LMFDB - Embedded newform 220.3.w.a.7.19

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			7.19
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37635 + 1.45109i) q^{2} +(-2.01897 + 1.02872i) q^{3} +(-0.211311 - 3.99441i) q^{4} +(4.19108 - 2.72669i) q^{5} +(1.28605 - 4.34558i) q^{6} +(-2.63142 + 5.16446i) q^{7} +(6.08708 + 5.19109i) q^{8} +(-2.27209 + 3.12726i) q^{9} +(-1.81173 + 9.83451i) q^{10} +(-9.84371 - 4.90931i) q^{11} +(4.53575 + 7.84722i) q^{12} +(-2.39288 - 15.1080i) q^{13} +(-3.87232 - 10.9265i) q^{14} +(-5.65667 + 9.81653i) q^{15} +(-15.9107 + 1.68813i) q^{16} +(-1.91459 + 12.0882i) q^{17} +(-1.41074 - 7.60122i) q^{18} +(-24.2978 - 7.89483i) q^{19} +(-11.7772 - 16.1647i) q^{20} -13.1339i q^{21} +(20.6723 - 7.52715i) q^{22} +(11.4273 + 11.4273i) q^{23} +(-17.6298 - 4.21877i) q^{24} +(10.1303 - 22.8556i) q^{25} +(25.2165 + 17.3217i) q^{26} +(4.56045 - 28.7936i) q^{27} +(21.1850 + 9.41969i) q^{28} +(-16.0454 - 49.3826i) q^{29} +(-6.45909 - 21.7193i) q^{30} +(7.84453 - 10.7971i) q^{31} +(19.4491 - 25.4113i) q^{32} +(24.9244 - 0.214638i) q^{33} +(-14.9059 - 19.4159i) q^{34} +(3.05338 + 28.8197i) q^{35} +(12.9717 + 8.41484i) q^{36} +(4.00077 - 7.85195i) q^{37} +(44.8984 - 24.3922i) q^{38} +(20.3730 + 28.0411i) q^{39} +(39.6660 + 5.15867i) q^{40} +(-75.7259 - 24.6048i) q^{41} +(19.0584 + 18.0768i) q^{42} +(-54.5989 + 54.5989i) q^{43} +(-17.5297 + 40.3573i) q^{44} +(-0.995428 + 19.3019i) q^{45} +(-32.3100 + 0.854028i) q^{46} +(-22.4582 - 44.0767i) q^{47} +(30.3866 - 19.7759i) q^{48} +(9.05424 + 12.4621i) q^{49} +(19.2226 + 46.1573i) q^{50} +(-8.56986 - 26.3753i) q^{51} +(-59.8422 + 12.7506i) 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} +(93.7425 + 44.6846i) q^{58} +(-15.0901 - 46.4424i) q^{59} +(40.4066 + 20.5207i) q^{60} +(55.4322 + 76.2959i) q^{61} +(4.87066 + 26.2437i) q^{62} +(-10.1718 - 19.9633i) q^{63} +(10.1052 + 63.1972i) q^{64} +(-51.2237 - 56.7944i) q^{65} +(-33.9933 + 36.4630i) q^{66} +(-5.11791 + 5.11791i) q^{67} +(48.6899 + 5.09328i) q^{68} +(-34.8268 - 11.3159i) q^{69} +(-46.0225 - 35.2354i) q^{70} +(10.7606 + 14.8107i) q^{71} +(-30.0643 + 7.24129i) q^{72} +(-46.5762 + 91.4110i) q^{73} +(5.88740 + 16.6125i) q^{74} +(3.05911 + 56.5659i) q^{75} +(-26.4008 + 98.7237i) q^{76} +(51.2569 - 37.9190i) q^{77} +(-68.7305 - 9.03133i) q^{78} +(47.7369 - 65.7043i) q^{79} +(-62.0800 + 50.4586i) q^{80} +(9.66242 + 29.7379i) q^{81} +(139.929 - 76.0200i) q^{82} +(9.70086 - 61.2488i) q^{83} +(-52.4621 + 2.77533i) q^{84} +(24.9367 + 55.8832i) q^{85} +(-4.08049 - 154.375i) q^{86} +(83.1957 + 83.1957i) q^{87} +(-34.4348 - 80.9830i) q^{88} -11.2250i q^{89} +(-26.6387 - 28.0107i) q^{90} +(84.3215 + 27.3977i) q^{91} +(43.2307 - 48.0601i) q^{92} +(-4.73074 + 29.8687i) q^{93} +(94.8695 + 28.0762i) q^{94} +(-123.361 + 33.1647i) q^{95} +(-13.1261 + 71.3121i) q^{96} +(7.98092 + 50.3895i) q^{97} +(-30.5454 - 4.01373i) 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 $

$2$	−1.37635	+	1.45109i	−0.688176	+	0.725544i
$2$	−1.37635	+	1.45109i	−0.688176	+	0.725544i
$3$	−2.01897	+	1.02872i	−0.672990	+	0.342905i	−0.756865	−	0.653571i	$-0.773270\pi$
$3$	−2.01897	+	1.02872i	−0.672990	+	0.342905i	0.0838758	+	0.996476i	$0.473270\pi$
$4$	−0.211311	−	3.99441i	−0.0528277	−	0.998604i
$5$	4.19108	−	2.72669i	0.838216	−	0.545338i
$5$	4.19108	−	2.72669i	0.838216	−	0.545338i
$6$	1.28605	−	4.34558i	0.214342	−	0.724263i
$7$	−2.63142	+	5.16446i	−0.375918	+	0.737780i	−0.999015	−	0.0443641i	$-0.985874\pi$
$7$	−2.63142	+	5.16446i	−0.375918	+	0.737780i	0.623098	+	0.782144i	$0.285874\pi$
$8$	6.08708	+	5.19109i	0.760885	+	0.648886i
$9$	−2.27209	+	3.12726i	−0.252454	+	0.347474i
$10$	−1.81173	+	9.83451i	−0.181173	+	0.983451i
$11$	−9.84371	−	4.90931i	−0.894883	−	0.446301i
$11$	−9.84371	−	4.90931i	−0.894883	−	0.446301i
$12$	4.53575	+	7.84722i	0.377979	+	0.653935i
$13$	−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	$-0.250211\pi$
$14$	−3.87232	−	10.9265i	−0.276594	−	0.780467i
$15$	−5.65667	+	9.81653i	−0.377111	+	0.654436i
$16$	−15.9107	+	1.68813i	−0.994418	+	0.105508i
$17$	−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	$0.932788\pi$
$18$	−1.41074	−	7.60122i	−0.0783743	−	0.422290i
$19$	−24.2978	−	7.89483i	−1.27883	−	0.415517i	−0.410663	−	0.911787i	$-0.634703\pi$
$19$	−24.2978	−	7.89483i	−1.27883	−	0.415517i	−0.868168	+	0.496270i	$0.834703\pi$
$20$	−11.7772	−	16.1647i	−0.588858	−	0.808237i
$21$		−	13.1339i		−	0.625422i
$22$	20.6723	−	7.52715i	0.939648	−	0.342143i
$23$	11.4273	+	11.4273i	0.496839	+	0.496839i	0.910453	−	0.413613i	$-0.135733\pi$
$23$	11.4273	+	11.4273i	0.496839	+	0.496839i	−0.413613	+	0.910453i	$0.635733\pi$
$24$	−17.6298	−	4.21877i	−0.734574	−	0.175782i
$25$	10.1303	−	22.8556i	0.405212	−	0.914223i
$26$	25.2165	+	17.3217i	0.969867	+	0.666220i
$27$	4.56045	−	28.7936i	0.168906	−	1.06643i
$28$	21.1850	+	9.41969i	0.756608	+	0.336417i
$29$	−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	$-0.452996\pi$
$30$	−6.45909	−	21.7193i	−0.215303	−	0.723978i
$31$	7.84453	−	10.7971i	0.253049	−	0.348292i	−0.663527	−	0.748152i	$-0.730941\pi$
$31$	7.84453	−	10.7971i	0.253049	−	0.348292i	0.916576	+	0.399860i	$0.130941\pi$
$32$	19.4491	−	25.4113i	0.607784	−	0.794102i
$33$	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
$36$	12.9717	+	8.41484i	0.360325	+	0.233746i
$37$	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	$0.112003\pi$
$38$	44.8984	−	24.3922i	1.18154	−	0.641899i
$39$	20.3730	+	28.0411i	0.522385	+	0.719002i
$40$	39.6660	+	5.15867i	0.991649	+	0.128967i
$41$	−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	$-0.823169\pi$
$42$	19.0584	+	18.0768i	0.453771	+	0.430400i
$43$	−54.5989	+	54.5989i	−1.26974	+	1.26974i	−0.323519	+	0.946222i	$0.604866\pi$
$43$	−54.5989	+	54.5989i	−1.26974	+	1.26974i	−0.946222	+	0.323519i	$0.895134\pi$
$44$	−17.5297	+	40.3573i	−0.398403	+	0.917210i
$45$	−0.995428	+	19.3019i	−0.0221206	+	0.428931i
$46$	−32.3100	+	0.854028i	−0.702391	+	0.0185658i
$47$	−22.4582	−	44.0767i	−0.477834	−	0.937802i	−0.996561	−	0.0828618i	$-0.973594\pi$
$47$	−22.4582	−	44.0767i	−0.477834	−	0.937802i	0.518727	−	0.854940i	$-0.326406\pi$
$48$	30.3866	−	19.7759i	0.633054	−	0.411997i
$49$	9.05424	+	12.4621i	0.184780	+	0.254328i
$50$	19.2226	+	46.1573i	0.384451	+	0.923145i
