LMFDB - Embedded newform 702.2.bb.a.71.9

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			71.9
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.51706 + 0.406496i) q^{5} +(4.52587 - 1.21270i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.51706 + 0.406496i) q^{5} +(4.52587 - 1.21270i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.36016 - 0.785290i) q^{10} +(1.08184 - 1.08184i) q^{11} +(-1.01269 - 3.46041i) q^{13} +(4.05778 + 2.34276i) q^{14} -1.00000 q^{16} +(2.99188 + 5.18209i) q^{17} +(5.70943 + 1.52984i) q^{19} +(-0.406496 - 1.51706i) q^{20} +1.52995 q^{22} +(2.48702 + 4.30764i) q^{23} +(-2.19388 + 1.26664i) q^{25} +(1.73080 - 3.16296i) q^{26} +(1.21270 + 4.52587i) q^{28} -6.86939i q^{29} +(-0.271305 - 1.01253i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.54871 + 5.77988i) q^{34} +(-6.37308 + 3.67950i) q^{35} +(-6.94881 + 1.86193i) q^{37} +(2.95542 + 5.11893i) q^{38} +(0.785290 - 1.36016i) q^{40} +(-1.34176 + 5.00750i) q^{41} +(10.6164 + 6.12935i) q^{43} +(1.08184 + 1.08184i) q^{44} +(-1.28737 + 4.80455i) q^{46} +(-6.14146 - 1.64560i) q^{47} +(12.9507 - 7.47708i) q^{49} +(-2.44696 - 0.655661i) q^{50} +(3.46041 - 1.01269i) q^{52} -2.78130i q^{53} +(-1.20146 + 2.08099i) q^{55} +(-2.34276 + 4.05778i) q^{56} +(4.85740 - 4.85740i) q^{58} +(4.22367 - 4.22367i) q^{59} +(-2.18623 + 3.78666i) q^{61} +(0.524122 - 0.907805i) q^{62} -1.00000i q^{64} +(2.94296 + 4.83801i) q^{65} +(-5.41695 - 1.45147i) q^{67} +(-5.18209 + 2.99188i) q^{68} +(-7.10824 - 1.90465i) q^{70} +(-0.0745019 + 0.278045i) q^{71} +(0.964880 + 0.964880i) q^{73} +(-6.23013 - 3.59697i) q^{74} +(-1.52984 + 5.70943i) q^{76} +(3.58432 - 6.20823i) q^{77} +(-0.0673941 - 0.116730i) q^{79} +(1.51706 - 0.406496i) q^{80} +(-4.48960 + 2.59207i) q^{82} +(3.00217 - 11.2043i) q^{83} +(-6.64538 - 6.64538i) q^{85} +(3.17279 + 11.8410i) q^{86} +1.52995i q^{88} +(-1.46167 - 5.45501i) q^{89} +(-8.77976 - 14.4333i) q^{91} +(-4.30764 + 2.48702i) q^{92} +(-3.17905 - 5.50628i) q^{94} -9.28344 q^{95} +(-1.72699 - 6.44523i) q^{97} +(14.4446 + 3.87042i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.51706	+	0.406496i	−0.678452	+	0.181791i	−0.581559	−	0.813504i	$-0.697557\pi$
$5$	−1.51706	+	0.406496i	−0.678452	+	0.181791i	−0.0968927	+	0.995295i	$0.530890\pi$
$6$		0			0
$7$	4.52587	−	1.21270i	1.71062	−	0.458359i	0.735042	−	0.678021i	$-0.237162\pi$
$7$	4.52587	−	1.21270i	1.71062	−	0.458359i	0.975576	+	0.219662i	$0.0704955\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−1.36016	−	0.785290i	−0.430121	−	0.248331i
$11$	1.08184	−	1.08184i	0.326187	−	0.326187i	−0.524947	−	0.851135i	$-0.675915\pi$
$11$	1.08184	−	1.08184i	0.326187	−	0.326187i	0.851135	+	0.524947i	$0.175915\pi$
$12$		0			0
$13$	−1.01269	−	3.46041i	−0.280869	−	0.959746i
$13$	−1.01269	−	3.46041i	−0.280869	−	0.959746i
$14$	4.05778	+	2.34276i	1.08449	+	0.626130i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.99188	+	5.18209i	0.725638	+	1.25684i	0.958711	+	0.284383i	$0.0917888\pi$
$17$	2.99188	+	5.18209i	0.725638	+	1.25684i	−0.233072	+	0.972459i	$0.574878\pi$
$18$		0			0
$19$	5.70943	+	1.52984i	1.30983	+	0.350968i	0.845160	−	0.534514i	$-0.179505\pi$
$19$	5.70943	+	1.52984i	1.30983	+	0.350968i	0.464673	+	0.885483i	$0.346172\pi$
$20$	−0.406496	−	1.51706i	−0.0908953	−	0.339226i
$21$		0			0
$22$	1.52995			0.326187
$23$	2.48702	+	4.30764i	0.518579	+	0.898204i	0.999767	+	0.0215873i	$0.00687197\pi$
$23$	2.48702	+	4.30764i	0.518579	+	0.898204i	−0.481188	+	0.876617i	$0.659795\pi$
$24$		0			0
$25$	−2.19388	+	1.26664i	−0.438777	+	0.253328i
$26$	1.73080	−	3.16296i	0.339438	−	0.620308i
$27$		0			0
$28$	1.21270	+	4.52587i	0.229179	+	0.855309i
$29$		−	6.86939i		−	1.27561i	−0.770196	−	0.637807i	$-0.779842\pi$
$29$		−	6.86939i		−	1.27561i	0.770196	−	0.637807i	$-0.220158\pi$
$30$		0			0
$31$	−0.271305	−	1.01253i	−0.0487279	−	0.181855i	0.937273	−	0.348597i	$-0.113342\pi$
$31$	−0.271305	−	1.01253i	−0.0487279	−	0.181855i	−0.986001	+	0.166742i	$0.946675\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	−1.54871	+	5.77988i	−0.265602	+	0.991240i
$35$	−6.37308	+	3.67950i	−1.07725	+	0.621949i
$36$		0			0
$37$	−6.94881	+	1.86193i	−1.14238	+	0.306099i	−0.779906	−	0.625896i	$-0.784733\pi$
$37$	−6.94881	+	1.86193i	−1.14238	+	0.306099i	−0.362471	+	0.931995i	$0.618067\pi$
$38$	2.95542	+	5.11893i	0.479432	+	0.830400i
$39$		0			0
$40$	0.785290	−	1.36016i	0.124165	−	0.215061i
$41$	−1.34176	+	5.00750i	−0.209547	+	0.782040i	0.778468	+	0.627684i	$0.215997\pi$
$41$	−1.34176	+	5.00750i	−0.209547	+	0.782040i	−0.988015	+	0.154356i	$0.950670\pi$
$42$		0			0
$43$	10.6164	+	6.12935i	1.61898	+	0.934718i	0.987185	+	0.159581i	$0.0510143\pi$
$43$	10.6164	+	6.12935i	1.61898	+	0.934718i	0.631794	+	0.775137i	$0.282319\pi$
$44$	1.08184	+	1.08184i	0.163094	+	0.163094i
$45$		0			0
$46$	−1.28737	+	4.80455i	−0.189813	+	0.708392i
$47$	−6.14146	−	1.64560i	−0.895823	−	0.240035i	−0.218602	−	0.975814i	$-0.570150\pi$
$47$	−6.14146	−	1.64560i	−0.895823	−	0.240035i	−0.677222	+	0.735779i	$0.736816\pi$
$48$		0			0
$49$	12.9507	−	7.47708i	1.85010	−	1.06815i
$50$	−2.44696	−	0.655661i	−0.346052	−	0.0927244i
$51$		0			0
$52$	3.46041	−	1.01269i	0.479873	−	0.140435i
$53$		−	2.78130i		−	0.382041i	−0.981586	−	0.191021i	$-0.938820\pi$
$53$		−	2.78130i		−	0.382041i	0.981586	−	0.191021i	$-0.0611798\pi$
$54$		0			0
$55$	−1.20146	+	2.08099i	−0.162005	+	0.280600i
$56$	−2.34276	+	4.05778i	−0.313065	+	0.542244i
$57$		0			0
$58$	4.85740	−	4.85740i	0.637807	−	0.637807i
$59$	4.22367	−	4.22367i	0.549875	−	0.549875i	−0.376529	−	0.926405i	$-0.622883\pi$
$59$	4.22367	−	4.22367i	0.549875	−	0.549875i	0.926405	+	0.376529i	$0.122883\pi$
$60$		0			0
$61$	−2.18623	+	3.78666i	−0.279918	+	0.484833i	−0.971364	−	0.237596i	$-0.923641\pi$
$61$	−2.18623	+	3.78666i	−0.279918	+	0.484833i	0.691446	+	0.722428i	$0.256974\pi$
