LMFDB - Embedded newform 220.3.w.a.7.15

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			7.15
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.57651 - 1.23070i) q^{2} +(-3.31218 + 1.68764i) q^{3} +(0.970777 + 3.88041i) q^{4} +(0.464993 + 4.97833i) q^{5} +(7.29866 + 1.41570i) q^{6} +(5.48368 - 10.7623i) q^{7} +(3.24516 - 7.31224i) q^{8} +(2.83235 - 3.89839i) q^{9} +(5.39374 - 8.42066i) q^{10} +(5.61283 + 9.46024i) q^{11} +(-9.76413 - 11.2143i) q^{12} +(0.930957 + 5.87783i) q^{13} +(-21.8902 + 10.2182i) q^{14} +(-9.94178 - 15.7044i) q^{15} +(-14.1152 + 7.53403i) q^{16} +(-2.47078 + 15.5999i) q^{17} +(-9.26297 + 2.66010i) q^{18} +(-17.8686 - 5.80587i) q^{19} +(-18.8666 + 6.63721i) q^{20} +44.9012i q^{21} +(2.79399 - 21.8219i) q^{22} +(-0.129068 - 0.129068i) q^{23} +(1.59187 + 29.6962i) q^{24} +(-24.5676 + 4.62978i) q^{25} +(5.76615 - 10.4122i) q^{26} +(2.43153 - 15.3521i) q^{27} +(47.0857 + 10.8311i) q^{28} +(9.02940 + 27.7896i) q^{29} +(-3.65401 + 36.9935i) q^{30} +(-24.5635 + 33.8088i) q^{31} +(31.5248 + 5.49402i) q^{32} +(-34.5562 - 21.8616i) q^{33} +(23.0939 - 21.5526i) q^{34} +(56.1283 + 22.2952i) q^{35} +(17.8770 + 7.20621i) q^{36} +(-5.76994 + 11.3241i) q^{37} +(21.0248 + 31.1438i) q^{38} +(-13.0032 - 17.8973i) q^{39} +(37.9117 + 12.7554i) q^{40} +(-24.3151 - 7.90045i) q^{41} +(55.2598 - 70.7873i) q^{42} +(-44.4485 + 44.4485i) q^{43} +(-31.2608 + 30.9639i) q^{44} +(20.7245 + 12.2876i) q^{45} +(0.0446339 + 0.362322i) q^{46} +(-24.9005 - 48.8700i) q^{47} +(34.0373 - 48.7754i) q^{48} +(-56.9554 - 78.3923i) q^{49} +(44.4289 + 22.9363i) q^{50} +(-18.1433 - 55.8394i) q^{51} +(-21.9046 + 9.31855i) q^{52} +(10.9664 - 1.73691i) q^{53} +(-22.7270 + 21.2102i) q^{54} +(-44.4863 + 32.3415i) q^{55} +(-60.9013 - 75.0235i) q^{56} +(68.9823 - 10.9257i) q^{57} +(19.9656 - 54.9231i) q^{58} +(8.53987 + 26.2830i) q^{59} +(51.2883 - 53.8236i) q^{60} +(26.8435 + 36.9469i) q^{61} +(80.3329 - 23.0697i) q^{62} +(-26.4241 - 51.8602i) q^{63} +(-42.9378 - 47.4589i) q^{64} +(-28.8289 + 7.36776i) q^{65} +(27.5733 + 76.9932i) q^{66} +(-79.0469 + 79.0469i) q^{67} +(-62.9325 + 5.55636i) q^{68} +(0.645319 + 0.209677i) q^{69} +(-61.0483 - 104.225i) q^{70} +(56.4177 + 77.6523i) q^{71} +(-19.3146 - 33.3618i) q^{72} +(10.9558 - 21.5021i) q^{73} +(23.0329 - 10.7516i) q^{74} +(73.5588 - 56.7959i) q^{75} +(5.18271 - 74.9738i) q^{76} +(132.593 - 8.53013i) q^{77} +(-1.52652 + 44.2183i) q^{78} +(27.9655 - 38.4912i) q^{79} +(-44.0703 - 66.7668i) q^{80} +(31.2566 + 96.1979i) q^{81} +(28.6100 + 42.3796i) q^{82} +(4.01934 - 25.3771i) q^{83} +(-174.235 + 43.5891i) q^{84} +(-78.8103 - 5.04652i) q^{85} +(124.776 - 15.3710i) q^{86} +(-76.8059 - 76.8059i) q^{87} +(87.3901 - 10.3423i) q^{88} +59.2376i q^{89} +(-17.5501 - 44.8772i) q^{90} +(68.3641 + 22.2129i) q^{91} +(0.375542 - 0.626135i) q^{92} +(24.3017 - 153.435i) q^{93} +(-20.8882 + 107.689i) q^{94} +(20.5947 - 91.6556i) q^{95} +(-113.688 + 35.0054i) q^{96} +(-28.7204 - 181.333i) q^{97} +(-6.68631 + 193.681i) q^{98} +(52.7772 + 4.91370i) 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 $

$2$	−1.57651	−	1.23070i	−0.788256	−	0.615348i
$2$	−1.57651	−	1.23070i	−0.788256	−	0.615348i
$3$	−3.31218	+	1.68764i	−1.10406	+	0.562547i	−0.908391	−	0.418123i	$-0.862688\pi$
$3$	−3.31218	+	1.68764i	−1.10406	+	0.562547i	−0.195670	+	0.980670i	$0.562688\pi$
$4$	0.970777	+	3.88041i	0.242694	+	0.970103i
$5$	0.464993	+	4.97833i	0.0929986	+	0.995666i
$5$	0.464993	+	4.97833i	0.0929986	+	0.995666i
$6$	7.29866	+	1.41570i	1.21644	+	0.235950i
$7$	5.48368	−	10.7623i	0.783382	−	1.53747i	−0.0587928	−	0.998270i	$-0.518725\pi$
$7$	5.48368	−	10.7623i	0.783382	−	1.53747i	0.842175	−	0.539204i	$-0.181275\pi$
$8$	3.24516	−	7.31224i	0.405646	−	0.914030i
$9$	2.83235	−	3.89839i	0.314705	−	0.433155i
$10$	5.39374	−	8.42066i	0.539374	−	0.842066i
$11$	5.61283	+	9.46024i	0.510257	+	0.860022i
$11$	5.61283	+	9.46024i	0.510257	+	0.860022i
$12$	−9.76413	−	11.2143i	−0.813678	−	0.934525i
$13$	0.930957	+	5.87783i	0.0716120	+	0.452141i	0.997274	+	0.0737888i	$0.0235091\pi$
$13$	0.930957	+	5.87783i	0.0716120	+	0.452141i	−0.925662	+	0.378352i	$0.876491\pi$
$14$	−21.8902	+	10.2182i	−1.56359	+	0.729870i
$15$	−9.94178	−	15.7044i	−0.662785	−	1.04696i
$16$	−14.1152	+	7.53403i	−0.882199	+	0.470877i
$17$	−2.47078	+	15.5999i	−0.145340	+	0.917640i	0.801980	+	0.597351i	$0.203780\pi$
$17$	−2.47078	+	15.5999i	−0.145340	+	0.917640i	−0.947320	+	0.320289i	$0.896220\pi$
$18$	−9.26297	+	2.66010i	−0.514609	+	0.147784i
$19$	−17.8686	−	5.80587i	−0.940454	−	0.305572i	−0.201623	−	0.979463i	$-0.564622\pi$
$19$	−17.8686	−	5.80587i	−0.940454	−	0.305572i	−0.738831	+	0.673891i	$0.764622\pi$
$20$	−18.8666	+	6.63721i	−0.943328	+	0.331861i
$21$			44.9012i			2.13815i
$22$	2.79399	−	21.8219i	0.127000	−	0.991903i
$23$	−0.129068	−	0.129068i	−0.00561167	−	0.00561167i	0.704295	−	0.709907i	$-0.251263\pi$
$23$	−0.129068	−	0.129068i	−0.00561167	−	0.00561167i	−0.709907	+	0.704295i	$0.751263\pi$
$24$	1.59187	+	29.6962i	0.0663278	+	1.23734i
$25$	−24.5676	+	4.62978i	−0.982703	+	0.185191i
$26$	5.76615	−	10.4122i	0.221775	−	0.400469i
$27$	2.43153	−	15.3521i	0.0900566	−	0.568595i
$28$	47.0857	+	10.8311i	1.68163	+	0.386825i
$29$	9.02940	+	27.7896i	0.311359	+	0.958263i	0.977227	+	0.212194i	$0.0680610\pi$
$29$	9.02940	+	27.7896i	0.311359	+	0.958263i	−0.665869	+	0.746069i	$0.731939\pi$
$30$	−3.65401	+	36.9935i	−0.121800	+	1.23312i
$31$	−24.5635	+	33.8088i	−0.792371	+	1.09060i	0.201438	+	0.979501i	$0.435439\pi$
$31$	−24.5635	+	33.8088i	−0.792371	+	1.09060i	−0.993809	+	0.111104i	$0.964561\pi$
$32$	31.5248	+	5.49402i	0.985151	+	0.171688i
$33$	−34.5562	−	21.8616i	−1.04716	−	0.662473i
$34$	23.0939	−	21.5526i	0.679233	−	0.633900i
$35$	56.1283	+	22.2952i	1.60366	+	0.637004i
$36$	17.8770	+	7.20621i	0.496582	+	0.200172i
$37$	−5.76994	+	11.3241i	−0.155944	+	0.306058i	−0.955739	−	0.294216i	$-0.904942\pi$
$37$	−5.76994	+	11.3241i	−0.155944	+	0.306058i	0.799795	+	0.600274i	$0.204942\pi$
$38$	21.0248	+	31.1438i	0.553285	+	0.819575i
$39$	−13.0032	−	17.8973i	−0.333414	−	0.458906i
$40$	37.9117	+	12.7554i	0.947794	+	0.318884i
$41$	−24.3151	−	7.90045i	−0.593051	−	0.192694i	−0.00291203	−	0.999996i	$-0.500927\pi$
$41$	−24.3151	−	7.90045i	−0.593051	−	0.192694i	−0.590139	+	0.807302i	$0.700927\pi$
$42$	55.2598	−	70.7873i	1.31571	−	1.68541i
$43$	−44.4485	+	44.4485i	−1.03369	+	1.03369i	−0.0342742	+	0.999412i	$0.510912\pi$
$43$	−44.4485	+	44.4485i	−1.03369	+	1.03369i	−0.999412	+	0.0342742i	$0.989088\pi$
$44$	−31.2608	+	30.9639i	−0.710473	+	0.703724i
$45$	20.7245	+	12.2876i	0.460545	+	0.273059i
$46$	0.0446339	+	0.362322i	0.000970302	+	0.00787656i
$47$	−24.9005	−	48.8700i	−0.529799	−	1.03979i	−0.988503	−	0.151199i	$-0.951686\pi$
$47$	−24.9005	−	48.8700i	−0.529799	−	1.03979i	0.458705	−	0.888589i	$-0.348314\pi$
$48$	34.0373	−	48.7754i	0.709111	−	1.01615i
$49$	−56.9554	−	78.3923i	−1.16235	−	1.59984i
$50$	44.4289	+	22.9363i	0.888578	+	0.458726i
$51$	−18.1433	−	55.8394i	−0.355752	−	1.09489i
$52$	−21.9046	+	9.31855i	−0.421243	+	0.179203i
$53$	10.9664	−	1.73691i	0.206913	−	0.0327718i	−0.0521174	−	0.998641i	$-0.516597\pi$
$53$	10.9664	−	1.73691i	0.206913	−	0.0327718i	0.259030	+	0.965869i	$0.416597\pi$
$54$	−22.7270	+	21.2102i	−0.420871	+	0.392782i
