LMFDB - Embedded newform 220.3.s.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(31,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 6]))

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

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

chi := DirichletCharacter("220.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.s (of order $10$, degree $4$, 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:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	220.31
Dual form			220.3.s.b.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96516 - 0.371672i) q^{2} +(0.447988 + 0.616603i) q^{3} +(3.72372 + 1.46079i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-0.651195 - 1.37823i) q^{6} +(-5.62557 + 7.74293i) q^{7} +(-6.77478 - 4.25469i) q^{8} +(2.60165 - 8.00705i) q^{9} +(0.567486 + 4.43598i) q^{10} +(-8.56295 - 6.90477i) q^{11} +(0.767455 + 2.95047i) q^{12} +(-0.964498 + 2.96842i) q^{13} +(13.9330 - 13.1252i) q^{14} +(1.00173 - 1.37877i) q^{15} +(11.7322 + 10.8791i) q^{16} +(-0.505552 - 1.55593i) q^{17} +(-8.08865 + 14.7682i) q^{18} +(-8.88888 - 12.2345i) q^{19} +(0.533527 - 8.92835i) q^{20} -7.29450 q^{21} +(14.2613 + 16.7516i) q^{22} -9.12329i q^{23} +(-0.411568 - 6.08339i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(2.99867 - 5.47495i) q^{26} +(12.6264 - 4.10257i) q^{27} +(-32.2588 + 20.6147i) q^{28} +(-40.1611 - 29.1787i) q^{29} +(-2.48101 + 2.33718i) q^{30} +(-33.6488 - 10.9332i) q^{31} +(-19.0122 - 25.7398i) q^{32} +(0.421397 - 8.37319i) q^{33} +(0.415197 + 3.24555i) q^{34} +(20.3535 + 6.61325i) q^{35} +(21.3844 - 26.0155i) q^{36} +(-42.9061 - 31.1731i) q^{37} +(12.9209 + 27.3465i) q^{38} +(-2.26242 + 0.735104i) q^{39} +(-4.36688 + 17.3473i) q^{40} +(-3.78700 + 2.75142i) q^{41} +(14.3349 + 2.71116i) q^{42} +24.1885i q^{43} +(-21.7996 - 38.2201i) q^{44} -18.8257 q^{45} +(-3.39087 + 17.9287i) q^{46} +(6.89694 + 9.49282i) q^{47} +(-1.45223 + 12.1078i) q^{48} +(-13.1641 - 40.5150i) q^{49} +(9.04156 - 4.27202i) q^{50} +(0.732909 - 1.00876i) q^{51} +(-7.92776 + 9.64464i) q^{52} +(-11.5593 + 35.5760i) q^{53} +(-26.3377 + 3.36933i) q^{54} +(-8.76701 + 22.9813i) q^{55} +(71.0557 - 28.5216i) q^{56} +(3.56171 - 10.9618i) q^{57} +(68.0781 + 72.2677i) q^{58} +(33.0063 - 45.4293i) q^{59} +(5.74425 - 3.67082i) q^{60} +(27.3220 + 84.0884i) q^{61} +(62.0618 + 33.9917i) q^{62} +(47.3623 + 65.1886i) q^{63} +(27.7953 + 57.6491i) q^{64} +6.97917 q^{65} +(-3.94019 + 16.2981i) q^{66} -58.1153i q^{67} +(0.390351 - 6.53235i) q^{68} +(5.62544 - 4.08712i) q^{69} +(-37.5399 - 20.5609i) q^{70} +(95.0277 - 30.8764i) q^{71} +(-51.6931 + 43.1768i) q^{72} +(-29.7244 - 21.5961i) q^{73} +(72.7312 + 77.2071i) q^{74} +(-3.62430 - 1.17761i) q^{75} +(-15.2277 - 58.5426i) q^{76} +(101.635 - 27.4591i) q^{77} +(4.71924 - 0.603722i) q^{78} +(70.8877 + 23.0328i) q^{79} +(15.0291 - 32.4673i) q^{80} +(-53.1147 - 38.5901i) q^{81} +(8.46469 - 3.99946i) q^{82} +(-38.8899 + 12.6361i) q^{83} +(-27.1627 - 10.6557i) q^{84} +(-2.95955 + 2.15024i) q^{85} +(8.99017 - 47.5343i) q^{86} -37.8351i q^{87} +(28.6345 + 83.2110i) q^{88} +116.343 q^{89} +(36.9955 + 6.99698i) q^{90} +(-17.5584 - 24.1671i) q^{91} +(13.3272 - 33.9726i) q^{92} +(-8.33285 - 25.6459i) q^{93} +(-10.0254 - 21.2183i) q^{94} +(-19.8761 + 27.3572i) q^{95} +(7.35400 - 23.2541i) q^{96} +(13.7668 - 42.3699i) q^{97} +(10.8113 + 84.5112i) q^{98} +(-77.5646 + 50.6002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} + 16 q^{4} - 120 q^{5} - 20 q^{6} - 10 q^{8} + 64 q^{9} - 10 q^{10} - 70 q^{12} + 20 q^{13} + 83 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} - 25 q^{20} + 35 q^{22} - 62 q^{24} - 120 q^{25}+ \cdots - 1042 q^{98}+O(q^{100}) $ 96 * q + 2 * q^2 + 16 * q^4 - 120 * q^5 - 20 * q^6 - 10 * q^8 + 64 * q^9 - 10 * q^10 - 70 * q^12 + 20 * q^13 + 83 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 - 25 * q^20 + 35 * q^22 - 62 * q^24 - 120 * q^25 - 88 * q^26 - 130 * q^28 - 8 * q^29 + 40 * q^30 + 152 * q^32 + 180 * q^33 - 126 * q^34 - 394 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 + 275 * q^42 + 113 * q^44 + 40 * q^45 - 85 * q^46 + 353 * q^48 + 292 * q^49 + 10 * q^50 + 62 * q^52 - 224 * q^53 - 328 * q^54 + 380 * q^56 - 364 * q^57 + 598 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 - 356 * q^64 - 40 * q^65 - 65 * q^66 - 117 * q^68 + 32 * q^69 - 165 * q^70 - 28 * q^72 + 16 * q^73 - 72 * q^74 - 720 * q^77 - 752 * q^78 - 235 * q^80 - 44 * q^81 + 49 * q^82 - 348 * q^84 + 60 * q^85 + 70 * q^86 - 165 * q^88 - 144 * q^89 + 778 * q^92 + 40 * q^93 + 254 * q^94 + 243 * q^96 + 204 * q^97 - 1042 * q^98

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.96516	−	0.371672i	−0.982581	−	0.185836i
$2$	−1.96516	−	0.371672i	−0.982581	−	0.185836i
$3$	0.447988	+	0.616603i	0.149329	+	0.205534i	0.877128	−	0.480257i	$-0.159456\pi$
$3$	0.447988	+	0.616603i	0.149329	+	0.205534i	−0.727799	+	0.685791i	$0.759456\pi$
$4$	3.72372	+	1.46079i	0.930930	+	0.365197i
$5$	−0.690983	−	2.12663i	−0.138197	−	0.425325i
$5$	−0.690983	−	2.12663i	−0.138197	−	0.425325i
$6$	−0.651195	−	1.37823i	−0.108533	−	0.229705i
$7$	−5.62557	+	7.74293i	−0.803652	+	1.10613i	0.188619	+	0.982050i	$0.439599\pi$
$7$	−5.62557	+	7.74293i	−0.803652	+	1.10613i	−0.992272	+	0.124082i	$0.960401\pi$
$8$	−6.77478	−	4.25469i	−0.846847	−	0.531836i
$9$	2.60165	−	8.00705i	0.289072	−	0.889672i
$10$	0.567486	+	4.43598i	0.0567486	+	0.443598i
$11$	−8.56295	−	6.90477i	−0.778450	−	0.627706i
$11$	−8.56295	−	6.90477i	−0.778450	−	0.627706i
$12$	0.767455	+	2.95047i	0.0639546	+	0.245873i
$13$	−0.964498	+	2.96842i	−0.0741921	+	0.228340i	−0.981275	−	0.192612i	$-0.938304\pi$
$13$	−0.964498	+	2.96842i	−0.0741921	+	0.228340i	0.907083	+	0.420952i	$0.138304\pi$
$14$	13.9330	−	13.1252i	0.995212	−	0.937517i
$15$	1.00173	−	1.37877i	0.0667821	−	0.0919177i
$16$	11.7322	+	10.8791i	0.733262	+	0.679946i
$17$	−0.505552	−	1.55593i	−0.0297384	−	0.0915253i	0.935086	−	0.354422i	$-0.115322\pi$
$17$	−0.505552	−	1.55593i	−0.0297384	−	0.0915253i	−0.964824	+	0.262896i	$0.915322\pi$
$18$	−8.08865	+	14.7682i	−0.449369	+	0.820455i
$19$	−8.88888	−	12.2345i	−0.467836	−	0.643921i	0.508275	−	0.861195i	$-0.330283\pi$
$19$	−8.88888	−	12.2345i	−0.467836	−	0.643921i	−0.976111	+	0.217274i	$0.930283\pi$
$20$	0.533527	−	8.92835i	0.0266763	−	0.446417i
$21$	−7.29450			−0.347357
$22$	14.2613	+	16.7516i	0.648240	+	0.761436i
$23$		−	9.12329i		−	0.396665i	−0.980135	−	0.198332i	$-0.936447\pi$
$23$		−	9.12329i		−	0.396665i	0.980135	−	0.198332i	$-0.0635525\pi$
$24$	−0.411568	−	6.08339i	−0.0171486	−	0.253475i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	2.99867	−	5.47495i	0.115334	−	0.210575i
$27$	12.6264	−	4.10257i	0.467645	−	0.151947i
$28$	−32.2588	+	20.6147i	−1.15210	+	0.736240i
$29$	−40.1611	−	29.1787i	−1.38486	−	1.00616i	−0.996407	−	0.0846969i	$-0.973008\pi$
$29$	−40.1611	−	29.1787i	−1.38486	−	1.00616i	−0.388458	−	0.921466i	$-0.626992\pi$
$30$	−2.48101	+	2.33718i	−0.0827004	+	0.0779060i
$31$	−33.6488	−	10.9332i	−1.08545	−	0.352683i	−0.288961	−	0.957341i	$-0.593310\pi$
$31$	−33.6488	−	10.9332i	−1.08545	−	0.352683i	−0.796485	+	0.604658i	$0.793310\pi$
$32$	−19.0122	−	25.7398i	−0.594131	−	0.804369i
$33$	0.421397	−	8.37319i	0.0127696	−	0.253733i
$34$	0.415197	+	3.24555i	0.0122117	+	0.0954574i
$35$	20.3535	+	6.61325i	0.581528	+	0.188950i
$36$	21.3844	−	26.0155i	0.594012	−	0.722654i
$37$	−42.9061	−	31.1731i	−1.15962	−	0.842516i	−0.169893	−	0.985462i	$-0.554342\pi$
$37$	−42.9061	−	31.1731i	−1.15962	−	0.842516i	−0.989730	+	0.142946i	$0.954342\pi$
$38$	12.9209	+	27.3465i	0.340023	+	0.719645i
$39$	−2.26242	+	0.735104i	−0.0580107	+	0.0188488i
$40$	−4.36688	+	17.3473i	−0.109172	+	0.433684i
$41$	−3.78700	+	2.75142i	−0.0923659	+	0.0671077i	−0.633010	−	0.774144i	$-0.718181\pi$
$41$	−3.78700	+	2.75142i	−0.0923659	+	0.0671077i	0.540644	+	0.841252i	$0.318181\pi$
$42$	14.3349	+	2.71116i	0.341306	+	0.0645513i
$43$			24.1885i			0.562523i	0.959631	+	0.281261i	$0.0907528\pi$
$43$			24.1885i			0.562523i	−0.959631	+	0.281261i	$0.909247\pi$
$44$	−21.7996	−	38.2201i	−0.495446	−	0.868639i
$45$	−18.8257			−0.418349
$46$	−3.39087	+	17.9287i	−0.0737145	+	0.389755i
$47$	6.89694	+	9.49282i	0.146743	+	0.201975i	0.876061	−	0.482200i	$-0.160162\pi$
$47$	6.89694	+	9.49282i	0.146743	+	0.201975i	−0.729318	+	0.684175i	$0.760162\pi$
$48$	−1.45223	+	12.1078i	−0.0302548	+	0.252246i
$49$	−13.1641	−	40.5150i	−0.268655	−	0.826836i
$50$	9.04156	−	4.27202i	0.180831	−	0.0854404i
$51$	0.732909	−	1.00876i	0.0143708	−	0.0197797i
$52$	−7.92776	+	9.64464i	−0.152457	+	0.185474i
$53$	−11.5593	+	35.5760i	−0.218101	+	0.671244i	0.780818	+	0.624758i	$0.214802\pi$
$53$	−11.5593	+	35.5760i	−0.218101	+	0.671244i	−0.998919	+	0.0464864i	$0.985198\pi$
$54$	−26.3377	+	3.36933i	−0.487736	+	0.0623951i
$55$	−8.76701	+	22.9813i	−0.159400	+	0.417842i
$56$	71.0557	−	28.5216i	1.26885	−	0.509314i
$57$	3.56171	−	10.9618i	0.0624861	−	0.192313i
$58$	68.0781	+	72.2677i	1.17376	+	1.24599i
$59$	33.0063	−	45.4293i	0.559430	−	0.769989i	−0.431824	−	0.901958i	$-0.642130\pi$
$59$	33.0063	−	45.4293i	0.559430	−	0.769989i	0.991254	+	0.131969i	$0.0421299\pi$
$60$	5.74425	−	3.67082i	0.0957376	−	0.0611803i
$61$	27.3220	+	84.0884i	0.447902	+	1.37850i	0.879270	+	0.476323i	$0.158031\pi$
$61$	27.3220	+	84.0884i	0.447902	+	1.37850i	−0.431369	+	0.902176i	$0.641969\pi$
$62$	62.0618	+	33.9917i	1.00100	+	0.548254i
