LMFDB - Embedded newform 756.2.bp.a.193.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 12]))

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

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

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (of order $9$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.8
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.844572 - 1.51218i) q^{3} +(-0.569103 + 0.207137i) q^{5} +(2.00271 + 1.72892i) q^{7} +(-1.57340 + 2.55430i) q^{9} +O(q^{10})$	\(q+(-0.844572 - 1.51218i) q^{3} +(-0.569103 + 0.207137i) q^{5} +(2.00271 + 1.72892i) q^{7} +(-1.57340 + 2.55430i) q^{9} +(-3.12667 - 1.13801i) q^{11} +(-2.37655 + 0.864994i) q^{13} +(0.793878 + 0.685647i) q^{15} +(-0.831106 - 1.43952i) q^{17} +(-3.18133 + 5.51023i) q^{19} +(0.923004 - 4.48866i) q^{21} +(-0.329380 + 1.86800i) q^{23} +(-3.54925 + 2.97817i) q^{25} +(5.19141 + 0.221975i) q^{27} +(-5.30432 - 1.93061i) q^{29} +(3.04436 - 1.10806i) q^{31} +(0.919812 + 5.68923i) q^{33} +(-1.49787 - 0.569097i) q^{35} -4.15961 q^{37} +(3.31520 + 2.86323i) q^{39} +(5.16301 - 1.87918i) q^{41} +(1.48333 + 8.41241i) q^{43} +(0.366336 - 1.77957i) q^{45} +(2.63058 + 0.957453i) q^{47} +(1.02170 + 6.92504i) q^{49} +(-1.47489 + 2.47256i) q^{51} +(-4.36492 + 7.56027i) q^{53} +2.01512 q^{55} +(11.0193 + 0.156970i) q^{57} +(5.41321 + 4.54223i) q^{59} +(-5.86567 - 2.13493i) q^{61} +(-7.56722 + 2.39525i) q^{63} +(1.17333 - 0.984542i) q^{65} +(-0.437715 + 2.48240i) q^{67} +(3.10295 - 1.07958i) q^{69} +(-5.23329 + 9.06432i) q^{71} +5.79537 q^{73} +(7.50114 + 2.85183i) q^{75} +(-4.29428 - 7.68486i) q^{77} +(0.191208 + 1.08440i) q^{79} +(-4.04885 - 8.03783i) q^{81} +(-8.09245 - 2.94541i) q^{83} +(0.771162 + 0.647082i) q^{85} +(1.56044 + 9.65164i) q^{87} +(4.25989 - 7.37835i) q^{89} +(-6.25504 - 2.37652i) q^{91} +(-4.24676 - 3.66779i) q^{93} +(0.669136 - 3.79486i) q^{95} +(-1.28660 - 7.29669i) q^{97} +(7.82631 - 6.19589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−0.844572	−	1.51218i	−0.487614	−	0.873059i
$3$	−0.844572	−	1.51218i	−0.487614	−	0.873059i
$4$		0			0
$5$	−0.569103	+	0.207137i	−0.254511	+	0.0926344i	−0.466125	−	0.884719i	$-0.654350\pi$
$5$	−0.569103	+	0.207137i	−0.254511	+	0.0926344i	0.211614	+	0.977353i	$0.432128\pi$
$6$		0			0
$7$	2.00271	+	1.72892i	0.756953	+	0.653469i
$7$	2.00271	+	1.72892i	0.756953	+	0.653469i
$8$		0			0
$9$	−1.57340	+	2.55430i	−0.524465	+	0.851432i
$10$		0			0
$11$	−3.12667	−	1.13801i	−0.942727	−	0.343124i	−0.175485	−	0.984482i	$-0.556149\pi$
$11$	−3.12667	−	1.13801i	−0.942727	−	0.343124i	−0.767242	+	0.641358i	$0.778371\pi$
$12$		0			0
$13$	−2.37655	+	0.864994i	−0.659136	+	0.239906i	−0.649863	−	0.760051i	$-0.725174\pi$
$13$	−2.37655	+	0.864994i	−0.659136	+	0.239906i	−0.00927297	+	0.999957i	$0.502952\pi$
$14$		0			0
$15$	0.793878	+	0.685647i	0.204978	+	0.177033i
$16$		0			0
$17$	−0.831106	−	1.43952i	−0.201573	−	0.349134i	0.747463	−	0.664304i	$-0.231272\pi$
$17$	−0.831106	−	1.43952i	−0.201573	−	0.349134i	−0.949035	+	0.315170i	$0.897939\pi$
$18$		0			0
$19$	−3.18133	+	5.51023i	−0.729847	+	1.26413i	0.227100	+	0.973871i	$0.427075\pi$
$19$	−3.18133	+	5.51023i	−0.729847	+	1.26413i	−0.956948	+	0.290261i	$0.906258\pi$
$20$		0			0
$21$	0.923004	−	4.48866i	0.201416	−	0.979506i
$22$		0			0
$23$	−0.329380	+	1.86800i	−0.0686804	+	0.389506i	0.931019	+	0.364972i	$0.118921\pi$
$23$	−0.329380	+	1.86800i	−0.0686804	+	0.389506i	−0.999699	+	0.0245342i	$0.992190\pi$
$24$		0			0
$25$	−3.54925	+	2.97817i	−0.709850	+	0.595635i
$26$		0			0
$27$	5.19141	+	0.221975i	0.999087	+	0.0427190i
$28$		0			0
$29$	−5.30432	−	1.93061i	−0.984987	−	0.358506i	−0.201210	−	0.979548i	$-0.564487\pi$
$29$	−5.30432	−	1.93061i	−0.984987	−	0.358506i	−0.783777	+	0.621042i	$0.786710\pi$
$30$		0			0
$31$	3.04436	−	1.10806i	0.546783	−	0.199013i	−0.0538338	−	0.998550i	$-0.517144\pi$
$31$	3.04436	−	1.10806i	0.546783	−	0.199013i	0.600616	+	0.799537i	$0.294922\pi$
$32$		0			0
$33$	0.919812	+	5.68923i	0.160119	+	0.990368i
$34$		0			0
$35$	−1.49787	−	0.569097i	−0.253186	−	0.0961950i
$36$		0			0
$37$	−4.15961			−0.683836			−0.341918	−	0.939730i	$-0.611076\pi$
$37$	−4.15961			−0.683836			−0.341918	+	0.939730i	$0.611076\pi$
$38$		0			0
$39$	3.31520	+	2.86323i	0.530856	+	0.458484i
$40$		0			0
$41$	5.16301	−	1.87918i	0.806326	−	0.293479i	0.0942209	−	0.995551i	$-0.469964\pi$
$41$	5.16301	−	1.87918i	0.806326	−	0.293479i	0.712105	+	0.702073i	$0.247742\pi$
$42$		0			0
$43$	1.48333	+	8.41241i	0.226206	+	1.28288i	0.860365	+	0.509678i	$0.170235\pi$
$43$	1.48333	+	8.41241i	0.226206	+	1.28288i	−0.634159	+	0.773203i	$0.718654\pi$
$44$		0			0
$45$	0.366336	−	1.77957i	0.0546102	−	0.265282i
$46$		0			0
$47$	2.63058	+	0.957453i	0.383710	+	0.139659i	0.526671	−	0.850069i	$-0.323440\pi$
$47$	2.63058	+	0.957453i	0.383710	+	0.139659i	−0.142961	+	0.989728i	$0.545662\pi$
$48$		0			0
$49$	1.02170	+	6.92504i	0.145957	+	0.989291i
$50$		0			0
$51$	−1.47489	+	2.47256i	−0.206525	+	0.346228i
$52$		0			0
$53$	−4.36492	+	7.56027i	−0.599568	+	1.03848i	0.393316	+	0.919403i	$0.371328\pi$
$53$	−4.36492	+	7.56027i	−0.599568	+	1.03848i	−0.992885	+	0.119080i	$0.962006\pi$
$54$		0			0
$55$	2.01512			0.271719
$56$		0			0
$57$	11.0193	+	0.156970i	1.45955	+	0.0207912i
$58$		0			0
$59$	5.41321	+	4.54223i	0.704740	+	0.591347i	0.923118	−	0.384517i	$-0.125632\pi$
$59$	5.41321	+	4.54223i	0.704740	+	0.591347i	−0.218378	+	0.975864i	$0.570076\pi$
$60$		0			0
$61$	−5.86567	−	2.13493i	−0.751022	−	0.273350i	−0.0619865	−	0.998077i	$-0.519744\pi$
$61$	−5.86567	−	2.13493i	−0.751022	−	0.273350i	−0.689036	+	0.724727i	$0.741966\pi$
$62$		0			0
$63$	−7.56722	+	2.39525i	−0.953380	+	0.301773i
$64$		0			0
$65$	1.17333	−	0.984542i	0.145534	−	0.122117i
$66$		0			0
$67$	−0.437715	+	2.48240i	−0.0534754	+	0.303274i	−0.999801	−	0.0199404i	$-0.993652\pi$
$67$	−0.437715	+	2.48240i	−0.0534754	+	0.303274i	0.946326	+	0.323214i	$0.104763\pi$
$68$		0			0
$69$	3.10295	−	1.07958i	0.373551	−	0.129966i
$70$		0			0
$71$	−5.23329	+	9.06432i	−0.621077	+	1.07574i	0.368209	+	0.929743i	$0.379971\pi$
$71$	−5.23329	+	9.06432i	−0.621077	+	1.07574i	−0.989286	+	0.145994i	$0.953362\pi$
$72$		0			0
$73$	5.79537			0.678297			0.339149	−	0.940733i	$-0.389861\pi$
$73$	5.79537			0.678297			0.339149	+	0.940733i	$0.389861\pi$
$74$		0			0
$75$	7.50114	+	2.85183i	0.866157	+	0.329301i
$76$		0			0
$77$	−4.29428	−	7.68486i	−0.489379	−	0.875772i
$78$		0			0
$79$	0.191208	+	1.08440i	0.0215126	+	0.122004i	0.993673	−	0.112313i	$-0.0358258\pi$
$79$	0.191208	+	1.08440i	0.0215126	+	0.122004i	−0.972160	+	0.234317i	$0.924715\pi$
$80$		0			0
$81$	−4.04885	−	8.03783i	−0.449873	−	0.893093i
$82$		0			0
$83$	−8.09245	−	2.94541i	−0.888261	−	0.323301i	−0.142722	−	0.989763i	$-0.545586\pi$