$55$	−44.4863	+	32.3415i	−0.808842	+	0.588026i
$56$	−60.9013	−	75.0235i	−1.08752	−	1.33970i
$57$	68.9823	−	10.9257i	1.21022	−	0.191679i
$58$	19.9656	−	54.9231i	0.344235	−	0.946950i
$59$	8.53987	+	26.2830i	0.144743	+	0.445475i	0.996978	−	0.0776854i	$-0.0247530\pi$
$59$	8.53987	+	26.2830i	0.144743	+	0.445475i	−0.852234	+	0.523160i	$0.824753\pi$
$60$	51.2883	−	53.8236i	0.854805	−	0.897061i
$61$	26.8435	+	36.9469i	0.440058	+	0.605688i	0.970225	−	0.242206i	$-0.0778708\pi$
$61$	26.8435	+	36.9469i	0.440058	+	0.605688i	−0.530167	+	0.847893i	$0.677871\pi$
$62$	80.3329	−	23.0697i	1.29569	−	0.372092i
$63$	−26.4241	−	51.8602i	−0.419430	−	0.823177i
$64$	−42.9378	−	47.4589i	−0.670903	−	0.741545i
$65$	−28.8289	+	7.36776i	−0.443521	+	0.113350i
$66$	27.5733	+	76.9932i	0.417777	+	1.16656i
$67$	−79.0469	+	79.0469i	−1.17980	+	1.17980i	−0.200010	+	0.979794i	$0.564098\pi$
$67$	−79.0469	+	79.0469i	−1.17980	+	1.17980i	−0.979794	+	0.200010i	$0.935902\pi$
$68$	−62.9325	+	5.55636i	−0.925478	+	0.0817112i
$69$	0.645319	+	0.209677i	0.00935245	+	0.00303879i
$70$	−61.0483	−	104.225i	−0.872119	−	1.48893i
$71$	56.4177	+	77.6523i	0.794616	+	1.09369i	0.993518	+	0.113675i	$0.0362624\pi$
$71$	56.4177	+	77.6523i	0.794616	+	1.09369i	−0.198902	+	0.980019i	$0.563738\pi$
$72$	−19.3146	−	33.3618i	−0.268258	−	0.463358i
$73$	10.9558	−	21.5021i	0.150080	−	0.294549i	−0.803711	−	0.595020i	$-0.797144\pi$
$73$	10.9558	−	21.5021i	0.150080	−	0.294549i	0.953791	+	0.300471i	$0.0971440\pi$
$74$	23.0329	−	10.7516i	0.311256	−	0.145292i
$75$	73.5588	−	56.7959i	0.980784	−	0.757279i
$76$	5.18271	−	74.9738i	0.0681936	−	0.986497i
$77$	132.593	−	8.53013i	1.72199	−	0.110781i
$78$	−1.52652	+	44.2183i	−0.0195707	+	0.566901i
$79$	27.9655	−	38.4912i	0.353994	−	0.487231i	−0.594469	−	0.804118i	$-0.702638\pi$
$79$	27.9655	−	38.4912i	0.353994	−	0.487231i	0.948463	+	0.316888i	$0.102638\pi$
$80$	−44.0703	−	66.7668i	−0.550879	−	0.834585i
$81$	31.2566	+	96.1979i	0.385884	+	1.18763i
$82$	28.6100	+	42.3796i	0.348902	+	0.516824i
$83$	4.01934	−	25.3771i	0.0484258	−	0.305749i	−0.951573	−	0.307424i	$-0.900533\pi$
$83$	4.01934	−	25.3771i	0.0484258	−	0.305749i	0.999999	+	0.00167499i	$0.000533166\pi$
$84$	−174.235	+	43.5891i	−2.07423	+	0.518918i
$85$	−78.8103	−	5.04652i	−0.927179	−	0.0593708i
$86$	124.776	−	15.3710i	1.45089	−	0.178733i
$87$	−76.8059	−	76.8059i	−0.882827	−	0.882827i
$88$	87.3901	−	10.3423i	0.993070	−	0.117526i
$89$			59.2376i			0.665591i	0.942999	+	0.332795i	$0.107992\pi$
$89$			59.2376i			0.665591i	−0.942999	+	0.332795i	$0.892008\pi$
$90$	−17.5501	−	44.8772i	−0.195001	−	0.498635i
$91$	68.3641	+	22.2129i	0.751254	+	0.244097i
$92$	0.375542	−	0.626135i	0.00408198	−	0.00680581i
$93$	24.3017	−	153.435i	0.261309	−	1.64984i
$94$	−20.8882	+	107.689i	−0.222215	+	1.14563i
$95$	20.5947	−	91.6556i	0.216787	−	0.964796i
$96$	−113.688	+	35.0054i	−1.18425	+	0.364640i
$97$	−28.7204	−	181.333i	−0.296087	−	1.86942i	−0.467180	−	0.884162i	$-0.654730\pi$
$97$	−28.7204	−	181.333i	−0.296087	−	1.86942i	0.171093	−	0.985255i	$-0.445270\pi$
$98$	−6.68631	+	193.681i	−0.0682277	+	1.97634i
$99$	52.7772	+	4.91370i	0.533103	+	0.0496333i
$100$	−41.8151	−	90.8378i	−0.418151	−	0.908378i
$101$	59.2466	−	81.5459i	0.586600	−	0.807386i	−0.407800	−	0.913071i	$-0.633704\pi$
$101$	59.2466	−	81.5459i	0.586600	−	0.807386i	0.994400	+	0.105686i	$0.0337038\pi$
$102$	−40.1182	+	110.360i	−0.393315	+	1.08196i
$103$	−35.9777	+	70.6103i	−0.349298	+	0.685537i	−0.997086	−	0.0762842i	$-0.975694\pi$
$103$	−35.9777	+	70.6103i	−0.349298	+	0.685537i	0.647788	+	0.761821i	$0.275694\pi$
$104$	46.0012	+	12.2671i	0.442319	+	0.117953i
$105$	−223.533	+	20.8788i	−2.12889	+	0.198845i
$106$	−19.4262	−	10.7580i	−0.183266	−	0.101491i
$107$	−55.9891	+	28.5279i	−0.523262	+	0.266615i	−0.695609	−	0.718421i	$-0.744865\pi$
$107$	−55.9891	+	28.5279i	−0.523262	+	0.266615i	0.172346	+	0.985036i	$0.444865\pi$
$108$	61.9328	−	5.46809i	0.573452	−	0.0506305i
$109$	149.379			1.37045			0.685224	−	0.728332i	$-0.259704\pi$
$109$	149.379			1.37045			0.685224	+	0.728332i	$0.259704\pi$
$110$	109.936	+	3.76241i	0.999415	+	0.0342038i
$111$		−	47.2452i		−	0.425632i
$112$	3.68050	+	193.226i	0.0328616	+	1.72523i
$113$	89.2953	+	175.252i	0.790224	+	1.55090i	0.833938	+	0.551858i	$0.186081\pi$
$113$	89.2953	+	175.252i	0.790224	+	1.55090i	−0.0437141	+	0.999044i	$0.513919\pi$
$114$	−122.198	−	67.6717i	−1.07191	−	0.593612i
$115$	0.582529	−	0.702561i	0.00506547	−	0.00610922i
$116$	−99.0697	+	62.0153i	−0.854049	+	0.534615i
$117$	25.5509	+	13.0188i	0.218384	+	0.111272i
$118$	18.8832	−	51.9454i	0.160027	−	0.440216i
$119$	154.342	+	112.136i	1.29699	+	0.942319i
$120$	−147.097	+	21.7333i	−1.22581	+	0.181111i
$121$	−57.9924	+	106.197i	−0.479276	+	0.877664i
$122$	3.15131	−	91.2835i	0.0258304	−	0.748225i
$123$	93.8691	−	14.8674i	0.763163	−	0.120873i
$124$	−155.038	−	62.4957i	−1.25030	−	0.503998i
$125$	−34.4723	−	120.153i	−0.275778	−	0.961221i
$126$	−22.1662	+	114.278i	−0.175922	+	0.906970i
$127$	−53.8942	−	8.53601i	−0.424364	−	0.0672127i	−0.0593999	−	0.998234i	$-0.518919\pi$
$127$	−53.8942	−	8.53601i	−0.424364	−	0.0672127i	−0.364964	+	0.931022i	$0.618919\pi$
$128$	9.28453	+	127.663i	0.0725354	+	0.997366i
$129$	72.2085	−	222.235i	0.559755	−	1.72275i
$130$	54.5165	+	23.8642i	0.419358	+	0.183571i
$131$	48.0065			0.366461			0.183231	−	0.983070i	$-0.441344\pi$
$131$	48.0065			0.366461			0.183231	+	0.983070i	$0.441344\pi$
$132$	51.2857	−	155.315i	0.388528	−	1.17663i
$133$	−160.470	+	160.470i	−1.20654	+	1.20654i
$134$	221.901	−	27.3357i	1.65598	−	0.203998i
$135$	77.5583	+	4.96635i	0.574506	+	0.0367878i
$136$	106.052	+	68.6911i	0.779794	+	0.505082i
$137$	−56.9257	−	9.01615i	−0.415516	−	0.0658113i	−0.0548237	−	0.998496i	$-0.517460\pi$
$137$	−56.9257	−	9.01615i	−0.415516	−	0.0658113i	−0.360693	+	0.932685i	$0.617460\pi$
$138$	−0.759304	−	1.12475i	−0.00550220	−	0.00815035i
$139$	155.921	−	50.6618i	1.12173	−	0.364474i	0.311305	−	0.950310i	$-0.399234\pi$
$139$	155.921	−	50.6618i	1.12173	−	0.364474i	0.810429	+	0.585836i	$0.199234\pi$
$140$	−32.0264	+	239.444i	−0.228760	+	1.71032i
$141$	164.950	+	119.843i	1.16986	+	0.849953i
$142$	6.62320	−	191.853i	0.0466422	−	1.35108i
$143$	−50.3804	+	41.7983i	−0.352310	+	0.292296i
$144$	−10.6085	+	76.3655i	−0.0736703	+	0.530316i
$145$	−134.147	+	57.8733i	−0.925154	+	0.399126i
$146$	−43.7345	+	20.4149i	−0.299551	+	0.139828i
$147$	320.945	+	163.529i	2.18330	+	1.11245i
$148$	−49.5437	−	11.3965i	−0.334754	−	0.0770035i
$149$	−111.889	+	81.2921i	−0.750933	+	0.545585i	−0.896116	−	0.443820i	$-0.853623\pi$
$149$	−111.889	+	81.2921i	−0.750933	+	0.545585i	0.145183	+	0.989405i	$0.453623\pi$
$150$	−185.865	−	0.989161i	−1.23910	−	0.00659441i
$151$	−7.39602	+	22.7626i	−0.0489803	+	0.150746i	−0.972555	−	0.232672i	$-0.925253\pi$
$151$	−7.39602	+	22.7626i	−0.0489803	+	0.150746i	0.923575	+	0.383418i	$0.125253\pi$
$152$	−100.441	+	111.819i	−0.660793	+	0.735649i
$153$	53.8164	+	53.8164i	0.351741	+	0.351741i
$154$	−219.532	−	149.734i	−1.42554	−	0.972298i
$155$	−179.733	−	106.564i	−1.15957	−	0.687512i
$156$	56.8258	−	67.8319i	0.364268	−	0.434820i
$157$	79.3251	−	40.4182i	0.505255	−	0.257441i	−0.182732	−	0.983163i	$-0.558494\pi$
$157$	79.3251	−	40.4182i	0.505255	−	0.257441i	0.687988	+	0.725722i	$0.258494\pi$
$158$	−91.4589	+	26.2648i	−0.578854	+	0.166233i
