LMFDB - Embedded newform 756.2.be.e.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.8
Character	$\chi$	$=$	756.107
Dual form			756.2.be.e.431.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04167 + 0.956516i) q^{2} +(0.170154 - 1.99275i) q^{4} +(0.835158 + 0.482179i) q^{5} +(2.03771 - 1.68753i) q^{7} +(1.72885 + 2.23854i) q^{8} +O(q^{10})$	\(q+(-1.04167 + 0.956516i) q^{2} +(0.170154 - 1.99275i) q^{4} +(0.835158 + 0.482179i) q^{5} +(2.03771 - 1.68753i) q^{7} +(1.72885 + 2.23854i) q^{8} +(-1.33117 + 0.296571i) q^{10} +(1.63178 + 2.82633i) q^{11} -2.66851 q^{13} +(-0.508474 + 3.70695i) q^{14} +(-3.94210 - 0.678147i) q^{16} +(-0.713843 + 0.412137i) q^{17} +(4.31465 + 2.49107i) q^{19} +(1.10297 - 1.58222i) q^{20} +(-4.40321 - 1.38328i) q^{22} +(4.08549 - 7.07628i) q^{23} +(-2.03501 - 3.52474i) q^{25} +(2.77971 - 2.55248i) q^{26} +(-3.01609 - 4.34778i) q^{28} +7.71232i q^{29} +(6.98679 - 4.03382i) q^{31} +(4.75502 - 3.06427i) q^{32} +(0.349373 - 1.11211i) q^{34} +(2.51550 - 0.426812i) q^{35} +(2.46063 - 4.26194i) q^{37} +(-6.87719 + 1.53217i) q^{38} +(0.364488 + 2.70315i) q^{40} +5.35061i q^{41} +8.09044i q^{43} +(5.90982 - 2.77082i) q^{44} +(2.51284 + 11.2790i) q^{46} +(-0.910519 + 1.57706i) q^{47} +(1.30451 - 6.87737i) q^{49} +(5.49127 + 1.72510i) q^{50} +(-0.454058 + 5.31768i) q^{52} +(7.39839 - 4.27147i) q^{53} +3.14724i q^{55} +(7.30049 + 1.64401i) q^{56} +(-7.37696 - 8.03369i) q^{58} +(0.238238 + 0.412641i) q^{59} +(-2.09383 + 3.62661i) q^{61} +(-3.41951 + 10.8849i) q^{62} +(-2.02214 + 7.74022i) q^{64} +(-2.22863 - 1.28670i) q^{65} +(7.36654 - 4.25307i) q^{67} +(0.699823 + 1.49264i) q^{68} +(-2.21207 + 2.85071i) q^{70} -7.12475 q^{71} +(5.84578 + 10.1252i) q^{73} +(1.51345 + 6.79317i) q^{74} +(5.69822 - 8.17416i) q^{76} +(8.09460 + 3.00556i) q^{77} +(3.28159 + 1.89463i) q^{79} +(-2.96528 - 2.46715i) q^{80} +(-5.11794 - 5.57357i) q^{82} +0.0674837 q^{83} -0.794896 q^{85} +(-7.73863 - 8.42757i) q^{86} +(-3.50575 + 8.53912i) q^{88} +(-13.7441 - 7.93517i) q^{89} +(-5.43765 + 4.50319i) q^{91} +(-13.4061 - 9.34541i) q^{92} +(-0.560027 - 2.51371i) q^{94} +(2.40228 + 4.16087i) q^{95} +7.41403 q^{97} +(5.21945 + 8.41174i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) $ 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.04167	+	0.956516i	−0.736572	+	0.676359i
$2$	−1.04167	+	0.956516i	−0.736572	+	0.676359i
$3$		0			0
$3$		0			0
$4$	0.170154	−	1.99275i	0.0850769	−	0.996374i
$5$	0.835158	+	0.482179i	0.373494	+	0.215637i	0.674984	−	0.737833i	$-0.264151\pi$
$5$	0.835158	+	0.482179i	0.373494	+	0.215637i	−0.301490	+	0.953469i	$0.597484\pi$
$6$		0			0
$7$	2.03771	−	1.68753i	0.770181	−	0.637825i
$7$	2.03771	−	1.68753i	0.770181	−	0.637825i
$8$	1.72885	+	2.23854i	0.611242	+	0.791444i
$9$		0			0
$10$	−1.33117	+	0.296571i	−0.420953	+	0.0937840i
$11$	1.63178	+	2.82633i	0.492001	+	0.852170i	0.999958	−	0.00921230i	$-0.00293241\pi$
$11$	1.63178	+	2.82633i	0.492001	+	0.852170i	−0.507957	+	0.861383i	$0.669599\pi$
$12$		0			0
$13$	−2.66851			−0.740113			−0.370056	−	0.929009i	$-0.620662\pi$
$13$	−2.66851			−0.740113			−0.370056	+	0.929009i	$0.620662\pi$
$14$	−0.508474	+	3.70695i	−0.135895	+	0.990723i
$15$		0			0
$16$	−3.94210	−	0.678147i	−0.985524	−	0.169537i
$17$	−0.713843	+	0.412137i	−0.173132	+	0.0999580i	−0.584062	−	0.811709i	$-0.698538\pi$
$17$	−0.713843	+	0.412137i	−0.173132	+	0.0999580i	0.410930	+	0.911667i	$0.365204\pi$
$18$		0			0
$19$	4.31465	+	2.49107i	0.989849	+	0.571490i	0.905229	−	0.424924i	$-0.139699\pi$
$19$	4.31465	+	2.49107i	0.989849	+	0.571490i	0.0846201	+	0.996413i	$0.473032\pi$
$20$	1.10297	−	1.58222i	0.246631	−	0.353794i
$21$		0			0
$22$	−4.40321	−	1.38328i	−0.938767	−	0.294916i
$23$	4.08549	−	7.07628i	0.851884	−	1.47551i	−0.0276221	−	0.999618i	$-0.508794\pi$
$23$	4.08549	−	7.07628i	0.851884	−	1.47551i	0.879506	−	0.475888i	$-0.157873\pi$
$24$		0			0
$25$	−2.03501	−	3.52474i	−0.407002	−	0.704947i
$26$	2.77971	−	2.55248i	0.545146	−	0.500582i
$27$		0			0
$28$	−3.01609	−	4.34778i	−0.569988	−	0.821653i
$29$			7.71232i			1.43214i	0.698028	+	0.716071i	$0.254061\pi$
$29$			7.71232i			1.43214i	−0.698028	+	0.716071i	$0.745939\pi$
$30$		0			0
$31$	6.98679	−	4.03382i	1.25486	−	0.724496i	0.282793	−	0.959181i	$-0.408739\pi$
$31$	6.98679	−	4.03382i	1.25486	−	0.724496i	0.972071	+	0.234685i	$0.0754059\pi$
$32$	4.75502	−	3.06427i	0.840577	−	0.541692i
$33$		0			0
$34$	0.349373	−	1.11211i	0.0599170	−	0.190726i
$35$	2.51550	−	0.426812i	0.425197	−	0.0721443i
$36$		0			0
$37$	2.46063	−	4.26194i	0.404526	−	0.700659i	−0.589740	−	0.807593i	$-0.700770\pi$
$37$	2.46063	−	4.26194i	0.404526	−	0.700659i	0.994266	+	0.106934i	$0.0341033\pi$
$38$	−6.87719	+	1.53217i	−1.11563	+	0.248550i
$39$		0			0
$40$	0.364488	+	2.70315i	0.0576306	+	0.427406i
$41$			5.35061i			0.835624i	0.908533	+	0.417812i	$0.137203\pi$
$41$			5.35061i			0.835624i	−0.908533	+	0.417812i	$0.862797\pi$
$42$		0			0
$43$			8.09044i			1.23378i	0.787049	+	0.616890i	$0.211608\pi$
$43$			8.09044i			1.23378i	−0.787049	+	0.616890i	$0.788392\pi$
$44$	5.90982	−	2.77082i	0.890938	−	0.417717i
$45$		0			0
$46$	2.51284	+	11.2790i	0.370498	+	1.66300i
$47$	−0.910519	+	1.57706i	−0.132813	+	0.230038i	−0.924760	−	0.380551i	$-0.875734\pi$
$47$	−0.910519	+	1.57706i	−0.132813	+	0.230038i	0.791947	+	0.610590i	$0.209068\pi$
$48$		0			0
$49$	1.30451	−	6.87737i	0.186359	−	0.982482i
$50$	5.49127	+	1.72510i	0.776583	+	0.243965i
$51$		0			0
$52$	−0.454058	+	5.31768i	−0.0629664	+	0.737429i
$53$	7.39839	−	4.27147i	1.01625	−	0.586731i	0.103233	−	0.994657i	$-0.467081\pi$
$53$	7.39839	−	4.27147i	1.01625	−	0.586731i	0.913015	+	0.407926i	$0.133748\pi$
$54$		0			0
$55$			3.14724i			0.424374i
$56$	7.30049	+	1.64401i	0.975570	+	0.219690i
$57$		0			0
$58$	−7.37696	−	8.03369i	−0.968642	−	1.05488i
$59$	0.238238	+	0.412641i	0.0310160	+	0.0537213i	0.881117	−	0.472899i	$-0.156792\pi$
$59$	0.238238	+	0.412641i	0.0310160	+	0.0537213i	−0.850101	+	0.526620i	$0.823459\pi$
$60$		0			0
$61$	−2.09383	+	3.62661i	−0.268087	+	0.464340i	−0.968368	−	0.249527i	$-0.919725\pi$
$61$	−2.09383	+	3.62661i	−0.268087	+	0.464340i	0.700281	+	0.713867i	$0.253058\pi$
$62$	−3.41951	+	10.8849i	−0.434278	+	1.38238i
$63$		0			0
$64$	−2.02214	+	7.74022i	−0.252767	+	0.967527i
$65$	−2.22863	−	1.28670i	−0.276428	−	0.159596i
$66$		0			0
$67$	7.36654	−	4.25307i	0.899966	−	0.519596i	0.0227769	−	0.999741i	$-0.492749\pi$
$67$	7.36654	−	4.25307i	0.899966	−	0.519596i	0.877189	+	0.480145i	$0.159416\pi$
$68$	0.699823	+	1.49264i	0.0848661	+	0.181009i
$69$		0			0
$70$	−2.21207	+	2.85071i	−0.264393	+	0.340725i
$71$	−7.12475			−0.845553			−0.422776	−	0.906234i	$-0.638944\pi$
$71$	−7.12475			−0.845553			−0.422776	+	0.906234i	$0.638944\pi$
$72$		0			0
$73$	5.84578	+	10.1252i	0.684197	+	1.18506i	0.973688	+	0.227883i	$0.0731805\pi$
$73$	5.84578	+	10.1252i	0.684197	+	1.18506i	−0.289491	+	0.957181i	$0.593486\pi$
$74$	1.51345	+	6.79317i	0.175935	+	0.789691i
$75$		0			0
$76$	5.69822	−	8.17416i	0.653631	−	0.937640i
$77$	8.09460	+	3.00556i	0.922465	+	0.342515i
$78$		0			0
$79$	3.28159	+	1.89463i	0.369208	+	0.213162i	0.673112	−	0.739540i	$-0.264957\pi$
$79$	3.28159	+	1.89463i	0.369208	+	0.213162i	−0.303905	+	0.952702i	$0.598290\pi$
$80$	−2.96528	−	2.46715i	−0.331529	−	0.275836i
$81$		0			0
$82$	−5.11794	−	5.57357i	−0.565182	−	0.615497i
