LMFDB - Embedded newform 185.2.p.a.103.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.p (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.16
Character	$\chi$	$=$	185.103
Dual form			185.2.p.a.97.16

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09500 + 1.89659i) q^{2} +(0.719938 + 2.68684i) q^{3} +(-1.39805 + 2.42149i) q^{4} +(0.538130 - 2.17035i) q^{5} +(-4.30752 + 4.30752i) q^{6} +(-0.548654 - 2.04761i) q^{7} -1.74345 q^{8} +(-4.10274 + 2.36872i) q^{9} +(4.70553 - 1.35592i) q^{10} -1.23973i q^{11} +(-7.51267 - 2.01301i) q^{12} +(2.36045 - 4.08842i) q^{13} +(3.28270 - 3.28270i) q^{14} +(6.21881 - 0.116643i) q^{15} +(0.887020 + 1.53636i) q^{16} +(0.0289241 - 0.0166994i) q^{17} +(-8.98500 - 5.18749i) q^{18} +(-7.22035 + 1.93469i) q^{19} +(4.50315 + 4.33733i) q^{20} +(5.10660 - 2.94830i) q^{21} +(2.35127 - 1.35751i) q^{22} -6.57468 q^{23} +(-1.25517 - 4.68438i) q^{24} +(-4.42083 - 2.33586i) q^{25} +10.3388 q^{26} +(-3.41738 - 3.41738i) q^{27} +(5.72530 + 1.53409i) q^{28} +(1.35173 - 1.35173i) q^{29} +(7.03082 + 11.6668i) q^{30} +(6.48877 + 6.48877i) q^{31} +(-3.68602 + 6.38438i) q^{32} +(3.33097 - 0.892530i) q^{33} +(0.0633438 + 0.0365716i) q^{34} +(-4.73927 + 0.0888923i) q^{35} -13.2463i q^{36} +(-3.03439 + 5.27186i) q^{37} +(-11.5756 - 11.5756i) q^{38} +(12.6843 + 3.39875i) q^{39} +(-0.938203 + 3.78389i) q^{40} +(-0.983566 - 0.567862i) q^{41} +(11.1834 + 6.45677i) q^{42} -1.39708 q^{43} +(3.00200 + 1.73320i) q^{44} +(2.93314 + 10.1791i) q^{45} +(-7.19927 - 12.4695i) q^{46} +(2.19251 - 2.19251i) q^{47} +(-3.48937 + 3.48937i) q^{48} +(2.17051 - 1.25315i) q^{49} +(-0.410624 - 10.9423i) q^{50} +(0.0656922 + 0.0656922i) q^{51} +(6.60004 + 11.4316i) q^{52} +(1.55300 - 5.79588i) q^{53} +(2.73936 - 10.2234i) q^{54} +(-2.69065 - 0.667138i) q^{55} +(0.956551 + 3.56990i) q^{56} +(-10.3964 - 18.0071i) q^{57} +(4.04382 + 1.08354i) q^{58} +(-2.33391 + 8.71027i) q^{59} +(-8.41174 + 15.2219i) q^{60} +(1.47405 - 0.394969i) q^{61} +(-5.20137 + 19.4118i) q^{62} +(7.10119 + 7.10119i) q^{63} -12.5967 q^{64} +(-7.60306 - 7.32310i) q^{65} +(5.34017 + 5.34017i) q^{66} +(9.51822 - 2.55040i) q^{67} +0.0933860i q^{68} +(-4.73336 - 17.6651i) q^{69} +(-5.35809 - 8.89113i) q^{70} +(-3.72842 + 6.45780i) q^{71} +(7.15292 - 4.12974i) q^{72} +(10.8733 - 10.8733i) q^{73} +(-13.3212 + 0.0176679i) q^{74} +(3.09337 - 13.5598i) q^{75} +(5.40957 - 20.1888i) q^{76} +(-2.53848 + 0.680184i) q^{77} +(7.44326 + 27.7786i) q^{78} +(8.39531 - 2.24952i) q^{79} +(3.81178 - 1.09838i) q^{80} +(-0.384493 + 0.665961i) q^{81} -2.48723i q^{82} +(-1.18288 + 4.41457i) q^{83} +16.4874i q^{84} +(-0.0206785 - 0.0717619i) q^{85} +(-1.52981 - 2.64970i) q^{86} +(4.60504 + 2.65872i) q^{87} +2.16141i q^{88} +(-8.74613 - 2.34352i) q^{89} +(-16.0938 + 16.7090i) q^{90} +(-9.66653 - 2.59014i) q^{91} +(9.19171 - 15.9205i) q^{92} +(-12.7628 + 22.1058i) q^{93} +(6.55910 + 1.75751i) q^{94} +(0.313456 + 16.7118i) q^{95} +(-19.8075 - 5.30741i) q^{96} +3.75535i q^{97} +(4.75342 + 2.74439i) q^{98} +(2.93658 + 5.08630i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.09500	+	1.89659i	0.774282	+	1.34110i	0.935197	+	0.354127i	$0.115222\pi$
$2$	1.09500	+	1.89659i	0.774282	+	1.34110i	−0.160916	+	0.986968i	$0.551445\pi$
$3$	0.719938	+	2.68684i	0.415656	+	1.55125i	0.783518	+	0.621369i	$0.213423\pi$
$3$	0.719938	+	2.68684i	0.415656	+	1.55125i	−0.367862	+	0.929881i	$0.619910\pi$
$4$	−1.39805	+	2.42149i	−0.699024	+	1.21075i
$5$	0.538130	−	2.17035i	0.240659	−	0.970610i
$5$	0.538130	−	2.17035i	0.240659	−	0.970610i
$6$	−4.30752	+	4.30752i	−1.75854	+	1.75854i
$7$	−0.548654	−	2.04761i	−0.207372	−	0.773922i	−0.988714	−	0.149819i	$-0.952131\pi$
$7$	−0.548654	−	2.04761i	−0.207372	−	0.773922i	0.781342	−	0.624103i	$-0.214536\pi$
$8$	−1.74345			−0.616402
$9$	−4.10274	+	2.36872i	−1.36758	+	0.789573i
$10$	4.70553	−	1.35592i	1.48802	−	0.428778i
$11$		−	1.23973i		−	0.373793i	−0.982380	−	0.186897i	$-0.940157\pi$
$11$		−	1.23973i		−	0.373793i	0.982380	−	0.186897i	$-0.0598430\pi$
$12$	−7.51267	−	2.01301i	−2.16872	−	0.581107i
$13$	2.36045	−	4.08842i	0.654671	−	1.13392i	−0.327306	−	0.944919i	$-0.606141\pi$
$13$	2.36045	−	4.08842i	0.654671	−	1.13392i	0.981976	−	0.189004i	$-0.0605260\pi$
$14$	3.28270	−	3.28270i	0.877339	−	0.877339i
$15$	6.21881	−	0.116643i	1.60569	−	0.0301172i
$16$	0.887020	+	1.53636i	0.221755	+	0.384091i
$17$	0.0289241	−	0.0166994i	0.00701514	−	0.00405019i	−0.496488	−	0.868043i	$-0.665377\pi$
$17$	0.0289241	−	0.0166994i	0.00701514	−	0.00405019i	0.503503	+	0.863993i	$0.332044\pi$
$18$	−8.98500	−	5.18749i	−2.11779	−	1.22270i
$19$	−7.22035	+	1.93469i	−1.65646	+	0.443847i	−0.961411	−	0.275115i	$-0.911284\pi$
$19$	−7.22035	+	1.93469i	−1.65646	+	0.443847i	−0.695049	+	0.718962i	$0.744618\pi$
$20$	4.50315	+	4.33733i	1.00693	+	0.969856i
$21$	5.10660	−	2.94830i	1.11435	−	0.643371i
$22$	2.35127	−	1.35751i	0.501292	−	0.289421i
$23$	−6.57468			−1.37091			−0.685457	−	0.728113i	$-0.740398\pi$
$23$	−6.57468			−1.37091			−0.685457	+	0.728113i	$0.740398\pi$
$24$	−1.25517	−	4.68438i	−0.256211	−	0.956194i
$25$	−4.42083	−	2.33586i	−0.884166	−	0.467172i
$26$	10.3388			2.02760
$27$	−3.41738	−	3.41738i	−0.657675	−	0.657675i
$28$	5.72530	+	1.53409i	1.08198	+	0.289916i
$29$	1.35173	−	1.35173i	0.251009	−	0.251009i	−0.570375	−	0.821384i	$-0.693202\pi$
$29$	1.35173	−	1.35173i	0.251009	−	0.251009i	0.821384	+	0.570375i	$0.193202\pi$
$30$	7.03082	+	11.6668i	1.28365	+	2.13006i
$31$	6.48877	+	6.48877i	1.16542	+	1.16542i	0.983271	+	0.182146i	$0.0583044\pi$
$31$	6.48877	+	6.48877i	1.16542	+	1.16542i	0.182146	+	0.983271i	$0.441696\pi$
$32$	−3.68602	+	6.38438i	−0.651603	+	1.12861i
$33$	3.33097	−	0.892530i	0.579847	−	0.155369i
$34$	0.0633438	+	0.0365716i	0.0108634	+	0.00627198i
$35$	−4.73927	+	0.0888923i	−0.801082	+	0.0150255i
$36$		−	13.2463i		−	2.20772i
$37$	−3.03439	+	5.27186i	−0.498851	+	0.866688i
$37$	−3.03439	+	5.27186i	−0.498851	+	0.866688i
$38$	−11.5756	−	11.5756i	−1.87781	−	1.87781i
$39$	12.6843	+	3.39875i	2.03112	+	0.544236i
$40$	−0.938203	+	3.78389i	−0.148343	+	0.598286i
$41$	−0.983566	−	0.567862i	−0.153607	−	0.0886851i	0.421226	−	0.906956i	$-0.361600\pi$
$41$	−0.983566	−	0.567862i	−0.153607	−	0.0886851i	−0.574833	+	0.818270i	$0.694933\pi$
$42$	11.1834	+	6.45677i	1.72564	+	0.996301i
$43$	−1.39708			−0.213053			−0.106527	−	0.994310i	$-0.533973\pi$
$43$	−1.39708			−0.213053			−0.106527	+	0.994310i	$0.533973\pi$
$44$	3.00200	+	1.73320i	0.452568	+	0.261290i
$45$	2.93314	+	10.1791i	0.437246	+	1.51741i
$46$	−7.19927	−	12.4695i	−1.06147	−	1.83853i
$47$	2.19251	−	2.19251i	0.319811	−	0.319811i	−0.528884	−	0.848694i	$-0.677389\pi$
$47$	2.19251	−	2.19251i	0.319811	−	0.319811i	0.848694	+	0.528884i	$0.177389\pi$
$48$	−3.48937	+	3.48937i	−0.503647	+	0.503647i
$49$	2.17051	−	1.25315i	0.310073	−	0.179021i
$50$	−0.410624	−	10.9423i	−0.0580710	−	1.54747i
$51$	0.0656922	+	0.0656922i	0.00919874	+	0.00919874i
$52$	6.60004	+	11.4316i	0.915261	+	1.58528i
$53$	1.55300	−	5.79588i	0.213321	−	0.796126i	−0.773429	−	0.633882i	$-0.781460\pi$
$53$	1.55300	−	5.79588i	0.213321	−	0.796126i	0.986751	−	0.162244i	$-0.0518730\pi$
$54$	2.73936	−	10.2234i	0.372779	−	1.39123i
$55$	−2.69065	−	0.667138i	−0.362807	−	0.0899568i
$56$	0.956551	+	3.56990i	0.127824	+	0.477047i
$57$	−10.3964	−	18.0071i	−1.37704	−	2.38510i
$58$	4.04382	+	1.08354i	0.530979	+	0.142275i
$59$	−2.33391	+	8.71027i	−0.303849	+	1.13398i	0.630083	+	0.776528i	$0.283021\pi$
$59$	−2.33391	+	8.71027i	−0.303849	+	1.13398i	−0.933932	+	0.357452i	$0.883646\pi$
$60$	−8.41174	+	15.2219i	−1.08595	+	1.96513i
$61$	1.47405	−	0.394969i	0.188732	−	0.0505706i	−0.163215	−	0.986591i	$-0.552186\pi$
$61$	1.47405	−	0.394969i	0.188732	−	0.0505706i	0.351947	+	0.936020i	$0.385520\pi$
$62$	−5.20137	+	19.4118i	−0.660574	+	2.46530i
$63$	7.10119	+	7.10119i	0.894666	+	0.894666i
$64$	−12.5967			−1.57459
$65$	−7.60306	−	7.32310i	−0.943044	−	0.908319i
$66$	5.34017	+	5.34017i	0.657330	+	0.657330i
$67$	9.51822	−	2.55040i	1.16284	−	0.311581i	0.374737	−	0.927131i	$-0.377733\pi$
$67$	9.51822	−	2.55040i	1.16284	−	0.311581i	0.788098	+	0.615550i	$0.211066\pi$
$68$			0.0933860i			0.0113247i
$69$	−4.73336	−	17.6651i	−0.569829	−	2.12663i
$70$	−5.35809	−	8.89113i	−0.640414	−	1.06269i
$71$	−3.72842	+	6.45780i	−0.442482	+	0.766400i	−0.997873	−	0.0651886i	$-0.979235\pi$
$71$	−3.72842	+	6.45780i	−0.442482	+	0.766400i	0.555391	+	0.831589i	$0.312568\pi$
$72$	7.15292	−	4.12974i	0.842980	−	0.486695i
$73$	10.8733	−	10.8733i	1.27262	−	1.27262i	0.327912	−	0.944708i	$-0.393655\pi$
$73$	10.8733	−	10.8733i	1.27262	−	1.27262i	0.944708	−	0.327912i	$-0.106345\pi$