$83$	−8.09245	−	2.94541i	−0.888261	−	0.323301i	−0.745539	+	0.666462i	$0.767808\pi$
$84$		0			0
$85$	0.771162	+	0.647082i	0.0836443	+	0.0701859i
$86$		0			0
$87$	1.56044	+	9.65164i	0.167297	+	1.03476i
$88$		0			0
$89$	4.25989	−	7.37835i	0.451548	−	0.782104i	−0.546935	−	0.837175i	$-0.684205\pi$
$89$	4.25989	−	7.37835i	0.451548	−	0.782104i	0.998482	+	0.0550717i	$0.0175387\pi$
$90$		0			0
$91$	−6.25504	−	2.37652i	−0.655707	−	0.249128i
$92$		0			0
$93$	−4.24676	−	3.66779i	−0.440369	−	0.380332i
$94$		0			0
$95$	0.669136	−	3.79486i	0.0686519	−	0.389344i
$96$		0			0
$97$	−1.28660	−	7.29669i	−0.130635	−	0.740866i	−0.977801	−	0.209538i	$-0.932804\pi$
$97$	−1.28660	−	7.29669i	−0.130635	−	0.740866i	0.847166	−	0.531329i	$-0.178307\pi$
$98$		0			0
$99$	7.82631	−	6.19589i	0.786574	−	0.622711i
$100$		0			0
$101$	−2.07363	−	11.7601i	−0.206334	−	1.17018i	−0.895327	−	0.445408i	$-0.853058\pi$
$101$	−2.07363	−	11.7601i	−0.206334	−	1.17018i	0.688994	−	0.724767i	$-0.258053\pi$
$102$		0			0
$103$	−3.81818	+	1.38970i	−0.376216	+	0.136932i	−0.523206	−	0.852207i	$-0.675264\pi$
$103$	−3.81818	+	1.38970i	−0.376216	+	0.136932i	0.146989	+	0.989138i	$0.453042\pi$
$104$		0			0
$105$	0.404481	+	2.74570i	0.0394733	+	0.267953i
$106$		0			0
$107$	−3.38001	−	5.85434i	−0.326758	−	0.565961i	0.655109	−	0.755534i	$-0.272623\pi$
$107$	−3.38001	−	5.85434i	−0.326758	−	0.565961i	−0.981866	+	0.189574i	$0.939289\pi$
$108$		0			0
$109$	0.279268	−	0.483706i	0.0267490	−	0.0463306i	−0.852341	−	0.522986i	$-0.824818\pi$
$109$	0.279268	−	0.483706i	0.0267490	−	0.0463306i	0.879090	+	0.476656i	$0.158151\pi$
$110$		0			0
$111$	3.51309	+	6.29009i	0.333448	+	0.597029i
$112$		0			0
$113$	2.84714	−	16.1469i	0.267836	−	1.51897i	−0.493000	−	0.870030i	$-0.664100\pi$
$113$	2.84714	−	16.1469i	0.267836	−	1.51897i	0.760836	−	0.648945i	$-0.224789\pi$
$114$		0			0
$115$	−0.199481	−	1.13131i	−0.0186017	−	0.105496i
$116$		0			0
$117$	1.52980	−	7.43139i	0.141430	−	0.687032i
$118$		0			0
$119$	0.824341	−	4.31985i	0.0755673	−	0.396000i
$120$		0			0
$121$	0.0544992	+	0.0457302i	0.00495447	+	0.00415729i
$122$		0			0
$123$	−7.20220	−	6.22031i	−0.649400	−	0.560866i
$124$		0			0
$125$	2.91707	−	5.05251i	0.260911	−	0.451910i
$126$		0			0
$127$	3.34719	+	5.79750i	0.297015	+	0.514445i	0.975452	−	0.220214i	$-0.0706755\pi$
$127$	3.34719	+	5.79750i	0.297015	+	0.514445i	−0.678437	+	0.734659i	$0.737342\pi$
$128$		0			0
$129$	11.4683	−	9.34796i	1.00973	−	0.823042i
$130$		0			0
$131$	0.263929	−	1.49682i	0.0230596	−	0.130778i	−0.971105	−	0.238654i	$-0.923294\pi$
$131$	0.263929	−	1.49682i	0.0230596	−	0.130778i	0.994164	+	0.107876i	$0.0344050\pi$
$132$		0			0
$133$	−15.8980	+	5.53513i	−1.37853	+	0.479957i
$134$		0			0
$135$	−3.00043	+	0.949005i	−0.258236	+	0.0816773i
$136$		0			0
$137$	−17.6779	+	14.8335i	−1.51032	+	1.26731i	−0.647197	+	0.762323i	$0.724059\pi$
$137$	−17.6779	+	14.8335i	−1.51032	+	1.26731i	−0.863126	+	0.504988i	$0.831497\pi$
$138$		0			0
$139$	8.32286	+	6.98371i	0.705936	+	0.592351i	0.923456	−	0.383705i	$-0.125352\pi$
$139$	8.32286	+	6.98371i	0.705936	+	0.592351i	−0.217519	+	0.976056i	$0.569797\pi$
$140$		0			0
$141$	−0.773871	−	4.78656i	−0.0651717	−	0.403101i
$142$		0			0
$143$	8.41506			0.703703
$144$		0			0
$145$	3.41861			0.283900
$146$		0			0
$147$	9.60903	−	7.39369i	0.792539	−	0.609821i
$148$		0			0
$149$	−16.8529	−	14.1412i	−1.38064	−	1.15850i	−0.968975	−	0.247160i	$-0.920503\pi$
$149$	−16.8529	−	14.1412i	−1.38064	−	1.15850i	−0.411666	−	0.911335i	$-0.635053\pi$
$150$		0			0
$151$	5.33046	+	1.94013i	0.433787	+	0.157885i	0.549678	−	0.835376i	$-0.314750\pi$
$151$	5.33046	+	1.94013i	0.433787	+	0.157885i	−0.115892	+	0.993262i	$0.536973\pi$
$152$		0			0
$153$	4.98461	+	0.142040i	0.402982	+	0.0114833i
$154$		0			0
$155$	−1.50303	+	1.26120i	−0.120727	+	0.101302i
$156$		0			0
$157$	18.0772	+	15.1686i	1.44272	+	1.21058i	0.937687	+	0.347481i	$0.112963\pi$
$157$	18.0772	+	15.1686i	1.44272	+	1.21058i	0.505030	+	0.863102i	$0.331482\pi$
$158$		0			0
$159$	15.1190	+	0.215370i	1.19902	+	0.0170799i
$160$		0			0
$161$	−3.88928	+	3.17160i	−0.306518	+	0.249957i
$162$		0			0
$163$	−12.3450	−	21.3822i	−0.966935	−	1.67478i	−0.704324	−	0.709878i	$-0.748750\pi$
$163$	−12.3450	−	21.3822i	−0.966935	−	1.67478i	−0.262610	−	0.964902i	$-0.584583\pi$
$164$		0			0
$165$	−1.70192	−	3.04724i	−0.132494	−	0.237227i
$166$		0			0
$167$	0.732072	−	4.15179i	0.0566495	−	0.321275i	−0.943293	−	0.331960i	$-0.892290\pi$
$167$	0.732072	−	4.15179i	0.0566495	−	0.321275i	0.999943	+	0.0106850i	$0.00340121\pi$
$168$		0			0
$169$	−5.05880	+	4.24484i	−0.389138	+	0.326526i
$170$		0			0
$171$	−9.06926	−	16.7958i	−0.693543	−	1.28441i
$172$		0			0
$173$	−6.91816	+	5.80502i	−0.525978	+	0.441348i	−0.866710	−	0.498813i	$-0.833770\pi$
$173$	−6.91816	+	5.80502i	−0.525978	+	0.441348i	0.340732	+	0.940160i	$0.389325\pi$
$174$		0			0
$175$	−12.2571	−	0.171936i	−0.926552	−	0.0129971i
$176$		0			0
$177$	2.29683	−	12.0220i	0.172640	−	0.903629i
$178$		0			0
$179$	11.9694	+	20.7317i	0.894638	+	1.54956i	0.834252	+	0.551383i	$0.185900\pi$
$179$	11.9694	+	20.7317i	0.894638	+	1.54956i	0.0603851	+	0.998175i	$0.480767\pi$
$180$		0			0
$181$	−3.43317	−	5.94643i	−0.255186	−	0.441995i	0.709760	−	0.704443i	$-0.248803\pi$
$181$	−3.43317	−	5.94643i	−0.255186	−	0.441995i	−0.964946	+	0.262449i	$0.915470\pi$
$182$		0			0
$183$	1.72558	+	10.6731i	0.127558	+	0.788976i
$184$		0			0
$185$	2.36725	−	0.861608i	0.174044	−	0.0633467i
$186$		0			0
$187$	0.960402	+	5.44671i	0.0702315	+	0.398303i
$188$		0			0
$189$	10.0131	+	9.42006i	0.728347	+	0.685209i
$190$		0			0
$191$	−0.0939779	−	0.532975i	−0.00680000	−	0.0385647i	0.981219	−	0.192897i	$-0.0617884\pi$
$191$	−0.0939779	−	0.532975i	−0.00680000	−	0.0385647i	−0.988019	+	0.154333i	$0.950677\pi$
$192$		0			0
$193$	15.7836	−	5.74478i	1.13613	−	0.413518i	0.295617	−	0.955307i	$-0.404475\pi$
$193$	15.7836	−	5.74478i	1.13613	−	0.413518i	0.840515	+	0.541789i	$0.182253\pi$
$194$		0			0
$195$	−2.47977	−	0.942775i	−0.177580	−	0.0675135i
$196$		0			0
$197$	−10.7176	−	18.5635i	−0.763599	−	1.32259i	−0.940984	−	0.338451i	$-0.890097\pi$
$197$	−10.7176	−	18.5635i	−0.763599	−	1.32259i	0.177384	−	0.984142i	$-0.443236\pi$
$198$		0			0
$199$	−5.19594	−	8.99964i	−0.368331	−	0.637968i	0.620974	−	0.783831i	$-0.286737\pi$
$199$	−5.19594	−	8.99964i	−0.368331	−	0.637968i	−0.989305	+	0.145864i	$0.953404\pi$
$200$		0			0
$201$	4.12353	−	1.43466i	0.290852	−	0.101193i
$202$		0			0
$203$	−7.28514	−	13.0372i	−0.511317	−	0.915031i
$204$		0			0
$205$	−2.54904	+	2.13890i	−0.178033	+	0.149387i
$206$		0			0
$207$	−4.25319	−	3.78044i	−0.295617	−	0.262759i
$208$		0			0
$209$	16.2177	−	13.6083i	1.12180	−	0.941303i
$210$		0			0
