LMFDB - Embedded newform 370.2.r.e.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (of order $12$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.1
Root			$0.117630 - 0.893490i$ of defining polynomial
Character	$\chi$	$=$	370.193
Dual form			370.2.r.e.347.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.392794 - 1.46593i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.19306 + 1.89119i) q^{5} +(1.07313 + 1.07313i) q^{6} +(-0.552037 - 2.06023i) q^{7} +1.00000i q^{8} +(0.603425 - 0.348387i) q^{9} +(0.0876265 - 2.23435i) q^{10} +1.24199i q^{11} +(-1.46593 - 0.392794i) q^{12} +(-3.60872 - 2.08350i) q^{13} +(1.50819 + 1.50819i) q^{14} +(3.24097 + 1.00609i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.82810 - 4.89842i) q^{17} +(-0.348387 + 0.603425i) q^{18} +(-0.647049 - 2.41482i) q^{19} +(1.04129 + 1.97882i) q^{20} +(-2.80331 + 1.61849i) q^{21} +(-0.620995 - 1.07560i) q^{22} +7.58025i q^{23} +(1.46593 - 0.392794i) q^{24} +(-2.15321 - 4.51262i) q^{25} +4.16699 q^{26} +(-3.96713 - 3.96713i) q^{27} +(-2.06023 - 0.552037i) q^{28} +(-7.29797 - 7.29797i) q^{29} +(-3.30981 + 0.749185i) q^{30} +(-6.72707 + 6.72707i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.82067 - 0.487846i) q^{33} +(4.89842 + 2.82810i) q^{34} +(4.55490 + 1.41398i) q^{35} -0.696775i q^{36} +(-0.586988 - 6.05437i) q^{37} +(1.76777 + 1.76777i) q^{38} +(-1.63677 + 6.10850i) q^{39} +(-1.89119 - 1.19306i) q^{40} +(4.66912 + 2.69572i) q^{41} +(1.61849 - 2.80331i) q^{42} -6.61187i q^{43} +(1.07560 + 0.620995i) q^{44} +(-0.0610560 + 1.55684i) q^{45} +(-3.79012 - 6.56469i) q^{46} +(-3.36364 + 3.36364i) q^{47} +(-1.07313 + 1.07313i) q^{48} +(2.12237 - 1.22535i) q^{49} +(4.12104 + 2.83144i) q^{50} +(-6.06986 + 6.06986i) q^{51} +(-3.60872 + 2.08350i) q^{52} +(1.86551 - 6.96219i) q^{53} +(5.41920 + 1.45207i) q^{54} +(-2.34884 - 1.48177i) q^{55} +(2.06023 - 0.552037i) q^{56} +(-3.28579 + 1.89705i) q^{57} +(9.96921 + 2.67124i) q^{58} +(11.7504 + 3.14851i) q^{59} +(2.49179 - 2.30372i) q^{60} +(0.279654 + 1.04368i) q^{61} +(2.46228 - 9.18935i) q^{62} +(-1.05087 - 1.05087i) q^{63} -1.00000 q^{64} +(8.24571 - 4.33904i) q^{65} +(-1.33282 + 1.33282i) q^{66} +(9.47979 - 2.54010i) q^{67} -5.65620 q^{68} +(11.1121 - 2.97747i) q^{69} +(-4.65165 + 1.05291i) q^{70} +(4.90681 - 8.49885i) q^{71} +(0.348387 + 0.603425i) q^{72} +(-10.7498 + 10.7498i) q^{73} +(3.53553 + 4.94975i) q^{74} +(-5.76939 + 4.92897i) q^{75} +(-2.41482 - 0.647049i) q^{76} +(2.55879 - 0.685625i) q^{77} +(-1.63677 - 6.10850i) q^{78} +(0.454017 + 1.69441i) q^{79} +(2.23435 + 0.0876265i) q^{80} +(-3.21209 + 5.56350i) q^{81} -5.39144 q^{82} +(-0.0295859 + 0.110416i) q^{83} +3.23698i q^{84} +(12.6379 + 0.495634i) q^{85} +(3.30593 + 5.72604i) q^{86} +(-7.83168 + 13.5649i) q^{87} -1.24199 q^{88} +(-1.84256 + 6.87653i) q^{89} +(-0.725543 - 1.37879i) q^{90} +(-2.30033 + 8.58496i) q^{91} +(6.56469 + 3.79012i) q^{92} +(12.5037 + 7.21903i) q^{93} +(1.23118 - 4.59481i) q^{94} +(5.33885 + 1.65734i) q^{95} +(0.392794 - 1.46593i) q^{96} +0.402849 q^{97} +(-1.22535 + 2.12237i) q^{98} +(0.432694 + 0.749448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} - 8 q^{6} + 24 q^{9} - 4 q^{10} - 8 q^{12} + 12 q^{13} - 8 q^{16} - 16 q^{17} + 24 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 16 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 - 8 * q^6 + 24 * q^9 - 4 * q^10 - 8 * q^12 + 12 * q^13 - 8 * q^16 - 16 * q^17 + 24 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 16 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 12 * q^33 - 8 * q^35 - 8 * q^40 - 36 * q^41 + 4 * q^42 + 20 * q^45 + 4 * q^46 + 32 * q^47 + 8 * q^48 - 24 * q^49 - 4 * q^50 - 16 * q^51 + 12 * q^52 + 24 * q^53 + 8 * q^54 - 12 * q^55 - 60 * q^57 + 8 * q^58 + 8 * q^59 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 16 * q^64 + 12 * q^65 - 24 * q^66 + 8 * q^67 - 32 * q^68 + 8 * q^69 - 20 * q^70 + 4 * q^71 - 48 * q^73 - 36 * q^75 + 24 * q^76 - 12 * q^77 - 20 * q^79 + 12 * q^80 + 16 * q^81 - 24 * q^82 - 48 * q^83 - 8 * q^85 + 8 * q^86 - 12 * q^87 + 16 * q^88 + 8 * q^89 + 4 * q^90 - 8 * q^91 + 12 * q^92 - 36 * q^93 + 28 * q^94 + 8 * q^95 + 16 * q^96 + 16 * q^97 - 8 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.392794	−	1.46593i	−0.226780	−	0.846353i	−0.981684	−	0.190518i	$-0.938983\pi$
$3$	−0.392794	−	1.46593i	−0.226780	−	0.846353i	0.754904	−	0.655835i	$-0.227683\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.19306	+	1.89119i	−0.533554	+	0.845766i
$5$	−1.19306	+	1.89119i	−0.533554	+	0.845766i
$6$	1.07313	+	1.07313i	0.438104	+	0.438104i
$7$	−0.552037	−	2.06023i	−0.208650	−	0.778694i	−0.988306	−	0.152485i	$-0.951272\pi$
$7$	−0.552037	−	2.06023i	−0.208650	−	0.778694i	0.779655	−	0.626209i	$-0.215394\pi$
$8$			1.00000i			0.353553i
$9$	0.603425	−	0.348387i	0.201142	−	0.116129i
$10$	0.0876265	−	2.23435i	0.0277099	−	0.706564i
$11$			1.24199i			0.374474i	0.982315	+	0.187237i	$0.0599533\pi$
$11$			1.24199i			0.374474i	−0.982315	+	0.187237i	$0.940047\pi$
$12$	−1.46593	−	0.392794i	−0.423176	−	0.113390i
$13$	−3.60872	−	2.08350i	−1.00088	−	0.577858i	−0.0923705	−	0.995725i	$-0.529444\pi$
$13$	−3.60872	−	2.08350i	−1.00088	−	0.577858i	−0.908508	+	0.417867i	$0.862778\pi$
$14$	1.50819	+	1.50819i	0.403082	+	0.403082i
$15$	3.24097	+	1.00609i	0.836816	+	0.259772i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.82810	−	4.89842i	−0.685916	−	1.18804i	−0.973148	−	0.230180i	$-0.926069\pi$
$17$	−2.82810	−	4.89842i	−0.685916	−	1.18804i	0.287233	−	0.957861i	$-0.407265\pi$
$18$	−0.348387	+	0.603425i	−0.0821157	+	0.142229i
$19$	−0.647049	−	2.41482i	−0.148443	−	0.553997i	−0.999578	−	0.0290502i	$-0.990752\pi$
$19$	−0.647049	−	2.41482i	−0.148443	−	0.553997i	0.851135	−	0.524947i	$-0.175915\pi$
$20$	1.04129	+	1.97882i	0.232839	+	0.442477i
$21$	−2.80331	+	1.61849i	−0.611732	+	0.353184i
$22$	−0.620995	−	1.07560i	−0.132397	−	0.229318i
$23$			7.58025i			1.58059i	0.612726	+	0.790296i	$0.290073\pi$
$23$			7.58025i			1.58059i	−0.612726	+	0.790296i	$0.709927\pi$
$24$	1.46593	−	0.392794i	0.299231	−	0.0801787i
$25$	−2.15321	−	4.51262i	−0.430641	−	0.902523i
$26$	4.16699			0.817214
$27$	−3.96713	−	3.96713i	−0.763474	−	0.763474i
$28$	−2.06023	−	0.552037i	−0.389347	−	0.104325i
$29$	−7.29797	−	7.29797i	−1.35520	−	1.35520i	−0.879736	−	0.475462i	$-0.842281\pi$
$29$	−7.29797	−	7.29797i	−1.35520	−	1.35520i	−0.475462	−	0.879736i	$-0.657719\pi$
$30$	−3.30981	+	0.749185i	−0.604286	+	0.136782i
$31$	−6.72707	+	6.72707i	−1.20822	+	1.20822i	−0.236613	+	0.971604i	$0.576037\pi$
$31$	−6.72707	+	6.72707i	−1.20822	+	1.20822i	−0.971604	+	0.236613i	$0.923963\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.82067	−	0.487846i	0.316937	−	0.0849231i
$34$	4.89842	+	2.82810i	0.840072	+	0.485016i
$35$	4.55490	+	1.41398i	0.769919	+	0.239005i
$36$		−	0.696775i		−	0.116129i
$37$	−0.586988	−	6.05437i	−0.0965003	−	0.995333i
$37$	−0.586988	−	6.05437i	−0.0965003	−	0.995333i
$38$	1.76777	+	1.76777i	0.286770	+	0.286770i
$39$	−1.63677	+	6.10850i	−0.262093	+	0.978143i
$40$	−1.89119	−	1.19306i	−0.299024	−	0.188640i
$41$	4.66912	+	2.69572i	0.729195	+	0.421001i	0.818128	−	0.575037i	$-0.195012\pi$
$41$	4.66912	+	2.69572i	0.729195	+	0.421001i	−0.0889327	+	0.996038i	$0.528346\pi$
$42$	1.61849	−	2.80331i	0.249739	−	0.432560i
$43$		−	6.61187i		−	1.00830i	−0.863616	−	0.504150i	$-0.831806\pi$
$43$		−	6.61187i		−	1.00830i	0.863616	−	0.504150i	$-0.168194\pi$
$44$	1.07560	+	0.620995i	0.162152	+	0.0936186i
$45$	−0.0610560	+	1.55684i	−0.00910168	+	0.232080i
$46$	−3.79012	−	6.56469i	−0.558823	−	0.967911i
$47$	−3.36364	+	3.36364i	−0.490637	+	0.490637i	−0.908507	−	0.417870i	$-0.862777\pi$
$47$	−3.36364	+	3.36364i	−0.490637	+	0.490637i	0.417870	+	0.908507i	$0.362777\pi$
$48$	−1.07313	+	1.07313i	−0.154893	+	0.154893i
$49$	2.12237	−	1.22535i	0.303196	−	0.175050i
$50$	4.12104	+	2.83144i	0.582803	+	0.400426i
$51$	−6.06986	+	6.06986i	−0.849950	+	0.849950i
$52$	−3.60872	+	2.08350i	−0.500439	+	0.288929i
$53$	1.86551	−	6.96219i	0.256248	−	0.956330i	−0.711144	−	0.703046i	$-0.751823\pi$
$53$	1.86551	−	6.96219i	0.256248	−	0.956330i	0.967392	−	0.253284i	$-0.0815107\pi$
$54$	5.41920	+	1.45207i	0.737459	+	0.197602i
$55$	−2.34884	−	1.48177i	−0.316718	−	0.199802i
$56$	2.06023	−	0.552037i	0.275310	−	0.0737691i
$57$	−3.28579	+	1.89705i	−0.435213	+	0.251271i
$58$	9.96921	+	2.67124i	1.30902	+	0.350751i
$59$	11.7504	+	3.14851i	1.52977	+	0.409900i	0.922944	−	0.384935i	$-0.125776\pi$
$59$	11.7504	+	3.14851i	1.52977	+	0.409900i	0.606826	+	0.794835i	$0.292443\pi$
$60$	2.49179	−	2.30372i	0.321688	−	0.297409i
$61$	0.279654	+	1.04368i	0.0358061	+	0.133630i	0.981515	−	0.191384i	$-0.0612976\pi$
$61$	0.279654	+	1.04368i	0.0358061	+	0.133630i	−0.945709	+	0.325014i	$0.894631\pi$
$62$	2.46228	−	9.18935i	0.312710	−	1.16705i
$63$	−1.05087	−	1.05087i	−0.132397	−	0.132397i
$64$	−1.00000			−0.125000
$65$	8.24571	−	4.33904i	1.02275	−	0.538191i
$66$	−1.33282	+	1.33282i	−0.164059	+	0.164059i
$67$	9.47979	−	2.54010i	1.15814	−	0.310323i	0.371918	−	0.928266i	$-0.378700\pi$
$67$	9.47979	−	2.54010i	1.15814	−	0.310323i	0.786223	+	0.617943i	$0.212034\pi$
$68$	−5.65620			−0.685916
$69$	11.1121	−	2.97747i	1.33774	−	0.358446i
