LMFDB - Embedded newform 432.3.bc.b.209.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			209.5
Character	$\chi$	$=$	432.209
Dual form			432.3.bc.b.401.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47205 + 2.61402i) q^{3} +(-4.32861 + 0.763252i) q^{5} +(2.73772 + 2.29722i) q^{7} +(-4.66616 + 7.69591i) q^{9} +O(q^{10})$	\(q+(1.47205 + 2.61402i) q^{3} +(-4.32861 + 0.763252i) q^{5} +(2.73772 + 2.29722i) q^{7} +(-4.66616 + 7.69591i) q^{9} +(14.4582 + 2.54938i) q^{11} +(-3.67778 - 1.33860i) q^{13} +(-8.36707 - 10.1915i) q^{15} +(-5.96626 + 3.44462i) q^{17} +(-14.1412 + 24.4932i) q^{19} +(-1.97492 + 10.5381i) q^{21} +(-0.832583 - 0.992234i) q^{23} +(-5.33796 + 1.94286i) q^{25} +(-26.9860 - 0.868674i) q^{27} +(-12.9959 - 35.7059i) q^{29} +(-41.7175 + 35.0052i) q^{31} +(14.6191 + 41.5469i) q^{33} +(-13.6039 - 7.85422i) q^{35} +(18.5334 + 32.1007i) q^{37} +(-1.91473 - 11.5842i) q^{39} +(-14.0768 + 38.6757i) q^{41} +(0.615899 - 3.49294i) q^{43} +(14.3241 - 36.8741i) q^{45} +(27.5222 - 32.7997i) q^{47} +(-6.29086 - 35.6773i) q^{49} +(-17.7869 - 10.5253i) q^{51} -47.8007i q^{53} -64.5299 q^{55} +(-84.8421 - 0.910069i) q^{57} +(61.1091 - 10.7752i) q^{59} +(-8.50896 - 7.13987i) q^{61} +(-30.4539 + 10.3501i) q^{63} +(16.9414 + 2.98722i) q^{65} +(105.153 + 38.2727i) q^{67} +(1.36811 - 3.63700i) q^{69} +(-90.9885 + 52.5322i) q^{71} +(-48.5118 + 84.0248i) q^{73} +(-12.9364 - 11.0935i) q^{75} +(33.7262 + 40.1933i) q^{77} +(104.299 - 37.9616i) q^{79} +(-37.4540 - 71.8206i) q^{81} +(44.8984 + 123.357i) q^{83} +(23.1965 - 19.4642i) q^{85} +(74.2053 - 86.5322i) q^{87} +(87.8638 + 50.7282i) q^{89} +(-6.99367 - 12.1134i) q^{91} +(-152.914 - 57.5210i) q^{93} +(42.5172 - 116.815i) q^{95} +(-28.7527 + 163.065i) q^{97} +(-87.0842 + 99.3734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{18}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.47205	+	2.61402i	0.490682	+	0.871339i
$3$	1.47205	+	2.61402i	0.490682	+	0.871339i
$4$		0			0
$5$	−4.32861	+	0.763252i	−0.865723	+	0.152650i	−0.588836	−	0.808252i	$-0.700414\pi$
$5$	−4.32861	+	0.763252i	−0.865723	+	0.152650i	−0.276887	+	0.960903i	$0.589303\pi$
$6$		0			0
$7$	2.73772	+	2.29722i	0.391103	+	0.328175i	0.817043	−	0.576577i	$-0.195612\pi$
$7$	2.73772	+	2.29722i	0.391103	+	0.328175i	−0.425939	+	0.904752i	$0.640056\pi$
$8$		0			0
$9$	−4.66616	+	7.69591i	−0.518462	+	0.855101i
$10$		0			0
$11$	14.4582	+	2.54938i	1.31438	+	0.231762i	0.786519	−	0.617566i	$-0.211881\pi$
$11$	14.4582	+	2.54938i	1.31438	+	0.231762i	0.527866	+	0.849328i	$0.322992\pi$
$12$		0			0
$13$	−3.67778	−	1.33860i	−0.282906	−	0.102969i	0.196670	−	0.980470i	$-0.436987\pi$
$13$	−3.67778	−	1.33860i	−0.282906	−	0.102969i	−0.479576	+	0.877500i	$0.659209\pi$
$14$		0			0
$15$	−8.36707	−	10.1915i	−0.557805	−	0.679435i
$16$		0			0
$17$	−5.96626	+	3.44462i	−0.350956	+	0.202625i	−0.665106	−	0.746749i	$-0.731614\pi$
$17$	−5.96626	+	3.44462i	−0.350956	+	0.202625i	0.314150	+	0.949373i	$0.398280\pi$
$18$		0			0
$19$	−14.1412	+	24.4932i	−0.744272	+	1.28912i	0.206263	+	0.978497i	$0.433870\pi$
$19$	−14.1412	+	24.4932i	−0.744272	+	1.28912i	−0.950534	+	0.310620i	$0.899463\pi$
$20$		0			0
$21$	−1.97492	+	10.5381i	−0.0940438	+	0.501813i
$22$		0			0
$23$	−0.832583	−	0.992234i	−0.0361993	−	0.0431406i	0.747641	−	0.664103i	$-0.231186\pi$
$23$	−0.832583	−	0.992234i	−0.0361993	−	0.0431406i	−0.783840	+	0.620962i	$0.786742\pi$
$24$		0			0
$25$	−5.33796	+	1.94286i	−0.213519	+	0.0777144i
$26$		0			0
$27$	−26.9860	−	0.868674i	−0.999482	−	0.0321731i
$28$		0			0
$29$	−12.9959	−	35.7059i	−0.448134	−	1.23124i	−0.934021	−	0.357217i	$-0.883726\pi$
$29$	−12.9959	−	35.7059i	−0.448134	−	1.23124i	0.485887	−	0.874021i	$-0.338496\pi$
$30$		0			0
$31$	−41.7175	+	35.0052i	−1.34573	+	1.12920i	−0.365612	+	0.930767i	$0.619140\pi$
$31$	−41.7175	+	35.0052i	−1.34573	+	1.12920i	−0.980115	+	0.198431i	$0.936415\pi$
$32$		0			0
$33$	14.6191	+	41.5469i	0.443003	+	1.25900i
$34$		0			0
$35$	−13.6039	−	7.85422i	−0.388683	−	0.224406i
$36$		0			0
$37$	18.5334	+	32.1007i	0.500902	+	0.867588i	0.999999	+	0.00104187i	$0.000331638\pi$
$37$	18.5334	+	32.1007i	0.500902	+	0.867588i	−0.499097	+	0.866546i	$0.666335\pi$
$38$		0			0
$39$	−1.91473	−	11.5842i	−0.0490957	−	0.297032i
$40$		0			0
$41$	−14.0768	+	38.6757i	−0.343336	+	0.943309i	0.641083	+	0.767472i	$0.278485\pi$
$41$	−14.0768	+	38.6757i	−0.343336	+	0.943309i	−0.984419	+	0.175837i	$0.943737\pi$
$42$		0			0
$43$	0.615899	−	3.49294i	0.0143232	−	0.0812311i	−0.976808	−	0.214116i	$-0.931313\pi$
$43$	0.615899	−	3.49294i	0.0143232	−	0.0812311i	0.991131	+	0.132885i	$0.0424241\pi$
$44$		0			0
$45$	14.3241	−	36.8741i	0.318313	−	0.819424i
$46$		0			0
$47$	27.5222	−	32.7997i	0.585578	−	0.697865i	−0.389171	−	0.921165i	$-0.627239\pi$
$47$	27.5222	−	32.7997i	0.585578	−	0.697865i	0.974750	+	0.223300i	$0.0716830\pi$
$48$		0			0
$49$	−6.29086	−	35.6773i	−0.128385	−	0.728107i
$50$		0			0
$51$	−17.7869	−	10.5253i	−0.348763	−	0.206377i
$52$		0			0
$53$		−	47.8007i		−	0.901900i	−0.892549	−	0.450950i	$-0.851085\pi$
$53$		−	47.8007i		−	0.901900i	0.892549	−	0.450950i	$-0.148915\pi$
$54$		0			0
$55$	−64.5299			−1.17327
$56$		0			0
$57$	−84.8421	−	0.910069i	−1.48846	−	0.0159661i
$58$		0			0
$59$	61.1091	−	10.7752i	1.03575	−	0.182630i	0.370174	−	0.928962i	$-0.379298\pi$
$59$	61.1091	−	10.7752i	1.03575	−	0.182630i	0.665574	+	0.746332i	$0.268187\pi$
$60$		0			0
$61$	−8.50896	−	7.13987i	−0.139491	−	0.117047i	0.570372	−	0.821386i	$-0.306799\pi$
$61$	−8.50896	−	7.13987i	−0.139491	−	0.117047i	−0.709863	+	0.704339i	$0.751243\pi$
$62$		0			0
$63$	−30.4539	+	10.3501i	−0.483395	+	0.164287i
$64$		0			0
$65$	16.9414	+	2.98722i	0.260636	+	0.0459572i
$66$		0			0
$67$	105.153	+	38.2727i	1.56945	+	0.571235i	0.972877	−	0.231321i	$-0.0743049\pi$
$67$	105.153	+	38.2727i	1.56945	+	0.571235i	0.596577	+	0.802556i	$0.296527\pi$
$68$		0			0
$69$	1.36811	−	3.63700i	0.0198277	−	0.0527101i
$70$		0			0
$71$	−90.9885	+	52.5322i	−1.28153	+	0.739890i	−0.977128	−	0.212654i	$-0.931789\pi$
$71$	−90.9885	+	52.5322i	−1.28153	+	0.739890i	−0.304400	+	0.952544i	$0.598456\pi$
$72$		0			0
$73$	−48.5118	+	84.0248i	−0.664545	+	1.15102i	0.314864	+	0.949137i	$0.398041\pi$
$73$	−48.5118	+	84.0248i	−0.664545	+	1.15102i	−0.979409	+	0.201888i	$0.935292\pi$
$74$		0			0
$75$	−12.9364	−	11.0935i	−0.172485	−	0.147914i
$76$		0			0
$77$	33.7262	+	40.1933i	0.438002	+	0.521991i
$78$		0			0
$79$	104.299	−	37.9616i	1.32024	−	0.480527i	0.416702	−	0.909043i	$-0.363186\pi$
$79$	104.299	−	37.9616i	1.32024	−	0.480527i	0.903534	+	0.428516i	$0.140963\pi$
$80$		0			0
$81$	−37.4540	−	71.8206i	−0.462395	−	0.886674i
$82$		0			0
$83$	44.8984	+	123.357i	0.540945	+	1.48623i	0.845624	+	0.533779i	$0.179229\pi$