$51$	−8.56986	−	26.3753i	−0.168036	−	0.517163i
$52$	−59.8422	+	12.7506i	−1.15081	+	0.245205i
$53$	−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
$58$	93.7425	+	44.6846i	1.61625	+	0.770423i
$59$	−15.0901	−	46.4424i	−0.255764	−	0.787159i	−0.993678	−	0.112265i	$-0.964189\pi$
$59$	−15.0901	−	46.4424i	−0.255764	−	0.787159i	0.737915	−	0.674894i	$-0.235811\pi$
$60$	40.4066	+	20.5207i	0.673444	+	0.342012i
$61$	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	$0.518751\pi$
$62$	4.87066	+	26.2437i	0.0785590	+	0.423285i
$63$	−10.1718	−	19.9633i	−0.161457	−	0.316877i
$64$	10.1052	+	63.1972i	0.157893	+	0.987456i
$65$	−51.2237	−	56.7944i	−0.788057	−	0.873760i
$66$	−33.9933	+	36.4630i	−0.515050	+	0.552469i
$67$	−5.11791	+	5.11791i	−0.0763867	+	0.0763867i	−0.744268	−	0.667881i	$-0.767201\pi$
$67$	−5.11791	+	5.11791i	−0.0763867	+	0.0763867i	0.667881	+	0.744268i	$0.267201\pi$
$68$	48.6899	+	5.09328i	0.716029	+	0.0749012i
$69$	−34.8268	−	11.3159i	−0.504736	−	0.163999i
$70$	−46.0225	−	35.2354i	−0.657464	−	0.503363i
$71$	10.7606	+	14.8107i	0.151558	+	0.208602i	0.878044	−	0.478579i	$-0.158848\pi$
$71$	10.7606	+	14.8107i	0.151558	+	0.208602i	−0.726486	+	0.687181i	$0.758848\pi$
$72$	−30.0643	+	7.24129i	−0.417560	+	0.100573i
$73$	−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	$0.901982\pi$
$74$	5.88740	+	16.6125i	0.0795595	+	0.224493i
$75$	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
$78$	−68.7305	−	9.03133i	−0.881161	−	0.115786i
$79$	47.7369	−	65.7043i	0.604265	−	0.831700i	−0.391825	−	0.920040i	$-0.628156\pi$
$79$	47.7369	−	65.7043i	0.604265	−	0.831700i	0.996090	+	0.0883400i	$0.0281562\pi$
$80$	−62.0800	+	50.4586i	−0.776000	+	0.630733i
$81$	9.66242	+	29.7379i	0.119289	+	0.367134i
$82$	139.929	−	76.0200i	1.70645	−	0.927073i
$83$	9.70086	−	61.2488i	0.116878	−	0.737937i	−0.857744	−	0.514078i	$-0.828134\pi$
$83$	9.70086	−	61.2488i	0.116878	−	0.737937i	0.974621	−	0.223860i	$-0.0718657\pi$
$84$	−52.4621	+	2.77533i	−0.624549	+	0.0330396i
$85$	24.9367	+	55.8832i	0.293373	+	0.657449i
$86$	−4.08049	−	154.375i	−0.0474475	−	1.79506i
$87$	83.1957	+	83.1957i	0.956273	+	0.956273i
$88$	−34.4348	−	80.9830i	−0.391305	−	0.920261i
$89$		−	11.2250i		−	0.126124i	−0.998010	−	0.0630619i	$-0.979913\pi$
$89$		−	11.2250i		−	0.126124i	0.998010	−	0.0630619i	$-0.0200865\pi$
$90$	−26.6387	−	28.0107i	−0.295985	−	0.311230i
$91$	84.3215	+	27.3977i	0.926610	+	0.301074i
$92$	43.2307	−	48.0601i	0.469899	−	0.522392i
$93$	−4.73074	+	29.8687i	−0.0508682	+	0.321169i
$94$	94.8695	+	28.0762i	1.00925	+	0.298683i
$95$	−123.361	+	33.1647i	−1.29853	+	0.349102i
$96$	−13.1261	+	71.3121i	−0.136731	+	0.742835i
$97$	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	$0.865295\pi$
$98$	−30.5454	−	4.01373i	−0.311688	−	0.0409564i
$99$	37.7185	−	19.6295i	0.380995	−	0.198278i
$100$	−93.4352	−	35.6350i	−0.934352	−	0.356350i
$101$	−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	$0.329275\pi$
$102$	50.0680	+	23.8661i	0.490863	+	0.233981i
$103$	−17.4529	+	34.2533i	−0.169446	+	0.332556i	−0.960077	−	0.279737i	$-0.909753\pi$
$103$	−17.4529	+	34.2533i	−0.169446	+	0.332556i	0.790631	+	0.612293i	$0.209753\pi$
$104$	63.8616	−	104.386i	0.614053	−	1.00371i
$105$	−35.8120	−	55.0451i	−0.341067	−	0.524239i
$106$	25.0929	−	36.5297i	0.236725	−	0.344619i
$107$	−2.13636	+	1.08853i	−0.0199660	+	0.0101732i	−0.463945	−	0.885864i	$-0.653566\pi$
$107$	−2.13636	+	1.08853i	−0.0199660	+	0.0101732i	0.443979	+	0.896037i	$0.353566\pi$
$108$	−115.977	−	12.1320i	−1.07386	−	0.112333i
$109$	35.3156			0.323997			0.161998	−	0.986791i	$-0.448206\pi$
$109$	35.3156			0.323997			0.161998	+	0.986791i	$0.448206\pi$
$110$	66.1149	−	87.9137i	0.601044	−	0.799216i
$111$			19.9685i			0.179896i
$112$	33.1495	−	86.6123i	0.295978	−	0.773324i
$113$	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	$0.609389\pi$
$114$	−65.5559	+	95.4347i	−0.575051	+	0.837147i
$115$	79.0515	+	16.7340i	0.687404	+	0.145513i
$116$	−193.864	+	74.5269i	−1.67124	+	0.642473i
$117$	52.6837	+	26.8437i	0.450288	+	0.229433i
$118$	88.1612	+	42.0241i	0.747129	+	0.356136i
$119$	−57.3910	−	41.6970i	−0.482278	−	0.350395i
$120$	−85.3911	+	30.3898i	−0.711593	+	0.253248i
$121$	72.7973	+	96.6517i	0.601631	+	0.798774i
$122$	−187.006	−	24.5730i	−1.53284	−	0.201418i
$123$	178.200	−	28.2240i	1.44878	−	0.229464i
$124$	−44.7856	−	29.0528i	−0.361174	−	0.234296i
$125$	−19.8632	−	123.412i	−0.158905	−	0.987294i
$126$	42.9684	+	12.7163i	0.341019	+	0.100923i
$127$	158.623	+	25.1234i	1.24900	+	0.197822i	0.745696	−	0.666286i	$-0.232117\pi$
$127$	158.623	+	25.1234i	1.24900	+	0.197822i	0.503305	+	0.864109i	$0.332117\pi$
$128$	−105.613	−	72.3181i	−0.825101	−	0.564985i
$129$	54.0667	−	166.400i	0.419121	−	1.28992i
$130$	152.916	+	3.83894i	1.17627	+	0.0295303i
$131$	64.7703			0.494430			0.247215	−	0.968961i	$-0.420485\pi$
$131$	64.7703			0.494430			0.247215	+	0.968961i	$0.420485\pi$
$132$	−6.12415	−	99.5132i	−0.0463951	−	0.753888i
$133$	104.710	−	104.710i	0.787295	−	0.787295i
$134$	−0.382491	−	14.4706i	−0.00285441	−	0.107989i
$135$	−59.3980	−	133.111i	−0.439985	−	0.986008i
$136$	−74.4053	+	63.6432i	−0.547098	+	0.467965i
$137$	−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	$0.735299\pi$
$138$	64.3543	−	34.9621i	0.466336	−	0.253348i
$139$	−157.194	+	51.0755i	−1.13089	+	0.367449i	−0.813915	−	0.580984i	$-0.802668\pi$
$139$	−157.194	+	51.0755i	−1.13089	+	0.367449i	−0.316978	+	0.948433i	$0.602668\pi$
$140$	114.473	−	18.2864i	0.817663	−	0.130617i
$141$	90.6847	+	65.8863i	0.643154	+	0.467279i
$142$	−36.3021	−	4.77016i	−0.255648	−	0.0335927i
$143$	−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
$146$	−68.5401	−	193.400i	−0.469452	−	1.32466i
$147$	−31.1002	−	15.8463i	−0.211566	−	0.107798i
$148$	−32.2093	−	14.3215i	−0.217631	−	0.0967670i
$149$	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	$0.249060\pi$
$150$	−86.2925	−	73.4155i	−0.575283	−	0.489437i
$151$	1.37473	−	4.23100i	0.00910420	−	0.0280198i	−0.946401	−	0.322993i	$-0.895311\pi$
$151$	1.37473	−	4.23100i	0.00910420	−	0.0280198i	0.955505	+	0.294974i	$0.0953108\pi$
$152$	−106.920	−	174.189i	−0.703421	−	1.14598i
$153$	−33.4529	−	33.4529i	−0.218647	−	0.218647i
$154$	−15.5238	+	126.568i	−0.100804	+	0.821871i
