LMFDB - Embedded newform 71.5.e.a.66.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,5,Mod(14,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("71.14");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	71.e (of order $10$, degree $4$, 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:	$7.33926737895$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$23$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			66.19
Character	$\chi$	$=$	71.66
Dual form			71.5.e.a.14.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30403 + 4.01340i) q^{2} +(-0.422249 - 1.29955i) q^{3} +(-1.46264 + 1.06267i) q^{4} +(-37.2304 - 27.0495i) q^{5} +(4.66499 - 3.38931i) q^{6} +(56.2511 - 18.2771i) q^{7} +(48.4518 + 35.2023i) q^{8} +(64.0198 - 46.5131i) q^{9} +O(q^{10})$	\(q+(1.30403 + 4.01340i) q^{2} +(-0.422249 - 1.29955i) q^{3} +(-1.46264 + 1.06267i) q^{4} +(-37.2304 - 27.0495i) q^{5} +(4.66499 - 3.38931i) q^{6} +(56.2511 - 18.2771i) q^{7} +(48.4518 + 35.2023i) q^{8} +(64.0198 - 46.5131i) q^{9} +(60.0108 - 184.694i) q^{10} +(91.9776 - 29.8853i) q^{11} +(1.99859 + 1.45206i) q^{12} +(-244.332 - 79.3883i) q^{13} +(146.707 + 201.924i) q^{14} +(-19.4316 + 59.8043i) q^{15} +(-87.0371 + 267.873i) q^{16} +(263.435 + 85.5953i) q^{17} +(270.160 + 196.283i) q^{18} +(-132.220 - 406.931i) q^{19} +83.1992 q^{20} +(-47.5039 - 65.3835i) q^{21} +(239.884 + 330.172i) q^{22} -764.871i q^{23} +(25.2884 - 77.8297i) q^{24} +(461.294 + 1419.72i) q^{25} -1084.13i q^{26} +(-177.021 - 128.613i) q^{27} +(-62.8524 + 86.5090i) q^{28} +(815.306 + 592.355i) q^{29} -265.358 q^{30} +(-759.202 + 246.680i) q^{31} -230.345 q^{32} +(-77.6749 - 106.910i) q^{33} +1168.89i q^{34} +(-2588.64 - 841.099i) q^{35} +(-44.2098 + 136.064i) q^{36} -1085.36 q^{37} +(1460.76 - 1061.30i) q^{38} +351.043i q^{39} +(-851.678 - 2621.19i) q^{40} +189.553i q^{41} +(200.464 - 275.915i) q^{42} +(231.695 + 168.336i) q^{43} +(-102.772 + 141.453i) q^{44} -3641.64 q^{45} +(3069.74 - 997.417i) q^{46} +(2948.78 + 958.118i) q^{47} +384.865 q^{48} +(887.682 - 644.939i) q^{49} +(-5096.35 + 3702.72i) q^{50} -378.489i q^{51} +(441.733 - 143.528i) q^{52} +(-618.623 + 851.462i) q^{53} +(285.335 - 878.172i) q^{54} +(-4232.75 - 1375.30i) q^{55} +(3368.86 + 1094.61i) q^{56} +(-472.997 + 343.652i) q^{57} +(-1314.17 + 4044.60i) q^{58} +(-594.609 + 818.409i) q^{59} +(-35.1308 - 108.121i) q^{60} +(-1923.51 - 624.987i) q^{61} +(-1980.05 - 2725.31i) q^{62} +(2751.06 - 3786.51i) q^{63} +(1092.22 + 3361.50i) q^{64} +(6949.18 + 9564.72i) q^{65} +(327.784 - 451.155i) q^{66} +(3102.79 + 4270.62i) q^{67} +(-476.270 + 154.749i) q^{68} +(-993.986 + 322.966i) q^{69} -11486.1i q^{70} +(-2342.52 + 4463.66i) q^{71} +4739.25 q^{72} +(32.3413 + 99.5363i) q^{73} +(-1415.34 - 4355.97i) q^{74} +(1650.21 - 1198.95i) q^{75} +(625.823 + 454.687i) q^{76} +(4627.62 - 3362.16i) q^{77} +(-1408.88 + 457.772i) q^{78} +(-4633.81 - 3366.66i) q^{79} +(10486.3 - 7618.71i) q^{80} +(1888.33 - 5811.69i) q^{81} +(-760.754 + 247.184i) q^{82} +(6894.17 + 5008.91i) q^{83} +(138.962 + 45.1515i) q^{84} +(-7492.50 - 10312.5i) q^{85} +(-373.463 + 1149.40i) q^{86} +(425.531 - 1309.65i) q^{87} +(5508.52 + 1789.83i) q^{88} +(9509.54 + 6909.09i) q^{89} +(-4748.83 - 14615.4i) q^{90} -15194.9 q^{91} +(812.804 + 1118.73i) q^{92} +(641.145 + 882.460i) q^{93} +13084.1i q^{94} +(-6084.67 + 18726.7i) q^{95} +(97.2629 + 299.344i) q^{96} +5328.12i q^{97} +(3745.97 + 2721.61i) q^{98} +(4498.33 - 6191.42i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 6 q^{2} - 13 q^{3} - 170 q^{4} - 9 q^{5} - 70 q^{6} - 5 q^{7} + 329 q^{8} - 742 q^{9}+O(q^{10}) $ 92 * q + 6 * q^2 - 13 * q^3 - 170 * q^4 - 9 * q^5 - 70 * q^6 - 5 * q^7 + 329 * q^8 - 742 * q^9	\( 92 q + 6 q^{2} - 13 q^{3} - 170 q^{4} - 9 q^{5} - 70 q^{6} - 5 q^{7} + 329 q^{8} - 742 q^{9} + 75 q^{10} - 395 q^{11} + 1306 q^{12} - 5 q^{13} - 1025 q^{14} + 303 q^{15} - 1430 q^{16} - 560 q^{17} - 420 q^{18} + 83 q^{19} + 1796 q^{20} - 5 q^{21} - 2380 q^{22} + 849 q^{24} - 968 q^{25} + 4880 q^{27} - 1230 q^{28} + 9 q^{29} + 4312 q^{30} + 2770 q^{31} - 7780 q^{32} - 1680 q^{33} + 355 q^{35} + 6392 q^{36} - 4722 q^{37} + 1703 q^{38} - 2741 q^{40} + 5485 q^{42} + 683 q^{43} + 11095 q^{44} - 18856 q^{45} + 20465 q^{46} - 12005 q^{47} - 23780 q^{48} + 5632 q^{49} + 12166 q^{50} + 19325 q^{52} - 1430 q^{53} + 23768 q^{54} - 10460 q^{55} - 14645 q^{56} + 1140 q^{57} - 17583 q^{58} + 3955 q^{59} + 5490 q^{60} + 13630 q^{61} - 21935 q^{62} - 5585 q^{63} + 12481 q^{64} + 3250 q^{65} + 66740 q^{66} - 46680 q^{67} - 4575 q^{68} - 5435 q^{69} - 12829 q^{71} - 29794 q^{72} + 4327 q^{73} + 4533 q^{74} - 8579 q^{75} - 22813 q^{76} + 39664 q^{77} + 13120 q^{78} - 34081 q^{79} + 39762 q^{80} - 41491 q^{81} - 60875 q^{82} - 17571 q^{83} + 122015 q^{84} - 33245 q^{85} - 32869 q^{86} - 34233 q^{87} - 113910 q^{88} - 36432 q^{89} - 9308 q^{90} + 68114 q^{91} + 68490 q^{92} + 24470 q^{93} + 57539 q^{95} + 36869 q^{96} + 117096 q^{98} - 24650 q^{99}+O(q^{100}) \) 92 * q + 6 * q^2 - 13 * q^3 - 170 * q^4 - 9 * q^5 - 70 * q^6 - 5 * q^7 + 329 * q^8 - 742 * q^9 + 75 * q^10 - 395 * q^11 + 1306 * q^12 - 5 * q^13 - 1025 * q^14 + 303 * q^15 - 1430 * q^16 - 560 * q^17 - 420 * q^18 + 83 * q^19 + 1796 * q^20 - 5 * q^21 - 2380 * q^22 + 849 * q^24 - 968 * q^25 + 4880 * q^27 - 1230 * q^28 + 9 * q^29 + 4312 * q^30 + 2770 * q^31 - 7780 * q^32 - 1680 * q^33 + 355 * q^35 + 6392 * q^36 - 4722 * q^37 + 1703 * q^38 - 2741 * q^40 + 5485 * q^42 + 683 * q^43 + 11095 * q^44 - 18856 * q^45 + 20465 * q^46 - 12005 * q^47 - 23780 * q^48 + 5632 * q^49 + 12166 * q^50 + 19325 * q^52 - 1430 * q^53 + 23768 * q^54 - 10460 * q^55 - 14645 * q^56 + 1140 * q^57 - 17583 * q^58 + 3955 * q^59 + 5490 * q^60 + 13630 * q^61 - 21935 * q^62 - 5585 * q^63 + 12481 * q^64 + 3250 * q^65 + 66740 * q^66 - 46680 * q^67 - 4575 * q^68 - 5435 * q^69 - 12829 * q^71 - 29794 * q^72 + 4327 * q^73 + 4533 * q^74 - 8579 * q^75 - 22813 * q^76 + 39664 * q^77 + 13120 * q^78 - 34081 * q^79 + 39762 * q^80 - 41491 * q^81 - 60875 * q^82 - 17571 * q^83 + 122015 * q^84 - 33245 * q^85 - 32869 * q^86 - 34233 * q^87 - 113910 * q^88 - 36432 * q^89 - 9308 * q^90 + 68114 * q^91 + 68490 * q^92 + 24470 * q^93 + 57539 * q^95 + 36869 * q^96 + 117096 * q^98 - 24650 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	1.30403	+	4.01340i	0.326009	+	1.00335i	0.970983	+	0.239147i	$0.0768679\pi$
$2$	1.30403	+	4.01340i	0.326009	+	1.00335i	−0.644975	+	0.764204i	$0.723132\pi$
$3$	−0.422249	−	1.29955i	−0.0469165	−	0.144394i	0.924854	−	0.380322i	$-0.124187\pi$
$3$	−0.422249	−	1.29955i	−0.0469165	−	0.144394i	−0.971770	+	0.235928i	$0.924187\pi$
$4$	−1.46264	+	1.06267i	−0.0914148	+	0.0664168i
$5$	−37.2304	−	27.0495i	−1.48922	−	1.08198i	−0.974438	−	0.224656i	$-0.927874\pi$
$5$	−37.2304	−	27.0495i	−1.48922	−	1.08198i	−0.514779	−	0.857323i	$-0.672126\pi$
$6$	4.66499	−	3.38931i	0.129583	−	0.0941475i
$7$	56.2511	−	18.2771i	1.14798	−	0.373002i	0.327599	−	0.944817i	$-0.393761\pi$
$7$	56.2511	−	18.2771i	1.14798	−	0.373002i	0.820382	+	0.571815i	$0.193761\pi$
$8$	48.4518	+	35.2023i	0.757060	+	0.550036i
$9$	64.0198	−	46.5131i	0.790368	−	0.574236i
$10$	60.0108	−	184.694i	0.600108	−	1.84694i
$11$	91.9776	−	29.8853i	0.760146	−	0.246986i	0.0968044	−	0.995303i	$-0.469138\pi$
$11$	91.9776	−	29.8853i	0.760146	−	0.246986i	0.663341	+	0.748317i	$0.269138\pi$
$12$	1.99859	+	1.45206i	0.0138791	+	0.0100837i
$13$	−244.332	−	79.3883i	−1.44575	−	0.469753i	−0.522067	−	0.852905i	$-0.674839\pi$
$13$	−244.332	−	79.3883i	−1.44575	−	0.469753i	−0.923686	+	0.383151i	$0.874839\pi$
$14$	146.707	+	201.924i	0.748503	+	1.03023i
$15$	−19.4316	+	59.8043i	−0.0863627	+	0.265797i
$16$	−87.0371	+	267.873i	−0.339989	+	1.04638i
$17$	263.435	+	85.5953i	0.911541	+	0.296177i	0.726992	−	0.686646i	$-0.240918\pi$
$17$	263.435	+	85.5953i	0.911541	+	0.296177i	0.184549	+	0.982823i	$0.440918\pi$
$18$	270.160	+	196.283i	0.833827	+	0.605811i
$19$	−132.220	−	406.931i	−0.366260	−	1.12723i	−0.949188	−	0.314709i	$-0.898093\pi$
$19$	−132.220	−	406.931i	−0.366260	−	1.12723i	0.582928	−	0.812524i	$-0.301907\pi$
$20$	83.1992			0.207998
$21$	−47.5039	−	65.3835i	−0.107719	−	0.148262i
$22$	239.884	+	330.172i	0.495628	+	0.682173i
$23$		−	764.871i		−	1.44588i	−0.690911	−	0.722940i	$-0.742790\pi$
$23$		−	764.871i		−	1.44588i	0.690911	−	0.722940i	$-0.257210\pi$
$24$	25.2884	−	77.8297i	0.0439035	−	0.135121i
$25$	461.294	+	1419.72i	0.738070	+	2.27155i
$26$		−	1084.13i		−	1.60374i
$27$	−177.021	−	128.613i	−0.242827	−	0.176424i
$28$	−62.8524	+	86.5090i	−0.0801689	+	0.110343i
$29$	815.306	+	592.355i	0.969449	+	0.704346i	0.955326	−	0.295555i	$-0.0955044\pi$
$29$	815.306	+	592.355i	0.969449	+	0.704346i	0.0141228	+	0.999900i	$0.495504\pi$
$30$	−265.358			−0.294843
$31$	−759.202	+	246.680i	−0.790013	+	0.256691i	−0.676109	−	0.736801i	$-0.736335\pi$
$31$	−759.202	+	246.680i	−0.790013	+	0.256691i	−0.113903	+	0.993492i	$0.536335\pi$
$32$	−230.345			−0.224946
$33$	−77.6749	−	106.910i	−0.0713268	−	0.0981729i
$34$			1168.89i			1.01115i
$35$	−2588.64	−	841.099i	−2.11317	−	0.686612i
$36$	−44.2098	+	136.064i	−0.0341125	+	0.104987i
$37$	−1085.36			−0.792809			−0.396405	−	0.918076i	$-0.629742\pi$
$37$	−1085.36			−0.792809			−0.396405	+	0.918076i	$0.629742\pi$
$38$	1460.76	−	1061.30i	1.01161	−	0.734975i
$39$			351.043i			0.230798i
$40$	−851.678	−	2621.19i	−0.532299	−	1.63825i
$41$			189.553i			0.112762i	0.998409	+	0.0563811i	$0.0179562\pi$
$41$			189.553i			0.112762i	−0.998409	+	0.0563811i	$0.982044\pi$