$83$	44.8984	+	123.357i	0.540945	+	1.48623i	−0.304679	+	0.952455i	$0.598549\pi$
$84$		0			0
$85$	23.1965	−	19.4642i	0.272900	−	0.228990i
$86$		0			0
$87$	74.2053	−	86.5322i	0.852934	−	0.994623i
$88$		0			0
$89$	87.8638	+	50.7282i	0.987233	+	0.569979i	0.904446	−	0.426588i	$-0.140285\pi$
$89$	87.8638	+	50.7282i	0.987233	+	0.569979i	0.0827871	+	0.996567i	$0.473618\pi$
$90$		0			0
$91$	−6.99367	−	12.1134i	−0.0768535	−	0.133114i
$92$		0			0
$93$	−152.914	−	57.5210i	−1.64424	−	0.618506i
$94$		0			0
$95$	42.5172	−	116.815i	0.447549	−	1.22963i
$96$		0			0
$97$	−28.7527	+	163.065i	−0.296420	+	1.68108i	0.364956	+	0.931025i	$0.381084\pi$
$97$	−28.7527	+	163.065i	−0.296420	+	1.68108i	−0.661376	+	0.750055i	$0.730027\pi$
$98$		0			0
$99$	−87.0842	+	99.3734i	−0.879638	+	1.00377i
$100$		0			0
$101$	14.2076	−	16.9319i	0.140669	−	0.167643i	−0.691110	−	0.722749i	$-0.742878\pi$
$101$	14.2076	−	16.9319i	0.140669	−	0.167643i	0.831779	+	0.555107i	$0.187323\pi$
$102$		0			0
$103$	4.91300	+	27.8630i	0.0476991	+	0.270515i	0.999325	−	0.0367451i	$-0.0116990\pi$
$103$	4.91300	+	27.8630i	0.0476991	+	0.270515i	−0.951626	+	0.307260i	$0.900588\pi$
$104$		0			0
$105$	0.505467	−	47.1226i	0.00481397	−	0.448787i
$106$		0			0
$107$		−	67.0830i		−	0.626944i	−0.949597	−	0.313472i	$-0.898508\pi$
$107$		−	67.0830i		−	0.626944i	0.949597	−	0.313472i	$-0.101492\pi$
$108$		0			0
$109$	82.0479			0.752733			0.376367	−	0.926471i	$-0.377173\pi$
$109$	82.0479			0.752733			0.376367	+	0.926471i	$0.377173\pi$
$110$		0			0
$111$	−56.6299	+	95.7003i	−0.510179	+	0.862165i
$112$		0			0
$113$	139.573	−	24.6104i	1.23516	−	0.217791i	0.482317	−	0.875997i	$-0.339795\pi$
$113$	139.573	−	24.6104i	1.23516	−	0.217791i	0.752839	+	0.658205i	$0.228684\pi$
$114$		0			0
$115$	4.36126	+	3.65953i	0.0379240	+	0.0318220i
$116$		0			0
$117$	27.4628	−	22.0577i	0.234725	−	0.188527i
$118$		0			0
$119$	−24.2470	−	4.27540i	−0.203757	−	0.0359278i
$120$		0			0
$121$	88.8384	+	32.3345i	0.734202	+	0.267228i
$122$		0			0
$123$	−121.820	+	20.1354i	−0.990410	+	0.163703i
$124$		0			0
$125$	116.786	−	67.4265i	0.934289	−	0.539412i
$126$		0			0
$127$	−36.1258	+	62.5718i	−0.284455	+	0.492691i	−0.972477	−	0.232999i	$-0.925146\pi$
$127$	−36.1258	+	62.5718i	−0.284455	+	0.492691i	0.688022	+	0.725690i	$0.258479\pi$
$128$		0			0
$129$	10.0372	−	3.53180i	0.0778079	−	0.0273783i
$130$		0			0
$131$	−80.4893	−	95.9234i	−0.614422	−	0.732239i	0.365679	−	0.930741i	$-0.380837\pi$
$131$	−80.4893	−	95.9234i	−0.614422	−	0.732239i	−0.980101	+	0.198502i	$0.936392\pi$
$132$		0			0
$133$	−94.9809	+	34.5702i	−0.714142	+	0.259927i
$134$		0			0
$135$	117.475	−	16.8370i	0.870186	−	0.124718i
$136$		0			0
$137$	−44.4879	−	122.229i	−0.324729	−	0.892186i	−0.989422	−	0.145069i	$-0.953660\pi$
$137$	−44.4879	−	122.229i	−0.324729	−	0.892186i	0.664693	−	0.747117i	$-0.268563\pi$
$138$		0			0
$139$	64.7192	−	54.3058i	0.465606	−	0.390689i	−0.379583	−	0.925158i	$-0.623933\pi$
$139$	64.7192	−	54.3058i	0.465606	−	0.390689i	0.845189	+	0.534468i	$0.179488\pi$
$140$		0			0
$141$	126.253	+	23.6608i	0.895410	+	0.167807i
$142$		0			0
$143$	−49.7615	−	28.7298i	−0.347983	−	0.200908i
$144$		0			0
$145$	83.5068	+	144.638i	0.575909	+	0.997503i
$146$		0			0
$147$	84.0005	−	68.9630i	0.571432	−	0.469136i
$148$		0			0
$149$	48.8305	−	134.161i	0.327722	−	0.900408i	−0.660966	−	0.750416i	$-0.729853\pi$
$149$	48.8305	−	134.161i	0.327722	−	0.900408i	0.988687	−	0.149992i	$-0.0479247\pi$
$150$		0			0
$151$	−7.41354	+	42.0443i	−0.0490963	+	0.278439i	−0.999466	−	0.0326849i	$-0.989594\pi$
$151$	−7.41354	+	42.0443i	−0.0490963	+	0.278439i	0.950369	+	0.311124i	$0.100705\pi$
$152$		0			0
$153$	1.33002	−	61.9889i	0.00869292	−	0.405156i
$154$		0			0
$155$	153.861	−	183.365i	0.992654	−	1.18300i
$156$		0			0
$157$	−11.8042	−	66.9447i	−0.0751857	−	0.426399i	−0.999046	−	0.0436696i	$-0.986095\pi$
$157$	−11.8042	−	66.9447i	−0.0751857	−	0.426399i	0.923860	−	0.382730i	$-0.125016\pi$
$158$		0			0
$159$	124.952	−	70.3649i	0.785861	−	0.442546i
$160$		0			0
$161$		−	4.62909i		−	0.0287521i
$162$		0			0
$163$	52.2555			0.320586			0.160293	−	0.987069i	$-0.448756\pi$
$163$	52.2555			0.320586			0.160293	+	0.987069i	$0.448756\pi$
$164$		0			0
$165$	−94.9911	−	168.682i	−0.575704	−	1.02232i
$166$		0			0
$167$	205.761	−	36.2813i	1.23210	−	0.217253i	0.480575	−	0.876953i	$-0.340428\pi$
$167$	205.761	−	36.2813i	1.23210	−	0.217253i	0.751529	+	0.659700i	$0.229317\pi$
$168$		0			0
$169$	−117.727	−	98.7850i	−0.696611	−	0.584526i
$170$		0			0
$171$	−122.513	−	223.118i	−0.716448	−	1.30478i
$172$		0			0
$173$	285.514	+	50.3439i	1.65037	+	0.291005i	0.919963	−	0.392005i	$-0.128218\pi$
$173$	285.514	+	50.3439i	1.65037	+	0.291005i	0.730409	+	0.683010i	$0.239329\pi$
$174$		0			0
$175$	−19.0771	−	6.94348i	−0.109012	−	0.0396770i
$176$		0			0
$177$	118.122	+	143.879i	0.667356	+	0.812874i
$178$		0			0
$179$	84.3915	−	48.7235i	0.471461	−	0.272198i	−0.245390	−	0.969424i	$-0.578916\pi$
$179$	84.3915	−	48.7235i	0.471461	−	0.272198i	0.716851	+	0.697226i	$0.245583\pi$
$180$		0			0
$181$	18.6602	−	32.3205i	0.103095	−	0.178566i	−0.809863	−	0.586619i	$-0.800459\pi$
$181$	18.6602	−	32.3205i	0.103095	−	0.178566i	0.912958	+	0.408053i	$0.133792\pi$
$182$		0			0
$183$	6.13813	−	32.7528i	0.0335417	−	0.178977i
$184$		0			0
$185$	−104.725	−	124.806i	−0.566080	−	0.674628i
$186$		0			0
$187$	−95.0432	+	34.5929i	−0.508252	+	0.184989i
$188$		0			0
$189$	−71.8847	−	64.3711i	−0.380342	−	0.340588i
$190$		0			0
$191$	119.816	+	329.191i	0.627307	+	1.72351i	0.688352	+	0.725377i	$0.258335\pi$
$191$	119.816	+	329.191i	0.627307	+	1.72351i	−0.0610446	+	0.998135i	$0.519443\pi$
$192$		0			0
$193$	8.46714	−	7.10477i	0.0438712	−	0.0368123i	−0.620588	−	0.784136i	$-0.713106\pi$
$193$	8.46714	−	7.10477i	0.0438712	−	0.0368123i	0.664460	+	0.747324i	$0.268662\pi$
$194$		0			0
$195$	17.1298	+	48.6823i	0.0878453	+	0.249653i
$196$		0			0
$197$	−275.483	−	159.050i	−1.39839	−	0.807362i	−0.404167	−	0.914685i	$-0.632439\pi$
$197$	−275.483	−	159.050i	−1.39839	−	0.807362i	−0.994224	+	0.107323i	$0.965772\pi$
$198$		0			0
$199$	88.3486	+	153.024i	0.443963	+	0.768966i	0.997979	−	0.0635397i	$-0.0202389\pi$
$199$	88.3486	+	153.024i	0.443963	+	0.768966i	−0.554017	+	0.832506i	$0.686906\pi$
$200$		0			0
$201$	54.7453	+	331.212i	0.272365	+	1.64782i
$202$		0			0
$203$	46.4453	−	127.607i	0.228794	−	0.628608i
$204$		0			0
$205$	31.4137	−	178.156i	0.153238	−	0.869054i
$206$		0			0
$207$	11.5211	−	1.77756i	0.0556575	−	0.00858726i
$208$		0			0
$209$	−266.899	+	318.077i	−1.27703	+	1.52190i
$210$		0			0
$211$	36.0058	+	204.199i	0.170644	+	0.967768i	0.943053	+	0.332643i	$0.107940\pi$
$211$	36.0058	+	204.199i	0.170644	+	0.967768i	−0.772409	+	0.635125i	$0.780949\pi$