$159$	−33.3914	+	24.2603i	−0.210009	+	0.152580i
$160$	−12.6922	+	159.496i	−0.0793263	+	0.996849i
$161$	−2.09684	+	0.681306i	−0.0130239	+	0.00423171i
$162$	69.1139	−	190.124i	0.426629	−	1.17361i
$163$	−39.5659	−	249.809i	−0.242736	−	1.53257i	−0.744532	−	0.667587i	$-0.767327\pi$
$163$	−39.5659	−	249.809i	−0.242736	−	1.53257i	0.501796	−	0.864986i	$-0.332673\pi$
$164$	7.05248	−	102.022i	0.0430029	−	0.622086i
$165$	92.7659	−	182.198i	0.562218	−	1.10423i
$166$	−37.5681	+	35.0607i	−0.226314	+	0.211209i
$167$	27.0235	+	170.619i	0.161817	+	1.02167i	0.926234	+	0.376950i	$0.123027\pi$
$167$	27.0235	+	170.619i	0.161817	+	1.02167i	−0.764416	+	0.644723i	$0.776973\pi$
$168$	328.329	+	145.712i	1.95434	+	0.867333i
$169$	127.046	−	41.2799i	0.751754	−	0.244260i
$170$	118.035	+	104.947i	0.694321	+	0.617337i
$171$	−73.2437	+	53.2147i	−0.428326	+	0.311197i
$172$	−215.628	−	129.329i	−1.25365	−	0.751913i
$173$	−66.6089	+	33.9389i	−0.385023	+	0.196179i	−0.635779	−	0.771871i	$-0.719321\pi$
$173$	−66.6089	+	33.9389i	−0.385023	+	0.196179i	0.250756	+	0.968050i	$0.419321\pi$
$174$	26.5607	+	215.610i	0.152648	+	1.23914i
$175$	−84.8934	+	289.792i	−0.485105	+	1.65596i
$176$	−150.500	−	91.2459i	−0.855112	−	0.518443i
$177$	−72.6419	−	72.6419i	−0.410406	−	0.410406i
$178$	72.9034	−	93.3887i	0.409570	−	0.524656i
$179$	−27.6616	+	85.1335i	−0.154534	+	0.475606i	−0.998113	−	0.0613979i	$-0.980444\pi$
$179$	−27.6616	+	85.1335i	−0.154534	+	0.475606i	0.843579	+	0.537004i	$0.180444\pi$
$180$	−27.5622	+	92.3482i	−0.153124	+	0.513046i
$181$	−47.2861	+	34.3553i	−0.261249	+	0.189809i	−0.710698	−	0.703498i	$-0.751621\pi$
$181$	−47.2861	+	34.3553i	−0.261249	+	0.189809i	0.449448	+	0.893306i	$0.351621\pi$
$182$	−80.4396	−	119.154i	−0.441976	−	0.654694i
$183$	−151.264	−	77.0728i	−0.826578	−	0.421163i
$184$	−1.36263	+	0.524931i	−0.00740558	+	0.00285289i
$185$	−59.0583	−	23.4590i	−0.319234	−	0.126806i
$186$	−227.144	+	211.984i	−1.22120	+	1.13970i
$187$	−161.447	+	64.1852i	−0.863351	+	0.343237i
$188$	165.463	−	144.066i	0.880123	−	0.766310i
$189$	−151.890	−	110.355i	−0.803651	−	0.583887i
$190$	−145.268	+	119.150i	−0.764568	+	0.627106i
$191$	−146.681	+	47.6595i	−0.767963	+	0.249526i	−0.666693	−	0.745333i	$-0.732291\pi$
$191$	−146.681	+	47.6595i	−0.767963	+	0.249526i	−0.101270	+	0.994859i	$0.532291\pi$
$192$	222.311	+	84.7288i	1.15787	+	0.441296i
$193$	262.236	+	41.5341i	1.35873	+	0.215202i	0.792918	−	0.609329i	$-0.208561\pi$
$193$	262.236	+	41.5341i	1.35873	+	0.215202i	0.565817	+	0.824531i	$0.308561\pi$
$194$	−177.888	+	321.220i	−0.916950	+	1.65578i
$195$	83.0524	−	73.0562i	0.425910	−	0.374647i
$196$	248.904	−	297.112i	1.26992	−	1.51588i
$197$	−159.635	+	159.635i	−0.810331	+	0.810331i	−0.984683	−	0.174353i	$-0.944217\pi$
$197$	−159.635	+	159.635i	−0.810331	+	0.810331i	0.174353	+	0.984683i	$0.444217\pi$
$198$	−77.1566	−	72.6992i	−0.389680	−	0.367168i
$199$	55.8178			0.280492			0.140246	−	0.990117i	$-0.455211\pi$
$199$	55.8178			0.280492			0.140246	+	0.990117i	$0.455211\pi$
$200$	−45.8717	+	194.668i	−0.229359	+	0.973342i
$201$	128.415	−	395.220i	0.638880	−	1.96627i
$202$	−193.761	+	55.6436i	−0.959214	+	0.275463i
$203$	348.595	+	55.2121i	1.71722	+	0.271981i
$204$	199.067	−	124.611i	0.975818	−	0.610839i
$205$	28.0247	−	124.722i	0.136706	−	0.608401i
$206$	143.619	−	67.0403i	0.697180	−	0.325438i
$207$	−0.868726	+	0.137593i	−0.00419674	+	0.000664699i
$208$	−57.4243	−	75.9528i	−0.276079	−	0.365158i
$209$	−45.3686	−	201.629i	−0.217074	−	0.964731i
$210$	378.098	+	242.186i	1.80047	+	1.15327i
$211$	−89.4763	−	65.0083i	−0.424058	−	0.308096i	0.355210	−	0.934786i	$-0.384409\pi$
$211$	−89.4763	−	65.0083i	−0.424058	−	0.308096i	−0.779269	+	0.626690i	$0.784409\pi$
$212$	17.3858	+	40.8680i	0.0820086	+	0.192773i
$213$	−317.915	−	161.986i	−1.49256	−	0.760497i
$214$	123.377	+	23.9310i	0.576526	+	0.111827i
$215$	−241.948	−	200.611i	−1.12534	−	0.933076i
$216$	−104.367	−	67.5999i	−0.483182	−	0.312962i
$217$	229.162	+	449.756i	1.05605	+	2.07261i
$218$	−235.497	−	183.840i	−1.08026	−	0.843302i
$219$			89.7083i			0.409627i
$220$	−168.684	−	141.229i	−0.766747	−	0.641949i
$221$	−93.9936			−0.425310
$222$	−58.1445	+	74.4826i	−0.261912	+	0.335507i
$223$	122.864	−	62.6025i	0.550961	−	0.280729i	−0.156266	−	0.987715i	$-0.549946\pi$
$223$	122.864	−	62.6025i	0.550961	−	0.280729i	0.707227	+	0.706986i	$0.249946\pi$
$224$	232.000	−	309.153i	1.03572	−	1.38015i
$225$	−51.5352	+	108.887i	−0.229045	+	0.483943i
$226$	74.9067	−	386.182i	0.331446	−	1.70877i
$227$	111.128	−	218.101i	0.489551	−	0.960798i	−0.505630	−	0.862750i	$-0.668740\pi$
$227$	111.128	−	218.101i	0.489551	−	0.960798i	0.995182	−	0.0980483i	$-0.0312600\pi$
$228$	109.363	+	257.073i	0.479661	+	1.12751i
$229$	110.738	−	152.418i	0.483572	−	0.665580i	−0.495614	−	0.868543i	$-0.665057\pi$
$229$	110.738	−	152.418i	0.483572	−	0.665580i	0.979186	+	0.202963i	$0.0650570\pi$
$230$	−1.78300	+	0.390679i	−0.00775218	+	0.00169861i
$231$	−424.777	+	252.023i	−1.83886	+	1.09101i
$232$	232.506	+	24.1568i	1.00218	+	0.104124i
$233$	35.6065	+	224.810i	0.152817	+	0.964851i	0.938264	+	0.345921i	$0.112434\pi$
$233$	35.6065	+	224.810i	0.152817	+	0.964851i	−0.785446	+	0.618930i	$0.787566\pi$
$234$	−24.2591	−	51.9697i	−0.103671	−	0.222093i
$235$	231.713	−	146.687i	0.986012	−	0.624201i
$236$	−93.6986	+	58.6531i	−0.397028	+	0.248530i
$237$	−27.6675	+	174.686i	−0.116740	+	0.737070i
$238$	−105.317	−	366.732i	−0.442507	−	1.54089i
$239$	12.7622	+	4.14669i	0.0533983	+	0.0173502i	0.335594	−	0.942007i	$-0.391063\pi$
$239$	12.7622	+	4.14669i	0.0533983	+	0.0173502i	−0.282196	+	0.959357i	$0.591063\pi$
$240$	258.647	+	146.769i	1.07770	+	0.611537i
$241$		−	359.741i		−	1.49270i	−0.665554	−	0.746350i	$-0.731805\pi$
$241$		−	359.741i		−	1.49270i	0.665554	−	0.746350i	$-0.268195\pi$
$242$	222.122	−	96.0505i	0.917861	−	0.396903i
$243$	−166.957	−	166.957i	−0.687067	−	0.687067i
$244$	−117.310	+	140.031i	−0.480780	+	0.573898i
$245$	363.779	−	319.994i	1.48481	−	1.30610i
$246$	−166.283	−	92.0856i	−0.675947	−	0.374332i
$247$	17.4910	−	110.434i	0.0708137	−	0.447100i
$248$	167.505	+	289.329i	0.675424	+	1.16665i
$249$	29.5147	+	90.8369i	0.118533	+	0.364807i
$250$	−93.5253	+	231.847i	−0.374101	+	0.927388i
$251$	97.6596	−	134.417i	0.389082	−	0.535525i	−0.568880	−	0.822421i	$-0.692623\pi$
$251$	97.6596	−	134.417i	0.389082	−	0.535525i	0.957962	+	0.286895i	$0.0926231\pi$
$252$	175.587	−	152.881i	0.696774	−	0.606670i
$253$	0.496580	−	1.94546i	0.00196277	−	0.00768955i
$254$	74.4596	+	79.7845i	0.293148	+	0.314112i
$255$	269.551	−	116.288i	1.05706	−	0.456033i
$256$	142.477	−	212.688i	0.556550	−	0.830814i
$257$	−112.801	+	221.385i	−0.438916	+	0.861422i	0.560530	+	0.828134i	$0.310598\pi$
$257$	−112.801	+	221.385i	−0.438916	+	0.861422i	−0.999446	+	0.0332872i	$0.989402\pi$
$258$	−387.341	+	261.489i	−1.50132	+	1.01352i
$259$	90.2336	+	124.196i	0.348392	+	0.479521i
$260$	−56.5763	−	104.715i	−0.217601	−	0.402752i
$261$	133.909	+	43.5098i	0.513063	+	0.166704i
$262$	−75.6827	−	59.0813i	−0.288865	−	0.225501i
$263$	226.093	−	226.093i	0.859669	−	0.859669i	−0.131630	−	0.991299i	$-0.542021\pi$
$263$	226.093	−	226.093i	0.859669	−	0.859669i	0.991299	+	0.131630i	$0.0420210\pi$
$264$	−271.998	+	181.739i	−1.03030	+	0.688404i