$42$	200.464	−	275.915i	0.113642	−	0.156414i
$43$	231.695	+	168.336i	0.125308	+	0.0910416i	0.648674	−	0.761066i	$-0.275324\pi$
$43$	231.695	+	168.336i	0.125308	+	0.0910416i	−0.523366	+	0.852108i	$0.675324\pi$
$44$	−102.772	+	141.453i	−0.0530845	+	0.0730646i
$45$	−3641.64			−1.79834
$46$	3069.74	−	997.417i	1.45073	−	0.471369i
$47$	2948.78	+	958.118i	1.33490	+	0.433734i	0.887585	−	0.460644i	$-0.152382\pi$
$47$	2948.78	+	958.118i	1.33490	+	0.433734i	0.447311	+	0.894378i	$0.352382\pi$
$48$	384.865			0.167042
$49$	887.682	−	644.939i	0.369714	−	0.268613i
$50$	−5096.35	+	3702.72i	−2.03854	+	1.48109i
$51$		−	378.489i		−	0.145517i
$52$	441.733	−	143.528i	0.163363	−	0.0530798i
$53$	−618.623	+	851.462i	−0.220229	+	0.303119i	−0.904808	−	0.425819i	$-0.859986\pi$
$53$	−618.623	+	851.462i	−0.220229	+	0.303119i	0.684579	+	0.728938i	$0.259986\pi$
$54$	285.335	−	878.172i	0.0978516	−	0.301156i
$55$	−4232.75	−	1375.30i	−1.39926	−	0.454646i
$56$	3368.86	+	1094.61i	1.07426	+	0.349047i
$57$	−472.997	+	343.652i	−0.145582	+	0.105772i
$58$	−1314.17	+	4044.60i	−0.390657	+	1.20232i
$59$	−594.609	+	818.409i	−0.170816	+	0.235108i	−0.885839	−	0.463993i	$-0.846416\pi$
$59$	−594.609	+	818.409i	−0.170816	+	0.235108i	0.715023	+	0.699101i	$0.246416\pi$
$60$	−35.1308	−	108.121i	−0.00975855	−	0.0300337i
$61$	−1923.51	−	624.987i	−0.516934	−	0.167962i	0.0389192	−	0.999242i	$-0.487609\pi$
$61$	−1923.51	−	624.987i	−0.516934	−	0.167962i	−0.555854	+	0.831280i	$0.687609\pi$
$62$	−1980.05	−	2725.31i	−0.515102	−	0.708977i
$63$	2751.06	−	3786.51i	0.693137	−	0.954021i
$64$	1092.22	+	3361.50i	0.266654	+	0.820678i
$65$	6949.18	+	9564.72i	1.64478	+	2.26384i
$66$	327.784	−	451.155i	0.0752488	−	0.103571i
$67$	3102.79	+	4270.62i	0.691197	+	0.951352i	1.00000		0.000225438i	$7.17590e-5\pi$
$67$	3102.79	+	4270.62i	0.691197	+	0.951352i	−0.308803	+	0.951126i	$0.599928\pi$
$68$	−476.270	+	154.749i	−0.102999	+	0.0334666i
$69$	−993.986	+	322.966i	−0.208777	+	0.0678357i
$70$		−	11486.1i		−	2.34410i
$71$	−2342.52	+	4463.66i	−0.464694	+	0.885472i
$71$	−2342.52	+	4463.66i	−0.464694	+	0.885472i
$72$	4739.25			0.914207
$73$	32.3413	+	99.5363i	0.00606892	+	0.0186782i	0.954045	−	0.299663i	$-0.0968742\pi$
$73$	32.3413	+	99.5363i	0.00606892	+	0.0186782i	−0.947976	+	0.318341i	$0.896874\pi$
$74$	−1415.34	−	4355.97i	−0.258463	−	0.795466i
$75$	1650.21	−	1198.95i	0.293371	−	0.213146i
$76$	625.823	+	454.687i	0.108349	+	0.0787200i
$77$	4627.62	−	3362.16i	0.780507	−	0.567071i
$78$	−1408.88	+	457.772i	−0.231571	+	0.0752420i
$79$	−4633.81	−	3366.66i	−0.742479	−	0.539442i	0.151008	−	0.988533i	$-0.451748\pi$
$79$	−4633.81	−	3366.66i	−0.742479	−	0.539442i	−0.893486	+	0.449090i	$0.851748\pi$
$80$	10486.3	−	7618.71i	1.63848	−	1.19042i
$81$	1888.33	−	5811.69i	0.287812	−	0.885794i
$82$	−760.754	+	247.184i	−0.113140	+	0.0367614i
$83$	6894.17	+	5008.91i	1.00075	+	0.727088i	0.962249	−	0.272170i	$-0.0877415\pi$
$83$	6894.17	+	5008.91i	1.00075	+	0.727088i	0.0385018	+	0.999259i	$0.487741\pi$
$84$	138.962	+	45.1515i	0.0196942	+	0.00639902i
$85$	−7492.50	−	10312.5i	−1.03702	−	1.42734i
$86$	−373.463	+	1149.40i	−0.0504952	+	0.155408i
$87$	425.531	−	1309.65i	0.0562203	−	0.173028i
$88$	5508.52	+	1789.83i	0.711327	+	0.231124i
$89$	9509.54	+	6909.09i	1.20055	+	0.872249i	0.994339	−	0.106258i	$-0.0338871\pi$
$89$	9509.54	+	6909.09i	1.20055	+	0.872249i	0.206210	+	0.978508i	$0.433887\pi$
$90$	−4748.83	−	14615.4i	−0.586275	−	1.80437i
$91$	−15194.9			−1.83492
$92$	812.804	+	1118.73i	0.0960307	+	0.132175i
$93$	641.145	+	882.460i	0.0741293	+	0.102030i
$94$			13084.1i			1.48077i
$95$	−6084.67	+	18726.7i	−0.674202	+	2.07498i
$96$	97.2629	+	299.344i	0.0105537	+	0.0324809i
$97$			5328.12i			0.566279i	0.959079	+	0.283139i	$0.0913759\pi$
$97$			5328.12i			0.566279i	−0.959079	+	0.283139i	$0.908624\pi$
$98$	3745.97	+	2721.61i	0.390043	+	0.283383i
$99$	4498.33	−	6191.42i	0.458967	−	0.631713i
$100$	−2183.39	−	1586.33i	−0.218339	−	0.158633i
$101$	−10495.1			−1.02884			−0.514418	−	0.857540i	$-0.671992\pi$
$101$	−10495.1			−1.02884			−0.514418	+	0.857540i	$0.671992\pi$
$102$	1519.03	−	493.563i	0.146004	−	0.0474397i
$103$	14293.0			1.34726			0.673628	−	0.739071i	$-0.264735\pi$
$103$	14293.0			1.34726			0.673628	+	0.739071i	$0.264735\pi$
$104$	−9043.69	−	12447.6i	−0.836140	−	1.15085i
$105$			3719.21i			0.337344i
$106$	−4223.97	−	1372.45i	−0.375931	−	0.122148i
$107$	3130.52	−	9634.74i	0.273432	−	0.841536i	−0.716199	−	0.697896i	$-0.754120\pi$
$107$	3130.52	−	9634.74i	0.273432	−	0.841536i	0.989630	−	0.143639i	$-0.0458805\pi$
$108$	395.590			0.0339155
$109$	10979.7	−	7977.24i	0.924142	−	0.671429i	−0.0204093	−	0.999792i	$-0.506497\pi$
$109$	10979.7	−	7977.24i	0.924142	−	0.671429i	0.944552	+	0.328363i	$0.106497\pi$
$110$		−	18781.2i		−	1.55216i
$111$	458.290	+	1410.47i	0.0371959	+	0.114477i
$112$			16658.9i			1.32804i
$113$	−12495.5	+	17198.6i	−0.978581	+	1.34690i	−0.0409906	+	0.999160i	$0.513051\pi$
$113$	−12495.5	+	17198.6i	−0.978581	+	1.34690i	−0.937590	+	0.347742i	$0.886949\pi$
$114$	−1996.02	−	1450.19i	−0.153587	−	0.111588i
$115$	−20689.4	+	28476.5i	−1.56441	+	2.15323i
$116$	−1821.97			−0.135402
$117$	−19334.7	+	6282.23i	−1.41243	+	0.458925i
$118$	−4060.00	−	1319.17i	−0.291583	−	0.0947410i
$119$	16382.9			1.15691
$120$	−3046.75	+	2213.59i	−0.211580	+	0.153722i
$121$	−4278.07	+	3108.20i	−0.292198	+	0.212294i
$122$		−	8534.84i		−	0.573424i
$123$	246.334	−	80.0386i	0.0162822	−	0.00529041i
$124$	848.299	−	1167.58i	0.0551703	−	0.0759354i
$125$	12340.5	−	37980.1i	0.789790	−	2.43072i
$126$	18784.3	+	6103.38i	1.18319	+	0.384441i
$127$	10167.9	+	3303.74i	0.630408	+	0.204832i	0.606756	−	0.794888i	$-0.292470\pi$
$127$	10167.9	+	3303.74i	0.630408	+	0.204832i	0.0236524	+	0.999720i	$0.492470\pi$
$128$	−15048.4	+	10933.3i	−0.918482	+	0.667316i
$129$	120.928	−	372.178i	0.00726687	−	0.0223651i
$130$	−29325.1	+	40362.6i	−1.73521	+	2.38832i
$131$	−780.342	−	2401.65i	−0.0454719	−	0.139948i	0.925743	−	0.378153i	$-0.123441\pi$
$131$	−780.342	−	2401.65i	−0.0454719	−	0.139948i	−0.971215	+	0.238205i	$0.923441\pi$
$132$	227.220	+	73.8284i	0.0130407	+	0.00423717i
$133$	−14875.0	−	20473.7i	−0.840920	−	1.15743i
$134$	−13093.6	+	18021.8i	−0.729203	+	1.00366i
$135$	3111.64	+	9576.64i	0.170735	+	0.525467i
$136$	9750.77	+	13420.8i	0.527183	+	0.725605i
$137$	12806.4	−	17626.6i	0.682319	−	0.939131i	−0.317640	−	0.948211i	$-0.602890\pi$
$137$	12806.4	−	17626.6i	0.682319	−	0.939131i	0.999959	+	0.00908029i	$0.00289038\pi$
$138$	−2592.38	−	3568.11i	−0.136126	−	0.187361i
$139$	14729.9	−	4786.02i	0.762376	−	0.247711i	0.0980778	−	0.995179i	$-0.468731\pi$
$139$	14729.9	−	4786.02i	0.762376	−	0.247711i	0.664298	+	0.747468i	$0.268731\pi$
$140$	4680.05	−	1520.64i	0.238778	−	0.0775836i
$141$		−	4236.65i		−	0.213101i
$142$	−20969.2	−	3580.71i	−1.03993	−	0.177580i
$143$	−24845.6			−1.21501
$144$	6887.50	+	21197.5i	0.332152	+	1.02226i
$145$	−14331.3	−	44107.2i	−0.681632	−	2.09785i
$146$	−357.305	+	259.597i	−0.0167623	+	0.0121785i
$147$	−1212.95	−	881.261i	−0.0561318	−	0.0407821i
$148$	1587.48	−	1153.37i	0.0724745	−	0.0526558i
$149$	7559.82	−	2456.33i	0.340517	−	0.110641i	−0.133767	−	0.991013i	$-0.542707\pi$
$149$	7559.82	−	2456.33i	0.340517	−	0.110641i	0.474283	+	0.880372i	$0.342707\pi$
$150$	6963.79	+	5059.49i	0.309502	+	0.224866i
$151$	−13268.6	+	9640.23i	−0.581932	+	0.422798i	−0.839420	−	0.543483i	$-0.817105\pi$
$151$	−13268.6	+	9640.23i	−0.581932	+	0.422798i	0.257488	+	0.966281i	$0.417105\pi$
$152$	7918.62	−	24371.0i	0.342738	−	1.05484i
$153$	20846.4	−	6773.40i	0.890529	−	0.289350i
$154$	19528.3	+	14188.1i	0.823423	+	0.598252i
$155$	34938.0	+	11352.0i	1.45423	+	0.472509i
$156$	−373.042	−	513.449i	−0.0153288	−	0.0210983i
$157$	9777.47	−	30092.0i	0.396668	−	1.22082i	−0.530987	−	0.847380i	$-0.678179\pi$
$157$	9777.47	−	30092.0i	0.396668	−	1.22082i	0.927655	−	0.373439i	$-0.121821\pi$
$158$	7469.12	−	22987.6i	0.299196	−	0.920830i
$159$	1367.73	+	444.402i	0.0541010	+	0.0175785i
$160$	8575.84	+	6230.71i	0.334994	+	0.243387i
$161$	−13979.6	−	43024.8i	−0.539316	−	1.65984i
$162$	25787.1			0.982591
$163$	−12080.6	−	16627.5i	−0.454686	−	0.625822i	0.518710	−	0.854950i	$-0.326412\pi$
$163$	−12080.6	−	16627.5i	−0.454686	−	0.625822i	−0.973396	+	0.229129i	$0.926412\pi$
$164$	−201.432	−	277.248i	−0.00748930	−	0.0103081i
$165$			6081.38i			0.223375i
$166$	−11112.5	+	34200.9i	−0.403271	+	1.24114i
$167$	−3014.61	−	9278.03i	−0.108093	−	0.332677i	0.882351	−	0.470592i	$-0.155960\pi$
$167$	−3014.61	−	9278.03i	−0.108093	−	0.332677i	−0.990444	+	0.137915i	$0.955960\pi$
$168$		−	4840.20i		−	0.171492i
$169$	30289.4	+	22006.5i	1.06052	+	0.770509i
$170$	31617.9	−	43518.3i	1.09405	−	1.50582i
$171$	−27392.3	−	19901.7i	−0.936779	−	0.680610i
$172$	−517.770			−0.0175017
$173$	−44412.9	+	14430.6i	−1.48394	+	0.482162i	−0.935288	−	0.353888i	$-0.884859\pi$
$173$	−44412.9	+	14430.6i	−1.48394	+	0.482162i	−0.548653	+	0.836050i	$0.684859\pi$
$174$	5811.07			0.191936
$175$	51896.6	+	71429.5i	1.69458	+	2.33239i
$176$			27239.4i			0.879372i
$177$	1314.64	+	427.151i	0.0419623	+	0.0136344i
$178$	−15328.2	+	47175.3i	−0.483783	+	1.48893i
$179$	−2546.05			−0.0794622			−0.0397311	−	0.999210i	$-0.512650\pi$
$179$	−2546.05			−0.0794622			−0.0397311	+	0.999210i	$0.512650\pi$
$180$	5326.40	−	3869.86i	0.164395	−	0.119440i
$181$			28668.7i			0.875085i	0.899198	+	0.437543i	$0.144151\pi$
$181$			28668.7i			0.875085i	−0.899198	+	0.437543i	$0.855849\pi$
$182$	−19814.7	−	60983.4i	−0.598198	−	1.84106i
$183$			2763.60i			0.0825226i
