LMFDB - Embedded newform 220.2.r.c.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.r (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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.4
Character	$\chi$	$=$	220.151
Dual form			220.2.r.c.51.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21274 - 0.727497i) q^{2} +(0.919215 - 0.298671i) q^{3} +(0.941497 + 1.76453i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-1.33205 - 0.306514i) q^{6} +(0.819704 - 2.52279i) q^{7} +(0.141898 - 2.82487i) q^{8} +(-1.67130 + 1.21427i) q^{9} +(-0.553519 - 1.30139i) q^{10} +(3.31523 - 0.0962271i) q^{11} +(1.39245 + 1.34079i) q^{12} +(3.18839 + 4.38844i) q^{13} +(-2.82941 + 2.46317i) q^{14} +(0.919215 + 0.298671i) q^{15} +(-2.22717 + 3.32261i) q^{16} +(2.85398 - 3.92817i) q^{17} +(2.91024 - 0.256734i) q^{18} +(-0.860525 - 2.64842i) q^{19} +(-0.275480 + 1.98094i) q^{20} -2.56381i q^{21} +(-4.09053 - 2.29512i) q^{22} -6.73882i q^{23} +(-0.713271 - 2.63904i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.674125 - 7.64160i) q^{26} +(-2.87793 + 3.96114i) q^{27} +(5.22330 - 0.928803i) q^{28} +(-5.27084 - 1.71260i) q^{29} +(-0.897490 - 1.03094i) q^{30} +(2.76888 + 3.81103i) q^{31} +(5.11817 - 2.40922i) q^{32} +(3.01867 - 1.07862i) q^{33} +(-6.31888 + 2.68760i) q^{34} +(2.14601 - 1.55917i) q^{35} +(-3.71615 - 1.80583i) q^{36} +(-2.07425 + 6.38388i) q^{37} +(-0.883122 + 3.83789i) q^{38} +(4.24151 + 3.08164i) q^{39} +(1.77521 - 2.20196i) q^{40} +(-5.13011 + 1.66687i) q^{41} +(-1.86516 + 3.10924i) q^{42} +5.61242 q^{43} +(3.29107 + 5.75924i) q^{44} -2.06584 q^{45} +(-4.90247 + 8.17247i) q^{46} +(-11.2770 + 3.66411i) q^{47} +(-1.05488 + 3.71938i) q^{48} +(-0.0294279 - 0.0213806i) q^{49} +(0.317132 - 1.37820i) q^{50} +(1.45019 - 4.46323i) q^{51} +(-4.74170 + 9.75773i) q^{52} +(4.06440 - 2.95296i) q^{53} +(6.37191 - 2.71016i) q^{54} +(2.73864 + 1.87079i) q^{55} +(-7.01022 - 2.67353i) q^{56} +(-1.58201 - 2.17746i) q^{57} +(5.14627 + 5.91147i) q^{58} +(-3.91889 - 1.27333i) q^{59} +(0.338423 + 1.90318i) q^{60} +(-4.69937 + 6.46813i) q^{61} +(-0.585426 - 6.63616i) q^{62} +(1.69338 + 5.21168i) q^{63} +(-7.95973 - 0.801684i) q^{64} +5.42441i q^{65} +(-4.44556 - 0.887985i) q^{66} -1.99522i q^{67} +(9.61840 + 1.33759i) q^{68} +(-2.01269 - 6.19443i) q^{69} +(-3.73685 + 0.329657i) q^{70} +(-7.82413 + 10.7690i) q^{71} +(3.19300 + 4.89350i) q^{72} +(-10.0453 - 3.26391i) q^{73} +(7.15978 - 6.23300i) q^{74} +(0.568106 + 0.781931i) q^{75} +(3.86305 - 4.01191i) q^{76} +(2.47474 - 8.44250i) q^{77} +(-2.90199 - 6.82293i) q^{78} +(-9.25186 + 6.72187i) q^{79} +(-3.75480 + 1.37895i) q^{80} +(0.452777 - 1.39350i) q^{81} +(7.43415 + 1.71065i) q^{82} +(-7.51368 - 5.45901i) q^{83} +(4.52392 - 2.41382i) q^{84} +(4.61784 - 1.50043i) q^{85} +(-6.80643 - 4.08302i) q^{86} -5.35654 q^{87} +(0.198595 - 9.37873i) q^{88} +14.5622 q^{89} +(2.50534 + 1.50289i) q^{90} +(13.6846 - 4.44641i) q^{91} +(11.8909 - 6.34458i) q^{92} +(3.68344 + 2.67617i) q^{93} +(16.3417 + 3.76033i) q^{94} +(0.860525 - 2.64842i) q^{95} +(3.98513 - 3.74324i) q^{96} +(2.55355 - 1.85526i) q^{97} +(0.0201342 + 0.0473379i) q^{98} +(-5.42390 + 4.18641i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q - 10 q^{2} - 2 q^{4} + 8 q^{5} - 15 q^{6} - 10 q^{8} + 10 q^{9} + 6 q^{12} - 10 q^{13} + 21 q^{14} - 34 q^{16} + 10 q^{17} - 25 q^{18} + 2 q^{20} - 36 q^{22} - 15 q^{24} - 8 q^{25} + 12 q^{26} + 30 q^{28}+ \cdots + 94 q^{97}+O(q^{100})$ 32 * q - 10 * q^2 - 2 * q^4 + 8 * q^5 - 15 * q^6 - 10 * q^8 + 10 * q^9 + 6 * q^12 - 10 * q^13 + 21 * q^14 - 34 * q^16 + 10 * q^17 - 25 * q^18 + 2 * q^20 - 36 * q^22 - 15 * q^24 - 8 * q^25 + 12 * q^26 + 30 * q^28 - 10 * q^29 + 10 * q^30 + 36 * q^33 + 18 * q^34 + 15 * q^36 - 44 * q^37 + 29 * q^38 - 10 * q^40 - 30 * q^41 + 18 * q^42 + 9 * q^44 + 60 * q^45 - 10 * q^46 + 38 * q^48 + 12 * q^49 + 10 * q^50 + 10 * q^52 - 14 * q^53 - 34 * q^56 - 60 * q^57 + 10 * q^58 - 11 * q^60 + 20 * q^61 + 40 * q^62 - 74 * q^64 - 118 * q^66 - 20 * q^68 - 22 * q^69 - 21 * q^70 + 70 * q^72 + 10 * q^73 + 20 * q^74 + 44 * q^77 - 92 * q^78 - 46 * q^80 - 58 * q^81 + 37 * q^82 + 100 * q^84 - 10 * q^85 + 57 * q^86 + 19 * q^88 - 72 * q^89 + 10 * q^90 - 63 * q^92 - 26 * q^93 - 25 * q^94 + 94 * q^97

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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

)

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

$2$	−1.21274	−	0.727497i	−0.857540	−	0.514418i
$2$	−1.21274	−	0.727497i	−0.857540	−	0.514418i
$3$	0.919215	−	0.298671i	0.530709	−	0.172438i	−0.0313910	−	0.999507i	$-0.509994\pi$
$3$	0.919215	−	0.298671i	0.530709	−	0.172438i	0.562100	+	0.827069i	$0.309994\pi$
$4$	0.941497	+	1.76453i	0.470749	+	0.882267i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−1.33205	−	0.306514i	−0.543809	−	0.125134i
$7$	0.819704	−	2.52279i	0.309819	−	0.953524i	−0.668016	−	0.744147i	$-0.732856\pi$
$7$	0.819704	−	2.52279i	0.309819	−	0.953524i	0.977835	−	0.209377i	$-0.0671437\pi$
$8$	0.141898	−	2.82487i	0.0501684	−	0.998741i
$9$	−1.67130	+	1.21427i	−0.557100	+	0.404757i
$10$	−0.553519	−	1.30139i	−0.175038	−	0.411536i
$11$	3.31523	−	0.0962271i	0.999579	−	0.0290136i
$11$	3.31523	−	0.0962271i	0.999579	−	0.0290136i
$12$	1.39245	+	1.34079i	0.401967	+	0.387052i
$13$	3.18839	+	4.38844i	0.884300	+	1.21713i	0.975211	+	0.221276i	$0.0710221\pi$
$13$	3.18839	+	4.38844i	0.884300	+	1.21713i	−0.0909110	+	0.995859i	$0.528978\pi$
$14$	−2.82941	+	2.46317i	−0.756192	+	0.658309i
$15$	0.919215	+	0.298671i	0.237340	+	0.0771165i
$16$	−2.22717	+	3.32261i	−0.556791	+	0.830652i
$17$	2.85398	−	3.92817i	0.692192	−	0.952720i	−0.307807	−	0.951449i	$-0.599595\pi$
$17$	2.85398	−	3.92817i	0.692192	−	0.952720i	0.999999	−	0.00127174i	$-0.000404807\pi$
$18$	2.91024	−	0.256734i	0.685949	−	0.0605129i
$19$	−0.860525	−	2.64842i	−0.197418	−	0.607590i	−0.999940	−	0.0109673i	$-0.996509\pi$
$19$	−0.860525	−	2.64842i	−0.197418	−	0.607590i	0.802522	−	0.596623i	$-0.203491\pi$
$20$	−0.275480	+	1.98094i	−0.0615993	+	0.442951i
$21$		−	2.56381i		−	0.559468i
$22$	−4.09053	−	2.29512i	−0.872104	−	0.489321i
$23$		−	6.73882i		−	1.40514i	−0.711614	−	0.702571i	$-0.752035\pi$
$23$		−	6.73882i		−	1.40514i	0.711614	−	0.702571i	$-0.247965\pi$
$24$	−0.713271	−	2.63904i	−0.145596	−	0.538691i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.674125	−	7.64160i	−0.132207	−	1.49864i
$27$	−2.87793	+	3.96114i	−0.553859	+	0.762321i
$28$	5.22330	−	0.928803i	0.987110	−	0.175527i
$29$	−5.27084	−	1.71260i	−0.978771	−	0.318022i	−0.224419	−	0.974493i	$-0.572048\pi$
$29$	−5.27084	−	1.71260i	−0.978771	−	0.318022i	−0.754351	+	0.656471i	$0.772048\pi$
$30$	−0.897490	−	1.03094i	−0.163859	−	0.188222i
$31$	2.76888	+	3.81103i	0.497305	+	0.684482i	0.981714	−	0.190360i	$-0.0609655\pi$
$31$	2.76888	+	3.81103i	0.497305	+	0.684482i	−0.484409	+	0.874841i	$0.660965\pi$
$32$	5.11817	−	2.40922i	0.904773	−	0.425894i
$33$	3.01867	−	1.07862i	0.525482	−	0.187763i
$34$	−6.31888	+	2.68760i	−1.08368	+	0.460920i
$35$	2.14601	−	1.55917i	0.362742	−	0.263548i
$36$	−3.71615	−	1.80583i	−0.619358	−	0.300972i
$37$	−2.07425	+	6.38388i	−0.341004	+	1.04950i	0.622684	+	0.782473i	$0.286042\pi$
$37$	−2.07425	+	6.38388i	−0.341004	+	1.04950i	−0.963688	+	0.267030i	$0.913958\pi$
$38$	−0.883122	+	3.83789i	−0.143261	+	0.622588i
$39$	4.24151	+	3.08164i	0.679186	+	0.493457i
$40$	1.77521	−	2.20196i	0.280686	−	0.348160i
$41$	−5.13011	+	1.66687i	−0.801188	+	0.260322i	−0.680861	−	0.732412i	$-0.738394\pi$
$41$	−5.13011	+	1.66687i	−0.801188	+	0.260322i	−0.120327	+	0.992734i	$0.538394\pi$
$42$	−1.86516	+	3.10924i	−0.287800	+	0.479766i
$43$	5.61242			0.855886			0.427943	−	0.903806i	$-0.359238\pi$
$43$	5.61242			0.855886			0.427943	+	0.903806i	$0.359238\pi$
$44$	3.29107	+	5.75924i	0.496148	+	0.868238i
$45$	−2.06584			−0.307957
$46$	−4.90247	+	8.17247i	−0.722830	+	1.20497i
$47$	−11.2770	+	3.66411i	−1.64491	+	0.534465i	−0.977629	−	0.210337i	$-0.932544\pi$
$47$	−11.2770	+	3.66411i	−1.64491	+	0.534465i	−0.667285	+	0.744802i	$0.732544\pi$
$48$	−1.05488	+	3.71938i	−0.152258	+	0.536846i
$49$	−0.0294279	−	0.0213806i	−0.00420398	−	0.00305437i
$50$	0.317132	−	1.37820i	0.0448492	−	0.194907i
$51$	1.45019	−	4.46323i	0.203067	−	0.624977i
$52$	−4.74170	+	9.75773i	−0.657555	+	1.35315i
$53$	4.06440	−	2.95296i	0.558288	−	0.405620i	−0.272544	−	0.962143i	$-0.587865\pi$
$53$	4.06440	−	2.95296i	0.558288	−	0.405620i	0.830832	+	0.556523i	$0.187865\pi$
$54$	6.37191	−	2.71016i	0.867107	−	0.368806i
$55$	2.73864	+	1.87079i	0.369278	+	0.252258i
$56$	−7.01022	−	2.67353i	−0.936781	−	0.357266i
$57$	−1.58201	−	2.17746i	−0.209543	−	0.288411i
$58$	5.14627	+	5.91147i	0.675739	+	0.776213i
$59$	−3.91889	−	1.27333i	−0.510196	−	0.165773i	0.0425952	−	0.999092i	$-0.486437\pi$
$59$	−3.91889	−	1.27333i	−0.510196	−	0.165773i	−0.552792	+	0.833320i	$0.686437\pi$
