LMFDB - Embedded newform 961.2.c.k.439.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(439,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("961.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.5
Character	$\chi$	$=$	961.439
Dual form			961.2.c.k.521.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.24512 q^{2} +(-1.33932 + 2.31977i) q^{3} -0.449667 q^{4} +(-1.30938 - 2.26791i) q^{5} +(1.66762 - 2.88840i) q^{6} +(-0.602271 + 1.04316i) q^{7} +3.05014 q^{8} +(-2.08754 - 3.61573i) q^{9} +(1.63034 + 2.82383i) q^{10} +(2.19849 + 3.80789i) q^{11} +(0.602246 - 1.04312i) q^{12} +(0.609148 + 1.05508i) q^{13} +(0.749903 - 1.29887i) q^{14} +7.01469 q^{15} -2.89847 q^{16} +(-1.82937 + 3.16857i) q^{17} +(2.59925 + 4.50203i) q^{18} +(-3.21488 + 5.56834i) q^{19} +(0.588784 + 1.01980i) q^{20} +(-1.61327 - 2.79426i) q^{21} +(-2.73739 - 4.74130i) q^{22} +3.94405 q^{23} +(-4.08510 + 7.07561i) q^{24} +(-0.928943 + 1.60898i) q^{25} +(-0.758465 - 1.31370i) q^{26} +3.14762 q^{27} +(0.270821 - 0.469076i) q^{28} -1.34040 q^{29} -8.73416 q^{30} -2.49133 q^{32} -11.7779 q^{33} +(2.27780 - 3.94526i) q^{34} +3.15440 q^{35} +(0.938698 + 1.62587i) q^{36} +(-3.21787 + 5.57351i) q^{37} +(4.00293 - 6.93327i) q^{38} -3.26337 q^{39} +(-3.99378 - 6.91744i) q^{40} +(-1.04404 - 1.80833i) q^{41} +(2.00872 + 3.47920i) q^{42} +(4.70654 - 8.15196i) q^{43} +(-0.988587 - 1.71228i) q^{44} +(-5.46676 + 9.46871i) q^{45} -4.91083 q^{46} +0.754009 q^{47} +(3.88197 - 6.72376i) q^{48} +(2.77454 + 4.80564i) q^{49} +(1.15665 - 2.00337i) q^{50} +(-4.90022 - 8.48743i) q^{51} +(-0.273914 - 0.474432i) q^{52} +(2.35700 + 4.08245i) q^{53} -3.91918 q^{54} +(5.75731 - 9.97195i) q^{55} +(-1.83701 + 3.18180i) q^{56} +(-8.61150 - 14.9156i) q^{57} +1.66896 q^{58} +(-1.99565 + 3.45658i) q^{59} -3.15427 q^{60} -2.21839 q^{61} +5.02907 q^{63} +8.89894 q^{64} +(1.59521 - 2.76299i) q^{65} +14.6649 q^{66} +(-6.00489 - 10.4008i) q^{67} +(0.822608 - 1.42480i) q^{68} +(-5.28233 + 9.14927i) q^{69} -3.92762 q^{70} +(3.76141 + 6.51496i) q^{71} +(-6.36729 - 11.0285i) q^{72} +(-4.96210 - 8.59461i) q^{73} +(4.00664 - 6.93971i) q^{74} +(-2.48830 - 4.30986i) q^{75} +(1.44563 - 2.50390i) q^{76} -5.29635 q^{77} +4.06330 q^{78} +(4.73043 - 8.19334i) q^{79} +(3.79519 + 6.57346i) q^{80} +(2.04696 - 3.54544i) q^{81} +(1.29996 + 2.25159i) q^{82} +(-2.80472 - 4.85793i) q^{83} +(0.725432 + 1.25648i) q^{84} +9.58136 q^{85} +(-5.86022 + 10.1502i) q^{86} +(1.79522 - 3.10941i) q^{87} +(6.70570 + 11.6146i) q^{88} -13.9443 q^{89} +(6.80680 - 11.7897i) q^{90} -1.46749 q^{91} -1.77351 q^{92} -0.938835 q^{94} +16.8380 q^{95} +(3.33668 - 5.77930i) q^{96} -4.50970 q^{97} +(-3.45464 - 5.98362i) q^{98} +(9.17888 - 15.8983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 32 q^{4} - 8 q^{5} - 8 q^{7} + 24 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} - 32 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} - 12 q^{25} + 20 q^{28} + 48 q^{32} - 80 q^{33} + 112 q^{35} - 40 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) $ 24 * q + 32 * q^4 - 8 * q^5 - 8 * q^7 + 24 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 - 32 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 - 12 * q^25 + 20 * q^28 + 48 * q^32 - 80 * q^33 + 112 * q^35 - 40 * q^36 - 36 * q^38 - 32 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 + 96 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 + 8 * q^56 - 40 * q^59 - 16 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 24 * q^69 + 24 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 - 208 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 - 64 * q^87 + 44 * q^90 + 32 * q^94 + 80 * q^95 - 16 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.24512			−0.880435			−0.440218	−	0.897891i	$-0.645099\pi$
$2$	−1.24512			−0.880435			−0.440218	+	0.897891i	$0.645099\pi$
$3$	−1.33932	+	2.31977i	−0.773255	+	1.33932i	0.162515	+	0.986706i	$0.448040\pi$
$3$	−1.33932	+	2.31977i	−0.773255	+	1.33932i	−0.935770	+	0.352611i	$0.885294\pi$
$4$	−0.449667			−0.224833
$5$	−1.30938	−	2.26791i	−0.585572	−	1.01424i	−0.994804	−	0.101810i	$-0.967537\pi$
$5$	−1.30938	−	2.26791i	−0.585572	−	1.01424i	0.409232	−	0.912430i	$-0.365797\pi$
$6$	1.66762	−	2.88840i	0.680801	−	1.17918i
$7$	−0.602271	+	1.04316i	−0.227637	+	0.394279i	−0.957107	−	0.289733i	$-0.906433\pi$
$7$	−0.602271	+	1.04316i	−0.227637	+	0.394279i	0.729470	+	0.684013i	$0.239767\pi$
$8$	3.05014			1.07839
$9$	−2.08754	−	3.61573i	−0.695847	−	1.20524i
$10$	1.63034	+	2.82383i	0.515558	+	0.892973i
$11$	2.19849	+	3.80789i	0.662869	+	1.14812i	0.979858	+	0.199694i	$0.0639949\pi$
$11$	2.19849	+	3.80789i	0.662869	+	1.14812i	−0.316989	+	0.948429i	$0.602672\pi$
$12$	0.602246	−	1.04312i	0.173854	−	0.301123i
$13$	0.609148	+	1.05508i	0.168947	+	0.292625i	0.938050	−	0.346500i	$-0.112630\pi$
$13$	0.609148	+	1.05508i	0.168947	+	0.292625i	−0.769103	+	0.639125i	$0.779297\pi$
$14$	0.749903	−	1.29887i	0.200420	−	0.347137i
$15$	7.01469			1.81119
$16$	−2.89847			−0.724617
$17$	−1.82937	+	3.16857i	−0.443688	+	0.768490i	−0.997960	−	0.0638454i	$-0.979664\pi$
$17$	−1.82937	+	3.16857i	−0.443688	+	0.768490i	0.554272	+	0.832336i	$0.312997\pi$
$18$	2.59925	+	4.50203i	0.612649	+	1.06114i
$19$	−3.21488	+	5.56834i	−0.737545	+	1.27746i	0.216053	+	0.976382i	$0.430682\pi$
$19$	−3.21488	+	5.56834i	−0.737545	+	1.27746i	−0.953598	+	0.301083i	$0.902652\pi$
$20$	0.588784	+	1.01980i	0.131656	+	0.228035i
$21$	−1.61327	−	2.79426i	−0.352043	−	0.609757i
$22$	−2.73739	−	4.74130i	−0.583614	−	1.01085i
$23$	3.94405			0.822391			0.411195	−	0.911547i	$-0.365111\pi$
$23$	3.94405			0.822391			0.411195	+	0.911547i	$0.365111\pi$
$24$	−4.08510	+	7.07561i	−0.833868	+	1.44430i
$25$	−0.928943	+	1.60898i	−0.185789	+	0.321795i
$26$	−0.758465	−	1.31370i	−0.148747	−	0.257638i
$27$	3.14762			0.605760
$28$	0.270821	−	0.469076i	0.0511804	−	0.0886471i
$29$	−1.34040			−0.248906			−0.124453	−	0.992226i	$-0.539718\pi$
$29$	−1.34040			−0.248906			−0.124453	+	0.992226i	$0.539718\pi$
$30$	−8.73416			−1.59463
$31$		0			0
$31$		0			0
$32$	−2.49133			−0.440409
$33$	−11.7779			−2.05027
$34$	2.27780	−	3.94526i	0.390639	−	0.676606i
$35$	3.15440			0.533192
$36$	0.938698	+	1.62587i	0.156450	+	0.270979i
$37$	−3.21787	+	5.57351i	−0.529014	+	0.916280i	0.470413	+	0.882446i	$0.344105\pi$
$37$	−3.21787	+	5.57351i	−0.529014	+	0.916280i	−0.999427	+	0.0338334i	$0.989228\pi$
$38$	4.00293	−	6.93327i	0.649361	−	1.12473i
$39$	−3.26337			−0.522558
$40$	−3.99378	−	6.91744i	−0.631473	−	1.09374i
$41$	−1.04404	−	1.80833i	−0.163051	−	0.282413i	0.772910	−	0.634515i	$-0.218800\pi$
$41$	−1.04404	−	1.80833i	−0.163051	−	0.282413i	−0.935962	+	0.352102i	$0.885467\pi$
$42$	2.00872	+	3.47920i	0.309951	+	0.536852i
$43$	4.70654	−	8.15196i	0.717740	−	1.24316i	−0.244153	−	0.969737i	$-0.578510\pi$
$43$	4.70654	−	8.15196i	0.717740	−	1.24316i	0.961893	−	0.273426i	$-0.0881568\pi$
$44$	−0.988587	−	1.71228i	−0.149035	−	0.258136i
$45$	−5.46676	+	9.46871i	−0.814937	+	1.41151i
$46$	−4.91083			−0.724062
$47$	0.754009			0.109984			0.0549918	−	0.998487i	$-0.482487\pi$
$47$	0.754009			0.109984			0.0549918	+	0.998487i	$0.482487\pi$
$48$	3.88197	−	6.72376i	0.560314	−	0.970492i
$49$	2.77454	+	4.80564i	0.396363	+	0.686520i
$50$	1.15665	−	2.00337i	0.163575	−	0.283320i
$51$	−4.90022	−	8.48743i	−0.686168	−	1.18848i
$52$	−0.273914	−	0.474432i	−0.0379850	−	0.0657919i
$53$	2.35700	+	4.08245i	0.323759	+	0.560767i	0.981260	−	0.192686i	$-0.0617199\pi$
$53$	2.35700	+	4.08245i	0.323759	+	0.560767i	−0.657501	+	0.753453i	$0.728387\pi$
$54$	−3.91918			−0.533333
$55$	5.75731	−	9.97195i	0.776315	−	1.34462i
$56$	−1.83701	+	3.18180i	−0.245481	+	0.425185i
$57$	−8.61150	−	14.9156i	−1.14062	−	1.97561i
$58$	1.66896			0.219145
$59$	−1.99565	+	3.45658i	−0.259812	+	0.450008i	−0.966191	−	0.257826i	$-0.916994\pi$
$59$	−1.99565	+	3.45658i	−0.259812	+	0.450008i	0.706379	+	0.707833i	$0.250327\pi$
$60$	−3.15427			−0.407215
$61$	−2.21839			−0.284036			−0.142018	−	0.989864i	$-0.545359\pi$
$61$	−2.21839			−0.284036			−0.142018	+	0.989864i	$0.545359\pi$
$62$		0			0
$63$	5.02907			0.633603
$64$	8.89894			1.11237
$65$	1.59521	−	2.76299i	0.197862	−	0.342706i
$66$	14.6649			1.80513
$67$	−6.00489	−	10.4008i	−0.733614	−	1.27066i	−0.955329	−	0.295545i	$-0.904499\pi$
$67$	−6.00489	−	10.4008i	−0.733614	−	1.27066i	0.221715	−	0.975112i	$-0.428835\pi$
$68$	0.822608	−	1.42480i	0.0997559	−	0.172782i
$69$	−5.28233	+	9.14927i	−0.635918	+	1.10144i
$70$	−3.92762			−0.469441
$71$	3.76141	+	6.51496i	0.446398	+	0.773183i	0.998148	−	0.0608256i	$-0.0193733\pi$