$184$	26925.2	−	37059.4i	0.795287	−	1.09462i
$185$	40408.3	+	29358.3i	1.18066	+	0.857803i
$186$	−2705.59	+	3723.93i	−0.0782054	+	0.107640i
$187$	26788.2			0.766055
$188$	−5331.16	+	1732.20i	−0.150836	+	0.0490097i
$189$	−12308.3	−	3999.20i	−0.344567	−	0.111957i
$190$	−83092.4			−2.30173
$191$	−14577.5	+	10591.2i	−0.399591	+	0.290320i	−0.769374	−	0.638798i	$-0.779432\pi$
$191$	−14577.5	+	10591.2i	−0.399591	+	0.290320i	0.369783	+	0.929118i	$0.379432\pi$
$192$	3907.24	−	2838.78i	0.105991	−	0.0770068i
$193$		−	19999.6i		−	0.536917i	−0.963291	−	0.268459i	$-0.913486\pi$
$193$		−	19999.6i		−	0.536917i	0.963291	−	0.268459i	$-0.0865143\pi$
$194$	−21383.9	+	6948.05i	−0.568176	+	0.184612i
$195$	9495.54	−	13069.5i	0.249718	−	0.343708i
$196$	−613.001	+	1886.62i	−0.0159569	+	0.0491104i
$197$	31269.2	+	10160.0i	0.805719	+	0.261794i	0.682784	−	0.730621i	$-0.260769\pi$
$197$	31269.2	+	10160.0i	0.805719	+	0.261794i	0.122936	+	0.992415i	$0.460769\pi$
$198$	30714.7	+	9979.80i	0.783457	+	0.254561i
$199$	−6236.90	+	4531.37i	−0.157493	+	0.114426i	−0.663741	−	0.747963i	$-0.731032\pi$
$199$	−6236.90	+	4531.37i	−0.157493	+	0.114426i	0.506247	+	0.862388i	$0.331032\pi$
$200$	−27626.8	+	85026.5i	−0.690670	+	2.12566i
$201$	4239.73	−	5835.48i	0.104941	−	0.144439i
$202$	−13686.0	−	42121.3i	−0.335409	−	1.03228i
$203$	56688.4	+	18419.2i	1.37563	+	0.446970i
$204$	402.209	+	553.593i	0.00966476	+	0.0133024i
$205$	5127.32	−	7057.15i	0.122006	−	0.167927i
$206$	18638.6	+	57363.7i	0.439217	+	1.35177i
$207$	−35576.5	−	48966.9i	−0.830277	−	1.14278i
$208$	42532.0	−	58540.2i	0.983080	−	1.35309i
$209$	−24322.5	−	33477.1i	−0.556822	−	0.766400i
$210$	−14926.7	+	4849.98i	−0.338474	+	0.109977i
$211$	−25281.5	+	8214.46i	−0.567856	+	0.184508i	−0.578853	−	0.815432i	$-0.696500\pi$
$211$	−25281.5	+	8214.46i	−0.567856	+	0.184508i	0.0109969	+	0.999940i	$0.496500\pi$
$212$		−	1902.77i		−	0.0423365i
$213$	6789.87	+	1159.44i	0.149659	+	0.0255558i
$214$	42750.4			0.933497
$215$	−4072.68	−	12534.4i	−0.0881057	−	0.271161i
$216$	−4049.50	−	12463.1i	−0.0867949	−	0.267127i
$217$	−38197.4	+	27752.0i	−0.811174	+	0.589352i
$218$	46333.9	+	33663.5i	0.974957	+	0.708348i
$219$	115.696	−	84.0582i	0.00241230	−	0.00175264i
$220$	7652.47	−	2486.44i	0.158109	−	0.0513727i
$221$	−57570.4	−	41827.4i	−1.17873	−	0.856399i
$222$	−5063.17	+	3678.61i	−0.102735	+	0.0746410i
$223$	9791.13	−	30134.0i	0.196890	−	0.605964i	−0.803060	−	0.595899i	$-0.796796\pi$
$223$	9791.13	−	30134.0i	0.196890	−	0.605964i	0.999949	−	0.0100655i	$-0.00320401\pi$
$224$	−12957.1	+	4210.03i	−0.258234	+	0.0839053i
$225$	95567.5	+	69433.8i	1.88775	+	1.37153i
$226$	−85319.4	−	27722.0i	−1.67044	−	0.542759i
$227$	−454.261	−	625.237i	−0.00881564	−	0.0121337i	0.804586	−	0.593836i	$-0.202387\pi$
$227$	−454.261	−	625.237i	−0.00881564	−	0.0121337i	−0.813402	+	0.581702i	$0.802387\pi$
$228$	326.634	−	1005.28i	0.00628337	−	0.0193382i
$229$	−18874.8	+	58090.7i	−0.359925	+	1.10773i	0.593174	+	0.805074i	$0.297875\pi$
$229$	−18874.8	+	58090.7i	−0.359925	+	1.10773i	−0.953099	+	0.302660i	$0.902125\pi$
$230$	−141267.	−	45900.5i	−2.67046	−	0.867684i
$231$	−6323.30	−	4594.15i	−0.118500	−	0.0860956i
$232$	18650.8	+	57401.4i	0.346515	+	1.06646i
$233$	65175.8			1.20053			0.600267	−	0.799800i	$-0.295061\pi$
$233$	65175.8			1.20053			0.600267	+	0.799800i	$0.295061\pi$
$234$	−50426.2	−	69405.8i	−0.920926	−	1.26755i
$235$	−83867.9	−	115434.i	−1.51866	−	2.09025i
$236$		−	1828.91i		−	0.0328373i
$237$	−2418.52	+	7443.43i	−0.0430579	+	0.132518i
$238$	21363.9	+	65751.4i	0.377161	+	1.16078i
$239$		−	1301.53i		−	0.0227855i	−0.999935	−	0.0113927i	$-0.996374\pi$
$239$		−	1301.53i		−	0.0227855i	0.999935	−	0.0113927i	$-0.00362650\pi$
$240$	−14328.7	−	10410.4i	−0.248762	−	0.180736i
$241$	−30888.7	+	42514.7i	−0.531821	+	0.731989i	−0.987407	−	0.158203i	$-0.949430\pi$
$241$	−30888.7	+	42514.7i	−0.531821	+	0.731989i	0.455585	+	0.890192i	$0.349430\pi$
$242$	−18053.2	−	13116.4i	−0.308265	−	0.223967i
$243$	−26073.5			−0.441557
$244$	3477.56	−	1129.93i	0.0584110	−	0.0189789i
$245$	−50494.0			−0.841217
$246$	642.455	+	884.263i	0.0106163	+	0.0146121i
$247$			109923.i			1.80175i
$248$	−45468.4	−	14773.6i	−0.739276	−	0.240205i
$249$	3598.26	−	11074.3i	0.0580356	−	0.178615i
$250$	168522.			2.69635
$251$	−4959.97	+	3603.63i	−0.0787284	+	0.0571995i	−0.626453	−	0.779459i	$-0.715494\pi$
$251$	−4959.97	+	3603.63i	−0.0787284	+	0.0571995i	0.547725	+	0.836659i	$0.315494\pi$
$252$			8461.76i			0.133248i
$253$	−22858.4	−	70351.0i	−0.357113	−	1.09908i
$254$			45115.9i			0.699298i
$255$	−10237.9	+	14091.3i	−0.157446	+	0.216706i
$256$	−17752.1	−	12897.6i	−0.270875	−	0.196802i
$257$	65868.2	−	90659.8i	0.997262	−	1.37261i	0.0702723	−	0.997528i	$-0.477613\pi$
$257$	65868.2	−	90659.8i	0.997262	−	1.37261i	0.926990	−	0.375086i	$-0.122387\pi$
$258$	1651.39			0.0248091
$259$	−61052.4	+	19837.1i	−0.910130	+	0.295719i
$260$	−20328.2	−	6605.05i	−0.300714	−	0.0977078i
$261$	79748.1			1.17068
$262$	8621.19	−	6263.66i	0.125593	−	0.0912485i
$263$	41833.6	−	30393.9i	0.604803	−	0.439415i	−0.242778	−	0.970082i	$-0.578059\pi$
$263$	41833.6	−	30393.9i	0.604803	−	0.439415i	0.847580	+	0.530667i	$0.178059\pi$
$264$		−	7914.34i		−	0.113555i
$265$	46063.2	−	14966.8i	0.655937	−	0.213127i
$266$	62771.8	−	86397.9i	0.887158	−	1.22107i
$267$	4963.30	−	15275.5i	0.0696222	−	0.214275i
$268$	−9076.50	−	2949.13i	−0.126371	−	0.0410605i
$269$	−29022.6	−	9430.02i	−0.401081	−	0.130319i	0.101529	−	0.994833i	$-0.467627\pi$
$269$	−29022.6	−	9430.02i	−0.401081	−	0.130319i	−0.502610	+	0.864514i	$0.667627\pi$
$270$	−34377.3	+	24976.5i	−0.471567	+	0.342614i
$271$	−27070.9	+	83315.6i	−0.368607	+	1.13446i	0.579084	+	0.815268i	$0.303410\pi$
$271$	−27070.9	+	83315.6i	−0.368607	+	1.13446i	−0.947691	+	0.319188i	$0.896590\pi$
$272$	−45857.3	+	63117.2i	−0.619827	+	0.853119i
$273$	6416.04	+	19746.6i	0.0860879	+	0.264951i
$274$	87442.5	+	28411.8i	1.16472	+	0.378440i
$275$	84857.4	+	116796.i	1.12208	+	1.54441i
$276$	1110.64	−	1528.66i	0.0145799	−	0.0200675i
$277$	−16523.1	−	50852.8i	−0.215343	−	0.662759i	−0.999129	−	0.0417273i	$-0.986714\pi$
$277$	−16523.1	−	50852.8i	−0.215343	−	0.662759i	0.783786	−	0.621031i	$-0.213286\pi$
$278$	38416.5	+	52875.8i	0.497082	+	0.684175i
$279$	−37130.2	+	51105.3i	−0.477000	+	0.656534i
$280$	−95815.6	−	131879.i	−1.22214	−	1.68213i
$281$	−24025.2	+	7806.25i	−0.304266	+	0.0988621i	−0.457171	−	0.889379i	$-0.651137\pi$
$281$	−24025.2	+	7806.25i	−0.304266	+	0.0988621i	0.152905	+	0.988241i	$0.451137\pi$
$282$	17003.4	−	5524.74i	0.213815	−	0.0694726i
$283$			64355.6i			0.803551i	0.915738	+	0.401775i	$0.131607\pi$
$283$			64355.6i			0.803551i	−0.915738	+	0.401775i	$0.868393\pi$
$284$	−1317.13	−	9018.04i	−0.0163303	−	0.111809i
$285$	26905.5			0.331246
$286$	−32399.6	−	99715.6i	−0.396102	−	1.21908i
$287$	3464.48	+	10662.6i	0.0420605	+	0.129449i
$288$	−14746.6	+	10714.1i	−0.177790	+	0.129172i
$289$	−5498.35	−	3994.79i	−0.0658320	−	0.0478297i
$290$	158332.	−	115035.i	1.88266	−	1.36783i
$291$	6924.15	−	2249.79i	0.0817674	−	0.0265678i
$292$	−153.078	−	111.217i	−0.00179534	−	0.00130439i
$293$	−70199.2	+	51002.7i	−0.817705	+	0.594098i	−0.916054	−	0.401054i	$-0.868644\pi$
$293$	−70199.2	+	51002.7i	−0.817705	+	0.594098i	0.0983491	+	0.995152i	$0.468644\pi$
$294$	1955.13	−	6017.26i	0.0226194	−	0.0696152i
$295$	44275.1	−	14385.8i	0.508763	−	0.165307i
$296$	−52587.5	−	38207.0i	−0.600204	−	0.436074i
$297$	−20125.6	−	6539.20i	−0.228158	−	0.0741331i
$298$	19716.5	+	27137.5i	0.222023	+	0.305588i
$299$	−60721.8	+	186883.i	−0.679207	+	2.09039i
$300$	−1139.57	+	3507.25i	−0.0126619	+	0.0389695i
$301$	16109.8	+	5234.38i	0.177810	+	0.0577739i
$302$	−55992.9	−	40681.2i	−0.613930	−	0.446046i
$303$	4431.56	+	13639.0i	0.0482694	+	0.148558i
$304$	120514.			1.30404
$305$	54707.6	+	75298.6i	0.588096	+	0.809444i
$306$	54368.8	+	74832.2i	0.580640	+	0.799182i
$307$			36632.6i			0.388679i	0.980934	+	0.194340i	$0.0622564\pi$
$307$			36632.6i			0.388679i	−0.980934	+	0.194340i	$0.937744\pi$
$308$	−3195.67	+	9835.26i	−0.0336868	+	0.103677i
$309$	−6035.22	−	18574.5i	−0.0632086	−	0.194536i
$310$			155024.i			1.61315i
$311$	79229.2	+	57563.4i	0.819152	+	0.595149i	0.916469	−	0.400105i	$-0.131026\pi$
$311$	79229.2	+	57563.4i	0.819152	+	0.595149i	−0.0973175	+	0.995253i	$0.531026\pi$
$312$	−12357.5	+	17008.7i	−0.126947	+	0.174728i
$313$	−90161.0	−	65505.8i	−0.920302	−	0.668638i	0.0232975	−	0.999729i	$-0.492583\pi$
$313$	−90161.0	−	65505.8i	−0.920302	−	0.668638i	−0.943599	+	0.331090i	$0.892583\pi$
$314$	133521.			1.35423
$315$	−204846.	+	66558.6i	−2.06446	+	0.670785i
$316$	10355.2			0.103702
$317$	−28169.6	−	38772.1i	−0.280325	−	0.385835i	0.645516	−	0.763747i	$-0.276642\pi$
$317$	−28169.6	−	38772.1i	−0.280325	−	0.385835i	−0.925842	+	0.377912i	$0.876642\pi$
$318$			6068.76i			0.0600131i
$319$	92692.7	+	30117.7i	0.910886	+	0.295965i
$320$	50263.1	−	154694.i	0.490850	−	1.51068i
$321$	−13842.7			−0.134341
$322$	154446.	−	112212.i	1.48958	−	1.08225i
$323$		−	118517.i		−	1.13600i
$324$	3413.95	+	10507.1i	0.0325213	+	0.100090i
$325$		−	383504.i		−	3.63081i
$326$	50979.2	−	70166.9i	0.479687	−	0.660233i
$327$	−15003.0	−	10900.3i	−0.140308	−	0.101940i
$328$	−6672.71	+	9184.20i	−0.0620233	+	0.0853677i
$329$	183384.			1.69422
$330$	−24407.0	+	7930.33i	−0.224123	+	0.0728221i
$331$	−16592.4	−	5391.19i	−0.151444	−	0.0492072i	0.232314	−	0.972641i	$-0.425370\pi$
$331$	−16592.4	−	5391.19i	−0.151444	−	0.0492072i	−0.383758	+	0.923434i	$0.625370\pi$
$332$	−15406.5			−0.139774