$212$		0			0
$213$	−271.259	−	160.515i	−1.27352	−	0.753594i
$214$		0			0
$215$			15.5897i			0.0725100i
$216$		0			0
$217$	−194.626			−0.896893
$218$		0			0
$219$	−291.054	−	3.12203i	−1.32901	−	0.0142558i
$220$		0			0
$221$	26.5535	−	4.68210i	0.120152	−	0.0211860i
$222$		0			0
$223$	−316.844	−	265.863i	−1.42082	−	1.19221i	−0.950897	−	0.309506i	$-0.899836\pi$
$223$	−316.844	−	265.863i	−1.42082	−	1.19221i	−0.469926	−	0.882706i	$-0.655719\pi$
$224$		0			0
$225$	9.95571	−	50.1462i	0.0442476	−	0.222872i
$226$		0			0
$227$	−94.9127	−	16.7357i	−0.418117	−	0.0737254i	−0.0393683	−	0.999225i	$-0.512535\pi$
$227$	−94.9127	−	16.7357i	−0.418117	−	0.0737254i	−0.378749	+	0.925499i	$0.623646\pi$
$228$		0			0
$229$	189.133	+	68.8386i	0.825906	+	0.300605i	0.720178	−	0.693790i	$-0.244060\pi$
$229$	189.133	+	68.8386i	0.825906	+	0.300605i	0.105729	+	0.994395i	$0.466283\pi$
$230$		0			0
$231$	−55.4194	+	147.327i	−0.239911	+	0.637780i
$232$		0			0
$233$	−303.285	+	175.101i	−1.30165	+	0.751508i	−0.980687	−	0.195583i	$-0.937340\pi$
$233$	−303.285	+	175.101i	−1.30165	+	0.751508i	−0.320964	+	0.947092i	$0.604007\pi$
$234$		0			0
$235$	−94.0985	+	162.983i	−0.400419	+	0.693547i
$236$		0			0
$237$	252.765	+	216.757i	1.06652	+	0.914587i
$238$		0			0
$239$	100.663	+	119.965i	0.421183	+	0.501947i	0.934357	−	0.356338i	$-0.115975\pi$
$239$	100.663	+	119.965i	0.421183	+	0.501947i	−0.513174	+	0.858285i	$0.671530\pi$
$240$		0			0
$241$	324.419	−	118.079i	1.34614	−	0.489954i	0.434397	−	0.900721i	$-0.356961\pi$
$241$	324.419	−	118.079i	1.34614	−	0.489954i	0.911740	+	0.410768i	$0.134739\pi$
$242$		0			0
$243$	132.606	−	203.629i	0.545705	−	0.837978i
$244$		0			0
$245$	54.4614	+	149.632i	0.222292	+	0.610741i
$246$		0			0
$247$	84.7946	−	71.1512i	0.343298	−	0.288061i
$248$		0			0
$249$	−256.366	+	298.953i	−1.02958	+	1.20062i
$250$		0			0
$251$	−22.8819	−	13.2109i	−0.0911628	−	0.0526329i	0.453726	−	0.891141i	$-0.350095\pi$
$251$	−22.8819	−	13.2109i	−0.0911628	−	0.0526329i	−0.544888	+	0.838509i	$0.683428\pi$
$252$		0			0
$253$	−9.50810	−	16.4685i	−0.0375814	−	0.0650930i
$254$		0			0
$255$	85.0261	+	31.9839i	0.333436	+	0.125427i
$256$		0			0
$257$	40.6520	−	111.691i	0.158179	−	0.434593i	−0.835134	−	0.550047i	$-0.814610\pi$
$257$	40.6520	−	111.691i	0.158179	−	0.434593i	0.993313	+	0.115453i	$0.0368321\pi$
$258$		0			0
$259$	−23.0033	+	130.458i	−0.0888159	+	0.503700i
$260$		0			0
$261$	335.430	+	66.5942i	1.28517	+	0.255150i
$262$		0			0
$263$	−110.151	+	131.272i	−0.418823	+	0.499134i	−0.933663	−	0.358152i	$-0.883407\pi$
$263$	−110.151	+	131.272i	−0.418823	+	0.499134i	0.514840	+	0.857286i	$0.327851\pi$
$264$		0			0
$265$	36.4840	+	206.911i	0.137675	+	0.780796i
$266$		0			0
$267$	−3.26466	+	304.351i	−0.0122272	+	1.13989i
$268$		0			0
$269$		−	147.131i		−	0.546957i	−0.961878	−	0.273478i	$-0.911826\pi$
$269$		−	147.131i		−	0.546957i	0.961878	−	0.273478i	$-0.0881742\pi$
$270$		0			0
$271$	−42.2256			−0.155814			−0.0779071	−	0.996961i	$-0.524824\pi$
$271$	−42.2256			−0.155814			−0.0779071	+	0.996961i	$0.524824\pi$
$272$		0			0
$273$	21.3696	−	36.1130i	0.0782769	−	0.132282i
$274$		0			0
$275$	−82.1306	+	14.4818i	−0.298657	+	0.0526612i
$276$		0			0
$277$	−241.990	−	203.054i	−0.873611	−	0.733046i	0.0912446	−	0.995829i	$-0.470916\pi$
$277$	−241.990	−	203.054i	−0.873611	−	0.733046i	−0.964855	+	0.262782i	$0.915360\pi$
$278$		0			0
$279$	−74.7359	−	484.394i	−0.267871	−	1.73618i
$280$		0			0
$281$	425.296	+	74.9912i	1.51351	+	0.266872i	0.867878	−	0.496777i	$-0.165483\pi$
$281$	425.296	+	74.9912i	1.51351	+	0.266872i	0.645631	+	0.763650i	$0.276594\pi$
$282$		0			0
$283$	51.4917	+	18.7414i	0.181949	+	0.0662242i	0.431388	−	0.902166i	$-0.358024\pi$
$283$	51.4917	+	18.7414i	0.181949	+	0.0662242i	−0.249439	+	0.968391i	$0.580246\pi$
$284$		0			0
$285$	367.943	−	60.8165i	1.29103	−	0.213391i
$286$		0			0
$287$	−127.385	+	73.5457i	−0.443850	+	0.256257i
$288$		0			0
$289$	−120.769	+	209.178i	−0.417886	+	0.723801i
$290$		0			0
$291$	−468.579	+	164.879i	−1.61024	+	0.566594i
$292$		0			0
$293$	−90.3507	−	107.676i	−0.308364	−	0.367494i	0.589499	−	0.807769i	$-0.299325\pi$
$293$	−90.3507	−	107.676i	−0.308364	−	0.367494i	−0.897863	+	0.440275i	$0.854881\pi$
$294$		0			0
$295$	−256.294	+	93.2833i	−0.868792	+	0.316214i
$296$		0			0
$297$	−387.956	−	81.3570i	−1.30625	−	0.273929i
$298$		0			0
$299$	1.73385	+	4.76371i	0.00579883	+	0.0159321i
$300$		0			0
$301$	9.71021	−	8.14784i	0.0322598	−	0.0270692i
$302$		0			0
$303$	65.1745	+	12.2142i	0.215097	+	0.0403110i
$304$		0			0
$305$	42.2815	+	24.4113i	0.138628	+	0.0800369i
$306$		0			0
$307$	213.941	+	370.556i	0.696876	+	1.20702i	0.969544	+	0.244916i	$0.0787603\pi$
$307$	213.941	+	370.556i	0.696876	+	1.20702i	−0.272669	+	0.962108i	$0.587906\pi$
$308$		0			0
$309$	−65.6022	+	53.8584i	−0.212305	+	0.174299i
$310$		0			0
$311$	−142.432	+	391.327i	−0.457979	+	1.25829i	0.469008	+	0.883194i	$0.344612\pi$
$311$	−142.432	+	391.327i	−0.457979	+	1.25829i	−0.926987	+	0.375094i	$0.877611\pi$
$312$		0			0
$313$	25.1171	−	142.446i	0.0802462	−	0.455099i	−0.918035	−	0.396499i	$-0.870225\pi$
$313$	25.1171	−	142.446i	0.0802462	−	0.455099i	0.998282	−	0.0586003i	$-0.0186638\pi$
$314$		0			0
$315$	123.923	−	68.0454i	0.393407	−	0.216017i
$316$		0			0
$317$	−348.939	+	415.849i	−1.10075	+	1.31183i	−0.154648	+	0.987970i	$0.549424\pi$
$317$	−348.939	+	415.849i	−1.10075	+	1.31183i	−0.946106	+	0.323858i	$0.895020\pi$
$318$		0			0
$319$	−96.8698	−	549.376i	−0.303667	−	1.72218i
$320$		0			0
$321$	175.356	−	98.7493i	0.546280	−	0.307630i
$322$		0			0
$323$		−	194.844i		−	0.603231i
$324$		0			0
$325$	22.2325			0.0684078
$326$		0			0
$327$	120.778	+	214.475i	0.369353	+	0.655886i
$328$		0			0
$329$	150.696	−	26.5718i	0.458043	−	0.0807654i
$330$		0			0
$331$	−169.745	−	142.433i	−0.512825	−	0.430311i	0.349297	−	0.937012i	$-0.386420\pi$
$331$	−169.745	−	142.433i	−0.512825	−	0.430311i	−0.862122	+	0.506701i	$0.830865\pi$
$332$		0			0
$333$	−333.524	−	7.15600i	−1.00157	−	0.0214895i
$334$		0			0
$335$	−484.380	−	85.4093i	−1.44591	−	0.254953i
$336$		0			0
$337$	36.2922	+	13.2093i	0.107692	+	0.0391967i	0.395304	−	0.918550i	$-0.370639\pi$
$337$	36.2922	+	13.2093i	0.107692	+	0.0391967i	−0.287612	+	0.957747i	$0.592861\pi$
$338$		0			0
$339$	269.789	+	328.617i	0.795839	+	0.969373i
$340$		0			0
$341$	−692.403	+	399.759i	−2.03051	+	1.17231i
$342$		0			0
$343$	152.295	−	263.783i	0.444009	−	0.769046i
$344$		0			0
$345$	−3.14609	+	16.7874i	−0.00911911	+	0.0486591i
$346$		0			0
$347$	−134.499	−	160.290i	−0.387607	−	0.461932i	0.536593	−	0.843841i	$-0.319711\pi$
$347$	−134.499	−	160.290i	−0.387607	−	0.461932i	−0.924200	+	0.381910i	$0.875267\pi$
$348$		0			0
