LMFDB - Embedded newform 220.3.w.a.7.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

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

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

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.11
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.75740 - 0.954750i) q^{2} +(2.01897 - 1.02872i) q^{3} +(2.17690 + 3.35575i) q^{4} +(4.19108 - 2.72669i) q^{5} +(-4.53030 - 0.119746i) q^{6} +(2.63142 - 5.16446i) q^{7} +(-0.621782 - 7.97580i) q^{8} +(-2.27209 + 3.12726i) q^{9} +(-9.96871 + 0.790451i) q^{10} +(9.84371 + 4.90931i) q^{11} +(7.84722 + 4.53575i) q^{12} +(-2.39288 - 15.1080i) q^{13} +(-9.55523 + 6.56366i) q^{14} +(5.65667 - 9.81653i) q^{15} +(-6.52218 + 14.6103i) q^{16} +(-1.91459 + 12.0882i) q^{17} +(6.97872 - 3.32657i) q^{18} +(24.2978 + 7.89483i) q^{19} +(18.2737 + 8.12849i) q^{20} -13.1339i q^{21} +(-12.6122 - 18.0259i) q^{22} +(-11.4273 - 11.4273i) q^{23} +(-9.46019 - 15.4633i) q^{24} +(10.1303 - 22.8556i) q^{25} +(-10.2192 + 28.8355i) q^{26} +(-4.56045 + 28.7936i) q^{27} +(23.0590 - 2.41212i) q^{28} +(-16.0454 - 49.3826i) q^{29} +(-19.3134 + 11.8509i) q^{30} +(-7.84453 + 10.7971i) q^{31} +(25.4113 - 19.4491i) q^{32} +(24.9244 - 0.214638i) q^{33} +(14.9059 - 19.4159i) q^{34} +(-3.05338 - 28.8197i) q^{35} +(-15.4404 - 0.816824i) q^{36} +(4.00077 - 7.85195i) q^{37} +(-35.1633 - 37.0727i) q^{38} +(-20.3730 - 28.0411i) q^{39} +(-24.3535 - 31.7318i) q^{40} +(-75.7259 - 24.6048i) q^{41} +(-12.5396 + 23.0814i) q^{42} +(54.5989 - 54.5989i) q^{43} +(4.95437 + 43.7202i) q^{44} +(-0.995428 + 19.3019i) q^{45} +(9.17211 + 30.9925i) q^{46} +(22.4582 + 44.0767i) q^{47} +(1.86179 + 36.2072i) q^{48} +(9.05424 + 12.4621i) q^{49} +(-39.6243 + 30.4944i) q^{50} +(8.56986 + 26.3753i) q^{51} +(45.4898 - 40.9187i) q^{52} +(-21.8861 + 3.46642i) q^{53} +(35.5052 - 46.2477i) q^{54} +(54.6420 - 6.26545i) q^{55} +(-42.8269 - 17.7765i) q^{56} +(57.1780 - 9.05611i) q^{57} +(-18.9499 + 102.104i) q^{58} +(15.0901 + 46.4424i) q^{59} +(45.2559 - 2.38726i) q^{60} +(55.4322 + 76.2959i) q^{61} +(24.0945 - 11.4852i) q^{62} +(10.1718 + 19.9633i) q^{63} +(-63.2268 + 9.91841i) q^{64} +(-51.2237 - 56.7944i) q^{65} +(-44.0071 - 23.4194i) q^{66} +(5.11791 - 5.11791i) q^{67} +(-44.7330 + 19.8900i) q^{68} +(-34.8268 - 11.3159i) q^{69} +(-22.1496 + 53.5630i) q^{70} +(-10.7606 - 14.8107i) q^{71} +(26.3552 + 16.1773i) q^{72} +(-46.5762 + 91.4110i) q^{73} +(-14.5276 + 9.97927i) q^{74} +(-3.05911 - 56.5659i) q^{75} +(26.4008 + 98.7237i) q^{76} +(51.2569 - 37.9190i) q^{77} +(9.03133 + 68.7305i) q^{78} +(-47.7369 + 65.7043i) q^{79} +(12.5028 + 79.0170i) q^{80} +(9.66242 + 29.7379i) q^{81} +(109.589 + 115.540i) q^{82} +(-9.70086 + 61.2488i) q^{83} +(44.0740 - 28.5912i) q^{84} +(24.9367 + 55.8832i) q^{85} +(-148.080 + 43.8237i) q^{86} +(-83.1957 - 83.1957i) q^{87} +(33.0350 - 81.5640i) q^{88} -11.2250i q^{89} +(20.1779 - 32.9708i) q^{90} +(-84.3215 - 27.3977i) q^{91} +(13.4711 - 63.2234i) q^{92} +(-4.73074 + 29.8687i) q^{93} +(2.61421 - 98.9023i) q^{94} +(123.361 - 33.1647i) q^{95} +(31.2970 - 65.4081i) q^{96} +(7.98092 + 50.3895i) q^{97} +(-4.01373 - 30.5454i) q^{98} +(-37.7185 + 19.6295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.75740	−	0.954750i	−0.878700	−	0.477375i
$2$	−1.75740	−	0.954750i	−0.878700	−	0.477375i
$3$	2.01897	−	1.02872i	0.672990	−	0.342905i	−0.0838758	−	0.996476i	$-0.526730\pi$
$3$	2.01897	−	1.02872i	0.672990	−	0.342905i	0.756865	+	0.653571i	$0.226730\pi$
$4$	2.17690	+	3.35575i	0.544226	+	0.838939i
$5$	4.19108	−	2.72669i	0.838216	−	0.545338i
$5$	4.19108	−	2.72669i	0.838216	−	0.545338i
$6$	−4.53030	−	0.119746i	−0.755050	−	0.0199577i
$7$	2.63142	−	5.16446i	0.375918	−	0.737780i	−0.623098	−	0.782144i	$-0.714126\pi$
$7$	2.63142	−	5.16446i	0.375918	−	0.737780i	0.999015	+	0.0443641i	$0.0141262\pi$
$8$	−0.621782	−	7.97580i	−0.0777227	−	0.996975i
$9$	−2.27209	+	3.12726i	−0.252454	+	0.347474i
$10$	−9.96871	+	0.790451i	−0.996871	+	0.0790451i
$11$	9.84371	+	4.90931i	0.894883	+	0.446301i
$11$	9.84371	+	4.90931i	0.894883	+	0.446301i
$12$	7.84722	+	4.53575i	0.653935	+	0.377979i
$13$	−2.39288	−	15.1080i	−0.184068	−	1.16216i	−0.890705	−	0.454582i	$-0.849789\pi$
$13$	−2.39288	−	15.1080i	−0.184068	−	1.16216i	0.706637	−	0.707576i	$-0.250211\pi$
$14$	−9.55523	+	6.56366i	−0.682516	+	0.468833i
$15$	5.65667	−	9.81653i	0.377111	−	0.654436i
$16$	−6.52218	+	14.6103i	−0.407636	+	0.913144i
$17$	−1.91459	+	12.0882i	−0.112623	+	0.711072i	0.865167	+	0.501484i	$0.167212\pi$
$17$	−1.91459	+	12.0882i	−0.112623	+	0.711072i	−0.977790	+	0.209588i	$0.932788\pi$
$18$	6.97872	−	3.32657i	0.387707	−	0.184810i
$19$	24.2978	+	7.89483i	1.27883	+	0.415517i	0.868168	−	0.496270i	$-0.165297\pi$
$19$	24.2978	+	7.89483i	1.27883	+	0.415517i	0.410663	+	0.911787i	$0.365297\pi$
$20$	18.2737	+	8.12849i	0.913684	+	0.406425i
$21$		−	13.1339i		−	0.625422i
$22$	−12.6122	−	18.0259i	−0.573280	−	0.819359i
$23$	−11.4273	−	11.4273i	−0.496839	−	0.496839i	0.413613	−	0.910453i	$-0.364267\pi$
$23$	−11.4273	−	11.4273i	−0.496839	−	0.496839i	−0.910453	+	0.413613i	$0.864267\pi$
$24$	−9.46019	−	15.4633i	−0.394175	−	0.644302i
$25$	10.1303	−	22.8556i	0.405212	−	0.914223i
$26$	−10.2192	+	28.8355i	−0.393045	+	1.10906i
$27$	−4.56045	+	28.7936i	−0.168906	+	1.06643i
$28$	23.0590	−	2.41212i	0.823536	−	0.0861471i
$29$	−16.0454	−	49.3826i	−0.553289	−	1.70285i	−0.700421	−	0.713730i	$-0.747004\pi$
$29$	−16.0454	−	49.3826i	−0.553289	−	1.70285i	0.147132	−	0.989117i	$-0.452996\pi$
$30$	−19.3134	+	11.8509i	−0.643779	+	0.395029i
$31$	−7.84453	+	10.7971i	−0.253049	+	0.348292i	−0.916576	−	0.399860i	$-0.869059\pi$
$31$	−7.84453	+	10.7971i	−0.253049	+	0.348292i	0.663527	+	0.748152i	$0.269059\pi$
$32$	25.4113	−	19.4491i	0.794102	−	0.607784i
$33$	24.9244	−	0.214638i	0.755286	−	0.00650418i
$34$	14.9059	−	19.4159i	0.438410	−	0.571055i
$35$	−3.05338	−	28.8197i	−0.0872394	−	0.823421i
$36$	−15.4404	−	0.816824i	−0.428901	−	0.0226896i
$37$	4.00077	−	7.85195i	0.108129	−	0.212215i	−0.830602	−	0.556867i	$-0.812003\pi$
$37$	4.00077	−	7.85195i	0.108129	−	0.212215i	0.938730	+	0.344652i	$0.112003\pi$
$38$	−35.1633	−	37.0727i	−0.925351	−	0.975597i
$39$	−20.3730	−	28.0411i	−0.522385	−	0.719002i
$40$	−24.3535	−	31.7318i	−0.608837	−	0.793295i
$41$	−75.7259	−	24.6048i	−1.84697	−	0.600118i	−0.997352	−	0.0727233i	$-0.976831\pi$
$41$	−75.7259	−	24.6048i	−1.84697	−	0.600118i	−0.849621	−	0.527395i	$-0.823169\pi$
$42$	−12.5396	+	23.0814i	−0.298561	+	0.549558i
$43$	54.5989	−	54.5989i	1.26974	−	1.26974i	0.323519	−	0.946222i	$-0.395134\pi$
$43$	54.5989	−	54.5989i	1.26974	−	1.26974i	0.946222	−	0.323519i	$-0.104866\pi$
$44$	4.95437	+	43.7202i	0.112599	+	0.993640i
$45$	−0.995428	+	19.3019i	−0.0221206	+	0.428931i
$46$	9.17211	+	30.9925i	0.199394	+	0.673751i
$47$	22.4582	+	44.0767i	0.477834	+	0.937802i	0.996561	+	0.0828618i	$0.0264060\pi$
$47$	22.4582	+	44.0767i	0.477834	+	0.937802i	−0.518727	+	0.854940i	$0.673594\pi$
$48$	1.86179	+	36.2072i	0.0387872	+	0.754317i
$49$	9.05424	+	12.4621i	0.184780	+	0.254328i
$50$	−39.6243	+	30.4944i	−0.792487	+	0.609889i
$51$	8.56986	+	26.3753i	0.168036	+	0.517163i
$52$	45.4898	−	40.9187i	0.874804	−	0.786898i
$53$	−21.8861	+	3.46642i	−0.412945	+	0.0654041i	−0.359451	−	0.933164i	$-0.617036\pi$