$71$	3.76141	+	6.51496i	0.446398	+	0.773183i	−0.551751	+	0.834009i	$0.686040\pi$
$72$	−6.36729	−	11.0285i	−0.750393	−	1.29972i
$73$	−4.96210	−	8.59461i	−0.580770	−	1.00592i	−0.995388	−	0.0959274i	$-0.969418\pi$
$73$	−4.96210	−	8.59461i	−0.580770	−	1.00592i	0.414619	−	0.909995i	$-0.363915\pi$
$74$	4.00664	−	6.93971i	0.465763	−	0.806725i
$75$	−2.48830	−	4.30986i	−0.287324	−	0.497660i
$76$	1.44563	−	2.50390i	0.165825	−	0.287217i
$77$	−5.29635			−0.603575
$78$	4.06330			0.460078
$79$	4.73043	−	8.19334i	0.532215	−	0.921823i	−0.467078	−	0.884216i	$-0.654693\pi$
$79$	4.73043	−	8.19334i	0.532215	−	0.921823i	0.999293	−	0.0376067i	$-0.0119734\pi$
$80$	3.79519	+	6.57346i	0.424315	+	0.734935i
$81$	2.04696	−	3.54544i	0.227440	−	0.393938i
$82$	1.29996	+	2.25159i	0.143556	+	0.248646i
$83$	−2.80472	−	4.85793i	−0.307859	−	0.533227i	0.670035	−	0.742329i	$-0.266279\pi$
$83$	−2.80472	−	4.85793i	−0.307859	−	0.533227i	−0.977894	+	0.209103i	$0.932946\pi$
$84$	0.725432	+	1.25648i	0.0791511	+	0.137094i
$85$	9.58136			1.03924
$86$	−5.86022	+	10.1502i	−0.631924	+	1.09452i
$87$	1.79522	−	3.10941i	0.192468	−	0.333364i
$88$	6.70570	+	11.6146i	0.714830	+	1.23812i
$89$	−13.9443			−1.47809			−0.739046	−	0.673655i	$-0.764723\pi$
$89$	−13.9443			−1.47809			−0.739046	+	0.673655i	$0.764723\pi$
$90$	6.80680	−	11.7897i	0.717500	−	1.24275i
$91$	−1.46749			−0.153835
$92$	−1.77351			−0.184901
$93$		0			0
$94$	−0.938835			−0.0968334
$95$	16.8380			1.72754
$96$	3.33668	−	5.77930i	0.340548	−	0.589847i
$97$	−4.50970			−0.457891			−0.228945	−	0.973439i	$-0.573528\pi$
$97$	−4.50970			−0.457891			−0.228945	+	0.973439i	$0.573528\pi$
$98$	−3.45464	−	5.98362i	−0.348972	−	0.604437i
$99$	9.17888	−	15.8983i	0.922512	−	1.59784i
$100$	0.417715	−	0.723503i	0.0417715	−	0.0723503i
$101$	1.88887			0.187950			0.0939749	−	0.995575i	$-0.470043\pi$
$101$	1.88887			0.187950			0.0939749	+	0.995575i	$0.470043\pi$
$102$	6.10138	+	10.5679i	0.604127	+	1.04638i
$103$	−5.64548	−	9.77825i	−0.556265	−	0.963480i	−0.997804	−	0.0662374i	$-0.978901\pi$
$103$	−5.64548	−	9.77825i	−0.556265	−	0.963480i	0.441539	−	0.897242i	$-0.354433\pi$
$104$	1.85799	+	3.21813i	0.182191	+	0.315563i
$105$	−4.22475	+	7.31748i	−0.412293	+	0.714113i
$106$	−2.93476	−	5.08315i	−0.285049	−	0.493719i
$107$	−2.42114	+	4.19354i	−0.234061	+	0.405405i	−0.958999	−	0.283409i	$-0.908535\pi$
$107$	−2.42114	+	4.19354i	−0.234061	+	0.405405i	0.724939	+	0.688813i	$0.241868\pi$
$108$	−1.41538			−0.136195
$109$	−12.7361			−1.21989			−0.609947	−	0.792442i	$-0.708809\pi$
$109$	−12.7361			−1.21989			−0.609947	+	0.792442i	$0.708809\pi$
$110$	−7.16856	+	12.4163i	−0.683495	+	1.18385i
$111$	−8.61949	−	14.9294i	−0.818126	−	1.41704i
$112$	1.74566	−	3.02358i	0.164950	−	0.285701i
$113$	−4.47100	−	7.74401i	−0.420597	−	0.728495i	0.575401	−	0.817871i	$-0.304846\pi$
$113$	−4.47100	−	7.74401i	−0.420597	−	0.728495i	−0.995998	+	0.0893765i	$0.971513\pi$
$114$	10.7224	+	18.5717i	1.00424	+	1.73940i
$115$	−5.16425	−	8.94475i	−0.481569	−	0.834102i
$116$	0.602732			0.0559623
$117$	2.54325	−	4.40503i	0.235123	−	0.407245i
$118$	2.48484	−	4.30386i	0.228748	−	0.396203i
$119$	−2.20356	−	3.81667i	−0.202000	−	0.349874i
$120$	21.3958			1.95316
$121$	−4.16671	+	7.21695i	−0.378792	+	0.656086i
$122$	2.76217			0.250075
$123$	5.59319			0.504321
$124$		0			0
$125$	−8.22843			−0.735973
$126$	−6.26181			−0.557847
$127$	−2.54914	+	4.41524i	−0.226199	+	0.391789i	−0.956679	−	0.291146i	$-0.905963\pi$
$127$	−2.54914	+	4.41524i	−0.226199	+	0.391789i	0.730479	+	0.682935i	$0.239297\pi$
$128$	−6.09763			−0.538960
$129$	12.6071	+	21.8361i	1.10999	+	1.92256i
$130$	−1.98624	+	3.44026i	−0.174204	+	0.301731i
$131$	−1.38724	+	2.40277i	−0.121204	+	0.209931i	−0.920243	−	0.391348i	$-0.872009\pi$
$131$	−1.38724	+	2.40277i	−0.121204	+	0.209931i	0.799039	+	0.601279i	$0.205342\pi$
$132$	5.29613			0.460969
$133$	−3.87246	−	6.70731i	−0.335785	−	0.581597i
$134$	7.47683	+	12.9502i	0.645900	+	1.11873i
$135$	−4.12143	−	7.13852i	−0.354716	−	0.614386i
$136$	−5.57984	+	9.66457i	−0.478467	+	0.828730i
$137$	5.17079	+	8.95607i	0.441770	+	0.765168i	0.997821	−	0.0659800i	$-0.0210173\pi$
$137$	5.17079	+	8.95607i	0.441770	+	0.765168i	−0.556051	+	0.831148i	$0.687684\pi$
$138$	6.57716	−	11.3920i	0.559885	−	0.969749i
$139$	−0.320787			−0.0272088			−0.0136044	−	0.999907i	$-0.504331\pi$
$139$	−0.320787			−0.0272088			−0.0136044	+	0.999907i	$0.504331\pi$
$140$	−1.41843			−0.119879
$141$	−1.00986	+	1.74912i	−0.0850454	+	0.147303i
$142$	−4.68343	−	8.11193i	−0.393024	−	0.680738i
$143$	−2.67841	+	4.63915i	−0.223980	+	0.387945i
$144$	6.05067	+	10.4801i	0.504223	+	0.873339i
$145$	1.75509	+	3.03990i	0.145752	+	0.252450i
$146$	6.17843	+	10.7014i	0.511330	+	0.885650i
$147$	−14.8639			−1.22596
$148$	1.44697	−	2.50622i	0.118940	−	0.206010i
$149$	−10.9051	+	18.8882i	−0.893382	+	1.54738i	−0.0575872	+	0.998340i	$0.518341\pi$
$149$	−10.9051	+	18.8882i	−0.893382	+	1.54738i	−0.835795	+	0.549042i	$0.814993\pi$
$150$	3.09824	+	5.36631i	0.252970	+	0.438157i
$151$	−3.57548			−0.290968			−0.145484	−	0.989361i	$-0.546474\pi$
$151$	−3.57548			−0.290968			−0.145484	+	0.989361i	$0.546474\pi$
$152$	−9.80584	+	16.9842i	−0.795358	+	1.37760i
$153$	15.2756			1.23496
$154$	6.59461			0.531409
$155$		0			0
$156$	1.46743			0.117488
$157$	−18.1350			−1.44733			−0.723665	−	0.690152i	$-0.757544\pi$
$157$	−18.1350			−1.44733			−0.723665	+	0.690152i	$0.757544\pi$
$158$	−5.88997	+	10.2017i	−0.468581	+	0.811606i
$159$	−12.6271			−1.00139
$160$	3.26209	+	5.65010i	0.257891	+	0.446680i
$161$	−2.37539	+	4.11429i	−0.187207	+	0.324252i
$162$	−2.54872	+	4.41451i	−0.200246	+	0.346837i
$163$	−7.86179			−0.615783			−0.307891	−	0.951422i	$-0.599623\pi$
$163$	−7.86179			−0.615783			−0.307891	+	0.951422i	$0.599623\pi$
$164$	0.469469	+	0.813144i	0.0366594	+	0.0634959i
$165$	15.4217	+	26.7112i	1.20058	+	2.07946i
$166$	3.49223	+	6.04872i	0.271050	+	0.469472i
$167$	−9.88676	+	17.1244i	−0.765061	+	1.32512i	0.175154	+	0.984541i	$0.443958\pi$
$167$	−9.88676	+	17.1244i	−0.765061	+	1.32512i	−0.940214	+	0.340583i	$0.889376\pi$
$168$	−4.92068	−	8.52287i	−0.379639	−	0.657554i
$169$	5.75788	−	9.97294i	0.442914	−	0.767149i
$170$	−11.9300			−0.914988
$171$	26.8448			2.05287
$172$	−2.11637	+	3.66567i	−0.161372	+	0.279504i
$173$	−8.07316	−	13.9831i	−0.613791	−	1.06312i	−0.990595	−	0.136824i	$-0.956310\pi$
$173$	−8.07316	−	13.9831i	−0.613791	−	1.06312i	0.376804	−	0.926293i	$-0.377023\pi$
$174$	−2.23527	+	3.87160i	−0.169455	+	0.293505i
$175$	−1.11895	−	1.93808i	−0.0845848	−	0.146505i
$176$	−6.37225	−	11.0371i	−0.480326	−	0.831949i
$177$	−5.34563	−	9.25890i	−0.401802	−	0.695942i
$178$	17.3624			1.30136
$179$	1.97997	−	3.42941i	0.147990	−	0.256326i	−0.782494	−	0.622658i	$-0.786053\pi$
$179$	1.97997	−	3.42941i	0.147990	−	0.256326i	0.930484	+	0.366331i	$0.119386\pi$
$180$	2.45822	−	4.25777i	0.183225	−	0.317355i
$181$	10.2011	+	17.6688i	0.758239	+	1.31331i	0.943748	+	0.330667i	$0.107274\pi$
$181$	10.2011	+	17.6688i	0.758239	+	1.31331i	−0.185508	+	0.982643i	$0.559393\pi$
$182$	1.82721			0.135442
$183$	2.97113	−	5.14615i	0.219632	−	0.380414i
$184$	12.0299			0.886856
$185$	16.8536			1.23910
$186$		0			0
$187$	−16.0874			−1.17643
$188$	−0.339053			−0.0247280
$189$	−1.89572	+	3.28349i	−0.137894	+	0.238839i
$190$	−20.9654			−1.52099
$191$	−9.50926	−	16.4705i	−0.688066	−	1.19176i	−0.972463	−	0.233058i	$-0.925127\pi$
$191$	−9.50926	−	16.4705i	−0.688066	−	1.19176i	0.284397	−	0.958707i	$-0.408207\pi$
$192$	−11.9185	+	20.6435i	−0.860144	+	1.48981i
$193$	10.5687	−	18.3056i	0.760754	−	1.31766i	−0.181708	−	0.983353i	$-0.558163\pi$
$193$	10.5687	−	18.3056i	0.760754	−	1.31766i	0.942462	−	0.334312i	$-0.108504\pi$
$194$	5.61514			0.403143
$195$	4.27299	+	7.40103i	0.305995	+	0.529999i
$196$	−1.24762	−	2.16094i	−0.0891155	−	0.154353i
$197$	−3.19082	−	5.52665i	−0.227336	−	0.393758i	0.729682	−	0.683787i	$-0.239668\pi$
$197$	−3.19082	−	5.52665i	−0.227336	−	0.393758i	−0.957018	+	0.290029i	$0.906335\pi$
$198$	−11.4288	+	19.7953i	−0.812212	+	1.40679i
$199$	7.73041	+	13.3895i	0.547994	+	0.949154i	0.998412	+	0.0563360i	$0.0179418\pi$
$199$	7.73041	+	13.3895i	0.547994	+	0.949154i	−0.450418	+	0.892818i	$0.648725\pi$
$200$	−2.83340	+	4.90760i	−0.200352	+	0.347020i
$201$	32.1698			2.26908
$202$	−2.35188			−0.165478
$203$	0.807283	−	1.39826i	0.0566602	−	0.0981383i
$204$	2.20347	+	3.81652i	0.154274	+	0.267210i
$205$	−2.73408	+	4.73556i	−0.190956	+	0.330746i
$206$	7.02932	+	12.1751i	0.489756	+	0.848282i
$207$	−8.23337	−	14.2606i	−0.572259	−	0.991181i
