LMFDB - Embedded newform 702.2.bb.a.71.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("702.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.14
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.71422 - 0.995221i) q^{5} +(2.11355 - 0.566325i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.71422 - 0.995221i) q^{5} +(2.11355 - 0.566325i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(3.33007 + 1.92262i) q^{10} +(-2.96155 + 2.96155i) q^{11} +(3.17583 - 1.70707i) q^{13} +(1.89496 + 1.09406i) q^{14} -1.00000 q^{16} +(-0.465866 - 0.806903i) q^{17} +(-1.86997 - 0.501056i) q^{19} +(0.995221 + 3.71422i) q^{20} -4.18826 q^{22} +(-3.91493 - 6.78085i) q^{23} +(8.47480 - 4.89293i) q^{25} +(3.45273 + 1.03857i) q^{26} +(0.566325 + 2.11355i) q^{28} +7.40705i q^{29} +(-0.333283 - 1.24383i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.241150 - 0.899984i) q^{34} +(7.28657 - 4.20690i) q^{35} +(4.93092 - 1.32124i) q^{37} +(-0.967965 - 1.67657i) q^{38} +(-1.92262 + 3.33007i) q^{40} +(-2.83325 + 10.5738i) q^{41} +(1.70588 + 0.984890i) q^{43} +(-2.96155 - 2.96155i) q^{44} +(2.02652 - 7.56306i) q^{46} +(-9.40830 - 2.52095i) q^{47} +(-1.91580 + 1.10609i) q^{49} +(9.45241 + 2.53277i) q^{50} +(1.70707 + 3.17583i) q^{52} +2.04197i q^{53} +(-8.05243 + 13.9472i) q^{55} +(-1.09406 + 1.89496i) q^{56} +(-5.23757 + 5.23757i) q^{58} +(4.46186 - 4.46186i) q^{59} +(-0.430522 + 0.745686i) q^{61} +(0.643854 - 1.11519i) q^{62} -1.00000i q^{64} +(10.0968 - 9.50108i) q^{65} +(-3.23147 - 0.865869i) q^{67} +(0.806903 - 0.465866i) q^{68} +(8.12711 + 2.17765i) q^{70} +(-2.90450 + 10.8397i) q^{71} +(-2.45316 - 2.45316i) q^{73} +(4.42095 + 2.55243i) q^{74} +(0.501056 - 1.86997i) q^{76} +(-4.58218 + 7.93658i) q^{77} +(6.38240 + 11.0546i) q^{79} +(-3.71422 + 0.995221i) q^{80} +(-9.48023 + 5.47341i) q^{82} +(1.45546 - 5.43185i) q^{83} +(-2.53337 - 2.53337i) q^{85} +(0.509817 + 1.90266i) q^{86} -4.18826i q^{88} +(-0.522663 - 1.95060i) q^{89} +(5.74553 - 5.40653i) q^{91} +(6.78085 - 3.91493i) q^{92} +(-4.87009 - 8.43525i) q^{94} -7.44412 q^{95} +(-4.55884 - 17.0138i) q^{97} +(-2.13680 - 0.572553i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	3.71422	−	0.995221i	1.66105	−	0.445076i	0.698372	−	0.715735i	$-0.253908\pi$
$5$	3.71422	−	0.995221i	1.66105	−	0.445076i	0.962675	+	0.270659i	$0.0872414\pi$
$6$		0			0
$7$	2.11355	−	0.566325i	0.798848	−	0.214051i	0.163770	−	0.986499i	$-0.447635\pi$
$7$	2.11355	−	0.566325i	0.798848	−	0.214051i	0.635078	+	0.772448i	$0.280968\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	3.33007	+	1.92262i	1.05306	+	0.607986i
$11$	−2.96155	+	2.96155i	−0.892940	+	0.892940i	−0.994799	−	0.101859i	$-0.967521\pi$
$11$	−2.96155	+	2.96155i	−0.892940	+	0.892940i	0.101859	+	0.994799i	$0.467521\pi$
$12$		0			0
$13$	3.17583	−	1.70707i	0.880818	−	0.473456i
$13$	3.17583	−	1.70707i	0.880818	−	0.473456i
$14$	1.89496	+	1.09406i	0.506449	+	0.292399i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.465866	−	0.806903i	−0.112989	−	0.195703i	0.803985	−	0.594649i	$-0.202709\pi$
$17$	−0.465866	−	0.806903i	−0.112989	−	0.195703i	−0.916974	+	0.398947i	$0.869376\pi$
$18$		0			0
$19$	−1.86997	−	0.501056i	−0.429000	−	0.114950i	0.0378569	−	0.999283i	$-0.487947\pi$
$19$	−1.86997	−	0.501056i	−0.429000	−	0.114950i	−0.466857	+	0.884333i	$0.654614\pi$
$20$	0.995221	+	3.71422i	0.222538	+	0.830524i
$21$		0			0
$22$	−4.18826			−0.892940
$23$	−3.91493	−	6.78085i	−0.816319	−	1.41391i	−0.908377	−	0.418152i	$-0.862678\pi$
$23$	−3.91493	−	6.78085i	−0.816319	−	1.41391i	0.0920584	−	0.995754i	$-0.470655\pi$
$24$		0			0
$25$	8.47480	−	4.89293i	1.69496	−	0.978586i
$26$	3.45273	+	1.03857i	0.677137	+	0.203681i
$27$		0			0
$28$	0.566325	+	2.11355i	0.107025	+	0.399424i
$29$			7.40705i			1.37545i	0.725969	+	0.687727i	$0.241391\pi$
$29$			7.40705i			1.37545i	−0.725969	+	0.687727i	$0.758609\pi$
$30$		0			0
$31$	−0.333283	−	1.24383i	−0.0598595	−	0.223399i	0.929516	−	0.368782i	$-0.120225\pi$
$31$	−0.333283	−	1.24383i	−0.0598595	−	0.223399i	−0.989375	+	0.145383i	$0.953558\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	0.241150	−	0.899984i	0.0413569	−	0.154346i
$35$	7.28657	−	4.20690i	1.23165	−	0.711096i
$36$		0			0
$37$	4.93092	−	1.32124i	0.810639	−	0.217210i	0.170389	−	0.985377i	$-0.445498\pi$
$37$	4.93092	−	1.32124i	0.810639	−	0.217210i	0.640250	+	0.768167i	$0.278831\pi$
$38$	−0.967965	−	1.67657i	−0.157025	−	0.271975i
$39$		0			0
$40$	−1.92262	+	3.33007i	−0.303993	+	0.526531i
$41$	−2.83325	+	10.5738i	−0.442479	+	1.65135i	0.280029	+	0.959991i	$0.409656\pi$
$41$	−2.83325	+	10.5738i	−0.442479	+	1.65135i	−0.722508	+	0.691362i	$0.757011\pi$
$42$		0			0
$43$	1.70588	+	0.984890i	0.260144	+	0.150194i	0.624400	−	0.781104i	$-0.285343\pi$
$43$	1.70588	+	0.984890i	0.260144	+	0.150194i	−0.364256	+	0.931299i	$0.618677\pi$
$44$	−2.96155	−	2.96155i	−0.446470	−	0.446470i
$45$		0			0
$46$	2.02652	−	7.56306i	0.298793	−	1.11511i
$47$	−9.40830	−	2.52095i	−1.37234	−	0.367718i	−0.504008	−	0.863699i	$-0.668142\pi$
$47$	−9.40830	−	2.52095i	−1.37234	−	0.367718i	−0.868333	+	0.495981i	$0.834809\pi$
$48$		0			0
$49$	−1.91580	+	1.10609i	−0.273686	+	0.158012i
$50$	9.45241	+	2.53277i	1.33677	+	0.358187i
$51$		0			0
$52$	1.70707	+	3.17583i	0.236728	+	0.440409i
$53$			2.04197i			0.280486i	0.990117	+	0.140243i	$0.0447883\pi$
$53$			2.04197i			0.280486i	−0.990117	+	0.140243i	$0.955212\pi$
$54$		0			0
$55$	−8.05243	+	13.9472i	−1.08579	+	1.88064i
$56$	−1.09406	+	1.89496i	−0.146199	+	0.253225i
$57$		0			0
$58$	−5.23757	+	5.23757i	−0.687727	+	0.687727i
$59$	4.46186	−	4.46186i	0.580884	−	0.580884i	−0.354262	−	0.935146i	$-0.615268\pi$
$59$	4.46186	−	4.46186i	0.580884	−	0.580884i	0.935146	+	0.354262i	$0.115268\pi$
$60$		0			0
$61$	−0.430522	+	0.745686i	−0.0551227	+	0.0954753i	−0.892270	−	0.451502i	$-0.850888\pi$