$349$	−262.851	+	95.6701i	−0.753156	+	0.274126i	−0.689933	−	0.723873i	$-0.742360\pi$
$349$	−262.851	+	95.6701i	−0.753156	+	0.274126i	−0.0632228	+	0.997999i	$0.520138\pi$
$350$		0			0
$351$	98.0857	+	39.3183i	0.279447	+	0.112018i
$352$		0			0
$353$	−28.7312	−	78.9384i	−0.0813916	−	0.223622i	0.892321	−	0.451401i	$-0.149076\pi$
$353$	−28.7312	−	78.9384i	−0.0813916	−	0.223622i	−0.973713	+	0.227780i	$0.926853\pi$
$354$		0			0
$355$	353.759	−	296.839i	0.996503	−	0.836166i
$356$		0			0
$357$	−24.5168	−	69.6757i	−0.0686745	−	0.195170i
$358$		0			0
$359$	221.262	+	127.746i	0.616330	+	0.355838i	0.775439	−	0.631423i	$-0.217529\pi$
$359$	221.262	+	127.746i	0.616330	+	0.355838i	−0.159109	+	0.987261i	$0.550862\pi$
$360$		0			0
$361$	−219.445	−	380.090i	−0.607880	−	1.05288i
$362$		0			0
$363$	46.2513	+	279.823i	0.127414	+	0.770862i
$364$		0			0
$365$	145.857	−	400.738i	0.399607	−	1.09791i
$366$		0			0
$367$	44.7221	−	253.632i	0.121859	−	0.691095i	−0.861265	−	0.508155i	$-0.830328\pi$
$367$	44.7221	−	253.632i	0.121859	−	0.691095i	0.983124	−	0.182940i	$-0.0585613\pi$
$368$		0			0
$369$	−231.960	−	288.800i	−0.628617	−	0.782657i
$370$		0			0
$371$	109.809	−	130.865i	0.295981	−	0.352736i
$372$		0			0
$373$	83.5846	+	474.032i	0.224087	+	1.27086i	0.864422	+	0.502767i	$0.167684\pi$
$373$	83.5846	+	474.032i	0.224087	+	1.27086i	−0.640335	+	0.768096i	$0.721204\pi$
$374$		0			0
$375$	348.168	+	206.026i	0.928449	+	0.549402i
$376$		0			0
$377$			148.715i			0.394469i
$378$		0			0
$379$	370.571			0.977759			0.488880	−	0.872351i	$-0.337406\pi$
$379$	370.571			0.977759			0.488880	+	0.872351i	$0.337406\pi$
$380$		0			0
$381$	−216.743	−	2.32492i	−0.568878	−	0.00610214i
$382$		0			0
$383$	−481.807	+	84.9556i	−1.25798	+	0.221816i	−0.762606	−	0.646863i	$-0.776081\pi$
$383$	−481.807	+	84.9556i	−1.25798	+	0.221816i	−0.495375	+	0.868679i	$0.664969\pi$
$384$		0			0
$385$	−176.665	−	148.240i	−0.458870	−	0.385038i
$386$		0			0
$387$	24.0074	+	21.0385i	0.0620347	+	0.0543630i
$388$		0			0
$389$	309.685	+	54.6057i	0.796104	+	0.140375i	0.556884	−	0.830591i	$-0.311997\pi$
$389$	309.685	+	54.6057i	0.796104	+	0.140375i	0.239221	+	0.970965i	$0.423108\pi$
$390$		0			0
$391$	8.38528	+	3.05199i	0.0214457	+	0.00780560i
$392$		0			0
$393$	132.261	−	351.604i	0.336543	−	0.894666i
$394$		0			0
$395$	−422.495	+	243.927i	−1.06961	+	0.617538i
$396$		0			0
$397$	−44.8022	+	77.5996i	−0.112852	+	0.195465i	−0.916919	−	0.399073i	$-0.869332\pi$
$397$	−44.8022	+	77.5996i	−0.112852	+	0.195465i	0.804067	+	0.594538i	$0.202665\pi$
$398$		0			0
$399$	−230.184	−	197.393i	−0.576901	−	0.494719i
$400$		0			0
$401$	−55.2456	−	65.8392i	−0.137770	−	0.164187i	0.692748	−	0.721180i	$-0.256400\pi$
$401$	−55.2456	−	65.8392i	−0.137770	−	0.164187i	−0.830518	+	0.556992i	$0.811955\pi$
$402$		0			0
$403$	200.286	−	72.8980i	0.496987	−	0.180888i
$404$		0			0
$405$	216.941	+	282.297i	0.535657	+	0.697030i
$406$		0			0
$407$	186.123	+	511.369i	0.457305	+	1.25643i
$408$		0			0
$409$	479.987	−	402.757i	1.17356	−	0.984736i	0.173563	−	0.984823i	$-0.444472\pi$
$409$	479.987	−	402.757i	1.17356	−	0.984736i	1.00000		8.63705e-5i	$2.74926e-5\pi$
$410$		0			0
$411$	254.021	−	296.219i	0.618057	−	0.720729i
$412$		0			0
$413$	192.053	+	110.882i	0.465019	+	0.268479i
$414$		0			0
$415$	−288.501	−	499.698i	−0.695183	−	1.20409i
$416$		0			0
$417$	237.226	+	89.2362i	0.568887	+	0.213996i
$418$		0			0
$419$	120.491	−	331.047i	0.287569	−	0.790089i	−0.708836	−	0.705373i	$-0.750780\pi$
$419$	120.491	−	331.047i	0.287569	−	0.790089i	0.996405	−	0.0847157i	$-0.0269982\pi$
$420$		0			0
$421$	26.8471	−	152.258i	0.0637699	−	0.361657i	−0.936179	−	0.351524i	$-0.885663\pi$
$421$	26.8471	−	152.258i	0.0637699	−	0.361657i	0.999949	−	0.0101329i	$-0.00322545\pi$
$422$		0			0
$423$	124.000	+	364.857i	0.293145	+	0.862545i
$424$		0			0
$425$	25.1553	−	29.9789i	0.0591888	−	0.0705385i
$426$		0			0
$427$	−6.89332	−	39.0940i	−0.0161436	−	0.0915549i
$428$		0			0
$429$	1.84894	−	172.369i	0.00430988	−	0.401793i
$430$		0			0
$431$		−	226.253i		−	0.524949i	−0.964939	−	0.262474i	$-0.915461\pi$
$431$		−	226.253i		−	0.524949i	0.964939	−	0.262474i	$-0.0845386\pi$
$432$		0			0
$433$	−648.539			−1.49778			−0.748890	−	0.662695i	$-0.769413\pi$
$433$	−648.539			−1.49778			−0.748890	+	0.662695i	$0.769413\pi$
$434$		0			0
$435$	−255.160	+	431.202i	−0.586575	+	0.991269i
$436$		0			0
$437$	36.0767	−	6.36129i	0.0825553	−	0.0145567i
$438$		0			0
$439$	−231.313	−	194.095i	−0.526909	−	0.442129i	0.340123	−	0.940381i	$-0.389531\pi$
$439$	−231.313	−	194.095i	−0.526909	−	0.442129i	−0.867032	+	0.498252i	$0.833976\pi$
$440$		0			0
$441$	303.923	+	118.062i	0.689168	+	0.267714i
$442$		0			0
$443$	−458.869	−	80.9110i	−1.03582	−	0.182643i	−0.370215	−	0.928946i	$-0.620716\pi$
$443$	−458.869	−	80.9110i	−1.03582	−	0.182643i	−0.665606	+	0.746303i	$0.731827\pi$
$444$		0			0
$445$	−419.047	−	152.521i	−0.941678	−	0.342743i
$446$		0			0
$447$	422.579	−	69.8472i	0.945367	−	0.156258i
$448$		0			0
$449$	35.8903	−	20.7213i	0.0799339	−	0.0461498i	−0.459500	−	0.888178i	$-0.651971\pi$
$449$	35.8903	−	20.7213i	0.0799339	−	0.0461498i	0.539434	+	0.842028i	$0.318638\pi$
$450$		0			0
$451$	−302.124	+	523.295i	−0.669899	+	1.16030i
$452$		0			0
$453$	−120.817	+	42.5120i	−0.266705	+	0.0938455i
$454$		0			0
$455$	39.5185	+	47.0963i	0.0868538	+	0.103508i
$456$		0			0
$457$	405.966	−	147.760i	0.888329	−	0.323325i	0.142763	−	0.989757i	$-0.454401\pi$
$457$	405.966	−	147.760i	0.888329	−	0.323325i	0.745566	+	0.666432i	$0.232179\pi$
$458$		0			0
$459$	163.998	−	87.7739i	0.357294	−	0.191229i
$460$		0			0
$461$	224.994	+	618.167i	0.488057	+	1.34093i	0.902437	+	0.430822i	$0.141776\pi$
$461$	224.994	+	618.167i	0.488057	+	1.34093i	−0.414380	+	0.910104i	$0.636002\pi$
$462$		0			0
$463$	415.550	−	348.688i	0.897516	−	0.753105i	−0.0721872	−	0.997391i	$-0.522998\pi$
$463$	415.550	−	348.688i	0.897516	−	0.753105i	0.969703	+	0.244286i	$0.0785535\pi$
$464$		0			0
$465$	705.810	+	132.274i	1.51787	+	0.284461i
$466$		0			0
$467$	71.4291	+	41.2396i	0.152953	+	0.0883075i	0.574523	−	0.818488i	$-0.305188\pi$
$467$	71.4291	+	41.2396i	0.152953	+	0.0883075i	−0.421570	+	0.906796i	$0.638521\pi$
$468$		0			0
$469$	199.960	+	346.341i	0.426354	+	0.738467i
$470$		0			0
$471$	157.618	−	129.402i	0.334646	−	0.274739i
$472$		0			0
$473$	17.8096	−	48.9315i	0.0376525	−	0.103449i
$474$		0			0
$475$	27.8981	−	158.218i	0.0587329	−	0.333091i
$476$		0			0
$477$	367.870	+	223.046i	0.771216	+	0.467601i
$478$		0			0
$479$	−54.1626	+	64.5485i	−0.113074	+	0.134757i	−0.819613	−	0.572918i	$-0.805811\pi$
$479$	−54.1626	+	64.5485i	−0.113074	+	0.134757i	0.706538	+	0.707675i	$0.250256\pi$
$480$		0			0
$481$	−25.1915	−	142.868i	−0.0523732	−	0.297023i