$211$	−0.876973	+	4.97356i	−0.0603733	+	0.342394i	0.939627	+	0.342201i	$0.111172\pi$
$211$	−0.876973	+	4.97356i	−0.0603733	+	0.342394i	−1.00000		0.000192737i	$0.999939\pi$
$212$		0			0
$213$	18.1268	+	0.258216i	1.24203	+	0.0176927i
$214$		0			0
$215$	−2.58669	−	4.48028i	−0.176411	−	0.305552i
$216$		0			0
$217$	8.01270	+	3.04432i	0.543937	+	0.206662i
$218$		0			0
$219$	−4.89461	−	8.76367i	−0.330747	−	0.592194i
$220$		0			0
$221$	3.22034	+	2.70219i	0.216623	+	0.181769i
$222$		0			0
$223$	−3.73384	+	3.13306i	−0.250036	+	0.209805i	−0.759188	−	0.650871i	$-0.774404\pi$
$223$	−3.73384	+	3.13306i	−0.250036	+	0.209805i	0.509152	+	0.860677i	$0.329959\pi$
$224$		0			0
$225$	−2.02276	−	13.7517i	−0.134851	−	0.916778i
$226$		0			0
$227$	−11.4828	−	4.17939i	−0.762138	−	0.277396i	−0.0684341	−	0.997656i	$-0.521800\pi$
$227$	−11.4828	−	4.17939i	−0.762138	−	0.277396i	−0.693704	+	0.720260i	$0.744023\pi$
$228$		0			0
$229$	18.0446	+	15.1412i	1.19242	+	1.00056i	0.999814	+	0.0192819i	$0.00613800\pi$
$229$	18.0446	+	15.1412i	1.19242	+	1.00056i	0.192605	+	0.981276i	$0.438306\pi$
$230$		0			0
$231$	−7.99409	+	12.9842i	−0.525973	+	0.854295i
$232$		0			0
$233$	14.2724			0.935017			0.467508	−	0.883989i	$-0.345152\pi$
$233$	14.2724			0.935017			0.467508	+	0.883989i	$0.345152\pi$
$234$		0			0
$235$	−1.69540			−0.110595
$236$		0			0
$237$	1.47832	−	1.20499i	0.0960270	−	0.0782727i
$238$		0			0
$239$	16.5721	+	13.9057i	1.07196	+	0.899483i	0.995229	−	0.0975691i	$-0.0311067\pi$
$239$	16.5721	+	13.9057i	1.07196	+	0.899483i	0.0767329	+	0.997052i	$0.475551\pi$
$240$		0			0
$241$	−5.33901	+	4.47996i	−0.343916	+	0.288579i	−0.798341	−	0.602205i	$-0.794289\pi$
$241$	−5.33901	+	4.47996i	−0.343916	+	0.288579i	0.454426	+	0.890785i	$0.349844\pi$
$242$		0			0
$243$	−8.73513	+	12.9111i	−0.560359	+	0.828250i
$244$		0			0
$245$	−2.01588	−	3.72943i	−0.128790	−	0.238265i
$246$		0			0
$247$	2.79428	−	15.8472i	0.177796	−	1.00833i
$248$		0			0
$249$	2.38066	+	14.7249i	0.150868	+	0.933151i
$250$		0			0
$251$	12.1938	+	21.1202i	0.769663	+	1.33310i	0.937746	+	0.347322i	$0.112909\pi$
$251$	12.1938	+	21.1202i	0.769663	+	1.33310i	−0.168083	+	0.985773i	$0.553758\pi$
$252$		0			0
$253$	3.15568	−	5.46580i	0.198396	−	0.343632i
$254$		0			0
$255$	0.327204	−	1.71265i	0.0204903	−	0.107250i
$256$		0			0
$257$	−17.5774	−	14.7492i	−1.09645	−	0.920031i	−0.0992691	−	0.995061i	$-0.531650\pi$
$257$	−17.5774	−	14.7492i	−1.09645	−	0.920031i	−0.997181	+	0.0750295i	$0.976095\pi$
$258$		0			0
$259$	−8.33050	−	7.19162i	−0.517632	−	0.446866i
$260$		0			0
$261$	13.2772	−	10.5112i	0.821835	−	0.650626i
$262$		0			0
$263$	0.661165	+	3.74965i	0.0407692	+	0.231214i	0.998383	−	0.0568408i	$-0.0181027\pi$
$263$	0.661165	+	3.74965i	0.0407692	+	0.231214i	−0.957614	+	0.288054i	$0.906992\pi$
$264$		0			0
$265$	0.918084	−	5.20671i	0.0563974	−	0.319846i
$266$		0			0
$267$	−14.7552	−	0.210187i	−0.903004	−	0.0128633i
$268$		0			0
$269$	−9.14104	+	15.8327i	−0.557339	+	0.965339i	0.440379	+	0.897812i	$0.354844\pi$
$269$	−9.14104	+	15.8327i	−0.557339	+	0.965339i	−0.997717	+	0.0675270i	$0.978489\pi$
$270$		0			0
$271$	−1.33887	−	2.31898i	−0.0813303	−	0.140868i	0.822491	−	0.568778i	$-0.192584\pi$
$271$	−1.33887	−	2.31898i	−0.0813303	−	0.140868i	−0.903822	+	0.427909i	$0.859250\pi$
$272$		0			0
$273$	1.68910	+	11.4659i	0.102229	+	0.693949i
$274$		0			0
$275$	14.4865	−	5.27267i	0.873571	−	0.317954i
$276$		0			0
$277$	3.41770	+	19.3828i	0.205350	+	1.16460i	0.896888	+	0.442258i	$0.145822\pi$
$277$	3.41770	+	19.3828i	0.205350	+	1.16460i	−0.691538	+	0.722340i	$0.743067\pi$
$278$		0			0
$279$	−1.95968	+	9.51960i	−0.117323	+	0.569923i
$280$		0			0
$281$	1.18454	+	6.71785i	0.0706636	+	0.400753i	0.999539	+	0.0303608i	$0.00966564\pi$
$281$	1.18454	+	6.71785i	0.0706636	+	0.400753i	−0.928875	+	0.370392i	$0.879223\pi$
$282$		0			0
$283$	3.64120	−	20.6503i	0.216447	−	1.22753i	−0.661931	−	0.749565i	$-0.730263\pi$
$283$	3.64120	−	20.6503i	0.216447	−	1.22753i	0.878378	−	0.477967i	$-0.158626\pi$
$284$		0			0
$285$	−6.30365	+	2.19318i	−0.373396	+	0.129913i
$286$		0			0
$287$	13.5890	+	5.16295i	0.802131	+	0.304759i
$288$		0			0
$289$	7.11853	−	12.3296i	0.418737	−	0.725273i
$290$		0			0
$291$	−9.94730	+	8.10816i	−0.583121	+	0.475309i
$292$		0			0
$293$	25.5191	+	21.4131i	1.49084	+	1.25097i	0.893567	+	0.448930i	$0.148195\pi$
$293$	25.5191	+	21.4131i	1.49084	+	1.25097i	0.597276	+	0.802036i	$0.296250\pi$
$294$		0			0
$295$	−4.02154	−	1.46372i	−0.234143	−	0.0852211i
$296$		0			0
$297$	−15.9792	−	6.60194i	−0.927208	−	0.383084i
$298$		0			0
$299$	−0.833025	−	4.72432i	−0.0481751	−	0.273214i
$300$		0			0
$301$	−11.5737	+	19.4122i	−0.667095	+	1.11890i
$302$		0			0
$303$	−16.0321	+	13.0680i	−0.921022	+	0.750735i
$304$		0			0
$305$	3.78040			0.216465
$306$		0			0
$307$	13.4168	−	23.2387i	0.765740	−	1.32630i	−0.174115	−	0.984725i	$-0.555706\pi$
$307$	13.4168	−	23.2387i	0.765740	−	1.32630i	0.939855	−	0.341575i	$-0.110960\pi$
$308$		0			0
$309$	5.32621	+	4.60008i	0.302998	+	0.261689i
$310$		0			0
$311$	1.10522	−	6.26800i	0.0626712	−	0.355426i	−0.937305	−	0.348510i	$-0.886688\pi$
$311$	1.10522	−	6.26800i	0.0626712	−	0.355426i	0.999976	−	0.00691549i	$-0.00220129\pi$
$312$		0			0
$313$	−19.6206	+	16.4636i	−1.10902	+	0.930580i	−0.997998	−	0.0632379i	$-0.979857\pi$
$313$	−19.6206	+	16.4636i	−1.10902	+	0.930580i	−0.111023	+	0.993818i	$0.535413\pi$
$314$		0			0
$315$	3.81039	−	2.93059i	0.214691	−	0.165120i
$316$		0			0
$317$	−6.77040	−	2.46422i	−0.380263	−	0.138405i	0.144814	−	0.989459i	$-0.453742\pi$
$317$	−6.77040	−	2.46422i	−0.380263	−	0.138405i	−0.525078	+	0.851054i	$0.675964\pi$
$318$		0			0
$319$	14.3878	+	12.0728i	0.805561	+	0.675946i
$320$		0			0
$321$	−5.99818	+	10.0556i	−0.334786	+	0.561249i
$322$		0			0
$323$	10.5761			0.588469
$324$		0			0
$325$	5.85887	−	10.1479i	0.324992	−	0.562902i
$326$		0			0
$327$	−0.967314	−	0.0137794i	−0.0534926	−	0.000762000i
$328$		0			0
$329$	3.61293	+	6.46555i	0.199187	+	0.356457i
$330$		0			0
$331$	2.40036	+	0.873661i	0.131936	+	0.0480208i	0.407144	−	0.913364i	$-0.366525\pi$
$331$	2.40036	+	0.873661i	0.131936	+	0.0480208i	−0.275208	+	0.961385i	$0.588747\pi$
$332$		0			0
$333$	6.54471	−	10.6249i	0.358648	−	0.582240i
$334$		0			0
$335$	−0.265092	−	1.50341i	−0.0144835	−	0.0821402i
$336$		0			0
$337$	−10.9461	+	3.98406i	−0.596273	+	0.217026i	−0.622486	−	0.782631i	$-0.713877\pi$
$337$	−10.9461	+	3.98406i	−0.596273	+	0.217026i	0.0262133	+	0.999656i	$0.491655\pi$
$338$		0			0
$339$	−26.8217	+	9.33185i	−1.45676	+	0.506836i
$340$		0			0
$341$	−10.7797			−0.583753
$342$		0			0
$343$	−9.92665	+	15.6353i	−0.535988	+	0.844225i
$344$		0			0
$345$	−1.54228	+	1.25713i	−0.0830335	+	0.0676816i
$346$		0			0
