LMFDB - Embedded newform 756.2.bf.d.271.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.6
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.d.703.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.577244 + 1.29104i) q^{2} +(-1.33358 - 1.49049i) q^{4} +(3.11886 + 1.80067i) q^{5} +(-0.838804 - 2.50926i) q^{7} +(2.69409 - 0.861330i) q^{8} +O(q^{10})$	\(q+(-0.577244 + 1.29104i) q^{2} +(-1.33358 - 1.49049i) q^{4} +(3.11886 + 1.80067i) q^{5} +(-0.838804 - 2.50926i) q^{7} +(2.69409 - 0.861330i) q^{8} +(-4.12508 + 2.98715i) q^{10} +(-4.13038 + 2.38467i) q^{11} +2.81834i q^{13} +(3.72376 + 0.365526i) q^{14} +(-0.443132 + 3.97538i) q^{16} +(1.10943 - 0.640529i) q^{17} +(-1.39801 + 2.42142i) q^{19} +(-1.47535 - 7.04997i) q^{20} +(-0.694481 - 6.70903i) q^{22} +(5.58646 + 3.22535i) q^{23} +(3.98484 + 6.90195i) q^{25} +(-3.63859 - 1.62687i) q^{26} +(-2.62143 + 4.59653i) q^{28} +7.78607 q^{29} +(5.30848 + 9.19455i) q^{31} +(-4.87659 - 2.86686i) q^{32} +(0.186539 + 1.80206i) q^{34} +(1.90225 - 9.33644i) q^{35} +(-0.554486 + 0.960399i) q^{37} +(-2.31917 - 3.20264i) q^{38} +(9.95344 + 2.16480i) q^{40} +3.06753i q^{41} -9.45594i q^{43} +(9.06252 + 2.97614i) q^{44} +(-7.38881 + 5.35055i) q^{46} +(-2.18192 + 3.77920i) q^{47} +(-5.59282 + 4.20956i) q^{49} +(-11.2109 + 1.16049i) q^{50} +(4.20071 - 3.75847i) q^{52} +(3.06328 + 5.30575i) q^{53} -17.1761 q^{55} +(-4.42112 - 6.03769i) q^{56} +(-4.49446 + 10.0521i) q^{58} +(-0.957733 - 1.65884i) q^{59} +(-8.59451 - 4.96204i) q^{61} +(-14.9348 + 1.54597i) q^{62} +(6.51622 - 4.64100i) q^{64} +(-5.07490 + 8.78998i) q^{65} +(8.12062 - 4.68844i) q^{67} +(-2.43421 - 0.799398i) q^{68} +(10.9557 + 7.84529i) q^{70} +2.12825i q^{71} +(-7.42074 + 4.28437i) q^{73} +(-0.919841 - 1.27025i) q^{74} +(5.47346 - 1.14544i) q^{76} +(9.44835 + 8.36393i) q^{77} +(-2.33401 - 1.34754i) q^{79} +(-8.54042 + 11.6007i) q^{80} +(-3.96031 - 1.77071i) q^{82} +2.62572 q^{83} +4.61353 q^{85} +(12.2080 + 5.45838i) q^{86} +(-9.07361 + 9.98214i) q^{88} +(4.78921 + 2.76505i) q^{89} +(7.07195 - 2.36403i) q^{91} +(-2.64264 - 12.6278i) q^{92} +(-3.61961 - 4.99847i) q^{94} +(-8.72037 + 5.03471i) q^{95} -7.51833i q^{97} +(-2.20630 - 9.65050i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{7}+O(q^{10}) $ 32 * q + 2 * q^7	$ 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) $ 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.577244	+	1.29104i	−0.408173	+	0.912905i
$2$	−0.577244	+	1.29104i	−0.408173	+	0.912905i
$3$		0			0
$3$		0			0
$4$	−1.33358	−	1.49049i	−0.666790	−	0.745246i
$5$	3.11886	+	1.80067i	1.39479	+	0.805285i	0.993841	−	0.110813i	$-0.0353456\pi$
$5$	3.11886	+	1.80067i	1.39479	+	0.805285i	0.400953	+	0.916098i	$0.368679\pi$
$6$		0			0
$7$	−0.838804	−	2.50926i	−0.317038	−	0.948413i
$7$	−0.838804	−	2.50926i	−0.317038	−	0.948413i
$8$	2.69409	−	0.861330i	0.952504	−	0.304526i
$9$		0			0
$10$	−4.12508	+	2.98715i	−1.30447	+	0.944619i
$11$	−4.13038	+	2.38467i	−1.24536	+	0.719006i	−0.970179	−	0.242388i	$-0.922069\pi$
$11$	−4.13038	+	2.38467i	−1.24536	+	0.719006i	−0.275176	+	0.961394i	$0.588736\pi$
$12$		0			0
$13$			2.81834i			0.781666i	0.920462	+	0.390833i	$0.127813\pi$
$13$			2.81834i			0.781666i	−0.920462	+	0.390833i	$0.872187\pi$
$14$	3.72376	+	0.365526i	0.995217	+	0.0976910i
$15$		0			0
$16$	−0.443132	+	3.97538i	−0.110783	+	0.993845i
$17$	1.10943	−	0.640529i	0.269076	−	0.155351i	−0.359392	−	0.933187i	$-0.617016\pi$
$17$	1.10943	−	0.640529i	0.269076	−	0.155351i	0.628468	+	0.777836i	$0.283682\pi$
$18$		0			0
$19$	−1.39801	+	2.42142i	−0.320725	+	0.555512i	−0.980638	−	0.195830i	$-0.937260\pi$
$19$	−1.39801	+	2.42142i	−0.320725	+	0.555512i	0.659913	+	0.751342i	$0.270593\pi$
$20$	−1.47535	−	7.04997i	−0.329899	−	1.57642i
$21$		0			0
$22$	−0.694481	−	6.70903i	−0.148064	−	1.43037i
$23$	5.58646	+	3.22535i	1.16486	+	0.672531i	0.952464	−	0.304653i	$-0.0985403\pi$
$23$	5.58646	+	3.22535i	1.16486	+	0.672531i	0.212395	+	0.977184i	$0.431874\pi$
$24$		0			0
$25$	3.98484	+	6.90195i	0.796968	+	1.38039i
$26$	−3.63859	−	1.62687i	−0.713586	−	0.319055i
$27$		0			0
$28$	−2.62143	+	4.59653i	−0.495403	+	0.868663i
$29$	7.78607			1.44584			0.722919	−	0.690933i	$-0.242800\pi$
$29$	7.78607			1.44584			0.722919	+	0.690933i	$0.242800\pi$
$30$		0			0
$31$	5.30848	+	9.19455i	0.953431	+	1.65139i	0.737919	+	0.674889i	$0.235809\pi$
$31$	5.30848	+	9.19455i	0.953431	+	1.65139i	0.215511	+	0.976501i	$0.430858\pi$
$32$	−4.87659	−	2.86686i	−0.862067	−	0.506795i
$33$		0			0
$34$	0.186539	+	1.80206i	0.0319912	+	0.309051i
$35$	1.90225	−	9.33644i	0.321540	−	1.57815i
$36$		0			0
$37$	−0.554486	+	0.960399i	−0.0911570	+	0.157889i	−0.907998	−	0.418974i	$-0.862390\pi$
$37$	−0.554486	+	0.960399i	−0.0911570	+	0.157889i	0.816841	+	0.576863i	$0.195723\pi$
$38$	−2.31917	−	3.20264i	−0.376218	−	0.519536i
$39$		0			0
$40$	9.95344	+	2.16480i	1.57378	+	0.342286i
$41$			3.06753i			0.479067i	0.970888	+	0.239534i	$0.0769945\pi$
$41$			3.06753i			0.479067i	−0.970888	+	0.239534i	$0.923005\pi$
$42$		0			0
$43$		−	9.45594i		−	1.44202i	−0.692926	−	0.721009i	$-0.743679\pi$
$43$		−	9.45594i		−	1.44202i	0.692926	−	0.721009i	$-0.256321\pi$
$44$	9.06252	+	2.97614i	1.36623	+	0.448670i
$45$		0			0
$46$	−7.38881	+	5.35055i	−1.08942	+	0.788896i
$47$	−2.18192	+	3.77920i	−0.318266	+	0.551253i	−0.980126	−	0.198374i	$-0.936434\pi$
$47$	−2.18192	+	3.77920i	−0.318266	+	0.551253i	0.661860	+	0.749627i	$0.269767\pi$
$48$		0			0
$49$	−5.59282	+	4.20956i	−0.798974	+	0.601366i
$50$	−11.2109	+	1.16049i	−1.58546	+	0.164118i
$51$		0			0
$52$	4.20071	−	3.75847i	0.582533	−	0.521207i
$53$	3.06328	+	5.30575i	0.420773	+	0.728801i	0.996015	−	0.0891825i	$-0.0284254\pi$
$53$	3.06328	+	5.30575i	0.420773	+	0.728801i	−0.575242	+	0.817983i	$0.695092\pi$
$54$		0			0
$55$	−17.1761			−2.31602
$56$	−4.42112	−	6.03769i	−0.590797	−	0.806821i
$57$		0			0
$58$	−4.49446	+	10.0521i	−0.590152	+	1.31991i
$59$	−0.957733	−	1.65884i	−0.124686	−	0.215963i	0.796924	−	0.604080i	$-0.206459\pi$
$59$	−0.957733	−	1.65884i	−0.124686	−	0.215963i	−0.921610	+	0.388117i	$0.873126\pi$
$60$		0			0
$61$	−8.59451	−	4.96204i	−1.10041	−	0.635324i	−0.164084	−	0.986446i	$-0.552467\pi$
$61$	−8.59451	−	4.96204i	−1.10041	−	0.635324i	−0.936330	+	0.351122i	$0.885800\pi$
$62$	−14.9348	+	1.54597i	−1.89673	+	0.196338i
$63$		0			0
$64$	6.51622	−	4.64100i	0.814528	−	0.580125i
$65$	−5.07490	+	8.78998i	−0.629464	+	1.09026i
$66$		0			0
$67$	8.12062	−	4.68844i	0.992092	−	0.572784i	0.0861928	−	0.996278i	$-0.472530\pi$
$67$	8.12062	−	4.68844i	0.992092	−	0.572784i	0.905899	+	0.423494i	$0.139197\pi$
$68$	−2.43421	−	0.799398i	−0.295192	−	0.0969412i
$69$		0			0
$70$	10.9557	+	7.84529i	1.30945	+	0.937692i
$71$			2.12825i			0.252577i	0.991994	+	0.126288i	$0.0403065\pi$
$71$			2.12825i			0.252577i	−0.991994	+	0.126288i	$0.959694\pi$
$72$		0			0
$73$	−7.42074	+	4.28437i	−0.868532	+	0.501447i	−0.866860	−	0.498552i	$-0.833865\pi$
$73$	−7.42074	+	4.28437i	−0.868532	+	0.501447i	−0.00167170	+	0.999999i	$0.500532\pi$
$74$	−0.919841	−	1.27025i	−0.106929	−	0.147664i
$75$		0			0
$76$	5.47346	−	1.14544i	0.627849	−	0.131391i
$77$	9.44835	+	8.36393i	1.07674	+	0.953159i
$78$		0			0
$79$	−2.33401	−	1.34754i	−0.262597	−	0.151610i	0.362922	−	0.931820i	$-0.381779\pi$
$79$	−2.33401	−	1.34754i	−0.262597	−	0.151610i	−0.625519	+	0.780209i	$0.715113\pi$
