LMFDB - Embedded newform 370.2.x.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(9,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 8]))

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

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

chi := DirichletCharacter("370.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.x (of order $18$, degree $6$, 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:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	370.49
Dual form			370.2.x.a.219.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 - 0.766044i) q^{2} +(-1.48887 + 1.77437i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.17115 - 0.534875i) q^{5} +2.31627 q^{6} +(-0.983118 - 2.70110i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.410698 - 2.32918i) q^{9} +(-1.80533 - 1.31939i) q^{10} +(-0.525341 - 0.909917i) q^{11} +(-1.48887 - 1.77437i) q^{12} +(2.47264 + 0.435993i) q^{13} +(-1.43722 + 2.48934i) q^{14} +(-2.28350 + 4.64878i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.02282 - 0.533005i) q^{17} +(-1.52027 + 1.81178i) q^{18} +(1.28623 + 1.07928i) q^{19} +(0.149732 + 2.23105i) q^{20} +(6.25647 + 2.27717i) q^{21} +(-0.359354 + 0.987318i) q^{22} +(6.21280 + 3.58696i) q^{23} +(-0.402216 + 2.28108i) q^{24} +(4.42782 - 2.32259i) q^{25} +(-1.25539 - 2.17440i) q^{26} +(-1.27355 - 0.735284i) q^{27} +(2.83078 - 0.499142i) q^{28} +(-0.697579 - 1.20824i) q^{29} +(5.02898 - 1.23892i) q^{30} +5.27408 q^{31} +(0.342020 + 0.939693i) q^{32} +(2.39669 + 0.422601i) q^{33} +(-2.35134 - 1.97300i) q^{34} +(-3.57925 - 5.33865i) q^{35} +2.36511 q^{36} +(6.01379 - 0.913429i) q^{37} -1.67905i q^{38} +(-4.45505 + 3.73823i) q^{39} +(1.61284 - 1.54879i) q^{40} +(-0.453911 + 2.57426i) q^{41} +(-2.27717 - 6.25647i) q^{42} +2.68546i q^{43} +(0.987318 - 0.359354i) q^{44} +(-2.13751 - 4.83734i) q^{45} +(-1.24574 - 7.06493i) q^{46} +(-0.462988 - 0.267306i) q^{47} +(2.00595 - 1.15814i) q^{48} +(-0.967083 + 0.811479i) q^{49} +(-4.62536 - 1.89897i) q^{50} +(-3.55484 + 6.15716i) q^{51} +(-0.858739 + 2.35937i) q^{52} +(2.13484 - 5.86544i) q^{53} +(0.255362 + 1.44823i) q^{54} +(-1.62729 - 1.69458i) q^{55} +(-2.20195 - 1.84766i) q^{56} +(-3.83006 + 0.675343i) q^{57} +(-0.477172 + 1.31102i) q^{58} +(-7.51204 - 2.73416i) q^{59} +(-4.18163 - 3.05606i) q^{60} +(-2.32708 + 13.1975i) q^{61} +(-3.39011 - 4.04018i) q^{62} +(-5.88758 + 3.39920i) q^{63} +(0.500000 - 0.866025i) q^{64} +(5.60168 - 0.375946i) q^{65} +(-1.21683 - 2.10762i) q^{66} +(0.740907 + 2.03563i) q^{67} +3.06945i q^{68} +(-15.6146 + 5.68326i) q^{69} +(-1.78894 + 6.17348i) q^{70} +(-10.0672 - 8.44738i) q^{71} +(-1.52027 - 1.81178i) q^{72} -10.1927i q^{73} +(-4.56532 - 4.01969i) q^{74} +(-2.47131 + 11.3146i) q^{75} +(-1.28623 + 1.07928i) q^{76} +(-1.94130 + 2.31355i) q^{77} +(5.72731 + 1.00988i) q^{78} +(5.67072 - 2.06397i) q^{79} +(-2.22316 - 0.239960i) q^{80} +(9.86826 - 3.59175i) q^{81} +(2.26376 - 1.30698i) q^{82} +(-12.4770 + 2.20004i) q^{83} +(-3.32900 + 5.76599i) q^{84} +(6.27791 - 2.77407i) q^{85} +(2.05718 - 1.72618i) q^{86} +(3.18247 + 0.561155i) q^{87} +(-0.909917 - 0.525341i) q^{88} +(5.80174 + 2.11166i) q^{89} +(-2.33165 + 4.74681i) q^{90} +(-1.25324 - 7.10747i) q^{91} +(-4.61131 + 5.49554i) q^{92} +(-7.85242 + 9.35815i) q^{93} +(0.0928345 + 0.526491i) q^{94} +(3.36988 + 1.65530i) q^{95} +(-2.17658 - 0.792212i) q^{96} +(10.7837 + 6.22595i) q^{97} +(1.24326 + 0.219220i) q^{98} +(-1.90361 + 1.59732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 12 q^{9} + 12 q^{11} - 6 q^{14} + 6 q^{19} - 24 q^{21} + 30 q^{25} + 48 q^{26} + 24 q^{30} - 192 q^{31} + 12 q^{34} + 30 q^{35} + 84 q^{36} + 24 q^{39} + 12 q^{40} - 108 q^{41} + 6 q^{44} - 30 q^{45}+ \cdots - 90 q^{99}+O(q^{100}) $ 108 * q - 12 * q^9 + 12 * q^11 - 6 * q^14 + 6 * q^19 - 24 * q^21 + 30 * q^25 + 48 * q^26 + 24 * q^30 - 192 * q^31 + 12 * q^34 + 30 * q^35 + 84 * q^36 + 24 * q^39 + 12 * q^40 - 108 * q^41 + 6 * q^44 - 30 * q^45 - 54 * q^46 + 60 * q^49 - 12 * q^50 + 30 * q^55 - 48 * q^59 + 24 * q^61 + 54 * q^64 - 6 * q^65 - 120 * q^69 - 12 * q^70 + 12 * q^71 - 60 * q^74 - 156 * q^75 - 6 * q^76 + 12 * q^80 + 120 * q^81 - 24 * q^84 - 30 * q^85 + 12 * q^86 + 54 * q^89 + 18 * q^90 - 138 * q^91 + 6 * q^94 + 84 * q^95 - 90 * q^99

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	−1.48887	+	1.77437i	−0.859600	+	1.02443i	0.139813	+	0.990178i	$0.455350\pi$
$3$	−1.48887	+	1.77437i	−0.859600	+	1.02443i	−0.999413	+	0.0342534i	$0.989095\pi$
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	2.17115	−	0.534875i	0.970969	−	0.239204i
$5$	2.17115	−	0.534875i	0.970969	−	0.239204i
$6$	2.31627			0.945614
$7$	−0.983118	−	2.70110i	−0.371584	−	1.02092i	−0.974749	−	0.223302i	$-0.928316\pi$
$7$	−0.983118	−	2.70110i	−0.371584	−	1.02092i	0.603166	−	0.797616i	$-0.293906\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.410698	−	2.32918i	−0.136899	−	0.776394i
$10$	−1.80533	−	1.31939i	−0.570895	−	0.417227i
$11$	−0.525341	−	0.909917i	−0.158396	−	0.274350i	0.775894	−	0.630863i	$-0.217299\pi$
$11$	−0.525341	−	0.909917i	−0.158396	−	0.274350i	−0.934291	+	0.356513i	$0.883966\pi$
$12$	−1.48887	−	1.77437i	−0.429800	−	0.512216i
$13$	2.47264	+	0.435993i	0.685787	+	0.120923i	0.505676	−	0.862723i	$-0.331243\pi$
$13$	2.47264	+	0.435993i	0.685787	+	0.120923i	0.180111	+	0.983646i	$0.442354\pi$
$14$	−1.43722	+	2.48934i	−0.384114	+	0.665305i
$15$	−2.28350	+	4.64878i	−0.589598	+	1.20031i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.02282	−	0.533005i	0.733141	−	0.129273i	0.205400	−	0.978678i	$-0.434150\pi$
$17$	3.02282	−	0.533005i	0.733141	−	0.129273i	0.527741	+	0.849405i	$0.323039\pi$
$18$	−1.52027	+	1.81178i	−0.358330	+	0.427041i
$19$	1.28623	+	1.07928i	0.295081	+	0.247603i	0.778294	−	0.627901i	$-0.216086\pi$
$19$	1.28623	+	1.07928i	0.295081	+	0.247603i	−0.483212	+	0.875503i	$0.660530\pi$
$20$	0.149732	+	2.23105i	0.0334812	+	0.498878i
$21$	6.25647	+	2.27717i	1.36527	+	0.496919i
$22$	−0.359354	+	0.987318i	−0.0766146	+	0.210497i
$23$	6.21280	+	3.58696i	1.29546	+	0.747933i	0.979616	−	0.200879i	$-0.0643799\pi$
$23$	6.21280	+	3.58696i	1.29546	+	0.747933i	0.315841	+	0.948812i	$0.397713\pi$
$24$	−0.402216	+	2.28108i	−0.0821021	+	0.465624i
$25$	4.42782	−	2.32259i	0.885563	−	0.464519i
$26$	−1.25539	−	2.17440i	−0.246203	−	0.426436i
$27$	−1.27355	−	0.735284i	−0.245095	−	0.141506i
$28$	2.83078	−	0.499142i	0.534966	−	0.0943290i
$29$	−0.697579	−	1.20824i	−0.129537	−	0.224365i	0.793960	−	0.607970i	$-0.208016\pi$
$29$	−0.697579	−	1.20824i	−0.129537	−	0.224365i	−0.923497	+	0.383605i	$0.874682\pi$
$30$	5.02898	−	1.23892i	0.918162	−	0.226194i
$31$	5.27408			0.947253			0.473626	−	0.880726i	$-0.342945\pi$
$31$	5.27408			0.947253			0.473626	+	0.880726i	$0.342945\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	2.39669	+	0.422601i	0.417211	+	0.0735655i
$34$	−2.35134	−	1.97300i	−0.403251	−	0.338368i
$35$	−3.57925	−	5.33865i	−0.605004	−	0.902396i
$36$	2.36511			0.394186
$37$	6.01379	−	0.913429i	0.988661	−	0.150167i
$37$	6.01379	−	0.913429i	0.988661	−	0.150167i
$38$		−	1.67905i		−	0.272379i
$39$	−4.45505	+	3.73823i	−0.713380	+	0.598597i
$40$	1.61284	−	1.54879i	0.255012	−	0.244886i
$41$	−0.453911	+	2.57426i	−0.0708890	+	0.402031i	0.928630	+	0.371008i	$0.120988\pi$
$41$	−0.453911	+	2.57426i	−0.0708890	+	0.402031i	−0.999519	+	0.0310233i	$0.990123\pi$
$42$	−2.27717	−	6.25647i	−0.351375	−	0.965394i
$43$			2.68546i			0.409529i	0.978811	+	0.204765i	$0.0656429\pi$
$43$			2.68546i			0.409529i	−0.978811	+	0.204765i	$0.934357\pi$
$44$	0.987318	−	0.359354i	0.148844	−	0.0541747i
$45$	−2.13751	−	4.83734i	−0.318641	−	0.721108i
$46$	−1.24574	−	7.06493i	−0.183674	−	1.04167i
$47$	−0.462988	−	0.267306i	−0.0675337	−	0.0389906i	0.465853	−	0.884862i	$-0.345748\pi$
$47$	−0.462988	−	0.267306i	−0.0675337	−	0.0389906i	−0.533387	+	0.845872i	$0.679081\pi$
$48$	2.00595	−	1.15814i	0.289534	−	0.167163i
$49$	−0.967083	+	0.811479i	−0.138155	+	0.115926i
$50$	−4.62536	−	1.89897i	−0.654124	−	0.268555i
$51$	−3.55484	+	6.15716i	−0.497777	+	0.862175i
$52$	−0.858739	+	2.35937i	−0.119086	+	0.327185i
$53$	2.13484	−	5.86544i	0.293243	−	0.805680i	−0.702344	−	0.711838i	$-0.747863\pi$
$53$	2.13484	−	5.86544i	0.293243	−	0.805680i	0.995587	−	0.0938417i	$-0.0299148\pi$
$54$	0.255362	+	1.44823i	0.0347503	+	0.197079i
$55$	−1.62729	−	1.69458i	−0.219424	−	0.228497i
$56$	−2.20195	−	1.84766i	−0.294248	−	0.246904i
$57$	−3.83006	+	0.675343i	−0.507304	+	0.0894514i
$58$	−0.477172	+	1.31102i	−0.0626558	+	0.172145i
$59$	−7.51204	−	2.73416i	−0.977985	−	0.355957i	−0.196928	−	0.980418i	$-0.563097\pi$
$59$	−7.51204	−	2.73416i	−0.977985	−	0.355957i	−0.781056	+	0.624461i	$0.785319\pi$
$60$	−4.18163	−	3.05606i	−0.539846	−	0.394536i
$61$	−2.32708	+	13.1975i	−0.297952	+	1.68977i	0.357004	+	0.934103i	$0.383798\pi$
$61$	−2.32708	+	13.1975i	−0.297952	+	1.68977i	−0.654956	+	0.755667i	$0.727313\pi$
$62$	−3.39011	−	4.04018i	−0.430545	−	0.513103i
$63$	−5.88758	+	3.39920i	−0.741765	+	0.428258i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	5.60168	−	0.375946i	0.694803	−	0.0466304i
$66$	−1.21683	−	2.10762i	−0.149782	−	0.259430i
$67$	0.740907	+	2.03563i	0.0905162	+	0.248691i	0.976687	−	0.214667i	$-0.0688666\pi$
$67$	0.740907	+	2.03563i	0.0905162	+	0.248691i	−0.886171	+	0.463358i	$0.846644\pi$
$68$			3.06945i			0.372226i
