LMFDB - Embedded newform 912.2.ci.b.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			751.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	912.751
Dual form			912.2.ci.b.895.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.907604 + 0.524005i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.907604 + 0.524005i) q^{7} +(0.173648 - 0.984808i) q^{9} +(3.79813 - 2.19285i) q^{11} +(-3.64543 + 4.34445i) q^{13} +(0.826352 - 0.300767i) q^{15} +(-0.539363 - 3.05888i) q^{17} +(4.28699 + 0.788496i) q^{19} +(-1.03209 + 0.181985i) q^{21} +(1.78699 + 4.90971i) q^{23} +(-3.23783 - 2.71686i) q^{25} +(0.500000 + 0.866025i) q^{27} +(6.30200 + 1.11121i) q^{29} +(3.40033 - 5.88954i) q^{31} +(-1.50000 + 4.12122i) q^{33} +(-0.592396 - 0.705990i) q^{35} +9.58186i q^{37} -5.67128i q^{39} +(4.50640 + 5.37051i) q^{41} +(-1.63429 + 4.49016i) q^{43} +(-0.439693 + 0.761570i) q^{45} +(11.1985 + 1.97459i) q^{47} +(-2.95084 - 5.11100i) q^{49} +(2.37939 + 1.99654i) q^{51} +(1.83022 + 5.02849i) q^{53} +(-3.79813 + 0.669713i) q^{55} +(-3.79086 + 2.15160i) q^{57} +(2.62314 + 14.8766i) q^{59} +(7.56418 - 2.75314i) q^{61} +(0.673648 - 0.802823i) q^{63} +(4.31908 - 2.49362i) q^{65} +(0.709141 - 4.02174i) q^{67} +(-4.52481 - 2.61240i) q^{69} +(3.59240 + 1.30753i) q^{71} +(-10.4474 + 8.76644i) q^{73} +4.22668 q^{75} +4.59627 q^{77} +(3.54710 - 2.97637i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-6.02481 - 3.47843i) q^{83} +(-0.474308 + 2.68993i) q^{85} +(-5.54189 + 3.19961i) q^{87} +(5.71941 - 6.81612i) q^{89} +(-5.58512 + 2.03282i) q^{91} +(1.18092 + 6.69734i) q^{93} +(-3.30541 - 1.94096i) q^{95} +(3.33022 - 0.587208i) q^{97} +(-1.50000 - 4.12122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} + 9 q^{7}+O(q^{10}) $ 6 * q - 6 * q^5 + 9 * q^7	$ 6 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 6 q^{13} + 6 q^{15} - 12 q^{17} + 18 q^{19} + 3 q^{21} + 3 q^{23} + 3 q^{27} + 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} + 39 q^{47} - 6 q^{49} + 3 q^{51} - 12 q^{53} - 9 q^{55} + 9 q^{57} + 12 q^{59} + 27 q^{61} + 3 q^{63} + 9 q^{65} + 36 q^{67} + 18 q^{71} - 9 q^{73} + 12 q^{75} - 18 q^{79} - 9 q^{83} + 27 q^{85} - 27 q^{87} + 3 q^{89} - 12 q^{91} + 24 q^{93} - 24 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 6 * q - 6 * q^5 + 9 * q^7 + 9 * q^11 - 6 * q^13 + 6 * q^15 - 12 * q^17 + 18 * q^19 + 3 * q^21 + 3 * q^23 + 3 * q^27 + 6 * q^31 - 9 * q^33 - 12 * q^41 + 3 * q^45 + 39 * q^47 - 6 * q^49 + 3 * q^51 - 12 * q^53 - 9 * q^55 + 9 * q^57 + 12 * q^59 + 27 * q^61 + 3 * q^63 + 9 * q^65 + 36 * q^67 + 18 * q^71 - 9 * q^73 + 12 * q^75 - 18 * q^79 - 9 * q^83 + 27 * q^85 - 27 * q^87 + 3 * q^89 - 12 * q^91 + 24 * q^93 - 24 * q^95 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$		0			0
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	0.150565	−	0.988600i	$-0.451891\pi$
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	−0.520121	+	0.854093i	$0.674113\pi$
$6$		0			0
$7$	0.907604	+	0.524005i	0.343042	+	0.198055i	0.661616	−	0.749842i	$-0.269871\pi$
$7$	0.907604	+	0.524005i	0.343042	+	0.198055i	−0.318574	+	0.947898i	$0.603204\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	3.79813	−	2.19285i	1.14518	−	0.661170i	0.197472	−	0.980308i	$-0.436727\pi$
$11$	3.79813	−	2.19285i	1.14518	−	0.661170i	0.947708	+	0.319138i	$0.103393\pi$
$12$		0			0
$13$	−3.64543	+	4.34445i	−1.01106	+	1.20493i	−0.0323947	+	0.999475i	$0.510313\pi$
$13$	−3.64543	+	4.34445i	−1.01106	+	1.20493i	−0.978666	+	0.205460i	$0.934131\pi$
$14$		0			0
$15$	0.826352	−	0.300767i	0.213363	−	0.0776578i
$16$		0			0
$17$	−0.539363	−	3.05888i	−0.130815	−	0.741887i	−0.977683	−	0.210085i	$-0.932626\pi$
$17$	−0.539363	−	3.05888i	−0.130815	−	0.741887i	0.846868	−	0.531802i	$-0.178485\pi$
$18$		0			0
$19$	4.28699	+	0.788496i	0.983503	+	0.180893i
$19$	4.28699	+	0.788496i	0.983503	+	0.180893i
$20$		0			0
$21$	−1.03209	+	0.181985i	−0.225220	+	0.0397124i
$22$		0			0
$23$	1.78699	+	4.90971i	0.372613	+	1.02375i	0.974347	+	0.225049i	$0.0722544\pi$
$23$	1.78699	+	4.90971i	0.372613	+	1.02375i	−0.601734	+	0.798696i	$0.705523\pi$
$24$		0			0
$25$	−3.23783	−	2.71686i	−0.647565	−	0.543372i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	6.30200	+	1.11121i	1.17025	+	0.206347i	0.724801	−	0.688959i	$-0.241932\pi$
$29$	6.30200	+	1.11121i	1.17025	+	0.206347i	0.445452	+	0.895306i	$0.353043\pi$
$30$		0			0
$31$	3.40033	−	5.88954i	0.610717	−	1.05779i	−0.380402	−	0.924821i	$-0.624215\pi$
$31$	3.40033	−	5.88954i	0.610717	−	1.05779i	0.991120	−	0.132972i	$-0.0424521\pi$
$32$		0			0
$33$	−1.50000	+	4.12122i	−0.261116	+	0.717412i
$34$		0			0
$35$	−0.592396	−	0.705990i	−0.100133	−	0.119334i
$36$		0			0
$37$			9.58186i			1.57525i	0.616156	+	0.787624i	$0.288689\pi$
$37$			9.58186i			1.57525i	−0.616156	+	0.787624i	$0.711311\pi$
$38$		0			0
$39$		−	5.67128i		−	0.908132i
$40$		0			0
$41$	4.50640	+	5.37051i	0.703781	+	0.838733i	0.992949	−	0.118545i	$-0.0378230\pi$
$41$	4.50640	+	5.37051i	0.703781	+	0.838733i	−0.289168	+	0.957278i	$0.593379\pi$
$42$		0			0
$43$	−1.63429	+	4.49016i	−0.249226	+	0.684743i	0.750489	+	0.660883i	$0.229818\pi$
$43$	−1.63429	+	4.49016i	−0.249226	+	0.684743i	−0.999715	+	0.0238605i	$0.992404\pi$
$44$		0			0
$45$	−0.439693	+	0.761570i	−0.0655455	+	0.113528i
$46$		0			0
$47$	11.1985	+	1.97459i	1.63346	+	0.288024i	0.913759	−	0.406257i	$-0.133166\pi$
$47$	11.1985	+	1.97459i	1.63346	+	0.288024i	0.719705	+	0.694280i	$0.244277\pi$
$48$		0			0
$49$	−2.95084	−	5.11100i	−0.421548	−	0.730143i
$50$		0			0
$51$	2.37939	+	1.99654i	0.333181	+	0.279572i
$52$		0			0
$53$	1.83022	+	5.02849i	0.251400	+	0.690717i	0.999628	+	0.0272747i	$0.00868288\pi$
$53$	1.83022	+	5.02849i	0.251400	+	0.690717i	−0.748228	+	0.663442i	$0.769095\pi$
$54$		0			0
$55$	−3.79813	+	0.669713i	−0.512140	+	0.0903041i
$56$		0			0
$57$	−3.79086	+	2.15160i	−0.502112	+	0.284986i
$58$		0			0
$59$	2.62314	+	14.8766i	0.341504	+	1.93676i	0.349866	+	0.936800i	$0.386227\pi$
$59$	2.62314	+	14.8766i	0.341504	+	1.93676i	−0.00836244	+	0.999965i	$0.502662\pi$
$60$		0			0
$61$	7.56418	−	2.75314i	0.968494	−	0.352503i	0.191137	−	0.981563i	$-0.438782\pi$
$61$	7.56418	−	2.75314i	0.968494	−	0.352503i	0.777356	+	0.629060i	$0.216560\pi$
$62$		0			0
$63$	0.673648	−	0.802823i	0.0848717	−	0.101146i
$64$		0			0
$65$	4.31908	−	2.49362i	0.535716	−	0.309296i
$66$		0			0
$67$	0.709141	−	4.02174i	0.0866353	−	0.491333i	−0.910356	−	0.413825i	$-0.864192\pi$
$67$	0.709141	−	4.02174i	0.0866353	−	0.491333i	0.996992	−	0.0775082i	$-0.0246964\pi$
$68$		0			0
$69$	−4.52481	−	2.61240i	−0.544724	−	0.314496i
$70$		0			0
$71$	3.59240	+	1.30753i	0.426339	+	0.155175i	0.546273	−	0.837607i	$-0.316046\pi$
$71$	3.59240	+	1.30753i	0.426339	+	0.155175i	−0.119934	+	0.992782i	$0.538268\pi$
$72$		0			0
$73$	−10.4474	+	8.76644i	−1.22278	+	1.02603i	−0.224105	+	0.974565i	$0.571946\pi$