$333$	−69484.3	+	50483.3i	−0.626611	+	0.455260i
$334$	33305.3	−	24197.7i	0.298552	−	0.216911i
$335$		−	242926.i		−	2.16463i
$336$	21649.1	−	7034.21i	0.191761	−	0.0623070i
$337$	81168.8	−	111719.i	0.714709	−	0.983713i	−0.284974	−	0.958535i	$-0.591985\pi$
$337$	81168.8	−	111719.i	0.714709	−	0.983713i	0.999683	−	0.0251773i	$-0.00801504\pi$
$338$	−48822.7	+	150261.i	−0.427354	+	1.31526i
$339$	27626.6	+	8976.43i	0.240396	+	0.0781095i
$340$	21917.6	+	7121.46i	0.189599	+	0.0616043i
$341$	−62457.5	+	45378.0i	−0.537126	+	0.390245i
$342$	44153.0	−	135889.i	0.377492	−	1.16180i
$343$	−45325.5	+	62385.2i	−0.385260	+	0.530265i
$344$	5300.21	+	16312.4i	0.0447895	+	0.137848i
$345$	45742.6	+	14862.7i	0.384311	+	0.124870i
$346$	−115832.	−	159429.i	−0.967555	−	1.33173i
$347$	−62077.1	+	85441.8i	−0.515552	+	0.709596i	−0.984843	−	0.173447i	$-0.944509\pi$
$347$	−62077.1	+	85441.8i	−0.515552	+	0.709596i	0.469291	+	0.883043i	$0.344509\pi$
$348$	769.326	+	2367.74i	0.00635261	+	0.0195513i
$349$	86970.8	+	119705.i	0.714040	+	0.982792i	0.999701	+	0.0244615i	$0.00778710\pi$
$349$	86970.8	+	119705.i	0.714040	+	0.982792i	−0.285660	+	0.958331i	$0.592213\pi$
$350$	−219001.	+	301428.i	−1.78776	+	2.46064i
$351$	33041.5	+	45477.7i	0.268192	+	0.369134i
$352$	−21186.6	+	6883.94i	−0.170992	+	0.0555586i
$353$	−138134.	+	44882.3i	−1.10854	+	0.360185i	−0.805382	−	0.592757i	$-0.798040\pi$
$353$	−138134.	+	44882.3i	−1.10854	+	0.360185i	−0.303154	+	0.952942i	$0.598040\pi$
$354$			5833.18i			0.0465478i
$355$	207953.	−	102820.i	1.65009	−	0.815870i
$356$	−21251.1			−0.167680
$357$	−6917.68	−	21290.4i	−0.0542780	−	0.167051i
$358$	−3320.14	−	10218.3i	−0.0259054	−	0.0797285i
$359$	−129744.	+	94264.4i	−1.00669	+	0.731406i	−0.963513	−	0.267661i	$-0.913749\pi$
$359$	−129744.	+	94264.4i	−1.00669	+	0.731406i	−0.0431811	+	0.999067i	$0.513749\pi$
$360$	−176444.	−	128194.i	−1.36145	−	0.989153i
$361$	−42678.9	+	31008.1i	−0.327491	+	0.237936i
$362$	−115059.	+	37384.9i	−0.878017	+	0.285285i
$363$	5845.67	+	4247.13i	0.0443630	+	0.0322316i
$364$	22224.7	−	16147.2i	0.167738	−	0.121869i
$365$	1488.32	−	4580.59i	0.0111715	−	0.0343824i
$366$	−11091.4	+	3603.83i	−0.0827991	+	0.0269031i
$367$	−127338.	−	92516.6i	−0.945424	−	0.686891i	0.00429623	−	0.999991i	$-0.498632\pi$
$367$	−127338.	−	92516.6i	−0.945424	−	0.686891i	−0.949720	+	0.313100i	$0.898632\pi$
$368$	204888.	+	66572.2i	1.51294	+	0.491583i
$369$	8816.72	+	12135.2i	0.0647521	+	0.0891237i
$370$	−65133.0	+	200459.i	−0.475771	+	1.46427i
$371$	−19236.0	+	59202.3i	−0.139755	+	0.430121i
$372$	−1875.52	−	609.395i	−0.0135530	−	0.00440365i
$373$	77527.5	+	56327.0i	0.557235	+	0.404855i	0.830446	−	0.557099i	$-0.188086\pi$
$373$	77527.5	+	56327.0i	0.557235	+	0.404855i	−0.273211	+	0.961954i	$0.588086\pi$
$374$	34932.7	+	107512.i	0.249741	+	0.768622i
$375$	−54567.7			−0.388037
$376$	109146.	+	150227.i	0.772027	+	1.06260i
$377$	−152180.	−	209457.i	−1.07071	−	1.47371i
$378$		−	54613.2i		−	0.382221i
$379$	−24722.3	+	76087.4i	−0.172112	+	0.529705i	−0.999490	−	0.0319401i	$-0.989831\pi$
$379$	−24722.3	+	76087.4i	−0.172112	+	0.529705i	0.827378	+	0.561645i	$0.189831\pi$
$380$	−11000.6	−	33856.4i	−0.0761814	−	0.234462i
$381$		−	14608.6i		−	0.100637i
$382$	−61516.1	−	44694.1i	−0.421563	−	0.306283i
$383$	32643.2	−	44929.5i	0.222533	−	0.306291i	−0.683123	−	0.730303i	$-0.739379\pi$
$383$	32643.2	−	44929.5i	0.222533	−	0.306291i	0.905656	+	0.424012i	$0.139379\pi$
$384$	20562.5	+	14939.6i	0.139449	+	0.101315i
$385$	−263233.			−1.77590
$386$	80266.6	−	26080.2i	0.538716	−	0.175040i
$387$	22662.9			0.151319
$388$	−5662.02	−	7793.10i	−0.0376104	−	0.0517663i
$389$		−	3616.31i		−	0.0238983i	−0.999929	−	0.0119491i	$-0.996196\pi$
$389$		−	3616.31i		−	0.0238983i	0.999929	−	0.0119491i	$-0.00380362\pi$
$390$	64835.6	+	21066.4i	0.426270	+	0.138503i
$391$	65469.3	−	201494.i	0.428237	−	1.31798i
$392$	65713.2			0.427642
$393$	−2791.56	+	2028.19i	−0.0180743	+	0.0131317i
$394$			138745.i			0.893766i
$395$	81452.3	+	250684.i	0.522046	+	1.60669i
$396$			13836.0i			0.0882310i
$397$	77846.6	−	107147.i	0.493922	−	0.679825i	−0.487183	−	0.873300i	$-0.661976\pi$
$397$	77846.6	−	107147.i	0.493922	−	0.679825i	0.981105	+	0.193474i	$0.0619756\pi$
$398$	−26319.4	−	19122.1i	−0.166153	−	0.120717i
$399$	−20325.6	+	27975.8i	−0.127673	+	0.175726i
$400$	−420453.			−2.62783
$401$	−21121.6	+	6862.82i	−0.131352	+	0.0426790i	−0.373956	−	0.927447i	$-0.621999\pi$
$401$	−21121.6	+	6862.82i	−0.131352	+	0.0426790i	0.242603	+	0.970126i	$0.421999\pi$
$402$	28948.9	+	9406.07i	0.179135	+	0.0582044i
$403$	205081.			1.26274
$404$	15350.6	−	11152.9i	0.0940508	−	0.0683319i
$405$	−227507.	+	165293.i	−1.38702	+	1.00773i
$406$			251533.i			1.52596i
$407$	−99828.4	+	32436.2i	−0.602650	+	0.195813i
$408$	13323.7	−	18338.5i	0.0800396	−	0.110165i
$409$	−56566.2	+	174093.i	−0.338151	+	1.04072i	0.626998	+	0.779021i	$0.284283\pi$
$409$	−56566.2	+	174093.i	−0.338151	+	1.04072i	−0.965149	+	0.261701i	$0.915717\pi$
$410$	35009.4	+	11375.2i	0.208265	+	0.0676695i
$411$	−28314.1	−	9199.80i	−0.167617	−	0.0544621i
$412$	−20905.5	+	15188.8i	−0.123159	+	0.0894804i
$413$	−18489.3	+	56904.1i	−0.108398	+	0.333614i
$414$	150131.	−	206638.i	0.875930	−	1.20561i
$415$	−121185.	−	372968.i	−0.703641	−	2.16558i
$416$	56280.7	+	18286.7i	0.325217	+	0.105669i
$417$	−12439.3	−	17121.3i	−0.0715361	−	0.0984610i
$418$	102640.	−	141272.i	0.587439	−	0.808541i
$419$	15666.8	+	48217.6i	0.0892387	+	0.274649i	0.985709	−	0.168454i	$-0.0538776\pi$
$419$	15666.8	+	48217.6i	0.0892387	+	0.274649i	−0.896471	+	0.443103i	$0.853878\pi$
$420$	−3952.29	−	5439.86i	−0.0224053	−	0.0308382i
$421$	106278.	−	146280.i	0.599626	−	0.825315i	−0.396048	−	0.918230i	$-0.629618\pi$
$421$	106278.	−	146280.i	0.599626	−	0.825315i	0.995674	+	0.0929150i	$0.0296185\pi$
$422$	−65935.9	−	90753.0i	−0.370252	−	0.509608i
$423$	233346.	−	75818.7i	1.30413	−	0.423736i
$424$	−59946.9	+	19477.9i	−0.333453	+	0.108345i
$425$			413488.i			2.28921i
$426$	4200.91	+	28762.5i	0.0231486	+	0.158492i
$427$	−119623.			−0.656081
$428$	5659.72	+	17418.8i	0.0308964	+	0.0950893i
$429$	10491.0	+	32288.1i	0.0570038	+	0.175440i
$430$	44994.8	−	32690.7i	0.243347	−	0.176802i
$431$	264127.	+	191899.i	1.42186	+	1.03304i	0.991461	+	0.130407i	$0.0416283\pi$
$431$	264127.	+	191899.i	1.42186	+	1.03304i	0.430402	+	0.902637i	$0.358372\pi$
$432$	49859.3	−	36224.9i	0.267165	−	0.194107i
$433$	169254.	−	54994.1i	0.902744	−	0.293319i	0.179375	−	0.983781i	$-0.442593\pi$
$433$	169254.	−	54994.1i	0.902744	−	0.293319i	0.723369	+	0.690462i	$0.242593\pi$
$434$	−161191.	−	117112.i	−0.855777	−	0.621758i
$435$	−51268.1	+	37248.5i	−0.270937	+	0.196847i
$436$	−7582.20	+	23335.6i	−0.0398862	+	0.122757i
$437$	−311250.	+	101131.i	−1.62984	+	0.529568i
$438$	488.231	+	354.721i	0.00254494	+	0.00184901i
$439$	−119194.	−	38728.6i	−0.618482	−	0.200957i	−0.0170159	−	0.999855i	$-0.505417\pi$
$439$	−119194.	−	38728.6i	−0.618482	−	0.200957i	−0.601466	+	0.798898i	$0.705417\pi$
$440$	−156671.	−	215639.i	−0.809249	−	1.11384i
$441$	26831.1	−	82577.8i	0.137963	−	0.424606i
$442$	92796.3	−	285598.i	0.474992	−	1.46187i
$443$	305075.	+	99124.9i	1.55453	+	0.505097i	0.955340	−	0.295509i	$-0.0954893\pi$
$443$	305075.	+	99124.9i	1.55453	+	0.505097i	0.599190	+	0.800607i	$0.295489\pi$
$444$	−2169.18	−	1576.00i	−0.0110035	−	0.00799448i
$445$	−167157.	−	514456.i	−0.844121	−	2.59794i
$446$	133708.			0.672183
$447$	−6384.25	−	8787.16i	−0.0319517	−	0.0439778i
$448$	122877.	+	169125.i	0.612229	+	0.842660i
$449$		−	330794.i		−	1.64083i	−0.571765	−	0.820417i	$-0.693741\pi$
$449$		−	330794.i		−	1.64083i	0.571765	−	0.820417i	$-0.306259\pi$
$450$	−154043.	+	474095.i	−0.760705	+	2.34121i
$451$	5664.86	+	17434.7i	0.0278507	+	0.0857157i
$452$		−	38433.9i		−	0.188121i
$453$	18130.6	+	13172.7i	0.0883519	+	0.0641914i
$454$	1916.96	−	2638.46i	0.00930038	−	0.0128009i
$455$	565714.	+	411015.i	2.73259	+	1.98534i
$456$	−35014.9			−0.168393
$457$	259701.	−	84382.1i	1.24349	−	0.404034i	0.387906	−	0.921699i	$-0.373199\pi$
$457$	259701.	−	84382.1i	1.24349	−	0.404034i	0.855583	+	0.517665i	$0.173199\pi$
$458$	−257755.			−1.22879
$459$	−35624.8	−	49033.4i	−0.169094	−	0.232738i
$460$		−	63636.6i		−	0.300740i
$461$	−54137.0	−	17590.2i	−0.254737	−	0.0827691i	0.178865	−	0.983874i	$-0.442758\pi$
$461$	−54137.0	−	17590.2i	−0.254737	−	0.0827691i	−0.433602	+	0.901105i	$0.642758\pi$
$462$	10192.4	−	31368.9i	0.0477520	−	0.146966i
$463$	−274711.			−1.28149			−0.640743	−	0.767755i	$-0.721374\pi$
$463$	−274711.			−1.28149			−0.640743	+	0.767755i	$0.721374\pi$
$464$	−229638.	+	166842.i	−1.06661	+	0.774940i
$465$		−	50197.0i		−	0.232152i
$466$	84991.4	+	261577.i	0.391384	+	1.20456i
$467$		−	128624.i		−	0.589778i	−0.955531	−	0.294889i	$-0.904717\pi$
$467$		−	128624.i		−	0.589778i	0.955531	−	0.294889i	$-0.0952827\pi$
$468$	21603.7	−	29735.0i	0.0986364	−	0.135761i
$469$	252589.	+	183517.i	1.14834	+	0.834316i
$470$	353918.	−	487126.i	1.60216	−	2.20519i
$471$	−43234.5			−0.194890
$472$	−57619.8	+	18721.8i	−0.258635	+	0.0840357i
$473$	26341.5	+	8558.87i	0.117738	+	0.0382555i
$474$	−33027.3			−0.147000
$475$	516735.	−	375430.i	2.29024	−	1.66395i
$476$	−23962.3	+	17409.6i	−0.105758	+	0.0768380i
$477$			83284.5i			0.366039i
$478$	5223.56	−	1697.24i	0.0228618	−	0.00742825i
$479$	224884.	−	309526.i	0.980137	−	1.34904i	0.0433817	−	0.999059i	$-0.486187\pi$
$479$	224884.	−	309526.i	0.980137	−	1.34904i	0.936755	−	0.349985i	$-0.113813\pi$
$480$	4475.97	−	13775.6i	0.0194270	−	0.0597900i
$481$	265187.	+	86164.6i	1.14621	+	0.372425i
