LMFDB - Embedded newform 425.2.k.c.86.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.9
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.135768 + 0.0986414i) q^{2} +(-0.267848 + 0.824353i) q^{3} +(-0.609331 + 1.87533i) q^{4} +(1.96067 + 1.07508i) q^{5} +(-0.0449500 - 0.138342i) q^{6} +2.33732 q^{7} +(-0.205975 - 0.633926i) q^{8} +(1.81924 + 1.32175i) q^{9} +(-0.372243 + 0.0474416i) q^{10} +(0.599060 - 0.435242i) q^{11} +(-1.38272 - 1.00461i) q^{12} +(-1.35955 - 0.987768i) q^{13} +(-0.317333 + 0.230556i) q^{14} +(-1.41140 + 1.32832i) q^{15} +(-3.10000 - 2.25228i) q^{16} +(-0.309017 - 0.951057i) q^{17} -0.377374 q^{18} +(0.352165 + 1.08385i) q^{19} +(-3.21082 + 3.02182i) q^{20} +(-0.626046 + 1.92677i) q^{21} +(-0.0384004 + 0.118184i) q^{22} +(1.57595 - 1.14500i) q^{23} +0.577748 q^{24} +(2.68842 + 4.21573i) q^{25} +0.282018 q^{26} +(-3.68058 + 2.67410i) q^{27} +(-1.42420 + 4.38324i) q^{28} +(-2.55643 + 7.86787i) q^{29} +(0.0605961 - 0.319567i) q^{30} +(-1.61653 - 4.97516i) q^{31} +1.97615 q^{32} +(0.198336 + 0.610415i) q^{33} +(0.135768 + 0.0986414i) q^{34} +(4.58270 + 2.51279i) q^{35} +(-3.58724 + 2.60628i) q^{36} +(-4.68730 - 3.40552i) q^{37} +(-0.154726 - 0.112415i) q^{38} +(1.17842 - 0.856173i) q^{39} +(0.277670 - 1.46436i) q^{40} +(-3.40711 - 2.47541i) q^{41} +(-0.105062 - 0.323349i) q^{42} +7.20187 q^{43} +(0.451197 + 1.38864i) q^{44} +(2.14593 + 4.54733i) q^{45} +(-0.101020 + 0.310909i) q^{46} +(0.925941 - 2.84975i) q^{47} +(2.68701 - 1.95222i) q^{48} -1.53695 q^{49} +(-0.780848 - 0.307173i) q^{50} +0.866776 q^{51} +(2.68080 - 1.94772i) q^{52} +(0.912506 - 2.80840i) q^{53} +(0.235929 - 0.726115i) q^{54} +(1.64247 - 0.209330i) q^{55} +(-0.481429 - 1.48168i) q^{56} -0.987803 q^{57} +(-0.429016 - 1.32038i) q^{58} +(2.73261 + 1.98535i) q^{59} +(-1.63103 - 3.45623i) q^{60} +(-2.94584 + 2.14028i) q^{61} +(0.710230 + 0.516012i) q^{62} +(4.25213 + 3.08935i) q^{63} +(5.93171 - 4.30964i) q^{64} +(-1.60369 - 3.39830i) q^{65} +(-0.0871399 - 0.0633109i) q^{66} +(-2.03304 - 6.25706i) q^{67} +1.97184 q^{68} +(0.521765 + 1.60583i) q^{69} +(-0.870050 + 0.110886i) q^{70} +(0.479377 - 1.47537i) q^{71} +(0.463176 - 1.42551i) q^{72} +(10.2810 - 7.46961i) q^{73} +0.972312 q^{74} +(-4.19534 + 1.08703i) q^{75} -2.24716 q^{76} +(1.40019 - 1.01730i) q^{77} +(-0.0755380 + 0.232482i) q^{78} +(0.804955 - 2.47740i) q^{79} +(-3.65669 - 7.74872i) q^{80} +(0.866098 + 2.66558i) q^{81} +0.706755 q^{82} +(-0.855933 - 2.63429i) q^{83} +(-3.23186 - 2.34809i) q^{84} +(0.416579 - 2.19692i) q^{85} +(-0.977785 + 0.710402i) q^{86} +(-5.80117 - 4.21479i) q^{87} +(-0.399303 - 0.290110i) q^{88} +(-6.88427 + 5.00172i) q^{89} +(-0.739905 - 0.405706i) q^{90} +(-3.17769 - 2.30873i) q^{91} +(1.18697 + 3.65311i) q^{92} +4.53427 q^{93} +(0.155390 + 0.478242i) q^{94} +(-0.474746 + 2.50368i) q^{95} +(-0.529308 + 1.62904i) q^{96} +(3.90595 - 12.0213i) q^{97} +(0.208669 - 0.151607i) q^{98} +1.66511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.135768	+	0.0986414i	−0.0960027	+	0.0697500i	−0.634751	−	0.772717i	$-0.718897\pi$
$2$	−0.135768	+	0.0986414i	−0.0960027	+	0.0697500i	0.538748	+	0.842467i	$0.318897\pi$
$3$	−0.267848	+	0.824353i	−0.154642	+	0.475940i	−0.998124	−	0.0612171i	$-0.980502\pi$
$3$	−0.267848	+	0.824353i	−0.154642	+	0.475940i	0.843482	+	0.537157i	$0.180502\pi$
$4$	−0.609331	+	1.87533i	−0.304666	+	0.937664i
$5$	1.96067	+	1.07508i	0.876836	+	0.480789i
$5$	1.96067	+	1.07508i	0.876836	+	0.480789i
$6$	−0.0449500	−	0.138342i	−0.0183508	−	0.0564778i
$7$	2.33732			0.883423			0.441711	−	0.897157i	$-0.354372\pi$
$7$	2.33732			0.883423			0.441711	+	0.897157i	$0.354372\pi$
$8$	−0.205975	−	0.633926i	−0.0728231	−	0.224127i
$9$	1.81924	+	1.32175i	0.606412	+	0.440584i
$10$	−0.372243	+	0.0474416i	−0.117714	+	0.0150024i
$11$	0.599060	−	0.435242i	0.180623	−	0.131230i	−0.493800	−	0.869576i	$-0.664392\pi$
$11$	0.599060	−	0.435242i	0.180623	−	0.131230i	0.674423	+	0.738345i	$0.264392\pi$
$12$	−1.38272	−	1.00461i	−0.399158	−	0.290005i
$13$	−1.35955	−	0.987768i	−0.377070	−	0.273957i	0.383067	−	0.923721i	$-0.374868\pi$
$13$	−1.35955	−	0.987768i	−0.377070	−	0.273957i	−0.760137	+	0.649763i	$0.774868\pi$
$14$	−0.317333	+	0.230556i	−0.0848109	+	0.0616187i
$15$	−1.41140	+	1.32832i	−0.364423	+	0.342971i
$16$	−3.10000	−	2.25228i	−0.775001	−	0.563071i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−0.377374			−0.0889479
$19$	0.352165	+	1.08385i	0.0807922	+	0.248653i	0.983291	−	0.182039i	$-0.0582697\pi$
$19$	0.352165	+	1.08385i	0.0807922	+	0.248653i	−0.902499	+	0.430692i	$0.858270\pi$
$20$	−3.21082	+	3.02182i	−0.717960	+	0.675698i
$21$	−0.626046	+	1.92677i	−0.136615	+	0.420456i
$22$	−0.0384004	+	0.118184i	−0.00818699	+	0.0251970i
$23$	1.57595	−	1.14500i	0.328609	−	0.238749i	−0.411231	−	0.911531i	$-0.634901\pi$
$23$	1.57595	−	1.14500i	0.328609	−	0.238749i	0.739840	+	0.672783i	$0.234901\pi$
$24$	0.577748			0.117932
$25$	2.68842	+	4.21573i	0.537684	+	0.843146i
$26$	0.282018			0.0553083
$27$	−3.68058	+	2.67410i	−0.708328	+	0.514630i
$28$	−1.42420	+	4.38324i	−0.269148	+	0.828354i
$29$	−2.55643	+	7.86787i	−0.474717	+	1.46103i	0.371623	+	0.928384i	$0.378801\pi$
$29$	−2.55643	+	7.86787i	−0.474717	+	1.46103i	−0.846340	+	0.532644i	$0.821199\pi$
$30$	0.0605961	−	0.319567i	0.0110633	−	0.0583447i
$31$	−1.61653	−	4.97516i	−0.290337	−	0.893565i	−0.984748	−	0.173987i	$-0.944335\pi$
$31$	−1.61653	−	4.97516i	−0.290337	−	0.893565i	0.694411	−	0.719578i	$-0.255665\pi$
$32$	1.97615			0.349337
$33$	0.198336	+	0.610415i	0.0345259	+	0.106260i
$34$	0.135768	+	0.0986414i	0.0232841	+	0.0169169i
$35$	4.58270	+	2.51279i	0.774617	+	0.424740i
$36$	−3.58724	+	2.60628i	−0.597873	+	0.434380i
$37$	−4.68730	−	3.40552i	−0.770587	−	0.559864i	0.131552	−	0.991309i	$-0.458004\pi$
$37$	−4.68730	−	3.40552i	−0.770587	−	0.559864i	−0.902139	+	0.431445i	$0.858004\pi$
$38$	−0.154726	−	0.112415i	−0.0250998	−	0.0182361i
$39$	1.17842	−	0.856173i	0.188698	−	0.137097i
$40$	0.277670	−	1.46436i	0.0439035	−	0.231535i
$41$	−3.40711	−	2.47541i	−0.532101	−	0.386594i	0.289042	−	0.957316i	$-0.406663\pi$
$41$	−3.40711	−	2.47541i	−0.532101	−	0.386594i	−0.821143	+	0.570722i	$0.806663\pi$
$42$	−0.105062	−	0.323349i	−0.0162115	−	0.0498938i
$43$	7.20187			1.09827			0.549137	−	0.835732i	$-0.314956\pi$
$43$	7.20187			1.09827			0.549137	+	0.835732i	$0.314956\pi$
$44$	0.451197	+	1.38864i	0.0680204	+	0.209345i
$45$	2.14593	+	4.54733i	0.319896	+	0.677877i
$46$	−0.101020	+	0.310909i	−0.0148946	+	0.0458410i
$47$	0.925941	−	2.84975i	0.135062	−	0.415679i	−0.860537	−	0.509387i	$-0.829872\pi$
$47$	0.925941	−	2.84975i	0.135062	−	0.415679i	0.995600	+	0.0937081i	$0.0298720\pi$
$48$	2.68701	−	1.95222i	0.387836	−	0.281779i
$49$	−1.53695			−0.219565
$50$	−0.780848	−	0.307173i	−0.110429	−	0.0434408i
$51$	0.866776			0.121373
$52$	2.68080	−	1.94772i	0.371760	−	0.270100i
$53$	0.912506	−	2.80840i	0.125342	−	0.385764i	−0.868621	−	0.495477i	$-0.834993\pi$
$53$	0.912506	−	2.80840i	0.125342	−	0.385764i	0.993963	+	0.109713i	$0.0349932\pi$
$54$	0.235929	−	0.726115i	0.0321059	−	0.0988117i
