LMFDB - Embedded newform 75.9.k.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(13,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.3788 + 3.38607i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(202.117 - 65.6718i) q^{4} +(611.912 + 127.235i) q^{5} +(312.802 - 962.707i) q^{6} +(-2654.08 + 2654.08i) q^{7} +(838.588 - 427.282i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-21.3788 + 3.38607i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(202.117 - 65.6718i) q^{4} +(611.912 + 127.235i) q^{5} +(312.802 - 962.707i) q^{6} +(-2654.08 + 2654.08i) q^{7} +(838.588 - 427.282i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-13512.8 - 648.155i) q^{10} +(-1504.19 - 1092.86i) q^{11} +(-1554.73 + 9816.15i) q^{12} +(-6400.36 - 1013.72i) q^{13} +(47754.1 - 65727.9i) q^{14} +(-18293.2 + 22796.0i) q^{15} +(-60495.6 + 43952.6i) q^{16} +(65940.1 + 129415. i) q^{17} +(33473.2 + 33473.2i) q^{18} +(207882. + 67544.8i) q^{19} +(132034. - 14469.0i) q^{20} +(-54242.0 - 166940. i) q^{21} +(35858.2 + 18270.7i) q^{22} +(28374.4 + 179149. i) q^{23} +44014.1i q^{24} +(358248. + 155713. i) q^{25} +140265. q^{26} +(101017. - 15999.5i) q^{27} +(-362137. + 710733. i) q^{28} +(-292915. + 95173.8i) q^{29} +(313898. - 549292. i) q^{30} +(113440. - 349132. i) q^{31} +(974126. - 974126. i) q^{32} +(77472.9 - 39474.4i) q^{33} +(-1.84793e6 - 2.54345e6i) q^{34} +(-1.96176e6 + 1.28637e6i) q^{35} +(-376013. - 273190. i) q^{36} +(-91982.6 + 580755. i) q^{37} +(-4.67297e6 - 740126. i) q^{38} +(178126. - 245170. i) q^{39} +(567507. - 154761. i) q^{40} +(-1.92092e6 + 1.39563e6i) q^{41} +(1.72490e6 + 3.38530e6i) q^{42} +(2.69998e6 + 2.69998e6i) q^{43} +(-375792. - 122102. i) q^{44} +(-561485. - 1.24623e6i) q^{45} +(-1.21322e6 - 3.73391e6i) q^{46} +(-4.30603e6 - 2.19403e6i) q^{47} +(-547044. - 3.45390e6i) q^{48} -8.32348e6i q^{49} +(-8.18616e6 - 2.11591e6i) q^{50} -6.79246e6 q^{51} +(-1.36020e6 + 215434. i) q^{52} +(-3.15602e6 + 6.19404e6i) q^{53} +(-2.10544e6 + 684099. i) q^{54} +(-781381. - 860118. i) q^{55} +(-1.09164e6 + 3.35972e6i) q^{56} +(-7.22802e6 + 7.22802e6i) q^{57} +(5.93990e6 - 3.02653e6i) q^{58} +(-6.93700e6 - 9.54796e6i) q^{59} +(-2.20031e6 + 5.80880e6i) q^{60} +(-1.62063e7 - 1.17745e7i) q^{61} +(-1.24302e6 + 7.84814e6i) q^{62} +(8.10770e6 + 1.28413e6i) q^{63} +(-6.27532e6 + 8.63724e6i) q^{64} +(-3.78748e6 - 1.43466e6i) q^{65} +(-1.52262e6 + 1.10624e6i) q^{66} +(-3.49256e6 - 6.85454e6i) q^{67} +(2.18265e7 + 2.18265e7i) q^{68} +(-8.06724e6 - 2.62121e6i) q^{69} +(3.75842e7 - 3.41437e7i) q^{70} +(9.09174e6 + 2.79815e7i) q^{71} +(-1.83399e6 - 934465. i) q^{72} +(-1.80754e6 - 1.14124e7i) q^{73} -1.27273e7i q^{74} +(-1.40943e7 + 1.16216e7i) q^{75} +4.64522e7 q^{76} +(6.89277e6 - 1.09171e6i) q^{77} +(-2.97796e6 + 5.84458e6i) q^{78} +(2.24349e7 - 7.28953e6i) q^{79} +(-4.26103e7 + 1.91980e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(3.63413e7 - 3.63413e7i) q^{82} +(6.24368e7 - 3.18131e7i) q^{83} +(-2.19265e7 - 3.01792e7i) q^{84} +(2.38834e7 + 8.75803e7i) q^{85} +(-6.68646e7 - 4.85799e7i) q^{86} +(2.25316e6 - 1.42259e7i) q^{87} +(-1.72835e6 - 273744. i) q^{88} +(1.31621e6 - 1.81160e6i) q^{89} +(1.62237e7 + 2.47416e7i) q^{90} +(1.96776e7 - 1.42966e7i) q^{91} +(1.75000e7 + 3.43457e7i) q^{92} +(1.21393e7 + 1.21393e7i) q^{93} +(9.94869e7 + 3.23252e7i) q^{94} +(1.18611e8 + 6.77813e7i) q^{95} +(1.99084e7 + 6.12718e7i) q^{96} +(-4.39238e7 - 2.23803e7i) q^{97} +(2.81839e7 + 1.77946e8i) q^{98} +4.06624e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−21.3788	+	3.38607i	−1.33617	+	0.211629i	−0.783305	−	0.621638i	$-0.786468\pi$
$2$	−21.3788	+	3.38607i	−1.33617	+	0.211629i	−0.552870	+	0.833267i	$0.686468\pi$
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$4$	202.117	−	65.6718i	0.789520	−	0.256531i
$5$	611.912	+	127.235i	0.979059	+	0.203576i
$5$	611.912	+	127.235i	0.979059	+	0.203576i
$6$	312.802	−	962.707i	0.241360	−	0.742829i
$7$	−2654.08	+	2654.08i	−1.10541	+	1.10541i	−0.111660	+	0.993747i	$0.535617\pi$
$7$	−2654.08	+	2654.08i	−1.10541	+	1.10541i	−0.993747	+	0.111660i	$0.964383\pi$
$8$	838.588	−	427.282i	0.204733	−	0.104317i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	−13512.8	−	648.155i	−1.35128	−	0.0648155i
$11$	−1504.19	−	1092.86i	−0.102738	−	0.0746436i	0.535230	−	0.844706i	$-0.320225\pi$
$11$	−1504.19	−	1092.86i	−0.102738	−	0.0746436i	−0.637968	+	0.770063i	$0.720225\pi$
$12$	−1554.73	+	9816.15i	−0.0749771	+	0.473387i
$13$	−6400.36	−	1013.72i	−0.224094	−	0.0354931i	0.0433774	−	0.999059i	$-0.486188\pi$
$13$	−6400.36	−	1013.72i	−0.224094	−	0.0354931i	−0.267472	+	0.963566i	$0.586188\pi$
$14$	47754.1	−	65727.9i	1.24308	−	1.71095i
$15$	−18293.2	+	22796.0i	−0.361347	+	0.450291i
$16$	−60495.6	+	43952.6i	−0.923089	+	0.670663i
$17$	65940.1	+	129415.i	0.789503	+	1.54949i	0.834826	+	0.550514i	$0.185568\pi$
$17$	65940.1	+	129415.i	0.789503	+	1.54949i	−0.0453227	+	0.998972i	$0.514432\pi$
$18$	33473.2	+	33473.2i	0.318865	+	0.318865i
$19$	207882.	+	67544.8i	1.59515	+	0.518296i	0.965902	−	0.258908i	$-0.0833627\pi$
$19$	207882.	+	67544.8i	1.59515	+	0.518296i	0.629249	+	0.777204i	$0.283363\pi$
$20$	132034.	−	14469.0i	0.825210	−	0.0904314i
$21$	−54242.0	−	166940.i	−0.278906	−	0.858386i
$22$	35858.2	+	18270.7i	0.153073	+	0.0779945i
$23$	28374.4	+	179149.i	0.101395	+	0.640181i	0.985080	+	0.172099i	$0.0550549\pi$
$23$	28374.4	+	179149.i	0.101395	+	0.640181i	−0.883685	+	0.468082i	$0.844945\pi$
$24$			44014.1i			0.132662i
$25$	358248.	+	155713.i	0.917114	+	0.398626i
$26$	140265.			0.306941
$27$	101017.	−	15999.5i	0.190081	−	0.0301058i
$28$	−362137.	+	710733.i	−0.589170	+	1.15631i
$29$	−292915.	+	95173.8i	−0.414142	+	0.134563i	−0.508675	−	0.860959i	$-0.669864\pi$
$29$	−292915.	+	95173.8i	−0.414142	+	0.134563i	0.0945326	+	0.995522i	$0.469864\pi$
$30$	313898.	−	549292.i	0.387528	−	0.678139i
$31$	113440.	−	349132.i	0.122834	−	0.378045i	−0.870666	−	0.491874i	$-0.836312\pi$
$31$	113440.	−	349132.i	0.122834	−	0.378045i	0.993500	+	0.113830i	$0.0363119\pi$
$32$	974126.	−	974126.i	0.928999	−	0.928999i
$33$	77472.9	−	39474.4i	0.0653272	−	0.0332859i
$34$	−1.84793e6	−	2.54345e6i	−1.38283	−	1.90330i
$35$	−1.96176e6	+	1.28637e6i	−1.30729	+	0.857224i
$36$	−376013.	−	273190.i	−0.223869	−	0.162650i
$37$	−91982.6	+	580755.i	−0.0490793	+	0.309875i	0.950921	+	0.309435i	$0.100140\pi$
$37$	−91982.6	+	580755.i	−0.0490793	+	0.309875i	−1.00000		0.000439635i	$0.999860\pi$
$38$	−4.67297e6	−	740126.i	−2.24109	−	0.354953i
$39$	178126.	−	245170.i	0.0769962	−	0.105976i
$40$	567507.	−	154761.i	0.221682	−	0.0604536i
$41$	−1.92092e6	+	1.39563e6i	−0.679790	+	0.493896i	−0.873288	−	0.487204i	$-0.838017\pi$
$41$	−1.92092e6	+	1.39563e6i	−0.679790	+	0.493896i	0.193498	+	0.981101i	$0.438017\pi$
$42$	1.72490e6	+	3.38530e6i	0.554327	+	1.08793i
$43$	2.69998e6	+	2.69998e6i	0.789744	+	0.789744i	0.981452	−	0.191708i	$-0.0614028\pi$
$43$	2.69998e6	+	2.69998e6i	0.789744	+	0.789744i	−0.191708	+	0.981452i	$0.561403\pi$
$44$	−375792.	−	122102.i	−0.100262	−	0.0325772i
$45$	−561485.	−	1.24623e6i	−0.136927	−	0.303911i
$46$	−1.21322e6	−	3.73391e6i	−0.270962	−	0.833936i
$47$	−4.30603e6	−	2.19403e6i	−0.882440	−	0.449626i	−0.0468010	−	0.998904i	$-0.514903\pi$
$47$	−4.30603e6	−	2.19403e6i	−0.882440	−	0.449626i	−0.835639	+	0.549278i	$0.814903\pi$
$48$	−547044.	−	3.45390e6i	−0.103052	−	0.650647i
$49$		−	8.32348e6i		−	1.44385i
$50$	−8.18616e6	−	2.11591e6i	−1.30979	−	0.338546i
$51$	−6.79246e6			−1.00403
$52$	−1.36020e6	+	215434.i	−0.186032	+	0.0294646i
$53$	−3.15602e6	+	6.19404e6i	−0.399978	+	0.785001i	−0.999886	−	0.0150675i	$-0.995204\pi$
$53$	−3.15602e6	+	6.19404e6i	−0.399978	+	0.785001i	0.599908	+	0.800069i	$0.295204\pi$
$54$	−2.10544e6	+	684099.i	−0.247610	+	0.0804533i
$55$	−781381.	−	860118.i	−0.0853911	−	0.0939955i
$56$	−1.09164e6	+	3.35972e6i	−0.111001	+	0.341626i
$57$	−7.22802e6	+	7.22802e6i	−0.684731	+	0.684731i
$58$	5.93990e6	−	3.02653e6i	0.524889	−	0.267444i
$59$	−6.93700e6	−	9.54796e6i	−0.572484	−	0.787957i	0.420362	−	0.907357i	$-0.361903\pi$
$59$	−6.93700e6	−	9.54796e6i	−0.572484	−	0.787957i	−0.992846	+	0.119399i	$0.961903\pi$
$60$	−2.20031e6	+	5.80880e6i	−0.169777	+	0.448210i
$61$	−1.62063e7	−	1.17745e7i	−1.17048	−	0.850403i	−0.179413	−	0.983774i	$-0.557420\pi$
$61$	−1.62063e7	−	1.17745e7i	−1.17048	−	0.850403i	−0.991066	+	0.133371i	$0.957420\pi$
$62$	−1.24302e6	+	7.84814e6i	−0.0841226	+	0.531129i
$63$	8.10770e6	+	1.28413e6i	0.514678	+	0.0815170i
$64$	−6.27532e6	+	8.63724e6i	−0.374038	+	0.514820i
$65$	−3.78748e6	−	1.43466e6i	−0.212176	−	0.0803700i
$66$	−1.52262e6	+	1.10624e6i	−0.0802443	+	0.0583009i
$67$	−3.49256e6	−	6.85454e6i	−0.173319	−	0.340157i	0.787964	−	0.615721i	$-0.211135\pi$
$67$	−3.49256e6	−	6.85454e6i	−0.173319	−	0.340157i	−0.961283	+	0.275564i	$0.911135\pi$
$68$	2.18265e7	+	2.18265e7i	1.02082	+	1.02082i
$69$	−8.06724e6	−	2.62121e6i	−0.355901	−	0.115639i
$70$	3.75842e7	−	3.41437e7i	1.56536	−	1.42206i
$71$	9.09174e6	+	2.79815e7i	0.357778	+	1.10113i	0.954381	+	0.298591i	$0.0965167\pi$
$71$	9.09174e6	+	2.79815e7i	0.357778	+	1.10113i	−0.596603	+	0.802536i	$0.703483\pi$
$72$	−1.83399e6	−	934465.i	−0.0682444	−	0.0347723i
$73$	−1.80754e6	−	1.14124e7i	−0.0636497	−	0.401868i	−0.998858	−	0.0477710i	$-0.984788\pi$
$73$	−1.80754e6	−	1.14124e7i	−0.0636497	−	0.401868i	0.935209	−	0.354097i	$-0.115212\pi$
$74$		−	1.27273e7i		−	0.424433i
$75$	−1.40943e7	+	1.16216e7i	−0.445448	+	0.367300i
$76$	4.64522e7			1.39236
$77$	6.89277e6	−	1.09171e6i	0.196079	−	0.0310558i
$78$	−2.97796e6	+	5.84458e6i	−0.0804527	+	0.157897i
$79$	2.24349e7	−	7.28953e6i	0.575990	−	0.187150i	−0.00651338	−	0.999979i	$-0.502073\pi$
$79$	2.24349e7	−	7.28953e6i	0.575990	−	0.187150i	0.582503	+	0.812828i	$0.302073\pi$
$80$	−4.26103e7	+	1.91980e7i	−1.04029	+	0.468700i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	3.63413e7	−	3.63413e7i	0.803795	−	0.803795i
