LMFDB - Embedded newform 672.2.bo.a.125.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.5
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39741 + 0.217363i) q^{2} +(-0.679260 - 1.59330i) q^{3} +(1.90551 - 0.607491i) q^{4} +(0.491250 + 1.18598i) q^{5} +(1.29553 + 2.07885i) q^{6} +(0.112587 + 2.64335i) q^{7} +(-2.53073 + 1.26310i) q^{8} +(-2.07721 + 2.16453i) q^{9} +O(q^{10})$	\(q+(-1.39741 + 0.217363i) q^{2} +(-0.679260 - 1.59330i) q^{3} +(1.90551 - 0.607491i) q^{4} +(0.491250 + 1.18598i) q^{5} +(1.29553 + 2.07885i) q^{6} +(0.112587 + 2.64335i) q^{7} +(-2.53073 + 1.26310i) q^{8} +(-2.07721 + 2.16453i) q^{9} +(-0.944266 - 1.55052i) q^{10} +(-1.77535 - 4.28607i) q^{11} +(-2.26225 - 2.62340i) q^{12} +(-0.783054 - 0.324352i) q^{13} +(-0.731898 - 3.66938i) q^{14} +(1.55594 - 1.58830i) q^{15} +(3.26191 - 2.31516i) q^{16} +1.90168i q^{17} +(2.43223 - 3.47624i) q^{18} +(-7.09674 - 2.93957i) q^{19} +(1.65655 + 1.96147i) q^{20} +(4.13518 - 1.97491i) q^{21} +(3.41252 + 5.60350i) q^{22} +(5.55180 - 5.55180i) q^{23} +(3.73152 + 3.17423i) q^{24} +(2.37031 - 2.37031i) q^{25} +(1.16475 + 0.283045i) q^{26} +(4.85971 + 1.83935i) q^{27} +(1.82035 + 4.96853i) q^{28} +(1.32060 - 3.18821i) q^{29} +(-1.82905 + 2.55771i) q^{30} -3.29238i q^{31} +(-4.05499 + 3.94424i) q^{32} +(-5.62307 + 5.74002i) q^{33} +(-0.413355 - 2.65742i) q^{34} +(-3.07966 + 1.43207i) q^{35} +(-2.64321 + 5.38641i) q^{36} +(-3.68551 - 8.89762i) q^{37} +(10.5560 + 2.56521i) q^{38} +(0.0151074 + 1.46796i) q^{39} +(-2.74123 - 2.38090i) q^{40} +(2.07087 + 2.07087i) q^{41} +(-5.34927 + 3.65859i) q^{42} +(-1.34745 + 0.558131i) q^{43} +(-5.98669 - 7.08863i) q^{44} +(-3.58752 - 1.40021i) q^{45} +(-6.55137 + 8.96489i) q^{46} -3.10014i q^{47} +(-5.90442 - 3.62461i) q^{48} +(-6.97465 + 0.595214i) q^{49} +(-2.79707 + 3.82751i) q^{50} +(3.02994 - 1.29173i) q^{51} +(-1.68916 - 0.142356i) q^{52} +(-2.74572 - 6.62876i) q^{53} +(-7.19081 - 1.51400i) q^{54} +(4.21106 - 4.21106i) q^{55} +(-3.62375 - 6.54740i) q^{56} +(0.136917 + 13.3040i) q^{57} +(-1.15242 + 4.74228i) q^{58} +(-3.16388 - 7.63828i) q^{59} +(1.99998 - 3.97173i) q^{60} +(-5.90476 + 14.2553i) q^{61} +(0.715642 + 4.60080i) q^{62} +(-5.95549 - 5.24711i) q^{63} +(4.80915 - 6.39312i) q^{64} -1.08803i q^{65} +(6.61007 - 9.24340i) q^{66} +(-0.559933 - 0.231932i) q^{67} +(1.15525 + 3.62366i) q^{68} +(-12.6168 - 5.07457i) q^{69} +(3.99227 - 2.67060i) q^{70} +(-2.74586 - 2.74586i) q^{71} +(2.52284 - 8.10156i) q^{72} +(6.19930 - 6.19930i) q^{73} +(7.08419 + 11.6325i) q^{74} +(-5.38667 - 2.16656i) q^{75} +(-15.3086 - 1.29016i) q^{76} +(11.1297 - 5.17543i) q^{77} +(-0.340192 - 2.04806i) q^{78} -7.15778i q^{79} +(4.34814 + 2.73125i) q^{80} +(-0.370373 - 8.99238i) q^{81} +(-3.34398 - 2.44372i) q^{82} +(4.51977 - 10.9117i) q^{83} +(6.67988 - 6.27529i) q^{84} +(-2.25535 + 0.934198i) q^{85} +(1.76162 - 1.07282i) q^{86} +(-5.97680 + 0.0615097i) q^{87} +(9.90666 + 8.60443i) q^{88} +(-8.06313 + 8.06313i) q^{89} +(5.31759 + 1.17687i) q^{90} +(0.769215 - 2.10641i) q^{91} +(7.20632 - 13.9516i) q^{92} +(-5.24575 + 2.23638i) q^{93} +(0.673856 + 4.33216i) q^{94} -9.86067i q^{95} +(9.03875 + 3.78166i) q^{96} +7.95920i q^{97} +(9.61706 - 2.34779i) q^{98} +(12.9651 + 5.06029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.39741	+	0.217363i	−0.988118	+	0.153699i
$2$	−1.39741	+	0.217363i	−0.988118	+	0.153699i
$3$	−0.679260	−	1.59330i	−0.392171	−	0.919892i
$3$	−0.679260	−	1.59330i	−0.392171	−	0.919892i
$4$	1.90551	−	0.607491i	0.952753	−	0.303745i
$5$	0.491250	+	1.18598i	0.219694	+	0.530387i	0.994847	−	0.101386i	$-0.0323276\pi$
$5$	0.491250	+	1.18598i	0.219694	+	0.530387i	−0.775154	+	0.631773i	$0.782328\pi$
$6$	1.29553	+	2.07885i	0.528897	+	0.848686i
$7$	0.112587	+	2.64335i	0.0425538	+	0.999094i
$7$	0.112587	+	2.64335i	0.0425538	+	0.999094i
$8$	−2.53073	+	1.26310i	−0.894747	+	0.446573i
$9$	−2.07721	+	2.16453i	−0.692404	+	0.721510i
$10$	−0.944266	−	1.55052i	−0.298603	−	0.490318i
$11$	−1.77535	−	4.28607i	−0.535288	−	1.29230i	−0.927980	−	0.372629i	$-0.878456\pi$
$11$	−1.77535	−	4.28607i	−0.535288	−	1.29230i	0.392693	−	0.919670i	$-0.371544\pi$
$12$	−2.26225	−	2.62340i	−0.653055	−	0.757310i
$13$	−0.783054	−	0.324352i	−0.217180	−	0.0899590i	0.271441	−	0.962455i	$-0.412500\pi$
$13$	−0.783054	−	0.324352i	−0.217180	−	0.0899590i	−0.488621	+	0.872496i	$0.662500\pi$
$14$	−0.731898	−	3.66938i	−0.195608	−	0.980682i
$15$	1.55594	−	1.58830i	0.401742	−	0.410097i
$16$	3.26191	−	2.31516i	0.815477	−	0.578789i
$17$			1.90168i			0.461224i	0.973046	+	0.230612i	$0.0740729\pi$
$17$			1.90168i			0.461224i	−0.973046	+	0.230612i	$0.925927\pi$
$18$	2.43223	−	3.47624i	0.573282	−	0.819358i
$19$	−7.09674	−	2.93957i	−1.62810	−	0.674383i	−0.633087	−	0.774081i	$-0.718212\pi$
$19$	−7.09674	−	2.93957i	−1.62810	−	0.674383i	−0.995018	+	0.0996979i	$0.968212\pi$
$20$	1.65655	+	1.96147i	0.370416	+	0.438597i
$21$	4.13518	−	1.97491i	0.902371	−	0.430960i
$22$	3.41252	+	5.60350i	0.727552	+	1.19467i
$23$	5.55180	−	5.55180i	1.15763	−	1.15763i	0.172645	−	0.984984i	$-0.444769\pi$
$23$	5.55180	−	5.55180i	1.15763	−	1.15763i	0.984984	−	0.172645i	$-0.0552314\pi$
$24$	3.73152	+	3.17423i	0.761693	+	0.647938i
$25$	2.37031	−	2.37031i	0.474062	−	0.474062i
$26$	1.16475	+	0.283045i	0.228426	+	0.0555097i
$27$	4.85971	+	1.83935i	0.935252	+	0.353983i
$28$	1.82035	+	4.96853i	0.344014	+	0.938965i
$29$	1.32060	−	3.18821i	0.245229	−	0.592035i	−0.752558	−	0.658526i	$-0.771180\pi$
$29$	1.32060	−	3.18821i	0.245229	−	0.592035i	0.997787	+	0.0664910i	$0.0211804\pi$
$30$	−1.82905	+	2.55771i	−0.333937	+	0.466971i
$31$		−	3.29238i		−	0.591329i	−0.955292	−	0.295664i	$-0.904459\pi$
$31$		−	3.29238i		−	0.591329i	0.955292	−	0.295664i	$-0.0955410\pi$
$32$	−4.05499	+	3.94424i	−0.716828	+	0.697250i
$33$	−5.62307	+	5.74002i	−0.978852	+	0.999209i
$34$	−0.413355	−	2.65742i	−0.0708897	−	0.455744i
$35$	−3.07966	+	1.43207i	−0.520558	+	0.242065i
$36$	−2.64321	+	5.38641i	−0.440535	+	0.897735i
$37$	−3.68551	−	8.89762i	−0.605895	−	1.46276i	−0.867427	−	0.497565i	$-0.834228\pi$
$37$	−3.68551	−	8.89762i	−0.605895	−	1.46276i	0.261532	−	0.965195i	$-0.415772\pi$
$38$	10.5560	+	2.56521i	1.71241	+	0.416132i
$39$	0.0151074	+	1.46796i	0.00241912	+	0.235062i
$40$	−2.74123	−	2.38090i	−0.433427	−	0.376453i
$41$	2.07087	+	2.07087i	0.323415	+	0.323415i	0.850076	−	0.526661i	$-0.176556\pi$
$41$	2.07087	+	2.07087i	0.323415	+	0.323415i	−0.526661	+	0.850076i	$0.676556\pi$
$42$	−5.34927	+	3.65859i	−0.825410	+	0.564533i
$43$	−1.34745	+	0.558131i	−0.205484	+	0.0851142i	−0.483052	−	0.875592i	$-0.660472\pi$
$43$	−1.34745	+	0.558131i	−0.205484	+	0.0851142i	0.277568	+	0.960706i	$0.410472\pi$
$44$	−5.98669	−	7.08863i	−0.902527	−	1.06865i
$45$	−3.58752	−	1.40021i	−0.534796	−	0.208731i
$46$	−6.55137	+	8.96489i	−0.965948	+	1.32180i
$47$		−	3.10014i		−	0.452202i	−0.974104	−	0.226101i	$-0.927402\pi$
$47$		−	3.10014i		−	0.452202i	0.974104	−	0.226101i	$-0.0725979\pi$
$48$	−5.90442	−	3.62461i	−0.852230	−	0.523167i
$49$	−6.97465	+	0.595214i	−0.996378	+	0.0850305i
$50$	−2.79707	+	3.82751i	−0.395566	+	0.541291i
$51$	3.02994	−	1.29173i	0.424277	−	0.180879i
$52$	−1.68916	−	0.142356i	−0.234244	−	0.0197412i
$53$	−2.74572	−	6.62876i	−0.377154	−	0.910530i	−0.992497	−	0.122270i	$-0.960983\pi$
$53$	−2.74572	−	6.62876i	−0.377154	−	0.910530i	0.615343	−	0.788259i	$-0.289017\pi$
$54$	−7.19081	−	1.51400i	−0.978546	−	0.206029i
$55$	4.21106	−	4.21106i	0.567819	−	0.567819i
$56$	−3.62375	−	6.54740i	−0.484244	−	0.874933i
$57$	0.136917	+	13.3040i	0.0181351	+	1.76215i
$58$	−1.15242	+	4.74228i	−0.151320	+	0.622692i
$59$	−3.16388	−	7.63828i	−0.411902	−	0.994420i	−0.984627	−	0.174672i	$-0.944114\pi$
$59$	−3.16388	−	7.63828i	−0.411902	−	0.994420i	0.572724	−	0.819748i	$-0.305886\pi$
$60$	1.99998	−	3.97173i	0.258196	−	0.512748i
$61$	−5.90476	+	14.2553i	−0.756027	+	1.82521i	−0.234119	+	0.972208i	$0.575221\pi$
$61$	−5.90476	+	14.2553i	−0.756027	+	1.82521i	−0.521907	+	0.853002i	$0.674779\pi$
$62$	0.715642	+	4.60080i	0.0908866	+	0.584302i
$63$	−5.95549	−	5.24711i	−0.750321	−	0.661074i
$64$	4.80915	−	6.39312i	0.601144	−	0.799141i
$65$		−	1.08803i		−	0.134953i
$66$	6.61007	−	9.24340i	0.813643	−	1.13778i
$67$	−0.559933	−	0.231932i	−0.0684068	−	0.0283350i	0.348218	−	0.937414i	$-0.386787\pi$
$67$	−0.559933	−	0.231932i	−0.0684068	−	0.0283350i	−0.416624	+	0.909079i	$0.636787\pi$
$68$	1.15525	+	3.62366i	0.140095	+	0.439433i
$69$	−12.6168	−	5.07457i	−1.51888	−	0.610906i
$70$	3.99227	−	2.67060i	0.477167	−	0.319197i
$71$	−2.74586	−	2.74586i	−0.325874	−	0.325874i	0.525141	−	0.851015i	$-0.324012\pi$
$71$	−2.74586	−	2.74586i	−0.325874	−	0.325874i	−0.851015	+	0.525141i	$0.824012\pi$
$72$	2.52284	−	8.10156i	0.297320	−	0.954778i
$73$	6.19930	−	6.19930i	0.725573	−	0.725573i	−0.244161	−	0.969735i	$-0.578513\pi$
$73$	6.19930	−	6.19930i	0.725573	−	0.725573i	0.969735	+	0.244161i	$0.0785127\pi$
$74$	7.08419	+	11.6325i	0.823520	+	1.35225i
$75$	−5.38667	−	2.16656i	−0.621999	−	0.250173i
$76$	−15.3086	−	1.29016i	−1.75602	−	0.147991i
$77$	11.1297	−	5.17543i	1.26835	−	0.589795i
$78$	−0.340192	−	2.04806i	−0.0385191	−	0.231897i
