LMFDB - Embedded newform 324.3.f.p.55.4

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			55.4
Root			$-0.437016 - 0.756934i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.p.271.3

$q$-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	$-0.901259\pi$
$5$	−3.70246	−	6.41285i	−0.740492	−	1.28257i	0.211780	−	0.977317i	$-0.432074\pi$
$6$		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	0.742244	−	0.670130i	$-0.233762\pi$
$11$	5.86319	+	3.38511i	0.533017	+	0.307737i	−0.209227	+	0.977867i	$0.567095\pi$
$12$		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	$-0.323589\pi$
$17$	17.8933			1.05255			0.526274	+	0.850315i	$0.323589\pi$
$18$		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	0.0493164	−	0.998783i	$-0.484296\pi$
$23$	21.5958	−	12.4683i	0.938946	−	0.542101i	0.889630	+	0.456682i	$0.150962\pi$
$24$		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	$0.337274\pi$
$29$	−14.8098	+	25.6514i	−0.510684	+	0.884531i	−0.999923	+	0.0123811i	$0.996059\pi$
$30$		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	0.808501	−	0.588495i	$-0.200279\pi$
$41$	−4.32145	−	7.48497i	−0.105401	−	0.182560i	−0.913902	+	0.405935i	$0.866946\pi$
$42$		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	−0.0627743	−	0.998028i	$-0.519995\pi$
$47$	−45.0485	−	26.0088i	−0.958479	−	0.553378i	−0.895705	+	0.444650i	$0.853328\pi$
$48$		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	$-0.784839\pi$
$53$	−82.6921			−1.56023			−0.780114	+	0.625637i	$0.784839\pi$
$54$		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	0.262132	−	0.965032i	$-0.415575\pi$
$59$	72.5075	−	41.8622i	1.22894	−	0.709529i	0.966808	+	0.255503i	$0.0822412\pi$
$60$		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	$-0.705999\pi$
$71$		−	113.287i		−	1.59559i	0.602928	−	0.797796i	$-0.294001\pi$
$72$		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	0.427693	−	0.903924i	$-0.359326\pi$
$83$	−11.7264	−	6.77022i	−0.141282	−	0.0815690i	−0.568975	+	0.822355i	$0.692660\pi$
$84$		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	$-0.467948\pi$
$89$	17.8933			0.201048			0.100524	+	0.994935i	$0.467948\pi$
$90$		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	−0.999802	−	0.0198821i	$-0.993671\pi$
$101$	−48.7510	+	84.4391i	−0.482683	+	0.836031i	0.517120	+	0.855913i	$0.327004\pi$
$102$		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	$0.150185\pi$
$107$			97.2648i			0.909017i	−0.890742	+	0.454509i	$0.849815\pi$
$108$		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	0.767125	−	0.641498i	$-0.221687\pi$
$113$	−19.4350	−	33.6625i	−0.171991	−	0.297898i	−0.939116	+	0.343600i	$0.888353\pi$
$114$		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	−0.668228	−	0.743956i	$-0.732947\pi$
$131$	−46.9055	+	27.0809i	−0.358057	+	0.206724i	0.310171	+	0.950681i	$0.399614\pi$
$132$		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	−0.855702	−	0.517469i	$-0.826874\pi$
$137$	2.77972	−	4.81461i	0.0202899	−	0.0351432i	0.875992	+	0.482325i	$0.160208\pi$
$138$		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	0.539280	−	0.842126i	$-0.318696\pi$
$149$	−68.4897	−	118.628i	−0.459663	−	0.796159i	−0.998943	+	0.0459672i	$0.985363\pi$
$150$		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	−0.921428	−	0.388550i	$-0.872976\pi$
$167$	−174.623	+	100.819i	−1.04565	+	0.603705i	−0.124220	+	0.992255i	$0.539643\pi$
$168$		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	−0.968212	−	0.250132i	$-0.919526\pi$
$173$	−46.2750	+	80.1506i	−0.267485	+	0.463298i	0.700726	+	0.713430i	$0.252859\pi$
$174$		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	$-0.996187\pi$
$179$		−	4.28851i		−	0.0239581i	0.999928	−	0.0119791i	$-0.00381315\pi$
$180$		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	0.275055	−	0.961429i	$-0.411304\pi$
