LMFDB - Embedded newform 702.2.bb.a.449.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			449.12
Character	$\chi$	$=$	702.449
Dual form			702.2.bb.a.197.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.491075 + 1.83272i) q^{5} +(-0.530631 - 1.98034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.64317 + 0.948684i) q^{10} +(4.07867 + 4.07867i) q^{11} +(3.34535 + 1.34484i) q^{13} +(-1.77553 - 1.02510i) q^{14} -1.00000 q^{16} +(-1.11311 - 1.92797i) q^{17} +(1.13029 - 4.21829i) q^{19} +(1.83272 - 0.491075i) q^{20} +5.76811 q^{22} +(2.96731 + 5.13954i) q^{23} +(1.21243 - 0.699997i) q^{25} +(3.31647 - 1.41458i) q^{26} +(-1.98034 + 0.530631i) q^{28} -6.12844i q^{29} +(-2.46576 + 0.660699i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.15037 - 0.576189i) q^{34} +(3.36883 - 1.94499i) q^{35} +(-0.585575 - 2.18540i) q^{37} +(-2.18355 - 3.78201i) q^{38} +(0.948684 - 1.64317i) q^{40} +(10.8182 + 2.89872i) q^{41} +(-5.13566 - 2.96507i) q^{43} +(4.07867 - 4.07867i) q^{44} +(5.73241 + 1.53599i) q^{46} +(-1.46521 + 5.46823i) q^{47} +(2.42199 - 1.39834i) q^{49} +(0.362345 - 1.35229i) q^{50} +(1.34484 - 3.34535i) q^{52} +2.73563i q^{53} +(-5.47212 + 9.47798i) q^{55} +(-1.02510 + 1.77553i) q^{56} +(-4.33346 - 4.33346i) q^{58} +(-4.65773 - 4.65773i) q^{59} +(-4.43478 + 7.68127i) q^{61} +(-1.27637 + 2.21074i) q^{62} +1.00000i q^{64} +(-0.821895 + 6.79151i) q^{65} +(-3.58735 + 13.3882i) q^{67} +(-1.92797 + 1.11311i) q^{68} +(1.00680 - 3.75744i) q^{70} +(-6.43432 - 1.72407i) q^{71} +(6.02332 - 6.02332i) q^{73} +(-1.95937 - 1.13124i) q^{74} +(-4.21829 - 1.13029i) q^{76} +(5.91289 - 10.2414i) q^{77} +(-5.25497 - 9.10187i) q^{79} +(-0.491075 - 1.83272i) q^{80} +(9.69930 - 5.59989i) q^{82} +(-2.70106 - 0.723746i) q^{83} +(2.98680 - 2.98680i) q^{85} +(-5.72808 + 1.53483i) q^{86} -5.76811i q^{88} +(-12.7827 + 3.42511i) q^{89} +(0.888099 - 7.33856i) q^{91} +(5.13954 - 2.96731i) q^{92} +(2.83056 + 4.90268i) q^{94} +8.28598 q^{95} +(6.05201 - 1.62163i) q^{97} +(0.723833 - 2.70138i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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
$5$	0.491075	+	1.83272i	0.219615	+	0.819616i	0.984491	+	0.175437i	$0.0561340\pi$
$5$	0.491075	+	1.83272i	0.219615	+	0.819616i	−0.764875	+	0.644179i	$0.777199\pi$
$6$		0			0
$7$	−0.530631	−	1.98034i	−0.200560	−	0.748499i	−0.990757	−	0.135647i	$-0.956689\pi$
$7$	−0.530631	−	1.98034i	−0.200560	−	0.748499i	0.790198	−	0.612852i	$-0.209978\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	1.64317	+	0.948684i	0.519616	+	0.300000i
$11$	4.07867	+	4.07867i	1.22977	+	1.22977i	0.964052	+	0.265713i	$0.0856075\pi$
$11$	4.07867	+	4.07867i	1.22977	+	1.22977i	0.265713	+	0.964052i	$0.414393\pi$
$12$		0			0
$13$	3.34535	+	1.34484i	0.927834	+	0.372992i
$13$	3.34535	+	1.34484i	0.927834	+	0.372992i
$14$	−1.77553	−	1.02510i	−0.474529	−	0.273970i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.11311	−	1.92797i	−0.269969	−	0.467601i	0.698884	−	0.715235i	$-0.253680\pi$
$17$	−1.11311	−	1.92797i	−0.269969	−	0.467601i	−0.968854	+	0.247634i	$0.920347\pi$
$18$		0			0
$19$	1.13029	−	4.21829i	0.259306	−	0.967742i	−0.706339	−	0.707874i	$-0.749654\pi$
$19$	1.13029	−	4.21829i	0.259306	−	0.967742i	0.965644	−	0.259868i	$-0.0836789\pi$
$20$	1.83272	−	0.491075i	0.409808	−	0.109808i
$21$		0			0
$22$	5.76811			1.22977
$23$	2.96731	+	5.13954i	0.618728	+	1.07167i	0.989718	+	0.143031i	$0.0456849\pi$
$23$	2.96731	+	5.13954i	0.618728	+	1.07167i	−0.370991	+	0.928637i	$0.620982\pi$
$24$		0			0
$25$	1.21243	−	0.699997i	0.242486	−	0.139999i
$26$	3.31647	−	1.41458i	0.650413	−	0.277421i
$27$		0			0
$28$	−1.98034	+	0.530631i	−0.374249	+	0.100280i
$29$		−	6.12844i		−	1.13802i	−0.822330	−	0.569011i	$-0.807326\pi$
$29$		−	6.12844i		−	1.13802i	0.822330	−	0.569011i	$-0.192674\pi$
$30$		0			0
$31$	−2.46576	+	0.660699i	−0.442864	+	0.118665i	−0.473359	−	0.880870i	$-0.656958\pi$
$31$	−2.46576	+	0.660699i	−0.442864	+	0.118665i	0.0304944	+	0.999535i	$0.490292\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	−2.15037	−	0.576189i	−0.368785	−	0.0988157i
$35$	3.36883	−	1.94499i	0.569436	−	0.328764i
$36$		0			0
$37$	−0.585575	−	2.18540i	−0.0962680	−	0.359277i	0.900941	−	0.433942i	$-0.142878\pi$
$37$	−0.585575	−	2.18540i	−0.0962680	−	0.359277i	−0.997209	+	0.0746653i	$0.976211\pi$
$38$	−2.18355	−	3.78201i	−0.354218	−	0.613524i
$39$		0			0
$40$	0.948684	−	1.64317i	0.150000	−	0.259808i
$41$	10.8182	+	2.89872i	1.68951	+	0.452704i	0.970264	−	0.242048i	$-0.0778192\pi$
$41$	10.8182	+	2.89872i	1.68951	+	0.452704i	0.719249	+	0.694752i	$0.244486\pi$
$42$		0			0
$43$	−5.13566	−	2.96507i	−0.783180	−	0.452169i	0.0543759	−	0.998521i	$-0.482683\pi$
$43$	−5.13566	−	2.96507i	−0.783180	−	0.452169i	−0.837556	+	0.546351i	$0.816016\pi$
$44$	4.07867	−	4.07867i	0.614883	−	0.614883i
$45$		0			0
$46$	5.73241	+	1.53599i	0.845198	+	0.226470i
$47$	−1.46521	+	5.46823i	−0.213723	+	0.797623i	0.772890	+	0.634540i	$0.218811\pi$
$47$	−1.46521	+	5.46823i	−0.213723	+	0.797623i	−0.986612	+	0.163083i	$0.947856\pi$
$48$		0			0
$49$	2.42199	−	1.39834i	0.345999	−	0.199763i
$50$	0.362345	−	1.35229i	0.0512433	−	0.191243i
$51$		0			0
$52$	1.34484	−	3.34535i	0.186496	−	0.463917i
$53$			2.73563i			0.375767i	0.982191	+	0.187884i	$0.0601628\pi$
$53$			2.73563i			0.375767i	−0.982191	+	0.187884i	$0.939837\pi$
$54$		0			0
$55$	−5.47212	+	9.47798i	−0.737860	+	1.27801i
$56$	−1.02510	+	1.77553i	−0.136985	+	0.237265i
$57$		0			0
$58$	−4.33346	−	4.33346i	−0.569011	−	0.569011i
$59$	−4.65773	−	4.65773i	−0.606384	−	0.606384i	0.335615	−	0.941999i	$-0.391056\pi$
$59$	−4.65773	−	4.65773i	−0.606384	−	0.606384i	−0.941999	+	0.335615i	$0.891056\pi$
$60$		0			0
$61$	−4.43478	+	7.68127i	−0.567815	+	0.983485i	0.428966	+	0.903321i	$0.358878\pi$
$61$	−4.43478	+	7.68127i	−0.567815	+	0.983485i	−0.996782	+	0.0801647i	$0.974455\pi$
$62$	−1.27637	+	2.21074i	−0.162100	+	0.280765i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.821895	+	6.79151i	−0.101944	+	0.842383i
$66$		0			0
$67$	−3.58735	+	13.3882i	−0.438264	+	1.63562i	0.294868	+	0.955538i	$0.404724\pi$
$67$	−3.58735	+	13.3882i	−0.438264	+	1.63562i	−0.733132	+	0.680086i	$0.761942\pi$
$68$	−1.92797	+	1.11311i	−0.233800	+	0.134985i
$69$		0			0
$70$	1.00680	−	3.75744i	0.120336	−	0.449100i
$71$	−6.43432	−	1.72407i	−0.763613	−	0.204609i	−0.144065	−	0.989568i	$-0.546017\pi$
$71$	−6.43432	−	1.72407i	−0.763613	−	0.204609i	−0.619548	+	0.784959i	$0.712684\pi$
$72$		0			0
$73$	6.02332	−	6.02332i	0.704976	−	0.704976i	−0.260498	−	0.965474i	$-0.583887\pi$
$73$	6.02332	−	6.02332i	0.704976	−	0.704976i	0.965474	+	0.260498i	$0.0838869\pi$
$74$	−1.95937	−	1.13124i	−0.227773	−	0.131505i
$75$		0			0
$76$	−4.21829	−	1.13029i	−0.483871	−	0.129653i
$77$	5.91289	−	10.2414i	0.673837	−	1.16712i
$78$		0			0
$79$	−5.25497	−	9.10187i	−0.591230	−	1.02404i	−0.994067	−	0.108769i	$-0.965309\pi$
$79$	−5.25497	−	9.10187i	−0.591230	−	1.02404i	0.402837	−	0.915272i	$-0.368024\pi$
$80$	−0.491075	−	1.83272i	−0.0549039	−	0.204904i
$81$		0			0
$82$	9.69930	−	5.59989i	1.07111	−	0.618405i
$83$	−2.70106	−	0.723746i	−0.296479	−	0.0794414i	0.107513	−	0.994204i	$-0.465711\pi$
$83$	−2.70106	−	0.723746i	−0.296479	−	0.0794414i	−0.403993	+	0.914762i	$0.632378\pi$
$84$		0			0
$85$	2.98680	−	2.98680i	0.323964	−	0.323964i