$79$		−	7.15778i		−	0.805313i	−0.915351	−	0.402657i	$-0.868087\pi$
$79$		−	7.15778i		−	0.805313i	0.915351	−	0.402657i	$-0.131913\pi$
$80$	4.34814	+	2.73125i	0.486137	+	0.305363i
$81$	−0.370373	−	8.99238i	−0.0411526	−	0.999153i
$82$	−3.34398	−	2.44372i	−0.369280	−	0.269863i
$83$	4.51977	−	10.9117i	0.496110	−	1.19771i	−0.455453	−	0.890260i	$-0.650523\pi$
$83$	4.51977	−	10.9117i	0.496110	−	1.19771i	0.951563	−	0.307455i	$-0.0994773\pi$
$84$	6.67988	−	6.27529i	0.728834	−	0.684690i
$85$	−2.25535	+	0.934198i	−0.244627	+	0.101328i
$86$	1.76162	−	1.07282i	0.189960	−	0.115686i
$87$	−5.97680	+	0.0615097i	−0.640780	+	0.00659453i
$88$	9.90666	+	8.60443i	1.05605	+	0.917235i
$89$	−8.06313	+	8.06313i	−0.854690	+	0.854690i	−0.990707	−	0.136016i	$-0.956570\pi$
$89$	−8.06313	+	8.06313i	−0.854690	+	0.854690i	0.136016	+	0.990707i	$0.456570\pi$
$90$	5.31759	+	1.17687i	0.560523	+	0.124053i
$91$	0.769215	−	2.10641i	0.0806356	−	0.220812i
$92$	7.20632	−	13.9516i	0.751310	−	1.45456i
$93$	−5.24575	+	2.23638i	−0.543959	+	0.231902i
$94$	0.673856	+	4.33216i	0.0695030	+	0.446829i
$95$		−	9.86067i		−	1.01168i
$96$	9.03875	+	3.78166i	0.922514	+	0.385964i
$97$			7.95920i			0.808134i	0.914729	+	0.404067i	$0.132404\pi$
$97$			7.95920i			0.808134i	−0.914729	+	0.404067i	$0.867596\pi$
$98$	9.61706	−	2.34779i	0.971470	−	0.237163i
$99$	12.9651	+	5.06029i	1.30304	+	0.508578i
$100$	3.07670	−	5.95658i	0.307670	−	0.595658i
$101$	1.75253	+	4.23099i	0.174383	+	0.420999i	0.986771	−	0.162119i	$-0.0518327\pi$
$101$	1.75253	+	4.23099i	0.174383	+	0.420999i	−0.812388	+	0.583117i	$0.801833\pi$
$102$	−3.95330	+	2.46368i	−0.391435	+	0.243940i
$103$	7.27569	+	7.27569i	0.716895	+	0.716895i	0.967968	−	0.251073i	$-0.0807835\pi$
$103$	7.27569	+	7.27569i	0.716895	+	0.716895i	−0.251073	+	0.967968i	$0.580783\pi$
$104$	2.39138	−	0.168231i	0.234495	−	0.0164964i
$105$	4.37361	+	3.93408i	0.426821	+	0.383927i
$106$	5.27774	+	8.66627i	0.512620	+	0.841742i
$107$	5.28270	+	12.7536i	0.510697	+	1.23293i	0.943479	+	0.331434i	$0.107532\pi$
$107$	5.28270	+	12.7536i	0.510697	+	1.23293i	−0.432781	+	0.901499i	$0.642468\pi$
$108$	10.3776	+	0.552657i	0.998585	+	0.0531795i
$109$	−1.81003	+	4.36979i	−0.173369	+	0.418550i	−0.986550	−	0.163461i	$-0.947734\pi$
$109$	−1.81003	+	4.36979i	−0.173369	+	0.418550i	0.813181	+	0.582012i	$0.197734\pi$
$110$	−4.96925	+	6.79991i	−0.473799	+	0.648346i
$111$	−11.6732	+	11.9159i	−1.10797	+	1.13101i
$112$	6.48703	+	8.36173i	0.612966	+	0.790109i
$113$	−12.5662			−1.18213			−0.591063	−	0.806625i	$-0.701292\pi$
$113$	−12.5662			−1.18213			−0.591063	+	0.806625i	$0.701292\pi$
$114$	−3.08312	−	18.5613i	−0.288761	−	1.73843i
$115$	9.31164	+	3.85701i	0.868315	+	0.359668i
$116$	0.579602	−	6.87740i	0.0538147	−	0.638550i
$117$	2.32864	−	1.02120i	0.215283	−	0.0944096i
$118$	6.08152	+	9.98610i	0.559849	+	0.919295i
$119$	−5.02681	+	0.214104i	−0.460807	+	0.0196268i
$120$	−1.93148	+	5.98485i	−0.176319	+	0.546340i
$121$	−7.44036	+	7.44036i	−0.676396	+	0.676396i
$122$	5.15278	−	21.2040i	0.466510	−	1.91972i
$123$	1.89286	−	4.70617i	0.170673	−	0.424341i
$124$	−2.00009	−	6.27365i	−0.179613	−	0.563390i
$125$	9.90546	+	4.10298i	0.885972	+	0.366981i
$126$	9.46278	+	6.03786i	0.843012	+	0.537896i
$127$	−5.03806			−0.447056			−0.223528	−	0.974698i	$-0.571757\pi$
$127$	−5.03806			−0.447056			−0.223528	+	0.974698i	$0.571757\pi$
$128$	−5.33073	+	9.97915i	−0.471174	+	0.882040i
$129$	1.80454	+	1.76777i	0.158881	+	0.155644i
$130$	0.236497	+	1.52042i	0.0207421	+	0.133349i
$131$	−17.1820	−	7.11704i	−1.50120	−	0.621818i	−0.527482	−	0.849566i	$-0.676864\pi$
$131$	−17.1820	−	7.11704i	−1.50120	−	0.621818i	−0.973720	+	0.227748i	$0.926864\pi$
$132$	−7.22780	+	14.3536i	−0.629099	+	1.24932i
$133$	6.97132	−	19.0902i	0.604490	−	1.65533i
$134$	0.832870	+	0.202395i	0.0719490	+	0.0174843i
$135$	0.205900	+	6.66711i	0.0177211	+	0.573813i
$136$	−2.40201	−	4.81262i	−0.205971	−	0.412679i
$137$	−0.943247	+	0.943247i	−0.0805870	+	0.0805870i	−0.746251	−	0.665664i	$-0.768148\pi$
$137$	−0.943247	+	0.943247i	−0.0805870	+	0.0805870i	0.665664	+	0.746251i	$0.268148\pi$
$138$	18.7338	+	4.34882i	1.59473	+	0.370196i
$139$	−2.05898	−	4.97081i	−0.174640	−	0.421619i	0.812187	−	0.583397i	$-0.198277\pi$
$139$	−2.05898	−	4.97081i	−0.174640	−	0.421619i	−0.986827	+	0.161779i	$0.948277\pi$
$140$	−4.99834	+	4.59969i	−0.422437	+	0.388745i
$141$	−4.93945	+	2.10580i	−0.415977	+	0.177340i
$142$	4.43394	+	3.24024i	0.372088	+	0.271915i
$143$			3.93206i			0.328816i
$144$	−1.76446	+	11.8696i	−0.147038	+	0.989131i
$145$	4.42990			0.367883
$146$	−7.31546	+	10.0105i	−0.605432	+	0.828472i
$147$	5.68595	+	10.7084i	0.468969	+	0.883214i
$148$	−12.4280	−	14.7156i	−1.02157	−	1.20961i
$149$	4.62948	+	11.1765i	0.379262	+	0.915618i	0.992105	+	0.125414i	$0.0400258\pi$
$149$	4.62948	+	11.1765i	0.379262	+	0.915618i	−0.612843	+	0.790205i	$0.709974\pi$
$150$	7.99831	+	1.85671i	0.653059	+	0.151599i
$151$	−3.50043	−	3.50043i	−0.284861	−	0.284861i	0.550183	−	0.835044i	$-0.314558\pi$
$151$	−3.50043	−	3.50043i	−0.284861	−	0.284861i	−0.835044	+	0.550183i	$0.814558\pi$
$152$	21.6729	−	1.52466i	1.75790	−	0.123666i
$153$	−4.11623	−	3.95019i	−0.332778	−	0.319354i
$154$	−14.4278	+	9.65139i	−1.16263	+	0.777731i
$155$	3.90470	−	1.61738i	0.313633	−	0.129911i
$156$	0.920559	+	2.78803i	0.0737037	+	0.223221i
$157$	0.602088	−	1.45357i	0.0480519	−	0.116008i	−0.898031	−	0.439932i	$-0.855002\pi$
$157$	0.602088	−	1.45357i	0.0480519	−	0.116008i	0.946083	+	0.323925i	$0.105002\pi$
$158$	1.55584	+	10.0024i	0.123776	+	0.795744i
$159$	−8.69654	+	8.87740i	−0.689681	+	0.704024i
$160$	−6.66981	−	2.87154i	−0.527295	−	0.227015i
$161$	15.3004	+	14.0503i	1.20584	+	1.10732i
$162$	2.47217	+	12.4855i	0.194232	+	0.980956i
$163$	17.1307	+	7.09575i	1.34178	+	0.555782i	0.933991	−	0.357295i	$-0.116301\pi$
$163$	17.1307	+	7.09575i	1.34178	+	0.555782i	0.407786	+	0.913078i	$0.366301\pi$
$164$	5.20408	+	2.68802i	0.406370	+	0.209899i
$165$	−9.56989	−	3.84908i	−0.745015	−	0.299651i
$166$	−3.94417	+	16.2305i	−0.306127	+	1.25973i
$167$	−3.54510	+	3.54510i	−0.274328	+	0.274328i	−0.830840	−	0.556512i	$-0.812139\pi$
$167$	−3.54510	+	3.54510i	−0.274328	+	0.274328i	0.556512	+	0.830840i	$0.312139\pi$
$168$	−7.97051	+	10.2211i	−0.614938	+	0.788575i
$169$	−8.68442	−	8.68442i	−0.668032	−	0.668032i
$170$	2.94859	−	1.79569i	0.226147	−	0.137723i
$171$	21.1042	−	9.25500i	1.61388	−	0.707748i
$172$	−2.22851	+	1.88208i	−0.169922	+	0.143508i
$173$	2.94986	−	7.12159i	0.224273	−	0.541444i	−0.771188	−	0.636607i	$-0.780337\pi$
$173$	2.94986	−	7.12159i	0.224273	−	0.541444i	0.995462	+	0.0951631i	$0.0303373\pi$
$174$	8.33866	−	1.38509i	0.632152	−	0.105003i
$175$	6.53243	+	5.99870i	0.493805	+	0.453459i
$176$	−15.7139	−	9.87056i	−1.18448	−	0.744022i
$177$	−10.0210	+	10.2294i	−0.753223	+	0.768888i
$178$	9.51487	−	13.0201i	0.713169	−	0.975900i
$179$	−1.69333	−	0.701401i	−0.126566	−	0.0524252i	0.318502	−	0.947922i	$-0.396820\pi$
$179$	−1.69333	−	0.701401i	−0.126566	−	0.0524252i	−0.445067	+	0.895497i	$0.646820\pi$
$180$	−7.68666	−	0.488726i	−0.572930	−	0.0364275i
$181$	−8.08486	−	19.5186i	−0.600943	−	1.45080i	−0.872612	−	0.488414i	$-0.837576\pi$
$181$	−8.08486	−	19.5186i	−0.600943	−	1.45080i	0.271669	−	0.962391i	$-0.412424\pi$
$182$	−0.617053	+	3.11071i	−0.0457390	+	0.230581i
$183$	26.7239	−	0.275027i	1.97549	−	0.0203306i
$184$	−7.03760	+	21.0626i	−0.518819	+	1.55275i
$185$	8.74191	−	8.74191i	0.642718	−	0.642718i
$186$	6.84435	−	4.26537i	0.501852	−	0.312752i
$187$	8.15072	−	3.37614i	0.596040	−	0.246888i
$188$	−1.88331	−	5.90733i	−0.137354	−	0.430837i
$189$	−4.31491	+	13.0530i	−0.313863	+	0.949468i
$190$	2.14335	+	13.7794i	0.155495	+	0.999662i
$191$		−	5.77863i		−	0.418127i	−0.977902	−	0.209063i	$-0.932958\pi$
$191$		−	5.77863i		−	0.418127i	0.977902	−	0.209063i	$-0.0670415\pi$
$192$	−13.4528	−	3.31984i	−0.970875	−	0.239589i
$193$	−1.27730			−0.0919422			−0.0459711	−	0.998943i	$-0.514638\pi$
$193$	−1.27730			−0.0919422			−0.0459711	+	0.998943i	$0.514638\pi$
$194$	−1.73004	−	11.1223i	−0.124209	−	0.798532i
$195$	−1.73355	+	0.739052i	−0.124142	+	0.0529246i
$196$	−12.9287	+	5.37122i	−0.923475	+	0.383658i
$197$	13.0945	−	5.42391i	0.932942	−	0.386437i	0.136148	−	0.990688i	$-0.456528\pi$
$197$	13.0945	−	5.42391i	0.932942	−	0.386437i	0.796794	+	0.604251i	$0.206528\pi$
$198$	−19.2175	−	4.25316i	−1.36573	−	0.302259i
$199$	16.8514	+	16.8514i	1.19456	+	1.19456i	0.975772	+	0.218792i	$0.0702116\pi$
$199$	16.8514	+	16.8514i	1.19456	+	1.19456i	0.218792	+	0.975772i	$0.429788\pi$
$200$	−3.00466	+	8.99254i	−0.212462	+	0.635868i
$201$	0.0108027	+	1.04968i	0.000761966	+	0.0740390i
$202$	−3.36866	−	5.53148i	−0.237018	−	0.389194i
$203$	8.57624	+	3.13186i	0.601934	+	0.219813i
$204$	4.98886	−	4.30207i	0.349290	−	0.301205i
$205$	−1.43870	+	3.47332i	−0.100483	+	0.242587i
$206$	−11.7486	−	8.58565i	−0.818563	−	0.598191i
$207$	0.484762	+	23.5493i	0.0336933	+	1.63679i
$208$	−3.30518	+	0.754886i	−0.229173	+	0.0523420i
$209$			35.6359i			2.46499i
$210$	−6.96685	−	4.54685i	−0.480758	−	0.313763i
$211$	3.67199	−	8.86497i	0.252790	−	0.610290i	−0.745637	−	0.666352i	$-0.767855\pi$
$211$	3.67199	−	8.86497i	0.252790	−	0.610290i	0.998427	+	0.0560627i	$0.0178547\pi$
