LMFDB - Embedded newform 108.3.k.a.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			77.2
Character	$\chi$	$=$	108.77
Dual form			108.3.k.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			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	−0.276887	−	0.960903i	$-0.589303\pi$
$5$	−4.32861	−	0.763252i	−0.865723	−	0.152650i	−0.588836	+	0.808252i	$0.700414\pi$
$6$		0			0
$7$	−2.73772	+	2.29722i	−0.391103	+	0.328175i	−0.817043	−	0.576577i	$-0.804388\pi$
$7$	−2.73772	+	2.29722i	−0.391103	+	0.328175i	0.425939	+	0.904752i	$0.359944\pi$
$8$		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	$-0.788119\pi$
$11$	−14.4582	+	2.54938i	−1.31438	+	0.231762i	−0.527866	+	0.849328i	$0.677008\pi$
$12$		0			0
$13$	−3.67778	+	1.33860i	−0.282906	+	0.102969i	−0.479576	−	0.877500i	$-0.659209\pi$
$13$	−3.67778	+	1.33860i	−0.282906	+	0.102969i	0.196670	+	0.980470i	$0.436987\pi$
$14$		0			0
$15$	8.36707	−	10.1915i	0.557805	−	0.679435i
$16$		0			0
$17$	−5.96626	−	3.44462i	−0.350956	−	0.202625i	0.314150	−	0.949373i	$-0.398280\pi$
$17$	−5.96626	−	3.44462i	−0.350956	−	0.202625i	−0.665106	+	0.746749i	$0.731614\pi$
$18$		0			0
$19$	14.1412	+	24.4932i	0.744272	+	1.28912i	0.950534	+	0.310620i	$0.100537\pi$
$19$	14.1412	+	24.4932i	0.744272	+	1.28912i	−0.206263	+	0.978497i	$0.566130\pi$
$20$		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	$-0.768814\pi$
$23$	0.832583	−	0.992234i	0.0361993	−	0.0431406i	0.783840	+	0.620962i	$0.213258\pi$
$24$		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	0.485887	+	0.874021i	$0.338496\pi$
$29$	−12.9959	+	35.7059i	−0.448134	+	1.23124i	−0.934021	+	0.357217i	$0.883726\pi$
$30$		0			0
$31$	41.7175	+	35.0052i	1.34573	+	1.12920i	0.980115	+	0.198431i	$0.0635846\pi$
$31$	41.7175	+	35.0052i	1.34573	+	1.12920i	0.365612	+	0.930767i	$0.380860\pi$
$32$		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	−0.499097	−	0.866546i	$-0.666335\pi$
$37$	18.5334	−	32.1007i	0.500902	−	0.867588i	0.999999	−	0.00104187i	$-0.000331638\pi$
$38$		0			0
$39$	1.91473	−	11.5842i	0.0490957	−	0.297032i
$40$		0			0
$41$	−14.0768	−	38.6757i	−0.343336	−	0.943309i	−0.984419	−	0.175837i	$-0.943737\pi$
$41$	−14.0768	−	38.6757i	−0.343336	−	0.943309i	0.641083	−	0.767472i	$-0.278485\pi$
$42$		0			0
$43$	−0.615899	−	3.49294i	−0.0143232	−	0.0812311i	0.976808	−	0.214116i	$-0.0686870\pi$
$43$	−0.615899	−	3.49294i	−0.0143232	−	0.0812311i	−0.991131	+	0.132885i	$0.957576\pi$
$44$		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	$-0.372761\pi$
$47$	−27.5222	−	32.7997i	−0.585578	−	0.697865i	−0.974750	+	0.223300i	$0.928317\pi$
$48$		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	$0.148915\pi$
$53$			47.8007i			0.901900i	−0.892549	+	0.450950i	$0.851085\pi$
$54$		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	$-0.620702\pi$
$59$	−61.1091	−	10.7752i	−1.03575	−	0.182630i	−0.665574	+	0.746332i	$0.731813\pi$
$60$		0			0
$61$	−8.50896	+	7.13987i	−0.139491	+	0.117047i	−0.709863	−	0.704339i	$-0.751243\pi$
$61$	−8.50896	+	7.13987i	−0.139491	+	0.117047i	0.570372	+	0.821386i	$0.306799\pi$
$62$		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	$-0.925695\pi$
$67$	−105.153	+	38.2727i	−1.56945	+	0.571235i	−0.596577	+	0.802556i	$0.703473\pi$
$68$		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	$-0.0682107\pi$
$71$	90.9885	+	52.5322i	1.28153	+	0.739890i	0.304400	+	0.952544i	$0.401544\pi$
$72$		0			0
$73$	−48.5118	−	84.0248i	−0.664545	−	1.15102i	−0.979409	−	0.201888i	$-0.935292\pi$
$73$	−48.5118	−	84.0248i	−0.664545	−	1.15102i	0.314864	−	0.949137i	$-0.398041\pi$
$74$		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	$-0.636814\pi$