$86$	−5.72808	+	1.53483i	−0.617675	+	0.165505i
$87$		0			0
$88$		−	5.76811i		−	0.614883i
$89$	−12.7827	+	3.42511i	−1.35496	+	0.363061i	−0.861965	−	0.506969i	$-0.830766\pi$
$89$	−12.7827	+	3.42511i	−1.35496	+	0.363061i	−0.492999	+	0.870030i	$0.664099\pi$
$90$		0			0
$91$	0.888099	−	7.33856i	0.0930981	−	0.769290i
$92$	5.13954	−	2.96731i	0.535834	−	0.309364i
$93$		0			0
$94$	2.83056	+	4.90268i	0.291950	+	0.505673i
$95$	8.28598			0.850124
$96$		0			0
$97$	6.05201	−	1.62163i	0.614489	−	0.164652i	0.0618676	−	0.998084i	$-0.480294\pi$
$97$	6.05201	−	1.62163i	0.614489	−	0.164652i	0.552621	+	0.833433i	$0.313628\pi$
$98$	0.723833	−	2.70138i	0.0731182	−	0.272881i
$99$		0			0
$100$	−0.699997	−	1.21243i	−0.0699997	−	0.121243i
$101$	−3.52832			−0.351081			−0.175540	−	0.984472i	$-0.556167\pi$
$101$	−3.52832			−0.351081			−0.175540	+	0.984472i	$0.556167\pi$
$102$		0			0
$103$	2.08972	+	1.20650i	0.205906	+	0.118880i	0.599407	−	0.800444i	$-0.295403\pi$
$103$	2.08972	+	1.20650i	0.205906	+	0.118880i	−0.393501	+	0.919324i	$0.628736\pi$
$104$	−1.41458	−	3.31647i	−0.138711	−	0.325207i
$105$		0			0
$106$	1.93438	+	1.93438i	0.187884	+	0.187884i
$107$	−11.9580	−	6.90393i	−1.15602	−	0.667428i	−0.205673	−	0.978621i	$-0.565938\pi$
$107$	−11.9580	−	6.90393i	−1.15602	−	0.667428i	−0.950347	+	0.311193i	$0.899272\pi$
$108$		0			0
$109$	−8.53541	−	8.53541i	−0.817544	−	0.817544i	0.168207	−	0.985752i	$-0.446202\pi$
$109$	−8.53541	−	8.53541i	−0.817544	−	0.817544i	−0.985752	+	0.168207i	$0.946202\pi$
$110$	2.83258	+	10.5713i	0.270075	+	1.00794i
$111$		0			0
$112$	0.530631	+	1.98034i	0.0501399	+	0.187125i
$113$			9.18211i			0.863781i	0.901926	+	0.431890i	$0.142153\pi$
$113$			9.18211i			0.863781i	−0.901926	+	0.431890i	$0.857847\pi$
$114$		0			0
$115$	−7.96214	+	7.96214i	−0.742474	+	0.742474i
$116$	−6.12844			−0.569011
$117$		0			0
$118$	−6.58702			−0.606384
$119$	−3.22738	+	3.22738i	−0.295854	+	0.295854i
$120$		0			0
$121$			22.2711i			2.02465i
$122$	2.29561	+	8.56734i	0.207835	+	0.775650i
$123$		0			0
$124$	0.660699	+	2.46576i	0.0593325	+	0.221432i
$125$	8.58650	+	8.58650i	0.768000	+	0.768000i
$126$		0			0
$127$	7.73808	+	4.46758i	0.686643	+	0.396434i	0.802353	−	0.596849i	$-0.203581\pi$
$127$	7.73808	+	4.46758i	0.686643	+	0.396434i	−0.115710	+	0.993283i	$0.536914\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	4.22115	+	5.38349i	0.370220	+	0.472163i
$131$	−16.1712	−	9.33646i	−1.41289	−	0.815731i	−0.417227	−	0.908802i	$-0.636998\pi$
$131$	−16.1712	−	9.33646i	−1.41289	−	0.815731i	−0.995659	+	0.0930716i	$0.970331\pi$
$132$		0			0
$133$	−8.95342			−0.776360
$134$	6.93022	+	12.0035i	0.598680	+	1.03694i
$135$		0			0
$136$	−0.576189	+	2.15037i	−0.0494078	+	0.184393i
$137$	−9.98001	+	2.67413i	−0.852649	+	0.228467i	−0.658570	−	0.752519i	$-0.728839\pi$
$137$	−9.98001	+	2.67413i	−0.852649	+	0.228467i	−0.194079	+	0.980986i	$0.562172\pi$
$138$		0			0
$139$	−18.6932			−1.58554			−0.792769	−	0.609523i	$-0.791361\pi$
$139$	−18.6932			−1.58554			−0.792769	+	0.609523i	$0.791361\pi$
$140$	−1.94499	−	3.36883i	−0.164382	−	0.284718i
$141$		0			0
$142$	−5.76885	+	3.33065i	−0.484111	+	0.279502i
$143$	8.15943	+	19.1298i	0.682326	+	1.59971i
$144$		0			0
$145$	11.2317	−	3.00952i	0.932741	−	0.249927i
$146$		−	8.51825i		−	0.704976i
$147$		0			0
$148$	−2.18540	+	0.585575i	−0.179639	+	0.0481340i
$149$	3.87791	−	3.87791i	0.317691	−	0.317691i	−0.530189	−	0.847880i	$-0.677879\pi$
$149$	3.87791	−	3.87791i	0.317691	−	0.317691i	0.847880	+	0.530189i	$0.177879\pi$
$150$		0			0
$151$	6.28851	+	1.68500i	0.511752	+	0.137124i	0.505449	−	0.862857i	$-0.331327\pi$
$151$	6.28851	+	1.68500i	0.511752	+	0.137124i	0.00630324	+	0.999980i	$0.497994\pi$
$152$	−3.78201	+	2.18355i	−0.306762	+	0.177109i
$153$		0			0
$154$	−3.06074	−	11.4228i	−0.246641	−	0.920478i
$155$	−2.42175	−	4.19459i	−0.194520	−	0.336918i
$156$		0			0
$157$	−5.12269	+	8.87276i	−0.408835	+	0.708123i	−0.994759	−	0.102243i	$-0.967398\pi$
$157$	−5.12269	+	8.87276i	−0.408835	+	0.708123i	0.585924	+	0.810366i	$0.300732\pi$
$158$	−10.1518	−	2.72017i	−0.807635	−	0.216405i
$159$		0			0
$160$	−1.64317	−	0.948684i	−0.129904	−	0.0750001i
$161$	8.60349	−	8.60349i	0.678050	−	0.678050i
$162$		0			0
$163$	15.5355	+	4.16272i	1.21683	+	0.326049i	0.809439	−	0.587203i	$-0.199771\pi$
$163$	15.5355	+	4.16272i	1.21683	+	0.326049i	0.407393	+	0.913253i	$0.366438\pi$
$164$	2.89872	−	10.8182i	0.226352	−	0.844757i
$165$		0			0
$166$	−2.42170	+	1.39817i	−0.187960	+	0.108519i
$167$	−1.46529	+	5.46853i	−0.113387	+	0.423167i	−0.999161	−	0.0409498i	$-0.986962\pi$
$167$	−1.46529	+	5.46853i	−0.113387	+	0.423167i	0.885774	+	0.464117i	$0.153628\pi$
$168$		0			0
$169$	9.38280	+	8.99795i	0.721754	+	0.692150i
$170$		−	4.22397i		−	0.323964i
$171$		0			0
$172$	−2.96507	+	5.13566i	−0.226085	+	0.391590i
$173$	−5.60823	+	9.71374i	−0.426386	+	0.738522i	−0.996549	−	0.0830097i	$-0.973547\pi$
$173$	−5.60823	+	9.71374i	−0.426386	+	0.738522i	0.570163	+	0.821532i	$0.306880\pi$
$174$		0			0
$175$	−2.02959	−	2.02959i	−0.153422	−	0.153422i
$176$	−4.07867	−	4.07867i	−0.307441	−	0.307441i
$177$		0			0
$178$	−6.61681	+	11.4607i	−0.495951	+	0.859012i
$179$	5.57461	−	9.65551i	0.416666	−	0.721687i	−0.578936	−	0.815373i	$-0.696532\pi$
$179$	5.57461	−	9.65551i	0.416666	−	0.721687i	0.995602	+	0.0936864i	$0.0298651\pi$
$180$		0			0
$181$			2.01561i			0.149819i	0.997190	+	0.0749094i	$0.0238668\pi$
$181$			2.01561i			0.149819i	−0.997190	+	0.0749094i	$0.976133\pi$
$182$	−4.56117	−	5.81713i	−0.338096	−	0.431194i
$183$		0			0
$184$	1.53599	−	5.73241i	0.113235	−	0.422599i
$185$	3.71765	−	2.14639i	0.273327	−	0.157806i
$186$		0			0
$187$	3.32352	−	12.4036i	0.243040	−	0.907038i
$188$	5.46823	+	1.46521i	0.398812	+	0.106861i
$189$		0			0
$190$	5.85908	−	5.85908i	0.425062	−	0.425062i
$191$	−0.486028	−	0.280608i	−0.0351677	−	0.0203041i	0.482313	−	0.875999i	$-0.339797\pi$
$191$	−0.486028	−	0.280608i	−0.0351677	−	0.0203041i	−0.517481	+	0.855695i	$0.673130\pi$
$192$		0			0
$193$	8.61775	+	2.30912i	0.620319	+	0.166214i	0.555273	−	0.831668i	$-0.312614\pi$
$193$	8.61775	+	2.30912i	0.620319	+	0.166214i	0.0650462	+	0.997882i	$0.479281\pi$
$194$	3.13275	−	5.42608i	0.224918	−	0.389570i
$195$		0			0
$196$	−1.39834	−	2.42199i	−0.0998813	−	0.173000i
$197$	−2.52062	−	9.40707i	−0.179586	−	0.670226i	−0.995725	−	0.0923693i	$-0.970556\pi$
$197$	−2.52062	−	9.40707i	−0.179586	−	0.670226i	0.816138	−	0.577857i	$-0.196111\pi$
$198$		0			0
$199$	−7.42000	+	4.28394i	−0.525990	+	0.303680i	−0.739382	−	0.673286i	$-0.764882\pi$
$199$	−7.42000	+	4.28394i	−0.525990	+	0.303680i	0.213392	+	0.976967i	$0.431549\pi$
$200$	−1.35229	−	0.362345i	−0.0956214	−	0.0256217i
$201$		0			0
$202$	−2.49490	+	2.49490i	−0.175540	+	0.175540i
$203$	−12.1364	+	3.25194i	−0.851808	+	0.228241i
$204$		0			0
$205$			21.2501i			1.48417i
$206$	2.33078	−	0.624531i	0.162393	−	0.0435131i
$207$		0			0
$208$	−3.34535	−	1.34484i	−0.231959	−	0.0932480i
$209$	21.8151	−	12.5949i	1.50898	−	0.871210i
$210$		0			0
$211$	−6.42173	−	11.1228i	−0.442090	−	0.765722i	0.555754	−	0.831347i	$-0.312429\pi$
$211$	−6.42173	−	11.1228i	−0.442090	−	0.765722i	−0.997844	+	0.0656241i	$0.979096\pi$
$212$	2.73563			0.187884
$213$		0			0
$214$	−13.3374	+	3.57374i	−0.911724	+	0.244296i
$215$	2.91215	−	10.8683i	0.198607	−	0.741211i
$216$		0			0