$74$	−13.3212	+	0.0176679i	−1.54856	+	0.00205385i
$75$	3.09337	−	13.5598i	0.357192	−	1.56575i
$76$	5.40957	−	20.1888i	0.620520	−	2.31581i
$77$	−2.53848	+	0.680184i	−0.289287	+	0.0775142i
$78$	7.44326	+	27.7786i	0.842784	+	3.14531i
$79$	8.39531	−	2.24952i	0.944546	−	0.253090i	0.246500	−	0.969143i	$-0.420720\pi$
$79$	8.39531	−	2.24952i	0.944546	−	0.253090i	0.698046	+	0.716052i	$0.254053\pi$
$80$	3.81178	−	1.09838i	0.426170	−	0.122802i
$81$	−0.384493	+	0.665961i	−0.0427214	+	0.0739956i
$82$		−	2.48723i		−	0.274669i
$83$	−1.18288	+	4.41457i	−0.129838	+	0.484562i	−0.999966	−	0.00826393i	$-0.997369\pi$
$83$	−1.18288	+	4.41457i	−0.129838	+	0.484562i	0.870128	+	0.492826i	$0.164036\pi$
$84$			16.4874i			1.79893i
$85$	−0.0206785	−	0.0717619i	−0.00224290	−	0.00778367i
$86$	−1.52981	−	2.64970i	−0.164963	−	0.285725i
$87$	4.60504	+	2.65872i	0.493712	+	0.285045i
$88$			2.16141i			0.230407i
$89$	−8.74613	−	2.34352i	−0.927088	−	0.248413i	−0.236476	−	0.971637i	$-0.575992\pi$
$89$	−8.74613	−	2.34352i	−0.927088	−	0.248413i	−0.690613	+	0.723225i	$0.742659\pi$
$90$	−16.0938	+	16.7090i	−1.69643	+	1.76129i
$91$	−9.66653	−	2.59014i	−1.01333	−	0.271520i
$92$	9.19171	−	15.9205i	0.958302	−	1.65983i
$93$	−12.7628	+	22.1058i	−1.32344	+	2.29227i
$94$	6.55910	+	1.75751i	0.676520	+	0.181273i
$95$	0.313456	+	16.7118i	0.0321599	+	1.71459i
$96$	−19.8075	−	5.30741i	−2.02160	−	0.541685i
$97$			3.75535i			0.381298i	0.981658	+	0.190649i	$0.0610593\pi$
$97$			3.75535i			0.381298i	−0.981658	+	0.190649i	$0.938941\pi$
$98$	4.75342	+	2.74439i	0.480168	+	0.277225i
$99$	2.93658	+	5.08630i	0.295137	+	0.511193i
$100$	11.8368	−	7.43935i	1.18368	−	0.743935i
$101$			4.09183i			0.407152i	0.979059	+	0.203576i	$0.0652565\pi$
$101$			4.09183i			0.407152i	−0.979059	+	0.203576i	$0.934744\pi$
$102$	−0.0526585	+	0.196524i	−0.00521397	+	0.0194588i
$103$		−	6.53109i		−	0.643527i	−0.946820	−	0.321764i	$-0.895724\pi$
$103$		−	6.53109i		−	0.643527i	0.946820	−	0.321764i	$-0.104276\pi$
$104$	−4.11532	+	7.12795i	−0.403541	+	0.698953i
$105$	−3.65082	−	12.6697i	−0.356283	−	1.23643i
$106$	12.6930	−	3.40107i	1.23285	−	0.330342i
$107$	−5.20333	−	19.4191i	−0.503025	−	1.87731i	−0.479408	−	0.877592i	$-0.659149\pi$
$107$	−5.20333	−	19.4191i	−0.503025	−	1.87731i	−0.0236166	−	0.999721i	$-0.507518\pi$
$108$	13.0528	−	3.49749i	1.25601	−	0.336546i
$109$	0.528705	−	1.97315i	0.0506407	−	0.188994i	−0.935972	−	0.352074i	$-0.885476\pi$
$109$	0.528705	−	1.97315i	0.0506407	−	0.188994i	0.986613	+	0.163081i	$0.0521431\pi$
$110$	−1.68097	−	5.83359i	−0.160274	−	0.556211i
$111$	−16.3492	−	4.35753i	−1.55180	−	0.413598i
$112$	2.65920	−	2.65920i	0.251271	−	0.251271i
$113$	−14.0235	+	8.09647i	−1.31922	+	0.761652i	−0.983603	−	0.180346i	$-0.942278\pi$
$113$	−14.0235	+	8.09647i	−1.31922	+	0.761652i	−0.335617	+	0.941999i	$0.608945\pi$
$114$	22.7681	−	39.4355i	2.13243	−	3.69347i
$115$	−3.53803	+	14.2693i	−0.329923	+	1.33062i
$116$	1.38341	+	5.16297i	0.128447	+	0.479370i
$117$			22.3650i			2.06764i
$118$	−19.0755	+	5.11126i	−1.75604	+	0.470529i
$119$	−0.0500631	−	0.0500631i	−0.00458927	−	0.00458927i
$120$	−10.8422	+	0.203362i	−0.989751	+	0.0185643i
$121$	9.46306			0.860279
$122$	2.36318	+	2.36318i	0.213952	+	0.213952i
$123$	0.817650	−	3.05151i	0.0737250	−	0.275146i
$124$	−24.7841	+	6.64088i	−2.22568	+	0.596369i
$125$	−7.44862	+	8.33775i	−0.666225	+	0.745751i
$126$	−5.69228	+	21.2439i	−0.507109	+	1.89256i
$127$	−0.438297	−	0.117441i	−0.0388925	−	0.0104212i	0.239320	−	0.970941i	$-0.423075\pi$
$127$	−0.438297	−	0.117441i	−0.0388925	−	0.0104212i	−0.278213	+	0.960519i	$0.589742\pi$
$128$	−6.42132	−	11.1221i	−0.567570	−	0.983061i
$129$	−1.00581	−	3.75374i	−0.0885569	−	0.330499i
$130$	5.56360	−	22.4387i	0.487960	−	1.96801i
$131$	−3.09915	+	11.5662i	−0.270774	+	1.01054i	0.687846	+	0.725856i	$0.258556\pi$
$131$	−3.09915	+	11.5662i	−0.270774	+	1.01054i	−0.958621	+	0.284687i	$0.908110\pi$
$132$	−2.49560	+	9.31370i	−0.217214	+	0.810654i
$133$	7.92294	+	13.7229i	0.687006	+	1.18993i
$134$	15.2595	+	15.2595i	1.31822	+	1.31822i
$135$	−9.25591	+	5.57791i	−0.796622	+	0.480070i
$136$	−0.0504278	+	0.0291145i	−0.00432415	+	0.00249655i
$137$	−0.454200	+	0.454200i	−0.0388049	+	0.0388049i	−0.726243	−	0.687438i	$-0.758735\pi$
$137$	−0.454200	+	0.454200i	−0.0388049	+	0.0388049i	0.687438	+	0.726243i	$0.258735\pi$
$138$	28.3206	−	28.3206i	2.41081	−	2.41081i
$139$	6.18063	+	10.7052i	0.524234	+	0.908000i	0.999602	+	0.0282126i	$0.00898155\pi$
$139$	6.18063	+	10.7052i	0.524234	+	0.908000i	−0.475368	+	0.879787i	$0.657685\pi$
$140$	6.41047	−	11.6004i	0.541783	−	0.980409i
$141$	7.46941	+	4.31246i	0.629037	+	0.363175i
$142$	−16.3305			−1.37042
$143$	−5.06854	−	2.92632i	−0.423853	−	0.244712i
$144$	−7.27843	−	4.20220i	−0.606536	−	0.350184i
$145$	−2.20631	−	3.66112i	−0.183224	−	0.304040i
$146$	32.5284	+	8.71596i	2.69207	+	0.721338i
$147$	4.92964	+	4.92964i	0.406590	+	0.406590i
$148$	−8.52352	−	14.7181i	−0.700629	−	1.20982i
$149$		−	0.733690i		−	0.0601063i	−0.999548	−	0.0300531i	$-0.990432\pi$
$149$		−	0.733690i		−	0.0601063i	0.999548	−	0.0300531i	$-0.00956765\pi$
$150$	29.1046	−	8.98105i	2.37638	−	0.733300i
$151$	−8.11344	−	4.68430i	−0.660262	−	0.381203i	0.132115	−	0.991234i	$-0.457823\pi$
$151$	−8.11344	−	4.68430i	−0.660262	−	0.381203i	−0.792377	+	0.610032i	$0.791157\pi$
$152$	12.5883	−	3.37303i	1.02105	−	0.273589i
$153$	−0.0791122	+	0.137026i	−0.00639584	+	0.0110779i
$154$	−4.06967	−	4.06967i	−0.327943	−	0.327943i
$155$	17.5747	−	10.5911i	1.41163	−	0.850697i
$156$	−25.9633	+	25.9633i	−2.07873	+	2.07873i
$157$	13.0554	+	3.49819i	1.04194	+	0.279186i	0.738915	−	0.673798i	$-0.235338\pi$
$157$	13.0554	+	3.49819i	1.04194	+	0.279186i	0.303020	+	0.952984i	$0.402005\pi$
$158$	13.4593	+	13.4593i	1.07076	+	1.07076i
$159$	16.6907			1.32366
$160$	11.8728	+	11.4356i	0.938625	+	0.904062i
$161$	3.60722	+	13.4623i	0.284289	+	1.06098i
$162$	−1.68408			−0.132314
$163$	11.9309	−	6.88834i	0.934504	−	0.539536i	0.0462707	−	0.998929i	$-0.485266\pi$
$163$	11.9309	−	6.88834i	0.934504	−	0.539536i	0.888233	+	0.459393i	$0.151933\pi$
$164$	2.75014	−	1.58780i	0.214750	−	0.123986i
$165$	−0.144607	−	7.70966i	−0.0112576	−	0.600196i
$166$	−9.66791	+	2.59051i	−0.750375	+	0.201062i
$167$	−11.1342	−	6.42833i	−0.861590	−	0.497439i	0.00295410	−	0.999996i	$-0.499060\pi$
$167$	−11.1342	−	6.42833i	−0.861590	−	0.497439i	−0.864545	+	0.502556i	$0.832393\pi$
$168$	−8.90309	+	5.14020i	−0.686889	+	0.396575i
$169$	−4.64344	−	8.04267i	−0.357187	−	0.618667i
$170$	0.113460	−	0.117798i	0.00870201	−	0.00903469i
$171$	25.0405	−	25.0405i	1.91489	−	1.91489i
$172$	1.95319	−	3.38302i	0.148929	−	0.257953i
$173$	1.77628	+	0.475953i	0.135048	+	0.0361860i	0.325710	−	0.945470i	$-0.394397\pi$
$173$	1.77628	+	0.475953i	0.135048	+	0.0361860i	−0.190662	+	0.981656i	$0.561063\pi$
$174$			11.6452i			0.882819i
$175$	−2.35742	+	10.3337i	−0.178204	+	0.781154i
$176$	1.90468	−	1.09967i	0.143571	−	0.0828905i
$177$	−25.0834			−1.88538
$178$	−5.13231	−	19.1540i	−0.384683	−	1.43565i
$179$	9.45565	−	9.45565i	0.706749	−	0.706749i	−0.259101	−	0.965850i	$-0.583426\pi$
$179$	9.45565	−	9.45565i	0.706749	−	0.706749i	0.965850	+	0.259101i	$0.0834264\pi$
$180$	−28.7492	−	7.12826i	−2.14284	−	0.531309i
$181$	0.584911	−	1.01310i	0.0434761	−	0.0753028i	−0.843469	−	0.537179i	$-0.819490\pi$
$181$	0.584911	−	1.01310i	0.0434761	−	0.0753028i	0.886945	+	0.461876i	$0.152823\pi$
$182$	−5.67240	−	21.1697i	−0.420467	−	1.56920i
$183$	2.12244	+	3.67618i	0.156895	+	0.271751i
$184$	11.4626			0.845035
$185$	9.80887	+	9.42264i	0.721162	+	0.692766i
$186$	−55.9011			−4.09886
$187$	−0.0207027	−	0.0358582i	−0.00151393	−	0.00262221i
$188$	2.24391	+	8.37438i	0.163654	+	0.610764i
$189$	−5.12249	+	8.87241i	−0.372606	+	0.645373i
$190$	−31.3522	+	18.8939i	−2.27453	+	1.37071i
$191$	17.2720	−	17.2720i	1.24976	−	1.24976i	0.293931	−	0.955826i	$-0.405036\pi$
$191$	17.2720	−	17.2720i	1.24976	−	1.24976i	0.955826	−	0.293931i	$-0.0949638\pi$
$192$	−9.06883	−	33.8453i	−0.654486	−	2.44258i
$193$	−15.3627			−1.10583			−0.552915	−	0.833237i	$-0.686485\pi$
$193$	−15.3627			−1.10583			−0.552915	+	0.833237i	$0.686485\pi$
$194$	−7.12239	+	4.11211i	−0.511357	+	0.295232i
$195$	14.2023	−	25.7004i	1.01705	−	1.84045i
$196$			7.00783i			0.500559i
$197$	−14.0673	−	3.76932i	−1.00225	−	0.268553i	−0.279863	−	0.960040i	$-0.590289\pi$
$197$	−14.0673	−	3.76932i	−1.00225	−	0.268553i	−0.722389	+	0.691487i	$0.756956\pi$
$198$	−6.43110	+	11.1390i	−0.457039	+	0.791614i
$199$	−11.3240	+	11.3240i	−0.802737	+	0.802737i	−0.983523	−	0.180786i	$-0.942136\pi$
$199$	−11.3240	+	11.3240i	−0.802737	+	0.802737i	0.180786	+	0.983523i	$0.442136\pi$