$79$	−104.299	−	37.9616i	−1.32024	−	0.480527i	−0.903534	+	0.428516i	$0.859037\pi$
$80$		0			0
$81$	−37.4540	+	71.8206i	−0.462395	+	0.886674i
$82$		0			0
$83$	−44.8984	+	123.357i	−0.540945	+	1.48623i	0.304679	+	0.952455i	$0.401451\pi$
$83$	−44.8984	+	123.357i	−0.540945	+	1.48623i	−0.845624	+	0.533779i	$0.820771\pi$
$84$		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	0.0827871	−	0.996567i	$-0.473618\pi$
$89$	87.8638	−	50.7282i	0.987233	−	0.569979i	0.904446	+	0.426588i	$0.140285\pi$
$90$		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	−0.661376	−	0.750055i	$-0.730027\pi$
$97$	−28.7527	−	163.065i	−0.296420	−	1.68108i	0.364956	−	0.931025i	$-0.381084\pi$
$98$		0			0
$99$	87.0842	+	99.3734i	0.879638	+	1.00377i
$100$		0			0
$101$	14.2076	+	16.9319i	0.140669	+	0.167643i	0.831779	−	0.555107i	$-0.187323\pi$
$101$	14.2076	+	16.9319i	0.140669	+	0.167643i	−0.691110	+	0.722749i	$0.742878\pi$
$102$		0			0
$103$	−4.91300	+	27.8630i	−0.0476991	+	0.270515i	−0.999325	−	0.0367451i	$-0.988301\pi$
$103$	−4.91300	+	27.8630i	−0.0476991	+	0.270515i	0.951626	+	0.307260i	$0.0994121\pi$
$104$		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	0.752839	−	0.658205i	$-0.228684\pi$
$113$	139.573	+	24.6104i	1.23516	+	0.217791i	0.482317	+	0.875997i	$0.339795\pi$
$114$		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	$-0.0748539\pi$
$127$	36.1258	+	62.5718i	0.284455	+	0.492691i	−0.688022	+	0.725690i	$0.741521\pi$
$128$		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	$-0.619163\pi$
$131$	80.4893	−	95.9234i	0.614422	−	0.732239i	0.980101	+	0.198502i	$0.0636076\pi$
$132$		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	0.664693	+	0.747117i	$0.268563\pi$
$137$	−44.4879	+	122.229i	−0.324729	+	0.892186i	−0.989422	+	0.145069i	$0.953660\pi$
$138$		0			0
$139$	−64.7192	−	54.3058i	−0.465606	−	0.390689i	0.379583	−	0.925158i	$-0.376067\pi$
$139$	−64.7192	−	54.3058i	−0.465606	−	0.390689i	−0.845189	+	0.534468i	$0.820512\pi$
$140$		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	0.988687	+	0.149992i	$0.0479247\pi$
$149$	48.8305	+	134.161i	0.327722	+	0.900408i	−0.660966	+	0.750416i	$0.729853\pi$
$150$		0			0
$151$	7.41354	+	42.0443i	0.0490963	+	0.278439i	0.999466	−	0.0326849i	$-0.0104058\pi$
$151$	7.41354	+	42.0443i	0.0490963	+	0.278439i	−0.950369	+	0.311124i	$0.899295\pi$
$152$		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	0.923860	+	0.382730i	$0.125016\pi$
$157$	−11.8042	+	66.9447i	−0.0751857	+	0.426399i	−0.999046	+	0.0436696i	$0.986095\pi$
$158$		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	$-0.551244\pi$
$163$	−52.2555			−0.320586			−0.160293	+	0.987069i	$0.551244\pi$
$164$		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	$-0.659572\pi$
$167$	−205.761	−	36.2813i	−1.23210	−	0.217253i	−0.751529	+	0.659700i	$0.770683\pi$
$168$		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	0.730409	−	0.683010i	$-0.239329\pi$
$173$	285.514	−	50.3439i	1.65037	−	0.291005i	0.919963	+	0.392005i	$0.128218\pi$
$174$		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	$-0.421084\pi$
$179$	−84.3915	−	48.7235i	−0.471461	−	0.272198i	−0.716851	+	0.697226i	$0.754417\pi$
$180$		0			0
$181$	18.6602	+	32.3205i	0.103095	+	0.178566i	0.912958	−	0.408053i	$-0.133792\pi$
$181$	18.6602	+	32.3205i	0.103095	+	0.178566i	−0.809863	+	0.586619i	$0.800459\pi$
$182$		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	0.0610446	+	0.998135i	$0.480557\pi$
$191$	−119.816	+	329.191i	−0.627307	+	1.72351i	−0.688352	+	0.725377i	$0.741665\pi$
$192$		0			0
$193$	8.46714	+	7.10477i	0.0438712	+	0.0368123i	0.664460	−	0.747324i	$-0.268662\pi$
$193$	8.46714	+	7.10477i	0.0438712	+	0.0368123i	−0.620588	+	0.784136i	$0.713106\pi$