$83$	0.0674837			0.00740730			0.00370365	−	0.999993i	$-0.498821\pi$
$83$	0.0674837			0.00740730			0.00370365	+	0.999993i	$0.498821\pi$
$84$		0			0
$85$	−0.794896			−0.0862185
$86$	−7.73863	−	8.42757i	−0.834478	−	0.908768i
$87$		0			0
$88$	−3.50575	+	8.53912i	−0.373714	+	0.910273i
$89$	−13.7441	−	7.93517i	−1.45687	−	0.841126i	−0.458018	−	0.888943i	$-0.651440\pi$
$89$	−13.7441	−	7.93517i	−1.45687	−	0.841126i	−0.998856	+	0.0478167i	$0.984774\pi$
$90$		0			0
$91$	−5.43765	+	4.50319i	−0.570021	+	0.472062i
$92$	−13.4061	−	9.34541i	−1.39768	−	0.974327i
$93$		0			0
$94$	−0.560027	−	2.51371i	−0.0577624	−	0.259269i
$95$	2.40228	+	4.16087i	0.246469	+	0.426896i
$96$		0			0
$97$	7.41403			0.752781			0.376390	−	0.926461i	$-0.377165\pi$
$97$	7.41403			0.752781			0.376390	+	0.926461i	$0.377165\pi$
$98$	5.21945	+	8.41174i	0.527244	+	0.849714i
$99$		0			0
$100$	−7.37018	+	3.45551i	−0.737018	+	0.345551i
$101$	−1.87642	+	1.08335i	−0.186711	+	0.107797i	−0.590442	−	0.807080i	$-0.701046\pi$
$101$	−1.87642	+	1.08335i	−0.186711	+	0.107797i	0.403731	+	0.914878i	$0.367713\pi$
$102$		0			0
$103$	15.2933	+	8.82956i	1.50689	+	0.870003i	0.999968	+	0.00801027i	$0.00254978\pi$
$103$	15.2933	+	8.82956i	1.50689	+	0.870003i	0.506921	+	0.861992i	$0.330784\pi$
$104$	−4.61347	−	5.97358i	−0.452388	−	0.585758i
$105$		0			0
$106$	−3.62096	+	11.5261i	−0.351699	+	1.11952i
$107$	−1.77753	+	3.07877i	−0.171840	+	0.297636i	−0.939063	−	0.343744i	$-0.888305\pi$
$107$	−1.77753	+	3.07877i	−0.171840	+	0.297636i	0.767223	+	0.641381i	$0.221638\pi$
$108$		0			0
$109$	−1.39239	−	2.41168i	−0.133366	−	0.230997i	0.791606	−	0.611032i	$-0.209245\pi$
$109$	−1.39239	−	2.41168i	−0.133366	−	0.230997i	−0.924972	+	0.380035i	$0.875912\pi$
$110$	−3.01039	−	3.27839i	−0.287029	−	0.312582i
$111$		0			0
$112$	−9.17723	+	5.27052i	−0.867167	+	0.498018i
$113$			3.09703i			0.291344i	0.989333	+	0.145672i	$0.0465344\pi$
$113$			3.09703i			0.291344i	−0.989333	+	0.145672i	$0.953466\pi$
$114$		0			0
$115$	6.82406	−	3.93987i	0.636347	−	0.367395i
$116$	15.3687	+	1.31228i	1.42695	+	0.121842i
$117$		0			0
$118$	−0.642864	−	0.201957i	−0.0591804	−	0.0185917i
$119$	−0.759111	+	2.04444i	−0.0695876	+	0.187414i
$120$		0			0
$121$	0.174577	−	0.302376i	0.0158706	−	0.0274887i
$122$	−1.28784	−	5.78051i	−0.116595	−	0.523343i
$123$		0			0
$124$	−6.84957	−	14.6093i	−0.615109	−	1.31195i
$125$		−	8.74674i		−	0.782332i
$126$		0			0
$127$		−	0.308166i		−	0.0273454i	−0.999907	−	0.0136727i	$-0.995648\pi$
$127$		−	0.308166i		−	0.0273454i	0.999907	−	0.0136727i	$-0.00435228\pi$
$128$	−5.29724	−	9.99696i	−0.468214	−	0.883615i
$129$		0			0
$130$	3.55225	−	0.791404i	0.311553	−	0.0694107i
$131$	−1.18854	+	2.05862i	−0.103843	+	0.179862i	−0.913265	−	0.407366i	$-0.866447\pi$
$131$	−1.18854	+	2.05862i	−0.103843	+	0.179862i	0.809422	+	0.587228i	$0.199781\pi$
$132$		0			0
$133$	12.9957	−	2.20502i	1.12687	−	0.191200i
$134$	−3.60537	+	11.4765i	−0.311457	+	0.991420i
$135$		0			0
$136$	−2.15672	−	0.885443i	−0.184937	−	0.0759261i
$137$	−2.58499	+	1.49245i	−0.220851	+	0.127508i	−0.606344	−	0.795202i	$-0.707365\pi$
$137$	−2.58499	+	1.49245i	−0.220851	+	0.127508i	0.385493	+	0.922711i	$0.374031\pi$
$138$		0			0
$139$		−	11.6534i		−	0.988427i	−0.869340	−	0.494214i	$-0.835456\pi$
$139$		−	11.6534i		−	0.988427i	0.869340	−	0.494214i	$-0.164544\pi$
$140$	−0.422507	−	5.08538i	−0.0357084	−	0.429793i
$141$		0			0
$142$	7.42164	−	6.81494i	0.622811	−	0.571897i
$143$	−4.35443	−	7.54210i	−0.364136	−	0.630702i
$144$		0			0
$145$	−3.71871	+	6.44100i	−0.308822	+	0.534896i
$146$	−15.7743	−	4.95553i	−1.30549	−	0.410122i
$147$		0			0
$148$	−8.07430	−	5.62861i	−0.663703	−	0.462669i
$149$	−10.3895	−	5.99838i	−0.851142	−	0.491407i	0.00989432	−	0.999951i	$-0.496850\pi$
$149$	−10.3895	−	5.99838i	−0.851142	−	0.491407i	−0.861036	+	0.508544i	$0.830184\pi$
$150$		0			0
$151$	−9.42801	+	5.44327i	−0.767241	+	0.442967i	−0.831889	−	0.554941i	$-0.812741\pi$
$151$	−9.42801	+	5.44327i	−0.767241	+	0.442967i	0.0646486	+	0.997908i	$0.479407\pi$
$152$	1.88304	+	13.9652i	0.152735	+	1.13273i
$153$		0			0
$154$	−11.3068	+	4.61181i	−0.911125	+	0.371631i
$155$	7.78009			0.624912
$156$		0			0
$157$	−3.33931	−	5.78386i	−0.266506	−	0.461602i	0.701451	−	0.712718i	$-0.252536\pi$
$157$	−3.33931	−	5.78386i	−0.266506	−	0.461602i	−0.967957	+	0.251115i	$0.919203\pi$
$158$	−5.23058	+	1.16532i	−0.416122	+	0.0927077i
$159$		0			0
$160$	5.44872	−	0.266381i	0.430759	−	0.0210593i
$161$	−3.61637	−	21.3138i	−0.285010	−	1.67976i
$162$		0			0
$163$	1.41872	+	0.819098i	0.111123	+	0.0641567i	0.554531	−	0.832163i	$-0.312898\pi$
$163$	1.41872	+	0.819098i	0.111123	+	0.0641567i	−0.443409	+	0.896320i	$0.646231\pi$
$164$	10.6624	+	0.910425i	0.832595	+	0.0710923i
$165$		0			0
$166$	−0.0702957	+	0.0645492i	−0.00545601	+	0.00500999i
$167$	−22.9045			−1.77240			−0.886201	−	0.463302i	$-0.846665\pi$
$167$	−22.9045			−1.77240			−0.886201	+	0.463302i	$0.846665\pi$
$168$		0			0
$169$	−5.87903			−0.452233
$170$	0.828019	−	0.760330i	0.0635062	−	0.0583147i
$171$		0			0
$172$	16.1222	+	1.37662i	1.22931	+	0.104966i
$173$	19.6628	+	11.3524i	1.49494	+	0.863103i	0.999983	−	0.00581508i	$-0.00185101\pi$
$173$	19.6628	+	11.3524i	1.49494	+	0.863103i	0.494956	+	0.868918i	$0.335184\pi$
$174$		0			0
$175$	−10.0948	−	3.74826i	−0.763098	−	0.283341i
$176$	−4.51597	−	12.2482i	−0.340404	−	0.923246i
$177$		0			0
$178$	21.9070	−	4.88064i	1.64200	−	0.365819i
$179$	2.13289	+	3.69428i	0.159420	+	0.276123i	0.934660	−	0.355544i	$-0.115704\pi$
$179$	2.13289	+	3.69428i	0.159420	+	0.276123i	−0.775240	+	0.631667i	$0.782371\pi$
$180$		0			0
$181$	−19.8046			−1.47206			−0.736032	−	0.676947i	$-0.763303\pi$
$181$	−19.8046			−1.47206			−0.736032	+	0.676947i	$0.763303\pi$
$182$	1.35687	−	9.89204i	0.100578	−	0.733247i
$183$		0			0
$184$	22.9038	−	3.08830i	1.68849	−	0.227672i
$185$	4.11004	−	2.37293i	0.302176	−	0.174461i
$186$		0			0
$187$	−2.32967	−	1.34504i	−0.170363	−	0.0983588i
$188$	2.98776	+	2.08278i	0.217905	+	0.151902i
$189$		0			0
$190$	−6.48232	−	2.03643i	−0.470277	−	0.147738i
$191$	9.06556	−	15.7020i	0.655961	−	1.13616i	−0.325691	−	0.945476i	$-0.605597\pi$
$191$	9.06556	−	15.7020i	0.655961	−	1.13616i	0.981652	−	0.190681i	$-0.0610697\pi$
$192$		0			0
$193$	−11.9282	−	20.6602i	−0.858610	−	1.48716i	−0.873255	−	0.487263i	$-0.837995\pi$
$193$	−11.9282	−	20.6602i	−0.858610	−	1.48716i	0.0146458	−	0.999893i	$-0.495338\pi$
$194$	−7.72297	+	7.09164i	−0.554477	+	0.509150i
$195$		0			0
$196$	−13.4829	−	3.76977i	−0.963065	−	0.269269i
$197$		−	17.9765i		−	1.28077i	−0.768052	−	0.640387i	$-0.778774\pi$
$197$		−	17.9765i		−	1.28077i	0.768052	−	0.640387i	$-0.221226\pi$
$198$		0			0
$199$	3.86082	−	2.22904i	0.273686	−	0.158013i	−0.356876	−	0.934152i	$-0.616158\pi$
$199$	3.86082	−	2.22904i	0.273686	−	0.158013i	0.630562	+	0.776139i	$0.282825\pi$
$200$	4.37204	−	10.6492i	0.309150	−	0.753012i
$201$		0			0
$202$	0.918367	−	2.92332i	0.0646161	−	0.205684i
$203$	13.0147	+	15.7155i	0.913456	+	1.10301i
$204$		0			0
$205$	−2.57995	+	4.46860i	−0.180191	+	0.312101i
$206$	−24.3761	+	5.43075i	−1.69837	+	0.378378i
$207$		0			0
$208$	10.5195	+	1.80965i	0.729399	+	0.125476i
$209$			16.2595i			1.12469i
$210$		0			0
$211$		−	1.53384i		−	0.105594i	−0.998605	−	0.0527970i	$-0.983186\pi$
$211$		−	1.53384i		−	0.105594i	0.998605	−	0.0527970i	$-0.0168136\pi$
$212$	−7.25309	−	15.4699i	−0.498144	−	1.06248i