$482$		0			0
$483$	12.1005	−	6.81424i	0.0250528	−	0.0141082i
$484$		0			0
$485$		−	727.790i		−	1.50060i
$486$		0			0
$487$	−566.361			−1.16296			−0.581479	−	0.813561i	$-0.697526\pi$
$487$	−566.361			−1.16296			−0.581479	+	0.813561i	$0.697526\pi$
$488$		0			0
$489$	76.9225	+	136.597i	0.157306	+	0.279339i
$490$		0			0
$491$	754.890	−	133.107i	1.53745	−	0.271095i	0.660188	−	0.751100i	$-0.270476\pi$
$491$	754.890	−	133.107i	1.53745	−	0.271095i	0.877266	+	0.480005i	$0.159365\pi$
$492$		0			0
$493$	200.530	+	168.265i	0.406755	+	0.341308i
$494$		0			0
$495$	301.107	−	496.616i	0.608297	−	1.00327i
$496$		0			0
$497$	−369.779	−	65.2021i	−0.744023	−	0.131191i
$498$		0			0
$499$	207.387	+	75.4828i	0.415606	+	0.151268i	0.541355	−	0.840794i	$-0.317911\pi$
$499$	207.387	+	75.4828i	0.415606	+	0.151268i	−0.125750	+	0.992062i	$0.540134\pi$
$500$		0			0
$501$	397.730	+	484.456i	0.793873	+	0.966978i
$502$		0			0
$503$	−783.399	+	452.296i	−1.55745	+	0.899196i	−0.559954	+	0.828524i	$0.689181\pi$
$503$	−783.399	+	452.296i	−1.55745	+	0.899196i	−0.997500	+	0.0706721i	$0.977486\pi$
$504$		0			0
$505$	−48.5757	+	84.1357i	−0.0961896	+	0.166605i
$506$		0			0
$507$	84.9253	−	453.157i	0.167506	−	0.893801i
$508$		0			0
$509$	220.212	+	262.439i	0.432637	+	0.515596i	0.937681	−	0.347497i	$-0.112968\pi$
$509$	220.212	+	262.439i	0.432637	+	0.515596i	−0.505044	+	0.863093i	$0.668524\pi$
$510$		0			0
$511$	−325.835	+	118.594i	−0.637643	+	0.232083i
$512$		0			0
$513$	402.890	−	648.690i	0.785361	−	1.26450i
$514$		0			0
$515$	−42.5330	−	116.858i	−0.0825884	−	0.226910i
$516$		0			0
$517$	481.541	−	404.061i	0.931414	−	0.781549i
$518$		0			0
$519$	288.691	+	820.448i	0.556244	+	1.58082i
$520$		0			0
$521$	−120.568	−	69.6099i	−0.231416	−	0.133608i	0.379809	−	0.925065i	$-0.375990\pi$
$521$	−120.568	−	69.6099i	−0.231416	−	0.133608i	−0.611225	+	0.791457i	$0.709323\pi$
$522$		0			0
$523$	12.3821	+	21.4464i	0.0236751	+	0.0410065i	0.877620	−	0.479357i	$-0.159130\pi$
$523$	12.3821	+	21.4464i	0.0236751	+	0.0410065i	−0.853945	+	0.520363i	$0.825797\pi$
$524$		0			0
$525$	−9.93195	−	60.0888i	−0.0189180	−	0.114455i
$526$		0			0
$527$	128.318	−	352.551i	0.243488	−	0.668977i
$528$		0			0
$529$	91.5686	−	519.311i	0.173097	−	0.981684i
$530$		0			0
$531$	−202.220	+	520.569i	−0.380828	+	0.980355i
$532$		0			0
$533$	103.543	−	123.397i	0.194264	−	0.231514i
$534$		0			0
$535$	51.2012	+	290.376i	0.0957032	+	0.542760i
$536$		0			0
$537$	251.592	+	148.878i	0.468514	+	0.277239i
$538$		0			0
$539$		−	531.868i		−	0.986768i
$540$		0			0
$541$	476.086			0.880011			0.440006	−	0.897995i	$-0.354976\pi$
$541$	476.086			0.880011			0.440006	+	0.897995i	$0.354976\pi$
$542$		0			0
$543$	111.955	+	1.20090i	0.206179	+	0.00221160i
$544$		0			0
$545$	−355.154	+	62.6232i	−0.651658	+	0.114905i
$546$		0			0
$547$	225.822	+	189.487i	0.412836	+	0.346411i	0.825430	−	0.564504i	$-0.190933\pi$
$547$	225.822	+	189.487i	0.412836	+	0.346411i	−0.412594	+	0.910915i	$0.635377\pi$
$548$		0			0
$549$	94.6519	−	32.1684i	0.172408	−	0.0585946i
$550$		0			0
$551$	1058.33	+	186.612i	1.92074	+	0.338679i
$552$		0			0
$553$	372.747	+	135.669i	0.674046	+	0.245333i
$554$		0			0
$555$	172.085	−	457.473i	0.310064	−	0.824275i
$556$		0			0
$557$	−756.664	+	436.860i	−1.35846	+	0.784309i	−0.989417	−	0.145101i	$-0.953649\pi$
$557$	−756.664	+	436.860i	−1.35846	+	0.784309i	−0.369047	+	0.929411i	$0.620316\pi$
$558$		0			0
$559$	−6.94078	+	12.0218i	−0.0124164	+	0.0215059i
$560$		0			0
$561$	−230.334	−	197.522i	−0.410578	−	0.352089i
$562$		0			0
$563$	327.795	+	390.651i	0.582230	+	0.693874i	0.974093	−	0.226149i	$-0.0726137\pi$
$563$	327.795	+	390.651i	0.582230	+	0.693874i	−0.391863	+	0.920024i	$0.628169\pi$
$564$		0			0
$565$	−585.372	+	213.058i	−1.03606	+	0.377094i
$566$		0			0
$567$	62.4494	−	282.665i	0.110140	−	0.498527i
$568$		0			0
$569$	−303.435	−	833.680i	−0.533277	−	1.46517i	−0.855148	−	0.518384i	$-0.826534\pi$
$569$	−303.435	−	833.680i	−0.533277	−	1.46517i	0.321871	−	0.946784i	$-0.395688\pi$
$570$		0			0
$571$	−403.162	+	338.293i	−0.706063	+	0.592457i	−0.923491	−	0.383619i	$-0.874677\pi$
$571$	−403.162	+	338.293i	−0.706063	+	0.592457i	0.217429	+	0.976076i	$0.430233\pi$
$572$		0			0
$573$	−684.136	+	797.784i	−1.19395	+	1.39229i
$574$		0			0
$575$	6.37207	+	3.67892i	0.0110819	+	0.00639812i
$576$		0			0
$577$	68.5779	+	118.780i	0.118853	+	0.205859i	0.919313	−	0.393527i	$-0.128745\pi$
$577$	68.5779	+	118.780i	0.118853	+	0.205859i	−0.800461	+	0.599385i	$0.795412\pi$
$578$		0			0
$579$	31.0360	+	11.6747i	0.0536028	+	0.0201635i
$580$		0			0
$581$	−160.460	+	440.860i	−0.276179	+	0.758796i
$582$		0			0
$583$	121.862	−	691.114i	0.209026	−	1.18544i
$584$		0			0
$585$	−102.040	+	116.440i	−0.174428	+	0.199043i
$586$		0			0
$587$	115.043	−	137.103i	0.195985	−	0.233566i	−0.659098	−	0.752057i	$-0.729062\pi$
$587$	115.043	−	137.103i	0.195985	−	0.233566i	0.855083	+	0.518491i	$0.173506\pi$
$588$		0			0
$589$	−267.454	−	1516.81i	−0.454082	−	2.57523i
$590$		0			0
$591$	10.2358	−	954.247i	0.0173195	−	1.61463i
$592$		0			0
$593$		−	52.0285i		−	0.0877377i	−0.999037	−	0.0438689i	$-0.986032\pi$
$593$		−	52.0285i		−	0.0877377i	0.999037	−	0.0438689i	$-0.0139684\pi$
$594$		0			0
$595$	108.219			0.181881
$596$		0			0
$597$	−269.954	+	456.203i	−0.452185	+	0.764160i
$598$		0			0
$599$	−114.494	+	20.1884i	−0.191142	+	0.0337035i	−0.268400	−	0.963308i	$-0.586495\pi$
$599$	−114.494	+	20.1884i	−0.191142	+	0.0337035i	0.0772575	+	0.997011i	$0.475384\pi$
$600$		0			0
$601$	−402.677	−	337.886i	−0.670011	−	0.562206i	0.243057	−	0.970012i	$-0.421850\pi$
$601$	−402.677	−	337.886i	−0.670011	−	0.562206i	−0.913069	+	0.407806i	$0.866294\pi$
$602$		0			0
$603$	−785.206	+	630.665i	−1.30217	+	1.04588i
$604$		0			0
$605$	−409.227	−	72.1577i	−0.676408	−	0.119269i
$606$		0			0
$607$	−80.4769	−	29.2912i	−0.132581	−	0.0482557i	0.274877	−	0.961479i	$-0.411363\pi$
$607$	−80.4769	−	29.2912i	−0.132581	−	0.0482557i	−0.407459	+	0.913224i	$0.633585\pi$
$608$		0			0
$609$	401.937	−	66.4353i	0.659995	−	0.109089i
$610$		0			0
$611$	−145.126	+	83.7886i	−0.237522	+	0.137134i
$612$		0			0
$613$	81.6463	−	141.416i	0.133191	−	0.230694i	−0.791714	−	0.610892i	$-0.790811\pi$
$613$	81.6463	−	141.416i	0.133191	−	0.230694i	0.924905	+	0.380198i	$0.124144\pi$
$614$		0			0
$615$	511.946	−	180.138i	0.832432	−	0.292908i
$616$		0			0
$617$	179.054	+	213.388i	0.290200	+	0.345847i	0.891372	−	0.453273i	$-0.149744\pi$
$617$	179.054	+	213.388i	0.290200	+	0.345847i	−0.601171	+	0.799120i	$0.705299\pi$
$618$		0			0
$619$	669.731	−	243.762i	1.08196	−	0.393800i	0.261321	−	0.965252i	$-0.415842\pi$
$619$	669.731	−	243.762i	1.08196	−	0.393800i	0.820636	+	0.571452i	$0.193620\pi$
$620$		0			0