$212$	−9.25890	−	10.9631i	−0.635904	−	0.752951i
$213$	−2.50983	+	6.24013i	−0.171971	+	0.427567i
$214$	−10.1542	−	16.6737i	−0.694130	−	1.13979i
$215$	−1.32387	−	1.32387i	−0.0902870	−	0.0902870i
$216$	−14.6219	+	1.48342i	−0.994893	+	0.100934i
$217$	8.70292	−	0.370678i	0.590793	−	0.0251633i
$218$	1.57952	−	6.49982i	0.106978	−	0.440224i
$219$	−14.0883	−	5.66641i	−0.951998	−	0.382901i
$220$	5.46602	−	10.5824i	0.368519	−	0.713464i
$221$	0.616812	−	1.48912i	0.0414913	−	0.100169i
$222$	13.7221	−	19.1887i	0.920967	−	1.28786i
$223$		−	12.6315i		−	0.845868i	−0.906160	−	0.422934i	$-0.861000\pi$
$223$		−	12.6315i		−	0.845868i	0.906160	−	0.422934i	$-0.139000\pi$
$224$	−10.8826	−	10.2747i	−0.727122	−	0.686508i
$225$	0.206967	+	10.0542i	0.0137978	+	0.670282i
$226$	17.5601	−	2.73142i	1.16808	−	0.181692i
$227$	22.2132	+	9.20100i	1.47434	+	0.610692i	0.967844	−	0.251550i	$-0.0809404\pi$
$227$	22.2132	+	9.20100i	1.47434	+	0.610692i	0.506496	+	0.862242i	$0.330940\pi$
$228$	8.34294	+	25.2676i	0.552525	+	1.67339i
$229$	−4.16120	+	1.72363i	−0.274980	+	0.113900i	−0.515912	−	0.856642i	$-0.672547\pi$
$229$	−4.16120	+	1.72363i	−0.274980	+	0.113900i	0.240932	+	0.970542i	$0.422547\pi$
$230$	−13.8506	−	3.36581i	−0.913278	−	0.221935i
$231$	−15.8060	−	14.2175i	−1.03996	−	0.935445i
$232$	0.684952	+	9.73652i	0.0449693	+	0.639234i
$233$	13.3240	−	13.3240i	0.872885	−	0.872885i	−0.119901	−	0.992786i	$-0.538258\pi$
$233$	13.3240	−	13.3240i	0.872885	−	0.872885i	0.992786	+	0.119901i	$0.0382576\pi$
$234$	−3.03209	+	1.93319i	−0.198214	+	0.126377i
$235$	3.67671	−	1.52294i	0.239842	−	0.0993458i
$236$	−10.6690	−	12.6328i	−0.694492	−	0.822323i
$237$	−11.4045	+	4.86199i	−0.740802	+	0.315820i
$238$	6.97797	−	1.39183i	0.452315	−	0.0902192i
$239$	−23.8830			−1.54486			−0.772430	−	0.635099i	$-0.780959\pi$
$239$	−23.8830			−1.54486			−0.772430	+	0.635099i	$0.780959\pi$
$240$	1.39818	−	8.78312i	0.0902519	−	0.566948i
$241$	7.77549			0.500863			0.250432	−	0.968134i	$-0.419427\pi$
$241$	7.77549			0.500863			0.250432	+	0.968134i	$0.419427\pi$
$242$	8.77996	−	12.0145i	0.564397	−	0.772320i
$243$	−14.0760	+	6.69827i	−0.902974	+	0.429694i
$244$	−2.59156	+	30.7507i	−0.165908	+	1.96861i
$245$	−4.13221	−	7.97941i	−0.263997	−	0.509786i
$246$	−1.62215	+	6.98788i	−0.103424	+	0.445531i
$247$	4.60368	+	4.60368i	0.292925	+	0.292925i
$248$	4.15860	+	8.33211i	0.264072	+	0.529089i
$249$	−20.4557	+	0.210518i	−1.29633	+	0.0133411i
$250$	−14.7338	−	3.58046i	−0.931849	−	0.226448i
$251$	6.98708	+	16.8683i	0.441020	+	1.06472i	0.975591	+	0.219594i	$0.0704732\pi$
$251$	6.98708	+	16.8683i	0.441020	+	1.06472i	−0.534571	+	0.845124i	$0.679527\pi$
$252$	−14.5358	−	6.38051i	−0.915669	−	0.401934i
$253$	−33.6517	−	13.9390i	−2.11567	−	0.876338i
$254$	7.04023	−	1.09509i	0.441743	−	0.0687120i
$255$	3.02043	+	2.95889i	0.189147	+	0.185293i
$256$	5.28011	−	15.1037i	0.330007	−	0.943979i
$257$	19.2639			1.20165			0.600824	−	0.799381i	$-0.294839\pi$
$257$	19.2639			1.20165			0.600824	+	0.799381i	$0.294839\pi$
$258$	−2.90593	−	2.07806i	−0.180915	−	0.129375i
$259$	23.1046	−	10.7439i	1.43565	−	0.667592i
$260$	−0.660966	−	2.07324i	−0.0409913	−	0.128577i
$261$	4.15780	+	9.48105i	0.257361	+	0.586862i
$262$	25.5573	+	6.21067i	1.57894	+	0.383696i
$263$	4.93554	+	4.93554i	0.304339	+	0.304339i	0.842709	−	0.538370i	$-0.180960\pi$
$263$	4.93554	+	4.93554i	0.304339	+	0.304339i	−0.538370	+	0.842709i	$0.680960\pi$
$264$	6.98025	−	21.6289i	0.429604	−	1.33117i
$265$	6.51275	−	6.51275i	0.400075	−	0.400075i
$266$	−5.59229	+	28.1921i	−0.342885	+	1.72857i
$267$	18.3239	+	7.37003i	1.12141	+	0.451039i
$268$	−1.20785	−	0.101794i	−0.0737814	−	0.00621803i
$269$	2.33774	−	5.64380i	0.142534	−	0.344108i	−0.836450	−	0.548043i	$-0.815373\pi$
$269$	2.33774	−	5.64380i	0.142534	−	0.344108i	0.978985	+	0.203935i	$0.0653730\pi$
$270$	−1.73691	−	9.27192i	−0.105705	−	0.564271i
$271$	−6.46559			−0.392757			−0.196378	−	0.980528i	$-0.562918\pi$
$271$	−6.46559			−0.392757			−0.196378	+	0.980528i	$0.562918\pi$
$272$	4.40268	+	6.20310i	0.266952	+	0.376118i
$273$	−3.87864	+	0.205207i	−0.234746	+	0.0124197i
$274$	1.11307	−	1.52313i	0.0672433	−	0.0920156i
$275$	−14.3674	−	5.95118i	−0.866388	−	0.358870i
$276$	−27.1241	−	2.00504i	−1.63268	−	0.120689i
$277$	30.1826	−	12.5021i	1.81350	−	0.751176i	0.833399	−	0.552672i	$-0.186392\pi$
$277$	30.1826	−	12.5021i	1.81350	−	0.751176i	0.980100	−	0.198504i	$-0.0636083\pi$
$278$	3.95770	+	6.49871i	0.237367	+	0.389767i
$279$	7.12645	+	6.83897i	0.426649	+	0.409438i
$280$	5.98493	−	7.51411i	0.357668	−	0.449054i
$281$	−2.86206	−	2.86206i	−0.170736	−	0.170736i	0.616567	−	0.787303i	$-0.288523\pi$
$281$	−2.86206	−	2.86206i	−0.170736	−	0.170736i	−0.787303	+	0.616567i	$0.788523\pi$
$282$	6.44471	−	4.01632i	0.383777	−	0.239168i
$283$	−11.3994	+	4.72179i	−0.677625	+	0.280681i	−0.694834	−	0.719171i	$-0.744522\pi$
$283$	−11.3994	+	4.72179i	−0.677625	+	0.280681i	0.0172088	+	0.999852i	$0.494522\pi$
$284$	−6.90034	−	3.56417i	−0.409460	−	0.211495i
$285$	−15.7110	+	6.69795i	−0.930640	+	0.396753i
$286$	−0.854686	−	5.49470i	−0.0505386	−	0.324908i
$287$	−5.24088	+	5.70718i	−0.309359	+	0.336884i
$288$	−0.114336	−	16.9702i	−0.00673732	−	0.999977i
$289$	13.3836			0.787272
$290$	−6.19038	+	0.962896i	−0.363512	+	0.0565432i
$291$	12.6814	−	5.40636i	0.743397	−	0.316927i
$292$	8.04679	−	15.5788i	0.470903	−	0.911682i
$293$	−1.18499	−	2.86082i	−0.0692279	−	0.167131i	0.885479	−	0.464680i	$-0.153831\pi$
$293$	−1.18499	−	2.86082i	−0.0692279	−	0.167131i	−0.954706	+	0.297549i	$0.903831\pi$
$294$	−10.2732	−	13.7281i	−0.599146	−	0.800640i
$295$	7.50461	−	7.50461i	0.436935	−	0.436935i
$296$	20.5656	+	17.8623i	1.19535	+	1.03822i
$297$	−0.744111	−	24.0945i	−0.0431777	−	1.39811i
$298$	−8.89865	−	14.6119i	−0.515485	−	0.846447i
$299$	−6.14809	+	2.54662i	−0.355553	+	0.147275i
$300$	−11.5805	−	0.856040i	−0.668600	−	0.0494235i
$301$	−1.62704	−	3.49894i	−0.0937812	−	0.201676i
$302$	5.65240	+	4.13067i	0.325259	+	0.237693i
$303$	5.55081	−	5.66625i	0.318886	−	0.325517i
$304$	−29.9545	+	6.84146i	−1.71801	+	0.392385i
$305$	−19.8073			−1.13416
$306$	6.61069	+	4.62531i	0.377908	+	0.264411i
$307$	−22.8449	−	9.46268i	−1.30383	−	0.540064i	−0.380752	−	0.924677i	$-0.624335\pi$
$307$	−22.8449	−	9.46268i	−1.30383	−	0.540064i	−0.923078	+	0.384614i	$0.874335\pi$
$308$	18.0637	−	16.6230i	1.02928	−	0.947184i
$309$	6.65028	−	16.5344i	0.378321	−	0.940612i
$310$	−5.10491	+	3.10888i	−0.289939	+	0.176572i
$311$	−15.4859	−	15.4859i	−0.878123	−	0.878123i	0.115218	−	0.993340i	$-0.463243\pi$
$311$	−15.4859	−	15.4859i	−0.878123	−	0.878123i	−0.993340	+	0.115218i	$0.963243\pi$
$312$	−1.89241	−	3.69592i	−0.107137	−	0.209240i
$313$	18.3792	+	18.3792i	1.03885	+	1.03885i	0.999214	+	0.0396384i	$0.0126206\pi$
$313$	18.3792	+	18.3792i	1.03885	+	1.03885i	0.0396384	+	0.999214i	$0.487379\pi$
$314$	−0.525411	+	2.16210i	−0.0296507	+	0.122015i
$315$	3.29735	−	9.64074i	0.185785	−	0.543194i
$316$	−4.34829	−	13.6392i	−0.244610	−	0.767265i
$317$	−8.39124	+	20.2582i	−0.471299	+	1.13782i	0.492291	+	0.870431i	$0.336160\pi$
$317$	−8.39124	+	20.2582i	−0.471299	+	1.13782i	−0.963590	+	0.267385i	$0.913840\pi$
$318$	10.2230	−	14.2957i	0.573278	−	0.801662i
$319$	−16.0094			−0.896354
$320$	9.94462	+	2.56295i	0.555921	+	0.143273i
$321$	16.7319	−	17.0799i	0.933885	−	0.953307i
$322$	−24.4350	−	16.3083i	−1.36171	−	0.908825i
$323$	5.59011	−	13.4957i	0.311042	−	0.750921i
$324$	−6.16853	−	16.9100i	−0.342696	−	0.939446i
$325$	−2.62489	+	1.08727i	−0.145603	+	0.0603107i
$326$	−25.4809	−	6.19210i	−1.41126	−	0.342948i
$327$	8.19187	−	0.0843060i	0.453012	−	0.00466213i
$328$	−7.85651	−	2.62508i	−0.433803	−	0.144946i
$329$	8.19477	−	0.349035i	0.451792	−	0.0192429i
$330$	14.2097	+	3.29860i	0.782218	+	0.181582i
$331$	−3.26758	+	1.35348i	−0.179603	+	0.0743938i	−0.470673	−	0.882308i	$-0.655989\pi$
$331$	−3.26758	+	1.35348i	−0.179603	+	0.0743938i	0.291070	+	0.956702i	$0.405989\pi$
$332$	1.98370	−	23.5380i	0.108870	−	1.29182i
$333$	26.9148	+	10.5048i	1.47492	+	0.575662i
$334$	4.18338	−	5.72453i	0.228905	−	0.313232i
$335$		−	0.778007i		−	0.0425071i
$336$	8.91637	−	16.0156i	0.486428	−	0.873721i
$337$			8.46912i			0.461342i	0.973032	+	0.230671i	$0.0740921\pi$
$337$			8.46912i			0.461342i	−0.973032	+	0.230671i	$0.925908\pi$
$338$	14.0234	+	10.2480i	0.762770	+	0.557419i
$339$	8.53569	+	20.0217i	0.463595	+	1.08743i
$340$	−3.73007	+	3.15023i	−0.202292	+	0.170845i
$341$	−14.1114	+	5.84512i	−0.764173	+	0.316531i
$342$	−27.4795	+	17.5203i	−1.48592	+	0.947390i
$343$	−2.35861	−	18.3695i	−0.127353	−	0.991857i
$344$	2.70505	−	3.11444i	0.145846	−	0.167919i
$345$	−0.179649	−	17.4562i	−0.00967195	−	0.939808i
$346$	−2.57419	+	10.5930i	−0.138389	+	0.569481i
$347$	−23.7703	+	9.84599i	−1.27606	+	0.528561i	−0.914801	−	0.403906i	$-0.867652\pi$
$347$	−23.7703	+	9.84599i	−1.27606	+	0.528561i	−0.361257	+	0.932466i	$0.617652\pi$
$348$	−11.3515	+	3.74806i	−0.608502	+	0.200917i
$349$	6.85875	−	16.5585i	0.367141	−	0.886356i	−0.627076	−	0.778958i	$-0.715748\pi$
$349$	6.85875	−	16.5585i	0.367141	−	0.886356i	0.994216	−	0.107397i	$-0.0342517\pi$