$53$	−21.8861	+	3.46642i	−0.412945	+	0.0654041i	−0.0534944	+	0.998568i	$0.517036\pi$
$54$	35.5052	−	46.2477i	0.657504	−	0.856439i
$55$	54.6420	−	6.26545i	0.993490	−	0.113917i
$56$	−42.8269	−	17.7765i	−0.764765	−	0.317438i
$57$	57.1780	−	9.05611i	1.00312	−	0.158879i
$58$	−18.9499	+	102.104i	−0.326722	+	1.76042i
$59$	15.0901	+	46.4424i	0.255764	+	0.787159i	0.993678	+	0.112265i	$0.0358107\pi$
$59$	15.0901	+	46.4424i	0.255764	+	0.787159i	−0.737915	+	0.674894i	$0.764189\pi$
$60$	45.2559	−	2.38726i	0.754265	−	0.0397877i
$61$	55.4322	+	76.2959i	0.908725	+	1.25075i	0.967600	+	0.252487i	$0.0812486\pi$
$61$	55.4322	+	76.2959i	0.908725	+	1.25075i	−0.0588751	+	0.998265i	$0.518751\pi$
$62$	24.0945	−	11.4852i	0.388620	−	0.185245i
$63$	10.1718	+	19.9633i	0.161457	+	0.316877i
$64$	−63.2268	+	9.91841i	−0.987918	+	0.154975i
$65$	−51.2237	−	56.7944i	−0.788057	−	0.873760i
$66$	−44.0071	−	23.4194i	−0.666774	−	0.354839i
$67$	5.11791	−	5.11791i	0.0763867	−	0.0763867i	−0.667881	−	0.744268i	$-0.732799\pi$
$67$	5.11791	−	5.11791i	0.0763867	−	0.0763867i	0.744268	+	0.667881i	$0.232799\pi$
$68$	−44.7330	+	19.8900i	−0.657838	+	0.292500i
$69$	−34.8268	−	11.3159i	−0.504736	−	0.163999i
$70$	−22.1496	+	53.5630i	−0.316423	+	0.765186i
$71$	−10.7606	−	14.8107i	−0.151558	−	0.208602i	0.726486	−	0.687181i	$-0.241152\pi$
$71$	−10.7606	−	14.8107i	−0.151558	−	0.208602i	−0.878044	+	0.478579i	$0.841152\pi$
$72$	26.3552	+	16.1773i	0.366044	+	0.224684i
$73$	−46.5762	+	91.4110i	−0.638030	+	1.25220i	0.314932	+	0.949114i	$0.398018\pi$
$73$	−46.5762	+	91.4110i	−0.638030	+	1.25220i	−0.952962	+	0.303090i	$0.901982\pi$
$74$	−14.5276	+	9.97927i	−0.196319	+	0.134855i
$75$	−3.05911	−	56.5659i	−0.0407882	−	0.754212i
$76$	26.4008	+	98.7237i	0.347380	+	1.29900i
$77$	51.2569	−	37.9190i	0.665674	−	0.492454i
$78$	9.03133	+	68.7305i	0.115786	+	0.881161i
$79$	−47.7369	+	65.7043i	−0.604265	+	0.831700i	−0.996090	−	0.0883400i	$-0.971844\pi$
$79$	−47.7369	+	65.7043i	−0.604265	+	0.831700i	0.391825	+	0.920040i	$0.371844\pi$
$80$	12.5028	+	79.0170i	0.156285	+	0.987712i
$81$	9.66242	+	29.7379i	0.119289	+	0.367134i
$82$	109.589	+	115.540i	1.33645	+	1.40902i
$83$	−9.70086	+	61.2488i	−0.116878	+	0.737937i	0.857744	+	0.514078i	$0.171866\pi$
$83$	−9.70086	+	61.2488i	−0.116878	+	0.737937i	−0.974621	+	0.223860i	$0.928134\pi$
$84$	44.0740	−	28.5912i	0.524691	−	0.340371i
$85$	24.9367	+	55.8832i	0.293373	+	0.657449i
$86$	−148.080	+	43.8237i	−1.72186	+	0.509578i
$87$	−83.1957	−	83.1957i	−0.956273	−	0.956273i
$88$	33.0350	−	81.5640i	0.375398	−	0.926864i
$89$		−	11.2250i		−	0.126124i	−0.998010	−	0.0630619i	$-0.979913\pi$
$89$		−	11.2250i		−	0.126124i	0.998010	−	0.0630619i	$-0.0200865\pi$
$90$	20.1779	−	32.9708i	0.224198	−	0.366342i
$91$	−84.3215	−	27.3977i	−0.926610	−	0.301074i
$92$	13.4711	−	63.2234i	0.146425	−	0.687210i
$93$	−4.73074	+	29.8687i	−0.0508682	+	0.321169i
$94$	2.61421	−	98.9023i	0.0278108	−	1.05215i
$95$	123.361	−	33.1647i	1.29853	−	0.349102i
$96$	31.2970	−	65.4081i	0.326010	−	0.681334i
$97$	7.98092	+	50.3895i	0.0822775	+	0.519480i	0.994062	+	0.108812i	$0.0347045\pi$
$97$	7.98092	+	50.3895i	0.0822775	+	0.519480i	−0.911785	+	0.410668i	$0.865295\pi$
$98$	−4.01373	−	30.5454i	−0.0409564	−	0.311688i
$99$	−37.7185	+	19.6295i	−0.380995	+	0.198278i
$100$	98.7504	−	15.7595i	0.987504	−	0.157595i
$101$	−46.9062	+	64.5609i	−0.464418	+	0.639216i	−0.975418	−	0.220364i	$-0.929275\pi$
$101$	−46.9062	+	64.5609i	−0.464418	+	0.639216i	0.511000	+	0.859581i	$0.329275\pi$
$102$	10.1212	−	54.5340i	0.0992272	−	0.534647i
$103$	17.4529	−	34.2533i	0.169446	−	0.332556i	−0.790631	−	0.612293i	$-0.790247\pi$
$103$	17.4529	−	34.2533i	0.169446	−	0.332556i	0.960077	+	0.279737i	$0.0902473\pi$
$104$	−119.011	+	28.4790i	−1.14434	+	0.273837i
$105$	−35.8120	−	55.0451i	−0.341067	−	0.524239i
$106$	41.7722	+	14.8039i	0.394077	+	0.139659i
$107$	2.13636	−	1.08853i	0.0199660	−	0.0101732i	−0.443979	−	0.896037i	$-0.646434\pi$
$107$	2.13636	−	1.08853i	0.0199660	−	0.0101732i	0.463945	+	0.885864i	$0.346434\pi$
$108$	−106.552	+	47.3771i	−0.986591	+	0.438677i
$109$	35.3156			0.323997			0.161998	−	0.986791i	$-0.448206\pi$
$109$	35.3156			0.323997			0.161998	+	0.986791i	$0.448206\pi$
$110$	−102.010	−	41.1585i	−0.927361	−	0.374168i
$111$		−	19.9685i		−	0.179896i
$112$	58.2917	+	72.1294i	0.520462	+	0.644013i
$113$	70.3792	+	138.127i	0.622825	+	1.22236i	0.959756	+	0.280834i	$0.0906110\pi$
$113$	70.3792	+	138.127i	0.622825	+	1.22236i	−0.336931	+	0.941529i	$0.609389\pi$
$114$	−109.131	−	38.6755i	−0.957289	−	0.339259i
$115$	−79.0515	−	16.7340i	−0.687404	−	0.145513i
$116$	130.787	−	161.345i	1.12747	−	1.39091i
$117$	52.6837	+	26.8437i	0.450288	+	0.229433i
$118$	17.8217	−	96.0251i	0.151031	−	0.813772i
$119$	57.3910	+	41.6970i	0.482278	+	0.350395i
$120$	−81.8119	−	39.0127i	−0.681766	−	0.325106i
$121$	72.7973	+	96.6517i	0.601631	+	0.798774i
$122$	−24.5730	−	187.006i	−0.201418	−	1.53284i
$123$	−178.200	+	28.2240i	−1.44878	+	0.229464i
$124$	−53.3091	−	2.82013i	−0.429912	−	0.0227430i
$125$	−19.8632	−	123.412i	−0.158905	−	0.987294i
$126$	1.18403	−	44.7949i	0.00939709	−	0.355515i
$127$	−158.623	−	25.1234i	−1.24900	−	0.197822i	−0.503305	−	0.864109i	$-0.667883\pi$
$127$	−158.623	−	25.1234i	−1.24900	−	0.197822i	−0.745696	+	0.666286i	$0.767883\pi$
$128$	120.584	+	42.9352i	0.942065	+	0.335431i
$129$	54.0667	−	166.400i	0.419121	−	1.28992i
$130$	35.7961	+	148.716i	0.275355	+	1.14397i
$131$	−64.7703			−0.494430			−0.247215	−	0.968961i	$-0.579515\pi$
$131$	−64.7703			−0.494430			−0.247215	+	0.968961i	$0.579515\pi$
$132$	54.9784	+	83.1730i	0.416503	+	0.630099i
$133$	104.710	−	104.710i	0.787295	−	0.787295i
$134$	−13.8805	+	4.10789i	−0.103586	+	0.0306559i
$135$	59.3980	+	133.111i	0.439985	+	0.986008i
$136$	97.6037	+	7.75412i	0.717674	+	0.0570156i
$137$	−148.793	−	23.5665i	−1.08608	−	0.172018i	−0.412371	−	0.911016i	$-0.635299\pi$
$137$	−148.793	−	23.5665i	−1.08608	−	0.172018i	−0.673708	+	0.738998i	$0.735299\pi$
$138$	50.4007	+	53.1375i	0.365223	+	0.385054i
$139$	157.194	−	51.0755i	1.13089	−	0.367449i	0.316978	−	0.948433i	$-0.397332\pi$
$139$	157.194	−	51.0755i	1.13089	−	0.367449i	0.813915	+	0.580984i	$0.197332\pi$
$140$	90.0650	−	72.9842i	0.643322	−	0.521316i
$141$	90.6847	+	65.8863i	0.643154	+	0.467279i
$142$	4.77016	+	36.3021i	0.0335927	+	0.255648i
$143$	50.6153	−	160.467i	0.353953	−	1.12214i
$144$	−30.8713	−	53.5925i	−0.214384	−	0.372170i
$145$	−201.898	−	163.216i	−1.39240	−	1.12562i
$146$	169.128	−	116.177i	1.15841	−	0.795732i
$147$	31.1002	+	15.8463i	0.211566	+	0.107798i
$148$	35.0585	−	3.66734i	0.236882	−	0.0247793i
$149$	38.4172	−	27.9117i	0.257834	−	0.187327i	−0.451358	−	0.892343i	$-0.649060\pi$
$149$	38.4172	−	27.9117i	0.257834	−	0.187327i	0.709191	+	0.705016i	$0.249060\pi$
$150$	−48.6302	+	102.330i	−0.324201	+	0.682197i
$151$	−1.37473	+	4.23100i	−0.00910420	+	0.0280198i	−0.955505	−	0.294974i	$-0.904689\pi$
$151$	−1.37473	+	4.23100i	−0.00910420	+	0.0280198i	0.946401	+	0.322993i	$0.104689\pi$
$152$	47.8597	−	198.703i	0.314866	−	1.30726i
$153$	−33.4529	−	33.4529i	−0.218647	−	0.218647i
$154$	−126.282	+	17.7012i	−0.820013	+	0.114943i
$155$	−3.43678	+	66.6410i	−0.0221727	+	0.429942i
$156$	49.7488	−	129.410i	0.318903	−	0.829549i
$157$	−16.4961	+	8.40517i	−0.105071	+	0.0535361i	−0.505736	−	0.862688i	$-0.668779\pi$
