LMFDB - Embedded newform 804.2.c.b.671.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.15
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28652 - 0.587251i) q^{2} +(1.29382 - 1.15153i) q^{3} +(1.31027 + 1.51102i) q^{4} +1.10955i q^{5} +(-2.34077 + 0.721672i) q^{6} -0.262541i q^{7} +(-0.798342 - 2.71342i) q^{8} +(0.347946 - 2.97975i) q^{9} +O(q^{10})$	\(q+(-1.28652 - 0.587251i) q^{2} +(1.29382 - 1.15153i) q^{3} +(1.31027 + 1.51102i) q^{4} +1.10955i q^{5} +(-2.34077 + 0.721672i) q^{6} -0.262541i q^{7} +(-0.798342 - 2.71342i) q^{8} +(0.347946 - 2.97975i) q^{9} +(0.651585 - 1.42746i) q^{10} -2.52769 q^{11} +(3.43525 + 0.446172i) q^{12} +2.54523 q^{13} +(-0.154178 + 0.337765i) q^{14} +(1.27768 + 1.43556i) q^{15} +(-0.566377 + 3.95970i) q^{16} -1.62641i q^{17} +(-2.19750 + 3.62918i) q^{18} -7.27510i q^{19} +(-1.67656 + 1.45381i) q^{20} +(-0.302325 - 0.339681i) q^{21} +(3.25193 + 1.48439i) q^{22} -2.35289 q^{23} +(-4.15750 - 2.59136i) q^{24} +3.76890 q^{25} +(-3.27450 - 1.49469i) q^{26} +(-2.98110 - 4.25594i) q^{27} +(0.396706 - 0.344000i) q^{28} -2.37144i q^{29} +(-0.800732 - 2.59720i) q^{30} -4.13270i q^{31} +(3.05399 - 4.76163i) q^{32} +(-3.27038 + 2.91072i) q^{33} +(-0.955110 + 2.09241i) q^{34} +0.291303 q^{35} +(4.95838 - 3.37853i) q^{36} +9.94276 q^{37} +(-4.27231 + 9.35956i) q^{38} +(3.29308 - 2.93092i) q^{39} +(3.01068 - 0.885801i) q^{40} -0.158753i q^{41} +(0.189469 + 0.614548i) q^{42} +0.426938i q^{43} +(-3.31196 - 3.81940i) q^{44} +(3.30619 + 0.386064i) q^{45} +(3.02704 + 1.38174i) q^{46} +6.49415 q^{47} +(3.82693 + 5.77534i) q^{48} +6.93107 q^{49} +(-4.84876 - 2.21329i) q^{50} +(-1.87286 - 2.10428i) q^{51} +(3.33495 + 3.84590i) q^{52} -2.11312i q^{53} +(1.33595 + 7.22601i) q^{54} -2.80460i q^{55} +(-0.712385 + 0.209598i) q^{56} +(-8.37751 - 9.41267i) q^{57} +(-1.39263 + 3.05091i) q^{58} +1.36081 q^{59} +(-0.495051 + 3.81158i) q^{60} -5.75065 q^{61} +(-2.42693 + 5.31680i) q^{62} +(-0.782308 - 0.0913501i) q^{63} +(-6.72530 + 4.33247i) q^{64} +2.82407i q^{65} +(5.91673 - 1.82416i) q^{66} -1.00000i q^{67} +(2.45754 - 2.13103i) q^{68} +(-3.04421 + 2.70943i) q^{69} +(-0.374767 - 0.171068i) q^{70} +4.23883 q^{71} +(-8.36311 + 1.43474i) q^{72} -15.0927 q^{73} +(-12.7916 - 5.83890i) q^{74} +(4.87628 - 4.34001i) q^{75} +(10.9928 - 9.53235i) q^{76} +0.663623i q^{77} +(-5.95780 + 1.83682i) q^{78} +11.8105i q^{79} +(-4.39349 - 0.628424i) q^{80} +(-8.75787 - 2.07359i) q^{81} +(-0.0932279 + 0.204239i) q^{82} +0.252949 q^{83} +(0.117139 - 0.901894i) q^{84} +1.80458 q^{85} +(0.250720 - 0.549264i) q^{86} +(-2.73079 - 3.06822i) q^{87} +(2.01796 + 6.85869i) q^{88} -7.08186i q^{89} +(-4.02676 - 2.43824i) q^{90} -0.668229i q^{91} +(-3.08292 - 3.55526i) q^{92} +(-4.75893 - 5.34697i) q^{93} +(-8.35486 - 3.81370i) q^{94} +8.07209 q^{95} +(-1.53185 - 9.67747i) q^{96} -9.60577 q^{97} +(-8.91697 - 4.07028i) q^{98} +(-0.879500 + 7.53190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.28652	−	0.587251i	−0.909708	−	0.415249i
$2$	−1.28652	−	0.587251i	−0.909708	−	0.415249i
$3$	1.29382	−	1.15153i	0.746988	−	0.664838i
$3$	1.29382	−	1.15153i	0.746988	−	0.664838i
$4$	1.31027	+	1.51102i	0.655136	+	0.755511i
$5$			1.10955i			0.496206i	0.968734	+	0.248103i	$0.0798072\pi$
$5$			1.10955i			0.496206i	−0.968734	+	0.248103i	$0.920193\pi$
$6$	−2.34077	+	0.721672i	−0.955614	+	0.294621i
$7$		−	0.262541i		−	0.0992313i	−0.998768	−	0.0496156i	$-0.984200\pi$
$7$		−	0.262541i		−	0.0992313i	0.998768	−	0.0496156i	$-0.0157996\pi$
$8$	−0.798342	−	2.71342i	−0.282256	−	0.959339i
$9$	0.347946	−	2.97975i	0.115982	−	0.993251i
$10$	0.651585	−	1.42746i	0.206049	−	0.451403i
$11$	−2.52769			−0.762127			−0.381064	−	0.924549i	$-0.624442\pi$
$11$	−2.52769			−0.762127			−0.381064	+	0.924549i	$0.624442\pi$
$12$	3.43525	+	0.446172i	0.991671	+	0.128799i
$13$	2.54523			0.705921			0.352960	−	0.935638i	$-0.385175\pi$
$13$	2.54523			0.705921			0.352960	+	0.935638i	$0.385175\pi$
$14$	−0.154178	+	0.337765i	−0.0412057	+	0.0902714i
$15$	1.27768	+	1.43556i	0.329897	+	0.370660i
$16$	−0.566377	+	3.95970i	−0.141594	+	0.989925i
$17$		−	1.62641i		−	0.394462i	−0.980357	−	0.197231i	$-0.936805\pi$
$17$		−	1.62641i		−	0.394462i	0.980357	−	0.197231i	$-0.0631948\pi$
$18$	−2.19750	+	3.62918i	−0.517957	+	0.855407i
$19$		−	7.27510i		−	1.66902i	−0.550992	−	0.834511i	$-0.685750\pi$
$19$		−	7.27510i		−	1.66902i	0.550992	−	0.834511i	$-0.314250\pi$
$20$	−1.67656	+	1.45381i	−0.374889	+	0.325082i
$21$	−0.302325	−	0.339681i	−0.0659727	−	0.0741245i
$22$	3.25193	+	1.48439i	0.693313	+	0.316473i
$23$	−2.35289			−0.490611			−0.245305	−	0.969446i	$-0.578888\pi$
$23$	−2.35289			−0.490611			−0.245305	+	0.969446i	$0.578888\pi$
$24$	−4.15750	−	2.59136i	−0.848647	−	0.528960i
$25$	3.76890			0.753779
$26$	−3.27450	−	1.49469i	−0.642182	−	0.293133i
$27$	−2.98110	−	4.25594i	−0.573714	−	0.819056i
$28$	0.396706	−	0.344000i	0.0749703	−	0.0650099i
$29$		−	2.37144i		−	0.440366i	−0.975459	−	0.220183i	$-0.929335\pi$
$29$		−	2.37144i		−	0.440366i	0.975459	−	0.220183i	$-0.0706654\pi$
$30$	−0.800732	−	2.59720i	−0.146193	−	0.474182i
$31$		−	4.13270i		−	0.742254i	−0.928582	−	0.371127i	$-0.878971\pi$
$31$		−	4.13270i		−	0.742254i	0.928582	−	0.371127i	$-0.121029\pi$
$32$	3.05399	−	4.76163i	0.539875	−	0.841745i
$33$	−3.27038	+	2.91072i	−0.569300	+	0.506691i
$34$	−0.955110	+	2.09241i	−0.163800	+	0.358845i
$35$	0.291303			0.0492392
$36$	4.95838	−	3.37853i	0.826396	−	0.563089i
$37$	9.94276			1.63458			0.817290	−	0.576226i	$-0.195475\pi$
$37$	9.94276			1.63458			0.817290	+	0.576226i	$0.195475\pi$
$38$	−4.27231	+	9.35956i	−0.693060	+	1.51832i
$39$	3.29308	−	2.93092i	0.527314	−	0.469323i
$40$	3.01068	−	0.885801i	0.476030	−	0.140057i
$41$		−	0.158753i		−	0.0247931i	−0.999923	−	0.0123965i	$-0.996054\pi$
$41$		−	0.158753i		−	0.0247931i	0.999923	−	0.0123965i	$-0.00394604\pi$
$42$	0.189469	+	0.614548i	0.0292357	+	0.0948268i
$43$			0.426938i			0.0651074i	0.999470	+	0.0325537i	$0.0103640\pi$
$43$			0.426938i			0.0651074i	−0.999470	+	0.0325537i	$0.989636\pi$
$44$	−3.31196	−	3.81940i	−0.499297	−	0.575796i
$45$	3.30619	+	0.386064i	0.492858	+	0.0575510i
$46$	3.02704	+	1.38174i	0.446312	+	0.203726i
$47$	6.49415			0.947270			0.473635	−	0.880721i	$-0.342942\pi$
$47$	6.49415			0.947270			0.473635	+	0.880721i	$0.342942\pi$
$48$	3.82693	+	5.77534i	0.552370	+	0.833599i
$49$	6.93107			0.990153
$50$	−4.84876	−	2.21329i	−0.685719	−	0.313006i
$51$	−1.87286	−	2.10428i	−0.262253	−	0.294658i
$52$	3.33495	+	3.84590i	0.462474	+	0.533331i
$53$		−	2.11312i		−	0.290259i	−0.989413	−	0.145129i	$-0.953640\pi$
$53$		−	2.11312i		−	0.290259i	0.989413	−	0.145129i	$-0.0463599\pi$
$54$	1.33595	+	7.22601i	0.181799	+	0.983336i
$55$		−	2.80460i		−	0.378172i
$56$	−0.712385	+	0.209598i	−0.0951964	+	0.0280087i
$57$	−8.37751	−	9.41267i	−1.10963	−	1.24674i
$58$	−1.39263	+	3.05091i	−0.182862	+	0.400604i
$59$	1.36081			0.177162			0.0885810	−	0.996069i	$-0.471767\pi$
$59$	1.36081			0.177162			0.0885810	+	0.996069i	$0.471767\pi$
$60$	−0.495051	+	3.81158i	−0.0639108	+	0.492073i
$61$	−5.75065			−0.736295			−0.368148	−	0.929767i	$-0.620008\pi$
$61$	−5.75065			−0.736295			−0.368148	+	0.929767i	$0.620008\pi$
$62$	−2.42693	+	5.31680i	−0.308221	+	0.675234i
$63$	−0.782308	−	0.0913501i	−0.0985616	−	0.0115090i
$64$	−6.72530	+	4.33247i	−0.840663	+	0.541559i
$65$			2.82407i			0.350282i
$66$	5.91673	−	1.82416i	0.728300	−	0.224539i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	2.45754	−	2.13103i	0.298020	−	0.258426i
$69$	−3.04421	+	2.70943i	−0.366480	+	0.326177i
$70$	−0.374767	−	0.171068i	−0.0447932	−	0.0204465i
$71$	4.23883			0.503056			0.251528	−	0.967850i	$-0.419067\pi$
$71$	4.23883			0.503056			0.251528	+	0.967850i	$0.419067\pi$
$72$	−8.36311	+	1.43474i	−0.985601	+	0.169086i
$73$	−15.0927			−1.76647			−0.883236	−	0.468929i	$-0.844640\pi$
$73$	−15.0927			−1.76647			−0.883236	+	0.468929i	$0.844640\pi$
$74$	−12.7916	−	5.83890i	−1.48699	−	0.678759i
$75$	4.87628	−	4.34001i	0.563064	−	0.501141i
$76$	10.9928	−	9.53235i	1.26096	−	1.09344i
$77$			0.663623i			0.0756269i
$78$	−5.95780	+	1.83682i	−0.674588	+	0.207979i
$79$			11.8105i			1.32878i	0.747386	+	0.664390i	$0.231309\pi$