$350$	−10.4324	−	6.96273i	−0.557634	−	0.372173i
$351$	−3.20882	−	3.01656i	−0.171274	−	0.161012i
$352$	24.1043	+	10.3776i	1.28476	+	0.553127i
$353$	−33.6488			−1.79095			−0.895474	−	0.445114i	$-0.853163\pi$
$353$	−33.6488			−1.79095			−0.895474	+	0.445114i	$0.853163\pi$
$354$	11.7799	−	16.4728i	0.626096	−	0.875522i
$355$	1.90764	−	4.60544i	0.101247	−	0.244432i
$356$	−10.4661	+	20.2626i	−0.554701	+	1.07392i
$357$	3.75564	+	7.86378i	0.198769	+	0.416195i
$358$	2.51874	+	0.612076i	0.133119	+	0.0323492i
$359$	10.1805	+	10.1805i	0.537304	+	0.537304i	0.922736	−	0.385432i	$-0.125948\pi$
$359$	10.1805	+	10.1805i	0.537304	+	0.537304i	−0.385432	+	0.922736i	$0.625948\pi$
$360$	10.8476	−	0.987847i	0.571721	−	0.0520641i
$361$	28.2877	+	28.2877i	1.48883	+	1.48883i
$362$	15.5405	+	25.5181i	0.816789	+	1.34120i
$363$	16.9087	+	6.80079i	0.887474	+	0.356949i
$364$	0.186121	−	4.48106i	0.00975537	−	0.234872i
$365$	10.3977	+	4.30685i	0.544238	+	0.225431i
$366$	−37.2845	+	6.19312i	−1.94889	+	0.323720i
$367$	−0.466030			−0.0243266			−0.0121633	−	0.999926i	$-0.503872\pi$
$367$	−0.466030			−0.0243266			−0.0121633	+	0.999926i	$0.503872\pi$
$368$	5.25618	−	30.9627i	0.273998	−	1.61404i
$369$	−8.78408	+	0.180820i	−0.457281	+	0.00941313i
$370$	−10.3159	+	14.1162i	−0.536296	+	0.733866i
$371$	17.2130	−	8.00422i	0.893656	−	0.415559i
$372$	−8.63723	+	7.44818i	−0.447819	+	0.386170i
$373$	−18.3001	+	7.58017i	−0.947545	+	0.392486i	−0.802308	−	0.596911i	$-0.796395\pi$
$373$	−18.3001	+	7.58017i	−0.947545	+	0.392486i	−0.145238	+	0.989397i	$0.546395\pi$
$374$	−10.6560	+	6.48951i	−0.551011	+	0.335565i
$375$	−0.191105	−	18.5694i	−0.00986862	−	0.958918i
$376$	3.91579	+	7.84560i	0.201941	+	0.404606i
$377$	−2.06820	+	2.06820i	−0.106518	+	0.106518i
$378$	3.19244	−	19.1783i	0.164202	−	0.986427i
$379$	−3.99179	−	9.63704i	−0.205045	−	0.495022i	0.787585	−	0.616206i	$-0.211331\pi$
$379$	−3.99179	−	9.63704i	−0.205045	−	0.495022i	−0.992630	+	0.121184i	$0.961331\pi$
$380$	−5.99027	−	18.7896i	−0.307294	−	0.963884i
$381$	3.42215	+	8.02714i	0.175322	+	0.411243i
$382$	1.25606	+	8.07511i	0.0642657	+	0.413159i
$383$	−26.2038			−1.33895			−0.669475	−	0.742835i	$-0.733481\pi$
$383$	−26.2038			−1.33895			−0.669475	+	0.742835i	$0.733481\pi$
$384$	19.5207	+	1.71502i	0.996163	+	0.0875193i
$385$	11.6054	+	10.6572i	0.591468	+	0.543142i
$386$	1.78491	−	0.277639i	0.0908497	−	0.0141314i
$387$	1.59084	−	4.07595i	0.0808672	−	0.207192i
$388$	4.83514	+	15.1663i	0.245467	+	0.769953i
$389$	19.7437	−	8.17811i	1.00105	−	0.414647i	0.178865	−	0.983874i	$-0.442757\pi$
$389$	19.7437	−	8.17811i	1.00105	−	0.414647i	0.822180	+	0.569227i	$0.192757\pi$
$390$	2.26184	−	1.40957i	0.114533	−	0.0713763i
$391$	10.5577	+	10.5577i	0.533927	+	0.533927i
$392$	16.8991	−	10.3160i	0.853534	−	0.521037i
$393$	0.331491	+	32.2105i	0.0167215	+	1.62480i
$394$	−17.1194	+	10.4257i	−0.862462	+	0.525238i
$395$	8.48900	−	3.51626i	0.427128	−	0.176922i
$396$	27.7792	+	1.76623i	1.39596	+	0.0887563i
$397$	5.98962	+	2.48098i	0.300610	+	0.124517i	0.527890	−	0.849313i	$-0.322983\pi$
$397$	5.98962	+	2.48098i	0.300610	+	0.124517i	−0.227280	+	0.973829i	$0.572983\pi$
$398$	−27.2112	−	19.8854i	−1.36397	−	0.996766i
$399$	−35.1517	+	1.85977i	−1.75979	+	0.0931050i
$400$	2.24410	−	13.2194i	0.112205	−	0.660968i
$401$	0.816177			0.0407579			0.0203790	−	0.999792i	$-0.493513\pi$
$401$	0.816177			0.0407579			0.0203790	+	0.999792i	$0.493513\pi$
$402$	−0.243259	−	1.46449i	−0.0121326	−	0.0730422i
$403$	−1.06789	+	2.57811i	−0.0531953	+	0.128425i
$404$	5.90975	+	6.99752i	0.294021	+	0.348140i
$405$	10.4828	−	4.85676i	0.520897	−	0.241334i
$406$	−12.6653	−	2.51233i	−0.628567	−	0.124685i
$407$	−31.5927	+	31.5927i	−1.56599	+	1.56599i
$408$	−6.03637	+	7.09614i	−0.298845	+	0.351311i
$409$	−21.8709	−	21.8709i	−1.08145	−	1.08145i	−0.996375	−	0.0850724i	$-0.972888\pi$
$409$	−21.8709	−	21.8709i	−1.08145	−	1.08145i	−0.0850724	−	0.996375i	$-0.527112\pi$
$410$	1.25548	−	5.16637i	0.0620035	−	0.255149i
$411$	2.14358	+	0.862166i	0.105735	+	0.0425275i
$412$	18.2838	+	9.44396i	0.900778	+	0.465270i
$413$	19.8345	−	9.22323i	0.975991	−	0.453845i
$414$	−5.79616	−	32.8026i	−0.284866	−	1.61216i
$415$	15.1614			0.744244
$416$	4.45460	−	1.77331i	0.218405	−	0.0869436i
$417$	−6.52141	+	6.65704i	−0.319355	+	0.325997i
$418$	−7.74593	−	49.7979i	−0.378866	−	2.43570i
$419$	−15.9496	−	6.60654i	−0.779189	−	0.322751i	−0.0426007	−	0.999092i	$-0.513564\pi$
$419$	−15.9496	−	6.60654i	−0.779189	−	0.322751i	−0.736588	+	0.676342i	$0.763564\pi$
$420$	10.7239	+	4.83948i	0.523271	+	0.236142i
$421$	1.41426	+	3.41432i	0.0689267	+	0.166404i	0.954589	−	0.297927i	$-0.0962950\pi$
$421$	1.41426	+	3.41432i	0.0689267	+	0.166404i	−0.885662	+	0.464330i	$0.846295\pi$
$422$	−3.20436	+	13.1861i	−0.155986	+	0.641892i
$423$	6.71034	+	6.43965i	0.326268	+	0.313106i
$424$	15.3215	+	13.3074i	0.744076	+	0.646267i
$425$	4.50756	+	4.50756i	0.218649	+	0.218649i
$426$	2.15088	−	9.26557i	0.104211	−	0.448918i
$427$	−38.3467	−	14.0034i	−1.85573	−	0.677672i
$428$	17.8139	+	21.0928i	0.861066	+	1.01956i
$429$	6.26496	−	2.67089i	0.302475	−	0.128952i
$430$	2.13774	+	1.56222i	0.103091	+	0.0753371i
$431$	−11.9755			−0.576841			−0.288421	−	0.957504i	$-0.593130\pi$
$431$	−11.9755			−0.576841			−0.288421	+	0.957504i	$0.593130\pi$
$432$	20.1103	−	5.25121i	0.967558	−	0.252649i
$433$	2.07294			0.0996192			0.0498096	−	0.998759i	$-0.484139\pi$
$433$	2.07294			0.0996192			0.0498096	+	0.998759i	$0.484139\pi$
$434$	−12.0810	+	2.40968i	−0.579905	+	0.115669i
$435$	−3.00905	−	7.05816i	−0.144273	−	0.338413i
$436$	−0.794410	+	9.42625i	−0.0380453	+	0.451435i
$437$	−55.7195	+	23.0798i	−2.66543	+	1.10406i
$438$	20.9188	+	4.85603i	0.999537	+	0.232030i
$439$	−4.89937	+	4.89937i	−0.233834	+	0.233834i	−0.814291	−	0.580457i	$-0.802874\pi$
$439$	−4.89937	+	4.89937i	−0.233834	+	0.233834i	0.580457	+	0.814291i	$0.302874\pi$
$440$	−5.33805	+	15.9760i	−0.254482	+	0.761628i
$441$	13.1995	−	16.3332i	0.628546	−	0.777772i
$442$	−0.538260	+	2.21498i	−0.0256024	+	0.105356i
$443$	−4.47527	+	1.85372i	−0.212626	+	0.0880728i	−0.486455	−	0.873706i	$-0.661710\pi$
$443$	−4.47527	+	1.85372i	−0.212626	+	0.0880728i	0.273828	+	0.961779i	$0.411710\pi$
$444$	−15.0045	+	29.7972i	−0.712081	+	1.41411i
$445$	−13.5237	−	5.60171i	−0.641087	−	0.265547i
$446$	2.74562	+	17.6514i	0.130009	+	0.835817i
$447$	14.6630	−	14.9679i	0.693535	−	0.707959i
$448$	17.4407	+	11.9925i	0.823998	+	0.566593i
$449$		−	1.12904i		−	0.0532829i	−0.999645	−	0.0266415i	$-0.991519\pi$
$449$		−	1.12904i		−	0.0532829i	0.999645	−	0.0266415i	$-0.00848124\pi$
$450$	−2.47464	−	14.0049i	−0.116656	−	0.660197i
$451$	5.19937	−	12.5524i	0.244829	−	0.591068i
$452$	−23.9449	+	7.63384i	−1.12627	+	0.359065i
$453$	−3.19954	+	7.95494i	−0.150327	+	0.373756i
$454$	−33.0409	−	8.02924i	−1.55068	−	0.376831i
$455$	2.87604	−	0.122497i	0.134831	−	0.00574276i
$456$	−17.1508	−	33.4958i	−0.803158	−	1.56858i
$457$	16.3309	+	16.3309i	0.763926	+	0.763926i	0.977030	−	0.213104i	$-0.0683572\pi$
$457$	16.3309	+	16.3309i	0.763926	+	0.763926i	−0.213104	+	0.977030i	$0.568357\pi$
$458$	5.44025	−	3.31310i	0.254206	−	0.154811i
$459$	−3.49784	+	9.24160i	−0.163265	+	0.431361i
$460$	20.0865	+	1.69282i	0.936538	+	0.0789280i
$461$	7.06664	−	17.0604i	0.329126	−	0.794581i	−0.669532	−	0.742784i	$-0.733505\pi$
$461$	7.06664	−	17.0604i	0.329126	−	0.794581i	0.998658	−	0.0517970i	$-0.0164949\pi$
$462$	25.1778	+	16.4321i	1.17138	+	0.764489i
$463$		−	26.4029i		−	1.22705i	−0.789676	−	0.613524i	$-0.789752\pi$
$463$		−	26.4029i		−	1.22705i	0.789676	−	0.613524i	$-0.210248\pi$
$464$	−3.07352	−	13.4570i	−0.142685	−	0.624727i
$465$	−5.22928	−	5.12274i	−0.242502	−	0.237561i
$466$	−15.7230	+	21.5153i	−0.728352	+	0.996675i
$467$	0.141822	−	0.342388i	0.00656273	−	0.0158438i	−0.920564	−	0.390591i	$-0.872271\pi$
$467$	0.141822	−	0.342388i	0.00656273	−	0.0158438i	0.927127	+	0.374747i	$0.122271\pi$
$468$	3.81687	−	3.36052i	0.176435	−	0.155340i
$469$	0.550038	−	1.50622i	0.0253984	−	0.0695506i
$470$	−4.80683	+	2.92736i	−0.221723	+	0.135029i
$471$	−2.72495	+	0.0280436i	−0.125559	+	0.00129218i
$472$	17.6548	+	15.3341i	0.812630	+	0.705810i
$473$	4.78438	+	4.78438i	0.219986	+	0.219986i
$474$	14.8799	−	9.27311i	0.683458	−	0.425928i
$475$	−23.7891	+	9.85379i	−1.09152	+	0.452123i
$476$	−9.44855	+	3.46171i	−0.433073	+	0.158667i
$477$	20.0516	+	7.82615i	0.918099	+	0.358335i
$478$	33.3743	−	5.19128i	1.52650	−	0.237444i
$479$	−5.11883			−0.233885			−0.116943	−	0.993139i	$-0.537309\pi$
$479$	−5.11883			−0.233885			−0.116943	+	0.993139i	$0.537309\pi$
$480$	−0.0446967	+	12.5775i	−0.00204011	+	0.574083i
$481$			8.16272i			0.372188i
$482$	−10.8655	+	1.69011i	−0.494912	+	0.0769822i
$483$	11.9934	−	33.9220i	0.545719	−	1.54350i
$484$	−9.65770	+	18.6976i	−0.438986	+	0.849891i
$485$	−9.43946	+	3.90995i	−0.428624	+	0.177542i
$486$	18.2139	−	12.4198i	0.826201	−	0.563375i
$487$	−5.87578	+	5.87578i	−0.266257	+	0.266257i	−0.827590	−	0.561333i	$-0.810289\pi$
$487$	−5.87578	+	5.87578i	−0.266257	+	0.266257i	0.561333	+	0.827590i	$0.310289\pi$
$488$	−3.06261	−	43.5347i	−0.138638	−	1.97072i
$489$	−0.330500	−	32.1142i	−0.0149457	−	1.45225i