$621$	21.6062	+	27.4997i	0.0347926	+	0.0442829i
$622$		0			0
$623$	124.013	+	340.722i	0.199057	+	0.546906i
$624$		0			0
$625$	−345.270	+	289.716i	−0.552432	+	0.463545i
$626$		0			0
$627$	−1224.35	−	229.452i	−1.95271	−	0.365953i
$628$		0			0
$629$	−221.150	−	127.681i	−0.351590	−	0.202990i
$630$		0			0
$631$	311.029	+	538.718i	0.492914	+	0.853753i	0.999967	−	0.00816241i	$-0.00259820\pi$
$631$	311.029	+	538.718i	0.492914	+	0.853753i	−0.507052	+	0.861915i	$0.669265\pi$
$632$		0			0
$633$	−480.777	+	394.710i	−0.759522	+	0.623555i
$634$		0			0
$635$	108.617	−	298.422i	0.171050	−	0.469956i
$636$		0			0
$637$	−24.6212	+	139.634i	−0.0386518	+	0.219206i
$638$		0			0
$639$	20.2834	−	945.362i	0.0317425	−	1.47944i
$640$		0			0
$641$	163.405	−	194.738i	0.254921	−	0.303804i	−0.623372	−	0.781925i	$-0.714238\pi$
$641$	163.405	−	194.738i	0.254921	−	0.303804i	0.878294	+	0.478122i	$0.158682\pi$
$642$		0			0
$643$	−36.8378	−	208.917i	−0.0572905	−	0.324910i	0.942671	−	0.333724i	$-0.108305\pi$
$643$	−36.8378	−	208.917i	−0.0572905	−	0.324910i	−0.999961	+	0.00881399i	$0.997194\pi$
$644$		0			0
$645$	−40.7516	+	22.9487i	−0.0631808	+	0.0355794i
$646$		0			0
$647$			330.267i			0.510459i	0.966880	+	0.255230i	$0.0821511\pi$
$647$			330.267i			0.510459i	−0.966880	+	0.255230i	$0.917849\pi$
$648$		0			0
$649$	911.000			1.40370
$650$		0			0
$651$	−286.498	−	508.755i	−0.440089	−	0.781497i
$652$		0			0
$653$	329.228	−	58.0518i	0.504178	−	0.0889002i	0.0842262	−	0.996447i	$-0.473158\pi$
$653$	329.228	−	58.0518i	0.504178	−	0.0889002i	0.419952	+	0.907546i	$0.362047\pi$
$654$		0			0
$655$	421.621	+	353.782i	0.643696	+	0.540125i
$656$		0			0
$657$	−420.284	−	765.415i	−0.639701	−	1.16502i
$658$		0			0
$659$	1021.20	+	180.064i	1.54962	+	0.273239i	0.881993	−	0.471262i	$-0.156201\pi$
$659$	1021.20	+	180.064i	1.54962	+	0.273239i	0.667622	+	0.744501i	$0.267312\pi$
$660$		0			0
$661$	397.057	+	144.517i	0.600692	+	0.218634i	0.624426	−	0.781084i	$-0.285333\pi$
$661$	397.057	+	144.517i	0.600692	+	0.218634i	−0.0237335	+	0.999718i	$0.507555\pi$
$662$		0			0
$663$	51.3271	+	62.5191i	0.0774165	+	0.0942972i
$664$		0			0
$665$	384.750	−	222.136i	0.578572	−	0.334038i
$666$		0			0
$667$	−24.6085	+	42.6231i	−0.0368942	+	0.0639027i
$668$		0			0
$669$	228.562	−	1219.60i	0.341648	−	1.82302i
$670$		0			0
$671$	−104.822	−	124.922i	−0.156218	−	0.186173i
$672$		0			0
$673$	−14.3659	+	5.22876i	−0.0213460	+	0.00776932i	−0.352671	−	0.935747i	$-0.614727\pi$
$673$	−14.3659	+	5.22876i	−0.0213460	+	0.00776932i	0.331325	+	0.943517i	$0.392504\pi$
$674$		0			0
$675$	145.738	−	47.7931i	0.215908	−	0.0708046i
$676$		0			0
$677$	103.653	+	284.784i	0.153106	+	0.420655i	0.992405	−	0.123015i	$-0.0392564\pi$
$677$	103.653	+	284.784i	0.153106	+	0.420655i	−0.839299	+	0.543670i	$0.817034\pi$
$678$		0			0
$679$	−453.313	+	380.375i	−0.667618	+	0.560198i
$680$		0			0
$681$	−95.9686	−	272.739i	−0.140923	−	0.400498i
$682$		0			0
$683$	−688.686	−	397.613i	−1.00833	−	0.582157i	−0.0976243	−	0.995223i	$-0.531124\pi$
$683$	−688.686	−	397.613i	−1.00833	−	0.582157i	−0.910701	+	0.413067i	$0.864458\pi$
$684$		0			0
$685$	285.863	+	495.129i	0.417318	+	0.722816i
$686$		0			0
$687$	98.4667	+	595.729i	0.143329	+	0.867146i
$688$		0			0
$689$	−63.9861	+	175.800i	−0.0928680	+	0.255153i
$690$		0			0
$691$	−8.31097	+	47.1339i	−0.0120275	+	0.0682111i	−0.990231	−	0.139438i	$-0.955470\pi$
$691$	−8.31097	+	47.1339i	−0.0120275	+	0.0682111i	0.978203	+	0.207650i	$0.0665814\pi$
$692$		0			0
$693$	−466.695	+	72.0053i	−0.673442	+	0.103904i
$694$		0			0
$695$	−238.695	+	284.466i	−0.343447	+	0.409304i
$696$		0			0
$697$	−49.2372	−	279.238i	−0.0706416	−	0.400629i
$698$		0			0
$699$	−904.167	−	535.033i	−1.29352	−	0.765427i
$700$		0			0
$701$			32.9301i			0.0469759i	0.999724	+	0.0234880i	$0.00747714\pi$
$701$			32.9301i			0.0469759i	−0.999724	+	0.0234880i	$0.992523\pi$
$702$		0			0
$703$	−1048.33			−1.49123
$704$		0			0
$705$	−564.559	−	6.05581i	−0.800793	−	0.00858980i
$706$		0			0
$707$	77.7927	−	13.7170i	0.110032	−	0.0194016i
$708$		0			0
$709$	705.725	+	592.173i	0.995380	+	0.835223i	0.986338	−	0.164736i	$-0.0526772\pi$
$709$	705.725	+	592.173i	0.995380	+	0.835223i	0.00904260	+	0.999959i	$0.497122\pi$
$710$		0			0
$711$	−194.525	+	979.808i	−0.273593	+	1.37807i
$712$		0			0
$713$	69.4666	+	12.2488i	0.0974286	+	0.0171793i
$714$		0			0
$715$	237.327	+	86.3798i	0.331925	+	0.120811i
$716$		0			0
$717$	−165.411	+	439.729i	−0.230698	+	0.613290i
$718$		0			0
$719$	−406.335	+	234.597i	−0.565139	+	0.326283i	−0.755205	−	0.655488i	$-0.772463\pi$
$719$	−406.335	+	234.597i	−0.565139	+	0.326283i	0.190067	+	0.981771i	$0.439130\pi$
$720$		0			0
$721$	−50.5571	+	87.5675i	−0.0701209	+	0.121453i
$722$		0			0
$723$	786.220	+	674.219i	1.08744	+	0.932530i
$724$		0			0
$725$	138.743	+	165.348i	0.191370	+	0.228066i
$726$		0			0
$727$	−53.3053	+	19.4016i	−0.0733223	+	0.0266871i	−0.378421	−	0.925634i	$-0.623533\pi$
$727$	−53.3053	+	19.4016i	−0.0733223	+	0.0266871i	0.305099	+	0.952321i	$0.401311\pi$
$728$		0			0
$729$	727.491	+	46.8841i	0.997930	+	0.0643129i
$730$		0			0
$731$	8.35723	+	22.9613i	0.0114326	+	0.0314108i
$732$		0			0
$733$	−773.970	+	649.438i	−1.05589	+	0.886000i	−0.993701	−	0.112064i	$-0.964254\pi$
$733$	−773.970	+	649.438i	−1.05589	+	0.886000i	−0.0621924	+	0.998064i	$0.519809\pi$
$734$		0			0
$735$	−310.970	+	362.628i	−0.423088	+	0.493371i
$736$		0			0
$737$	1422.76	+	821.432i	1.93048	+	1.11456i
$738$		0			0
$739$	−368.682	−	638.576i	−0.498893	−	0.864108i	0.501106	−	0.865386i	$-0.332927\pi$
$739$	−368.682	−	638.576i	−0.498893	−	0.864108i	−0.999999	+	0.00127777i	$0.999593\pi$
$740$		0			0
$741$	310.812	+	116.917i	0.419449	+	0.157782i
$742$		0			0
$743$	31.4911	−	86.5211i	0.0423837	−	0.116448i	−0.916695	−	0.399587i	$-0.869153\pi$
$743$	31.4911	−	86.5211i	0.0423837	−	0.116448i	0.959079	+	0.283139i	$0.0913757\pi$
$744$		0			0
$745$	−108.970	+	618.000i	−0.146269	+	0.829531i
$746$		0			0
$747$	−1158.85	−	230.071i	−1.55134	−	0.307993i
$748$		0			0
$749$	154.105	−	183.655i	0.205747	−	0.245200i
$750$		0			0
$751$	65.4270	+	371.055i	0.0871199	+	0.494081i	0.996879	+	0.0789448i	$0.0251551\pi$
$751$	65.4270	+	371.055i	0.0871199	+	0.494081i	−0.909759	+	0.415137i	$0.863734\pi$
$752$		0			0
$753$	0.850199	−	79.2606i	0.00112908	−	0.105260i
$754$		0			0
$755$		−	187.652i		−	0.248545i
$756$		0			0
$757$	98.9786			0.130751			0.0653755	−	0.997861i	$-0.479175\pi$
$757$	98.9786			0.130751			0.0653755	+	0.997861i	$0.479175\pi$
$758$		0			0
$759$	29.0526	−	49.0968i	0.0382775	−	0.0646861i
$760$		0			0
$761$	−1035.32	+	182.555i	−1.36047	+	0.239888i	−0.805804	−	0.592183i	$-0.798266\pi$
$761$	−1035.32	+	182.555i	−1.36047	+	0.239888i	−0.554669	+	0.832071i	$0.687155\pi$