$194$		0			0
$195$	−17.1298	+	48.6823i	−0.0878453	+	0.249653i
$196$		0			0
$197$	−275.483	+	159.050i	−1.39839	+	0.807362i	−0.994224	−	0.107323i	$-0.965772\pi$
$197$	−275.483	+	159.050i	−1.39839	+	0.807362i	−0.404167	+	0.914685i	$0.632439\pi$
$198$		0			0
$199$	−88.3486	+	153.024i	−0.443963	+	0.768966i	−0.997979	−	0.0635397i	$-0.979761\pi$
$199$	−88.3486	+	153.024i	−0.443963	+	0.768966i	0.554017	+	0.832506i	$0.313094\pi$
$200$		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	0.772409	+	0.635125i	$0.219051\pi$
$211$	−36.0058	+	204.199i	−0.170644	+	0.967768i	−0.943053	+	0.332643i	$0.892060\pi$
$212$		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	0.469926	−	0.882706i	$-0.344281\pi$
$223$	316.844	−	265.863i	1.42082	−	1.19221i	0.950897	−	0.309506i	$-0.100164\pi$
$224$		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	$-0.487465\pi$
$227$	94.9127	−	16.7357i	0.418117	−	0.0737254i	0.378749	+	0.925499i	$0.376354\pi$
$228$		0			0
$229$	189.133	−	68.8386i	0.825906	−	0.300605i	0.105729	−	0.994395i	$-0.466283\pi$
$229$	189.133	−	68.8386i	0.825906	−	0.300605i	0.720178	+	0.693790i	$0.244060\pi$
$230$		0			0
$231$	55.4194	+	147.327i	0.239911	+	0.637780i
$232$		0			0
$233$	−303.285	−	175.101i	−1.30165	−	0.751508i	−0.320964	−	0.947092i	$-0.604007\pi$
$233$	−303.285	−	175.101i	−1.30165	−	0.751508i	−0.980687	+	0.195583i	$0.937340\pi$
$234$		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	$-0.884025\pi$
$239$	−100.663	+	119.965i	−0.421183	+	0.501947i	0.513174	+	0.858285i	$0.328470\pi$
$240$		0			0
$241$	324.419	+	118.079i	1.34614	+	0.489954i	0.911740	−	0.410768i	$-0.134739\pi$
$241$	324.419	+	118.079i	1.34614	+	0.489954i	0.434397	+	0.900721i	$0.356961\pi$
$242$		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	$-0.649905\pi$
$251$	22.8819	−	13.2109i	0.0911628	−	0.0526329i	0.544888	+	0.838509i	$0.316572\pi$
$252$		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	0.993313	−	0.115453i	$-0.0368321\pi$
$257$	40.6520	+	111.691i	0.158179	+	0.434593i	−0.835134	+	0.550047i	$0.814610\pi$
$258$		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	$-0.116593\pi$
$263$	110.151	+	131.272i	0.418823	+	0.499134i	−0.514840	+	0.857286i	$0.672149\pi$
$264$		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	$0.0881742\pi$
$269$			147.131i			0.546957i	−0.961878	+	0.273478i	$0.911826\pi$
$270$		0			0
$271$	42.2256			0.155814			0.0779071	−	0.996961i	$-0.475176\pi$
$271$	42.2256			0.155814			0.0779071	+	0.996961i	$0.475176\pi$
$272$		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	−0.964855	−	0.262782i	$-0.915360\pi$
$277$	−241.990	+	203.054i	−0.873611	+	0.733046i	0.0912446	+	0.995829i	$0.470916\pi$
$278$		0			0
$279$	74.7359	−	484.394i	0.267871	−	1.73618i
$280$		0			0
$281$	425.296	−	74.9912i	1.51351	−	0.266872i	0.645631	−	0.763650i	$-0.276594\pi$
$281$	425.296	−	74.9912i	1.51351	−	0.266872i	0.867878	+	0.496777i	$0.165483\pi$
$282$		0			0
$283$	−51.4917	+	18.7414i	−0.181949	+	0.0662242i	−0.431388	−	0.902166i	$-0.641976\pi$
$283$	−51.4917	+	18.7414i	−0.181949	+	0.0662242i	0.249439	+	0.968391i	$0.419754\pi$
$284$		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	−0.897863	−	0.440275i	$-0.854881\pi$
$293$	−90.3507	+	107.676i	−0.308364	+	0.367494i	0.589499	+	0.807769i	$0.299325\pi$
$294$		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	0.272669	+	0.962108i	$0.412094\pi$
$307$	−213.941	+	370.556i	−0.696876	+	1.20702i	−0.969544	+	0.244916i	$0.921240\pi$
$308$		0			0
$309$	−65.6022	−	53.8584i	−0.212305	−	0.174299i
$310$		0			0
$311$	142.432	+	391.327i	0.457979	+	1.25829i	0.926987	+	0.375094i	$0.122389\pi$
