LMFDB - Embedded newform 324.3.f.p.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, not 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.207360000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.1
Root			$0.437016 + 0.756934i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.p.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58114 - 1.22474i) q^{2} +(1.00000 + 3.87298i) q^{4} +(3.70246 + 6.41285i) q^{5} +(8.20820 + 4.73901i) q^{7} +(3.16228 - 7.34847i) q^{8} +O(q^{10})$	\(q+(-1.58114 - 1.22474i) q^{2} +(1.00000 + 3.87298i) q^{4} +(3.70246 + 6.41285i) q^{5} +(8.20820 + 4.73901i) q^{7} +(3.16228 - 7.34847i) q^{8} +(2.00000 - 14.6742i) q^{10} +(-5.86319 - 3.38511i) q^{11} +(7.20820 + 12.4850i) q^{13} +(-7.17423 - 17.5460i) q^{14} +(-14.0000 + 7.74597i) q^{16} -17.8933 q^{17} +5.19615i q^{19} +(-21.1344 + 20.7524i) q^{20} +(5.12461 + 12.5332i) q^{22} +(-21.5958 + 12.4683i) q^{23} +(-14.9164 + 25.8360i) q^{25} +(3.89374 - 28.5687i) q^{26} +(-10.1459 + 36.5292i) q^{28} +(14.8098 - 25.6514i) q^{29} +(14.8328 - 8.56373i) q^{31} +(31.6228 + 4.89898i) q^{32} +(28.2918 + 21.9147i) q^{34} +70.1839i q^{35} +6.41641 q^{37} +(6.36396 - 8.21584i) q^{38} +(58.8328 - 6.92820i) q^{40} +(4.32145 + 7.48497i) q^{41} +(-43.4164 - 25.0665i) q^{43} +(7.24730 - 26.0931i) q^{44} +(49.4164 + 6.73516i) q^{46} +(45.0485 + 26.0088i) q^{47} +(20.4164 + 35.3623i) q^{49} +(55.2274 - 22.5815i) q^{50} +(-41.1459 + 40.4022i) q^{52} +82.6921 q^{53} -50.1329i q^{55} +(60.7811 - 45.3317i) q^{56} +(-54.8328 + 22.4201i) q^{58} +(-72.5075 + 41.8622i) q^{59} +(4.20820 - 7.28882i) q^{61} +(-33.9411 - 4.62597i) q^{62} +(-44.0000 - 46.4758i) q^{64} +(-53.3762 + 92.4502i) q^{65} +(-25.1656 + 14.5294i) q^{67} +(-17.8933 - 69.3005i) q^{68} +(85.9574 - 110.971i) q^{70} +113.287i q^{71} +2.16718 q^{73} +(-10.1452 - 7.85846i) q^{74} +(-20.1246 + 5.19615i) q^{76} +(-32.0841 - 55.5714i) q^{77} +(129.457 + 74.7423i) q^{79} +(-101.508 - 61.1007i) q^{80} +(2.33437 - 17.1275i) q^{82} +(11.7264 + 6.77022i) q^{83} +(-66.2492 - 114.747i) q^{85} +(37.9473 + 92.8076i) q^{86} +(-43.4164 + 32.3808i) q^{88} -17.8933 q^{89} +136.639i q^{91} +(-69.8854 - 71.1717i) q^{92} +(-39.3738 - 96.2964i) q^{94} +(-33.3221 + 19.2385i) q^{95} +(69.1656 - 119.798i) q^{97} +(11.0286 - 80.9175i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 12 q^{7}+O(q^{10}) $ 8 * q + 8 * q^4 + 12 * q^7	$ 8 q + 8 q^{4} + 12 q^{7} + 16 q^{10} + 4 q^{13} - 112 q^{16} - 120 q^{22} - 12 q^{25} - 108 q^{28} - 96 q^{31} + 280 q^{34} - 56 q^{37} + 256 q^{40} - 240 q^{43} + 288 q^{46} + 56 q^{49} - 356 q^{52} - 224 q^{58} - 20 q^{61} - 352 q^{64} + 228 q^{67} + 312 q^{70} + 232 q^{73} + 660 q^{79} + 448 q^{82} - 208 q^{85} - 240 q^{88} + 168 q^{94} + 124 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 + 12 * q^7 + 16 * q^10 + 4 * q^13 - 112 * q^16 - 120 * q^22 - 12 * q^25 - 108 * q^28 - 96 * q^31 + 280 * q^34 - 56 * q^37 + 256 * q^40 - 240 * q^43 + 288 * q^46 + 56 * q^49 - 356 * q^52 - 224 * q^58 - 20 * q^61 - 352 * q^64 + 228 * q^67 + 312 * q^70 + 232 * q^73 + 660 * q^79 + 448 * q^82 - 208 * q^85 - 240 * q^88 + 168 * q^94 + 124 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.58114	−	1.22474i	−0.790569	−	0.612372i
$2$	−1.58114	−	1.22474i	−0.790569	−	0.612372i
$3$		0			0
$3$		0			0
$4$	1.00000	+	3.87298i	0.250000	+	0.968246i
$5$	3.70246	+	6.41285i	0.740492	+	1.28257i	0.952272	+	0.305252i	$0.0987407\pi$
$5$	3.70246	+	6.41285i	0.740492	+	1.28257i	−0.211780	+	0.977317i	$0.567926\pi$
$6$		0			0
$7$	8.20820	+	4.73901i	1.17260	+	0.677001i	0.954291	−	0.298878i	$-0.0966125\pi$
$7$	8.20820	+	4.73901i	1.17260	+	0.677001i	0.218309	+	0.975880i	$0.429946\pi$
$8$	3.16228	−	7.34847i	0.395285	−	0.918559i
$9$		0			0
$10$	2.00000	−	14.6742i	0.200000	−	1.46742i
$11$	−5.86319	−	3.38511i	−0.533017	−	0.307737i	0.209227	−	0.977867i	$-0.432905\pi$
$11$	−5.86319	−	3.38511i	−0.533017	−	0.307737i	−0.742244	+	0.670130i	$0.766238\pi$
$12$		0			0
$13$	7.20820	+	12.4850i	0.554477	+	0.960383i	0.997944	+	0.0640919i	$0.0204151\pi$
$13$	7.20820	+	12.4850i	0.554477	+	0.960383i	−0.443467	+	0.896291i	$0.646252\pi$
$14$	−7.17423	−	17.5460i	−0.512445	−	1.25328i
$15$		0			0
$16$	−14.0000	+	7.74597i	−0.875000	+	0.484123i
$17$	−17.8933			−1.05255			−0.526274	−	0.850315i	$-0.676411\pi$
$17$	−17.8933			−1.05255			−0.526274	+	0.850315i	$0.676411\pi$
$18$		0			0
$19$			5.19615i			0.273482i	0.990607	+	0.136741i	$0.0436628\pi$
$19$			5.19615i			0.273482i	−0.990607	+	0.136741i	$0.956337\pi$
$20$	−21.1344	+	20.7524i	−1.05672	+	1.03762i
$21$		0			0
$22$	5.12461	+	12.5332i	0.232937	+	0.569693i
$23$	−21.5958	+	12.4683i	−0.938946	+	0.542101i	−0.889630	−	0.456682i	$-0.849038\pi$
$23$	−21.5958	+	12.4683i	−0.938946	+	0.542101i	−0.0493164	+	0.998783i	$0.515704\pi$
$24$		0			0
$25$	−14.9164	+	25.8360i	−0.596656	+	1.03344i
$26$	3.89374	−	28.5687i	0.149759	−	1.09880i
$27$		0			0
$28$	−10.1459	+	36.5292i	−0.362354	+	1.30462i
$29$	14.8098	−	25.6514i	0.510684	−	0.884531i	−0.489239	−	0.872150i	$-0.662726\pi$
$29$	14.8098	−	25.6514i	0.510684	−	0.884531i	0.999923	−	0.0123811i	$-0.00394113\pi$
$30$		0			0
$31$	14.8328	−	8.56373i	0.478478	−	0.276249i	−0.241304	−	0.970450i	$-0.577575\pi$
$31$	14.8328	−	8.56373i	0.478478	−	0.276249i	0.719782	+	0.694200i	$0.244242\pi$
$32$	31.6228	+	4.89898i	0.988212	+	0.153093i
$33$		0			0
$34$	28.2918	+	21.9147i	0.832112	+	0.644551i
$35$			70.1839i			2.00526i
$36$		0			0
$37$	6.41641			0.173416			0.0867082	−	0.996234i	$-0.472365\pi$
$37$	6.41641			0.173416			0.0867082	+	0.996234i	$0.472365\pi$
$38$	6.36396	−	8.21584i	0.167473	−	0.216206i
$39$		0			0
$40$	58.8328	−	6.92820i	1.47082	−	0.173205i
$41$	4.32145	+	7.48497i	0.105401	+	0.182560i	0.913902	−	0.405935i	$-0.133054\pi$
$41$	4.32145	+	7.48497i	0.105401	+	0.182560i	−0.808501	+	0.588495i	$0.799721\pi$
$42$		0			0
$43$	−43.4164	−	25.0665i	−1.00968	−	0.582941i	−0.0985848	−	0.995129i	$-0.531432\pi$
$43$	−43.4164	−	25.0665i	−1.00968	−	0.582941i	−0.911099	+	0.412187i	$0.864765\pi$
$44$	7.24730	−	26.0931i	0.164711	−	0.593026i
$45$		0			0
$46$	49.4164	+	6.73516i	1.07427	+	0.146416i
$47$	45.0485	+	26.0088i	0.958479	+	0.553378i	0.895705	−	0.444650i	$-0.146672\pi$
$47$	45.0485	+	26.0088i	0.958479	+	0.553378i	0.0627743	+	0.998028i	$0.480005\pi$
$48$		0			0
$49$	20.4164	+	35.3623i	0.416661	+	0.721679i
$50$	55.2274	−	22.5815i	1.10455	−	0.451629i
$51$		0			0
$52$	−41.1459	+	40.4022i	−0.791267	+	0.776966i
$53$	82.6921			1.56023			0.780114	−	0.625637i	$-0.215161\pi$
$53$	82.6921			1.56023			0.780114	+	0.625637i	$0.215161\pi$
$54$		0			0
$55$		−	50.1329i		−	0.911508i
$56$	60.7811	−	45.3317i	1.08538	−	0.809494i
$57$		0			0
$58$	−54.8328	+	22.4201i	−0.945393	+	0.386554i
$59$	−72.5075	+	41.8622i	−1.22894	+	0.709529i	−0.966808	−	0.255503i	$-0.917759\pi$
$59$	−72.5075	+	41.8622i	−1.22894	+	0.709529i	−0.262132	+	0.965032i	$0.584425\pi$
$60$		0			0
$61$	4.20820	−	7.28882i	0.0689869	−	0.119489i	−0.829469	−	0.558553i	$-0.811357\pi$
$61$	4.20820	−	7.28882i	0.0689869	−	0.119489i	0.898456	+	0.439064i	$0.144690\pi$
$62$	−33.9411	−	4.62597i	−0.547438	−	0.0746124i
$63$		0			0
$64$	−44.0000	−	46.4758i	−0.687500	−	0.726184i
$65$	−53.3762	+	92.4502i	−0.821172	+	1.42231i
$66$		0			0
$67$	−25.1656	+	14.5294i	−0.375606	+	0.216856i	−0.675905	−	0.736989i	$-0.736247\pi$
$67$	−25.1656	+	14.5294i	−0.375606	+	0.216856i	0.300299	+	0.953845i	$0.402914\pi$
$68$	−17.8933	−	69.3005i	−0.263137	−	1.01912i
$69$		0			0
$70$	85.9574	−	110.971i	1.22796	−	1.58529i