$191$	−80.2276	−	46.3194i	−0.420040	−	0.242510i	−0.695094	+	0.718919i	$0.744637\pi$
$192$		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	$-0.615141\pi$
$197$	−139.432			−0.707779			−0.353890	+	0.935287i	$0.615141\pi$
$198$		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	0.893502	−	0.449060i	$-0.148241\pi$
$227$	215.958	+	124.683i	0.951355	+	0.549265i	0.0578535	+	0.998325i	$0.481574\pi$
$228$		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	$-0.767165\pi$
$233$	−346.793			−1.48838			−0.744191	+	0.667966i	$0.767165\pi$
$234$		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	−0.299526	−	0.954088i	$-0.596829\pi$
$239$	90.0970	−	52.0175i	0.376975	−	0.217647i	0.676501	+	0.736441i	$0.263495\pi$
$240$		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	$0.181880\pi$
$251$			271.484i			1.08161i	−0.841148	+	0.540804i	$0.818120\pi$
$252$		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	$0.184879\pi$
$257$	229.552	+	397.597i	0.893200	+	1.54707i	0.0571840	+	0.998364i	$0.481788\pi$
$258$		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	0.125439	−	0.992101i	$-0.459966\pi$
$263$	−176.480	−	101.891i	−0.671027	−	0.387418i	−0.796466	+	0.604684i	$0.793299\pi$
$264$		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	$-0.294750\pi$
$269$	323.363			1.20209			0.601047	+	0.799213i	$0.294750\pi$
$270$		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	−0.891174	−	0.453662i	$-0.850117\pi$
$281$	−14.8098	+	25.6514i	−0.0527040	+	0.0912861i	0.838470	+	0.544948i	$0.183451\pi$
$282$		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	0.519521	−	0.854458i	$-0.326110\pi$
$293$	−140.705	−	243.708i	−0.480222	−	0.831768i	−0.999743	+	0.0226894i	$0.992777\pi$
$294$		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	−0.521679	−	0.853142i	$-0.674694\pi$
$311$	−13.5833	+	7.84235i	−0.0436764	+	0.0252166i	0.478003	+	0.878358i	$0.341361\pi$
$312$		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	$-0.547276\pi$
$317$	248.053	−	429.641i	0.782502	−	1.35533i	0.930480	−	0.366343i	$-0.119390\pi$
$318$		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	$-0.241797\pi$
$347$	584.358	−	337.379i	1.68403	−	0.972275i	0.958936	−	0.283624i	$-0.0915368\pi$
$348$		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	$0.510984\pi$
$353$	−311.614	+	539.731i	−0.882759	+	1.52898i	−0.848260	+	0.529579i	$0.822350\pi$
$354$		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	$-0.928312\pi$
$359$		−	160.341i		−	0.446633i	0.974746	−	0.223316i	$-0.0716883\pi$
$360$		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	−0.937202	−	0.348788i	$-0.886593\pi$
$383$	−422.734	+	244.065i	−1.10374	+	0.637247i	−0.166542	+	0.986034i	$0.553260\pi$
$384$		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	$0.346180\pi$
$389$	−207.934	+	360.152i	−0.534534	+	0.925840i	−0.999186	+	0.0403465i	$0.987154\pi$
$390$		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	0.928651	−	0.370955i	$-0.120969\pi$
$401$	57.3709	+	99.3693i	0.143070	+	0.247804i	−0.785582	+	0.618758i	$0.787636\pi$
$402$		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	0.170914	−	0.985286i	$-0.445328\pi$
$419$	464.945	−	268.436i	1.10965	−	0.640659i	0.938740	+	0.344627i	$0.111995\pi$
$420$		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	$-0.674733\pi$
$431$		−	735.353i		−	1.70616i	0.521784	−	0.853078i	$-0.325267\pi$
$432$		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	0.357203	−	0.934027i	$-0.383731\pi$
$443$	−120.978	−	69.8465i	−0.273087	−	0.157667i	−0.630290	+	0.776360i	$0.717064\pi$
$444$		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	$-0.403853\pi$
$449$	267.139			0.594963			0.297482	+	0.954728i	$0.403853\pi$