$63$	47.3623	+	65.1886i	0.751782	+	1.03474i
$64$	27.7953	+	57.6491i	0.434301	+	0.900768i
$65$	6.97917			0.107372
$66$	−3.94019	+	16.2981i	−0.0596999	+	0.246940i
$67$		−	58.1153i		−	0.867392i	−0.901059	−	0.433696i	$-0.857209\pi$
$67$		−	58.1153i		−	0.867392i	0.901059	−	0.433696i	$-0.142791\pi$
$68$	0.390351	−	6.53235i	0.00574045	−	0.0960640i
$69$	5.62544	−	4.08712i	0.0815281	−	0.0592337i
$70$	−37.5399	−	20.5609i	−0.536285	−	0.293727i
$71$	95.0277	−	30.8764i	1.33842	−	0.434878i	0.449637	−	0.893211i	$-0.351553\pi$
$71$	95.0277	−	30.8764i	1.33842	−	0.434878i	0.888781	+	0.458333i	$0.151553\pi$
$72$	−51.6931	+	43.1768i	−0.717959	+	0.599677i
$73$	−29.7244	−	21.5961i	−0.407184	−	0.295836i	0.365277	−	0.930899i	$-0.380974\pi$
$73$	−29.7244	−	21.5961i	−0.407184	−	0.295836i	−0.772461	+	0.635063i	$0.780974\pi$
$74$	72.7312	+	77.2071i	0.982855	+	1.04334i
$75$	−3.62430	−	1.17761i	−0.0483240	−	0.0157014i
$76$	−15.2277	−	58.5426i	−0.200364	−	0.770298i
$77$	101.635	−	27.4591i	1.31993	−	0.356612i
$78$	4.71924	−	0.603722i	0.0605030	−	0.00774003i
$79$	70.8877	+	23.0328i	0.897313	+	0.291555i	0.721127	−	0.692802i	$-0.243624\pi$
$79$	70.8877	+	23.0328i	0.897313	+	0.291555i	0.176185	+	0.984357i	$0.443624\pi$
$80$	15.0291	−	32.4673i	0.187864	−	0.405841i
$81$	−53.1147	−	38.5901i	−0.655737	−	0.476421i
$82$	8.46469	−	3.99946i	0.103228	−	0.0487739i
$83$	−38.8899	+	12.6361i	−0.468553	+	0.152242i	−0.533771	−	0.845629i	$-0.679226\pi$
$83$	−38.8899	+	12.6361i	−0.468553	+	0.152242i	0.0652183	+	0.997871i	$0.479226\pi$
$84$	−27.1627	−	10.6557i	−0.323365	−	0.126854i
$85$	−2.95955	+	2.15024i	−0.0348183	+	0.0252970i
$86$	8.99017	−	47.5343i	0.104537	−	0.552724i
$87$		−	37.8351i		−	0.434887i
$88$	28.6345	+	83.2110i	0.325392	+	0.945579i
$89$	116.343			1.30722			0.653612	−	0.756830i	$-0.273253\pi$
$89$	116.343			1.30722			0.653612	+	0.756830i	$0.273253\pi$
$90$	36.9955	+	6.99698i	0.411062	+	0.0777442i
$91$	−17.5584	−	24.1671i	−0.192950	−	0.265572i
$92$	13.3272	−	33.9726i	0.144861	−	0.369267i
$93$	−8.33285	−	25.6459i	−0.0896005	−	0.275762i
$94$	−10.0254	−	21.2183i	−0.106653	−	0.225727i
$95$	−19.8761	+	27.3572i	−0.209223	+	0.287970i
$96$	7.35400	−	23.2541i	0.0766041	−	0.242230i
$97$	13.7668	−	42.3699i	0.141926	−	0.436803i	−0.854677	−	0.519160i	$-0.826245\pi$
$97$	13.7668	−	42.3699i	0.141926	−	0.436803i	0.996603	+	0.0823573i	$0.0262449\pi$
$98$	10.8113	+	84.5112i	0.110320	+	0.862359i
$99$	−77.5646	+	50.6002i	−0.783481	+	0.511113i
$100$	−19.3559	+	5.03472i	−0.193559	+	0.0503472i
$101$	−38.1746	+	117.489i	−0.377967	+	1.16326i	0.563489	+	0.826124i	$0.309459\pi$
$101$	−38.1746	+	117.489i	−0.377967	+	1.16326i	−0.941455	+	0.337138i	$0.890541\pi$
$102$	−1.81521	+	1.70998i	−0.0177962	+	0.0167645i
$103$	−115.343	+	158.756i	−1.11983	+	1.54132i	−0.313761	+	0.949502i	$0.601589\pi$
$103$	−115.343	+	158.756i	−1.11983	+	1.54132i	−0.806073	+	0.591816i	$0.798411\pi$
$104$	19.1640	−	16.0067i	0.184269	−	0.153911i
$105$	5.04037	+	15.5127i	0.0480035	+	0.147740i
$106$	35.9385	−	65.6162i	0.339043	−	0.619021i
$107$	28.1635	+	38.7638i	0.263211	+	0.362278i	0.920083	−	0.391723i	$-0.128121\pi$
$107$	28.1635	+	38.7638i	0.263211	+	0.362278i	−0.656872	+	0.754002i	$0.728121\pi$
$108$	53.0102	+	3.16771i	0.490835	+	0.0293306i
$109$	11.5938			0.106365			0.0531824	−	0.998585i	$-0.483064\pi$
$109$	11.5938			0.106365			0.0531824	+	0.998585i	$0.483064\pi$
$110$	25.7701	−	41.9035i	0.234273	−	0.380941i
$111$		−	40.4212i		−	0.364155i
$112$	−150.237	+	29.6401i	−1.34140	+	0.264644i
$113$	−108.027	+	78.4859i	−0.955988	+	0.694566i	−0.952215	−	0.305427i	$-0.901201\pi$
$113$	−108.027	+	78.4859i	−0.955988	+	0.694566i	−0.00377227	+	0.999993i	$0.501201\pi$
$114$	−11.0735	+	20.2179i	−0.0971362	+	0.177350i
$115$	−19.4018	+	6.30404i	−0.168712	+	0.0548177i
$116$	−106.925	−	167.320i	−0.921764	−	1.44242i
$117$	21.2590	+	15.4456i	0.181701	+	0.132013i
$118$	−81.7476	+	77.0085i	−0.692776	+	0.652614i
$119$	14.8915	+	4.83853i	0.125138	+	0.0406599i
$120$	−12.6527	+	5.07877i	−0.105439	+	0.0423231i
$121$	25.6484	+	118.250i	0.211970	+	0.977276i
$122$	−22.4388	−	175.402i	−0.183925	−	1.43772i
$123$	−3.39306	−	1.10247i	−0.0275859	−	0.00896319i
$124$	−109.328	−	89.8659i	−0.881675	−	0.724725i
$125$	9.04508	+	6.57164i	0.0723607	+	0.0525731i
$126$	−68.8458	−	145.709i	−0.546395	−	1.15642i
$127$	−4.42432	+	1.43755i	−0.0348372	+	0.0113193i	−0.326384	−	0.945237i	$-0.605830\pi$
$127$	−4.42432	+	1.43755i	−0.0348372	+	0.0113193i	0.291547	+	0.956557i	$0.405830\pi$
$128$	−33.1956	−	123.621i	−0.259341	−	0.965786i
$129$	−14.9147	+	10.8361i	−0.115618	+	0.0840012i
$130$	−13.7152	−	2.59396i	−0.105502	−	0.0199535i
$131$		−	234.292i		−	1.78849i	−0.447576	−	0.894246i	$-0.647712\pi$
$131$		−	234.292i		−	1.78849i	0.447576	−	0.894246i	$-0.352288\pi$
$132$	13.8006	−	30.5639i	0.104550	−	0.231544i
$133$	144.736			1.08824
$134$	−21.5998	+	114.206i	−0.161193	+	0.852283i
$135$	−17.4493	−	24.0169i	−0.129254	−	0.177903i
$136$	−3.19499	+	12.6920i	−0.0234926	+	0.0933239i
$137$	−18.7864	−	57.8185i	−0.137127	−	0.422033i	0.858788	−	0.512331i	$-0.171218\pi$
$137$	−18.7864	−	57.8185i	−0.137127	−	0.422033i	−0.995915	+	0.0902985i	$0.971218\pi$
$138$	−12.5740	+	5.94104i	−0.0911157	+	0.0430510i
$139$	4.30579	−	5.92642i	0.0309769	−	0.0426361i	−0.793248	−	0.608899i	$-0.791611\pi$
$139$	4.30579	−	5.92642i	0.0309769	−	0.0426361i	0.824225	+	0.566263i	$0.191611\pi$
$140$	66.1301	+	54.3581i	0.472358	+	0.388272i
$141$	−2.76355	+	8.50534i	−0.0195997	+	0.0603215i
$142$	−198.221	+	25.3580i	−1.39592	+	0.178577i
$143$	28.7552	−	18.7588i	0.201085	−	0.131180i
$144$	117.633	−	65.6365i	0.816895	−	0.455809i
$145$	−34.3017	+	105.570i	−0.236563	+	0.728067i
$146$	50.3867	+	53.4875i	0.345114	+	0.366353i
$147$	19.0843	−	26.2672i	0.129825	−	0.178689i
$148$	−114.233	−	178.757i	−0.771844	−	1.20782i
$149$	−22.0579	−	67.8872i	−0.148039	−	0.455619i	0.849350	−	0.527830i	$-0.176994\pi$
$149$	−22.0579	−	67.8872i	−0.148039	−	0.455619i	−0.997389	+	0.0722117i	$0.976994\pi$
$150$	6.68465	+	3.66123i	0.0445643	+	0.0244082i
$151$	−26.4721	−	36.4357i	−0.175312	−	0.241296i	0.712315	−	0.701860i	$-0.247647\pi$
$151$	−26.4721	−	36.4357i	−0.175312	−	0.241296i	−0.887626	+	0.460565i	$0.847647\pi$
$152$	8.16624	+	120.705i	0.0537252	+	0.794115i
$153$	−13.7737			−0.0900240
$154$	−209.934	+	16.1869i	−1.36321	+	0.105110i
$155$			79.1131i			0.510407i
$156$	−9.49845	−	0.567594i	−0.0608875	−	0.00363842i
$157$	215.708	−	156.721i	1.37393	−	0.998222i	0.376517	−	0.926410i	$-0.377122\pi$
$157$	215.708	−	156.721i	1.37393	−	0.998222i	0.997418	−	0.0718124i	$-0.0228783\pi$
$158$	−130.745	−	71.6101i	−0.827501	−	0.453229i
$159$	−27.1147	+	8.81009i	−0.170532	+	0.0554094i
$160$	−41.6019	+	58.2176i	−0.260012	+	0.363860i
$161$	70.6410	+	51.3237i	0.438764	+	0.318781i
$162$	90.0361	+	95.5769i	0.555778	+	0.589981i
$163$	−73.9072	−	24.0139i	−0.453418	−	0.147324i	0.0733999	−	0.997303i	$-0.476615\pi$
$163$	−73.9072	−	24.0139i	−0.453418	−	0.147324i	−0.526818	+	0.849978i	$0.676615\pi$
$164$	−18.1210	+	4.71350i	−0.110494	+	0.0287408i
$165$	−18.0978	+	4.88958i	−0.109684	+	0.0296338i
$166$	81.1214	−	10.3777i	0.488683	−	0.0625162i
$167$	35.7406	+	11.6128i	0.214016	+	0.0695379i	0.414063	−	0.910248i	$-0.364109\pi$
$167$	35.7406	+	11.6128i	0.214016	+	0.0695379i	−0.200047	+	0.979786i	$0.564109\pi$
$168$	49.4186	+	31.0358i	0.294158	+	0.184737i
$169$	128.843	+	93.6096i	0.762382	+	0.553903i
$170$	6.61519	−	3.12559i	0.0389129	−	0.0183858i
$171$	−121.088	+	39.3439i	−0.708117	+	0.230081i
$172$	−35.3343	+	90.0712i	−0.205432	+	0.523670i
$173$	243.517	−	176.926i	1.40761	−	1.02269i	0.413949	−	0.910300i	$-0.364149\pi$
$173$	243.517	−	176.926i	1.40761	−	1.02269i	0.993664	−	0.112391i	$-0.0358509\pi$
$174$	−14.0622	+	74.3522i	−0.0808175	+	0.427311i
$175$		−	47.8539i		−	0.273451i
$176$	−25.3442	−	174.166i	−0.144001	−	0.989577i
$177$	42.7983			0.241798
$178$	−228.633	−	43.2413i	−1.28445	−	0.242929i
$179$	−183.916	−	253.139i	−1.02746	−	1.41418i	−0.906835	−	0.421486i	$-0.861509\pi$
$179$	−183.916	−	253.139i	−1.02746	−	1.41418i	−0.120629	−	0.992698i	$-0.538491\pi$
$180$	−70.1016	−	27.5004i	−0.389454	−	0.152780i
$181$	73.7817	+	227.077i	0.407634	+	1.25457i	0.918676	+	0.395012i	$0.129260\pi$
$181$	73.7817	+	227.077i	0.407634	+	1.25457i	−0.511042	+	0.859556i	$0.670740\pi$
$182$	25.5229	+	54.0182i	0.140236	+	0.296803i
$183$	−39.6092	+	54.5174i	−0.216444	+	0.297909i
$184$	−38.8167	+	61.8083i	−0.210961	+	0.335914i
$185$	−36.6462	+	112.785i	−0.198087	+	0.609650i
$186$	6.84355	+	53.4953i	0.0367933	+	0.287609i
$187$	−6.41431	+	16.8141i	−0.0343011	+	0.0899149i
$188$	11.8153	+	45.4236i	0.0628471	+	0.241615i
$189$	−39.2648	+	120.845i	−0.207750	+	0.639390i
$190$	49.2277	−	46.3739i	0.259093	−	0.244073i
$191$	−181.210	+	249.414i	−0.948742	+	1.30583i	0.00334140	+	0.999994i	$0.498936\pi$
$191$	−181.210	+	249.414i	−0.948742	+	1.30583i	−0.952084	+	0.305837i	$0.901064\pi$
$192$	−23.0947	+	42.9647i	−0.120285	+	0.223775i
$193$	−105.817	−	325.671i	−0.548274	−	1.68741i	−0.713075	−	0.701088i	$-0.752698\pi$
$193$	−105.817	−	325.671i	−0.548274	−	1.68741i	0.164801	−	0.986327i	$-0.447302\pi$
$194$	−42.8017	+	78.1469i	−0.220627	+	0.402819i
$195$	3.12659	+	4.30338i	0.0160338	+	0.0220686i
$196$	10.1644	−	170.096i	0.0518590	−	0.867839i
$197$	−310.061			−1.57391			−0.786956	−	0.617009i	$-0.788344\pi$
$197$	−310.061			−1.57391			−0.786956	+	0.617009i	$0.788344\pi$