$62$	0.524122	−	0.907805i	0.0665635	−	0.115291i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.94296	+	4.83801i	0.365029	+	0.600082i
$66$		0			0
$67$	−5.41695	−	1.45147i	−0.661785	−	0.177325i	−0.0877337	−	0.996144i	$-0.527962\pi$
$67$	−5.41695	−	1.45147i	−0.661785	−	0.177325i	−0.574052	+	0.818819i	$0.694629\pi$
$68$	−5.18209	+	2.99188i	−0.628421	+	0.362819i
$69$		0			0
$70$	−7.10824	−	1.90465i	−0.849598	−	0.227649i
$71$	−0.0745019	+	0.278045i	−0.00884175	+	0.0329979i	−0.970206	−	0.242282i	$-0.922104\pi$
$71$	−0.0745019	+	0.278045i	−0.00884175	+	0.0329979i	0.961364	+	0.275280i	$0.0887706\pi$
$72$		0			0
$73$	0.964880	+	0.964880i	0.112931	+	0.112931i	0.761314	−	0.648383i	$-0.224555\pi$
$73$	0.964880	+	0.964880i	0.112931	+	0.112931i	−0.648383	+	0.761314i	$0.724555\pi$
$74$	−6.23013	−	3.59697i	−0.724238	−	0.418139i
$75$		0			0
$76$	−1.52984	+	5.70943i	−0.175484	+	0.654916i
$77$	3.58432	−	6.20823i	0.408471	−	0.707493i
$78$		0			0
$79$	−0.0673941	−	0.116730i	−0.00758243	−	0.0131331i	0.862209	−	0.506552i	$-0.169080\pi$
$79$	−0.0673941	−	0.116730i	−0.00758243	−	0.0131331i	−0.869792	+	0.493419i	$0.835747\pi$
$80$	1.51706	−	0.406496i	0.169613	−	0.0454476i
$81$		0			0
$82$	−4.48960	+	2.59207i	−0.495794	+	0.286247i
$83$	3.00217	−	11.2043i	0.329531	−	1.22983i	−0.580147	−	0.814512i	$-0.697005\pi$
$83$	3.00217	−	11.2043i	0.329531	−	1.22983i	0.909678	−	0.415314i	$-0.136328\pi$
$84$		0			0
$85$	−6.64538	−	6.64538i	−0.720793	−	0.720793i
$86$	3.17279	+	11.8410i	0.342130	+	1.27685i
$87$		0			0
$88$			1.52995i			0.163094i
$89$	−1.46167	−	5.45501i	−0.154936	−	0.578230i	−0.999111	−	0.0421616i	$-0.986576\pi$
$89$	−1.46167	−	5.45501i	−0.154936	−	0.578230i	0.844175	−	0.536068i	$-0.180091\pi$
$90$		0			0
$91$	−8.77976	−	14.4333i	−0.920368	−	1.51302i
$92$	−4.30764	+	2.48702i	−0.449102	+	0.259289i
$93$		0			0
$94$	−3.17905	−	5.50628i	−0.327894	−	0.567929i
$95$	−9.28344			−0.952461
$96$		0			0
$97$	−1.72699	−	6.44523i	−0.175350	−	0.654414i	−0.996492	−	0.0836903i	$-0.973329\pi$
$97$	−1.72699	−	6.44523i	−0.175350	−	0.654414i	0.821142	−	0.570724i	$-0.193337\pi$
$98$	14.4446	+	3.87042i	1.45913	+	0.390972i
$99$		0			0
$100$	−1.26664	−	2.19388i	−0.126664	−	0.219388i
$101$	−7.65990			−0.762188			−0.381094	−	0.924536i	$-0.624453\pi$
$101$	−7.65990			−0.762188			−0.381094	+	0.924536i	$0.624453\pi$
$102$		0			0
$103$	−2.46359	−	1.42235i	−0.242744	−	0.140149i	0.373693	−	0.927552i	$-0.378091\pi$
$103$	−2.46359	−	1.42235i	−0.242744	−	0.140149i	−0.616437	+	0.787404i	$0.711425\pi$
$104$	3.16296	+	1.73080i	0.310154	+	0.169719i
$105$		0			0
$106$	1.96668	−	1.96668i	0.191021	−	0.191021i
$107$	−14.7551	−	8.51888i	−1.42643	−	0.823551i	−0.429595	−	0.903022i	$-0.641344\pi$
$107$	−14.7551	−	8.51888i	−1.42643	−	0.823551i	−0.996837	+	0.0794704i	$0.974677\pi$
$108$		0			0
$109$	−1.44362	+	1.44362i	−0.138274	+	0.138274i	−0.772856	−	0.634582i	$-0.781172\pi$
$109$	−1.44362	+	1.44362i	−0.138274	+	0.138274i	0.634582	+	0.772856i	$0.281172\pi$
$110$	−2.32104	+	0.621920i	−0.221302	+	0.0592978i
$111$		0			0
$112$	−4.52587	+	1.21270i	−0.427655	+	0.114590i
$113$		−	8.31066i		−	0.781802i	−0.920433	−	0.390901i	$-0.872164\pi$
$113$		−	8.31066i		−	0.781802i	0.920433	−	0.390901i	$-0.127836\pi$
$114$		0			0
$115$	−5.52400	−	5.52400i	−0.515116	−	0.515116i
$116$	6.86939			0.637807
$117$		0			0
$118$	5.97318			0.549875
$119$	19.8252	+	19.8252i	1.81738	+	1.81738i
$120$		0			0
$121$			8.65924i			0.787204i
$122$	−4.22347	+	1.13168i	−0.382375	+	0.102457i
$123$		0			0
$124$	1.01253	−	0.271305i	0.0909275	−	0.0243639i
$125$	8.36622	−	8.36622i	0.748297	−	0.748297i
$126$		0			0
$127$	−10.0790	−	5.81914i	−0.894371	−	0.516365i	−0.0190013	−	0.999819i	$-0.506049\pi$
$127$	−10.0790	−	5.81914i	−0.894371	−	0.516365i	−0.875370	+	0.483454i	$0.839382\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−1.34001	+	5.50198i	−0.117526	+	0.482555i
$131$	−4.72499	−	2.72798i	−0.412825	−	0.238344i	0.279178	−	0.960239i	$-0.409938\pi$
$131$	−4.72499	−	2.72798i	−0.412825	−	0.238344i	−0.692003	+	0.721895i	$0.743271\pi$
$132$		0			0
$133$	27.6954			2.40149
$134$	−2.80402	−	4.85670i	−0.242230	−	0.419555i
$135$		0			0
$136$	−5.77988	−	1.54871i	−0.495620	−	0.132801i
$137$	−0.379002	−	1.41446i	−0.0323803	−	0.120845i	0.947844	−	0.318735i	$-0.103258\pi$
$137$	−0.379002	−	1.41446i	−0.0323803	−	0.120845i	−0.980224	+	0.197890i	$0.936591\pi$
$138$		0			0
$139$	−7.49403			−0.635636			−0.317818	−	0.948152i	$-0.602950\pi$
$139$	−7.49403			−0.635636			−0.317818	+	0.948152i	$0.602950\pi$
$140$	−3.67950	−	6.37308i	−0.310974	−	0.538623i
$141$		0			0
$142$	−0.249288	+	0.143927i	−0.0209198	+	0.0120781i
$143$	−4.83919	−	2.64805i	−0.404673	−	0.221441i
$144$		0			0
$145$	2.79238	+	10.4213i	0.231895	+	0.865443i
$146$			1.36455i			0.112931i
$147$		0			0
$148$	−1.86193	−	6.94881i	−0.153049	−	0.571188i
$149$	0.424349	+	0.424349i	0.0347641	+	0.0347641i	0.724275	−	0.689511i	$-0.242175\pi$
$149$	0.424349	+	0.424349i	0.0347641	+	0.0347641i	−0.689511	+	0.724275i	$0.742175\pi$
$150$		0			0
$151$	0.470936	−	1.75756i	0.0383242	−	0.143028i	−0.944113	−	0.329623i	$-0.893078\pi$
$151$	0.470936	−	1.75756i	0.0383242	−	0.143028i	0.982437	+	0.186595i	$0.0597451\pi$
$152$	−5.11893	+	2.95542i	−0.415200	+	0.239716i
$153$		0			0
$154$	6.92438	−	1.85538i	0.557982	−	0.149511i
$155$	0.823175	+	1.42578i	0.0661190	+	0.114521i
$156$		0			0
$157$	−1.01577	+	1.75937i	−0.0810676	+	0.140413i	−0.903709	−	0.428148i	$-0.859166\pi$
$157$	−1.01577	+	1.75937i	−0.0810676	+	0.140413i	0.822641	+	0.568561i	$0.192500\pi$
$158$	0.0348857	−	0.130195i	0.00277536	−	0.0103578i
$159$		0			0
$160$	1.36016	+	0.785290i	0.107530	+	0.0620826i
$161$	16.4798	+	16.4798i	1.29879	+	1.29879i
$162$		0			0
$163$	−2.35591	+	8.79238i	−0.184529	+	0.688672i	0.810202	+	0.586151i	$0.199358\pi$
$163$	−2.35591	+	8.79238i	−0.184529	+	0.688672i	−0.994731	+	0.102521i	$0.967309\pi$