$265$	13.7462	+	53.7867i	0.0518724	+	0.202969i
$266$	450.473	−	55.4932i	1.69351	−	0.208621i
$267$	−99.9718	−	196.206i	−0.374426	−	0.734853i
$268$	−383.471	−	229.998i	−1.43086	−	0.858200i
$269$	249.996	+	344.090i	0.929354	+	1.27915i	0.960111	+	0.279620i	$0.0902084\pi$
$269$	249.996	+	344.090i	0.929354	+	1.27915i	−0.0307564	+	0.999527i	$0.509792\pi$
$270$	−116.159	−	103.280i	−0.430220	−	0.382519i
$271$	−143.115	−	440.463i	−0.528099	−	1.62532i	−0.758104	−	0.652133i	$-0.773874\pi$
$271$	−143.115	−	440.463i	−0.528099	−	1.62532i	0.230005	−	0.973190i	$-0.426126\pi$
$272$	−82.6544	−	238.810i	−0.303876	−	0.877978i
$273$	−263.922	+	41.8011i	−0.966746	+	0.153118i
$274$	78.6480	+	84.2723i	0.287036	+	0.307563i
$275$	−181.692	−	206.429i	−0.660699	−	0.750651i
$276$	−0.187172	+	2.70765i	−0.000678158	+	0.00981033i
$277$	−295.462	+	46.7965i	−1.06665	+	0.168941i	−0.664993	−	0.746850i	$-0.731565\pi$
$277$	−295.462	+	46.7965i	−1.06665	+	0.168941i	−0.401656	+	0.915791i	$0.631565\pi$
$278$	−308.161	−	112.022i	−1.10849	−	0.402958i
$279$	62.2274	+	191.516i	0.223037	+	0.686439i
$280$	345.173	−	338.072i	1.23276	−	1.20740i
$281$	1.43885	+	1.98041i	0.00512046	+	0.00704771i	0.811570	−	0.584256i	$-0.198614\pi$
$281$	1.43885	+	1.98041i	0.00512046	+	0.00704771i	−0.806449	+	0.591304i	$0.798614\pi$
$282$	−112.555	−	391.938i	−0.399132	−	1.38985i
$283$	243.363	+	477.627i	0.859941	+	1.68773i	0.715952	+	0.698150i	$0.245993\pi$
$283$	243.363	+	477.627i	0.859941	+	1.68773i	0.143989	+	0.989579i	$0.454007\pi$
$284$	−246.554	+	294.307i	−0.868148	+	1.03629i
$285$	86.4682	+	338.336i	0.303397	+	1.18715i
$286$	130.866	−	3.89259i	0.457574	−	0.0136105i
$287$	−218.363	+	218.363i	−0.760847	+	0.760847i
$288$	110.707	−	107.335i	0.384400	−	0.372692i
$289$	37.6039	+	12.2182i	0.130117	+	0.0422776i
$290$	282.709	+	73.8566i	0.974860	+	0.254678i
$291$	401.153	+	552.140i	1.37853	+	1.89739i
$292$	94.0725	+	21.6395i	0.322166	+	0.0741079i
$293$	13.7530	−	26.9919i	0.0469387	−	0.0921224i	−0.866346	−	0.499445i	$-0.833537\pi$
$293$	13.7530	−	26.9919i	0.0469387	−	0.0921224i	0.913285	+	0.407322i	$0.133537\pi$
$294$	−304.718	−	652.791i	−1.03646	−	2.22038i
$295$	−126.875	+	54.7357i	−0.430083	+	0.185545i
$296$	64.0805	+	78.9399i	0.216488	+	0.266689i
$297$	158.882	−	63.1656i	0.534956	−	0.212679i
$298$	276.440	+	9.54335i	0.927652	+	0.0320247i
$299$	0.638485	−	0.878799i	0.00213540	−	0.00293913i
$300$	291.801	+	230.302i	0.972669	+	0.767675i
$301$	234.628	+	722.111i	0.779495	+	2.39904i
$302$	39.6738	−	26.7833i	0.131370	−	0.0886863i
$303$	−58.6152	+	370.082i	−0.193450	+	1.22139i
$304$	295.960	−	52.6718i	0.973554	−	0.173262i
$305$	−171.452	+	150.816i	−0.562138	+	0.494479i
$306$	−18.6106	−	151.074i	−0.0608188	−	0.493705i
$307$	−53.1474	−	53.1474i	−0.173119	−	0.173119i	0.615229	−	0.788348i	$-0.289063\pi$
$307$	−53.1474	−	53.1474i	−0.173119	−	0.173119i	−0.788348	+	0.615229i	$0.789063\pi$
$308$	161.819	+	506.235i	0.525385	+	1.64362i
$309$		−	294.592i		−	0.953371i
$310$	152.203	+	389.197i	0.490977	+	1.25547i
$311$	−205.532	−	66.7814i	−0.660875	−	0.214731i	−0.0406718	−	0.999173i	$-0.512950\pi$
$311$	−205.532	−	66.7814i	−0.660875	−	0.214731i	−0.620203	+	0.784441i	$0.712950\pi$
$312$	−173.067	+	37.0025i	−0.554702	+	0.118598i
$313$	27.5293	−	173.813i	0.0879530	−	0.555313i	−0.903882	−	0.427783i	$-0.859295\pi$
$313$	27.5293	−	173.813i	0.0879530	−	0.555313i	0.991835	−	0.127531i	$-0.0407051\pi$
$314$	−174.799	−	33.9054i	−0.556686	−	0.107979i
$315$	245.890	−	155.662i	0.780604	−	0.494166i
$316$	176.510	+	71.1513i	0.558576	+	0.225162i
$317$	−0.798535	−	5.04175i	−0.00251904	−	0.0159046i	0.986397	−	0.164382i	$-0.0525629\pi$
$317$	−0.798535	−	5.04175i	−0.00251904	−	0.0159046i	−0.988916	+	0.148477i	$0.952563\pi$
$318$	82.4990	+	2.84805i	0.259431	+	0.00895614i
$319$	−212.216	+	241.399i	−0.665255	+	0.756736i
$320$	216.300	−	235.827i	0.675938	−	0.736958i
$321$	137.301	−	188.979i	0.427730	−	0.588719i
$322$	4.14418	+	1.50649i	0.0128701	+	0.00467854i
$323$	134.720	−	264.403i	0.417090	−	0.818586i
$324$	−342.944	+	214.675i	−1.05847	+	0.662577i
$325$	−50.0844	−	140.094i	−0.154106	−	0.431058i
$326$	−245.063	+	442.521i	−0.751727	+	1.35743i
$327$	−494.770	+	252.098i	−1.51306	+	0.770941i
$328$	−136.676	+	152.160i	−0.416696	+	0.463901i
$329$	−662.502			−2.01368
$330$	−370.476	+	173.070i	−1.12266	+	0.524455i
$331$			116.596i			0.352255i	0.984367	+	0.176128i	$0.0563571\pi$
$331$			116.596i			0.352255i	−0.984367	+	0.176128i	$0.943643\pi$
$332$	102.376	−	9.03882i	0.308360	−	0.0272254i
$333$	27.8035	+	54.5674i	0.0834940	+	0.163866i
$334$	167.378	−	302.241i	0.501131	−	0.904913i
$335$	−430.278	−	356.765i	−1.28441	−	1.06497i
$336$	−338.287	−	633.789i	−1.00681	−	1.88628i
$337$	540.321	+	275.307i	1.60333	+	0.816936i	0.999808	+	0.0195870i	$0.00623512\pi$
$337$	540.321	+	275.307i	1.60333	+	0.816936i	0.603519	+	0.797349i	$0.293765\pi$
$338$	−251.093	−	91.2772i	−0.742879	−	0.270051i
$339$	−591.525	−	429.768i	−1.74491	−	1.26775i
$340$	−56.9246	−	310.715i	−0.167425	−	0.913868i
$341$	−457.710	−	42.6140i	−1.34226	−	0.124968i
$342$	180.961	+	6.24717i	0.529125	+	0.0182666i
$343$	−571.432	+	90.5059i	−1.66598	+	0.263866i
$344$	180.776	+	469.261i	0.525511	+	1.36413i
$345$	−0.743772	+	3.31011i	−0.00215586	+	0.00959452i
$346$	146.778	+	28.4702i	0.424215	+	0.0822838i
$347$	299.264	+	47.3987i	0.862431	+	0.136596i	0.571953	−	0.820286i	$-0.306186\pi$
$347$	299.264	+	47.3987i	0.862431	+	0.136596i	0.290478	+	0.956882i	$0.406186\pi$
$348$	223.477	−	372.600i	0.642176	−	1.07069i
$349$	53.2811	−	163.982i	0.152668	−	0.469863i	−0.845249	−	0.534372i	$-0.820548\pi$
$349$	53.2811	−	163.982i	0.152668	−	0.469863i	0.997917	+	0.0645088i	$0.0205481\pi$
$350$	490.481	−	352.383i	1.40138	−	1.00681i
$351$	92.5004			0.263534
$352$	124.969	+	329.070i	0.355025	+	0.934857i
$353$	297.793	−	297.793i	0.843606	−	0.843606i	−0.145720	−	0.989326i	$-0.546550\pi$
$353$	297.793	−	297.793i	0.843606	−	0.843606i	0.989326	+	0.145720i	$0.0465499\pi$
$354$	25.1207	+	203.921i	0.0709625	+	0.576047i
$355$	−360.345	+	316.974i	−1.01506	+	0.892884i
$356$	−229.866	+	57.5065i	−0.645692	+	0.161535i
$357$	−700.454	−	110.941i	−1.96206	−	0.310759i
$358$	148.382	−	100.171i	0.414476	−	0.279807i
$359$	368.041	−	119.584i	1.02518	−	0.333102i	0.252299	−	0.967649i	$-0.418813\pi$
$359$	368.041	−	119.584i	1.02518	−	0.333102i	0.772884	+	0.634547i	$0.218813\pi$
$360$	157.105	−	111.667i	0.436402	−	0.310187i
$361$	−6.47571	−	4.70488i	−0.0179382	−	0.0130329i
$362$	116.828	+	4.03317i	0.322729	+	0.0111414i
$363$	12.8582	−	449.615i	0.0354220	−	1.23861i
$364$	−19.8287	+	286.845i	−0.0544745	+	0.788035i
$365$	112.139	+	44.5435i	0.307230	+	0.122037i
$366$	143.616	+	307.666i	0.392393	+	0.840617i
$367$	−327.698	−	166.971i	−0.892911	−	0.454961i	−0.0535687	−	0.998564i	$-0.517060\pi$
$367$	−327.698	−	166.971i	−0.892911	−	0.454961i	−0.839342	+	0.543603i	$0.817060\pi$
$368$	2.79423	+	0.849419i	0.00759301	+	0.00230820i
$369$	−99.6678	+	72.4129i	−0.270103	+	0.196241i
$370$	64.2352	+	109.666i	0.173609	+	0.296395i
$371$	41.4430	−	127.548i	0.111706	−	0.343796i
$372$	618.983	−	54.6505i	1.66393	−	0.146910i
$373$	−279.881	−	279.881i	−0.750350	−	0.750350i	0.224194	−	0.974545i	$-0.428025\pi$
$373$	−279.881	−	279.881i	−0.750350	−	0.750350i	−0.974545	+	0.224194i	$0.928025\pi$