$60$	0.338423	+	1.90318i	0.0436902	+	0.245700i
$61$	−4.69937	+	6.46813i	−0.601693	+	0.828159i	−0.995862	−	0.0908788i	$-0.971032\pi$
$61$	−4.69937	+	6.46813i	−0.601693	+	0.828159i	0.394169	+	0.919038i	$0.371032\pi$
$62$	−0.585426	−	6.63616i	−0.0743492	−	0.842793i
$63$	1.69338	+	5.21168i	0.213345	+	0.656610i
$64$	−7.95973	−	0.801684i	−0.994966	−	0.100211i
$65$			5.42441i			0.672816i
$66$	−4.44556	−	0.887985i	−0.547211	−	0.109303i
$67$		−	1.99522i		−	0.243755i	−0.992545	−	0.121877i	$-0.961108\pi$
$67$		−	1.99522i		−	0.243755i	0.992545	−	0.121877i	$-0.0388915\pi$
$68$	9.61840	+	1.33759i	1.16640	+	0.162207i
$69$	−2.01269	−	6.19443i	−0.242300	−	0.745721i
$70$	−3.73685	+	0.329657i	−0.446639	+	0.0394015i
$71$	−7.82413	+	10.7690i	−0.928553	+	1.27804i	0.0318679	+	0.999492i	$0.489854\pi$
$71$	−7.82413	+	10.7690i	−0.928553	+	1.27804i	−0.960421	+	0.278552i	$0.910146\pi$
$72$	3.19300	+	4.89350i	0.376298	+	0.576704i
$73$	−10.0453	−	3.26391i	−1.17571	−	0.382012i	−0.344939	−	0.938625i	$-0.612101\pi$
$73$	−10.0453	−	3.26391i	−1.17571	−	0.382012i	−0.830772	+	0.556613i	$0.812101\pi$
$74$	7.15978	−	6.23300i	0.832308	−	0.724572i
$75$	0.568106	+	0.781931i	0.0655992	+	0.0902896i
$76$	3.86305	−	4.01191i	0.443123	−	0.460198i
$77$	2.47474	−	8.44250i	0.282023	−	0.962112i
$78$	−2.90199	−	6.82293i	−0.328586	−	0.772545i
$79$	−9.25186	+	6.72187i	−1.04092	+	0.756269i	−0.970464	−	0.241246i	$-0.922444\pi$
$79$	−9.25186	+	6.72187i	−1.04092	+	0.756269i	−0.0704513	+	0.997515i	$0.522444\pi$
$80$	−3.75480	+	1.37895i	−0.419799	+	0.154172i
$81$	0.452777	−	1.39350i	0.0503085	−	0.154834i
$82$	7.43415	+	1.71065i	0.820965	+	0.188909i
$83$	−7.51368	−	5.45901i	−0.824733	−	0.599204i	0.0933312	−	0.995635i	$-0.470248\pi$
$83$	−7.51368	−	5.45901i	−0.824733	−	0.599204i	−0.918064	+	0.396431i	$0.870248\pi$
$84$	4.52392	−	2.41382i	0.493601	−	0.263369i
$85$	4.61784	−	1.50043i	0.500875	−	0.162744i
$86$	−6.80643	−	4.08302i	−0.733956	−	0.440283i
$87$	−5.35654			−0.574281
$88$	0.198595	−	9.37873i	0.0211703	−	0.999776i
$89$	14.5622			1.54359			0.771796	−	0.635870i	$-0.219358\pi$
$89$	14.5622			1.54359			0.771796	+	0.635870i	$0.219358\pi$
$90$	2.50534	+	1.50289i	0.264086	+	0.158419i
$91$	13.6846	−	4.44641i	1.43454	−	0.466111i
$92$	11.8909	−	6.34458i	1.23971	−	0.661469i
$93$	3.68344	+	2.67617i	0.381955	+	0.277506i
$94$	16.3417	+	3.76033i	1.68552	+	0.387848i
$95$	0.860525	−	2.64842i	0.0882880	−	0.271722i
$96$	3.98513	−	3.74324i	0.406731	−	0.382043i
$97$	2.55355	−	1.85526i	0.259273	−	0.188373i	−0.450553	−	0.892750i	$-0.648773\pi$
$97$	2.55355	−	1.85526i	0.259273	−	0.188373i	0.709827	+	0.704376i	$0.248773\pi$
$98$	0.0201342	+	0.0473379i	0.00203386	+	0.00478185i
$99$	−5.42390	+	4.18641i	−0.545122	+	0.420750i
$100$	−1.38723	+	1.44069i	−0.138723	+	0.144069i
$101$	1.12706	+	1.55127i	0.112147	+	0.154357i	0.861401	−	0.507926i	$-0.169588\pi$
$101$	1.12706	+	1.55127i	0.112147	+	0.154357i	−0.749254	+	0.662283i	$0.769588\pi$
$102$	−5.00570	+	4.35775i	−0.495638	+	0.431481i
$103$	−4.44936	−	1.44568i	−0.438408	−	0.142447i	0.0814928	−	0.996674i	$-0.474031\pi$
$103$	−4.44936	−	1.44568i	−0.438408	−	0.142447i	−0.519901	+	0.854226i	$0.674031\pi$
$104$	12.8492	−	8.38406i	1.25997	−	0.822125i
$105$	1.50697	−	2.07416i	0.147065	−	0.202418i
$106$	−7.07735	+	0.624347i	−0.687413	+	0.0606420i
$107$	0.107374	+	0.330465i	0.0103803	+	0.0319472i	0.956113	−	0.293000i	$-0.0946535\pi$
$107$	0.107374	+	0.330465i	0.0103803	+	0.0319472i	−0.945732	+	0.324947i	$0.894654\pi$
$108$	−9.69913	−	1.34882i	−0.933299	−	0.129790i
$109$		−	3.33111i		−	0.319062i	−0.987193	−	0.159531i	$-0.949002\pi$
$109$		−	3.33111i		−	0.319062i	0.987193	−	0.159531i	$-0.0509983\pi$
$110$	−1.96027	−	4.26114i	−0.186904	−	0.406284i
$111$			6.48767i			0.615783i
$112$	6.55662	+	8.34222i	0.619543	+	0.788266i
$113$	0.465946	+	1.43403i	0.0438325	+	0.134902i	0.970578	−	0.240788i	$-0.0774057\pi$
$113$	0.465946	+	1.43403i	0.0438325	+	0.134902i	−0.926745	+	0.375690i	$0.877406\pi$
$114$	0.334487	+	3.79161i	0.0313276	+	0.355116i
$115$	3.96098	−	5.45182i	0.369363	−	0.508385i
$116$	−1.94054	−	10.9130i	−0.180175	−	1.01325i
$117$	−10.6575	−	3.46284i	−0.985287	−	0.320139i
$118$	3.82627	+	4.39520i	0.352237	+	0.404611i
$119$	−7.57052	−	10.4199i	−0.693988	−	0.955193i
$120$	0.974140	−	2.55428i	0.0889264	−	0.233173i
$121$	10.9815	−	0.638030i	0.998316	−	0.0580027i
$122$	10.4047	−	4.42541i	0.941995	−	0.400658i
$123$	−4.21782	+	3.06443i	−0.380308	+	0.276310i
$124$	−4.11781	+	8.47386i	−0.369790	+	0.760975i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	1.73785	−	7.55236i	0.154820	−	0.672818i
$127$	−9.20456	−	6.68750i	−0.816772	−	0.593420i	0.0990139	−	0.995086i	$-0.468431\pi$
$127$	−9.20456	−	6.68750i	−0.816772	−	0.593420i	−0.915786	+	0.401666i	$0.868431\pi$
$128$	9.06989	+	6.76291i	0.801673	+	0.597763i
$129$	5.15902	−	1.67627i	0.454226	−	0.147587i
$130$	3.94624	−	6.57843i	0.346108	−	0.576966i
$131$	13.7361			1.20013			0.600066	−	0.799951i	$-0.295141\pi$
$131$	13.7361			1.20013			0.600066	+	0.799951i	$0.295141\pi$
$132$	4.74532	+	4.31103i	0.413027	+	0.375227i
$133$	−7.38679			−0.640516
$134$	−1.45152	+	2.41969i	−0.125392	+	0.209030i
$135$	−4.65659	+	1.51302i	−0.400776	+	0.130220i
$136$	−10.6916	−	8.61951i	−0.916795	−	0.739117i
$137$	4.55581	+	3.30999i	0.389229	+	0.282791i	0.765139	−	0.643865i	$-0.222670\pi$
$137$	4.55581	+	3.30999i	0.389229	+	0.282791i	−0.375911	+	0.926656i	$0.622670\pi$
$138$	−2.06554	+	8.97648i	−0.175831	+	0.764129i
$139$	2.89662	−	8.91487i	0.245688	−	0.756149i	−0.749835	−	0.661625i	$-0.769867\pi$
$139$	2.89662	−	8.91487i	0.245688	−	0.756149i	0.995523	−	0.0945243i	$-0.0301330\pi$
$140$	4.77167	+	2.31876i	0.403280	+	0.195971i
$141$	−9.27159	+	6.73620i	−0.780808	+	0.567291i
$142$	17.3231	−	7.36800i	1.45372	−	0.618309i
$143$	10.9925	+	14.2419i	0.919241	+	1.19097i
$144$	−0.312284	−	8.25746i	−0.0260237	−	0.688121i
$145$	−3.25756	−	4.48365i	−0.270526	−	0.372346i
$146$	9.80787	+	11.2662i	0.811705	+	0.932397i
$147$	−0.0334363	−	0.0108641i	−0.00275778	−	0.000896056i
$148$	−13.2175	+	2.35032i	−1.08647	+	0.193195i
$149$	1.01118	−	1.39177i	0.0828393	−	0.114019i	−0.765586	−	0.643333i	$-0.777551\pi$
$149$	1.01118	−	1.39177i	0.0828393	−	0.114019i	0.848426	+	0.529315i	$0.177551\pi$
$150$	−0.120115	−	1.36158i	−0.00980736	−	0.111172i
$151$	−3.18023	−	9.78774i	−0.258803	−	0.796515i	−0.993056	−	0.117639i	$-0.962467\pi$
$151$	−3.18023	−	9.78774i	−0.258803	−	0.796515i	0.734253	−	0.678876i	$-0.237533\pi$
$152$	−7.60355	+	2.05506i	−0.616729	+	0.166688i
$153$			10.0306i			0.810930i
$154$	−9.14312	+	8.43822i	−0.736774	+	0.679971i
$155$			4.71070i			0.378372i
$156$	−1.44429	+	10.3857i	−0.115636	+	0.831518i
$157$	−3.66619	−	11.2834i	−0.292593	−	0.900510i	−0.984019	−	0.178063i	$-0.943017\pi$
$157$	−3.66619	−	11.2834i	−0.292593	−	0.900510i	0.691426	−	0.722448i	$-0.256983\pi$
$158$	16.1103	−	1.42121i	1.28166	−	0.113066i
$159$	2.85409	−	3.92832i	0.226344	−	0.311536i
$160$	5.55679	+	1.05929i	0.439303	+	0.0837438i
$161$	−17.0006	−	5.52384i	−1.33984	−	0.435339i
$162$	−1.56287	+	1.36057i	−0.122791	+	0.106896i
$163$	−6.30118	−	8.67283i	−0.493546	−	0.679308i	0.487491	−	0.873128i	$-0.337912\pi$
$163$	−6.30118	−	8.67283i	−0.493546	−	0.679308i	−0.981037	+	0.193820i	$0.937912\pi$
$164$	−7.77124	−	7.48290i	−0.606832	−	0.584316i
$165$	3.07615	+	0.901709i	0.239478	+	0.0701980i
$166$	5.14076	+	12.0866i	0.399000	+	0.938098i
$167$	−12.8253	+	9.31810i	−0.992449	+	0.721056i	−0.960456	−	0.278432i	$-0.910185\pi$
$167$	−12.8253	+	9.31810i	−0.992449	+	0.721056i	−0.0319930	+	0.999488i	$0.510185\pi$
$168$	−7.24241	−	0.363798i	−0.558764	−	0.0280676i
$169$	−5.07537	+	15.6204i	−0.390413	+	1.20157i
$170$	−6.69181	−	1.53983i	−0.513238	−	0.118099i
$171$	4.65410	+	3.38140i	0.355908	+	0.258582i
$172$	5.28408	+	9.90331i	0.402907	+	0.755120i
$173$	−1.88681	+	0.613063i	−0.143452	+	0.0466103i	−0.379863	−	0.925043i	$-0.624029\pi$
$173$	−1.88681	+	0.613063i	−0.143452	+	0.0466103i	0.236411	+	0.971653i	$0.424029\pi$
$174$	6.49611	+	3.89686i	0.492469	+	0.295420i
$175$	2.65262			0.200519
$176$	−7.06384	+	11.2295i	−0.532457	+	0.846457i
$177$	−3.98261			−0.299351
$178$	−17.6603	−	10.5940i	−1.32369	−	0.794052i
$179$	10.5044	−	3.41308i	0.785135	−	0.255106i	0.111104	−	0.993809i	$-0.464561\pi$
$179$	10.5044	−	3.41308i	0.785135	−	0.255106i	0.674031	+	0.738703i	$0.264561\pi$
$180$	−1.94498	−	3.64525i	−0.144970	−	0.271701i
$181$	12.7806	+	9.28562i	0.949971	+	0.690194i	0.950800	−	0.309805i	$-0.100264\pi$
$181$	12.7806	+	9.28562i	0.949971	+	0.690194i	−0.000828970		1.00000i	$0.500264\pi$
$182$	−19.8307	−	4.56317i	−1.46995	−	0.338245i
$183$	−2.38789	+	7.34916i	−0.176518	+	0.543266i
$184$	−19.0363	−	0.956224i	−1.40337	−	0.0704938i
$185$	−5.43045	+	3.94545i	−0.399255	+	0.290076i
$186$	−2.52016	−	5.92520i	−0.184787	−	0.434457i