$70$	−4.65165	+	1.05291i	−0.555979	+	0.125847i
$71$	4.90681	−	8.49885i	0.582332	−	1.00863i	−0.412871	−	0.910790i	$-0.635474\pi$
$71$	4.90681	−	8.49885i	0.582332	−	1.00863i	0.995202	−	0.0978382i	$-0.0311928\pi$
$72$	0.348387	+	0.603425i	0.0410578	+	0.0711143i
$73$	−10.7498	+	10.7498i	−1.25816	+	1.25816i	−0.306196	+	0.951969i	$0.599056\pi$
$73$	−10.7498	+	10.7498i	−1.25816	+	1.25816i	−0.951969	+	0.306196i	$0.900944\pi$
$74$	3.53553	+	4.94975i	0.410997	+	0.575396i
$75$	−5.76939	+	4.92897i	−0.666192	+	0.569148i
$76$	−2.41482	−	0.647049i	−0.276999	−	0.0742216i
$77$	2.55879	−	0.685625i	0.291601	−	0.0781342i
$78$	−1.63677	−	6.10850i	−0.185327	−	0.691651i
$79$	0.454017	+	1.69441i	0.0510809	+	0.190637i	0.986752	−	0.162238i	$-0.0518711\pi$
$79$	0.454017	+	1.69441i	0.0510809	+	0.190637i	−0.935671	+	0.352874i	$0.885204\pi$
$80$	2.23435	+	0.0876265i	0.249808	+	0.00979695i
$81$	−3.21209	+	5.56350i	−0.356899	+	0.618167i
$82$	−5.39144			−0.595385
$83$	−0.0295859	+	0.110416i	−0.00324747	+	0.0121197i	−0.967531	−	0.252754i	$-0.918664\pi$
$83$	−0.0295859	+	0.110416i	−0.00324747	+	0.0121197i	0.964283	+	0.264874i	$0.0853303\pi$
$84$			3.23698i			0.353184i
$85$	12.6379	+	0.495634i	1.37078	+	0.0537590i
$86$	3.30593	+	5.72604i	0.356488	+	0.617455i
$87$	−7.83168	+	13.5649i	−0.839645	+	1.45431i
$88$	−1.24199			−0.132397
$89$	−1.84256	+	6.87653i	−0.195311	+	0.728910i	0.796875	+	0.604144i	$0.206485\pi$
$89$	−1.84256	+	6.87653i	−0.195311	+	0.728910i	−0.992186	+	0.124766i	$0.960182\pi$
$90$	−0.725543	−	1.37879i	−0.0764790	−	0.145337i
$91$	−2.30033	+	8.58496i	−0.241140	+	0.899948i
$92$	6.56469	+	3.79012i	0.684416	+	0.395148i
$93$	12.5037	+	7.21903i	1.29658	+	0.748579i
$94$	1.23118	−	4.59481i	0.126986	−	0.473919i
$95$	5.33885	+	1.65734i	0.547755	+	0.170039i
$96$	0.392794	−	1.46593i	0.0400893	−	0.149615i
$97$	0.402849			0.0409031			0.0204516	−	0.999791i	$-0.493490\pi$
$97$	0.402849			0.0409031			0.0204516	+	0.999791i	$0.493490\pi$
$98$	−1.22535	+	2.12237i	−0.123779	+	0.214392i
$99$	0.432694	+	0.749448i	0.0434874	+	0.0753223i
$100$	−4.98464	−	0.391577i	−0.498464	−	0.0391577i
$101$			10.2921i			1.02410i	0.858956	+	0.512049i	$0.171114\pi$
$101$			10.2921i			1.02410i	−0.858956	+	0.512049i	$0.828886\pi$
$102$	2.22172	−	8.29158i	0.219983	−	0.820988i
$103$	7.89579			0.777995			0.388997	−	0.921239i	$-0.372821\pi$
$103$	7.89579			0.777995			0.388997	+	0.921239i	$0.372821\pi$
$104$	2.08350	−	3.60872i	0.204303	−	0.353864i
$105$	0.283646	−	7.23255i	0.0276810	−	0.705825i
$106$	1.86551	+	6.96219i	0.181195	+	0.676228i
$107$	0.879327	+	3.28169i	0.0850078	+	0.317253i	0.995316	−	0.0966784i	$-0.0308218\pi$
$107$	0.879327	+	3.28169i	0.0850078	+	0.317253i	−0.910308	+	0.413932i	$0.864155\pi$
$108$	−5.41920	+	1.45207i	−0.521463	+	0.139725i
$109$	−3.45589	−	0.926002i	−0.331014	−	0.0886949i	0.0894844	−	0.995988i	$-0.471478\pi$
$109$	−3.45589	−	0.926002i	−0.331014	−	0.0886949i	−0.420498	+	0.907293i	$0.638145\pi$
$110$	2.77504	+	0.108831i	0.264590	+	0.0103767i
$111$	−8.64470	+	3.23860i	−0.820518	+	0.307394i
$112$	−1.50819	+	1.50819i	−0.142511	+	0.142511i
$113$	−1.99492	−	3.45530i	−0.187666	−	0.325048i	0.756805	−	0.653640i	$-0.226759\pi$
$113$	−1.99492	−	3.45530i	−0.187666	−	0.325048i	−0.944472	+	0.328593i	$0.893426\pi$
$114$	1.89705	−	3.28579i	0.177675	−	0.307742i
$115$	−14.3357	−	9.04371i	−1.33681	−	0.843330i
$116$	−9.96921	+	2.67124i	−0.925618	+	0.248019i
$117$	−2.90345			−0.268424
$118$	−11.7504	+	3.14851i	−1.08171	+	0.289843i
$119$	−8.53065	+	8.53065i	−0.782003	+	0.782003i
$120$	−1.00609	+	3.24097i	−0.0918433	+	0.295859i
$121$	9.45746			0.859769
$122$	−0.764030	−	0.764030i	−0.0691720	−	0.0691720i
$123$	2.11772	−	7.90345i	0.190949	−	0.712630i
$124$	2.46228	+	9.18935i	0.221119	+	0.825228i
$125$	11.1031	+	1.31171i	0.993094	+	0.117323i
$126$	1.43552	+	0.384645i	0.127886	+	0.0342669i
$127$	6.97904	+	1.87003i	0.619290	+	0.165938i	0.554805	−	0.831980i	$-0.312793\pi$
$127$	6.97904	+	1.87003i	0.619290	+	0.165938i	0.0644850	+	0.997919i	$0.479460\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−9.69251	+	2.59710i	−0.853378	+	0.228662i
$130$	−4.97148	+	7.88057i	−0.436027	+	0.691172i
$131$	−3.93914	−	1.05549i	−0.344164	−	0.0922184i	0.0825968	−	0.996583i	$-0.473679\pi$
$131$	−3.93914	−	1.05549i	−0.344164	−	0.0922184i	−0.426761	+	0.904365i	$0.640345\pi$
$132$	0.487846	−	1.82067i	0.0424616	−	0.158469i
$133$	−4.61789	+	2.66614i	−0.400422	+	0.231184i
$134$	−6.93969	+	6.93969i	−0.599498	+	0.599498i
$135$	12.2356	−	2.76957i	1.05307	−	0.238366i
$136$	4.89842	−	2.82810i	0.420036	−	0.242508i
$137$	7.39158	−	7.39158i	0.631505	−	0.631505i	−0.316940	−	0.948446i	$-0.602655\pi$
$137$	7.39158	−	7.39158i	0.631505	−	0.631505i	0.948446	+	0.316940i	$0.102655\pi$
$138$	−8.13461	+	8.13461i	−0.692464	+	0.692464i
$139$	−10.5923	−	18.3463i	−0.898424	−	1.55612i	−0.829509	−	0.558494i	$-0.811380\pi$
$139$	−10.5923	−	18.3463i	−0.898424	−	1.55612i	−0.0689152	−	0.997623i	$-0.521954\pi$
$140$	3.50199	−	3.23767i	0.295972	−	0.273633i
$141$	6.25206	+	3.60963i	0.526518	+	0.303985i
$142$			9.81363i			0.823541i
$143$	2.58768	−	4.48200i	0.216393	−	0.374803i
$144$	−0.603425	−	0.348387i	−0.0502854	−	0.0290323i
$145$	22.5088	−	5.09492i	1.86925	−	0.423110i
$146$	3.93469	−	14.6844i	0.325637	−	1.21529i
$147$	−2.62993	−	2.62993i	−0.216913	−	0.216913i
$148$	−5.53674	−	2.51884i	−0.455117	−	0.207047i
$149$		−	17.9119i		−	1.46740i	−0.679473	−	0.733700i	$-0.737792\pi$
$149$		−	17.9119i		−	1.46740i	0.679473	−	0.733700i	$-0.262208\pi$
$150$	2.53196	−	7.15331i	0.206734	−	0.584065i
$151$	−4.95829	−	2.86267i	−0.403500	−	0.232961i	0.284493	−	0.958678i	$-0.408175\pi$
$151$	−4.95829	−	2.86267i	−0.403500	−	0.232961i	−0.687993	+	0.725717i	$0.741508\pi$
$152$	2.41482	−	0.647049i	0.195868	−	0.0524826i
$153$	−3.41309	−	1.97055i	−0.275932	−	0.159310i
$154$	−1.87316	+	1.87316i	−0.150944	+	0.150944i
$155$	−4.69636	−	20.7480i	−0.377221	−	1.66652i
$156$	4.47173	+	4.47173i	0.358025	+	0.358025i
$157$	−7.02982	−	1.88363i	−0.561040	−	0.150330i	−0.0328561	−	0.999460i	$-0.510460\pi$
$157$	−7.02982	−	1.88363i	−0.561040	−	0.150330i	−0.528184	+	0.849130i	$0.677127\pi$
$158$	−1.24040	−	1.24040i	−0.0986807	−	0.0986807i
$159$	−10.9388			−0.867505
$160$	−1.97882	+	1.04129i	−0.156439	+	0.0823211i
$161$	15.6171	−	4.18458i	1.23080	−	0.329791i
$162$		−	6.42418i		−	0.504731i
$163$	8.87349	+	15.3693i	0.695025	+	1.20382i	0.970172	+	0.242417i	$0.0779401\pi$
$163$	8.87349	+	15.3693i	0.695025	+	1.20382i	−0.275147	+	0.961402i	$0.588727\pi$
$164$	4.66912	−	2.69572i	0.364597	−	0.210500i
$165$	−1.24956	+	4.02526i	−0.0972780	+	0.313366i
$166$	−0.0295859	−	0.110416i	−0.00229631	−	0.00856995i
$167$	−5.00522	+	8.66929i	−0.387315	+	0.670850i	−0.992087	−	0.125549i	$-0.959931\pi$
$167$	−5.00522	+	8.66929i	−0.387315	+	0.670850i	0.604772	+	0.796398i	$0.293264\pi$
$168$	−1.61849	−	2.80331i	−0.124869	−	0.216280i
$169$	2.18190	+	3.77917i	0.167839	+	0.290705i
$170$	−11.1926	+	5.88974i	−0.858433	+	0.451722i
$171$	−1.23174	−	1.23174i	−0.0941933	−	0.0941933i
$172$	−5.72604	−	3.30593i	−0.436607	−	0.252075i
$173$	2.46568	+	0.660678i	0.187463	+	0.0502304i	0.351329	−	0.936252i	$-0.385730\pi$
$173$	2.46568	+	0.660678i	0.187463	+	0.0502304i	−0.163866	+	0.986483i	$0.552397\pi$
$174$		−	15.6634i		−	1.18744i
$175$	−8.10838	+	6.92723i	−0.612936	+	0.523650i
$176$	1.07560	−	0.620995i	0.0810761	−	0.0468093i
$177$		−	18.4619i		−	1.38768i
$178$	−1.84256	−	6.87653i	−0.138106	−	0.515417i
$179$	−3.90524	−	3.90524i	−0.291892	−	0.291892i	0.545936	−	0.837827i	$-0.316174\pi$
$179$	−3.90524	−	3.90524i	−0.291892	−	0.291892i	−0.837827	+	0.545936i	$0.816174\pi$
$180$	1.31773	+	0.831295i	0.0982181	+	0.0619611i
$181$	10.4223	−	18.0520i	0.774685	−	1.34179i	−0.160287	−	0.987071i	$-0.551242\pi$
$181$	10.4223	−	18.0520i	0.774685	−	1.34179i	0.934971	−	0.354723i	$-0.115425\pi$
$182$	−2.30033	−	8.58496i	−0.170512	−	0.636360i
$183$	1.42012	−	0.819905i	0.104978	−	0.0606091i
$184$	−7.58025			−0.558823
$185$	12.1503	+	6.11314i	0.893307	+	0.449447i
$186$	−14.4381			−1.05865
$187$	6.08379	−	3.51248i	0.444891	−	0.256858i
$188$	1.23118	+	4.59481i	0.0897928	+	0.335111i
$189$	−5.98320	+	10.3632i	−0.435214	+	0.753812i
$190$	−5.45225	+	1.23413i	−0.395548	+	0.0895333i
$191$	−1.86603	−	1.86603i	−0.135021	−	0.135021i	0.636366	−	0.771387i	$-0.280437\pi$
$191$	−1.86603	−	1.86603i	−0.135021	−	0.135021i	−0.771387	+	0.636366i	$0.780437\pi$
$192$	0.392794	+	1.46593i	0.0283474	+	0.105794i
$193$		−	19.7620i		−	1.42250i	−0.702938	−	0.711251i	$-0.748129\pi$
$193$		−	19.7620i		−	1.42250i	0.702938	−	0.711251i	$-0.251871\pi$
$194$	−0.348877	+	0.201424i	−0.0250479	+	0.0144614i
$195$	−9.59957	−	10.3833i	−0.687440	−	0.743560i
$196$		−	2.45070i		−	0.175050i
$197$	−11.6260	−	3.11519i	−0.828321	−	0.221948i	−0.180340	−	0.983604i	$-0.557720\pi$
$197$	−11.6260	−	3.11519i	−0.828321	−	0.221948i	−0.647981	+	0.761656i	$0.724386\pi$
$198$	−0.749448	−	0.432694i	−0.0532609	−	0.0307502i
$199$	1.28100	+	1.28100i	0.0908079	+	0.0908079i	0.751052	−	0.660244i	$-0.229547\pi$
$199$	1.28100	+	1.28100i	0.0908079	+	0.0908079i	−0.660244	+	0.751052i	$0.729547\pi$
$200$	4.51262	−	2.15321i	0.319090	−	0.152255i
$201$	−7.44720	−	12.8989i	−0.525285	−	0.909821i
$202$	−5.14603	−	8.91319i	−0.362074	−	0.627130i