$164$	−5.00750	−	1.34176i	−0.391020	−	0.104774i
$165$		0			0
$166$	10.0455	−	5.79975i	0.779679	−	0.450148i
$167$	−3.61344	−	0.968219i	−0.279617	−	0.0749231i	0.116285	−	0.993216i	$-0.462901\pi$
$167$	−3.61344	−	0.968219i	−0.279617	−	0.0749231i	−0.395902	+	0.918293i	$0.629568\pi$
$168$		0			0
$169$	−10.9489	+	7.00865i	−0.842225	+	0.539127i
$170$		−	9.39799i		−	0.720793i
$171$		0			0
$172$	−6.12935	+	10.6164i	−0.467359	+	0.809489i
$173$	−0.507126	+	0.878368i	−0.0385561	+	0.0667811i	−0.884659	−	0.466238i	$-0.845609\pi$
$173$	−0.507126	+	0.878368i	−0.0385561	+	0.0667811i	0.846103	+	0.533019i	$0.178942\pi$
$174$		0			0
$175$	−8.39317	+	8.39317i	−0.634464	+	0.634464i
$176$	−1.08184	+	1.08184i	−0.0815468	+	0.0815468i
$177$		0			0
$178$	2.82372	−	4.89083i	0.211647	−	0.366583i
$179$	−11.6793	+	20.2291i	−0.872951	+	1.51200i	−0.0140213	+	0.999902i	$0.504463\pi$
$179$	−11.6793	+	20.2291i	−0.872951	+	1.51200i	−0.858930	+	0.512094i	$0.828870\pi$
$180$		0			0
$181$		−	8.51778i		−	0.633122i	−0.948572	−	0.316561i	$-0.897472\pi$
$181$		−	8.51778i		−	0.633122i	0.948572	−	0.316561i	$-0.102528\pi$
$182$	3.99765	−	16.4141i	0.296326	−	1.21669i
$183$		0			0
$184$	−4.80455	−	1.28737i	−0.354196	−	0.0949065i
$185$	9.78492	−	5.64933i	0.719401	−	0.415347i
$186$		0			0
$187$	8.84295	+	2.36946i	0.646660	+	0.173272i
$188$	1.64560	−	6.14146i	0.120018	−	0.447912i
$189$		0			0
$190$	−6.56438	−	6.56438i	−0.476230	−	0.476230i
$191$	−13.5364	−	7.81525i	−0.979461	−	0.565492i	−0.0773534	−	0.997004i	$-0.524647\pi$
$191$	−13.5364	−	7.81525i	−0.979461	−	0.565492i	−0.902107	+	0.431512i	$0.857980\pi$
$192$		0			0
$193$	−4.09187	+	15.2711i	−0.294540	+	1.09924i	0.647043	+	0.762454i	$0.276005\pi$
$193$	−4.09187	+	15.2711i	−0.294540	+	1.09924i	−0.941582	+	0.336783i	$0.890661\pi$
$194$	3.33630	−	5.77864i	0.239532	−	0.414882i
$195$		0			0
$196$	7.47708	+	12.9507i	0.534077	+	0.925049i
$197$	13.3907	−	3.58802i	0.954045	−	0.255635i	0.251967	−	0.967736i	$-0.418923\pi$
$197$	13.3907	−	3.58802i	0.954045	−	0.255635i	0.702078	+	0.712100i	$0.252256\pi$
$198$		0			0
$199$	−10.8199	+	6.24687i	−0.767002	+	0.442829i	−0.831804	−	0.555069i	$-0.812692\pi$
$199$	−10.8199	+	6.24687i	−0.767002	+	0.442829i	0.0648021	+	0.997898i	$0.479358\pi$
$200$	0.655661	−	2.44696i	0.0463622	−	0.173026i
$201$		0			0
$202$	−5.41637	−	5.41637i	−0.381094	−	0.381094i
$203$	−8.33054	−	31.0900i	−0.584689	−	2.18209i
$204$		0			0
$205$		−	8.14212i		−	0.568670i
$206$	−0.736264	−	2.74777i	−0.0512979	−	0.191446i
$207$		0			0
$208$	1.01269	+	3.46041i	0.0702174	+	0.239936i
$209$	7.83173	−	4.52165i	0.541732	−	0.312769i
$210$		0			0
$211$	−3.90948	−	6.77143i	−0.269140	−	0.466164i	0.699500	−	0.714633i	$-0.253406\pi$
$211$	−3.90948	−	6.77143i	−0.269140	−	0.466164i	−0.968640	+	0.248468i	$0.920073\pi$
$212$	2.78130			0.191021
$213$		0			0
$214$	−4.40970	−	16.4572i	−0.301441	−	1.12499i
$215$	−18.5972	−	4.98312i	−1.26832	−	0.339846i
$216$		0			0
$217$	−2.45579	−	4.25355i	−0.166710	−	0.288750i
$218$	−2.04159			−0.138274
$219$		0			0
$220$	−2.08099	−	1.20146i	−0.140300	−	0.0810023i
$221$	14.9023	−	15.6010i	1.00244	−	1.04944i
$222$		0			0
$223$	−1.50200	+	1.50200i	−0.100581	+	0.100581i	−0.755607	−	0.655026i	$-0.772658\pi$
$223$	−1.50200	+	1.50200i	−0.100581	+	0.100581i	0.655026	+	0.755607i	$0.272658\pi$
$224$	−4.05778	−	2.34276i	−0.271122	−	0.156532i
$225$		0			0
$226$	5.87653	−	5.87653i	0.390901	−	0.390901i
$227$	18.1107	−	4.85274i	1.20205	−	0.322088i	0.398411	−	0.917207i	$-0.369562\pi$
$227$	18.1107	−	4.85274i	1.20205	−	0.322088i	0.803637	+	0.595119i	$0.202895\pi$
$228$		0			0
$229$	21.4410	−	5.74509i	1.41686	−	0.379646i	0.532491	−	0.846436i	$-0.321256\pi$
$229$	21.4410	−	5.74509i	1.41686	−	0.379646i	0.884369	+	0.466789i	$0.154589\pi$
$230$		−	7.81211i		−	0.515116i
$231$		0			0
$232$	4.85740	+	4.85740i	0.318904	+	0.318904i
$233$	−18.3697			−1.20344			−0.601721	−	0.798707i	$-0.705518\pi$
$233$	−18.3697			−1.20344			−0.601721	+	0.798707i	$0.705518\pi$
$234$		0			0
$235$	9.98591			0.651409
$236$	4.22367	+	4.22367i	0.274938	+	0.274938i
$237$		0			0
$238$			28.0371i			1.81738i
$239$	−8.67535	+	2.32455i	−0.561161	+	0.150363i	−0.528240	−	0.849095i	$-0.677148\pi$
$239$	−8.67535	+	2.32455i	−0.561161	+	0.150363i	−0.0329216	+	0.999458i	$0.510481\pi$
$240$		0			0
$241$	−4.08094	+	1.09348i	−0.262876	+	0.0704375i	−0.387850	−	0.921723i	$-0.626782\pi$
$241$	−4.08094	+	1.09348i	−0.262876	+	0.0704375i	0.124974	+	0.992160i	$0.460115\pi$
$242$	−6.12301	+	6.12301i	−0.393602	+	0.393602i
$243$		0			0
$244$	−3.78666	−	2.18623i	−0.242416	−	0.139959i
$245$	−16.6076	+	16.6076i	−1.06102	+	1.06102i
$246$		0			0
$247$	−0.488008	−	21.3062i	−0.0310512	−	1.35568i
$248$	0.907805	+	0.524122i	0.0576457	+	0.0332818i
$249$		0			0
$250$	11.8316			0.748297
$251$	−0.0344162	−	0.0596107i	−0.00217233	−	0.00376259i	0.864937	−	0.501880i	$-0.167358\pi$
$251$	−0.0344162	−	0.0596107i	−0.00217233	−	0.00376259i	−0.867110	+	0.498118i	$0.834025\pi$
$252$		0			0
$253$	7.35074	+	1.96962i	0.462137	+	0.123829i
$254$	−3.01221	−	11.2417i	−0.189003	−	0.705368i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.98389	+	12.0965i	0.435643	+	0.754556i	0.997348	−	0.0727815i	$-0.0231876\pi$
$257$	6.98389	+	12.0965i	0.435643	+	0.754556i	−0.561705	+	0.827338i	$0.689854\pi$
$258$		0			0
$259$	−29.1914	+	16.8537i	−1.81387	+	1.04724i
$260$	−4.83801	+	2.94296i	−0.300041	+	0.182515i
$261$		0			0
$262$	−1.41210	−	5.27005i	−0.0872401	−	0.325584i
$263$			23.9692i			1.47800i	0.673705	+	0.739001i	$0.264702\pi$
$263$			23.9692i			1.47800i	−0.673705	+	0.739001i	$0.735298\pi$
$264$		0			0
$265$	1.13059	+	4.21942i	0.0694515	+	0.259197i
$266$	19.5836	+	19.5836i	1.20075	+	1.20075i
$267$		0			0
$268$	1.45147	−	5.41695i	0.0886624	−	0.330893i
$269$	22.7826	−	13.1536i	1.38908	−	0.801987i	0.395870	−	0.918307i	$-0.370443\pi$
$269$	22.7826	−	13.1536i	1.38908	−	0.801987i	0.993212	+	0.116320i	$0.0371099\pi$
