LMFDB - Embedded newform 75.9.k.a.13.1

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			13.1
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-31.1680 + 4.93653i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(703.605 - 228.615i) q^{4} +(559.718 + 278.101i) q^{5} +(456.033 - 1403.52i) q^{6} +(1699.82 - 1699.82i) q^{7} +(-13603.4 + 6931.29i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-31.1680 + 4.93653i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(703.605 - 228.615i) q^{4} +(559.718 + 278.101i) q^{5} +(456.033 - 1403.52i) q^{6} +(1699.82 - 1699.82i) q^{7} +(-13603.4 + 6931.29i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-18818.2 - 5904.80i) q^{10} +(-18185.6 - 13212.6i) q^{11} +(-5412.27 + 34171.7i) q^{12} +(10727.3 + 1699.04i) q^{13} +(-44588.7 + 61371.1i) q^{14} +(-23471.4 + 17418.1i) q^{15} +(236553. - 171866. i) q^{16} +(-6535.32 - 12826.3i) q^{17} +(48800.3 + 48800.3i) q^{18} +(-150659. - 48952.2i) q^{19} +(457399. + 67713.3i) q^{20} +(34739.5 + 106917. i) q^{21} +(632032. + 322037. i) q^{22} +(26432.6 + 166889. i) q^{23} -713989. i q^{24} +(235944. + 311317. i) q^{25} -342736. q^{26} +(101017. - 15999.5i) q^{27} +(807396. - 1.58460e6i) q^{28} +(-293712. + 95432.7i) q^{29} +(645572. - 658755. i) q^{30} +(188248. - 579367. i) q^{31} +(-3.76077e6 + 3.76077e6i) q^{32} +(936644. - 477244. i) q^{33} +(267010. + 367508. i) q^{34} +(1.42414e6 - 478698. i) q^{35} +(-1.30897e6 - 951020. i) q^{36} +(-484958. + 3.06190e6i) q^{37} +(4.93740e6 + 782008. i) q^{38} +(-298548. + 410916. i) q^{39} +(-9.54169e6 + 96441.0i) q^{40} +(-3.24571e6 + 2.35815e6i) q^{41} +(-1.61056e6 - 3.16091e6i) q^{42} +(-2.45683e6 - 2.45683e6i) q^{43} +(-1.58161e7 - 5.13895e6i) q^{44} +(-227460. - 1.34782e6i) q^{45} +(-1.64770e6 - 5.07111e6i) q^{46} +(7.83833e6 + 3.99383e6i) q^{47} +(2.13909e6 + 1.35057e7i) q^{48} -13957.9i q^{49} +(-8.89074e6 - 8.53838e6i) q^{50} +673200. q^{51} +(7.93621e6 - 1.25697e6i) q^{52} +(-3.58128e6 + 7.02865e6i) q^{53} +(-3.06951e6 + 997343. i) q^{54} +(-6.50436e6 - 1.24528e7i) q^{55} +(-1.13414e7 + 3.49053e7i) q^{56} +(5.23841e6 - 5.23841e6i) q^{57} +(8.68330e6 - 4.42436e6i) q^{58} +(6.16795e6 + 8.48945e6i) q^{59} +(-1.25325e7 + 1.76214e7i) q^{60} +(4.90436e6 + 3.56322e6i) q^{61} +(-3.00725e6 + 1.89870e7i) q^{62} +(-5.19261e6 - 822429. i) q^{63} +(5.46527e7 - 7.52230e7i) q^{64} +(5.53177e6 + 3.93426e6i) q^{65} +(-2.68374e7 + 1.94985e7i) q^{66} +(-2.43463e6 - 4.77823e6i) q^{67} +(-7.53056e6 - 7.53056e6i) q^{68} +(-7.51516e6 - 2.44183e6i) q^{69} +(-4.20245e7 + 2.19504e7i) q^{70} +(-3.26073e6 - 1.00355e7i) q^{71} +(2.97507e7 + 1.51587e7i) q^{72} +(4.96651e6 + 3.13573e7i) q^{73} -9.78274e7i q^{74} +(-1.79814e7 + 3.22181e6i) q^{75} -1.17196e8 q^{76} +(-5.33711e7 + 8.45316e6i) q^{77} +(7.27664e6 - 1.42812e7i) q^{78} +(-2.87628e7 + 9.34560e6i) q^{79} +(1.80199e8 - 3.04108e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(8.95214e7 - 8.95214e7i) q^{82} +(-2.42958e7 + 1.23793e7i) q^{83} +(4.88858e7 + 6.72855e7i) q^{84} +(-90931.5 - 8.99659e6i) q^{85} +(8.87025e7 + 6.44462e7i) q^{86} +(2.25929e6 - 1.42646e7i) q^{87} +(3.38966e8 + 5.36870e7i) q^{88} +(9.28965e6 - 1.27861e7i) q^{89} +(1.37430e7 + 4.08859e7i) q^{90} +(2.11225e7 - 1.53464e7i) q^{91} +(5.67514e7 + 1.11381e8i) q^{92} +(2.01445e7 + 2.01445e7i) q^{93} +(-2.64021e8 - 8.57855e7i) q^{94} +(-7.07131e7 - 6.92980e7i) q^{95} +(-7.68596e7 - 2.36550e8i) q^{96} +(-9.10671e6 - 4.64010e6i) q^{97} +(68903.7 + 435041. i) q^{98} +4.91607e7i 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 $

$2$	−31.1680	+	4.93653i	−1.94800	+	0.308533i	−0.999954	−	0.00959950i	$-0.996944\pi$
$2$	−31.1680	+	4.93653i	−1.94800	+	0.308533i	−0.948046	+	0.318132i	$0.896944\pi$
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$4$	703.605	−	228.615i	2.74846	−	0.893027i
$5$	559.718	+	278.101i	0.895549	+	0.444962i
$5$	559.718	+	278.101i	0.895549	+	0.444962i
$6$	456.033	−	1403.52i	0.351877	−	1.08297i
$7$	1699.82	−	1699.82i	0.707962	−	0.707962i	−0.258144	−	0.966106i	$-0.583111\pi$
$7$	1699.82	−	1699.82i	0.707962	−	0.707962i	0.966106	+	0.258144i	$0.0831109\pi$
$8$	−13603.4	+	6931.29i	−3.32115	+	1.69221i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	−18818.2	−	5904.80i	−1.88182	−	0.590480i
$11$	−18185.6	−	13212.6i	−1.24210	−	0.902438i	−0.244363	−	0.969684i	$-0.578579\pi$
$11$	−18185.6	−	13212.6i	−1.24210	−	0.902438i	−0.997736	+	0.0672461i	$0.978579\pi$
$12$	−5412.27	+	34171.7i	−0.261008	+	1.64794i
$13$	10727.3	+	1699.04i	0.375593	+	0.0594881i	0.341377	−	0.939926i	$-0.389107\pi$
$13$	10727.3	+	1699.04i	0.375593	+	0.0594881i	0.0342157	+	0.999414i	$0.489107\pi$
$14$	−44588.7	+	61371.1i	−1.16068	+	1.59754i
$15$	−23471.4	+	17418.1i	−0.463632	+	0.344061i
$16$	236553.	−	171866.i	3.60952	−	2.62247i
$17$	−6535.32	−	12826.3i	−0.0782476	−	0.153570i	0.848568	−	0.529086i	$-0.177465\pi$
$17$	−6535.32	−	12826.3i	−0.0782476	−	0.153570i	−0.926816	+	0.375517i	$0.877465\pi$
$18$	48800.3	+	48800.3i	0.464871	+	0.464871i
$19$	−150659.	−	48952.2i	−1.15606	−	0.375628i	−0.332639	−	0.943054i	$-0.607939\pi$
$19$	−150659.	−	48952.2i	−1.15606	−	0.375628i	−0.823424	+	0.567426i	$0.807939\pi$
$20$	457399.	+	67713.3i	2.85874	+	0.423208i
$21$	34739.5	+	106917.i	0.178627	+	0.549757i
$22$	632032.	+	322037.i	2.69804	+	1.37472i
$23$	26432.6	+	166889.i	0.0944559	+	0.596371i	0.988830	+	0.149050i	$0.0476217\pi$
$23$	26432.6	+	166889.i	0.0944559	+	0.596371i	−0.894374	+	0.447320i	$0.852378\pi$
$24$		−	713989.i		−	2.15202i
$25$	235944.	+	311317.i	0.604018	+	0.796971i
$26$	−342736.			−0.750009
$27$	101017.	−	15999.5i	0.190081	−	0.0301058i
$28$	807396.	−	1.58460e6i	1.31357	−	2.57803i
$29$	−293712.	+	95432.7i	−0.415269	+	0.134929i	−0.509197	−	0.860650i	$-0.670058\pi$
$29$	−293712.	+	95432.7i	−0.415269	+	0.134929i	0.0939283	+	0.995579i	$0.470058\pi$
$30$	645572.	−	658755.i	0.797002	−	0.813278i
$31$	188248.	−	579367.i	0.203837	−	0.627346i	−0.795922	−	0.605399i	$-0.793014\pi$
$31$	188248.	−	579367.i	0.203837	−	0.627346i	0.999759	−	0.0219469i	$-0.00698648\pi$
$32$	−3.76077e6	+	3.76077e6i	−3.58655	+	3.58655i
$33$	936644.	−	477244.i	0.789803	−	0.402425i
$34$	267010.	+	367508.i	0.199808	+	0.275012i
$35$	1.42414e6	−	478698.i	0.949032	−	0.318999i
$36$	−1.30897e6	−	951020.i	−0.779325	−	0.566213i
$37$	−484958.	+	3.06190e6i	−0.258760	+	1.63375i	0.425820	+	0.904808i	$0.359986\pi$
$37$	−484958.	+	3.06190e6i	−0.258760	+	1.63375i	−0.684580	+	0.728938i	$0.740014\pi$
$38$	4.93740e6	+	782008.i	2.36791	+	0.375039i
$39$	−298548.	+	410916.i	−0.129049	+	0.177621i
$40$	−9.54169e6	+	96441.0i	−3.72722	+	0.0376723i
$41$	−3.24571e6	+	2.35815e6i	−1.14862	+	0.834519i	−0.988296	−	0.152547i	$-0.951253\pi$
$41$	−3.24571e6	+	2.35815e6i	−1.14862	+	0.834519i	−0.160320	+	0.987065i	$0.551253\pi$
$42$	−1.61056e6	−	3.16091e6i	−0.517583	−	1.01581i
$43$	−2.45683e6	−	2.45683e6i	−0.718622	−	0.718622i	0.249701	−	0.968323i	$-0.419668\pi$
$43$	−2.45683e6	−	2.45683e6i	−0.718622	−	0.718622i	−0.968323	+	0.249701i	$0.919668\pi$
$44$	−1.58161e7	−	5.13895e6i	−4.21976	−	1.37108i
$45$	−227460.	−	1.34782e6i	−0.0554696	−	0.328686i
$46$	−1.64770e6	−	5.07111e6i	−0.368000	−	1.13259i
$47$	7.83833e6	+	3.99383e6i	1.60632	+	0.818461i	0.999725	+	0.0234493i	$0.00746483\pi$
$47$	7.83833e6	+	3.99383e6i	1.60632	+	0.818461i	0.606595	+	0.795011i	$0.292535\pi$
$48$	2.13909e6	+	1.35057e7i	0.402961	+	2.54420i
$49$		−	13957.9i		−	0.00242123i
$50$	−8.89074e6	−	8.53838e6i	−1.42252	−	1.36614i
$51$	673200.			0.0995093
$52$	7.93621e6	−	1.25697e6i	1.08542	−	0.171914i
$53$	−3.58128e6	+	7.02865e6i	−0.453873	+	0.890776i	0.544764	+	0.838589i	$0.316619\pi$
$53$	−3.58128e6	+	7.02865e6i	−0.453873	+	0.890776i	−0.998637	+	0.0521869i	$0.983381\pi$
$54$	−3.06951e6	+	997343.i	−0.360989	+	0.117292i
$55$	−6.50436e6	−	1.24528e7i	−0.710811	−	1.36086i
$56$	−1.13414e7	+	3.49053e7i	−1.15323	+	3.54927i
$57$	5.23841e6	−	5.23841e6i	0.496249	−	0.496249i
$58$	8.68330e6	−	4.42436e6i	0.767313	−	0.390966i
$59$	6.16795e6	+	8.48945e6i	0.509018	+	0.700603i	0.983753	−	0.179526i	$-0.0574563\pi$
$59$	6.16795e6	+	8.48945e6i	0.509018	+	0.700603i	−0.474736	+	0.880128i	$0.657456\pi$
$60$	−1.25325e7	+	1.76214e7i	−0.967017	+	1.35967i
$61$	4.90436e6	+	3.56322e6i	0.354212	+	0.257350i	0.750634	−	0.660719i	$-0.229748\pi$
$61$	4.90436e6	+	3.56322e6i	0.354212	+	0.257350i	−0.396422	+	0.918068i	$0.629748\pi$
$62$	−3.00725e6	+	1.89870e7i	−0.203518	+	1.28496i
$63$	−5.19261e6	−	822429.i	−0.329628	−	0.0522079i
$64$	5.46527e7	−	7.52230e7i	3.25756	−	4.48364i
$65$	5.53177e6	+	3.93426e6i	0.309892	+	0.220399i
$66$	−2.68374e7	+	1.94985e7i	−1.41438	+	1.02760i
$67$	−2.43463e6	−	4.77823e6i	−0.120819	−	0.237120i	0.822674	−	0.568513i	$-0.192481\pi$
$67$	−2.43463e6	−	4.77823e6i	−0.120819	−	0.237120i	−0.943493	+	0.331394i	$0.892481\pi$
$68$	−7.53056e6	−	7.53056e6i	−0.352202	−	0.352202i
$69$	−7.51516e6	−	2.44183e6i	−0.331545	−	0.107725i
$70$	−4.20245e7	+	2.19504e7i	−1.75029	+	0.914217i
$71$	−3.26073e6	−	1.00355e7i	−0.128316	−	0.394916i	0.866175	−	0.499742i	$-0.166572\pi$
$71$	−3.26073e6	−	1.00355e7i	−0.128316	−	0.394916i	−0.994491	+	0.104825i	$0.966572\pi$
$72$	2.97507e7	+	1.51587e7i	1.10705	+	0.564070i
$73$	4.96651e6	+	3.13573e7i	0.174888	+	1.10420i	0.906416	+	0.422387i	$0.138808\pi$
$73$	4.96651e6	+	3.13573e7i	0.174888	+	1.10420i	−0.731528	+	0.681812i	$0.761192\pi$
$74$		−	9.78274e7i		−	3.26237i
$75$	−1.79814e7	+	3.22181e6i	−0.568300	+	0.101825i
$76$	−1.17196e8			−3.51284
$77$	−5.33711e7	+	8.45316e6i	−1.51825	+	0.240467i
$78$	7.27664e6	−	1.42812e7i	0.196586	−	0.385822i
$79$	−2.87628e7	+	9.34560e6i	−0.738453	+	0.239938i	−0.654005	−	0.756490i	$-0.726913\pi$
$79$	−2.87628e7	+	9.34560e6i	−0.738453	+	0.239938i	−0.0844479	+	0.996428i	$0.526913\pi$
$80$	1.80199e8	−	3.04108e7i	4.39940	−	0.742451i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	8.95214e7	−	8.95214e7i	1.98003	−	1.98003i