$55$	1.64247	−	0.209330i	0.221471	−	0.0282261i
$56$	−0.481429	−	1.48168i	−0.0643336	−	0.197998i
$57$	−0.987803			−0.130838
$58$	−0.429016	−	1.32038i	−0.0563326	−	0.173374i
$59$	2.73261	+	1.98535i	0.355755	+	0.258471i	0.751279	−	0.659984i	$-0.229437\pi$
$59$	2.73261	+	1.98535i	0.355755	+	0.258471i	−0.395524	+	0.918455i	$0.629437\pi$
$60$	−1.63103	−	3.45623i	−0.210565	−	0.446198i
$61$	−2.94584	+	2.14028i	−0.377176	+	0.274035i	−0.760180	−	0.649712i	$-0.774890\pi$
$61$	−2.94584	+	2.14028i	−0.377176	+	0.274035i	0.383004	+	0.923747i	$0.374890\pi$
$62$	0.710230	+	0.516012i	0.0901993	+	0.0655336i
$63$	4.25213	+	3.08935i	0.535718	+	0.389222i
$64$	5.93171	−	4.30964i	0.741463	−	0.538705i
$65$	−1.60369	−	3.39830i	−0.198913	−	0.421507i
$66$	−0.0871399	−	0.0633109i	−0.0107262	−	0.00779303i
$67$	−2.03304	−	6.25706i	−0.248376	−	0.764422i	−0.995063	−	0.0992466i	$-0.968357\pi$
$67$	−2.03304	−	6.25706i	−0.248376	−	0.764422i	0.746687	−	0.665175i	$-0.231643\pi$
$68$	1.97184			0.239120
$69$	0.521765	+	1.60583i	0.0628131	+	0.193319i
$70$	−0.870050	+	0.110886i	−0.103991	+	0.0132534i
$71$	0.479377	−	1.47537i	0.0568916	−	0.175094i	−0.918573	−	0.395252i	$-0.870657\pi$
$71$	0.479377	−	1.47537i	0.0568916	−	0.175094i	0.975464	+	0.220158i	$0.0706572\pi$
$72$	0.463176	−	1.42551i	0.0545858	−	0.167998i
$73$	10.2810	−	7.46961i	1.20330	−	0.874252i	0.208699	−	0.977980i	$-0.433077\pi$
$73$	10.2810	−	7.46961i	1.20330	−	0.874252i	0.994606	+	0.103728i	$0.0330771\pi$
$74$	0.972312			0.113029
$75$	−4.19534	+	1.08703i	−0.484436	+	0.125520i
$76$	−2.24716			−0.257767
$77$	1.40019	−	1.01730i	0.159567	−	0.115932i
$78$	−0.0755380	+	0.232482i	−0.00855300	+	0.0263234i
$79$	0.804955	−	2.47740i	0.0905645	−	0.278729i	−0.895508	−	0.445046i	$-0.853187\pi$
$79$	0.804955	−	2.47740i	0.0905645	−	0.278729i	0.986072	+	0.166317i	$0.0531874\pi$
$80$	−3.65669	−	7.74872i	−0.408831	−	0.866333i
$81$	0.866098	+	2.66558i	0.0962332	+	0.296175i
$82$	0.706755			0.0780481
$83$	−0.855933	−	2.63429i	−0.0939508	−	0.289151i	0.893028	−	0.450001i	$-0.148576\pi$
$83$	−0.855933	−	2.63429i	−0.0939508	−	0.289151i	−0.986979	+	0.160850i	$0.948576\pi$
$84$	−3.23186	−	2.34809i	−0.352625	−	0.256197i
$85$	0.416579	−	2.19692i	0.0451844	−	0.238290i
$86$	−0.977785	+	0.710402i	−0.105437	+	0.0766047i
$87$	−5.80117	−	4.21479i	−0.621950	−	0.451873i
$88$	−0.399303	−	0.290110i	−0.0425658	−	0.0309259i
$89$	−6.88427	+	5.00172i	−0.729731	+	0.530181i	−0.889478	−	0.456977i	$-0.848932\pi$
$89$	−6.88427	+	5.00172i	−0.729731	+	0.530181i	0.159747	+	0.987158i	$0.448932\pi$
$90$	−0.739905	−	0.405706i	−0.0779928	−	0.0427652i
$91$	−3.17769	−	2.30873i	−0.333112	−	0.242020i
$92$	1.18697	+	3.65311i	0.123750	+	0.380863i
$93$	4.53427			0.470182
$94$	0.155390	+	0.478242i	0.0160273	+	0.0493269i
$95$	−0.474746	+	2.50368i	−0.0487079	+	0.256872i
$96$	−0.529308	+	1.62904i	−0.0540223	+	0.166263i
$97$	3.90595	−	12.0213i	0.396589	−	1.22058i	−0.531128	−	0.847292i	$-0.678232\pi$
$97$	3.90595	−	12.0213i	0.396589	−	1.22058i	0.927717	−	0.373284i	$-0.121768\pi$
$98$	0.208669	−	0.151607i	0.0210788	−	0.0153146i
$99$	1.66511			0.167350
$100$	−9.54402	+	2.47290i	−0.954402	+	0.247290i
$101$	−7.28612			−0.724996			−0.362498	−	0.931985i	$-0.618076\pi$
$101$	−7.28612			−0.724996			−0.362498	+	0.931985i	$0.618076\pi$
$102$	−0.117681	+	0.0855000i	−0.0116521	+	0.00846576i
$103$	1.53266	−	4.71706i	0.151018	−	0.464785i	−0.846718	−	0.532042i	$-0.821425\pi$
$103$	1.53266	−	4.71706i	0.151018	−	0.464785i	0.997736	+	0.0672570i	$0.0214247\pi$
$104$	−0.346139	+	1.06531i	−0.0339417	+	0.104462i
$105$	−3.29890	+	3.10471i	−0.321939	+	0.302989i
$106$	0.153136	+	0.471303i	0.0148738	+	0.0457770i
$107$	11.2433			1.08694			0.543468	−	0.839430i	$-0.317111\pi$
$107$	11.2433			1.08694			0.543468	+	0.839430i	$0.317111\pi$
$108$	−2.77212	−	8.53170i	−0.266747	−	0.820963i
$109$	3.38845	+	2.46185i	0.324554	+	0.235803i	0.738116	−	0.674673i	$-0.235716\pi$
$109$	3.38845	+	2.46185i	0.324554	+	0.235803i	−0.413562	+	0.910476i	$0.635716\pi$
$110$	−0.202347	+	0.190436i	−0.0192931	+	0.0181574i
$111$	4.06284	−	2.95182i	0.385627	−	0.280175i
$112$	−7.24569	−	5.26430i	−0.684653	−	0.497430i
$113$	4.40482	+	3.20029i	0.414370	+	0.301058i	0.775369	−	0.631509i	$-0.217564\pi$
$113$	4.40482	+	3.20029i	0.414370	+	0.301058i	−0.360998	+	0.932566i	$0.617564\pi$
$114$	0.134112	−	0.0974383i	0.0125608	−	0.00912593i
$115$	4.32088	−	0.550687i	0.402924	−	0.0513519i
$116$	−13.1971	−	9.58828i	−1.22532	−	0.890249i
$117$	−1.16775	−	3.59397i	−0.107959	−	0.332262i
$118$	−0.566839			−0.0521818
$119$	−0.722271	−	2.22292i	−0.0662104	−	0.203775i
$120$	1.13277	+	0.621123i	0.103407	+	0.0567006i
$121$	−3.22975	+	9.94015i	−0.293614	+	0.903650i
$122$	0.188832	−	0.581164i	0.0170960	−	0.0526161i
$123$	2.95320	−	2.14562i	0.266281	−	0.193464i
$124$	10.3151			0.926319
$125$	0.738866	+	11.1559i	0.0660862	+	0.997814i
$126$	−0.882043			−0.0785786
$127$	5.07819	−	3.68952i	0.450617	−	0.327392i	−0.339222	−	0.940706i	$-0.610164\pi$
$127$	5.07819	−	3.68952i	0.450617	−	0.327392i	0.789839	+	0.613314i	$0.210164\pi$
$128$	−1.60156	+	4.92908i	−0.141559	+	0.435673i
$129$	−1.92901	+	5.93688i	−0.169840	+	0.522713i
$130$	0.552943	+	0.303191i	0.0484963	+	0.0265916i
$131$	0.635371	+	1.95547i	0.0555126	+	0.170850i	0.974969	−	0.222343i	$-0.0713704\pi$
$131$	0.635371	+	1.95547i	0.0555126	+	0.170850i	−0.919456	+	0.393193i	$0.871370\pi$
$132$	−1.26558			−0.110155
$133$	0.823121	+	2.53331i	0.0713736	+	0.219665i
$134$	0.893229	+	0.648969i	0.0771632	+	0.0560623i
$135$	−10.0912	+	1.28611i	−0.868516	+	0.110691i
$136$	−0.539249	+	0.391788i	−0.0462403	+	0.0335955i
$137$	−1.46629	−	1.06532i	−0.125274	−	0.0910168i	0.523384	−	0.852097i	$-0.324669\pi$
$137$	−1.46629	−	1.06532i	−0.125274	−	0.0910168i	−0.648658	+	0.761080i	$0.724669\pi$
$138$	−0.229240	−	0.166553i	−0.0195142	−	0.0141779i
$139$	13.6401	−	9.91012i	1.15694	−	0.840566i	0.167551	−	0.985863i	$-0.446414\pi$
$139$	13.6401	−	9.91012i	1.15694	−	0.840566i	0.989388	+	0.145298i	$0.0464140\pi$
$140$	−7.50469	+	7.06294i	−0.634262	+	0.596927i
$141$	2.10119	+	1.52660i	0.176952	+	0.128563i
$142$	0.0804485	+	0.247595i	0.00675109	+	0.0207777i
$143$	−1.24437			−0.104059
$144$	−2.66268	−	8.19488i	−0.221890	−	0.682906i
$145$	−13.4709	+	12.6779i	−1.11869	+	1.05284i
$146$	−0.659026	+	2.02827i	−0.0545414	+	0.167861i
$147$	0.411670	−	1.26699i	0.0339540	−	0.104500i
$148$	9.24259	−	6.71513i	0.759736	−	0.551981i
$149$	5.74751			0.470855			0.235427	−	0.971892i	$-0.424351\pi$
$149$	5.74751			0.470855			0.235427	+	0.971892i	$0.424351\pi$
$150$	0.462367	−	0.561418i	0.0377521	−	0.0458396i
$151$	10.0338			0.816536			0.408268	−	0.912862i	$-0.366133\pi$
$151$	10.0338			0.816536			0.408268	+	0.912862i	$0.366133\pi$
$152$	0.614545	−	0.446493i	0.0498461	−	0.0362153i
$153$	0.694887	−	2.13864i	0.0561783	−	0.172899i
$154$	−0.0897538	+	0.276234i	−0.00723257	+	0.0222596i
$155$	2.17921	−	11.4925i	0.175038	−	0.923101i
$156$	0.887557	+	2.73162i	0.0710614	+	0.218705i
$157$	9.06169			0.723202			0.361601	−	0.932333i	$-0.382230\pi$
$157$	9.06169			0.723202			0.361601	+	0.932333i	$0.382230\pi$
