LMFDB - Embedded newform 805.2.k.a.622.15

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			622.15
Character	$\chi$	$=$	805.622
Dual form			805.2.k.a.783.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49985 - 1.49985i) q^{2} +(-1.75798 - 1.75798i) q^{3} +2.49908i q^{4} +(-0.277450 - 2.21879i) q^{5} +5.27339i q^{6} +(-2.59761 - 0.502421i) q^{7} +(0.748540 - 0.748540i) q^{8} +3.18096i q^{9} +O(q^{10})$	\(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} +(-2.59761 - 0.502421i) 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} +(1.25559 - 6.49163i) 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} +(-0.394061 + 5.90294i) 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} +(2.64946 - 13.6982i) 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} +(1.59818 - 8.26290i) 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} +(9.44454 - 8.26247i) 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} +(14.1932 + 2.74520i) 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} +(-5.82684 - 13.6566i) 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 $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

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

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	−0.998045	−	0.0625069i	$-0.980090\pi$
$2$	−1.49985	−	1.49985i	−1.06055	−	1.06055i	−0.0625069	−	0.998045i	$-0.519910\pi$
$3$	−1.75798	−	1.75798i	−1.01497	−	1.01497i	−0.999886	−	0.0150820i	$-0.995199\pi$
$3$	−1.75798	−	1.75798i	−1.01497	−	1.01497i	−0.0150820	−	0.999886i	$-0.504801\pi$
$4$			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
$7$	−2.59761	−	0.502421i	−0.981804	−	0.189897i
$7$	−2.59761	−	0.502421i	−0.981804	−	0.189897i
$8$	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	$-0.444376\pi$
$13$	−2.92379	−	2.92379i	−0.810912	−	0.810912i	−0.984771	+	0.173858i	$0.944376\pi$
$14$	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	$-0.512075\pi$
$17$	3.96376	−	3.96376i	0.961354	−	0.961354i	0.999281	+	0.0379269i	$0.0120754\pi$
$18$	4.77096	−	4.77096i	1.12453	−	1.12453i
$19$	−2.35096			−0.539346			−0.269673	−	0.962952i	$-0.586916\pi$
$19$	−2.35096			−0.539346			−0.269673	+	0.962952i	$0.586916\pi$
$20$	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
$28$	1.25559	−	6.49163i	0.237284	−	1.22680i
$29$			4.74229i			0.880621i	0.897846	+	0.440311i	$0.145132\pi$
$29$			4.74229i			0.880621i	−0.897846	+	0.440311i	$0.854868\pi$
$30$	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
$35$	−0.394061	+	5.90294i	−0.0666085	+	0.997779i
$36$	−7.94947			−1.32491
$37$	−3.00442	−	3.00442i	−0.493924	−	0.493924i	0.415616	−	0.909540i	$-0.363566\pi$
$37$	−3.00442	−	3.00442i	−0.493924	−	0.493924i	−0.909540	+	0.415616i	$0.863566\pi$
$38$	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	$-0.233535\pi$
$42$	2.64946	−	13.6982i	0.408821	−	2.11368i
$43$	−7.01938	+	7.01938i	−1.07045	+	1.07045i	−0.0731231	+	0.997323i	$0.523297\pi$
$43$	−7.01938	+	7.01938i	−1.07045	+	1.07045i	−0.997323	+	0.0731231i	$0.976703\pi$
$44$		−	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	$-0.572016\pi$
$47$	5.14309	−	5.14309i	0.750197	−	0.750197i	0.974516	+	0.224319i	$0.0720158\pi$
$48$	−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	0.274380	−	0.961621i	$-0.411528\pi$
$53$	8.99822	−	8.99822i	1.23600	−	1.23600i	0.961621	−	0.274380i	$-0.0884724\pi$
$54$	−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	$-0.293005\pi$
$59$	9.30065			1.21084			0.605421	+	0.795906i	$0.293005\pi$
$60$	−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
$63$	1.59818	−	8.26290i	0.201352	−	1.04103i
$64$			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	0.0792611	−	0.996854i	$-0.474744\pi$
$67$	−7.51082	−	7.51082i	−0.917593	−	0.917593i	−0.996854	+	0.0792611i	$0.974744\pi$
$68$	9.90575	+	9.90575i	1.20125	+	1.20125i
$69$	−2.48615			−0.299298
$70$	9.44454	−	8.26247i	1.12884	−	0.987554i
$71$	−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	$-0.352909\pi$
$73$	−3.83871	−	3.83871i	−0.449287	−	0.449287i	−0.895118	+	0.445830i	$0.852909\pi$
$74$			9.01235i			1.04766i