$490$	7.50881	+	10.2523i	0.339214	+	0.463152i
$491$	12.6872	+	30.6295i	0.572564	+	1.38229i	0.899365	+	0.437198i	$0.144029\pi$
$491$	12.6872	+	30.6295i	0.572564	+	1.38229i	−0.326801	+	0.945093i	$0.605971\pi$
$492$	0.747896	−	10.1175i	0.0337178	−	0.456133i
$493$	6.06294	+	2.51135i	0.273061	+	0.113106i
$494$	−7.43390	−	5.43256i	−0.334467	−	0.244422i
$495$	0.367694	+	17.8622i	0.0165266	+	0.802848i
$496$	−7.62237	−	10.7394i	−0.342254	−	0.482215i
$497$	6.94914	−	7.56743i	0.311711	−	0.339446i
$498$	28.5392	−	4.74050i	1.27887	−	0.212427i
$499$	−4.88317	+	11.7890i	−0.218601	+	0.527749i	−0.994695	−	0.102868i	$-0.967198\pi$
$499$	−4.88317	+	11.7890i	−0.218601	+	0.527749i	0.776094	+	0.630617i	$0.217198\pi$
$500$	21.3674	+	1.80077i	0.955581	+	0.0805329i
$501$	8.05646	+	3.24037i	0.359936	+	0.144769i
$502$	−13.4304	−	22.0532i	−0.599426	−	0.984282i
$503$	−6.94461	−	6.94461i	−0.309645	−	0.309645i	0.535127	−	0.844772i	$-0.320264\pi$
$503$	−6.94461	−	6.94461i	−0.309645	−	0.309645i	−0.844772	+	0.535127i	$0.820264\pi$
$504$	21.6993	+	5.75663i	0.966565	+	0.256421i
$505$	−4.15694	+	4.15694i	−0.184981	+	0.184981i
$506$	50.0551	+	12.1639i	2.22522	+	0.540749i
$507$	−7.93791	+	19.7359i	−0.352535	+	0.876500i
$508$	−9.60006	+	3.06058i	−0.425934	+	0.135791i
$509$	13.6808	+	5.66678i	0.606391	+	0.251176i	0.664685	−	0.747124i	$-0.268566\pi$
$509$	13.6808	+	5.66678i	0.606391	+	0.251176i	−0.0582934	+	0.998299i	$0.518566\pi$
$510$	−4.86393	−	3.47826i	−0.215378	−	0.154020i
$511$	17.0849	+	15.6890i	0.755792	+	0.694040i
$512$	−4.09550	+	22.2537i	−0.180997	+	0.983484i
$513$	−29.0812	−	27.3388i	−1.28397	−	1.20704i
$514$	−26.9195	+	4.18726i	−1.18737	+	0.184692i
$515$	−5.05465	+	12.2030i	−0.222735	+	0.537729i
$516$	4.51246	+	2.27226i	0.198650	+	0.100031i
$517$	−13.2874	+	5.50383i	−0.584380	+	0.242058i
$518$	−29.9513	+	20.0357i	−1.31598	+	0.880318i
$519$	−13.3505	+	0.137396i	−0.586024	+	0.00603101i
$520$	1.37429	+	2.75350i	0.0602664	+	0.120749i
$521$	4.41255	+	4.41255i	0.193317	+	0.193317i	0.797128	−	0.603811i	$-0.206352\pi$
$521$	4.41255	+	4.41255i	0.193317	+	0.193317i	−0.603811	+	0.797128i	$0.706352\pi$
$522$	−7.87098	−	12.3452i	−0.344504	−	0.540333i
$523$	9.66135	+	23.3246i	0.422461	+	1.01991i	0.981619	+	0.190851i	$0.0611246\pi$
$523$	9.66135	+	23.3246i	0.422461	+	1.01991i	−0.559158	+	0.829061i	$0.688875\pi$
$524$	−37.0640	−	3.12362i	−1.61915	−	0.136456i
$525$	5.12051	−	14.4828i	0.223478	−	0.632081i
$526$	−7.96978	−	5.82417i	−0.347499	−	0.253946i
$527$	6.26104			0.272735
$528$	−5.05293	+	31.7417i	−0.219901	+	1.38138i
$529$		−	38.6449i		−	1.68021i
$530$	−7.68535	+	10.5166i	−0.333830	+	0.456812i
$531$	23.1053	+	9.01803i	1.00269	+	0.391349i
$532$	1.68679	−	40.6114i	0.0731318	−	1.76073i
$533$	−0.949911	−	2.29329i	−0.0411452	−	0.0993333i
$534$	−27.2080	−	6.31600i	−1.17741	−	0.273320i
$535$	−12.5304	+	12.5304i	−0.541735	+	0.541735i
$536$	1.70999	−	0.120296i	0.0738604	−	0.00519598i
$537$	0.0326693	+	3.17442i	0.00140978	+	0.136986i
$538$	−2.04002	+	8.39484i	−0.0879516	+	0.361927i
$539$	14.9336	+	28.8371i	0.643234	+	1.24210i
$540$	4.44255	+	12.5791i	0.191177	+	0.541320i
$541$	7.42860	+	3.07703i	0.319381	+	0.132292i	0.536614	−	0.843828i	$-0.319703\pi$
$541$	7.42860	+	3.07703i	0.319381	+	0.132292i	−0.217233	+	0.976120i	$0.569703\pi$
$542$	9.03508	−	1.40538i	0.388090	−	0.0603663i
$543$	−25.6072	+	26.1398i	−1.09891	+	1.12177i
$544$	−7.50067	−	7.71129i	−0.321589	−	0.330619i
$545$	−6.07167			−0.260082
$546$	5.37544	−	1.12983i	0.230048	−	0.0483523i
$547$	2.47351	+	1.02456i	0.105760	+	0.0438071i	0.434936	−	0.900461i	$-0.356771\pi$
$547$	2.47351	+	1.02456i	0.105760	+	0.0438071i	−0.329176	+	0.944268i	$0.606771\pi$
$548$	−1.22435	+	2.37038i	−0.0523016	+	0.101257i
$549$	−18.5907	−	42.3924i	−0.793431	−	1.80926i
$550$	21.3707	+	5.19329i	0.911252	+	0.221443i
$551$	−18.7439	+	18.7439i	−0.798516	+	0.798516i
$552$	38.3393	−	3.09393i	1.63183	−	0.131686i
$553$	18.9206	−	0.805871i	0.804584	−	0.0342691i
$554$	−39.4600	+	24.0311i	−1.67650	+	1.02098i
$555$	−19.8665	−	7.99046i	−0.843286	−	0.339176i
$556$	−6.94311	−	8.22110i	−0.294454	−	0.348652i
$557$	−6.26019	−	2.59306i	−0.265253	−	0.109871i	0.246093	−	0.969246i	$-0.420853\pi$
$557$	−6.26019	−	2.59306i	−0.265253	−	0.109871i	−0.511346	+	0.859375i	$0.670853\pi$
$558$	−11.4451	−	8.00781i	−0.484510	−	0.338998i
$559$	1.23616			0.0522838
$560$	−6.73011	+	11.8012i	−0.284399	+	0.498691i
$561$	−10.9157	−	10.6933i	−0.460859	−	0.451470i
$562$	4.62157	+	3.37736i	0.194949	+	0.142465i
$563$	3.37074	−	8.13769i	0.142060	−	0.342963i	−0.836796	−	0.547515i	$-0.815574\pi$
$563$	3.37074	−	8.13769i	0.142060	−	0.342963i	0.978856	+	0.204552i	$0.0655738\pi$
$564$	−8.13291	+	7.01329i	−0.342457	+	0.295313i
$565$	−6.17313	−	14.9033i	−0.259706	−	0.626985i
$566$	14.9033	−	9.07609i	0.626433	−	0.381496i
$567$	23.7283	−	1.99145i	0.996497	−	0.0836331i
$568$	10.4173	+	3.48072i	0.437101	+	0.146048i
$569$	0.670180	+	0.670180i	0.0280954	+	0.0280954i	0.721015	−	0.692920i	$-0.243676\pi$
$569$	0.670180	+	0.670180i	0.0280954	+	0.0280954i	−0.692920	+	0.721015i	$0.743676\pi$
$570$	20.4988	−	12.7748i	0.858601	−	0.535077i
$571$	16.2279	+	39.1777i	0.679118	+	1.63953i	0.765628	+	0.643284i	$0.222429\pi$
$571$	16.2279	+	39.1777i	0.679118	+	1.63953i	−0.0865100	+	0.996251i	$0.527571\pi$
$572$	2.38869	+	7.49257i	0.0998762	+	0.313280i
$573$	−9.20709	+	3.92519i	−0.384632	+	0.163977i
$574$	6.08312	−	9.11445i	0.253905	−	0.380430i
$575$		−	26.3189i		−	1.09758i
$576$	3.84847	+	23.6894i	0.160353	+	0.987060i
$577$			10.2989i			0.428750i	0.976751	+	0.214375i	$0.0687715\pi$
$577$			10.2989i			0.428750i	−0.976751	+	0.214375i	$0.931229\pi$
$578$	−18.7024	+	2.90911i	−0.777917	+	0.121003i
$579$	0.867620	+	2.03513i	0.0360570	+	0.0845770i
$580$	8.44120	−	2.69112i	0.350502	−	0.111743i
$581$	29.3524	+	10.7189i	1.21774	+	0.444693i
$582$	−16.5460	+	10.3114i	−0.685852	+	0.427420i
$583$	−23.5367	+	23.5367i	−0.974791	+	0.974791i
$584$	−7.85839	+	23.5191i	−0.325183	+	0.973226i
$585$	2.35506	+	2.26006i	0.0973699	+	0.0934420i
$586$	2.27775	+	3.74016i	0.0940932	+	0.154505i
$587$	3.22485	−	1.33578i	0.133104	−	0.0551333i	−0.315137	−	0.949046i	$-0.602051\pi$
$587$	3.22485	−	1.33578i	0.133104	−	0.0551333i	0.448241	+	0.893913i	$0.352051\pi$
$588$	17.3399	+	16.9508i	0.715084	+	0.699038i
$589$	−9.67817	+	23.3652i	−0.398782	+	0.962745i
$590$	−8.85579	+	12.1182i	−0.364587	+	0.498900i
$591$	−17.5365	−	17.1792i	−0.721353	−	0.706657i
$592$	−32.6212	−	20.4907i	−1.34072	−	0.842162i
$593$		−	12.7937i		−	0.525373i	−0.964881	−	0.262686i	$-0.915392\pi$
$593$		−	12.7937i		−	0.525373i	0.964881	−	0.262686i	$-0.0846085\pi$
$594$	6.27710	+	33.5082i	0.257552	+	1.37486i
$595$	−2.72334	−	5.85652i	−0.111646	−	0.240094i
$596$	15.6112	+	18.4846i	0.639458	+	0.757159i
$597$	15.4029	−	38.2958i	0.630397	−	1.56734i
$598$	8.03786	−	4.89504i	0.328692	−	0.200173i
$599$	9.46156	−	9.46156i	0.386589	−	0.386589i	−0.486880	−	0.873469i	$-0.661865\pi$
$599$	9.46156	−	9.46156i	0.386589	−	0.386589i	0.873469	+	0.486880i	$0.161865\pi$
$600$	16.3688	−	1.32093i	0.668252	−	0.0539269i
$601$	26.5750	+	26.5750i	1.08402	+	1.08402i	0.996130	+	0.0878866i	$0.0280113\pi$
$601$	26.5750	+	26.5750i	1.08402	+	1.08402i	0.0878866	+	0.996130i	$0.471989\pi$
$602$	3.03419	+	4.53580i	0.123664	+	0.184865i
$603$	1.66512	−	0.730220i	0.0678091	−	0.0297369i
$604$	−8.79658	−	4.54362i	−0.357928	−	0.184877i
$605$	−12.4792	−	5.16905i	−0.507352	−	0.210152i
$606$	−6.52512	+	9.12461i	−0.265065	+	0.370662i
$607$		−	25.9850i		−	1.05470i	−0.849649	−	0.527348i	$-0.823186\pi$
$607$		−	25.9850i		−	1.05470i	0.849649	−	0.527348i	$-0.176814\pi$
$608$	40.3716	−	16.0713i	1.63728	−	0.651778i
$609$	−0.835500	−	15.7919i	−0.0338562	−	0.639919i
$610$	27.6789	−	4.30538i	1.12069	−	0.174320i
$611$	−1.00554	+	2.42758i	−0.0406796	+	0.0982092i
$612$	−10.2432	−	5.02653i	−0.414057	−	0.203186i
$613$	14.5692	+	35.1731i	0.588443	+	1.42063i	0.884991	+	0.465609i	$0.154165\pi$
$613$	14.5692	+	35.1731i	0.588443	+	1.42063i	−0.296548	+	0.955018i	$0.595835\pi$
$614$	33.9806	+	8.25759i	1.37134	+	0.333249i
$615$	6.51129	−	0.0670104i	0.262561	−	0.00270212i
$616$	−21.6292	+	27.1556i	−0.871465	+	1.09413i
$617$	24.4432	−	24.4432i	0.984048	−	0.984048i	−0.0158270	−	0.999875i	$-0.505038\pi$
$617$	24.4432	−	24.4432i	0.984048	−	0.984048i	0.999875	+	0.0158270i	$0.00503809\pi$
$618$	−5.69918	+	24.5509i	−0.229255	+	0.987582i
$619$	16.9475	+	40.9150i	0.681179	+	1.64451i	0.761836	+	0.647770i	$0.224298\pi$
$619$	16.9475	+	40.9150i	0.681179	+	1.64451i	−0.0806567	+	0.996742i	$0.525702\pi$
$620$	6.45789	−	5.45400i	0.259355	−	0.219038i
$621$	37.1918	−	16.7684i	1.49246	−	0.672895i
$622$	25.0061	+	18.2740i	1.00265	+	0.732722i
$623$	−22.2215	−	20.4059i	−0.890286	−	0.817546i
$624$	3.44783	+	4.75338i	0.138024	+	0.190287i
$625$		−	2.99732i		−	0.119893i
$626$	−29.6782	−	21.6883i	−1.18618	−	0.866838i
$627$	56.7787	−	24.2060i	2.26752	−	0.966695i
$628$	0.264253	−	3.13555i	0.0105448	−	0.125122i
$629$	16.9204	−	7.00866i	0.674660	−	0.279454i
$630$	−2.51221	+	14.1888i	−0.100089	+	0.565295i
$631$	−23.5625	−	23.5625i	−0.938008	−	0.938008i	0.0601800	−	0.998188i	$-0.480833\pi$