$270$		0			0
$271$	4.66870	−	1.25097i	0.283603	−	0.0759913i	−0.114213	−	0.993456i	$-0.536435\pi$
$271$	4.66870	−	1.25097i	0.283603	−	0.0759913i	0.397817	+	0.917465i	$0.369768\pi$
$272$	−2.99188	−	5.18209i	−0.181410	−	0.314211i
$273$		0			0
$274$	0.732176	−	1.26817i	0.0442324	−	0.0766127i
$275$	−1.00313	+	3.74374i	−0.0604911	+	0.225756i
$276$		0			0
$277$	−12.6229	−	7.28781i	−0.758434	−	0.437882i	0.0702994	−	0.997526i	$-0.477605\pi$
$277$	−12.6229	−	7.28781i	−0.758434	−	0.437882i	−0.828733	+	0.559644i	$0.810938\pi$
$278$	−5.29908	−	5.29908i	−0.317818	−	0.317818i
$279$		0			0
$280$	1.90465	−	7.10824i	0.113824	−	0.424799i
$281$	22.2228	+	5.95459i	1.32570	+	0.355221i	0.851112	−	0.524985i	$-0.175929\pi$
$281$	22.2228	+	5.95459i	1.32570	+	0.355221i	0.474592	+	0.880206i	$0.342596\pi$
$282$		0			0
$283$	12.4400	−	7.18223i	0.739480	−	0.426939i	−0.0824000	−	0.996599i	$-0.526258\pi$
$283$	12.4400	−	7.18223i	0.739480	−	0.426939i	0.821880	+	0.569660i	$0.192925\pi$
$284$	−0.278045	−	0.0745019i	−0.0164989	−	0.00442087i
$285$		0			0
$286$	−1.54937	−	5.29427i	−0.0916161	−	0.313057i
$287$			24.2905i			1.43382i
$288$		0			0
$289$	−9.40274	+	16.2860i	−0.553102	+	0.958001i
$290$	−5.39447	+	9.34349i	−0.316774	+	0.548669i
$291$		0			0
$292$	−0.964880	+	0.964880i	−0.0564653	+	0.0564653i
$293$	−8.61260	+	8.61260i	−0.503153	+	0.503153i	−0.912416	−	0.409263i	$-0.865786\pi$
$293$	−8.61260	+	8.61260i	−0.503153	+	0.503153i	0.409263	+	0.912416i	$0.365786\pi$
$294$		0			0
$295$	−4.69068	+	8.12449i	−0.273102	+	0.473026i
$296$	3.59697	−	6.23013i	0.209069	−	0.362119i
$297$		0			0
$298$			0.600121i			0.0347641i
$299$	12.3876	−	12.9684i	0.716395	−	0.749982i
$300$		0			0
$301$	55.4813	+	14.8662i	3.19789	+	0.856872i
$302$	1.57578	−	0.909778i	0.0906761	−	0.0523519i
$303$		0			0
$304$	−5.70943	−	1.52984i	−0.327458	−	0.0877421i
$305$	1.77739	−	6.63330i	0.101773	−	0.379822i
$306$		0			0
$307$	−6.82241	−	6.82241i	−0.389375	−	0.389375i	0.485089	−	0.874465i	$-0.338787\pi$
$307$	−6.82241	−	6.82241i	−0.389375	−	0.389375i	−0.874465	+	0.485089i	$0.838787\pi$
$308$	6.20823	+	3.58432i	0.353747	+	0.204236i
$309$		0			0
$310$	−0.426107	+	1.59025i	−0.0242012	+	0.0903203i
$311$	−7.73754	+	13.4018i	−0.438756	+	0.759947i	−0.997594	−	0.0693297i	$-0.977914\pi$
$311$	−7.73754	+	13.4018i	−0.438756	+	0.759947i	0.558838	+	0.829277i	$0.311247\pi$
$312$		0			0
$313$	13.3960	+	23.2026i	0.757189	+	1.31149i	0.944279	+	0.329146i	$0.106761\pi$
$313$	13.3960	+	23.2026i	0.757189	+	1.31149i	−0.187090	+	0.982343i	$0.559906\pi$
$314$	−1.96232	+	0.525803i	−0.110740	+	0.0296728i
$315$		0			0
$316$	0.116730	−	0.0673941i	0.00656657	−	0.00379121i
$317$	−3.72829	+	13.9142i	−0.209402	+	0.781498i	0.778661	+	0.627445i	$0.215899\pi$
$317$	−3.72829	+	13.9142i	−0.209402	+	0.781498i	−0.988063	+	0.154053i	$0.950767\pi$
$318$		0			0
$319$	−7.43159	−	7.43159i	−0.416089	−	0.416089i
$320$	0.406496	+	1.51706i	0.0227238	+	0.0848065i
$321$		0			0
$322$			23.3060i			1.29879i
$323$	9.15418	+	34.1639i	0.509352	+	1.90093i
$324$		0			0
$325$	6.60482	+	6.30903i	0.366369	+	0.349962i
$326$	−7.88303	+	4.55127i	−0.436601	+	0.252072i
$327$		0			0
$328$	−2.59207	−	4.48960i	−0.143123	−	0.247897i
$329$	−29.7911			−1.64243
$330$		0			0
$331$	−7.95647	−	29.6940i	−0.437327	−	1.63213i	−0.735435	−	0.677596i	$-0.763022\pi$
$331$	−7.95647	−	29.6940i	−0.437327	−	1.63213i	0.298107	−	0.954532i	$-0.403645\pi$
$332$	11.2043	+	3.00217i	0.614913	+	0.164765i
$333$		0			0
$334$	−1.87046	−	3.23973i	−0.102347	−	0.177270i
$335$	8.80787			0.481225
$336$		0			0
$337$	−26.0523	−	15.0413i	−1.41916	−	0.819353i	−0.422936	−	0.906159i	$-0.639001\pi$
$337$	−26.0523	−	15.0413i	−1.41916	−	0.819353i	−0.996225	+	0.0868060i	$0.972334\pi$
$338$	−12.6979	−	2.78620i	−0.690676	−	0.151549i
$339$		0			0
$340$	6.64538	−	6.64538i	0.360396	−	0.360396i
$341$	−1.38890	−	0.801882i	−0.0752132	−	0.0434244i
$342$		0			0
$343$	26.3535	−	26.3535i	1.42295	−	1.42295i
$344$	−11.8410	+	3.17279i	−0.638424	+	0.171065i
$345$		0			0
$346$	−0.979692	+	0.262508i	−0.0526686	+	0.0141125i
$347$			17.1041i			0.918194i	0.888386	+	0.459097i	$0.151827\pi$
$347$			17.1041i			0.918194i	−0.888386	+	0.459097i	$0.848173\pi$
$348$		0			0
$349$	−1.97713	−	1.97713i	−0.105833	−	0.105833i	0.652207	−	0.758041i	$-0.273843\pi$
$349$	−1.97713	−	1.97713i	−0.105833	−	0.105833i	−0.758041	+	0.652207i	$0.773843\pi$
$350$	−11.8697			−0.634464
$351$		0			0
$352$	−1.52995			−0.0815468
$353$	23.6505	+	23.6505i	1.25879	+	1.25879i	0.951671	+	0.307119i	$0.0993650\pi$
$353$	23.6505	+	23.6505i	1.25879	+	1.25879i	0.307119	+	0.951671i	$0.400635\pi$
$354$		0			0
$355$		−	0.452097i		−	0.0239948i
$356$	5.45501	−	1.46167i	0.289115	−	0.0774681i
$357$		0			0
$358$	−22.5626	+	6.04564i	−1.19247	+	0.319522i
$359$	−4.06738	+	4.06738i	−0.214668	+	0.214668i	−0.806247	−	0.591579i	$-0.798505\pi$
$359$	−4.06738	+	4.06738i	−0.214668	+	0.214668i	0.591579	+	0.806247i	$0.298505\pi$
$360$		0			0
$361$	13.8027	+	7.96897i	0.726456	+	0.419420i
$362$	6.02298	−	6.02298i	0.316561	−	0.316561i
$363$		0			0
$364$	14.4333	−	8.77976i	0.756510	−	0.460184i
$365$	−1.85601	−	1.07157i	−0.0971477	−	0.0560883i
$366$		0			0
$367$	2.87993			0.150331			0.0751656	−	0.997171i	$-0.476051\pi$
$367$	2.87993			0.150331			0.0751656	+	0.997171i	$0.476051\pi$
$368$	−2.48702	−	4.30764i	−0.129645	−	0.224551i
$369$		0			0
$370$	10.9137	+	2.92431i	0.567374	+	0.152027i
$371$	−3.37290	−	12.5878i	−0.175112	−	0.653527i
$372$		0			0
$373$	−17.0979			−0.885297			−0.442648	−	0.896695i	$-0.645961\pi$
$373$	−17.0979			−0.885297			−0.442648	+	0.896695i	$0.645961\pi$
$374$	4.57745	+	7.92837i	0.236694	+	0.409966i
$375$		0			0
$376$	5.50628	−	3.17905i	0.283965	−	0.163947i
$377$	−23.7709	+	6.95656i	−1.22427	+	0.358281i
$378$		0			0
$379$	5.27326	+	19.6801i	0.270869	+	1.01090i	0.958559	+	0.284893i	$0.0919581\pi$
