LMFDB - Embedded newform 805.2.k.a.783.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(622,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("805.622");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.k (of order $4$, degree $2$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$88$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			783.16
Character	$\chi$	$=$	805.783
Dual form			805.2.k.a.622.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49985 + 1.49985i) q^{2} +(1.75798 - 1.75798i) q^{3} -2.49908i q^{4} +(0.277450 - 2.21879i) q^{5} +5.27339i q^{6} +(-0.502421 + 2.59761i) q^{7} +(0.748540 + 0.748540i) q^{8} -3.18096i q^{9} +O(q^{10})$	\(q+(-1.49985 + 1.49985i) q^{2} +(1.75798 - 1.75798i) q^{3} -2.49908i q^{4} +(0.277450 - 2.21879i) q^{5} +5.27339i q^{6} +(-0.502421 + 2.59761i) q^{7} +(0.748540 + 0.748540i) q^{8} -3.18096i q^{9} +(2.91171 + 3.74397i) q^{10} -5.46394 q^{11} +(-4.39332 - 4.39332i) q^{12} +(2.92379 - 2.92379i) q^{13} +(-3.14246 - 4.64957i) q^{14} +(-3.41283 - 4.38833i) q^{15} +2.75277 q^{16} +(-3.96376 - 3.96376i) q^{17} +(4.77096 + 4.77096i) q^{18} +2.35096 q^{19} +(-5.54492 - 0.693368i) q^{20} +(3.68329 + 5.44978i) q^{21} +(8.19507 - 8.19507i) q^{22} +(0.707107 + 0.707107i) q^{23} +2.63183 q^{24} +(-4.84604 - 1.23120i) q^{25} +8.77046i q^{26} +(-0.318129 - 0.318129i) q^{27} +(6.49163 + 1.25559i) q^{28} -4.74229i q^{29} +(11.7005 + 1.46310i) q^{30} -1.70183i q^{31} +(-5.62581 + 5.62581i) q^{32} +(-9.60548 + 9.60548i) q^{33} +11.8901 q^{34} +(5.62415 + 1.83547i) q^{35} -7.94947 q^{36} +(-3.00442 + 3.00442i) q^{37} +(-3.52607 + 3.52607i) q^{38} -10.2799i q^{39} +(1.86853 - 1.45317i) q^{40} -8.57508i q^{41} +(-13.6982 - 2.64946i) q^{42} +(-7.01938 - 7.01938i) q^{43} +13.6548i q^{44} +(-7.05788 - 0.882557i) q^{45} -2.12110 q^{46} +(-5.14309 - 5.14309i) q^{47} +(4.83930 - 4.83930i) q^{48} +(-6.49515 - 2.61019i) q^{49} +(9.11494 - 5.42170i) q^{50} -13.9364 q^{51} +(-7.30677 - 7.30677i) q^{52} +(8.99822 + 8.99822i) q^{53} +0.954290 q^{54} +(-1.51597 + 12.1233i) q^{55} +(-2.32050 + 1.56833i) q^{56} +(4.13293 - 4.13293i) q^{57} +(7.11271 + 7.11271i) q^{58} -9.30065 q^{59} +(-10.9668 + 8.52892i) q^{60} -9.11442i q^{61} +(2.55249 + 2.55249i) q^{62} +(8.26290 + 1.59818i) q^{63} -11.3702i q^{64} +(-5.67606 - 7.29846i) q^{65} -28.8135i q^{66} +(-7.51082 + 7.51082i) q^{67} +(-9.90575 + 9.90575i) q^{68} +2.48615 q^{69} +(-11.1883 + 5.68243i) q^{70} -1.02237 q^{71} +(2.38108 - 2.38108i) q^{72} +(3.83871 - 3.83871i) q^{73} -9.01235i q^{74} +(-10.6837 + 6.35480i) q^{75} -5.87522i q^{76} +(2.74520 - 14.1932i) q^{77} +(15.4183 + 15.4183i) q^{78} +9.70176i q^{79} +(0.763754 - 6.10781i) q^{80} +8.42436 q^{81} +(12.8613 + 12.8613i) q^{82} +(-6.88435 + 6.88435i) q^{83} +(13.6194 - 9.20483i) q^{84} +(-9.89449 + 7.69501i) q^{85} +21.0560 q^{86} +(-8.33684 - 8.33684i) q^{87} +(-4.08997 - 4.08997i) q^{88} +14.6482 q^{89} +(11.9094 - 9.26204i) q^{90} +(6.12588 + 9.06382i) q^{91} +(1.76711 - 1.76711i) q^{92} +(-2.99178 - 2.99178i) q^{93} +15.4277 q^{94} +(0.652272 - 5.21628i) q^{95} +19.7801i q^{96} +(7.56301 + 7.56301i) q^{97} +(13.6566 - 5.82684i) q^{98} +17.3806i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 176 * q - 8 * q^7 + 24 * q^8	$ 176 q - 8 q^{7} + 24 q^{8} + 8 q^{11} - 8 q^{15} - 208 q^{16} + 16 q^{21} - 16 q^{22} + 36 q^{28} + 88 q^{30} + 8 q^{32} - 48 q^{35} - 144 q^{36} + 24 q^{37} + 24 q^{50} - 24 q^{51} - 8 q^{53} + 104 q^{56} - 40 q^{57} - 80 q^{58} + 40 q^{60} + 60 q^{63} - 8 q^{65} - 64 q^{67} + 68 q^{70} + 40 q^{71} + 80 q^{72} + 4 q^{77} + 168 q^{78} - 160 q^{81} - 16 q^{85} - 128 q^{86} - 88 q^{88} - 112 q^{91} - 32 q^{93} + 24 q^{98}+O(q^{100}) $ 176 * q - 8 * q^7 + 24 * q^8 + 8 * q^11 - 8 * q^15 - 208 * q^16 + 16 * q^21 - 16 * q^22 + 36 * q^28 + 88 * q^30 + 8 * q^32 - 48 * q^35 - 144 * q^36 + 24 * q^37 + 24 * q^50 - 24 * q^51 - 8 * q^53 + 104 * q^56 - 40 * q^57 - 80 * q^58 + 40 * q^60 + 60 * q^63 - 8 * q^65 - 64 * q^67 + 68 * q^70 + 40 * q^71 + 80 * q^72 + 4 * q^77 + 168 * q^78 - 160 * q^81 - 16 * q^85 - 128 * q^86 - 88 * q^88 - 112 * q^91 - 32 * q^93 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−1.49985	+	1.49985i	−1.06055	+	1.06055i	−0.0625069	+	0.998045i	$0.519910\pi$
$2$	−1.49985	+	1.49985i	−1.06055	+	1.06055i	−0.998045	+	0.0625069i	$0.980090\pi$
$3$	1.75798	−	1.75798i	1.01497	−	1.01497i	0.0150820	−	0.999886i	$-0.495199\pi$
$3$	1.75798	−	1.75798i	1.01497	−	1.01497i	0.999886	−	0.0150820i	$-0.00480093\pi$
$4$		−	2.49908i		−	1.24954i
$5$	0.277450	−	2.21879i	0.124079	−	0.992272i
$5$	0.277450	−	2.21879i	0.124079	−	0.992272i
$6$			5.27339i			2.15285i
$7$	−0.502421	+	2.59761i	−0.189897	+	0.981804i
$7$	−0.502421	+	2.59761i	−0.189897	+	0.981804i
$8$	0.748540	+	0.748540i	0.264649	+	0.264649i
$9$		−	3.18096i		−	1.06032i
$10$	2.91171	+	3.74397i	0.920763	+	1.18395i
$11$	−5.46394			−1.64744			−0.823720	−	0.566997i	$-0.808105\pi$
$11$	−5.46394			−1.64744			−0.823720	+	0.566997i	$0.808105\pi$
$12$	−4.39332	−	4.39332i	−1.26824	−	1.26824i
$13$	2.92379	−	2.92379i	0.810912	−	0.810912i	−0.173858	−	0.984771i	$-0.555624\pi$
$13$	2.92379	−	2.92379i	0.810912	−	0.810912i	0.984771	+	0.173858i	$0.0556235\pi$
$14$	−3.14246	−	4.64957i	−0.839858	−	1.24265i
$15$	−3.41283	−	4.38833i	−0.881188	−	1.13306i
$16$	2.75277			0.688192
$17$	−3.96376	−	3.96376i	−0.961354	−	0.961354i	0.0379269	−	0.999281i	$-0.487925\pi$
$17$	−3.96376	−	3.96376i	−0.961354	−	0.961354i	−0.999281	+	0.0379269i	$0.987925\pi$
$18$	4.77096	+	4.77096i	1.12453	+	1.12453i
$19$	2.35096			0.539346			0.269673	−	0.962952i	$-0.413084\pi$
$19$	2.35096			0.539346			0.269673	+	0.962952i	$0.413084\pi$
$20$	−5.54492	−	0.693368i	−1.23988	−	0.155042i
$21$	3.68329	+	5.44978i	0.803760	+	1.18924i
$22$	8.19507	−	8.19507i	1.74719	−	1.74719i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	2.63183			0.537220
$25$	−4.84604	−	1.23120i	−0.969209	−	0.246241i
$26$			8.77046i			1.72003i
$27$	−0.318129	−	0.318129i	−0.0612240	−	0.0612240i
$28$	6.49163	+	1.25559i	1.22680	+	0.237284i
$29$		−	4.74229i		−	0.880621i	−0.897846	−	0.440311i	$-0.854868\pi$
$29$		−	4.74229i		−	0.880621i	0.897846	−	0.440311i	$-0.145132\pi$
$30$	11.7005	+	1.46310i	2.13622	+	0.267124i
$31$		−	1.70183i		−	0.305658i	−0.988253	−	0.152829i	$-0.951162\pi$
$31$		−	1.70183i		−	0.305658i	0.988253	−	0.152829i	$-0.0488384\pi$
$32$	−5.62581	+	5.62581i	−0.994511	+	0.994511i
$33$	−9.60548	+	9.60548i	−1.67210	+	1.67210i
$34$	11.8901			2.03913
$35$	5.62415	+	1.83547i	0.950655	+	0.310251i
$36$	−7.94947			−1.32491
$37$	−3.00442	+	3.00442i	−0.493924	+	0.493924i	−0.909540	−	0.415616i	$-0.863566\pi$
$37$	−3.00442	+	3.00442i	−0.493924	+	0.493924i	0.415616	+	0.909540i	$0.363566\pi$
$38$	−3.52607	+	3.52607i	−0.572005	+	0.572005i
$39$		−	10.2799i		−	1.64610i
$40$	1.86853	−	1.45317i	0.295441	−	0.229766i
$41$		−	8.57508i		−	1.33920i	−0.742721	−	0.669601i	$-0.766465\pi$
$41$		−	8.57508i		−	1.33920i	0.742721	−	0.669601i	$-0.233535\pi$
$42$	−13.6982	−	2.64946i	−2.11368	−	0.408821i
$43$	−7.01938	−	7.01938i	−1.07045	−	1.07045i	−0.997323	−	0.0731231i	$-0.976703\pi$
$43$	−7.01938	−	7.01938i	−1.07045	−	1.07045i	−0.0731231	−	0.997323i	$-0.523297\pi$
$44$			13.6548i			2.05854i
$45$	−7.05788	−	0.882557i	−1.05213	−	0.131564i
$46$	−2.12110			−0.312740
$47$	−5.14309	−	5.14309i	−0.750197	−	0.750197i	0.224319	−	0.974516i	$-0.427984\pi$
$47$	−5.14309	−	5.14309i	−0.750197	−	0.750197i	−0.974516	+	0.224319i	$0.927984\pi$
$48$	4.83930	−	4.83930i	0.698493	−	0.698493i
$49$	−6.49515	−	2.61019i	−0.927878	−	0.372884i
$50$	9.11494	−	5.42170i	1.28905	−	0.766745i
$51$	−13.9364			−1.95149
$52$	−7.30677	−	7.30677i	−1.01327	−	1.01327i
$53$	8.99822	+	8.99822i	1.23600	+	1.23600i	0.961621	+	0.274380i	$0.0884724\pi$
$53$	8.99822	+	8.99822i	1.23600	+	1.23600i	0.274380	+	0.961621i	$0.411528\pi$
$54$	0.954290			0.129862
$55$	−1.51597	+	12.1233i	−0.204413	+	1.63471i
$56$	−2.32050	+	1.56833i	−0.310089	+	0.209577i
$57$	4.13293	−	4.13293i	0.547420	−	0.547420i
$58$	7.11271	+	7.11271i	0.933944	+	0.933944i
$59$	−9.30065			−1.21084			−0.605421	−	0.795906i	$-0.706995\pi$
$59$	−9.30065			−1.21084			−0.605421	+	0.795906i	$0.706995\pi$
$60$	−10.9668	+	8.52892i	−1.41580	+	1.10108i
$61$		−	9.11442i		−	1.16698i	−0.812120	−	0.583491i	$-0.801686\pi$
$61$		−	9.11442i		−	1.16698i	0.812120	−	0.583491i	$-0.198314\pi$
$62$	2.55249	+	2.55249i	0.324166	+	0.324166i
$63$	8.26290	+	1.59818i	1.04103	+	0.201352i