$71$			113.287i			1.59559i	0.602928	+	0.797796i	$0.294001\pi$
$71$			113.287i			1.59559i	−0.602928	+	0.797796i	$0.705999\pi$
$72$		0			0
$73$	2.16718			0.0296875			0.0148437	−	0.999890i	$-0.495275\pi$
$73$	2.16718			0.0296875			0.0148437	+	0.999890i	$0.495275\pi$
$74$	−10.1452	−	7.85846i	−0.137098	−	0.106195i
$75$		0			0
$76$	−20.1246	+	5.19615i	−0.264798	+	0.0683704i
$77$	−32.0841	−	55.5714i	−0.416677	−	0.721706i
$78$		0			0
$79$	129.457	+	74.7423i	1.63870	+	0.946105i	0.981281	+	0.192581i	$0.0616858\pi$
$79$	129.457	+	74.7423i	1.63870	+	0.946105i	0.657421	+	0.753524i	$0.271648\pi$
$80$	−101.508	−	61.1007i	−1.26885	−	0.763759i
$81$		0			0
$82$	2.33437	−	17.1275i	0.0284679	−	0.208871i
$83$	11.7264	+	6.77022i	0.141282	+	0.0815690i	0.568975	−	0.822355i	$-0.307340\pi$
$83$	11.7264	+	6.77022i	0.141282	+	0.0815690i	−0.427693	+	0.903924i	$0.640674\pi$
$84$		0			0
$85$	−66.2492	−	114.747i	−0.779403	−	1.34996i
$86$	37.9473	+	92.8076i	0.441248	+	1.07916i
$87$		0			0
$88$	−43.4164	+	32.3808i	−0.493368	+	0.367963i
$89$	−17.8933			−0.201048			−0.100524	−	0.994935i	$-0.532052\pi$
$89$	−17.8933			−0.201048			−0.100524	+	0.994935i	$0.532052\pi$
$90$		0			0
$91$			136.639i			1.50153i
$92$	−69.8854	−	71.1717i	−0.759623	−	0.773606i
$93$		0			0
$94$	−39.3738	−	96.2964i	−0.418871	−	1.02443i
$95$	−33.3221	+	19.2385i	−0.350759	+	0.202511i
$96$		0			0
$97$	69.1656	−	119.798i	0.713048	−	1.23503i	−0.250660	−	0.968075i	$-0.580648\pi$
$97$	69.1656	−	119.798i	0.713048	−	1.23503i	0.963708	−	0.266960i	$-0.0860191\pi$
$98$	11.0286	−	80.9175i	0.112536	−	0.825689i
$99$		0			0
$100$	−114.979	−	31.9350i	−1.14979	−	0.319350i
$101$	48.7510	−	84.4391i	0.482683	−	0.836031i	−0.517120	−	0.855913i	$-0.672996\pi$
$101$	48.7510	−	84.4391i	0.482683	−	0.836031i	0.999802	+	0.0198821i	$0.00632907\pi$
$102$		0			0
$103$	−36.7918	+	21.2418i	−0.357202	+	0.206231i	−0.667853	−	0.744294i	$-0.732786\pi$
$103$	−36.7918	+	21.2418i	−0.357202	+	0.206231i	0.310651	+	0.950524i	$0.399453\pi$
$104$	114.540	−	13.4883i	1.10134	−	0.129695i
$105$		0			0
$106$	−130.748	−	101.277i	−1.23347	−	0.955441i
$107$		−	97.2648i		−	0.909017i	−0.890742	−	0.454509i	$-0.849815\pi$
$107$		−	97.2648i		−	0.909017i	0.890742	−	0.454509i	$-0.150185\pi$
$108$		0			0
$109$	−96.8328			−0.888374			−0.444187	−	0.895934i	$-0.646507\pi$
$109$	−96.8328			−0.888374			−0.444187	+	0.895934i	$0.646507\pi$
$110$	−61.4001	+	79.2672i	−0.558182	+	0.720610i
$111$		0			0
$112$	−151.623	−	2.76565i	−1.35378	−	0.0246933i
$113$	19.4350	+	33.6625i	0.171991	+	0.297898i	0.939116	−	0.343600i	$-0.111647\pi$
$113$	19.4350	+	33.6625i	0.171991	+	0.297898i	−0.767125	+	0.641498i	$0.778313\pi$
$114$		0			0
$115$	−159.915	−	92.3269i	−1.39056	−	0.802842i
$116$	114.157	+	31.7069i	0.984114	+	0.273335i
$117$		0			0
$118$	165.915	+	22.6132i	1.40606	+	0.191637i
$119$	−146.872	−	84.7965i	−1.23422	−	0.712576i
$120$		0			0
$121$	−37.5820	−	65.0940i	−0.310595	−	0.537967i
$122$	−15.5807	+	6.37066i	−0.127711	+	0.0522186i
$123$		0			0
$124$	48.0000	+	48.8835i	0.387097	+	0.394222i
$125$	−35.7866			−0.286293
$126$		0			0
$127$		−	99.0165i		−	0.779657i	−0.920887	−	0.389829i	$-0.872534\pi$
$127$		−	99.0165i		−	0.779657i	0.920887	−	0.389829i	$-0.127466\pi$
$128$	12.6491	+	127.373i	0.0988212	+	0.995105i
$129$		0			0
$130$	197.623	−	80.8045i	1.52018	−	0.621573i
$131$	46.9055	−	27.0809i	0.358057	−	0.206724i	−0.310171	−	0.950681i	$-0.600386\pi$
$131$	46.9055	−	27.0809i	0.358057	−	0.206724i	0.668228	+	0.743956i	$0.267053\pi$
$132$		0			0
$133$	−24.6246	+	42.6511i	−0.185147	+	0.320685i
$134$	57.5851	+	7.84850i	0.429740	+	0.0585709i
$135$		0			0
$136$	−56.5836	+	131.488i	−0.416056	+	0.966826i
$137$	−2.77972	+	4.81461i	−0.0202899	+	0.0351432i	−0.875992	−	0.482325i	$-0.839792\pi$
$137$	−2.77972	+	4.81461i	−0.0202899	+	0.0351432i	0.855702	+	0.517469i	$0.173126\pi$
$138$		0			0
$139$	132.084	−	76.2585i	0.950242	−	0.548622i	0.0570857	−	0.998369i	$-0.481819\pi$
$139$	132.084	−	76.2585i	0.950242	−	0.548622i	0.893156	+	0.449747i	$0.148486\pi$
$140$	−271.821	+	70.1839i	−1.94158	+	0.501314i
$141$		0			0
$142$	138.748	−	179.122i	0.977096	−	1.26143i
$143$		−	97.6023i		−	0.682534i
$144$		0			0
$145$	219.331			1.51263
$146$	−3.42662	−	2.65425i	−0.0234700	−	0.0181798i
$147$		0			0
$148$	6.41641	+	24.8506i	0.0433541	+	0.167910i
$149$	68.4897	+	118.628i	0.459663	+	0.796159i	0.998943	−	0.0459672i	$-0.0146370\pi$
$149$	68.4897	+	118.628i	0.459663	+	0.796159i	−0.539280	+	0.842126i	$0.681304\pi$
$150$		0			0
$151$	−67.5395	−	38.9939i	−0.447281	−	0.258238i	0.259400	−	0.965770i	$-0.416475\pi$
$151$	−67.5395	−	38.9939i	−0.447281	−	0.258238i	−0.706681	+	0.707532i	$0.749809\pi$
$152$	38.1838	+	16.4317i	0.251209	+	0.108103i
$153$		0			0
$154$	−17.3313	+	127.161i	−0.112541	+	0.825720i
$155$	109.836	+	63.4137i	0.708618	+	0.409121i
$156$		0			0
$157$	36.0820	+	62.4959i	0.229822	+	0.398063i	0.957755	−	0.287585i	$-0.0928523\pi$
$157$	36.0820	+	62.4959i	0.229822	+	0.398063i	−0.727933	+	0.685648i	$0.759519\pi$
$158$	−113.150	−	276.730i	−0.716139	−	1.75146i
$159$		0			0
$160$	85.6656	+	220.930i	0.535410	+	1.38081i
$161$	−236.350			−1.46801
$162$		0			0
$163$		−	56.5785i		−	0.347108i	−0.984824	−	0.173554i	$-0.944475\pi$
$163$		−	56.5785i		−	0.347108i	0.984824	−	0.173554i	$-0.0555250\pi$
$164$	−24.6677	+	24.2219i	−0.150413	+	0.147694i
$165$		0			0
$166$	−10.2492	−	25.0665i	−0.0617423	−	0.151003i
$167$	174.623	−	100.819i	1.04565	−	0.603705i	0.124220	−	0.992255i	$-0.460357\pi$
$167$	174.623	−	100.819i	1.04565	−	0.603705i	0.921428	+	0.388550i	$0.127024\pi$
$168$		0			0
$169$	−19.4164	+	33.6302i	−0.114890	+	0.198995i
$170$	−35.7866	+	262.569i	−0.210509	+	1.54453i
$171$		0			0
$172$	53.6656	−	193.217i	0.312009	−	1.12336i
$173$	46.2750	−	80.1506i	0.267485	−	0.463298i	−0.700726	−	0.713430i	$-0.747141\pi$
$173$	46.2750	−	80.1506i	0.267485	−	0.463298i	0.968212	+	0.250132i	$0.0804739\pi$
$174$		0			0
$175$	−244.874	+	141.378i	−1.39928	+	0.807874i
$176$	108.306	+	1.97552i	0.615372	+	0.0112246i
$177$		0			0
$178$	28.2918	+	21.9147i	0.158943	+	0.123116i
$179$			4.28851i			0.0239581i	0.999928	+	0.0119791i	$0.00381315\pi$
$179$			4.28851i			0.0239581i	−0.999928	+	0.0119791i	$0.996187\pi$
$180$		0			0
$181$	−289.748			−1.60082			−0.800408	−	0.599456i	$-0.795384\pi$
$181$	−289.748			−1.60082			−0.800408	+	0.599456i	$0.795384\pi$
$182$	167.348	−	216.045i	0.919494	−	1.18706i
$183$		0			0
$184$	23.3313	+	198.124i	0.126800	+	1.07676i
$185$	23.7565	+	41.1474i	0.128413	+	0.222419i
$186$		0			0
$187$	104.912	+	60.5708i	0.561025	+	0.323908i
$188$	−55.6830	+	200.481i	−0.296186	+	1.06639i
$189$		0			0
$190$	76.2492	+	10.3923i	0.401312	+	0.0546963i
$191$	80.2276	+	46.3194i	0.420040	+	0.242510i	0.695094	−	0.718919i	$-0.255363\pi$
$191$	80.2276	+	46.3194i	0.420040	+	0.242510i	−0.275055	+	0.961429i	$0.588696\pi$
$192$		0			0
$193$	121.582	+	210.586i	0.629959	+	1.09112i	0.987559	+	0.157246i	$0.0502616\pi$
$193$	121.582	+	210.586i	0.629959	+	1.09112i	−0.357601	+	0.933875i	$0.616405\pi$
$194$	−256.083	+	104.708i	−1.32002	+	0.539730i
$195$		0			0
$196$	−116.541	+	114.435i	−0.594597	+	0.583850i
$197$	139.432			0.707779			0.353890	−	0.935287i	$-0.384859\pi$
$197$	139.432			0.707779			0.353890	+	0.935287i	$0.384859\pi$
$198$		0			0
$199$		−	110.993i		−	0.557756i	−0.960327	−	0.278878i	$-0.910038\pi$
$199$		−	110.993i		−	0.557756i	0.960327	−	0.278878i	$-0.0899624\pi$
$200$	142.685	+	191.313i	0.713425	+	0.956566i
$201$		0			0
$202$	−180.498	+	73.8025i	−0.893557	+	0.365359i
$203$	243.124	−	140.368i	1.19766	−	0.691467i