$200$	7.70749	+	4.07246i	0.545002	+	0.287966i
$201$	13.7050	+	23.7378i	0.966679	+	1.67434i
$202$	−7.76055	+	4.48055i	−0.546030	+	0.315251i
$203$	−3.50943	−	2.02617i	−0.246314	−	0.142209i
$204$	−0.250914	+	0.0672321i	−0.0175675	+	0.00470719i
$205$	−1.76175	+	1.82910i	−0.123046	+	0.127750i
$206$	12.3868	−	7.15154i	0.863031	−	0.498271i
$207$	26.9742	−	15.5736i	1.87484	−	1.08244i
$208$	8.37506			0.580706
$209$	2.39849	+	8.95129i	0.165907	+	0.619174i
$210$	20.0316	−	20.7974i	1.38231	−	1.43516i
$211$	−14.8333			−1.02117			−0.510584	−	0.859828i	$-0.670571\pi$
$211$	−14.8333			−1.02117			−0.510584	+	0.859828i	$0.670571\pi$
$212$	11.8635	+	11.8635i	0.814789	+	0.814789i
$213$	−20.0353	−	5.36845i	−1.37280	−	0.367840i
$214$	31.1325	−	31.1325i	2.12817	−	2.12817i
$215$	−0.751813	+	3.03216i	−0.0512732	+	0.206792i
$216$	5.95803	+	5.95803i	0.405393	+	0.405393i
$217$	9.72635	−	16.8465i	0.660268	−	1.14362i
$218$	4.32120	−	1.15786i	0.292669	−	0.0784204i
$219$	37.0429	+	21.3867i	2.50312	+	1.44518i
$220$	5.37713	−	5.58270i	0.362526	−	0.376385i
$221$		−	0.157672i		−	0.0106062i
$222$	−9.63793	−	35.7794i	−0.646855	−	2.40135i
$223$	3.28516	+	3.28516i	0.219990	+	0.219990i	0.808494	−	0.588504i	$-0.200283\pi$
$223$	3.28516	+	3.28516i	0.219990	+	0.219990i	−0.588504	+	0.808494i	$0.700283\pi$
$224$	15.0950	+	4.04470i	1.00858	+	0.270248i
$225$	23.6705	−	0.888268i	1.57804	−	0.0592179i
$226$	−30.7115	−	17.7313i	−2.04290	−	1.17947i
$227$	13.6262	+	7.86711i	0.904405	+	0.522158i	0.878627	−	0.477509i	$-0.158460\pi$
$227$	13.6262	+	7.86711i	0.904405	+	0.522158i	0.0257781	+	0.999668i	$0.491794\pi$
$228$	58.1386			3.85033
$229$	6.18242	+	3.56942i	0.408546	+	0.235874i	0.690165	−	0.723652i	$-0.257538\pi$
$229$	6.18242	+	3.56942i	0.408546	+	0.235874i	−0.281619	+	0.959526i	$0.590871\pi$
$230$	−30.9373	+	8.91471i	−2.03995	+	0.587818i
$231$	−3.65510	−	6.33081i	−0.240488	−	0.416537i
$232$	−2.35667	+	2.35667i	−0.154723	+	0.154723i
$233$	3.03747	−	3.03747i	0.198992	−	0.198992i	−0.600576	−	0.799568i	$-0.705062\pi$
$233$	3.03747	−	3.03747i	0.198992	−	0.198992i	0.799568	+	0.600576i	$0.205062\pi$
$234$	−42.4173	+	24.4896i	−2.77290	+	1.60094i
$235$	−3.57866	−	5.93837i	−0.233446	−	0.387377i
$236$	−17.8289	−	17.8289i	−1.16056	−	1.16056i
$237$	12.0882	+	20.9374i	0.785213	+	1.36003i
$238$	0.0401303	−	0.149768i	0.00260126	−	0.00970804i
$239$	−4.17069	+	15.5652i	−0.269779	+	1.00683i	0.689480	+	0.724304i	$0.257839\pi$
$239$	−4.17069	+	15.5652i	−0.269779	+	1.00683i	−0.959260	+	0.282526i	$0.908828\pi$
$240$	5.69541	+	9.45089i	0.367637	+	0.610052i
$241$	−0.716932	−	2.67563i	−0.0461817	−	0.172352i	0.938983	−	0.343963i	$-0.111770\pi$
$241$	−0.716932	−	2.67563i	−0.0461817	−	0.172352i	−0.985165	+	0.171611i	$0.945103\pi$
$242$	10.3621	+	17.9476i	0.666098	+	1.15372i
$243$	−16.0708	−	4.30617i	−1.03094	−	0.276241i
$244$	−1.10437	+	4.12157i	−0.0707002	+	0.263857i
$245$	−1.55175	−	5.38513i	−0.0991374	−	0.344043i
$246$	6.68281	−	1.79065i	0.426080	−	0.114168i
$247$	−9.13345	+	34.0865i	−0.581148	+	2.16887i
$248$	−11.3128	−	11.3128i	−0.718366	−	0.718366i
$249$	−12.7129			−0.805645
$250$	−23.9696	−	4.99718i	−1.51597	−	0.316050i
$251$	−0.234209	−	0.234209i	−0.0147832	−	0.0147832i	0.699677	−	0.714460i	$-0.253327\pi$
$251$	−0.234209	−	0.234209i	−0.0147832	−	0.0147832i	−0.714460	+	0.699677i	$0.753327\pi$
$252$	−27.1233	+	7.26766i	−1.70861	+	0.457819i
$253$			8.15084i			0.512439i
$254$	−0.257196	−	0.959869i	−0.0161379	−	0.0602276i
$255$	0.177926	−	0.107224i	0.0111422	−	0.00671463i
$256$	1.46601	−	2.53920i	0.0916254	−	0.158700i
$257$	−6.78901	+	3.91964i	−0.423487	+	0.244500i	−0.696568	−	0.717491i	$-0.745291\pi$
$257$	−6.78901	+	3.91964i	−0.423487	+	0.244500i	0.273081	+	0.961991i	$0.411957\pi$
$258$	6.01797	−	6.01797i	0.374662	−	0.374662i
$259$	12.4595	+	3.32081i	0.774196	+	0.206345i
$260$	28.3623	−	8.17270i	1.75895	−	0.506849i
$261$	−2.34393	+	8.74765i	−0.145085	+	0.541466i
$262$	−25.3300	+	6.78714i	−1.56489	+	0.419311i
$263$	−4.76520	−	17.7840i	−0.293835	−	1.09661i	−0.942138	−	0.335225i	$-0.891188\pi$
$263$	−4.76520	−	17.7840i	−0.293835	−	1.09661i	0.648303	−	0.761382i	$-0.275479\pi$
$264$	−5.80737	+	1.55608i	−0.357419	+	0.0957701i
$265$	−11.7434	−	6.48950i	−0.721390	−	0.398647i
$266$	−17.3512	+	30.0532i	−1.06387	+	1.84268i
$267$		−	25.1867i		−	1.54140i
$268$	−7.13116	+	26.6138i	−0.435605	+	1.62570i
$269$			11.0064i			0.671074i	0.942027	+	0.335537i	$0.108918\pi$
$269$			11.0064i			0.671074i	−0.942027	+	0.335537i	$0.891082\pi$
$270$	−20.7143	−	11.4469i	−1.26063	−	0.696636i
$271$	11.7063	+	20.2758i	0.711105	+	1.23167i	0.964443	+	0.264292i	$0.0851383\pi$
$271$	11.7063	+	20.2758i	0.711105	+	1.23167i	−0.253338	+	0.967378i	$0.581528\pi$
$272$	0.0513126	+	0.0296253i	0.00311128	+	0.00179630i
$273$		−	27.8372i		−	1.68478i
$274$	−1.35878	−	0.364085i	−0.0820870	−	0.0219952i
$275$	−2.89584	+	5.48065i	−0.174626	+	0.330495i
$276$	49.3934	+	13.2349i	2.97313	+	0.796648i
$277$	8.81023	−	15.2598i	0.529355	−	0.916871i	−0.470058	−	0.882635i	$-0.655767\pi$
$277$	8.81023	−	15.2598i	0.529355	−	0.916871i	0.999414	−	0.0342352i	$-0.0108995\pi$
$278$	−13.5356	+	23.4443i	−0.811809	+	1.40609i
$279$	−41.9918	−	11.2517i	−2.51399	−	0.673620i
$280$	8.26267	−	0.154979i	0.493789	−	0.00926178i
$281$	−16.0243	−	4.29370i	−0.955930	−	0.256141i	−0.253053	−	0.967452i	$-0.581435\pi$
$281$	−16.0243	−	4.29370i	−0.955930	−	0.256141i	−0.702877	+	0.711312i	$0.748101\pi$
$282$			18.8886i			1.12480i
$283$	16.5747	+	9.56940i	0.985262	+	0.568841i	0.903855	−	0.427839i	$-0.140725\pi$
$283$	16.5747	+	9.56940i	0.985262	+	0.568841i	0.0814076	+	0.996681i	$0.474058\pi$
$284$	−10.4250	−	18.0566i	−0.618610	−	1.07146i
$285$	−44.6763	+	12.8736i	−2.64639	+	0.762569i
$286$		−	12.8173i		−	0.757903i
$287$	−0.623120	+	2.32551i	−0.0367816	+	0.137271i
$288$		−	34.9246i		−	2.05795i
$289$	−8.49944	+	14.7215i	−0.499967	+	0.865969i
$290$	4.52776	−	8.19341i	0.265879	−	0.481134i
$291$	−10.0900	+	2.70362i	−0.591489	+	0.158489i
$292$	11.1282	+	41.5309i	0.651227	+	2.43041i
$293$	25.6321	−	6.86811i	1.49745	−	0.401239i	0.585202	−	0.810888i	$-0.301015\pi$
$293$	25.6321	−	6.86811i	1.49745	−	0.401239i	0.912243	+	0.409648i	$0.134349\pi$
$294$	−3.95158	+	14.7475i	−0.230461	+	0.860091i
$295$	17.6484	+	9.75266i	1.02753	+	0.567822i
$296$	5.29031	−	9.19121i	0.307493	−	0.534228i
$297$	−4.23664	+	4.23664i	−0.245835	+	0.245835i
$298$	1.39151	−	0.803391i	0.0806082	−	0.0465392i
$299$	−15.5192	+	26.8800i	−0.897498	+	1.55451i
$300$	28.5101	+	26.4478i	1.64603	+	1.52696i
$301$	0.766516	+	2.86068i	0.0441812	+	0.164887i
$302$		−	20.5172i		−	1.18063i
$303$	−10.9941	+	2.94586i	−0.631595	+	0.169235i
$304$	−9.37697	−	9.37697i	−0.537806	−	0.537806i
$305$	−0.0639925	−	3.41174i	−0.00366420	−	0.195356i
$306$	−0.346511			−0.0198087
$307$	2.20110	+	2.20110i	0.125624	+	0.125624i	0.767123	−	0.641500i	$-0.221687\pi$
$307$	2.20110	+	2.20110i	0.125624	+	0.125624i	−0.641500	+	0.767123i	$0.721687\pi$
$308$	1.90186	−	7.09784i	0.108369	−	0.404437i
$309$	17.5480	−	4.70198i	0.998272	−	0.267486i
$310$	39.3313	+	21.7349i	2.23387	+	1.23446i
$311$	2.19712	−	8.19978i	0.124588	−	0.464967i	−0.875237	−	0.483694i	$-0.839295\pi$
$311$	2.19712	−	8.19978i	0.124588	−	0.464967i	0.999825	+	0.0187272i	$0.00596139\pi$
$312$	−22.1145	−	5.92555i	−1.25198	−	0.335468i
$313$	−4.88505	−	8.46115i	−0.276119	−	0.478253i	0.694298	−	0.719688i	$-0.255715\pi$
$313$	−4.88505	−	8.46115i	−0.276119	−	0.478253i	−0.970417	+	0.241435i	$0.922382\pi$
$314$	7.66103	+	28.5913i	0.432337	+	1.61350i
$315$	19.2334	−	11.5907i	1.08368	−	0.653062i
$316$	−6.28986	+	23.4741i	−0.353833	+	1.32052i
$317$	−2.80299	+	10.4609i	−0.157432	+	0.587543i	0.841453	+	0.540330i	$0.181701\pi$
$317$	−2.80299	+	10.4609i	−0.157432	+	0.587543i	−0.998885	+	0.0472130i	$0.984966\pi$
$318$	18.2763	+	31.6555i	1.02488	+	1.77515i
$319$	−1.67578	−	1.67578i	−0.0938256	−	0.0938256i
$320$	−6.77866	+	27.3392i	−0.378939	+	1.52831i
$321$	48.4300	−	27.9611i	2.70310	−	1.56063i
$322$	−21.5827	+	21.5827i	−1.20276	+	1.20276i
$323$	−0.176534	+	0.176534i	−0.00982263	+	0.00982263i
$324$	−1.07508	−	1.86209i	−0.0597266	−	0.103449i
$325$	−19.9851	+	12.5605i	−1.10858	+	0.696732i
$326$	26.1288	+	15.0854i	1.44714	+	0.835506i
$327$	5.68219			0.314226
$328$	1.71480	+	0.990038i	0.0946838	+	0.0546657i
$329$	−5.69233	−	3.28647i	−0.313828	−	0.181189i
$330$	14.4638	−	8.71633i	0.796203	−	0.479818i
$331$	−17.8711	−	4.78853i	−0.982282	−	0.263202i	−0.268277	−	0.963342i	$-0.586454\pi$
$331$	−17.8711	−	4.78853i	−0.982282	−	0.263202i	−0.714005	+	0.700140i	$0.753121\pi$
$332$	−9.03612	−	9.03612i	−0.495921	−	0.495921i
