LMFDB - Embedded newform 425.2.r.a.69.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, 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:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.7
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.85902 + 0.604031i) q^{2} +(-1.84553 - 2.54016i) q^{3} +(1.47306 - 1.07024i) q^{4} +(-1.33190 - 1.79612i) q^{5} +(4.96521 + 3.60744i) q^{6} +3.19704i q^{7} +(0.205893 - 0.283388i) q^{8} +(-2.11936 + 6.52273i) q^{9} +(3.56094 + 2.53450i) q^{10} +(0.299302 + 0.921156i) q^{11} +(-5.43715 - 1.76664i) q^{12} +(-5.27770 - 1.71483i) q^{13} +(-1.93111 - 5.94336i) q^{14} +(-2.10435 + 6.69804i) q^{15} +(-1.33690 + 4.11455i) q^{16} +(-0.587785 + 0.809017i) q^{17} -13.4060i q^{18} +(3.19489 + 2.32122i) q^{19} +(-3.88424 - 1.22033i) q^{20} +(8.12100 - 5.90025i) q^{21} +(-1.11281 - 1.53166i) q^{22} +(2.21517 - 0.719754i) q^{23} -1.09983 q^{24} +(-1.45206 + 4.78451i) q^{25} +10.8471 q^{26} +(11.5217 - 3.74363i) q^{27} +(3.42160 + 4.70942i) q^{28} +(6.75371 - 4.90685i) q^{29} +(-0.133808 - 13.7229i) q^{30} +(-5.25911 - 3.82097i) q^{31} -7.75597i q^{32} +(1.78751 - 2.46030i) q^{33} +(0.604031 - 1.85902i) q^{34} +(5.74226 - 4.25816i) q^{35} +(3.85893 + 11.8766i) q^{36} +(7.36049 + 2.39157i) q^{37} +(-7.34145 - 2.38538i) q^{38} +(5.38424 + 16.5710i) q^{39} +(-0.783227 + 0.00763705i) q^{40} +(-2.64384 + 8.13692i) q^{41} +(-11.5331 + 15.8740i) q^{42} -4.68498i q^{43} +(1.42674 + 1.03659i) q^{44} +(14.5384 - 4.88103i) q^{45} +(-3.68329 + 2.67607i) q^{46} +(-2.21169 - 3.04413i) q^{47} +(12.9189 - 4.19761i) q^{48} -3.22110 q^{49} +(-0.190578 - 9.77157i) q^{50} +3.13981 q^{51} +(-9.60962 + 3.12235i) q^{52} +(3.90172 + 5.37025i) q^{53} +(-19.1578 + 13.9190i) q^{54} +(1.25586 - 1.76447i) q^{55} +(0.906003 + 0.658250i) q^{56} -12.3994i q^{57} +(-9.59136 + 13.2014i) q^{58} +(3.31406 - 10.1996i) q^{59} +(4.06867 + 12.1187i) q^{60} +(1.77287 + 5.45633i) q^{61} +(12.0848 + 3.92658i) q^{62} +(-20.8535 - 6.77570i) q^{63} +(2.01105 + 6.18938i) q^{64} +(3.94936 + 11.7633i) q^{65} +(-1.83692 + 5.65345i) q^{66} +(-3.03778 + 4.18115i) q^{67} +1.82080i q^{68} +(-5.91647 - 4.29857i) q^{69} +(-8.10290 + 11.3845i) q^{70} +(8.40244 - 6.10473i) q^{71} +(1.41210 + 1.94359i) q^{72} +(0.183701 - 0.0596879i) q^{73} -15.1278 q^{74} +(14.8332 - 5.14149i) q^{75} +7.19051 q^{76} +(-2.94498 + 0.956881i) q^{77} +(-20.0188 - 27.5535i) q^{78} +(-0.139692 + 0.101492i) q^{79} +(9.17083 - 3.07896i) q^{80} +(-14.1275 - 10.2642i) q^{81} -16.7236i q^{82} +(-0.926093 + 1.27466i) q^{83} +(5.64801 - 17.3828i) q^{84} +(2.23596 - 0.0218023i) q^{85} +(2.82987 + 8.70945i) q^{86} +(-24.9284 - 8.09972i) q^{87} +(0.322669 + 0.104841i) q^{88} +(0.910731 + 2.80294i) q^{89} +(-24.0788 + 17.8555i) q^{90} +(5.48238 - 16.8730i) q^{91} +(2.49277 - 3.43100i) q^{92} +20.4107i q^{93} +(5.95031 + 4.32316i) q^{94} +(-0.0860994 - 8.83004i) q^{95} +(-19.7014 + 14.3139i) q^{96} +(7.06616 + 9.72573i) q^{97} +(5.98807 - 1.94564i) q^{98} -6.64278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−1.85902	+	0.604031i	−1.31452	+	0.427115i	−0.880611	−	0.473840i	$-0.842867\pi$
$2$	−1.85902	+	0.604031i	−1.31452	+	0.427115i	−0.433913	+	0.900955i	$0.642867\pi$
$3$	−1.84553	−	2.54016i	−1.06552	−	1.46656i	−0.874531	−	0.484969i	$-0.838831\pi$
$3$	−1.84553	−	2.54016i	−1.06552	−	1.46656i	−0.190988	−	0.981592i	$-0.561169\pi$
$4$	1.47306	−	1.07024i	0.736528	−	0.535119i
$5$	−1.33190	−	1.79612i	−0.595645	−	0.803247i
$5$	−1.33190	−	1.79612i	−0.595645	−	0.803247i
$6$	4.96521	+	3.60744i	2.02704	+	1.47273i
$7$			3.19704i			1.20837i	0.796844	+	0.604185i	$0.206501\pi$
$7$			3.19704i			1.20837i	−0.796844	+	0.604185i	$0.793499\pi$
$8$	0.205893	−	0.283388i	0.0727943	−	0.100193i
$9$	−2.11936	+	6.52273i	−0.706455	+	2.17424i
$10$	3.56094	+	2.53450i	1.12607	+	0.801479i
$11$	0.299302	+	0.921156i	0.0902428	+	0.277739i	0.985985	−	0.166836i	$-0.0533549\pi$
$11$	0.299302	+	0.921156i	0.0902428	+	0.277739i	−0.895742	+	0.444574i	$0.853355\pi$
$12$	−5.43715	−	1.76664i	−1.56957	−	0.509984i
$13$	−5.27770	−	1.71483i	−1.46377	−	0.475608i	−0.534551	−	0.845136i	$-0.679519\pi$
$13$	−5.27770	−	1.71483i	−1.46377	−	0.475608i	−0.929219	+	0.369528i	$0.879519\pi$
$14$	−1.93111	−	5.94336i	−0.516112	−	1.58843i
$15$	−2.10435	+	6.69804i	−0.543340	+	1.72943i
$16$	−1.33690	+	4.11455i	−0.334225	+	1.02864i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$		−	13.4060i		−	3.15983i
$19$	3.19489	+	2.32122i	0.732958	+	0.532525i	0.890498	−	0.454987i	$-0.150356\pi$
$19$	3.19489	+	2.32122i	0.732958	+	0.532525i	−0.157540	+	0.987513i	$0.550356\pi$
$20$	−3.88424	−	1.22033i	−0.868542	−	0.272873i
$21$	8.12100	−	5.90025i	1.77215	−	1.28754i
$22$	−1.11281	−	1.53166i	−0.237253	−	0.326550i
$23$	2.21517	−	0.719754i	0.461896	−	0.150079i	−0.0688197	−	0.997629i	$-0.521923\pi$
$23$	2.21517	−	0.719754i	0.461896	−	0.150079i	0.530715	+	0.847550i	$0.321923\pi$
$24$	−1.09983			−0.224503
$25$	−1.45206	+	4.78451i	−0.290413	+	0.956901i
$26$	10.8471			2.12730
$27$	11.5217	−	3.74363i	2.21736	−	0.720463i
$28$	3.42160	+	4.70942i	0.646621	+	0.889997i
$29$	6.75371	−	4.90685i	1.25413	−	0.911180i	0.255678	−	0.966762i	$-0.417701\pi$
$29$	6.75371	−	4.90685i	1.25413	−	0.911180i	0.998454	+	0.0555821i	$0.0177014\pi$
$30$	−0.133808	−	13.7229i	−0.0244299	−	2.50544i
$31$	−5.25911	−	3.82097i	−0.944565	−	0.686266i	0.00495033	−	0.999988i	$-0.498424\pi$
$31$	−5.25911	−	3.82097i	−0.944565	−	0.686266i	−0.949515	+	0.313721i	$0.898424\pi$
$32$		−	7.75597i		−	1.37107i
$33$	1.78751	−	2.46030i	0.311166	−	0.428283i
$34$	0.604031	−	1.85902i	0.103590	−	0.318819i
$35$	5.74226	−	4.25816i	0.970620	−	0.719760i
$36$	3.85893	+	11.8766i	0.643155	+	1.97943i
$37$	7.36049	+	2.39157i	1.21006	+	0.393171i	0.843451	−	0.537205i	$-0.180520\pi$
$37$	7.36049	+	2.39157i	1.21006	+	0.393171i	0.366605	+	0.930377i	$0.380520\pi$
$38$	−7.34145	−	2.38538i	−1.19094	−	0.386960i
$39$	5.38424	+	16.5710i	0.862168	+	2.65348i
$40$	−0.783227	+	0.00763705i	−0.123839	+	0.00120752i
$41$	−2.64384	+	8.13692i	−0.412899	+	1.27077i	0.501218	+	0.865321i	$0.332886\pi$
$41$	−2.64384	+	8.13692i	−0.412899	+	1.27077i	−0.914117	+	0.405451i	$0.867114\pi$
$42$	−11.5331	+	15.8740i	−1.77960	+	2.44941i
$43$		−	4.68498i		−	0.714452i	−0.934018	−	0.357226i	$-0.883723\pi$
$43$		−	4.68498i		−	0.714452i	0.934018	−	0.357226i	$-0.116277\pi$
$44$	1.42674	+	1.03659i	0.215090	+	0.156272i
$45$	14.5384	−	4.88103i	2.16725	−	0.727620i
$46$	−3.68329	+	2.67607i	−0.543072	+	0.394565i
$47$	−2.21169	−	3.04413i	−0.322608	−	0.444032i	0.616653	−	0.787235i	$-0.288488\pi$
$47$	−2.21169	−	3.04413i	−0.322608	−	0.444032i	−0.939261	+	0.343203i	$0.888488\pi$
$48$	12.9189	−	4.19761i	1.86468	−	0.605872i
$49$	−3.22110			−0.460156
$50$	−0.190578	−	9.77157i	−0.0269518	−	1.38191i
$51$	3.13981			0.439661
$52$	−9.60962	+	3.12235i	−1.33261	+	0.432993i
$53$	3.90172	+	5.37025i	0.535942	+	0.737661i	0.988021	−	0.154317i	$-0.0493177\pi$
$53$	3.90172	+	5.37025i	0.535942	+	0.737661i	−0.452080	+	0.891978i	$0.649318\pi$