$198$	171.234	−	70.6090i	0.864816	−	0.356611i
$199$			275.222i			1.38302i	0.722365	+	0.691512i	$0.243055\pi$
$199$			275.222i			1.38302i	−0.722365	+	0.691512i	$0.756945\pi$
$200$	39.9088	−	2.70000i	0.199544	−	0.0135000i
$201$	35.8340	−	26.0349i	0.178279	−	0.129527i
$202$	118.687	−	216.697i	0.587559	−	1.07276i
$203$	451.858	−	146.817i	2.22590	−	0.723239i
$204$	4.20274	−	2.68572i	0.0206017	−	0.0131653i
$205$	8.46799	+	6.15236i	0.0413073	+	0.0300115i
$206$	285.672	−	269.111i	1.38676	−	1.30636i
$207$	−73.0506	−	23.7356i	−0.352901	−	0.114665i
$208$	−43.6095	+	24.3331i	−0.209661	+	0.116986i
$209$	−8.36127	+	166.139i	−0.0400061	+	0.794924i
$210$	−4.13953	−	32.3583i	−0.0197120	−	0.154087i
$211$	158.344	+	51.4490i	0.750445	+	0.243834i	0.659173	−	0.751992i	$-0.270907\pi$
$211$	158.344	+	51.4490i	0.750445	+	0.243834i	0.0912723	+	0.995826i	$0.470907\pi$
$212$	−95.0127	+	115.589i	−0.448173	+	0.545232i
$213$	61.6097	+	44.7621i	0.289247	+	0.210151i
$214$	−40.9385	−	86.6447i	−0.191301	−	0.404882i
$215$	51.4399	−	16.7138i	0.239255	−	0.0777388i
$216$	−102.996	−	25.9274i	−0.476835	−	0.120034i
$217$	273.948	−	199.035i	1.26243	−	0.917212i
$218$	−22.7836	−	4.30907i	−0.104512	−	0.0197664i
$219$		−	28.0029i		−	0.127867i
$220$	−66.2167	+	72.7691i	−0.300985	+	0.330769i
$221$	5.10626			0.0231052
$222$	−15.0234	+	79.4341i	−0.0676730	+	0.357811i
$223$	157.104	+	216.236i	0.704504	+	0.969666i	0.999898	+	0.0142908i	$0.00454904\pi$
$223$	157.104	+	216.236i	0.704504	+	0.969666i	−0.295394	+	0.955375i	$0.595451\pi$
$224$	306.256	−	2.40899i	1.36721	−	0.0107544i
$225$	13.0082	+	40.0352i	0.0578144	+	0.177934i
$226$	241.461	−	114.087i	1.06841	−	0.504810i
$227$	−76.5696	+	105.389i	−0.337311	+	0.464269i	−0.943654	−	0.330935i	$-0.892636\pi$
$227$	−76.5696	+	105.389i	−0.337311	+	0.464269i	0.606342	+	0.795204i	$0.292636\pi$
$228$	29.2757	−	35.6158i	0.128402	−	0.156210i
$229$	85.0594	−	261.786i	0.371438	−	1.14317i	−0.574412	−	0.818566i	$-0.694769\pi$
$229$	85.0594	−	261.786i	0.371438	−	1.14317i	0.945850	−	0.324603i	$-0.105231\pi$
$230$	40.4708	−	5.17734i	0.175960	−	0.0225102i
$231$	62.4624	+	50.3668i	0.270400	+	0.218038i
$232$	147.936	+	368.552i	0.637655	+	1.58859i
$233$	−117.614	+	361.980i	−0.504783	+	1.55356i	0.296353	+	0.955079i	$0.404230\pi$
$233$	−117.614	+	361.980i	−0.504783	+	1.55356i	−0.801136	+	0.598483i	$0.795770\pi$
$234$	−36.0367	−	38.2544i	−0.154003	−	0.163480i
$235$	15.4220	−	21.2266i	0.0656256	−	0.0903259i
$236$	189.269	−	120.951i	0.801988	−	0.512504i
$237$	17.5547	+	54.0280i	0.0740707	+	0.227966i
$238$	−27.4658	−	15.0432i	−0.115403	−	0.0632069i
$239$	−34.6444	−	47.6840i	−0.144956	−	0.199514i	0.730365	−	0.683057i	$-0.239350\pi$
$239$	−34.6444	−	47.6840i	−0.144956	−	0.199514i	−0.875321	+	0.483542i	$0.839350\pi$
$240$	26.7523	−	5.27795i	0.111468	−	0.0219915i
$241$	−370.100			−1.53568			−0.767842	−	0.640639i	$-0.778670\pi$
$241$	−370.100			−1.53568			−0.767842	+	0.640639i	$0.778670\pi$
$242$	−6.45285	−	241.914i	−0.0266647	−	0.999644i
$243$		−	169.524i		−	0.697631i
$244$	−21.0961	+	353.034i	−0.0864592	+	1.44686i
$245$	−77.0640	+	55.9903i	−0.314547	+	0.228532i
$246$	6.25816	+	3.42764i	0.0254397	+	0.0139335i
$247$	44.8904	−	14.5858i	0.181743	−	0.0590518i
$248$	181.446	+	217.235i	0.731637	+	0.875947i
$249$	−25.2136	−	18.3188i	−0.101260	−	0.0735694i
$250$	−15.3326	−	16.2761i	−0.0613302	−	0.0651045i
$251$	−125.908	−	40.9099i	−0.501624	−	0.162988i	0.0472655	−	0.998882i	$-0.484949\pi$
$251$	−125.908	−	40.9099i	−0.501624	−	0.162988i	−0.548890	+	0.835895i	$0.684949\pi$
$252$	81.1371	+	311.930i	0.321972	+	1.23782i
$253$	−62.9942	+	78.1223i	−0.248989	+	0.308784i
$254$	9.22880	−	1.18062i	0.0363339	−	0.00464812i
$255$	−2.65169	−	0.861586i	−0.0103988	−	0.00337877i
$256$	19.2885	+	255.272i	0.0753456	+	0.997157i
$257$	−250.554	−	182.038i	−0.974917	−	0.708319i	−0.0183500	−	0.999832i	$-0.505841\pi$
$257$	−250.554	−	182.038i	−0.974917	−	0.708319i	−0.956567	+	0.291513i	$0.905841\pi$
$258$	33.3372	−	15.7514i	0.129214	−	0.0610520i
$259$	482.742	−	156.852i	1.86387	−	0.605608i
$260$	25.9885	+	10.1951i	0.0999557	+	0.0392119i
$261$	−338.120	+	245.659i	−1.29548	+	0.941222i
$262$	−87.0799	+	460.423i	−0.332366	+	1.75734i
$263$		−	189.659i		−	0.721138i	−0.932733	−	0.360569i	$-0.882583\pi$
$263$		−	189.659i		−	0.721138i	0.932733	−	0.360569i	$-0.117417\pi$
$264$	−38.4802	+	54.9336i	−0.145758	+	0.208082i
$265$	83.6441			0.315638
$266$	−284.429	−	53.7942i	−1.06928	−	0.202234i
$267$	52.1202	+	71.7373i	0.195207	+	0.268679i
$268$	84.8942	−	216.405i	0.316769	−	0.807482i
$269$	−102.424	−	315.227i	−0.380757	−	1.17185i	−0.939512	−	0.342516i	$-0.888721\pi$
$269$	−102.424	−	315.227i	−0.380757	−	1.17185i	0.558755	−	0.829333i	$-0.311279\pi$
$270$	25.3643	+	53.6824i	0.0939417	+	0.198824i
$271$	15.6229	−	21.5031i	0.0576491	−	0.0793471i	−0.779219	−	0.626752i	$-0.784384\pi$
$271$	15.6229	−	21.5031i	0.0576491	−	0.0793471i	0.836868	+	0.547405i	$0.184384\pi$
$272$	10.9960	−	23.7544i	0.0404263	−	0.0873325i
$273$	7.03553	−	21.6531i	0.0257712	−	0.0793155i
$274$	15.4287	+	120.605i	0.0563093	+	0.440164i
$275$	54.9305	+	2.76448i	0.199747	+	0.0100527i
$276$	26.9180	−	7.00172i	0.0975290	−	0.0253685i
$277$	94.9161	−	292.122i	0.342657	−	1.05459i	−0.620169	−	0.784469i	$-0.712936\pi$
$277$	94.9161	−	292.122i	0.342657	−	1.05459i	0.962826	−	0.270123i	$-0.0870642\pi$
$278$	−10.6643	+	10.0460i	−0.0383607	+	0.0361368i
$279$	−175.085	+	240.983i	−0.627544	+	0.863740i
$280$	−109.753	−	131.401i	−0.391975	−	0.469290i
$281$	52.6783	+	162.127i	0.187467	+	0.576965i	0.999982	−	0.00597528i	$-0.00190200\pi$
$281$	52.6783	+	162.127i	0.187467	+	0.576965i	−0.812515	+	0.582941i	$0.801902\pi$
$282$	8.59202	−	15.6872i	0.0304681	−	0.0556285i
$283$	−219.344	−	301.901i	−0.775066	−	1.06679i	−0.995809	−	0.0914550i	$-0.970848\pi$
$283$	−219.344	−	301.901i	−0.775066	−	1.06679i	0.220743	−	0.975332i	$-0.429152\pi$
$284$	398.960	+	23.8405i	1.40479	+	0.0839454i
$285$	−25.7728			−0.0904308
$286$	−63.4807	+	26.1766i	−0.221961	+	0.0915265i
$287$		−	44.8008i		−	0.156100i
$288$	−255.563	+	85.2655i	−0.887371	+	0.296061i
$289$	231.641	−	168.297i	0.801524	−	0.582342i
$290$	106.646	−	194.712i	0.367743	−	0.671422i
$291$	32.2927	−	10.4925i	0.110972	−	0.0360568i
$292$	−79.1381	−	123.839i	−0.271021	−	0.424105i
$293$	−253.670	−	184.302i	−0.865769	−	0.629018i	0.0636796	−	0.997970i	$-0.479716\pi$
$293$	−253.670	−	184.302i	−0.865769	−	0.629018i	−0.929448	+	0.368953i	$0.879716\pi$
$294$	−47.2664	+	44.5263i	−0.160770	+	0.151450i
$295$	−119.418	−	38.8013i	−0.404807	−	0.131530i
$296$	158.047	+	393.743i	0.533944	+	1.33021i
$297$	−136.447	−	52.0523i	−0.459416	−	0.175260i
$298$	18.1156	+	141.608i	0.0607905	+	0.475193i
$299$	27.0817	+	8.79939i	0.0905744	+	0.0294294i
$300$	−11.7756	−	9.67941i	−0.0392521	−	0.0322647i
$301$	−187.290	−	136.074i	−0.622225	−	0.452073i
$302$	38.4798	+	81.4409i	0.127417	+	0.269672i
$303$	−89.5461	+	29.0953i	−0.295532	+	0.0960240i
$304$	28.8148	−	240.241i	0.0947855	−	0.790266i
$305$	159.946	−	116.207i	0.524412	−	0.381008i
$306$	27.0675	+	5.11928i	0.0884559	+	0.0167297i
$307$		−	265.822i		−	0.865871i	−0.901425	−	0.432935i	$-0.857478\pi$
$307$		−	265.822i		−	0.865871i	0.901425	−	0.432935i	$-0.142522\pi$
$308$	418.571	+	46.2167i	1.35900	+	0.150054i
$309$	−149.561			−0.484018
$310$	29.4041	−	155.470i	0.0948519	−	0.501516i
$311$	197.511	+	271.850i	0.635082	+	0.874116i	0.998341	−	0.0575722i	$-0.0183359\pi$
$311$	197.511	+	271.850i	0.635082	+	0.874116i	−0.363259	+	0.931688i	$0.618336\pi$
$312$	18.4550	+	4.64572i	0.0591507	+	0.0148901i
$313$	−104.875	−	322.772i	−0.335064	−	1.03122i	−0.966690	−	0.255949i	$-0.917612\pi$
$313$	−104.875	−	322.772i	−0.335064	−	1.03122i	0.631626	−	0.775273i	$-0.282388\pi$
$314$	−482.149	+	227.809i	−1.53551	+	0.725508i
$315$	105.905	−	145.766i	0.336207	−	0.462749i
$316$	230.320	+	189.320i	0.728860	+	0.599113i
$317$	−11.9209	+	36.6887i	−0.0376053	+	0.115737i	−0.968097	−	0.250576i	$-0.919380\pi$
$317$	−11.9209	+	36.6887i	−0.0376053	+	0.115737i	0.930492	+	0.366313i	$0.119380\pi$
$318$	56.5592	−	7.23550i	0.177859	−	0.0227531i
$319$	142.425	+	527.159i	0.446474	+	1.65254i
$320$	103.392	−	98.9447i	0.323101	−	0.309202i
$321$	−11.2849	+	34.7314i	−0.0351555	+	0.108198i
$322$	−119.745	−	127.115i	−0.371880	−	0.394766i
$323$	−14.5422	+	20.0157i	−0.0450224	+	0.0619680i
$324$	−141.412	−	221.288i	−0.436458	−	0.682988i
$325$	−4.82249	−	14.8421i	−0.0148384	−	0.0456680i
$326$	136.314	+	74.6604i	0.418142	+	0.229020i
$327$	5.19386	+	7.14874i	0.0158834	+	0.0218616i
$328$	37.3625	−	2.52773i	0.113910	−	0.00770650i
$329$	−112.301			−0.341342
$330$	37.3825	−	2.88236i	0.113280	−	0.00873443i
$331$			276.676i			0.835878i	0.908475	+	0.417939i	$0.137247\pi$
$331$			276.676i			0.835878i	−0.908475	+	0.417939i	$0.862753\pi$
$332$	−163.274	−	9.75667i	−0.491788	−	0.0293876i
$333$	−361.231	+	262.450i	−1.08478	+	0.788137i
$334$	−65.9199	−	36.1049i	−0.197365	−	0.108098i
$335$	−123.590	+	40.1567i	−0.368924	+	0.119871i
$336$	−85.5804	−	79.3579i	−0.254704	−	0.236184i
$337$	28.3271	+	20.5808i	0.0840567	+	0.0610707i	0.629020	−	0.777389i	$-0.283456\pi$
$337$	28.3271	+	20.5808i	0.0840567	+	0.0610707i	−0.544963	+	0.838460i	$0.683456\pi$
$338$	−218.405	−	231.845i	−0.646167	−	0.685933i
$339$	−96.7892	−	31.4487i	−0.285514	−	0.0927691i
$340$	−14.1616	+	3.68361i	−0.0416518	+	0.0108342i
$341$	212.642	+	325.957i	0.623584	+	0.955887i