$155$	3.43678	−	66.6410i	0.0221727	−	0.429942i
$156$	107.703	−	87.3037i	0.690402	−	0.559639i
$157$	−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	$0.368779\pi$
$158$	29.6398	+	159.703i	0.187594	+	1.01078i
$159$	40.6214	−	29.5132i	0.255480	−	0.185617i
$160$	12.2240	−	159.532i	0.0764002	−	0.997077i
$161$	−89.0859	+	28.9458i	−0.553328	+	0.179787i
$162$	−56.4511	−	26.9088i	−0.348464	−	0.166103i
$163$	−22.6295	−	142.877i	−0.138831	−	0.876546i	−0.954540	−	0.298083i	$-0.903653\pi$
$163$	−22.6295	−	142.877i	−0.138831	−	0.876546i	0.815709	−	0.578463i	$-0.196347\pi$
$164$	−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	0.998995	−	0.0448205i	$-0.0142716\pi$
$167$	5.85235	+	36.9503i	0.0350440	+	0.221259i	−0.963951	+	0.266080i	$0.914272\pi$
$168$	68.1791	−	79.9469i	0.405828	−	0.475875i
$169$	−61.7986	+	20.0796i	−0.365672	+	0.118814i
$170$	−115.413	−	40.7297i	−0.678900	−	0.239586i
$171$	79.8960	−	58.0478i	0.467228	−	0.339461i
$172$	229.628	+	206.553i	1.33505	+	1.20089i
$173$	−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	$0.484526\pi$
$174$	−235.231	+	6.21769i	−1.35190	+	0.0357339i
$175$	91.3795	+	112.460i	0.522169	+	0.642630i
$176$	164.908	+	61.4931i	0.936976	+	0.349393i
$177$	78.2424	+	78.2424i	0.442047	+	0.442047i
$178$	16.2885	+	15.4496i	0.0915083	+	0.0867953i
$179$	51.3148	−	157.931i	0.286675	−	0.882294i	−0.699217	−	0.714909i	$-0.746468\pi$
$179$	51.3148	−	157.931i	0.286675	−	0.882294i	0.985892	−	0.167384i	$-0.0535321\pi$
$180$	77.3101	−	0.102547i	0.429501	−	0.000569705i
$181$	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	$0.262402\pi$
$182$	−155.813	+	84.6490i	−0.856113	+	0.465105i
$183$	−190.403	−	97.0150i	−1.04045	−	0.530137i
$184$	10.2388	+	128.879i	0.0556456	+	0.700430i
$185$	−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
$188$	−171.315	+	99.0212i	−0.911249	+	0.526708i
$189$	136.703	+	99.3203i	0.723295	+	0.525504i
$190$	121.663	−	224.654i	0.640331	−	1.18239i
$191$	226.751	−	73.6758i	1.18718	−	0.385737i	0.352149	−	0.935944i	$-0.385451\pi$
$191$	226.751	−	73.6758i	1.18718	−	0.385737i	0.835029	+	0.550207i	$0.185451\pi$
$192$	−85.4140	−	117.198i	−0.444865	−	0.610405i
$193$	−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	$0.588595\pi$
$194$	−84.1042	−	57.7727i	−0.433527	−	0.297798i
$195$	161.844	+	61.9714i	0.829971	+	0.317802i
$196$	47.8655	−	38.7997i	0.244212	−	0.197958i
$197$	−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	$0.360019\pi$
$198$	−23.4298	+	81.7499i	−0.118333	+	0.412878i
$199$	−335.923			−1.68806			−0.844028	−	0.536299i	$-0.819822\pi$
$199$	−335.923			−1.68806			−0.844028	+	0.536299i	$0.819822\pi$
$200$	180.309	−	86.5364i	0.901547	−	0.432682i
$201$	5.06802	−	15.5978i	0.0252141	−	0.0776009i
$202$	−29.1240	−	156.923i	−0.144178	−	0.776849i
$203$	297.256	+	47.0808i	1.46432	+	0.231925i
$204$	−103.543	+	39.8049i	−0.507564	+	0.195122i
$205$	−384.463	+	103.360i	−1.87543	+	0.504197i
$206$	−25.6832	−	72.4703i	−0.124676	−	0.351797i
$207$	−61.7000	+	9.77232i	−0.298068	+	0.0472093i
$208$	63.5767	+	236.340i	0.305657	+	1.13625i
$209$	200.422	+	197.000i	0.958958	+	0.942583i
$210$	129.165	+	23.7951i	0.615072	+	0.113310i
$211$	90.9735	+	66.0961i	0.431154	+	0.313252i	0.782110	−	0.623140i	$-0.214143\pi$
$211$	90.9735	+	66.0961i	0.431154	+	0.313252i	−0.350956	+	0.936392i	$0.614143\pi$
$212$	18.4711	+	86.6896i	0.0871277	+	0.408913i
$213$	−36.9614	−	18.8328i	−0.173528	−	0.0884167i
$214$	1.36083	−	4.59824i	0.00635902	−	0.0214871i
$215$	−79.9539	+	377.702i	−0.371879	+	1.75676i
$216$	177.230	−	151.595i	0.820509	−	0.701830i
$217$	35.1187	+	68.9244i	0.161837	+	0.317624i
$218$	−48.6068	+	51.2461i	−0.222967	+	0.235074i
$219$		−	232.470i		−	1.06150i
$220$	36.5732	+	216.939i	0.166242	+	0.986085i
$221$	187.211			0.847108
$222$	−28.9760	−	27.4837i	−0.130523	−	0.123800i
$223$	−206.304	+	105.117i	−0.925131	+	0.471378i	−0.850584	−	0.525840i	$-0.823751\pi$
$223$	−206.304	+	105.117i	−0.925131	+	0.471378i	−0.0745471	+	0.997217i	$0.523751\pi$
$224$	80.0566	+	167.312i	0.357396	+	0.746928i
$225$	48.4584	+	83.6100i	0.215371	+	0.371600i
$226$	−297.301	−	87.9850i	−1.31549	−	0.389314i
$227$	40.9502	−	80.3693i	0.180397	−	0.354050i	−0.783045	−	0.621965i	$-0.786335\pi$
$227$	40.9502	−	80.3693i	0.180397	−	0.354050i	0.963443	+	0.267915i	$0.0863347\pi$
$228$	−48.2562	−	226.479i	−0.211650	−	0.993329i
$229$	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	$0.120566\pi$
$230$	−133.085	+	91.6787i	−0.578631	+	0.398603i
$231$	−64.4782	+	129.286i	−0.279127	+	0.559680i
$232$	158.680	−	383.889i	0.683965	−	1.65469i
$233$	−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	$-0.121148\pi$
$234$	−111.464	+	39.5023i	−0.476341	+	0.168813i
$235$	−214.308	−	123.492i	−0.911947	−	0.525499i
$236$	−182.322	+	70.0897i	−0.772549	+	0.296990i
$237$	−28.7884	+	181.763i	−0.121470	+	0.766931i
$238$	139.496	−	25.8896i	0.586119	−	0.108780i
$239$	−91.4706	−	29.7206i	−0.382722	−	0.124354i	0.111336	−	0.993783i	$-0.464487\pi$
$239$	−91.4706	−	29.7206i	−0.382722	−	0.124354i	−0.494058	+	0.869429i	$0.664487\pi$
$240$	73.4300	−	165.737i	0.305958	−	0.690571i
$241$			144.550i			0.599791i	0.953972	+	0.299895i	$0.0969518\pi$
$241$			144.550i			0.599791i	−0.953972	+	0.299895i	$0.903048\pi$
$242$	−240.445	−	27.3914i	−0.993574	−	0.113188i
$243$	135.425	+	135.425i	0.557306	+	0.557306i
$244$	293.044	−	237.541i	1.20100	−	0.973531i
$245$	71.9273	+	27.5415i	0.293581	+	0.112414i
$246$	−204.310	+	297.429i	−0.830527	+	1.20906i
$247$	−61.1338	+	385.984i	−0.247505	+	1.56269i
$248$	103.799	−	25.0010i	0.418544	−	0.100810i
$249$	43.4219	+	133.639i	0.174385	+	0.536702i
$250$	206.420	+	141.035i	0.825680	+	0.564139i
$251$	58.6480	−	80.7220i	0.233657	−	0.321602i	−0.676047	−	0.736859i	$-0.736308\pi$
$251$	58.6480	−	80.7220i	0.233657	−	0.321602i	0.909704	+	0.415257i	$0.136308\pi$
$252$	−77.5921	+	44.8488i	−0.307905	+	0.177971i
$253$	−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
$256$	250.300	−	53.7185i	0.977736	−	0.209838i
$257$	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	$-0.0899475\pi$
$258$	167.046	+	307.481i	0.647466	+	1.19178i
$259$	30.0233	+	41.3236i	0.115920	+	0.159551i
$260$	−216.036	+	216.610i	−0.830908	+	0.833116i
$261$	190.889	+	62.0235i	0.731375	+	0.237638i
$262$	−89.1467	+	93.9874i	−0.340255	+	0.358730i