$64$		−	11.3702i		−	1.42127i
$65$	−5.67606	−	7.29846i	−0.704028	−	0.905263i
$66$		−	28.8135i		−	3.54669i
$67$	−7.51082	+	7.51082i	−0.917593	+	0.917593i	−0.996854	−	0.0792611i	$-0.974744\pi$
$67$	−7.51082	+	7.51082i	−0.917593	+	0.917593i	0.0792611	+	0.996854i	$0.474744\pi$
$68$	−9.90575	+	9.90575i	−1.20125	+	1.20125i
$69$	2.48615			0.299298
$70$	−11.1883	+	5.68243i	−1.33726	+	0.679180i
$71$	−1.02237			−0.121333			−0.0606666	−	0.998158i	$-0.519323\pi$
$71$	−1.02237			−0.121333			−0.0606666	+	0.998158i	$0.519323\pi$
$72$	2.38108	−	2.38108i	0.280613	−	0.280613i
$73$	3.83871	−	3.83871i	0.449287	−	0.449287i	−0.445830	−	0.895118i	$-0.647091\pi$
$73$	3.83871	−	3.83871i	0.449287	−	0.449287i	0.895118	+	0.445830i	$0.147091\pi$
$74$		−	9.01235i		−	1.04766i
$75$	−10.6837	+	6.35480i	−1.23364	+	0.733789i
$76$		−	5.87522i		−	0.673934i
$77$	2.74520	−	14.1932i	0.312845	−	1.61746i
$78$	15.4183	+	15.4183i	1.74577	+	1.74577i
$79$			9.70176i			1.09153i	0.837937	+	0.545767i	$0.183762\pi$
$79$			9.70176i			1.09153i	−0.837937	+	0.545767i	$0.816238\pi$
$80$	0.763754	−	6.10781i	0.0853903	−	0.682874i
$81$	8.42436			0.936040
$82$	12.8613	+	12.8613i	1.42029	+	1.42029i
$83$	−6.88435	+	6.88435i	−0.755655	+	0.755655i	−0.975528	−	0.219873i	$-0.929436\pi$
$83$	−6.88435	+	6.88435i	−0.755655	+	0.755655i	0.219873	+	0.975528i	$0.429436\pi$
$84$	13.6194	−	9.20483i	1.48600	−	1.00433i
$85$	−9.89449	+	7.69501i	−1.07321	+	0.834641i
$86$	21.0560			2.27053
$87$	−8.33684	−	8.33684i	−0.893803	−	0.893803i
$88$	−4.08997	−	4.08997i	−0.435993	−	0.435993i
$89$	14.6482			1.55271			0.776354	−	0.630297i	$-0.217067\pi$
$89$	14.6482			1.55271			0.776354	+	0.630297i	$0.217067\pi$
$90$	11.9094	−	9.26204i	1.25537	−	0.976305i
$91$	6.12588	+	9.06382i	0.642167	+	0.950147i
$92$	1.76711	−	1.76711i	0.184234	−	0.184234i
$93$	−2.99178	−	2.99178i	−0.310234	−	0.310234i
$94$	15.4277			1.59124
$95$	0.652272	−	5.21628i	0.0669217	−	0.535179i
$96$			19.7801i			2.01879i
$97$	7.56301	+	7.56301i	0.767907	+	0.767907i	0.977738	−	0.209831i	$-0.0672913\pi$
$97$	7.56301	+	7.56301i	0.767907	+	0.767907i	−0.209831	+	0.977738i	$0.567291\pi$
$98$	13.6566	−	5.82684i	1.37953	−	0.588599i
$99$			17.3806i			1.74681i
$100$	−3.07687	+	12.1106i	−0.307687	+	1.21106i
$101$		−	7.47187i		−	0.743478i	−0.928337	−	0.371739i	$-0.878762\pi$
$101$		−	7.47187i		−	0.743478i	0.928337	−	0.371739i	$-0.121238\pi$
$102$	20.9025	−	20.9025i	2.06965	−	2.06965i
$103$	4.93048	−	4.93048i	0.485815	−	0.485815i	−0.421168	−	0.906983i	$-0.638380\pi$
$103$	4.93048	−	4.93048i	0.485815	−	0.485815i	0.906983	+	0.421168i	$0.138380\pi$
$104$	4.37714			0.429214
$105$	13.1138	−	6.66040i	1.27978	−	0.649989i
$106$	−26.9919			−2.62169
$107$	−1.45572	+	1.45572i	−0.140730	+	0.140730i	−0.773962	−	0.633232i	$-0.781728\pi$
$107$	−1.45572	+	1.45572i	−0.140730	+	0.140730i	0.633232	+	0.773962i	$0.281728\pi$
$108$	−0.795030	+	0.795030i	−0.0765018	+	0.0765018i
$109$		−	12.6744i		−	1.21399i	−0.794705	−	0.606995i	$-0.792375\pi$
$109$		−	12.6744i		−	1.21399i	0.794705	−	0.606995i	$-0.207625\pi$
$110$	−15.9094	−	20.4568i	−1.51690	−	1.95048i
$111$			10.5634i			1.00264i
$112$	−1.38305	+	7.15061i	−0.130686	+	0.675669i
$113$	9.55334	+	9.55334i	0.898703	+	0.898703i	0.995321	−	0.0966186i	$-0.0308027\pi$
$113$	9.55334	+	9.55334i	0.898703	+	0.898703i	−0.0966186	+	0.995321i	$0.530803\pi$
$114$			12.3975i			1.16113i
$115$	1.76511	−	1.37273i	0.164597	−	0.128008i
$116$	−11.8514			−1.10037
$117$	−9.30045	−	9.30045i	−0.859827	−	0.859827i
$118$	13.9495	−	13.9495i	1.28416	−	1.28416i
$119$	12.2878	−	8.30483i	1.12642	−	0.761302i
$120$	0.730200	−	5.83947i	0.0666579	−	0.533069i
$121$	18.8546			1.71406
$122$	13.6702	+	13.6702i	1.23764	+	1.23764i
$123$	−15.0748	−	15.0748i	−1.35925	−	1.35925i
$124$	−4.25301			−0.381932
$125$	−4.07631	+	10.4107i	−0.364597	+	0.931166i
$126$	−14.7901	+	9.99605i	−1.31761	+	0.890519i
$127$	7.13760	−	7.13760i	0.633359	−	0.633359i	−0.315550	−	0.948909i	$-0.602189\pi$
$127$	7.13760	−	7.13760i	0.633359	−	0.633359i	0.948909	+	0.315550i	$0.102189\pi$
$128$	5.80187	+	5.80187i	0.512818	+	0.512818i
$129$	−24.6798			−2.17294
$130$	19.4598	+	2.43336i	1.70674	+	0.213420i
$131$		−	13.6703i		−	1.19438i	−0.802100	−	0.597190i	$-0.796284\pi$
$131$		−	13.6703i		−	1.19438i	0.802100	−	0.597190i	$-0.203716\pi$
$132$	24.0048	+	24.0048i	2.08935	+	2.08935i
$133$	−1.18117	+	6.10687i	−0.102421	+	0.529532i
$134$		−	22.5302i		−	1.94631i
$135$	−0.794127	+	0.617597i	−0.0683475	+	0.0531543i
$136$		−	5.93407i		−	0.508842i
$137$	3.24432	−	3.24432i	0.277181	−	0.277181i	−0.554801	−	0.831983i	$-0.687206\pi$
$137$	3.24432	−	3.24432i	0.277181	−	0.277181i	0.831983	+	0.554801i	$0.187206\pi$
$138$	−3.72885	+	3.72885i	−0.317421	+	0.317421i
$139$	4.39193			0.372519			0.186259	−	0.982501i	$-0.440363\pi$
$139$	4.39193			0.372519			0.186259	+	0.982501i	$0.440363\pi$
$140$	4.58699	−	14.0552i	0.387671	−	1.18788i
$141$	−18.0829			−1.52285
$142$	1.53340	−	1.53340i	0.128680	−	0.128680i
$143$	−15.9754	+	15.9754i	−1.33593	+	1.33593i
$144$		−	8.75645i		−	0.729704i
$145$	−10.5221	−	1.31575i	−0.873816	−	0.109267i
$146$			11.5150i			0.952985i
$147$	−16.0070	+	6.82966i	−1.32023	+	0.563301i
$148$	7.50829	+	7.50829i	0.617178	+	0.617178i
$149$		−	14.1331i		−	1.15783i	−0.815388	−	0.578914i	$-0.803477\pi$
$149$		−	14.1331i		−	1.15783i	0.815388	−	0.578914i	$-0.196523\pi$
$150$	6.49262	−	25.5551i	0.530120	−	2.08656i
$151$	10.7310			0.873277			0.436638	−	0.899637i	$-0.356169\pi$
$151$	10.7310			0.873277			0.436638	+	0.899637i	$0.356169\pi$
$152$	1.75978	+	1.75978i	0.142737	+	0.142737i
$153$	−12.6086	+	12.6086i	−1.01934	+	1.01934i
$154$	17.1702	+	25.4050i	1.38361	+	2.04719i
$155$	−3.77601	−	0.472173i	−0.303296	−	0.0379259i
$156$	−25.6902			−2.05687
$157$	8.33434	+	8.33434i	0.665153	+	0.665153i	0.956590	−	0.291437i	$-0.0941334\pi$
$157$	8.33434	+	8.33434i	0.665153	+	0.665153i	−0.291437	+	0.956590i	$0.594133\pi$
$158$	−14.5512	−	14.5512i	−1.15763	−	1.15763i
$159$	31.6373			2.50900
$160$	10.9216	+	14.0433i	0.863428	+	1.11022i
$161$	−2.19205	+	1.48152i	−0.172758	+	0.116760i
$162$	−12.6352	+	12.6352i	−0.992719	+	0.992719i
$163$	−1.18699	−	1.18699i	−0.0929725	−	0.0929725i	0.659091	−	0.752063i	$-0.270941\pi$
$163$	−1.18699	−	1.18699i	−0.0929725	−	0.0929725i	−0.752063	+	0.659091i	$0.770941\pi$
$164$	−21.4298			−1.67338
$165$	18.6475	+	23.9776i	1.45170	+	1.86665i
$166$		−	20.6509i		−	1.60282i
$167$	14.5798	+	14.5798i	1.12822	+	1.12822i	0.990467	+	0.137752i	$0.0439876\pi$
$167$	14.5798	+	14.5798i	1.12822	+	1.12822i	0.137752	+	0.990467i	$0.456012\pi$
$168$	−1.32229	+	6.83647i	−0.102017	+	0.527445i
$169$		−	4.09704i		−	0.315157i
$170$	3.29890	−	26.3815i	0.253014	−	2.02337i
$171$		−	7.47831i		−	0.571880i
$172$	−17.5420	+	17.5420i	−1.33756	+	1.33756i
$173$	−4.13373	+	4.13373i	−0.314281	+	0.314281i	−0.846566	−	0.532284i	$-0.821334\pi$
$173$	−4.13373	+	4.13373i	−0.314281	+	0.314281i	0.532284	+	0.846566i	$0.321334\pi$
$174$	25.0079			1.89585
$175$	5.63294	−	11.9695i	0.425810	−	0.904812i
$176$	−15.0409			−1.13375
$177$	−16.3503	+	16.3503i	−1.22897	+	1.22897i
$178$	−21.9701	+	21.9701i	−1.64673	+	1.64673i
$179$		−	10.7040i		−	0.800054i	−0.916503	−	0.400027i	$-0.869001\pi$
$179$		−	10.7040i		−	0.800054i	0.916503	−	0.400027i	$-0.130999\pi$
$180$	−2.20558	+	17.6382i	−0.164394	+	1.31467i
$181$		−	3.52721i		−	0.262176i	−0.991371	−	0.131088i	$-0.958153\pi$
$181$		−	3.52721i		−	0.262176i	0.991371	−	0.131088i	$-0.0418470\pi$
$182$	−22.7822	−	4.40647i	−1.68873	−	0.326629i
$183$	−16.0229	−	16.0229i	−1.18445	−	1.18445i
$184$			1.05859i			0.0780406i
$185$	5.83261	+	7.49976i	0.428822	+	0.551393i
$186$	8.97443			0.658037
$187$	21.6578	+	21.6578i	1.58377	+	1.58377i
$188$	−12.8530	+	12.8530i	−0.937400	+	0.937400i
$189$	0.986211	−	0.666541i	0.0717363	−	0.0484837i
$190$	6.84530	+	8.80192i	0.496610	+	0.638558i
$191$	21.9902			1.59115			0.795577	−	0.605853i	$-0.207168\pi$
$191$	21.9902			1.59115			0.795577	+	0.605853i	$0.207168\pi$
$192$	−19.9885	−	19.9885i	−1.44254	−	1.44254i
$193$	−0.204250	−	0.204250i	−0.0147022	−	0.0147022i	0.699717	−	0.714420i	$-0.253309\pi$
$193$	−0.204250	−	0.204250i	−0.0147022	−	0.0147022i	−0.714420	+	0.699717i	$0.753309\pi$
$194$	−22.6867			−1.62881
$195$	−22.8089	−	2.85215i	−1.63338	−	0.204247i
$196$	−6.52307	+	16.2319i	−0.465933	+	1.15942i
$197$	−5.29465	+	5.29465i	−0.377228	+	0.377228i	−0.870101	−	0.492873i	$-0.835947\pi$
$197$	−5.29465	+	5.29465i	−0.377228	+	0.377228i	0.492873	+	0.870101i	$0.335947\pi$