$69$	−15.6146	+	5.68326i	−1.87978	+	0.684184i
$70$	−1.78894	+	6.17348i	−0.213820	+	0.737872i
$71$	−10.0672	−	8.44738i	−1.19476	−	1.00252i	−0.999764	−	0.0217144i	$-0.993088\pi$
$71$	−10.0672	−	8.44738i	−1.19476	−	1.00252i	−0.194992	−	0.980805i	$-0.562468\pi$
$72$	−1.52027	−	1.81178i	−0.179165	−	0.213521i
$73$		−	10.1927i		−	1.19297i	−0.802624	−	0.596485i	$-0.796564\pi$
$73$		−	10.1927i		−	1.19297i	0.802624	−	0.596485i	$-0.203436\pi$
$74$	−4.56532	−	4.01969i	−0.530707	−	0.467279i
$75$	−2.47131	+	11.3146i	−0.285363	+	1.30650i
$76$	−1.28623	+	1.07928i	−0.147541	+	0.123801i
$77$	−1.94130	+	2.31355i	−0.221232	+	0.263654i
$78$	5.72731	+	1.00988i	0.648490	+	0.114346i
$79$	5.67072	−	2.06397i	0.638006	−	0.232215i	−0.00270620	−	0.999996i	$-0.500861\pi$
$79$	5.67072	−	2.06397i	0.638006	−	0.232215i	0.640712	+	0.767781i	$0.278639\pi$
$80$	−2.22316	−	0.239960i	−0.248556	−	0.0268283i
$81$	9.86826	−	3.59175i	1.09647	−	0.399083i
$82$	2.26376	−	1.30698i	0.249991	−	0.144332i
$83$	−12.4770	+	2.20004i	−1.36953	+	0.241486i	−0.809566	−	0.587029i	$-0.800297\pi$
$83$	−12.4770	+	2.20004i	−1.36953	+	0.241486i	−0.559967	+	0.828515i	$0.689186\pi$
$84$	−3.32900	+	5.76599i	−0.363223	+	0.629122i
$85$	6.27791	−	2.77407i	0.680935	−	0.300890i
$86$	2.05718	−	1.72618i	0.221832	−	0.186139i
$87$	3.18247	+	0.561155i	0.341197	+	0.0601622i
$88$	−0.909917	−	0.525341i	−0.0969975	−	0.0560015i
$89$	5.80174	+	2.11166i	0.614983	+	0.223836i	0.630682	−	0.776041i	$-0.282775\pi$
$89$	5.80174	+	2.11166i	0.614983	+	0.223836i	−0.0156989	+	0.999877i	$0.504997\pi$
$90$	−2.33165	+	4.74681i	−0.245778	+	0.500358i
$91$	−1.25324	−	7.10747i	−0.131375	−	0.745065i
$92$	−4.61131	+	5.49554i	−0.480762	+	0.572950i
$93$	−7.85242	+	9.35815i	−0.814258	+	0.970395i
$94$	0.0928345	+	0.526491i	0.00957515	+	0.0543034i
$95$	3.36988	+	1.65530i	0.345742	+	0.169830i
$96$	−2.17658	−	0.792212i	−0.222147	−	0.0808548i
$97$	10.7837	+	6.22595i	1.09491	+	0.632149i	0.934881	−	0.354962i	$-0.115506\pi$
$97$	10.7837	+	6.22595i	1.09491	+	0.632149i	0.160034	+	0.987111i	$0.448840\pi$
$98$	1.24326	+	0.219220i	0.125588	+	0.0221446i
$99$	−1.90361	+	1.59732i	−0.191320	+	0.160536i
$100$	1.51843	+	4.76386i	0.151843	+	0.476386i
$101$	2.53524	−	4.39116i	0.252265	−	0.436936i	−0.711884	−	0.702297i	$-0.752158\pi$
$101$	2.53524	−	4.39116i	0.252265	−	0.436936i	0.964149	+	0.265361i	$0.0854911\pi$
$102$	7.00167	−	1.23458i	0.693269	−	0.122242i
$103$	−7.53678	+	4.35136i	−0.742621	+	0.428752i	−0.823021	−	0.568010i	$-0.807713\pi$
$103$	−7.53678	+	4.35136i	−0.742621	+	0.428752i	0.0804006	+	0.996763i	$0.474380\pi$
$104$	2.35937	−	0.858739i	0.231355	−	0.0842063i
$105$	14.8018	+	1.59765i	1.44450	+	0.155915i
$106$	−5.86544	+	2.13484i	−0.569702	+	0.207354i
$107$	0.185150	+	0.0326469i	0.0178991	+	0.00315610i	0.182591	−	0.983189i	$-0.441552\pi$
$107$	0.185150	+	0.0326469i	0.0178991	+	0.00315610i	−0.164691	+	0.986345i	$0.552663\pi$
$108$	0.945263	−	1.12652i	0.0909580	−	0.108400i
$109$	−13.9770	+	11.7281i	−1.33875	+	1.12334i	−0.356804	+	0.934179i	$0.616133\pi$
$109$	−13.9770	+	11.7281i	−1.33875	+	1.12334i	−0.981945	+	0.189164i	$0.939422\pi$
$110$	−0.252122	+	2.33583i	−0.0240389	+	0.222713i
$111$	−7.33300	+	12.0306i	−0.696017	+	1.14190i
$112$			2.87445i			0.271610i
$113$	−10.1289	−	12.0712i	−0.952850	−	1.13556i	−0.990671	−	0.136278i	$-0.956486\pi$
$113$	−10.1289	−	12.0712i	−0.952850	−	1.13556i	0.0378208	−	0.999285i	$-0.487958\pi$
$114$	2.97926	+	2.49989i	0.279033	+	0.234137i
$115$	15.4075	+	4.46477i	1.43676	+	0.416342i
$116$	1.31102	−	0.477172i	0.121725	−	0.0443043i
$117$		−	5.93829i		−	0.548995i
$118$	2.73416	+	7.51204i	0.251700	+	0.691539i
$119$	−4.41148	−	7.64091i	−0.404400	−	0.700442i
$120$	0.346821	+	5.16772i	0.0316603	+	0.471746i
$121$	4.94803	−	8.57025i	0.449821	−	0.779113i
$122$	11.6057	−	6.70056i	1.05073	−	0.606640i
$123$	−3.89186	−	4.63814i	−0.350917	−	0.418207i
$124$	−0.915834	+	5.19395i	−0.0822443	+	0.466431i
$125$	8.37117	−	7.41104i	0.748741	−	0.662863i
$126$	6.38840	+	2.32519i	0.569124	+	0.207144i
$127$	1.00863	−	2.77118i	0.0895011	−	0.245902i	−0.886864	−	0.462031i	$-0.847121\pi$
$127$	1.00863	−	2.77118i	0.0895011	−	0.245902i	0.976365	+	0.216129i	$0.0693431\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	−4.76499	−	3.99831i	−0.419534	−	0.352031i
$130$	−3.88868	−	4.04949i	−0.341060	−	0.355163i
$131$	−3.01797	−	17.1158i	−0.263682	−	1.49541i	−0.772763	−	0.634695i	$-0.781126\pi$
$131$	−3.01797	−	17.1158i	−0.263682	−	1.49541i	0.509081	−	0.860718i	$-0.329985\pi$
$132$	−0.832362	+	2.28690i	−0.0724479	+	0.199049i
$133$	1.65071	−	4.53528i	0.143135	−	0.393259i
$134$	1.08313	−	1.87604i	0.0935685	−	0.162065i
$135$	−3.15836	−	0.915225i	−0.271828	−	0.0787700i
$136$	2.35134	−	1.97300i	0.201625	−	0.169184i
$137$	−12.7181	+	7.34282i	−1.08658	+	0.627340i	−0.932665	−	0.360744i	$-0.882523\pi$
$137$	−12.7181	+	7.34282i	−1.08658	+	0.627340i	−0.153919	+	0.988083i	$0.549190\pi$
$138$	14.3905	+	8.30837i	1.22500	+	0.707256i
$139$	1.12574	+	6.38436i	0.0954836	+	0.541515i	0.994598	+	0.103801i	$0.0331005\pi$
$139$	1.12574	+	6.38436i	0.0954836	+	0.541515i	−0.899114	+	0.437714i	$0.855788\pi$
$140$	5.87907	−	2.59783i	0.496872	−	0.219556i
$141$	1.16363	−	0.423526i	0.0979952	−	0.0356673i
$142$			13.1418i			1.10283i
$143$	−0.902262	−	2.47894i	−0.0754509	−	0.207300i
$144$	−0.410698	+	2.32918i	−0.0342248	+	0.194099i
$145$	−2.16081	−	2.25016i	−0.179446	−	0.186866i
$146$	−7.80809	+	6.55176i	−0.646202	+	0.542228i
$147$		−	2.92415i		−	0.241180i
$148$	−0.144732	+	6.08104i	−0.0118969	+	0.499858i
$149$	−21.4945			−1.76090			−0.880449	−	0.474140i	$-0.842759\pi$
$149$	−21.4945			−1.76090			−0.880449	+	0.474140i	$0.842759\pi$
$150$	10.2560	−	5.37976i	0.837401	−	0.439255i
$151$	9.33309	+	7.83139i	0.759516	+	0.637310i	0.938001	−	0.346633i	$-0.112675\pi$
$151$	9.33309	+	7.83139i	0.759516	+	0.637310i	−0.178485	+	0.983943i	$0.557119\pi$
$152$	1.65355	+	0.291565i	0.134120	+	0.0236490i
$153$	−2.48293	−	6.82179i	−0.200733	−	0.551509i
$154$	3.02013			0.243369
$155$	11.4508	−	2.82097i	0.919753	−	0.226586i
$156$	−2.90783	−	5.03651i	−0.232813	−	0.403243i
$157$	0.163592	−	0.0288457i	0.0130561	−	0.00230214i	−0.167116	−	0.985937i	$-0.553446\pi$
$157$	0.163592	−	0.0288457i	0.0130561	−	0.00230214i	0.180172	+	0.983635i	$0.442334\pi$
$158$	−5.22616	−	3.01733i	−0.415771	−	0.240046i
$159$	7.22893	+	12.5209i	0.573291	+	0.992970i
$160$	1.24520	+	1.85728i	0.0984414	+	0.146831i
$161$	3.58081	−	20.3078i	0.282207	−	1.60048i
$162$	−9.09463	−	5.25079i	−0.714542	−	0.412541i
$163$	4.56528	−	12.5430i	0.357581	−	0.982445i	−0.622286	−	0.782790i	$-0.713796\pi$
$163$	4.56528	−	12.5430i	0.357581	−	0.982445i	0.979866	−	0.199654i	$-0.0639820\pi$
$164$	−2.45633	−	0.894030i	−0.191807	−	0.0698120i
$165$	5.42963	−	0.364399i	0.422696	−	0.0283684i
$166$	9.70541	+	8.14381i	0.753286	+	0.632082i
$167$	−9.82407	+	11.7079i	−0.760210	+	0.905983i	−0.997861	−	0.0653679i	$-0.979178\pi$
$167$	−9.82407	+	11.7079i	−0.760210	+	0.905983i	0.237652	+	0.971350i	$0.423622\pi$
$168$	6.55685	−	1.15615i	0.505872	−	0.0891988i
$169$	−6.29214	−	2.29015i	−0.484011	−	0.176166i
$170$	−6.16042	−	3.02603i	−0.472483	−	0.232086i
$171$	1.98558	−	3.43912i	0.151841	−	0.262996i
$172$	−2.64466	−	0.466326i	−0.201654	−	0.0355570i
$173$	−5.37146	−	6.40145i	−0.408384	−	0.486694i	0.522173	−	0.852840i	$-0.325122\pi$
$173$	−5.37146	−	6.40145i	−0.408384	−	0.486694i	−0.930557	+	0.366146i	$0.880677\pi$
$174$	−1.61578	−	2.79862i	−0.122492	−	0.212163i
$175$	−10.6266	−	9.67657i	−0.803296	−	0.731480i
$176$	0.182449	+	1.03472i	0.0137526	+	0.0779949i
$177$	16.0359	−	9.25831i	1.20533	−	0.695897i
$178$	−2.11166	−	5.80174i	−0.158276	−	0.434859i
$179$	22.3731			1.67225			0.836123	−	0.548542i	$-0.184817\pi$
$179$	22.3731			1.67225			0.836123	+	0.548542i	$0.184817\pi$
$180$	5.13503	−	1.26504i	0.382742	−	0.0942906i
$181$	−4.51315	+	25.5953i	−0.335460	+	1.90249i	0.0871873	+	0.996192i	$0.472212\pi$
$181$	−4.51315	+	25.5953i	−0.335460	+	1.90249i	−0.422647	+	0.906294i	$0.638899\pi$
$182$	−4.63907	+	5.52863i	−0.343871	+	0.409809i
$183$	−19.9525	−	23.7785i	−1.47493	−	1.75776i
$184$	7.17392			0.528868
$185$	12.5683	−	5.19982i	0.924039	−	0.382298i
$186$	12.2162			0.895735
$187$	−2.07300	−	2.47051i	−0.151593	−	0.180661i
$188$	0.343642	−	0.409537i	0.0250627	−	0.0298685i
$189$	−0.734023	+	4.16285i	−0.0533923	+	0.302803i
$190$	−0.898084	−	3.64548i	−0.0651539	−	0.264471i
$191$	13.0838			0.946712			0.473356	−	0.880871i	$-0.343043\pi$
$191$	13.0838			0.946712			0.473356	+	0.880871i	$0.343043\pi$
$192$	0.792212	+	2.17658i	0.0571729	+	0.157081i
$193$	−14.8665	+	8.58315i	−1.07011	+	0.617829i	−0.928212	−	0.372052i	$-0.878654\pi$
$193$	−14.8665	+	8.58315i	−1.07011	+	0.617829i	−0.141899	+	0.989881i	$0.545321\pi$
$194$	−2.16225	−	12.2627i	−0.155240	−	0.880412i
$195$	−7.67312	+	10.4992i	−0.549483	+	0.751862i
$196$	−0.631219	−	1.09330i	−0.0450870	−	0.0780930i
$197$	−3.70533	−	4.41584i	−0.263994	−	0.314616i	0.617722	−	0.786397i	$-0.288056\pi$
$197$	−3.70533	−	4.41584i	−0.263994	−	0.314616i	−0.881716	+	0.471781i	$0.843611\pi$
$198$	2.44723	+	0.431513i	0.173917	+	0.0306663i
$199$	10.5881	−	18.3391i	0.750570	−	1.30003i	−0.196976	−	0.980408i	$-0.563112\pi$
$199$	10.5881	−	18.3391i	0.750570	−	1.30003i	0.947547	−	0.319618i	$-0.103554\pi$
$200$	2.67331	−	4.22533i	0.189031	−	0.298776i
$201$	−4.71506	−	1.71614i	−0.332575	−	0.121047i