$79$			11.8105i			1.32878i	−0.747386	+	0.664390i	$0.768691\pi$
$80$	−4.39349	−	0.628424i	−0.491207	−	0.0702599i
$81$	−8.75787	−	2.07359i	−0.973096	−	0.230398i
$82$	−0.0932279	+	0.204239i	−0.0102953	+	0.0225544i
$83$	0.252949			0.0277648			0.0138824	−	0.999904i	$-0.495581\pi$
$83$	0.252949			0.0277648			0.0138824	+	0.999904i	$0.495581\pi$
$84$	0.117139	−	0.901894i	0.0127809	−	0.0984047i
$85$	1.80458			0.195734
$86$	0.250720	−	0.549264i	0.0270358	−	0.0592287i
$87$	−2.73079	−	3.06822i	−0.292772	−	0.328948i
$88$	2.01796	+	6.85869i	0.215115	+	0.731138i
$89$		−	7.08186i		−	0.750675i	−0.926888	−	0.375338i	$-0.877527\pi$
$89$		−	7.08186i		−	0.750675i	0.926888	−	0.375338i	$-0.122473\pi$
$90$	−4.02676	−	2.43824i	−0.424458	−	0.257013i
$91$		−	0.668229i		−	0.0700494i
$92$	−3.08292	−	3.55526i	−0.321417	−	0.370662i
$93$	−4.75893	−	5.34697i	−0.493478	−	0.554455i
$94$	−8.35486	−	3.81370i	−0.861738	−	0.393353i
$95$	8.07209			0.828179
$96$	−1.53185	−	9.67747i	−0.156344	−	0.987703i
$97$	−9.60577			−0.975318			−0.487659	−	0.873034i	$-0.662149\pi$
$97$	−9.60577			−0.975318			−0.487659	+	0.873034i	$0.662149\pi$
$98$	−8.91697	−	4.07028i	−0.900750	−	0.411161i
$99$	−0.879500	+	7.53190i	−0.0883930	+	0.756984i
$100$	4.93828	+	5.69489i	0.493828	+	0.569489i
$101$		−	0.353964i		−	0.0352207i	−0.999845	−	0.0176104i	$-0.994394\pi$
$101$		−	0.353964i		−	0.0352207i	0.999845	−	0.0176104i	$-0.00560584\pi$
$102$	1.17373	+	3.80704i	0.116217	+	0.376953i
$103$			0.502968i			0.0495589i	0.999693	+	0.0247794i	$0.00788835\pi$
$103$			0.502968i			0.0495589i	−0.999693	+	0.0247794i	$0.992112\pi$
$104$	−2.03197	−	6.90629i	−0.199251	−	0.677217i
$105$	0.376894	−	0.335445i	0.0367811	−	0.0327360i
$106$	−1.24093	+	2.71857i	−0.120530	+	0.264051i
$107$	−11.9462			−1.15488			−0.577440	−	0.816433i	$-0.695948\pi$
$107$	−11.9462			−1.15488			−0.577440	+	0.816433i	$0.695948\pi$
$108$	2.52476	−	10.0810i	0.242946	−	0.970040i
$109$	2.85495			0.273455			0.136727	−	0.990609i	$-0.456342\pi$
$109$	2.85495			0.273455			0.136727	+	0.990609i	$0.456342\pi$
$110$	−1.64701	+	3.60818i	−0.157036	+	0.344026i
$111$	12.8642	−	11.4494i	1.22101	−	1.08673i
$112$	1.03958	+	0.148697i	0.0982315	+	0.0140506i
$113$		−	4.89451i		−	0.460437i	−0.973139	−	0.230218i	$-0.926056\pi$
$113$		−	4.89451i		−	0.460437i	0.973139	−	0.230218i	$-0.0739440\pi$
$114$	5.25023	+	17.0293i	0.491730	+	1.59494i
$115$		−	2.61065i		−	0.243444i
$116$	3.58330	−	3.10723i	0.332701	−	0.288499i
$117$	0.885604	−	7.58417i	0.0818741	−	0.701157i
$118$	−1.75071	−	0.799136i	−0.161166	−	0.0735664i
$119$	−0.426999			−0.0391429
$120$	2.87525	−	4.61296i	0.262473	−	0.421104i
$121$	−4.61078			−0.419162
$122$	7.39833	+	3.37708i	0.669814	+	0.305746i
$123$	−0.182809	−	0.205398i	−0.0164834	−	0.0185201i
$124$	6.24460	−	5.41495i	0.560781	−	0.486277i
$125$			9.72954i			0.870236i
$126$	0.952810	+	0.576935i	0.0848831	+	0.0513975i
$127$		−	7.16672i		−	0.635943i	−0.948100	−	0.317972i	$-0.896998\pi$
$127$		−	7.16672i		−	0.635943i	0.948100	−	0.317972i	$-0.103002\pi$
$128$	11.1965	−	1.62437i	0.989639	−	0.143576i
$129$	0.491633	+	0.552381i	0.0432858	+	0.0486344i
$130$	1.65844	−	3.63322i	0.145455	−	0.318654i
$131$	18.8378			1.64586			0.822932	−	0.568140i	$-0.192337\pi$
$131$	18.8378			1.64586			0.822932	+	0.568140i	$0.192337\pi$
$132$	−8.68324	−	1.12779i	−0.755779	−	0.0981611i
$133$	−1.91001			−0.165619
$134$	−0.587251	+	1.28652i	−0.0507308	+	0.111138i
$135$	4.72218	−	3.30769i	0.406421	−	0.284680i
$136$	−4.41312	+	1.29843i	−0.378422	+	0.111339i
$137$			19.8598i			1.69673i	0.529409	+	0.848367i	$0.322414\pi$
$137$			19.8598i			1.69673i	−0.529409	+	0.848367i	$0.677586\pi$
$138$	5.50756	−	1.69801i	0.468835	−	0.144544i
$139$			15.9768i			1.35514i	0.735459	+	0.677569i	$0.236966\pi$
$139$			15.9768i			1.35514i	−0.735459	+	0.677569i	$0.763034\pi$
$140$	0.381686	+	0.440165i	0.0322583	+	0.0372007i
$141$	8.40227	−	7.47823i	0.707599	−	0.629781i
$142$	−5.45334	−	2.48926i	−0.457634	−	0.208894i
$143$	−6.43356			−0.538002
$144$	11.6019	+	3.06542i	0.966822	+	0.255452i
$145$	2.63123			0.218512
$146$	19.4171	+	8.86323i	1.60697	+	0.733526i
$147$	8.96757	−	7.98135i	0.739632	−	0.658291i
$148$	13.0277	+	15.0237i	1.07087	+	1.23494i
$149$			12.0139i			0.984216i	0.870534	+	0.492108i	$0.163773\pi$
$149$			12.0139i			0.984216i	−0.870534	+	0.492108i	$0.836227\pi$
$150$	−8.82211	+	2.71991i	−0.720322	+	0.222080i
$151$		−	6.15058i		−	0.500527i	−0.968178	−	0.250263i	$-0.919483\pi$
$151$		−	6.15058i		−	0.500527i	0.968178	−	0.250263i	$-0.0805172\pi$
$152$	−19.7404	+	5.80801i	−1.60116	+	0.471092i
$153$	−4.84629	−	0.565901i	−0.391799	−	0.0457504i
$154$	0.389714	−	0.853765i	0.0314040	−	0.0687983i
$155$	4.58544			0.368311
$156$	8.74351	+	1.13561i	0.700041	+	0.0909218i
$157$	0.311590			0.0248676			0.0124338	−	0.999923i	$-0.496042\pi$
$157$	0.311590			0.0248676			0.0124338	+	0.999923i	$0.496042\pi$
$158$	6.93571	−	15.1944i	0.551775	−	1.20880i
$159$	−2.43332	−	2.73400i	−0.192975	−	0.216820i
$160$	5.28327	+	3.38856i	0.417679	+	0.267889i
$161$			0.617730i			0.0486839i
$162$	10.0495	+	7.81078i	0.789560	+	0.613673i
$163$			8.18013i			0.640717i	0.947296	+	0.320358i	$0.103803\pi$
$163$			8.18013i			0.640717i	−0.947296	+	0.320358i	$0.896197\pi$
$164$	0.239879	−	0.208010i	0.0187314	−	0.0162428i
$165$	−3.22959	−	3.62865i	−0.251423	−	0.282490i
$166$	−0.325425	−	0.148545i	−0.0252579	−	0.0115293i
$167$	−12.5370			−0.970143			−0.485072	−	0.874474i	$-0.661206\pi$
$167$	−12.5370			−0.970143			−0.485072	+	0.874474i	$0.661206\pi$
$168$	−0.680340	+	1.09152i	−0.0524894	+	0.0842123i
$169$	−6.52179			−0.501676
$170$	−2.32163	−	1.05974i	−0.178061	−	0.0812786i
$171$	−21.6780	−	2.53134i	−1.65776	−	0.193576i
$172$	−0.645112	+	0.559404i	−0.0491894	+	0.0426542i
$173$		−	4.00346i		−	0.304378i	−0.988351	−	0.152189i	$-0.951368\pi$
$173$		−	4.00346i		−	0.304378i	0.988351	−	0.152189i	$-0.0486322\pi$
$174$	1.71140	+	5.55099i	0.129741	+	0.420820i
$175$		−	0.989491i		−	0.0747985i
$176$	1.43163	−	10.0089i	0.107913	−	0.754449i
$177$	1.76064	−	1.56701i	0.132338	−	0.117784i
$178$	−4.15883	+	9.11096i	−0.311718	+	0.682895i
$179$	21.7282			1.62404			0.812020	−	0.583630i	$-0.198368\pi$
$179$	21.7282			1.62404			0.812020	+	0.583630i	$0.198368\pi$
$180$	3.74865	+	5.50157i	0.279408	+	0.410063i
$181$	−14.5887			−1.08437			−0.542183	−	0.840260i	$-0.682402\pi$
$181$	−14.5887			−1.08437			−0.542183	+	0.840260i	$0.682402\pi$
$182$	−0.392418	+	0.859690i	−0.0290880	+	0.0637245i
$183$	−7.44031	+	6.62206i	−0.550004	+	0.489517i
$184$	1.87841	+	6.38437i	0.138478	+	0.470662i
$185$			11.0320i			0.811089i
$186$	2.98245	+	9.67368i	0.218684	+	0.709309i
$187$			4.11105i			0.300630i
$188$	8.50911	+	9.81281i	0.620590	+	0.715673i
$189$	−1.11736	+	0.782663i	−0.0812759	+	0.0569303i
$190$	−10.3849	−	4.74035i	−0.753401	−	0.343901i
$191$	21.8420			1.58043			0.790217	−	0.612827i	$-0.209968\pi$
$191$	21.8420			1.58043			0.790217	+	0.612827i	$0.209968\pi$
$192$	−3.71235	+	13.3498i	−0.267916	+	0.963442i
$193$	3.19092			0.229688			0.114844	−	0.993384i	$-0.463363\pi$
$193$	3.19092			0.229688			0.114844	+	0.993384i	$0.463363\pi$
$194$	12.3580	+	5.64100i	0.887254	+	0.405000i
$195$	3.25200	+	3.65384i	0.232881	+	0.261657i
$196$	9.08159	+	10.4730i	0.648685	+	0.748072i
$197$		−	4.90985i		−	0.349812i	−0.984585	−	0.174906i	$-0.944038\pi$
$197$		−	4.90985i		−	0.349812i	0.984585	−	0.174906i	$-0.0559622\pi$
$198$	5.55461	−	9.17345i	0.394749	−	0.651929i
$199$			23.5288i			1.66791i	0.551832	+	0.833956i	$0.313929\pi$
$199$			23.5288i			1.66791i	−0.551832	+	0.833956i	$0.686071\pi$
$200$	−3.00887	−	10.2266i	−0.212759	−	0.723130i
$201$	−1.15153	−	1.29382i	−0.0812228	−	0.0912591i
$202$	−0.207866	+	0.455382i	−0.0146254	+	0.0320405i
$203$	−0.622601			−0.0436980
$204$	0.725657	−	5.58711i	0.0508062	−	0.391176i
$205$	0.176145			0.0123025
$206$	0.295368	−	0.647078i	0.0205793	−	0.0450841i
$207$	−0.818677	+	7.01102i	−0.0569020	+	0.487300i
$208$	−1.44156	+	10.0784i	−0.0999543	+	0.698809i
$209$			18.3892i			1.27201i
$210$	−0.681872	+	0.210225i	−0.0470536	+	0.0145069i
$211$			3.78622i			0.260654i	0.991471	+	0.130327i	$0.0416028\pi$