$158$	0.135087	+	0.415754i	0.0107469	+	0.0330756i
$159$	2.07070	+	1.50445i	0.164217	+	0.119311i
$160$	3.87457	+	2.12451i	0.306311	+	0.167957i
$161$	3.68350	−	2.67622i	0.290301	−	0.210916i
$162$	−0.380525	−	0.276468i	−0.0298969	−	0.0217213i
$163$	−3.20279	−	2.32697i	−0.250862	−	0.182262i	0.455247	−	0.890365i	$-0.349551\pi$
$163$	−3.20279	−	2.32697i	−0.250862	−	0.182262i	−0.706109	+	0.708103i	$0.749551\pi$
$164$	6.71826	−	4.88110i	0.524608	−	0.381150i
$165$	−0.267372	+	1.41005i	−0.0208149	+	0.109772i
$166$	0.376059	+	0.273222i	0.0291878	+	0.0212062i
$167$	1.05556	+	3.24868i	0.0816816	+	0.251390i	0.983555	−	0.180611i	$-0.0578076\pi$
$167$	1.05556	+	3.24868i	0.0816816	+	0.251390i	−0.901873	+	0.432001i	$0.857808\pi$
$168$	1.35038			0.104184
$169$	−3.14454	−	9.67790i	−0.241888	−	0.744454i
$170$	0.160149	+	0.339364i	0.0122829	+	0.0260280i
$171$	−0.791913	+	2.43726i	−0.0605591	+	0.186382i
$172$	−4.38832	+	13.5059i	−0.334606	+	1.02981i
$173$	−9.97699	+	7.24871i	−0.758537	+	0.551109i	−0.898461	−	0.439053i	$-0.855314\pi$
$173$	−9.97699	+	7.24871i	−0.758537	+	0.551109i	0.139925	+	0.990162i	$0.455314\pi$
$174$	1.20337			0.0912271
$175$	6.28369	+	9.85350i	0.475003	+	0.744854i
$176$	−2.83738			−0.213875
$177$	−2.36856	+	1.72086i	−0.178032	+	0.129347i
$178$	0.441289	−	1.35815i	0.0330760	−	0.101798i
$179$	−5.44216	+	16.7492i	−0.406766	+	1.25190i	0.512645	+	0.858601i	$0.328666\pi$
$179$	−5.44216	+	16.7492i	−0.406766	+	1.25190i	−0.919411	+	0.393297i	$0.871334\pi$
$180$	−9.83533	+	1.25349i	−0.733082	+	0.0934298i
$181$	2.88990	+	8.89421i	0.214805	+	0.661101i	0.999167	+	0.0407987i	$0.0129902\pi$
$181$	2.88990	+	8.89421i	0.214805	+	0.661101i	−0.784363	+	0.620303i	$0.787010\pi$
$182$	0.659165			0.0488606
$183$	−0.975306	−	3.00168i	−0.0720967	−	0.221891i
$184$	−1.05045	−	0.763197i	−0.0774402	−	0.0562636i
$185$	−5.52903	−	11.7163i	−0.406503	−	0.861399i
$186$	−0.615610	+	0.447267i	−0.0451387	+	0.0327952i
$187$	−0.599060	−	0.435242i	−0.0438076	−	0.0318281i
$188$	4.78002	+	3.47289i	0.348619	+	0.253286i
$189$	−8.60268	+	6.25021i	−0.625753	+	0.454636i
$190$	−0.182511	−	0.386749i	−0.0132407	−	0.0280577i
$191$	−21.1484	−	15.3652i	−1.53024	−	1.11179i	−0.956104	−	0.293027i	$-0.905337\pi$
$191$	−21.1484	−	15.3652i	−1.53024	−	1.11179i	−0.574138	−	0.818759i	$-0.694663\pi$
$192$	1.96386	+	6.04415i	0.141730	+	0.436199i
$193$	−17.6472			−1.27028			−0.635138	−	0.772399i	$-0.719057\pi$
$193$	−17.6472			−1.27028			−0.635138	+	0.772399i	$0.719057\pi$
$194$	0.655492	+	2.01740i	0.0470616	+	0.144841i
$195$	3.23094	−	0.411777i	0.231372	−	0.0294879i
$196$	0.936512	−	2.88229i	0.0668937	−	0.205878i
$197$	0.759863	−	2.33862i	0.0541380	−	0.166620i	−0.920332	−	0.391139i	$-0.872081\pi$
$197$	0.759863	−	2.33862i	0.0541380	−	0.166620i	0.974470	+	0.224519i	$0.0720812\pi$
$198$	−0.226070	+	0.164249i	−0.0160661	+	0.0116727i
$199$	17.5490			1.24402			0.622009	−	0.783010i	$-0.286317\pi$
$199$	17.5490			1.24402			0.622009	+	0.783010i	$0.286317\pi$
$200$	2.11871	−	2.57259i	0.149816	−	0.181910i
$201$	5.70257			0.402229
$202$	0.989224	−	0.718713i	0.0696015	−	0.0505685i
$203$	−5.97518	+	18.3897i	−0.419375	+	1.29070i
$204$	−0.528153	+	1.62549i	−0.0369781	+	0.113807i
$205$	−4.01895	−	8.51635i	−0.280696	−	0.594808i
$206$	0.257210	+	0.791611i	0.0179207	+	0.0551541i
$207$	4.38044			0.304461
$208$	1.98986	+	6.12416i	0.137972	+	0.424634i
$209$	0.682706	+	0.496015i	0.0472238	+	0.0343101i
$210$	0.141632	−	0.746929i	0.00977356	−	0.0515430i
$211$	14.9143	−	10.8359i	1.02675	−	0.745974i	0.0590904	−	0.998253i	$-0.481180\pi$
$211$	14.9143	−	10.8359i	1.02675	−	0.745974i	0.967655	+	0.252279i	$0.0811800\pi$
$212$	4.71066	+	3.42250i	0.323530	+	0.235058i
$213$	1.08783	+	0.790351i	0.0745365	+	0.0541540i
$214$	−1.52649	+	1.10906i	−0.104349	+	0.0758138i
$215$	14.1205	+	7.74256i	0.963007	+	0.528038i
$216$	2.45329	+	1.78242i	0.166925	+	0.121278i
$217$	−3.77834	−	11.6285i	−0.256490	−	0.789395i
$218$	−0.702884			−0.0476053
$219$	3.40383	+	10.4759i	0.230010	+	0.707897i
$220$	−0.608248	+	3.20773i	−0.0410081	+	0.216265i
$221$	−0.519300	+	1.59824i	−0.0349319	+	0.107509i
$222$	−0.260432	+	0.801528i	−0.0174791	+	0.0537950i
$223$	10.0333	−	7.28964i	0.671881	−	0.488150i	−0.198773	−	0.980046i	$-0.563696\pi$
$223$	10.0333	−	7.28964i	0.671881	−	0.488150i	0.870654	+	0.491895i	$0.163696\pi$
$224$	4.61888			0.308612
$225$	−0.681278	+	11.2228i	−0.0454185	+	0.748189i
$226$	−0.913715			−0.0607794
$227$	−19.2759	+	14.0048i	−1.27939	+	0.929529i	−0.999534	−	0.0305146i	$-0.990285\pi$
$227$	−19.2759	+	14.0048i	−1.27939	+	0.929529i	−0.279852	+	0.960043i	$0.590285\pi$
$228$	0.601899	−	1.85246i	0.0398617	−	0.122682i
$229$	−2.20456	+	6.78494i	−0.145681	+	0.448361i	−0.997098	−	0.0761288i	$-0.975744\pi$
$229$	−2.20456	+	6.78494i	−0.145681	+	0.448361i	0.851417	+	0.524490i	$0.175744\pi$
$230$	−0.532318	+	0.500984i	−0.0351000	+	0.0330339i
$231$	0.463574	+	1.42673i	0.0305009	+	0.0938722i
$232$	5.51421			0.362025
$233$	7.39791	+	22.7684i	0.484653	+	1.49161i	0.832482	+	0.554052i	$0.186919\pi$
$233$	7.39791	+	22.7684i	0.484653	+	1.49161i	−0.347829	+	0.937558i	$0.613081\pi$
$234$	0.513057	+	0.372758i	0.0335396	+	0.0243680i
$235$	4.87916	−	4.59196i	0.318282	−	0.299546i
$236$	−5.38825	+	3.91479i	−0.350745	+	0.254831i
$237$	1.82664	+	1.32713i	0.118653	+	0.0862066i
$238$	0.317333	+	0.230556i	0.0205697	+	0.0149447i
$239$	−23.4153	+	17.0122i	−1.51461	+	1.10043i	−0.550532	+	0.834814i	$0.685575\pi$
$239$	−23.4153	+	17.0122i	−1.51461	+	1.10043i	−0.964079	+	0.265615i	$0.914425\pi$
$240$	7.36711	−	0.938923i	0.475545	−	0.0606072i
$241$	−14.5668	−	10.5834i	−0.938331	−	0.681737i	0.00968721	−	0.999953i	$-0.496916\pi$
$241$	−14.5668	−	10.5834i	−0.938331	−	0.681737i	−0.948018	+	0.318216i	$0.896916\pi$
$242$	−0.542013	−	1.66814i	−0.0348419	−	0.107232i
$243$	−16.0777			−1.03138
$244$	−2.21873	−	6.82856i	−0.142040	−	0.437154i
$245$	−3.01345	−	1.65234i	−0.192522	−	0.105564i
$246$	−0.189303	+	0.582615i	−0.0120695	+	0.0371462i
$247$	0.591810	−	1.82140i	0.0376560	−	0.115893i
$248$	−2.82092	+	2.04952i	−0.179128	+	0.130144i
$249$	2.40084			0.152147
$250$	−1.20075	−	1.44173i	−0.0759420	−	0.0911833i
$251$	29.8448			1.88378			0.941892	−	0.335916i	$-0.109046\pi$
$251$	29.8448			1.88378			0.941892	+	0.335916i	$0.109046\pi$
$252$	−8.38451	+	6.09170i	−0.528175	+	0.383741i
$253$	0.445739	−	1.37184i	0.0280234	−	0.0862471i
$254$	−0.325518	+	1.00184i	−0.0204248	+	0.0628610i
$255$	1.69946	+	0.931850i	0.106424	+	0.0583547i
$256$	4.26265	+	13.1191i	0.266416	+	0.819943i
$257$	−22.0356			−1.37454			−0.687271	−	0.726401i	$-0.741191\pi$
$257$	−22.0356			−1.37454			−0.687271	+	0.726401i	$0.741191\pi$
$258$	−0.323724	−	0.996320i	−0.0201542	−	0.0620282i
$259$	−10.9557	−	7.95978i	−0.680754	−	0.494597i
$260$	7.35010	−	0.936755i	0.455834	−	0.0580951i
$261$	−15.0501	+	10.9346i	−0.931580	+	0.676832i
$262$	−0.279154	−	0.202817i	−0.0172462	−	0.0125301i
$263$	8.40098	+	6.10367i	0.518027	+	0.376369i	0.815860	−	0.578249i	$-0.196264\pi$
$263$	8.40098	+	6.10367i	0.518027	+	0.376369i	−0.297833	+	0.954618i	$0.596264\pi$
