LMFDB - Embedded newform 756.2.bf.d.271.11

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			271.11
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.d.703.11

$q$-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	−0.400953	−	0.916098i	$-0.631321\pi$
$5$	−3.11886	−	1.80067i	−1.39479	−	0.805285i	−0.993841	+	0.110813i	$0.964654\pi$
$6$		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	0.275176	−	0.961394i	$-0.411264\pi$
$11$	4.13038	−	2.38467i	1.24536	−	0.719006i	0.970179	+	0.242388i	$0.0779306\pi$
$12$		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	−0.628468	−	0.777836i	$-0.716318\pi$
$17$	−1.10943	+	0.640529i	−0.269076	+	0.155351i	0.359392	+	0.933187i	$0.382984\pi$
$18$		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	−0.212395	−	0.977184i	$-0.568126\pi$
$23$	−5.58646	−	3.22535i	−1.16486	−	0.672531i	−0.952464	+	0.304653i	$0.901460\pi$
$24$		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	$-0.757200\pi$
$29$	−7.78607			−1.44584			−0.722919	+	0.690933i	$0.757200\pi$
$30$		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	$-0.923005\pi$
$41$		−	3.06753i		−	0.479067i	0.970888	−	0.239534i	$-0.0769945\pi$
$42$		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	−0.661860	−	0.749627i	$-0.730233\pi$
$47$	2.18192	−	3.77920i	0.318266	−	0.551253i	0.980126	+	0.198374i	$0.0635661\pi$
$48$		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	0.575242	−	0.817983i	$-0.304908\pi$
$53$	−3.06328	−	5.30575i	−0.420773	−	0.728801i	−0.996015	+	0.0891825i	$0.971575\pi$
$54$		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	0.921610	−	0.388117i	$-0.126874\pi$
$59$	0.957733	+	1.65884i	0.124686	+	0.215963i	−0.796924	+	0.604080i	$0.793541\pi$
$60$		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	$-0.959694\pi$
$71$		−	2.12825i		−	0.252577i	0.991994	−	0.126288i	$-0.0403065\pi$
$72$		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	$-0.546030\pi$
$83$	−2.62572			−0.288210			−0.144105	+	0.989562i	$0.546030\pi$
$84$		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	0.224214	−	0.974540i	$-0.428019\pi$
$89$	−4.78921	−	2.76505i	−0.507655	−	0.293095i	−0.731869	+	0.681445i	$0.761352\pi$
$90$		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	−0.656682	−	0.754168i	$-0.728041\pi$
$101$	−3.33550	+	1.92575i	−0.331895	+	0.191619i	0.324787	+	0.945787i	$0.394707\pi$
$102$		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	0.642057	−	0.766657i	$-0.278081\pi$
$107$	3.09433	+	1.78651i	0.299141	+	0.172709i	−0.342916	+	0.939366i	$0.611415\pi$
$108$		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	$-0.237989\pi$
$113$	15.5897			1.46656			0.733278	+	0.679929i	$0.237989\pi$
$114$		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	−0.994387	−	0.105800i	$-0.966260\pi$
$131$	−4.64194	+	8.04008i	−0.405568	+	0.702465i	0.588819	+	0.808265i	$0.299593\pi$
$132$		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	0.902055	−	0.431621i	$-0.142058\pi$
$137$	0.903992	+	1.56576i	0.0772332	+	0.133772i	−0.824822	+	0.565392i	$0.808725\pi$
$138$		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	$0.424787\pi$
$149$	−8.84870	+	15.3264i	−0.724914	+	1.25559i	−0.959010	+	0.283374i	$0.908546\pi$
$150$		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	$-0.680409\pi$
$167$	−13.8768			−1.07382			−0.536911	+	0.843639i	$0.680409\pi$
$168$		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	0.271424	−	0.962460i	$-0.412505\pi$
$173$	−5.60814	−	3.23786i	−0.426379	−	0.246170i	−0.697803	+	0.716290i	$0.745839\pi$
$174$		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	−0.611054	−	0.791589i	$-0.709254\pi$
$179$	−3.09116	+	1.78468i	−0.231044	+	0.133393i	0.380010	+	0.924983i	$0.375921\pi$