$213$		0			0
$214$	−1.09330	−	4.90730i	−0.0747362	−	0.335456i
$215$	−3.90104	+	6.75679i	−0.266048	+	0.460809i
$216$		0			0
$217$	7.42985	−	20.0101i	0.504371	−	1.35838i
$218$	3.75722	+	1.18034i	0.254471	+	0.0799426i
$219$		0			0
$220$	6.27166	+	0.535515i	0.422835	+	0.0361044i
$221$	1.90490	−	1.09979i	0.128137	−	0.0739802i
$222$		0			0
$223$		−	0.996362i		−	0.0667213i	−0.999443	−	0.0333607i	$-0.989379\pi$
$223$		−	0.996362i		−	0.0667213i	0.999443	−	0.0333607i	$-0.0106210\pi$
$224$	4.51831	−	14.2683i	0.301892	−	0.953342i
$225$		0			0
$226$	−2.96236	−	3.22608i	−0.197053	−	0.214596i
$227$	−14.2085	−	24.6099i	−0.943053	−	1.63342i	−0.759603	−	0.650387i	$-0.774607\pi$
$227$	−14.2085	−	24.6099i	−0.943053	−	1.63342i	−0.183450	−	0.983029i	$-0.558727\pi$
$228$		0			0
$229$	−13.5125	+	23.4043i	−0.892932	+	1.54660i	−0.0565877	+	0.998398i	$0.518022\pi$
$229$	−13.5125	+	23.4043i	−0.892932	+	1.54660i	−0.836344	+	0.548205i	$0.815311\pi$
$230$	−3.33987	+	10.6314i	−0.220224	+	0.701012i
$231$		0			0
$232$	−17.2643	+	13.3335i	−1.13346	+	0.875384i
$233$	−15.9500	−	9.20872i	−1.04492	−	0.603283i	−0.123695	−	0.992320i	$-0.539475\pi$
$233$	−15.9500	−	9.20872i	−1.04492	−	0.603283i	−0.921222	+	0.389037i	$0.872808\pi$
$234$		0			0
$235$	−1.52085	+	0.878065i	−0.0992095	+	0.0572787i
$236$	0.862827	−	0.404537i	0.0561653	−	0.0263331i
$237$		0			0
$238$	−1.16480	−	2.85574i	−0.0755028	−	0.185110i
$239$	−0.547163			−0.0353930			−0.0176965	−	0.999843i	$-0.505633\pi$
$239$	−0.547163			−0.0353930			−0.0176965	+	0.999843i	$0.505633\pi$
$240$		0			0
$241$	5.94128	+	10.2906i	0.382712	+	0.662876i	0.991449	−	0.130496i	$-0.0416569\pi$
$241$	5.94128	+	10.2906i	0.382712	+	0.662876i	−0.608737	+	0.793372i	$0.708324\pi$
$242$	0.107376	+	0.481962i	0.00690240	+	0.0309817i
$243$		0			0
$244$	6.87066	+	4.78955i	0.439849	+	0.306620i
$245$	4.40559	−	5.11469i	0.281463	−	0.326765i
$246$		0			0
$247$	−11.5137	−	6.64744i	−0.732600	−	0.422967i
$248$	21.1090	+	8.66633i	1.34042	+	0.550313i
$249$		0			0
$250$	8.36639	+	9.11121i	0.529137	+	0.576244i
$251$	−20.1885			−1.27429			−0.637143	−	0.770746i	$-0.719884\pi$
$251$	−20.1885			−1.27429			−0.637143	+	0.770746i	$0.719884\pi$
$252$		0			0
$253$	26.6665			1.67651
$254$	0.294766	+	0.321008i	0.0184953	+	0.0201418i
$255$		0			0
$256$	15.0802	+	5.34664i	0.942515	+	0.334165i
$257$	−7.44631	−	4.29913i	−0.464488	−	0.268172i	0.249442	−	0.968390i	$-0.419753\pi$
$257$	−7.44631	−	4.29913i	−0.464488	−	0.268172i	−0.713929	+	0.700218i	$0.753086\pi$
$258$		0			0
$259$	−2.17809	−	12.8370i	−0.135340	−	0.797651i
$260$	−2.94328	+	4.22216i	−0.182534	+	0.261847i
$261$		0			0
$262$	−0.731030	−	3.28126i	−0.0451632	−	0.202717i
$263$	8.76014	+	15.1730i	0.540173	+	0.935607i	0.998894	+	0.0470268i	$0.0149746\pi$
$263$	8.76014	+	15.1730i	0.540173	+	0.935607i	−0.458720	+	0.888581i	$0.651692\pi$
$264$		0			0
$265$	8.23844			0.506083
$266$	−11.4281	+	14.7275i	−0.700704	+	0.903004i
$267$		0			0
$268$	−7.22186	−	15.4033i	−0.441145	−	0.940909i
$269$	−6.65653	+	3.84315i	−0.405856	+	0.234321i	−0.689008	−	0.724754i	$-0.741953\pi$
$269$	−6.65653	+	3.84315i	−0.405856	+	0.234321i	0.283152	+	0.959075i	$0.408620\pi$
$270$		0			0
$271$	−20.4624	−	11.8140i	−1.24300	−	0.717649i	−0.273300	−	0.961929i	$-0.588115\pi$
$271$	−20.4624	−	11.8140i	−1.24300	−	0.717649i	−0.969705	+	0.244280i	$0.921448\pi$
$272$	3.09353	−	1.14059i	0.187573	−	0.0691587i
$273$		0			0
$274$	1.26516	−	4.02722i	0.0764312	−	0.243294i
$275$	6.64138	−	11.5032i	0.400490	−	0.693669i
$276$		0			0
$277$	−11.9596	−	20.7147i	−0.718584	−	1.24462i	−0.961561	−	0.274592i	$-0.911457\pi$
$277$	−11.9596	−	20.7147i	−0.718584	−	1.24462i	0.242977	−	0.970032i	$-0.421876\pi$
$278$	11.1467	+	12.1390i	0.668532	+	0.728048i
$279$		0			0
$280$	5.30436	+	4.89315i	0.316996	+	0.292422i
$281$		−	2.87579i		−	0.171555i	−0.996314	−	0.0857777i	$-0.972663\pi$
$281$		−	2.87579i		−	0.171555i	0.996314	−	0.0857777i	$-0.0273375\pi$
$282$		0			0
$283$	−10.2157	+	5.89802i	−0.607258	+	0.350601i	−0.771892	−	0.635754i	$-0.780689\pi$
$283$	−10.2157	+	5.89802i	−0.607258	+	0.350601i	0.164633	+	0.986355i	$0.447356\pi$
$284$	−1.21230	+	14.1978i	−0.0719370	+	0.842487i
$285$		0			0
$286$	11.7500	+	3.69129i	0.694793	+	0.218271i
$287$	9.02929	+	10.9030i	0.532982	+	0.643582i
$288$		0			0
$289$	−8.16029	+	14.1340i	−0.480017	+	0.831413i
$290$	−2.28725	−	10.2664i	−0.134312	−	0.602864i
$291$		0			0
$292$	21.1716	−	9.92633i	1.23898	−	0.580895i
$293$			29.0652i			1.69801i	0.528387	+	0.849003i	$0.322797\pi$
$293$			29.0652i			1.69801i	−0.528387	+	0.849003i	$0.677203\pi$
$294$		0			0
$295$			0.459494i			0.0267528i
$296$	13.7946	−	1.86004i	0.801795	−	0.108113i
$297$		0			0
$298$	16.5600	−	3.68939i	0.959295	−	0.213721i
$299$	−10.9022	+	18.8831i	−0.630490	+	1.09204i
$300$		0			0
$301$	13.6528	+	16.4859i	0.786936	+	0.950234i
$302$	4.61431	−	14.6881i	0.265524	−	0.845207i
$303$		0			0
$304$	−15.3195	−	12.7460i	−0.878632	−	0.731033i
$305$	−3.49735	+	2.01920i	−0.200258	+	0.115619i
$306$		0			0
$307$			30.4085i			1.73551i	0.496995	+	0.867754i	$0.334437\pi$
$307$			30.4085i			1.73551i	−0.496995	+	0.867754i	$0.665563\pi$
$308$	7.36665	−	15.6191i	0.419754	−	0.889981i
$309$		0			0
$310$	−8.10429	+	7.44179i	−0.460293	+	0.422665i
$311$	12.8735	+	22.2975i	0.729988	+	1.26438i	0.956888	+	0.290458i	$0.0938077\pi$
$311$	12.8735	+	22.2975i	0.729988	+	1.26438i	−0.226900	+	0.973918i	$0.572859\pi$
$312$		0			0
$313$	−14.5546	+	25.2092i	−0.822673	+	1.42491i	0.0810126	+	0.996713i	$0.474185\pi$
$313$	−14.5546	+	25.2092i	−0.822673	+	1.42491i	−0.903685	+	0.428198i	$0.859149\pi$
$314$	9.01082	+	2.83077i	0.508510	+	0.159750i
$315$		0			0
$316$	4.33389	−	6.21701i	0.243800	−	0.349734i
$317$	23.3028	+	13.4539i	1.30881	+	0.755644i	0.981898	−	0.189410i	$-0.0606576\pi$
$317$	23.3028	+	13.4539i	1.30881	+	0.755644i	0.326915	+	0.945054i	$0.393991\pi$
$318$		0			0
$319$	−21.7975	+	12.5848i	−1.22043	+	0.704615i
$320$	−5.42097	+	5.48927i	−0.303042	+	0.306860i
$321$		0			0
$322$	24.1540	+	18.7428i	1.34605	+	1.04450i
$323$	−4.10665			−0.228500
$324$		0			0
$325$	5.43045	+	9.40581i	0.301227	+	0.521740i
$326$	−2.26132	+	0.503798i	−0.125243	+	0.0279028i
$327$		0			0
$328$	−11.9776	+	9.25041i	−0.661350	+	0.510768i
$329$	0.805967	+	4.75012i	0.0444344	+	0.261883i
$330$		0			0
$331$	−13.1236	−	7.57689i	−0.721336	−	0.416464i	0.0939082	−	0.995581i	$-0.470064\pi$
$331$	−13.1236	−	7.57689i	−0.721336	−	0.416464i	−0.815244	+	0.579117i	$0.803397\pi$
$332$	0.0114826	−	0.134478i	0.000630189	−	0.00738044i
$333$		0			0
$334$	23.8589	−	21.9085i	1.30550	−	1.19878i
$335$	8.20296			0.448176
$336$		0			0
$337$	16.6582			0.907429			0.453715	−	0.891147i	$-0.350099\pi$
$337$	16.6582			0.907429			0.453715	+	0.891147i	$0.350099\pi$
$338$	6.12401	−	5.62339i	0.333103	−	0.305872i
$339$		0			0
$340$	−0.135254	+	1.58403i	−0.00733520	+	0.0859059i
$341$	22.8018	+	13.1646i	1.23479	+	0.712905i
$342$		0			0
$343$	−8.94754	−	16.2155i	−0.483122	−	0.875553i
$344$	−18.1108	+	13.9872i	−0.976468	+	0.754138i
$345$		0			0
$346$	−31.3409	+	6.98243i	−1.68490	+	0.375378i
$347$	−10.2420	−	17.7397i	−0.549822	−	0.952319i	−0.998286	−	0.0585187i	$-0.981362\pi$
$347$	−10.2420	−	17.7397i	−0.549822	−	0.952319i	0.448464	−	0.893801i	$-0.351971\pi$
$348$		0			0
$349$	−6.97866			−0.373559			−0.186780	−	0.982402i	$-0.559805\pi$