$73$	−10.4474	+	8.76644i	−1.22278	+	1.02603i	−0.998675	+	0.0514689i	$0.983610\pi$
$74$		0			0
$75$	4.22668			0.488055
$76$		0			0
$77$	4.59627			0.523793
$78$		0			0
$79$	3.54710	−	2.97637i	0.399080	−	0.334868i	−0.421058	−	0.907034i	$-0.638341\pi$
$79$	3.54710	−	2.97637i	0.399080	−	0.334868i	0.820138	+	0.572166i	$0.193897\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	−6.02481	−	3.47843i	−0.661309	−	0.381807i	0.131466	−	0.991321i	$-0.458031\pi$
$83$	−6.02481	−	3.47843i	−0.661309	−	0.381807i	−0.792776	+	0.609514i	$0.791365\pi$
$84$		0			0
$85$	−0.474308	+	2.68993i	−0.0514459	+	0.291764i
$86$		0			0
$87$	−5.54189	+	3.19961i	−0.594153	+	0.343034i
$88$		0			0
$89$	5.71941	−	6.81612i	0.606256	−	0.722508i	−0.372386	−	0.928078i	$-0.621460\pi$
$89$	5.71941	−	6.81612i	0.606256	−	0.722508i	0.978642	+	0.205570i	$0.0659048\pi$
$90$		0			0
$91$	−5.58512	+	2.03282i	−0.585480	+	0.213097i
$92$		0			0
$93$	1.18092	+	6.69734i	0.122456	+	0.694482i
$94$		0			0
$95$	−3.30541	−	1.94096i	−0.339128	−	0.199138i
$96$		0			0
$97$	3.33022	−	0.587208i	0.338133	−	0.0596219i	−0.00200373	−	0.999998i	$-0.500638\pi$
$97$	3.33022	−	0.587208i	0.338133	−	0.0596219i	0.340137	+	0.940376i	$0.389527\pi$
$98$		0			0
$99$	−1.50000	−	4.12122i	−0.150756	−	0.414198i
$100$		0			0
$101$	−7.74376	−	6.49778i	−0.770532	−	0.646554i	0.170313	−	0.985390i	$-0.445522\pi$
$101$	−7.74376	−	6.49778i	−0.770532	−	0.646554i	−0.940845	+	0.338837i	$0.889967\pi$
$102$		0			0
$103$	3.61334	+	6.25849i	0.356033	+	0.616667i	0.987294	−	0.158903i	$-0.0507957\pi$
$103$	3.61334	+	6.25849i	0.356033	+	0.616667i	−0.631261	+	0.775570i	$0.717462\pi$
$104$		0			0
$105$	0.907604	+	0.160035i	0.0885731	+	0.0156178i
$106$		0			0
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$		0			0
$109$	−2.74123	+	7.53147i	−0.262562	+	0.721384i	0.736431	+	0.676513i	$0.236510\pi$
$109$	−2.74123	+	7.53147i	−0.262562	+	0.721384i	−0.998993	+	0.0448706i	$0.985712\pi$
$110$		0			0
$111$	−6.15910	−	7.34013i	−0.584596	−	0.696694i
$112$		0			0
$113$		−	20.4241i		−	1.92134i	−0.277697	−	0.960669i	$-0.589571\pi$
$113$		−	20.4241i		−	1.92134i	0.277697	−	0.960669i	$-0.410429\pi$
$114$		0			0
$115$		−	4.59462i		−	0.428450i
$116$		0			0
$117$	3.64543	+	4.34445i	0.337020	+	0.401645i
$118$		0			0
$119$	1.11334	−	3.05888i	0.102060	−	0.280407i
$120$		0			0
$121$	4.11721	−	7.13122i	0.374292	−	0.648293i
$122$		0			0
$123$	−6.90420	−	1.21740i	−0.622531	−	0.109769i
$124$		0			0
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$		0			0
$127$	−8.32888	−	6.98876i	−0.739068	−	0.620152i	0.193519	−	0.981097i	$-0.438010\pi$
$127$	−8.32888	−	6.98876i	−0.739068	−	0.620152i	−0.932587	+	0.360945i	$0.882454\pi$
$128$		0			0
$129$	−1.63429	−	4.49016i	−0.143891	−	0.395337i
$130$		0			0
$131$	−4.63429	+	0.817150i	−0.404899	+	0.0713947i	−0.372389	−	0.928077i	$-0.621461\pi$
$131$	−4.63429	+	0.817150i	−0.404899	+	0.0713947i	−0.0325103	+	0.999471i	$0.510350\pi$
$132$		0			0
$133$	3.47771	+	2.96205i	0.301556	+	0.256842i
$134$		0			0
$135$	−0.152704	−	0.866025i	−0.0131426	−	0.0745356i
$136$		0			0
$137$	5.81908	−	2.11797i	0.497157	−	0.180950i	−0.0812576	−	0.996693i	$-0.525894\pi$
$137$	5.81908	−	2.11797i	0.497157	−	0.180950i	0.578415	+	0.815743i	$0.303671\pi$
$138$		0			0
$139$	−4.28446	+	5.10602i	−0.363403	+	0.433087i	−0.916503	−	0.400028i	$-0.869000\pi$
$139$	−4.28446	+	5.10602i	−0.363403	+	0.433087i	0.553100	+	0.833115i	$0.313445\pi$
$140$		0			0
$141$	−9.84776	+	5.68561i	−0.829331	+	0.478815i
$142$		0			0
$143$	−4.31908	+	24.4947i	−0.361179	+	2.04835i
$144$		0			0
$145$	−4.87346	−	2.81369i	−0.404718	−	0.233664i
$146$		0			0
$147$	5.54576	+	2.01849i	0.457407	+	0.166482i
$148$		0			0
$149$	−0.190722	+	0.160035i	−0.0156246	+	0.0131106i	−0.650566	−	0.759449i	$-0.725468\pi$
$149$	−0.190722	+	0.160035i	−0.0156246	+	0.0131106i	0.634942	+	0.772560i	$0.281024\pi$
$150$		0			0
$151$	15.2199			1.23858			0.619288	−	0.785164i	$-0.287421\pi$
$151$	15.2199			1.23858			0.619288	+	0.785164i	$0.287421\pi$
$152$		0			0
$153$	−3.10607			−0.251111
$154$		0			0
$155$	−4.58125	+	3.84413i	−0.367975	+	0.308768i
$156$		0			0
$157$	−10.6912	−	3.89127i	−0.853250	−	0.310558i	−0.121885	−	0.992544i	$-0.538894\pi$
$157$	−10.6912	−	3.89127i	−0.853250	−	0.310558i	−0.731365	+	0.681987i	$0.761116\pi$
$158$		0			0
$159$	−4.63429	−	2.67561i	−0.367523	−	0.212189i
$160$		0			0
$161$	−0.950837	+	5.39246i	−0.0749365	+	0.424986i
$162$		0			0
$163$	6.83157	−	3.94421i	0.535090	−	0.308934i	−0.207997	−	0.978129i	$-0.566694\pi$
$163$	6.83157	−	3.94421i	0.535090	−	0.308934i	0.743087	+	0.669195i	$0.233361\pi$
$164$		0			0
$165$	2.47906	−	2.95442i	0.192994	−	0.230002i
$166$		0			0
$167$	−1.65270	+	0.601535i	−0.127890	+	0.0465482i	−0.405172	−	0.914240i	$-0.632788\pi$
$167$	−1.65270	+	0.601535i	−0.127890	+	0.0465482i	0.277282	+	0.960788i	$0.410566\pi$
$168$		0			0
$169$	−3.32770	−	18.8723i	−0.255977	−	1.45172i
$170$		0			0
$171$	1.52094	−	4.08494i	0.116310	−	0.312383i
$172$		0			0
$173$	3.76011	−	0.663010i	0.285876	−	0.0504077i	−0.0288712	−	0.999583i	$-0.509191\pi$
$173$	3.76011	−	0.663010i	0.285876	−	0.0504077i	0.314747	+	0.949175i	$0.398080\pi$
$174$		0			0
$175$	−1.51501	−	4.16247i	−0.114524	−	0.314653i
$176$		0			0
$177$	−11.5719	−	9.70999i	−0.869799	−	0.729848i
$178$		0			0
$179$	−10.0039	−	17.3272i	−0.747724	−	1.29510i	−0.948911	−	0.315544i	$-0.897813\pi$
$179$	−10.0039	−	17.3272i	−0.747724	−	1.29510i	0.201187	−	0.979553i	$-0.435520\pi$
$180$		0			0
$181$	−7.42514	−	1.30925i	−0.551907	−	0.0973160i	−0.109262	−	0.994013i	$-0.534849\pi$
$181$	−7.42514	−	1.30925i	−0.551907	−	0.0973160i	−0.442645	+	0.896697i	$0.645960\pi$
$182$		0			0
$183$	−4.02481	+	6.97118i	−0.297523	+	0.515325i
$184$		0			0
$185$	2.88191	−	7.91799i	0.211882	−	0.582142i
$186$		0			0
$187$	−8.75624	−	10.4353i	−0.640320	−	0.763104i
$188$		0			0
$189$			1.04801i			0.0762315i
$190$		0			0
$191$		−	5.01590i		−	0.362937i	−0.983397	−	0.181469i	$-0.941915\pi$
$191$		−	5.01590i		−	0.362937i	0.983397	−	0.181469i	$-0.0580851\pi$
$192$		0			0
$193$	3.82635	+	4.56007i	0.275427	+	0.328241i	0.885970	−	0.463742i	$-0.153493\pi$
$193$	3.82635	+	4.56007i	0.275427	+	0.328241i	−0.610544	+	0.791983i	$0.709049\pi$
$194$		0			0
$195$	−1.70574	+	4.68647i	−0.122150	+	0.335605i
$196$		0			0
$197$	12.0594	−	20.8875i	0.859199	−	1.48818i	−0.0134954	−	0.999909i	$-0.504296\pi$
$197$	12.0594	−	20.8875i	0.859199	−	1.48818i	0.872694	−	0.488267i	$-0.162371\pi$
$198$		0			0
$199$	−24.4859	−	4.31753i	−1.73576	−	0.306061i	−0.785812	−	0.618466i	$-0.787754\pi$
$199$	−24.4859	−	4.31753i	−1.73576	−	0.306061i	−0.949949	+	0.312404i	$0.898866\pi$
$200$		0			0
$201$	2.04189	+	3.53666i	0.144024	+	0.249456i
$202$		0			0
$203$	5.13744	+	4.31082i	0.360578	+	0.302561i
$204$		0			0
$205$	−2.10859	−	5.79331i	−0.147271	−	0.404622i