$80$	−8.54042	+	11.6007i	−0.954848	+	1.29700i
$81$		0			0
$82$	−3.96031	−	1.77071i	−0.437343	−	0.195542i
$83$	2.62572			0.288210			0.144105	−	0.989562i	$-0.453970\pi$
$83$	2.62572			0.288210			0.144105	+	0.989562i	$0.453970\pi$
$84$		0			0
$85$	4.61353			0.500407
$86$	12.2080	+	5.45838i	1.31642	+	0.588592i
$87$		0			0
$88$	−9.07361	+	9.98214i	−0.967250	+	1.06410i
$89$	4.78921	+	2.76505i	0.507655	+	0.293095i	0.731869	−	0.681445i	$-0.238648\pi$
$89$	4.78921	+	2.76505i	0.507655	+	0.293095i	−0.224214	+	0.974540i	$0.571981\pi$
$90$		0			0
$91$	7.07195	−	2.36403i	0.741342	−	0.247818i
$92$	−2.64264	−	12.6278i	−0.275514	−	1.31654i
$93$		0			0
$94$	−3.61961	−	4.99847i	−0.373334	−	0.515553i
$95$	−8.72037	+	5.03471i	−0.894691	+	0.516550i
$96$		0			0
$97$		−	7.51833i		−	0.763371i	−0.924292	−	0.381685i	$-0.875344\pi$
$97$		−	7.51833i		−	0.763371i	0.924292	−	0.381685i	$-0.124656\pi$
$98$	−2.20630	−	9.65050i	−0.222870	−	0.974848i
$99$		0			0
$100$	4.97319	−	15.1437i	0.497319	−	1.51437i
$101$	3.33550	−	1.92575i	0.331895	−	0.191619i	−0.324787	−	0.945787i	$-0.605293\pi$
$101$	3.33550	−	1.92575i	0.331895	−	0.191619i	0.656682	+	0.754168i	$0.271959\pi$
$102$		0			0
$103$	3.48956	−	6.04409i	0.343836	−	0.595542i	−0.641305	−	0.767286i	$-0.721607\pi$
$103$	3.48956	−	6.04409i	0.343836	−	0.595542i	0.985142	+	0.171744i	$0.0549401\pi$
$104$	2.42752	+	7.59284i	0.238038	+	0.744540i
$105$		0			0
$106$	−8.61820	+	0.892108i	−0.837074	+	0.0866492i
$107$	−3.09433	−	1.78651i	−0.299141	−	0.172709i	0.342916	−	0.939366i	$-0.388585\pi$
$107$	−3.09433	−	1.78651i	−0.299141	−	0.172709i	−0.642057	+	0.766657i	$0.721919\pi$
$108$		0			0
$109$	−7.84566	−	13.5891i	−0.751478	−	1.30160i	−0.947106	−	0.320920i	$-0.896008\pi$
$109$	−7.84566	−	13.5891i	−0.751478	−	1.30160i	0.195628	−	0.980678i	$-0.437325\pi$
$110$	9.91477	−	22.1750i	0.945337	−	2.11431i
$111$		0			0
$112$	10.3470	−	2.22263i	0.977697	−	0.210019i
$113$	−15.5897			−1.46656			−0.733278	−	0.679929i	$-0.762011\pi$
$113$	−15.5897			−1.46656			−0.733278	+	0.679929i	$0.762011\pi$
$114$		0			0
$115$	11.6156	+	20.1188i	1.08316	+	1.87609i
$116$	−10.3833	−	11.6051i	−0.964070	−	1.07750i
$117$		0			0
$118$	2.69448	−	0.278917i	0.248047	−	0.0256764i
$119$	−2.53785	−	2.24657i	−0.232644	−	0.205943i
$120$		0			0
$121$	5.87334	−	10.1729i	0.533940	−	0.924811i
$122$	11.3673	−	8.23156i	1.02915	−	0.745251i
$123$		0			0
$124$	6.62513	−	20.1739i	0.594954	−	1.81167i
$125$			10.6948i			0.956575i
$126$		0			0
$127$			5.46225i			0.484696i	0.970189	+	0.242348i	$0.0779176\pi$
$127$			5.46225i			0.484696i	−0.970189	+	0.242348i	$0.922082\pi$
$128$	2.23028	+	11.0917i	0.197131	+	0.980377i
$129$		0			0
$130$	−8.41878	−	11.6259i	−0.738376	−	1.01966i
$131$	4.64194	−	8.04008i	0.405568	−	0.702465i	−0.588819	−	0.808265i	$-0.700407\pi$
$131$	4.64194	−	8.04008i	0.405568	−	0.702465i	0.994387	+	0.105800i	$0.0337403\pi$
$132$		0			0
$133$	7.24864	+	1.47687i	0.628537	+	0.128061i
$134$	1.36540	+	13.1904i	0.117953	+	1.13948i
$135$		0			0
$136$	2.43719	−	2.68122i	0.208987	−	0.229913i
$137$	−0.903992	−	1.56576i	−0.0772332	−	0.133772i	0.824822	−	0.565392i	$-0.191275\pi$
$137$	−0.903992	−	1.56576i	−0.0772332	−	0.133772i	−0.902055	+	0.431621i	$0.857942\pi$
$138$		0			0
$139$	−8.73545			−0.740932			−0.370466	−	0.928846i	$-0.620802\pi$
$139$	−8.73545			−0.740932			−0.370466	+	0.928846i	$0.620802\pi$
$140$	−16.4527	+	9.61559i	−1.39051	+	0.812666i
$141$		0			0
$142$	−2.74766	−	1.22852i	−0.230579	−	0.103095i
$143$	−6.72081	−	11.6408i	−0.562022	−	0.973451i
$144$		0			0
$145$	24.2836	+	14.0202i	2.01665	+	1.16431i
$146$	−1.24772	−	12.0536i	−0.103262	−	0.997564i
$147$		0			0
$148$	2.17092	−	0.454310i	0.178448	−	0.0373441i
$149$	8.84870	−	15.3264i	0.724914	−	1.25559i	−0.234096	−	0.972214i	$-0.575213\pi$
$149$	8.84870	−	15.3264i	0.724914	−	1.25559i	0.959010	−	0.283374i	$-0.0914537\pi$
$150$		0			0
$151$	−6.53951	+	3.77559i	−0.532178	+	0.307253i	−0.741903	−	0.670508i	$-0.766076\pi$
$151$	−6.53951	+	3.77559i	−0.532178	+	0.307253i	0.209725	+	0.977760i	$0.432743\pi$
$152$	−1.68071	+	7.72767i	−0.136324	+	0.626797i
$153$		0			0
$154$	−16.2522	+	7.37019i	−1.30964	+	0.593907i
$155$			38.2353i			3.07113i
$156$		0			0
$157$	7.54440	−	4.35576i	0.602109	−	0.347628i	−0.167762	−	0.985828i	$-0.553654\pi$
$157$	7.54440	−	4.35576i	0.602109	−	0.347628i	0.769871	+	0.638200i	$0.220321\pi$
$158$	3.08703	−	2.23545i	0.245591	−	0.177843i
$159$		0			0
$160$	−10.0471	−	17.7225i	−0.794292	−	1.40108i
$161$	3.40730	−	16.7234i	0.268533	−	1.31798i
$162$		0			0
$163$	−12.5919	−	7.26992i	−0.986271	−	0.569424i	−0.0821135	−	0.996623i	$-0.526167\pi$
$163$	−12.5919	−	7.26992i	−0.986271	−	0.569424i	−0.904158	+	0.427199i	$0.859500\pi$
$164$	4.57212	−	4.09079i	0.357023	−	0.319437i
$165$		0			0
$166$	−1.51568	+	3.38991i	−0.117640	+	0.263108i
$167$	13.8768			1.07382			0.536911	−	0.843639i	$-0.319591\pi$
$167$	13.8768			1.07382			0.536911	+	0.843639i	$0.319591\pi$
$168$		0			0
$169$	5.05699			0.388999
$170$	−2.66313	+	5.95626i	−0.204253	+	0.456824i
$171$		0			0
$172$	−14.0940	+	12.6102i	−1.07466	+	0.961522i
$173$	5.60814	+	3.23786i	0.426379	+	0.246170i	0.697803	−	0.716290i	$-0.254161\pi$
$173$	5.60814	+	3.23786i	0.426379	+	0.246170i	−0.271424	+	0.962460i	$0.587495\pi$
$174$		0			0
$175$	13.9763	−	15.7884i	1.05651	−	1.19349i
$176$	−7.64968	−	17.4765i	−0.576616	−	1.31734i
$177$		0			0
$178$	−6.33434	+	4.58696i	−0.474779	+	0.343808i
$179$	3.09116	−	1.78468i	0.231044	−	0.133393i	−0.380010	−	0.924983i	$-0.624079\pi$
$179$	3.09116	−	1.78468i	0.231044	−	0.133393i	0.611054	+	0.791589i	$0.290746\pi$
$180$		0			0
$181$		−	14.7047i		−	1.09299i	−0.837462	−	0.546495i	$-0.815962\pi$
$181$		−	14.7047i		−	1.09299i	0.837462	−	0.546495i	$-0.184038\pi$
$182$	−1.03018	+	10.4948i	−0.0763617	+	0.777927i
$183$		0			0
$184$	17.8285	+	3.87758i	1.31434	+	0.285859i
$185$	−3.45873	+	1.99690i	−0.254291	+	0.146815i
$186$		0			0
$187$	−3.05490	+	5.29125i	−0.223397	+	0.386934i
$188$	8.54264	−	1.78773i	0.623036	−	0.130383i
$189$		0			0
$190$	−1.46624	−	14.1646i	−0.106372	−	1.02761i
$191$	−3.61448	−	2.08682i	−0.261535	−	0.150997i	0.363500	−	0.931594i	$-0.381582\pi$
$191$	−3.61448	−	2.08682i	−0.261535	−	0.150997i	−0.625034	+	0.780597i	$0.714915\pi$
$192$		0			0
$193$	0.889958	+	1.54145i	0.0640605	+	0.110956i	0.896277	−	0.443495i	$-0.146262\pi$
$193$	0.889958	+	1.54145i	0.0640605	+	0.110956i	−0.832216	+	0.554451i	$0.812928\pi$
$194$	9.70648	+	4.33991i	0.696885	+	0.311587i
$195$		0			0
$196$	13.7328	+	2.72226i	0.980913	+	0.194447i
$197$	16.1128			1.14799			0.573995	−	0.818859i	$-0.305393\pi$
$197$	16.1128			1.14799			0.573995	+	0.818859i	$0.305393\pi$
$198$		0			0
$199$	6.91690	+	11.9804i	0.490326	+	0.849270i	0.999938	−	0.0111347i	$-0.00354437\pi$
$199$	6.91690	+	11.9804i	0.490326	+	0.849270i	−0.509612	+	0.860404i	$0.670211\pi$
$200$	16.6804	+	15.1622i	1.17948	+	1.07213i
$201$		0			0
$202$	0.560830	+	5.41790i	0.0394599	+	0.381202i
$203$	−6.53099	−	19.5373i	−0.458385	−	1.37125i
$204$		0			0
$205$	−5.52361	+	9.56717i	−0.385786	+	0.668200i
$206$	5.78885	+	7.99408i	0.403328	+	0.556974i
$207$		0			0
$208$	−11.2040	−	1.24889i	−0.776854	−	0.0865952i
$209$		−	13.3352i		−	0.922413i
$210$		0			0
$211$		−	13.2074i		−	0.909238i	−0.890686	−	0.454619i	$-0.849776\pi$
$211$		−	13.2074i		−	0.909238i	0.890686	−	0.454619i	$-0.150224\pi$