$342$	252.580	−	32.3121i	0.738539	−	0.0944798i
$343$	−58.2556	−	18.9284i	−0.169841	−	0.0551848i
$344$	102.914	−	163.872i	0.299170	−	0.476371i
$345$	−12.5789	−	9.13909i	−0.0364605	−	0.0264901i
$346$	−544.309	+	257.179i	−1.57315	+	0.743292i
$347$	254.573	−	82.7158i	0.733640	−	0.238374i	0.0817130	−	0.996656i	$-0.473961\pi$
$347$	254.573	−	82.7158i	0.733640	−	0.238374i	0.651927	+	0.758282i	$0.273961\pi$
$348$	55.2692	−	140.888i	0.158819	−	0.404849i
$349$	−81.7493	+	59.3944i	−0.234239	+	0.170184i	−0.698713	−	0.715402i	$-0.746243\pi$
$349$	−81.7493	+	59.3944i	−0.234239	+	0.170184i	0.464474	+	0.885587i	$0.346243\pi$
$350$	−17.7859	+	94.0407i	−0.0508170	+	0.268688i
$351$			41.4374i			0.118055i
$352$	−14.9269	+	351.683i	−0.0424060	+	0.999100i
$353$	265.736			0.752792			0.376396	−	0.926459i	$-0.377163\pi$
$353$	265.736			0.752792			0.376396	+	0.926459i	$0.377163\pi$
$354$	−84.1056	−	15.9069i	−0.237586	−	0.0449348i
$355$	−131.325	−	180.753i	−0.369930	−	0.509165i
$356$	433.228	+	169.952i	1.21693	+	0.477394i
$357$	3.68775	+	11.3497i	0.0103298	+	0.0317919i
$358$	267.340	+	565.815i	0.746761	+	1.58049i
$359$	338.315	−	465.651i	0.942383	−	1.29708i	−0.0124461	−	0.999923i	$-0.503962\pi$
$359$	338.315	−	465.651i	0.942383	−	1.29708i	0.954829	−	0.297156i	$-0.0960382\pi$
$360$	127.540	+	80.0975i	0.354278	+	0.222493i
$361$	40.8845	−	125.829i	0.113253	−	0.348558i
$362$	−60.5950	−	473.665i	−0.167389	−	1.30847i
$363$	−61.4233	+	68.7896i	−0.169210	+	0.189503i
$364$	−30.0796	−	115.641i	−0.0826363	−	0.317694i
$365$	−25.3877	+	78.1353i	−0.0695553	+	0.214069i
$366$	98.1011	−	92.4139i	0.268036	−	0.252497i
$367$	−220.806	+	303.914i	−0.601652	+	0.828103i	−0.995858	−	0.0909189i	$-0.971020\pi$
$367$	−220.806	+	303.914i	−0.601652	+	0.828103i	0.394206	+	0.919022i	$0.371020\pi$
$368$	99.2536	−	107.036i	0.269711	−	0.290859i
$369$	12.1783	+	37.4809i	0.0330035	+	0.101574i
$370$	113.935	−	208.021i	0.307932	−	0.562219i
$371$	−210.434	−	289.638i	−0.567208	−	0.780695i
$372$	6.43402	−	107.671i	0.0172957	−	0.289437i
$373$	569.644			1.52719			0.763597	−	0.645693i	$-0.223431\pi$
$373$	569.644			1.52719			0.763597	+	0.645693i	$0.223431\pi$
$374$	18.8545	−	30.6584i	0.0504130	−	0.0819742i
$375$			8.52124i			0.0227233i
$376$	−6.33623	−	93.6561i	−0.0168517	−	0.249085i
$377$	125.350	−	91.0721i	0.332493	−	0.241571i
$378$	122.076	−	222.886i	0.322953	−	0.589645i
$379$	−338.309	+	109.923i	−0.892635	+	0.290035i	−0.719194	−	0.694810i	$-0.755489\pi$
$379$	−338.309	+	109.923i	−0.892635	+	0.290035i	−0.173441	+	0.984844i	$0.555489\pi$
$380$	−113.976	+	72.8356i	−0.299938	+	0.191673i
$381$	−2.86844	−	2.08404i	−0.00752871	−	0.00546993i
$382$	448.807	−	422.788i	1.17489	−	1.10678i
$383$	−476.382	−	154.786i	−1.24382	−	0.404140i	−0.388115	−	0.921611i	$-0.626874\pi$
$383$	−476.382	−	154.786i	−1.24382	−	0.404140i	−0.855701	+	0.517471i	$0.826874\pi$
$384$	61.3535	−	75.8490i	0.159775	−	0.197524i
$385$	−128.623	−	197.165i	−0.334086	−	0.512117i
$386$	86.9047	+	679.325i	0.225142	+	1.75991i
$387$	193.678	+	62.9299i	0.500461	+	0.162610i
$388$	113.157	−	137.663i	0.291642	−	0.354802i
$389$	−546.381	−	396.969i	−1.40458	−	1.02049i	−0.994083	−	0.108623i	$-0.965356\pi$
$389$	−546.381	−	396.969i	−1.40458	−	1.02049i	−0.410495	−	0.911863i	$-0.634644\pi$
$390$	−4.54480	−	9.61889i	−0.0116533	−	0.0246638i
$391$	−14.1952	+	4.61230i	−0.0363049	+	0.0117962i
$392$	−83.1946	+	330.489i	−0.212231	+	0.843084i
$393$	144.465	−	104.960i	0.367596	−	0.267074i
$394$	609.319	+	115.241i	1.54650	+	0.292489i
$395$		−	166.667i		−	0.421942i
$396$	−362.745	+	75.1155i	−0.916023	+	0.189686i
$397$	−25.3917			−0.0639590			−0.0319795	−	0.999489i	$-0.510181\pi$
$397$	−25.3917			−0.0639590			−0.0319795	+	0.999489i	$0.510181\pi$
$398$	102.292	−	540.856i	0.257015	−	1.35893i
$399$	64.8399	+	89.2445i	0.162506	+	0.223670i
$400$	−79.4307	−	9.52702i	−0.198577	−	0.0238176i
$401$	−3.42431	−	10.5389i	−0.00853942	−	0.0262816i	0.946696	−	0.322128i	$-0.104398\pi$
$401$	−3.42431	−	10.5389i	−0.00853942	−	0.0262816i	−0.955235	+	0.295847i	$0.904398\pi$
$402$	−80.0961	+	37.8444i	−0.199244	+	0.0941403i
$403$	64.9084	−	89.3388i	0.161063	−	0.221684i
$404$	−313.779	+	381.733i	−0.776681	+	0.944883i
$405$	−45.3654	+	139.620i	−0.112013	+	0.344741i
$406$	−942.541	+	120.577i	−2.32153	+	0.296989i
$407$	152.160	+	563.190i	0.373857	+	1.38376i
$408$	−9.25727	+	3.71584i	−0.0226894	+	0.00910746i
$409$	81.7829	−	251.702i	0.199958	−	0.615408i	−0.799925	−	0.600101i	$-0.795127\pi$
$409$	81.7829	−	251.702i	0.199958	−	0.615408i	0.999883	−	0.0153078i	$-0.00487281\pi$
$410$	−14.3543	−	15.2377i	−0.0350105	−	0.0371651i
$411$	27.2349	−	37.4857i	0.0662651	−	0.0912060i
$412$	−661.413	+	422.671i	−1.60537	+	1.02590i
$413$	166.077	+	511.132i	0.402123	+	1.23761i
$414$	134.734	+	73.7951i	0.325445	+	0.178249i
$415$	53.7445	+	73.9729i	0.129505	+	0.178248i
$416$	94.7437	−	31.6101i	0.227749	−	0.0759859i
$417$	5.58319			0.0133889
$418$	78.1804	−	323.383i	0.187035	−	0.773642i
$419$		−	179.325i		−	0.427983i	−0.976836	−	0.213992i	$-0.931353\pi$
$419$		−	179.325i		−	0.427983i	0.976836	−	0.213992i	$-0.0686465\pi$
$420$	−3.89181	+	65.1278i	−0.00926621	+	0.155066i
$421$	360.024	−	261.573i	0.855163	−	0.621312i	−0.0714016	−	0.997448i	$-0.522747\pi$
$421$	360.024	−	261.573i	0.855163	−	0.621312i	0.926565	+	0.376135i	$0.122747\pi$
$422$	−292.049	−	159.958i	−0.692060	−	0.379046i
$423$	93.9528	−	30.5271i	0.222111	−	0.0721682i
$424$	229.677	−	191.838i	0.541690	−	0.452448i
$425$	6.61777	+	4.80809i	0.0155712	+	0.0113131i
$426$	−104.436	−	110.863i	−0.245155	−	0.260242i
$427$	−804.793	−	261.493i	−1.88476	−	0.612396i
$428$	48.2474	+	185.486i	0.112728	+	0.433380i
$429$	24.4487	+	9.32681i	0.0569900	+	0.0217408i
$430$	−107.300	+	13.7266i	−0.249534	+	0.0319224i
$431$	200.900	+	65.2764i	0.466125	+	0.151453i	0.532657	−	0.846331i	$-0.321193\pi$
$431$	200.900	+	65.2764i	0.466125	+	0.151453i	−0.0665320	+	0.997784i	$0.521193\pi$
$432$	192.768	+	89.2324i	0.446222	+	0.206557i
$433$	292.628	+	212.607i	0.675816	+	0.491009i	0.871967	−	0.489565i	$-0.162844\pi$
$433$	292.628	+	212.607i	0.675816	+	0.491009i	−0.196151	+	0.980574i	$0.562844\pi$
$434$	−612.328	+	289.317i	−1.41089	+	0.666630i
$435$	−80.4612	+	26.1434i	−0.184968	+	0.0600999i
$436$	43.1719	+	16.9360i	0.0990181	+	0.0388441i
$437$	−111.619	+	81.0958i	−0.255421	+	0.185574i
$438$	−10.4079	+	55.0303i	−0.0237623	+	0.125640i
$439$		−	568.506i		−	1.29500i	−0.762064	−	0.647502i	$-0.775814\pi$
$439$		−	568.506i		−	1.29500i	0.762064	−	0.647502i	$-0.224186\pi$
$440$	157.173	−	118.392i	0.357211	−	0.269073i
$441$	−358.654			−0.813273
$442$	−10.0346	−	1.89785i	−0.0227028	−	0.00429378i
$443$	−320.253	−	440.790i	−0.722919	−	0.995012i	−0.999422	−	0.0339992i	$-0.989176\pi$
$443$	−320.253	−	440.790i	−0.722919	−	0.995012i	0.276503	−	0.961013i	$-0.410824\pi$
$444$	59.0468	−	150.517i	0.132988	−	0.339003i
$445$	−80.3909	−	247.418i	−0.180654	−	0.555995i
$446$	−228.367	−	483.329i	−0.512033	−	1.08370i
$447$	31.9777	−	44.0136i	0.0715386	−	0.0984644i
$448$	−602.737	−	109.092i	−1.34540	−	0.243510i
$449$	−114.167	+	351.370i	−0.254270	+	0.782561i	0.739703	+	0.672933i	$0.234966\pi$
$449$	−114.167	+	351.370i	−0.254270	+	0.782561i	−0.993973	+	0.109628i	$0.965034\pi$
$450$	−10.6833	−	83.5105i	−0.0237407	−	0.185579i
$451$	51.4258	+	2.58810i	0.114026	+	0.00573859i
$452$	−516.912	+	134.456i	−1.14361	+	0.297468i
$453$	10.6072	−	32.6455i	0.0234154	−	0.0720651i
$454$	189.642	−	178.648i	0.417713	−	0.393497i
$455$	−39.2618	+	54.0392i	−0.0862897	+	0.118768i
$456$	−70.7689	+	59.1099i	−0.155195	+	0.129627i
$457$	74.5127	+	229.327i	0.163048	+	0.501809i	0.998887	−	0.0471650i	$-0.0150187\pi$
$457$	74.5127	+	229.327i	0.163048	+	0.501809i	−0.835840	+	0.548974i	$0.815019\pi$
$458$	−264.454	+	482.837i	−0.577410	+	1.05423i
$459$	−12.7666	−	17.5717i	−0.0278140	−	0.0382827i
$460$	−81.4559	−	4.86752i	−0.177078	−	0.0105816i
$461$	−81.6794			−0.177179			−0.0885894	−	0.996068i	$-0.528236\pi$
$461$	−81.6794			−0.177179			−0.0885894	+	0.996068i	$0.528236\pi$
$462$	−104.029	−	122.194i	−0.225171	−	0.264490i
$463$			196.860i			0.425183i	0.977141	+	0.212592i	$0.0681904\pi$
$463$			196.860i			0.425183i	−0.977141	+	0.212592i	$0.931810\pi$
$464$	−153.738	−	779.249i	−0.331331	−	1.67942i
$465$	−48.7813	+	35.4417i	−0.104906	+	0.0762187i
$466$	365.669	−	667.635i	0.784697	−	1.43269i
$467$	276.586	−	89.8681i	0.592261	−	0.192437i	0.00247492	−	0.999997i	$-0.499212\pi$
$467$	276.586	−	89.8681i	0.592261	−	0.192437i	0.589786	+	0.807560i	$0.299212\pi$
$468$	56.5998	+	88.5699i	0.120940	+	0.189252i
$469$	449.983	+	326.931i	0.959451	+	0.697082i
$470$	−38.1961	+	35.9817i	−0.0812682	+	0.0765569i
$471$	193.269	+	62.7969i	0.410338	+	0.133327i
$472$	−416.898	+	167.342i	−0.883259	+	0.354538i
$473$	167.016	−	207.125i	0.353099	−	0.437896i
$474$	−14.4173	−	112.698i	−0.0304162	−	0.237760i
$475$	71.9126	+	23.3658i	0.151395	+	0.0491912i
$476$	48.3836	+	39.7706i	0.101646	+	0.0835518i
$477$	254.785	+	185.112i	0.534141	+	0.388076i
$478$	50.3591	+	106.583i	0.105354	+	0.222977i
$479$	−372.369	+	120.990i	−0.777388	+	0.252589i	−0.670725	−	0.741706i	$-0.734017\pi$
$479$	−372.369	+	120.990i	−0.777388	+	0.252589i	−0.106663	+	0.994295i	$0.534017\pi$
$480$	−54.5342	+	0.428963i	−0.113613	+	0.000893673i
$481$	133.918	−	97.2969i	0.278415	−	0.202280i
$482$	727.306	+	137.556i	1.50893	+	0.285385i
$483$			66.5498i			0.137784i