$202$	−4.99344	+	0.880478i	−0.351337	+	0.0619502i
$203$	−2.57777	+	3.07207i	−0.180924	+	0.215617i
$204$	−5.44633	−	4.57001i	−0.381319	−	0.319965i
$205$	0.391396	+	5.83189i	0.0273363	+	0.407317i
$206$	8.17788	+	2.97651i	0.569780	+	0.207383i
$207$	5.80310	−	15.9439i	0.403343	−	1.10818i
$208$	−2.17440	−	1.25539i	−0.150768	−	0.0870458i
$209$	0.306342	−	1.73735i	0.0211901	−	0.120175i
$210$	−8.29052	−	12.3658i	−0.572100	−	0.853318i
$211$	11.9835	+	20.7561i	0.824980	+	1.42891i	0.901934	+	0.431873i	$0.142147\pi$
$211$	11.9835	+	20.7561i	0.824980	+	1.42891i	−0.0769543	+	0.997035i	$0.524520\pi$
$212$	5.40562	+	3.12093i	0.371259	+	0.214347i
$213$	29.9775	−	5.28584i	2.05402	−	0.362180i
$214$	−0.0940030	−	0.162818i	−0.00642591	−	0.0111300i
$215$	1.43639	+	5.83055i	0.0979608	+	0.397640i
$216$	−1.47057			−0.100060
$217$	−5.18504	−	14.2458i	−0.351984	−	0.967067i
$218$	17.9684	+	3.16832i	1.21698	+	0.214586i
$219$	18.0857	+	15.1757i	1.22212	+	1.02548i
$220$	1.95141	−	1.30831i	0.131564	−	0.0882060i
$221$	7.70673			0.518411
$222$	13.9296	−	2.11575i	0.934891	−	0.142000i
$223$			6.42981i			0.430572i	0.976551	+	0.215286i	$0.0690684\pi$
$223$			6.42981i			0.430572i	−0.976551	+	0.215286i	$0.930932\pi$
$224$	2.20195	−	1.84766i	0.147124	−	0.123452i
$225$	−7.22824	−	9.35931i	−0.481882	−	0.623954i
$226$	−2.73632	+	15.5184i	−0.182017	+	1.03227i
$227$	9.20223	+	25.2829i	0.610774	+	1.67809i	0.728504	+	0.685041i	$0.240216\pi$
$227$	9.20223	+	25.2829i	0.610774	+	1.67809i	−0.117731	+	0.993046i	$0.537562\pi$
$228$		−	3.88914i		−	0.257565i
$229$	9.59566	−	3.49253i	0.634099	−	0.230793i	−0.00491543	−	0.999988i	$-0.501565\pi$
$229$	9.59566	−	3.49253i	0.634099	−	0.230793i	0.639014	+	0.769195i	$0.279342\pi$
$230$	−6.48354	−	14.6727i	−0.427512	−	0.967491i
$231$	−1.21474	−	6.88916i	−0.0799244	−	0.453274i
$232$	−1.20824	−	0.697579i	−0.0793250	−	0.0457983i
$233$	−12.6122	+	7.28167i	−0.826254	+	0.477038i	−0.852568	−	0.522616i	$-0.824956\pi$
$233$	−12.6122	+	7.28167i	−0.826254	+	0.477038i	0.0263146	+	0.999654i	$0.491623\pi$
$234$	−4.54900	+	3.81706i	−0.297377	+	0.249529i
$235$	−1.14819	−	0.332722i	−0.0748999	−	0.0217044i
$236$	3.99707	−	6.92314i	0.260187	−	0.450658i
$237$	−4.78072	+	13.1349i	−0.310541	+	0.853205i
$238$	−3.01763	+	8.29088i	−0.195604	+	0.537418i
$239$	4.07823	+	23.1288i	0.263799	+	1.49608i	0.772434	+	0.635095i	$0.219039\pi$
$239$	4.07823	+	23.1288i	0.263799	+	1.49608i	−0.508635	+	0.860982i	$0.669850\pi$
$240$	3.73577	−	3.58742i	0.241143	−	0.231567i
$241$	−10.1880	−	8.54872i	−0.656265	−	0.550672i	0.252700	−	0.967545i	$-0.418682\pi$
$241$	−10.1880	−	8.54872i	−0.656265	−	0.550672i	−0.908965	+	0.416873i	$0.863126\pi$
$242$	−9.74572	+	1.71843i	−0.626479	+	0.110465i
$243$	−6.81058	+	18.7119i	−0.436899	+	1.20037i
$244$	−12.5929	−	4.58345i	−0.806180	−	0.293425i
$245$	−1.66565	+	2.27911i	−0.106414	+	0.145607i
$246$	−1.05138	+	5.96268i	−0.0670336	+	0.380166i
$247$	2.70983	+	3.22945i	0.172422	+	0.205485i
$248$	4.56749	−	2.63704i	0.290036	−	0.167452i
$249$	14.6730	−	25.4144i	0.929865	−	1.61057i
$250$	−11.0581	−	1.64897i	−0.699374	−	0.104290i
$251$	−2.32121	−	4.02046i	−0.146514	−	0.253769i	0.783423	−	0.621489i	$-0.213472\pi$
$251$	−2.32121	−	4.02046i	−0.146514	−	0.253769i	−0.929937	+	0.367720i	$0.880139\pi$
$252$	−2.32519	−	6.38840i	−0.146473	−	0.402431i
$253$		−	7.53751i		−	0.473879i
$254$	−2.77118	+	1.00863i	−0.173879	+	0.0632868i
$255$	−4.42479	+	15.2695i	−0.277091	+	0.956216i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	19.6770	+	23.4501i	1.22742	+	1.46278i	0.841513	+	0.540237i	$0.181666\pi$
$257$	19.6770	+	23.4501i	1.22742	+	1.46278i	0.385903	+	0.922539i	$0.373890\pi$
$258$			6.22026i			0.387256i
$259$	−8.37952	−	15.3458i	−0.520678	−	0.953542i
$260$	−0.602488	+	5.58186i	−0.0373647	+	0.346173i
$261$	−2.52772	+	2.12101i	−0.156462	+	0.131287i
$262$	−11.1715	+	13.3137i	−0.690180	+	0.822524i
$263$	−3.95613	−	0.697573i	−0.243946	−	0.0430142i	0.0503383	−	0.998732i	$-0.483970\pi$
$263$	−3.95613	−	0.697573i	−0.243946	−	0.0430142i	−0.294284	+	0.955718i	$0.595081\pi$
$264$	2.28690	−	0.832362i	0.140749	−	0.0512284i
$265$	1.49780	−	13.8766i	0.0920090	−	0.852435i
$266$	−4.53528	+	1.65071i	−0.278076	+	0.101211i
$267$	−12.3849	+	7.15043i	−0.757944	+	0.437599i
$268$	−2.13336	+	0.376168i	−0.130315	+	0.0229781i
$269$	−6.03731	+	10.4569i	−0.368101	+	0.637570i	−0.989269	−	0.146108i	$-0.953325\pi$
$269$	−6.03731	+	10.4569i	−0.368101	+	0.637570i	0.621167	+	0.783678i	$0.286659\pi$
$270$	1.32905	+	3.00774i	0.0808834	+	0.183045i
$271$	4.17575	−	3.50387i	0.253659	−	0.212845i	−0.507087	−	0.861895i	$-0.669278\pi$
$271$	4.17575	−	3.50387i	0.253659	−	0.212845i	0.760746	+	0.649050i	$0.224833\pi$
$272$	−3.02282	−	0.533005i	−0.183285	−	0.0323181i
$273$	14.4772	+	8.35840i	0.876198	+	0.505873i
$274$	13.8000	+	5.02279i	0.833688	+	0.303438i
$275$	−4.43948	−	2.80879i	−0.267711	−	0.169377i
$276$	−2.88547	−	16.3643i	−0.173685	−	0.985015i
$277$	−16.0960	+	19.1825i	−0.967115	+	1.15256i	0.0211442	+	0.999776i	$0.493269\pi$
$277$	−16.0960	+	19.1825i	−0.967115	+	1.15256i	−0.988259	+	0.152786i	$0.951175\pi$
$278$	4.16710	−	4.96615i	0.249926	−	0.297850i
$279$	−2.16605	−	12.2843i	−0.129678	−	0.735441i
$280$	−5.76905	−	2.83378i	−0.344766	−	0.169351i
$281$	−17.7029	−	6.44334i	−1.05607	−	0.384377i	−0.245118	−	0.969493i	$-0.578827\pi$
$281$	−17.7029	−	6.44334i	−1.05607	−	0.384377i	−0.810950	+	0.585116i	$0.801049\pi$
$282$	−1.07241	−	0.619154i	−0.0638608	−	0.0368701i
$283$	17.0728	+	3.01040i	1.01487	+	0.178950i	0.656259	−	0.754536i	$-0.272138\pi$
$283$	17.0728	+	3.01040i	1.01487	+	0.178950i	0.358615	+	0.933485i	$0.383249\pi$
$284$	10.0672	−	8.44738i	0.597378	−	0.501260i
$285$	−7.95442	+	3.51488i	−0.471179	+	0.208203i
$286$	−1.31902	+	2.28461i	−0.0779952	+	0.135092i
$287$	7.39956	−	1.30474i	0.436782	−	0.0770165i
$288$	2.04825	−	1.18256i	0.120694	−	0.0696828i
$289$	−7.12144	+	2.59199i	−0.418908	+	0.152470i
$290$	−0.334782	+	3.10165i	−0.0196591	+	0.182135i
$291$	−27.1026	+	9.86454i	−1.58878	+	0.578269i
$292$	10.0379	+	1.76995i	0.587423	+	0.103578i
$293$	−0.782127	+	0.932103i	−0.0456923	+	0.0544540i	−0.788407	−	0.615154i	$-0.789094\pi$
$293$	−0.782127	+	0.932103i	−0.0456923	+	0.0544540i	0.742714	+	0.669608i	$0.233538\pi$
$294$	−2.24003	+	1.87961i	−0.130641	+	0.109621i
$295$	−17.7722	−	1.91828i	−1.03474	−	0.111686i
$296$	4.75138	−	3.79795i	0.276168	−	0.220751i
$297$			1.54510i			0.0896558i
$298$	13.8164	+	16.4657i	0.800363	+	0.953835i
$299$	13.7981	+	11.5780i	0.797966	+	0.669573i
$300$	−10.7136	−	4.39853i	−0.618549	−	0.253949i
$301$	7.25369	−	2.64013i	0.418096	−	0.152174i
$302$		−	12.1835i		−	0.701081i
$303$	4.01689	+	11.0363i	0.230764	+	0.634019i
$304$	−0.839527	−	1.45410i	−0.0481502	−	0.0833985i
$305$	2.00658	+	29.8985i	0.114897	+	1.71199i
$306$	−3.62980	+	6.28700i	−0.207502	+	0.359404i
$307$	2.98048	−	1.72078i	0.170105	−	0.0982103i	−0.412530	−	0.910944i	$-0.635355\pi$
$307$	2.98048	−	1.72078i	0.170105	−	0.0982103i	0.582635	+	0.812734i	$0.302022\pi$
$308$	−1.94130	−	2.31355i	−0.110616	−	0.131827i
$309$	3.50038	−	19.8516i	0.199129	−	1.12932i
$310$	−9.52145	−	6.95856i	−0.540782	−	0.395220i
$311$	−18.1203	−	6.59524i	−1.02751	−	0.373982i	−0.227375	−	0.973807i	$-0.573014\pi$
$311$	−18.1203	−	6.59524i	−1.02751	−	0.373982i	−0.800131	+	0.599826i	$0.795237\pi$
$312$	−1.98907	+	5.46493i	−0.112609	+	0.309391i
$313$	26.9427	−	4.75072i	1.52289	−	0.268526i	0.651321	−	0.758802i	$-0.274215\pi$
$313$	26.9427	−	4.75072i	1.52289	−	0.268526i	0.871567	+	0.490276i	$0.163104\pi$
$314$	−0.127252	−	0.106777i	−0.00718125	−	0.00602579i
$315$	−10.9647	+	10.5293i	−0.617791	+	0.593259i
$316$	1.04791	+	5.94298i	0.0589494	+	0.334318i
$317$	−2.14226	+	5.88580i	−0.120321	+	0.330579i	−0.985202	−	0.171398i	$-0.945172\pi$
$317$	−2.14226	+	5.88580i	−0.120321	+	0.330579i	0.864881	+	0.501977i	$0.167394\pi$
$318$	4.94488	−	13.5859i	0.277295	−	0.761862i
$319$	−0.732934	+	1.26948i	−0.0410364	+	0.0710771i
$320$	0.622361	−	2.14771i	0.0347911	−	0.120061i
$321$	−0.333592	+	0.279917i	−0.0186193	+	0.0156234i
$322$	−17.8583	+	10.3105i	−0.995206	+	0.574583i
$323$	4.46330	+	2.57689i	0.248345	+	0.143382i
$324$	1.82358	+	10.3420i	0.101310	+	0.574558i
$325$	11.9610	−	3.81244i	0.663479	−	0.211476i
$326$	−12.5430	+	4.56528i	−0.694693	+	0.252848i
$327$		−	42.2618i		−	2.33708i
$328$	0.894030	+	2.45633i	0.0493645	+	0.135628i
$329$	−0.266848	+	1.51337i	−0.0147118	+	0.0834347i
$330$	−3.76924	−	3.92510i	−0.207490	−	0.216070i
$331$	0.716461	−	0.601182i	0.0393803	−	0.0330440i	−0.622885	−	0.782313i	$-0.714040\pi$
$331$	0.716461	−	0.601182i	0.0393803	−	0.0330440i	0.662265	+	0.749269i	$0.269595\pi$
$332$		−	12.6695i		−	0.695330i
$333$	−4.59739	−	13.6321i	−0.251935	−	0.747033i
$334$	15.2835			0.836278
$335$	2.69743	+	4.02336i	0.147376	+	0.219820i
$336$	−5.10032	−	4.27968i	−0.278245	−	0.233476i
$337$	−32.0084	−	5.64394i	−1.74361	−	0.307445i	−0.791038	−	0.611767i	$-0.790459\pi$
$337$	−32.0084	−	5.64394i	−1.74361	−	0.307445i	−0.952569	+	0.304322i	$0.901570\pi$
$338$	2.29015	+	6.29214i	0.124568	+	0.342247i
$339$	36.4994			1.98238
$340$	1.64177	+	6.66425i	0.0890377	+	0.361420i
$341$	−2.77069	−	4.79898i	−0.150041	−	0.259879i
$342$	−3.91082	+	0.689584i	−0.211473	+	0.0372884i
$343$	−14.2828	−	8.24616i	−0.771197	−	0.445251i
$344$	1.34273	+	2.32568i	0.0723952	+	0.125392i