$198$	−26.0682	−	26.0682i	−1.85259	−	1.85259i
$199$	−11.3300			−0.803160			−0.401580	−	0.915824i	$-0.631539\pi$
$199$	−11.3300			−0.803160			−0.401580	+	0.915824i	$0.631539\pi$
$200$	−2.70585	−	4.54906i	−0.191333	−	0.321667i
$201$			26.4077i			1.86266i
$202$	11.2067	+	11.2067i	0.788497	+	0.788497i
$203$	12.3186	+	2.38263i	0.864597	+	0.167228i
$204$			34.8282i			2.43846i
$205$	−19.0263	−	2.37915i	−1.32885	−	0.166167i
$206$			14.7899i			1.03046i
$207$	2.24928	−	2.24928i	0.156336	−	0.156336i
$208$	8.04850	−	8.04850i	0.558063	−	0.558063i
$209$	−12.8455			−0.888541
$210$	−9.67916	+	29.6583i	−0.667926	+	2.04662i
$211$	10.3977			0.715806			0.357903	−	0.933759i	$-0.383492\pi$
$211$	10.3977			0.715806			0.357903	+	0.933759i	$0.383492\pi$
$212$	22.4873	−	22.4873i	1.54443	−	1.54443i
$213$	−1.79730	+	1.79730i	−0.123149	+	0.123149i
$214$		−	4.36672i		−	0.298503i
$215$	−17.5221	+	13.6270i	−1.19499	+	0.929354i
$216$		−	0.476265i		−	0.0324057i
$217$	4.42070	+	0.855038i	0.300097	+	0.0580438i
$218$	19.0097	+	19.0097i	1.28750	+	1.28750i
$219$		−	13.4967i		−	0.912025i
$220$	30.2971	+	3.78852i	2.04263	+	0.255422i
$221$	−23.1784			−1.55915
$222$	−15.8435	−	15.8435i	−1.06335	−	1.06335i
$223$	−10.7394	+	10.7394i	−0.719161	+	0.719161i	−0.968433	−	0.249272i	$-0.919809\pi$
$223$	−10.7394	+	10.7394i	−0.719161	+	0.719161i	0.249272	+	0.968433i	$0.419809\pi$
$224$	−11.7871	−	17.4402i	−0.787560	−	1.16527i
$225$	−3.91641	+	15.4151i	−0.261094	+	1.02767i
$226$	−28.6571			−1.90624
$227$	6.13651	+	6.13651i	0.407294	+	0.407294i	0.880794	−	0.473500i	$-0.157010\pi$
$227$	6.13651	+	6.13651i	0.407294	+	0.407294i	−0.473500	+	0.880794i	$0.657010\pi$
$228$	−10.3285	−	10.3285i	−0.684022	−	0.684022i
$229$	6.24110			0.412424			0.206212	−	0.978507i	$-0.433886\pi$
$229$	6.24110			0.412424			0.206212	+	0.978507i	$0.433886\pi$
$230$	−0.588499	+	4.70628i	−0.0388045	+	0.310323i
$231$	−20.1253	−	29.7773i	−1.32415	−	1.95920i
$232$	3.54979	−	3.54979i	0.233055	−	0.233055i
$233$	−4.35986	−	4.35986i	−0.285624	−	0.285624i	0.549723	−	0.835347i	$-0.314733\pi$
$233$	−4.35986	−	4.35986i	−0.285624	−	0.285624i	−0.835347	+	0.549723i	$0.814733\pi$
$234$	27.8985			1.82378
$235$	−12.8384	+	9.98448i	−0.837483	+	0.651316i
$236$			23.2430i			1.51299i
$237$	17.0555	+	17.0555i	1.10787	+	1.10787i
$238$	−5.97383	+	30.8858i	−0.387226	+	2.00203i
$239$			9.47916i			0.613156i	0.951846	+	0.306578i	$0.0991840\pi$
$239$			9.47916i			0.613156i	−0.951846	+	0.306578i	$0.900816\pi$
$240$	−9.39472	−	12.0800i	−0.606426	−	0.779763i
$241$		−	2.75940i		−	0.177749i	−0.996043	−	0.0888744i	$-0.971673\pi$
$241$		−	2.75940i		−	0.177749i	0.996043	−	0.0888744i	$-0.0283270\pi$
$242$	−28.2790	+	28.2790i	−1.81784	+	1.81784i
$243$	15.7642	−	15.7642i	1.01128	−	1.01128i
$244$	−22.7776			−1.45819
$245$	−7.59353	+	13.6872i	−0.485133	+	0.874440i
$246$	45.2197			2.88310
$247$	6.87369	−	6.87369i	0.437363	−	0.437363i
$248$	1.27389	−	1.27389i	0.0808921	−	0.0808921i
$249$			24.2050i			1.53393i
$250$	−9.50068	−	21.7284i	−0.600876	−	1.37422i
$251$			0.820683i			0.0518010i	0.999665	+	0.0259005i	$0.00824531\pi$
$251$			0.820683i			0.0518010i	−0.999665	+	0.0259005i	$0.991755\pi$
$252$	3.99399	−	20.6496i	0.251598	−	1.30080i
$253$	−3.86359	−	3.86359i	−0.242902	−	0.242902i
$254$			21.4106i			1.34342i
$255$	−3.86665	+	30.9219i	−0.242139	+	1.93641i
$256$	5.33648			0.333530
$257$	−4.43475	−	4.43475i	−0.276632	−	0.276632i	0.555131	−	0.831763i	$-0.312668\pi$
$257$	−4.43475	−	4.43475i	−0.276632	−	0.276632i	−0.831763	+	0.555131i	$0.812668\pi$
$258$	37.0159	−	37.0159i	2.30451	−	2.30451i
$259$	−6.29483	−	9.31381i	−0.391142	−	0.578732i
$260$	−18.2394	+	14.1849i	−1.13116	+	0.879711i
$261$	−15.0851			−0.933741
$262$	20.5034	+	20.5034i	1.26670	+	1.26670i
$263$	−17.9979	−	17.9979i	−1.10980	−	1.10980i	−0.993176	−	0.116623i	$-0.962793\pi$
$263$	−17.9979	−	17.9979i	−1.10980	−	1.10980i	−0.116623	−	0.993176i	$-0.537207\pi$
$264$	−14.3802			−0.885037
$265$	22.4617	−	17.4686i	1.37981	−	1.07309i
$266$	−7.38779	−	10.9309i	−0.452974	−	0.670219i
$267$	25.7512	−	25.7512i	1.57595	−	1.57595i
$268$	18.7701	+	18.7701i	1.14657	+	1.14657i
$269$	−2.00033			−0.121962			−0.0609811	−	0.998139i	$-0.519423\pi$
$269$	−2.00033			−0.121962			−0.0609811	+	0.998139i	$0.519423\pi$
$270$	0.264767	−	2.11737i	0.0161132	−	0.128859i
$271$			4.64097i			0.281919i	0.990015	+	0.140960i	$0.0450187\pi$
$271$			4.64097i			0.281919i	−0.990015	+	0.140960i	$0.954981\pi$
$272$	−10.9113	−	10.9113i	−0.661596	−	0.661596i
$273$	26.7031	+	5.16484i	1.61615	+	0.312590i
$274$			9.73198i			0.587930i
$275$	26.4785	+	6.72722i	1.59671	+	0.405667i
$276$		−	6.21309i		−	0.373984i
$277$	13.9263	−	13.9263i	0.836752	−	0.836752i	−0.151678	−	0.988430i	$-0.548468\pi$
$277$	13.9263	−	13.9263i	0.836752	−	0.836752i	0.988430	+	0.151678i	$0.0484675\pi$
$278$	−6.58723	+	6.58723i	−0.395076	+	0.395076i
$279$	−5.41347			−0.324096
$280$	2.83597	+	5.58382i	0.169482	+	0.333697i
$281$	24.2518			1.44674			0.723370	−	0.690461i	$-0.242592\pi$
$281$	24.2518			1.44674			0.723370	+	0.690461i	$0.242592\pi$
$282$	27.1215	−	27.1215i	1.61506	−	1.61506i
$283$	6.29920	−	6.29920i	0.374449	−	0.374449i	−0.494646	−	0.869095i	$-0.664702\pi$
$283$	6.29920	−	6.29920i	0.374449	−	0.374449i	0.869095	+	0.494646i	$0.164702\pi$
$284$			2.55499i			0.151610i
$285$	−8.02341	−	10.3168i	−0.475266	−	0.611113i
$286$		−	47.9212i		−	2.83364i
$287$	22.2747	+	4.30830i	1.31483	+	0.254311i
$288$	17.8955	+	17.8955i	1.05450	+	1.05450i
$289$			14.4228i			0.848402i
$290$	17.7550	−	13.8082i	1.04261	−	0.810844i
$291$	26.5912			1.55880
$292$	−9.59324	−	9.59324i	−0.561402	−	0.561402i
$293$	−2.28857	+	2.28857i	−0.133700	+	0.133700i	−0.770790	−	0.637090i	$-0.780138\pi$
$293$	−2.28857	+	2.28857i	−0.133700	+	0.133700i	0.637090	+	0.770790i	$0.280138\pi$
$294$	13.7645	−	34.2514i	0.802764	−	1.99758i
$295$	−2.58046	+	20.6362i	−0.150240	+	1.20148i
$296$	−4.49786			−0.261433
$297$	1.73824	+	1.73824i	0.100863	+	0.100863i
$298$	21.1975	+	21.1975i	1.22794	+	1.22794i
$299$	4.13486			0.239125
$300$	15.8811	+	26.6993i	0.916898	+	1.54148i
$301$	21.7603	−	14.7069i	1.25424	−	0.847693i
$302$	−16.0949	+	16.0949i	−0.926155	+	0.926155i
$303$	−13.1354	−	13.1354i	−0.754607	−	0.754607i
$304$	6.47163			0.371174
$305$	−20.2230	−	2.52879i	−1.15796	−	0.144798i
$306$		−	37.8219i		−	2.16213i
$307$	16.2737	+	16.2737i	0.928792	+	0.928792i	0.997628	−	0.0688364i	$-0.0219287\pi$
$307$	16.2737	+	16.2737i	0.928792	+	0.928792i	−0.0688364	+	0.997628i	$0.521929\pi$
$308$	−35.4698	−	6.86047i	−2.02108	−	0.390911i
$309$		−	17.3354i		−	0.986174i
$310$	6.37162	−	4.95525i	0.361884	−	0.281439i
$311$			0.604612i			0.0342844i	0.999853	+	0.0171422i	$0.00545680\pi$
$311$			0.604612i			0.0342844i	−0.999853	+	0.0171422i	$0.994543\pi$
$312$	7.69491	−	7.69491i	0.435638	−	0.435638i
$313$	0.458911	−	0.458911i	0.0259392	−	0.0259392i	−0.694018	−	0.719957i	$-0.744161\pi$
$313$	0.458911	−	0.458911i	0.0259392	−	0.0259392i	0.719957	+	0.694018i	$0.244161\pi$
$314$	−25.0005			−1.41086
$315$	5.83857	−	17.8902i	0.328966	−	1.00800i
$316$	24.2455			1.36391
$317$	−17.4912	+	17.4912i	−0.982406	+	0.982406i	−0.999848	−	0.0174423i	$-0.994448\pi$
$317$	−17.4912	+	17.4912i	−0.982406	+	0.982406i	0.0174423	+	0.999848i	$0.494448\pi$
$318$	−47.4511	+	47.4511i	−2.66093	+	2.66093i
$319$			25.9116i			1.45077i
$320$	−25.2280	−	3.15464i	−1.41029	−	0.176350i
$321$			5.11825i			0.285673i
$322$	1.06569	−	5.50980i	0.0593885	−	0.307049i
$323$	−9.31863	−	9.31863i	−0.518503	−	0.518503i
$324$		−	21.0531i		−	1.16962i
$325$	−17.7686	+	10.5690i	−0.985623	+	0.586263i
$326$	3.56062			0.197204
$327$	−22.2814	−	22.2814i	−1.23216	−	1.23216i
$328$	6.41878	−	6.41878i	0.354418	−	0.354418i
$329$	15.9437	−	10.7757i	0.879007	−	0.594086i
$330$	−63.9310	−	7.99429i	−3.51929	−	0.440071i
$331$	−11.4347			−0.628509			−0.314255	−	0.949339i	$-0.601755\pi$
$331$	−11.4347			−0.628509			−0.314255	+	0.949339i	$0.601755\pi$
$332$	17.2045	+	17.2045i	0.944221	+	0.944221i
$333$	9.55696	+	9.55696i	0.523718	+	0.523718i
$334$	−43.7349			−2.39307
$335$	14.5810	+	18.7488i	0.796648	+	1.02436i
$336$	10.1392	+	15.0020i	0.553141	+	0.818425i
$337$	7.62055	−	7.62055i	0.415118	−	0.415118i	−0.468399	−	0.883517i	$-0.655169\pi$
$337$	7.62055	−	7.62055i	0.415118	−	0.415118i	0.883517	+	0.468399i	$0.155169\pi$
$338$	6.14493	+	6.14493i	0.334240	+	0.334240i
$339$	33.5891			1.82431
$340$	19.2304	+	24.7271i	1.04292	+	1.34102i
$341$			9.29871i			0.503554i
