LMFDB - Embedded newform 336.2.u.a.139.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (of order $4$, degree $2$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.3
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27023 - 0.621708i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.22696 + 1.57942i) q^{4} +(1.90169 - 1.90169i) q^{5} +(1.33780 - 0.458573i) q^{6} +(2.22978 - 1.42411i) q^{7} +(-0.576579 - 2.76904i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.27023 - 0.621708i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.22696 + 1.57942i) q^{4} +(1.90169 - 1.90169i) q^{5} +(1.33780 - 0.458573i) q^{6} +(2.22978 - 1.42411i) q^{7} +(-0.576579 - 2.76904i) q^{8} -1.00000i q^{9} +(-3.59788 + 1.23329i) q^{10} +(-3.56463 + 3.56463i) q^{11} +(-1.98441 - 0.249229i) q^{12} +(1.66932 + 1.66932i) q^{13} +(-3.71771 + 0.422676i) q^{14} +2.68940i q^{15} +(-0.989144 + 3.87577i) q^{16} -7.15496i q^{17} +(-0.621708 + 1.27023i) q^{18} +(3.10260 - 3.10260i) q^{19} +(5.33687 + 0.670275i) q^{20} +(-0.569692 + 2.58369i) q^{21} +(6.74404 - 2.31173i) q^{22} +3.63389 q^{23} +(2.36571 + 1.55030i) q^{24} -2.23286i q^{25} +(-1.08259 - 3.15825i) q^{26} +(0.707107 + 0.707107i) q^{27} +(4.98512 + 1.77443i) q^{28} +(5.29845 - 5.29845i) q^{29} +(1.67202 - 3.41615i) q^{30} -0.906641 q^{31} +(3.66604 - 4.30815i) q^{32} -5.04114i q^{33} +(-4.44830 + 9.08843i) q^{34} +(1.53213 - 6.94857i) q^{35} +(1.57942 - 1.22696i) q^{36} +(2.51619 + 2.51619i) q^{37} +(-5.86992 + 2.01210i) q^{38} -2.36078 q^{39} +(-6.36233 - 4.16938i) q^{40} -2.37705 q^{41} +(2.32994 - 2.92769i) q^{42} +(-1.93434 + 1.93434i) q^{43} +(-10.0037 - 1.25640i) q^{44} +(-1.90169 - 1.90169i) q^{45} +(-4.61587 - 2.25922i) q^{46} -0.550905 q^{47} +(-2.04115 - 3.44001i) q^{48} +(2.94382 - 6.35090i) q^{49} +(-1.38819 + 2.83624i) q^{50} +(5.05932 + 5.05932i) q^{51} +(-0.588373 + 4.68475i) q^{52} +(3.05130 + 3.05130i) q^{53} +(-0.458573 - 1.33780i) q^{54} +13.5576i q^{55} +(-5.22906 - 5.35322i) q^{56} +4.38774i q^{57} +(-10.0243 + 3.43615i) q^{58} +(9.17593 + 9.17593i) q^{59} +(-4.24769 + 3.29978i) q^{60} +(-5.62319 - 5.62319i) q^{61} +(1.15164 + 0.563666i) q^{62} +(-1.42411 - 2.22978i) q^{63} +(-7.33511 + 3.19313i) q^{64} +6.34907 q^{65} +(-3.13412 + 6.40340i) q^{66} +(1.68616 + 1.68616i) q^{67} +(11.3007 - 8.77884i) q^{68} +(-2.56955 + 2.56955i) q^{69} +(-6.26613 + 7.87373i) q^{70} -11.6715 q^{71} +(-2.76904 + 0.576579i) q^{72} +8.41083 q^{73} +(-1.63180 - 4.76048i) q^{74} +(1.57887 + 1.57887i) q^{75} +(8.70707 + 1.09355i) q^{76} +(-2.87190 + 13.0247i) q^{77} +(2.99872 + 1.46771i) q^{78} -12.6448i q^{79} +(5.48947 + 9.25157i) q^{80} -1.00000 q^{81} +(3.01939 + 1.47783i) q^{82} +(-3.82605 + 3.82605i) q^{83} +(-4.77972 + 2.27030i) q^{84} +(-13.6065 - 13.6065i) q^{85} +(3.65964 - 1.25446i) q^{86} +7.49314i q^{87} +(11.9259 + 7.81529i) q^{88} -14.6937 q^{89} +(1.23329 + 3.59788i) q^{90} +(6.09951 + 1.34492i) q^{91} +(4.45864 + 5.73945i) q^{92} +(0.641092 - 0.641092i) q^{93} +(0.699775 + 0.342502i) q^{94} -11.8004i q^{95} +(0.454046 + 5.63860i) q^{96} +6.22825i q^{97} +(-7.68772 + 6.23690i) q^{98} +(3.56463 + 3.56463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.27023	−	0.621708i	−0.898187	−	0.439614i
$2$	−1.27023	−	0.621708i	−0.898187	−	0.439614i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.22696	+	1.57942i	0.613479	+	0.789711i
$5$	1.90169	−	1.90169i	0.850462	−	0.850462i	−0.139728	−	0.990190i	$-0.544623\pi$
$5$	1.90169	−	1.90169i	0.850462	−	0.850462i	0.990190	+	0.139728i	$0.0446227\pi$
$6$	1.33780	−	0.458573i	0.546155	−	0.187212i
$7$	2.22978	−	1.42411i	0.842777	−	0.538263i
$7$	2.22978	−	1.42411i	0.842777	−	0.538263i
$8$	−0.576579	−	2.76904i	−0.203851	−	0.979002i
$9$		−	1.00000i		−	0.333333i
$10$	−3.59788	+	1.23329i	−1.13775	+	0.389999i
$11$	−3.56463	+	3.56463i	−1.07477	+	1.07477i	−0.0778065	+	0.996968i	$0.524792\pi$
$11$	−3.56463	+	3.56463i	−1.07477	+	1.07477i	−0.996968	+	0.0778065i	$0.975208\pi$
$12$	−1.98441	−	0.249229i	−0.572850	−	0.0719461i
$13$	1.66932	+	1.66932i	0.462986	+	0.462986i	0.899633	−	0.436647i	$-0.143834\pi$
$13$	1.66932	+	1.66932i	0.462986	+	0.462986i	−0.436647	+	0.899633i	$0.643834\pi$
$14$	−3.71771	+	0.422676i	−0.993599	+	0.112965i
$15$			2.68940i			0.694400i
$16$	−0.989144	+	3.87577i	−0.247286	+	0.968943i
$17$		−	7.15496i		−	1.73533i	−0.497147	−	0.867667i	$-0.665619\pi$
$17$		−	7.15496i		−	1.73533i	0.497147	−	0.867667i	$-0.334381\pi$
$18$	−0.621708	+	1.27023i	−0.146538	+	0.299396i
$19$	3.10260	−	3.10260i	0.711785	−	0.711785i	−0.255123	−	0.966908i	$-0.582116\pi$
$19$	3.10260	−	3.10260i	0.711785	−	0.711785i	0.966908	+	0.255123i	$0.0821161\pi$
$20$	5.33687	+	0.670275i	1.19336	+	0.149878i
$21$	−0.569692	+	2.58369i	−0.124317	+	0.563807i
$22$	6.74404	−	2.31173i	1.43783	−	0.492863i
$23$	3.63389			0.757719			0.378860	−	0.925454i	$-0.376316\pi$
$23$	3.63389			0.757719			0.378860	+	0.925454i	$0.376316\pi$
$24$	2.36571	+	1.55030i	0.482898	+	0.316454i
$25$		−	2.23286i		−	0.446572i
$26$	−1.08259	−	3.15825i	−0.212313	−	0.619383i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	4.98512	+	1.77443i	0.942098	+	0.335336i
$29$	5.29845	−	5.29845i	0.983898	−	0.983898i	−0.0159747	−	0.999872i	$-0.505085\pi$
$29$	5.29845	−	5.29845i	0.983898	−	0.983898i	0.999872	+	0.0159747i	$0.00508512\pi$
$30$	1.67202	−	3.41615i	0.305268	−	0.623701i
$31$	−0.906641			−0.162838			−0.0814188	−	0.996680i	$-0.525945\pi$
$31$	−0.906641			−0.162838			−0.0814188	+	0.996680i	$0.525945\pi$
$32$	3.66604	−	4.30815i	0.648070	−	0.761581i
$33$		−	5.04114i		−	0.877550i
$34$	−4.44830	+	9.08843i	−0.762876	+	1.55865i
$35$	1.53213	−	6.94857i	0.258977	−	1.17452i
$36$	1.57942	−	1.22696i	0.263237	−	0.204493i
$37$	2.51619	+	2.51619i	0.413660	+	0.413660i	0.883011	−	0.469352i	$-0.155512\pi$
$37$	2.51619	+	2.51619i	0.413660	+	0.413660i	−0.469352	+	0.883011i	$0.655512\pi$
$38$	−5.86992	+	2.01210i	−0.952226	+	0.326405i
$39$	−2.36078			−0.378027
$40$	−6.36233	−	4.16938i	−1.00597	−	0.659236i
$41$	−2.37705			−0.371232			−0.185616	−	0.982622i	$-0.559428\pi$
$41$	−2.37705			−0.371232			−0.185616	+	0.982622i	$0.559428\pi$
$42$	2.32994	−	2.92769i	0.359517	−	0.451753i
$43$	−1.93434	+	1.93434i	−0.294984	+	0.294984i	−0.839045	−	0.544062i	$-0.816886\pi$
$43$	−1.93434	+	1.93434i	−0.294984	+	0.294984i	0.544062	+	0.839045i	$0.316886\pi$
$44$	−10.0037	−	1.25640i	−1.50811	−	0.189409i
$45$	−1.90169	−	1.90169i	−0.283487	−	0.283487i
$46$	−4.61587	−	2.25922i	−0.680573	−	0.333104i
$47$	−0.550905			−0.0803577			−0.0401789	−	0.999193i	$-0.512793\pi$
$47$	−0.550905			−0.0803577			−0.0401789	+	0.999193i	$0.512793\pi$
$48$	−2.04115	−	3.44001i	−0.294615	−	0.496523i
$49$	2.94382	−	6.35090i	0.420545	−	0.907272i
$50$	−1.38819	+	2.83624i	−0.196319	+	0.401106i
$51$	5.05932	+	5.05932i	0.708447	+	0.708447i
$52$	−0.588373	+	4.68475i	−0.0815927	+	0.649658i
$53$	3.05130	+	3.05130i	0.419128	+	0.419128i	0.884903	−	0.465775i	$-0.154224\pi$
$53$	3.05130	+	3.05130i	0.419128	+	0.419128i	−0.465775	+	0.884903i	$0.654224\pi$
$54$	−0.458573	−	1.33780i	−0.0624039	−	0.182052i
$55$			13.5576i			1.82811i
$56$	−5.22906	−	5.35322i	−0.698762	−	0.715354i
$57$			4.38774i			0.581170i
$58$	−10.0243	+	3.43615i	−1.31626	+	0.451189i
$59$	9.17593	+	9.17593i	1.19460	+	1.19460i	0.975760	+	0.218845i	$0.0702289\pi$
$59$	9.17593	+	9.17593i	1.19460	+	1.19460i	0.218845	+	0.975760i	$0.429771\pi$
$60$	−4.24769	+	3.29978i	−0.548375	+	0.426000i
$61$	−5.62319	−	5.62319i	−0.719976	−	0.719976i	0.248624	−	0.968600i	$-0.420022\pi$
$61$	−5.62319	−	5.62319i	−0.719976	−	0.719976i	−0.968600	+	0.248624i	$0.920022\pi$
$62$	1.15164	+	0.563666i	0.146259	+	0.0715856i
$63$	−1.42411	−	2.22978i	−0.179421	−	0.280926i
$64$	−7.33511	+	3.19313i	−0.916889	+	0.399142i
$65$	6.34907			0.787505
$66$	−3.13412	+	6.40340i	−0.385783	+	0.788204i
$67$	1.68616	+	1.68616i	0.205997	+	0.205997i	0.802564	−	0.596567i	$-0.203469\pi$
$67$	1.68616	+	1.68616i	0.205997	+	0.205997i	−0.596567	+	0.802564i	$0.703469\pi$