$264$	0.346106	−	0.251460i	0.0213013	−	0.0154763i
$265$	4.80837	−	4.52533i	0.295376	−	0.277989i
$266$	−0.361643	−	0.262749i	−0.0221737	−	0.0161102i
$267$	−2.27924	−	7.01477i	−0.139487	−	0.429297i
$268$	12.9728			0.792443
$269$	3.84101	+	11.8214i	0.234190	+	0.720764i	0.997228	+	0.0744096i	$0.0237072\pi$
$269$	3.84101	+	11.8214i	0.234190	+	0.720764i	−0.763037	+	0.646354i	$0.776293\pi$
$270$	1.24321	−	1.17003i	0.0756592	−	0.0712056i
$271$	−6.86493	+	21.1281i	−0.417015	+	1.28344i	0.493421	+	0.869791i	$0.335746\pi$
$271$	−6.86493	+	21.1281i	−0.417015	+	1.28344i	−0.910436	+	0.413650i	$0.864254\pi$
$272$	−1.18410	+	3.64427i	−0.0717963	+	0.220966i
$273$	2.75434	−	2.00115i	0.166700	−	0.121115i
$274$	0.304161			0.0183750
$275$	3.44539	+	1.35536i	0.207765	+	0.0817312i
$276$	−3.32938			−0.200405
$277$	21.8908	−	15.9046i	1.31529	−	0.955613i	0.315310	−	0.948989i	$-0.397892\pi$
$277$	21.8908	−	15.9046i	1.31529	−	0.955613i	0.999978	−	0.00662369i	$-0.00210840\pi$
$278$	−0.874346	+	2.69096i	−0.0524398	+	0.161393i
$279$	3.63509	−	11.1876i	0.217627	−	0.669787i
$280$	0.649004	−	3.42266i	0.0387854	−	0.204543i
$281$	−4.76212	−	14.6563i	−0.284084	−	0.874321i	−0.986672	−	0.162723i	$-0.947972\pi$
$281$	−4.76212	−	14.6563i	−0.284084	−	0.874321i	0.702588	−	0.711597i	$-0.252028\pi$
$282$	−0.435861			−0.0259552
$283$	−7.98424	−	24.5730i	−0.474614	−	1.46071i	−0.846478	−	0.532424i	$-0.821281\pi$
$283$	−7.98424	−	24.5730i	−0.474614	−	1.46071i	0.371864	−	0.928287i	$-0.378719\pi$
$284$	2.47470	+	1.79798i	0.146847	+	0.106690i
$285$	−1.93675	−	1.06196i	−0.114723	−	0.0629053i
$286$	0.168946	−	0.122746i	0.00998996	−	0.00725813i
$287$	−7.96349	−	5.78582i	−0.470070	−	0.341526i
$288$	3.59508	+	2.61198i	0.211842	+	0.153912i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	0.578348	−	3.05004i	0.0339618	−	0.179105i
$291$	8.86357	+	6.43976i	0.519592	+	0.377505i
$292$	7.74342	+	23.8318i	0.453149	+	1.39465i
$293$	−28.7553			−1.67990			−0.839950	−	0.542663i	$-0.817416\pi$
$293$	−28.7553			−1.67990			−0.839950	+	0.542663i	$0.817416\pi$
$294$	0.0690860	+	0.212625i	0.00402917	+	0.0124005i
$295$	3.22332	+	6.83037i	0.187669	+	0.397680i
$296$	−1.19338	+	3.67285i	−0.0693639	+	0.213480i
$297$	−1.04101	+	3.20389i	−0.0604053	+	0.185908i
$298$	−0.780330	+	0.566943i	−0.0452033	+	0.0328421i
$299$	−3.27357			−0.189316
$300$	0.517810	−	8.53000i	0.0298958	−	0.492480i
$301$	16.8330			0.970240
$302$	−1.36227	+	0.989745i	−0.0783897	+	0.0569534i
$303$	1.95158	−	6.00633i	0.112115	−	0.345055i
$304$	1.34943	−	4.15312i	0.0773952	−	0.238198i
$305$	−8.07678	+	1.02937i	−0.462475	+	0.0589415i
$306$	0.116615	+	0.358904i	0.00666644	+	0.0205172i
$307$	−16.8097			−0.959381			−0.479691	−	0.877438i	$-0.659251\pi$
$307$	−16.8097			−0.959381			−0.479691	+	0.877438i	$0.659251\pi$
$308$	1.05459	+	3.24569i	0.0600908	+	0.184940i
$309$	3.47799	+	2.52691i	0.197856	+	0.143751i
$310$	0.837771	+	1.77528i	0.0475822	+	0.100829i
$311$	20.2425	−	14.7071i	1.14785	−	0.833961i	0.159655	−	0.987173i	$-0.448962\pi$
$311$	20.2425	−	14.7071i	1.14785	−	0.833961i	0.988193	+	0.153212i	$0.0489617\pi$
$312$	−0.785475	−	0.570681i	−0.0444688	−	0.0323084i
$313$	8.66253	+	6.29370i	0.489635	+	0.355741i	0.805044	−	0.593215i	$-0.202142\pi$
$313$	8.66253	+	6.29370i	0.489635	+	0.355741i	−0.315409	+	0.948956i	$0.602142\pi$
$314$	−1.23029	+	0.893858i	−0.0694293	+	0.0504433i
$315$	5.01572	+	10.6286i	0.282604	+	0.598851i
$316$	4.15545	+	3.01911i	0.233762	+	0.169838i
$317$	−6.93911	−	21.3564i	−0.389739	−	1.19949i	−0.932983	−	0.359920i	$-0.882804\pi$
$317$	−6.93911	−	21.3564i	−0.389739	−	1.19949i	0.543244	−	0.839575i	$-0.317196\pi$
$318$	−0.429537			−0.0240872
$319$	1.89298	+	5.82599i	0.105986	+	0.326193i
$320$	16.2633	−	2.07272i	0.909145	−	0.115869i
$321$	−3.01151	+	9.26848i	−0.168086	+	0.517316i
$322$	−0.236117	+	0.726692i	−0.0131583	+	0.0404970i
$323$	0.921980	−	0.669858i	0.0513003	−	0.0372719i
$324$	−5.52657			−0.307032
$325$	0.509130	−	8.38701i	0.0282415	−	0.465228i
$326$	0.664373			0.0367962
$327$	−2.93702	+	2.13387i	−0.162418	+	0.118003i
$328$	−0.867447	+	2.66973i	−0.0478967	+	0.147411i
$329$	2.16422	−	6.66078i	0.119317	−	0.367220i
$330$	−0.102788	−	0.217814i	−0.00565831	−	0.0119902i
$331$	−8.25744	−	25.4138i	−0.453870	−	1.39687i	−0.872456	−	0.488692i	$-0.837474\pi$
$331$	−8.25744	−	25.4138i	−0.453870	−	1.39687i	0.418586	−	0.908177i	$-0.362526\pi$
$332$	5.46170			0.299750
$333$	−4.02605	−	12.3909i	−0.220626	−	0.679017i
$334$	−0.463766	−	0.336945i	−0.0253761	−	0.0184368i
$335$	2.74070	−	14.4537i	0.149741	−	0.789690i
$336$	6.28038	−	4.56297i	0.342623	−	0.248930i
$337$	19.6939	+	14.3085i	1.07280	+	0.779432i	0.976413	−	0.215912i	$-0.0692725\pi$
$337$	19.6939	+	14.3085i	1.07280	+	0.779432i	0.0963836	+	0.995344i	$0.469272\pi$
$338$	1.38157	+	1.00377i	0.0751476	+	0.0545979i
$339$	−3.81799	+	2.77393i	−0.207365	+	0.150659i
$340$	3.86611	+	2.11987i	0.209669	+	0.114966i
$341$	−3.13380	−	2.27684i	−0.169705	−	0.123298i
$342$	−0.132898	−	0.409018i	−0.00718630	−	0.0221172i
$343$	−19.9536			−1.07739
$344$	−1.48340	−	4.56545i	−0.0799798	−	0.246152i
$345$	−0.703380	+	3.70943i	−0.0378687	+	0.199709i
$346$	0.639536	−	1.96829i	0.0343817	−	0.105816i
$347$	−1.48215	+	4.56160i	−0.0795661	+	0.244879i	−0.982925	−	0.184006i	$-0.941093\pi$
$347$	−1.48215	+	4.56160i	−0.0795661	+	0.244879i	0.903359	+	0.428885i	$0.141093\pi$
$348$	11.4390	−	8.31089i	0.613192	−	0.445510i
$349$	−37.3215			−1.99777			−0.998887	−	0.0471628i	$-0.984982\pi$
$349$	−37.3215			−1.99777			−0.998887	+	0.0471628i	$0.984982\pi$
$350$	−1.82509	−	0.717960i	−0.0975551	−	0.0383766i
$351$	7.64530			0.408076
$352$	1.18383	−	0.860103i	0.0630984	−	0.0458437i
$353$	0.109721	−	0.337685i	0.00583984	−	0.0179732i	−0.948094	−	0.317990i	$-0.896992\pi$
$353$	0.109721	−	0.337685i	0.00583984	−	0.0179732i	0.953934	+	0.300017i	$0.0969922\pi$
$354$	0.151827	−	0.467275i	0.00806951	−	0.0248354i
$355$	2.52603	−	2.37734i	0.134068	−	0.126176i
$356$	−5.18506	−	15.9580i	−0.274808	−	0.845771i
$357$	2.02593			0.107224
$358$	−0.913297	−	2.81084i	−0.0482692	−	0.148557i
$359$	−10.2385	−	7.43868i	−0.540365	−	0.392598i	0.283855	−	0.958867i	$-0.408386\pi$
$359$	−10.2385	−	7.43868i	−0.540365	−	0.392598i	−0.824221	+	0.566269i	$0.808386\pi$
$360$	2.44066	−	2.29700i	0.128634	−	0.121062i
$361$	14.3206	−	10.4045i	0.753716	−	0.547607i
$362$	−1.26969	−	0.922487i	−0.0667337	−	0.0484849i
$363$	−7.32910	−	5.32491i	−0.384678	−	0.279485i
$364$	6.26588	−	4.55243i	0.328421	−	0.238612i
$365$	28.1881	−	3.59251i	1.47543	−	0.188041i
$366$	0.428506	+	0.311328i	0.0223984	+	0.0162734i
$367$	−4.55183	−	14.0091i	−0.237603	−	0.731268i	−0.996765	−	0.0803664i	$-0.974391\pi$
$367$	−4.55183	−	14.0091i	−0.237603	−	0.731268i	0.759162	−	0.650902i	$-0.225609\pi$
$368$	−7.46432			−0.389105
$369$	−2.92646	−	9.00671i	−0.152345	−	0.468871i
$370$	1.90638	+	1.04531i	0.0991079	+	0.0543431i
$371$	2.13282	−	6.56413i	0.110730	−	0.340793i
$372$	−2.76287	+	8.50324i	−0.143248	+	0.440873i
$373$	−24.7589	+	17.9884i	−1.28197	+	0.931404i	−0.999611	−	0.0279049i	$-0.991116\pi$