$450$		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	−0.657377	−	0.753562i	$-0.728334\pi$
$461$	149.325	−	258.638i	0.323915	−	0.561037i	0.981292	+	0.192524i	$0.0616675\pi$
$462$		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	$0.161683\pi$
$467$			454.280i			0.972762i	−0.873747	+	0.486381i	$0.838317\pi$
$468$		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	0.503263	−	0.864133i	$-0.332133\pi$
$479$	3.12946	+	1.80679i	0.00653332	+	0.00377201i	−0.496730	+	0.867905i	$0.665466\pi$
$480$		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	−0.945934	−	0.324360i	$-0.894851\pi$
$491$	−558.756	+	322.598i	−1.13800	+	0.657022i	−0.192063	+	0.981383i	$0.561518\pi$
$492$		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	$-0.840576\pi$
$503$		−	483.048i		−	0.960334i	0.877177	−	0.480167i	$-0.159424\pi$
$504$		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	0.740214	−	0.672372i	$-0.234724\pi$
$509$	−108.002	−	187.065i	−0.212184	−	0.367514i	−0.952398	+	0.304858i	$0.901391\pi$
$510$		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	$-0.643773\pi$
$521$	−454.806			−0.872949			−0.436475	+	0.899717i	$0.643773\pi$
$522$		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	$-0.621029\pi$
$557$	−413.437			−0.742258			−0.371129	+	0.928581i	$0.621029\pi$
$558$		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	−0.0469843	−	0.998896i	$-0.514961\pi$
$563$	447.356	−	258.281i	0.794592	−	0.458758i	0.841577	+	0.540137i	$0.181628\pi$
$564$		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	−0.583500	−	0.812113i	$-0.698317\pi$
$569$	234.178	−	405.608i	0.411560	−	0.712843i	0.995061	+	0.0992699i	$0.0316507\pi$
$570$		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	0.653744	−	0.756716i	$-0.273197\pi$
$587$	190.940	+	110.239i	0.325281	+	0.187801i	−0.328463	+	0.944517i	$0.606531\pi$
$588$		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	$-0.183896\pi$
$593$	993.520			1.67541			0.837707	+	0.546121i	$0.183896\pi$
$594$		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	−0.689020	−	0.724743i	$-0.741959\pi$
$599$	−243.124	+	140.368i	−0.405884	+	0.234337i	0.283136	+	0.959080i	$0.408625\pi$
$600$		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	0.998089	−	0.0617910i	$-0.0196812\pi$
$617$	274.893	+	476.129i	0.445532	+	0.771684i	−0.552557	+	0.833475i	$0.686348\pi$
$618$		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	−0.985643	−	0.168842i	$-0.945997\pi$
$641$	−222.171	+	384.811i	−0.346600	+	0.600329i	0.639043	+	0.769171i	$0.279331\pi$
$642$		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	$0.231857\pi$
$647$			861.386i			1.33135i	−0.746240	+	0.665677i	$0.768143\pi$
$648$		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	$0.0674605\pi$
$653$	438.151	+	758.900i	0.670982	+	1.16217i	−0.306644	+	0.951824i	$0.599206\pi$
$654$		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	0.823338	−	0.567551i	$-0.192109\pi$
$659$	489.963	+	282.880i	0.743494	+	0.429257i	−0.0798443	+	0.996807i	$0.525442\pi$
$660$		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	−0.986880	−	0.161454i	$-0.948382\pi$
$677$	−239.399	+	414.651i	−0.353617	+	0.612483i	0.633263	+	0.773937i	$0.281715\pi$
$678$		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	$0.0748879\pi$
$683$			318.418i			0.466206i	−0.972452	+	0.233103i	$0.925112\pi$
$684$		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	$-0.595283\pi$
$701$	−413.437			−0.589782			−0.294891	+	0.955531i	$0.595283\pi$
$702$		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	$0.0638173\pi$
$719$			286.374i			0.398295i	−0.979970	+	0.199148i	$0.936183\pi$
$720$		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	−0.976669	−	0.214748i	$-0.931107\pi$
$743$	−950.317	+	548.666i	−1.27903	+	0.738447i	−0.302357	+	0.953195i	$0.597774\pi$