$68$	11.3007	−	8.77884i	1.37041	−	1.06459i
$69$	−2.56955	+	2.56955i	−0.309338	+	0.309338i
$70$	−6.26613	+	7.87373i	−0.748946	+	0.941091i
$71$	−11.6715			−1.38515			−0.692577	−	0.721344i	$-0.743525\pi$
$71$	−11.6715			−1.38515			−0.692577	+	0.721344i	$0.743525\pi$
$72$	−2.76904	+	0.576579i	−0.326334	+	0.0679505i
$73$	8.41083			0.984414			0.492207	−	0.870478i	$-0.336190\pi$
$73$	8.41083			0.984414			0.492207	+	0.870478i	$0.336190\pi$
$74$	−1.63180	−	4.76048i	−0.189693	−	0.553394i
$75$	1.57887	+	1.57887i	0.182312	+	0.182312i
$76$	8.70707	+	1.09355i	0.998770	+	0.125439i
$77$	−2.87190	+	13.0247i	−0.327283	+	1.48431i
$78$	2.99872	+	1.46771i	0.339539	+	0.166186i
$79$		−	12.6448i		−	1.42265i	−0.702862	−	0.711327i	$-0.748095\pi$
$79$		−	12.6448i		−	1.42265i	0.702862	−	0.711327i	$-0.251905\pi$
$80$	5.48947	+	9.25157i	0.613742	+	1.03436i
$81$	−1.00000			−0.111111
$82$	3.01939	+	1.47783i	0.333436	+	0.163199i
$83$	−3.82605	+	3.82605i	−0.419964	+	0.419964i	−0.885191	−	0.465227i	$-0.845973\pi$
$83$	−3.82605	+	3.82605i	−0.419964	+	0.419964i	0.465227	+	0.885191i	$0.345973\pi$
$84$	−4.77972	+	2.27030i	−0.521511	+	0.247710i
$85$	−13.6065	−	13.6065i	−1.47584	−	1.47584i
$86$	3.65964	−	1.25446i	0.394629	−	0.135272i
$87$			7.49314i			0.803349i
$88$	11.9259	+	7.81529i	1.27130	+	0.833112i
$89$	−14.6937			−1.55753			−0.778765	−	0.627315i	$-0.784154\pi$
$89$	−14.6937			−1.55753			−0.778765	+	0.627315i	$0.784154\pi$
$90$	1.23329	+	3.59788i	0.130000	+	0.379250i
$91$	6.09951	+	1.34492i	0.639403	+	0.140986i
$92$	4.45864	+	5.73945i	0.464845	+	0.598379i
$93$	0.641092	−	0.641092i	0.0664782	−	0.0664782i
$94$	0.699775	+	0.342502i	0.0721762	+	0.0353264i
$95$		−	11.8004i		−	1.21069i
$96$	0.454046	+	5.63860i	0.0463409	+	0.575487i
$97$			6.22825i			0.632383i	0.948695	+	0.316191i	$0.102404\pi$
$97$			6.22825i			0.632383i	−0.948695	+	0.316191i	$0.897596\pi$
$98$	−7.68772	+	6.23690i	−0.776577	+	0.630022i
$99$	3.56463	+	3.56463i	0.358258	+	0.358258i
$100$	3.52663	−	2.73963i	0.352663	−	0.273963i
$101$	−13.7348	+	13.7348i	−1.36666	+	1.36666i	−0.501512	+	0.865150i	$0.667223\pi$
$101$	−13.7348	+	13.7348i	−1.36666	+	1.36666i	−0.865150	+	0.501512i	$0.832777\pi$
$102$	−3.28107	−	9.57191i	−0.324875	−	0.947761i
$103$			2.12589i			0.209471i	0.994500	+	0.104735i	$0.0333995\pi$
$103$			2.12589i			0.209471i	−0.994500	+	0.104735i	$0.966600\pi$
$104$	3.65991	−	5.58490i	0.358884	−	0.547645i
$105$	3.83000	+	5.99676i	0.373770	+	0.585224i
$106$	−1.97883	−	5.77286i	−0.192201	−	0.560710i
$107$	−9.07831	+	9.07831i	−0.877634	+	0.877634i	−0.993289	−	0.115656i	$-0.963103\pi$
$107$	−9.07831	+	9.07831i	−0.877634	+	0.877634i	0.115656	+	0.993289i	$0.463103\pi$
$108$	−0.249229	+	1.98441i	−0.0239820	+	0.190950i
$109$	−7.77089	+	7.77089i	−0.744316	+	0.744316i	−0.973405	−	0.229090i	$-0.926425\pi$
$109$	−7.77089	+	7.77089i	−0.744316	+	0.744316i	0.229090	+	0.973405i	$0.426425\pi$
$110$	8.42889	−	17.2213i	0.803663	−	1.64199i
$111$	−3.55843			−0.337752
$112$	3.31395	+	10.0508i	0.313139	+	0.949707i
$113$	7.32742			0.689306			0.344653	−	0.938730i	$-0.387997\pi$
$113$	7.32742			0.689306			0.344653	+	0.938730i	$0.387997\pi$
$114$	2.72789	−	5.57343i	0.255490	−	0.521999i
$115$	6.91054	−	6.91054i	0.644412	−	0.644412i
$116$	14.8695	+	1.86751i	1.38060	+	0.173394i
$117$	1.66932	−	1.66932i	0.154329	−	0.154329i
$118$	−5.95078	−	17.3603i	−0.547814	−	1.59814i
$119$	−10.1895	−	15.9540i	−0.934066	−	1.46250i
$120$	7.44704	−	1.55065i	0.679818	−	0.141554i
$121$		−	14.4131i		−	1.31028i
$122$	3.64675	+	10.6387i	0.330161	+	0.963184i
$123$	1.68083	−	1.68083i	0.151555	−	0.151555i
$124$	−1.11241	−	1.43197i	−0.0998975	−	0.128595i
$125$	5.26224	+	5.26224i	0.470669	+	0.470669i
$126$	0.422676	+	3.71771i	0.0376549	+	0.331200i
$127$			14.6589i			1.30076i	0.759608	+	0.650382i	$0.225391\pi$
$127$			14.6589i			1.30076i	−0.759608	+	0.650382i	$0.774609\pi$
$128$	11.3025	+	0.504288i	0.999006	+	0.0445732i
$129$		−	2.73556i		−	0.240853i
$130$	−8.06476	−	3.94726i	−0.707326	−	0.346198i
$131$	−5.52527	+	5.52527i	−0.482745	+	0.482745i	−0.906007	−	0.423262i	$-0.860885\pi$
$131$	−5.52527	+	5.52527i	−0.482745	+	0.482745i	0.423262	+	0.906007i	$0.360885\pi$
$132$	7.96209	−	6.18527i	0.693011	−	0.538359i
$133$	2.49966	−	11.3365i	0.216748	−	0.983004i
$134$	−1.09351	−	3.19010i	−0.0944646	−	0.275583i
$135$	2.68940			0.231467
$136$	−19.8123	+	4.12540i	−1.69889	+	0.353750i
$137$		−	3.43937i		−	0.293845i	−0.989148	−	0.146923i	$-0.953063\pi$
$137$		−	3.43937i		−	0.293845i	0.989148	−	0.146923i	$-0.0469368\pi$
$138$	4.86143	−	1.66641i	0.413832	−	0.141854i
$139$	−5.21179	−	5.21179i	−0.442058	−	0.442058i	0.450645	−	0.892703i	$-0.351194\pi$
$139$	−5.21179	−	5.21179i	−0.442058	−	0.442058i	−0.892703	+	0.450645i	$0.851194\pi$
$140$	12.8546	−	6.10573i	1.08641	−	0.516028i
$141$	0.389548	−	0.389548i	0.0328059	−	0.0328059i
$142$	14.8255	+	7.25628i	1.24413	+	0.608933i
$143$	−11.9010			−0.995212
$144$	3.87577	+	0.989144i	0.322981	+	0.0824287i
$145$		−	20.1520i		−	1.67354i
$146$	−10.6837	−	5.22908i	−0.884187	−	0.432762i
$147$	2.40917	+	6.57236i	0.198705	+	0.542079i
$148$	−0.886864	+	7.06139i	−0.0728998	+	0.580443i
$149$	8.38511	+	8.38511i	0.686935	+	0.686935i	0.961553	−	0.274618i	$-0.0885514\pi$
$149$	8.38511	+	8.38511i	0.686935	+	0.686935i	−0.274618	+	0.961553i	$0.588551\pi$
$150$	−1.02393	−	2.98712i	−0.0836036	−	0.243898i
$151$	3.21093			0.261302			0.130651	−	0.991428i	$-0.458293\pi$
$151$	3.21093			0.261302			0.130651	+	0.991428i	$0.458293\pi$
$152$	−10.3801	−	6.80231i	−0.841937	−	0.551740i
$153$	−7.15496			−0.578444
$154$	11.7456	−	14.7589i	0.946484	−	1.18931i
$155$	−1.72415	+	1.72415i	−0.138487	+	0.138487i
$156$	−2.89657	−	3.72866i	−0.231912	−	0.298532i
$157$	0.574508	+	0.574508i	0.0458508	+	0.0458508i	0.729660	−	0.683810i	$-0.239678\pi$
$157$	0.574508	+	0.574508i	0.0458508	+	0.0458508i	−0.683810	+	0.729660i	$0.739678\pi$
$158$	−7.86138	+	16.0618i	−0.625418	+	1.27781i
$159$	−4.31519			−0.342217
$160$	−1.22111	−	15.1644i	−0.0965373	−	1.19885i
$161$	8.10277	−	5.17507i	0.638588	−	0.407852i
$162$	1.27023	+	0.621708i	0.0997985	+	0.0488460i
$163$	−13.8383	−	13.8383i	−1.08390	−	1.08390i	−0.996142	−	0.0877597i	$-0.972029\pi$
$163$	−13.8383	−	13.8383i	−1.08390	−	1.08390i	−0.0877597	−	0.996142i	$-0.527971\pi$
$164$	−2.91654	−	3.75436i	−0.227743	−	0.293166i
$165$	−9.58670	−	9.58670i	−0.746323	−	0.746323i
$166$	7.23865	−	2.48127i	0.561828	−	0.192584i
$167$		−	9.71401i		−	0.751692i	−0.926682	−	0.375846i	$-0.877352\pi$
$167$		−	9.71401i		−	0.751692i	0.926682	−	0.375846i	$-0.122648\pi$
$168$	7.48280	+	0.0877976i	0.577311	+	0.00677373i
$169$		−	7.42674i		−	0.571287i
$170$	8.82411	+	25.7427i	0.676778	+	1.97437i
$171$	−3.10260	−	3.10260i	−0.237262	−	0.237262i
$172$	−5.42848	−	0.681781i	−0.413918	−	0.0519853i
$173$	3.57505	+	3.57505i	0.271806	+	0.271806i	0.829827	−	0.558021i	$-0.188439\pi$
$173$	3.57505	+	3.57505i	0.271806	+	0.271806i	−0.558021	+	0.829827i	$0.688439\pi$
$174$	4.65854	−	9.51800i	0.353163	−	0.721558i
$175$	−3.17984	−	4.97879i	−0.240374	−	0.376361i
$176$	−10.2897	−	17.3416i	−0.775618	−	1.30717i
$177$	−12.9767			−0.975391
$178$	18.6644	+	9.13520i	1.39895	+	0.684712i
$179$	12.0824	+	12.0824i	0.903078	+	0.903078i	0.995701	−	0.0926229i	$-0.0295251\pi$
$179$	12.0824	+	12.0824i	0.903078	+	0.903078i	−0.0926229	+	0.995701i	$0.529525\pi$
$180$	0.670275	−	5.33687i	0.0499594	−	0.397787i
$181$	−14.7072	+	14.7072i	−1.09318	+	1.09318i	−0.0979893	+	0.995187i	$0.531241\pi$
$181$	−14.7072	+	14.7072i	−1.09318	+	1.09318i	−0.995187	+	0.0979893i	$0.968759\pi$
$182$	−6.91163	−	5.50046i	−0.512324	−	0.407722i
$183$	7.95239			0.587858
$184$	−2.09523	−	10.0624i	−0.154462	−	0.741808i
$185$	9.57005			0.703604
$186$	−1.21291	+	0.415761i	−0.0889345	+	0.0304851i
$187$	25.5048	+	25.5048i	1.86509	+	1.86509i
$188$	−0.675937	−	0.870111i	−0.0492978	−	0.0634593i
$189$	2.58369	+	0.569692i	0.187936	+	0.0414390i
$190$	−7.33638	+	14.9892i	−0.532237	+	1.08743i
$191$			4.83855i			0.350105i	0.984559	+	0.175052i	$0.0560095\pi$