$373$	−24.7589	+	17.9884i	−1.28197	+	0.931404i	−0.282358	+	0.959309i	$0.591116\pi$
$374$	0.124266			0.00642565
$375$	−9.39430	−	2.37900i	−0.485119	−	0.122851i
$376$	−1.99725			−0.103000
$377$	11.2472	−	8.17158i	0.579261	−	0.420858i
$378$	0.551441	−	1.69716i	0.0283631	−	0.0872925i
$379$	5.94586	−	18.2995i	0.305418	−	0.939981i	−0.674102	−	0.738638i	$-0.735469\pi$
$379$	5.94586	−	18.2995i	0.305418	−	0.939981i	0.979521	−	0.201343i	$-0.0645307\pi$
$380$	−4.40594	−	2.41587i	−0.226020	−	0.123932i
$381$	1.68128	+	5.17445i	0.0861347	+	0.265095i
$382$	4.38692			0.224454
$383$	−10.1347	−	31.1914i	−0.517858	−	1.59380i	−0.778020	−	0.628239i	$-0.783776\pi$
$383$	−10.1347	−	31.1914i	−0.517858	−	1.59380i	0.260162	−	0.965565i	$-0.416224\pi$
$384$	−3.63433	−	2.64049i	−0.185463	−	0.134747i
$385$	3.83898	−	0.489270i	0.195653	−	0.0249355i
$386$	2.39593	−	1.74075i	0.121950	−	0.0886018i
$387$	13.1019	+	9.51909i	0.666007	+	0.483882i
$388$	20.1638	+	14.6499i	1.02366	+	0.743735i
$389$	−14.6677	+	10.6567i	−0.743679	+	0.540315i	−0.893861	−	0.448344i	$-0.852014\pi$
$389$	−14.6677	+	10.6567i	−0.743679	+	0.540315i	0.150182	+	0.988658i	$0.452014\pi$
$390$	−0.398041	+	0.374611i	−0.0201556	+	0.0189692i
$391$	−1.57595	−	1.14500i	−0.0796994	−	0.0579050i
$392$	0.316574	+	0.974313i	0.0159894	+	0.0492102i
$393$	−1.78218			−0.0898991
$394$	0.127519	+	0.392464i	0.00642433	+	0.0197721i
$395$	4.24164	−	3.99196i	0.213420	−	0.200857i
$396$	−1.01461	+	3.12264i	−0.0509859	+	0.156918i
$397$	−6.27251	+	19.3048i	−0.314808	+	0.968880i	0.661025	+	0.750364i	$0.270122\pi$
$397$	−6.27251	+	19.3048i	−0.314808	+	0.968880i	−0.975833	+	0.218516i	$0.929878\pi$
$398$	−2.38260	+	1.73106i	−0.119429	+	0.0867702i
$399$	−2.30881			−0.115585
$400$	1.16091	−	19.1239i	0.0580453	−	0.956193i
$401$	25.7985			1.28832			0.644159	−	0.764892i	$-0.277208\pi$
$401$	25.7985			1.28832			0.644159	+	0.764892i	$0.277208\pi$
$402$	−0.774229	+	0.562510i	−0.0386150	+	0.0280554i
$403$	−2.71656	+	8.36071i	−0.135321	+	0.416477i
$404$	4.43966	−	13.6639i	0.220881	−	0.679803i
$405$	−1.16757	+	6.15743i	−0.0580169	+	0.305965i
$406$	−1.00275	−	3.08614i	−0.0497655	−	0.153163i
$407$	−4.29020			−0.212657
$408$	−0.178534	−	0.549471i	−0.00883875	−	0.0272029i
$409$	−10.4536	−	7.59497i	−0.516896	−	0.375547i	0.298537	−	0.954398i	$-0.403501\pi$
$409$	−10.4536	−	7.59497i	−0.516896	−	0.375547i	−0.815433	+	0.578851i	$0.803501\pi$
$410$	1.38571	+	0.759816i	0.0684354	+	0.0375246i
$411$	1.27095	−	0.923397i	0.0626912	−	0.0455478i
$412$	7.91213	+	5.74850i	0.389803	+	0.283208i
$413$	6.38696	+	4.64040i	0.314282	+	0.228339i
$414$	−0.594724	+	0.432093i	−0.0292291	+	0.0212362i
$415$	1.15386	−	6.08515i	0.0566410	−	0.298708i
$416$	−2.68666	−	1.95198i	−0.131725	−	0.0957035i
$417$	4.51595	+	13.8987i	0.221147	+	0.680621i
$418$	−0.141617			−0.00692674
$419$	−4.84966	−	14.9257i	−0.236922	−	0.729170i	−0.996861	−	0.0791753i	$-0.974771\pi$
$419$	−4.84966	−	14.9257i	−0.236922	−	0.729170i	0.759939	−	0.649994i	$-0.225229\pi$
$420$	−3.81223	−	8.07831i	−0.186018	−	0.394181i
$421$	−9.36192	+	28.8130i	−0.456272	+	1.40426i	0.413363	+	0.910566i	$0.364354\pi$
$421$	−9.36192	+	28.8130i	−0.456272	+	1.40426i	−0.869635	+	0.493695i	$0.835646\pi$
$422$	−0.956025	+	2.94234i	−0.0465386	+	0.143231i
$423$	5.45118	−	3.96051i	0.265045	−	0.192567i
$424$	−1.96827			−0.0955878
$425$	3.17863	−	3.85957i	0.154186	−	0.187217i
$426$	−0.225653			−0.0109329
$427$	−6.88536	+	5.00251i	−0.333206	+	0.242088i
$428$	−6.85092	+	21.0850i	−0.331152	+	1.01918i
$429$	0.333302	−	1.02580i	0.0160920	−	0.0495260i
$430$	−2.68085	+	0.341668i	−0.129282	+	0.0164767i
$431$	2.36645	+	7.28319i	0.113988	+	0.350819i	0.991735	−	0.128306i	$-0.0409540\pi$
$431$	2.36645	+	7.28319i	0.113988	+	0.350819i	−0.877747	+	0.479125i	$0.840954\pi$
$432$	17.4326			0.838728
$433$	−5.76301	−	17.7367i	−0.276952	−	0.852372i	−0.988696	−	0.149933i	$-0.952094\pi$
$433$	−5.76301	−	17.7367i	−0.276952	−	0.852372i	0.711744	−	0.702439i	$-0.247906\pi$
$434$	1.66003	+	1.20608i	0.0796841	+	0.0578939i
$435$	−6.84292	−	14.5005i	−0.328093	−	0.695246i
$436$	−6.68147	+	4.85437i	−0.319984	+	0.232482i
$437$	1.79600	+	1.30487i	0.0859145	+	0.0624206i
$438$	−1.49549	−	1.08654i	−0.0714574	−	0.0519168i
$439$	10.1782	−	7.39491i	0.485780	−	0.352940i	−0.317779	−	0.948165i	$-0.602937\pi$
$439$	10.1782	−	7.39491i	0.485780	−	0.352940i	0.803559	+	0.595225i	$0.202937\pi$
$440$	−0.471008	−	0.998090i	−0.0224544	−	0.0475821i
$441$	−2.79608	−	2.03147i	−0.133147	−	0.0967367i
$442$	−0.0871483	−	0.268215i	−0.00414522	−	0.0127577i
$443$	−15.9434			−0.757495			−0.378747	−	0.925500i	$-0.623645\pi$
$443$	−15.9434			−0.757495			−0.378747	+	0.925500i	$0.623645\pi$
$444$	3.06003	+	9.41779i	0.145222	+	0.446949i
$445$	−18.8750	+	2.40558i	−0.894760	+	0.114035i
$446$	−0.643147	+	1.97940i	−0.0304539	+	0.0937275i
$447$	−1.53946	+	4.73798i	−0.0728141	+	0.224099i
$448$	13.8643	−	10.0730i	0.655026	−	0.475904i
$449$	7.07163			0.333731			0.166865	−	0.985980i	$-0.446635\pi$
$449$	7.07163			0.333731			0.166865	+	0.985980i	$0.446635\pi$
$450$	−1.01454	−	1.59091i	−0.0478259	−	0.0749961i
$451$	−3.11846			−0.146843
$452$	−8.68558	+	6.31045i	−0.408535	+	0.296818i
$453$	−2.68753	+	8.27136i	−0.126271	+	0.388622i
$454$	1.23561	−	3.80280i	0.0579899	−	0.178474i
$455$	−3.74833	−	7.94290i	−0.175724	−	0.372369i
$456$	0.203463	+	0.626194i	0.00952801	+	0.0293242i
$457$	−11.8771			−0.555587			−0.277794	−	0.960641i	$-0.589603\pi$
$457$	−11.8771			−0.555587			−0.277794	+	0.960641i	$0.589603\pi$
$458$	−0.369966	−	1.13864i	−0.0172874	−	0.0532051i
$459$	3.68058	+	2.67410i	0.171795	+	0.124816i
$460$	−1.60013	+	8.43862i	−0.0746063	+	0.393453i
$461$	8.99108	−	6.53240i	0.418756	−	0.304244i	−0.358381	−	0.933575i	$-0.616671\pi$
$461$	8.99108	−	6.53240i	0.418756	−	0.304244i	0.777137	+	0.629331i	$0.216671\pi$
$462$	−0.203674	−	0.147978i	−0.00947576	−	0.00688454i
$463$	−20.9179	−	15.1978i	−0.972138	−	0.706300i	−0.0162004	−	0.999869i	$-0.505157\pi$
$463$	−20.9179	−	15.1978i	−0.972138	−	0.706300i	−0.955938	+	0.293569i	$0.905157\pi$
$464$	25.6456	−	18.6326i	1.19057	−	0.864998i
$465$	8.89019	+	4.87468i	0.412273	+	0.226058i
$466$	−3.25031	−	2.36149i	−0.150568	−	0.109394i
$467$	12.6052	+	38.7947i	0.583297	+	1.79520i	0.606003	+	0.795462i	$0.292772\pi$
$467$	12.6052	+	38.7947i	0.583297	+	1.79520i	−0.0227055	+	0.999742i	$0.507228\pi$
$468$	7.45141			0.344442
$469$	−4.75187	−	14.6247i	−0.219421	−	0.675308i
$470$	−0.209478	+	1.10473i	−0.00966251	+	0.0509574i
$471$	−2.42716	+	7.47003i	−0.111838	+	0.344201i
$472$	0.695719	−	2.14120i	0.0320230	−	0.0985568i
$473$	4.31435	−	3.13456i	0.198374	−	0.144127i
$474$	−0.378910			−0.0174039
$475$	−3.62246	+	4.39849i	−0.166210	+	0.201816i
$476$	4.60881			0.211244
$477$	5.37208	−	3.90305i	0.245971	−	0.178708i
$478$	1.50095	−	4.61944i	0.0686517	−	0.211288i
$479$	9.95256	−	30.6308i	0.454744	−	1.39956i	−0.416692	−	0.909048i	$-0.636811\pi$
$479$	9.95256	−	30.6308i	0.454744	−	1.39956i	0.871436	−	0.490510i	$-0.163189\pi$
$480$	−2.78914	+	2.62496i	−0.127306	+	0.119813i
$481$	3.00873	+	9.25993i	0.137186	+	0.422216i
$482$	3.02167			0.137633