$379$	5.27326	+	19.6801i	0.270869	+	1.01090i	−0.687690	+	0.726004i	$0.741375\pi$
$380$		−	9.28344i		−	0.476230i
$381$		0			0
$382$	−4.04547	−	15.0979i	−0.206984	−	0.772476i
$383$	11.4042	+	11.4042i	0.582726	+	0.582726i	0.935651	−	0.352925i	$-0.114813\pi$
$383$	11.4042	+	11.4042i	0.582726	+	0.582726i	−0.352925	+	0.935651i	$0.614813\pi$
$384$		0			0
$385$	−2.91402	+	10.8753i	−0.148512	+	0.554256i
$386$	−13.6917	+	7.90489i	−0.696888	+	0.402348i
$387$		0			0
$388$	6.44523	−	1.72699i	0.327207	−	0.0876749i
$389$	−18.1024	−	31.3543i	−0.917828	−	1.58972i	−0.802707	−	0.596373i	$-0.796608\pi$
$389$	−18.1024	−	31.3543i	−0.917828	−	1.58972i	−0.115121	−	0.993351i	$-0.536726\pi$
$390$		0			0
$391$	−14.8817	+	25.7759i	−0.752601	+	1.30354i
$392$	−3.87042	+	14.4446i	−0.195486	+	0.729563i
$393$		0			0
$394$	12.0057	+	6.93151i	0.604840	+	0.349205i
$395$	0.149691	+	0.149691i	0.00753179	+	0.00753179i
$396$		0			0
$397$	−0.170003	+	0.634461i	−0.00853223	+	0.0318427i	−0.970061	−	0.242863i	$-0.921914\pi$
$397$	−0.170003	+	0.634461i	−0.00853223	+	0.0318427i	0.961528	+	0.274705i	$0.0885803\pi$
$398$	−12.0680	−	3.23362i	−0.604915	−	0.162087i
$399$		0			0
$400$	2.19388	−	1.26664i	0.109694	−	0.0633319i
$401$	2.91390	+	0.780777i	0.145513	+	0.0389902i	0.330840	−	0.943687i	$-0.392668\pi$
$401$	2.91390	+	0.780777i	0.145513	+	0.0389902i	−0.185327	+	0.982677i	$0.559334\pi$
$402$		0			0
$403$	−3.22901	+	1.96420i	−0.160848	+	0.0978439i
$404$		−	7.65990i		−	0.381094i
$405$		0			0
$406$	16.0934	−	27.8745i	0.798700	−	1.38339i
$407$	−5.50320	+	9.53181i	−0.272783	+	0.472475i
$408$		0			0
$409$	1.66863	−	1.66863i	0.0825083	−	0.0825083i	−0.664648	−	0.747156i	$-0.731419\pi$
$409$	1.66863	−	1.66863i	0.0825083	−	0.0825083i	0.747156	+	0.664648i	$0.231419\pi$
$410$	5.75735	−	5.75735i	0.284335	−	0.284335i
$411$		0			0
$412$	1.42235	−	2.46359i	0.0700743	−	0.121372i
$413$	13.9937	−	24.2379i	0.688587	−	1.19267i
$414$		0			0
$415$			18.2179i			0.894283i
$416$	−1.73080	+	3.16296i	−0.0848596	+	0.155077i
$417$		0			0
$418$	8.73516	+	2.34058i	0.427251	+	0.114481i
$419$	19.7189	−	11.3847i	0.963333	−	0.556181i	0.0661358	−	0.997811i	$-0.478933\pi$
$419$	19.7189	−	11.3847i	0.963333	−	0.556181i	0.897197	+	0.441630i	$0.145600\pi$
$420$		0			0
$421$	−32.9974	−	8.84164i	−1.60820	−	0.430915i	−0.660692	−	0.750657i	$-0.729737\pi$
$421$	−32.9974	−	8.84164i	−1.60820	−	0.430915i	−0.947505	+	0.319742i	$0.896404\pi$
$422$	2.02370	−	7.55254i	0.0985121	−	0.367652i
$423$		0			0
$424$	1.96668	+	1.96668i	0.0955104	+	0.0955104i
$425$	−13.1277	−	7.57927i	−0.636786	−	0.367649i
$426$		0			0
$427$	−5.30250	+	19.7892i	−0.256606	+	0.957666i
$428$	8.51888	−	14.7551i	0.411776	−	0.713216i
$429$		0			0
$430$	−9.62664	−	16.6738i	−0.464238	−	0.804084i
$431$	6.97762	−	1.86965i	0.336100	−	0.0900578i	−0.0868218	−	0.996224i	$-0.527671\pi$
$431$	6.97762	−	1.86965i	0.336100	−	0.0900578i	0.422922	+	0.906166i	$0.361004\pi$
$432$		0			0
$433$	16.0208	−	9.24961i	0.769910	−	0.444508i	−0.0629325	−	0.998018i	$-0.520045\pi$
$433$	16.0208	−	9.24961i	0.769910	−	0.444508i	0.832842	+	0.553510i	$0.186712\pi$
$434$	1.27121	−	4.74421i	0.0610200	−	0.227730i
$435$		0			0
$436$	−1.44362	−	1.44362i	−0.0691369	−	0.0691369i
$437$	7.60945	+	28.3989i	0.364010	+	1.35850i
$438$		0			0
$439$		−	20.3207i		−	0.969855i	−0.874554	−	0.484927i	$-0.838846\pi$
$439$		−	20.3207i		−	0.969855i	0.874554	−	0.484927i	$-0.161154\pi$
$440$	−0.621920	−	2.32104i	−0.0296489	−	0.110651i
$441$		0			0
$442$	21.5691	−	0.494029i	1.02594	−	0.0234986i
$443$	−8.71411	+	5.03109i	−0.414020	+	0.239034i	−0.692515	−	0.721403i	$-0.743498\pi$
$443$	−8.71411	+	5.03109i	−0.414020	+	0.239034i	0.278496	+	0.960437i	$0.410164\pi$
$444$		0			0
$445$	4.43488	+	7.68144i	0.210234	+	0.364135i
$446$	−2.12414			−0.100581
$447$		0			0
$448$	−1.21270	−	4.52587i	−0.0572949	−	0.213827i
$449$	−22.3408	−	5.98619i	−1.05433	−	0.282506i	−0.310288	−	0.950643i	$-0.600426\pi$
$449$	−22.3408	−	5.98619i	−1.05433	−	0.282506i	−0.744039	+	0.668137i	$0.767092\pi$
$450$		0			0
$451$	3.96575	+	6.86889i	0.186740	+	0.323443i
$452$	8.31066			0.390901
$453$		0			0
$454$	16.2376	+	9.37478i	0.762068	+	0.439980i
$455$	19.1865	+	18.3273i	0.899478	+	0.859197i
$456$		0			0
$457$	15.7054	−	15.7054i	0.734667	−	0.734667i	−0.236874	−	0.971540i	$-0.576123\pi$
$457$	15.7054	−	15.7054i	0.734667	−	0.734667i	0.971540	+	0.236874i	$0.0761228\pi$
$458$	19.2235	+	11.0987i	0.898253	+	0.518607i
$459$		0			0
$460$	5.52400	−	5.52400i	0.257558	−	0.257558i
$461$	−23.0977	+	6.18902i	−1.07577	+	0.288251i	−0.752861	−	0.658180i	$-0.771327\pi$
$461$	−23.0977	+	6.18902i	−1.07577	+	0.288251i	−0.322907	+	0.946431i	$0.604660\pi$
$462$		0			0
$463$	−14.9267	+	3.99959i	−0.693702	+	0.185877i	−0.588408	−	0.808564i	$-0.700245\pi$
$463$	−14.9267	+	3.99959i	−0.693702	+	0.185877i	−0.105294	+	0.994441i	$0.533578\pi$
$464$			6.86939i			0.318904i
$465$		0			0
$466$	−12.9894	−	12.9894i	−0.601721	−	0.601721i
$467$	30.0205			1.38918			0.694591	−	0.719405i	$-0.255585\pi$
$467$	30.0205			1.38918			0.694591	+	0.719405i	$0.255585\pi$
$468$		0			0
$469$	−26.2766			−1.21334
$470$	7.06111	+	7.06111i	0.325705	+	0.325705i
$471$		0			0
$472$			5.97318i			0.274938i
$473$	18.1162	−	4.85422i	0.832983	−	0.223197i
$474$		0			0
$475$	−14.4636	+	3.87550i	−0.663634	+	0.177820i
$476$	−19.8252	+	19.8252i	−0.908688	+	0.908688i
$477$		0			0
$478$	−7.77810	−	4.49069i	−0.355762	−	0.205399i
$479$	0.352246	−	0.352246i	0.0160945	−	0.0160945i	−0.699014	−	0.715108i	$-0.746377\pi$
$479$	0.352246	−	0.352246i	0.0160945	−	0.0160945i	0.715108	+	0.699014i	$0.246377\pi$
$480$		0			0
$481$	13.4800	+	22.1602i	0.614636	+	1.01042i
$482$	−3.65887	−	2.11245i	−0.166657	−	0.0962194i
$483$		0			0
$484$	−8.65924			−0.393602
$485$	5.23992	+	9.07581i	0.237933	+	0.412111i
$486$		0			0
$487$	22.2998	+	5.97522i	1.01050	+	0.270763i	0.725839	−	0.687865i	$-0.241452\pi$
