LMFDB - Embedded newform 756.2.be.e.107.14

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			107.14
Character	$\chi$	$=$	756.107
Dual form			756.2.be.e.431.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.307532 + 1.38037i) q^{2} +(-1.81085 - 0.849017i) q^{4} +(-0.835158 - 0.482179i) q^{5} +(-2.03771 + 1.68753i) q^{7} +(1.72885 - 2.23854i) q^{8} +O(q^{10})$	\(q+(-0.307532 + 1.38037i) q^{2} +(-1.81085 - 0.849017i) q^{4} +(-0.835158 - 0.482179i) q^{5} +(-2.03771 + 1.68753i) q^{7} +(1.72885 - 2.23854i) q^{8} +(0.922423 - 1.00454i) q^{10} +(1.63178 + 2.82633i) q^{11} -2.66851 q^{13} +(-1.70275 - 3.33176i) q^{14} +(2.55834 + 3.07488i) q^{16} +(0.713843 - 0.412137i) q^{17} +(-4.31465 - 2.49107i) q^{19} +(1.10297 + 1.58222i) q^{20} +(-4.40321 + 1.38328i) q^{22} +(4.08549 - 7.07628i) q^{23} +(-2.03501 - 3.52474i) q^{25} +(0.820654 - 3.68354i) q^{26} +(5.12272 - 1.32580i) q^{28} -7.71232i q^{29} +(-6.98679 + 4.03382i) q^{31} +(-5.03125 + 2.58583i) q^{32} +(0.349373 + 1.11211i) q^{34} +(2.51550 - 0.426812i) q^{35} +(2.46063 - 4.26194i) q^{37} +(4.76549 - 5.18974i) q^{38} +(-2.52324 + 1.03592i) q^{40} -5.35061i q^{41} -8.09044i q^{43} +(-0.555307 - 6.50346i) q^{44} +(8.51147 + 7.81568i) q^{46} +(-0.910519 + 1.57706i) q^{47} +(1.30451 - 6.87737i) q^{49} +(5.49127 - 1.72510i) q^{50} +(4.83227 + 2.26561i) q^{52} +(-7.39839 + 4.27147i) q^{53} -3.14724i q^{55} +(0.254702 + 7.47898i) q^{56} +(10.6459 + 2.37179i) q^{58} +(0.238238 + 0.412641i) q^{59} +(-2.09383 + 3.62661i) q^{61} +(-3.41951 - 10.8849i) q^{62} +(-2.02214 - 7.74022i) q^{64} +(2.22863 + 1.28670i) q^{65} +(-7.36654 + 4.25307i) q^{67} +(-1.64257 + 0.140253i) q^{68} +(-0.184438 + 3.60358i) q^{70} -7.12475 q^{71} +(5.84578 + 10.1252i) q^{73} +(5.12634 + 4.70727i) q^{74} +(5.69822 + 8.17416i) q^{76} +(-8.09460 - 3.00556i) q^{77} +(-3.28159 - 1.89463i) q^{79} +(-0.653976 - 3.80159i) q^{80} +(7.38582 + 1.64548i) q^{82} +0.0674837 q^{83} -0.794896 q^{85} +(11.1678 + 2.48807i) q^{86} +(9.14796 + 1.23349i) q^{88} +(13.7441 + 7.93517i) q^{89} +(5.43765 - 4.50319i) q^{91} +(-13.4061 + 9.34541i) q^{92} +(-1.89692 - 1.74185i) q^{94} +(2.40228 + 4.16087i) q^{95} +7.41403 q^{97} +(9.09215 + 3.91572i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.307532	+	1.38037i	−0.217458	+	0.976070i
$2$	−0.307532	+	1.38037i	−0.217458	+	0.976070i
$3$		0			0
$3$		0			0
$4$	−1.81085	−	0.849017i	−0.905424	−	0.424508i
$5$	−0.835158	−	0.482179i	−0.373494	−	0.215637i	0.301490	−	0.953469i	$-0.402516\pi$
$5$	−0.835158	−	0.482179i	−0.373494	−	0.215637i	−0.674984	+	0.737833i	$0.735849\pi$
$6$		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
$10$	0.922423	−	1.00454i	0.291696	−	0.317664i
$11$	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	$0.620662\pi$
$14$	−1.70275	−	3.33176i	−0.455079	−	0.890451i
$15$		0			0
$16$	2.55834	+	3.07488i	0.639585	+	0.768720i
$17$	0.713843	−	0.412137i	0.173132	−	0.0999580i	−0.410930	−	0.911667i	$-0.634796\pi$
$17$	0.713843	−	0.412137i	0.173132	−	0.0999580i	0.584062	+	0.811709i	$0.301462\pi$
$18$		0			0
$19$	−4.31465	−	2.49107i	−0.989849	−	0.571490i	−0.0846201	−	0.996413i	$-0.526968\pi$
$19$	−4.31465	−	2.49107i	−0.989849	−	0.571490i	−0.905229	+	0.424924i	$0.860301\pi$
$20$	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
$26$	0.820654	−	3.68354i	0.160943	−	0.722401i
$27$		0			0
$28$	5.12272	−	1.32580i	0.968103	−	0.250554i
$29$		−	7.71232i		−	1.43214i	−0.698028	−	0.716071i	$-0.745939\pi$
$29$		−	7.71232i		−	1.43214i	0.698028	−	0.716071i	$-0.254061\pi$
$30$		0			0
$31$	−6.98679	+	4.03382i	−1.25486	+	0.724496i	−0.972071	−	0.234685i	$-0.924594\pi$
$31$	−6.98679	+	4.03382i	−1.25486	+	0.724496i	−0.282793	+	0.959181i	$0.591261\pi$
$32$	−5.03125	+	2.58583i	−0.889408	+	0.457115i
$33$		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	$0.0341033\pi$
$38$	4.76549	−	5.18974i	0.773065	−	0.841887i
$39$		0			0
$40$	−2.52324	+	1.03592i	−0.398960	+	0.163793i
$41$		−	5.35061i		−	0.835624i	−0.908533	−	0.417812i	$-0.862797\pi$
$41$		−	5.35061i		−	0.835624i	0.908533	−	0.417812i	$-0.137203\pi$
$42$		0			0
$43$		−	8.09044i		−	1.23378i	−0.787049	−	0.616890i	$-0.788392\pi$
$43$		−	8.09044i		−	1.23378i	0.787049	−	0.616890i	$-0.211608\pi$
$44$	−0.555307	−	6.50346i	−0.0837157	−	0.980434i
$45$		0			0
$46$	8.51147	+	7.81568i	1.25495	+	1.15236i
$47$	−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
$52$	4.83227	+	2.26561i	0.670116	+	0.314184i
$53$	−7.39839	+	4.27147i	−1.01625	+	0.586731i	−0.913015	−	0.407926i	$-0.866252\pi$
$53$	−7.39839	+	4.27147i	−1.01625	+	0.586731i	−0.103233	+	0.994657i	$0.532919\pi$
$54$		0			0
$55$		−	3.14724i		−	0.424374i
$56$	0.254702	+	7.47898i	0.0340359	+	0.999421i
$57$		0			0
$58$	10.6459	+	2.37179i	1.39787	+	0.311431i
$59$	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	−0.877189	−	0.480145i	$-0.840584\pi$
$67$	−7.36654	+	4.25307i	−0.899966	+	0.519596i	−0.0227769	+	0.999741i	$0.507251\pi$
$68$	−1.64257	+	0.140253i	−0.199191	+	0.0170082i