$311$	142.432	+	391.327i	0.457979	+	1.25829i	−0.469008	+	0.883194i	$0.655388\pi$
$312$		0			0
$313$	25.1171	+	142.446i	0.0802462	+	0.455099i	0.998282	+	0.0586003i	$0.0186638\pi$
$313$	25.1171	+	142.446i	0.0802462	+	0.455099i	−0.918035	+	0.396499i	$0.870225\pi$
$314$		0			0
$315$	−123.923	−	68.0454i	−0.393407	−	0.216017i
$316$		0			0
$317$	−348.939	−	415.849i	−1.10075	−	1.31183i	−0.946106	−	0.323858i	$-0.895020\pi$
$317$	−348.939	−	415.849i	−1.10075	−	1.31183i	−0.154648	−	0.987970i	$-0.549424\pi$
$318$		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	$-0.613580\pi$
$331$	169.745	−	142.433i	0.512825	−	0.430311i	0.862122	+	0.506701i	$0.169135\pi$
$332$		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	−0.287612	−	0.957747i	$-0.592861\pi$
$337$	36.2922	−	13.2093i	0.107692	−	0.0391967i	0.395304	+	0.918550i	$0.370639\pi$
$338$		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	$-0.680289\pi$
$347$	134.499	−	160.290i	0.387607	−	0.461932i	0.924200	+	0.381910i	$0.124733\pi$
$348$		0			0
$349$	−262.851	−	95.6701i	−0.753156	−	0.274126i	−0.0632228	−	0.997999i	$-0.520138\pi$
$349$	−262.851	−	95.6701i	−0.753156	−	0.274126i	−0.689933	+	0.723873i	$0.742360\pi$
$350$		0			0
$351$	−98.0857	+	39.3183i	−0.279447	+	0.112018i
$352$		0			0
$353$	−28.7312	+	78.9384i	−0.0813916	+	0.223622i	−0.973713	−	0.227780i	$-0.926853\pi$
$353$	−28.7312	+	78.9384i	−0.0813916	+	0.223622i	0.892321	+	0.451401i	$0.149076\pi$
$354$		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	$-0.782471\pi$
$359$	−221.262	+	127.746i	−0.616330	+	0.355838i	0.159109	+	0.987261i	$0.449138\pi$
$360$		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	−0.983124	−	0.182940i	$-0.941439\pi$
$367$	−44.7221	−	253.632i	−0.121859	−	0.691095i	0.861265	−	0.508155i	$-0.169672\pi$
$368$		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	−0.640335	−	0.768096i	$-0.721204\pi$
$373$	83.5846	−	474.032i	0.224087	−	1.27086i	0.864422	−	0.502767i	$-0.167684\pi$
$374$		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	$-0.662594\pi$
$379$	−370.571			−0.977759			−0.488880	+	0.872351i	$0.662594\pi$
$380$		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	$-0.223919\pi$
$383$	481.807	+	84.9556i	1.25798	+	0.221816i	0.495375	+	0.868679i	$0.335031\pi$
$384$		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	0.239221	−	0.970965i	$-0.423108\pi$
$389$	309.685	−	54.6057i	0.796104	−	0.140375i	0.556884	+	0.830591i	$0.311997\pi$
$390$		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	0.804067	−	0.594538i	$-0.202665\pi$
$397$	−44.8022	−	77.5996i	−0.112852	−	0.195465i	−0.916919	+	0.399073i	$0.869332\pi$
$398$		0			0
$399$	230.184	−	197.393i	0.576901	−	0.494719i
$400$		0			0
$401$	−55.2456	+	65.8392i	−0.137770	+	0.164187i	−0.830518	−	0.556992i	$-0.811955\pi$
$401$	−55.2456	+	65.8392i	−0.137770	+	0.164187i	0.692748	+	0.721180i	$0.256400\pi$
$402$		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	1.00000		8.63705e-5i	$-2.74926e-5\pi$
$409$	479.987	+	402.757i	1.17356	+	0.984736i	0.173563	+	0.984823i	$0.444472\pi$
$410$		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	−0.996405	−	0.0847157i	$-0.973002\pi$
$419$	−120.491	−	331.047i	−0.287569	−	0.790089i	0.708836	−	0.705373i	$-0.249220\pi$
$420$		0			0
$421$	26.8471	+	152.258i	0.0637699	+	0.361657i	0.999949	+	0.0101329i	$0.00322545\pi$
$421$	26.8471	+	152.258i	0.0637699	+	0.361657i	−0.936179	+	0.351524i	$0.885663\pi$
$422$		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	$-0.610469\pi$
$439$	231.313	−	194.095i	0.526909	−	0.442129i	0.867032	+	0.498252i	$0.166024\pi$
$440$		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	$-0.379284\pi$