$75$	10.6837	+	6.35480i	1.23364	+	0.733789i
$76$		−	5.87522i		−	0.673934i
$77$	14.1932	+	2.74520i	1.61746	+	0.312845i
$78$	15.4183	−	15.4183i	1.74577	−	1.74577i
$79$		−	9.70176i		−	1.09153i	−0.837937	−	0.545767i	$-0.816238\pi$
$79$		−	9.70176i		−	1.09153i	0.837937	−	0.545767i	$-0.183762\pi$
$80$	−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	$-0.0705643\pi$
$83$	6.88435	+	6.88435i	0.755655	+	0.755655i	−0.219873	+	0.975528i	$0.570564\pi$
$84$	−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	$-0.782933\pi$
$89$	−14.6482			−1.55271			−0.776354	+	0.630297i	$0.782933\pi$
$90$	−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	$-0.932709\pi$
$97$	−7.56301	+	7.56301i	−0.767907	+	0.767907i	0.209831	+	0.977738i	$0.432709\pi$
$98$	−5.82684	−	13.6566i	−0.588599	−	1.37953i
$99$		−	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	$-0.361620\pi$
$103$	−4.93048	−	4.93048i	−0.485815	−	0.485815i	−0.906983	+	0.421168i	$0.861620\pi$
$104$	−4.37714			−0.429214
$105$	11.0700	−	9.68448i	1.08032	−	0.945109i
$106$	−26.9919			−2.62169
$107$	−1.45572	−	1.45572i	−0.140730	−	0.140730i	0.633232	−	0.773962i	$-0.281728\pi$
$107$	−1.45572	−	1.45572i	−0.140730	−	0.140730i	−0.773962	+	0.633232i	$0.781728\pi$
$108$	0.795030	+	0.795030i	0.0765018	+	0.0765018i
$109$			12.6744i			1.21399i	0.794705	+	0.606995i	$0.207625\pi$
$109$			12.6744i			1.21399i	−0.794705	+	0.606995i	$0.792375\pi$
$110$	15.9094	−	20.4568i	1.51690	−	1.95048i
$111$			10.5634i			1.00264i
$112$	−7.15061	−	1.38305i	−0.675669	−	0.130686i
$113$	9.55334	−	9.55334i	0.898703	−	0.898703i	−0.0966186	−	0.995321i	$-0.530803\pi$
$113$	9.55334	−	9.55334i	0.898703	−	0.898703i	0.995321	+	0.0966186i	$0.0308027\pi$
$114$		−	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	0.948909	−	0.315550i	$-0.102189\pi$
$127$	7.13760	+	7.13760i	0.633359	+	0.633359i	−0.315550	+	0.948909i	$0.602189\pi$
$128$	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
$133$	6.10687	+	1.18117i	0.529532	+	0.102421i
$134$			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	0.831983	−	0.554801i	$-0.187206\pi$
$137$	3.24432	+	3.24432i	0.277181	+	0.277181i	−0.554801	+	0.831983i	$0.687206\pi$
$138$	3.72885	+	3.72885i	0.317421	+	0.317421i
$139$	−4.39193			−0.372519			−0.186259	−	0.982501i	$-0.559637\pi$
$139$	−4.39193			−0.372519			−0.186259	+	0.982501i	$0.559637\pi$
$140$	−14.7519	−	0.984790i	−1.24676	−	0.0832299i
$141$	−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
$147$	−6.82966	−	16.0070i	−0.563301	−	1.32023i
$148$	7.50829	−	7.50829i	0.617178	−	0.617178i
$149$			14.1331i			1.15783i	0.815388	+	0.578914i	$0.196523\pi$
$149$			14.1331i			1.15783i	−0.815388	+	0.578914i	$0.803477\pi$
$150$	−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	$-0.905867\pi$
$157$	−8.33434	+	8.33434i	−0.665153	+	0.665153i	0.291437	+	0.956590i	$0.405867\pi$
$158$	−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	−0.752063	−	0.659091i	$-0.770941\pi$
$163$	−1.18699	+	1.18699i	−0.0929725	+	0.0929725i	0.659091	+	0.752063i	$0.270941\pi$
$164$	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	−0.137752	+	0.990467i	$0.543988\pi$
$167$	−14.5798	+	14.5798i	−1.12822	+	1.12822i	−0.990467	+	0.137752i	$0.956012\pi$
$168$	6.83647	+	1.32229i	0.527445	+	0.102017i
$169$			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	$-0.178666\pi$
$173$	4.13373	+	4.13373i	0.314281	+	0.314281i	−0.532284	+	0.846566i	$0.678666\pi$
$174$	−25.0079			−1.89585
$175$	13.2067	−	0.763430i	0.998333	−	0.0577099i
$176$	−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	$0.130999\pi$
$179$			10.7040i			0.800054i	−0.916503	+	0.400027i	$0.869001\pi$
$180$	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	$-0.0418470\pi$
$182$	4.40647	−	22.7822i	0.326629	−	1.68873i
$183$	−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	−0.714420	−	0.699717i	$-0.753309\pi$
$193$	−0.204250	+	0.204250i	−0.0147022	+	0.0147022i	0.699717	+	0.714420i	$0.253309\pi$
$194$	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	0.492873	−	0.870101i	$-0.335947\pi$