$482$	−210908.	−	68528.3i	−0.907820	−	0.294969i
$483$	−50009.9	+	36334.3i	−0.214369	+	0.155748i
$484$	2954.28	−	9092.34i	0.0126113	−	0.0388137i
$485$	144123.	−	198368.i	0.612702	−	0.843312i
$486$	−34000.7	−	104644.i	−0.143951	−	0.443037i
$487$	−312973.	−	101691.i	−1.31962	−	0.428771i	−0.437256	−	0.899337i	$-0.644049\pi$
$487$	−312973.	−	101691.i	−1.31962	−	0.428771i	−0.882364	+	0.470567i	$0.844049\pi$
$488$	−71196.7	−	97993.9i	−0.298965	−	0.411490i
$489$	−16507.2	+	22720.2i	−0.0690327	+	0.0950154i
$490$	−65846.0	−	202653.i	−0.274244	−	0.844036i
$491$	60053.1	+	82656.0i	0.249099	+	0.342856i	0.915196	−	0.403010i	$-0.132036\pi$
$491$	60053.1	+	82656.0i	0.249099	+	0.342856i	−0.666096	+	0.745866i	$0.732036\pi$
$492$	−275.242	+	378.838i	−0.00113706	+	0.00156503i
$493$	164078.	+	225833.i	0.675080	+	0.929169i
$494$	−441166.	+	143343.i	−1.80779	+	0.587387i
$495$	−334950.	+	108832.i	−1.36700	+	0.444166i
$496$		−	224840.i		−	0.913924i
$497$	−50186.6	+	293900.i	−0.203177	+	1.18984i
$498$	49138.0			0.198134
$499$	67513.6	+	207786.i	0.271138	+	0.834477i	0.990215	+	0.139547i	$0.0445646\pi$
$499$	67513.6	+	207786.i	0.271138	+	0.834477i	−0.719077	+	0.694930i	$0.755435\pi$
$500$	22310.6	+	68664.9i	0.0892423	+	0.274659i
$501$	−10784.3	+	7835.27i	−0.0429653	+	0.0312161i
$502$	−20930.8	−	15207.1i	−0.0830573	−	0.0603447i
$503$	−152662.	+	110916.i	−0.603386	+	0.438386i	−0.847079	−	0.531467i	$-0.821641\pi$
$503$	−152662.	+	110916.i	−0.603386	+	0.438386i	0.243693	+	0.969852i	$0.421641\pi$
$504$	266588.	−	86619.7i	1.04949	−	0.341001i
$505$	390739.	+	283888.i	1.53216	+	1.11318i
$506$	252539.	−	183480.i	0.986341	−	0.716619i
$507$	15808.9	−	48654.7i	0.0615014	−	0.189282i
$508$	−18382.7	+	5972.89i	−0.0712330	+	0.0231450i
$509$	99593.0	+	72358.6i	0.384409	+	0.279289i	0.763161	−	0.646209i	$-0.223647\pi$
$509$	99593.0	+	72358.6i	0.384409	+	0.279289i	−0.378752	+	0.925498i	$0.623647\pi$
$510$	−69904.8	−	22713.4i	−0.268761	−	0.0873258i
$511$	3638.47	+	5007.92i	0.0139340	+	0.0191785i
$512$	−63353.6	+	194982.i	−0.241675	+	0.743799i
$513$	−28931.0	+	89040.5i	−0.109933	+	0.338340i
$514$	449749.	+	146132.i	1.70233	+	0.553120i
$515$	−532136.	−	386619.i	−2.00636	−	1.45770i
$516$	218.628	+	672.868i	0.000821119	+	0.00252715i
$517$	299856.			1.12184
$518$	−159229.	−	219160.i	−0.593420	−	0.816773i
$519$	37506.6	+	51623.4i	0.139243	+	0.191651i
$520$			708056.i			2.61855i
$521$	71376.9	−	219675.i	0.262955	−	0.809293i	−0.729202	−	0.684298i	$-0.760109\pi$
$521$	71376.9	−	219675.i	0.262955	−	0.809293i	0.992157	−	0.124995i	$-0.0398914\pi$
$522$	103994.	+	320061.i	0.381652	+	1.17461i
$523$		−	32714.8i		−	0.119603i	−0.998210	−	0.0598013i	$-0.980953\pi$
$523$		−	32714.8i		−	0.119603i	0.998210	−	0.0598013i	$-0.0190467\pi$
$524$	3693.51	+	2683.49i	0.0134517	+	0.00977323i
$525$	70912.8	−	97603.1i	0.257280	−	0.354116i
$526$	176535.	+	128260.i	0.638058	+	0.463576i
$527$	−221115.			−0.796155
$528$	35399.0	−	11501.8i	0.126976	−	0.0412571i
$529$	−305186.			−1.09057
$530$	120136.	+	165353.i	0.427682	+	0.588654i
$531$			80051.6i			0.283910i
$532$	43513.5	+	14138.4i	0.153745	+	0.0499548i
$533$	15048.3	−	46314.0i	0.0529704	−	0.163026i
$534$	67778.9			0.237691
$535$	−377165.	+	274027.i	−1.31772	+	0.957382i
$536$			316145.i			1.10041i
$537$	1075.07	+	3308.71i	0.00372809	+	0.0114739i
$538$		−	128777.i		−	0.444910i
$539$	62372.7	−	85848.6i	0.214692	−	0.295499i
$540$	−14728.0	−	10700.5i	−0.0505075	−	0.0366959i
$541$	−126587.	+	174232.i	−0.432508	+	0.595296i	−0.968527	−	0.248910i	$-0.919928\pi$
$541$	−126587.	+	174232.i	−0.432508	+	0.595296i	0.536019	+	0.844206i	$0.319928\pi$
$542$	−369680.			−1.25843
$543$	37256.3	−	12105.3i	0.126357	−	0.0410560i
$544$	−60681.0	−	19716.4i	−0.205048	−	0.0666240i
$545$	−624560.			−2.10272
$546$	−70884.2	+	51500.4i	−0.237774	+	0.172753i
$547$	−315237.	+	229033.i	−1.05357	+	0.765462i	−0.972888	−	0.231278i	$-0.925709\pi$
$547$	−315237.	+	229033.i	−1.05357	+	0.765462i	−0.0806803	+	0.996740i	$0.525709\pi$
$548$			39390.2i			0.131168i
$549$	−152213.	+	49457.0i	−0.505019	+	0.164090i
$550$	−358094.	+	492873.i	−1.18378	+	1.62933i
$551$	133248.	−	410095.i	0.438891	−	1.35077i
$552$	−59529.6	−	19342.3i	−0.195369	−	0.0634791i
$553$	−322190.	−	104686.i	−1.05356	−	0.342324i
$554$	182546.	−	132628.i	0.594776	−	0.432130i
$555$	21090.2	−	64909.0i	0.0684692	−	0.210726i
$556$	−16458.5	+	22653.2i	−0.0532403	+	0.0732790i
$557$	−85142.4	−	262041.i	−0.274432	−	0.844616i	−0.989369	−	0.145427i	$-0.953544\pi$
$557$	−85142.4	−	262041.i	−0.274432	−	0.844616i	0.714937	−	0.699189i	$-0.246456\pi$
$558$	−253525.	−	82375.3i	−0.814240	−	0.264563i
$559$	−43246.5	−	59523.7i	−0.138397	−	0.190488i
$560$	450615.	−	620219.i	1.43691	−	1.97774i
$561$	−11311.3	−	34812.5i	−0.0359407	−	0.110614i
$562$	−62659.3	−	86243.1i	−0.198387	−	0.273056i
$563$	−67881.2	+	93430.5i	−0.214157	+	0.294762i	−0.902558	−	0.430568i	$-0.858313\pi$
$563$	−67881.2	+	93430.5i	−0.214157	+	0.294762i	0.688401	+	0.725331i	$0.258313\pi$
$564$	4502.16	+	6196.69i	0.0141535	+	0.0194806i
$565$	930425.	−	302314.i	2.91464	−	0.947023i
$566$	−258285.	+	83921.9i	−0.806244	+	0.261964i
$567$		−	361427.i		−	1.12423i
$568$	−270631.	+	133811.i	−0.838842	+	0.414757i
$569$	−518583.			−1.60175			−0.800874	−	0.598833i	$-0.795631\pi$
$569$	−518583.			−1.60175			−0.800874	+	0.598833i	$0.795631\pi$
$570$	35085.7	+	107983.i	0.107989	+	0.332357i
$571$	−186769.	−	574816.i	−0.572839	−	1.76302i	−0.643422	−	0.765512i	$-0.722486\pi$
$571$	−186769.	−	574816.i	−0.572839	−	1.76302i	0.0705829	−	0.997506i	$-0.477514\pi$
$572$	36340.2	−	26402.7i	0.111069	−	0.0806967i
$573$	19919.0	+	14472.0i	0.0606679	+	0.0440778i
$574$	−38275.4	+	27808.7i	−0.116171	+	0.0844029i
$575$	1.08590e6	−	352830.i	3.28438	−	1.06716i
$576$	226277.	+	164400.i	0.682018	+	0.495515i
$577$	−394830.	+	286861.i	−1.18593	+	0.861628i	−0.992828	−	0.119550i	$-0.961855\pi$
$577$	−394830.	+	286861.i	−1.18593	+	0.861628i	−0.193102	+	0.981179i	$0.561855\pi$
$578$	8862.65	−	27276.4i	0.0265282	−	0.0816455i
$579$	−25990.5	+	8444.82i	−0.0775278	+	0.0251903i
$580$	67832.9	+	49283.5i	0.201643	+	0.146503i
$581$	479353.	+	155751.i	1.42005	+	0.461402i
$582$	18058.6	+	24855.6i	0.0533137	+	0.0733801i
$583$	−31453.3	+	96803.2i	−0.0925398	+	0.284808i
$584$	−1936.91	+	5961.21i	−0.00567916	+	0.0174787i
$585$	889770.	+	289104.i	2.59996	+	0.844777i
$586$	−296236.	−	215228.i	−0.862667	−	0.626764i
$587$	116238.	+	357743.i	0.337342	+	1.03823i	0.965557	+	0.260192i	$0.0837859\pi$
$587$	116238.	+	357743.i	0.337342	+	1.03823i	−0.628215	+	0.778040i	$0.716214\pi$
$588$	2710.60			0.00783990
$589$	200763.	+	276327.i	0.578700	+	0.796513i
$590$	115472.	+	158934.i	0.331722	+	0.456576i
$591$		−	44925.8i		−	0.128624i
$592$	94466.3	−	290737.i	0.269546	−	0.829578i
$593$	−115485.	−	355426.i	−0.328409	−	1.01074i	−0.969878	−	0.243591i	$-0.921675\pi$
$593$	−115485.	−	355426.i	−0.328409	−	1.01074i	0.641469	−	0.767149i	$-0.278325\pi$
$594$		−	89299.5i		−	0.253091i
$595$	−609944.	−	443150.i	−1.72288	−	1.25175i
$596$	−8447.00	+	11626.3i	−0.0237799	+	0.0327302i
$597$	8522.26	+	6191.78i	0.0239115	+	0.0173727i
$598$	−829218.			−2.31882
$599$	−515913.	+	167630.i	−1.43788	+	0.467196i	−0.921236	−	0.389004i	$-0.872819\pi$
$599$	−515913.	+	167630.i	−1.43788	+	0.467196i	−0.516645	+	0.856200i	$0.672819\pi$
$600$	122161.			0.339337
$601$	149557.	+	205848.i	0.414056	+	0.569899i	0.964202	−	0.265169i	$-0.0854279\pi$
$601$	149557.	+	205848.i	0.414056	+	0.569899i	−0.550146	+	0.835069i	$0.685428\pi$
$602$			71480.8i			0.197241i
$603$	397280.	+	129084.i	1.09260	+	0.355008i
$604$	9162.84	−	28200.3i	0.0251163	−	0.0773001i
$605$	243350.			0.664844
$606$	−48959.7	+	35571.3i	−0.133320	+	0.0968623i
$607$		−	520152.i		−	1.41173i	−0.708344	−	0.705867i	$-0.750558\pi$
$607$		−	520152.i		−	1.41173i	0.708344	−	0.705867i	$-0.249442\pi$
$608$	30456.2	+	93734.5i	0.0823888	+	0.253567i
$609$		−	81446.8i		−	0.219604i
$610$	−230863.	+	317756.i	−0.620433	+	0.853952i
$611$	−644420.	−	468198.i	−1.72618	−	1.25414i
$612$	−23292.8	+	32059.8i	−0.0621898	+	0.0855969i
$613$	−306217.			−0.814908			−0.407454	−	0.913226i	$-0.633583\pi$
$613$	−306217.			−0.814908			−0.407454	+	0.913226i	$0.633583\pi$
$614$	−147021.	+	47770.2i	−0.389982	+	0.126713i
$615$	−11336.1	−	3683.32i	−0.0299719	−	0.00973845i
$616$	342573.			0.902800
$617$	−150430.	+	109294.i	−0.395151	+	0.287094i	−0.767563	−	0.640973i	$-0.778531\pi$
$617$	−150430.	+	109294.i	−0.395151	+	0.287094i	0.372412	+	0.928068i	$0.378531\pi$
$618$	66676.8	−	48443.5i	0.174581	−	0.126841i
$619$			589370.i			1.53818i	0.639141	+	0.769090i	$0.279290\pi$
$619$			589370.i			1.53818i	−0.639141	+	0.769090i	$0.720710\pi$
$620$	−63165.0	+	20523.6i	−0.164321	+	0.0533912i
$621$	−98372.4	+	135398.i	−0.255088	+	0.351099i
$622$	−127708.	+	393043.i	−0.330093	+	1.01592i
$623$	661200.	+	214837.i	1.70356	+	0.553519i
$624$	−94034.9	−	30553.8i	−0.241502	−	0.0784686i
$625$	−731979.	+	531814.i	−1.87387	+	1.36144i
$626$	145328.	−	447274.i	0.370853	−	1.14137i
$627$	−33235.0	+	45744.0i	−0.0845396	+	0.116359i
$628$	17676.9	+	54403.8i	0.0448215	+	0.137946i
$629$	−285921.	−	92901.3i	−0.722678	−	0.234812i
$630$	−534253.	−	735336.i	−1.34606	−	1.85270i
$631$	45361.0	−	62434.0i	0.113926	−	0.156806i	−0.748246	−	0.663422i	$-0.769104\pi$
$631$	45361.0	−	62434.0i	0.113926	−	0.156806i	0.862172	+	0.506616i	$0.169104\pi$
$632$	−106002.	−	326242.i	−0.265388	−	0.816781i
$633$	21350.2	+	29386.0i	0.0532837	+	0.0733387i
$634$	118874.	−	163616.i	0.295739	−	0.407050i