$206$		0			0
$207$	5.14543	−	0.907278i	0.357632	−	0.0630602i
$208$		0			0
$209$	18.0116	−	6.40593i	1.24589	−	0.443107i
$210$		0			0
$211$	0.440570	+	2.49860i	0.0303301	+	0.172010i	0.996210	−	0.0869795i	$-0.0277215\pi$
$211$	0.440570	+	2.49860i	0.0303301	+	0.172010i	−0.965880	+	0.258990i	$0.916610\pi$
$212$		0			0
$213$	−3.59240	+	1.30753i	−0.246147	+	0.0895902i
$214$		0			0
$215$	2.70099	−	3.21891i	0.184206	−	0.219528i
$216$		0			0
$217$	6.17230	−	3.56358i	0.419003	−	0.241912i
$218$		0			0
$219$	2.36824	−	13.4310i	0.160031	−	0.907580i
$220$		0			0
$221$	15.2554	+	8.80769i	1.02619	+	0.592469i
$222$		0			0
$223$	−20.9884	−	7.63917i	−1.40549	−	0.511557i	−0.475687	−	0.879614i	$-0.657801\pi$
$223$	−20.9884	−	7.63917i	−1.40549	−	0.511557i	−0.929803	+	0.368058i	$0.880023\pi$
$224$		0			0
$225$	−3.23783	+	2.71686i	−0.215855	+	0.181124i
$226$		0			0
$227$	2.58172			0.171355			0.0856773	−	0.996323i	$-0.472695\pi$
$227$	2.58172			0.171355			0.0856773	+	0.996323i	$0.472695\pi$
$228$		0			0
$229$	−5.16756			−0.341482			−0.170741	−	0.985316i	$-0.554616\pi$
$229$	−5.16756			−0.341482			−0.170741	+	0.985316i	$0.554616\pi$
$230$		0			0
$231$	−3.52094	+	2.95442i	−0.231661	+	0.194387i
$232$		0			0
$233$	8.12361	+	2.95675i	0.532195	+	0.193703i	0.594118	−	0.804378i	$-0.297501\pi$
$233$	8.12361	+	2.95675i	0.532195	+	0.193703i	−0.0619230	+	0.998081i	$0.519723\pi$
$234$		0			0
$235$	−8.65998	−	4.99984i	−0.564915	−	0.326154i
$236$		0			0
$237$	−0.804063	+	4.56007i	−0.0522295	+	0.296208i
$238$		0			0
$239$	3.04664	−	1.75898i	0.197071	−	0.113779i	−0.398218	−	0.917291i	$-0.630371\pi$
$239$	3.04664	−	1.75898i	0.197071	−	0.113779i	0.595288	+	0.803512i	$0.297038\pi$
$240$		0			0
$241$	−9.78611	+	11.6626i	−0.630379	+	0.751256i	−0.982818	−	0.184579i	$-0.940908\pi$
$241$	−9.78611	+	11.6626i	−0.630379	+	0.751256i	0.352439	+	0.935835i	$0.385352\pi$
$242$		0			0
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$		0			0
$245$	0.901207	+	5.11100i	0.0575760	+	0.326530i
$246$		0			0
$247$	−19.0535	+	15.7502i	−1.21235	+	1.00216i
$248$		0			0
$249$	6.85117	−	1.20805i	0.434175	−	0.0765568i
$250$		0			0
$251$	5.95218	+	16.3535i	0.375698	+	1.03222i	0.973121	+	0.230296i	$0.0739694\pi$
$251$	5.95218	+	16.3535i	0.375698	+	1.03222i	−0.597422	+	0.801927i	$0.703808\pi$
$252$		0			0
$253$	17.5535	+	14.7291i	1.10358	+	0.926013i
$254$		0			0
$255$	−1.36571	−	2.36549i	−0.0855244	−	0.148133i
$256$		0			0
$257$	−31.1976	−	5.50098i	−1.94605	−	0.343141i	−0.999806	−	0.0196932i	$-0.993731\pi$
$257$	−31.1976	−	5.50098i	−1.94605	−	0.343141i	−0.946246	−	0.323448i	$-0.895158\pi$
$258$		0			0
$259$	−5.02094	+	8.69653i	−0.311986	+	0.540376i
$260$		0			0
$261$	2.18866	−	6.01330i	0.135475	−	0.372214i
$262$		0			0
$263$	−0.985452	−	1.17442i	−0.0607656	−	0.0724176i	0.734805	−	0.678278i	$-0.237273\pi$
$263$	−0.985452	−	1.17442i	−0.0607656	−	0.0724176i	−0.795571	+	0.605860i	$0.792829\pi$
$264$		0			0
$265$		−	4.70578i		−	0.289074i
$266$		0			0
$267$			8.89782i			0.544538i
$268$		0			0
$269$	14.9932	+	17.8682i	0.914151	+	1.08944i	0.995687	+	0.0927725i	$0.0295729\pi$
$269$	14.9932	+	17.8682i	0.914151	+	1.08944i	−0.0815362	+	0.996670i	$0.525983\pi$
$270$		0			0
$271$	−7.75237	+	21.2995i	−0.470923	+	1.29385i	0.446088	+	0.894989i	$0.352817\pi$
$271$	−7.75237	+	21.2995i	−0.470923	+	1.29385i	−0.917011	+	0.398862i	$0.869405\pi$
$272$		0			0
$273$	2.97178	−	5.14728i	0.179860	−	0.311527i
$274$		0			0
$275$	−18.2554	−	3.21891i	−1.10084	−	0.194108i
$276$		0			0
$277$	−10.7947	−	18.6970i	−0.648592	−	1.12340i	−0.983459	−	0.181130i	$-0.942025\pi$
$277$	−10.7947	−	18.6970i	−0.648592	−	1.12340i	0.334867	−	0.942265i	$-0.391309\pi$
$278$		0			0
$279$	−5.20961	−	4.37138i	−0.311891	−	0.261708i
$280$		0			0
$281$	−9.31299	−	25.5872i	−0.555566	−	1.52641i	−0.826002	−	0.563667i	$-0.809390\pi$
$281$	−9.31299	−	25.5872i	−0.555566	−	1.52641i	0.270436	−	0.962738i	$-0.412832\pi$
$282$		0			0
$283$	25.2788	−	4.45734i	1.50267	−	0.264961i	0.639074	−	0.769145i	$-0.279318\pi$
$283$	25.2788	−	4.45734i	1.50267	−	0.264961i	0.863597	+	0.504184i	$0.168206\pi$
$284$		0			0
$285$	3.77972	−	0.637812i	0.223891	−	0.0377807i
$286$		0			0
$287$	1.27584	+	7.23567i	0.0753107	+	0.427108i
$288$		0			0
$289$	6.90895	−	2.51465i	0.406409	−	0.147921i
$290$		0			0
$291$	−2.17365	+	2.59045i	−0.127422	+	0.151855i
$292$		0			0
$293$	−16.7087	+	9.64679i	−0.976134	+	0.563571i	−0.901101	−	0.433610i	$-0.857240\pi$
$293$	−16.7087	+	9.64679i	−0.976134	+	0.563571i	−0.0750336	+	0.997181i	$0.523906\pi$
$294$		0			0
$295$	2.30675	−	13.0822i	0.134304	−	0.761677i
$296$		0			0
$297$	3.79813	+	2.19285i	0.220390	+	0.127242i
$298$		0			0
$299$	−27.8444	−	10.1345i	−1.61028	−	0.586094i
$300$		0			0
$301$	−3.83615	+	3.21891i	−0.221112	+	0.185535i
$302$		0			0
$303$	10.1088			0.580733
$304$		0			0
$305$	−7.07873			−0.405327
$306$		0			0
$307$	−2.83615	+	2.37981i	−0.161868	+	0.135823i	−0.720124	−	0.693845i	$-0.755915\pi$
$307$	−2.83615	+	2.37981i	−0.161868	+	0.135823i	0.558256	+	0.829669i	$0.311471\pi$
$308$		0			0
$309$	−6.79086	−	2.47167i	−0.386318	−	0.140608i
$310$		0			0
$311$	14.7724	+	8.52887i	0.837668	+	0.483628i	0.856471	−	0.516195i	$-0.172652\pi$
$311$	14.7724	+	8.52887i	0.837668	+	0.483628i	−0.0188027	+	0.999823i	$0.505985\pi$
$312$		0			0
$313$	−5.35962	+	30.3959i	−0.302944	+	1.71808i	0.330085	+	0.943951i	$0.392923\pi$
$313$	−5.35962	+	30.3959i	−0.302944	+	1.71808i	−0.633029	+	0.774128i	$0.718188\pi$
$314$		0			0
$315$	−0.798133	+	0.460802i	−0.0449697	+	0.0259633i
$316$		0			0
$317$	−13.9329	+	16.6046i	−0.782549	+	0.932605i	−0.999046	−	0.0436780i	$-0.986092\pi$
$317$	−13.9329	+	16.6046i	−0.782549	+	0.932605i	0.216497	+	0.976283i	$0.430537\pi$
$318$		0			0
$319$	26.3726	−	9.59883i	1.47658	−	0.537431i
$320$		0			0
$321$	1.04189	+	5.90885i	0.0581526	+	0.329800i
$322$		0			0
$323$	0.0996702	−	13.5387i	0.00554580	−	0.753311i
$324$		0			0
$325$	23.6065	−	4.16247i	1.30945	−	0.230892i
$326$		0			0
$327$	−2.74123	−	7.53147i	−0.151590	−	0.416491i
$328$		0			0
$329$	9.12907	+	7.66020i	0.503302	+	0.422320i
$330$		0			0
$331$	1.32383	+	2.29293i	0.0727640	+	0.126031i	0.900112	−	0.435659i	$-0.143485\pi$
$331$	1.32383	+	2.29293i	0.0727640	+	0.126031i	−0.827348	+	0.561690i	$0.810151\pi$
$332$		0			0
$333$	9.43629	+	1.66387i	0.517105	+	0.0911796i
$334$		0			0
$335$	−1.79561	+	3.11008i	−0.0981045	+	0.169922i
$336$		0			0
$337$	8.05556	−	22.1325i	0.438814	−	1.20563i	−0.501450	−	0.865187i	$-0.667200\pi$
$337$	8.05556	−	22.1325i	0.438814	−	1.20563i	0.940264	−	0.340446i	$-0.110578\pi$
$338$		0			0
$339$	13.1284	+	15.6458i	0.713034	+	0.849761i
$340$		0			0
$341$		−	29.8257i		−	1.61515i
$342$		0			0
$343$		−	13.5211i		−	0.730070i
$344$		0			0
$345$	2.95336	+	3.51968i	0.159004	+	0.189493i
$346$		0			0
$347$	5.43923	−	14.9442i	0.291993	−	0.802244i	−0.703782	−	0.710416i	$-0.748507\pi$