$54$	−19.1578	+	13.9190i	−2.60705	+	1.89413i
$55$	1.25586	−	1.76447i	0.169340	−	0.237921i
$56$	0.906003	+	0.658250i	0.121070	+	0.0879624i
$57$		−	12.3994i		−	1.64234i
$58$	−9.59136	+	13.2014i	−1.25941	+	1.73343i
$59$	3.31406	−	10.1996i	0.431454	−	1.32788i	−0.465223	−	0.885194i	$-0.654026\pi$
$59$	3.31406	−	10.1996i	0.431454	−	1.32788i	0.896677	−	0.442686i	$-0.145974\pi$
$60$	4.06867	+	12.1187i	0.525263	+	1.56452i
$61$	1.77287	+	5.45633i	0.226993	+	0.698611i	0.998083	+	0.0618860i	$0.0197115\pi$
$61$	1.77287	+	5.45633i	0.226993	+	0.698611i	−0.771091	+	0.636725i	$0.780288\pi$
$62$	12.0848	+	3.92658i	1.53477	+	0.498676i
$63$	−20.8535	−	6.77570i	−2.62729	−	0.853658i
$64$	2.01105	+	6.18938i	0.251381	+	0.773672i
$65$	3.94936	+	11.7633i	0.489857	+	1.45906i
$66$	−1.83692	+	5.65345i	−0.226109	+	0.695891i
$67$	−3.03778	+	4.18115i	−0.371124	+	0.510808i	−0.953206	−	0.302322i	$-0.902238\pi$
$67$	−3.03778	+	4.18115i	−0.371124	+	0.510808i	0.582082	+	0.813130i	$0.302238\pi$
$68$			1.82080i			0.220804i
$69$	−5.91647	−	4.29857i	−0.712259	−	0.517486i
$70$	−8.10290	+	11.3845i	−0.968482	+	1.36071i
$71$	8.40244	−	6.10473i	0.997187	−	0.724499i	0.0357036	−	0.999362i	$-0.488633\pi$
$71$	8.40244	−	6.10473i	0.997187	−	0.724499i	0.961483	+	0.274864i	$0.0886328\pi$
$72$	1.41210	+	1.94359i	0.166418	+	0.229054i
$73$	0.183701	−	0.0596879i	0.0215005	−	0.00698594i	−0.298247	−	0.954489i	$-0.596402\pi$
$73$	0.183701	−	0.0596879i	0.0215005	−	0.00698594i	0.319748	+	0.947503i	$0.396402\pi$
$74$	−15.1278			−1.75858
$75$	14.8332	−	5.14149i	1.71280	−	0.593688i
$76$	7.19051			0.824808
$77$	−2.94498	+	0.956881i	−0.335611	+	0.109047i
$78$	−20.0188	−	27.5535i	−2.26668	−	3.11982i
$79$	−0.139692	+	0.101492i	−0.0157165	+	0.0114187i	−0.595616	−	0.803269i	$-0.703092\pi$
$79$	−0.139692	+	0.101492i	−0.0157165	+	0.0114187i	0.579899	+	0.814688i	$0.303092\pi$
$80$	9.17083	−	3.07896i	1.02533	−	0.344238i
$81$	−14.1275	−	10.2642i	−1.56972	−	1.14047i
$82$		−	16.7236i		−	1.84682i
$83$	−0.926093	+	1.27466i	−0.101652	+	0.139912i	−0.856813	−	0.515628i	$-0.827559\pi$
$83$	−0.926093	+	1.27466i	−0.101652	+	0.139912i	0.755161	+	0.655540i	$0.227559\pi$
$84$	5.64801	−	17.3828i	0.616249	−	1.89662i
$85$	2.23596	−	0.0218023i	0.242524	−	0.00236479i
$86$	2.82987	+	8.70945i	0.305153	+	0.939164i
$87$	−24.9284	−	8.09972i	−2.67260	−	0.868382i
$88$	0.322669	+	0.104841i	0.0343966	+	0.0111761i
$89$	0.910731	+	2.80294i	0.0965373	+	0.297111i	0.987651	−	0.156668i	$-0.0500753\pi$
$89$	0.910731	+	2.80294i	0.0965373	+	0.297111i	−0.891114	+	0.453780i	$0.850075\pi$
$90$	−24.0788	+	17.8555i	−2.53813	+	1.88214i
$91$	5.48238	−	16.8730i	0.574710	−	1.76878i
$92$	2.49277	−	3.43100i	0.259889	−	0.357706i
$93$			20.4107i			2.11649i
$94$	5.95031	+	4.32316i	0.613728	+	0.445899i
$95$	−0.0860994	−	8.83004i	−0.00883361	−	0.905943i
$96$	−19.7014	+	14.3139i	−2.01077	+	1.46091i
$97$	7.06616	+	9.72573i	0.717459	+	0.987498i	0.999604	+	0.0281264i	$0.00895408\pi$
$97$	7.06616	+	9.72573i	0.717459	+	0.987498i	−0.282145	+	0.959372i	$0.591046\pi$
$98$	5.98807	−	1.94564i	0.604886	−	0.196539i
$99$	−6.64278			−0.667625
$100$	2.98159	+	8.60190i	0.298159	+	0.860190i
$101$	−9.21688			−0.917114			−0.458557	−	0.888665i	$-0.651634\pi$
$101$	−9.21688			−0.917114			−0.458557	+	0.888665i	$0.651634\pi$
$102$	−5.83696	+	1.89654i	−0.577945	+	0.187786i
$103$	7.31951	+	10.0744i	0.721213	+	0.992665i	0.999483	+	0.0321617i	$0.0102392\pi$
$103$	7.31951	+	10.0744i	0.721213	+	0.992665i	−0.278270	+	0.960503i	$0.589761\pi$
$104$	−1.57260	+	1.14256i	−0.154207	+	0.112038i
$105$	−21.4139	−	6.72769i	−2.08979	−	0.656556i
$106$	−10.4972	−	7.62663i	−1.01957	−	0.740764i
$107$			6.10323i			0.590022i	0.955494	+	0.295011i	$0.0953233\pi$
$107$			6.10323i			0.590022i	−0.955494	+	0.295011i	$0.904677\pi$
$108$	12.9656	−	17.8456i	1.24761	−	1.71719i
$109$	−2.02394	+	6.22905i	−0.193859	+	0.596635i	0.806129	+	0.591739i	$0.201558\pi$
$109$	−2.02394	+	6.22905i	−0.193859	+	0.596635i	−0.999988	+	0.00489604i	$0.998442\pi$
$110$	−1.26887	+	4.03876i	−0.120982	+	0.385081i
$111$	−7.50907	−	23.1105i	−0.712729	−	2.19355i
$112$	−13.1544	−	4.27412i	−1.24297	−	0.403867i
$113$	18.4494	+	5.99459i	1.73558	+	0.563923i	0.994237	−	0.107206i	$-0.0341905\pi$
$113$	18.4494	+	5.99459i	1.73558	+	0.563923i	0.741340	+	0.671129i	$0.234191\pi$
$114$	7.48964	+	23.0507i	0.701469	+	2.15890i
$115$	−4.24316	−	3.02007i	−0.395677	−	0.281623i
$116$	4.69708	−	14.4561i	0.436113	−	1.34222i
$117$	22.3707	−	30.7907i	2.06817	−	2.84660i
$118$			20.9631i			1.92981i
$119$	−2.58646	−	1.87918i	−0.237101	−	0.172264i
$120$	1.46487	+	1.97543i	0.133724	+	0.180331i
$121$	8.14024	−	5.91423i	0.740022	−	0.537657i
$122$	−6.59159	−	9.07254i	−0.596774	−	0.821389i
$123$	25.5484	−	8.30117i	2.30362	−	0.748491i
$124$	−11.8363			−1.06293
$125$	10.5275	−	3.76443i	0.941612	−	0.336700i
$126$	42.8597			3.81824
$127$	−18.6482	+	6.05917i	−1.65476	+	0.537665i	−0.979764	−	0.200156i	$-0.935855\pi$
$127$	−18.6482	+	6.05917i	−1.65476	+	0.537665i	−0.674997	+	0.737820i	$0.735855\pi$
$128$	1.64053	+	2.25800i	0.145004	+	0.199581i
$129$	−11.9006	+	8.64628i	−1.04779	+	0.761263i
$130$	−14.4473	−	19.4827i	−1.26712	−	1.70875i
$131$	−0.921594	−	0.669577i	−0.0805200	−	0.0585012i	0.546797	−	0.837265i	$-0.315847\pi$
$131$	−0.921594	−	0.669577i	−0.0805200	−	0.0585012i	−0.627317	+	0.778764i	$0.715847\pi$
$132$		−	5.53722i		−	0.481953i
$133$	−7.42106	+	10.2142i	−0.643487	+	0.885684i
$134$	3.12174	−	9.60774i	0.269677	−	0.829982i
$135$	−22.0698	−	15.7082i	−1.89947	−	1.35195i
$136$	0.108245	+	0.333142i	0.00928189	+	0.0285667i
$137$	−1.64402	−	0.534175i	−0.140458	−	0.0456376i	0.237944	−	0.971279i	$-0.423526\pi$
$137$	−1.64402	−	0.534175i	−0.140458	−	0.0456376i	−0.378402	+	0.925641i	$0.623526\pi$
$138$	13.5953	+	4.41737i	1.15731	+	0.376032i
$139$	0.340745	+	1.04870i	0.0289016	+	0.0889499i	0.964467	−	0.264204i	$-0.0851092\pi$
$139$	0.340745	+	1.04870i	0.0289016	+	0.0889499i	−0.935565	+	0.353154i	$0.885109\pi$
$140$	3.90143	−	12.4181i	0.329731	−	1.04952i
$141$	−3.65082	+	11.2361i	−0.307455	+	0.946249i
$142$	−11.9328	+	16.4241i	−1.00138	+	1.37828i
$143$		−	5.37483i		−	0.449466i
$144$	−24.0047	−	17.4405i	−2.00039	−	1.45337i
$145$	−17.8086	−	5.59498i	−1.47892	−	0.464638i
$146$	−0.305449	+	0.221922i	−0.0252791	+	0.0183664i
$147$	5.94464	+	8.18210i	0.490306	+	0.674848i
$148$	13.4019	−	4.35456i	1.10163	−	0.357942i
$149$	−4.07559			−0.333885			−0.166943	−	0.985967i	$-0.553389\pi$
$149$	−4.07559			−0.333885			−0.166943	+	0.985967i	$0.553389\pi$
$150$	−24.4696	+	18.5179i	−1.99794	+	1.51198i
$151$	21.2557			1.72977			0.864884	−	0.501972i	$-0.167392\pi$
$151$	21.2557			1.72977			0.864884	+	0.501972i	$0.167392\pi$
$152$	1.31561	−	0.427469i	0.106710	−	0.0346723i
$153$	−4.03127	−	5.54857i	−0.325909	−	0.448575i
$154$	4.89677	−	3.55771i	0.394593	−	0.286689i
$155$	0.141728	+	14.5351i	0.0113839	+	1.16749i
$156$	25.6662	+	18.6476i	2.05494	+	1.49300i
$157$			10.5255i			0.840024i	0.907519	+	0.420012i	$0.137974\pi$