$83$	−2.42958e7	+	1.23793e7i	−0.511939	+	0.260846i	−0.690823	−	0.723024i	$-0.742752\pi$
$83$	−2.42958e7	+	1.23793e7i	−0.511939	+	0.260846i	0.178883	+	0.983870i	$0.442752\pi$
$84$	4.88858e7	+	6.72855e7i	0.981896	+	1.35146i
$85$	−90931.5	−	8.99659e6i	−0.00174196	−	0.172346i
$86$	8.87025e7	+	6.44462e7i	1.62159	+	1.17816i
$87$	2.25929e6	−	1.42646e7i	0.0394362	−	0.248990i
$88$	3.38966e8	+	5.36870e7i	5.65231	+	0.895238i
$89$	9.28965e6	−	1.27861e7i	0.148060	−	0.203788i	−0.728544	−	0.684999i	$-0.759803\pi$
$89$	9.28965e6	−	1.27861e7i	0.148060	−	0.203788i	0.876605	+	0.481211i	$0.159803\pi$
$90$	1.37430e7	+	4.08859e7i	0.209465	+	0.623165i
$91$	2.11225e7	−	1.53464e7i	0.308021	−	0.223790i
$92$	5.67514e7	+	1.11381e8i	0.792183	+	1.55475i
$93$	2.01445e7	+	2.01445e7i	0.269293	+	0.269293i
$94$	−2.64021e8	−	8.57855e7i	−3.38163	−	1.09876i
$95$	−7.07131e7	−	6.92980e7i	−0.868172	−	0.850798i
$96$	−7.68596e7	−	2.36550e8i	−0.904926	−	2.78508i
$97$	−9.10671e6	−	4.64010e6i	−0.102867	−	0.0524132i	0.401800	−	0.915727i	$-0.368385\pi$
$97$	−9.10671e6	−	4.64010e6i	−0.102867	−	0.0524132i	−0.504667	+	0.863314i	$0.668385\pi$
$98$	68903.7	+	435041.i	0.000747030	+	0.00471656i
$99$			4.91607e7i			0.511773i
$100$	2.37183e8	+	1.65104e8i	2.37183	+	1.65104i
$101$	−4.66982e7			−0.448760			−0.224380	−	0.974502i	$-0.572036\pi$
$101$	−4.66982e7			−0.448760			−0.224380	+	0.974502i	$0.572036\pi$
$102$	−2.09823e7	+	3.32327e6i	−0.193844	+	0.0307019i
$103$	−7.66909e7	+	1.50514e8i	−0.681388	+	1.33730i	0.248203	+	0.968708i	$0.420160\pi$
$103$	−7.66909e7	+	1.50514e8i	−0.681388	+	1.33730i	−0.929591	+	0.368592i	$0.879840\pi$
$104$	−1.57705e8	+	5.12413e7i	−1.34807	+	0.438013i
$105$	−1.02895e7	+	6.95047e7i	−0.0846518	+	0.571817i
$106$	7.69241e7	−	2.36748e8i	0.609311	−	1.87527i
$107$	−7.10833e7	+	7.10833e7i	−0.542291	+	0.542291i	−0.924200	−	0.381909i	$-0.875267\pi$
$107$	−7.10833e7	+	7.10833e7i	−0.542291	+	0.542291i	0.381909	+	0.924200i	$0.375267\pi$
$108$	6.74181e7	−	3.43512e7i	0.495543	−	0.252492i
$109$	2.96834e7	+	4.08557e7i	0.210285	+	0.289432i	0.901111	−	0.433589i	$-0.142753\pi$
$109$	2.96834e7	+	4.08557e7i	0.210285	+	0.289432i	−0.690826	+	0.723021i	$0.742753\pi$
$110$	2.64201e8	+	3.56019e8i	1.80453	+	2.43166i
$111$	−1.17288e8	−	8.52147e7i	−0.772612	−	0.561336i
$112$	1.09957e8	−	6.94239e8i	0.698794	−	4.41201i
$113$	−2.42874e8	−	3.84675e7i	−1.48959	−	0.235928i	−0.642052	−	0.766661i	$-0.721917\pi$
$113$	−2.42874e8	−	3.84675e7i	−1.48959	−	0.235928i	−0.847539	+	0.530733i	$0.821917\pi$
$114$	−1.37411e8	+	1.89130e8i	−0.813584	+	1.11980i
$115$	−3.16172e7	+	1.00762e8i	−0.180773	+	0.576109i
$116$	−1.84840e8	+	1.34294e8i	−1.02085	+	0.741693i
$117$	−1.07837e7	−	2.11641e7i	−0.0575470	−	0.112942i
$118$	−2.34151e8	−	2.34151e8i	−1.20773	−	1.20773i
$119$	−3.29112e7	−	1.06935e7i	−0.164118	−	0.0533251i
$120$	1.98561e8	−	3.99633e8i	0.957568	−	1.92724i
$121$	8.99019e7	+	2.76690e8i	0.419399	+	1.29078i
$122$	−1.70449e8	−	8.68481e7i	−0.769405	−	0.392031i
$123$	−2.93501e7	−	1.85309e8i	−0.128230	−	0.809611i
$124$		−	4.50682e8i		−	1.90626i
$125$	4.54848e7	+	2.39866e8i	0.186306	+	0.982492i
$126$	1.65903e8			0.658223
$127$	−1.39909e8	+	2.21594e7i	−0.537812	+	0.0851811i	−0.419431	−	0.907787i	$-0.637770\pi$
$127$	−1.39909e8	+	2.21594e7i	−0.537812	+	0.0851811i	−0.118381	+	0.992968i	$0.537770\pi$
$128$	−7.13949e8	+	1.40120e9i	−2.65967	+	5.21989i
$129$	1.54533e8	−	5.02107e7i	0.558035	−	0.181316i
$130$	−1.91836e8	−	9.53154e7i	−0.671670	−	0.333726i
$131$	−1.06408e7	+	3.27490e7i	−0.0361317	+	0.111202i	−0.967496	−	0.252887i	$-0.918620\pi$
$131$	−1.06408e7	+	3.27490e7i	−0.0361317	+	0.111202i	0.931364	+	0.364089i	$0.118620\pi$
$132$	5.49922e8	−	5.49922e8i	1.81136	−	1.81136i
$133$	−3.39303e8	+	1.72884e8i	−1.08438	+	0.552519i
$134$	9.94704e7	+	1.36909e8i	0.308514	+	0.424633i
$135$	6.09904e7	+	1.91377e7i	0.183623	+	0.0576175i
$136$	1.77805e8	+	1.29183e8i	0.519744	+	0.377616i
$137$	8.87256e7	−	5.60191e8i	0.251864	−	1.59021i	−0.460018	−	0.887910i	$-0.652157\pi$
$137$	8.87256e7	−	5.60191e8i	0.251864	−	1.59021i	0.711882	−	0.702299i	$-0.247843\pi$
$138$	2.46287e8	+	3.90080e7i	0.679086	+	0.107557i
$139$	−2.73973e8	+	3.77091e8i	−0.733919	+	1.01015i	0.265026	+	0.964241i	$0.414619\pi$
$139$	−2.73973e8	+	3.77091e8i	−0.733919	+	1.01015i	−0.998945	+	0.0459122i	$0.985381\pi$
$140$	8.92594e8	−	6.62394e8i	2.32350	−	1.72427i
$141$	−3.32832e8	+	2.41816e8i	−0.842070	+	0.611799i
$142$	1.51171e8	+	2.96690e8i	0.371805	+	0.729708i
$143$	−1.72634e8	−	1.72634e8i	−0.412839	−	0.412839i
$144$	−6.08172e8	−	1.97607e8i	−1.41441	−	0.459571i
$145$	−1.90936e8	−	2.82662e7i	−0.431932	−	0.0639432i
$146$	−3.09592e8	−	9.52827e8i	−0.681363	−	2.09702i
$147$	581603.	+	296341.i	0.00124554	+	0.000634633i
$148$	3.58778e8	+	2.26524e9i	0.747790	+	4.72136i
$149$		−	1.04262e8i		−	0.211534i	−0.994391	−	0.105767i	$-0.966270\pi$
$149$		−	1.04262e8i		−	0.211534i	0.994391	−	0.105767i	$-0.0337297\pi$
$150$	5.44539e8	−	1.89183e8i	1.07563	−	0.373695i
$151$	3.60102e8			0.692656			0.346328	−	0.938114i	$-0.387428\pi$
$151$	3.60102e8			0.692656			0.346328	+	0.938114i	$0.387428\pi$
$152$	2.38878e9	−	3.78346e8i	4.47510	−	0.708786i
$153$	−1.42927e7	+	2.80511e7i	−0.0260825	+	0.0511898i
$154$	1.62174e9	−	5.26936e8i	2.88336	−	0.936861i
$155$	2.66489e8	−	2.71931e8i	0.461691	−	0.471120i
$156$	−1.16118e8	+	3.57375e8i	−0.196066	+	0.603428i
$157$	9.85223e7	−	9.85223e7i	0.162157	−	0.162157i	−0.621365	−	0.783522i	$-0.713421\pi$
$157$	9.85223e7	−	9.85223e7i	0.162157	−	0.162157i	0.783522	+	0.621365i	$0.213421\pi$
$158$	8.50345e8	−	4.33272e8i	1.36448	−	0.695236i
$159$	−2.16837e8	−	2.98451e8i	−0.339270	−	0.466965i
$160$	−3.15084e9	+	1.05910e9i	−4.80781	+	1.61605i
$161$	3.28611e8	+	2.38750e8i	0.489079	+	0.355337i
$162$	2.36113e7	−	1.49076e8i	0.0342814	−	0.216444i
$163$	6.50743e7	+	1.03068e7i	0.0921847	+	0.0146006i	0.202356	−	0.979312i	$-0.435140\pi$
$163$	6.50743e7	+	1.03068e7i	0.0921847	+	0.0146006i	−0.110172	+	0.993913i	$0.535140\pi$
$164$	−1.74459e9	+	2.40122e9i	−2.41167	+	3.31938i
$165$	6.56979e8	−	6.64031e6i	0.886371	−	0.00895885i
$166$	6.96140e8	−	5.05775e8i	0.916778	−	0.666078i
$167$	−7.92272e7	−	1.55492e8i	−0.101861	−	0.199914i	0.834451	−	0.551081i	$-0.185785\pi$
$167$	−7.92272e7	−	1.55492e8i	−0.101861	−	0.199914i	−0.936313	+	0.351168i	$0.885785\pi$
$168$	−1.21365e9	−	1.21365e9i	−1.52355	−	1.52355i
$169$	−6.63618e8	−	2.15622e8i	−0.813525	−	0.264330i
$170$	4.72460e7	+	2.79957e8i	0.0565679	+	0.335193i
$171$	1.07058e8	+	3.29492e8i	0.125209	+	0.385354i
$172$	−2.29030e9	−	1.16697e9i	−2.61685	−	1.33335i
$173$	−2.38849e8	−	1.50803e9i	−0.266648	−	1.68355i	−0.649989	−	0.759943i	$-0.725227\pi$
$173$	−2.38849e8	−	1.50803e9i	−0.266648	−	1.68355i	0.383341	−	0.923607i	$-0.374773\pi$
$174$			4.55752e8i			0.497200i
$175$	9.30244e8	+	1.28119e8i	0.991847	+	0.136604i
$176$	−6.57265e9			−6.84999
$177$	−4.84693e8	+	7.67678e7i	−0.493825	+	0.0782143i
$178$	−2.26421e8	+	4.44376e8i	−0.225547	+	0.442660i
$179$	8.59292e8	−	2.79201e8i	0.837006	−	0.271960i	0.141012	−	0.990008i	$-0.454964\pi$
$179$	8.59292e8	−	2.79201e8i	0.837006	−	0.271960i	0.695993	+	0.718048i	$0.254964\pi$
$180$	−4.68173e8	−	8.96329e8i	−0.445981	−	0.853842i
$181$	−2.08762e8	+	6.42504e8i	−0.194508	+	0.598634i	0.805474	+	0.592631i	$0.201911\pi$
$181$	−2.08762e8	+	6.42504e8i	−0.194508	+	0.598634i	−0.999982	+	0.00600278i	$0.998089\pi$
$182$	−5.82589e8	+	5.82589e8i	−0.530978	+	0.530978i
$183$	−2.52598e8	+	1.28705e8i	−0.225230	+	0.114760i
$184$	−1.51633e9	−	2.08705e9i	−1.32289	−	1.82080i
$185$	−1.12296e9	+	1.57894e9i	−0.958687	+	1.34796i
$186$	−7.27309e8	−	5.28421e8i	−0.607669	−	0.441497i
$187$	−5.06199e7	+	3.19602e8i	−0.0413957	+	0.261362i
$188$	6.42813e9	+	1.01812e9i	5.14581	+	0.815016i
$189$	1.44514e8	−	1.98906e8i	0.113256	−	0.155884i
$190$	2.54608e9	+	1.81080e9i	1.95370	+	1.38949i
$191$	4.61519e8	−	3.35313e8i	0.346782	−	0.251952i	−0.400736	−	0.916194i	$-0.631246\pi$
$191$	4.61519e8	−	3.35313e8i	0.346782	−	0.251952i	0.747518	+	0.664242i	$0.231246\pi$
$192$	1.97408e9	+	3.87435e9i	1.45264	+	2.85098i
$193$	9.73045e8	+	9.73045e8i	0.701300	+	0.701300i	0.964690	−	0.263390i	$-0.0848404\pi$
$193$	9.73045e8	+	9.73045e8i	0.701300	+	0.701300i	−0.263390	+	0.964690i	$0.584840\pi$
$194$	3.06744e8	+	9.96672e7i	0.216556	+	0.0703631i
$195$	−2.81379e8	+	1.46971e8i	−0.194605	+	0.101646i
$196$	−3.19099e6	−	9.82087e6i	−0.00216223	−	0.00665465i
$197$	1.06882e9	+	5.44590e8i	0.709641	+	0.361580i	0.771261	−	0.636519i	$-0.219627\pi$
$197$	1.06882e9	+	5.44590e8i	0.709641	+	0.361580i	−0.0616195	+	0.998100i	$0.519627\pi$
$198$	−2.42683e8	−	1.53224e9i	−0.157899	−	0.996934i
$199$		−	2.55300e9i		−	1.62794i	−0.580906	−	0.813971i	$-0.697302\pi$
$199$		−	2.55300e9i		−	1.62794i	0.580906	−	0.813971i	$-0.302698\pi$
$200$	−5.36748e9	−	2.59958e9i	−3.35467	−	1.62473i
$201$	2.50790e8			0.153648
$202$	1.45549e9	−	2.30527e8i	0.874185	−	0.138457i
$203$	−3.37038e8	+	6.61474e8i	−0.198470	+	0.389519i
$204$	4.73667e8	−	1.53904e8i	0.273497	−	0.0888645i
$205$	−2.47249e9	+	4.17262e8i	−1.39997	+	0.236262i
$206$	1.64728e9	−	5.06982e9i	0.914744	−	2.81529i
$207$	2.61301e8	−	2.61301e8i	0.142318	−	0.142318i
$208$	2.82959e9	−	1.44175e9i	1.51171	−	0.770257i
$209$	2.09304e9	+	2.88082e9i	1.09696	+	1.50984i
$210$	−2.24091e7	−	2.21712e9i	−0.0115225	−	1.14002i
$211$	2.30382e9	+	1.67382e9i	1.16230	+	0.844461i	0.990067	−	0.140595i	$-0.0449015\pi$
$211$	2.30382e9	+	1.67382e9i	1.16230	+	0.844461i	0.172234	+	0.985056i	$0.444902\pi$
$212$	−9.12948e8	+	5.76413e9i	−0.451963	+	2.85358i
$213$	4.87390e8	+	7.71950e7i	0.236787	+	0.0375034i
$214$	1.86462e9	−	2.56643e9i	0.889068	−	1.22370i
$215$	−6.91884e8	−	2.05838e9i	−0.323802	−	0.963321i
$216$	−1.26328e9	+	9.17823e8i	−0.580341	+	0.421642i
$217$	−6.64832e8	−	1.30481e9i	−0.299828	−	0.588446i