$69$		0			0
$70$	−0.184438	+	3.60358i	−0.0220446	+	0.430710i
$71$	−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	$0.593486\pi$
$74$	5.12634	+	4.70727i	0.595925	+	0.547209i
$75$		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	0.303905	−	0.952702i	$-0.401710\pi$
$79$	−3.28159	−	1.89463i	−0.369208	−	0.213162i	−0.673112	+	0.739540i	$0.735043\pi$
$80$	−0.653976	−	3.80159i	−0.0731168	−	0.425031i
$81$		0			0
$82$	7.38582	+	1.64548i	0.815627	+	0.181713i
$83$	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
$86$	11.1678	+	2.48807i	1.20426	+	0.268295i
$87$		0			0
$88$	9.14796	+	1.23349i	0.975176	+	0.131491i
$89$	13.7441	+	7.93517i	1.45687	+	0.841126i	0.998856	−	0.0478167i	$-0.0152263\pi$
$89$	13.7441	+	7.93517i	1.45687	+	0.841126i	0.458018	+	0.888943i	$0.348560\pi$
$90$		0			0
$91$	5.43765	−	4.50319i	0.570021	−	0.472062i
$92$	−13.4061	+	9.34541i	−1.39768	+	0.974327i
$93$		0			0
$94$	−1.89692	−	1.74185i	−0.195652	−	0.179658i
$95$	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	$0.377165\pi$
$98$	9.09215	+	3.91572i	0.918446	+	0.395548i
$99$		0			0
$100$	0.692528	+	8.11052i	0.0692528	+	0.811052i
$101$	1.87642	−	1.08335i	0.186711	−	0.107797i	−0.403731	−	0.914878i	$-0.632287\pi$
$101$	1.87642	−	1.08335i	0.186711	−	0.107797i	0.590442	+	0.807080i	$0.298954\pi$
$102$		0			0
$103$	−15.2933	−	8.82956i	−1.50689	−	0.870003i	−0.999968	−	0.00801027i	$-0.997450\pi$
$103$	−15.2933	−	8.82956i	−1.50689	−	0.870003i	−0.506921	−	0.861992i	$-0.669216\pi$
$104$	−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	$0.875912\pi$
$110$	4.34436	+	0.967878i	0.414218	+	0.0922835i
$111$		0			0
$112$	−10.4021	−	1.94844i	−0.982906	−	0.184111i
$113$		−	3.09703i		−	0.291344i	−0.989333	−	0.145672i	$-0.953466\pi$
$113$		−	3.09703i		−	0.291344i	0.989333	−	0.145672i	$-0.0465344\pi$
$114$		0			0
$115$	−6.82406	+	3.93987i	−0.636347	+	0.367395i
$116$	−6.54789	+	13.9658i	−0.607956	+	1.29670i
$117$		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
$122$	−4.36215	−	4.00556i	−0.394931	−	0.362646i
$123$		0			0
$124$	16.0768	−	1.37274i	1.44374	−	0.123276i
$125$			8.74674i			0.782332i
$126$		0			0
$127$			0.308166i			0.0273454i	0.999907	+	0.0136727i	$0.00435228\pi$
$127$			0.308166i			0.0273454i	−0.999907	+	0.0136727i	$0.995648\pi$
$128$	11.3062	−	0.410937i	0.999340	−	0.0363220i
$129$		0			0
$130$	−2.46150	+	2.68063i	−0.215888	+	0.235107i
$131$	−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
$136$	0.311542	−	2.31049i	0.0267145	−	0.198123i
$137$	2.58499	−	1.49245i	0.220851	−	0.127508i	−0.385493	−	0.922711i	$-0.625969\pi$
$137$	2.58499	−	1.49245i	0.220851	−	0.127508i	0.606344	+	0.795202i	$0.292635\pi$
$138$		0			0
$139$			11.6534i			0.988427i	0.869340	+	0.494214i	$0.164544\pi$
$139$			11.6534i			0.988427i	−0.869340	+	0.494214i	$0.835456\pi$
$140$	−4.91755	−	1.36281i	−0.415609	−	0.115178i
$141$		0			0
$142$	2.19109	−	9.83480i	0.183872	−	0.825318i
$143$	−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	0.861036	−	0.508544i	$-0.169816\pi$
$149$	10.3895	+	5.99838i	0.851142	+	0.491407i	−0.00989432	+	0.999951i	$0.503150\pi$
$150$		0			0
$151$	9.42801	−	5.44327i	0.767241	−	0.442967i	−0.0646486	−	0.997908i	$-0.520593\pi$
$151$	9.42801	−	5.44327i	0.767241	−	0.442967i	0.831889	+	0.554941i	$0.187259\pi$
$152$	−13.0358	+	5.35185i	−1.05734	+	0.434092i
$153$		0			0
$154$	6.63814	−	10.2492i	0.534916	−	0.825908i
$155$	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	$0.919203\pi$
$158$	3.62448	−	3.94715i	0.288348	−	0.314019i
$159$		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	0.443409	−	0.896320i	$-0.353769\pi$
$163$	−1.41872	−	0.819098i	−0.111123	−	0.0641567i	−0.554531	+	0.832163i	$0.687102\pi$
$164$	−4.54276	+	9.68913i	−0.354730	+	0.756594i
$165$		0			0
$166$	−0.0207534	+	0.0931525i	−0.00161078	+	0.00723004i
$167$	−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
$170$	0.244456	−	1.09725i	0.0187489	−	0.0841553i
$171$		0			0
$172$	−6.86892	+	14.6505i	−0.523750	+	1.11709i
$173$	−19.6628	−	11.3524i	−1.49494	−	0.863103i	−0.494956	−	0.868918i	$-0.664816\pi$
$173$	−19.6628	−	11.3524i	−1.49494	−	0.863103i	−0.999983	+	0.00581508i	$0.998149\pi$
$174$		0			0
$175$	10.0948	+	3.74826i	0.763098	+	0.283341i
$176$	−4.51597	+	12.2482i	−0.340404	+	0.923246i
$177$		0			0
$178$	−15.1802	+	16.5317i	−1.13781	+	1.23910i
$179$	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	$0.763303\pi$
$182$	4.54382	+	8.89085i	0.336810	+	0.659034i
$183$		0			0
$184$	−8.77734	−	21.3794i	−0.647074	−	1.57611i
$185$	−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	$-0.495338\pi$
$194$	−2.28005	+	10.2341i	−0.163698	+	0.734766i
$195$		0			0
$196$	−8.20127	+	11.3463i	−0.585805	+	0.810452i
$197$			17.9765i			1.28077i	0.768052	+	0.640387i	$0.221226\pi$
$197$			17.9765i			1.28077i	−0.768052	+	0.640387i	$0.778774\pi$
$198$		0			0
$199$	−3.86082	+	2.22904i	−0.273686	+	0.158013i	−0.630562	−	0.776139i	$-0.717175\pi$