$374$	333.515	+	97.5029i	0.891751	+	0.260703i
$375$	316.953	+	339.791i	0.845208	+	0.906108i
$376$	−438.156	+	23.4874i	−1.16531	+	0.0624665i
$377$	−154.937	+	78.9442i	−0.410973	+	0.209401i
$378$	103.644	+	360.906i	0.274189	+	0.954777i
$379$	−275.031	+	199.822i	−0.725677	+	0.527235i	−0.888193	−	0.459471i	$-0.848039\pi$
$379$	−275.031	+	199.822i	−0.725677	+	0.527235i	0.162516	+	0.986706i	$0.448039\pi$
$380$	375.654	−	9.06103i	0.988564	−	0.0238448i
$381$	192.913	−	62.6813i	0.506334	−	0.164518i
$382$	289.899	+	105.384i	0.758897	+	0.275874i
$383$	−9.91794	−	62.6194i	−0.0258954	−	0.163497i	0.971352	−	0.237646i	$-0.0763759\pi$
$383$	−9.91794	−	62.6194i	−0.0258954	−	0.163497i	−0.997247	+	0.0741491i	$0.976376\pi$
$384$	−246.201	−	407.174i	−0.641149	−	1.06035i
$385$	104.121	+	656.126i	0.270443	+	1.70422i
$386$	−362.302	−	388.211i	−0.938606	−	1.00573i
$387$	47.3841	+	299.172i	0.122440	+	0.773053i
$388$	675.767	−	287.481i	1.74167	−	0.740931i
$389$	155.583	−	50.5519i	0.399956	−	0.129954i	−0.102130	−	0.994771i	$-0.532566\pi$
$389$	155.583	−	50.5519i	0.399956	−	0.129954i	0.502086	+	0.864817i	$0.332566\pi$
$390$	−220.843	+	12.9617i	−0.566264	+	0.0332351i
$391$	2.33235	−	1.69455i	0.00596509	−	0.00433389i
$392$	−758.053	+	162.075i	−1.93381	+	0.413458i
$393$	−159.006	+	81.0177i	−0.404596	+	0.206152i
$394$	448.129	−	55.2044i	1.13738	−	0.140113i
$395$	204.626	+	121.323i	0.518040	+	0.307148i
$396$	32.1677	+	209.567i	0.0812317	+	0.529211i
$397$	−64.1963	−	64.1963i	−0.161703	−	0.161703i	0.621617	−	0.783321i	$-0.286476\pi$
$397$	−64.1963	−	64.1963i	−0.161703	−	0.161703i	−0.783321	+	0.621617i	$0.786476\pi$
$398$	−87.9974	−	68.6948i	−0.221099	−	0.172600i
$399$	260.691	−	802.323i	0.653360	−	2.01083i
$400$	311.895	−	250.443i	0.779737	−	0.626107i
$401$	225.848	−	164.088i	0.563212	−	0.409197i	−0.269421	−	0.963022i	$-0.586832\pi$
$401$	225.848	−	164.088i	0.563212	−	0.409197i	0.832633	+	0.553825i	$0.186832\pi$
$402$	−688.844	+	465.030i	−1.71354	+	1.15679i
$403$	−221.590	−	112.906i	−0.549850	−	0.280163i
$404$	373.947	+	150.738i	0.925611	+	0.373115i
$405$	−464.371	+	200.337i	−1.14659	+	0.494659i
$406$	−481.615	−	516.057i	−1.18624	−	1.27108i
$407$	−139.515	+	8.97543i	−0.342788	+	0.0220526i
$408$	−467.190	−	48.5397i	−1.14507	−	0.118970i
$409$	−21.8694	−	15.8890i	−0.0534703	−	0.0388485i	0.560729	−	0.827999i	$-0.310521\pi$
$409$	−21.8694	−	15.8890i	−0.0534703	−	0.0388485i	−0.614199	+	0.789151i	$0.710521\pi$
$410$	−197.676	+	162.136i	−0.482137	+	0.395454i
$411$	203.764	−	66.2071i	0.495777	−	0.161088i
$412$	−308.923	−	71.0616i	−0.749814	−	0.172480i
$413$	329.696	+	52.2187i	0.798295	+	0.126438i
$414$	1.53889	+	0.852221i	0.00371713	+	0.00205850i
$415$	128.205	+	8.20943i	0.308927	+	0.0197818i
$416$	−2.94463	+	190.412i	−0.00707845	+	0.457722i
$417$	−430.940	+	430.940i	−1.03343	+	1.03343i
$418$	−176.620	+	373.705i	−0.422535	+	0.894031i
$419$	388.971			0.928333			0.464166	−	0.885748i	$-0.346354\pi$
$419$	388.971			0.928333			0.464166	+	0.885748i	$0.346354\pi$
$420$	−298.019	−	847.132i	−0.709569	−	2.01698i
$421$	−209.353	+	644.323i	−0.497276	+	1.53046i	0.316104	+	0.948724i	$0.397625\pi$
$421$	−209.353	+	644.323i	−0.497276	+	1.53046i	−0.813380	+	0.581733i	$0.802375\pi$
$422$	61.0549	+	212.604i	0.144680	+	0.503802i
$423$	−261.042	−	41.3449i	−0.617120	−	0.0977422i
$424$	22.8871	−	85.8255i	0.0539789	−	0.202419i
$425$	−11.5230	−	394.690i	−0.0271129	−	0.928683i
$426$	301.841	+	646.629i	0.708548	+	1.51791i
$427$	544.836	−	86.2935i	1.27596	−	0.202093i
$428$	−165.053	−	189.566i	−0.385637	−	0.442912i
$429$	96.3285	−	223.468i	0.224542	−	0.520903i
$430$	134.542	+	614.030i	0.312888	+	1.42798i
$431$	572.582	+	416.005i	1.32850	+	0.965208i	0.999784	+	0.0207780i	$0.00661432\pi$
$431$	572.582	+	416.005i	1.32850	+	0.965208i	0.328711	+	0.944430i	$0.393386\pi$
$432$	81.3413	+	235.016i	0.188290	+	0.544019i
$433$	144.774	+	73.7661i	0.334351	+	0.170360i	0.613103	−	0.790003i	$-0.289921\pi$
$433$	144.774	+	73.7661i	0.334351	+	0.170360i	−0.278752	+	0.960363i	$0.589921\pi$
$434$	192.236	−	991.075i	0.442941	−	2.28358i
$435$	346.651	−	418.080i	0.796899	−	0.961102i
$436$	145.013	+	579.651i	0.332600	+	1.32948i
$437$	1.55692	+	3.05563i	0.00356274	+	0.00699228i
$438$	110.404	−	141.426i	0.252063	−	0.322891i
$439$			526.297i			1.19885i	0.800430	+	0.599427i	$0.204605\pi$
$439$			526.297i			1.19885i	−0.800430	+	0.599427i	$0.795395\pi$
$440$	92.1232	+	430.248i	0.209371	+	0.977836i
$441$	−466.922			−1.05878
$442$	148.182	+	115.677i	0.335253	+	0.261714i
$443$	−344.694	+	175.631i	−0.778091	+	0.396457i	−0.797473	−	0.603355i	$-0.793830\pi$
$443$	−344.694	+	175.631i	−0.778091	+	0.396457i	0.0193816	+	0.999812i	$0.493830\pi$
$444$	183.331	−	45.8645i	0.412907	−	0.103299i
$445$	−294.904	+	27.5451i	−0.662706	+	0.0618990i
$446$	−270.742	−	52.5150i	−0.607044	−	0.117747i
$447$	233.405	−	458.083i	0.522159	−	1.02479i
$448$	−746.225	+	201.861i	−1.66568	+	0.450584i
$449$	508.848	−	700.370i	1.13329	−	1.55984i	0.351633	−	0.936138i	$-0.385626\pi$
$449$	508.848	−	700.370i	1.13329	−	1.55984i	0.781659	−	0.623706i	$-0.214374\pi$
$450$	215.253	−	108.238i	0.478340	−	0.240528i
$451$	−61.7362	−	274.370i	−0.136887	−	0.608360i
$452$	−593.364	+	516.633i	−1.31275	+	1.14299i
$453$	−13.9182	−	87.8758i	−0.0307244	−	0.193986i
$454$	−443.611	+	207.074i	−0.977117	+	0.456111i
$455$	−78.7941	+	350.668i	−0.173174	+	0.770699i
$456$	143.967	−	539.871i	0.315718	−	1.18393i
$457$	66.5232	−	420.011i	0.145565	−	0.919062i	−0.801494	−	0.598003i	$-0.795961\pi$
$457$	66.5232	−	420.011i	0.145565	−	0.919062i	0.947059	−	0.321059i	$-0.104039\pi$
$458$	−362.160	+	104.004i	−0.790742	+	0.227082i
$459$	233.482	+	75.8631i	0.508676	+	0.165279i
$460$	3.29173	+	1.57842i	0.00715594	+	0.00343135i
$461$		−	241.927i		−	0.524787i	−0.964961	−	0.262394i	$-0.915488\pi$
$461$		−	241.927i		−	0.524787i	0.964961	−	0.262394i	$-0.0845119\pi$
$462$	979.829	+	125.454i	2.12084	+	0.271545i
$463$	256.350	+	256.350i	0.553671	+	0.553671i	0.927498	−	0.373827i	$-0.121955\pi$
$463$	256.350	+	256.350i	0.553671	+	0.553671i	−0.373827	+	0.927498i	$0.621955\pi$
$464$	−336.819	−	324.228i	−0.725904	−	0.698767i
$465$	775.151	+	49.6358i	1.66699	+	0.106744i
$466$	220.539	−	398.237i	0.473260	−	0.854585i
$467$	−60.3982	+	381.339i	−0.129332	+	0.816573i	0.834684	+	0.550729i	$0.185650\pi$
$467$	−60.3982	+	381.339i	−0.129332	+	0.816573i	−0.964016	+	0.265843i	$0.914350\pi$
$468$	−25.7142	+	111.786i	−0.0549449	+	0.238860i
$469$	417.260	+	1284.20i	0.889681	+	2.73816i
$470$	−545.825	−	53.9136i	−1.16133	−	0.114710i
$471$	−194.528	+	267.745i	−0.413010	+	0.568460i
$472$	219.901	+	22.8471i	0.465892	+	0.0484049i
$473$	−669.976	−	171.012i	−1.41644	−	0.361548i
$474$	258.603	−	241.344i	0.545576	−	0.509164i
$475$	465.868	+	59.9083i	0.980775	+	0.126123i
$476$	−285.302	+	707.769i	−0.599374	+	1.48691i
$477$	24.2895	−	47.6708i	0.0509214	−	0.0999389i
$478$	−15.0164	−	22.2437i	−0.0314151	−	0.0465349i
$479$	116.193	+	159.926i	0.242574	+	0.333875i	0.912893	−	0.408198i	$-0.133843\pi$
$479$	116.193	+	159.926i	0.242574	+	0.333875i	−0.670319	+	0.742073i	$0.733843\pi$
$480$	−227.133	−	549.699i	−0.473193	−	1.14521i
$481$	−71.9329	−	23.3724i	−0.149549	−	0.0485913i
$482$	−442.731	+	567.135i	−0.918530	+	1.17663i
$483$	5.79533	−	5.79533i	0.0119986	−	0.0119986i