$212$	3.82305	−	11.6414i	0.262568	−	0.799536i
$213$		0			0
$214$	4.09265	−	2.96366i	0.279768	−	0.202592i
$215$	17.0270	−	29.4917i	1.16123	−	2.01132i
$216$		0			0
$217$	18.6188	−	21.0328i	1.26393	−	1.42780i
$218$	22.0729	−	2.28487i	1.49497	−	0.154751i
$219$		0			0
$220$	22.9056	+	25.6008i	1.54430	+	1.72600i
$221$	1.80522	+	3.12674i	0.121433	+	0.210327i
$222$		0			0
$223$	16.4648			1.10256			0.551282	−	0.834319i	$-0.314139\pi$
$223$	16.4648			1.10256			0.551282	+	0.834319i	$0.314139\pi$
$224$	−3.10322	+	14.6414i	−0.207343	+	0.978268i
$225$		0			0
$226$	8.99906	−	20.1270i	0.598608	−	1.33883i
$227$	13.0078	+	22.5302i	0.863357	+	1.49538i	0.868669	+	0.495393i	$0.164976\pi$
$227$	13.0078	+	22.5302i	0.863357	+	1.49538i	−0.00531177	+	0.999986i	$0.501691\pi$
$228$		0			0
$229$	−14.7020	−	8.48819i	−0.971534	−	0.560916i	−0.0718306	−	0.997417i	$-0.522884\pi$
$229$	−14.7020	−	8.48819i	−0.971534	−	0.560916i	−0.899704	+	0.436501i	$0.856217\pi$
$230$	−32.6792	+	3.38277i	−2.15480	+	0.223053i
$231$		0			0
$232$	20.9764	−	6.70638i	1.37717	−	0.440295i
$233$	−6.30918	+	10.9278i	−0.413328	+	0.715906i	−0.995251	−	0.0973382i	$-0.968967\pi$
$233$	−6.30918	+	10.9278i	−0.413328	+	0.715906i	0.581923	+	0.813244i	$0.302300\pi$
$234$		0			0
$235$	−13.6102	+	7.85785i	−0.887832	+	0.512590i
$236$	−1.19528	+	3.63969i	−0.0778060	+	0.236924i
$237$		0			0
$238$	4.36537	−	1.97965i	0.282965	−	0.128322i
$239$			13.6404i			0.882321i	0.897428	+	0.441161i	$0.145433\pi$
$239$			13.6404i			0.882321i	−0.897428	+	0.441161i	$0.854567\pi$
$240$		0			0
$241$	2.54798	−	1.47108i	0.164130	−	0.0947603i	−0.415685	−	0.909509i	$-0.636458\pi$
$241$	2.54798	−	1.47108i	0.164130	−	0.0947603i	0.579815	+	0.814748i	$0.303125\pi$
$242$	9.74332	+	13.4550i	0.626324	+	0.864919i
$243$		0			0
$244$	4.06558	+	19.4273i	0.260272	+	1.24371i
$245$	−25.0232	+	3.05818i	−1.59868	+	0.195380i
$246$		0			0
$247$	−6.82438	−	3.94006i	−0.434225	−	0.250700i
$248$	22.2211	+	20.1986i	1.41104	+	1.28261i
$249$		0			0
$250$	−13.8075	−	6.17353i	−0.873262	−	0.390448i
$251$	15.0809			0.951900			0.475950	−	0.879472i	$-0.342104\pi$
$251$	15.0809			0.951900			0.475950	+	0.879472i	$0.342104\pi$
$252$		0			0
$253$	−30.7656			−1.93422
$254$	−7.05199	−	3.15305i	−0.442481	−	0.197840i
$255$		0			0
$256$	−15.6073	−	3.52323i	−0.975454	−	0.220202i
$257$	−2.61842	−	1.51175i	−0.163333	−	0.0943001i	0.416106	−	0.909316i	$-0.363395\pi$
$257$	−2.61842	−	1.51175i	−0.163333	−	0.0943001i	−0.579438	+	0.815016i	$0.696728\pi$
$258$		0			0
$259$	2.87500	+	0.585767i	0.178644	+	0.0363978i
$260$	19.8692	−	4.15804i	1.23223	−	0.257871i
$261$		0			0
$262$	7.70055	+	10.6340i	0.475742	+	0.656973i
$263$	−23.4171	+	13.5199i	−1.44396	+	0.833670i	−0.998111	−	0.0614382i	$-0.980431\pi$
$263$	−23.4171	+	13.5199i	−1.44396	+	0.833670i	−0.445848	+	0.895109i	$0.647098\pi$
$264$		0			0
$265$			22.0638i			1.35537i
$266$	−6.09094	+	8.50578i	−0.373459	+	0.521523i
$267$		0			0
$268$	−17.8176	−	5.85131i	−1.08838	−	0.357426i
$269$	−7.35220	+	4.24479i	−0.448271	+	0.258810i	−0.707100	−	0.707114i	$-0.749997\pi$
$269$	−7.35220	+	4.24479i	−0.448271	+	0.258810i	0.258829	+	0.965923i	$0.416664\pi$
$270$		0			0
$271$	2.68880	−	4.65714i	0.163333	−	0.282901i	−0.772729	−	0.634736i	$-0.781109\pi$
$271$	2.68880	−	4.65714i	0.163333	−	0.282901i	0.936062	+	0.351835i	$0.114442\pi$
$272$	2.05472	+	4.69424i	0.124586	+	0.284630i
$273$		0			0
$274$	2.54329	−	0.263267i	0.153645	−	0.0159045i
$275$	−32.9178	−	19.0051i	−1.98502	−	1.14605i
$276$		0			0
$277$	−10.4066	−	18.0248i	−0.625272	−	1.08300i	−0.988488	−	0.151298i	$-0.951655\pi$
$277$	−10.4066	−	18.0248i	−0.625272	−	1.08300i	0.363216	−	0.931705i	$-0.381679\pi$
$278$	5.04249	−	11.2778i	0.302428	−	0.676400i
$279$		0			0
$280$	−2.91692	−	26.7917i	−0.174319	−	1.60111i
$281$	−16.7084			−0.996738			−0.498369	−	0.866965i	$-0.666068\pi$
$281$	−16.7084			−0.996738			−0.498369	+	0.866965i	$0.666068\pi$
$282$		0			0
$283$	1.62998	+	2.82320i	0.0968920	+	0.167822i	0.910397	−	0.413736i	$-0.135777\pi$
$283$	1.62998	+	2.82320i	0.0968920	+	0.167822i	−0.813505	+	0.581558i	$0.802443\pi$
$284$	3.17214	−	2.83819i	0.188232	−	0.168416i
$285$		0			0
$286$	18.9083	−	1.95728i	1.11807	−	0.115736i
$287$	7.69724	−	2.57305i	0.454353	−	0.151883i
$288$		0			0
$289$	−7.67945	+	13.3012i	−0.451732	+	0.782423i
$290$	−32.1182	+	23.2581i	−1.88605	+	1.36577i
$291$		0			0
$292$	16.2820	+	5.34701i	0.952829	+	0.312910i
$293$		−	25.0184i		−	1.46159i	−0.682597	−	0.730795i	$-0.739150\pi$
$293$		−	25.0184i		−	1.46159i	0.682597	−	0.730795i	$-0.260850\pi$
$294$		0			0
$295$		−	6.89825i		−	0.401632i
$296$	−0.666615	+	3.06499i	−0.0387462	+	0.178149i
$297$		0			0
$298$	14.6792	+	20.2711i	0.850341	+	1.17427i
$299$	−9.09011	+	15.7445i	−0.525695	+	0.910530i
$300$		0			0
$301$	−23.7275	+	7.93168i	−1.36763	+	0.457174i
$302$	−1.09955	−	10.6222i	−0.0632721	−	0.611240i
$303$		0			0
$304$	−9.00656	−	6.63062i	−0.516562	−	0.380292i
$305$	−17.8700	−	30.9518i	−1.02323	−	1.77229i
$306$		0			0
$307$	22.9210			1.30817			0.654086	−	0.756421i	$-0.273054\pi$
$307$	22.9210			1.30817			0.654086	+	0.756421i	$0.273054\pi$
$308$	−0.133754	−	25.2367i	−0.00762136	−	1.43799i
$309$		0			0
$310$	−49.3634	−	22.0711i	−2.80365	−	1.25355i
$311$	−4.27939	−	7.41212i	−0.242662	−	0.420303i	0.718810	−	0.695207i	$-0.244687\pi$
$311$	−4.27939	−	7.41212i	−0.242662	−	0.420303i	−0.961472	+	0.274904i	$0.911354\pi$
$312$		0			0
$313$	−9.54575	−	5.51124i	−0.539557	−	0.311514i	0.205342	−	0.978690i	$-0.434169\pi$
$313$	−9.54575	−	5.51124i	−0.539557	−	0.311514i	−0.744900	+	0.667177i	$0.767503\pi$
$314$	1.26851	+	12.2545i	0.0715864	+	0.691560i
$315$		0			0
$316$	1.10409	+	5.27588i	0.0621099	+	0.296791i
$317$	1.90705	−	3.30310i	0.107110	−	0.185521i	−0.807488	−	0.589884i	$-0.799174\pi$
$317$	1.90705	−	3.30310i	0.107110	−	0.185521i	0.914598	+	0.404363i	$0.132507\pi$
$318$		0			0
$319$	−32.1594	+	18.5672i	−1.80058	+	1.03957i
$320$	28.6801	−	2.74103i	1.60326	−	0.153228i
$321$		0			0
$322$	19.6237	+	14.0524i	1.09359	+	0.783111i
$323$			3.58186i			0.199300i
$324$		0			0
$325$	−19.4520	+	11.2306i	−1.07900	+	0.622962i
$326$	16.6543	−	12.0601i	0.922399	−	0.667948i
$327$		0			0
$328$	2.64215	+	8.26419i	0.145889	+	0.456313i
$329$	11.3132	+	2.30501i	0.623718	+	0.127080i
$330$		0			0
$331$	−1.92269	−	1.11007i	−0.105681	−	0.0610147i	0.446228	−	0.894919i	$-0.352767\pi$
$331$	−1.92269	−	1.11007i	−0.105681	−	0.0610147i	−0.551909	+	0.833905i	$0.686100\pi$
$332$	−3.50161	−	3.91361i	−0.192176	−	0.214787i
$333$		0			0
$334$	−8.01031	+	17.9156i	−0.438305	+	0.980296i
$335$	33.7694			1.84502
$336$		0			0
$337$	18.1020			0.986077			0.493038	−	0.870008i	$-0.335886\pi$
$337$	18.1020			0.986077			0.493038	+	0.870008i	$0.335886\pi$
$338$	−2.91911	+	6.52878i	−0.158779	+	0.355119i
$339$		0			0
$340$	−6.15251	−	6.87643i	−0.333667	−	0.372927i
$341$	−43.8520	−	25.3180i	−2.37472	−	1.37105i
$342$		0			0
$343$	15.2542	+	10.5029i	0.823648	+	0.567101i
$344$	−8.14469	−	25.4751i	−0.439132	−	1.37353i
$345$		0			0
$346$	−7.41747	+	5.37131i	−0.398766	+	0.288763i
$347$	12.9940	−	7.50209i	0.697555	−	0.402733i	−0.108881	−	0.994055i	$-0.534727\pi$
$347$	12.9940	−	7.50209i	0.697555	−	0.402733i	0.806436	+	0.591321i	$0.201394\pi$
$348$		0			0
$349$		−	1.81356i		−	0.0970777i	−0.998821	−	0.0485388i	$-0.984544\pi$