$180$		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	0.625034	−	0.780597i	$-0.285085\pi$
$191$	3.61448	+	2.08682i	0.261535	+	0.150997i	−0.363500	+	0.931594i	$0.618418\pi$
$192$		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	$-0.694607\pi$
$197$	−16.1128			−1.14799			−0.573995	+	0.818859i	$0.694607\pi$
$198$		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	$-0.835024\pi$
$227$	−13.0078	−	22.5302i	−0.863357	−	1.49538i	0.00531177	−	0.999986i	$-0.498309\pi$
$228$		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	−0.581923	−	0.813244i	$-0.697700\pi$
$233$	6.30918	−	10.9278i	0.413328	−	0.715906i	0.995251	+	0.0973382i	$0.0310328\pi$
$234$		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	$-0.854567\pi$
$239$		−	13.6404i		−	0.882321i	0.897428	−	0.441161i	$-0.145433\pi$
$240$		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	$-0.657896\pi$
$251$	−15.0809			−0.951900			−0.475950	+	0.879472i	$0.657896\pi$
$252$		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	0.579438	−	0.815016i	$-0.303272\pi$
$257$	2.61842	+	1.51175i	0.163333	+	0.0943001i	−0.416106	+	0.909316i	$0.636605\pi$
$258$		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	0.445848	−	0.895109i	$-0.352902\pi$
$263$	23.4171	−	13.5199i	1.44396	−	0.833670i	0.998111	+	0.0614382i	$0.0195687\pi$
$264$		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	−0.258829	−	0.965923i	$-0.583336\pi$
$269$	7.35220	−	4.24479i	0.448271	−	0.258810i	0.707100	+	0.707114i	$0.250003\pi$
$270$		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	$-0.333932\pi$
$281$	16.7084			0.996738			0.498369	+	0.866965i	$0.333932\pi$
$282$		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	$0.260850\pi$
$293$			25.0184i			1.46159i	−0.682597	+	0.730795i	$0.739150\pi$
$294$		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	0.961472	−	0.274904i	$-0.0886461\pi$
$311$	4.27939	+	7.41212i	0.242662	+	0.420303i	−0.718810	+	0.695207i	$0.755313\pi$
$312$		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	−0.914598	−	0.404363i	$-0.867493\pi$
$317$	−1.90705	+	3.30310i	−0.107110	+	0.185521i	0.807488	+	0.589884i	$0.200826\pi$
$318$		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	−0.806436	−	0.591321i	$-0.798606\pi$
$347$	−12.9940	+	7.50209i	−0.697555	+	0.402733i	0.108881	+	0.994055i	$0.465273\pi$
$348$		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	−0.655541	−	0.755159i	$-0.727560\pi$
$353$	−6.18746	+	3.57233i	−0.329325	+	0.190136i	0.326216	+	0.945295i	$0.394226\pi$
$354$		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	0.980426	−	0.196886i	$-0.0630829\pi$
$359$	24.6340	+	14.2224i	1.30013	+	0.750631i	0.319705	+	0.947517i	$0.396416\pi$
$360$		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	$-0.600417\pi$
$383$	13.0761	−	22.6484i	0.668156	−	1.15728i	0.978419	−	0.206629i	$-0.0662493\pi$
$384$		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	$0.130355\pi$
$389$	15.8471	+	27.4480i	0.803481	+	1.39167i	−0.113830	+	0.993500i	$0.536312\pi$
$390$		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	−0.899651	−	0.436610i	$-0.856179\pi$
$401$	−1.43600	+	2.48722i	−0.0717102	+	0.124206i	0.827941	+	0.560816i	$0.189512\pi$
$402$		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	$-0.654197\pi$
$419$	−19.0652			−0.931395			−0.465698	+	0.884944i	$0.654197\pi$
$420$		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	−0.185176	−	0.982705i	$-0.559286\pi$
$431$	11.9017	−	6.87144i	0.573284	−	0.330986i	0.758460	+	0.651720i	$0.225952\pi$
$432$		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	0.645105	−	0.764094i	$-0.276814\pi$
$443$	6.43914	+	3.71764i	0.305933	+	0.176630i	−0.339172	+	0.940724i	$0.610147\pi$
$444$		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	$-0.618720\pi$