$208$	−1.76560	−	3.05810i	−0.122422	−	0.212041i
$209$	−28.2715			−1.95558
$210$	5.26034	−	9.11117i	0.362998	−	0.628730i
$211$	13.3454	−	23.1150i	0.918738	−	1.59130i	0.117402	−	0.993084i	$-0.462543\pi$
$211$	13.3454	−	23.1150i	0.918738	−	1.59130i	0.801335	−	0.598216i	$-0.204123\pi$
$212$	−1.05987	−	1.83574i	−0.0727918	−	0.126079i
$213$	−20.1509			−1.38072
$214$	3.01462	−	5.22148i	0.206075	−	0.356933i
$215$	−24.6505			−1.68115
$216$	9.60068			0.653244
$217$		0			0
$218$	15.8580			1.07404
$219$	26.5833			1.79633
$220$	−2.58887	+	4.48405i	−0.174542	+	0.302315i
$221$	−4.45744			−0.299840
$222$	10.7323	+	18.5890i	0.720307	+	1.24761i
$223$	6.33493	−	10.9724i	0.424218	−	0.734768i	−0.572129	−	0.820164i	$-0.693882\pi$
$223$	6.33493	−	10.9724i	0.424218	−	0.734768i	0.996347	+	0.0853960i	$0.0272155\pi$
$224$	1.50046	−	2.59886i	0.100253	−	0.173644i
$225$	7.75683			0.517122
$226$	5.56695	+	9.64225i	0.370308	+	0.641393i
$227$	5.78852	+	10.0260i	0.384198	+	0.665450i	0.991658	−	0.128900i	$-0.0411448\pi$
$227$	5.78852	+	10.0260i	0.384198	+	0.665450i	−0.607460	+	0.794350i	$0.707811\pi$
$228$	3.87230	+	6.70703i	0.256450	+	0.444184i
$229$	14.3657	−	24.8820i	0.949309	−	1.64425i	0.202424	−	0.979298i	$-0.435118\pi$
$229$	14.3657	−	24.8820i	0.949309	−	1.64425i	0.746885	−	0.664953i	$-0.231549\pi$
$230$	6.43013	+	11.1373i	0.423990	+	0.734373i
$231$	7.09349	−	12.2863i	0.466718	−	0.808378i
$232$	−4.08840			−0.268416
$233$	11.4456			0.749826			0.374913	−	0.927060i	$-0.377672\pi$
$233$	11.4456			0.749826			0.374913	+	0.927060i	$0.377672\pi$
$234$	−3.16666	+	5.48481i	−0.207011	+	0.358553i
$235$	−0.987283	−	1.71002i	−0.0644033	−	0.111550i
$236$	0.897380	−	1.55431i	0.0584144	−	0.101177i
$237$	12.6711	+	21.9470i	0.823076	+	1.42561i
$238$	2.74370	+	4.75223i	0.177848	+	0.308041i
$239$	12.6075	+	21.8368i	0.815511	+	1.41251i	0.908960	+	0.416883i	$0.136878\pi$
$239$	12.6075	+	21.8368i	0.815511	+	1.41251i	−0.0934489	+	0.995624i	$0.529789\pi$
$240$	−20.3318			−1.31242
$241$	−5.18886	+	8.98737i	−0.334244	+	0.578927i	−0.983339	−	0.181780i	$-0.941814\pi$
$241$	−5.18886	+	8.98737i	−0.334244	+	0.578927i	0.649095	+	0.760707i	$0.275148\pi$
$242$	5.18807	−	8.98600i	0.333502	−	0.577642i
$243$	10.2045	+	17.6747i	0.654619	+	1.13383i
$244$	0.997536			0.0638607
$245$	7.26584	−	12.5848i	0.464197	−	0.804014i
$246$	−6.96421			−0.444022
$247$	−7.83336			−0.498425
$248$		0			0
$249$	15.0257			0.952213
$250$	10.2454			0.647977
$251$	−0.738530	+	1.27917i	−0.0466156	+	0.0807406i	−0.888392	−	0.459086i	$-0.848177\pi$
$251$	−0.738530	+	1.27917i	−0.0466156	+	0.0807406i	0.841776	+	0.539827i	$0.181510\pi$
$252$	−2.26140			−0.142455
$253$	8.67095	+	15.0185i	0.545138	+	0.944206i
$254$	3.17399	−	5.49752i	0.199154	−	0.344945i
$255$	−12.8325	+	22.2265i	−0.803602	+	1.39188i
$256$	−10.2056			−0.637849
$257$	−8.43218	−	14.6050i	−0.525985	−	0.911032i	−0.999542	−	0.0302693i	$-0.990364\pi$
$257$	−8.43218	−	14.6050i	−0.525985	−	0.911032i	0.473557	−	0.880763i	$-0.342970\pi$
$258$	−15.6974	−	27.1887i	−0.977277	−	1.69269i
$259$	−3.87606	−	6.71353i	−0.240847	−	0.417159i
$260$	−0.717313	+	1.24242i	−0.0444859	+	0.0770518i
$261$	2.79814	+	4.84651i	0.173200	+	0.299992i
$262$	1.72728	−	2.99174i	0.106712	−	0.184830i
$263$	−23.4826			−1.44800			−0.723998	−	0.689802i	$-0.757698\pi$
$263$	−23.4826			−1.44800			−0.723998	+	0.689802i	$0.757698\pi$
$264$	−35.9242			−2.21098
$265$	6.17241	−	10.6909i	0.379168	−	0.656739i
$266$	4.82170	+	8.35143i	0.295637	+	0.512059i
$267$	18.6758	−	32.3475i	1.14294	−	1.97963i
$268$	2.70020	+	4.67688i	0.164941	+	0.285686i
$269$	6.56148	+	11.3648i	0.400061	+	0.692925i	0.993733	−	0.111782i	$-0.0356557\pi$
$269$	6.56148	+	11.3648i	0.400061	+	0.692925i	−0.593672	+	0.804707i	$0.702322\pi$
$270$	5.13169	+	8.88834i	0.312305	+	0.540927i
$271$	11.2629			0.684171			0.342086	−	0.939669i	$-0.388867\pi$
$271$	11.2629			0.684171			0.342086	+	0.939669i	$0.388867\pi$
$272$	5.30238	−	9.18398i	0.321504	−	0.556861i
$273$	1.96544	−	3.40423i	0.118954	−	0.206034i
$274$	−6.43827	−	11.1514i	−0.388950	−	0.673681i
$275$	−8.16908			−0.492614
$276$	2.37529	−	4.11412i	0.142976	−	0.247641i
$277$	−2.23182			−0.134097			−0.0670486	−	0.997750i	$-0.521358\pi$
$277$	−2.23182			−0.134097			−0.0670486	+	0.997750i	$0.521358\pi$
$278$	0.399420			0.0239556
$279$		0			0
$280$	9.62137			0.574987
$281$	−5.33651			−0.318349			−0.159175	−	0.987250i	$-0.550883\pi$
$281$	−5.33651			−0.318349			−0.159175	+	0.987250i	$0.550883\pi$
$282$	1.25740	−	2.17788i	0.0748769	−	0.129691i
$283$	11.8335			0.703429			0.351714	−	0.936107i	$-0.385599\pi$
$283$	11.8335			0.703429			0.351714	+	0.936107i	$0.385599\pi$
$284$	−1.69138	−	2.92956i	−0.100365	−	0.173837i
$285$	−22.5514	+	39.0602i	−1.33583	+	2.31373i
$286$	3.33495	−	5.77631i	0.197200	−	0.341560i
$287$	2.51518			0.148466
$288$	5.20075	+	9.00796i	0.306457	+	0.530799i
$289$	1.80679	+	3.12945i	0.106282	+	0.184085i
$290$	−2.18530	−	3.78505i	−0.128325	−	0.222266i
$291$	6.03992	−	10.4615i	0.354066	−	0.613261i
$292$	2.23129	+	3.86471i	0.130576	+	0.226165i
$293$	−13.3680	+	23.1540i	−0.780966	+	1.35267i	0.150413	+	0.988623i	$0.451940\pi$
$293$	−13.3680	+	23.1540i	−0.780966	+	1.35267i	−0.931379	+	0.364050i	$0.881394\pi$
$294$	18.5075			1.07938
$295$	10.4523			0.608555
$296$	−9.81494	+	17.0000i	−0.570482	+	0.988104i
$297$	6.92001	+	11.9858i	0.401540	+	0.695488i
$298$	13.5782	−	23.5182i	0.786565	−	1.36237i
$299$	2.40251	+	4.16127i	0.138941	+	0.240652i
$300$	1.11890	+	1.93800i	0.0646000	+	0.111890i
$301$	5.66923	+	9.81939i	0.326769	+	0.565980i
$302$	4.45192			0.256179
$303$	−2.52980	+	4.38174i	−0.145333	+	0.251724i
$304$	9.31823	−	16.1396i	0.534437	−	0.925672i
$305$	2.90471	+	5.03111i	0.166323	+	0.288080i
$306$	−19.0200			−1.08730
$307$	7.12583	−	12.3423i	0.406692	−	0.704412i	−0.587824	−	0.808989i	$-0.700015\pi$
$307$	7.12583	−	12.3423i	0.406692	−	0.704412i	0.994517	+	0.104577i	$0.0333487\pi$
$308$	2.38159			0.135704
$309$	30.2443			1.72054
$310$		0			0
$311$	20.2466			1.14808			0.574040	−	0.818827i	$-0.305375\pi$
$311$	20.2466			1.14808			0.574040	+	0.818827i	$0.305375\pi$
$312$	−9.95374			−0.563519
$313$	−4.52300	+	7.83407i	−0.255655	+	0.442808i	−0.965073	−	0.261980i	$-0.915624\pi$
$313$	−4.52300	+	7.83407i	−0.255655	+	0.442808i	0.709418	+	0.704788i	$0.248958\pi$
$314$	22.5803			1.27428
$315$	−6.58495	−	11.4055i	−0.371020	−	0.642626i
$316$	−2.12712	+	3.68427i	−0.119660	+	0.207257i
$317$	15.0248	−	26.0238i	0.843880	−	1.46164i	−0.0427111	−	0.999087i	$-0.513600\pi$
$317$	15.0248	−	26.0238i	0.843880	−	1.46164i	0.886591	−	0.462555i	$-0.153067\pi$
$318$	15.7223			0.881663
$319$	−2.94685	−	5.10409i	−0.164992	−	0.285774i
$320$	−11.6521	−	20.1820i	−0.651371	−	1.12821i
$321$	−6.48535	−	11.2330i	−0.361977	−	0.626963i
$322$	2.95765	−	5.12280i	0.164823	−	0.285483i
$323$	−11.7624	−	20.3731i	−0.654480	−	1.13359i
$324$	−0.920450	+	1.59427i	−0.0511361	+	0.0885704i
$325$	−2.26346			−0.125554
$326$	9.78890			0.542157
$327$	17.0576	−	29.5447i	0.943289	−	1.63382i
$328$	−3.18446	−	5.51564i	−0.175832	−	0.304550i
$329$	−0.454118	+	0.786556i	−0.0250363	+	0.0433642i
$330$	−19.2020	−	33.2588i	−1.05703	−	1.83083i
$331$	7.63333	+	13.2213i	0.419566	+	0.726709i	0.995896	−	0.0905081i	$-0.0288491\pi$
$331$	7.63333	+	13.2213i	0.419566	+	0.726709i	−0.576330	+	0.817217i	$0.695516\pi$
$332$	1.26119	+	2.18445i	0.0692169	+	0.119887i
$333$	26.8697			1.47245
$334$	12.3102	−	21.3220i	0.673587	−	1.16669i
$335$	−15.7253	+	27.2371i	−0.859167	+	1.48812i
$336$	4.67600	+	8.09906i	0.255096	+	0.441840i
$337$	8.23132			0.448388			0.224194	−	0.974544i	$-0.428025\pi$
$337$	8.23132			0.448388			0.224194	+	0.974544i	$0.428025\pi$
$338$	−7.16927	+	12.4175i	−0.389957	+	0.675425i
$339$	23.9524			1.30091
$340$	−4.30842			−0.233657
$341$		0			0
$342$	−33.4251			−1.80742
$343$	−15.1159			−0.816182
$344$	14.3556	−	24.8646i	0.774001	−	1.34061i
$345$	27.6663			1.48950
$346$	10.0521	+	17.4107i	0.540403	+	0.936006i
$347$	1.74062	−	3.01484i	0.0934413	−	0.161845i	−0.815516	−	0.578735i	$-0.803547\pi$
$347$	1.74062	−	3.01484i	0.0934413	−	0.161845i	0.908957	+	0.416890i	$0.136880\pi$
$348$	−0.807250	+	1.39820i	−0.0432731	+	0.0749512i
$349$	−17.7490			−0.950081			−0.475040	−	0.879964i	$-0.657567\pi$
$349$	−17.7490			−0.950081			−0.475040	+	0.879964i	$0.657567\pi$
$350$	1.39323	+	2.41315i	0.0744714	+	0.128988i
$351$	1.91737	+	3.32098i	0.102342	+	0.177261i
$352$	−5.47716	−	9.48671i	−0.291933	−	0.505643i
$353$	−2.54899	+	4.41498i	−0.135669	+	0.234986i	−0.925853	−	0.377884i	$-0.876652\pi$