$443$	458.869	−	80.9110i	1.03582	−	0.182643i	0.665606	+	0.746303i	$0.268173\pi$
$444$		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	0.539434	−	0.842028i	$-0.318638\pi$
$449$	35.8903	+	20.7213i	0.0799339	+	0.0461498i	−0.459500	+	0.888178i	$0.651971\pi$
$450$		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	0.745566	−	0.666432i	$-0.232179\pi$
$457$	405.966	+	147.760i	0.888329	+	0.323325i	0.142763	+	0.989757i	$0.454401\pi$
$458$		0			0
$459$	−163.998	−	87.7739i	−0.357294	−	0.191229i
$460$		0			0
$461$	224.994	−	618.167i	0.488057	−	1.34093i	−0.414380	−	0.910104i	$-0.636002\pi$
$461$	224.994	−	618.167i	0.488057	−	1.34093i	0.902437	−	0.430822i	$-0.141776\pi$
$462$		0			0
$463$	−415.550	−	348.688i	−0.897516	−	0.753105i	0.0721872	−	0.997391i	$-0.477002\pi$
$463$	−415.550	−	348.688i	−0.897516	−	0.753105i	−0.969703	+	0.244286i	$0.921447\pi$
$464$		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	$-0.694812\pi$
$467$	−71.4291	+	41.2396i	−0.152953	+	0.0883075i	0.421570	+	0.906796i	$0.361479\pi$
$468$		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	$-0.194189\pi$
$479$	54.1626	+	64.5485i	0.113074	+	0.134757i	−0.706538	+	0.707675i	$0.749744\pi$
$480$		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	$-0.302474\pi$
$487$	566.361			1.16296			0.581479	+	0.813561i	$0.302474\pi$
$488$		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	$-0.729524\pi$
$491$	−754.890	−	133.107i	−1.53745	−	0.271095i	−0.877266	+	0.480005i	$0.840635\pi$
$492$		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	$-0.682089\pi$
$499$	−207.387	+	75.4828i	−0.415606	+	0.151268i	0.125750	+	0.992062i	$0.459866\pi$
$500$		0			0
$501$	397.730	−	484.456i	0.793873	−	0.966978i
$502$		0			0
$503$	783.399	+	452.296i	1.55745	+	0.899196i	0.997500	+	0.0706721i	$0.0225144\pi$
$503$	783.399	+	452.296i	1.55745	+	0.899196i	0.559954	+	0.828524i	$0.310819\pi$
$504$		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	−0.505044	−	0.863093i	$-0.668524\pi$
$509$	220.212	−	262.439i	0.432637	−	0.515596i	0.937681	+	0.347497i	$0.112968\pi$
$510$		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	−0.611225	−	0.791457i	$-0.709323\pi$
$521$	−120.568	+	69.6099i	−0.231416	+	0.133608i	0.379809	+	0.925065i	$0.375990\pi$
$522$		0			0
$523$	−12.3821	+	21.4464i	−0.0236751	+	0.0410065i	−0.877620	−	0.479357i	$-0.840870\pi$
$523$	−12.3821	+	21.4464i	−0.0236751	+	0.0410065i	0.853945	+	0.520363i	$0.174203\pi$
$524$		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	$-0.809067\pi$
$547$	−225.822	+	189.487i	−0.412836	+	0.346411i	0.412594	+	0.910915i	$0.364623\pi$
$548$		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	−0.369047	−	0.929411i	$-0.620316\pi$
$557$	−756.664	−	436.860i	−1.35846	−	0.784309i	−0.989417	+	0.145101i	$0.953649\pi$
$558$		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	$-0.927386\pi$
$563$	−327.795	+	390.651i	−0.582230	+	0.693874i	0.391863	+	0.920024i	$0.371831\pi$
$564$		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	0.321871	+	0.946784i	$0.395688\pi$
$569$	−303.435	+	833.680i	−0.533277	+	1.46517i	−0.855148	+	0.518384i	$0.826534\pi$
$570$		0			0
$571$	403.162	+	338.293i	0.706063	+	0.592457i	0.923491	−	0.383619i	$-0.125323\pi$
$571$	403.162	+	338.293i	0.706063	+	0.592457i	−0.217429	+	0.976076i	$0.569767\pi$
$572$		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	−0.800461	−	0.599385i	$-0.795412\pi$
$577$	68.5779	−	118.780i	0.118853	−	0.205859i	0.919313	+	0.393527i	$0.128745\pi$
$578$		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	$-0.270938\pi$
$587$	−115.043	−	137.103i	−0.195985	−	0.233566i	−0.855083	+	0.518491i	$0.826494\pi$
$588$		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	$0.0139684\pi$