$199$	−3.86082	+	2.22904i	−0.273686	+	0.158013i	0.356876	+	0.934152i	$0.383842\pi$
$200$	−11.4085	−	1.53830i	−0.806703	−	0.108774i
$201$		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
$206$	16.8912	−	18.3950i	1.17687	−	1.28164i
$207$		0			0
$208$	−6.82697	−	8.20536i	−0.473365	−	0.568940i
$209$		−	16.2595i		−	1.12469i
$210$		0			0
$211$			1.53384i			0.105594i	0.998605	+	0.0527970i	$0.0168136\pi$
$211$			1.53384i			0.105594i	−0.998605	+	0.0527970i	$0.983186\pi$
$212$	17.0239	−	1.45361i	1.16921	−	0.0998344i
$213$		0			0
$214$	−3.70320	−	3.40047i	−0.253146	−	0.232452i
$215$	−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
$220$	−2.67206	+	5.69918i	−0.180150	+	0.384238i
$221$	−1.90490	+	1.09979i	−0.128137	+	0.0739802i
$222$		0			0
$223$			0.996362i			0.0667213i	0.999443	+	0.0333607i	$0.0106210\pi$
$223$			0.996362i			0.0667213i	−0.999443	+	0.0333607i	$0.989379\pi$
$224$	5.88855	−	13.7595i	0.393446	−	0.919348i
$225$		0			0
$226$	4.27505	+	0.952436i	0.284372	+	0.0633551i
$227$	−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	0.921222	−	0.389037i	$-0.127192\pi$
$233$	15.9500	+	9.20872i	1.04492	+	0.603283i	0.123695	+	0.992320i	$0.460525\pi$
$234$		0			0
$235$	1.52085	−	0.878065i	0.0992095	−	0.0572787i
$236$	−0.0810743	−	0.949499i	−0.00527749	−	0.0618071i
$237$		0			0
$238$	−2.58864	−	1.67659i	−0.167797	−	0.108677i
$239$	−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	$0.708324\pi$
$242$	0.363703	+	0.333971i	0.0233797	+	0.0214685i
$243$		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
$248$	−3.04924	+	22.6141i	−0.193627	+	1.43600i
$249$		0			0
$250$	−12.0737	−	2.68990i	−0.763610	−	0.170124i
$251$	−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
$254$	−0.425384	−	0.0947711i	−0.0266910	−	0.00594647i
$255$		0			0
$256$	−2.90979	+	15.7332i	−0.181862	+	0.983324i
$257$	7.44631	+	4.29913i	0.464488	+	0.268172i	0.713929	−	0.700218i	$-0.246914\pi$
$257$	7.44631	+	4.29913i	0.464488	+	0.268172i	−0.249442	+	0.968390i	$0.580247\pi$
$258$		0			0
$259$	2.17809	+	12.8370i	0.135340	+	0.797651i
$260$	−2.94328	−	4.22216i	−0.182534	−	0.261847i
$261$		0			0
$262$	−2.47614	−	2.27372i	−0.152976	−	0.140471i
$263$	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
$266$	−0.952857	+	18.6171i	−0.0584234	+	1.14149i
$267$		0			0
$268$	16.9506	−	1.44735i	1.03542	−	0.0884111i
$269$	6.65653	−	3.84315i	0.405856	−	0.234321i	−0.283152	−	0.959075i	$-0.591380\pi$
$269$	6.65653	−	3.84315i	0.405856	−	0.234321i	0.689008	+	0.724754i	$0.258047\pi$
$270$		0			0
$271$	20.4624	+	11.8140i	1.24300	+	0.717649i	0.969705	−	0.244280i	$-0.0785516\pi$
$271$	20.4624	+	11.8140i	1.24300	+	0.717649i	0.273300	+	0.961929i	$0.411885\pi$
$272$	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	$-0.421876\pi$
$278$	−16.0860	−	3.58379i	−0.964774	−	0.214942i
$279$		0			0
$280$	3.39349	−	6.36894i	0.202800	−	0.380617i
$281$			2.87579i			0.171555i	0.996314	+	0.0857777i	$0.0273375\pi$
$281$			2.87579i			0.171555i	−0.996314	+	0.0857777i	$0.972663\pi$
$282$		0			0
$283$	10.2157	−	5.89802i	0.607258	−	0.350601i	−0.164633	−	0.986355i	$-0.552644\pi$
$283$	10.2157	−	5.89802i	0.607258	−	0.350601i	0.771892	+	0.635754i	$0.219311\pi$
$284$	12.9018	+	6.04904i	0.765584	+	0.358944i
$285$		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
$290$	−7.74735	−	7.11402i	−0.454940	−	0.417750i
$291$		0			0
$292$	−1.98936	−	23.2983i	−0.116419	−	1.36343i
$293$		−	29.0652i		−	1.69801i	−0.528387	−	0.849003i	$-0.677203\pi$
$293$		−	29.0652i		−	1.69801i	0.528387	−	0.849003i	$-0.322797\pi$
$294$		0			0
$295$		−	0.459494i		−	0.0267528i
$296$	−5.28646	−	12.8765i	−0.307270	−	0.748431i
$297$		0			0
$298$	−11.4751	+	12.4967i	−0.664735	+	0.723913i
$299$	−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
$304$	−3.37862	−	19.6400i	−0.193777	−	1.12643i
$305$	3.49735	−	2.01920i	0.200258	−	0.115619i
$306$		0			0
$307$		−	30.4085i		−	1.73551i	−0.496995	−	0.867754i	$-0.665563\pi$
$307$		−	30.4085i		−	1.73551i	0.496995	−	0.867754i	$-0.334437\pi$
$308$	12.1063	+	12.3151i	0.689821	+	0.701716i
$309$		0			0
$310$	−2.39263	+	10.7394i	−0.135892	+	0.609958i
$311$	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	−0.326915	−	0.945054i	$-0.606009\pi$
$317$	−23.3028	−	13.4539i	−1.30881	−	0.755644i	−0.981898	+	0.189410i	$0.939342\pi$
$318$		0			0
$319$	21.7975	−	12.5848i	1.22043	−	0.704615i
$320$	−2.04336	+	7.43934i	−0.114227	+	0.415871i
$321$		0			0
$322$	−30.5331	−	1.56274i	−1.70154	−	0.0870881i
$323$	−4.10665			−0.228500
$324$		0			0
$325$	5.43045	+	9.40581i	0.301227	+	0.521740i
$326$	1.56696	−	1.70646i	0.0867859	−	0.0945121i
$327$		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	0.815244	−	0.579117i	$-0.196603\pi$
$331$	13.1236	+	7.57689i	0.721336	+	0.416464i	−0.0939082	+	0.995581i	$0.529936\pi$
$332$	−0.122203	−	0.0572948i	−0.00670674	−	0.00314446i
$333$		0			0
$334$	7.04386	−	31.6167i	0.385423	−	1.72999i
$335$	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	$0.350099\pi$