$204$		0			0
$205$	−32.0000	+	55.4256i	−0.156098	+	0.270369i
$206$	84.1887	+	11.4744i	0.408683	+	0.0557010i
$207$		0			0
$208$	−197.623	−	118.955i	−0.950111	−	0.571900i
$209$	17.5896	−	30.4660i	0.0841606	−	0.145770i
$210$		0			0
$211$	229.579	−	132.547i	1.08805	−	0.628187i	0.154995	−	0.987915i	$-0.450464\pi$
$211$	229.579	−	132.547i	1.08805	−	0.628187i	0.933057	+	0.359728i	$0.117131\pi$
$212$	82.6921	+	320.265i	0.390057	+	1.51068i
$213$		0			0
$214$	−119.125	+	153.789i	−0.556657	+	0.718641i
$215$		−	371.230i		−	1.72665i
$216$		0			0
$217$	162.334			0.748085
$218$	153.106	+	118.595i	0.702322	+	0.544016i
$219$		0			0
$220$	194.164	−	50.1329i	0.882564	−	0.227877i
$221$	−128.979	−	223.397i	−0.583613	−	1.01085i
$222$		0			0
$223$	275.331	+	158.963i	1.23467	+	0.712837i	0.968000	−	0.250951i	$-0.0807434\pi$
$223$	275.331	+	158.963i	1.23467	+	0.712837i	0.266670	+	0.963788i	$0.414077\pi$
$224$	236.350	+	190.072i	1.05513	+	0.848538i
$225$		0			0
$226$	10.4984	−	77.0280i	0.0464533	−	0.340832i
$227$	−215.958	−	124.683i	−0.951355	−	0.549265i	−0.0578535	−	0.998325i	$-0.518426\pi$
$227$	−215.958	−	124.683i	−0.951355	−	0.549265i	−0.893502	+	0.449060i	$0.851759\pi$
$228$		0			0
$229$	−76.1672	−	131.925i	−0.332608	−	0.576094i	0.650415	−	0.759579i	$-0.274595\pi$
$229$	−76.1672	−	131.925i	−0.332608	−	0.576094i	−0.983022	+	0.183486i	$0.941262\pi$
$230$	139.771	+	341.837i	0.607699	+	1.48625i
$231$		0			0
$232$	−141.666	−	189.946i	−0.610628	−	0.818735i
$233$	346.793			1.48838			0.744191	−	0.667966i	$-0.232835\pi$
$233$	346.793			1.48838			0.744191	+	0.667966i	$0.232835\pi$
$234$		0			0
$235$			385.186i			1.63909i
$236$	−234.639	−	238.958i	−0.994233	−	1.01253i
$237$		0			0
$238$	128.371	+	313.956i	0.539373	+	1.31914i
$239$	−90.0970	+	52.0175i	−0.376975	+	0.217647i	−0.676501	−	0.736441i	$-0.736505\pi$
$239$	−90.0970	+	52.0175i	−0.376975	+	0.217647i	0.299526	+	0.954088i	$0.403171\pi$
$240$		0			0
$241$	−140.913	+	244.069i	−0.584702	+	1.01273i	0.410210	+	0.911991i	$0.365455\pi$
$241$	−140.913	+	244.069i	−0.584702	+	1.01273i	−0.994912	+	0.100743i	$0.967878\pi$
$242$	−20.3011	+	148.951i	−0.0838889	+	0.615500i
$243$		0			0
$244$	32.4377	+	9.00948i	0.132941	+	0.0369241i
$245$	−151.182	+	261.855i	−0.617069	+	1.06879i
$246$		0			0
$247$	−64.8738	+	37.4549i	−0.262647	+	0.151639i
$248$	−16.0248	−	136.079i	−0.0646162	−	0.548707i
$249$		0			0
$250$	56.5836	+	43.8295i	0.226334	+	0.175318i
$251$		−	271.484i		−	1.08161i	−0.841148	−	0.540804i	$-0.818120\pi$
$251$		−	271.484i		−	1.08161i	0.841148	−	0.540804i	$-0.181880\pi$
$252$		0			0
$253$	168.827			0.667299
$254$	−121.270	+	156.559i	−0.477441	+	0.616373i
$255$		0			0
$256$	136.000	−	216.887i	0.531250	−	0.847215i
$257$	−229.552	−	397.597i	−0.893200	−	1.54707i	−0.836016	−	0.548705i	$-0.815121\pi$
$257$	−229.552	−	397.597i	−0.893200	−	1.54707i	−0.0571840	−	0.998364i	$-0.518212\pi$
$258$		0			0
$259$	52.6672	+	30.4074i	0.203348	+	0.117403i
$260$	−411.434	−	114.275i	−1.58244	−	0.439518i
$261$		0			0
$262$	−107.331	−	14.6286i	−0.409661	−	0.0558343i
$263$	176.480	+	101.891i	0.671027	+	0.387418i	0.796466	−	0.604684i	$-0.206701\pi$
$263$	176.480	+	101.891i	0.671027	+	0.387418i	−0.125439	+	0.992101i	$0.540034\pi$
$264$		0			0
$265$	306.164	+	530.292i	1.15534	+	2.00110i
$266$	91.1716	−	37.2784i	0.342750	−	0.140144i
$267$		0			0
$268$	−81.4377	−	82.9367i	−0.303872	−	0.309465i
$269$	−323.363			−1.20209			−0.601047	−	0.799213i	$-0.705250\pi$
$269$	−323.363			−1.20209			−0.601047	+	0.799213i	$0.705250\pi$
$270$		0			0
$271$			104.928i			0.387190i	0.981082	+	0.193595i	$0.0620148\pi$
$271$			104.928i			0.387190i	−0.981082	+	0.193595i	$0.937985\pi$
$272$	250.506	−	138.601i	0.920979	−	0.509562i
$273$		0			0
$274$	10.2918	−	4.20813i	0.0375613	−	0.0153581i
$275$	174.915	−	100.987i	0.636056	−	0.367227i
$276$		0			0
$277$	24.4164	−	42.2905i	0.0881459	−	0.152673i	−0.818582	−	0.574390i	$-0.805239\pi$
$277$	24.4164	−	42.2905i	0.0881459	−	0.152673i	0.906727	+	0.421717i	$0.138573\pi$
$278$	−302.240	−	41.1934i	−1.08719	−	0.148178i
$279$		0			0
$280$	515.745	+	221.941i	1.84194	+	0.792647i
$281$	14.8098	−	25.6514i	0.0527040	−	0.0912861i	−0.838470	−	0.544948i	$-0.816549\pi$
$281$	14.8098	−	25.6514i	0.0527040	−	0.0912861i	0.891174	+	0.453662i	$0.149883\pi$
$282$		0			0
$283$	333.580	−	192.593i	1.17873	−	0.680540i	0.223009	−	0.974816i	$-0.428412\pi$
$283$	333.580	−	192.593i	1.17873	−	0.680540i	0.955720	+	0.294276i	$0.0950786\pi$
$284$	−438.759	+	113.287i	−1.54492	+	0.398898i
$285$		0			0
$286$	−119.538	+	154.323i	−0.417965	+	0.539590i
$287$			81.9176i			0.285427i
$288$		0			0
$289$	31.1703			0.107856
$290$	−346.793	−	268.625i	−1.19584	−	0.926293i
$291$		0			0
$292$	2.16718	+	8.39347i	0.00742186	+	0.0287448i
$293$	140.705	+	243.708i	0.480222	+	0.831768i	0.999743	−	0.0226894i	$-0.00722289\pi$
$293$	140.705	+	243.708i	0.480222	+	0.831768i	−0.519521	+	0.854458i	$0.673890\pi$
$294$		0			0
$295$	−536.912	−	309.986i	−1.82004	−	1.05080i
$296$	20.2905	−	47.1508i	0.0685489	−	0.159293i
$297$		0			0
$298$	36.9969	−	271.449i	0.124151	−	0.910904i
$299$	−311.333	−	179.748i	−1.04125	−	0.601165i
$300$		0			0
$301$	−237.580	−	411.501i	−0.789304	−	1.36711i
$302$	59.0317	+	144.373i	0.195469	+	0.478058i
$303$		0			0
$304$	−40.2492	−	72.7461i	−0.132399	−	0.239296i
$305$	62.3228			0.204337
$306$		0			0
$307$		−	553.961i		−	1.80443i	−0.431282	−	0.902217i	$-0.641939\pi$
$307$		−	553.961i		−	1.80443i	0.431282	−	0.902217i	$-0.358061\pi$
$308$	183.143	−	179.833i	0.594620	−	0.583873i
$309$		0			0
$310$	−96.0000	−	234.787i	−0.309677	−	0.757377i
$311$	13.5833	−	7.84235i	0.0436764	−	0.0252166i	−0.478003	−	0.878358i	$-0.658639\pi$
$311$	13.5833	−	7.84235i	0.0436764	−	0.0252166i	0.521679	+	0.853142i	$0.325306\pi$
$312$		0			0
$313$	154.080	−	266.875i	0.492270	−	0.852637i	−0.507690	−	0.861540i	$-0.669501\pi$
$313$	154.080	−	266.875i	0.492270	−	0.852637i	0.999960	+	0.00890304i	$0.00283396\pi$
$314$	19.4909	−	143.006i	0.0620728	−	0.455433i
$315$		0			0
$316$	−160.018	+	576.129i	−0.506387	+	1.82319i
$317$	−248.053	+	429.641i	−0.782502	+	1.35533i	0.147977	+	0.988991i	$0.452724\pi$
$317$	−248.053	+	429.641i	−0.782502	+	1.35533i	−0.930480	+	0.366343i	$0.880610\pi$
$318$		0			0
$319$	−173.666	+	100.266i	−0.544406	+	0.314313i
$320$	135.134	−	454.240i	0.422294	−	1.41950i
$321$		0			0
$322$	373.702	+	289.468i	1.16057	+	0.898970i
$323$		−	92.9763i		−	0.287852i
$324$		0			0
$325$	−430.082			−1.32333
$326$	−69.2943	+	89.4585i	−0.212559	+	0.274413i
$327$		0			0
$328$	68.6687	−	8.08649i	0.209356	−	0.0246539i
$329$	246.512	+	426.970i	0.749275	+	1.29778i
$330$		0			0
$331$	−74.9164	−	43.2530i	−0.226334	−	0.130674i	0.382546	−	0.923936i	$-0.375047\pi$
$331$	−74.9164	−	43.2530i	−0.226334	−	0.130674i	−0.608879	+	0.793263i	$0.708381\pi$
$332$	−14.4946	+	52.1863i	−0.0436584	+	0.157188i
$333$		0			0
$334$	−399.580	−	54.4604i	−1.19635	−	0.163055i
$335$	−186.349	−	107.589i	−0.556267	−	0.321161i
$336$		0			0
$337$	−160.330	−	277.699i	−0.475756	−	0.824033i	0.523858	−	0.851805i	$-0.324492\pi$
$337$	−160.330	−	277.699i	−0.475756	−	0.824033i	−0.999614	+	0.0277721i	$0.991159\pi$
$338$	71.8885	−	29.3939i	0.212688	−	0.0869641i
$339$		0			0
$340$	378.164	−	371.329i	1.11225	−	1.09214i
$341$	−115.957			−0.340049
$342$		0			0
$343$		−	77.4087i		−	0.225681i
$344$	−321.495	+	239.777i	−0.934578	+	0.697026i
$345$		0			0
$346$	−171.331	+	70.0542i	−0.495177	+	0.202469i
$347$	−584.358	+	337.379i	−1.68403	+	0.972275i	−0.725093	+	0.688650i	$0.758203\pi$