$345$	−30.8619	+	20.6911i	−1.66155	+	1.11397i
$346$	−1.45109	+	8.22955i	−0.0780112	+	0.442423i
$347$	−3.00265	−	1.73358i	−0.161191	−	0.0930635i	0.417235	−	0.908799i	$-0.362999\pi$
$347$	−3.00265	−	1.73358i	−0.161191	−	0.0930635i	−0.578425	+	0.815735i	$0.696333\pi$
$348$	−1.10526	+	3.03668i	−0.0592482	+	0.162783i
$349$	−4.19965	−	1.52855i	−0.224802	−	0.0818213i	0.227163	−	0.973857i	$-0.427055\pi$
$349$	−4.19965	−	1.52855i	−0.224802	−	0.0818213i	−0.451966	+	0.892035i	$0.649277\pi$
$350$	−0.582029	+	14.3604i	−0.0311108	+	0.767598i
$351$	−2.82845	−	2.37335i	−0.150972	−	0.126680i
$352$	0.675365	−	0.804869i	0.0359971	−	0.0428997i
$353$	2.55165	−	0.449924i	0.135811	−	0.0239471i	−0.105330	−	0.994437i	$-0.533590\pi$
$353$	2.55165	−	0.449924i	0.135811	−	0.0239471i	0.241140	+	0.970490i	$0.422479\pi$
$354$	−17.3999	−	6.33306i	−0.924796	−	0.336598i
$355$	−26.3757	−	12.9559i	−1.39988	−	0.687626i
$356$	−3.08704	+	5.34692i	−0.163613	+	0.283386i
$357$	20.1259	+	3.54874i	1.06518	+	0.187819i
$358$	−14.3812	−	17.1388i	−0.760068	−	0.905814i
$359$	−15.3669	−	26.6162i	−0.811033	−	1.40475i	−0.912142	−	0.409875i	$-0.865572\pi$
$359$	−15.3669	−	26.6162i	−0.811033	−	1.40475i	0.101109	−	0.994875i	$-0.467761\pi$
$360$	−4.26981	−	3.12051i	−0.225039	−	0.164465i
$361$	−2.80976	−	15.9350i	−0.147882	−	0.838682i
$362$	22.5082	−	12.9951i	1.18300	−	0.683007i
$363$	7.83978	+	21.5396i	0.411482	+	1.13054i
$364$	7.21711			0.378280
$365$	−5.45184	−	22.1300i	−0.285362	−	1.15834i
$366$	−5.39015	+	30.5690i	−0.281748	+	1.59787i
$367$	−1.49103	+	1.77694i	−0.0778312	+	0.0927556i	−0.803555	−	0.595231i	$-0.797061\pi$
$367$	−1.49103	+	1.77694i	−0.0778312	+	0.0927556i	0.725724	+	0.687986i	$0.241505\pi$
$368$	−4.61131	−	5.49554i	−0.240381	−	0.286475i
$369$	6.18233			0.321839
$370$	−12.0620	−	6.28549i	−0.627075	−	0.326767i
$371$	−17.9419			−0.931497
$372$	−7.85242	−	9.35815i	−0.407129	−	0.485198i
$373$	9.99515	−	11.9118i	0.517529	−	0.616768i	−0.442465	−	0.896786i	$-0.645896\pi$
$373$	9.99515	−	11.9118i	0.517529	−	0.616768i	0.959995	+	0.280018i	$0.0903405\pi$
$374$	−0.560018	+	3.17602i	−0.0289579	+	0.164228i
$375$	0.686303	+	25.8876i	0.0354406	+	1.33683i
$376$	−0.534612			−0.0275705
$377$	−1.19808	−	3.29169i	−0.0617041	−	0.169531i
$378$	3.66075	−	2.11353i	0.188289	−	0.108708i
$379$	−1.83834	−	10.4258i	−0.0944292	−	0.535535i	−0.994921	−	0.100661i	$-0.967904\pi$
$379$	−1.83834	−	10.4258i	−0.0944292	−	0.535535i	0.900492	−	0.434874i	$-0.143207\pi$
$380$	−2.21533	+	3.03124i	−0.113644	+	0.155500i
$381$	3.41537	+	5.91560i	0.174975	+	0.303065i
$382$	−8.41011	−	10.0228i	−0.430299	−	0.512810i
$383$	−32.6590	−	5.75866i	−1.66880	−	0.294254i	−0.742162	−	0.670220i	$-0.766200\pi$
$383$	−32.6590	−	5.75866i	−1.66880	−	0.294254i	−0.926633	+	0.375967i	$0.877311\pi$
$384$	1.15814	−	2.00595i	0.0591009	−	0.102366i
$385$	−2.97740	+	6.06143i	−0.151742	+	0.308919i
$386$	16.1311	+	5.87122i	0.821049	+	0.298837i
$387$	6.25493	−	1.10291i	0.317956	−	0.0560642i
$388$	−8.00393	+	9.53871i	−0.406338	+	0.484255i
$389$	5.91738	+	4.96527i	0.300023	+	0.251749i	0.780354	−	0.625338i	$-0.215039\pi$
$389$	5.91738	+	4.96527i	0.300023	+	0.251749i	−0.480331	+	0.877087i	$0.659483\pi$
$390$	12.9750	−	0.870793i	0.657016	−	0.0440943i
$391$	20.6920	+	7.53128i	1.04644	+	0.380873i
$392$	−0.431779	+	1.18630i	−0.0218081	+	0.0599173i
$393$	34.8631	+	20.1282i	1.75861	+	1.01533i
$394$	−1.00099	+	5.67690i	−0.0504292	+	0.285998i
$395$	11.2080	−	7.51433i	0.563938	−	0.378087i
$396$	−1.24249	−	2.15206i	−0.0624375	−	0.108145i
$397$	−6.66058	−	3.84549i	−0.334285	−	0.193000i	0.323457	−	0.946243i	$-0.395155\pi$
$397$	−6.66058	−	3.84549i	−0.334285	−	0.193000i	−0.657742	+	0.753243i	$0.728488\pi$
$398$	−20.8545	+	3.67721i	−1.04534	+	0.184322i
$399$	5.58957	+	9.68141i	0.279828	+	0.484677i
$400$	−4.95516	+	0.668121i	−0.247758	+	0.0334060i
$401$	−15.0989			−0.754005			−0.377002	−	0.926212i	$-0.623045\pi$
$401$	−15.0989			−0.754005			−0.377002	+	0.926212i	$0.623045\pi$
$402$	1.71614	+	4.71506i	0.0855934	+	0.235166i
$403$	13.0409	+	2.29946i	0.649614	+	0.114544i
$404$	3.88421	+	3.25924i	0.193246	+	0.162153i
$405$	19.5044	−	13.0765i	0.969179	−	0.649778i
$406$	4.01031			0.199028
$407$	−3.99043	−	4.99219i	−0.197798	−	0.247454i
$408$			7.10968i			0.351982i
$409$	−0.709304	+	0.595177i	−0.0350728	+	0.0294296i	−0.660156	−	0.751129i	$-0.729510\pi$
$409$	−0.709304	+	0.595177i	−0.0350728	+	0.0294296i	0.625083	+	0.780558i	$0.285065\pi$
$410$	4.21590	−	4.04849i	0.208209	−	0.199941i
$411$	5.90681	−	33.4992i	0.291361	−	1.65239i
$412$	−2.97651	−	8.17788i	−0.146642	−	0.402895i
$413$			22.9787i			1.13071i
$414$	−15.9439	+	5.80310i	−0.783599	+	0.285207i
$415$	−25.9128	+	11.4503i	−1.27201	+	0.562072i
$416$	0.435993	+	2.47264i	0.0213763	+	0.121231i
$417$	−13.0043	−	7.50802i	−0.636822	−	0.367669i
$418$	−1.52780	+	0.882076i	−0.0747272	+	0.0431437i
$419$	−17.2526	+	14.4766i	−0.842844	+	0.707230i	−0.958202	−	0.286094i	$-0.907643\pi$
$419$	−17.2526	+	14.4766i	−0.842844	+	0.707230i	0.115358	+	0.993324i	$0.463199\pi$
$420$	−4.14368	+	14.2995i	−0.202191	+	0.697742i
$421$	−10.7263	+	18.5786i	−0.522770	+	0.905464i	0.476879	+	0.878969i	$0.341768\pi$
$421$	−10.7263	+	18.5786i	−0.522770	+	0.905464i	−0.999649	+	0.0264951i	$0.991565\pi$
$422$	8.19722	−	22.5217i	0.399034	−	1.09634i
$423$	−0.432457	+	1.18817i	−0.0210268	+	0.0577706i
$424$	−1.08389	−	6.14704i	−0.0526383	−	0.298527i
$425$	12.1465	−	9.38082i	0.589194	−	0.455037i
$426$	−23.3184	−	19.5664i	−1.12978	−	0.947996i
$427$	37.9356	−	6.68906i	1.83583	−	0.323706i
$428$	−0.0643019	+	0.176668i	−0.00310815	+	0.00853957i
$429$	5.74191	+	2.08988i	0.277222	+	0.100901i
$430$	3.54317	−	4.84814i	0.170867	−	0.233798i
$431$	−2.63854	+	14.9639i	−0.127094	+	0.720785i	0.852948	+	0.521995i	$0.174812\pi$
$431$	−2.63854	+	14.9639i	−0.127094	+	0.720785i	−0.980042	+	0.198789i	$0.936299\pi$
$432$	0.945263	+	1.12652i	0.0454790	+	0.0541998i
$433$	−14.6564	+	8.46188i	−0.704342	+	0.406652i	−0.808962	−	0.587860i	$-0.799970\pi$
$433$	−14.6564	+	8.46188i	−0.704342	+	0.406652i	0.104621	+	0.994512i	$0.466637\pi$
$434$	−7.58003	+	13.1290i	−0.363853	+	0.630212i
$435$	7.20978	−	0.483870i	0.345682	−	0.0231998i
$436$	−9.12281	−	15.8012i	−0.436903	−	0.756739i
$437$	4.11977	+	11.3190i	0.197075	+	0.541460i
$438$		−	23.6091i		−	1.12809i
$439$	−2.08662	+	0.759469i	−0.0995891	+	0.0362475i	−0.391334	−	0.920249i	$-0.627986\pi$
$439$	−2.08662	+	0.759469i	−0.0995891	+	0.0362475i	0.291745	+	0.956496i	$0.405764\pi$
$440$	−2.25656	−	0.653904i	−0.107577	−	0.0311736i
$441$	2.28726	+	1.91924i	0.108917	+	0.0913924i
$442$	−4.95379	−	5.90370i	−0.235628	−	0.280810i
$443$			13.4852i			0.640701i	0.947299	+	0.320351i	$0.103801\pi$
$443$			13.4852i			0.640701i	−0.947299	+	0.320351i	$0.896199\pi$
$444$	−10.5745	−	9.31069i	−0.501844	−	0.441866i
$445$	13.7260	+	1.48153i	0.650672	+	0.0702314i
$446$	4.92552	−	4.13300i	0.233230	−	0.195703i
$447$	32.0025	−	38.1391i	1.51367	−	1.80392i
$448$	−2.83078	−	0.499142i	−0.133742	−	0.0235823i
$449$	9.37420	−	3.41193i	0.442396	−	0.161019i	−0.111211	−	0.993797i	$-0.535473\pi$
$449$	9.37420	−	3.41193i	0.442396	−	0.161019i	0.553607	+	0.832778i	$0.313251\pi$
$450$	−2.52343	+	11.5532i	−0.118955	+	0.544623i
$451$	2.58082	−	0.939341i	0.121526	−	0.0442318i
$452$	13.6467	−	7.87891i	0.641886	−	0.370593i
$453$	−27.7915	+	4.90040i	−1.30576	+	0.230241i
$454$	13.4528	−	23.3009i	0.631370	−	1.09356i
$455$	−6.52258	−	14.7611i	−0.305783	−	0.692010i
$456$	−2.97926	+	2.49989i	−0.139517	+	0.117068i
$457$	8.11252	+	1.43046i	0.379488	+	0.0669139i	0.360138	−	0.932899i	$-0.382729\pi$
$457$	8.11252	+	1.43046i	0.379488	+	0.0669139i	0.0193492	+	0.999813i	$0.493841\pi$
$458$	−8.84341	−	5.10574i	−0.413225	−	0.238576i
$459$	−4.24162	−	1.54382i	−0.197982	−	0.0720595i
$460$	−7.07242	+	14.3981i	−0.329753	+	0.671317i
$461$	0.842244	+	4.77660i	0.0392272	+	0.222469i	0.998119	−	0.0613027i	$-0.0195255\pi$
$461$	0.842244	+	4.77660i	0.0392272	+	0.222469i	−0.958892	+	0.283771i	$0.908414\pi$
$462$	−4.49658	+	5.35882i	−0.209200	+	0.249315i
$463$	20.8087	−	24.7988i	0.967060	−	1.15250i	−0.0212087	−	0.999775i	$-0.506751\pi$
$463$	20.8087	−	24.7988i	0.967060	−	1.15250i	0.988269	−	0.152723i	$-0.0488041\pi$
$464$	0.242267	+	1.37396i	0.0112469	+	0.0637846i
$465$	−12.0434	+	24.5181i	−0.558498	+	1.13700i
$466$	13.6851	+	4.98095i	0.633948	+	0.230738i
$467$	2.68238	+	1.54867i	0.124126	+	0.0716641i	0.560777	−	0.827967i	$-0.310502\pi$
$467$	2.68238	+	1.54867i	0.124126	+	0.0716641i	−0.436651	+	0.899631i	$0.643836\pi$
$468$	5.84808	+	1.03117i	0.270327	+	0.0476660i
$469$	4.77002	−	4.00252i	0.220259	−	0.184819i
$470$	0.483165	+	1.09344i	0.0222867	+	0.0504365i
$471$	−0.192385	+	0.333220i	−0.00886462	+	0.0153540i
$472$	−7.87270	+	1.38817i	−0.362370	+	0.0638957i
$473$	2.44355	−	1.41078i	0.112354	−	0.0648679i
$474$	13.1349	−	4.78072i	0.603307	−	0.219586i
$475$	8.20191	+	1.79144i	0.376329	+	0.0821971i
$476$	8.29088	−	3.01763i	0.380012	−	0.138313i
$477$	−14.5384	−	2.56352i	−0.665670	−	0.117376i
$478$	15.0963	−	17.9910i	0.690487	−	0.822890i
$479$	15.4155	−	12.9352i	0.704354	−	0.591023i	−0.218655	−	0.975802i	$-0.570167\pi$
$479$	15.4155	−	12.9352i	0.704354	−	0.591023i	0.923009	+	0.384779i	$0.125722\pi$
$480$	−5.14943	−	0.555812i	−0.235038	−	0.0253692i
$481$	15.2682	+	0.363390i	0.696169	+	0.0165692i
$482$			13.2995i			0.605774i