$263$	−145.248	+	145.248i	−0.552275	+	0.552275i	−0.927097	−	0.374822i	$-0.877704\pi$
$263$	−145.248	+	145.248i	−0.552275	+	0.552275i	0.374822	+	0.927097i	$0.377704\pi$
$264$	152.831	+	128.078i	0.578906	+	0.485146i
$265$	−82.2745	+	74.2047i	−0.310470	+	0.280018i
$266$	7.82560	+	296.062i	0.0294196	+	1.11302i
$267$	11.5473	+	22.6629i	0.0432485	+	0.0848799i
$268$	21.5245	+	19.3616i	0.0803154	+	0.0722447i
$269$	−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	$0.888943\pi$
$270$	274.908	+	97.0161i	1.01818	+	0.359319i
$271$	−117.527	−	361.712i	−0.433680	−	1.33473i	−0.894433	−	0.447202i	$-0.852421\pi$
$271$	−117.527	−	361.712i	−0.433680	−	1.33473i	0.460753	−	0.887528i	$-0.347579\pi$
$272$	10.0560	−	195.564i	0.0369704	−	0.718986i
$273$	−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	$0.460822\pi$
$278$	142.239	−	298.400i	0.511653	−	1.07338i
$279$	15.9418	+	49.0638i	0.0571390	+	0.175856i
$280$	−131.020	+	191.279i	−0.467927	+	0.683138i
$281$	−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	$-0.438934\pi$
$282$	−220.421	+	40.9087i	−0.781635	+	0.145066i
$283$	201.552	+	395.568i	0.712197	+	1.39777i	0.908779	+	0.417278i	$0.137016\pi$
$283$	201.552	+	395.568i	0.712197	+	1.39777i	−0.196582	+	0.980487i	$0.562984\pi$
$284$	56.8863	−	46.1120i	0.200304	−	0.162366i
$285$	214.944	−	193.862i	0.754191	−	0.680216i
$286$	−163.187	−	294.306i	−0.570583	−	1.02904i
$287$	326.337	−	326.337i	1.13706	−	1.13706i
$288$	35.2776	+	118.559i	0.122492	+	0.411664i
$289$	132.396	+	43.0180i	0.458117	+	0.148851i
$290$	514.723	−	68.3303i	1.77491	−	0.235622i
$291$	−67.9498	−	93.5248i	−0.233504	−	0.321391i
$292$	374.975	+	166.729i	1.28416	+	0.570988i
$293$	−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	$0.263364\pi$
$294$	65.7992	−	23.3189i	0.223807	−	0.0793161i
$295$	−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
$298$	−12.3732	+	94.1631i	−0.0415209	+	0.315984i
$299$	145.300	−	199.988i	0.485953	−	0.668857i
$300$	225.301	−	24.1723i	0.751004	−	0.0805745i
$301$	−138.301	−	425.646i	−0.459471	−	1.41411i
$302$	4.24743	+	7.81820i	0.0140643	+	0.0258881i
$303$	28.2874	−	178.600i	0.0933577	−	0.589437i
$304$	399.922	+	84.5945i	1.31553	+	0.278271i
$305$	440.356	+	168.616i	1.44379	+	0.552838i
$306$	94.5862	−	2.50013i	0.309105	−	0.00817036i
$307$	197.102	+	197.102i	0.642027	+	0.642027i	0.951054	−	0.309026i	$-0.100003\pi$
$307$	197.102	+	197.102i	0.642027	+	0.642027i	−0.309026	+	0.951054i	$0.600003\pi$
$308$	−162.295	−	196.729i	−0.526932	−	0.638729i
$309$		−	87.1104i		−	0.281911i
$310$	91.9717	+	96.7085i	0.296683	+	0.311963i
$311$	−444.086	−	144.292i	−1.42793	−	0.463962i	−0.509816	−	0.860283i	$-0.670287\pi$
$311$	−444.086	−	144.292i	−1.42793	−	0.463962i	−0.918112	+	0.396322i	$0.870287\pi$
$312$	−21.5514	+	276.447i	−0.0690749	+	0.886047i
$313$	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	$-0.277119\pi$
$314$	10.5078	−	35.5057i	0.0334642	−	0.113076i
$315$	−97.0645	−	55.9323i	−0.308141	−	0.177563i
$316$	−272.537	−	176.797i	−0.862460	−	0.559485i
$317$	−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	$0.956208\pi$
$318$	−13.0831	+	99.5657i	−0.0411419	+	0.313100i
$319$	−84.4884	+	564.879i	−0.264854	+	1.77078i
$320$	214.671	+	237.311i	0.670846	+	0.741596i
$321$	3.19345	−	4.39541i	0.00994845	−	0.0136929i
$322$	80.6107	−	169.111i	0.250344	−	0.525189i
$323$	141.955	−	278.602i	0.439488	−	0.862544i
$324$	116.744	−	44.8796i	0.360320	−	0.138517i
$325$	−369.544	−	98.3585i	−1.13706	−	0.302642i
$326$	238.473	+	163.812i	0.731513	+	0.502490i
$327$	−71.3012	+	36.3298i	−0.218046	+	0.111100i
$328$	−333.224	−	542.871i	−1.01593	−	1.65510i
$329$	286.729			0.871517
$330$	−43.0455	+	245.508i	−0.130441	+	0.743965i
$331$			236.741i			0.715229i	0.933869	+	0.357614i	$0.116410\pi$
$331$			236.741i			0.715229i	−0.933869	+	0.357614i	$0.883590\pi$
$332$	−246.703	−	25.8067i	−0.743081	−	0.0777311i
$333$	15.4650	+	30.3518i	0.0464415	+	0.0911465i
$334$	−61.6730	−	42.3643i	−0.184650	−	0.126839i
$335$	−7.49461	+	35.4045i	−0.0223720	+	0.105685i
$336$	22.1716	+	208.969i	0.0659870	+	0.621931i
$337$	−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	$0.720035\pi$
$338$	55.9194	−	117.312i	0.165442	−	0.347076i
$339$	−284.187	−	206.474i	−0.838310	−	0.609068i
$340$	217.951	−	111.416i	0.641033	−	0.327694i
$341$	−130.225	+	67.7720i	−0.381893	+	0.198745i
$342$	−25.7325	+	195.830i	−0.0752412	+	0.572603i
$343$	−368.703	+	58.3968i	−1.07494	+	0.170253i
$344$	−615.775	+	48.9202i	−1.79004	+	0.142210i
$345$	−176.817	+	47.5360i	−0.512513	+	0.137786i
$346$	80.5447	−	272.161i	0.232788	−	0.786591i
$347$	−203.667	−	32.2577i	−0.586937	−	0.0929616i	−0.144099	−	0.989563i	$-0.546028\pi$
$347$	−203.667	−	32.2577i	−0.586937	−	0.0929616i	−0.442838	+	0.896602i	$0.646028\pi$
$348$	314.738	−	349.898i	0.904420	−	1.00546i
$349$	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	$0.0184401\pi$
$350$	−288.960	−	22.1852i	−0.825600	−	0.0633862i
$351$	−445.927			−1.27045
$352$	−316.203	+	154.660i	−0.898304	+	0.439374i
$353$	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	$0.130514\pi$
$354$	−221.226	+	5.84750i	−0.624931	+	0.0165184i
$355$	85.4829	+	32.7320i	0.240797	+	0.0922029i
$356$	−44.8373	+	2.37197i	−0.125948	+	0.00666283i
$357$	158.765	+	25.1459i	0.444720	+	0.0704367i
$358$	158.544	+	291.830i	0.442860	+	0.815168i
$359$	113.014	−	36.7204i	0.314802	−	0.102285i	−0.147355	−	0.989084i	$-0.547076\pi$
$359$	113.014	−	36.7204i	0.314802	−	0.102285i	0.462156	+	0.886798i	$0.347076\pi$
$360$	−106.257	+	112.325i	−0.295159	+	0.312014i
$361$	235.999	+	171.464i	0.653738	+	0.474968i
$362$	−11.1154	+	84.5910i	−0.0307056	+	0.233677i
$363$	−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
$366$	402.839	−	142.764i	1.10065	−	0.390066i
$367$	373.233	+	190.172i	1.01698	+	0.518179i	0.881292	−	0.472572i	$-0.156674\pi$
$367$	373.233	+	190.172i	1.01698	+	0.518179i	0.135692	+	0.990751i	$0.456674\pi$
$368$	−201.107	−	162.526i	−0.546486	−	0.441646i
$369$	249.002	−	180.910i	0.674802	−	0.490272i
$370$	69.9717	+	53.5712i	0.189113	+	0.144787i
$371$	39.6894	−	122.151i	0.106980	−	0.329249i
$372$	120.308	+	12.5850i	0.323408	+	0.0338305i
$373$	−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	$-0.541018\pi$
$374$	51.4110	+	264.302i	0.137463	+	0.706690i