$347$	−584.358	+	337.379i	−1.68403	+	0.972275i	−0.958936	+	0.283624i	$0.908463\pi$
$348$		0			0
$349$	−76.9590	+	133.297i	−0.220513	+	0.381939i	−0.954964	−	0.296722i	$-0.904106\pi$
$349$	−76.9590	+	133.297i	−0.220513	+	0.381939i	0.734451	+	0.678662i	$0.237440\pi$
$350$	560.331	+	76.3698i	1.60095	+	0.218199i
$351$		0			0
$352$	−168.827	−	135.770i	−0.479621	−	0.385711i
$353$	311.614	−	539.731i	0.882759	−	1.52898i	0.0344990	−	0.999405i	$-0.489016\pi$
$353$	311.614	−	539.731i	0.882759	−	1.52898i	0.848260	−	0.529579i	$-0.177650\pi$
$354$		0			0
$355$	−726.492	+	419.440i	−2.04646	+	1.18152i
$356$	−17.8933	−	69.3005i	−0.0502621	−	0.194664i
$357$		0			0
$358$	5.25233	−	6.78073i	0.0146713	−	0.0189406i
$359$			160.341i			0.446633i	0.974746	+	0.223316i	$0.0716883\pi$
$359$			160.341i			0.446633i	−0.974746	+	0.223316i	$0.928312\pi$
$360$		0			0
$361$	334.000			0.925208
$362$	458.131	+	354.867i	1.26556	+	0.980296i
$363$		0			0
$364$	−529.200	+	136.639i	−1.45385	+	0.375382i
$365$	8.02391	+	13.8978i	0.0219833	+	0.0380762i
$366$		0			0
$367$	246.457	+	142.292i	0.671546	+	0.387717i	0.796662	−	0.604425i	$-0.206597\pi$
$367$	246.457	+	142.292i	0.671546	+	0.387717i	−0.125116	+	0.992142i	$0.539930\pi$
$368$	205.761	−	341.837i	0.559134	−	0.928904i
$369$		0			0
$370$	12.8328	−	94.1555i	0.0346833	−	0.254474i
$371$	678.754	+	391.879i	1.82952	+	1.05628i
$372$		0			0
$373$	−150.710	−	261.037i	−0.404048	−	0.699831i	0.590163	−	0.807284i	$-0.299064\pi$
$373$	−150.710	−	261.037i	−0.404048	−	0.699831i	−0.994210	+	0.107453i	$0.965730\pi$
$374$	−91.6962	−	224.261i	−0.245177	−	0.599628i
$375$		0			0
$376$	333.580	−	248.791i	0.887182	−	0.661677i
$377$	427.009			1.13265
$378$		0			0
$379$			248.547i			0.655796i	0.944713	+	0.327898i	$0.106340\pi$
$379$			248.547i			0.655796i	−0.944713	+	0.327898i	$0.893660\pi$
$380$	−107.833	−	109.818i	−0.283770	−	0.288993i
$381$		0			0
$382$	−70.1215	−	171.496i	−0.183564	−	0.448942i
$383$	422.734	−	244.065i	1.10374	−	0.637247i	0.166542	−	0.986034i	$-0.446740\pi$
$383$	422.734	−	244.065i	1.10374	−	0.637247i	0.937202	+	0.348788i	$0.113407\pi$
$384$		0			0
$385$	237.580	−	411.501i	0.617092	−	1.06883i
$386$	65.6764	−	481.873i	0.170146	−	1.24838i
$387$		0			0
$388$	533.143	+	148.079i	1.37408	+	0.381647i
$389$	207.934	−	360.152i	0.534534	−	0.925840i	−0.464652	−	0.885493i	$-0.653820\pi$
$389$	207.934	−	360.152i	0.534534	−	0.925840i	0.999186	−	0.0403465i	$-0.0128462\pi$
$390$		0			0
$391$	386.420	−	223.099i	0.988285	−	0.570587i
$392$	324.421	−	38.2041i	0.827604	−	0.0974594i
$393$		0			0
$394$	−220.462	−	170.769i	−0.559548	−	0.433424i
$395$			1106.92i			2.80233i
$396$		0			0
$397$	−670.827			−1.68974			−0.844870	−	0.534972i	$-0.820322\pi$
$397$	−670.827			−1.68974			−0.844870	+	0.534972i	$0.820322\pi$
$398$	−135.939	+	175.496i	−0.341554	+	0.440944i
$399$		0			0
$400$	8.70510	−	477.246i	0.0217627	−	1.19311i
$401$	−57.3709	−	99.3693i	−0.143070	−	0.247804i	0.785582	−	0.618758i	$-0.212364\pi$
$401$	−57.3709	−	99.3693i	−0.143070	−	0.247804i	−0.928651	+	0.370955i	$0.879031\pi$
$402$		0			0
$403$	213.836	+	123.458i	0.530610	+	0.306348i
$404$	375.782	+	104.373i	0.930154	+	0.258348i
$405$		0			0
$406$	−556.328	−	75.8241i	−1.37027	−	0.186759i
$407$	−37.6206	−	21.7203i	−0.0924339	−	0.0533667i
$408$		0			0
$409$	73.3359	+	127.022i	0.179305	+	0.310566i	0.941643	−	0.336614i	$-0.109282\pi$
$409$	73.3359	+	127.022i	0.179305	+	0.310566i	−0.762337	+	0.647180i	$0.775948\pi$
$410$	118.479	−	48.4438i	0.288972	−	0.118156i
$411$		0			0
$412$	−119.061	−	121.252i	−0.288982	−	0.294302i
$413$	−793.541			−1.92141
$414$		0			0
$415$			100.266i			0.241605i
$416$	166.780	+	430.122i	0.400913	+	1.03395i
$417$		0			0
$418$	−65.1246	+	26.6283i	−0.155801	+	0.0637040i
$419$	−464.945	+	268.436i	−1.10965	+	0.640659i	−0.938740	−	0.344627i	$-0.888005\pi$
$419$	−464.945	+	268.436i	−1.10965	+	0.640659i	−0.170914	+	0.985286i	$0.554672\pi$
$420$		0			0
$421$	183.707	−	318.189i	0.436358	−	0.755794i	−0.561048	−	0.827784i	$-0.689602\pi$
$421$	183.707	−	318.189i	0.436358	−	0.755794i	0.997405	+	0.0719896i	$0.0229349\pi$
$422$	−525.333	−	71.5997i	−1.24486	−	0.169668i
$423$		0			0
$424$	261.495	−	607.660i	0.616734	−	1.43316i
$425$	266.904	−	462.291i	0.628009	−	1.08774i
$426$		0			0
$427$	69.0836	−	39.8854i	0.161788	−	0.0934085i
$428$	376.705	−	97.2648i	0.880152	−	0.227254i
$429$		0			0
$430$	−454.663	+	586.967i	−1.05735	+	1.36504i
$431$			735.353i			1.70616i	0.521784	+	0.853078i	$0.325267\pi$
$431$			735.353i			1.70616i	−0.521784	+	0.853078i	$0.674733\pi$
$432$		0			0
$433$	765.161			1.76712			0.883558	−	0.468322i	$-0.155141\pi$
$433$	765.161			1.76712			0.883558	+	0.468322i	$0.155141\pi$
$434$	−256.673	−	198.818i	−0.591413	−	0.458106i
$435$		0			0
$436$	−96.8328	−	375.032i	−0.222094	−	0.860165i
$437$	−64.7873	−	112.215i	−0.148255	−	0.256785i
$438$		0			0
$439$	−40.1703	−	23.1923i	−0.0915041	−	0.0528299i	0.453550	−	0.891231i	$-0.350157\pi$
$439$	−40.1703	−	23.1923i	−0.0915041	−	0.0528299i	−0.545054	+	0.838401i	$0.683491\pi$
$440$	−368.400	−	158.534i	−0.837274	−	0.360305i
$441$		0			0
$442$	−69.6718	+	511.188i	−0.157629	+	1.15653i
$443$	120.978	+	69.8465i	0.273087	+	0.157667i	0.630290	−	0.776360i	$-0.282936\pi$
$443$	120.978	+	69.8465i	0.273087	+	0.157667i	−0.357203	+	0.934027i	$0.616269\pi$
$444$		0			0
$445$	−66.2492	−	114.747i	−0.148875	−	0.257858i
$446$	−240.648	−	588.552i	−0.539570	−	1.31962i
$447$		0			0
$448$	−140.912	−	589.999i	−0.314535	−	1.31696i
$449$	−267.139			−0.594963			−0.297482	−	0.954728i	$-0.596147\pi$
$449$	−267.139			−0.594963			−0.297482	+	0.954728i	$0.596147\pi$
$450$		0			0
$451$		−	58.5144i		−	0.129744i
$452$	−110.939	+	108.934i	−0.245441	+	0.241005i
$453$		0			0
$454$	188.754	+	461.634i	0.415757	+	1.01682i
$455$	−876.245	+	505.900i	−1.92581	+	1.11187i
$456$		0			0
$457$	−118.915	+	205.967i	−0.260208	+	0.450693i	−0.966297	−	0.257430i	$-0.917124\pi$
$457$	−118.915	+	205.967i	−0.260208	+	0.450693i	0.706089	+	0.708123i	$0.250458\pi$
$458$	−41.1441	+	301.878i	−0.0898343	+	0.659122i
$459$		0			0
$460$	197.666	−	711.674i	0.429708	−	1.54712i
$461$	−149.325	+	258.638i	−0.323915	+	0.561037i	−0.981292	−	0.192524i	$-0.938333\pi$
$461$	−149.325	+	258.638i	−0.323915	+	0.561037i	0.657377	+	0.753562i	$0.271666\pi$
$462$		0			0
$463$	423.950	−	244.767i	0.915658	−	0.528655i	0.0334107	−	0.999442i	$-0.489363\pi$
$463$	423.950	−	244.767i	0.915658	−	0.528655i	0.882247	+	0.470786i	$0.156030\pi$
$464$	−8.64290	+	473.836i	−0.0186269	+	1.02120i
$465$		0			0
$466$	−548.328	−	424.733i	−1.17667	−	0.911445i
$467$		−	454.280i		−	0.972762i	−0.873747	−	0.486381i	$-0.838317\pi$
$467$		−	454.280i		−	0.972762i	0.873747	−	0.486381i	$-0.161683\pi$
$468$		0			0
$469$	−275.420			−0.587248
$470$	471.754	−	609.032i	1.00373	−	1.29581i
$471$		0			0
$472$	78.3344	+	665.199i	0.165963	+	1.40932i
$473$	169.706	+	293.939i	0.358786	+	0.621435i
$474$		0			0
$475$	−134.248	−	77.5079i	−0.282627	−	0.163175i
$476$	181.544	−	653.629i	0.381394	−	1.37317i
$477$		0			0
$478$	206.164	+	28.0989i	0.431306	+	0.0587843i
$479$	−3.12946	−	1.80679i	−0.00653332	−	0.00377201i	0.496730	−	0.867905i	$-0.334534\pi$
$479$	−3.12946	−	1.80679i	−0.00653332	−	0.00377201i	−0.503263	+	0.864133i	$0.667867\pi$
$480$		0			0
$481$	46.2508	+	80.1087i	0.0961555	+	0.166546i
$482$	521.726	−	213.324i	1.08242	−	0.442581i
$483$		0			0
$484$	214.526	−	210.649i	0.443235	−	0.435224i
$485$	1024.33			2.11202
$486$		0			0
$487$			874.538i			1.79577i	0.440234	+	0.897883i	$0.354896\pi$
$487$			874.538i			1.79577i	−0.440234	+	0.897883i	$0.645104\pi$