$593$			52.0285i			0.0877377i	−0.999037	+	0.0438689i	$0.986032\pi$
$594$		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	$-0.413505\pi$
$599$	114.494	+	20.1884i	0.191142	+	0.0337035i	−0.0772575	+	0.997011i	$0.524616\pi$
$600$		0			0
$601$	−402.677	+	337.886i	−0.670011	+	0.562206i	−0.913069	−	0.407806i	$-0.866294\pi$
$601$	−402.677	+	337.886i	−0.670011	+	0.562206i	0.243057	+	0.970012i	$0.421850\pi$
$602$		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	$-0.588637\pi$
$607$	80.4769	−	29.2912i	0.132581	−	0.0482557i	0.407459	+	0.913224i	$0.366415\pi$
$608$		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	0.924905	−	0.380198i	$-0.124144\pi$
$613$	81.6463	+	141.416i	0.133191	+	0.230694i	−0.791714	+	0.610892i	$0.790811\pi$
$614$		0			0
$615$	−511.946	−	180.138i	−0.832432	−	0.292908i
$616$		0			0
$617$	179.054	−	213.388i	0.290200	−	0.345847i	−0.601171	−	0.799120i	$-0.705299\pi$
$617$	179.054	−	213.388i	0.290200	−	0.345847i	0.891372	+	0.453273i	$0.149744\pi$
$618$		0			0
$619$	−669.731	−	243.762i	−1.08196	−	0.393800i	−0.261321	−	0.965252i	$-0.584158\pi$
$619$	−669.731	−	243.762i	−1.08196	−	0.393800i	−0.820636	+	0.571452i	$0.806380\pi$
$620$		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	$-0.997402\pi$
$631$	−311.029	+	538.718i	−0.492914	+	0.853753i	0.507052	+	0.861915i	$0.330735\pi$
$632$		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	0.878294	−	0.478122i	$-0.158682\pi$
$641$	163.405	+	194.738i	0.254921	+	0.303804i	−0.623372	+	0.781925i	$0.714238\pi$
$642$		0			0
$643$	36.8378	−	208.917i	0.0572905	−	0.324910i	−0.942671	−	0.333724i	$-0.891695\pi$
$643$	36.8378	−	208.917i	0.0572905	−	0.324910i	0.999961	+	0.00881399i	$0.00280562\pi$
$644$		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	0.419952	−	0.907546i	$-0.362047\pi$
$653$	329.228	+	58.0518i	0.504178	+	0.0889002i	0.0842262	+	0.996447i	$0.473158\pi$
$654$		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	$-0.843799\pi$
$659$	−1021.20	+	180.064i	−1.54962	+	0.273239i	−0.667622	+	0.744501i	$0.732688\pi$
$660$		0			0
$661$	397.057	−	144.517i	0.600692	−	0.218634i	−0.0237335	−	0.999718i	$-0.507555\pi$
$661$	397.057	−	144.517i	0.600692	−	0.218634i	0.624426	+	0.781084i	$0.285333\pi$
$662$		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	0.331325	−	0.943517i	$-0.392504\pi$
$673$	−14.3659	−	5.22876i	−0.0213460	−	0.00776932i	−0.352671	+	0.935747i	$0.614727\pi$
$674$		0			0
$675$	−145.738	−	47.7931i	−0.215908	−	0.0708046i
$676$		0			0
$677$	103.653	−	284.784i	0.153106	−	0.420655i	−0.839299	−	0.543670i	$-0.817034\pi$
$677$	103.653	−	284.784i	0.153106	−	0.420655i	0.992405	+	0.123015i	$0.0392564\pi$
$678$		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	$-0.468876\pi$
$683$	688.686	−	397.613i	1.00833	−	0.582157i	0.910701	+	0.413067i	$0.135542\pi$
$684$		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	$-0.0445297\pi$
$691$	8.31097	+	47.1339i	0.0120275	+	0.0682111i	−0.978203	+	0.207650i	$0.933419\pi$
$692$		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	$-0.992523\pi$
$701$		−	32.9301i		−	0.0469759i	0.999724	−	0.0234880i	$-0.00747714\pi$
$702$		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	0.00904260	−	0.999959i	$-0.497122\pi$
$709$	705.725	−	592.173i	0.995380	−	0.835223i	0.986338	+	0.164736i	$0.0526772\pi$
$710$		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	$-0.227537\pi$
$719$	406.335	+	234.597i	0.565139	+	0.326283i	−0.190067	+	0.981771i	$0.560870\pi$
$720$		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	$-0.376467\pi$
$727$	53.3053	+	19.4016i	0.0733223	+	0.0266871i	−0.305099	+	0.952321i	$0.598689\pi$