$157$			10.5255i			0.840024i	−0.907519	+	0.420012i	$0.862026\pi$
$158$	0.198385	−	0.273053i	0.0157826	−	0.0217229i
$159$	6.44055	−	19.8220i	0.510768	−	1.57198i
$160$	−13.9306	+	10.3302i	−1.10131	+	0.816674i
$161$	2.30108	+	7.08201i	0.181351	+	0.558141i
$162$	32.4631	+	10.5479i	2.55054	+	0.828721i
$163$	10.3040	+	3.34796i	0.807068	+	0.262232i	0.683355	−	0.730086i	$-0.260520\pi$
$163$	10.3040	+	3.34796i	0.807068	+	0.262232i	0.123712	+	0.992318i	$0.460520\pi$
$164$	4.81390	+	14.8157i	0.375903	+	1.15691i
$165$	−6.79977	+	0.0663028i	−0.529362	+	0.00516167i
$166$	0.951689	−	2.92900i	0.0738654	−	0.227334i
$167$	2.89195	−	3.98043i	0.223786	−	0.308015i	−0.682330	−	0.731044i	$-0.739033\pi$
$167$	2.89195	−	3.98043i	0.223786	−	0.308015i	0.906116	+	0.423029i	$0.139033\pi$
$168$		−	3.51622i		−	0.271282i
$169$	14.3963	+	10.4595i	1.10740	+	0.804576i
$170$	−4.14352	+	1.39112i	−0.317794	+	0.106694i
$171$	−21.9119	+	15.9199i	−1.67564	+	1.21742i
$172$	−5.01404	−	6.90123i	−0.382317	−	0.526214i
$173$	−7.21916	+	2.34565i	−0.548863	+	0.178336i	−0.570304	−	0.821434i	$-0.693175\pi$
$173$	−7.21916	+	2.34565i	−0.548863	+	0.178336i	0.0214413	+	0.999770i	$0.493175\pi$
$174$	51.2348			3.88410
$175$	−15.2963	−	4.64232i	−1.15629	−	0.350926i
$176$	−4.19028			−0.315854
$177$	−32.0249	+	10.4055i	−2.40714	+	0.782127i
$178$	−3.38613	−	4.66061i	−0.253801	−	0.349327i
$179$	−10.7067	+	7.77886i	−0.800255	+	0.581419i	−0.910989	−	0.412431i	$-0.864680\pi$
$179$	−10.7067	+	7.77886i	−0.800255	+	0.581419i	0.110734	+	0.993850i	$0.464680\pi$
$180$	16.1920	−	22.7495i	1.20688	−	1.69565i
$181$	9.12526	+	6.62989i	0.678275	+	0.492796i	0.872785	−	0.488105i	$-0.162312\pi$
$181$	9.12526	+	6.62989i	0.678275	+	0.492796i	−0.194510	+	0.980901i	$0.562312\pi$
$182$			34.6788i			2.57056i
$183$	10.5881	−	14.5732i	0.782692	−	1.07728i
$184$	0.252120	−	0.775946i	0.0185865	−	0.0572035i
$185$	−5.50793	−	16.4056i	−0.404951	−	1.20617i
$186$	−12.3287	−	37.9439i	−0.903985	−	2.78218i
$187$	−0.921156	−	0.299302i	−0.0673616	−	0.0218871i
$188$	−6.51588	−	2.11714i	−0.475219	−	0.154408i
$189$	11.9686	+	36.8355i	0.870585	+	2.67939i
$190$	5.49368	+	16.3632i	0.398553	+	1.18711i
$191$	1.25752	−	3.87025i	0.0909909	−	0.280041i	−0.895197	−	0.445670i	$-0.852965\pi$
$191$	1.25752	−	3.87025i	0.0909909	−	0.280041i	0.986188	+	0.165629i	$0.0529654\pi$
$192$	12.0105	−	16.5311i	0.866787	−	1.19303i
$193$			25.6866i			1.84896i	0.381228	+	0.924481i	$0.375501\pi$
$193$			25.6866i			1.84896i	−0.381228	+	0.924481i	$0.624499\pi$
$194$	−19.0107	−	13.8121i	−1.36489	−	0.991652i
$195$	22.5921	−	31.7417i	1.61785	−	2.27307i
$196$	−4.74485	+	3.44734i	−0.338918	+	0.246238i
$197$	13.5038	+	18.5864i	0.962107	+	1.32423i	0.945935	+	0.324357i	$0.105148\pi$
$197$	13.5038	+	18.5864i	0.962107	+	1.32423i	0.0161724	+	0.999869i	$0.494852\pi$
$198$	12.3490	−	4.01245i	0.877608	−	0.285152i
$199$	9.40113			0.666428			0.333214	−	0.942851i	$-0.391867\pi$
$199$	9.40113			0.666428			0.333214	+	0.942851i	$0.391867\pi$
$200$	1.05690	+	1.39660i	0.0747341	+	0.0987542i
$201$	16.2271			1.14457
$202$	17.1343	−	5.56728i	1.20557	−	0.391713i
$203$	15.6874	+	21.5919i	1.10104	+	1.51545i
$204$	4.62511	−	3.36034i	0.323823	−	0.235271i
$205$	18.1362	−	6.08894i	1.26669	−	0.425270i
$206$	−19.6924	−	14.3074i	−1.37203	−	0.996840i
$207$			15.9744i			1.11030i
$208$	14.1115	−	19.4228i	0.978456	−	1.34673i
$209$	−1.18197	+	3.63774i	−0.0817588	+	0.251628i
$210$	43.8726	−	0.427790i	3.02750	−	0.0295203i
$211$	0.846592	+	2.60554i	0.0582818	+	0.179373i	0.975959	−	0.217953i	$-0.0699381\pi$
$211$	0.846592	+	2.60554i	0.0582818	+	0.179373i	−0.917677	+	0.397326i	$0.869938\pi$
$212$	11.4949	+	3.73491i	0.789472	+	0.256515i
$213$	−31.0140	−	10.0771i	−2.12504	−	0.690469i
$214$	−3.68654	−	11.3460i	−0.252007	−	0.775597i
$215$	−8.41476	+	6.23994i	−0.573882	+	0.425560i
$216$	1.31135	−	4.03591i	0.0892257	−	0.274609i
$217$	12.2158	−	16.8136i	0.829263	−	1.14138i
$218$		−	12.8024i		−	0.867091i
$219$	−0.490642	−	0.356472i	−0.0331545	−	0.0240882i
$220$	−0.0384494	−	3.94323i	−0.00259226	−	0.265853i
$221$	4.48948	−	3.26180i	0.301995	−	0.219412i
$222$	27.9190	+	38.4271i	1.87380	+	2.57906i
$223$	24.6584	−	8.01200i	1.65125	−	0.536523i	0.672239	−	0.740334i	$-0.265333\pi$
$223$	24.6584	−	8.01200i	1.65125	−	0.536523i	0.979010	+	0.203811i	$0.0653327\pi$
$224$	24.7962			1.65676
$225$	−28.1306	−	19.6115i	−1.87537	−	1.30744i
$226$	−37.9187			−2.52232
$227$	6.46877	−	2.10183i	0.429348	−	0.139503i	−0.0863681	−	0.996263i	$-0.527526\pi$
$227$	6.46877	−	2.10183i	0.429348	−	0.139503i	0.515716	+	0.856760i	$0.327526\pi$
$228$	−13.2703	−	18.2650i	−0.878849	−	1.20963i
$229$	3.93122	−	2.85620i	0.259782	−	0.188743i	−0.450269	−	0.892893i	$-0.648672\pi$
$229$	3.93122	−	2.85620i	0.259782	−	0.188743i	0.710051	+	0.704150i	$0.248672\pi$
$230$	9.71232	+	3.05135i	0.640411	+	0.201200i
$231$	7.86568	+	5.71475i	0.517524	+	0.376003i
$232$		−	2.92421i		−	0.191984i
$233$	−8.37804	+	11.5314i	−0.548864	+	0.755446i	−0.989857	−	0.142064i	$-0.954626\pi$
$233$	−8.37804	+	11.5314i	−0.548864	+	0.755446i	0.440994	+	0.897510i	$0.354626\pi$
$234$	−22.9890	+	70.7530i	−1.50284	+	4.62527i
$235$	−2.52185	+	8.02693i	−0.164507	+	0.523619i
$236$	−6.03423	−	18.5715i	−0.392795	−	1.20890i
$237$	0.515611	+	0.167532i	0.0334925	+	0.0108824i
$238$	5.94336	+	1.93111i	0.385251	+	0.125176i
$239$	2.45246	+	7.54790i	0.158636	+	0.488233i	0.998511	−	0.0545475i	$-0.0173716\pi$
$239$	2.45246	+	7.54790i	0.158636	+	0.488233i	−0.839875	+	0.542780i	$0.817372\pi$
$240$	−24.7461	−	17.6130i	−1.59736	−	1.13692i
$241$	−1.37769	+	4.24009i	−0.0887447	+	0.273128i	−0.985573	−	0.169251i	$-0.945865\pi$
$241$	−1.37769	+	4.24009i	−0.0887447	+	0.273128i	0.896828	+	0.442379i	$0.145865\pi$
$242$	−11.5605	+	15.9116i	−0.743135	+	1.02284i
$243$			18.4850i			1.18581i
$244$	8.45110	+	6.14008i	0.541026	+	0.393079i
$245$	4.29019	+	5.78546i	0.274090	+	0.369620i
$246$	−42.4807	+	30.8640i	−2.70847	+	1.96782i
$247$	−12.8812	−	17.7294i	−0.819609	−	1.12810i
$248$	−2.16563	+	0.703657i	−0.137518	+	0.0446822i
$249$	4.94697			0.313501
$250$	−17.2970	+	13.3571i	−1.09396	+	0.844777i
$251$	−16.9443			−1.06951			−0.534756	−	0.845007i	$-0.679596\pi$
$251$	−16.9443			−1.06951			−0.534756	+	0.845007i	$0.679596\pi$
$252$	−37.9699	+	12.3372i	−2.39188	+	0.777169i
$253$	1.32601	+	1.82510i	0.0833656	+	0.114743i
$254$	31.0074	−	22.5282i	1.94558	−	1.41355i
$255$	−4.18192	−	5.63946i	−0.261882	−	0.353157i
$256$	−14.9437	−	10.8572i	−0.933980	−	0.678576i
$257$		−	17.4123i		−	1.08615i	−0.839685	−	0.543074i	$-0.817260\pi$
$257$		−	17.4123i		−	1.08615i	0.839685	−	0.543074i	$-0.182740\pi$
$258$	16.9008	−	23.2619i	1.05220	−	1.44822i
$259$	−7.64595	+	23.5318i	−0.475096	+	1.46220i
$260$	18.4072	+	13.1013i	1.14157	+	0.812509i
$261$	17.6925	+	54.4520i	1.09514	+	3.37050i
$262$	2.11770	+	0.688084i	0.130832	+	0.0425100i
$263$	−24.6613	−	8.01295i	−1.52068	−	0.494099i	−0.574712	−	0.818355i	$-0.694886\pi$
$263$	−24.6613	−	8.01295i	−1.52068	−	0.494099i	−0.945969	+	0.324256i	$0.894886\pi$