$347$	−6.33016	+	2.30399i	−0.339821	+	0.123685i	−0.506293	−	0.862361i	$-0.668985\pi$
$347$	−6.33016	+	2.30399i	−0.339821	+	0.123685i	0.166472	+	0.986046i	$0.446762\pi$
$348$		0			0
$349$	−0.796250	−	0.289811i	−0.0426223	−	0.0155132i	0.320621	−	0.947208i	$-0.396108\pi$
$349$	−0.796250	−	0.289811i	−0.0426223	−	0.0155132i	−0.363243	+	0.931694i	$0.618331\pi$
$350$		0			0
$351$	−12.5297	+	3.96300i	−0.668783	+	0.211529i
$352$		0			0
$353$	−15.1039	+	12.6737i	−0.803899	+	0.674551i	−0.949143	−	0.314845i	$-0.898048\pi$
$353$	−15.1039	+	12.6737i	−0.803899	+	0.674551i	0.145245	+	0.989396i	$0.453603\pi$
$354$		0			0
$355$	1.10073	−	6.24254i	0.0584206	−	0.331320i
$356$		0			0
$357$	−7.22862	+	2.40187i	−0.382579	+	0.127120i
$358$		0			0
$359$	−4.46009	+	7.72511i	−0.235395	+	0.407716i	−0.959387	−	0.282092i	$-0.908972\pi$
$359$	−4.46009	+	7.72511i	−0.235395	+	0.407716i	0.723993	+	0.689808i	$0.242305\pi$
$360$		0			0
$361$	−10.7417	−	18.6052i	−0.565354	−	0.979222i
$362$		0			0
$363$	0.0231240	−	0.121035i	0.00121369	−	0.00635270i
$364$		0			0
$365$	−3.29817	+	1.20043i	−0.172634	+	0.0628336i
$366$		0			0
$367$	−23.6782	−	8.61817i	−1.23599	−	0.449865i	−0.360347	−	0.932818i	$-0.617342\pi$
$367$	−23.6782	−	8.61817i	−1.23599	−	0.449865i	−0.875646	+	0.482954i	$0.839564\pi$
$368$		0			0
$369$	−3.32347	+	16.1445i	−0.173013	+	0.840451i
$370$		0			0
$371$	−21.8128	+	7.59444i	−1.13246	+	0.394284i
$372$		0			0
$373$	4.45457	−	1.62133i	0.230649	−	0.0839494i	−0.224110	−	0.974564i	$-0.571948\pi$
$373$	4.45457	−	1.62133i	0.230649	−	0.0839494i	0.454759	+	0.890614i	$0.349725\pi$
$374$		0			0
$375$	−10.1040	−	0.143931i	−0.521768	−	0.00743257i
$376$		0			0
$377$	14.2759			0.735249
$378$		0			0
$379$	35.1210			1.80405			0.902023	−	0.431688i	$-0.142082\pi$
$379$	35.1210			1.80405			0.902023	+	0.431688i	$0.142082\pi$
$380$		0			0
$381$	5.93994	−	9.95797i	0.304312	−	0.510162i
$382$		0			0
$383$	16.4206	−	5.97661i	0.839053	−	0.305390i	0.113484	−	0.993540i	$-0.463799\pi$
$383$	16.4206	−	5.97661i	0.839053	−	0.305390i	0.725569	+	0.688149i	$0.241577\pi$
$384$		0			0
$385$	4.03571	+	3.48398i	0.205679	+	0.177560i
$386$		0			0
$387$	−23.8217	−	9.44717i	−1.21092	−	0.480227i
$388$		0			0
$389$	−34.2545	−	12.4676i	−1.73677	−	0.632134i	−0.737699	−	0.675130i	$-0.764088\pi$
$389$	−34.2545	−	12.4676i	−1.73677	−	0.632134i	−0.999075	+	0.0429958i	$0.986310\pi$
$390$		0			0
$391$	2.96278	−	1.07836i	0.149834	−	0.0545351i
$392$		0			0
$393$	−2.48637	+	0.865061i	−0.125421	+	0.0436366i
$394$		0			0
$395$	−0.333436	−	0.577527i	−0.0167770	−	0.0290586i
$396$		0			0
$397$	3.83070	−	6.63496i	0.192257	−	0.332999i	−0.753741	−	0.657172i	$-0.771753\pi$
$397$	3.83070	−	6.63496i	0.192257	−	0.332999i	0.945998	+	0.324173i	$0.105086\pi$
$398$		0			0
$399$	21.7971	+	19.3659i	1.09122	+	0.969506i
$400$		0			0
$401$	−4.55788	+	25.8490i	−0.227610	+	1.29084i	0.630023	+	0.776576i	$0.283045\pi$
$401$	−4.55788	+	25.8490i	−0.227610	+	1.29084i	−0.857633	+	0.514262i	$0.828066\pi$
$402$		0			0
$403$	−6.27661	+	5.26670i	−0.312660	+	0.262353i
$404$		0			0
$405$	3.96915	+	3.73569i	0.197229	+	0.185628i
$406$		0			0
$407$	13.0057	+	4.73370i	0.644670	+	0.234641i
$408$		0			0
$409$	−0.533774	+	0.194278i	−0.0263934	+	0.00960642i	−0.355183	−	0.934797i	$-0.615581\pi$
$409$	−0.533774	+	0.194278i	−0.0263934	+	0.00960642i	0.328790	+	0.944403i	$0.393359\pi$
$410$		0			0
$411$	37.3612	+	14.2042i	1.84289	+	0.700643i
$412$		0			0
$413$	2.98797	+	18.4558i	0.147028	+	0.908148i
$414$		0			0
$415$	5.21554			0.256021
$416$		0			0
$417$	3.53139	−	18.4839i	0.172933	−	0.905163i
$418$		0			0
$419$	34.6971	−	12.6287i	1.69506	−	0.616952i	0.699815	−	0.714325i	$-0.253266\pi$
$419$	34.6971	−	12.6287i	1.69506	−	0.616952i	0.995248	+	0.0973722i	$0.0310437\pi$
$420$		0			0
$421$	−3.41620	−	19.3742i	−0.166495	−	0.944241i	−0.947509	−	0.319728i	$-0.896408\pi$
$421$	−3.41620	−	19.3742i	−0.166495	−	0.944241i	0.781014	−	0.624513i	$-0.214703\pi$
$422$		0			0
$423$	−6.58456	+	5.21283i	−0.320152	+	0.253456i
$424$		0			0
$425$	7.23694	+	2.63403i	0.351043	+	0.127769i
$426$		0			0
$427$	−8.05613	−	14.4169i	−0.389863	−	0.697683i
$428$		0			0
$429$	−7.10713	−	12.7251i	−0.343135	−	0.614374i
$430$		0			0
$431$	−12.6134	+	21.8471i	−0.607568	+	1.05234i	0.384072	+	0.923303i	$0.374521\pi$
$431$	−12.6134	+	21.8471i	−0.607568	+	1.05234i	−0.991640	+	0.129035i	$0.958812\pi$
$432$		0			0
$433$	−8.98965			−0.432015			−0.216008	−	0.976392i	$-0.569304\pi$
$433$	−8.98965			−0.432015			−0.216008	+	0.976392i	$0.569304\pi$
$434$		0			0
$435$	−2.88726	−	5.16956i	−0.138434	−	0.247861i
$436$		0			0
$437$	−9.24526	−	7.75770i	−0.442261	−	0.371101i
$438$		0			0
$439$	20.8090	+	7.57385i	0.993158	+	0.361480i	0.786942	−	0.617026i	$-0.211663\pi$
$439$	20.8090	+	7.57385i	0.993158	+	0.361480i	0.206216	+	0.978507i	$0.433885\pi$
$440$		0			0
$441$	−19.2961	−	8.28610i	−0.918863	−	0.394576i
$442$		0			0
$443$	9.23911	−	7.75253i	0.438963	−	0.368334i	−0.396358	−	0.918096i	$-0.629726\pi$
$443$	9.23911	−	7.75253i	0.438963	−	0.368334i	0.835321	+	0.549762i	$0.185282\pi$
$444$		0			0
$445$	−0.895992	+	5.08142i	−0.0424741	+	0.240883i
$446$		0			0
$447$	−7.15067	+	37.4279i	−0.338215	+	1.77028i
$448$		0			0
$449$	−4.95505	+	8.58241i	−0.233843	+	0.405029i	−0.958936	−	0.283623i	$-0.908464\pi$
$449$	−4.95505	+	8.58241i	−0.233843	+	0.405029i	0.725092	+	0.688652i	$0.241797\pi$
$450$		0			0
$451$	−18.2816			−0.860845
$452$		0			0
$453$	−1.56813	−	9.69921i	−0.0736771	−	0.455709i
$454$		0			0
$455$	4.05203	+	0.0568395i	0.189962	+	0.00266468i
$456$		0			0
$457$	−1.23775	−	7.01964i	−0.0578996	−	0.328365i	0.942076	−	0.335400i	$-0.108872\pi$
$457$	−1.23775	−	7.01964i	−0.0578996	−	0.328365i	−0.999975	+	0.00703561i	$0.997760\pi$
$458$		0			0
$459$	−3.99508	−	7.65761i	−0.186474	−	0.357427i
$460$		0			0
$461$	27.0552	+	9.84728i	1.26009	+	0.458634i	0.883798	−	0.467869i	$-0.154978\pi$
$461$	27.0552	+	9.84728i	1.26009	+	0.458634i	0.376288	+	0.926503i	$0.377200\pi$
$462$		0			0
$463$	−3.45229	−	2.89682i	−0.160442	−	0.134627i	0.559032	−	0.829146i	$-0.311173\pi$
$463$	−3.45229	−	2.89682i	−0.160442	−	0.134627i	−0.719474	+	0.694519i	$0.755617\pi$
$464$		0			0
$465$	3.17658	+	1.20769i	0.147310	+	0.0560054i
$466$		0			0
$467$	−10.2778	+	17.8016i	−0.475598	+	0.823759i	−0.999609	−	0.0279517i	$-0.991102\pi$
$467$	−10.2778	+	17.8016i	−0.475598	+	0.823759i	0.524012	+	0.851711i	$0.324435\pi$
$468$		0			0
$469$	−5.16849	+	4.21476i	−0.238658	+	0.194620i
$470$		0			0
$471$	7.67015	−	40.1470i	0.353422	−	1.84987i
$472$		0			0
$473$	4.93555	−	27.9909i	0.226937	−	1.28702i
$474$		0			0
$475$	−5.11907	−	29.0317i	−0.234879	−	1.33207i
$476$		0			0
$477$	−12.4434	−	23.0446i	−0.569745	−	1.05514i
$478$		0			0