$483$	30.7021	+	36.5893i	1.39699	+	1.66487i
$484$	7.58083	+	6.36107i	0.344583	+	0.289140i
$485$	26.7431	+	7.74958i	1.21434	+	0.351890i
$486$	18.7119	−	6.81058i	0.848790	−	0.308934i
$487$			1.79585i			0.0813778i	0.999172	+	0.0406889i	$0.0129553\pi$
$487$			1.79585i			0.0813778i	−0.999172	+	0.0406889i	$0.987045\pi$
$488$	4.58345	+	12.5929i	0.207483	+	0.570055i
$489$	15.4588	+	26.7754i	0.699071	+	1.21083i
$490$	2.81656	−	0.189028i	0.127239	−	0.00853941i
$491$	−2.77151	+	4.80040i	−0.125077	+	0.216639i	−0.921763	−	0.387754i	$-0.873251\pi$
$491$	−2.77151	+	4.80040i	−0.125077	+	0.216639i	0.796686	+	0.604393i	$0.206584\pi$
$492$	5.24349	−	3.02733i	0.236395	−	0.136483i
$493$	−2.75265	−	3.28048i	−0.123973	−	0.147746i
$494$	0.732056	−	4.15170i	0.0329368	−	0.186794i
$495$	−3.27866	+	4.48621i	−0.147365	+	0.201640i
$496$	−4.95601	−	1.80384i	−0.222532	−	0.0809949i
$497$	−12.9199	+	35.4972i	−0.579538	+	1.59227i
$498$	−28.9002	+	5.09588i	−1.29505	+	0.228352i
$499$	−24.2344	−	20.3351i	−1.08488	−	0.910323i	−0.0885636	−	0.996071i	$-0.528228\pi$
$499$	−24.2344	−	20.3351i	−1.08488	−	0.910323i	−0.996317	+	0.0857478i	$0.972672\pi$
$500$	5.84481	+	9.53091i	0.261388	+	0.426235i
$501$	−6.14729	−	34.8630i	−0.274641	−	1.55756i
$502$	−1.58780	+	4.36245i	−0.0708671	+	0.194706i
$503$	13.6123	−	37.3994i	0.606942	−	1.66756i	−0.129928	−	0.991523i	$-0.541475\pi$
$503$	13.6123	−	37.3994i	0.606942	−	1.66756i	0.736870	−	0.676035i	$-0.236303\pi$
$504$	−3.39920	+	5.88758i	−0.151412	+	0.262254i
$505$	3.15566	−	10.8899i	0.140425	−	0.484595i
$506$	−5.77407	+	4.84502i	−0.256689	+	0.215387i
$507$	13.4318	−	7.75483i	0.596525	−	0.344404i
$508$	2.55393	+	1.47451i	0.113312	+	0.0654209i
$509$	−2.06324	−	11.7012i	−0.0914514	−	0.518647i	−0.995777	−	0.0918037i	$-0.970737\pi$
$509$	−2.06324	−	11.7012i	−0.0914514	−	0.518647i	0.904326	−	0.426843i	$-0.140374\pi$
$510$	14.5414	−	6.42549i	0.643902	−	0.284525i
$511$	−27.5315	+	10.0207i	−1.21792	+	0.443288i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.844504	−	2.32026i	−0.0372858	−	0.102442i
$514$	5.31571	−	30.1469i	0.234466	−	1.32972i
$515$	−14.0361	+	13.4787i	−0.618503	+	0.593943i
$516$	4.76499	−	3.99831i	0.209767	−	0.176016i
$517$			0.561708i			0.0247039i
$518$	−6.36932	+	16.2832i	−0.279852	+	0.715442i
$519$	19.3559			0.849631
$520$	4.66323	−	3.12642i	0.204496	−	0.137103i
$521$	19.6236	+	16.4661i	0.859725	+	0.721395i	0.961909	−	0.273371i	$-0.0881385\pi$
$521$	19.6236	+	16.4661i	0.859725	+	0.721395i	−0.102184	+	0.994766i	$0.532583\pi$
$522$	3.24958	+	0.572988i	0.142230	+	0.0250790i
$523$	8.81070	+	24.2072i	0.385265	+	1.05851i	0.969107	+	0.246640i	$0.0793264\pi$
$523$	8.81070	+	24.2072i	0.385265	+	1.05851i	−0.583842	+	0.811867i	$0.698451\pi$
$524$	17.3798			0.759241
$525$	32.9914	−	4.44835i	1.43986	−	0.194142i
$526$	2.00858	+	3.47897i	0.0875783	+	0.151690i
$527$	15.9426	−	2.81111i	0.694470	−	0.122454i
$528$	−2.10762	−	1.21683i	−0.0917222	−	0.0529558i
$529$	14.2325	+	24.6515i	0.618806	+	1.07180i
$530$	−11.5929	+	7.77235i	−0.503563	+	0.337609i
$531$	−3.28318	+	18.6198i	−0.142478	+	0.808032i
$532$	4.17974	+	2.41317i	0.181215	+	0.104624i
$533$	−2.24472	+	6.16731i	−0.0972295	+	0.267136i
$534$	13.4384	+	4.89118i	0.581537	+	0.211662i
$535$	0.419451	−	0.0281506i	0.0181344	−	0.00121706i
$536$	1.65946	+	1.39245i	0.0716776	+	0.0601447i
$537$	−33.3107	+	39.6981i	−1.43746	+	1.71310i
$538$	11.8912	−	2.09674i	0.512665	−	0.0903967i
$539$	1.24643	+	0.453662i	0.0536874	+	0.0195406i
$540$	1.44976	−	2.95145i	0.0623879	−	0.127010i
$541$	−3.01111	+	5.21539i	−0.129458	+	0.224227i	−0.923467	−	0.383679i	$-0.874657\pi$
$541$	−3.01111	+	5.21539i	−0.129458	+	0.224227i	0.794009	+	0.607906i	$0.207990\pi$
$542$	−5.36824	−	0.946566i	−0.230586	−	0.0406585i
$543$	−38.6960	−	46.1161i	−1.66061	−	1.97903i
$544$	1.53473	+	2.65822i	0.0658008	+	0.113970i
$545$	−24.0731	+	32.9393i	−1.03118	+	1.41097i
$546$	−2.90284	−	16.4628i	−0.124230	−	0.704544i
$547$	−10.7753	+	6.22111i	−0.460718	+	0.265995i	−0.712346	−	0.701829i	$-0.752367\pi$
$547$	−10.7753	+	6.22111i	−0.460718	+	0.265995i	0.251628	+	0.967824i	$0.419034\pi$
$548$	−5.02279	−	13.8000i	−0.214563	−	0.589507i
$549$	31.6952			1.35272
$550$	0.701983	+	5.20630i	0.0299326	+	0.221997i
$551$	0.406779	−	2.30696i	0.0173294	−	0.0982797i
$552$	−10.6810	+	12.7292i	−0.454615	+	0.541789i
$553$	−11.1500	−	13.2880i	−0.474145	−	0.565064i
$554$	25.0409			1.06389
$555$	−9.48617	+	30.0426i	−0.402665	+	1.27524i
$556$	−6.48285			−0.274934
$557$	−10.5357	−	12.5559i	−0.446410	−	0.532011i	0.495172	−	0.868795i	$-0.335105\pi$
$557$	−10.5357	−	12.5559i	−0.446410	−	0.532011i	−0.941582	+	0.336784i	$0.890661\pi$
$558$	−8.01800	+	9.55548i	−0.339429	+	0.404516i
$559$	−1.17084	+	6.64018i	−0.0495214	+	0.280850i
$560$	1.53747	+	6.24086i	0.0649700	+	0.263725i
$561$	7.47001			0.315384
$562$	6.44334	+	17.7029i	0.271796	+	0.746753i
$563$	−15.9273	+	9.19564i	−0.671256	+	0.387550i	−0.796553	−	0.604569i	$-0.793345\pi$
$563$	−15.9273	+	9.19564i	−0.671256	+	0.387550i	0.125296	+	0.992119i	$0.460012\pi$
$564$	0.215030	+	1.21950i	0.00905439	+	0.0513500i
$565$	−28.4481	−	20.7907i	−1.19682	−	0.874671i
$566$	−8.66810	−	15.0136i	−0.364347	−	0.631068i
$567$	−19.4033	−	23.1240i	−0.814863	−	0.971116i
$568$	−12.9421	−	2.28205i	−0.543040	−	0.0957526i
$569$	−9.65896	+	16.7298i	−0.404925	+	0.701350i	−0.994313	−	0.106500i	$-0.966036\pi$
$569$	−9.65896	+	16.7298i	−0.404925	+	0.701350i	0.589388	+	0.807850i	$0.299369\pi$
$570$	7.80556	+	3.83412i	0.326939	+	0.160594i
$571$	34.5136	+	12.5619i	1.44435	+	0.525700i	0.941007	−	0.338388i	$-0.109881\pi$
$571$	34.5136	+	12.5619i	1.44435	+	0.525700i	0.503342	+	0.864087i	$0.332104\pi$
$572$	2.59796	−	0.458090i	0.108626	−	0.0191537i
$573$	−19.4801	+	23.2155i	−0.813793	+	0.969841i
$574$	−5.75583	−	4.82972i	−0.240244	−	0.201589i
$575$	35.8402	+	1.45260i	1.49464	+	0.0605777i
$576$	−2.22248	−	0.808917i	−0.0926033	−	0.0337049i
$577$	11.1810	−	30.7196i	0.465472	−	1.27887i	−0.455844	−	0.890060i	$-0.650663\pi$
$577$	11.1810	−	30.7196i	0.465472	−	1.27887i	0.921316	−	0.388814i	$-0.127115\pi$
$578$	6.56315	+	3.78924i	0.272991	+	0.157611i
$579$	6.90457	−	39.1578i	0.286944	−	1.62734i
$580$	2.59120	−	1.73725i	0.107594	−	0.0721352i
$581$	18.2089	+	31.5388i	0.755433	+	1.30845i
$582$	24.9779	+	14.4210i	1.03537	+	0.597769i
$583$	−6.45858	+	1.13882i	−0.267487	+	0.0471652i
$584$	−5.09637	−	8.82717i	−0.210889	−	0.365271i
$585$	−3.17625	−	12.8929i	−0.131322	−	0.533058i
$586$	1.21677			0.0502645
$587$	0.0413219	+	0.113531i	0.00170554	+	0.00468592i	0.940542	−	0.339676i	$-0.110317\pi$
$587$	0.0413219	+	0.113531i	0.00170554	+	0.00468592i	−0.938837	+	0.344362i	$0.888095\pi$
$588$	2.87972	+	0.507773i	0.118758	+	0.0209402i
$589$	6.78368	+	5.69218i	0.279517	+	0.234542i
$590$	9.95429	+	14.8474i	0.409811	+	0.611256i
$591$	13.3521			0.549232
$592$	−5.96352	−	1.19849i	−0.245099	−	0.0492578i
$593$		−	12.5915i		−	0.517071i	−0.966002	−	0.258536i	$-0.916760\pi$
$593$		−	12.5915i		−	0.517071i	0.966002	−	0.258536i	$-0.0832400\pi$
$594$	1.18362	−	0.993171i	0.0485643	−	0.0407503i
$595$	−13.6649	−	14.2300i	−0.560208	−	0.583373i
$596$	3.73248	−	21.1680i	0.152888	−	0.867073i
$597$	16.7760	+	46.0917i	0.686597	+	1.88641i
$598$		−	18.0122i		−	0.736572i
$599$	−16.9227	+	6.15935i	−0.691442	+	0.251664i	−0.663752	−	0.747952i	$-0.731037\pi$
$599$	−16.9227	+	6.15935i	−0.691442	+	0.251664i	−0.0276894	+	0.999617i	$0.508815\pi$
$600$	3.51709	+	11.0344i	0.143584	+	0.450477i
$601$	2.00267	+	11.3577i	0.0816904	+	0.463289i	0.998022	+	0.0628687i	$0.0200249\pi$
$601$	2.00267	+	11.3577i	0.0816904	+	0.463289i	−0.916331	+	0.400421i	$0.868864\pi$
$602$	−6.68503	−	3.85961i	−0.272462	−	0.157306i
$603$	4.43705	−	2.56173i	0.180691	−	0.104322i
$604$	−9.33309	+	7.83139i	−0.379758	+	0.318655i
$605$	6.15893	−	21.2539i	0.250396	−	0.864094i
$606$	5.87229	−	10.1711i	0.238546	−	0.413173i
$607$	6.51220	−	17.8921i	0.264322	−	0.726219i	−0.734542	−	0.678563i	$-0.762603\pi$
$607$	6.51220	−	17.8921i	0.264322	−	0.726219i	0.998864	−	0.0476553i	$-0.0151749\pi$
$608$	−0.574270	+	1.57779i	−0.0232897	+	0.0639880i
$609$	−1.61301	−	9.14784i	−0.0653625	−	0.370689i
$610$	21.6138	−	20.7555i	0.875118	−	0.840368i
$611$	−1.02826	−	0.862812i	−0.0415989	−	0.0349056i
$612$	7.14931	−	1.26062i	0.288994	−	0.0509574i
$613$	7.77465	−	21.3607i	0.314015	−	0.862750i	−0.677820	−	0.735228i	$-0.737075\pi$
$613$	7.77465	−	21.3607i	0.314015	−	0.862750i	0.991836	−	0.127522i	$-0.0407025\pi$
$614$	−3.23401	−	1.17708i	−0.130514	−	0.0475033i
$615$	−10.9307	−	7.98845i	−0.440766	−	0.322125i
$616$	−0.524440	+	2.97425i	−0.0211303	+	0.119836i
$617$	−14.1216	−	16.8295i	−0.568514	−	0.677528i	0.402812	−	0.915283i	$-0.368033\pi$
$617$	−14.1216	−	16.8295i	−0.568514	−	0.677528i	−0.971325	+	0.237755i	$0.923589\pi$
$618$	−17.4572	+	10.0789i	−0.702233	+	0.405434i
$619$	−3.61006	+	6.25281i	−0.145101	+	0.251322i	−0.929411	−	0.369048i	$-0.879684\pi$
$619$	−3.61006	+	6.25281i	−0.145101	+	0.251322i	0.784310	+	0.620369i	$0.213017\pi$
$620$	0.789701	+	11.7667i	0.0317151	+	0.472563i
$621$	−5.27487	−	9.13634i	−0.211673	−	0.366629i
$622$	6.59524	+	18.1203i	0.264445	+	0.726556i
$623$		−	17.7471i		−	0.711021i
$624$	5.46493	−	1.98907i	0.218772	−	0.0796266i
$625$	14.2111	−	20.5680i	0.568445	−	0.822721i
$626$	−20.9577	−	17.5856i	−0.837637	−	0.702861i
$627$	2.62659	+	3.13025i	0.104896	+	0.125010i