$484$	−77.2316	+	477.798i	−0.159570	+	0.987187i
$485$	−99.6175			−0.205397
$486$	−63.0074	+	333.143i	−0.129645	+	0.685479i
$487$	256.315	+	352.787i	0.526314	+	0.724409i	0.986563	−	0.163381i	$-0.0522400\pi$
$487$	256.315	+	352.787i	0.526314	+	0.724409i	−0.460249	+	0.887790i	$0.652240\pi$
$488$	172.670	−	685.927i	0.353831	−	1.40559i
$489$	−18.3025	−	56.3293i	−0.0374284	−	0.115193i
$490$	172.253	−	81.3875i	0.351537	−	0.166097i
$491$	−561.929	+	773.429i	−1.14446	+	1.57521i	−0.387337	+	0.921938i	$0.626605\pi$
$491$	−561.929	+	773.429i	−1.14446	+	1.57521i	−0.757122	+	0.653274i	$0.773395\pi$
$492$	−11.0243	−	9.06185i	−0.0224072	−	0.0184184i
$493$	−25.0965	+	77.2392i	−0.0509058	+	0.156672i
$494$	−93.6381	+	11.9789i	−0.189551	+	0.0242488i
$495$	161.204	+	129.987i	0.325664	+	0.262600i
$496$	−275.831	−	494.340i	−0.556110	−	0.996653i
$497$	−295.511	+	909.490i	−0.594590	+	1.82996i
$498$	42.7403	+	45.3706i	0.0858239	+	0.0911055i
$499$	−87.5613	+	120.518i	−0.175474	+	0.241519i	−0.887690	−	0.460441i	$-0.847691\pi$
$499$	−87.5613	+	120.518i	−0.175474	+	0.241519i	0.712217	+	0.701960i	$0.247691\pi$
$500$	24.0816	+	37.6839i	0.0481632	+	0.0753678i
$501$	8.85087	+	27.2402i	0.0176664	+	0.0543716i
$502$	232.224	+	127.191i	0.462597	+	0.253368i
$503$	−168.942	−	232.529i	−0.335870	−	0.462285i	0.607360	−	0.794427i	$-0.292229\pi$
$503$	−168.942	−	232.529i	−0.335870	−	0.462285i	−0.943229	+	0.332142i	$0.892229\pi$
$504$	−43.5118	−	643.150i	−0.0863330	−	1.27609i
$505$	276.234			0.546999
$506$	152.830	−	130.110i	0.302035	−	0.257134i
$507$			121.381i			0.239410i
$508$	−18.5749	−	1.10997i	−0.0365647	−	0.00218498i
$509$	−79.7845	+	57.9668i	−0.156747	+	0.113884i	−0.663394	−	0.748270i	$-0.730885\pi$
$509$	−79.7845	+	57.9668i	−0.156747	+	0.113884i	0.506647	+	0.862154i	$0.330885\pi$
$510$	4.89077	+	2.67871i	0.00958975	+	0.00525238i
$511$	334.433	−	108.664i	0.654469	−	0.212650i
$512$	56.9725	−	508.820i	0.111274	−	0.993790i
$513$	−162.428	−	118.011i	−0.316623	−	0.230040i
$514$	424.720	+	450.857i	0.826304	+	0.877155i
$515$	417.314	+	135.594i	0.810319	+	0.263289i
$516$	−71.3674	+	18.5636i	−0.138309	+	0.0359759i
$517$	6.48756	−	128.908i	0.0125485	−	0.249339i
$518$	−1006.96	+	128.819i	−1.94395	+	0.248685i
$519$	218.185	+	70.8928i	0.420396	+	0.136595i
$520$	−47.2823	−	29.6942i	−0.0909276	−	0.0571042i
$521$	267.153	+	194.098i	0.512770	+	0.372549i	0.813874	−	0.581042i	$-0.197355\pi$
$521$	267.153	+	194.098i	0.512770	+	0.372549i	−0.301103	+	0.953592i	$0.597355\pi$
$522$	755.766	−	357.090i	1.44783	−	0.684080i
$523$	836.001	−	271.633i	1.59847	−	0.519375i	0.631744	−	0.775177i	$-0.282339\pi$
$523$	836.001	−	271.633i	1.59847	−	0.519375i	0.966729	+	0.255802i	$0.0823395\pi$
$524$	342.252	−	872.440i	0.653153	−	1.66496i
$525$	29.5069	−	21.4380i	0.0562035	−	0.0408343i
$526$	−70.4910	+	372.711i	−0.134013	+	0.708576i
$527$			57.8825i			0.109834i
$528$	96.0371	−	93.6514i	0.181888	−	0.177370i
$529$	445.766			0.842657
$530$	−164.374	−	31.0881i	−0.310140	−	0.0586569i
$531$	−277.884	−	382.475i	−0.523322	−	0.720291i
$532$	538.956	+	211.429i	1.01307	+	0.397422i
$533$	−4.51481	−	13.8951i	−0.00847055	−	0.0260697i
$534$	−75.7619	−	160.347i	−0.141876	−	0.300275i
$535$	62.9756	−	86.6784i	0.117711	−	0.162016i
$536$	−247.262	+	393.718i	−0.461311	+	0.734549i
$537$	73.6938	−	226.806i	0.137232	−	0.422358i
$538$	84.1178	+	657.541i	0.156353	+	1.22219i
$539$	−167.023	+	437.823i	−0.309875	+	0.812287i
$540$	−29.8926	−	114.922i	−0.0553567	−	0.212818i
$541$	236.223	−	727.020i	0.436641	−	1.34384i	−0.454754	−	0.890617i	$-0.650273\pi$
$541$	236.223	−	727.020i	0.436641	−	1.34384i	0.891395	−	0.453227i	$-0.149727\pi$
$542$	−38.6936	+	36.4504i	−0.0713904	+	0.0672517i
$543$	−106.963	+	147.222i	−0.196985	+	0.271126i
$544$	−30.4377	+	42.5944i	−0.0559516	+	0.0782986i
$545$	−8.01109	−	24.6556i	−0.0146992	−	0.0452396i
$546$	−21.8738	+	39.9370i	−0.0400619	+	0.0731447i
$547$	−219.118	−	301.590i	−0.400581	−	0.551353i	0.560308	−	0.828284i	$-0.310683\pi$
$547$	−219.118	−	301.590i	−0.400581	−	0.551353i	−0.960890	+	0.276931i	$0.910683\pi$
$548$	14.5055	−	242.743i	0.0264698	−	0.442961i
$549$	744.382			1.35589
$550$	−106.920	−	25.8488i	−0.194400	−	0.0469977i
$551$			750.717i			1.36246i
$552$	−55.5006	+	3.75485i	−0.100544	+	0.00680226i
$553$	−577.125	+	419.306i	−1.04363	+	0.758238i
$554$	−295.099	+	538.789i	−0.532669	+	0.972543i
$555$	−85.9608	+	27.9303i	−0.154884	+	0.0503249i
$556$	24.6908	−	15.7785i	0.0444080	−	0.0283785i
$557$	90.6342	+	65.8496i	0.162719	+	0.118222i	0.666165	−	0.745805i	$-0.267935\pi$
$557$	90.6342	+	65.8496i	0.162719	+	0.118222i	−0.503446	+	0.864027i	$0.667935\pi$
$558$	433.636	−	408.497i	0.777126	−	0.732074i
$559$	−71.8016	−	23.3297i	−0.128446	−	0.0417348i
$560$	166.845	+	299.016i	0.297937	+	0.533958i
$561$	−13.2411	+	3.57742i	−0.0236027	+	0.00637687i
$562$	−43.2634	−	338.185i	−0.0769811	−	0.601753i
$563$	846.470	+	275.035i	1.50350	+	0.488517i	0.941036	−	0.338306i	$-0.109854\pi$
$563$	846.470	+	275.035i	1.50350	+	0.488517i	0.562463	+	0.826822i	$0.309854\pi$
$564$	−22.7152	+	27.6345i	−0.0402752	+	0.0489974i
$565$	241.555	+	175.500i	0.427531	+	0.310619i
$566$	318.838	+	674.808i	0.563318	+	1.19224i
$567$	597.600	−	194.172i	1.05397	−	0.342455i
$568$	−775.161	−	195.133i	−1.36472	−	0.343543i
$569$	−443.404	+	322.152i	−0.779268	+	0.566172i	−0.904759	−	0.425923i	$-0.859949\pi$
$569$	−443.404	+	322.152i	−0.779268	+	0.566172i	0.125491	+	0.992095i	$0.459949\pi$
$570$	50.6477	+	9.57901i	0.0888555	+	0.0168053i
$571$		−	546.540i		−	0.957163i	−0.878043	−	0.478581i	$-0.841151\pi$
$571$		−	546.540i		−	0.957163i	0.878043	−	0.478581i	$-0.158849\pi$
$572$	134.479	−	27.8473i	0.235103	−	0.0486840i
$573$	−234.969			−0.410068
$574$	−16.6512	+	88.0407i	−0.0290090	+	0.153381i
$575$	26.8127	+	36.9045i	0.0466307	+	0.0641817i
$576$	533.913	−	72.5751i	0.926932	−	0.125999i
$577$	262.876	+	809.048i	0.455590	+	1.40216i	0.870441	+	0.492273i	$0.163834\pi$
$577$	262.876	+	809.048i	0.455590	+	1.40216i	−0.414850	+	0.909890i	$0.636166\pi$
$578$	−517.762	+	244.636i	−0.895783	+	0.423246i
$579$	153.405	−	211.144i	0.264948	−	0.364670i
$580$	−281.945	+	343.004i	−0.486112	+	0.591387i
$581$	120.937	−	372.207i	0.208154	−	0.640631i
$582$	−67.3602	+	8.61725i	−0.115739	+	0.0148063i
$583$	344.626	−	224.821i	0.591125	−	0.385627i
$584$	109.492	+	272.777i	0.187486	+	0.467083i
$585$	18.1573	−	55.8826i	0.0310382	−	0.0955258i
$586$	430.003	+	456.466i	0.733794	+	0.778952i
$587$	−141.943	+	195.368i	−0.241811	+	0.332825i	−0.912622	−	0.408804i	$-0.865946\pi$
$587$	−141.943	+	195.368i	−0.241811	+	0.332825i	0.670811	+	0.741628i	$0.265946\pi$
$588$	109.435	−	69.9337i	0.186115	−	0.118935i
$589$	165.339	+	508.860i	0.280711	+	0.863938i
$590$	220.255	+	120.635i	0.373313	+	0.204466i
$591$	−138.903	−	191.184i	−0.235031	−	0.323493i
$592$	−164.246	−	832.510i	−0.277442	−	1.40627i
$593$	542.114			0.914189			0.457094	−	0.889418i	$-0.348890\pi$
$593$	542.114			0.914189			0.457094	+	0.889418i	$0.348890\pi$
$594$	248.793	+	153.005i	0.418844	+	0.257583i
$595$		−	35.0120i		−	0.0588436i
$596$	17.0315	−	285.015i	0.0285763	−	0.478213i
$597$	−169.703	+	123.296i	−0.284259	+	0.206526i
$598$	−49.9495	−	27.3577i	−0.0835276	−	0.0457487i
$599$	−224.218	+	72.8527i	−0.374320	+	0.121624i	−0.490134	−	0.871647i	$-0.663052\pi$
$599$	−224.218	+	72.8527i	−0.374320	+	0.121624i	0.115814	+	0.993271i	$0.463052\pi$
$600$	19.5435	+	23.3983i	0.0325725	+	0.0389971i
$601$	123.566	+	89.7761i	0.205601	+	0.149378i	0.685821	−	0.727770i	$-0.259443\pi$
$601$	123.566	+	89.7761i	0.205601	+	0.149378i	−0.480220	+	0.877148i	$0.659443\pi$
$602$	317.480	+	337.018i	0.527375	+	0.559830i
$603$	−465.332	−	151.195i	−0.771695	−	0.250739i
$604$	−45.3497	−	174.346i	−0.0750823	−	0.288653i
$605$	233.752	−	136.254i	0.386367	−	0.225212i
$606$	186.786	−	23.8952i	0.308228	−	0.0394310i
$607$	2.97708	+	0.967311i	0.00490457	+	0.00159359i	0.311468	−	0.950257i	$-0.399179\pi$
$607$	2.97708	+	0.967311i	0.00490457	+	0.00159359i	−0.306564	+	0.951850i	$0.599179\pi$
$608$	−145.916	+	461.402i	−0.239994	+	0.758886i
$609$	292.955	+	212.844i	0.481042	+	0.349498i
$610$	−357.510	+	168.919i	−0.586082	+	0.276916i
$611$	−34.8307	+	11.3172i	−0.0570061	+	0.0185224i
$612$	−51.2893	−	20.1204i	−0.0838061	−	0.0328765i
$613$	−162.834	+	118.306i	−0.265635	+	0.192995i	−0.712627	−	0.701543i	$-0.752495\pi$
$613$	−162.834	+	118.306i	−0.265635	+	0.192995i	0.446993	+	0.894538i	$0.352495\pi$
$614$	−98.7986	+	522.384i	−0.160910	+	0.850788i
$615$			7.97757i			0.0129717i
$616$	−805.382	−	246.394i	−1.30744	−	0.399991i
$617$	−463.153			−0.750654			−0.375327	−	0.926893i	$-0.622470\pi$
$617$	−463.153			−0.750654			−0.375327	+	0.926893i	$0.622470\pi$
$618$	293.912	+	55.5877i	0.475586	+	0.0899478i
$619$	169.667	+	233.527i	0.274099	+	0.377265i	0.923768	−	0.382952i	$-0.125093\pi$
$619$	169.667	+	233.527i	0.274099	+	0.377265i	−0.649669	+	0.760217i	$0.725093\pi$
$620$	−115.568	+	294.595i	−0.186399	+	0.475153i
$621$	−37.4289	−	115.194i	−0.0602720	−	0.185498i
$622$	−287.101	−	607.638i	−0.461578	−	0.976911i
$623$	−654.495	+	900.835i	−1.05055	+	1.44596i
$624$	−34.5404	−	15.9888i	−0.0553532	−	0.0256231i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$	86.1312	+	673.279i	0.137590	+	1.07553i
$627$	−106.188	+	69.2727i	−0.169358	+	0.110483i
$628$	1032.17	−	268.481i	1.64359	−	0.427518i
$629$	−26.8119	+	82.5185i	−0.0426262	+	0.131190i