$349$		−	1.81356i		−	0.0970777i	0.998821	−	0.0485388i	$-0.0154565\pi$
$350$	12.3157	+	27.1578i	0.658304	+	1.45164i
$351$		0			0
$352$	26.9787	+	0.212160i	1.43797	+	0.0113082i
$353$	6.18746	−	3.57233i	0.329325	−	0.190136i	−0.326216	−	0.945295i	$-0.605774\pi$
$353$	6.18746	−	3.57233i	0.329325	−	0.190136i	0.655541	+	0.755159i	$0.272440\pi$
$354$		0			0
$355$	−3.83228	+	6.63771i	−0.203396	+	0.352293i
$356$	−2.26551	−	10.8257i	−0.120072	−	0.573761i
$357$		0			0
$358$	0.519747	+	5.02101i	0.0274695	+	0.265369i
$359$	−24.6340	−	14.2224i	−1.30013	−	0.750631i	−0.319705	−	0.947517i	$-0.603584\pi$
$359$	−24.6340	−	14.2224i	−1.30013	−	0.750631i	−0.980426	+	0.196886i	$0.936917\pi$
$360$		0			0
$361$	5.59115	+	9.68415i	0.294271	+	0.509692i
$362$	18.9844	+	8.48818i	0.997796	+	0.446129i
$363$		0			0
$364$	−12.9546	−	7.38806i	−0.679004	−	0.387240i
$365$	−30.8589			−1.61523
$366$		0			0
$367$	−14.8432	−	25.7091i	−0.774806	−	1.34200i	−0.934903	−	0.354902i	$-0.884514\pi$
$367$	−14.8432	−	25.7091i	−0.774806	−	1.34200i	0.160097	−	0.987101i	$-0.448819\pi$
$368$	−15.2975	+	20.7791i	−0.797438	+	1.08318i
$369$		0			0
$370$	−0.581550	−	5.61806i	−0.0302333	−	0.292069i
$371$	10.7440	−	12.1371i	0.557803	−	0.630124i
$372$		0			0
$373$	12.1273	−	21.0051i	0.627929	−	1.08760i	−0.360038	−	0.932938i	$-0.617236\pi$
$373$	12.1273	−	21.0051i	0.627929	−	1.08760i	0.987967	−	0.154667i	$-0.0494305\pi$
$374$	−5.06780	−	6.99835i	−0.262050	−	0.361876i
$375$		0			0
$376$	−2.62315	+	12.0609i	−0.135279	+	0.621991i
$377$			21.9438i			1.13016i
$378$		0			0
$379$		−	28.3124i		−	1.45431i	−0.686472	−	0.727156i	$-0.740842\pi$
$379$		−	28.3124i		−	1.45431i	0.686472	−	0.727156i	$-0.259158\pi$
$380$	19.1335	+	6.28346i	0.981528	+	0.322335i
$381$		0			0
$382$	4.78061	−	3.46184i	0.244597	−	0.177123i
$383$	−13.0761	+	22.6484i	−0.668156	+	1.15728i	0.310264	+	0.950650i	$0.399583\pi$
$383$	−13.0761	+	22.6484i	−0.668156	+	1.15728i	−0.978419	+	0.206629i	$0.933751\pi$
$384$		0			0
$385$	14.4073	+	43.0993i	0.734266	+	2.19654i
$386$	−2.50380	+	0.259179i	−0.127440	+	0.0131919i
$387$		0			0
$388$	−11.2060	+	10.0263i	−0.568899	+	0.509008i
$389$	−15.8471	−	27.4480i	−0.803481	−	1.39167i	−0.917312	−	0.398170i	$-0.869645\pi$
$389$	−15.8471	−	27.4480i	−0.803481	−	1.39167i	0.113830	−	0.993500i	$-0.463688\pi$
$390$		0			0
$391$	8.26371			0.417914
$392$	−11.4417	+	16.1582i	−0.577894	+	0.816112i
$393$		0			0
$394$	−9.30101	+	20.8023i	−0.468578	+	1.04800i
$395$	−4.85296	−	8.40558i	−0.244179	−	0.422931i
$396$		0			0
$397$	30.7223	+	17.7375i	1.54191	+	0.890222i	0.998718	+	0.0506125i	$0.0161174\pi$
$397$	30.7223	+	17.7375i	1.54191	+	0.890222i	0.543191	+	0.839609i	$0.317216\pi$
$398$	−19.4600	+	2.01439i	−0.975440	+	0.100972i
$399$		0			0
$400$	−29.2037	+	12.7828i	−1.46018	+	0.639139i
$401$	1.43600	−	2.48722i	0.0717102	−	0.124206i	−0.827941	−	0.560816i	$-0.810488\pi$
$401$	1.43600	−	2.48722i	0.0717102	−	0.124206i	0.899651	+	0.436610i	$0.143821\pi$
$402$		0			0
$403$	−25.9133	+	14.9611i	−1.29084	+	0.745264i
$404$	−7.31847	−	2.40339i	−0.364107	−	0.119573i
$405$		0			0
$406$	28.9935	+	2.84601i	1.43892	+	0.141245i
$407$		−	5.28908i		−	0.262170i
$408$		0			0
$409$	−1.14804	+	0.662818i	−0.0567667	+	0.0327743i	−0.528115	−	0.849173i	$-0.677101\pi$
$409$	−1.14804	+	0.662818i	−0.0567667	+	0.0327743i	0.471348	+	0.881947i	$0.343768\pi$
$410$	−9.16315	−	12.6538i	−0.452536	−	0.624927i
$411$		0			0
$412$	−13.6623	+	2.85912i	−0.673092	+	0.140859i
$413$	−3.35912	+	3.79465i	−0.165292	+	0.186722i
$414$		0			0
$415$	8.18924	+	4.72806i	0.401994	+	0.232091i
$416$	8.07978	−	13.7439i	0.396144	−	0.673848i
$417$		0			0
$418$	17.2163	+	7.69764i	0.842075	+	0.376504i
$419$	19.0652			0.931395			0.465698	−	0.884944i	$-0.345803\pi$
$419$	19.0652			0.931395			0.465698	+	0.884944i	$0.345803\pi$
$420$		0			0
$421$	18.7522			0.913925			0.456963	−	0.889486i	$-0.348937\pi$
$421$	18.7522			0.913925			0.456963	+	0.889486i	$0.348937\pi$
$422$	17.0514	+	7.62391i	0.830047	+	0.371126i
$423$		0			0
$424$	12.8227	+	11.6557i	0.622727	+	0.566049i
$425$	8.84179	+	5.10481i	0.428890	+	0.247620i
$426$		0			0
$427$	−5.24197	+	25.7281i	−0.253677	+	1.24507i
$428$	1.46376	+	6.99454i	0.0707533	+	0.338094i
$429$		0			0
$430$	28.2463	+	39.0065i	1.36216	+	1.88106i
$431$	−11.9017	+	6.87144i	−0.573284	+	0.330986i	−0.758460	−	0.651720i	$-0.774048\pi$
$431$	−11.9017	+	6.87144i	−0.573284	+	0.330986i	0.185176	+	0.982705i	$0.440714\pi$
$432$		0			0
$433$			36.5119i			1.75465i	0.479899	+	0.877324i	$0.340673\pi$
$433$			36.5119i			1.75465i	−0.479899	+	0.877324i	$0.659327\pi$
$434$	16.4066	+	36.1787i	0.787544	+	1.73663i
$435$		0			0
$436$	−9.79160	+	29.8160i	−0.468933	+	1.42793i
$437$	−15.6198	+	9.01812i	−0.747199	+	0.431395i
$438$		0			0
$439$	17.1013	−	29.6203i	0.816200	−	1.41370i	−0.0922635	−	0.995735i	$-0.529410\pi$
$439$	17.1013	−	29.6203i	0.816200	−	1.41370i	0.908463	−	0.417965i	$-0.137256\pi$
$440$	−46.2738	+	14.7943i	−2.20602	+	0.705289i
$441$		0			0
$442$	−5.07881	+	0.525730i	−0.241574	+	0.0250064i
$443$	−6.43914	−	3.71764i	−0.305933	−	0.176630i	0.339172	−	0.940724i	$-0.389853\pi$
$443$	−6.43914	−	3.71764i	−0.305933	−	0.176630i	−0.645105	+	0.764094i	$0.723186\pi$
$444$		0			0
$445$	9.95791	+	17.2476i	0.472050	+	0.817615i
$446$	−9.50420	+	21.2567i	−0.450037	+	1.00654i
$447$		0			0
$448$	−17.1113	−	12.4580i	−0.808434	−	0.588587i
$449$	15.4423			0.728767			0.364384	−	0.931249i	$-0.381280\pi$
$449$	15.4423			0.728767			0.364384	+	0.931249i	$0.381280\pi$
$450$		0			0
$451$	−7.31505	−	12.6700i	−0.344452	−	0.596609i
$452$	20.7901	+	23.2363i	0.977884	+	1.09294i
$453$		0			0
$454$	−36.5960	+	3.78822i	−1.71754	+	0.177790i
$455$	26.3132	+	5.36119i	1.23358	+	0.251337i
$456$		0			0
$457$	−4.29272	+	7.43521i	−0.200805	+	0.347805i	−0.948788	−	0.315913i	$-0.897689\pi$
$457$	−4.29272	+	7.43521i	−0.200805	+	0.347805i	0.747983	+	0.663718i	$0.231022\pi$
$458$	19.4452	−	14.0811i	0.908616	−	0.657968i
$459$		0			0
$460$	14.4966	−	44.1429i	0.675906	−	2.05817i
$461$			36.2424i			1.68798i	0.536362	+	0.843988i	$0.319798\pi$
$461$			36.2424i			1.68798i	−0.536362	+	0.843988i	$0.680202\pi$
$462$		0			0
$463$			23.4578i			1.09018i	0.838378	+	0.545089i	$0.183504\pi$
$463$			23.4578i			1.09018i	−0.838378	+	0.545089i	$0.816496\pi$
$464$	−3.45026	+	30.9526i	−0.160174	+	1.43694i
$465$		0			0
$466$	−10.4663	−	14.4534i	−0.484844	−	0.669543i
$467$	−19.4469	+	33.6830i	−0.899895	+	1.55866i	−0.0722679	+	0.997385i	$0.523024\pi$
$467$	−19.4469	+	33.6830i	−0.899895	+	1.55866i	−0.827627	+	0.561278i	$0.810310\pi$
$468$		0			0
$469$	−18.5761	−	16.4441i	−0.857767	−	0.759318i
$470$	−2.28842	−	22.1072i	−0.105557	−	1.01973i
$471$		0			0
$472$	−4.00903	−	3.64414i	−0.184530	−	0.167735i
$473$	22.5493	+	39.0566i	1.03682	+	1.79582i
$474$		0			0
$475$	−22.2834			−1.02243
$476$	0.0359267	+	6.77862i	0.00164670	+	0.310698i
$477$		0			0
$478$	−17.6103	−	7.87381i	−0.805475	−	0.360140i
$479$	−21.3331	−	36.9500i	−0.974733	−	1.68829i	−0.680814	−	0.732456i	$-0.738374\pi$
$479$	−21.3331	−	36.9500i	−0.974733	−	1.68829i	−0.293919	−	0.955830i	$-0.594960\pi$
$480$		0			0
$481$	−2.70673	−	1.56273i	−0.123416	−	0.0712543i
$482$	0.428417	+	4.13872i	0.0195138	+	0.188513i
$483$		0			0
$484$	−22.9952	+	4.81223i	−1.04524	+	0.218738i
$485$	13.5380	−	23.4486i	0.614731	−	1.06475i
$486$		0			0