$375$	167.059	+	228.731i	0.445490	+	0.609949i
$376$	92.1011	−	384.881i	0.244950	−	1.02362i
$377$	−707.679	+	360.581i	−1.87713	+	0.956447i
$378$	−332.274	+	61.6679i	−0.879031	+	0.163143i
$379$	346.843	−	251.996i	0.915153	−	0.664897i	−0.0271600	−	0.999631i	$-0.508646\pi$
$379$	346.843	−	251.996i	0.915153	−	0.664897i	0.942313	+	0.334734i	$0.108646\pi$
$380$	158.541	+	485.746i	0.417213	+	1.27828i
$381$	−346.100	+	112.455i	−0.908399	+	0.295157i
$382$	−205.179	+	430.439i	−0.537118	+	1.12680i
$383$	29.4309	+	185.820i	0.0768431	+	0.485168i	0.995856	+	0.0909415i	$0.0289876\pi$
$383$	29.4309	+	185.820i	0.0768431	+	0.485168i	−0.919013	+	0.394227i	$0.871012\pi$
$384$	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
$388$	199.590	−	42.5270i	0.514408	−	0.109606i
$389$	−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	$0.746891\pi$
$390$	−312.681	+	149.556i	−0.801746	+	0.383477i
$391$	−160.014	+	116.257i	−0.409244	+	0.297333i
$392$	−9.57792	+	122.859i	−0.0244335	+	0.313416i
$393$	−130.769	+	66.6302i	−0.332746	+	0.169543i
$394$	−7.05415	−	266.876i	−0.0179039	−	0.677351i
$395$	20.9141	−	405.536i	0.0529471	−	1.02667i
$396$	−86.3786	−	146.515i	−0.218128	−	0.369988i
$397$	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	$0.711589\pi$
$398$	462.349	−	487.454i	1.16168	−	1.22476i
$399$	−103.690	+	319.124i	−0.259874	+	0.799809i
$400$	−122.597	+	380.749i	−0.306493	+	0.951873i
$401$	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	$-0.0811647\pi$
$402$	15.6584	+	28.8222i	0.0389511	+	0.0716970i
$403$	−181.894	−	92.6794i	−0.451349	−	0.229974i
$404$	267.795	+	173.720i	0.662858	+	0.430001i
$405$	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
$408$	84.7511	−	205.036i	0.207723	−	0.502538i
$409$	−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	$0.759859\pi$
$410$	379.172	−	700.150i	0.924809	−	1.70768i
$411$	324.651	−	105.486i	0.789906	−	0.256656i
$412$	140.510	+	62.4761i	0.341043	+	0.151641i
$413$	279.558	+	44.2777i	0.676896	+	0.107210i
$414$	70.7405	−	102.982i	0.170871	−	0.248750i
$415$	−126.350	−	283.150i	−0.304457	−	0.682289i
$416$	−430.454	−	233.032i	−1.03475	−	0.560172i
$417$	264.828	−	264.828i	0.635079	−	0.635079i
$418$	−561.716	+	19.6892i	−1.34382	+	0.0471033i
$419$	148.419			0.354222			0.177111	−	0.984191i	$-0.443325\pi$
$419$	148.419			0.354222			0.177111	+	0.984191i	$0.443325\pi$
$420$	−212.305	+	154.680i	−0.505489	+	0.368285i
$421$	−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	$0.766833\pi$
$422$	−221.123	+	41.0390i	−0.523988	+	0.0972488i
$423$	188.866	+	29.9135i	0.446493	+	0.0707175i
$424$	−151.217	−	92.5123i	−0.356644	−	0.218189i
$425$	256.888	+	166.216i	0.604442	+	0.391097i
$426$	78.1998	−	27.7137i	0.183568	−	0.0650556i
$427$	−539.893	+	85.5106i	−1.26439	+	0.200259i
$428$	4.79947	+	8.30348i	0.0112137	+	0.0194007i
$429$	−62.8839	−	376.046i	−0.146583	−	0.876564i
$430$	−438.035	−	635.872i	−1.01868	−	1.47877i
$431$	389.660	+	283.105i	0.904084	+	0.656855i	0.939512	−	0.342517i	$-0.111279\pi$
$431$	389.660	+	283.105i	0.904084	+	0.656855i	−0.0354281	+	0.999372i	$0.511279\pi$
$432$	−23.9528	+	465.824i	−0.0554463	+	1.07830i
$433$	−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	$0.671238\pi$
$434$	−148.351	−	43.9038i	−0.341823	−	0.101161i
$435$	575.529	+	121.831i	1.32306	+	0.280071i
$436$	−7.46258	−	141.065i	−0.0171160	−	0.323544i
$437$	−187.442	−	367.875i	−0.428928	−	0.841819i
$438$	337.334	+	319.960i	0.770168	+	0.730502i
$439$		−	396.815i		−	0.903906i	−0.892042	−	0.451953i	$-0.850727\pi$
$439$		−	396.815i		−	0.903906i	0.892042	−	0.451953i	$-0.149273\pi$
$440$	−365.135	−	245.513i	−0.829852	−	0.557984i
$441$	−59.5443			−0.135021
$442$	−257.668	+	271.659i	−0.582959	+	0.614614i
$443$	−404.354	+	206.029i	−0.912763	+	0.465076i	−0.846296	−	0.532713i	$-0.821173\pi$
$443$	−404.354	+	206.029i	−0.912763	+	0.465076i	−0.0664669	+	0.997789i	$0.521173\pi$
$444$	79.7624	−	4.21956i	0.179645	−	0.00950351i
$445$	−30.6071	−	47.0449i	−0.0687801	−	0.105719i
$446$	131.413	−	444.044i	0.294648	−	0.995614i
$447$	−48.8499	+	95.8733i	−0.109284	+	0.214482i
$448$	−352.970	−	114.111i	−0.787880	−	0.254712i
$449$	−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	$0.213499\pi$
$450$	−188.021	−	44.7594i	−0.417825	−	0.0994654i
$451$	624.631	+	613.965i	1.38499	+	1.36134i
$452$	536.865	−	310.312i	1.18775	−	0.686530i
$453$	1.57695	+	9.95646i	0.00348112	+	0.0219789i
$454$	60.2610	+	170.039i	0.132733	+	0.374535i
$455$	428.104	−	115.093i	0.940887	−	0.252951i
$456$	395.058	+	241.691i	0.866356	+	0.530024i
$457$	−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	$0.0828277\pi$
$458$	41.2806	+	222.425i	0.0901323	+	0.485643i
$459$	339.332	+	110.256i	0.739285	+	0.240208i
$460$	50.1381	−	319.300i	0.108996	−	0.694131i
$461$		−	566.953i		−	1.22983i	−0.788592	−	0.614916i	$-0.789190\pi$
$461$		−	566.953i		−	1.22983i	0.788592	−	0.614916i	$-0.210810\pi$
$462$	−98.8606	−	271.507i	−0.213984	−	0.587677i
$463$	122.032	+	122.032i	0.263569	+	0.263569i	0.826502	−	0.562933i	$-0.190327\pi$
$463$	122.032	+	122.032i	0.263569	+	0.263569i	−0.562933	+	0.826502i	$0.690327\pi$
$464$	338.657	+	758.624i	0.729864	+	1.63497i
$465$	61.6159	+	138.081i	0.132507	+	0.296949i
$466$	170.285	+	116.972i	0.365418	+	0.251013i
$467$	0.555465	−	3.50707i	0.00118943	−	0.00750979i	−0.987086	−	0.160188i	$-0.948790\pi$
$467$	0.555465	−	3.50707i	0.00118943	−	0.00750979i	0.988276	+	0.152678i	$0.0487899\pi$
$468$	96.0921	−	216.113i	0.205325	−	0.461779i
$469$	−12.9638	−	39.8986i	−0.0276415	−	0.0850717i
$470$	474.161	−	141.010i	1.00885	−	0.300022i
$471$	24.6585	−	33.9396i	0.0523536	−	0.0720585i
$472$	149.232	−	361.033i	0.316170	−	0.764900i
$473$	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
$476$	−154.428	+	238.055i	−0.324428	+	0.500115i
$477$	38.8868	−	76.3196i	0.0815236	−	0.159999i
$478$	169.023	−	91.8259i	0.353605	−	0.192104i
$479$	−274.282	−	377.516i	−0.572613	−	0.788134i	0.420248	−	0.907409i	$-0.361943\pi$
$479$	−274.282	−	377.516i	−0.572613	−	0.788134i	−0.992861	+	0.119275i	$0.961943\pi$
$480$	139.434	+	334.666i	0.290486	+	0.697221i
$481$	−128.201	−	41.6550i	−0.266530	−	0.0866008i
$482$	−209.754	−	198.951i	−0.435175	−	0.412762i
$483$	150.085	−	150.085i	0.310734	−	0.310734i
$484$	370.684	−	311.206i	0.765876	−	0.642988i