$83$	6.24368e7	−	3.18131e7i	1.31561	−	0.670338i	0.351589	−	0.936154i	$-0.385641\pi$
$83$	6.24368e7	−	3.18131e7i	1.31561	−	0.670338i	0.964024	+	0.265816i	$0.0856415\pi$
$84$	−2.19265e7	−	3.01792e7i	−0.440404	−	0.606165i
$85$	2.38834e7	+	8.75803e7i	0.457532	+	1.67776i
$86$	−6.68646e7	−	4.85799e7i	−1.22237	−	0.888103i
$87$	2.25316e6	−	1.42259e7i	0.0393292	−	0.248315i
$88$	−1.72835e6	−	273744.i	−0.0288205	−	0.00456472i
$89$	1.31621e6	−	1.81160e6i	0.0209780	−	0.0288738i	−0.798399	−	0.602129i	$-0.794319\pi$
$89$	1.31621e6	−	1.81160e6i	0.0209780	−	0.0288738i	0.819377	+	0.573255i	$0.194319\pi$
$90$	1.62237e7	+	2.47416e7i	0.247275	+	0.377101i
$91$	1.96776e7	−	1.42966e7i	0.286950	−	0.208481i
$92$	1.75000e7	+	3.43457e7i	0.244279	+	0.479425i
$93$	1.21393e7	+	1.21393e7i	0.162279	+	0.162279i
$94$	9.94869e7	+	3.23252e7i	1.27425	+	0.414029i
$95$	1.18611e8	+	6.77813e7i	1.45623	+	0.832177i
$96$	1.99084e7	+	6.12718e7i	0.234397	+	0.721400i
$97$	−4.39238e7	−	2.23803e7i	−0.496150	−	0.252801i	0.187964	−	0.982176i	$-0.439811\pi$
$97$	−4.39238e7	−	2.23803e7i	−0.496150	−	0.252801i	−0.684114	+	0.729375i	$0.739811\pi$
$98$	2.81839e7	+	1.77946e8i	0.305560	+	1.92923i
$99$			4.06624e6i			0.0423304i
$100$	8.26339e7	+	7.94553e6i	0.826339	+	0.0794553i
$101$	−2.01783e8			−1.93910			−0.969550	−	0.244894i	$-0.921247\pi$
$101$	−2.01783e8			−1.93910			−0.969550	+	0.244894i	$0.921247\pi$
$102$	1.45215e8	−	2.29997e7i	1.34156	−	0.212482i
$103$	−8.96383e7	+	1.75925e8i	−0.796425	+	1.56307i	0.0296827	+	0.999559i	$0.490550\pi$
$103$	−8.96383e7	+	1.75925e8i	−0.796425	+	1.56307i	−0.826108	+	0.563512i	$0.809450\pi$
$104$	−5.80041e6	+	1.88467e6i	−0.0495821	+	0.0161102i
$105$	−1.19508e7	−	1.09054e8i	−0.0983192	−	0.897189i
$106$	4.64985e7	−	1.43108e8i	0.368311	−	1.13355i
$107$	−1.83003e7	+	1.83003e7i	−0.139612	+	0.139612i	−0.773459	−	0.633847i	$-0.781475\pi$
$107$	−1.83003e7	+	1.83003e7i	−0.139612	+	0.139612i	0.633847	+	0.773459i	$0.281475\pi$
$108$	1.93665e7	−	9.86772e6i	0.142349	−	0.0725307i
$109$	−1.17876e8	−	1.62242e8i	−0.835062	−	1.14936i	−0.986960	−	0.160968i	$-0.948538\pi$
$109$	−1.17876e8	−	1.62242e8i	−0.835062	−	1.14936i	0.151898	−	0.988396i	$-0.451462\pi$
$110$	1.96174e7	+	1.57425e7i	0.133990	+	0.107523i
$111$	−2.22462e7	−	1.61628e7i	−0.146542	−	0.106469i
$112$	4.39063e7	−	2.77214e8i	0.279033	−	1.76174i
$113$	−2.21277e8	−	3.50469e7i	−1.35713	−	0.214949i	−0.564897	−	0.825162i	$-0.691084\pi$
$113$	−2.21277e8	−	3.50469e7i	−1.35713	−	0.214949i	−0.792238	+	0.610213i	$0.791084\pi$
$114$	1.30052e8	−	1.79001e8i	0.770011	−	1.05983i
$115$	−5.43137e6	+	1.13234e8i	−0.0310540	+	0.647417i
$116$	−5.29528e7	+	3.84725e7i	−0.292454	+	0.212480i
$117$	6.43398e6	+	1.26274e7i	0.0343350	+	0.0673862i
$118$	1.80635e8	+	1.80635e8i	0.931694	+	0.931694i
$119$	−5.18487e8	−	1.68467e8i	−2.58553	−	0.840091i
$120$	−5.60013e6	+	2.69328e7i	−0.0270068	+	0.129884i
$121$	−6.51723e7	−	2.00580e8i	−0.304034	−	0.935719i
$122$	3.86340e8	+	1.96850e8i	1.74393	+	0.888579i
$123$	−1.73704e7	−	1.09672e8i	−0.0758908	−	0.479155i
$124$		−	7.80154e7i		−	0.329984i
$125$	1.99404e8	+	1.40864e8i	0.816758	+	0.576981i
$126$	−1.77681e8			−0.704951
$127$	3.51059e8	−	5.56023e7i	1.34948	−	0.213736i	0.560497	−	0.828156i	$-0.310610\pi$
$127$	3.51059e8	−	5.56023e7i	1.34948	−	0.213736i	0.788979	+	0.614420i	$0.210610\pi$
$128$	−5.51968e7	+	1.08330e8i	−0.205624	+	0.403560i
$129$	−1.69827e8	+	5.51800e7i	−0.613263	+	0.199261i
$130$	8.58295e7	+	1.78466e7i	0.300513	+	0.0624857i
$131$	4.42513e7	−	1.36192e8i	0.150259	−	0.462450i	−0.847391	−	0.530970i	$-0.821828\pi$
$131$	4.42513e7	−	1.36192e8i	0.150259	−	0.462450i	0.997650	+	0.0685198i	$0.0218276\pi$
$132$	1.30662e7	−	1.30662e7i	0.0430383	−	0.0430383i
$133$	−7.31004e8	+	3.72465e8i	−2.33622	+	1.19036i
$134$	9.78768e7	+	1.34716e8i	0.303571	+	0.417830i
$135$	6.38490e7	+	3.06259e6i	0.192229	+	0.00922048i
$136$	1.10593e8	+	8.03506e7i	0.323275	+	0.234873i
$137$	5.03158e7	−	3.17681e8i	0.142831	−	0.901798i	−0.807344	−	0.590081i	$-0.799096\pi$
$137$	5.03158e7	−	3.17681e8i	0.142831	−	0.901798i	0.950175	−	0.311717i	$-0.100904\pi$
$138$	1.81344e8	+	2.87220e7i	0.500018	+	0.0791951i
$139$	−6.18704e7	+	8.51573e7i	−0.165739	+	0.228120i	−0.883806	−	0.467854i	$-0.845027\pi$
$139$	−6.18704e7	+	8.51573e7i	−0.165739	+	0.228120i	0.718067	+	0.695974i	$0.245027\pi$
$140$	−3.12026e8	+	3.88830e8i	−0.812229	+	1.01216i
$141$	1.82843e8	−	1.32843e8i	0.462596	−	0.336095i
$142$	−2.89118e8	−	5.67426e8i	−0.711085	−	1.39558i
$143$	8.51950e6	+	8.51950e6i	0.0203737	+	0.0203737i
$144$	1.55532e8	+	5.05355e7i	0.361719	+	0.117530i
$145$	−1.91347e8	+	2.09690e7i	−0.432863	+	0.0474357i
$146$	7.72860e7	+	2.37862e8i	0.170094	+	0.523496i
$147$	3.46825e8	+	1.76716e8i	0.742747	+	0.378448i
$148$	1.95480e7	+	1.23421e8i	0.0407432	+	0.257243i
$149$			5.07248e8i			1.02914i	0.857448	+	0.514571i	$0.172049\pi$
$149$			5.07248e8i			1.02914i	−0.857448	+	0.514571i	$0.827951\pi$
$150$	2.61967e8	−	2.96180e8i	0.517465	−	0.585047i
$151$	1.32218e8			0.254322			0.127161	−	0.991882i	$-0.459413\pi$
$151$	1.32218e8			0.254322			0.127161	+	0.991882i	$0.459413\pi$
$152$	2.03188e8	−	3.21818e7i	0.380647	−	0.0602886i
$153$	1.44211e8	−	2.83030e8i	0.263168	−	0.516496i
$154$	−1.43663e8	+	4.66788e7i	−0.255423	+	0.0829921i
$155$	1.13837e8	−	1.99205e8i	0.197223	−	0.345122i
$156$	1.99016e7	−	6.12508e7i	0.0336039	−	0.103422i
$157$	−3.94787e8	+	3.94787e8i	−0.649777	+	0.649777i	−0.952939	−	0.303162i	$-0.901958\pi$
$157$	−3.94787e8	+	3.94787e8i	−0.649777	+	0.649777i	0.303162	+	0.952939i	$0.401958\pi$
$158$	−4.54947e8	+	2.31807e8i	−0.730017	+	0.371962i
$159$	−1.91089e8	−	2.63012e8i	−0.298984	−	0.411516i
$160$	7.20022e8	−	4.72136e8i	1.09867	−	0.720423i
$161$	−5.50784e8	−	4.00168e8i	−0.819742	−	0.595578i
$162$	1.61955e7	−	1.02254e8i	0.0235144	−	0.148464i
$163$	1.20448e9	+	1.90771e8i	1.70628	+	0.270248i	0.931964	−	0.362550i	$-0.118094\pi$
$163$	1.20448e9	+	1.90771e8i	1.70628	+	0.270248i	0.774317	+	0.632798i	$0.218094\pi$
$164$	−2.96598e8	+	4.08232e8i	−0.410008	+	0.564328i
$165$	5.24291e7	−	1.42976e7i	0.0707354	−	0.0192898i
$166$	−1.22710e9	+	8.91542e8i	−1.61603	+	1.17411i
$167$	−3.05412e8	−	5.99404e8i	−0.392663	−	0.770644i	0.607049	−	0.794665i	$-0.292353\pi$
$167$	−3.05412e8	−	5.99404e8i	−0.392663	−	0.770644i	−0.999711	+	0.0240205i	$0.992353\pi$
$168$	−1.16817e8	−	1.16817e8i	−0.146646	−	0.146646i
$169$	−7.35869e8	−	2.39098e8i	−0.902098	−	0.293109i
$170$	−8.07152e8	−	1.79149e9i	−0.966406	−	2.14496i
$171$	−1.47721e8	−	4.54637e8i	−0.172765	−	0.531717i
$172$	7.23024e8	+	3.68399e8i	0.826112	+	0.420925i
$173$	2.78248e8	+	1.75679e9i	0.310633	+	1.96126i	0.273175	+	0.961964i	$0.411926\pi$
$173$	2.78248e8	+	1.75679e9i	0.310633	+	1.96126i	0.0374587	+	0.999298i	$0.488074\pi$
$174$			3.11762e8i			0.340115i
$175$	−1.36409e9	+	5.37542e8i	−1.45443	+	0.573140i
$176$	1.39031e8			0.144897
$177$	5.45127e8	−	8.63396e7i	0.555398	−	0.0879664i
$178$	−2.20047e7	+	4.31867e7i	−0.0219198	+	0.0430200i
$179$	4.43548e8	−	1.44118e8i	0.432045	−	0.140380i	−0.0849177	−	0.996388i	$-0.527063\pi$
$179$	4.43548e8	−	1.44118e8i	0.432045	−	0.140380i	0.516962	+	0.856008i	$0.327063\pi$
$180$	−1.95328e8	−	2.15010e8i	−0.186069	−	0.204818i
$181$	1.84776e8	−	5.68683e8i	0.172160	−	0.529854i	−0.827332	−	0.561713i	$-0.810143\pi$
$181$	1.84776e8	−	5.68683e8i	0.172160	−	0.529854i	0.999492	+	0.0318587i	$0.0101426\pi$
$182$	−3.72273e8	+	3.72273e8i	−0.339294	+	0.339294i
$183$	8.34700e8	−	4.25301e8i	0.744263	−	0.379221i
$184$	1.00341e8	+	1.38108e8i	0.0875406	+	0.120489i
$185$	−1.30178e8	+	3.43668e8i	−0.111135	+	0.293394i
$186$	−3.00628e8	−	2.18419e8i	−0.251175	−	0.182490i
$187$	4.22454e7	−	2.66727e8i	0.0345472	−	0.218123i
$188$	−1.01441e9	−	1.60666e8i	−0.812047	−	0.128616i
$189$	−2.25642e8	+	3.10570e8i	−0.176837	+	0.243396i
$190$	−2.76528e9	−	1.04746e9i	−2.12190	−	0.803752i
$191$	−1.64209e9	+	1.19305e9i	−1.23385	+	0.896446i	−0.997173	−	0.0751413i	$-0.976059\pi$
$191$	−1.64209e9	+	1.19305e9i	−1.23385	+	0.896446i	−0.236680	+	0.971588i	$0.576059\pi$
$192$	−2.26667e8	−	4.44859e8i	−0.166795	−	0.327354i
$193$	−4.08787e8	−	4.08787e8i	−0.294624	−	0.294624i	0.544280	−	0.838904i	$-0.316803\pi$
$193$	−4.08787e8	−	4.08787e8i	−0.294624	−	0.294624i	−0.838904	+	0.544280i	$0.816803\pi$
$194$	1.01482e9	+	3.29735e8i	0.716444	+	0.232787i
$195$	1.40192e8	−	1.27358e8i	0.0969580	−	0.0880823i
$196$	−5.46618e8	−	1.68232e9i	−0.370390	−	1.13994i
$197$	1.70495e8	+	8.68717e7i	0.113200	+	0.0576784i	0.509674	−	0.860368i	$-0.329766\pi$
$197$	1.70495e8	+	8.68717e7i	0.113200	+	0.0576784i	−0.396473	+	0.918046i	$0.629766\pi$
$198$	−1.37686e7	−	8.69314e7i	−0.00895836	−	0.0565609i
$199$		−	2.75682e8i		−	0.175791i	−0.996130	−	0.0878955i	$-0.971986\pi$
$199$		−	2.75682e8i		−	0.175791i	0.996130	−	0.0878955i	$-0.0280141\pi$
$200$	3.66955e8	−	2.24935e7i	0.229347	−	0.0140584i
$201$	3.59768e8			0.220413
$202$	4.31389e9	−	6.83253e8i	2.59098	−	0.410370i
$203$	5.24820e8	−	1.03002e9i	0.309048	−	0.606542i
$204$	−1.37287e9	+	4.46073e8i	−0.792701	+	0.257564i
$205$	−1.35301e9	+	6.09596e8i	−0.766100	+	0.345165i
$206$	1.32067e9	−	4.06459e9i	0.733371	−	2.25708i
$207$	2.80497e8	−	2.80497e8i	0.152773	−	0.152773i
$208$	4.31749e8	−	2.19987e8i	0.230663	−	0.117529i
$209$	−2.38876e8	−	3.28785e8i	−0.125195	−	0.172317i
$210$	6.24757e8	+	2.29098e9i	0.321243	+	1.17799i
$211$	2.77677e9	+	2.01744e9i	1.40091	+	1.01782i	0.994567	+	0.104100i	$0.0331963\pi$
$211$	2.77677e9	+	2.01744e9i	1.40091	+	1.01782i	0.406343	+	0.913720i	$0.366804\pi$
$212$	−2.31112e8	+	1.45918e9i	−0.114414	+	0.722381i
$213$	−1.35897e9	−	2.15239e8i	−0.660223	−	0.104569i
$214$	3.29273e8	−	4.53205e8i	0.157000	−	0.216092i
$215$	1.30862e9	+	1.99568e9i	0.612433	+	0.933978i
$216$	7.78751e7	−	5.65795e7i	0.0357753	−	0.0259923i
$217$	6.25546e8	+	1.22770e9i	0.282111	+	0.553674i
$218$	3.06941e9	+	3.06941e9i	1.35903	+	1.35903i