$264$	−0.329182	−	1.01312i	−0.0202597	−	0.0623531i
$265$	4.44888	−	14.1606i	0.273293	−	0.869878i
$266$	7.62617	−	23.4709i	0.467590	−	1.43910i
$267$	5.43914	−	7.48633i	0.332870	−	0.458156i
$268$			9.41021i			0.574820i
$269$	−13.3017	−	9.66425i	−0.811019	−	0.589240i	0.103107	−	0.994670i	$-0.467122\pi$
$269$	−13.3017	−	9.66425i	−0.811019	−	0.589240i	−0.914126	+	0.405430i	$0.867122\pi$
$270$	50.5164	+	15.8709i	3.07433	+	0.965874i
$271$	−1.82633	+	1.32691i	−0.110942	+	0.0806038i	−0.641873	−	0.766811i	$-0.721842\pi$
$271$	−1.82633	+	1.32691i	−0.110942	+	0.0806038i	0.530931	+	0.847415i	$0.321842\pi$
$272$	−2.54293	−	3.50004i	−0.154188	−	0.212221i
$273$	−52.9781	+	17.2136i	−3.20638	+	1.04182i
$274$	3.37892			0.204128
$275$	−4.84188	+	0.0944328i	−0.291976	+	0.00569451i
$276$	−13.3158			−0.801515
$277$	3.15566	−	1.02534i	0.189605	−	0.0616065i	−0.212675	−	0.977123i	$-0.568218\pi$
$277$	3.15566	−	1.02534i	0.189605	−	0.0616065i	0.402281	+	0.915516i	$0.368218\pi$
$278$	−1.26690	−	1.74374i	−0.0759836	−	0.104582i
$279$	36.0691	−	26.2058i	2.15940	−	1.56890i
$280$	−0.0244160	−	2.50401i	−0.00145913	−	0.149643i
$281$	−9.91912	−	7.20666i	−0.591725	−	0.429913i	0.251207	−	0.967933i	$-0.419173\pi$
$281$	−9.91912	−	7.20666i	−0.591725	−	0.429913i	−0.842932	+	0.538020i	$0.819173\pi$
$282$		−	23.0933i		−	1.37518i
$283$	1.28631	−	1.77046i	0.0764635	−	0.105243i	−0.769072	−	0.639162i	$-0.779281\pi$
$283$	1.28631	−	1.77046i	0.0764635	−	0.105243i	0.845536	+	0.533919i	$0.179281\pi$
$284$	5.84375	−	17.9852i	0.346763	−	1.06723i
$285$	−22.2708	+	16.5148i	−1.31921	+	0.978255i
$286$	3.24657	+	9.99191i	0.191974	+	0.590834i
$287$	−26.0141	−	8.45249i	−1.53556	−	0.498935i
$288$	50.5901	+	16.4377i	2.98105	+	0.968602i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	36.4860	−	0.355765i	2.14253	−	0.0208912i
$291$	11.6641	−	35.8983i	0.683760	−	2.10440i
$292$	0.206721	−	0.284527i	0.0120974	−	0.0166507i
$293$		−	15.1187i		−	0.883245i	−0.897201	−	0.441622i	$-0.854403\pi$
$293$		−	15.1187i		−	0.883245i	0.897201	−	0.441622i	$-0.145597\pi$
$294$	−15.9934	−	11.6199i	−0.932755	−	0.677687i
$295$	−22.7337	+	7.63249i	−1.32361	+	0.444381i
$296$	2.19322	−	1.59346i	0.127478	−	0.0926182i
$297$	6.89694	+	9.49283i	0.400201	+	0.550830i
$298$	7.57658	−	2.46178i	0.438900	−	0.142607i
$299$	−12.9253			−0.747488
$300$	16.3476	−	23.4488i	0.943828	−	1.35382i
$301$	14.9781			0.863322
$302$	−39.5148	+	12.8391i	−2.27382	+	0.738809i
$303$	17.0101	+	23.4124i	0.977203	+	1.34500i
$304$	−13.8220	+	10.0423i	−0.792748	+	0.575965i
$305$	7.43891	−	10.4516i	0.425951	−	0.598456i
$306$	10.8457	+	7.87986i	0.620008	+	0.450462i
$307$		−	16.1363i		−	0.920949i	−0.887673	−	0.460475i	$-0.847679\pi$
$307$		−	16.1363i		−	0.920949i	0.887673	−	0.460475i	$-0.152321\pi$
$308$	−3.31402	+	4.56136i	−0.188834	+	0.259908i
$309$	12.0823	−	37.1855i	0.687337	−	2.11541i
$310$	−9.04315	−	26.9355i	−0.513617	−	1.52983i
$311$	0.584245	+	1.79812i	0.0331295	+	0.101962i	0.966254	−	0.257592i	$-0.0829289\pi$
$311$	0.584245	+	1.79812i	0.0331295	+	0.101962i	−0.933124	+	0.359554i	$0.882929\pi$
$312$	5.80459	+	1.88603i	0.328620	+	0.106775i
$313$	−22.7453	−	7.39039i	−1.28564	−	0.417730i	−0.415077	−	0.909786i	$-0.636245\pi$
$313$	−22.7453	−	7.39039i	−1.28564	−	0.417730i	−0.870563	+	0.492057i	$0.836245\pi$
$314$	−6.35771	−	19.5670i	−0.358786	−	1.10423i
$315$	15.6049	+	46.4798i	0.879234	+	2.61884i
$316$	−0.0971530	+	0.299006i	−0.00546528	+	0.0168204i
$317$	7.35498	−	10.1233i	0.413097	−	0.568579i	−0.550874	−	0.834589i	$-0.685705\pi$
$317$	7.35498	−	10.1233i	0.413097	−	0.568579i	0.963970	+	0.266010i	$0.0857053\pi$
$318$			40.7396i			2.28457i
$319$	6.54137	+	4.75259i	0.366247	+	0.266094i
$320$	8.43832	−	11.8557i	0.471716	−	0.662756i
$321$	15.5032	−	11.2637i	0.865303	−	0.628680i
$322$	−8.55551	−	11.7756i	−0.476780	−	0.656231i
$323$	−3.75582	+	1.22034i	−0.208979	+	0.0679015i
$324$	−31.7957			−1.76643
$325$	15.8682	−	22.7611i	0.880208	−	1.26256i
$326$	−21.1775			−1.17291
$327$	19.5580	−	6.35479i	1.08156	−	0.351421i
$328$	1.76155	+	2.42457i	0.0972655	+	0.133874i
$329$	9.73221	−	7.07087i	0.536554	−	0.389829i
$330$	12.6008	−	4.23053i	0.693654	−	0.232883i
$331$	−3.21289	−	2.33430i	−0.176597	−	0.128305i	0.495976	−	0.868336i	$-0.334811\pi$
$331$	−3.21289	−	2.33430i	−0.176597	−	0.128305i	−0.672572	+	0.740032i	$0.734811\pi$
$332$			2.86878i			0.157445i
$333$	−31.1991	+	42.9419i	−1.70970	+	2.35320i
$334$	−2.97188	+	9.14652i	−0.162614	+	0.500475i
$335$	11.5559	−	0.112678i	0.631364	−	0.00615626i
$336$	13.4199	+	41.3023i	0.732117	+	2.25323i
$337$	22.1340	+	7.19177i	1.20572	+	0.391761i	0.841861	−	0.539695i	$-0.181461\pi$
$337$	22.1340	+	7.19177i	1.20572	+	0.391761i	0.363855	+	0.931456i	$0.381461\pi$
$338$	−33.0807	−	10.7486i	−1.79936	−	0.584646i
$339$	−18.8219	−	57.9277i	−1.02226	−	3.14620i
$340$	3.27036	−	2.42513i	0.177360	−	0.131521i
$341$	1.94565	−	5.98809i	0.105363	−	0.324273i
$342$	31.1184	−	42.8308i	1.68269	−	2.31602i
$343$			12.0813i			0.652330i
$344$	−1.32767	−	0.964605i	−0.0715829	−	0.0520080i
$345$	0.159443	+	16.3519i	0.00858415	+	0.880359i
$346$	12.0037	−	8.72119i	0.645323	−	0.468854i
$347$	−1.89693	−	2.61090i	−0.101833	−	0.140161i	0.755060	−	0.655656i	$-0.227608\pi$
$347$	−1.89693	−	2.61090i	−0.101833	−	0.140161i	−0.856892	+	0.515496i	$0.827608\pi$
$348$	−45.3895	+	14.7479i	−2.43313	+	0.790573i
$349$	26.9466			1.44242			0.721208	−	0.692719i	$-0.243587\pi$
$349$	26.9466			1.44242			0.721208	+	0.692719i	$0.243587\pi$
$350$	31.2401	−	0.609287i	1.66986	−	0.0325678i
$351$	−67.2279			−3.58836
$352$	7.14446	−	2.32137i	0.380801	−	0.123730i
$353$	15.7854	+	21.7268i	0.840173	+	1.15640i	0.985943	+	0.167081i	$0.0534340\pi$
$353$	15.7854	+	21.7268i	0.840173	+	1.15640i	−0.145770	+	0.989319i	$0.546566\pi$
$354$	53.2496	−	38.6881i	2.83018	−	2.05625i
$355$	−22.1561	−	6.96085i	−1.17592	−	0.369443i
$356$	4.34137	+	3.15419i	0.230092	+	0.167172i
$357$			10.0381i			0.531273i
$358$	15.2052	−	20.9282i	0.803621	−	1.10609i
$359$	1.68467	−	5.18487i	0.0889134	−	0.273647i	−0.896706	−	0.442626i	$-0.854047\pi$
$359$	1.68467	−	5.18487i	0.0889134	−	0.273647i	0.985620	+	0.168979i	$0.0540469\pi$
$360$	1.61013	−	5.12497i	0.0848613	−	0.270109i
$361$	−1.05208	−	3.23796i	−0.0553725	−	0.170419i
$362$	−20.9687	−	6.81313i	−1.10209	−	0.358090i
$363$	−30.0462	−	9.76260i	−1.57702	−	0.512403i
$364$	−9.98231	−	30.7224i	−0.523215	−	1.61029i
$365$	−0.351878	−	0.250449i	−0.0184181	−	0.0131091i
$366$	−10.8807	+	33.4874i	−0.568743	+	1.75041i
$367$	−3.98595	+	5.48619i	−0.208065	+	0.286377i	−0.900277	−	0.435317i	$-0.856636\pi$
$367$	−3.98595	+	5.48619i	−0.208065	+	0.286377i	0.692212	+	0.721694i	$0.256636\pi$
$368$			10.0767i			0.525283i
$369$	−47.4716	−	34.4902i	−2.47128	−	1.79549i
$370$	20.1488	+	27.1714i	1.04749	+	1.41257i
$371$	−17.1689	+	12.4740i	−0.891367	+	0.647616i
$372$	21.8443	+	30.0661i	1.13257	+	1.55886i
$373$	21.7140	−	7.05531i	1.12431	−	0.365310i	0.312898	−	0.949787i	$-0.398700\pi$
$373$	21.7140	−	7.05531i	1.12431	−	0.365310i	0.811411	+	0.584476i	$0.198700\pi$