$487$	−1.96989	+	1.13732i	−0.0892641	+	0.0515367i	−0.543968	−	0.839106i	$-0.683079\pi$
$487$	−1.96989	+	1.13732i	−0.0892641	+	0.0515367i	0.454703	+	0.890643i	$0.349745\pi$
$488$	−27.4283	−	5.96547i	−1.24162	−	0.270044i
$489$		0			0
$490$	10.4963	−	34.0714i	0.474173	−	1.53919i
$491$		−	9.76471i		−	0.440675i	−0.975424	−	0.220338i	$-0.929284\pi$
$491$		−	9.76471i		−	0.440675i	0.975424	−	0.220338i	$-0.0707159\pi$
$492$		0			0
$493$	8.63809	−	4.98720i	0.389040	−	0.224612i
$494$	9.02611	−	6.53619i	0.406104	−	0.294077i
$495$		0			0
$496$	−38.9042	+	17.0288i	−1.74685	+	0.764616i
$497$	5.34034	−	1.78518i	0.239547	−	0.0800765i
$498$		0			0
$499$	14.2123	+	8.20548i	0.636231	+	0.367328i	0.783161	−	0.621819i	$-0.213606\pi$
$499$	14.2123	+	8.20548i	0.636231	+	0.367328i	−0.146930	+	0.989147i	$0.546939\pi$
$500$	15.9406	−	14.2624i	0.712884	−	0.637835i
$501$		0			0
$502$	−8.70537	+	19.4701i	−0.388540	+	0.868994i
$503$	33.1594			1.47851			0.739253	−	0.673428i	$-0.235179\pi$
$503$	33.1594			1.47851			0.739253	+	0.673428i	$0.235179\pi$
$504$		0			0
$505$	13.8706			0.617233
$506$	17.7592	−	39.7197i	0.789495	−	1.76576i
$507$		0			0
$508$	8.14144	−	7.28434i	0.361218	−	0.323190i
$509$	−10.3036	−	5.94878i	−0.456698	−	0.263675i	0.253957	−	0.967216i	$-0.418268\pi$
$509$	−10.3036	−	5.94878i	−0.456698	−	0.263675i	−0.710655	+	0.703541i	$0.751601\pi$
$510$		0			0
$511$	16.9751	+	15.0269i	0.750936	+	0.664749i
$512$	13.5578	−	18.1159i	0.599178	−	0.800616i
$513$		0			0
$514$	3.46320	−	2.50785i	0.152755	−	0.110616i
$515$	21.7669	−	12.5671i	0.959162	−	0.553773i
$516$		0			0
$517$		−	20.8127i		−	0.915341i
$518$	−2.41583	+	3.37362i	−0.106145	+	0.148228i
$519$		0			0
$520$	−6.10115	+	28.0521i	−0.267553	+	1.23017i
$521$	3.26685	−	1.88612i	0.143123	−	0.0826323i	−0.426728	−	0.904380i	$-0.640334\pi$
$521$	3.26685	−	1.88612i	0.143123	−	0.0826323i	0.569852	+	0.821748i	$0.307001\pi$
$522$		0			0
$523$	12.1769	−	21.0910i	0.532459	−	0.922246i	−0.466823	−	0.884351i	$-0.654601\pi$
$523$	12.1769	−	21.0910i	0.532459	−	0.922246i	0.999282	−	0.0378952i	$-0.0120653\pi$
$524$	−18.1741	+	3.80331i	−0.793938	+	0.166148i
$525$		0			0
$526$	−3.93734	−	38.0367i	−0.171676	−	1.65848i
$527$	11.7787	+	6.80046i	0.513090	+	0.296233i
$528$		0			0
$529$	9.30573	+	16.1180i	0.404597	+	0.700782i
$530$	−28.4853	−	12.7362i	−1.23732	−	0.553225i
$531$		0			0
$532$	−7.46537	−	12.7736i	−0.323665	−	0.553804i
$533$	−8.64532			−0.374470
$534$		0			0
$535$	−6.43386	−	11.1438i	−0.278160	−	0.481787i
$536$	17.8394	−	19.6256i	0.770543	−	0.847697i
$537$		0			0
$538$	−1.23620	−	11.9423i	−0.0532962	−	0.514868i
$539$	13.0620	−	30.7241i	0.562620	−	1.32338i
$540$		0			0
$541$	10.8730	−	18.8326i	0.467467	−	0.809677i	−0.531842	−	0.846844i	$-0.678500\pi$
$541$	10.8730	−	18.8326i	0.467467	−	0.809677i	0.999309	+	0.0371667i	$0.0118332\pi$
$542$	4.46047	+	6.15966i	0.191594	+	0.264580i
$543$		0			0
$544$	−7.24653	−	0.0569867i	−0.310692	−	0.00244328i
$545$		−	56.5098i		−	2.42062i
$546$		0			0
$547$			25.6113i			1.09506i	0.836787	+	0.547529i	$0.184432\pi$
$547$			25.6113i			1.09506i	−0.836787	+	0.547529i	$0.815568\pi$
$548$	−1.12821	+	3.43546i	−0.0481946	+	0.146755i
$549$		0			0
$550$	43.5379	−	31.5277i	1.85646	−	1.34434i
$551$	−10.8850	+	18.8534i	−0.463716	+	0.803180i
$552$		0			0
$553$	−1.42356	+	6.98698i	−0.0605360	+	0.297116i
$554$	29.2779	−	3.03068i	1.24390	−	0.128761i
$555$		0			0
$556$	11.6494	+	13.0201i	0.494046	+	0.552176i
$557$	9.84326	+	17.0490i	0.417072	+	0.722391i	0.995644	−	0.0932413i	$-0.0297228\pi$
$557$	9.84326	+	17.0490i	0.417072	+	0.722391i	−0.578571	+	0.815632i	$0.696389\pi$
$558$		0			0
$559$	26.6500			1.12718
$560$	36.2729	+	11.6995i	1.53281	+	0.494392i
$561$		0			0
$562$	9.64480	−	21.5712i	0.406841	−	0.909927i
$563$	5.53366	+	9.58459i	0.233216	+	0.403942i	0.958753	−	0.284241i	$-0.0917417\pi$
$563$	5.53366	+	9.58459i	0.233216	+	0.403942i	−0.725537	+	0.688184i	$0.758408\pi$
$564$		0			0
$565$	−48.6220	−	28.0719i	−2.04554	−	1.18100i
$566$	−4.58577	+	0.474693i	−0.192754	+	0.0199528i
$567$		0			0
$568$	1.83313	+	5.73369i	0.0769163	+	0.240580i
$569$	12.7180	−	22.0283i	0.533167	−	0.923473i	−0.466082	−	0.884741i	$-0.654335\pi$
$569$	12.7180	−	22.0283i	0.533167	−	0.923473i	0.999250	−	0.0387316i	$-0.0123317\pi$
$570$		0			0
$571$	−17.5661	+	10.1418i	−0.735117	+	0.424420i	−0.820291	−	0.571946i	$-0.806189\pi$
$571$	−17.5661	+	10.1418i	−0.735117	+	0.424420i	0.0851743	+	0.996366i	$0.472855\pi$
$572$	−8.38776	+	25.5412i	−0.350710	+	1.06793i
$573$		0			0
$574$	−1.12126	+	11.4227i	−0.0468005	+	0.476776i
$575$			51.4100i			2.14394i
$576$		0			0
$577$	13.3573	−	7.71187i	0.556074	−	0.321049i	−0.195494	−	0.980705i	$-0.562631\pi$
$577$	13.3573	−	7.71187i	0.556074	−	0.321049i	0.751568	+	0.659656i	$0.229298\pi$
$578$	−12.7395	−	17.5925i	−0.529893	−	0.731752i
$579$		0			0
$580$	−11.4872	−	54.8916i	−0.476981	−	2.27925i
$581$	−2.20246	−	6.58863i	−0.0913736	−	0.273342i
$582$		0			0
$583$	−25.3050	−	14.6098i	−1.04802	−	0.605077i
$584$	−16.3019	+	17.9342i	−0.674576	+	0.742121i
$585$		0			0
$586$	32.2998	+	14.4417i	1.33429	+	0.596581i
$587$	−31.8321			−1.31385			−0.656925	−	0.753956i	$-0.728143\pi$
$587$	−31.8321			−1.31385			−0.656925	+	0.753956i	$0.728143\pi$
$588$		0			0
$589$	−29.6852			−1.22316
$590$	8.90593	+	3.98197i	0.366652	+	0.163935i
$591$		0			0
$592$	−3.57224	−	2.62988i	−0.146818	−	0.108087i
$593$	31.6740	+	18.2870i	1.30070	+	0.750957i	0.980523	−	0.196403i	$-0.0629259\pi$
$593$	31.6740	+	18.2870i	1.30070	+	0.750957i	0.320172	+	0.947359i	$0.396259\pi$
$594$		0			0
$595$	−3.86984	−	11.5766i	−0.158648	−	0.474593i
$596$	−34.6443	+	7.25005i	−1.41909	+	0.296974i
$597$		0			0
$598$	−15.0796	−	20.8241i	−0.616653	−	0.851563i
$599$	−28.1544	+	16.2550i	−1.15036	+	0.664160i	−0.948975	−	0.315352i	$-0.897877\pi$
$599$	−28.1544	+	16.2550i	−1.15036	+	0.664160i	−0.201384	+	0.979512i	$0.564544\pi$
$600$		0			0
$601$		−	22.0349i		−	0.898823i	−0.893325	−	0.449411i	$-0.851634\pi$
$601$		−	22.0349i		−	0.898823i	0.893325	−	0.449411i	$-0.148366\pi$
$602$	3.45639	−	35.2117i	0.140872	−	1.43512i
$603$		0			0
$604$	14.3484	+	4.71204i	0.583829	+	0.191730i
$605$	36.6362	−	21.1519i	1.48947	−	0.859948i
$606$		0			0
$607$	−4.32882	+	7.49773i	−0.175701	+	0.304324i	−0.940404	−	0.340060i	$-0.889553\pi$
$607$	−4.32882	+	7.49773i	−0.175701	+	0.304324i	0.764702	+	0.644384i	$0.222886\pi$
$608$	13.7594	−	7.80037i	0.558017	−	0.316347i
$609$		0			0
$610$	50.2754	−	5.20423i	2.03559	−	0.210713i
$611$	−10.6511	−	6.14939i	−0.430896	−	0.248778i
$612$		0			0
$613$	−16.5860	−	28.7278i	−0.669903	−	1.16031i	−0.977931	−	0.208928i	$-0.933003\pi$
$613$	−16.5860	−	28.7278i	−0.669903	−	1.16031i	0.308028	−	0.951377i	$-0.400331\pi$
$614$	−13.2310	+	29.5920i	−0.533960	+	1.19424i
$615$		0			0
$616$	32.6588	+	14.3950i	1.31586	+	0.579992i
$617$	28.0026			1.12734			0.563671	−	0.825999i	$-0.309388\pi$
$617$	28.0026			1.12734			0.563671	+	0.825999i	$0.309388\pi$
$618$		0			0
$619$	2.71629	+	4.70476i	0.109177	+	0.189100i	0.915437	−	0.402461i	$-0.131845\pi$
$619$	2.71629	+	4.70476i	0.109177	+	0.189100i	−0.806260	+	0.591561i	$0.798512\pi$
$620$	56.9894	−	50.9898i	2.28875	−	2.04780i
$621$		0			0
$622$	12.0396	−	1.24627i	0.482744	−	0.0499710i
$623$	2.92104	−	14.3367i	0.117029	−	0.574389i
$624$		0			0
$625$	0.666302	−	1.15407i	0.0266521	−	0.0461627i
$626$	12.6255	−	9.14263i	0.504615	−	0.365413i