$479$	2.53961	+	14.4029i	0.116038	+	0.658083i	0.986231	+	0.165373i	$0.0528827\pi$
$479$	2.53961	+	14.4029i	0.116038	+	0.658083i	−0.870193	+	0.492710i	$0.836006\pi$
$480$		0			0
$481$	9.88553	−	3.59804i	0.450741	−	0.164056i
$482$		0			0
$483$	8.08082	+	3.20265i	0.367690	+	0.145726i
$484$		0			0
$485$	2.24362	+	3.88607i	0.101878	+	0.176457i
$486$		0			0
$487$	−3.28695	+	5.69316i	−0.148946	+	0.257982i	−0.930838	−	0.365432i	$-0.880921\pi$
$487$	−3.28695	+	5.69316i	−0.148946	+	0.257982i	0.781892	+	0.623413i	$0.214255\pi$
$488$		0			0
$489$	−21.9075	+	36.7267i	−0.990691	+	1.66084i
$490$		0			0
$491$	−2.77355	+	15.7296i	−0.125168	+	0.709865i	0.856039	+	0.516911i	$0.172918\pi$
$491$	−2.77355	+	15.7296i	−0.125168	+	0.709865i	−0.981208	+	0.192954i	$0.938193\pi$
$492$		0			0
$493$	1.62930	+	9.24021i	0.0733799	+	0.416158i
$494$		0			0
$495$	−3.17059	+	5.14722i	−0.142507	+	0.231350i
$496$		0			0
$497$	−26.1522	+	9.10529i	−1.17309	+	0.408428i
$498$		0			0
$499$	1.63596	+	1.37274i	0.0732358	+	0.0614521i	0.678671	−	0.734443i	$-0.262556\pi$
$499$	1.63596	+	1.37274i	0.0732358	+	0.0614521i	−0.605435	+	0.795895i	$0.707001\pi$
$500$		0			0
$501$	−6.89655	+	2.39946i	−0.308115	+	0.107200i
$502$		0			0
$503$	−9.60345	+	16.6337i	−0.428197	+	0.741659i	−0.996713	−	0.0810135i	$-0.974184\pi$
$503$	−9.60345	+	16.6337i	−0.428197	+	0.741659i	0.568516	+	0.822672i	$0.307518\pi$
$504$		0			0
$505$	3.61606	+	6.26320i	0.160913	+	0.278709i
$506$		0			0
$507$	10.6915	+	4.06476i	0.474826	+	0.180522i
$508$		0			0
$509$	−6.05397	+	34.3337i	−0.268337	+	1.52182i	0.491023	+	0.871146i	$0.336623\pi$
$509$	−6.05397	+	34.3337i	−0.268337	+	1.52182i	−0.759361	+	0.650670i	$0.774488\pi$
$510$		0			0
$511$	11.6065	+	10.0197i	0.513439	+	0.443246i
$512$		0			0
$513$	−17.7387	+	27.8997i	−0.783183	+	1.23180i
$514$		0			0
$515$	1.88508	−	1.58177i	0.0830666	−	0.0697011i
$516$		0			0
$517$	−7.13536	−	5.98728i	−0.313813	−	0.263320i
$518$		0			0
$519$	14.6211	+	5.55876i	0.641797	+	0.244002i
$520$		0			0
$521$	39.3686			1.72477			0.862386	−	0.506251i	$-0.168969\pi$
$521$	39.3686			1.72477			0.862386	+	0.506251i	$0.168969\pi$
$522$		0			0
$523$	−28.3648			−1.24031			−0.620154	−	0.784480i	$-0.712930\pi$
$523$	−28.3648			−1.24031			−0.620154	+	0.784480i	$0.712930\pi$
$524$		0			0
$525$	10.0920	+	18.6802i	0.440452	+	0.815272i
$526$		0			0
$527$	−4.12525	−	3.46149i	−0.179699	−	0.150785i
$528$		0			0
$529$	18.2320	+	6.63590i	0.792695	+	0.288517i
$530$		0			0
$531$	−20.1193	+	6.68023i	−0.873104	+	0.289897i
$532$		0			0
$533$	−10.6447	+	8.93194i	−0.461072	+	0.386885i
$534$		0			0
$535$	3.13622	+	2.63160i	0.135591	+	0.113774i
$536$		0			0
$537$	21.2410	−	35.6094i	0.916618	−	1.53666i
$538$		0			0
$539$	4.68629	−	22.8150i	0.201853	−	0.982712i
$540$		0			0
$541$	7.84798	+	13.5931i	0.337411	+	0.584413i	0.983945	−	0.178472i	$-0.0571154\pi$
$541$	7.84798	+	13.5931i	0.337411	+	0.584413i	−0.646534	+	0.762885i	$0.723782\pi$
$542$		0			0
$543$	−6.09253	+	10.2138i	−0.261456	+	0.438315i
$544$		0			0
$545$	−0.0587390	+	0.333125i	−0.00251610	+	0.0142695i
$546$		0			0
$547$	22.0320	−	18.4871i	0.942021	−	0.790449i	−0.0359149	−	0.999355i	$-0.511435\pi$
$547$	22.0320	−	18.4871i	0.942021	−	0.790449i	0.977936	+	0.208905i	$0.0669901\pi$
$548$		0			0
$549$	14.6823	−	11.6236i	0.626624	−	0.496082i
$550$		0			0
$551$	27.5129	−	23.0861i	1.17209	−	0.983500i
$552$		0			0
$553$	−1.49190	+	2.50232i	−0.0634419	+	0.106409i
$554$		0			0
$555$	−3.30222	−	2.85202i	−0.140172	−	0.121062i
$556$		0			0
$557$	11.9028	+	20.6162i	0.504336	+	0.873536i	0.999987	+	0.00501448i	$0.00159616\pi$
$557$	11.9028	+	20.6162i	0.504336	+	0.873536i	−0.495651	+	0.868522i	$0.665071\pi$
$558$		0			0
$559$	−10.8019	−	18.7094i	−0.456872	−	0.791325i
$560$		0			0
$561$	7.42529	−	6.05244i	0.313496	−	0.255534i
$562$		0			0
$563$	−3.46371	+	1.26069i	−0.145978	+	0.0531316i	−0.413976	−	0.910288i	$-0.635860\pi$
$563$	−3.46371	+	1.26069i	−0.145978	+	0.0531316i	0.267998	+	0.963419i	$0.413638\pi$
$564$		0			0
$565$	1.72430	+	9.77901i	0.0725420	+	0.411406i
$566$		0			0
$567$	5.78806	−	23.0976i	0.243076	−	0.970007i
$568$		0			0
$569$	5.35209	+	30.3532i	0.224371	+	1.27247i	0.863883	+	0.503692i	$0.168025\pi$
$569$	5.35209	+	30.3532i	0.224371	+	1.27247i	−0.639512	+	0.768781i	$0.720864\pi$
$570$		0			0
$571$	41.2887	−	15.0279i	1.72788	−	0.628896i	0.729403	−	0.684084i	$-0.239798\pi$
$571$	41.2887	−	15.0279i	1.72788	−	0.628896i	0.998476	+	0.0551879i	$0.0175758\pi$
$572$		0			0
$573$	−0.726585	+	0.592248i	−0.0303535	+	0.0247415i
$574$		0			0
$575$	−4.39419	−	7.61096i	−0.183251	−	0.317399i
$576$		0			0
$577$	8.23897	+	14.2703i	0.342993	+	0.594081i	0.984987	−	0.172629i	$-0.0552261\pi$
$577$	8.23897	+	14.2703i	0.342993	+	0.594081i	−0.641994	+	0.766709i	$0.721893\pi$
$578$		0			0
$579$	−22.0176	−	19.0159i	−0.915019	−	0.790273i
$580$		0			0
$581$	−11.1145	−	19.8900i	−0.461106	−	0.825175i
$582$		0			0
$583$	22.2514	−	18.6711i	0.921558	−	0.773279i
$584$		0			0
$585$	0.668697	+	4.54611i	0.0276472	+	0.187958i
$586$		0			0
$587$	15.5810	−	13.0740i	0.643098	−	0.539623i	−0.261870	−	0.965103i	$-0.584339\pi$
$587$	15.5810	−	13.0740i	0.643098	−	0.539623i	0.904968	+	0.425480i	$0.139895\pi$
$588$		0			0
$589$	−3.57947	+	20.3002i	−0.147489	+	0.836454i
$590$		0			0
$591$	−19.0196	+	31.8852i	−0.782360	+	1.31158i
$592$		0			0
$593$	−9.45247	−	16.3722i	−0.388166	−	0.672324i	0.604037	−	0.796957i	$-0.293558\pi$
$593$	−9.45247	−	16.3722i	−0.388166	−	0.672324i	−0.992203	+	0.124633i	$0.960225\pi$
$594$		0			0
$595$	0.425664	+	2.62919i	0.0174505	+	0.107786i
$596$		0			0
$597$	−9.22075	+	15.4581i	−0.377380	+	0.632656i
$598$		0			0
$599$	32.2953	+	27.0990i	1.31955	+	1.10724i	0.986400	+	0.164362i	$0.0525564\pi$
$599$	32.2953	+	27.0990i	1.31955	+	1.10724i	0.333151	+	0.942873i	$0.391888\pi$
$600$		0			0
$601$	5.45945	−	4.58102i	0.222696	−	0.186864i	−0.524613	−	0.851341i	$-0.675790\pi$
$601$	5.45945	−	4.58102i	0.222696	−	0.186864i	0.747309	+	0.664477i	$0.231346\pi$
$602$		0			0
$603$	−5.65210	−	5.02386i	−0.230171	−	0.204587i
$604$		0			0
$605$	−0.0404881	−	0.0147365i	−0.00164607	−	0.000599122i
$606$		0			0
$607$	7.54820	+	6.33370i	0.306372	+	0.257077i	0.782991	−	0.622033i	$-0.213693\pi$
$607$	7.54820	+	6.33370i	0.306372	+	0.257077i	−0.476618	+	0.879110i	$0.658138\pi$
$608$		0			0
$609$	−13.5618	+	22.0273i	−0.549551	+	0.892592i
$610$		0			0
$611$	−7.07990			−0.286422
$612$		0			0
$613$	3.62780			0.146525			0.0732627	−	0.997313i	$-0.476659\pi$
$613$	3.62780			0.146525			0.0732627	+	0.997313i	$0.476659\pi$
$614$		0			0
$615$	5.38725	+	2.04816i	0.217235	+	0.0825898i
$616$		0			0
$617$	−31.6551	−	26.5618i	−1.27439	−	1.06934i	−0.993992	−	0.109452i	$-0.965090\pi$
$617$	−31.6551	−	26.5618i	−1.27439	−	1.06934i	−0.280394	−	0.959885i	$-0.590465\pi$