$342$	11.2163	+	11.2163i	0.606509	+	0.606509i
$343$	10.0436	−	15.5604i	0.542301	−	0.840184i
$344$		−	10.5086i		−	0.566584i
$345$	0.689783	−	5.51625i	0.0371366	−	0.296985i
$346$		−	12.3999i		−	0.666623i
$347$	−8.64885	+	8.64885i	−0.464294	+	0.464294i	−0.900060	−	0.435766i	$-0.856478\pi$
$347$	−8.64885	+	8.64885i	−0.464294	+	0.464294i	0.435766	+	0.900060i	$0.356478\pi$
$348$	−20.8344	+	20.8344i	−1.11684	+	1.11684i
$349$	7.30774			0.391174			0.195587	−	0.980686i	$-0.437339\pi$
$349$	7.30774			0.391174			0.195587	+	0.980686i	$0.437339\pi$
$350$	9.50393	+	26.4010i	0.508006	+	1.41119i
$351$	−1.86028			−0.0992946
$352$	30.7391	−	30.7391i	1.63840	−	1.63840i
$353$	9.53049	−	9.53049i	0.507257	−	0.507257i	−0.406427	−	0.913683i	$-0.633225\pi$
$353$	9.53049	−	9.53049i	0.507257	−	0.507257i	0.913683	+	0.406427i	$0.133225\pi$
$354$		−	49.0459i		−	2.60676i
$355$	−0.283657	+	2.26843i	−0.0150549	+	0.120396i
$356$		−	36.6070i		−	1.94017i
$357$	7.00195	−	36.2013i	0.370582	−	1.91598i
$358$	16.0543	+	16.0543i	0.848498	+	0.848498i
$359$			7.49263i			0.395446i	0.980258	+	0.197723i	$0.0633546\pi$
$359$			7.49263i			0.395446i	−0.980258	+	0.197723i	$0.936645\pi$
$360$	−4.62248	−	5.94373i	−0.243626	−	0.313262i
$361$	−13.4730			−0.709105
$362$	5.29028	+	5.29028i	0.278051	+	0.278051i
$363$	33.1460	−	33.1460i	1.73971	−	1.73971i
$364$	22.6512	−	15.3090i	1.18725	−	0.802412i
$365$	−7.45224	−	9.58234i	−0.390068	−	0.501563i
$366$	48.0639			2.51234
$367$	−17.7571	−	17.7571i	−0.926911	−	0.926911i	0.0705939	−	0.997505i	$-0.477511\pi$
$367$	−17.7571	−	17.7571i	−0.926911	−	0.926911i	−0.997505	+	0.0705939i	$0.977511\pi$
$368$	1.94650	+	1.94650i	0.101468	+	0.101468i
$369$	−27.2770			−1.41998
$370$	−19.9965	−	2.50047i	−1.03957	−	0.129993i
$371$	−27.8948	+	18.8530i	−1.44822	+	0.978797i
$372$	−7.47670	+	7.47670i	−0.387649	+	0.387649i
$373$	0.927491	+	0.927491i	0.0480237	+	0.0480237i	0.730711	−	0.682687i	$-0.239189\pi$
$373$	0.927491	+	0.927491i	0.0480237	+	0.0480237i	−0.682687	+	0.730711i	$0.739189\pi$
$374$	−64.9666			−3.35934
$375$	11.1358	+	25.4679i	0.575050	+	1.31516i
$376$		−	7.69961i		−	0.397077i
$377$	−13.8654	−	13.8654i	−0.714106	−	0.714106i
$378$	−0.479456	+	2.47887i	−0.0246606	+	0.127499i
$379$			9.07840i			0.466326i	0.972438	+	0.233163i	$0.0749076\pi$
$379$			9.07840i			0.466326i	−0.972438	+	0.233163i	$0.925092\pi$
$380$	−13.0359	−	1.63008i	−0.668726	−	0.0836213i
$381$		−	25.0955i		−	1.28568i
$382$	−32.9819	+	32.9819i	−1.68750	+	1.68750i
$383$	7.42961	−	7.42961i	0.379635	−	0.379635i	−0.491335	−	0.870970i	$-0.663491\pi$
$383$	7.42961	−	7.42961i	0.379635	−	0.379635i	0.870970	+	0.491335i	$0.163491\pi$
$384$	20.3991			1.04099
$385$	−30.7300	−	10.0289i	−1.56615	−	0.511121i
$386$	0.612686			0.0311849
$387$	−22.3284	+	22.3284i	−1.13502	+	1.13502i
$388$	18.9005	−	18.9005i	0.959530	−	0.959530i
$389$			3.17676i			0.161068i	0.996752	+	0.0805341i	$0.0256626\pi$
$389$			3.17676i			0.161068i	−0.996752	+	0.0805341i	$0.974337\pi$
$390$	38.4876	−	29.9321i	1.94890	−	1.51567i
$391$		−	5.60561i		−	0.283488i
$392$	−2.90804	−	6.81570i	−0.146878	−	0.344245i
$393$	−24.0321	−	24.0321i	−1.21226	−	1.21226i
$394$		−	15.8823i		−	0.800140i
$395$	21.5262	+	2.69175i	1.08310	+	0.135437i
$396$	43.4354			2.18271
$397$	−0.721827	−	0.721827i	−0.0362274	−	0.0362274i	0.688761	−	0.724988i	$-0.258155\pi$
$397$	−0.721827	−	0.721827i	−0.0362274	−	0.0362274i	−0.724988	+	0.688761i	$0.758155\pi$
$398$	16.9932	−	16.9932i	0.851793	−	0.851793i
$399$	8.65926	+	12.8122i	0.433505	+	0.641412i
$400$	−13.3400	−	3.38922i	−0.667001	−	0.169461i
$401$	17.9170			0.894732			0.447366	−	0.894351i	$-0.352362\pi$
$401$	17.9170			0.894732			0.447366	+	0.894351i	$0.352362\pi$
$402$	−39.6075	−	39.6075i	−1.97544	−	1.97544i
$403$	−4.97580	−	4.97580i	−0.247862	−	0.247862i
$404$	−18.6728			−0.929005
$405$	2.33734	−	18.6919i	0.116143	−	0.928807i
$406$	−22.0496	+	14.9025i	−1.09430	+	0.739596i
$407$	16.4160	−	16.4160i	0.813710	−	0.813710i
$408$	−10.4319	−	10.4319i	−0.516458	−	0.516458i
$409$	−11.7347			−0.580243			−0.290121	−	0.956990i	$-0.593696\pi$
$409$	−11.7347			−0.580243			−0.290121	+	0.956990i	$0.593696\pi$
$410$	32.1049	−	24.9681i	1.58555	−	1.23309i
$411$		−	11.4069i		−	0.562661i
$412$	−12.3217	−	12.3217i	−0.607045	−	0.607045i
$413$	4.67284	−	24.1594i	0.229936	−	1.18881i
$414$			6.74715i			0.331604i
$415$	13.3649	+	17.1850i	0.656055	+	0.843577i
$416$			32.8973i			1.61292i
$417$	7.72092	−	7.72092i	0.378095	−	0.378095i
$418$	19.2662	−	19.2662i	0.942343	−	0.942343i
$419$	17.3094			0.845617			0.422809	−	0.906219i	$-0.361044\pi$
$419$	17.3094			0.845617			0.422809	+	0.906219i	$0.361044\pi$
$420$	−16.6449	−	32.7725i	−0.812186	−	1.59913i
$421$	−36.5210			−1.77992			−0.889961	−	0.456036i	$-0.849269\pi$
$421$	−36.5210			−1.77992			−0.889961	+	0.456036i	$0.849269\pi$
$422$	−15.5949	+	15.5949i	−0.759149	+	0.759149i
$423$	−16.3600	+	16.3600i	−0.795449	+	0.795449i
$424$			13.4711i			0.654212i
$425$	14.3284	+	24.0888i	0.695028	+	1.16848i
$426$		−	5.39136i		−	0.261212i
$427$	23.6757	+	4.57928i	1.14575	+	0.221607i
$428$	3.63797	+	3.63797i	0.175848	+	0.175848i
$429$			56.1687i			2.71185i
$430$	5.84198	−	46.7188i	0.281725	−	2.25298i
$431$	−23.7702			−1.14497			−0.572484	−	0.819916i	$-0.694020\pi$
$431$	−23.7702			−1.14497			−0.572484	+	0.819916i	$0.694020\pi$
$432$	−0.875736	−	0.875736i	−0.0421339	−	0.0421339i
$433$	−27.5738	+	27.5738i	−1.32511	+	1.32511i	−0.415539	+	0.909576i	$0.636407\pi$
$433$	−27.5738	+	27.5738i	−1.32511	+	1.32511i	−0.909576	+	0.415539i	$0.863593\pi$
$434$	−7.91279	+	5.34794i	−0.379826	+	0.256709i
$435$	−20.8107	+	16.1846i	−0.997798	+	0.775993i
$436$	−31.6744			−1.51693
$437$	1.66238	+	1.66238i	0.0795223	+	0.0795223i
$438$	20.2430	+	20.2430i	0.967249	+	0.967249i
$439$	12.8939			0.615393			0.307696	−	0.951485i	$-0.400442\pi$
$439$	12.8939			0.615393			0.307696	+	0.951485i	$0.400442\pi$
$440$	−10.2095	+	7.94002i	−0.486721	+	0.378526i
$441$	−8.30292	+	20.6608i	−0.395377	+	0.983849i
$442$	34.7640	−	34.7640i	1.65356	−	1.65356i
$443$	−3.81406	−	3.81406i	−0.181211	−	0.181211i	0.610672	−	0.791884i	$-0.290899\pi$
$443$	−3.81406	−	3.81406i	−0.181211	−	0.181211i	−0.791884	+	0.610672i	$0.790899\pi$
$444$	26.3988			1.25283
$445$	4.06414	−	32.5013i	0.192659	−	1.54071i
$446$		−	32.2148i		−	1.52542i
$447$	−24.8457	−	24.8457i	−1.17516	−	1.17516i
$448$	29.5352	+	5.71261i	1.39541	+	0.269895i
$449$		−	19.4935i		−	0.919953i	−0.887931	−	0.459977i	$-0.847858\pi$
$449$		−	19.4935i		−	0.919953i	0.887931	−	0.459977i	$-0.152142\pi$
$450$	−17.2462	−	28.9943i	−0.812996	−	1.36680i
$451$			46.8537i			2.20625i
$452$	23.8745	−	23.8745i	1.12296	−	1.12296i
$453$	18.8649	−	18.8649i	0.886348	−	0.886348i
$454$	−18.4076			−0.863913
$455$	21.8103	−	11.0773i	1.02248	−	0.519311i
$456$	6.18732			0.289748
$457$	−0.461167	+	0.461167i	−0.0215725	+	0.0215725i	−0.717811	−	0.696238i	$-0.754856\pi$
$457$	−0.461167	+	0.461167i	−0.0215725	+	0.0215725i	0.696238	+	0.717811i	$0.254856\pi$
$458$	−9.36070	+	9.36070i	−0.437397	+	0.437397i
$459$			2.52198i			0.117716i
$460$	−3.43057	−	4.41114i	−0.159951	−	0.205670i
$461$		−	13.2565i		−	0.617417i	−0.951157	−	0.308709i	$-0.900103\pi$
$461$		−	13.2565i		−	0.617417i	0.951157	−	0.308709i	$-0.0998968\pi$
$462$	74.8461	+	14.4765i	3.48216	+	0.673508i
$463$	19.2417	+	19.2417i	0.894238	+	0.894238i	0.994919	−	0.100681i	$-0.0321022\pi$
$463$	19.2417	+	19.2417i	0.894238	+	0.894238i	−0.100681	+	0.994919i	$0.532102\pi$
$464$		−	13.0544i		−	0.606036i
$465$	−7.46820	+	5.80807i	−0.346330	+	0.269343i
$466$	13.0782			0.605837
$467$	−3.32523	−	3.32523i	−0.153873	−	0.153873i	0.625972	−	0.779845i	$-0.284702\pi$
$467$	−3.32523	−	3.32523i	−0.153873	−	0.153873i	−0.779845	+	0.625972i	$0.784702\pi$
$468$	−23.2426	+	23.2426i	−1.07439	+	1.07439i
$469$	−15.7366	−	23.2838i	−0.726648	−	1.07514i
$470$	4.28041	−	34.2308i	0.197440	−	1.57895i
$471$	29.3032			1.35022
$472$	−6.96190	−	6.96190i	−0.320448	−	0.320448i
$473$	38.3535	+	38.3535i	1.76349	+	1.76349i
$474$	−51.1612			−2.34991
$475$	−11.3928	−	2.89451i	−0.522739	−	0.132809i
$476$	−20.7544	−	30.7081i	−0.951277	−	1.40750i
$477$	28.6230	−	28.6230i	1.31056	−	1.31056i
$478$	−14.2173	−	14.2173i	−0.650283	−	0.650283i
$479$	8.10066			0.370128			0.185064	−	0.982726i	$-0.440751\pi$
$479$	8.10066			0.370128			0.185064	+	0.982726i	$0.440751\pi$
$480$	43.8878	+	5.48797i	2.00319	+	0.250491i
$481$			17.5686i			0.801059i
$482$	4.13868	+	4.13868i	0.188512	+	0.188512i