$333$	−0.0382194	−	28.8167i	−0.00209441	−	1.57915i
$334$		−	28.1561i		−	1.54063i
$335$	−0.413213	−	22.0303i	−0.0225762	−	1.20364i
$336$	9.05931	+	5.23039i	0.494226	+	0.285341i
$337$	11.0258	−	2.95437i	0.600616	−	0.160935i	0.0543154	−	0.998524i	$-0.482702\pi$
$337$	11.0258	−	2.95437i	0.600616	−	0.160935i	0.546300	+	0.837589i	$0.316036\pi$
$338$	10.1691	−	17.6134i	0.553127	−	0.958045i
$339$	−31.8500	−	31.8500i	−1.72985	−	1.72985i
$340$	0.202680	+	0.0502539i	0.0109919	+	0.00272540i
$341$	8.04434	−	8.04434i	0.435625	−	0.435625i
$342$	74.9110	+	20.0723i	4.05072	+	1.08539i
$343$	−14.2495	−	14.2495i	−0.769399	−	0.769399i
$344$	2.43574			0.131327
$345$	−40.8867	+	0.766893i	−2.20126	+	0.0412881i
$346$	1.04234	+	3.89005i	0.0560363	+	0.209130i
$347$	9.88289			0.530542			0.265271	−	0.964174i	$-0.414539\pi$
$347$	9.88289			0.530542			0.265271	+	0.964174i	$0.414539\pi$
$348$	−12.8761	+	7.43403i	−0.690233	+	0.398506i
$349$	23.0009	−	13.2796i	1.23121	−	0.710840i	0.263929	−	0.964542i	$-0.414982\pi$
$349$	23.0009	−	13.2796i	1.23121	−	0.710840i	0.967282	+	0.253702i	$0.0816483\pi$
$350$	−22.1802	+	6.84433i	−1.18558	+	0.365845i
$351$	−22.0382	+	5.90513i	−1.17631	+	0.315192i
$352$	7.91492	+	4.56968i	0.421867	+	0.243565i
$353$	−25.2989	+	14.6063i	−1.34652	+	0.777415i	−0.987755	−	0.156012i	$-0.950136\pi$
$353$	−25.2989	+	14.6063i	−1.34652	+	0.777415i	−0.358767	+	0.933427i	$0.616803\pi$
$354$	−27.4663	−	47.5730i	−1.45982	−	2.52848i
$355$	12.0093	+	11.5671i	0.637388	+	0.613918i
$356$	17.9023	−	17.9023i	0.948821	−	0.948821i
$357$	0.0984693	−	0.170554i	0.00521155	−	0.00902667i
$358$	28.2875	+	7.57961i	1.49504	+	0.400595i
$359$		−	11.9936i		−	0.633000i	−0.948593	−	0.316500i	$-0.897492\pi$
$359$		−	11.9936i		−	0.633000i	0.948593	−	0.316500i	$-0.102508\pi$
$360$	−5.11378	−	17.7467i	−0.269520	−	0.935332i
$361$	31.9359	−	18.4382i	1.68084	−	0.970431i
$362$	2.56191			0.134651
$363$	6.81282	+	25.4258i	0.357580	+	1.33451i
$364$	19.7863	−	19.7863i	1.03708	−	1.03708i
$365$	−17.7476	−	29.4500i	−0.928950	−	1.54149i
$366$	−4.64814	+	8.05082i	−0.242962	+	0.420823i
$367$	3.94255	+	14.7138i	0.205799	+	0.768053i	0.989204	+	0.146542i	$0.0468143\pi$
$367$	3.94255	+	14.7138i	0.205799	+	0.768053i	−0.783405	+	0.621511i	$0.786519\pi$
$368$	−5.83187	−	10.1011i	−0.304007	−	0.526556i
$369$	5.38042			0.280094
$370$	−7.13022	+	28.9212i	−0.370682	+	1.50354i
$371$	−12.7197			−0.660376
$372$	−35.6860	−	61.8100i	−1.85023	−	3.20470i
$373$	1.56441	+	5.83844i	0.0810018	+	0.302303i	0.994527	−	0.104479i	$-0.0333175\pi$
$373$	1.56441	+	5.83844i	0.0810018	+	0.302303i	−0.913525	+	0.406782i	$0.866651\pi$
$374$	0.0453390	−	0.0785294i	0.00234442	−	0.00406066i
$375$	−27.7648	−	14.0106i	−1.43377	−	0.723505i
$376$	−3.82253	+	3.82253i	−0.197132	+	0.197132i
$377$	−2.33574	−	8.71710i	−0.120297	−	0.448954i
$378$	−22.4365			−1.15401
$379$	−17.3786	+	10.0335i	−0.892678	+	0.515388i	−0.874817	−	0.484453i	$-0.839019\pi$
$379$	−17.3786	+	10.0335i	−0.892678	+	0.515388i	−0.0178603	+	0.999840i	$0.505685\pi$
$380$	−40.9056	−	22.6048i	−2.09842	−	1.15960i
$381$		−	1.26219i		−	0.0646637i
$382$	51.6708	+	13.8452i	2.64371	+	0.708380i
$383$	−3.42470	+	5.93175i	−0.174994	+	0.303098i	−0.940159	−	0.340736i	$-0.889324\pi$
$383$	−3.42470	+	5.93175i	−0.174994	+	0.303098i	0.765165	+	0.643834i	$0.222657\pi$
$384$	25.2603	−	25.2603i	1.28906	−	1.28906i
$385$	0.110203	+	5.87542i	0.00561645	+	0.299439i
$386$	−16.8221	−	29.1368i	−0.856224	−	1.48302i
$387$	5.73187	−	3.30930i	0.291368	−	0.168221i
$388$	−9.09355	−	5.25016i	−0.461655	−	0.266537i
$389$	16.3576	−	4.38300i	0.829362	−	0.222227i	0.180926	−	0.983497i	$-0.442090\pi$
$389$	16.3576	−	4.38300i	0.829362	−	0.222227i	0.648435	+	0.761270i	$0.275424\pi$
$390$	64.2948	−	1.20595i	3.25569	−	0.0610656i
$391$	−0.190167	+	0.109793i	−0.00961715	+	0.00555247i
$392$	−3.78418	+	2.18480i	−0.191130	+	0.110349i
$393$	−33.3078			−1.68015
$394$	−8.25480	−	30.8073i	−0.415871	−	1.55205i
$395$	−0.364464	−	19.4313i	−0.0183382	−	0.977694i
$396$	−16.4219			−0.825232
$397$	−15.6633	−	15.6633i	−0.786117	−	0.786117i	0.194738	−	0.980855i	$-0.437614\pi$
$397$	−15.6633	−	15.6633i	−0.786117	−	0.786117i	−0.980855	+	0.194738i	$0.937614\pi$
$398$	−33.8768	−	9.07726i	−1.69809	−	0.455002i
$399$	−31.1674	+	31.1674i	−1.56032	+	1.56032i
$400$	−0.332632	−	8.86396i	−0.0166316	−	0.443198i
$401$	−27.4615	−	27.4615i	−1.37136	−	1.37136i	−0.858429	−	0.512932i	$-0.828559\pi$
$401$	−27.4615	−	27.4615i	−1.37136	−	1.37136i	−0.512932	−	0.858429i	$-0.671441\pi$
$402$	−30.0140	+	51.9858i	−1.49696	+	2.59282i
$403$	41.8452	−	11.2124i	2.08446	−	0.558529i
$404$	−9.90833	−	5.72058i	−0.492958	−	0.284609i
$405$	1.23846	+	1.19286i	0.0615396	+	0.0592735i
$406$		−	8.87463i		−	0.440440i
$407$	6.53569	+	3.76183i	0.323962	+	0.186467i
$408$	−0.114531	−	0.114531i	−0.00567013	−	0.00567013i
$409$	15.1481	+	4.05891i	0.749023	+	0.200700i	0.613085	−	0.790017i	$-0.289928\pi$
$409$	15.1481	+	4.05891i	0.749023	+	0.200700i	0.135938	+	0.990717i	$0.456595\pi$
$410$	−5.39817	−	1.33846i	−0.266596	−	0.0661017i
$411$	−1.54736	−	0.893369i	−0.0763256	−	0.0440666i
$412$	15.8150	+	9.13077i	0.779147	+	0.449841i
$413$	19.1157			0.940622
$414$	59.0735	+	34.1061i	2.90330	+	1.67622i
$415$	8.94462	+	4.94288i	0.439074	+	0.242636i
$416$	17.4013	+	30.1400i	0.853170	+	1.47773i
$417$	−24.3134	+	24.3134i	−1.19063	+	1.19063i
$418$	−14.3506	+	14.3506i	−0.701912	+	0.701912i
$419$	12.0917	−	6.98112i	0.590716	−	0.341050i	−0.174665	−	0.984628i	$-0.555884\pi$
$419$	12.0917	−	6.98112i	0.590716	−	0.341050i	0.765381	+	0.643578i	$0.222551\pi$
$420$	35.7835	+	8.87239i	1.74606	+	0.432928i
$421$	−7.68957	−	7.68957i	−0.374767	−	0.374767i	0.494443	−	0.869210i	$-0.335372\pi$
$421$	−7.68957	−	7.68957i	−0.374767	−	0.374767i	−0.869210	+	0.494443i	$0.835372\pi$
$422$	−16.2425	−	28.1328i	−0.790672	−	1.36948i
$423$	−3.80187	+	14.1888i	−0.184853	+	0.689881i
$424$	−2.70758	+	10.1048i	−0.131492	+	0.490734i
$425$	−0.166876	+	0.00626225i	−0.00809468	+	0.000303764i
$426$	−11.7569	−	43.8774i	−0.569624	−	2.12587i
$427$	−1.61748	−	2.80156i	−0.0782754	−	0.135577i
$428$	54.2976	+	14.5490i	2.62457	+	0.703252i
$429$	4.21354	−	15.7252i	0.203432	−	0.759217i
$430$	−6.57401	+	1.89433i	−0.317027	+	0.0913526i
$431$	−32.3472	+	8.66742i	−1.55811	+	0.417495i	−0.932065	−	0.362291i	$-0.881995\pi$
$431$	−32.3472	+	8.66742i	−1.55811	+	0.417495i	−0.626047	+	0.779786i	$0.715328\pi$
$432$	2.21905	−	8.28162i	0.106764	−	0.398450i
$433$	4.25204	+	4.25204i	0.204340	+	0.204340i	0.801857	−	0.597516i	$-0.203846\pi$
$433$	4.25204	+	4.25204i	0.204340	+	0.204340i	−0.597516	+	0.801857i	$0.703846\pi$
$434$	42.6014			2.04493
$435$	8.24846	−	8.56380i	0.395483	−	0.410603i
$436$	4.03882	+	4.03882i	0.193424	+	0.193424i
$437$	47.4714	−	12.7199i	2.27087	−	0.608477i
$438$			93.6737i			4.47590i
$439$	0.642178	+	2.39664i	0.0306495	+	0.114385i	0.979556	−	0.201172i	$-0.0644751\pi$
$439$	0.642178	+	2.39664i	0.0306495	+	0.114385i	−0.948906	+	0.315558i	$0.897808\pi$
$440$	4.69101	+	1.16312i	0.223635	+	0.0554496i
$441$	−5.93670	+	10.2827i	−0.282700	+	0.489651i
$442$	0.299040	−	0.172651i	0.0142239	−	0.00821216i
$443$	7.09829	−	7.09829i	0.337250	−	0.337250i	−0.518081	−	0.855331i	$-0.673354\pi$
$443$	7.09829	−	7.09829i	0.337250	−	0.337250i	0.855331	+	0.518081i	$0.173354\pi$
$444$	33.4087	−	33.4975i	1.58551	−	1.58972i
$445$	−9.79282	+	17.7210i	−0.464224	+	0.840058i
$446$	−2.63337	+	9.82785i	−0.124693	+	0.465362i
$447$	1.97131	−	0.528211i	0.0932398	−	0.0249835i
$448$	6.91123	+	25.7930i	0.326525	+	1.21861i
$449$	7.50385	−	2.01065i	0.354129	−	0.0948885i	−0.0773691	−	0.997003i	$-0.524652\pi$
$449$	7.50385	−	2.01065i	0.354129	−	0.0948885i	0.431498	+	0.902114i	$0.357985\pi$
$450$	27.6039	+	43.9208i	1.30126	+	2.07044i
$451$	−0.703997	+	1.21936i	−0.0331499	+	0.0574173i
$452$		−	45.2770i		−	2.12965i
$453$	6.74480	−	25.1719i	0.316898	−	1.18268i
$454$			34.4579i			1.61719i
$455$	−10.8234	+	19.5859i	−0.507407	+	0.918202i
$456$	18.1256	+	31.3944i	0.848808	+	1.47018i
$457$	−27.5019	−	15.8782i	−1.28648	−	0.742751i	−0.308458	−	0.951238i	$-0.599813\pi$
$457$	−27.5019	−	15.8782i	−1.28648	−	0.742751i	−0.978025	+	0.208487i	$0.933146\pi$
$458$			15.6341i			0.730532i
$459$	−0.155913	−	0.0417767i	−0.00727739	−	0.00194997i
$460$	−29.6067	−	28.5165i	−1.38042	−	1.32959i
$461$	1.79169	+	0.480083i	0.0834475	+	0.0223597i	0.300301	−	0.953844i	$-0.402913\pi$
$461$	1.79169	+	0.480083i	0.0834475	+	0.0223597i	−0.216854	+	0.976204i	$0.569579\pi$
$462$	8.00466	−	13.8645i	0.372410	−	0.645034i
$463$	10.6253	−	18.4035i	0.493799	−	0.855285i	−0.506175	−	0.862431i	$-0.668941\pi$