$191$			4.83855i			0.350105i	−0.984559	+	0.175052i	$0.943991\pi$
$192$	2.92882	−	7.44460i	0.211369	−	0.537267i
$193$	23.3996			1.68434			0.842169	−	0.539213i	$-0.181278\pi$
$193$	23.3996			1.68434			0.842169	+	0.539213i	$0.181278\pi$
$194$	3.87215	−	7.91129i	0.278004	−	0.567998i
$195$	−4.48947	+	4.48947i	−0.321497	+	0.321497i
$196$	13.6427	−	3.14277i	0.974478	−	0.224483i
$197$	5.84458	+	5.84458i	0.416409	+	0.416409i	0.883964	−	0.467555i	$-0.154865\pi$
$197$	5.84458	+	5.84458i	0.416409	+	0.416409i	−0.467555	+	0.883964i	$0.654865\pi$
$198$	−2.31173	−	6.74404i	−0.164288	−	0.479278i
$199$			4.28359i			0.303655i	0.988407	+	0.151828i	$0.0485159\pi$
$199$			4.28359i			0.303655i	−0.988407	+	0.151828i	$0.951484\pi$
$200$	−6.18287	+	1.28742i	−0.437195	+	0.0910344i
$201$	−2.38459			−0.168196
$202$	25.9853	−	8.90729i	1.82832	−	0.626715i
$203$	4.26879	−	19.3600i	0.299610	−	1.35880i
$204$	−1.78322	+	14.1984i	−0.124851	+	0.994086i
$205$	−4.52041	+	4.52041i	−0.315719	+	0.315719i
$206$	1.32168	−	2.70037i	0.0920861	−	0.188144i
$207$		−	3.63389i		−	0.252573i
$208$	−8.12110	+	4.81870i	−0.563097	+	0.334117i
$209$			22.1192i			1.53002i
$210$	−1.13674	−	9.99839i	−0.0784427	−	0.689955i
$211$	−5.34715	−	5.34715i	−0.368113	−	0.368113i	0.498676	−	0.866789i	$-0.333820\pi$
$211$	−5.34715	−	5.34715i	−0.368113	−	0.368113i	−0.866789	+	0.498676i	$0.833820\pi$
$212$	−1.07547	+	8.56311i	−0.0738635	+	0.588117i
$213$	8.25301	−	8.25301i	0.565487	−	0.565487i
$214$	17.1756	−	5.88747i	1.17410	−	0.402459i
$215$			7.35702i			0.501745i
$216$	1.55030	−	2.36571i	0.105485	−	0.160966i
$217$	−2.02161	+	1.29116i	−0.137236	+	0.0876495i
$218$	14.7020	−	5.03958i	0.995746	−	0.341323i
$219$	−5.94736	+	5.94736i	−0.401885	+	0.401885i
$220$	−21.4132	+	16.6347i	−1.44368	+	1.12151i
$221$	11.9439	−	11.9439i	0.803435	−	0.803435i
$222$	4.52002	+	2.21231i	0.303364	+	0.148480i
$223$	−28.4331			−1.90402			−0.952009	−	0.306070i	$-0.900986\pi$
$223$	−28.4331			−1.90402			−0.952009	+	0.306070i	$0.900986\pi$
$224$	2.03916	−	14.8271i	0.136247	−	0.990675i
$225$	−2.23286			−0.148857
$226$	−9.30750	−	4.55552i	−0.619126	−	0.303028i
$227$	19.1228	−	19.1228i	1.26923	−	1.26923i	0.322739	−	0.946488i	$-0.395396\pi$
$227$	19.1228	−	19.1228i	1.26923	−	1.26923i	0.946488	−	0.322739i	$-0.104604\pi$
$228$	−6.93009	+	5.38357i	−0.458956	+	0.356536i
$229$	2.11755	−	2.11755i	0.139932	−	0.139932i	−0.633671	−	0.773603i	$-0.718453\pi$
$229$	2.11755	−	2.11755i	0.139932	−	0.139932i	0.773603	+	0.633671i	$0.218453\pi$
$230$	−13.0743	+	4.48163i	−0.862094	+	0.295510i
$231$	−7.17914	−	11.2406i	−0.472353	−	0.739579i
$232$	−17.7266	−	11.6166i	−1.16381	−	0.762669i
$233$			23.1104i			1.51401i	0.653408	+	0.757006i	$0.273339\pi$
$233$			23.1104i			1.51401i	−0.653408	+	0.757006i	$0.726661\pi$
$234$	−3.15825	+	1.08259i	−0.206461	+	0.0707710i
$235$	−1.04765	+	1.04765i	−0.0683412	+	0.0683412i
$236$	−3.23417	+	25.7512i	−0.210527	+	1.67626i
$237$	8.94124	+	8.94124i	0.580796	+	0.580796i
$238$	3.02423	+	26.6001i	0.196032	+	1.72423i
$239$		−	9.94538i		−	0.643313i	−0.946856	−	0.321657i	$-0.895760\pi$
$239$		−	9.94538i		−	0.643313i	0.946856	−	0.321657i	$-0.104240\pi$
$240$	−10.4235	−	2.66020i	−0.672833	−	0.171715i
$241$			11.4287i			0.736187i	0.929789	+	0.368093i	$0.119989\pi$
$241$			11.4287i			0.736187i	−0.929789	+	0.368093i	$0.880011\pi$
$242$	−8.96074	+	18.3079i	−0.576018	+	1.17688i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	1.98196	−	15.7808i	0.126882	−	1.01026i
$245$	−6.47922	−	17.6757i	−0.413942	−	1.12926i
$246$	−3.18001	+	1.09005i	−0.202750	+	0.0694990i
$247$	10.3585			0.659093
$248$	0.522750	+	2.51052i	0.0331947	+	0.159418i
$249$		−	5.41086i		−	0.342899i
$250$	−3.41267	−	9.95583i	−0.215836	−	0.629662i
$251$	−11.4020	−	11.4020i	−0.719687	−	0.719687i	0.248854	−	0.968541i	$-0.419946\pi$
$251$	−11.4020	−	11.4020i	−0.719687	−	0.719687i	−0.968541	+	0.248854i	$0.919946\pi$
$252$	1.77443	−	4.98512i	0.111779	−	0.314033i
$253$	−12.9535	+	12.9535i	−0.814378	+	0.814378i
$254$	9.11352	−	18.6201i	0.571833	−	1.16833i
$255$	19.2425			1.20501
$256$	−14.0432	−	7.66739i	−0.877699	−	0.479212i
$257$			8.41347i			0.524818i	0.964957	+	0.262409i	$0.0845169\pi$
$257$			8.41347i			0.524818i	−0.964957	+	0.262409i	$0.915483\pi$
$258$	−1.70072	+	3.47479i	−0.105882	+	0.216331i
$259$	9.19389	+	2.02721i	0.571280	+	0.125965i
$260$	7.79004	+	10.0279i	0.483118	+	0.621901i
$261$	−5.29845	−	5.29845i	−0.327966	−	0.327966i
$262$	10.4535	−	3.58325i	0.645817	−	0.221374i
$263$	−6.67247			−0.411442			−0.205721	−	0.978611i	$-0.565954\pi$
$263$	−6.67247			−0.411442			−0.205721	+	0.978611i	$0.565954\pi$
$264$	−13.9591	+	2.90662i	−0.859123	+	0.178890i
$265$	11.6053			0.712906
$266$	−10.2232	+	12.8459i	−0.626822	+	0.787635i
$267$	10.3900	−	10.3900i	0.635859	−	0.635859i
$268$	−0.594307	+	4.73200i	−0.0363031	+	0.289053i
$269$	1.02225	+	1.02225i	0.0623274	+	0.0623274i	0.737583	−	0.675256i	$-0.235967\pi$
$269$	1.02225	+	1.02225i	0.0623274	+	0.0623274i	−0.675256	+	0.737583i	$0.735967\pi$
$270$	−3.41615	−	1.67202i	−0.207900	−	0.101756i
$271$	−5.47375			−0.332507			−0.166253	−	0.986083i	$-0.553167\pi$
$271$	−5.47375			−0.332507			−0.166253	+	0.986083i	$0.553167\pi$
$272$	27.7310	+	7.07729i	1.68144	+	0.429124i
$273$	−5.26401	+	3.36201i	−0.318592	+	0.203478i
$274$	−2.13828	+	4.36878i	−0.129178	+	0.263928i
$275$	7.95932	+	7.95932i	0.479965	+	0.479965i
$276$	−7.21114	−	0.905671i	−0.434059	−	0.0545150i
$277$	9.91118	+	9.91118i	0.595505	+	0.595505i	0.939113	−	0.343608i	$-0.111649\pi$
$277$	9.91118	+	9.91118i	0.595505	+	0.595505i	−0.343608	+	0.939113i	$0.611649\pi$
$278$	3.37995	+	9.86038i	0.202716	+	0.591386i
$279$			0.906641i			0.0542792i
$280$	−20.1242	−	0.236123i	−1.20265	−	0.0141110i
$281$			19.6432i			1.17182i	0.810378	+	0.585908i	$0.199262\pi$
$281$			19.6432i			1.17182i	−0.810378	+	0.585908i	$0.800738\pi$
$282$	−0.737001	+	0.252630i	−0.0438877	+	0.0150439i
$283$	−20.3051	−	20.3051i	−1.20701	−	1.20701i	−0.971990	−	0.235022i	$-0.924484\pi$
$283$	−20.3051	−	20.3051i	−1.20701	−	1.20701i	−0.235022	−	0.971990i	$-0.575516\pi$
$284$	−14.3205	−	18.4343i	−0.849764	−	1.09387i
$285$	8.34412	+	8.34412i	0.494263	+	0.494263i
$286$	15.1170	+	7.39895i	0.893886	+	0.437509i
$287$	−5.30028	+	3.38518i	−0.312866	+	0.199821i
$288$	−4.30815	−	3.66604i	−0.253860	−	0.216023i
$289$	−34.1935			−2.01138
$290$	−12.5287	+	25.5977i	−0.735710	+	1.50315i
$291$	−4.40404	−	4.40404i	−0.258169	−	0.258169i
$292$	10.3197	+	13.2842i	0.603917	+	0.777402i
$293$	−11.7526	+	11.7526i	−0.686597	+	0.686597i	−0.961478	−	0.274881i	$-0.911361\pi$
$293$	−11.7526	+	11.7526i	−0.686597	+	0.686597i	0.274881	+	0.961478i	$0.411361\pi$
$294$	1.02589	−	9.84619i	0.0598310	−	0.574242i
$295$	34.8996			2.03193
$296$	5.51664	−	8.41821i	0.320648	−	0.489299i
$297$	−5.04114			−0.292517
$298$	−5.43792	−	15.8641i	−0.315010	−	0.918983i
$299$	6.06613	+	6.06613i	0.350814	+	0.350814i
$300$	−0.556493	+	4.43092i	−0.0321292	+	0.255819i
$301$	−1.55843	+	7.06785i	−0.0898264	+	0.407384i
$302$	−4.07861	−	1.99626i	−0.234698	−	0.114872i
$303$		−	19.4239i		−	1.11588i
$304$	8.95604	+	15.0939i	0.513664	+	0.865693i
$305$	−21.3871			−1.22462
$306$	9.08843	+	4.44830i	0.519551	+	0.254292i
$307$	19.0195	−	19.0195i	1.08550	−	1.08550i	0.0895163	−	0.995985i	$-0.471468\pi$
$307$	19.0195	−	19.0195i	1.08550	−	1.08550i	0.995985	−	0.0895163i	$-0.0285321\pi$
$308$	−24.0953	+	11.4449i	−1.37295	+	0.652133i
$309$	−1.50323	−	1.50323i	−0.0855160	−	0.0855160i
$310$	3.26199	−	1.11815i	0.185268	−	0.0635065i
$311$			13.7113i			0.777499i	0.921344	+	0.388749i	$0.127093\pi$
$311$			13.7113i			0.777499i	−0.921344	+	0.388749i	$0.872907\pi$
$312$	1.36117	+	6.53707i	0.0770613	+	0.370089i
$313$	−4.84337			−0.273764			−0.136882	−	0.990587i	$-0.543708\pi$
$313$	−4.84337			−0.273764			−0.136882	+	0.990587i	$0.543708\pi$
$314$	−0.372580	−	1.08693i	−0.0210259	−	0.0613392i
$315$	−6.94857	−	1.53213i	−0.391508	−	0.0863257i
$316$	19.9715	−	15.5147i	1.12348	−	0.872768i