$483$	−1.24910	+	6.45806i	−0.0568359	+	0.293852i
$484$		−	47.1192i		−	2.14178i
$485$	18.8791	−	14.6824i	0.857254	−	0.666692i
$486$			47.2878i			2.14502i
$487$	8.06395	−	8.06395i	0.365412	−	0.365412i	−0.500389	−	0.865801i	$-0.666809\pi$
$487$	8.06395	−	8.06395i	0.365412	−	0.365412i	0.865801	+	0.500389i	$0.166809\pi$
$488$	6.82250	−	6.82250i	0.308840	−	0.308840i
$489$	−4.17341			−0.188728
$490$	−9.13950	−	31.9178i	−0.412880	−	1.44190i
$491$	38.5724			1.74075			0.870375	−	0.492390i	$-0.163877\pi$
$491$	38.5724			1.74075			0.870375	+	0.492390i	$0.163877\pi$
$492$	−37.6730	+	37.6730i	−1.69843	+	1.69843i
$493$	−18.7973	+	18.7973i	−0.846588	+	0.846588i
$494$			20.6190i			0.927691i
$495$	38.5638	+	4.82224i	1.73332	+	0.216743i
$496$		−	4.68475i		−	0.210352i
$497$	0.513661	−	2.65572i	0.0230409	−	0.119125i
$498$	−36.3038	−	36.3038i	−1.62681	−	1.62681i
$499$			9.53903i			0.427026i	0.976940	+	0.213513i	$0.0684905\pi$
$499$			9.53903i			0.427026i	−0.976940	+	0.213513i	$0.931509\pi$
$500$	26.0173	+	10.1870i	1.16353	+	0.455578i
$501$	51.2619			2.29021
$502$	−1.23090	−	1.23090i	−0.0549377	−	0.0549377i
$503$	2.24839	−	2.24839i	0.100251	−	0.100251i	−0.655203	−	0.755453i	$-0.727417\pi$
$503$	2.24839	−	2.24839i	0.100251	−	0.100251i	0.755453	+	0.655203i	$0.227417\pi$
$504$	4.98880	+	7.38141i	0.222219	+	0.328794i
$505$	−16.5785	−	2.07307i	−0.737733	−	0.0922502i
$506$	11.5896			0.515219
$507$	−7.20250	−	7.20250i	−0.319874	−	0.319874i
$508$	−17.8374	−	17.8374i	−0.791407	−	0.791407i
$509$	−30.1275			−1.33538			−0.667690	−	0.744439i	$-0.732717\pi$
$509$	−30.1275			−1.33538			−0.667690	+	0.744439i	$0.732717\pi$
$510$	−40.5788	−	52.1775i	−1.79686	−	2.31046i
$511$	8.04283	+	11.9001i	0.355794	+	0.526431i
$512$	−19.6076	+	19.6076i	−0.866543	+	0.866543i
$513$	−0.747908	−	0.747908i	−0.0330210	−	0.0330210i
$514$	13.3029			0.586765
$515$	−9.57174	−	12.3077i	−0.421781	−	0.542340i
$516$			61.6768i			2.71517i
$517$	28.1015	+	28.1015i	1.23590	+	1.23590i
$518$	23.4106	+	4.52800i	1.02860	+	0.198949i
$519$			14.5340i			0.637971i
$520$	1.21444	−	9.71194i	0.0532565	−	0.425897i
$521$			11.9379i			0.523008i	0.965202	+	0.261504i	$0.0842184\pi$
$521$			11.9379i			0.523008i	−0.965202	+	0.261504i	$0.915782\pi$
$522$	22.6253	−	22.6253i	0.990281	−	0.990281i
$523$	20.4563	−	20.4563i	0.894489	−	0.894489i	−0.100452	−	0.994942i	$-0.532029\pi$
$523$	20.4563	−	20.4563i	0.894489	−	0.894489i	0.994942	+	0.100452i	$0.0320290\pi$
$524$	−34.1632			−1.49242
$525$	−11.1396	−	30.9448i	−0.486172	−	1.35054i
$526$	53.9882			2.35400
$527$	−6.74567	+	6.74567i	−0.293846	+	0.293846i
$528$	−26.4416	+	26.4416i	−1.15072	+	1.15072i
$529$			1.00000i			0.0434783i
$530$	−7.48889	+	59.8893i	−0.325297	+	2.60143i
$531$			29.5850i			1.28388i
$532$	15.2615	+	2.95184i	0.661671	+	0.127978i
$533$	−25.0717	−	25.0717i	−1.08598	−	1.08598i
$534$			77.2457i			3.34275i
$535$	2.82605	+	3.63383i	0.122181	+	0.157104i
$536$	−11.2443			−0.485679
$537$	−18.8174	−	18.8174i	−0.812029	−	0.812029i
$538$	3.00019	−	3.00019i	0.129347	−	0.129347i
$539$	35.4891	+	14.2619i	1.52862	+	0.614304i
$540$	1.54342	+	1.98458i	0.0664183	+	0.0854029i
$541$	1.80848			0.0777527			0.0388764	−	0.999244i	$-0.487622\pi$
$541$	1.80848			0.0777527			0.0388764	+	0.999244i	$0.487622\pi$
$542$	−6.96075	−	6.96075i	−0.298990	−	0.298990i
$543$	−6.20076	−	6.20076i	−0.266100	−	0.266100i
$544$	44.5987			1.91215
$545$	−28.1219	−	3.51652i	−1.20461	−	0.150631i
$546$	−47.7971	+	32.3041i	−2.04553	+	1.38249i
$547$	−11.2022	+	11.2022i	−0.478970	+	0.478970i	−0.904802	−	0.425832i	$-0.859981\pi$
$547$	−11.2022	+	11.2022i	−0.478970	+	0.478970i	0.425832	+	0.904802i	$0.359981\pi$
$548$	−8.10782	−	8.10782i	−0.346349	−	0.346349i
$549$	−28.9926			−1.23738
$550$	−49.8034	+	29.6239i	−2.12363	+	1.26317i
$551$		−	11.1489i		−	0.474960i
$552$	1.86098	+	1.86098i	0.0792088	+	0.0792088i
$553$	−25.2014	−	4.87437i	−1.07167	−	0.207279i
$554$			41.7747i			1.77484i
$555$	23.4380	+	2.93082i	0.994887	+	0.124406i
$556$		−	10.9758i		−	0.465477i
$557$	3.66717	−	3.66717i	0.155383	−	0.155383i	−0.625134	−	0.780517i	$-0.714956\pi$
$557$	3.66717	−	3.66717i	0.155383	−	0.155383i	0.780517	+	0.625134i	$0.214956\pi$
$558$	8.11937	−	8.11937i	0.343721	−	0.343721i
$559$	−41.0463			−1.73608
$560$	15.4820	+	5.05263i	0.654232	+	0.213512i
$561$	76.1476			3.21496
$562$	−36.3739	+	36.3739i	−1.53434	+	1.53434i
$563$	30.7561	−	30.7561i	1.29622	−	1.29622i	0.365341	−	0.930874i	$-0.380952\pi$
$563$	30.7561	−	30.7561i	1.29622	−	1.29622i	0.930874	−	0.365341i	$-0.119048\pi$
$564$			45.1905i			1.90286i
$565$	23.8474	−	18.5463i	1.00327	−	0.780248i
$566$			18.8957i			0.794244i
$567$	−4.23258	+	21.8832i	−0.177752	+	0.919008i
$568$	−0.765285	−	0.765285i	−0.0321107	−	0.0321107i
$569$			45.8253i			1.92110i	0.278114	+	0.960548i	$0.410291\pi$
$569$			45.8253i			1.92110i	−0.278114	+	0.960548i	$0.589709\pi$
$570$	27.5074	+	3.43968i	1.15216	+	0.144073i
$571$	−36.0464			−1.50849			−0.754247	−	0.656590i	$-0.771998\pi$
$571$	−36.0464			−1.50849			−0.754247	+	0.656590i	$0.771998\pi$
$572$	39.9237	+	39.9237i	1.66929	+	1.66929i
$573$	38.6582	−	38.6582i	1.61497	−	1.61497i
$574$	−39.8704	+	26.9468i	−1.66416	+	1.12474i
$575$	−2.55608	−	4.29726i	−0.106596	−	0.179208i
$576$	−36.1680			−1.50700
$577$	−10.2740	−	10.2740i	−0.427712	−	0.427712i	0.460136	−	0.887848i	$-0.347801\pi$
$577$	−10.2740	−	10.2740i	−0.427712	−	0.427712i	−0.887848	+	0.460136i	$0.847801\pi$
$578$	−21.6320	−	21.6320i	−0.899774	−	0.899774i
$579$	−0.718132			−0.0298446
$580$	−3.28815	+	26.2956i	−0.136533	+	1.09187i
$581$	−14.4240	−	21.3417i	−0.598408	−	0.885403i
$582$	−39.8827	+	39.8827i	−1.65319	+	1.65319i
$583$	−49.1657	−	49.1657i	−2.03624	−	2.03624i
$584$	5.74686			0.237807
$585$	−23.2161	+	18.0553i	−0.959870	+	0.746496i
$586$		−	6.86501i		−	0.283591i
$587$	−10.5298	−	10.5298i	−0.434611	−	0.434611i	0.455582	−	0.890194i	$-0.349431\pi$
$587$	−10.5298	−	10.5298i	−0.434611	−	0.434611i	−0.890194	+	0.455582i	$0.849431\pi$
$588$	17.0679	+	40.0026i	0.703866	+	1.64968i
$589$		−	4.00094i		−	0.164856i
$590$	−27.0808	−	34.8214i	−1.11490	−	1.43357i
$591$			18.6157i			0.765749i
$592$	−8.27048	+	8.27048i	−0.339915	+	0.339915i
$593$	−12.2692	+	12.2692i	−0.503836	+	0.503836i	−0.912628	−	0.408791i	$-0.865950\pi$
$593$	−12.2692	+	12.2692i	−0.503836	+	0.503836i	0.408791	+	0.912628i	$0.365950\pi$
$594$	−5.21418			−0.213941
$595$	−15.0174	−	29.5682i	−0.615654	−	1.21218i
$596$	−35.3197			−1.44675
$597$	−19.9178	+	19.9178i	−0.815182	+	0.815182i
$598$	−6.20165	+	6.20165i	−0.253604	+	0.253604i
$599$			2.48130i			0.101383i	0.998714	+	0.0506917i	$0.0161426\pi$
$599$			2.48130i			0.101383i	−0.998714	+	0.0506917i	$0.983857\pi$
$600$	−12.7540	−	3.24032i	−0.520678	−	0.132285i
$601$			8.61072i			0.351239i	0.984458	+	0.175619i	$0.0561928\pi$
$601$			8.61072i			0.351239i	−0.984458	+	0.175619i	$0.943807\pi$
$602$	−10.5790	+	54.6952i	−0.431167	+	2.22921i
$603$	23.8916	+	23.8916i	0.972943	+	0.972943i
$604$		−	26.8176i		−	1.09119i
$605$	5.23121	−	41.8344i	0.212679	−	1.70081i
$606$	39.4021			1.60060
$607$	−7.02880	−	7.02880i	−0.285290	−	0.285290i	0.549924	−	0.835214i	$-0.314657\pi$
$607$	−7.02880	−	7.02880i	−0.285290	−	0.285290i	−0.835214	+	0.549924i	$0.814657\pi$
$608$	−13.2260	+	13.2260i	−0.536386	+	0.536386i
$609$	25.8444	−	17.4672i	1.04727	−	0.707808i
$610$	34.1241	−	26.5385i	1.38165	−	1.07451i
$611$	−30.0746			−1.21669
$612$	31.5098	+	31.5098i	1.27371	+	1.27371i
$613$	−21.2341	−	21.2341i	−0.857636	−	0.857636i	0.133423	−	0.991059i	$-0.457403\pi$
$613$	−21.2341	−	21.2341i	−0.857636	−	0.857636i	−0.991059	+	0.133423i	$0.957403\pi$
$614$	−48.8162			−1.97006
$615$	−37.6302	+	29.2653i	−1.51740	+	1.18009i
$616$	12.6790	−	8.56926i	0.510853	−	0.345265i
$617$	14.5680	−	14.5680i	0.586486	−	0.586486i	−0.350192	−	0.936678i	$-0.613884\pi$
$617$	14.5680	−	14.5680i	0.586486	−	0.586486i	0.936678	+	0.350192i	$0.113884\pi$
$618$	26.0004	+	26.0004i	1.04589	+	1.04589i
$619$	1.12180			0.0450889			0.0225444	−	0.999746i	$-0.492823\pi$
$619$	1.12180			0.0450889			0.0225444	+	0.999746i	$0.492823\pi$
$620$	−1.18000	+	9.43654i	−0.0473898	+	0.378981i
$621$		−	0.449903i		−	0.0180540i
$622$	−0.906825	−	0.906825i	−0.0363604	−	0.0363604i
$623$	−7.35958	+	38.0503i	−0.294855	+	1.52445i
$624$		−	28.2981i		−	1.13283i
$625$	21.9683	+	11.9329i	0.878731	+	0.477317i
$626$			1.37659i			0.0550197i
$627$	−22.5821	+	22.5821i	−0.901840	+	0.901840i
$628$	20.8282	−	20.8282i	0.831134	−	0.831134i
$629$	23.8177			0.949672