$762$		0			0
$763$	224.625	+	188.482i	0.294396	+	0.247028i
$764$		0			0
$765$	41.5560	+	269.341i	0.0543216	+	0.352080i
$766$		0			0
$767$	−239.169	−	42.1720i	−0.311824	−	0.0549830i
$768$		0			0
$769$	14.0610	+	5.11778i	0.0182848	+	0.00665511i	0.351146	−	0.936321i	$-0.385792\pi$
$769$	14.0610	+	5.11778i	0.0182848	+	0.00665511i	−0.332862	+	0.942976i	$0.608014\pi$
$770$		0			0
$771$	351.802	−	58.1486i	0.456294	−	0.0754198i
$772$		0			0
$773$	453.509	−	261.834i	0.586687	−	0.338724i	−0.177099	−	0.984193i	$-0.556671\pi$
$773$	453.509	−	261.834i	0.586687	−	0.338724i	0.763787	+	0.645469i	$0.223338\pi$
$774$		0			0
$775$	154.677	−	267.908i	0.199583	−	0.345687i
$776$		0			0
$777$	−374.882	+	131.910i	−0.482473	+	0.169768i
$778$		0			0
$779$	−748.229	−	891.705i	−0.960499	−	1.14468i
$780$		0			0
$781$	−1449.46	+	527.559i	−1.85590	+	0.675492i
$782$		0			0
$783$	319.691	+	974.850i	0.408289	+	1.24502i
$784$		0			0
$785$	102.191	+	280.768i	0.130180	+	0.357667i
$786$		0			0
$787$	−120.730	+	101.305i	−0.153406	+	0.128723i	−0.716260	−	0.697833i	$-0.754148\pi$
$787$	−120.730	+	101.305i	−0.153406	+	0.128723i	0.562854	+	0.826556i	$0.309703\pi$
$788$		0			0
$789$	−505.294	−	94.6963i	−0.640424	−	0.120021i
$790$		0			0
$791$	438.647	+	253.253i	0.554547	+	0.320168i
$792$		0			0
$793$	21.7366	+	37.6489i	0.0274106	+	0.0474766i
$794$		0			0
$795$	−487.162	+	399.952i	−0.612783	+	0.503085i
$796$		0			0
$797$	5.59137	−	15.3622i	0.00701552	−	0.0192750i	−0.936135	−	0.351640i	$-0.885624\pi$
$797$	5.59137	−	15.3622i	0.00701552	−	0.0192750i	0.943151	+	0.332365i	$0.107846\pi$
$798$		0			0
$799$	−51.2221	+	290.495i	−0.0641077	+	0.363573i
$800$		0			0
$801$	−800.385	+	439.486i	−0.999233	+	0.548671i
$802$		0			0
$803$	−915.605	+	1091.18i	−1.14023	+	1.35887i
$804$		0			0
$805$	3.53316	+	20.0376i	0.00438902	+	0.0248914i
$806$		0			0
$807$	384.604	−	216.584i	0.476585	−	0.268382i
$808$		0			0
$809$		−	1248.37i		−	1.54310i	−0.636168	−	0.771551i	$-0.719481\pi$
$809$		−	1248.37i		−	1.54310i	0.636168	−	0.771551i	$-0.280519\pi$
$810$		0			0
$811$	796.242			0.981803			0.490901	−	0.871215i	$-0.336668\pi$
$811$	796.242			0.981803			0.490901	+	0.871215i	$0.336668\pi$
$812$		0			0
$813$	−62.1581	−	110.379i	−0.0764553	−	0.135767i
$814$		0			0
$815$	−226.194	+	39.8841i	−0.277538	+	0.0489375i
$816$		0			0
$817$	76.8437	+	64.4795i	0.0940559	+	0.0789223i
$818$		0			0
$819$	125.857	+	2.70035i	0.153672	+	0.00329714i
$820$		0			0
$821$	−1369.41	−	241.464i	−1.66798	−	0.294110i	−0.741640	−	0.670798i	$-0.765952\pi$
$821$	−1369.41	−	241.464i	−1.66798	−	0.294110i	−0.926340	+	0.376688i	$0.877063\pi$
$822$		0			0
$823$	21.0770	+	7.67138i	0.0256099	+	0.00932124i	0.354793	−	0.934945i	$-0.384551\pi$
$823$	21.0770	+	7.67138i	0.0256099	+	0.00932124i	−0.329183	+	0.944266i	$0.606773\pi$
$824$		0			0
$825$	−158.756	−	193.373i	−0.192431	−	0.234391i
$826$		0			0
$827$	−79.4904	+	45.8938i	−0.0961190	+	0.0554943i	−0.547289	−	0.836944i	$-0.684340\pi$
$827$	−79.4904	+	45.8938i	−0.0961190	+	0.0554943i	0.451170	+	0.892438i	$0.351007\pi$
$828$		0			0
$829$	−398.805	+	690.751i	−0.481068	+	0.833234i	−0.999764	−	0.0217246i	$-0.993084\pi$
$829$	−398.805	+	690.751i	−0.481068	+	0.833234i	0.518696	+	0.854959i	$0.326418\pi$
$830$		0			0
$831$	174.565	−	931.471i	0.210066	−	1.12090i
$832$		0			0
$833$	160.428	+	191.190i	0.192590	+	0.229520i
$834$		0			0
$835$	−862.970	+	314.095i	−1.03350	+	0.376162i
$836$		0			0
$837$	1156.20	−	908.411i	1.38136	−	1.08532i
$838$		0			0
$839$	−566.496	−	1556.43i	−0.675203	−	1.85511i	−0.488158	−	0.872755i	$-0.662331\pi$
$839$	−566.496	−	1556.43i	−0.675203	−	1.85511i	−0.187045	−	0.982351i	$-0.559891\pi$
$840$		0			0
$841$	−461.775	+	387.476i	−0.549079	+	0.460732i
$842$		0			0
$843$	430.028	+	1222.12i	0.510116	+	1.44973i
$844$		0			0
$845$	584.994	+	337.746i	0.692301	+	0.399700i
$846$		0			0
$847$	168.935	+	292.605i	0.199451	+	0.345460i
$848$		0			0
$849$	26.8077	+	162.188i	0.0315757	+	0.191035i
$850$		0			0
$851$	16.4209	−	45.1160i	0.0192960	−	0.0530153i
$852$		0			0
$853$	−215.597	+	1222.71i	−0.252752	+	1.43343i	0.549027	+	0.835805i	$0.314998\pi$
$853$	−215.597	+	1222.71i	−0.252752	+	1.43343i	−0.801779	+	0.597621i	$0.796113\pi$
$854$		0			0
$855$	700.605	+	872.285i	0.819421	+	1.02022i
$856$		0			0
$857$	949.464	−	1131.53i	1.10789	−	1.32033i	0.165355	−	0.986234i	$-0.447123\pi$
$857$	949.464	−	1131.53i	1.10789	−	1.32033i	0.942537	−	0.334101i	$-0.108433\pi$
$858$		0			0
$859$	173.038	+	981.345i	0.201441	+	1.14243i	0.902943	+	0.429760i	$0.141402\pi$
$859$	173.038	+	981.345i	0.201441	+	1.14243i	−0.701503	+	0.712667i	$0.747487\pi$
$860$		0			0
$861$	−379.766	−	224.724i	−0.441076	−	0.261003i
$862$		0			0
$863$		−	671.209i		−	0.777763i	−0.921288	−	0.388881i	$-0.872862\pi$
$863$		−	671.209i		−	0.777763i	0.921288	−	0.388881i	$-0.127138\pi$
$864$		0			0
$865$	−1274.31			−1.47319
$866$		0			0
$867$	−724.573	−	7.77223i	−0.835725	−	0.00896451i
$868$		0			0
$869$	1604.75	−	282.961i	1.84667	−	0.325617i
$870$		0			0
$871$	−335.499	−	281.517i	−0.385188	−	0.323211i
$872$		0			0
$873$	−1120.77	−	982.164i	−1.28381	−	1.12504i
$874$		0			0
$875$	474.622	+	83.6886i	0.542425	+	0.0956441i
$876$		0			0
$877$	−610.614	−	222.245i	−0.696253	−	0.253415i	−0.0304427	−	0.999537i	$-0.509692\pi$
$877$	−610.614	−	222.245i	−0.696253	−	0.253415i	−0.665810	+	0.746121i	$0.731914\pi$
$878$		0			0
$879$	148.466	−	394.682i	0.168903	−	0.449013i
$880$		0			0
$881$	−196.446	+	113.418i	−0.222980	+	0.128738i	−0.607330	−	0.794450i	$-0.707759\pi$
$881$	−196.446	+	113.418i	−0.222980	+	0.128738i	0.384349	+	0.923188i	$0.374426\pi$
$882$		0			0
$883$	−34.4995	+	59.7548i	−0.0390707	+	0.0676725i	−0.884900	−	0.465782i	$-0.845773\pi$
$883$	−34.4995	+	59.7548i	−0.0390707	+	0.0676725i	0.845829	+	0.533454i	$0.179106\pi$
$884$		0			0
$885$	−621.120	−	532.638i	−0.701831	−	0.601851i
$886$		0			0
$887$	581.417	+	692.906i	0.655488	+	0.781180i	0.986731	−	0.162366i	$-0.0519125\pi$
$887$	581.417	+	692.906i	0.655488	+	0.781180i	−0.331243	+	0.943545i	$0.607468\pi$
$888$		0			0
$889$	−242.644	+	88.3151i	−0.272940	+	0.0993421i
$890$		0			0
$891$	−358.420	−	1133.88i	−0.402267	−	1.27260i
$892$		0			0
$893$	414.173	+	1137.93i	0.463800	+	1.27428i
$894$		0			0
$895$	−328.110	+	275.317i	−0.366603	+	0.307617i
$896$		0			0
$897$	−9.90011	+	11.5447i	−0.0110369	+	0.0128704i
$898$		0			0
$899$	1792.05	+	1034.64i	1.99338	+	1.15088i
$900$		0			0
$901$	164.655	+	285.191i	0.182747	+	0.316528i
$902$		0			0
$903$	35.5925	+	13.3887i	0.0394158	+	0.0148269i
$904$		0			0
$905$	−56.1043	+	154.145i	−0.0619937	+	0.170326i
$906$		0			0
$907$	28.0243	−	158.934i	0.0308978	−	0.175230i	−0.965454	−	0.260575i	$-0.916088\pi$