$203$	−11.0067	+	19.0642i	−0.772522	+	1.33805i
$204$	2.22172	+	8.29158i	0.155552	+	0.580526i
$205$	−10.6687	+	5.61404i	−0.745133	+	0.392102i
$206$	−6.83795	+	3.94789i	−0.476423	+	0.275063i
$207$	2.64086	+	4.57411i	0.183553	+	0.317923i
$208$			4.16699i			0.288929i
$209$	2.99918	−	0.803629i	0.207458	−	0.0555882i
$210$	3.37063	+	6.40540i	0.232596	+	0.442014i
$211$	−2.01843			−0.138955			−0.0694773	−	0.997584i	$-0.522133\pi$
$211$	−2.01843			−0.138955			−0.0694773	+	0.997584i	$0.522133\pi$
$212$	−5.09668	−	5.09668i	−0.350041	−	0.350041i
$213$	−14.3860	−	3.85473i	−0.985716	−	0.264122i
$214$	−2.40237	−	2.40237i	−0.164222	−	0.164222i
$215$	12.5043	+	7.88837i	0.852786	+	0.537982i
$216$	3.96713	−	3.96713i	0.269929	−	0.269929i
$217$	17.5729	+	10.1457i	1.19293	+	0.688736i
$218$	3.45589	−	0.926002i	0.234062	−	0.0627168i
$219$	19.9808	+	11.5359i	1.35018	+	0.779525i
$220$	−2.45767	+	1.29327i	−0.165696	+	0.0871923i
$221$			23.5693i			1.58545i
$222$	5.86723	−	7.12706i	0.393783	−	0.478337i
$223$	9.90448	+	9.90448i	0.663253	+	0.663253i	0.956145	−	0.292892i	$-0.0946177\pi$
$223$	9.90448	+	9.90448i	0.663253	+	0.663253i	−0.292892	+	0.956145i	$0.594618\pi$
$224$	0.552037	−	2.06023i	0.0368845	−	0.137655i
$225$	−2.87144	−	1.97287i	−0.191429	−	0.131525i
$226$	3.45530	+	1.99492i	0.229843	+	0.132700i
$227$	−9.89342	+	17.1359i	−0.656649	+	1.13735i	0.324829	+	0.945773i	$0.394693\pi$
$227$	−9.89342	+	17.1359i	−0.656649	+	1.13735i	−0.981478	+	0.191577i	$0.938640\pi$
$228$			3.79410i			0.251271i
$229$	−6.54334	−	3.77780i	−0.432396	−	0.249644i	0.267971	−	0.963427i	$-0.413647\pi$
$229$	−6.54334	−	3.77780i	−0.432396	−	0.249644i	−0.700367	+	0.713783i	$0.746980\pi$
$230$	16.9369	+	0.664231i	1.11679	+	0.0437981i
$231$	−2.01015	−	3.48168i	−0.132258	−	0.229078i
$232$	7.29797	−	7.29797i	0.479135	−	0.479135i
$233$	−9.92585	+	9.92585i	−0.650264	+	0.650264i	−0.953056	−	0.302793i	$-0.902081\pi$
$233$	−9.92585	+	9.92585i	−0.650264	+	0.650264i	0.302793	+	0.953056i	$0.402081\pi$
$234$	2.51446	−	1.45173i	0.164376	−	0.0949023i
$235$	−2.34825	−	10.3743i	−0.153183	−	0.676745i
$236$	8.60188	−	8.60188i	0.559934	−	0.559934i
$237$	2.30555	−	1.33111i	0.149762	−	0.0864649i
$238$	3.12243	−	11.6531i	0.202397	−	0.755357i
$239$	−8.58662	−	2.30078i	−0.555423	−	0.148825i	−0.0298200	−	0.999555i	$-0.509493\pi$
$239$	−8.58662	−	2.30078i	−0.555423	−	0.148825i	−0.525603	+	0.850730i	$0.676160\pi$
$240$	−0.749185	−	3.30981i	−0.0483597	−	0.213647i
$241$	−8.80585	+	2.35952i	−0.567234	+	0.151990i	−0.531028	−	0.847354i	$-0.678194\pi$
$241$	−8.80585	+	2.35952i	−0.567234	+	0.151990i	−0.0362065	+	0.999344i	$0.511527\pi$
$242$	−8.19040	+	4.72873i	−0.526499	+	0.303974i
$243$	−6.84022	−	1.83283i	−0.438800	−	0.117576i
$244$	1.04368	+	0.279654i	0.0668150	+	0.0179030i
$245$	−0.214747	+	5.47573i	−0.0137197	+	0.349832i
$246$	2.11772	+	7.90345i	0.135021	+	0.503906i
$247$	−2.69625	+	10.0625i	−0.171558	+	0.640263i
$248$	−6.72707	−	6.72707i	−0.427169	−	0.427169i
$249$	0.173483			0.0109940
$250$	−10.2714	+	4.41559i	−0.649623	+	0.279267i
$251$	0.286913	−	0.286913i	0.0181098	−	0.0181098i	−0.697994	−	0.716104i	$-0.745924\pi$
$251$	0.286913	−	0.286913i	0.0181098	−	0.0181098i	0.716104	+	0.697994i	$0.245924\pi$
$252$	−1.43552	+	0.384645i	−0.0904290	+	0.0242304i
$253$	−9.41460			−0.591891
$254$	−6.97904	+	1.87003i	−0.437904	+	0.117336i
$255$	−4.23754	−	18.7210i	−0.265365	−	1.17235i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.54430	+	13.0671i	0.470600	+	0.815103i	0.999435	−	0.0336216i	$-0.0107041\pi$
$257$	7.54430	+	13.0671i	0.470600	+	0.815103i	−0.528834	+	0.848725i	$0.677371\pi$
$258$	7.09541	−	7.09541i	0.441741	−	0.441741i
$259$	−12.1494	+	4.55157i	−0.754925	+	0.282821i
$260$	0.365139	−	9.31052i	0.0226450	−	0.577414i
$261$	−6.94629	−	1.86125i	−0.429965	−	0.115209i
$262$	3.93914	−	1.05549i	0.243361	−	0.0652083i
$263$	5.31582	+	19.8389i	0.327787	+	1.22332i	0.911480	+	0.411344i	$0.134941\pi$
$263$	5.31582	+	19.8389i	0.327787	+	1.22332i	−0.583693	+	0.811974i	$0.698393\pi$
$264$	0.487846	+	1.82067i	0.0300249	+	0.112054i
$265$	10.9412	+	11.8344i	0.672110	+	0.726979i
$266$	2.66614	−	4.61789i	0.163471	−	0.283141i
$267$	10.8042			0.661208
$268$	2.54010	−	9.47979i	0.155161	−	0.579070i
$269$		−	6.60785i		−	0.402888i	−0.979500	−	0.201444i	$-0.935437\pi$
$269$		−	6.60785i		−	0.402888i	0.979500	−	0.201444i	$-0.0645634\pi$
$270$	−9.21158	+	8.51633i	−0.560599	+	0.518287i
$271$	−6.90495	−	11.9597i	−0.419446	−	0.726501i	0.576438	−	0.817141i	$-0.304442\pi$
$271$	−6.90495	−	11.9597i	−0.419446	−	0.726501i	−0.995884	+	0.0906397i	$0.971109\pi$
$272$	−2.82810	+	4.89842i	−0.171479	+	0.297010i
$273$	13.4885			0.816359
$274$	−2.70551	+	10.0971i	−0.163446	+	0.609987i
$275$	5.60463	−	2.67426i	0.337972	−	0.161264i
$276$	2.97747	−	11.1121i	0.179223	−	0.668869i
$277$	0.200429	+	0.115718i	0.0120426	+	0.00695279i	0.506009	−	0.862528i	$-0.331120\pi$
$277$	0.200429	+	0.115718i	0.0120426	+	0.00695279i	−0.493967	+	0.869481i	$0.664454\pi$
$278$	18.3463	+	10.5923i	1.10034	+	0.635282i
$279$	−1.71565	+	6.40290i	−0.102713	+	0.383332i
$280$	−1.41398	+	4.55490i	−0.0845012	+	0.272208i
$281$	4.01948	−	15.0009i	0.239782	−	0.894879i	−0.736153	−	0.676816i	$-0.763359\pi$
$281$	4.01948	−	15.0009i	0.239782	−	0.894879i	0.975935	−	0.218063i	$-0.0699739\pi$
$282$	−7.21925			−0.429900
$283$	15.3798	−	26.6386i	0.914235	−	1.58350i	0.106217	−	0.994343i	$-0.466126\pi$
$283$	15.3798	−	26.6386i	0.914235	−	1.58350i	0.808018	−	0.589158i	$-0.200541\pi$
$284$	−4.90681	−	8.49885i	−0.291166	−	0.504314i
$285$	0.332464	−	8.47735i	0.0196935	−	0.502155i
$286$			5.17536i			0.306026i
$287$	2.97628	−	11.1076i	0.175684	−	0.655662i
$288$	0.696775			0.0410578
$289$	−7.49632	+	12.9840i	−0.440960	+	0.763766i
$290$	−16.9457	+	15.6667i	−0.995086	+	0.919981i
$291$	−0.158236	−	0.590547i	−0.00927599	−	0.0346185i
$292$	3.93469	+	14.6844i	0.230260	+	0.859342i
$293$	6.11166	−	1.63761i	0.357047	−	0.0956704i	−0.0758367	−	0.997120i	$-0.524163\pi$
$293$	6.11166	−	1.63761i	0.357047	−	0.0956704i	0.432884	+	0.901450i	$0.357496\pi$
$294$	3.59255	+	0.962621i	0.209522	+	0.0561412i
$295$	−19.9734	+	18.4659i	−1.16289	+	1.07512i
$296$	6.05437	−	0.586988i	0.351903	−	0.0341180i
$297$	4.92714	−	4.92714i	0.285901	−	0.285901i
$298$	8.95595	+	15.5122i	0.518804	+	0.898595i
$299$	15.7934	−	27.3550i	0.913357	−	1.58198i
$300$	1.38391	+	7.46093i	0.0799003	+	0.430757i
$301$	−13.6220	+	3.65000i	−0.785157	+	0.210382i
$302$	5.72534			0.329456
$303$	15.0874	−	4.04266i	0.866749	−	0.232245i
$304$	−1.76777	+	1.76777i	−0.101389	+	0.101389i
$305$	−2.30745	−	0.716300i	−0.132124	−	0.0410152i
$306$	3.94110			0.225298
$307$	13.1849	+	13.1849i	0.752500	+	0.752500i	0.974945	−	0.222445i	$-0.0714039\pi$
$307$	13.1849	+	13.1849i	0.752500	+	0.752500i	−0.222445	+	0.974945i	$0.571404\pi$
$308$	0.685625	−	2.55879i	0.0390671	−	0.145800i
$309$	−3.10141	−	11.5746i	−0.176433	−	0.658458i
$310$	14.4412	+	15.6201i	0.820203	+	0.887162i
$311$	1.39722	+	0.374385i	0.0792292	+	0.0212294i	0.298216	−	0.954498i	$-0.403608\pi$
$311$	1.39722	+	0.374385i	0.0792292	+	0.0212294i	−0.218987	+	0.975728i	$0.570275\pi$
$312$	−6.10850	−	1.63677i	−0.345826	−	0.0926637i
$313$	−5.24388	+	3.02756i	−0.296402	+	0.171128i	−0.640825	−	0.767687i	$-0.721408\pi$
$313$	−5.24388	+	3.02756i	−0.296402	+	0.171128i	0.344424	+	0.938814i	$0.388074\pi$
$314$	7.02982	−	1.88363i	0.396715	−	0.106300i
$315$	3.24115	−	0.733643i	0.182618	−	0.0413361i
$316$	1.69441	+	0.454017i	0.0953183	+	0.0255405i
$317$	−4.63520	+	17.2988i	−0.260339	+	0.971598i	0.704703	+	0.709502i	$0.251080\pi$
$317$	−4.63520	+	17.2988i	−0.260339	+	0.971598i	−0.965042	+	0.262095i	$0.915586\pi$
$318$	9.47329	−	5.46941i	0.531236	−	0.306709i
$319$	9.06401	−	9.06401i	0.507487	−	0.507487i
$320$	1.19306	−	1.89119i	0.0666942	−	0.105721i
$321$	4.46533	−	2.57806i	0.249230	−	0.143893i
$322$	−11.4325	+	11.4325i	−0.637107	+	0.637107i
$323$	−9.99887	+	9.99887i	−0.556352	+	0.556352i
$324$	3.21209	+	5.56350i	0.178449	+	0.309084i
$325$	−1.63170	+	20.7710i	−0.0905102	+	1.15217i
$326$	−15.3693	−	8.87349i	−0.851229	−	0.491457i
$327$			5.42980i			0.300269i
$328$	−2.69572	+	4.66912i	−0.148846	+	0.257809i
$329$	8.78672	+	5.07301i	0.484427	+	0.279684i
$330$	−0.930480	−	4.11076i	−0.0512213	−	0.226290i
$331$	1.42272	−	5.30966i	0.0781997	−	0.291845i	−0.915740	−	0.401771i	$-0.868395\pi$
$331$	1.42272	−	5.30966i	0.0781997	−	0.291845i	0.993940	+	0.109926i	$0.0350614\pi$
$332$	0.0808302	+	0.0808302i	0.00443613	+	0.00443613i
$333$	−2.46347	−	3.44886i	−0.134997	−	0.188996i
$334$		−	10.0104i		−	0.547746i
$335$	−6.50616	+	20.9586i	−0.355469	+	1.14509i
$336$	2.80331	+	1.61849i	0.152933	+	0.0882959i
$337$	−7.29082	+	1.95357i	−0.397156	+	0.106418i	−0.451869	−	0.892084i	$-0.649242\pi$
$337$	−7.29082	+	1.95357i	−0.397156	+	0.106418i	0.0547125	+	0.998502i	$0.482576\pi$
$338$	−3.77917	−	2.18190i	−0.205560	−	0.118680i
$339$	−4.28163	+	4.28163i	−0.232546	+	0.232546i
$340$	6.74820	−	10.6970i	0.365973	−	0.580124i
$341$	−8.35496	−	8.35496i	−0.452446	−	0.452446i
$342$	1.68258	+	0.450847i	0.0909837	+	0.0243790i
$343$	−14.2535	−	14.2535i	−0.769616	−	0.769616i
$344$	6.61187			0.356488
$345$	−7.62643	+	24.5674i	−0.410593	+	1.32266i
$346$	−2.46568	+	0.660678i	−0.132556	+	0.0355183i