$353$	−2.54899	+	4.41498i	−0.135669	+	0.234986i	0.790184	+	0.612870i	$0.209985\pi$
$354$	6.65597	+	11.5285i	0.353761	+	0.612732i
$355$	9.85023	−	17.0611i	0.522796	−	0.905509i
$356$	6.27028			0.332324
$357$	11.8051			0.624790
$358$	−2.46531	+	4.27004i	−0.130296	+	0.225679i
$359$	3.87846	+	6.71769i	0.204697	+	0.354546i	0.950036	−	0.312140i	$-0.101046\pi$
$359$	3.87846	+	6.71769i	0.204697	+	0.354546i	−0.745339	+	0.666686i	$0.767712\pi$
$360$	−16.6744	+	28.8809i	−0.878817	+	1.52216i
$361$	−11.1709	−	19.3486i	−0.587944	−	1.01835i
$362$	−12.7016	−	21.9998i	−0.667581	−	1.15628i
$363$	−11.1611	−	19.3316i	−0.585805	−	1.01464i
$364$	0.659882			0.0345872
$365$	−12.9945	+	22.5072i	−0.680165	+	1.17808i
$366$	−3.69942	+	6.40759i	−0.193372	+	0.334930i
$367$	−15.1302	−	26.2063i	−0.789791	−	1.36796i	−0.926095	−	0.377291i	$-0.876856\pi$
$367$	−15.1302	−	26.2063i	−0.789791	−	1.36796i	0.136303	−	0.990667i	$-0.456478\pi$
$368$	−11.4317			−0.595918
$369$	−4.35894	+	7.54991i	−0.226918	+	0.393033i
$370$	−20.9849			−1.09095
$371$	−5.67822			−0.294798
$372$		0			0
$373$	−11.6354			−0.602458			−0.301229	−	0.953552i	$-0.597397\pi$
$373$	−11.6354			−0.602458			−0.301229	+	0.953552i	$0.597397\pi$
$374$	20.0308			1.03577
$375$	11.0205	−	19.0880i	0.569095	−	0.985702i
$376$	2.29983			0.118605
$377$	−0.816501	−	1.41422i	−0.0420519	−	0.0728361i
$378$	2.36041	−	4.08835i	0.121406	−	0.210282i
$379$	−17.0765	+	29.5774i	−0.877161	+	1.51929i	−0.0227192	+	0.999742i	$0.507232\pi$
$379$	−17.0765	+	29.5774i	−0.877161	+	1.51929i	−0.854442	+	0.519546i	$0.826101\pi$
$380$	−7.57148			−0.388409
$381$	−6.82821	−	11.8268i	−0.349820	−	0.605906i
$382$	11.8402	+	20.5078i	0.605797	+	1.04927i
$383$	−0.293185	−	0.507812i	−0.0149811	−	0.0259480i	0.858438	−	0.512918i	$-0.171435\pi$
$383$	−0.293185	−	0.507812i	−0.0149811	−	0.0259480i	−0.873419	+	0.486970i	$0.838102\pi$
$384$	8.16666	−	14.1451i	0.416753	−	0.721838i
$385$	6.93492	+	12.0116i	0.353436	+	0.612170i
$386$	−13.1594	+	22.7927i	−0.669795	+	1.16012i
$387$	−39.3004			−1.99775
$388$	2.02786			0.102949
$389$	−9.30710	+	16.1204i	−0.471889	+	0.817335i	−0.999483	−	0.0321615i	$-0.989761\pi$
$389$	−9.30710	+	16.1204i	−0.471889	+	0.817335i	0.527594	+	0.849497i	$0.323094\pi$
$390$	−5.32040	−	9.21520i	−0.269409	−	0.466630i
$391$	−7.21514	+	12.4970i	−0.364885	+	0.632000i
$392$	8.46273	+	14.6579i	0.427432	+	0.740334i
$393$	−3.71590	−	6.43614i	−0.187443	−	0.324660i
$394$	3.97296	+	6.88137i	0.200155	+	0.346678i
$395$	−24.7757			−1.24660
$396$	−4.12744	+	7.14893i	−0.207411	+	0.359247i
$397$	−6.98331	+	12.0954i	−0.350482	+	0.607053i	−0.986334	−	0.164758i	$-0.947316\pi$
$397$	−6.98331	+	12.0954i	−0.350482	+	0.607053i	0.635852	+	0.771811i	$0.280649\pi$
$398$	−9.62532	−	16.6715i	−0.482474	−	0.835669i
$399$	20.7458			1.03859
$400$	2.69251	−	4.66356i	0.134625	−	0.233178i
$401$	−3.54741			−0.177149			−0.0885747	−	0.996070i	$-0.528231\pi$
$401$	−3.54741			−0.177149			−0.0885747	+	0.996070i	$0.528231\pi$
$402$	−40.0554			−1.99778
$403$		0			0
$404$	−0.849363			−0.0422574
$405$	−10.7210			−0.532730
$406$	−1.00517	+	1.74100i	−0.0498856	+	0.0864044i
$407$	−28.2978			−1.40267
$408$	−14.9464	−	25.8878i	−0.739955	−	1.28164i
$409$	8.56426	−	14.8337i	0.423476	−	0.733481i	−0.572801	−	0.819694i	$-0.694143\pi$
$409$	8.56426	−	14.8337i	0.423476	−	0.733481i	0.996277	+	0.0862131i	$0.0274766\pi$
$410$	3.40427	−	5.89636i	0.168125	−	0.291201i
$411$	−27.7013			−1.36640
$412$	2.53858	+	4.39695i	0.125067	+	0.216622i
$413$	−2.40385	−	4.16359i	−0.118286	−	0.204877i
$414$	10.2516	+	17.7562i	0.503837	+	0.872671i
$415$	−7.34489	+	12.7217i	−0.360547	+	0.624485i
$416$	−1.51759	−	2.62854i	−0.0744059	−	0.128875i
$417$	0.429636	−	0.744151i	0.0210394	−	0.0364412i
$418$	35.2016			1.72176
$419$	−18.2169			−0.889954			−0.444977	−	0.895542i	$-0.646788\pi$
$419$	−18.2169			−0.889954			−0.444977	+	0.895542i	$0.646788\pi$
$420$	1.89973	−	3.29043i	0.0926973	−	0.160556i
$421$	1.74399	+	3.02067i	0.0849966	+	0.147219i	0.905390	−	0.424581i	$-0.139579\pi$
$421$	1.74399	+	3.02067i	0.0849966	+	0.147219i	−0.820393	+	0.571800i	$0.806245\pi$
$422$	−16.6167	+	28.7810i	−0.808889	+	1.40104i
$423$	−1.57403	−	2.72629i	−0.0765318	−	0.132557i
$424$	7.18918	+	12.4520i	0.349138	+	0.604724i
$425$	−3.39877	−	5.88683i	−0.164864	−	0.285553i
$426$	25.0904			1.21563
$427$	1.33607	−	2.31415i	0.0646571	−	0.111989i
$428$	1.08871	−	1.88570i	0.0526246	−	0.0911485i
$429$	−7.17449	−	12.4266i	−0.346387	−	0.599961i
$430$	30.6930			1.48015
$431$	−7.11038	+	12.3155i	−0.342495	+	0.593219i	−0.984895	−	0.173150i	$-0.944605\pi$
$431$	−7.11038	+	12.3155i	−0.342495	+	0.593219i	0.642400	+	0.766369i	$0.277939\pi$
$432$	−9.12328			−0.438944
$433$	−32.1386			−1.54448			−0.772242	−	0.635328i	$-0.780865\pi$
$433$	−32.1386			−1.54448			−0.772242	+	0.635328i	$0.780865\pi$
$434$		0			0
$435$	−9.40247			−0.450814
$436$	5.72698			0.274273
$437$	−12.6797	+	21.9618i	−0.606550	+	1.05058i
$438$	−33.0995			−1.58156
$439$	−5.93040	−	10.2718i	−0.283043	−	0.490244i	0.689090	−	0.724676i	$-0.258011\pi$
$439$	−5.93040	−	10.2718i	−0.283043	−	0.490244i	−0.972133	+	0.234431i	$0.924677\pi$
$440$	17.5606	−	30.4158i	0.837168	−	1.45002i
$441$	11.5839	−	20.0640i	0.551616	−	0.955427i
$442$	5.55006			0.263990
$443$	17.0208	+	29.4808i	0.808681	+	1.40068i	0.913777	+	0.406215i	$0.133152\pi$
$443$	17.0208	+	29.4808i	0.808681	+	1.40068i	−0.105096	+	0.994462i	$0.533515\pi$
$444$	3.87590	+	6.71326i	0.183942	+	0.318597i
$445$	18.2583	+	31.6244i	0.865529	+	1.49914i
$446$	−7.88777	+	13.6620i	−0.373497	+	0.646916i
$447$	−29.2108	−	50.5946i	−1.38162	−	2.39304i
$448$	−5.35958	+	9.28306i	−0.253216	+	0.438584i
$449$	−10.8469			−0.511896			−0.255948	−	0.966690i	$-0.582388\pi$
$449$	−10.8469			−0.511896			−0.255948	+	0.966690i	$0.582388\pi$
$450$	−9.65821			−0.455293
$451$	4.59061	−	7.95117i	0.216163	−	0.374406i
$452$	2.01046	+	3.48222i	0.0945642	+	0.163790i
$453$	4.78870	−	8.29428i	0.224993	−	0.389699i
$454$	−7.20743	−	12.4836i	−0.338261	−	0.585886i
$455$	1.92150	+	3.32814i	0.0900813	+	0.156025i
$456$	−26.2663	−	45.4945i	−1.23003	−	2.13047i
$457$	−11.7064			−0.547603			−0.273802	−	0.961786i	$-0.588281\pi$
$457$	−11.7064			−0.547603			−0.273802	+	0.961786i	$0.588281\pi$
$458$	−17.8870	+	30.9812i	−0.835805	+	1.44766i
$459$	−5.75818	+	9.97345i	−0.268769	+	0.465521i
$460$	2.32219	+	4.02215i	0.108273	+	0.187534i
$461$	36.4085			1.69571			0.847857	−	0.530224i	$-0.177892\pi$
$461$	36.4085			1.69571			0.847857	+	0.530224i	$0.177892\pi$
$462$	−8.83228	+	15.2980i	−0.410915	+	0.711725i
$463$	18.1673			0.844306			0.422153	−	0.906525i	$-0.361274\pi$
$463$	18.1673			0.844306			0.422153	+	0.906525i	$0.361274\pi$
$464$	3.88510			0.180361
$465$		0			0
$466$	−14.2512			−0.660174
$467$	−4.99940			−0.231345			−0.115672	−	0.993287i	$-0.536902\pi$
$467$	−4.99940			−0.231345			−0.115672	+	0.993287i	$0.536902\pi$
$468$	−1.14361	+	1.98080i	−0.0528635	+	0.0915623i
$469$	14.4663			0.667991
$470$	1.22929	+	2.12919i	0.0567029	+	0.0982123i
$471$	24.2885	−	42.0689i	1.11915	−	1.93843i
$472$	−6.08702	+	10.5430i	−0.280178	+	0.485282i
$473$	41.3891			1.90307
$474$	−15.7771	−	27.3267i	−0.724665	−	1.25516i
$475$	−5.97288	−	10.3453i	−0.274055	−	0.474677i
$476$	0.990867	+	1.71623i	0.0454163	+	0.0786634i
$477$	9.84068	−	17.0446i	0.450574	−	0.780417i
$478$	−15.6979	−	27.1896i	−0.718005	−	1.24362i
$479$	1.32191	−	2.28962i	0.0603998	−	0.104615i	−0.834244	−	0.551395i	$-0.814096\pi$
$479$	1.32191	−	2.28962i	0.0603998	−	0.104615i	0.894644	+	0.446779i	$0.147429\pi$
$480$	−17.4759			−0.797662
$481$	−7.84064			−0.357502
$482$	6.46077	−	11.1904i	0.294280	−	0.509708i
$483$	−6.36280	−	11.0207i	−0.289517	−	0.501459i
$484$	1.87363	−	3.24522i	0.0851650	−	0.147510i
$485$	5.90490	+	10.2276i	0.268128	+	0.464411i
$486$	−12.7059	−	22.0072i	−0.576350	−	0.998267i
$487$	−11.6852	−	20.2394i	−0.529507	−	0.917133i	−0.999408	−	0.0344138i	$-0.989044\pi$
$487$	−11.6852	−	20.2394i	−0.529507	−	0.917133i	0.469901	−	0.882719i	$-0.344290\pi$
$488$	−6.76640			−0.306300
$489$	10.5294	−	18.2375i	0.476157	−	0.824728i
$490$	−9.04687	+	15.6696i	−0.408696	+	0.707882i
$491$	2.49844	+	4.32742i	0.112753	+	0.195294i	0.916879	−	0.399165i	$-0.130700\pi$
$491$	2.49844	+	4.32742i	0.112753	+	0.195294i	−0.804126	+	0.594458i	$0.797366\pi$
$492$	−2.51507			−0.113388
$493$	2.45209	−	4.24714i	0.110436	−	0.191282i
$494$	9.75351			0.438831
$495$	−48.0745			−2.16079
$496$		0			0
$497$	−9.06157			−0.406467
$498$	−18.7088			−0.838362
$499$	−8.68746	+	15.0471i	−0.388904	+	0.673602i	−0.992302	−	0.123838i	$-0.960480\pi$