$630$	18.0756	+	35.5895i	0.720149	+	1.41792i
$631$	−6.50164			−0.258826			−0.129413	−	0.991591i	$-0.541309\pi$
$631$	−6.50164			−0.258826			−0.129413	+	0.991591i	$0.541309\pi$
$632$	−7.26215	+	7.26215i	−0.288873	+	0.288873i
$633$	18.2789	−	18.2789i	0.726521	−	0.726521i
$634$		−	52.4683i		−	2.08378i
$635$	−13.8565	−	17.8171i	−0.549878	−	0.707052i
$636$		−	79.0641i		−	3.13510i
$637$	−26.6220	+	11.3588i	−1.05480	+	0.450051i
$638$	−38.8634	−	38.8634i	−1.53862	−	1.53862i
$639$			3.25213i			0.128652i
$640$	14.4829	−	11.2634i	0.572485	−	0.445225i
$641$	−8.28637			−0.327292			−0.163646	−	0.986519i	$-0.552326\pi$
$641$	−8.28637			−0.327292			−0.163646	+	0.986519i	$0.552326\pi$
$642$	−7.67659	−	7.67659i	−0.302971	−	0.302971i
$643$	13.3798	−	13.3798i	0.527648	−	0.527648i	−0.392222	−	0.919871i	$-0.628294\pi$
$643$	13.3798	−	13.3798i	0.527648	−	0.527648i	0.919871	+	0.392222i	$0.128294\pi$
$644$	3.70244	+	5.47811i	0.145896	+	0.215868i
$645$	−6.84741	+	54.7593i	−0.269616	+	2.15615i
$646$	27.9530			1.09980
$647$	−1.45577	−	1.45577i	−0.0572321	−	0.0572321i	0.677911	−	0.735144i	$-0.262885\pi$
$647$	−1.45577	−	1.45577i	−0.0572321	−	0.0572321i	−0.735144	+	0.677911i	$0.762885\pi$
$648$	6.30597	+	6.30597i	0.247722	+	0.247722i
$649$	50.8182			1.99479
$650$	10.7982	−	42.5020i	0.423541	−	1.66707i
$651$	9.27462	−	6.26835i	0.363501	−	0.245676i
$652$	−2.96639	+	2.96639i	−0.116173	+	0.116173i
$653$	−7.00067	−	7.00067i	−0.273958	−	0.273958i	0.556734	−	0.830691i	$-0.312054\pi$
$653$	−7.00067	−	7.00067i	−0.273958	−	0.273958i	−0.830691	+	0.556734i	$0.812054\pi$
$654$	66.8372			2.61354
$655$	−30.3315	−	3.79282i	−1.18515	−	0.148198i
$656$		−	23.6052i		−	0.921628i
$657$	−12.2108	−	12.2108i	−0.476389	−	0.476389i
$658$	−7.75120	+	40.0751i	−0.302173	+	1.56229i
$659$			37.2812i			1.45227i	0.687553	+	0.726134i	$0.258685\pi$
$659$			37.2812i			1.45227i	−0.687553	+	0.726134i	$0.741315\pi$
$660$	59.9218	−	46.6015i	2.33245	−	1.81396i
$661$		−	27.9771i		−	1.08818i	−0.839026	−	0.544091i	$-0.816875\pi$
$661$		−	27.9771i		−	1.08818i	0.839026	−	0.544091i	$-0.183125\pi$
$662$	17.1503	−	17.1503i	0.666566	−	0.666566i
$663$	−40.7471	+	40.7471i	−1.58248	+	1.58248i
$664$	−10.3064			−0.399966
$665$	13.2221	+	4.31512i	0.512732	+	0.167333i
$666$	−28.6680			−1.11086
$667$	3.35331	−	3.35331i	0.129841	−	0.129841i
$668$	36.4360	−	36.4360i	1.40975	−	1.40975i
$669$			37.7591i			1.45985i
$670$	−49.9896	−	6.25098i	−1.93127	−	0.241497i
$671$			49.8006i			1.92253i
$672$	−51.3809	−	9.93793i	−1.98206	−	0.383364i
$673$	−12.3284	−	12.3284i	−0.475224	−	0.475224i	0.428376	−	0.903600i	$-0.359086\pi$
$673$	−12.3284	−	12.3284i	−0.475224	−	0.475224i	−0.903600	+	0.428376i	$0.859086\pi$
$674$			22.8593i			0.880507i
$675$	1.14999	+	1.93335i	0.0442630	+	0.0744147i
$676$	−10.2388			−0.393801
$677$	−0.346340	−	0.346340i	−0.0133109	−	0.0133109i	0.700420	−	0.713731i	$-0.252996\pi$
$677$	−0.346340	−	0.346340i	−0.0133109	−	0.0133109i	−0.713731	+	0.700420i	$0.752996\pi$
$678$	−50.3785	+	50.3785i	−1.93477	+	1.93477i
$679$	−23.4456	+	15.8459i	−0.899758	+	0.608111i
$680$	−13.1664	−	1.64640i	−0.504910	−	0.0631367i
$681$	21.5757			0.826781
$682$	−13.9466	−	13.9466i	−0.534045	−	0.534045i
$683$	15.3145	+	15.3145i	0.585994	+	0.585994i	0.936544	−	0.350550i	$-0.114005\pi$
$683$	15.3145	+	15.3145i	0.585994	+	0.585994i	−0.350550	+	0.936544i	$0.614005\pi$
$684$	−18.6889			−0.714587
$685$	−6.29833	−	8.09861i	−0.240647	−	0.309432i
$686$	8.27447	+	38.4020i	0.315921	+	1.46620i
$687$	10.9717	−	10.9717i	0.418597	−	0.418597i
$688$	−19.3227	−	19.3227i	−0.736672	−	0.736672i
$689$	52.6177			2.00458
$690$	7.23896	+	9.30810i	0.275582	+	0.354353i
$691$			7.31939i			0.278443i	0.990261	+	0.139221i	$0.0444599\pi$
$691$			7.31939i			0.278443i	−0.990261	+	0.139221i	$0.955540\pi$
$692$	10.3305	+	10.3305i	0.392707	+	0.392707i
$693$	−45.1480	−	8.73238i	−1.71503	−	0.331716i
$694$		−	25.9439i		−	0.984816i
$695$	1.21854	−	9.74477i	0.0462219	−	0.369640i
$696$		−	12.4809i		−	0.473087i
$697$	−33.9896	+	33.9896i	−1.28745	+	1.28745i
$698$	−10.9605	+	10.9605i	−0.414860	+	0.414860i
$699$	−15.3291			−0.579798
$700$	−29.9128	−	14.0772i	−1.13060	−	0.532067i
$701$	−23.7409			−0.896682			−0.448341	−	0.893863i	$-0.647985\pi$
$701$	−23.7409			−0.896682			−0.448341	+	0.893863i	$0.647985\pi$
$702$	2.79014	−	2.79014i	0.105307	−	0.105307i
$703$	−7.06327	+	7.06327i	−0.266396	+	0.266396i
$704$			62.1258i			2.34145i
$705$	−5.01708	+	40.1220i	−0.188954	+	1.51108i
$706$			28.5885i			1.07594i
$707$	19.4090	+	3.75403i	0.729950	+	0.141185i
$708$	40.8607	+	40.8607i	1.53564	+	1.53564i
$709$		−	32.0809i		−	1.20482i	−0.798185	−	0.602412i	$-0.794207\pi$
$709$		−	32.0809i		−	1.20482i	0.798185	−	0.602412i	$-0.205793\pi$
$710$	−2.97685	−	3.82773i	−0.111719	−	0.143652i
$711$	30.8609			1.15738
$712$	10.9648	+	10.9648i	0.410922	+	0.410922i
$713$	1.20338	−	1.20338i	0.0450669	−	0.0450669i
$714$	43.7946	+	64.7983i	1.63897	+	2.42501i
$715$	31.0136	+	39.8784i	1.15984	+	1.49137i
$716$	−26.7501			−0.999698
$717$	16.6641	+	16.6641i	0.622334	+	0.622334i
$718$	−11.2378	−	11.2378i	−0.419391	−	0.419391i
$719$	35.7355			1.33271			0.666354	−	0.745636i	$-0.267854\pi$
$719$	35.7355			1.33271			0.666354	+	0.745636i	$0.267854\pi$
$720$	−19.4287	−	2.42947i	−0.724065	−	0.0905411i
$721$	10.3303	+	15.2847i	0.384720	+	0.569230i
$722$	20.2074	−	20.2074i	0.752043	−	0.752043i
$723$	−4.85097	−	4.85097i	−0.180409	−	0.180409i
$724$	−8.81478			−0.327599
$725$	−5.83873	+	22.9813i	−0.216845	+	0.853506i
$726$			99.4277i			3.69011i
$727$	−2.22970	−	2.22970i	−0.0826952	−	0.0826952i	0.664549	−	0.747244i	$-0.268624\pi$
$727$	−2.22970	−	2.22970i	−0.0826952	−	0.0826952i	−0.747244	+	0.664549i	$0.768624\pi$
$728$	−2.19917	+	11.3701i	−0.0815066	+	0.421404i
$729$		−	30.1532i		−	1.11678i
$730$	25.5493	+	3.19482i	0.945621	+	0.118246i
$731$			55.6463i			2.05815i
$732$	−40.0426	+	40.0426i	−1.48002	+	1.48002i
$733$	−0.709245	+	0.709245i	−0.0261966	+	0.0261966i	−0.720084	−	0.693887i	$-0.755897\pi$
$733$	−0.709245	+	0.709245i	−0.0261966	+	0.0261966i	0.693887	+	0.720084i	$0.255897\pi$
$734$	53.2657			1.96607
$735$	10.7124	+	37.4110i	0.395135	+	1.37992i
$736$	−7.95609			−0.293265
$737$	41.0387	−	41.0387i	1.51168	−	1.51168i
$738$	40.9113	−	40.9113i	1.50597	−	1.50597i
$739$		−	52.0563i		−	1.91492i	−0.288565	−	0.957460i	$-0.593178\pi$
$739$		−	52.0563i		−	1.91492i	0.288565	−	0.957460i	$-0.406822\pi$
$740$	18.7425	−	14.5761i	0.688987	−	0.535829i
$741$		−	24.1676i		−	0.887818i
$742$	13.5613	−	70.1144i	0.497851	−	2.57398i
$743$	3.57228	+	3.57228i	0.131054	+	0.131054i	0.769591	−	0.638537i	$-0.220460\pi$
$743$	3.57228	+	3.57228i	0.131054	+	0.131054i	−0.638537	+	0.769591i	$0.720460\pi$
$744$		−	4.47894i		−	0.164206i
$745$	−31.3584	−	3.92122i	−1.14888	−	0.143662i
$746$	−2.78219			−0.101863
$747$	21.8989	+	21.8989i	0.801237	+	0.801237i
$748$	54.1244	−	54.1244i	1.97898	−	1.97898i
$749$	−3.05001	−	4.51279i	−0.111445	−	0.164894i
$750$	−54.8999	−	21.4960i	−2.00466	−	0.784923i
$751$	−46.6939			−1.70388			−0.851941	−	0.523637i	$-0.824575\pi$
$751$	−46.6939			−1.70388			−0.851941	+	0.523637i	$0.824575\pi$
$752$	−14.1577	−	14.1577i	−0.516279	−	0.516279i
$753$	1.44274	+	1.44274i	0.0525764	+	0.0525764i
$754$	41.5921			1.51469
$755$	2.97731	−	23.8098i	0.108356	−	0.866528i
$756$	−1.66574	−	2.46462i	−0.0605823	−	0.0896373i
$757$	22.0223	−	22.0223i	0.800415	−	0.800415i	−0.182745	−	0.983160i	$-0.558498\pi$
$757$	22.0223	−	22.0223i	0.800415	−	0.800415i	0.983160	+	0.182745i	$0.0584983\pi$
$758$	−13.6162	−	13.6162i	−0.494563	−	0.494563i
$759$	−13.5842			−0.493075
$760$	4.39284	−	3.41634i	0.159345	−	0.123924i
$761$		−	47.4739i		−	1.72093i	−0.509512	−	0.860463i	$-0.670174\pi$
$761$		−	47.4739i		−	1.72093i	0.509512	−	0.860463i	$-0.329826\pi$
$762$	37.6393	+	37.6393i	1.36353	+	1.36353i
$763$	32.9232	+	6.36791i	1.19190	+	0.230534i
$764$		−	54.9552i		−	1.98821i
$765$	24.4775	+	31.4740i	0.884987	+	1.13795i
$766$			22.2865i			0.805245i
$767$	−27.1931	+	27.1931i	−0.981886	+	0.981886i
$768$	9.38140	−	9.38140i	0.338522	−	0.338522i
$769$	25.9511			0.935819			0.467910	−	0.883776i	$-0.345007\pi$
$769$	25.9511			0.935819			0.467910	+	0.883776i	$0.345007\pi$
$770$	61.1321	−	31.0484i	2.20305	−	1.11891i
$771$	−15.5924			−0.561545
$772$	−0.510436	+	0.510436i	−0.0183710	+	0.0183710i
$773$	−16.2625	+	16.2625i	−0.584922	+	0.584922i	−0.936252	−	0.351330i	$-0.885730\pi$
$773$	−16.2625	+	16.2625i	−0.584922	+	0.584922i	0.351330	+	0.936252i	$0.385730\pi$