$463$	10.6253	−	18.4035i	0.493799	−	0.855285i	0.999974	+	0.00714545i	$0.00227449\pi$
$464$	3.27575	+	0.877735i	0.152073	+	0.0407478i
$465$	41.1093	+	39.5956i	1.90640	+	1.83620i
$466$	9.08689	+	2.43483i	0.420942	+	0.112791i
$467$		−	14.1946i		−	0.656850i	−0.944530	−	0.328425i	$-0.893482\pi$
$467$		−	14.1946i		−	0.656850i	0.944530	−	0.328425i	$-0.106518\pi$
$468$	−54.1565	−	31.2673i	−2.50339	−	1.44533i
$469$	−10.4444	−	18.0903i	−0.482278	−	0.835331i
$470$	7.34406	−	13.2898i	0.338756	−	0.613012i
$471$			37.5963i			1.73235i
$472$	4.06905	−	15.1859i	0.187293	−	0.698988i
$473$			1.73201i			0.0796379i
$474$	−26.4731	+	45.8528i	−1.21595	+	2.10609i
$475$	36.4391	+	8.31281i	1.67194	+	0.381418i
$476$	0.191218	−	0.0512366i	0.00876445	−	0.00234843i
$477$	7.35726	+	27.4577i	0.336866	+	1.25720i
$478$	−34.0878	+	9.13380i	−1.55914	+	0.417770i
$479$	0.811398	−	3.02818i	0.0370737	−	0.138361i	−0.944908	−	0.327335i	$-0.893849\pi$
$479$	0.811398	−	3.02818i	0.0370737	−	0.138361i	0.981982	+	0.188974i	$0.0605161\pi$
$480$	−22.1780	+	40.1332i	−1.01228	+	1.83182i
$481$	14.3910	+	24.8498i	0.656174	+	1.13305i
$482$	4.28954	−	4.28954i	0.195383	−	0.195383i
$483$	−33.5742	+	19.3841i	−1.52768	+	0.882007i
$484$	−13.2298	+	22.9147i	−0.601355	+	1.04158i
$485$	8.15043	+	2.02087i	0.370092	+	0.0917630i
$486$	−9.43050	−	35.1951i	−0.427776	−	1.59648i
$487$		−	4.64386i		−	0.210433i	−0.994449	−	0.105217i	$-0.966446\pi$
$487$		−	4.64386i		−	0.210433i	0.994449	−	0.105217i	$-0.0335536\pi$
$488$	−2.56992	+	0.688609i	−0.116335	+	0.0311719i
$489$	27.0974	+	27.0974i	1.22539	+	1.22539i
$490$	8.51424	−	8.83974i	0.384634	−	0.399339i
$491$	1.23861			0.0558978			0.0279489	−	0.999609i	$-0.491102\pi$
$491$	1.23861			0.0558978			0.0279489	+	0.999609i	$0.491102\pi$
$492$	6.24609	+	6.24609i	0.281596	+	0.281596i
$493$	0.0165246	−	0.0616705i	0.000744229	−	0.00277750i
$494$	−74.6494	+	20.0023i	−3.35864	+	0.899944i
$495$	12.6193	−	3.63631i	0.567196	−	0.163440i
$496$	−4.21344	+	15.7248i	−0.189189	+	0.706063i
$497$	15.2686	+	4.09122i	0.684892	+	0.183516i
$498$	−13.9206	−	24.1112i	−0.623796	−	1.08045i
$499$	−4.19924	−	15.6718i	−0.187984	−	0.701566i	−0.993972	−	0.109634i	$-0.965032\pi$
$499$	−4.19924	−	15.6718i	−0.187984	−	0.701566i	0.805988	−	0.591932i	$-0.201635\pi$
$500$	−9.77625	−	29.6933i	−0.437207	−	1.32793i
$501$	9.25600	−	34.5439i	0.413528	−	1.54331i
$502$	0.187741	−	0.700659i	0.00837929	−	0.0312719i
$503$	−5.77808	−	10.0079i	−0.257632	−	0.446232i	0.707975	−	0.706237i	$-0.249609\pi$
$503$	−5.77808	−	10.0079i	−0.257632	−	0.446232i	−0.965607	+	0.260006i	$0.916276\pi$
$504$	−12.3806	−	12.3806i	−0.551474	−	0.551474i
$505$	8.88070	+	2.20194i	0.395186	+	0.0979850i
$506$	−15.4588	+	8.92516i	−0.687229	+	0.396772i
$507$	18.2664	−	18.2664i	0.811240	−	0.811240i
$508$	0.897143	−	0.897143i	0.0398043	−	0.0398043i
$509$	0.707015	+	1.22459i	0.0313379	+	0.0542788i	0.881269	−	0.472615i	$-0.156690\pi$
$509$	0.707015	+	1.22459i	0.0313379	+	0.0542788i	−0.849931	+	0.526894i	$0.823357\pi$
$510$	0.398189	+	0.220043i	0.0176321	+	0.00974367i
$511$	−28.2298	−	16.2985i	−1.24881	−	0.721003i
$512$	−19.2642			−0.851365
$513$	31.2862	+	18.0631i	1.38132	+	0.797506i
$514$	−14.8679	−	8.58400i	−0.655796	−	0.378624i
$515$	−14.1747	−	3.51458i	−0.624614	−	0.154871i
$516$	10.4958	+	2.81235i	0.462053	+	0.123807i
$517$	−2.71813	−	2.71813i	−0.119543	−	0.119543i
$518$	7.34493	+	27.2669i	0.322718	+	1.19804i
$519$			5.11524i			0.224534i
$520$	13.2556	+	12.7675i	0.581295	+	0.559890i
$521$	6.98004	+	4.02993i	0.305801	+	0.176554i	0.645046	−	0.764144i	$-0.276838\pi$
$521$	6.98004	+	4.02993i	0.305801	+	0.176554i	−0.339245	+	0.940698i	$0.610172\pi$
$522$	−19.1573	+	5.13319i	−0.838494	+	0.224674i
$523$	−5.88038	+	10.1851i	−0.257131	+	0.445364i	−0.965472	−	0.260506i	$-0.916111\pi$
$523$	−5.88038	+	10.1851i	−0.257131	+	0.445364i	0.708341	+	0.705870i	$0.249444\pi$
$524$	−23.6747	−	23.6747i	−1.03423	−	1.03423i
$525$	−29.4622	+	1.10561i	−1.28584	+	0.0482527i
$526$	28.5111	−	28.5111i	1.24314	−	1.24314i
$527$	0.296040	+	0.0793238i	0.0128957	+	0.00345540i
$528$	4.32588	+	4.32588i	0.188260	+	0.188260i
$529$	20.2264			0.879407
$530$	−0.551038	−	29.3784i	−0.0239356	−	1.27612i
$531$	−11.0568	−	41.2644i	−0.479822	−	1.79072i
$532$	−44.3066			−1.92094
$533$	−4.64331	+	2.68082i	−0.201124	+	0.116119i
$534$	47.7689	−	27.5794i	2.06716	−	1.19348i
$535$	−44.9463	+	0.843037i	−1.94320	+	0.0364477i
$536$	−16.5945	+	4.44649i	−0.716774	+	0.192059i
$537$	32.2133	+	18.5984i	1.39011	+	0.802580i
$538$	−20.8748	+	12.0520i	−0.899975	+	0.519601i
$539$	−1.55357	−	2.69085i	−0.0669168	−	0.115903i
$540$	−0.566660	−	30.2113i	−0.0243851	−	1.30009i
$541$	24.2210	−	24.2210i	1.04134	−	1.04134i	0.0422359	−	0.999108i	$-0.486552\pi$
$541$	24.2210	−	24.2210i	1.04134	−	1.04134i	0.999108	−	0.0422359i	$-0.0134481\pi$
$542$	−25.6367	+	44.4041i	−1.10119	+	1.90732i
$543$	3.14313	+	0.842199i	0.134885	+	0.0361422i
$544$			0.246217i			0.0105565i
$545$	−3.99792	−	2.20929i	−0.171252	−	0.0946355i
$546$	52.7959	−	30.4817i	2.25946	−	1.30450i
$547$	−19.3178			−0.825969			−0.412985	−	0.910738i	$-0.635514\pi$
$547$	−19.3178			−0.825969			−0.412985	+	0.910738i	$0.635514\pi$
$548$	−0.464847	−	1.73483i	−0.0198573	−	0.0741084i
$549$	−5.11206	+	5.11206i	−0.218177	+	0.218177i
$550$	−13.5655	+	0.509064i	−0.578435	+	0.0217066i
$551$	−7.14477	+	12.3751i	−0.304377	+	0.527197i
$552$	8.25237	+	30.7982i	0.351244	+	1.31086i
$553$	−9.21224	−	15.9561i	−0.391744	−	0.678521i
$554$	38.5888			1.63948
$555$	−18.2554	+	33.1386i	−0.774898	+	1.40666i
$556$	−34.5632			−1.46581
$557$	16.1462	+	27.9660i	0.684136	+	1.18496i	0.973707	+	0.227802i	$0.0731540\pi$
$557$	16.1462	+	27.9660i	0.684136	+	1.18496i	−0.289571	+	0.957157i	$0.593513\pi$
$558$	−24.6412	−	91.9621i	−1.04314	−	3.89307i
$559$	−3.29774	+	5.71186i	−0.139480	+	0.241586i
$560$	−4.34039	−	7.20239i	−0.183415	−	0.304356i
$561$	0.0814407	−	0.0814407i	0.00343843	−	0.00343843i
$562$	−9.40320	−	35.0932i	−0.396650	−	1.48032i
$563$	21.1834			0.892774			0.446387	−	0.894840i	$-0.352711\pi$
$563$	21.1834			0.892774			0.446387	+	0.894840i	$0.352711\pi$
$564$	−20.8852	+	12.0581i	−0.879425	+	0.507736i
$565$	10.0257	+	34.7929i	0.421784	+	1.46375i
$566$			41.9139i			1.76177i
$567$	1.57458	+	0.421907i	0.0661260	+	0.0177184i
$568$	6.50030	−	11.2589i	0.272747	−	0.472411i
$569$	2.78046	−	2.78046i	0.116563	−	0.116563i	−0.646419	−	0.762982i	$-0.723734\pi$
$569$	2.78046	−	2.78046i	0.116563	−	0.116563i	0.762982	+	0.646419i	$0.223734\pi$
$570$	−73.3366	−	70.6362i	−3.07173	−	2.95862i
$571$	7.98743	+	13.8346i	0.334264	+	0.578962i	0.983343	−	0.181759i	$-0.0581791\pi$
$571$	7.98743	+	13.8346i	0.334264	+	0.578962i	−0.649079	+	0.760721i	$0.724846\pi$
$572$	14.1721	−	8.18228i	0.592567	−	0.342118i
$573$	58.8419	+	33.9724i	2.45816	+	1.41922i
$574$	−5.09287	+	1.36463i	−0.212572	+	0.0569586i
$575$	29.0655	+	15.3575i	1.21212	+	0.640454i
$576$	51.6810	−	29.8380i	2.15337	−	1.24325i
$577$	−4.21277	+	2.43224i	−0.175380	+	0.101256i	−0.585120	−	0.810947i	$-0.698953\pi$
$577$	−4.21277	+	2.43224i	−0.175380	+	0.101256i	0.409740	+	0.912202i	$0.365619\pi$
$578$	−37.2275			−1.54846
$579$	−11.0602	−	41.2772i	−0.459645	−	1.71542i
$580$	11.9499	−	0.224139i	0.496193	−	0.00930687i
$581$	9.68829			0.401938
$582$	−16.1763	−	16.1763i	−0.670528	−	0.670528i
$583$	−7.18534	−	1.92531i	−0.297587	−	0.0797381i
$584$	−18.9570	+	18.9570i	−0.784446	+	0.784446i
$585$	48.5398	+	12.0353i	2.00687	+	0.497597i
$586$	41.0932	+	41.0932i	1.69754	+	1.69754i
$587$	6.46649	−	11.2003i	0.266901	−	0.462286i	−0.701159	−	0.713005i	$-0.747334\pi$
$587$	6.46649	−	11.2003i	0.266901	−	0.462286i	0.968060	+	0.250719i	$0.0806671\pi$
$588$	−18.8290	+	5.04520i	−0.776493	+	0.208061i
$589$	−59.4049	−	34.2974i	−2.44774	−	1.41320i
$590$	0.828120	+	44.1510i	0.0340932	+	1.81767i
$591$		−	40.5103i		−	1.66637i
$592$	−10.7911	+	0.0143121i	−0.443510	+	0.000588224i
$593$	7.50423	+	7.50423i	0.308162	+	0.308162i	0.844196	−	0.536034i	$-0.180078\pi$
$593$	7.50423	+	7.50423i	0.308162	+	0.308162i	−0.536034	+	0.844196i	$0.680078\pi$
$594$	−12.6743	−	3.39607i	−0.520033	−	0.139342i
$595$	−0.135595	+	0.0817138i	−0.00555884	+	0.00334994i
$596$	1.77662	+	1.02573i	0.0727734	+	0.0420157i
$597$	−38.5784	−	22.2732i	−1.57891	−	0.911583i
$598$	−67.9740			−2.77966
$599$	3.87945	+	2.23980i	0.158510	+	0.0915159i	0.577157	−	0.816633i	$-0.304162\pi$
$599$	3.87945	+	2.23980i	0.158510	+	0.0915159i	−0.418647	+	0.908149i	$0.637495\pi$
$600$	−5.39314	+	23.6407i	−0.220174	+	0.965129i
$601$	1.17640	+	2.03759i	0.0479865	+	0.0831151i	0.889021	−	0.457866i	$-0.151386\pi$
$601$	1.17640	+	2.03759i	0.0479865	+	0.0831151i	−0.841034	+	0.540982i	$0.818053\pi$