$499$	−8.68746	+	15.0471i	−0.388904	+	0.673602i	0.603398	+	0.797440i	$0.293813\pi$
$500$	3.70005			0.165471
$501$	−26.4830	−	45.8700i	−1.18317	−	2.04932i
$502$	0.919561	−	1.59273i	0.0410420	−	0.0710869i
$503$	−1.94567	+	3.36999i	−0.0867530	+	0.150261i	−0.906137	−	0.422985i	$-0.860982\pi$
$503$	−1.94567	+	3.36999i	−0.0867530	+	0.150261i	0.819384	+	0.573245i	$0.194316\pi$
$504$	15.3394			0.683269
$505$	−2.47325	−	4.28379i	−0.110058	−	0.190626i
$506$	−10.7964	−	18.6999i	−0.479959	−	0.831313i
$507$	15.4232	+	26.7139i	0.684971	+	1.18640i
$508$	1.14626	−	1.98538i	0.0508572	−	0.0880872i
$509$	7.90327	+	13.6889i	0.350306	+	0.606748i	0.986303	−	0.164943i	$-0.0527441\pi$
$509$	7.90327	+	13.6889i	0.350306	+	0.606748i	−0.635997	+	0.771692i	$0.719411\pi$
$510$	15.9780	−	27.6748i	0.707519	−	1.22546i
$511$	11.9541			0.528819
$512$	24.9025			1.10054
$513$	−10.1192	+	17.5270i	−0.446775	+	0.773837i
$514$	10.4991	+	18.1850i	0.463096	+	0.802105i
$515$	−14.7841	+	25.6069i	−0.651466	+	1.12837i
$516$	−5.66899	−	9.81898i	−0.249563	−	0.432256i
$517$	1.65768	+	2.87119i	0.0729047	+	0.126275i
$518$	4.82618	+	8.35918i	0.212050	+	0.367281i
$519$	43.2501			1.89847
$520$	4.86561	−	8.42749i	0.213371	−	0.369570i
$521$	15.4138	−	26.6975i	0.675291	−	1.16964i	−0.301093	−	0.953595i	$-0.597352\pi$
$521$	15.4138	−	26.6975i	0.675291	−	1.16964i	0.976384	−	0.216043i	$-0.0693151\pi$
$522$	−3.48403	−	6.03451i	−0.152492	−	0.264123i
$523$	1.29385			0.0565763			0.0282881	−	0.999600i	$-0.490994\pi$
$523$	1.29385			0.0565763			0.0282881	+	0.999600i	$0.490994\pi$
$524$	0.623795	−	1.08044i	0.0272506	−	0.0471994i
$525$	5.99452			0.261622
$526$	29.2387			1.27487
$527$		0			0
$528$	34.1378			1.48566
$529$	−7.44448			−0.323673
$530$	−7.68542	+	13.3115i	−0.333833	+	0.578216i
$531$	16.6641			0.723158
$532$	1.74132	+	3.01605i	0.0754957	+	0.130762i
$533$	1.27195	−	2.20308i	0.0550941	−	0.0954259i
$534$	−23.2537	+	40.2766i	−1.00629	+	1.74294i
$535$	12.6808			0.548237
$536$	−18.3157	−	31.7238i	−0.791119	−	1.37026i
$537$	5.30362	+	9.18614i	0.228868	+	0.396411i
$538$	−8.16986	−	14.1506i	−0.352228	−	0.610076i
$539$	−12.1996	+	21.1303i	−0.525473	+	0.910146i
$540$	1.85327	+	3.20996i	0.0797520	+	0.138135i
$541$	6.56375	−	11.3687i	0.282198	−	0.488781i	−0.689728	−	0.724068i	$-0.742270\pi$
$541$	6.56375	−	11.3687i	0.282198	−	0.488781i	0.971926	+	0.235288i	$0.0756033\pi$
$542$	−14.0237			−0.602369
$543$	−54.6499			−2.34525
$544$	4.55757	−	7.89394i	0.195404	−	0.338450i
$545$	16.6763	+	28.8842i	0.714335	+	1.23726i
$546$	−2.44721	+	4.23869i	−0.104731	+	0.181399i
$547$	−15.0282	−	26.0295i	−0.642558	−	1.11294i	−0.984860	−	0.173352i	$-0.944540\pi$
$547$	−15.0282	−	26.0295i	−0.642558	−	1.11294i	0.342302	−	0.939590i	$-0.388793\pi$
$548$	−2.32513	−	4.02724i	−0.0993247	−	0.172035i
$549$	4.63098	+	8.02110i	0.197646	+	0.342332i
$550$	10.1715			0.433715
$551$	4.30922	−	7.46379i	0.183579	−	0.317968i
$552$	−16.1118	+	27.9065i	−0.685766	+	1.18778i
$553$	5.69800	+	9.86923i	0.242304	+	0.419682i
$554$	2.77889			0.118064
$555$	−22.5724	+	39.0965i	−0.958143	+	1.65955i
$556$	0.144247			0.00611745
$557$	12.8904			0.546184			0.273092	−	0.961988i	$-0.411954\pi$
$557$	12.8904			0.546184			0.273092	+	0.961988i	$0.411954\pi$
$558$		0			0
$559$	11.4679			0.485041
$560$	−9.14294			−0.386360
$561$	21.5462	−	37.3191i	0.909680	−	1.57561i
$562$	6.64461			0.280286
$563$	−6.37499	−	11.0418i	−0.268674	−	0.465357i	0.699846	−	0.714294i	$-0.253252\pi$
$563$	−6.37499	−	11.0418i	−0.268674	−	0.465357i	−0.968520	+	0.248937i	$0.919919\pi$
$564$	0.454099	−	0.786523i	0.0191210	−	0.0331186i
$565$	−11.7085	+	20.2797i	−0.492579	+	0.853172i
$566$	−14.7342			−0.619324
$567$	2.46565	+	4.27064i	0.103548	+	0.179350i
$568$	11.4728	+	19.8715i	0.481389	+	0.833791i
$569$	−1.67976	−	2.90943i	−0.0704193	−	0.121970i	0.828666	−	0.559744i	$-0.189100\pi$
$569$	−1.67976	−	2.90943i	−0.0704193	−	0.121970i	−0.899085	+	0.437774i	$0.855767\pi$
$570$	28.0793	−	48.6348i	1.17611	−	2.03709i
$571$	4.03832	+	6.99458i	0.168998	+	0.292714i	0.938068	−	0.346451i	$-0.112613\pi$
$571$	4.03832	+	6.99458i	0.168998	+	0.292714i	−0.769070	+	0.639165i	$0.779280\pi$
$572$	1.20439	−	2.08607i	0.0503582	−	0.0872229i
$573$	50.9436			2.12820
$574$	−3.13170			−0.130715
$575$	−3.66380	+	6.34588i	−0.152791	+	0.264641i
$576$	−18.5769	−	32.1762i	−0.774038	−	1.34067i
$577$	−9.03396	+	15.6473i	−0.376089	+	0.651405i	−0.990489	−	0.137589i	$-0.956065\pi$
$577$	−9.03396	+	15.6473i	−0.376089	+	0.651405i	0.614401	+	0.788994i	$0.289398\pi$
$578$	−2.24968	−	3.89655i	−0.0935742	−	0.162075i
$579$	28.3098	+	49.0340i	1.17651	+	2.03778i
$580$	−0.789204	−	1.36694i	−0.0327699	−	0.0567592i
$581$	6.75682			0.280320
$582$	−7.52045	+	13.0258i	−0.311733	+	0.539937i
$583$	−10.3637	+	17.9504i	−0.429220	+	0.743431i
$584$	−15.1351	−	26.2147i	−0.626294	−	1.08477i
$585$	−13.3203			−0.550726
$586$	16.6448	−	28.8296i	0.687590	−	1.19094i
$587$	16.6650			0.687839			0.343920	−	0.938999i	$-0.388245\pi$
$587$	16.6650			0.687839			0.343920	+	0.938999i	$0.388245\pi$
$588$	6.68382			0.275636
$589$		0			0
$590$	−13.0144			−0.535793
$591$	17.0941			0.703156
$592$	9.32688	−	16.1546i	0.383333	−	0.663951i
$593$	32.6571			1.34107			0.670533	−	0.741880i	$-0.266066\pi$
$593$	32.6571			1.34107			0.670533	+	0.741880i	$0.266066\pi$
$594$	−8.61627	−	14.9238i	−0.353530	−	0.612332i
$595$	−5.77058	+	9.99494i	−0.236571	+	0.409753i
$596$	4.90367	−	8.49340i	0.200862	−	0.347903i
$597$	−41.4139			−1.69496
$598$	−2.99142	−	5.18130i	−0.122328	−	0.211879i
$599$	−10.5165	−	18.2150i	−0.429691	−	0.744246i	0.567155	−	0.823611i	$-0.308044\pi$
$599$	−10.5165	−	18.2150i	−0.429691	−	0.744246i	−0.996846	+	0.0793652i	$0.974711\pi$
$600$	−7.58965	−	13.1457i	−0.309846	−	0.536670i
$601$	−8.36666	+	14.4915i	−0.341283	+	0.591120i	−0.984671	−	0.174420i	$-0.944195\pi$
$601$	−8.36666	+	14.4915i	−0.341283	+	0.591120i	0.643388	+	0.765540i	$0.277528\pi$
$602$	−7.05889	−	12.2264i	−0.287699	−	0.498309i
$603$	−25.0709	+	43.4241i	−1.02097	+	1.76837i
$604$	1.60777			0.0654194
$605$	21.8232			0.887239
$606$	3.14991	−	5.45581i	0.127956	−	0.221627i
$607$	0.787887	+	1.36466i	0.0319793	+	0.0553898i	0.881572	−	0.472049i	$-0.156486\pi$
$607$	0.787887	+	1.36466i	0.0319793	+	0.0553898i	−0.849593	+	0.527439i	$0.823152\pi$
$608$	8.00933	−	13.8726i	0.324821	−	0.562607i
$609$	2.16242	+	3.74542i	0.0876255	+	0.151772i
$610$	−3.61673	−	6.26435i	−0.146437	−	0.253636i
$611$	0.459303	+	0.795537i	0.0185814	+	0.0321840i
$612$	−6.86892			−0.277660
$613$	−22.5131	+	38.9938i	−0.909294	+	1.57494i	−0.0942459	+	0.995549i	$0.530044\pi$
$613$	−22.5131	+	38.9938i	−0.909294	+	1.57494i	−0.815048	+	0.579394i	$0.803289\pi$
$614$	−8.87254	+	15.3677i	−0.358066	+	0.620189i
$615$	−7.32360	−	12.6848i	−0.295316	−	0.511502i
$616$	−16.1546			−0.650887
$617$	16.7177	−	28.9559i	0.673029	−	1.16572i	−0.304012	−	0.952668i	$-0.598326\pi$
$617$	16.7177	−	28.9559i	0.673029	−	1.16572i	0.977041	−	0.213052i	$-0.0683403\pi$
$618$	−37.6579			−1.51482
$619$	10.7700			0.432881			0.216440	−	0.976296i	$-0.430555\pi$
$619$	10.7700			0.432881			0.216440	+	0.976296i	$0.430555\pi$
$620$		0			0
$621$	12.4144			0.498172
$622$	−25.2095			−1.01081
$623$	8.39825	−	14.5462i	0.336469	−	0.582781i
$624$	9.45877			0.378654
$625$	15.4188	+	26.7062i	0.616754	+	1.06825i
$626$	5.63170	−	9.75438i	0.225088	−	0.389864i
$627$	37.8646	−	65.5834i	1.51217	−	2.61915i
$628$	8.15470			0.325408
$629$	−11.7734	−	20.3921i	−0.469435	−	0.813085i
$630$	8.19908	+	14.2012i	0.326659	+	0.565790i
$631$	−9.22183	−	15.9727i	−0.367115	−	0.635862i	0.621998	−	0.783019i	$-0.286321\pi$
$631$	−9.22183	−	15.9727i	−0.367115	−	0.635862i	−0.989113	+	0.147157i	$0.952988\pi$
$632$	14.4285	−	24.9908i	0.573933	−	0.994082i
$633$	35.7475	+	61.9166i	1.42084	+	2.46096i
$634$	−18.7078	+	32.4029i	−0.742982	+	1.28688i
$635$	13.3511			0.529824
$636$	5.67798			0.225147
$637$	−3.38021	+	5.85470i	−0.133929	+	0.231972i
$638$	3.66919	+	6.35523i	0.145265	+	0.251606i
$639$	15.7042	−	27.2005i	0.621249	−	1.07604i
$640$	7.98411	+	13.8289i	0.315600	+	0.546634i
$641$	−18.9818	−	32.8774i	−0.749734	−	1.29858i	−0.947950	−	0.318419i	$-0.896848\pi$
$641$	−18.9818	−	32.8774i	−0.749734	−	1.29858i	0.198216	−	0.980158i	$-0.436485\pi$
$642$	8.07507	+	13.9864i	0.318697	+	0.552000i
$643$	−16.1193			−0.635682			−0.317841	−	0.948144i	$-0.602958\pi$
$643$	−16.1193			−0.635682			−0.317841	+	0.948144i	$0.602958\pi$
$644$	1.06813	−	1.85006i	0.0420903	−	0.0729026i
$645$	33.0149	−	57.1835i	1.29996	−	2.25160i
$646$	14.6457	+	25.3671i	0.576227	+	0.998055i
$647$	−6.89869			−0.271215			−0.135608	−	0.990763i	$-0.543299\pi$