$219$	5.13909e8	+	1.66979e8i	0.223414	+	0.0725914i
$220$	−2.14416e8	−	1.22530e8i	−0.0915307	−	0.0523059i
$221$	−2.90850e8	−	8.95145e8i	−0.121927	−	0.375253i
$222$	5.30325e8	+	2.70214e8i	0.218338	+	0.111249i
$223$	−6.47837e7	−	4.09028e8i	−0.0261967	−	0.165399i	0.971122	−	0.238585i	$-0.0766835\pi$
$223$	−6.47837e7	−	4.09028e8i	−0.0261967	−	0.165399i	−0.997318	+	0.0731855i	$0.976683\pi$
$224$			5.17082e9i			2.05384i
$225$	−1.85016e8	−	8.34022e8i	−0.0721903	−	0.325422i
$226$	4.84931e9			1.85886
$227$	−6.29859e8	+	9.97598e7i	−0.237214	+	0.0375709i	−0.273909	−	0.961756i	$-0.588317\pi$
$227$	−6.29859e8	+	9.97598e7i	−0.237214	+	0.0375709i	0.0366956	+	0.999326i	$0.488317\pi$
$228$	−9.86229e8	+	1.93558e9i	−0.364954	+	0.716263i
$229$	5.06432e9	−	1.64550e9i	1.84153	−	0.598350i	0.843399	−	0.537288i	$-0.180551\pi$
$229$	5.06432e9	−	1.64550e9i	1.84153	−	0.598350i	0.998134	−	0.0610624i	$-0.0194489\pi$
$230$	−2.67301e8	−	2.43919e9i	−0.0955187	−	0.871634i
$231$	−1.00851e8	+	3.10388e8i	−0.0354187	+	0.109008i
$232$	−2.04969e8	+	2.04969e8i	−0.0707515	+	0.0707515i
$233$	−1.32458e9	+	6.74907e8i	−0.449422	+	0.228992i	−0.664026	−	0.747709i	$-0.731154\pi$
$233$	−1.32458e9	+	6.74907e8i	−0.449422	+	0.228992i	0.214604	+	0.976701i	$0.431154\pi$
$234$	−1.80308e8	−	2.48173e8i	−0.0601384	−	0.0827734i
$235$	−2.35575e9	−	1.89043e9i	−0.772428	−	0.619854i
$236$	−2.02912e9	−	1.47424e9i	−0.654123	−	0.475248i
$237$	−1.72573e8	+	1.08959e9i	−0.0546991	+	0.345357i
$238$	1.16551e10	+	1.84598e9i	3.63251	+	0.575334i
$239$	−3.30967e9	+	4.55538e9i	−1.01436	+	1.39615i	−0.0982825	+	0.995159i	$0.531335\pi$
$239$	−3.30967e9	+	4.55538e9i	−1.01436	+	1.39615i	−0.916081	+	0.400993i	$0.868665\pi$
$240$	1.04714e8	−	2.18309e9i	0.0315617	−	0.658001i
$241$	1.43515e9	−	1.04269e9i	0.425430	−	0.309093i	−0.354389	−	0.935098i	$-0.615311\pi$
$241$	1.43515e9	−	1.04269e9i	0.425430	−	0.309093i	0.779819	+	0.626005i	$0.215311\pi$
$242$	2.07248e9	+	4.06747e9i	0.604268	+	1.18594i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	−4.04882e9	−	1.31554e9i	−1.14227	−	0.371146i
$245$	1.05904e9	−	5.09324e9i	0.293932	−	1.41361i
$246$	7.42716e8	+	2.28584e9i	0.202807	+	0.624175i
$247$	−1.26205e9	−	6.43044e8i	−0.339068	−	0.172764i
$248$	−5.40485e7	−	3.41249e8i	−0.0142882	−	0.0902120i
$249$			3.27706e9i			0.852485i
$250$	−4.73999e9	−	2.33632e9i	−1.21344	−	0.598097i
$251$	5.64593e8			0.142246			0.0711231	−	0.997468i	$-0.477342\pi$
$251$	5.64593e8			0.142246			0.0711231	+	0.997468i	$0.477342\pi$
$252$	1.72304e9	−	2.72902e8i	0.427260	−	0.0676714i
$253$	1.53104e8	−	3.00483e8i	0.0373683	−	0.0733395i
$254$	−7.31695e9	+	2.37742e9i	−1.75790	+	0.571177i
$255$	−4.15639e9	−	8.64238e8i	−0.983004	−	0.204396i
$256$	1.65781e9	−	5.10221e9i	0.385988	−	1.18795i
$257$	3.14885e8	−	3.14885e8i	0.0721804	−	0.0721804i	−0.670095	−	0.742275i	$-0.733747\pi$
$257$	3.14885e8	−	3.14885e8i	0.0721804	−	0.0721804i	0.742275	+	0.670095i	$0.233747\pi$
$258$	3.44384e9	−	1.75473e9i	0.777257	−	0.396032i
$259$	−1.29724e9	−	1.78550e9i	−0.288285	−	0.396790i
$260$	−8.59730e8	−	4.12379e7i	−0.188135	−	0.00902408i
$261$	5.44931e8	+	3.95915e8i	0.117430	+	0.0853179i
$262$	−4.84886e8	+	3.06145e9i	−0.102905	+	0.649714i
$263$	−4.80621e8	−	7.61229e7i	−0.100457	−	0.0159108i	0.106004	−	0.994366i	$-0.466194\pi$
$263$	−4.80621e8	−	7.61229e7i	−0.100457	−	0.0159108i	−0.206461	+	0.978455i	$0.566194\pi$
$264$	4.81011e7	−	6.62055e7i	0.00990238	−	0.0136295i
$265$	−2.71930e9	+	3.38865e9i	−0.551410	+	0.687137i
$266$	1.43668e10	−	1.04381e10i	2.86968	−	2.08494i
$267$	4.75419e7	+	9.33063e7i	0.00935474	+	0.0183597i
$268$	−1.15606e9	−	1.15606e9i	−0.224099	−	0.224099i
$269$	7.18292e9	+	2.33387e9i	1.37180	+	0.445726i	0.899966	−	0.435960i	$-0.143591\pi$
$269$	7.18292e9	+	2.33387e9i	1.37180	+	0.445726i	0.471837	+	0.881686i	$0.343591\pi$
$270$	−1.37539e9	+	1.50723e8i	−0.258803	+	0.0283611i
$271$	1.19974e9	+	3.69240e9i	0.222438	+	0.684593i	0.998542	+	0.0539876i	$0.0171931\pi$
$271$	1.19974e9	+	3.69240e9i	0.222438	+	0.684593i	−0.776104	+	0.630605i	$0.782807\pi$
$272$	−9.67719e9	−	4.93078e9i	−1.76797	−	0.900823i
$273$	1.77939e8	+	1.12346e9i	0.0320346	+	0.202259i
$274$			6.96202e9i			1.23519i
$275$	−3.68700e8	−	6.25735e8i	−0.0644677	−	0.109411i
$276$	−1.80267e9			−0.310656
$277$	−6.61486e8	+	1.04769e8i	−0.112357	+	0.0177957i	−0.212360	−	0.977192i	$-0.568115\pi$
$277$	−6.61486e8	+	1.04769e8i	−0.112357	+	0.0177957i	0.100002	+	0.994987i	$0.468115\pi$
$278$	1.03437e9	−	2.03006e9i	0.173179	−	0.339883i
$279$	−7.63552e8	+	2.48093e8i	−0.126015	+	0.0409447i
$280$	−1.09546e9	+	1.91696e9i	−0.178223	+	0.311875i
$281$	3.40678e9	−	1.04850e10i	0.546411	−	1.68168i	−0.171201	−	0.985236i	$-0.554765\pi$
$281$	3.40678e9	−	1.04850e10i	0.546411	−	1.68168i	0.717612	−	0.696443i	$-0.245235\pi$
$282$	−3.45914e9	+	3.45914e9i	−0.546981	+	0.546981i
$283$	−1.00990e10	+	5.14572e9i	−1.57447	+	0.802232i	−0.999869	−	0.0162012i	$-0.994843\pi$
$283$	−1.00990e10	+	5.14572e9i	−1.57447	+	0.802232i	−0.574601	+	0.818434i	$0.694843\pi$
$284$	3.67519e9	+	5.05847e9i	0.564946	+	0.777581i
$285$	−5.34257e9	+	3.50325e9i	−0.809786	+	0.530997i
$286$	−2.10984e8	−	1.53289e8i	−0.0315345	−	0.0229112i
$287$	1.39416e9	−	8.80241e9i	0.205488	−	1.29740i
$288$	−2.97577e9	−	4.71315e8i	−0.432543	−	0.0685080i
$289$	−8.29982e9	+	1.14237e10i	−1.18981	+	1.63763i
$290$	4.01978e9	−	1.09621e9i	0.568342	−	0.154989i
$291$	1.86510e9	−	1.35507e9i	0.260093	−	0.188969i
$292$	−1.11480e9	−	2.18793e9i	−0.153344	−	0.300955i
$293$	−1.58645e9	−	1.58645e9i	−0.215256	−	0.215256i	0.591240	−	0.806496i	$-0.298639\pi$
$293$	−1.58645e9	−	1.58645e9i	−0.215256	−	0.215256i	−0.806496	+	0.591240i	$0.798639\pi$
$294$	−8.01307e9	−	2.60360e9i	−1.07253	−	0.348486i
$295$	−3.03000e9	−	6.72514e9i	−0.400087	−	0.888001i
$296$	1.71011e8	+	5.26317e8i	0.0222770	+	0.0685615i
$297$	−1.69433e8	−	8.63306e7i	−0.0217757	−	0.0110953i
$298$	−1.71758e9	−	1.08444e10i	−0.217797	−	1.37511i
$299$		−	1.17538e9i		−	0.147060i
$300$	−2.08548e9	+	3.27452e9i	−0.257467	+	0.404262i
$301$	−1.43319e10			−1.74597
$302$	−2.82667e9	+	4.47701e8i	−0.339819	+	0.0538220i
$303$	4.28407e9	−	8.40796e9i	0.508260	−	0.997517i
$304$	−1.55447e10	+	5.05077e9i	−1.82007	+	0.591376i
$305$	−8.41867e9	−	9.26699e9i	−0.972847	−	1.07088i
$306$	−2.12470e9	+	6.53915e9i	−0.242332	+	0.745822i
$307$	3.36951e9	−	3.36951e9i	0.379327	−	0.379327i	−0.491532	−	0.870859i	$-0.663563\pi$
$307$	3.36951e9	−	3.36951e9i	0.379327	−	0.379327i	0.870859	+	0.491532i	$0.163563\pi$
$308$	1.32145e9	−	6.73313e8i	0.146841	−	0.0748194i
$309$	−5.42738e9	−	7.47014e9i	−0.595328	−	0.819398i
$310$	−1.75918e9	+	4.64422e9i	−0.190486	+	0.502881i
$311$	1.75416e9	+	1.27447e9i	0.187512	+	0.136235i	0.677581	−	0.735448i	$-0.263028\pi$
$311$	1.75416e9	+	1.27447e9i	0.187512	+	0.136235i	−0.490069	+	0.871684i	$0.663028\pi$
$312$	4.46179e7	−	2.81706e8i	0.00470859	−	0.0297288i
$313$	−5.33326e9	−	8.44705e8i	−0.555668	−	0.0880091i	−0.127716	−	0.991811i	$-0.540765\pi$
$313$	−5.33326e9	−	8.44705e8i	−0.555668	−	0.0880091i	−0.427952	+	0.903802i	$0.640765\pi$
$314$	7.10330e9	−	9.77685e9i	0.730704	−	1.00573i
$315$	4.79781e9	+	1.81736e9i	0.487305	+	0.184586i
$316$	4.05575e9	−	2.94668e9i	0.406746	−	0.295518i
$317$	−2.54554e9	−	4.99591e9i	−0.252083	−	0.494741i	0.729938	−	0.683514i	$-0.239549\pi$
$317$	−2.54554e9	−	4.99591e9i	−0.252083	−	0.494741i	−0.982021	+	0.188773i	$0.939549\pi$
$318$	4.97583e9	+	4.97583e9i	0.486583	+	0.486583i
$319$	5.44610e8	+	1.76955e8i	0.0525924	+	0.0170883i
$320$	−4.93890e9	+	4.48679e9i	−0.471011	+	0.427894i
$321$	−3.74008e8	−	1.15108e9i	−0.0352257	−	0.108414i
$322$	1.31301e10	+	6.69011e9i	1.22136	+	0.622315i
$323$	4.96644e9	+	3.13568e10i	0.456284	+	2.88086i
$324$			1.01647e9i			0.0922389i
$325$	−2.13506e9	−	1.35978e9i	−0.191372	−	0.121881i
$326$	−2.63964e10			−2.33708
$327$	9.26297e9	−	1.46711e9i	0.810138	−	0.128313i
$328$	−1.01453e9	+	1.99114e9i	−0.0876540	+	0.172031i
$329$	1.72517e10	−	5.60541e9i	1.47247	−	0.478436i
$330$	−1.07246e9	+	4.83194e8i	−0.0904326	+	0.0407442i
$331$	−2.73204e9	+	8.40836e9i	−0.227602	+	0.700485i	0.770416	+	0.637542i	$0.220049\pi$
$331$	−2.73204e9	+	8.40836e9i	−0.227602	+	0.700485i	−0.998017	+	0.0629434i	$0.979951\pi$
$332$	1.05303e10	−	1.05303e10i	0.866740	−	0.866740i
$333$	1.14578e9	−	5.83806e8i	0.0931807	−	0.0474779i
$334$	8.55896e9	+	1.17804e10i	0.687757	+	0.946617i
$335$	−1.26500e9	−	4.63875e9i	−0.100441	−	0.368317i
$336$	1.06188e10	+	7.71503e9i	0.833143	+	0.605314i
$337$	−1.49328e9	+	9.42820e9i	−0.115777	+	0.730986i	0.859686	+	0.510822i	$0.170659\pi$
$337$	−1.49328e9	+	9.42820e9i	−0.115777	+	0.730986i	−0.975463	+	0.220163i	$0.929341\pi$
$338$	1.65416e10	+	2.61993e9i	1.26739	+	0.200735i
$339$	6.15828e9	−	8.47615e9i	0.466295	−	0.641800i
$340$	1.05788e10	+	1.61330e10i	0.791628	+	1.20726i
$341$	−5.52187e8	+	4.01187e8i	−0.0408384	+	0.0296708i
$342$	4.69752e9	+	9.21940e9i	0.343372	+	0.673905i
$343$	6.79094e9	+	6.79094e9i	0.490629	+	0.490629i
$344$	3.41782e9	+	1.11052e9i	0.244070	+	0.0793033i
$345$	−4.60293e9	−	2.63038e9i	−0.324906	−	0.185670i
$346$	−1.18972e10	−	3.66159e10i	−0.830121	−	2.55485i
$347$	2.39557e9	+	1.22060e9i	0.165231	+	0.0841892i	0.534650	−	0.845074i	$-0.320443\pi$
$347$	2.39557e9	+	1.22060e9i	0.165231	+	0.0841892i	−0.369419	+	0.929263i	$0.620443\pi$
$348$	−4.78838e8	−	3.02326e9i	−0.0326491	−	0.206138i
$349$		−	2.06149e10i		−	1.38957i	−0.719220	−	0.694783i	$-0.755501\pi$
$349$		−	2.06149e10i		−	1.38957i	0.719220	−	0.694783i	$-0.244499\pi$
$350$	2.73425e10	−	1.61109e10i	1.82207	−	1.07361i
$351$	−6.62762e8			−0.0436646
$352$	−2.52985e9	+	4.00689e8i	−0.164787	+	0.0260998i
$353$	−9.18670e9	+	1.80299e10i	−0.591644	+	1.16117i	0.380059	+	0.924962i	$0.375904\pi$
$353$	−9.18670e9	+	1.80299e10i	−0.591644	+	1.16117i	−0.971703	+	0.236205i	$0.924096\pi$
$354$	−1.13618e10	+	3.69167e9i	−0.723493	+	0.235077i
$355$	2.00312e9	+	1.82790e10i	0.126123	+	1.15090i