$197$	−5.29465	−	5.29465i	−0.377228	−	0.377228i	−0.870101	+	0.492873i	$0.835947\pi$
$198$	−26.0682	+	26.0682i	−1.85259	+	1.85259i
$199$	11.3300			0.803160			0.401580	−	0.915824i	$-0.368461\pi$
$199$	11.3300			0.803160			0.401580	+	0.915824i	$0.368461\pi$
$200$	−2.70585	+	4.54906i	−0.191333	+	0.321667i
$201$			26.4077i			1.86266i
$202$	−11.2067	+	11.2067i	−0.788497	+	0.788497i
$203$	2.38263	−	12.3186i	0.167228	−	0.864597i
$204$		−	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
$210$	−31.1285	−	2.07804i	−2.14807	−	0.143398i
$211$	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
$217$	−0.855038	+	4.42070i	−0.0580438	+	0.300097i
$218$	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	$-0.0801914\pi$
$223$	10.7394	+	10.7394i	0.719161	+	0.719161i	−0.249272	+	0.968433i	$0.580191\pi$
$224$	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	$-0.842990\pi$
$227$	−6.13651	+	6.13651i	−0.407294	+	0.407294i	0.473500	+	0.880794i	$0.342990\pi$
$228$	−10.3285	+	10.3285i	−0.684022	+	0.684022i
$229$	−6.24110			−0.412424			−0.206212	−	0.978507i	$-0.566114\pi$
$229$	−6.24110			−0.412424			−0.206212	+	0.978507i	$0.566114\pi$
$230$	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	−0.835347	−	0.549723i	$-0.814733\pi$
$233$	−4.35986	+	4.35986i	−0.285624	+	0.285624i	0.549723	+	0.835347i	$0.314733\pi$
$234$	−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
$238$	30.8858	+	5.97383i	2.00203	+	0.387226i
$239$		−	9.47916i		−	0.613156i	−0.951846	−	0.306578i	$-0.900816\pi$
$239$		−	9.47916i		−	0.613156i	0.951846	−	0.306578i	$-0.0991840\pi$
$240$	−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
$245$	3.98938	−	15.1355i	0.254872	−	0.966975i
$246$	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	$0.991755\pi$
$252$	20.6496	+	3.99399i	1.30080	+	0.251598i
$253$	−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	$-0.687332\pi$
$257$	4.43475	−	4.43475i	0.276632	−	0.276632i	0.831763	+	0.555131i	$0.187332\pi$
$258$	−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	−0.116623	+	0.993176i	$0.537207\pi$
$263$	−17.9979	+	17.9979i	−1.10980	+	1.10980i	−0.993176	+	0.116623i	$0.962793\pi$
$264$	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	$-0.480577\pi$
$269$	2.00033			0.121962			0.0609811	+	0.998139i	$0.480577\pi$
$270$	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
$273$	5.16484	−	26.7031i	0.312590	−	1.61615i
$274$		−	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	0.988430	−	0.151678i	$-0.0484675\pi$
$277$	13.9263	+	13.9263i	0.836752	+	0.836752i	−0.151678	+	0.988430i	$0.548468\pi$
$278$	6.58723	+	6.58723i	0.395076	+	0.395076i
$279$	5.41347			0.324096
$280$	4.12361	+	4.71356i	0.246433	+	0.281689i
$281$	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	$-0.335298\pi$
$283$	−6.29920	−	6.29920i	−0.374449	−	0.374449i	−0.869095	+	0.494646i	$0.835298\pi$
$284$		−	2.55499i		−	0.151610i
$285$	8.02341	−	10.3168i	0.475266	−	0.611113i
$286$		−	47.9212i		−	2.83364i
$287$	−4.30830	+	22.2747i	−0.254311	+	1.31483i
$288$	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	$-0.219862\pi$
$293$	2.28857	+	2.28857i	0.133700	+	0.133700i	−0.637090	+	0.770790i	$0.719862\pi$
$294$	−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	$-0.978071\pi$
$307$	−16.2737	+	16.2737i	−0.928792	+	0.928792i	0.0688364	+	0.997628i	$0.478071\pi$
$308$	−6.86047	+	35.4698i	−0.390911	+	2.02108i
$309$			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	$-0.255839\pi$
$313$	−0.458911	−	0.458911i	−0.0259392	−	0.0259392i	−0.719957	+	0.694018i	$0.755839\pi$
$314$	25.0005			1.41086
$315$	−18.7770	−	1.25349i	−1.05797	−	0.0706264i
$316$	24.2455			1.36391
$317$	−17.4912	−	17.4912i	−0.982406	−	0.982406i	0.0174423	−	0.999848i	$-0.494448\pi$
$317$	−17.4912	−	17.4912i	−0.982406	−	0.982406i	−0.999848	+	0.0174423i	$0.994448\pi$
$318$	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
$322$	5.50980	+	1.06569i	0.307049	+	0.0593885i
$323$	−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	0.883517	−	0.468399i	$-0.155169\pi$
$337$	7.62055	+	7.62055i	0.415118	+	0.415118i	−0.468399	+	0.883517i	$0.655169\pi$