$317$	−2.72533	+	2.72533i	−0.153070	+	0.153070i	−0.779488	−	0.626418i	$-0.784520\pi$
$317$	−2.72533	+	2.72533i	−0.153070	+	0.153070i	0.626418	+	0.779488i	$0.284520\pi$
$318$	5.48128	+	2.68279i	0.307375	+	0.150443i
$319$			37.7740i			2.11494i
$320$	−7.87677	+	20.0215i	−0.440325	+	1.11923i
$321$		−	12.8387i		−	0.716585i
$322$	−13.5098	+	1.53596i	−0.752869	+	0.0855956i
$323$	−22.1990	−	22.1990i	−1.23518	−	1.23518i
$324$	−1.22696	−	1.57942i	−0.0681644	−	0.0877456i
$325$	3.72736	−	3.72736i	0.206757	−	0.206757i
$326$	8.97444	+	26.1812i	0.497048	+	1.45004i
$327$		−	10.9897i		−	0.607731i
$328$	1.37055	+	6.58212i	0.0756762	+	0.363437i
$329$	−1.22839	+	0.784549i	−0.0677236	+	0.0432536i
$330$	6.21717	+	18.1374i	0.342244	+	0.998432i
$331$	6.93803	−	6.93803i	0.381349	−	0.381349i	−0.490239	−	0.871588i	$-0.663091\pi$
$331$	6.93803	−	6.93803i	0.381349	−	0.381349i	0.871588	+	0.490239i	$0.163091\pi$
$332$	−10.7374	−	1.34854i	−0.589289	−	0.0740108i
$333$	2.51619	−	2.51619i	0.137887	−	0.137887i
$334$	−6.03927	+	12.3390i	−0.330454	+	0.675160i
$335$	6.41310			0.350385
$336$	−9.45028	−	4.76364i	−0.515555	−	0.259878i
$337$	2.95698			0.161077			0.0805384	−	0.996752i	$-0.474336\pi$
$337$	2.95698			0.161077			0.0805384	+	0.996752i	$0.474336\pi$
$338$	−4.61726	+	9.43365i	−0.251146	+	0.513123i
$339$	−5.18127	+	5.18127i	−0.281408	+	0.281408i
$340$	4.79579	−	38.1851i	0.260088	−	2.07088i
$341$	3.23184	−	3.23184i	0.175014	−	0.175014i
$342$	2.01210	+	5.86992i	0.108802	+	0.317409i
$343$	−2.48033	−	18.3534i	−0.133925	−	0.990991i
$344$	6.47154	+	4.24095i	0.348922	+	0.228657i
$345$			9.77299i			0.526160i
$346$	−2.31849	−	6.76376i	−0.124643	−	0.363622i
$347$	−3.16858	+	3.16858i	−0.170098	+	0.170098i	−0.787023	−	0.616924i	$-0.788378\pi$
$347$	−3.16858	+	3.16858i	−0.170098	+	0.170098i	0.616924	+	0.787023i	$0.288378\pi$
$348$	−11.8348	+	9.19378i	−0.634413	+	0.492838i
$349$	11.0951	+	11.0951i	0.593908	+	0.593908i	0.938685	−	0.344777i	$-0.112045\pi$
$349$	11.0951	+	11.0951i	0.593908	+	0.593908i	−0.344777	+	0.938685i	$0.612045\pi$
$350$	0.943776	+	8.30113i	0.0504470	+	0.443714i
$351$			2.36078i			0.126009i
$352$	2.28891	+	28.4250i	0.121999	+	1.51506i
$353$		−	30.8984i		−	1.64455i	−0.569087	−	0.822277i	$-0.692703\pi$
$353$		−	30.8984i		−	1.64455i	0.569087	−	0.822277i	$-0.307297\pi$
$354$	16.4834	+	8.06773i	0.876083	+	0.428795i
$355$	−22.1956	+	22.1956i	−1.17802	+	1.17802i
$356$	−18.0286	−	23.2076i	−0.955513	−	1.23000i
$357$	18.4862	+	4.07613i	0.978393	+	0.215732i
$358$	−7.83566	−	22.8591i	−0.414127	−	1.20814i
$359$	0.943215			0.0497810			0.0248905	−	0.999690i	$-0.492076\pi$
$359$	0.943215			0.0497810			0.0248905	+	0.999690i	$0.492076\pi$
$360$	−4.16938	+	6.36233i	−0.219745	+	0.335324i
$361$		−	0.252238i		−	0.0132757i
$362$	27.8251	−	9.53791i	1.46245	−	0.501301i
$363$	10.1916	+	10.1916i	0.534921	+	0.534921i
$364$	5.35966	+	11.2839i	0.280923	+	0.591435i
$365$	15.9948	−	15.9948i	0.837207	−	0.837207i
$366$	−10.1014	−	4.94406i	−0.528006	−	0.258430i
$367$	3.56906			0.186304			0.0931518	−	0.995652i	$-0.470306\pi$
$367$	3.56906			0.186304			0.0931518	+	0.995652i	$0.470306\pi$
$368$	−3.59444	+	14.0841i	−0.187373	+	0.734186i
$369$			2.37705i			0.123744i
$370$	−12.1561	−	5.94977i	−0.631968	−	0.309314i
$371$	11.1491	+	2.45833i	0.578833	+	0.127630i
$372$	1.79915	+	0.225961i	0.0932815	+	0.0117155i
$373$	−0.693026	−	0.693026i	−0.0358835	−	0.0358835i	0.688937	−	0.724821i	$-0.258077\pi$
$373$	−0.693026	−	0.693026i	−0.0358835	−	0.0358835i	−0.724821	+	0.688937i	$0.758077\pi$
$374$	−16.5404	−	48.2534i	−0.855281	−	2.49512i
$375$	−7.44194			−0.384300
$376$	0.317640	+	1.52547i	0.0163810	+	0.0786703i
$377$	17.6896			0.911062
$378$	−2.92769	−	2.32994i	−0.150584	−	0.119839i
$379$	6.55229	−	6.55229i	0.336569	−	0.336569i	−0.518506	−	0.855074i	$-0.673511\pi$
$379$	6.55229	−	6.55229i	0.336569	−	0.336569i	0.855074	+	0.518506i	$0.173511\pi$
$380$	18.6378	−	14.4786i	0.956097	−	0.742735i
$381$	−10.3654	−	10.3654i	−0.531034	−	0.531034i
$382$	3.00816	−	6.14606i	0.153911	−	0.314460i
$383$	25.4405			1.29995			0.649975	−	0.759956i	$-0.274779\pi$
$383$	25.4405			1.29995			0.649975	+	0.759956i	$0.274779\pi$
$384$	−8.34863	+	7.63546i	−0.426039	+	0.389646i
$385$	19.3076	+	30.2305i	0.984005	+	1.54069i
$386$	−29.7228	−	14.5477i	−1.51285	−	0.740459i
$387$	1.93434	+	1.93434i	0.0983278	+	0.0983278i
$388$	−9.83703	+	7.64180i	−0.499399	+	0.387954i
$389$	−11.6405	−	11.6405i	−0.590199	−	0.590199i	0.347486	−	0.937685i	$-0.387035\pi$
$389$	−11.6405	−	11.6405i	−0.590199	−	0.590199i	−0.937685	+	0.347486i	$0.887035\pi$
$390$	8.49379	−	2.91151i	0.430100	−	0.147430i
$391$		−	26.0004i		−	1.31490i
$392$	−19.2832	−	4.48974i	−0.973949	−	0.226766i
$393$		−	7.81392i		−	0.394160i
$394$	−3.79033	−	11.0576i	−0.190954	−	0.557072i
$395$	−24.0465	−	24.0465i	−1.20991	−	1.20991i
$396$	−1.25640	+	10.0037i	−0.0631363	+	0.502705i
$397$	−18.3501	−	18.3501i	−0.920963	−	0.920963i	0.0761349	−	0.997098i	$-0.475742\pi$
$397$	−18.3501	−	18.3501i	−0.920963	−	0.920963i	−0.997098	+	0.0761349i	$0.975742\pi$
$398$	2.66314	−	5.44113i	0.133491	−	0.272739i
$399$	6.24862	+	9.78368i	0.312822	+	0.489797i
$400$	8.65406	+	2.20862i	0.432703	+	0.110431i
$401$	22.2529			1.11126			0.555630	−	0.831430i	$-0.312477\pi$
$401$	22.2529			1.11126			0.555630	+	0.831430i	$0.312477\pi$
$402$	3.02897	+	1.48252i	0.151071	+	0.0739412i
$403$	−1.51347	−	1.51347i	−0.0753916	−	0.0753916i
$404$	−38.5450	−	4.84100i	−1.91769	−	0.240849i
$405$	−1.90169	+	1.90169i	−0.0944958	+	0.0944958i
$406$	−17.4586	+	21.9376i	−0.866454	+	1.08875i
$407$	−17.9386			−0.889182
$408$	11.0923	−	16.9265i	0.549153	−	0.837989i
$409$	27.1395			1.34196			0.670981	−	0.741475i	$-0.265873\pi$
$409$	27.1395			1.34196			0.670981	+	0.741475i	$0.265873\pi$
$410$	8.55232	−	2.93158i	0.422369	−	0.144780i
$411$	2.43200	+	2.43200i	0.119962	+	0.119962i
$412$	−3.35768	+	2.60838i	−0.165421	+	0.128506i
$413$	33.5278	+	7.39274i	1.64980	+	0.363773i
$414$	−2.25922	+	4.61587i	−0.111035	+	0.226858i
$415$			14.5519i			0.714327i
$416$	13.3115	−	1.07190i	0.652649	−	0.0525543i
$417$	7.37059			0.360939
$418$	13.7517	−	28.0964i	0.672617	−	1.37424i
$419$	−14.0335	+	14.0335i	−0.685582	+	0.685582i	−0.961252	−	0.275670i	$-0.911100\pi$
$419$	−14.0335	+	14.0335i	−0.685582	+	0.685582i	0.275670	+	0.961252i	$0.411100\pi$
$420$	−4.77216	+	13.4070i	−0.232857	+	0.654193i
$421$	18.7350	+	18.7350i	0.913087	+	0.913087i	0.996514	−	0.0834270i	$-0.0265866\pi$
$421$	18.7350	+	18.7350i	0.913087	+	0.913087i	−0.0834270	+	0.996514i	$0.526587\pi$
$422$	3.46774	+	10.1165i	0.168807	+	0.492462i
$423$			0.550905i			0.0267859i
$424$	6.68984	−	10.2085i	0.324887	−	0.495767i
$425$	−15.9760			−0.774952
$426$	−15.6142	+	5.35225i	−0.756509	+	0.259317i
$427$	−20.5465	−	4.53042i	−0.994315	−	0.219242i
$428$	−25.4772	−	3.19977i	−1.23149	−	0.154667i
$429$	8.41528	−	8.41528i	0.406294	−	0.406294i
$430$	4.57392	−	9.34510i	0.220574	−	0.450661i
$431$		−	24.5106i		−	1.18063i	−0.807172	−	0.590317i	$-0.799003\pi$
$431$		−	24.5106i		−	1.18063i	0.807172	−	0.590317i	$-0.200997\pi$
$432$	−3.44001	+	2.04115i	−0.165508	+	0.0982050i
$433$			10.3532i			0.497542i	0.968562	+	0.248771i	$0.0800267\pi$
$433$			10.3532i			0.497542i	−0.968562	+	0.248771i	$0.919973\pi$
$434$	3.37063	−	0.383215i	0.161795	−	0.0183949i
$435$	14.2496	+	14.2496i	0.683218	+	0.683218i
$436$	−21.8081	−	2.73895i	−1.04442	−	0.131172i
$437$	11.2745	−	11.2745i	0.539333	−	0.539333i
$438$	11.2520	−	3.85698i	0.537642	−	0.184294i
$439$			21.8589i			1.04327i	0.853170	+	0.521634i	$0.174677\pi$
$439$			21.8589i			1.04327i	−0.853170	+	0.521634i	$0.825323\pi$
$440$	37.5416	−	7.81705i	1.78972	−	0.372663i
$441$	−6.35090	−	2.94382i	−0.302424	−	0.140182i
$442$	−22.5971	+	7.74588i	−1.07484	+	0.368434i
$443$	8.82244	−	8.82244i	0.419167	−	0.419167i	−0.465750	−	0.884916i	$-0.654215\pi$
$443$	8.82244	−	8.82244i	0.419167	−	0.419167i	0.884916	+	0.465750i	$0.154215\pi$
$444$	−4.36605	−	5.62027i	−0.207204	−	0.266726i