$774$		−	66.9783i		−	2.40749i
$775$	−2.09530	+	8.24716i	−0.0752656	+	0.296247i
$776$			11.3224i			0.406451i
$777$	−27.4396	−	5.30729i	−0.984391	−	0.190398i
$778$	−4.76466	−	4.76466i	−0.170821	−	0.170821i
$779$		−	20.1596i		−	0.722294i
$780$	−7.12775	+	57.0012i	−0.255214	+	2.04097i
$781$	5.58617			0.199889
$782$	8.40755	+	8.40755i	0.300653	+	0.300653i
$783$	−1.50866	+	1.50866i	−0.0539152	+	0.0539152i
$784$	−17.8796	−	7.18524i	−0.638558	−	0.256616i
$785$	20.8045	−	16.1798i	0.742545	−	0.577481i
$786$	72.0889			2.57132
$787$	−27.1411	−	27.1411i	−0.967475	−	0.967475i	0.0320129	−	0.999487i	$-0.489808\pi$
$787$	−27.1411	−	27.1411i	−0.967475	−	0.967475i	−0.999487	+	0.0320129i	$0.989808\pi$
$788$	13.2317	+	13.2317i	0.471361	+	0.471361i
$789$	−63.2799			−2.25282
$790$	−36.3231	+	28.2487i	−1.29232	+	1.00504i
$791$	−29.6157	+	20.0160i	−1.05301	+	0.711689i
$792$	−13.0101	+	13.0101i	−0.462292	+	0.462292i
$793$	−26.6486	−	26.6486i	−0.946320	−	0.946320i
$794$	2.16526			0.0768421
$795$	8.77777	−	70.1965i	0.311315	−	2.48961i
$796$			28.3145i			1.00358i
$797$	−22.1509	−	22.1509i	−0.784625	−	0.784625i	0.195982	−	0.980607i	$-0.437210\pi$
$797$	−22.1509	−	22.1509i	−0.784625	−	0.784625i	−0.980607	+	0.195982i	$0.937210\pi$
$798$	−32.2039	−	6.22877i	−1.14001	−	0.220496i
$799$			40.7720i			1.44241i
$800$	34.1894	−	20.3364i	1.20878	−	0.719000i
$801$		−	46.5954i		−	1.64637i
$802$	−26.8727	+	26.8727i	−0.948909	+	0.948909i
$803$	−20.9745	+	20.9745i	−0.740174	+	0.740174i
$804$	65.9949			2.32746
$805$	2.67900	+	5.27475i	0.0944223	+	0.185910i
$806$	14.9259			0.525741
$807$	−3.51653	+	3.51653i	−0.123788	+	0.123788i
$808$	5.59299	−	5.59299i	0.196761	−	0.196761i
$809$		−	40.2197i		−	1.41405i	−0.707189	−	0.707025i	$-0.750037\pi$
$809$		−	40.2197i		−	1.41405i	0.707189	−	0.707025i	$-0.249963\pi$
$810$	24.5293	+	31.5406i	0.861872	+	1.10822i
$811$		−	8.08434i		−	0.283879i	−0.989875	−	0.141940i	$-0.954666\pi$
$811$		−	8.08434i		−	0.283879i	0.989875	−	0.141940i	$-0.0453339\pi$
$812$	5.95437	−	30.7852i	0.208958	−	1.08035i
$813$	8.15872	+	8.15872i	0.286139	+	0.286139i
$814$			49.2429i			1.72596i
$815$	−2.96302	+	2.30436i	−0.103790	+	0.0807181i
$816$	−38.3637			−1.34300
$817$	−16.5023	−	16.5023i	−0.577341	−	0.577341i
$818$	17.6002	−	17.6002i	0.615377	−	0.615377i
$819$	28.8317	−	19.4862i	1.00746	−	0.680903i
$820$	−5.94568	+	47.5481i	−0.207632	+	1.66045i
$821$	−31.9771			−1.11601			−0.558004	−	0.829838i	$-0.688433\pi$
$821$	−31.9771			−1.11601			−0.558004	+	0.829838i	$0.688433\pi$
$822$	17.1086	+	17.1086i	0.596731	+	0.596731i
$823$	−2.32945	−	2.32945i	−0.0811997	−	0.0811997i	0.665340	−	0.746540i	$-0.268286\pi$
$823$	−2.32945	−	2.32945i	−0.0811997	−	0.0811997i	−0.746540	+	0.665340i	$0.768286\pi$
$824$	7.38132			0.257141
$825$	58.3748	−	34.7223i	2.03235	−	1.20887i
$826$	29.2269	+	43.2440i	1.01693	+	1.50465i
$827$	−18.8953	+	18.8953i	−0.657055	+	0.657055i	−0.954682	−	0.297627i	$-0.903805\pi$
$827$	−18.8953	+	18.8953i	−0.657055	+	0.657055i	0.297627	+	0.954682i	$0.403805\pi$
$828$	−5.62113	−	5.62113i	−0.195348	−	0.195348i
$829$	20.0327			0.695765			0.347882	−	0.937538i	$-0.386901\pi$
$829$	20.0327			0.695765			0.347882	+	0.937538i	$0.386901\pi$
$830$	−45.8200	−	5.72959i	−1.59044	−	0.198877i
$831$		−	48.9643i		−	1.69855i
$832$	−33.2439	−	33.2439i	−1.15252	−	1.15252i
$833$	15.3990	+	36.0914i	0.533545	+	1.25049i
$834$			23.1604i			0.801978i
$835$	36.3946	−	28.3043i	1.25949	−	0.979512i
$836$			32.1019i			1.11027i
$837$	−0.541403	+	0.541403i	−0.0187136	+	0.0187136i
$838$	−25.9614	+	25.9614i	−0.896821	+	0.896821i
$839$	−37.1097			−1.28117			−0.640585	−	0.767887i	$-0.721308\pi$
$839$	−37.1097			−1.28117			−0.640585	+	0.767887i	$0.721308\pi$
$840$	14.8018	+	4.83065i	0.510711	+	0.166673i
$841$	6.51068			0.224506
$842$	54.7758	−	54.7758i	1.88770	−	1.88770i
$843$	42.6341	−	42.6341i	1.46840	−	1.46840i
$844$		−	25.9846i		−	0.894428i
$845$	−9.09047	−	1.13672i	−0.312722	−	0.0391044i
$846$		−	49.0749i		−	1.68723i
$847$	−9.47297	+	48.9769i	−0.325495	+	1.68287i
$848$	24.7700	+	24.7700i	0.850606	+	0.850606i
$849$		−	22.1477i		−	0.760107i
$850$	−57.6198	−	14.6391i	−1.97634	−	0.502117i
$851$	−4.24890			−0.145650
$852$	4.49160	+	4.49160i	0.153880	+	0.153880i
$853$	−19.9487	+	19.9487i	−0.683029	+	0.683029i	−0.960682	−	0.277653i	$-0.910444\pi$
$853$	−19.9487	+	19.9487i	−0.683029	+	0.683029i	0.277653	+	0.960682i	$0.410444\pi$
$854$	−42.3781	+	28.6417i	−1.45015	+	0.980098i
$855$	−16.5928	−	2.07485i	−0.567461	−	0.0709585i
$856$	−2.17933			−0.0744881
$857$	35.3663	+	35.3663i	1.20809	+	1.20809i	0.971645	+	0.236446i	$0.0759828\pi$
$857$	35.3663	+	35.3663i	1.20809	+	1.20809i	0.236446	+	0.971645i	$0.424017\pi$
$858$	−84.2444	−	84.2444i	−2.87606	−	2.87606i
$859$	16.2950			0.555978			0.277989	−	0.960584i	$-0.410332\pi$
$859$	16.2950			0.555978			0.277989	+	0.960584i	$0.410332\pi$
$860$	34.0549	+	43.7890i	1.16126	+	1.49319i
$861$	46.7323	−	31.5845i	1.59263	−	1.07640i
$862$	35.6516	−	35.6516i	1.21430	−	1.21430i
$863$	25.3390	+	25.3390i	0.862550	+	0.862550i	0.991634	−	0.129084i	$-0.0412036\pi$
$863$	25.3390	+	25.3390i	0.862550	+	0.862550i	−0.129084	+	0.991634i	$0.541204\pi$
$864$	3.57947			0.121776
$865$	8.02496	+	10.3188i	0.272857	+	0.350848i
$866$		−	82.7130i		−	2.81070i
$867$	25.3550	+	25.3550i	0.861101	+	0.861101i
$868$	2.13681	−	11.0477i	0.0725279	−	0.374982i
$869$		−	53.0098i		−	1.79824i
$870$	6.93844	−	55.4873i	0.235235	−	1.88120i
$871$			43.9201i			1.48817i
$872$	9.48731	−	9.48731i	0.321281	−	0.321281i
$873$	24.0576	−	24.0576i	0.814228	−	0.814228i
$874$	−4.98662			−0.168675
$875$	−24.9950	−	15.8193i	−0.844986	−	0.534788i
$876$	−33.7294			−1.13961
$877$	1.86436	−	1.86436i	0.0629549	−	0.0629549i	−0.674928	−	0.737883i	$-0.735825\pi$
$877$	1.86436	−	1.86436i	0.0629549	−	0.0629549i	0.737883	+	0.674928i	$0.235825\pi$
$878$	−19.3389	+	19.3389i	−0.652656	+	0.652656i
$879$			8.04651i			0.271402i
$880$	−4.17310	+	33.3727i	−0.140675	+	1.12499i
$881$		−	21.9858i		−	0.740721i	−0.928888	−	0.370361i	$-0.879234\pi$
$881$		−	21.9858i		−	0.740721i	0.928888	−	0.370361i	$-0.120766\pi$
$882$	−18.5350	−	43.4411i	−0.624104	−	1.46274i
$883$	6.60804	+	6.60804i	0.222378	+	0.222378i	0.809499	−	0.587121i	$-0.199739\pi$
$883$	6.60804	+	6.60804i	0.222378	+	0.222378i	−0.587121	+	0.809499i	$0.699739\pi$
$884$			57.9246i			1.94821i
$885$	31.7415	+	40.8143i	1.06698	+	1.37196i
$886$	11.4410			0.384368
$887$	−29.2386	−	29.2386i	−0.981737	−	0.981737i	0.0180995	−	0.999836i	$-0.494238\pi$
$887$	−29.2386	−	29.2386i	−0.981737	−	0.981737i	−0.999836	+	0.0180995i	$0.994238\pi$
$888$	−7.90714	+	7.90714i	−0.265346	+	0.265346i
$889$	14.9546	+	22.1268i	0.501561	+	0.742108i
$890$	42.6513	+	54.8425i	1.42968	+	1.83833i
$891$	−46.0302			−1.54207
$892$	26.8385	+	26.8385i	0.898620	+	0.898620i
$893$	−12.0912	−	12.0912i	−0.404616	−	0.404616i
$894$	74.5293			2.49263
$895$	−23.7499	−	2.96982i	−0.793871	−	0.0992700i
$896$	−17.9860	+	12.1560i	−0.600869	+	0.406104i
$897$	7.26898	−	7.26898i	0.242704	−	0.242704i
$898$	29.2372	+	29.2372i	0.975658	+	0.975658i
$899$	−8.07059			−0.269169
$900$	38.5235	+	9.78742i	1.28412	+	0.326247i
$901$		−	71.3336i		−	2.37647i
$902$	−70.2733	−	70.2733i	−2.33985	−	2.33985i
$903$	12.3997	−	64.1085i	0.412635	−	2.13340i
$904$			14.3021i			0.475681i
$905$	−7.82614	−	0.978624i	−0.260150	−	0.0325306i
$906$			56.5888i			1.88004i
$907$	40.0930	−	40.0930i	1.33127	−	1.33127i	0.427027	−	0.904239i	$-0.359561\pi$
$907$	40.0930	−	40.0930i	1.33127	−	1.33127i	0.904239	−	0.427027i	$-0.140439\pi$
$908$	15.3356	−	15.3356i	0.508930	−	0.508930i
$909$	−23.7677			−0.788326
$910$	−16.0979	+	49.3263i	−0.533641	+	1.63515i
$911$	14.8733			0.492775			0.246388	−	0.969171i	$-0.420756\pi$
$911$	14.8733			0.492775			0.246388	+	0.969171i	$0.420756\pi$
$912$	11.3770	−	11.3770i	0.376730	−	0.376730i
$913$	37.6157	−	37.6157i	1.24490	−	1.24490i
$914$		−	1.38336i		−	0.0457575i
$915$	−39.9971	+	31.1059i	−1.32226	+	1.02833i
$916$		−	15.5970i		−	0.515339i
$917$	35.5101	+	6.86826i	1.17265	+	0.226810i
$918$	−3.78258	−	3.78258i	−0.124844	−	0.124844i
$919$		−	46.8697i		−	1.54609i	−0.634352	−	0.773045i	$-0.718733\pi$
$919$		−	46.8697i		−	1.54609i	0.634352	−	0.773045i	$-0.281267\pi$
$920$	2.34880	+	0.293707i	0.0774376	+	0.00968322i
$921$	57.2177			1.88539
$922$	19.8827	+	19.8827i	0.654803	+	0.654803i
$923$	−2.98919	+	2.98919i	−0.0983905	+	0.0983905i
$924$	−74.4157	+	50.2946i	−2.44810	+	1.65457i