$627$		0			0
$628$	−16.5533	−	5.43611i	−0.660548	−	0.216925i
$629$			1.42066i			0.0566453i
$630$		0			0
$631$		−	16.4332i		−	0.654195i	−0.944991	−	0.327098i	$-0.893929\pi$
$631$		−	16.4332i		−	0.654195i	0.944991	−	0.327098i	$-0.106071\pi$
$632$	−7.44871	−	1.62004i	−0.296294	−	0.0644418i
$633$		0			0
$634$	3.16361	+	4.36877i	0.125643	+	0.173506i
$635$	−9.83572	+	17.0360i	−0.390319	+	0.676052i
$636$		0			0
$637$	−11.8640	−	15.7624i	−0.470067	−	0.624530i
$638$	−5.40728	−	52.2370i	−0.214076	−	2.06808i
$639$		0			0
$640$	−13.0166	+	38.6094i	−0.514527	+	1.52617i
$641$	−6.33951	−	10.9804i	−0.250396	−	0.433698i	0.713239	−	0.700921i	$-0.247227\pi$
$641$	−6.33951	−	10.9804i	−0.250396	−	0.433698i	−0.963635	+	0.267223i	$0.913894\pi$
$642$		0			0
$643$	−4.22290			−0.166535			−0.0832674	−	0.996527i	$-0.526536\pi$
$643$	−4.22290			−0.166535			−0.0832674	+	0.996527i	$0.526536\pi$
$644$	−29.4699	+	17.2234i	−1.16128	+	0.678696i
$645$		0			0
$646$	−4.62433	−	2.06760i	−0.181942	−	0.0813488i
$647$	−9.70483	−	16.8093i	−0.381536	−	0.660840i	0.609746	−	0.792597i	$-0.291271\pi$
$647$	−9.70483	−	16.8093i	−0.381536	−	0.660840i	−0.991282	+	0.131757i	$0.957938\pi$
$648$		0			0
$649$	7.91160	+	4.56776i	0.310557	+	0.179300i
$650$	−3.27066	−	31.5961i	−0.128286	−	1.23930i
$651$		0			0
$652$	5.95650	+	28.4631i	0.233275	+	1.11470i
$653$	−17.2417	+	29.8635i	−0.674720	+	1.16865i	0.301831	+	0.953362i	$0.402402\pi$
$653$	−17.2417	+	29.8635i	−0.674720	+	1.16865i	−0.976551	+	0.215288i	$0.930931\pi$
$654$		0			0
$655$	28.9551	−	16.7172i	1.13137	−	0.653196i
$656$	−12.1946	−	1.35932i	−0.476118	−	0.0530725i
$657$		0			0
$658$	−9.50635	+	13.2753i	−0.370596	+	0.517525i
$659$			8.56812i			0.333767i	0.985977	+	0.166883i	$0.0533703\pi$
$659$			8.56812i			0.333767i	−0.985977	+	0.166883i	$0.946630\pi$
$660$		0			0
$661$	−16.4212	+	9.48077i	−0.638710	+	0.368759i	−0.784117	−	0.620612i	$-0.786884\pi$
$661$	−16.4212	+	9.48077i	−0.638710	+	0.368759i	0.145407	+	0.989372i	$0.453551\pi$
$662$	2.54300	−	1.84150i	0.0988366	−	0.0715717i
$663$		0			0
$664$	7.07392	−	2.26161i	0.274521	−	0.0877676i
$665$	19.9481	+	17.6586i	0.773554	+	0.684770i
$666$		0			0
$667$	43.4966	+	25.1128i	1.68420	+	0.972371i
$668$	−18.5059	−	20.6833i	−0.716013	−	0.800261i
$669$		0			0
$670$	−19.4932	+	43.5977i	−0.753087	+	1.68433i
$671$	47.3314			1.82721
$672$		0			0
$673$	−6.56771			−0.253167			−0.126583	−	0.991956i	$-0.540401\pi$
$673$	−6.56771			−0.253167			−0.126583	+	0.991956i	$0.540401\pi$
$674$	−10.4492	+	23.3704i	−0.402490	+	0.900194i
$675$		0			0
$676$	−6.74389	−	7.53740i	−0.259380	−	0.289900i
$677$	−5.35071	−	3.08923i	−0.205644	−	0.118729i	0.393641	−	0.919264i	$-0.371215\pi$
$677$	−5.35071	−	3.08923i	−0.205644	−	0.118729i	−0.599286	+	0.800535i	$0.704549\pi$
$678$		0			0
$679$	−18.8655	+	6.30640i	−0.723991	+	0.242018i
$680$	12.4293	−	3.97377i	0.476640	−	0.152387i
$681$		0			0
$682$	57.9999	−	42.0002i	2.22093	−	1.60827i
$683$	16.7278	−	9.65777i	0.640070	−	0.369544i	−0.144572	−	0.989494i	$-0.546180\pi$
$683$	16.7278	−	9.65777i	0.640070	−	0.369544i	0.784641	+	0.619950i	$0.212847\pi$
$684$		0			0
$685$		−	6.51117i		−	0.248779i
$686$	−22.3650	+	13.6311i	−0.853900	+	0.520437i
$687$		0			0
$688$	37.5909	+	4.19023i	1.43314	+	0.159751i
$689$	−14.9534	+	8.63334i	−0.569679	+	0.328904i
$690$		0			0
$691$	6.17003	−	10.6868i	0.234719	−	0.406546i	−0.724472	−	0.689304i	$-0.757916\pi$
$691$	6.17003	−	10.6868i	0.234719	−	0.406546i	0.959191	+	0.282759i	$0.0912496\pi$
$692$	−2.65289	−	12.6768i	−0.100848	−	0.481901i
$693$		0			0
$694$	2.18481	+	21.1063i	0.0829342	+	0.801186i
$695$	−27.2446	−	15.7297i	−1.03345	−	0.596661i
$696$		0			0
$697$	1.96484	+	3.40320i	0.0744236	+	0.128905i
$698$	2.34138	+	1.04687i	0.0886227	+	0.0396245i
$699$		0			0
$700$	−42.1710	+	0.223506i	−1.59391	+	0.00844774i
$701$	5.88673			0.222339			0.111169	−	0.993801i	$-0.464540\pi$
$701$	5.88673			0.222339			0.111169	+	0.993801i	$0.464540\pi$
$702$		0			0
$703$	−1.55035	−	2.68529i	−0.0584727	−	0.101278i
$704$	−15.8472	+	34.7081i	−0.597263	+	1.30811i
$705$		0			0
$706$	1.04036	+	10.0504i	0.0391544	+	0.378251i
$707$	−7.63005	−	6.75432i	−0.286957	−	0.254022i
$708$		0			0
$709$	−11.5925	+	20.0787i	−0.435364	+	0.754073i	−0.997325	−	0.0730907i	$-0.976714\pi$
$709$	−11.5925	+	20.0787i	−0.435364	+	0.754073i	0.561961	+	0.827164i	$0.310047\pi$
$710$	−6.35740	−	8.77921i	−0.238589	−	0.329478i
$711$		0			0
$712$	15.2842	+	3.32420i	0.572799	+	0.124580i
$713$			68.4867i			2.56485i
$714$		0			0
$715$		−	48.4079i		−	1.81035i
$716$	−6.78236	−	2.22733i	−0.253469	−	0.0832393i
$717$		0			0
$718$	32.5816	−	23.5937i	1.21593	−	0.880509i
$719$	−7.32342	+	12.6845i	−0.273117	+	0.473053i	−0.969658	−	0.244464i	$-0.921388\pi$
$719$	−7.32342	+	12.6845i	−0.273117	+	0.473053i	0.696541	+	0.717517i	$0.254721\pi$
$720$		0			0
$721$	−18.0933	−	3.68642i	−0.673829	−	0.137289i
$722$	−15.7301	+	1.62829i	−0.585414	+	0.0605987i
$723$		0			0
$724$	−21.9172	+	19.6099i	−0.814547	+	0.728795i
$725$	31.0263	+	53.7390i	1.15229	+	1.99582i
$726$		0			0
$727$	−6.86577			−0.254637			−0.127319	−	0.991862i	$-0.540637\pi$
$727$	−6.86577			−0.254637			−0.127319	+	0.991862i	$0.540637\pi$
$728$	17.0162	−	12.4602i	0.630664	−	0.461805i
$729$		0			0
$730$	17.8131	−	39.8402i	0.659294	−	1.47455i
$731$	−6.05680	−	10.4907i	−0.224019	−	0.388012i
$732$		0			0
$733$	−1.76365	−	1.01825i	−0.0651420	−	0.0376098i	0.467075	−	0.884218i	$-0.345308\pi$
$733$	−1.76365	−	1.01825i	−0.0651420	−	0.0376098i	−0.532217	+	0.846608i	$0.678641\pi$
$734$	41.7596	−	4.32272i	1.54138	−	0.159555i
$735$		0			0
$736$	−17.9962	−	31.7443i	−0.663350	−	1.17011i
$737$	−22.3608	+	38.7301i	−0.823671	+	1.42664i
$738$		0			0
$739$	26.0135	−	15.0189i	0.956921	−	0.552478i	0.0616967	−	0.998095i	$-0.480349\pi$
$739$	26.0135	−	15.0189i	0.956921	−	0.552478i	0.895224	+	0.445617i	$0.147016\pi$
$740$	7.58884	+	2.49218i	0.278971	+	0.0916145i
$741$		0			0
$742$	9.46752	+	20.8770i	0.347563	+	0.766421i
$743$			35.5890i			1.30563i	0.757516	+	0.652816i	$0.226413\pi$
$743$			35.5890i			1.30563i	−0.757516	+	0.652816i	$0.773587\pi$
$744$		0			0
$745$	55.1956	−	31.8672i	2.02221	−	1.16752i
$746$	20.1181	+	27.7820i	0.736576	+	1.01717i
$747$		0			0
$748$	11.9605	−	2.50299i	0.437320	−	0.0915184i
$749$	−1.88730	+	9.26304i	−0.0689604	+	0.338464i
$750$		0			0
$751$	−14.2416	−	8.22238i	−0.519683	−	0.300039i	0.217122	−	0.976144i	$-0.430333\pi$
$751$	−14.2416	−	8.22238i	−0.519683	−	0.300039i	−0.736805	+	0.676106i	$0.763666\pi$
$752$	−14.0569	−	10.3487i	−0.512602	−	0.377377i
$753$		0			0
$754$	−28.3303	−	12.6669i	−1.03173	−	0.461301i
$755$	−27.1944			−0.989704
$756$		0			0
$757$	11.0638			0.402119			0.201060	−	0.979579i	$-0.435561\pi$
$757$	11.0638			0.402119			0.201060	+	0.979579i	$0.435561\pi$
$758$	36.5526	+	16.3432i	1.32765	+	0.593611i
$759$		0			0
$760$	−19.1569	+	21.0751i	−0.694894	+	0.764473i
$761$	−0.693929	−	0.400640i	−0.0251549	−	0.0145232i	0.487370	−	0.873196i	$-0.337956\pi$
$761$	−0.693929	−	0.400640i	−0.0251549	−	0.0145232i	−0.512525	+	0.858672i	$0.671290\pi$
$762$		0			0
$763$	−27.5176	+	31.0854i	−0.996205	+	1.12537i
$764$	1.70981	+	8.17029i	0.0618586	+	0.295591i
$765$		0			0
$766$	−21.6920	−	29.9554i	−0.783763	−	1.08233i
$767$	4.67517	−	2.69921i	0.168811	−	0.0974629i
$768$		0			0
$769$		−	16.0686i		−	0.579449i	−0.957110	−	0.289724i	$-0.906436\pi$