$338$	1.80799	−	8.11525i	0.0983418	−	0.441411i
$339$		0			0
$340$	1.43944	+	0.674880i	0.0780643	+	0.0366005i
$341$	−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
$346$	21.7174	−	23.6508i	1.16754	−	1.27148i
$347$	−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	$0.559805\pi$
$350$	−8.27847	+	12.7819i	−0.442503	+	0.683222i
$351$		0			0
$352$	−15.5183	−	10.0004i	−0.827129	−	0.533026i
$353$	25.7521	−	14.8680i	1.37064	−	0.791342i	0.379635	−	0.925136i	$-0.376049\pi$
$353$	25.7521	−	14.8680i	1.37064	−	0.791342i	0.991009	+	0.133794i	$0.0427161\pi$
$354$		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
$362$	6.09055	−	27.3377i	0.320112	−	1.43684i
$363$		0			0
$364$	−13.6700	+	3.53793i	−0.716505	+	0.185438i
$365$		−	11.2748i		−	0.590152i
$366$		0			0
$367$	11.5077	−	6.64395i	0.600695	−	0.346811i	−0.168620	−	0.985681i	$-0.553931\pi$
$367$	11.5077	−	6.64395i	0.600695	−	0.346811i	0.769315	+	0.638870i	$0.220598\pi$
$368$	32.2108	−	5.54113i	1.67910	−	0.288851i
$369$		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	$0.178338\pi$
$374$	−2.57310	+	2.80217i	−0.133052	+	0.144897i
$375$		0			0
$376$	1.95617	+	4.76475i	0.100882	+	0.245723i
$377$			20.5804i			1.05995i
$378$		0			0
$379$			32.9449i			1.69227i	0.532972	+	0.846133i	$0.321075\pi$
$379$			32.9449i			1.69227i	−0.532972	+	0.846133i	$0.678925\pi$
$380$	−0.817513	−	9.57427i	−0.0419375	−	0.491150i
$381$		0			0
$382$	18.8866	+	17.3427i	0.966325	+	0.887330i
$383$	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
$388$	−13.4257	−	6.29464i	−0.681586	−	0.319562i
$389$	−14.4005	+	8.31416i	−0.730136	+	0.421545i	−0.818472	−	0.574546i	$-0.805179\pi$
$389$	−14.4005	+	8.31416i	−0.730136	+	0.421545i	0.0883356	+	0.996091i	$0.471845\pi$
$390$		0			0
$391$		−	6.73514i		−	0.340611i
$392$	−13.1400	−	14.8102i	−0.663669	−	0.748026i
$393$		0			0
$394$	−24.8143	−	5.52836i	−1.25013	−	0.278515i
$395$	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	0.803872	−	0.594802i	$-0.202770\pi$
$401$	13.8311	+	7.98541i	0.690694	+	0.398772i	−0.113178	+	0.993575i	$0.536103\pi$
$402$		0			0
$403$	18.6443	−	10.7643i	0.928741	−	0.536209i
$404$	−4.31769	+	0.368672i	−0.214813	+	0.0183421i
$405$		0			0
$406$	−25.6956	+	13.1322i	−1.27525	+	0.651738i
$407$	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	$0.639239\pi$
$410$	−5.37491	−	4.93552i	−0.265448	−	0.243748i
$411$		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
$416$	13.4260	−	6.90033i	0.658262	−	0.338317i
$417$		0			0
$418$	22.4441	+	5.00032i	1.09778	+	0.244574i
$419$	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	$0.378782\pi$
$422$	−2.11727	−	0.471706i	−0.103067	−	0.0229623i
$423$		0			0
$424$	−3.22888	+	23.9463i	−0.156808	+	1.16294i
$425$	−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
$430$	−8.12719	−	7.46281i	−0.391928	−	0.359889i
$431$	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	$0.904298\pi$
$434$	25.3365	+	16.4097i	1.21619	+	0.787691i
$435$		0			0
$436$	0.473839	+	5.54935i	0.0226928	+	0.265766i
$437$	−35.2550	+	20.3545i	−1.68647	+	0.973686i
$438$		0			0
$439$	−0.349336	−	0.201689i	−0.0166729	−	0.00962611i	0.491640	−	0.870798i	$-0.336397\pi$
$439$	−0.349336	−	0.201689i	−0.0166729	−	0.00962611i	−0.508313	+	0.861172i	$0.669731\pi$
$440$	−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
$446$	−1.37535	−	0.306413i	−0.0651247	−	0.0145091i
$447$		0			0
$448$	17.1823	+	12.3599i	0.811790	+	0.583950i
$449$		−	21.3129i		−	1.00582i	−0.864339	−	0.502910i	$-0.832263\pi$
$449$		−	21.3129i		−	1.00582i	0.864339	−	0.502910i	$-0.167737\pi$
$450$		0			0
$451$	15.1226	−	8.73102i	0.712094	−	0.411128i
$452$	−2.62943	+	5.60825i	−0.123678	+	0.263790i
$453$		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	$0.0257842\pi$
$458$	−28.1512	−	25.8499i	−1.31542	−	1.20788i
$459$		0			0
$460$	15.7024	−	1.34077i	0.732126	−	0.0625136i
$461$		−	13.5275i		−	0.630040i	−0.949085	−	0.315020i	$-0.897989\pi$
$461$		−	13.5275i		−	0.630040i	0.949085	−	0.315020i	$-0.102011\pi$
$462$		0			0
$463$		−	11.7296i		−	0.545121i	−0.962139	−	0.272560i	$-0.912130\pi$
$463$		−	11.7296i		−	0.545121i	0.962139	−	0.272560i	$-0.0878704\pi$
$464$	23.7145	−	19.7307i	1.10092	−	0.915976i
$465$		0			0
$466$	−17.6166	+	19.1849i	−0.816072	+	0.888724i
$467$	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
$472$	1.33559	+	0.180089i	0.0614757	+	0.00828926i
$473$	22.8662	−	13.2018i	1.05139	−	0.607021i
$474$		0			0
$475$			20.2774i			0.930389i
$476$	3.11040	−	3.05768i	0.142565	−	0.140149i
$477$		0			0
$478$	0.168270	−	0.755288i	0.00769650	−	0.0345460i
$479$	−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	−0.890372	−	0.455233i	$-0.849556\pi$
$487$	−20.7730	+	11.9933i	−0.941314	+	0.543468i	−0.0509423	+	0.998702i	$0.516222\pi$
$488$	4.49841	+	10.9570i	0.203633	+	0.496000i
$489$		0			0
$490$	−5.70530	−	7.65428i	−0.257739	−	0.345785i
$491$	−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
$494$	−12.7168	+	13.8489i	−0.572155	+	0.623091i