$347$	5.43923	−	14.9442i	0.291993	−	0.802244i	0.995775	−	0.0918280i	$-0.0292710\pi$
$348$		0			0
$349$	−8.73917	+	15.1367i	−0.467797	+	0.810248i	−0.999323	−	0.0367938i	$-0.988286\pi$
$349$	−8.73917	+	15.1367i	−0.467797	+	0.810248i	0.531526	+	0.847042i	$0.321619\pi$
$350$		0			0
$351$	−5.58512	−	0.984808i	−0.298112	−	0.0525651i
$352$		0			0
$353$	−5.56552	−	9.63977i	−0.296223	−	0.513073i	0.679046	−	0.734096i	$-0.262394\pi$
$353$	−5.56552	−	9.63977i	−0.296223	−	0.513073i	−0.975269	+	0.221023i	$0.929060\pi$
$354$		0			0
$355$	−2.57532	−	2.16095i	−0.136684	−	0.114691i
$356$		0			0
$357$	1.11334	+	3.05888i	0.0589242	+	0.161893i
$358$		0			0
$359$	−7.24304	+	1.27714i	−0.382273	+	0.0674051i	−0.361483	−	0.932379i	$-0.617729\pi$
$359$	−7.24304	+	1.27714i	−0.382273	+	0.0674051i	−0.0207903	+	0.999784i	$0.506618\pi$
$360$		0			0
$361$	17.7565	+	6.76055i	0.934555	+	0.355818i
$362$		0			0
$363$	1.42989	+	8.10932i	0.0750499	+	0.425629i
$364$		0			0
$365$	11.2699	−	4.10191i	0.589894	−	0.214704i
$366$		0			0
$367$	−0.682266	+	0.813093i	−0.0356140	+	0.0424431i	−0.783557	−	0.621319i	$-0.786597\pi$
$367$	−0.682266	+	0.813093i	−0.0356140	+	0.0424431i	0.747943	+	0.663762i	$0.231041\pi$
$368$		0			0
$369$	6.07145	−	3.50535i	0.316067	−	0.182481i
$370$		0			0
$371$	−0.973841	+	5.52293i	−0.0505593	+	0.286736i
$372$		0			0
$373$	−16.6723	−	9.62576i	−0.863259	−	0.498403i	0.00184317	−	0.999998i	$-0.499413\pi$
$373$	−16.6723	−	9.62576i	−0.863259	−	0.498403i	−0.865102	+	0.501595i	$0.832747\pi$
$374$		0			0
$375$	−7.62449	−	2.77509i	−0.393727	−	0.143305i
$376$		0			0
$377$	−27.8011	+	23.3279i	−1.43183	+	1.20145i
$378$		0			0
$379$	21.3651			1.09745			0.548727	−	0.836002i	$-0.315113\pi$
$379$	21.3651			1.09745			0.548727	+	0.836002i	$0.315113\pi$
$380$		0			0
$381$	10.8726			0.557019
$382$		0			0
$383$	12.8027	−	10.7428i	0.654188	−	0.548929i	−0.254150	−	0.967165i	$-0.581796\pi$
$383$	12.8027	−	10.7428i	0.654188	−	0.548929i	0.908339	+	0.418236i	$0.137351\pi$
$384$		0			0
$385$	−3.79813	−	1.38241i	−0.193571	−	0.0704540i
$386$		0			0
$387$	4.13816	+	2.38917i	0.210354	+	0.121448i
$388$		0			0
$389$	−1.17799	+	6.68069i	−0.0597262	+	0.338724i	−0.999999	−	0.00169891i	$-0.999459\pi$
$389$	−1.17799	+	6.68069i	−0.0597262	+	0.338724i	0.940272	+	0.340423i	$0.110570\pi$
$390$		0			0
$391$	14.0544	−	8.11430i	0.710760	−	0.410358i
$392$		0			0
$393$	3.02481	−	3.60483i	0.152582	−	0.181840i
$394$		0			0
$395$	−3.82635	+	1.39268i	−0.192525	+	0.0700732i
$396$		0			0
$397$	3.76857	+	21.3726i	0.189139	+	1.07266i	0.920521	+	0.390693i	$0.127765\pi$
$397$	3.76857	+	21.3726i	0.189139	+	1.07266i	−0.731382	+	0.681968i	$0.761124\pi$
$398$		0			0
$399$	−4.56805	−	0.0336295i	−0.228688	−	0.00168358i
$400$		0			0
$401$	9.63223	−	1.69842i	0.481010	−	0.0848151i	0.0721149	−	0.997396i	$-0.477025\pi$
$401$	9.63223	−	1.69842i	0.481010	−	0.0848151i	0.408895	+	0.912581i	$0.365914\pi$
$402$		0			0
$403$	13.1912	+	36.2425i	0.657100	+	1.80537i
$404$		0			0
$405$	0.673648	+	0.565258i	0.0334738	+	0.0280879i
$406$		0			0
$407$	21.0116	+	36.3932i	1.04151	+	1.80394i
$408$		0			0
$409$	−1.51842	−	0.267738i	−0.0750810	−	0.0132388i	0.135981	−	0.990711i	$-0.456581\pi$
$409$	−1.51842	−	0.267738i	−0.0750810	−	0.0132388i	−0.211062	+	0.977473i	$0.567692\pi$
$410$		0			0
$411$	−3.09627	+	5.36289i	−0.152728	+	0.264532i
$412$		0			0
$413$	−5.41463	+	14.8766i	−0.266436	+	0.732028i
$414$		0			0
$415$	3.93242	+	4.68647i	0.193035	+	0.230050i
$416$		0			0
$417$		−	6.66544i		−	0.326408i
$418$		0			0
$419$		−	14.1279i		−	0.690194i	−0.938567	−	0.345097i	$-0.887846\pi$
$419$		−	14.1279i		−	0.690194i	0.938567	−	0.345097i	$-0.112154\pi$
$420$		0			0
$421$	10.3285	+	12.3090i	0.503379	+	0.599903i	0.956567	−	0.291511i	$-0.0941581\pi$
$421$	10.3285	+	12.3090i	0.503379	+	0.599903i	−0.453189	+	0.891415i	$0.649714\pi$
$422$		0			0
$423$	3.88919	−	10.6854i	0.189099	−	0.519544i
$424$		0			0
$425$	−6.56418	+	11.3695i	−0.318409	+	0.551501i
$426$		0			0
$427$	8.30793	+	1.46491i	0.402049	+	0.0708921i
$428$		0			0
$429$	−12.4363	−	21.5403i	−0.600430	−	1.03997i
$430$		0			0
$431$	10.0155	+	8.40399i	0.482429	+	0.404806i	0.851304	−	0.524673i	$-0.175812\pi$
$431$	10.0155	+	8.40399i	0.482429	+	0.404806i	−0.368875	+	0.929479i	$0.620257\pi$
$432$		0			0
$433$	−0.853388	−	2.34466i	−0.0410112	−	0.112677i	0.917497	−	0.397744i	$-0.130207\pi$
$433$	−0.853388	−	2.34466i	−0.0410112	−	0.112677i	−0.958508	+	0.285066i	$0.907984\pi$
$434$		0			0
$435$	5.54189	−	0.977185i	0.265713	−	0.0468524i
$436$		0			0
$437$	3.78952	+	22.4569i	0.181277	+	1.07426i
$438$		0			0
$439$	−1.02616	−	5.81964i	−0.0489759	−	0.277756i	0.950478	−	0.310791i	$-0.100594\pi$
$439$	−1.02616	−	5.81964i	−0.0489759	−	0.277756i	−0.999454	+	0.0330348i	$0.989483\pi$
$440$		0			0
$441$	−5.54576	+	2.01849i	−0.264084	+	0.0961186i
$442$		0			0
$443$	10.4838	−	12.4941i	0.498101	−	0.593613i	−0.457158	−	0.889386i	$-0.651133\pi$
$443$	10.4838	−	12.4941i	0.498101	−	0.593613i	0.955258	+	0.295772i	$0.0955770\pi$
$444$		0			0
$445$	−6.77631	+	3.91231i	−0.321228	+	0.185461i
$446$		0			0
$447$	0.0432332	−	0.245188i	0.00204486	−	0.0115970i
$448$		0			0
$449$	12.6218	+	7.28720i	0.595659	+	0.343904i	0.767332	−	0.641250i	$-0.221584\pi$
$449$	12.6218	+	7.28720i	0.595659	+	0.343904i	−0.171673	+	0.985154i	$0.554917\pi$
$450$		0			0
$451$	28.8926	+	10.5161i	1.36050	+	0.495182i
$452$		0			0
$453$	−11.6591	+	9.78315i	−0.547792	+	0.459652i
$454$		0			0
$455$	5.22668			0.245031
$456$		0			0
$457$	11.9813			0.560463			0.280232	−	0.959932i	$-0.409589\pi$
$457$	11.9813			0.560463			0.280232	+	0.959932i	$0.409589\pi$
$458$		0			0
$459$	2.37939	−	1.99654i	0.111060	−	0.0931906i
$460$		0			0
$461$	−28.0719	−	10.2173i	−1.30744	−	0.475869i	−0.408027	−	0.912970i	$-0.633783\pi$
$461$	−28.0719	−	10.2173i	−1.30744	−	0.475869i	−0.899413	+	0.437101i	$0.856005\pi$
$462$		0			0
$463$	11.5079	+	6.64409i	0.534818	+	0.308777i	0.742976	−	0.669318i	$-0.233414\pi$
$463$	11.5079	+	6.64409i	0.534818	+	0.308777i	−0.208158	+	0.978095i	$0.566747\pi$
$464$		0			0
$465$	1.03849	−	5.88954i	0.0481586	−	0.273121i
$466$		0			0
$467$	19.3571	−	11.1758i	0.895740	−	0.517156i	0.0199241	−	0.999801i	$-0.493658\pi$
$467$	19.3571	−	11.1758i	0.895740	−	0.517156i	0.875816	+	0.482646i	$0.160324\pi$
$468$		0			0
$469$	2.75103	−	3.27855i	0.127031	−	0.151389i
$470$		0			0
$471$	10.6912	−	3.89127i	0.492624	−	0.179300i
$472$		0			0
$473$	3.63903	+	20.6380i	0.167323	+	0.948935i
$474$		0			0
$475$	−11.7383	−	14.2002i	−0.538590	−	0.651548i
$476$		0			0
$477$	5.26991	−	0.929228i	0.241293	−	0.0425464i
$478$		0			0
$479$	4.16234	+	11.4359i	0.190182	+	0.522521i	0.997734	−	0.0672746i	$-0.0214304\pi$
$479$	4.16234	+	11.4359i	0.190182	+	0.522521i	−0.807552	+	0.589796i	$0.799208\pi$
$480$		0			0
$481$	−41.6279	−	34.9300i	−1.89807	−	1.59267i