$338$	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
$343$	−15.5604	−	10.0436i	−0.840184	−	0.542301i
$344$			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	0.435766	−	0.900060i	$-0.356478\pi$
$347$	−8.64885	−	8.64885i	−0.464294	−	0.464294i	−0.900060	+	0.435766i	$0.856478\pi$
$348$	20.8344	+	20.8344i	1.11684	+	1.11684i
$349$	−7.30774			−0.391174			−0.195587	−	0.980686i	$-0.562661\pi$
$349$	−7.30774			−0.391174			−0.195587	+	0.980686i	$0.562661\pi$
$350$	−20.9531	−	18.6630i	−1.11999	−	0.997580i
$351$	−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	$-0.366775\pi$
$353$	−9.53049	−	9.53049i	−0.507257	−	0.507257i	−0.913683	+	0.406427i	$0.866775\pi$
$354$			49.0459i			2.60676i
$355$	0.283657	+	2.26843i	0.0150549	+	0.120396i
$356$		−	36.6070i		−	1.94017i
$357$	36.2013	+	7.00195i	1.91598	+	0.370582i
$358$	16.0543	−	16.0543i	0.848498	−	0.848498i
$359$		−	7.49263i		−	0.395446i	−0.980258	−	0.197723i	$-0.936645\pi$
$359$		−	7.49263i		−	0.395446i	0.980258	−	0.197723i	$-0.0633546\pi$
$360$	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	$-0.522489\pi$
$367$	17.7571	−	17.7571i	0.926911	−	0.926911i	0.997505	+	0.0705939i	$0.0224894\pi$
$368$	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	−0.682687	−	0.730711i	$-0.739189\pi$
$373$	0.927491	−	0.927491i	0.0480237	−	0.0480237i	0.730711	+	0.682687i	$0.239189\pi$
$374$	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
$378$	2.47887	+	0.479456i	0.127499	+	0.0246606i
$379$		−	9.07840i		−	0.466326i	−0.972438	−	0.233163i	$-0.925092\pi$
$379$		−	9.07840i		−	0.466326i	0.972438	−	0.233163i	$-0.0749076\pi$
$380$	−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	$-0.336509\pi$
$383$	−7.42961	−	7.42961i	−0.379635	−	0.379635i	−0.870970	+	0.491335i	$0.836509\pi$
$384$	−20.3991			−1.04099
$385$	2.15313	−	32.2533i	0.109733	−	1.64378i
$386$	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	$-0.974337\pi$
$389$		−	3.17676i		−	0.161068i	0.996752	−	0.0805341i	$-0.0256626\pi$
$390$	−38.4876	−	29.9321i	−1.94890	−	1.51567i
$391$		−	5.60561i		−	0.283488i
$392$	6.81570	−	2.90804i	0.344245	−	0.146878i
$393$	−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	$-0.741845\pi$
$397$	0.721827	−	0.721827i	0.0362274	−	0.0362274i	0.724988	+	0.688761i	$0.241845\pi$
$398$	−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	$-0.406304\pi$
$409$	11.7347			0.580243			0.290121	+	0.956990i	$0.406304\pi$
$410$	32.1049	+	24.9681i	1.58555	+	1.23309i
$411$		−	11.4069i		−	0.562661i
$412$	12.3217	−	12.3217i	0.607045	−	0.607045i
$413$	−24.1594	−	4.67284i	−1.18881	−	0.229936i
$414$		−	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	$-0.638956\pi$
$419$	−17.3094			−0.845617			−0.422809	+	0.906219i	$0.638956\pi$
$420$	24.2023	+	27.6647i	1.18095	+	1.34990i
$421$	−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
$427$	−4.57928	+	23.6757i	−0.221607	+	1.14575i
$428$	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	0.909576	+	0.415539i	$0.136407\pi$
$433$	27.5738	+	27.5738i	1.32511	+	1.32511i	0.415539	+	0.909576i	$0.363593\pi$
$434$	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	$-0.599558\pi$
$439$	−12.8939			−0.615393			−0.307696	+	0.951485i	$0.599558\pi$
$440$	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	−0.791884	−	0.610672i	$-0.790899\pi$
$443$	−3.81406	+	3.81406i	−0.181211	+	0.181211i	0.610672	+	0.791884i	$0.290899\pi$
$444$	−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
$448$	5.71261	−	29.5352i	0.269895	−	1.39541i
$449$			19.4935i			0.919953i	0.887931	+	0.459977i	$0.152142\pi$
$449$			19.4935i			0.919953i	−0.887931	+	0.459977i	$0.847858\pi$
$450$	−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
$455$	18.4111	−	16.1068i	0.863125	−	0.755098i
$456$	6.18732			0.289748
$457$	−0.461167	−	0.461167i	−0.0215725	−	0.0215725i	0.696238	−	0.717811i	$-0.254856\pi$
$457$	−0.461167	−	0.461167i	−0.0215725	−	0.0215725i	−0.717811	+	0.696238i	$0.754856\pi$
$458$	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	$-0.0998968\pi$
$462$	−14.4765	+	74.8461i	−0.673508	+	3.48216i