$217$	2.61682	+	4.53247i	0.177641	+	0.307684i
$218$	−12.0709			−0.817544
$219$		0			0
$220$	9.47798	+	5.47212i	0.639005	+	0.368930i
$221$	−1.13094	−	7.94670i	−0.0760755	−	0.534553i
$222$		0			0
$223$	−8.53473	−	8.53473i	−0.571528	−	0.571528i	0.361027	−	0.932555i	$-0.382426\pi$
$223$	−8.53473	−	8.53473i	−0.571528	−	0.571528i	−0.932555	+	0.361027i	$0.882426\pi$
$224$	1.77553	+	1.02510i	0.118632	+	0.0684924i
$225$		0			0
$226$	6.49274	+	6.49274i	0.431890	+	0.431890i
$227$	−3.32670	−	12.4154i	−0.220801	−	0.824039i	−0.984044	−	0.177928i	$-0.943061\pi$
$227$	−3.32670	−	12.4154i	−0.220801	−	0.824039i	0.763243	−	0.646112i	$-0.223606\pi$
$228$		0			0
$229$	−5.03556	−	18.7930i	−0.332759	−	1.24187i	−0.906278	−	0.422682i	$-0.861089\pi$
$229$	−5.03556	−	18.7930i	−0.332759	−	1.24187i	0.573519	−	0.819192i	$-0.305578\pi$
$230$			11.2602i			0.742474i
$231$		0			0
$232$	−4.33346	+	4.33346i	−0.284506	+	0.284506i
$233$	−4.00407			−0.262316			−0.131158	−	0.991361i	$-0.541869\pi$
$233$	−4.00407			−0.262316			−0.131158	+	0.991361i	$0.541869\pi$
$234$		0			0
$235$	−10.7412			−0.700682
$236$	−4.65773	+	4.65773i	−0.303192	+	0.303192i
$237$		0			0
$238$			4.56421i			0.295854i
$239$	−2.37469	−	8.86245i	−0.153606	−	0.573264i	−0.999221	−	0.0394708i	$-0.987433\pi$
$239$	−2.37469	−	8.86245i	−0.153606	−	0.573264i	0.845615	−	0.533793i	$-0.179234\pi$
$240$		0			0
$241$	−5.01123	−	18.7022i	−0.322802	−	1.20471i	−0.916503	−	0.400028i	$-0.869001\pi$
$241$	−5.01123	−	18.7022i	−0.322802	−	1.20471i	0.593701	−	0.804686i	$-0.297666\pi$
$242$	15.7480	+	15.7480i	1.01232	+	1.01232i
$243$		0			0
$244$	7.68127	+	4.43478i	0.491743	+	0.283908i
$245$	3.75214	+	3.75214i	0.239715	+	0.239715i
$246$		0			0
$247$	9.45414	−	12.5916i	0.601553	−	0.801185i
$248$	2.21074	+	1.27637i	0.140382	+	0.0810498i
$249$		0			0
$250$	12.1431			0.768000
$251$	7.58584	+	13.1391i	0.478814	+	0.829331i	0.999705	−	0.0242928i	$-0.00773340\pi$
$251$	7.58584	+	13.1391i	0.478814	+	0.829331i	−0.520891	+	0.853623i	$0.674400\pi$
$252$		0			0
$253$	−8.85979	+	33.0652i	−0.557010	+	2.07879i
$254$	8.63070	−	2.31259i	0.541539	−	0.145105i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.56492	+	6.17463i	0.222374	+	0.385163i	0.955528	−	0.294899i	$-0.0952861\pi$
$257$	3.56492	+	6.17463i	0.222374	+	0.385163i	−0.733154	+	0.680062i	$0.761953\pi$
$258$		0			0
$259$	−4.01711	+	2.31928i	−0.249611	+	0.144113i
$260$	6.79151	+	0.821895i	0.421191	+	0.0509718i
$261$		0			0
$262$	−18.0367	+	4.83291i	−1.11431	+	0.298578i
$263$			10.3460i			0.637964i	0.947761	+	0.318982i	$0.103341\pi$
$263$			10.3460i			0.637964i	−0.947761	+	0.318982i	$0.896659\pi$
$264$		0			0
$265$	−5.01363	+	1.34340i	−0.307985	+	0.0825243i
$266$	−6.33102	+	6.33102i	−0.388180	+	0.388180i
$267$		0			0
$268$	13.3882	+	3.58735i	0.817812	+	0.219132i
$269$	−16.9068	+	9.76113i	−1.03082	+	0.595146i	−0.917221	−	0.398380i	$-0.869573\pi$
$269$	−16.9068	+	9.76113i	−1.03082	+	0.595146i	−0.113603	+	0.993526i	$0.536239\pi$
$270$		0			0
$271$	−4.18848	−	15.6316i	−0.254432	−	0.949553i	−0.968406	−	0.249380i	$-0.919773\pi$
$271$	−4.18848	−	15.6316i	−0.254432	−	0.949553i	0.713974	−	0.700172i	$-0.246894\pi$
$272$	1.11311	+	1.92797i	0.0674924	+	0.116900i
$273$		0			0
$274$	−5.16603	+	8.94783i	−0.312091	+	0.540558i
$275$	7.80016	+	2.09005i	0.470367	+	0.126035i
$276$		0			0
$277$	26.7062	+	15.4188i	1.60462	+	0.926427i	0.990547	+	0.137176i	$0.0438026\pi$
$277$	26.7062	+	15.4188i	1.60462	+	0.926427i	0.614071	+	0.789251i	$0.289531\pi$
$278$	−13.2181	+	13.2181i	−0.792769	+	0.792769i
$279$		0			0
$280$	−3.75744	−	1.00680i	−0.224550	−	0.0601679i
$281$	2.35439	−	8.78669i	0.140451	−	0.524170i	−0.859465	−	0.511195i	$-0.829203\pi$
$281$	2.35439	−	8.78669i	0.140451	−	0.524170i	0.999916	−	0.0129751i	$-0.00413023\pi$
$282$		0			0
$283$	14.8593	−	8.57903i	0.883295	−	0.509970i	0.0115513	−	0.999933i	$-0.496323\pi$
$283$	14.8593	−	8.57903i	0.883295	−	0.509970i	0.871743	+	0.489963i	$0.162990\pi$
$284$	−1.72407	+	6.43432i	−0.102305	+	0.381806i
$285$		0			0
$286$	19.2964	+	7.75720i	1.14102	+	0.458693i
$287$		−	22.9618i		−	1.35539i
$288$		0			0
$289$	6.02196	−	10.4303i	0.354233	−	0.613550i
$290$	5.81395	−	10.0701i	0.341407	−	0.591334i
$291$		0			0
$292$	−6.02332	−	6.02332i	−0.352488	−	0.352488i
$293$	−7.41306	−	7.41306i	−0.433075	−	0.433075i	0.456598	−	0.889673i	$-0.349068\pi$
$293$	−7.41306	−	7.41306i	−0.433075	−	0.433075i	−0.889673	+	0.456598i	$0.849068\pi$
$294$		0			0
$295$	6.24900	−	10.8236i	0.363831	−	0.630174i
$296$	−1.13124	+	1.95937i	−0.0657523	+	0.113886i
$297$		0			0
$298$		−	5.48419i		−	0.317691i
$299$	3.01485	+	21.1841i	0.174353	+	1.22511i
$300$		0			0
$301$	−3.14672	+	11.7437i	−0.181374	+	0.676897i
$302$	5.63813	−	3.25517i	0.324438	−	0.187314i
$303$		0			0
$304$	−1.13029	+	4.21829i	−0.0648264	+	0.241935i
$305$	−16.2554	−	4.35562i	−0.930781	−	0.249402i
$306$		0			0
$307$	6.92368	−	6.92368i	0.395155	−	0.395155i	−0.481365	−	0.876520i	$-0.659859\pi$
$307$	6.92368	−	6.92368i	0.395155	−	0.395155i	0.876520	+	0.481365i	$0.159859\pi$
$308$	−10.2414	−	5.91289i	−0.583560	−	0.336918i
$309$		0			0
$310$	−4.67846	−	1.25359i	−0.265719	−	0.0711991i
$311$	−7.54546	+	13.0691i	−0.427864	+	0.741082i	−0.996683	−	0.0813809i	$-0.974067\pi$
$311$	−7.54546	+	13.0691i	−0.427864	+	0.741082i	0.568819	+	0.822462i	$0.307400\pi$
$312$		0			0
$313$	−13.2146	−	22.8883i	−0.746933	−	1.29373i	−0.949286	−	0.314413i	$-0.898192\pi$
$313$	−13.2146	−	22.8883i	−0.746933	−	1.29373i	0.202353	−	0.979313i	$-0.435141\pi$
$314$	2.65170	+	9.89627i	0.149644	+	0.558479i
$315$		0			0
$316$	−9.10187	+	5.25497i	−0.512020	+	0.295615i
$317$	29.4867	+	7.90095i	1.65614	+	0.443761i	0.961323	−	0.275425i	$-0.0888185\pi$
$317$	29.4867	+	7.90095i	1.65614	+	0.443761i	0.694817	+	0.719186i	$0.255485\pi$
$318$		0			0
$319$	24.9959	−	24.9959i	1.39950	−	1.39950i
$320$	−1.83272	+	0.491075i	−0.102452	+	0.0274519i
$321$		0			0
$322$		−	12.1672i		−	0.678050i
$323$	−9.39086	+	2.51627i	−0.522521	+	0.140009i
$324$		0			0
$325$	4.99739	−	0.711210i	0.277206	−	0.0394509i
$326$	13.9287	−	8.04176i	0.771441	−	0.445392i
$327$		0			0
$328$	−5.59989	−	9.69930i	−0.309202	−	0.535554i
$329$	11.6065			0.639884
$330$		0			0
$331$	10.1636	−	2.72333i	0.558642	−	0.149688i	0.0315596	−	0.999502i	$-0.489953\pi$
$331$	10.1636	−	2.72333i	0.558642	−	0.149688i	0.527082	+	0.849814i	$0.323286\pi$
$332$	−0.723746	+	2.70106i	−0.0397207	+	0.148240i
$333$		0			0
$334$	2.83072	+	4.90295i	0.154890	+	0.268277i
$335$	−26.2984			−1.43683
$336$		0			0
$337$	−0.605437	−	0.349549i	−0.0329803	−	0.0190412i	0.483419	−	0.875389i	$-0.339395\pi$
$337$	−0.605437	−	0.349549i	−0.0329803	−	0.0190412i	−0.516399	+	0.856348i	$0.672728\pi$
$338$	12.9972	−	0.272128i	0.706952	−	0.0148018i
$339$		0			0
$340$	−2.98680	−	2.98680i	−0.161982	−	0.161982i
$341$	−12.7518	−	7.36226i	−0.690549	−	0.398689i
$342$		0			0
$343$	−14.2023	−	14.2023i	−0.766855	−	0.766855i
$344$	1.53483	+	5.72808i	0.0827527	+	0.308837i
$345$		0			0
$346$	2.90303	+	10.8343i	0.156068	+	0.582454i
$347$		−	23.1261i		−	1.24147i	−0.784019	−	0.620737i	$-0.786834\pi$
$347$		−	23.1261i		−	1.24147i	0.784019	−	0.620737i	$-0.213166\pi$
$348$		0			0
$349$	−2.29084	+	2.29084i	−0.122626	+	0.122626i	−0.765756	−	0.643131i	$-0.777635\pi$
$349$	−2.29084	+	2.29084i	−0.122626	+	0.122626i	0.643131	+	0.765756i	$0.277635\pi$