$482$		0			0
$483$	−2.73783	−	4.74205i	−0.124575	−	0.215771i
$484$		0			0
$485$	−2.92855	−	0.516382i	−0.132979	−	0.0234477i
$486$		0			0
$487$	−4.92380	+	8.52827i	−0.223119	+	0.386453i	−0.955753	−	0.294169i	$-0.904957\pi$
$487$	−4.92380	+	8.52827i	−0.223119	+	0.386453i	0.732635	+	0.680622i	$0.238290\pi$
$488$		0			0
$489$	−2.69800	+	7.41268i	−0.122008	+	0.335213i
$490$		0			0
$491$	−25.2973	−	30.1481i	−1.14165	−	1.36056i	−0.923018	−	0.384757i	$-0.874285\pi$
$491$	−25.2973	−	30.1481i	−1.14165	−	1.36056i	−0.218631	−	0.975808i	$-0.570159\pi$
$492$		0			0
$493$		−	19.8764i		−	0.895189i
$494$		0			0
$495$			3.85673i			0.173347i
$496$		0			0
$497$	2.57532	+	3.06915i	0.115519	+	0.137670i
$498$		0			0
$499$	5.79544	−	15.9229i	0.259440	−	0.712805i	−0.739762	−	0.672868i	$-0.765062\pi$
$499$	5.79544	−	15.9229i	0.259440	−	0.712805i	0.999202	−	0.0399367i	$-0.0127156\pi$
$500$		0			0
$501$	0.879385	−	1.52314i	0.0392880	−	0.0680489i
$502$		0			0
$503$	12.4547	+	2.19610i	0.555328	+	0.0979193i	0.444267	−	0.895894i	$-0.353464\pi$
$503$	12.4547	+	2.19610i	0.555328	+	0.0979193i	0.111061	+	0.993814i	$0.464575\pi$
$504$		0			0
$505$	4.44475	+	7.69852i	0.197789	+	0.342580i
$506$		0			0
$507$	14.6800	+	12.3180i	0.651964	+	0.547062i
$508$		0			0
$509$	−0.703678	−	1.93334i	−0.0311900	−	0.0856937i	0.923120	−	0.384511i	$-0.125630\pi$
$509$	−0.703678	−	1.93334i	−0.0311900	−	0.0856937i	−0.954310	+	0.298818i	$0.903408\pi$
$510$		0			0
$511$	−14.0758	+	2.48194i	−0.622676	+	0.109795i
$512$		0			0
$513$	1.46064	+	4.10689i	0.0644887	+	0.181324i
$514$		0			0
$515$	−1.10354	−	6.25849i	−0.0486278	−	0.275782i
$516$		0			0
$517$	46.8632	−	17.0568i	2.06104	−	0.750158i
$518$		0			0
$519$	−2.45424	+	2.92485i	−0.107729	+	0.128387i
$520$		0			0
$521$	−25.8460	+	14.9222i	−1.13233	+	0.653753i	−0.944521	−	0.328451i	$-0.893473\pi$
$521$	−25.8460	+	14.9222i	−1.13233	+	0.653753i	−0.187813	+	0.982205i	$0.560140\pi$
$522$		0			0
$523$	−6.18644	+	35.0851i	−0.270514	+	1.53416i	0.482345	+	0.875981i	$0.339785\pi$
$523$	−6.18644	+	35.0851i	−0.270514	+	1.53416i	−0.752860	+	0.658181i	$0.771326\pi$
$524$		0			0
$525$	3.83615	+	2.21480i	0.167423	+	0.0966619i
$526$		0			0
$527$	−19.8494	−	7.22460i	−0.864654	−	0.314708i
$528$		0			0
$529$	−3.29292	+	2.76309i	−0.143170	+	0.120134i
$530$		0			0
$531$	15.1061			0.655547
$532$		0			0
$533$	−39.7597			−1.72218
$534$		0			0
$535$	−4.04189	+	3.39155i	−0.174746	+	0.146629i
$536$		0			0
$537$	18.8011	+	6.84305i	0.811328	+	0.295299i
$538$		0			0
$539$	−22.4153	−	12.9415i	−0.965497	−	0.557430i
$540$		0			0
$541$	−1.92097	+	10.8944i	−0.0825889	+	0.468385i	0.915262	+	0.402859i	$0.131984\pi$
$541$	−1.92097	+	10.8944i	−0.0825889	+	0.468385i	−0.997851	+	0.0655259i	$0.979128\pi$
$542$		0			0
$543$	6.52956	−	3.76984i	0.280210	−	0.161780i
$544$		0			0
$545$	4.53044	−	5.39917i	0.194063	−	0.231275i
$546$		0			0
$547$	25.0398	−	9.11375i	1.07063	−	0.389676i	0.254215	−	0.967148i	$-0.418183\pi$
$547$	25.0398	−	9.11375i	1.07063	−	0.389676i	0.816411	+	0.577472i	$0.195961\pi$
$548$		0			0
$549$	−1.39780	−	7.92734i	−0.0596568	−	0.338331i
$550$		0			0
$551$	26.1404	+	9.73286i	1.11362	+	0.414634i
$552$		0			0
$553$	4.77900	−	0.842667i	0.203224	−	0.0358338i
$554$		0			0
$555$	2.88191	+	7.91799i	0.122330	+	0.336100i
$556$		0			0
$557$	−22.6655	−	19.0186i	−0.960368	−	0.805844i	0.0206450	−	0.999787i	$-0.493428\pi$
$557$	−22.6655	−	19.0186i	−0.960368	−	0.805844i	−0.981013	+	0.193942i	$0.937872\pi$
$558$		0			0
$559$	−13.5496	−	23.4686i	−0.573088	−	0.992618i
$560$		0			0
$561$	13.4153	+	2.36549i	0.566396	+	0.0998709i
$562$		0			0
$563$	6.79473	−	11.7688i	0.286364	−	0.495997i	−0.686575	−	0.727059i	$-0.740887\pi$
$563$	6.79473	−	11.7688i	0.286364	−	0.495997i	0.972939	+	0.231062i	$0.0742201\pi$
$564$		0			0
$565$	−6.14290	+	16.8775i	−0.258434	+	0.710041i
$566$		0			0
$567$	−0.673648	−	0.802823i	−0.0282906	−	0.0337154i
$568$		0			0
$569$			28.9965i			1.21560i	0.794091	+	0.607799i	$0.207947\pi$
$569$			28.9965i			1.21560i	−0.794091	+	0.607799i	$0.792053\pi$
$570$		0			0
$571$			16.3619i			0.684725i	0.939568	+	0.342362i	$0.111227\pi$
$571$			16.3619i			0.684725i	−0.939568	+	0.342362i	$0.888773\pi$
$572$		0			0
$573$	3.22416	+	3.84240i	0.134691	+	0.160519i
$574$		0			0
$575$	7.55303	−	20.7518i	0.314983	−	0.865409i
$576$		0			0
$577$	−1.09920	+	1.90388i	−0.0457604	+	0.0792594i	−0.887998	−	0.459847i	$-0.847904\pi$
$577$	−1.09920	+	1.90388i	−0.0457604	+	0.0792594i	0.842238	+	0.539106i	$0.181238\pi$
$578$		0			0
$579$	−5.86231	−	1.03368i	−0.243629	−	0.0429584i
$580$		0			0
$581$	−3.64543	−	6.31407i	−0.151238	−	0.261952i
$582$		0			0
$583$	17.9782	+	15.0855i	0.744580	+	0.624777i
$584$		0			0
$585$	−1.70574	−	4.68647i	−0.0705235	−	0.193762i
$586$		0			0
$587$	25.9231	−	4.57094i	1.06996	−	0.188663i	0.389188	−	0.921158i	$-0.372756\pi$
$587$	25.9231	−	4.57094i	1.06996	−	0.188663i	0.680772	+	0.732495i	$0.261644\pi$
$588$		0			0
$589$	19.2211	−	22.5673i	0.791990	−	0.929868i
$590$		0			0
$591$	4.18820	+	23.7524i	0.172279	+	0.977045i
$592$		0			0
$593$	−5.84167	+	2.12619i	−0.239889	+	0.0873123i	−0.459167	−	0.888350i	$-0.651852\pi$
$593$	−5.84167	+	2.12619i	−0.239889	+	0.0873123i	0.219278	+	0.975662i	$0.429630\pi$
$594$		0			0
$595$	−1.84002	+	2.19285i	−0.0754336	+	0.0898982i
$596$		0			0
$597$	21.5326	−	12.4318i	0.881269	−	0.508801i
$598$		0			0
$599$	−1.34952	+	7.65350i	−0.0551398	+	0.312713i	−0.999886	−	0.0150889i	$-0.995197\pi$
$599$	−1.34952	+	7.65350i	−0.0551398	+	0.312713i	0.944746	+	0.327802i	$0.106308\pi$
$600$		0			0
$601$	1.34090	+	0.774169i	0.0546964	+	0.0315790i	0.527099	−	0.849804i	$-0.323280\pi$
$601$	1.34090	+	0.774169i	0.0546964	+	0.0315790i	−0.472402	+	0.881383i	$0.656613\pi$
$602$		0			0
$603$	−3.83750	−	1.39673i	−0.156275	−	0.0568794i
$604$		0			0
$605$	−5.54710	+	4.65457i	−0.225522	+	0.189235i
$606$		0			0
$607$	2.46110			0.0998931			0.0499466	−	0.998752i	$-0.484095\pi$
$607$	2.46110			0.0998931			0.0499466	+	0.998752i	$0.484095\pi$
$608$		0			0
$609$	−6.70645			−0.271759
$610$		0			0
$611$	−49.4017	+	41.4530i	−1.99858	+	1.67701i
$612$		0			0
$613$	−12.1686	−	4.42901i	−0.491485	−	0.178886i	0.0843753	−	0.996434i	$-0.473111\pi$
$613$	−12.1686	−	4.42901i	−0.491485	−	0.178886i	−0.575860	+	0.817548i	$0.695333\pi$
$614$		0			0
$615$	5.33915	+	3.08256i	0.215295	+	0.124301i
$616$		0			0
$617$	−7.56805	+	42.9205i	−0.304678	+	1.72792i	0.320338	+	0.947303i	$0.396204\pi$
$617$	−7.56805	+	42.9205i	−0.304678	+	1.72792i	−0.625016	+	0.780612i	$0.714907\pi$
$618$		0			0
$619$	−22.0956	+	12.7569i	−0.888095	+	0.512742i	−0.873319	−	0.487149i	$-0.838037\pi$
$619$	−22.0956	+	12.7569i	−0.888095	+	0.512742i	−0.0147762	+	0.999891i	$0.504704\pi$
$620$		0			0
$621$	−3.35844	+	4.00243i	−0.134770	+	0.160612i
$622$		0			0
$623$	8.76264	−	3.18934i	0.351068	−	0.127778i