$463$	19.2417	−	19.2417i	0.894238	−	0.894238i	−0.100681	−	0.994919i	$-0.532102\pi$
$463$	19.2417	−	19.2417i	0.894238	−	0.894238i	0.994919	+	0.100681i	$0.0321022\pi$
$464$			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	$-0.715298\pi$
$467$	3.32523	−	3.32523i	0.153873	−	0.153873i	0.779845	+	0.625972i	$0.215298\pi$
$468$	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	$-0.559249\pi$
$479$	−8.10066			−0.370128			−0.185064	+	0.982726i	$0.559249\pi$
$480$	43.8878	−	5.48797i	2.00319	−	0.250491i
$481$			17.5686i			0.801059i
$482$	−4.13868	+	4.13868i	−0.188512	+	0.188512i
$483$	6.45806	+	1.24910i	0.293852	+	0.0568359i
$484$			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	0.865801	−	0.500389i	$-0.166809\pi$
$487$	8.06395	+	8.06395i	0.365412	+	0.365412i	−0.500389	+	0.865801i	$0.666809\pi$
$488$	−6.82250	−	6.82250i	−0.308840	−	0.308840i
$489$	4.17341			0.188728
$490$	−28.6845	+	16.7175i	−1.29583	+	0.755221i
$491$	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
$497$	2.65572	+	0.513661i	0.119125	+	0.0230409i
$498$	−36.3038	+	36.3038i	−1.62681	+	1.62681i
$499$		−	9.53903i		−	0.427026i	−0.976940	−	0.213513i	$-0.931509\pi$
$499$		−	9.53903i		−	0.427026i	0.976940	−	0.213513i	$-0.0684905\pi$
$500$	−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	$-0.272583\pi$
$503$	−2.24839	−	2.24839i	−0.100251	−	0.100251i	−0.755453	+	0.655203i	$0.772583\pi$
$504$	−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	$-0.267283\pi$
$509$	30.1275			1.33538			0.667690	+	0.744439i	$0.267283\pi$
$510$	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
$518$	4.52800	−	23.4106i	0.198949	−	1.02860i
$519$		−	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	$-0.467971\pi$
$523$	−20.4563	−	20.4563i	−0.894489	−	0.894489i	−0.994942	+	0.100452i	$0.967971\pi$
$524$	34.1632			1.49242
$525$	−24.5592	−	21.8750i	−1.07185	−	0.954703i
$526$	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
$532$	−2.95184	+	15.2615i	−0.127978	+	0.661671i
$533$	−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	0.425832	−	0.904802i	$-0.359981\pi$
$547$	−11.2022	−	11.2022i	−0.478970	−	0.478970i	−0.904802	+	0.425832i	$0.859981\pi$
$548$	−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
$553$	−4.87437	+	25.2014i	−0.207279	+	1.07167i
$554$		−	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	0.780517	−	0.625134i	$-0.214956\pi$
$557$	3.66717	+	3.66717i	0.155383	+	0.155383i	−0.625134	+	0.780517i	$0.714956\pi$
$558$	−8.11937	−	8.11937i	−0.343721	−	0.343721i
$559$	41.0463			1.73608
$560$	−1.08476	+	16.2494i	−0.0458394	+	0.686663i
$561$	76.1476			3.21496
$562$	−36.3739	−	36.3739i	−1.53434	−	1.53434i
$563$	−30.7561	−	30.7561i	−1.29622	−	1.29622i	−0.930874	−	0.365341i	$-0.880952\pi$
$563$	−30.7561	−	30.7561i	−1.29622	−	1.29622i	−0.365341	−	0.930874i	$-0.619048\pi$
$564$		−	45.1905i		−	1.90286i
$565$	−23.8474	−	18.5463i	−1.00327	−	0.780248i
$566$			18.8957i			0.794244i
$567$	−21.8832	−	4.23258i	−0.919008	−	0.177752i
$568$	−0.765285	+	0.765285i	−0.0321107	+	0.0321107i
$569$		−	45.8253i		−	1.92110i	−0.278114	−	0.960548i	$-0.589709\pi$
$569$		−	45.8253i		−	1.92110i	0.278114	−	0.960548i	$-0.410291\pi$
$570$	−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	$-0.652199\pi$
$577$	10.2740	−	10.2740i	0.427712	−	0.427712i	0.887848	+	0.460136i	$0.152199\pi$
$578$	−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	$-0.650569\pi$
$587$	10.5298	−	10.5298i	0.434611	−	0.434611i	0.890194	+	0.455582i	$0.150569\pi$
$588$	40.0026	−	17.0679i	1.64968	−	0.703866i
$589$			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	$-0.134050\pi$
$593$	12.2692	+	12.2692i	0.503836	+	0.503836i	−0.408791	+	0.912628i	$0.634050\pi$
$594$	5.21418			0.213941
$595$	21.8359	+	24.9598i	0.895184	+	1.02325i
$596$	−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	$-0.983857\pi$
$599$		−	2.48130i		−	0.101383i	0.998714	−	0.0506917i	$-0.0161426\pi$
$600$	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	$0.943807\pi$
$602$	−54.6952	−	10.5790i	−2.22921	−	0.431167i
$603$	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	$-0.685343\pi$