$157$	−16.4961	+	8.40517i	−0.105071	+	0.0535361i	0.400665	+	0.916224i	$0.368779\pi$
$158$	146.624	−	69.8918i	0.928000	−	0.442353i
$159$	−40.6214	+	29.5132i	−0.255480	+	0.185617i
$160$	53.4690	−	150.801i	0.334181	−	0.942509i
$161$	−89.0859	+	28.9458i	−0.553328	+	0.179787i
$162$	11.4115	−	61.4865i	0.0704414	−	0.379546i
$163$	22.6295	+	142.877i	0.138831	+	0.876546i	0.954540	+	0.298083i	$0.0963473\pi$
$163$	22.6295	+	142.877i	0.138831	+	0.876546i	−0.815709	+	0.578463i	$0.803653\pi$
$164$	−82.2802	−	307.680i	−0.501709	−	1.87610i
$165$	103.875	−	68.8608i	0.629546	−	0.417338i
$166$	75.5256	−	98.3767i	0.454973	−	0.592631i
$167$	−5.85235	−	36.9503i	−0.0350440	−	0.221259i	0.963951	−	0.266080i	$-0.0857284\pi$
$167$	−5.85235	−	36.9503i	−0.0350440	−	0.221259i	−0.998995	+	0.0448205i	$0.985728\pi$
$168$	−104.753	+	8.16640i	−0.623530	+	0.0486095i
$169$	−61.7986	+	20.0796i	−0.365672	+	0.118814i
$170$	9.53081	−	122.017i	0.0560636	−	0.717749i
$171$	−79.8960	+	58.0478i	−0.467228	+	0.339461i
$172$	302.077	+	64.3639i	1.75626	+	0.374209i
$173$	−126.447	+	64.4278i	−0.730906	+	0.372415i	−0.779499	−	0.626404i	$-0.784526\pi$
$173$	−126.447	+	64.4278i	−0.730906	+	0.372415i	0.0485932	+	0.998819i	$0.484526\pi$
$174$	66.7770	+	225.639i	0.383776	+	1.29678i
$175$	−91.3795	−	112.460i	−0.522169	−	0.642630i
$176$	−135.929	+	111.800i	−0.772324	+	0.635229i
$177$	78.2424	+	78.2424i	0.442047	+	0.442047i
$178$	−10.7171	+	19.7268i	−0.0602083	+	0.110825i
$179$	−51.3148	+	157.931i	−0.286675	+	0.882294i	0.699217	+	0.714909i	$0.253532\pi$
$179$	−51.3148	+	157.931i	−0.286675	+	0.882294i	−0.985892	+	0.167384i	$0.946468\pi$
$180$	−66.9394	+	38.6780i	−0.371885	+	0.214878i
$181$	34.5119	−	25.0744i	0.190674	−	0.138533i	−0.488353	−	0.872646i	$-0.662402\pi$
$181$	34.5119	−	25.0744i	0.190674	−	0.138533i	0.679027	+	0.734114i	$0.262402\pi$
$182$	122.029	+	128.655i	0.670487	+	0.706894i
$183$	190.403	+	97.0150i	1.04045	+	0.530137i
$184$	−84.0366	+	98.2472i	−0.456721	+	0.533952i
$185$	−4.64230	−	43.8170i	−0.0250935	−	0.236849i
$186$	36.8310	−	47.9746i	0.198016	−	0.257928i
$187$	−78.1915	+	109.594i	−0.418136	+	0.586062i
$188$	−99.0212	+	171.315i	−0.526708	+	0.911249i
$189$	136.703	+	99.3203i	0.723295	+	0.525504i
$190$	−248.458	−	59.4951i	−1.30767	−	0.313132i
$191$	−226.751	+	73.6758i	−1.18718	+	0.385737i	−0.835029	−	0.550207i	$-0.814549\pi$
$191$	−226.751	+	73.6758i	−1.18718	+	0.385737i	−0.352149	+	0.935944i	$0.614549\pi$
$192$	−117.450	+	85.0673i	−0.611717	+	0.443059i
$193$	−46.1134	−	7.30364i	−0.238929	−	0.0378427i	0.0358212	−	0.999358i	$-0.488595\pi$
$193$	−46.1134	−	7.30364i	−0.238929	−	0.0378427i	−0.274751	+	0.961516i	$0.588595\pi$
$194$	34.0838	−	96.1743i	0.175690	−	0.495744i
$195$	−161.844	−	61.9714i	−0.829971	−	0.317802i
$196$	−22.1095	+	57.5126i	−0.112804	+	0.293431i
$197$	−94.3879	+	94.3879i	−0.479126	+	0.479126i	−0.904852	−	0.425726i	$-0.860019\pi$
$197$	−94.3879	+	94.3879i	−0.479126	+	0.479126i	0.425726	+	0.904852i	$0.360019\pi$
$198$	85.0277	+	1.51491i	0.429433	+	0.00765108i
$199$	335.923			1.68806			0.844028	−	0.536299i	$-0.180178\pi$
$199$	335.923			1.68806			0.844028	+	0.536299i	$0.180178\pi$
$200$	−188.590	−	66.5861i	−0.942951	−	0.332931i
$201$	5.06802	−	15.5978i	0.0252141	−	0.0776009i
$202$	144.072	−	68.6755i	0.713230	−	0.339978i
$203$	−297.256	−	47.0808i	−1.46432	−	0.231925i
$204$	−69.8533	+	86.1748i	−0.342418	+	0.422426i
$205$	−384.463	+	103.360i	−1.87543	+	0.504197i
$206$	−63.3751	+	43.5335i	−0.307646	+	0.211328i
$207$	61.7000	−	9.77232i	0.298068	−	0.0472093i
$208$	236.340	+	63.5767i	1.13625	+	0.305657i
$209$	200.422	+	197.000i	0.958958	+	0.942583i
$210$	10.3817	+	130.928i	0.0494365	+	0.623465i
$211$	−90.9735	−	66.0961i	−0.431154	−	0.313252i	0.350956	−	0.936392i	$-0.385857\pi$
$211$	−90.9735	−	66.0961i	−0.431154	−	0.313252i	−0.782110	+	0.623140i	$0.785857\pi$
$212$	−59.2764	−	65.8983i	−0.279606	−	0.310841i
$213$	−36.9614	−	18.8328i	−0.173528	−	0.0884167i
$214$	−4.79371	−	0.126709i	−0.0224005	−	0.000592097i
$215$	79.9539	−	377.702i	0.371879	−	1.75676i
$216$	232.487	+	18.4700i	1.07633	+	0.0855090i
$217$	35.1187	+	68.9244i	0.161837	+	0.317624i
$218$	−62.0637	−	33.7176i	−0.284696	−	0.154668i
$219$			232.470i			1.06150i
$220$	139.976	+	169.726i	0.636253	+	0.771481i
$221$	187.211			0.847108
$222$	−19.0649	+	35.0926i	−0.0858780	+	0.158075i
$223$	206.304	−	105.117i	0.925131	−	0.471378i	0.0745471	−	0.997217i	$-0.476249\pi$
$223$	206.304	−	105.117i	0.925131	−	0.471378i	0.850584	+	0.525840i	$0.176249\pi$
$224$	−33.5763	−	182.414i	−0.149894	−	0.814349i
$225$	48.4584	+	83.6100i	0.215371	+	0.371600i
$226$	8.19240	−	309.939i	0.0362496	−	1.37141i
$227$	−40.9502	+	80.3693i	−0.180397	+	0.354050i	−0.963443	−	0.267915i	$-0.913665\pi$
$227$	−40.9502	+	80.3693i	−0.180397	+	0.354050i	0.783045	+	0.621965i	$0.213665\pi$
$228$	154.861	+	172.161i	0.679216	+	0.755093i
$229$	66.4852	−	91.5091i	0.290329	−	0.399603i	−0.638792	−	0.769379i	$-0.720566\pi$
$229$	66.4852	−	91.5091i	0.290329	−	0.399603i	0.929121	+	0.369776i	$0.120566\pi$
$230$	122.948	+	104.883i	0.534557	+	0.456012i
$231$	64.4782	−	129.286i	0.279127	−	0.559680i
$232$	−383.889	+	158.680i	−1.65469	+	0.683965i
$233$	−16.1589	−	102.023i	−0.0693514	−	0.437868i	−0.997794	−	0.0663909i	$-0.978852\pi$
$233$	−16.1589	−	102.023i	−0.0693514	−	0.437868i	0.928442	−	0.371477i	$-0.121148\pi$
$234$	−66.9572	−	97.4748i	−0.286142	−	0.416559i
$235$	214.308	+	123.492i	0.911947	+	0.525499i
$236$	−123.000	+	151.739i	−0.521185	+	0.642963i
$237$	−28.7884	+	181.763i	−0.121470	+	0.766931i
$238$	−61.0487	−	128.072i	−0.256507	−	0.538119i
$239$	91.4706	+	29.7206i	0.382722	+	0.124354i	0.494058	−	0.869429i	$-0.335513\pi$
$239$	91.4706	+	29.7206i	0.382722	+	0.124354i	−0.111336	+	0.993783i	$0.535513\pi$
$240$	106.529	+	146.671i	0.443870	+	0.611129i
$241$			144.550i			0.599791i	0.953972	+	0.299895i	$0.0969518\pi$
$241$			144.550i			0.599791i	−0.953972	+	0.299895i	$0.903048\pi$
$242$	−35.6557	−	239.359i	−0.147338	−	0.989086i
$243$	−135.425	−	135.425i	−0.557306	−	0.557306i
$244$	−135.360	+	352.106i	−0.554753	+	1.44306i
$245$	71.9273	+	27.5415i	0.293581	+	0.112414i
$246$	340.115	+	120.535i	1.38258	+	0.489980i
$247$	61.1338	−	385.984i	0.247505	−	1.56269i
$248$	90.9928	+	55.8530i	0.366906	+	0.225214i
$249$	43.4219	+	133.639i	0.174385	+	0.536702i
$250$	−82.9199	+	235.848i	−0.331680	+	0.943392i
$251$	−58.6480	+	80.7220i	−0.233657	+	0.321602i	−0.909704	−	0.415257i	$-0.863692\pi$
$251$	−58.6480	+	80.7220i	−0.233657	+	0.321602i	0.676047	+	0.736859i	$0.263692\pi$
$252$	−44.8488	+	77.5921i	−0.177971	+	0.307905i
$253$	−56.3869	−	168.587i	−0.222873	−	0.666353i
$254$	254.778	+	195.597i	1.00306	+	0.770069i
$255$	107.834	+	87.1737i	0.422880	+	0.341858i
$256$	−170.922	−	190.582i	−0.667666	−	0.744461i
$257$	159.712	−	313.452i	0.621447	−	1.21966i	−0.338893	−	0.940825i	$-0.610052\pi$
$257$	159.712	−	313.452i	0.621447	−	1.21966i	0.960340	−	0.278833i	$-0.0899475\pi$
$258$	−253.887	+	240.811i	−0.984059	+	0.933377i
$259$	−30.0233	−	41.3236i	−0.115920	−	0.159551i
$260$	79.0789	−	295.530i	0.304150	−	1.13665i
$261$	190.889	+	62.0235i	0.731375	+	0.237638i
$262$	113.827	+	61.8395i	0.434455	+	0.236028i
$263$	145.248	−	145.248i	0.552275	−	0.552275i	−0.374822	−	0.927097i	$-0.622296\pi$
$263$	145.248	−	145.248i	0.552275	−	0.552275i	0.927097	+	0.374822i	$0.122296\pi$