$61$	−0.430522	+	0.745686i	−0.0551227	+	0.0954753i	0.837147	+	0.546977i	$0.184222\pi$
$62$	0.643854	−	1.11519i	0.0817696	−	0.141629i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	10.0968	−	9.50108i	1.25236	−	1.17846i
$66$		0			0
$67$	−3.23147	−	0.865869i	−0.394786	−	0.105783i	0.0559639	−	0.998433i	$-0.482177\pi$
$67$	−3.23147	−	0.865869i	−0.394786	−	0.105783i	−0.450750	+	0.892650i	$0.648843\pi$
$68$	0.806903	−	0.465866i	0.0978514	−	0.0564945i
$69$		0			0
$70$	8.12711	+	2.17765i	0.971376	+	0.260279i
$71$	−2.90450	+	10.8397i	−0.344700	+	1.28644i	0.548262	+	0.836307i	$0.315290\pi$
$71$	−2.90450	+	10.8397i	−0.344700	+	1.28644i	−0.892962	+	0.450132i	$0.851377\pi$
$72$		0			0
$73$	−2.45316	−	2.45316i	−0.287121	−	0.287121i	0.548820	−	0.835941i	$-0.315077\pi$
$73$	−2.45316	−	2.45316i	−0.287121	−	0.287121i	−0.835941	+	0.548820i	$0.815077\pi$
$74$	4.42095	+	2.55243i	0.513925	+	0.296714i
$75$		0			0
$76$	0.501056	−	1.86997i	0.0574750	−	0.214500i
$77$	−4.58218	+	7.93658i	−0.522188	+	0.904457i
$78$		0			0
$79$	6.38240	+	11.0546i	0.718076	+	1.24374i	0.961761	+	0.273889i	$0.0883102\pi$
$79$	6.38240	+	11.0546i	0.718076	+	1.24374i	−0.243686	+	0.969854i	$0.578357\pi$
$80$	−3.71422	+	0.995221i	−0.415262	+	0.111269i
$81$		0			0
$82$	−9.48023	+	5.47341i	−1.04692	+	0.604437i
$83$	1.45546	−	5.43185i	0.159757	−	0.596223i	−0.838893	−	0.544296i	$-0.816797\pi$
$83$	1.45546	−	5.43185i	0.159757	−	0.596223i	0.998651	−	0.0519272i	$-0.0165364\pi$
$84$		0			0
$85$	−2.53337	−	2.53337i	−0.274783	−	0.274783i
$86$	0.509817	+	1.90266i	0.0549749	+	0.205169i
$87$		0			0
$88$		−	4.18826i		−	0.446470i
$89$	−0.522663	−	1.95060i	−0.0554022	−	0.206764i	0.932676	−	0.360714i	$-0.117467\pi$
$89$	−0.522663	−	1.95060i	−0.0554022	−	0.206764i	−0.988079	+	0.153951i	$0.950800\pi$
$90$		0			0
$91$	5.74553	−	5.40653i	0.602295	−	0.566759i
$92$	6.78085	−	3.91493i	0.706953	−	0.408159i
$93$		0			0
$94$	−4.87009	−	8.43525i	−0.502312	−	0.870030i
$95$	−7.44412			−0.763750
$96$		0			0
$97$	−4.55884	−	17.0138i	−0.462880	−	1.72749i	−0.663825	−	0.747888i	$-0.731068\pi$
$97$	−4.55884	−	17.0138i	−0.462880	−	1.72749i	0.200945	−	0.979603i	$-0.435599\pi$
$98$	−2.13680	−	0.572553i	−0.215849	−	0.0578366i
$99$		0			0
$100$	4.89293	+	8.47480i	0.489293	+	0.847480i
$101$	−5.95775			−0.592818			−0.296409	−	0.955061i	$-0.595789\pi$
$101$	−5.95775			−0.592818			−0.296409	+	0.955061i	$0.595789\pi$
$102$		0			0
$103$	−3.14153	−	1.81377i	−0.309544	−	0.178716i	0.337178	−	0.941441i	$-0.390528\pi$
$103$	−3.14153	−	1.81377i	−0.309544	−	0.178716i	−0.646723	+	0.762725i	$0.723861\pi$
$104$	−1.03857	+	3.45273i	−0.101840	+	0.338568i
$105$		0			0
$106$	−1.44389	+	1.44389i	−0.140243	+	0.140243i
$107$	3.85034	+	2.22300i	0.372227	+	0.214905i	0.674431	−	0.738338i	$-0.264389\pi$
$107$	3.85034	+	2.22300i	0.372227	+	0.214905i	−0.302204	+	0.953243i	$0.597722\pi$
$108$		0			0
$109$	5.79714	−	5.79714i	0.555266	−	0.555266i	−0.372690	−	0.927956i	$-0.621565\pi$
$109$	5.79714	−	5.79714i	0.555266	−	0.555266i	0.927956	+	0.372690i	$0.121565\pi$
$110$	−15.5561	+	4.16824i	−1.48322	+	0.397426i
$111$		0			0
$112$	−2.11355	+	0.566325i	−0.199712	+	0.0535126i
$113$		−	12.5666i		−	1.18217i	−0.806610	−	0.591084i	$-0.798700\pi$
$113$		−	12.5666i		−	1.18217i	0.806610	−	0.591084i	$-0.201300\pi$
$114$		0			0
$115$	−21.2893	−	21.2893i	−1.98524	−	1.98524i
$116$	−7.40705			−0.687727
$117$		0			0
$118$	6.31002			0.580884
$119$	−1.44160	−	1.44160i	−0.132151	−	0.132151i
$120$		0			0
$121$		−	6.54150i		−	0.594682i
$122$	−0.831705	+	0.222855i	−0.0752990	+	0.0201763i
$123$		0			0
$124$	1.24383	−	0.333283i	0.111699	−	0.0299297i
$125$	13.0127	−	13.0127i	1.16389	−	1.16389i
$126$		0			0
$127$	0.0921603	+	0.0532087i	0.00817790	+	0.00472151i	0.504083	−	0.863655i	$-0.331830\pi$
$127$	0.0921603	+	0.0532087i	0.00817790	+	0.00472151i	−0.495905	+	0.868377i	$0.665164\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	13.8578	+	0.421249i	1.21541	+	0.0369460i
$131$	−10.7216	−	6.19013i	−0.936752	−	0.540834i	−0.0478111	−	0.998856i	$-0.515225\pi$
$131$	−10.7216	−	6.19013i	−0.936752	−	0.540834i	−0.888941	+	0.458023i	$0.848558\pi$
$132$		0			0
$133$	−4.23603			−0.367310
$134$	−1.67273	−	2.89725i	−0.144502	−	0.250284i
$135$		0			0
$136$	0.899984	+	0.241150i	0.0771729	+	0.0206784i
$137$	−0.681728	−	2.54424i	−0.0582439	−	0.217369i	0.930670	−	0.365860i	$-0.119225\pi$
$137$	−0.681728	−	2.54424i	−0.0582439	−	0.217369i	−0.988914	+	0.148491i	$0.952558\pi$
$138$		0			0
$139$	−14.6578			−1.24326			−0.621629	−	0.783312i	$-0.713529\pi$
$139$	−14.6578			−1.24326			−0.621629	+	0.783312i	$0.713529\pi$
$140$	4.20690	+	7.28657i	0.355548	+	0.615827i
$141$		0			0
$142$	−9.71863	+	5.61105i	−0.815569	+	0.470869i
$143$	−4.34981	+	14.4609i	−0.363749	+	1.20928i
$144$		0			0
$145$	7.37165	+	27.5114i	0.612182	+	2.28470i
$146$		−	3.46929i		−	0.287121i
$147$		0			0
$148$	1.32124	+	4.93092i	0.108605	+	0.405320i
$149$	4.33712	+	4.33712i	0.355311	+	0.355311i	0.862081	−	0.506770i	$-0.169161\pi$
$149$	4.33712	+	4.33712i	0.355311	+	0.355311i	−0.506770	+	0.862081i	$0.669161\pi$
$150$		0			0
$151$	1.02381	−	3.82090i	0.0833163	−	0.310941i	−0.911674	−	0.410915i	$-0.865209\pi$
$151$	1.02381	−	3.82090i	0.0833163	−	0.310941i	0.994990	+	0.0999742i	$0.0318760\pi$
$152$	1.67657	−	0.967965i	0.135987	−	0.0785124i
$153$		0			0
$154$	−8.85210	+	2.37191i	−0.713323	+	0.191134i
$155$	−2.47577	−	4.28816i	−0.198859	−	0.344434i
$156$		0			0
$157$	−4.23403	+	7.33355i	−0.337912	+	0.585281i	−0.984040	−	0.177948i	$-0.943054\pi$
$157$	−4.23403	+	7.33355i	−0.337912	+	0.585281i	0.646128	+	0.763229i	$0.276387\pi$
$158$	−3.30377	+	12.3298i	−0.262834	+	0.980910i
$159$		0			0
$160$	−3.33007	−	1.92262i	−0.263265	−	0.151996i
$161$	−12.1146	−	12.1146i	−0.954761	−	0.954761i
$162$		0			0
$163$	−0.512492	+	1.91264i	−0.0401414	+	0.149810i	−0.983088	−	0.183135i	$-0.941376\pi$
$163$	−0.512492	+	1.91264i	−0.0401414	+	0.149810i	0.942946	+	0.332945i	$0.108042\pi$