$624$		0			0
$625$	2.43077	+	13.7856i	0.0972308	+	0.551423i
$626$		0			0
$627$	−9.68004	+	16.4849i	−0.386584	+	0.658342i
$628$		0			0
$629$	29.3097	−	5.16810i	1.16866	−	0.206066i
$630$		0			0
$631$	−8.07057	−	22.1737i	−0.321284	−	0.882722i	−0.990234	−	0.139414i	$-0.955478\pi$
$631$	−8.07057	−	22.1737i	−0.321284	−	0.882722i	0.668950	−	0.743308i	$-0.266744\pi$
$632$		0			0
$633$	−1.94356	−	1.63084i	−0.0772497	−	0.0648202i
$634$		0			0
$635$	4.78059	+	8.28023i	0.189712	+	0.328591i
$636$		0			0
$637$	32.9616	+	5.81201i	1.30598	+	0.230280i
$638$		0			0
$639$	1.91147	−	3.31077i	0.0756167	−	0.130972i
$640$		0			0
$641$	−9.47272	+	26.0261i	−0.374150	+	1.02797i	0.599591	+	0.800307i	$0.295330\pi$
$641$	−9.47272	+	26.0261i	−0.374150	+	1.02797i	−0.973740	+	0.227661i	$0.926892\pi$
$642$		0			0
$643$	−15.3833	−	18.3331i	−0.606656	−	0.722985i	0.372059	−	0.928209i	$-0.378652\pi$
$643$	−15.3833	−	18.3331i	−0.606656	−	0.722985i	−0.978715	+	0.205224i	$0.934208\pi$
$644$		0			0
$645$			4.20199i			0.165453i
$646$		0			0
$647$			2.85382i			0.112195i	0.998425	+	0.0560975i	$0.0178658\pi$
$647$			2.85382i			0.112195i	−0.998425	+	0.0560975i	$0.982134\pi$
$648$		0			0
$649$	42.5852	+	50.7510i	1.67161	+	1.99215i
$650$		0			0
$651$	−2.43763	+	6.69734i	−0.0955384	+	0.262490i
$652$		0			0
$653$	3.06283	−	5.30498i	0.119858	−	0.207600i	−0.799853	−	0.600196i	$-0.795089\pi$
$653$	3.06283	−	5.30498i	0.119858	−	0.207600i	0.919711	+	0.392596i	$0.128423\pi$
$654$		0			0
$655$	4.07532	+	0.718589i	0.159236	+	0.0280776i
$656$		0			0
$657$	6.81908	+	11.8110i	0.266038	+	0.460791i
$658$		0			0
$659$	−35.0009	−	29.3693i	−1.36344	−	1.14406i	−0.974902	−	0.222633i	$-0.928535\pi$
$659$	−35.0009	−	29.3693i	−1.36344	−	1.14406i	−0.388540	−	0.921432i	$-0.627021\pi$
$660$		0			0
$661$	−11.3858	−	31.2822i	−0.442856	−	1.21674i	−0.937606	−	0.347700i	$-0.886963\pi$
$661$	−11.3858	−	31.2822i	−0.442856	−	1.21674i	0.494750	−	0.869035i	$-0.335260\pi$
$662$		0			0
$663$	−17.3478	+	3.05888i	−0.673731	+	0.118797i
$664$		0			0
$665$	−1.98293	−	3.49367i	−0.0768946	−	0.135479i
$666$		0			0
$667$	5.80587	+	32.9267i	0.224804	+	1.27493i
$668$		0			0
$669$	20.9884	−	7.63917i	0.811460	−	0.295347i
$670$		0			0
$671$	22.6925	−	27.0439i	0.876036	−	1.04402i
$672$		0			0
$673$	22.1716	−	12.8008i	0.854652	−	0.493434i	−0.00756578	−	0.999971i	$-0.502408\pi$
$673$	22.1716	−	12.8008i	0.854652	−	0.493434i	0.862218	+	0.506538i	$0.169075\pi$
$674$		0			0
$675$	0.733956	−	4.16247i	0.0282500	−	0.160213i
$676$		0			0
$677$	−18.0831	−	10.4403i	−0.694989	−	0.401252i	0.110490	−	0.993877i	$-0.464758\pi$
$677$	−18.0831	−	10.4403i	−0.694989	−	0.401252i	−0.805478	+	0.592625i	$0.798091\pi$
$678$		0			0
$679$	3.33022	+	1.21210i	0.127802	+	0.0465162i
$680$		0			0
$681$	−1.97771	+	1.65950i	−0.0757861	+	0.0635921i
$682$		0			0
$683$	3.65808			0.139973			0.0699863	−	0.997548i	$-0.477704\pi$
$683$	3.65808			0.139973			0.0699863	+	0.997548i	$0.477704\pi$
$684$		0			0
$685$	−5.44562			−0.208067
$686$		0			0
$687$	3.95858	−	3.32164i	0.151029	−	0.126729i
$688$		0			0
$689$	−28.5180	−	10.3797i	−1.08645	−	0.395435i
$690$		0			0
$691$	38.9097	+	22.4645i	1.48020	+	0.854591i	0.999748	−	0.0224324i	$-0.00714106\pi$
$691$	38.9097	+	22.4645i	1.48020	+	0.854591i	0.480447	+	0.877024i	$0.340474\pi$
$692$		0			0
$693$	0.798133	−	4.52644i	0.0303186	−	0.171945i
$694$		0			0
$695$	5.07620	−	2.93075i	0.192551	−	0.111169i
$696$		0			0
$697$	13.9972	−	16.6812i	0.530181	−	0.631845i
$698$		0			0
$699$	−8.12361	+	2.95675i	−0.307263	+	0.111835i
$700$		0			0
$701$	1.28905	+	7.31056i	0.0486867	+	0.276116i	0.999426	−	0.0338754i	$-0.0107849\pi$
$701$	1.28905	+	7.31056i	0.0486867	+	0.276116i	−0.950739	+	0.309991i	$0.899674\pi$
$702$		0			0
$703$	−7.55525	+	41.0773i	−0.284952	+	1.54926i
$704$		0			0
$705$	9.84776	−	1.73643i	0.370888	−	0.0653976i
$706$		0			0
$707$	−3.62339	−	9.95518i	−0.136272	−	0.374403i
$708$		0			0
$709$	−38.9673	−	32.6974i	−1.46345	−	1.22798i	−0.921970	−	0.387260i	$-0.873421\pi$
$709$	−38.9673	−	32.6974i	−1.46345	−	1.22798i	−0.541475	−	0.840717i	$-0.682134\pi$
$710$		0			0
$711$	−2.31521	−	4.01006i	−0.0868271	−	0.150389i
$712$		0			0
$713$	34.9923	+	6.17009i	1.31047	+	0.231072i
$714$		0			0
$715$	10.9363	−	18.9422i	0.408994	−	0.708398i
$716$		0			0
$717$	−1.20321	+	3.30579i	−0.0449347	+	0.123457i
$718$		0			0
$719$	−24.6246	−	29.3465i	−0.918344	−	1.09444i	−0.995245	−	0.0974015i	$-0.968947\pi$
$719$	−24.6246	−	29.3465i	−0.918344	−	1.09444i	0.0769008	−	0.997039i	$-0.475498\pi$
$720$		0			0
$721$			7.57364i			0.282057i
$722$		0			0
$723$		−	15.2245i		−	0.566205i
$724$		0			0
$725$	−17.3858	−	20.7196i	−0.645692	−	0.769505i
$726$		0			0
$727$	13.8712	−	38.1109i	0.514456	−	1.41346i	−0.362093	−	0.932142i	$-0.617938\pi$
$727$	13.8712	−	38.1109i	0.514456	−	1.41346i	0.876549	−	0.481313i	$-0.159840\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	14.6163	+	2.57725i	0.540605	+	0.0953232i
$732$		0			0
$733$	−4.55391	−	7.88760i	−0.168203	−	0.291335i	0.769585	−	0.638544i	$-0.220463\pi$
$733$	−4.55391	−	7.88760i	−0.168203	−	0.291335i	−0.937788	+	0.347209i	$0.887130\pi$
$734$		0			0
$735$	−3.97565	−	3.33597i	−0.146644	−	0.123049i
$736$		0			0
$737$	−6.12567	−	16.8301i	−0.225642	−	0.619946i
$738$		0			0
$739$	−34.0087	+	5.99665i	−1.25103	+	0.220590i	−0.759637	−	0.650348i	$-0.774623\pi$
$739$	−34.0087	+	5.99665i	−1.25103	+	0.220590i	−0.491393	+	0.870938i	$0.663512\pi$
$740$		0			0
$741$	4.47178	−	24.3127i	0.164275	−	0.893150i
$742$		0			0
$743$	2.02094	+	11.4613i	0.0741413	+	0.420476i	0.999176	+	0.0405929i	$0.0129247\pi$
$743$	2.02094	+	11.4613i	0.0741413	+	0.420476i	−0.925035	+	0.379883i	$0.875964\pi$
$744$		0			0
$745$	0.205737	−	0.0748822i	0.00753762	−	0.00274347i
$746$		0			0
$747$	−4.47178	+	5.32926i	−0.163614	+	0.194987i
$748$		0			0
$749$	5.44562	−	3.14403i	0.198979	−	0.114880i
$750$		0			0
$751$	0.805874	−	4.57034i	0.0294068	−	0.166774i	−0.966568	−	0.256412i	$-0.917460\pi$
$751$	0.805874	−	4.57034i	0.0294068	−	0.166774i	0.995974	+	0.0896375i	$0.0285709\pi$
$752$		0			0
$753$	−15.0715	−	8.70151i	−0.549234	−	0.317101i
$754$		0			0
$755$	−12.5770	−	4.57764i	−0.457723	−	0.166597i
$756$		0			0
$757$	−40.7131	+	34.1623i	−1.47974	+	1.24165i	−0.573282	+	0.819358i	$0.694330\pi$
$757$	−40.7131	+	34.1623i	−1.47974	+	1.24165i	−0.906460	+	0.422292i	$0.861226\pi$
$758$		0			0
$759$	−22.9145			−0.831742
$760$		0			0
$761$	19.7324			0.715298			0.357649	−	0.933856i	$-0.383578\pi$
$761$	19.7324			0.715298			0.357649	+	0.933856i	$0.383578\pi$
$762$		0			0
$763$	−6.43448	+	5.39917i	−0.232944	+	0.195463i
$764$		0			0
$765$	2.56670	+	0.934204i	0.0927994	+	0.0337762i
$766$		0			0
$767$	−74.1931	−	42.8354i	−2.67896	−	1.54670i
$768$		0			0
$769$	4.18155	−	23.7148i	0.150791	−	0.855176i	−0.811743	−	0.584014i	$-0.801481\pi$