$631$	−23.5625	−	23.5625i	−0.938008	−	0.938008i	−0.998188	+	0.0601800i	$0.980833\pi$
$632$	9.04100	+	18.1144i	0.359632	+	0.720552i
$633$	−16.6188	+	0.171031i	−0.660538	+	0.00679787i
$634$	7.32260	−	30.1330i	0.290817	−	1.19673i
$635$	−2.47495	−	5.97505i	−0.0982152	−	0.237112i
$636$	−11.1784	+	22.1990i	−0.443252	+	0.880249i
$637$	5.65459	+	1.79615i	0.224043	+	0.0711662i
$638$	22.3717	−	3.47985i	0.885703	−	0.137769i
$639$	11.6472	−	0.239758i	0.460757	−	0.00948470i
$640$	−14.4538	−	1.41989i	−0.571337	−	0.0561262i
$641$			6.47610i			0.255790i	0.991788	+	0.127895i	$0.0408221\pi$
$641$			6.47610i			0.255790i	−0.991788	+	0.127895i	$0.959178\pi$
$642$	−19.6688	+	27.5045i	−0.776266	+	1.08552i
$643$	−8.28119	+	19.9926i	−0.326578	+	0.788430i	0.672263	+	0.740312i	$0.265322\pi$
$643$	−8.28119	+	19.9926i	−0.326578	+	0.788430i	−0.998842	+	0.0481179i	$0.984678\pi$
$644$	37.6905	+	17.4781i	1.48521	+	0.688733i
$645$	−1.21007	+	3.00857i	−0.0476464	+	0.118462i
$646$	−4.87820	+	20.0741i	−0.191930	+	0.789806i
$647$	21.0983	−	21.0983i	0.829458	−	0.829458i	−0.157984	−	0.987442i	$-0.550499\pi$
$647$	21.0983	−	21.0983i	0.829458	−	0.829458i	0.987442	+	0.157984i	$0.0504994\pi$
$648$	12.2956	+	22.2894i	0.483016	+	0.875611i
$649$	−27.1212	+	27.1212i	−1.06460	+	1.06460i
$650$	3.43172	−	2.08991i	0.134603	−	0.0819731i
$651$	−6.50215	−	13.6146i	−0.254839	−	0.533598i
$652$	36.9532	+	3.11428i	1.44720	+	0.121965i
$653$	21.3062	+	8.82533i	0.833778	+	0.345362i	0.758397	−	0.651793i	$-0.225983\pi$
$653$	21.3062	+	8.82533i	0.833778	+	0.345362i	0.0753805	+	0.997155i	$0.475983\pi$
$654$	−11.4291	+	1.89842i	−0.446912	+	0.0742342i
$655$		−	23.8738i		−	0.932828i
$656$	11.5494	+	1.96060i	0.450926	+	0.0765486i
$657$	0.541300	+	26.2958i	0.0211181	+	1.02590i
$658$	−11.3756	+	2.26899i	−0.443466	+	0.0884543i
$659$	16.3666	+	6.77928i	0.637553	+	0.264083i	0.677959	−	0.735100i	$-0.262865\pi$
$659$	16.3666	+	6.77928i	0.637553	+	0.264083i	−0.0404052	+	0.999183i	$0.512865\pi$
$660$	−20.5738	−	1.52083i	−0.800833	−	0.0591982i
$661$	−12.5870	−	30.3878i	−0.489579	−	1.18195i	−0.954933	−	0.296823i	$-0.904073\pi$
$661$	−12.5870	−	30.3878i	−0.489579	−	1.18195i	0.465354	−	0.885125i	$-0.345927\pi$
$662$	4.27196	−	2.60161i	0.166034	−	0.101115i
$663$	−2.79158	+	0.0287294i	−0.108416	+	0.00111576i
$664$	2.34426	+	33.3235i	0.0909750	+	1.29320i
$665$	26.0652	−	1.11018i	1.01077	−	0.0430510i
$666$	−39.8943	−	8.82929i	−1.54587	−	0.342128i
$667$	−10.3686	−	25.0319i	−0.401473	−	0.969241i
$668$	−4.60160	+	8.90883i	−0.178041	+	0.344693i
$669$	−20.1258	+	8.58007i	−0.778108	+	0.331725i
$670$	0.169110	+	1.08719i	0.00653330	+	0.0420020i
$671$	71.5824			2.76341
$672$	−8.97863	+	24.3184i	−0.346358	+	0.938102i
$673$	−35.4030			−1.36469			−0.682343	−	0.731032i	$-0.739039\pi$
$673$	−35.4030			−1.36469			−0.682343	+	0.731032i	$0.739039\pi$
$674$	−1.84087	−	11.8348i	−0.0709078	−	0.455860i
$675$	15.8788	−	7.15919i	0.611177	−	0.275558i
$676$	−21.8239	−	11.2725i	−0.839382	−	0.433558i
$677$	−8.22253	−	19.8509i	−0.316017	−	0.762933i	−0.999458	−	0.0329271i	$-0.989517\pi$
$677$	−8.22253	−	19.8509i	−0.316017	−	0.762933i	0.683440	−	0.730006i	$-0.260483\pi$
$678$	−16.2798	−	26.1232i	−0.625223	−	1.00325i
$679$	−21.0390	+	0.896101i	−0.807402	+	0.0343892i
$680$	4.52770	−	5.21294i	0.173629	−	0.199907i
$681$	−0.428557	−	41.6421i	−0.0164223	−	1.59573i
$682$	18.4488	−	11.2353i	0.706442	−	0.430222i
$683$	0.314108	+	0.758323i	0.0120190	+	0.0290164i	0.929775	−	0.368128i	$-0.120001\pi$
$683$	0.314108	+	0.758323i	0.0120190	+	0.0290164i	−0.917756	+	0.397144i	$0.870001\pi$
$684$	34.5919	−	30.4561i	1.32265	−	1.16452i
$685$	−1.58204	−	0.655304i	−0.0604468	−	0.0250379i
$686$	7.28879	+	25.1570i	0.278287	+	0.960498i
$687$	5.57279	+	5.45925i	0.212615	+	0.208284i
$688$	−3.10309	+	4.94012i	−0.118304	+	0.188340i
$689$			6.08125i			0.231677i
$690$	4.04537	+	24.3544i	0.154005	+	0.927154i
$691$	−20.4739	−	8.48058i	−0.778865	−	0.322616i	−0.0424075	−	0.999100i	$-0.513503\pi$
$691$	−20.4739	−	8.48058i	−0.778865	−	0.322616i	−0.736457	+	0.676484i	$0.763503\pi$
$692$	1.29467	−	15.3622i	0.0492161	−	0.583985i
$693$	−11.9164	+	34.8411i	−0.452668	+	1.32350i
$694$	31.0767	−	18.9257i	1.17966	−	0.718409i
$695$	4.88382	−	4.88382i	0.185254	−	0.185254i
$696$	15.0479	−	7.70496i	0.570391	−	0.292056i
$697$	−3.93812	+	3.93812i	−0.149167	+	0.149167i
$698$	−5.98528	+	24.6298i	−0.226546	+	0.932253i
$699$	−30.2796	−	12.1787i	−1.14528	−	0.460641i
$700$	16.0917	+	7.46217i	0.608211	+	0.282043i
$701$	15.2144	−	36.7308i	0.574640	−	1.38730i	−0.322927	−	0.946424i	$-0.604667\pi$
$701$	15.2144	−	36.7308i	0.574640	−	1.38730i	0.897567	−	0.440879i	$-0.145333\pi$
$702$	5.13973	+	3.51790i	0.193987	+	0.132774i
$703$			73.9779i			2.79013i
$704$	−35.9393	−	9.26235i	−1.35451	−	0.349088i
$705$	−4.92394	−	4.82363i	−0.185446	−	0.181668i
$706$	47.0212	−	7.31402i	1.76967	−	0.275267i
$707$	−10.9867	+	5.10892i	−0.413197	+	0.192141i
$708$	−12.8808	+	25.5798i	−0.484090	+	0.961349i
$709$	−12.2861	−	29.6612i	−0.461414	−	1.11395i	−0.967817	−	0.251654i	$-0.919025\pi$
$709$	−12.2861	−	29.6612i	−0.461414	−	1.11395i	0.506404	−	0.862297i	$-0.330975\pi$
$710$	−1.66470	+	6.85034i	−0.0624749	+	0.257089i
$711$	15.4932	+	14.8682i	0.581041	+	0.557602i
$712$	10.2210	−	30.5901i	0.383049	−	1.14641i
$713$	−18.2786	−	18.2786i	−0.684539	−	0.684539i
$714$	−6.95746	−	10.1726i	−0.260376	−	0.380699i
$715$	−4.66335	+	1.93162i	−0.174400	+	0.0722386i
$716$	−3.65275	−	0.307841i	−0.136510	−	0.0115045i
$717$	16.2227	+	38.0527i	0.605849	+	1.42111i
$718$	−16.4391	−	12.0134i	−0.613503	−	0.448337i
$719$			11.5801i			0.431864i	0.976408	+	0.215932i	$0.0692789\pi$
$719$			11.5801i			0.431864i	−0.976408	+	0.215932i	$0.930721\pi$
$720$	−14.9439	+	3.73831i	−0.556926	+	0.139318i
$721$	−18.4131	+	20.0514i	−0.685739	+	0.746752i
$722$	−45.6782	−	33.3808i	−1.69997	−	1.24230i
$723$	−5.28158	−	12.3887i	−0.196424	−	0.460740i
$724$	−27.2631	−	32.2813i	−1.01323	−	1.19972i
$725$	−4.42680	−	10.6872i	−0.164407	−	0.396914i
$726$	−25.1066	−	5.82817i	−0.931792	−	0.216304i
$727$	18.8079	−	18.8079i	0.697547	−	0.697547i	−0.266334	−	0.963881i	$-0.585812\pi$
$727$	18.8079	−	18.8079i	0.697547	−	0.697547i	0.963881	+	0.266334i	$0.0858124\pi$
$728$	0.713932	+	6.30234i	0.0264601	+	0.233580i
$729$	20.2336	+	17.8774i	0.749393	+	0.662126i
$730$	−15.4659	−	3.75837i	−0.572420	−	0.139103i
$731$	−1.06139	−	2.56241i	−0.0392567	−	0.0947742i
$732$	50.7555	−	16.7586i	1.87598	−	0.619416i
$733$	−6.12274	+	14.7816i	−0.226148	+	0.545971i	−0.995702	−	0.0926112i	$-0.970479\pi$
$733$	−6.12274	+	14.7816i	−0.226148	+	0.545971i	0.769554	+	0.638582i	$0.220479\pi$
$734$	0.651235	−	0.101298i	0.0240375	−	0.00373897i
$735$	−9.90675	+	12.0039i	−0.365416	+	0.442772i
$736$	−0.614885	+	44.4101i	−0.0226650	+	1.63698i
$737$			2.81167i			0.103569i
$738$	12.2356	−	2.16202i	0.450400	−	0.0795849i
$739$	−33.2434	−	13.7699i	−1.22288	−	0.506533i	−0.324555	−	0.945867i	$-0.605214\pi$
$739$	−33.2434	−	13.7699i	−1.22288	−	0.506533i	−0.898324	+	0.439334i	$0.855214\pi$
$740$	11.3471	−	21.9684i	0.417129	−	0.807574i
$741$	4.20795	−	10.4621i	0.154583	−	0.384336i
$742$	−22.3138	+	14.9267i	−0.819166	+	0.547975i
$743$	21.7102	+	21.7102i	0.796472	+	0.796472i	0.982537	−	0.186066i	$-0.0595737\pi$
$743$	21.7102	+	21.7102i	0.796472	+	0.796472i	−0.186066	+	0.982537i	$0.559574\pi$
$744$	10.4508	−	12.2856i	0.383144	−	0.450411i
$745$	−10.9810	+	10.9810i	−0.402311	+	0.402311i
$746$	23.9251	−	14.5704i	0.875962	−	0.533459i
$747$	14.2302	+	32.4491i	0.520654	+	1.18725i
$748$	13.4803	−	11.3847i	0.492888	−	0.416267i
$749$	−33.1174	+	15.3999i	−1.21008	+	0.562701i
$750$	4.30335	+	25.9075i	0.157136	+	0.946007i
$751$		−	38.7252i		−	1.41310i	−0.707662	−	0.706551i	$-0.750250\pi$
$751$		−	38.7252i		−	1.41310i	0.707662	−	0.706551i	$-0.249750\pi$
$752$	−7.17730	−	10.1124i	−0.261729	−	0.368760i
$753$	22.1302	−	22.5905i	0.806470	−	0.823242i
$754$	2.44057	−	3.33967i	0.0888803	−	0.121624i
$755$	2.43186	−	5.87103i	0.0885045	−	0.213669i
$756$	−0.292488	+	27.4939i	−0.0106377	+	0.999943i
$757$	32.8313	−	13.5992i	1.19327	−	0.494271i	0.304455	−	0.952527i	$-0.401526\pi$
$757$	32.8313	−	13.5992i	1.19327	−	0.494271i	0.888820	+	0.458256i	$0.151526\pi$
$758$	7.67291	+	12.5992i	0.278693	+	0.457624i
$759$	0.649240	+	63.0856i	0.0235659	+	2.28986i
$760$	12.4550	+	24.9547i	0.451791	+	0.905201i
$761$	−0.854654	+	0.854654i	−0.0309812	+	0.0309812i	−0.722428	−	0.691446i	$-0.756974\pi$
$761$	−0.854654	+	0.854654i	−0.0309812	+	0.0309812i	0.691446	+	0.722428i	$0.256974\pi$
$762$	−6.52695	−	10.4734i	−0.236446	−	0.379410i
$763$	−11.7547	−	4.29256i	−0.425549	−	0.155401i
$764$	−3.51046	−	11.0112i	−0.127004	−	0.398372i
$765$	2.66275	−	6.82231i	0.0962720	−	0.246661i
$766$	36.6174	−	5.69574i	1.32304	−	0.205795i
$767$			7.00740i			0.253023i
$768$	−27.6512	+	1.84650i	−0.997778	+	0.0666299i
$769$		−	10.2705i		−	0.370364i	−0.982704	−	0.185182i	$-0.940713\pi$
$769$		−	10.2705i		−	0.370364i	0.982704	−	0.185182i	$-0.0592874\pi$
$770$	−18.5340	−	12.3699i	−0.667920	−	0.445780i
$771$	−13.0852	−	30.6932i	−0.471251	−	1.10539i
$772$	−2.43391	+	0.775949i	−0.0875982	+	0.0279270i
$773$	11.8746	+	28.6679i	0.427101	+	1.03111i	0.980202	+	0.197999i	$0.0634441\pi$