$602$	−4.58621	+	4.58621i	−0.186920	+	0.186920i
$603$	−33.0096	+	33.0096i	−1.34426	+	1.34426i
$604$	22.6860	−	13.0977i	0.923078	−	0.532939i
$605$	5.09236	−	20.5382i	0.207034	−	0.834995i
$606$	−17.6257	−	17.6257i	−0.715993	−	0.715993i
$607$	−12.6038	−	21.8304i	−0.511572	−	0.886068i	−0.999910	−	0.0134136i	$-0.995730\pi$
$607$	−12.6038	−	21.8304i	−0.511572	−	0.886068i	0.488338	−	0.872654i	$-0.337603\pi$
$608$	14.2626	−	53.2287i	0.578424	−	2.15871i
$609$	2.91743	−	10.8880i	0.118220	−	0.441205i
$610$	6.40061	−	3.85722i	0.259153	−	0.156174i
$611$	−3.78859	−	14.1392i	−0.153270	−	0.572011i
$612$	−0.221205	−	0.383139i	−0.00894170	−	0.0154875i
$613$	27.7991	+	7.44875i	1.12280	+	0.300852i	0.772014	−	0.635605i	$-0.219249\pi$
$613$	27.7991	+	7.44875i	1.12280	+	0.300852i	0.350782	+	0.936457i	$0.385916\pi$
$614$	−1.76440	+	6.58481i	−0.0712052	+	0.265741i
$615$	−6.18285	−	3.41670i	−0.249316	−	0.137775i
$616$	4.42571	−	1.18587i	0.178317	−	0.0477799i
$617$	−1.34445	+	5.01754i	−0.0541254	+	0.201999i	−0.987694	−	0.156401i	$-0.950011\pi$
$617$	−1.34445	+	5.01754i	−0.0541254	+	0.201999i	0.933568	+	0.358400i	$0.116677\pi$
$618$	28.1328	+	28.1328i	1.13167	+	1.13167i
$619$	10.0009			0.401968			0.200984	−	0.979594i	$-0.435586\pi$
$619$	10.0009			0.401968			0.200984	+	0.979594i	$0.435586\pi$
$620$	1.07595	+	57.3638i	0.0432111	+	2.30379i
$621$	22.4682	+	22.4682i	0.901617	+	0.901617i
$622$	17.9575	−	4.81170i	0.720031	−	0.192932i
$623$			19.1944i			0.769008i
$624$	6.02952	+	22.5025i	0.241374	+	0.900820i
$625$	14.0875	+	20.6529i	0.563500	+	0.826116i
$626$	10.6983	−	18.5299i	0.427588	−	0.740604i
$627$	−22.3240	+	12.8887i	−0.891533	+	0.514727i
$628$	−26.7229	+	26.7229i	−1.06636	+	1.06636i
$629$	0.000269445		0.203156i	1.07435e−5		0.00810037i
$630$	43.0434	+	23.7862i	1.71489	+	0.947665i
$631$	−10.6979	+	39.9251i	−0.425877	+	1.58939i	0.336125	+	0.941818i	$0.390884\pi$
$631$	−10.6979	+	39.9251i	−0.425877	+	1.58939i	−0.762001	+	0.647576i	$0.775783\pi$
$632$	−14.6368	+	3.92192i	−0.582221	+	0.156006i
$633$	−10.6791	−	39.8548i	−0.424455	−	1.58409i
$634$	−22.9094	+	6.13855i	−0.909848	+	0.243793i
$635$	−0.490749	+	0.888058i	−0.0194748	+	0.0352415i
$636$	−23.3344	+	40.4164i	−0.925269	+	1.60261i
$637$		−	11.8319i		−	0.468799i
$638$	1.34330	−	5.01325i	0.0531816	−	0.198477i
$639$		−	35.3263i		−	1.39749i
$640$	−27.5943	+	7.95140i	−1.09076	+	0.314307i
$641$	−10.8959	−	18.8722i	−0.430361	−	0.745407i	0.566543	−	0.824032i	$-0.308280\pi$
$641$	−10.8959	−	18.8722i	−0.430361	−	0.745407i	−0.996904	+	0.0786250i	$0.974947\pi$
$642$	106.062	+	61.2347i	4.18592	+	2.41674i
$643$		−	2.18918i		−	0.0863329i	−0.999068	−	0.0431665i	$-0.986255\pi$
$643$		−	2.18918i		−	0.0863329i	0.999068	−	0.0431665i	$-0.0137446\pi$
$644$	−37.6420	−	10.0861i	−1.48330	−	0.397450i
$645$	−8.68820	+	0.162961i	−0.342097	+	0.00641657i
$646$	−0.528119	−	0.141509i	−0.0207786	−	0.00556760i
$647$	13.3113	−	23.0558i	0.523321	−	0.906418i	−0.476311	−	0.879277i	$-0.658026\pi$
$647$	13.3113	−	23.0558i	0.523321	−	0.906418i	0.999632	−	0.0271412i	$-0.00864037\pi$
$648$	0.670343	−	1.16107i	0.0263336	−	0.0456111i
$649$	10.7984	+	2.89342i	0.423874	+	0.113577i
$650$	−45.7059	−	24.1499i	−1.79273	−	0.947238i
$651$	52.2664	+	14.0047i	2.04848	+	0.548889i
$652$			38.5209i			1.50859i
$653$	−13.9888	−	8.07644i	−0.547425	−	0.316056i	0.200658	−	0.979661i	$-0.435692\pi$
$653$	−13.9888	−	8.07644i	−0.547425	−	0.316056i	−0.748083	+	0.663606i	$0.769025\pi$
$654$	6.22199	+	10.7768i	0.243299	+	0.421407i
$655$	23.4349	+	12.9504i	0.915679	+	0.506013i
$656$		−	2.01482i		−	0.0786655i
$657$	−18.8545	+	70.3660i	−0.735584	+	2.74524i
$658$		−	14.3947i		−	0.561165i
$659$	5.08003	−	8.79888i	0.197890	−	0.342756i	−0.749954	−	0.661490i	$-0.769924\pi$
$659$	5.08003	−	8.79888i	0.197890	−	0.342756i	0.947844	+	0.318734i	$0.103258\pi$
$660$	18.8710	+	10.4283i	0.734554	+	0.405921i
$661$	−31.5621	+	8.45703i	−1.22762	+	0.328940i	−0.813653	−	0.581351i	$-0.802524\pi$
$661$	−31.5621	+	8.45703i	−1.22762	+	0.328940i	−0.413969	+	0.910291i	$0.635858\pi$
$662$	−10.4869	−	39.1376i	−0.407584	−	1.52113i
$663$	0.423640	−	0.113514i	0.0164528	−	0.00440852i
$664$	2.06229	−	7.69658i	0.0800325	−	0.298685i
$665$	34.0472	−	9.81082i	1.32029	−	0.380447i
$666$	54.6117	−	31.6268i	2.11616	−	1.22551i
$667$	−8.88716	+	8.88716i	−0.344112	+	0.344112i
$668$	31.1323	−	17.9742i	1.20454	−	0.695444i
$669$	−6.46159	+	11.1918i	−0.249820	+	0.432700i
$670$	41.3301	−	24.9069i	1.59672	−	0.962236i
$671$	−0.489656	−	1.82742i	−0.0189030	−	0.0705468i
$672$			43.4699i			1.67689i
$673$	40.3503	−	10.8118i	1.55539	−	0.416765i	0.624188	−	0.781274i	$-0.285430\pi$
$673$	40.3503	−	10.8118i	1.55539	−	0.416765i	0.931200	+	0.364509i	$0.118763\pi$
$674$	17.6765	+	17.6765i	0.680874	+	0.680874i
$675$	7.12513	+	23.0902i	0.274246	+	0.888742i
$676$	25.9670			0.998730
$677$	−2.28433	−	2.28433i	−0.0877938	−	0.0877938i	0.661846	−	0.749640i	$-0.269773\pi$
$677$	−2.28433	−	2.28433i	−0.0877938	−	0.0877938i	−0.749640	+	0.661846i	$0.769773\pi$
$678$	25.5308	−	95.2823i	0.980505	−	3.65929i
$679$	7.68948	−	2.06039i	0.295095	−	0.0790705i
$680$	0.0360519	+	0.125113i	0.00138253	+	0.00479787i
$681$	−11.3277	+	42.2754i	−0.434077	+	1.62000i
$682$	24.0654	+	6.44830i	0.921512	+	0.246918i
$683$	19.2927	+	33.4159i	0.738214	+	1.27862i	0.953299	+	0.302029i	$0.0976641\pi$
$683$	19.2927	+	33.4159i	0.738214	+	1.27862i	−0.215084	+	0.976596i	$0.569003\pi$
$684$	25.6275	+	95.6431i	0.979892	+	3.65701i
$685$	0.741354	+	1.23019i	0.0283257	+	0.0470032i
$686$	11.4223	−	42.6286i	0.436106	−	1.62757i
$687$	−5.13952	+	19.1810i	−0.196085	+	0.731800i
$688$	−1.23924	−	2.14643i	−0.0472456	−	0.0818318i
$689$	−20.0302	−	20.0302i	−0.763090	−	0.763090i
$690$	−46.2254	−	76.7057i	−1.75977	−	2.92013i
$691$	−18.4725	+	10.6651i	−0.702725	+	0.405719i	−0.808362	−	0.588686i	$-0.799645\pi$
$691$	−18.4725	+	10.6651i	−0.702725	+	0.405719i	0.105636	+	0.994405i	$0.466312\pi$
$692$	−3.63584	+	3.63584i	−0.138214	+	0.138214i
$693$	8.80357	−	8.80357i	0.334420	−	0.334420i
$694$	10.8218	+	18.7438i	0.410789	+	0.711507i
$695$	26.5599	−	7.65334i	1.00747	−	0.290308i
$696$	−8.02865	−	4.63534i	−0.304325	−	0.175702i
$697$	−0.0379317			−0.00143677
$698$	50.3720	+	29.0823i	1.90661	+	1.10078i
$699$	10.3480	+	5.97443i	0.391398	+	0.225974i
$700$	−21.7272	−	20.1555i	−0.821210	−	0.761805i
$701$	10.6288	+	2.84798i	0.401444	+	0.107567i	0.453891	−	0.891057i	$-0.350036\pi$
$701$	10.6288	+	2.84798i	0.401444	+	0.107567i	−0.0524473	+	0.998624i	$0.516702\pi$
$702$	−35.3315	−	35.3315i	−1.33350	−	1.33350i
$703$	11.7100	−	43.9352i	0.441650	−	1.65705i
$704$			15.6165i			0.588570i
$705$	13.3791	−	13.8906i	0.503885	−	0.523148i
$706$	−55.4045	−	31.9878i	−2.08517	−	1.20388i
$707$	8.37846	−	2.24500i	0.315104	−	0.0844319i
$708$	35.0678	−	60.7392i	1.31793	−	2.28272i
$709$	0.00480033	+	0.00480033i	0.000180280	+	0.000180280i	0.707197	−	0.707017i	$-0.249959\pi$
$709$	0.00480033	+	0.00480033i	0.000180280	+	0.000180280i	−0.707017	+	0.707197i	$0.749959\pi$
$710$	−8.78791	+	35.4428i	−0.329805	+	1.33014i
$711$	−29.1153	+	29.1153i	−1.09191	+	1.09191i
$712$	15.2484	+	4.08581i	0.571459	+	0.153122i
$713$	−42.6616	−	42.6616i	−1.59769	−	1.59769i
$714$	0.431295			0.0161408
$715$	−9.07868	+	9.42576i	−0.339523	+	0.352504i
$716$	9.67732	+	36.1162i	0.361658	+	1.34973i
$717$	−44.8239			−1.67398
$718$	22.7471	−	13.1330i	0.848913	−	0.490120i
$719$	−25.8790	+	14.9412i	−0.965124	+	0.557214i	−0.897746	−	0.440513i	$-0.854797\pi$
$719$	−25.8790	+	14.9412i	−0.965124	+	0.557214i	−0.0673775	+	0.997728i	$0.521463\pi$
$720$	−13.0370	+	13.5354i	−0.485860	+	0.504435i
$721$	−13.3731	+	3.58331i	−0.498040	+	0.133449i
$722$	69.9396	+	40.3796i	2.60288	+	1.50277i
$723$	6.67285	−	3.85257i	0.248166	−	0.143279i
$724$	1.63547	+	2.83271i	0.0607817	+	0.105277i
$725$	−9.13320	+	2.81831i	−0.339199	+	0.104669i
$726$	−40.7624	+	40.7624i	−1.51283	+	1.51283i
$727$	−11.5115	+	19.9385i	−0.426938	+	0.739478i	−0.996599	−	0.0824017i	$-0.973741\pi$
$727$	−11.5115	+	19.9385i	−0.426938	+	0.739478i	0.569662	+	0.821879i	$0.307074\pi$
$728$	16.8531	+	4.51578i	0.624618	+	0.167366i
$729$		−	43.9730i		−	1.62863i
$730$	36.4212	−	65.9077i	1.34801	−	2.43935i
$731$	−0.0404094	+	0.0233304i	−0.00149460	+	0.000862906i
$732$	−11.8691			−0.438694
$733$	5.67438	+	21.1771i	0.209588	+	0.782193i	0.988002	+	0.154442i	$0.0493579\pi$
$733$	5.67438	+	21.1771i	0.209588	+	0.782193i	−0.778414	+	0.627751i	$0.783975\pi$
$734$	−23.5890	+	23.5890i	−0.870686	+	0.870686i
$735$	13.3518	−	8.04625i	0.492490	−	0.296790i
$736$	24.2344	−	41.9752i	0.893292	−	1.54723i
$737$	−3.16181	−	11.8000i	−0.116467	−	0.434660i