$164$	−10.5738	−	2.83325i	−0.825677	−	0.221239i
$165$		0			0
$166$	4.87006	−	2.81173i	0.377990	−	0.218233i
$167$	−21.6497	−	5.80101i	−1.67530	−	0.448896i	−0.708770	−	0.705440i	$-0.750750\pi$
$167$	−21.6497	−	5.80101i	−1.67530	−	0.448896i	−0.966533	+	0.256544i	$0.917416\pi$
$168$		0			0
$169$	7.17183	−	10.8427i	0.551679	−	0.834056i
$170$		−	3.58273i		−	0.274783i
$171$		0			0
$172$	−0.984890	+	1.70588i	−0.0750971	+	0.130072i
$173$	9.52249	−	16.4934i	0.723981	−	1.25397i	−0.235411	−	0.971896i	$-0.575644\pi$
$173$	9.52249	−	16.4934i	0.723981	−	1.25397i	0.959392	−	0.282076i	$-0.0910232\pi$
$174$		0			0
$175$	15.1409	−	15.1409i	1.14455	−	1.14455i
$176$	2.96155	−	2.96155i	0.223235	−	0.223235i
$177$		0			0
$178$	1.00971	−	1.74886i	0.0756808	−	0.131083i
$179$	0.255705	−	0.442894i	0.0191123	−	0.0331035i	−0.856311	−	0.516460i	$-0.827249\pi$
$179$	0.255705	−	0.442894i	0.0191123	−	0.0331035i	0.875423	+	0.483357i	$0.160583\pi$
$180$		0			0
$181$		−	2.38215i		−	0.177064i	−0.996073	−	0.0885319i	$-0.971782\pi$
$181$		−	2.38215i		−	0.177064i	0.996073	−	0.0885319i	$-0.0282175\pi$
$182$	7.88570	+	0.239709i	0.584527	+	0.0177684i
$183$		0			0
$184$	7.56306	+	2.02652i	0.557556	+	0.149397i
$185$	16.9996	−	9.81472i	1.24983	−	0.721592i
$186$		0			0
$187$	3.76936	+	1.01000i	0.275643	+	0.0738584i
$188$	2.52095	−	9.40830i	0.183859	−	0.686171i
$189$		0			0
$190$	−5.26379	−	5.26379i	−0.381875	−	0.381875i
$191$	20.4524	+	11.8082i	1.47989	+	0.854412i	0.999741	−	0.0227772i	$-0.00725084\pi$
$191$	20.4524	+	11.8082i	1.47989	+	0.854412i	0.480145	+	0.877189i	$0.340584\pi$
$192$		0			0
$193$	−4.08516	+	15.2460i	−0.294056	+	1.09743i	0.647908	+	0.761719i	$0.275644\pi$
$193$	−4.08516	+	15.2460i	−0.294056	+	1.09743i	−0.941964	+	0.335714i	$0.891022\pi$
$194$	8.80700	−	15.2542i	0.632306	−	1.09519i
$195$		0			0
$196$	−1.10609	−	1.91580i	−0.0790062	−	0.136843i
$197$	−18.2302	+	4.88476i	−1.29885	+	0.348025i	−0.841014	−	0.541014i	$-0.818041\pi$
$197$	−18.2302	+	4.88476i	−1.29885	+	0.348025i	−0.457833	+	0.889038i	$0.651374\pi$
$198$		0			0
$199$	−4.30172	+	2.48360i	−0.304941	+	0.176058i	−0.644660	−	0.764469i	$-0.723001\pi$
$199$	−4.30172	+	2.48360i	−0.304941	+	0.176058i	0.339719	+	0.940527i	$0.389668\pi$
$200$	−2.53277	+	9.45241i	−0.179094	+	0.668387i
$201$		0			0
$202$	−4.21276	−	4.21276i	−0.296409	−	0.296409i
$203$	4.19479	+	15.6552i	0.294417	+	1.09878i
$204$		0			0
$205$			42.0932i			2.93991i
$206$	−0.938874	−	3.50392i	−0.0654144	−	0.244130i
$207$		0			0
$208$	−3.17583	+	1.70707i	−0.220204	+	0.118364i
$209$	7.02189	−	4.05409i	0.485714	−	0.280427i
$210$		0			0
$211$	6.62163	+	11.4690i	0.455852	+	0.789559i	0.998737	−	0.0502484i	$-0.0160013\pi$
$211$	6.62163	+	11.4690i	0.455852	+	0.789559i	−0.542885	+	0.839807i	$0.682668\pi$
$212$	−2.04197			−0.140243
$213$		0			0
$214$	1.15071	+	4.29450i	0.0786607	+	0.293566i
$215$	7.31619	+	1.96037i	0.498960	+	0.133696i
$216$		0			0
$217$	−1.40882	−	2.44015i	−0.0956372	−	0.165648i
$218$	8.19840			0.555266
$219$		0			0
$220$	−13.9472	−	8.05243i	−0.940321	−	0.542894i
$221$	−2.85695	−	1.76732i	−0.192179	−	0.118883i
$222$		0			0
$223$	−5.75133	+	5.75133i	−0.385137	+	0.385137i	−0.872949	−	0.487812i	$-0.837795\pi$
$223$	−5.75133	+	5.75133i	−0.385137	+	0.385137i	0.487812	+	0.872949i	$0.337795\pi$
$224$	−1.89496	−	1.09406i	−0.126612	−	0.0730996i
$225$		0			0
$226$	8.88595	−	8.88595i	0.591084	−	0.591084i
$227$	10.1846	−	2.72896i	0.675977	−	0.181128i	0.0955315	−	0.995426i	$-0.469545\pi$
$227$	10.1846	−	2.72896i	0.675977	−	0.181128i	0.580446	+	0.814299i	$0.302878\pi$
$228$		0			0
$229$	−14.1016	+	3.77851i	−0.931859	+	0.249691i	−0.692647	−	0.721276i	$-0.743556\pi$
$229$	−14.1016	+	3.77851i	−0.931859	+	0.249691i	−0.239212	+	0.970967i	$0.576889\pi$
$230$		−	30.1077i		−	1.98524i
$231$		0			0
$232$	−5.23757	−	5.23757i	−0.343864	−	0.343864i
$233$	17.7535			1.16307			0.581536	−	0.813521i	$-0.302452\pi$
$233$	17.7535			1.16307			0.581536	+	0.813521i	$0.302452\pi$
$234$		0			0
$235$	−37.4533			−2.44319
$236$	4.46186	+	4.46186i	0.290442	+	0.290442i
$237$		0			0
$238$		−	2.03873i		−	0.132151i
$239$	10.7752	−	2.88720i	0.696988	−	0.186757i	0.107107	−	0.994247i	$-0.465841\pi$
$239$	10.7752	−	2.88720i	0.696988	−	0.186757i	0.589881	+	0.807490i	$0.299175\pi$
$240$		0			0
$241$	2.55136	−	0.683636i	0.164348	−	0.0440368i	−0.175707	−	0.984443i	$-0.556221\pi$
$241$	2.55136	−	0.683636i	0.164348	−	0.0440368i	0.340055	+	0.940406i	$0.389554\pi$
$242$	4.62554	−	4.62554i	0.297341	−	0.297341i
$243$		0			0
$244$	−0.745686	−	0.430522i	−0.0477377	−	0.0275614i
$245$	−6.01489	+	6.01489i	−0.384277	+	0.384277i
$246$		0			0
$247$	−6.79404	+	1.60089i	−0.432294	+	0.101862i
$248$	1.11519	+	0.643854i	0.0708145	+	0.0408848i
$249$		0			0
$250$	18.4028			1.16389
$251$	−3.16017	−	5.47357i	−0.199468	−	0.345489i	0.748888	−	0.662697i	$-0.230588\pi$
$251$	−3.16017	−	5.47357i	−0.199468	−	0.345489i	−0.948356	+	0.317208i	$0.897255\pi$
$252$		0			0
$253$	31.6760	+	8.48757i	1.99146	+	0.533609i
$254$	0.0275429	+	0.102791i	0.00172819	+	0.00644971i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−0.511580	−	0.886083i	−0.0319115	−	0.0552723i	0.849629	−	0.527382i	$-0.176826\pi$
$257$	−0.511580	−	0.886083i	−0.0319115	−	0.0552723i	−0.881540	+	0.472109i	$0.843493\pi$
$258$		0			0
$259$	9.67352	−	5.58501i	0.601083	−	0.347035i
$260$	9.50108	+	10.0968i	0.589232	+	0.626178i
$261$		0			0
$262$	−3.20424	−	11.9584i	−0.197959	−	0.738793i
$263$		−	11.6474i		−	0.718209i	−0.933297	−	0.359105i	$-0.883082\pi$
$263$		−	11.6474i		−	0.718209i	0.933297	−	0.359105i	$-0.116918\pi$
$264$		0			0
$265$	2.03221	+	7.58430i	0.124837	+	0.465900i
$266$	−2.99533	−	2.99533i	−0.183655	−	0.183655i
$267$		0			0
$268$	0.865869	−	3.23147i	0.0528913	−	0.197393i
$269$	−24.3789	+	14.0752i	−1.48641	+	0.858178i	−0.999880	−	0.0154875i	$-0.995070\pi$