$630$	−262.298	+	247.092i	−0.416346	+	0.392209i
$631$	−31.4364	+	43.2685i	−0.0498199	+	0.0685713i	−0.833200	−	0.552972i	$-0.813494\pi$
$631$	−31.4364	+	43.2685i	−0.0498199	+	0.0685713i	0.783380	+	0.621543i	$0.213494\pi$
$632$	−382.251	−	457.647i	−0.604828	−	0.724125i
$633$	39.2125	+	120.684i	0.0619471	+	0.190654i
$634$	37.0626	−	67.6686i	0.0584584	−	0.106733i
$635$	6.11426	+	8.41556i	0.00962875	+	0.0132528i
$636$	−113.837	−	6.80251i	−0.178989	−	0.0106958i
$637$	132.962			0.208732
$638$	−83.9583	−	1088.89i	−0.131596	−	1.70672i
$639$		−	841.221i		−	1.31646i
$640$	−239.957	+	156.014i	−0.374933	+	0.243773i
$641$	708.110	−	514.472i	1.10470	−	0.802609i	0.122876	−	0.992422i	$-0.460788\pi$
$641$	708.110	−	514.472i	1.10470	−	0.802609i	0.981820	+	0.189813i	$0.0607883\pi$
$642$	35.0854	−	64.0585i	0.0546501	−	0.0997797i
$643$	1023.68	−	332.614i	1.59204	−	0.517284i	0.626916	−	0.779087i	$-0.284317\pi$
$643$	1023.68	−	332.614i	1.59204	−	0.517284i	0.965121	+	0.261803i	$0.0843169\pi$
$644$	188.074	+	294.307i	0.292041	+	0.456998i
$645$	33.3502	+	24.2304i	0.0517058	+	0.0375665i
$646$	36.0171	−	33.9291i	0.0557540	−	0.0525218i
$647$	−215.802	−	70.1183i	−0.333542	−	0.108374i	0.137458	−	0.990508i	$-0.456107\pi$
$647$	−215.802	−	70.1183i	−0.333542	−	0.108374i	−0.471000	+	0.882133i	$0.656107\pi$
$648$	195.651	+	487.426i	0.301931	+	0.752200i
$649$	−596.311	+	161.108i	−0.918815	+	0.248241i
$650$	3.96059	+	30.9595i	0.00609321	+	0.0476300i
$651$	245.451	+	79.7519i	0.377037	+	0.122507i
$652$	−240.130	−	197.384i	−0.368298	−	0.302736i
$653$	−495.163	−	359.757i	−0.758289	−	0.550929i	0.140096	−	0.990138i	$-0.455259\pi$
$653$	−495.163	−	359.757i	−0.758289	−	0.550929i	−0.898385	+	0.439208i	$0.855259\pi$
$654$	−7.54980	−	15.9788i	−0.0115440	−	0.0244325i
$655$	−498.253	+	161.892i	−0.760691	+	0.247164i
$656$	−74.3629	−	8.91918i	−0.113358	−	0.0135963i
$657$	−250.253	+	181.820i	−0.380903	+	0.276742i
$658$	220.690	+	41.7392i	0.335396	+	0.0634335i
$659$		−	312.111i		−	0.473613i	−0.971557	−	0.236807i	$-0.923899\pi$
$659$		−	312.111i		−	0.473613i	0.971557	−	0.236807i	$-0.0761008\pi$
$660$	−74.5339	−	8.22970i	−0.112930	−	0.0124692i
$661$	−101.013			−0.152819			−0.0764095	−	0.997077i	$-0.524346\pi$
$661$	−101.013			−0.152819			−0.0764095	+	0.997077i	$0.524346\pi$
$662$	102.832	−	543.712i	0.155336	−	0.821318i
$663$	2.28754	+	3.14853i	0.00345029	+	0.00474892i
$664$	317.233	+	79.8576i	0.477760	+	0.120268i
$665$	−100.010	−	307.799i	−0.150391	−	0.462856i
$666$	807.422	−	381.497i	1.21235	−	0.572818i
$667$	−266.206	+	366.401i	−0.399109	+	0.549327i
$668$	116.124	+	95.4525i	0.173839	+	0.142893i
$669$	−62.9505	+	193.742i	−0.0940965	+	0.289599i
$670$	257.799	−	32.9796i	0.384774	−	0.0492233i
$671$	346.654	−	908.698i	0.516623	−	1.35424i
$672$	138.684	+	187.759i	0.206375	+	0.279403i
$673$	125.465	−	386.143i	0.186427	−	0.573763i	−0.813543	−	0.581505i	$-0.802464\pi$
$673$	125.465	−	386.143i	0.186427	−	0.573763i	0.999970	+	0.00774135i	$0.00246417\pi$
$674$	−48.0180	−	50.9731i	−0.0712433	−	0.0756277i
$675$	−39.0178	+	53.7033i	−0.0578041	+	0.0795605i
$676$	343.030	+	536.788i	0.507441	+	0.794065i
$677$	−169.613	−	522.014i	−0.250536	−	0.771070i	−0.994676	−	0.103047i	$-0.967141\pi$
$677$	−169.613	−	522.014i	−0.250536	−	0.771070i	0.744141	−	0.668023i	$-0.232859\pi$
$678$	178.518	+	97.7756i	0.263301	+	0.144212i
$679$	250.621	+	344.950i	0.369103	+	0.508026i
$680$	29.1989	−	1.97543i	0.0429396	−	0.00290505i
$681$	−99.2854			−0.145794
$682$	−296.727	−	719.592i	−0.435084	−	1.05512i
$683$			914.777i			1.33935i	0.742654	+	0.669675i	$0.233567\pi$
$683$			914.777i			1.33935i	−0.742654	+	0.669675i	$0.766433\pi$
$684$	−508.371	−	30.3785i	−0.743232	−	0.0444130i
$685$	−109.977	+	79.9031i	−0.160551	+	0.116647i
$686$	107.446	+	58.8493i	0.156628	+	0.0857861i
$687$	199.523	−	64.8291i	0.290427	−	0.0943655i
$688$	−263.150	+	283.784i	−0.382485	+	0.412477i
$689$	−94.4554	−	68.6259i	−0.137091	−	0.0996021i
$690$	21.3228	+	22.6350i	0.0309026	+	0.0328043i
$691$	−117.626	−	38.2189i	−0.170225	−	0.0553095i	0.222665	−	0.974895i	$-0.428525\pi$
$691$	−117.626	−	38.2189i	−0.170225	−	0.0553095i	−0.392890	+	0.919586i	$0.628525\pi$
$692$	1165.24	−	303.094i	1.68387	−	0.437997i
$693$	44.5510	−	885.232i	0.0642872	−	1.27739i
$694$	−531.020	+	67.9323i	−0.765159	+	0.0978852i
$695$	−15.5785	−	5.06177i	−0.0224151	−	0.00728312i
$696$	−160.977	+	256.325i	−0.231288	+	0.368283i
$697$	6.19554	+	4.50132i	0.00888887	+	0.00645814i
$698$	182.726	−	86.3356i	0.261785	−	0.123690i
$699$	−275.887	+	89.6413i	−0.394689	+	0.128242i
$700$	69.9045	−	178.195i	0.0998636	−	0.254564i
$701$	431.259	−	313.328i	0.615205	−	0.446972i	−0.236038	−	0.971744i	$-0.575849\pi$
$701$	431.259	−	313.328i	0.615205	−	0.446972i	0.851243	+	0.524771i	$0.175849\pi$
$702$	15.4011	−	81.4312i	0.0219389	−	0.115999i
$703$			802.028i			1.14087i
$704$	160.045	−	685.567i	0.227336	−	0.973816i
$705$	19.9972			0.0283649
$706$	−522.213	−	98.7663i	−0.739679	−	0.139896i
$707$	−694.958	−	956.528i	−0.982968	−	1.35294i
$708$	159.369	+	62.5193i	0.225097	+	0.0883041i
$709$	340.137	+	1046.83i	0.479742	+	1.47649i	0.839454	+	0.543431i	$0.182875\pi$
$709$	340.137	+	1046.83i	0.479742	+	1.47649i	−0.359712	+	0.933063i	$0.617125\pi$
$710$	190.894	+	404.019i	0.268865	+	0.569041i
$711$	368.850	−	507.678i	0.518776	−	0.714034i
$712$	−788.197	−	495.003i	−1.10702	−	0.695228i
$713$	−99.7464	+	306.988i	−0.139897	+	0.430558i
$714$	−3.02865	−	23.6747i	−0.00424181	−	0.0331578i
$715$	−59.7623	−	48.1896i	−0.0835837	−	0.0673980i
$716$	−315.070	−	1211.28i	−0.440041	−	1.69173i
$717$	13.8818	−	42.7237i	0.0193609	−	0.0595867i
$718$	−837.914	+	789.338i	−1.16701	+	1.09936i
$719$	−595.573	+	819.736i	−0.828335	+	1.14011i	0.159896	+	0.987134i	$0.448884\pi$
$719$	−595.573	+	819.736i	−0.828335	+	1.14011i	−0.988231	+	0.152971i	$0.951116\pi$
$720$	−220.867	−	204.807i	−0.306759	−	0.284455i
$721$	−580.366	−	1786.18i	−0.804946	−	2.47737i
$722$	−127.112	+	232.080i	−0.176055	+	0.321440i
$723$	−165.800	−	228.205i	−0.229323	−	0.315636i
$724$	−56.9689	+	953.350i	−0.0786863	+	1.31678i
$725$	248.209			0.342357
$726$	146.274	−	112.353i	0.201479	−	0.154757i
$727$		−	1172.43i		−	1.61270i	−0.591438	−	0.806350i	$-0.701440\pi$
$727$		−	1172.43i		−	1.61270i	0.591438	−	0.806350i	$-0.298560\pi$
$728$	16.1310	+	238.432i	0.0221579	+	0.327517i
$729$	−373.503	+	271.366i	−0.512350	+	0.372244i
$730$	78.9316	−	144.113i	0.108125	−	0.197414i
$731$	37.6356	−	12.2285i	0.0514851	−	0.0167285i
$732$	−227.132	+	145.147i	−0.310290	+	0.198288i
$733$	−618.263	−	449.195i	−0.843470	−	0.612817i	0.0798680	−	0.996805i	$-0.474550\pi$
$733$	−618.263	−	449.195i	−0.843470	−	0.612817i	−0.923338	+	0.383989i	$0.874550\pi$
$734$	546.876	−	515.172i	0.745063	−	0.701870i
$735$	−69.0475	−	22.4349i	−0.0939422	−	0.0305237i
$736$	−234.832	+	173.454i	−0.319065	+	0.235671i
$737$	−401.273	+	497.639i	−0.544468	+	0.675222i
$738$	−10.0017	−	78.1824i	−0.0135525	−	0.105938i
$739$	598.384	+	194.427i	0.809721	+	0.263094i	0.684480	−	0.729032i	$-0.260029\pi$
$739$	598.384	+	194.427i	0.809721	+	0.263094i	0.125242	+	0.992126i	$0.460029\pi$
$740$	−301.216	+	366.449i	−0.407048	+	0.495201i
$741$	29.1040	+	21.1453i	0.0392767	+	0.0285362i
$742$	305.887	+	647.398i	0.412247	+	0.872504i
$743$	−780.309	+	253.538i	−1.05021	+	0.341235i	−0.782752	−	0.622333i	$-0.786185\pi$
$743$	−780.309	+	253.538i	−1.05021	+	0.341235i	−0.267462	+	0.963568i	$0.586185\pi$
$744$	−52.6620	+	209.199i	−0.0707822	+	0.281181i
$745$	−129.129	+	93.8178i	−0.173328	+	0.125930i
$746$	−1119.44	−	211.720i	−1.50059	−	0.283807i
$747$			344.268i			0.460867i
$748$	−48.4469	+	53.2410i	−0.0647686	+	0.0711778i
$749$	−458.581			−0.612258
$750$	3.16710	−	16.7456i	0.00422280	−	0.0223275i
$751$	−118.603	−	163.244i	−0.157927	−	0.217368i	0.722720	−	0.691141i	$-0.242892\pi$
$751$	−118.603	−	163.244i	−0.157927	−	0.217368i	−0.880647	+	0.473773i	$0.842892\pi$
$752$	−22.3576	+	186.404i	−0.0297308	+	0.247878i
$753$	−31.1800	−	95.9621i	−0.0414077	−	0.127440i
$754$	−280.182	+	132.382i	−0.371594	+	0.175573i
$755$	−59.1933	+	81.4726i	−0.0784018	+	0.107911i
$756$	−322.740	+	392.634i	−0.426905	+	0.519357i
$757$	−66.7243	+	205.356i	−0.0881431	+	0.271277i	−0.985406	−	0.170220i	$-0.945552\pi$
$757$	−66.7243	+	205.356i	−0.0881431	+	0.271277i	0.897263	+	0.441496i	$0.145552\pi$
$758$	705.686	−	90.2770i	0.930985	−	0.119099i
$759$	−76.3910	−	3.84453i	−0.100647	−	0.00506525i
$760$	251.053	−	100.772i	0.330332	−	0.132595i
$761$	161.955	−	498.446i	0.212818	−	0.654988i	−0.786483	−	0.617612i	$-0.788100\pi$
$761$	161.955	−	498.446i	0.212818	−	0.654988i	0.999301	−	0.0373757i	$-0.0118998\pi$
$762$	4.86236	+	5.16160i	0.00638106	+	0.00677375i
$763$	−65.2215	+	89.7696i	−0.0854803	+	0.117654i
$764$	−1039.12	+	664.038i	−1.36010	+	0.869160i
$765$	9.51737	+	29.2915i	0.0124410	+	0.0382895i
$766$	878.637	+	481.236i	1.14705	+	0.628246i
$767$	103.019	+	141.793i	0.134314	+	0.184867i
$768$	−148.761	+	126.252i	−0.193699	+	0.164391i
$769$	−714.080			−0.928583			−0.464291	−	0.885683i	$-0.653691\pi$
$769$	−714.080			−0.928583			−0.464291	+	0.885683i	$0.653691\pi$
$770$	179.484	+	435.267i	0.233097	+	0.565282i
$771$		−	236.043i		−	0.306151i
$772$	81.7041	−	1367.28i	0.105834	−	1.77109i
$773$	−346.430	+	251.696i	−0.448163	+	0.325609i	−0.788870	−	0.614560i	$-0.789334\pi$
$773$	−346.430	+	251.696i	−0.448163	+	0.325609i	0.340707	+	0.940169i	$0.389334\pi$