$488$	−40.2542	−	53.9731i	−0.0824881	−	0.110601i
$489$		0			0
$490$	559.745	−	228.869i	1.14234	−	0.467080i
$491$	558.756	−	322.598i	1.13800	−	0.657022i	0.192063	−	0.981383i	$-0.438482\pi$
$491$	558.756	−	322.598i	1.13800	−	0.657022i	0.945934	+	0.324360i	$0.105149\pi$
$492$		0			0
$493$	−264.997	+	458.988i	−0.537519	+	0.931010i
$494$	148.447	+	20.2325i	0.300501	+	0.0409564i
$495$		0			0
$496$	−141.325	+	234.787i	−0.284930	+	0.473360i
$497$	−536.868	+	929.883i	−1.08022	+	1.87099i
$498$		0			0
$499$	−489.167	+	282.421i	−0.980295	+	0.565974i	−0.902359	−	0.430985i	$-0.858166\pi$
$499$	−489.167	+	282.421i	−0.980295	+	0.565974i	−0.0779358	+	0.996958i	$0.524833\pi$
$500$	−35.7866	−	138.601i	−0.0715732	−	0.277202i
$501$		0			0
$502$	−332.498	+	429.254i	−0.662348	+	0.855087i
$503$			483.048i			0.960334i	0.877177	+	0.480167i	$0.159424\pi$
$503$			483.048i			0.960334i	−0.877177	+	0.480167i	$0.840576\pi$
$504$		0			0
$505$	721.994			1.42969
$506$	−266.938	−	206.770i	−0.527546	−	0.408635i
$507$		0			0
$508$	383.489	−	99.0165i	0.754900	−	0.194914i
$509$	108.002	+	187.065i	0.212184	+	0.367514i	0.952398	−	0.304858i	$-0.0986090\pi$
$509$	108.002	+	187.065i	0.212184	+	0.367514i	−0.740214	+	0.672372i	$0.765276\pi$
$510$		0			0
$511$	17.7887	+	10.2703i	0.0348115	+	0.0200984i
$512$	−480.666	+	176.363i	−0.938801	+	0.344459i
$513$		0			0
$514$	−124.000	+	909.799i	−0.241245	+	1.77004i
$515$	−272.440	−	157.293i	−0.529010	−	0.305424i
$516$		0			0
$517$	−176.085	−	304.988i	−0.340590	−	0.589920i
$518$	−46.0328	−	112.582i	−0.0888664	−	0.217340i
$519$		0			0
$520$	510.577	+	684.586i	0.981880	+	1.31651i
$521$	454.806			0.872949			0.436475	−	0.899717i	$-0.356227\pi$
$521$	454.806			0.872949			0.436475	+	0.899717i	$0.356227\pi$
$522$		0			0
$523$		−	325.041i		−	0.621493i	−0.950493	−	0.310747i	$-0.899421\pi$
$523$		−	325.041i		−	0.621493i	0.950493	−	0.310747i	$-0.100579\pi$
$524$	151.789	+	154.583i	0.289674	+	0.295006i
$525$		0			0
$526$	−154.249	−	377.247i	−0.293249	−	0.717199i
$527$	−265.408	+	153.233i	−0.503621	+	0.290765i
$528$		0			0
$529$	46.4180	−	80.3983i	0.0877466	−	0.151982i
$530$	165.384	−	1213.44i	0.312046	−	2.28951i
$531$		0			0
$532$	−189.812	−	52.7196i	−0.356789	−	0.0990971i
$533$	−62.2998	+	107.906i	−0.116885	+	0.202451i
$534$		0			0
$535$	623.745	−	360.119i	1.16588	−	0.673120i
$536$	27.1880	+	230.875i	0.0507239	+	0.430737i
$537$		0			0
$538$	511.282	+	396.038i	0.950339	+	0.736130i
$539$		−	276.447i		−	0.512889i
$540$		0			0
$541$	−962.574			−1.77925			−0.889625	−	0.456692i	$-0.849034\pi$
$541$	−962.574			−1.77925			−0.889625	+	0.456692i	$0.849034\pi$
$542$	128.511	−	165.906i	0.237104	−	0.306101i
$543$		0			0
$544$	−565.836	−	87.6589i	−1.04014	−	0.161138i
$545$	−358.520	−	620.974i	−0.657834	−	1.13940i
$546$		0			0
$547$	115.588	+	66.7349i	0.211313	+	0.122002i	0.601921	−	0.798555i	$-0.294402\pi$
$547$	115.588	+	66.7349i	0.211313	+	0.122002i	−0.390608	+	0.920557i	$0.627735\pi$
$548$	−21.4266	−	5.95119i	−0.0390997	−	0.0108598i
$549$		0			0
$550$	−400.249	−	54.5515i	−0.727726	−	0.0991846i
$551$	133.289	+	76.9542i	0.241903	+	0.139663i
$552$		0			0
$553$	708.409	+	1227.00i	1.28103	+	2.21881i
$554$	−90.4008	+	36.9632i	−0.163178	+	0.0667206i
$555$		0			0
$556$	427.431	+	435.299i	0.768762	+	0.782912i
$557$	413.437			0.742258			0.371129	−	0.928581i	$-0.378971\pi$
$557$	413.437			0.742258			0.371129	+	0.928581i	$0.378971\pi$
$558$		0			0
$559$		−	722.737i		−	1.29291i
$560$	−543.643	−	982.575i	−0.970790	−	1.75460i
$561$		0			0
$562$	−54.8328	+	22.4201i	−0.0975673	+	0.0398935i
$563$	−447.356	+	258.281i	−0.794592	+	0.458758i	−0.841577	−	0.540137i	$-0.818372\pi$
$563$	−447.356	+	258.281i	−0.794592	+	0.458758i	0.0469843	+	0.998896i	$0.485039\pi$
$564$		0			0
$565$	−143.915	+	249.268i	−0.254717	+	0.441182i
$566$	−763.314	−	104.035i	−1.34861	−	0.183808i
$567$		0			0
$568$	832.486	+	358.245i	1.46564	+	0.630713i
$569$	−234.178	+	405.608i	−0.411560	+	0.712843i	−0.995061	−	0.0992699i	$-0.968349\pi$
$569$	−234.178	+	405.608i	−0.411560	+	0.712843i	0.583500	+	0.812113i	$0.301683\pi$
$570$		0			0
$571$	−585.409	+	337.986i	−1.02523	+	0.591919i	−0.915616	−	0.402055i	$-0.868296\pi$
$571$	−585.409	+	337.986i	−1.02523	+	0.591919i	−0.109618	+	0.993974i	$0.534963\pi$
$572$	378.012	−	97.6023i	0.660860	−	0.170633i
$573$		0			0
$574$	100.328	−	129.523i	0.174788	−	0.225650i
$575$		−	743.930i		−	1.29379i
$576$		0			0
$577$	−354.823			−0.614945			−0.307473	−	0.951557i	$-0.599483\pi$
$577$	−354.823			−0.614945			−0.307473	+	0.951557i	$0.599483\pi$
$578$	−49.2846	−	38.1757i	−0.0852674	−	0.0660478i
$579$		0			0
$580$	219.331	+	849.466i	0.378157	+	1.46460i
$581$	64.1683	+	111.143i	0.110445	+	0.191296i
$582$		0			0
$583$	−484.839	−	279.922i	−0.831628	−	0.480141i
$584$	6.85324	−	15.9255i	0.0117350	−	0.0272697i
$585$		0			0
$586$	76.0062	−	557.664i	0.129703	−	0.951645i
$587$	−190.940	−	110.239i	−0.325281	−	0.187801i	0.328463	−	0.944517i	$-0.393469\pi$
$587$	−190.940	−	110.239i	−0.325281	−	0.187801i	−0.653744	+	0.756716i	$0.726803\pi$
$588$		0			0
$589$	44.4984	+	77.0736i	0.0755491	+	0.130855i
$590$	469.278	+	1147.71i	0.795387	+	1.94527i
$591$		0			0
$592$	−89.8297	+	49.7013i	−0.151739	+	0.0839549i
$593$	−993.520			−1.67541			−0.837707	−	0.546121i	$-0.816104\pi$
$593$	−993.520			−1.67541			−0.837707	+	0.546121i	$0.816104\pi$
$594$		0			0
$595$		−	1255.82i		−	2.11063i
$596$	−390.953	+	383.887i	−0.655962	+	0.644106i
$597$		0			0
$598$	272.115	+	665.511i	0.455042	+	1.11289i
$599$	243.124	−	140.368i	0.405884	−	0.234337i	−0.283136	−	0.959080i	$-0.591375\pi$
$599$	243.124	−	140.368i	0.405884	−	0.234337i	0.689020	+	0.724743i	$0.258041\pi$
$600$		0			0
$601$	−280.915	+	486.559i	−0.467412	+	0.809582i	−0.999307	−	0.0372287i	$-0.988147\pi$
$601$	−280.915	+	486.559i	−0.467412	+	0.809582i	0.531894	+	0.846811i	$0.321480\pi$
$602$	−128.337	+	941.616i	−0.213184	+	1.56415i
$603$		0			0
$604$	83.4834	−	300.573i	0.138218	−	0.497638i
$605$	278.292	−	482.016i	0.459987	−	0.796720i
$606$		0			0
$607$	−72.7918	+	42.0264i	−0.119921	+	0.0692362i	−0.558760	−	0.829329i	$-0.688723\pi$
$607$	−72.7918	+	42.0264i	−0.119921	+	0.0692362i	0.438840	+	0.898565i	$0.355390\pi$
$608$	−25.4558	+	164.317i	−0.0418682	+	0.270258i
$609$		0			0
$610$	−98.5410	−	76.3295i	−0.161543	−	0.125130i
$611$			749.906i			1.22734i
$612$		0			0
$613$	730.234			1.19125			0.595623	−	0.803264i	$-0.296905\pi$
$613$	730.234			1.19125			0.595623	+	0.803264i	$0.296905\pi$
$614$	−678.461	+	875.890i	−1.10499	+	1.42653i
$615$		0			0
$616$	−509.823	+	60.0373i	−0.827636	+	0.0974631i
$617$	−274.893	−	476.129i	−0.445532	−	0.771684i	0.552557	−	0.833475i	$-0.313652\pi$
$617$	−274.893	−	476.129i	−0.445532	−	0.771684i	−0.998089	+	0.0617910i	$0.980319\pi$
$618$		0			0
$619$	63.3297	+	36.5634i	0.102310	+	0.0590685i	0.550282	−	0.834979i	$-0.314520\pi$
$619$	63.3297	+	36.5634i	0.102310	+	0.0590685i	−0.447972	+	0.894048i	$0.647854\pi$
$620$	−135.765	+	488.806i	−0.218975	+	0.788397i
$621$		0			0
$622$	−31.0820	−	4.23629i	−0.0499711	−	0.00681076i
$623$	−146.872	−	84.7965i	−0.235749	−	0.136110i
$624$		0			0
$625$	240.412	+	416.405i	0.384659	+	0.666249i
$626$	−570.477	+	233.258i	−0.911305	+	0.372616i
$627$		0			0
$628$	−205.964	+	202.241i	−0.327968	+	0.322040i
$629$	−114.811			−0.182529
$630$		0			0
$631$			779.849i			1.23589i	0.786220	+	0.617947i	$0.212035\pi$
$631$			779.849i			1.23589i	−0.786220	+	0.617947i	$0.787965\pi$
$632$	958.622	−	714.958i	1.51681	−	1.13126i
$633$		0			0