$607$	7.02880	−	7.02880i	0.285290	−	0.285290i	0.835214	+	0.549924i	$0.185343\pi$
$608$	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	−0.991059	−	0.133423i	$-0.957403\pi$
$613$	−21.2341	+	21.2341i	−0.857636	+	0.857636i	0.133423	+	0.991059i	$0.457403\pi$
$614$	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	0.936678	−	0.350192i	$-0.113884\pi$
$617$	14.5680	+	14.5680i	0.586486	+	0.586486i	−0.350192	+	0.936678i	$0.613884\pi$
$618$	26.0004	−	26.0004i	1.04589	−	1.04589i
$619$	−1.12180			−0.0450889			−0.0225444	−	0.999746i	$-0.507177\pi$
$619$	−1.12180			−0.0450889			−0.0225444	+	0.999746i	$0.507177\pi$
$620$	−1.18000	−	9.43654i	−0.0473898	−	0.378981i
$621$		−	0.449903i		−	0.0180540i
$622$	0.906825	−	0.906825i	0.0363604	−	0.0363604i
$623$	38.0503	+	7.35958i	1.52445	+	0.294855i
$624$			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
$630$	26.2826	+	30.0427i	1.04712	+	1.19693i
$631$	−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
$637$	−11.3588	−	26.6220i	−0.450051	−	1.05480i
$638$	−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	$-0.371706\pi$
$643$	−13.3798	−	13.3798i	−0.527648	−	0.527648i	−0.919871	+	0.392222i	$0.871706\pi$
$644$	−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	$-0.737115\pi$
$647$	1.45577	−	1.45577i	0.0572321	−	0.0572321i	0.735144	+	0.677911i	$0.237115\pi$
$648$	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	−0.830691	−	0.556734i	$-0.812054\pi$
$653$	−7.00067	+	7.00067i	−0.273958	+	0.273958i	0.556734	+	0.830691i	$0.312054\pi$
$654$	−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
$658$	40.0751	+	7.75120i	1.56229	+	0.302173i
$659$		−	37.2812i		−	1.45227i	−0.687553	−	0.726134i	$-0.741315\pi$
$659$		−	37.2812i		−	1.45227i	0.687553	−	0.726134i	$-0.258685\pi$
$660$	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
$665$	0.926421	−	13.8776i	0.0359251	−	0.538149i
$666$	−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
$672$	9.93793	−	51.3809i	0.383364	−	1.98206i
$673$	−12.3284	+	12.3284i	−0.475224	+	0.475224i	−0.903600	−	0.428376i	$-0.859086\pi$
$673$	−12.3284	+	12.3284i	−0.475224	+	0.475224i	0.428376	+	0.903600i	$0.359086\pi$
$674$		−	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	$-0.747004\pi$
$677$	0.346340	−	0.346340i	0.0133109	−	0.0133109i	0.713731	+	0.700420i	$0.247004\pi$
$678$	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	−0.350550	−	0.936544i	$-0.614005\pi$
$683$	15.3145	−	15.3145i	0.585994	−	0.585994i	0.936544	+	0.350550i	$0.114005\pi$
$684$	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
$693$	−8.73238	+	45.1480i	−0.331716	+	1.71503i
$694$			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
$700$	1.90787	+	33.0046i	0.0721108	+	1.24746i
$701$	−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
$707$	−3.75403	+	19.4090i	−0.141185	+	0.729950i
$708$	40.8607	−	40.8607i	1.53564	−	1.53564i
$709$			32.0809i			1.20482i	0.798185	+	0.602412i	$0.205793\pi$
$709$			32.0809i			1.20482i	−0.798185	+	0.602412i	$0.794207\pi$
$710$	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	$-0.732146\pi$
$719$	−35.7355			−1.33271			−0.666354	+	0.745636i	$0.732146\pi$
$720$	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	$-0.731376\pi$
$727$	2.22970	−	2.22970i	0.0826952	−	0.0826952i	0.747244	+	0.664549i	$0.231376\pi$
$728$	11.3701	+	2.19917i	0.421404	+	0.0815066i
$729$			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	$-0.244103\pi$
$733$	0.709245	+	0.709245i	0.0261966	+	0.0261966i	−0.693887	+	0.720084i	$0.744103\pi$
$734$	−53.2657			−1.96607
$735$	−33.6212	+	19.5947i	−1.24014	+	0.722761i
$736$	−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	$0.406822\pi$
$739$			52.0563i			1.91492i	−0.288565	+	0.957460i	$0.593178\pi$
$740$	−18.7425	−	14.5761i	−0.688987	−	0.535829i
$741$		−	24.1676i		−	0.887818i
$742$	70.1144	+	13.5613i	2.57398	+	0.497851i
$743$	3.57228	−	3.57228i	0.131054	−	0.131054i	−0.638537	−	0.769591i	$-0.720460\pi$
$743$	3.57228	−	3.57228i	0.131054	−	0.131054i	0.769591	+	0.638537i	$0.220460\pi$
$744$			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	0.983160	−	0.182745i	$-0.0584983\pi$