$218$	−1.12686e9	−	1.12686e9i	−0.498934	−	0.498934i
$219$	−1.41205e9	−	4.58802e8i	−0.613865	−	0.199457i
$220$	−7.42339e9	−	7.27483e9i	−3.16892	−	3.10550i
$221$	−4.83140e7	−	1.48695e8i	−0.0202537	−	0.0623344i
$222$	4.07630e9	+	2.07698e9i	1.67824	+	0.855106i
$223$	2.81893e8	+	1.77980e9i	0.113989	+	0.719700i	0.976797	+	0.214168i	$0.0687040\pi$
$223$	2.81893e8	+	1.77980e9i	0.113989	+	0.719700i	−0.862808	+	0.505533i	$0.831296\pi$
$224$			1.27852e10i			5.07828i
$225$	2.47516e8	−	8.17655e8i	0.0965768	−	0.319036i
$226$	7.75979e9			2.97452
$227$	1.99828e9	−	3.16497e8i	0.752581	−	0.119197i	0.231654	−	0.972798i	$-0.425586\pi$
$227$	1.99828e9	−	3.16497e8i	0.752581	−	0.119197i	0.520927	+	0.853601i	$0.325586\pi$
$228$	2.48819e9	−	4.88335e9i	0.920755	−	1.80708i
$229$	−2.50753e9	+	8.14746e8i	−0.911809	+	0.296265i	−0.727103	−	0.686529i	$-0.759134\pi$
$229$	−2.50753e9	+	8.14746e8i	−0.911809	+	0.296265i	−0.184707	+	0.982794i	$0.559134\pi$
$230$	4.88032e8	−	3.29662e9i	0.174396	−	1.17803i
$231$	7.80896e8	−	2.40335e9i	0.274249	−	0.844052i
$232$	3.33401e9	−	3.33401e9i	1.15084	−	1.15084i
$233$	−2.82229e9	+	1.43803e9i	−0.957586	+	0.487914i	−0.861667	−	0.507475i	$-0.830579\pi$
$233$	−2.82229e9	+	1.43803e9i	−0.957586	+	0.487914i	−0.0959193	+	0.995389i	$0.530579\pi$
$234$	4.40583e8	+	6.06410e8i	0.146948	+	0.202257i
$235$	3.27657e9	+	4.41527e9i	1.07435	+	1.44772i
$236$	6.28062e9	+	4.56313e9i	2.02467	+	1.47101i
$237$	2.21249e8	−	1.39691e9i	0.0701275	−	0.442768i
$238$	1.07856e9	+	1.70828e8i	0.336154	+	0.0532416i
$239$	2.26679e9	−	3.11997e9i	0.694735	−	0.956221i	−0.305257	−	0.952270i	$-0.598742\pi$
$239$	2.26679e9	−	3.11997e9i	0.694735	−	0.956221i	0.999992	−	0.00395082i	$-0.00125759\pi$
$240$	−2.55866e9	+	8.15425e9i	−0.771200	+	2.45776i
$241$	−2.79923e9	+	2.03376e9i	−0.829795	+	0.602881i	−0.919501	−	0.393087i	$-0.871407\pi$
$241$	−2.79923e9	+	2.03376e9i	−0.829795	+	0.602881i	0.0897062	+	0.995968i	$0.471407\pi$
$242$	−4.16795e9	−	8.18006e9i	−1.21524	−	2.38504i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	4.26534e9	+	1.38589e9i	1.20336	+	0.390994i
$245$	3.88172e6	−	7.81251e6i	0.00107736	−	0.00216833i
$246$	1.82957e9	+	5.63083e9i	0.499584	+	1.53756i
$247$	−1.53300e9	−	7.81101e8i	−0.411864	−	0.209855i
$248$	1.45495e9	+	9.18618e9i	0.384628	+	2.42844i
$249$		−	1.27519e9i		−	0.331724i
$250$	−2.60178e9	−	7.25161e9i	−0.666055	−	1.85641i
$251$	−4.05102e9			−1.02063			−0.510316	−	0.859987i	$-0.670472\pi$
$251$	−4.05102e9			−1.02063			−0.510316	+	0.859987i	$0.670472\pi$
$252$	−3.84157e9	+	6.08444e8i	−0.952590	+	0.150876i
$253$	1.72434e9	−	3.38422e9i	0.420864	−	0.825992i
$254$	4.25129e9	−	1.38133e9i	1.02138	−	0.331865i
$255$	3.76803e8	+	1.87218e8i	0.0891155	+	0.0442779i
$256$	7.97972e9	−	2.45591e10i	1.85792	−	5.71810i
$257$	−2.22682e9	+	2.22682e9i	−0.510449	+	0.510449i	−0.914664	−	0.404215i	$-0.867545\pi$
$257$	−2.22682e9	+	2.22682e9i	−0.510449	+	0.510449i	0.404215	+	0.914664i	$0.367545\pi$
$258$	−4.56861e9	+	2.32782e9i	−1.03111	+	0.525377i
$259$	4.38034e9	+	6.02902e9i	0.973438	+	1.33982i
$260$	4.79161e9	+	1.50352e9i	1.04855	+	0.329015i
$261$	5.46413e8	+	3.96992e8i	0.117750	+	0.0855501i
$262$	1.69986e8	−	1.07325e9i	0.0360751	−	0.227769i
$263$	−5.49090e9	−	8.69673e8i	−1.14768	−	0.181775i	−0.446516	−	0.894776i	$-0.647336\pi$
$263$	−5.49090e9	−	8.69673e8i	−1.14768	−	0.181775i	−0.701163	+	0.713001i	$0.747336\pi$
$264$	−9.43365e9	+	1.29843e10i	−1.94207	+	2.67302i
$265$	−3.95918e9	+	2.93811e9i	−0.802827	+	0.595778i
$266$	9.72196e9	−	7.06342e9i	1.94190	−	1.41087i
$267$	3.35546e8	+	6.58545e8i	0.0660247	+	0.129581i
$268$	−2.80539e9	−	2.80539e9i	−0.543819	−	0.543819i
$269$	−4.61416e9	−	1.49923e9i	−0.881219	−	0.286325i	−0.166756	−	0.985998i	$-0.553329\pi$
$269$	−4.61416e9	−	1.49923e9i	−0.881219	−	0.286325i	−0.714463	+	0.699673i	$0.753329\pi$
$270$	−1.99542e9	−	2.95402e8i	−0.375474	−	0.0555852i
$271$	−8.90173e8	−	2.73967e9i	−0.165043	−	0.507950i	0.833996	−	0.551770i	$-0.186047\pi$
$271$	−8.90173e8	−	2.73967e9i	−0.165043	−	0.507950i	−0.999039	+	0.0438195i	$0.986047\pi$
$272$	−3.75035e9	−	1.91090e9i	−0.685167	−	0.349110i
$273$	1.91005e8	+	1.20596e9i	0.0343870	+	0.217111i
$274$			1.78980e10i			3.17543i
$275$	−1.77481e8	−	8.77891e9i	−0.0310328	−	1.53501i
$276$	−5.84594e9			−1.00744
$277$	−3.18360e9	+	5.04233e8i	−0.540754	+	0.0856470i	−0.420836	−	0.907137i	$-0.638263\pi$
$277$	−3.18360e9	+	5.04233e8i	−0.540754	+	0.0856470i	−0.119918	+	0.992784i	$0.538263\pi$
$278$	6.67767e9	−	1.31057e10i	1.11801	−	2.19422i
$279$	−1.26708e9	+	4.11698e8i	−0.209115	+	0.0679457i
$280$	−1.60552e10	+	1.63831e10i	−2.61206	+	2.66540i
$281$	2.30140e8	−	7.08298e8i	0.0369119	−	0.113603i	−0.930903	−	0.365267i	$-0.880978\pi$
$281$	2.30140e8	−	7.08298e8i	0.0369119	−	0.113603i	0.967815	+	0.251664i	$0.0809777\pi$
$282$	9.17996e9	−	9.17996e9i	1.45159	−	1.45159i
$283$	−7.05283e9	+	3.59359e9i	−1.09956	+	0.560252i	−0.907041	−	0.421042i	$-0.861664\pi$
$283$	−7.05283e9	+	3.59359e9i	−1.09956	+	0.560252i	−0.192515	+	0.981294i	$0.561664\pi$
$284$	−4.58853e9	−	6.31557e9i	−0.705342	−	0.970821i
$285$	4.38884e9	−	1.47522e9i	0.665228	−	0.223604i
$286$	6.23285e9	+	4.52843e9i	0.931586	+	0.676836i
$287$	−1.50870e9	+	9.52555e9i	−0.222369	+	1.40398i
$288$	1.14884e10	+	1.81959e9i	1.66990	+	0.264486i
$289$	3.97844e9	−	5.47586e9i	0.570324	−	0.784984i
$290$	6.09062e9	−	6.15600e7i	0.861132	−	0.00870375i
$291$	3.86690e8	−	2.80947e8i	0.0539251	−	0.0391789i
$292$	1.06632e10	+	2.09277e10i	1.46675	+	2.87866i
$293$	9.96474e8	+	9.96474e8i	0.135206	+	0.135206i	0.771471	−	0.636265i	$-0.219521\pi$
$293$	9.96474e8	+	9.96474e8i	0.135206	+	0.135206i	−0.636265	+	0.771471i	$0.719521\pi$
$294$	−1.95903e7	−	6.36527e6i	−0.00262211	−	0.000851976i
$295$	1.09139e9	+	6.46702e9i	0.144109	+	0.853918i
$296$	−1.46259e10	−	4.50137e10i	−1.90526	−	5.86379i
$297$	−2.04844e9	−	1.04373e9i	−0.263268	−	0.134142i
$298$	5.14691e8	+	3.24963e9i	0.0652652	+	0.412068i
$299$			1.83518e9i			0.229612i
$300$	−1.19152e10	+	6.37769e9i	−1.47102	+	0.787369i
$301$	−8.35231e9			−1.01751
$302$	−1.12237e10	+	1.77765e9i	−1.34929	+	0.213707i
$303$	9.91451e8	−	1.94583e9i	0.117625	−	0.230853i
$304$	−4.40522e10	+	1.43134e10i	−5.15790	+	1.67590i
$305$	1.75412e9	+	3.35831e9i	0.202703	+	0.388080i
$306$	3.07001e8	−	9.44853e8i	0.0350150	−	0.107765i
$307$	−3.24515e9	+	3.24515e9i	−0.365327	+	0.365327i	−0.865769	−	0.500443i	$-0.833170\pi$
$307$	−3.24515e9	+	3.24515e9i	−0.365327	+	0.365327i	0.500443	+	0.865769i	$0.333170\pi$
$308$	−3.56197e10	+	1.81491e10i	−3.95810	+	2.01675i
$309$	−4.64344e9	−	6.39115e9i	−0.509338	−	0.701043i
$310$	−6.96352e9	+	9.79106e9i	−0.754019	+	1.06019i
$311$	1.38577e10	+	1.00682e10i	1.48132	+	1.07624i	0.977127	+	0.212655i	$0.0682110\pi$
$311$	1.38577e10	+	1.00682e10i	1.48132	+	1.07624i	0.504196	+	0.863589i	$0.331789\pi$
$312$	1.21310e9	−	7.65918e9i	0.128020	−	0.808284i
$313$	4.93550e8	+	7.81707e7i	0.0514226	+	0.00814454i	0.182093	−	0.983281i	$-0.441713\pi$
$313$	4.93550e8	+	7.81707e7i	0.0514226	+	0.00814454i	−0.130670	+	0.991426i	$0.541713\pi$
$314$	−2.58439e9	+	3.55710e9i	−0.265851	+	0.365913i
$315$	−2.67768e9	−	1.90440e9i	−0.271967	−	0.193427i
$316$	−1.81011e10	+	1.31512e10i	−1.81533	+	1.31892i
$317$	−6.80446e9	−	1.33545e10i	−0.673840	−	1.32248i	−0.934123	−	0.356952i	$-0.883816\pi$
$317$	−6.80446e9	−	1.33545e10i	−0.673840	−	1.32248i	0.260283	−	0.965532i	$-0.416184\pi$
$318$	8.23170e9	+	8.23170e9i	0.804973	+	0.804973i
$319$	6.60223e9	+	2.14519e9i	0.637570	+	0.207159i
$320$	5.15098e10	−	2.69047e10i	4.91235	−	2.56583i
$321$	−1.45274e9	−	4.47109e9i	−0.136826	−	0.421108i
$322$	−1.14208e10	−	5.81917e9i	−1.06236	−	0.541299i
$323$	3.56732e8	+	2.25232e9i	0.0327742	+	0.206928i
$324$			3.53851e9i			0.321100i
$325$	2.00211e9	+	3.74047e9i	0.179454	+	0.335268i
$326$	−2.07911e9			−0.184081
$327$	−2.33260e9	+	3.69447e8i	−0.204009	+	0.0323118i
$328$	2.78078e10	−	5.45759e10i	2.40254	−	4.71526i
$329$	2.01125e10	−	6.53495e9i	1.71665	−	0.557774i
$330$	−2.04439e10	+	3.45016e9i	−1.72389	+	0.290927i
$331$	−2.55698e9	+	7.86957e9i	−0.213017	+	0.655600i	0.786271	+	0.617882i	$0.212009\pi$
$331$	−2.55698e9	+	7.86957e9i	−0.213017	+	0.655600i	−0.999288	+	0.0377182i	$0.987991\pi$
$332$	−1.42645e10	+	1.42645e10i	−1.17410	+	1.17410i
$333$	6.04089e9	−	3.07799e9i	0.491275	−	0.250317i
$334$	3.23694e9	+	4.45527e9i	0.260105	+	0.358004i
$335$	−3.38751e7	−	3.35154e9i	−0.00268968	−	0.266112i
$336$	2.65932e10	+	1.93211e10i	2.08648	+	1.51591i
$337$	2.13716e9	−	1.34935e10i	0.165698	−	1.04617i	−0.754951	−	0.655782i	$-0.772339\pi$
$337$	2.13716e9	−	1.34935e10i	0.165698	−	1.04617i	0.920648	−	0.390393i	$-0.127661\pi$
$338$	2.17481e10	+	3.44455e9i	1.66630	+	0.263916i
$339$	6.75934e9	−	9.30343e9i	0.511806	−	0.704440i
$340$	−2.12073e9	−	6.30925e9i	−0.158698	−	0.472131i
$341$	−1.10783e10	+	8.04888e9i	−0.819327	+	0.595276i
$342$	−4.96334e9	−	9.74111e9i	−0.362802	−	0.712039i
$343$	9.77538e9	+	9.77538e9i	0.706248	+	0.706248i
$344$	5.04502e10	+	1.63923e10i	3.60271	+	1.17059i
$345$	−3.52730e9	−	3.45671e9i	−0.248981	−	0.243998i
$346$	1.48889e10	+	4.58233e10i	1.03886	+	3.19729i
$347$	−4.92096e9	−	2.50736e9i	−0.339416	−	0.172941i	0.275972	−	0.961166i	$-0.411000\pi$
$347$	−4.92096e9	−	2.50736e9i	−0.339416	−	0.172941i	−0.615387	+	0.788225i	$0.711000\pi$
$348$	−1.67145e9	−	1.05531e10i	−0.113966	−	0.719556i
$349$		−	1.68656e10i		−	1.13684i	−0.822737	−	0.568422i	$-0.807554\pi$
$349$		−	1.68656e10i		−	1.13684i	0.822737	−	0.568422i	$-0.192446\pi$
$350$	−2.96263e10	+	5.98947e8i	−1.97427	+	0.0399132i
$351$	1.11082e9			0.0731839
$352$	1.18081e11	−	1.87022e10i	7.69148	−	1.21821i
$353$	−1.05196e10	+	2.06459e10i	−0.677487	+	1.32964i	0.254472	+	0.967080i	$0.418098\pi$
$353$	−1.05196e10	+	2.06459e10i	−0.677487	+	1.32964i	−0.931959	+	0.362563i	$0.881902\pi$
$354$	1.47279e10	−	4.78540e9i	0.937840	−	0.304723i
$355$	9.65793e8	−	6.52386e9i	0.0608094	−	0.410763i