$269$	−24.3789	+	14.0752i	−1.48641	+	0.858178i	−0.486527	+	0.873665i	$0.661737\pi$
$270$		0			0
$271$	1.95393	−	0.523554i	0.118693	−	0.0318037i	−0.198984	−	0.980003i	$-0.563764\pi$
$271$	1.95393	−	0.523554i	0.118693	−	0.0318037i	0.317677	+	0.948199i	$0.397097\pi$
$272$	0.465866	+	0.806903i	0.0282473	+	0.0489257i
$273$		0			0
$274$	1.31700	−	2.28111i	0.0795627	−	0.137807i
$275$	−10.6079	+	39.5891i	−0.639679	+	2.38732i
$276$		0			0
$277$	−13.6892	−	7.90346i	−0.822504	−	0.474873i	0.0287755	−	0.999586i	$-0.490839\pi$
$277$	−13.6892	−	7.90346i	−0.822504	−	0.474873i	−0.851279	+	0.524713i	$0.824173\pi$
$278$	−10.3646	−	10.3646i	−0.621629	−	0.621629i
$279$		0			0
$280$	−2.17765	+	8.12711i	−0.130140	+	0.485688i
$281$	18.9089	+	5.06663i	1.12801	+	0.302250i	0.774122	−	0.633037i	$-0.218192\pi$
$281$	18.9089	+	5.06663i	1.12801	+	0.302250i	0.353891	+	0.935287i	$0.384858\pi$
$282$		0			0
$283$	28.1378	−	16.2454i	1.67262	−	0.965687i	0.706456	−	0.707757i	$-0.250293\pi$
$283$	28.1378	−	16.2454i	1.67262	−	0.965687i	0.966164	−	0.257930i	$-0.0830403\pi$
$284$	−10.8397	−	2.90450i	−0.643219	−	0.172350i
$285$		0			0
$286$	−13.3012	+	7.14965i	−0.786517	+	0.422767i
$287$			23.9529i			1.41389i
$288$		0			0
$289$	8.06594	−	13.9706i	0.474467	−	0.821801i
$290$	−14.2409	+	24.6660i	−0.836256	+	1.44844i
$291$		0			0
$292$	2.45316	−	2.45316i	0.143560	−	0.143560i
$293$	10.2821	−	10.2821i	0.600684	−	0.600684i	−0.339810	−	0.940494i	$-0.610363\pi$
$293$	10.2821	−	10.2821i	0.600684	−	0.600684i	0.940494	+	0.339810i	$0.110363\pi$
$294$		0			0
$295$	12.1318	−	21.0128i	0.706338	−	1.22341i
$296$	−2.55243	+	4.42095i	−0.148357	+	0.256962i
$297$		0			0
$298$			6.13362i			0.355311i
$299$	−24.0085	−	14.8518i	−1.38845	−	0.858902i
$300$		0			0
$301$	4.16323	+	1.11553i	0.239965	+	0.0642983i
$302$	3.42573	−	1.97784i	0.197128	−	0.113812i
$303$		0			0
$304$	1.86997	+	0.501056i	0.107250	+	0.0287375i
$305$	−0.856929	+	3.19810i	−0.0490676	+	0.183123i
$306$		0			0
$307$	6.00502	+	6.00502i	0.342724	+	0.342724i	0.857391	−	0.514666i	$-0.172084\pi$
$307$	6.00502	+	6.00502i	0.342724	+	0.342724i	−0.514666	+	0.857391i	$0.672084\pi$
$308$	−7.93658	−	4.58218i	−0.452228	−	0.261094i
$309$		0			0
$310$	1.28155	−	4.78283i	0.0727874	−	0.271646i
$311$	−7.13805	+	12.3635i	−0.404762	+	0.701068i	−0.994294	−	0.106677i	$-0.965979\pi$
$311$	−7.13805	+	12.3635i	−0.404762	+	0.701068i	0.589532	+	0.807745i	$0.299312\pi$
$312$		0			0
$313$	−0.0856946	−	0.148427i	−0.00484375	−	0.00838962i	0.863593	−	0.504189i	$-0.168208\pi$
$313$	−0.0856946	−	0.148427i	−0.00484375	−	0.00838962i	−0.868437	+	0.495799i	$0.834875\pi$
$314$	−8.17951	+	2.19169i	−0.461597	+	0.123684i
$315$		0			0
$316$	−11.0546	+	6.38240i	−0.621872	+	0.359038i
$317$	−5.12627	+	19.1315i	−0.287920	+	1.07453i	0.658759	+	0.752354i	$0.271082\pi$
$317$	−5.12627	+	19.1315i	−0.287920	+	1.07453i	−0.946679	+	0.322178i	$0.895585\pi$
$318$		0			0
$319$	−21.9363	−	21.9363i	−1.22820	−	1.22820i
$320$	−0.995221	−	3.71422i	−0.0556345	−	0.207631i
$321$		0			0
$322$		−	17.1326i		−	0.954761i
$323$	0.466849	+	1.74231i	0.0259762	+	0.0969445i
$324$		0			0
$325$	18.5620	−	30.0062i	1.02963	−	1.66444i
$326$	−1.71483	+	0.990058i	−0.0949757	+	0.0548342i
$327$		0			0
$328$	−5.47341	−	9.48023i	−0.302219	−	0.523458i
$329$	−21.3126			−1.17500
$330$		0			0
$331$	6.29719	+	23.5014i	0.346125	+	1.29176i	0.891292	+	0.453429i	$0.149799\pi$
$331$	6.29719	+	23.5014i	0.346125	+	1.29176i	−0.545167	+	0.838327i	$0.683534\pi$
$332$	5.43185	+	1.45546i	0.298111	+	0.0798787i
$333$		0			0
$334$	−11.2067	−	19.4106i	−0.613203	−	1.06210i
$335$	−12.8641			−0.702840
$336$		0			0
$337$	−8.81745	−	5.09076i	−0.480317	−	0.277311i	0.240232	−	0.970716i	$-0.422777\pi$
$337$	−8.81745	−	5.09076i	−0.480317	−	0.277311i	−0.720549	+	0.693404i	$0.756110\pi$
$338$	12.7382	−	2.59572i	0.692868	−	0.141189i
$339$		0			0
$340$	2.53337	−	2.53337i	0.137391	−	0.137391i
$341$	4.67070	+	2.69663i	0.252932	+	0.146031i
$342$		0			0
$343$	−14.2533	+	14.2533i	−0.769607	+	0.769607i
$344$	−1.90266	+	0.509817i	−0.102585	+	0.0274875i
$345$		0			0
$346$	18.3960	−	4.92920i	0.988977	−	0.264996i
$347$		−	16.1265i		−	0.865715i	−0.901462	−	0.432857i	$-0.857505\pi$
$347$		−	16.1265i		−	0.865715i	0.901462	−	0.432857i	$-0.142495\pi$
$348$		0			0
$349$	20.7759	+	20.7759i	1.11211	+	1.11211i	0.992865	+	0.119243i	$0.0380466\pi$
$349$	20.7759	+	20.7759i	1.11211	+	1.11211i	0.119243	+	0.992865i	$0.461953\pi$
$350$	21.4125			1.14455
$351$		0			0
$352$	4.18826			0.223235
$353$	15.0529	+	15.0529i	0.801184	+	0.801184i	0.983281	−	0.182096i	$-0.0582883\pi$
$353$	15.0529	+	15.0529i	0.801184	+	0.801184i	−0.182096	+	0.983281i	$0.558288\pi$
$354$		0			0
$355$			43.1517i			2.29025i
$356$	1.95060	−	0.522663i	0.103382	−	0.0277011i
$357$		0			0
$358$	0.493984	−	0.132363i	0.0261079	−	0.00699558i
$359$	11.8574	−	11.8574i	0.625809	−	0.625809i	−0.321202	−	0.947011i	$-0.604087\pi$
$359$	11.8574	−	11.8574i	0.625809	−	0.625809i	0.947011	+	0.321202i	$0.104087\pi$
$360$		0			0
$361$	−13.2088	−	7.62609i	−0.695198	−	0.401373i
$362$	1.68443	−	1.68443i	0.0885319	−	0.0885319i
$363$		0			0
$364$	5.40653	+	5.74553i	0.283379	+	0.301148i
$365$	−11.5530	−	6.67013i	−0.604712	−	0.349131i
$366$		0			0
$367$	9.73112			0.507960			0.253980	−	0.967209i	$-0.418260\pi$
$367$	9.73112			0.507960			0.253980	+	0.967209i	$0.418260\pi$
$368$	3.91493	+	6.78085i	0.204080	+	0.353476i
$369$		0			0
$370$	18.9606	+	5.08047i	0.985714	+	0.264121i
$371$	1.15642	+	4.31580i	0.0600381	+	0.224065i
$372$		0			0
$373$	23.7302			1.22870			0.614351	−	0.789032i	$-0.289418\pi$
$373$	23.7302			1.22870			0.614351	+	0.789032i	$0.289418\pi$
$374$	1.95117	+	3.37952i	0.100892	+	0.174751i
$375$		0			0
$376$	8.43525	−	4.87009i	0.435015	−	0.251156i
$377$	12.6443	+	23.5235i	0.651217	+	1.21152i
$378$		0			0
$379$	−0.0380534	−	0.142017i	−0.00195467	−	0.00729493i	0.964942	−	0.262465i	$-0.0845353\pi$