$356$	1.47057e8	−	4.52594e8i	0.00915556	−	0.0281779i
$357$	1.80277e10	−	1.80277e10i	1.10986	−	1.10986i
$358$	−8.99453e9	+	4.58294e9i	−0.547579	+	0.279005i
$359$	−2.60529e8	−	3.58588e8i	−0.0156848	−	0.0215883i	0.801103	−	0.598527i	$-0.204247\pi$
$359$	−2.60529e8	−	3.58588e8i	−0.0156848	−	0.0215883i	−0.816787	+	0.576939i	$0.804247\pi$
$360$	−1.00334e9	−	8.05158e8i	−0.0597365	−	0.0479370i
$361$	2.49125e10	+	1.81000e10i	1.46686	+	1.06573i
$362$	−2.02470e9	+	1.27834e10i	−0.117903	+	0.744412i
$363$	9.74148e9	+	1.54290e9i	0.561046	+	0.0888609i
$364$	3.03829e9	−	4.18184e9i	0.173071	−	0.238211i
$365$	3.45995e8	−	7.21334e9i	0.0194939	−	0.406410i
$366$	−1.64048e10	+	1.19188e10i	−0.914211	+	0.664213i
$367$	1.17561e10	+	2.30726e10i	0.648035	+	1.27184i	0.948115	+	0.317926i	$0.102987\pi$
$367$	1.17561e10	+	2.30726e10i	0.648035	+	1.27184i	−0.300080	+	0.953914i	$0.597013\pi$
$368$	−9.59059e9	−	9.59059e9i	−0.522942	−	0.522942i
$369$	4.93864e9	+	1.60466e9i	0.266380	+	0.0865522i
$370$	1.61936e9	−	7.78799e9i	0.0864044	−	0.415545i
$371$	−8.06314e9	−	2.48158e10i	−0.425607	−	1.30988i
$372$	3.25076e9	+	1.65635e9i	0.169752	+	0.0864927i
$373$	−3.39395e9	−	2.14285e10i	−0.175335	−	1.10702i	−0.905685	−	0.423951i	$-0.860643\pi$
$373$	−3.39395e9	−	2.14285e10i	−0.175335	−	1.10702i	0.730350	−	0.683074i	$-0.239357\pi$
$374$			5.84535e9i			0.298761i
$375$	−1.01031e10	+	5.31811e9i	−0.510894	+	0.268926i
$376$	−4.54845e9			−0.227569
$377$	1.97124e9	−	3.12214e8i	0.0975829	−	0.0154556i
$378$	3.77235e9	−	7.40366e9i	0.184776	−	0.362643i
$379$	8.20155e9	−	2.66484e9i	0.397502	−	0.129156i	−0.103443	−	0.994635i	$-0.532986\pi$
$379$	8.20155e9	−	2.66484e9i	0.397502	−	0.129156i	0.500945	+	0.865479i	$0.332986\pi$
$380$	2.84247e10	+	5.91035e9i	1.36320	+	0.283451i
$381$	−5.13650e9	+	1.58085e10i	−0.243763	+	0.750224i
$382$	3.10662e10	−	3.10662e10i	1.45893	−	1.45893i
$383$	−3.25301e10	+	1.65749e10i	−1.51179	+	0.770294i	−0.996246	−	0.0865713i	$-0.972409\pi$
$383$	−3.25301e10	+	1.65749e10i	−1.51179	+	0.770294i	−0.515541	+	0.856865i	$0.672409\pi$
$384$	−3.34203e9	−	4.59991e9i	−0.153704	−	0.211556i
$385$	4.35667e9	+	2.08972e8i	0.198295	+	0.00951144i
$386$	1.01236e10	+	7.35520e9i	0.456020	+	0.331318i
$387$	1.30634e9	−	8.24790e9i	0.0582388	−	0.367705i
$388$	−1.03475e10	−	1.63888e9i	−0.456572	−	0.0723139i
$389$	2.96330e9	−	4.07863e9i	0.129413	−	0.178121i	−0.739394	−	0.673273i	$-0.764888\pi$
$389$	2.96330e9	−	4.07863e9i	0.129413	−	0.178121i	0.868806	+	0.495152i	$0.164888\pi$
$390$	−2.56588e9	+	3.19747e9i	−0.110912	+	0.138213i
$391$	−2.13135e10	+	1.54852e10i	−0.911901	+	0.662535i
$392$	−3.55647e9	−	6.97997e9i	−0.150617	−	0.295603i
$393$	4.73536e9	+	4.73536e9i	0.198510	+	0.198510i
$394$	−3.93914e9	−	1.27990e9i	−0.163462	−	0.0531120i
$395$	1.46556e10	−	1.60605e9i	0.602028	−	0.0659737i
$396$	2.67038e8	+	8.21858e8i	0.0108591	+	0.0334207i
$397$	−2.62636e10	−	1.33820e10i	−1.05729	−	0.538714i	−0.163192	−	0.986594i	$-0.552179\pi$
$397$	−2.62636e10	−	1.33820e10i	−1.05729	−	0.538714i	−0.894094	+	0.447880i	$0.852179\pi$
$398$	9.33479e8	+	5.89375e9i	0.0372025	+	0.234887i
$399$		−	3.83675e10i		−	1.51381i
$400$	−2.85164e10	+	6.32595e9i	−1.11392	+	0.247107i
$401$	−1.35651e10			−0.524621			−0.262311	−	0.964983i	$-0.584485\pi$
$401$	−1.35651e10			−0.524621			−0.262311	+	0.964983i	$0.584485\pi$
$402$	−7.69140e9	+	1.21820e9i	−0.294511	+	0.0466459i
$403$	−1.07998e9	+	2.11958e9i	−0.0409444	+	0.0803579i
$404$	−4.07839e10	+	1.32515e10i	−1.53096	+	0.497438i
$405$	−1.48319e9	+	2.59545e9i	−0.0551287	+	0.0964702i
$406$	−7.73232e9	+	2.37976e10i	−0.284581	+	0.875849i
$407$	7.73042e8	−	7.73042e8i	0.0281725	−	0.0281725i
$408$	−5.69607e9	+	2.90229e9i	−0.205558	+	0.104737i
$409$	−1.28321e10	−	1.76619e10i	−0.458570	−	0.631167i	0.515642	−	0.856804i	$-0.327554\pi$
$409$	−1.28321e10	−	1.76619e10i	−0.458570	−	0.631167i	−0.974211	+	0.225637i	$0.927554\pi$
$410$	2.68616e10	−	1.76138e10i	0.950597	−	0.623330i
$411$	1.21690e10	+	8.84127e9i	0.426468	+	0.309847i
$412$	−6.56412e9	+	4.14442e10i	−0.227818	+	1.43838i
$413$	4.37524e10	+	6.92970e9i	1.50384	+	0.238185i
$414$	−5.04691e9	+	6.94647e9i	−0.171800	+	0.236463i
$415$	4.22535e10	−	1.15227e10i	1.42453	−	0.388474i
$416$	−7.22225e9	+	5.24727e9i	−0.241156	+	0.175210i
$417$	−2.23478e9	−	4.38601e9i	−0.0739080	−	0.145053i
$418$	6.22018e9	+	6.22018e9i	0.203750	+	0.203750i
$419$	4.04629e10	+	1.31472e10i	1.31281	+	0.426557i	0.880019	−	0.474938i	$-0.157530\pi$
$419$	4.04629e10	+	1.31472e10i	1.31281	+	0.426557i	0.432789	+	0.901495i	$0.357530\pi$
$420$	−9.57722e9	−	2.12568e10i	−0.307781	−	0.683127i
$421$	5.78430e9	+	1.78022e10i	0.184129	+	0.566691i	0.999932	−	0.0116386i	$-0.00370477\pi$
$421$	5.78430e9	+	1.78022e10i	0.184129	+	0.566691i	−0.815803	+	0.578330i	$0.803705\pi$
$422$	−6.61952e10	−	3.37282e10i	−2.08726	−	1.06351i
$423$	1.65340e9	+	1.04391e10i	0.0516435	+	0.326064i
$424$			6.54275e9i			0.202440i
$425$	3.47129e9	+	5.66302e10i	0.106399	+	1.73577i
$426$	2.97819e10			0.904303
$427$	7.42633e10	−	1.17622e10i	2.23389	−	0.353814i
$428$	−2.49699e9	+	4.90062e9i	−0.0744118	+	0.146041i
$429$	−5.35871e8	+	1.74115e8i	−0.0158209	+	0.00514052i
$430$	−3.47342e10	−	3.82342e10i	−1.01597	−	1.11835i
$431$	2.09743e8	−	6.45523e8i	0.00607825	−	0.0187069i	−0.947971	−	0.318356i	$-0.896869\pi$
$431$	2.09743e8	−	6.45523e8i	0.00607825	−	0.0187069i	0.954050	+	0.299649i	$0.0968694\pi$
$432$	−5.40784e9	+	5.40784e9i	−0.155271	+	0.155271i
$433$	3.07083e10	−	1.56466e10i	0.873582	−	0.445112i	0.0410943	−	0.999155i	$-0.486916\pi$
$433$	3.07083e10	−	1.56466e10i	0.873582	−	0.445112i	0.832488	+	0.554043i	$0.186916\pi$
$434$	−1.75305e10	−	2.41287e10i	−0.494124	−	0.680103i
$435$	3.18876e9	−	8.41831e9i	0.0890564	−	0.235108i
$436$	−3.44795e10	−	2.50508e10i	−0.954145	−	0.693227i
$437$	−6.20207e9	+	3.91583e10i	−0.170063	+	1.07374i
$438$	−1.15522e10	−	1.82968e9i	−0.313882	−	0.0497140i
$439$	3.88734e10	−	5.35047e10i	1.04663	−	1.44057i	0.154943	−	0.987923i	$-0.450481\pi$
$439$	3.88734e10	−	5.35047e10i	1.04663	−	1.44057i	0.891691	−	0.452644i	$-0.149519\pi$
$440$	−1.02277e9	−	3.87414e8i	−0.0272877	−	0.0103363i
$441$	−1.47269e10	+	1.06997e10i	−0.389365	+	0.282890i
$442$	9.24905e9	+	1.81523e10i	0.242331	+	0.475601i
$443$	−1.78197e10	−	1.78197e10i	−0.462685	−	0.462685i	0.436850	−	0.899535i	$-0.356094\pi$
$443$	−1.78197e10	−	1.78197e10i	−0.462685	−	0.462685i	−0.899535	+	0.436850i	$0.856094\pi$
$444$	−5.55777e9	−	1.80583e9i	−0.143011	−	0.0464670i
$445$	1.03590e9	−	9.41075e8i	0.0264167	−	0.0239985i
$446$	2.77000e9	+	8.52517e9i	0.0700067	+	0.215458i
$447$	−2.11361e10	−	1.07694e10i	−0.529414	−	0.269750i
$448$	−6.26872e9	−	3.95791e10i	−0.155620	−	0.982549i
$449$			3.58408e10i			0.881846i	0.897545	+	0.440923i	$0.145349\pi$
$449$			3.58408e10i			0.881846i	−0.897545	+	0.440923i	$0.854651\pi$
$450$	6.77947e9	+	1.72039e10i	0.165328	+	0.419544i
$451$	4.41466e9			0.106707
$452$	−4.70255e10	+	7.44811e9i	−1.12663	+	0.178440i
$453$	−2.80713e9	+	5.50931e9i	−0.0666608	+	0.130829i
$454$	1.31278e10	−	4.26549e9i	0.309008	−	0.100403i
$455$	1.38600e10	−	6.24458e9i	0.323382	−	0.145699i
$456$	−2.97293e9	+	9.14973e9i	−0.0687582	+	0.211616i
$457$	4.25412e9	−	4.25412e9i	0.0975316	−	0.0975316i	−0.656657	−	0.754189i	$-0.728030\pi$
$457$	4.25412e9	−	4.25412e9i	0.0975316	−	0.0975316i	0.754189	+	0.656657i	$0.228030\pi$
$458$	−1.02697e11	+	5.23269e10i	−2.33398	+	1.18922i
$459$	8.73161e9	+	1.20180e10i	0.196718	+	0.270759i
$460$	6.33848e9	+	2.32431e10i	0.141564	+	0.519115i
$461$	2.81453e10	+	2.04488e10i	0.623164	+	0.452755i	0.854025	−	0.520231i	$-0.174154\pi$
$461$	2.81453e10	+	2.04488e10i	0.623164	+	0.452755i	−0.230861	+	0.972987i	$0.574154\pi$
$462$	1.10508e9	−	6.97720e9i	0.0242564	−	0.153149i
$463$	−5.29058e10	−	8.37946e9i	−1.15128	−	0.182344i	−0.448518	−	0.893774i	$-0.648048\pi$
$463$	−5.29058e10	−	8.37946e9i	−1.15128	−	0.182344i	−0.702758	+	0.711429i	$0.748048\pi$
$464$	1.35369e10	−	1.86319e10i	0.292043	−	0.401963i
$465$	5.88363e9	+	8.97271e9i	0.125844	+	0.191916i
$466$	2.60326e10	−	1.89138e10i	0.552045	−	0.401084i
$467$	−3.33416e10	−	6.54367e10i	−0.701002	−	1.37579i	−0.916796	−	0.399356i	$-0.869234\pi$
$467$	−3.33416e10	−	6.54367e10i	−0.701002	−	1.37579i	0.215794	−	0.976439i	$-0.430766\pi$
$468$	2.12968e9	+	2.12968e9i	0.0443948	+	0.0443948i
$469$	2.74620e10	+	8.92296e9i	0.567599	+	0.184424i
$470$	5.67643e10	+	3.24384e10i	1.16328	+	0.664765i
$471$	−8.06835e9	−	2.48318e10i	−0.163946	−	0.504574i
$472$	−9.89695e9	−	5.04275e9i	−0.199404	−	0.101601i
$473$	−1.11059e9	−	7.01196e9i	−0.0221875	−	0.140086i
$474$		−	2.38784e10i		−	0.473033i
$475$	6.39555e10	+	5.65677e10i	1.25633	+	1.11120i
$476$	−1.15859e11			−2.25684
$477$	1.50163e10	−	2.37834e9i	0.290060	−	0.0459410i
$478$	5.53320e10	−	1.08595e11i	1.05990	−	2.08017i
$479$	−1.25069e10	+	4.06375e9i	−0.237580	+	0.0771943i	−0.425387	−	0.905012i	$-0.639862\pi$
$479$	−1.25069e10	+	4.06375e9i	−0.237580	+	0.0771943i	0.187807	+	0.982206i	$0.439862\pi$
$480$	4.38628e9	+	4.00260e10i	0.0826289	+	0.754011i
$481$	1.17744e9	−	3.62380e9i	0.0219968	−	0.0676992i
$482$	−2.71510e10	+	2.71510e10i	−0.503035	+	0.503035i
$483$	2.83680e10	−	1.44542e10i	0.521243	−	0.265586i
$484$	−2.63449e10	−	3.62606e10i	−0.480081	−	0.660775i
$485$	−2.40300e10	−	1.92834e10i	−0.434296	−	0.348512i
$486$	3.91690e9	+	2.84580e9i	0.0702098	+	0.0510104i
$487$	−1.49781e9	+	9.45679e9i	−0.0266281	+	0.168123i	−0.997419	−	0.0718052i	$-0.977124\pi$
$487$	−1.49781e9	+	9.45679e9i	−0.0266281	+	0.168123i	0.970791	+	0.239929i	$0.0771240\pi$
$488$	−1.86214e10	−	2.94934e9i	−0.328347	−	0.0520051i
$489$	−3.35216e10	+	4.61385e10i	−0.586258	+	0.806915i
$490$	−5.39490e9	+	1.12473e11i	−0.0935835	+	1.95103i
$491$	4.26108e10	−	3.09586e10i	0.733151	−	0.532666i	−0.157407	−	0.987534i	$-0.550314\pi$
$491$	4.26108e10	−	3.09586e10i	0.733151	−	0.532666i	0.890559	+	0.454868i	$0.150314\pi$