$187$	9.08360	−	13.2974i	0.664259	−	0.972402i
$188$	−17.0827	−	16.4488i	−1.24588	−	1.19966i
$189$	7.63405	+	10.5074i	0.555296	+	0.764299i
$190$	−2.97032	+	2.58583i	−0.215489	+	0.187596i
$191$	13.3317	+	4.33172i	0.964646	+	0.313433i	0.748653	−	0.662962i	$-0.230701\pi$
$191$	13.3317	+	4.33172i	0.964646	+	0.313433i	0.215994	+	0.976395i	$0.430701\pi$
$192$	−7.55614	+	1.64042i	−0.545317	+	0.118387i
$193$	4.77833	−	6.57680i	0.343951	−	0.473408i	−0.601639	−	0.798768i	$-0.705485\pi$
$193$	4.77833	−	6.57680i	0.343951	−	0.473408i	0.945590	+	0.325360i	$0.105485\pi$
$194$	−4.44649	+	0.392259i	−0.319240	+	0.0281626i
$195$	1.62011	+	4.98620i	0.116019	+	0.357069i
$196$	0.0100205	−	0.0720562i	0.000715753	−	0.00514687i
$197$		−	1.14642i		−	0.0816789i	−0.999166	−	0.0408394i	$-0.986997\pi$
$197$		−	1.14642i		−	0.0816789i	0.999166	−	0.0408394i	$-0.0130032\pi$
$198$	9.62340	−	1.13118i	0.683905	−	0.0803892i
$199$			15.4162i			1.09282i	0.837517	+	0.546411i	$0.184006\pi$
$199$			15.4162i			1.09282i	−0.837517	+	0.546411i	$0.815994\pi$
$200$	2.73046	−	0.737979i	0.193072	−	0.0521830i
$201$	−0.595914	−	1.83404i	−0.0420326	−	0.129363i
$202$	−0.238296	−	2.70123i	−0.0167665	−	0.190058i
$203$	−8.64106	+	11.8934i	−0.606483	+	0.834752i
$204$	9.24087	−	1.64321i	0.646991	−	0.115047i
$205$	−5.13011	−	1.66687i	−0.358302	−	0.116419i
$206$	4.34420	+	4.99014i	0.302675	+	0.347679i
$207$	8.18276	+	11.2626i	0.568741	+	0.782805i
$208$	−21.6822	+	0.819985i	−1.50339	+	0.0568557i
$209$	−3.10769	−	8.69732i	−0.214963	−	0.601606i
$210$	−3.33651	+	1.41911i	−0.230241	+	0.0979282i
$211$	5.95726	−	4.32820i	0.410115	−	0.297966i	−0.363534	−	0.931581i	$-0.618430\pi$
$211$	5.95726	−	4.32820i	0.410115	−	0.297966i	0.773648	+	0.633615i	$0.218430\pi$
$212$	9.03722	+	4.39157i	0.620679	+	0.301614i
$213$	−3.97567	+	12.2359i	−0.272408	+	0.838387i
$214$	0.110194	−	0.478884i	0.00753271	−	0.0327358i
$215$	4.54054	+	3.29890i	0.309662	+	0.224983i
$216$	10.7813	+	8.69185i	0.733575	+	0.591406i
$217$	11.8841	−	3.86137i	0.806744	−	0.262127i
$218$	−2.42337	+	4.03978i	−0.164131	+	0.273609i
$219$	−10.2086			−0.689833
$220$	−0.722660	+	6.59377i	−0.0487217	+	0.444552i
$221$	26.3381			1.77169
$222$	4.71976	−	7.86789i	0.316770	−	0.528058i
$223$	15.4342	−	5.01489i	1.03355	−	0.335822i	0.257359	−	0.966316i	$-0.417148\pi$
$223$	15.4342	−	5.01489i	1.03355	−	0.335822i	0.776194	+	0.630494i	$0.217148\pi$
$224$	−1.88257	−	14.8869i	−0.125784	−	0.994673i
$225$	−1.67130	−	1.21427i	−0.111420	−	0.0809514i
$226$	0.478181	−	2.07809i	0.0318082	−	0.138232i
$227$	5.32020	−	16.3739i	0.353114	−	1.08677i	−0.603981	−	0.796999i	$-0.706420\pi$
$227$	5.32020	−	16.3739i	0.353114	−	1.08677i	0.957095	−	0.289774i	$-0.0935802\pi$
$228$	2.35273	−	4.84159i	0.155814	−	0.320642i
$229$	4.83613	−	3.51365i	0.319580	−	0.232189i	−0.416416	−	0.909174i	$-0.636714\pi$
$229$	4.83613	−	3.51365i	0.319580	−	0.232189i	0.735996	+	0.676985i	$0.236714\pi$
$230$	−8.76984	+	3.73007i	−0.578266	+	0.245953i
$231$	−0.246708	−	8.49960i	−0.0162322	−	0.559233i
$232$	−5.58579	+	14.6464i	−0.366725	+	0.961583i
$233$	−12.7024	−	17.4834i	−0.832163	−	1.14537i	−0.987517	−	0.157515i	$-0.949652\pi$
$233$	−12.7024	−	17.4834i	−0.832163	−	1.14537i	0.155354	−	0.987859i	$-0.450348\pi$
$234$	10.4056	+	11.9528i	0.680238	+	0.781381i
$235$	−11.2770	−	3.66411i	−0.735628	−	0.239020i
$236$	−1.44280	−	8.11385i	−0.0939183	−	0.528167i
$237$	−6.49682	+	8.94210i	−0.422014	+	0.580852i
$238$	1.60064	+	18.1442i	0.103754	+	1.17612i
$239$	3.77012	+	11.6032i	0.243869	+	0.750551i	0.995820	+	0.0913328i	$0.0291127\pi$
$239$	3.77012	+	11.6032i	0.243869	+	0.750551i	−0.751952	+	0.659218i	$0.770887\pi$
$240$	−3.03961	+	2.38900i	−0.196206	+	0.154209i
$241$			4.27559i			0.275415i	0.990473	+	0.137707i	$0.0439734\pi$
$241$			4.27559i			0.275415i	−0.990473	+	0.137707i	$0.956027\pi$
$242$	−13.7819	−	7.21522i	−0.885934	−	0.463812i
$243$		−	16.1049i		−	1.03313i
$244$	−15.8377	−	2.20248i	−1.01390	−	0.140999i
$245$	−0.0112404	−	0.0345945i	−0.000718125	−	0.00221016i
$246$	7.34450	−	0.647915i	0.468268	−	0.0413096i
$247$	8.87876	−	12.2206i	0.564942	−	0.777576i
$248$	11.1586	−	7.28093i	0.708569	−	0.462339i
$249$	−8.53713	−	2.77388i	−0.541018	−	0.175788i
$250$	1.06665	−	0.928579i	0.0674608	−	0.0587285i
$251$	−7.02506	−	9.66916i	−0.443418	−	0.610312i	0.527550	−	0.849524i	$-0.323111\pi$
$251$	−7.02506	−	9.66916i	−0.443418	−	0.610312i	−0.970967	+	0.239212i	$0.923111\pi$
$252$	−7.60188	+	7.89480i	−0.478873	+	0.497326i
$253$	−0.648457	−	22.3407i	−0.0407682	−	1.40455i
$254$	6.29764	+	14.8065i	0.395149	+	0.929043i
$255$	3.79665	−	2.75843i	0.237755	−	0.172739i
$256$	−6.07946	−	14.8000i	−0.379967	−	0.925000i
$257$	−5.48456	+	16.8798i	−0.342118	+	1.05293i	0.620991	+	0.783818i	$0.286730\pi$
$257$	−5.48456	+	16.8798i	−0.342118	+	1.05293i	−0.963109	+	0.269112i	$0.913270\pi$
$258$	−7.47605	−	1.72029i	−0.465438	−	0.107100i
$259$	14.4049	+	10.4658i	0.895077	+	0.650312i
$260$	−9.57157	+	5.10707i	−0.593603	+	0.316727i
$261$	10.8887	−	3.53796i	0.673995	−	0.218994i
$262$	−16.6584	−	9.99299i	−1.02916	−	0.617369i
$263$	−20.9424			−1.29136			−0.645681	−	0.763607i	$-0.723426\pi$
$263$	−20.9424			−1.29136			−0.645681	+	0.763607i	$0.723426\pi$
$264$	−2.61860	−	8.68038i	−0.161164	−	0.534240i
$265$	5.02388			0.308614
$266$	8.95828	+	5.37386i	0.549268	+	0.329493i
$267$	13.3858	−	4.34931i	0.819198	−	0.266174i
$268$	3.52064	−	1.87849i	0.215057	−	0.114747i
$269$	−8.96012	−	6.50991i	−0.546308	−	0.396916i	0.280114	−	0.959967i	$-0.409628\pi$
$269$	−8.96012	−	6.50991i	−0.546308	−	0.396916i	−0.826422	+	0.563051i	$0.809628\pi$
$270$	6.74797	+	1.55275i	0.410669	+	0.0944974i
$271$	2.12198	−	6.53078i	0.128901	−	0.396717i	−0.865691	−	0.500579i	$-0.833120\pi$
$271$	2.12198	−	6.53078i	0.128901	−	0.396717i	0.994592	+	0.103863i	$0.0331203\pi$
$272$	6.69548	+	18.2313i	0.405973	+	1.10544i
$273$	11.2511	−	8.17441i	0.680948	−	0.494738i
$274$	−3.11702	−	7.32850i	−0.188306	−	0.442731i
$275$	1.11598	+	3.12323i	0.0672961	+	0.188338i
$276$	9.03534	−	9.38350i	0.543863	−	0.564820i
$277$	14.5656	+	20.0478i	0.875161	+	1.20456i	0.977738	+	0.209830i	$0.0672912\pi$
$277$	14.5656	+	20.0478i	0.875161	+	1.20456i	−0.102577	+	0.994725i	$0.532709\pi$
$278$	−9.99839	+	8.70418i	−0.599664	+	0.522042i
$279$	−9.25525	−	3.00721i	−0.554097	−	0.180037i
$280$	−4.09993	−	6.28344i	−0.245018	−	0.375507i
$281$	−14.4474	+	19.8851i	−0.861859	+	1.18625i	0.119264	+	0.992863i	$0.461947\pi$
$281$	−14.4474	+	19.8851i	−0.861859	+	1.18625i	−0.981123	+	0.193385i	$0.938053\pi$
$282$	16.1446	−	1.42424i	0.961399	−	0.0848124i
$283$	3.26201	+	10.0394i	0.193906	+	0.596782i	0.999988	+	0.00497747i	$0.00158439\pi$
$283$	3.26201	+	10.0394i	0.193906	+	0.596782i	−0.806081	+	0.591805i	$0.798416\pi$
$284$	−26.3687	−	3.66697i	−1.56469	−	0.217595i
$285$		−	2.69148i		−	0.159430i
$286$	−2.97021	−	25.2688i	−0.175632	−	1.49417i
$287$			14.3085i			0.844605i
$288$	−5.62855	+	10.2414i	−0.331666	+	0.603479i
$289$	−2.03200	−	6.25386i	−0.119530	−	0.367874i
$290$	0.688749	+	7.80738i	0.0404447	+	0.458465i
$291$	1.79314	−	2.46805i	0.105116	−	0.144680i
$292$	−3.69832	−	20.7982i	−0.216428	−	1.21712i
$293$	7.92528	+	2.57508i	0.463000	+	0.150438i	0.531223	−	0.847232i	$-0.321733\pi$
$293$	7.92528	+	2.57508i	0.463000	+	0.150438i	−0.0682226	+	0.997670i	$0.521733\pi$
$294$	0.0326461	+	0.0375002i	0.00190396	+	0.00218705i
$295$	−2.42201	−	3.33361i	−0.141015	−	0.194090i
$296$	17.7393	+	6.76533i	1.03107	+	0.393227i
$297$	−9.15984	+	13.4090i	−0.531508	+	0.778069i
$298$	−2.23882	+	0.952233i	−0.129691	+	0.0551614i
$299$	29.5729	−	21.4860i	1.71025	−	1.24257i
$300$	−0.844874	+	1.73863i	−0.0487788	+	0.100380i
$301$	4.60052	−	14.1589i	0.265170	−	0.816108i
$302$	−3.26374	+	14.1836i	−0.187807	+	0.816176i
$303$	1.49933	+	1.08933i	0.0861344	+	0.0625803i
$304$	10.7162	+	3.03929i	0.614617	+	0.174315i
$305$	−7.60374	+	2.47061i	−0.435389	+	0.141466i
$306$	7.29726	−	12.1646i	0.417157	−	0.695405i
$307$	−5.12122			−0.292283			−0.146142	−	0.989264i	$-0.546686\pi$
$307$	−5.12122			−0.292283			−0.146142	+	0.989264i	$0.546686\pi$
$308$	17.2270	−	3.58182i	0.981602	−	0.204093i
$309$	−4.52170			−0.257230
$310$	3.42701	−	5.71287i	0.194641	−	0.324469i
$311$	−9.53518	+	3.09817i	−0.540690	+	0.175681i	−0.566615	−	0.823983i	$-0.691747\pi$
$311$	−9.53518	+	3.09817i	−0.540690	+	0.175681i	0.0259242	+	0.999664i	$0.491747\pi$
$312$	9.30708	−	11.5444i	0.526910	−	0.653575i
$313$	12.6954	+	9.22374i	0.717586	+	0.521357i	0.885612	−	0.464426i	$-0.153739\pi$
$313$	12.6954	+	9.22374i	0.717586	+	0.521357i	−0.168026	+	0.985783i	$0.553739\pi$
$314$	−3.76246	+	16.3510i	−0.212328	+	0.922739i
$315$	−1.69338	+	5.21168i	−0.0954110	+	0.293645i
$316$	−20.5716	−	9.99660i	−1.15724	−	0.562353i
$317$	12.4944	−	9.07771i	0.701755	−	0.509855i	−0.178748	−	0.983895i	$-0.557205\pi$