$374$	1.89323			0.0978967
$375$	−28.9912	−	19.7943i	−1.49710	−	1.02217i
$376$	−1.31804			−0.0679727
$377$	−44.0584	+	14.3155i	−2.26913	+	0.737284i
$378$	−44.4995	−	61.2484i	−2.28881	−	3.15028i
$379$	6.72907	−	4.88896i	0.345649	−	0.251129i	−0.401392	−	0.915906i	$-0.631474\pi$
$379$	6.72907	−	4.88896i	0.345649	−	0.251129i	0.747041	+	0.664777i	$0.231474\pi$
$380$	−9.57707	−	12.9150i	−0.491293	−	0.662525i
$381$	49.8072	+	36.1870i	2.55170	+	1.85392i
$382$			7.95444i			0.406984i
$383$	−6.54770	+	9.01213i	−0.334572	+	0.460498i	−0.942846	−	0.333228i	$-0.891862\pi$
$383$	−6.54770	+	9.01213i	−0.334572	+	0.460498i	0.608274	+	0.793727i	$0.291862\pi$
$384$	2.70802	−	8.33444i	0.138193	−	0.425315i
$385$	5.64109	+	4.01505i	0.287497	+	0.204626i
$386$	−15.5155	−	47.7518i	−0.789719	−	2.43050i
$387$	30.5588	+	9.92917i	1.55339	+	0.504728i
$388$	20.8177	+	6.76407i	1.05686	+	0.343394i
$389$	1.77207	+	5.45386i	0.0898474	+	0.276522i	0.985877	−	0.167473i	$-0.0535608\pi$
$389$	1.77207	+	5.45386i	0.0898474	+	0.276522i	−0.896029	+	0.443995i	$0.853561\pi$
$390$	−22.8262	+	72.6546i	−1.15585	+	3.67901i
$391$	−0.719754	+	2.21517i	−0.0363995	+	0.112026i
$392$	−0.663202	+	0.912819i	−0.0334968	+	0.0461043i
$393$			3.57672i			0.180422i
$394$	−36.3306	−	26.3957i	−1.83031	−	1.32980i
$395$	0.368347	+	0.115725i	0.0185335	+	0.00582275i
$396$	−9.78518	+	7.10935i	−0.491724	+	0.357258i
$397$	−18.4525	−	25.3976i	−0.926103	−	1.27467i	−0.961360	−	0.275293i	$-0.911225\pi$
$397$	−18.4525	−	25.3976i	−0.926103	−	1.27467i	0.0352576	−	0.999378i	$-0.488775\pi$
$398$	−17.4769	+	5.67857i	−0.876036	+	0.284641i
$399$	39.6415			1.98456
$400$	−17.7448	−	12.3710i	−0.887241	−	0.618550i
$401$	−9.47687			−0.473252			−0.236626	−	0.971601i	$-0.576042\pi$
$401$	−9.47687			−0.473252			−0.236626	+	0.971601i	$0.576042\pi$
$402$	−30.1665	+	9.80168i	−1.50457	+	0.488863i
$403$	21.2037	+	29.1844i	1.05623	+	1.45378i
$404$	−13.5770	+	9.86425i	−0.675480	+	0.490765i
$405$	0.380722	+	39.0455i	0.0189182	+	1.94019i
$406$	−42.2054	−	30.6640i	−2.09462	−	1.52183i
$407$			7.49596i			0.371561i
$408$	0.646466	−	0.889784i	0.0320048	−	0.0440509i
$409$	−8.72079	+	26.8398i	−0.431215	+	1.32714i	0.465700	+	0.884943i	$0.345803\pi$
$409$	−8.72079	+	26.8398i	−0.431215	+	1.32714i	−0.896916	+	0.442202i	$0.854197\pi$
$410$	−30.0376	+	22.2743i	−1.48345	+	1.10005i
$411$	1.67721	+	5.16191i	0.0827305	+	0.254618i
$412$	21.5641	+	7.00660i	1.06239	+	0.345190i
$413$	32.6087	+	10.5952i	1.60457	+	0.521356i
$414$	−9.64904	−	29.6967i	−0.474224	−	1.45951i
$415$	3.52290	−	0.0343509i	0.172932	−	0.00168622i
$416$	−13.3002	+	40.9337i	−0.652094	+	2.00694i
$417$	2.03502	−	2.80096i	0.0996554	−	0.137164i
$418$		−	7.47656i		−	0.365691i
$419$	14.5226	+	10.5513i	0.709474	+	0.515463i	0.883004	−	0.469366i	$-0.155517\pi$
$419$	14.5226	+	10.5513i	0.709474	+	0.515463i	−0.173530	+	0.984829i	$0.555517\pi$
$420$	−38.7441	+	13.0077i	−1.89052	+	0.634712i
$421$	19.7136	−	14.3227i	0.960781	−	0.698048i	0.00744880	−	0.999972i	$-0.497629\pi$
$421$	19.7136	−	14.3227i	0.960781	−	0.698048i	0.953332	+	0.301924i	$0.0976289\pi$
$422$	−3.14766	−	4.33238i	−0.153225	−	0.210897i
$423$	24.5434	−	7.97463i	1.19334	−	0.387740i
$424$	2.32520			0.112922
$425$	−3.01725	−	3.98701i	−0.146358	−	0.193398i
$426$	63.7424			3.08833
$427$	−17.4441	+	5.66794i	−0.844181	+	0.274291i
$428$	6.53191	+	8.99040i	0.315732	+	0.434567i
$429$	−13.6529	+	9.91944i	−0.659170	+	0.478915i
$430$	11.8741	−	16.6829i	0.572618	−	0.804522i
$431$	−8.28626	−	6.02032i	−0.399135	−	0.289989i	0.370054	−	0.929010i	$-0.379339\pi$
$431$	−8.28626	−	6.02032i	−0.399135	−	0.289989i	−0.769189	+	0.639022i	$0.779339\pi$
$432$			52.4116i			2.52165i
$433$	−18.1924	+	25.0397i	−0.874271	+	1.20333i	0.103704	+	0.994608i	$0.466931\pi$
$433$	−18.1924	+	25.0397i	−0.874271	+	1.20333i	−0.977975	+	0.208723i	$0.933069\pi$
$434$	−12.5534	+	38.6355i	−0.602585	+	1.85457i
$435$	18.6542	+	55.5623i	0.894399	+	2.66401i
$436$	3.68519	+	11.3418i	0.176488	+	0.543176i
$437$	8.74795	+	2.84238i	0.418471	+	0.135969i
$438$	1.12743	+	0.366325i	0.0538708	+	0.0175037i
$439$	9.39801	+	28.9241i	0.448543	+	1.38047i	0.878551	+	0.477648i	$0.158510\pi$
$439$	9.39801	+	28.9241i	0.448543	+	1.38047i	−0.430009	+	0.902825i	$0.641490\pi$
$440$	−0.241456	−	0.719189i	−0.0115110	−	0.0342860i
$441$	6.82667	−	21.0103i	0.325080	−	1.00049i
$442$	−6.37579	+	8.77552i	−0.303265	+	0.417409i
$443$		−	30.3496i		−	1.44195i	−0.692960	−	0.720976i	$-0.743694\pi$
$443$		−	30.3496i		−	1.44195i	0.692960	−	0.720976i	$-0.256306\pi$
$444$	−35.7950	−	26.0066i	−1.69876	−	1.23422i
$445$	3.82140	−	5.36903i	0.181152	−	0.254516i
$446$	−41.0009	+	29.7889i	−1.94145	+	1.41055i
$447$	7.52163	+	10.3526i	0.355761	+	0.489663i
$448$	−19.7877	+	6.42942i	−0.934882	+	0.303762i
$449$	−12.6070			−0.594960			−0.297480	−	0.954728i	$-0.596146\pi$
$449$	−12.6070			−0.594960			−0.297480	+	0.954728i	$0.596146\pi$
$450$	64.1412	+	19.4664i	3.02365	+	0.917656i
$451$	−8.28667			−0.390204
$452$	33.5927	−	10.9149i	1.58007	−	0.513395i
$453$	−39.2282	−	53.9930i	−1.84310	−	2.53681i
$454$	−10.7560	+	7.81468i	−0.504803	+	0.366761i
$455$	−37.6079	+	12.6263i	−1.76309	+	0.591929i
$456$	−3.51385	−	2.55296i	−0.164551	−	0.119553i
$457$		−	11.2778i		−	0.527551i	−0.964584	−	0.263776i	$-0.915032\pi$
$457$		−	11.2778i		−	0.527551i	0.964584	−	0.263776i	$-0.0849678\pi$
$458$	−5.58297	+	7.68430i	−0.260875	+	0.359064i
$459$	−3.74363	+	11.5217i	−0.174738	+	0.537788i
$460$	−9.48260	+	0.0924623i	−0.442128	+	0.00431108i
$461$	8.81205	+	27.1207i	0.410418	+	1.26314i	0.916285	+	0.400526i	$0.131173\pi$
$461$	8.81205	+	27.1207i	0.410418	+	1.26314i	−0.505867	+	0.862611i	$0.668827\pi$
$462$	−18.0743	−	5.87270i	−0.840894	−	0.273223i
$463$	−20.2342	−	6.57448i	−0.940361	−	0.305542i	−0.201568	−	0.979474i	$-0.564604\pi$
$463$	−20.2342	−	6.57448i	−0.940361	−	0.305542i	−0.738793	+	0.673932i	$0.764604\pi$
$464$	11.1605	+	34.3484i	0.518112	+	1.59459i
$465$	36.6600	−	27.1851i	1.70007	−	1.26068i
$466$	8.60960	−	26.4976i	0.398832	−	1.22748i
$467$	10.8677	−	14.9581i	0.502898	−	0.692180i	−0.479803	−	0.877376i	$-0.659292\pi$
$467$	10.8677	−	14.9581i	0.502898	−	0.692180i	0.982702	+	0.185196i	$0.0592920\pi$
$468$		−	69.2983i		−	3.20332i
$469$	−13.3673	−	9.71192i	−0.617245	−	0.448455i
$470$	−0.160356	−	16.4455i	−0.00739665	−	0.758573i
$471$	26.7364	−	19.4251i	1.23195	−	0.895062i
$472$	−2.20811	−	3.03920i	−0.101636	−	0.139891i
$473$	4.31559	−	1.40222i	0.198431	−	0.0644742i
$474$	−1.05972			−0.0486747
$475$	−15.7451	+	11.9154i	−0.722435	+	0.546716i
$476$	−5.82117			−0.266813
$477$	−43.2979	+	14.0683i	−1.98247	+	0.644144i
$478$	−9.11833	−	12.5503i	−0.417063	−	0.574038i
$479$	17.7246	−	12.8777i	0.809859	−	0.588397i	−0.103931	−	0.994585i	$-0.533142\pi$
$479$	17.7246	−	12.8777i	0.809859	−	0.588397i	0.913790	+	0.406188i	$0.133142\pi$
$480$	51.9498	+	16.3213i	2.37117	+	0.744960i
$481$	−34.7453	−	25.2439i	−1.58425	−	1.15102i
$482$		−	8.71456i		−	0.396937i
$483$	13.7427	−	18.9152i	0.625315	−	0.860672i