$264$	−17.2095	−	198.659i	−0.0651874	−	0.752496i
$265$	−82.2745	+	74.2047i	−0.310470	+	0.280018i
$266$	−283.990	+	84.0456i	−1.06763	+	0.315961i
$267$	−11.5473	−	22.6629i	−0.0432485	−	0.0848799i
$268$	28.3157	+	6.03325i	0.105655	+	0.0225121i
$269$	−87.2157	−	120.042i	−0.324222	−	0.446253i	0.615528	−	0.788115i	$-0.288943\pi$
$269$	−87.2157	−	120.042i	−0.324222	−	0.446253i	−0.939750	+	0.341861i	$0.888943\pi$
$270$	22.7019	−	290.640i	0.0840813	−	1.07644i
$271$	117.527	+	361.712i	0.433680	+	1.33473i	0.894433	+	0.447202i	$0.147579\pi$
$271$	117.527	+	361.712i	0.433680	+	1.33473i	−0.460753	+	0.887528i	$0.652421\pi$
$272$	−164.125	−	106.814i	−0.603402	−	0.392699i
$273$	−198.427	+	31.4278i	−0.726839	+	0.115120i
$274$	238.988	+	183.476i	0.872220	+	0.669619i
$275$	211.925	−	175.251i	0.770636	−	0.637276i
$276$	−37.8412	−	141.504i	−0.137106	−	0.512695i
$277$	−18.6000	+	2.94595i	−0.0671480	+	0.0106352i	−0.189918	−	0.981800i	$-0.560822\pi$
$277$	−18.6000	+	2.94595i	−0.0671480	+	0.0106352i	0.122770	+	0.992435i	$0.460822\pi$
$278$	−325.017	−	60.3212i	−1.16913	−	0.216983i
$279$	−15.9418	−	49.0638i	−0.0571390	−	0.175856i
$280$	−227.962	+	42.2727i	−0.814150	+	0.150974i
$281$	−225.323	−	310.130i	−0.801860	−	1.10366i	−0.992529	−	0.122011i	$-0.961066\pi$
$281$	−225.323	−	310.130i	−0.801860	−	1.10366i	0.190669	−	0.981654i	$-0.438934\pi$
$282$	−96.4643	−	202.370i	−0.342072	−	0.717624i
$283$	−201.552	−	395.568i	−0.712197	−	1.39777i	−0.908779	−	0.417278i	$-0.862984\pi$
$283$	−201.552	−	395.568i	−0.712197	−	1.39777i	0.196582	−	0.980487i	$-0.437016\pi$
$284$	26.2763	−	68.3515i	0.0925222	−	0.240674i
$285$	214.944	−	193.862i	0.754191	−	0.680216i
$286$	−242.157	+	233.679i	−0.846702	+	0.817059i
$287$	−326.337	+	326.337i	−1.13706	+	1.13706i
$288$	3.08576	+	123.658i	0.0107145	+	0.429367i
$289$	132.396	+	43.0180i	0.458117	+	0.148851i
$290$	198.986	+	479.597i	0.686159	+	1.65378i
$291$	67.9498	+	93.5248i	0.233504	+	0.321391i
$292$	−408.145	+	42.6945i	−1.39776	+	0.146214i
$293$	−92.7576	+	182.047i	−0.316579	+	0.621321i	−0.993384	−	0.114842i	$-0.963364\pi$
$293$	−92.7576	+	182.047i	−0.316579	+	0.621321i	0.676805	+	0.736162i	$0.263364\pi$
$294$	−39.5261	−	57.5412i	−0.134443	−	0.195718i
$295$	189.878	+	153.498i	0.643653	+	0.520332i
$296$	−65.1132	−	27.0271i	−0.219977	−	0.0913078i
$297$	−186.248	+	261.047i	−0.627099	+	0.878946i
$298$	−94.1631	+	12.3732i	−0.315984	+	0.0415209i
$299$	−145.300	+	199.988i	−0.485953	+	0.668857i
$300$	183.162	−	133.404i	0.610539	−	0.444680i
$301$	−138.301	−	425.646i	−0.459471	−	1.41411i
$302$	6.45550	−	6.12302i	0.0213758	−	0.0202749i
$303$	−28.2874	+	178.600i	−0.0933577	+	0.589437i
$304$	−273.820	+	303.507i	−0.900725	+	0.998378i
$305$	440.356	+	168.616i	1.44379	+	0.552838i
$306$	26.8510	+	90.7294i	0.0877483	+	0.296501i
$307$	−197.102	−	197.102i	−0.642027	−	0.642027i	0.309026	−	0.951054i	$-0.399997\pi$
$307$	−197.102	−	197.102i	−0.642027	−	0.642027i	−0.951054	+	0.309026i	$0.899997\pi$
$308$	238.828	+	89.4596i	0.775416	+	0.290453i
$309$		−	87.1104i		−	0.281911i
$310$	69.6653	−	113.834i	0.224727	−	0.367205i
$311$	444.086	+	144.292i	1.42793	+	0.463962i	0.918112	−	0.396322i	$-0.129713\pi$
$311$	444.086	+	144.292i	1.42793	+	0.463962i	0.509816	+	0.860283i	$0.329713\pi$
$312$	−210.982	+	179.927i	−0.676226	+	0.576688i
$313$	83.8361	−	529.321i	0.267847	−	1.69112i	−0.376524	−	0.926407i	$-0.622881\pi$
$313$	83.8361	−	529.321i	0.267847	−	1.69112i	0.644371	−	0.764713i	$-0.277119\pi$
$314$	37.0150	+	0.978393i	0.117882	+	0.00311590i
$315$	97.0645	+	55.9323i	0.308141	+	0.177563i
$316$	−324.406	−	17.1616i	−1.02660	−	0.0543088i
$317$	−1.93423	−	12.2122i	−0.00610166	−	0.0385244i	0.984450	−	0.175667i	$-0.0562082\pi$
$317$	−1.93423	−	12.2122i	−0.00610166	−	0.0385244i	−0.990551	+	0.137143i	$0.956208\pi$
$318$	99.5657	−	13.0831i	0.313100	−	0.0411419i
$319$	84.4884	−	564.879i	0.264854	−	1.77078i
$320$	−237.944	+	213.969i	−0.743575	+	0.668652i
$321$	3.19345	−	4.39541i	0.00994845	−	0.0136929i
$322$	184.195	+	34.1855i	0.572035	+	0.106166i
$323$	−141.955	+	278.602i	−0.439488	+	0.862544i
$324$	−78.7588	+	97.1612i	−0.243083	+	0.299880i
$325$	−369.544	−	98.3585i	−1.13706	−	0.302642i
$326$	96.6428	−	272.698i	0.296450	−	0.836496i
$327$	71.3012	−	36.3298i	0.218046	−	0.111100i
$328$	−149.158	+	619.273i	−0.454751	+	1.88803i
$329$	286.729			0.871517
$330$	−248.295	+	21.8412i	−0.752408	+	0.0661854i
$331$		−	236.741i		−	0.715229i	−0.933869	−	0.357614i	$-0.883590\pi$
$331$		−	236.741i		−	0.715229i	0.933869	−	0.357614i	$-0.116410\pi$
$332$	−226.654	+	100.779i	−0.682692	+	0.303551i
$333$	15.4650	+	30.3518i	0.0464415	+	0.0911465i
$334$	−24.9934	+	70.5239i	−0.0748305	+	0.211150i
$335$	7.49461	−	35.4045i	0.0223720	−	0.105685i
$336$	191.890	+	85.6614i	0.571101	+	0.254945i
$337$	−131.068	−	66.7824i	−0.388925	−	0.198167i	0.248583	−	0.968610i	$-0.420035\pi$
$337$	−131.068	−	66.7824i	−0.388925	−	0.198167i	−0.637509	+	0.770443i	$0.720035\pi$
$338$	127.776	+	23.7144i	0.378035	+	0.0701609i
$339$	284.187	+	206.474i	0.838310	+	0.609068i
$340$	−133.246	+	205.334i	−0.391899	+	0.603923i
$341$	−130.225	+	67.7720i	−0.381893	+	0.198745i
$342$	195.830	−	25.7325i	0.572603	−	0.0752412i
$343$	368.703	−	58.3968i	1.07494	−	0.170253i
$344$	−469.418	−	401.521i	−1.36459	−	1.16721i
$345$	−176.817	+	47.5360i	−0.512513	+	0.137786i
$346$	283.730	+	7.49963i	0.820028	+	0.0216752i
$347$	203.667	+	32.2577i	0.586937	+	0.0929616i	0.442838	−	0.896602i	$-0.353972\pi$
$347$	203.667	+	32.2577i	0.586937	+	0.0929616i	0.144099	+	0.989563i	$0.453972\pi$
$348$	98.0753	−	460.294i	0.281826	−	1.32268i
$349$	54.6641	−	168.239i	0.156631	−	0.482059i	−0.841692	−	0.539958i	$-0.818440\pi$
$349$	54.6641	−	168.239i	0.156631	−	0.482059i	0.998322	+	0.0578988i	$0.0184401\pi$
$350$	53.2188	+	284.882i	0.152054	+	0.813949i
$351$	445.927			1.27045
$352$	345.623	−	66.6995i	0.981883	−	0.189487i
$353$	183.025	−	183.025i	0.518484	−	0.518484i	−0.398628	−	0.917113i	$-0.630514\pi$
$353$	183.025	−	183.025i	0.518484	−	0.518484i	0.917113	+	0.398628i	$0.130514\pi$
$354$	−62.8012	−	212.205i	−0.177404	−	0.599449i
$355$	−85.4829	−	32.7320i	−0.240797	−	0.0922029i
$356$	37.6684	−	24.4358i	0.105810	−	0.0686398i
$357$	158.765	+	25.1459i	0.444720	+	0.0704367i
$358$	240.965	−	228.554i	0.673086	−	0.638420i
$359$	−113.014	+	36.7204i	−0.314802	+	0.102285i	−0.462156	−	0.886798i	$-0.652924\pi$
$359$	−113.014	+	36.7204i	−0.314802	+	0.102285i	0.147355	+	0.989084i	$0.452924\pi$
$360$	154.567	−	4.06223i	0.429353	−	0.0112840i
$361$	235.999	+	171.464i	0.653738	+	0.474968i
$362$	−84.5910	+	11.1154i	−0.233677	+	0.0307056i
$363$	246.403	+	120.249i	0.678795	+	0.331264i
$364$	−91.6198	−	342.605i	−0.251703	−	0.941222i
$365$	54.0449	+	510.110i	0.148068	+	1.39756i
$366$	−241.988	−	352.281i	−0.661171	−	0.962517i
$367$	−373.233	−	190.172i	−1.01698	−	0.518179i	−0.135692	−	0.990751i	$-0.543326\pi$
$367$	−373.233	−	190.172i	−1.01698	−	0.518179i	−0.881292	+	0.472572i	$0.843326\pi$
$368$	241.487	−	92.4255i	0.656216	−	0.251156i
$369$	249.002	−	180.910i	0.674802	−	0.490272i
$370$	−33.6759	+	81.4362i	−0.0910160	+	0.220098i
$371$	−39.6894	+	122.151i	−0.106980	+	0.329249i
$372$	−110.530	+	49.1461i	−0.297125	+	0.132113i
$373$	−417.840	−	417.840i	−1.12022	−	1.12022i	−0.991709	−	0.128507i	$-0.958982\pi$