$347$		−	13.7347i		−	0.737316i	−0.929565	−	0.368658i	$-0.879817\pi$
$347$		−	13.7347i		−	0.737316i	0.929565	−	0.368658i	$-0.120183\pi$
$348$	7.83168	+	13.5649i	0.419822	+	0.727154i
$349$	−5.31791	+	3.07030i	−0.284661	+	0.164349i	−0.635532	−	0.772075i	$-0.719219\pi$
$349$	−5.31791	+	3.07030i	−0.284661	+	0.164349i	0.350871	+	0.936424i	$0.385886\pi$
$350$	3.55845	−	10.0533i	0.190207	−	0.537374i
$351$	6.05076	+	22.5817i	0.322966	+	1.20532i
$352$	−0.620995	+	1.07560i	−0.0330992	+	0.0573294i
$353$	−15.3041	−	26.5075i	−0.814556	−	1.41085i	−0.909647	−	0.415383i	$-0.863648\pi$
$353$	−15.3041	−	26.5075i	−0.814556	−	1.41085i	0.0950909	−	0.995469i	$-0.469686\pi$
$354$	9.23095	+	15.9885i	0.490619	+	0.849778i
$355$	10.2188	+	19.4194i	0.542358	+	1.03067i
$356$	5.03397	+	5.03397i	0.266800	+	0.266800i
$357$	15.8561	+	9.15452i	0.839193	+	0.484508i
$358$	5.33466	+	1.42942i	0.281946	+	0.0755471i
$359$			10.8846i			0.574467i	0.957861	+	0.287234i	$0.0927356\pi$
$359$			10.8846i			0.574467i	−0.957861	+	0.287234i	$0.907264\pi$
$360$	−1.55684	−	0.0610560i	−0.0820526	−	0.00321793i
$361$	11.0418	−	6.37499i	0.581148	−	0.335526i
$362$			20.8446i			1.09557i
$363$	−3.71483	−	13.8639i	−0.194978	−	0.727668i
$364$	6.28463	+	6.28463i	0.329404	+	0.329404i
$365$	−7.50472	−	33.1550i	−0.392815	−	1.73541i
$366$	−0.819905	+	1.42012i	−0.0428571	+	0.0742307i
$367$	−3.29675	−	12.3036i	−0.172089	−	0.642244i	−0.997029	−	0.0770245i	$-0.975458\pi$
$367$	−3.29675	−	12.3036i	−0.172089	−	0.642244i	0.824940	−	0.565220i	$-0.191209\pi$
$368$	6.56469	−	3.79012i	0.342208	−	0.197574i
$369$	3.75662			0.195562
$370$	−13.5790	+	0.781014i	−0.705940	+	0.0406030i
$371$	−15.3736			−0.798155
$372$	12.5037	−	7.21903i	0.648288	−	0.374289i
$373$	4.47900	+	16.7159i	0.231914	+	0.865514i	0.979516	+	0.201367i	$0.0645384\pi$
$373$	4.47900	+	16.7159i	0.231914	+	0.865514i	−0.747602	+	0.664147i	$0.768795\pi$
$374$	−3.51248	+	6.08379i	−0.181626	+	0.314585i
$375$	−2.43837	−	16.7916i	−0.125917	−	0.867114i
$376$	−3.36364	−	3.36364i	−0.173466	−	0.173466i
$377$	11.1310	+	41.5416i	0.573278	+	2.13950i
$378$		−	11.9664i		−	0.615485i
$379$	23.2093	−	13.3999i	1.19218	−	0.688308i	0.233382	−	0.972385i	$-0.425021\pi$
$379$	23.2093	−	13.3999i	1.19218	−	0.688308i	0.958801	+	0.284077i	$0.0916873\pi$
$380$	4.10472	−	3.79491i	0.210568	−	0.194675i
$381$		−	10.9653i		−	0.561769i
$382$	2.54904	+	0.683014i	0.130420	+	0.0349460i
$383$	1.80031	+	1.03941i	0.0919915	+	0.0531113i	0.545290	−	0.838247i	$-0.316420\pi$
$383$	1.80031	+	1.03941i	0.0919915	+	0.0531113i	−0.453299	+	0.891359i	$0.649753\pi$
$384$	−1.07313	−	1.07313i	−0.0547630	−	0.0547630i
$385$	−1.75614	+	5.65715i	−0.0895014	+	0.288315i
$386$	9.88101	+	17.1144i	0.502930	+	0.871101i
$387$	−2.30349	−	3.98976i	−0.117093	−	0.202811i
$388$	0.201424	−	0.348877i	0.0102258	−	0.0177116i
$389$	6.45889	+	24.1049i	0.327479	+	1.22217i	0.911797	+	0.410642i	$0.134695\pi$
$389$	6.45889	+	24.1049i	0.327479	+	1.22217i	−0.584318	+	0.811525i	$0.698638\pi$
$390$	13.5051	+	4.19238i	0.683857	+	0.212289i
$391$	37.1312	−	21.4377i	1.87781	−	1.08415i
$392$	1.22535	+	2.12237i	0.0618896	+	0.107196i
$393$			6.18907i			0.312197i
$394$	11.6260	−	3.11519i	0.585712	−	0.156941i
$395$	−3.74613	−	1.16291i	−0.188488	−	0.0585123i
$396$	0.865388			0.0434874
$397$	−6.29578	−	6.29578i	−0.315976	−	0.315976i	0.531243	−	0.847219i	$-0.321725\pi$
$397$	−6.29578	−	6.29578i	−0.315976	−	0.315976i	−0.847219	+	0.531243i	$0.821725\pi$
$398$	−1.74988	−	0.468880i	−0.0877137	−	0.0235028i
$399$	5.72224	+	5.72224i	0.286470	+	0.286470i
$400$	−2.83144	+	4.12104i	−0.141572	+	0.206052i
$401$	15.3810	−	15.3810i	0.768091	−	0.768091i	−0.209680	−	0.977770i	$-0.567242\pi$
$401$	15.3810	−	15.3810i	0.768091	−	0.768091i	0.977770	+	0.209680i	$0.0672421\pi$
$402$	12.8989	+	7.44720i	0.643340	+	0.371433i
$403$	38.2919	−	10.2603i	1.90746	−	0.511101i
$404$	8.91319	+	5.14603i	0.443448	+	0.256025i
$405$	−6.68943	−	12.7123i	−0.332400	−	0.631678i
$406$		−	22.0135i		−	1.09251i
$407$	7.51948	−	0.729034i	0.372727	−	0.0361369i
$408$	−6.06986	−	6.06986i	−0.300503	−	0.300503i
$409$	8.95667	−	33.4267i	0.442879	−	1.65285i	−0.278598	−	0.960408i	$-0.589870\pi$
$409$	8.95667	−	33.4267i	0.442879	−	1.65285i	0.721477	−	0.692438i	$-0.243464\pi$
$410$	6.43232	−	10.1962i	0.317670	−	0.503557i
$411$	−13.7389	−	7.93214i	−0.677689	−	0.391264i
$412$	3.94789	−	6.83795i	0.194499	−	0.336882i
$413$		−	25.9466i		−	1.27675i
$414$	−4.57411	−	2.64086i	−0.224805	−	0.129791i
$415$	−0.173520	−	0.187686i	−0.00851776	−	0.00921313i
$416$	−2.08350	−	3.60872i	−0.102152	−	0.176932i
$417$	−22.7338	+	22.7338i	−1.11328	+	1.11328i
$418$	−2.19555	+	2.19555i	−0.107388	+	0.107388i
$419$	−33.4282	+	19.2998i	−1.63307	+	0.942855i	−0.649935	+	0.759990i	$0.725204\pi$
$419$	−33.4282	+	19.2998i	−1.63307	+	0.942855i	−0.983138	+	0.182865i	$0.941463\pi$
$420$	−6.12175	−	3.86192i	−0.298711	−	0.188442i
$421$	−10.7713	+	10.7713i	−0.524962	+	0.524962i	−0.919066	−	0.394104i	$-0.871055\pi$
$421$	−10.7713	+	10.7713i	−0.524962	+	0.524962i	0.394104	+	0.919066i	$0.371055\pi$
$422$	1.74801	−	1.00922i	0.0850920	−	0.0491279i
$423$	−0.857852	+	3.20155i	−0.0417102	+	0.155665i
$424$	6.96219	+	1.86551i	0.338114	+	0.0905973i
$425$	−16.0152	+	23.3094i	−0.776851	+	1.13067i
$426$	14.3860	−	3.85473i	0.697006	−	0.186762i
$427$	1.99585	−	1.15230i	0.0965860	−	0.0557639i
$428$	3.28169	+	0.879327i	0.158627	+	0.0425039i
$429$	−7.58670	−	2.03285i	−0.366289	−	0.0981469i
$430$	−14.7732	−	0.579375i	−0.712428	−	0.0279399i
$431$	2.95967	+	11.0456i	0.142562	+	0.532050i	0.999852	+	0.0172153i	$0.00548006\pi$
$431$	2.95967	+	11.0456i	0.142562	+	0.532050i	−0.857289	+	0.514835i	$0.827853\pi$
$432$	−1.45207	+	5.41920i	−0.0698627	+	0.260731i
$433$	22.3552	+	22.3552i	1.07432	+	1.07432i	0.997007	+	0.0773168i	$0.0246353\pi$
$433$	22.3552	+	22.3552i	1.07432	+	1.07432i	0.0773168	+	0.997007i	$0.475365\pi$
$434$	−20.2914			−0.974020
$435$	−16.3101	−	30.9949i	−0.782009	−	1.48609i
$436$	−2.52989	+	2.52989i	−0.121160	+	0.121160i
$437$	18.3049	−	4.90479i	0.875643	−	0.234628i
$438$	−23.0718			−1.10241
$439$	10.0097	−	2.68209i	0.477737	−	0.128009i	−0.0119114	−	0.999929i	$-0.503792\pi$
$439$	10.0097	−	2.68209i	0.477737	−	0.128009i	0.489649	+	0.871920i	$0.337125\pi$
$440$	1.48177	−	2.34884i	0.0706407	−	0.111977i
$441$	0.853794	−	1.47882i	0.0406569	−	0.0704198i
$442$	−11.7847	−	20.4117i	−0.560540	−	0.970883i
$443$	−10.5760	+	10.5760i	−0.502480	+	0.502480i	−0.912208	−	0.409728i	$-0.865624\pi$
$443$	−10.5760	+	10.5760i	−0.502480	+	0.502480i	0.409728	+	0.912208i	$0.365624\pi$
$444$	−1.51764	+	9.10583i	−0.0720239	+	0.432143i
$445$	−10.8065	−	11.6888i	−0.512279	−	0.554100i
$446$	−13.5298	−	3.62529i	−0.640653	−	0.171663i
$447$	−26.2575	+	7.03568i	−1.24194	+	0.332776i
$448$	0.552037	+	2.06023i	0.0260813	+	0.0973368i
$449$	−9.97134	−	37.2136i	−0.470577	−	1.75622i	−0.637705	−	0.770281i	$-0.720116\pi$
$449$	−9.97134	−	37.2136i	−0.470577	−	1.75622i	0.167128	−	0.985935i	$-0.446551\pi$
$450$	3.47317	+	0.272841i	0.163727	+	0.0128618i
$451$	−3.34806	+	5.79901i	−0.157654	+	0.273065i
$452$	−3.98984			−0.187666
$453$	−2.24888	+	8.39293i	−0.105662	+	0.394334i
$454$		−	19.7868i		−	0.928642i
$455$	−13.4914	−	14.5928i	−0.632485	−	0.684119i
$456$	−1.89705	−	3.28579i	−0.0888375	−	0.153871i
$457$	16.2870	−	28.2100i	0.761875	−	1.31961i	−0.180008	−	0.983665i	$-0.557612\pi$
$457$	16.2870	−	28.2100i	0.761875	−	1.31961i	0.941883	−	0.335941i	$-0.109054\pi$
$458$	7.55560			0.353050
$459$	−8.21320	+	30.6521i	−0.383359	+	1.43072i
$460$	−14.9999	+	7.89323i	−0.699375	+	0.368024i
$461$	2.39516	−	8.93886i	0.111554	−	0.416324i	−0.887452	−	0.460900i	$-0.847527\pi$
$461$	2.39516	−	8.93886i	0.111554	−	0.416324i	0.999006	+	0.0445754i	$0.0141935\pi$
$462$	3.48168	+	2.01015i	0.161983	+	0.0935207i
$463$	18.2579	+	10.5412i	0.848518	+	0.489892i	0.860150	−	0.510040i	$-0.170370\pi$
$463$	18.2579	+	10.5412i	0.848518	+	0.489892i	−0.0116328	+	0.999932i	$0.503703\pi$
$464$	−2.67124	+	9.96921i	−0.124009	+	0.462809i
$465$	−28.5703	+	15.0342i	−1.32492	+	0.697194i
$466$	3.63311	−	13.5590i	0.168301	−	0.628107i
$467$	−25.5763			−1.18353			−0.591764	−	0.806111i	$-0.701568\pi$
$467$	−25.5763			−1.18353			−0.591764	+	0.806111i	$0.701568\pi$
$468$	−1.45173	+	2.51446i	−0.0671061	+	0.116231i
$469$	−10.4664	−	18.1283i	−0.483293	−	0.837088i
$470$	7.22080	+	7.81028i	0.333071	+	0.360262i
$471$			11.0451i			0.508930i
$472$	−3.14851	+	11.7504i	−0.144922	+	0.540855i
$473$	8.21188			0.377583
$474$	−1.33111	+	2.30555i	−0.0611399	+	0.105897i
$475$	−9.50392	+	8.11948i	−0.436070	+	0.372548i
$476$	3.12243	+	11.6531i	0.143117	+	0.534118i
$477$	−1.29984	−	4.85108i	−0.0595157	−	0.222116i
$478$	8.58662	−	2.30078i	0.392743	−	0.105235i
$479$	7.17989	+	1.92385i	0.328058	+	0.0879027i	0.419089	−	0.907945i	$-0.362350\pi$
$479$	7.17989	+	1.92385i	0.328058	+	0.0879027i	−0.0910312	+	0.995848i	$0.529016\pi$
$480$	2.30372	+	2.49179i	0.105150	+	0.113734i
$481$	−10.4960	+	23.0715i	−0.478576	+	1.05197i
$482$	6.44633	−	6.44633i	0.293622	−	0.293622i
$483$	−12.2686	−	21.2498i	−0.558239	−	0.966898i
$484$	4.72873	−	8.19040i	0.214942	−	0.372291i
$485$	−0.480624	+	0.761864i	−0.0218240	+	0.0345945i
$486$	6.84022	−	1.83283i	0.310279	−	0.0831389i