$317$	12.4944	−	9.07771i	0.701755	−	0.509855i	0.880503	+	0.474040i	$0.157205\pi$
$318$	−6.31913	+	2.68771i	−0.354359	+	0.150719i
$319$	−17.6388	−	5.17046i	−0.987586	−	0.289490i
$320$	−5.96834	−	5.32719i	−0.333640	−	0.297799i
$321$	0.197400	+	0.271698i	0.0110178	+	0.0151647i
$322$	16.5988	+	19.0669i	0.925017	+	1.06256i
$323$	−12.8594	−	4.17826i	−0.715514	−	0.232485i
$324$	2.88517	−	0.513039i	0.160287	−	0.0285022i
$325$	−3.18839	+	4.38844i	−0.176860	+	0.243427i
$326$	1.33226	+	15.1020i	0.0737873	+	0.836423i
$327$	−0.994906	−	3.06200i	−0.0550184	−	0.169329i
$328$	3.98074	+	14.7284i	0.219800	+	0.813239i
$329$			31.4529i			1.73405i
$330$	−3.07459	−	3.33143i	−0.169251	−	0.183389i
$331$			14.9466i			0.821541i	0.911739	+	0.410770i	$0.134740\pi$
$331$			14.9466i			0.821541i	−0.911739	+	0.410770i	$0.865260\pi$
$332$	2.55850	−	18.3978i	0.140416	−	1.00971i
$333$	−4.28507	−	13.1881i	−0.234820	−	0.722702i
$334$	22.3327	−	1.97014i	1.22199	−	0.107801i
$335$	1.17276	−	1.61417i	0.0640748	−	0.0881914i
$336$	8.51852	+	5.71002i	0.464724	+	0.311507i
$337$	13.3418	+	4.33502i	0.726776	+	0.236144i	0.648958	−	0.760824i	$-0.275205\pi$
$337$	13.3418	+	4.33502i	0.726776	+	0.236144i	0.0778173	+	0.996968i	$0.475205\pi$
$338$	17.5189	−	15.2512i	0.952904	−	0.829557i
$339$	0.856608	+	1.17902i	0.0465246	+	0.0640356i
$340$	6.99524	+	6.73569i	0.379370	+	0.365294i
$341$	9.54618	+	12.3680i	0.516955	+	0.669765i
$342$	−3.18427	−	7.48661i	−0.172186	−	0.404830i
$343$	14.9440	−	10.8575i	0.806901	−	0.586248i
$344$	0.796390	−	15.8543i	0.0429385	−	0.854808i
$345$	2.01269	−	6.19443i	0.108360	−	0.333497i
$346$	2.73422	+	0.629162i	0.146993	+	0.0338240i
$347$	9.90524	+	7.19658i	0.531741	+	0.386333i	0.821009	−	0.570916i	$-0.193412\pi$
$347$	9.90524	+	7.19658i	0.531741	+	0.386333i	−0.289267	+	0.957248i	$0.593412\pi$
$348$	−5.04317	−	9.45180i	−0.270342	−	0.506670i
$349$	−19.5066	+	6.33807i	−1.04416	+	0.339269i	−0.780375	−	0.625311i	$-0.784972\pi$
$349$	−19.5066	+	6.33807i	−1.04416	+	0.339269i	−0.263788	+	0.964581i	$0.584972\pi$
$350$	−3.21695	−	1.92977i	−0.171953	−	0.103151i
$351$	−26.5592			−1.41762
$352$	16.7361	−	8.47962i	0.892036	−	0.451965i
$353$	−23.8846			−1.27125			−0.635625	−	0.771998i	$-0.719258\pi$
$353$	−23.8846			−1.27125			−0.635625	+	0.771998i	$0.719258\pi$
$354$	4.82989	+	2.89733i	0.256706	+	0.153992i
$355$	−12.6597	+	4.11339i	−0.671907	+	0.218316i
$356$	13.7103	+	25.6956i	0.726644	+	1.36186i
$357$	−10.0711	−	7.31705i	−0.533017	−	0.387259i
$358$	−15.2222	−	3.50271i	−0.804516	−	0.185124i
$359$	3.90705	−	12.0247i	0.206206	−	0.634638i	−0.793455	−	0.608629i	$-0.791720\pi$
$359$	3.90705	−	12.0247i	0.206206	−	0.634638i	0.999662	−	0.0260095i	$-0.00828001\pi$
$360$	−0.293138	+	5.83572i	−0.0154497	+	0.307569i
$361$	9.09768	−	6.60985i	0.478825	−	0.347887i
$362$	−8.74429	−	20.5589i	−0.459590	−	1.08055i
$363$	9.90378	−	3.86634i	0.519813	−	0.202930i
$364$	20.7299	+	19.9607i	1.08654	+	1.04623i
$365$	−6.20832	−	8.54503i	−0.324959	−	0.447267i
$366$	8.24239	−	7.17548i	0.430837	−	0.375068i
$367$	2.88231	+	0.936519i	0.150455	+	0.0488859i	0.383276	−	0.923634i	$-0.374796\pi$
$367$	2.88231	+	0.936519i	0.150455	+	0.0488859i	−0.232821	+	0.972520i	$0.574796\pi$
$368$	22.3905	+	15.0085i	1.16718	+	0.782371i
$369$	6.54991	−	9.01518i	0.340975	−	0.469312i
$370$	9.45605	−	0.834191i	0.491597	−	0.0433675i
$371$	−4.11809	−	12.6742i	−0.213801	−	0.658010i
$372$	−1.25426	+	9.01916i	−0.0650301	+	0.467622i
$373$			14.5626i			0.754024i	0.926208	+	0.377012i	$0.123048\pi$
$373$			14.5626i			0.754024i	−0.926208	+	0.377012i	$0.876952\pi$
$374$	−20.6899	+	9.51806i	−1.06985	+	0.492167i
$375$			0.966519i			0.0499108i
$376$	8.75043	+	32.3758i	0.451269	+	1.66966i
$377$	−9.28985	−	28.5912i	−0.478452	−	1.47252i
$378$	−1.61408	−	18.2965i	−0.0830191	−	0.941071i
$379$	−5.26442	+	7.24585i	−0.270415	+	0.372194i	−0.922530	−	0.385926i	$-0.873882\pi$
$379$	−5.26442	+	7.24585i	−0.270415	+	0.372194i	0.652115	+	0.758120i	$0.273882\pi$
$380$	5.48342	−	0.975057i	0.281293	−	0.0500194i
$381$	−10.4583	−	3.39812i	−0.535796	−	0.174091i
$382$	−13.0166	−	14.9520i	−0.665987	−	0.765012i
$383$	16.6378	+	22.9000i	0.850153	+	1.17014i	0.983829	+	0.179111i	$0.0573220\pi$
$383$	16.6378	+	22.9000i	0.850153	+	1.17014i	−0.133676	+	0.991025i	$0.542678\pi$
$384$	10.3571	+	3.50766i	0.528532	+	0.178999i
$385$	6.96449	−	5.37551i	0.354943	−	0.273961i
$386$	−10.5795	+	4.49976i	−0.538482	+	0.229032i
$387$	−9.38003	+	6.81499i	−0.476814	+	0.346426i
$388$	5.67782	+	2.75910i	0.288248	+	0.140072i
$389$	1.23493	−	3.80071i	0.0626132	−	0.192704i	−0.914857	−	0.403779i	$-0.867697\pi$
$389$	1.23493	−	3.80071i	0.0626132	−	0.192704i	0.977470	+	0.211075i	$0.0676965\pi$
$390$	1.66266	−	7.22561i	0.0841920	−	0.365883i
$391$	−26.4712	−	19.2325i	−1.33871	−	0.972628i
$392$	−0.0645730	+	0.0800959i	−0.00326143	+	0.00404545i
$393$	12.6265	−	4.10258i	0.636920	−	0.206948i
$394$	−0.834015	+	1.39031i	−0.0420171	+	0.0700429i
$395$	−11.4359			−0.575404
$396$	−12.4936	−	5.62916i	−0.627829	−	0.282876i
$397$	32.8863			1.65052			0.825258	−	0.564756i	$-0.191030\pi$
$397$	32.8863			1.65052			0.825258	+	0.564756i	$0.191030\pi$
$398$	11.2152	−	18.6959i	0.562167	−	0.937139i
$399$	−6.79004	+	2.20622i	−0.339927	+	0.110449i
$400$	−3.84822	−	1.09142i	−0.192411	−	0.0545709i
$401$	−7.71754	−	5.60712i	−0.385396	−	0.280006i	0.378170	−	0.925736i	$-0.376553\pi$
$401$	−7.71754	−	5.60712i	−0.385396	−	0.280006i	−0.763566	+	0.645730i	$0.776553\pi$
$402$	−0.611563	+	2.65774i	−0.0305020	+	0.132556i
$403$	−7.89624	+	24.3021i	−0.393340	+	1.21057i
$404$	−1.67614	+	3.44926i	−0.0833912	+	0.171607i
$405$	1.18538	−	0.861233i	0.0589023	−	0.0427950i
$406$	19.1318	−	8.13730i	0.949495	−	0.403848i
$407$	−6.26230	+	21.3636i	−0.310411	+	1.05896i
$408$	−12.4022	−	4.72992i	−0.614003	−	0.234166i
$409$	−10.1638	−	13.9892i	−0.502565	−	0.691722i	0.480078	−	0.877226i	$-0.340608\pi$
$409$	−10.1638	−	13.9892i	−0.502565	−	0.691722i	−0.982644	+	0.185504i	$0.940608\pi$
$410$	5.00886	+	5.75363i	0.247370	+	0.284151i
$411$	5.17636	+	1.68190i	0.255331	+	0.0829621i
$412$	−1.63810	−	9.21215i	−0.0807033	−	0.453850i
$413$	−6.42466	+	8.84279i	−0.316137	+	0.435125i
$414$	−1.73009	−	19.6116i	−0.0850292	−	0.963856i
$415$	−2.86997	−	8.83286i	−0.140881	−	0.433588i
$416$	26.8914	+	14.7793i	1.31846	+	0.724613i
$417$		−	9.05981i		−	0.443661i
$418$	−2.55844	+	12.8085i	−0.125138	+	0.626482i
$419$			3.65753i			0.178682i	0.996001	+	0.0893409i	$0.0284761\pi$
$419$			3.65753i			0.178682i	−0.996001	+	0.0893409i	$0.971524\pi$
$420$	5.07874	+	0.706278i	0.247817	+	0.0344628i
$421$	−10.9062	−	33.5659i	−0.531537	−	1.63590i	−0.751015	−	0.660285i	$-0.770435\pi$
$421$	−10.9062	−	33.5659i	−0.531537	−	1.63590i	0.219478	−	0.975617i	$-0.429565\pi$
$422$	−10.3734	+	0.915116i	−0.504969	+	0.0445472i
$423$	14.3980	−	19.8171i	0.700053	−	0.963541i
$424$	−7.76499	−	11.9004i	−0.377101	−	0.577935i
$425$	4.61784	+	1.50043i	0.223998	+	0.0727814i
$426$	13.7230	−	11.9467i	0.664882	−	0.578818i
$427$	12.4656	+	17.1575i	0.603254	+	0.830308i
$428$	−0.482023	+	0.500597i	−0.0232995	+	0.0241973i
$429$	14.3581	+	9.80820i	0.693217	+	0.473544i
$430$	−3.10658	−	7.30395i	−0.149813	−	0.352228i
$431$	−19.8732	+	14.4387i	−0.957256	+	0.695488i	−0.952512	−	0.304501i	$-0.901510\pi$
$431$	−19.8732	+	14.4387i	−0.957256	+	0.695488i	−0.00474449	+	0.999989i	$0.501510\pi$
$432$	−6.75167	−	18.3844i	−0.324840	−	0.884518i
$433$	−5.27457	+	16.2335i	−0.253480	+	0.780130i	0.740646	+	0.671896i	$0.234520\pi$
$433$	−5.27457	+	16.2335i	−0.253480	+	0.780130i	−0.994125	+	0.108234i	$0.965480\pi$
$434$	−17.2215	−	3.96277i	−0.826658	−	0.190219i
$435$	−4.33353	−	3.14849i	−0.207777	−	0.150959i
$436$	5.87786	−	3.13623i	0.281498	−	0.150198i
$437$	−17.8473	+	5.79893i	−0.853750	+	0.277400i
$438$	12.3804	+	7.42672i	0.591560	+	0.354863i
$439$	13.6245			0.650261			0.325130	−	0.945669i	$-0.394592\pi$
$439$	13.6245			0.650261			0.325130	+	0.945669i	$0.394592\pi$
$440$	5.67335	−	7.47082i	0.270466	−	0.356157i
$441$	0.0751446			0.00357831
$442$	−31.9414	−	19.1609i	−1.51930	−	0.911391i
$443$	−32.3766	+	10.5198i	−1.53826	+	0.499811i	−0.950895	−	0.309513i	$-0.899834\pi$
$443$	−32.3766	+	10.5198i	−1.53826	+	0.499811i	−0.587363	+	0.809323i	$0.699834\pi$
$444$	−11.4477	+	6.10813i	−0.543285	+	0.289879i
$445$	11.7811	+	8.55946i	0.558477	+	0.405757i
$446$	−22.3661	−	5.14658i	−1.05906	−	0.243697i
$447$	0.513812	−	1.58135i	0.0243025	−	0.0747953i
$448$	−8.54710	+	19.4236i	−0.403812	+	0.917677i
$449$	22.0313	−	16.0067i	1.03972	−	0.755403i	0.0694912	−	0.997583i	$-0.477862\pi$
$449$	22.0313	−	16.0067i	1.03972	−	0.755403i	0.970231	+	0.242180i	$0.0778624\pi$
$450$	1.14348	+	2.68846i	0.0539042	+	0.126735i
$451$	−16.8471	+	6.01972i	−0.793298	+	0.283458i
$452$	−2.09171	+	2.17232i	−0.0983860	+	0.102177i
$453$	−5.84663	−	8.04719i	−0.274698	−	0.378090i
$454$	−18.3640	+	15.9869i	−0.861865	+	0.750303i