$495$		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	0.662443	−	0.749112i	$-0.269520\pi$
$499$	7.70480	+	4.44837i	0.344914	+	0.199136i	−0.317529	+	0.948249i	$0.602853\pi$
$500$	7.42613	−	15.8390i	0.332106	−	0.708342i
$501$		0			0
$502$	6.20861	−	27.8676i	0.277104	−	1.24379i
$503$	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
$506$	−8.20081	+	36.8097i	−0.364571	+	1.63639i
$507$		0			0
$508$	0.261639	−	0.558043i	0.0116083	−	0.0247591i
$509$	−17.7650	−	10.2566i	−0.787421	−	0.454618i	0.0516327	−	0.998666i	$-0.483557\pi$
$509$	−17.7650	−	10.2566i	−0.787421	−	0.454618i	−0.839054	+	0.544048i	$0.816891\pi$
$510$		0			0
$511$	−28.9985	−	10.7673i	−1.28282	−	0.476316i
$512$	−20.8228	−	8.85505i	−0.920246	−	0.391342i
$513$		0			0
$514$	−8.22437	+	8.95654i	−0.362761	+	0.395056i
$515$	8.51485	+	14.7482i	0.375209	+	0.649882i
$516$		0			0
$517$	−5.94307			−0.261376
$518$	−18.3896	−	0.941217i	−0.807994	−	0.0413547i
$519$		0			0
$520$	6.73331	−	2.76437i	0.295275	−	0.121226i
$521$	13.5376	−	7.81591i	0.593091	−	0.342421i	−0.173228	−	0.984882i	$-0.555420\pi$
$521$	13.5376	−	7.81591i	0.593091	−	0.342421i	0.766319	+	0.642460i	$0.222086\pi$
$522$		0			0
$523$	−22.5412	−	13.0142i	−0.985657	−	0.569069i	−0.0816838	−	0.996658i	$-0.526030\pi$
$523$	−22.5412	−	13.0142i	−0.985657	−	0.569069i	−0.903973	+	0.427589i	$0.859363\pi$
$524$	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
$530$	−2.53358	+	11.3721i	−0.110052	+	0.493972i
$531$		0			0
$532$	−25.4054	−	7.04064i	−1.10146	−	0.305251i
$533$			14.2782i			0.618456i
$534$		0			0
$535$	2.96904	−	1.71417i	0.128363	−	0.0741102i
$536$	−3.21498	+	23.8432i	−0.138866	+	1.02987i
$537$		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	$0.882879\pi$
$542$	−22.6006	+	24.6126i	−0.970777	+	1.05720i
$543$		0			0
$544$	−2.52580	+	3.91945i	−0.108293	+	0.168045i
$545$			2.68551i			0.115035i
$546$		0			0
$547$			32.5689i			1.39255i	0.717777	+	0.696273i	$0.245160\pi$
$547$			32.5689i			1.39255i	−0.717777	+	0.696273i	$0.754840\pi$
$548$	−5.94814	+	0.507891i	−0.254092	+	0.0216960i
$549$		0			0
$550$	13.8362	+	12.7052i	0.589980	+	0.541750i
$551$	−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
$556$	9.89392	−	21.1025i	0.419596	−	0.894946i
$557$	−15.6704	+	9.04732i	−0.663977	+	0.383347i	−0.793791	−	0.608191i	$-0.791895\pi$
$557$	−15.6704	+	9.04732i	−0.663977	+	0.383347i	0.129814	+	0.991538i	$0.458562\pi$
$558$		0			0
$559$			21.5894i			0.913136i
$560$	7.74789	+	6.64293i	0.327408	+	0.280715i
$561$		0			0
$562$	−3.96966	−	0.884399i	−0.167450	−	0.0373061i
$563$	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	$0.0513814\pi$
$569$	38.6356	+	22.3063i	1.61969	+	0.935127i	0.632687	+	0.774407i	$0.281952\pi$
$570$		0			0
$571$	22.2316	−	12.8354i	0.930363	−	0.537145i	0.0434368	−	0.999056i	$-0.486169\pi$
$571$	22.2316	−	12.8354i	0.930363	−	0.537145i	0.886926	+	0.461911i	$0.152836\pi$
$572$	1.48185	+	17.3546i	0.0619591	+	0.725631i
$573$		0			0
$574$	−17.8269	+	9.11075i	−0.744082	+	0.380275i
$575$	−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	$-0.333812\pi$
$578$	−17.0007	−	15.6109i	−0.707134	−	0.649327i
$579$		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
$584$	32.7722	+	4.41893i	1.35612	+	0.182857i
$585$		0			0
$586$	40.1208	+	8.93848i	1.65737	+	0.369245i
$587$	−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
$590$	0.634272	+	0.141309i	0.0261126	+	0.00581761i
$591$		0			0
$592$	19.4001	−	3.33734i	0.797339	−	0.137164i
$593$	13.8913	+	8.02017i	0.570449	+	0.329349i	0.757329	−	0.653034i	$-0.226504\pi$
$593$	13.8913	+	8.02017i	0.570449	+	0.329349i	−0.186879	+	0.982383i	$0.559837\pi$
$594$		0			0
$595$	1.61977	−	1.34141i	0.0664039	−	0.0549923i
$596$	−13.7211	−	19.6830i	−0.562038	−	0.806248i
$597$		0			0
$598$	−22.7130	−	20.8562i	−0.928803	−	0.852875i
$599$	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	$0.543184\pi$
$602$	−26.9554	+	13.7760i	−1.09862	+	0.561468i
$603$		0			0
$604$	−21.6941	+	1.85238i	−0.882721	+	0.0753724i
$605$	−0.291599	+	0.168355i	−0.0118552	+	0.00684459i
$606$		0			0
$607$	−0.127387	−	0.0735469i	−0.00517048	−	0.00298518i	0.497413	−	0.867514i	$-0.334284\pi$
$607$	−0.127387	−	0.0735469i	−0.00517048	−	0.00298518i	−0.502583	+	0.864529i	$0.667617\pi$
$608$	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	$0.984080\pi$
$614$	41.9751	+	9.35160i	1.69398	+	0.377400i
$615$		0			0
$616$	−20.7224	+	12.9239i	−0.834931	+	0.520720i
$617$			35.8659i			1.44391i	0.691941	+	0.721954i	$0.256756\pi$
$617$			35.8659i			1.44391i	−0.691941	+	0.721954i	$0.743244\pi$
$618$		0			0
$619$	−9.40387	+	5.42933i	−0.377973	+	0.218223i	−0.676936	−	0.736042i	$-0.736693\pi$
$619$	−9.40387	+	5.42933i	−0.377973	+	0.218223i	0.298963	+	0.954265i	$0.403359\pi$
$620$	−14.0886	−	6.60543i	−0.565810	−	0.265281i
$621$		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
$626$	−30.3221	−	27.8433i	−1.21192	−	1.11284i
$627$		0			0
$628$	1.13639	+	13.3088i	0.0453470	+	0.531080i