$211$			3.78622i			0.260654i	−0.991471	+	0.130327i	$0.958397\pi$
$212$	3.19297	−	2.76876i	0.219294	−	0.190159i
$213$	5.48429	−	4.88115i	0.375777	−	0.334451i
$214$	15.3690	+	7.01541i	1.05060	+	0.479564i
$215$	−0.473709			−0.0323067
$216$	−9.16821	+	11.4867i	−0.623818	+	0.781570i
$217$	−1.08500			−0.0736548
$218$	−3.67296	−	1.67657i	−0.248764	−	0.113552i
$219$	−19.5273	+	17.3798i	−1.31953	+	1.17442i
$220$	4.23782	−	3.67479i	0.285713	−	0.247754i
$221$		−	4.13958i		−	0.278459i
$222$	−23.2737	+	7.17542i	−1.56203	+	0.481582i
$223$		−	3.36904i		−	0.225608i	−0.993617	−	0.112804i	$-0.964017\pi$
$223$		−	3.36904i		−	0.225608i	0.993617	−	0.112804i	$-0.0359832\pi$
$224$	−1.25012	−	0.801799i	−0.0835274	−	0.0535725i
$225$	1.31137	−	11.2304i	0.0874248	−	0.748692i
$226$	−2.87431	+	6.29689i	−0.191196	+	0.418863i
$227$	−19.5547			−1.29789			−0.648945	−	0.760835i	$-0.724789\pi$
$227$	−19.5547			−1.29789			−0.648945	+	0.760835i	$0.724789\pi$
$228$	3.24595	−	24.9918i	0.214968	−	1.65512i
$229$	5.62695			0.371839			0.185920	−	0.982565i	$-0.440474\pi$
$229$	5.62695			0.371839			0.185920	+	0.982565i	$0.440474\pi$
$230$	−1.53311	+	3.35865i	−0.101090	+	0.221463i
$231$	0.764183	+	0.858609i	0.0502796	+	0.0564923i
$232$	−6.43472	+	1.89322i	−0.422460	+	0.124296i
$233$			27.4599i			1.79896i	0.436961	+	0.899480i	$0.356055\pi$
$233$			27.4599i			1.79896i	−0.436961	+	0.899480i	$0.643945\pi$
$234$	−5.59316	+	9.23712i	−0.365636	+	0.603849i
$235$			7.20559i			0.470041i
$236$	1.78303	+	2.05621i	0.116065	+	0.133848i
$237$	13.6001	+	15.2806i	0.883423	+	0.992583i
$238$	0.549343	+	0.250756i	0.0356086	+	0.0162541i
$239$	18.0672			1.16867			0.584336	−	0.811512i	$-0.301355\pi$
$239$	18.0672			1.16867			0.584336	+	0.811512i	$0.301355\pi$
$240$	−6.40804	+	4.24618i	−0.413637	+	0.274089i
$241$	20.0664			1.29259			0.646294	−	0.763089i	$-0.276318\pi$
$241$	20.0664			1.29259			0.646294	+	0.763089i	$0.276318\pi$
$242$	5.93187	+	2.70769i	0.381315	+	0.174057i
$243$	−13.7189	+	7.40212i	−0.880069	+	0.474846i
$244$	−7.53492	−	8.68936i	−0.482374	−	0.556279i
$245$			7.69038i			0.491320i
$246$	0.114568	+	0.371604i	0.00730457	+	0.0236926i
$247$		−	18.5168i		−	1.17820i
$248$	−11.2137	+	3.29930i	−0.712073	+	0.209506i
$249$	0.327271	−	0.291280i	0.0207400	−	0.0184591i
$250$	5.71368	−	12.5173i	0.361365	−	0.791661i
$251$	0.410017			0.0258800			0.0129400	−	0.999916i	$-0.495881\pi$
$251$	0.410017			0.0258800			0.0129400	+	0.999916i	$0.495881\pi$
$252$	−0.887004	−	1.30178i	−0.0558760	−	0.0820043i
$253$	5.94737			0.373908
$254$	−4.20866	+	9.22013i	−0.264075	+	0.578522i
$255$	2.33480	−	2.07803i	0.146211	−	0.130132i
$256$	−15.3584	−	4.48536i	−0.959902	−	0.280335i
$257$			28.2650i			1.76312i	0.472068	+	0.881562i	$0.343508\pi$
$257$			28.2650i			1.76312i	−0.472068	+	0.881562i	$0.656492\pi$
$258$	−0.308109	−	0.999361i	−0.0191820	−	0.0622175i
$259$		−	2.61039i		−	0.162201i
$260$	−4.26723	+	3.70029i	−0.264642	+	0.229482i
$261$	−7.06631	−	0.825133i	−0.437394	−	0.0510745i
$262$	−24.2352	−	11.0625i	−1.49725	−	0.683444i
$263$	10.9958			0.678033			0.339016	−	0.940780i	$-0.389906\pi$
$263$	10.9958			0.678033			0.339016	+	0.940780i	$0.389906\pi$
$264$	10.5089	+	6.55017i	0.646777	+	0.403135i
$265$	2.34461			0.144028
$266$	2.45727	+	1.12166i	0.150665	+	0.0687732i
$267$	−8.15499	−	9.16266i	−0.499077	−	0.560745i
$268$	1.51102	−	1.31027i	0.0923004	−	0.0800376i
$269$			0.709047i			0.0432314i	0.999766	+	0.0216157i	$0.00688102\pi$
$269$			0.709047i			0.0432314i	−0.999766	+	0.0216157i	$0.993119\pi$
$270$	−8.01763	+	1.48230i	−0.487937	+	0.0902099i
$271$			8.50829i			0.516842i	0.966032	+	0.258421i	$0.0832022\pi$
$271$			8.50829i			0.516842i	−0.966032	+	0.258421i	$0.916798\pi$
$272$	6.44008	+	0.921159i	0.390487	+	0.0558535i
$273$	−0.769487	−	0.864568i	−0.0465715	−	0.0523261i
$274$	11.6627	−	25.5500i	0.704568	−	1.54353i
$275$	−9.52660			−0.574476
$276$	−8.08275	−	1.04979i	−0.486524	−	0.0631901i
$277$	29.7481			1.78739			0.893695	−	0.448674i	$-0.148104\pi$
$277$	29.7481			1.78739			0.893695	+	0.448674i	$0.148104\pi$
$278$	9.38242	−	20.5545i	0.562720	−	1.23278i
$279$	−12.3144	−	1.43795i	−0.737245	−	0.0860881i
$280$	−0.232559	−	0.790427i	−0.0138981	−	0.0472371i
$281$		−	8.92122i		−	0.532195i	−0.963946	−	0.266098i	$-0.914266\pi$
$281$		−	8.92122i		−	0.532195i	0.963946	−	0.266098i	$-0.0857344\pi$
$282$	−15.2013	+	4.68665i	−0.905224	+	0.279086i
$283$			5.10047i			0.303191i	0.988443	+	0.151596i	$0.0484412\pi$
$283$			5.10047i			0.303191i	−0.988443	+	0.151596i	$0.951559\pi$
$284$	5.55402	+	6.40496i	0.329570	+	0.380065i
$285$	10.4438	−	9.29527i	0.618640	−	0.550604i
$286$	8.27691	+	3.77812i	0.489424	+	0.223405i
$287$	−0.0416792			−0.00246025
$288$	−13.1259	−	10.7569i	−0.773449	−	0.633859i
$289$	14.3548			0.844400
$290$	−3.38514	−	1.54520i	−0.198782	−	0.0907370i
$291$	−12.4281	+	11.0614i	−0.728551	+	0.648428i
$292$	−19.7756	−	22.8055i	−1.15728	−	1.33459i
$293$		−	22.5544i		−	1.31764i	−0.752300	−	0.658820i	$-0.771056\pi$
$293$		−	22.5544i		−	1.31764i	0.752300	−	0.658820i	$-0.228944\pi$
$294$	−16.2240	+	5.00196i	−0.946204	+	0.291720i
$295$			1.50988i			0.0879089i
$296$	−7.93772	−	26.9789i	−0.461371	−	1.56812i
$297$	7.53531	+	10.7577i	0.437243	+	0.624225i
$298$	7.05517	−	15.4561i	0.408695	−	0.895349i
$299$	−5.98865			−0.346332
$300$	12.9471	+	1.68158i	0.747501	+	0.0970859i
$301$	0.112089			0.00646069
$302$	−3.61193	+	7.91284i	−0.207843	+	0.455333i
$303$	−0.407601	−	0.457966i	−0.0234160	−	0.0263094i
$304$	28.8072	+	4.12045i	1.65221	+	0.236324i
$305$		−	6.38064i		−	0.365354i
$306$	5.90253	+	3.57404i	0.337425	+	0.204314i
$307$		−	22.0167i		−	1.25656i	−0.777988	−	0.628280i	$-0.783759\pi$
$307$		−	22.0167i		−	1.25656i	0.777988	−	0.628280i	$-0.216241\pi$
$308$	−1.00275	+	0.869526i	−0.0571369	+	0.0495459i
$309$	0.579184	+	0.650750i	0.0329486	+	0.0370199i
$310$	−5.89926	−	2.69280i	−0.335055	−	0.152941i
$311$	17.5997			0.997986			0.498993	−	0.866606i	$-0.333703\pi$
$311$	17.5997			0.997986			0.498993	+	0.866606i	$0.333703\pi$
$312$	−10.5818	−	6.59563i	−0.599077	−	0.373404i
$313$	7.38797			0.417593			0.208796	−	0.977959i	$-0.433045\pi$
$313$	7.38797			0.417593			0.208796	+	0.977959i	$0.433045\pi$
$314$	−0.400867	−	0.182982i	−0.0226222	−	0.0103263i
$315$	0.101358	−	0.868011i	0.00571086	−	0.0489069i
$316$	−17.8459	+	15.4749i	−1.00391	+	0.870531i
$317$		−	28.7508i		−	1.61481i	−0.590001	−	0.807403i	$-0.700873\pi$
$317$		−	28.7508i		−	1.61481i	0.590001	−	0.807403i	$-0.299127\pi$
$318$	1.52498	+	4.94631i	0.0855165	+	0.277376i
$319$			5.99427i			0.335615i
$320$	−4.80710	−	7.46206i	−0.268725	−	0.417142i
$321$	−15.4562	+	13.7564i	−0.862682	+	0.767808i
$322$	0.362763	−	0.794722i	0.0202160	−	0.0442881i
$323$	−11.8323			−0.658365
$324$	−8.34195	−	15.9503i	−0.463442	−	0.886127i
$325$	9.59272			0.532109
$326$	4.80379	−	10.5239i	0.266057	−	0.582865i
$327$	3.69380	−	3.28757i	0.204267	−	0.181803i
$328$	−0.430764	+	0.126739i	−0.0237849	+	0.00699800i
$329$		−	1.70498i		−	0.0939988i
$330$	2.02400	+	6.56492i	0.111418	+	0.361387i
$331$		−	9.08046i		−	0.499107i	−0.968361	−	0.249553i	$-0.919716\pi$
$331$		−	9.08046i		−	0.499107i	0.968361	−	0.249553i	$-0.0802838\pi$
$332$	0.331433	+	0.382212i	0.0181897	+	0.0209766i
$333$	3.45954	−	29.6270i	0.189582	−	1.62355i
$334$	16.1291	+	7.36238i	0.882547	+	0.402851i
$335$	1.10955			0.0606212
$336$	1.51627	−	1.00473i	0.0827191	−	0.0548124i
$337$	−20.0677			−1.09316			−0.546579	−	0.837408i	$-0.684070\pi$
$337$	−20.0677			−1.09316			−0.546579	+	0.837408i	$0.684070\pi$
$338$	8.39041	+	3.82993i	0.456378	+	0.208321i
$339$	−5.63618	−	6.33262i	−0.306116	−	0.343941i
$340$	2.36449	+	2.72676i	0.128233	+	0.147879i
$341$			10.4462i			0.565692i
$342$	26.4027	+	15.9871i	1.42769	+	0.864481i
$343$		−	3.65748i		−	0.197485i
$344$	1.15846	−	0.340842i	0.0624600	−	0.0183770i
$345$	−3.00625	−	3.37771i	−0.161851	−	0.181850i
$346$	−2.35104	+	5.15054i	−0.126393	+	0.276895i
$347$	−12.6600			−0.679625			−0.339812	−	0.940493i	$-0.610364\pi$
$347$	−12.6600			−0.679625			−0.339812	+	0.940493i	$0.610364\pi$
$348$	1.05807	−	8.14649i	0.0567186	−	0.436698i
$349$	11.0888			0.593571			0.296786	−	0.954944i	$-0.404085\pi$