$635$	−289189.	−	398035.i	−0.717191	−	0.987128i
$636$	−2472.74	+	803.443i	−0.00611314	+	0.00198628i
$637$	−268090.	+	87107.7i	−0.660696	+	0.214673i
$638$			411288.i			1.01043i
$639$	57651.2	+	394721.i	0.141191	+	0.966693i
$640$	855999.			2.08984
$641$	95353.8	+	293469.i	0.232071	+	0.714243i	0.997496	+	0.0707174i	$0.0225288\pi$
$641$	95353.8	+	293469.i	0.232071	+	0.714243i	−0.765425	+	0.643525i	$0.777471\pi$
$642$	−18051.3	−	55556.2i	−0.0437964	−	0.134792i
$643$	409995.	−	297879.i	0.991645	−	0.720473i	0.0313646	−	0.999508i	$-0.490015\pi$
$643$	409995.	−	297879.i	0.991645	−	0.720473i	0.960281	+	0.279035i	$0.0900147\pi$
$644$	66168.2	+	48074.0i	0.159543	+	0.115915i
$645$	−14569.4	+	10585.3i	−0.0350205	+	0.0254439i
$646$	475658.	−	154551.i	1.13980	−	0.370345i
$647$	109048.	+	79227.9i	0.260500	+	0.189265i	0.710368	−	0.703831i	$-0.248529\pi$
$647$	109048.	+	79227.9i	0.260500	+	0.189265i	−0.449867	+	0.893095i	$0.648529\pi$
$648$	296078.	−	215114.i	0.705110	−	0.512292i
$649$	−30232.3	+	93045.4i	−0.0717764	+	0.220905i
$650$	1.53916e6	−	500102.i	3.64297	−	1.18367i
$651$	52193.9	+	37921.1i	0.123157	+	0.0894785i
$652$	35338.9	+	11482.3i	0.0831301	+	0.0270106i
$653$	179880.	+	247583.i	0.421848	+	0.580624i	0.966058	−	0.258325i	$-0.0831705\pi$
$653$	179880.	+	247583.i	0.421848	+	0.580624i	−0.544210	+	0.838949i	$0.683171\pi$
$654$	24182.9	−	74427.5i	0.0565397	−	0.174011i
$655$	−35910.8	+	110522.i	−0.0837034	+	0.257612i
$656$	−50776.2	−	16498.2i	−0.117992	−	0.0383379i
$657$	6700.23	+	4868.00i	0.0155224	+	0.0112777i
$658$	239139.	+	735994.i	0.552330	+	1.69990i
$659$	−395933.			−0.911698			−0.455849	−	0.890057i	$-0.650664\pi$
$659$	−395933.			−0.911698			−0.455849	+	0.890057i	$0.650664\pi$
$660$	−6462.49	−	8894.85i	−0.0148358	−	0.0204198i
$661$	−154306.	−	212384.i	−0.353166	−	0.486091i	0.595063	−	0.803679i	$-0.297127\pi$
$661$	−154306.	−	212384.i	−0.353166	−	0.486091i	−0.948229	+	0.317588i	$0.897127\pi$
$662$		−	73622.3i		−	0.167994i
$663$	−30047.6	+	92477.1i	−0.0683570	+	0.210381i
$664$	157710.	+	485382.i	0.357704	+	1.10090i
$665$			1.16461e6i			2.63352i
$666$	−293220.	−	213037.i	−0.661066	−	0.480293i
$667$	453075.	−	623604.i	1.01840	−	1.40171i
$668$	14268.8	+	10366.9i	0.0319767	+	0.0232324i
$669$	−43294.9			−0.0967351
$670$	974959.	−	316783.i	2.17188	−	0.705688i
$671$	−195598.			−0.434430
$672$	10942.3	+	15060.8i	0.0242309	+	0.0333510i
$673$		−	279812.i		−	0.617784i	−0.951097	−	0.308892i	$-0.900042\pi$
$673$		−	279812.i		−	0.617784i	0.951097	−	0.308892i	$-0.0999582\pi$
$674$	554221.	+	180077.i	1.22001	+	0.396405i
$675$	100936.	−	310648.i	0.221532	−	0.681806i
$676$	−67688.0			−0.148122
$677$	304514.	−	221242.i	0.664401	−	0.482715i	−0.203745	−	0.979024i	$-0.565311\pi$
$677$	304514.	−	221242.i	0.664401	−	0.482715i	0.868146	+	0.496308i	$0.165311\pi$
$678$			122582.i			0.266666i
$679$	97382.4	+	299712.i	0.211223	+	0.650077i
$680$		−	763415.i		−	1.65098i
$681$	−620.714	+	854.340i	−0.00133844	+	0.00184220i
$682$	−263567.	−	191493.i	−0.566660	−	0.411702i
$683$	205119.	−	282322.i	0.439707	−	0.605205i	−0.530440	−	0.847723i	$-0.677973\pi$
$683$	205119.	−	282322.i	0.439707	−	0.605205i	0.970147	+	0.242517i	$0.0779731\pi$
$684$	61214.0			0.130839
$685$	−953578.	+	309836.i	−2.03224	+	0.660315i
$686$	−309483.	−	100557.i	−0.657640	−	0.213680i
$687$	83461.5			0.176837
$688$	−65258.7	+	47413.2i	−0.137867	+	0.100166i
$689$	218746.	−	158928.i	0.460788	−	0.334782i
$690$			202965.i			0.426307i
$691$	−147075.	+	47787.7i	−0.308024	+	0.100083i	−0.458950	−	0.888462i	$-0.651774\pi$
$691$	−147075.	+	47787.7i	−0.308024	+	0.100083i	0.150926	+	0.988545i	$0.451774\pi$
$692$	49625.0	−	68302.9i	0.103631	−	0.142635i
$693$	139875.	−	430491.i	0.291255	−	0.896390i
$694$	−423863.	−	137721.i	−0.880049	−	0.285945i
$695$	−677858.	−	220250.i	−1.40336	−	0.455980i
$696$	66720.6	−	48475.3i	0.137734	−	0.100070i
$697$	−16224.9	+	49935.0i	−0.0333976	+	0.102787i
$698$	−367012.	+	505149.i	−0.753303	+	1.03683i
$699$	−27520.4	−	84699.1i	−0.0563249	−	0.173350i
$700$	−151812.	−	49326.6i	−0.309820	−	0.100667i
$701$	89018.7	+	122524.i	0.181153	+	0.249336i	0.889930	−	0.456097i	$-0.150753\pi$
$701$	89018.7	+	122524.i	0.181153	+	0.249336i	−0.708777	+	0.705432i	$0.750753\pi$
$702$	−139433.	+	191913.i	−0.282939	+	0.389431i
$703$	143506.	+	441665.i	0.290374	+	0.893681i
$704$	200919.	+	276541.i	0.405392	+	0.557975i
$705$	−114599.	+	157732.i	−0.230570	+	0.317353i
$706$	−360262.	−	495858.i	−0.722784	−	0.994827i
$707$	−590363.	+	191821.i	−1.18108	+	0.383757i
$708$	−2376.75	+	772.254i	−0.00474152	+	0.00154061i
$709$		−	120214.i		−	0.239145i	−0.992825	−	0.119572i	$-0.961848\pi$
$709$		−	120214.i		−	0.239145i	0.992825	−	0.119572i	$-0.0381524\pi$
$710$	683836.	+	700518.i	1.35655	+	1.38964i
$711$	−453250.			−0.896599
$712$	217539.	+	669516.i	0.429118	+	1.32069i
$713$	188678.	+	580691.i	0.371144	+	1.14226i
$714$	76426.2	−	55526.9i	0.149915	−	0.108920i
$715$	925014.	+	672062.i	1.80941	+	1.31461i
$716$	3723.95	−	2705.61i	0.00726403	−	0.00527762i
$717$	−1691.40	+	549.569i	−0.00329009	+	0.00106901i
$718$	−547511.	−	397790.i	−1.06205	−	0.771623i
$719$	671398.	−	487799.i	1.29874	−	0.943590i	0.298797	−	0.954317i	$-0.403415\pi$
$719$	671398.	−	487799.i	1.29874	−	0.943590i	0.999942	+	0.0107271i	$0.00341459\pi$
$720$	316958.	−	975497.i	0.611416	−	1.88175i
$721$	803999.	−	261235.i	1.54662	−	0.502529i
$722$	−180103.	−	130852.i	−0.345498	−	0.251019i
$723$	68292.6	+	22189.6i	0.130646	+	0.0424495i
$724$	−30465.3	−	41931.8i	−0.0581203	−	0.0799957i
$725$	−464880.	+	1.43075e6i	−0.884433	+	2.72200i
$726$	−9422.48	+	28999.4i	−0.0178769	+	0.0550194i
$727$	186118.	+	60473.5i	0.352144	+	0.114418i	0.479747	−	0.877407i	$-0.340728\pi$
$727$	186118.	+	60473.5i	0.352144	+	0.114418i	−0.127603	+	0.991825i	$0.540728\pi$
$728$	−736223.	−	534897.i	−1.38914	−	1.00927i
$729$	−141946.	−	436863.i	−0.267096	−	0.822035i
$730$	20324.6			0.0381396
$731$	46627.7	+	64177.6i	0.0872589	+	0.120102i
$732$	−2936.79	−	4042.14i	−0.00548088	−	0.00754379i
$733$		−	615177.i		−	1.14497i	−0.819917	−	0.572483i	$-0.805980\pi$
$733$		−	615177.i		−	1.14497i	0.819917	−	0.572483i	$-0.194020\pi$
$734$	205253.	−	631704.i	0.380976	−	1.17252i
$735$	21321.1	+	65619.5i	0.0394670	+	0.121467i
$736$			176184.i			0.325245i
$737$	413016.	+	300073.i	0.760381	+	0.552449i
$738$	−37206.0	+	51209.7i	−0.0683126	+	0.0940242i
$739$	−473358.	−	343915.i	−0.866764	−	0.629741i	0.0629524	−	0.998017i	$-0.479948\pi$
$739$	−473358.	−	343915.i	−0.866764	−	0.629741i	−0.929717	+	0.368275i	$0.879948\pi$
$740$	−90300.8			−0.164903
$741$	142850.	−	46414.9i	0.260163	−	0.0845320i
$742$	−262687.			−0.477123
$743$	93889.5	+	129228.i	0.170075	+	0.234088i	0.885543	−	0.464558i	$-0.153787\pi$
$743$	93889.5	+	129228.i	0.170075	+	0.234088i	−0.715468	+	0.698645i	$0.753787\pi$
$744$			65326.6i			0.118017i
$745$	−347898.	−	113039.i	−0.626814	−	0.203664i
$746$	−124965.	+	384602.i	−0.224548	+	0.691088i
$747$	674344.			1.20848
$748$	−39181.4	+	28467.0i	−0.0700288	+	0.0508789i
$749$		−	599181.i		−	1.06806i
$750$	−71158.1	−	219002.i	−0.126503	−	0.389337i
$751$		−	105252.i		−	0.186616i	−0.995637	−	0.0933081i	$-0.970256\pi$
$751$		−	105252.i		−	0.186616i	0.995637	−	0.0933081i	$-0.0297442\pi$
$752$	−513308.	+	706507.i	−0.907699	+	1.24934i
$753$	6777.43	+	4924.09i	0.0119529	+	0.00868432i
$754$	642189.	−	883897.i	1.12959	−	1.55474i
$755$	754760.			1.32408
$756$	22252.4	−	7230.24i	0.0389343	−	0.0126505i
$757$	−438882.	−	142601.i	−0.765872	−	0.248847i	−0.100075	−	0.994980i	$-0.531908\pi$
$757$	−438882.	−	142601.i	−0.765872	−	0.248847i	−0.665797	+	0.746133i	$0.731908\pi$
$758$	−337608.			−0.587590
$759$	−81772.6	+	59411.2i	−0.141946	+	0.103130i
$760$	−954037.	+	693148.i	−1.65173	+	1.20005i
$761$		−	339156.i		−	0.585640i	−0.956168	−	0.292820i	$-0.905406\pi$
$761$		−	339156.i		−	0.585640i	0.956168	−	0.292820i	$-0.0945936\pi$
$762$	58630.3	−	19050.1i	0.100975	−	0.0328086i
$763$	471821.	−	649406.i	0.810454	−	1.11549i
$764$	10066.7	−	30982.0i	0.0172464	−	0.0530791i
$765$	−959337.	−	311707.i	−1.63926	−	0.532628i
$766$	222888.	+	72420.7i	0.379865	+	0.123426i
$767$	210254.	−	152759.i	0.357400	−	0.259666i
$768$	−9265.30	+	28515.7i	−0.0157086	+	0.0483460i
$769$	255132.	−	351159.i	0.431432	−	0.593816i	−0.536849	−	0.843678i	$-0.680385\pi$
$769$	255132.	−	351159.i	0.431432	−	0.593816i	0.968281	+	0.249863i	$0.0803855\pi$
$770$	−343265.	−	1.05646e6i	−0.578959	−	1.78185i
$771$	−145630.	−	47317.9i	−0.244986	−	0.0796007i
$772$	21253.0	+	29252.2i	0.0356603	+	0.0490822i
$773$	52555.7	−	72336.7i	0.0879550	−	0.121060i	−0.762772	−	0.646668i	$-0.776162\pi$
$773$	52555.7	−	72336.7i	0.0879550	−	0.121060i	0.850727	+	0.525608i	$0.176162\pi$
$774$	29553.2	+	90955.3i	0.0493313	+	0.151826i
$775$	−700431.	−	964060.i	−1.16617	−	1.60510i
$776$	−187562.	+	258157.i	−0.311474	+	0.428707i
$777$	51558.6	+	70964.4i	0.0854003	+	0.117543i
$778$	14513.7	−	4715.79i	0.0239784	−	0.00779104i
$779$	77135.1	−	25062.7i	0.127109	−	0.0413003i
$780$			29206.5i			0.0480054i
$781$	−82061.4	+	480564.i	−0.134535	+	0.787860i
$782$	894051.			1.46200
$783$	−68141.6	−	209718.i	−0.111145	−	0.342068i
$784$	95500.3	+	293920.i	0.155372	+	0.478186i
$785$	−1.17799e6	+	855861.i	−1.91163	+	1.38888i
$786$	−11780.2	−	8558.83i	−0.0190681	−	0.0138538i
$787$	−357427.	+	259686.i	−0.577083	+	0.419275i	−0.837671	−	0.546175i	$-0.816083\pi$
$787$	−357427.	+	259686.i	−0.577083	+	0.419275i	0.260588	+	0.965450i	$0.416083\pi$
$788$	−56532.1	+	18368.4i	−0.0910422	+	0.0295814i
$789$	−57162.5	−	41531.0i	−0.0918242	−	0.0667142i