$483$	1.21953	+	3.75333i	0.0554905	+	0.170782i
$484$	−16.6731	−	12.1137i	−0.757866	−	0.550622i
$485$	20.5821	−	19.3705i	0.934583	−	0.879570i
$486$	2.18284	−	1.58593i	0.0990156	−	0.0719391i
$487$	17.4619	+	12.6868i	0.791276	+	0.574895i	0.908342	−	0.418229i	$-0.137349\pi$
$487$	17.4619	+	12.6868i	0.791276	+	0.574895i	−0.117066	+	0.993124i	$0.537349\pi$
$488$	1.96355	+	1.42660i	0.0888856	+	0.0645792i
$489$	2.77610	−	2.01696i	0.125540	−	0.0912099i
$490$	0.572120	−	0.0729155i	0.0258457	−	0.00329399i
$491$	3.81701	+	2.77322i	0.172259	+	0.125154i	0.670574	−	0.741842i	$-0.266048\pi$
$491$	3.81701	+	2.77322i	0.172259	+	0.125154i	−0.498315	+	0.866996i	$0.666048\pi$
$492$	2.22427	+	6.84561i	0.100278	+	0.308624i
$493$	8.27277			0.372587
$494$	0.0993168	+	0.305666i	0.00446848	+	0.0137526i
$495$	3.26473	+	1.79012i	0.146739	+	0.0804601i
$496$	−6.19423	+	19.0639i	−0.278129	+	0.855994i
$497$	1.12046	−	3.44841i	0.0502593	−	0.154682i
$498$	−0.325958	+	0.236823i	−0.0146065	+	0.0106123i
$499$	−24.6490			−1.10344			−0.551721	−	0.834029i	$-0.686029\pi$
$499$	−24.6490			−1.10344			−0.551721	+	0.834029i	$0.686029\pi$
$500$	−21.3712	−	5.41202i	−0.955749	−	0.242033i
$501$	−2.96079			−0.132278
$502$	−4.05197	+	2.94393i	−0.180848	+	0.131394i
$503$	−4.05027	+	12.4654i	−0.180592	+	0.555806i	−0.999845	−	0.0176270i	$-0.994389\pi$
$503$	−4.05027	+	12.4654i	−0.180592	+	0.555806i	0.819252	+	0.573433i	$0.194389\pi$
$504$	1.08259	−	3.33187i	0.0482223	−	0.148413i
$505$	−14.2856	−	7.83313i	−0.635703	−	0.348570i
$506$	0.0748034	+	0.230221i	0.00332542	+	0.0102346i
$507$	8.82027			0.391722
$508$	3.82477	+	11.7714i	0.169697	+	0.522272i
$509$	25.3510	+	18.4186i	1.12366	+	0.816390i	0.984761	−	0.173915i	$-0.0556419\pi$
$509$	25.3510	+	18.4186i	1.12366	+	0.816390i	0.138904	+	0.990306i	$0.455642\pi$
$510$	−0.322651	+	0.0411213i	−0.0142872	+	0.00182088i
$511$	24.0300	−	17.4589i	1.06303	−	0.772334i
$512$	−10.2587	−	7.45336i	−0.453374	−	0.329395i
$513$	−4.19450	−	3.04748i	−0.185192	−	0.134550i
$514$	2.99173	−	2.17362i	0.131960	−	0.0958743i
$515$	8.07624	−	7.60084i	0.355881	−	0.334933i
$516$	−9.95819	−	7.23505i	−0.438385	−	0.318505i
$517$	−0.685639	−	2.11018i	−0.0301544	−	0.0928056i
$518$	2.27260			0.0998524
$519$	−3.30317	−	10.1661i	−0.144993	−	0.446243i
$520$	−1.82395	+	1.71658i	−0.0799854	+	0.0752772i
$521$	9.69500	−	29.8381i	0.424745	−	1.30723i	−0.478492	−	0.878092i	$-0.658817\pi$
$521$	9.69500	−	29.8381i	0.424745	−	1.30723i	0.903238	−	0.429140i	$-0.141183\pi$
$522$	0.964729	−	2.96913i	0.0422251	−	0.129955i
$523$	−19.0034	+	13.8068i	−0.830961	+	0.603728i	−0.919831	−	0.392315i	$-0.871674\pi$
$523$	−19.0034	+	13.8068i	−0.830961	+	0.603728i	0.0888702	+	0.996043i	$0.471674\pi$
$524$	−4.05430			−0.177113
$525$	−9.80583	+	2.54074i	−0.427962	+	0.110887i
$526$	−1.74266			−0.0759837
$527$	−4.23212	+	3.07482i	−0.184354	+	0.133941i
$528$	0.759986	−	2.33900i	0.0330742	−	0.101792i
$529$	−5.93478	+	18.2654i	−0.258034	+	0.794147i
$530$	−0.206439	+	1.08870i	−0.00896713	+	0.0472901i
$531$	2.34711	+	7.22366i	0.101856	+	0.313480i
$532$	−5.25233			−0.227718
$533$	2.18699	+	6.73086i	0.0947291	+	0.291546i
$534$	1.00139	+	0.727556i	0.0433346	+	0.0314844i
$535$	22.0444	+	12.0875i	0.953065	+	0.522586i
$536$	−3.54776	+	2.57760i	−0.153240	+	0.111335i
$537$	−12.3496	−	8.97252i	−0.532925	−	0.387193i
$538$	−1.68757	−	1.22609i	−0.0727562	−	0.0528605i
$539$	−0.920726	+	0.668946i	−0.0396585	+	0.0288136i
$540$	3.73703	−	19.7081i	0.160816	−	0.848100i
$541$	−20.8245	−	15.1299i	−0.895314	−	0.650483i	0.0419443	−	0.999120i	$-0.486645\pi$
$541$	−20.8245	−	15.1299i	−0.895314	−	0.650483i	−0.937258	+	0.348636i	$0.886645\pi$
$542$	−1.15206	−	3.54569i	−0.0494854	−	0.152300i
$543$	−8.10602			−0.347863
$544$	−0.610663	−	1.87943i	−0.0261820	−	0.0805798i
$545$	3.99694	+	8.46971i	0.171210	+	0.362802i
$546$	−0.176556	+	0.543384i	−0.00755591	+	0.0232547i
$547$	−0.947753	+	2.91688i	−0.0405230	+	0.124717i	−0.969271	−	0.245994i	$-0.920886\pi$
$547$	−0.947753	+	2.91688i	−0.0405230	+	0.124717i	0.928748	+	0.370710i	$0.120886\pi$
$548$	2.89129	−	2.10064i	0.123510	−	0.0897351i
$549$	−8.18810			−0.349460
$550$	−0.601469	+	0.155843i	−0.0256467	+	0.00664518i
$551$	−9.42790			−0.401642
$552$	0.910505	−	0.661520i	0.0387537	−	0.0281562i
$553$	1.88143	−	5.79046i	0.0800067	−	0.246235i
$554$	−1.40322	+	4.31867i	−0.0596171	+	0.183483i
$555$	11.1393	−	1.41968i	0.472837	−	0.0602621i
$556$	10.2734	+	31.6182i	0.435689	+	1.34091i
$557$	4.34924			0.184283			0.0921416	−	0.995746i	$-0.470629\pi$
$557$	4.34924			0.184283			0.0921416	+	0.995746i	$0.470629\pi$
$558$	0.610036	+	1.87750i	0.0258249	+	0.0794808i
$559$	−9.79127	−	7.11377i	−0.414126	−	0.300880i
$560$	−8.54685	−	18.1112i	−0.361170	−	0.765338i
$561$	0.519250	−	0.377257i	0.0219228	−	0.0159278i
$562$	2.09226	+	1.52012i	0.0882567	+	0.0641222i
$563$	17.9834	+	13.0657i	0.757911	+	0.550655i	0.898269	−	0.439446i	$-0.144825\pi$
$563$	17.9834	+	13.0657i	0.757911	+	0.550655i	−0.140358	+	0.990101i	$0.544825\pi$
$564$	−4.14320	+	3.01021i	−0.174460	+	0.126753i
$565$	5.19582	+	11.0102i	0.218590	+	0.463203i
$566$	3.50792	+	2.54865i	0.147449	+	0.107128i
$567$	2.02435	+	6.23030i	0.0850145	+	0.261648i
$568$	−1.03401			−0.0433863
$569$	6.04237	+	18.5965i	0.253309	+	0.779605i	0.994158	+	0.107934i	$0.0344234\pi$
$569$	6.04237	+	18.5965i	0.253309	+	0.779605i	−0.740849	+	0.671672i	$0.765577\pi$
$570$	0.367703	−	0.0468630i	0.0154014	−	0.00196287i
$571$	−14.0906	+	43.3663i	−0.589672	+	1.81482i	−0.0100338	+	0.999950i	$0.503194\pi$
$571$	−14.0906	+	43.3663i	−0.589672	+	1.81482i	−0.579638	+	0.814874i	$0.696806\pi$
$572$	0.758232	−	2.33360i	0.0317033	−	0.0975726i
$573$	18.3309	−	13.3182i	0.765784	−	0.556374i
$574$	1.65191			0.0689494
$575$	9.06383	+	3.56556i	0.377988	+	0.148694i
$576$	16.4875			0.686977
$577$	−3.52730	+	2.56273i	−0.146843	+	0.106688i	−0.658781	−	0.752335i	$-0.728928\pi$
$577$	−3.52730	+	2.56273i	−0.146843	+	0.106688i	0.511938	+	0.859022i	$0.328928\pi$
$578$	0.0518589	−	0.159605i	0.00215704	−	0.00663870i
$579$	4.72678	−	14.5475i	0.196438	−	0.604575i
$580$	−15.5670	−	32.9873i	−0.646386	−	1.36972i
$581$	−2.00059	−	6.15717i	−0.0829983	−	0.255442i
$582$	−1.83862			−0.0762132
$583$	−0.675691	−	2.07956i	−0.0279843	−	0.0861267i
$584$	−6.85282	−	4.97886i	−0.283572	−	0.206027i
$585$	1.57422	−	8.30199i	0.0650859	−	0.343245i
$586$	3.90405	−	2.83646i	0.161275	−	0.117173i
$587$	10.0346	+	7.29053i	0.414170	+	0.300912i	0.775288	−	0.631608i	$-0.217605\pi$
$587$	10.0346	+	7.29053i	0.414170	+	0.300912i	−0.361118	+	0.932520i	$0.617605\pi$
$588$	2.12518	+	1.54403i	0.0876409	+	0.0636748i
$589$	4.82305	−	3.50415i	0.198730	−	0.144386i
$590$	−1.11138	−	0.609395i	−0.0457549	−	0.0250884i
$591$	1.72432	+	1.25279i	0.0709290	+	0.0515329i
$592$	6.86044	+	21.1143i	0.281962	+	0.867791i
$593$	−15.3195			−0.629094			−0.314547	−	0.949242i	$-0.601853\pi$
$593$	−15.3195			−0.629094			−0.314547	+	0.949242i	$0.601853\pi$
$594$	−0.174700	−	0.537672i	−0.00716804	−	0.0220610i
$595$	0.973677	−	5.13490i	0.0399169	−	0.210510i
$596$	−3.50214	+	10.7785i	−0.143453	+	0.441504i