$728$		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	−0.0621924	−	0.998064i	$-0.519809\pi$
$733$	−773.970	−	649.438i	−1.05589	−	0.886000i	−0.993701	+	0.112064i	$0.964254\pi$
$734$		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	$-0.667073\pi$
$739$	368.682	−	638.576i	0.498893	−	0.864108i	0.999999	+	0.00127777i	$0.000406727\pi$
$740$		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	$-0.130847\pi$
$743$	−31.4911	−	86.5211i	−0.0423837	−	0.116448i	−0.959079	+	0.283139i	$0.908624\pi$
$744$		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	0.909759	+	0.415137i	$0.136266\pi$
$751$	−65.4270	+	371.055i	−0.0871199	+	0.494081i	−0.996879	+	0.0789448i	$0.974845\pi$
$752$		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	−0.554669	−	0.832071i	$-0.687155\pi$
$761$	−1035.32	−	182.555i	−1.36047	−	0.239888i	−0.805804	+	0.592183i	$0.798266\pi$
$762$		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	−0.332862	−	0.942976i	$-0.608014\pi$
$769$	14.0610	−	5.11778i	0.0182848	−	0.00665511i	0.351146	+	0.936321i	$0.385792\pi$
$770$		0			0
$771$	−351.802	−	58.1486i	−0.456294	−	0.0754198i
$772$		0			0
$773$	453.509	+	261.834i	0.586687	+	0.338724i	0.763787	−	0.645469i	$-0.223338\pi$
$773$	453.509	+	261.834i	0.586687	+	0.338724i	−0.177099	+	0.984193i	$0.556671\pi$
$774$		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	$-0.245852\pi$
$787$	120.730	+	101.305i	0.153406	+	0.128723i	−0.562854	+	0.826556i	$0.690297\pi$
$788$		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	0.943151	−	0.332365i	$-0.107846\pi$
$797$	5.59137	+	15.3622i	0.00701552	+	0.0192750i	−0.936135	+	0.351640i	$0.885624\pi$
$798$		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	$0.280519\pi$
$809$			1248.37i			1.54310i	−0.636168	+	0.771551i	$0.719481\pi$
$810$		0			0
$811$	−796.242			−0.981803			−0.490901	−	0.871215i	$-0.663332\pi$
$811$	−796.242			−0.981803			−0.490901	+	0.871215i	$0.663332\pi$
$812$		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	−0.926340	−	0.376688i	$-0.877063\pi$
$821$	−1369.41	+	241.464i	−1.66798	+	0.294110i	−0.741640	+	0.670798i	$0.765952\pi$
$822$		0			0
$823$	−21.0770	+	7.67138i	−0.0256099	+	0.00932124i	−0.354793	−	0.934945i	$-0.615449\pi$
$823$	−21.0770	+	7.67138i	−0.0256099	+	0.00932124i	0.329183	+	0.944266i	$0.393227\pi$
$824$		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	$-0.315660\pi$
$827$	79.4904	+	45.8938i	0.0961190	+	0.0554943i	−0.451170	+	0.892438i	$0.648993\pi$
$828$		0			0
$829$	−398.805	−	690.751i	−0.481068	−	0.833234i	0.518696	−	0.854959i	$-0.326418\pi$
$829$	−398.805	−	690.751i	−0.481068	−	0.833234i	−0.999764	+	0.0217246i	$0.993084\pi$
$830$		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	0.187045	−	0.982351i	$-0.440109\pi$
$839$	566.496	−	1556.43i	0.675203	−	1.85511i	0.488158	−	0.872755i	$-0.337669\pi$
$840$		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	−0.801779	−	0.597621i	$-0.796113\pi$
$853$	−215.597	−	1222.71i	−0.252752	−	1.43343i	0.549027	−	0.835805i	$-0.314998\pi$
$854$		0			0
$855$	−700.605	+	872.285i	−0.819421	+	1.02022i
$856$		0			0
$857$	949.464	+	1131.53i	1.10789	+	1.32033i	0.942537	+	0.334101i	$0.108433\pi$
$857$	949.464	+	1131.53i	1.10789	+	1.32033i	0.165355	+	0.986234i	$0.447123\pi$
$858$		0			0
$859$	−173.038	+	981.345i	−0.201441	+	1.14243i	0.701503	+	0.712667i	$0.252513\pi$
$859$	−173.038	+	981.345i	−0.201441	+	1.14243i	−0.902943	+	0.429760i	$0.858598\pi$
$860$		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	−0.665810	−	0.746121i	$-0.731914\pi$
$877$	−610.614	+	222.245i	−0.696253	+	0.253415i	−0.0304427	+	0.999537i	$0.509692\pi$
$878$		0			0
$879$	−148.466	−	394.682i	−0.168903	−	0.449013i