$349$	−6.97866			−0.373559			−0.186780	+	0.982402i	$0.559805\pi$
$350$	14.1008	−	5.75143i	0.753717	−	0.307427i
$351$		0			0
$352$	16.4198	+	8.43903i	0.875178	+	0.449802i
$353$	−25.7521	+	14.8680i	−1.37064	+	0.791342i	−0.991009	−	0.133794i	$-0.957284\pi$
$353$	−25.7521	+	14.8680i	−1.37064	+	0.791342i	−0.379635	+	0.925136i	$0.623951\pi$
$354$		0			0
$355$	−5.95029	−	3.43540i	−0.315809	−	0.182332i
$356$	−18.1514	+	26.0384i	−0.962023	+	1.38003i
$357$		0			0
$358$	−5.75541	−	1.80807i	−0.304183	−	0.0955597i
$359$	1.93429	−	3.35029i	0.102088	−	0.176821i	−0.810457	−	0.585798i	$-0.800781\pi$
$359$	1.93429	−	3.35029i	0.102088	−	0.176821i	0.912545	+	0.408977i	$0.134114\pi$
$360$		0			0
$361$	2.91082	+	5.04169i	0.153201	+	0.265352i
$362$	20.6298	−	18.9434i	1.08428	−	0.995643i
$363$		0			0
$364$	8.04848	+	11.6021i	0.421855	+	0.608116i
$365$			11.2748i			0.590152i
$366$		0			0
$367$	−11.5077	+	6.64395i	−0.600695	+	0.346811i	−0.769315	−	0.638870i	$-0.779402\pi$
$367$	−11.5077	+	6.64395i	−0.600695	+	0.346811i	0.168620	+	0.985681i	$0.446069\pi$
$368$	−20.9042	+	25.1248i	−1.08970	+	1.30972i
$369$		0			0
$370$	−2.01156	+	6.40313i	−0.104576	+	0.332883i
$371$	7.86756	−	21.1890i	0.408463	−	1.10008i
$372$		0			0
$373$	−0.708016	+	1.22632i	−0.0366597	+	0.0634964i	−0.883773	−	0.467916i	$-0.845005\pi$
$373$	−0.708016	+	1.22632i	−0.0366597	+	0.0634964i	0.847113	+	0.531412i	$0.178338\pi$
$374$	3.71330	−	0.827284i	0.192010	−	0.0427778i
$375$		0			0
$376$	−5.10448	+	0.688278i	−0.263243	+	0.0354952i
$377$		−	20.5804i		−	1.05995i
$378$		0			0
$379$		−	32.9449i		−	1.69227i	−0.532972	−	0.846133i	$-0.678925\pi$
$379$		−	32.9449i		−	1.69227i	0.532972	−	0.846133i	$-0.321075\pi$
$380$	8.70032	−	4.07915i	0.446317	−	0.209256i
$381$		0			0
$382$	5.57590	+	25.0277i	0.285288	+	1.28053i
$383$	18.6554	−	32.3121i	0.953245	−	1.65107i	0.214911	−	0.976634i	$-0.431054\pi$
$383$	18.6554	−	32.3121i	0.953245	−	1.65107i	0.738334	−	0.674435i	$-0.235613\pi$
$384$		0			0
$385$	5.31105	+	6.41316i	0.270676	+	0.326845i
$386$	32.1871	+	10.1116i	1.63828	+	0.514669i
$387$		0			0
$388$	1.26152	−	14.7743i	0.0640442	−	0.750051i
$389$	14.4005	−	8.31416i	0.730136	−	0.421545i	−0.0883356	−	0.996091i	$-0.528155\pi$
$389$	14.4005	−	8.31416i	0.730136	−	0.421545i	0.818472	+	0.574546i	$0.194821\pi$
$390$		0			0
$391$			6.73514i			0.340611i
$392$	17.6506	−	8.96976i	0.891489	−	0.453041i
$393$		0			0
$394$	17.1948	+	18.7256i	0.866264	+	0.943383i
$395$	1.82710	+	3.16463i	0.0919313	+	0.159230i
$396$		0			0
$397$	4.47847	−	7.75695i	0.224768	−	0.389310i	−0.731482	−	0.681861i	$-0.761171\pi$
$397$	4.47847	−	7.75695i	0.224768	−	0.389310i	0.956250	+	0.292551i	$0.0945042\pi$
$398$	−1.88958	+	6.01486i	−0.0947161	+	0.301498i
$399$		0			0
$400$	5.63190	+	15.2749i	0.281595	+	0.763744i
$401$	−13.8311	−	7.98541i	−0.690694	−	0.398772i	0.113178	−	0.993575i	$-0.463897\pi$
$401$	−13.8311	−	7.98541i	−0.690694	−	0.398772i	−0.803872	+	0.594802i	$0.797230\pi$
$402$		0			0
$403$	−18.6443	+	10.7643i	−0.928741	+	0.536209i
$404$	1.83957	+	3.92357i	0.0915218	+	0.195205i
$405$		0			0
$406$	−28.5891	−	3.92151i	−1.41886	−	0.194621i
$407$	16.0609			0.796108
$408$		0			0
$409$	11.5816	+	20.0600i	0.572674	+	0.991901i	0.996290	+	0.0860589i	$0.0274273\pi$
$409$	11.5816	+	20.0600i	0.572674	+	0.991901i	−0.423616	+	0.905842i	$0.639239\pi$
$410$	−1.58683	−	7.12257i	−0.0783681	−	0.351759i
$411$		0			0
$412$	20.1973	−	28.9732i	0.995050	−	1.42741i
$413$	1.18180	+	0.438809i	0.0581527	+	0.0215924i
$414$		0			0
$415$	0.0563595	+	0.0325392i	0.00276658	+	0.00159729i
$416$	−12.6888	+	8.17705i	−0.622122	+	0.400913i
$417$		0			0
$418$	−15.5525	−	16.9370i	−0.760697	−	0.828418i
$419$	8.76342			0.428121			0.214061	−	0.976820i	$-0.431331\pi$
$419$	8.76342			0.428121			0.214061	+	0.976820i	$0.431331\pi$
$420$		0			0
$421$	15.2524			0.743356			0.371678	−	0.928362i	$-0.378782\pi$
$421$	15.2524			0.743356			0.371678	+	0.928362i	$0.378782\pi$
$422$	1.46714	+	1.59776i	0.0714195	+	0.0777776i
$423$		0			0
$424$	22.3526	+	9.17688i	1.08554	+	0.445669i
$425$	2.90535	+	1.67741i	0.140930	+	0.0813661i
$426$		0			0
$427$	1.85340	+	10.9234i	0.0896922	+	0.528619i
$428$	5.83277	+	4.06604i	0.281938	+	0.196539i
$429$		0			0
$430$	−2.39939	−	10.7698i	−0.115709	−	0.519364i
$431$	1.89646	+	3.28476i	0.0913492	+	0.158221i	0.908079	−	0.418799i	$-0.137549\pi$
$431$	1.89646	+	3.28476i	0.0913492	+	0.158221i	−0.816730	+	0.577020i	$0.804215\pi$
$432$		0			0
$433$	−39.7504			−1.91028			−0.955142	−	0.296147i	$-0.904298\pi$
$433$	−39.7504			−1.91028			−0.955142	+	0.296147i	$0.904298\pi$
$434$	11.4006	+	27.9507i	0.547245	+	1.34168i
$435$		0			0
$436$	−5.04280	+	2.36432i	−0.241506	+	0.113230i
$437$	35.2550	−	20.3545i	1.68647	−	0.973686i
$438$		0			0
$439$	0.349336	+	0.201689i	0.0166729	+	0.00962611i	0.508313	−	0.861172i	$-0.330269\pi$
$439$	0.349336	+	0.201689i	0.0166729	+	0.00962611i	−0.491640	+	0.870798i	$0.663603\pi$
$440$	−7.04523	+	5.44112i	−0.335868	+	0.259395i
$441$		0			0
$442$	−0.932306	+	2.96769i	−0.0443453	+	0.141159i
$443$	2.07536	−	3.59463i	0.0986032	−	0.170786i	−0.812504	−	0.582956i	$-0.801896\pi$
$443$	2.07536	−	3.59463i	0.0986032	−	0.170786i	0.911107	+	0.412171i	$0.135229\pi$
$444$		0			0
$445$	−7.65234	−	13.2542i	−0.362756	−	0.628311i
$446$	0.953036	+	1.03788i	0.0451276	+	0.0491451i
$447$		0			0
$448$	8.94129	+	19.1847i	0.422436	+	0.906393i
$449$			21.3129i			1.00582i	0.864339	+	0.502910i	$0.167737\pi$
$449$			21.3129i			1.00582i	−0.864339	+	0.502910i	$0.832263\pi$
$450$		0			0
$451$	−15.1226	+	8.73102i	−0.712094	+	0.411128i
$452$	6.17160	+	0.526971i	0.290288	+	0.0247866i
$453$		0			0
$454$	38.3404	+	12.0447i	1.79940	+	0.565286i
$455$	−6.71264	+	1.13895i	−0.314693	+	0.0533949i
$456$		0			0
$457$	9.15571	−	15.8582i	0.428286	−	0.741813i	−0.568435	−	0.822728i	$-0.692451\pi$
$457$	9.15571	−	15.8582i	0.428286	−	0.741813i	0.996721	+	0.0809150i	$0.0257842\pi$
$458$	−8.31106	−	37.3045i	−0.388350	−	1.74313i
$459$		0			0
$460$	−6.69004	−	14.2690i	−0.311925	−	0.665297i
$461$			13.5275i			0.630040i	0.949085	+	0.315020i	$0.102011\pi$
$461$			13.5275i			0.630040i	−0.949085	+	0.315020i	$0.897989\pi$
$462$		0			0
$463$			11.7296i			0.545121i	0.962139	+	0.272560i	$0.0878704\pi$
$463$			11.7296i			0.545121i	−0.962139	+	0.272560i	$0.912130\pi$
$464$	5.23009	−	30.4027i	0.242801	−	1.41141i
$465$		0			0
$466$	25.4229	−	5.66396i	1.17769	−	0.262378i
$467$	2.64703	−	4.58479i	0.122490	−	0.212159i	−0.798259	−	0.602314i	$-0.794245\pi$
$467$	2.64703	−	4.58479i	0.122490	−	0.212159i	0.920749	+	0.390155i	$0.127579\pi$
$468$		0			0
$469$	7.83368	−	21.0978i	0.361726	−	0.974204i
$470$	0.744344	−	2.36938i	0.0343340	−	0.109291i
$471$		0			0
$472$	−0.511835	+	1.24670i	−0.0235591	+	0.0573841i
$473$	−22.8662	+	13.2018i	−1.05139	+	0.607021i
$474$		0			0
$475$		−	20.2774i		−	0.930389i
$476$	3.94490	+	1.86059i	0.180814	+	0.0852799i
$477$		0			0
$478$	0.569963	−	0.523370i	0.0260695	−	0.0239384i
$479$	−1.19209	−	2.06475i	−0.0544678	−	0.0943410i	0.837506	−	0.546428i	$-0.184013\pi$
$479$	−1.19209	−	2.06475i	−0.0544678	−	0.0943410i	−0.891974	+	0.452087i	$0.850680\pi$
$480$		0			0
$481$	−6.56624	+	11.3731i	−0.299395	+	0.518567i
$482$	−16.0320	−	5.03648i	−0.730237	−	0.229406i
$483$		0			0
$484$	−0.572855	−	0.399339i	−0.0260389	−	0.0181518i
$485$	6.19189	+	3.57489i	0.281159	+	0.162327i
$486$		0			0