$618$		0			0
$619$	−0.0725035	+	0.0608377i	−0.00291416	+	0.00244527i	−0.644244	−	0.764820i	$-0.722828\pi$
$619$	−0.0725035	+	0.0608377i	−0.00291416	+	0.00244527i	0.641329	+	0.767266i	$0.278383\pi$
$620$		0			0
$621$	−2.12459	+	9.62446i	−0.0852570	+	0.386216i
$622$		0			0
$623$	21.2879	−	7.41170i	0.852881	−	0.296944i
$624$		0			0
$625$	3.40919	−	19.3345i	0.136368	−	0.773380i
$626$		0			0
$627$	−34.2752	−	13.0310i	−1.36882	−	0.520406i
$628$		0			0
$629$	3.45708	+	5.98784i	0.137843	+	0.238751i
$630$		0			0
$631$	3.96494	−	6.86748i	0.157842	−	0.273390i	−0.776248	−	0.630427i	$-0.782880\pi$
$631$	3.96494	−	6.86748i	0.157842	−	0.273390i	0.934090	+	0.357037i	$0.116213\pi$
$632$		0			0
$633$	8.26160	−	2.87439i	0.328369	−	0.114247i
$634$		0			0
$635$	−3.10577	−	2.60605i	−0.123249	−	0.103418i
$636$		0			0
$637$	−8.41823	−	15.5739i	−0.333542	−	0.617062i
$638$		0			0
$639$	−14.9189	−	27.6291i	−0.590183	−	1.09299i
$640$		0			0
$641$	2.21259	+	12.5482i	0.0873922	+	0.495626i	0.996815	+	0.0797523i	$0.0254129\pi$
$641$	2.21259	+	12.5482i	0.0873922	+	0.495626i	−0.909423	+	0.415873i	$0.863476\pi$
$642$		0			0
$643$	5.84747	−	33.1627i	0.230602	−	1.30781i	−0.621080	−	0.783747i	$-0.713306\pi$
$643$	5.84747	−	33.1627i	0.230602	−	1.30781i	0.851681	−	0.524060i	$-0.175583\pi$
$644$		0			0
$645$	−4.59035	+	7.69547i	−0.180745	+	0.303009i
$646$		0			0
$647$	3.11628	−	5.39755i	0.122514	−	0.212200i	−0.798245	−	0.602333i	$-0.794238\pi$
$647$	3.11628	−	5.39755i	0.122514	−	0.212200i	0.920758	+	0.390134i	$0.127571\pi$
$648$		0			0
$649$	−11.7562	−	20.3624i	−0.461472	−	0.799292i
$650$		0			0
$651$	−2.16373	−	14.6878i	−0.0848032	−	0.575661i
$652$		0			0
$653$	21.2129	−	7.72086i	0.830124	−	0.302140i	0.108214	−	0.994128i	$-0.465487\pi$
$653$	21.2129	−	7.72086i	0.830124	−	0.302140i	0.721910	+	0.691987i	$0.243265\pi$
$654$		0			0
$655$	0.159843	+	0.906513i	0.00624557	+	0.0354204i
$656$		0			0
$657$	−9.11841	+	14.8031i	−0.355743	+	0.577524i
$658$		0			0
$659$	0.939206	+	5.32650i	0.0365863	+	0.207491i	0.997621	−	0.0689365i	$-0.0219606\pi$
$659$	0.939206	+	5.32650i	0.0365863	+	0.207491i	−0.961035	+	0.276427i	$0.910849\pi$
$660$		0			0
$661$	−0.510032	+	2.89253i	−0.0198379	+	0.112507i	−0.993119	−	0.117111i	$-0.962637\pi$
$661$	−0.510032	+	2.89253i	−0.0198379	+	0.112507i	0.973281	+	0.229618i	$0.0737477\pi$
$662$		0			0
$663$	1.36639	−	7.15193i	0.0530662	−	0.277758i
$664$		0			0
$665$	7.90108	−	6.44312i	0.306391	−	0.249854i
$666$		0			0
$667$	5.35353	−	9.27259i	0.207290	−	0.359036i
$668$		0			0
$669$	7.89126	+	3.00015i	0.305094	+	0.115993i
$670$		0			0
$671$	15.9104	+	13.3504i	0.614216	+	0.515388i
$672$		0			0
$673$	−10.3952	−	3.78353i	−0.400704	−	0.145844i	0.133804	−	0.991008i	$-0.457281\pi$
$673$	−10.3952	−	3.78353i	−0.400704	−	0.145844i	−0.534508	+	0.845163i	$0.679503\pi$
$674$		0			0
$675$	−19.0867	+	14.6731i	−0.734647	+	0.564767i
$676$		0			0
$677$	−5.87315	−	33.3083i	−0.225724	−	1.28014i	−0.861297	−	0.508102i	$-0.830347\pi$
$677$	−5.87315	−	33.3083i	−0.225724	−	1.28014i	0.635573	−	0.772040i	$-0.280764\pi$
$678$		0			0
$679$	10.0387	−	16.8376i	0.385249	−	0.646167i
$680$		0			0
$681$	3.37803	+	20.8939i	0.129446	+	0.800654i
$682$		0			0
$683$	−31.6204			−1.20992			−0.604961	−	0.796255i	$-0.706811\pi$
$683$	−31.6204			−1.20992			−0.604961	+	0.796255i	$0.706811\pi$
$684$		0			0
$685$	6.98798	−	12.1035i	0.266997	−	0.462452i
$686$		0			0
$687$	7.65631	−	40.0745i	0.292107	−	1.52894i
$688$		0			0
$689$	3.83388	−	21.7430i	0.146059	−	0.828342i
$690$		0			0
$691$	−11.5553	+	9.69604i	−0.439584	+	0.368855i	−0.835554	−	0.549409i	$-0.814853\pi$
$691$	−11.5553	+	9.69604i	−0.439584	+	0.368855i	0.395970	+	0.918264i	$0.370409\pi$
$692$		0			0
$693$	26.3860	+	1.12246i	1.00232	+	0.0426389i
$694$		0			0
$695$	−6.18315	−	2.25048i	−0.234540	−	0.0853657i
$696$		0			0
$697$	−6.99612	−	5.87044i	−0.264997	−	0.222359i
$698$		0			0
$699$	−12.0541	−	21.5825i	−0.455927	−	0.816325i
$700$		0			0
$701$	23.6233			0.892240			0.446120	−	0.894973i	$-0.352805\pi$
$701$	23.6233			0.892240			0.446120	+	0.894973i	$0.352805\pi$
$702$		0			0
$703$	13.2331	−	22.9204i	0.499096	−	0.864459i
$704$		0			0
$705$	1.43188	+	2.56375i	0.0539279	+	0.0965564i
$706$		0			0
$707$	16.1794	−	27.1372i	0.608489	−	1.02060i
$708$		0			0
$709$	−24.7942	−	9.02435i	−0.931166	−	0.338917i	−0.168494	−	0.985703i	$-0.553891\pi$
$709$	−24.7942	−	9.02435i	−0.931166	−	0.338917i	−0.762672	+	0.646786i	$0.776113\pi$
$710$		0			0
$711$	−3.07072	−	1.21778i	−0.115161	−	0.0456704i
$712$		0			0
$713$	1.06710	+	6.05184i	0.0399633	+	0.226643i
$714$		0			0
$715$	−4.78904	+	1.74307i	−0.179100	+	0.0651871i
$716$		0			0
$717$	7.03155	−	36.8044i	0.262598	−	1.37449i
$718$		0			0
$719$	−19.0450			−0.710258			−0.355129	−	0.934817i	$-0.615563\pi$
$719$	−19.0450			−0.710258			−0.355129	+	0.934817i	$0.615563\pi$
$720$		0			0
$721$	−10.0494	−	3.81814i	−0.374259	−	0.142195i
$722$		0			0
$723$	11.2837	+	4.28991i	0.419645	+	0.159543i
$724$		0			0
$725$	24.5761	−	8.94495i	0.912732	−	0.332207i
$726$		0			0
$727$	−38.0628	−	13.8537i	−1.41167	−	0.513806i	−0.480050	−	0.877241i	$-0.659382\pi$
$727$	−38.0628	−	13.8537i	−1.41167	−	0.513806i	−0.931619	+	0.363435i	$0.881604\pi$
$728$		0			0
$729$	26.9015	+	2.30472i	0.996350	+	0.0853601i
$730$		0			0
$731$	10.8770	−	9.12689i	0.402301	−	0.337570i
$732$		0			0
$733$	−8.16367	+	46.2985i	−0.301532	+	1.71007i	0.337864	+	0.941195i	$0.390296\pi$
$733$	−8.16367	+	46.2985i	−0.301532	+	1.71007i	−0.639396	+	0.768878i	$0.720815\pi$
$734$		0			0
$735$	−3.93703	+	6.19815i	−0.145219	+	0.228622i
$736$		0			0
$737$	4.19360	−	7.26353i	0.154473	−	0.267556i
$738$		0			0
$739$	−1.09738	−	1.90072i	−0.0403678	−	0.0699191i	0.845136	−	0.534552i	$-0.179520\pi$
$739$	−1.09738	−	1.90072i	−0.0403678	−	0.0699191i	−0.885503	+	0.464633i	$0.846186\pi$
$740$		0			0
$741$	−26.3238	+	9.15860i	−0.967028	+	0.336450i
$742$		0			0
$743$	−30.4203	+	11.0721i	−1.11601	+	0.406196i	−0.833196	−	0.552978i	$-0.813491\pi$
$743$	−30.4203	+	11.0721i	−1.11601	+	0.406196i	−0.282818	+	0.959174i	$0.591269\pi$
$744$		0			0
$745$	12.5202	+	4.55698i	0.458704	+	0.166955i
$746$		0			0
$747$	20.2561	−	16.0362i	0.741131	−	0.586734i
$748$		0			0
$749$	3.35249	−	17.5683i	0.122497	−	0.641932i
$750$		0			0
$751$	−2.56254	+	0.932690i	−0.0935086	+	0.0340343i	−0.388351	−	0.921512i	$-0.626955\pi$
$751$	−2.56254	+	0.932690i	−0.0935086	+	0.0340343i	0.294842	+	0.955546i	$0.404733\pi$
$752$		0			0
$753$	21.6391	−	36.2767i	0.788573	−	1.32200i
$754$		0			0
$755$	−3.43545			−0.125029
$756$		0			0
$757$	−15.2787			−0.555313			−0.277656	−	0.960680i	$-0.589558\pi$
$757$	−15.2787			−0.555313			−0.277656	+	0.960680i	$0.589558\pi$
$758$		0			0