$773$	11.8746	+	28.6679i	0.427101	+	1.03111i	−0.553102	+	0.833114i	$0.686556\pi$
$774$	−1.33710	+	6.04156i	−0.0480611	+	0.217159i
$775$	−7.80395	−	7.80395i	−0.280326	−	0.280326i
$776$	−10.0533	−	20.1426i	−0.360891	−	0.723076i
$777$	−32.8123	−	29.5147i	−1.17713	−	1.05884i
$778$	−25.8124	+	15.7197i	−0.925420	+	0.563579i
$779$	−8.60895	−	20.7838i	−0.308448	−	0.744659i
$780$	−2.85433	+	2.46138i	−0.102201	+	0.0881317i
$781$	−6.89409	+	16.6438i	−0.246690	+	0.595562i
$782$	−17.0483	−	12.4586i	−0.609647	−	0.445519i
$783$	12.2819	−	13.0647i	0.438921	−	0.466895i
$784$	−21.3727	+	18.0889i	−0.763309	+	0.646033i
$785$	2.01968			0.0720856
$786$	−7.46460	−	44.9392i	−0.266254	−	1.60293i
$787$	−24.2088	−	10.0276i	−0.862951	−	0.357446i	−0.0930901	−	0.995658i	$-0.529674\pi$
$787$	−24.2088	−	10.0276i	−0.862951	−	0.357446i	−0.769861	+	0.638212i	$0.779674\pi$
$788$	21.6566	−	18.2901i	0.771485	−	0.651556i
$789$	4.51129	−	11.2163i	0.160606	−	0.399312i
$790$	−11.0983	+	6.75885i	−0.394860	+	0.240469i
$791$	−1.41479	−	33.2169i	−0.0503040	−	1.18106i
$792$	−39.2028	+	3.57002i	−1.39301	+	0.126855i
$793$	9.24749	−	9.24749i	0.328388	−	0.328388i
$794$	−8.90922	−	2.16502i	−0.316176	−	0.0768338i
$795$	−14.8006	−	5.95292i	−0.524924	−	0.211128i
$796$	42.3475	+	21.8734i	1.50097	+	0.775281i
$797$	−7.49626	−	3.10505i	−0.265531	−	0.109987i	0.245946	−	0.969284i	$-0.420901\pi$
$797$	−7.49626	−	3.10505i	−0.265531	−	0.109987i	−0.511477	+	0.859297i	$0.670901\pi$
$798$	48.7171	−	10.2395i	1.72457	−	0.362476i
$799$	5.89546			0.208566
$800$	−0.262522	+	18.9606i	−0.00928154	+	0.670360i
$801$	−0.704043	−	34.2017i	−0.0248761	−	1.20846i
$802$	−1.14053	+	0.177407i	−0.0402736	+	0.00626445i
$803$	−37.5765	−	15.5647i	−1.32605	−	0.549267i
$804$	0.658258	+	1.99362i	0.0232150	+	0.0703095i
$805$	−9.14708	+	25.0482i	−0.322392	+	0.882834i
$806$	0.931891	−	3.83480i	0.0328245	−	0.135075i
$807$	−10.5802	+	0.108885i	−0.372441	+	0.00383294i
$808$	−9.77934	−	8.49384i	−0.344036	−	0.298812i
$809$	15.6991	−	15.6991i	0.551951	−	0.551951i	−0.375053	−	0.927003i	$-0.622375\pi$
$809$	15.6991	−	15.6991i	0.551951	−	0.551951i	0.927003	+	0.375053i	$0.122375\pi$
$810$	−13.5931	+	9.06546i	−0.477615	+	0.318528i
$811$	−2.36034	−	5.69837i	−0.0828829	−	0.200097i	0.877005	−	0.480481i	$-0.159538\pi$
$811$	−2.36034	−	5.69837i	−0.0828829	−	0.200097i	−0.959888	+	0.280384i	$0.909538\pi$
$812$	18.2447	+	0.757790i	0.640262	+	0.0265932i
$813$	4.39182	+	10.3016i	0.154028	+	0.361294i
$814$	37.2809	−	51.0151i	1.30669	−	1.78808i
$815$			23.8024i			0.833763i
$816$	6.89284	−	11.2283i	0.241298	−	0.393069i
$817$	11.2032			0.391949
$818$	35.3166	+	25.8087i	1.23481	+	0.902380i
$819$	2.96156	+	6.04045i	0.103485	+	0.211070i
$820$	−0.631435	+	7.49243i	−0.0220507	+	0.261647i
$821$	13.1530	+	31.7541i	0.459041	+	1.10822i	0.968786	+	0.247898i	$0.0797399\pi$
$821$	13.1530	+	31.7541i	0.459041	+	1.10822i	−0.509745	+	0.860326i	$0.670260\pi$
$822$	−3.18287	−	0.738863i	−0.111015	−	0.0257708i
$823$	32.5081	+	32.5081i	1.13316	+	1.13316i	0.989649	+	0.143511i	$0.0458392\pi$
$823$	32.5081	+	32.5081i	1.13316	+	1.13316i	0.143511	+	0.989649i	$0.454161\pi$
$824$	−27.6027	−	9.22285i	−0.961586	−	0.321293i
$825$	0.277189	+	26.9340i	0.00965049	+	0.937722i
$826$	−25.7121	+	17.1999i	−0.894639	+	0.598462i
$827$	8.61595	−	3.56884i	0.299606	−	0.124101i	−0.227816	−	0.973704i	$-0.573159\pi$
$827$	8.61595	−	3.56884i	0.299606	−	0.124101i	0.527422	+	0.849603i	$0.323159\pi$
$828$	15.2297	+	44.5788i	0.529268	+	1.54922i
$829$	20.9131	−	50.4888i	0.726344	−	1.75355i	0.0719329	−	0.997409i	$-0.477083\pi$
$829$	20.9131	−	50.4888i	0.726344	−	1.75355i	0.654411	−	0.756139i	$-0.272917\pi$
$830$	−21.1867	+	3.29553i	−0.735401	+	0.114390i
$831$	−40.4214	−	39.5979i	−1.40220	−	1.37363i
$832$	−5.83945	+	3.44631i	−0.202446	+	0.119479i
$833$	−1.13190	−	13.2635i	−0.0392181	−	0.459554i
$834$	7.66609	−	10.7201i	0.265455	−	0.371208i
$835$	−5.94595	−	2.46290i	−0.205768	−	0.0852320i
$836$	21.6485	+	67.9044i	0.748728	+	2.34852i
$837$	6.05583	−	16.0000i	0.209320	−	0.553041i
$838$	23.7241	+	5.76519i	0.819537	+	0.199155i
$839$	22.7361	−	22.7361i	0.784937	−	0.784937i	−0.195723	−	0.980659i	$-0.562705\pi$
$839$	22.7361	−	22.7361i	0.784937	−	0.784937i	0.980659	+	0.195723i	$0.0627052\pi$
$840$	−16.0376	−	4.43176i	−0.553348	−	0.152910i
$841$	12.0854	+	12.0854i	0.416739	+	0.416739i
$842$	−2.71845	−	4.46380i	−0.0936838	−	0.153833i
$843$	−2.61604	+	6.50420i	−0.0901011	+	0.224016i
$844$	1.61161	−	19.1230i	0.0554740	−	0.658239i
$845$	6.03334	−	14.5658i	0.207553	−	0.501078i
$846$	−10.7768	−	7.54024i	−0.370515	−	0.259239i
$847$	−20.5052	−	18.8298i	−0.704567	−	0.647000i
$848$	−24.3029	−	15.2656i	−0.834565	−	0.524224i
$849$	15.2664	+	14.9554i	0.523941	+	0.513267i
$850$	−7.27868	−	5.31913i	−0.249657	−	0.182445i
$851$	−69.8590	−	28.9365i	−2.39474	−	0.991932i
$852$	−0.991671	+	13.4153i	−0.0339741	+	0.459601i
$853$	−6.58810	−	15.9051i	−0.225572	−	0.544580i	0.770057	−	0.637975i	$-0.220228\pi$
$853$	−6.58810	−	15.9051i	−0.225572	−	0.544580i	−0.995629	+	0.0933956i	$0.970228\pi$
$854$	56.6299	+	11.2333i	1.93784	+	0.384396i
$855$	21.3437	+	20.4827i	0.729939	+	0.700494i
$856$	−29.4781	−	25.6032i	−1.00754	−	0.875099i
$857$	6.47594	−	6.47594i	0.221214	−	0.221214i	−0.587796	−	0.809010i	$-0.700004\pi$
$857$	6.47594	−	6.47594i	0.221214	−	0.221214i	0.809010	+	0.587796i	$0.200004\pi$
$858$	−8.17416	+	5.09410i	−0.279061	+	0.173910i
$859$	−39.4456	+	16.3389i	−1.34587	+	0.557476i	−0.935139	−	0.354281i	$-0.884725\pi$
$859$	−39.4456	+	16.3389i	−1.34587	+	0.557476i	−0.410728	+	0.911758i	$0.634725\pi$
$860$	−3.32687	−	1.71840i	−0.113445	−	0.0585969i
$861$	12.6532	+	4.47364i	0.431219	+	0.152461i
$862$	16.7347	−	2.60304i	0.569987	−	0.0886600i
$863$		−	21.6558i		−	0.737172i	−0.929594	−	0.368586i	$-0.879842\pi$
$863$		−	21.6558i		−	0.737172i	0.929594	−	0.368586i	$-0.120158\pi$
$864$	−26.9609	+	11.7093i	−0.917229	+	0.398359i
$865$	9.89519			0.336446
$866$	−2.89675	+	0.450581i	−0.0984355	+	0.0153114i
$867$	−9.09096	−	21.3241i	−0.308745	−	0.724206i
$868$	16.3583	−	5.99328i	0.555237	−	0.203425i
$869$	−30.6787	+	12.7076i	−1.04071	+	0.431074i
$870$	5.73906	+	9.20908i	0.194572	+	0.312217i
$871$	0.363231	+	0.363231i	0.0123076	+	0.0123076i
$872$	−0.938803	−	13.3450i	−0.0317919	−	0.451919i
$873$	−17.2279	−	16.5330i	−0.583077	−	0.559556i
$874$	72.8463	−	44.3633i	2.46406	−	1.50061i
$875$	−9.73040	+	26.6456i	−0.328948	+	0.900785i
$876$	−30.2876	−	2.23889i	−1.02332	−	0.0756449i
$877$	3.55455	−	8.58145i	0.120029	−	0.289775i	−0.852433	−	0.522836i	$-0.824874\pi$
$877$	3.55455	−	8.58145i	0.120029	−	0.289775i	0.972462	+	0.233061i	$0.0748741\pi$
$878$	5.78148	−	7.91137i	0.195116	−	0.266996i
$879$	−3.75323	+	3.83129i	−0.126593	+	0.129226i
$880$	3.98684	−	23.4854i	0.134396	−	0.791691i
$881$		−	32.6691i		−	1.10065i	−0.834951	−	0.550325i	$-0.814504\pi$
$881$		−	32.6691i		−	1.10065i	0.834951	−	0.550325i	$-0.185496\pi$
$882$	−14.8948	+	25.6933i	−0.501535	+	0.865137i
$883$	−18.5221	+	44.7163i	−0.623318	+	1.50482i	0.224467	+	0.974482i	$0.427936\pi$
$883$	−18.5221	+	44.7163i	−0.623318	+	1.50482i	−0.847785	+	0.530340i	$0.822064\pi$
$884$	0.270715	−	3.21223i	0.00910513	−	0.108039i
$885$	−17.0547	−	6.85952i	−0.573287	−	0.230580i
$886$	5.85085	−	3.56316i	0.196563	−	0.119707i
$887$	5.07169	+	5.07169i	0.170291	+	0.170291i	0.787107	−	0.616816i	$-0.211578\pi$
$887$	5.07169	+	5.07169i	0.170291	+	0.170291i	−0.616816	+	0.787107i	$0.711578\pi$
$888$	14.4906	−	44.9003i	0.486272	−	1.50676i
$889$	−0.567219	−	13.3174i	−0.0190239	−	0.446651i
$890$	20.1158	+	4.88833i	0.674283	+	0.163857i
$891$	−37.8844	+	17.5520i	−1.26918	+	0.588016i
$892$	−7.67352	−	24.0694i	−0.256929	−	0.805904i
$893$	−9.11307	+	22.0009i	−0.304957	+	0.736232i
$894$	−17.2367	+	24.1035i	−0.576482	+	0.806142i
$895$		−	2.35282i		−	0.0786462i
$896$	−26.9786	−	12.9675i	−0.901291	−	0.433213i
$897$	8.23368	+	8.06594i	0.274915	+	0.269314i
$898$	0.245413	+	1.57774i	0.00818953	+	0.0526498i
$899$	−10.4968	−	4.34791i	−0.350087	−	0.145011i
$900$	6.50223	+	19.0327i	0.216741	+	0.634423i
$901$	12.6058	−	5.22147i	0.419959	−	0.173953i
$902$	−4.53722	+	18.6710i	−0.151073	+	0.621675i
$903$	−4.46968	+	4.96906i	−0.148742	+	0.165360i
$904$	31.8016	−	15.8723i	1.05770	−	0.527906i
$905$	19.1770	−	19.1770i	0.637465	−	0.637465i
$906$	2.74195	−	11.8118i	0.0910953	−	0.392420i
$907$	−7.19146	+	2.97880i	−0.238789	+	0.0989095i	−0.498869	−	0.866678i	$-0.666251\pi$
$907$	−7.19146	+	2.97880i	−0.238789	+	0.0989095i	0.260080	+	0.965587i	$0.416251\pi$
$908$	47.9169	+	4.03826i	1.59018	+	0.134014i
$909$	−12.7985	−	4.99525i	−0.424499	−	0.165682i
$910$	−3.99238	+	0.796324i	−0.132346	+	0.0263979i
$911$	2.06944			0.0685637			0.0342819	−	0.999412i	$-0.489086\pi$
$911$	2.06944			0.0685637			0.0342819	+	0.999412i	$0.489086\pi$
$912$	31.2474	+	43.0794i	1.03470	+	1.42650i
$913$	−54.7925			−1.81337
$914$	−26.3706	−	19.2712i	−0.872263	−	0.637434i
$915$	13.4543	+	31.5590i	0.444785	+	1.04331i
$916$	−6.88211	+	5.81227i	−0.227391	+	0.192043i
$917$	16.8784	−	46.2195i	0.557373	−	1.52630i
$918$	2.87914	−	13.6746i	0.0950256	−	0.451329i