$769$		−	16.0686i		−	0.579449i	0.957110	−	0.289724i	$-0.0935636\pi$
$770$	−63.9595	−	6.27830i	−2.30494	−	0.226254i
$771$		0			0
$772$	1.11069	−	3.38212i	0.0399747	−	0.121725i
$773$	12.2616	−	7.07927i	0.441021	−	0.254624i	−0.263010	−	0.964793i	$-0.584715\pi$
$773$	12.2616	−	7.07927i	0.441021	−	0.254624i	0.704031	+	0.710170i	$0.251382\pi$
$774$		0			0
$775$	−42.3069	+	73.2776i	−1.51971	+	2.63221i
$776$	−6.47577	−	20.2550i	−0.232466	−	0.727114i
$777$		0			0
$778$	44.5842	−	4.61511i	1.59842	−	0.165460i
$779$	−7.42777	−	4.28843i	−0.266128	−	0.153649i
$780$		0			0
$781$	−5.07518	−	8.79048i	−0.181604	−	0.314548i
$782$	−4.77017	+	10.6688i	−0.170581	+	0.381515i
$783$		0			0
$784$	−14.2562	−	24.0990i	−0.509152	−	0.860677i
$785$	31.3732			1.11976
$786$		0			0
$787$	−2.47090	−	4.27972i	−0.0880779	−	0.152555i	0.818621	−	0.574335i	$-0.194739\pi$
$787$	−2.47090	−	4.27972i	−0.0880779	−	0.152555i	−0.906699	+	0.421779i	$0.861406\pi$
$788$	−21.4877	−	24.0160i	−0.765468	−	0.855534i
$789$		0			0
$790$	13.6533	−	1.41331i	0.485763	−	0.0502834i
$791$	13.0767	+	39.1187i	0.464954	+	1.39090i
$792$		0			0
$793$	13.9847	−	24.2222i	0.496611	−	0.860156i
$794$	−40.6342	+	29.4249i	−1.44205	+	1.04425i
$795$		0			0
$796$	8.63249	−	26.2864i	0.305970	−	0.931698i
$797$		−	11.2762i		−	0.399425i	−0.979855	−	0.199713i	$-0.935999\pi$
$797$		−	11.2762i		−	0.399425i	0.979855	−	0.199713i	$-0.0640008\pi$
$798$		0			0
$799$			5.59034i			0.197772i
$800$	0.354524	−	45.0819i	0.0125343	−	1.59389i
$801$		0			0
$802$	2.38218	+	3.28966i	0.0841179	+	0.116162i
$803$	20.4336	−	35.3921i	0.721087	−	1.24896i
$804$		0			0
$805$	40.7402	−	46.0223i	1.43590	−	1.62207i
$806$	−4.35706	−	42.0914i	−0.153471	−	1.48261i
$807$		0			0
$808$	7.32742	−	8.06111i	0.257778	−	0.283589i
$809$	−13.3092	−	23.0522i	−0.467926	−	0.810471i	0.531403	−	0.847119i	$-0.321665\pi$
$809$	−13.3092	−	23.0522i	−0.467926	−	0.810471i	−0.999328	+	0.0366484i	$0.988332\pi$
$810$		0			0
$811$	−19.0545			−0.669094			−0.334547	−	0.942379i	$-0.608583\pi$
$811$	−19.0545			−0.669094			−0.334547	+	0.942379i	$0.608583\pi$
$812$	−20.4106	+	35.7889i	−0.716272	+	1.25595i
$813$		0			0
$814$	6.82842	+	3.05309i	0.239336	+	0.107011i
$815$	−26.1815	−	45.3476i	−0.917097	−	1.58846i
$816$		0			0
$817$	22.8968	+	13.2195i	0.801058	+	0.462491i
$818$	−0.193030	−	1.86477i	−0.00674915	−	0.0652001i
$819$		0			0
$820$	21.6260	−	4.52569i	0.755211	−	0.158044i
$821$	−11.7702	+	20.3866i	−0.410783	+	0.711496i	−0.994976	−	0.100118i	$-0.968078\pi$
$821$	−11.7702	+	20.3866i	−0.410783	+	0.711496i	0.584193	+	0.811615i	$0.301411\pi$
$822$		0			0
$823$	31.9586	−	18.4513i	1.11401	−	0.643173i	0.174143	−	0.984720i	$-0.444284\pi$
$823$	31.9586	−	18.4513i	1.11401	−	0.643173i	0.939864	+	0.341548i	$0.110951\pi$
$824$	4.19522	−	19.2890i	0.146147	−	0.671963i
$825$		0			0
$826$	−2.96002	−	6.52721i	−0.102992	−	0.227111i
$827$			1.44687i			0.0503126i	0.999684	+	0.0251563i	$0.00800834\pi$
$827$			1.44687i			0.0503126i	−0.999684	+	0.0251563i	$0.991992\pi$
$828$		0			0
$829$	−43.1883	+	24.9348i	−1.49999	+	0.866020i	−1.00000		9.98631e-6i	$-0.999997\pi$
$829$	−43.1883	+	24.9348i	−1.49999	+	0.866020i	−0.499991	+	0.866030i	$0.666663\pi$
$830$	−10.8313	+	7.84341i	−0.375960	+	0.272249i
$831$		0			0
$832$	13.0799	+	18.3649i	0.453464	+	0.636688i
$833$	−3.50848	+	8.25256i	−0.121562	+	0.285934i
$834$		0			0
$835$	43.2798	+	24.9876i	1.49776	+	0.864732i
$836$	−19.8760	+	17.7835i	−0.687425	+	0.615056i
$837$		0			0
$838$	−11.0053	+	24.6140i	−0.380170	+	0.850275i
$839$	52.2470			1.80377			0.901883	−	0.431981i	$-0.142185\pi$
$839$	52.2470			1.80377			0.901883	+	0.431981i	$0.142185\pi$
$840$		0			0
$841$	31.6229			1.09045
$842$	−10.8246	+	24.2099i	−0.373040	+	0.834327i
$843$		0			0
$844$	−19.6856	+	17.6132i	−0.677606	+	0.606270i
$845$	15.7720	+	9.10597i	0.542574	+	0.313255i
$846$		0			0
$847$	−30.4531	−	6.20468i	−1.04638	−	0.213195i
$848$	−22.4498	+	9.82654i	−0.770929	+	0.337445i
$849$		0			0
$850$	−11.6944	+	8.46840i	−0.401114	+	0.290464i
$851$	−6.19524	+	3.57682i	−0.212370	+	0.122612i
$852$		0			0
$853$			9.36179i			0.320542i	0.987073	+	0.160271i	$0.0512367\pi$
$853$			9.36179i			0.320542i	−0.987073	+	0.160271i	$0.948763\pi$
$854$	−30.1901	−	21.6190i	−1.03308	−	0.739786i
$855$		0			0
$856$	−9.87519	−	2.14778i	−0.337527	−	0.0734098i
$857$	23.6623	−	13.6614i	0.808289	−	0.466666i	−0.0380721	−	0.999275i	$-0.512122\pi$
$857$	23.6623	−	13.6614i	0.808289	−	0.466666i	0.846361	+	0.532609i	$0.178788\pi$
$858$		0			0
$859$	13.9535	−	24.1682i	0.476089	−	0.824610i	−0.523536	−	0.852004i	$-0.675387\pi$
$859$	13.9535	−	24.1682i	0.476089	−	0.824610i	0.999625	+	0.0273936i	$0.00872074\pi$
$860$	−66.6641	+	13.9509i	−2.27323	+	0.475721i
$861$		0			0
$862$	−2.00115	−	19.3321i	−0.0681593	−	0.658453i
$863$	−14.3385	−	8.27836i	−0.488090	−	0.281799i	0.235692	−	0.971828i	$-0.424264\pi$
$863$	−14.3385	−	8.27836i	−0.488090	−	0.281799i	−0.723782	+	0.690029i	$0.757598\pi$
$864$		0			0
$865$	11.6606	+	20.1968i	0.396474	+	0.686713i
$866$	−47.1383	−	21.0762i	−1.60183	−	0.716200i
$867$		0			0
$868$	−56.1789	+	0.297748i	−1.90683	+	0.0101062i
$869$	12.8538			0.436035
$870$		0			0
$871$	13.2136	+	22.8866i	0.447726	+	0.775484i
$872$	−32.8416	−	29.8525i	−1.11216	−	1.01093i
$873$		0			0
$874$	−2.62632	−	25.3715i	−0.0888365	−	0.858205i
$875$	26.8362	−	8.97087i	0.907228	−	0.303271i
$876$		0			0
$877$	−6.78956	+	11.7599i	−0.229267	+	0.397103i	−0.957591	−	0.288130i	$-0.906966\pi$
$877$	−6.78956	+	11.7599i	−0.229267	+	0.397103i	0.728324	+	0.685233i	$0.240300\pi$
$878$	28.3694	+	39.1766i	0.957422	+	1.32215i
$879$		0			0
$880$	7.61126	−	68.2813i	0.256576	−	2.30176i
$881$			7.57867i			0.255332i	0.991817	+	0.127666i	$0.0407485\pi$
$881$			7.57867i			0.255332i	−0.991817	+	0.127666i	$0.959251\pi$
$882$		0			0
$883$			5.56097i			0.187141i	0.995613	+	0.0935707i	$0.0298281\pi$
$883$			5.56097i			0.187141i	−0.995613	+	0.0935707i	$0.970172\pi$
$884$	2.25297	−	6.86043i	0.0757756	−	0.230741i
$885$		0			0
$886$	8.51658	−	6.16721i	0.286120	−	0.207192i
$887$	16.4181	−	28.4370i	0.551266	−	0.954821i	−0.446917	−	0.894575i	$-0.647478\pi$
$887$	16.4181	−	28.4370i	0.551266	−	0.954821i	0.998184	−	0.0602460i	$-0.0191885\pi$
$888$		0			0
$889$	13.7062	−	4.58176i	0.459692	−	0.153667i
$890$	−28.0155	+	2.90001i	−0.939082	+	0.0972085i
$891$		0			0
$892$	−21.9571	−	24.5406i	−0.735179	−	0.821682i
$893$	−6.10069	−	10.5667i	−0.204152	−	0.353601i
$894$		0			0
$895$	12.8545			0.429679
$896$	25.9613	−	14.9001i	0.867304	−	0.497778i
$897$		0			0
$898$	−8.91397	+	19.9367i	−0.297463	+	0.665295i
$899$	41.3322	+	71.5895i	1.37851	+	2.38764i
$900$		0			0
$901$	6.79697	+	3.92423i	0.226440	+	0.130735i
$902$	20.5801	−	2.13034i	0.685243	−	0.0709325i
$903$		0			0
$904$	−42.0000	+	13.4279i	−1.39690	+	0.446605i
$905$	26.4783	−	45.8618i	0.880169	−	1.52450i
$906$		0			0
$907$	33.1907	−	19.1626i	1.10208	−	0.636285i	0.165312	−	0.986241i	$-0.447137\pi$
$907$	33.1907	−	19.1626i	1.10208	−	0.636285i	0.936766	+	0.349956i	$0.113804\pi$
$908$	16.2341	−	49.4338i	0.538747	−	1.64052i
$909$		0			0
$910$	−22.1107	+	30.8768i	−0.732962	+	1.02356i
$911$		−	52.3031i		−	1.73288i	−0.499282	−	0.866440i	$-0.666403\pi$
$911$		−	52.3031i		−	1.73288i	0.499282	−	0.866440i	$-0.333597\pi$
$912$		0			0
$913$	−10.8452	+	6.26149i	−0.358924	+	0.207225i