$487$	−8.24270			−0.373512			−0.186756	−	0.982406i	$-0.559797\pi$
$487$	−8.24270			−0.373512			−0.186756	+	0.982406i	$0.559797\pi$
$488$	−1.04368	+	0.279654i	−0.0472454	+	0.0126594i
$489$	19.0449	−	19.0449i	0.861238	−	0.861238i
$490$	−2.55189	−	4.84950i	−0.115283	−	0.219078i
$491$	−16.2420			−0.732990			−0.366495	−	0.930420i	$-0.619442\pi$
$491$	−16.2420			−0.732990			−0.366495	+	0.930420i	$0.619442\pi$
$492$	−5.78573	−	5.78573i	−0.260841	−	0.260841i
$493$	−15.1091	+	56.3879i	−0.680479	+	2.53958i
$494$	−2.69625	−	10.0625i	−0.121310	−	0.452734i
$495$	−1.93358	−	0.0758309i	−0.0869079	−	0.00340835i
$496$	9.18935	+	2.46228i	0.412614	+	0.110560i
$497$	−20.2183	−	5.41749i	−0.906916	−	0.243007i
$498$	−0.150241	+	0.0867414i	−0.00673244	+	0.00388698i
$499$	15.4708	−	4.14540i	0.692570	−	0.185574i	0.104670	−	0.994507i	$-0.466621\pi$
$499$	15.4708	−	4.14540i	0.692570	−	0.185574i	0.587900	+	0.808934i	$0.299955\pi$
$500$	6.68753	−	8.95974i	0.299076	−	0.400692i
$501$	14.6745	+	3.93203i	0.655611	+	0.175670i
$502$	−0.105017	+	0.391930i	−0.00468716	+	0.0174927i
$503$	25.4176	−	14.6748i	1.13331	−	0.654318i	0.188547	−	0.982064i	$-0.439622\pi$
$503$	25.4176	−	14.6748i	1.13331	−	0.654318i	0.944766	+	0.327746i	$0.106289\pi$
$504$	1.05087	−	1.05087i	0.0468095	−	0.0468095i
$505$	−19.4643	−	12.2791i	−0.866148	−	0.546412i
$506$	8.15328	−	4.70730i	0.362458	−	0.209265i
$507$	4.68294	−	4.68294i	0.207977	−	0.207977i
$508$	5.10901	−	5.10901i	0.226676	−	0.226676i
$509$	−3.64938	−	6.32090i	−0.161756	−	0.280169i	0.773743	−	0.633500i	$-0.218382\pi$
$509$	−3.64938	−	6.32090i	−0.161756	−	0.280169i	−0.935498	+	0.353331i	$0.885049\pi$
$510$	13.0303	+	14.0941i	0.576991	+	0.624096i
$511$	28.0813	+	16.2127i	1.24224	+	0.717208i
$512$		−	1.00000i		−	0.0441942i
$513$	−7.01297	+	12.1468i	−0.309630	+	0.536295i
$514$	−13.0671	−	7.54430i	−0.576365	−	0.332765i
$515$	−9.42016	+	14.9324i	−0.415102	+	0.658002i
$516$	−2.59710	+	9.69251i	−0.114331	+	0.426689i
$517$	−4.17761	−	4.17761i	−0.183731	−	0.183731i
$518$	8.24588	−	10.0165i	0.362303	−	0.440098i
$519$		−	3.87402i		−	0.170051i
$520$	4.33904	+	8.24571i	0.190279	+	0.361598i
$521$	−17.5971	−	10.1597i	−0.770942	−	0.445104i	0.0622684	−	0.998059i	$-0.480167\pi$
$521$	−17.5971	−	10.1597i	−0.770942	−	0.445104i	−0.833211	+	0.552956i	$0.813500\pi$
$522$	6.94629	−	1.86125i	0.304031	−	0.0814648i
$523$	−6.63703	−	3.83189i	−0.290217	−	0.167557i	0.347823	−	0.937560i	$-0.386921\pi$
$523$	−6.63703	−	3.83189i	−0.290217	−	0.167557i	−0.638040	+	0.770003i	$0.720254\pi$
$524$	−2.88365	+	2.88365i	−0.125973	+	0.125973i
$525$	13.3397	+	9.16531i	0.582194	+	0.400007i
$526$	−14.5231	−	14.5231i	−0.633236	−	0.633236i
$527$	51.9768	+	13.9271i	2.26415	+	0.606676i
$528$	−1.33282	−	1.33282i	−0.0580036	−	0.0580036i
$529$	−34.4602			−1.49827
$530$	−15.3925	−	4.77828i	−0.668608	−	0.207555i
$531$	8.18737	−	2.19380i	0.355302	−	0.0952028i
$532$			5.33228i			0.231184i
$533$	−11.2330	−	19.4562i	−0.486557	−	0.842741i
$534$	−9.35673	+	5.40211i	−0.404905	+	0.233772i
$535$	−7.25540	−	2.25229i	−0.313678	−	0.0973750i
$536$	2.54010	+	9.47979i	0.109716	+	0.409465i
$537$	−4.19084	+	7.25875i	−0.180848	+	0.313238i
$538$	3.30393	+	5.72257i	0.142442	+	0.246717i
$539$	1.52188	+	2.63597i	0.0655519	+	0.113539i
$540$	3.71930	−	11.9811i	0.160053	−	0.515586i
$541$	29.5324	+	29.5324i	1.26970	+	1.26970i	0.946245	+	0.323450i	$0.104843\pi$
$541$	29.5324	+	29.5324i	1.26970	+	1.26970i	0.323450	+	0.946245i	$0.395157\pi$
$542$	11.9597	+	6.90495i	0.513714	+	0.296593i
$543$	−30.5567	−	8.18764i	−1.31131	−	0.351365i
$544$		−	5.65620i		−	0.242508i
$545$	5.87434	−	5.43097i	0.251629	−	0.232637i
$546$	−11.6814	+	6.74424i	−0.499916	+	0.288627i
$547$		−	6.72856i		−	0.287693i	−0.989600	−	0.143846i	$-0.954053\pi$
$547$		−	6.72856i		−	0.287693i	0.989600	−	0.143846i	$-0.0459471\pi$
$548$	−2.70551	−	10.0971i	−0.115573	−	0.431326i
$549$	0.532357	+	0.532357i	0.0227204	+	0.0227204i
$550$	−3.51662	+	5.11829i	−0.149949	+	0.218245i
$551$	−12.9011	+	22.3454i	−0.549606	+	0.951946i
$552$	2.97747	+	11.1121i	0.126730	+	0.472962i
$553$	3.24025	−	1.87076i	0.137789	−	0.0795528i
$554$	−0.231435			−0.00983274
$555$	4.18885	−	20.2126i	0.177807	−	0.857978i
$556$	−21.1845			−0.898424
$557$	0.851828	−	0.491803i	0.0360931	−	0.0208384i	−0.481845	−	0.876257i	$-0.660033\pi$
$557$	0.851828	−	0.491803i	0.0360931	−	0.0208384i	0.517938	+	0.855418i	$0.326700\pi$
$558$	−1.71565	−	6.40290i	−0.0726294	−	0.271057i
$559$	−13.7758	+	23.8604i	−0.582654	+	1.00919i
$560$	−1.05291	−	4.65165i	−0.0444937	−	0.196568i
$561$	−7.53870	−	7.53870i	−0.318284	−	0.318284i
$562$	4.01948	+	15.0009i	0.169552	+	0.632775i
$563$		−	31.0003i		−	1.30651i	−0.757139	−	0.653254i	$-0.773403\pi$
$563$		−	31.0003i		−	1.30651i	0.757139	−	0.653254i	$-0.226597\pi$
$564$	6.25206	−	3.60963i	0.263259	−	0.151993i
$565$	8.91470	+	0.349616i	0.375044	+	0.0147085i
$566$			30.7596i			1.29292i
$567$	13.2353	+	3.54639i	0.555830	+	0.148934i
$568$	8.49885	+	4.90681i	0.356604	+	0.205885i
$569$	5.62158	+	5.62158i	0.235669	+	0.235669i	0.815054	−	0.579385i	$-0.196707\pi$
$569$	5.62158	+	5.62158i	0.235669	+	0.235669i	−0.579385	+	0.815054i	$0.696707\pi$
$570$	3.95075	+	7.50783i	0.165479	+	0.314469i
$571$	−7.18338	−	12.4420i	−0.300615	−	0.520680i	0.675660	−	0.737213i	$-0.263859\pi$
$571$	−7.18338	−	12.4420i	−0.300615	−	0.520680i	−0.976275	+	0.216533i	$0.930525\pi$
$572$	−2.58768	−	4.48200i	−0.108196	−	0.187402i
$573$	−2.00249	+	3.46842i	−0.0836554	+	0.144895i
$574$	2.97628	+	11.1076i	0.124227	+	0.463623i
$575$	34.2068	−	16.3218i	1.42652	−	0.680668i
$576$	−0.603425	+	0.348387i	−0.0251427	+	0.0145161i
$577$	−0.183869	−	0.318471i	−0.00765458	−	0.0132581i	0.862173	−	0.506614i	$-0.169103\pi$
$577$	−0.183869	−	0.318471i	−0.00765458	−	0.0132581i	−0.869827	+	0.493356i	$0.835770\pi$
$578$		−	14.9926i		−	0.623612i
$579$	−28.9697	+	7.76240i	−1.20394	+	0.322594i
$580$	6.84206	−	22.0406i	0.284101	−	0.915187i
$581$	0.243815			0.0101152
$582$	0.432310	+	0.432310i	0.0179198	+	0.0179198i
$583$	8.64698	+	2.31695i	0.358121	+	0.0959583i
$584$	−10.7498	−	10.7498i	−0.444828	−	0.444828i
$585$	3.46400	−	5.49098i	0.143219	−	0.227024i
$586$	−4.47404	+	4.47404i	−0.184821	+	0.184821i
$587$	−2.89163	−	1.66948i	−0.119350	−	0.0689068i	0.439136	−	0.898420i	$-0.355284\pi$
$587$	−2.89163	−	1.66948i	−0.119350	−	0.0689068i	−0.558487	+	0.829514i	$0.688618\pi$
$588$	−3.59255	+	0.962621i	−0.148154	+	0.0396978i
$589$	20.5974	+	11.8919i	0.848701	+	0.489998i
$590$	8.06451	−	25.9786i	0.332011	−	1.06952i
$591$			18.2665i			0.751385i
$592$	−4.94975	+	3.53553i	−0.203433	+	0.145310i
$593$	−30.9214	−	30.9214i	−1.26979	−	1.26979i	−0.946196	−	0.323595i	$-0.895108\pi$
$593$	−30.9214	−	30.9214i	−1.26979	−	1.26979i	−0.323595	−	0.946196i	$-0.604892\pi$
$594$	−1.80346	+	6.73059i	−0.0739967	+	0.276160i
$595$	−5.95549	−	26.3107i	−0.244151	−	1.07863i
$596$	−15.5122	−	8.95595i	−0.635403	−	0.366850i
$597$	1.37469	−	2.38103i	0.0562622	−	0.0974489i
$598$			31.5868i			1.29168i
$599$	−10.3730	−	5.98884i	−0.423828	−	0.244697i	0.272886	−	0.962047i	$-0.412022\pi$
$599$	−10.3730	−	5.98884i	−0.423828	−	0.244697i	−0.696714	+	0.717349i	$0.745355\pi$
$600$	−4.92897	−	5.76939i	−0.201224	−	0.235535i
$601$	−2.65131	−	4.59220i	−0.108149	−	0.187320i	0.806871	−	0.590727i	$-0.201159\pi$
$601$	−2.65131	−	4.59220i	−0.108149	−	0.187320i	−0.915020	+	0.403407i	$0.867826\pi$
$602$	9.97197	−	9.97197i	0.406427	−	0.406427i
$603$	4.83540	−	4.83540i	0.196913	−	0.196913i
$604$	−4.95829	+	2.86267i	−0.201750	+	0.116480i
$605$	−11.2833	+	17.8859i	−0.458733	+	0.727164i
$606$	−11.0447	+	11.0447i	−0.448662	+	0.448662i
$607$	20.5512	−	11.8652i	0.834148	−	0.481595i	−0.0211229	−	0.999777i	$-0.506724\pi$
$607$	20.5512	−	11.8652i	0.834148	−	0.481595i	0.855271	+	0.518181i	$0.173391\pi$
$608$	0.647049	−	2.41482i	0.0262413	−	0.0979338i
$609$	32.2701	+	8.64676i	1.30765	+	0.350384i
$610$	2.35646	−	0.533391i	0.0954103	−	0.0215964i
$611$	19.1465	−	5.13030i	0.774586	−	0.207550i
$612$	−3.41309	+	1.97055i	−0.137966	+	0.0796548i
$613$	31.6675	+	8.48528i	1.27904	+	0.342717i	0.833487	−	0.552539i	$-0.186341\pi$
$613$	31.6675	+	8.48528i	1.27904	+	0.342717i	0.445551	+	0.895256i	$0.353008\pi$
$614$	−18.0109	−	4.82599i	−0.726859	−	0.194761i
$615$	12.4204	+	13.4343i	0.500837	+	0.541724i
$616$	0.685625	+	2.55879i	0.0276246	+	0.103096i
$617$	−10.9431	+	40.8403i	−0.440553	+	1.64417i	0.286863	+	0.957972i	$0.407387\pi$
$617$	−10.9431	+	40.8403i	−0.440553	+	1.64417i	−0.727417	+	0.686196i	$0.759279\pi$
$618$	8.47322	+	8.47322i	0.340843	+	0.340843i
$619$	−26.3358			−1.05853			−0.529263	−	0.848458i	$-0.677532\pi$
$619$	−26.3358			−1.05853			−0.529263	+	0.848458i	$0.677532\pi$
$620$	−20.3165	−	6.30682i	−0.815929	−	0.253288i
$621$	30.0718	−	30.0718i	1.20674	−	1.20674i
$622$	−1.39722	+	0.374385i	−0.0560235	+	0.0150115i
$623$	15.1844			0.608350
$624$	6.10850	−	1.63677i	0.244536	−	0.0655231i
$625$	−15.7274	+	19.4332i	−0.629096	+	0.777327i
$626$	3.02756	−	5.24388i	0.121006	−	0.209588i
$627$	−2.35612	−	4.08092i	−0.0940944	−	0.162976i
$628$	−5.14618	+	5.14618i	−0.205355	+	0.205355i
$629$	−27.9968	+	19.9977i	−1.11630	+	0.797361i
$630$	−2.44010	+	2.25593i	−0.0972158	+	0.0898784i
$631$	−25.9691	−	6.95841i	−1.03381	−	0.277010i	−0.298267	−	0.954483i	$-0.596409\pi$