$774$	−357.220	−	195.652i	−0.461525	−	0.252781i
$775$	168.244	−	54.6658i	0.217089	−	0.0705365i
$776$	−273.538	+	228.473i	−0.352497	+	0.294424i
$777$	312.978	+	227.392i	0.402803	+	0.292654i
$778$	926.185	+	983.183i	1.19047	+	1.26373i
$779$	67.3244	+	21.8750i	0.0864241	+	0.0280809i
$780$	5.35620	+	20.5918i	0.00686693	+	0.0263998i
$781$	−1026.91	−	391.751i	−1.31487	−	0.501602i
$782$	29.6101	−	3.78796i	0.0378646	−	0.00484394i
$783$	−626.798	−	203.659i	−0.800508	−	0.260101i
$784$	286.324	−	618.543i	0.365209	−	0.788958i
$785$	−482.337	−	350.439i	−0.614442	−	0.446419i
$786$	−322.908	+	152.570i	−0.410825	+	0.194110i
$787$	−5.56864	+	1.80936i	−0.00707578	+	0.00229906i	−0.312553	−	0.949900i	$-0.601184\pi$
$787$	−5.56864	+	1.80936i	−0.00707578	+	0.00229906i	0.305477	+	0.952199i	$0.401184\pi$
$788$	−1154.58	−	452.933i	−1.46520	−	0.574788i
$789$	116.944	−	84.9651i	0.148218	−	0.107687i
$790$	−61.9454	+	327.528i	−0.0784119	+	0.414592i
$791$		−	1277.97i		−	1.61564i
$792$	740.771	−	12.7920i	0.935317	−	0.0161515i
$793$	−275.962			−0.347997
$794$	49.8989	+	9.43739i	0.0628449	+	0.0118859i
$795$	37.4715	+	51.5752i	0.0471340	+	0.0648744i
$796$	−402.041	+	1024.85i	−0.505077	+	1.28750i
$797$	88.5703	+	272.591i	0.111130	+	0.342022i	0.991120	−	0.132969i	$-0.0424512\pi$
$797$	88.5703	+	272.591i	0.111130	+	0.342022i	−0.879991	+	0.474991i	$0.842451\pi$
$798$	−94.2513	−	199.479i	−0.118109	−	0.249974i
$799$	11.2834	−	15.5303i	0.0141219	−	0.0194371i
$800$	152.553	+	48.2443i	0.190692	+	0.0603053i
$801$	302.683	−	931.563i	0.377882	−	1.16300i
$802$	2.81230	+	21.9834i	0.00350660	+	0.0274108i
$803$	105.413	+	390.166i	0.131274	+	0.485886i
$804$	171.467	−	44.6009i	0.213268	−	0.0554737i
$805$	60.3346	−	185.691i	0.0749498	−	0.230672i
$806$	−160.760	+	151.440i	−0.199454	+	0.187891i
$807$	148.485	−	204.373i	0.183997	−	0.253250i
$808$	758.506	−	633.544i	0.938745	−	0.784089i
$809$	−395.973	−	1218.68i	−0.489459	−	1.50640i	−0.825417	−	0.564524i	$-0.809060\pi$
$809$	−395.973	−	1218.68i	−0.489459	−	1.50640i	0.335958	−	0.941877i	$-0.390940\pi$
$810$	141.043	−	257.515i	0.174127	−	0.317920i
$811$	−24.4211	−	33.6128i	−0.0301124	−	0.0414461i	0.793695	−	0.608315i	$-0.208154\pi$
$811$	−24.4211	−	33.6128i	−0.0301124	−	0.0414461i	−0.823808	+	0.566869i	$0.808154\pi$
$812$	1897.06	+	113.362i	2.33628	+	0.139608i
$813$	20.2577			0.0249172
$814$	−89.6968	−	1163.31i	−0.110193	−	1.42913i
$815$			173.766i			0.213210i
$816$	19.5731	−	3.86157i	0.0239866	−	0.00473232i
$817$	295.934	−	215.009i	0.362220	−	0.263168i
$818$	−254.267	+	464.239i	−0.310840	+	0.567529i
$819$	−239.188	+	77.7168i	−0.292049	+	0.0948923i
$820$	22.5451	+	35.2796i	0.0274941	+	0.0430239i
$821$	360.162	+	261.673i	0.438688	+	0.318725i	0.785113	−	0.619352i	$-0.212605\pi$
$821$	360.162	+	261.673i	0.438688	+	0.318725i	−0.346426	+	0.938077i	$0.612605\pi$
$822$	−67.4534	+	63.5430i	−0.0820601	+	0.0773029i
$823$	−471.551	−	153.216i	−0.572966	−	0.186168i	0.00818108	−	0.999967i	$-0.497396\pi$
$823$	−471.551	−	153.216i	−0.572966	−	0.186168i	−0.581147	+	0.813799i	$0.697396\pi$
$824$	1456.88	−	584.788i	1.76806	−	0.709694i
$825$	22.9036	+	35.1087i	0.0277619	+	0.0425560i
$826$	−136.395	−	1066.18i	−0.165127	−	1.29078i
$827$	323.516	+	105.117i	0.391192	+	0.127106i	0.498007	−	0.867173i	$-0.334065\pi$
$827$	323.516	+	105.117i	0.391192	+	0.127106i	−0.106815	+	0.994279i	$0.534065\pi$
$828$	−237.347	−	195.096i	−0.286651	−	0.235623i
$829$	157.617	+	114.515i	0.190128	+	0.138136i	0.678777	−	0.734344i	$-0.262510\pi$
$829$	157.617	+	114.515i	0.190128	+	0.138136i	−0.488649	+	0.872480i	$0.662510\pi$
$830$	−78.1230	−	165.344i	−0.0941241	−	0.199210i
$831$	222.644	−	72.3415i	0.267923	−	0.0870536i
$832$	−197.935	+	26.9055i	−0.237903	+	0.0323383i
$833$	−56.3833	+	40.9649i	−0.0676870	+	0.0491775i
$834$	−10.9719	−	2.07511i	−0.0131557	−	0.00248814i
$835$		−	84.0313i		−	0.100636i
$836$	−273.829	+	606.441i	−0.327547	+	0.725408i
$837$	−469.718			−0.561192
$838$	−66.6500	+	352.402i	−0.0795346	+	0.420528i
$839$	−705.545	−	971.100i	−0.840936	−	1.15745i	−0.985788	−	0.167996i	$-0.946271\pi$
$839$	−705.545	−	971.100i	−0.840936	−	1.15745i	0.144852	−	0.989453i	$-0.453729\pi$
$840$	31.8542	−	126.540i	0.0379216	−	0.150643i
$841$	501.631	+	1543.86i	0.596469	+	1.83574i
$842$	−804.724	+	380.222i	−0.955729	+	0.451570i
$843$	−76.3688	+	105.113i	−0.0905917	+	0.124689i
$844$	514.472	+	422.889i	0.609564	+	0.501053i
$845$	110.045	−	338.683i	0.130230	−	0.400808i
$846$	−195.979	+	25.0711i	−0.231653	+	0.0296349i
$847$	−1059.89	−	466.632i	−1.25135	−	0.550924i
$848$	−522.652	+	291.628i	−0.616335	+	0.343901i
$849$	87.8894	−	270.496i	0.103521	−	0.318605i
$850$	−11.2179	−	11.9083i	−0.0131976	−	0.0140098i
$851$	−284.401	+	391.445i	−0.334196	+	0.459982i
$852$	164.029	+	256.680i	0.192523	+	0.301268i
$853$	321.857	+	990.574i	0.377323	+	1.16128i	0.941898	+	0.335900i	$0.109040\pi$
$853$	321.857	+	990.574i	0.377323	+	1.16128i	−0.564574	+	0.825382i	$0.690960\pi$
$854$	1484.36	+	812.994i	1.73812	+	0.951984i
$855$	167.339	+	230.323i	0.195719	+	0.269384i
$856$	−25.8739	−	382.443i	−0.0302265	−	0.446779i
$857$	−681.252			−0.794926			−0.397463	−	0.917618i	$-0.630109\pi$
$857$	−681.252			−0.794926			−0.397463	+	0.917618i	$0.630109\pi$
$858$	−44.5792	−	27.4156i	−0.0519571	−	0.0319529i
$859$		−	856.203i		−	0.996744i	−0.866963	−	0.498372i	$-0.833931\pi$
$859$		−	856.203i		−	0.996744i	0.866963	−	0.498372i	$-0.166069\pi$
$860$	215.963	+	12.9052i	0.251120	+	0.0150061i
$861$	27.6243	−	20.0702i	0.0320839	−	0.0233103i
$862$	−370.540	−	202.947i	−0.429860	−	0.235438i
$863$	−630.616	+	204.900i	−0.730725	+	0.237427i	−0.650667	−	0.759363i	$-0.725511\pi$
$863$	−630.616	+	204.900i	−0.730725	+	0.237427i	−0.0800582	+	0.996790i	$0.525511\pi$
$864$	−345.655	−	247.002i	−0.400063	−	0.285882i
$865$	−544.521	−	395.618i	−0.629504	−	0.457361i
$866$	−496.042	−	526.568i	−0.572797	−	0.608047i
$867$	207.544	+	67.4353i	0.239382	+	0.0777800i
$868$	1310.86	−	340.970i	1.51020	−	0.392823i
$869$	−447.972	−	686.692i	−0.515503	−	0.790209i
$870$	167.836	−	21.4709i	0.192915	−	0.0246792i
$871$	172.511	+	56.0521i	0.198060	+	0.0643537i
$872$	−78.5451	−	49.3278i	−0.0900747	−	0.0565686i
$873$	−303.441	−	220.463i	−0.347584	−	0.252535i
$874$	249.490	−	117.881i	0.285458	−	0.134875i
$875$	−101.767	+	33.0663i	−0.116306	+	0.0377900i
$876$	40.9064	−	104.275i	0.0466968	−	0.119035i
$877$	−1166.19	+	847.283i	−1.32974	+	0.966116i	−0.329989	+	0.943985i	$0.607045\pi$
$877$	−1166.19	+	847.283i	−1.32974	+	0.966116i	−0.999755	+	0.0221308i	$0.992955\pi$
$878$	−211.298	+	1117.21i	−0.240658	+	1.27245i
$879$		−	238.979i		−	0.271876i
$880$	−352.873	+	174.243i	−0.400992	+	0.198004i
$881$	338.683			0.384431			0.192215	−	0.981353i	$-0.438433\pi$
$881$	338.683			0.384431			0.192215	+	0.981353i	$0.438433\pi$
$882$	704.812	+	133.301i	0.799107	+	0.151135i
$883$	783.323	+	1078.15i	0.887116	+	1.22101i	0.974399	+	0.224827i	$0.0721816\pi$
$883$	783.323	+	1078.15i	0.887116	+	1.22101i	−0.0872829	+	0.996184i	$0.527818\pi$
$884$	19.0143	+	7.45917i	0.0215094	+	0.00843797i
$885$	−29.5729	−	91.0160i	−0.0334157	−	0.102843i
$886$	465.520	+	985.253i	0.525417	+	1.11202i
$887$	952.972	−	1311.65i	1.07438	−	1.47875i	0.208811	−	0.977956i	$-0.433041\pi$
$887$	952.972	−	1311.65i	1.07438	−	1.47875i	0.865565	−	0.500796i	$-0.166959\pi$
$888$	−171.979	+	273.844i	−0.193671	+	0.308383i
$889$	13.7585	−	42.3442i	0.0154763	−	0.0476313i
$890$	66.0230	+	516.095i	0.0741831	+	0.579882i
$891$	188.363	+	697.190i	0.211406	+	0.782480i
$892$	269.138	+	1034.70i	0.301724	+	1.15997i
$893$	54.8338	−	168.761i	0.0614040	−	0.188982i
$894$	−79.2000	+	74.6086i	−0.0885906	+	0.0834548i
$895$	−411.249	+	566.036i	−0.459496	+	0.632442i
$896$	1143.93	+	438.405i	1.27671	+	0.489291i
$897$	6.70657	+	20.6407i	0.00747666	+	0.0230108i
$898$	354.951	−	648.066i	0.395268	−	0.721677i
$899$	1032.36	+	1420.92i	1.14834	+	1.58055i
$900$	−10.0440	+	168.082i	−0.0111600	+	0.186758i
$901$	61.1975			0.0679218
$902$	−100.098	−	24.1996i	−0.110974	−	0.0268288i
$903$		−	176.443i		−	0.195396i
$904$	1065.79	−	72.1052i	1.17897	−	0.0797624i
$905$	431.926	−	313.812i	0.477266	−	0.346754i
$906$	−32.9782	+	60.2113i	−0.0363998	+	0.0664584i
$907$	−702.346	+	228.206i	−0.774362	+	0.251605i	−0.669431	−	0.742874i	$-0.733462\pi$
$907$	−702.346	+	228.206i	−0.774362	+	0.251605i	−0.104931	+	0.994480i	$0.533462\pi$
$908$	−439.075	+	280.587i	−0.483563	+	0.309017i
$909$	841.427	+	611.332i	0.925662	+	0.672533i
$910$	97.2406	−	91.6033i	0.106858	−	0.100663i
$911$	1556.35	+	505.690i	1.70840	+	0.555093i	0.990066	−	0.140603i	$-0.0449042\pi$
$911$	1556.35	+	505.690i	1.70840	+	0.555093i	0.718336	+	0.695697i	$0.244904\pi$
$912$	161.042	−	89.8577i	0.176581	−	0.0985282i
$913$	420.262	+	160.323i	0.460308	+	0.175601i
$914$	−61.1954	−	478.358i	−0.0669534	−	0.523368i
$915$	143.308	+	46.5634i	0.156620	+	0.0508890i
$916$	699.151	−	850.563i	0.763266	−	0.928563i
$917$	1814.11	+	1318.03i	1.97831	+	1.43733i
$918$	18.5576	+	39.2763i	0.0202152	+	0.0427847i
$919$	855.560	−	277.988i	0.930968	−	0.302490i	0.196010	−	0.980602i	$-0.437202\pi$
$919$	855.560	−	277.988i	0.930968	−	0.302490i	0.734959	+	0.678112i	$0.237202\pi$
$920$	158.265	+	39.8403i	0.172027	+	0.0433047i
$921$	163.907	−	119.085i	0.177966	−	0.129300i
$922$	160.513	+	30.3579i	0.174092	+	0.0329262i
$923$			311.862i			0.337879i
$924$	159.017	+	278.796i	0.172097	+	0.301728i