$484$	5.66139	−	17.4240i	0.257336	−	0.791999i
$485$	8.05710	−	25.6454i	0.365854	−	1.16450i
$486$	−11.1655	−	34.3639i	−0.506477	−	1.55878i
$487$	24.6806	+	8.01923i	1.11839	+	0.363386i	0.809152	−	0.587600i	$-0.199927\pi$
$487$	24.6806	+	8.01923i	1.11839	+	0.363386i	0.309235	+	0.950986i	$0.399927\pi$
$488$	1.91128	+	0.621012i	0.0865195	+	0.0281119i
$489$	−10.5119	−	32.3525i	−0.475367	−	1.46303i
$490$	−11.4701	−	8.16386i	−0.518168	−	0.368806i
$491$	−11.4571	+	35.2613i	−0.517052	+	1.59132i	0.262465	+	0.964941i	$0.415464\pi$
$491$	−11.4571	+	35.2613i	−0.517052	+	1.59132i	−0.779517	+	0.626381i	$0.784536\pi$
$492$	28.7499	−	39.5709i	1.29615	−	1.78399i
$493$			8.34804i			0.375977i
$494$	34.6554	+	25.1786i	1.55922	+	1.13284i
$495$	8.84754	+	11.9312i	0.397667	+	0.536268i
$496$	22.7525	−	16.5306i	1.02162	−	0.742248i
$497$	19.5171	+	26.8630i	0.875462	+	1.20497i
$498$	−9.19650	+	2.98812i	−0.412105	+	0.133901i
$499$	−21.0515			−0.942393			−0.471197	−	0.882028i	$-0.656178\pi$
$499$	−21.0515			−0.942393			−0.471197	+	0.882028i	$0.656178\pi$
$500$	11.4788	−	16.8122i	0.513348	−	0.751863i
$501$	−15.4481			−0.690171
$502$	31.4996	−	10.2349i	1.40590	−	0.456804i
$503$	−0.619626	−	0.852842i	−0.0276277	−	0.0380263i	0.794980	−	0.606636i	$-0.207481\pi$
$503$	−0.619626	−	0.852842i	−0.0276277	−	0.0380263i	−0.822607	+	0.568610i	$0.807481\pi$
$504$	−6.21374	+	4.51455i	−0.276782	+	0.201094i
$505$	12.2760	+	16.5546i	0.546275	+	0.736670i
$506$	−3.56749	−	2.59193i	−0.158594	−	0.115226i
$507$		−	55.8721i		−	2.48137i
$508$	−20.9851	+	28.8835i	−0.931063	+	1.28150i
$509$	−8.20517	+	25.2529i	−0.363688	+	1.11932i	0.587111	+	0.809507i	$0.300265\pi$
$509$	−8.20517	+	25.2529i	−0.363688	+	1.11932i	−0.950799	+	0.309810i	$0.899735\pi$
$510$	11.1807	+	7.95784i	0.495089	+	0.352379i
$511$	0.190825	+	0.587299i	0.00844160	+	0.0259806i
$512$	29.0298	+	9.43235i	1.28295	+	0.416855i
$513$	45.5005	+	14.7840i	2.00889	+	0.652729i
$514$	10.5176	+	32.3697i	0.463910	+	1.42777i
$515$	8.34599	−	26.5649i	0.367768	−	1.17059i
$516$	−8.27665	+	25.4729i	−0.364359	+	1.12138i
$517$	2.14215	−	2.94842i	0.0942118	−	0.129671i
$518$		−	48.3644i		−	2.12501i
$519$	19.2815	+	14.0088i	0.846365	+	0.614920i
$520$	4.14674	+	1.30279i	0.181846	+	0.0571313i
$521$	2.27772	−	1.65486i	0.0997888	−	0.0725008i	−0.536772	−	0.843727i	$-0.680356\pi$
$521$	2.27772	−	1.65486i	0.0997888	−	0.0725008i	0.636561	+	0.771227i	$0.280356\pi$
$522$	−65.7814	−	90.5404i	−2.87917	−	3.96284i
$523$	−17.3699	+	5.64383i	−0.759534	+	0.246787i	−0.663078	−	0.748550i	$-0.730750\pi$
$523$	−17.3699	+	5.64383i	−0.759534	+	0.246787i	−0.0964552	+	0.995337i	$0.530750\pi$
$524$	−2.07417			−0.0906103
$525$	16.4376	+	47.4225i	0.717395	+	2.06969i
$526$	50.6859			2.21001
$527$	6.18246	−	2.00880i	0.269312	−	0.0875048i
$528$	7.73330	+	10.6440i	0.336549	+	0.463219i
$529$	−14.2184	+	10.3303i	−0.618193	+	0.449144i
$530$	0.282889	+	29.0120i	0.0122879	+	1.26020i
$531$	59.5058	+	43.2335i	2.58233	+	1.87617i
$532$			22.9884i			0.996673i
$533$	27.9068	−	38.4105i	1.20878	−	1.66374i
$534$	−5.58947	+	17.2026i	−0.241880	+	0.744430i
$535$	10.9621	−	8.12892i	0.473934	−	0.351444i
$536$	0.559427	+	1.72174i	0.0241636	+	0.0743678i
$537$	39.5191	+	12.8405i	1.70537	+	0.554110i
$538$	30.5656	+	9.93136i	1.31778	+	0.428171i
$539$	−0.964079	−	2.96713i	−0.0415258	−	0.127803i
$540$	−49.3216	+	0.480922i	−2.12246	+	0.0206956i
$541$	−1.88518	+	5.80199i	−0.0810503	+	0.249447i	−0.983368	−	0.181625i	$-0.941864\pi$
$541$	−1.88518	+	5.80199i	−0.0810503	+	0.249447i	0.902318	+	0.431072i	$0.141864\pi$
$542$	2.59369	−	3.56990i	0.111408	−	0.153340i
$543$		−	35.4153i		−	1.51982i
$544$	6.27471	+	4.55885i	0.269026	+	0.195459i
$545$	13.8838	−	4.66127i	0.594717	−	0.199667i
$546$	88.0897	−	64.0009i	3.76989	−	2.73899i
$547$	0.938035	+	1.29109i	0.0401075	+	0.0552032i	0.828600	−	0.559841i	$-0.189138\pi$
$547$	0.938035	+	1.29109i	0.0401075	+	0.0552032i	−0.788492	+	0.615045i	$0.789138\pi$
$548$	−2.99343	+	0.972624i	−0.127873	+	0.0415484i
$549$	−39.3475			−1.67931
$550$	8.94410	−	3.10020i	0.381378	−	0.132193i
$551$	32.9673			1.40445
$552$	−2.43632	+	0.791609i	−0.103697	+	0.0336931i
$553$	−0.324474	−	0.446600i	−0.0137980	−	0.0189914i
$554$	−5.24709	+	3.81224i	−0.222928	+	0.161966i
$555$	−31.5078	+	44.2682i	−1.33743	+	1.87908i
$556$	1.62430	+	1.18012i	0.0688856	+	0.0500483i
$557$			6.55596i			0.277785i	0.990307	+	0.138892i	$0.0443542\pi$
$557$			6.55596i			0.277785i	−0.990307	+	0.138892i	$0.955646\pi$
$558$	−51.2240	+	70.5038i	−2.16849	+	2.98466i
$559$	−8.03393	+	24.7259i	−0.339799	+	1.04579i
$560$	9.84357	+	29.3195i	0.415967	+	1.23898i
$561$	0.939750	+	2.89225i	0.0396763	+	0.122111i
$562$	22.7929	+	7.40585i	0.961459	+	0.312397i
$563$	−10.4488	−	3.39502i	−0.440365	−	0.143083i	0.0804392	−	0.996760i	$-0.474368\pi$
$563$	−10.4488	−	3.39502i	−0.440365	−	0.143083i	−0.520804	+	0.853676i	$0.674368\pi$
$564$	6.64741	+	20.4586i	0.279906	+	0.861463i
$565$	−13.8059	−	41.1215i	−0.580819	−	1.73000i
$566$	−1.32187	+	4.06829i	−0.0555622	+	0.171003i
$567$	32.8151	−	45.1661i	1.37811	−	1.89680i
$568$		−	3.63807i		−	0.152650i
$569$	−2.72410	−	1.97918i	−0.114200	−	0.0829714i	0.529219	−	0.848485i	$-0.322485\pi$
$569$	−2.72410	−	1.97918i	−0.114200	−	0.0829714i	−0.643420	+	0.765514i	$0.722485\pi$
$570$	31.4263	−	44.1536i	1.31630	−	1.84939i
$571$	6.66945	−	4.84564i	0.279108	−	0.202784i	−0.439420	−	0.898282i	$-0.644816\pi$
$571$	6.66945	−	4.84564i	0.279108	−	0.202784i	0.718528	+	0.695498i	$0.244816\pi$
$572$	−5.75235	−	7.91743i	−0.240518	−	0.331044i
$573$	−12.1518	+	3.94837i	−0.507650	+	0.164946i
$574$	53.4662			2.23164
$575$	0.227090	+	11.6436i	0.00947030	+	0.485574i
$576$	−44.6338			−1.85974
$577$	−13.8174	+	4.48954i	−0.575225	+	0.186902i	−0.582160	−	0.813074i	$-0.697792\pi$
$577$	−13.8174	+	4.48954i	−0.575225	+	0.186902i	0.00693539	+	0.999976i	$0.497792\pi$
$578$	1.14894	+	1.58137i	0.0477894	+	0.0657765i
$579$	65.2481	−	47.4055i	2.71162	−	1.97011i
$580$	−32.2210	+	10.8177i	−1.33790	+	0.449180i
$581$	−4.07514	−	2.96076i	−0.169065	−	0.122833i
$582$			73.7810i			3.05832i
$583$	−3.77905	+	5.20141i	−0.156512	+	0.215421i
$584$	0.0209079	−	0.0643478i	0.000865174	−	0.00266273i
$585$	−85.0993	+	0.829781i	−3.51842	+	0.0343072i
$586$	9.13217	+	28.1059i	0.377247	+	1.16105i
$587$	26.2518	+	8.52973i	1.08353	+	0.352060i	0.795742	−	0.605635i	$-0.207081\pi$
$587$	26.2518	+	8.52973i	1.08353	+	0.352060i	0.287786	+	0.957695i	$0.407081\pi$
$588$	17.5136	+	5.69050i	0.722247	+	0.234672i
$589$	−7.93297	−	24.4152i	−0.326872	−	1.00601i
$590$	37.6521	−	27.9208i	1.55011	−	1.14948i
$591$	22.2907	−	68.6037i	0.916916	−	2.82198i
$592$	−19.6804	+	27.0878i	−0.808861	+	1.11330i
$593$			0.780422i			0.0320481i	0.999872	+	0.0160240i	$0.00510083\pi$
$593$			0.780422i			0.0320481i	−0.999872	+	0.0160240i	$0.994899\pi$
$594$	−18.5555	−	13.4814i	−0.761341	−	0.553147i
$595$	0.0697029	+	7.14847i	0.00285754	+	0.293059i
$596$	−6.00356	+	4.36185i	−0.245916	+	0.178668i