$373$	−417.840	−	417.840i	−1.12022	−	1.12022i	−0.128507	−	0.991709i	$-0.541018\pi$
$374$	242.048	−	117.947i	0.647188	−	0.315365i
$375$	−167.059	−	228.731i	−0.445490	−	0.609949i
$376$	337.583	−	206.528i	0.897826	−	0.549277i
$377$	−707.679	+	360.581i	−1.87713	+	0.956447i
$378$	−145.415	−	305.062i	−0.384696	−	0.807044i
$379$	−346.843	+	251.996i	−0.915153	+	0.664897i	−0.942313	−	0.334734i	$-0.891354\pi$
$379$	−346.843	+	251.996i	−0.915153	+	0.664897i	0.0271600	+	0.999631i	$0.491354\pi$
$380$	379.837	+	341.772i	0.999572	+	0.899400i
$381$	−346.100	+	112.455i	−0.908399	+	0.295157i
$382$	468.834	+	87.0126i	1.22731	+	0.227782i
$383$	−29.4309	−	185.820i	−0.0768431	−	0.485168i	−0.995856	−	0.0909415i	$-0.971012\pi$
$383$	−29.4309	−	185.820i	−0.0768431	−	0.485168i	0.919013	−	0.394227i	$-0.128988\pi$
$384$	287.624	−	37.3622i	0.749021	−	0.0972975i
$385$	111.428	−	298.683i	0.289425	−	0.775800i
$386$	74.0665	+	56.8622i	0.191882	+	0.147311i
$387$	46.6915	+	294.798i	0.120650	+	0.761753i
$388$	−151.721	+	136.475i	−0.391034	+	0.351740i
$389$	−655.963	+	213.135i	−1.68628	+	0.547906i	−0.986113	−	0.166074i	$-0.946891\pi$
$389$	−655.963	+	213.135i	−1.68628	+	0.547906i	−0.700167	+	0.713980i	$0.746891\pi$
$390$	225.258	+	263.429i	0.577585	+	0.675460i
$391$	160.014	−	116.257i	0.409244	−	0.297333i
$392$	93.7654	−	79.9635i	0.239197	−	0.203988i
$393$	−130.769	+	66.6302i	−0.332746	+	0.169543i
$394$	255.994	−	75.7604i	0.649731	−	0.192285i
$395$	−20.9141	+	405.536i	−0.0529471	+	1.02667i
$396$	−147.981	−	83.8425i	−0.373690	−	0.211724i
$397$	67.5852	+	67.5852i	0.170240	+	0.170240i	0.787085	−	0.616845i	$-0.211589\pi$
$397$	67.5852	+	67.5852i	0.170240	+	0.170240i	−0.616845	+	0.787085i	$0.711589\pi$
$398$	−590.351	−	320.723i	−1.48329	−	0.805836i
$399$	103.690	−	319.124i	0.259874	−	0.799809i
$400$	267.855	+	297.075i	0.669638	+	0.742688i
$401$	604.138	−	438.932i	1.50658	−	1.09459i	0.538913	−	0.842362i	$-0.318835\pi$
$401$	604.138	−	438.932i	1.50658	−	1.09459i	0.967667	−	0.252232i	$-0.0811647\pi$
$402$	−23.7985	+	22.5728i	−0.0592003	+	0.0561513i
$403$	181.894	+	92.6794i	0.451349	+	0.229974i
$404$	−318.761	−	16.8629i	−0.789012	−	0.0417400i
$405$	121.582	+	98.2874i	0.300202	+	0.242685i
$406$	477.448	+	366.545i	1.17598	+	0.902821i
$407$	77.9300	−	57.6513i	0.191474	−	0.141649i
$408$	205.036	−	84.7511i	0.502538	−	0.207723i
$409$	−123.716	−	89.8852i	−0.302485	−	0.219768i	0.426180	−	0.904638i	$-0.359859\pi$
$409$	−123.716	−	89.8852i	−0.302485	−	0.219768i	−0.728665	+	0.684870i	$0.759859\pi$
$410$	774.338	+	185.421i	1.88863	+	0.452246i
$411$	−324.651	+	105.486i	−0.789906	+	0.256656i
$412$	152.939	−	15.9984i	0.371211	−	0.0388310i
$413$	279.558	+	44.2777i	0.676896	+	0.107210i
$414$	−117.762	−	41.7342i	−0.284449	−	0.100807i
$415$	126.350	+	283.150i	0.304457	+	0.682289i
$416$	−354.644	−	337.375i	−0.852510	−	0.810998i
$417$	264.828	−	264.828i	0.635079	−	0.635079i
$418$	−164.136	−	537.561i	−0.392671	−	1.28603i
$419$	−148.419			−0.354222			−0.177111	−	0.984191i	$-0.556675\pi$
$419$	−148.419			−0.354222			−0.177111	+	0.984191i	$0.556675\pi$
$420$	106.759	−	240.004i	0.254187	−	0.571438i
$421$	−225.265	+	693.295i	−0.535071	+	1.64678i	0.208423	+	0.978039i	$0.433167\pi$
$421$	−225.265	+	693.295i	−0.535071	+	1.64678i	−0.743495	+	0.668742i	$0.766833\pi$
$422$	96.7715	+	203.014i	0.229316	+	0.481076i
$423$	−188.866	−	29.9135i	−0.446493	−	0.0707175i
$424$	41.2558	+	172.404i	0.0973015	+	0.406613i
$425$	256.888	+	166.216i	0.604442	+	0.391097i
$426$	46.9753	+	68.3856i	0.110271	+	0.160529i
$427$	539.893	−	85.5106i	1.26439	−	0.200259i
$428$	8.30348	+	4.79947i	0.0194007	+	0.0112137i
$429$	−62.8839	−	376.046i	−0.146583	−	0.876564i
$430$	−501.122	+	587.438i	−1.16540	+	1.36613i
$431$	−389.660	−	283.105i	−0.904084	−	0.656855i	0.0354281	−	0.999372i	$-0.488721\pi$
$431$	−389.660	−	283.105i	−0.904084	−	0.656855i	−0.939512	+	0.342517i	$0.888721\pi$
$432$	−390.939	−	254.426i	−0.904951	−	0.588950i
$433$	−51.4435	−	26.2118i	−0.118807	−	0.0605353i	0.393577	−	0.919292i	$-0.371238\pi$
$433$	−51.4435	−	26.2118i	−0.118807	−	0.0605353i	−0.512384	+	0.858756i	$0.671238\pi$
$434$	4.08795	−	154.657i	0.00941923	−	0.356353i
$435$	−575.529	−	121.831i	−1.32306	−	0.280071i
$436$	76.8788	+	118.511i	0.176327	+	0.271813i
$437$	−187.442	−	367.875i	−0.428928	−	0.841819i
$438$	221.950	−	408.542i	0.506736	−	0.932744i
$439$			396.815i			0.903906i	0.892042	+	0.451953i	$0.149273\pi$
$439$			396.815i			0.903906i	−0.892042	+	0.451953i	$0.850727\pi$
$440$	−83.9474	−	431.918i	−0.190789	−	0.981631i
$441$	−59.5443			−0.135021
$442$	−329.004	−	178.740i	−0.744353	−	0.404388i
$443$	404.354	−	206.029i	0.912763	−	0.465076i	0.0664669	−	0.997789i	$-0.478827\pi$
$443$	404.354	−	206.029i	0.912763	−	0.465076i	0.846296	+	0.532713i	$0.178827\pi$
$444$	67.0093	−	43.4695i	0.150922	−	0.0979042i
$445$	−30.6071	−	47.0449i	−0.0687801	−	0.105719i
$446$	−462.919	−	12.2360i	−1.03794	−	0.0274350i
$447$	48.8499	−	95.8733i	0.109284	−	0.214482i
$448$	−115.153	+	352.632i	−0.257038	+	0.787124i
$449$	−22.3783	+	30.8011i	−0.0498403	+	0.0685992i	−0.833210	−	0.552957i	$-0.813499\pi$
$449$	−22.3783	+	30.8011i	−0.0498403	+	0.0685992i	0.783369	+	0.621556i	$0.213499\pi$
$450$	−5.33407	−	193.202i	−0.0118535	−	0.429338i
$451$	−624.631	−	613.965i	−1.38499	−	1.36134i
$452$	−310.312	+	536.865i	−0.686530	+	1.18775i
$453$	1.57695	+	9.95646i	0.00348112	+	0.0219789i
$454$	148.698	−	102.144i	0.327529	−	0.224986i
$455$	−428.104	+	115.093i	−0.940887	+	0.252951i
$456$	−107.782	−	450.410i	−0.236364	−	0.987740i
$457$	−14.7197	+	92.9365i	−0.0322094	+	0.203362i	−0.998545	−	0.0539222i	$-0.982828\pi$
$457$	−14.7197	+	92.9365i	−0.0322094	+	0.203362i	0.966336	+	0.257284i	$0.0828277\pi$
$458$	−204.209	+	97.3412i	−0.445872	+	0.212535i
$459$	−339.332	−	110.256i	−0.739285	−	0.240208i
$460$	−115.932	−	301.706i	−0.252027	−	0.655882i
$461$		−	566.953i		−	1.22983i	−0.788592	−	0.614916i	$-0.789190\pi$
$461$		−	566.953i		−	1.22983i	0.788592	−	0.614916i	$-0.210810\pi$
$462$	−236.750	+	165.646i	−0.512445	+	0.358542i
$463$	−122.032	−	122.032i	−0.263569	−	0.263569i	0.562933	−	0.826502i	$-0.309673\pi$
$463$	−122.032	−	122.032i	−0.263569	−	0.263569i	−0.826502	+	0.562933i	$0.809673\pi$
$464$	826.145	+	87.6541i	1.78049	+	0.188910i
$465$	61.6159	+	138.081i	0.132507	+	0.296949i
$466$	−69.0090	+	194.723i	−0.148088	+	0.417861i
$467$	−0.555465	+	3.50707i	−0.00118943	+	0.00750979i	−0.988276	−	0.152678i	$-0.951210\pi$
$467$	−0.555465	+	3.50707i	−0.00118943	+	0.00750979i	0.987086	+	0.160188i	$0.0512101\pi$
$468$	24.6065	+	235.230i	0.0525780	+	0.502627i
$469$	−12.9638	−	39.8986i	−0.0276415	−	0.0850717i
$470$	−258.720	−	421.635i	−0.550467	−	0.897097i
$471$	−24.6585	+	33.9396i	−0.0523536	+	0.0720585i
$472$	361.033	−	149.232i	0.764900	−	0.316170i
$473$	805.498	−	269.413i	1.70296	−	0.569583i
$474$	224.131	−	291.944i	0.472849	−	0.615915i
$475$	426.585	−	475.363i	0.898074	−	1.00076i
$476$	−14.9902	+	283.361i	−0.0314921	+	0.595295i
$477$	38.8868	−	76.3196i	0.0815236	−	0.159999i
$478$	−132.375	−	139.563i	−0.276934	−	0.291972i
$479$	274.282	+	377.516i	0.572613	+	0.788134i	0.992861	−	0.119275i	$-0.0380570\pi$
$479$	274.282	+	377.516i	0.572613	+	0.788134i	−0.420248	+	0.907409i	$0.638057\pi$
$480$	−47.1796	−	359.468i	−0.0982909	−	0.748891i