$349$	11.0888			0.593571			0.296786	+	0.954944i	$0.404085\pi$
$350$	−0.581080	+	1.27300i	−0.0310600	+	0.0680447i
$351$	−7.58761	−	10.8324i	−0.404996	−	0.578189i
$352$	−7.71955	+	12.0359i	−0.411454	+	0.641517i
$353$			4.79771i			0.255356i	0.991816	+	0.127678i	$0.0407525\pi$
$353$			4.79771i			0.255356i	−0.991816	+	0.127678i	$0.959248\pi$
$354$	−3.18533	+	0.982056i	−0.169298	+	0.0521957i
$355$			4.70320i			0.249620i
$356$	10.7008	−	9.27916i	0.567144	−	0.491794i
$357$	−0.552460	+	0.491703i	−0.0292393	+	0.0260237i
$358$	−27.9537	−	12.7599i	−1.47740	−	0.674381i
$359$	−27.5490			−1.45398			−0.726989	−	0.686649i	$-0.759081\pi$
$359$	−27.5490			−1.45398			−0.726989	+	0.686649i	$0.759081\pi$
$360$	−1.59192	−	9.27929i	−0.0839013	−	0.489062i
$361$	−33.9270			−1.78563
$362$	18.7686	+	8.56721i	0.986456	+	0.450282i
$363$	−5.96553	+	5.30946i	−0.313109	+	0.278675i
$364$	1.00971	−	0.875561i	0.0529231	−	0.0458919i
$365$		−	16.7462i		−	0.876534i
$366$	13.4609	−	4.15009i	0.703614	−	0.216928i
$367$			32.3136i			1.68676i	0.537320	+	0.843379i	$0.319437\pi$
$367$			32.3136i			1.68676i	−0.537320	+	0.843379i	$0.680563\pi$
$368$	1.33262	−	9.31672i	0.0694677	−	0.485668i
$369$	−0.473045	−	0.0552375i	−0.0246257	−	0.00287555i
$370$	6.47856	−	14.1929i	0.336804	−	0.737854i
$371$	−0.554780			−0.0288028
$372$	1.84389	−	14.1968i	0.0956015	−	0.736072i
$373$	−5.16397			−0.267380			−0.133690	−	0.991023i	$-0.542683\pi$
$373$	−5.16397			−0.267380			−0.133690	+	0.991023i	$0.542683\pi$
$374$	2.41422	−	5.28895i	0.124836	−	0.273485i
$375$	11.2039	+	12.5883i	0.578566	+	0.650056i
$376$	−5.18455	−	17.6214i	−0.267373	−	0.908753i
$377$		−	6.03587i		−	0.310863i
$378$	1.89713	−	0.350741i	0.0975776	−	0.0180402i
$379$		−	14.0877i		−	0.723636i	−0.932249	−	0.361818i	$-0.882156\pi$
$379$		−	14.0877i		−	0.723636i	0.932249	−	0.361818i	$-0.117844\pi$
$380$	10.5766	+	12.1971i	0.542570	+	0.625698i
$381$	−8.25271	−	9.27245i	−0.422799	−	0.475042i
$382$	−28.1002	−	12.8268i	−1.43773	−	0.656274i
$383$	−7.22905			−0.369387			−0.184694	−	0.982796i	$-0.559129\pi$
$383$	−7.22905			−0.369387			−0.184694	+	0.982796i	$0.559129\pi$
$384$	12.6157	−	14.9948i	0.643794	−	0.765199i
$385$	−0.736323			−0.0375265
$386$	−4.10519	−	1.87387i	−0.208949	−	0.0953776i
$387$	1.27217	+	0.148551i	0.0646680	+	0.00755128i
$388$	−12.5862	−	14.5145i	−0.638966	−	0.736864i
$389$			15.3857i			0.780085i	0.920797	+	0.390042i	$0.127540\pi$
$389$			15.3857i			0.780085i	−0.920797	+	0.390042i	$0.872460\pi$
$390$	−2.03805	−	6.61048i	−0.103201	−	0.334735i
$391$			3.82675i			0.193527i
$392$	−5.53336	−	18.8069i	−0.279477	−	0.949893i
$393$	24.3727	−	21.6923i	1.22944	−	1.09423i
$394$	−2.88332	+	6.31662i	−0.145259	+	0.318227i
$395$	−13.1043			−0.659349
$396$	−12.5332	+	8.53989i	−0.629819	+	0.429145i
$397$	30.3383			1.52263			0.761317	−	0.648380i	$-0.224553\pi$
$397$	30.3383			1.52263			0.761317	+	0.648380i	$0.224553\pi$
$398$	13.8173	−	30.2703i	0.692599	−	1.51731i
$399$	−2.47121	+	2.19944i	−0.123715	+	0.110110i
$400$	−2.13462	+	14.9237i	−0.106731	+	0.746185i
$401$			32.8331i			1.63961i	0.572646	+	0.819803i	$0.305917\pi$
$401$			32.8331i			1.63961i	−0.572646	+	0.819803i	$0.694083\pi$
$402$	0.721672	+	2.34077i	0.0359937	+	0.116747i
$403$		−	10.5187i		−	0.523973i
$404$	0.534847	−	0.463789i	0.0266096	−	0.0230743i
$405$	2.30075	−	9.71730i	0.114325	−	0.482857i
$406$	0.800989	+	0.365623i	0.0397524	+	0.0181456i
$407$	−25.1322			−1.24576
$408$	−4.21461	+	6.76179i	−0.208654	+	0.334759i
$409$	−12.4009			−0.613184			−0.306592	−	0.951841i	$-0.599189\pi$
$409$	−12.4009			−0.613184			−0.306592	+	0.951841i	$0.599189\pi$
$410$	−0.226614	−	0.103441i	−0.0111916	−	0.00510859i
$411$	22.8692	+	25.6950i	1.12805	+	1.26744i
$412$	−0.759995	+	0.659024i	−0.0374423	+	0.0324678i
$413$		−	0.357268i		−	0.0175800i
$414$	5.17048	−	8.53906i	0.254115	−	0.419672i
$415$			0.280660i			0.0137771i
$416$	7.77313	−	12.1195i	0.381109	−	0.594205i
$417$	18.3978	+	20.6712i	0.900946	+	1.01227i
$418$	10.7991	−	23.6581i	0.528200	−	1.15715i
$419$	21.6380			1.05709			0.528543	−	0.848907i	$-0.322739\pi$
$419$	21.6380			1.05709			0.528543	+	0.848907i	$0.322739\pi$
$420$	1.00070	+	0.129971i	0.0488290	+	0.00634195i
$421$	−22.6818			−1.10544			−0.552721	−	0.833366i	$-0.686411\pi$
$421$	−22.6818			−1.10544			−0.552721	+	0.833366i	$0.686411\pi$
$422$	2.22346	−	4.87105i	0.108237	−	0.237119i
$423$	2.25961	−	19.3510i	0.109866	−	0.940877i
$424$	−5.73377	+	1.68699i	−0.278457	+	0.0819274i
$425$		−	6.12976i		−	0.297337i
$426$	−9.92211	+	3.05904i	−0.480728	+	0.148211i
$427$			1.50978i			0.0730635i
$428$	−15.6527	−	18.0509i	−0.756604	−	0.872525i
$429$	−8.32388	+	7.40846i	−0.401881	+	0.357684i
$430$	0.609437	+	0.278186i	0.0293896	+	0.0134153i
$431$	22.4935			1.08347			0.541736	−	0.840549i	$-0.317767\pi$
$431$	22.4935			1.08347			0.541736	+	0.840549i	$0.317767\pi$
$432$	18.5407	−	9.39381i	0.892038	−	0.451960i
$433$	−19.6531			−0.944468			−0.472234	−	0.881473i	$-0.656552\pi$
$433$	−19.6531			−0.944468			−0.472234	+	0.881473i	$0.656552\pi$
$434$	1.39588	+	0.637170i	0.0670043	+	0.0305851i
$435$	3.40435	−	3.02995i	0.163226	−	0.145275i
$436$	3.74076	+	4.31390i	0.179150	+	0.206598i
$437$			17.1175i			0.818840i
$438$	35.3286	−	10.8920i	1.68806	−	0.520440i
$439$			21.9774i			1.04892i	0.851434	+	0.524462i	$0.175733\pi$
$439$			21.9774i			1.04892i	−0.851434	+	0.524462i	$0.824267\pi$
$440$	−7.61006	+	2.23903i	−0.362795	+	0.106742i
$441$	2.41164	−	20.6529i	0.114840	−	0.983471i
$442$	−2.43098	+	5.32566i	−0.115630	+	0.253316i
$443$	1.97577			0.0938716			0.0469358	−	0.998898i	$-0.485054\pi$
$443$	1.97577			0.0938716			0.0469358	+	0.998898i	$0.485054\pi$
$444$	34.1559	+	4.43619i	1.62097	+	0.210532i
$445$	7.85768			0.372490
$446$	−1.97848	+	4.33435i	−0.0936836	+	0.205237i
$447$	13.8344	+	15.5438i	0.654344	+	0.735197i
$448$	1.13745	+	1.76567i	0.0537396	+	0.0834200i
$449$		−	6.86064i		−	0.323774i	−0.986809	−	0.161887i	$-0.948242\pi$
$449$		−	6.86064i		−	0.323774i	0.986809	−	0.161887i	$-0.0517580\pi$
$450$	−8.28217	+	13.6780i	−0.390425	+	0.644788i
$451$			0.401278i			0.0188955i
$452$	7.39571	−	6.41313i	0.347865	−	0.301648i
$453$	−7.08259	−	7.95774i	−0.332769	−	0.373887i
$454$	25.1575	+	11.4835i	1.18070	+	0.538948i
$455$	0.741434			0.0347590
$456$	−18.8524	+	30.2462i	−0.882846	+	1.41641i
$457$	−7.92873			−0.370890			−0.185445	−	0.982655i	$-0.559373\pi$
$457$	−7.92873			−0.370890			−0.185445	+	0.982655i	$0.559373\pi$
$458$	−7.23919	−	3.30443i	−0.338265	−	0.154406i
$459$	−6.92189	+	4.84849i	−0.323086	+	0.226308i
$460$	3.94475	−	3.42066i	0.183925	−	0.159489i
$461$		−	27.6962i		−	1.28994i	−0.764208	−	0.644970i	$-0.776870\pi$
$461$		−	27.6962i		−	1.28994i	0.764208	−	0.644970i	$-0.223130\pi$
$462$	−0.478918	−	1.55339i	−0.0222813	−	0.0722701i
$463$		−	39.6611i		−	1.84321i	−0.388131	−	0.921604i	$-0.626879\pi$
$463$		−	39.6611i		−	1.84321i	0.388131	−	0.921604i	$-0.373121\pi$
$464$	9.39019	+	1.34313i	0.435929	+	0.0623532i
$465$	5.93274	−	5.28028i	0.275124	−	0.244867i
$466$	16.1259	−	35.3278i	0.747017	−	1.63653i
$467$	−39.8079			−1.84209			−0.921045	−	0.389456i	$-0.872663\pi$
$467$	−39.8079			−1.84209			−0.921045	+	0.389456i	$0.872663\pi$
$468$	12.6202	−	8.59916i	0.583370	−	0.397496i
$469$	−0.262541			−0.0121230
$470$	4.23150	−	9.27015i	0.195184	−	0.427600i
$471$	0.403142	−	0.358806i	0.0185758	−	0.0165329i
$472$	−1.08639	−	3.69244i	−0.0500051	−	0.169958i
$473$		−	1.07917i		−	0.0496201i
$474$	−8.52328	−	27.6455i	−0.391487	−	1.26980i
$475$		−	27.4191i		−	1.25807i
$476$	−0.559484	−	0.645205i	−0.0256439	−	0.0295729i
$477$	−6.29657	−	0.735250i	−0.288300	−	0.0336648i
$478$	−23.2439	−	10.6100i	−1.06315	−	0.485291i
$479$	6.76561			0.309129			0.154564	−	0.987983i	$-0.450603\pi$
$479$	6.76561			0.309129			0.154564	+	0.987983i	$0.450603\pi$
$480$	10.7376	−	1.69966i	0.490104	−	0.0775787i
$481$	25.3067			1.15388
$482$	−25.8158	−	11.7840i	−1.17588	−	0.536746i
$483$	0.711336	+	0.799232i	0.0323669	+	0.0363663i
$484$	−6.04138	−	6.96699i	−0.274608	−	0.316681i
$485$		−	10.6581i		−	0.483959i
$486$	21.9966	−	1.46653i	0.997785	−	0.0665231i
$487$			33.2472i			1.50658i	0.657690	+	0.753288i	$0.271534\pi$