$379$	−0.0380534	−	0.142017i	−0.00195467	−	0.00729493i	−0.966896	+	0.255170i	$0.917869\pi$
$380$		−	7.44412i		−	0.381875i
$381$		0			0
$382$	6.11238	+	22.8117i	0.312737	+	1.16715i
$383$	16.2995	+	16.2995i	0.832867	+	0.832867i	0.987908	−	0.155041i	$-0.0495509\pi$
$383$	16.2995	+	16.2995i	0.832867	+	0.832867i	−0.155041	+	0.987908i	$0.549551\pi$
$384$		0			0
$385$	−9.12057	+	34.0384i	−0.464827	+	1.73476i
$386$	−13.6692	+	7.89192i	−0.695744	+	0.401688i
$387$		0			0
$388$	17.0138	−	4.55884i	0.863745	−	0.231440i
$389$	−16.4933	−	28.5672i	−0.836243	−	1.44841i	−0.893015	−	0.450028i	$-0.851414\pi$
$389$	−16.4933	−	28.5672i	−0.836243	−	1.44841i	0.0567717	−	0.998387i	$-0.481919\pi$
$390$		0			0
$391$	−3.64766	+	6.31793i	−0.184470	+	0.319512i
$392$	0.572553	−	2.13680i	0.0289183	−	0.107925i
$393$		0			0
$394$	−16.3447	−	9.43664i	−0.823436	−	0.475411i
$395$	34.7074	+	34.7074i	1.74632	+	1.74632i
$396$		0			0
$397$	5.53019	−	20.6390i	0.277552	−	1.03584i	−0.676559	−	0.736388i	$-0.736530\pi$
$397$	5.53019	−	20.6390i	0.277552	−	1.03584i	0.954112	−	0.299451i	$-0.0968037\pi$
$398$	−4.79795	−	1.28561i	−0.240499	−	0.0644416i
$399$		0			0
$400$	−8.47480	+	4.89293i	−0.423740	+	0.244646i
$401$	26.3984	+	7.07343i	1.31827	+	0.353230i	0.848331	−	0.529467i	$-0.177608\pi$
$401$	26.3984	+	7.07343i	1.31827	+	0.353230i	0.469943	+	0.882697i	$0.344275\pi$
$402$		0			0
$403$	−3.18176	−	3.38126i	−0.158495	−	0.168433i
$404$		−	5.95775i		−	0.296409i
$405$		0			0
$406$	−8.10372	+	14.0361i	−0.402181	+	0.696598i
$407$	−10.6903	+	18.5161i	−0.529896	+	0.917807i
$408$		0			0
$409$	−12.3294	+	12.3294i	−0.609648	+	0.609648i	−0.942854	−	0.333206i	$-0.891869\pi$
$409$	−12.3294	+	12.3294i	−0.609648	+	0.609648i	0.333206	+	0.942854i	$0.391869\pi$
$410$	−29.7644	+	29.7644i	−1.46996	+	1.46996i
$411$		0			0
$412$	1.81377	−	3.14153i	0.0893578	−	0.154772i
$413$	6.90351	−	11.9572i	0.339699	−	0.588377i
$414$		0			0
$415$		−	21.6236i		−	1.06146i
$416$	−3.45273	−	1.03857i	−0.169284	−	0.0509202i
$417$		0			0
$418$	7.83190	+	2.09855i	0.383071	+	0.102643i
$419$	−17.0583	+	9.84862i	−0.833353	+	0.481137i	−0.854999	−	0.518629i	$-0.826443\pi$
$419$	−17.0583	+	9.84862i	−0.833353	+	0.481137i	0.0216462	+	0.999766i	$0.493109\pi$
$420$		0			0
$421$	−4.34449	−	1.16410i	−0.211737	−	0.0567348i	0.151391	−	0.988474i	$-0.451625\pi$
$421$	−4.34449	−	1.16410i	−0.211737	−	0.0567348i	−0.363128	+	0.931739i	$0.618291\pi$
$422$	−3.42761	+	12.7920i	−0.166853	+	0.622705i
$423$		0			0
$424$	−1.44389	−	1.44389i	−0.0701214	−	0.0701214i
$425$	−7.89624	−	4.55890i	−0.383024	−	0.221139i
$426$		0			0
$427$	−0.487630	+	1.81986i	−0.0235981	+	0.0880693i
$428$	−2.22300	+	3.85034i	−0.107453	+	0.186113i
$429$		0			0
$430$	3.78714	+	6.55951i	0.182632	+	0.316328i
$431$	0.579994	−	0.155409i	0.0279373	−	0.00748579i	−0.244823	−	0.969568i	$-0.578730\pi$
$431$	0.579994	−	0.155409i	0.0279373	−	0.00748579i	0.272761	+	0.962082i	$0.412063\pi$
$432$		0			0
$433$	−7.94515	+	4.58713i	−0.381819	+	0.220444i	−0.678610	−	0.734499i	$-0.737417\pi$
$433$	−7.94515	+	4.58713i	−0.381819	+	0.220444i	0.296790	+	0.954943i	$0.404084\pi$
$434$	0.729261	−	2.72164i	0.0350056	−	0.130643i
$435$		0			0
$436$	5.79714	+	5.79714i	0.277633	+	0.277633i
$437$	3.92319	+	14.6416i	0.187672	+	0.700401i
$438$		0			0
$439$			15.4681i			0.738252i	0.929379	+	0.369126i	$0.120343\pi$
$439$			15.4681i			0.738252i	−0.929379	+	0.369126i	$0.879657\pi$
$440$	−4.16824	−	15.5561i	−0.198713	−	0.741608i
$441$		0			0
$442$	−0.770483	−	3.26986i	−0.0366481	−	0.155531i
$443$	15.2867	−	8.82576i	0.726292	−	0.419325i	−0.0907723	−	0.995872i	$-0.528934\pi$
$443$	15.2867	−	8.82576i	0.726292	−	0.419325i	0.817064	+	0.576547i	$0.195600\pi$
$444$		0			0
$445$	−3.88257	−	6.72480i	−0.184051	−	0.318786i
$446$	−8.13360			−0.385137
$447$		0			0
$448$	−0.566325	−	2.11355i	−0.0267563	−	0.0998559i
$449$	17.1746	+	4.60193i	0.810521	+	0.217178i	0.640198	−	0.768210i	$-0.278852\pi$
$449$	17.1746	+	4.60193i	0.810521	+	0.217178i	0.170323	+	0.985388i	$0.445519\pi$
$450$		0			0
$451$	−22.9241	−	39.7056i	−1.07945	−	1.86967i
$452$	12.5666			0.591084
$453$		0			0
$454$	9.13129	+	5.27195i	0.428552	+	0.247425i
$455$	15.9594	−	25.7991i	0.748191	−	1.20948i
$456$		0			0
$457$	−18.5795	+	18.5795i	−0.869111	+	0.869111i	−0.992374	−	0.123263i	$-0.960664\pi$
$457$	−18.5795	+	18.5795i	−0.869111	+	0.869111i	0.123263	+	0.992374i	$0.460664\pi$
$458$	−12.6431	−	7.29952i	−0.590775	−	0.341084i
$459$		0			0
$460$	21.2893	−	21.2893i	0.992620	−	0.992620i
$461$	35.3774	−	9.47934i	1.64769	−	0.441497i	0.688725	−	0.725023i	$-0.258171\pi$
$461$	35.3774	−	9.47934i	1.64769	−	0.441497i	0.958965	+	0.283526i	$0.0915041\pi$
$462$		0			0
$463$	27.7142	−	7.42600i	1.28799	−	0.345115i	0.451092	−	0.892477i	$-0.351035\pi$
$463$	27.7142	−	7.42600i	1.28799	−	0.345115i	0.836896	+	0.547362i	$0.184368\pi$
$464$		−	7.40705i		−	0.343864i
$465$		0			0
$466$	12.5536	+	12.5536i	0.581536	+	0.581536i
$467$	30.1627			1.39576			0.697881	−	0.716214i	$-0.254126\pi$
$467$	30.1627			1.39576			0.697881	+	0.716214i	$0.254126\pi$
$468$		0			0
$469$	−7.32023			−0.338017
$470$	−26.4835	−	26.4835i	−1.22159	−	1.22159i
$471$		0			0
$472$			6.31002i			0.290442i
$473$	−7.96884	+	2.13524i	−0.366407	+	0.0981786i
$474$		0			0
$475$	−18.2992	+	4.90326i	−0.839626	+	0.224977i
$476$	1.44160	−	1.44160i	0.0660757	−	0.0660757i
$477$		0			0
$478$	9.66076	+	5.57764i	0.441873	+	0.255115i
$479$	−8.40895	+	8.40895i	−0.384215	+	0.384215i	−0.872618	−	0.488403i	$-0.837580\pi$
$479$	−8.40895	+	8.40895i	−0.384215	+	0.384215i	0.488403	+	0.872618i	$0.337580\pi$
$480$		0			0
$481$	13.4043	−	12.6135i	0.611186	−	0.575124i
$482$	2.28749	+	1.32068i	0.104192	+	0.0601554i
$483$		0			0
$484$	6.54150			0.297341
$485$	−33.8650	−	58.6559i	−1.53773	−	2.66343i
$486$		0			0
$487$	20.6057	+	5.52129i	0.933735	+	0.250194i	0.693447	−	0.720508i	$-0.256091\pi$