$790$	−899881.	+	653802.i	−1.44189	+	1.04759i
$791$	−388545.	+	1.19582e6i	−0.620996	+	1.91123i
$792$	435905.	−	141634.i	0.694931	−	0.225797i
$793$	420359.	+	305409.i	0.668458	+	0.485663i
$794$	531537.	+	172707.i	0.843126	+	0.273948i
$795$	−38900.3	−	53541.6i	−0.0615486	−	0.0847144i
$796$	4306.97	−	13255.5i	0.00679745	−	0.0209204i
$797$	208942.	−	643058.i	0.328935	−	1.01236i	−0.640698	−	0.767793i	$-0.721355\pi$
$797$	208942.	−	643058.i	0.328935	−	1.01236i	0.969633	−	0.244564i	$-0.0786449\pi$
$798$	−138784.	−	45093.5i	−0.217938	−	0.0708123i
$799$	694803.	+	504804.i	1.08835	+	0.790732i
$800$	−106257.	−	327025.i	−0.166026	−	0.510976i
$801$	930163.			1.44975
$802$	−55086.6	−	75820.2i	−0.0856440	−	0.117879i
$803$	5949.35	+	8188.58i	0.00922653	+	0.0126992i
$804$			13040.6i			0.0201737i
$805$	−643332.	+	1.97997e6i	−0.992758	+	3.05540i
$806$	267433.	+	823073.i	0.411665	+	1.26698i
$807$			41698.1i			0.0640279i
$808$	−508509.	−	369454.i	−0.778890	−	0.565897i
$809$	−223538.	+	307674.i	−0.341550	+	0.470104i	−0.944893	−	0.327378i	$-0.893835\pi$
$809$	−223538.	+	307674.i	−0.341550	+	0.470104i	0.603343	+	0.797482i	$0.293835\pi$
$810$	−960066.	−	697528.i	−1.46329	−	1.06314i
$811$	−592832.			−0.901343			−0.450671	−	0.892690i	$-0.648815\pi$
$811$	−592832.			−0.901343			−0.450671	+	0.892690i	$0.648815\pi$
$812$	−102488.	+	33300.4i	−0.155439	+	0.0505053i
$813$	119703.			0.181103
$814$	−260359.	−	358354.i	−0.392938	−	0.540833i
$815$			945820.i			1.42394i
$816$	101387.	+	32942.6i	0.152266	+	0.0494741i
$817$	37866.5	−	116541.i	0.0567298	−	0.174596i
$818$	−772469.			−1.15445
$819$	−972777.	+	706764.i	−1.45026	+	1.05368i
$820$			15770.7i			0.0234543i
$821$	−301057.	−	926558.i	−0.446645	−	1.37463i	−0.880670	−	0.473731i	$-0.842907\pi$
$821$	−301057.	−	926558.i	−0.446645	−	1.37463i	0.434025	−	0.900901i	$-0.357093\pi$
$822$		−	125633.i		−	0.185934i
$823$	358283.	−	493134.i	0.528965	−	0.728057i	−0.458008	−	0.888948i	$-0.651437\pi$
$823$	358283.	−	493134.i	0.528965	−	0.728057i	0.986972	+	0.160891i	$0.0514368\pi$
$824$	692524.	+	503148.i	1.01995	+	0.741040i
$825$	115951.	−	159593.i	0.170360	−	0.234481i
$826$	−252490.			−0.370070
$827$	529714.	−	172114.i	0.774516	−	0.251655i	0.105019	−	0.994470i	$-0.466510\pi$
$827$	529714.	−	172114.i	0.774516	−	0.251655i	0.669497	+	0.742815i	$0.266510\pi$
$828$	104071.	+	33814.8i	0.151799	+	0.0493226i
$829$	−870021.			−1.26596			−0.632981	−	0.774167i	$-0.718169\pi$
$829$	−870021.			−1.26596			−0.632981	+	0.774167i	$0.718169\pi$
$830$	1.33884e6	−	972725.i	1.94345	−	1.41200i
$831$	−59108.8	+	42945.1i	−0.0855954	+	0.0621887i
$832$		−	908031.i		−	1.31176i
$833$	289051.	−	93918.2i	0.416566	−	0.135350i
$834$	52493.3	−	72250.8i	0.0754695	−	0.103875i
$835$	−138731.	+	426969.i	−0.198975	+	0.612383i
$836$	71150.1	+	23118.1i	0.101804	+	0.0330780i
$837$	166121.	+	53975.9i	0.237123	+	0.0770458i
$838$	−173086.	+	125755.i	−0.246476	+	0.179076i
$839$	−189846.	+	584286.i	−0.269698	+	0.830045i	0.720876	+	0.693064i	$0.243740\pi$
$839$	−189846.	+	584286.i	−0.269698	+	0.830045i	−0.990574	+	0.136981i	$0.956260\pi$
$840$	−130925.	+	180203.i	−0.185551	+	0.255389i
$841$	95278.5	+	293237.i	0.134711	+	0.414598i
$842$	725670.	+	235784.i	1.02356	+	0.332576i
$843$	20289.2	+	27925.7i	0.0285502	+	0.0392960i
$844$	28248.4	−	38880.6i	0.0396561	−	0.0545819i
$845$	−532421.	−	1.63862e6i	−0.745662	−	2.29491i
$846$	608582.	+	837641.i	0.850312	+	1.17035i
$847$	−183837.	+	253030.i	−0.256252	+	0.352700i
$848$	−174240.	−	239821.i	−0.242302	−	0.333500i
$849$	83633.2	−	27174.1i	0.116028	−	0.0376998i
$850$	−1.65949e6	+	539202.i	−2.29688	+	0.746301i
$851$			830157.i			1.14631i
$852$	−11163.2	+	5519.54i	−0.0153784	+	0.00760367i
$853$	496460.			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$853$	496460.			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$854$	−155992.	−	480094.i	−0.213888	−	0.658280i
$855$	481498.	+	1.48190e6i	0.658661	+	2.02715i
$856$	490845.	−	356620.i	0.669879	−	0.486696i
$857$	264270.	+	192003.i	0.359820	+	0.261425i	0.752977	−	0.658047i	$-0.228617\pi$
$857$	264270.	+	192003.i	0.359820	+	0.261425i	−0.393157	+	0.919471i	$0.628617\pi$
$858$	−115905.	+	84209.6i	−0.157444	+	0.114390i
$859$	754492.	−	245149.i	1.02251	−	0.332234i	0.250686	−	0.968069i	$-0.419344\pi$
$859$	754492.	−	245149.i	1.02251	−	0.332234i	0.771825	+	0.635834i	$0.219344\pi$
$860$	19276.8	+	14005.4i	0.0260638	+	0.0189365i
$861$	12393.7	−	9004.52i	0.0167183	−	0.0121466i
$862$	−425739.	+	1.31029e6i	−0.572966	+	1.76341i
$863$	−1.12505e6	+	365550.i	−1.51060	+	0.490824i	−0.943089	−	0.332542i	$-0.892094\pi$
$863$	−1.12505e6	+	365550.i	−1.51060	+	0.490824i	−0.567512	+	0.823365i	$0.692094\pi$
$864$	40775.8	+	29625.4i	0.0546230	+	0.0396859i
$865$	2.04385e6	+	664087.i	2.73160	+	0.887550i
$866$	441427.	+	607573.i	0.588604	+	0.810144i
$867$	−2869.75	+	8832.17i	−0.00381773	+	0.0117498i
$868$	26377.7	−	81182.2i	0.0350104	−	0.107751i
$869$	−526821.	−	171174.i	−0.697627	−	0.226673i
$870$	−216348.	−	157186.i	−0.285835	−	0.207671i
$871$	−419073.	−	1.28977e6i	−0.552400	−	1.70011i
$872$	812806.			1.06894
$873$	247827.	+	341105.i	0.325178	+	0.447569i
$874$	−811760.	−	1.11729e6i	−1.06269	−	1.46266i
$875$		−	2.36197e6i		−	3.08502i
$876$	−79.8955	+	245.893i	−0.000104115	+	0.000320434i
$877$	−47077.1	−	144888.i	−0.0612083	−	0.188380i	0.915777	−	0.401688i	$-0.131576\pi$
$877$	−47077.1	−	144888.i	−0.0612083	−	0.188380i	−0.976985	+	0.213308i	$0.931576\pi$
$878$		−	528879.i		−	0.686068i
$879$	95922.0	+	69691.4i	0.124148	+	0.0901989i
$880$	736813.	−	1.01414e6i	0.951463	−	1.30958i
$881$	232266.	+	168751.i	0.299250	+	0.217418i	0.727270	−	0.686351i	$-0.240789\pi$
$881$	232266.	+	168751.i	0.299250	+	0.217418i	−0.428020	+	0.903769i	$0.640789\pi$
$882$	366407.			0.471006
$883$	−308134.	+	100119.i	−0.395202	+	0.128409i	−0.499874	−	0.866098i	$-0.666620\pi$
$883$	−308134.	+	100119.i	−0.395202	+	0.128409i	0.104673	+	0.994507i	$0.466620\pi$
$884$	128653.			0.164633
$885$	−37390.2	−	51463.2i	−0.0477388	−	0.0657068i
$886$			1.35365e6i			1.72441i
$887$	130661.	+	42454.2i	0.166072	+	0.0539602i	0.390873	−	0.920445i	$-0.372173\pi$
$887$	130661.	+	42454.2i	0.166072	+	0.0539602i	−0.224801	+	0.974405i	$0.572173\pi$
$888$	−27446.9	+	84472.9i	−0.0348071	+	0.107125i
$889$	632336.			0.800100
$890$	1.84674e6	−	1.34174e6i	2.33145	−	1.69390i
$891$		−	590979.i		−	0.744418i
$892$	17701.6	+	54479.8i	0.0222475	+	0.0684709i
$893$		−	1.32663e6i		−	1.66360i
$894$	26941.2	−	37081.3i	0.0337086	−	0.0463960i
$895$	94790.5	+	68869.3i	0.118337	+	0.0859765i
$896$	−646660.	+	890051.i	−0.805490	+	1.10866i
$897$	268503.			0.333706
$898$	1.32761e6	−	431367.i	1.64633	−	0.534926i
$899$	−765104.	−	248597.i	−0.946676	−	0.307594i
$900$	−213566.			−0.263661
$901$	−235848.	+	171354.i	−0.290525	+	0.211079i
$902$	−62585.1	+	45470.8i	−0.0769233	+	0.0558881i
$903$		−	23145.6i		−	0.0283853i
$904$	−1.21086e6	+	393432.i	−1.48169	+	0.481430i
$905$	775472.	−	1.06735e6i	0.946824	−	1.30319i
$906$	−29224.3	+	89943.1i	−0.0356031	+	0.109575i
$907$	984378.	+	319844.i	1.19660	+	0.388798i	0.838508	−	0.544890i	$-0.183429\pi$
$907$	984378.	+	319844.i	1.19660	+	0.388798i	0.358088	+	0.933688i	$0.383429\pi$
$908$	1328.84	+	431.766i	0.00161176	+	0.000523693i
$909$	−671898.	+	488162.i	−0.813159	+	0.590795i
$910$	−911860.	+	2.80642e6i	−1.10115	+	3.38898i
$911$	298637.	−	411039.i	0.359838	−	0.495275i	−0.590265	−	0.807209i	$-0.700977\pi$
$911$	298637.	−	411039.i	0.359838	−	0.495275i	0.950104	+	0.311934i	$0.100977\pi$
$912$	−50886.8	−	156614.i	−0.0611809	−	0.188295i
$913$	783803.	+	254673.i	0.940297	+	0.305521i
$914$	677319.	+	932250.i	0.810776	+	1.11594i
$915$	74753.9	−	102890.i	0.0892877	−	0.122894i
$916$	−34124.1	−	105023.i	−0.0406697	−	0.125168i
$917$	−87790.2	−	120833.i	−0.104402	−	0.143697i
$918$	150335.	−	206918.i	0.178391	−	0.245535i
$919$	−771764.	−	1.06224e6i	−0.913805	−	1.25774i	−0.965851	−	0.259100i	$-0.916574\pi$
$919$	−771764.	−	1.06224e6i	−0.913805	−	1.25774i	0.0520456	−	0.998645i	$-0.483426\pi$
$920$	−2.00487e6	+	651423.i	−2.36871	+	0.769640i
$921$	47605.9	−	15468.1i	0.0561230	−	0.0182355i
$922$		−	240212.i		−	0.282574i
$923$	926716.	−	904648.i	1.08779	−	1.06188i
$924$	14130.8			0.0165509
$925$	−500668.	−	1.54090e6i	−0.585149	−	1.80090i
$926$	−358232.	−	1.10253e6i	−0.417775	−	1.28578i
$927$	915038.	−	664814.i	1.06483	−	0.773643i
$928$	−187802.	−	136446.i	−0.218074	−	0.158440i
$929$	929645.	−	675427.i	1.07717	−	0.782613i	0.0999861	−	0.994989i	$-0.468120\pi$
$929$	929645.	−	675427.i	1.07717	−	0.782613i	0.977188	+	0.212376i	$0.0681202\pi$
$930$	201461.	−	65458.6i	0.232930	−	0.0756834i
$931$	−379815.	−	275952.i	−0.438200	−	0.318371i
$932$	−95328.5	+	69260.2i	−0.109747	+	0.0797356i
$933$	41352.0	−	127268.i	0.0475043	−	0.146203i
$934$	516221.	−	167730.i	0.591755	−	0.192273i
$935$	−997335.	−	724607.i	−1.14082	−	0.828856i
$936$	−1.15795e6	−	376241.i	−1.32172	−	0.429452i
$937$	508038.	+	699255.i	0.578652	+	0.796446i	0.993547	−	0.113423i	$-0.0361817\pi$
$937$	508038.	+	699255.i	0.578652	+	0.796446i	−0.414895	+	0.909869i	$0.636182\pi$
$938$	−407143.	+	1.25306e6i	−0.462744	+	1.42418i
$939$	−47057.6	+	144828.i	−0.0533702	+	0.164256i
$940$	245337.	+	79714.7i	0.277656	+	0.0902158i
$941$	726148.	+	527578.i	0.820061	+	0.595809i	0.916730	−	0.399507i	$-0.130819\pi$
$941$	726148.	+	527578.i	0.820061	+	0.595809i	−0.0966690	+	0.995317i	$0.530819\pi$
$942$	−56379.3	−	173518.i	−0.0635357	−	0.195543i
$943$	144984.			0.163041
$944$	−167476.	−	230512.i	−0.187936	−	0.258672i