$484$	−468.387	−	121.940i	−0.967742	−	0.251943i
$485$	889.383	−	227.298i	1.83378	−	0.468657i
$486$	57.7365	+	468.684i	0.118799	+	0.964369i
$487$	−201.108	−	394.697i	−0.412953	−	0.810467i	−1.00000		0.000913301i	$-0.999709\pi$
$487$	−201.108	−	394.697i	−0.412953	−	0.810467i	0.587046	−	0.809553i	$-0.300291\pi$
$488$	357.277	−	76.3875i	0.732124	−	0.156532i
$489$	552.638	+	760.641i	1.13014	+	1.55550i
$490$	−967.318	+	56.7737i	−1.97412	+	0.115865i
$491$	192.146	+	591.366i	0.391337	+	1.20441i	0.931778	+	0.363029i	$0.118257\pi$
$491$	192.146	+	591.366i	0.391337	+	1.20441i	−0.540441	+	0.841382i	$0.681743\pi$
$492$	148.818	+	349.818i	0.302475	+	0.711012i
$493$	−455.825	+	72.1955i	−0.924593	+	0.146441i
$494$	−163.485	+	152.574i	−0.330941	+	0.308854i
$495$	0.0790169	+	265.027i	0.000159630	+	0.535409i
$496$	92.0023	−	662.279i	0.185488	−	1.33524i
$497$	1145.10	−	181.365i	2.30402	−	0.364920i
$498$	65.2623	−	179.529i	0.131049	−	0.360500i
$499$	100.394	+	308.981i	0.201190	+	0.619200i	0.999848	+	0.0174150i	$0.00554366\pi$
$499$	100.394	+	308.981i	0.201190	+	0.619200i	−0.798658	+	0.601785i	$0.794456\pi$
$500$	432.777	−	250.408i	0.865554	−	0.500816i
$501$	−377.451	−	519.517i	−0.753395	−	1.03696i
$502$	−319.388	+	91.7205i	−0.636230	+	0.182710i
$503$	−44.2849	−	86.9140i	−0.0880415	−	0.172791i	0.842787	−	0.538247i	$-0.180913\pi$
$503$	−44.2849	−	86.9140i	−0.0880415	−	0.172791i	−0.930829	+	0.365456i	$0.880913\pi$
$504$	−464.965	+	24.9245i	−0.922549	+	0.0494534i
$505$	433.512	+	257.031i	0.858440	+	0.508972i
$506$	−3.17713	+	2.45590i	−0.00627891	+	0.00485355i
$507$	−351.135	+	351.135i	−0.692574	+	0.692574i
$508$	−19.1960	−	217.418i	−0.0377875	−	0.427989i
$509$	−507.945	−	165.041i	−0.997926	−	0.324246i	−0.235890	−	0.971780i	$-0.575800\pi$
$509$	−507.945	−	165.041i	−0.997926	−	0.324246i	−0.762037	+	0.647534i	$0.775800\pi$
$510$	−568.065	−	148.405i	−1.11385	−	0.290990i
$511$	−171.334	−	235.821i	−0.335291	−	0.461489i
$512$	−486.371	+	159.960i	−0.949944	+	0.312422i
$513$	−132.580	+	260.203i	−0.258441	+	0.507218i
$514$	450.291	−	210.192i	0.876052	−	0.408934i
$515$	−368.251	−	146.276i	−0.715050	−	0.284031i
$516$	932.461	+	64.4582i	1.80709	+	0.124919i
$517$	322.560	−	509.864i	0.623907	−	0.986198i
$518$	10.5930	−	306.846i	0.0204499	−	0.592367i
$519$	163.344	−	224.824i	0.314729	−	0.433187i
$520$	−39.6796	+	234.713i	−0.0763070	+	0.451372i
$521$	−69.4558	−	213.763i	−0.133313	−	0.410294i	0.862011	−	0.506889i	$-0.169205\pi$
$521$	−69.4558	−	213.763i	−0.133313	−	0.410294i	−0.995324	+	0.0965954i	$0.969205\pi$
$522$	−157.562	−	233.395i	−0.301844	−	0.447117i
$523$	−95.1567	+	600.796i	−0.181944	+	1.14875i	0.712534	+	0.701637i	$0.247547\pi$
$523$	−95.1567	+	600.796i	−0.181944	+	1.14875i	−0.894478	+	0.447112i	$0.852453\pi$
$524$	46.6035	+	186.285i	0.0889381	+	0.355505i
$525$	−207.883	−	1103.11i	−0.395967	−	2.10117i
$526$	−634.690	+	78.1865i	−1.20663	+	0.148644i
$527$	−466.721	−	466.721i	−0.885619	−	0.885619i
$528$	652.473	+	48.2334i	1.23574	+	0.0913511i
$529$		−	528.967i		−	0.999937i
$530$	44.5240	−	101.713i	0.0840076	−	0.191911i
$531$	126.649	+	41.1509i	0.238511	+	0.0774970i
$532$	−778.472	−	466.910i	−1.46329	−	0.877650i
$533$	23.8012	−	150.275i	0.0446551	−	0.281941i
$534$	−83.8628	+	432.355i	−0.157046	+	0.809654i
$535$	−168.056	−	265.467i	−0.314123	−	0.496200i
$536$	321.490	+	834.530i	0.599795	+	1.55696i
$537$	−52.0547	−	328.661i	−0.0969362	−	0.612031i
$538$	29.3485	−	850.132i	0.0545511	−	1.58017i
$539$	421.930	−	978.814i	0.782801	−	1.81598i
$540$	56.0203	+	305.779i	0.103741	+	0.566258i
$541$	107.381	−	147.797i	0.198486	−	0.273192i	−0.698159	−	0.715943i	$-0.745997\pi$
$541$	107.381	−	147.797i	0.198486	−	0.273192i	0.896645	+	0.442750i	$0.145997\pi$
$542$	−316.453	+	870.525i	−0.583861	+	1.60613i
$543$	98.6406	−	193.593i	0.181659	−	0.356525i
$544$	−163.597	+	478.209i	−0.300730	+	0.879061i
$545$	69.4601	+	743.657i	0.127450	+	1.36451i
$546$	467.520	+	258.907i	0.856264	+	0.474189i
$547$	780.949	−	397.913i	1.42769	−	0.727446i	0.442162	−	0.896935i	$-0.354212\pi$
$547$	780.949	−	397.913i	1.42769	−	0.727446i	0.985532	+	0.169489i	$0.0542116\pi$
$548$	−20.2758	−	229.648i	−0.0369997	−	0.419066i
$549$	220.064			0.400845
$550$	32.3888	+	549.046i	0.0588886	+	0.998265i
$551$		−	548.986i		−	0.996344i
$552$	3.62737	−	4.03829i	0.00657133	−	0.00731575i
$553$	−260.901	−	512.047i	−0.471792	−	0.925944i
$554$	523.391	+	289.848i	0.944749	+	0.523192i
$555$	235.202	−	21.9687i	0.423788	−	0.0395832i
$556$	347.953	+	555.857i	0.625815	+	0.999742i
$557$	−137.014	−	69.8124i	−0.245986	−	0.125336i	0.326651	−	0.945145i	$-0.394080\pi$
$557$	−137.014	−	69.8124i	−0.245986	−	0.125336i	−0.572638	+	0.819809i	$0.694080\pi$
$558$	137.596	−	378.511i	0.246588	−	0.678335i
$559$	−302.640	−	219.881i	−0.541396	−	0.393347i
$560$	−960.233	+	108.172i	−1.71470	+	0.193164i
$561$	426.419	−	485.057i	0.760105	−	0.864630i
$562$	0.168915	−	4.89292i	0.000300560	−	0.00870626i
$563$	−616.382	+	97.6254i	−1.09482	+	0.173402i	−0.677619	−	0.735413i	$-0.736988\pi$
$563$	−616.382	+	97.6254i	−1.09482	+	0.173402i	−0.417199	+	0.908815i	$0.636988\pi$
$564$	−304.912	+	756.416i	−0.540623	+	1.34116i
$565$	−830.940	+	526.033i	−1.47069	+	0.931031i
$566$	204.149	−	1052.49i	0.360687	−	1.85952i
$567$	1206.71	+	191.125i	2.12824	+	0.337080i
$568$	750.898	−	160.546i	1.32200	−	0.282651i
$569$	−61.7366	+	190.006i	−0.108500	+	0.333929i	−0.990536	−	0.137253i	$-0.956173\pi$
$569$	−61.7366	+	190.006i	−0.108500	+	0.333929i	0.882036	+	0.471182i	$0.156173\pi$
$570$	280.071	−	639.807i	0.491353	−	1.12247i
$571$	602.534			1.05523			0.527613	−	0.849485i	$-0.323087\pi$
$571$	602.534			1.05523			0.527613	+	0.849485i	$0.323087\pi$
$572$	−211.103	−	154.920i	−0.369061	−	0.270839i
$573$	405.402	−	405.402i	0.707508	−	0.707508i
$574$	612.991	−	75.5134i	1.06793	−	0.131557i
$575$	3.76845	+	2.57334i	0.00655383	+	0.00447537i
$576$	−306.628	+	32.9684i	−0.532341	+	0.0572369i
$577$	431.747	+	68.3820i	0.748261	+	0.118513i	0.518908	−	0.854830i	$-0.326339\pi$
$577$	431.747	+	68.3820i	0.748261	+	0.118513i	0.229354	+	0.973343i	$0.426339\pi$
$578$	−44.2460	−	65.5411i	−0.0765502	−	0.113393i
$579$	−938.667	+	304.991i	−1.62119	+	0.526755i
$580$	−354.799	−	464.365i	−0.611723	−	0.800629i
$581$	−251.076	−	182.417i	−0.432145	−	0.313971i
$582$	47.0936	−	1364.15i	0.0809169	−	2.34390i
$583$	77.9840	+	93.9958i	0.133763	+	0.161228i
$584$	−121.675	−	149.890i	−0.208347	−	0.256660i
$585$	−52.9310	+	133.254i	−0.0904804	+	0.227785i
$586$	−54.9006	+	25.6272i	−0.0936871	+	0.0437324i
$587$	903.490	+	460.351i	1.53917	+	0.784244i	0.998379	−	0.0569155i	$-0.0181265\pi$
$587$	903.490	+	460.351i	1.53917	+	0.784244i	0.540787	+	0.841160i	$0.318127\pi$
$588$	−322.996	+	1404.15i	−0.549313	+	2.38801i
$589$	635.205	−	461.503i	1.07845	−	0.783537i
$590$	267.382	+	69.8525i	0.453190	+	0.118394i
$591$	259.334	−	798.147i	0.438805	−	1.35050i
$592$	−3.87263	−	203.313i	−0.00654160	−	0.343435i
$593$	155.131	+	155.131i	0.261604	+	0.261604i	0.825706	−	0.564101i	$-0.190777\pi$
$593$	155.131	+	155.131i	0.261604	+	0.261604i	−0.564101	+	0.825706i	$0.690777\pi$
$594$	−328.217	−	95.9540i	−0.552554	−	0.161539i
$595$	−486.482	+	820.508i	−0.817617	+	1.37900i
$596$	−424.066	−	355.259i	−0.711521	−	0.596072i
$597$	−184.879	+	94.2005i	−0.309680	+	0.157790i