$919$	2.31318	+	2.31318i	0.0763047	+	0.0763047i	0.744229	−	0.667924i	$-0.232817\pi$
$919$	2.31318	+	2.31318i	0.0763047	+	0.0763047i	−0.667924	+	0.744229i	$0.732817\pi$
$920$	−28.4370	+	2.00051i	−0.937541	+	0.0659548i
$921$	0.440745	+	42.8265i	0.0145230	+	1.41118i
$922$	−6.16669	+	25.3764i	−0.203089	+	0.835726i
$923$	1.25953	+	3.04078i	0.0414580	+	0.100089i
$924$	−38.7554	−	17.4896i	−1.27496	−	0.575366i
$925$	−29.8259	−	12.3543i	−0.980670	−	0.406207i
$926$	5.73902	+	36.8957i	0.188596	+	1.21247i
$927$	−30.8616	+	0.635286i	−1.01363	+	0.0208655i
$928$	7.22003	+	18.1369i	0.237009	+	0.595373i
$929$	−23.9455			−0.785627			−0.392813	−	0.919618i	$-0.628498\pi$
$929$	−23.9455			−0.785627			−0.392813	+	0.919618i	$0.628498\pi$
$930$	8.42094	+	6.02191i	0.276133	+	0.197466i
$931$	51.2470	+	16.2784i	1.67955	+	0.533502i
$932$	17.2948	−	33.4832i	0.566509	−	1.09678i
$933$	−14.1547	+	35.1925i	−0.463404	+	1.15215i
$934$	−0.123761	+	0.509283i	−0.00404957	+	0.0166643i
$935$	8.00808	+	8.00808i	0.261892	+	0.261892i
$936$	−4.60327	+	5.52567i	−0.150463	+	0.180612i
$937$	5.00364	−	5.00364i	0.163462	−	0.163462i	−0.620637	−	0.784098i	$-0.713126\pi$
$937$	5.00364	−	5.00364i	0.163462	−	0.163462i	0.784098	+	0.620637i	$0.213126\pi$
$938$	−0.441232	+	2.22436i	−0.0144067	+	0.0726278i
$939$	16.7993	−	41.7678i	0.548225	−	1.36304i
$940$	6.08082	−	5.13554i	0.198334	−	0.167503i
$941$	−0.454949	+	1.09834i	−0.0148309	+	0.0358050i	−0.931122	−	0.364709i	$-0.881168\pi$
$941$	−0.454949	+	1.09834i	−0.0148309	+	0.0358050i	0.916291	+	0.400514i	$0.131168\pi$
$942$	3.80177	−	0.631492i	0.123868	−	0.0205751i
$943$	22.9940			0.748789
$944$	−28.0041	−	17.5905i	−0.911456	−	0.572523i
$945$	−17.6004	+	1.29490i	−0.572539	+	0.0421229i
$946$	−7.72568	−	5.64579i	−0.251184	−	0.183560i
$947$	−22.5818	−	9.35369i	−0.733810	−	0.303954i	−0.0156932	−	0.999877i	$-0.504996\pi$
$947$	−22.5818	−	9.35369i	−0.733810	−	0.303954i	−0.718116	+	0.695923i	$0.754996\pi$
$948$	−18.7777	+	16.1927i	−0.609872	+	0.525914i
$949$	−6.86514	+	2.84363i	−0.222852	+	0.0923083i
$950$	31.1013	−	18.9407i	1.00906	−	0.614516i
$951$	37.9773	−	0.390840i	1.23150	−	0.0126739i
$952$	12.4510	−	6.89120i	0.403540	−	0.223345i
$953$	−6.17054	−	6.17054i	−0.199883	−	0.199883i	0.600067	−	0.799950i	$-0.295141\pi$
$953$	−6.17054	−	6.17054i	−0.199883	−	0.199883i	−0.799950	+	0.600067i	$0.795141\pi$
$954$	−29.7214	−	6.57785i	−0.962266	−	0.212966i
$955$	6.85335	−	2.83875i	0.221769	−	0.0918598i
$956$	−45.5092	+	14.5087i	−1.47187	+	0.469244i
$957$	10.8745	+	25.5078i	0.351524	+	0.824549i
$958$	7.15310	−	1.11265i	0.231106	−	0.0359479i
$959$	−2.59953	−	2.38714i	−0.0839433	−	0.0770847i
$960$	−2.67143	−	17.5857i	−0.0862202	−	0.567575i
$961$	20.1602			0.650331
$962$	−1.77428	−	11.4067i	−0.0572049	−	0.367766i
$963$	−38.5787	−	15.0573i	−1.24318	−	0.485215i
$964$	14.8162	−	4.72354i	0.477199	−	0.152135i
$965$	−0.627474	−	1.51486i	−0.0201991	−	0.0487650i
$966$	−9.38630	+	50.0098i	−0.301999	+	1.60904i
$967$	−16.5213	+	16.5213i	−0.531290	+	0.531290i	−0.920956	−	0.389666i	$-0.872590\pi$
$967$	−16.5213	+	16.5213i	−0.531290	+	0.531290i	0.389666	+	0.920956i	$0.372590\pi$
$968$	9.43159	−	28.2274i	0.303143	−	0.907264i
$969$	−25.2999	+	0.260371i	−0.812748	+	0.00836433i
$970$	12.3409	−	7.51560i	0.396243	−	0.241311i
$971$	21.4043	−	8.86594i	0.686896	−	0.284522i	−0.0118104	−	0.999930i	$-0.503759\pi$
$971$	21.4043	−	8.86594i	0.686896	−	0.284522i	0.698706	+	0.715409i	$0.253759\pi$
$972$	−22.7527	+	21.3146i	−0.729794	+	0.683667i
$973$	12.9078	−	6.00225i	0.413805	−	0.192423i
$974$	6.93369	−	9.48805i	0.222170	−	0.304017i
$975$	3.51532	+	3.44371i	0.112580	+	0.110287i
$976$	13.7426	+	60.1701i	0.439889	+	1.92600i
$977$	12.2739			0.392678			0.196339	−	0.980536i	$-0.437095\pi$
$977$	12.2739			0.392678			0.196339	+	0.980536i	$0.437095\pi$
$978$	7.44228	+	44.8048i	0.237978	+	1.43270i
$979$	48.8740	+	20.2443i	1.56202	+	0.647010i
$980$	−12.7214	−	12.6945i	−0.406369	−	0.405512i
$981$	−5.69873	−	12.9948i	−0.181947	−	0.414894i
$982$	−24.3869	−	40.0443i	−0.778217	−	1.27786i
$983$	9.50897	+	9.50897i	0.303289	+	0.303289i	0.842299	−	0.539010i	$-0.181202\pi$
$983$	9.50897	+	9.50897i	0.303289	+	0.303289i	−0.539010	+	0.842299i	$0.681202\pi$
$984$	1.15406	+	14.3009i	0.0367901	+	0.455896i
$985$	12.8653	+	12.8653i	0.409923	+	0.409923i
$986$	−9.01828	−	2.19153i	−0.287201	−	0.0697924i
$987$	−6.12249	−	12.8196i	−0.194881	−	0.408054i
$988$	11.5690	+	5.97565i	0.368060	+	0.190111i
$989$	−4.38212	+	10.5794i	−0.139343	+	0.336405i
$990$	−4.39641	−	24.8809i	−0.139727	−	0.790768i
$991$	61.1699			1.94313			0.971563	−	0.236782i	$-0.0760928\pi$
$991$	61.1699			1.94313			0.971563	+	0.236782i	$0.0760928\pi$
$992$	12.9859	+	13.3506i	0.412304	+	0.423881i
$993$	4.37603	+	4.28688i	0.138869	+	0.136040i
$994$	−8.06591	+	12.0853i	−0.255835	+	0.383322i
$995$	−11.7072	+	28.2637i	−0.371143	+	0.896019i
$996$	−38.8506	+	12.8278i	−1.23103	+	0.406465i
$997$	19.2385	−	7.96884i	0.609289	−	0.252376i	−0.0566357	−	0.998395i	$-0.518037\pi$
$997$	19.2385	−	7.96884i	0.609289	−	0.252376i	0.665924	+	0.746019i	$0.268037\pi$
$998$	4.26129	−	17.5355i	0.134889	−	0.555077i
$999$	−1.54473	−	50.0188i	−0.0488731	−	1.58253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.5	✓	496
3.2	odd	2	inner	672.2.bo.a.125.120	yes	496
7.6	odd	2	inner	672.2.bo.a.125.6	yes	496
21.20	even	2	inner	672.2.bo.a.125.119	yes	496
32.21	even	8	inner	672.2.bo.a.629.119	yes	496
96.53	odd	8	inner	672.2.bo.a.629.6	yes	496
224.181	odd	8	inner	672.2.bo.a.629.120	yes	496
672.629	even	8	inner	672.2.bo.a.629.5	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.5	✓	496	1.1	even	1	trivial
672.2.bo.a.125.6	yes	496	7.6	odd	2	inner
672.2.bo.a.125.119	yes	496	21.20	even	2	inner
672.2.bo.a.125.120	yes	496	3.2	odd	2	inner
672.2.bo.a.629.5	yes	496	672.629	even	8	inner
672.2.bo.a.629.6	yes	496	96.53	odd	8	inner
672.2.bo.a.629.119	yes	496	32.21	even	8	inner
672.2.bo.a.629.120	yes	496	224.181	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39741 + 0.217363i) q^{2} +(-0.679260 - 1.59330i) q^{3} +(1.90551 - 0.607491i) q^{4} +(0.491250 + 1.18598i) q^{5} +(1.29553 + 2.07885i) q^{6} +(0.112587 + 2.64335i) q^{7} +(-2.53073 + 1.26310i) q^{8} +(-2.07721 + 2.16453i) q^{9} +O(q^{10})\)	\(q+(-1.39741 + 0.217363i) q^{2} +(-0.679260 - 1.59330i) q^{3} +(1.90551 - 0.607491i) q^{4} +(0.491250 + 1.18598i) q^{5} +(1.29553 + 2.07885i) q^{6} +(0.112587 + 2.64335i) q^{7} +(-2.53073 + 1.26310i) q^{8} +(-2.07721 + 2.16453i) q^{9} +(-0.944266 - 1.55052i) q^{10} +(-1.77535 - 4.28607i) q^{11} +(-2.26225 - 2.62340i) q^{12} +(-0.783054 - 0.324352i) q^{13} +(-0.731898 - 3.66938i) q^{14} +(1.55594 - 1.58830i) q^{15} +(3.26191 - 2.31516i) q^{16} +1.90168i q^{17} +(2.43223 - 3.47624i) q^{18} +(-7.09674 - 2.93957i) q^{19} +(1.65655 + 1.96147i) q^{20} +(4.13518 - 1.97491i) q^{21} +(3.41252 + 5.60350i) q^{22} +(5.55180 - 5.55180i) q^{23} +(3.73152 + 3.17423i) q^{24} +(2.37031 - 2.37031i) q^{25} +(1.16475 + 0.283045i) q^{26} +(4.85971 + 1.83935i) q^{27} +(1.82035 + 4.96853i) q^{28} +(1.32060 - 3.18821i) q^{29} +(-1.82905 + 2.55771i) q^{30} -3.29238i q^{31} +(-4.05499 + 3.94424i) q^{32} +(-5.62307 + 5.74002i) q^{33} +(-0.413355 - 2.65742i) q^{34} +(-3.07966 + 1.43207i) q^{35} +(-2.64321 + 5.38641i) q^{36} +(-3.68551 - 8.89762i) q^{37} +(10.5560 + 2.56521i) q^{38} +(0.0151074 + 1.46796i) q^{39} +(-2.74123 - 2.38090i) q^{40} +(2.07087 + 2.07087i) q^{41} +(-5.34927 + 3.65859i) q^{42} +(-1.34745 + 0.558131i) q^{43} +(-5.98669 - 7.08863i) q^{44} +(-3.58752 - 1.40021i) q^{45} +(-6.55137 + 8.96489i) q^{46} -3.10014i q^{47} +(-5.90442 - 3.62461i) q^{48} +(-6.97465 + 0.595214i) q^{49} +(-2.79707 + 3.82751i) q^{50} +(3.02994 - 1.29173i) q^{51} +(-1.68916 - 0.142356i) q^{52} +(-2.74572 - 6.62876i) q^{53} +(-7.19081 - 1.51400i) q^{54} +(4.21106 - 4.21106i) q^{55} +(-3.62375 - 6.54740i) q^{56} +(0.136917 + 13.3040i) q^{57} +(-1.15242 + 4.74228i) q^{58} +(-3.16388 - 7.63828i) q^{59} +(1.99998 - 3.97173i) q^{60} +(-5.90476 + 14.2553i) q^{61} +(0.715642 + 4.60080i) q^{62} +(-5.95549 - 5.24711i) q^{63} +(4.80915 - 6.39312i) q^{64} -1.08803i q^{65} +(6.61007 - 9.24340i) q^{66} +(-0.559933 - 0.231932i) q^{67} +(1.15525 + 3.62366i) q^{68} +(-12.6168 - 5.07457i) q^{69} +(3.99227 - 2.67060i) q^{70} +(-2.74586 - 2.74586i) q^{71} +(2.52284 - 8.10156i) q^{72} +(6.19930 - 6.19930i) q^{73} +(7.08419 + 11.6325i) q^{74} +(-5.38667 - 2.16656i) q^{75} +(-15.3086 - 1.29016i) q^{76} +(11.1297 - 5.17543i) q^{77} +(-0.340192 - 2.04806i) q^{78} -7.15778i q^{79} +(4.34814 + 2.73125i) q^{80} +(-0.370373 - 8.99238i) q^{81} +(-3.34398 - 2.44372i) q^{82} +(4.51977 - 10.9117i) q^{83} +(6.67988 - 6.27529i) q^{84} +(-2.25535 + 0.934198i) q^{85} +(1.76162 - 1.07282i) q^{86} +(-5.97680 + 0.0615097i) q^{87} +(9.90666 + 8.60443i) q^{88} +(-8.06313 + 8.06313i) q^{89} +(5.31759 + 1.17687i) q^{90} +(0.769215 - 2.10641i) q^{91} +(7.20632 - 13.9516i) q^{92} +(-5.24575 + 2.23638i) q^{93} +(0.673856 + 4.33216i) q^{94} -9.86067i q^{95} +(9.03875 + 3.78166i) q^{96} +7.95920i q^{97} +(9.61706 - 2.34779i) q^{98} +(12.9651 + 5.06029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more