$481$	−128.201	−	41.6550i	−0.266530	−	0.0866008i
$482$	138.009	−	254.031i	0.286325	−	0.527036i
$483$	−150.085	+	150.085i	−0.310734	+	0.310734i
$484$	−165.867	+	454.691i	−0.342699	+	0.939445i
$485$	170.845	+	189.425i	0.352259	+	0.390567i
$486$	108.699	+	367.294i	0.223661	+	0.755749i
$487$	−59.4939	−	116.763i	−0.122164	−	0.239761i	0.821823	−	0.569743i	$-0.192957\pi$
$487$	−59.4939	−	116.763i	−0.122164	−	0.239761i	−0.943987	+	0.329982i	$0.892957\pi$
$488$	574.054	−	489.556i	1.17634	−	1.00319i
$489$	192.668	+	265.185i	0.394004	+	0.542301i
$490$	−100.110	−	117.074i	−0.204306	−	0.238927i
$491$	260.437	+	801.543i	0.530422	+	1.63247i	0.753338	+	0.657633i	$0.228442\pi$
$491$	260.437	+	801.543i	0.530422	+	1.63247i	−0.222916	+	0.974838i	$0.571558\pi$
$492$	−482.636	−	536.553i	−0.980968	−	1.09055i
$493$	627.668	−	99.4128i	1.27316	−	0.201649i
$494$	−475.954	+	619.960i	−0.963470	+	1.25498i
$495$	−104.558	+	185.115i	−0.211228	+	0.373971i
$496$	−106.585	−	185.031i	−0.214889	−	0.373047i
$497$	−104.805	+	16.5995i	−0.210875	+	0.0333994i
$498$	51.2821	−	276.314i	0.102976	−	0.554847i
$499$	−67.0271	−	206.288i	−0.134323	−	0.413404i	0.861161	−	0.508332i	$-0.169738\pi$
$499$	−67.0271	−	206.288i	−0.134323	−	0.413404i	−0.995484	+	0.0949285i	$0.969738\pi$
$500$	370.899	−	335.311i	0.741799	−	0.670623i
$501$	−49.8271	−	68.5811i	−0.0994552	−	0.136888i
$502$	180.137	−	85.8666i	0.358839	−	0.171049i
$503$	−2.37690	−	4.66493i	−0.00472545	−	0.00927421i	0.888632	−	0.458621i	$-0.151657\pi$
$503$	−2.37690	−	4.66493i	−0.00472545	−	0.00927421i	−0.893357	+	0.449347i	$0.851657\pi$
$504$	152.898	−	93.5410i	0.303370	−	0.185597i
$505$	−20.5501	+	398.479i	−0.0406933	+	0.789066i
$506$	−61.8644	+	350.110i	−0.122262	+	0.691918i
$507$	−104.113	+	104.113i	−0.205352	+	0.205352i
$508$	−260.999	−	586.992i	−0.513778	−	1.15550i
$509$	324.222	+	105.346i	0.636978	+	0.206967i	0.609664	−	0.792660i	$-0.291304\pi$
$509$	324.222	+	105.346i	0.636978	+	0.206967i	0.0273144	+	0.999627i	$0.491304\pi$
$510$	−106.279	−	256.154i	−0.208390	−	0.502262i
$511$	349.526	+	481.082i	0.684005	+	0.941452i
$512$	118.421	+	498.117i	0.231290	+	0.972885i
$513$	−338.129	+	663.616i	−0.659122	+	1.29360i
$514$	−579.946	+	398.376i	−1.12830	+	0.775050i
$515$	−20.2516	−	191.147i	−0.0393234	−	0.371159i
$516$	676.096	−	180.803i	1.31026	−	0.350392i
$517$	4.68582	+	544.132i	0.00906349	+	1.05248i
$518$	13.3093	+	101.287i	0.0256936	+	0.195534i
$519$	−189.014	+	260.155i	−0.364189	+	0.501263i
$520$	−421.131	+	443.864i	−0.809867	+	0.853584i
$521$	−73.1392	−	225.099i	−0.140382	−	0.432052i	0.856006	−	0.516966i	$-0.172939\pi$
$521$	−73.1392	−	225.099i	−0.140382	−	0.432052i	−0.996388	+	0.0849136i	$0.972939\pi$
$522$	−276.251	−	291.251i	−0.529216	−	0.557953i
$523$	−153.156	+	966.991i	−0.292842	+	1.84893i	0.201275	+	0.979535i	$0.435492\pi$
$523$	−153.156	+	966.991i	−0.292842	+	1.84893i	−0.494117	+	0.869396i	$0.664508\pi$
$524$	−140.999	−	217.353i	−0.269081	−	0.414796i
$525$	−300.182	−	133.050i	−0.571775	−	0.253429i
$526$	−393.935	+	116.584i	−0.748927	+	0.221642i
$527$	−115.498	−	115.498i	−0.219162	−	0.219162i
$528$	−159.426	+	365.554i	−0.301943	+	0.692336i
$529$		−	267.834i		−	0.506302i
$530$	215.436	−	51.8556i	0.406483	−	0.0978407i
$531$	−179.524	−	58.3307i	−0.338086	−	0.109851i
$532$	579.326	+	123.438i	1.08896	+	0.232026i
$533$	−190.528	+	1202.95i	−0.357463	+	2.25694i
$534$	−1.34415	+	50.8527i	−0.00251714	+	0.0952297i
$535$	5.98557	−	10.3873i	0.0111880	−	0.0194155i
$536$	−44.0017	−	37.6372i	−0.0820926	−	0.0702187i
$537$	58.8628	+	371.645i	0.109614	+	0.692077i
$538$	38.6626	+	294.231i	0.0718635	+	0.546898i
$539$	27.9470	+	167.123i	0.0518498	+	0.310062i
$540$	−317.385	+	489.095i	−0.587749	+	0.905732i
$541$	173.455	−	238.741i	0.320620	−	0.441295i	−0.618036	−	0.786149i	$-0.712072\pi$
$541$	173.455	−	238.741i	0.320620	−	0.441295i	0.938656	+	0.344854i	$0.112072\pi$
$542$	138.802	−	747.881i	0.256092	−	1.37985i
$543$	43.8841	−	86.1274i	0.0808178	−	0.158614i
$544$	186.453	+	344.414i	0.342744	+	0.633114i
$545$	148.011	−	96.2949i	0.271579	−	0.176688i
$546$	378.721	+	134.217i	0.693628	+	0.245819i
$547$	600.518	−	305.979i	1.09784	−	0.559377i	0.191314	−	0.981529i	$-0.438725\pi$
$547$	600.518	−	305.979i	1.09784	−	0.559377i	0.906525	+	0.422152i	$0.138725\pi$
$548$	−244.824	−	550.614i	−0.446760	−	1.00477i
$549$	−364.544			−0.664015
$550$	−539.757	+	105.650i	−0.981377	+	0.192091i
$551$		−	1326.56i		−	2.40756i
$552$	−68.5988	+	284.808i	−0.124273	+	0.515956i
$553$	213.711	+	419.431i	0.386457	+	0.758465i
$554$	35.5003	+	12.5811i	0.0640799	+	0.0227097i
$555$	−54.4479	−	83.6895i	−0.0981043	−	0.150792i
$556$	513.593	+	416.319i	0.923729	+	0.748774i
$557$	134.416	+	68.4883i	0.241321	+	0.122959i	0.570469	−	0.821319i	$-0.306761\pi$
$557$	134.416	+	68.4883i	0.241321	+	0.122959i	−0.329148	+	0.944278i	$0.606761\pi$
$558$	−18.8276	+	101.445i	−0.0337412	+	0.181801i
$559$	−955.530	−	694.233i	−1.70936	−	1.24192i
$560$	440.980	+	143.357i	0.787464	+	0.255994i
$561$	−45.1254	+	301.703i	−0.0804374	+	0.537795i
$562$	99.8851	+	760.149i	0.177731	+	1.35258i
$563$	−761.878	+	120.670i	−1.35325	+	0.214333i	−0.790584	−	0.612353i	$-0.790223\pi$
$563$	−761.878	+	120.670i	−1.35325	+	0.214333i	−0.562663	+	0.826686i	$0.690223\pi$
$564$	−23.6864	+	447.744i	−0.0419971	+	0.793872i
$565$	671.595	+	386.999i	1.18866	+	0.684954i
$566$	−23.4614	+	887.602i	−0.0414512	+	1.56820i
$567$	179.006	+	28.3517i	0.315707	+	0.0500031i
$568$	−111.437	+	95.0336i	−0.196191	+	0.167313i
$569$	−228.564	+	703.449i	−0.401695	+	1.23629i	0.521929	+	0.852989i	$0.325213\pi$
$569$	−228.564	+	703.449i	−0.401695	+	1.23629i	−0.923624	+	0.383300i	$0.874787\pi$
$570$	−562.833	+	135.474i	−0.987426	+	0.237674i
$571$	−856.728			−1.50040			−0.750200	−	0.661211i	$-0.770043\pi$
$571$	−856.728			−1.50040			−0.750200	+	0.661211i	$0.770043\pi$
$572$	648.671	−	179.468i	1.13404	−	0.313755i
$573$	−382.011	+	382.011i	−0.666687	+	0.666687i
$574$	885.076	−	261.934i	1.54194	−	0.456332i
$575$	−376.939	+	145.415i	−0.655547	+	0.252896i
$576$	112.639	−	220.262i	0.195555	−	0.382400i
$577$	−819.702	−	129.828i	−1.42063	−	0.225005i	−0.601617	−	0.798784i	$-0.705477\pi$
$577$	−819.702	−	129.828i	−1.42063	−	0.225005i	−0.819010	+	0.573779i	$0.805477\pi$
$578$	−191.601	−	202.005i	−0.331489	−	0.349489i
$579$	−100.615	+	32.6917i	−0.173773	+	0.0564624i
$580$	108.198	−	1032.83i	0.186548	−	1.78073i
$581$	290.790	+	211.271i	0.500499	+	0.363634i
$582$	−30.1220	−	229.235i	−0.0517560	−	0.393875i
$583$	−232.458	−	73.3232i	−0.398727	−	0.125769i
$584$	758.036	+	314.645i	1.29801	+	0.538775i
$585$	293.996	−	31.1481i	0.502557	−	0.0532447i
$586$	336.821	−	231.369i	0.574781	−	0.394827i
$587$	−239.702	−	122.134i	−0.408351	−	0.208065i	0.237735	−	0.971330i	$-0.423595\pi$
$587$	−239.702	−	122.134i	−0.408351	−	0.208065i	−0.646086	+	0.763265i	$0.723595\pi$
$588$	14.5257	+	138.860i	0.0247036	+	0.236157i
$589$	−275.846	+	200.414i	−0.468329	+	0.340261i
$590$	−187.139	−	451.043i	−0.317184	−	0.764480i
$591$	−93.4679	+	287.665i	−0.158152	+	0.486742i
$592$	88.6257	+	109.664i	0.149706	+	0.185244i
$593$	−210.325	−	210.325i	−0.354680	−	0.354680i	0.507167	−	0.861848i	$-0.330693\pi$
$593$	−210.325	−	210.325i	−0.354680	−	0.354680i	−0.861848	+	0.507167i	$0.830693\pi$
$594$	576.547	−	280.943i	0.970619	−	0.472968i