$455$	13.6846	+	4.44641i	0.641546	+	0.208451i
$456$	−6.37550	+	4.16000i	−0.298560	+	0.194810i
$457$	2.29671	−	3.16115i	0.107436	−	0.147872i	−0.751914	−	0.659262i	$-0.770869\pi$
$457$	2.29671	−	3.16115i	0.107436	−	0.147872i	0.859349	+	0.511389i	$0.170869\pi$
$458$	−8.42116	+	0.742895i	−0.393495	+	0.0347132i
$459$	7.34644	+	22.6100i	0.342902	+	1.05534i
$460$	13.3492	+	1.85641i	0.622409	+	0.0865557i
$461$		−	14.1170i		−	0.657493i	−0.944418	−	0.328746i	$-0.893374\pi$
$461$		−	14.1170i		−	0.657493i	0.944418	−	0.328746i	$-0.106626\pi$
$462$	−5.88424	+	10.4873i	−0.273760	+	0.487914i
$463$		−	27.2847i		−	1.26803i	−0.773321	−	0.634014i	$-0.781406\pi$
$463$		−	27.2847i		−	1.26803i	0.773321	−	0.634014i	$-0.218594\pi$
$464$	17.4293	−	13.6987i	0.809137	−	0.635946i
$465$	1.40695	+	4.33014i	0.0652456	+	0.200805i
$466$	2.68568	+	30.4438i	0.124412	+	1.41028i
$467$	10.4982	−	14.4496i	0.485800	−	0.668647i	−0.493806	−	0.869572i	$-0.664395\pi$
$467$	10.4982	−	14.4496i	0.485800	−	0.668647i	0.979607	+	0.200925i	$0.0643948\pi$
$468$	−3.92372	−	22.0658i	−0.181374	−	1.01999i
$469$	−5.03352	−	1.63549i	−0.232426	−	0.0755199i
$470$	11.0104	+	12.6476i	0.507874	+	0.583389i
$471$	−6.74002	−	9.27685i	−0.310564	−	0.427454i
$472$	−4.15305	+	10.8897i	−0.191160	+	0.501237i
$473$	18.6064	−	0.540067i	0.855525	−	0.0248323i
$474$	14.3843	−	6.11807i	0.660694	−	0.281012i
$475$	2.25288	−	1.63682i	0.103369	−	0.0751022i
$476$	11.2587	−	23.1688i	0.516041	−	1.06194i
$477$	−3.20714	+	9.87056i	−0.146845	+	0.451942i
$478$	3.86913	−	16.8145i	0.176970	−	0.769078i
$479$	7.41160	+	5.38484i	0.338645	+	0.246040i	0.744090	−	0.668080i	$-0.232883\pi$
$479$	7.41160	+	5.38484i	0.338645	+	0.246040i	−0.405445	+	0.914119i	$0.632883\pi$
$480$	5.42426	−	0.685941i	0.247582	−	0.0313088i
$481$	−34.6288	+	11.2516i	−1.57894	+	0.513028i
$482$	3.11048	−	5.18520i	0.141678	−	0.236179i
$483$	−17.2770			−0.786132
$484$	11.4649	+	18.7765i	0.521130	+	0.853477i
$485$	3.15636			0.143323
$486$	−11.7162	+	19.5311i	−0.531459	+	0.885948i
$487$	16.1027	−	5.23208i	0.729683	−	0.237088i	0.0794667	−	0.996838i	$-0.474678\pi$
$487$	16.1027	−	5.23208i	0.729683	−	0.237088i	0.650216	+	0.759749i	$0.274678\pi$
$488$	17.6048	+	14.1929i	0.796930	+	0.642483i
$489$	−8.38245	−	6.09021i	−0.379068	−	0.275409i
$490$	−0.0115356	+	0.0501317i	−0.000521126	+	0.00226472i
$491$	−9.47795	+	29.1701i	−0.427734	+	1.31643i	0.472618	+	0.881268i	$0.343309\pi$
$491$	−9.47795	+	29.1701i	−0.427734	+	1.31643i	−0.900352	+	0.435163i	$0.856691\pi$
$492$	−9.37836	−	4.55735i	−0.422809	−	0.205461i
$493$	−21.7703	+	15.8170i	−0.980483	+	0.712363i
$494$	−19.6581	+	8.36115i	−0.884459	+	0.376186i
$495$	−6.84873	+	0.198790i	−0.307828	+	0.00893494i
$496$	−18.8293	+	0.712095i	−0.845461	+	0.0319740i
$497$	20.7544	+	28.5660i	0.930963	+	1.28136i
$498$	8.33536	+	9.57474i	0.373517	+	0.429054i
$499$	−31.5527	−	10.2521i	−1.41249	−	0.458947i	−0.499284	−	0.866438i	$-0.666404\pi$
$499$	−31.5527	−	10.2521i	−1.41249	−	0.458947i	−0.913209	+	0.407491i	$0.866404\pi$
$500$	−1.96911	+	0.350146i	−0.0880613	+	0.0156590i
$501$	−9.00613	+	12.3959i	−0.402364	+	0.553807i
$502$	1.48531	+	16.8369i	0.0662928	+	0.751469i
$503$	0.950044	+	2.92393i	0.0423604	+	0.130372i	0.970000	−	0.243104i	$-0.0781658\pi$
$503$	0.950044	+	2.92393i	0.0423604	+	0.130372i	−0.927640	+	0.373476i	$0.878166\pi$
$504$	14.9626	−	4.04404i	0.666486	−	0.180136i
$505$			1.91747i			0.0853265i
$506$	−15.4664	+	27.5654i	−0.687565	+	1.22543i
$507$			15.8744i			0.705005i
$508$	3.13426	−	22.5380i	0.139060	−	0.999963i
$509$	10.9332	+	33.6488i	0.484604	+	1.49146i	0.832554	+	0.553943i	$0.186878\pi$
$509$	10.9332	+	33.6488i	0.484604	+	1.49146i	−0.347951	+	0.937513i	$0.613122\pi$
$510$	−6.61111	+	0.583217i	−0.292745	+	0.0258253i
$511$	−16.4683	+	22.6667i	−0.728515	+	1.00271i
$512$	−3.39412	+	22.3714i	−0.150000	+	0.988686i
$513$	12.9673	+	4.21333i	0.572520	+	0.186023i
$514$	18.9313	−	16.4808i	0.835026	−	0.726938i
$515$	−2.74985	−	3.78485i	−0.121173	−	0.166780i
$516$	7.81503	+	7.52506i	0.344038	+	0.331273i
$517$	−37.0331	+	13.2325i	−1.62871	+	0.581965i
$518$	−9.85565	−	23.1718i	−0.433032	−	1.01811i
$519$	−1.55128	+	1.12707i	−0.0680937	+	0.0494730i
$520$	15.3232	+	0.769712i	0.671968	+	0.0337541i
$521$	13.1608	−	40.5047i	0.576584	−	1.77454i	−0.0541373	−	0.998534i	$-0.517241\pi$
$521$	13.1608	−	40.5047i	0.576584	−	1.77454i	0.630721	−	0.776009i	$-0.282759\pi$
$522$	−15.7791	−	3.63087i	−0.690632	−	0.158919i
$523$	6.11055	+	4.43957i	0.267196	+	0.194129i	0.713313	−	0.700845i	$-0.247194\pi$
$523$	6.11055	+	4.43957i	0.267196	+	0.194129i	−0.446118	+	0.894974i	$0.647194\pi$
$524$	12.9325	+	24.2379i	0.564960	+	1.05884i
$525$	2.43832	−	0.792259i	0.106417	−	0.0345770i
$526$	25.3977	+	15.2355i	1.10739	+	0.664300i
$527$	22.8727			0.996350
$528$	−3.13925	+	12.4321i	−0.136618	+	0.541038i
$529$	−22.4118			−0.974424
$530$	−6.09268	−	3.65485i	−0.264649	−	0.158757i
$531$	8.09581	−	2.63049i	0.351328	−	0.114153i
$532$	−6.95464	−	13.0342i	−0.301522	−	0.565106i
$533$	−23.6718	−	17.1985i	−1.02534	−	0.744952i
$534$	−19.3977	−	4.46353i	−0.839419	−	0.193156i
$535$	−0.107374	+	0.330465i	−0.00464220	+	0.0142872i
$536$	−5.63623	−	0.283117i	−0.243448	−	0.0122288i
$537$	8.63640	−	6.27471i	0.372688	−	0.270774i
$538$	6.13040	+	14.4133i	0.264300	+	0.621402i
$539$	−0.0996175	−	0.0680498i	−0.00429083	−	0.00293111i
$540$	−7.05395	−	6.79222i	−0.303553	−	0.292291i
$541$	−25.2002	−	34.6852i	−1.08344	−	1.49123i	−0.855674	−	0.517516i	$-0.826857\pi$
$541$	−25.2002	−	34.6852i	−1.08344	−	1.49123i	−0.227769	−	0.973715i	$-0.573143\pi$
$542$	−7.32454	+	6.37643i	−0.314616	+	0.273891i
$543$	14.5214	+	4.71829i	0.623174	+	0.202481i
$544$	5.14334	−	26.9809i	0.220519	−	1.15680i
$545$	1.95798	−	2.69492i	0.0838705	−	0.115438i
$546$	−19.5916	+	1.72832i	−0.838442	+	0.0739654i
$547$	−9.08694	−	27.9667i	−0.388530	−	1.19577i	−0.933887	−	0.357568i	$-0.883606\pi$
$547$	−9.08694	−	27.9667i	−0.388530	−	1.19577i	0.545358	−	0.838203i	$-0.316394\pi$
$548$	−1.55131	+	11.1552i	−0.0662686	+	0.476528i
$549$		−	16.5165i		−	0.704907i
$550$	0.918745	−	4.59956i	0.0391754	−	0.196126i
$551$			15.4332i			0.657474i
$552$	−17.7840	+	4.80661i	−0.756938	+	0.204583i
$553$	9.37407	+	28.8504i	0.398626	+	1.22684i
$554$	−3.07961	−	34.9093i	−0.130840	−	1.48315i
$555$	−3.81336	+	5.24864i	−0.161868	+	0.222792i
$556$	18.4578	−	3.28214i	0.782783	−	0.139194i
$557$	−26.1937	−	8.51085i	−1.10986	−	0.360616i	−0.303973	−	0.952681i	$-0.598313\pi$
$557$	−26.1937	−	8.51085i	−1.10986	−	0.360616i	−0.805891	+	0.592064i	$0.798313\pi$
$558$	9.03651	+	10.3801i	0.382546	+	0.439426i
$559$	17.8946	+	24.6298i	0.756860	+	1.04173i
$560$	0.400985	+	10.6029i	0.0169447	+	0.448054i
$561$	4.37823	−	14.9362i	0.184849	−	0.630606i
$562$	31.9874	−	13.6051i	1.34931	−	0.573899i
$563$	17.0684	−	12.4009i	0.719345	−	0.522635i	−0.166830	−	0.985986i	$-0.553353\pi$
$563$	17.0684	−	12.4009i	0.719345	−	0.522635i	0.886175	+	0.463351i	$0.153353\pi$
$564$	−20.6154	−	10.0179i	−0.868066	−	0.421831i
$565$	−0.465946	+	1.43403i	−0.0196025	+	0.0603302i
$566$	3.34767	−	14.5484i	0.140713	−	0.611513i
$567$	−3.14437	−	2.28452i	−0.132051	−	0.0959408i
$568$	29.3107	+	23.6302i	1.22985	+	0.991502i
$569$	18.1317	−	5.89136i	0.760122	−	0.246979i	0.0967909	−	0.995305i	$-0.469142\pi$
$569$	18.1317	−	5.89136i	0.760122	−	0.246979i	0.663331	+	0.748326i	$0.269142\pi$
$570$	−1.95804	+	3.26408i	−0.0820135	+	0.136717i
$571$	39.2808			1.64385			0.821924	−	0.569597i	$-0.192901\pi$
$571$	39.2808			1.64385			0.821924	+	0.569597i	$0.192901\pi$
$572$	−14.7809	+	32.8054i	−0.618019	+	1.37166i
$573$	13.5484			0.565994
$574$	10.4094	−	17.3526i	0.434480	−	0.724282i
$575$	6.40900	−	2.08241i	0.267274	−	0.0868426i
$576$	14.2766	−	8.32541i	0.594857	−	0.346892i
$577$	−3.36110	−	2.44198i	−0.139924	−	0.101661i	0.515621	−	0.856817i	$-0.327561\pi$
$577$	−3.36110	−	2.44198i	−0.139924	−	0.101661i	−0.655545	+	0.755156i	$0.727561\pi$
$578$	−2.08536	+	9.06261i	−0.0867397	+	0.376955i
$579$	2.42801	−	7.47264i	0.100905	−	0.310552i
$580$	4.84457	−	9.96942i	0.201160	−	0.413957i
$581$	−19.9309	+	14.4806i	−0.826873	+	0.600759i
$582$	−3.97012	+	1.68861i	−0.164567	+	0.0699951i
$583$	13.1903	−	10.1808i	0.546285	−	0.421647i
$584$	−10.6455	+	27.9134i	−0.440514	+	1.15507i
$585$	−6.58670	−	9.06582i	−0.272327	−	0.374826i
$586$	−7.73798	−	8.88853i	−0.319653	−	0.367182i
$587$	17.4871	+	5.68191i	0.721770	+	0.234517i	0.646790	−	0.762668i	$-0.276111\pi$
$587$	17.4871	+	5.68191i	0.721770	+	0.234517i	0.0749797	+	0.997185i	$0.476111\pi$
$588$	−0.0123101	−	0.0692280i	−0.000507659	−	0.00285491i
$589$	7.71054	−	10.6126i	0.317707	−	0.437286i
$590$	0.512088	+	5.80482i	0.0210823	+	0.238981i
$591$	−0.342402	−	1.05380i	−0.0140845	−	0.0433477i
$592$	−16.5914	−	21.1099i	−0.681904	−	0.867611i
$593$			31.9880i			1.31359i	0.754069	+	0.656795i	$0.228088\pi$