$487$	22.2998	+	5.97522i	1.01050	+	0.270763i	0.284663	+	0.958628i	$0.408118\pi$
$488$	−1.13168	−	4.22347i	−0.0512286	−	0.191188i
$489$		0			0
$490$	−23.4867			−1.06102
$491$	−1.59861	−	2.76887i	−0.0721442	−	0.124957i	0.827697	−	0.561176i	$-0.189651\pi$
$491$	−1.59861	−	2.76887i	−0.0721442	−	0.124957i	−0.899841	+	0.436218i	$0.856318\pi$
$492$		0			0
$493$	35.5978	−	20.5524i	1.60325	−	0.925635i
$494$	14.7207	−	15.4108i	0.662316	−	0.693367i
$495$		0			0
$496$	0.271305	+	1.01253i	0.0121820	+	0.0454637i
$497$			1.34874i			0.0604994i
$498$		0			0
$499$	8.82459	+	32.9338i	0.395043	+	1.47432i	0.821707	+	0.569910i	$0.193022\pi$
$499$	8.82459	+	32.9338i	0.395043	+	1.47432i	−0.426664	+	0.904410i	$0.640311\pi$
$500$	8.36622	+	8.36622i	0.374149	+	0.374149i
$501$		0			0
$502$	0.0178152	−	0.0664871i	0.000795129	−	0.00296746i
$503$	0.778425	−	0.449424i	0.0347083	−	0.0200388i	−0.482545	−	0.875871i	$-0.660288\pi$
$503$	0.778425	−	0.449424i	0.0347083	−	0.0200388i	0.517254	+	0.855832i	$0.326954\pi$
$504$		0			0
$505$	11.6206	−	3.11372i	0.517108	−	0.138559i
$506$	3.80502	+	6.59049i	0.169154	+	0.292983i
$507$		0			0
$508$	5.81914	−	10.0790i	0.258183	−	0.447185i
$509$	1.25690	−	4.69081i	0.0557111	−	0.207917i	−0.932460	−	0.361274i	$-0.882342\pi$
$509$	1.25690	−	4.69081i	0.0557111	−	0.207917i	0.988171	+	0.153357i	$0.0490086\pi$
$510$		0			0
$511$	5.53704	+	3.19681i	0.244944	+	0.141419i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−3.61513	+	13.4918i	−0.159457	+	0.595100i
$515$	4.31560	+	1.15636i	0.190168	+	0.0509554i
$516$		0			0
$517$	−8.42436	+	4.86380i	−0.370503	+	0.213910i
$518$	−32.5588	−	8.72411i	−1.43055	−	0.383315i
$519$		0			0
$520$	−5.50198	−	1.34001i	−0.241278	−	0.0587632i
$521$		−	14.7602i		−	0.646655i	−0.946287	−	0.323327i	$-0.895198\pi$
$521$		−	14.7602i		−	0.646655i	0.946287	−	0.323327i	$-0.104802\pi$
$522$		0			0
$523$	−7.04052	+	12.1945i	−0.307860	+	0.533230i	−0.977894	−	0.209101i	$-0.932946\pi$
$523$	−7.04052	+	12.1945i	−0.307860	+	0.533230i	0.670034	+	0.742331i	$0.266280\pi$
$524$	2.72798	−	4.72499i	0.119172	−	0.206412i
$525$		0			0
$526$	−16.9488	+	16.9488i	−0.739001	+	0.739001i
$527$	4.43529	−	4.43529i	0.193204	−	0.193204i
$528$		0			0
$529$	−0.870493	+	1.50774i	−0.0378475	+	0.0655538i
$530$	−2.18413	+	3.78302i	−0.0948726	+	0.164324i
$531$		0			0
$532$			27.6954i			1.20075i
$533$	18.6868	−	0.428011i	0.809415	−	0.0185392i
$534$		0			0
$535$	25.8474	+	6.92578i	1.11748	+	0.299428i
$536$	4.85670	−	2.80402i	0.209778	−	0.121115i
$537$		0			0
$538$	25.4107	+	6.80878i	1.09553	+	0.293547i
$539$	5.92157	−	22.0996i	0.255060	−	0.951897i
$540$		0			0
$541$	22.4390	+	22.4390i	0.964730	+	0.964730i	0.999399	−	0.0346688i	$-0.0110376\pi$
$541$	22.4390	+	22.4390i	0.964730	+	0.964730i	−0.0346688	+	0.999399i	$0.511038\pi$
$542$	4.18584	+	2.41670i	0.179797	+	0.103806i
$543$		0			0
$544$	1.54871	−	5.77988i	0.0664005	−	0.247810i
$545$	1.60324	−	2.77689i	0.0686752	−	0.118949i
$546$		0			0
$547$	1.46832	+	2.54321i	0.0627810	+	0.108740i	0.895708	−	0.444644i	$-0.146670\pi$
$547$	1.46832	+	2.54321i	0.0627810	+	0.108740i	−0.832927	+	0.553384i	$0.813336\pi$
$548$	1.41446	−	0.379002i	0.0604225	−	0.0161902i
$549$		0			0
$550$	−3.35654	+	1.93790i	−0.143123	+	0.0826323i
$551$	10.5090	−	39.2203i	0.447700	−	1.67084i
$552$		0			0
$553$	−0.446576	−	0.446576i	−0.0189903	−	0.0189903i
$554$	−3.77245	−	14.0790i	−0.160276	−	0.598158i
$555$		0			0
$556$		−	7.49403i		−	0.317818i
$557$	3.80383	+	14.1961i	0.161173	+	0.601507i	0.998497	+	0.0548002i	$0.0174522\pi$
$557$	3.80383	+	14.1961i	0.161173	+	0.601507i	−0.837324	+	0.546707i	$0.815881\pi$
$558$		0			0
$559$	10.4590	−	42.9441i	0.442370	−	1.81634i
$560$	6.37308	−	3.67950i	0.269312	−	0.155487i
$561$		0			0
$562$	11.5034	+	19.9245i	0.485241	+	0.840462i
$563$	−28.7217			−1.21047			−0.605237	−	0.796045i	$-0.706922\pi$
$563$	−28.7217			−1.21047			−0.605237	+	0.796045i	$0.706922\pi$
$564$		0			0
$565$	3.37825	+	12.6078i	0.142124	+	0.530415i
$566$	13.8750	+	3.71780i	0.583210	+	0.156271i
$567$		0			0
$568$	−0.143927	−	0.249288i	−0.00603903	−	0.0104599i
$569$	11.2305			0.470807			0.235403	−	0.971898i	$-0.424359\pi$
$569$	11.2305			0.470807			0.235403	+	0.971898i	$0.424359\pi$
$570$		0			0
$571$	−35.2056	−	20.3260i	−1.47331	−	0.850615i	−0.473760	−	0.880654i	$-0.657103\pi$
$571$	−35.2056	−	20.3260i	−1.47331	−	0.850615i	−0.999549	+	0.0300392i	$0.990437\pi$
$572$	2.64805	−	4.83919i	0.110720	−	0.202337i
$573$		0			0
$574$	−17.1759	+	17.1759i	−0.716910	+	0.716910i
$575$	−10.9124	−	6.30030i	−0.455080	−	0.262741i
$576$		0			0
$577$	−9.12182	+	9.12182i	−0.379746	+	0.379746i	−0.871011	−	0.491264i	$-0.836535\pi$
$577$	−9.12182	+	9.12182i	−0.379746	+	0.379746i	0.491264	+	0.871011i	$0.336535\pi$
$578$	−18.1647	+	4.86721i	−0.755552	+	0.202449i
$579$		0			0
$580$	−10.4213	+	2.79238i	−0.432721	+	0.115947i
$581$		−	54.3497i		−	2.25481i
$582$		0			0
$583$	−3.00893	−	3.00893i	−0.124617	−	0.124617i
$584$	−1.36455			−0.0564653
$585$		0			0
$586$	−12.1801			−0.503153
$587$	−25.9757	−	25.9757i	−1.07213	−	1.07213i	−0.997188	−	0.0749440i	$-0.976122\pi$
$587$	−25.9757	−	25.9757i	−1.07213	−	1.07213i	−0.0749440	−	0.997188i	$-0.523878\pi$
$588$		0			0
$589$		−	6.19599i		−	0.255301i
$590$	−9.06169	+	2.42807i	−0.373064	+	0.0999622i
$591$		0			0
$592$	6.94881	−	1.86193i	0.285594	−	0.0765247i
$593$	27.5996	−	27.5996i	1.13338	−	1.13338i	0.143768	−	0.989611i	$-0.454078\pi$
$593$	27.5996	−	27.5996i	1.13338	−	1.13338i	0.989611	−	0.143768i	$-0.0459219\pi$
$594$		0			0
$595$	−38.1350	−	22.0173i	−1.56338	−	0.902619i
$596$	−0.424349	+	0.424349i	−0.0173820	+	0.0173820i
$597$		0			0
$598$	17.9294	−	0.410664i	0.733189	−	0.0167933i
$599$	−40.1298	−	23.1689i	−1.63966	−	0.946657i	−0.980950	−	0.194259i	$-0.937770\pi$
$599$	−40.1298	−	23.1689i	−1.63966	−	0.946657i	−0.658708	−	0.752399i	$-0.728897\pi$
$600$		0			0