$350$	−2.87027			−0.153422
$351$		0			0
$352$	−5.76811			−0.307441
$353$	8.06932	−	8.06932i	0.429487	−	0.429487i	−0.458967	−	0.888453i	$-0.651780\pi$
$353$	8.06932	−	8.06932i	0.429487	−	0.429487i	0.888453	+	0.458967i	$0.151780\pi$
$354$		0			0
$355$		−	12.6389i		−	0.670805i
$356$	3.42511	+	12.7827i	0.181531	+	0.677482i
$357$		0			0
$358$	−2.88563	−	10.7693i	−0.152510	−	0.569176i
$359$	20.7218	+	20.7218i	1.09366	+	1.09366i	0.995135	+	0.0985204i	$0.0314110\pi$
$359$	20.7218	+	20.7218i	1.09366	+	1.09366i	0.0985204	+	0.995135i	$0.468589\pi$
$360$		0			0
$361$	−0.0619225	−	0.0357510i	−0.00325908	−	0.00188163i
$362$	1.42525	+	1.42525i	0.0749094	+	0.0749094i
$363$		0			0
$364$	−7.33856	−	0.888099i	−0.384645	−	0.0465490i
$365$	13.9969	+	8.08113i	0.732633	+	0.422986i
$366$		0			0
$367$	−12.3031			−0.642218			−0.321109	−	0.947042i	$-0.604056\pi$
$367$	−12.3031			−0.642218			−0.321109	+	0.947042i	$0.604056\pi$
$368$	−2.96731	−	5.13954i	−0.154682	−	0.267917i
$369$		0			0
$370$	1.11105	−	4.14650i	0.0577608	−	0.215566i
$371$	5.41747	−	1.45161i	0.281261	−	0.0753637i
$372$		0			0
$373$	28.3376			1.46727			0.733633	−	0.679546i	$-0.237823\pi$
$373$	28.3376			1.46727			0.733633	+	0.679546i	$0.237823\pi$
$374$	−6.42056	−	11.1207i	−0.331999	−	0.575039i
$375$		0			0
$376$	4.90268	−	2.83056i	0.252836	−	0.145975i
$377$	8.24178	−	20.5018i	0.424473	−	1.05590i
$378$		0			0
$379$	−17.5171	+	4.69369i	−0.899793	+	0.241099i	−0.678927	−	0.734206i	$-0.737555\pi$
$379$	−17.5171	+	4.69369i	−0.899793	+	0.241099i	−0.220866	+	0.975304i	$0.570888\pi$
$380$		−	8.28598i		−	0.425062i
$381$		0			0
$382$	−0.542094	+	0.145254i	−0.0277359	+	0.00743182i
$383$	−14.2918	+	14.2918i	−0.730279	+	0.730279i	−0.970675	−	0.240396i	$-0.922723\pi$
$383$	−14.2918	+	14.2918i	−0.730279	+	0.730279i	0.240396	+	0.970675i	$0.422723\pi$
$384$		0			0
$385$	21.6733	+	5.80735i	1.10457	+	0.295970i
$386$	7.72646	−	4.46087i	0.393266	−	0.227052i
$387$		0			0
$388$	−1.62163	−	6.05201i	−0.0823259	−	0.307244i
$389$	13.1281	+	22.7385i	0.665620	+	1.15289i	0.979117	+	0.203298i	$0.0651660\pi$
$389$	13.1281	+	22.7385i	0.665620	+	1.15289i	−0.313497	+	0.949589i	$0.601501\pi$
$390$		0			0
$391$	6.60591	−	11.4418i	0.334075	−	0.578635i
$392$	−2.70138	−	0.723833i	−0.136440	−	0.0365591i
$393$		0			0
$394$	−8.43415	−	4.86946i	−0.424906	−	0.245320i
$395$	14.1006	−	14.1006i	0.709477	−	0.709477i
$396$		0			0
$397$	−29.4918	−	7.90232i	−1.48015	−	0.396606i	−0.573754	−	0.819028i	$-0.694513\pi$
$397$	−29.4918	−	7.90232i	−1.48015	−	0.396606i	−0.906399	+	0.422422i	$0.861180\pi$
$398$	−2.21753	+	8.27594i	−0.111155	+	0.414835i
$399$		0			0
$400$	−1.21243	+	0.699997i	−0.0606215	+	0.0349998i
$401$	0.794274	−	2.96427i	0.0396641	−	0.148029i	−0.943254	−	0.332072i	$-0.892252\pi$
$401$	0.794274	−	2.96427i	0.0396641	−	0.148029i	0.982918	+	0.184044i	$0.0589188\pi$
$402$		0			0
$403$	−9.13739	−	1.10579i	−0.455166	−	0.0550833i
$404$			3.52832i			0.175540i
$405$		0			0
$406$	−6.28226	+	10.8812i	−0.311783	+	0.540025i
$407$	6.52515	−	11.3019i	0.323439	−	0.560214i
$408$		0			0
$409$	−12.9762	−	12.9762i	−0.641633	−	0.641633i	0.309324	−	0.950957i	$-0.399897\pi$
$409$	−12.9762	−	12.9762i	−0.641633	−	0.641633i	−0.950957	+	0.309324i	$0.899897\pi$
$410$	15.0261	+	15.0261i	0.742087	+	0.742087i
$411$		0			0
$412$	1.20650	−	2.08972i	0.0594400	−	0.102953i
$413$	−6.75236	+	11.6954i	−0.332262	+	0.575494i
$414$		0			0
$415$		−	5.30568i		−	0.260446i
$416$	−3.31647	+	1.41458i	−0.162603	+	0.0693553i
$417$		0			0
$418$	6.51962	−	24.3316i	0.318885	−	1.19010i
$419$	−16.4771	+	9.51305i	−0.804958	+	0.464743i	−0.845202	−	0.534447i	$-0.820520\pi$
$419$	−16.4771	+	9.51305i	−0.804958	+	0.464743i	0.0402436	+	0.999190i	$0.487187\pi$
$420$		0			0
$421$	8.19483	−	30.5835i	0.399392	−	1.49055i	−0.414777	−	0.909923i	$-0.636141\pi$
$421$	8.19483	−	30.5835i	0.399392	−	1.49055i	0.814169	−	0.580628i	$-0.197193\pi$
$422$	−12.4058	−	3.32413i	−0.603906	−	0.161816i
$423$		0			0
$424$	1.93438	−	1.93438i	0.0939418	−	0.0939418i
$425$	−2.69914	−	1.55835i	−0.130928	−	0.0755911i
$426$		0			0
$427$	17.5648	+	4.70646i	0.850018	+	0.227762i
$428$	−6.90393	+	11.9580i	−0.333714	+	0.578010i
$429$		0			0
$430$	−5.62584	−	9.74423i	−0.271302	−	0.469909i
$431$	−2.93713	−	10.9615i	−0.141477	−	0.527999i	−0.999887	−	0.0150347i	$-0.995214\pi$
$431$	−2.93713	−	10.9615i	−0.141477	−	0.527999i	0.858410	−	0.512964i	$-0.171453\pi$
$432$		0			0
$433$	19.3513	−	11.1725i	0.929963	−	0.536915i	0.0431634	−	0.999068i	$-0.486256\pi$
$433$	19.3513	−	11.1725i	0.929963	−	0.536915i	0.886800	+	0.462153i	$0.152923\pi$
$434$	5.05531	+	1.35457i	0.242663	+	0.0650212i
$435$		0			0
$436$	−8.53541	+	8.53541i	−0.408772	+	0.408772i
$437$	25.0340	−	6.70783i	1.19754	−	0.320879i
$438$		0			0
$439$			31.5696i			1.50674i	0.657599	+	0.753368i	$0.271572\pi$
$439$			31.5696i			1.50674i	−0.657599	+	0.753368i	$0.728428\pi$
$440$	10.5713	−	2.83258i	0.503968	−	0.135038i
$441$		0			0
$442$	−6.41886	−	4.81946i	−0.305314	−	0.229239i
$443$	−4.41781	+	2.55062i	−0.209897	+	0.121184i	−0.601263	−	0.799051i	$-0.705336\pi$
$443$	−4.41781	+	2.55062i	−0.209897	+	0.121184i	0.391367	+	0.920235i	$0.372002\pi$
$444$		0			0
$445$	−12.5545	−	21.7451i	−0.595142	−	1.03082i
$446$	−12.0699			−0.571528
$447$		0			0
$448$	1.98034	−	0.530631i	0.0935624	−	0.0250700i
$449$	7.26523	−	27.1142i	0.342867	−	1.27960i	−0.552216	−	0.833701i	$-0.686218\pi$
$449$	7.26523	−	27.1142i	0.342867	−	1.27960i	0.895084	−	0.445898i	$-0.147116\pi$
$450$		0			0
$451$	32.3008	+	55.9466i	1.52099	+	2.63442i
$452$	9.18211			0.431890
$453$		0			0
$454$	−11.1313	−	6.42669i	−0.522420	−	0.301619i
$455$	13.8856	−	1.97615i	0.650968	−	0.0926434i
$456$		0			0
$457$	25.1956	+	25.1956i	1.17860	+	1.17860i	0.980101	+	0.198498i	$0.0636062\pi$
$457$	25.1956	+	25.1956i	1.17860	+	1.17860i	0.198498	+	0.980101i	$0.436394\pi$
$458$	−16.8493	−	9.72795i	−0.787316	−	0.454557i
$459$		0			0
$460$	7.96214	+	7.96214i	0.371237	+	0.371237i
$461$	−4.60677	−	17.1927i	−0.214559	−	0.800743i	−0.986321	−	0.164833i	$-0.947291\pi$
$461$	−4.60677	−	17.1927i	−0.214559	−	0.800743i	0.771763	−	0.635910i	$-0.219375\pi$
$462$		0			0
$463$	7.13200	+	26.6170i	0.331452	+	1.23700i	0.907665	+	0.419696i	$0.137863\pi$
$463$	7.13200	+	26.6170i	0.331452	+	1.23700i	−0.576212	+	0.817300i	$0.695470\pi$
$464$			6.12844i			0.284506i
$465$		0			0
$466$	−2.83131	+	2.83131i	−0.131158	+	0.131158i
$467$	−16.8628			−0.780315			−0.390158	−	0.920748i	$-0.627580\pi$
$467$	−16.8628			−0.780315			−0.390158	+	0.920748i	$0.627580\pi$
$468$		0			0
$469$	28.4167			1.31216
$470$	−7.59521	+	7.59521i	−0.350341	+	0.350341i
$471$		0			0
$472$			6.58702i			0.303192i
$473$	−8.85310	−	33.0402i	−0.407066	−	1.51919i
$474$		0			0
$475$	−1.58239	−	5.90558i	−0.0726052	−	0.270966i
$476$	3.22738	+	3.22738i	0.147927	+	0.147927i
$477$		0			0
$478$	−7.94585	−	4.58754i	−0.363435	−	0.209829i
$479$	−26.9687	−	26.9687i	−1.23223	−	1.23223i	−0.963104	−	0.269128i	$-0.913264\pi$
$479$	−26.9687	−	26.9687i	−1.23223	−	1.23223i	−0.269128	−	0.963104i	$-0.586736\pi$
$480$		0			0
$481$	0.980057	−	8.09844i	0.0446868	−	0.369257i
$482$	−16.7679	−	9.68096i	−0.763757	−	0.440956i
$483$		0			0
$484$	22.2711			1.01232
$485$	5.94398	+	10.2953i	0.269902	+	0.467485i
$486$		0			0