$744$		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	$-0.871993\pi$
$761$	−608.092	−	1053.25i	−0.799069	−	1.38403i	0.121154	−	0.992634i	$-0.461341\pi$
$762$		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	$-0.420403\pi$
$773$	382.580			0.494929			0.247464	+	0.968897i	$0.420403\pi$
$774$		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	0.981073	−	0.193639i	$-0.0620290\pi$
$797$	257.304	+	445.663i	0.322840	+	0.559176i	−0.658233	+	0.752815i	$0.728696\pi$
$798$		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	$-0.140123\pi$
$809$	1463.74			1.80932			0.904662	+	0.426129i	$0.140123\pi$
$810$		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	−0.960448	−	0.278461i	$-0.910176\pi$
$821$	−196.276	+	339.961i	−0.239070	+	0.414081i	0.721378	+	0.692542i	$0.243509\pi$
$822$		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	$0.310398\pi$
$827$			1369.15i			1.65557i	−0.561049	+	0.827783i	$0.689602\pi$
$828$		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	0.968940	−	0.247297i	$-0.0795423\pi$
$839$	1039.73	+	600.286i	1.23924	+	0.715478i	0.270305	+	0.962775i	$0.412876\pi$
$840$		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	−0.677593	−	0.735437i	$-0.736977\pi$
$857$	255.481	−	442.506i	0.298111	−	0.516344i	0.975704	+	0.219094i	$0.0703101\pi$
$858$		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	$0.203149\pi$
$863$			1028.28i			1.19152i	−0.803163	+	0.595759i	$0.796851\pi$
$864$		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	$-0.706767\pi$
$881$	−1065.75			−1.20970			−0.604851	+	0.796339i	$0.706767\pi$
$882$		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	−0.791569	−	0.611079i	$-0.790736\pi$
$887$	−583.774	+	337.042i	−0.658144	+	0.379980i	0.133426	+	0.991059i	$0.457402\pi$
$888$		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	−0.340973	−	0.940073i	$-0.610756\pi$
$911$	−1207.61	−	697.213i	−1.32559	−	0.765328i	−0.984614	+	0.174746i	$0.944090\pi$
$912$		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	−0.817704	−	0.575639i	$-0.804753\pi$
$929$	83.2996	−	144.279i	0.0896659	−	0.155306i	0.907370	+	0.420333i	$0.138087\pi$
$930$		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	0.564296	−	0.825572i	$-0.309147\pi$
$941$	−407.282	−	705.433i	−0.432818	−	0.749663i	−0.997115	+	0.0759090i	$0.975814\pi$
$942$		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	0.745780	−	0.666192i	$-0.232077\pi$
$947$	513.020	+	296.192i	0.541731	+	0.312769i	−0.204049	+	0.978961i	$0.565410\pi$
$948$		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	$-0.646162\pi$
$953$	−844.768			−0.886430			−0.443215	+	0.896415i	$0.646162\pi$
$954$		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	$-0.932054\pi$
$971$		−	411.395i		−	0.423682i	0.977304	−	0.211841i	$-0.0679458\pi$
$972$		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	$-0.811109\pi$
$977$	−878.125	−	1520.96i	−0.898797	−	1.55676i	−0.0697635	−	0.997564i	$-0.522224\pi$
$978$		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	0.810132	−	0.586247i	$-0.199395\pi$
$983$	695.466	+	401.528i	0.707494	+	0.408472i	−0.102639	+	0.994719i	$0.532729\pi$
$984$		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.55.4		8
3.2	odd	2	inner	324.3.f.p.55.1		8
4.3	odd	2		324.3.f.o.55.1		8
9.2	odd	6		108.3.d.d.55.4	yes	8
9.4	even	3		324.3.f.o.271.1		8
9.5	odd	6		324.3.f.o.271.4		8
9.7	even	3		108.3.d.d.55.5	yes	8
12.11	even	2		324.3.f.o.55.4		8
36.7	odd	6		108.3.d.d.55.6	yes	8
36.11	even	6		108.3.d.d.55.3	✓	8
36.23	even	6	inner	324.3.f.p.271.2		8
36.31	odd	6	inner	324.3.f.p.271.3		8
72.11	even	6		1728.3.g.l.703.8		8
72.29	odd	6		1728.3.g.l.703.7		8
72.43	odd	6		1728.3.g.l.703.2		8
72.61	even	6		1728.3.g.l.703.1		8

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