$492$	−1.07132e10	−	2.10259e10i	−0.182835	−	0.358835i
$493$	−3.16317e10	−	3.16317e10i	−0.535470	−	0.535470i
$494$	2.91584e10	+	9.47414e9i	0.489617	+	0.159086i
$495$	−5.17369e8	+	2.48818e9i	−0.00861746	+	0.0414440i
$496$	8.48265e9	+	2.61069e10i	0.140154	+	0.431349i
$497$	−9.83953e10	−	5.01349e10i	−1.61268	−	0.821703i
$498$	−1.10963e10	−	7.00595e10i	−0.180411	−	1.13907i
$499$		−	1.05521e11i		−	1.70191i	−0.525241	−	0.850954i	$-0.676025\pi$
$499$		−	1.05521e11i		−	1.70191i	0.525241	−	0.850954i	$-0.323975\pi$
$500$	4.95537e10	+	1.53759e10i	0.792860	+	0.246014i
$501$	3.14603e10			0.499358
$502$	−1.20703e10	+	1.91175e9i	−0.190066	+	0.0301035i
$503$	−2.76681e10	+	5.43018e10i	−0.432223	+	0.848286i	0.567467	+	0.823396i	$0.307923\pi$
$503$	−2.76681e10	+	5.43018e10i	−0.432223	+	0.848286i	−0.999690	+	0.0248896i	$0.992077\pi$
$504$	7.34770e9	−	2.38741e9i	0.113875	−	0.0370003i
$505$	−1.23474e11	−	2.56739e10i	−1.89849	−	0.394754i
$506$	−2.25572e9	+	6.94239e9i	−0.0344098	+	0.105903i
$507$	2.55861e10	−	2.55861e10i	0.387232	−	0.387232i
$508$	6.73035e10	−	3.42929e10i	1.01061	−	0.514931i
$509$	5.27606e10	+	7.26187e10i	0.786029	+	1.08188i	0.994591	+	0.103867i	$0.0331217\pi$
$509$	5.27606e10	+	7.26187e10i	0.786029	+	1.08188i	−0.208562	+	0.978009i	$0.566878\pi$
$510$	9.17849e10	+	4.40256e9i	1.35672	+	0.0650766i
$511$	3.50866e10	+	2.54919e10i	0.514586	+	0.373869i
$512$	−1.32965e10	+	8.39509e10i	−0.193490	+	1.22165i
$513$	2.20802e10	+	3.49716e9i	0.318811	+	0.0504947i
$514$	−5.66564e9	+	7.79808e9i	−0.0811702	+	0.111721i
$515$	−7.72346e10	+	9.62456e10i	−1.09795	+	1.36821i
$516$	−3.07011e10	+	2.23056e10i	−0.433067	+	0.314641i
$517$	4.07932e9	+	8.00611e9i	0.0570986	+	0.112062i
$518$	3.37793e10	+	3.37793e10i	0.469171	+	0.469171i
$519$	−7.91099e10	−	2.57044e10i	−1.09034	−	0.354273i
$520$	−3.78913e9	+	4.15235e8i	−0.0518235	+	0.00567912i
$521$	3.38133e10	+	1.04066e11i	0.458919	+	1.41241i	0.866472	+	0.499226i	$0.166382\pi$
$521$	3.38133e10	+	1.04066e11i	0.458919	+	1.41241i	−0.407553	+	0.913182i	$0.633618\pi$
$522$	−1.29906e10	−	6.61902e9i	−0.174963	−	0.0891480i
$523$	−9.59640e9	−	6.05893e10i	−0.128263	−	0.809821i	−0.965007	−	0.262226i	$-0.915543\pi$
$523$	−9.59640e9	−	6.05893e10i	−0.128263	−	0.809821i	0.836743	−	0.547595i	$-0.184457\pi$
$524$		−	3.04327e10i		−	0.403660i
$525$	6.56266e9	−	6.82519e10i	0.0863858	−	0.898417i
$526$	1.05329e10			0.137595
$527$	5.26631e10	−	8.34101e9i	0.682753	−	0.108137i
$528$	−2.95176e9	+	5.79316e9i	−0.0379792	+	0.0745384i
$529$	4.31889e10	−	1.40329e10i	0.551506	−	0.179195i
$530$	4.66613e10	−	8.16530e10i	0.591361	−	1.03483i
$531$	−7.97598e9	+	2.45475e10i	−0.100324	+	0.308766i
$532$	−1.23288e11	+	1.23288e11i	−1.53913	+	1.53913i
$533$	1.37094e10	−	6.98528e9i	0.169867	−	0.0865516i
$534$	−1.33233e9	−	1.83380e9i	−0.0163850	−	0.0225521i
$535$	−1.35266e10	+	8.86974e9i	−0.165110	+	0.108267i
$536$	−5.85764e9	−	4.25583e9i	−0.0709682	−	0.0515614i
$537$	−3.41186e9	+	2.15416e10i	−0.0410293	+	0.259049i
$538$	−1.61465e11	−	2.55735e10i	−1.92730	−	0.305254i
$539$	−9.09637e9	+	1.25201e10i	−0.107774	+	0.148338i
$540$	1.31061e10	−	3.57408e9i	0.154134	−	0.0420329i
$541$	1.11401e11	−	8.09377e10i	1.30047	−	0.944848i	0.300512	−	0.953778i	$-0.402843\pi$
$541$	1.11401e11	−	8.09377e10i	1.30047	−	0.944848i	0.999960	+	0.00893013i	$0.00284259\pi$
$542$	−3.81516e10	−	7.48768e10i	−0.442095	−	0.867661i
$543$	1.97730e10	+	1.97730e10i	0.227444	+	0.227444i
$544$	1.90300e11	+	6.18323e10i	2.17292	+	0.706024i
$545$	−5.14867e10	−	1.14276e11i	−0.583592	−	1.29529i
$546$	−7.60823e9	−	2.34157e10i	−0.0856077	−	0.263474i
$547$	−4.25135e10	−	2.16617e10i	−0.474873	−	0.241960i	0.200138	−	0.979768i	$-0.435861\pi$
$547$	−4.25135e10	−	2.16617e10i	−0.474873	−	0.241960i	−0.675011	+	0.737808i	$0.735861\pi$
$548$	−1.06930e10	−	6.75132e10i	−0.118571	−	0.748628i
$549$			4.38101e10i			0.482264i
$550$	1.00011e10	+	1.21290e10i	0.109295	+	0.132549i
$551$	−6.73201e10			−0.730362
$552$	−7.88508e9	+	1.24887e9i	−0.0849278	+	0.0134512i
$553$	−4.01969e10	+	7.88909e10i	−0.429826	+	0.843580i
$554$	1.37870e10	−	4.47968e9i	0.146363	−	0.0475563i
$555$	−1.15562e10	−	1.27207e10i	−0.121799	−	0.134072i
$556$	−6.91263e9	+	2.12749e10i	−0.0723343	+	0.222622i
$557$	−8.04665e10	+	8.04665e10i	−0.835977	+	0.835977i	−0.988327	−	0.152350i	$-0.951316\pi$
$557$	−8.04665e10	+	8.04665e10i	−0.835977	+	0.835977i	0.152350	+	0.988327i	$0.451316\pi$
$558$	1.54838e10	−	7.88937e9i	0.159713	−	0.0813777i
$559$	−1.45438e10	−	2.00178e10i	−0.148947	−	0.205008i
$560$	6.21381e10	−	1.64044e11i	0.631838	−	1.66805i
$561$	1.02171e10	+	7.42319e9i	0.103152	+	0.0749444i
$562$	−3.73300e10	+	2.35692e11i	−0.374208	+	2.36265i
$563$	1.07118e11	+	1.69659e10i	1.06618	+	0.168866i	0.664782	−	0.747038i	$-0.268525\pi$
$563$	1.07118e11	+	1.69659e10i	1.06618	+	0.168866i	0.401397	+	0.915904i	$0.368525\pi$
$564$	2.82316e10	−	3.88575e10i	0.279010	−	0.384024i
$565$	−1.30943e11	−	4.95998e10i	−1.28496	−	0.486728i
$566$	1.98482e11	−	1.44205e11i	1.93399	−	1.40513i
$567$	−8.15030e9	−	1.59959e10i	−0.0788572	−	0.154766i
$568$	1.95802e10	+	1.95802e10i	0.188115	+	0.188115i
$569$	−3.70998e10	−	1.20544e10i	−0.353934	−	0.115000i	0.126653	−	0.991947i	$-0.459576\pi$
$569$	−3.70998e10	−	1.20544e10i	−0.353934	−	0.115000i	−0.480587	+	0.876947i	$0.659576\pi$
$570$	1.02355e11	−	9.29857e10i	0.969642	−	0.880880i
$571$	4.41223e9	+	1.35795e10i	0.0415063	+	0.127743i	0.969662	−	0.244448i	$-0.0786066\pi$
$571$	4.41223e9	+	1.35795e10i	0.0415063	+	0.127743i	−0.928156	+	0.372191i	$0.878607\pi$
$572$	2.28143e9	+	1.16245e9i	0.0213119	+	0.0108590i
$573$	−1.48490e10	−	9.37526e10i	−0.137746	−	0.869691i
$574$			1.92906e11i			1.77704i
$575$	−1.77308e10	+	6.85979e10i	−0.162202	+	0.627537i
$576$	2.33489e10			0.212117
$577$	−1.21124e11	+	1.91841e10i	−1.09276	+	0.173077i	−0.676699	−	0.736259i	$-0.736590\pi$
$577$	−1.21124e11	+	1.91841e10i	−1.09276	+	0.173077i	−0.416063	+	0.909336i	$0.636590\pi$
$578$	1.38759e11	−	2.72329e11i	1.24322	−	2.43996i
$579$	2.57124e10	−	8.35447e9i	0.228786	−	0.0743369i
$580$	−3.72975e10	+	1.68043e10i	−0.329585	+	0.148494i
$581$	−8.12776e10	+	2.50147e11i	−0.713290	+	2.19528i
$582$	−3.52852e10	+	3.52852e10i	−0.307539	+	0.307539i
$583$	1.15164e10	−	5.86792e9i	0.0996883	−	0.0507937i
$584$	−6.39207e9	−	8.79793e9i	−0.0549528	−	0.0756361i
$585$	2.33038e9	+	8.54549e9i	0.0198978	+	0.0729648i
$586$	3.92882e10	+	2.85445e10i	0.333174	+	0.242065i
$587$	−7.20219e9	+	4.54728e10i	−0.0606614	+	0.383001i	0.938615	+	0.344966i	$0.112110\pi$
$587$	−7.20219e9	+	4.54728e10i	−0.0606614	+	0.383001i	−0.999276	+	0.0380344i	$0.987890\pi$
$588$	8.17045e10	+	1.29407e10i	0.683497	+	0.108255i
$589$	4.71641e10	−	6.49159e10i	0.391878	−	0.539374i
$590$	8.75495e10	+	1.33516e11i	0.722513	+	1.10185i
$591$	−7.23958e9	+	5.25986e9i	−0.0593422	+	0.0431146i
$592$	−1.99612e10	−	3.91760e10i	−0.162517	−	0.318958i
$593$	−8.47075e10	−	8.47075e10i	−0.685020	−	0.685020i	0.276107	−	0.961127i	$-0.410956\pi$
$593$	−8.47075e10	−	8.47075e10i	−0.685020	−	0.685020i	−0.961127	+	0.276107i	$0.910956\pi$
$594$	3.91460e9	+	1.27193e9i	0.0314443	+	0.0102169i
$595$	−2.95834e11	−	1.69056e11i	−2.36037	−	1.34885i
$596$	3.33119e10	+	1.02524e11i	0.264006	+	0.812528i
$597$	1.14872e10	+	5.85302e9i	0.0904309	+	0.0460768i
$598$	3.97992e9	+	2.51282e10i	0.0311222	+	0.196498i
$599$		−	6.98459e10i		−	0.542542i	−0.962503	−	0.271271i	$-0.912556\pi$
$599$		−	6.98459e10i		−	0.542542i	0.962503	−	0.271271i	$-0.0874440\pi$
$600$	−6.85358e9	+	1.57679e10i	−0.0528826	+	0.121666i
$601$	2.19620e11			1.68335			0.841676	−	0.539983i	$-0.181569\pi$
$601$	2.19620e11			1.68335			0.841676	+	0.539983i	$0.181569\pi$
$602$	3.06399e11	−	4.85288e10i	2.33293	−	0.369499i
$603$	−7.63824e9	+	1.49909e10i	−0.0577729	+	0.113386i
$604$	2.67236e10	−	8.68303e9i	0.200793	−	0.0652414i
$605$	−1.43590e10	−	1.31029e11i	−0.107177	−	0.978018i
$606$	−6.31184e10	+	1.94258e11i	−0.468021	+	1.44042i
$607$	6.33895e10	−	6.33895e10i	0.466942	−	0.466942i	−0.433981	−	0.900922i	$-0.642891\pi$
$607$	6.33895e10	−	6.33895e10i	0.466942	−	0.466942i	0.900922	+	0.433981i	$0.142891\pi$
$608$	2.68300e11	−	1.36706e11i	1.96339	−	1.00040i
$609$	3.17766e10	+	4.37367e10i	0.231014	+	0.317963i
$610$	2.11360e11	+	1.69611e11i	1.52652	+	1.22499i
$611$	2.53360e10	+	1.84077e10i	0.181791	+	0.132079i
$612$	1.05604e10	−	6.66758e10i	0.0752792	−	0.475294i
$613$	−6.58592e10	−	1.04311e10i	−0.466417	−	0.0738732i	−0.0811972	−	0.996698i	$-0.525874\pi$
$613$	−6.58592e10	−	1.04311e10i	−0.466417	−	0.0738732i	−0.385220	+	0.922825i	$0.625874\pi$
$614$	−6.06268e10	+	8.34456e10i	−0.426571	+	0.587124i
$615$	3.32500e9	−	6.93199e10i	0.0232430	−	0.484571i
$616$	5.31372e9	−	3.86065e9i	0.0369042	−	0.0268125i
$617$	4.50326e10	+	8.83815e10i	0.310732	+	0.609847i	0.992572	−	0.121655i	$-0.0388200\pi$
$617$	4.50326e10	+	8.83815e10i	0.310732	+	0.609847i	−0.681840	+	0.731501i	$0.738820\pi$
$618$	1.41325e11	+	1.41325e11i	0.968871	+	0.968871i
$619$	2.06048e11	+	6.69490e10i	1.40348	+	0.456018i	0.910314	−	0.413919i	$-0.135840\pi$
$619$	2.06048e11	+	6.69490e10i	1.40348	+	0.456018i	0.493164	+	0.869936i	$0.335840\pi$
$620$	9.92629e9	−	4.77385e10i	0.0671769	−	0.323074i
$621$	5.73258e9	+	1.76431e10i	0.0385464	+	0.118634i
$622$	−4.18173e10	−	2.13070e10i	−0.279380	−	0.142351i
$623$	1.31482e9	+	8.30146e9i	0.00872800	+	0.0551064i
$624$			2.26608e10i			0.149464i
$625$	1.04095e11	+	1.11568e11i	0.682195	+	0.731170i
$626$	1.16879e11			0.761095
$627$	1.87715e10	−	2.97311e9i	0.121459	−	0.0192372i
$628$	−5.38669e10	+	1.05720e11i	−0.346324	+	0.679700i
$629$	−8.12236e10	+	2.63911e10i	−0.518895	+	0.168599i
$630$	−1.08725e11	−	2.26072e10i	−0.690189	−	0.143511i
$631$	−5.41857e10	+	1.66766e11i	−0.341796	+	1.05194i	0.621481	+	0.783429i	$0.286531\pi$
$631$	−5.41857e10	+	1.66766e11i	−0.341796	+	1.05194i	−0.963277	+	0.268510i	$0.913469\pi$
$632$	1.56989e10	−	1.56989e10i	0.0984014	−	0.0984014i