$485$	170.845	+	189.425i	0.352259	+	0.390567i
$486$	−382.907	+	10.1211i	−0.787875	+	0.0208253i
$487$	59.4939	+	116.763i	0.122164	+	0.239761i	0.943987	−	0.329982i	$-0.107043\pi$
$487$	59.4939	+	116.763i	0.122164	+	0.239761i	−0.821823	+	0.569743i	$0.807043\pi$
$488$	−58.6383	+	752.173i	−0.120161	+	1.54134i
$489$	192.668	+	265.185i	0.394004	+	0.542301i
$490$	−138.962	+	66.4660i	−0.283597	+	0.135645i
$491$	−260.437	−	801.543i	−0.530422	−	1.63247i	−0.753338	−	0.657633i	$-0.771558\pi$
$491$	−260.437	−	801.543i	−0.530422	−	1.63247i	0.222916	−	0.974838i	$-0.428442\pi$
$492$	−150.394	−	705.839i	−0.305679	−	1.43463i
$493$	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
$498$	−253.685	−	120.925i	−0.509409	−	0.242821i
$499$	67.0271	+	206.288i	0.134323	+	0.413404i	0.995484	−	0.0949285i	$-0.0302623\pi$
$499$	67.0271	+	206.288i	0.134323	+	0.413404i	−0.861161	+	0.508332i	$0.830262\pi$
$500$	−488.760	+	105.420i	−0.977521	+	0.210840i
$501$	−49.8271	−	68.5811i	−0.0994552	−	0.136888i
$502$	36.4145	+	196.205i	0.0725388	+	0.390847i
$503$	2.37690	+	4.66493i	0.00472545	+	0.00927421i	0.893357	−	0.449347i	$-0.148343\pi$
$503$	2.37690	+	4.66493i	0.00472545	+	0.00927421i	−0.888632	+	0.458621i	$0.848343\pi$
$504$	41.7145	−	174.321i	0.0827670	−	0.345874i
$505$	−20.5501	+	398.479i	−0.0406933	+	0.789066i
$506$	322.243	+	150.213i	0.636844	+	0.296864i
$507$	104.113	−	104.113i	0.205352	−	0.205352i
$508$	66.8347	−	638.916i	0.131564	−	1.25771i
$509$	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	$0.491304\pi$
$510$	274.915	−	36.4953i	0.539048	−	0.0715595i
$511$	−349.526	−	481.082i	−0.684005	−	0.941452i
$512$	−266.551	+	437.143i	−0.520608	+	0.853796i
$513$	−338.129	+	663.616i	−0.659122	+	1.29360i
$514$	235.027	+	663.176i	0.457251	+	1.29023i
$515$	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
$518$	−101.287	−	13.3093i	−0.195534	−	0.0256936i
$519$	189.014	−	260.155i	0.364189	−	0.501263i
$520$	−16.9784	−	611.619i	−0.0326507	−	1.17619i
$521$	−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	$0.972939\pi$
$522$	−352.732	+	191.630i	−0.675731	+	0.367108i
$523$	153.156	−	966.991i	0.292842	−	1.84893i	−0.201275	−	0.979535i	$-0.564508\pi$
$523$	153.156	−	966.991i	0.292842	−	1.84893i	0.494117	−	0.869396i	$-0.335492\pi$
$524$	−13.6867	−	258.719i	−0.0261196	−	0.493739i
$525$	−300.182	−	133.050i	−0.571775	−	0.253429i
$526$	−10.8553	−	410.681i	−0.0206374	−	0.780763i
$527$	115.498	+	115.498i	0.219162	+	0.219162i
$528$	−396.203	+	45.4906i	−0.750384	+	0.0861565i
$529$		−	267.834i		−	0.506302i
$530$	5.56124	−	221.519i	0.0104929	−	0.417961i
$531$	179.524	+	58.3307i	0.338086	+	0.109851i
$532$	−440.383	−	396.130i	−0.827787	−	0.744605i
$533$	−190.528	+	1202.95i	−0.357463	+	2.25694i
$534$	−48.7791	−	14.4360i	−0.0913467	−	0.0270337i
$535$	−5.98557	+	10.3873i	−0.0111880	+	0.0194155i
$536$	−57.7207	+	4.58562i	−0.107688	+	0.00855526i
$537$	58.8628	+	371.645i	0.109614	+	0.692077i
$538$	294.231	+	38.6626i	0.546898	+	0.0718635i
$539$	−27.9470	−	167.123i	−0.0518498	−	0.310062i
$540$	−519.150	+	265.388i	−0.961388	+	0.491459i
$541$	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	$0.112072\pi$
$542$	686.634	+	327.300i	1.26685	+	0.603875i
$543$	−43.8841	+	86.1274i	−0.0808178	+	0.158614i
$544$	269.940	+	283.757i	0.496213	+	0.521612i
$545$	148.011	−	96.2949i	0.271579	−	0.176688i
$546$	227.501	−	331.191i	0.416668	−	0.606576i
$547$	−600.518	+	305.979i	−1.09784	+	0.559377i	−0.906525	−	0.422152i	$-0.861275\pi$
$547$	−600.518	+	305.979i	−1.09784	+	0.559377i	−0.191314	+	0.981529i	$0.561275\pi$
$548$	−62.6927	+	599.320i	−0.114403	+	1.09365i
$549$	−364.544			−0.664015
$550$	37.3790	−	548.728i	0.0679618	−	0.997688i
$551$			1326.56i			2.40756i
$552$	−153.252	−	249.670i	−0.277630	−	0.452301i
$553$	213.711	+	419.431i	0.386457	+	0.758465i
$554$	21.3253	−	31.0449i	0.0384934	−	0.0560377i
$555$	54.4479	+	83.6895i	0.0981043	+	0.150792i
$556$	237.233	+	617.106i	0.426679	+	1.10990i
$557$	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	$0.606761\pi$
$558$	−93.1374	−	44.3961i	−0.166913	−	0.0795629i
$559$	955.530	+	694.233i	1.70936	+	1.24192i
$560$	−97.2327	−	453.388i	−0.173630	−	0.809621i
$561$	−45.1254	+	301.703i	−0.0804374	+	0.537795i
$562$	760.149	+	99.8851i	1.35258	+	0.177731i
$563$	761.878	−	120.670i	1.35325	−	0.214333i	0.562663	−	0.826686i	$-0.309777\pi$
$563$	761.878	−	120.670i	1.35325	−	0.214333i	0.790584	+	0.612353i	$0.209777\pi$
$564$	244.015	−	376.155i	0.432650	−	0.666941i
$565$	671.595	+	386.999i	1.18866	+	0.684954i
$566$	−851.410	−	251.971i	−1.50426	−	0.445179i
$567$	−179.006	−	28.3517i	−0.315707	−	0.0500031i
$568$	−11.3830	+	146.013i	−0.0200405	+	0.257066i
$569$	−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	$0.874787\pi$
$570$	−14.5289	+	578.725i	−0.0254893	+	1.01531i
$571$	856.728			1.50040			0.750200	−	0.661211i	$-0.229957\pi$
$571$	856.728			1.50040			0.750200	+	0.661211i	$0.229957\pi$
$572$	651.666	+	168.270i	1.13928	+	0.294178i
$573$	−382.011	+	382.011i	−0.666687	+	0.666687i
$574$	24.3891	+	922.699i	0.0424897	+	1.60749i
$575$	376.939	−	145.415i	0.655547	−	0.252896i
$576$	−220.594	−	111.988i	−0.382976	−	0.194424i
$577$	−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	$0.805477\pi$
$578$	−244.646	+	132.910i	−0.423263	+	0.229948i
$579$	100.615	−	32.6917i	0.173773	−	0.0564624i
$580$	−609.287	+	840.955i	−1.05050	+	1.44992i
$581$	290.790	+	211.271i	0.500499	+	0.363634i
$582$	229.235	+	30.1220i	0.393875	+	0.0517560i
$583$	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
$586$	−136.499	−	385.160i	−0.232934	−	0.657270i
$587$	239.702	+	122.134i	0.408351	+	0.208065i	0.646086	−	0.763265i	$-0.276405\pi$
$587$	239.702	+	122.134i	0.408351	+	0.208065i	−0.237735	+	0.971330i	$0.576405\pi$
$588$	−56.7250	+	127.575i	−0.0964711	+	0.216965i
$589$	−275.846	+	200.414i	−0.468329	+	0.340261i
$590$	484.077	−	64.2621i	0.820470	−	0.108919i
$591$	93.4679	−	287.665i	0.158152	−	0.486742i
$592$	−50.3999	+	131.684i	−0.0851350	+	0.222439i
$593$	−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	$0.830693\pi$
$594$	−122.459	−	629.555i	−0.206159	−	1.05986i
$595$	−354.225	−	18.2679i	−0.595337	−	0.0307024i
$596$	−119.609	−	147.556i	−0.200686	−	0.247578i
$597$	678.218	−	345.570i	1.13604	−	0.578843i