$629$		−	4.05648i		−	0.161742i
$630$		0			0
$631$			22.1335i			0.881121i	0.897723	+	0.440561i	$0.145220\pi$
$631$			22.1335i			0.881121i	−0.897723	+	0.440561i	$0.854780\pi$
$632$	−9.91459	+	4.07045i	−0.394381	+	0.161914i
$633$		0			0
$634$	25.7377	−	28.0290i	1.02217	−	1.11317i
$635$	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
$640$	−9.64064	−	5.10843i	−0.381080	−	0.201929i
$641$	−18.3363	+	10.5865i	−0.724242	+	0.418141i	−0.816312	−	0.577611i	$-0.803985\pi$
$641$	−18.3363	+	10.5865i	−0.724242	+	0.418141i	0.0920699	+	0.995753i	$0.470652\pi$
$642$		0			0
$643$		−	14.5277i		−	0.572917i	−0.958093	−	0.286458i	$-0.907522\pi$
$643$		−	14.5277i		−	0.572917i	0.958093	−	0.286458i	$-0.0924780\pi$
$644$	11.5471	−	41.6663i	0.455018	−	1.64188i
$645$		0			0
$646$	1.26293	−	5.66870i	0.0496892	−	0.223032i
$647$	−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	0.100816	−	0.994905i	$-0.467855\pi$
$653$	−18.1532	−	10.4808i	−0.710390	−	0.410144i	−0.811205	+	0.584762i	$0.801188\pi$
$654$		0			0
$655$	1.98524	−	1.14618i	0.0775698	−	0.0447849i
$656$	16.4525	−	13.6887i	0.642361	−	0.534453i
$657$		0			0
$658$	6.80479	+	0.348282i	0.265278	+	0.0135775i
$659$	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	$0.829934\pi$
$662$	−14.4948	+	15.7852i	−0.563358	+	0.613511i
$663$		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
$668$	41.4765	+	19.4463i	1.60477	+	0.752399i
$669$		0			0
$670$	−2.52268	+	11.3231i	−0.0974595	+	0.437451i
$671$	−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	$0.268174\pi$
$674$	−5.12293	+	22.9945i	−0.197328	+	0.885714i
$675$		0			0
$676$	10.6460	+	4.99140i	0.409463	+	0.191977i
$677$	25.6248	+	14.7945i	0.984841	+	0.568598i	0.903728	−	0.428107i	$-0.140819\pi$
$677$	25.6248	+	14.7945i	0.984841	+	0.568598i	0.0811126	+	0.996705i	$0.474153\pi$
$678$		0			0
$679$	−15.1076	+	12.5114i	−0.579778	+	0.480142i
$680$	−1.37426	+	1.77941i	−0.0527004	+	0.0682371i
$681$		0			0
$682$	25.1844	−	27.4264i	0.964360	−	1.05021i
$683$	−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
$686$	−25.1350	+	7.36414i	−0.959660	+	0.281164i
$687$		0			0
$688$	24.8771	−	20.6981i	0.948432	−	0.789107i
$689$	19.7427	−	11.3985i	0.752138	−	0.434247i
$690$		0			0
$691$	−33.9683	−	19.6116i	−1.29221	−	0.746060i	−0.313167	−	0.949698i	$-0.601390\pi$
$691$	−33.9683	−	19.6116i	−1.29221	−	0.746060i	−0.979046	+	0.203638i	$0.934723\pi$
$692$	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
$698$	2.14616	−	9.63314i	0.0812334	−	0.364620i
$699$		0			0
$700$	−15.0979	−	15.3582i	−0.570646	−	0.580486i
$701$		−	30.7510i		−	1.16145i	−0.814100	−	0.580725i	$-0.802769\pi$
$701$		−	30.7510i		−	1.16145i	0.814100	−	0.580725i	$-0.197231\pi$
$702$		0			0
$703$	−21.2336	+	12.2592i	−0.800839	+	0.462365i
$704$	18.5767	−	18.3456i	0.700136	−	0.691425i
$705$		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	$0.251421\pi$
$710$	−6.57204	+	7.15712i	−0.246644	+	0.268602i
$711$		0			0
$712$	41.5248	−	17.0480i	1.55621	−	0.638903i
$713$			65.9206i			2.46875i
$714$		0			0
$715$			8.39846i			0.314084i
$716$	−0.725839	−	8.50064i	−0.0271259	−	0.317684i
$717$		0			0
$718$	4.02978	+	3.70036i	0.150390	+	0.138096i
$719$	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
$724$	35.8631	+	16.8144i	1.33284	+	0.624903i
$725$	−27.1839	+	15.6946i	−1.00958	+	0.582884i
$726$		0			0
$727$		−	24.5723i		−	0.911336i	−0.890150	−	0.455668i	$-0.849400\pi$
$727$		−	24.5723i		−	0.911336i	0.890150	−	0.455668i	$-0.150600\pi$
$728$	−0.679675	−	19.9578i	−0.0251904	−	0.739684i
$729$		0			0
$730$	15.5635	+	3.46738i	0.576030	+	0.128333i
$731$	−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	−0.529349	−	0.848404i	$-0.677564\pi$
$739$	−1.61163	+	0.930477i	−0.0592849	+	0.0342282i	0.470065	+	0.882632i	$0.344231\pi$
$740$	9.45731	−	0.807526i	0.347658	−	0.0296852i
$741$		0			0
$742$	26.8291	+	17.3764i	0.984928	+	0.637909i
$743$	−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
$746$	−1.47504	−	1.35446i	−0.0540050	−	0.0495902i
$747$		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	−0.351069	−	0.936350i	$-0.614182\pi$
$751$	−36.6535	−	21.1619i	−1.33751	−	0.772210i	−0.986437	+	0.164140i	$0.947515\pi$
$752$	−7.17870	+	1.23493i	−0.261780	+	0.0450333i
$753$		0			0
$754$	−28.4086	−	6.32914i	−1.03458	−	0.230494i
$755$	−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	$0.395204\pi$
$758$	−45.4762	−	10.1316i	−1.65177	−	0.367997i
$759$		0			0
$760$	13.4675	+	1.81593i	0.488516	+	0.0658705i
$761$	32.0604	+	18.5101i	1.16219	+	0.670991i	0.951828	−	0.306633i	$-0.0992025\pi$
$761$	32.0604	+	18.5101i	1.16219	+	0.670991i	0.210362	+	0.977624i	$0.432536\pi$
$762$		0			0
$763$	6.90705	+	2.56462i	0.250052	+	0.0928454i
$764$	−29.7476	+	20.7371i	−1.07623	+	0.750243i
$765$		0			0
$766$	38.8655	+	35.6883i	1.40427	+	1.28947i
$767$	−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	$0.598587\pi$
$770$	−10.4859	+	5.35897i	−0.377884	+	0.193124i
$771$		0			0