$647$	−6.89869			−0.271215			−0.135608	+	0.990763i	$0.543299\pi$
$648$	6.24352	−	10.8141i	0.245268	−	0.424817i
$649$	−17.5497			−0.688886
$650$	2.81828			0.110542
$651$		0			0
$652$	3.53518			0.138448
$653$	8.08319			0.316320			0.158160	−	0.987414i	$-0.449444\pi$
$653$	8.08319			0.316320			0.158160	+	0.987414i	$0.449444\pi$
$654$	−21.2389	+	36.7868i	−0.830505	+	1.43848i
$655$	7.26568			0.283894
$656$	3.02611	+	5.24137i	0.118150	+	0.204641i
$657$	−20.7172	+	35.8832i	−0.808254	+	1.39994i
$658$	0.565433	−	0.979359i	0.0220429	−	0.0381794i
$659$	24.7700			0.964901			0.482450	−	0.875923i	$-0.339747\pi$
$659$	24.7700			0.964901			0.482450	+	0.875923i	$0.339747\pi$
$660$	−6.93464	−	12.0111i	−0.269930	−	0.467533i
$661$	−19.8835	−	34.4392i	−0.773379	−	1.33953i	−0.935701	−	0.352793i	$-0.885232\pi$
$661$	−19.8835	−	34.4392i	−0.773379	−	1.33953i	0.162323	−	0.986738i	$-0.448101\pi$
$662$	−9.50444	−	16.4622i	−0.369400	−	0.639820i
$663$	5.96992	−	10.3402i	0.231853	−	0.401581i
$664$	−8.55480	−	14.8173i	−0.331991	−	0.575025i
$665$	−10.1410	+	17.5648i	−0.393253	+	0.681134i
$666$	−33.4562			−1.29640
$667$	−5.28659			−0.204698
$668$	4.44575	−	7.70026i	0.172011	−	0.297932i
$669$	16.9690	+	29.3911i	0.656058	+	1.13633i
$670$	19.5800	−	33.9135i	0.756441	−	1.31019i
$671$	−4.87711	−	8.44740i	−0.188279	−	0.326108i
$672$	4.01917	+	6.96141i	0.155043	+	0.268542i
$673$	−7.28014	−	12.6096i	−0.280629	−	0.486063i	0.690911	−	0.722940i	$-0.257210\pi$
$673$	−7.28014	−	12.6096i	−0.280629	−	0.486063i	−0.971540	+	0.236877i	$0.923876\pi$
$674$	−10.2490			−0.394777
$675$	−2.92396	+	5.06445i	−0.112543	+	0.194931i
$676$	−2.58913	+	4.48450i	−0.0995818	+	0.172481i
$677$	0.110509	+	0.191408i	0.00424722	+	0.00735641i	0.868141	−	0.496317i	$-0.165315\pi$
$677$	0.110509	+	0.191408i	0.00424722	+	0.00735641i	−0.863894	+	0.503674i	$0.831981\pi$
$678$	−29.8237			−1.14537
$679$	2.71606	−	4.70436i	0.104233	−	0.180537i
$680$	29.2245			1.12071
$681$	−31.0107			−1.18833
$682$		0			0
$683$	−16.3674			−0.626280			−0.313140	−	0.949707i	$-0.601381\pi$
$683$	−16.3674			−0.626280			−0.313140	+	0.949707i	$0.601381\pi$
$684$	−12.0712			−0.461555
$685$	13.5410	−	23.4538i	0.517376	−	0.896122i
$686$	18.8212			0.718596
$687$	38.4803	+	66.6499i	1.46812	+	2.54285i
$688$	−13.6417	+	23.6282i	−0.520086	+	0.900816i
$689$	−2.87153	+	4.97363i	−0.109396	+	0.189480i
$690$	−34.4480			−1.31141
$691$	23.6536	+	40.9692i	0.899824	+	1.55854i	0.827718	+	0.561144i	$0.189639\pi$
$691$	23.6536	+	40.9692i	0.899824	+	1.55854i	0.0721057	+	0.997397i	$0.477028\pi$
$692$	3.63023	+	6.28775i	0.138001	+	0.239024i
$693$	11.0564	+	19.1502i	0.419996	+	0.727455i
$694$	−2.16728	+	3.75385i	−0.0822690	+	0.142494i
$695$	0.420032	+	0.727517i	0.0159327	+	0.0275963i
$696$	5.47566	−	9.48412i	0.207554	−	0.359495i
$697$	7.63973			0.289376
$698$	22.0997			0.836485
$699$	−15.3293	+	26.5511i	−0.579807	+	1.00426i
$700$	0.503155	+	0.871490i	0.0190175	+	0.0329392i
$701$	−12.1609	+	21.0634i	−0.459312	+	0.795553i	−0.998925	−	0.0463611i	$-0.985238\pi$
$701$	−12.1609	+	21.0634i	−0.459312	+	0.795553i	0.539612	+	0.841914i	$0.318571\pi$
$702$	−2.38736	−	4.13503i	−0.0901052	−	0.156067i
$703$	−20.6901	−	35.8364i	−0.780343	−	1.35159i
$704$	19.5642	+	33.8862i	0.737355	+	1.27714i
$705$	5.28914			0.199201
$706$	3.17381	−	5.49719i	0.119448	−	0.206890i
$707$	−1.13761	+	1.97040i	−0.0427844	+	0.0741047i
$708$	2.40375	+	4.16342i	0.0903385	+	0.156471i
$709$	−18.0141			−0.676535			−0.338268	−	0.941050i	$-0.609841\pi$
$709$	−18.0141			−0.676535			−0.338268	+	0.941050i	$0.609841\pi$
$710$	−12.2648	+	21.2432i	−0.460288	+	0.797242i
$711$	−39.4999			−1.48136
$712$	−42.5320			−1.59395
$713$		0			0
$714$	−14.6988			−0.550087
$715$	14.0282			0.524626
$716$	−0.890327	+	1.54209i	−0.0332731	+	0.0576307i
$717$	−67.5418			−2.52239
$718$	−4.82916	−	8.36435i	−0.180223	−	0.312155i
$719$	−15.6914	+	27.1784i	−0.585192	+	1.01358i	0.409660	+	0.912238i	$0.365647\pi$
$719$	−15.6914	+	27.1784i	−0.585192	+	1.01358i	−0.994852	+	0.101343i	$0.967686\pi$
$720$	15.8452	−	27.4448i	0.590517	−	1.02281i
$721$	13.6004			0.506507
$722$	13.9092	+	24.0915i	0.517647	+	0.896591i
$723$	−13.8991	−	24.0739i	−0.516912	−	0.895317i
$724$	−4.58708	−	7.94506i	−0.170478	−	0.295276i
$725$	1.24515	−	2.15667i	0.0462438	−	0.0800966i
$726$	13.8969	+	24.0702i	0.515764	+	0.893329i
$727$	2.32820	−	4.03256i	0.0863481	−	0.149559i	−0.819617	−	0.572912i	$-0.805814\pi$
$727$	2.32820	−	4.03256i	0.0863481	−	0.149559i	0.905965	+	0.423353i	$0.139147\pi$
$728$	−4.47605			−0.165893
$729$	−42.3865			−1.56987
$730$	16.1798	−	28.0242i	0.598841	−	1.03722i
$731$	17.2200	+	29.8260i	0.636906	+	1.10315i
$732$	−1.33602	+	2.31405i	−0.0493806	+	0.0855298i
$733$	24.8925	+	43.1151i	0.919425	+	1.59249i	0.800290	+	0.599613i	$0.204679\pi$
$733$	24.8925	+	43.1151i	0.919425	+	1.59249i	0.119135	+	0.992878i	$0.461988\pi$
$734$	18.8390	+	32.6301i	0.695360	+	1.20440i
$735$	19.4625	+	33.7101i	0.717886	+	1.24342i
$736$	−9.82592			−0.362188
$737$	26.4034	−	45.7320i	0.972580	−	1.68456i
$738$	5.42742	−	9.40058i	0.199786	−	0.346040i
$739$	−16.3597	−	28.3359i	−0.601802	−	1.04235i	−0.992548	−	0.121853i	$-0.961116\pi$
$739$	−16.3597	−	28.3359i	−0.601802	−	1.04235i	0.390746	−	0.920498i	$-0.372217\pi$
$740$	−7.57852			−0.278592
$741$	10.4914	−	18.1716i	0.385410	−	0.667549i
$742$	7.07009			0.259551
$743$	34.5763			1.26848			0.634241	−	0.773136i	$-0.281313\pi$
$743$	34.5763			1.26848			0.634241	+	0.773136i	$0.281313\pi$
$744$		0			0
$745$	57.1157			2.09256
$746$	14.4875			0.530425
$747$	−11.7100	+	20.2823i	−0.428445	+	0.742089i
$748$	7.23398			0.264501
$749$	−2.91637	−	5.05130i	−0.106562	−	0.184570i
$750$	−13.7219	+	23.7670i	−0.501052	+	0.867847i
$751$	−8.13227	+	14.0855i	−0.296751	+	0.513988i	−0.975391	−	0.220484i	$-0.929236\pi$
$751$	−8.13227	+	14.0855i	−0.296751	+	0.513988i	0.678640	+	0.734471i	$0.262570\pi$
$752$	−2.18547			−0.0796959
$753$	−1.97825	−	3.42643i	−0.0720915	−	0.124866i
$754$	1.01664	+	1.76088i	0.0370240	+	0.0641275i
$755$	4.68166	+	8.10887i	0.170383	+	0.295112i
$756$	0.852444	−	1.47648i	0.0310031	−	0.0536989i
$757$	−20.4826	−	35.4769i	−0.744453	−	1.28943i	−0.950450	−	0.310878i	$-0.899377\pi$
$757$	−20.4826	−	35.4769i	−0.744453	−	1.28943i	0.205996	−	0.978553i	$-0.433957\pi$
$758$	21.2624	−	36.8275i	0.772284	−	1.33764i
$759$	−46.4526			−1.68612
$760$	51.3582			1.86296
$761$	−0.0315345	+	0.0546193i	−0.00114312	+	0.00197995i	−0.866596	−	0.499010i	$-0.833697\pi$
$761$	−0.0315345	+	0.0546193i	−0.00114312	+	0.00197995i	0.865453	+	0.500990i	$0.167031\pi$
$762$	8.50197	+	14.7258i	0.307994	+	0.533461i
$763$	7.67057	−	13.2858i	0.277693	−	0.480979i
$764$	4.27600	+	7.40624i	0.154700	+	0.267948i
$765$	−20.0015	−	34.6436i	−0.723156	−	1.25254i
$766$	0.365052	+	0.632289i	0.0131899	+	0.0228455i
$767$	−4.86260			−0.175578
$768$	13.6685	−	23.6746i	0.493220	−	0.854282i
$769$	20.2449	−	35.0652i	0.730050	−	1.26448i	−0.226811	−	0.973939i	$-0.572830\pi$
$769$	20.2449	−	35.0652i	0.730050	−	1.26448i	0.956861	−	0.290545i	$-0.0938368\pi$
$770$	−8.63484	−	14.9560i	−0.311178	−	0.538976i
$771$	45.1735			1.62688
$772$	−4.75241	+	8.23141i	−0.171043	+	0.296255i
$773$	−36.7190			−1.32069			−0.660345	−	0.750963i	$-0.729590\pi$
$773$	−36.7190			−1.32069			−0.660345	+	0.750963i	$0.729590\pi$
$774$	48.9338			1.75889
$775$		0			0
$776$	−13.7552			−0.493783
$777$	20.7651			0.744944
$778$	11.5885	−	20.0719i	0.415468	−	0.719611i
$779$	13.4258			0.481030
$780$	−1.92142	−	3.32800i	−0.0687979	−	0.119161i
$781$	−16.5389	+	28.6461i	−0.591807	+	1.02504i
$782$	8.98374	−	15.5603i	0.321258	−	0.556435i
$783$	−4.21906			−0.150777
$784$	−8.04191	−	13.9290i	−0.287211	−	0.497464i
$785$	23.7455	+	41.1285i	0.847515	+	1.46794i
$786$	4.62676	+	8.01379i	0.165031	+	0.285842i
$787$	3.38010	−	5.85451i	0.120488	−	0.208691i	−0.799472	−	0.600703i	$-0.794888\pi$
$787$	3.38010	−	5.85451i	0.120488	−	0.208691i	0.919960	+	0.392012i	$0.128221\pi$
$788$	1.43480	+	2.48515i	0.0511128	+	0.0885299i
$789$	31.4506	−	54.4740i	1.11967	−	1.93933i
$790$	30.8488			1.09755
$791$	10.7710			0.382974
$792$	27.9968	−	48.4920i	0.994825	−	1.72309i
$793$	−1.35133	−	2.34057i	−0.0479871	−	0.0831161i
$794$	8.69508	−	15.0603i	0.308577	−	0.534471i
$795$	16.5336	+	28.6371i	0.586388	+	1.01565i
$796$	−3.47611	−	6.02080i	−0.123207	−	0.213401i
$797$	11.0398	+	19.1215i	0.391051	+	0.677319i	0.992588	−	0.121525i	$-0.0387784\pi$
$797$	11.0398	+	19.1215i	0.391051	+	0.677319i	−0.601538	+	0.798844i	$0.705445\pi$
$798$	−25.8311			−0.914412