$487$			33.2472i			1.50658i	−0.657690	+	0.753288i	$0.728466\pi$
$488$	4.59098	+	15.6039i	0.207824	+	0.706357i
$489$	9.41968	+	10.5836i	0.425973	+	0.478608i
$490$	4.51619	−	9.89383i	0.204020	−	0.446958i
$491$	9.36873			0.422805			0.211403	−	0.977399i	$-0.432197\pi$
$491$	9.36873			0.422805			0.211403	+	0.977399i	$0.432197\pi$
$492$	0.0708312	−	0.545356i	0.00319332	−	0.0245865i
$493$	−3.85693			−0.173707
$494$	−10.8740	+	23.8223i	−0.489246	+	1.07181i
$495$	−8.35702	−	0.975850i	−0.375620	−	0.0438612i
$496$	16.3642	+	2.34066i	0.734776	+	0.105099i
$497$		−	1.11287i		−	0.0499189i
$498$	−0.592096	+	0.182547i	−0.0265324	+	0.00818011i
$499$			14.4248i			0.645742i	0.946443	+	0.322871i	$0.104648\pi$
$499$			14.4248i			0.645742i	−0.946443	+	0.322871i	$0.895352\pi$
$500$	−14.7015	+	12.7483i	−0.657473	+	0.570123i
$501$	−16.2207	+	14.4368i	−0.724685	+	0.644988i
$502$	−0.527495	−	0.240783i	−0.0235433	−	0.0107467i
$503$	−31.2772			−1.39458			−0.697292	−	0.716787i	$-0.745612\pi$
$503$	−31.2772			−1.39458			−0.697292	+	0.716787i	$0.745612\pi$
$504$	0.376678	+	2.19566i	0.0167786	+	0.0978025i
$505$	0.392741			0.0174767
$506$	−7.65142	−	3.49260i	−0.340147	−	0.155265i
$507$	−8.43802	+	7.51005i	−0.374746	+	0.333533i
$508$	10.8291	−	9.39034i	0.480462	−	0.416629i
$509$			32.5296i			1.44185i	0.693014	+	0.720924i	$0.256282\pi$
$509$			32.5296i			1.44185i	−0.693014	+	0.720924i	$0.743718\pi$
$510$	−4.22410	+	1.30232i	−0.187046	+	0.0576675i
$511$			3.96247i			0.175289i
$512$	17.1249	+	14.7898i	0.756821	+	0.653622i
$513$	−30.9624	+	21.6878i	−1.36702	+	0.957540i
$514$	16.5987	−	36.3635i	0.732136	−	1.60393i
$515$	−0.558068			−0.0245914
$516$	−0.190488	+	1.46664i	−0.00838575	+	0.0645651i
$517$	−16.4152			−0.721940
$518$	−1.53295	+	3.35831i	−0.0673541	+	0.147556i
$519$	−4.61012	−	5.17977i	−0.202362	−	0.227367i
$520$	7.66288	−	2.25457i	0.336040	−	0.0988694i
$521$		−	11.5579i		−	0.506360i	−0.967419	−	0.253180i	$-0.918524\pi$
$521$		−	11.5579i		−	0.506360i	0.967419	−	0.253180i	$-0.0814764\pi$
$522$	8.60640	+	5.21125i	0.376692	+	0.228090i
$523$		−	4.09487i		−	0.179056i	−0.995984	−	0.0895281i	$-0.971464\pi$
$523$		−	4.09487i		−	0.179056i	0.995984	−	0.0895281i	$-0.0285359\pi$
$524$	24.6826	+	28.4643i	1.07826	+	1.24347i
$525$	−1.13943	−	1.28022i	−0.0497288	−	0.0558736i
$526$	−14.1464	−	6.45732i	−0.616812	−	0.281553i
$527$	−6.72144			−0.292791
$528$	−9.67330	−	14.5983i	−0.420976	−	0.635309i
$529$	−17.4639			−0.759301
$530$	−3.01639	−	1.37688i	−0.131024	−	0.0598077i
$531$	0.473487	−	4.05487i	0.0205476	−	0.175966i
$532$	−2.50264	−	2.88607i	−0.108503	−	0.125127i
$533$		−	0.404064i		−	0.0175019i
$534$	5.11078	+	16.5770i	0.221165	+	0.717356i
$535$		−	13.2549i		−	0.573059i
$536$	−2.71342	+	0.798342i	−0.117202	+	0.0344831i
$537$	28.1124	−	25.0207i	1.21314	−	1.07972i
$538$	0.416389	−	0.912204i	0.0179518	−	0.0393279i
$539$	−17.5196			−0.754623
$540$	11.1853	+	2.80135i	0.481340	+	0.120551i
$541$	8.60038			0.369759			0.184880	−	0.982761i	$-0.440810\pi$
$541$	8.60038			0.369759			0.184880	+	0.982761i	$0.440810\pi$
$542$	4.99651	−	10.9461i	0.214618	−	0.470175i
$543$	−18.8751	+	16.7993i	−0.810008	+	0.720927i
$544$	−7.74435	−	4.96704i	−0.332036	−	0.212960i
$545$			3.16771i			0.135690i
$546$	0.482242	+	1.56417i	0.0206381	+	0.0669402i
$547$			19.3459i			0.827169i	0.910466	+	0.413585i	$0.135723\pi$
$547$			19.3459i			0.827169i	−0.910466	+	0.413585i	$0.864277\pi$
$548$	−30.0085	+	26.0217i	−1.28190	+	1.11159i
$549$	−2.00092	+	17.1355i	−0.0853970	+	0.731326i
$550$	12.2562	+	5.59451i	0.522605	+	0.238551i
$551$	−17.2525			−0.734980
$552$	9.78213	+	6.09719i	0.416355	+	0.259514i
$553$	3.10073			0.131857
$554$	−38.2716	−	17.4696i	−1.62600	−	0.742213i
$555$	12.7037	+	14.2734i	0.539242	+	0.605874i
$556$	−24.1414	+	20.9340i	−1.02382	+	0.887799i
$557$		−	22.1267i		−	0.937536i	−0.883321	−	0.468768i	$-0.844698\pi$
$557$		−	22.1267i		−	0.937536i	0.883321	−	0.468768i	$-0.155302\pi$
$558$	14.9983	+	9.08162i	0.634929	+	0.384456i
$559$			1.08666i			0.0459607i
$560$	−0.164987	+	1.15347i	−0.00697198	+	0.0487431i
$561$	4.73401	+	5.31897i	0.199870	+	0.224567i
$562$	−5.23900	+	11.4773i	−0.220994	+	0.484142i
$563$	32.7218			1.37906			0.689530	−	0.724257i	$-0.257817\pi$
$563$	32.7218			1.37906			0.689530	+	0.724257i	$0.257817\pi$
$564$	22.3090	+	2.89751i	0.939380	+	0.122007i
$565$	5.43071			0.228472
$566$	2.99526	−	6.56186i	0.125900	−	0.275815i
$567$	−0.544402	+	2.29930i	−0.0228627	+	0.0965616i
$568$	−3.38403	−	11.5017i	−0.141991	−	0.482602i
$569$			17.1204i			0.717725i	0.933390	+	0.358862i	$0.116835\pi$
$569$			17.1204i			0.717725i	−0.933390	+	0.358862i	$0.883165\pi$
$570$	−18.8949	+	5.82540i	−0.791419	+	0.243999i
$571$		−	27.6118i		−	1.15552i	−0.816207	−	0.577760i	$-0.803927\pi$
$571$		−	27.6118i		−	1.15552i	0.816207	−	0.577760i	$-0.196073\pi$
$572$	−8.42971	−	9.72126i	−0.352464	−	0.406466i
$573$	28.2597	−	25.1518i	1.18057	−	1.05073i
$574$	0.0536212	+	0.0244762i	0.00223810	+	0.00102162i
$575$	−8.86779			−0.369812
$576$	10.5697	+	21.5472i	0.440403	+	0.897800i
$577$	−16.6041			−0.691237			−0.345618	−	0.938375i	$-0.612331\pi$
$577$	−16.6041			−0.691237			−0.345618	+	0.938375i	$0.612331\pi$
$578$	−18.4678	−	8.42988i	−0.768157	−	0.350637i
$579$	4.12848	−	3.67445i	0.171574	−	0.152705i
$580$	3.44763	+	3.97585i	0.143155	+	0.165088i
$581$		−	0.0664097i		−	0.00275514i
$582$	22.4849	−	6.93222i	0.932028	−	0.287350i
$583$			5.34131i			0.221214i
$584$	12.0492	+	40.9529i	0.498598	+	1.69464i
$585$	8.41502	+	0.982622i	0.347918	+	0.0406264i
$586$	−13.2451	+	29.0167i	−0.547150	+	1.19867i
$587$	29.1091			1.20146			0.600731	−	0.799451i	$-0.294876\pi$
$587$	29.1091			1.20146			0.600731	+	0.799451i	$0.294876\pi$
$588$	23.8100	+	3.09245i	0.981906	+	0.127531i
$589$	−30.0658			−1.23884
$590$	0.886682	−	1.94250i	0.0365041	−	0.0799714i
$591$	−5.65385	−	6.35247i	−0.232568	−	0.261306i
$592$	−5.63135	+	39.3704i	−0.231447	+	1.61811i
$593$			22.6210i			0.928931i	0.885591	+	0.464466i	$0.153754\pi$
$593$			22.6210i			0.928931i	−0.885591	+	0.464466i	$0.846246\pi$
$594$	−3.37686	−	18.2651i	−0.138554	−	0.749427i
$595$		−	0.473777i		−	0.0194230i
$596$	−18.1532	+	15.7415i	−0.743586	+	0.644795i
$597$	27.0942	+	30.4420i	1.10889	+	1.24591i
$598$	7.70452	+	3.51684i	0.315061	+	0.143814i
$599$	−11.2359			−0.459087			−0.229544	−	0.973298i	$-0.573723\pi$
$599$	−11.2359			−0.459087			−0.229544	+	0.973298i	$0.573723\pi$
$600$	−15.6692	−	9.76658i	−0.639692	−	0.398719i
$601$	4.66316			0.190214			0.0951071	−	0.995467i	$-0.469681\pi$
$601$	4.66316			0.190214			0.0951071	+	0.995467i	$0.469681\pi$
$602$	−0.144204	−	0.0658243i	−0.00587734	−	0.00268280i
$603$	−2.97975	−	0.347946i	−0.121345	−	0.0141695i
$604$	9.29366	−	8.05892i	0.378154	−	0.327913i
$605$		−	5.11590i		−	0.207991i
$606$	0.255446	+	0.828546i	0.0103768	+	0.0336574i
$607$		−	12.7184i		−	0.516223i	−0.966115	−	0.258111i	$-0.916900\pi$
$607$		−	12.7184i		−	0.516223i	0.966115	−	0.258111i	$-0.0831002\pi$
$608$	−34.6413	−	22.2181i	−1.40489	−	0.901063i
$609$	−0.805534	+	0.716945i	−0.0326419	+	0.0290521i
$610$	−3.74704	+	8.20883i	−0.151713	+	0.332366i
$611$	16.5291			0.668697
$612$	−5.49487	−	8.06434i	−0.222117	−	0.325982i
$613$	−4.53277			−0.183077			−0.0915385	−	0.995802i	$-0.529178\pi$
$613$	−4.53277			−0.183077			−0.0915385	+	0.995802i	$0.529178\pi$
$614$	−12.9293	+	28.3249i	−0.521786	+	1.14310i
$615$	0.227900	−	0.202836i	0.00918980	−	0.00817914i
$616$	1.80069	−	0.529798i	0.0725518	−	0.0213462i
$617$		−	2.32331i		−	0.0935328i	−0.998906	−	0.0467664i	$-0.985108\pi$
$617$		−	2.32331i		−	0.0935328i	0.998906	−	0.0467664i	$-0.0148916\pi$
$618$	−0.362978	−	1.17733i	−0.0146011	−	0.0473592i
$619$		−	8.70358i		−	0.349826i	−0.984584	−	0.174913i	$-0.944036\pi$
$619$		−	8.70358i		−	0.349826i	0.984584	−	0.174913i	$-0.0559645\pi$
$620$	6.00817	+	6.92870i	0.241294	+	0.278263i
$621$	7.01420	+	10.0137i	0.281470	+	0.401838i
$622$	−22.6423	−	10.3354i	−0.907875	−	0.414413i
$623$	−1.85928			−0.0744905
$624$	9.74044	+	14.6996i	0.389930	+	0.588455i
$625$	8.04907			0.321963
$626$	−9.50477	−	4.33859i	−0.379887	−	0.173405i
$627$	21.1757	+	23.7923i	0.845678	+	0.950174i
$628$	0.408267	+	0.470819i	0.0162916	+	0.0187877i