$487$	20.7730	−	11.9933i	0.941314	−	0.543468i	0.0509423	−	0.998702i	$-0.483778\pi$
$487$	20.7730	−	11.9933i	0.941314	−	0.543468i	0.890372	+	0.455233i	$0.150444\pi$
$488$	−11.7382	+	1.58276i	−0.531365	+	0.0716482i
$489$		0			0
$490$	0.303103	+	9.54184i	0.0136928	+	0.431056i
$491$	−19.8907			−0.897654			−0.448827	−	0.893619i	$-0.648158\pi$
$491$	−19.8907			−0.897654			−0.448827	+	0.893619i	$0.648158\pi$
$492$		0			0
$493$	−3.17854	−	5.50538i	−0.143154	−	0.247950i
$494$	18.3519	−	4.08861i	0.825690	−	0.183955i
$495$		0			0
$496$	−30.2781	+	11.1636i	−1.35953	+	0.501263i
$497$	−14.5182	+	12.0232i	−0.651229	+	0.539315i
$498$		0			0
$499$	−7.70480	−	4.44837i	−0.344914	−	0.199136i	0.317529	−	0.948249i	$-0.397147\pi$
$499$	−7.70480	−	4.44837i	−0.344914	−	0.199136i	−0.662443	+	0.749112i	$0.730480\pi$
$500$	−17.4300	−	1.48829i	−0.779495	−	0.0665583i
$501$		0			0
$502$	21.0297	−	19.3106i	0.938604	−	0.861875i
$503$	21.6446			0.965086			0.482543	−	0.875872i	$-0.339713\pi$
$503$	21.6446			0.965086			0.482543	+	0.875872i	$0.339713\pi$
$504$		0			0
$505$	−2.08947			−0.0929804
$506$	−27.7777	+	25.5070i	−1.23487	+	1.13392i
$507$		0			0
$508$	−0.614098	−	0.0524357i	−0.0272462	−	0.00232646i
$509$	17.7650	+	10.2566i	0.787421	+	0.454618i	0.839054	−	0.544048i	$-0.183109\pi$
$509$	17.7650	+	10.2566i	0.787421	+	0.454618i	−0.0516327	+	0.998666i	$0.516443\pi$
$510$		0			0
$511$	28.9985	+	10.7673i	1.28282	+	0.476316i
$512$	−20.8228	+	8.85505i	−0.920246	+	0.391342i
$513$		0			0
$514$	11.8688	−	2.64424i	0.523509	−	0.116632i
$515$	8.51485	+	14.7482i	0.375209	+	0.649882i
$516$		0			0
$517$	−5.94307			−0.261376
$518$	14.5476	+	11.2885i	0.639186	+	0.495989i
$519$		0			0
$520$	−0.972640	−	7.21340i	−0.0426531	−	0.316328i
$521$	−13.5376	+	7.81591i	−0.593091	+	0.342421i	−0.766319	−	0.642460i	$-0.777914\pi$
$521$	−13.5376	+	7.81591i	−0.593091	+	0.342421i	0.173228	+	0.984882i	$0.444580\pi$
$522$		0			0
$523$	22.5412	+	13.0142i	0.985657	+	0.569069i	0.903973	−	0.427589i	$-0.140637\pi$
$523$	22.5412	+	13.0142i	0.985657	+	0.569069i	0.0816838	+	0.996658i	$0.473970\pi$
$524$	3.90007	+	2.71875i	0.170375	+	0.118769i
$525$		0			0
$526$	−23.6384	−	7.42605i	−1.03068	−	0.323791i
$527$	−3.32498	+	5.75903i	−0.144838	+	0.250867i
$528$		0			0
$529$	−21.8825	−	37.9016i	−0.951412	−	1.64789i
$530$	−8.58174	+	7.88020i	−0.372767	+	0.342294i
$531$		0			0
$532$	−2.18279	−	26.2724i	−0.0946358	−	1.13906i
$533$		−	14.2782i		−	0.618456i
$534$		0			0
$535$	−2.96904	+	1.71417i	−0.128363	+	0.0741102i
$536$	22.2563	+	9.13737i	0.961328	+	0.394674i
$537$		0			0
$538$	3.25788	−	10.3704i	0.140457	−	0.447099i
$539$	21.5664	−	7.53540i	0.928930	−	0.324573i
$540$		0			0
$541$	−18.0968	+	31.3446i	−0.778044	+	1.34761i	0.155024	+	0.987911i	$0.450455\pi$
$541$	−18.0968	+	31.3446i	−0.778044	+	1.34761i	−0.933068	+	0.359701i	$0.882879\pi$
$542$	32.6154	−	7.26637i	1.40095	−	0.312117i
$543$		0			0
$544$	−2.13144	+	4.14713i	−0.0913847	+	0.177807i
$545$		−	2.68551i		−	0.115035i
$546$		0			0
$547$		−	32.5689i		−	1.39255i	−0.717777	−	0.696273i	$-0.754840\pi$
$547$		−	32.5689i		−	1.39255i	0.717777	−	0.696273i	$-0.245160\pi$
$548$	2.53422	+	5.40519i	0.108257	+	0.230898i
$549$		0			0
$550$	4.08487	+	18.3351i	0.174180	+	0.781812i
$551$	−19.2119	+	33.2760i	−0.818454	+	1.41760i
$552$		0			0
$553$	9.88416	−	1.67707i	0.420317	−	0.0713164i
$554$	32.2719	+	10.1383i	1.37110	+	0.430735i
$555$		0			0
$556$	−23.2223	−	1.98287i	−0.984844	−	0.0840923i
$557$	15.6704	−	9.04732i	0.663977	−	0.383347i	−0.129814	−	0.991538i	$-0.541438\pi$
$557$	15.6704	−	9.04732i	0.663977	−	0.383347i	0.793791	+	0.608191i	$0.208105\pi$
$558$		0			0
$559$		−	21.5894i		−	0.913136i
$560$	−10.2058	−	0.0233456i	−0.431273	−	0.000986532i
$561$		0			0
$562$	2.75074	+	2.99563i	0.116033	+	0.126363i
$563$	9.24225	+	16.0081i	0.389515	+	0.674659i	0.992384	−	0.123181i	$-0.0393094\pi$
$563$	9.24225	+	16.0081i	0.389515	+	0.674659i	−0.602870	+	0.797840i	$0.705976\pi$
$564$		0			0
$565$	−1.49332	+	2.58651i	−0.0628245	+	0.108815i
$566$	4.99980	−	15.9152i	0.210157	−	0.668967i
$567$		0			0
$568$	−12.3176	−	15.9491i	−0.516837	−	0.669208i
$569$	−38.6356	−	22.3063i	−1.61969	−	0.935127i	−0.987000	−	0.160719i	$-0.948619\pi$
$569$	−38.6356	−	22.3063i	−1.61969	−	0.935127i	−0.632687	−	0.774407i	$-0.718048\pi$
$570$		0			0
$571$	−22.2316	+	12.8354i	−0.930363	+	0.537145i	−0.886926	−	0.461911i	$-0.847164\pi$
$571$	−22.2316	+	12.8354i	−0.930363	+	0.537145i	−0.0434368	+	0.999056i	$0.513831\pi$
$572$	−15.7704	+	7.39397i	−0.659395	+	0.309158i
$573$		0			0
$574$	−19.8344	−	2.72064i	−0.827872	−	0.113557i
$575$	−33.2560			−1.38687
$576$		0			0
$577$	−12.0417	−	20.8568i	−0.501302	−	0.868281i	−0.999999	−	0.00150416i	$-0.999521\pi$
$577$	−12.0417	−	20.8568i	−0.501302	−	0.868281i	0.498697	−	0.866777i	$-0.333812\pi$
$578$	−5.01910	−	22.5284i	−0.208767	−	0.937060i
$579$		0			0
$580$	12.2025	+	8.50642i	0.506683	+	0.353210i
$581$	0.137512	−	0.113880i	0.00570496	−	0.00472456i
$582$		0			0
$583$	24.1451	+	13.9402i	0.999989	+	0.577344i
$584$	−12.5592	+	30.5910i	−0.519702	+	1.26586i
$585$		0			0
$586$	−27.8013	−	30.2764i	−1.14846	−	1.25070i
$587$	−13.1811			−0.544044			−0.272022	−	0.962291i	$-0.587692\pi$
$587$	−13.1811			−0.544044			−0.272022	+	0.962291i	$0.587692\pi$
$588$		0			0
$589$	40.1941			1.65617
$590$	−0.439513	−	0.478641i	−0.0180945	−	0.0197053i
$591$		0			0
$592$	−12.5903	+	15.1323i	−0.517457	+	0.621934i
$593$	−13.8913	−	8.02017i	−0.570449	−	0.329349i	0.186879	−	0.982383i	$-0.440163\pi$
$593$	−13.8913	−	8.02017i	−0.570449	−	0.329349i	−0.757329	+	0.653034i	$0.773496\pi$
$594$		0			0
$595$	−1.61977	+	1.34141i	−0.0664039	+	0.0549923i
$596$	−13.7211	+	19.6830i	−0.562038	+	0.806248i
$597$		0			0
$598$	−6.70555	−	30.0981i	−0.274210	−	1.23080i
$599$	2.93188	+	5.07816i	0.119793	+	0.207488i	0.919686	−	0.392655i	$-0.128444\pi$
$599$	2.93188	+	5.07816i	0.119793	+	0.207488i	−0.799892	+	0.600143i	$0.795110\pi$
$600$		0			0
$601$	−6.63145			−0.270503			−0.135251	−	0.990811i	$-0.543184\pi$
$601$	−6.63145			−0.270503			−0.135251	+	0.990811i	$0.543184\pi$
$602$	−29.9908	−	4.11378i	−1.22233	−	0.167665i
$603$		0			0
$604$	9.24285	+	19.7139i	0.376086	+	0.802145i
$605$	0.291599	−	0.168355i	0.0118552	−	0.00684459i
$606$		0			0
$607$	0.127387	+	0.0735469i	0.00517048	+	0.00298518i	0.502583	−	0.864529i	$-0.332383\pi$
$607$	0.127387	+	0.0735469i	0.00517048	+	0.00298518i	−0.497413	+	0.867514i	$0.665716\pi$
$608$	28.1496	−	1.37620i	1.14162	−	0.0558121i
$609$		0			0
$610$	1.71169	−	5.44861i	0.0693044	−	0.220608i
$611$	2.42973	−	4.20842i	0.0982964	−	0.170254i
$612$		0			0
$613$	−11.2920	−	19.5583i	−0.456080	−	0.789954i	0.542669	−	0.839946i	$-0.317414\pi$
$613$	−11.2920	−	19.5583i	−0.456080	−	0.789954i	−0.998750	+	0.0499922i	$0.984080\pi$
$614$	−29.0863	−	31.6757i	−1.17383	−	1.27833i
$615$		0			0
$616$	7.26630	+	23.3163i	0.292767	+	0.939439i
$617$		−	35.8659i		−	1.44391i	−0.691941	−	0.721954i	$-0.743244\pi$
$617$		−	35.8659i		−	1.44391i	0.691941	−	0.721954i	$-0.256756\pi$
$618$		0			0
$619$	9.40387	−	5.42933i	0.377973	−	0.218223i	−0.298963	−	0.954265i	$-0.596641\pi$
$619$	9.40387	−	5.42933i	0.377973	−	0.218223i	0.676936	+	0.736042i	$0.263307\pi$
$620$	1.32381	−	15.5038i	0.0531656	−	0.622646i
$621$		0			0
$622$	−34.7379	−	10.9130i	−1.39286	−	0.437570i
$623$	−41.3973	+	7.02400i	−1.65855	+	0.281411i
$624$		0			0