$631$	−25.9691	−	6.95841i	−1.03381	−	0.277010i	−0.735548	+	0.677473i	$0.763075\pi$
$632$	−1.69441	+	0.454017i	−0.0674002	+	0.0180598i
$633$	0.792828	+	2.95887i	0.0315121	+	0.117605i
$634$	−4.63520	−	17.2988i	−0.184087	−	0.687023i
$635$	−11.8630	+	10.9676i	−0.470769	+	0.435238i
$636$	−5.46941	+	9.47329i	−0.216876	+	0.375641i
$637$	−10.2121			−0.404617
$638$	−3.31766	+	12.3817i	−0.131347	+	0.490195i
$639$		−	6.83789i		−	0.270503i
$640$	−0.0876265	+	2.23435i	−0.00346374	+	0.0883205i
$641$	−7.65325	−	13.2558i	−0.302285	−	0.523573i	0.674368	−	0.738395i	$-0.264416\pi$
$641$	−7.65325	−	13.2558i	−0.302285	−	0.523573i	−0.976653	+	0.214822i	$0.931083\pi$
$642$	−2.57806	+	4.46533i	−0.101748	+	0.176232i
$643$	36.8625			1.45372			0.726858	−	0.686788i	$-0.240980\pi$
$643$	36.8625			1.45372			0.726858	+	0.686788i	$0.240980\pi$
$644$	4.18458	−	15.6171i	0.164896	−	0.615398i
$645$	6.65215	−	21.4289i	0.261928	−	0.843761i
$646$	3.65984	−	13.6587i	0.143994	−	0.537395i
$647$	−31.6509	−	18.2737i	−1.24433	−	0.718413i	−0.274355	−	0.961629i	$-0.588464\pi$
$647$	−31.6509	−	18.2737i	−1.24433	−	0.718413i	−0.969972	+	0.243216i	$0.921798\pi$
$648$	−5.56350	−	3.21209i	−0.218555	−	0.126183i
$649$	−3.91041	+	14.5939i	−0.153497	+	0.572859i
$650$	−8.97239	−	18.8040i	−0.351926	−	0.737555i
$651$	7.97035	−	29.7457i	0.312383	−	1.16583i
$652$	17.7470			0.695025
$653$	1.49778	−	2.59423i	0.0586126	−	0.101520i	−0.835230	−	0.549900i	$-0.814666\pi$
$653$	1.49778	−	2.59423i	0.0586126	−	0.101520i	0.893843	+	0.448380i	$0.147999\pi$
$654$	−2.71490	−	4.70235i	−0.106161	−	0.183876i
$655$	6.69576	−	6.19039i	0.261625	−	0.241879i
$656$		−	5.39144i		−	0.210500i
$657$	−2.74159	+	10.2317i	−0.106960	+	0.399179i
$658$	−10.1460			−0.395533
$659$	−8.79071	+	15.2259i	−0.342437	+	0.593119i	−0.984885	−	0.173211i	$-0.944586\pi$
$659$	−8.79071	+	15.2259i	−0.342437	+	0.593119i	0.642447	+	0.766330i	$0.277919\pi$
$660$	2.86120	+	3.09478i	0.111372	+	0.120464i
$661$	−6.22906	−	23.2472i	−0.242282	−	0.904210i	−0.974730	−	0.223386i	$-0.928289\pi$
$661$	−6.22906	−	23.2472i	−0.242282	−	0.904210i	0.732448	−	0.680823i	$-0.238378\pi$
$662$	1.42272	+	5.30966i	0.0552955	+	0.206366i
$663$	34.5509	−	9.25789i	1.34185	−	0.359547i
$664$	−0.110416	−	0.0295859i	−0.00428497	−	0.00114816i
$665$	0.467249	−	11.9142i	0.0181191	−	0.462012i
$666$	3.85786	+	1.75506i	0.149489	+	0.0680073i
$667$	55.3204	−	55.3204i	2.14201	−	2.14201i
$668$	5.00522	+	8.66929i	0.193658	+	0.335425i
$669$	10.6288	−	18.4097i	0.410934	−	0.711758i
$670$	−4.84480	−	21.4038i	−0.187171	−	0.826899i
$671$	−1.29625	+	0.347328i	−0.0500410	+	0.0134085i
$672$	−3.23698			−0.124869
$673$	13.0415	−	3.49445i	0.502712	−	0.134701i	0.00145339	−	0.999999i	$-0.499537\pi$
$673$	13.0415	−	3.49445i	0.502712	−	0.134701i	0.501258	+	0.865298i	$0.332871\pi$
$674$	5.33725	−	5.33725i	0.205583	−	0.205583i
$675$	−9.36008	+	26.4442i	−0.360270	+	1.01784i
$676$	4.36381			0.167839
$677$	−22.4520	−	22.4520i	−0.862902	−	0.862902i	0.128772	−	0.991674i	$-0.458896\pi$
$677$	−22.4520	−	22.4520i	−0.862902	−	0.862902i	−0.991674	+	0.128772i	$0.958896\pi$
$678$	1.56718	−	5.84881i	0.0601873	−	0.224622i
$679$	−0.222388	−	0.829962i	−0.00853445	−	0.0318510i
$680$	−0.495634	+	12.6379i	−0.0190067	+	0.484643i
$681$	29.0060	+	7.77214i	1.11151	+	0.297829i
$682$	11.4131	+	3.05813i	0.437030	+	0.117102i
$683$	−17.9138	+	10.3425i	−0.685453	+	0.395747i	−0.801906	−	0.597450i	$-0.796181\pi$
$683$	−17.9138	+	10.3425i	−0.685453	+	0.395747i	0.116453	+	0.993196i	$0.462847\pi$
$684$	−1.68258	+	0.450847i	−0.0643352	+	0.0172386i
$685$	5.16028	+	22.7975i	0.197164	+	0.871048i
$686$	19.4706	+	5.21714i	0.743392	+	0.199191i
$687$	−2.96779	+	11.0759i	−0.113228	+	0.422574i
$688$	−5.72604	+	3.30593i	−0.218303	+	0.126038i
$689$	−21.2378	+	21.2378i	−0.809096	+	0.809096i
$690$	−5.67901	−	25.0892i	−0.216196	−	0.955129i
$691$	−29.7824	+	17.1949i	−1.13297	+	0.654123i	−0.944681	−	0.327990i	$-0.893629\pi$
$691$	−29.7824	+	17.1949i	−1.13297	+	0.654123i	−0.188293	+	0.982113i	$0.560295\pi$
$692$	1.80501	−	1.80501i	0.0686160	−	0.0686160i
$693$	1.30517	−	1.30517i	0.0495794	−	0.0495794i
$694$	6.86734	+	11.8946i	0.260681	+	0.451512i
$695$	47.3337	+	1.85633i	1.79547	+	0.0704145i
$696$	−13.5649	−	7.83168i	−0.514175	−	0.296859i
$697$		−	30.4951i		−	1.15508i
$698$	3.07030	−	5.31791i	0.116212	−	0.201286i
$699$	18.4494	+	10.6517i	0.697819	+	0.402886i
$700$	1.94497	+	10.4857i	0.0735129	+	0.396321i
$701$	−6.71711	+	25.0686i	−0.253702	+	0.946827i	0.715107	+	0.699015i	$0.246378\pi$
$701$	−6.71711	+	25.0686i	−0.253702	+	0.946827i	−0.968808	+	0.247812i	$0.920289\pi$
$702$	−16.5310	−	16.5310i	−0.623922	−	0.623922i
$703$	−14.2404	+	5.33495i	−0.537087	+	0.201211i
$704$		−	1.24199i		−	0.0468093i
$705$	−14.2856	+	7.51732i	−0.538026	+	0.283119i
$706$	26.5075	+	15.3041i	0.997623	+	0.575978i
$707$	21.2040	−	5.68160i	0.797460	−	0.213679i
$708$	−15.9885	−	9.23095i	−0.600884	−	0.346920i
$709$	−7.52915	+	7.52915i	−0.282763	+	0.282763i	−0.834210	−	0.551447i	$-0.814076\pi$
$709$	−7.52915	+	7.52915i	−0.282763	+	0.282763i	0.551447	+	0.834210i	$0.314076\pi$
$710$	−18.5594	−	11.7083i	−0.696523	−	0.439403i
$711$	0.864278	+	0.864278i	0.0324129	+	0.0324129i
$712$	−6.87653	−	1.84256i	−0.257709	−	0.0690528i
$713$	−50.9929	−	50.9929i	−1.90970	−	1.90970i
$714$	−18.3090			−0.685198
$715$	5.38905	+	10.2411i	0.201539	+	0.382995i
$716$	−5.33466	+	1.42942i	−0.199366	+	0.0534199i
$717$			13.4911i			0.503834i
$718$	−5.44230	−	9.42634i	−0.203105	−	0.351788i
$719$	44.8295	−	25.8823i	1.67186	−	0.965248i	0.705262	−	0.708947i	$-0.250829\pi$
$719$	44.8295	−	25.8823i	1.67186	−	0.965248i	0.966597	−	0.256301i	$-0.0825039\pi$
$720$	1.37879	−	0.725543i	0.0513845	−	0.0270394i
$721$	−4.35877	−	16.2671i	−0.162329	−	0.605820i
$722$	−6.37499	+	11.0418i	−0.237253	+	0.410933i
$723$	6.91776	+	11.9819i	0.257274	+	0.445612i
$724$	−10.4223	−	18.0520i	−0.387342	−	0.670897i
$725$	−17.2189	+	48.6470i	−0.639494	+	1.80670i
$726$	10.1491	+	10.1491i	0.376669	+	0.376669i
$727$	−22.8390	−	13.1861i	−0.847052	−	0.489046i	0.0126028	−	0.999921i	$-0.495988\pi$
$727$	−22.8390	−	13.1861i	−0.847052	−	0.489046i	−0.859655	+	0.510875i	$0.829322\pi$
$728$	−8.58496	−	2.30033i	−0.318180	−	0.0852560i
$729$			30.0197i			1.11184i
$730$	23.0768	+	24.9607i	0.854109	+	0.923837i
$731$	−32.3877	+	18.6990i	−1.19790	+	0.691609i
$732$		−	1.63981i		−	0.0606091i
$733$	−9.72011	−	36.2759i	−0.359020	−	1.33988i	−0.875349	−	0.483492i	$-0.839368\pi$
$733$	−9.72011	−	36.2759i	−0.359020	−	1.33988i	0.516329	−	0.856391i	$-0.327298\pi$
$734$	9.00688	+	9.00688i	0.332450	+	0.332450i
$735$	8.11137	−	1.83603i	0.299192	−	0.0677230i
$736$	−3.79012	+	6.56469i	−0.139706	+	0.241978i
$737$	3.15478	+	11.7738i	0.116208	+	0.433694i
$738$	−3.25333	+	1.87831i	−0.119757	+	0.0691415i
$739$	39.7737			1.46310			0.731549	−	0.681788i	$-0.238798\pi$
$739$	39.7737			1.46310			0.731549	+	0.681788i	$0.238798\pi$
$740$	11.3693	−	7.46589i	0.417943	−	0.274452i
$741$	15.8100			0.580794
$742$	13.3139	−	7.68678i	0.488768	−	0.282190i
$743$	10.1080	+	37.7236i	0.370827	+	1.38395i	0.859347	+	0.511393i	$0.170870\pi$
$743$	10.1080	+	37.7236i	0.370827	+	1.38395i	−0.488520	+	0.872553i	$0.662463\pi$
$744$	−7.21903	+	12.5037i	−0.264663	+	0.458409i
$745$	33.8748	+	21.3700i	1.24108	+	0.782937i
$746$	−12.2369	−	12.2369i	−0.448023	−	0.448023i
$747$	0.0206147	+	0.0769351i	0.000754252	+	0.00281491i
$748$		−	7.02495i		−	0.256858i
$749$	6.27563	−	3.62323i	0.229306	−	0.132390i
$750$	10.5075	+	13.3228i	0.383679	+	0.486478i
$751$		−	21.9626i		−	0.801428i	−0.916203	−	0.400714i	$-0.868762\pi$
$751$		−	21.9626i		−	0.801428i	0.916203	−	0.400714i	$-0.131238\pi$
$752$	4.59481	+	1.23118i	0.167556	+	0.0448964i
$753$	−0.533290	−	0.307895i	−0.0194342	−	0.0112203i
$754$	−30.4106	−	30.4106i	−1.10749	−	1.10749i
$755$	11.3294	−	5.96173i	0.412319	−	0.216970i
$756$	5.98320	+	10.3632i	0.217607	+	0.376906i
$757$	0.0633581	+	0.109739i	0.00230279	+	0.00398855i	0.867175	−	0.498004i	$-0.165934\pi$
$757$	0.0633581	+	0.109739i	0.00230279	+	0.00398855i	−0.864872	+	0.501993i	$0.832600\pi$
$758$	−13.3999	+	23.2093i	−0.486707	+	0.843001i
$759$	3.69800	+	13.8011i	0.134229	+	0.500948i
$760$	−1.65734	+	5.33885i	−0.0601179	+	0.193661i
$761$	9.07376	−	5.23874i	0.328923	−	0.189904i	−0.326440	−	0.945218i	$-0.605849\pi$
$761$	9.07376	−	5.23874i	0.328923	−	0.189904i	0.655363	+	0.755314i	$0.272516\pi$
$762$	5.48265	+	9.49623i	0.198615	+	0.344012i
$763$			7.63111i			0.276265i
$764$	−2.54904	+	0.683014i	−0.0922211	+	0.0247106i
$765$	7.79872	−	4.10382i	0.281963	−	0.148374i
$766$	−2.07882			−0.0751107
$767$	−35.8439	−	35.8439i	−1.29425	−	1.29425i
$768$	1.46593	+	0.392794i	0.0528970	+	0.0141737i
$769$	25.1503	+	25.1503i	0.906945	+	0.906945i	0.996024	−	0.0890797i	$-0.0283926\pi$
$769$	25.1503	+	25.1503i	0.906945	+	0.906945i	−0.0890797	+	0.996024i	$0.528393\pi$
$770$	−1.30771	−	5.77731i	−0.0471266	−	0.208200i
$771$	16.1921	−	16.1921i	0.583142	−	0.583142i
$772$	−17.1144	−	9.88101i	−0.615961	−	0.355625i
$773$	43.6165	−	11.6870i	1.56878	−	0.420352i	0.633348	−	0.773867i	$-0.281680\pi$
$773$	43.6165	−	11.6870i	1.56878	−	0.420352i	0.935429	+	0.353515i	$0.115014\pi$
$774$	3.98976	+	2.30349i	0.143409	+	0.0827972i