$907$	28.0243	−	158.934i	0.0308978	−	0.175230i	0.996352	+	0.0853445i	$0.0271991\pi$
$908$		0			0
$909$	64.0117	+	188.347i	0.0704199	+	0.207202i
$910$		0			0
$911$	−51.9472	+	61.9082i	−0.0570221	+	0.0679563i	−0.793802	−	0.608177i	$-0.791901\pi$
$911$	−51.9472	+	61.9082i	−0.0570221	+	0.0679563i	0.736779	+	0.676133i	$0.236346\pi$
$912$		0			0
$913$	334.668	+	1897.99i	0.366558	+	2.07885i
$914$		0			0
$915$	−1.57101	+	146.459i	−0.00171695	+	0.160065i
$916$		0			0
$917$		−	447.513i		−	0.488019i
$918$		0			0
$919$	656.985			0.714891			0.357445	−	0.933934i	$-0.383648\pi$
$919$	656.985			0.714891			0.357445	+	0.933934i	$0.383648\pi$
$920$		0			0
$921$	−653.709	+	1104.72i	−0.709782	+	1.19948i
$922$		0			0
$923$	404.955	−	71.4045i	0.438738	−	0.0773613i
$924$		0			0
$925$	−161.298	−	135.345i	−0.174376	−	0.146319i
$926$		0			0
$927$	−237.356	−	92.2033i	−0.256048	−	0.0994641i
$928$		0			0
$929$	−244.546	−	43.1200i	−0.263235	−	0.0464155i	0.0404727	−	0.999181i	$-0.487114\pi$
$929$	−244.546	−	43.1200i	−0.263235	−	0.0464155i	−0.303708	+	0.952765i	$0.598225\pi$
$930$		0			0
$931$	962.811	+	350.434i	1.03417	+	0.376406i
$932$		0			0
$933$	−1232.60	+	203.734i	−1.32112	+	0.218364i
$934$		0			0
$935$	385.002	−	222.281i	0.411767	−	0.237734i
$936$		0			0
$937$	468.473	−	811.418i	0.499971	−	0.865975i	−0.500029	−	0.866008i	$-0.666677\pi$
$937$	468.473	−	811.418i	0.499971	−	0.865975i	1.00000		3.38875e-5i	$1.07867e-5\pi$
$938$		0			0
$939$	409.330	−	144.031i	0.435921	−	0.153387i
$940$		0			0
$941$	−899.429	−	1071.90i	−0.955823	−	1.13911i	−0.990194	−	0.139696i	$-0.955387\pi$
$941$	−899.429	−	1071.90i	−0.955823	−	1.13911i	0.0343714	−	0.999409i	$-0.489057\pi$
$942$		0			0
$943$	50.0954	−	18.2332i	0.0531234	−	0.0193354i
$944$		0			0
$945$	360.293	+	223.772i	0.381262	+	0.236795i
$946$		0			0
$947$	−249.635	−	685.866i	−0.263606	−	0.724252i	−0.998917	−	0.0465220i	$-0.985186\pi$
$947$	−249.635	−	685.866i	−0.263606	−	0.724252i	0.735311	−	0.677730i	$-0.237036\pi$
$948$		0			0
$949$	290.891	−	244.087i	0.306524	−	0.257204i
$950$		0			0
$951$	−1600.69	−	299.982i	−1.68317	−	0.315439i
$952$		0			0
$953$	1167.46	+	674.032i	1.22503	+	0.707274i	0.965987	−	0.258591i	$-0.0832581\pi$
$953$	1167.46	+	674.032i	1.22503	+	0.707274i	0.259047	+	0.965865i	$0.416591\pi$
$954$		0			0
$955$	−769.891	−	1333.49i	−0.806169	−	1.39633i
$956$		0			0
$957$	1293.48	−	1061.93i	1.35160	−	1.10964i
$958$		0			0
$959$	158.993	−	436.829i	0.165790	−	0.455505i
$960$		0			0
$961$	348.115	−	1974.26i	0.362242	−	2.05438i
$962$		0			0
$963$	516.264	+	313.020i	0.536100	+	0.325046i
$964$		0			0
$965$	−31.2283	+	37.2164i	−0.0323609	+	0.0385662i
$966$		0			0
$967$	−124.207	−	704.414i	−0.128446	−	0.728453i	−0.979201	−	0.202891i	$-0.934966\pi$
$967$	−124.207	−	704.414i	−0.128446	−	0.728453i	0.850755	−	0.525562i	$-0.176145\pi$
$968$		0			0
$969$	509.325	−	286.819i	0.525619	−	0.295995i
$970$		0			0
$971$		−	1288.41i		−	1.32689i	−0.748226	−	0.663444i	$-0.769094\pi$
$971$		−	1288.41i		−	1.32689i	0.748226	−	0.663444i	$-0.230906\pi$
$972$		0			0
$973$	301.936			0.310314
$974$		0			0
$975$	32.7273	+	58.1162i	0.0335665	+	0.0596064i
$976$		0			0
$977$	−830.119	+	146.372i	−0.849661	+	0.149818i	−0.581491	−	0.813553i	$-0.697530\pi$
$977$	−830.119	+	146.372i	−0.849661	+	0.149818i	−0.268171	+	0.963371i	$0.586419\pi$
$978$		0			0
$979$	1141.03	+	957.437i	1.16551	+	0.977975i
$980$		0			0
$981$	−382.848	+	631.433i	−0.390263	+	0.643663i
$982$		0			0
$983$	−502.601	−	88.6222i	−0.511293	−	0.0901548i	−0.0879514	−	0.996125i	$-0.528032\pi$
$983$	−502.601	−	88.6222i	−0.511293	−	0.0901548i	−0.423342	+	0.905970i	$0.639143\pi$
$984$		0			0
$985$	1313.86	+	478.204i	1.33386	+	0.485487i
$986$		0			0
$987$	291.291	+	354.807i	0.295128	+	0.359481i
$988$		0			0
$989$	−3.97860	+	2.29704i	−0.00402285	+	0.00232259i
$990$		0			0
$991$	186.798	−	323.544i	0.188495	−	0.326483i	−0.756254	−	0.654278i	$-0.772972\pi$
$991$	186.798	−	323.544i	0.188495	−	0.326483i	0.944749	+	0.327796i	$0.106306\pi$
$992$		0			0
$993$	122.450	−	653.385i	0.123313	−	0.657991i
$994$		0			0
$995$	−499.223	−	594.951i	−0.501732	−	0.597940i
$996$		0			0
$997$	1763.31	−	641.793i	1.76862	−	0.643724i	0.768625	−	0.639699i	$-0.220941\pi$
$997$	1763.31	−	641.793i	1.76862	−	0.643724i	0.999992	−	0.00402483i	$-0.00128115\pi$
$998$		0			0
$999$	−472.257	−	882.371i	−0.472730	−	0.883254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.b.209.5		36
4.3	odd	2		108.3.k.a.101.2	yes	36
12.11	even	2		324.3.k.a.305.4		36
27.23	odd	18	inner	432.3.bc.b.401.5		36
108.23	even	18		108.3.k.a.77.2	✓	36
108.31	odd	18		324.3.k.a.17.4		36
108.79	odd	18		2916.3.c.b.1457.28		36
108.83	even	18		2916.3.c.b.1457.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.2	✓	36	108.23	even	18
108.3.k.a.101.2	yes	36	4.3	odd	2
324.3.k.a.17.4		36	108.31	odd	18
324.3.k.a.305.4		36	12.11	even	2
432.3.bc.b.209.5		36	1.1	even	1	trivial
432.3.bc.b.401.5		36	27.23	odd	18	inner
2916.3.c.b.1457.9		36	108.83	even	18
2916.3.c.b.1457.28		36	108.79	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.47205 + 2.61402i) q^{3} +(-4.32861 + 0.763252i) q^{5} +(2.73772 + 2.29722i) q^{7} +(-4.66616 + 7.69591i) q^{9} +O(q^{10})\)	\(q+(1.47205 + 2.61402i) q^{3} +(-4.32861 + 0.763252i) q^{5} +(2.73772 + 2.29722i) q^{7} +(-4.66616 + 7.69591i) q^{9} +(14.4582 + 2.54938i) q^{11} +(-3.67778 - 1.33860i) q^{13} +(-8.36707 - 10.1915i) q^{15} +(-5.96626 + 3.44462i) q^{17} +(-14.1412 + 24.4932i) q^{19} +(-1.97492 + 10.5381i) q^{21} +(-0.832583 - 0.992234i) q^{23} +(-5.33796 + 1.94286i) q^{25} +(-26.9860 - 0.868674i) q^{27} +(-12.9959 - 35.7059i) q^{29} +(-41.7175 + 35.0052i) q^{31} +(14.6191 + 41.5469i) q^{33} +(-13.6039 - 7.85422i) q^{35} +(18.5334 + 32.1007i) q^{37} +(-1.91473 - 11.5842i) q^{39} +(-14.0768 + 38.6757i) q^{41} +(0.615899 - 3.49294i) q^{43} +(14.3241 - 36.8741i) q^{45} +(27.5222 - 32.7997i) q^{47} +(-6.29086 - 35.6773i) q^{49} +(-17.7869 - 10.5253i) q^{51} -47.8007i q^{53} -64.5299 q^{55} +(-84.8421 - 0.910069i) q^{57} +(61.1091 - 10.7752i) q^{59} +(-8.50896 - 7.13987i) q^{61} +(-30.4539 + 10.3501i) q^{63} +(16.9414 + 2.98722i) q^{65} +(105.153 + 38.2727i) q^{67} +(1.36811 - 3.63700i) q^{69} +(-90.9885 + 52.5322i) q^{71} +(-48.5118 + 84.0248i) q^{73} +(-12.9364 - 11.0935i) q^{75} +(33.7262 + 40.1933i) q^{77} +(104.299 - 37.9616i) q^{79} +(-37.4540 - 71.8206i) q^{81} +(44.8984 + 123.357i) q^{83} +(23.1965 - 19.4642i) q^{85} +(74.2053 - 86.5322i) q^{87} +(87.8638 + 50.7282i) q^{89} +(-6.99367 - 12.1134i) q^{91} +(-152.914 - 57.5210i) q^{93} +(42.5172 - 116.815i) q^{95} +(-28.7527 + 163.065i) q^{97} +(-87.0842 + 99.3734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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