$593$			31.9880i			1.31359i	−0.754069	+	0.656795i	$0.771912\pi$
$594$	20.8635	−	9.59794i	0.856042	−	0.393808i
$595$		−	12.8797i		−	0.528017i
$596$	3.40786	+	0.473916i	0.139591	+	0.0194124i
$597$	4.60436	+	14.1708i	0.188444	+	0.579970i
$598$	−51.4954	+	4.54281i	−2.10580	+	0.185769i
$599$	22.1391	−	30.4718i	0.904579	−	1.24505i	−0.0644055	−	0.997924i	$-0.520515\pi$
$599$	22.1391	−	30.4718i	0.904579	−	1.24505i	0.968984	−	0.247122i	$-0.0794849\pi$
$600$	2.28946	−	1.49387i	0.0934669	−	0.0609869i
$601$	38.2253	+	12.4201i	1.55924	+	0.506628i	0.956605	−	0.291388i	$-0.0941172\pi$
$601$	38.2253	+	12.4201i	1.55924	+	0.506628i	0.602636	+	0.798016i	$0.294117\pi$
$602$	−15.8798	+	13.8243i	−0.647214	+	0.563437i
$603$	2.42274	+	3.33461i	0.0986615	+	0.135796i
$604$	14.2766	−	14.8268i	0.580908	−	0.603292i
$605$	9.25923	+	5.93858i	0.376441	+	0.241437i
$606$	−1.02582	−	2.41184i	−0.0416712	−	0.0979741i
$607$	5.87169	−	4.26603i	0.238324	−	0.173153i	−0.462212	−	0.886769i	$-0.652944\pi$
$607$	5.87169	−	4.26603i	0.238324	−	0.173153i	0.700536	+	0.713617i	$0.252944\pi$
$608$	−10.7849	−	11.4819i	−0.437387	−	0.465652i
$609$	−4.39077	+	13.5134i	−0.177923	+	0.547591i
$610$	11.0188	+	2.53548i	0.446136	+	0.102659i
$611$	−52.0351	−	37.8057i	−2.10511	−	1.52945i
$612$	−17.6994	+	9.44383i	−0.715457	+	0.381744i
$613$	18.0790	−	5.87421i	0.730203	−	0.237257i	0.0797617	−	0.996814i	$-0.474584\pi$
$613$	18.0790	−	5.87421i	0.730203	−	0.237257i	0.650441	+	0.759557i	$0.274584\pi$
$614$	6.21073	+	3.72567i	0.250645	+	0.150356i
$615$	−5.21352			−0.210229
$616$	−23.4978	−	8.18879i	−0.946752	−	0.329936i
$617$	−44.9665			−1.81028			−0.905142	−	0.425110i	$-0.860235\pi$
$617$	−44.9665			−1.81028			−0.905142	+	0.425110i	$0.860235\pi$
$618$	5.48366	+	3.28952i	0.220585	+	0.132324i
$619$	6.01378	−	1.95400i	0.241714	−	0.0785378i	−0.185655	−	0.982615i	$-0.559441\pi$
$619$	6.01378	−	1.95400i	0.241714	−	0.0785378i	0.427369	+	0.904077i	$0.359441\pi$
$620$	−8.31219	+	4.43511i	−0.333825	+	0.178118i
$621$	26.6934	+	19.3939i	1.07117	+	0.778250i
$622$	13.8176	+	3.17953i	0.554037	+	0.127487i
$623$	11.9367	−	36.7374i	0.478234	−	1.47185i
$624$	−19.6856	+	7.22957i	−0.788057	+	0.289414i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−8.68602	−	20.4219i	−0.347163	−	0.816223i
$627$	−5.45427	−	7.06653i	−0.217822	−	0.282210i
$628$	16.4582	−	17.0924i	0.656753	−	0.682060i
$629$	19.1571	+	26.3675i	0.763843	+	1.05134i
$630$	5.84511	−	5.08851i	0.232875	−	0.202731i
$631$	−20.7108	−	6.72934i	−0.824483	−	0.267891i	−0.133763	−	0.991013i	$-0.542706\pi$
$631$	−20.7108	−	6.72934i	−0.824483	−	0.267891i	−0.690720	+	0.723122i	$0.742706\pi$
$632$	17.6756	+	27.0891i	0.703096	+	1.07755i
$633$	4.18329	−	5.75781i	0.166271	−	0.228852i
$634$	−21.7565	+	1.91931i	−0.864062	+	0.0762255i
$635$	−3.51583	−	10.8206i	−0.139521	−	0.429403i
$636$	9.61878	+	1.33764i	0.381410	+	0.0530410i
$637$		−	0.197312i		−	0.00781779i
$638$	17.6299	+	19.1026i	0.697975	+	0.756281i
$639$		−	27.4988i		−	1.08784i
$640$	3.36256	+	10.8025i	0.132917	+	0.427005i
$641$	8.29228	+	25.5210i	0.327525	+	1.00802i	0.970288	+	0.241954i	$0.0777883\pi$
$641$	8.29228	+	25.5210i	0.327525	+	1.00802i	−0.642762	+	0.766066i	$0.722212\pi$
$642$	−0.0417365	−	0.473109i	−0.00164721	−	0.0186721i
$643$	−12.7023	+	17.4833i	−0.500931	+	0.689473i	−0.982357	−	0.187014i	$-0.940119\pi$
$643$	−12.7023	+	17.4833i	−0.500931	+	0.689473i	0.481426	+	0.876487i	$0.340119\pi$
$644$	−6.25904	−	35.1989i	−0.246641	−	1.38703i
$645$	5.15902	+	1.67627i	0.203136	+	0.0660029i
$646$	12.5555	+	14.4223i	0.493988	+	0.567438i
$647$	−4.35021	−	5.98754i	−0.171024	−	0.235395i	0.714898	−	0.699229i	$-0.246473\pi$
$647$	−4.35021	−	5.98754i	−0.171024	−	0.235395i	−0.885922	+	0.463834i	$0.846473\pi$
$648$	−3.87221	−	1.47677i	−0.152115	−	0.0580129i
$649$	−13.1146	−	3.84426i	−0.514791	−	0.150900i
$650$	7.05928	−	3.00252i	0.276888	−	0.117768i
$651$	9.77075	−	7.09886i	0.382946	−	0.278226i
$652$	9.37096	−	19.2841i	0.366995	−	0.755223i
$653$	8.45502	−	26.0219i	0.330870	−	1.01831i	−0.637850	−	0.770160i	$-0.720176\pi$
$653$	8.45502	−	26.0219i	0.330870	−	1.01831i	0.968721	−	0.248154i	$-0.0798238\pi$
$654$	−1.02103	+	4.43722i	−0.0399255	+	0.173509i
$655$	11.1128	+	8.07390i	0.434212	+	0.315473i
$656$	5.88723	−	20.7577i	0.229858	−	0.810454i
$657$	20.7519	−	6.74272i	0.809610	−	0.263058i
$658$	22.8819	−	38.1443i	0.892028	−	1.48702i
$659$	24.7789			0.965248			0.482624	−	0.875828i	$-0.339684\pi$
$659$	24.7789			0.965248			0.482624	+	0.875828i	$0.339684\pi$
$660$	1.30509	+	6.27692i	0.0508004	+	0.244329i
$661$	38.5830			1.50070			0.750352	−	0.661039i	$-0.229884\pi$
$661$	38.5830			1.50070			0.750352	+	0.661039i	$0.229884\pi$
$662$	10.8736	−	18.1264i	0.422615	−	0.704504i
$663$	24.2104	−	7.86644i	0.940254	−	0.305507i
$664$	−16.4871	+	20.4505i	−0.639825	+	0.793634i
$665$	−5.97604	−	4.34184i	−0.231741	−	0.168369i
$666$	−4.39759	+	19.1111i	−0.170403	+	0.740541i
$667$	−11.5409	+	35.5193i	−0.446866	+	1.37531i
$668$	−28.5171	−	13.8577i	−1.10336	−	0.536169i
$669$	12.6896	−	9.21951i	0.490607	−	0.356447i
$670$	−2.59656	+	1.10439i	−0.100314	+	0.0426664i
$671$	−14.9571	+	21.8955i	−0.577412	+	0.845268i
$672$	−6.17677	−	13.1220i	−0.238274	−	0.506192i
$673$	−4.23354	−	5.82697i	−0.163191	−	0.224613i	0.719589	−	0.694401i	$-0.244330\pi$
$673$	−4.23354	−	5.82697i	−0.163191	−	0.224613i	−0.882779	+	0.469788i	$0.844330\pi$
$674$	−13.0265	−	14.9634i	−0.501762	−	0.576369i
$675$	−4.65659	−	1.51302i	−0.179232	−	0.0582361i
$676$	−32.3412	+	5.75089i	−1.24389	+	0.221188i
$677$	10.1679	−	13.9949i	0.390785	−	0.537869i	−0.567616	−	0.823293i	$-0.692134\pi$
$677$	10.1679	−	13.9949i	0.390785	−	0.537869i	0.958401	+	0.285424i	$0.0921343\pi$
$678$	−0.181113	−	2.05303i	−0.00695562	−	0.0788461i
$679$	−2.58728	−	7.96282i	−0.0992905	−	0.305585i
$680$	−3.58324	−	13.2577i	−0.137411	−	0.508409i
$681$		−	16.6401i		−	0.637650i
$682$	−2.57940	−	21.9440i	−0.0987704	−	0.840281i
$683$		−	5.72289i		−	0.218980i	−0.993988	−	0.109490i	$-0.965078\pi$
$683$		−	5.72289i		−	0.218980i	0.993988	−	0.109490i	$-0.0349218\pi$
$684$	−1.58478	+	11.3959i	−0.0605955	+	0.435733i
$685$	1.74016	+	5.35567i	0.0664882	+	0.204630i
$686$	−26.0220	+	2.29561i	−0.993526	+	0.0876466i
$687$	3.39601	−	4.67421i	0.129566	−	0.178332i
$688$	−12.4998	+	18.6479i	−0.476550	+	0.710944i
$689$	25.9178	+	8.42120i	0.987389	+	0.320822i
$690$	−6.94730	+	6.04803i	−0.264479	+	0.230245i
$691$	11.7754	+	16.2075i	0.447958	+	0.616562i	0.971957	−	0.235157i	$-0.0755605\pi$
$691$	11.7754	+	16.2075i	0.447958	+	0.616562i	−0.523999	+	0.851719i	$0.675560\pi$
$692$	−2.85820	−	2.75215i	−0.108652	−	0.104621i
$693$	6.11544	+	17.1150i	0.232306	+	0.650143i
$694$	−6.77704	−	15.9336i	−0.257253	−	0.604833i
$695$	7.58344	−	5.50969i	0.287656	−	0.208995i
$696$	−0.760081	+	15.1315i	−0.0288108	+	0.573558i
$697$	−8.09347	+	24.9091i	−0.306562	+	0.943501i
$698$	28.2674	+	6.50451i	1.06994	+	0.246199i
$699$	−16.8980	−	12.2771i	−0.639142	−	0.464364i
$700$	2.49743	+	4.68063i	0.0943940	+	0.176911i
$701$	−30.1048	+	9.78165i	−1.13704	+	0.369448i	−0.816249	−	0.577701i	$-0.803950\pi$
$701$	−30.1048	+	9.78165i	−1.13704	+	0.369448i	−0.320795	+	0.947149i	$0.603950\pi$
$702$	32.2095	+	19.3217i	1.21567	+	0.729251i
$703$	18.6922			0.704988
$704$	−26.4655	−	1.89182i	−0.997455	−	0.0713008i
$705$	−11.4603			−0.431620
$706$	28.9659	+	17.3760i	1.09015	+	0.653954i
$707$	4.83738	−	1.57176i	0.181928	−	0.0591121i
$708$	−3.74961	−	7.02745i	−0.140919	−	0.264108i
$709$	1.22468	+	0.889781i	0.0459938	+	0.0334164i	0.610545	−	0.791982i	$-0.290951\pi$
$709$	1.22468	+	0.889781i	0.0459938	+	0.0334164i	−0.564551	+	0.825398i	$0.690951\pi$
$710$	18.3455	+	4.22141i	0.688493	+	0.158427i
$711$	7.30046	−	22.4685i	0.273789	−	0.842635i
$712$	2.06635	−	41.1363i	0.0774396	−	1.54165i
$713$	25.6819	−	18.6590i	0.961794	−	0.698784i
$714$	6.89049	+	16.2004i	0.257870	+	0.606284i
$715$	0.521975	+	17.9832i	0.0195208	+	0.672532i
$716$	15.9124	+	15.3220i	0.594673	+	0.572609i
$717$	6.93110	+	9.53984i	0.258847	+	0.356272i
$718$	−13.4862	+	11.7405i	−0.503299	+	0.438151i
$719$	26.5476	+	8.62583i	0.990058	+	0.321689i	0.758886	−	0.651224i	$-0.225744\pi$
$719$	26.5476	+	8.62583i	0.990058	+	0.321689i	0.231172	+	0.972913i	$0.425744\pi$
$720$	4.60097	−	6.86398i	0.171468	−	0.255805i
$721$	−7.29431	+	10.0398i	−0.271654	+	0.373900i
$722$	−15.8418	+	1.39753i	−0.589571	+	0.0520106i
$723$	1.27699	+	3.93018i	0.0474919	+	0.146165i
$724$	−4.35194	+	31.2941i	−0.161738	+	1.16304i
$725$		−	5.54209i		−	0.205828i
$726$	−14.8235	−	2.51609i	−0.550151	−	0.0933808i
$727$		−	24.0348i		−	0.891400i	−0.895182	−	0.445700i	$-0.852955\pi$
$727$		−	24.0348i		−	0.891400i	0.895182	−	0.445700i	$-0.147045\pi$
$728$	−10.6187	−	39.2882i	−0.393555	−	1.45612i
$729$	−3.45172	−	10.6233i	−0.127842	−	0.393456i
$730$	1.31263	+	14.8795i	0.0485827	+	0.550714i