$598$	−2.08811	+	0.599656i	−0.00349183	+	0.00100277i
$599$	−813.931	+	591.355i	−1.35882	+	0.987237i	−0.360296	+	0.932838i	$0.617324\pi$
$599$	−813.931	+	591.355i	−1.35882	+	0.987237i	−0.998519	+	0.0543995i	$0.982676\pi$
$600$	−176.595	−	722.192i	−0.294325	−	1.20365i
$601$	78.3368	−	25.4532i	0.130344	−	0.0423514i	−0.243119	−	0.969997i	$-0.578170\pi$
$601$	78.3368	−	25.4532i	0.130344	−	0.0423514i	0.373463	+	0.927645i	$0.378170\pi$
$602$	518.805	−	1427.17i	0.861802	−	2.37072i
$603$	84.2675	+	532.044i	0.139747	+	0.882329i
$604$	−95.5082	−	6.60219i	−0.158126	−	0.0109308i
$605$	−555.652	−	239.324i	−0.918433	−	0.395577i
$606$	547.866	−	511.301i	0.904069	−	0.843731i
$607$	−128.828	−	813.390i	−0.212238	−	1.34002i	−0.831803	−	0.555071i	$-0.812691\pi$
$607$	−128.828	−	813.390i	−0.212238	−	1.34002i	0.619565	−	0.784945i	$-0.287309\pi$
$608$	−531.408	−	281.200i	−0.874026	−	0.462499i
$609$	−1247.79	+	405.431i	−2.04891	+	0.665733i
$610$	455.905	−	26.7579i	0.747385	−	0.0438654i
$611$	264.068	−	191.857i	0.432191	−	0.314005i
$612$	−156.586	+	261.073i	−0.255859	+	0.426590i
$613$	481.593	−	245.384i	0.785633	−	0.400300i	−0.0146724	−	0.999892i	$-0.504671\pi$
$613$	481.593	−	245.384i	0.785633	−	0.400300i	0.800306	+	0.599592i	$0.204671\pi$
$614$	18.3792	+	149.196i	0.0299336	+	0.242990i
$615$	117.663	+	460.398i	0.191322	+	0.748615i
$616$	367.912	−	997.235i	0.597260	−	1.61889i
$617$	−796.010	−	796.010i	−1.29013	−	1.29013i	−0.934704	−	0.355426i	$-0.884336\pi$
$617$	−796.010	−	796.010i	−1.29013	−	1.29013i	−0.355426	−	0.934704i	$-0.615664\pi$
$618$	−362.553	+	464.427i	−0.586655	+	0.751500i
$619$	173.080	−	532.686i	0.279613	−	0.860560i	−0.708349	−	0.705862i	$-0.750560\pi$
$619$	173.080	−	532.686i	0.279613	−	0.860560i	0.987962	−	0.154697i	$-0.0494403\pi$
$620$	239.033	−	800.888i	0.385537	−	1.29176i
$621$	−2.29530	+	1.66763i	−0.00369613	+	0.00268540i
$622$	241.836	+	358.229i	0.388804	+	0.575931i
$623$	637.534	+	324.840i	1.02333	+	0.521412i
$624$	318.381	+	154.658i	0.510226	+	0.247849i
$625$	582.130	−	227.485i	0.931409	−	0.363976i
$626$	−257.311	+	240.138i	−0.411040	+	0.383607i
$627$	490.546	+	591.265i	0.782370	+	0.943007i
$628$	233.846	+	268.577i	0.372366	+	0.427670i
$629$	−162.399	−	117.990i	−0.258186	−	0.187583i
$630$	−579.222	−	57.2123i	−0.919400	−	0.0908131i
$631$	−160.423	+	52.1246i	−0.254236	+	0.0826064i	−0.433362	−	0.901220i	$-0.642673\pi$
$631$	−160.423	+	52.1246i	−0.254236	+	0.0826064i	0.179126	+	0.983826i	$0.442673\pi$
$632$	−190.704	−	329.401i	−0.301748	−	0.521204i
$633$	406.073	+	64.3156i	0.641505	+	0.101604i
$634$	−4.94596	+	8.93113i	−0.00780120	+	0.0140870i
$635$	17.4346	−	272.273i	0.0274561	−	0.428776i
$636$	−126.555	−	106.021i	−0.198987	−	0.166700i
$637$	407.754	−	407.754i	0.640116	−	0.640116i
$638$	631.650	−	119.394i	0.990046	−	0.187138i
$639$	462.514			0.723809
$640$	−631.231	+	105.584i	−0.986298	+	0.164975i
$641$	29.5245	−	90.8670i	0.0460600	−	0.141758i	−0.925382	−	0.379037i	$-0.876255\pi$
$641$	29.5245	−	90.8670i	0.0460600	−	0.141758i	0.971442	+	0.237279i	$0.0762554\pi$
$642$	−449.032	+	128.951i	−0.699427	+	0.200859i
$643$	207.812	+	32.9143i	0.323192	+	0.0511886i	0.315923	−	0.948785i	$-0.397686\pi$
$643$	207.812	+	32.9143i	0.323192	+	0.0511886i	0.00726947	+	0.999974i	$0.497686\pi$
$644$	−4.67931	−	7.47522i	−0.00726602	−	0.0116075i
$645$	1139.93	+	256.140i	1.76734	+	0.397116i
$646$	−537.788	+	251.035i	−0.832489	+	0.388599i
$647$	−398.129	+	63.0575i	−0.615347	+	0.0974613i	−0.456324	−	0.889814i	$-0.650834\pi$
$647$	−398.129	+	63.0575i	−0.615347	+	0.0974613i	−0.159022	+	0.987275i	$0.550834\pi$
$648$	804.855	+	83.6222i	1.24206	+	0.129047i
$649$	−200.711	+	228.311i	−0.309262	+	0.351789i
$650$	−93.4542	+	282.498i	−0.143776	+	0.434612i
$651$	−1518.05	−	1102.93i	−2.33188	−	1.69421i
$652$	930.953	−	396.041i	1.42784	−	0.607425i
$653$	113.590	+	57.8772i	0.173952	+	0.0886327i	0.538798	−	0.842435i	$-0.318879\pi$
$653$	113.590	+	57.8772i	0.173952	+	0.0886327i	−0.364847	+	0.931068i	$0.618879\pi$
$654$	1090.27	+	211.476i	1.66707	+	0.323358i
$655$	22.3227	+	238.992i	0.0340804	+	0.364873i
$656$	402.734	−	71.6741i	0.613924	−	0.109259i
$657$	−52.7927	−	103.612i	−0.0803542	−	0.157704i
$658$	1044.44	+	815.338i	1.58730	+	1.23912i
$659$		−	118.415i		−	0.179688i	−0.995956	−	0.0898442i	$-0.971363\pi$
$659$		−	118.415i		−	0.179688i	0.995956	−	0.0898442i	$-0.0286369\pi$
$660$	797.057	+	183.097i	1.20766	+	0.277419i
$661$	−755.354			−1.14274			−0.571372	−	0.820691i	$-0.693589\pi$
$661$	−755.354			−1.14274			−0.571372	+	0.820691i	$0.693589\pi$
$662$	143.495	−	183.816i	0.216759	−	0.277667i
$663$	311.324	−	158.627i	0.469568	−	0.239257i
$664$	−172.520	−	111.743i	−0.259820	−	0.168288i
$665$	−873.492	−	724.257i	−1.31352	−	1.08911i
$666$	23.3234	−	120.244i	0.0350201	−	0.180546i
$667$	2.42135	−	4.75217i	0.00363021	−	0.00712469i
$668$	−635.840	+	270.495i	−0.951856	+	0.404933i
$669$	−301.298	+	414.702i	−0.450371	+	0.619883i
$670$	239.268	+	1091.99i	0.357117	+	1.62983i
$671$	−198.859	+	461.323i	−0.296362	+	0.687516i
$672$	−246.688	+	1415.50i	−0.367096	+	2.10641i
$673$	170.117	+	1074.08i	0.252775	+	1.59596i	0.708418	+	0.705793i	$0.249409\pi$
$673$	170.117	+	1074.08i	0.252775	+	1.59596i	−0.455643	+	0.890162i	$0.650591\pi$
$674$	−513.003	−	1099.00i	−0.761132	−	1.63056i
$675$	11.3399	+	388.420i	0.0167999	+	0.575437i
$676$	283.517	+	452.919i	0.419403	+	0.669998i
$677$	−117.878	+	744.252i	−0.174118	+	1.09934i	0.733546	+	0.679640i	$0.237864\pi$
$677$	−117.878	+	744.252i	−0.174118	+	1.09934i	−0.907664	+	0.419698i	$0.862136\pi$
$678$	403.632	+	1405.52i	0.595327	+	2.07304i
$679$	−2109.06	−	685.276i	−3.10613	−	1.00924i
$680$	−292.654	+	559.903i	−0.430373	+	0.823387i
$681$			909.935i			1.33618i
$682$	669.140	+	630.483i	0.981143	+	0.924461i
$683$	−80.3888	−	80.3888i	−0.117700	−	0.117700i	0.645804	−	0.763503i	$-0.276522\pi$
$683$	−80.3888	−	80.3888i	−0.117700	−	0.117700i	−0.763503	+	0.645804i	$0.776522\pi$
$684$	−277.598	−	232.556i	−0.405845	−	0.339994i
$685$	18.4153	−	287.588i	0.0268837	−	0.419836i
$686$	1012.25	+	560.575i	1.47559	+	0.817165i
$687$	−109.558	+	691.721i	−0.159473	+	1.00687i
$688$	292.523	−	962.276i	0.425179	−	1.39866i
$689$	20.4185	+	62.8416i	0.0296349	+	0.0912069i
$690$	5.24630	−	4.30307i	0.00760334	−	0.00623633i
$691$	−499.950	+	688.122i	−0.723516	+	0.995835i	0.275884	+	0.961191i	$0.411030\pi$
$691$	−499.950	+	688.122i	−0.723516	+	0.995835i	−0.999400	+	0.0346436i	$0.988970\pi$
$692$	−196.359	−	225.523i	−0.283756	−	0.325900i
$693$	342.296	−	541.060i	0.493934	−	0.780751i
$694$	−413.459	−	443.027i	−0.595762	−	0.638367i
$695$	324.714	+	752.669i	0.467214	+	1.08298i
$696$	−810.872	+	312.376i	−1.16505	+	0.448816i
$697$	183.323	−	359.792i	0.263017	−	0.516201i
$698$	−285.811	+	192.947i	−0.409471	+	0.276429i
$699$	−497.334	−	684.522i	−0.711494	−	0.979287i
$700$	−1206.93	−	48.0978i	−1.72418	−	0.0687112i
$701$	30.6036	+	9.94371i	0.0436570	+	0.0141850i	0.330764	−	0.943713i	$-0.392694\pi$
$701$	30.6036	+	9.94371i	0.0436570	+	0.0141850i	−0.287107	+	0.957898i	$0.592694\pi$
$702$	−145.828	−	113.840i	−0.207732	−	0.162165i
$703$	168.847	−	168.847i	0.240181	−	0.240181i
$704$	207.970	−	672.580i	0.295412	−	0.955370i
$705$	−519.919	+	876.903i	−0.737474	+	1.24383i
$706$	−835.966	+	102.981i	−1.18409	+	0.145866i