$598$	90.2166	+	486.097i	0.150864	+	0.812872i
$599$	−869.672	+	631.853i	−1.45187	+	1.05485i	−0.466483	+	0.884530i	$0.654479\pi$
$599$	−869.672	+	631.853i	−1.45187	+	1.05485i	−0.985389	+	0.170317i	$0.945521\pi$
$600$	−275.017	+	360.201i	−0.458362	+	0.600336i
$601$	−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	$0.548331\pi$
$602$	808.000	+	385.152i	1.34219	+	0.639788i
$603$	−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	$-0.780629\pi$
$607$	−142.206	−	897.855i	−0.234277	−	1.47917i	0.537494	−	0.843267i	$-0.319371\pi$
$608$	−673.188	+	463.890i	−1.10722	+	0.762978i
$609$	−648.584	+	210.738i	−1.06500	+	0.346039i
$610$	−850.761	+	406.921i	−1.39469	+	0.667084i
$611$	−612.173	+	444.769i	−1.00192	+	0.727937i
$612$	−126.556	+	140.694i	−0.206791	+	0.229892i
$613$	−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	$0.423986\pi$
$614$	−557.295	+	14.7306i	−0.907647	+	0.0239912i
$615$	669.890	−	604.184i	1.08925	−	0.982414i
$616$	508.846	+	35.2632i	0.826048	+	0.0572455i
$617$	−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	$0.824063\pi$
$618$	126.405	+	119.895i	0.204539	+	0.194004i
$619$	−92.1660	+	283.658i	−0.148895	+	0.458252i	−0.997491	−	0.0707893i	$-0.977448\pi$
$619$	−92.1660	+	283.658i	−0.148895	+	0.458252i	0.848596	+	0.529041i	$0.177448\pi$
$620$	−266.918	+	0.354049i	−0.430513	+	0.000571048i
$621$	381.147	−	276.919i	0.613763	−	0.445925i
$622$	820.599	−	445.810i	1.31929	−	0.716737i
$623$	57.9711	+	29.5377i	0.0930515	+	0.0474121i
$624$	−371.486	−	411.761i	−0.595330	−	0.659873i
$625$	−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
$628$	37.0596	+	64.1161i	0.0590120	+	0.102096i
$629$	87.2563	+	63.3954i	0.138722	+	0.100788i
$630$	214.758	−	63.8665i	0.340885	−	0.101375i
$631$	−181.799	+	59.0701i	−0.288113	+	0.0936135i	−0.449508	−	0.893276i	$-0.648401\pi$
$631$	−181.799	+	59.0701i	−0.288113	+	0.0936135i	0.161395	+	0.986890i	$0.448401\pi$
$632$	631.656	−	152.141i	0.999455	−	0.240729i
$633$	−251.667	−	39.8601i	−0.397578	−	0.0629701i
$634$	20.3832	+	14.0016i	0.0321501	+	0.0220845i
$635$	733.306	−	327.222i	1.15481	−	0.515310i
$636$	−126.472	−	156.022i	−0.198855	−	0.245318i
$637$	166.612	−	166.612i	0.261557	−	0.261557i
$638$	−703.404	−	900.073i	−1.10251	−	1.41077i
$639$	−70.7661			−0.110745
$640$	−639.821	−	15.1170i	−0.999721	−	0.0236203i
$641$	−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	$0.959746\pi$
$642$	1.98281	+	10.6836i	0.00308849	+	0.0166411i
$643$	87.4537	+	13.8513i	0.136009	+	0.0215417i	0.224068	−	0.974574i	$-0.428066\pi$
$643$	87.4537	+	13.8513i	0.136009	+	0.0215417i	−0.0880588	+	0.996115i	$0.528066\pi$
$644$	134.446	+	349.729i	0.208767	+	0.543058i
$645$	−227.124	−	844.819i	−0.352130	−	1.30980i
$646$	208.896	+	589.443i	0.323368	+	0.912450i
$647$	512.994	−	81.2502i	0.792881	−	0.125580i	0.253160	−	0.967424i	$-0.418530\pi$
$647$	512.994	−	81.2502i	0.792881	−	0.125580i	0.539720	+	0.841844i	$0.318530\pi$
$648$	−95.5560	+	231.175i	−0.147463	+	0.356752i
$649$	−79.4581	+	531.247i	−0.122432	+	0.818563i
$650$	651.349	−	400.864i	1.00208	−	0.616714i
$651$	−141.807	−	103.029i	−0.217830	−	0.158263i
$652$	−565.928	+	120.583i	−0.867988	+	0.184943i
$653$	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	$0.536936\pi$
$654$	45.4178	−	153.467i	0.0694462	−	0.234659i
$655$	271.457	−	176.609i	0.414439	−	0.269631i
$656$	1246.39	+	263.645i	1.89998	+	0.401898i
$657$	−180.041	−	353.350i	−0.274035	−	0.537823i
$658$	−394.640	+	416.069i	−0.599757	+	0.632324i
$659$			513.775i			0.779628i	0.920894	+	0.389814i	$0.127461\pi$
$659$			513.775i			0.779628i	−0.920894	+	0.389814i	$0.872539\pi$
$660$	−297.008	−	400.369i	−0.450013	−	0.606620i
$661$	98.3245			0.148751			0.0743756	−	0.997230i	$-0.476304\pi$
$661$	98.3245			0.148751			0.0743756	+	0.997230i	$0.476304\pi$
$662$	−343.532	−	325.839i	−0.518930	−	0.492203i
$663$	−377.973	+	192.587i	−0.570095	+	0.290478i
$664$	376.998	−	322.469i	0.567768	−	0.485645i
$665$	153.337	−	724.362i	0.230581	−	1.08927i
$666$	−65.3284	−	19.3337i	−0.0980907	−	0.0290295i
$667$	380.954	−	747.665i	0.571146	−	1.12094i
$668$	146.358	−	31.1847i	0.219099	−	0.0466837i
$669$	308.386	−	424.457i	0.460965	−	0.634464i
$670$	−41.0599	−	59.6044i	−0.0612834	−	0.0889618i
$671$	−171.099	−	1023.17i	−0.254990	−	1.52484i
$672$	−333.748	−	255.442i	−0.496649	−	0.380122i
$673$	−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	$-0.147480\pi$
$674$	277.302	−	98.2748i	0.411428	−	0.145808i
$675$	−611.895	−	395.920i	−0.906511	−	0.586547i
$676$	93.2649	+	242.606i	0.137966	+	0.358885i
$677$	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	$-0.118820\pi$
$678$	690.753	−	128.199i	1.01881	−	0.189085i
$679$	−281.236	−	91.3791i	−0.414191	−	0.134579i
$680$	−138.303	+	469.614i	−0.203387	+	0.690609i
$681$			204.389i			0.300131i
$682$	80.8929	−	282.247i	0.118611	−	0.413851i
$683$	−522.218	−	522.218i	−0.764595	−	0.764595i	0.212555	−	0.977149i	$-0.431822\pi$
$683$	−522.218	−	522.218i	−0.764595	−	0.764595i	−0.977149	+	0.212555i	$0.931822\pi$
$684$	−248.750	−	306.872i	−0.363670	−	0.448643i
$685$	−687.861	+	306.943i	−1.00418	+	0.448092i
$686$	422.726	−	615.395i	0.616219	−	0.897077i
$687$	−40.0948	+	253.148i	−0.0583621	+	0.368484i
$688$	776.536	−	960.875i	1.12869	−	1.39662i
$689$	104.742	+	322.361i	0.152020	+	0.467868i
$690$	174.383	−	322.003i	0.252730	−	0.466671i
$691$	−687.245	+	945.912i	−0.994566	+	1.36890i	−0.0659660	+	0.997822i	$0.521013\pi$
$691$	−687.245	+	945.912i	−0.994566	+	1.36890i	−0.928600	+	0.371081i	$0.878987\pi$
$692$	284.071	+	491.466i	0.410507	+	0.710211i
$693$	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
$696$	74.5429	+	938.296i	0.107102	+	1.34813i
$697$	442.412	−	868.283i	0.634738	−	1.24574i
$698$	168.892	+	310.878i	0.241966	+	0.445384i
$699$	137.577	+	189.359i	0.196820	+	0.270899i
$700$	429.903	−	388.772i	0.614147	−	0.555388i
$701$	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	$0.542036\pi$
$702$	613.753	−	647.080i	0.874292	−	0.921766i
$703$	−159.200	+	159.200i	−0.226457	+	0.226457i
$704$	210.782	−	671.704i	0.299407	−	0.954126i
$705$	559.719	+	28.8655i	0.793927	+	0.0409440i
$706$	13.6785	+	517.492i	0.0193747	+	0.732991i
$707$	−209.992	−	412.132i	−0.297018	−	0.582931i
$708$	295.999	−	329.066i	0.418078	−	0.464782i