$757$	22.0223	+	22.0223i	0.800415	+	0.800415i	−0.182745	+	0.983160i	$0.558498\pi$
$758$	−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
$763$	6.36791	−	32.9232i	0.230534	−	1.19190i
$764$			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	$-0.654993\pi$
$769$	−25.9511			−0.935819			−0.467910	+	0.883776i	$0.654993\pi$
$770$	−51.6044	+	45.1456i	−1.85969	+	1.62694i
$771$	−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	$-0.114270\pi$
$773$	16.2625	+	16.2625i	0.584922	+	0.584922i	−0.351330	+	0.936252i	$0.614270\pi$
$774$			66.9783i			2.40749i
$775$	2.09530	+	8.24716i	0.0752656	+	0.296247i
$776$			11.3224i			0.406451i
$777$	5.30729	−	27.4396i	0.190398	−	0.984391i
$778$	−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	$-0.510192\pi$
$787$	27.1411	−	27.1411i	0.967475	−	0.967475i	0.999487	+	0.0320129i	$0.0101918\pi$
$788$	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	$-0.562790\pi$
$797$	22.1509	−	22.1509i	0.784625	−	0.784625i	0.980607	+	0.195982i	$0.0627895\pi$
$798$	−6.22877	+	32.2039i	−0.220496	+	1.14001i
$799$		−	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
$805$	3.89537	+	4.45265i	0.137294	+	0.156935i
$806$	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	$0.249963\pi$
$809$			40.2197i			1.41405i	−0.707189	+	0.707025i	$0.750037\pi$
$810$	−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	$-0.0453339\pi$
$812$	30.7852	+	5.95437i	1.08035	+	0.208958i
$813$	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	−0.746540	−	0.665340i	$-0.768286\pi$
$823$	−2.32945	+	2.32945i	−0.0811997	+	0.0811997i	0.665340	+	0.746540i	$0.268286\pi$
$824$	−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	0.297627	−	0.954682i	$-0.403805\pi$
$827$	−18.8953	−	18.8953i	−0.657055	−	0.657055i	−0.954682	+	0.297627i	$0.903805\pi$
$828$	−5.62113	+	5.62113i	−0.195348	+	0.195348i
$829$	−20.0327			−0.695765			−0.347882	−	0.937538i	$-0.613099\pi$
$829$	−20.0327			−0.695765			−0.347882	+	0.937538i	$0.613099\pi$
$830$	−45.8200	+	5.72959i	−1.59044	+	0.198877i
$831$		−	48.9643i		−	1.69855i
$832$	33.2439	−	33.2439i	1.15252	−	1.15252i
$833$	36.0914	−	15.3990i	1.25049	−	0.533545i
$834$		−	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	$-0.278692\pi$
$839$	37.1097			1.28117			0.640585	+	0.767887i	$0.278692\pi$
$840$	1.03710	−	15.5355i	0.0357834	−	0.536027i
$841$	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
$847$	−48.9769	−	9.47297i	−1.68287	−	0.325495i
$848$	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	$-0.0895564\pi$
$853$	19.9487	+	19.9487i	0.683029	+	0.683029i	−0.277653	+	0.960682i	$0.589556\pi$
$854$	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	−0.236446	+	0.971645i	$0.575983\pi$
$857$	−35.3663	+	35.3663i	−1.20809	+	1.20809i	−0.971645	+	0.236446i	$0.924017\pi$
$858$	−84.2444	+	84.2444i	−2.87606	+	2.87606i
$859$	−16.2950			−0.555978			−0.277989	−	0.960584i	$-0.589668\pi$
$859$	−16.2950			−0.555978			−0.277989	+	0.960584i	$0.589668\pi$
$860$	−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	−0.129084	−	0.991634i	$-0.541204\pi$
$863$	25.3390	−	25.3390i	0.862550	−	0.862550i	0.991634	+	0.129084i	$0.0412036\pi$
$864$	−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
$868$	−11.0477	−	2.13681i	−0.374982	−	0.0725279i
$869$			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
$875$	−5.35809	−	29.0911i	−0.181136	−	0.983458i
$876$	−33.7294			−1.13961
$877$	1.86436	+	1.86436i	0.0629549	+	0.0629549i	0.737883	−	0.674928i	$-0.235825\pi$
$877$	1.86436	+	1.86436i	0.0629549	+	0.0629549i	−0.674928	+	0.737883i	$0.735825\pi$
$878$	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	$-0.120766\pi$
$882$	43.4411	−	18.5350i	1.46274	−	0.624104i
$883$	6.60804	−	6.60804i	0.222378	−	0.222378i	−0.587121	−	0.809499i	$-0.699739\pi$
$883$	6.60804	−	6.60804i	0.222378	−	0.222378i	0.809499	+	0.587121i	$0.199739\pi$
$884$		−	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	$-0.505762\pi$
$887$	29.2386	−	29.2386i	0.981737	−	0.981737i	0.999836	+	0.0180995i	$0.00576157\pi$