$487$	20.6057	+	5.52129i	0.933735	+	0.250194i	0.240288	+	0.970702i	$0.422758\pi$
$488$	−0.222855	−	0.831705i	−0.0100882	−	0.0376495i
$489$		0			0
$490$	−8.50634			−0.384277
$491$	9.99582	+	17.3133i	0.451105	+	0.781337i	0.998455	−	0.0555669i	$-0.0176966\pi$
$491$	9.99582	+	17.3133i	0.451105	+	0.781337i	−0.547350	+	0.836904i	$0.684363\pi$
$492$		0			0
$493$	5.97677	−	3.45069i	0.269180	−	0.155411i
$494$	−5.93611	−	3.67211i	−0.267078	−	0.165216i
$495$		0			0
$496$	0.333283	+	1.24383i	0.0149649	+	0.0558497i
$497$			24.5552i			1.10145i
$498$		0			0
$499$	−0.0739605	−	0.276024i	−0.00331093	−	0.0123565i	0.964251	−	0.264992i	$-0.0853693\pi$
$499$	−0.0739605	−	0.276024i	−0.00331093	−	0.0123565i	−0.967562	+	0.252635i	$0.918703\pi$
$500$	13.0127	+	13.0127i	0.581947	+	0.581947i
$501$		0			0
$502$	1.63582	−	6.10498i	0.0730104	−	0.272478i
$503$	6.95762	−	4.01698i	0.310225	−	0.179108i	−0.336802	−	0.941575i	$-0.609345\pi$
$503$	6.95762	−	4.01698i	0.310225	−	0.179108i	0.647027	+	0.762467i	$0.276012\pi$
$504$		0			0
$505$	−22.1284	+	5.92927i	−0.984699	+	0.263849i
$506$	16.3967	+	28.4000i	0.728923	+	1.26253i
$507$		0			0
$508$	−0.0532087	+	0.0921603i	−0.00236076	+	0.00408895i
$509$	7.97104	−	29.7483i	0.353310	−	1.31857i	−0.529288	−	0.848442i	$-0.677541\pi$
$509$	7.97104	−	29.7483i	0.353310	−	1.31857i	0.882598	−	0.470129i	$-0.155792\pi$
$510$		0			0
$511$	−6.57417	−	3.79560i	−0.290824	−	0.167907i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	0.264813	−	0.988297i	0.0116804	−	0.0435919i
$515$	−13.4734	−	3.61019i	−0.593710	−	0.159084i
$516$		0			0
$517$	35.3290	−	20.3972i	1.55377	−	0.897068i
$518$	10.7894	+	2.89101i	0.474059	+	0.127024i
$519$		0			0
$520$	−0.421249	+	13.8578i	−0.0184730	+	0.607705i
$521$		−	5.90138i		−	0.258544i	−0.991609	−	0.129272i	$-0.958736\pi$
$521$		−	5.90138i		−	0.258544i	0.991609	−	0.129272i	$-0.0412640\pi$
$522$		0			0
$523$	5.66854	−	9.81820i	0.247868	−	0.429320i	−0.715066	−	0.699057i	$-0.753603\pi$
$523$	5.66854	−	9.81820i	0.247868	−	0.429320i	0.962934	+	0.269737i	$0.0869368\pi$
$524$	6.19013	−	10.7216i	0.270417	−	0.468376i
$525$		0			0
$526$	8.23595	−	8.23595i	0.359105	−	0.359105i
$527$	−0.848386	+	0.848386i	−0.0369563	+	0.0369563i
$528$		0			0
$529$	−19.1533	+	33.1745i	−0.832752	+	1.44237i
$530$	−3.92592	+	6.79990i	−0.170531	+	0.295369i
$531$		0			0
$532$		−	4.23603i		−	0.183655i
$533$	9.05233	+	38.4172i	0.392100	+	1.66404i
$534$		0			0
$535$	16.5134	+	4.42474i	0.713935	+	0.191298i
$536$	2.89725	−	1.67273i	0.125142	−	0.0722509i
$537$		0			0
$538$	−27.1911	−	7.28584i	−1.17229	−	0.314115i
$539$	2.39800	−	8.94945i	0.103289	−	0.385480i
$540$		0			0
$541$	1.72650	+	1.72650i	0.0742279	+	0.0742279i	0.743246	−	0.669018i	$-0.233285\pi$
$541$	1.72650	+	1.72650i	0.0742279	+	0.0742279i	−0.669018	+	0.743246i	$0.733285\pi$
$542$	1.75185	+	1.01143i	0.0752483	+	0.0434446i
$543$		0			0
$544$	−0.241150	+	0.899984i	−0.0103392	+	0.0385865i
$545$	15.7624	−	27.3013i	0.675187	−	1.16946i
$546$		0			0
$547$	−9.56787	−	16.5720i	−0.409092	−	0.708569i	0.585696	−	0.810531i	$-0.300821\pi$
$547$	−9.56787	−	16.5720i	−0.409092	−	0.708569i	−0.994788	+	0.101962i	$0.967488\pi$
$548$	2.54424	−	0.681728i	0.108685	−	0.0291220i
$549$		0			0
$550$	−35.4947	+	20.4929i	−1.51350	+	0.873818i
$551$	3.71134	−	13.8509i	0.158109	−	0.590069i
$552$		0			0
$553$	19.7500	+	19.7500i	0.839857	+	0.839857i
$554$	−4.09113	−	15.2683i	−0.173815	−	0.648688i
$555$		0			0
$556$		−	14.6578i		−	0.621629i
$557$	−5.72596	−	21.3696i	−0.242617	−	0.905457i	−0.974566	−	0.224099i	$-0.928056\pi$
$557$	−5.72596	−	21.3696i	−0.242617	−	0.905457i	0.731950	−	0.681359i	$-0.238611\pi$
$558$		0			0
$559$	7.09886	+	0.215791i	0.300250	+	0.00912699i
$560$	−7.28657	+	4.20690i	−0.307914	+	0.177774i
$561$		0			0
$562$	9.78798	+	16.9533i	0.412881	+	0.715131i
$563$	−16.2778			−0.686026			−0.343013	−	0.939331i	$-0.611448\pi$
$563$	−16.2778			−0.686026			−0.343013	+	0.939331i	$0.611448\pi$
$564$		0			0
$565$	−12.5066	−	46.6752i	−0.526155	−	1.96364i
$566$	31.3837	+	8.40922i	1.31915	+	0.353466i
$567$		0			0
$568$	−5.61105	−	9.71863i	−0.235435	−	0.407785i
$569$	−14.6047			−0.612260			−0.306130	−	0.951990i	$-0.599034\pi$
$569$	−14.6047			−0.612260			−0.306130	+	0.951990i	$0.599034\pi$
$570$		0			0
$571$	−17.7611	−	10.2544i	−0.743278	−	0.429132i	0.0799818	−	0.996796i	$-0.474514\pi$
$571$	−17.7611	−	10.2544i	−0.743278	−	0.429132i	−0.823260	+	0.567664i	$0.807847\pi$
$572$	−14.4609	−	4.34981i	−0.604642	−	0.181875i
$573$		0			0
$574$	−16.9372	+	16.9372i	−0.706946	+	0.706946i
$575$	−66.3565	−	38.3109i	−2.76726	−	1.59768i
$576$		0			0
$577$	−21.6621	+	21.6621i	−0.901806	+	0.901806i	−0.995592	−	0.0937859i	$-0.970103\pi$
$577$	−21.6621	+	21.6621i	−0.901806	+	0.901806i	0.0937859	+	0.995592i	$0.470103\pi$
$578$	15.5822	−	4.17524i	0.648134	−	0.173667i
$579$		0			0
$580$	−27.5114	+	7.37165i	−1.14235	+	0.306091i
$581$		−	12.3048i		−	0.510487i
$582$		0			0
$583$	−6.04737	−	6.04737i	−0.250457	−	0.250457i
$584$	3.46929			0.143560
$585$		0			0
$586$	14.5410			0.600684
$587$	10.9465	+	10.9465i	0.451811	+	0.451811i	0.895955	−	0.444144i	$-0.146492\pi$
$587$	10.9465	+	10.9465i	0.451811	+	0.451811i	−0.444144	+	0.895955i	$0.646492\pi$
$588$		0			0
$589$			2.49291i			0.102719i
$590$	23.4368	−	6.27986i	0.964876	−	0.258538i
$591$		0			0
$592$	−4.93092	+	1.32124i	−0.202660	+	0.0543025i
$593$	−15.6420	+	15.6420i	−0.642338	+	0.642338i	−0.951130	−	0.308791i	$-0.900075\pi$
$593$	−15.6420	+	15.6420i	−0.642338	+	0.642338i	0.308791	+	0.951130i	$0.400075\pi$
$594$		0			0
$595$	−6.78913	−	3.91970i	−0.278327	−	0.160692i
$596$	−4.33712	+	4.33712i	−0.177655	+	0.177655i
$597$		0			0
$598$	−6.47479	−	27.4784i	−0.264774	−	1.12368i
$599$	−23.9942	−	13.8531i	−0.980378	−	0.566022i	−0.0779938	−	0.996954i	$-0.524851\pi$
$599$	−23.9942	−	13.8531i	−0.980378	−	0.566022i	−0.902384	+	0.430932i	$0.858185\pi$