$625$	−5.95755	+	10.3188i	−0.238302	+	0.412751i
$626$	−8.95199	−	40.1814i	−0.357794	−	1.60597i
$627$		0			0
$628$	−12.0940	+	5.67027i	−0.482602	+	0.226268i
$629$			4.05648i			0.161742i
$630$		0			0
$631$		−	22.1335i		−	0.881121i	−0.897723	−	0.440561i	$-0.854780\pi$
$631$		−	22.1335i		−	0.881121i	0.897723	−	0.440561i	$-0.145220\pi$
$632$	1.43218	+	10.6215i	0.0569692	+	0.422501i
$633$		0			0
$634$	−37.1426	+	8.27498i	−1.47512	+	0.328642i
$635$	0.148591	−	0.257368i	0.00589667	−	0.0102133i
$636$		0			0
$637$	−3.48110	+	18.3524i	−0.137926	+	0.727147i
$638$	10.6683	−	33.9589i	0.422361	−	1.34445i
$639$		0			0
$640$	0.396290	−	10.9033i	0.0156647	−	0.430989i
$641$	18.3363	−	10.5865i	0.724242	−	0.418141i	−0.0920699	−	0.995753i	$-0.529348\pi$
$641$	18.3363	−	10.5865i	0.724242	−	0.418141i	0.816312	+	0.577611i	$0.196015\pi$
$642$		0			0
$643$			14.5277i			0.572917i	0.958093	+	0.286458i	$0.0924780\pi$
$643$			14.5277i			0.572917i	−0.958093	+	0.286458i	$0.907522\pi$
$644$	−43.0883	+	3.57989i	−1.69792	+	0.141068i
$645$		0			0
$646$	4.27777	−	3.92807i	0.168307	−	0.154548i
$647$	−12.9409	−	22.4143i	−0.508760	−	0.881198i	−0.999949	−	0.0101447i	$-0.996771\pi$
$647$	−12.9409	−	22.4143i	−0.508760	−	0.881198i	0.491189	−	0.871053i	$-0.336563\pi$
$648$		0			0
$649$	−0.777506	+	1.34668i	−0.0305198	+	0.0528618i
$650$	−14.6535	−	4.60344i	−0.574759	−	0.180562i
$651$		0			0
$652$	1.87366	−	2.68778i	0.0733780	−	0.105262i
$653$	18.1532	+	10.4808i	0.710390	+	0.410144i	0.811205	−	0.584762i	$-0.198812\pi$
$653$	18.1532	+	10.4808i	0.710390	+	0.410144i	−0.100816	+	0.994905i	$0.532145\pi$
$654$		0			0
$655$	−1.98524	+	1.14618i	−0.0775698	+	0.0447849i
$656$	3.62850	−	21.0926i	0.141669	−	0.823528i
$657$		0			0
$658$	−5.38312	−	4.17714i	−0.209856	−	0.162842i
$659$	16.0912			0.626826			0.313413	−	0.949617i	$-0.398528\pi$
$659$	16.0912			0.626826			0.313413	+	0.949617i	$0.398528\pi$
$660$		0			0
$661$	0.274559	+	0.475551i	0.0106791	+	0.0184968i	0.871316	−	0.490723i	$-0.163267\pi$
$661$	0.274559	+	0.475551i	0.0106791	+	0.0184968i	−0.860636	+	0.509220i	$0.829934\pi$
$662$	20.9178	−	4.66028i	0.812995	−	0.181127i
$663$		0			0
$664$	0.116669	+	0.151065i	0.00452765	+	0.00586246i
$665$	11.9167	+	4.42473i	0.462110	+	0.171584i
$666$		0			0
$667$	54.5745	+	31.5086i	2.11313	+	1.22002i
$668$	−3.89728	+	45.6429i	−0.150790	+	1.76598i
$669$		0			0
$670$	−8.54478	+	7.84627i	−0.330114	+	0.303128i
$671$	−13.6667			−0.527596
$672$		0			0
$673$	34.5345			1.33121			0.665604	−	0.746305i	$-0.268174\pi$
$673$	34.5345			1.33121			0.665604	+	0.746305i	$0.268174\pi$
$674$	−17.3523	+	15.9338i	−0.668387	+	0.613748i
$675$		0			0
$676$	−1.00034	+	11.7154i	−0.0384746	+	0.450594i
$677$	−25.6248	−	14.7945i	−0.984841	−	0.568598i	−0.0811126	−	0.996705i	$-0.525847\pi$
$677$	−25.6248	−	14.7945i	−0.984841	−	0.568598i	−0.903728	+	0.428107i	$0.859181\pi$
$678$		0			0
$679$	15.1076	−	12.5114i	0.579778	−	0.480142i
$680$	−1.37426	−	1.77941i	−0.0527004	−	0.0682371i
$681$		0			0
$682$	−36.3442	+	8.09710i	−1.39169	+	0.310054i
$683$	−2.69521	−	4.66823i	−0.103129	−	0.178625i	0.809843	−	0.586647i	$-0.199552\pi$
$683$	−2.69521	−	4.66823i	−0.103129	−	0.178625i	−0.912972	+	0.408021i	$0.866219\pi$
$684$		0			0
$685$	−2.87850			−0.109982
$686$	24.8307	+	8.33271i	0.948042	+	0.318144i
$687$		0			0
$688$	5.48651	−	31.8933i	0.209171	−	1.21592i
$689$	−19.7427	+	11.3985i	−0.752138	+	0.434247i
$690$		0			0
$691$	33.9683	+	19.6116i	1.29221	+	0.746060i	0.979046	−	0.203638i	$-0.0652766\pi$
$691$	33.9683	+	19.6116i	1.29221	+	0.746060i	0.313167	+	0.949698i	$0.398610\pi$
$692$	25.9681	−	37.2515i	0.987159	−	1.41609i
$693$		0			0
$694$	27.6372	+	8.68228i	1.04909	+	0.329575i
$695$	5.61901	−	9.73242i	0.213141	−	0.369172i
$696$		0			0
$697$	−2.20519	−	3.81949i	−0.0835273	−	0.144674i
$698$	7.26946	−	6.67520i	0.275153	−	0.252660i
$699$		0			0
$700$	−9.18701	+	19.4787i	−0.347236	+	0.736225i
$701$			30.7510i			1.16145i	0.814100	+	0.580725i	$0.197231\pi$
$701$			30.7510i			1.16145i	−0.814100	+	0.580725i	$0.802769\pi$
$702$		0			0
$703$	21.2336	−	12.2592i	0.800839	−	0.462365i
$704$	−25.1761	+	6.91511i	−0.948859	+	0.260623i
$705$		0			0
$706$	12.6037	−	40.1198i	0.474347	−	1.50993i
$707$	−1.99541	+	5.37406i	−0.0750451	+	0.202112i
$708$		0			0
$709$	−7.00634	+	12.1353i	−0.263129	+	0.455752i	−0.967072	−	0.254504i	$-0.918088\pi$
$709$	−7.00634	+	12.1353i	−0.263129	+	0.455752i	0.703943	+	0.710256i	$0.251421\pi$
$710$	9.48426	−	2.11299i	0.355938	−	0.0792993i
$711$		0			0
$712$	−5.99834	−	44.4855i	−0.224797	−	1.66717i
$713$		−	65.9206i		−	2.46875i
$714$		0			0
$715$		−	8.39846i		−	0.314084i
$716$	7.72469	−	3.62172i	0.288685	−	0.135350i
$717$		0			0
$718$	1.18971	+	5.34007i	0.0443997	+	0.199290i
$719$	18.1147	−	31.3756i	0.675565	−	1.17011i	−0.300739	−	0.953707i	$-0.597233\pi$
$719$	18.1147	−	31.3756i	0.675565	−	1.17011i	0.976304	−	0.216406i	$-0.0694334\pi$
$720$		0			0
$721$	46.0633	−	7.81569i	1.71549	−	0.291072i
$722$	−7.85458	−	2.46753i	−0.292317	−	0.0918320i
$723$		0			0
$724$	−3.36982	+	39.4656i	−0.125239	+	1.46673i
$725$	27.1839	−	15.6946i	1.00958	−	0.582884i
$726$		0			0
$727$			24.5723i			0.911336i	0.890150	+	0.455668i	$0.150600\pi$
$727$			24.5723i			0.911336i	−0.890150	+	0.455668i	$0.849400\pi$
$728$	−19.4815	−	4.38707i	−0.722031	−	0.162596i
$729$		0			0
$730$	−10.7846	−	11.7447i	−0.399155	−	0.434690i
$731$	−3.33437	−	5.77530i	−0.123326	−	0.213607i
$732$		0			0
$733$	1.84390	−	3.19373i	0.0681061	−	0.117963i	−0.829962	−	0.557821i	$-0.811638\pi$
$733$	1.84390	−	3.19373i	0.0681061	−	0.117963i	0.898068	+	0.439857i	$0.144971\pi$
$734$	5.63214	−	17.9281i	0.207886	−	0.661737i
$735$		0			0
$736$	−2.25704	−	46.1669i	−0.0831957	−	1.70174i
$737$	24.0412	+	13.8802i	0.885568	+	0.511283i
$738$		0			0
$739$	1.61163	−	0.930477i	0.0592849	−	0.0342282i	−0.470065	−	0.882632i	$-0.655769\pi$
$739$	1.61163	−	0.930477i	0.0592849	−	0.0342282i	0.529349	+	0.848404i	$0.322436\pi$
$740$	−4.02932	−	8.59403i	−0.148121	−	0.315923i
$741$		0			0
$742$	12.0722	+	29.5974i	0.443185	+	1.08655i
$743$	−13.7224			−0.503425			−0.251713	−	0.967802i	$-0.580994\pi$
$743$	−13.7224			−0.503425			−0.251713	+	0.967802i	$0.580994\pi$
$744$		0			0
$745$	−5.78459	−	10.0192i	−0.211931	−	0.367075i
$746$	−0.435475	−	1.95465i	−0.0159439	−	0.0715648i
$747$		0			0
$748$	−3.07672	+	4.41359i	−0.112496	+	0.161377i
$749$	1.57342	+	9.27327i	0.0574916	+	0.338838i
$750$		0			0
$751$	36.6535	+	21.1619i	1.33751	+	0.772210i	0.986437	−	0.164140i	$-0.0524849\pi$
$751$	36.6535	+	21.1619i	1.33751	+	0.772210i	0.351069	+	0.936350i	$0.385818\pi$
$752$	4.65883	−	5.59947i	0.169890	−	0.204192i
$753$		0			0
$754$	19.6855	+	21.4380i	0.716904	+	0.780726i
$755$	−10.4985			−0.382080
$756$		0			0
$757$	17.7909			0.646622			0.323311	−	0.946293i	$-0.395204\pi$
$757$	17.7909			0.646622			0.323311	+	0.946293i	$0.395204\pi$
$758$	31.5123	+	34.3177i	1.14458	+	1.24648i
$759$		0			0
$760$	−5.16109	+	12.5711i	−0.187212	+	0.456003i
$761$	−32.0604	−	18.5101i	−1.16219	−	0.670991i	−0.210362	−	0.977624i	$-0.567464\pi$
$761$	−32.0604	−	18.5101i	−1.16219	−	0.670991i	−0.951828	+	0.306633i	$0.900798\pi$
$762$		0			0
$763$	−6.90705	−	2.56462i	−0.250052	−	0.0928454i
$764$	−29.7476	−	20.7371i	−1.07623	−	0.750243i
$765$		0			0
$766$	11.4743	+	51.5027i	0.414582	+	1.86087i
$767$	−0.635743	−	1.10114i	−0.0229553	−	0.0397598i
$768$		0			0