$925$	18.2586	−	10.8605i	0.600340	−	0.357091i
$926$	−57.7192			−1.89677
$927$	−15.6837	−	15.6837i	−0.515120	−	0.515120i
$928$	26.6792	+	26.6792i	0.875788	+	0.875788i
$929$	48.4740			1.59038			0.795190	−	0.606360i	$-0.207371\pi$
$929$	48.4740			1.59038			0.795190	+	0.606360i	$0.207371\pi$
$930$	2.48995	−	19.9124i	0.0816488	−	0.652952i
$931$	−15.2698	−	6.13644i	−0.500448	−	0.201114i
$932$	−10.8956	+	10.8956i	−0.356898	+	0.356898i
$933$	1.06289	+	1.06289i	0.0347976	+	0.0347976i
$934$	9.97466			0.326381
$935$	54.0629	−	42.0450i	1.76805	−	1.37502i
$936$		−	13.9235i		−	0.455104i
$937$	7.65052	+	7.65052i	0.249932	+	0.249932i	0.820942	−	0.571011i	$-0.193449\pi$
$937$	7.65052	+	7.65052i	0.249932	+	0.249932i	−0.571011	+	0.820942i	$0.693449\pi$
$938$	58.5245	+	11.3196i	1.91089	+	0.369599i
$939$		−	1.61351i		−	0.0526549i
$940$	24.9520	+	32.0841i	0.813844	+	1.04647i
$941$			24.9746i			0.814148i	0.913395	+	0.407074i	$0.133451\pi$
$941$			24.9746i			0.814148i	−0.913395	+	0.407074i	$0.866549\pi$
$942$	−43.9502	+	43.9502i	−1.43198	+	1.43198i
$943$	6.06349	−	6.06349i	0.197455	−	0.197455i
$944$	−25.6025			−0.833291
$945$	−1.20529	−	2.37312i	−0.0392081	−	0.0771977i
$946$	−115.049			−3.74055
$947$	13.2073	−	13.2073i	0.429178	−	0.429178i	−0.459170	−	0.888348i	$-0.651853\pi$
$947$	13.2073	−	13.2073i	0.429178	−	0.429178i	0.888348	+	0.459170i	$0.151853\pi$
$948$	42.6229	−	42.6229i	1.38433	−	1.38433i
$949$		−	22.4472i		−	0.728665i
$950$	21.4288	−	12.7462i	0.695243	−	0.413541i
$951$			61.4984i			1.99422i
$952$	15.4144	+	2.98140i	0.499583	+	0.0966278i
$953$	10.1786	+	10.1786i	0.329718	+	0.329718i	0.852479	−	0.522761i	$-0.175098\pi$
$953$	10.1786	+	10.1786i	0.329718	+	0.329718i	−0.522761	+	0.852479i	$0.675098\pi$
$954$			85.8603i			2.77983i
$955$	6.10117	−	48.7916i	0.197429	−	1.57886i
$956$	23.6891			0.766162
$957$	45.5520	+	45.5520i	1.47249	+	1.47249i
$958$	−12.1497	+	12.1497i	−0.392540	+	0.392540i
$959$	6.79747	+	10.0575i	0.219502	+	0.324774i
$960$	−49.8960	+	38.8044i	−1.61039	+	1.25241i
$961$	28.1038			0.906573
$962$	−26.3502	−	26.3502i	−0.849564	−	0.849564i
$963$	4.63060	+	4.63060i	0.149219	+	0.149219i
$964$	−6.89596			−0.222104
$965$	−0.509856	+	0.396518i	−0.0164128	+	0.0127644i
$966$	−7.81264	−	11.5595i	−0.251368	−	0.371922i
$967$	39.2710	−	39.2710i	1.26287	−	1.26287i	0.313173	−	0.949696i	$-0.398608\pi$
$967$	39.2710	−	39.2710i	1.26287	−	1.26287i	0.949696	−	0.313173i	$-0.101392\pi$
$968$	14.1134	+	14.1134i	0.453623	+	0.453623i
$969$	−32.7639			−1.05253
$970$	−6.29441	+	50.3370i	−0.202101	+	1.61622i
$971$		−	22.3608i		−	0.717592i	−0.933416	−	0.358796i	$-0.883187\pi$
$971$		−	22.3608i		−	0.717592i	0.933416	−	0.358796i	$-0.116813\pi$
$972$	−39.3960	−	39.3960i	−1.26363	−	1.26363i
$973$	−2.20660	+	11.4085i	−0.0707404	+	0.365741i
$974$			24.1894i			0.775077i
$975$	−12.6566	+	49.8168i	−0.405337	+	1.59541i
$976$		−	25.0899i		−	0.803107i
$977$	−13.7201	+	13.7201i	−0.438946	+	0.438946i	−0.891657	−	0.452711i	$-0.850457\pi$
$977$	−13.7201	+	13.7201i	−0.438946	+	0.438946i	0.452711	+	0.891657i	$0.350457\pi$
$978$	6.25948	−	6.25948i	0.200156	−	0.200156i
$979$	−80.0369			−2.55799
$980$	34.2053	+	18.9768i	1.09265	+	0.606193i
$981$	−40.3169			−1.28722
$982$	−57.8527	+	57.8527i	−1.84615	+	1.84615i
$983$	13.6587	−	13.6587i	0.435643	−	0.435643i	−0.454899	−	0.890543i	$-0.650325\pi$
$983$	13.6587	−	13.6587i	0.435643	−	0.435643i	0.890543	+	0.454899i	$0.150325\pi$
$984$		−	22.5681i		−	0.719446i
$985$	10.2787	+	13.2167i	0.327507	+	0.421119i
$986$		−	56.3862i		−	1.79570i
$987$	9.08522	−	46.9722i	0.289186	−	1.49514i
$988$	−17.1779	−	17.1779i	−0.546501	−	0.546501i
$989$		−	9.92691i		−	0.315657i
$990$	−65.0725	+	50.6072i	−2.06814	+	1.60840i
$991$	−13.2776			−0.421778			−0.210889	−	0.977510i	$-0.567636\pi$
$991$	−13.2776			−0.421778			−0.210889	+	0.977510i	$0.567636\pi$
$992$	9.57419	+	9.57419i	0.303981	+	0.303981i
$993$	−20.1020	+	20.1020i	−0.637917	+	0.637917i
$994$	3.21276	+	4.75359i	0.101903	+	0.150775i
$995$	−3.14350	+	25.1388i	−0.0996555	+	0.796954i
$996$	60.4903			1.91671
$997$	−41.1105	−	41.1105i	−1.30198	−	1.30198i	−0.927054	−	0.374928i	$-0.877667\pi$
$997$	−41.1105	−	41.1105i	−1.30198	−	1.30198i	−0.374928	−	0.927054i	$-0.622333\pi$
$998$	−14.3071	−	14.3071i	−0.452883	−	0.452883i
$999$	1.91159			0.0604801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.k.a.783.16	yes	176
5.2	odd	4	inner	805.2.k.a.622.15	✓	176
7.6	odd	2	inner	805.2.k.a.783.15	yes	176
35.27	even	4	inner	805.2.k.a.622.16	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.k.a.622.15	✓	176	5.2	odd	4	inner
805.2.k.a.622.16	yes	176	35.27	even	4	inner
805.2.k.a.783.15	yes	176	7.6	odd	2	inner
805.2.k.a.783.16	yes	176	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49985 + 1.49985i) q^{2} +(1.75798 - 1.75798i) q^{3} -2.49908i q^{4} +(0.277450 - 2.21879i) q^{5} +5.27339i q^{6} +(-0.502421 + 2.59761i) q^{7} +(0.748540 + 0.748540i) q^{8} -3.18096i q^{9} +O(q^{10})\)	\(q+(-1.49985 + 1.49985i) q^{2} +(1.75798 - 1.75798i) q^{3} -2.49908i q^{4} +(0.277450 - 2.21879i) q^{5} +5.27339i q^{6} +(-0.502421 + 2.59761i) q^{7} +(0.748540 + 0.748540i) q^{8} -3.18096i q^{9} +(2.91171 + 3.74397i) q^{10} -5.46394 q^{11} +(-4.39332 - 4.39332i) q^{12} +(2.92379 - 2.92379i) q^{13} +(-3.14246 - 4.64957i) q^{14} +(-3.41283 - 4.38833i) q^{15} +2.75277 q^{16} +(-3.96376 - 3.96376i) q^{17} +(4.77096 + 4.77096i) q^{18} +2.35096 q^{19} +(-5.54492 - 0.693368i) q^{20} +(3.68329 + 5.44978i) q^{21} +(8.19507 - 8.19507i) q^{22} +(0.707107 + 0.707107i) q^{23} +2.63183 q^{24} +(-4.84604 - 1.23120i) q^{25} +8.77046i q^{26} +(-0.318129 - 0.318129i) q^{27} +(6.49163 + 1.25559i) q^{28} -4.74229i q^{29} +(11.7005 + 1.46310i) q^{30} -1.70183i q^{31} +(-5.62581 + 5.62581i) q^{32} +(-9.60548 + 9.60548i) q^{33} +11.8901 q^{34} +(5.62415 + 1.83547i) q^{35} -7.94947 q^{36} +(-3.00442 + 3.00442i) q^{37} +(-3.52607 + 3.52607i) q^{38} -10.2799i q^{39} +(1.86853 - 1.45317i) q^{40} -8.57508i q^{41} +(-13.6982 - 2.64946i) q^{42} +(-7.01938 - 7.01938i) q^{43} +13.6548i q^{44} +(-7.05788 - 0.882557i) q^{45} -2.12110 q^{46} +(-5.14309 - 5.14309i) q^{47} +(4.83930 - 4.83930i) q^{48} +(-6.49515 - 2.61019i) q^{49} +(9.11494 - 5.42170i) q^{50} -13.9364 q^{51} +(-7.30677 - 7.30677i) q^{52} +(8.99822 + 8.99822i) q^{53} +0.954290 q^{54} +(-1.51597 + 12.1233i) q^{55} +(-2.32050 + 1.56833i) q^{56} +(4.13293 - 4.13293i) q^{57} +(7.11271 + 7.11271i) q^{58} -9.30065 q^{59} +(-10.9668 + 8.52892i) q^{60} -9.11442i q^{61} +(2.55249 + 2.55249i) q^{62} +(8.26290 + 1.59818i) q^{63} -11.3702i q^{64} +(-5.67606 - 7.29846i) q^{65} -28.8135i q^{66} +(-7.51082 + 7.51082i) q^{67} +(-9.90575 + 9.90575i) q^{68} +2.48615 q^{69} +(-11.1883 + 5.68243i) q^{70} -1.02237 q^{71} +(2.38108 - 2.38108i) q^{72} +(3.83871 - 3.83871i) q^{73} -9.01235i q^{74} +(-10.6837 + 6.35480i) q^{75} -5.87522i q^{76} +(2.74520 - 14.1932i) q^{77} +(15.4183 + 15.4183i) q^{78} +9.70176i q^{79} +(0.763754 - 6.10781i) q^{80} +8.42436 q^{81} +(12.8613 + 12.8613i) q^{82} +(-6.88435 + 6.88435i) q^{83} +(13.6194 - 9.20483i) q^{84} +(-9.89449 + 7.69501i) q^{85} +21.0560 q^{86} +(-8.33684 - 8.33684i) q^{87} +(-4.08997 - 4.08997i) q^{88} +14.6482 q^{89} +(11.9094 - 9.26204i) q^{90} +(6.12588 + 9.06382i) q^{91} +(1.76711 - 1.76711i) q^{92} +(-2.99178 - 2.99178i) q^{93} +15.4277 q^{94} +(0.652272 - 5.21628i) q^{95} +19.7801i q^{96} +(7.56301 + 7.56301i) q^{97} +(13.6566 - 5.82684i) q^{98} +17.3806i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 176 * q - 8 * q^7 + 24 * q^8	\( 176 q - 8 q^{7} + 24 q^{8} + 8 q^{11} - 8 q^{15} - 208 q^{16} + 16 q^{21} - 16 q^{22} + 36 q^{28} + 88 q^{30} + 8 q^{32} - 48 q^{35} - 144 q^{36} + 24 q^{37} + 24 q^{50} - 24 q^{51} - 8 q^{53} + 104 q^{56} - 40 q^{57} - 80 q^{58} + 40 q^{60} + 60 q^{63} - 8 q^{65} - 64 q^{67} + 68 q^{70} + 40 q^{71} + 80 q^{72} + 4 q^{77} + 168 q^{78} - 160 q^{81} - 16 q^{85} - 128 q^{86} - 88 q^{88} - 112 q^{91} - 32 q^{93} + 24 q^{98}+O(q^{100}) \) 176 * q - 8 * q^7 + 24 * q^8 + 8 * q^11 - 8 * q^15 - 208 * q^16 + 16 * q^21 - 16 * q^22 + 36 * q^28 + 88 * q^30 + 8 * q^32 - 48 * q^35 - 144 * q^36 + 24 * q^37 + 24 * q^50 - 24 * q^51 - 8 * q^53 + 104 * q^56 - 40 * q^57 - 80 * q^58 + 40 * q^60 + 60 * q^63 - 8 * q^65 - 64 * q^67 + 68 * q^70 + 40 * q^71 + 80 * q^72 + 4 * q^77 + 168 * q^78 - 160 * q^81 - 16 * q^85 - 128 * q^86 - 88 * q^88 - 112 * q^91 - 32 * q^93 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more