$356$	3.61314e9	−	1.11201e10i	0.224950	−	0.692324i
$357$	1.14432e9	−	1.14432e9i	0.0704488	−	0.0704488i
$358$	−2.54041e10	+	1.29440e10i	−1.54658	+	0.788022i
$359$	−1.35761e10	−	1.86859e10i	−0.817330	−	1.12496i	−0.990151	−	0.140005i	$-0.955288\pi$
$359$	−1.35761e10	−	1.86859e10i	−0.817330	−	1.12496i	0.172821	−	0.984953i	$-0.444712\pi$
$360$	1.24363e10	+	1.67583e10i	0.740428	+	0.997747i
$361$	6.56193e9	+	4.76752e9i	0.386369	+	0.280714i
$362$	3.33496e9	−	2.10561e10i	0.194203	−	1.22615i
$363$	−1.34379e10	−	2.12835e9i	−0.773935	−	0.122579i
$364$	1.13535e10	−	1.56267e10i	0.646731	−	0.890149i
$365$	−5.94066e9	+	1.89325e10i	−0.334706	+	1.06668i
$366$	7.23762e9	−	5.25844e9i	0.403340	−	0.293044i
$367$	3.35848e9	+	6.59139e9i	0.185131	+	0.363340i	0.964855	−	0.262784i	$-0.0846406\pi$
$367$	3.35848e9	+	6.59139e9i	0.185131	+	0.363340i	−0.779724	+	0.626123i	$0.784641\pi$
$368$	3.49353e10	+	3.49353e10i	1.90490	+	1.90490i
$369$	8.34464e9	+	2.71134e9i	0.450093	+	0.146244i
$370$	2.72059e10	−	5.47558e10i	1.45163	−	2.92162i
$371$	5.85991e9	+	1.80349e10i	0.309311	+	0.951961i
$372$	1.87791e10	+	9.56844e9i	0.980626	+	0.499654i
$373$	4.65071e9	+	2.93634e10i	0.240261	+	1.51695i	0.752780	+	0.658273i	$0.228713\pi$
$373$	4.65071e9	+	2.93634e10i	0.240261	+	1.51695i	−0.512518	+	0.858676i	$0.671287\pi$
$374$		−	1.02112e10i		−	0.521906i
$375$	−1.09605e10	−	3.19734e9i	−0.554249	−	0.161683i
$376$	−1.34310e11			−6.71983
$377$	−3.31288e9	+	5.24709e8i	−0.163999	+	0.0259748i
$378$	−3.52230e9	+	6.91290e9i	−0.172528	+	0.338605i
$379$	−2.80952e10	+	9.12868e9i	−1.36168	+	0.442437i	−0.896604	−	0.442833i	$-0.853973\pi$
$379$	−2.80952e10	+	9.12868e9i	−1.36168	+	0.442437i	−0.465077	+	0.885270i	$0.653973\pi$
$380$	−6.55967e10	−	3.25923e10i	−3.14592	−	1.56308i
$381$	2.04707e9	−	6.30023e9i	0.0971477	−	0.298990i
$382$	−1.27293e10	+	1.27293e10i	−0.597796	+	0.597796i
$383$	1.16317e10	−	5.92667e9i	0.540567	−	0.275433i	−0.162315	−	0.986739i	$-0.551896\pi$
$383$	1.16317e10	−	5.92667e9i	0.540567	−	0.275433i	0.702882	+	0.711306i	$0.251896\pi$
$384$	−4.32278e10	−	5.94980e10i	−1.98810	−	2.73639i
$385$	−3.22236e10	−	1.01112e10i	−1.46667	−	0.460214i
$386$	−3.51313e10	−	2.55244e10i	−1.58251	−	1.14976i
$387$	−1.18870e9	+	7.50513e9i	−0.0529940	+	0.334591i
$388$	−7.46832e9	−	1.18287e9i	−0.329531	−	0.0521926i
$389$	1.55773e10	−	2.14404e10i	0.680291	−	0.936340i	−0.319646	−	0.947537i	$-0.603564\pi$
$389$	1.55773e10	−	2.14404e10i	0.680291	−	0.936340i	0.999937	+	0.0111966i	$0.00356406\pi$
$390$	8.04449e9	−	5.96981e9i	0.347729	−	0.258049i
$391$	1.96782e9	−	1.42970e9i	0.0841935	−	0.0611701i
$392$	9.67465e7	+	1.89876e8i	0.00409723	+	0.00804128i
$393$	−1.13868e9	−	1.13868e9i	−0.0477343	−	0.0477343i
$394$	−3.60013e10	−	1.16975e10i	−1.49394	−	0.485411i
$395$	−1.86981e10	−	2.76807e9i	−0.768085	−	0.113707i
$396$	1.12389e10	+	3.45897e10i	0.457027	+	1.40659i
$397$	3.32826e10	+	1.69583e10i	1.33985	+	0.682686i	0.969243	−	0.246105i	$-0.0791508\pi$
$397$	3.32826e10	+	1.69583e10i	1.33985	+	0.682686i	0.370604	+	0.928791i	$0.379151\pi$
$398$	1.26030e10	+	7.95720e10i	0.502274	+	3.17123i
$399$		−	1.78087e10i		−	0.702651i
$400$	1.09318e11	+	3.30922e10i	4.27024	+	1.29266i
$401$	1.04599e9			0.0404527			0.0202264	−	0.999795i	$-0.493561\pi$
$401$	1.04599e9			0.0404527			0.0202264	+	0.999795i	$0.493561\pi$
$402$	−7.81663e9	+	1.23803e9i	−0.299306	+	0.0474054i
$403$	3.00376e9	−	5.89521e9i	0.113879	−	0.223501i
$404$	−3.28571e10	+	1.06759e10i	−1.23340	+	0.400755i
$405$	−2.09232e9	+	2.13505e9i	−0.0777693	+	0.0793575i
$406$	7.23942e9	−	2.22806e10i	0.266440	−	0.820018i
$407$	4.92749e10	−	4.92749e10i	1.79576	−	1.79576i
$408$	−9.15783e9	+	4.66615e9i	−0.330485	+	0.168391i
$409$	2.73533e10	+	3.76486e10i	0.977499	+	1.34541i	0.938166	+	0.346186i	$0.112523\pi$
$409$	2.73533e10	+	3.76486e10i	0.977499	+	1.34541i	0.0393333	+	0.999226i	$0.487477\pi$
$410$	7.50028e10	−	2.52108e10i	2.65425	−	0.892176i
$411$	2.14585e10	+	1.55905e10i	0.752023	+	0.546377i
$412$	−1.95502e10	+	1.23435e11i	−0.678520	+	4.28401i
$413$	2.49149e10	+	3.94613e9i	0.856365	+	0.135635i
$414$	−6.85432e9	+	9.43416e9i	−0.233326	+	0.321146i
$415$	−1.70415e10	+	1.72244e8i	−0.574534	+	0.00580700i
$416$	−4.67326e10	+	3.39532e10i	−1.56044	+	1.13372i
$417$	−9.89601e9	−	1.94220e10i	−0.327277	−	0.642318i
$418$	−7.94572e10	−	7.94572e10i	−2.60272	−	2.60272i
$419$	1.27456e10	+	4.14128e9i	0.413526	+	0.134363i	0.508389	−	0.861128i	$-0.330241\pi$
$419$	1.27456e10	+	4.14128e9i	0.413526	+	0.134363i	−0.0948630	+	0.995490i	$0.530241\pi$
$420$	8.65009e9	+	5.12562e10i	0.277986	+	1.64721i
$421$	−5.13916e9	−	1.58167e10i	−0.163593	−	0.503486i	0.835337	−	0.549738i	$-0.185272\pi$
$421$	−5.13916e9	−	1.58167e10i	−0.163593	−	0.503486i	−0.998930	+	0.0462516i	$0.985272\pi$
$422$	−8.00683e10	−	4.07969e10i	−2.52471	−	1.28640i
$423$	−3.00970e9	−	1.90025e10i	−0.0940074	−	0.593540i
$424$		−	1.20437e11i		−	3.72645i
$425$	2.45107e9	−	5.06084e9i	0.0751276	−	0.155120i
$426$	−1.55720e10			−0.472833
$427$	1.43933e10	−	2.27968e9i	0.432962	−	0.0685745i
$428$	−3.37638e10	+	6.62652e10i	−1.00618	+	1.97474i
$429$	1.08585e10	−	3.52815e9i	0.320584	−	0.104164i
$430$	3.17259e10	+	6.07400e10i	0.927983	+	1.77665i
$431$	1.20877e10	−	3.72020e10i	0.350295	−	1.07810i	−0.608393	−	0.793636i	$-0.708186\pi$
$431$	1.20877e10	−	3.72020e10i	0.350295	−	1.07810i	0.958688	−	0.284460i	$-0.0918144\pi$
$432$	2.11461e10	−	2.11461e10i	0.607148	−	0.607148i
$433$	−4.67272e9	+	2.38087e9i	−0.132929	+	0.0677305i	−0.519190	−	0.854659i	$-0.673766\pi$
$433$	−4.67272e9	+	2.38087e9i	−0.132929	+	0.0677305i	0.386261	+	0.922389i	$0.373766\pi$
$434$	2.71627e10	+	3.73862e10i	0.765621	+	1.05379i
$435$	5.23156e9	−	7.35584e9i	0.146108	−	0.205435i
$436$	3.02256e10	+	2.19602e10i	0.836429	+	0.607701i
$437$	4.18726e9	−	2.64373e10i	0.114816	−	0.724923i
$438$	4.62756e10	+	7.32934e9i	1.25735	+	0.199144i
$439$	3.24961e10	−	4.47270e10i	0.874930	−	1.20424i	−0.102870	−	0.994695i	$-0.532803\pi$
$439$	3.24961e10	−	4.47270e10i	0.874930	−	1.20424i	0.977800	−	0.209542i	$-0.0671974\pi$
$440$	1.74795e11	+	1.24317e11i	4.66357	+	3.31679i
$441$	−2.46961e7	+	1.79427e7i	−0.000652940	+	0.000474389i
$442$	2.23989e9	+	4.39603e9i	0.0586864	+	0.115179i
$443$	−1.07382e10	−	1.07382e10i	−0.278815	−	0.278815i	0.553821	−	0.832636i	$-0.313169\pi$
$443$	−1.07382e10	−	1.07382e10i	−0.278815	−	0.278815i	−0.832636	+	0.553821i	$0.813169\pi$
$444$	−1.02006e11	−	3.31437e10i	−2.62478	−	0.852842i
$445$	8.75542e9	−	4.57315e9i	0.223273	−	0.116621i
$446$	−1.75721e10	−	5.40812e10i	−0.444103	−	1.36681i
$447$	4.34440e9	+	2.21358e9i	0.108818	+	0.0554455i
$448$	−3.49658e10	−	2.20765e11i	−0.868022	−	5.48048i
$449$			4.21231e10i			1.03642i	0.855254	+	0.518209i	$0.173401\pi$
$449$			4.21231e10i			1.03642i	−0.855254	+	0.518209i	$0.826599\pi$
$450$	−3.67820e9	+	2.67065e10i	−0.0896986	+	0.651279i
$451$	9.01825e10			2.17980
$452$	−1.79682e11	+	2.84588e10i	−4.30477	+	0.681808i
$453$	−7.64533e9	+	1.50048e10i	−0.181553	+	0.356318i
$454$	−6.07200e10	+	1.97291e10i	−1.42925	+	0.464392i
$455$	1.60905e10	−	2.71547e9i	0.375426	−	0.0633576i
$456$	−3.49513e10	+	1.07569e11i	−0.808359	+	2.48787i
$457$	3.48708e10	−	3.48708e10i	0.799460	−	0.799460i	−0.183550	−	0.983010i	$-0.558759\pi$
$457$	3.48708e10	−	3.48708e10i	0.799460	−	0.799460i	0.983010	+	0.183550i	$0.0587589\pi$
$458$	7.41327e10	−	3.77725e10i	1.68480	−	0.858447i
$459$	−8.65390e8	−	1.19111e9i	−0.0194967	−	0.0268349i
$460$	7.89632e8	+	7.81246e10i	0.0176357	+	1.74484i
$461$	1.76701e10	+	1.28381e10i	0.391232	+	0.284247i	0.765960	−	0.642888i	$-0.222264\pi$
$461$	1.76701e10	+	1.28381e10i	0.391232	+	0.284247i	−0.374728	+	0.927135i	$0.622264\pi$
$462$	−1.24748e10	+	7.87626e10i	−0.273820	+	1.72883i
$463$	3.36822e9	+	5.33473e8i	0.0732953	+	0.0116088i	0.192974	−	0.981204i	$-0.438187\pi$
$463$	3.36822e9	+	5.33473e8i	0.0732953	+	0.0116088i	−0.119679	+	0.992813i	$0.538187\pi$
$464$	−5.30768e10	+	7.30540e10i	−1.14507	+	1.57606i
$465$	5.67304e9	+	1.68775e10i	0.121340	+	0.360990i
$466$	8.08662e10	−	5.87528e10i	1.71484	−	1.24590i
$467$	1.40064e9	+	2.74891e9i	0.0294482	+	0.0577953i	0.905262	−	0.424854i	$-0.139675\pi$
$467$	1.40064e9	+	2.74891e9i	0.0294482	+	0.0577953i	−0.875814	+	0.482649i	$0.839675\pi$
$468$	−1.24259e10	−	1.24259e10i	−0.259026	−	0.259026i
$469$	−1.22605e10	−	3.98369e9i	−0.253407	−	0.0823369i
$470$	−1.23920e11	−	1.21440e11i	−2.53951	−	2.48869i
$471$	2.01352e9	+	6.19698e9i	0.0409141	+	0.125921i
$472$	−1.42748e11	−	7.27338e10i	−2.87609	−	1.46544i
$473$	1.22177e10	+	7.71398e10i	0.244088	+	1.54111i
$474$			4.46312e10i			0.884148i
$475$	−2.03076e10	−	5.84528e10i	−0.398918	−	1.14823i
$476$	−2.56012e10			−0.498691
$477$	1.70396e10	−	2.69881e9i	0.329144	−	0.0521313i
$478$	−5.52494e10	+	1.08433e11i	−1.05832	+	2.07707i
$479$	5.87747e10	−	1.90971e10i	1.11647	−	0.362764i	0.308053	−	0.951369i	$-0.400323\pi$
$479$	5.87747e10	−	1.90971e10i	1.11647	−	0.362764i	0.808421	+	0.588605i	$0.200323\pi$
$480$	2.27650e10	−	1.53776e11i	0.428847	−	2.89683i
$481$	−1.04046e10	+	3.20220e10i	−0.194377	+	0.598230i
$482$	7.72068e10	−	7.72068e10i	1.43043	−	1.43043i
$483$	−1.69251e10	+	8.62375e9i	−0.310987	+	0.158456i
$484$	1.26511e11	+	1.74127e11i	2.30540	+	3.17311i
$485$	−3.80678e9	−	5.12974e9i	−0.0688003	−	0.0927104i
$486$	5.71043e9	+	4.14887e9i	0.102358	+	0.0743677i
$487$	7.19127e9	−	4.54039e10i	0.127847	−	0.807193i	−0.837541	−	0.546375i	$-0.816008\pi$
$487$	7.19127e9	−	4.54039e10i	0.127847	−	0.807193i	0.965388	−	0.260819i	$-0.0839925\pi$
$488$	−9.14138e10	−	1.44785e10i	−1.61188	−	0.255296i
$489$	−1.81106e9	+	2.49271e9i	−0.0316736	+	0.0435949i
$490$	−8.24188e7	+	2.62663e8i	−0.00142969	+	0.00455632i
$491$	−3.12277e9	+	2.26883e9i	−0.0537297	+	0.0390369i	−0.614326	−	0.789052i	$-0.710572\pi$
$491$	−3.12277e9	+	2.26883e9i	−0.0537297	+	0.0390369i	0.560596	+	0.828089i	$0.310572\pi$