$487$	−3.49748	+	13.0528i	−0.158486	+	0.591478i	0.840296	+	0.542128i	$0.182381\pi$
$487$	−3.49748	+	13.0528i	−0.158486	+	0.591478i	−0.998782	+	0.0493492i	$0.984285\pi$
$488$	8.56734	−	2.29561i	0.387825	−	0.103917i
$489$		0			0
$490$	5.30633			0.239715
$491$	15.2485	+	26.4112i	0.688155	+	1.19192i	0.972434	+	0.233178i	$0.0749124\pi$
$491$	15.2485	+	26.4112i	0.688155	+	1.19192i	−0.284279	+	0.958742i	$0.591754\pi$
$492$		0			0
$493$	−11.8154	+	6.82164i	−0.532140	+	0.307231i
$494$	−2.21853	−	15.5887i	−0.0998162	−	0.701369i
$495$		0			0
$496$	2.46576	−	0.660699i	0.110716	−	0.0296663i
$497$			13.6570i			0.612600i
$498$		0			0
$499$	0.802501	−	0.215030i	0.0359249	−	0.00962605i	−0.240812	−	0.970572i	$-0.577414\pi$
$499$	0.802501	−	0.215030i	0.0359249	−	0.00962605i	0.276737	+	0.960946i	$0.410747\pi$
$500$	8.58650	−	8.58650i	0.384000	−	0.384000i
$501$		0			0
$502$	14.6547	+	3.92672i	0.654072	+	0.175258i
$503$	−1.71989	+	0.992977i	−0.0766860	+	0.0442747i	−0.537853	−	0.843039i	$-0.680764\pi$
$503$	−1.71989	+	0.992977i	−0.0766860	+	0.0442747i	0.461167	+	0.887314i	$0.347431\pi$
$504$		0			0
$505$	−1.73267	−	6.46640i	−0.0771027	−	0.287751i
$506$	17.1158	+	29.6454i	0.760890	+	1.31790i
$507$		0			0
$508$	4.46758	−	7.73808i	0.198217	−	0.343322i
$509$	16.4919	+	4.41899i	0.730991	+	0.195868i	0.605070	−	0.796172i	$-0.293145\pi$
$509$	16.4919	+	4.41899i	0.730991	+	0.195868i	0.125920	+	0.992040i	$0.459812\pi$
$510$		0			0
$511$	−15.1244	−	8.73207i	−0.669063	−	0.386284i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	6.88691	+	1.84534i	0.303768	+	0.0813945i
$515$	−1.18497	+	4.42235i	−0.0522158	+	0.194872i
$516$		0			0
$517$	−28.2792	+	16.3270i	−1.24372	+	0.718061i
$518$	−1.20055	+	4.48050i	−0.0527490	+	0.196862i
$519$		0			0
$520$	5.38349	−	4.22115i	0.236082	−	0.185110i
$521$			14.9970i			0.657030i	0.944499	+	0.328515i	$0.106548\pi$
$521$			14.9970i			0.657030i	−0.944499	+	0.328515i	$0.893452\pi$
$522$		0			0
$523$	−18.1632	+	31.4596i	−0.794221	+	1.37563i	0.129112	+	0.991630i	$0.458787\pi$
$523$	−18.1632	+	31.4596i	−0.794221	+	1.37563i	−0.923333	+	0.384001i	$0.874546\pi$
$524$	−9.33646	+	16.1712i	−0.407865	+	0.706443i
$525$		0			0
$526$	7.31576	+	7.31576i	0.318982	+	0.318982i
$527$	4.01848	+	4.01848i	0.175048	+	0.175048i
$528$		0			0
$529$	−6.10989	+	10.5826i	−0.265648	+	0.460115i
$530$	−2.59524	+	4.49510i	−0.112730	+	0.195254i
$531$		0			0
$532$			8.95342i			0.388180i
$533$	32.2923	+	24.2460i	1.39873	+	1.05021i
$534$		0			0
$535$	6.78070	−	25.3059i	0.293155	−	1.09407i
$536$	12.0035	−	6.93022i	0.518472	−	0.299340i
$537$		0			0
$538$	−5.05273	+	18.8570i	−0.217839	+	0.812985i
$539$	15.5819	+	4.17515i	0.671159	+	0.179836i
$540$		0			0
$541$	−12.6107	+	12.6107i	−0.542176	+	0.542176i	−0.924166	−	0.381990i	$-0.875239\pi$
$541$	−12.6107	+	12.6107i	−0.542176	+	0.542176i	0.381990	+	0.924166i	$0.375239\pi$
$542$	−14.0149	−	8.09152i	−0.601992	−	0.347560i
$543$		0			0
$544$	2.15037	+	0.576189i	0.0921963	+	0.0247039i
$545$	11.4515	−	19.8345i	0.490527	−	0.849618i
$546$		0			0
$547$	3.89564	+	6.74745i	0.166566	+	0.288500i	0.937210	−	0.348765i	$-0.113399\pi$
$547$	3.89564	+	6.74745i	0.166566	+	0.288500i	−0.770644	+	0.637265i	$0.780066\pi$
$548$	2.67413	+	9.98001i	0.114233	+	0.426325i
$549$		0			0
$550$	6.99343	−	4.03766i	0.298201	−	0.172166i
$551$	−25.8515	−	6.92689i	−1.10131	−	0.295095i
$552$		0			0
$553$	−15.2364	+	15.2364i	−0.647916	+	0.647916i
$554$	29.7869	−	7.98136i	1.26552	−	0.339096i
$555$		0			0
$556$			18.6932i			0.792769i
$557$	18.3374	−	4.91350i	0.776982	−	0.208192i	0.151528	−	0.988453i	$-0.451581\pi$
$557$	18.3374	−	4.91350i	0.776982	−	0.208192i	0.625454	+	0.780261i	$0.284914\pi$
$558$		0			0
$559$	−13.1930	−	16.8259i	−0.558006	−	0.711659i
$560$	−3.36883	+	1.94499i	−0.142359	+	0.0821909i
$561$		0			0
$562$	−4.54832	−	7.87793i	−0.191859	−	0.332310i
$563$	−29.3305			−1.23613			−0.618066	−	0.786126i	$-0.712084\pi$
$563$	−29.3305			−1.23613			−0.618066	+	0.786126i	$0.712084\pi$
$564$		0			0
$565$	−16.8282	+	4.50911i	−0.707968	+	0.189700i
$566$	4.44083	−	16.5734i	0.186662	−	0.696632i
$567$		0			0
$568$	3.33065	+	5.76885i	0.139751	+	0.242056i
$569$	4.67830			0.196124			0.0980622	−	0.995180i	$-0.468736\pi$
$569$	4.67830			0.196124			0.0980622	+	0.995180i	$0.468736\pi$
$570$		0			0
$571$	1.98594	+	1.14658i	0.0831088	+	0.0479829i	0.540978	−	0.841036i	$-0.318054\pi$
$571$	1.98594	+	1.14658i	0.0831088	+	0.0479829i	−0.457870	+	0.889019i	$0.651387\pi$
$572$	19.1298	−	8.15943i	0.799856	−	0.341163i
$573$		0			0
$574$	−16.2365	−	16.2365i	−0.677697	−	0.677697i
$575$	7.19532	+	4.15422i	0.300066	+	0.173243i
$576$		0			0
$577$	13.7676	+	13.7676i	0.573154	+	0.573154i	0.933008	−	0.359854i	$-0.117174\pi$
$577$	13.7676	+	13.7676i	0.573154	+	0.573154i	−0.359854	+	0.933008i	$0.617174\pi$
$578$	−3.11720	−	11.6335i	−0.129658	−	0.483891i
$579$		0			0
$580$	−3.00952	−	11.2317i	−0.124964	−	0.466371i
$581$			5.73305i			0.237847i
$582$		0			0
$583$	−11.1577	+	11.1577i	−0.462105	+	0.462105i
$584$	−8.51825			−0.352488
$585$		0			0
$586$	−10.4836			−0.433075
$587$	12.6269	−	12.6269i	0.521170	−	0.521170i	−0.396755	−	0.917925i	$-0.629864\pi$
$587$	12.6269	−	12.6269i	0.521170	−	0.521170i	0.917925	+	0.396755i	$0.129864\pi$
$588$		0			0
$589$			11.1481i			0.459349i
$590$	−3.23472	−	12.0721i	−0.133171	−	0.497002i
$591$		0			0
$592$	0.585575	+	2.18540i	0.0240670	+	0.0898193i
$593$	1.54480	+	1.54480i	0.0634372	+	0.0634372i	0.738114	−	0.674676i	$-0.235717\pi$
$593$	1.54480	+	1.54480i	0.0634372	+	0.0634372i	−0.674676	+	0.738114i	$0.735717\pi$
$594$		0			0
$595$	−7.49977	−	4.32999i	−0.307460	−	0.177512i
$596$	−3.87791	−	3.87791i	−0.158845	−	0.158845i
$597$		0			0
$598$	17.1113	+	12.8476i	0.699732	+	0.525379i
$599$	−6.23611	−	3.60042i	−0.254801	−	0.147109i	0.367160	−	0.930158i	$-0.380330\pi$
$599$	−6.23611	−	3.60042i	−0.254801	−	0.147109i	−0.621960	+	0.783049i	$0.713664\pi$
$600$		0			0
$601$	7.62636			0.311086			0.155543	−	0.987829i	$-0.450287\pi$
$601$	7.62636			0.311086			0.155543	+	0.987829i	$0.450287\pi$
$602$	6.07899	+	10.5291i	0.247761	+	0.429135i
$603$		0			0
$604$	1.68500	−	6.28851i	0.0685618	−	0.255876i
$605$	−40.8166	+	10.9368i	−1.65943	+	0.444643i
$606$		0			0
$607$	−41.8829			−1.69997			−0.849987	−	0.526804i	$-0.823390\pi$
$607$	−41.8829			−1.69997			−0.849987	+	0.526804i	$0.823390\pi$
$608$	2.18355	+	3.78201i	0.0885545	+	0.153381i
$609$		0			0
$610$	−14.5742	+	8.41441i	−0.590092	+	0.340690i
$611$	−12.2555	+	16.3227i	−0.495806	+	0.660346i
$612$		0			0
$613$	−27.6735	+	7.41508i	−1.11772	+	0.299492i	−0.769961	−	0.638091i	$-0.779724\pi$
$613$	−27.6735	+	7.41508i	−1.11772	+	0.299492i	−0.347760	+	0.937584i	$0.613058\pi$
$614$		−	9.79156i		−	0.395155i
$615$		0			0
$616$	−11.4228	+	3.06074i	−0.460239	+	0.123321i
$617$	6.98237	−	6.98237i	0.281100	−	0.281100i	−0.552448	−	0.833547i	$-0.686306\pi$
$617$	6.98237	−	6.98237i	0.281100	−	0.281100i	0.833547	+	0.552448i	$0.186306\pi$
$618$		0			0
$619$	37.7062	+	10.1033i	1.51554	+	0.406088i	0.918271	−	0.395953i	$-0.129586\pi$
$619$	37.7062	+	10.1033i	1.51554	+	0.406088i	0.597269	+	0.802041i	$0.296252\pi$
$620$	−4.19459	+	2.42175i	−0.168459	+	0.0972598i
$621$		0			0
$622$	3.90582	+	14.5767i	0.156609	+	0.584473i
$623$	13.5658	+	23.4966i	0.543502	+	0.941373i
$624$		0			0
$625$	−8.02002	+	13.8911i	−0.320801	+	0.555644i