$799$	−1.37936	+	2.38913i	−0.0487984	+	0.0845213i
$800$	2.31430	−	4.00849i	0.0818229	−	0.141721i
$801$	29.1093	+	50.4188i	1.02853	+	1.78146i
$802$	4.41697			0.155969
$803$	21.8182	−	37.7903i	0.769949	−	1.33359i
$804$	−14.4657			−0.510166
$805$	12.4411			0.438492
$806$		0			0
$807$	−35.1516			−1.23740
$808$	5.76132			0.202683
$809$	−12.5081	+	21.6647i	−0.439762	+	0.761691i	−0.997671	−	0.0682118i	$-0.978271\pi$
$809$	−12.5081	+	21.6647i	−0.439762	+	0.761691i	0.557909	+	0.829902i	$0.311604\pi$
$810$	13.3490			0.469034
$811$	−1.30069	−	2.25286i	−0.0456734	−	0.0791087i	0.842285	−	0.539033i	$-0.181210\pi$
$811$	−1.30069	−	2.25286i	−0.0456734	−	0.0791087i	−0.887958	+	0.459924i	$0.847877\pi$
$812$	−0.363008	+	0.628749i	−0.0127391	+	0.0220648i
$813$	−15.0846	+	26.1272i	−0.529039	+	0.916323i
$814$	35.2343			1.23496
$815$	10.2941	+	17.8298i	0.360585	+	0.624551i
$816$	14.2031	+	24.6005i	0.497209	+	0.861191i
$817$	30.2619	+	52.4152i	1.05873	+	1.83378i
$818$	−10.6636	+	18.4698i	−0.372843	+	0.645783i
$819$	3.06345	+	5.30605i	0.107046	+	0.185408i
$820$	1.22942	−	2.12943i	0.0429334	−	0.0743628i
$821$	25.9258			0.904818			0.452409	−	0.891811i	$-0.350565\pi$
$821$	25.9258			0.904818			0.452409	+	0.891811i	$0.350565\pi$
$822$	34.4915			1.20303
$823$	−16.0449	+	27.7906i	−0.559290	+	0.968720i	0.438265	+	0.898846i	$0.355593\pi$
$823$	−16.0449	+	27.7906i	−0.559290	+	0.968720i	−0.997556	+	0.0698739i	$0.977740\pi$
$824$	−17.2195	−	29.8250i	−0.599869	−	1.03900i
$825$	10.9410	−	18.9504i	0.380917	−	0.659767i
$826$	2.99309	+	5.18419i	0.104143	+	0.180381i
$827$	10.8717	+	18.8303i	0.378045	+	0.654793i	0.990778	−	0.135497i	$-0.0432632\pi$
$827$	10.8717	+	18.8303i	0.378045	+	0.654793i	−0.612733	+	0.790290i	$0.709930\pi$
$828$	3.70227	+	6.41252i	0.128663	+	0.222851i
$829$	−20.6366			−0.716740			−0.358370	−	0.933580i	$-0.616667\pi$
$829$	−20.6366			−0.716740			−0.358370	+	0.933580i	$0.616667\pi$
$830$	9.14530	−	15.8401i	0.317438	−	0.549819i
$831$	2.98912	−	5.17730i	0.103691	−	0.179599i
$832$	5.42078	+	9.38906i	0.187932	+	0.325507i
$833$	−20.3027			−0.703446
$834$	−0.534950	+	0.926561i	−0.0185238	+	0.0320842i
$835$	51.7821			1.79199
$836$	12.7128			0.439680
$837$		0			0
$838$	22.6823			0.783547
$839$	−7.68971			−0.265478			−0.132739	−	0.991151i	$-0.542377\pi$
$839$	−7.68971			−0.265478			−0.132739	+	0.991151i	$0.542377\pi$
$840$	−12.8861	+	22.3193i	−0.444612	+	0.770090i
$841$	−27.2033			−0.938046
$842$	−2.17148	−	3.76111i	−0.0748341	−	0.129616i
$843$	7.14728	−	12.3795i	0.246165	−	0.426371i
$844$	−6.00100	+	10.3940i	−0.206563	+	0.357777i
$845$	−30.1570			−1.03743
$846$	1.95986	+	3.39457i	0.0673813	+	0.116708i
$847$	−5.01898	−	8.69313i	−0.172454	−	0.298699i
$848$	−6.83169	−	11.8328i	−0.234601	−	0.406341i
$849$	−15.8488	+	27.4510i	−0.543930	+	0.942114i
$850$	4.23188	+	7.32984i	0.145152	+	0.251411i
$851$	−12.6914	+	21.9822i	−0.435057	+	0.753540i
$852$	9.06119			0.310431
$853$	−0.888830			−0.0304330			−0.0152165	−	0.999884i	$-0.504844\pi$
$853$	−0.888830			−0.0304330			−0.0152165	+	0.999884i	$0.504844\pi$
$854$	−1.66358	+	2.88140i	−0.0569264	+	0.0985994i
$855$	−35.1500	−	60.8816i	−1.20211	−	2.08211i
$856$	−7.38482	+	12.7909i	−0.252408	+	0.437183i
$857$	−7.42802	−	12.8657i	−0.253736	−	0.439484i	0.710815	−	0.703379i	$-0.248326\pi$
$857$	−7.42802	−	12.8657i	−0.253736	−	0.439484i	−0.964552	+	0.263894i	$0.914993\pi$
$858$	8.93312	+	15.4726i	0.304972	+	0.528227i
$859$	−20.7316	−	35.9081i	−0.707352	−	1.22517i	−0.965836	−	0.259154i	$-0.916556\pi$
$859$	−20.7316	−	35.9081i	−0.707352	−	1.22517i	0.258484	−	0.966016i	$-0.416777\pi$
$860$	11.0845			0.377979
$861$	−3.36862	+	5.83462i	−0.114802	+	0.198843i
$862$	8.85330	−	15.3344i	0.301545	−	0.522291i
$863$	11.1992	+	19.3977i	0.381227	+	0.660304i	0.991238	−	0.132089i	$-0.0421685\pi$
$863$	11.1992	+	19.3977i	0.381227	+	0.660304i	−0.610011	+	0.792393i	$0.708835\pi$
$864$	−7.84176			−0.266782
$865$	−21.1416	+	36.6184i	−0.718837	+	1.24506i
$866$	40.0166			1.35982
$867$	−9.67946			−0.328732
$868$		0			0
$869$	41.5992			1.41116
$870$	11.7072			0.396913
$871$	7.31573	−	12.6712i	0.247884	−	0.429348i
$872$	−38.8467			−1.31552
$873$	9.41419	+	16.3059i	0.318622	+	0.551870i
$874$	15.7877	−	27.3452i	0.534028	−	0.924964i
$875$	4.95575	−	8.58361i	0.167535	−	0.290179i
$876$	−11.9536			−0.403876
$877$	15.3948	+	26.6646i	0.519846	+	0.900400i	0.999734	+	0.0230700i	$0.00734405\pi$
$877$	15.3948	+	26.6646i	0.519846	+	0.900400i	−0.479888	+	0.877330i	$0.659323\pi$
$878$	7.38409	+	12.7896i	0.249201	+	0.431629i
$879$	−35.8080	−	62.0212i	−1.20777	−	2.09192i
$880$	−16.6874	+	28.9034i	−0.562531	+	0.974332i
$881$	1.42973	+	2.47637i	0.0481689	+	0.0834310i	0.889105	−	0.457704i	$-0.151328\pi$
$881$	1.42973	+	2.47637i	0.0481689	+	0.0834310i	−0.840936	+	0.541135i	$0.817995\pi$
$882$	−14.4234	+	24.9821i	−0.485662	+	0.841191i
$883$	−23.9316			−0.805362			−0.402681	−	0.915340i	$-0.631922\pi$
$883$	−23.9316			−0.805362			−0.402681	+	0.915340i	$0.631922\pi$
$884$	2.00436			0.0674140
$885$	−13.9989	+	24.2468i	−0.470568	+	0.815048i
$886$	−21.1930	−	36.7073i	−0.711992	−	1.23321i
$887$	−13.1926	+	22.8503i	−0.442964	+	0.767237i	−0.997908	−	0.0646512i	$-0.979407\pi$
$887$	−13.1926	+	22.8503i	−0.442964	+	0.767237i	0.554944	+	0.831888i	$0.312740\pi$
$888$	−26.2907	−	45.5367i	−0.882257	−	1.52811i
$889$	−3.07055	−	5.31834i	−0.102983	−	0.178371i
$890$	−22.7339	−	39.3763i	−0.762042	−	1.31990i
$891$	18.0009			0.603052
$892$	−2.84861	+	4.93393i	−0.0953785	+	0.165200i
$893$	−2.42405	+	4.19858i	−0.0811178	+	0.140500i
$894$	36.3711	+	62.9966i	1.21643	+	2.10692i
$895$	−10.3701			−0.346635
$896$	3.67243	−	6.36083i	0.122687	−	0.212501i
$897$	−12.8709			−0.429747
$898$	13.5057			0.450692
$899$		0			0
$900$	−3.48799			−0.116266
$901$	−17.2473			−0.574592
$902$	−5.71588	+	9.90019i	−0.190318	+	0.329640i
$903$	−30.3716			−1.01070
$904$	−13.6372	−	23.6203i	−0.453566	−	0.785599i
$905$	26.7141	−	46.2702i	0.888007	−	1.53807i
$906$	−5.96253	+	10.3274i	−0.198092	+	0.343105i
$907$	10.2177			0.339273			0.169636	−	0.985507i	$-0.445741\pi$
$907$	10.2177			0.339273			0.169636	+	0.985507i	$0.445741\pi$
$908$	−2.60291	−	4.50837i	−0.0863805	−	0.149615i
$909$	−3.94310	−	6.82965i	−0.130784	−	0.226525i
$910$	−2.39251	−	4.14394i	−0.0793108	−	0.137370i
$911$	−3.19642	+	5.53636i	−0.105902	+	0.183428i	−0.914106	−	0.405474i	$-0.867106\pi$
$911$	−3.19642	+	5.53636i	−0.105902	+	0.183428i	0.808204	+	0.588902i	$0.200440\pi$
$912$	24.9601	+	43.2322i	0.826513	+	1.43156i
$913$	12.3323	−	21.3602i	0.408140	−	0.706919i
$914$	14.5759			0.482129
$915$	−15.5613			−0.514442
$916$	−6.45975	+	11.1886i	−0.213436	+	0.369683i
$917$	−1.67099	−	2.89424i	−0.0551809	−	0.0955761i
$918$	7.16964	−	12.4182i	0.236633	−	0.409861i
$919$	13.6444	+	23.6328i	0.450088	+	0.779576i	0.998391	−	0.0567043i	$-0.0180592\pi$
$919$	13.6444	+	23.6328i	0.450088	+	0.779576i	−0.548303	+	0.836280i	$0.684726\pi$
$920$	−15.7517	−	27.2827i	−0.519318	−	0.899484i
$921$	19.0875	+	33.0605i	0.628954	+	1.08938i
$922$	−45.3331			−1.49297
$923$	−4.58252	+	7.93715i	−0.150835	+	0.261255i
$924$	−3.18971	+	5.52474i	−0.104934	+	0.181750i
$925$	−5.97843	−	10.3549i	−0.196570	−	0.340469i
$926$	−22.6205			−0.743357
$927$	−23.5703	+	40.8250i	−0.774151	+	1.34087i
$928$	3.33937			0.109620
$929$	−6.67079			−0.218861			−0.109431	−	0.993994i	$-0.534903\pi$
$929$	−6.67079			−0.218861			−0.109431	+	0.993994i	$0.534903\pi$
$930$		0			0
$931$	−35.6793			−1.16934
$932$	−5.14671			−0.168586
$933$	−27.1166	+	46.9674i	−0.887759	+	1.53764i
$934$	6.22487			0.203684
$935$	21.0645	+	36.4848i	0.688884	+	1.19318i
$936$	7.75725	−	13.4360i	0.253554	−	0.439168i
$937$	−0.232350	+	0.402443i	−0.00759056	+	0.0131472i	−0.869796	−	0.493412i	$-0.835750\pi$
$937$	−0.232350	+	0.402443i	−0.00759056	+	0.0131472i	0.862205	+	0.506559i	$0.169083\pi$
$938$	−18.0123			−0.588123
$939$	−12.1155	−	20.9846i	−0.395373	−	0.684807i
$940$	0.443948	+	0.768941i	0.0144800	+	0.0250801i
$941$	−21.4150	−	37.0918i	−0.698108	−	1.20916i	−0.969122	−	0.246583i	$-0.920692\pi$
$941$	−21.4150	−	37.0918i	−0.698108	−	1.20916i	0.271013	−	0.962576i	$-0.412641\pi$
$942$	−30.2422	+	52.3810i	−0.985344	+	1.70667i
$943$	−4.11773	−	7.13212i	−0.134092	−	0.232254i
$944$	5.78434	−	10.0188i	0.188264	−	0.326083i
$945$	9.92887			0.322986
$946$	−51.5345			−1.67553
$947$	−11.6590	+	20.1939i	−0.378866	+	0.656215i	−0.990898	−	0.134618i	$-0.957019\pi$
$947$	−11.6590	+	20.1939i	−0.378866	+	0.656215i	0.612032	+	0.790833i	$0.290352\pi$
$948$	−5.69777	−	9.86882i	−0.185055	−	0.320524i
$949$	6.04531	−	10.4708i	0.196239	−	0.339896i