$769$	−16.9042			−0.609583			−0.304791	−	0.952419i	$-0.598587\pi$
$769$	−16.9042			−0.609583			−0.304791	+	0.952419i	$0.598587\pi$
$770$	−11.6667	−	1.60029i	−0.420437	−	0.0576704i
$771$		0			0
$772$	−43.2003	+	20.2545i	−1.55481	+	0.728974i
$773$	4.25588	−	2.45713i	0.153073	−	0.0883769i	−0.421507	−	0.906825i	$-0.638499\pi$
$773$	4.25588	−	2.45713i	0.153073	−	0.0883769i	0.574580	+	0.818448i	$0.305165\pi$
$774$		0			0
$775$	−28.4363	−	16.4177i	−1.02146	−	0.589742i
$776$	12.8178	+	16.5966i	0.460131	+	0.595784i
$777$		0			0
$778$	−7.04799	+	22.4350i	−0.252683	+	0.804332i
$779$	−13.3287	+	23.0860i	−0.477551	+	0.827142i
$780$		0			0
$781$	−11.6260	−	20.1369i	−0.416013	−	0.720555i
$782$	−6.44227	−	7.01579i	−0.230375	−	0.250884i
$783$		0			0
$784$	−9.80637	+	26.2266i	−0.350228	+	0.936665i
$785$		−	6.44058i		−	0.229874i
$786$		0			0
$787$	13.4861	−	7.78620i	0.480727	−	0.277548i	−0.239992	−	0.970775i	$-0.577145\pi$
$787$	13.4861	−	7.78620i	0.480727	−	0.277548i	0.720719	+	0.693227i	$0.243812\pi$
$788$	−35.8227	−	3.05877i	−1.27613	−	0.108964i
$789$		0			0
$790$	−4.93025	−	1.54885i	−0.175410	−	0.0551055i
$791$	5.22632	+	6.31084i	0.185827	+	0.224388i
$792$		0			0
$793$	5.58740	−	9.67767i	0.198415	−	0.343664i
$794$	2.75455	+	12.3639i	0.0977553	+	0.438779i
$795$		0			0
$796$	−3.78499	−	8.07292i	−0.134155	−	0.286137i
$797$		−	30.5378i		−	1.08170i	−0.841118	−	0.540852i	$-0.818102\pi$
$797$		−	30.5378i		−	1.08170i	0.841118	−	0.540852i	$-0.181898\pi$
$798$		0			0
$799$		−	1.50104i		−	0.0531028i
$800$	−20.4773	−	10.5244i	−0.723980	−	0.372093i
$801$		0			0
$802$	22.0457	−	4.91154i	0.778459	−	0.173433i
$803$	−19.0781	+	33.0442i	−0.673251	+	1.16610i
$804$		0			0
$805$	7.25681	−	19.5441i	0.255769	−	0.688839i
$806$	9.12501	−	29.0465i	0.321415	−	1.02312i
$807$		0			0
$808$	−5.66918	−	2.32749i	−0.199441	−	0.0818807i
$809$	−23.8487	+	13.7690i	−0.838474	+	0.484093i	−0.856745	−	0.515740i	$-0.827517\pi$
$809$	−23.8487	+	13.7690i	−0.838474	+	0.484093i	0.0182712	+	0.999833i	$0.494184\pi$
$810$		0			0
$811$			44.3302i			1.55665i	0.627865	+	0.778323i	$0.283929\pi$
$811$			44.3302i			1.55665i	−0.627865	+	0.778323i	$0.716071\pi$
$812$	33.5315	−	23.2611i	1.17672	−	0.816303i
$813$		0			0
$814$	−16.7301	+	15.3625i	−0.586391	+	0.538455i
$815$	0.789903	+	1.36815i	0.0276691	+	0.0479243i
$816$		0			0
$817$	−20.1538	+	34.9074i	−0.705093	+	1.22126i
$818$	−31.2519	−	9.81785i	−1.09270	−	0.343273i
$819$		0			0
$820$	8.46581	+	5.90154i	0.295639	+	0.206091i
$821$	−8.92840	−	5.15482i	−0.311603	−	0.179904i	0.336040	−	0.941848i	$-0.390912\pi$
$821$	−8.92840	−	5.15482i	−0.311603	−	0.179904i	−0.647644	+	0.761943i	$0.724245\pi$
$822$		0			0
$823$	8.74721	−	5.05020i	0.304908	−	0.176039i	−0.339737	−	0.940520i	$-0.610338\pi$
$823$	8.74721	−	5.05020i	0.304908	−	0.176039i	0.644646	+	0.764481i	$0.277005\pi$
$824$	6.67443	+	49.4996i	0.232515	+	1.72440i
$825$		0			0
$826$	−1.65078	+	0.673320i	−0.0574379	+	0.0234278i
$827$	20.6380			0.717653			0.358827	−	0.933404i	$-0.383177\pi$
$827$	20.6380			0.717653			0.358827	+	0.933404i	$0.383177\pi$
$828$		0			0
$829$	−0.0292908	−	0.0507332i	−0.00101731	−	0.00176204i	0.865516	−	0.500881i	$-0.166990\pi$
$829$	−0.0292908	−	0.0507332i	−0.00101731	−	0.00176204i	−0.866534	+	0.499119i	$0.833657\pi$
$830$	−0.0898323	+	0.0200137i	−0.00311812	+	0.000694685i
$831$		0			0
$832$	5.39611	−	20.6549i	0.187076	−	0.716079i
$833$	1.90321	+	5.44700i	0.0659422	+	0.188727i
$834$		0			0
$835$	−19.1289	−	11.0440i	−0.661981	−	0.382195i
$836$	32.4011	+	2.76662i	1.12062	+	0.0956854i
$837$		0			0
$838$	−9.12859	+	8.38235i	−0.315342	+	0.289564i
$839$	13.8295			0.477447			0.238724	−	0.971088i	$-0.423271\pi$
$839$	13.8295			0.477447			0.238724	+	0.971088i	$0.423271\pi$
$840$		0			0
$841$	−30.4798			−1.05103
$842$	−15.8880	+	14.5892i	−0.547536	+	0.502776i
$843$		0			0
$844$	−3.05656	−	0.260989i	−0.105211	−	0.00898361i
$845$	−4.90992	−	2.83474i	−0.168906	−	0.0975182i
$846$		0			0
$847$	−0.154531	−	0.910758i	−0.00530974	−	0.0312940i
$848$	−32.0619	+	11.8213i	−1.10101	+	0.405946i
$849$		0			0
$850$	−4.63088	+	1.03171i	−0.158838	+	0.0353874i
$851$	−20.1058	−	34.8243i	−0.689218	−	1.19376i
$852$		0			0
$853$	43.8632			1.50185			0.750923	−	0.660389i	$-0.229609\pi$
$853$	43.8632			1.50185			0.750923	+	0.660389i	$0.229609\pi$
$854$	−12.3790	−	9.60574i	−0.423601	−	0.328702i
$855$		0			0
$856$	−9.96505	+	1.34367i	−0.340598	+	0.0459256i
$857$	10.8122	−	6.24242i	0.369337	−	0.213237i	−0.303832	−	0.952726i	$-0.598266\pi$
$857$	10.8122	−	6.24242i	0.369337	−	0.213237i	0.673169	+	0.739489i	$0.264933\pi$
$858$		0			0
$859$	8.19286	+	4.73015i	0.279537	+	0.161391i	0.633214	−	0.773977i	$-0.281735\pi$
$859$	8.19286	+	4.73015i	0.279537	+	0.161391i	−0.353677	+	0.935368i	$0.615069\pi$
$860$	12.8008	+	8.92348i	0.436504	+	0.304288i
$861$		0			0
$862$	−5.11741	−	1.60765i	−0.174300	−	0.0547566i
$863$	−22.9830	+	39.8077i	−0.782350	+	1.35507i	0.148220	+	0.988954i	$0.452646\pi$
$863$	−22.9830	+	39.8077i	−0.782350	+	1.35507i	−0.930570	+	0.366115i	$0.880688\pi$
$864$		0			0
$865$	10.9477	+	18.9620i	0.372234	+	0.644728i
$866$	41.4069	−	38.0219i	1.40706	−	1.29204i
$867$		0			0
$868$	−38.6110	−	18.2106i	−1.31054	−	0.618109i
$869$			12.3665i			0.419504i
$870$		0			0
$871$	−19.6577	+	11.3494i	−0.666076	+	0.384559i
$872$	2.99142	−	7.28636i	0.101302	−	0.246747i
$873$		0			0
$874$	−17.2547	+	54.9246i	−0.583648	+	1.85785i
$875$	−14.7603	−	17.8233i	−0.498991	−	0.602537i
$876$		0			0
$877$	5.82605	−	10.0910i	0.196732	−	0.340749i	−0.750735	−	0.660603i	$-0.770301\pi$
$877$	5.82605	−	10.0910i	0.196732	−	0.340749i	0.947467	+	0.319854i	$0.103634\pi$
$878$	−0.556812	+	0.124052i	−0.0187915	+	0.00418655i
$879$		0			0
$880$	2.13429	−	12.4067i	0.0719470	−	0.418231i
$881$			49.9833i			1.68398i	0.539493	+	0.841990i	$0.318616\pi$
$881$			49.9833i			1.68398i	−0.539493	+	0.841990i	$0.681384\pi$
$882$		0			0
$883$			57.7771i			1.94435i	0.234250	+	0.972176i	$0.424737\pi$
$883$			57.7771i			1.94435i	−0.234250	+	0.972176i	$0.575263\pi$
$884$	−1.86749	−	3.98312i	−0.0628104	−	0.133967i
$885$		0			0
$886$	1.27648	+	5.72953i	0.0428841	+	0.192487i
$887$	24.9323	−	43.1840i	0.837144	−	1.44998i	−0.0551292	−	0.998479i	$-0.517557\pi$
$887$	24.9323	−	43.1840i	0.837144	−	1.44998i	0.892273	−	0.451496i	$-0.149110\pi$
$888$		0			0
$889$	−0.520039	−	0.627953i	−0.0174416	−	0.0210609i
$890$	20.6491	+	6.48696i	0.692160	+	0.217443i
$891$		0			0
$892$	−1.98550	−	0.169535i	−0.0664794	−	0.00567644i
$893$	−7.85714	+	4.53632i	−0.262929	+	0.151802i
$894$		0			0
$895$			4.11374i			0.137507i
$896$	−27.6644	−	11.4317i	−0.924202	−	0.381905i
$897$		0			0
$898$	−20.3862	−	22.2011i	−0.680295	−	0.740859i
$899$	31.1101	+	53.8843i	1.03758	+	1.79714i
$900$		0			0
$901$	−3.52086	+	6.09831i	−0.117297	+	0.203164i
$902$	7.40137	−	23.5598i	0.246439	−	0.784456i
$903$		0			0
$904$	−6.93283	+	5.35431i	−0.230583	+	0.178082i
$905$	−16.5400	−	9.54935i	−0.549807	−	0.317431i
$906$		0			0
$907$	22.1632	−	12.7960i	0.735918	−	0.424883i	−0.0846650	−	0.996409i	$-0.526982\pi$
$907$	22.1632	−	12.7960i	0.735918	−	0.424883i	0.820583	+	0.571527i	$0.193649\pi$
$908$	−51.4590	+	24.1266i	−1.70773	+	0.800668i
$909$		0			0
$910$	5.90293	−	7.60716i	0.195680	−	0.252175i
$911$	40.5778			1.34440			0.672201	−	0.740369i	$-0.265349\pi$
$911$	40.5778			1.34440			0.672201	+	0.740369i	$0.265349\pi$
$912$		0			0