$888$	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
$903$	−64.1085	−	12.3997i	−2.13340	−	0.412635i
$904$		−	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	0.904239	+	0.427027i	$0.140439\pi$
$907$	40.0930	+	40.0930i	1.33127	+	1.33127i	0.427027	+	0.904239i	$0.359561\pi$
$908$	−15.3356	−	15.3356i	−0.508930	−	0.508930i
$909$	23.7677			0.788326
$910$	−51.7715	−	3.45610i	−1.71621	−	0.114569i
$911$	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
$917$	−6.86826	+	35.5101i	−0.226810	+	1.17265i
$918$	−3.78258	+	3.78258i	−0.124844	+	0.124844i
$919$			46.8697i			1.54609i	0.634352	+	0.773045i	$0.281267\pi$
$919$			46.8697i			1.54609i	−0.634352	+	0.773045i	$0.718733\pi$
$920$	−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	$-0.792629\pi$
$929$	−48.4740			−1.59038			−0.795190	+	0.606360i	$0.792629\pi$
$930$	−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	$-0.806551\pi$
$937$	−7.65052	+	7.65052i	−0.249932	+	0.249932i	0.571011	+	0.820942i	$0.306551\pi$
$938$	11.3196	−	58.5245i	0.369599	−	1.91089i
$939$			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
$945$	1.75254	+	2.00326i	0.0570100	+	0.0651661i
$946$	−115.049			−3.74055
$947$	13.2073	+	13.2073i	0.429178	+	0.429178i	0.888348	−	0.459170i	$-0.151853\pi$
$947$	13.2073	+	13.2073i	0.429178	+	0.429178i	−0.459170	+	0.888348i	$0.651853\pi$
$948$	−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
$952$	−2.98140	+	15.4144i	−0.0966278	+	0.499583i
$953$	10.1786	−	10.1786i	0.329718	−	0.329718i	−0.522761	−	0.852479i	$-0.675098\pi$
$953$	10.1786	−	10.1786i	0.329718	−	0.329718i	0.852479	+	0.522761i	$0.175098\pi$
$954$		−	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	0.949696	+	0.313173i	$0.101392\pi$
$967$	39.2710	+	39.2710i	1.26287	+	1.26287i	0.313173	+	0.949696i	$0.398608\pi$
$968$	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
$973$	11.4085	+	2.20660i	0.365741	+	0.0707404i
$974$		−	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	0.452711	−	0.891657i	$-0.350457\pi$
$977$	−13.7201	−	13.7201i	−0.438946	−	0.438946i	−0.891657	+	0.452711i	$0.850457\pi$
$978$	−6.25948	−	6.25948i	−0.200156	−	0.200156i
$979$	80.0369			2.55799
$980$	37.8249	+	9.96977i	1.20827	+	0.318473i
$981$	−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	$-0.349675\pi$
$983$	−13.6587	−	13.6587i	−0.435643	−	0.435643i	−0.890543	+	0.454899i	$0.849675\pi$
$984$			22.5681i			0.719446i
$985$	−10.2787	+	13.2167i	−0.327507	+	0.421119i
$986$		−	56.3862i		−	1.79570i
$987$	46.9722	+	9.08522i	1.49514	+	0.289186i
$988$	−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	0.374928	−	0.927054i	$-0.377667\pi$
$997$	41.1105	−	41.1105i	1.30198	−	1.30198i	0.927054	−	0.374928i	$-0.122333\pi$
$998$	−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.622.15	✓	176
5.3	odd	4	inner	805.2.k.a.783.16	yes	176
7.6	odd	2	inner	805.2.k.a.622.16	yes	176
35.13	even	4	inner	805.2.k.a.783.15	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.k.a.622.15	✓	176	1.1	even	1	trivial
805.2.k.a.622.16	yes	176	7.6	odd	2	inner
805.2.k.a.783.15	yes	176	35.13	even	4	inner
805.2.k.a.783.16	yes	176	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49985 - 1.49985i) q^{2} +(-1.75798 - 1.75798i) q^{3} +2.49908i q^{4} +(-0.277450 - 2.21879i) q^{5} +5.27339i q^{6} +(-2.59761 - 0.502421i) q^{7} +(0.748540 - 0.748540i) q^{8} +3.18096i q^{9} +O(q^{10})\)	\(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} +(-2.59761 - 0.502421i) 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} +(1.25559 - 6.49163i) 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} +(-0.394061 + 5.90294i) 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} +(2.64946 - 13.6982i) 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} +(1.59818 - 8.26290i) 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} +(9.44454 - 8.26247i) 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} +(14.1932 + 2.74520i) 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} +(-5.82684 - 13.6566i) 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

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