$731$	16.0177	−	22.0465i	0.592437	−	0.815420i
$732$	−15.2160	+	2.70571i	−0.562401	+	0.100006i
$733$	26.1669	+	8.50215i	0.966498	+	0.314034i	0.749401	−	0.662116i	$-0.230341\pi$
$733$	26.1669	+	8.50215i	0.966498	+	0.314034i	0.217096	+	0.976150i	$0.430341\pi$
$734$	−2.81419	−	3.23263i	−0.103874	−	0.119319i
$735$	−0.0206648	−	0.0284426i	−0.000762231	−	0.00104912i
$736$	−16.2353	−	34.4904i	−0.598441	−	1.27133i
$737$	−0.191994	−	6.61461i	−0.00707220	−	0.243652i
$738$	−14.5019	+	6.16807i	−0.533822	+	0.227050i
$739$	−31.7775	+	23.0877i	−1.16895	+	0.849295i	−0.990883	−	0.134723i	$-0.956986\pi$
$739$	−31.7775	+	23.0877i	−1.16895	+	0.849295i	−0.178071	+	0.984018i	$0.556986\pi$
$740$	−12.0746	−	5.86759i	−0.443873	−	0.215697i
$741$	4.51156	−	13.8852i	0.165736	−	0.510084i
$742$	−4.22623	+	18.3664i	−0.155150	+	0.674253i
$743$	17.8946	+	13.0012i	0.656491	+	0.476968i	0.865476	−	0.500950i	$-0.167016\pi$
$743$	17.8946	+	13.0012i	0.656491	+	0.476968i	−0.208985	+	0.977919i	$0.567016\pi$
$744$	8.08250	−	10.0255i	0.296319	−	0.367552i
$745$	1.63613	−	0.531610i	0.0599431	−	0.0194767i
$746$	10.5943	−	17.6607i	0.387883	−	0.646605i
$747$	19.1863			0.701991
$748$	32.0159	+	3.50886i	1.17062	+	0.128297i
$749$	0.921707			0.0336785
$750$	0.703140	−	1.17214i	0.0256750	−	0.0428005i
$751$	−11.1682	+	3.62877i	−0.407534	+	0.132416i	−0.505608	−	0.862763i	$-0.668732\pi$
$751$	−11.1682	+	3.62877i	−0.407534	+	0.132416i	0.0980741	+	0.995179i	$0.468732\pi$
$752$	12.9413	−	45.6295i	0.471920	−	1.66394i
$753$	−9.34543	−	6.78985i	−0.340566	−	0.247436i
$754$	−9.53380	+	41.4322i	−0.347201	+	1.50887i
$755$	3.18023	−	9.78774i	0.115740	−	0.356212i
$756$	−11.3532	+	23.3632i	−0.412911	+	0.849712i
$757$	33.2187	−	24.1348i	1.20735	−	0.877194i	0.212366	−	0.977190i	$-0.431883\pi$
$757$	33.2187	−	24.1348i	1.20735	−	0.877194i	0.994988	+	0.0999962i	$0.0318831\pi$
$758$	11.6557	−	4.95752i	0.423355	−	0.180065i
$759$	−7.26860	−	20.3423i	−0.263834	−	0.738377i
$760$	−7.35933	−	2.80667i	−0.266951	−	0.101809i
$761$	−21.0539	−	28.9782i	−0.763202	−	1.05046i	−0.996941	−	0.0781579i	$-0.975096\pi$
$761$	−21.0539	−	28.9782i	−0.763202	−	1.05046i	0.233739	−	0.972299i	$-0.424904\pi$
$762$	10.2112	+	11.7294i	0.369911	+	0.424913i
$763$	−8.40369	−	2.73052i	−0.304234	−	0.0988516i
$764$	4.90826	+	27.6025i	0.177575	+	0.998624i
$765$	−5.89587	+	8.11497i	−0.213166	+	0.293397i
$766$	−3.51775	−	39.8758i	−0.127102	−	1.44077i
$767$	−6.90704	−	21.2577i	−0.249399	−	0.767571i
$768$	−10.0087	−	11.7886i	−0.361157	−	0.425385i
$769$		−	27.3914i		−	0.987761i	−0.869530	−	0.493880i	$-0.835578\pi$
$769$		−	27.3914i		−	0.987761i	0.869530	−	0.493880i	$-0.164422\pi$
$770$	−12.3568	+	1.45247i	−0.445308	+	0.0523435i
$771$			17.1542i			0.617793i
$772$	16.1038	+	2.23948i	0.579587	+	0.0806007i
$773$	1.94520	+	5.98670i	0.0699638	+	0.215327i	0.979925	−	0.199367i	$-0.0638887\pi$
$773$	1.94520	+	5.98670i	0.0699638	+	0.215327i	−0.909961	+	0.414694i	$0.863889\pi$
$774$	16.3335	−	1.44090i	0.587094	−	0.0517921i
$775$	−2.76888	+	3.81103i	−0.0994610	+	0.136896i
$776$	−4.87852	−	7.47668i	−0.175128	−	0.268397i
$777$	16.3670	+	5.31797i	0.587164	+	0.190781i
$778$	−4.26265	+	3.71088i	−0.152823	+	0.133042i
$779$	8.82917	+	12.1523i	0.316338	+	0.435402i
$780$	−7.27299	+	7.55324i	−0.260415	+	0.270449i
$781$	−24.9025	+	36.4546i	−0.891082	+	1.30445i
$782$	18.1113	+	42.5818i	0.647658	+	1.52272i
$783$	21.9530	−	15.9498i	0.784535	−	0.569998i
$784$	0.136580	−	0.0501591i	0.00487786	−	0.00179140i
$785$	3.66619	−	11.2834i	0.130852	−	0.402720i
$786$	−18.2973	−	4.21032i	−0.652642	−	0.150177i
$787$	33.4661	+	24.3145i	1.19294	+	0.866719i	0.993572	−	0.113206i	$-0.0361121\pi$
$787$	33.4661	+	24.3145i	1.19294	+	0.866719i	0.199365	+	0.979925i	$0.436112\pi$
$788$	2.02289	−	1.07935i	0.0720626	−	0.0384502i
$789$	−19.2505	+	6.25488i	−0.685337	+	0.222680i
$790$	13.8689	+	8.31960i	0.493432	+	0.295998i
$791$	3.99970			0.142213
$792$	11.0564	+	15.9158i	0.392872	+	0.565544i
$793$	−43.3684			−1.54006
$794$	−39.8827	−	23.9247i	−1.41538	−	0.849055i
$795$	4.61802	−	1.50049i	0.163784	−	0.0532167i
$796$	−27.2023	+	14.5143i	−0.964162	+	0.514445i
$797$	−14.8957	−	10.8224i	−0.527634	−	0.383349i	0.291838	−	0.956468i	$-0.405733\pi$
$797$	−14.8957	−	10.8224i	−0.527634	−	0.383349i	−0.819472	+	0.573119i	$0.805733\pi$
$798$	9.83960	+	2.26415i	0.348318	+	0.0801502i
$799$	−17.7910	+	54.7551i	−0.629401	+	1.93710i
$800$	3.87291	+	4.12318i	0.136928	+	0.145776i
$801$	−24.3378	+	17.6825i	−0.859935	+	0.624780i
$802$	5.28024	+	12.4145i	0.186452	+	0.438371i
$803$	−33.6165	−	9.85398i	−1.18630	−	0.347739i
$804$	2.67517	−	2.77825i	0.0943459	−	0.0979814i
$805$	−10.5070	−	14.4616i	−0.370322	−	0.509704i
$806$	27.2558	−	23.7278i	0.960045	−	0.835775i
$807$	−10.1806	−	3.30788i	−0.358374	−	0.116443i
$808$	4.54205	−	2.96368i	0.159789	−	0.104262i
$809$	−18.6127	+	25.6181i	−0.654386	+	0.900685i	−0.999279	−	0.0379568i	$-0.987915\pi$
$809$	−18.6127	+	25.6181i	−0.654386	+	0.900685i	0.344893	+	0.938642i	$0.387915\pi$
$810$	−2.06411	+	0.182091i	−0.0725255	+	0.00639804i
$811$	−2.74635	−	8.45240i	−0.0964374	−	0.296804i	0.891188	−	0.453634i	$-0.149873\pi$
$811$	−2.74635	−	8.45240i	−0.0964374	−	0.296804i	−0.987626	+	0.156830i	$0.949873\pi$
$812$	−29.1218	−	4.04985i	−1.02198	−	0.142122i
$813$		−	6.63696i		−	0.232768i
$814$	23.1365	−	21.3528i	0.810935	−	0.748415i
$815$		−	10.7202i		−	0.375512i
$816$	11.5998	+	14.7588i	0.406073	+	0.516660i
$817$	−4.82963	−	14.8641i	−0.168967	−	0.520028i
$818$	2.14893	+	24.3594i	0.0751357	+	0.851708i
$819$	−17.4720	+	24.0481i	−0.610521	+	0.840310i
$820$	−1.88873	−	10.6216i	−0.0659572	−	0.370923i
$821$	−8.03960	−	2.61222i	−0.280584	−	0.0911673i	0.165344	−	0.986236i	$-0.447126\pi$
$821$	−8.03960	−	2.61222i	−0.280584	−	0.0911673i	−0.445928	+	0.895069i	$0.647126\pi$
$822$	−5.05403	−	5.80550i	−0.176279	−	0.202490i
$823$	−4.39558	−	6.05000i	−0.153220	−	0.210890i	0.725506	−	0.688216i	$-0.241606\pi$
$823$	−4.39558	−	6.05000i	−0.153220	−	0.210890i	−0.878726	+	0.477326i	$0.841606\pi$
$824$	−4.71522	+	12.3637i	−0.164262	+	0.430710i
$825$	1.95864	+	2.53761i	0.0681912	+	0.0883483i
$826$	14.2246	−	6.05012i	0.494936	−	0.210511i
$827$	−41.4448	+	30.1114i	−1.44118	+	1.04708i	−0.453383	+	0.891316i	$0.649783\pi$
$827$	−41.4448	+	30.1114i	−1.44118	+	1.04708i	−0.987795	+	0.155761i	$0.950217\pi$
$828$	−12.1692	+	25.0425i	−0.422909	+	0.870286i
$829$	−6.90572	+	21.2536i	−0.239846	+	0.738169i	0.756596	+	0.653883i	$0.226861\pi$
$829$	−6.90572	+	21.2536i	−0.239846	+	0.738169i	−0.996442	+	0.0842863i	$0.973139\pi$
$830$	−2.94534	+	12.7999i	−0.102234	+	0.444291i
$831$	19.3766	+	14.0779i	0.672166	+	0.488357i
$832$	−21.8606	−	37.4869i	−0.757879	−	1.29962i
$833$	−0.167973	+	0.0545778i	−0.00581992	+	0.00189101i
$834$	−6.59098	+	10.9872i	−0.228227	+	0.380457i
$835$	−15.8529			−0.548612
$836$	12.4208	−	13.6721i	0.429584	−	0.472860i
$837$	−23.0647			−0.797231
$838$	2.66084	−	4.43564i	0.0919171	−	0.153227i
$839$	−8.38967	+	2.72597i	−0.289643	+	0.0941109i	−0.450235	−	0.892910i	$-0.648660\pi$
$839$	−8.38967	+	2.72597i	−0.289643	+	0.0941109i	0.160592	+	0.987021i	$0.448660\pi$
$840$	−5.64539	−	4.55130i	−0.194785	−	0.157035i
$841$	1.38727	+	1.00791i	0.0478371	+	0.0347557i
$842$	−11.1926	+	48.6411i	−0.385723	+	1.67628i
$843$	−7.34114	+	22.5937i	−0.252842	+	0.778169i
$844$	13.2460	+	6.43680i	0.455946	+	0.221564i
$845$	−13.2875	+	9.65394i	−0.457104	+	0.332105i
$846$	−31.8779	+	13.5586i	−1.09599	+	0.466154i
$847$	7.39195	−	28.2269i	0.253990	−	0.969889i
$848$	0.759437	+	20.0811i	0.0260792	+	0.689589i
$849$	5.99697	+	8.25413i	0.205816	+	0.283281i
$850$	−4.50870	−	5.17909i	−0.154647	−	0.177641i
$851$	43.0198	+	13.9780i	1.47470	+	0.479159i
$852$	−25.3337	+	4.50481i	−0.867917	+	0.154332i
$853$	10.3300	−	14.2181i	0.353694	−	0.486818i	−0.594684	−	0.803959i	$-0.702723\pi$
$853$	10.3300	−	14.2181i	0.353694	−	0.486818i	0.948378	+	0.317141i	$0.102723\pi$
$854$	−2.63562	−	29.8763i	−0.0901891	−	1.02235i
$855$	1.77771	+	5.47122i	0.0607963	+	0.187112i
$856$	0.948754	−	0.256426i	0.0324277	−	0.00876447i
$857$			26.3527i			0.900191i	0.892980	+	0.450096i	$0.148610\pi$
$857$			26.3527i			0.900191i	−0.892980	+	0.450096i	$0.851390\pi$
$858$	−10.2773	−	22.3403i	−0.350862	−	0.762686i
$859$			27.3129i			0.931905i	0.884810	+	0.465952i	$0.154288\pi$
$859$			27.3129i			0.931905i	−0.884810	+	0.465952i	$0.845712\pi$
$860$	−1.54611	+	11.1178i	−0.0527219	+	0.379115i
$861$	4.27354	+	13.1526i	0.145642	+	0.448239i
$862$	34.6052	−	3.05279i	1.17866	−	0.103978i
$863$	−19.3262	+	26.6003i	−0.657873	+	0.905484i	−0.999409	−	0.0343846i	$-0.989053\pi$
$863$	−19.3262	+	26.6003i	−0.657873	+	0.905484i	0.341536	+	0.939869i	$0.389053\pi$
$864$	−5.18651	+	27.2073i	−0.176449	+	0.925612i
$865$	−1.88681	−	0.613063i	−0.0641536	−	0.0208448i
$866$	18.2065	−	15.8498i	0.618682	−	0.538598i