$492$	−6.30153e10	−	1.23675e11i	−1.07544	−	2.11067i
$493$	3.14355e9	+	3.14355e9i	0.0532148	+	0.0532148i
$494$	5.16364e10	+	1.67777e10i	0.867058	+	0.281724i
$495$	−1.36717e10	+	2.75162e10i	−0.227720	+	0.458318i
$496$	−5.50429e10	−	1.69405e11i	−0.909441	−	2.79897i
$497$	−2.26011e10	−	1.15159e10i	−0.370429	−	0.188743i
$498$	6.29500e9	+	3.97451e10i	0.102348	+	0.646199i
$499$		−	2.82331e10i		−	0.455362i	−0.973736	−	0.227681i	$-0.926886\pi$
$499$		−	2.82331e10i		−	0.455362i	0.973736	−	0.227681i	$-0.0731144\pi$
$500$	8.68403e10	+	1.58372e11i	1.38944	+	2.53396i
$501$	8.16116e9			0.129539
$502$	1.26262e11	−	1.99980e10i	1.98819	−	0.314899i
$503$	−2.70243e10	+	5.30382e10i	−0.422166	+	0.828547i	0.577758	+	0.816208i	$0.303928\pi$
$503$	−2.70243e10	+	5.30382e10i	−0.422166	+	0.828547i	−0.999924	+	0.0123389i	$0.996072\pi$
$504$	7.63378e10	−	2.48037e10i	1.18309	−	0.384409i
$505$	−2.61378e10	−	1.29868e10i	−0.401887	−	0.199681i
$506$	−3.70381e10	+	1.13992e11i	−0.564997	+	1.73888i
$507$	2.30739e10	−	2.30739e10i	0.349212	−	0.349212i
$508$	−9.33746e10	+	4.75767e10i	−1.40208	+	0.714397i
$509$	−2.71684e10	−	3.73941e10i	−0.404756	−	0.557099i	0.557174	−	0.830396i	$-0.311886\pi$
$509$	−2.71684e10	−	3.73941e10i	−0.404756	−	0.557099i	−0.961930	+	0.273297i	$0.911886\pi$
$510$	−1.26684e10	−	3.97511e9i	−0.187258	−	0.0587582i
$511$	6.17439e10	+	4.48595e10i	0.905545	+	0.657917i
$512$	−6.44970e10	+	4.07218e11i	−0.938554	+	5.92580i
$513$	−1.60023e10	−	2.53452e9i	−0.231054	−	0.0365954i
$514$	5.84127e10	−	8.03982e10i	0.836864	−	1.15185i
$515$	−8.47835e10	+	6.29178e10i	−1.20526	+	0.894426i
$516$	9.72509e10	−	7.06569e10i	1.37181	−	0.996681i
$517$	−8.97757e10	−	1.76195e11i	−1.25660	−	2.46621i
$518$	−1.66289e11	−	1.66289e11i	−2.30964	−	2.30964i
$519$	6.79081e10	+	2.20647e10i	0.935948	+	0.304108i
$520$	−1.02520e11	−	1.51771e10i	−1.40216	−	0.207576i
$521$	3.13747e10	+	9.65613e10i	0.425822	+	1.31055i	0.902205	+	0.431307i	$0.141948\pi$
$521$	3.13747e10	+	9.65613e10i	0.425822	+	1.31055i	−0.476383	+	0.879238i	$0.658052\pi$
$522$	−1.89904e10	−	9.67608e9i	−0.255771	−	0.130322i
$523$	−1.20635e9	−	7.61663e9i	−0.0161238	−	0.101802i	0.978314	−	0.207128i	$-0.0664115\pi$
$523$	−1.20635e9	−	7.61663e9i	−0.0161238	−	0.101802i	−0.994438	+	0.105326i	$0.966412\pi$
$524$			2.54750e10i			0.337900i
$525$	−2.50886e10	+	3.60415e10i	−0.330247	+	0.474423i
$526$	1.75434e11			2.29176
$527$	−8.66139e9	+	1.37183e9i	−0.112291	+	0.0177851i
$528$	1.39544e11	−	2.73871e11i	1.79546	−	3.52379i
$529$	4.73249e10	−	1.53768e10i	0.604320	−	0.196356i
$530$	1.08896e11	−	1.11120e11i	1.38009	−	1.40827i
$531$	7.09175e9	−	2.18262e10i	0.0892021	−	0.274536i
$532$	−1.99212e11	+	1.99212e11i	−2.48695	+	2.48695i
$533$	−3.88244e10	+	1.97820e10i	−0.481056	+	0.245110i
$534$	−1.37092e10	−	1.88691e10i	−0.168596	−	0.232053i
$535$	−5.95550e10	+	2.00183e10i	−0.726947	+	0.244349i
$536$	6.62386e10	+	4.81251e10i	0.802513	+	0.583060i
$537$	−6.60984e9	+	4.17329e10i	−0.0794866	+	0.501859i
$538$	1.51215e11	+	2.39501e10i	1.80496	+	0.285877i
$539$	−1.84420e8	+	2.53833e8i	−0.00218501	+	0.00300741i
$540$	4.72883e10	−	4.77958e8i	0.556133	−	0.00562102i
$541$	−6.12299e10	+	4.44862e10i	−0.714784	+	0.519321i	−0.884713	−	0.466135i	$-0.845646\pi$
$541$	−6.12299e10	+	4.44862e10i	−0.714784	+	0.519321i	0.169930	+	0.985456i	$0.445646\pi$
$542$	4.12694e10	+	8.09957e10i	0.478223	+	0.938566i
$543$	−2.23398e10	−	2.23398e10i	−0.256968	−	0.256968i
$544$	7.28144e10	+	2.36588e10i	0.831423	+	0.270146i
$545$	5.25232e9	+	3.11227e10i	0.0595341	+	0.352770i
$546$	−1.19065e10	−	3.66444e10i	−0.133972	−	0.412323i
$547$	−1.38917e11	−	7.07819e10i	−1.55170	−	0.790630i	−0.552614	−	0.833437i	$-0.686370\pi$
$547$	−1.38917e11	−	7.07819e10i	−1.55170	−	0.790630i	−0.999083	+	0.0428075i	$0.986370\pi$
$548$	−6.56404e10	−	4.14437e11i	−0.727862	−	4.59554i
$549$		−	1.32579e10i		−	0.145943i
$550$	4.88691e10	+	2.72745e11i	0.534052	+	2.98062i
$551$	4.89220e10			0.530760
$552$	1.19157e11	−	1.88726e10i	1.28340	−	0.203271i
$553$	−3.30057e10	+	6.47774e10i	−0.352930	+	0.692664i
$554$	9.67373e10	−	3.14319e10i	1.02696	−	0.333681i
$555$	−4.19499e10	−	8.03142e10i	−0.442139	−	0.846487i
$556$	−1.06560e11	+	3.27958e11i	−1.11505	+	3.43177i
$557$	−1.00702e11	+	1.00702e11i	−1.04621	+	1.04621i	−0.0473256	+	0.998880i	$0.515070\pi$
$557$	−1.00702e11	+	1.00702e11i	−1.04621	+	1.04621i	−0.998880	+	0.0473256i	$0.984930\pi$
$558$	3.74599e10	−	1.90868e10i	0.386393	−	0.196877i
$559$	−2.21809e10	−	3.05294e10i	−0.227160	−	0.312659i
$560$	2.54613e11	−	3.57999e11i	2.58898	−	3.64024i
$561$	−1.22425e10	−	8.89472e9i	−0.123600	−	0.0898009i
$562$	−3.67647e9	+	2.32123e10i	−0.0368541	+	0.232688i
$563$	−1.72346e10	−	2.72969e9i	−0.171541	−	0.0271694i	0.0700731	−	0.997542i	$-0.477677\pi$
$563$	−1.72346e10	−	2.72969e9i	−0.171541	−	0.0271694i	−0.241614	+	0.970372i	$0.577677\pi$
$564$	−1.78899e11	+	2.46233e11i	−1.76804	+	2.43350i
$565$	−1.25243e11	−	8.90745e10i	−1.22902	−	0.874097i
$566$	2.02083e11	−	1.46822e11i	1.96908	−	1.43062i
$567$	5.21989e9	+	1.02446e10i	0.0505044	+	0.0991205i
$568$	1.13916e11	+	1.13916e11i	1.09444	+	1.09444i
$569$	−3.70897e10	−	1.20512e10i	−0.353838	−	0.114969i	0.126704	−	0.991941i	$-0.459560\pi$
$569$	−3.70897e10	−	1.20512e10i	−0.353838	−	0.114969i	−0.480542	+	0.876972i	$0.659560\pi$
$570$	−1.29509e11	+	6.76454e10i	−1.22687	+	0.640824i
$571$	−4.26794e10	−	1.31354e11i	−0.401489	−	1.23566i	−0.923792	−	0.382896i	$-0.874927\pi$
$571$	−4.26794e10	−	1.31354e11i	−0.401489	−	1.23566i	0.522303	−	0.852760i	$-0.325073\pi$
$572$	−1.60932e11	−	8.19991e10i	−1.50335	−	0.765994i
$573$	4.17339e9	+	2.63497e10i	0.0387142	+	0.244432i
$574$		−	3.04340e11i		−	2.80357i
$575$	−4.57187e10	+	4.76054e10i	−0.418237	+	0.435497i
$576$	−2.03349e11			−1.84736
$577$	5.25796e10	−	8.32779e9i	0.474366	−	0.0751322i	0.0853262	−	0.996353i	$-0.472807\pi$
$577$	5.25796e10	−	8.32779e9i	0.474366	−	0.0751322i	0.389040	+	0.921221i	$0.372807\pi$
$578$	−9.69684e10	+	1.90311e11i	−0.868798	+	1.70511i
$579$	−6.12039e10	+	1.98863e10i	−0.544584	+	0.176946i
$580$	−1.40805e11	+	2.37626e10i	−1.24425	+	0.209982i
$581$	−2.02558e10	+	6.23410e10i	−0.177765	+	0.547103i
$582$	−1.06655e10	+	1.06655e10i	−0.0929581	+	0.0929581i
$583$	1.57994e11	−	8.05021e10i	1.36763	−	0.696840i
$584$	−2.84908e11	−	3.92142e11i	−2.44936	−	3.37126i
$585$	−1.50042e8	−	1.48449e10i	−0.00128112	−	0.126752i
$586$	−3.59772e10	−	2.61390e10i	−0.305097	−	0.221666i
$587$	−9.58901e9	+	6.05426e10i	−0.0807646	+	0.509928i	0.913830	+	0.406096i	$0.133110\pi$
$587$	−9.58901e9	+	6.05426e10i	−0.0807646	+	0.509928i	−0.994595	+	0.103831i	$0.966890\pi$
$588$	4.76966e8	+	7.55441e7i	0.00399005	+	0.000631962i
$589$	−5.67226e10	+	7.80719e10i	−0.471297	+	0.648685i
$590$	−6.59410e10	−	1.96176e11i	−0.544186	−	1.61897i
$591$	−4.53842e10	+	3.29736e10i	−0.372010	+	0.270281i
$592$	4.11519e11	+	8.07651e11i	3.35045	+	6.57563i
$593$	6.92367e10	+	6.92367e10i	0.559909	+	0.559909i	0.929281	−	0.369372i	$-0.120427\pi$
$593$	6.92367e10	+	6.92367e10i	0.559909	+	0.559909i	−0.369372	+	0.929281i	$0.620427\pi$
$594$	6.89982e10	+	2.24189e10i	0.554233	+	0.180081i
$595$	−1.54471e10	−	1.51380e10i	−0.123248	−	0.120781i
$596$	−2.38358e10	−	7.33590e10i	−0.188906	−	0.581391i
$597$	1.06379e11	+	5.42029e10i	0.837450	+	0.426702i
$598$	−9.05941e9	−	5.71989e10i	−0.0708427	−	0.447283i
$599$			1.77506e11i			1.37881i	0.724376	+	0.689405i	$0.242128\pi$
$599$			1.77506e11i			1.37881i	−0.724376	+	0.689405i	$0.757872\pi$
$600$	2.22277e11	−	1.68462e11i	1.71510	−	1.29986i
$601$	−5.73457e10			−0.439544			−0.219772	−	0.975551i	$-0.570531\pi$
$601$	−5.73457e10			−0.439544			−0.219772	+	0.975551i	$0.570531\pi$
$602$	2.60325e11	−	4.12314e10i	1.98212	−	0.313937i
$603$	−5.32453e9	+	1.04500e10i	−0.0402729	+	0.0790399i
$604$	2.53369e11	−	8.23247e10i	1.90373	−	0.618561i
$605$	−2.66280e10	+	1.79870e11i	−0.198755	+	1.34257i
$606$	−2.12959e10	+	6.55420e10i	−0.157908	+	0.485992i
$607$	1.70188e10	−	1.70188e10i	0.125364	−	0.125364i	−0.641641	−	0.767005i	$-0.721746\pi$
$607$	1.70188e10	−	1.70188e10i	0.125364	−	0.125364i	0.767005	+	0.641641i	$0.221746\pi$
$608$	7.50692e11	−	3.82497e11i	5.49348	−	2.79907i
$609$	−2.04068e10	−	2.80876e10i	−0.148356	−	0.204195i
$610$	−7.12509e10	−	9.60126e10i	−0.514601	−	0.693440i
$611$	7.72985e10	+	5.61606e10i	0.554634	+	0.402965i
$612$	−3.64354e9	+	2.30044e10i	−0.0259727	+	0.163985i
$613$	−1.56762e11	−	2.48287e10i	−1.11020	−	0.175838i	−0.425707	−	0.904861i	$-0.639974\pi$
$613$	−1.56762e11	−	2.48287e10i	−1.11020	−	0.175838i	−0.684489	+	0.729024i	$0.739974\pi$
$614$	8.51251e10	−	1.17165e11i	0.598941	−	0.824371i
$615$	3.51069e10	−	1.11883e11i	0.245410	−	0.782104i
$616$	6.67439e11	−	4.84923e11i	4.63542	−	3.36783i
$617$	6.19876e10	+	1.21657e11i	0.427724	+	0.839456i	0.999814	+	0.0192653i	$0.00613271\pi$
$617$	6.19876e10	+	1.21657e11i	0.427724	+	0.839456i	−0.572090	+	0.820191i	$0.693867\pi$
$618$	1.76277e11	+	1.76277e11i	1.20849	+	1.20849i
$619$	2.48060e10	+	8.05996e9i	0.168964	+	0.0548998i	0.392277	−	0.919847i	$-0.371687\pi$
$619$	2.48060e10	+	8.05996e9i	0.168964	+	0.0548998i	−0.223313	+	0.974747i	$0.571687\pi$
$620$	1.25335e11	−	2.52255e11i	0.848216	−	1.70715i
$621$	5.34027e9	+	1.64357e10i	0.0359085	+	0.110515i
$622$	−4.81619e11	−	2.45397e11i	−3.21767	−	1.63949i
$623$	−5.94333e9	−	3.75247e10i	−0.0394528	−	0.249095i
$624$			1.48514e11i			0.979554i
$625$	−4.12484e10	+	1.46907e11i	−0.270326	+	0.962769i
$626$	−1.57689e10			−0.102684
$627$	−1.64476e11	+	2.60505e10i	−1.06422	+	0.168557i
$628$	4.67971e10	−	9.18444e10i	0.300871	−	0.590492i
$629$	4.24422e10	−	1.37903e10i	0.271141	−	0.0880991i
$630$	9.28591e10	+	4.61379e10i	0.589471	+	0.292884i
$631$	−3.91689e10	+	1.20550e11i	−0.247072	+	0.760411i	0.748216	+	0.663455i	$0.230911\pi$
$631$	−3.91689e10	+	1.20550e11i	−0.247072	+	0.760411i	−0.995289	+	0.0969558i	$0.969089\pi$