$445$	−27.9429	+	27.9429i	−1.32462	+	1.32462i
$446$	36.1165	+	17.6771i	1.71016	+	0.837033i
$447$	−11.8583			−0.560880
$448$	−11.8083	+	17.5660i	−0.557889	+	0.829915i
$449$	−15.3552			−0.724657			−0.362329	−	0.932050i	$-0.618018\pi$
$449$	−15.3552			−0.724657			−0.362329	+	0.932050i	$0.618018\pi$
$450$	2.83624	+	1.38819i	0.133702	+	0.0654398i
$451$	8.47328	−	8.47328i	0.398991	−	0.398991i
$452$	8.99045	+	11.5731i	0.422875	+	0.544352i
$453$	−2.27047	+	2.27047i	−0.106676	+	0.106676i
$454$	−36.1792	+	12.4015i	−1.69797	+	0.582033i
$455$	14.1570	−	9.04177i	0.663691	−	0.423885i
$456$	12.1498	−	2.52988i	0.568966	−	0.118472i
$457$		−	34.0509i		−	1.59283i	−0.604748	−	0.796417i	$-0.706726\pi$
$457$		−	34.0509i		−	1.59283i	0.604748	−	0.796417i	$-0.293274\pi$
$458$	−4.00627	+	1.37327i	−0.187201	+	0.0641689i
$459$	5.05932	−	5.05932i	0.236149	−	0.236149i
$460$	19.3936	+	2.43571i	0.904232	+	0.113566i
$461$	−17.5033	−	17.5033i	−0.815210	−	0.815210i	0.170200	−	0.985410i	$-0.445559\pi$
$461$	−17.5033	−	17.5033i	−0.815210	−	0.815210i	−0.985410	+	0.170200i	$0.945559\pi$
$462$	2.13077	+	18.7415i	0.0991323	+	0.871933i
$463$			0.0530223i			0.00246416i	0.999999	+	0.00123208i	$0.000392183\pi$
$463$			0.0530223i			0.00246416i	−0.999999	+	0.00123208i	$0.999608\pi$
$464$	15.2946	+	25.7765i	0.710036	+	1.19664i
$465$		−	2.43832i		−	0.113074i
$466$	14.3679	−	29.3555i	0.665581	−	1.35987i
$467$	−8.39635	+	8.39635i	−0.388537	+	0.388537i	−0.874165	−	0.485629i	$-0.838591\pi$
$467$	−8.39635	+	8.39635i	−0.388537	+	0.388537i	0.485629	+	0.874165i	$0.338591\pi$
$468$	4.68475	+	0.588373i	0.216553	+	0.0271976i
$469$	6.16103	+	1.35848i	0.284490	+	0.0627288i
$470$	1.98209	−	0.679423i	0.0914269	−	0.0313394i
$471$	−0.812478			−0.0374370
$472$	20.1178	−	30.6991i	0.925998	−	1.41304i
$473$		−	13.7904i		−	0.634082i
$474$	−5.79857	−	16.9162i	−0.266337	−	0.776989i
$475$	−6.92768	−	6.92768i	−0.317864	−	0.317864i
$476$	12.6960	−	35.6683i	0.581920	−	1.63485i
$477$	3.05130	−	3.05130i	0.139709	−	0.139709i
$478$	−6.18312	+	12.6329i	−0.282809	+	0.577816i
$479$	36.9533			1.68844			0.844220	−	0.535997i	$-0.180064\pi$
$479$	36.9533			1.68844			0.844220	+	0.535997i	$0.180064\pi$
$480$	11.5863	+	9.85943i	0.528842	+	0.450019i
$481$			8.40067i			0.383037i
$482$	7.10531	−	14.5170i	0.323638	−	0.661233i
$483$	−2.07020	+	9.38885i	−0.0941974	+	0.427208i
$484$	22.7644	−	17.6843i	1.03474	−	0.803831i
$485$	11.8442	+	11.8442i	0.537818	+	0.537818i
$486$	−1.33780	+	0.458573i	−0.0606839	+	0.0208013i
$487$	14.6233			0.662647			0.331324	−	0.943517i	$-0.392505\pi$
$487$	14.6233			0.662647			0.331324	+	0.943517i	$0.392505\pi$
$488$	−12.3286	+	18.8130i	−0.558089	+	0.851626i
$489$	19.5703			0.885002
$490$	−2.75902	+	26.4803i	−0.124640	+	1.19626i
$491$	6.45924	−	6.45924i	0.291502	−	0.291502i	−0.546172	−	0.837673i	$-0.683915\pi$
$491$	6.45924	−	6.45924i	0.291502	−	0.291502i	0.837673	+	0.546172i	$0.183915\pi$
$492$	4.71703	+	0.592428i	0.212660	+	0.0267087i
$493$	−37.9102	−	37.9102i	−1.70739	−	1.70739i
$494$	−13.1576	−	6.43994i	−0.591989	−	0.289747i
$495$	13.5576			0.609370
$496$	0.896799	−	3.51393i	0.0402675	−	0.157780i
$497$	−26.0249	+	16.6215i	−1.16738	+	0.745578i
$498$	−3.36397	+	6.87302i	−0.150743	+	0.307987i
$499$	0.0937570	+	0.0937570i	0.00419714	+	0.00419714i	0.709202	−	0.705005i	$-0.249055\pi$
$499$	0.0937570	+	0.0937570i	0.00419714	+	0.00419714i	−0.705005	+	0.709202i	$0.749055\pi$
$500$	−1.85474	+	14.7679i	−0.0829467	+	0.660439i
$501$	6.86884	+	6.86884i	0.306877	+	0.306877i
$502$	7.39442	+	21.5718i	0.330029	+	0.962798i
$503$			8.91797i			0.397633i	0.980037	+	0.198816i	$0.0637097\pi$
$503$			8.91797i			0.397633i	−0.980037	+	0.198816i	$0.936290\pi$
$504$	−5.35322	+	5.22906i	−0.238451	+	0.232921i
$505$			52.2387i			2.32459i
$506$	24.5071	−	8.40059i	1.08947	−	0.373452i
$507$	5.25150	+	5.25150i	0.233227	+	0.233227i
$508$	−23.1525	+	17.9858i	−1.02723	+	0.797991i
$509$	−8.24799	−	8.24799i	−0.365586	−	0.365586i	0.500279	−	0.865864i	$-0.333231\pi$
$509$	−8.24799	−	8.24799i	−0.365586	−	0.365586i	−0.865864	+	0.500279i	$0.833231\pi$
$510$	−24.4424	−	11.9632i	−1.08233	−	0.529741i
$511$	18.7543	−	11.9780i	0.829641	−	0.529874i
$512$	13.0712	+	18.4701i	0.577670	+	0.816271i
$513$	4.38774			0.193723
$514$	5.23072	−	10.6870i	0.230717	−	0.471384i
$515$	4.04279	+	4.04279i	0.178147	+	0.178147i
$516$	4.32061	−	3.35643i	0.190204	−	0.147758i
$517$	1.96377	−	1.96377i	0.0863664	−	0.0863664i
$518$	−10.4180	−	8.29093i	−0.457741	−	0.364283i
$519$	−5.05588			−0.221929
$520$	−3.66074	−	17.5808i	−0.160534	−	0.770969i
$521$	22.1437			0.970135			0.485068	−	0.874477i	$-0.338795\pi$
$521$	22.1437			0.970135			0.485068	+	0.874477i	$0.338795\pi$
$522$	3.43615	+	10.0243i	0.150396	+	0.438753i
$523$	1.49811	+	1.49811i	0.0655079	+	0.0655079i	0.739102	−	0.673594i	$-0.235250\pi$
$523$	1.49811	+	1.49811i	0.0655079	+	0.0655079i	−0.673594	+	0.739102i	$0.735250\pi$
$524$	−15.5060	−	1.94745i	−0.677383	−	0.0850748i
$525$	5.76902	+	1.27204i	0.251781	+	0.0555166i
$526$	8.47555	+	4.14832i	0.369552	+	0.180876i
$527$			6.48698i			0.282577i
$528$	19.5383	+	4.98642i	0.850296	+	0.217006i
$529$	−9.79482			−0.425862
$530$	−14.7413	−	7.21508i	−0.640322	−	0.313403i
$531$	9.17593	−	9.17593i	0.398202	−	0.398202i
$532$	20.9722	−	9.96146i	0.909259	−	0.431884i
$533$	−3.96805	−	3.96805i	−0.171875	−	0.171875i
$534$	−19.6573	+	6.73814i	−0.850653	+	0.291588i
$535$			34.5283i			1.49279i
$536$	3.69683	−	5.64123i	0.159679	−	0.243664i
$537$	−17.0870			−0.737360
$538$	−0.662947	−	1.93402i	−0.0285817	−	0.0833817i
$539$	12.1450	+	33.1322i	0.523121	+	1.42710i
$540$	3.29978	+	4.24769i	0.142000	+	0.182792i
$541$	3.10477	−	3.10477i	0.133485	−	0.133485i	−0.637208	−	0.770692i	$-0.719911\pi$
$541$	3.10477	−	3.10477i	0.133485	−	0.133485i	0.770692	+	0.637208i	$0.219911\pi$
$542$	6.95292	+	3.40308i	0.298653	+	0.146175i
$543$		−	20.7991i		−	0.892575i
$544$	−30.8247	−	26.2303i	−1.32160	−	1.12462i
$545$			29.5557i			1.26603i
$546$	8.77667	−	0.997842i	0.375607	−	0.0427037i
$547$	−1.79963	−	1.79963i	−0.0769465	−	0.0769465i	0.667586	−	0.744533i	$-0.267328\pi$
$547$	−1.79963	−	1.79963i	−0.0769465	−	0.0769465i	−0.744533	+	0.667586i	$0.767328\pi$
$548$	5.43221	−	4.21996i	0.232053	−	0.180268i
$549$	−5.62319	+	5.62319i	−0.239992	+	0.239992i
$550$	−5.16178	−	15.0585i	−0.220099	−	0.642097i
$551$		−	32.8779i		−	1.40065i
$552$	8.59673	+	5.63363i	0.365901	+	0.239783i
$553$	−18.0076	−	28.1951i	−0.765762	−	1.19898i
$554$	−6.42760	−	18.7513i	−0.273083	−	0.796667i
$555$	−6.76704	+	6.76704i	−0.287245	+	0.287245i
$556$	1.83696	−	14.6263i	0.0779045	−	0.620292i
$557$	−11.8995	+	11.8995i	−0.504196	+	0.504196i	−0.912739	−	0.408543i	$-0.866037\pi$
$557$	−11.8995	+	11.8995i	−0.504196	+	0.504196i	0.408543	+	0.912739i	$0.366037\pi$
$558$	0.563666	−	1.15164i	0.0238619	−	0.0487529i
$559$	−6.45806			−0.273147
$560$	25.4156	+	12.8113i	1.07400	+	0.541377i
$561$	−36.0692			−1.52284
$562$	12.2123	−	24.9514i	0.515146	−	1.05251i
$563$	−0.635961	+	0.635961i	−0.0268026	+	0.0268026i	−0.720381	−	0.693578i	$-0.756033\pi$
$563$	−0.635961	+	0.635961i	−0.0268026	+	0.0268026i	0.693578	+	0.720381i	$0.256033\pi$
$564$	1.09322	+	0.137301i	0.0460329	+	0.00578143i
$565$	13.9345	−	13.9345i	0.586229	−	0.586229i
$566$	13.1683	+	38.4159i	0.553503	+	1.61474i
$567$	−2.22978	+	1.42411i	−0.0936419	+	0.0598070i
$568$	6.72955	+	32.3189i	0.282366	+	1.35607i
$569$		−	0.425156i		−	0.0178235i	−0.999960	−	0.00891174i	$-0.997163\pi$
$569$		−	0.425156i		−	0.0178235i	0.999960	−	0.00891174i	$-0.00283673\pi$
$570$	−5.41133	−	15.7865i	−0.226656	−	0.661226i
$571$	−20.0961	+	20.0961i	−0.840997	+	0.840997i	−0.988989	−	0.147992i	$-0.952719\pi$
$571$	−20.0961	+	20.0961i	−0.840997	+	0.840997i	0.147992	+	0.988989i	$0.452719\pi$
$572$	−14.6020	−	18.7967i	−0.610542	−	0.785930i
$573$	−3.42137	−	3.42137i	−0.142930	−	0.142930i
$574$	8.83716	−	1.00472i	0.368856	−	0.0419362i
$575$		−	8.11398i		−	0.338376i
$576$	3.19313	+	7.33511i	0.133047	+	0.305630i
$577$			10.2508i			0.426748i	0.976971	+	0.213374i	$0.0684453\pi$