$707$	−552.734	−	1084.80i	−0.781803	−	1.53437i
$708$	211.361	−	352.399i	0.298533	−	0.497739i
$709$	467.485	+	643.437i	0.659358	+	0.907528i	0.999460	−	0.0328605i	$-0.0104617\pi$
$709$	467.485	+	643.437i	0.659358	+	0.907528i	−0.340102	+	0.940388i	$0.610462\pi$
$710$	958.187	−	56.2377i	1.34956	−	0.0792081i
$711$	−70.8459	−	218.041i	−0.0996426	−	0.306668i
$712$	433.160	+	192.236i	0.608370	+	0.269994i
$713$	7.53401	−	1.19327i	0.0105666	−	0.00167359i
$714$	967.739	+	1036.95i	1.35538	+	1.45230i
$715$	−231.512	−	231.374i	−0.323793	−	0.323600i
$716$	−357.206	−	24.6926i	−0.498892	−	0.0344869i
$717$	−49.2688	+	7.80342i	−0.0687152	+	0.0108834i
$718$	−727.391	−	264.421i	−1.01308	−	0.368274i
$719$	225.753	+	694.796i	0.313982	+	0.966337i	0.976171	+	0.217001i	$0.0696274\pi$
$719$	225.753	+	694.796i	0.313982	+	0.966337i	−0.662190	+	0.749336i	$0.730373\pi$
$720$	−385.106	−	17.3033i	−0.534869	−	0.0240324i
$721$	562.640	+	774.408i	0.780361	+	1.07407i
$722$	4.41876	+	15.3869i	0.00612016	+	0.0213115i
$723$	607.113	+	1191.53i	0.839714	+	1.64803i
$724$	−179.217	−	150.138i	−0.247537	−	0.207373i
$725$	−350.490	−	640.919i	−0.483435	−	0.884027i
$726$	−573.611	+	692.999i	−0.790097	+	0.954544i
$727$	−371.698	+	371.698i	−0.511277	+	0.511277i	−0.914917	−	0.403641i	$-0.867745\pi$
$727$	−371.698	+	371.698i	−0.511277	+	0.511277i	0.403641	+	0.914917i	$0.367745\pi$
$728$	384.279	−	427.811i	0.527855	−	0.587652i
$729$	−31.0243	−	10.0804i	−0.0425574	−	0.0138277i
$730$	−121.969	−	208.232i	−0.167080	−	0.285249i
$731$	−583.569	−	803.214i	−0.798316	−	1.09879i
$732$	152.231	−	661.786i	0.207965	−	0.904079i
$733$	13.0615	−	25.6346i	0.0178192	−	0.0349721i	−0.881925	−	0.471389i	$-0.843753\pi$
$733$	13.0615	−	25.6346i	0.0178192	−	0.0349721i	0.899745	+	0.436417i	$0.143753\pi$
$734$	311.130	+	666.528i	0.423883	+	0.908076i
$735$	−664.867	+	1673.81i	−0.904581	+	2.27729i
$736$	−3.35976	−	4.77796i	−0.00456489	−	0.00649180i
$737$	−1191.48	−	304.126i	−1.61666	−	0.412654i
$738$	246.246	+	8.50097i	0.333666	+	0.0115189i
$739$	−296.352	+	407.893i	−0.401017	+	0.551953i	−0.960999	−	0.276552i	$-0.910808\pi$
$739$	−296.352	+	407.893i	−0.401017	+	0.551953i	0.559982	+	0.828505i	$0.310808\pi$
$740$	33.6982	−	251.944i	0.0455381	−	0.340465i
$741$	128.439	+	395.295i	0.173332	+	0.533461i
$742$	−222.309	+	150.078i	−0.299607	+	0.202261i
$743$	−45.6112	+	287.978i	−0.0613879	+	0.387588i	0.937796	+	0.347188i	$0.112863\pi$
$743$	−45.6112	+	287.978i	−0.0613879	+	0.387588i	−0.999184	+	0.0404004i	$0.987137\pi$
$744$	−1043.09	−	675.622i	−1.40200	−	0.908094i
$745$	−456.727	−	519.220i	−0.613056	−	0.696940i
$746$	96.7872	+	785.683i	0.129742	+	1.05319i
$747$	−87.5459	−	87.5459i	−0.117197	−	0.117197i
$748$	−405.794	−	564.170i	−0.542505	−	0.754238i
$749$			759.010i			1.01336i
$750$	−81.5014	−	925.756i	−0.108669	−	1.23434i
$751$	37.9272	+	12.3233i	0.0505023	+	0.0164092i	0.334159	−	0.942517i	$-0.391548\pi$
$751$	37.9272	+	12.3233i	0.0505023	+	0.0164092i	−0.283657	+	0.958926i	$0.591548\pi$
$752$	719.664	+	502.209i	0.957000	+	0.667830i
$753$	−96.6189	+	610.027i	−0.128312	+	0.810129i
$754$	341.416	+	66.2235i	0.452806	+	0.0878296i
$755$	−116.759	−	26.2354i	−0.154648	−	0.0347489i
$756$	280.770	−	696.526i	0.371389	−	0.921330i
$757$	20.5321	+	129.634i	0.0271229	+	0.171247i	0.997531	−	0.0702218i	$-0.0223707\pi$
$757$	20.5321	+	129.634i	0.0271229	+	0.171247i	−0.970408	+	0.241469i	$0.922371\pi$
$758$	679.510	+	23.4583i	0.896452	+	0.0309476i
$759$	1.63847	+	7.28175i	0.00215872	+	0.00959388i
$760$	−603.375	−	448.031i	−0.793914	−	0.589515i
$761$	−177.360	+	244.115i	−0.233061	+	0.320781i	−0.909489	−	0.415727i	$-0.863527\pi$
$761$	−177.360	+	244.115i	−0.233061	+	0.320781i	0.676428	+	0.736509i	$0.263527\pi$
$762$	−381.271	−	138.600i	−0.500356	−	0.181889i
$763$	819.145	−	1607.66i	1.07358	−	2.10703i
$764$	−327.333	−	522.916i	−0.428446	−	0.684445i
$765$	−242.891	+	292.940i	−0.317505	+	0.382928i
$766$	−61.4297	+	110.926i	−0.0801954	+	0.144812i
$767$	−146.537	+	74.6642i	−0.191052	+	0.0973458i
$768$	−112.968	+	944.912i	−0.147094	+	1.23035i
$769$	−1022.88			−1.33014			−0.665070	−	0.746781i	$-0.731598\pi$
$769$	−1022.88			−1.33014			−0.665070	+	0.746781i	$0.731598\pi$

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+(-1.57651 - 1.23070i) q^{2} +(-3.31218 + 1.68764i) q^{3} +(0.970777 + 3.88041i) q^{4} +(0.464993 + 4.97833i) q^{5} +(7.29866 + 1.41570i) q^{6} +(5.48368 - 10.7623i) q^{7} +(3.24516 - 7.31224i) q^{8} +(2.83235 - 3.89839i) q^{9} +(5.39374 - 8.42066i) q^{10} +(5.61283 + 9.46024i) q^{11} +(-9.76413 - 11.2143i) q^{12} +(0.930957 + 5.87783i) q^{13} +(-21.8902 + 10.2182i) q^{14} +(-9.94178 - 15.7044i) q^{15} +(-14.1152 + 7.53403i) q^{16} +(-2.47078 + 15.5999i) q^{17} +(-9.26297 + 2.66010i) q^{18} +(-17.8686 - 5.80587i) q^{19} +(-18.8666 + 6.63721i) q^{20} +44.9012i q^{21} +(2.79399 - 21.8219i) q^{22} +(-0.129068 - 0.129068i) q^{23} +(1.59187 + 29.6962i) q^{24} +(-24.5676 + 4.62978i) q^{25} +(5.76615 - 10.4122i) q^{26} +(2.43153 - 15.3521i) q^{27} +(47.0857 + 10.8311i) q^{28} +(9.02940 + 27.7896i) q^{29} +(-3.65401 + 36.9935i) q^{30} +(-24.5635 + 33.8088i) q^{31} +(31.5248 + 5.49402i) q^{32} +(-34.5562 - 21.8616i) q^{33} +(23.0939 - 21.5526i) q^{34} +(56.1283 + 22.2952i) q^{35} +(17.8770 + 7.20621i) q^{36} +(-5.76994 + 11.3241i) q^{37} +(21.0248 + 31.1438i) q^{38} +(-13.0032 - 17.8973i) q^{39} +(37.9117 + 12.7554i) q^{40} +(-24.3151 - 7.90045i) q^{41} +(55.2598 - 70.7873i) q^{42} +(-44.4485 + 44.4485i) q^{43} +(-31.2608 + 30.9639i) q^{44} +(20.7245 + 12.2876i) q^{45} +(0.0446339 + 0.362322i) q^{46} +(-24.9005 - 48.8700i) q^{47} +(34.0373 - 48.7754i) q^{48} +(-56.9554 - 78.3923i) q^{49} +(44.4289 + 22.9363i) q^{50} +(-18.1433 - 55.8394i) q^{51} +(-21.9046 + 9.31855i) q^{52} +(10.9664 - 1.73691i) q^{53} +(-22.7270 + 21.2102i) q^{54} +(-44.4863 + 32.3415i) q^{55} +(-60.9013 - 75.0235i) q^{56} +(68.9823 - 10.9257i) q^{57} +(19.9656 - 54.9231i) q^{58} +(8.53987 + 26.2830i) q^{59} +(51.2883 - 53.8236i) q^{60} +(26.8435 + 36.9469i) q^{61} +(80.3329 - 23.0697i) q^{62} +(-26.4241 - 51.8602i) q^{63} +(-42.9378 - 47.4589i) q^{64} +(-28.8289 + 7.36776i) q^{65} +(27.5733 + 76.9932i) q^{66} +(-79.0469 + 79.0469i) q^{67} +(-62.9325 + 5.55636i) q^{68} +(0.645319 + 0.209677i) q^{69} +(-61.0483 - 104.225i) q^{70} +(56.4177 + 77.6523i) q^{71} +(-19.3146 - 33.3618i) q^{72} +(10.9558 - 21.5021i) q^{73} +(23.0329 - 10.7516i) q^{74} +(73.5588 - 56.7959i) q^{75} +(5.18271 - 74.9738i) q^{76} +(132.593 - 8.53013i) q^{77} +(-1.52652 + 44.2183i) q^{78} +(27.9655 - 38.4912i) q^{79} +(-44.0703 - 66.7668i) q^{80} +(31.2566 + 96.1979i) q^{81} +(28.6100 + 42.3796i) q^{82} +(4.01934 - 25.3771i) q^{83} +(-174.235 + 43.5891i) q^{84} +(-78.8103 - 5.04652i) q^{85} +(124.776 - 15.3710i) q^{86} +(-76.8059 - 76.8059i) q^{87} +(87.3901 - 10.3423i) q^{88} +59.2376i q^{89} +(-17.5501 - 44.8772i) q^{90} +(68.3641 + 22.2129i) q^{91} +(0.375542 - 0.626135i) q^{92} +(24.3017 - 153.435i) q^{93} +(-20.8882 + 107.689i) q^{94} +(20.5947 - 91.6556i) q^{95} +(-113.688 + 35.0054i) q^{96} +(-28.7204 - 181.333i) q^{97} +(-6.68631 + 193.681i) q^{98} +(52.7772 + 4.91370i) 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

Representations

Groups

Database

Properties

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