$709$	−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	$0.839854\pi$
$710$	−165.152	+	78.9924i	−0.232608	+	0.111257i
$711$	97.0119	+	298.572i	0.136444	+	0.419932i
$712$	58.2700	−	68.3276i	0.0818399	−	0.0959657i
$713$	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
$718$	−102.262	+	214.533i	−0.142426	+	0.298793i
$719$	−165.942	−	510.715i	−0.230795	−	0.710314i	−0.997651	−	0.0684951i	$-0.978180\pi$
$719$	−165.942	−	510.715i	−0.230795	−	0.710314i	0.766857	−	0.641818i	$-0.221820\pi$
$720$	−16.7461	−	308.787i	−0.0232584	−	0.428871i
$721$	−130.974	−	180.270i	−0.181656	−	0.250027i
$722$	−573.627	+	106.462i	−0.794497	+	0.147454i
$723$	−148.700	−	291.841i	−0.205671	−	0.403653i
$724$	−107.450	−	132.556i	−0.148412	−	0.183089i
$725$	−1291.21	−	133.535i	−1.78098	−	0.184186i
$726$	513.629	−	192.047i	0.707477	−	0.264527i
$727$	311.604	−	311.604i	0.428616	−	0.428616i	−0.459541	−	0.888157i	$-0.651986\pi$
$727$	311.604	−	311.604i	0.428616	−	0.428616i	0.888157	+	0.459541i	$0.151986\pi$
$728$	371.048	+	604.493i	0.509682	+	0.830347i
$729$	−680.375	−	221.067i	−0.933299	−	0.303247i
$730$	−814.598	−	623.666i	−1.11589	−	0.854338i
$731$	−555.469	−	764.537i	−0.759875	−	1.04588i
$732$	−347.284	+	781.048i	−0.474432	+	1.06701i
$733$	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	$0.0110285\pi$
$734$	−789.656	+	279.851i	−1.07583	+	0.381268i
$735$	−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
$738$	−80.1973	+	610.320i	−0.108668	+	0.826992i
$739$	−570.920	+	785.804i	−0.772558	+	1.06333i	0.223506	+	0.974702i	$0.428250\pi$
$739$	−570.920	+	785.804i	−0.772558	+	1.06333i	−0.996064	+	0.0886324i	$0.971750\pi$
$740$	−174.042	+	27.8023i	−0.235192	+	0.0375707i
$741$	−273.640	−	842.178i	−0.369285	−	1.13654i
$742$	122.626	+	225.716i	0.165264	+	0.304200i
$743$	53.6467	−	338.712i	0.0722028	−	0.455870i	−0.924926	−	0.380147i	$-0.875873\pi$
$743$	53.6467	−	338.712i	0.0722028	−	0.455870i	0.997129	−	0.0757234i	$-0.0241266\pi$
$744$	−183.848	+	157.256i	−0.247107	+	0.211365i
$745$	84.9029	−	221.732i	0.113964	−	0.297627i
$746$	1181.42	−	31.2276i	1.58367	−	0.0418601i
$747$	169.500	+	169.500i	0.226908	+	0.226908i
$748$	−454.285	−	289.171i	−0.607333	−	0.386592i
$749$		−	13.8975i		−	0.0185548i
$750$	−561.840	−	72.3974i	−0.749120	−	0.0965298i
$751$	183.845	+	59.7347i	0.244800	+	0.0795402i	0.428847	−	0.903377i	$-0.358920\pi$
$751$	183.845	+	59.7347i	0.244800	+	0.0795402i	−0.184047	+	0.982917i	$0.558920\pi$
$752$	431.732	+	663.378i	0.574112	+	0.882152i
$753$	−35.3684	+	223.307i	−0.0469700	+	0.296557i
$754$	450.782	−	1523.19i	0.597854	−	2.02015i
$755$	−5.77500	−	21.4809i	−0.00764901	−	0.0284515i
$756$	367.840	−	567.035i	0.486561	−	0.750046i
$757$	−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	$0.982213\pi$
$758$	−111.709	+	850.135i	−0.147374	+	1.12155i
$759$	287.272	+	282.366i	0.378487	+	0.372024i
$760$	−923.068	−	438.500i	−1.21456	−	0.576974i
$761$	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	$0.0570904\pi$
$762$	313.174	−	656.999i	0.410989	−	0.862203i
$763$	−92.9304	+	182.386i	−0.121796	+	0.239038i
$764$	−342.207	−	890.169i	−0.447915	−	1.16514i
$765$	−231.420	−	48.9881i	−0.302510	−	0.0640367i
$766$	−310.148	−	213.046i	−0.404893	−	0.278128i
$767$	−665.545	+	339.112i	−0.867725	+	0.442128i
$768$	−450.088	+	365.944i	−0.586052	+	0.476490i
$769$	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+(-1.37635 + 1.45109i) q^{2} +(-2.01897 + 1.02872i) q^{3} +(-0.211311 - 3.99441i) q^{4} +(4.19108 - 2.72669i) q^{5} +(1.28605 - 4.34558i) q^{6} +(-2.63142 + 5.16446i) q^{7} +(6.08708 + 5.19109i) q^{8} +(-2.27209 + 3.12726i) q^{9} +(-1.81173 + 9.83451i) q^{10} +(-9.84371 - 4.90931i) q^{11} +(4.53575 + 7.84722i) q^{12} +(-2.39288 - 15.1080i) q^{13} +(-3.87232 - 10.9265i) q^{14} +(-5.65667 + 9.81653i) q^{15} +(-15.9107 + 1.68813i) q^{16} +(-1.91459 + 12.0882i) q^{17} +(-1.41074 - 7.60122i) q^{18} +(-24.2978 - 7.89483i) q^{19} +(-11.7772 - 16.1647i) q^{20} -13.1339i q^{21} +(20.6723 - 7.52715i) q^{22} +(11.4273 + 11.4273i) q^{23} +(-17.6298 - 4.21877i) q^{24} +(10.1303 - 22.8556i) q^{25} +(25.2165 + 17.3217i) q^{26} +(4.56045 - 28.7936i) q^{27} +(21.1850 + 9.41969i) q^{28} +(-16.0454 - 49.3826i) q^{29} +(-6.45909 - 21.7193i) q^{30} +(7.84453 - 10.7971i) q^{31} +(19.4491 - 25.4113i) q^{32} +(24.9244 - 0.214638i) q^{33} +(-14.9059 - 19.4159i) q^{34} +(3.05338 + 28.8197i) q^{35} +(12.9717 + 8.41484i) q^{36} +(4.00077 - 7.85195i) q^{37} +(44.8984 - 24.3922i) q^{38} +(20.3730 + 28.0411i) q^{39} +(39.6660 + 5.15867i) q^{40} +(-75.7259 - 24.6048i) q^{41} +(19.0584 + 18.0768i) q^{42} +(-54.5989 + 54.5989i) q^{43} +(-17.5297 + 40.3573i) q^{44} +(-0.995428 + 19.3019i) q^{45} +(-32.3100 + 0.854028i) q^{46} +(-22.4582 - 44.0767i) q^{47} +(30.3866 - 19.7759i) q^{48} +(9.05424 + 12.4621i) q^{49} +(19.2226 + 46.1573i) q^{50} +(-8.56986 - 26.3753i) q^{51} +(-59.8422 + 12.7506i) 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} +(93.7425 + 44.6846i) q^{58} +(-15.0901 - 46.4424i) q^{59} +(40.4066 + 20.5207i) q^{60} +(55.4322 + 76.2959i) q^{61} +(4.87066 + 26.2437i) q^{62} +(-10.1718 - 19.9633i) q^{63} +(10.1052 + 63.1972i) q^{64} +(-51.2237 - 56.7944i) q^{65} +(-33.9933 + 36.4630i) q^{66} +(-5.11791 + 5.11791i) q^{67} +(48.6899 + 5.09328i) q^{68} +(-34.8268 - 11.3159i) q^{69} +(-46.0225 - 35.2354i) q^{70} +(10.7606 + 14.8107i) q^{71} +(-30.0643 + 7.24129i) q^{72} +(-46.5762 + 91.4110i) q^{73} +(5.88740 + 16.6125i) q^{74} +(3.05911 + 56.5659i) q^{75} +(-26.4008 + 98.7237i) q^{76} +(51.2569 - 37.9190i) q^{77} +(-68.7305 - 9.03133i) q^{78} +(47.7369 - 65.7043i) q^{79} +(-62.0800 + 50.4586i) q^{80} +(9.66242 + 29.7379i) q^{81} +(139.929 - 76.0200i) q^{82} +(9.70086 - 61.2488i) q^{83} +(-52.4621 + 2.77533i) q^{84} +(24.9367 + 55.8832i) q^{85} +(-4.08049 - 154.375i) q^{86} +(83.1957 + 83.1957i) q^{87} +(-34.4348 - 80.9830i) q^{88} -11.2250i q^{89} +(-26.6387 - 28.0107i) q^{90} +(84.3215 + 27.3977i) q^{91} +(43.2307 - 48.0601i) q^{92} +(-4.73074 + 29.8687i) q^{93} +(94.8695 + 28.0762i) q^{94} +(-123.361 + 33.1647i) q^{95} +(-13.1261 + 71.3121i) q^{96} +(7.98092 + 50.3895i) q^{97} +(-30.5454 - 4.01373i) 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

Modular forms

Varieties

Fields

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