$577$			10.2508i			0.426748i	−0.976971	+	0.213374i	$0.931555\pi$
$578$	43.4335	+	21.2584i	1.80660	+	0.884231i
$579$	−16.5460	+	16.5460i	−0.687628	+	0.687628i
$580$	31.8286	−	24.7257i	1.32161	−	1.02668i
$581$	−3.08252	+	13.9800i	−0.127885	+	0.579987i
$582$	2.85611	+	8.33215i	0.118389	+	0.345379i
$583$	−21.7535			−0.900937
$584$	−4.84951	−	23.2899i	−0.200674	−	0.963743i
$585$		−	6.34907i		−	0.262502i
$586$	22.2353	−	7.62183i	0.918530	−	0.314855i
$587$	−19.3706	−	19.3706i	−0.799510	−	0.799510i	0.183508	−	0.983018i	$-0.441255\pi$
$587$	−19.3706	−	19.3706i	−0.799510	−	0.799510i	−0.983018	+	0.183508i	$0.941255\pi$
$588$	−7.42457	+	11.8691i	−0.306184	+	0.489474i
$589$	−2.81294	+	2.81294i	−0.115905	+	0.115905i
$590$	−44.3304	−	21.6973i	−1.82506	−	0.893266i
$591$	−8.26548			−0.339997
$592$	−12.2411	+	7.26331i	−0.503105	+	0.298520i
$593$		−	33.1941i		−	1.36312i	−0.731764	−	0.681559i	$-0.761302\pi$
$593$		−	33.1941i		−	1.36312i	0.731764	−	0.681559i	$-0.238698\pi$
$594$	6.40340	+	3.13412i	0.262735	+	0.128594i
$595$	−49.7167	−	10.9623i	−2.03819	−	0.449412i
$596$	−2.95544	+	23.5318i	−0.121060	+	0.963901i
$597$	−3.02895	−	3.02895i	−0.123967	−	0.123967i
$598$	−3.93401	−	11.4767i	−0.160874	−	0.469319i
$599$	−1.68554			−0.0688694			−0.0344347	−	0.999407i	$-0.510963\pi$
$599$	−1.68554			−0.0688694			−0.0344347	+	0.999407i	$0.510963\pi$
$600$	3.46161	−	5.28230i	0.141320	−	0.215649i
$601$	2.90830			0.118632			0.0593160	−	0.998239i	$-0.481108\pi$
$601$	2.90830			0.118632			0.0593160	+	0.998239i	$0.481108\pi$
$602$	6.37370	−	8.00889i	0.259773	−	0.326418i
$603$	1.68616	−	1.68616i	0.0686656	−	0.0686656i
$604$	3.93968	+	5.07141i	0.160303	+	0.206353i
$605$	−27.4093	−	27.4093i	−1.11435	−	1.11435i
$606$	−12.0760	+	24.6728i	−0.490554	+	1.00226i
$607$	21.5383			0.874213			0.437106	−	0.899410i	$-0.356003\pi$
$607$	21.5383			0.874213			0.437106	+	0.899410i	$0.356003\pi$
$608$	−1.99224	−	24.7407i	−0.0807958	−	1.00337i
$609$	10.6711	+	16.7080i	0.432413	+	0.677044i
$610$	27.1666	+	13.2966i	1.09994	+	0.538362i
$611$	−0.919637	−	0.919637i	−0.0372045	−	0.0372045i
$612$	−8.77884	−	11.3007i	−0.354864	−	0.456804i
$613$	19.8687	+	19.8687i	0.802488	+	0.802488i	0.983484	−	0.180996i	$-0.0579321\pi$
$613$	19.8687	+	19.8687i	0.802488	+	0.802488i	−0.180996	+	0.983484i	$0.557932\pi$
$614$	−35.9837	+	12.3345i	−1.45218	+	0.497782i
$615$		−	6.39282i		−	0.257783i
$616$	37.7219	+	0.442600i	1.51986	+	0.0178329i
$617$		−	31.7899i		−	1.27981i	−0.768453	−	0.639906i	$-0.778973\pi$
$617$		−	31.7899i		−	1.27981i	0.768453	−	0.639906i	$-0.221027\pi$
$618$	0.974878	+	2.84402i	0.0392153	+	0.114403i
$619$	−14.2152	−	14.2152i	−0.571358	−	0.571358i	0.361150	−	0.932508i	$-0.382384\pi$
$619$	−14.2152	−	14.2152i	−0.571358	−	0.571358i	−0.932508	+	0.361150i	$0.882384\pi$
$620$	−4.83863	−	0.607699i	−0.194324	−	0.0244058i
$621$	2.56955	+	2.56955i	0.103113	+	0.103113i
$622$	8.52445	−	17.4165i	0.341799	−	0.698339i
$623$	−32.7637	+	20.9255i	−1.31265	+	0.838362i
$624$	2.33515	−	9.14983i	0.0934807	−	0.366286i
$625$	31.1786			1.24715
$626$	6.15219	+	3.01116i	0.245891	+	0.120350i
$627$	−15.6406	−	15.6406i	−0.624627	−	0.624627i
$628$	−0.202493	+	1.61229i	−0.00808034	+	0.0643373i
$629$	18.0033	−	18.0033i	0.717837	−	0.717837i
$630$	7.87373	+	6.26613i	0.313697	+	0.249649i
$631$	7.63145			0.303803			0.151902	−	0.988396i	$-0.451460\pi$
$631$	7.63145			0.303803			0.151902	+	0.988396i	$0.451460\pi$
$632$	−35.0139	+	7.29074i	−1.39278	+	0.290010i
$633$	7.56202			0.300563
$634$	5.15616	−	1.76743i	0.204777	−	0.0701938i
$635$	27.8766	+	27.8766i	1.10625	+	1.10625i
$636$	−5.29456	−	6.81550i	−0.209943	−	0.270252i
$637$	15.5159	−	5.68752i	0.614761	−	0.225348i
$638$	23.4844	−	47.9816i	0.929756	−	1.89961i
$639$			11.6715i			0.461718i
$640$	22.4528	−	20.5348i	0.887525	−	0.811709i
$641$	−24.3462			−0.961616			−0.480808	−	0.876826i	$-0.659657\pi$
$641$	−24.3462			−0.961616			−0.480808	+	0.876826i	$0.659657\pi$
$642$	−7.98190	+	16.3080i	−0.315021	+	0.643627i
$643$	−21.6002	+	21.6002i	−0.851829	+	0.851829i	−0.990358	−	0.138529i	$-0.955763\pi$
$643$	−21.6002	+	21.6002i	−0.851829	+	0.851829i	0.138529	+	0.990358i	$0.455763\pi$
$644$	18.1154	+	6.44810i	0.713846	+	0.254091i
$645$	−5.20220	−	5.20220i	−0.204836	−	0.204836i
$646$	14.3965	+	41.9990i	0.566422	+	1.65243i
$647$			34.5047i			1.35652i	0.734823	+	0.678259i	$0.237265\pi$
$647$			34.5047i			1.35652i	−0.734823	+	0.678259i	$0.762735\pi$
$648$	0.576579	+	2.76904i	0.0226502	+	0.108778i
$649$	−65.4175			−2.56786
$650$	−7.05193	+	2.41727i	−0.276600	+	0.0948132i
$651$	0.516507	−	2.34248i	0.0202435	−	0.0918090i
$652$	4.87749	−	38.8356i	0.191017	−	1.52092i
$653$	10.7862	−	10.7862i	0.422097	−	0.422097i	−0.463828	−	0.885925i	$-0.653525\pi$
$653$	10.7862	−	10.7862i	0.422097	−	0.422097i	0.885925	+	0.463828i	$0.153525\pi$
$654$	−6.83238	+	13.9594i	−0.267167	+	0.545856i
$655$			21.0147i			0.821113i
$656$	2.35124	−	9.21288i	0.0918005	−	0.359703i
$657$		−	8.41083i		−	0.328138i
$658$	2.04810	−	0.232854i	0.0798433	−	0.00907759i
$659$	−14.5491	−	14.5491i	−0.566754	−	0.566754i	0.364464	−	0.931217i	$-0.381252\pi$
$659$	−14.5491	−	14.5491i	−0.566754	−	0.566754i	−0.931217	+	0.364464i	$0.881252\pi$
$660$	3.37895	−	26.9039i	0.131526	−	1.04723i
$661$	−25.2625	+	25.2625i	−0.982596	+	0.982596i	−0.999851	−	0.0172555i	$-0.994507\pi$
$661$	−25.2625	+	25.2625i	−0.982596	+	0.982596i	0.0172555	+	0.999851i	$0.494507\pi$
$662$	−13.1263	+	4.49946i	−0.510169	+	0.174876i
$663$			16.8913i			0.656002i
$664$	12.8005	+	8.38845i	0.496756	+	0.325535i
$665$	−16.8050	−	26.3122i	−0.651671	−	1.02034i
$666$	−4.76048	+	1.63180i	−0.184465	+	0.0632310i
$667$	19.2540	−	19.2540i	0.745518	−	0.745518i
$668$	15.3425	−	11.9187i	0.593620	−	0.461148i
$669$	20.1052	−	20.1052i	0.777312	−	0.777312i
$670$	−8.14610	−	3.98708i	−0.314711	−	0.154034i
$671$	40.0891			1.54762
$672$	9.04242	+	11.9262i	0.348819	+	0.460064i
$673$	10.5919			0.408287			0.204144	−	0.978941i	$-0.434559\pi$
$673$	10.5919			0.408287			0.204144	+	0.978941i	$0.434559\pi$
$674$	−3.75603	−	1.83838i	−0.144677	−	0.0708116i
$675$	1.57887	−	1.57887i	0.0607708	−	0.0607708i
$676$	11.7299	−	9.11230i	0.451152	−	0.350473i
$677$	27.0595	−	27.0595i	1.03998	−	1.03998i	0.0408138	−	0.999167i	$-0.487005\pi$
$677$	27.0595	−	27.0595i	1.03998	−	1.03998i	0.999167	−	0.0408138i	$-0.0129951\pi$
$678$	9.80263	−	3.36016i	0.376468	−	0.129046i
$679$	8.86971	+	13.8876i	0.340388	+	0.532957i
$680$	−29.8317	+	45.5222i	−1.14399	+	1.74570i
$681$			27.0438i			1.03632i
$682$	−6.11443	+	2.09591i	−0.234133	+	0.0802566i
$683$	28.1993	−	28.1993i	1.07901	−	1.07901i	0.0824168	−	0.996598i	$-0.473736\pi$
$683$	28.1993	−	28.1993i	1.07901	−	1.07901i	0.996598	−	0.0824168i	$-0.0262639\pi$
$684$	1.09355	−	8.70707i	0.0418129	−	0.332923i
$685$	−6.54062	−	6.54062i	−0.249904	−	0.249904i
$686$	−8.25988	+	24.8551i	−0.315364	+	0.948971i
$687$			2.99467i			0.114254i
$688$	−5.58371	−	9.41038i	−0.212877	−	0.358767i
$689$			10.1872i			0.388101i
$690$	6.07594	−	12.4139i	0.231307	−	0.472590i
$691$	2.94281	−	2.94281i	0.111950	−	0.111950i	−0.648913	−	0.760863i	$-0.724776\pi$
$691$	2.94281	−	2.94281i	0.111950	−	0.111950i	0.760863	+	0.648913i	$0.224776\pi$
$692$	−1.26007	+	10.0329i	−0.0479007	+	0.381395i
$693$	13.0247	+	2.87190i	0.494769	+	0.109094i
$694$	5.99475	−	2.05489i	0.227558	−	0.0780025i
$695$	−19.8224			−0.751908
$696$	20.7488	−	4.32039i	0.786480	−	0.163764i
$697$			17.0077i			0.644211i
$698$	−7.19541	−	20.9913i	−0.272350	−	0.794531i
$699$	−16.3415	−	16.3415i	−0.618093	−	0.618093i
$700$	3.96206	−	11.1311i	0.149752	−	0.420715i
$701$	14.0610	−	14.0610i	0.531077	−	0.531077i	−0.389816	−	0.920893i	$-0.627461\pi$
$701$	14.0610	−	14.0610i	0.531077	−	0.531077i	0.920893	+	0.389816i	$0.127461\pi$
$702$	1.46771	−	2.99872i	0.0553953	−	0.113180i
$703$	15.6135			0.588873
$704$	14.7646	−	37.5293i	0.556462	−	1.41444i
$705$		−	1.48160i		−	0.0558004i
$706$	−19.2098	+	39.2480i	−0.722969	+	1.47712i