$633$	−1.43017e11	+	7.28708e10i	−0.890785	+	0.453878i
$634$	7.13372e10	+	9.81872e10i	0.441529	+	0.607712i
$635$	2.21892e11	+	1.06433e10i	1.36473	+	0.0654607i
$636$	−5.58948e10	−	4.06100e10i	−0.341620	−	0.248201i
$637$	−8.43766e9	+	5.32733e10i	−0.0512465	+	0.323558i
$638$	−1.22423e10	−	1.93899e9i	−0.0738891	−	0.0117029i
$639$	3.78209e10	−	5.20560e10i	0.226845	−	0.312225i
$640$	−4.75590e10	+	5.92654e10i	−0.283473	+	0.353249i
$641$	−1.91290e11	+	1.38980e11i	−1.13308	+	0.823229i	−0.986140	−	0.165917i	$-0.946942\pi$
$641$	−1.91290e11	+	1.38980e11i	−1.13308	+	0.823229i	−0.146937	+	0.989146i	$0.546942\pi$
$642$	1.18935e10	+	2.33422e10i	0.0700113	+	0.137405i
$643$	−7.38060e10	−	7.38060e10i	−0.431765	−	0.431765i	0.457463	−	0.889229i	$-0.348758\pi$
$643$	−7.38060e10	−	7.38060e10i	−0.431765	−	0.431765i	−0.889229	+	0.457463i	$0.848758\pi$
$644$	−1.37603e11	−	4.47098e10i	−0.799987	−	0.259932i
$645$	−1.10940e11	+	1.21574e10i	−0.640986	+	0.0702429i
$646$	−2.12353e11	−	6.53555e11i	−1.21935	−	3.75277i
$647$	−4.16619e10	−	2.12278e10i	−0.237751	−	0.121140i	0.331056	−	0.943611i	$-0.392595\pi$
$647$	−4.16619e10	−	2.12278e10i	−0.237751	−	0.121140i	−0.568807	+	0.822471i	$0.692595\pi$
$648$	7.04203e8	+	4.44616e9i	0.00399390	+	0.0252165i
$649$			2.19431e10i			0.123686i
$650$	5.02494e10	+	2.18410e10i	0.281499	+	0.122354i
$651$	−6.44372e10			−0.358767
$652$	2.55975e11	−	4.05425e10i	1.41647	−	0.224347i
$653$	−5.14882e10	+	1.01051e11i	−0.283175	+	0.555762i	−0.988154	−	0.153466i	$-0.950956\pi$
$653$	−5.14882e10	+	1.01051e11i	−0.283175	+	0.555762i	0.704979	+	0.709228i	$0.250956\pi$
$654$	−1.93063e11	+	6.27301e10i	−1.05533	+	0.342898i
$655$	4.44062e10	−	7.77069e10i	0.241256	−	0.422177i
$656$	5.48657e10	−	1.68859e11i	0.296268	−	0.911821i
$657$	−1.78685e10	+	1.78685e10i	−0.0959020	+	0.0959020i
$658$	−3.49840e11	+	1.78252e11i	−1.86623	+	0.950893i
$659$	−6.26084e10	−	8.61730e10i	−0.331964	−	0.456909i	0.610109	−	0.792317i	$-0.291126\pi$
$659$	−6.26084e10	−	8.61730e10i	−0.331964	−	0.456909i	−0.942073	+	0.335409i	$0.891126\pi$
$660$	9.65788e9	−	6.33291e9i	0.0508986	−	0.0333755i
$661$	3.54196e10	+	2.57338e10i	0.185540	+	0.134803i	0.676678	−	0.736279i	$-0.263419\pi$
$661$	3.54196e10	+	2.57338e10i	0.185540	+	0.134803i	−0.491138	+	0.871082i	$0.663419\pi$
$662$	2.99365e10	−	1.89011e11i	0.155872	−	0.984138i
$663$	4.34742e10	+	6.88563e9i	0.224997	+	0.0356361i
$664$	3.87655e10	−	5.33562e10i	0.199422	−	0.274481i
$665$	−4.94701e11	+	1.34907e11i	−2.52962	+	0.689837i
$666$	−2.25187e10	+	1.63608e10i	−0.114458	+	0.0831586i
$667$	−2.53616e10	−	4.97749e10i	−0.128136	−	0.251482i
$668$	−1.01093e11	−	1.01093e11i	−0.507709	−	0.507709i
$669$	1.84189e10	+	5.98467e9i	0.0919516	+	0.0298769i
$670$	4.27514e10	+	9.48876e10i	0.212154	+	0.470880i
$671$	1.15094e10	+	3.54223e10i	0.0567757	+	0.174738i
$672$	−2.15459e11	−	1.09782e11i	−1.05654	−	0.538336i
$673$	−7.92488e9	−	5.00357e10i	−0.0386307	−	0.243905i	0.960815	−	0.277190i	$-0.0894031\pi$
$673$	−7.92488e9	−	5.00357e10i	−0.0386307	−	0.243905i	−0.999446	+	0.0332851i	$0.989403\pi$
$674$		−	2.06620e11i		−	1.00123i
$675$	3.86803e10	+	9.99786e9i	0.186327	+	0.0481606i
$676$	−1.64434e11			−0.787416
$677$	1.17980e11	−	1.86862e10i	0.561635	−	0.0889542i	0.130839	−	0.991404i	$-0.458233\pi$
$677$	1.17980e11	−	1.86862e10i	0.561635	−	0.0889542i	0.430796	+	0.902449i	$0.358233\pi$
$678$	−1.02956e11	+	2.02062e11i	−0.487228	+	0.956239i
$679$	1.75976e11	−	5.71782e10i	0.827895	−	0.269000i
$680$	5.74498e10	+	6.32388e10i	0.268691	+	0.295766i
$681$	9.21573e9	−	2.83631e10i	0.0428491	−	0.131876i
$682$	1.04466e10	−	1.04466e10i	0.0482880	−	0.0482880i
$683$	2.05069e11	−	1.04488e11i	0.942359	−	0.480156i	0.0858618	−	0.996307i	$-0.472636\pi$
$683$	2.05069e11	−	1.04488e11i	0.942359	−	0.480156i	0.856498	+	0.516151i	$0.172636\pi$
$684$	−5.97137e10	−	8.21889e10i	−0.272803	−	0.375482i
$685$	7.12090e10	−	1.87991e11i	0.323424	−	0.853837i
$686$	−1.68177e11	−	1.22188e11i	−0.759398	−	0.551735i
$687$	−3.89558e10	+	2.45957e11i	−0.174882	+	1.10416i
$688$	−2.82007e11	−	4.46656e10i	−1.25866	−	0.199351i
$689$	2.64787e10	−	3.64448e10i	0.117495	−	0.161718i
$690$	1.07312e11	+	4.06486e10i	0.473425	+	0.179328i
$691$	−1.49570e11	+	1.08669e11i	−0.656045	+	0.476645i	−0.865325	−	0.501211i	$-0.832888\pi$
$691$	−1.49570e11	+	1.08669e11i	−0.656045	+	0.476645i	0.209280	+	0.977856i	$0.432888\pi$
$692$	1.71610e11	+	3.36805e11i	0.748375	+	1.46877i
$693$	−1.07921e10	−	1.07921e10i	−0.0467923	−	0.0467923i
$694$	−5.53474e10	−	1.79835e10i	−0.238594	−	0.0775239i
$695$	−4.86942e10	+	4.42367e10i	−0.208708	+	0.189602i
$696$	−4.18899e9	−	1.28924e10i	−0.0178514	−	0.0549410i
$697$	−3.07281e11	−	1.56568e11i	−1.30198	−	0.663393i
$698$	6.98034e10	+	4.40721e11i	0.294073	+	1.85670i
$699$		−	6.95219e10i		−	0.291214i
$700$	−2.40405e11	+	1.98229e11i	−1.00127	+	0.825610i
$701$	−4.07337e11			−1.68687			−0.843436	−	0.537230i	$-0.819471\pi$
$701$	−4.07337e11			−1.68687			−0.843436	+	0.537230i	$0.819471\pi$
$702$	1.41691e10	−	2.24416e9i	0.0583435	−	0.00924070i
$703$	−5.83485e10	+	1.14515e11i	−0.238896	+	0.468859i
$704$	1.88785e10	−	6.13401e9i	0.0768560	−	0.0249720i
$705$	1.28786e11	−	5.80243e10i	0.521329	−	0.234884i
$706$	1.35350e11	−	4.16565e11i	0.544803	−	1.67673i
$707$	5.35549e11	−	5.35549e11i	2.14349	−	2.14349i
$708$	1.04509e11	−	5.32502e10i	0.415932	−	0.211928i
$709$	1.12834e11	+	1.55303e11i	0.446535	+	0.614602i	0.971649	−	0.236430i	$-0.0759772\pi$
$709$	1.12834e11	+	1.55303e11i	0.446535	+	0.614602i	−0.525114	+	0.851032i	$0.675977\pi$
$710$	−1.04718e11	−	3.84000e11i	−0.412087	−	1.51112i
$711$	−4.17372e10	−	3.03239e10i	−0.163322	−	0.118660i
$712$	3.29690e8	−	2.08158e9i	0.00128288	−	0.00809978i
$713$	6.57654e10	+	1.04162e10i	0.254472	+	0.0403044i
$714$	−3.24368e11	+	4.46454e11i	−1.24809	+	1.71785i
$715$	4.12921e9	+	6.29716e9i	0.0157995	+	0.0240947i
$716$	8.01842e10	−	5.82572e10i	0.305096	−	0.221665i
$717$	−1.19547e11	−	2.34624e11i	−0.452336	−	0.887759i
$718$	6.78400e9	+	6.78400e9i	0.0255263	+	0.0255263i
$719$	−2.99760e11	−	9.73980e10i	−1.12165	−	0.364447i	−0.311255	−	0.950326i	$-0.600749\pi$
$719$	−2.99760e11	−	9.73980e10i	−1.12165	−	0.364447i	−0.810398	+	0.585879i	$0.800749\pi$
$720$	8.87423e10	+	5.07125e10i	0.330218	+	0.188706i
$721$	−2.29012e11	−	7.04827e11i	−0.847456	−	2.60820i
$722$	−5.93887e11	−	3.02600e11i	−2.18552	−	1.11358i
$723$	1.29776e10	+	8.19375e10i	0.0474943	+	0.299867i
$724$		−	1.27075e11i		−	0.462495i
$725$	−1.19756e11	−	1.15149e10i	−0.433455	−	0.0416782i
$726$	−2.13486e11			−0.768461
$727$	5.21197e11	−	8.25495e10i	1.86580	−	0.295513i	0.881520	−	0.472146i	$-0.156521\pi$
$727$	5.21197e11	−	8.25495e10i	1.86580	−	0.295513i	0.984277	+	0.176633i	$0.0565206\pi$
$728$	1.03927e10	−	2.03968e10i	0.0370000	−	0.0726167i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	1.70279e10	+	1.55384e11i	0.0599611	+	0.547161i
$731$	−1.71380e11	+	5.27453e11i	−0.600192	+	1.84720i
$732$	1.40777e11	−	1.40777e11i	0.490329	−	0.490329i
$733$	−8.72629e9	+	4.44627e9i	−0.0302283	+	0.0154021i	−0.469039	−	0.883177i	$-0.655400\pi$
$733$	−8.72629e9	+	4.44627e9i	−0.0302283	+	0.0154021i	0.438811	+	0.898579i	$0.355400\pi$
$734$	−3.29456e11	−	4.53458e11i	−1.13505	−	1.56226i
$735$	1.89742e11	+	1.52263e11i	0.650150	+	0.521729i
$736$	2.02154e11	+	1.46873e11i	0.688923	+	0.500532i
$737$	−2.23756e9	+	1.41274e10i	−0.00758411	+	0.0478842i
$738$	−1.11016e11	−	1.75832e10i	−0.374248	−	0.0592750i
$739$	−2.11185e11	+	2.90671e11i	−0.708085	+	0.974596i	0.291751	+	0.956494i	$0.405762\pi$
$739$	−2.11185e11	+	2.90671e11i	−0.708085	+	0.974596i	−0.999836	+	0.0181016i	$0.994238\pi$
$740$	−3.74184e9	+	7.80101e10i	−0.0124784	+	0.260150i
$741$	5.35891e10	−	3.89347e10i	0.177747	−	0.129141i
$742$	2.56408e11	+	5.03230e11i	0.845895	+	1.66016i
$743$	9.09671e9	+	9.09671e9i	0.0298490	+	0.0298490i	0.721874	−	0.692025i	$-0.243281\pi$
$743$	9.09671e9	+	9.09671e9i	0.0298490	+	0.0298490i	−0.692025	+	0.721874i	$0.743281\pi$
$744$	1.53667e10	+	4.99296e9i	0.0501522	+	0.0162954i
$745$	−6.45397e10	+	3.10391e11i	−0.209509	+	1.00759i
$746$	1.45117e11	+	4.46624e11i	0.468558	+	1.44207i
$747$	−1.36549e11	−	6.95753e10i	−0.438538	−	0.223446i
$748$	−8.97794e9	−	5.66845e10i	−0.0286794	−	0.181075i
$749$		−	9.71410e10i		−	0.308656i
$750$	1.97985e11	−	1.47905e11i	0.625731	−	0.467452i
$751$	3.04930e11			0.958606			0.479303	−	0.877649i	$-0.340889\pi$
$751$	3.04930e11			0.958606			0.479303	+	0.877649i	$0.340889\pi$
$752$	3.56929e11	−	5.65320e10i	1.11612	−	0.176776i
$753$	−1.19869e10	+	2.35256e10i	−0.0372844	+	0.0731747i
$754$	−4.10855e10	+	1.33495e10i	−0.127117	+	0.0413028i
$755$	8.09061e10	+	1.68228e10i	0.248997	+	0.0517739i
$756$	−2.52105e10	+	7.75899e10i	−0.0771781	+	0.237530i
$757$	−3.08337e9	+	3.08337e9i	−0.00938950	+	0.00938950i	−0.711786	−	0.702396i	$-0.752113\pi$
$757$	−3.08337e9	+	3.08337e9i	−0.00938950	+	0.00938950i	0.702396	+	0.711786i	$0.252113\pi$
$758$	−1.66316e11	+	8.47422e10i	−0.503799	+	0.256698i
$759$	9.27005e9	+	1.27591e10i	0.0279328	+	0.0384462i
$760$	1.28428e11	+	6.16017e9i	0.384950	+	0.0184645i
$761$	4.20842e11	+	3.05759e11i	1.25482	+	0.911677i	0.998491	−	0.0549134i	$-0.0174883\pi$
$761$	4.20842e11	+	3.05759e11i	1.25482	+	0.911677i	0.256325	+	0.966591i	$0.417488\pi$
$762$	5.62834e10	−	3.55359e11i	0.166940	−	1.05402i
$763$	7.43455e11	+	1.17752e11i	2.19360	+	0.347432i
$764$	−2.53545e11	+	3.48974e11i	−0.744185	+	1.02428i
$765$	1.24256e11	−	1.54841e11i	0.362803	−	0.452105i
$766$	6.39331e11	−	4.64501e11i	1.85699	−	1.34919i
$767$	3.47204e10	+	6.81425e10i	0.100324	+	0.196896i
$768$	1.77403e11	+	1.77403e11i	0.509937	+	0.509937i
$769$	−3.08852e11	−	1.00352e11i	−0.883172	−	0.286960i	−0.167898	−	0.985804i	$-0.553698\pi$
$769$	−3.08852e11	−	1.00352e11i	−0.883172	−	0.286960i	−0.715274	+	0.698844i	$0.753698\pi$
$770$	−9.38480e10	+	1.02844e10i	−0.266970	+	0.0292561i