$626$	−25.5286	−	6.84038i	−1.02033	−	0.273396i
$627$		0			0
$628$	8.87276	+	5.12269i	0.354062	+	0.204418i
$629$	−3.56156	+	3.56156i	−0.142009	+	0.142009i
$630$		0			0
$631$	−28.3493	−	7.59618i	−1.12857	−	0.302399i	−0.354223	−	0.935161i	$-0.615254\pi$
$631$	−28.3493	−	7.59618i	−1.12857	−	0.302399i	−0.774346	+	0.632762i	$0.781921\pi$
$632$	−2.72017	+	10.1518i	−0.108203	+	0.403818i
$633$		0			0
$634$	26.4371	−	15.2635i	1.04995	−	0.606189i
$635$	−4.38784	+	16.3756i	−0.174126	+	0.649847i
$636$		0			0
$637$	9.98297	−	1.42074i	0.395540	−	0.0562917i
$638$		−	35.3495i		−	1.39950i
$639$		0			0
$640$	−0.948684	+	1.64317i	−0.0375000	+	0.0649520i
$641$	6.79302	−	11.7659i	0.268308	−	0.464723i	−0.700117	−	0.714028i	$-0.746869\pi$
$641$	6.79302	−	11.7659i	0.268308	−	0.464723i	0.968425	+	0.249305i	$0.0802021\pi$
$642$		0			0
$643$	13.2878	+	13.2878i	0.524018	+	0.524018i	0.918782	−	0.394764i	$-0.129174\pi$
$643$	13.2878	+	13.2878i	0.524018	+	0.524018i	−0.394764	+	0.918782i	$0.629174\pi$
$644$	−8.60349	−	8.60349i	−0.339025	−	0.339025i
$645$		0			0
$646$	−4.86107	+	8.41961i	−0.191256	+	0.331265i
$647$	−11.7916	+	20.4237i	−0.463576	+	0.802937i	−0.999136	−	0.0415601i	$-0.986767\pi$
$647$	−11.7916	+	20.4237i	−0.463576	+	0.802937i	0.535560	+	0.844497i	$0.320101\pi$
$648$		0			0
$649$		−	37.9947i		−	1.49142i
$650$	3.03079	−	4.03659i	0.118877	−	0.158328i
$651$		0			0
$652$	4.16272	−	15.5355i	0.163025	−	0.608416i
$653$	−33.1389	+	19.1327i	−1.29683	+	0.748722i	−0.979854	−	0.199713i	$-0.935999\pi$
$653$	−33.1389	+	19.1327i	−1.29683	+	0.748722i	−0.316971	+	0.948435i	$0.602666\pi$
$654$		0			0
$655$	9.16981	−	34.2222i	0.358294	−	1.33717i
$656$	−10.8182	−	2.89872i	−0.422378	−	0.113176i
$657$		0			0
$658$	8.20700	−	8.20700i	0.319942	−	0.319942i
$659$	−31.8257	−	18.3746i	−1.23975	−	0.715771i	−0.270708	−	0.962661i	$-0.587258\pi$
$659$	−31.8257	−	18.3746i	−1.23975	−	0.715771i	−0.969043	+	0.246890i	$0.920591\pi$
$660$		0			0
$661$	5.70295	+	1.52810i	0.221819	+	0.0594363i	0.368017	−	0.929819i	$-0.380037\pi$
$661$	5.70295	+	1.52810i	0.221819	+	0.0594363i	−0.146198	+	0.989255i	$0.546704\pi$
$662$	5.26107	−	9.11243i	0.204477	−	0.354165i
$663$		0			0
$664$	1.39817	+	2.42170i	0.0542595	+	0.0939802i
$665$	−4.39680	−	16.4091i	−0.170501	−	0.636317i
$666$		0			0
$667$	31.4973	−	18.1850i	1.21958	−	0.704126i
$668$	5.46853	+	1.46529i	0.211584	+	0.0566937i
$669$		0			0
$670$	−18.5958	+	18.5958i	−0.718417	+	0.718417i
$671$	−49.4174	+	13.2413i	−1.90774	+	0.511176i
$672$		0			0
$673$			21.4564i			0.827085i	0.910485	+	0.413543i	$0.135709\pi$
$673$			21.4564i			0.827085i	−0.910485	+	0.413543i	$0.864291\pi$
$674$	−0.675277	+	0.180940i	−0.0260107	+	0.00696955i
$675$		0			0
$676$	8.99795	−	9.38280i	0.346075	−	0.360877i
$677$	−12.9054	+	7.45094i	−0.495995	+	0.286363i	−0.727058	−	0.686576i	$-0.759113\pi$
$677$	−12.9054	+	7.45094i	−0.495995	+	0.286363i	0.231063	+	0.972939i	$0.425780\pi$
$678$		0			0
$679$	−6.42277	−	11.1246i	−0.246483	−	0.426922i
$680$	−4.22397			−0.161982
$681$		0			0
$682$	−14.2228	+	3.81099i	−0.544619	+	0.145930i
$683$	6.54752	−	24.4357i	0.250534	−	0.935005i	−0.719987	−	0.693988i	$-0.755852\pi$
$683$	6.54752	−	24.4357i	0.250534	−	0.935005i	0.970521	−	0.241018i	$-0.0774811\pi$
$684$		0			0
$685$	−9.80186	−	16.9773i	−0.374510	−	0.648670i
$686$	−20.0852			−0.766855
$687$		0			0
$688$	5.13566	+	2.96507i	0.195795	+	0.113042i
$689$	−3.67899	+	9.15164i	−0.140158	+	0.348650i
$690$		0			0
$691$	27.0050	+	27.0050i	1.02732	+	1.02732i	0.999616	+	0.0277021i	$0.00881897\pi$
$691$	27.0050	+	27.0050i	1.02732	+	1.02732i	0.0277021	+	0.999616i	$0.491181\pi$
$692$	9.71374	+	5.60823i	0.369261	+	0.213193i
$693$		0			0
$694$	−16.3526	−	16.3526i	−0.620737	−	0.620737i
$695$	−9.17977	−	34.2594i	−0.348209	−	1.29953i
$696$		0			0
$697$	−6.45320	−	24.0837i	−0.244432	−	0.912234i
$698$			3.23974i			0.122626i
$699$		0			0
$700$	−2.02959	+	2.02959i	−0.0767111	+	0.0767111i
$701$	5.62024			0.212274			0.106137	−	0.994352i	$-0.466152\pi$
$701$	5.62024			0.212274			0.106137	+	0.994352i	$0.466152\pi$
$702$		0			0
$703$	−9.88050			−0.372650
$704$	−4.07867	+	4.07867i	−0.153721	+	0.153721i
$705$		0			0
$706$		−	11.4117i		−	0.429487i
$707$	1.87223	+	6.98727i	0.0704126	+	0.262783i
$708$		0			0
$709$	−2.25710	−	8.42362i	−0.0847672	−	0.316356i	0.910503	−	0.413503i	$-0.135695\pi$
$709$	−2.25710	−	8.42362i	−0.0847672	−	0.316356i	−0.995270	+	0.0971473i	$0.969028\pi$
$710$	−8.93707	−	8.93707i	−0.335402	−	0.335402i
$711$		0			0
$712$	11.4607	+	6.61681i	0.429506	+	0.247976i
$713$	−10.7124	−	10.7124i	−0.401182	−	0.401182i
$714$		0			0
$715$	−31.0526	+	24.3481i	−1.16130	+	0.910567i
$716$	−9.65551	−	5.57461i	−0.360843	−	0.208333i
$717$		0			0
$718$	29.3051			1.09366
$719$	17.1214	+	29.6552i	0.638522	+	1.10595i	0.985757	+	0.168175i	$0.0537873\pi$
$719$	17.1214	+	29.6552i	0.638522	+	1.10595i	−0.347235	+	0.937778i	$0.612879\pi$
$720$		0			0
$721$	1.28041	−	4.77857i	0.0476851	−	0.177963i
$722$	−0.0690656	+	0.0185061i	−0.00257036	+	0.000688725i
$723$		0			0
$724$	2.01561			0.0749094
$725$	−4.28989	−	7.43030i	−0.159322	−	0.275954i
$726$		0			0
$727$	27.5561	−	15.9095i	1.02200	−	0.590052i	0.107318	−	0.994225i	$-0.465774\pi$
$727$	27.5561	−	15.9095i	1.02200	−	0.590052i	0.914683	+	0.404172i	$0.132440\pi$
$728$	−5.81713	+	4.56117i	−0.215597	+	0.169048i
$729$		0			0
$730$	15.6115	−	4.18310i	0.577809	−	0.154824i
$731$			13.2018i			0.488288i
$732$		0			0
$733$	−12.2727	+	3.28845i	−0.453301	+	0.121462i	−0.478244	−	0.878227i	$-0.658726\pi$
$733$	−12.2727	+	3.28845i	−0.453301	+	0.121462i	0.0249426	+	0.999689i	$0.492060\pi$
$734$	−8.69962	+	8.69962i	−0.321109	+	0.321109i
$735$		0			0
$736$	−5.73241	−	1.53599i	−0.211299	−	0.0566175i
$737$	−69.2375	+	39.9743i	−2.55040	+	1.47247i
$738$		0			0
$739$	−7.36509	−	27.4869i	−0.270929	−	1.01112i	−0.958521	−	0.285024i	$-0.907999\pi$
$739$	−7.36509	−	27.4869i	−0.270929	−	1.01112i	0.687591	−	0.726098i	$-0.258668\pi$
$740$	−2.14639	−	3.71765i	−0.0789028	−	0.136664i
$741$		0			0
$742$	2.80429	−	4.85717i	0.102949	−	0.178312i
$743$	25.1804	+	6.74708i	0.923781	+	0.247526i	0.689201	−	0.724571i	$-0.257962\pi$
$743$	25.1804	+	6.74708i	0.923781	+	0.247526i	0.234580	+	0.972097i	$0.424629\pi$
$744$		0			0
$745$	9.01145	+	5.20276i	0.330154	+	0.190615i
$746$	20.0377	−	20.0377i	0.733633	−	0.733633i
$747$		0			0
$748$	−12.4036	−	3.32352i	−0.453519	−	0.121520i
$749$	−7.32688	+	27.3443i	−0.267718	+	0.999138i
$750$		0			0
$751$	−23.5480	+	13.5954i	−0.859279	+	0.496105i	−0.863771	−	0.503885i	$-0.831904\pi$
$751$	−23.5480	+	13.5954i	−0.859279	+	0.496105i	0.00449183	+	0.999990i	$0.498570\pi$
$752$	1.46521	−	5.46823i	0.0534306	−	0.199406i
$753$		0			0
$754$	−8.66914	−	20.3248i	−0.315711	−	0.740185i
$755$			12.3525i			0.449555i
$756$		0			0
$757$	−22.3587	+	38.7264i	−0.812640	+	1.40753i	0.0983707	+	0.995150i	$0.468637\pi$
$757$	−22.3587	+	38.7264i	−0.812640	+	1.40753i	−0.911010	+	0.412383i	$0.864696\pi$
$758$	−9.06752	+	15.7054i	−0.329347	+	0.570446i
$759$		0			0
$760$	−5.85908	−	5.85908i	−0.212531	−	0.212531i
$761$	35.5609	+	35.5609i	1.28908	+	1.28908i	0.935345	+	0.353737i	$0.115089\pi$
$761$	35.5609	+	35.5609i	1.28908	+	1.28908i	0.353737	+	0.935345i	$0.384911\pi$
$762$		0			0
$763$	−12.3739	+	21.4322i	−0.447965	+	0.775897i
$764$	−0.280608	+	0.486028i	−0.0101521	+	0.0175839i