$634$	918.407	−	375.520i	1.44859	−	0.592303i
$635$	634.977	−	366.604i	0.999965	−	0.577330i
$636$		0			0
$637$	−294.331	+	509.797i	−0.462058	+	0.800309i
$638$	397.390	+	54.1618i	0.622868	+	0.0848931i
$639$		0			0
$640$	−769.994	+	552.712i	−1.20312	+	0.863612i
$641$	222.171	−	384.811i	0.346600	−	0.600329i	−0.639043	−	0.769171i	$-0.720669\pi$
$641$	222.171	−	384.811i	0.346600	−	0.600329i	0.985643	+	0.168842i	$0.0540028\pi$
$642$		0			0
$643$	−386.420	+	223.099i	−0.600963	+	0.346966i	−0.769421	−	0.638743i	$-0.779455\pi$
$643$	−386.420	+	223.099i	−0.600963	+	0.346966i	0.168457	+	0.985709i	$0.446122\pi$
$644$	−236.350	−	915.379i	−0.367003	−	1.42140i
$645$		0			0
$646$	−113.872	+	147.008i	−0.176273	+	0.227567i
$647$		−	861.386i		−	1.33135i	−0.746240	−	0.665677i	$-0.768143\pi$
$647$		−	861.386i		−	1.33135i	0.746240	−	0.665677i	$-0.231857\pi$
$648$		0			0
$649$	566.833			0.873394
$650$	680.019	+	526.741i	1.04618	+	0.810370i
$651$		0			0
$652$	219.128	−	56.5785i	0.336085	−	0.0867769i
$653$	−438.151	−	758.900i	−0.670982	−	1.16217i	−0.977626	−	0.210350i	$-0.932539\pi$
$653$	−438.151	−	758.900i	−0.670982	−	1.16217i	0.306644	−	0.951824i	$-0.400794\pi$
$654$		0			0
$655$	347.331	+	200.532i	0.530277	+	0.306155i
$656$	−118.479	−	71.3158i	−0.180608	−	0.108713i
$657$		0			0
$658$	133.161	−	977.013i	0.202372	−	1.48482i
$659$	−489.963	−	282.880i	−0.743494	−	0.429257i	0.0798443	−	0.996807i	$-0.474558\pi$
$659$	−489.963	−	282.880i	−0.743494	−	0.429257i	−0.823338	+	0.567551i	$0.807891\pi$
$660$		0			0
$661$	−316.290	−	547.831i	−0.478503	−	0.828791i	0.521194	−	0.853438i	$-0.325487\pi$
$661$	−316.290	−	547.831i	−0.478503	−	0.828791i	−0.999696	+	0.0246476i	$0.992154\pi$
$662$	65.4793	+	160.142i	0.0989114	+	0.241907i
$663$		0			0
$664$	86.8328	−	64.7615i	0.130772	−	0.0975325i
$665$	−364.686			−0.548401
$666$		0			0
$667$			738.615i			1.10737i
$668$	565.092	+	575.494i	0.845946	+	0.861517i
$669$		0			0
$670$	162.875	+	398.344i	0.243098	+	0.594543i
$671$	−49.3470	+	28.4905i	−0.0735424	+	0.0424597i
$672$		0			0
$673$	536.330	−	928.950i	0.796924	−	1.38031i	−0.124687	−	0.992196i	$-0.539793\pi$
$673$	536.330	−	928.950i	0.796924	−	1.38031i	0.921610	−	0.388116i	$-0.126874\pi$
$674$	−86.6071	+	635.444i	−0.128497	+	0.942795i
$675$		0			0
$676$	−149.666	−	41.5692i	−0.221399	−	0.0614929i
$677$	239.399	−	414.651i	0.353617	−	0.612483i	−0.633263	−	0.773937i	$-0.718285\pi$
$677$	239.399	−	414.651i	0.353617	−	0.612483i	0.986880	+	0.161454i	$0.0516182\pi$
$678$		0			0
$679$	1135.45	−	655.553i	1.67224	−	0.965468i
$680$	−1052.71	+	123.968i	−1.54811	+	0.182307i
$681$		0			0
$682$	183.344	+	142.017i	0.268832	+	0.208237i
$683$		−	318.418i		−	0.466206i	−0.972452	−	0.233103i	$-0.925112\pi$
$683$		−	318.418i		−	0.466206i	0.972452	−	0.233103i	$-0.0748879\pi$
$684$		0			0
$685$	−41.1672			−0.0600981
$686$	−94.8059	+	122.394i	−0.138201	+	0.178417i
$687$		0			0
$688$	801.994	+	14.6286i	1.16569	+	0.0212625i
$689$	596.061	+	1032.41i	0.865111	+	1.49842i
$690$		0			0
$691$	971.076	+	560.651i	1.40532	+	0.811362i	0.994932	−	0.100550i	$-0.0320601\pi$
$691$	971.076	+	560.651i	1.40532	+	0.811362i	0.410388	+	0.911911i	$0.365393\pi$
$692$	356.697	+	99.0716i	0.515458	+	0.143167i
$693$		0			0
$694$	1337.15	+	182.246i	1.92674	+	0.262602i
$695$	978.068	+	564.688i	1.40729	+	0.812501i
$696$		0			0
$697$	−77.3251	−	133.931i	−0.110940	−	0.192153i
$698$	284.937	−	116.506i	0.408220	−	0.166914i
$699$		0			0
$700$	−792.428	−	807.014i	−1.13204	−	1.15288i
$701$	413.437			0.589782			0.294891	−	0.955531i	$-0.404717\pi$
$701$	413.437			0.589782			0.294891	+	0.955531i	$0.404717\pi$
$702$		0			0
$703$			33.3406i			0.0474262i
$704$	100.654	+	421.441i	0.142975	+	0.598638i
$705$		0			0
$706$	−1153.74	+	471.743i	−1.63419	+	0.668191i
$707$	800.316	−	462.062i	1.13199	−	0.653554i
$708$		0			0
$709$	341.457	−	591.422i	0.481604	−	0.834163i	−0.518173	−	0.855276i	$-0.673388\pi$
$709$	341.457	−	591.422i	0.481604	−	0.834163i	0.999777	+	0.0211129i	$0.00672093\pi$
$710$	1662.39	+	226.574i	2.34140	+	0.319118i
$711$		0			0
$712$	−56.5836	+	131.488i	−0.0794713	+	0.184675i
$713$	−213.551	+	369.881i	−0.299510	+	0.518767i
$714$		0			0
$715$	625.909	−	361.369i	0.875397	−	0.505411i
$716$	−16.6093	+	4.28851i	−0.0231974	+	0.00598954i
$717$		0			0
$718$	196.377	−	253.522i	0.273505	−	0.353094i
$719$		−	286.374i		−	0.398295i	−0.979970	−	0.199148i	$-0.936183\pi$
$719$		−	286.374i		−	0.398295i	0.979970	−	0.199148i	$-0.0638173\pi$
$720$		0			0
$721$	−402.659			−0.558474
$722$	−528.100	−	409.065i	−0.731441	−	0.566572i
$723$		0			0
$724$	−289.748	−	1122.19i	−0.400204	−	1.54998i
$725$	441.819	+	765.253i	0.609406	+	1.05552i
$726$		0			0
$727$	−279.659	−	161.461i	−0.384676	−	0.222093i	0.295175	−	0.955443i	$-0.404622\pi$
$727$	−279.659	−	161.461i	−0.384676	−	0.222093i	−0.679851	+	0.733351i	$0.737955\pi$
$728$	1004.09	+	432.090i	1.37924	+	0.593531i
$729$		0			0
$730$	4.33437	−	31.8016i	0.00593749	−	0.0435639i
$731$	776.863	+	448.522i	1.06274	+	0.613573i
$732$		0			0
$733$	260.915	+	451.918i	0.355955	+	0.616532i	0.987281	−	0.158986i	$-0.0508224\pi$
$733$	260.915	+	451.918i	0.355955	+	0.616532i	−0.631326	+	0.775517i	$0.717489\pi$
$734$	−215.412	−	526.831i	−0.293476	−	0.717754i
$735$		0			0
$736$	−744.000	+	288.486i	−1.01087	+	0.391964i
$737$	196.734			0.266939
$738$		0			0
$739$			965.020i			1.30585i	0.757424	+	0.652923i	$0.226458\pi$
$739$			965.020i			1.30585i	−0.757424	+	0.652923i	$0.773542\pi$
$740$	−135.607	+	133.156i	−0.183253	+	0.179940i
$741$		0			0
$742$	−593.252	−	1450.91i	−0.799531	−	1.95541i
$743$	950.317	−	548.666i	1.27903	−	0.738447i	0.302357	−	0.953195i	$-0.402226\pi$
$743$	950.317	−	548.666i	1.27903	−	0.738447i	0.976669	+	0.214748i	$0.0688930\pi$
$744$		0			0
$745$	−507.161	+	878.429i	−0.680753	+	1.17910i
$746$	−81.4106	+	597.317i	−0.109130	+	0.800693i
$747$		0			0
$748$	−129.678	+	466.892i	−0.173366	+	0.624188i
$749$	460.939	−	798.370i	0.615406	−	1.06591i
$750$		0			0
$751$	−1196.02	+	690.524i	−1.59257	+	0.919472i	−0.599709	+	0.800218i	$0.704717\pi$
$751$	−1196.02	+	690.524i	−1.59257	+	0.919472i	−0.992864	+	0.119255i	$0.961950\pi$
$752$	−832.142	−	15.1785i	−1.10657	−	0.0201842i
$753$		0			0
$754$	−675.161	−	522.977i	−0.895439	−	0.693604i
$755$		−	577.494i		−	0.764892i
$756$		0			0
$757$	−516.252			−0.681971			−0.340986	−	0.940068i	$-0.610761\pi$
$757$	−516.252			−0.681971			−0.340986	+	0.940068i	$0.610761\pi$
$758$	304.406	−	392.987i	0.401591	−	0.518452i
$759$		0			0
$760$	36.0000	+	305.704i	0.0473684	+	0.402242i
$761$	608.092	+	1053.25i	0.799069	+	1.38403i	0.920223	+	0.391394i	$0.128007\pi$
$761$	608.092	+	1053.25i	0.799069	+	1.38403i	−0.121154	+	0.992634i	$0.538659\pi$
$762$		0			0
$763$	−794.823	−	458.892i	−1.04171	−	0.601431i
$764$	−99.1668	+	357.040i	−0.129799	+	0.467329i
$765$		0			0
$766$	−967.319	−	131.840i	−1.26282	−	0.172114i
$767$	−1045.30	−	603.502i	−1.36284	−	0.786835i
$768$		0			0
$769$	−502.163	−	869.771i	−0.653007	−	1.13104i	−0.982389	−	0.186845i	$-0.940174\pi$
$769$	−502.163	−	869.771i	−0.653007	−	1.13104i	0.329382	−	0.944197i	$-0.393160\pi$
$770$	−879.632	+	359.665i	−1.14238	+	0.467098i
$771$		0			0
$772$	−694.015	+	681.471i	−0.898983	+	0.882735i
$773$	−382.580			−0.494929			−0.247464	−	0.968897i	$-0.579597\pi$
$773$	−382.580			−0.494929			−0.247464	+	0.968897i	$0.579597\pi$
$774$		0			0
$775$			510.960i			0.659304i
$776$	−661.614	−	887.097i	−0.852595	−	1.14317i
$777$		0			0
$778$	−769.866	+	314.784i	−0.989545	+	0.404607i
$779$	−38.8931	+	22.4549i	−0.0499269	+	0.0288253i
$780$		0			0