$628$			0.166116i			0.00662874i
$629$	17.6917	−	5.96651i	0.705415	−	0.237900i
$630$	15.1139	+	1.63134i	0.602151	+	0.0649942i
$631$	−23.5711	+	19.7785i	−0.938350	+	0.787369i	−0.977297	−	0.211872i	$-0.932044\pi$
$631$	−23.5711	+	19.7785i	−0.938350	+	0.787369i	0.0389473	+	0.999241i	$0.487600\pi$
$632$	3.87900	−	4.62281i	0.154298	−	0.183886i
$633$	−54.6708	−	9.63994i	−2.17297	−	0.383153i
$634$	5.88580	−	2.14226i	0.233755	−	0.0850798i
$635$	0.707648	−	6.55614i	0.0280821	−	0.260172i
$636$	−13.5859	+	4.94488i	−0.538718	+	0.196077i
$637$	−2.74505	+	1.58485i	−0.108763	+	0.0627942i
$638$	1.44360	−	0.254545i	0.0571526	−	0.0100775i
$639$	−15.5409	+	26.9176i	−0.614789	+	1.06485i
$640$	−2.04529	+	0.903766i	−0.0808471	+	0.0357245i
$641$	30.7667	−	25.8163i	1.21521	−	1.01968i	0.216150	−	0.976360i	$-0.430650\pi$
$641$	30.7667	−	25.8163i	1.21521	−	1.01968i	0.999061	−	0.0433234i	$-0.0137946\pi$
$642$	0.428857	+	0.0756191i	0.0169256	+	0.00298445i
$643$	14.5439	+	8.39695i	0.573557	+	0.331143i	0.758569	−	0.651593i	$-0.225899\pi$
$643$	14.5439	+	8.39695i	0.573557	+	0.331143i	−0.185012	+	0.982736i	$0.559232\pi$
$644$	19.3774	+	7.05281i	0.763578	+	0.277920i
$645$	−12.4841	−	6.13226i	−0.491562	−	0.241457i
$646$	−0.894943	−	5.07548i	−0.0352111	−	0.199692i
$647$	25.2181	−	30.0538i	0.991426	−	1.18154i	0.00804795	−	0.999968i	$-0.497438\pi$
$647$	25.2181	−	30.0538i	0.991426	−	1.18154i	0.983378	−	0.181568i	$-0.0581173\pi$
$648$	6.75028	−	8.04468i	0.265176	−	0.316025i
$649$	1.45852	+	8.27170i	0.0572521	+	0.324693i
$650$	−10.6089	−	6.71210i	−0.416115	−	0.263270i
$651$	32.9971	+	12.0100i	1.29326	+	0.470708i
$652$	11.5597	+	6.67400i	0.452713	+	0.261374i
$653$	−6.39892	−	1.12830i	−0.250409	−	0.0441539i	0.0470345	−	0.998893i	$-0.485023\pi$
$653$	−6.39892	−	1.12830i	−0.250409	−	0.0441539i	−0.297444	+	0.954739i	$0.596134\pi$
$654$	−32.3744	+	27.1654i	−1.26594	+	1.06225i
$655$	−15.7073	−	35.5468i	−0.613735	−	1.38893i
$656$	1.30698	−	2.26376i	0.0510292	−	0.0883851i
$657$	−23.7407	+	4.18613i	−0.926214	+	0.163317i
$658$	1.33083	−	0.768357i	0.0518813	−	0.0299537i
$659$	−2.06610	+	0.752001i	−0.0804840	+	0.0292938i	−0.381948	−	0.924184i	$-0.624747\pi$
$659$	−2.06610	+	0.752001i	−0.0804840	+	0.0292938i	0.301464	+	0.953477i	$0.402525\pi$
$660$	−0.583982	+	5.41042i	−0.0227315	+	0.210600i
$661$	14.8195	−	5.39384i	0.576410	−	0.209796i	−0.0373315	−	0.999303i	$-0.511886\pi$
$661$	14.8195	−	5.39384i	0.576410	−	0.209796i	0.613742	+	0.789507i	$0.289664\pi$
$662$	−0.921065	−	0.162409i	−0.0357982	−	0.00631219i
$663$	−11.4743	+	13.6746i	−0.445626	+	0.531076i
$664$	−9.70541	+	8.14381i	−0.376643	+	0.316041i
$665$	1.15813	−	10.7297i	0.0449104	−	0.416081i
$666$	−7.48762	+	12.2843i	−0.290140	+	0.476008i
$667$		−	10.0087i		−	0.387540i
$668$	−9.82407	−	11.7079i	−0.380105	−	0.452991i
$669$	−11.4088	−	9.57316i	−0.441091	−	0.370120i
$670$	1.34820	−	4.65252i	0.0520855	−	0.179742i
$671$	13.2312	−	4.81575i	0.510783	−	0.185910i
$672$			6.65800i			0.256838i
$673$	−8.14861	−	22.3881i	−0.314106	−	0.862999i	−0.991817	−	0.127670i	$-0.959250\pi$
$673$	−8.14861	−	22.3881i	−0.314106	−	0.862999i	0.677711	−	0.735329i	$-0.262972\pi$
$674$	16.2511	+	28.1477i	0.625968	+	1.08421i
$675$	−7.34681	−	0.297766i	−0.282779	−	0.0114610i
$676$	3.34798	−	5.79887i	0.128768	−	0.223033i
$677$	18.4034	−	10.6252i	0.707302	−	0.408361i	−0.102759	−	0.994706i	$-0.532767\pi$
$677$	18.4034	−	10.6252i	0.707302	−	0.408361i	0.810061	+	0.586345i	$0.199434\pi$
$678$	−23.4614	−	27.9602i	−0.901028	−	1.07380i
$679$	6.21527	−	35.2485i	0.238520	−	1.35271i
$680$	4.04980	−	5.54137i	0.155303	−	0.212502i
$681$	−58.5621	−	21.3149i	−2.24411	−	0.816788i
$682$	−1.89526	+	5.20719i	−0.0725734	+	0.199394i
$683$	−3.57104	+	0.629670i	−0.136642	+	0.0240937i	−0.241551	−	0.970388i	$-0.577656\pi$
$683$	−3.57104	+	0.629670i	−0.136642	+	0.0240937i	0.104909	+	0.994482i	$0.466545\pi$
$684$	3.04208	+	2.55261i	0.116317	+	0.0976014i
$685$	−23.6856	+	22.7450i	−0.904978	+	0.869043i
$686$	2.86386	+	16.2418i	0.109343	+	0.620113i
$687$	−8.08966	+	22.2262i	−0.308640	+	0.847981i
$688$	0.918482	−	2.52351i	0.0350168	−	0.0962079i
$689$	7.83599	−	13.5723i	0.298528	−	0.517065i
$690$	35.6880	+	10.3416i	1.35862	+	0.393699i
$691$	17.0216	−	14.2828i	0.647530	−	0.543343i	−0.258790	−	0.965934i	$-0.583324\pi$
$691$	17.0216	−	14.2828i	0.647530	−	0.543343i	0.906320	+	0.422591i	$0.138879\pi$
$692$	7.23695	−	4.17825i	0.275107	−	0.158833i
$693$	6.18597	+	3.57147i	0.234986	+	0.135669i
$694$	0.602066	+	3.41449i	0.0228541	+	0.129612i
$695$	5.85898	+	13.2593i	0.222244	+	0.502954i
$696$	3.03668	−	1.10526i	0.115105	−	0.0418948i
$697$			8.02345i			0.303910i
$698$	1.52855	+	4.19965i	0.0578564	+	0.158959i
$699$	5.85761	−	33.2202i	0.221555	−	1.25650i
$700$	11.3749	−	8.78485i	0.429929	−	0.332036i
$701$	−25.2801	+	21.2125i	−0.954814	+	0.801184i	−0.980102	−	0.198496i	$-0.936394\pi$
$701$	−25.2801	+	21.2125i	−0.954814	+	0.801184i	0.0252873	+	0.999680i	$0.491950\pi$
$702$			3.69228i			0.139356i
$703$	8.72095	+	5.31565i	0.328917	+	0.200484i
$704$	−1.05068			−0.0395991
$705$	2.29988	−	1.54194i	0.0866186	−	0.0580727i
$706$	−1.98483	−	1.66547i	−0.0747001	−	0.0626808i
$707$	−14.3534	−	2.53089i	−0.539814	−	0.0951838i
$708$	6.33306	+	17.3999i	0.238011	+	0.653929i
$709$	−45.5646			−1.71121			−0.855607	−	0.517626i	$-0.826816\pi$
$709$	−45.5646			−1.71121			−0.855607	+	0.517626i	$0.826816\pi$
$710$	7.02922	+	28.5328i	0.263802	+	1.07082i
$711$	−7.13632	−	12.3605i	−0.267633	−	0.463554i
$712$	6.08029	−	1.07212i	0.227868	−	0.0401793i
$713$	32.7668	+	18.9179i	1.22713	+	0.708481i
$714$	−10.2182	−	17.6984i	−0.382406	−	0.662347i
$715$	−3.28487	−	4.89957i	−0.122847	−	0.183234i
$716$	−3.88505	+	22.0332i	−0.145191	+	0.823420i
$717$	−47.1109	−	27.1995i	−1.75939	−	1.01578i
$718$	−10.5116	+	28.8803i	−0.392288	+	1.07780i
$719$	3.18941	+	1.16085i	0.118945	+	0.0432924i	0.400807	−	0.916163i	$-0.368730\pi$
$719$	3.18941	+	1.16085i	0.118945	+	0.0432924i	−0.281862	+	0.959455i	$0.590952\pi$
$720$	0.354134	+	5.27669i	0.0131978	+	0.196650i
$721$	19.1630	+	16.0797i	0.713667	+	0.598838i
$722$	−10.4008	+	12.3952i	−0.387078	+	0.461301i
$723$	30.3371	−	5.34926i	1.12825	−	0.198941i
$724$	−24.4228	−	8.88917i	−0.907666	−	0.330363i
$725$	−5.89501	−	3.72968i	−0.218935	−	0.138517i
$726$	11.4610	−	19.8510i	0.425357	−	0.736740i
$727$	49.9030	+	8.79925i	1.85080	+	0.326346i	0.984800	−	0.173694i	$-0.0555705\pi$
$727$	49.9030	+	8.79925i	1.85080	+	0.326346i	0.866002	+	0.500041i	$0.166682\pi$
$728$	−4.63907	−	5.52863i	−0.171935	−	0.204905i
$729$	−7.30936	−	12.6602i	−0.270717	−	0.468896i
$730$	−13.4482	+	18.4012i	−0.497740	+	0.681060i
$731$	1.43136	+	8.11766i	0.0529409	+	0.300243i
$732$	26.8820	−	15.5203i	0.993586	−	0.573647i
$733$	4.21567	+	11.5824i	0.155709	+	0.427807i	0.992878	−	0.119138i	$-0.0380129\pi$
$733$	4.21567	+	11.5824i	0.155709	+	0.427807i	−0.837169	+	0.546945i	$0.815791\pi$
$734$	2.31963			0.0856192
$735$	−1.56405	−	6.34877i	−0.0576910	−	0.234178i
$736$	−1.24574	+	7.06493i	−0.0459185	+	0.260417i
$737$	1.46302	−	1.74356i	0.0538911	−	0.0642249i
$738$	−3.97393	−	4.73594i	−0.146282	−	0.174332i
$739$	−38.5263			−1.41721			−0.708606	−	0.705604i	$-0.750676\pi$
$739$	−38.5263			−1.41721			−0.708606	+	0.705604i	$0.750676\pi$
$740$	2.93836	+	13.2803i	0.108016	+	0.488193i
$741$	−9.76481			−0.358719
$742$	11.5328	+	13.7443i	0.423384	+	0.504569i
$743$	13.0249	−	15.5224i	0.477836	−	0.569463i	−0.472245	−	0.881468i	$-0.656556\pi$
$743$	13.0249	−	15.5224i	0.477836	−	0.569463i	0.950080	+	0.312005i	$0.101001\pi$
$744$	−2.12132	+	12.0306i	−0.0777714	+	0.441063i
$745$	−46.6679	+	11.4969i	−1.70978	+	0.421213i
$746$	−15.5497			−0.569315
$747$	10.2486	+	28.1577i	0.374976	+	1.03024i
$748$	2.79295	−	1.61251i	0.102120	−	0.0589591i
$749$	−0.0938418	−	0.532203i	−0.00342890	−	0.0194463i
$750$	19.3899	−	17.1660i	0.708019	−	0.626813i
$751$	14.6236	+	25.3288i	0.533623	+	0.924262i	0.999229	+	0.0392700i	$0.0125032\pi$
$751$	14.6236	+	25.3288i	0.533623	+	0.924262i	−0.465606	+	0.884992i	$0.654163\pi$
$752$	0.343642	+	0.409537i	0.0125313	+	0.0149343i
$753$	10.5898	+	1.86726i	0.385912	+	0.0680467i
$754$	−1.75147	+	3.03364i	−0.0637848	+	0.110479i
$755$	24.4524	+	12.0111i	0.889914	+	0.437129i
$756$	−3.97215	−	1.44574i	−0.144466	−	0.0525812i
$757$	−7.67693	+	1.35365i	−0.279023	+	0.0491992i	−0.311408	−	0.950276i	$-0.600801\pi$
$757$	−7.67693	+	1.35365i	−0.279023	+	0.0491992i	0.0323856	+	0.999475i	$0.489690\pi$
$758$	−6.80493	+	8.10979i	−0.247166	+	0.294561i
$759$	13.3743	+	11.2224i	0.485456	+	0.407346i
$760$	3.74605	−	0.251409i	0.135884	−	0.00911956i
$761$	9.19817	+	3.34786i	0.333433	+	0.121360i	0.503311	−	0.864105i	$-0.332115\pi$
$761$	9.19817	+	3.34786i	0.333433	+	0.121360i	−0.169878	+	0.985465i	$0.554337\pi$
$762$	2.33625	−	6.41880i	0.0846335	−	0.232528i
$763$	45.4196	+	26.2230i	1.64430	+	0.949337i
$764$	−2.27198	+	12.8850i	−0.0821974	+	0.466164i
$765$	−9.03963	−	13.4831i	−0.326829	−	0.487483i
$766$	16.5814	+	28.7198i	0.599110	+	1.03769i
$767$	−17.3825	−	10.0358i	−0.627646	−	0.362371i
$768$	−2.28108	+	0.402216i	−0.0823115	+	0.0145137i
$769$	2.86689	+	4.96559i	0.103383	+	0.179064i	0.913076	−	0.407789i	$-0.133700\pi$
$769$	2.86689	+	4.96559i	0.103383	+	0.179064i	−0.809694	+	0.586853i	$0.800367\pi$
$770$	6.55716	−	1.61539i	0.236304	−	0.0582147i
$771$	−70.9055			−2.55360
$772$	−5.87122	−	16.1311i	−0.211310	−	0.580569i