$597$	−4.70048	+	14.4666i	−0.192378	+	0.592078i
$598$	0.444447	−	0.322910i	0.0181748	−	0.0132048i
$599$	−33.1389			−1.35402			−0.677009	−	0.735975i	$-0.736724\pi$
$599$	−33.1389			−1.35402			−0.677009	+	0.735975i	$0.736724\pi$
$600$	1.55323	+	2.43563i	0.0634104	+	0.0994342i
$601$	3.08632			0.125894			0.0629468	−	0.998017i	$-0.479950\pi$
$601$	3.08632			0.125894			0.0629468	+	0.998017i	$0.479950\pi$
$602$	−2.28539	+	1.66044i	−0.0931457	+	0.0676743i
$603$	4.57171	−	14.0703i	0.186174	−	0.572985i
$604$	−6.11389	+	18.8166i	−0.248771	+	0.765637i
$605$	−17.0189	+	16.0171i	−0.691916	+	0.651187i
$606$	0.327511	+	1.00798i	0.0133042	+	0.0409462i
$607$	−36.2260			−1.47037			−0.735184	−	0.677868i	$-0.762904\pi$
$607$	−36.2260			−1.47037			−0.735184	+	0.677868i	$0.762904\pi$
$608$	0.695930	+	2.14185i	0.0282237	+	0.0868636i
$609$	−13.5592	−	9.85131i	−0.549445	−	0.399195i
$610$	0.995031	−	0.936460i	0.0402876	−	0.0379162i
$611$	−4.07375	+	2.95975i	−0.164806	+	0.119739i
$612$	3.58724	+	2.60628i	0.145005	+	0.105353i
$613$	12.3522	+	8.97443i	0.498902	+	0.362474i	0.808598	−	0.588362i	$-0.200227\pi$
$613$	12.3522	+	8.97443i	0.498902	+	0.362474i	−0.309695	+	0.950836i	$0.600227\pi$
$614$	2.28223	−	1.65813i	0.0921032	−	0.0669169i
$615$	8.09695	−	1.03194i	0.326500	−	0.0416118i
$616$	−0.933296	−	0.678080i	−0.0376036	−	0.0273206i
$617$	−5.70189	−	17.5486i	−0.229550	−	0.706481i	−0.997798	−	0.0663288i	$-0.978871\pi$
$617$	−5.70189	−	17.5486i	−0.229550	−	0.706481i	0.768248	−	0.640152i	$-0.221129\pi$
$618$	−0.721459			−0.0290214
$619$	1.51124	+	4.65111i	0.0607417	+	0.186944i	0.976823	−	0.214049i	$-0.0686652\pi$
$619$	1.51124	+	4.65111i	0.0607417	+	0.186944i	−0.916081	+	0.400993i	$0.868665\pi$
$620$	20.2244	+	11.0895i	0.812231	+	0.445364i
$621$	−2.73859	+	8.42851i	−0.109896	+	0.338224i
$622$	−1.29757	+	3.99350i	−0.0520277	+	0.160125i
$623$	−16.0907	+	11.6906i	−0.644661	+	0.468374i
$624$	−5.58145			−0.223437
$625$	−10.5448	+	22.6673i	−0.421791	+	0.906693i
$626$	−1.79692			−0.0718192
$627$	−0.591753	+	0.429934i	−0.0236323	+	0.0171699i
$628$	−5.52157	+	16.9936i	−0.220335	+	0.678120i
$629$	−1.79039	+	5.51025i	−0.0713875	+	0.219708i
$630$	−1.72939	−	0.948263i	−0.0689006	−	0.0377797i
$631$	5.35214	+	16.4722i	0.213065	+	0.655747i	0.999285	+	0.0378007i	$0.0120352\pi$
$631$	5.35214	+	16.4722i	0.213065	+	0.655747i	−0.786220	+	0.617947i	$0.787965\pi$
$632$	−1.73629			−0.0690657
$633$	4.93782	+	15.1970i	0.196261	+	0.604028i
$634$	3.04874	+	2.21504i	0.121081	+	0.0879703i
$635$	13.9232	−	1.77448i	0.552524	−	0.0704180i
$636$	−4.08309	+	2.96654i	−0.161905	+	0.117631i
$637$	2.08956	+	1.51815i	0.0827912	+	0.0601513i
$638$	−0.831690	−	0.604258i	−0.0329269	−	0.0239228i
$639$	2.82218	−	2.05043i	0.111644	−	0.0811138i
$640$	−8.43925	+	7.94249i	−0.333591	+	0.313954i
$641$	32.0610	+	23.2936i	1.26633	+	0.920044i	0.999050	−	0.0435748i	$-0.0138747\pi$
$641$	32.0610	+	23.2936i	1.26633	+	0.920044i	0.267281	+	0.963619i	$0.413875\pi$
$642$	−0.505388	−	1.55543i	−0.0199461	−	0.0613877i
$643$	22.7771			0.898241			0.449120	−	0.893471i	$-0.351737\pi$
$643$	22.7771			0.898241			0.449120	+	0.893471i	$0.351737\pi$
$644$	2.77432	+	8.53848i	0.109324	+	0.336463i
$645$	−10.1647	+	9.56640i	−0.400236	+	0.376677i
$646$	−0.0590999	+	0.181891i	−0.00232525	+	0.00715640i
$647$	2.99706	−	9.22400i	0.117827	−	0.362633i	−0.874700	−	0.484666i	$-0.838941\pi$
$647$	2.99706	−	9.22400i	0.117827	−	0.362633i	0.992526	+	0.122033i	$0.0389413\pi$
$648$	1.51138	−	1.09808i	0.0593727	−	0.0431368i
$649$	2.50110			0.0981769
$650$	0.758183	+	1.18891i	0.0297384	+	0.0466329i
$651$	10.5980			0.415369
$652$	6.31539	−	4.58840i	0.247330	−	0.179695i
$653$	−15.0652	+	46.3660i	−0.589548	+	1.81444i	−0.00936280	+	0.999956i	$0.502980\pi$
$653$	−15.0652	+	46.3660i	−0.589548	+	1.81444i	−0.580185	+	0.814485i	$0.697020\pi$
$654$	0.188266	−	0.579424i	0.00736180	−	0.0226573i
$655$	−0.856530	+	4.51710i	−0.0334674	+	0.176498i
$656$	4.98672	+	15.3476i	0.194699	+	0.599221i
$657$	28.5766			1.11488
$658$	0.363196	+	1.11780i	0.0141589	+	0.0435765i
$659$	15.3229	+	11.1328i	0.596897	+	0.433671i	0.844776	−	0.535120i	$-0.179734\pi$
$659$	15.3229	+	11.1328i	0.596897	+	0.433671i	−0.247879	+	0.968791i	$0.579734\pi$
$660$	−2.48138	−	1.36060i	−0.0965877	−	0.0529611i
$661$	2.52711	−	1.83606i	0.0982933	−	0.0714143i	−0.537553	−	0.843230i	$-0.680651\pi$
$661$	2.52711	−	1.83606i	0.0982933	−	0.0714143i	0.635846	+	0.771816i	$0.280651\pi$
$662$	3.62795	+	2.63586i	0.141004	+	0.102446i
$663$	−1.17842	−	0.856173i	−0.0457661	−	0.0332510i
$664$	−1.49364	+	1.08520i	−0.0579646	+	0.0421137i
$665$	−1.10963	+	5.85188i	−0.0430297	+	0.226926i
$666$	1.76887	+	1.28516i	0.0685422	+	0.0497988i
$667$	4.97989	+	15.3265i	0.192822	+	0.593445i
$668$	−6.73552			−0.260605
$669$	3.32182	+	10.2235i	0.128429	+	0.395264i
$670$	1.05363	+	2.23270i	0.0407054	+	0.0862567i
$671$	−0.833195	+	2.56431i	−0.0321651	+	0.0989941i
$672$	−1.23716	+	3.80759i	−0.0477245	+	0.146881i
$673$	−19.3245	+	14.0401i	−0.744905	+	0.541205i	−0.894244	−	0.447581i	$-0.852286\pi$
$673$	−19.3245	+	14.0401i	−0.744905	+	0.541205i	0.149338	+	0.988786i	$0.452286\pi$
$674$	−4.08522			−0.157357
$675$	−21.1682	−	8.32723i	−0.814765	−	0.320515i
$676$	20.0653			0.771743
$677$	−7.59341	+	5.51694i	−0.291839	+	0.212033i	−0.724065	−	0.689732i	$-0.757728\pi$
$677$	−7.59341	+	5.51694i	−0.291839	+	0.212033i	0.432226	+	0.901765i	$0.357728\pi$
$678$	0.244737	−	0.753224i	0.00939908	−	0.0289274i
$679$	9.12944	−	28.0975i	0.350356	−	1.07828i
$680$	−1.47849	+	0.188430i	−0.0566975	+	0.00722598i
$681$	−6.38184	−	19.6413i	−0.244553	−	0.752656i
$682$	0.650060			0.0248921
$683$	9.03681	+	27.8125i	0.345784	+	1.06421i	0.961163	+	0.275982i	$0.0890031\pi$
$683$	9.03681	+	27.8125i	0.345784	+	1.06421i	−0.615379	+	0.788232i	$0.710997\pi$
$684$	−4.08812	−	2.97020i	−0.156313	−	0.113568i
$685$	−1.72961	−	3.66512i	−0.0660848	−	0.140037i
$686$	2.70906	−	1.96825i	0.103432	−	0.0751480i
$687$	−5.00269	−	3.63467i	−0.190865	−	0.138671i
$688$	−22.3258	−	16.2206i	−0.851164	−	0.618406i
$689$	−4.01464	+	2.91681i	−0.152946	+	0.111122i
$690$	−0.270407	−	0.573005i	−0.0102942	−	0.0218139i
$691$	−1.77659	−	1.29077i	−0.0675848	−	0.0491032i	0.553480	−	0.832863i	$-0.313300\pi$
$691$	−1.77659	−	1.29077i	−0.0675848	−	0.0491032i	−0.621065	+	0.783759i	$0.713300\pi$
$692$	−7.51442	−	23.1270i	−0.285655	−	0.879157i
$693$	3.89190			0.147841
$694$	−0.248733	−	0.765522i	−0.00944178	−	0.0290588i
$695$	37.3978	−	4.76628i	1.41858	−	0.180795i
$696$	−1.47697	+	4.54565i	−0.0559844	+	0.172302i
$697$	−1.30140	+	4.00530i	−0.0492940	+	0.151711i
$698$	5.06708	−	3.68145i	0.191792	−	0.139345i
$699$	−20.7507			−0.784865
$700$	−22.3074	+	5.77995i	−0.843140	+	0.218461i
$701$	24.5922			0.928834			0.464417	−	0.885617i	$-0.346264\pi$
$701$	24.5922			0.928834			0.464417	+	0.885617i	$0.346264\pi$
$702$	−1.03799	+	0.754143i	−0.0391764	+	0.0284633i
$703$	2.04038	−	6.27965i	0.0769544	−	0.236841i
$704$	1.67771	−	5.16346i	0.0632311	−	0.194605i
$705$	2.47852	+	5.25210i	0.0933463	+	0.197805i
$706$	0.0184132	+	0.0566699i	0.000692989	+	0.00213280i