$781$	383.489	−	664.223i	0.491023	−	0.850477i
$782$	−884.223	−	120.514i	−1.13072	−	0.154110i
$783$		0			0
$784$	−559.745	−	336.927i	−0.713960	−	0.429754i
$785$	−267.185	+	462.777i	−0.340362	+	0.589525i
$786$		0			0
$787$	413.327	−	238.634i	0.525193	−	0.303220i	−0.213864	−	0.976863i	$-0.568605\pi$
$787$	413.327	−	238.634i	0.525193	−	0.303220i	0.739057	+	0.673643i	$0.235272\pi$
$788$	139.432	+	540.020i	0.176945	+	0.685304i
$789$		0			0
$790$	1355.70	−	1750.20i	1.71607	−	2.21544i
$791$			368.411i			0.465754i
$792$		0			0
$793$	121.334			0.153007
$794$	1060.67	+	821.591i	1.33586	+	1.03475i
$795$		0			0
$796$	429.875	−	110.993i	0.540044	−	0.139439i
$797$	−257.304	−	445.663i	−0.322840	−	0.559176i	0.658233	−	0.752815i	$-0.271304\pi$
$797$	−257.304	−	445.663i	−0.322840	−	0.559176i	−0.981073	+	0.193639i	$0.937971\pi$
$798$		0			0
$799$	−806.067	−	465.383i	−1.00884	−	0.582456i
$800$	−598.268	+	743.930i	−0.747835	+	0.929913i
$801$		0			0
$802$	−30.9907	+	227.381i	−0.0386417	+	0.283518i
$803$	−12.7066	−	7.33616i	−0.0158239	−	0.00913594i
$804$		0			0
$805$	−875.076	−	1515.68i	−1.08705	−	1.88283i
$806$	−186.899	−	457.099i	−0.231885	−	0.567120i
$807$		0			0
$808$	−466.334	−	625.265i	−0.577146	−	0.773843i
$809$	−1463.74			−1.80932			−0.904662	−	0.426129i	$-0.859877\pi$
$809$	−1463.74			−1.80932			−0.904662	+	0.426129i	$0.859877\pi$
$810$		0			0
$811$		−	1163.05i		−	1.43410i	−0.697023	−	0.717049i	$-0.745492\pi$
$811$		−	1163.05i		−	1.43410i	0.697023	−	0.717049i	$-0.254508\pi$
$812$	786.767	+	801.249i	0.968925	+	0.986759i
$813$		0			0
$814$	32.8816	+	80.4184i	0.0403951	+	0.0987941i
$815$	362.830	−	209.480i	0.445190	−	0.257030i
$816$		0			0
$817$	130.249	−	225.598i	0.159424	−	0.276130i
$818$	39.6147	−	290.656i	0.0484287	−	0.355326i
$819$		0			0
$820$	−246.663	−	68.5098i	−0.300808	−	0.0835486i
$821$	196.276	−	339.961i	0.239070	−	0.414081i	−0.721378	−	0.692542i	$-0.756491\pi$
$821$	196.276	−	339.961i	0.239070	−	0.414081i	0.960448	+	0.278461i	$0.0898242\pi$
$822$		0			0
$823$	−1081.53	+	624.422i	−1.31413	+	0.758714i	−0.982778	−	0.184792i	$-0.940839\pi$
$823$	−1081.53	+	624.422i	−1.31413	+	0.758714i	−0.331354	+	0.943507i	$0.607505\pi$
$824$	39.7485	+	337.536i	0.0482385	+	0.409631i
$825$		0			0
$826$	1254.70	+	971.886i	1.51901	+	1.17662i
$827$		−	1369.15i		−	1.65557i	−0.561049	−	0.827783i	$-0.689602\pi$
$827$		−	1369.15i		−	1.65557i	0.561049	−	0.827783i	$-0.310398\pi$
$828$		0			0
$829$	−73.7477			−0.0889598			−0.0444799	−	0.999010i	$-0.514163\pi$
$829$	−73.7477			−0.0889598			−0.0444799	+	0.999010i	$0.514163\pi$
$830$	122.800	−	158.534i	0.147952	−	0.191005i
$831$		0			0
$832$	263.088	−	884.346i	0.316212	−	1.06292i
$833$	−365.317	−	632.748i	−0.438556	−	0.759601i
$834$		0			0
$835$	1293.07	+	746.554i	1.54859	+	0.894077i
$836$	135.584	+	37.6581i	0.162182	+	0.0450455i
$837$		0			0
$838$	1063.91	+	145.004i	1.26958	+	0.173036i
$839$	−1039.73	−	600.286i	−1.23924	−	0.715478i	−0.270305	−	0.962775i	$-0.587124\pi$
$839$	−1039.73	−	600.286i	−1.23924	−	0.715478i	−0.968940	+	0.247297i	$0.920458\pi$
$840$		0			0
$841$	−18.1625	−	31.4584i	−0.0215963	−	0.0374060i
$842$	−680.166	+	278.108i	−0.807799	+	0.330294i
$843$		0			0
$844$	742.933	+	756.608i	0.880252	+	0.896455i
$845$	−287.554			−0.340300
$846$		0			0
$847$		−	712.406i		−	0.841094i
$848$	−1157.69	+	640.530i	−1.36520	+	0.755342i
$849$		0			0
$850$	−988.200	+	404.057i	−1.16259	+	0.475361i
$851$	−138.567	+	80.0018i	−0.162829	+	0.0940092i
$852$		0			0
$853$	219.539	−	380.254i	0.257373	−	0.445784i	−0.708164	−	0.706048i	$-0.750476\pi$
$853$	219.539	−	380.254i	0.257373	−	0.445784i	0.965537	+	0.260264i	$0.0838097\pi$
$854$	−158.080	−	21.5454i	−0.185106	−	0.0252288i
$855$		0			0
$856$	−714.748	−	307.578i	−0.834986	−	0.359321i
$857$	−255.481	+	442.506i	−0.298111	+	0.516344i	−0.975704	−	0.219094i	$-0.929690\pi$
$857$	−255.481	+	442.506i	−0.298111	+	0.516344i	0.677593	+	0.735437i	$0.263023\pi$
$858$		0			0
$859$	153.093	−	88.3882i	0.178222	−	0.102897i	−0.408235	−	0.912877i	$-0.633856\pi$
$859$	153.093	−	88.3882i	0.178222	−	0.102897i	0.586457	+	0.809980i	$0.300522\pi$
$860$	1437.77	−	371.230i	1.67182	−	0.431663i
$861$		0			0
$862$	900.620	−	1162.70i	1.04480	−	1.34883i
$863$		−	1028.28i		−	1.19152i	−0.803163	−	0.595759i	$-0.796851\pi$
$863$		−	1028.28i		−	1.19152i	0.803163	−	0.595759i	$-0.203149\pi$
$864$		0			0
$865$	685.325			0.792283
$866$	−1209.83	−	937.127i	−1.39703	−	1.08213i
$867$		0			0
$868$	162.334	+	628.718i	0.187021	+	0.724330i
$869$	−506.022	−	876.456i	−0.582304	−	1.00858i
$870$		0			0
$871$	−362.798	−	209.462i	−0.416530	−	0.240484i
$872$	−306.212	+	711.573i	−0.351161	+	0.816024i
$873$		0			0
$874$	−34.9969	+	256.775i	−0.0400422	+	0.293793i
$875$	−293.744	−	169.593i	−0.335707	−	0.193821i
$876$		0			0
$877$	470.457	+	814.856i	0.536439	+	0.929140i	0.999092	+	0.0426008i	$0.0135644\pi$
$877$	470.457	+	814.856i	0.536439	+	0.929140i	−0.462653	+	0.886540i	$0.653102\pi$
$878$	35.1101	+	85.8686i	0.0399887	+	0.0978003i
$879$		0			0
$880$	388.328	+	701.861i	0.441282	+	0.797570i
$881$	1065.75			1.20970			0.604851	−	0.796339i	$-0.293233\pi$
$881$	1065.75			1.20970			0.604851	+	0.796339i	$0.293233\pi$
$882$		0			0
$883$		−	1001.97i		−	1.13474i	−0.823464	−	0.567368i	$-0.807962\pi$
$883$		−	1001.97i		−	1.13474i	0.823464	−	0.567368i	$-0.192038\pi$
$884$	736.236	−	722.929i	0.832846	−	0.817793i
$885$		0			0
$886$	−105.738	−	258.604i	−0.119344	−	0.291878i
$887$	583.774	−	337.042i	0.658144	−	0.379980i	−0.133426	−	0.991059i	$-0.542598\pi$
$887$	583.774	−	337.042i	0.658144	−	0.379980i	0.791569	+	0.611079i	$0.209264\pi$
$888$		0			0
$889$	469.240	−	812.747i	0.527829	−	0.914227i
$890$	−35.7866	+	262.569i	−0.0402097	+	0.295022i
$891$		0			0
$892$	−340.328	+	1225.32i	−0.381534	+	1.37367i
$893$	−135.146	+	234.079i	−0.151339	+	0.262126i
$894$		0			0
$895$	−27.5016	+	15.8780i	−0.0307280	+	0.0177408i
$896$	−499.797	+	1105.45i	−0.557810	+	1.23376i
$897$		0			0
$898$	422.383	+	327.177i	0.470360	+	0.364339i
$899$		−	507.310i		−	0.564305i
$900$		0			0
$901$	−1479.63			−1.64221
$902$	−71.6652	+	92.5194i	−0.0794514	+	0.102571i
$903$		0			0
$904$	308.827	−	36.3677i	0.341622	−	0.0402297i
$905$	−1072.78	−	1858.11i	−1.18539	−	2.05316i
$906$		0			0
$907$	−1023.16	−	590.723i	−1.12807	−	0.651293i	−0.184624	−	0.982809i	$-0.559107\pi$
$907$	−1023.16	−	590.723i	−1.12807	−	0.651293i	−0.943450	+	0.331516i	$0.892440\pi$
$908$	266.938	−	961.083i	0.293985	−	1.05846i
$909$		0			0
$910$	2005.06	+	273.278i	2.20337	+	0.300305i
$911$	1207.61	+	697.213i	1.32559	+	0.765328i	0.984614	−	0.174746i	$-0.0559103\pi$
$911$	1207.61	+	697.213i	1.32559	+	0.765328i	0.340973	+	0.940073i	$0.389244\pi$
$912$		0			0
$913$	−45.8359	−	79.3901i	−0.0502036	−	0.0869553i
$914$	440.277	−	180.021i	0.481704	−	0.196960i
$915$		0			0
$916$	434.778	−	426.920i	0.474648	−	0.466070i
$917$	513.346			0.559811
$918$		0			0
$919$		−	210.163i		−	0.228686i	−0.993441	−	0.114343i	$-0.963524\pi$
$919$		−	210.163i		−	0.228686i	0.993441	−	0.114343i	$-0.0364763\pi$
$920$	−1184.16	+	883.166i	−1.28713	+	0.959963i
$921$		0			0
$922$	552.869	−	226.058i	0.599641	−	0.245182i
$923$	−1414.39	+	816.596i	−1.53238	+	0.884719i
$924$		0			0
$925$	−95.7098	+	165.774i	−0.103470	+	0.179215i
$926$	−970.101	−	132.219i	−1.04763	−	0.142785i
$927$		0			0
$928$	593.994	−	738.615i	0.640080	−	0.795921i
$929$	−83.2996	+	144.279i	−0.0896659	+	0.155306i	−0.907370	−	0.420333i	$-0.861913\pi$
$929$	−83.2996	+	144.279i	−0.0896659	+	0.155306i	0.817704	+	0.575639i	$0.195247\pi$
$930$		0			0