$772$	4.05925	+	47.5398i	0.146096	+	1.71099i
$773$	−4.25588	+	2.45713i	−0.153073	+	0.0883769i	−0.574580	−	0.818448i	$-0.694835\pi$
$773$	−4.25588	+	2.45713i	−0.153073	+	0.0883769i	0.421507	+	0.906825i	$0.361501\pi$
$774$		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
$782$	9.29699	+	2.07127i	0.332460	+	0.0740685i
$783$		0			0
$784$	24.4845	−	13.5834i	0.874446	−	0.485123i
$785$			6.44058i			0.229874i
$786$		0			0
$787$	−13.4861	+	7.78620i	−0.480727	+	0.277548i	−0.720719	−	0.693227i	$-0.756188\pi$
$787$	−13.4861	+	7.78620i	−0.480727	+	0.277548i	0.239992	+	0.970775i	$0.422855\pi$
$788$	15.2624	−	32.5528i	0.543700	−	1.15964i
$789$		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
$794$	9.33019	+	8.56747i	0.331116	+	0.304048i
$795$		0			0
$796$	8.88384	−	0.758560i	0.314880	−	0.0268864i
$797$			30.5378i			1.08170i	0.841118	+	0.540852i	$0.181898\pi$
$797$			30.5378i			1.08170i	−0.841118	+	0.540852i	$0.818102\pi$
$798$		0			0
$799$			1.50104i			0.0531028i
$800$	19.3530	+	12.4716i	0.684232	+	0.440939i
$801$		0			0
$802$	−15.2764	+	16.6363i	−0.539427	+	0.587449i
$803$	−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
$808$	0.818924	−	6.07339i	0.0288097	−	0.213661i
$809$	23.8487	−	13.7690i	0.838474	−	0.484093i	−0.0182712	−	0.999833i	$-0.505816\pi$
$809$	23.8487	−	13.7690i	0.838474	−	0.484093i	0.856745	+	0.515740i	$0.172483\pi$
$810$		0			0
$811$		−	44.3302i		−	1.55665i	−0.627865	−	0.778323i	$-0.716071\pi$
$811$		−	44.3302i		−	1.55665i	0.627865	−	0.778323i	$-0.283929\pi$
$812$	−10.2250	−	39.5080i	−0.358828	−	1.38646i
$813$		0			0
$814$	−4.93923	+	22.1700i	−0.173120	+	0.777057i
$815$	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	0.647644	−	0.761943i	$-0.275755\pi$
$821$	8.92840	+	5.15482i	0.311603	+	0.179904i	−0.336040	+	0.941848i	$0.609088\pi$
$822$		0			0
$823$	−8.74721	+	5.05020i	−0.304908	+	0.176039i	−0.644646	−	0.764481i	$-0.722995\pi$
$823$	−8.74721	+	5.05020i	−0.304908	+	0.176039i	0.339737	+	0.940520i	$0.389662\pi$
$824$	−46.2051	+	18.9696i	−1.60963	+	0.660836i
$825$		0			0
$826$	0.969161	−	1.49638i	0.0337214	−	0.0520657i
$827$	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	$0.833657\pi$
$830$	0.0622485	−	0.0677902i	0.00216068	−	0.00235303i
$831$		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
$836$	−13.8046	+	29.4435i	−0.477442	+	1.01832i
$837$		0			0
$838$	−2.69503	+	12.0968i	−0.0930984	+	0.417876i
$839$	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
$842$	−4.69060	+	21.0540i	−0.161649	+	0.725568i
$843$		0			0
$844$	1.30226	−	2.77755i	0.0448256	−	0.0956074i
$845$	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
$850$	3.20893	−	3.49461i	0.110065	−	0.119864i
$851$	−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	$0.229609\pi$
$854$	15.6483	+	0.800909i	0.535473	+	0.0274065i
$855$		0			0
$856$	3.81888	+	9.30182i	0.130526	+	0.317930i
$857$	−10.8122	+	6.24242i	−0.369337	+	0.213237i	−0.673169	−	0.739489i	$-0.735067\pi$
$857$	−10.8122	+	6.24242i	−0.369337	+	0.213237i	0.303832	+	0.952726i	$0.401734\pi$
$858$		0			0
$859$	−8.19286	−	4.73015i	−0.279537	−	0.161391i	0.353677	−	0.935368i	$-0.384931\pi$
$859$	−8.19286	−	4.73015i	−0.279537	−	0.161391i	−0.633214	+	0.773977i	$0.718265\pi$
$860$	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
$866$	12.2245	−	54.8704i	0.415407	−	1.86457i
$867$		0			0
$868$	−30.4433	+	29.9273i	−1.03331	+	1.01580i
$869$		−	12.3665i		−	0.419504i
$870$		0			0
$871$	19.6577	−	11.3494i	0.666076	−	0.384559i
$872$	−7.80588	−	1.05253i	−0.264341	−	0.0356432i
$873$		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	$0.103634\pi$
$878$	0.385838	−	0.420188i	0.0130214	−	0.0141806i
$879$		0			0
$880$	9.67739	−	8.05171i	0.326225	−	0.271423i
$881$		−	49.9833i		−	1.68398i	−0.539493	−	0.841990i	$-0.681384\pi$
$881$		−	49.9833i		−	1.68398i	0.539493	−	0.841990i	$-0.318616\pi$
$882$		0			0
$883$		−	57.7771i		−	1.94435i	−0.234250	−	0.972176i	$-0.575263\pi$
$883$		−	57.7771i		−	1.94435i	0.234250	−	0.972176i	$-0.424737\pi$
$884$	4.38323	−	0.374268i	0.147424	−	0.0125880i
$885$		0			0
$886$	4.32368	+	3.97023i	0.145257	+	0.133382i
$887$	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
$892$	0.845928	−	1.80426i	0.0283238	−	0.0604111i
$893$	7.85714	−	4.53632i	0.262929	−	0.151802i
$894$		0			0
$895$		−	4.11374i		−	0.137507i
$896$	−22.3454	+	19.9170i	−0.746506	+	0.665379i
$897$		0			0
$898$	29.4198	+	6.55441i	0.981750	+	0.218724i
$899$	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	−0.820583	−	0.571527i	$-0.806351\pi$
$907$	−22.1632	+	12.7960i	−0.735918	+	0.424883i	0.0846650	+	0.996409i	$0.473018\pi$
$908$	4.83527	+	56.6281i	0.160464	+	1.87927i
$909$		0			0
$910$	0.492176	−	9.61620i	0.0163155	−	0.318774i
$911$	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
$914$	19.0745	+	17.5152i	0.630927	+	0.579350i
$915$		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	0.826678	−	0.562676i	$-0.190228\pi$