$595$	354.225	+	18.2679i	0.595337	+	0.0307024i
$596$	177.296	+	68.1576i	0.297476	+	0.114358i
$597$	678.218	−	345.570i	1.13604	−	0.578843i
$598$	446.289	−	212.734i	0.746303	−	0.355743i
$599$	869.672	−	631.853i	1.45187	−	1.05485i	0.466483	−	0.884530i	$-0.345521\pi$
$599$	869.672	−	631.853i	1.45187	−	1.05485i	0.985389	−	0.170317i	$-0.0544792\pi$
$600$	−449.256	+	59.5705i	−0.748760	+	0.0992842i
$601$	−513.641	+	166.892i	−0.854644	+	0.277691i	−0.703390	−	0.710804i	$-0.748331\pi$
$601$	−513.641	+	166.892i	−0.854644	+	0.277691i	−0.151254	+	0.988495i	$0.548331\pi$
$602$	−163.336	+	880.073i	−0.271322	+	1.46192i
$603$	4.37670	+	27.6334i	0.00725821	+	0.0458265i
$604$	−17.1908	+	4.59720i	−0.0284617	+	0.00761126i
$605$	568.639	+	206.579i	0.939899	+	0.341453i
$606$	220.230	−	286.863i	0.363416	−	0.473372i
$607$	142.206	+	897.855i	0.234277	+	1.47917i	0.771771	+	0.635900i	$0.219371\pi$
$607$	142.206	+	897.855i	0.234277	+	1.47917i	−0.537494	+	0.843267i	$0.680629\pi$
$608$	770.985	−	271.952i	1.26807	−	0.447290i
$609$	−648.584	+	210.738i	−1.06500	+	0.346039i
$610$	−612.896	−	716.755i	−1.00475	−	1.17501i
$611$	612.173	−	444.769i	1.00192	−	0.727937i
$612$	39.4360	−	185.084i	0.0644379	−	0.302424i
$613$	−251.624	+	128.209i	−0.410480	+	0.209150i	−0.647022	−	0.762471i	$-0.723986\pi$
$613$	−251.624	+	128.209i	−0.410480	+	0.209150i	0.236542	+	0.971621i	$0.423986\pi$
$614$	158.204	+	534.571i	0.257661	+	0.870637i
$615$	−669.890	+	604.184i	−1.08925	+	0.982414i
$616$	−334.305	−	385.237i	−0.542702	−	0.625385i
$617$	−201.200	−	201.200i	−0.326094	−	0.326094i	0.525005	−	0.851099i	$-0.324063\pi$
$617$	−201.200	−	201.200i	−0.326094	−	0.326094i	−0.851099	+	0.525005i	$0.824063\pi$
$618$	−83.1687	+	153.088i	−0.134577	+	0.247715i
$619$	92.1660	−	283.658i	0.148895	−	0.458252i	−0.848596	−	0.529041i	$-0.822552\pi$
$619$	92.1660	−	283.658i	0.148895	−	0.458252i	0.997491	+	0.0707893i	$0.0225518\pi$
$620$	−231.112	+	133.538i	−0.372762	+	0.215384i
$621$	381.147	−	276.919i	0.613763	−	0.445925i
$622$	−642.673	−	677.570i	−1.03324	−	1.08934i
$623$	−57.9711	−	29.5377i	−0.0930515	−	0.0474121i
$624$	542.565	−	114.767i	0.869496	−	0.183922i
$625$	−419.754	−	463.068i	−0.671606	−	0.740908i
$626$	−652.703	+	850.185i	−1.04266	+	1.35812i
$627$	607.303	+	191.559i	0.968586	+	0.305517i
$628$	−64.1161	−	37.0596i	−0.102096	−	0.0590120i
$629$	87.2563	+	63.3954i	0.138722	+	0.100788i
$630$	−117.180	−	190.968i	−0.185999	−	0.303123i
$631$	181.799	−	59.0701i	0.288113	−	0.0936135i	−0.161395	−	0.986890i	$-0.551599\pi$
$631$	181.799	−	59.0701i	0.288113	−	0.0936135i	0.449508	+	0.893276i	$0.351599\pi$
$632$	553.726	+	339.887i	0.876149	+	0.537795i
$633$	−251.667	−	39.8601i	−0.397578	−	0.0629701i
$634$	−8.26042	+	23.3085i	−0.0130291	+	0.0367641i
$635$	−733.306	+	327.222i	−1.15481	+	0.515310i
$636$	−187.468	−	72.0681i	−0.294761	−	0.113315i
$637$	166.612	−	166.612i	0.261557	−	0.261557i
$638$	−687.799	+	912.053i	−1.07805	+	1.42955i
$639$	70.7661			0.110745
$640$	622.449	−	148.851i	0.972577	−	0.232580i
$641$	−168.963	+	520.014i	−0.263593	+	0.811255i	0.728422	+	0.685129i	$0.240254\pi$
$641$	−168.963	+	520.014i	−0.263593	+	0.811255i	−0.992014	+	0.126126i	$0.959746\pi$
$642$	−9.80869	+	4.67554i	−0.0152783	+	0.00728277i
$643$	−87.4537	−	13.8513i	−0.136009	−	0.0215417i	0.0880588	−	0.996115i	$-0.471934\pi$
$643$	−87.4537	−	13.8513i	−0.136009	−	0.0215417i	−0.224068	+	0.974574i	$0.571934\pi$
$644$	−291.066	−	235.938i	−0.451966	−	0.366364i
$645$	−227.124	−	844.819i	−0.352130	−	1.30980i
$646$	515.466	−	354.083i	0.797935	−	0.548117i
$647$	−512.994	+	81.2502i	−0.792881	+	0.125580i	−0.539720	−	0.841844i	$-0.681470\pi$
$647$	−512.994	+	81.2502i	−0.792881	+	0.125580i	−0.253160	+	0.967424i	$0.581470\pi$
$648$	231.175	−	95.5560i	0.356752	−	0.147463i
$649$	−79.4581	+	531.247i	−0.122432	+	0.818563i
$650$	555.528	+	525.677i	0.854658	+	0.808734i
$651$	141.807	+	103.029i	0.217830	+	0.158263i
$652$	−430.198	+	386.969i	−0.659813	+	0.593510i
$653$	404.694	+	206.202i	0.619747	+	0.315777i	0.735524	−	0.677499i	$-0.236936\pi$
$653$	404.694	+	206.202i	0.619747	+	0.315777i	−0.115778	+	0.993275i	$0.536936\pi$
$654$	−159.990	−	4.22892i	−0.244634	−	0.00646623i
$655$	−271.457	+	176.609i	−0.414439	+	0.269631i
$656$	853.382	−	945.902i	1.30089	−	1.44192i
$657$	−180.041	−	353.350i	−0.274035	−	0.537823i
$658$	−503.897	−	273.755i	−0.765802	−	0.416041i
$659$		−	513.775i		−	0.779628i	−0.920894	−	0.389814i	$-0.872539\pi$
$659$		−	513.775i		−	0.779628i	0.920894	−	0.389814i	$-0.127461\pi$
$660$	457.206	+	198.676i	0.692736	+	0.301024i
$661$	98.3245			0.148751			0.0743756	−	0.997230i	$-0.476304\pi$
$661$	98.3245			0.148751			0.0743756	+	0.997230i	$0.476304\pi$
$662$	−226.028	+	416.048i	−0.341432	+	0.628471i
$663$	377.973	−	192.587i	0.570095	−	0.290478i
$664$	494.540	+	39.2887i	0.744789	+	0.0591698i
$665$	153.337	−	724.362i	0.230581	−	1.08927i
$666$	1.80018	−	68.1054i	0.00270298	−	0.102260i
$667$	−380.954	+	747.665i	−0.571146	+	1.12094i
$668$	111.256	−	100.076i	0.166551	−	0.149815i
$669$	308.386	−	424.457i	0.460965	−	0.634464i
$670$	−46.9735	+	55.0644i	−0.0701097	+	0.0821857i
$671$	171.099	+	1023.17i	0.254990	+	1.52484i
$672$	−255.442	−	333.748i	−0.380122	−	0.496649i
$673$	−63.4796	−	400.795i	−0.0943234	−	0.595534i	−0.988896	−	0.148611i	$-0.952520\pi$
$673$	−63.4796	−	400.795i	−0.0943234	−	0.595534i	0.894572	−	0.446923i	$-0.147480\pi$
$674$	166.578	+	242.500i	0.247148	+	0.359793i
$675$	611.895	+	395.920i	0.906511	+	0.586547i
$676$	−201.912	−	163.670i	−0.298686	−	0.242115i
$677$	107.145	−	676.485i	0.158264	−	0.999239i	−0.772871	−	0.634564i	$-0.781180\pi$
$677$	107.145	−	676.485i	0.158264	−	0.999239i	0.931135	−	0.364676i	$-0.118820\pi$
$678$	−302.299	−	634.185i	−0.445869	−	0.935375i
$679$	281.236	+	91.3791i	0.414191	+	0.134579i
$680$	430.208	−	233.637i	0.632659	−	0.343584i
$681$			204.389i			0.300131i
$682$	293.563	+	5.23033i	0.430445	+	0.00766910i
$683$	522.218	+	522.218i	0.764595	+	0.764595i	0.977149	−	0.212555i	$-0.0681783\pi$
$683$	522.218	+	522.218i	0.764595	+	0.764595i	−0.212555	+	0.977149i	$0.568178\pi$
$684$	−368.720	−	141.747i	−0.539065	−	0.207232i
$685$	−687.861	+	306.943i	−1.00418	+	0.448092i
$686$	−703.713	−	249.393i	−1.02582	−	0.363546i
$687$	40.0948	−	253.148i	0.0583621	−	0.368484i
$688$	441.603	+	1153.81i	0.641864	+	1.67705i
$689$	104.742	+	322.361i	0.152020	+	0.467868i
$690$	356.123	+	85.2762i	0.516120	+	0.123589i
$691$	687.245	−	945.912i	0.994566	−	1.36890i	0.0659660	−	0.997822i	$-0.478987\pi$
$691$	687.245	−	945.912i	0.994566	−	1.36890i	0.928600	−	0.371081i	$-0.121013\pi$
$692$	−491.466	−	284.071i	−0.710211	−	0.410507i
$693$	2.12231	+	246.449i	0.00306249	+	0.355626i
$694$	−327.126	−	251.141i	−0.471363	−	0.361874i
$695$	519.546	−	642.681i	0.747549	−	0.924721i
$696$	−611.823	+	715.282i	−0.879056	+	1.02770i
$697$	442.412	−	868.283i	0.634738	−	1.24574i
$698$	−256.693	+	243.472i	−0.367754	+	0.348814i
$699$	−137.577	−	189.359i	−0.196820	−	0.270899i
$700$	178.464	−	551.462i	0.254949	−	0.787803i
$701$	241.466	+	78.4571i	0.344459	+	0.111922i	0.476137	−	0.879371i	$-0.342036\pi$
$701$	241.466	+	78.4571i	0.344459	+	0.111922i	−0.131678	+	0.991293i	$0.542036\pi$
$702$	−783.672	−	425.749i	−1.11634	−	0.606480i
$703$	159.200	−	159.200i	0.226457	−	0.226457i
$704$	−671.079	−	212.766i	−0.953237	−	0.302224i