$601$	−21.0902			−0.860289			−0.430145	−	0.902760i	$-0.641537\pi$
$601$	−21.0902			−0.860289			−0.430145	+	0.902760i	$0.641537\pi$
$602$	28.7192	+	49.7432i	1.17051	+	2.02738i
$603$		0			0
$604$	1.75756	+	0.470936i	0.0715140	+	0.0191621i
$605$	−3.51995	−	13.1366i	−0.143106	−	0.534080i
$606$		0			0
$607$	10.2282			0.415151			0.207576	−	0.978219i	$-0.433443\pi$
$607$	10.2282			0.415151			0.207576	+	0.978219i	$0.433443\pi$
$608$	−2.95542	−	5.11893i	−0.119858	−	0.207600i
$609$		0			0
$610$	5.94726	−	3.43365i	0.240797	−	0.139024i
$611$	0.524935	+	22.9185i	0.0212366	+	0.927182i
$612$		0			0
$613$	−12.0361	−	44.9194i	−0.486134	−	1.81428i	−0.574900	−	0.818224i	$-0.694959\pi$
$613$	−12.0361	−	44.9194i	−0.486134	−	1.81428i	0.0887657	−	0.996053i	$-0.471708\pi$
$614$		−	9.64834i		−	0.389375i
$615$		0			0
$616$	1.85538	+	6.92438i	0.0747554	+	0.278991i
$617$	16.1123	+	16.1123i	0.648657	+	0.648657i	0.952668	−	0.304012i	$-0.0983262\pi$
$617$	16.1123	+	16.1123i	0.648657	+	0.648657i	−0.304012	+	0.952668i	$0.598326\pi$
$618$		0			0
$619$	−7.63393	+	28.4902i	−0.306834	+	1.14512i	0.624522	+	0.781007i	$0.285294\pi$
$619$	−7.63393	+	28.4902i	−0.306834	+	1.14512i	−0.931355	+	0.364111i	$0.881373\pi$
$620$	−1.42578	+	0.823175i	−0.0572607	+	0.0330595i
$621$		0			0
$622$	−14.9478	+	4.00525i	−0.599351	+	0.160596i
$623$	−13.2306	−	22.9161i	−0.530074	−	0.918115i
$624$		0			0
$625$	−2.95806	+	5.12350i	−0.118322	+	0.204940i
$626$	−6.93430	+	25.8792i	−0.277150	+	1.03434i
$627$		0			0
$628$	−1.75937	−	1.01577i	−0.0702066	−	0.0405338i
$629$	−30.4387	−	30.4387i	−1.21367	−	1.21367i
$630$		0			0
$631$	11.3620	−	42.4037i	0.452315	−	1.68806i	−0.243548	−	0.969889i	$-0.578311\pi$
$631$	11.3620	−	42.4037i	0.452315	−	1.68806i	0.695863	−	0.718174i	$-0.255022\pi$
$632$	0.130195	+	0.0348857i	0.00517889	+	0.00138768i
$633$		0			0
$634$	−12.4751	+	7.20250i	−0.495450	+	0.286048i
$635$	17.6560	+	4.73092i	0.700658	+	0.187741i
$636$		0			0
$637$	−38.9888	−	37.2428i	−1.54479	−	1.47561i
$638$		−	10.5099i		−	0.416089i
$639$		0			0
$640$	−0.785290	+	1.36016i	−0.0310413	+	0.0537651i
$641$	−22.6855	+	39.2924i	−0.896022	+	1.55196i	−0.0634878	+	0.997983i	$0.520222\pi$
$641$	−22.6855	+	39.2924i	−0.896022	+	1.55196i	−0.832534	+	0.553973i	$0.813111\pi$
$642$		0			0
$643$	19.4333	−	19.4333i	0.766375	−	0.766375i	−0.211091	−	0.977466i	$-0.567702\pi$
$643$	19.4333	−	19.4333i	0.766375	−	0.766375i	0.977466	+	0.211091i	$0.0677017\pi$
$644$	−16.4798	+	16.4798i	−0.649395	+	0.649395i
$645$		0			0
$646$	−17.6845	+	30.6305i	−0.695788	+	1.20514i
$647$	1.29346	−	2.24034i	0.0508513	−	0.0880770i	−0.839479	−	0.543392i	$-0.817140\pi$
$647$	1.29346	−	2.24034i	0.0508513	−	0.0880770i	0.890331	+	0.455315i	$0.150473\pi$
$648$		0			0
$649$		−	9.13869i		−	0.358725i
$650$	0.209151	+	9.13147i	0.00820360	+	0.358166i
$651$		0			0
$652$	−8.79238	−	2.35591i	−0.344336	−	0.0922646i
$653$	−1.89876	+	1.09625i	−0.0743042	+	0.0428995i	−0.536692	−	0.843778i	$-0.680326\pi$
$653$	−1.89876	+	1.09625i	−0.0743042	+	0.0428995i	0.462388	+	0.886678i	$0.346993\pi$
$654$		0			0
$655$	8.27703	+	2.21782i	0.323410	+	0.0866575i
$656$	1.34176	−	5.00750i	0.0523868	−	0.195510i
$657$		0			0
$658$	−21.0655	−	21.0655i	−0.821217	−	0.821217i
$659$	19.3027	+	11.1444i	0.751925	+	0.434124i	0.826389	−	0.563099i	$-0.190391\pi$
$659$	19.3027	+	11.1444i	0.751925	+	0.434124i	−0.0744639	+	0.997224i	$0.523725\pi$
$660$		0			0
$661$	6.60372	−	24.6454i	0.256855	−	0.958596i	−0.710194	−	0.704006i	$-0.751393\pi$
$661$	6.60372	−	24.6454i	0.256855	−	0.958596i	0.967049	−	0.254590i	$-0.0819406\pi$
$662$	15.3707	−	26.6229i	0.597400	−	1.03473i
$663$		0			0
$664$	5.79975	+	10.0455i	0.225074	+	0.389839i
$665$	−42.0156	+	11.2581i	−1.62930	+	0.436569i
$666$		0			0
$667$	29.5909	−	17.0843i	1.14576	−	0.661506i
$668$	0.968219	−	3.61344i	0.0374615	−	0.139808i
$669$		0			0
$670$	6.22810	+	6.22810i	0.240613	+	0.240613i
$671$	1.73141	+	6.46172i	0.0668405	+	0.249452i
$672$		0			0
$673$			17.3697i			0.669552i	0.942298	+	0.334776i	$0.108661\pi$
$673$			17.3697i			0.669552i	−0.942298	+	0.334776i	$0.891339\pi$
$674$	−7.78596	−	29.0576i	−0.299904	−	1.11926i
$675$		0			0
$676$	−7.00865	−	10.9489i	−0.269563	−	0.421112i
$677$	1.50598	−	0.869476i	0.0578794	−	0.0334167i	−0.470781	−	0.882250i	$-0.656028\pi$
$677$	1.50598	−	0.869476i	0.0578794	−	0.0334167i	0.528660	+	0.848833i	$0.322694\pi$
$678$		0			0
$679$	−15.6323	−	27.0760i	−0.599913	−	1.03908i
$680$	9.39799			0.360396
$681$		0			0
$682$	−0.415085	−	1.54912i	−0.0158944	−	0.0593188i
$683$	40.4081	+	10.8273i	1.54617	+	0.414296i	0.928254	−	0.371947i	$-0.121310\pi$
$683$	40.4081	+	10.8273i	1.54617	+	0.414296i	0.617918	+	0.786243i	$0.287976\pi$
$684$		0			0
$685$	1.14994	+	1.99176i	0.0439370	+	0.0761011i
$686$	37.2694			1.42295
$687$		0			0
$688$	−10.6164	−	6.12935i	−0.404745	−	0.233679i
$689$	−9.62446	+	2.81660i	−0.366663	+	0.107304i
$690$		0			0
$691$	6.97222	−	6.97222i	0.265236	−	0.265236i	−0.561941	−	0.827177i	$-0.689945\pi$
$691$	6.97222	−	6.97222i	0.265236	−	0.265236i	0.827177	+	0.561941i	$0.189945\pi$
$692$	−0.878368	−	0.507126i	−0.0333905	−	0.0192780i
$693$		0			0
$694$	−12.0944	+	12.0944i	−0.459097	+	0.459097i
$695$	11.3689	−	3.04629i	0.431248	−	0.115553i
$696$		0			0
$697$	−29.9637	+	8.02875i	−1.13496	+	0.304111i
$698$		−	2.79608i		−	0.105833i
$699$		0			0
$700$	−8.39317	−	8.39317i	−0.317232	−	0.317232i
$701$	9.99927			0.377667			0.188834	−	0.982009i	$-0.439529\pi$
$701$	9.99927			0.377667			0.188834	+	0.982009i	$0.439529\pi$
$702$		0			0
$703$	−42.5221			−1.60375
$704$	−1.08184	−	1.08184i	−0.0407734	−	0.0407734i
$705$		0			0
$706$			33.4469i			1.25879i
$707$	−34.6677	+	9.28919i	−1.30381	+	0.349356i
$708$		0			0
$709$	19.6851	−	5.27462i	0.739291	−	0.198092i	0.130528	−	0.991445i	$-0.458333\pi$
$709$	19.6851	−	5.27462i	0.739291	−	0.198092i	0.608763	+	0.793352i	$0.291666\pi$
$710$	0.319681	−	0.319681i	0.0119974	−	0.0119974i