$919$	22.8189	+	13.1745i	0.752725	+	0.434586i	−0.0739526	+	0.997262i	$0.523561\pi$
$920$	−2.97822	+	22.0874i	−0.0981891	+	0.728200i
$921$		0			0
$922$	18.6730	+	4.16015i	0.614963	+	0.137007i
$923$	19.0125			0.625804
$924$		0			0
$925$	−20.0296			−0.658570
$926$	16.1912	+	3.60723i	0.532076	+	0.118541i
$927$		0			0
$928$	19.9428	+	38.8026i	0.654654	+	1.27376i
$929$	−16.7968	−	9.69765i	−0.551086	−	0.318170i	0.198474	−	0.980106i	$-0.436402\pi$
$929$	−16.7968	−	9.69765i	−0.551086	−	0.318170i	−0.749560	+	0.661936i	$0.769735\pi$
$930$		0			0
$931$	−22.7605	+	26.4239i	−0.745945	+	0.866007i
$932$	−21.0646	−	30.2174i	−0.689995	−	0.989804i
$933$		0			0
$934$	5.51467	+	5.06386i	0.180445	+	0.165694i
$935$	−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	$0.554708\pi$
$938$	26.7136	+	17.3016i	0.872230	+	0.564918i
$939$		0			0
$940$	−3.49953	+	0.298812i	−0.114142	+	0.00974618i
$941$	−8.83717	+	5.10214i	−0.288083	+	0.166325i	−0.637077	−	0.770800i	$-0.719857\pi$
$941$	−8.83717	+	5.10214i	−0.288083	+	0.166325i	0.348994	+	0.937125i	$0.386523\pi$
$942$		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
$950$	−27.9903	−	6.23594i	−0.908124	−	0.202321i
$951$		0			0
$952$	3.26418	+	5.23385i	0.105793	+	0.169630i
$953$			4.47642i			0.145005i	0.997368	+	0.0725027i	$0.0230986\pi$
$953$			4.47642i			0.145005i	−0.997368	+	0.0725027i	$0.976901\pi$
$954$		0			0
$955$	−15.1423	+	8.74244i	−0.489995	+	0.282899i
$956$	0.990829	+	0.464550i	0.0320457	+	0.0150246i
$957$		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
$962$	−13.6797	−	12.5614i	−0.441051	−	0.404996i
$963$		0			0
$964$	−2.02186	−	23.6790i	−0.0651198	−	0.762648i
$965$			23.0061i			0.740591i
$966$		0			0
$967$		−	23.9578i		−	0.770430i	−0.922827	−	0.385215i	$-0.874127\pi$
$967$		−	23.9578i		−	0.770430i	0.922827	−	0.385215i	$-0.125873\pi$
$968$	−0.375064	−	0.913562i	−0.0120550	−	0.0293630i
$969$		0			0
$970$	6.83887	−	7.44771i	0.219583	−	0.239131i
$971$	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
$976$	−16.5081	+	2.83984i	−0.528412	+	0.0909012i
$977$	20.6125	−	11.9006i	0.659453	−	0.380735i	−0.132616	−	0.991168i	$-0.542338\pi$
$977$	20.6125	−	11.9006i	0.659453	−	0.380735i	0.792068	+	0.610432i	$0.209004\pi$
$978$		0			0
$979$			51.7939i			1.65534i
$980$	12.3203	−	5.52149i	0.393558	−	0.176378i
$981$		0			0
$982$	6.11703	−	27.4565i	0.195202	−	0.876173i
$983$	−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	−0.559648	−	0.828730i	$-0.689064\pi$
$991$	−3.83336	+	2.21319i	−0.121771	+	0.0703044i	0.437877	+	0.899035i	$0.355730\pi$
$992$	24.7215	−	38.3618i	0.784907	−	1.21799i
$993$		0			0
$994$	12.1317	+	23.7380i	0.384794	+	0.752923i
$995$	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	$0.700917\pi$
$998$	−8.50987	+	9.26746i	−0.269375	+	0.293356i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.307532 + 1.38037i) q^{2} +(-1.81085 - 0.849017i) q^{4} +(-0.835158 - 0.482179i) q^{5} +(-2.03771 + 1.68753i) q^{7} +(1.72885 - 2.23854i) q^{8} +O(q^{10})\)	\(q+(-0.307532 + 1.38037i) q^{2} +(-1.81085 - 0.849017i) q^{4} +(-0.835158 - 0.482179i) q^{5} +(-2.03771 + 1.68753i) q^{7} +(1.72885 - 2.23854i) q^{8} +(0.922423 - 1.00454i) q^{10} +(1.63178 + 2.82633i) q^{11} -2.66851 q^{13} +(-1.70275 - 3.33176i) q^{14} +(2.55834 + 3.07488i) q^{16} +(0.713843 - 0.412137i) q^{17} +(-4.31465 - 2.49107i) q^{19} +(1.10297 + 1.58222i) q^{20} +(-4.40321 + 1.38328i) q^{22} +(4.08549 - 7.07628i) q^{23} +(-2.03501 - 3.52474i) q^{25} +(0.820654 - 3.68354i) q^{26} +(5.12272 - 1.32580i) q^{28} -7.71232i q^{29} +(-6.98679 + 4.03382i) q^{31} +(-5.03125 + 2.58583i) q^{32} +(0.349373 + 1.11211i) q^{34} +(2.51550 - 0.426812i) q^{35} +(2.46063 - 4.26194i) q^{37} +(4.76549 - 5.18974i) q^{38} +(-2.52324 + 1.03592i) q^{40} -5.35061i q^{41} -8.09044i q^{43} +(-0.555307 - 6.50346i) q^{44} +(8.51147 + 7.81568i) q^{46} +(-0.910519 + 1.57706i) q^{47} +(1.30451 - 6.87737i) q^{49} +(5.49127 - 1.72510i) q^{50} +(4.83227 + 2.26561i) q^{52} +(-7.39839 + 4.27147i) q^{53} -3.14724i q^{55} +(0.254702 + 7.47898i) q^{56} +(10.6459 + 2.37179i) q^{58} +(0.238238 + 0.412641i) q^{59} +(-2.09383 + 3.62661i) q^{61} +(-3.41951 - 10.8849i) q^{62} +(-2.02214 - 7.74022i) q^{64} +(2.22863 + 1.28670i) q^{65} +(-7.36654 + 4.25307i) q^{67} +(-1.64257 + 0.140253i) q^{68} +(-0.184438 + 3.60358i) q^{70} -7.12475 q^{71} +(5.84578 + 10.1252i) q^{73} +(5.12634 + 4.70727i) q^{74} +(5.69822 + 8.17416i) q^{76} +(-8.09460 - 3.00556i) q^{77} +(-3.28159 - 1.89463i) q^{79} +(-0.653976 - 3.80159i) q^{80} +(7.38582 + 1.64548i) q^{82} +0.0674837 q^{83} -0.794896 q^{85} +(11.1678 + 2.48807i) q^{86} +(9.14796 + 1.23349i) q^{88} +(13.7441 + 7.93517i) q^{89} +(5.43765 - 4.50319i) q^{91} +(-13.4061 + 9.34541i) q^{92} +(-1.89692 - 1.74185i) q^{94} +(2.40228 + 4.16087i) q^{95} +7.41403 q^{97} +(9.09215 + 3.91572i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 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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