$632$	3.26496e11	−	3.26496e11i	2.04649	−	2.04649i
$633$	−1.18658e11	+	6.04591e10i	−0.739063	+	0.376571i
$634$	2.78006e11	+	3.82643e11i	1.72067	+	2.36830i
$635$	−8.44721e10	−	2.65058e10i	−0.519540	−	0.163022i
$636$	−2.20798e11	−	1.60419e11i	−1.34948	−	0.980456i
$637$	2.37151e7	−	1.49731e8i	0.000144035	−	0.000909398i
$638$	−2.16368e11	−	3.42693e10i	−1.30590	−	0.206834i
$639$	−1.35644e10	+	1.86698e10i	−0.0813573	+	0.111979i
$640$	−7.89287e11	+	5.85729e11i	−4.70451	+	3.49122i
$641$	−1.06628e11	+	7.74699e10i	−0.631597	+	0.458882i	−0.856953	−	0.515394i	$-0.827645\pi$
$641$	−1.06628e11	+	7.74699e10i	−0.631597	+	0.458882i	0.225356	+	0.974276i	$0.427645\pi$
$642$	6.73508e10	+	1.32183e11i	0.396463	+	0.778102i
$643$	1.41512e11	+	1.41512e11i	0.827846	+	0.827846i	0.987218	−	0.159373i	$-0.0509472\pi$
$643$	1.41512e11	+	1.41512e11i	0.827846	+	0.827846i	−0.159373	+	0.987218i	$0.550947\pi$
$644$	2.85794e11	+	9.28602e10i	1.66154	+	0.539866i
$645$	1.00458e11	+	1.48719e10i	0.580427	+	0.0859264i
$646$	−2.22373e10	−	6.84392e10i	−0.127688	−	0.392984i
$647$	4.03559e10	+	2.05624e10i	0.230298	+	0.117343i	0.565332	−	0.824863i	$-0.308748\pi$
$647$	4.03559e10	+	2.05624e10i	0.230298	+	0.117343i	−0.335034	+	0.942206i	$0.608748\pi$
$648$	−1.14234e10	−	7.21248e10i	−0.0647884	−	0.409058i
$649$		−	2.35880e11i		−	1.32957i
$650$	−8.08666e10	−	1.06700e11i	−0.453019	−	0.597735i
$651$	6.84840e10			0.381299
$652$	4.81428e10	−	7.62508e9i	0.266404	−	0.0421943i
$653$	7.99987e10	−	1.57006e11i	0.439977	−	0.863504i	−0.559423	−	0.828882i	$-0.688977\pi$
$653$	7.99987e10	−	1.57006e11i	0.439977	−	0.863504i	0.999400	−	0.0346220i	$-0.0110227\pi$
$654$	7.08786e10	−	2.30298e10i	0.387439	−	0.125887i
$655$	−1.50634e10	+	1.53710e10i	−0.0818384	+	0.0835096i
$656$	−3.62499e11	+	1.11566e12i	−1.95745	+	6.02442i
$657$	4.90967e10	−	4.90967e10i	0.263506	−	0.263506i
$658$	−5.94607e11	+	3.02967e11i	−3.17195	+	1.61619i
$659$	−8.94685e10	−	1.23143e11i	−0.474382	−	0.652931i	0.503031	−	0.864268i	$-0.332218\pi$
$659$	−8.94685e10	−	1.23143e11i	−0.474382	−	0.652931i	−0.977413	+	0.211337i	$0.932218\pi$
$660$	4.60735e11	−	1.54867e11i	2.42815	−	0.816177i
$661$	1.04112e11	+	7.56415e10i	0.545372	+	0.396236i	0.826076	−	0.563558i	$-0.190568\pi$
$661$	1.04112e11	+	7.56415e10i	0.545372	+	0.396236i	−0.280704	+	0.959794i	$0.590568\pi$
$662$	4.08476e10	−	2.57901e11i	0.212684	−	1.34283i
$663$	7.22163e9	+	1.14379e9i	0.0373750	+	0.00591961i
$664$	2.44701e11	−	3.36802e11i	1.25882	−	1.73262i
$665$	−2.37993e11	+	2.40548e9i	−1.21697	+	0.0123003i
$666$	−1.73088e11	+	1.25756e11i	−0.879772	+	0.639192i
$667$	−2.36902e10	−	4.64947e10i	−0.119692	−	0.234909i
$668$	−9.12924e10	−	9.12924e10i	−0.458489	−	0.458489i
$669$	−8.01460e10	−	2.60410e10i	−0.400108	−	0.130003i
$670$	1.76008e10	+	1.04293e11i	0.0873439	+	0.517557i
$671$	−4.21091e10	−	1.29599e11i	−0.207724	−	0.639308i
$672$	−5.32738e11	−	2.71444e11i	−2.61238	−	1.33108i
$673$	6.63765e9	+	4.19085e10i	0.0323560	+	0.204287i	0.998570	−	0.0534520i	$-0.0170224\pi$
$673$	6.63765e9	+	4.19085e10i	0.0323560	+	0.204287i	−0.966214	+	0.257739i	$0.917022\pi$
$674$			4.31115e11i			2.08907i
$675$	2.88152e10	+	2.76732e10i	0.138806	+	0.133304i
$676$	−5.16219e11			−2.47199
$677$	1.72288e11	−	2.72877e10i	0.820163	−	0.129901i	0.267768	−	0.963483i	$-0.413714\pi$
$677$	1.72288e11	−	2.72877e10i	0.820163	−	0.129901i	0.552395	+	0.833582i	$0.313714\pi$
$678$	−1.64748e11	+	3.23337e11i	−0.779655	+	1.53016i
$679$	−2.33671e10	+	7.59242e9i	−0.109932	+	0.0357192i
$680$	6.35949e10	+	1.21754e11i	0.297431	+	0.569440i
$681$	−2.92377e10	+	8.99844e10i	−0.135942	+	0.418388i
$682$	3.05556e11	−	3.05556e11i	1.41239	−	1.41239i
$683$	−9.23024e10	+	4.70304e10i	−0.424160	+	0.216121i	−0.653023	−	0.757338i	$-0.726499\pi$
$683$	−9.23024e10	+	4.70304e10i	−0.424160	+	0.216121i	0.228862	+	0.973459i	$0.426499\pi$
$684$	1.50654e11	+	2.07357e11i	0.688264	+	0.947314i
$685$	2.05451e11	−	2.88875e11i	0.933139	−	1.31204i
$686$	−3.52936e11	−	2.56423e11i	−1.59367	−	1.15787i
$687$	1.92884e10	−	1.21782e11i	0.0865904	−	0.546710i
$688$	−1.00342e12	−	1.58925e11i	−4.47844	−	0.709316i
$689$	−5.03594e10	+	6.93138e10i	−0.223462	+	0.307569i
$690$	1.27003e11	+	9.03262e10i	0.560297	+	0.398490i
$691$	1.53713e11	−	1.11679e11i	0.674216	−	0.489847i	−0.197218	−	0.980360i	$-0.563191\pi$
$691$	1.53713e11	−	1.11679e11i	0.674216	−	0.489847i	0.871434	+	0.490513i	$0.163191\pi$
$692$	−5.12814e11	−	1.00645e12i	−2.23633	−	4.38904i
$693$	8.35642e10	+	8.35642e10i	0.362316	+	0.362316i
$694$	1.65754e11	+	5.38568e10i	0.714540	+	0.232168i
$695$	−2.58217e11	+	1.34873e11i	−1.10674	+	0.578076i
$696$	6.81379e10	+	2.09707e11i	0.290370	+	0.893667i
$697$	5.14581e10	+	2.62192e10i	0.218033	+	0.111093i
$698$	8.32576e10	+	5.25668e11i	0.350754	+	2.21457i
$699$		−	1.48131e11i		−	0.620492i
$700$	6.83814e11	−	1.22522e11i	2.84804	−	0.510297i
$701$	2.14010e11			0.886261			0.443131	−	0.896457i	$-0.353868\pi$
$701$	2.14010e11			0.886261			0.443131	+	0.896457i	$0.353868\pi$
$702$	−3.46221e10	+	5.48360e9i	−0.142562	+	0.0225796i
$703$	2.22950e11	−	4.37565e11i	0.912823	−	1.79152i
$704$	−1.98778e12	+	6.45870e11i	−8.09242	+	2.62939i
$705$	−2.53541e11	+	4.27881e10i	−1.02634	+	0.173208i
$706$	2.25956e11	−	6.95422e11i	0.909506	−	2.79917i
$707$	−7.93784e10	+	7.93784e10i	−0.317705	+	0.317705i
$708$	−3.23482e11	+	1.64822e11i	−1.28741	+	0.655968i
$709$	−2.12770e11	−	2.92852e11i	−0.842024	−	1.15895i	−0.985564	−	0.169302i	$-0.945849\pi$
$709$	−2.12770e11	−	2.92852e11i	−0.842024	−	1.15895i	0.143540	−	0.989644i	$-0.454151\pi$
$710$	2.10337e9	+	2.08103e11i	0.00827718	+	0.818928i
$711$	5.35096e10	+	3.88770e10i	0.209389	+	0.152130i
$712$	−3.77468e10	+	2.38324e11i	−0.146879	+	0.927358i
$713$	1.01666e11	+	1.61023e10i	0.393384	+	0.0623060i
$714$	−3.00171e10	+	4.13151e10i	−0.115499	+	0.158970i
$715$	−4.86166e10	−	1.44636e11i	−0.186020	−	0.553416i
$716$	5.40772e11	−	3.92894e11i	2.05761	−	1.49494i
$717$	8.18773e10	+	1.60693e11i	0.309804	+	0.608024i
$718$	5.15384e11	+	5.15384e11i	1.93925	+	1.93925i
$719$	2.20926e11	+	7.17831e10i	0.826667	+	0.268600i	0.691641	−	0.722242i	$-0.256888\pi$
$719$	2.20926e11	+	7.17831e10i	0.826667	+	0.268600i	0.135026	+	0.990842i	$0.456888\pi$
$720$	−2.85450e11	−	2.79738e11i	−1.06219	−	1.04093i
$721$	1.25486e11	+	3.86207e11i	0.464361	+	1.42916i
$722$	−2.28057e11	−	1.16201e11i	−0.839257	−	0.427623i
$723$	−2.53127e10	−	1.59818e11i	−0.0926371	−	0.584888i
$724$			4.99795e11i			1.81902i
$725$	−9.90094e10	−	6.89206e10i	−0.358364	−	0.249458i
$726$	4.29339e11			1.54545
$727$	−4.76131e10	+	7.54117e9i	−0.170447	+	0.0269961i	−0.241074	−	0.970507i	$-0.577500\pi$
$727$	−4.76131e10	+	7.54117e9i	−0.170447	+	0.0269961i	0.0706277	+	0.997503i	$0.477500\pi$
$728$	−1.80968e11	+	3.55170e11i	−0.644283	+	1.26448i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	9.16980e10	−	6.19413e11i	0.322900	−	2.18117i
$731$	−1.54558e10	+	4.75681e10i	−0.0541280	+	0.166589i
$732$	−1.48305e11	+	1.48305e11i	−0.516549	+	0.516549i
$733$	−3.20159e11	+	1.63129e11i	−1.10905	+	0.565087i	−0.909877	−	0.414878i	$-0.863824\pi$
$733$	−3.20159e11	+	1.63129e11i	−1.10905	+	0.565087i	−0.199169	+	0.979965i	$0.563824\pi$
$734$	−1.37216e11	−	1.88861e11i	−0.472737	−	0.650667i
$735$	2.43121e8	+	3.27612e8i	0.000833053	+	0.00112256i
$736$	−7.27037e11	−	5.28224e11i	−2.47768	−	1.80014i
$737$	−1.88577e10	+	1.19063e11i	−0.0639172	+	0.403558i
$738$	−2.73471e11	−	4.33135e10i	−0.921903	−	0.146015i
$739$	1.24428e11	−	1.71260e11i	0.417195	−	0.574220i	−0.547760	−	0.836636i	$-0.684519\pi$
$739$	1.24428e11	−	1.71260e11i	0.417195	−	0.574220i	0.964955	+	0.262416i	$0.0845192\pi$
$740$	−4.29151e11	+	1.36767e12i	−1.43114	+	4.56095i
$741$	6.50942e10	−	4.72937e10i	0.215909	−	0.156867i
$742$	−2.71672e11	−	5.33186e11i	−0.896249	−	1.75899i
$743$	1.83848e11	+	1.83848e11i	0.603260	+	0.603260i	0.941176	−	0.337916i	$-0.109722\pi$
$743$	1.83848e11	+	1.83848e11i	0.603260	+	0.603260i	−0.337916	+	0.941176i	$0.609722\pi$
$744$	−4.13662e11	−	1.34407e11i	−1.35006	−	0.438662i
$745$	2.89953e10	−	5.83572e10i	0.0941245	−	0.189439i
$746$	−2.89906e11	−	8.92240e11i	−0.936057	−	2.88089i
$747$	5.31349e10	+	2.70736e10i	0.170646	+	0.0869487i
$748$	3.74493e10	+	2.36446e11i	0.119629	+	0.755310i
$749$			2.41657e11i			0.767843i
$750$	3.57400e11	+	4.55478e10i	1.12956	+	0.143954i
$751$	−8.35838e9			−0.0262762			−0.0131381	−	0.999914i	$-0.504182\pi$
$751$	−8.35838e9			−0.0262762			−0.0131381	+	0.999914i	$0.504182\pi$
$752$	2.54059e12	−	4.02389e11i	7.94443	−	1.25827i
$753$	8.60073e10	−	1.68799e11i	0.267519	−	0.525037i
$754$	1.00666e11	−	3.27082e10i	0.311455	−	0.101198i
$755$	2.01556e11	+	1.00145e11i	0.620307	+	0.308206i
$756$	5.62076e10	−	1.72989e11i	0.172071	−	0.529581i
$757$	−1.60293e10	+	1.60293e10i	−0.0488124	+	0.0488124i	−0.731092	−	0.682279i	$-0.760989\pi$
$757$	−1.60293e10	+	1.60293e10i	−0.0488124	+	0.0488124i	0.682279	+	0.731092i	$0.260989\pi$
$758$	8.30607e11	−	4.23216e11i	2.51605	−	1.28199i
$759$	1.04405e11	+	1.43701e11i	0.314596	+	0.433004i
$760$	1.44227e12	+	4.52557e11i	4.32305	+	1.35650i
$761$	−8.49776e10	−	6.17399e10i	−0.253376	−	0.184089i	0.453846	−	0.891080i	$-0.350052\pi$
$761$	−8.49776e10	−	6.17399e10i	−0.253376	−	0.184089i	−0.707222	+	0.706992i	$0.750052\pi$
$762$	−3.27018e10	+	2.06471e11i	−0.0969955	+	0.612405i
$763$	1.19904e11	+	1.89909e10i	0.353781	+	0.0560334i
$764$	2.48069e11	−	3.41438e11i	0.728115	−	1.00216i
$765$	−1.58010e10	+	1.17259e10i	−0.0461357	+	0.0342373i
$766$	−3.33281e11	+	2.42143e11i	−0.968045	+	0.703326i
$767$	5.17416e10	+	1.01549e11i	0.149506	+	0.293422i
$768$	8.53915e11	+	8.53915e11i	2.45454	+	2.45454i
$769$	−3.21968e11	−	1.04614e11i	−0.920678	−	0.299146i	−0.189933	−	0.981797i	$-0.560827\pi$
$769$	−3.21968e11	−	1.04614e11i	−0.920678	−	0.299146i	−0.730745	+	0.682651i	$0.760827\pi$
$770$	1.05426e12	+	1.56073e11i	2.99906	+	0.443981i