$759$	−10.9305	−	0.155704i	−0.396751	−	0.00565171i
$760$		0			0
$761$	28.4834	−	10.3671i	1.03252	−	0.375807i	0.230481	−	0.973077i	$-0.425970\pi$
$761$	28.4834	−	10.3671i	1.03252	−	0.375807i	0.802041	+	0.597269i	$0.203748\pi$
$762$		0			0
$763$	1.39558	−	0.485892i	0.0505234	−	0.0175905i
$764$		0			0
$765$	−2.86618	+	0.951661i	−0.103627	+	0.0344074i
$766$		0			0
$767$	−16.7938	−	6.11243i	−0.606388	−	0.220707i
$768$		0			0
$769$	−3.11874	+	1.13513i	−0.112465	+	0.0409338i	−0.397640	−	0.917542i	$-0.630171\pi$
$769$	−3.11874	+	1.13513i	−0.112465	+	0.0409338i	0.285175	+	0.958476i	$0.407948\pi$
$770$		0			0
$771$	−7.45811	+	39.0371i	−0.268597	+	1.40589i
$772$		0			0
$773$	−8.70425	−	15.0762i	−0.313070	−	0.542254i	0.665955	−	0.745992i	$-0.268024\pi$
$773$	−8.70425	−	15.0762i	−0.313070	−	0.542254i	−0.979025	+	0.203738i	$0.934691\pi$
$774$		0			0
$775$	−7.50520	+	12.9994i	−0.269595	+	0.466952i
$776$		0			0
$777$	−3.83934	+	18.6711i	−0.137736	+	0.669821i
$778$		0			0
$779$	−6.07052	+	34.4276i	−0.217499	+	1.23350i
$780$		0			0
$781$	26.6781	−	22.3856i	0.954617	−	0.801019i
$782$		0			0
$783$	−27.1083	−	11.2000i	−0.968773	−	0.400256i
$784$		0			0
$785$	−13.4298	−	4.88803i	−0.479329	−	0.174461i
$786$		0			0
$787$	−32.9707	+	12.0004i	−1.17528	+	0.427766i	−0.854532	−	0.519399i	$-0.826156\pi$
$787$	−32.9707	+	12.0004i	−1.17528	+	0.427766i	−0.320746	+	0.947165i	$0.603934\pi$
$788$		0			0
$789$	5.11176	−	4.16666i	0.181984	−	0.148337i
$790$		0			0
$791$	33.6187	−	27.4151i	1.19534	−	0.974770i
$792$		0			0
$793$	15.7868			0.560604
$794$		0			0
$795$	−8.64889	+	3.00913i	−0.306745	+	0.106723i
$796$		0			0
$797$	−21.5581	+	7.84652i	−0.763629	+	0.277938i	−0.694329	−	0.719658i	$-0.744299\pi$
$797$	−21.5581	+	7.84652i	−0.763629	+	0.277938i	−0.0692998	+	0.997596i	$0.522077\pi$
$798$		0			0
$799$	−0.808021	−	4.58251i	−0.0285857	−	0.162118i
$800$		0			0
$801$	12.1440	+	22.4901i	0.429087	+	0.794648i
$802$		0			0
$803$	−18.1202	−	6.59522i	−0.639449	−	0.232740i
$804$		0			0
$805$	1.55645	−	2.61058i	0.0548575	−	0.0920109i
$806$		0			0
$807$	31.6623	+	0.451028i	1.11456	+	0.0158769i
$808$		0			0
$809$	−17.4133	+	30.1606i	−0.612217	+	1.06039i	0.378649	+	0.925541i	$0.376389\pi$
$809$	−17.4133	+	30.1606i	−0.612217	+	1.06039i	−0.990866	+	0.134851i	$0.956944\pi$
$810$		0			0
$811$	−15.2819			−0.536620			−0.268310	−	0.963333i	$-0.586465\pi$
$811$	−15.2819			−0.536620			−0.268310	+	0.963333i	$0.586465\pi$
$812$		0			0
$813$	−2.37596	+	3.98316i	−0.0833285	+	0.139695i
$814$		0			0
$815$	11.4546	+	9.61156i	0.401238	+	0.336678i
$816$		0			0
$817$	−51.0733	−	18.5891i	−1.78683	−	0.650352i
$818$		0			0
$819$	15.9120	−	12.2380i	0.556010	−	0.427631i
$820$		0			0
$821$	−8.89580	+	7.46446i	−0.310466	+	0.260512i	−0.784684	−	0.619895i	$-0.787175\pi$
$821$	−8.89580	+	7.46446i	−0.310466	+	0.260512i	0.474219	+	0.880407i	$0.342731\pi$
$822$		0			0
$823$	8.21198	−	46.5725i	0.286252	−	1.62341i	−0.414528	−	0.910037i	$-0.636053\pi$
$823$	8.21198	−	46.5725i	0.286252	−	1.62341i	0.700780	−	0.713378i	$-0.252836\pi$
$824$		0			0
$825$	−20.2082	−	17.4531i	−0.703558	−	0.607641i
$826$		0			0
$827$	3.94740	−	6.83710i	0.137265	−	0.237749i	−0.789196	−	0.614142i	$-0.789502\pi$
$827$	3.94740	−	6.83710i	0.137265	−	0.237749i	0.926460	+	0.376393i	$0.122836\pi$
$828$		0			0
$829$	46.3525			1.60989			0.804944	−	0.593350i	$-0.202195\pi$
$829$	46.3525			1.60989			0.804944	+	0.593350i	$0.202195\pi$
$830$		0			0
$831$	26.4238	−	21.5383i	0.916631	−	0.747157i
$832$		0			0
$833$	9.11958	−	7.22619i	0.315975	−	0.250373i
$834$		0			0
$835$	0.443363	+	2.51444i	0.0153432	+	0.0870156i
$836$		0			0
$837$	16.0505	−	5.07660i	0.554785	−	0.175473i
$838$		0			0
$839$	3.58823	+	1.30601i	0.123879	+	0.0450884i	0.403216	−	0.915105i	$-0.367892\pi$
$839$	3.58823	+	1.30601i	0.123879	+	0.0450884i	−0.279337	+	0.960193i	$0.590115\pi$
$840$		0			0
$841$	2.19324	+	1.84035i	0.0756289	+	0.0634602i
$842$		0			0
$843$	9.15819	−	7.46495i	0.315425	−	0.257106i
$844$		0			0
$845$	1.99972	−	3.46361i	0.0687924	−	0.119152i
$846$		0			0
$847$	0.0300823	+	0.185809i	0.00103364	+	0.00638447i
$848$		0			0
$849$	−34.3023	+	11.9345i	−1.17725	+	0.409591i
$850$		0			0
$851$	1.37009	−	7.77017i	0.0469661	−	0.266358i
$852$		0			0
$853$	7.54758	+	42.8044i	0.258424	+	1.46560i	0.787128	+	0.616790i	$0.211567\pi$
$853$	7.54758	+	42.8044i	0.258424	+	1.46560i	−0.528704	+	0.848806i	$0.677322\pi$
$854$		0			0
$855$	8.64038	+	7.67998i	0.295495	+	0.262650i
$856$		0			0
$857$	2.46951	+	14.0053i	0.0843569	+	0.478412i	0.997494	+	0.0707582i	$0.0225419\pi$
$857$	2.46951	+	14.0053i	0.0843569	+	0.478412i	−0.913137	+	0.407654i	$0.866347\pi$
$858$		0			0
$859$	0.596011	−	0.216930i	0.0203356	−	0.00740156i	−0.331832	−	0.943338i	$-0.607667\pi$
$859$	0.596011	−	0.216930i	0.0203356	−	0.00740156i	0.352168	+	0.935937i	$0.385445\pi$
$860$		0			0
$861$	−3.66953	−	24.9095i	−0.125057	−	0.848913i
$862$		0			0
$863$	16.5317	+	28.6338i	0.562746	+	0.974705i	0.997255	+	0.0740375i	$0.0235884\pi$
$863$	16.5317	+	28.6338i	0.562746	+	0.974705i	−0.434509	+	0.900667i	$0.643078\pi$
$864$		0			0
$865$	2.73471	−	4.73666i	0.0929831	−	0.161051i
$866$		0			0
$867$	−24.6568	−	0.351235i	−0.837389	−	0.0119286i
$868$		0			0
$869$	0.636214	−	3.60815i	0.0215821	−	0.122398i
$870$		0			0
$871$	−1.10701	−	6.27818i	−0.0375097	−	0.212728i
$872$		0			0
$873$	20.6622	+	8.19421i	0.699310	+	0.277332i
$874$		0			0
$875$	14.5774	−	5.07535i	0.492807	−	0.171578i
$876$		0			0
$877$	36.9546	+	31.0086i	1.24787	+	1.04709i	0.996867	+	0.0790981i	$0.0252040\pi$
$877$	36.9546	+	31.0086i	1.24787	+	1.04709i	0.251001	+	0.967987i	$0.419240\pi$
$878$		0			0
$879$	10.8278	−	56.6745i	0.365211	−	1.91158i
$880$		0			0
$881$	11.0502	−	19.1394i	0.372289	−	0.644824i	−0.617628	−	0.786470i	$-0.711906\pi$
$881$	11.0502	−	19.1394i	0.372289	−	0.644824i	0.989917	+	0.141647i	$0.0452396\pi$
$882$		0			0
$883$	1.35462	+	2.34627i	0.0455866	+	0.0789583i	0.887918	−	0.460001i	$-0.152151\pi$
$883$	1.35462	+	2.34627i	0.0455866	+	0.0789583i	−0.842332	+	0.538959i	$0.818818\pi$
$884$		0			0
$885$	1.18307	+	7.31752i	0.0397684	+	0.245976i
$886$		0			0
$887$	−7.49202	+	42.4893i	−0.251557	+	1.42665i	0.553200	+	0.833048i	$0.313407\pi$
$887$	−7.49202	+	42.4893i	−0.251557	+	1.42665i	−0.804757	+	0.593604i	$0.797705\pi$
$888$		0			0
$889$	−3.31994	+	17.3977i	−0.111347	+	0.583501i
$890$		0			0
$891$	3.51226	+	29.7393i	0.117665	+	0.996304i
$892$		0			0
$893$	−13.6445	+	11.4491i	−0.456597	+	0.383130i
$894$		0			0
$895$	−11.1061	−	9.31916i	−0.371237	−	0.311505i
$896$		0			0
$897$	−6.44049	+	5.24972i	−0.215042	+	0.175283i
$898$		0			0
$899$	−18.2875			−0.609921
$900$		0			0
$901$	14.5109			0.483427
$902$		0			0
$903$	39.1296	+	1.10651i	1.30215	+	0.0368222i
$904$		0			0