$773$	18.5359	+	3.26837i	0.666689	+	0.117555i	0.496742	−	0.867898i	$-0.334529\pi$
$773$	18.5359	+	3.26837i	0.666689	+	0.117555i	0.169947	+	0.985453i	$0.445641\pi$
$774$	−4.86547	−	4.08262i	−0.174886	−	0.146747i
$775$	23.3527	−	12.2495i	0.838852	−	0.440016i
$776$	12.4519			0.446997
$777$	39.7051	+	7.97957i	1.42441	+	0.286266i
$778$		−	7.72459i		−	0.276940i
$779$	−3.36216	+	2.82119i	−0.120462	+	0.101080i
$780$	−9.00725	−	9.37971i	−0.322511	−	0.335847i
$781$	−2.39771	+	13.5981i	−0.0857967	+	0.486577i
$782$	−7.53128	−	20.6920i	−0.269318	−	0.739945i
$783$			2.05168i			0.0733209i
$784$	1.18630	−	0.431779i	0.0423680	−	0.0154207i
$785$	0.339755	−	0.150130i	0.0121264	−	0.00535836i
$786$	−6.99045	−	39.6448i	−0.249341	−	1.41408i
$787$	−31.3851	−	18.1202i	−1.11876	−	0.645915i	−0.177674	−	0.984089i	$-0.556857\pi$
$787$	−31.3851	−	18.1202i	−1.11876	−	0.645915i	−0.941083	+	0.338175i	$0.890190\pi$
$788$	4.99218	−	2.88224i	0.177839	−	0.102675i
$789$	7.12792	−	5.98104i	0.253761	−	0.212931i
$790$	−12.9607	−	3.75574i	−0.461121	−	0.133623i
$791$	−22.6475	+	39.2266i	−0.805252	+	1.39474i
$792$	−0.849914	+	2.33512i	−0.0302004	+	0.0829749i
$793$	−11.5081	+	31.6181i	−0.408663	+	1.12279i
$794$	1.33552	+	7.57413i	0.0473960	+	0.268796i
$795$	22.3922	+	23.3182i	0.794170	+	0.827010i
$796$	16.2219	+	13.6118i	0.574970	+	0.482457i
$797$	9.02198	−	1.59082i	0.319575	−	0.0563497i	−0.0115598	−	0.999933i	$-0.503680\pi$
$797$	9.02198	−	1.59082i	0.319575	−	0.0563497i	0.331135	+	0.943584i	$0.392569\pi$
$798$	3.82349	−	10.5050i	0.135350	−	0.371871i
$799$	−1.54200	−	0.561244i	−0.0545522	−	0.0198554i
$800$	3.69693	+	3.36641i	0.130706	+	0.119021i
$801$	2.53568	−	14.3806i	0.0895940	−	0.508113i
$802$	9.70541	+	11.5665i	0.342710	+	0.408426i
$803$	−9.27455	+	5.35466i	−0.327292	+	0.188962i
$804$	2.50883	−	4.34542i	0.0884797	−	0.153251i
$805$	−3.08764	−	46.0065i	−0.108825	−	1.62152i
$806$	−6.62104	−	11.4680i	−0.233216	−	0.403942i
$807$	−9.56566	−	26.2814i	−0.336727	−	0.925150i
$808$		−	5.07047i		−	0.178379i
$809$	20.6851	−	7.52875i	0.727248	−	0.264697i	0.0482487	−	0.998835i	$-0.484636\pi$
$809$	20.6851	−	7.52875i	0.727248	−	0.264697i	0.679000	+	0.734139i	$0.262414\pi$
$810$	−22.5544	−	6.53578i	−0.792480	−	0.229644i
$811$	15.9886	+	13.4160i	0.561436	+	0.471101i	0.878792	−	0.477206i	$-0.158350\pi$
$811$	15.9886	+	13.4160i	0.561436	+	0.471101i	−0.317355	+	0.948307i	$0.602795\pi$
$812$	−2.57777	−	3.07207i	−0.0904622	−	0.107809i
$813$			12.6261i			0.442817i
$814$	−1.25924	+	6.26577i	−0.0441362	+	0.219615i
$815$	3.20298	−	29.6747i	0.112196	−	1.03946i
$816$	5.44633	−	4.57001i	0.190660	−	0.159983i
$817$	−2.89835	+	3.45412i	−0.101400	+	0.120844i
$818$	0.911864	+	0.160786i	0.0318826	+	0.00562176i
$819$	−16.0399	+	5.83804i	−0.560479	+	0.203998i
$820$	−5.81126	−	0.627248i	−0.202938	−	0.0219044i
$821$	−24.5544	+	8.93707i	−0.856954	+	0.311906i	−0.732872	−	0.680366i	$-0.761821\pi$
$821$	−24.5544	+	8.93707i	−0.856954	+	0.311906i	−0.124082	+	0.992272i	$0.539599\pi$
$822$	−29.4587	+	17.0080i	−1.02749	+	0.593221i
$823$	−9.69313	+	1.70916i	−0.337881	+	0.0595776i	−0.340015	−	0.940420i	$-0.610432\pi$
$823$	−9.69313	+	1.70916i	−0.337881	+	0.0595776i	0.00213345	+	0.999998i	$0.499321\pi$
$824$	−4.35136	+	7.53678i	−0.151587	+	0.262556i
$825$	11.5936	−	3.69534i	0.403639	−	0.128655i
$826$	17.6027	−	14.7705i	0.612478	−	0.513930i
$827$	−21.8000	−	3.84393i	−0.758060	−	0.133666i	−0.218758	−	0.975779i	$-0.570201\pi$
$827$	−21.8000	−	3.84393i	−0.758060	−	0.133666i	−0.539302	+	0.842113i	$0.681312\pi$
$828$	14.6940	+	8.48357i	0.510651	+	0.294824i
$829$	−15.0185	−	5.46628i	−0.521613	−	0.189852i	0.0677764	−	0.997701i	$-0.478410\pi$
$829$	−15.0185	−	5.46628i	−0.521613	−	0.189852i	−0.589390	+	0.807849i	$0.700632\pi$
$830$	25.4279	+	12.4903i	0.882614	+	0.433544i
$831$	−10.0719	−	57.1204i	−0.349389	−	1.98149i
$832$	1.61390	−	1.92337i	0.0559520	−	0.0666810i
$833$	−2.49079	+	2.96841i	−0.0863009	+	0.102849i
$834$	2.60751	+	14.7879i	0.0902906	+	0.512064i
$835$	−15.0673	+	30.6742i	−0.521426	+	1.06153i
$836$	1.65776	+	0.603375i	0.0573348	+	0.0208682i
$837$	−6.71680	−	3.87795i	−0.232167	−	0.134041i
$838$	22.1795	+	3.91084i	0.766178	+	0.135098i
$839$	−39.2827	+	32.9621i	−1.35619	+	1.13798i	−0.379050	+	0.925376i	$0.623749\pi$
$839$	−39.2827	+	32.9621i	−1.35619	+	1.13798i	−0.977139	+	0.212601i	$0.931807\pi$
$840$	13.6175	−	6.01727i	0.469849	−	0.207616i
$841$	13.5268	−	23.4290i	0.466440	−	0.807898i
$842$	21.1268	−	3.72522i	0.728076	−	0.128380i
$843$	37.7902	−	21.8182i	1.30156	−	0.751458i
$844$	−22.5217	+	8.19722i	−0.775228	+	0.282160i
$845$	−14.8862	−	1.60676i	−0.512099	−	0.0552743i
$846$	1.18817	−	0.432457i	0.0408500	−	0.0148682i
$847$	−28.0136	−	4.93955i	−0.962557	−	0.169725i
$848$	−4.01219	+	4.78155i	−0.137779	+	0.164199i
$849$	−30.7608	+	25.8114i	−1.05571	+	0.885844i
$850$	−14.9938	−	3.27491i	−0.514282	−	0.112328i
$851$	40.6389	+	15.8963i	1.39308	+	0.544917i
$852$			30.4399i			1.04286i
$853$	−13.5285	−	16.1227i	−0.463208	−	0.552030i	0.482987	−	0.875628i	$-0.339552\pi$
$853$	−13.5285	−	16.1227i	−0.463208	−	0.552030i	−0.946195	+	0.323598i	$0.895107\pi$
$854$	−29.5086	−	24.7607i	−1.00976	−	0.847293i
$855$	2.47149	−	8.52889i	0.0845232	−	0.291682i
$856$	0.176668	−	0.0643019i	0.00603838	−	0.00219779i
$857$			34.6817i			1.18470i	0.805679	+	0.592352i	$0.201800\pi$
$857$			34.6817i			1.18470i	−0.805679	+	0.592352i	$0.798200\pi$
$858$	−2.08988	−	5.74191i	−0.0713474	−	0.196025i
$859$	6.79939	+	11.7769i	0.231992	+	0.401822i	0.958394	−	0.285448i	$-0.0921422\pi$
$859$	6.79939	+	11.7769i	0.231992	+	0.401822i	−0.726402	+	0.687270i	$0.758809\pi$
$860$	−5.99140	+	0.402101i	−0.204305	+	0.0137115i
$861$	−8.70189	+	15.0721i	−0.296560	+	0.513657i
$862$	13.1590	−	7.59736i	0.448198	−	0.258767i
$863$	−6.99287	−	8.33377i	−0.238040	−	0.283685i	0.633778	−	0.773515i	$-0.281503\pi$
$863$	−6.99287	−	8.33377i	−0.238040	−	0.283685i	−0.871818	+	0.489830i	$0.837059\pi$
$864$	0.255362	−	1.44823i	0.00868758	−	0.0492697i
$865$	−15.0862	−	11.0255i	−0.512948	−	0.374878i
$866$	15.9031	+	5.78826i	0.540410	+	0.196693i
$867$	6.00375	−	16.4952i	0.203898	−	0.560206i
$868$	14.9297	−	2.63252i	0.506748	−	0.0893534i
$869$	−4.85711	−	4.07560i	−0.164766	−	0.138255i
$870$	−5.00502	−	5.21199i	−0.169686	−	0.176703i
$871$	0.944478	+	5.35640i	0.0320024	+	0.181495i
$872$	−6.24037	+	17.1453i	−0.211325	+	0.580612i
$873$	10.0725	−	27.6741i	0.340904	−	0.936626i
$874$	6.02270	−	10.4316i	0.203721	−	0.352855i
$875$	−28.2478	−	15.3254i	−0.954949	−	0.518093i
$876$	−18.0857	+	15.1757i	−0.611058	+	0.512738i
$877$	−35.7673	+	20.6503i	−1.20778	+	0.697310i	−0.962273	−	0.272085i	$-0.912287\pi$
$877$	−35.7673	+	20.6503i	−1.20778	+	0.697310i	−0.245504	+	0.969396i	$0.578953\pi$
$878$	1.92304	+	1.11027i	0.0648996	+	0.0374698i
$879$	−0.489406	−	2.77556i	−0.0165073	−	0.0936173i
$880$	0.949571	+	2.14895i	0.0320100	+	0.0724410i
$881$	−13.0616	+	4.75403i	−0.440056	+	0.160167i	−0.552540	−	0.833486i	$-0.686341\pi$
$881$	−13.0616	+	4.75403i	−0.440056	+	0.160167i	0.112484	+	0.993654i	$0.464119\pi$
$882$		−	2.98581i		−	0.100537i
$883$	14.9856	+	41.1727i	0.504307	+	1.38557i	0.887031	+	0.461709i	$0.152764\pi$
$883$	14.9856	+	41.1727i	0.504307	+	1.38557i	−0.382725	+	0.923862i	$0.625014\pi$
$884$	−1.33826	+	7.58965i	−0.0450105	+	0.255267i
$885$	29.8643	−	28.6784i	1.00388	−	0.964014i
$886$	10.3303	−	8.66812i	0.347052	−	0.291211i
$887$			16.6933i			0.560505i	0.959926	+	0.280252i	$0.0904181\pi$
$887$			16.6933i			0.560505i	−0.959926	+	0.280252i	$0.909582\pi$
$888$	−0.335238	+	14.0853i	−0.0112499	+	0.472673i
$889$	−8.47681			−0.284303
$890$	−7.68795	−	11.4670i	−0.257701	−	0.384375i
$891$	−8.45240	−	7.09240i	−0.283166	−	0.237604i
$892$	−6.33213	−	1.11652i	−0.212015	−	0.0373840i
$893$	−0.307012	−	0.843509i	−0.0102738	−	0.0282269i
$894$	−49.7871			−1.66513
$895$	48.5755	−	11.9668i	1.62370	−	0.400007i
$896$	1.43722	+	2.48934i	0.0480142	+	0.0831631i
$897$	−41.0872	+	7.24479i	−1.37186	+	0.241896i
$898$	−8.63931	−	4.98791i	−0.288298	−	0.166449i
$899$	−3.67909	−	6.37236i	−0.122704	−	0.212530i
$900$	10.4723	−	5.49320i	0.349076	−	0.183107i
$901$	3.32694	−	18.8680i	0.110837	−	0.628585i
$902$	−2.37849	−	1.37322i	−0.0791952	−	0.0457234i
$903$	−6.11525	+	16.8015i	−0.203503	+	0.559119i
$904$	−14.8075	−	5.38949i	−0.492490	−	0.179252i
$905$	3.89157	+	57.9854i	0.129360	+	1.92750i
$906$	21.6180	+	18.1396i	0.718209	+	0.602649i
$907$	11.7216	−	13.9693i	0.389210	−	0.463842i	−0.535489	−	0.844542i	$-0.679873\pi$
$907$	11.7216	−	13.9693i	0.389210	−	0.463842i	0.924699	+	0.380700i	$0.124317\pi$
$908$	−26.4968	+	4.67210i	−0.879326	+	0.155049i
$909$	−11.2690	−	4.10159i	−0.373770	−	0.136041i
$910$	−7.11501	+	14.4848i	−0.235860	+	0.480168i
$911$	25.2935	−	43.8096i	0.838010	−	1.45148i	−0.0535460	−	0.998565i	$-0.517052\pi$
$911$	25.2935	−	43.8096i	0.838010	−	1.45148i	0.891556	−	0.452911i	$-0.149614\pi$
$912$	3.83006	+	0.675343i	0.126826	+	0.0223628i
$913$	8.55655	+	10.1973i	0.283180	+	0.337481i
$914$	−4.11883	−	7.13403i	−0.136239	−	0.235973i
$915$	−56.0385	−	40.9547i	−1.85258	−	1.35392i
$916$	1.77321	+	10.0564i	0.0585884	+	0.332271i
$917$	−43.2643	+	24.9787i	−1.42871	+	0.824869i
$918$	1.54382	+	4.24162i	0.0509538	+	0.139994i
$919$	−43.9106			−1.44848			−0.724239	−	0.689549i	$-0.757809\pi$
$919$	−43.9106			−1.44848			−0.724239	+	0.689549i	$0.757809\pi$