$913$	0.110119	+	0.190731i	0.00364439	+	0.00631228i
$914$	5.63135	+	25.2766i	0.186269	+	0.836074i
$915$		0			0
$916$	44.3398	+	30.9094i	1.46503	+	1.02127i
$917$	1.05207	+	6.20055i	0.0347423	+	0.204760i
$918$		0			0
$919$	−22.8189	−	13.1745i	−0.752725	−	0.434586i	0.0739526	−	0.997262i	$-0.476439\pi$
$919$	−22.8189	−	13.1745i	−0.752725	−	0.434586i	−0.826678	+	0.562676i	$0.809772\pi$
$920$	20.6174	+	8.46449i	0.679734	+	0.279066i
$921$		0			0
$922$	−12.9393	−	14.0912i	−0.426133	−	0.464070i
$923$	19.0125			0.625804
$924$		0			0
$925$	−20.0296			−0.658570
$926$	−11.2196	−	12.2184i	−0.368697	−	0.401521i
$927$		0			0
$928$	23.6326	+	36.6722i	0.775779	+	1.20383i
$929$	16.7968	+	9.69765i	0.551086	+	0.318170i	0.749560	−	0.661936i	$-0.230265\pi$
$929$	16.7968	+	9.69765i	0.551086	+	0.318170i	−0.198474	+	0.980106i	$0.563598\pi$
$930$		0			0
$931$	22.7605	−	26.4239i	0.745945	−	0.866007i
$932$	−21.0646	+	30.2174i	−0.689995	+	0.989804i
$933$		0			0
$934$	1.62810	+	7.30777i	0.0532729	+	0.239118i
$935$	−1.29710	−	2.24664i	−0.0424196	−	0.0734729i
$936$		0			0
$937$	−10.4703			−0.342048			−0.171024	−	0.985267i	$-0.554708\pi$
$937$	−10.4703			−0.342048			−0.171024	+	0.985267i	$0.554708\pi$
$938$	12.0202	+	29.4699i	0.392474	+	0.962228i
$939$		0			0
$940$	1.49098	+	3.18009i	0.0486306	+	0.103723i
$941$	8.83717	−	5.10214i	0.288083	−	0.166325i	−0.348994	−	0.937125i	$-0.613477\pi$
$941$	8.83717	−	5.10214i	0.288083	−	0.166325i	0.637077	+	0.770800i	$0.280143\pi$
$942$		0			0
$943$	37.8624	+	21.8599i	1.23297	+	0.711855i
$944$	−0.659327	−	1.78823i	−0.0214593	−	0.0582020i
$945$		0			0
$946$	11.1913	−	35.6239i	0.363861	−	1.15823i
$947$	−16.2233	+	28.0997i	−0.527188	+	0.913116i	0.472310	+	0.881432i	$0.343420\pi$
$947$	−16.2233	+	28.0997i	−0.527188	+	0.913116i	−0.999498	+	0.0316837i	$0.989913\pi$
$948$		0			0
$949$	−15.5995	−	27.0192i	−0.506383	−	0.877081i
$950$	19.3956	+	21.1223i	0.629277	+	0.685298i
$951$		0			0
$952$	−5.88897	+	1.83524i	−0.190863	+	0.0594805i
$953$		−	4.47642i		−	0.145005i	−0.997368	−	0.0725027i	$-0.976901\pi$
$953$		−	4.47642i		−	0.145005i	0.997368	−	0.0725027i	$-0.0230986\pi$
$954$		0			0
$955$	15.1423	−	8.74244i	0.489995	−	0.282899i
$956$	−0.0931018	+	1.09036i	−0.00301113	+	0.0352647i
$957$		0			0
$958$	3.21673	+	1.01054i	0.103928	+	0.0326491i
$959$	−2.74892	+	7.40341i	−0.0887672	+	0.239069i
$960$		0			0
$961$	17.0435	−	29.5201i	0.549789	−	0.952263i
$962$	−4.03866	−	18.1277i	−0.130212	−	0.584460i
$963$		0			0
$964$	21.5175	−	10.0885i	0.693033	−	0.324929i
$965$		−	23.0061i		−	0.740591i
$966$		0			0
$967$			23.9578i			0.770430i	0.922827	+	0.385215i	$0.125873\pi$
$967$			23.9578i			0.770430i	−0.922827	+	0.385215i	$0.874127\pi$
$968$	0.978700	−	0.131966i	0.0314566	−	0.00424155i
$969$		0			0
$970$	−9.86934	+	2.19879i	−0.316885	+	0.0705987i
$971$	10.6584	−	18.4609i	0.342045	−	0.592440i	−0.642767	−	0.766062i	$-0.722214\pi$
$971$	10.6584	−	18.4609i	0.342045	−	0.592440i	0.984812	+	0.173622i	$0.0555470\pi$
$972$		0			0
$973$	−19.6654	−	23.7462i	−0.630444	−	0.761268i
$974$	−10.1668	+	32.3628i	−0.325766	+	1.03697i
$975$		0			0
$976$	10.7134	−	12.8765i	0.342929	−	0.412168i
$977$	−20.6125	+	11.9006i	−0.659453	+	0.380735i	−0.792068	−	0.610432i	$-0.790996\pi$
$977$	−20.6125	+	11.9006i	−0.659453	+	0.380735i	0.132616	+	0.991168i	$0.457662\pi$
$978$		0			0
$979$		−	51.7939i		−	1.65534i
$980$	−9.44265	−	9.64952i	−0.301635	−	0.308243i
$981$		0			0
$982$	20.7195	−	19.0258i	0.661187	−	0.607137i
$983$	−31.1545	−	53.9613i	−0.993676	−	1.72110i	−0.594082	−	0.804404i	$-0.702485\pi$
$983$	−31.1545	−	53.9613i	−0.993676	−	1.72110i	−0.399594	−	0.916692i	$-0.630849\pi$
$984$		0			0
$985$	8.66790	−	15.0132i	0.276182	−	0.478362i
$986$	8.57697	+	2.69447i	0.273147	+	0.0858096i
$987$		0			0
$988$	−15.2058	+	21.8128i	−0.483761	+	0.693959i
$989$	57.2502	+	33.0534i	1.82045	+	1.05104i
$990$		0			0
$991$	3.83336	−	2.21319i	0.121771	−	0.0703044i	−0.437877	−	0.899035i	$-0.644270\pi$
$991$	3.83336	−	2.21319i	0.121771	−	0.0703044i	0.559648	+	0.828730i	$0.310936\pi$
$992$	20.8616	−	40.5903i	0.662356	−	1.28874i
$993$		0			0
$994$	3.62275	−	26.4111i	0.114907	−	0.837709i
$995$	4.29919			0.136293
$996$		0			0
$997$	12.7597	+	22.1004i	0.404103	+	0.699928i	0.994217	−	0.107393i	$-0.0342502\pi$
$997$	12.7597	+	22.1004i	0.404103	+	0.699928i	−0.590113	+	0.807320i	$0.700917\pi$
$998$	12.2808	−	2.73603i	0.388742	−	0.0866076i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.e.107.8	✓	64
3.2	odd	2	inner	756.2.be.e.107.25	yes	64
4.3	odd	2	inner	756.2.be.e.107.19	yes	64
7.4	even	3	inner	756.2.be.e.431.14	yes	64
12.11	even	2	inner	756.2.be.e.107.14	yes	64
21.11	odd	6	inner	756.2.be.e.431.19	yes	64
28.11	odd	6	inner	756.2.be.e.431.25	yes	64
84.11	even	6	inner	756.2.be.e.431.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.e.107.8	✓	64	1.1	even	1	trivial
756.2.be.e.107.14	yes	64	12.11	even	2	inner
756.2.be.e.107.19	yes	64	4.3	odd	2	inner
756.2.be.e.107.25	yes	64	3.2	odd	2	inner
756.2.be.e.431.8	yes	64	84.11	even	6	inner
756.2.be.e.431.14	yes	64	7.4	even	3	inner
756.2.be.e.431.19	yes	64	21.11	odd	6	inner
756.2.be.e.431.25	yes	64	28.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.04167 + 0.956516i) q^{2} +(0.170154 - 1.99275i) q^{4} +(0.835158 + 0.482179i) q^{5} +(2.03771 - 1.68753i) q^{7} +(1.72885 + 2.23854i) q^{8} +O(q^{10})\)	\(q+(-1.04167 + 0.956516i) q^{2} +(0.170154 - 1.99275i) q^{4} +(0.835158 + 0.482179i) q^{5} +(2.03771 - 1.68753i) q^{7} +(1.72885 + 2.23854i) q^{8} +(-1.33117 + 0.296571i) q^{10} +(1.63178 + 2.82633i) q^{11} -2.66851 q^{13} +(-0.508474 + 3.70695i) q^{14} +(-3.94210 - 0.678147i) q^{16} +(-0.713843 + 0.412137i) q^{17} +(4.31465 + 2.49107i) q^{19} +(1.10297 - 1.58222i) q^{20} +(-4.40321 - 1.38328i) q^{22} +(4.08549 - 7.07628i) q^{23} +(-2.03501 - 3.52474i) q^{25} +(2.77971 - 2.55248i) q^{26} +(-3.01609 - 4.34778i) q^{28} +7.71232i q^{29} +(6.98679 - 4.03382i) q^{31} +(4.75502 - 3.06427i) q^{32} +(0.349373 - 1.11211i) q^{34} +(2.51550 - 0.426812i) q^{35} +(2.46063 - 4.26194i) q^{37} +(-6.87719 + 1.53217i) q^{38} +(0.364488 + 2.70315i) q^{40} +5.35061i q^{41} +8.09044i q^{43} +(5.90982 - 2.77082i) q^{44} +(2.51284 + 11.2790i) q^{46} +(-0.910519 + 1.57706i) q^{47} +(1.30451 - 6.87737i) q^{49} +(5.49127 + 1.72510i) q^{50} +(-0.454058 + 5.31768i) q^{52} +(7.39839 - 4.27147i) q^{53} +3.14724i q^{55} +(7.30049 + 1.64401i) q^{56} +(-7.37696 - 8.03369i) q^{58} +(0.238238 + 0.412641i) q^{59} +(-2.09383 + 3.62661i) q^{61} +(-3.41951 + 10.8849i) q^{62} +(-2.02214 + 7.74022i) q^{64} +(-2.22863 - 1.28670i) q^{65} +(7.36654 - 4.25307i) q^{67} +(0.699823 + 1.49264i) q^{68} +(-2.21207 + 2.85071i) q^{70} -7.12475 q^{71} +(5.84578 + 10.1252i) q^{73} +(1.51345 + 6.79317i) q^{74} +(5.69822 - 8.17416i) q^{76} +(8.09460 + 3.00556i) q^{77} +(3.28159 + 1.89463i) q^{79} +(-2.96528 - 2.46715i) q^{80} +(-5.11794 - 5.57357i) q^{82} +0.0674837 q^{83} -0.794896 q^{85} +(-7.73863 - 8.42757i) q^{86} +(-3.50575 + 8.53912i) q^{88} +(-13.7441 - 7.93517i) q^{89} +(-5.43765 + 4.50319i) q^{91} +(-13.4061 - 9.34541i) q^{92} +(-0.560027 - 2.51371i) q^{94} +(2.40228 + 4.16087i) q^{95} +7.41403 q^{97} +(5.21945 + 8.41174i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) \) 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

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