$769$	4.18155	−	23.7148i	0.150791	−	0.855176i	0.962534	−	0.271161i	$-0.0874077\pi$
$770$		0			0
$771$	27.4347	−	15.8394i	0.988036	−	0.570443i
$772$		0			0
$773$	−26.9247	+	32.0876i	−0.968415	+	1.15411i	0.0196079	+	0.999808i	$0.493758\pi$
$773$	−26.9247	+	32.0876i	−0.968415	+	1.15411i	−0.988023	+	0.154305i	$0.950686\pi$
$774$		0			0
$775$	−27.0107	+	9.83110i	−0.970254	+	0.353144i
$776$		0			0
$777$	−1.74376	−	9.88933i	−0.0625569	−	0.354778i
$778$		0			0
$779$	15.0842	+	26.5766i	0.540449	+	0.952206i
$780$		0			0
$781$	16.5116	−	2.91144i	0.590832	−	0.104180i
$782$		0			0
$783$	2.18866	+	6.01330i	0.0782164	+	0.214898i
$784$		0			0
$785$	7.66431	+	6.43112i	0.273551	+	0.229537i
$786$		0			0
$787$	8.76011	+	15.1730i	0.312264	+	0.540858i	0.978852	−	0.204569i	$-0.0655792\pi$
$787$	8.76011	+	15.1730i	0.312264	+	0.540858i	−0.666588	+	0.745426i	$0.732246\pi$
$788$		0			0
$789$	1.50980	+	0.266219i	0.0537503	+	0.00947763i
$790$		0			0
$791$	10.7023	−	18.5370i	0.380531	−	0.659099i
$792$		0			0
$793$	−15.6138	+	42.8986i	−0.554463	+	1.52337i
$794$		0			0
$795$	3.02481	+	3.60483i	0.107279	+	0.127850i
$796$		0			0
$797$		−	39.9751i		−	1.41599i	−0.706216	−	0.707996i	$-0.749599\pi$
$797$		−	39.9751i		−	1.41599i	0.706216	−	0.707996i	$-0.250401\pi$
$798$		0			0
$799$		−	35.3198i		−	1.24952i
$800$		0			0
$801$	−5.71941	−	6.81612i	−0.202085	−	0.240836i
$802$		0			0
$803$	−20.4572	+	56.2058i	−0.721920	+	1.98346i
$804$		0			0
$805$	2.40760	−	4.17009i	0.0848569	−	0.146976i
$806$		0			0
$807$	−22.9709	−	4.05039i	−0.808614	−	0.142580i
$808$		0			0
$809$	−19.8418	−	34.3671i	−0.697602	−	1.20828i	−0.969296	−	0.245898i	$-0.920917\pi$
$809$	−19.8418	−	34.3671i	−0.697602	−	1.20828i	0.271694	−	0.962384i	$-0.412416\pi$
$810$		0			0
$811$	−31.4918	−	26.4248i	−1.10583	−	0.927900i	−0.108025	−	0.994148i	$-0.534453\pi$
$811$	−31.4918	−	26.4248i	−1.10583	−	0.927900i	−0.997803	+	0.0662480i	$0.978897\pi$
$812$		0			0
$813$	−7.75237	−	21.2995i	−0.271888	−	0.747005i
$814$		0			0
$815$	−6.83157	+	1.20459i	−0.239299	+	0.0421949i
$816$		0			0
$817$	−10.5466	+	17.9606i	−0.368980	+	0.628364i
$818$		0			0
$819$	1.03209	+	5.85327i	0.0360641	+	0.204530i
$820$		0			0
$821$	24.0993	−	8.77141i	0.841070	−	0.306124i	0.114676	−	0.993403i	$-0.463417\pi$
$821$	24.0993	−	8.77141i	0.841070	−	0.306124i	0.726394	+	0.687279i	$0.241195\pi$
$822$		0			0
$823$	2.80928	−	3.34797i	0.0979253	−	0.116703i	−0.714856	−	0.699271i	$-0.753508\pi$
$823$	2.80928	−	3.34797i	0.0979253	−	0.116703i	0.812781	+	0.582569i	$0.197952\pi$
$824$		0			0
$825$	16.0535	−	9.26849i	0.558911	−	0.322687i
$826$		0			0
$827$	3.64125	−	20.6506i	0.126619	−	0.718091i	−0.853714	−	0.520742i	$-0.825656\pi$
$827$	3.64125	−	20.6506i	0.126619	−	0.718091i	0.980333	−	0.197349i	$-0.0632334\pi$
$828$		0			0
$829$	28.6038	+	16.5144i	0.993453	+	0.573570i	0.906305	−	0.422625i	$-0.138891\pi$
$829$	28.6038	+	16.5144i	0.993453	+	0.573570i	0.0871481	+	0.996195i	$0.472225\pi$
$830$		0			0
$831$	20.2875	+	7.38403i	0.703764	+	0.256149i
$832$		0			0
$833$	−14.0424	+	11.7829i	−0.486539	+	0.408255i
$834$		0			0
$835$	1.54664			0.0535236
$836$		0			0
$837$	6.80066			0.235065
$838$		0			0
$839$	−26.9702	+	22.6307i	−0.931114	+	0.781298i	−0.976017	−	0.217694i	$-0.930147\pi$
$839$	−26.9702	+	22.6307i	−0.931114	+	0.781298i	0.0449028	+	0.998991i	$0.485702\pi$
$840$		0			0
$841$	11.2294	+	4.08716i	0.387220	+	0.140936i
$842$		0			0
$843$	23.5813	+	13.6147i	0.812183	+	0.468914i
$844$		0			0
$845$	−2.92633	+	16.5960i	−0.100669	+	0.570921i
$846$		0			0
$847$	7.47359	−	4.31488i	0.256796	−	0.148261i
$848$		0			0
$849$	−16.4996	+	19.6634i	−0.566264	+	0.674848i
$850$		0			0
$851$	−47.0442	+	17.1227i	−1.61265	+	0.586958i
$852$		0			0
$853$	−8.14755	−	46.2070i	−0.278967	−	1.58210i	−0.726073	−	0.687618i	$-0.758657\pi$
$853$	−8.14755	−	46.2070i	−0.278967	−	1.58210i	0.447106	−	0.894481i	$-0.352455\pi$
$854$		0			0
$855$	−2.48545	+	2.91815i	−0.0850007	+	0.0997985i
$856$		0			0
$857$	14.3846	−	2.53639i	0.491369	−	0.0866415i	0.0775266	−	0.996990i	$-0.475298\pi$
$857$	14.3846	−	2.53639i	0.491369	−	0.0866415i	0.413842	+	0.910349i	$0.364187\pi$
$858$		0			0
$859$	−12.1009	−	33.2468i	−0.412876	−	1.13437i	−0.955654	−	0.294491i	$-0.904850\pi$
$859$	−12.1009	−	33.2468i	−0.412876	−	1.13437i	0.542779	−	0.839876i	$-0.317372\pi$
$860$		0			0
$861$	−5.62836	−	4.72275i	−0.191814	−	0.160951i
$862$		0			0
$863$	16.8366	+	29.1619i	0.573125	+	0.992682i	0.996243	+	0.0866070i	$0.0276025\pi$
$863$	16.8366	+	29.1619i	0.573125	+	0.992682i	−0.423117	+	0.906075i	$0.639064\pi$
$864$		0			0
$865$	−3.30659	−	0.583041i	−0.112427	−	0.0198240i
$866$		0			0
$867$	−3.67617	+	6.36732i	−0.124849	+	0.216246i
$868$		0			0
$869$	6.94562	−	19.0829i	0.235614	−	0.647344i
$870$		0			0
$871$	14.8871	+	17.7418i	0.504431	+	0.601157i
$872$		0			0
$873$		−	3.38160i		−	0.114450i
$874$		0			0
$875$			8.50336i			0.287466i
$876$		0			0
$877$	−5.80587	−	6.91917i	−0.196050	−	0.233644i	0.659059	−	0.752091i	$-0.270955\pi$
$877$	−5.80587	−	6.91917i	−0.196050	−	0.233644i	−0.855110	+	0.518447i	$0.826510\pi$
$878$		0			0
$879$	6.59879	−	18.1300i	0.222572	−	0.611511i
$880$		0			0
$881$	−6.43330	+	11.1428i	−0.216743	+	0.375410i	−0.953810	−	0.300409i	$-0.902877\pi$
$881$	−6.43330	+	11.1428i	−0.216743	+	0.375410i	0.737067	+	0.675819i	$0.236210\pi$
$882$		0			0
$883$	−14.7078	−	2.59338i	−0.494957	−	0.0872742i	−0.0794025	−	0.996843i	$-0.525301\pi$
$883$	−14.7078	−	2.59338i	−0.494957	−	0.0872742i	−0.415554	+	0.909568i	$0.636412\pi$
$884$		0			0
$885$	6.64203	+	11.5043i	0.223269	+	0.386714i
$886$		0			0
$887$	13.9185	+	11.6790i	0.467337	+	0.392143i	0.845822	−	0.533465i	$-0.179110\pi$
$887$	13.9185	+	11.6790i	0.467337	+	0.392143i	−0.378485	+	0.925608i	$0.623555\pi$
$888$		0			0
$889$	−3.89717	−	10.7074i	−0.130707	−	0.359115i
$890$		0			0
$891$	−4.31908	+	0.761570i	−0.144695	+	0.0255136i
$892$		0			0
$893$	46.4507	+	17.2950i	1.55441	+	0.578755i
$894$		0			0
$895$	3.05525	+	17.3272i	0.102126	+	0.579185i
$896$		0			0
$897$	27.8444	−	10.1345i	0.929696	−	0.338382i
$898$		0			0
$899$	27.9734	−	33.3374i	0.932966	−	1.11187i
$900$		0			0
$901$	14.3944	−	8.31061i	0.479547	−	0.276867i
$902$		0			0
$903$	0.869585	−	4.93166i	0.0289380	−	0.164115i
$904$		0			0
$905$	5.74200	+	3.31515i	0.190871	+	0.110199i
$906$		0			0
$907$	−15.6186	−	5.68469i	−0.518606	−	0.188757i	0.0694379	−	0.997586i	$-0.477879\pi$
$907$	−15.6186	−	5.68469i	−0.518606	−	0.188757i	−0.588044	+	0.808829i	$0.700102\pi$
$908$		0			0
$909$	−7.74376	+	6.49778i	−0.256844	+	0.215518i
$910$		0			0
$911$	−9.37464			−0.310596			−0.155298	−	0.987868i	$-0.549634\pi$
$911$	−9.37464			−0.310596			−0.155298	+	0.987868i	$0.549634\pi$
$912$		0			0
$913$	−30.5107			−1.00976
$914$		0			0
$915$	5.42262	−	4.55012i	0.179266	−	0.150422i
$916$		0			0
$917$	−4.63429	−	1.68674i	−0.153038	−	0.0557011i
$918$		0			0