$867$	−3.73569	−	5.14174i	−0.126871	−	0.174623i
$868$	18.0024	+	17.3344i	0.611040	+	0.588368i
$869$	−30.0252	+	23.1748i	−1.01854	+	0.786152i
$870$	2.96495	+	6.97095i	0.100521	+	0.236337i
$871$	8.75591	−	6.36154i	0.296683	−	0.215553i
$872$	−9.40994	−	0.472677i	−0.318661	−	0.0160069i
$873$	−2.01495	+	6.20139i	−0.0681958	+	0.209885i
$874$	25.8629	+	5.95121i	0.874824	+	0.201303i
$875$	2.14601	+	1.55917i	0.0725484	+	0.0527095i
$876$	−9.61137	−	18.0134i	−0.324738	−	0.608618i
$877$	14.6212	−	4.75073i	0.493724	−	0.160421i	−0.0515635	−	0.998670i	$-0.516420\pi$
$877$	14.6212	−	4.75073i	0.493724	−	0.160421i	0.545288	+	0.838249i	$0.316420\pi$
$878$	−16.5230	−	9.91176i	−0.557625	−	0.334506i
$879$	8.05414			0.271659
$880$	−12.3153	+	4.93285i	−0.415149	+	0.166286i
$881$	54.1311			1.82372			0.911861	−	0.410499i	$-0.134645\pi$
$881$	54.1311			1.82372			0.911861	+	0.410499i	$0.134645\pi$
$882$	−0.0911312	−	0.0546674i	−0.00306855	−	0.00184075i
$883$	−39.1111	+	12.7080i	−1.31619	+	0.427657i	−0.881186	−	0.472769i	$-0.843254\pi$
$883$	−39.1111	+	12.7080i	−1.31619	+	0.427657i	−0.435008	+	0.900427i	$0.643254\pi$
$884$	24.7973	+	46.4746i	0.834023	+	1.56311i
$885$	−3.22200	−	2.34092i	−0.108306	−	0.0786891i
$886$	46.9176	+	10.7960i	1.57623	+	0.362700i
$887$	−11.2378	+	34.5865i	−0.377329	+	1.16130i	0.564564	+	0.825389i	$0.309044\pi$
$887$	−11.2378	+	34.5865i	−0.377329	+	1.16130i	−0.941894	+	0.335911i	$0.890956\pi$
$888$	18.3268	+	0.920586i	0.615007	+	0.0308929i
$889$	−24.4162	+	17.7394i	−0.818892	+	0.594960i
$890$	−8.06047	−	18.9511i	−0.270187	−	0.635244i
$891$	1.36697	−	4.66335i	0.0457951	−	0.156228i
$892$	23.3802	+	22.5127i	0.782828	+	0.753782i
$893$	19.4082	+	26.7131i	0.649471	+	0.893920i
$894$	−1.77355	+	1.54398i	−0.0593163	+	0.0516383i
$895$	10.5044	+	3.41308i	0.351123	+	0.114087i
$896$	24.4960	−	17.3378i	0.818355	−	0.579216i
$897$	20.7666	−	28.5828i	0.693378	−	0.954353i
$898$	−38.3632	+	3.38431i	−1.28020	+	0.112936i
$899$	−8.06754	−	24.8293i	−0.269067	−	0.828104i
$900$	0.569098	−	4.09230i	0.0189699	−	0.136410i
$901$		−	24.3933i		−	0.812660i
$902$	24.8105	+	4.95581i	0.826100	+	0.165011i
$903$		−	14.3891i		−	0.478841i
$904$	4.11707	−	1.11275i	0.136932	−	0.0370094i
$905$	4.88174	+	15.0244i	0.162274	+	0.499429i
$906$	1.23616	+	14.0126i	0.0410686	+	0.465537i
$907$	−6.22295	+	8.56516i	−0.206630	+	0.284401i	−0.899736	−	0.436434i	$-0.856241\pi$
$907$	−6.22295	+	8.56516i	−0.206630	+	0.284401i	0.693107	+	0.720835i	$0.256241\pi$
$908$	33.9012	−	6.02829i	1.12505	−	0.200056i
$909$	−3.76732	−	1.22408i	−0.124954	−	0.0406001i
$910$	−13.3612	−	15.3479i	−0.442920	−	0.508778i
$911$	−23.2220	−	31.9623i	−0.769378	−	1.05896i	−0.996376	−	0.0850623i	$-0.972891\pi$
$911$	−23.2220	−	31.9623i	−0.769378	−	1.05896i	0.226998	−	0.973895i	$-0.427109\pi$
$912$	10.7582	−	0.406860i	0.356241	−	0.0134725i
$913$	−25.4349	−	17.3748i	−0.841771	−	0.575023i
$914$	−5.08505	+	2.16282i	−0.168199	+	0.0715397i
$915$	−6.25157	+	4.54203i	−0.206671	+	0.150155i
$916$	10.7532	+	5.22542i	0.355295	+	0.172653i
$917$	11.2596	−	34.6534i	0.371823	−	1.14435i
$918$	7.53936	−	32.7647i	0.248836	−	1.08140i
$919$	−32.6232	−	23.7021i	−1.07614	−	0.781861i	−0.0991334	−	0.995074i	$-0.531607\pi$
$919$	−32.6232	−	23.7021i	−1.07614	−	0.781861i	−0.977006	+	0.213213i	$0.931607\pi$
$920$	−14.8386	−	11.9628i	−0.489215	−	0.394403i
$921$	−4.70750	+	1.52956i	−0.155117	+	0.0504007i
$922$	−10.2700	+	17.1203i	−0.338226	+	0.563826i
$923$	−72.2055			−2.37667
$924$	14.7656	−	8.43768i	0.485751	−	0.277579i
$925$	−6.71241			−0.220703
$926$	−19.8495	+	33.0894i	−0.652296	+	1.08738i
$927$	9.19166	−	2.98655i	0.301894	−	0.0980912i
$928$	−31.1031	+	3.93324i	−1.02101	+	0.129115i
$929$	−8.03705	−	5.83926i	−0.263687	−	0.191580i	0.448084	−	0.893991i	$-0.352107\pi$
$929$	−8.03705	−	5.83926i	−0.263687	−	0.191580i	−0.711771	+	0.702412i	$0.752107\pi$
$930$	1.44389	−	6.27490i	0.0473472	−	0.205762i
$931$	−0.0313014	+	0.0963359i	−0.00102586	+	0.00315728i
$932$	18.8907	−	38.8744i	0.618786	−	1.27337i
$933$	−7.83954	+	5.69576i	−0.256655	+	0.186471i
$934$	−23.2437	+	9.88621i	−0.760557	+	0.323487i
$935$	15.1648	−	5.41862i	0.495942	−	0.177208i
$936$	−11.2943	+	29.6147i	−0.369166	+	0.967986i
$937$	−10.0136	−	13.7825i	−0.327129	−	0.450254i	0.613498	−	0.789696i	$-0.289762\pi$
$937$	−10.0136	−	13.7825i	−0.327129	−	0.450254i	−0.940627	+	0.339442i	$0.889762\pi$
$938$	4.91456	+	5.64530i	0.160466	+	0.184326i
$939$	14.4247	+	4.68685i	0.470731	+	0.152950i
$940$	−4.15178	−	23.3483i	−0.135416	−	0.761539i
$941$	13.9992	−	19.2683i	0.456362	−	0.628129i	−0.517387	−	0.855751i	$-0.673095\pi$
$941$	13.9992	−	19.2683i	0.456362	−	0.628129i	0.973749	+	0.227623i	$0.0730952\pi$
$942$	1.42505	+	16.1538i	0.0464306	+	0.526319i
$943$	11.2328	+	34.5709i	0.365789	+	1.12578i
$944$	12.9588	−	10.1850i	0.421773	−	0.331495i
$945$			12.9878i			0.422494i
$946$	−22.9578	−	12.8812i	−0.746421	−	0.418803i
$947$		−	37.4645i		−	1.21743i	−0.793389	−	0.608716i	$-0.791685\pi$
$947$		−	37.4645i		−	1.21743i	0.793389	−	0.608716i	$-0.208315\pi$
$948$	−21.8954	−	3.04490i	−0.711129	−	0.0988936i
$949$	−17.7048	−	54.4898i	−0.574722	−	1.76881i
$950$	−3.92295	+	0.346074i	−0.127277	+	0.0112281i
$951$	8.77379	−	12.0761i	0.284510	−	0.391594i
$952$	−30.5091	+	19.9071i	−0.988806	+	0.645194i
$953$	−7.79494	−	2.53273i	−0.252503	−	0.0820432i	0.180031	−	0.983661i	$-0.442380\pi$
$953$	−7.79494	−	2.53273i	−0.252503	−	0.0820432i	−0.432534	+	0.901618i	$0.642380\pi$
$954$	11.0702	−	9.63728i	0.358412	−	0.312019i
$955$	8.23943	+	11.3406i	0.266622	+	0.366973i
$956$	−16.9248	+	17.5769i	−0.547386	+	0.568478i
$957$	−17.7581	+	0.515444i	−0.574039	+	0.0166619i
$958$	−5.07092	−	11.9223i	−0.163834	−	0.385194i
$959$	12.0848	−	8.78013i	0.390239	−	0.283525i
$960$	−7.07726	−	3.11426i	−0.228418	−	0.100512i
$961$	2.72224	−	8.37819i	0.0878142	−	0.270264i
$962$	50.1814	+	11.5470i	1.61791	+	0.372292i
$963$	−0.580728	−	0.421924i	−0.0187137	−	0.0135963i
$964$	−7.54443	+	4.02546i	−0.242990	+	0.129651i
$965$	7.73149	−	2.51211i	0.248886	−	0.0808678i
$966$	20.9526	+	12.5690i	0.674140	+	0.404400i
$967$	−54.8530			−1.76395			−0.881976	−	0.471294i	$-0.843787\pi$
$967$	−54.8530			−1.76395			−0.881976	+	0.471294i	$0.843787\pi$
$968$	−0.244100	−	31.1117i	−0.00784568	−	0.999969i
$969$	−13.0684			−0.419819
$970$	−3.82785	−	2.29624i	−0.122905	−	0.0737278i
$971$	13.0728	−	4.24761i	0.419526	−	0.136312i	−0.0916439	−	0.995792i	$-0.529212\pi$
$971$	13.0728	−	4.24761i	0.419526	−	0.136312i	0.511170	+	0.859479i	$0.329212\pi$
$972$	28.4176	−	15.1627i	0.911494	−	0.486343i
$973$	−20.1160	−	14.6151i	−0.644888	−	0.468539i
$974$	−23.3348	−	5.36948i	−0.747695	−	0.172049i
$975$	−1.62011	+	4.98620i	−0.0518852	+	0.159686i
$976$	−11.0248	−	30.0198i	−0.352895	−	0.960909i
$977$	−24.5295	+	17.8217i	−0.784769	+	0.570168i	−0.906406	−	0.422407i	$-0.861185\pi$
$977$	−24.5295	+	17.8217i	−0.784769	+	0.570168i	0.121638	+	0.992575i	$0.461185\pi$
$978$	5.73517	+	13.4841i	0.183390	+	0.431173i
$979$	48.2771	−	1.40128i	1.54294	−	0.0447851i
$980$	0.0504604	−	0.0524048i	0.00161190	−	0.00167401i
$981$	4.04487	+	5.56728i	0.129143	+	0.177750i
$982$	32.7155	−	28.4807i	1.04399	−	0.908857i
$983$	11.3903	+	3.70093i	0.363294	+	0.118041i	0.484975	−	0.874528i	$-0.338829\pi$
$983$	11.3903	+	3.70093i	0.363294	+	0.118041i	−0.121681	+	0.992569i	$0.538829\pi$
$984$	8.05810	+	12.3496i	0.256883	+	0.393692i
$985$	0.673847	−	0.927472i	0.0214706	−	0.0295517i
$986$	37.9086	−	3.34421i	1.20726	−	0.106501i
$987$	9.39406	+	28.9119i	0.299016	+	0.920277i
$988$	29.9230	+	4.16125i	0.951976	+	0.132387i
$989$		−	37.8211i		−	1.20264i
$990$	8.45038	+	4.74135i	0.268571	+	0.150690i
$991$			3.20128i			0.101692i	0.998707	+	0.0508459i	$0.0161917\pi$
$991$			3.20128i			0.101692i	−0.998707	+	0.0508459i	$0.983808\pi$
$992$	23.3532	+	12.8347i	0.741465	+	0.407501i
$993$	4.46412	+	13.7392i	0.141665	+	0.435999i
$994$	−4.38813	−	49.7420i	−0.139183	−	1.57772i
$995$	−9.06139	+	12.4719i	−0.287265	+	0.395387i
$996$	−3.14307	−	17.6757i	−0.0995921	−	0.560075i
$997$	24.4373	+	7.94017i	0.773938	+	0.251468i	0.669250	−	0.743038i	$-0.266616\pi$
$997$	24.4373	+	7.94017i	0.773938	+	0.251468i	0.104688	+	0.994505i	$0.466616\pi$
$998$	30.8070	+	35.3877i	0.975178	+	1.12018i
$999$	−19.3179	−	26.5888i	−0.611190	−	0.841231i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.c.151.4	yes	32
4.3	odd	2	inner	220.2.r.c.151.5	yes	32
11.7	odd	10	inner	220.2.r.c.51.5	yes	32
44.7	even	10	inner	220.2.r.c.51.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.c.51.4	✓	32	44.7	even	10	inner
220.2.r.c.51.5	yes	32	11.7	odd	10	inner
220.2.r.c.151.4	yes	32	1.1	even	1	trivial
220.2.r.c.151.5	yes	32	4.3	odd	2	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.r.c.151.4

Level	$220$
Weight	$2$
Character	220.151
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$