$600$		0			0
$601$	46.3112			1.88907			0.944536	−	0.328407i	$-0.106512\pi$
$601$	46.3112			1.88907			0.944536	+	0.328407i	$0.106512\pi$
$602$	2.15505	+	3.73265i	0.0878332	+	0.152132i
$603$		0			0
$604$	3.82090	+	1.02381i	0.155470	+	0.0416581i
$605$	−6.51024	−	24.2966i	−0.264679	−	0.987795i
$606$		0			0
$607$	−0.676366			−0.0274528			−0.0137264	−	0.999906i	$-0.504369\pi$
$607$	−0.676366			−0.0274528			−0.0137264	+	0.999906i	$0.504369\pi$
$608$	0.967965	+	1.67657i	0.0392562	+	0.0679937i
$609$		0			0
$610$	−2.86734	+	1.65546i	−0.116095	+	0.0670276i
$611$	−34.1826	+	8.05452i	−1.38288	+	0.325851i
$612$		0			0
$613$	6.69356	+	24.9807i	0.270351	+	1.00896i	0.958893	+	0.283766i	$0.0915840\pi$
$613$	6.69356	+	24.9807i	0.270351	+	1.00896i	−0.688543	+	0.725196i	$0.741749\pi$
$614$			8.49238i			0.342724i
$615$		0			0
$616$	−2.37191	−	8.85210i	−0.0955671	−	0.356661i
$617$	16.4300	+	16.4300i	0.661445	+	0.661445i	0.955721	−	0.294275i	$-0.0950783\pi$
$617$	16.4300	+	16.4300i	0.661445	+	0.661445i	−0.294275	+	0.955721i	$0.595078\pi$
$618$		0			0
$619$	−2.71346	+	10.1268i	−0.109063	+	0.407029i	−0.998774	−	0.0494944i	$-0.984239\pi$
$619$	−2.71346	+	10.1268i	−0.109063	+	0.407029i	0.889711	+	0.456524i	$0.150906\pi$
$620$	4.28816	−	2.47577i	0.172217	−	0.0994294i
$621$		0			0
$622$	−13.7896	+	3.69493i	−0.552915	+	0.148153i
$623$	−2.20935	−	3.82671i	−0.0885158	−	0.153314i
$624$		0			0
$625$	10.9169	−	18.9086i	0.436675	−	0.756343i
$626$	0.0443588	−	0.165549i	0.00177293	−	0.00661668i
$627$		0			0
$628$	−7.33355	−	4.23403i	−0.292640	−	0.168956i
$629$	−3.36326	−	3.36326i	−0.134102	−	0.134102i
$630$		0			0
$631$	−6.92325	+	25.8379i	−0.275610	+	1.02859i	0.679821	+	0.733378i	$0.262057\pi$
$631$	−6.92325	+	25.8379i	−0.275610	+	1.02859i	−0.955431	+	0.295213i	$0.904609\pi$
$632$	−12.3298	−	3.30377i	−0.490455	−	0.131417i
$633$		0			0
$634$	−17.1528	+	9.90320i	−0.681226	+	0.393306i
$635$	0.395257	+	0.105909i	0.0156853	+	0.00420287i
$636$		0			0
$637$	−4.19609	+	6.78315i	−0.166255	+	0.268758i
$638$		−	31.0226i		−	1.22820i
$639$		0			0
$640$	1.92262	−	3.33007i	0.0759982	−	0.131633i
$641$	8.11862	−	14.0619i	0.320666	−	0.555410i	−0.659959	−	0.751301i	$-0.729427\pi$
$641$	8.11862	−	14.0619i	0.320666	−	0.555410i	0.980626	+	0.195891i	$0.0627598\pi$
$642$		0			0
$643$	−28.2088	+	28.2088i	−1.11245	+	1.11245i	−0.119629	+	0.992819i	$0.538170\pi$
$643$	−28.2088	+	28.2088i	−1.11245	+	1.11245i	−0.992819	+	0.119629i	$0.961830\pi$
$644$	12.1146	−	12.1146i	0.477381	−	0.477381i
$645$		0			0
$646$	−0.901884	+	1.56211i	−0.0354841	+	0.0614603i
$647$	1.17726	−	2.03908i	0.0462830	−	0.0801645i	−0.841956	−	0.539546i	$-0.818596\pi$
$647$	1.17726	−	2.03908i	0.0462830	−	0.0801645i	0.888239	+	0.459382i	$0.151929\pi$
$648$		0			0
$649$			26.4280i			1.03739i
$650$	34.3429	−	8.09228i	1.34704	−	0.317405i
$651$		0			0
$652$	−1.91264	−	0.512492i	−0.0749049	−	0.0200707i
$653$	12.6180	−	7.28502i	0.493782	−	0.285085i	−0.232360	−	0.972630i	$-0.574645\pi$
$653$	12.6180	−	7.28502i	0.493782	−	0.285085i	0.726142	+	0.687545i	$0.241312\pi$
$654$		0			0
$655$	−45.9829	−	12.3211i	−1.79670	−	0.481425i
$656$	2.83325	−	10.5738i	0.110620	−	0.412838i
$657$		0			0
$658$	−15.0703	−	15.0703i	−0.587501	−	0.587501i
$659$	−3.83999	−	2.21702i	−0.149585	−	0.0863628i	0.423339	−	0.905971i	$-0.360858\pi$
$659$	−3.83999	−	2.21702i	−0.149585	−	0.0863628i	−0.572924	+	0.819608i	$0.694191\pi$
$660$		0			0
$661$	5.45199	−	20.3471i	0.212058	−	0.791411i	−0.775124	−	0.631809i	$-0.782313\pi$
$661$	5.45199	−	20.3471i	0.212058	−	0.791411i	0.987182	−	0.159601i	$-0.0510208\pi$
$662$	−12.1652	+	21.0708i	−0.472816	+	0.818941i
$663$		0			0
$664$	2.81173	+	4.87006i	0.109116	+	0.188995i
$665$	−15.7335	+	4.21579i	−0.610120	+	0.163481i
$666$		0			0
$667$	50.2261	−	28.9981i	1.94476	−	1.12281i
$668$	5.80101	−	21.6497i	0.224448	−	0.837651i
$669$		0			0
$670$	−9.09628	−	9.09628i	−0.351420	−	0.351420i
$671$	−0.933373	−	3.48339i	−0.0360325	−	0.134475i
$672$		0			0
$673$		−	32.8052i		−	1.26455i	−0.774745	−	0.632274i	$-0.782122\pi$
$673$		−	32.8052i		−	1.26455i	0.774745	−	0.632274i	$-0.217878\pi$
$674$	−2.63517	−	9.83459i	−0.101503	−	0.378814i
$675$		0			0
$676$	10.8427	+	7.17183i	0.417028	+	0.275840i
$677$	−19.6014	+	11.3169i	−0.753344	+	0.434944i	−0.826901	−	0.562347i	$-0.809898\pi$
$677$	−19.6014	+	11.3169i	−0.753344	+	0.434944i	0.0735566	+	0.997291i	$0.476565\pi$
$678$		0			0
$679$	−19.2707	−	33.3778i	−0.739541	−	1.28092i
$680$	3.58273			0.137391
$681$		0			0
$682$	1.39588	+	5.20948i	0.0534509	+	0.199481i
$683$	−11.5934	−	3.10645i	−0.443611	−	0.118865i	0.0300976	−	0.999547i	$-0.490418\pi$
$683$	−11.5934	−	3.10645i	−0.443611	−	0.118865i	−0.473708	+	0.880682i	$0.657085\pi$
$684$		0			0
$685$	−5.06417	−	8.77140i	−0.193492	−	0.335138i
$686$	−20.1573			−0.769607
$687$		0			0
$688$	−1.70588	−	0.984890i	−0.0650360	−	0.0375486i
$689$	3.48578	+	6.48494i	0.132798	+	0.247057i
$690$		0			0
$691$	−15.6544	+	15.6544i	−0.595522	+	0.595522i	−0.939118	−	0.343596i	$-0.888355\pi$
$691$	−15.6544	+	15.6544i	−0.595522	+	0.595522i	0.343596	+	0.939118i	$0.388355\pi$
$692$	16.4934	+	9.52249i	0.626986	+	0.361991i
$693$		0			0
$694$	11.4031	−	11.4031i	0.432857	−	0.432857i
$695$	−54.4422	+	14.5877i	−2.06511	+	0.553345i
$696$		0			0
$697$	9.85196	−	2.63983i	0.373170	−	0.0999905i
$698$			29.3815i			1.11211i
$699$		0			0
$700$	15.1409	+	15.1409i	0.572274	+	0.572274i
$701$	−26.8651			−1.01468			−0.507341	−	0.861746i	$-0.669371\pi$
$701$	−26.8651			−1.01468			−0.507341	+	0.861746i	$0.669371\pi$
$702$		0			0
$703$	−9.88267			−0.372732
$704$	2.96155	+	2.96155i	0.111617	+	0.111617i
$705$		0			0
$706$			21.2880i			0.801184i
$707$	−12.5920	+	3.37402i	−0.473571	+	0.126893i
$708$		0			0
$709$	18.0428	−	4.83455i	0.677611	−	0.181565i	0.0964301	−	0.995340i	$-0.469258\pi$
$709$	18.0428	−	4.83455i	0.677611	−	0.181565i	0.581181	+	0.813774i	$0.302591\pi$