$765$		0			0
$766$			20.2117i			0.730279i
$767$	−9.31784	−	21.8457i	−0.336448	−	0.788801i
$768$		0			0
$769$	10.6831	−	39.8699i	0.385243	−	1.43774i	−0.452542	−	0.891743i	$-0.649483\pi$
$769$	10.6831	−	39.8699i	0.385243	−	1.43774i	0.837784	−	0.546002i	$-0.183851\pi$
$770$	19.4318	−	11.2189i	0.700272	−	0.404302i
$771$		0			0
$772$	2.30912	−	8.61775i	0.0831070	−	0.310159i
$773$	13.9509	+	3.73812i	0.501778	+	0.134451i	0.500825	−	0.865549i	$-0.333030\pi$
$773$	13.9509	+	3.73812i	0.501778	+	0.134451i	0.000952768		1.00000i	$0.499697\pi$
$774$		0			0
$775$	−2.52708	+	2.52708i	−0.0907753	+	0.0907753i
$776$	−5.42608	−	3.13275i	−0.194785	−	0.112459i
$777$		0			0
$778$	25.3615	+	6.79559i	0.909253	+	0.243634i
$779$	24.4553	−	42.3578i	0.876201	−	1.51762i
$780$		0			0
$781$	−19.2115	−	33.2754i	−0.687443	−	1.19069i
$782$	−3.41947	−	12.7616i	−0.122280	−	0.456355i
$783$		0			0
$784$	−2.42199	+	1.39834i	−0.0864998	+	0.0499407i
$785$	−18.7769	−	5.03125i	−0.670175	−	0.179573i
$786$		0			0
$787$	−19.0283	+	19.0283i	−0.678286	+	0.678286i	−0.959612	−	0.281327i	$-0.909226\pi$
$787$	−19.0283	+	19.0283i	−0.678286	+	0.678286i	0.281327	+	0.959612i	$0.409226\pi$
$788$	−9.40707	+	2.52062i	−0.335113	+	0.0897932i
$789$		0			0
$790$		−	19.9412i		−	0.709477i
$791$	18.1837	−	4.87231i	0.646539	−	0.173240i
$792$		0			0
$793$	−25.1660	+	19.7325i	−0.893671	+	0.700721i
$794$	−26.4417	+	15.2661i	−0.938380	+	0.541774i
$795$		0			0
$796$	4.28394	+	7.42000i	0.151840	+	0.262995i
$797$	−20.6809			−0.732555			−0.366278	−	0.930506i	$-0.619368\pi$
$797$	−20.6809			−0.732555			−0.366278	+	0.930506i	$0.619368\pi$
$798$		0			0
$799$	12.1735	−	3.26188i	0.430668	−	0.115397i
$800$	−0.362345	+	1.35229i	−0.0128108	+	0.0478107i
$801$		0			0
$802$	−1.53442	−	2.65769i	−0.0541822	−	0.0938463i
$803$	49.1342			1.73391
$804$		0			0
$805$	19.9927	+	11.5428i	0.704651	+	0.406830i
$806$	−7.24302	+	5.67920i	−0.255125	+	0.200041i
$807$		0			0
$808$	2.49490	+	2.49490i	0.0877701	+	0.0877701i
$809$	10.9263	+	6.30829i	0.384147	+	0.221788i	0.679621	−	0.733563i	$-0.262144\pi$
$809$	10.9263	+	6.30829i	0.384147	+	0.221788i	−0.295474	+	0.955351i	$0.595478\pi$
$810$		0			0
$811$	−0.473478	−	0.473478i	−0.0166261	−	0.0166261i	0.698745	−	0.715371i	$-0.253742\pi$
$811$	−0.473478	−	0.473478i	−0.0166261	−	0.0166261i	−0.715371	+	0.698745i	$0.753742\pi$
$812$	3.25194	+	12.1364i	0.114121	+	0.425904i
$813$		0			0
$814$	−3.37766	−	12.6056i	−0.118387	−	0.441827i
$815$			30.5164i			1.06894i
$816$		0			0
$817$	−18.3123	+	18.3123i	−0.640666	+	0.640666i
$818$	−18.3511			−0.641633
$819$		0			0
$820$	21.2501			0.742087
$821$	−35.4309	+	35.4309i	−1.23655	+	1.23655i	−0.275145	+	0.961403i	$0.588726\pi$
$821$	−35.4309	+	35.4309i	−1.23655	+	1.23655i	−0.961403	+	0.275145i	$0.911274\pi$
$822$		0			0
$823$			31.6644i			1.10375i	0.833926	+	0.551877i	$0.186088\pi$
$823$			31.6644i			1.10375i	−0.833926	+	0.551877i	$0.813912\pi$
$824$	−0.624531	−	2.33078i	−0.0217566	−	0.0811966i
$825$		0			0
$826$	3.49528	+	13.0446i	0.121616	+	0.453878i
$827$	20.7929	+	20.7929i	0.723039	+	0.723039i	0.969223	−	0.246184i	$-0.0791769\pi$
$827$	20.7929	+	20.7929i	0.723039	+	0.723039i	−0.246184	+	0.969223i	$0.579177\pi$
$828$		0			0
$829$	1.10256	+	0.636564i	0.0382935	+	0.0221088i	0.519025	−	0.854759i	$-0.326295\pi$
$829$	1.10256	+	0.636564i	0.0382935	+	0.0221088i	−0.480731	+	0.876868i	$0.659629\pi$
$830$	−3.75168	−	3.75168i	−0.130223	−	0.130223i
$831$		0			0
$832$	−1.34484	+	3.34535i	−0.0466240	+	0.115979i
$833$	−5.39190	−	3.11302i	−0.186818	−	0.107860i
$834$		0			0
$835$	−10.7418			−0.371736
$836$	−12.5949	−	21.8151i	−0.435605	−	0.754490i
$837$		0			0
$838$	−4.92432	+	18.3778i	−0.170108	+	0.634851i
$839$	44.0635	−	11.8068i	1.52124	−	0.407616i	0.601091	−	0.799180i	$-0.294733\pi$
$839$	44.0635	−	11.8068i	1.52124	−	0.407616i	0.920151	+	0.391565i	$0.128066\pi$
$840$		0			0
$841$	−8.55774			−0.295094
$842$	−15.8312	−	27.4205i	−0.545579	−	0.944971i
$843$		0			0
$844$	−11.1228	+	6.42173i	−0.382861	+	0.221045i
$845$	−11.8830	+	21.6147i	−0.408789	+	0.743568i
$846$		0			0
$847$	44.1044	−	11.8177i	1.51545	−	0.406062i
$848$		−	2.73563i		−	0.0939418i
$849$		0			0
$850$	−3.01050	+	0.806662i	−0.103259	+	0.0276683i
$851$	9.49434	−	9.49434i	0.325462	−	0.325462i
$852$		0			0
$853$	−11.3909	−	3.05217i	−0.390016	−	0.104504i	0.0584818	−	0.998288i	$-0.481374\pi$
$853$	−11.3909	−	3.05217i	−0.390016	−	0.104504i	−0.448498	+	0.893784i	$0.648041\pi$
$854$	15.7481	−	9.09219i	0.538890	−	0.311128i
$855$		0			0
$856$	3.57374	+	13.3374i	0.122148	+	0.455862i
$857$	−21.4436	−	37.1414i	−0.732499	−	1.26872i	−0.955812	−	0.293978i	$-0.905021\pi$
$857$	−21.4436	−	37.1414i	−0.732499	−	1.26872i	0.223314	−	0.974747i	$-0.428313\pi$
$858$		0			0
$859$	−9.82545	+	17.0182i	−0.335240	+	0.580653i	−0.983531	−	0.180740i	$-0.942151\pi$
$859$	−9.82545	+	17.0182i	−0.335240	+	0.580653i	0.648291	+	0.761393i	$0.275484\pi$
$860$	−10.8683	−	2.91215i	−0.370605	−	0.0993034i
$861$		0			0
$862$	−9.82784	−	5.67411i	−0.334738	−	0.193261i
$863$	13.1900	−	13.1900i	0.448992	−	0.448992i	−0.446027	−	0.895019i	$-0.647162\pi$
$863$	13.1900	−	13.1900i	0.448992	−	0.448992i	0.895019	+	0.446027i	$0.147162\pi$
$864$		0			0
$865$	−20.5566	−	5.50812i	−0.698945	−	0.187282i
$866$	5.78330	−	21.5836i	0.196524	−	0.733439i
$867$		0			0
$868$	4.53247	−	2.61682i	0.153842	−	0.0888207i
$869$	15.6902	−	58.5568i	0.532255	−	1.98640i
$870$		0			0
$871$	−30.0059	+	39.9637i	−1.01671	+	1.35412i
$872$			12.0709i			0.408772i
$873$		0			0
$874$	12.9585	−	22.4448i	0.438329	−	0.759208i
$875$	12.4479	−	21.5605i	0.420817	−	0.728877i
$876$		0			0
$877$	31.8045	+	31.8045i	1.07396	+	1.07396i	0.997037	+	0.0769245i	$0.0245100\pi$
$877$	31.8045	+	31.8045i	1.07396	+	1.07396i	0.0769245	+	0.997037i	$0.475490\pi$
$878$	22.3231	+	22.3231i	0.753368	+	0.753368i
$879$		0			0
$880$	5.47212	−	9.47798i	0.184465	−	0.319503i
$881$	−6.29938	+	10.9108i	−0.212232	+	0.367596i	−0.952413	−	0.304812i	$-0.901406\pi$
$881$	−6.29938	+	10.9108i	−0.212232	+	0.367596i	0.740181	+	0.672408i	$0.234740\pi$
$882$		0			0
$883$		−	36.0877i		−	1.21445i	−0.794531	−	0.607224i	$-0.792283\pi$
$883$		−	36.0877i		−	1.21445i	0.794531	−	0.607224i	$-0.207717\pi$
$884$	−7.94670	+	1.13094i	−0.267276	+	0.0380378i
$885$		0			0
$886$	−1.32030	+	4.92743i	−0.0443564	+	0.165540i
$887$	−15.0027	+	8.66181i	−0.503741	+	0.290835i	−0.730257	−	0.683172i	$-0.760600\pi$
$887$	−15.0027	+	8.66181i	−0.503741	+	0.290835i	0.226516	+	0.974007i	$0.427266\pi$
$888$		0			0
$889$	4.74127	−	17.6947i	0.159017	−	0.593460i
$890$	−24.2535	−	6.49870i	−0.812979	−	0.217837i
$891$		0			0
$892$	−8.53473	+	8.53473i	−0.285764	+	0.285764i
$893$	21.4105	+	12.3613i	0.716474	+	0.413656i
$894$		0			0
$895$	20.4334	+	5.47511i	0.683012	+	0.183013i
$896$	1.02510	−	1.77553i	0.0342462	−	0.0593162i
$897$		0			0
$898$	−14.0353	−	24.3099i	−0.468366	−	0.811233i
$899$	4.04905	+	15.1113i	0.135043	+	0.503989i
$900$		0			0
$901$	5.27420	−	3.04506i	0.175709	−	0.101446i
$902$	62.4004	+	16.7201i	2.07771	+	0.556719i
$903$		0			0
$904$	6.49274	−	6.49274i	0.215945	−	0.215945i
$905$	−3.69403	+	0.989813i	−0.122794	+	0.0329025i
$906$		0			0
$907$		−	40.8301i		−	1.35574i	−0.735181	−	0.677871i	$-0.762903\pi$
$907$		−	40.8301i		−	1.35574i	0.735181	−	0.677871i	$-0.237097\pi$