$449$	−15.4423			−0.728767			−0.364384	+	0.931249i	$0.618720\pi$
$450$		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	$-0.680202\pi$
$461$		−	36.2424i		−	1.68798i	0.536362	−	0.843988i	$-0.319798\pi$
$462$		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	$-0.476976\pi$
$467$	19.4469	−	33.6830i	0.899895	−	1.55866i	0.827627	−	0.561278i	$-0.189690\pi$
$468$		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	$0.261626\pi$
$479$	21.3331	+	36.9500i	0.974733	+	1.68829i	0.293919	+	0.955830i	$0.405040\pi$
$480$		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	$0.0707159\pi$
$491$			9.76471i			0.440675i	−0.975424	+	0.220338i	$0.929284\pi$
$492$		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	$-0.764821\pi$
$503$	−33.1594			−1.47851			−0.739253	+	0.673428i	$0.764821\pi$
$504$		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	0.710655	−	0.703541i	$-0.248399\pi$
$509$	10.3036	+	5.94878i	0.456698	+	0.263675i	−0.253957	+	0.967216i	$0.581732\pi$
$510$		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	−0.569852	−	0.821748i	$-0.692999\pi$
$521$	−3.26685	+	1.88612i	−0.143123	+	0.0826323i	0.426728	+	0.904380i	$0.359666\pi$
$522$		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	0.578571	−	0.815632i	$-0.303611\pi$
$557$	−9.84326	−	17.0490i	−0.417072	−	0.722391i	−0.995644	+	0.0932413i	$0.970277\pi$
$558$		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	0.725537	−	0.688184i	$-0.241592\pi$
$563$	−5.53366	−	9.58459i	−0.233216	−	0.403942i	−0.958753	+	0.284241i	$0.908258\pi$
$564$		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	$0.345665\pi$
$569$	−12.7180	+	22.0283i	−0.533167	+	0.923473i	−0.999250	+	0.0387316i	$0.987668\pi$
$570$		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	$-0.271857\pi$
$587$	31.8321			1.31385			0.656925	+	0.753956i	$0.271857\pi$
$588$		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	−0.320172	−	0.947359i	$-0.603741\pi$
$593$	−31.6740	−	18.2870i	−1.30070	−	0.750957i	−0.980523	+	0.196403i	$0.937074\pi$
$594$		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	0.201384	−	0.979512i	$-0.435456\pi$
$599$	28.1544	−	16.2550i	1.15036	−	0.664160i	0.948975	+	0.315352i	$0.102123\pi$
$600$		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	$-0.690612\pi$
$617$	−28.0026			−1.12734			−0.563671	+	0.825999i	$0.690612\pi$
$618$		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	0.963635	−	0.267223i	$-0.0861060\pi$
$641$	6.33951	+	10.9804i	0.250396	+	0.433698i	−0.713239	+	0.700921i	$0.752773\pi$
$642$		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	0.991282	−	0.131757i	$-0.0420619\pi$
$647$	9.70483	+	16.8093i	0.381536	+	0.660840i	−0.609746	+	0.792597i	$0.708729\pi$
$648$		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	$-0.597598\pi$
$653$	17.2417	−	29.8635i	0.674720	−	1.16865i	0.976551	−	0.215288i	$-0.0690689\pi$
$654$		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	$-0.946630\pi$
$659$		−	8.56812i		−	0.333767i	0.985977	−	0.166883i	$-0.0533703\pi$
$660$		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	0.599286	−	0.800535i	$-0.295451\pi$
$677$	5.35071	+	3.08923i	0.205644	+	0.118729i	−0.393641	+	0.919264i	$0.628785\pi$
$678$		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	−0.784641	−	0.619950i	$-0.787153\pi$
$683$	−16.7278	+	9.65777i	−0.640070	+	0.369544i	0.144572	+	0.989494i	$0.453820\pi$
$684$		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	$-0.535460\pi$
$701$	−5.88673			−0.222339			−0.111169	+	0.993801i	$0.535460\pi$
$702$		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	−0.696541	−	0.717517i	$-0.745279\pi$
$719$	7.32342	−	12.6845i	0.273117	−	0.473053i	0.969658	+	0.244464i	$0.0786119\pi$