$705$	559.719	+	28.8655i	0.793927	+	0.0409440i
$706$	−496.391	+	146.905i	−0.703103	+	0.208080i
$707$	209.992	+	412.132i	0.297018	+	0.582931i
$708$	−92.2361	+	432.888i	−0.130277	+	0.611424i
$709$	−104.083	−	143.258i	−0.146803	−	0.202057i	0.729283	−	0.684213i	$-0.239854\pi$
$709$	−104.083	−	143.258i	−0.146803	−	0.202057i	−0.876086	+	0.482156i	$0.839854\pi$
$710$	118.977	+	139.138i	0.167573	+	0.195969i
$711$	−97.0119	−	298.572i	−0.136444	−	0.419932i
$712$	−89.5284	+	6.97951i	−0.125742	+	0.00980268i
$713$	213.023	−	33.7395i	0.298770	−	0.0473205i
$714$	−255.006	−	195.772i	−0.357151	−	0.274191i
$715$	−225.410	−	810.541i	−0.315259	−	1.13362i
$716$	−641.684	+	171.600i	−0.896206	+	0.239665i
$717$	215.250	−	34.0923i	0.300210	−	0.0475486i
$718$	233.669	+	43.3675i	0.325444	+	0.0604005i
$719$	165.942	+	510.715i	0.230795	+	0.710314i	0.997651	+	0.0684951i	$0.0218197\pi$
$719$	165.942	+	510.715i	0.230795	+	0.710314i	−0.766857	+	0.641818i	$0.778180\pi$
$720$	−275.514	−	140.434i	−0.382659	−	0.195047i
$721$	−130.974	−	180.270i	−0.181656	−	0.250027i
$722$	−251.040	−	526.650i	−0.347701	−	0.729432i
$723$	148.700	+	291.841i	0.205671	+	0.403653i
$724$	159.273	+	61.2290i	0.219990	+	0.0845705i
$725$	−1291.21	−	133.535i	−1.78098	−	0.184186i
$726$	−318.220	−	446.578i	−0.438320	−	0.615122i
$727$	−311.604	+	311.604i	−0.428616	+	0.428616i	−0.888157	−	0.459541i	$-0.848014\pi$
$727$	−311.604	+	311.604i	−0.428616	+	0.428616i	0.459541	+	0.888157i	$0.348014\pi$
$728$	−166.089	+	689.567i	−0.228145	+	0.947208i
$729$	−680.375	−	221.067i	−0.933299	−	0.303247i
$730$	392.049	−	948.066i	0.537053	−	1.29872i
$731$	555.469	+	764.537i	0.759875	+	1.04588i
$732$	88.9298	+	850.137i	0.121489	+	1.16139i
$733$	281.430	−	552.338i	0.383943	−	0.753531i	−0.615457	−	0.788171i	$-0.711028\pi$
$733$	281.430	−	552.338i	0.383943	−	0.753531i	0.999400	+	0.0346400i	$0.0110285\pi$
$734$	474.353	+	690.552i	0.646257	+	0.940807i
$735$	173.551	−	18.3873i	0.236124	−	0.0250168i
$736$	−512.633	−	68.1315i	−0.696512	−	0.0925700i
$737$	75.5047	−	25.2538i	0.102449	−	0.0342657i
$738$	−610.320	+	80.1973i	−0.826992	+	0.108668i
$739$	570.920	−	785.804i	0.772558	−	1.06333i	−0.223506	−	0.974702i	$-0.571750\pi$
$739$	570.920	−	785.804i	0.772558	−	1.06333i	0.996064	−	0.0886324i	$-0.0282496\pi$
$740$	136.933	−	110.964i	0.185045	−	0.149951i
$741$	−273.640	−	842.178i	−0.369285	−	1.13654i
$742$	186.374	−	176.775i	0.251178	−	0.238242i
$743$	−53.6467	+	338.712i	−0.0722028	+	0.455870i	0.924926	+	0.380147i	$0.124127\pi$
$743$	−53.6467	+	338.712i	−0.0722028	+	0.455870i	−0.997129	+	0.0757234i	$0.975873\pi$
$744$	241.168	+	19.1596i	0.324151	+	0.0257522i
$745$	84.9029	−	221.732i	0.113964	−	0.297627i
$746$	335.379	+	1133.25i	0.449570	+	1.51910i
$747$	−169.500	−	169.500i	−0.226908	−	0.226908i
$748$	−537.985	−	23.8165i	−0.719231	−	0.0318403i
$749$		−	13.8975i		−	0.0185548i
$750$	75.2079	+	561.471i	0.100277	+	0.748628i
$751$	−183.845	−	59.7347i	−0.244800	−	0.0795402i	0.184047	−	0.982917i	$-0.441080\pi$
$751$	−183.845	−	59.7347i	−0.244800	−	0.0795402i	−0.428847	+	0.903377i	$0.641080\pi$
$752$	−790.450	+	40.6452i	−1.05113	+	0.0540494i
$753$	−35.3684	+	223.307i	−0.0469700	+	0.296557i
$754$	1587.94	+	41.9729i	2.10602	+	0.0556670i
$755$	5.77500	+	21.4809i	0.00764901	+	0.0284515i
$756$	−35.7060	+	674.952i	−0.0472302	+	0.892793i
$757$	−23.9273	−	151.071i	−0.0316080	−	0.199565i	0.966831	−	0.255417i	$-0.0822126\pi$
$757$	−23.9273	−	151.071i	−0.0316080	−	0.199565i	−0.998439	+	0.0558515i	$0.982213\pi$
$758$	850.135	−	111.709i	1.12155	−	0.147374i
$759$	−287.272	−	282.366i	−0.378487	−	0.372024i
$760$	−341.219	−	963.280i	−0.448972	−	1.26747i
$761$	388.289	−	534.434i	0.510236	−	0.702279i	−0.473723	−	0.880674i	$-0.657090\pi$
$761$	388.289	−	534.434i	0.510236	−	0.702279i	0.983959	+	0.178395i	$0.0570904\pi$
$762$	715.602	+	132.811i	0.939110	+	0.174293i
$763$	92.9304	−	182.386i	0.121796	−	0.239038i
$764$	−740.853	−	600.535i	−0.969703	−	0.786041i
$765$	−231.420	−	48.9881i	−0.302510	−	0.0640367i
$766$	−125.689	+	354.658i	−0.164085	+	0.463000i
$767$	665.545	−	339.112i	0.867725	−	0.442128i
$768$	−541.142	−	208.949i	−0.704612	−	0.272069i
$769$	13.4574			0.0174999			0.00874994	−	0.999962i	$-0.497215\pi$

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75740 - 0.954750i) q^{2} +(2.01897 - 1.02872i) q^{3} +(2.17690 + 3.35575i) q^{4} +(4.19108 - 2.72669i) q^{5} +(-4.53030 - 0.119746i) q^{6} +(2.63142 - 5.16446i) q^{7} +(-0.621782 - 7.97580i) q^{8} +(-2.27209 + 3.12726i) q^{9} +(-9.96871 + 0.790451i) q^{10} +(9.84371 + 4.90931i) q^{11} +(7.84722 + 4.53575i) q^{12} +(-2.39288 - 15.1080i) q^{13} +(-9.55523 + 6.56366i) q^{14} +(5.65667 - 9.81653i) q^{15} +(-6.52218 + 14.6103i) q^{16} +(-1.91459 + 12.0882i) q^{17} +(6.97872 - 3.32657i) q^{18} +(24.2978 + 7.89483i) q^{19} +(18.2737 + 8.12849i) q^{20} -13.1339i q^{21} +(-12.6122 - 18.0259i) q^{22} +(-11.4273 - 11.4273i) q^{23} +(-9.46019 - 15.4633i) q^{24} +(10.1303 - 22.8556i) q^{25} +(-10.2192 + 28.8355i) q^{26} +(-4.56045 + 28.7936i) q^{27} +(23.0590 - 2.41212i) q^{28} +(-16.0454 - 49.3826i) q^{29} +(-19.3134 + 11.8509i) q^{30} +(-7.84453 + 10.7971i) q^{31} +(25.4113 - 19.4491i) q^{32} +(24.9244 - 0.214638i) q^{33} +(14.9059 - 19.4159i) q^{34} +(-3.05338 - 28.8197i) q^{35} +(-15.4404 - 0.816824i) q^{36} +(4.00077 - 7.85195i) q^{37} +(-35.1633 - 37.0727i) q^{38} +(-20.3730 - 28.0411i) q^{39} +(-24.3535 - 31.7318i) q^{40} +(-75.7259 - 24.6048i) q^{41} +(-12.5396 + 23.0814i) q^{42} +(54.5989 - 54.5989i) q^{43} +(4.95437 + 43.7202i) q^{44} +(-0.995428 + 19.3019i) q^{45} +(9.17211 + 30.9925i) q^{46} +(22.4582 + 44.0767i) q^{47} +(1.86179 + 36.2072i) q^{48} +(9.05424 + 12.4621i) q^{49} +(-39.6243 + 30.4944i) q^{50} +(8.56986 + 26.3753i) q^{51} +(45.4898 - 40.9187i) q^{52} +(-21.8861 + 3.46642i) q^{53} +(35.5052 - 46.2477i) q^{54} +(54.6420 - 6.26545i) q^{55} +(-42.8269 - 17.7765i) q^{56} +(57.1780 - 9.05611i) q^{57} +(-18.9499 + 102.104i) q^{58} +(15.0901 + 46.4424i) q^{59} +(45.2559 - 2.38726i) q^{60} +(55.4322 + 76.2959i) q^{61} +(24.0945 - 11.4852i) q^{62} +(10.1718 + 19.9633i) q^{63} +(-63.2268 + 9.91841i) q^{64} +(-51.2237 - 56.7944i) q^{65} +(-44.0071 - 23.4194i) q^{66} +(5.11791 - 5.11791i) q^{67} +(-44.7330 + 19.8900i) q^{68} +(-34.8268 - 11.3159i) q^{69} +(-22.1496 + 53.5630i) q^{70} +(-10.7606 - 14.8107i) q^{71} +(26.3552 + 16.1773i) q^{72} +(-46.5762 + 91.4110i) q^{73} +(-14.5276 + 9.97927i) q^{74} +(-3.05911 - 56.5659i) q^{75} +(26.4008 + 98.7237i) q^{76} +(51.2569 - 37.9190i) q^{77} +(9.03133 + 68.7305i) q^{78} +(-47.7369 + 65.7043i) q^{79} +(12.5028 + 79.0170i) q^{80} +(9.66242 + 29.7379i) q^{81} +(109.589 + 115.540i) q^{82} +(-9.70086 + 61.2488i) q^{83} +(44.0740 - 28.5912i) q^{84} +(24.9367 + 55.8832i) q^{85} +(-148.080 + 43.8237i) q^{86} +(-83.1957 - 83.1957i) q^{87} +(33.0350 - 81.5640i) q^{88} -11.2250i q^{89} +(20.1779 - 32.9708i) q^{90} +(-84.3215 - 27.3977i) q^{91} +(13.4711 - 63.2234i) q^{92} +(-4.73074 + 29.8687i) q^{93} +(2.61421 - 98.9023i) q^{94} +(123.361 - 33.1647i) q^{95} +(31.2970 - 65.4081i) q^{96} +(7.98092 + 50.3895i) q^{97} +(-4.01373 - 30.5454i) q^{98} +(-37.7185 + 19.6295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

L-functions

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