$738$	5.89156	+	10.2045i	0.216871	+	0.375632i
$739$	−41.5119			−1.52704			−0.763520	−	0.645784i	$-0.776531\pi$
$739$	−41.5119			−1.52704			−0.763520	+	0.645784i	$0.776531\pi$
$740$	−36.5301	+	10.5788i	−1.34287	+	0.388884i
$741$	−98.1606			−3.60602
$742$	−13.9281	−	24.1242i	−0.511317	−	0.885627i
$743$	7.87005	+	29.3714i	0.288724	+	1.07753i	0.946075	+	0.323948i	$0.105010\pi$
$743$	7.87005	+	29.3714i	0.288724	+	1.07753i	−0.657351	+	0.753585i	$0.728323\pi$
$744$	22.2513	−	38.5404i	0.815772	−	1.41296i
$745$	−1.59236	−	0.394821i	−0.0583397	−	0.0144651i
$746$	−9.36013	+	9.36013i	−0.342699	+	0.342699i
$747$	−5.60383	−	20.9138i	−0.205033	−	0.765195i
$748$	0.115774			0.00423310
$749$	−36.9078	+	21.3087i	−1.34858	+	0.778604i
$750$	−3.82994	−	68.0001i	−0.139850	−	2.48301i
$751$			10.3889i			0.379096i	0.981871	+	0.189548i	$0.0607022\pi$
$751$			10.3889i			0.379096i	−0.981871	+	0.189548i	$0.939298\pi$
$752$	5.31329	+	1.42369i	0.193756	+	0.0519167i
$753$	0.460668	−	0.797900i	0.0167877	−	0.0290771i
$754$	13.9752	−	13.9752i	0.508946	−	0.508946i
$755$	−14.5326	+	15.0882i	−0.528897	+	0.549117i
$756$	−14.3230	−	24.8081i	−0.520921	−	0.902262i
$757$	21.0689	−	12.1641i	0.765761	−	0.442112i	−0.0655993	−	0.997846i	$-0.520896\pi$
$757$	21.0689	−	12.1641i	0.765761	−	0.442112i	0.831360	+	0.555734i	$0.187563\pi$
$758$	−38.0591	−	21.9734i	−1.38237	−	0.798110i
$759$	−21.9000	+	5.86809i	−0.794921	+	0.212998i
$760$	−0.546494	−	29.1361i	−0.0198234	−	1.05688i
$761$	−6.45000	+	3.72391i	−0.233812	+	0.134992i	−0.612330	−	0.790603i	$-0.709767\pi$
$761$	−6.45000	+	3.72391i	−0.233812	+	0.134992i	0.378517	+	0.925594i	$0.376434\pi$
$762$	2.39385	−	1.38209i	0.0867202	−	0.0500679i
$763$	−4.33031			−0.156768
$764$	17.6769	+	65.9711i	0.639527	+	2.38675i
$765$	0.254822	+	0.245439i	0.00921312	+	0.00887387i
$766$	−15.0002			−0.541978
$767$	30.1021	+	30.1021i	1.08692	+	1.08692i
$768$	7.87786	+	2.11087i	0.284268	+	0.0761693i
$769$	10.7914	−	10.7914i	0.389149	−	0.389149i	−0.485235	−	0.874384i	$-0.661266\pi$
$769$	10.7914	−	10.7914i	0.389149	−	0.389149i	0.874384	+	0.485235i	$0.161266\pi$
$770$	−11.0226	+	6.64259i	−0.397228	+	0.239382i
$771$	−15.4191	−	15.4191i	−0.555306	−	0.555306i
$772$	21.4778	−	37.2006i	0.773002	−	1.33888i
$773$	4.08855	−	1.09552i	0.147055	−	0.0394032i	−0.184541	−	0.982825i	$-0.559080\pi$
$773$	4.08855	−	1.09552i	0.147055	−	0.0394032i	0.331596	+	0.943422i	$0.392413\pi$
$774$	12.5528	+	7.24736i	0.451201	+	0.260501i
$775$	−13.5289	−	43.8426i	−0.485972	−	1.57487i
$776$		−	6.54727i		−	0.235033i
$777$	0.0475709	+	35.8675i	0.00170660	+	1.28674i
$778$	26.2243	+	26.2243i	0.940187	+	0.940187i
$779$	8.20032	+	2.19727i	0.293807	+	0.0787253i
$780$	42.3778	+	70.3211i	1.51737	+	2.51790i
$781$	8.00595	+	4.62224i	0.286475	+	0.165397i
$782$	−0.416465	−	0.240446i	−0.0148928	−	0.00859834i
$783$	−9.23873			−0.330165
$784$	3.85058	+	2.22313i	0.137521	+	0.0793975i
$785$	14.6178	−	26.4523i	0.521732	−	0.944124i
$786$	−36.4720	−	63.1713i	−1.30091	−	2.25325i
$787$	3.18353	−	3.18353i	0.113481	−	0.113481i	−0.648086	−	0.761567i	$-0.724430\pi$
$787$	3.18353	−	3.18353i	0.113481	−	0.113481i	0.761567	+	0.648086i	$0.224430\pi$
$788$	28.7941	−	28.7941i	1.02575	−	1.02575i
$789$	44.3521	−	25.6067i	1.57898	−	0.911623i
$790$	36.4542	−	21.9685i	1.29698	−	0.781604i
$791$	24.2724	+	24.2724i	0.863028	+	0.863028i
$792$	−5.11977	−	8.86771i	−0.181923	−	0.315100i
$793$	1.86461	−	6.95882i	0.0662142	−	0.247115i
$794$	12.5556	−	46.8582i	0.445582	−	1.66293i
$795$	8.98177	−	36.2246i	0.318551	−	1.28476i
$796$	−11.5895	−	43.2524i	−0.410777	−	1.53304i
$797$	2.97131	+	5.14646i	0.105249	+	0.182297i	0.913840	−	0.406074i	$-0.133103\pi$
$797$	2.97131	+	5.14646i	0.105249	+	0.182297i	−0.808591	+	0.588371i	$0.799769\pi$
$798$	−93.2401	−	24.9836i	−3.30067	−	0.884411i
$799$	0.0268030	−	0.100030i	0.000948221	−	0.00353881i
$800$	31.2083	−	19.6142i	1.10338	−	0.693467i
$801$	41.4343	−	11.1023i	1.46401	−	0.392280i
$802$	22.0130	−	82.1536i	0.777306	−	2.90095i
$803$	−13.4799	−	13.4799i	−0.475697	−	0.475697i
$804$	−76.6412			−2.70293
$805$	31.1591	−	0.584438i	1.09822	−	0.0205987i
$806$	67.0859	+	67.0859i	2.36300	+	2.36300i
$807$	−29.5726	+	7.92395i	−1.04100	+	0.278936i
$808$		−	7.13390i		−	0.250970i
$809$	12.6920	+	47.3671i	0.446226	+	1.66534i	0.712680	+	0.701490i	$0.247481\pi$
$809$	12.6920	+	47.3671i	0.446226	+	1.66534i	−0.266454	+	0.963848i	$0.585852\pi$
$810$	−0.906253	+	3.65503i	−0.0318425	+	0.128425i
$811$	−16.0707	+	27.8353i	−0.564319	+	0.977428i	0.432794	+	0.901493i	$0.357528\pi$
$811$	−16.0707	+	27.8353i	−0.564319	+	0.977428i	−0.997113	+	0.0759357i	$0.975806\pi$
$812$	9.81271	−	5.66537i	0.344359	−	0.198816i
$813$	−46.0503	+	46.0503i	−1.61505	+	1.61505i
$814$	0.0219034	+	16.5148i	0.000767715	+	0.578842i
$815$	−8.52969	−	29.6011i	−0.298782	−	1.03688i
$816$	−0.0426568	+	0.159197i	−0.00149329	+	0.00557302i
$817$	10.0874	−	2.70292i	0.352914	−	0.0945631i
$818$	8.88901	+	33.1742i	0.310797	+	1.15991i
$819$	45.7946	−	12.2706i	1.60019	−	0.428771i
$820$	−1.96614	−	6.82321i	−0.0686605	−	0.238277i
$821$	−7.36263	+	12.7525i	−0.256958	+	0.445064i	−0.965425	−	0.260679i	$-0.916053\pi$
$821$	−7.36263	+	12.7525i	−0.256958	+	0.445064i	0.708468	+	0.705743i	$0.249387\pi$
$822$		−	3.91295i		−	0.136480i
$823$	−5.30290	+	19.7907i	−0.184847	+	0.689860i	0.809816	+	0.586684i	$0.199567\pi$
$823$	−5.30290	+	19.7907i	−0.184847	+	0.689860i	−0.994663	+	0.103175i	$0.967100\pi$
$824$			11.3866i			0.396672i
$825$	−16.8105	−	3.83496i	−0.585265	−	0.133516i
$826$	20.9317	+	36.2547i	0.728306	+	1.26146i
$827$	21.9826	+	12.6917i	0.764411	+	0.441333i	0.830877	−	0.556456i	$-0.187839\pi$
$827$	21.9826	+	12.6917i	0.764411	+	0.441333i	−0.0664665	+	0.997789i	$0.521173\pi$
$828$			87.0904i			3.02660i
$829$	14.0425	+	3.76268i	0.487716	+	0.130683i	0.494293	−	0.869295i	$-0.335427\pi$
$829$	14.0425	+	3.76268i	0.487716	+	0.130683i	−0.00657707	+	0.999978i	$0.502094\pi$
$830$	0.419711	+	22.3768i	0.0145684	+	0.776709i
$831$	47.3434	+	12.6856i	1.64233	+	0.440060i
$832$	−29.7338	+	51.5005i	−1.03084	+	1.78546i
$833$	0.0418535	−	0.0724923i	0.00145014	−	0.00251171i
$834$	−72.7359	−	19.4895i	−2.51864	−	0.674867i
$835$	−19.9434	+	20.7058i	−0.690169	+	0.716555i
$836$	−25.0287	−	6.70641i	−0.865635	−	0.231946i
$837$		−	44.3492i		−	1.53293i
$838$	26.4807	+	15.2886i	0.914761	+	0.528138i
$839$	−5.10617	−	8.84414i	−0.176284	−	0.305334i	0.764321	−	0.644836i	$-0.223075\pi$
$839$	−5.10617	−	8.84414i	−0.176284	−	0.305334i	−0.940605	+	0.339503i	$0.889741\pi$
$840$	6.36501	+	22.0889i	0.219614	+	0.762140i
$841$			25.3457i			0.873989i
$842$	6.16392	−	23.0041i	0.212423	−	0.792773i
$843$		−	46.1460i		−	1.58935i
$844$	20.7377	−	35.9187i	0.713821	−	1.23637i
$845$	−19.9542	+	5.74987i	−0.686444	+	0.197802i
$846$	−31.0734	+	8.32608i	−1.06832	+	0.286257i
$847$	−5.19195	−	19.3766i	−0.178397	−	0.665789i
$848$	10.2821	−	2.75509i	0.353090	−	0.0946101i
$849$	−13.7787	+	51.4229i	−0.472885	+	1.76483i
$850$	−0.194606	−	0.309639i	−0.00667494	−	0.0106205i
$851$	19.9501	−	34.6607i	0.683882	−	1.18815i
$852$	41.0100	−	41.0100i	1.40498	−	1.40498i
$853$	−13.1435	+	7.58839i	−0.450024	+	0.259821i	−0.707840	−	0.706372i	$-0.750330\pi$
$853$	−13.1435	+	7.58839i	−0.450024	+	0.259821i	0.257816	+	0.966194i	$0.416997\pi$
$854$	3.54228	−	6.13542i	0.121214	−	0.209950i
$855$	−40.8716	−	67.8217i	−1.39778	−	2.31945i
$856$	9.07174	+	33.8562i	0.310066	+	1.15718i
$857$			23.5625i			0.804880i	0.915446	+	0.402440i	$0.131838\pi$
$857$			23.5625i			0.804880i	−0.915446	+	0.402440i	$0.868162\pi$
$858$	34.4381	−	9.22765i	1.17570	−	0.315027i
$859$	−0.0767505	−	0.0767505i	−0.00261869	−	0.00261869i	0.705796	−	0.708415i	$-0.250589\pi$
$859$	−0.0767505	−	0.0767505i	−0.00261869	−	0.00261869i	−0.708415	+	0.705796i	$0.750589\pi$
$860$	−6.29127	−	6.05961i	−0.214531	−	0.206631i
$861$	−6.69690			−0.228230
$862$	−51.8588	−	51.8588i	−1.76632	−	1.76632i
$863$	−4.02089	+	15.0062i	−0.136873	+	0.510816i	0.863110	+	0.505015i	$0.168513\pi$
$863$	−4.02089	+	15.0062i	−0.136873	+	0.510816i	−0.999983	+	0.00580085i	$0.998154\pi$
$864$	34.4144	−	9.22131i	1.17080	−	0.313715i
$865$	1.98885	−	3.59902i	0.0676231	−	0.122370i
$866$	−3.40842	+	12.7204i	−0.115823	+	0.432256i
$867$	−45.6733	−	12.2381i	−1.55115	−	0.415629i
$868$	27.1958	+	47.1045i	0.923086	+	1.59883i
$869$	−2.78880	−	10.4079i	−0.0946035	−	0.353065i
$870$	25.2741	+	6.26663i	0.856873	+	0.212459i
$871$	12.0402	−	44.9345i	0.407966	−	1.52255i
$872$	−0.921770	+	3.44009i	−0.0312151	+	0.116496i
$873$	−8.89538	−	15.4073i	−0.301063	−	0.521456i
$874$	76.1057	+	76.1057i	2.57432	+	2.57432i
$875$	21.1591	+	10.6773i	0.715309	+	0.360958i