$950$	7.43698	+	12.8812i	0.241288	+	0.417922i
$951$	40.2461	+	69.7083i	1.30507	+	2.26045i
$952$	−6.72116	−	11.6414i	−0.217834	−	0.377300i
$953$	24.9169			0.807138			0.403569	−	0.914949i	$-0.367770\pi$
$953$	24.9169			0.807138			0.403569	+	0.914949i	$0.367770\pi$
$954$	−12.2529	+	21.2226i	−0.396701	+	0.687107i
$955$	−24.9024	+	43.1323i	−0.805824	+	1.39573i
$956$	−5.66917	−	9.81930i	−0.183354	−	0.317579i
$957$	15.7871			0.510323
$958$	−1.64595	+	2.85086i	−0.0531781	+	0.0921072i
$959$	−12.4569			−0.402253
$960$	62.4234			2.01470
$961$		0			0
$962$	9.76256			0.314758
$963$	20.2169			0.651482
$964$	2.33326	−	4.04132i	0.0751492	−	0.130162i
$965$	−55.3539			−1.78190
$966$	7.92247	+	13.7221i	0.254901	+	0.441502i
$967$	−11.2887	+	19.5526i	−0.363021	+	0.628771i	−0.988456	−	0.151505i	$-0.951588\pi$
$967$	−11.2887	+	19.5526i	−0.363021	+	0.628771i	0.625436	+	0.780276i	$0.284921\pi$
$968$	−12.7090	+	22.0127i	−0.408484	+	0.707515i
$969$	63.0146			2.02432
$970$	−7.35234	−	12.7346i	−0.236069	−	0.408884i
$971$	3.04810	+	5.27947i	0.0978183	+	0.169426i	0.910781	−	0.412889i	$-0.135480\pi$
$971$	3.04810	+	5.27947i	0.0978183	+	0.169426i	−0.812963	+	0.582315i	$0.802147\pi$
$972$	−4.58862	−	7.94773i	−0.147180	−	0.254923i
$973$	0.193201	−	0.334634i	0.00619374	−	0.0107279i
$974$	14.5495	+	25.2005i	0.466197	+	0.807477i
$975$	3.03149	−	5.25069i	0.0970852	−	0.168157i
$976$	6.42993			0.205817
$977$	−13.4726			−0.431027			−0.215514	−	0.976501i	$-0.569143\pi$
$977$	−13.4726			−0.431027			−0.215514	+	0.976501i	$0.569143\pi$
$978$	−13.1104	+	22.7080i	−0.419226	+	0.726120i
$979$	−30.6564	−	53.0984i	−0.979782	−	1.69703i
$980$	−3.26721	+	5.65897i	−0.104367	+	0.180769i
$981$	26.5871	+	46.0501i	0.848860	+	1.47027i
$982$	−3.11086	−	5.38817i	−0.0992716	−	0.171944i
$983$	−9.37992	−	16.2465i	−0.299173	−	0.518183i	0.676774	−	0.736191i	$-0.263377\pi$
$983$	−9.37992	−	16.2465i	−0.299173	−	0.518183i	−0.975947	+	0.218008i	$0.930044\pi$
$984$	17.0600			0.543853
$985$	−8.35597	+	14.4730i	−0.266243	+	0.461147i
$986$	−3.05315	+	5.28821i	−0.0972322	+	0.168411i
$987$	−1.21642	−	2.10690i	−0.0387190	−	0.0670632i
$988$	3.52240			0.112063
$989$	18.5628	−	32.1517i	0.590263	−	1.02237i
$990$	59.8587			1.90243
$991$	57.0730			1.81298			0.906491	−	0.422225i	$-0.138751\pi$
$991$	57.0730			1.81298			0.906491	+	0.422225i	$0.138751\pi$
$992$		0			0
$993$	−40.8938			−1.29773
$994$	11.2828			0.357868
$995$	20.2441	−	35.0638i	0.641780	−	1.11160i
$996$	−6.75654			−0.214089
$997$	12.4444	+	21.5544i	0.394119	+	0.682635i	0.992988	−	0.118212i	$-0.0377163\pi$
$997$	12.4444	+	21.5544i	0.394119	+	0.682635i	−0.598869	+	0.800847i	$0.704383\pi$
$998$	10.8170	−	18.7355i	0.342405	−	0.593063i
$999$	−10.1286	+	17.5433i	−0.320456	+	0.555046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.k.439.5		24
31.2	even	5		961.2.g.v.547.6		96
31.3	odd	30		961.2.g.v.448.5		96
31.4	even	5		961.2.g.v.235.8		96
31.5	even	3		961.2.a.k.1.6	yes	12
31.6	odd	6	inner	961.2.c.k.521.6		24
31.7	even	15		961.2.g.v.338.7		96
31.8	even	5		961.2.g.v.816.7		96
31.9	even	15		961.2.d.r.374.7		48
31.10	even	15		961.2.d.r.531.6		48
31.11	odd	30		961.2.d.r.388.8		48
31.12	odd	30		961.2.g.v.844.6		96
31.13	odd	30		961.2.d.r.628.5		48
31.14	even	15		961.2.g.v.732.8		96
31.15	odd	10		961.2.g.v.846.6		96
31.16	even	5		961.2.g.v.846.5		96
31.17	odd	30		961.2.g.v.732.7		96
31.18	even	15		961.2.d.r.628.6		48
31.19	even	15		961.2.g.v.844.5		96
31.20	even	15		961.2.d.r.388.7		48
31.21	odd	30		961.2.d.r.531.5		48
31.22	odd	30		961.2.d.r.374.8		48
31.23	odd	10		961.2.g.v.816.8		96
31.24	odd	30		961.2.g.v.338.8		96
31.25	even	3	inner	961.2.c.k.521.5		24
31.26	odd	6		961.2.a.k.1.5	✓	12
31.27	odd	10		961.2.g.v.235.7		96
31.28	even	15		961.2.g.v.448.6		96
31.29	odd	10		961.2.g.v.547.5		96
31.30	odd	2	inner	961.2.c.k.439.6		24
93.5	odd	6		8649.2.a.bp.1.8		12
93.26	even	6		8649.2.a.bp.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.5	✓	12	31.26	odd	6
961.2.a.k.1.6	yes	12	31.5	even	3
961.2.c.k.439.5		24	1.1	even	1	trivial
961.2.c.k.439.6		24	31.30	odd	2	inner
961.2.c.k.521.5		24	31.25	even	3	inner
961.2.c.k.521.6		24	31.6	odd	6	inner
961.2.d.r.374.7		48	31.9	even	15
961.2.d.r.374.8		48	31.22	odd	30
961.2.d.r.388.7		48	31.20	even	15
961.2.d.r.388.8		48	31.11	odd	30
961.2.d.r.531.5		48	31.21	odd	30
961.2.d.r.531.6		48	31.10	even	15
961.2.d.r.628.5		48	31.13	odd	30
961.2.d.r.628.6		48	31.18	even	15
961.2.g.v.235.7		96	31.27	odd	10
961.2.g.v.235.8		96	31.4	even	5
961.2.g.v.338.7		96	31.7	even	15
961.2.g.v.338.8		96	31.24	odd	30
961.2.g.v.448.5		96	31.3	odd	30
961.2.g.v.448.6		96	31.28	even	15
961.2.g.v.547.5		96	31.29	odd	10
961.2.g.v.547.6		96	31.2	even	5
961.2.g.v.732.7		96	31.17	odd	30
961.2.g.v.732.8		96	31.14	even	15
961.2.g.v.816.7		96	31.8	even	5
961.2.g.v.816.8		96	31.23	odd	10
961.2.g.v.844.5		96	31.19	even	15
961.2.g.v.844.6		96	31.12	odd	30
961.2.g.v.846.5		96	31.16	even	5
961.2.g.v.846.6		96	31.15	odd	10
8649.2.a.bp.1.7		12	93.26	even	6
8649.2.a.bp.1.8		12	93.5	odd	6

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.24512 q^{2} +(-1.33932 + 2.31977i) q^{3} -0.449667 q^{4} +(-1.30938 - 2.26791i) q^{5} +(1.66762 - 2.88840i) q^{6} +(-0.602271 + 1.04316i) q^{7} +3.05014 q^{8} +(-2.08754 - 3.61573i) q^{9} +(1.63034 + 2.82383i) q^{10} +(2.19849 + 3.80789i) q^{11} +(0.602246 - 1.04312i) q^{12} +(0.609148 + 1.05508i) q^{13} +(0.749903 - 1.29887i) q^{14} +7.01469 q^{15} -2.89847 q^{16} +(-1.82937 + 3.16857i) q^{17} +(2.59925 + 4.50203i) q^{18} +(-3.21488 + 5.56834i) q^{19} +(0.588784 + 1.01980i) q^{20} +(-1.61327 - 2.79426i) q^{21} +(-2.73739 - 4.74130i) q^{22} +3.94405 q^{23} +(-4.08510 + 7.07561i) q^{24} +(-0.928943 + 1.60898i) q^{25} +(-0.758465 - 1.31370i) q^{26} +3.14762 q^{27} +(0.270821 - 0.469076i) q^{28} -1.34040 q^{29} -8.73416 q^{30} -2.49133 q^{32} -11.7779 q^{33} +(2.27780 - 3.94526i) q^{34} +3.15440 q^{35} +(0.938698 + 1.62587i) q^{36} +(-3.21787 + 5.57351i) q^{37} +(4.00293 - 6.93327i) q^{38} -3.26337 q^{39} +(-3.99378 - 6.91744i) q^{40} +(-1.04404 - 1.80833i) q^{41} +(2.00872 + 3.47920i) q^{42} +(4.70654 - 8.15196i) q^{43} +(-0.988587 - 1.71228i) q^{44} +(-5.46676 + 9.46871i) q^{45} -4.91083 q^{46} +0.754009 q^{47} +(3.88197 - 6.72376i) q^{48} +(2.77454 + 4.80564i) q^{49} +(1.15665 - 2.00337i) q^{50} +(-4.90022 - 8.48743i) q^{51} +(-0.273914 - 0.474432i) q^{52} +(2.35700 + 4.08245i) q^{53} -3.91918 q^{54} +(5.75731 - 9.97195i) q^{55} +(-1.83701 + 3.18180i) q^{56} +(-8.61150 - 14.9156i) q^{57} +1.66896 q^{58} +(-1.99565 + 3.45658i) q^{59} -3.15427 q^{60} -2.21839 q^{61} +5.02907 q^{63} +8.89894 q^{64} +(1.59521 - 2.76299i) q^{65} +14.6649 q^{66} +(-6.00489 - 10.4008i) q^{67} +(0.822608 - 1.42480i) q^{68} +(-5.28233 + 9.14927i) q^{69} -3.92762 q^{70} +(3.76141 + 6.51496i) q^{71} +(-6.36729 - 11.0285i) q^{72} +(-4.96210 - 8.59461i) q^{73} +(4.00664 - 6.93971i) q^{74} +(-2.48830 - 4.30986i) q^{75} +(1.44563 - 2.50390i) q^{76} -5.29635 q^{77} +4.06330 q^{78} +(4.73043 - 8.19334i) q^{79} +(3.79519 + 6.57346i) q^{80} +(2.04696 - 3.54544i) q^{81} +(1.29996 + 2.25159i) q^{82} +(-2.80472 - 4.85793i) q^{83} +(0.725432 + 1.25648i) q^{84} +9.58136 q^{85} +(-5.86022 + 10.1502i) q^{86} +(1.79522 - 3.10941i) q^{87} +(6.70570 + 11.6146i) q^{88} -13.9443 q^{89} +(6.80680 - 11.7897i) q^{90} -1.46749 q^{91} -1.77351 q^{92} -0.938835 q^{94} +16.8380 q^{95} +(3.33668 - 5.77930i) q^{96} -4.50970 q^{97} +(-3.45464 - 5.98362i) q^{98} +(9.17888 - 15.8983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 32 q^{4} - 8 q^{5} - 8 q^{7} + 24 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} - 32 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} - 12 q^{25} + 20 q^{28} + 48 q^{32} - 80 q^{33} + 112 q^{35} - 40 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) \) 24 * q + 32 * q^4 - 8 * q^5 - 8 * q^7 + 24 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 - 32 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 - 12 * q^25 + 20 * q^28 + 48 * q^32 - 80 * q^33 + 112 * q^35 - 40 * q^36 - 36 * q^38 - 32 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 + 96 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 + 8 * q^56 - 40 * q^59 - 16 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 24 * q^69 + 24 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 - 208 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 - 64 * q^87 + 44 * q^90 + 32 * q^94 + 80 * q^95 - 16 * q^97 - 4 * q^98

Introduction

L-functions

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