$707$	−11.0657	+	50.1854i	−0.416167	+	1.88742i
$708$	−15.9219	−	20.4957i	−0.598382	−	0.770276i
$709$	−17.0650	−	17.0650i	−0.640890	−	0.640890i	0.309884	−	0.950774i	$-0.399710\pi$
$709$	−17.0650	−	17.0650i	−0.640890	−	0.640890i	−0.950774	+	0.309884i	$0.899710\pi$
$710$	41.9927	−	14.3943i	1.57596	−	0.540209i
$711$	−12.6448			−0.474218
$712$	8.47209	+	40.6874i	0.317505	+	1.52483i
$713$	−3.29464			−0.123385
$714$	−20.9475	−	16.6706i	−0.783942	−	0.623882i
$715$	−22.6320	+	22.6320i	−0.846390	+	0.846390i
$716$	−4.25858	+	33.9077i	−0.159151	+	1.26719i
$717$	7.03245	+	7.03245i	0.262632	+	0.262632i
$718$	−1.19810	−	0.586404i	−0.0447126	−	0.0218844i
$719$	4.08011			0.152162			0.0760812	−	0.997102i	$-0.475759\pi$
$719$	4.08011			0.152162			0.0760812	+	0.997102i	$0.475759\pi$
$720$	9.25157	−	5.48947i	0.344786	−	0.204581i
$721$	3.02751	+	4.74027i	0.112750	+	0.176537i
$722$	−0.156819	+	0.320400i	−0.00583618	+	0.0119241i
$723$	−8.08131	−	8.08131i	−0.300547	−	0.300547i
$724$	−41.2740	−	5.18373i	−1.53393	−	0.192652i
$725$	−11.8307	−	11.8307i	−0.439382	−	0.439382i
$726$	−6.60946	−	19.2819i	−0.245300	−	0.715617i
$727$			29.7494i			1.10334i	0.834061	+	0.551672i	$0.186010\pi$
$727$			29.7494i			1.10334i	−0.834061	+	0.551672i	$0.813990\pi$
$728$	0.207271	−	17.6652i	0.00768196	−	0.654716i
$729$			1.00000i			0.0370370i
$730$	−30.2612	+	10.3730i	−1.12002	+	0.383920i
$731$	13.8401	+	13.8401i	0.511895	+	0.511895i
$732$	9.75726	+	12.5602i	0.360639	+	0.464238i
$733$	12.3461	+	12.3461i	0.456014	+	0.456014i	0.897345	−	0.441330i	$-0.145493\pi$
$733$	12.3461	+	12.3461i	0.456014	+	0.456014i	−0.441330	+	0.897345i	$0.645493\pi$
$734$	−4.53352	−	2.21891i	−0.167335	−	0.0819016i
$735$	17.0801	+	7.91709i	0.630009	+	0.292026i
$736$	13.3220	−	15.6554i	0.491055	−	0.577065i
$737$	−12.0210			−0.442801
$738$	1.47783	−	3.01939i	0.0543996	−	0.111145i
$739$	−12.7621	−	12.7621i	−0.469462	−	0.469462i	0.432278	−	0.901740i	$-0.357710\pi$
$739$	−12.7621	−	12.7621i	−0.469462	−	0.469462i	−0.901740	+	0.432278i	$0.857710\pi$
$740$	11.7421	+	15.1151i	0.431646	+	0.555643i
$741$	−7.32454	+	7.32454i	−0.269074	+	0.269074i
$742$	−12.6335	−	10.0541i	−0.463792	−	0.369099i
$743$	−14.3254			−0.525547			−0.262774	−	0.964858i	$-0.584637\pi$
$743$	−14.3254			−0.525547			−0.262774	+	0.964858i	$0.584637\pi$
$744$	−2.14485	−	1.40557i	−0.0786339	−	0.0515306i
$745$	31.8918			1.16843
$746$	0.449441	+	1.31116i	0.0164552	+	0.0480050i
$747$	3.82605	+	3.82605i	0.139988	+	0.139988i
$748$	−8.98947	+	71.5760i	−0.328688	+	2.61708i
$749$	−7.31409	+	33.1711i	−0.267251	+	1.21205i
$750$	9.45296	+	4.62671i	0.345173	+	0.168944i
$751$			51.1794i			1.86756i	0.357846	+	0.933781i	$0.383511\pi$
$751$			51.1794i			1.86756i	−0.357846	+	0.933781i	$0.616489\pi$
$752$	0.544924	−	2.13518i	0.0198713	−	0.0778620i
$753$	16.1248			0.587622
$754$	−22.4699	−	10.9978i	−0.818304	−	0.400516i
$755$	6.10620	−	6.10620i	0.222227	−	0.222227i
$756$	2.27030	+	4.77972i	0.0825699	+	0.173837i
$757$	−14.4521	−	14.4521i	−0.525271	−	0.525271i	0.393888	−	0.919159i	$-0.371130\pi$
$757$	−14.4521	−	14.4521i	−0.525271	−	0.525271i	−0.919159	+	0.393888i	$0.871130\pi$
$758$	−12.3965	+	4.24929i	−0.450262	+	0.154341i
$759$		−	18.3190i		−	0.664936i
$760$	−32.6756	+	6.80385i	−1.18527	+	0.246801i
$761$	6.59268			0.238985			0.119492	−	0.992835i	$-0.461873\pi$
$761$	6.59268			0.238985			0.119492	+	0.992835i	$0.461873\pi$
$762$	6.72216	+	19.6106i	0.243518	+	0.710418i
$763$	−6.26074	+	28.3939i	−0.226654	+	1.02793i
$764$	−7.64210	+	5.93670i	−0.276482	+	0.214782i
$765$	−13.6065	+	13.6065i	−0.491945	+	0.491945i
$766$	−32.3153	−	15.8166i	−1.16760	−	0.571476i
$767$			30.6351i			1.10617i
$768$	15.3517	−	4.50837i	0.553957	−	0.162682i
$769$		−	2.21522i		−	0.0798829i	−0.999202	−	0.0399414i	$-0.987283\pi$
$769$		−	2.21522i		−	0.0798829i	0.999202	−	0.0399414i	$-0.0127171\pi$
$770$	−5.73048	−	50.4033i	−0.206512	−	1.81641i
$771$	−5.94922	−	5.94922i	−0.214256	−	0.214256i
$772$	28.7103	+	36.9578i	1.03331	+	1.33014i
$773$	−17.1592	+	17.1592i	−0.617173	+	0.617173i	−0.944805	−	0.327633i	$-0.893749\pi$
$773$	−17.1592	+	17.1592i	−0.617173	+	0.617173i	0.327633	+	0.944805i	$0.393749\pi$
$774$	−1.25446	−	3.65964i	−0.0450905	−	0.131543i
$775$			2.02440i			0.0727188i
$776$	17.2462	−	3.59108i	0.619104	−	0.128912i
$777$	−7.93452	+	5.06760i	−0.284649	+	0.181799i
$778$	7.54913	+	22.0232i	0.270649	+	0.789568i
$779$	−7.37502	+	7.37502i	−0.264237	+	0.264237i
$780$	−12.5992	−	1.58237i	−0.451122	−	0.0566579i
$781$	41.6046	−	41.6046i	1.48873	−	1.48873i
$782$	−16.1646	+	33.0264i	−0.578046	+	1.18102i
$783$	7.49314			0.267783
$784$	21.7028	+	17.6915i	0.775099	+	0.631840i
$785$	2.18508			0.0779887
$786$	−4.85797	+	9.92546i	−0.173278	+	0.354029i
$787$	18.9133	−	18.9133i	0.674188	−	0.674188i	−0.284491	−	0.958679i	$-0.591825\pi$
$787$	18.9133	−	18.9133i	0.674188	−	0.674188i	0.958679	+	0.284491i	$0.0918246\pi$
$788$	−2.06000	+	16.4021i	−0.0733843	+	0.584301i
$789$	4.71815	−	4.71815i	0.167970	−	0.167970i
$790$	15.5947	+	45.4945i	0.554834	+	1.61862i
$791$	16.3385	−	10.4351i	0.580931	−	0.371028i
$792$	7.81529	−	11.9259i	0.277704	−	0.423767i
$793$		−	18.7738i		−	0.666678i
$794$	11.9004	+	34.7171i	0.422329	+	1.23206i
$795$	−8.20616	+	8.20616i	−0.291043	+	0.291043i
$796$	−6.76559	+	5.25578i	−0.239800	+	0.186286i
$797$	−0.285537	−	0.285537i	−0.0101142	−	0.0101142i	0.702032	−	0.712146i	$-0.252277\pi$
$797$	−0.285537	−	0.285537i	−0.0101142	−	0.0101142i	−0.712146	+	0.702032i	$0.752277\pi$
$798$	−1.85459	−	16.3123i	−0.0656517	−	0.577450i
$799$			3.94170i			0.139447i
$800$	−9.61951	−	8.18575i	−0.340101	−	0.289410i
$801$			14.6937i			0.519177i
$802$	−28.2663	−	13.8348i	−0.998118	−	0.488525i
$803$	−29.9815	+	29.9815i	−1.05802	+	1.05802i
$804$	−2.92579	−	3.76627i	−0.103185	−	0.132826i
$805$	5.56760	−	25.2504i	0.196232	−	0.889958i
$806$	0.981519	+	2.86340i	0.0345725	+	0.100859i
$807$	−1.44567			−0.0508901
$808$	45.9513	+	30.1129i	1.61656	+	1.05937i
$809$			20.9610i			0.736948i	0.929638	+	0.368474i	$0.120120\pi$
$809$			20.9610i			0.736948i	−0.929638	+	0.368474i	$0.879880\pi$
$810$	3.59788	−	1.23329i	0.126417	−	0.0433332i
$811$	8.09740	+	8.09740i	0.284338	+	0.284338i	0.834836	−	0.550498i	$-0.185562\pi$
$811$	8.09740	+	8.09740i	0.284338	+	0.284338i	−0.550498	+	0.834836i	$0.685562\pi$
$812$	35.8151	−	17.0116i	1.25687	−	0.596992i
$813$	3.87053	−	3.87053i	0.135745	−	0.135745i
$814$	22.7861	+	11.1525i	0.798651	+	0.390897i
$815$	−52.6325			−1.84363
$816$	−24.6132	+	14.6044i	−0.861633	+	0.511255i
$817$			12.0029i			0.419930i
$818$	−34.4734	−	16.8728i	−1.20533	−	0.589945i
$819$	1.34492	−	6.09951i	0.0469952	−	0.213134i
$820$	−12.6860	−	1.59327i	−0.443014	−	0.0556396i
$821$	−33.6935	−	33.6935i	−1.17591	−	1.17591i	−0.980776	−	0.195136i	$-0.937485\pi$
$821$	−33.6935	−	33.6935i	−1.17591	−	1.17591i	−0.195136	−	0.980776i	$-0.562515\pi$
$822$	−1.57720	−	4.60119i	−0.0550112	−	0.160485i
$823$	−46.3245			−1.61477			−0.807386	−	0.590023i	$-0.799118\pi$
$823$	−46.3245			−1.61477			−0.807386	+	0.590023i	$0.799118\pi$
$824$	5.88668	−	1.22575i	0.205072	−	0.0427009i
$825$	−11.2562			−0.391890
$826$	−37.9919	−	30.2350i	−1.32191	−	1.05201i
$827$	−13.5597	+	13.5597i	−0.471516	+	0.471516i	−0.902405	−	0.430889i	$-0.858200\pi$
$827$	−13.5597	+	13.5597i	−0.471516	+	0.471516i	0.430889	+	0.902405i	$0.358200\pi$
$828$	5.73945	−	4.45864i	0.199460	−	0.154948i
$829$	−19.5380	−	19.5380i	−0.678582	−	0.678582i	0.281097	−	0.959679i	$-0.409302\pi$
$829$	−19.5380	−	19.5380i	−0.678582	−	0.678582i	−0.959679	+	0.281097i	$0.909302\pi$
$830$	9.04706	−	18.4843i	0.314028	−	0.641599i
$831$	−14.0165			−0.486228
$832$	−17.5750	−	6.91429i	−0.609304	−	0.239710i
$833$	−45.4405	−	21.0629i	−1.57442	−	0.729786i
$834$	−9.36233	−	4.58235i	−0.324191	−	0.158674i
$835$	−18.4730	−	18.4730i	−0.639286	−	0.639286i
$836$	−34.9355	+	27.1394i	−1.20827	+	0.938634i
$837$	−0.641092	−	0.641092i	−0.0221594	−	0.0221594i
$838$	26.5505	−	9.10102i	0.917173	−	0.314390i
$839$			1.94803i			0.0672534i	0.999434	+	0.0336267i	$0.0107057\pi$