$775$	44.8414	+	15.8719i	1.61075	+	0.570136i
$776$			0.402849i			0.0144614i
$777$	11.4445	+	16.0222i	0.410568	+	0.574795i
$778$	−17.6460	−	17.6460i	−0.632640	−	0.632640i
$779$	3.48852	−	13.0194i	0.124989	−	0.466467i
$780$	−13.7919	+	3.12184i	−0.493831	+	0.111780i
$781$	10.5555	+	6.09422i	0.377705	+	0.218068i
$782$	−21.4377	+	37.1312i	−0.766611	+	1.32781i
$783$			57.9039i			2.06932i
$784$	−2.12237	−	1.22535i	−0.0757990	−	0.0437626i
$785$	11.9493	−	11.0474i	0.426489	−	0.394300i
$786$	−3.09453	−	5.35989i	−0.110378	−	0.191181i
$787$	4.28839	−	4.28839i	0.152865	−	0.152865i	−0.626532	−	0.779396i	$-0.715526\pi$
$787$	4.28839	−	4.28839i	0.152865	−	0.152865i	0.779396	+	0.626532i	$0.215526\pi$
$788$	−8.51085	+	8.51085i	−0.303187	+	0.303187i
$789$	26.9943	−	15.5852i	0.961024	−	0.554847i
$790$	3.82570	−	0.865957i	0.136112	−	0.0308094i
$791$	−6.01745	+	6.01745i	−0.213956	+	0.213956i
$792$	−0.749448	+	0.432694i	−0.0266305	+	0.0153751i
$793$	1.16532	−	4.34902i	0.0413816	−	0.154438i
$794$	8.60020	+	2.30442i	0.305210	+	0.0817807i
$795$	13.0507	−	20.6874i	0.462860	−	0.733706i
$796$	1.74988	−	0.468880i	0.0620230	−	0.0166190i
$797$	−46.5814	+	26.8938i	−1.65000	+	0.952628i	−0.672930	+	0.739706i	$0.734965\pi$
$797$	−46.5814	+	26.8938i	−1.65000	+	0.952628i	−0.977069	+	0.212922i	$0.931702\pi$
$798$	−7.81672	−	2.09449i	−0.276709	−	0.0741440i
$799$	25.9892	+	6.96378i	0.919432	+	0.246361i
$800$	0.391577	−	4.98464i	0.0138443	−	0.176234i
$801$	1.28385	+	4.79139i	0.0453626	+	0.169295i
$802$	−5.62984	+	21.0108i	−0.198796	+	0.741918i
$803$	−13.3511	−	13.3511i	−0.471150	−	0.471150i
$804$	−14.8944			−0.525285
$805$	−10.7183	+	34.5273i	−0.377770	+	1.21693i
$806$	−28.0316	+	28.0316i	−0.987372	+	0.987372i
$807$	−9.68662	+	2.59552i	−0.340985	+	0.0913667i
$808$	−10.2921			−0.362074
$809$	−4.87488	+	1.30622i	−0.171392	+	0.0459243i	−0.343494	−	0.939155i	$-0.611611\pi$
$809$	−4.87488	+	1.30622i	−0.171392	+	0.0459243i	0.172103	+	0.985079i	$0.444944\pi$
$810$	12.1494	+	7.66445i	0.426885	+	0.269301i
$811$	−0.576314	+	0.998205i	−0.0202371	+	0.0350517i	−0.875967	−	0.482372i	$-0.839775\pi$
$811$	−0.576314	+	0.998205i	−0.0202371	+	0.0350517i	0.855729	+	0.517423i	$0.173109\pi$
$812$	11.0067	+	19.0642i	0.386261	+	0.669024i
$813$	−14.8198	+	14.8198i	−0.519754	+	0.519754i
$814$	−6.14754	+	4.39110i	−0.215471	+	0.153908i
$815$	−39.6530	−	1.55511i	−1.38898	−	0.0544730i
$816$	8.29158	+	2.22172i	0.290263	+	0.0777758i
$817$	−15.9665	+	4.27820i	−0.558596	+	0.149675i
$818$	8.95667	+	33.4267i	0.313163	+	1.16874i
$819$	1.60281	+	5.98178i	0.0560069	+	0.209020i
$820$	−0.472433	+	12.0464i	−0.0164981	+	0.420677i
$821$	26.8808	−	46.5589i	0.938145	−	1.62492i	0.169218	−	0.985579i	$-0.445876\pi$
$821$	26.8808	−	46.5589i	0.938145	−	1.62492i	0.768927	−	0.639337i	$-0.220791\pi$
$822$	15.8643			0.553330
$823$	−12.3170	+	45.9677i	−0.429344	+	1.60233i	0.324907	+	0.945746i	$0.394667\pi$
$823$	−12.3170	+	45.9677i	−0.429344	+	1.60233i	−0.754251	+	0.656587i	$0.772000\pi$
$824$			7.89579i			0.275063i
$825$	−6.12173	−	7.16554i	−0.213131	−	0.249472i
$826$	12.9733	+	22.4704i	0.451399	+	0.781845i
$827$	−1.56275	+	2.70676i	−0.0543422	+	0.0941234i	−0.891917	−	0.452199i	$-0.850640\pi$
$827$	−1.56275	+	2.70676i	−0.0543422	+	0.0941234i	0.837575	+	0.546323i	$0.183973\pi$
$828$	5.28173			0.183553
$829$	1.17247	−	4.37573i	0.0407217	−	0.151975i	−0.942571	−	0.334005i	$-0.891600\pi$
$829$	1.17247	−	4.37573i	0.0407217	−	0.151975i	0.983293	+	0.182029i	$0.0582666\pi$
$830$	0.244116	+	0.0757806i	0.00847338	+	0.00263038i
$831$	0.0909062	−	0.339267i	0.00315350	−	0.0117690i
$832$	3.60872	+	2.08350i	0.125110	+	0.0722322i
$833$	−12.0046	−	6.93084i	−0.415934	−	0.240139i
$834$	8.32115	−	31.0549i	0.288138	−	1.07534i
$835$	−10.4237	−	19.8088i	−0.360729	−	0.685512i
$836$	0.803629	−	2.99918i	0.0277941	−	0.103729i
$837$	53.3743			1.84489
$838$	19.2998	−	33.4282i	0.666699	−	1.15476i
$839$	−1.29920	−	2.25028i	−0.0448534	−	0.0776884i	0.842727	−	0.538341i	$-0.180949\pi$
$839$	−1.29920	−	2.25028i	−0.0448534	−	0.0776884i	−0.887581	+	0.460653i	$0.847615\pi$
$840$	7.23255	+	0.283646i	0.249547	+	0.00978670i
$841$			77.5206i			2.67313i
$842$	3.94257	−	14.7139i	0.135870	−	0.507074i
$843$	−23.5690			−0.811761
$844$	−1.00922	+	1.74801i	−0.0347387	+	0.0601691i
$845$	−9.75027	−	0.382385i	−0.335420	−	0.0131545i
$846$	−0.857852	−	3.20155i	−0.0294936	−	0.110072i
$847$	−5.22087	−	19.4845i	−0.179391	−	0.669497i
$848$	−6.96219	+	1.86551i	−0.239083	+	0.0640620i
$849$	−45.0913	−	12.0822i	−1.54753	−	0.414659i
$850$	2.21484	−	28.1942i	0.0759683	−	0.967052i
$851$	45.8937	−	4.44952i	1.57321	−	0.152528i
$852$	−10.5313	+	10.5313i	−0.360797	+	0.360797i
$853$	2.72407	+	4.71823i	0.0932704	+	0.161549i	0.908885	−	0.417046i	$-0.136935\pi$
$853$	2.72407	+	4.71823i	0.0932704	+	0.161549i	−0.815615	+	0.578595i	$0.803601\pi$
$854$	−1.15230	+	1.99585i	−0.0394311	+	0.0682966i
$855$	3.79899	−	0.859911i	0.129923	−	0.0294083i
$856$	−3.28169	+	0.879327i	−0.112166	+	0.0300548i
$857$	18.8571			0.644145			0.322072	−	0.946715i	$-0.395621\pi$
$857$	18.8571			0.644145			0.322072	+	0.946715i	$0.395621\pi$
$858$	7.58670	−	2.03285i	0.259006	−	0.0694004i
$859$	−7.44096	+	7.44096i	−0.253882	+	0.253882i	−0.822560	−	0.568678i	$-0.807455\pi$
$859$	−7.44096	+	7.44096i	−0.253882	+	0.253882i	0.568678	+	0.822560i	$0.307455\pi$
$860$	13.0837	−	6.88486i	0.446150	−	0.234772i
$861$	−17.4520			−0.594762
$862$	−8.08597	−	8.08597i	−0.275409	−	0.275409i
$863$	5.09357	−	19.0095i	0.173387	−	0.647090i	−0.823433	−	0.567413i	$-0.807944\pi$
$863$	5.09357	−	19.0095i	0.173387	−	0.647090i	0.996821	−	0.0796772i	$-0.0253889\pi$
$864$	−1.45207	−	5.41920i	−0.0494004	−	0.184365i
$865$	−4.19118	+	3.87485i	−0.142504	+	0.131749i
$866$	−30.5378	−	8.18258i	−1.03772	−	0.278055i
$867$	21.9781	+	5.88902i	0.746416	+	0.200002i
$868$	17.5729	−	10.1457i	0.596463	−	0.344368i
$869$	−2.10445	+	0.563885i	−0.0713885	+	0.0191285i
$870$	29.6224	+	18.6874i	1.00429	+	0.633561i
$871$	−39.5022	−	10.5846i	−1.33848	−	0.358645i
$872$	0.926002	−	3.45589i	0.0313584	−	0.117031i
$873$	0.243089	−	0.140347i	0.00822731	−	0.00475004i
$874$	−13.4001	+	13.4001i	−0.453266	+	0.453266i
$875$	−3.42692	−	23.5991i	−0.115851	−	0.797796i
$876$	19.9808	−	11.5359i	0.675088	−	0.389762i
$877$	−10.4044	+	10.4044i	−0.351331	+	0.351331i	−0.860605	−	0.509274i	$-0.829914\pi$
$877$	−10.4044	+	10.4044i	−0.351331	+	0.351331i	0.509274	+	0.860605i	$0.329914\pi$
$878$	−7.32762	+	7.32762i	−0.247295	+	0.247295i
$879$	−4.80124	−	8.31599i	−0.161942	−	0.280491i
$880$	−0.108831	+	2.77504i	−0.00366870	+	0.0935467i
$881$	24.3451	+	14.0557i	0.820209	+	0.473548i	0.850488	−	0.525994i	$-0.176306\pi$
$881$	24.3451	+	14.0557i	0.820209	+	0.473548i	−0.0302797	+	0.999541i	$0.509640\pi$
$882$			1.70759i			0.0574975i
$883$	2.79091	−	4.83400i	0.0939216	−	0.162677i	−0.815236	−	0.579128i	$-0.803393\pi$
$883$	2.79091	−	4.83400i	0.0939216	−	0.162677i	0.909158	+	0.416451i	$0.136726\pi$
$884$	20.4117	+	11.7847i	0.686518	+	0.396361i
$885$	34.9150	+	22.0262i	1.17365	+	0.740402i
$886$	3.87108	−	14.4471i	0.130051	−	0.485359i
$887$	−12.3904	−	12.3904i	−0.416030	−	0.416030i	0.467803	−	0.883833i	$-0.345046\pi$
$887$	−12.3904	−	12.3904i	−0.416030	−	0.416030i	−0.883833	+	0.467803i	$0.845046\pi$
$888$	−3.23860	−	8.64470i	−0.108680	−	0.290097i
$889$		−	15.4108i		−	0.516860i
$890$	15.2031	+	4.71949i	0.509609	+	0.158198i
$891$	−6.90982	−	3.98939i	−0.231488	−	0.133650i
$892$	13.5298	−	3.62529i	0.453010	−	0.121384i
$893$	10.2990	+	5.94613i	0.344643	+	0.198980i
$894$	19.2218	−	19.2218i	0.642874	−	0.642874i
$895$	12.0448	−	2.72636i	0.402612	−	0.0911323i
$896$	−1.50819	−	1.50819i	−0.0503852	−	0.0503852i
$897$	−46.3039	−	12.4071i	−1.54604	−	0.414261i
$898$	27.2422	+	27.2422i	0.909084	+	0.909084i
$899$	98.1878			3.27475
$900$	−3.14428	+	1.50030i	−0.104809	+	0.0500100i
$901$	−39.3796	+	10.5517i	−1.31192	+	0.351529i
$902$		−	6.69612i		−	0.222956i
$903$	10.7012	+	18.5351i	0.356115	+	0.616810i
$904$	3.45530	−	1.99492i	0.114922	−	0.0663501i
$905$	21.7053	+	41.2477i	0.721508	+	1.37112i
$906$	−2.24888	−	8.39293i	−0.0747140	−	0.278836i
$907$	−0.331736	+	0.574584i	−0.0110151	+	0.0190788i	−0.871480	−	0.490430i	$-0.836840\pi$
$907$	−0.331736	+	0.574584i	−0.0110151	+	0.0190788i	0.860465	+	0.509509i	$0.170173\pi$
$908$	9.89342	+	17.1359i	0.328325	+	0.568675i
$909$	3.58563	+	6.21049i	0.118928	+	0.205989i
$910$	18.9802	+	5.89202i	0.629189	+	0.195319i
$911$	−27.6384	−	27.6384i	−0.915702	−	0.915702i	0.0810110	−	0.996713i	$-0.474185\pi$
$911$	−27.6384	−	27.6384i	−0.915702	−	0.915702i	−0.996713	+	0.0810110i	$0.974185\pi$
$912$	3.28579	+	1.89705i	0.108803	+	0.0628176i
$913$	−0.137136	−	0.0367454i	−0.00453853	−	0.00121610i
$914$			32.5741i			1.07745i
$915$	−0.143691	+	3.66391i	−0.00475027	+	0.121125i
$916$	−6.54334	+	3.77780i	−0.216198	+	0.124822i
$917$			8.69820i			0.287240i
$918$	−8.21320	−	30.6521i	−0.271076	−	1.01167i
$919$	−16.7230	−	16.7230i	−0.551641	−	0.551641i	0.375273	−	0.926914i	$-0.377549\pi$
$919$	−16.7230	−	16.7230i	−0.551641	−	0.551641i	−0.926914	+	0.375273i	$0.877549\pi$
$920$	9.04371	−	14.3357i	0.298162	−	0.472634i
$921$	14.1491	−	24.5070i	0.466229	−	0.807532i
$922$	2.39516	+	8.93886i	0.0788804	+	0.294386i