$920$	15.5757	−	3.83715i	0.513515	−	0.126507i
$921$	−1.38425	+	7.85049i	−0.0456127	+	0.258683i
$922$	3.11771	−	3.71554i	0.102676	−	0.122365i
$923$	−21.2095	−	25.2766i	−0.698121	−	0.831988i
$924$	6.99544			0.230133
$925$	24.5064	−	18.0121i	0.805766	−	0.592233i
$926$	−32.3725			−1.06383
$927$	13.2305	+	15.7674i	0.434545	+	0.517871i
$928$	0.896790	−	1.06875i	0.0294386	−	0.0350835i
$929$	−6.90996	+	39.1884i	−0.226709	+	1.28573i	0.632683	+	0.774411i	$0.281954\pi$
$929$	−6.90996	+	39.1884i	−0.226709	+	1.28573i	−0.859392	+	0.511318i	$0.829158\pi$
$930$	26.5232	−	6.53414i	0.869732	−	0.214263i
$931$	−2.11970			−0.0694704
$932$	−4.98095	−	13.6851i	−0.163157	−	0.448269i
$933$	38.6811	−	22.3325i	1.26636	−	0.731135i
$934$	−0.537849	−	3.05029i	−0.0175990	−	0.0998086i
$935$	−5.82222	−	4.25505i	−0.190407	−	0.139155i
$936$	−2.96915	−	5.14271i	−0.0970496	−	0.168095i
$937$	20.1987	+	24.0718i	0.659861	+	0.786392i	0.987366	−	0.158457i	$-0.0506520\pi$
$937$	20.1987	+	24.0718i	0.659861	+	0.786392i	−0.327504	+	0.944850i	$0.606208\pi$
$938$	−6.13222	−	1.08128i	−0.200224	−	0.0353049i
$939$	−31.6846	+	54.8794i	−1.03399	+	1.79092i
$940$	0.527049	−	1.07297i	0.0171904	−	0.0349965i
$941$	−24.5887	−	8.94957i	−0.801570	−	0.291748i	−0.0914332	−	0.995811i	$-0.529145\pi$
$941$	−24.5887	−	8.94957i	−0.801570	−	0.291748i	−0.710137	+	0.704064i	$0.751367\pi$
$942$	0.378924	−	0.0668145i	0.0123460	−	0.00217693i
$943$	−12.0538	+	14.3652i	−0.392526	+	0.467794i
$944$	6.12387	+	5.13854i	0.199315	+	0.167245i
$945$	0.632929	+	9.43080i	0.0205892	+	0.306784i
$946$	−2.65141	−	0.965033i	−0.0862046	−	0.0313759i
$947$	11.0412	−	30.3355i	0.358791	−	0.985770i	−0.620659	−	0.784081i	$-0.713135\pi$
$947$	11.0412	−	30.3355i	0.358791	−	0.985770i	0.979450	−	0.201689i	$-0.0646431\pi$
$948$	−12.1052	−	6.98895i	−0.393159	−	0.226991i
$949$	4.44396	−	25.2030i	0.144257	−	0.818123i
$950$	−3.89976	−	7.43454i	−0.126525	−	0.241208i
$951$	−7.25403	−	12.5643i	−0.235228	−	0.407427i
$952$	−7.64091	−	4.41148i	−0.247643	−	0.142977i
$953$	49.9817	−	8.81313i	1.61907	−	0.285485i	0.710649	−	0.703547i	$-0.248402\pi$
$953$	49.9817	−	8.81313i	1.61907	−	0.285485i	0.908419	+	0.418062i	$0.137290\pi$
$954$	7.38136	+	12.7849i	0.238980	+	0.413926i
$955$	28.4070	−	6.99821i	0.919228	−	0.226457i
$956$	−23.4856			−0.759579
$957$	−1.16128	−	3.19058i	−0.0375388	−	0.103137i
$958$	−19.8178	−	3.49442i	−0.640285	−	0.112900i
$959$	32.3371	+	27.1341i	1.04422	+	0.876204i
$960$	2.88421	+	4.30196i	0.0930876	+	0.138845i
$961$	−3.18409			−0.102713
$962$	−9.53583	−	11.9297i	−0.307447	−	0.384629i
$963$		−	0.444656i		−	0.0143288i
$964$	10.1880	−	8.54872i	0.328133	−	0.275336i
$965$	−27.6865	+	26.5871i	−0.891258	+	0.855867i
$966$	8.29412	−	47.0383i	0.266859	−	1.51343i
$967$	16.2623	+	44.6804i	0.522962	+	1.43683i	0.867208	+	0.497946i	$0.165912\pi$
$967$	16.2623	+	44.6804i	0.522962	+	1.43683i	−0.344246	+	0.938879i	$0.611866\pi$
$968$		−	9.89607i		−	0.318072i
$969$	−11.2176	+	4.08288i	−0.360362	+	0.131161i
$970$	−11.2536	−	25.4677i	−0.361332	−	0.817720i
$971$	1.67375	+	9.49232i	0.0537133	+	0.304623i	0.999815	−	0.0192472i	$-0.00612696\pi$
$971$	1.67375	+	9.49232i	0.0537133	+	0.304623i	−0.946101	+	0.323870i	$0.895016\pi$
$972$	−17.2450	−	9.95640i	−0.553133	−	0.319352i
$973$	16.1380	−	9.31730i	0.517362	−	0.298699i
$974$	1.37570	−	1.15435i	0.0440803	−	0.0369878i
$975$	−11.0438	+	26.8995i	−0.353684	+	0.861473i
$976$	6.70056	−	11.6057i	0.214480	−	0.371490i
$977$	−8.28750	+	22.7697i	−0.265141	+	0.728468i	0.733660	+	0.679516i	$0.237810\pi$
$977$	−8.28750	+	22.7697i	−0.265141	+	0.728468i	−0.998801	+	0.0489519i	$0.984412\pi$
$978$	10.5744	−	29.0530i	0.338133	−	0.929013i
$979$	−1.12646	−	6.38845i	−0.0360017	−	0.204176i
$980$	−1.95525	−	2.03610i	−0.0624583	−	0.0650410i
$981$	33.0571	+	27.7382i	1.05543	+	0.885612i
$982$	5.45882	−	0.962536i	0.174198	−	0.0307158i
$983$	1.37555	−	3.77930i	0.0438734	−	0.120541i	−0.915821	−	0.401586i	$-0.868459\pi$
$983$	1.37555	−	3.77930i	0.0438734	−	0.120541i	0.959694	+	0.281045i	$0.0906811\pi$
$984$	−5.68952	−	2.07082i	−0.181375	−	0.0660152i
$985$	−10.4068	−	7.60559i	−0.331587	−	0.242334i
$986$	−0.743625	+	4.21731i	−0.0236819	+	0.134306i
$987$	−2.28797	−	2.72670i	−0.0728269	−	0.0867917i
$988$	−3.65094	+	2.10787i	−0.116152	+	0.0670603i
$989$	−9.63264	+	16.6842i	−0.306300	+	0.530527i
$990$	5.54412	−	0.372083i	0.176204	−	0.0118256i
$991$	−21.8491	−	37.8438i	−0.694060	−	1.20215i	−0.970497	−	0.241115i	$-0.922487\pi$
$991$	−21.8491	−	37.8438i	−0.694060	−	1.20215i	0.276436	−	0.961032i	$-0.410846\pi$
$992$	1.80384	+	4.95601i	0.0572720	+	0.157354i
$993$			2.16635i			0.0687470i
$994$	35.4972	−	12.9199i	1.12590	−	0.409795i
$995$	13.1792	−	45.4804i	0.417810	−	1.44182i
$996$	22.4804	+	18.8633i	0.712318	+	0.597705i
$997$	−9.09007	−	10.8331i	−0.287885	−	0.343089i	0.602647	−	0.798008i	$-0.294113\pi$
$997$	−9.09007	−	10.8331i	−0.287885	−	0.343089i	−0.890533	+	0.454919i	$0.849668\pi$
$998$			31.6358i			1.00141i
$999$	−8.33049	−	3.25855i	−0.263565	−	0.103096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.x.a.49.2	✓	108
5.4	even	2	inner	370.2.x.a.49.17	yes	108
37.34	even	9	inner	370.2.x.a.219.17	yes	108
185.34	even	18	inner	370.2.x.a.219.2	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.x.a.49.2	✓	108	1.1	even	1	trivial
370.2.x.a.49.17	yes	108	5.4	even	2	inner
370.2.x.a.219.2	yes	108	185.34	even	18	inner
370.2.x.a.219.17	yes	108	37.34	even	9	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.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-1.48887 + 1.77437i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.17115 - 0.534875i) q^{5} +2.31627 q^{6} +(-0.983118 - 2.70110i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.410698 - 2.32918i) q^{9} +(-1.80533 - 1.31939i) q^{10} +(-0.525341 - 0.909917i) q^{11} +(-1.48887 - 1.77437i) q^{12} +(2.47264 + 0.435993i) q^{13} +(-1.43722 + 2.48934i) q^{14} +(-2.28350 + 4.64878i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.02282 - 0.533005i) q^{17} +(-1.52027 + 1.81178i) q^{18} +(1.28623 + 1.07928i) q^{19} +(0.149732 + 2.23105i) q^{20} +(6.25647 + 2.27717i) q^{21} +(-0.359354 + 0.987318i) q^{22} +(6.21280 + 3.58696i) q^{23} +(-0.402216 + 2.28108i) q^{24} +(4.42782 - 2.32259i) q^{25} +(-1.25539 - 2.17440i) q^{26} +(-1.27355 - 0.735284i) q^{27} +(2.83078 - 0.499142i) q^{28} +(-0.697579 - 1.20824i) q^{29} +(5.02898 - 1.23892i) q^{30} +5.27408 q^{31} +(0.342020 + 0.939693i) q^{32} +(2.39669 + 0.422601i) q^{33} +(-2.35134 - 1.97300i) q^{34} +(-3.57925 - 5.33865i) q^{35} +2.36511 q^{36} +(6.01379 - 0.913429i) q^{37} -1.67905i q^{38} +(-4.45505 + 3.73823i) q^{39} +(1.61284 - 1.54879i) q^{40} +(-0.453911 + 2.57426i) q^{41} +(-2.27717 - 6.25647i) q^{42} +2.68546i q^{43} +(0.987318 - 0.359354i) q^{44} +(-2.13751 - 4.83734i) q^{45} +(-1.24574 - 7.06493i) q^{46} +(-0.462988 - 0.267306i) q^{47} +(2.00595 - 1.15814i) q^{48} +(-0.967083 + 0.811479i) q^{49} +(-4.62536 - 1.89897i) q^{50} +(-3.55484 + 6.15716i) q^{51} +(-0.858739 + 2.35937i) q^{52} +(2.13484 - 5.86544i) q^{53} +(0.255362 + 1.44823i) q^{54} +(-1.62729 - 1.69458i) q^{55} +(-2.20195 - 1.84766i) q^{56} +(-3.83006 + 0.675343i) q^{57} +(-0.477172 + 1.31102i) q^{58} +(-7.51204 - 2.73416i) q^{59} +(-4.18163 - 3.05606i) q^{60} +(-2.32708 + 13.1975i) q^{61} +(-3.39011 - 4.04018i) q^{62} +(-5.88758 + 3.39920i) q^{63} +(0.500000 - 0.866025i) q^{64} +(5.60168 - 0.375946i) q^{65} +(-1.21683 - 2.10762i) q^{66} +(0.740907 + 2.03563i) q^{67} +3.06945i q^{68} +(-15.6146 + 5.68326i) q^{69} +(-1.78894 + 6.17348i) q^{70} +(-10.0672 - 8.44738i) q^{71} +(-1.52027 - 1.81178i) q^{72} -10.1927i q^{73} +(-4.56532 - 4.01969i) q^{74} +(-2.47131 + 11.3146i) q^{75} +(-1.28623 + 1.07928i) q^{76} +(-1.94130 + 2.31355i) q^{77} +(5.72731 + 1.00988i) q^{78} +(5.67072 - 2.06397i) q^{79} +(-2.22316 - 0.239960i) q^{80} +(9.86826 - 3.59175i) q^{81} +(2.26376 - 1.30698i) q^{82} +(-12.4770 + 2.20004i) q^{83} +(-3.32900 + 5.76599i) q^{84} +(6.27791 - 2.77407i) q^{85} +(2.05718 - 1.72618i) q^{86} +(3.18247 + 0.561155i) q^{87} +(-0.909917 - 0.525341i) q^{88} +(5.80174 + 2.11166i) q^{89} +(-2.33165 + 4.74681i) q^{90} +(-1.25324 - 7.10747i) q^{91} +(-4.61131 + 5.49554i) q^{92} +(-7.85242 + 9.35815i) q^{93} +(0.0928345 + 0.526491i) q^{94} +(3.36988 + 1.65530i) q^{95} +(-2.17658 - 0.792212i) q^{96} +(10.7837 + 6.22595i) q^{97} +(1.24326 + 0.219220i) q^{98} +(-1.90361 + 1.59732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 12 q^{9} + 12 q^{11} - 6 q^{14} + 6 q^{19} - 24 q^{21} + 30 q^{25} + 48 q^{26} + 24 q^{30} - 192 q^{31} + 12 q^{34} + 30 q^{35} + 84 q^{36} + 24 q^{39} + 12 q^{40} - 108 q^{41} + 6 q^{44} - 30 q^{45}+ \cdots - 90 q^{99}+O(q^{100}) \) 108 * q - 12 * q^9 + 12 * q^11 - 6 * q^14 + 6 * q^19 - 24 * q^21 + 30 * q^25 + 48 * q^26 + 24 * q^30 - 192 * q^31 + 12 * q^34 + 30 * q^35 + 84 * q^36 + 24 * q^39 + 12 * q^40 - 108 * q^41 + 6 * q^44 - 30 * q^45 - 54 * q^46 + 60 * q^49 - 12 * q^50 + 30 * q^55 - 48 * q^59 + 24 * q^61 + 54 * q^64 - 6 * q^65 - 120 * q^69 - 12 * q^70 + 12 * q^71 - 60 * q^74 - 156 * q^75 - 6 * q^76 + 12 * q^80 + 120 * q^81 - 24 * q^84 - 30 * q^85 + 12 * q^86 + 54 * q^89 + 18 * q^90 - 138 * q^91 + 6 * q^94 + 84 * q^95 - 90 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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