$720$		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	$-0.773587\pi$
$743$		−	35.5890i		−	1.30563i	0.757516	−	0.652816i	$-0.226413\pi$
$744$		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	0.512525	−	0.858672i	$-0.328710\pi$
$761$	0.693929	+	0.400640i	0.0251549	+	0.0145232i	−0.487370	+	0.873196i	$0.662044\pi$
$762$		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	−0.704031	−	0.710170i	$-0.748618\pi$
$773$	−12.2616	+	7.07927i	−0.441021	+	0.254624i	0.263010	+	0.964793i	$0.415285\pi$
$774$		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	$0.0640008\pi$
$797$			11.2762i			0.399425i	−0.979855	+	0.199713i	$0.935999\pi$
$798$		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	0.999328	−	0.0366484i	$-0.0116682\pi$
$809$	13.3092	+	23.0522i	0.467926	+	0.810471i	−0.531403	+	0.847119i	$0.678335\pi$
$810$		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	−0.584193	−	0.811615i	$-0.698589\pi$
$821$	11.7702	−	20.3866i	0.410783	−	0.711496i	0.994976	+	0.100118i	$0.0319222\pi$
$822$		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	$-0.991992\pi$
$827$		−	1.44687i		−	0.0503126i	0.999684	−	0.0251563i	$-0.00800834\pi$
$828$		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	$-0.857815\pi$
$839$	−52.2470			−1.80377			−0.901883	+	0.431981i	$0.857815\pi$
$840$		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	−0.846361	−	0.532609i	$-0.821212\pi$
$857$	−23.6623	+	13.6614i	−0.808289	+	0.466666i	0.0380721	+	0.999275i	$0.487878\pi$
$858$		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	0.723782	−	0.690029i	$-0.242402\pi$
$863$	14.3385	+	8.27836i	0.488090	+	0.281799i	−0.235692	+	0.971828i	$0.575736\pi$
$864$		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	$-0.959251\pi$
$881$		−	7.57867i		−	0.255332i	0.991817	−	0.127666i	$-0.0407485\pi$
$882$		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	$0.352522\pi$
$887$	−16.4181	+	28.4370i	−0.551266	+	0.954821i	−0.998184	+	0.0602460i	$0.980811\pi$
$888$		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	$0.333597\pi$
$911$			52.3031i			1.73288i	−0.499282	+	0.866440i	$0.666403\pi$
$912$		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	0.115421	−	0.993317i	$-0.463178\pi$
$929$	−20.9426	−	12.0912i	−0.687106	−	0.396701i	−0.802527	+	0.596616i	$0.796512\pi$
$930$		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	0.373229	−	0.927739i	$-0.378251\pi$
$941$	41.8199	−	24.1447i	1.36329	−	0.787096i	0.990060	+	0.140644i	$0.0449172\pi$
$942$		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	0.999722	−	0.0235578i	$-0.00749937\pi$
$947$	45.5194	+	26.2806i	1.47918	+	0.854006i	0.479460	+	0.877564i	$0.340833\pi$
$948$		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	$-0.297359\pi$
$953$	36.7039			1.18895			0.594477	+	0.804112i	$0.297359\pi$
$954$		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	$-0.608908\pi$
$971$	20.1945	−	34.9780i	0.648074	−	1.12250i	0.983582	−	0.180459i	$-0.0577585\pi$
$972$		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	$-0.996893\pi$
$977$	−15.8920	−	27.5257i	−0.508429	−	0.880625i	0.491523	−	0.870864i	$-0.336440\pi$
$978$		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	0.562515	−	0.826787i	$-0.309834\pi$
$983$	−13.6310	−	23.6096i	−0.434761	−	0.753028i	−0.997276	+	0.0737588i	$0.976500\pi$
$984$		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.271.11	yes	32
3.2	odd	2	inner	756.2.bf.d.271.6	yes	32
4.3	odd	2		756.2.bf.a.271.11	yes	32
7.3	odd	6		756.2.bf.a.703.11	yes	32
12.11	even	2		756.2.bf.a.271.6	✓	32
21.17	even	6		756.2.bf.a.703.6	yes	32
28.3	even	6	inner	756.2.bf.d.703.11	yes	32
84.59	odd	6	inner	756.2.bf.d.703.6	yes	32

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