$914$	−7.12123	−	9.83402i	−0.235549	−	0.325280i
$915$		0			0
$916$	6.95468	+	33.2329i	0.229789	+	1.09804i
$917$	−24.0684	−	4.90381i	−0.794808	−	0.161938i
$918$		0			0
$919$	−3.81590	−	2.20311i	−0.125875	−	0.0726739i	0.435740	−	0.900072i	$-0.356487\pi$
$919$	−3.81590	−	2.20311i	−0.125875	−	0.0726739i	−0.561615	+	0.827398i	$0.689820\pi$
$920$	48.6223	+	44.1969i	1.60303	+	1.45713i
$921$		0			0
$922$	−46.7905	−	20.9207i	−1.54096	−	0.688986i
$923$	−5.99812			−0.197431
$924$		0			0
$925$	−8.83816			−0.290597
$926$	−30.2851	−	13.5409i	−0.995229	−	0.444981i
$927$		0			0
$928$	−37.9695	−	22.3216i	−1.24641	−	0.732743i
$929$	20.9426	+	12.0912i	0.687106	+	0.396701i	0.802527	−	0.596616i	$-0.203488\pi$
$929$	20.9426	+	12.0912i	0.687106	+	0.396701i	−0.115421	+	0.993317i	$0.536822\pi$
$930$		0			0
$931$	−2.37432	−	19.4276i	−0.0778151	−	0.636713i
$932$	24.7016	−	5.16934i	0.809129	−	0.169327i
$933$		0			0
$934$	−32.2606	−	44.5501i	−1.05560	−	1.45772i
$935$	−19.0556	+	11.0018i	−0.623185	+	0.359796i
$936$		0			0
$937$		−	7.17084i		−	0.234261i	−0.993117	−	0.117130i	$-0.962630\pi$
$937$		−	7.17084i		−	0.234261i	0.993117	−	0.117130i	$-0.0373696\pi$
$938$	31.9530	−	14.4903i	1.04330	−	0.473126i
$939$		0			0
$940$	29.8624	+	9.80682i	0.974003	+	0.319863i
$941$	−41.8199	+	24.1447i	−1.36329	+	0.787096i	−0.990060	−	0.140644i	$-0.955083\pi$
$941$	−41.8199	+	24.1447i	−1.36329	+	0.787096i	−0.373229	+	0.927739i	$0.621749\pi$
$942$		0			0
$943$	−9.89384	+	17.1366i	−0.322188	+	0.558045i
$944$	7.01893	−	3.07227i	0.228447	−	0.0999937i
$945$		0			0
$946$	−63.4402	+	6.56697i	−2.06262	+	0.213511i
$947$	−45.5194	−	26.2806i	−1.47918	−	0.854006i	−0.479460	−	0.877564i	$-0.659167\pi$
$947$	−45.5194	−	26.2806i	−1.47918	−	0.854006i	−0.999722	+	0.0235578i	$0.992501\pi$
$948$		0			0
$949$	−12.0748	−	20.9141i	−0.391964	−	0.678901i
$950$	12.8629	−	28.7687i	0.417328	−	0.933381i
$951$		0			0
$952$	−8.77223	−	3.86653i	−0.284309	−	0.125315i
$953$	−36.7039			−1.18895			−0.594477	−	0.804112i	$-0.702641\pi$
$953$	−36.7039			−1.18895			−0.594477	+	0.804112i	$0.702641\pi$
$954$		0			0
$955$	−7.51536	−	13.0170i	−0.243191	−	0.421220i
$956$	20.3308	−	18.1905i	0.657546	−	0.588323i
$957$		0			0
$958$	60.0183	−	6.21276i	1.93910	−	0.200725i
$959$	−3.17063	+	3.58172i	−0.102385	+	0.115660i
$960$		0			0
$961$	−40.8599	+	70.7714i	−1.31806	+	2.28295i
$962$	3.57999	−	2.59242i	0.115423	−	0.0835830i
$963$		0			0
$964$	−5.59056	−	1.83594i	−0.180060	−	0.0591318i
$965$			6.41009i			0.206348i
$966$		0			0
$967$			45.4657i			1.46208i	0.682336	+	0.731039i	$0.260964\pi$
$967$			45.4657i			1.46208i	−0.682336	+	0.731039i	$0.739036\pi$
$968$	7.06105	−	32.4656i	0.226951	−	1.04348i
$969$		0			0
$970$	22.4584	+	31.0137i	0.721095	+	0.995791i
$971$	−20.1945	+	34.9780i	−0.648074	+	1.12250i	0.335509	+	0.942037i	$0.391092\pi$
$971$	−20.1945	+	34.9780i	−0.648074	+	1.12250i	−0.983582	+	0.180459i	$0.942242\pi$
$972$		0			0
$973$	7.32733	+	21.9196i	0.234903	+	0.702709i
$974$	−0.331217	−	3.19972i	−0.0106129	−	0.102526i
$975$		0			0
$976$	23.5345	−	31.9676i	0.753321	−	1.02326i
$977$	15.8920	+	27.5257i	0.508429	+	0.880625i	0.999952	+	0.00976068i	$0.00310697\pi$
$977$	15.8920	+	27.5257i	0.508429	+	0.880625i	−0.491523	+	0.870864i	$0.663560\pi$
$978$		0			0
$979$	−26.3750			−0.842948
$980$	37.9287	+	33.2186i	1.21159	+	1.06113i
$981$		0			0
$982$	12.6067	+	5.63662i	0.402295	+	0.179872i
$983$	13.6310	+	23.6096i	0.434761	+	0.753028i	0.997276	−	0.0737588i	$-0.0234995\pi$
$983$	13.6310	+	23.6096i	0.434761	+	0.753028i	−0.562515	+	0.826787i	$0.690166\pi$
$984$		0			0
$985$	50.2535	+	29.0139i	1.60121	+	0.924459i
$986$	1.45241	+	14.0310i	0.0462540	+	0.446837i
$987$		0			0
$988$	3.22823	+	15.4261i	0.102704	+	0.490768i
$989$	30.4987	−	52.8253i	0.969802	−	1.67975i
$990$		0			0
$991$	−16.9636	+	9.79395i	−0.538867	+	0.311115i	−0.744620	−	0.667489i	$-0.767369\pi$
$991$	−16.9636	+	9.79395i	−0.538867	+	0.311115i	0.205753	+	0.978604i	$0.434036\pi$
$992$	0.472285	−	60.0567i	0.0149951	−	1.90680i
$993$		0			0
$994$	−0.777931	+	7.92510i	−0.0246745	+	0.251369i
$995$			49.8203i			1.57941i
$996$		0			0
$997$	37.9200	−	21.8931i	1.20094	−	0.693363i	0.240176	−	0.970729i	$-0.422795\pi$
$997$	37.9200	−	21.8931i	1.20094	−	0.693363i	0.960764	+	0.277366i	$0.0894616\pi$
$998$	−18.7976	+	13.6121i	−0.595028	+	0.430885i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.d.271.6	yes	32
3.2	odd	2	inner	756.2.bf.d.271.11	yes	32
4.3	odd	2		756.2.bf.a.271.6	✓	32
7.3	odd	6		756.2.bf.a.703.6	yes	32
12.11	even	2		756.2.bf.a.271.11	yes	32
21.17	even	6		756.2.bf.a.703.11	yes	32
28.3	even	6	inner	756.2.bf.d.703.6	yes	32
84.59	odd	6	inner	756.2.bf.d.703.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.a.271.6	✓	32	4.3	odd	2
756.2.bf.a.271.11	yes	32	12.11	even	2
756.2.bf.a.703.6	yes	32	7.3	odd	6
756.2.bf.a.703.11	yes	32	21.17	even	6
756.2.bf.d.271.6	yes	32	1.1	even	1	trivial
756.2.bf.d.271.11	yes	32	3.2	odd	2	inner
756.2.bf.d.703.6	yes	32	28.3	even	6	inner
756.2.bf.d.703.11	yes	32	84.59	odd	6	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.577244 + 1.29104i) q^{2} +(-1.33358 - 1.49049i) q^{4} +(3.11886 + 1.80067i) q^{5} +(-0.838804 - 2.50926i) q^{7} +(2.69409 - 0.861330i) q^{8} +O(q^{10})\)	\(q+(-0.577244 + 1.29104i) q^{2} +(-1.33358 - 1.49049i) q^{4} +(3.11886 + 1.80067i) q^{5} +(-0.838804 - 2.50926i) q^{7} +(2.69409 - 0.861330i) q^{8} +(-4.12508 + 2.98715i) q^{10} +(-4.13038 + 2.38467i) q^{11} +2.81834i q^{13} +(3.72376 + 0.365526i) q^{14} +(-0.443132 + 3.97538i) q^{16} +(1.10943 - 0.640529i) q^{17} +(-1.39801 + 2.42142i) q^{19} +(-1.47535 - 7.04997i) q^{20} +(-0.694481 - 6.70903i) q^{22} +(5.58646 + 3.22535i) q^{23} +(3.98484 + 6.90195i) q^{25} +(-3.63859 - 1.62687i) q^{26} +(-2.62143 + 4.59653i) q^{28} +7.78607 q^{29} +(5.30848 + 9.19455i) q^{31} +(-4.87659 - 2.86686i) q^{32} +(0.186539 + 1.80206i) q^{34} +(1.90225 - 9.33644i) q^{35} +(-0.554486 + 0.960399i) q^{37} +(-2.31917 - 3.20264i) q^{38} +(9.95344 + 2.16480i) q^{40} +3.06753i q^{41} -9.45594i q^{43} +(9.06252 + 2.97614i) q^{44} +(-7.38881 + 5.35055i) q^{46} +(-2.18192 + 3.77920i) q^{47} +(-5.59282 + 4.20956i) q^{49} +(-11.2109 + 1.16049i) q^{50} +(4.20071 - 3.75847i) q^{52} +(3.06328 + 5.30575i) q^{53} -17.1761 q^{55} +(-4.42112 - 6.03769i) q^{56} +(-4.49446 + 10.0521i) q^{58} +(-0.957733 - 1.65884i) q^{59} +(-8.59451 - 4.96204i) q^{61} +(-14.9348 + 1.54597i) q^{62} +(6.51622 - 4.64100i) q^{64} +(-5.07490 + 8.78998i) q^{65} +(8.12062 - 4.68844i) q^{67} +(-2.43421 - 0.799398i) q^{68} +(10.9557 + 7.84529i) q^{70} +2.12825i q^{71} +(-7.42074 + 4.28437i) q^{73} +(-0.919841 - 1.27025i) q^{74} +(5.47346 - 1.14544i) q^{76} +(9.44835 + 8.36393i) q^{77} +(-2.33401 - 1.34754i) q^{79} +(-8.54042 + 11.6007i) q^{80} +(-3.96031 - 1.77071i) q^{82} +2.62572 q^{83} +4.61353 q^{85} +(12.2080 + 5.45838i) q^{86} +(-9.07361 + 9.98214i) q^{88} +(4.78921 + 2.76505i) q^{89} +(7.07195 - 2.36403i) q^{91} +(-2.64264 - 12.6278i) q^{92} +(-3.61961 - 4.99847i) q^{94} +(-8.72037 + 5.03471i) q^{95} -7.51833i q^{97} +(-2.20630 - 9.65050i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{7}+O(q^{10}) \) 32 * q + 2 * q^7	\( 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) \) 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

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