$597$	−17.3501	−	23.8804i	−0.710092	−	0.977358i
$598$	24.0283	−	7.80727i	0.982591	−	0.319263i
$599$	−7.40940			−0.302740			−0.151370	−	0.988477i	$-0.548368\pi$
$599$	−7.40940			−0.302740			−0.151370	+	0.988477i	$0.548368\pi$
$600$	1.59703	−	5.26216i	0.0651984	−	0.214827i
$601$	−27.0382			−1.10291			−0.551455	−	0.834205i	$-0.685927\pi$
$601$	−27.0382			−1.10291			−0.551455	+	0.834205i	$0.685927\pi$
$602$	−27.8445	+	9.04723i	−1.13486	+	0.368737i
$603$	−20.8343	−	28.6760i	−0.848440	−	1.16778i
$604$	31.3109	−	22.7487i	1.27402	−	0.925631i
$605$	−21.4647	−	6.74363i	−0.872663	−	0.274168i
$606$	−45.7638	−	33.2493i	−1.85903	−	1.35066i
$607$		−	45.3497i		−	1.84069i	−0.391110	−	0.920344i	$-0.627909\pi$
$607$		−	45.3497i		−	1.84069i	0.391110	−	0.920344i	$-0.372091\pi$
$608$	18.0033	−	24.7795i	0.730132	−	1.00494i
$609$	25.8952	−	79.6972i	1.04933	−	3.22949i
$610$	−7.51597	+	23.9230i	−0.304313	+	0.968614i
$611$	6.45247	+	19.8587i	0.261039	+	0.803395i
$612$	−11.8766	−	3.85893i	−0.480082	−	0.155988i
$613$	−38.4845	−	12.5044i	−1.55438	−	0.505047i	−0.599077	−	0.800691i	$-0.704466\pi$
$613$	−38.4845	−	12.5044i	−1.55438	−	0.505047i	−0.955298	+	0.295644i	$0.904466\pi$
$614$	9.74685	+	29.9977i	0.393351	+	1.21061i
$615$	−48.9378	−	34.8315i	−1.97336	−	1.40454i
$616$	−0.335182	+	1.03159i	−0.0135049	+	0.0415638i
$617$	−14.3775	+	19.7890i	−0.578817	+	0.796673i	−0.993565	−	0.113263i	$-0.963870\pi$
$617$	−14.3775	+	19.7890i	−0.578817	+	0.796673i	0.414748	+	0.909936i	$0.363870\pi$
$618$			76.4265i			3.07432i
$619$	2.45254	+	1.78188i	0.0985760	+	0.0716197i	0.635981	−	0.771704i	$-0.280595\pi$
$619$	2.45254	+	1.78188i	0.0985760	+	0.0716197i	−0.537405	+	0.843324i	$0.680595\pi$
$620$	15.7648	+	21.2594i	0.633131	+	0.853798i
$621$	22.8281	−	16.5856i	0.916061	−	0.665557i
$622$	−2.17224	−	2.98983i	−0.0870990	−	0.119881i
$623$	−8.96114	+	2.91165i	−0.359020	+	0.116653i
$624$	−75.3803			−3.01763
$625$	−20.7830	−	13.8948i	−0.831321	−	0.555793i
$626$	46.7479			1.86842
$627$	11.4218	−	3.71117i	0.456143	−	0.148210i
$628$	11.2647	+	15.5046i	0.449512	+	0.618701i
$629$	−6.26120	+	4.54903i	−0.249651	+	0.181382i
$630$	−57.0849	−	76.9809i	−2.27432	−	3.06699i
$631$	16.5058	+	11.9922i	0.657085	+	0.477400i	0.865677	−	0.500602i	$-0.166888\pi$
$631$	16.5058	+	11.9922i	0.657085	+	0.477400i	−0.208592	+	0.978003i	$0.566888\pi$
$632$			0.0604834i			0.00240590i
$633$	5.05608	−	6.95909i	0.200961	−	0.276599i
$634$	−7.55827	+	23.2619i	−0.300177	+	0.923850i
$635$	35.7206	+	25.4241i	1.41753	+	1.00893i
$636$	−11.7269	−	36.0918i	−0.465003	−	1.43113i
$637$	17.0000	+	5.52363i	0.673563	+	0.218854i
$638$	−15.0312	−	4.88394i	−0.595092	−	0.193357i
$639$	22.0117	+	67.7450i	0.870769	+	2.67995i
$640$	1.87060	−	5.95403i	0.0739419	−	0.235354i
$641$	−12.9198	+	39.7631i	−0.510302	+	1.57055i	0.281369	+	0.959600i	$0.409212\pi$
$641$	−12.9198	+	39.7631i	−0.510302	+	1.57055i	−0.791671	+	0.610948i	$0.790788\pi$
$642$	−22.0170	+	30.3039i	−0.868943	+	1.19600i
$643$			32.2857i			1.27322i	0.771185	+	0.636611i	$0.219664\pi$
$643$			32.2857i			1.27322i	−0.771185	+	0.636611i	$0.780336\pi$
$644$	10.9691	+	7.96949i	0.432241	+	0.314042i
$645$	31.3802	+	9.85882i	1.23559	+	0.388191i
$646$	6.24501	−	4.53726i	0.245707	−	0.178516i
$647$	18.7857	+	25.8563i	0.738542	+	1.01652i	0.998701	+	0.0509497i	$0.0162248\pi$
$647$	18.7857	+	25.8563i	0.738542	+	1.01652i	−0.260160	+	0.965566i	$0.583775\pi$
$648$	−5.81750	+	1.89022i	−0.228533	+	0.0742549i
$649$	10.3874			0.407739
$650$	−15.7508	+	51.8982i	−0.617795	+	2.03562i
$651$	−65.2540			−2.55751
$652$	18.7614	−	6.09595i	0.734753	−	0.238736i
$653$	−12.1372	−	16.7054i	−0.474965	−	0.653733i	0.502562	−	0.864541i	$-0.332391\pi$
$653$	−12.1372	−	16.7054i	−0.474965	−	0.653733i	−0.977528	+	0.210807i	$0.932391\pi$
$654$	−32.5202	+	23.6273i	−1.27164	+	0.923902i
$655$	0.0248361	+	2.54710i	0.000970428	+	0.0995235i
$656$	−29.9452	−	21.7565i	−1.16916	−	0.849447i
$657$			1.32473i			0.0516826i
$658$	−13.8213	+	19.0234i	−0.538811	+	0.741610i
$659$	−6.93788	+	21.3526i	−0.270261	+	0.831779i	0.720173	+	0.693794i	$0.244062\pi$
$659$	−6.93788	+	21.3526i	−0.270261	+	0.831779i	−0.990434	+	0.137984i	$0.955938\pi$
$660$	−9.94548	+	7.37504i	−0.387127	+	0.287073i
$661$	−7.53993	−	23.2055i	−0.293269	−	0.902591i	−0.983797	−	0.179285i	$-0.942622\pi$
$661$	−7.53993	−	23.2055i	−0.293269	−	0.902591i	0.690528	−	0.723306i	$-0.257378\pi$
$662$	7.38282	+	2.39882i	0.286941	+	0.0932329i
$663$	−16.5710	−	5.38424i	−0.643563	−	0.209106i
$664$	0.170546	+	0.524887i	0.00661847	+	0.0203696i
$665$	28.2300	−	0.275264i	1.09471	−	0.0106743i
$666$	32.0614	−	98.6749i	1.24235	−	3.82357i
$667$	11.4289	−	15.7305i	0.442529	−	0.609089i
$668$		−	8.95847i		−	0.346614i
$669$	−65.8597	−	47.8499i	−2.54628	−	1.84998i
$670$	−21.4145	+	7.18957i	−0.827313	+	0.277757i
$671$	−4.49551	+	3.26618i	−0.173547	+	0.126089i
$672$	−45.7622	−	62.9863i	−1.76532	−	2.42975i
$673$	25.6998	−	8.35036i	0.990653	−	0.321883i	0.231529	−	0.972828i	$-0.425627\pi$
$673$	25.6998	−	8.35036i	0.990653	−	0.321883i	0.759125	+	0.650945i	$0.225627\pi$
$674$	−45.4915			−1.75227
$675$	1.18116	+	60.5618i	0.0454627	+	2.33102i
$676$	32.4006			1.24618
$677$	15.9812	−	5.19261i	0.614208	−	0.199568i	0.0146412	−	0.999893i	$-0.495339\pi$
$677$	15.9812	−	5.19261i	0.614208	−	0.199568i	0.599567	+	0.800324i	$0.295339\pi$
$678$	69.9803	+	96.3196i	2.68758	+	3.69913i
$679$	−31.0936	+	22.5908i	−1.19326	+	0.866956i
$680$	0.454191	−	0.638133i	0.0174174	−	0.0244713i
$681$	−17.2773	−	12.5527i	−0.662069	−	0.481021i
$682$			12.3072i			0.471266i
$683$	14.5528	−	20.0302i	0.556848	−	0.766435i	−0.434074	−	0.900877i	$-0.642924\pi$
$683$	14.5528	−	20.0302i	0.556848	−	0.766435i	0.990921	+	0.134442i	$0.0429242\pi$
$684$	−15.2393	+	46.9018i	−0.582689	+	1.79333i
$685$	1.23024	+	3.66432i	0.0470050	+	0.140007i
$686$	−7.29750	−	22.4594i	−0.278620	−	0.857503i
$687$	−14.5104	−	4.71471i	−0.553606	−	0.179878i
$688$	19.2766	+	6.26334i	0.734912	+	0.238787i
$689$	−11.3830	−	35.0333i	−0.433659	−	1.33466i
$690$	−10.1735	−	30.3022i	−0.387298	−	1.15359i
$691$	−3.26344	+	10.0438i	−0.124147	+	0.382085i	−0.993745	−	0.111676i	$-0.964378\pi$
$691$	−3.26344	+	10.0438i	−0.124147	+	0.382085i	0.869598	+	0.493761i	$0.164378\pi$
$692$	−8.12382	+	11.1815i	−0.308821	+	0.425056i
$693$		−	21.2373i		−	0.806737i
$694$	5.10349	+	3.70790i	0.193726	+	0.140750i
$695$	1.42976	−	2.00879i	0.0542337	−	0.0761977i
$696$	−7.42795	+	5.39672i	−0.281556	+	0.204562i
$697$	−5.02889	−	6.92167i	−0.190483	−	0.262177i
$698$	−50.0941	+	16.2766i	−1.89609	+	0.616077i
$699$	44.7535			1.69273
$700$	−27.5007	+	9.53226i	−1.03943	+	0.360286i
$701$	−14.2390			−0.537798			−0.268899	−	0.963168i	$-0.586660\pi$
$701$	−14.2390			−0.537798			−0.268899	+	0.963168i	$0.586660\pi$
$702$	124.978	−	40.6077i	4.71698	−	1.53264i
$703$	17.9646	+	24.7261i	0.677547	+	0.932564i
$704$	−5.09947	+	3.70498i	−0.192194	+	0.139637i
$705$	25.0439	−	8.40808i	0.943206	−	0.316666i
$706$	−42.4690	−	30.8555i	−1.59834	−	1.16126i
$707$		−	29.4668i		−	1.10821i