$771$	−4.55100e10	−	1.40065e11i	−0.128792	−	0.396381i
$772$	9.07092e11	+	4.62186e11i	2.55377	+	1.30121i
$773$	−1.98989e10	−	1.25637e11i	−0.0557329	−	0.351883i	−0.999758	−	0.0220093i	$-0.992994\pi$
$773$	−1.98989e10	−	1.25637e11i	−0.0557329	−	0.351883i	0.944025	−	0.329874i	$-0.107006\pi$
$774$		−	2.39788e11i		−	0.668134i
$775$	2.24783e11	−	7.80937e10i	0.623098	−	0.216476i
$776$	1.56044e11			0.430330
$777$	−3.44218e11	+	5.45187e10i	−0.944385	+	0.149576i
$778$	−3.79674e11	+	7.45151e11i	−1.03632	+	2.03388i
$779$	6.04434e11	−	1.96392e11i	1.64134	−	0.533304i
$780$	−1.64380e11	+	1.67737e11i	−0.444089	+	0.453158i
$781$	−7.32966e10	+	2.25584e11i	−0.197006	+	0.606323i
$782$	−5.42752e10	+	5.42752e10i	−0.145136	+	0.145136i
$783$	−2.81429e10	+	1.43395e10i	−0.0748724	+	0.0381494i
$784$	−2.39890e9	−	3.30180e9i	−0.00634961	−	0.00873949i
$785$	8.25439e10	−	2.77456e10i	0.217373	−	0.0730659i
$786$	4.11114e10	+	2.98692e10i	0.107714	+	0.0782588i
$787$	−2.59858e10	+	1.64068e11i	−0.0677388	+	0.427686i	0.930392	+	0.366567i	$0.119467\pi$
$787$	−2.59858e10	+	1.64068e11i	−0.0677388	+	0.427686i	−0.998130	+	0.0611190i	$0.980533\pi$
$788$	8.76527e11	+	1.38828e11i	2.27332	+	0.360058i
$789$	1.52815e11	−	2.10332e11i	0.394329	−	0.542747i
$790$	5.96447e11	−	6.02849e9i	1.53131	−	0.0154775i
$791$	−4.78229e11	+	3.47454e11i	−1.22160	+	0.887546i
$792$	−3.40747e11	−	6.68754e11i	−0.866027	−	1.69967i
$793$	4.65565e10	+	4.65565e10i	0.117730	+	0.117730i
$794$	−1.12107e12	−	3.64257e11i	−2.82065	−	0.916486i
$795$	−3.83683e10	−	2.27351e11i	−0.0960514	−	0.569153i
$796$	−5.83655e11	−	1.79630e12i	−1.45380	−	4.47433i
$797$	−5.05675e11	−	2.57654e11i	−1.25325	−	0.638564i	−0.303878	−	0.952711i	$-0.598281\pi$
$797$	−5.05675e11	−	2.57654e11i	−1.25325	−	0.638564i	−0.949374	+	0.314147i	$0.898281\pi$
$798$	8.79130e10	+	5.55061e11i	0.216791	+	1.36876i
$799$		−	1.26638e11i		−	0.310724i
$800$	−2.05812e12	−	2.83458e11i	−5.02471	−	0.692037i
$801$	−3.45644e10			−0.0839652
$802$	−3.26013e10	+	5.16353e9i	−0.0788020	+	0.0124810i
$803$	3.23992e11	−	6.35871e11i	0.779243	−	1.52935i
$804$	1.76457e11	−	5.73344e10i	0.422294	−	0.137212i
$805$	1.17533e11	+	2.25020e11i	0.279883	+	0.535843i
$806$	−6.45193e10	+	1.98570e11i	−0.152880	+	0.470515i
$807$	1.60434e11	−	1.60434e11i	0.378270	−	0.378270i
$808$	6.35255e11	−	3.23679e11i	1.49040	−	0.759396i
$809$	−7.94994e9	−	1.09421e10i	−0.0185596	−	0.0255452i	0.799636	−	0.600485i	$-0.205026\pi$
$809$	−7.94994e9	−	1.09421e10i	−0.0185596	−	0.0255452i	−0.818196	+	0.574939i	$0.805026\pi$
$810$	5.46738e10	−	7.68740e10i	0.127010	−	0.178583i
$811$	1.38666e11	+	1.00747e11i	0.320544	+	0.232889i	0.736408	−	0.676538i	$-0.236521\pi$
$811$	1.38666e11	+	1.00747e11i	0.320544	+	0.232889i	−0.415864	+	0.909427i	$0.636521\pi$
$812$	−8.59186e10	+	5.42468e11i	−0.197635	+	1.24782i
$813$	1.33057e11	+	2.10741e10i	0.304561	+	0.0482377i
$814$	−1.29255e12	+	1.77905e12i	−2.94409	+	4.05219i
$815$	3.35569e10	+	2.38661e10i	0.0760592	+	0.0540943i
$816$	1.59248e11	−	1.15700e11i	0.359181	−	0.260960i
$817$	2.49877e11	+	4.90411e11i	0.560838	+	1.10071i
$818$	−1.03840e12	−	1.03840e12i	−2.31927	−	2.31927i
$819$	−5.43054e10	−	1.76449e10i	−0.120700	−	0.0392178i
$820$	−1.64426e12	+	8.58836e11i	−3.63677	+	1.89957i
$821$	6.04310e10	+	1.85988e11i	0.133011	+	0.409365i	0.995275	−	0.0970929i	$-0.0309544\pi$
$821$	6.04310e10	+	1.85988e11i	0.133011	+	0.409365i	−0.862264	+	0.506458i	$0.830954\pi$
$822$	−7.45780e11	−	3.79994e11i	−1.63352	−	0.832318i
$823$	−6.53207e10	−	4.12419e11i	−0.142381	−	0.898957i	−0.950677	−	0.310182i	$-0.899610\pi$
$823$	−6.53207e10	−	4.12419e11i	−0.142381	−	0.898957i	0.808297	−	0.588776i	$-0.200390\pi$
$824$		−	2.57908e12i		−	5.59442i
$825$	3.69570e11	+	1.78990e11i	0.797776	+	0.386379i
$826$	−7.96028e11			−1.71005
$827$	6.73459e11	−	1.06665e11i	1.43976	−	0.228035i	0.612773	−	0.790259i	$-0.290054\pi$
$827$	6.73459e11	−	1.06665e11i	1.43976	−	0.228035i	0.826985	+	0.562224i	$0.190054\pi$
$828$	1.24115e11	−	2.43590e11i	0.264061	−	0.518249i
$829$	−2.60160e11	+	8.45309e10i	−0.550835	+	0.178977i	−0.571193	−	0.820816i	$-0.693519\pi$
$829$	−2.60160e11	+	8.45309e10i	−0.550835	+	0.178977i	0.0203582	+	0.999793i	$0.493519\pi$
$830$	5.30299e11	−	8.94943e10i	1.11740	−	0.188575i
$831$	4.65806e10	−	1.43360e11i	0.0976790	−	0.300625i
$832$	7.14084e11	−	7.14084e11i	1.49024	−	1.49024i
$833$	−1.79028e8	+	9.12195e7i	−0.000371828	+	0.000189456i
$834$	4.04316e11	+	5.56493e11i	0.835712	+	1.15026i
$835$	−1.10236e9	−	1.09065e11i	−0.00226765	−	0.224357i
$836$	2.13127e12	+	1.54846e12i	4.36329	+	3.17012i
$837$	9.74660e9	−	6.15376e10i	0.0198587	−	0.125383i
$838$	−4.17697e11	−	6.61567e10i	−0.847004	−	0.134152i
$839$	1.64458e11	−	2.26356e11i	0.331899	−	0.456820i	−0.610155	−	0.792282i	$-0.708893\pi$
$839$	1.64458e11	−	2.26356e11i	0.331899	−	0.456820i	0.942053	+	0.335463i	$0.108893\pi$
$840$	−3.41785e11	−	1.01682e12i	−0.686492	−	2.04234i
$841$	−3.27549e11	+	2.37978e11i	−0.654775	+	0.475722i
$842$	2.38257e11	+	4.67606e11i	0.474021	+	0.930318i
$843$	2.46274e10	+	2.46274e10i	0.0487650	+	0.0487650i
$844$	2.00364e12	+	6.51022e11i	3.94866	+	1.28300i
$845$	−3.11474e11	−	3.05241e11i	−0.610935	−	0.598709i
$846$	1.87613e11	+	5.77413e11i	0.366253	+	1.12721i
$847$	6.23139e11	+	3.17505e11i	1.21074	+	0.616903i
$848$	3.60824e11	+	2.27815e12i	0.697769	+	4.40554i
$849$		−	3.70175e11i		−	0.712485i
$850$	−5.14119e10	+	1.69836e11i	−0.0984890	+	0.325353i
$851$	−5.23817e11			−0.998760
$852$	3.60578e11	−	5.71099e10i	0.684291	−	0.108381i
$853$	−1.18461e10	+	2.32492e10i	−0.0223758	+	0.0439150i	−0.901924	−	0.431895i	$-0.857845\pi$
$853$	−1.18461e10	+	2.32492e10i	−0.0223758	+	0.0439150i	0.879548	+	0.475810i	$0.157845\pi$
$854$	−4.37358e11	+	1.42106e11i	−0.822253	+	0.267166i
$855$	−3.17096e10	+	2.14196e11i	−0.0593370	+	0.400817i
$856$	4.74277e11	−	1.45967e12i	0.883358	−	2.71870i
$857$	1.40270e11	−	1.40270e11i	0.260041	−	0.260041i	−0.565030	−	0.825071i	$-0.691135\pi$
$857$	1.40270e11	−	1.40270e11i	0.260041	−	0.260041i	0.825071	+	0.565030i	$0.191135\pi$
$858$	−3.21022e11	+	1.63569e11i	−0.592359	+	0.301822i
$859$	4.44237e10	+	6.11440e10i	0.0815910	+	0.112300i	0.847862	−	0.530218i	$-0.177890\pi$
$859$	4.44237e10	+	6.11440e10i	0.0815910	+	0.112300i	−0.766271	+	0.642518i	$0.777890\pi$
$860$	−9.57389e11	−	1.29011e12i	−1.75023	−	2.35848i
$861$	−3.64882e11	−	2.65102e11i	−0.663956	−	0.482392i
$862$	−1.93100e11	+	1.21918e12i	−0.349746	+	2.20821i
$863$	5.83605e11	+	9.24340e10i	1.05215	+	0.166644i	0.658471	−	0.752606i	$-0.271203\pi$
$863$	5.83605e11	+	9.24340e10i	1.05215	+	0.166644i	0.393675	+	0.919250i	$0.371203\pi$
$864$	−3.19730e11	+	4.40070e11i	−0.573757	+	0.789709i
$865$	2.85698e11	−	9.10497e11i	0.510319	−	1.62635i
$866$	1.33886e11	−	9.72740e10i	0.238048	−	0.172952i
$867$	1.43703e11	+	2.82033e11i	0.254325	+	0.499141i
$868$	−7.66077e11	−	7.66077e11i	−1.34956	−	1.34956i
$869$	6.46548e11	+	2.10076e11i	1.13376	+	0.368381i
$870$	−1.26745e11	+	2.55093e11i	−0.221235	+	0.445267i
$871$	−1.79986e10	−	5.53941e10i	−0.0312728	−	0.0962478i
$872$	−6.86979e11	−	3.50033e11i	−1.18817	−	0.605401i
$873$	3.49673e9	+	2.20775e10i	0.00602012	+	0.0380095i
$874$			8.44669e11i			1.44757i
$875$	4.85045e11	+	3.30413e11i	0.827465	+	0.563670i
$876$	−1.09841e12			−1.86530
$877$	1.18745e11	−	1.88074e10i	0.200732	−	0.0317929i	−0.0552585	−	0.998472i	$-0.517598\pi$
$877$	1.18745e11	−	1.88074e10i	0.200732	−	0.0317929i	0.255991	+	0.966679i	$0.417598\pi$
$878$	−7.92042e11	+	1.55447e12i	−1.33282	+	2.61580i
$879$	−6.26775e10	+	2.03652e10i	−0.104992	+	0.0341140i
$880$	−3.67884e12	−	1.82786e12i	−6.13451	−	3.04799i
$881$	−9.20377e10	+	2.83263e11i	−0.152779	+	0.470204i	−0.997929	−	0.0643245i	$-0.979511\pi$
$881$	−9.20377e10	+	2.83263e11i	−0.152779	+	0.470204i	0.845151	+	0.534528i	$0.179511\pi$
$882$	6.81152e8	−	6.81152e8i	0.00112556	−	0.00112556i
$883$	3.39112e11	−	1.72786e11i	0.557829	−	0.284228i	−0.152260	−	0.988341i	$-0.548655\pi$
$883$	3.39112e11	−	1.72786e11i	0.557829	−	0.284228i	0.710088	+	0.704113i	$0.248655\pi$
$884$	−6.79879e10	−	9.35774e10i	−0.111333	−	0.153236i
$885$	−2.92641e11	−	9.18253e10i	−0.477047	−	0.149689i
$886$	3.87697e11	+	2.81678e11i	0.629155	+	0.457108i
$887$	1.40017e11	−	8.84030e11i	0.226196	−	1.42815i	−0.569272	−	0.822149i	$-0.692775\pi$
$887$	1.40017e11	−	8.84030e11i	0.226196	−	1.42815i	0.795468	−	0.605996i	$-0.207225\pi$
$888$	2.18617e12	+	3.46255e11i	3.51586	+	0.556857i
$889$	−2.00153e11	+	2.75487e11i	−0.320446	+	0.441056i
$890$	−2.50313e11	+	1.85757e11i	−0.398955	+	0.296064i
$891$	8.69810e10	−	6.31954e10i	0.138011	−	0.100271i
$892$	6.05230e11	+	1.18783e12i	0.956007	+	1.87627i
$893$	−9.85411e11	−	9.85411e11i	−1.54957	−	1.54957i
$894$	−1.46334e11	−	4.75467e10i	−0.229084	−	0.0744339i
$895$	5.58608e11	+	8.26963e10i	0.870592	+	0.128883i
$896$	1.16821e12	+	3.59537e12i	1.81254	+	5.57843i
$897$	−7.64687e10	−	3.89628e10i	−0.118117	−	0.0601839i
$898$	−2.07942e11	−	1.31289e12i	−0.319769	−	2.01894i
$899$			1.88132e11i			0.288021i
$900$	−1.27748e10	−	6.31891e11i	−0.0194708	−	0.963102i
$901$	1.13556e11			0.172311
$902$	−2.81081e12	+	4.45188e11i	−4.24624	+	0.672539i
$903$	1.77328e11	−	3.48026e11i	0.266702	−	0.523433i
$904$	3.57055e12	−	1.16014e12i	5.34639	−	1.73715i
$905$	−2.95529e11	+	3.01564e11i	−0.440561	+	0.449558i
$906$	1.64218e11	−	5.05411e11i	0.243730	−	0.750123i
$907$	−8.13844e11	+	8.13844e11i	−1.20257	+	1.20257i	−0.229194	+	0.973381i	$0.573609\pi$
$907$	−8.13844e11	+	8.13844e11i	−1.20257	+	1.20257i	−0.973381	+	0.229194i	$0.926391\pi$
$908$	1.33364e12	−	6.79526e11i	1.96199	−	0.999683i
$909$	6.00299e10	+	8.26240e10i	0.0879249	+	0.121018i
$910$	−4.88104e11	+	1.64067e11i	−0.711782	+	0.239252i
$911$	−4.34326e11	−	3.15556e11i	−0.630583	−	0.458146i	0.226019	−	0.974123i	$-0.427429\pi$
$911$	−4.34326e11	−	3.15556e11i	−0.630583	−	0.458146i	−0.856602	+	0.515977i	$0.827429\pi$