$880$		0			0
$881$	−196.446	−	113.418i	−0.222980	−	0.128738i	0.384349	−	0.923188i	$-0.374426\pi$
$881$	−196.446	−	113.418i	−0.222980	−	0.128738i	−0.607330	+	0.794450i	$0.707759\pi$
$882$		0			0
$883$	34.4995	+	59.7548i	0.0390707	+	0.0676725i	0.884900	−	0.465782i	$-0.154227\pi$
$883$	34.4995	+	59.7548i	0.0390707	+	0.0676725i	−0.845829	+	0.533454i	$0.820894\pi$
$884$		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	$-0.948088\pi$
$887$	−581.417	+	692.906i	−0.655488	+	0.781180i	0.331243	+	0.943545i	$0.392532\pi$
$888$		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	$-0.0839120\pi$
$907$	−28.0243	−	158.934i	−0.0308978	−	0.175230i	−0.996352	+	0.0853445i	$0.972801\pi$
$908$		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	$-0.208099\pi$
$911$	51.9472	+	61.9082i	0.0570221	+	0.0679563i	−0.736779	+	0.676133i	$0.763654\pi$
$912$		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	$-0.616352\pi$
$919$	−656.985			−0.714891			−0.357445	+	0.933934i	$0.616352\pi$
$920$		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	−0.303708	−	0.952765i	$-0.598225\pi$
$929$	−244.546	+	43.1200i	−0.263235	+	0.0464155i	0.0404727	+	0.999181i	$0.487114\pi$
$930$		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	1.00000		3.38875e-5i	$-1.07867e-5\pi$
$937$	468.473	+	811.418i	0.499971	+	0.865975i	−0.500029	+	0.866008i	$0.666677\pi$
$938$		0			0
$939$	−409.330	−	144.031i	−0.435921	−	0.153387i
$940$		0			0
$941$	−899.429	+	1071.90i	−0.955823	+	1.13911i	0.0343714	+	0.999409i	$0.489057\pi$
$941$	−899.429	+	1071.90i	−0.955823	+	1.13911i	−0.990194	+	0.139696i	$0.955387\pi$
$942$		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	−0.735311	−	0.677730i	$-0.762964\pi$
$947$	249.635	−	685.866i	0.263606	−	0.724252i	0.998917	−	0.0465220i	$-0.0148138\pi$
$948$		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	0.259047	−	0.965865i	$-0.416591\pi$
$953$	1167.46	−	674.032i	1.22503	−	0.707274i	0.965987	+	0.258591i	$0.0832581\pi$
$954$		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	−0.850755	−	0.525562i	$-0.823855\pi$
$967$	124.207	−	704.414i	0.128446	−	0.728453i	0.979201	−	0.202891i	$-0.0650337\pi$
$968$		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	−0.268171	−	0.963371i	$-0.586419\pi$
$977$	−830.119	−	146.372i	−0.849661	−	0.149818i	−0.581491	+	0.813553i	$0.697530\pi$
$978$		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	$-0.471968\pi$
$983$	502.601	−	88.6222i	0.511293	−	0.0901548i	0.423342	+	0.905970i	$0.360857\pi$
$984$		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	$-0.227028\pi$
$991$	−186.798	−	323.544i	−0.188495	−	0.326483i	−0.944749	+	0.327796i	$0.893694\pi$
$992$		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	0.999992	+	0.00402483i	$0.00128115\pi$
$997$	1763.31	+	641.793i	1.76862	+	0.643724i	0.768625	+	0.639699i	$0.220941\pi$
$998$		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	108.3.k.a.77.2	✓	36
3.2	odd	2		324.3.k.a.17.4		36
4.3	odd	2		432.3.bc.b.401.5		36
27.7	even	9		324.3.k.a.305.4		36
27.13	even	9		2916.3.c.b.1457.9		36
27.14	odd	18		2916.3.c.b.1457.28		36
27.20	odd	18	inner	108.3.k.a.101.2	yes	36
108.47	even	18		432.3.bc.b.209.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.2	✓	36	1.1	even	1	trivial
108.3.k.a.101.2	yes	36	27.20	odd	18	inner
324.3.k.a.17.4		36	3.2	odd	2
324.3.k.a.305.4		36	27.7	even	9
432.3.bc.b.209.5		36	108.47	even	18
432.3.bc.b.401.5		36	4.3	odd	2
2916.3.c.b.1457.9		36	27.13	even	9
2916.3.c.b.1457.28		36	27.14	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), 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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