$708$	−36.0381	+	49.6022i	−1.35439	+	1.86416i
$709$	3.79864	−	11.6910i	0.142661	−	0.439065i	−0.854042	−	0.520204i	$-0.825856\pi$
$709$	3.79864	−	11.6910i	0.142661	−	0.439065i	0.996703	+	0.0811392i	$0.0258558\pi$
$710$	45.3930	−	0.442616i	1.70357	−	0.0166111i
$711$	−0.365947	−	1.12627i	−0.0137241	−	0.0422384i
$712$	0.981833	+	0.319017i	0.0367958	+	0.0119557i
$713$	−14.4000	−	4.67885i	−0.539285	−	0.175224i
$714$	−6.06333	−	18.6610i	−0.226915	−	0.698371i
$715$	−9.65383	+	7.15876i	−0.361033	+	0.267723i
$716$	−7.44631	+	22.9174i	−0.278282	+	0.856463i
$717$	14.6468	−	20.1595i	0.546993	−	0.752872i
$718$			10.6564i			0.397692i
$719$	22.7310	+	16.5150i	0.847723	+	0.615906i	0.924517	−	0.381140i	$-0.124469\pi$
$719$	22.7310	+	16.5150i	0.847723	+	0.615906i	−0.0767946	+	0.997047i	$0.524469\pi$
$720$	0.646906	+	66.3443i	0.0241088	+	2.47250i
$721$	−32.2085	+	23.4008i	−1.19951	+	0.871492i
$722$	3.91166	+	5.38394i	0.145577	+	0.200369i
$723$	13.3131	−	4.32568i	0.495118	−	0.160874i
$724$	20.5376			0.763273
$725$	13.6701	+	39.4382i	0.507693	+	1.46470i
$726$	61.7533			2.29188
$727$	21.3501	−	6.93707i	0.791832	−	0.257282i	0.114948	−	0.993372i	$-0.463330\pi$
$727$	21.3501	−	6.93707i	0.791832	−	0.257282i	0.676884	+	0.736090i	$0.263330\pi$
$728$	−3.65283	−	5.02769i	−0.135383	−	0.186338i
$729$	4.57237	−	3.32202i	0.169347	−	0.123038i
$730$	0.805426	+	0.253043i	0.0298101	+	0.00936556i
$731$	3.79023	+	2.75376i	0.140187	+	0.101852i
$732$		−	32.7989i		−	1.21228i
$733$	7.43210	−	10.2294i	0.274511	−	0.377832i	−0.649395	−	0.760451i	$-0.724978\pi$
$733$	7.43210	−	10.2294i	0.274511	−	0.377832i	0.923906	+	0.382619i	$0.124978\pi$
$734$	4.09612	−	12.6065i	0.151190	−	0.465316i
$735$	6.77830	−	21.5750i	0.250021	−	0.795807i
$736$	−5.58239	−	17.1808i	−0.205770	−	0.633294i
$737$	−4.76070	−	1.54685i	−0.175363	−	0.0569788i
$738$	109.084	+	35.4434i	4.01543	+	1.30469i
$739$	3.22987	+	9.94051i	0.118813	+	0.365668i	0.992723	−	0.120419i	$-0.0384239\pi$
$739$	3.22987	+	9.94051i	0.118813	+	0.365668i	−0.873911	+	0.486087i	$0.838424\pi$
$740$	−25.6714	−	18.2716i	−0.943699	−	0.671677i
$741$	−21.2629	+	65.4405i	−0.781112	+	2.40402i
$742$	24.3827	−	33.5599i	0.895116	−	1.23202i
$743$		−	34.8760i		−	1.27948i	−0.768593	−	0.639738i	$-0.779043\pi$
$743$		−	34.8760i		−	1.27948i	0.768593	−	0.639738i	$-0.220957\pi$
$744$	5.78415	+	4.20243i	0.212057	+	0.154069i
$745$	5.42829	+	7.32023i	0.198877	+	0.268192i
$746$	−36.1051	+	26.2319i	−1.32190	+	0.960418i
$747$	−6.35152	−	8.74212i	−0.232390	−	0.319857i
$748$	−1.67724	+	0.544967i	−0.0613259	+	0.0199260i
$749$	−19.5123			−0.712964
$750$	65.8514	+	19.2863i	2.40455	+	0.704235i
$751$	15.0312			0.548495			0.274248	−	0.961659i	$-0.411571\pi$
$751$	15.0312			0.548495			0.274248	+	0.961659i	$0.411571\pi$
$752$	15.4820	−	5.03041i	0.564571	−	0.183440i
$753$	31.2712	+	43.0411i	1.13959	+	1.56850i
$754$	73.2584	−	53.2253i	2.66791	−	1.93835i
$755$	−28.3106	−	38.1778i	−1.03033	−	1.38943i
$756$	57.0531	+	41.4515i	2.07500	+	1.50758i
$757$			19.9967i			0.726794i	0.931634	+	0.363397i	$0.118383\pi$
$757$			19.9967i			0.726794i	−0.931634	+	0.363397i	$0.881617\pi$
$758$	−9.55637	+	13.1532i	−0.347103	+	0.477746i
$759$	2.18884	−	6.73656i	0.0794498	−	0.244521i
$760$	−2.52005	−	1.79365i	−0.0914119	−	0.0650624i
$761$	1.84145	+	5.66740i	0.0667525	+	0.205443i	0.978869	−	0.204488i	$-0.0655528\pi$
$761$	1.84145	+	5.66740i	0.0667525	+	0.205443i	−0.912117	+	0.409931i	$0.865553\pi$
$762$	−114.450	−	37.1872i	−4.14610	−	1.34715i
$763$	−19.9146	−	6.47063i	−0.720956	−	0.234253i
$764$	−2.28969	−	7.04693i	−0.0828380	−	0.254949i
$765$	−4.59661	+	14.6308i	−0.166191	+	0.528977i
$766$	6.72867	−	20.7087i	0.243117	−	0.748236i
$767$	−34.9812	+	48.1476i	−1.26310	+	1.73851i
$768$			57.9967i			2.09278i
$769$	−27.4007	−	19.9078i	−0.988094	−	0.717892i	−0.0285908	−	0.999591i	$-0.509102\pi$
$769$	−27.4007	−	19.9078i	−0.988094	−	0.717892i	−0.959503	+	0.281699i	$0.909102\pi$
$770$	−12.9121	−	4.05664i	−0.465320	−	0.146191i
$771$	−44.2300	+	32.1350i	−1.59290	+	1.15731i
$772$	27.4908	+

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.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85902 + 0.604031i) q^{2} +(-1.84553 - 2.54016i) q^{3} +(1.47306 - 1.07024i) q^{4} +(-1.33190 - 1.79612i) q^{5} +(4.96521 + 3.60744i) q^{6} +3.19704i q^{7} +(0.205893 - 0.283388i) q^{8} +(-2.11936 + 6.52273i) q^{9} +(3.56094 + 2.53450i) q^{10} +(0.299302 + 0.921156i) q^{11} +(-5.43715 - 1.76664i) q^{12} +(-5.27770 - 1.71483i) q^{13} +(-1.93111 - 5.94336i) q^{14} +(-2.10435 + 6.69804i) q^{15} +(-1.33690 + 4.11455i) q^{16} +(-0.587785 + 0.809017i) q^{17} -13.4060i q^{18} +(3.19489 + 2.32122i) q^{19} +(-3.88424 - 1.22033i) q^{20} +(8.12100 - 5.90025i) q^{21} +(-1.11281 - 1.53166i) q^{22} +(2.21517 - 0.719754i) q^{23} -1.09983 q^{24} +(-1.45206 + 4.78451i) q^{25} +10.8471 q^{26} +(11.5217 - 3.74363i) q^{27} +(3.42160 + 4.70942i) q^{28} +(6.75371 - 4.90685i) q^{29} +(-0.133808 - 13.7229i) q^{30} +(-5.25911 - 3.82097i) q^{31} -7.75597i q^{32} +(1.78751 - 2.46030i) q^{33} +(0.604031 - 1.85902i) q^{34} +(5.74226 - 4.25816i) q^{35} +(3.85893 + 11.8766i) q^{36} +(7.36049 + 2.39157i) q^{37} +(-7.34145 - 2.38538i) q^{38} +(5.38424 + 16.5710i) q^{39} +(-0.783227 + 0.00763705i) q^{40} +(-2.64384 + 8.13692i) q^{41} +(-11.5331 + 15.8740i) q^{42} -4.68498i q^{43} +(1.42674 + 1.03659i) q^{44} +(14.5384 - 4.88103i) q^{45} +(-3.68329 + 2.67607i) q^{46} +(-2.21169 - 3.04413i) q^{47} +(12.9189 - 4.19761i) q^{48} -3.22110 q^{49} +(-0.190578 - 9.77157i) q^{50} +3.13981 q^{51} +(-9.60962 + 3.12235i) q^{52} +(3.90172 + 5.37025i) q^{53} +(-19.1578 + 13.9190i) q^{54} +(1.25586 - 1.76447i) q^{55} +(0.906003 + 0.658250i) q^{56} -12.3994i q^{57} +(-9.59136 + 13.2014i) q^{58} +(3.31406 - 10.1996i) q^{59} +(4.06867 + 12.1187i) q^{60} +(1.77287 + 5.45633i) q^{61} +(12.0848 + 3.92658i) q^{62} +(-20.8535 - 6.77570i) q^{63} +(2.01105 + 6.18938i) q^{64} +(3.94936 + 11.7633i) q^{65} +(-1.83692 + 5.65345i) q^{66} +(-3.03778 + 4.18115i) q^{67} +1.82080i q^{68} +(-5.91647 - 4.29857i) q^{69} +(-8.10290 + 11.3845i) q^{70} +(8.40244 - 6.10473i) q^{71} +(1.41210 + 1.94359i) q^{72} +(0.183701 - 0.0596879i) q^{73} -15.1278 q^{74} +(14.8332 - 5.14149i) q^{75} +7.19051 q^{76} +(-2.94498 + 0.956881i) q^{77} +(-20.0188 - 27.5535i) q^{78} +(-0.139692 + 0.101492i) q^{79} +(9.17083 - 3.07896i) q^{80} +(-14.1275 - 10.2642i) q^{81} -16.7236i q^{82} +(-0.926093 + 1.27466i) q^{83} +(5.64801 - 17.3828i) q^{84} +(2.23596 - 0.0218023i) q^{85} +(2.82987 + 8.70945i) q^{86} +(-24.9284 - 8.09972i) q^{87} +(0.322669 + 0.104841i) q^{88} +(0.910731 + 2.80294i) q^{89} +(-24.0788 + 17.8555i) q^{90} +(5.48238 - 16.8730i) q^{91} +(2.49277 - 3.43100i) q^{92} +20.4107i q^{93} +(5.95031 + 4.32316i) q^{94} +(-0.0860994 - 8.83004i) q^{95} +(-19.7014 + 14.3139i) q^{96} +(7.06616 + 9.72573i) q^{97} +(5.98807 - 1.94564i) q^{98} -6.64278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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