$919$	−34.1072	−	19.6918i	−1.12509	−	0.649572i	−0.182396	−	0.983225i	$-0.558385\pi$
$919$	−34.1072	−	19.6918i	−1.12509	−	0.649572i	−0.942696	+	0.333653i	$0.891719\pi$
$920$		0			0
$921$	0.642903	−	3.64609i	0.0211844	−	0.120143i
$922$		0			0
$923$	−18.7763	+	10.8405i	−0.618030	+	0.356820i
$924$		0			0
$925$	26.0326	−	31.0244i	0.855945	−	1.02008i
$926$		0			0
$927$	6.79086	−	2.47167i	0.223041	−	0.0811803i
$928$		0			0
$929$	−9.04804	−	51.3140i	−0.296856	−	1.68356i	−0.659560	−	0.751652i	$-0.729257\pi$
$929$	−9.04804	−	51.3140i	−0.296856	−	1.68356i	0.362703	−	0.931905i	$-0.381854\pi$
$930$		0			0
$931$	−8.62020	−	24.2375i	−0.282516	−	0.794353i
$932$		0			0
$933$	−16.7986	+	2.96205i	−0.549961	+	0.0969730i
$934$		0			0
$935$	4.09714	+	11.2568i	0.133991	+	0.368137i
$936$		0			0
$937$	−2.21024	−	1.85461i	−0.0722053	−	0.0605874i	0.605971	−	0.795487i	$-0.292785\pi$
$937$	−2.21024	−	1.85461i	−0.0722053	−	0.0605874i	−0.678176	+	0.734900i	$0.737229\pi$
$938$		0			0
$939$	−15.4324	−	26.7297i	−0.503618	−	0.872292i
$940$		0			0
$941$	−30.5424	−	5.38544i	−0.995652	−	0.175560i	−0.347999	−	0.937495i	$-0.613139\pi$
$941$	−30.5424	−	5.38544i	−0.995652	−	0.175560i	−0.647654	+	0.761935i	$0.724250\pi$
$942$		0			0
$943$	−18.3148	+	31.7222i	−0.596412	+	1.03302i
$944$		0			0
$945$	0.315207	−	0.866025i	0.0102537	−	0.0281718i
$946$		0			0
$947$	−33.4749	−	39.8939i	−1.08779	−	1.29638i	−0.952154	−	0.305618i	$-0.901137\pi$
$947$	−33.4749	−	39.8939i	−1.08779	−	1.29638i	−0.135635	−	0.990759i	$-0.543307\pi$
$948$		0			0
$949$		−	77.3458i		−	2.51075i
$950$		0			0
$951$		−	21.6757i		−	0.702883i
$952$		0			0
$953$	5.62418	+	6.70264i	0.182185	+	0.217120i	0.849406	−	0.527740i	$-0.176961\pi$
$953$	5.62418	+	6.70264i	0.182185	+	0.217120i	−0.667221	+	0.744860i	$0.732516\pi$
$954$		0			0
$955$	−1.50862	+	4.14489i	−0.0488177	+	0.134126i
$956$		0			0
$957$	−14.0326	+	24.3051i	−0.453608	+	0.785672i
$958$		0			0
$959$	6.39124	+	1.12695i	0.206384	+	0.0363911i
$960$		0			0
$961$	−7.62449	−	13.2060i	−0.245951	−	0.426000i
$962$		0			0
$963$	−4.59627	−	3.85673i	−0.148113	−	0.124281i
$964$		0			0
$965$	−1.79039	−	4.91906i	−0.0576348	−	0.158350i
$966$		0			0
$967$	−45.9320	+	8.09905i	−1.47707	+	0.260448i	−0.853408	−	0.521243i	$-0.825468\pi$
$967$	−45.9320	+	8.09905i	−1.47707	+	0.260448i	−0.623666	+	0.781691i	$0.714357\pi$
$968$		0			0
$969$	8.62613	+	10.4353i	0.277111	+	0.335230i
$970$		0			0
$971$	−5.25372	−	29.7953i	−0.168600	−	0.956177i	−0.945275	−	0.326276i	$-0.894206\pi$
$971$	−5.25372	−	29.7953i	−0.168600	−	0.956177i	0.776675	−	0.629902i	$-0.216905\pi$
$972$		0			0
$973$	−6.56418	+	2.38917i	−0.210438	+	0.0765931i
$974$		0			0
$975$	−15.4081	+	18.3626i	−0.493453	+	0.588075i
$976$		0			0
$977$	7.31150	−	4.22130i	0.233916	−	0.135051i	−0.378462	−	0.925617i	$-0.623547\pi$
$977$	7.31150	−	4.22130i	0.233916	−	0.135051i	0.612377	+	0.790566i	$0.290213\pi$
$978$		0			0
$979$	6.77631	−	38.4304i	0.216572	−	1.22824i
$980$		0			0
$981$	6.94104	+	4.00741i	0.221610	+	0.127947i
$982$		0			0
$983$	12.2892	+	4.47291i	0.391965	+	0.142664i	0.530481	−	0.847697i	$-0.322011\pi$
$983$	12.2892	+	4.47291i	0.391965	+	0.142664i	−0.138516	+	0.990360i	$0.544233\pi$
$984$		0			0
$985$	−16.2476	+	13.6334i	−0.517692	+	0.434396i
$986$		0			0
$987$	−11.9172			−0.379327
$988$		0			0
$989$	−24.9659			−0.793868
$990$		0			0
$991$	−12.7556	+	10.7032i	−0.405195	+	0.339999i	−0.822498	−	0.568768i	$-0.807420\pi$
$991$	−12.7556	+	10.7032i	−0.405195	+	0.339999i	0.417302	+	0.908768i	$0.362976\pi$
$992$		0			0
$993$	−2.48798	−	0.905550i	−0.0789536	−	0.0287368i
$994$		0			0
$995$	18.9354	+	10.9324i	0.600293	+	0.346579i
$996$		0			0
$997$	−0.364533	+	2.06737i	−0.0115449	+	0.0654742i	−0.990036	−	0.140815i	$-0.955028\pi$
$997$	−0.364533	+	2.06737i	−0.0115449	+	0.0654742i	0.978491	+	0.206289i	$0.0661388\pi$
$998$		0			0
$999$	−8.29813	+	4.79093i	−0.262541	+	0.151578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.b.751.1	yes	6
4.3	odd	2		912.2.ci.a.751.1	✓	6
19.2	odd	18		912.2.ci.a.895.1	yes	6
76.59	even	18	inner	912.2.ci.b.895.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.a.751.1	✓	6	4.3	odd	2
912.2.ci.a.895.1	yes	6	19.2	odd	18
912.2.ci.b.751.1	yes	6	1.1	even	1	trivial
912.2.ci.b.895.1	yes	6	76.59	even	18	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.907604 + 0.524005i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.907604 + 0.524005i) q^{7} +(0.173648 - 0.984808i) q^{9} +(3.79813 - 2.19285i) q^{11} +(-3.64543 + 4.34445i) q^{13} +(0.826352 - 0.300767i) q^{15} +(-0.539363 - 3.05888i) q^{17} +(4.28699 + 0.788496i) q^{19} +(-1.03209 + 0.181985i) q^{21} +(1.78699 + 4.90971i) q^{23} +(-3.23783 - 2.71686i) q^{25} +(0.500000 + 0.866025i) q^{27} +(6.30200 + 1.11121i) q^{29} +(3.40033 - 5.88954i) q^{31} +(-1.50000 + 4.12122i) q^{33} +(-0.592396 - 0.705990i) q^{35} +9.58186i q^{37} -5.67128i q^{39} +(4.50640 + 5.37051i) q^{41} +(-1.63429 + 4.49016i) q^{43} +(-0.439693 + 0.761570i) q^{45} +(11.1985 + 1.97459i) q^{47} +(-2.95084 - 5.11100i) q^{49} +(2.37939 + 1.99654i) q^{51} +(1.83022 + 5.02849i) q^{53} +(-3.79813 + 0.669713i) q^{55} +(-3.79086 + 2.15160i) q^{57} +(2.62314 + 14.8766i) q^{59} +(7.56418 - 2.75314i) q^{61} +(0.673648 - 0.802823i) q^{63} +(4.31908 - 2.49362i) q^{65} +(0.709141 - 4.02174i) q^{67} +(-4.52481 - 2.61240i) q^{69} +(3.59240 + 1.30753i) q^{71} +(-10.4474 + 8.76644i) q^{73} +4.22668 q^{75} +4.59627 q^{77} +(3.54710 - 2.97637i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-6.02481 - 3.47843i) q^{83} +(-0.474308 + 2.68993i) q^{85} +(-5.54189 + 3.19961i) q^{87} +(5.71941 - 6.81612i) q^{89} +(-5.58512 + 2.03282i) q^{91} +(1.18092 + 6.69734i) q^{93} +(-3.30541 - 1.94096i) q^{95} +(3.33022 - 0.587208i) q^{97} +(-1.50000 - 4.12122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} + 9 q^{7}+O(q^{10}) \) 6 * q - 6 * q^5 + 9 * q^7	\( 6 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 6 q^{13} + 6 q^{15} - 12 q^{17} + 18 q^{19} + 3 q^{21} + 3 q^{23} + 3 q^{27} + 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} + 39 q^{47} - 6 q^{49} + 3 q^{51} - 12 q^{53} - 9 q^{55} + 9 q^{57} + 12 q^{59} + 27 q^{61} + 3 q^{63} + 9 q^{65} + 36 q^{67} + 18 q^{71} - 9 q^{73} + 12 q^{75} - 18 q^{79} - 9 q^{83} + 27 q^{85} - 27 q^{87} + 3 q^{89} - 12 q^{91} + 24 q^{93} - 24 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^5 + 9 * q^7 + 9 * q^11 - 6 * q^13 + 6 * q^15 - 12 * q^17 + 18 * q^19 + 3 * q^21 + 3 * q^23 + 3 * q^27 + 6 * q^31 - 9 * q^33 - 12 * q^41 + 3 * q^45 + 39 * q^47 - 6 * q^49 + 3 * q^51 - 12 * q^53 - 9 * q^55 + 9 * q^57 + 12 * q^59 + 27 * q^61 + 3 * q^63 + 9 * q^65 + 36 * q^67 + 18 * q^71 - 9 * q^73 + 12 * q^75 - 18 * q^79 - 9 * q^83 + 27 * q^85 - 27 * q^87 + 3 * q^89 - 12 * q^91 + 24 * q^93 - 24 * q^95 - 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more