$905$	3.18556	+	2.67300i	0.105891	+	0.0888535i
$906$		0			0
$907$	50.0130	+	18.2032i	1.66065	+	0.604429i	0.990465	−	0.137762i	$-0.0439911\pi$
$907$	50.0130	+	18.2032i	1.66065	+	0.604429i	0.670188	+	0.742191i	$0.266213\pi$
$908$		0			0
$909$	33.3015	+	13.2067i	1.10454	+	0.438037i
$910$		0			0
$911$	−17.7256	+	14.8735i	−0.587274	+	0.492782i	−0.887327	−	0.461141i	$-0.847440\pi$
$911$	−17.7256	+	14.8735i	−0.587274	+	0.492782i	0.300053	+	0.953923i	$0.402996\pi$
$912$		0			0
$913$	21.9505	+	18.4187i	0.726455	+	0.609568i
$914$		0			0
$915$	−3.19282	−	5.71665i	−0.105551	−	0.188987i
$916$		0			0
$917$	3.11645	−	2.54138i	0.102914	−	0.0839237i
$918$		0			0
$919$	18.3338	+	31.7550i	0.604775	+	1.04750i	0.992087	+	0.125553i	$0.0400704\pi$
$919$	18.3338	+	31.7550i	0.604775	+	1.04750i	−0.387312	+	0.921949i	$0.626596\pi$
$920$		0			0
$921$	−46.4726	−	0.662001i	−1.53132	−	0.0218137i
$922$		0			0
$923$	4.59659	−	26.0686i	0.151299	−	0.858057i
$924$		0			0
$925$	14.7635	−	12.3880i	0.485421	−	0.407316i
$926$		0			0
$927$	2.45779	−	11.9393i	0.0807245	−	0.392138i
$928$		0			0
$929$	3.89062	−	3.26462i	0.127647	−	0.107109i	−0.576729	−	0.816935i	$-0.695671\pi$
$929$	3.89062	−	3.26462i	0.127647	−	0.107109i	0.704376	+	0.709827i	$0.251227\pi$
$930$		0			0
$931$	−41.4089	−	16.4010i	−1.35712	−	0.537523i
$932$		0			0
$933$	−10.4118	+	3.62249i	−0.340867	+	0.118595i
$934$		0			0
$935$	−1.67478	−	2.90081i	−0.0547712	−	0.0948665i
$936$		0			0
$937$	−19.9489	−	34.5524i	−0.651701	−	1.12878i	−0.982710	−	0.185151i	$-0.940723\pi$
$937$	−19.9489	−	34.5524i	−0.651701	−	1.12878i	0.331009	−	0.943627i	$-0.392611\pi$
$938$		0			0
$939$	41.4671	+	15.7652i	1.35323	+	0.514478i
$940$		0			0
$941$	−50.8748	+	18.5169i	−1.65847	+	0.603635i	−0.990122	−	0.140211i	$-0.955222\pi$
$941$	−50.8748	+	18.5169i	−1.65847	+	0.603635i	−0.668351	+	0.743846i	$0.733000\pi$
$942$		0			0
$943$	1.80973	+	10.2635i	0.0589329	+	0.334225i
$944$		0			0
$945$	−7.64974	−	3.28691i	−0.248846	−	0.106923i
$946$		0			0
$947$	2.87839	+	16.3242i	0.0935351	+	0.530464i	0.995186	+	0.0980001i	$0.0312445\pi$
$947$	2.87839	+	16.3242i	0.0935351	+	0.530464i	−0.901651	+	0.432464i	$0.857644\pi$
$948$		0			0
$949$	−13.7730	+	5.01296i	−0.447090	+	0.162728i
$950$		0			0
$951$	1.99173	+	12.3193i	0.0645864	+	0.399480i
$952$		0			0
$953$	−5.60934	−	9.71566i	−0.181704	−	0.314721i	0.760757	−	0.649037i	$-0.224828\pi$
$953$	−5.60934	−	9.71566i	−0.181704	−	0.314721i	−0.942461	+	0.334316i	$0.891495\pi$
$954$		0			0
$955$	0.163882	+	0.283852i	0.00530309	+	0.00918522i
$956$		0			0
$957$	6.10474	−	31.9533i	0.197338	−	1.03290i
$958$		0			0
$959$	−61.0495	−	0.856366i	−1.97139	−	0.0276535i
$960$		0			0
$961$	−15.7071	+	13.1798i	−0.506679	+	0.425154i
$962$		0			0
$963$	20.2718	+	0.577660i	0.653250	+	0.0186148i
$964$		0			0
$965$	−7.79257	+	6.53874i	−0.250852	+	0.210490i
$966$		0			0
$967$	−8.76237	+	49.6939i	−0.281779	+	1.59805i	0.434791	+	0.900532i	$0.356822\pi$
$967$	−8.76237	+	49.6939i	−0.281779	+	1.59805i	−0.716569	+	0.697516i	$0.754289\pi$
$968$		0			0
$969$	−8.93227	−	15.9930i	−0.286946	−	0.513769i
$970$		0			0
$971$	−28.6651	−	49.6494i	−0.919907	−	1.59333i	−0.799553	−	0.600595i	$-0.794930\pi$
$971$	−28.6651	−	49.6494i	−0.919907	−	1.59333i	−0.120354	−	0.992731i	$-0.538403\pi$
$972$		0			0
$973$	4.59403	+	28.3759i	0.147278	+	0.909689i
$974$		0			0
$975$	−20.2937	−	0.289083i	−0.649917	−	0.00925805i
$976$		0			0
$977$	−6.78130	−	5.69018i	−0.216953	−	0.182045i	0.527834	−	0.849348i	$-0.323004\pi$
$977$	−6.78130	−	5.69018i	−0.216953	−	0.182045i	−0.744787	+	0.667303i	$0.767449\pi$
$978$		0			0
$979$	−21.7160	+	18.2218i	−0.694045	+	0.582373i
$980$		0			0
$981$	0.796130	+	1.47439i	0.0254185	+	0.0470738i
$982$		0			0
$983$	42.1313	+	15.3345i	1.34378	+	0.489096i	0.911001	−	0.412404i	$-0.135311\pi$
$983$	42.1313	+	15.3345i	1.34378	+	0.489096i	0.432779	+	0.901500i	$0.357533\pi$
$984$		0			0
$985$	9.94462	+	8.34453i	0.316862	+	0.265879i
$986$		0			0
$987$	6.72572	−	10.9240i	0.214082	−	0.347716i
$988$		0			0
$989$	−16.2030			−0.515226
$990$		0			0
$991$	−13.7456			−0.436642			−0.218321	−	0.975877i	$-0.570058\pi$
$991$	−13.7456			−0.436642			−0.218321	+	0.975877i	$0.570058\pi$
$992$		0			0
$993$	−0.706145	−	4.36766i	−0.0224088	−	0.138603i
$994$		0			0
$995$	4.82119	+	4.04545i	0.152842	+	0.128250i
$996$		0			0
$997$	12.7496	−	10.6982i	0.403783	−	0.338814i	−0.418171	−	0.908369i	$-0.637329\pi$
$997$	12.7496	−	10.6982i	0.403783	−	0.338814i	0.821954	+	0.569554i	$0.192884\pi$
$998$		0			0
$999$	−21.5942	−	0.923328i	−0.683212	−	0.0292128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.8	✓	144
7.2	even	3		756.2.bq.a.625.24	yes	144
27.7	even	9		756.2.bq.a.277.24	yes	144
189.142	even	9	inner	756.2.bp.a.709.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.8	✓	144	1.1	even	1	trivial
756.2.bp.a.709.8	yes	144	189.142	even	9	inner
756.2.bq.a.277.24	yes	144	27.7	even	9
756.2.bq.a.625.24	yes	144	7.2	even	3

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.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.844572 - 1.51218i) q^{3} +(-0.569103 + 0.207137i) q^{5} +(2.00271 + 1.72892i) q^{7} +(-1.57340 + 2.55430i) q^{9} +O(q^{10})\)	\(q+(-0.844572 - 1.51218i) q^{3} +(-0.569103 + 0.207137i) q^{5} +(2.00271 + 1.72892i) q^{7} +(-1.57340 + 2.55430i) q^{9} +(-3.12667 - 1.13801i) q^{11} +(-2.37655 + 0.864994i) q^{13} +(0.793878 + 0.685647i) q^{15} +(-0.831106 - 1.43952i) q^{17} +(-3.18133 + 5.51023i) q^{19} +(0.923004 - 4.48866i) q^{21} +(-0.329380 + 1.86800i) q^{23} +(-3.54925 + 2.97817i) q^{25} +(5.19141 + 0.221975i) q^{27} +(-5.30432 - 1.93061i) q^{29} +(3.04436 - 1.10806i) q^{31} +(0.919812 + 5.68923i) q^{33} +(-1.49787 - 0.569097i) q^{35} -4.15961 q^{37} +(3.31520 + 2.86323i) q^{39} +(5.16301 - 1.87918i) q^{41} +(1.48333 + 8.41241i) q^{43} +(0.366336 - 1.77957i) q^{45} +(2.63058 + 0.957453i) q^{47} +(1.02170 + 6.92504i) q^{49} +(-1.47489 + 2.47256i) q^{51} +(-4.36492 + 7.56027i) q^{53} +2.01512 q^{55} +(11.0193 + 0.156970i) q^{57} +(5.41321 + 4.54223i) q^{59} +(-5.86567 - 2.13493i) q^{61} +(-7.56722 + 2.39525i) q^{63} +(1.17333 - 0.984542i) q^{65} +(-0.437715 + 2.48240i) q^{67} +(3.10295 - 1.07958i) q^{69} +(-5.23329 + 9.06432i) q^{71} +5.79537 q^{73} +(7.50114 + 2.85183i) q^{75} +(-4.29428 - 7.68486i) q^{77} +(0.191208 + 1.08440i) q^{79} +(-4.04885 - 8.03783i) q^{81} +(-8.09245 - 2.94541i) q^{83} +(0.771162 + 0.647082i) q^{85} +(1.56044 + 9.65164i) q^{87} +(4.25989 - 7.37835i) q^{89} +(-6.25504 - 2.37652i) q^{91} +(-4.24676 - 3.66779i) q^{93} +(0.669136 - 3.79486i) q^{95} +(-1.28660 - 7.29669i) q^{97} +(7.82631 - 6.19589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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