$707$	−17.0300			−0.640478
$708$	−1.78394	−	5.49039i	−0.0670444	−	0.206341i
$709$	21.6541	+	15.7326i	0.813235	+	0.590850i	0.914767	−	0.403982i	$-0.132374\pi$
$709$	21.6541	+	15.7326i	0.813235	+	0.590850i	−0.101532	+	0.994832i	$0.532374\pi$
$710$	−0.108451	+	0.571939i	−0.00407009	+	0.0214645i
$711$	4.73891	−	3.44302i	0.177723	−	0.129123i
$712$	4.58870	+	3.33389i	0.171969	+	0.124943i
$713$	−8.24412	−	5.98970i	−0.308745	−	0.224316i
$714$	−0.275057	+	0.199840i	−0.0102937	+	0.00747884i
$715$	−2.43979	−	1.33779i	−0.0912429	−	0.0500305i
$716$	−28.0943	−	20.4117i	−1.04993	−	0.762820i
$717$	−7.75232	−	23.8592i	−0.289516	−	0.891037i
$718$	2.12382			0.0792603
$719$	1.27676	+	3.92945i	0.0476150	+	0.146544i	0.972037	−	0.234827i	$-0.0754522\pi$
$719$	1.27676	+	3.92945i	0.0476150	+	0.146544i	−0.924422	+	0.381370i	$0.875452\pi$
$720$	3.58950	−	18.9300i	0.133773	−	0.705479i
$721$	3.58232	−	11.0253i	0.133413	−	0.410602i
$722$	−0.917966	+	2.82521i	−0.0341632	+	0.105143i
$723$	12.6262	−	9.17344i	0.469572	−	0.341164i
$724$	−18.4405			−0.685335
$725$	−40.0416	+	10.3750i	−1.48711	+	0.385316i
$726$	1.52032			0.0564242
$727$	39.7186	−	28.8573i	1.47308	−	1.07026i	0.493376	−	0.869816i	$-0.335763\pi$
$727$	39.7186	−	28.8573i	1.47308	−	1.07026i	0.979706	−	0.200440i	$-0.0642372\pi$
$728$	−0.809036	+	2.48996i	−0.0299849	+	0.0922840i
$729$	1.70809	−	5.25696i	0.0632625	−	0.194702i
$730$	−3.47268	+	3.26826i	−0.128530	+	0.120964i
$731$	−2.22550	−	6.84938i	−0.0823131	−	0.253334i
$732$	6.22342			0.230024
$733$	−7.51224	−	23.1203i	−0.277471	−	0.853968i	−0.988555	−	0.150861i	$-0.951796\pi$
$733$	−7.51224	−	23.1203i	−0.277471	−	0.853968i	0.711084	−	0.703107i	$-0.248204\pi$
$734$	1.99987	+	1.45299i	0.0738165	+	0.0536308i
$735$	2.16926	−	2.04157i	0.0800143	−	0.0753043i
$736$	3.11432	−	2.26269i	0.114795	−	0.0834037i
$737$	−3.94125	−	2.86349i	−0.145178	−	0.105478i
$738$	1.28576	+	0.934156i	0.0473293	+	0.0343867i
$739$	−29.7998	+	21.6508i	−1.09620	+	0.796438i	−0.980436	−	0.196838i	$-0.936933\pi$
$739$	−29.7998	+	21.6508i	−1.09620	+	0.796438i	−0.115767	+	0.993276i	$0.536933\pi$
$740$	25.3409	−	3.22965i	0.931550	−	0.118724i
$741$	1.34296	+	0.975720i	0.0493350	+	0.0358440i
$742$	0.357926	+	1.10158i	0.0131399	+	0.0404404i
$743$	−46.8116			−1.71735			−0.858676	−	0.512519i	$-0.828712\pi$
$743$	−46.8116			−1.71735			−0.858676	+	0.512519i	$0.828712\pi$
$744$	−0.933946	−	2.87439i	−0.0342401	−	0.105380i
$745$	11.2690	+	6.17902i	0.412863	+	0.226382i
$746$	1.58707	−	4.88451i	0.0581069	−	0.178835i
$747$	1.92474	−	5.92373i	0.0704224	−	0.216738i
$748$	1.18125	−	0.858227i	0.0431907	−	0.0313799i
$749$	26.2793			0.960223
$750$	1.51012	−	0.603674i	0.0551416	−	0.0220430i
$751$	3.06377			0.111798			0.0558992	−	0.998436i	$-0.482197\pi$
$751$	3.06377			0.111798			0.0558992	+	0.998436i	$0.482197\pi$
$752$	−9.28887	+	6.74876i	−0.338730	+	0.246102i
$753$	−7.99387	+	24.6026i	−0.291313	+	0.896568i
$754$	−0.720958	+	2.21888i	−0.0262557	+	0.0808069i
$755$	19.6729	+	10.7871i	0.715969	+	0.392582i
$756$	−6.47932	−	19.9413i	−0.235651	−	0.725258i
$757$	−37.5712			−1.36555			−0.682775	−	0.730629i	$-0.739227\pi$
$757$	−37.5712			−1.36555			−0.682775	+	0.730629i	$0.739227\pi$
$758$	0.997827	+	3.07100i	0.0362427	+	0.111544i
$759$	1.01149	+	0.734892i	0.0367148	+	0.0266749i
$760$	1.68493	−	0.214741i	0.0611189	−	0.00778947i
$761$	−5.41803	+	3.93643i	−0.196404	+	0.142695i	−0.681641	−	0.731687i	$-0.738733\pi$
$761$	−5.41803	+	3.93643i	−0.196404	+	0.142695i	0.485237	+	0.874383i	$0.338733\pi$
$762$	−0.738680	−	0.536683i	−0.0267596	−	0.0194420i
$763$	7.91987	+	5.75413i	0.286719	+	0.208313i
$764$	41.7011	−	30.2976i	1.50869	−	1.09613i
$765$	3.66164	−	3.44610i	0.132387	−	0.124594i
$766$	4.45273	+	3.23510i	0.160884	+	0.116889i
$767$	−1.75403	−	5.39836i	−0.0633345	−	0.194923i
$768$	−11.9565			−0.431443
$769$	7.54562	+	23.2230i	0.272102	+	0.837444i	0.989972	+	0.141266i	$0.0451174\pi$
$769$	7.54562	+	23.2230i	0.272102	+	0.837444i	−0.717870	+	0.696178i	$0.754883\pi$
$770$	−0.472950	+	0.445110i	−0.0170439	+	0.0160407i
$771$	5.90219	−	18.1651i	0.212562	−	0.654200i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.135768 + 0.0986414i) q^{2} +(-0.267848 + 0.824353i) q^{3} +(-0.609331 + 1.87533i) q^{4} +(1.96067 + 1.07508i) q^{5} +(-0.0449500 - 0.138342i) q^{6} +2.33732 q^{7} +(-0.205975 - 0.633926i) q^{8} +(1.81924 + 1.32175i) q^{9} +(-0.372243 + 0.0474416i) q^{10} +(0.599060 - 0.435242i) q^{11} +(-1.38272 - 1.00461i) q^{12} +(-1.35955 - 0.987768i) q^{13} +(-0.317333 + 0.230556i) q^{14} +(-1.41140 + 1.32832i) q^{15} +(-3.10000 - 2.25228i) q^{16} +(-0.309017 - 0.951057i) q^{17} -0.377374 q^{18} +(0.352165 + 1.08385i) q^{19} +(-3.21082 + 3.02182i) q^{20} +(-0.626046 + 1.92677i) q^{21} +(-0.0384004 + 0.118184i) q^{22} +(1.57595 - 1.14500i) q^{23} +0.577748 q^{24} +(2.68842 + 4.21573i) q^{25} +0.282018 q^{26} +(-3.68058 + 2.67410i) q^{27} +(-1.42420 + 4.38324i) q^{28} +(-2.55643 + 7.86787i) q^{29} +(0.0605961 - 0.319567i) q^{30} +(-1.61653 - 4.97516i) q^{31} +1.97615 q^{32} +(0.198336 + 0.610415i) q^{33} +(0.135768 + 0.0986414i) q^{34} +(4.58270 + 2.51279i) q^{35} +(-3.58724 + 2.60628i) q^{36} +(-4.68730 - 3.40552i) q^{37} +(-0.154726 - 0.112415i) q^{38} +(1.17842 - 0.856173i) q^{39} +(0.277670 - 1.46436i) q^{40} +(-3.40711 - 2.47541i) q^{41} +(-0.105062 - 0.323349i) q^{42} +7.20187 q^{43} +(0.451197 + 1.38864i) q^{44} +(2.14593 + 4.54733i) q^{45} +(-0.101020 + 0.310909i) q^{46} +(0.925941 - 2.84975i) q^{47} +(2.68701 - 1.95222i) q^{48} -1.53695 q^{49} +(-0.780848 - 0.307173i) q^{50} +0.866776 q^{51} +(2.68080 - 1.94772i) q^{52} +(0.912506 - 2.80840i) q^{53} +(0.235929 - 0.726115i) q^{54} +(1.64247 - 0.209330i) q^{55} +(-0.481429 - 1.48168i) q^{56} -0.987803 q^{57} +(-0.429016 - 1.32038i) q^{58} +(2.73261 + 1.98535i) q^{59} +(-1.63103 - 3.45623i) q^{60} +(-2.94584 + 2.14028i) q^{61} +(0.710230 + 0.516012i) q^{62} +(4.25213 + 3.08935i) q^{63} +(5.93171 - 4.30964i) q^{64} +(-1.60369 - 3.39830i) q^{65} +(-0.0871399 - 0.0633109i) q^{66} +(-2.03304 - 6.25706i) q^{67} +1.97184 q^{68} +(0.521765 + 1.60583i) q^{69} +(-0.870050 + 0.110886i) q^{70} +(0.479377 - 1.47537i) q^{71} +(0.463176 - 1.42551i) q^{72} +(10.2810 - 7.46961i) q^{73} +0.972312 q^{74} +(-4.19534 + 1.08703i) q^{75} -2.24716 q^{76} +(1.40019 - 1.01730i) q^{77} +(-0.0755380 + 0.232482i) q^{78} +(0.804955 - 2.47740i) q^{79} +(-3.65669 - 7.74872i) q^{80} +(0.866098 + 2.66558i) q^{81} +0.706755 q^{82} +(-0.855933 - 2.63429i) q^{83} +(-3.23186 - 2.34809i) q^{84} +(0.416579 - 2.19692i) q^{85} +(-0.977785 + 0.710402i) q^{86} +(-5.80117 - 4.21479i) q^{87} +(-0.399303 - 0.290110i) q^{88} +(-6.88427 + 5.00172i) q^{89} +(-0.739905 - 0.405706i) q^{90} +(-3.17769 - 2.30873i) q^{91} +(1.18697 + 3.65311i) q^{92} +4.53427 q^{93} +(0.155390 + 0.478242i) q^{94} +(-0.474746 + 2.50368i) q^{95} +(-0.529308 + 1.62904i) q^{96} +(3.90595 - 12.0213i) q^{97} +(0.208669 - 0.151607i) q^{98} +1.66511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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