$925$	265.174			0.286675
$926$	73.1672	−	386.861i	0.0790142	−	0.417777i
$927$	971.084	+	1336.58i	1.04756	+	1.44184i
$928$	12.4950	+	1588.49i	0.0134644	+	1.71173i
$929$	−140.272	−	431.712i	−0.150992	−	0.464707i	0.846741	−	0.532006i	$-0.178562\pi$
$929$	−140.272	−	431.712i	−0.150992	−	0.464707i	−0.997733	+	0.0672996i	$0.978562\pi$
$930$	109.036	−	51.5181i	0.117243	−	0.0553958i
$931$	−378.666	+	521.189i	−0.406730	+	0.559816i
$932$	−966.739	+	1176.10i	−1.03727	+	1.26191i
$933$	−79.1411	+	243.571i	−0.0848243	+	0.261062i
$934$	−576.937	+	73.8064i	−0.617706	+	0.0790218i
$935$	40.1895	+	2.02261i	0.0429834	+	0.00216322i
$936$	−78.3089	−	195.091i	−0.0836634	−	0.208430i
$937$	336.677	−	1036.19i	0.359314	−	1.10585i	−0.594152	−	0.804353i	$-0.702512\pi$
$937$	336.677	−	1036.19i	0.359314	−	1.10585i	0.953466	−	0.301501i	$-0.0974877\pi$
$938$	−762.777	−	809.719i	−0.813195	−	0.863240i
$939$	152.039	−	209.264i	0.161916	−	0.222859i
$940$	88.4349	−	56.5136i	0.0940796	−	0.0601208i
$941$	−524.773	−	1615.08i	−0.557676	−	1.71635i	−0.688771	−	0.724979i	$-0.741849\pi$
$941$	−524.773	−	1615.08i	−0.557676	−	1.71635i	0.131095	−	0.991370i	$-0.458151\pi$
$942$	−356.465	−	195.239i	−0.378413	−	0.207260i
$943$	25.1020	+	34.5499i	0.0266193	+	0.0366383i
$944$	881.469	−	173.905i	0.933760	−	0.184221i
$945$	284.123			0.300659
$946$	−405.196	+	344.959i	−0.428325	+	0.364650i
$947$		−	343.409i		−	0.362628i	−0.983425	−	0.181314i	$-0.941965\pi$
$947$		−	343.409i		−	0.362628i	0.983425	−	0.181314i	$-0.0580350\pi$
$948$	−13.5545	+	226.829i	−0.0142980	+	0.239271i
$949$	92.7753	−	67.4052i	0.0977611	−	0.0710276i
$950$	−132.635	−	72.6454i	−0.139616	−	0.0764689i
$951$	−27.9628	+	9.08566i	−0.0294035	+	0.00955379i
$952$	−80.3000	−	96.1386i	−0.0843487	−	0.100986i
$953$	793.582	+	576.571i	0.832720	+	0.605006i	0.920327	−	0.391149i	$-0.127922\pi$
$953$	793.582	+	576.571i	0.832720	+	0.605006i	−0.0876078	+	0.996155i	$0.527922\pi$
$954$	−431.893	−	458.472i	−0.452718	−	0.480578i
$955$	655.623	+	213.025i	0.686516	+	0.223063i
$956$	−59.3499	−	228.170i	−0.0620815	−	0.238672i
$957$	−261.243	+	323.981i	−0.272981	+	0.338538i
$958$	776.734	−	99.3660i	0.810787	−	0.103722i
$959$	553.368	+	179.800i	0.577026	+	0.187487i
$960$	107.328	+	19.4258i	0.111800	+	0.0202353i
$961$	235.243	+	170.914i	0.244790	+	0.177850i
$962$	−299.332	+	141.431i	−0.311156	+	0.147017i
$963$	383.655	−	124.657i	0.398396	−	0.129447i
$964$	−1378.15	−	540.638i	−1.42962	−	0.560828i
$965$	−619.463	+	450.066i	−0.641931	+	0.466390i
$966$	24.7347	−	130.781i	0.0256052	−	0.135384i
$967$			1153.83i			1.19321i	0.802536	+	0.596604i	$0.203484\pi$
$967$			1153.83i			1.19321i	−0.802536	+	0.596604i	$0.796516\pi$
$968$	329.357	−	910.246i	0.340245	−	0.940337i
$969$	−18.8564			−0.0194597
$970$	195.765	+	37.0250i	0.201819	+	0.0381701i
$971$	−92.5275	−	127.353i	−0.0952910	−	0.131157i	0.758709	−	0.651429i	$-0.225830\pi$
$971$	−92.5275	−	127.353i	−0.0952910	−	0.131157i	−0.854000	+	0.520273i	$0.825830\pi$
$972$	247.639	−	631.261i	0.254773	−	0.649445i
$973$	21.6653	+	66.6789i	0.0222665	+	0.0685292i
$974$	−372.579	−	788.548i	−0.382525	−	0.809598i
$975$	6.99126	−	9.62264i	0.00717052	−	0.00986937i
$976$	−594.264	+	1283.78i	−0.608877	+	1.31535i
$977$	95.6163	−	294.277i	0.0978672	−	0.301204i	−0.890123	−	0.455720i	$-0.849382\pi$
$977$	95.6163	−	294.277i	0.0978672	−	0.301204i	0.987990	+	0.154516i	$0.0493818\pi$
$978$	15.0314	+	117.499i	0.0153695	+	0.120142i
$979$	−996.239	−	803.321i	−1.01761	−	0.820552i
$980$	−368.755	+	95.9179i	−0.376281	+	0.0978754i
$981$	30.1629	−	92.8318i	0.0307471	−	0.0946297i
$982$	1391.74	−	1311.06i	1.41725	−	1.33509i
$983$	719.649	−	990.512i	0.732094	−	1.00764i	−0.266940	−	0.963713i	$-0.586013\pi$
$983$	719.649	−	990.512i	0.732094	−	1.00764i	0.999035	−	0.0439284i	$-0.0139873\pi$
$984$	18.2966	+	21.9054i	0.0185941	+	0.0222616i
$985$	214.247	+	659.383i	0.217509	+	0.669425i
$986$	78.0264	−	142.460i	0.0791343	−	0.144483i
$987$	−50.3097	−	69.2453i	−0.0509723	−	0.0701574i
$988$	188.466	+	11.2621i	0.190755	+	0.0113989i
$989$	220.679			0.223133
$990$	−268.479	−	315.360i	−0.271191	−	0.318546i
$991$			2.98244i			0.00300952i	0.999999	+	0.00150476i	$0.000478980\pi$
$991$			2.98244i			0.00300952i	−0.999999	+	0.00150476i	$0.999521\pi$
$992$	358.320	+	1073.98i	0.361209	+	1.08264i
$993$	−170.599	+	123.947i	−0.171802	+	0.124821i
$994$	918.759	−	1677.46i	0.924304	−	1.68759i
$995$	585.294	−	190.174i	0.588236	−	0.191129i
$996$	−67.1287	−	105.046i	−0.0673983	−	0.105468i
$997$	−1322.62	−	960.939i	−1.32660	−	0.963830i	−0.999825	−	0.0187281i	$-0.994038\pi$
$997$	−1322.62	−	960.939i	−1.32660	−	0.963830i	−0.326774	−	0.945102i	$-0.605962\pi$
$998$	216.865	−	204.293i	0.217300	−	0.204702i
$999$	−669.640	−	217.579i	−0.670310	−	0.217797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.s.b.31.2	✓	96
4.3	odd	2	inner	220.3.s.b.31.21	yes	96
11.5	even	5	inner	220.3.s.b.71.21	yes	96
44.27	odd	10	inner	220.3.s.b.71.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.s.b.31.2	✓	96	1.1	even	1	trivial
220.3.s.b.31.21	yes	96	4.3	odd	2	inner
220.3.s.b.71.2	yes	96	44.27	odd	10	inner
220.3.s.b.71.21	yes	96	11.5	even	5	inner

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.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96516 - 0.371672i) q^{2} +(0.447988 + 0.616603i) q^{3} +(3.72372 + 1.46079i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-0.651195 - 1.37823i) q^{6} +(-5.62557 + 7.74293i) q^{7} +(-6.77478 - 4.25469i) q^{8} +(2.60165 - 8.00705i) q^{9} +(0.567486 + 4.43598i) q^{10} +(-8.56295 - 6.90477i) q^{11} +(0.767455 + 2.95047i) q^{12} +(-0.964498 + 2.96842i) q^{13} +(13.9330 - 13.1252i) q^{14} +(1.00173 - 1.37877i) q^{15} +(11.7322 + 10.8791i) q^{16} +(-0.505552 - 1.55593i) q^{17} +(-8.08865 + 14.7682i) q^{18} +(-8.88888 - 12.2345i) q^{19} +(0.533527 - 8.92835i) q^{20} -7.29450 q^{21} +(14.2613 + 16.7516i) q^{22} -9.12329i q^{23} +(-0.411568 - 6.08339i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(2.99867 - 5.47495i) q^{26} +(12.6264 - 4.10257i) q^{27} +(-32.2588 + 20.6147i) q^{28} +(-40.1611 - 29.1787i) q^{29} +(-2.48101 + 2.33718i) q^{30} +(-33.6488 - 10.9332i) q^{31} +(-19.0122 - 25.7398i) q^{32} +(0.421397 - 8.37319i) q^{33} +(0.415197 + 3.24555i) q^{34} +(20.3535 + 6.61325i) q^{35} +(21.3844 - 26.0155i) q^{36} +(-42.9061 - 31.1731i) q^{37} +(12.9209 + 27.3465i) q^{38} +(-2.26242 + 0.735104i) q^{39} +(-4.36688 + 17.3473i) q^{40} +(-3.78700 + 2.75142i) q^{41} +(14.3349 + 2.71116i) q^{42} +24.1885i q^{43} +(-21.7996 - 38.2201i) q^{44} -18.8257 q^{45} +(-3.39087 + 17.9287i) q^{46} +(6.89694 + 9.49282i) q^{47} +(-1.45223 + 12.1078i) q^{48} +(-13.1641 - 40.5150i) q^{49} +(9.04156 - 4.27202i) q^{50} +(0.732909 - 1.00876i) q^{51} +(-7.92776 + 9.64464i) q^{52} +(-11.5593 + 35.5760i) q^{53} +(-26.3377 + 3.36933i) q^{54} +(-8.76701 + 22.9813i) q^{55} +(71.0557 - 28.5216i) q^{56} +(3.56171 - 10.9618i) q^{57} +(68.0781 + 72.2677i) q^{58} +(33.0063 - 45.4293i) q^{59} +(5.74425 - 3.67082i) q^{60} +(27.3220 + 84.0884i) q^{61} +(62.0618 + 33.9917i) q^{62} +(47.3623 + 65.1886i) q^{63} +(27.7953 + 57.6491i) q^{64} +6.97917 q^{65} +(-3.94019 + 16.2981i) q^{66} -58.1153i q^{67} +(0.390351 - 6.53235i) q^{68} +(5.62544 - 4.08712i) q^{69} +(-37.5399 - 20.5609i) q^{70} +(95.0277 - 30.8764i) q^{71} +(-51.6931 + 43.1768i) q^{72} +(-29.7244 - 21.5961i) q^{73} +(72.7312 + 77.2071i) q^{74} +(-3.62430 - 1.17761i) q^{75} +(-15.2277 - 58.5426i) q^{76} +(101.635 - 27.4591i) q^{77} +(4.71924 - 0.603722i) q^{78} +(70.8877 + 23.0328i) q^{79} +(15.0291 - 32.4673i) q^{80} +(-53.1147 - 38.5901i) q^{81} +(8.46469 - 3.99946i) q^{82} +(-38.8899 + 12.6361i) q^{83} +(-27.1627 - 10.6557i) q^{84} +(-2.95955 + 2.15024i) q^{85} +(8.99017 - 47.5343i) q^{86} -37.8351i q^{87} +(28.6345 + 83.2110i) q^{88} +116.343 q^{89} +(36.9955 + 6.99698i) q^{90} +(-17.5584 - 24.1671i) q^{91} +(13.3272 - 33.9726i) q^{92} +(-8.33285 - 25.6459i) q^{93} +(-10.0254 - 21.2183i) q^{94} +(-19.8761 + 27.3572i) q^{95} +(7.35400 - 23.2541i) q^{96} +(13.7668 - 42.3699i) q^{97} +(10.8113 + 84.5112i) q^{98} +(-77.5646 + 50.6002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} + 16 q^{4} - 120 q^{5} - 20 q^{6} - 10 q^{8} + 64 q^{9} - 10 q^{10} - 70 q^{12} + 20 q^{13} + 83 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} - 25 q^{20} + 35 q^{22} - 62 q^{24} - 120 q^{25}+ \cdots - 1042 q^{98}+O(q^{100}) \) 96 * q + 2 * q^2 + 16 * q^4 - 120 * q^5 - 20 * q^6 - 10 * q^8 + 64 * q^9 - 10 * q^10 - 70 * q^12 + 20 * q^13 + 83 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 - 25 * q^20 + 35 * q^22 - 62 * q^24 - 120 * q^25 - 88 * q^26 - 130 * q^28 - 8 * q^29 + 40 * q^30 + 152 * q^32 + 180 * q^33 - 126 * q^34 - 394 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 + 275 * q^42 + 113 * q^44 + 40 * q^45 - 85 * q^46 + 353 * q^48 + 292 * q^49 + 10 * q^50 + 62 * q^52 - 224 * q^53 - 328 * q^54 + 380 * q^56 - 364 * q^57 + 598 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 - 356 * q^64 - 40 * q^65 - 65 * q^66 - 117 * q^68 + 32 * q^69 - 165 * q^70 - 28 * q^72 + 16 * q^73 - 72 * q^74 - 720 * q^77 - 752 * q^78 - 235 * q^80 - 44 * q^81 + 49 * q^82 - 348 * q^84 + 60 * q^85 + 70 * q^86 - 165 * q^88 - 144 * q^89 + 778 * q^92 + 40 * q^93 + 254 * q^94 + 243 * q^96 + 204 * q^97 - 1042 * q^98

Introduction

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