$629$		−	16.1710i		−	0.644779i
$630$	−0.640139	+	1.05719i	−0.0255038	+	0.0421195i
$631$		−	18.9935i		−	0.756119i	−0.925781	−	0.378059i	$-0.876592\pi$
$631$		−	18.9935i		−	0.756119i	0.925781	−	0.378059i	$-0.123408\pi$
$632$	32.0467	−	9.42878i	1.27475	−	0.375057i
$633$	4.35996	+	4.89869i	0.173293	+	0.194706i
$634$	−16.8839	+	36.9885i	−0.670547	+	1.46900i
$635$	7.95184			0.315559
$636$	0.942814	−	7.25908i	0.0373850	−	0.287841i
$637$	17.6412			0.698970
$638$	3.52014	−	7.71175i	0.139364	−	0.305311i
$639$	1.47488	−	12.6307i	0.0583455	−	0.499661i
$640$	1.80233	+	12.4231i	0.0712432	+	0.491065i
$641$		−	6.25712i		−	0.247141i	−0.992336	−	0.123571i	$-0.960565\pi$
$641$		−	6.25712i		−	0.247141i	0.992336	−	0.123571i	$-0.0394346\pi$
$642$	27.9632	−	8.62123i	1.10362	−	0.340253i
$643$		−	34.6109i		−	1.36492i	−0.730923	−	0.682460i	$-0.760910\pi$
$643$		−	34.6109i		−	1.36492i	0.730923	−	0.682460i	$-0.239090\pi$
$644$	−0.933404	+	0.809394i	−0.0367813	+	0.0318946i
$645$	−0.612895	+	0.545491i	−0.0241327	+	0.0214787i
$646$	15.2225	+	6.94851i	0.598919	+	0.273386i
$647$	−5.84844			−0.229926			−0.114963	−	0.993370i	$-0.536675\pi$
$647$	−5.84844			−0.229926			−0.114963	+	0.993370i	$0.536675\pi$
$648$	1.36526	+	25.4192i	0.0536324	+	0.998561i
$649$	−3.43970			−0.135020
$650$	−12.3412	−	5.63334i	−0.484063	−	0.220958i
$651$	−1.40380	+	1.24942i	−0.0550193	+	0.0489685i
$652$	−12.3604	+	10.7182i	−0.484069	+	0.419757i
$653$			37.8822i			1.48244i	0.671260	+	0.741222i	$0.265753\pi$
$653$			37.8822i			1.48244i	−0.671260	+	0.741222i	$0.734247\pi$
$654$	−6.68278	+	2.06034i	−0.261317	+	0.0805657i
$655$			20.9015i			0.816688i
$656$	0.628614	+	0.0899140i	0.0245433	+	0.00351055i
$657$	−5.25146	+	44.9726i	−0.204879	+	1.75455i
$658$	−1.00125	+	2.19350i	−0.0390329	+	0.0855114i
$659$	22.5539			0.878574			0.439287	−	0.898347i	$-0.355231\pi$
$659$	22.5539			0.878574			0.439287	+	0.898347i	$0.355231\pi$
$660$	1.25134	−	9.63450i	0.0487082	−	0.375022i
$661$	−3.76797			−0.146557			−0.0732786	−	0.997312i	$-0.523346\pi$
$661$	−3.76797			−0.146557			−0.0732786	+	0.997312i	$0.523346\pi$
$662$	−5.33251	+	11.6822i	−0.207254	+	0.454041i
$663$	−4.76687	−	5.35588i	−0.185130	−	0.208005i
$664$	−0.201940	−	0.686358i	−0.00783680	−	0.0266359i
$665$		−	2.11926i		−	0.0821812i
$666$	−21.8493	+	36.0841i	−0.846642	+	1.39823i
$667$			5.57973i			0.216048i
$668$	−16.4269	−	18.9437i	−0.635576	−	0.732954i
$669$	−3.87956	−	4.35894i	−0.149993	−	0.168526i
$670$	−1.42746	−	0.651585i	−0.0551476	−	0.0251729i
$671$	14.5359			0.561151
$672$	−2.54073	+	0.402173i	−0.0980110	+	0.0155142i
$673$	−36.4192			−1.40386			−0.701929	−	0.712247i	$-0.747678\pi$
$673$	−36.4192			−1.40386			−0.701929	+	0.712247i	$0.747678\pi$
$674$	25.8175	+	11.7848i	0.994454	+	0.453933i
$675$	−11.2355	−	16.0402i	−0.432454	−	0.617387i
$676$	−8.54531	−	9.85456i	−0.328666	−	0.379022i
$677$		−	21.9603i		−	0.844004i	−0.906595	−	0.422002i	$-0.861328\pi$
$677$		−	21.9603i		−	0.844004i	0.906595	−	0.422002i	$-0.138672\pi$
$678$	3.53223	+	11.4569i	0.135654	+	0.440000i
$679$			2.52191i			0.0967821i
$680$	−1.44067	−	4.89659i	−0.0552473	−	0.187776i
$681$	−25.3003	+	22.5179i	−0.969508	+	0.862886i
$682$	6.13453	−	13.4392i	0.234903	−	0.514615i
$683$	−13.2126			−0.505566			−0.252783	−	0.967523i	$-0.581346\pi$
$683$	−13.2126			−0.505566			−0.252783	+	0.967523i	$0.581346\pi$
$684$	−24.5792	−	36.0727i	−0.939807	−	1.37927i
$685$	−22.0354			−0.841930
$686$	−2.14786	+	4.70542i	−0.0820057	+	0.179654i
$687$	7.28027	−	6.47962i	0.277760	−	0.247213i
$688$	−1.69054	−	0.241808i	−0.0644514	−	0.00921883i
$689$		−	5.37838i		−	0.204900i
$690$	1.88403	+	6.11092i	0.0717239	+	0.232639i
$691$			37.0974i			1.41125i	0.708585	+	0.705626i	$0.249334\pi$
$691$			37.0974i			1.41125i	−0.708585	+	0.705626i	$0.750666\pi$
$692$	6.04932	−	5.24563i	0.229961	−	0.199409i
$693$	1.97743	+	0.230905i	0.0751165	+	0.00877135i
$694$	16.2874	+	7.43461i	0.618260	+	0.282214i
$695$	−17.7271			−0.672428
$696$	−6.14527	+	9.85927i	−0.232936	+	0.373715i
$697$	−0.258197			−0.00977991
$698$	−14.2660	−	6.51193i	−0.539976	−	0.246480i
$699$	31.6210	+	35.5283i	1.19602	+	1.34380i
$700$	1.49514	−	1.29650i	0.0565111	−	0.0490032i
$701$		−	17.0565i		−	0.644214i	−0.946703	−	0.322107i	$-0.895609\pi$
$701$		−	17.0565i		−	0.644214i	0.946703	−	0.322107i	$-0.104391\pi$
$702$	3.40029	+	18.3919i	0.128336	+	0.694157i
$703$		−	72.3346i		−	2.72815i
$704$	16.9995	−	10.9512i	0.640692	−	0.412737i
$705$	8.29748	+	9.32275i	0.312501	+	0.351115i
$706$	2.81746	−	6.17235i	0.106037	−	0.232300i
$707$	−0.0929301			−0.00349499
$708$	4.67471	+	0.607154i	0.175686	+	0.0228182i
$709$	37.6031			1.41222			0.706108	−	0.708104i	$-0.250449\pi$
$709$	37.6031			1.41222			0.706108	+	0.708104i	$0.250449\pi$
$710$	2.76196	−	6.05076i	0.103654	−	0.227081i
$711$	35.1923	+	4.10940i	1.31981	+	0.154115i
$712$	−19.2161	+	5.65374i	−0.720152	+	0.211883i
$713$			9.72377i			0.364158i
$714$	0.999505	−	0.308153i	0.0374055	−	0.0115323i
$715$		−	7.13837i		−	0.266960i
$716$	28.4698	+	32.8317i	1.06397	+	1.22698i
$717$	23.3758	−	20.8050i	0.872985	−	0.776978i
$718$	35.4423	+	16.1782i	1.32270	+	0.603764i
$719$	−28.7377			−1.07174			−0.535868	−	0.844301i	$-0.680016\pi$
$719$	−28.7377			−1.07174			−0.535868	+	0.844301i	$0.680016\pi$
$720$	−3.40124	+	12.8729i	−0.126757	+	0.479743i
$721$	0.132050			0.00491779
$722$	43.6478	+	19.9237i	1.62440	+	0.741483i
$723$	25.9623	−	23.1071i	0.965548	−	0.859361i
$724$	−19.1151	−	22.0438i	−0.710407	−	0.819251i
$725$		−	8.93772i		−	0.331938i
$726$	10.7928	−	3.32747i	0.400557	−	0.123494i
$727$			46.5471i			1.72634i	0.504918	+	0.863168i	$0.331523\pi$
$727$			46.5471i			1.72634i	−0.504918	+	0.863168i	$0.668477\pi$
$728$	−1.81319	+	0.533475i	−0.0672011	+	0.0197719i
$729$	−9.22604	+	25.3748i	−0.341705	+	0.939807i
$730$	−9.83421	+	21.5443i	−0.363980	+	0.797390i
$731$	0.694374			0.0256824
$732$	−19.7549	−	2.56578i	−0.730163	−	0.0948340i
$733$	3.78994			0.139985			0.0699923	−	0.997548i	$-0.477703\pi$
$733$	3.78994			0.139985			0.0699923	+	0.997548i	$0.477703\pi$
$734$	18.9762	−	41.5721i	0.700425	−	1.53446i
$735$	8.85572	+	9.94997i	0.326648	+	0.367010i
$736$	−7.18570	+	11.2036i	−0.264869	+	0.412969i
$737$			2.52769i			0.0931087i
$738$	0.576144	+	0.348860i	0.0212081	+	0.0128417i
$739$		−	18.1767i		−	0.668641i	−0.942460	−	0.334320i	$-0.891493\pi$
$739$		−	18.1767i		−	0.668641i	0.942460	−	0.334320i	$-0.108507\pi$
$740$	−16.6696	+	14.4549i	−0.612787	+	0.531373i
$741$	−21.3227	−	23.9575i	−0.783310	−	0.880099i
$742$	0.713736	+	0.325795i	0.0262021	+	0.0119603i
$743$	43.5376			1.59724			0.798619	−	0.601836i	$-0.205564\pi$
$743$	43.5376			1.59724			0.798619	+	0.601836i	$0.205564\pi$
$744$	−10.7093	+	17.1817i	−0.392623	+	0.629912i
$745$	−13.3300			−0.488374
$746$	6.64355	+	3.03255i	0.243238	+	0.111029i
$747$	0.0880127	−	0.753727i	0.00322022	−	0.0275774i
$748$	−6.21189	+	5.38660i	−0.227129	+	0.196953i
$749$			3.13636i			0.114600i
$750$	−7.02154	−	22.7746i	−0.256390	−	0.831610i
$751$			36.0638i			1.31599i	0.753024	+	0.657993i	$0.228595\pi$
$751$			36.0638i			1.31599i	−0.753024	+	0.657993i	$0.771405\pi$
$752$	−3.67814	+	25.7149i	−0.134128	+	0.937726i
$753$	0.530488	−	0.472147i	0.0193321	−	0.0172060i
$754$	−3.54457	+	7.76527i	−0.129086	+	0.282795i
$755$	6.82438			0.248365
$756$	−2.64667	−	0.662855i	−0.0962583	−	0.0241078i
$757$	27.7730			1.00943			0.504713	−	0.863287i	$-0.331598\pi$
$757$	27.7730			1.00943			0.504713	+	0.863287i	$0.331598\pi$
$758$	−8.27302	+	18.1241i	−0.300490	+	0.658297i
$759$	7.69483	−	6.84859i	0.279305	−	0.248588i
$760$	−6.44429	−	21.9030i	−0.233759	−	0.794504i
$761$		−	19.2103i		−	0.696373i	−0.937425	−	0.348186i	$-0.886798\pi$
$761$		−	19.2103i		−	0.696373i	0.937425	−	0.348186i	$-0.113202\pi$
$762$	5.17202	+	16.7756i	0.187362	+	0.607716i
$763$		−	0.749543i		−	0.0271353i
$764$	28.6190	+	33.0038i	1.03540	+	1.19404i
$765$	0.627897	−	5.37721i	0.0227016	−	0.194413i
$766$	9.30033	+	4.24527i	0.336034	+	0.153388i
$767$	3.46357			0.125062
$768$	−25.0361	+	11.8825i	−0.903413	+	0.428772i
$769$	−43.8641			−1.58178			−0.790890	−	0.611958i	$-0.790382\pi$
$769$	−43.8641			−1.58178			−0.790890	+	0.611958i	$0.790382\pi$