$923$	−35.4146	+	20.4466i	−1.16569	+	0.673009i
$924$	−4.02030			−0.132258
$925$	−26.0572	+	15.6852i	−0.856754	+	0.515725i
$926$	−21.0824			−0.692812
$927$	4.76451	−	2.75079i	0.156487	−	0.0903479i
$928$	−2.67124	−	9.96921i	−0.0876878	−	0.327255i
$929$	−8.45362	+	14.6421i	−0.277354	+	0.480392i	−0.970726	−	0.240188i	$-0.922791\pi$
$929$	−8.45362	+	14.6421i	−0.277354	+	0.480392i	0.693372	+	0.720580i	$0.256124\pi$
$930$	17.2255	−	27.3051i	0.564847	−	0.895371i
$931$	−4.33228	−	4.33228i	−0.141985	−	0.141985i
$932$	3.63311	+	13.5590i	0.119007	+	0.444139i
$933$		−	2.19528i		−	0.0718702i
$934$	22.1497	−	12.7881i	0.724760	−	0.418440i
$935$	−0.615573	+	15.6962i	−0.0201314	+	0.513321i
$936$		−	2.90345i		−	0.0949023i
$937$	8.78346	+	2.35352i	0.286943	+	0.0768862i	0.399420	−	0.916768i	$-0.369212\pi$
$937$	8.78346	+	2.35352i	0.286943	+	0.0768862i	−0.112477	+	0.993654i	$0.535878\pi$
$938$	18.1283	+	10.4664i	0.591911	+	0.341740i
$939$	6.49794	+	6.49794i	0.212052	+	0.212052i
$940$	−10.1585	−	3.15351i	−0.331335	−	0.102856i
$941$	−0.722576	−	1.25154i	−0.0235553	−	0.0407990i	0.854007	−	0.520261i	$-0.174165\pi$
$941$	−0.722576	−	1.25154i	−0.0235553	−	0.0407990i	−0.877563	+	0.479462i	$0.840832\pi$
$942$	−5.52253	−	9.56531i	−0.179934	−	0.311655i
$943$	−20.4342	+	35.3931i	−0.665430	+	1.15256i
$944$	−3.14851	−	11.7504i	−0.102475	−	0.382442i
$945$	−12.4605	−	23.6793i	−0.405339	−	0.770288i
$946$	−7.11169	+	4.10594i	−0.231221	+	0.133496i
$947$	−25.4993	−	44.1661i	−0.828616	−	1.43520i	−0.899124	−	0.437693i	$-0.855796\pi$
$947$	−25.4993	−	44.1661i	−0.828616	−	1.43520i	0.0705085	−	0.997511i	$-0.477538\pi$
$948$		−	2.66222i		−	0.0864649i
$949$	61.1899	−	16.3958i	1.98631	−	0.532230i
$950$	4.17089	−	11.7836i	0.135322	−	0.382312i
$951$	27.1794			0.881354
$952$	−8.53065	−	8.53065i	−0.276480	−	0.276480i
$953$	−34.3639	−	9.20777i	−1.11315	−	0.298269i	−0.345044	−	0.938586i	$-0.612136\pi$
$953$	−34.3639	−	9.20777i	−1.11315	−	0.298269i	−0.768110	+	0.640317i	$0.778803\pi$
$954$	3.55124	+	3.55124i	0.114975	+	0.114975i
$955$	5.75530	−	1.30273i	0.186237	−	0.0421553i
$956$	−6.28584	+	6.28584i	−0.203299	+	0.203299i
$957$	−16.8474	−	9.72688i	−0.544601	−	0.314425i
$958$	−7.17989	+	1.92385i	−0.231972	+	0.0621566i
$959$	−19.3088	−	11.1479i	−0.623513	−	0.359986i
$960$	−3.24097	−	1.00609i	−0.104602	−	0.0324715i
$961$		−	59.5069i		−	1.91958i
$962$	−2.44598	−	25.2285i	−0.0788614	−	0.813400i
$963$	1.67391	+	1.67391i	0.0539410	+	0.0539410i
$964$	−2.35952	+	8.80585i	−0.0759950	+	0.283617i
$965$	37.3738	+	23.5773i	1.20310	+	0.758981i
$966$	21.2498	+	12.2686i	0.683700	+	0.394735i
$967$	23.7442	−	41.1262i	0.763563	−	1.32253i	−0.177439	−	0.984132i	$-0.556781\pi$
$967$	23.7442	−	41.1262i	0.763563	−	1.32253i	0.941003	−	0.338399i	$-0.109885\pi$
$968$			9.45746i			0.303974i
$969$	18.5851	+	10.7301i	0.597039	+	0.344701i
$970$	0.0353003	−	0.900105i	0.00113342	−	0.0289006i
$971$	30.3430	+	52.5556i	0.973753	+	1.68659i	0.683989	+	0.729492i	$0.260244\pi$
$971$	30.3430	+	52.5556i	0.973753	+	1.68659i	0.289764	+	0.957098i	$0.406423\pi$
$972$	−5.00739	+	5.00739i	−0.160612	+	0.160612i
$973$	−31.9504	+	31.9504i	−1.02428	+	1.02428i
$974$	7.13839	−	4.12135i	0.228729	−	0.132057i
$975$	31.0896	−	5.76675i	0.995664	−	0.184684i
$976$	0.764030	−	0.764030i	0.0244560	−	0.0244560i
$977$	−13.7786	+	7.95510i	−0.440818	+	0.254506i	−0.703944	−	0.710255i	$-0.748580\pi$
$977$	−13.7786	+	7.95510i	−0.440818	+	0.254506i	0.263127	+	0.964761i	$0.415246\pi$
$978$	−6.97090	+	26.0158i	−0.222905	+	0.831892i
$979$	−8.54058	−	2.28844i	−0.272958	−	0.0731389i
$980$	4.63475	+	2.92384i	0.148052	+	0.0933987i
$981$	−2.40797	+	0.645215i	−0.0768807	+	0.0206001i
$982$	14.0660	−	8.12099i	0.448863	−	0.259151i
$983$	3.74405	+	1.00321i	0.119417	+	0.0319976i	0.318032	−	0.948080i	$-0.396978\pi$
$983$	3.74405	+	1.00321i	0.119417	+	0.0319976i	−0.198616	+	0.980077i	$0.563645\pi$
$984$	7.90345	+	2.11772i	0.251953	+	0.0675106i
$985$	19.7620	−	18.2705i	0.629670	−	0.582145i
$986$	−15.1091	−	56.3879i	−0.481171	−	1.79576i
$987$	3.98530	−	14.8733i	0.126853	−	0.473423i
$988$	7.36628	+	7.36628i	0.234353	+	0.234353i
$989$	50.1196			1.59371
$990$	1.71244	−	0.901118i	0.0544251	−	0.0286394i
$991$	−37.7253	+	37.7253i	−1.19838	+	1.19838i	−0.223732	+	0.974651i	$0.571824\pi$
$991$	−37.7253	+	37.7253i	−1.19838	+	1.19838i	−0.974651	+	0.223732i	$0.928176\pi$
$992$	−9.18935	+	2.46228i	−0.291762	+	0.0781774i
$993$	−8.34240			−0.264738
$994$	20.2183	−	5.41749i	0.641287	−	0.171832i
$995$	−3.95094	+	0.894306i	−0.125253	+	0.0283514i
$996$	0.0867414	−	0.150241i	0.00274851	−	0.00476056i
$997$	−7.17533	−	12.4280i	−0.227245	−	0.393600i	0.729746	−	0.683719i	$-0.239639\pi$
$997$	−7.17533	−	12.4280i	−0.227245	−	0.393600i	−0.956991	+	0.290119i	$0.906305\pi$
$998$	−11.3254	+	11.3254i	−0.358501	+	0.358501i
$999$	−21.6898	+	26.3471i	−0.686235	+	0.833586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.e.193.1	yes	16
5.2	odd	4		370.2.q.e.267.1	✓	16
37.14	odd	12		370.2.q.e.273.1	yes	16
185.162	even	12	inner	370.2.r.e.347.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.e.267.1	✓	16	5.2	odd	4
370.2.q.e.273.1	yes	16	37.14	odd	12
370.2.r.e.193.1	yes	16	1.1	even	1	trivial
370.2.r.e.347.1	yes	16	185.162	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.392794 - 1.46593i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.19306 + 1.89119i) q^{5} +(1.07313 + 1.07313i) q^{6} +(-0.552037 - 2.06023i) q^{7} +1.00000i q^{8} +(0.603425 - 0.348387i) q^{9} +(0.0876265 - 2.23435i) q^{10} +1.24199i q^{11} +(-1.46593 - 0.392794i) q^{12} +(-3.60872 - 2.08350i) q^{13} +(1.50819 + 1.50819i) q^{14} +(3.24097 + 1.00609i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.82810 - 4.89842i) q^{17} +(-0.348387 + 0.603425i) q^{18} +(-0.647049 - 2.41482i) q^{19} +(1.04129 + 1.97882i) q^{20} +(-2.80331 + 1.61849i) q^{21} +(-0.620995 - 1.07560i) q^{22} +7.58025i q^{23} +(1.46593 - 0.392794i) q^{24} +(-2.15321 - 4.51262i) q^{25} +4.16699 q^{26} +(-3.96713 - 3.96713i) q^{27} +(-2.06023 - 0.552037i) q^{28} +(-7.29797 - 7.29797i) q^{29} +(-3.30981 + 0.749185i) q^{30} +(-6.72707 + 6.72707i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.82067 - 0.487846i) q^{33} +(4.89842 + 2.82810i) q^{34} +(4.55490 + 1.41398i) q^{35} -0.696775i q^{36} +(-0.586988 - 6.05437i) q^{37} +(1.76777 + 1.76777i) q^{38} +(-1.63677 + 6.10850i) q^{39} +(-1.89119 - 1.19306i) q^{40} +(4.66912 + 2.69572i) q^{41} +(1.61849 - 2.80331i) q^{42} -6.61187i q^{43} +(1.07560 + 0.620995i) q^{44} +(-0.0610560 + 1.55684i) q^{45} +(-3.79012 - 6.56469i) q^{46} +(-3.36364 + 3.36364i) q^{47} +(-1.07313 + 1.07313i) q^{48} +(2.12237 - 1.22535i) q^{49} +(4.12104 + 2.83144i) q^{50} +(-6.06986 + 6.06986i) q^{51} +(-3.60872 + 2.08350i) q^{52} +(1.86551 - 6.96219i) q^{53} +(5.41920 + 1.45207i) q^{54} +(-2.34884 - 1.48177i) q^{55} +(2.06023 - 0.552037i) q^{56} +(-3.28579 + 1.89705i) q^{57} +(9.96921 + 2.67124i) q^{58} +(11.7504 + 3.14851i) q^{59} +(2.49179 - 2.30372i) q^{60} +(0.279654 + 1.04368i) q^{61} +(2.46228 - 9.18935i) q^{62} +(-1.05087 - 1.05087i) q^{63} -1.00000 q^{64} +(8.24571 - 4.33904i) q^{65} +(-1.33282 + 1.33282i) q^{66} +(9.47979 - 2.54010i) q^{67} -5.65620 q^{68} +(11.1121 - 2.97747i) q^{69} +(-4.65165 + 1.05291i) q^{70} +(4.90681 - 8.49885i) q^{71} +(0.348387 + 0.603425i) q^{72} +(-10.7498 + 10.7498i) q^{73} +(3.53553 + 4.94975i) q^{74} +(-5.76939 + 4.92897i) q^{75} +(-2.41482 - 0.647049i) q^{76} +(2.55879 - 0.685625i) q^{77} +(-1.63677 - 6.10850i) q^{78} +(0.454017 + 1.69441i) q^{79} +(2.23435 + 0.0876265i) q^{80} +(-3.21209 + 5.56350i) q^{81} -5.39144 q^{82} +(-0.0295859 + 0.110416i) q^{83} +3.23698i q^{84} +(12.6379 + 0.495634i) q^{85} +(3.30593 + 5.72604i) q^{86} +(-7.83168 + 13.5649i) q^{87} -1.24199 q^{88} +(-1.84256 + 6.87653i) q^{89} +(-0.725543 - 1.37879i) q^{90} +(-2.30033 + 8.58496i) q^{91} +(6.56469 + 3.79012i) q^{92} +(12.5037 + 7.21903i) q^{93} +(1.23118 - 4.59481i) q^{94} +(5.33885 + 1.65734i) q^{95} +(0.392794 - 1.46593i) q^{96} +0.402849 q^{97} +(-1.22535 + 2.12237i) q^{98} +(0.432694 + 0.749448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} - 8 q^{6} + 24 q^{9} - 4 q^{10} - 8 q^{12} + 12 q^{13} - 8 q^{16} - 16 q^{17} + 24 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 16 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 - 8 * q^6 + 24 * q^9 - 4 * q^10 - 8 * q^12 + 12 * q^13 - 8 * q^16 - 16 * q^17 + 24 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 16 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 12 * q^33 - 8 * q^35 - 8 * q^40 - 36 * q^41 + 4 * q^42 + 20 * q^45 + 4 * q^46 + 32 * q^47 + 8 * q^48 - 24 * q^49 - 4 * q^50 - 16 * q^51 + 12 * q^52 + 24 * q^53 + 8 * q^54 - 12 * q^55 - 60 * q^57 + 8 * q^58 + 8 * q^59 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 16 * q^64 + 12 * q^65 - 24 * q^66 + 8 * q^67 - 32 * q^68 + 8 * q^69 - 20 * q^70 + 4 * q^71 - 48 * q^73 - 36 * q^75 + 24 * q^76 - 12 * q^77 - 20 * q^79 + 12 * q^80 + 16 * q^81 - 24 * q^82 - 48 * q^83 - 8 * q^85 + 8 * q^86 - 12 * q^87 + 16 * q^88 + 8 * q^89 + 4 * q^90 - 8 * q^91 + 12 * q^92 - 36 * q^93 + 28 * q^94 + 8 * q^95 + 16 * q^96 + 16 * q^97 - 8 * q^98 - 8 * q^99

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