$876$	−103.575	+	59.7993i	−3.49949	+	2.02043i
$877$	27.8746	−	27.8746i	0.941257	−	0.941257i	−0.0571111	−	0.998368i	$-0.518189\pi$
$877$	27.8746	−	27.8746i	0.941257	−	0.941257i	0.998368	+	0.0571111i	$0.0181889\pi$
$878$	−3.84227	+	3.84227i	−0.129670	+	0.129670i
$879$	36.9071	+	63.9249i	1.24484	+	2.15613i
$880$	−1.36170	−	4.72558i	−0.0459027	−	0.159299i
$881$	33.4368	+	19.3048i	1.12652	+	0.650394i	0.943056	−	0.332633i	$-0.107937\pi$
$881$	33.4368	+	19.3048i	1.12652	+	0.650394i	0.183460	+	0.983027i	$0.441270\pi$
$882$	−26.0027			−0.875558
$883$	−18.5450	−	10.7070i	−0.624091	−	0.360319i	0.154369	−	0.988013i	$-0.450665\pi$
$883$	−18.5450	−	10.7070i	−0.624091	−	0.360319i	−0.778460	+	0.627694i	$0.783999\pi$
$884$	0.381801	+	0.220433i	0.0128414	+	0.00741396i
$885$	−13.4981	+	54.4397i	−0.453735	+	1.82997i
$886$	21.2352	+	5.68996i	0.713411	+	0.191158i
$887$	−35.8175	−	35.8175i	−1.20264	−	1.20264i	−0.973362	−	0.229273i	$-0.926365\pi$
$887$	−35.8175	−	35.8175i	−1.20264	−	1.20264i	−0.229273	−	0.973362i	$-0.573635\pi$
$888$	28.5040	+	7.59713i	0.956533	+	0.254943i
$889$			0.961893i			0.0322609i
$890$	−44.3328	+	0.831531i	−1.48604	+	0.0278730i
$891$	0.825613	+	0.476668i	0.0276591	+	0.0159690i
$892$	−12.5478	+	3.36217i	−0.420131	+	0.112574i
$893$	−11.5889	+	20.0725i	−0.387807	+	0.671701i
$894$	3.16039	+	3.16039i	0.105699	+	0.105699i
$895$	−15.4337	−	25.6104i	−0.515892	−	0.856063i
$896$	−19.2505	+	19.2505i	−0.643114	+	0.643114i
$897$	−83.3952	−	22.3457i	−2.78449	−	0.746101i
$898$	12.0301	+	12.0301i	0.401450	+	0.401450i
$899$	17.5421			0.585061
$900$	−30.9416	+	58.5598i	−1.03139	+	1.95199i
$901$	−0.0518683	−	0.193575i	−0.00172798	−	0.00644892i
$902$	−3.08350			−0.102669
$903$	−7.13434	+	4.11902i	−0.237416	+	0.137072i
$904$	24.4493	−	14.1158i	0.813170	−	0.469484i
$905$	−1.88401	−	1.81464i	−0.0626267	−	0.0603206i
$906$	55.1265	−	14.7711i	1.83146	−	0.490737i
$907$	−34.1906	−	19.7400i	−1.13528	−	0.655455i	−0.190023	−	0.981780i	$-0.560856\pi$
$907$	−34.1906	−	19.7400i	−1.13528	−	0.655455i	−0.945258	+	0.326325i	$0.894190\pi$
$908$	−38.1002	+	21.9972i	−1.26440	+	0.730002i
$909$	−9.69240	−	16.7877i	−0.321477	−	0.556814i
$910$	−48.9981	+	0.919037i	−1.62427	+	0.0304658i
$911$	27.4566	−	27.4566i	0.909679	−	0.909679i	−0.0865667	−	0.996246i	$-0.527590\pi$
$911$	27.4566	−	27.4566i	0.909679	−	0.909679i	0.996246	+	0.0865667i	$0.0275896\pi$
$912$	18.4436	−	31.9453i	0.610729	−	1.05781i
$913$	5.47289	+	1.46646i	0.181126	+	0.0485326i
$914$		−	69.5465i		−	2.30039i
$915$	9.12074	−	2.62818i	0.301522	−	0.0868848i
$916$	−17.2866	+	9.98045i	−0.571167	+	0.329763i
$917$	25.3834			0.838232
$918$	−0.0914910	−	0.341449i	−0.00301965	−	0.0112695i
$919$	−30.3936	+	30.3936i	−1.00259	+	1.00259i	−0.00259591	+	0.999997i	$0.500826\pi$
$919$	−30.3936	+	30.3936i	−1.00259	+	1.00259i	−0.999997	+	0.00259591i	$0.999174\pi$
$920$	6.16838	−	24.8779i	0.203366	−	0.820199i
$921$	−4.32937	+	7.49868i	−0.142657	+	0.247090i
$922$	1.05138	+	3.92381i	0.0346254	+	0.129224i
$923$	17.6015	+	30.4866i	0.579359	+	1.00348i
$924$	20.4400			0.672427
$925$	25.7289	−	16.2181i	0.845960	−	0.533247i
$926$	46.5387			1.52936
$927$	15.4703	+	26.7954i	0.508112	+	0.880076i
$928$	3.64744	+	13.6124i	0.119733	+	0.446850i
$929$	25.9335	−	44.9181i	0.850850	−	1.47372i	−0.0295925	−	0.999562i	$-0.509421\pi$
$929$	25.9335	−	44.9181i	0.850850	−	1.47372i	0.880442	−	0.474153i	$-0.157246\pi$
$930$	−30.0821	+	121.325i	−0.986430	+	3.97840i
$931$	−13.2474	+	13.2474i	−0.434166	+	0.434166i
$932$	3.10868	+	11.6018i	0.101828	+	0.380028i
$933$	23.6133			0.773066
$934$	26.9215	−	15.5431i	0.880898	−	0.508587i
$935$	−0.0889656	+	0.0256358i	−0.00290949	+	0.000838380i
$936$		−	38.9922i		−	1.27450i
$937$	12.0945	+	3.24072i	0.395111	+	0.105870i	0.450904	−	0.892573i	$-0.351102\pi$
$937$	12.0945	+	3.24072i	0.395111	+	0.105870i	−0.0557924	+	0.998442i	$0.517768\pi$
$938$	22.8733	−	39.6177i	0.746838	−	1.29356i
$939$	19.2169	−	19.2169i	0.627119	−	0.627119i
$940$	19.3828	−	0.363556i	0.632199	−	0.0118579i
$941$	7.13070	+	12.3507i	0.232454	+	0.402623i	0.958530	−	0.284992i	$-0.0919911\pi$
$941$	7.13070	+	12.3507i	0.232454	+	0.402623i	−0.726075	+	0.687615i	$0.758658\pi$
$942$	−71.3050	+	41.1680i	−2.32324	+	1.34132i
$943$	6.46663	+	3.73351i	0.210582	+	0.121580i
$944$	−15.4524	+	4.14045i	−0.502931	+	0.134760i
$945$	16.4997	+	15.8921i	0.536734	+	0.516970i
$946$	−3.28492	+	1.89655i	−0.106802	+	0.0616621i
$947$	−16.0794	+	9.28347i	−0.522512	+	0.301672i	−0.737962	−	0.674843i	$-0.764212\pi$
$947$	−16.0794	+	9.28347i	−0.522512	+	0.301672i	0.215450	+	0.976515i	$0.430878\pi$
$948$	−67.5995			−2.19553
$949$	−18.7887	−	70.1203i	−0.609906	−	2.27620i
$950$	24.1347	+	78.2127i	0.783035	+	2.53756i
$951$	−30.1248			−0.976864
$952$	0.0872824	+	0.0872824i	0.00282884	+	0.00282884i
$953$	−30.4791	−	8.16684i	−0.987314	−	0.264550i	−0.271192	−	0.962525i	$-0.587418\pi$
$953$	−30.4791	−	8.16684i	−0.987314	−	0.264550i	−0.716122	+	0.697975i	$0.754085\pi$
$954$	−44.0198	+	44.0198i	−1.42520	+	1.42520i
$955$	−28.1917	−	46.7809i	−0.912261	−	1.51379i
$956$	−31.8602	−	31.8602i	−1.03043	−	1.03043i
$957$	3.29610	−	5.70901i	0.106548	−	0.184546i
$958$	6.63171	−	1.77696i	0.214261	−	0.0574110i
$959$	1.17922	+	0.680823i	0.0380790	+	0.0219849i
$960$	−78.3364	+	1.46932i	−2.52830	+	0.0474222i
$961$			53.2083i			1.71640i
$962$	−31.3719	+	54.5045i	−1.01147	+	1.75729i
$963$	67.3463	+	67.3463i	2.17020	+	2.17020i
$964$	7.48131	+	2.00461i	0.240957	+	0.0645642i
$965$	−8.26713	+	33.3424i	−0.266128	+	1.07333i
$966$	−73.5275	−	42.4511i	−2.36571	−	1.36584i
$967$	24.2104	+	13.9779i	0.778555	+	0.449499i	0.835918	−	0.548854i	$-0.184936\pi$
$967$	24.2104	+	13.9779i	0.778555	+	0.449499i	−0.0573627	+	0.998353i	$0.518269\pi$
$968$	−16.4984			−0.530278
$969$	−0.601414	−	0.347226i	−0.0193202	−	0.0111545i
$970$	5.09194	+	17.6709i	0.163492	+	0.567379i
$971$	−15.4403	−	26.7434i	−0.495504	−	0.858237i	0.504483	−	0.863422i	$-0.331683\pi$
$971$	−15.4403	−	26.7434i	−0.495504	−	0.858237i	−0.999987	+	0.00518425i	$0.998350\pi$
$972$	32.8951	−	32.8951i	1.05511	−	1.05511i
$973$	18.5289	−	18.5289i	0.594010	−	0.594010i
$974$	8.80752	−	5.08502i	0.282211	−	0.162935i
$975$	−48.1362	−	44.6541i	−1.54159	−	1.43008i
$976$	1.91432	+	1.91432i	0.0612760	+	0.0612760i
$977$	21.2312	+	36.7735i	0.679247	+	1.17649i	0.975208	+	0.221290i	$0.0710267\pi$
$977$	21.2312	+	36.7735i	0.679247	+	1.17649i	−0.295961	+	0.955200i	$0.595640\pi$
$978$	−21.7212	+	81.0645i	−0.694566	+	2.59216i
$979$	−2.90534	+	10.8429i	−0.0928550	+	0.346539i
$980$	15.2094	+	3.77113i	0.485848	+	0.120464i
$981$	2.50471	+	9.34769i	0.0799691	+	0.298449i
$982$	1.35628	+	2.34915i	0.0432806	+	0.0749642i
$983$	−35.6415	−	9.55012i	−1.13679	−	0.304602i	−0.359130	−	0.933288i	$-0.616926\pi$
$983$	−35.6415	−	9.55012i	−1.13679	−	0.304602i	−0.777659	+	0.628686i	$0.783593\pi$
$984$	−1.42553	+	5.32016i	−0.0454443	+	0.169600i
$985$	−15.7508	+	28.5025i	−0.501861	+	0.908166i
$986$	0.135058	−	0.0361888i	0.00430113	−	0.00115249i
$987$	4.73210	−	17.6604i	0.150624	−	0.562138i
$988$	−69.7711	−	69.7711i	−2.21972	−	2.21972i
$989$	9.18537			0.292078
$990$	20.7147	+	19.9520i	0.658358	+	0.634115i
$991$	−36.6089	−	36.6089i	−1.16292	−	1.16292i	−0.983833	−	0.179088i	$-0.942685\pi$
$991$	−36.6089	−	36.6089i	−1.16292	−	1.16292i	−0.179088	−	0.983833i	$-0.557315\pi$
$992$	−65.3445	+	17.5090i	−2.07469	+	0.555912i
$993$		−	51.4642i		−	1.63317i
$994$	8.95977	+	33.4383i	0.284187	+	1.06060i
$995$	18.4832	+	30.6708i	0.585958	+	0.972330i
$996$	17.7732	−	30.7841i	0.563165	−	0.975431i
$997$	33.6213	−	19.4113i	1.06480	−	0.614761i	0.138042	−	0.990426i	$-0.455919\pi$
$997$	33.6213	−	19.4113i	1.06480	−	0.614761i	0.926755	+	0.375666i	$0.122586\pi$
$998$	25.1249	−	25.1249i	0.795314	−	0.795314i
$999$	28.3856	−	7.64627i	0.898081	−	0.241917i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.103.16	yes	68
5.2	odd	4		185.2.u.a.177.2	yes	68
5.3	odd	4		925.2.y.b.732.16		68
5.4	even	2		925.2.t.b.843.2		68
37.23	odd	12		185.2.u.a.23.2	yes	68
185.23	even	12		925.2.t.b.282.2		68
185.97	even	12	inner	185.2.p.a.97.16	✓	68
185.134	odd	12		925.2.y.b.393.16		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.16	✓	68	185.97	even	12	inner
185.2.p.a.103.16	yes	68	1.1	even	1	trivial
185.2.u.a.23.2	yes	68	37.23	odd	12
185.2.u.a.177.2	yes	68	5.2	odd	4
925.2.t.b.282.2		68	185.23	even	12
925.2.t.b.843.2		68	5.4	even	2
925.2.y.b.393.16		68	185.134	odd	12
925.2.y.b.732.16		68	5.3	odd	4

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.p.a.103.16

Level	$185$
Weight	$2$
Character	185.103
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$