$770$	0.947295	+	0.432407i	0.0341382	+	0.0155829i
$771$	32.5481	+	36.5699i	1.17219	+	1.31703i
$772$	4.18097	+	4.82155i	0.150477	+	0.173532i
$773$		−	51.2239i		−	1.84240i	−0.389094	−	0.921198i	$-0.627212\pi$
$773$		−	51.2239i		−	1.84240i	0.389094	−	0.921198i	$-0.372788\pi$
$774$	−1.54944	−	0.938197i	−0.0556933	−	0.0337228i
$775$		−	15.5757i		−	0.559496i
$776$	7.66869	+	26.0645i	0.275290	+	0.935661i
$777$	−3.00594	−	3.37737i	−0.107838	−	0.121163i
$778$	9.03526	−	19.7940i	0.323930	−	0.709649i
$779$	−1.15494			−0.0413801
$780$	−1.26002	+	9.70137i	−0.0451160	+	0.347365i
$781$	−10.7144			−0.383393
$782$	2.24726	−	4.92319i	0.0803620	−	0.176053i
$783$	−10.0927	+	7.06951i	−0.360684	+	0.252644i
$784$	−3.92560	+	27.4450i	−0.140200	+	0.980177i
$785$			0.345725i			0.0123395i
$786$	−44.0948	+	13.5947i	−1.57281	+	0.484907i
$787$		−	16.5745i		−	0.590817i	−0.955371	−	0.295408i	$-0.904544\pi$
$787$		−	16.5745i		−	0.590817i	0.955371	−	0.295408i	$-0.0954557\pi$
$788$	7.41889	−	6.43324i	0.264287	−	0.229175i
$789$	14.2267	−	12.6621i	0.506482	−	0.450782i
$790$	16.8590	+	7.69552i	0.599815	+	0.273794i
$791$	−1.28501			−0.0456897
$792$	21.1393	−	3.62657i	0.751154	−	0.128865i
$793$	−14.6368			−0.519766
$794$	−39.0308	−	17.8162i	−1.38515	−	0.632273i
$795$	3.03351	−	2.69990i	0.107587	−	0.0957554i
$796$	−35.5525	+	30.8291i	−1.26013	+	1.09271i
$797$			36.8215i			1.30428i	0.758097	+	0.652142i	$0.226129\pi$
$797$			36.8215i			1.30428i	−0.758097	+	0.652142i	$0.773871\pi$
$798$	4.47089	−	1.37840i	0.158268	−	0.0487949i
$799$		−	10.5621i		−	0.373661i
$800$	11.5102	−	17.9461i	0.406947	−	0.634490i
$801$	−21.1022	−	2.46410i	−0.745609	−	0.0870648i
$802$	19.2813	−	42.2404i	0.680846	−	1.49156i
$803$	38.1498			1.34628
$804$	0.446172	−	3.43525i	0.0157353	−	0.121152i
$805$	−0.685403			−0.0241573
$806$	−6.17711	+	13.5325i	−0.217579	+	0.476662i
$807$	0.816491	+	0.917380i	0.0287418	+	0.0322933i
$808$	−0.960452	+	0.282584i	−0.0337886	+	0.00994127i
$809$		−	50.6456i		−	1.78061i	−0.455369	−	0.890303i	$-0.650493\pi$
$809$		−	50.6456i		−	1.78061i	0.455369	−	0.890303i	$-0.349507\pi$
$810$	−8.66646	+	11.1504i	−0.304508	+	0.391785i
$811$		−	17.0163i		−	0.597525i	−0.954328	−	0.298762i	$-0.903426\pi$
$811$		−	17.0163i		−	0.597525i	0.954328	−	0.298762i	$-0.0965738\pi$
$812$	−0.815776	−	0.940764i	−0.0286281	−	0.0330143i
$813$	9.79758	+	11.0082i	0.343616	+	0.386075i
$814$	32.3331	+	14.7589i	1.13328	+	0.517300i
$815$	−9.07627			−0.317928
$816$	9.39306	−	6.22415i	0.328823	−	0.217889i
$817$	3.10601			0.108666
$818$	15.9540	+	7.28244i	0.557818	+	0.254624i
$819$	−1.99116	−	0.232507i	−0.0695767	−	0.00812447i
$820$	0.230797	+	0.266158i	0.00805979	+	0.00929465i
$821$		−	7.62323i		−	0.266053i	−0.991113	−	0.133026i	$-0.957531\pi$
$821$		−	7.62323i		−	0.266053i	0.991113	−	0.133026i	$-0.0424695\pi$
$822$	−14.3322	−	46.4871i	−0.499894	−	1.62142i
$823$			29.3274i			1.02229i	0.859495	+	0.511144i	$0.170778\pi$
$823$			29.3274i			1.02229i	−0.859495	+	0.511144i	$0.829222\pi$
$824$	1.36476	−	0.401540i	0.0475438	−	0.0139883i
$825$	−12.3257	+	10.9702i	−0.429127	+	0.381933i
$826$	−0.209806	+	0.459632i	−0.00730009	+	0.0159927i
$827$	9.28781			0.322969			0.161484	−	0.986875i	$-0.448372\pi$
$827$	9.28781			0.322969			0.161484	+	0.986875i	$0.448372\pi$
$828$	−11.6665	+	7.94931i	−0.405439	+	0.276257i
$829$	21.2676			0.738653			0.369326	−	0.929300i	$-0.379588\pi$
$829$	21.2676			0.738653			0.369326	+	0.929300i	$0.379588\pi$
$830$	0.164818	−	0.361075i	0.00572092	−	0.0125331i
$831$	38.4887	−	34.2559i	1.33516	−	1.18832i
$832$	−17.1175	+	11.0272i	−0.593441	+	0.382298i
$833$		−	11.2727i		−	0.390577i
$834$	−11.5300	−	37.3980i	−0.399253	−	1.29499i
$835$		−	13.9105i		−	0.481391i
$836$	−27.7865	+	24.0948i	−0.961015	+	0.833337i
$837$	−17.5885	+	12.3200i	−0.607948	+	0.425841i
$838$	−27.8377	−	12.7069i	−0.961639	−	0.438954i
$839$	29.4475			1.01664			0.508320	−	0.861168i	$-0.330267\pi$
$839$	29.4475			1.01664			0.508320	+	0.861168i	$0.330267\pi$
$840$	−1.21109	−	0.754872i	−0.0417867	−	0.0260456i
$841$	23.3763			0.806078
$842$	29.1806	+	13.3199i	1.00563	+	0.459034i
$843$	−10.2731	−	11.5425i	−0.353823	−	0.397543i
$844$	−5.72107	+	4.96098i	−0.196927	+	0.170764i
$845$		−	7.23625i		−	0.248935i
$846$	−14.2709	+	23.5685i	−0.490645	+	0.810301i
$847$			1.21052i			0.0415940i
$848$	8.36731	+	1.19682i	0.287335	+	0.0410990i
$849$	5.87335	+	6.59909i	0.201573	+	0.226480i
$850$	−3.59971	+	7.88606i	−0.123469	+	0.270490i
$851$	−23.3942			−0.801943
$852$	14.5614	+	1.89125i	0.498866	+	0.0647931i
$853$	26.5368			0.908603			0.454301	−	0.890848i	$-0.349889\pi$
$853$	26.5368			0.908603			0.454301	+	0.890848i	$0.349889\pi$
$854$	0.886622	−	1.94237i	0.0303396	−	0.0664664i
$855$	2.80865	−	24.0528i	0.0960538	−	0.822590i
$856$	9.53713	+	32.4150i	0.325972	+	1.10792i
$857$			10.5691i			0.361035i	0.983572	+	0.180518i	$0.0577773\pi$
$857$			10.5691i			0.361035i	−0.983572	+	0.180518i	$0.942223\pi$
$858$	15.0595	−	4.64292i	0.514122	−	0.158507i
$859$		−	3.53190i		−	0.120507i	−0.998183	−	0.0602534i	$-0.980809\pi$
$859$		−	3.53190i		−	0.120507i	0.998183	−	0.0602534i	$-0.0191909\pi$
$860$	−0.620688	−	0.715785i	−0.0211653	−	0.0244081i
$861$	−0.0539254	+	0.0479950i	−0.00183777	+	0.00163566i
$862$	−28.9383	−	13.2093i	−0.985643	−	0.449911i
$863$	−26.7043			−0.909025			−0.454513	−	0.890740i	$-0.650187\pi$
$863$	−26.7043			−0.909025			−0.454513	+	0.890740i	$0.650187\pi$
$864$	−29.3695	+	1.19730i	−0.999170	+	0.0407329i
$865$	4.44205			0.151034
$866$	25.2841	+	11.5413i	0.859190	+	0.392190i
$867$	18.5725	−	16.5300i	0.630757	−	0.561389i
$868$	−1.42165	−	1.63946i	−0.0482539	−	0.0556470i
$869$		−	29.8532i		−	1.01270i
$870$	−6.15911	+	1.89889i	−0.208813	+	0.0643784i
$871$		−	2.54523i		−	0.0862420i
$872$	−2.27923	−	7.74669i	−0.0771844	−	0.262336i
$873$	−3.34229	+	28.6228i	−0.113119	+	0.968736i
$874$	10.0523	−	22.0220i	0.340023	−	0.744905i
$875$	2.55440			0.0863546
$876$	−51.8473	−	6.73396i	−1.75176	−	0.227519i
$877$	−39.2152			−1.32420			−0.662102	−	0.749413i	$-0.730336\pi$
$877$	−39.2152			−1.32420			−0.662102	+	0.749413i	$0.730336\pi$
$878$	12.9063	−	28.2744i	0.435565	−	0.954214i
$879$	−25.9721	−	29.1813i	−0.876017	−	0.984262i
$880$	11.1054	+	1.58846i	0.374362	+	0.0535470i
$881$		−	33.8690i		−	1.14108i	−0.821271	−	0.570538i	$-0.806735\pi$
$881$		−	33.8690i		−	1.14108i	0.821271	−	0.570538i	$-0.193265\pi$
$882$	−15.2311	+	25.1541i	−0.512857	+	0.846984i
$883$		−	40.6781i		−	1.36893i	−0.729047	−	0.684464i	$-0.760036\pi$
$883$		−	40.6781i		−	1.36893i	0.729047	−	0.684464i	$-0.239964\pi$
$884$	6.25501	−	5.42398i	0.210379	−	0.182428i
$885$	1.73868	+	1.95352i	0.0584451	+	0.0656669i
$886$	−2.54187	−	1.16027i	−0.0853957	−	0.0389801i
$887$	5.22124			0.175312			0.0876561	−	0.996151i	$-0.472062\pi$
$887$	5.22124			0.175312			0.0876561	+	0.996151i	$0.472062\pi$
$888$	−41.3371	−	25.7653i	−1.38718	−	0.864628i
$889$	−1.88156			−0.0631054
$890$	−10.1091	−	4.61443i	−0.338857	−	0.154676i
$891$	22.1372	+	5.24138i	0.741623	+	0.175593i
$892$	5.09070	−	4.41436i	0.170449	−	0.147804i
$893$		−	47.2456i		−	1.58101i
$894$	−8.67009	−	28.1217i	−0.289971	−	0.940530i
$895$			24.1085i			0.805858i
$896$	−0.426465	−	2.93954i	−0.0142472	−	0.0982032i
$897$	−7.74824	+	6.89612i	−0.258706	+	0.230255i
$898$	−4.02892	+	8.82636i	−0.134447	+	0.294540i
$899$	−9.80045			−0.326863
$900$	18.6876	−	12.7333i	0.622921	−	0.424445i
$901$	−3.43679			−0.114496
$902$	0.235651	−	0.516253i	0.00784633	−	0.0171893i
$903$	0.145023	−	0.129074i	0.00482606	−	0.00429531i
$904$	−13.2809	+	3.90749i	−0.441715	+	0.129961i
$905$		−	16.1869i		−	0.538069i
$906$	4.43870	+	14.3971i	0.147466	+	0.478310i
$907$		−	3.95274i		−	0.131249i	−0.997844	−	0.0656243i	$-0.979096\pi$
$907$		−	3.95274i		−	0.131249i	0.997844	−	0.0656243i	$-0.0209039\pi$
$908$	−25.6219	−	29.5476i	−0.850294	−	0.980570i
$909$	−1.05472	−	0.123160i	−0.0349830	−	0.00408497i
$910$	−0.953870	−	0.435408i	−0.0316205	−	0.0144336i
$911$	56.1163			1.85922			0.929609	−	0.368549i	$-0.120145\pi$
$911$	56.1163			1.85922			0.929609	+	0.368549i	$0.120145\pi$
$912$	42.0162	−	27.8413i	1.39129	−	0.921917i
$913$	−0.639378			−0.0211603