$771$	6.43537e9	+	1.98060e10i	0.0182119	+	0.0560506i
$772$	−1.09469e11	−	5.57771e10i	−0.308192	−	0.157031i
$773$	7.97643e10	+	5.03612e11i	0.223404	+	1.41052i	0.803178	+	0.595739i	$0.203141\pi$
$773$	7.97643e10	+	5.03612e11i	0.223404	+	1.41052i	−0.579774	+	0.814777i	$0.696859\pi$
$774$			1.80754e11i			0.503643i
$775$	9.50040e10	−	1.07412e11i	0.263351	−	0.297745i
$776$	−4.63967e10			−0.127950
$777$	1.01940e11	−	1.61458e10i	0.279681	−	0.0442971i
$778$	−4.95412e10	+	9.72301e10i	−0.135222	+	0.265389i
$779$	−4.93593e11	+	1.60378e11i	−1.34035	+	0.435507i
$780$	1.99713e10	−	3.49479e10i	0.0539545	−	0.0944155i
$781$	1.69041e10	−	5.20254e10i	0.0454347	−	0.139834i
$782$	4.03223e11	−	4.03223e11i	1.07825	−	1.07825i
$783$	−2.80665e10	+	1.43006e10i	−0.0746693	+	0.0380459i
$784$	3.65839e11	+	5.03534e11i	0.968334	+	1.33280i
$785$	−2.91806e11	+	1.91344e11i	−0.768449	+	0.503891i
$786$	−1.17271e11	−	8.52021e10i	−0.307255	−	0.223234i
$787$	−9.94626e10	+	6.27982e11i	−0.259275	+	1.63700i	0.423161	+	0.906054i	$0.360920\pi$
$787$	−9.94626e10	+	6.27982e11i	−0.259275	+	1.63700i	−0.682436	+	0.730945i	$0.739080\pi$
$788$	4.01650e10	+	6.36152e9i	0.104170	+	0.0164989i
$789$	1.33760e10	−	1.84105e10i	0.0345158	−	0.0475069i
$790$	−3.07882e11	+	8.39604e10i	−0.790452	+	0.215559i
$791$	6.80304e11	−	4.94270e11i	1.73779	−	1.26258i
$792$	1.73743e9	+	3.40990e9i	0.00441578	+	0.00866645i
$793$	9.17899e10	+	9.17899e10i	0.232114	+	0.232114i
$794$	6.06797e11	+	1.97160e11i	1.52673	+	0.496064i
$795$	−8.34655e10	−	1.85253e11i	−0.208948	−	0.463764i
$796$	−1.81046e10	−	5.57201e10i	−0.0450958	−	0.138790i
$797$	5.89190e11	+	3.00207e11i	1.46023	+	0.744026i	0.990335	−	0.138696i	$-0.0442910\pi$
$797$	5.89190e11	+	3.00207e11i	1.46023	+	0.744026i	0.469897	+	0.882721i	$0.344291\pi$
$798$	1.29915e11	+	8.20250e11i	0.320367	+	2.02272i
$799$		−	7.01938e11i		−	1.72231i
$800$	5.00663e11	−	1.97294e11i	1.22232	−	0.481675i
$801$	−4.89727e9			−0.0118966
$802$	2.90006e11	−	4.59324e10i	0.700986	−	0.111025i
$803$	−9.75319e9	+	1.91417e10i	−0.0234576	+	0.0460382i
$804$	7.27152e10	−	2.36266e10i	0.174021	−	0.0565428i
$805$	−2.86116e11	−	3.14946e11i	−0.681331	−	0.749986i
$806$	1.59116e10	−	4.89708e10i	0.0377028	−	0.116037i
$807$	−2.49749e11	+	2.49749e11i	−0.588857	+	0.588857i
$808$	−1.69213e11	+	8.62184e10i	−0.396998	+	0.202281i
$809$	−2.59044e11	−	3.56543e11i	−0.604754	−	0.832373i	0.391379	−	0.920230i	$-0.371998\pi$
$809$	−2.59044e11	−	3.56543e11i	−0.604754	−	0.832373i	−0.996133	+	0.0878569i	$0.971998\pi$
$810$	2.29205e10	−	6.05099e10i	0.0532456	−	0.140568i
$811$	−5.15094e11	−	3.74238e11i	−1.19070	−	0.865096i	−0.197364	−	0.980330i	$-0.563238\pi$
$811$	−5.15094e11	−	3.74238e11i	−1.19070	−	0.865096i	−0.993338	+	0.115234i	$0.963238\pi$
$812$	3.84320e10	−	2.42650e11i	0.0884034	−	0.558157i
$813$	−1.79328e11	−	2.84027e10i	−0.410473	−	0.0650126i
$814$	−1.39091e10	+	1.91443e10i	−0.0316812	+	0.0436055i
$815$	7.12765e11	+	2.69988e11i	1.61553	+	0.611947i
$816$	4.10914e11	−	2.98546e11i	0.926808	−	0.673366i
$817$	3.78906e11	+	7.43645e11i	0.850439	+	1.66908i
$818$	3.34140e11	+	3.34140e11i	0.746303	+	0.746303i
$819$	−5.05905e10	−	1.64378e10i	−0.112443	−	0.0365350i
$820$	−2.33433e11	+	2.12064e11i	−0.516306	+	0.469043i
$821$	−1.09992e11	−	3.38522e11i	−0.242097	−	0.745099i	−0.996100	−	0.0882281i	$-0.971880\pi$
$821$	−1.09992e11	−	3.38522e11i	−0.242097	−	0.745099i	0.754003	−	0.656871i	$-0.228120\pi$
$822$	−2.90095e11	−	1.47811e11i	−0.635409	−	0.323757i
$823$	−1.99568e10	−	1.26002e11i	−0.0435002	−	0.274650i	0.956345	−	0.292240i	$-0.0944006\pi$
$823$	−1.99568e10	−	1.26002e11i	−0.0435002	−	0.274650i	−0.999845	+	0.0175902i	$0.994401\pi$
$824$			1.85829e11i			0.403093i
$825$	3.39012e10	−	2.07806e9i	0.0731811	−	0.00448582i
$826$	−9.58838e11			−2.05980
$827$	4.28049e10	−	6.77963e9i	0.0915106	−	0.0144938i	−0.110511	−	0.993875i	$-0.535249\pi$
$827$	4.28049e10	−	6.77963e9i	0.0915106	−	0.0144938i	0.202022	+	0.979381i	$0.435249\pi$
$828$	3.82725e10	−	7.51140e10i	0.0814264	−	0.159808i
$829$	4.34597e11	−	1.41209e11i	0.920171	−	0.298982i	0.189634	−	0.981855i	$-0.439270\pi$
$829$	4.34597e11	−	1.41209e11i	0.920171	−	0.298982i	0.730537	+	0.682873i	$0.239270\pi$
$830$	−8.64313e11	+	3.89415e11i	−1.82121	+	0.820540i
$831$	9.67849e9	−	2.97873e10i	0.0202957	−	0.0624637i
$832$	4.89200e10	−	4.89200e10i	0.102092	−	0.102092i
$833$	1.07718e12	−	5.48851e11i	2.23722	−	1.13992i
$834$	6.26283e10	+	8.62005e10i	0.129451	+	0.178175i
$835$	−1.10620e11	−	4.05642e11i	−0.227556	−	0.834443i
$836$	−6.98729e10	−	5.07657e10i	−0.143049	−	0.103931i
$837$	5.87339e9	−	3.70831e10i	0.0119671	−	0.0755570i
$838$	−9.09566e11	−	1.44061e11i	−1.84441	−	0.292126i
$839$	3.07102e11	−	4.22690e11i	0.619777	−	0.853050i	−0.377560	−	0.925985i	$-0.623237\pi$
$839$	3.07102e11	−	4.22690e11i	0.619777	−	0.853050i	0.997337	+	0.0729354i	$0.0232367\pi$
$840$	−5.66185e10	−	8.63449e10i	−0.113721	−	0.173428i
$841$	−3.27967e11	+	2.38282e11i	−0.655611	+	0.476329i
$842$	−1.83941e11	−	3.61005e11i	−0.365957	−	0.718231i
$843$	3.64562e11	+	3.64562e11i	0.721874	+	0.721874i
$844$	6.93722e11	+	2.25404e11i	1.36715	+	0.444214i
$845$	−4.19865e11	−	2.39935e11i	−0.823537	−	0.470617i
$846$	−7.06953e10	−	2.17578e11i	−0.138010	−	0.424750i
$847$	7.05327e11	+	3.59382e11i	1.37043	+	0.698269i
$848$	−8.13188e10	−	5.13427e11i	−0.157256	−	0.992877i
$849$		−	5.30058e11i		−	1.02022i
$850$	−2.65966e11	−	1.19893e12i	−0.509507	−	2.29678i
$851$	−1.06652e11			−0.203352
$852$	−2.88806e11	+	4.57423e10i	−0.548084	+	0.0868080i
$853$	1.20540e11	−	2.36572e11i	0.227685	−	0.446856i	−0.748696	−	0.662914i	$-0.769320\pi$
$853$	1.20540e11	−	2.36572e11i	0.227685	−	0.446856i	0.976381	+	0.216057i	$0.0693197\pi$
$854$	−1.54783e12	+	5.02921e11i	−2.91000	+	0.945515i
$855$	−3.25462e10	−	2.96993e11i	−0.0609027	−	0.555753i
$856$	−7.52703e9	+	2.31658e10i	−0.0140194	+	0.0431472i
$857$	−2.75313e11	+	2.75313e11i	−0.510392	+	0.510392i	−0.914647	−	0.404254i	$-0.867531\pi$
$857$	−2.75313e11	+	2.75313e11i	−0.510392	+	0.510392i	0.404254	+	0.914647i	$0.367531\pi$
$858$	1.08667e10	−	5.53686e9i	0.0200516	−	0.0102168i
$859$	1.16599e11	+	1.60485e11i	0.214152	+	0.294755i	0.902556	−	0.430573i	$-0.141688\pi$
$859$	1.16599e11	+	1.60485e11i	0.214152	+	0.294755i	−0.688404	+	0.725327i	$0.741688\pi$
$860$	3.95554e11	+	3.17422e11i	0.723122	+	0.580287i
$861$	3.37181e11	+	2.44977e11i	0.613551	+	0.445771i
$862$	−2.29827e9	+	1.45107e10i	−0.00416267	+	0.0262821i
$863$	8.53420e11	+	1.35168e11i	1.53858	+	0.243687i	0.867401	−	0.497610i	$-0.165789\pi$
$863$	8.53420e11	+	1.35168e11i	1.53858	+	0.243687i	0.671177	+	0.741297i	$0.265789\pi$
$864$	8.28175e10	−	1.13988e11i	0.148617	−	0.204553i
$865$	−5.32618e10	+	1.11040e12i	−0.0951374	+	1.98343i
$866$	−6.03526e11	+	4.38487e11i	−1.07306	+	0.779624i
$867$	−2.99793e11	−	5.88376e11i	−0.530573	−	1.04131i
$868$	2.07059e11	+	2.07059e11i	0.364767	+	0.364767i
$869$	−4.17127e10	−	1.35533e10i	−0.0731457	−	0.0237665i
$870$	−3.96670e10	+	1.90771e11i	−0.0692392	+	0.332993i
$871$	1.54051e10	+	4.74120e10i	0.0267665	+	0.0823789i
$872$	−1.68172e11	−	8.56881e10i	−0.290863	−	0.148202i
$873$	1.68655e10	+	1.06485e11i	0.0290364	+	0.183329i
$874$		−	8.58158e11i		−	1.47069i
$875$	−9.03099e11	+	1.55368e11i	−1.54065	+	0.265051i
$876$	1.14836e11			0.195011
$877$	−1.21593e11	+	1.92585e10i	−0.205547	+	0.0325555i	−0.258359	−	0.966049i	$-0.583182\pi$
$877$	−1.21593e11	+	1.92585e10i	−0.205547	+	0.0325555i	0.0528116	+	0.998604i	$0.483182\pi$
$878$	−6.49897e11	+	1.27549e12i	−1.09362	+	2.14635i
$879$	9.97865e10	−	3.24226e10i	0.167154	−	0.0543116i
$880$	8.50745e10	+	1.76896e10i	0.141863	+	0.0294976i
$881$	−4.76329e10	+	1.46599e11i	−0.0790685	+	0.243348i	−0.982775	−	0.184804i	$-0.940835\pi$
$881$	−4.76329e10	+	1.46599e11i	−0.0790685	+	0.243348i	0.903707	+	0.428152i	$0.140835\pi$
$882$	2.78613e11	−	2.78613e11i	0.460392	−	0.460392i
$883$	1.08815e11	−	5.54439e10i	0.178997	−	0.0912034i	−0.362196	−	0.932102i	$-0.617973\pi$
$883$	1.08815e11	−	5.54439e10i	0.178997	−	0.0912034i	0.541193	+	0.840899i	$0.317973\pi$
$884$	−1.17572e11	−	1.61824e11i	−0.192528	−	0.264992i
$885$	3.44555e11	+	1.65269e10i	0.561675	+	0.0269414i
$886$	4.41302e11	+	3.20625e11i	0.716146	+	0.520310i
$887$	−1.02070e11	+	6.44447e11i	−0.164894	+	1.04110i	0.756931	+	0.653495i	$0.226698\pi$
$887$	−1.02070e11	+	6.44447e11i	−0.164894	+	1.04110i	−0.921825	+	0.387606i	$0.873302\pi$
$888$	−2.55614e10	−	4.04853e9i	−0.0411086	−	0.00651097i
$889$	−7.84166e11	+	1.07931e12i	−1.25545	+	1.72798i
$890$	−1.89598e10	+	2.36267e10i	−0.0302186	+	0.0376567i
$891$	7.19449e9	−	5.22710e9i	0.0114153	−	0.00829373i
$892$	−3.99555e10	−	7.84171e10i	−0.0631128	−	0.123866i
$893$	−7.46949e11	−	7.46949e11i	−1.17459	−	1.17459i
$894$	4.88331e11	+	1.58668e11i	0.764477	+	0.248394i
$895$	2.89749e11	−	3.17524e10i	0.451575	−	0.0494862i
$896$	−1.41019e11	−	4.34013e11i	−0.218800	−	0.673396i
$897$	4.89761e10	+	2.49546e10i	0.0756509	+	0.0385461i
$898$	−1.21360e11	−	7.66234e11i	−0.186624	−	1.17830i
$899$			1.13062e11i			0.173093i
$900$	−9.21666e10	−	1.56420e11i	−0.140476	−	0.238408i
$901$	−1.00971e12			−1.53213
$902$	−9.43801e10	+	1.49483e10i	−0.142579	+	0.0225822i
$903$	3.04281e11	−	5.97185e11i	0.457640	−	0.898169i
$904$	−2.00535e11	+	6.51578e10i	−0.300273	+	0.0975647i
$905$	1.85423e11	−	3.24474e11i	0.276420	−	0.483711i
$906$	4.13583e10	−	1.27288e11i	0.0613832	−	0.188918i
$907$	−1.28773e11	+	1.28773e11i	−0.190281	+	0.190281i	−0.795818	−	0.605536i	$-0.792959\pi$
$907$	−1.28773e11	+	1.28773e11i	−0.190281	+	0.190281i	0.605536	+	0.795818i	$0.292959\pi$
$908$	−1.20754e11	+	6.15271e10i	−0.177647	+	0.0905156i
$909$	2.59390e11	+	3.57020e11i	0.379925	+	0.522921i
$910$	−2.75165e11	+	1.80432e11i	−0.401261	+	0.263117i
$911$	1.43269e11	+	1.04091e11i	0.208007	+	0.151126i	0.686912	−	0.726741i	$-0.258966\pi$
$911$	1.43269e11	+	1.04091e11i	0.208007	+	0.151126i	−0.478904	+	0.877867i	$0.658966\pi$