$710$	−30.5128	+	30.5128i	−1.14513	+	1.14513i
$711$		0			0
$712$	1.74886	+	1.00971i	0.0655415	+	0.0378404i
$713$	−7.12945	+	7.12945i	−0.267000	+	0.267000i
$714$		0			0
$715$	−1.76430	+	58.0401i	−0.0659811	+	2.17057i
$716$	0.442894	+	0.255705i	0.0165517	+	0.00955615i
$717$		0			0
$718$	16.7689			0.625809
$719$	14.5977	+	25.2840i	0.544404	+	0.942936i	0.998644	+	0.0520563i	$0.0165775\pi$
$719$	14.5977	+	25.2840i	0.544404	+	0.942936i	−0.454240	+	0.890879i	$0.650089\pi$
$720$		0			0
$721$	−7.66697	−	2.05436i	−0.285533	−	0.0765083i
$722$	−3.94755	−	14.7325i	−0.146913	−	0.548286i
$723$		0			0
$724$	2.38215			0.0885319
$725$	36.2422	+	62.7733i	1.34600	+	2.33134i
$726$		0			0
$727$	36.4712	−	21.0566i	1.35264	−	0.780948i	0.364022	−	0.931390i	$-0.381403\pi$
$727$	36.4712	−	21.0566i	1.35264	−	0.780948i	0.988619	+	0.150443i	$0.0480699\pi$
$728$	−0.239709	+	7.88570i	−0.00888422	+	0.292264i
$729$		0			0
$730$	−3.45271	−	12.8857i	−0.127791	−	0.476921i
$731$		−	1.83531i		−	0.0678812i
$732$		0			0
$733$	−10.0518	−	37.5139i	−0.371272	−	1.38561i	−0.858716	−	0.512452i	$-0.828737\pi$
$733$	−10.0518	−	37.5139i	−0.371272	−	1.38561i	0.487444	−	0.873154i	$-0.337929\pi$
$734$	6.88094	+	6.88094i	0.253980	+	0.253980i
$735$		0			0
$736$	−2.02652	+	7.56306i	−0.0746983	+	0.278778i
$737$	12.1344	−	7.00582i	0.446978	−	0.258063i
$738$		0			0
$739$	−13.9922	+	3.74921i	−0.514713	+	0.137917i	−0.506820	−	0.862052i	$-0.669179\pi$
$739$	−13.9922	+	3.74921i	−0.514713	+	0.137917i	−0.00789285	+	0.999969i	$0.502512\pi$
$740$	9.81472	+	16.9996i	0.360796	+	0.624917i
$741$		0			0
$742$	−2.23402	+	3.86944i	−0.0820135	+	0.142052i
$743$	3.45307	−	12.8870i	0.126681	−	0.472780i	−0.873213	−	0.487339i	$-0.837968\pi$
$743$	3.45307	−	12.8870i	0.126681	−	0.472780i	0.999894	+	0.0145589i	$0.00463440\pi$
$744$		0			0
$745$	20.4254	+	11.7926i	0.748329	+	0.432048i
$746$	16.7798	+	16.7798i	0.614351	+	0.614351i
$747$		0			0
$748$	−1.01000	+	3.76936i	−0.0369292	+	0.137822i
$749$	9.39684	+	2.51787i	0.343353	+	0.0920011i
$750$		0			0
$751$	26.4563	−	15.2745i	0.965402	−	0.557375i	0.0675709	−	0.997714i	$-0.478475\pi$
$751$	26.4563	−	15.2745i	0.965402	−	0.557375i	0.897832	+	0.440339i	$0.145142\pi$
$752$	9.40830	+	2.52095i	0.343085	+	0.0919295i
$753$		0			0
$754$	−7.69276	+	25.5746i	−0.280154	+	0.931371i
$755$		−	15.2106i		−	0.553569i
$756$		0			0
$757$	−22.0323	+	38.1611i	−0.800778	+	1.38699i	0.118326	+	0.992975i	$0.462247\pi$
$757$	−22.0323	+	38.1611i	−0.800778	+	1.38699i	−0.919105	+	0.394014i	$0.871086\pi$
$758$	0.0735135	−	0.127329i	0.00267013	−	0.00462480i
$759$		0			0
$760$	5.26379	−	5.26379i	0.190938	−	0.190938i
$761$	16.2670	−	16.2670i	0.589680	−	0.589680i	−0.347865	−	0.937545i	$-0.613093\pi$
$761$	16.2670	−	16.2670i	0.589680	−	0.589680i	0.937545	+	0.347865i	$0.113093\pi$
$762$		0			0
$763$	8.96950	−	15.5356i	0.324718	−	0.562427i
$764$	−11.8082	+	20.4524i	−0.427206	+	0.739943i
$765$		0			0
$766$			23.0510i			0.832867i
$767$	6.55341	−	21.7868i	0.236630	−	0.786676i
$768$		0			0
$769$	35.2148	+	9.43577i	1.26988	+	0.340262i	0.829984	−	0.557788i	$-0.188350\pi$
$769$	35.2148	+	9.43577i	1.26988	+	0.340262i	0.439893	+	0.898050i	$0.355016\pi$
$770$	−30.5180	+	17.6196i	−1.09979	+	0.634966i
$771$		0			0
$772$	−15.2460	−	4.08516i	−0.548716	−	0.147028i
$773$	−1.87114	+	6.98319i	−0.0673002	+	0.251168i	−0.991377	−	0.131038i	$-0.958169\pi$
$773$	−1.87114	+	6.98319i	−0.0673002	+	0.251168i	0.924077	+	0.382206i	$0.124836\pi$
$774$		0			0
$775$	−8.91049	−	8.91049i	−0.320074	−	0.320074i
$776$	15.2542	+	8.80700i	0.547593	+	0.316153i
$777$		0			0
$778$	8.53755	−	31.8626i	0.306086	−	1.14233i
$779$	10.5962	−	18.3531i	0.379646	−	0.657567i
$780$		0			0
$781$	−23.5005	−	40.7041i	−0.840916	−	1.45651i
$782$	−7.04674	+	1.88817i	−0.251991	+	0.0675208i
$783$		0			0
$784$	1.91580	−	1.10609i	0.0

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.71422 - 0.995221i) q^{5} +(2.11355 - 0.566325i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.71422 - 0.995221i) q^{5} +(2.11355 - 0.566325i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(3.33007 + 1.92262i) q^{10} +(-2.96155 + 2.96155i) q^{11} +(3.17583 - 1.70707i) q^{13} +(1.89496 + 1.09406i) q^{14} -1.00000 q^{16} +(-0.465866 - 0.806903i) q^{17} +(-1.86997 - 0.501056i) q^{19} +(0.995221 + 3.71422i) q^{20} -4.18826 q^{22} +(-3.91493 - 6.78085i) q^{23} +(8.47480 - 4.89293i) q^{25} +(3.45273 + 1.03857i) q^{26} +(0.566325 + 2.11355i) q^{28} +7.40705i q^{29} +(-0.333283 - 1.24383i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.241150 - 0.899984i) q^{34} +(7.28657 - 4.20690i) q^{35} +(4.93092 - 1.32124i) q^{37} +(-0.967965 - 1.67657i) q^{38} +(-1.92262 + 3.33007i) q^{40} +(-2.83325 + 10.5738i) q^{41} +(1.70588 + 0.984890i) q^{43} +(-2.96155 - 2.96155i) q^{44} +(2.02652 - 7.56306i) q^{46} +(-9.40830 - 2.52095i) q^{47} +(-1.91580 + 1.10609i) q^{49} +(9.45241 + 2.53277i) q^{50} +(1.70707 + 3.17583i) q^{52} +2.04197i q^{53} +(-8.05243 + 13.9472i) q^{55} +(-1.09406 + 1.89496i) q^{56} +(-5.23757 + 5.23757i) q^{58} +(4.46186 - 4.46186i) q^{59} +(-0.430522 + 0.745686i) q^{61} +(0.643854 - 1.11519i) q^{62} -1.00000i q^{64} +(10.0968 - 9.50108i) q^{65} +(-3.23147 - 0.865869i) q^{67} +(0.806903 - 0.465866i) q^{68} +(8.12711 + 2.17765i) q^{70} +(-2.90450 + 10.8397i) q^{71} +(-2.45316 - 2.45316i) q^{73} +(4.42095 + 2.55243i) q^{74} +(0.501056 - 1.86997i) q^{76} +(-4.58218 + 7.93658i) q^{77} +(6.38240 + 11.0546i) q^{79} +(-3.71422 + 0.995221i) q^{80} +(-9.48023 + 5.47341i) q^{82} +(1.45546 - 5.43185i) q^{83} +(-2.53337 - 2.53337i) q^{85} +(0.509817 + 1.90266i) q^{86} -4.18826i q^{88} +(-0.522663 - 1.95060i) q^{89} +(5.74553 - 5.40653i) q^{91} +(6.78085 - 3.91493i) q^{92} +(-4.87009 - 8.43525i) q^{94} -7.44412 q^{95} +(-4.55884 - 17.0138i) q^{97} +(-2.13680 - 0.572553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more