$914$	10.2005	+	4.65616i	0.337402	+	0.154012i
$915$	−7.34751	−	8.25541i	−0.242901	−	0.272915i
$916$	7.37283	+	8.50245i	0.243605	+	0.280929i
$917$		−	4.94569i		−	0.163321i
$918$	11.7524	−	2.17279i	0.387888	−	0.0717128i
$919$			32.2898i			1.06514i	0.846385	+	0.532572i	$0.178774\pi$
$919$			32.2898i			1.06514i	−0.846385	+	0.532572i	$0.821226\pi$
$920$	−7.08379	+	2.08419i	−0.233545	+	0.0687137i
$921$	−25.3529	−	28.4857i	−0.835408	−	0.938635i
$922$	−16.2646	+	35.6317i	−0.535647	+	1.17347i
$923$	10.7888			0.355118
$924$	−0.296090	+	2.27971i	−0.00974065	+	0.0749969i
$925$	37.4732			1.23211
$926$	−23.2910	+	51.0249i	−0.765391	+	1.67678i
$927$	1.49872	+	0.175006i	0.0492244	+	0.00574794i
$928$	−11.2919	−	7.24237i	−0.370676	−	0.237742i
$929$			41.5257i			1.36241i	0.732091	+	0.681207i	$0.238545\pi$
$929$			41.5257i			1.36241i	−0.732091	+	0.681207i	$0.761455\pi$
$930$	−10.7334	+	3.30918i	−0.351963	+	0.108512i
$931$		−	50.4242i		−	1.65259i
$932$	−41.4926	+	35.9800i	−1.35913	+	1.17856i
$933$	22.7708	−	20.2666i	0.745484	−	0.663499i
$934$	51.2137	+	23.3772i	1.67576	+	0.764927i
$935$	−4.56142			−0.149174
$936$	−21.2861	+	3.65174i	−0.695757	+	0.119361i
$937$	−17.7134			−0.578672			−0.289336	−	0.957228i	$-0.593435\pi$
$937$	−17.7134			−0.578672			−0.289336	+	0.957228i	$0.593435\pi$
$938$	0.337765	+	0.154178i	0.0110284	+	0.00503408i
$939$	9.55871	−	8.50748i	0.311937	−	0.277631i
$940$	−10.8878	+	9.44129i	−0.355121	+	0.307941i
$941$			19.9777i			0.651256i	0.945498	+	0.325628i	$0.105576\pi$
$941$			19.9777i			0.651256i	−0.945498	+	0.325628i	$0.894424\pi$
$942$	−0.729359	+	0.224866i	−0.0237638	+	0.00732652i
$943$			0.373528i			0.0121637i
$944$	−0.770729	+	5.38838i	−0.0250851	+	0.175377i
$945$	−0.868404	−	1.23977i	−0.0282492	−	0.0403296i
$946$	−0.633742	+	1.38837i	−0.0206047	+	0.0451398i
$947$	25.8875			0.841231			0.420616	−	0.907239i	$-0.361814\pi$
$947$	25.8875			0.841231			0.420616	+	0.907239i	$0.361814\pi$
$948$	−5.26950	+	40.5718i	−0.171145	+	1.31771i
$949$	−38.4145			−1.24699
$950$	−16.1019	+	35.2752i	−0.522414	+	1.14448i
$951$	−33.1075	−	37.1984i	−1.07358	−	1.20624i
$952$	0.340891	+	1.15863i	0.0110483	+	0.0375513i
$953$		−	29.5172i		−	0.956155i	−0.878318	−	0.478078i	$-0.841334\pi$
$953$		−	29.5172i		−	0.956155i	0.878318	−	0.478078i	$-0.158666\pi$
$954$	7.66889	+	4.64358i	0.248289	+	0.150342i
$955$			24.2349i			0.784221i
$956$	23.6730	+	27.3000i	0.765639	+	0.882945i
$957$	6.90260	+	7.75551i	0.223129	+	0.250700i
$958$	−8.70410	−	3.97312i	−0.281217	−	0.128366i
$959$	5.21401			0.168369
$960$	−14.8123	−	4.11904i	−0.478066	−	0.132942i
$961$	13.9208			0.449059
$962$	−32.5575	−	14.8614i	−1.04970	−	0.479150i
$963$	−4.15662	+	35.5967i	−0.133945	+	1.14709i
$964$	26.2924	+	30.3207i	0.846821	+	0.976565i
$965$			3.54049i			0.113972i
$966$	−0.445798	−	1.44596i	−0.0143433	−	0.0465230i
$967$		−	1.14166i		−	0.0367134i	−0.999832	−	0.0183567i	$-0.994157\pi$
$967$		−	1.14166i		−	0.0367134i	0.999832	−	0.0183567i	$-0.00584345\pi$
$968$	3.68098	+	12.5110i	0.118311	+	0.402118i
$969$	−15.3088	+	13.6252i	−0.491791	+	0.437706i
$970$	−6.25898	+	13.7119i	−0.200964	+	0.440261i
$971$	32.3916			1.03950			0.519748	−	0.854319i	$-0.326026\pi$
$971$	32.3916			1.03950			0.519748	+	0.854319i	$0.326026\pi$
$972$	−29.1603	−	11.0308i	−0.935316	−	0.353813i
$973$	4.19458			0.134472
$974$	19.5245	−	42.7733i	0.625605	−	1.37054i
$975$	12.4113	−	11.0463i	0.397479	−	0.353766i
$976$	3.25704	−	22.7708i	0.104255	−	0.728877i
$977$			32.2338i			1.03125i	0.856814	+	0.515625i	$0.172440\pi$
$977$			32.2338i			1.03125i	−0.856814	+	0.515625i	$0.827560\pi$
$978$	−5.90337	−	19.1478i	−0.188769	−	0.612278i
$979$			17.9007i			0.572110i
$980$	−11.6203	+	10.0765i	−0.371198	+	0.321881i
$981$	0.993369	−	8.50706i	0.0317158	−	0.271609i
$982$	−12.0531	−	5.50180i	−0.384629	−	0.175570i
$983$	−8.24942			−0.263116			−0.131558	−	0.991309i	$-0.541998\pi$
$983$	−8.24942			−0.263116			−0.131558	+	0.991309i	$0.541998\pi$
$984$	−0.411387	+	0.660016i	−0.0131145	+	0.0210405i
$985$	5.44773			0.173579
$986$	4.96202	+	2.26499i	0.158023	+	0.0721319i
$987$	−1.96334	−	2.20594i	−0.0624939	−	0.0702159i
$988$	27.9793	−	24.2621i	0.890141	−	0.771879i
$989$		−	1.00454i		−	0.0319424i
$990$	10.1784	+	6.16312i	0.323491	+	0.195877i
$991$		−	33.0301i		−	1.04924i	−0.851337	−	0.524619i	$-0.824208\pi$
$991$		−	33.0301i		−	1.04924i	0.851337	−	0.524619i	$-0.175792\pi$
$992$	−19.6784	−	12.6212i	−0.624789	−	0.400725i
$993$	−10.4564	−	11.7485i	−0.331825	−	0.372827i
$994$	−0.653533	+	1.43173i	−0.0207288	+	0.0454116i
$995$	−26.1064			−0.827628
$996$	0.868944	+	0.112859i	0.0275336	+	0.00357608i
$997$	−12.6422			−0.400383			−0.200192	−	0.979757i	$-0.564156\pi$
$997$	−12.6422			−0.400383			−0.200192	+	0.979757i	$0.564156\pi$
$998$	8.47098	−	18.5578i	0.268144	−	0.587437i
$999$	−29.6404	−	42.3158i	−0.937781	−	1.33881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.15	✓	128
3.2	odd	2	inner	804.2.c.b.671.114	yes	128
4.3	odd	2	inner	804.2.c.b.671.113	yes	128
12.11	even	2	inner	804.2.c.b.671.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.15	✓	128	1.1	even	1	trivial
804.2.c.b.671.16	yes	128	12.11	even	2	inner
804.2.c.b.671.113	yes	128	4.3	odd	2	inner
804.2.c.b.671.114	yes	128	3.2	odd	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28652 - 0.587251i) q^{2} +(1.29382 - 1.15153i) q^{3} +(1.31027 + 1.51102i) q^{4} +1.10955i q^{5} +(-2.34077 + 0.721672i) q^{6} -0.262541i q^{7} +(-0.798342 - 2.71342i) q^{8} +(0.347946 - 2.97975i) q^{9} +O(q^{10})\)	\(q+(-1.28652 - 0.587251i) q^{2} +(1.29382 - 1.15153i) q^{3} +(1.31027 + 1.51102i) q^{4} +1.10955i q^{5} +(-2.34077 + 0.721672i) q^{6} -0.262541i q^{7} +(-0.798342 - 2.71342i) q^{8} +(0.347946 - 2.97975i) q^{9} +(0.651585 - 1.42746i) q^{10} -2.52769 q^{11} +(3.43525 + 0.446172i) q^{12} +2.54523 q^{13} +(-0.154178 + 0.337765i) q^{14} +(1.27768 + 1.43556i) q^{15} +(-0.566377 + 3.95970i) q^{16} -1.62641i q^{17} +(-2.19750 + 3.62918i) q^{18} -7.27510i q^{19} +(-1.67656 + 1.45381i) q^{20} +(-0.302325 - 0.339681i) q^{21} +(3.25193 + 1.48439i) q^{22} -2.35289 q^{23} +(-4.15750 - 2.59136i) q^{24} +3.76890 q^{25} +(-3.27450 - 1.49469i) q^{26} +(-2.98110 - 4.25594i) q^{27} +(0.396706 - 0.344000i) q^{28} -2.37144i q^{29} +(-0.800732 - 2.59720i) q^{30} -4.13270i q^{31} +(3.05399 - 4.76163i) q^{32} +(-3.27038 + 2.91072i) q^{33} +(-0.955110 + 2.09241i) q^{34} +0.291303 q^{35} +(4.95838 - 3.37853i) q^{36} +9.94276 q^{37} +(-4.27231 + 9.35956i) q^{38} +(3.29308 - 2.93092i) q^{39} +(3.01068 - 0.885801i) q^{40} -0.158753i q^{41} +(0.189469 + 0.614548i) q^{42} +0.426938i q^{43} +(-3.31196 - 3.81940i) q^{44} +(3.30619 + 0.386064i) q^{45} +(3.02704 + 1.38174i) q^{46} +6.49415 q^{47} +(3.82693 + 5.77534i) q^{48} +6.93107 q^{49} +(-4.84876 - 2.21329i) q^{50} +(-1.87286 - 2.10428i) q^{51} +(3.33495 + 3.84590i) q^{52} -2.11312i q^{53} +(1.33595 + 7.22601i) q^{54} -2.80460i q^{55} +(-0.712385 + 0.209598i) q^{56} +(-8.37751 - 9.41267i) q^{57} +(-1.39263 + 3.05091i) q^{58} +1.36081 q^{59} +(-0.495051 + 3.81158i) q^{60} -5.75065 q^{61} +(-2.42693 + 5.31680i) q^{62} +(-0.782308 - 0.0913501i) q^{63} +(-6.72530 + 4.33247i) q^{64} +2.82407i q^{65} +(5.91673 - 1.82416i) q^{66} -1.00000i q^{67} +(2.45754 - 2.13103i) q^{68} +(-3.04421 + 2.70943i) q^{69} +(-0.374767 - 0.171068i) q^{70} +4.23883 q^{71} +(-8.36311 + 1.43474i) q^{72} -15.0927 q^{73} +(-12.7916 - 5.83890i) q^{74} +(4.87628 - 4.34001i) q^{75} +(10.9928 - 9.53235i) q^{76} +0.663623i q^{77} +(-5.95780 + 1.83682i) q^{78} +11.8105i q^{79} +(-4.39349 - 0.628424i) q^{80} +(-8.75787 - 2.07359i) q^{81} +(-0.0932279 + 0.204239i) q^{82} +0.252949 q^{83} +(0.117139 - 0.901894i) q^{84} +1.80458 q^{85} +(0.250720 - 0.549264i) q^{86} +(-2.73079 - 3.06822i) q^{87} +(2.01796 + 6.85869i) q^{88} -7.08186i q^{89} +(-4.02676 - 2.43824i) q^{90} -0.668229i q^{91} +(-3.08292 - 3.55526i) q^{92} +(-4.75893 - 5.34697i) q^{93} +(-8.35486 - 3.81370i) q^{94} +8.07209 q^{95} +(-1.53185 - 9.67747i) q^{96} -9.60577 q^{97} +(-8.91697 - 4.07028i) q^{98} +(-0.879500 + 7.53190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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