$931$	−183.748	+	106.087i	−0.197366	+	0.113949i
$932$	346.793	+	1343.12i	0.372096	+	1.44112i
$933$		0			0
$934$	−556.377	+	718.280i	−0.595693	+	0.769036i
$935$			897.044i			0.959405i
$936$		0			0
$937$	251.158			0.268045			0.134022	−	0.990978i	$-0.457211\pi$
$937$	251.158			0.268045			0.134022	+	0.990978i	$0.457211\pi$
$938$	435.476	+	337.319i	0.464261	+	0.359615i
$939$		0			0
$940$	−1491.82	+	385.186i	−1.58704	+	0.409772i
$941$	407.282	+	705.433i	0.432818	+	0.749663i	0.997115	−	0.0759090i	$-0.0241858\pi$
$941$	407.282	+	705.433i	0.432818	+	0.749663i	−0.564296	+	0.825572i	$0.690853\pi$
$942$		0			0
$943$	−186.650	−	107.762i	−0.197932	−	0.114276i
$944$	690.841	−	1147.71i	0.731823	−	1.21580i
$945$		0			0
$946$	91.6718	−	672.604i	0.0969047	−	0.710998i
$947$	−513.020	−	296.192i	−0.541731	−	0.312769i	0.204049	−	0.978961i	$-0.434590\pi$
$947$	−513.020	−	296.192i	−0.541731	−	0.312769i	−0.745780	+	0.666192i	$0.767923\pi$
$948$		0			0
$949$	15.6215	+	27.0572i	0.0164610	+	0.0285113i
$950$	117.337	+	286.970i	0.123512	+	0.302074i
$951$		0			0
$952$	−1087.57	+	811.133i	−1.14241	+	0.852031i
$953$	844.768			0.886430			0.443215	−	0.896415i	$-0.353838\pi$
$953$	844.768			0.886430			0.443215	+	0.896415i	$0.353838\pi$
$954$		0			0
$955$			685.983i			0.718307i
$956$	−291.560	−	296.927i	−0.304979	−	0.310593i
$957$		0			0
$958$	2.73525	+	6.68958i	0.00285517	+	0.00698286i
$959$	−45.6330	+	26.3462i	−0.0475839	+	0.0274726i
$960$		0			0
$961$	−333.825	+	578.202i	−0.347373	+	0.601667i
$962$	24.9838	−	183.308i	0.0259707	−	0.190549i
$963$		0			0
$964$	−1086.19	−	301.686i	−1.12675	−	0.312952i
$965$	−900.305	+	1559.37i	−0.932959	+	1.61593i
$966$		0			0
$967$	−156.035	+	90.0867i	−0.161360	+	0.0931611i	−0.578505	−	0.815679i	$-0.696364\pi$
$967$	−156.035	+	90.0867i	−0.161360	+	0.0931611i	0.417146	+	0.908840i	$0.363030\pi$
$968$	−597.186	+	70.3252i	−0.616928	+	0.0726500i
$969$		0			0
$970$	−1619.61	−	1254.55i	−1.66970	−	1.29335i
$971$			411.395i			0.423682i	0.977304	+	0.211841i	$0.0679458\pi$
$971$			411.395i			0.423682i	−0.977304	+	0.211841i	$0.932054\pi$
$972$		0			0
$973$	1445.56			1.48567
$974$	1071.09	−	1382.77i	1.09968	−	1.41968i
$975$		0			0
$976$	−2.45587	+	134.640i	−0.00251627	+	0.137951i
$977$	878.125	+	1520.96i	0.898797	+	1.55676i	0.829034	+	0.559199i	$0.188891\pi$
$977$	878.125	+	1520.96i	0.898797	+	1.55676i	0.0697635	+	0.997564i	$0.477776\pi$
$978$		0			0
$979$	104.912	+	60.5708i	0.107162	+	0.0618701i
$980$	−1165.34	−	323.670i	−1.18912	−	0.330276i
$981$		0			0
$982$	−1278.57	−	174.261i	−1.30201	−	0.177456i
$983$	−695.466	−	401.528i	−0.707494	−	0.408472i	0.102639	−	0.994719i	$-0.467271\pi$
$983$	−695.466	−	401.528i	−0.707494	−	0.408472i	−0.810132	+	0.586247i	$0.800605\pi$
$984$		0			0
$985$	516.243	+	894.159i	0.524105	+	0.907776i
$986$	981.140	−	401.170i	0.995071	−	0.406866i
$987$		0			0
$988$	−209.936	−	213.800i	−0.212486	−	0.216397i
$989$	1250.15			1.26405
$990$		0			0
$991$		−	338.466i		−	0.341540i	−0.985311	−	0.170770i	$-0.945375\pi$
$991$		−	338.466i		−	0.341540i	0.985311	−	0.170770i	$-0.0546254\pi$
$992$	511.008	−	198.143i	0.515129	−	0.199741i
$993$		0			0
$994$	1987.73	−	812.747i	1.99973	−	0.817653i
$995$	711.783	−	410.948i	0.715360	−	0.413013i
$996$		0			0
$997$	−295.906	+	512.523i	−0.296796	+	0.514066i	−0.975401	−	0.220438i	$-0.929251\pi$
$997$	−295.906	+	512.523i	−0.296796	+	0.514066i	0.678605	+	0.734503i	$0.262585\pi$
$998$	1119.33	+	152.558i	1.12158	+	0.152864i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.p.55.1		8
3.2	odd	2	inner	324.3.f.p.55.4		8
4.3	odd	2		324.3.f.o.55.4		8
9.2	odd	6		108.3.d.d.55.5	yes	8
9.4	even	3		324.3.f.o.271.4		8
9.5	odd	6		324.3.f.o.271.1		8
9.7	even	3		108.3.d.d.55.4	yes	8
12.11	even	2		324.3.f.o.55.1		8
36.7	odd	6		108.3.d.d.55.3	✓	8
36.11	even	6		108.3.d.d.55.6	yes	8
36.23	even	6	inner	324.3.f.p.271.3		8
36.31	odd	6	inner	324.3.f.p.271.2		8
72.11	even	6		1728.3.g.l.703.2		8
72.29	odd	6		1728.3.g.l.703.1		8
72.43	odd	6		1728.3.g.l.703.8		8
72.61	even	6		1728.3.g.l.703.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.d.55.3	✓	8	36.7	odd	6
108.3.d.d.55.4	yes	8	9.7	even	3
108.3.d.d.55.5	yes	8	9.2	odd	6
108.3.d.d.55.6	yes	8	36.11	even	6
324.3.f.o.55.1		8	12.11	even	2
324.3.f.o.55.4		8	4.3	odd	2
324.3.f.o.271.1		8	9.5	odd	6
324.3.f.o.271.4		8	9.4	even	3
324.3.f.p.55.1		8	1.1	even	1	trivial
324.3.f.p.55.4		8	3.2	odd	2	inner
324.3.f.p.271.2		8	36.31	odd	6	inner
324.3.f.p.271.3		8	36.23	even	6	inner
1728.3.g.l.703.1		8	72.29	odd	6
1728.3.g.l.703.2		8	72.11	even	6
1728.3.g.l.703.7		8	72.61	even	6
1728.3.g.l.703.8		8	72.43	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.58114 - 1.22474i) q^{2} +(1.00000 + 3.87298i) q^{4} +(3.70246 + 6.41285i) q^{5} +(8.20820 + 4.73901i) q^{7} +(3.16228 - 7.34847i) q^{8} +O(q^{10})\)	\(q+(-1.58114 - 1.22474i) q^{2} +(1.00000 + 3.87298i) q^{4} +(3.70246 + 6.41285i) q^{5} +(8.20820 + 4.73901i) q^{7} +(3.16228 - 7.34847i) q^{8} +(2.00000 - 14.6742i) q^{10} +(-5.86319 - 3.38511i) q^{11} +(7.20820 + 12.4850i) q^{13} +(-7.17423 - 17.5460i) q^{14} +(-14.0000 + 7.74597i) q^{16} -17.8933 q^{17} +5.19615i q^{19} +(-21.1344 + 20.7524i) q^{20} +(5.12461 + 12.5332i) q^{22} +(-21.5958 + 12.4683i) q^{23} +(-14.9164 + 25.8360i) q^{25} +(3.89374 - 28.5687i) q^{26} +(-10.1459 + 36.5292i) q^{28} +(14.8098 - 25.6514i) q^{29} +(14.8328 - 8.56373i) q^{31} +(31.6228 + 4.89898i) q^{32} +(28.2918 + 21.9147i) q^{34} +70.1839i q^{35} +6.41641 q^{37} +(6.36396 - 8.21584i) q^{38} +(58.8328 - 6.92820i) q^{40} +(4.32145 + 7.48497i) q^{41} +(-43.4164 - 25.0665i) q^{43} +(7.24730 - 26.0931i) q^{44} +(49.4164 + 6.73516i) q^{46} +(45.0485 + 26.0088i) q^{47} +(20.4164 + 35.3623i) q^{49} +(55.2274 - 22.5815i) q^{50} +(-41.1459 + 40.4022i) q^{52} +82.6921 q^{53} -50.1329i q^{55} +(60.7811 - 45.3317i) q^{56} +(-54.8328 + 22.4201i) q^{58} +(-72.5075 + 41.8622i) q^{59} +(4.20820 - 7.28882i) q^{61} +(-33.9411 - 4.62597i) q^{62} +(-44.0000 - 46.4758i) q^{64} +(-53.3762 + 92.4502i) q^{65} +(-25.1656 + 14.5294i) q^{67} +(-17.8933 - 69.3005i) q^{68} +(85.9574 - 110.971i) q^{70} +113.287i q^{71} +2.16718 q^{73} +(-10.1452 - 7.85846i) q^{74} +(-20.1246 + 5.19615i) q^{76} +(-32.0841 - 55.5714i) q^{77} +(129.457 + 74.7423i) q^{79} +(-101.508 - 61.1007i) q^{80} +(2.33437 - 17.1275i) q^{82} +(11.7264 + 6.77022i) q^{83} +(-66.2492 - 114.747i) q^{85} +(37.9473 + 92.8076i) q^{86} +(-43.4164 + 32.3808i) q^{88} -17.8933 q^{89} +136.639i q^{91} +(-69.8854 - 71.1717i) q^{92} +(-39.3738 - 96.2964i) q^{94} +(-33.3221 + 19.2385i) q^{95} +(69.1656 - 119.798i) q^{97} +(11.0286 - 80.9175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 12 q^{7}+O(q^{10}) \) 8 * q + 8 * q^4 + 12 * q^7	\( 8 q + 8 q^{4} + 12 q^{7} + 16 q^{10} + 4 q^{13} - 112 q^{16} - 120 q^{22} - 12 q^{25} - 108 q^{28} - 96 q^{31} + 280 q^{34} - 56 q^{37} + 256 q^{40} - 240 q^{43} + 288 q^{46} + 56 q^{49} - 356 q^{52} - 224 q^{58} - 20 q^{61} - 352 q^{64} + 228 q^{67} + 312 q^{70} + 232 q^{73} + 660 q^{79} + 448 q^{82} - 208 q^{85} - 240 q^{88} + 168 q^{94} + 124 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 + 12 * q^7 + 16 * q^10 + 4 * q^13 - 112 * q^16 - 120 * q^22 - 12 * q^25 - 108 * q^28 - 96 * q^31 + 280 * q^34 - 56 * q^37 + 256 * q^40 - 240 * q^43 + 288 * q^46 + 56 * q^49 - 356 * q^52 - 224 * q^58 - 20 * q^61 - 352 * q^64 + 228 * q^67 + 312 * q^70 + 232 * q^73 + 660 * q^79 + 448 * q^82 - 208 * q^85 - 240 * q^88 + 168 * q^94 + 124 * q^97

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