$912$	3.38858e11	−	2.13947e12i	0.489822	−	3.09262i
$913$	6.05396e11	+	9.58852e10i	0.871277	+	0.137997i
$914$	−9.14712e11	+	1.25899e12i	−1.31069	+	1.80401i
$915$	−1.77177e11	+	1.79078e9i	−0.252768	+	0.00255481i
$916$	−1.57805e12	+	1.14652e12i	−2.24149	+	1.62854i
$917$	3.75799e10	+	7.37546e10i	0.0531469	+	0.104307i
$918$	3.28524e10	+	3.28524e10i	0.0462590	+	0.0462590i
$919$	−7.49298e11	−	2.43462e11i	−1.05049	−	0.341325i	−0.267630	−	0.963522i	$-0.586240\pi$
$919$	−7.49298e11	−	2.43462e11i	−1.05049	−	0.341325i	−0.782861	+	0.622197i	$0.786240\pi$
$920$	−2.68307e11	−	1.58985e12i	−0.374524	−	2.21925i
$921$	−6.63218e10	−	2.04118e11i	−0.0921760	−	0.283689i
$922$	−6.14116e11	−	3.12908e11i	−0.849820	−	0.433005i
$923$	−1.79282e10	−	1.13194e11i	−0.0247018	−	0.155961i
$924$		−	1.86953e12i		−	2.56475i
$925$	−1.06765e12	+	5.71463e11i	−1.45834	+	0.780587i
$926$	−1.07614e11			−0.146361
$927$	3.64893e11	−	5.77934e10i	0.494136	−	0.0782635i
$928$	7.45681e11	−	1.46348e12i	1.00545	−	1.97331i
$929$	−1.18818e12	+	3.86063e11i	−1.59521	+	0.518316i	−0.965918	−	0.258849i	$-0.916657\pi$
$929$	−1.18818e12	+	3.86063e11i	−1.59521	+	0.518316i	−0.629296	+	0.777165i	$0.716657\pi$
$930$	−2.60134e11	−	4.98032e11i	−0.347748	−	0.665772i
$931$	−6.83271e8	+	2.10289e9i	−0.000909483	+	0.00279910i
$932$	−1.65702e12	+	1.65702e12i	−2.19616	+	2.19616i
$933$	−7.13738e11	+	3.63668e11i	−0.941916	+	0.479930i
$934$	−5.72251e10	−	7.87636e10i	−0.0751968	−	0.103499i
$935$	−1.17215e11	+	1.64810e11i	−0.153368	+	0.215643i
$936$	2.93389e11	+	2.13160e11i	0.382244	+	0.277717i
$937$	−2.07122e11	+	1.30772e12i	−0.268700	+	1.69651i	0.371610	+	0.928389i	$0.378806\pi$
$937$	−2.07122e11	+	1.30772e12i	−0.268700	+	1.69651i	−0.640310	+	0.768117i	$0.721194\pi$
$938$	4.01802e11	+	6.36392e10i	0.519040	+	0.0822079i
$939$	−1.37358e10	+	1.89057e10i	−0.0176682	+	0.0243182i
$940$	3.31480e12	+	2.35753e12i	4.24567	+	3.01958i
$941$	−1.56389e11	+	1.13623e11i	−0.199456	+	0.144914i	−0.683030	−	0.730390i	$-0.739338\pi$
$941$	−1.56389e11	+	1.13623e11i	−0.199456	+	0.144914i	0.483574	+	0.875303i	$0.339338\pi$
$942$	−9.33490e10	−	1.83208e11i	−0.118551	−	0.232670i
$943$	−4.79342e11	−	4.79342e11i	−0.606176	−	0.606176i
$944$	2.91810e12	+	9.48148e11i	3.67462	+	1.19396i
$945$	1.36203e11	−	7.11419e10i	0.170789	−	0.0892069i
$946$	−7.61606e11	−	2.34398e12i	−0.950967	−	2.92678i
$947$	1.25275e12	+	6.38307e11i	1.55763	+	0.793651i	0.999352	−	0.0360042i	$-0.0114630\pi$
$947$	1.25275e12	+	6.38307e11i	1.55763	+	0.793651i	0.558276	+	0.829655i	$0.311463\pi$
$948$	−1.63683e11	−	1.03346e12i	−0.202661	−	1.27955i
$949$			3.44818e11i			0.425133i
$950$	9.21500e11	+	1.72161e12i	1.13136	+	2.11368i
$951$	7.00924e11			0.856937
$952$	5.21824e11	−	8.26489e10i	0.635297	−	0.100621i
$953$	9.77020e10	−	1.91751e11i	0.118449	−	0.232470i	−0.824168	−	0.566346i	$-0.808357\pi$
$953$	9.77020e10	−	1.91751e11i	0.118449	−	0.232470i	0.942617	+	0.333876i	$0.108357\pi$
$954$	−5.17768e11	+	1.68233e11i	−0.625089	+	0.203104i
$955$	3.51572e11	−	5.93319e10i	0.422669	−	0.0713305i
$956$	8.81651e11	−	2.71344e12i	1.05552	−	3.24855i
$957$	−2.29559e11	+	2.29559e11i	−0.273682	+	0.273682i
$958$	−1.73762e12	+	8.85361e11i	−2.06297	+	1.05113i
$959$	−8.01406e11	−	1.10304e12i	−0.947497	−	1.30412i
$960$	2.74671e10	+	2.71754e12i	0.0323390	+	3.19956i
$961$	3.89774e11	+	2.83188e11i	0.457004	+	0.332032i
$962$	1.66213e11	−	1.04942e12i	0.194072	−	1.22532i
$963$	2.17146e11	+	3.43925e10i	0.252491	+	0.0399907i
$964$	−1.50461e12	+	2.07091e12i	−1.74227	+	2.39802i
$965$	2.74026e11	+	8.15237e11i	0.315997	+	0.940101i
$966$	4.84949e11	−	3.52336e11i	0.556913	−	0.404621i
$967$	−6.38135e11	−	1.25241e12i	−0.729805	−	1.43232i	−0.895002	−	0.446063i	$-0.852826\pi$
$967$	−6.38135e11	−	1.25241e12i	−0.729805	−	1.43232i	0.165197	−	0.986261i	$-0.447174\pi$
$968$	−3.14079e12	−	3.14079e12i	−3.57715	−	3.57715i
$969$	−1.01424e11	−	3.29546e10i	−0.115039	−	0.0373785i
$970$	1.43973e11	+	1.41091e11i	0.162627	+	0.159373i
$971$	−5.56692e10	−	1.71332e11i	−0.0626236	−	0.192736i	0.914850	−	0.403794i	$-0.132309\pi$
$971$	−5.56692e10	−	1.71332e11i	−0.0626236	−	0.192736i	−0.977473	+	0.211059i	$0.932309\pi$
$972$	−1.47443e11	−	7.51261e10i	−0.165181	−	0.0841639i
$973$	1.75283e11	+	1.10669e12i	0.195563	+	1.23474i
$974$			1.45065e12i			1.61186i
$975$	−1.98366e11	+	4.01031e9i	−0.219507	+	0.00443771i
$976$	1.77254e12			1.95342
$977$	−4.98993e10	+	7.90327e9i	−0.0547667	+	0.00867419i	−0.183758	−	0.982972i	$-0.558826\pi$
$977$	−4.98993e10	+	7.90327e9i	−0.0547667	+	0.00867419i	0.128991	+	0.991646i	$0.458826\pi$
$978$	4.41418e10	−	8.66331e10i	0.0482497	−	0.0946953i
$979$	−3.37875e11	+	1.09782e11i	−0.367812	+	0.119509i
$980$	9.45138e8	−	6.38434e9i	0.00102469	−	0.00692168i
$981$	3.41292e10	−	1.05039e11i	0.0368511	−	0.113416i
$982$	8.61305e10	−	8.61305e10i	0.0926213	−	0.0926213i
$983$	1.22131e12	−	6.22291e11i	1.30802	−	0.666468i	0.345687	−	0.938350i	$-0.387646\pi$
$983$	1.22131e12	−	6.22291e11i	1.30802	−	0.666468i	0.962331	+	0.271882i	$0.0876459\pi$
$984$	1.68369e12	+	2.31741e12i	1.79590	+	2.47185i
$985$	4.46786e11	+	6.02057e11i	0.474629	+	0.639576i
$986$	−1.13496e11	−	8.24598e10i	−0.120081	−	0.0872439i
$987$	−1.54709e11	+	9.76797e11i	−0.163023	+	1.02928i
$988$	−1.25720e12	−	1.99120e11i	−1.31940	−	0.208972i
$989$	3.45077e11	−	4.74958e11i	0.360687	−	0.496443i
$990$	2.90284e11	−	9.25114e11i	0.302192	−	0.963062i
$991$	2.38185e11	−	1.73052e11i	0.246957	−	0.179424i	−0.457420	−	0.889251i	$-0.651227\pi$
$991$	2.38185e11	−	1.73052e11i	0.246957	−	0.179424i	0.704377	+	0.709826i	$0.251227\pi$
$992$	1.47091e12	+	2.88682e12i	1.51893	+	2.98108i
$993$	−2.73624e11	−	2.73624e11i	−0.281421	−	0.281421i
$994$	7.61281e11	+	2.47355e11i	0.779829	+	0.253382i
$995$	7.09993e11	−	1.42896e12i	0.724372	−	1.45790i
$996$	−2.91527e11	−	8.97229e11i	−0.296239	−	0.911729i
$997$	1.30205e12	+	6.63427e11i	1.31779	+	0.671449i	0.964505	−	0.264066i	$-0.0850637\pi$
$997$	1.30205e12	+	6.63427e11i	1.31779	+	0.671449i	0.353288	+	0.935515i	$0.385064\pi$
$998$	1.39374e11	+	8.79970e11i	0.140494	+	0.887045i
$999$			3.17062e11i			0.318334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.1	✓	320
25.2	odd	20	inner	75.9.k.a.52.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.1	✓	320	1.1	even	1	trivial
75.9.k.a.52.1	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)

\(f(q)\)	\(=\)	\(q+(-31.1680 + 4.93653i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(703.605 - 228.615i) q^{4} +(559.718 + 278.101i) q^{5} +(456.033 - 1403.52i) q^{6} +(1699.82 - 1699.82i) q^{7} +(-13603.4 + 6931.29i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-31.1680 + 4.93653i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(703.605 - 228.615i) q^{4} +(559.718 + 278.101i) q^{5} +(456.033 - 1403.52i) q^{6} +(1699.82 - 1699.82i) q^{7} +(-13603.4 + 6931.29i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-18818.2 - 5904.80i) q^{10} +(-18185.6 - 13212.6i) q^{11} +(-5412.27 + 34171.7i) q^{12} +(10727.3 + 1699.04i) q^{13} +(-44588.7 + 61371.1i) q^{14} +(-23471.4 + 17418.1i) q^{15} +(236553. - 171866. i) q^{16} +(-6535.32 - 12826.3i) q^{17} +(48800.3 + 48800.3i) q^{18} +(-150659. - 48952.2i) q^{19} +(457399. + 67713.3i) q^{20} +(34739.5 + 106917. i) q^{21} +(632032. + 322037. i) q^{22} +(26432.6 + 166889. i) q^{23} -713989. i q^{24} +(235944. + 311317. i) q^{25} -342736. q^{26} +(101017. - 15999.5i) q^{27} +(807396. - 1.58460e6i) q^{28} +(-293712. + 95432.7i) q^{29} +(645572. - 658755. i) q^{30} +(188248. - 579367. i) q^{31} +(-3.76077e6 + 3.76077e6i) q^{32} +(936644. - 477244. i) q^{33} +(267010. + 367508. i) q^{34} +(1.42414e6 - 478698. i) q^{35} +(-1.30897e6 - 951020. i) q^{36} +(-484958. + 3.06190e6i) q^{37} +(4.93740e6 + 782008. i) q^{38} +(-298548. + 410916. i) q^{39} +(-9.54169e6 + 96441.0i) q^{40} +(-3.24571e6 + 2.35815e6i) q^{41} +(-1.61056e6 - 3.16091e6i) q^{42} +(-2.45683e6 - 2.45683e6i) q^{43} +(-1.58161e7 - 5.13895e6i) q^{44} +(-227460. - 1.34782e6i) q^{45} +(-1.64770e6 - 5.07111e6i) q^{46} +(7.83833e6 + 3.99383e6i) q^{47} +(2.13909e6 + 1.35057e7i) q^{48} -13957.9i q^{49} +(-8.89074e6 - 8.53838e6i) q^{50} +673200. q^{51} +(7.93621e6 - 1.25697e6i) q^{52} +(-3.58128e6 + 7.02865e6i) q^{53} +(-3.06951e6 + 997343. i) q^{54} +(-6.50436e6 - 1.24528e7i) q^{55} +(-1.13414e7 + 3.49053e7i) q^{56} +(5.23841e6 - 5.23841e6i) q^{57} +(8.68330e6 - 4.42436e6i) q^{58} +(6.16795e6 + 8.48945e6i) q^{59} +(-1.25325e7 + 1.76214e7i) q^{60} +(4.90436e6 + 3.56322e6i) q^{61} +(-3.00725e6 + 1.89870e7i) q^{62} +(-5.19261e6 - 822429. i) q^{63} +(5.46527e7 - 7.52230e7i) q^{64} +(5.53177e6 + 3.93426e6i) q^{65} +(-2.68374e7 + 1.94985e7i) q^{66} +(-2.43463e6 - 4.77823e6i) q^{67} +(-7.53056e6 - 7.53056e6i) q^{68} +(-7.51516e6 - 2.44183e6i) q^{69} +(-4.20245e7 + 2.19504e7i) q^{70} +(-3.26073e6 - 1.00355e7i) q^{71} +(2.97507e7 + 1.51587e7i) q^{72} +(4.96651e6 + 3.13573e7i) q^{73} -9.78274e7i q^{74} +(-1.79814e7 + 3.22181e6i) q^{75} -1.17196e8 q^{76} +(-5.33711e7 + 8.45316e6i) q^{77} +(7.27664e6 - 1.42812e7i) q^{78} +(-2.87628e7 + 9.34560e6i) q^{79} +(1.80199e8 - 3.04108e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(8.95214e7 - 8.95214e7i) q^{82} +(-2.42958e7 + 1.23793e7i) q^{83} +(4.88858e7 + 6.72855e7i) q^{84} +(-90931.5 - 8.99659e6i) q^{85} +(8.87025e7 + 6.44462e7i) q^{86} +(2.25929e6 - 1.42646e7i) q^{87} +(3.38966e8 + 5.36870e7i) q^{88} +(9.28965e6 - 1.27861e7i) q^{89} +(1.37430e7 + 4.08859e7i) q^{90} +(2.11225e7 - 1.53464e7i) q^{91} +(5.67514e7 + 1.11381e8i) q^{92} +(2.01445e7 + 2.01445e7i) q^{93} +(-2.64021e8 - 8.57855e7i) q^{94} +(-7.07131e7 - 6.92980e7i) q^{95} +(-7.68596e7 - 2.36550e8i) q^{96} +(-9.10671e6 - 4.64010e6i) q^{97} +(68903.7 + 435041. i) q^{98} +4.91607e7i 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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