$711$		0			0
$712$	4.89083	+	2.82372i	0.183292	+	0.105823i
$713$	3.68685	−	3.68685i	0.138074	−	0.138074i
$714$		0			0
$715$	8.41778	+	2.05015i	0.314807	+	0.0766712i
$716$	−20.2291	−	11.6793i	−0.755998	−	0.436475i
$717$		0			0
$718$	−5.75214			−0.214668
$719$	−9.70859	−	16.8158i	−0.362069	−	0.627123i	0.626232	−	0.779637i	$-0.284596\pi$
$719$	−9.70859	−	16.8158i	−0.362069	−	0.627123i	−0.988301	+	0.152514i	$0.951263\pi$
$720$		0			0
$721$	−12.8748	−	3.44978i	−0.479481	−	0.128477i
$722$	4.12504	+	15.3949i	0.153518	+	0.572938i
$723$		0			0
$724$	8.51778			0.316561
$725$	8.70104	+	15.0706i	0.323149	+	0.559710i
$726$		0			0
$727$	38.1818	−	22.0442i	1.41608	−	0.817576i	0.420131	−	0.907464i	$-0.361984\pi$
$727$	38.1818	−	22.0442i	1.41608	−	0.817576i	0.995952	+	0.0898878i	$0.0286508\pi$
$728$	16.4141	+	3.99765i	0.608347	+	0.148163i
$729$		0			0
$730$	−0.554683	−	2.07010i	−0.0205297	−	0.0766180i
$731$			73.3533i			2.71307i
$732$		0			0
$733$	9.30736	+	34.7355i	0.343775	+	1.28299i	0.894037	+	0.447994i	$0.147861\pi$
$733$	9.30736	+	34.7355i	0.343775	+	1.28299i	−0.550261	+	0.834992i	$0.685472\pi$
$734$	2.03642	+	2.03642i	0.0751656	+	0.0751656i
$735$		0			0
$736$	1.28737	−	4.80455i	0.0474532	−	0.177098i
$737$	−7.43053	+	4.29002i	−0.273707	+	0.158025i
$738$		0			0
$739$	−40.1431	+	10.7563i	−1.47669	+	0.395677i	−0.905219	−	0.424946i	$-0.860293\pi$
$739$	−40.1431	+	10.7563i	−1.47669	+	0.395677i	−0.571470	+	0.820623i	$0.693627\pi$
$740$	5.64933	+	9.78492i	0.207673	+	0.359701i
$741$		0			0
$742$	6.51594	−	11.2859i	0.239208	−	0.414320i
$743$	6.90641	−	25.7751i	0.253372	−	0.945596i	−0.715617	−	0.698492i	$-0.753855\pi$
$743$	6.90641	−	25.7751i	0.253372	−	0.945596i	0.968989	−	0.247103i	$-0.0794787\pi$
$744$		0			0
$745$	−0.816261	−	0.471269i	−0.0299055	−	0.0172660i
$746$	−12.0901	−	12.0901i	−0.442648	−	0.442648i
$747$		0			0
$748$	−2.36946	+	8.84295i	−0.0866360	+	0.323330i
$749$	−77.1107	−	20.6617i	−2.81756	−	0.754964i
$750$		0			0
$751$	3.69581	−	2.13378i	0.134862	−	0.0778626i	−0.431051	−	0.902328i	$-0.641857\pi$
$751$	3.69581	−	2.13378i	0.134862	−	0.0778626i	0.565913	+	0.824465i	$0.308524\pi$
$752$	6.14146	+	1.64560i	0.223956	+	0.0600088i
$753$		0			0
$754$	−21.7276	−	11.8896i	−0.791273	−	0.432992i
$755$			2.85776i			0.104005i
$756$		0			0
$757$	8.81337	−	15.2652i	0.320327	−	0.554823i	−0.660228	−	0.751065i	$-0.729540\pi$
$757$	8.81337	−	15.2652i	0.320327	−	0.554823i	0.980556	+	0.196242i	$0.0628738\pi$
$758$	−10.1872	+	17.6447i	−0.370014	+	0.640883i
$759$		0			0
$760$	6.56438	−	6.56438i	0.238115	−	0.238115i
$761$	5.20787	−	5.20787i	0.188785	−	0.188785i	−0.606386	−	0.795171i	$-0.707381\pi$
$761$	5.20787	−	5.20787i	0.188785	−	0.188785i	0.795171	+	0.606386i	$0.207381\pi$
$762$		0			0
$763$	−4.78296	+	8.28433i	−0.173155	+	0.299913i
$764$	7.81525	−	13.5364i	0.282746	−	0.489730i
$765$		0			0
$766$			16.1279i			0.582726i
$767$	−18.8929	−	10.3384i	−0.682184	−	0.373298i
$768$		0			0
$769$	−11.3565	−	3.04296i	−0.409525	−	0.109732i	0.0481743	−	0.998839i	$-0.484660\pi$
$769$	−11.3565	−	3.04296i	−0.409525	−	0.109732i	−0.457699	+	0.889107i	$0.651326\pi$
$770$	−9.75052	+	5.62946i	−0.351384	+	0.202872i
$771$		0			0
$772$	−15.2711	−	4.09187i	−0.549618	−	0.147270i
$773$	−1.81323	+	6.76707i	−0.0652173	+	0.243394i	−0.990838	−	0.135059i	$-0.956877\pi$
$773$	−1.81323	+	6.76707i	−0.0652173	+	0.243394i	0.925620	+	0.378454i	$0.123544\pi$
$774$		0			0
$775$	1.87772	+	1.87772i	0.0674496	+	0.0674496i
$776$	5.77864	+	3.33630i	0.207441	+	0.119766i
$777$		0			0
$778$	9.37049	−	34.9712i	0.335948	−	1.25378i
$779$	−15.3213	+	26.5373i	−0.548943	+	0.950797i
$780$		0			0
$781$	0.220201	+	0.381400i	0.00787942	+	0.0136476i
$782$	−28.7493	+	7.70335i	−1.02807	+	0.275471i
$783$		0			0
$784$	−12.9507	+

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.51706 + 0.406496i) q^{5} +(4.52587 - 1.21270i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.51706 + 0.406496i) q^{5} +(4.52587 - 1.21270i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.36016 - 0.785290i) q^{10} +(1.08184 - 1.08184i) q^{11} +(-1.01269 - 3.46041i) q^{13} +(4.05778 + 2.34276i) q^{14} -1.00000 q^{16} +(2.99188 + 5.18209i) q^{17} +(5.70943 + 1.52984i) q^{19} +(-0.406496 - 1.51706i) q^{20} +1.52995 q^{22} +(2.48702 + 4.30764i) q^{23} +(-2.19388 + 1.26664i) q^{25} +(1.73080 - 3.16296i) q^{26} +(1.21270 + 4.52587i) q^{28} -6.86939i q^{29} +(-0.271305 - 1.01253i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.54871 + 5.77988i) q^{34} +(-6.37308 + 3.67950i) q^{35} +(-6.94881 + 1.86193i) q^{37} +(2.95542 + 5.11893i) q^{38} +(0.785290 - 1.36016i) q^{40} +(-1.34176 + 5.00750i) q^{41} +(10.6164 + 6.12935i) q^{43} +(1.08184 + 1.08184i) q^{44} +(-1.28737 + 4.80455i) q^{46} +(-6.14146 - 1.64560i) q^{47} +(12.9507 - 7.47708i) q^{49} +(-2.44696 - 0.655661i) q^{50} +(3.46041 - 1.01269i) q^{52} -2.78130i q^{53} +(-1.20146 + 2.08099i) q^{55} +(-2.34276 + 4.05778i) q^{56} +(4.85740 - 4.85740i) q^{58} +(4.22367 - 4.22367i) q^{59} +(-2.18623 + 3.78666i) q^{61} +(0.524122 - 0.907805i) q^{62} -1.00000i q^{64} +(2.94296 + 4.83801i) q^{65} +(-5.41695 - 1.45147i) q^{67} +(-5.18209 + 2.99188i) q^{68} +(-7.10824 - 1.90465i) q^{70} +(-0.0745019 + 0.278045i) q^{71} +(0.964880 + 0.964880i) q^{73} +(-6.23013 - 3.59697i) q^{74} +(-1.52984 + 5.70943i) q^{76} +(3.58432 - 6.20823i) q^{77} +(-0.0673941 - 0.116730i) q^{79} +(1.51706 - 0.406496i) q^{80} +(-4.48960 + 2.59207i) q^{82} +(3.00217 - 11.2043i) q^{83} +(-6.64538 - 6.64538i) q^{85} +(3.17279 + 11.8410i) q^{86} +1.52995i q^{88} +(-1.46167 - 5.45501i) q^{89} +(-8.77976 - 14.4333i) q^{91} +(-4.30764 + 2.48702i) q^{92} +(-3.17905 - 5.50628i) q^{94} -9.28344 q^{95} +(-1.72699 - 6.44523i) q^{97} +(14.4446 + 3.87042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 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