$912$	1.19573e11	−	7.54953e11i	0.172844	−	1.09129i
$913$	−1.28684e11	−	2.03815e10i	−0.185200	−	0.0293328i
$914$	−7.65433e10	+	1.05353e11i	−0.109679	+	0.150960i
$915$	5.64876e11	−	1.54044e11i	0.805877	−	0.219766i
$916$	9.15524e11	−	6.65167e11i	1.30043	−	0.944819i
$917$	2.44017e11	+	4.78910e11i	0.345098	+	0.677293i
$918$	−2.27365e11	−	2.27365e11i	−0.320150	−	0.320150i
$919$	−1.17558e11	−	3.81968e10i	−0.164812	−	0.0535507i	0.225449	−	0.974255i	$-0.427615\pi$
$919$	−1.17558e11	−	3.81968e10i	−0.164812	−	0.0535507i	−0.390261	+	0.920704i	$0.627615\pi$
$920$	4.38280e10	+	9.72770e10i	0.0611787	+	0.135787i
$921$	6.88635e10	+	2.11940e11i	0.0957085	+	0.294560i
$922$	−6.70954e11	−	3.41868e11i	−0.928473	−	0.473081i
$923$	−2.98251e10	−	1.88308e11i	−0.0410937	−	0.259455i
$924$			6.93577e10i			0.0951496i
$925$	−1.23384e11	+	1.93731e11i	−0.168535	+	0.264626i
$926$	1.15944e12			1.57690
$927$	4.26497e11	−	6.75504e10i	0.577560	−	0.0914764i
$928$	−1.92625e11	+	3.78047e11i	−0.259729	+	0.509746i
$929$	−2.14902e11	+	6.98260e10i	−0.288521	+	0.0937463i	−0.449702	−	0.893179i	$-0.648470\pi$
$929$	−2.14902e11	+	6.98260e10i	−0.288521	+	0.0937463i	0.161181	+	0.986925i	$0.448470\pi$
$930$	−1.56167e11	−	1.71903e11i	−0.208765	−	0.229801i
$931$	5.62208e11	−	1.73030e12i	0.748339	−	2.30315i
$932$	−2.23398e11	+	2.23398e11i	−0.296084	+	0.296084i
$933$	−9.03477e10	+	4.60345e10i	−0.119231	+	0.0607514i
$934$	9.34377e11	+	1.28606e12i	1.22782	+	1.68995i
$935$	5.97875e10	−	1.57838e11i	0.0782283	−	0.206522i
$936$	1.07909e10	+	7.84006e9i	0.0140590	+	0.0102145i
$937$	7.33849e10	−	4.63334e11i	0.0952025	−	0.601085i	−0.893251	−	0.449559i	$-0.851581\pi$
$937$	7.33849e10	−	4.63334e11i	0.0952025	−	0.601085i	0.988453	−	0.151526i	$-0.0484187\pi$
$938$	−6.17319e11	−	9.77738e10i	−0.797441	−	0.126302i
$939$	1.48428e11	−	2.04294e11i	0.190921	−	0.262780i
$940$	−6.00286e11	−	2.27382e11i	−0.768859	−	0.291236i
$941$	−1.16916e12	+	8.49444e11i	−1.49113	+	1.08337i	−0.517377	+	0.855757i	$0.673092\pi$
$941$	−1.16916e12	+	8.49444e11i	−1.49113	+	1.08337i	−0.973752	+	0.227611i	$0.926908\pi$
$942$	2.56574e11	+	5.03555e11i	0.325843	+	0.639504i
$943$	−3.04531e11	−	3.04531e11i	−0.385110	−	0.385110i
$944$	8.39315e11	+	2.72710e11i	1.05691	+	0.343410i
$945$	−1.77589e11	+	1.61332e11i	−0.222684	+	0.202299i
$946$	4.74860e10	+	1.46147e11i	0.0592926	+	0.182484i
$947$	−6.22246e11	−	3.17050e11i	−0.773682	−	0.394210i	0.0221298	−	0.999755i	$-0.492955\pi$
$947$	−6.22246e11	−	3.17050e11i	−0.773682	−	0.394210i	−0.795811	+	0.605545i	$0.792955\pi$
$948$	3.66750e10	+	2.31557e11i	0.0454085	+	0.286698i
$949$			7.48755e10i			0.0923155i
$950$	−1.55883e12	−	9.92792e11i	−1.91384	−	1.21889i
$951$	2.62215e11			0.320580
$952$	−5.06780e11	+	8.02660e10i	−0.616980	+	0.0977201i
$953$	4.49188e11	−	8.81580e11i	0.544573	−	1.06878i	−0.440677	−	0.897666i	$-0.645262\pi$
$953$	4.49188e11	−	8.81580e11i	0.544573	−	1.06878i	0.985250	−	0.171119i	$-0.0547383\pi$
$954$	−3.12976e11	+	1.01692e11i	−0.377849	+	0.122770i
$955$	−1.15661e12	+	5.21109e11i	−1.39051	+	0.626491i
$956$	−3.69782e11	+	1.13807e12i	−0.442705	+	1.36251i
$957$	−1.89360e10	+	1.89360e10i	−0.0225757	+	0.0225757i
$958$	2.53623e11	−	1.29228e11i	0.301111	−	0.153424i
$959$	7.09609e11	+	9.76694e11i	0.838967	+	1.15474i
$960$	−8.20987e10	−	3.01055e11i	−0.0966610	−	0.354455i
$961$	5.80979e11	+	4.22106e11i	0.681188	+	0.494912i
$962$	−1.29019e10	+	8.14593e10i	−0.0150644	+	0.0951132i
$963$	5.59039e10	+	8.85431e9i	0.0650036	+	0.0102956i
$964$	2.21592e11	−	3.04995e11i	0.256593	−	0.353171i
$965$	−1.98130e11	−	3.02154e11i	−0.228476	−	0.348433i
$966$	−5.57531e11	+	4.05070e11i	−0.640266	+	0.465180i
$967$	4.20648e11	+	8.25568e11i	0.481075	+	0.944163i	0.996204	+	0.0870499i	$0.0277440\pi$
$967$	4.20648e11	+	8.25568e11i	0.481075	+	0.944163i	−0.515129	+	0.857113i	$0.672256\pi$
$968$	−1.40357e11	−	1.40357e11i	−0.159857	−	0.159857i
$969$	−1.41203e12	−	4.58796e11i	−1.60158	−	0.520384i
$970$	5.79027e11	+	3.30889e11i	0.654051	+	0.373763i
$971$	−1.16492e11	−	3.58527e11i	−0.131045	−	0.403315i	0.863909	−	0.503648i	$-0.168009\pi$
$971$	−1.16492e11	−	3.58527e11i	−0.131045	−	0.403315i	−0.994954	+	0.100333i	$0.968009\pi$
$972$	−4.23545e10	−	2.15807e10i	−0.0474498	−	0.0241769i
$973$	−6.18053e10	−	3.90223e11i	−0.0689564	−	0.435374i
$974$		−	2.07247e11i		−	0.230278i
$975$	1.01989e11	−	6.00948e10i	0.112859	−	0.0664995i
$976$	1.49793e12			1.65079
$977$	6.20595e10	−	9.82926e9i	0.0681130	−	0.0107880i	−0.122285	−	0.992495i	$-0.539022\pi$
$977$	6.20595e10	−	9.82926e9i	0.0681130	−	0.0107880i	0.190398	+	0.981707i	$0.439022\pi$
$978$	5.60423e11	−	1.09989e12i	0.612576	−	1.20225i
$979$	−3.95965e9	+	1.28657e9i	−0.00431048	+	0.00140056i
$980$	−1.20433e11	−	1.09898e12i	−0.130569	−	1.19148i
$981$	−1.35531e11	+	4.17120e11i	−0.146339	+	0.450386i
$982$	−8.06140e11	+	8.06140e11i	−0.866891	+	0.866891i
$983$	9.26296e11	−	4.71972e11i	0.992055	−	0.505477i	0.118893	−	0.992907i	$-0.462065\pi$
$983$	9.26296e11	−	4.71972e11i	0.992055	−	0.505477i	0.873162	+	0.487430i	$0.162065\pi$
$984$	−6.14276e10	−	8.45478e10i	−0.0655214	−	0.0901824i
$985$	9.32750e10	+	7.48508e10i	0.0990878	+	0.0795154i
$986$	7.83355e11	+	5.69141e11i	0.828802	+	0.602160i
$987$	−1.32703e11	+	8.37856e11i	−0.139834	+	0.882878i
$988$	−2.97311e11	−	4.70894e10i	−0.312021	−	0.0494192i
$989$	−4.07088e11	+	5.60308e11i	−0.425503	+	0.585655i
$990$	2.63556e9	−	5.49462e10i	0.00274367	−	0.0572001i
$991$	−4.49200e11	+	3.26363e11i	−0.465742	+	0.338381i	−0.795779	−	0.605587i	$-0.792939\pi$
$991$	−4.49200e11	+	3.26363e11i	−0.465742	+	0.338381i	0.330038	+	0.943968i	$0.392939\pi$
$992$	−2.29594e11	−	4.50603e11i	−0.237090	−	0.465316i
$993$	−2.92357e11	−	2.92357e11i	−0.300689	−	0.300689i
$994$	2.27333e12	+	7.38651e11i	2.32872	+	0.756648i
$995$	3.50764e10	−	1.68693e11i	0.0357868	−	0.172110i
$996$	2.15210e11	+	6.62349e11i	0.218688	+	0.673054i
$997$	−2.91416e10	−	1.48484e10i	−0.0294940	−	0.0150279i	0.439181	−	0.898398i	$-0.355269\pi$
$997$	−2.91416e10	−	1.48484e10i	−0.0294940	−	0.0150279i	−0.468675	+	0.883371i	$0.655269\pi$
$998$	3.57301e11	+	2.25591e12i	0.360174	+	2.27405i
$999$			6.01376e10i			0.0603788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.8	✓	320
25.2	odd	20	inner	75.9.k.a.52.8	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.8	✓	320	1.1	even	1	trivial
75.9.k.a.52.8	yes	320	25.2	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.3788 + 3.38607i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(202.117 - 65.6718i) q^{4} +(611.912 + 127.235i) q^{5} +(312.802 - 962.707i) q^{6} +(-2654.08 + 2654.08i) q^{7} +(838.588 - 427.282i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-21.3788 + 3.38607i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(202.117 - 65.6718i) q^{4} +(611.912 + 127.235i) q^{5} +(312.802 - 962.707i) q^{6} +(-2654.08 + 2654.08i) q^{7} +(838.588 - 427.282i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-13512.8 - 648.155i) q^{10} +(-1504.19 - 1092.86i) q^{11} +(-1554.73 + 9816.15i) q^{12} +(-6400.36 - 1013.72i) q^{13} +(47754.1 - 65727.9i) q^{14} +(-18293.2 + 22796.0i) q^{15} +(-60495.6 + 43952.6i) q^{16} +(65940.1 + 129415. i) q^{17} +(33473.2 + 33473.2i) q^{18} +(207882. + 67544.8i) q^{19} +(132034. - 14469.0i) q^{20} +(-54242.0 - 166940. i) q^{21} +(35858.2 + 18270.7i) q^{22} +(28374.4 + 179149. i) q^{23} +44014.1i q^{24} +(358248. + 155713. i) q^{25} +140265. q^{26} +(101017. - 15999.5i) q^{27} +(-362137. + 710733. i) q^{28} +(-292915. + 95173.8i) q^{29} +(313898. - 549292. i) q^{30} +(113440. - 349132. i) q^{31} +(974126. - 974126. i) q^{32} +(77472.9 - 39474.4i) q^{33} +(-1.84793e6 - 2.54345e6i) q^{34} +(-1.96176e6 + 1.28637e6i) q^{35} +(-376013. - 273190. i) q^{36} +(-91982.6 + 580755. i) q^{37} +(-4.67297e6 - 740126. i) q^{38} +(178126. - 245170. i) q^{39} +(567507. - 154761. i) q^{40} +(-1.92092e6 + 1.39563e6i) q^{41} +(1.72490e6 + 3.38530e6i) q^{42} +(2.69998e6 + 2.69998e6i) q^{43} +(-375792. - 122102. i) q^{44} +(-561485. - 1.24623e6i) q^{45} +(-1.21322e6 - 3.73391e6i) q^{46} +(-4.30603e6 - 2.19403e6i) q^{47} +(-547044. - 3.45390e6i) q^{48} -8.32348e6i q^{49} +(-8.18616e6 - 2.11591e6i) q^{50} -6.79246e6 q^{51} +(-1.36020e6 + 215434. i) q^{52} +(-3.15602e6 + 6.19404e6i) q^{53} +(-2.10544e6 + 684099. i) q^{54} +(-781381. - 860118. i) q^{55} +(-1.09164e6 + 3.35972e6i) q^{56} +(-7.22802e6 + 7.22802e6i) q^{57} +(5.93990e6 - 3.02653e6i) q^{58} +(-6.93700e6 - 9.54796e6i) q^{59} +(-2.20031e6 + 5.80880e6i) q^{60} +(-1.62063e7 - 1.17745e7i) q^{61} +(-1.24302e6 + 7.84814e6i) q^{62} +(8.10770e6 + 1.28413e6i) q^{63} +(-6.27532e6 + 8.63724e6i) q^{64} +(-3.78748e6 - 1.43466e6i) q^{65} +(-1.52262e6 + 1.10624e6i) q^{66} +(-3.49256e6 - 6.85454e6i) q^{67} +(2.18265e7 + 2.18265e7i) q^{68} +(-8.06724e6 - 2.62121e6i) q^{69} +(3.75842e7 - 3.41437e7i) q^{70} +(9.09174e6 + 2.79815e7i) q^{71} +(-1.83399e6 - 934465. i) q^{72} +(-1.80754e6 - 1.14124e7i) q^{73} -1.27273e7i q^{74} +(-1.40943e7 + 1.16216e7i) q^{75} +4.64522e7 q^{76} +(6.89277e6 - 1.09171e6i) q^{77} +(-2.97796e6 + 5.84458e6i) q^{78} +(2.24349e7 - 7.28953e6i) q^{79} +(-4.26103e7 + 1.91980e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(3.63413e7 - 3.63413e7i) q^{82} +(6.24368e7 - 3.18131e7i) q^{83} +(-2.19265e7 - 3.01792e7i) q^{84} +(2.38834e7 + 8.75803e7i) q^{85} +(-6.68646e7 - 4.85799e7i) q^{86} +(2.25316e6 - 1.42259e7i) q^{87} +(-1.72835e6 - 273744. i) q^{88} +(1.31621e6 - 1.81160e6i) q^{89} +(1.62237e7 + 2.47416e7i) q^{90} +(1.96776e7 - 1.42966e7i) q^{91} +(1.75000e7 + 3.43457e7i) q^{92} +(1.21393e7 + 1.21393e7i) q^{93} +(9.94869e7 + 3.23252e7i) q^{94} +(1.18611e8 + 6.77813e7i) q^{95} +(1.99084e7 + 6.12718e7i) q^{96} +(-4.39238e7 - 2.23803e7i) q^{97} +(2.81839e7 + 1.77946e8i) q^{98} +4.06624e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

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