$908$	−12.4154	+	3.32670i	−0.412020	+	0.110400i
$909$		0			0
$910$	8.42127	−	11.2160i	0.279162	−	0.371806i
$911$	33.7655	−	19.4945i	1.11870	−	0.645883i	0.177632	−	0.984097i	$-0.443156\pi$
$911$	33.7655	−	19.4945i	1.11870	−	0.645883i	0.941069	+	0.338214i	$0.109823\pi$
$912$		0			0
$913$	−8.06479	−	13.9686i	−0.266906	−	0.462294i
$914$	35.6319			1.17860
$915$		0			0
$916$	−18.7930	+	5.03556i	−0.620937	+	0.166380i
$917$	−9.90843	+	36.9788i	−0.327205	+	1.22115i
$918$		0			0
$919$	18.8145	+	32.5876i	0.620632	+	1.07497i	0.989368	+	0.145432i	$0.0464573\pi$
$919$	18.8145	+	32.5876i	0.620632	+	1.07497i	−0.368736	+	0.929534i	$0.620209\pi$
$920$	11.2602			0.371237
$921$		0			0
$922$	−15.4145	−	8.89959i	−0.507651	−	0.293092i
$923$	−19.2065	−	14.4208i	−0.632188	−	0.474665i
$924$		0			0
$925$	−2.23974	−	2.23974i	−0.0736422	−	0.0736422i
$926$	23.8641	+	13.7780i	0.784224	+	0.452772i
$927$		0			0
$928$	4.33346	+	4.33346i	0.142253	+	0.142253i
$929$	2.15479	+	8.04179i	0.0706964	+	0.263843i	0.992223	−	0.124473i	$-0.0397239\pi$
$929$	2.15479	+	8.04179i	0.0706964	+	0.263843i	−0.921527	+	0.388315i	$0.873057\pi$
$930$		0			0
$931$	−3.16105	−	11.7972i	−0.103599	−	0.386637i
$932$			4.00407i			0.131158i
$933$		0			0
$934$	−11.9238	+	11.9238i	−0.390158	+	0.390158i
$935$	24.3643			0.796799
$936$		0			0
$937$	37.9409			1.23948			0.619738	−	0.784809i	$-0.287239\pi$
$937$	37.9409			1.23948			0.619738	+	0.784809i	$0.287239\pi$
$938$	20.0936	−	20.0936i	0.656080	−	0.656080i
$939$		0			0
$940$			10.7412i			0.350341i
$941$	0.283676	+	1.05869i	0.00924757	+	0.0345124i	0.970395	−	0.241522i	$-0.0776464\pi$
$941$	0.283676	+	1.05869i	0.00924757	+	0.0345124i	−0.961148	+	0.276034i	$0.910980\pi$
$942$		0			0
$943$	17.2028	+	64.2018i	0.560201	+	2.09070i
$944$	4.65773	+	4.65773i	0.151596	+	0.151596i
$945$		0			0
$946$	−29.6230	−	17.1029i	−0.963128	−	0.556062i
$947$	16.2492	+	16.2492i	0.528028	+	0.528028i	0.919984	−	0.391956i	$-0.128202\pi$
$947$	16.2492	+	16.2492i	0.528028	+	0.528028i	−0.391956	+	0.919984i	$0.628202\pi$
$948$		0			0
$949$	28.2505	−	12.0497i	0.917051	−	0.391150i
$950$	−5.29480	−	3.05695i	−0.171786	−	0.0991806i
$951$		0			0
$952$	4.56421			0.147927
$953$	−23.9953	−	41.5611i	−0.777285	−	1.34630i	−0.933501	−	0.358575i	$-0.883263\pi$
$953$	−23.9953	−	41.5611i	−0.777285	−	1.34630i	0.156216	−	0.987723i	$-0.450070\pi$
$954$		0			0
$955$	0.275599	−	1.02855i	0.00891819	−	0.0332831i
$956$	−8.86245	+	2.37469i	−0.286632	+	0.0768028i
$957$		0			0
$958$	−38.1395			−1.23223
$959$	10.5914	+	18.3448i	0.342014	+	0.592386i
$960$		0			0
$961$	−21.2033	+	12.2417i	−0.683978	+	0.394895i
$962$	−5.03345	−	6.41946i	−0.162285	−	0.206972i
$963$		0			0
$964$	−18.7022	+	5.01123i	−0.602357	+	0.161401i
$965$			16.9278i			0.544926i
$966$		0			0
$967$	35.7214	−	9.57153i	1.14872	−	0.307800i	0.366270	−	0.930509i	$-0.380635\pi$
$967$	35.7214	−	9.57153i	1.14872	−	0.307800i	0.782454	+	0.622709i	$0.213968\pi$
$968$	15.7480	−	15.7480i	0.506161	−	0.506161i
$969$		0			0
$970$	11.4829	+	3.07683i	0.368693	+	0.0987911i
$971$	17.1597	−	9.90717i	0.550682	−	0.317936i	−0.198715	−	0.980057i	$-0.563677\pi$
$971$	17.1597	−	9.90717i	0.550682	−	0.317936i	0.749397	+	0.662121i	$0.230344\pi$
$972$		0			0
$973$	9.91920	+	37.0189i	0.317995	+	1.18677i
$974$	6.75661	+	11.7028i	0.216496	+	0.374982i
$975$		0			0
$976$	4.43478	−	7.68127i	0.141954	−	0.245871i
$977$	−31.3554	−	8.40164i	−1.00315	−	0.268792i	−0.280384	−	0.959888i	$-0.590462\pi$
$977$	−31.3554	−	8.40164i	−1.00315	−	0.268792i	−0.722763	+	0.691096i	$0.757128\pi$
$978$		0			0
$979$	−66.1063	−	38.1665i	−2.11277	−	1.21981i
$980$	3.75214	−	3.75214i	0.119858	−	0.119858i
$981$		0			0
$982$	29.4578	+	7.89320i	0.940037	+	0.251882i
$983$	−5.57467	+	20.8049i	−0.177804	+	0.663575i	0.818253	+	0.574859i	$0.194943\pi$
$983$	−5.57467	+	20.8049i	−0.177804	+	0.663575i	−0.996057	+	0.0887159i	$0.971724\pi$
$984$		0			0
$985$	16.0027	−	9.23915i	0.509888	−	0.294384i
$986$	−3.53114	+	13.1784i	−0.112454	+	0.419686i
$987$		0			0
$988$	−12.5916	−	9.45414i	−0.400593	−	0.300776i
$989$		−	35.1932i		−	1.11908i
$990$		0			0
$991$	5.50674	−	9.53796i	0.174927	−	0.302983i	−0.765209	−	0.643782i	$-0.777364\pi$
$991$	5.50674	−	9.53796i	0.174927	−	0.302983i	0.940136	+	0.340799i	$0.110698\pi$
$992$	1.27637	−	2.21074i	0.0405249	−	0.0701911i
$993$		0			0
$994$	9.65695	+	9.65695i	0.306300	+	0.306300i
$995$	−11.4950	−	11.4950i	−0.364417	−	0.364417i
$996$		0			0
$997$	21.1614	−	36.6526i	0.670188	−	1.16080i	−0.307662	−	0.951496i	$-0.599547\pi$
$997$	21.1614	−	36.6526i	0.670188	−	1.16080i	0.977851	−	0.209304i	$-0.0671199\pi$
$998$	0.415405	−	0.719503i	0.0131494	−	0.0227755i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.449.12		56
3.2	odd	2		234.2.y.a.59.2	✓	56
9.2	odd	6		702.2.bc.a.683.12		56
9.7	even	3		234.2.z.a.137.3	yes	56
13.2	odd	12		702.2.bc.a.665.12		56
39.2	even	12		234.2.z.a.41.3	yes	56
117.2	even	12	inner	702.2.bb.a.197.12		56
117.106	odd	12		234.2.y.a.119.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.2	✓	56	3.2	odd	2
234.2.y.a.119.2	yes	56	117.106	odd	12
234.2.z.a.41.3	yes	56	39.2	even	12
234.2.z.a.137.3	yes	56	9.7	even	3
702.2.bb.a.197.12		56	117.2	even	12	inner
702.2.bb.a.449.12		56	1.1	even	1	trivial
702.2.bc.a.665.12		56	13.2	odd	12
702.2.bc.a.683.12		56	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.491075 + 1.83272i) q^{5} +(-0.530631 - 1.98034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.64317 + 0.948684i) q^{10} +(4.07867 + 4.07867i) q^{11} +(3.34535 + 1.34484i) q^{13} +(-1.77553 - 1.02510i) q^{14} -1.00000 q^{16} +(-1.11311 - 1.92797i) q^{17} +(1.13029 - 4.21829i) q^{19} +(1.83272 - 0.491075i) q^{20} +5.76811 q^{22} +(2.96731 + 5.13954i) q^{23} +(1.21243 - 0.699997i) q^{25} +(3.31647 - 1.41458i) q^{26} +(-1.98034 + 0.530631i) q^{28} -6.12844i q^{29} +(-2.46576 + 0.660699i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.15037 - 0.576189i) q^{34} +(3.36883 - 1.94499i) q^{35} +(-0.585575 - 2.18540i) q^{37} +(-2.18355 - 3.78201i) q^{38} +(0.948684 - 1.64317i) q^{40} +(10.8182 + 2.89872i) q^{41} +(-5.13566 - 2.96507i) q^{43} +(4.07867 - 4.07867i) q^{44} +(5.73241 + 1.53599i) q^{46} +(-1.46521 + 5.46823i) q^{47} +(2.42199 - 1.39834i) q^{49} +(0.362345 - 1.35229i) q^{50} +(1.34484 - 3.34535i) q^{52} +2.73563i q^{53} +(-5.47212 + 9.47798i) q^{55} +(-1.02510 + 1.77553i) q^{56} +(-4.33346 - 4.33346i) q^{58} +(-4.65773 - 4.65773i) q^{59} +(-4.43478 + 7.68127i) q^{61} +(-1.27637 + 2.21074i) q^{62} +1.00000i q^{64} +(-0.821895 + 6.79151i) q^{65} +(-3.58735 + 13.3882i) q^{67} +(-1.92797 + 1.11311i) q^{68} +(1.00680 - 3.75744i) q^{70} +(-6.43432 - 1.72407i) q^{71} +(6.02332 - 6.02332i) q^{73} +(-1.95937 - 1.13124i) q^{74} +(-4.21829 - 1.13029i) q^{76} +(5.91289 - 10.2414i) q^{77} +(-5.25497 - 9.10187i) q^{79} +(-0.491075 - 1.83272i) q^{80} +(9.69930 - 5.59989i) q^{82} +(-2.70106 - 0.723746i) q^{83} +(2.98680 - 2.98680i) q^{85} +(-5.72808 + 1.53483i) q^{86} -5.76811i q^{88} +(-12.7827 + 3.42511i) q^{89} +(0.888099 - 7.33856i) q^{91} +(5.13954 - 2.96731i) q^{92} +(2.83056 + 4.90268i) q^{94} +8.28598 q^{95} +(6.05201 - 1.62163i) q^{97} +(0.723833 - 2.70138i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 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

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