$945$	350066.	+	481825.i	0.392000	+	0.539542i
$946$			116880.i			0.130605i
$947$	−396930.	+	1.22162e6i	−0.442602	+	1.36219i	0.442489	+	0.896774i	$0.354095\pi$
$947$	−396930.	+	1.22162e6i	−0.442602	+	1.36219i	−0.885092	+	0.465416i	$0.845905\pi$
$948$	−4372.48	−	13457.1i	−0.00486532	−	0.0149739i
$949$		−	26887.4i		−	0.0298550i
$950$	2.18059e6	+	1.58429e6i	2.41617	+	1.75545i
$951$	−38491.7	+	52979.3i	−0.0425604	+	0.0585794i
$952$	793784.	+	576718.i	0.875847	+	0.636340i
$953$	−1.37442e6			−1.51333			−0.756664	−	0.653804i	$-0.773172\pi$
$953$	−1.37442e6			−1.51333			−0.756664	+	0.653804i	$0.773172\pi$
$954$	−334255.	+	108606.i	−0.367266	+	0.119332i
$955$	829211.			0.909197
$956$	1383.09	+	1903.66i	0.00151334	+	0.00208293i
$957$		−	133176.i		−	0.145412i
$958$	1.53551e6	+	498917.i	1.67310	+	0.543622i
$959$	398214.	−	1.22558e6i	0.432992	−	1.33261i
$960$	−222256.			−0.241163
$961$	−231607.	+	168272.i	−0.250787	+	0.182207i
$962$			1.17667e6i			1.27146i
$963$	−247727.	−	762425.i	−0.267129	−	0.822138i
$964$		−	95008.0i		−	0.102237i
$965$	−540980.	+	744595.i	−0.580933	+	0.799586i
$966$	−211039.	−	153329.i	−0.226156	−	0.164312i
$967$	840403.	−	1.15672e6i	0.898742	−	1.23701i	−0.0721261	−	0.997396i	$-0.522978\pi$
$967$	840403.	−	1.15672e6i	0.898742	−	1.23701i	0.970868	−	0.239616i	$-0.0770216\pi$
$968$	−316696.			−0.337981
$969$	−154019.	+	50043.8i	−0.164031	+	0.0532970i
$970$	984072.	+	319744.i	1.04588	+	0.339828i
$971$	−1.79141e6			−1.90001			−0.950007	−	0.312229i	$-0.898924\pi$
$971$	−1.79141e6			−1.90001			−0.950007	+	0.312229i	$0.898924\pi$
$972$	38136.1	−	27707.5i	0.0403649	−	0.0293268i
$973$	741096.	−	538438.i	0.782796	−	0.568735i
$974$		−	1.38870e6i		−	1.46383i
$975$	−498382.	+	161934.i	−0.524268	+	0.170345i
$976$	334834.	−	460860.i	0.351504	−	0.483804i
$977$	−490787.	+	1.51049e6i	−0.514166	+	1.58244i	0.270627	+	0.962684i	$0.412769\pi$
$977$	−490787.	+	1.51049e6i	−0.514166	+	1.58244i	−0.784794	+	0.619757i	$0.787231\pi$
$978$	−112711.	−	36622.1i	−0.117839	−	0.0382882i
$979$	1.08115e6	+	351285.i	1.12803	+	0.366518i
$980$	73854.5	−	53658.4i	0.0768997	−	0.0558709i
$981$	331874.	−	1.02140e6i	0.344854	−	1.06135i
$982$	−253421.	+	348804.i	−0.262796	+	0.361708i
$983$	478264.	+	1.47194e6i	0.494949	+	1.52330i	0.817036	+	0.576587i	$0.195616\pi$
$983$	478264.	+	1.47194e6i	0.494949	+	1.52330i	−0.322087	+	0.946710i	$0.604384\pi$
$984$	14752.9	+	4793.50i	0.0152365	+	0.00495065i
$985$	−889342.	−	1.22407e6i	−0.916635	−	1.26164i
$986$	−692398.	+	953004.i	−0.712200	+	0.980260i
$987$	−77433.7	−	238316.i	−0.0794869	−	0.244635i
$988$	−116812.	−	160778.i	−0.119667	−	0.164707i
$989$	128755.	−	177216.i	0.131635	−	0.181180i
$990$	−873571.	−	1.20237e6i	−0.891308	−	1.22678i
$991$	189390.	−	61536.5i	0.192845	−	0.0626593i	−0.211002	−	0.977486i	$-0.567673\pi$
$991$	189390.	−	61536.5i	0.192845	−	0.0626593i	0.403847	+	0.914826i	$0.367673\pi$
$992$	174878.	−	56821.4i	0.177710	−	0.0577416i
$993$			23839.0i			0.0241763i
$994$	−1.24499e6	+	181837.i	−1.26006	+	0.184039i
$995$	354774.			0.358348
$996$	6505.37	+	20021.5i	0.00655773	+	0.0201826i
$997$	−282228.	−	868608.i	−0.283929	−	0.873843i	−0.986718	−	0.162445i	$-0.948062\pi$
$997$	−282228.	−	868608.i	−0.283929	−	0.873843i	0.702789	−	0.711399i	$-0.251938\pi$
$998$	−745888.	+	541919.i	−0.748880	+	0.544093i
$999$	192131.	+	139591.i	0.192515	+	0.139871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.5.e.a.66.19	yes	92
71.14	odd	10	inner	71.5.e.a.14.19	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.5.e.a.14.19	✓	92	71.14	odd	10	inner
71.5.e.a.66.19	yes	92	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	71.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30403 + 4.01340i) q^{2} +(-0.422249 - 1.29955i) q^{3} +(-1.46264 + 1.06267i) q^{4} +(-37.2304 - 27.0495i) q^{5} +(4.66499 - 3.38931i) q^{6} +(56.2511 - 18.2771i) q^{7} +(48.4518 + 35.2023i) q^{8} +(64.0198 - 46.5131i) q^{9} +O(q^{10})\)	\(q+(1.30403 + 4.01340i) q^{2} +(-0.422249 - 1.29955i) q^{3} +(-1.46264 + 1.06267i) q^{4} +(-37.2304 - 27.0495i) q^{5} +(4.66499 - 3.38931i) q^{6} +(56.2511 - 18.2771i) q^{7} +(48.4518 + 35.2023i) q^{8} +(64.0198 - 46.5131i) q^{9} +(60.0108 - 184.694i) q^{10} +(91.9776 - 29.8853i) q^{11} +(1.99859 + 1.45206i) q^{12} +(-244.332 - 79.3883i) q^{13} +(146.707 + 201.924i) q^{14} +(-19.4316 + 59.8043i) q^{15} +(-87.0371 + 267.873i) q^{16} +(263.435 + 85.5953i) q^{17} +(270.160 + 196.283i) q^{18} +(-132.220 - 406.931i) q^{19} +83.1992 q^{20} +(-47.5039 - 65.3835i) q^{21} +(239.884 + 330.172i) q^{22} -764.871i q^{23} +(25.2884 - 77.8297i) q^{24} +(461.294 + 1419.72i) q^{25} -1084.13i q^{26} +(-177.021 - 128.613i) q^{27} +(-62.8524 + 86.5090i) q^{28} +(815.306 + 592.355i) q^{29} -265.358 q^{30} +(-759.202 + 246.680i) q^{31} -230.345 q^{32} +(-77.6749 - 106.910i) q^{33} +1168.89i q^{34} +(-2588.64 - 841.099i) q^{35} +(-44.2098 + 136.064i) q^{36} -1085.36 q^{37} +(1460.76 - 1061.30i) q^{38} +351.043i q^{39} +(-851.678 - 2621.19i) q^{40} +189.553i q^{41} +(200.464 - 275.915i) q^{42} +(231.695 + 168.336i) q^{43} +(-102.772 + 141.453i) q^{44} -3641.64 q^{45} +(3069.74 - 997.417i) q^{46} +(2948.78 + 958.118i) q^{47} +384.865 q^{48} +(887.682 - 644.939i) q^{49} +(-5096.35 + 3702.72i) q^{50} -378.489i q^{51} +(441.733 - 143.528i) q^{52} +(-618.623 + 851.462i) q^{53} +(285.335 - 878.172i) q^{54} +(-4232.75 - 1375.30i) q^{55} +(3368.86 + 1094.61i) q^{56} +(-472.997 + 343.652i) q^{57} +(-1314.17 + 4044.60i) q^{58} +(-594.609 + 818.409i) q^{59} +(-35.1308 - 108.121i) q^{60} +(-1923.51 - 624.987i) q^{61} +(-1980.05 - 2725.31i) q^{62} +(2751.06 - 3786.51i) q^{63} +(1092.22 + 3361.50i) q^{64} +(6949.18 + 9564.72i) q^{65} +(327.784 - 451.155i) q^{66} +(3102.79 + 4270.62i) q^{67} +(-476.270 + 154.749i) q^{68} +(-993.986 + 322.966i) q^{69} -11486.1i q^{70} +(-2342.52 + 4463.66i) q^{71} +4739.25 q^{72} +(32.3413 + 99.5363i) q^{73} +(-1415.34 - 4355.97i) q^{74} +(1650.21 - 1198.95i) q^{75} +(625.823 + 454.687i) q^{76} +(4627.62 - 3362.16i) q^{77} +(-1408.88 + 457.772i) q^{78} +(-4633.81 - 3366.66i) q^{79} +(10486.3 - 7618.71i) q^{80} +(1888.33 - 5811.69i) q^{81} +(-760.754 + 247.184i) q^{82} +(6894.17 + 5008.91i) q^{83} +(138.962 + 45.1515i) q^{84} +(-7492.50 - 10312.5i) q^{85} +(-373.463 + 1149.40i) q^{86} +(425.531 - 1309.65i) q^{87} +(5508.52 + 1789.83i) q^{88} +(9509.54 + 6909.09i) q^{89} +(-4748.83 - 14615.4i) q^{90} -15194.9 q^{91} +(812.804 + 1118.73i) q^{92} +(641.145 + 882.460i) q^{93} +13084.1i q^{94} +(-6084.67 + 18726.7i) q^{95} +(97.2629 + 299.344i) q^{96} +5328.12i q^{97} +(3745.97 + 2721.61i) q^{98} +(4498.33 - 6191.42i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 6 q^{2} - 13 q^{3} - 170 q^{4} - 9 q^{5} - 70 q^{6} - 5 q^{7} + 329 q^{8} - 742 q^{9}+O(q^{10}) \) 92 * q + 6 * q^2 - 13 * q^3 - 170 * q^4 - 9 * q^5 - 70 * q^6 - 5 * q^7 + 329 * q^8 - 742 * q^9	\( 92 q + 6 q^{2} - 13 q^{3} - 170 q^{4} - 9 q^{5} - 70 q^{6} - 5 q^{7} + 329 q^{8} - 742 q^{9} + 75 q^{10} - 395 q^{11} + 1306 q^{12} - 5 q^{13} - 1025 q^{14} + 303 q^{15} - 1430 q^{16} - 560 q^{17} - 420 q^{18} + 83 q^{19} + 1796 q^{20} - 5 q^{21} - 2380 q^{22} + 849 q^{24} - 968 q^{25} + 4880 q^{27} - 1230 q^{28} + 9 q^{29} + 4312 q^{30} + 2770 q^{31} - 7780 q^{32} - 1680 q^{33} + 355 q^{35} + 6392 q^{36} - 4722 q^{37} + 1703 q^{38} - 2741 q^{40} + 5485 q^{42} + 683 q^{43} + 11095 q^{44} - 18856 q^{45} + 20465 q^{46} - 12005 q^{47} - 23780 q^{48} + 5632 q^{49} + 12166 q^{50} + 19325 q^{52} - 1430 q^{53} + 23768 q^{54} - 10460 q^{55} - 14645 q^{56} + 1140 q^{57} - 17583 q^{58} + 3955 q^{59} + 5490 q^{60} + 13630 q^{61} - 21935 q^{62} - 5585 q^{63} + 12481 q^{64} + 3250 q^{65} + 66740 q^{66} - 46680 q^{67} - 4575 q^{68} - 5435 q^{69} - 12829 q^{71} - 29794 q^{72} + 4327 q^{73} + 4533 q^{74} - 8579 q^{75} - 22813 q^{76} + 39664 q^{77} + 13120 q^{78} - 34081 q^{79} + 39762 q^{80} - 41491 q^{81} - 60875 q^{82} - 17571 q^{83} + 122015 q^{84} - 33245 q^{85} - 32869 q^{86} - 34233 q^{87} - 113910 q^{88} - 36432 q^{89} - 9308 q^{90} + 68114 q^{91} + 68490 q^{92} + 24470 q^{93} + 57539 q^{95} + 36869 q^{96} + 117096 q^{98} - 24650 q^{99}+O(q^{100}) \) 92 * q + 6 * q^2 - 13 * q^3 - 170 * q^4 - 9 * q^5 - 70 * q^6 - 5 * q^7 + 329 * q^8 - 742 * q^9 + 75 * q^10 - 395 * q^11 + 1306 * q^12 - 5 * q^13 - 1025 * q^14 + 303 * q^15 - 1430 * q^16 - 560 * q^17 - 420 * q^18 + 83 * q^19 + 1796 * q^20 - 5 * q^21 - 2380 * q^22 + 849 * q^24 - 968 * q^25 + 4880 * q^27 - 1230 * q^28 + 9 * q^29 + 4312 * q^30 + 2770 * q^31 - 7780 * q^32 - 1680 * q^33 + 355 * q^35 + 6392 * q^36 - 4722 * q^37 + 1703 * q^38 - 2741 * q^40 + 5485 * q^42 + 683 * q^43 + 11095 * q^44 - 18856 * q^45 + 20465 * q^46 - 12005 * q^47 - 23780 * q^48 + 5632 * q^49 + 12166 * q^50 + 19325 * q^52 - 1430 * q^53 + 23768 * q^54 - 10460 * q^55 - 14645 * q^56 + 1140 * q^57 - 17583 * q^58 + 3955 * q^59 + 5490 * q^60 + 13630 * q^61 - 21935 * q^62 - 5585 * q^63 + 12481 * q^64 + 3250 * q^65 + 66740 * q^66 - 46680 * q^67 - 4575 * q^68 - 5435 * q^69 - 12829 * q^71 - 29794 * q^72 + 4327 * q^73 + 4533 * q^74 - 8579 * q^75 - 22813 * q^76 + 39664 * q^77 + 13120 * q^78 - 34081 * q^79 + 39762 * q^80 - 41491 * q^81 - 60875 * q^82 - 17571 * q^83 + 122015 * q^84 - 33245 * q^85 - 32869 * q^86 - 34233 * q^87 - 113910 * q^88 - 36432 * q^89 - 9308 * q^90 + 68114 * q^91 + 68490 * q^92 + 24470 * q^93 + 57539 * q^95 + 36869 * q^96 + 117096 * q^98 - 24650 * q^99

Introduction

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