$839$			1.94803i			0.0672534i	−0.999434	+	0.0336267i	$0.989294\pi$
$840$	14.3969	−	14.0630i	0.496742	−	0.485220i
$841$		−	27.1472i		−	0.936109i
$842$	−12.1500	−	35.4454i	−0.418717	−	1.22153i
$843$	−13.8898	−	13.8898i	−0.478392	−	0.478392i
$844$	1.88467	−	15.0061i	0.0648731	−	0.516533i
$845$	−14.1234	−	14.1234i	−0.485858	−	0.485858i
$846$	0.342502	−	0.699775i	0.0117755	−	0.0240587i
$847$	−20.5259	−	32.1380i	−0.705277	−	1.10428i
$848$	−14.8443	+	8.80796i	−0.509756	+	0.302467i
$849$	28.7157			0.985521
$850$	20.2932	+	9.93243i	0.696052	+	0.340680i
$851$	9.14358	+	9.14358i	0.313438	+	0.313438i
$852$	23.1611	+	2.90888i	0.793486	+	0.0996565i
$853$	15.1509	−	15.1509i	0.518756	−	0.518756i	−0.398439	−	0.917195i	$-0.630448\pi$
$853$	15.1509	−	15.1509i	0.518756	−	0.518756i	0.917195	+	0.398439i	$0.130448\pi$
$854$	23.2822	+	18.5286i	0.796699	+	0.634035i
$855$	−11.8004			−0.403564
$856$	30.3725	+	19.9038i	1.03811	+	0.680298i
$857$	−28.4917			−0.973259			−0.486629	−	0.873609i	$-0.661774\pi$
$857$	−28.4917			−0.973259			−0.486629	+	0.873609i	$0.661774\pi$
$858$	−15.9212	+	5.45748i	−0.543540	+	0.186315i
$859$	4.12583	+	4.12583i	0.140772	+	0.140772i	0.773981	−	0.633209i	$-0.218263\pi$
$859$	4.12583	+	4.12583i	0.140772	+	0.140772i	−0.633209	+	0.773981i	$0.718263\pi$
$860$	−11.6198	+	9.02676i	−0.396233	+	0.307810i
$861$	1.35418	−	6.14155i	0.0461505	−	0.209303i
$862$	−15.2384	+	31.1340i	−0.519023	+	1.06043i
$863$			13.9231i			0.473949i	0.971516	+	0.236974i	$0.0761557\pi$
$863$			13.9231i			0.473949i	−0.971516	+	0.236974i	$0.923844\pi$
$864$	5.63860	−	0.454046i	0.191829	−	0.0154470i
$865$	13.5973			0.462321
$866$	6.43666	−	13.1509i	0.218726	−	0.446886i
$867$	24.1784	−	24.1784i	0.821143	−	0.821143i
$868$	−4.51971	−	1.60877i	−0.153409	−	0.0546054i
$869$	45.0740	+	45.0740i	1.52903	+	1.52903i
$870$	−9.24118	−	26.9594i	−0.313305	−	0.914010i
$871$			5.62947i			0.190747i
$872$	25.9984	+	17.0373i	0.880416	+	0.576957i
$873$	6.22825			0.210794
$874$	−21.3307	+	7.31175i	−0.721520	+	0.247324i
$875$	19.2276	+	4.23961i	0.650013	+	0.143325i
$876$	−16.6905	−	2.09622i	−0.563921	−	0.0708247i
$877$	28.6830	−	28.6830i	0.968557	−	0.968557i	−0.0309635	−	0.999521i	$-0.509858\pi$
$877$	28.6830	−	28.6830i	0.968557	−	0.968557i	0.999521	+	0.0309635i	$0.00985756\pi$
$878$	13.5898	−	27.7658i	0.458635	−	0.937049i
$879$		−	16.6208i		−	0.560604i
$880$	−52.5463	−	13.4105i	−1.77133	−	0.452066i
$881$			4.92697i			0.165994i	0.996550	+	0.0829969i	$0.0264492\pi$
$881$			4.92697i			0.165994i	−0.996550	+	0.0829969i	$0.973551\pi$
$882$	6.23690	+	7.68772i	0.210007	+	0.258859i
$883$	33.0133	+	33.0133i	1.11099	+	1.11099i	0.993017	+	0.117971i	$0.0376389\pi$
$883$	33.0133	+	33.0133i	1.11099	+	1.11099i	0.117971	+	0.993017i	$0.462361\pi$
$884$	33.5192	+	4.20979i	1.12737	+	0.141590i
$885$	−24.6777	+	24.6777i	−0.829533	+	0.829533i
$886$	−16.6915	+	5.72153i	−0.560762	+	0.192219i
$887$			6.48099i			0.217610i	0.994063	+	0.108805i	$0.0347025\pi$
$887$			6.48099i			0.217610i	−0.994063	+	0.108805i	$0.965298\pi$
$888$	2.05172	+	9.85343i	0.0688511	+	0.330659i
$889$	20.8758	+	32.6860i	0.700153	+	1.09625i
$890$	52.8662	−	18.1215i	1.77208	−	0.607436i
$891$	3.56463	−	3.56463i	0.119419	−	0.119419i
$892$	−34.8862	−	44.9078i	−1.16808	−	1.50362i
$893$	−1.70924	+	1.70924i	−0.0571974	+	0.0571974i
$894$	15.0628	+	7.37242i	0.503775	+	0.246571i
$895$	45.9539			1.53607
$896$	25.9201	−	14.9715i	0.865931	−	0.500163i
$897$	−8.57881			−0.286438
$898$	19.5046	+	9.54646i	0.650878	+	0.318569i
$899$	−4.80379	+	4.80379i	−0.160216	+	0.160216i
$900$	−2.73963	−	3.52663i	−0.0913210	−	0.117554i
$901$	21.8319	−	21.8319i	0.727327	−	0.727327i
$902$	−16.0309	+	5.49509i	−0.533770	+	0.182967i
$903$	−3.89575	−	6.09970i	−0.129642	−	0.202985i
$904$	−4.22484	−	20.2899i	−0.140516	−	0.674832i
$905$			55.9371i			1.85941i
$906$	4.29558	−	1.47245i	0.142711	−	0.0489187i
$907$	33.5078	−	33.5078i	1.11261	−	1.11261i	0.119810	−	0.992797i	$-0.461771\pi$
$907$	33.5078	−	33.5078i	1.11261	−	1.11261i	0.992797	−	0.119810i	$-0.0382286\pi$
$908$	53.6659	+	6.74008i	1.78097	+	0.223678i
$909$	13.7348	+	13.7348i	0.455554	+	0.455554i
$910$	−23.6040	+	2.68359i	−0.782464	+	0.0889603i
$911$			12.4867i			0.413702i	0.978372	+	0.206851i	$0.0663215\pi$
$911$			12.4867i			0.413702i	−0.978372	+	0.206851i	$0.933679\pi$
$912$	−17.0059	−	4.34010i	−0.563120	−	0.143715i
$913$		−	27.2769i		−	0.902733i
$914$	−21.1697	+	43.2524i	−0.700232	+	1.43066i
$915$	15.1230	−	15.1230i	0.499951	−	0.499951i
$916$	5.94265	+	0.746357i	0.196351	+	0.0246603i
$917$	−4.45153	+	20.1887i	−0.147002	+	0.666691i
$918$	−9.57191	+	3.28107i	−0.315920	+	0.108292i
$919$	−23.3667			−0.770796			−0.385398	−	0.922751i	$-0.625936\pi$
$919$	−23.3667			−0.770796			−0.385398	+	0.922751i	$0.625936\pi$
$920$	−23.1200	−	15.1511i	−0.762244	−	0.499516i
$921$			26.8977i			0.886308i
$922$	11.3512	+	33.1151i	0.373833	+	1.09059i
$923$	−19.4835	−	19.4835i	−0.641308	−	0.641308i
$924$	8.94517	−	25.1307i	0.294274	−	0.826739i
$925$	5.61831	−	5.61831i	0.184729	−	0.184729i
$926$	0.0329644	−	0.0673505i	0.00108328	−	0.00221327i
$927$	2.12589			0.0698235
$928$	−3.40223	−	42.2509i	−0.111684	−	1.38695i
$929$		−	22.6572i		−	0.743357i	−0.928361	−	0.371679i	$-0.878782\pi$
$929$		−	22.6572i		−	0.743357i	0.928361	−	0.371679i	$-0.121218\pi$
$930$	−1.51592	+	3.09722i	−0.0497090	+	0.101562i
$931$	−10.5708	−	28.8378i	−0.346445	−	0.945120i
$932$	−36.5011	+	28.3555i	−1.19563	+	0.928815i
$933$	−9.69538	−	9.69538i	−0.317413	−	0.317413i
$934$	15.8854	−	5.44520i	0.519785	−	0.178172i
$935$	97.0044			3.17238
$936$	−5.58490	−	3.65991i	−0.182548	−	0.119628i
$937$	23.8889			0.780417			0.390208	−	0.920727i	$-0.372403\pi$
$937$	23.8889			0.780417			0.390208	+	0.920727i	$0.372403\pi$
$938$	−6.98133	−	5.55594i	−0.227949	−	0.181408i
$939$	3.42478	−	3.42478i	0.111764	−	0.111764i
$940$	−2.94011	−	0.369258i	−0.0958957	−	0.0120439i
$941$	13.2546	+	13.2546i	0.432088	+	0.432088i	0.889338	−	0.457250i	$-0.151166\pi$
$941$	13.2546	+	13.2546i	0.432088	+	0.432088i	−0.457250	+	0.889338i	$0.651166\pi$
$942$	1.03203	+	0.505124i	0.0336254	+	0.0164578i
$943$	−8.63793			−0.281290
$944$	−44.6401	+	26.4875i	−1.45291	+	0.862094i
$945$	5.99676	−	3.83000i	0.195075	−	0.124590i
$946$	−8.57358	+	17.5169i	−0.278751	+	0.569524i
$947$	7.30455	+	7.30455i	0.237366	+	0.237366i	0.815759	−	0.578393i	$-0.196320\pi$
$947$	7.30455	+	7.30455i	0.237366	+	0.237366i	−0.578393	+	0.815759i	$0.696320\pi$
$948$	−3.15145	+	25.0925i	−0.102354	+	0.814967i
$949$	14.0404	+	14.0404i	0.455770	+	0.455770i
$950$	4.49274	+	13.1067i	0.145764	+	0.425238i
$951$		−	3.85421i		−	0.124981i
$952$	−38.3021	+	37.4137i	−1.24138	+	1.21258i
$953$		−	27.8206i		−	0.901198i	−0.892726	−	0.450599i	$-0.851210\pi$
$953$		−	27.8206i		−	0.901198i	0.892726	−	0.450599i	$-0.148790\pi$
$954$	−5.77286	+	1.97883i	−0.186903	+	0.0640670i
$955$	9.20142	+	9.20142i	0.297751	+	0.297751i
$956$	15.7080	−	12.2026i	0.508031	−	0.394660i
$957$	−26.7102	−	26.7102i	−0.863419	−	0.863419i
$958$	−46.9391	−	22.9742i	−1.51653	−	0.742262i
$959$	−4.89804	−	7.66903i	−0.158166	−	0.247646i
$960$	−8.58761	−	19.7270i	−0.277164	−	0.636687i
$961$	−30.1780			−0.973484
$962$	5.22276	−	10.6708i	0.168389	−	0.344039i
$963$	9.07831	+	9.07831i	0.292545	+	0.292545i
$964$	−18.0507	+	14.0225i	−0.581375	+	0.451635i
$965$	44.4988	−	44.4988i	1.43247	−	1.43247i
$966$	8.46675	−	10.6389i	0.272413	−	0.342302i
$967$	23.9412			0.769898			0.384949	−	0.922938i	$-0.374219\pi$
$967$	23.9412			0.769898			0.384949	+	0.922938i	$0.374219\pi$
$968$	−39.9104	+	8.31029i	−1.28277	+	0.267103i
$969$	31.3941			1.00852
$970$	−7.68121	−	22.4085i	−0.246629	−	0.719493i
$971$	18.4212	+	18.4212i	0.591165	+	0.591165i	0.937946	−	0.346781i	$-0.112725\pi$
$971$	18.4212	+	18.4212i	0.591165	+	0.591165i	−0.346781	+	0.937946i	$0.612725\pi$
$972$	1.98441	+	0.249229i	0.0636500	+	0.00799401i
$973$	−19.0433	−	4.19897i	−0.610500	−	0.134613i
$974$	−18.5750	−	9.09145i	−0.595181	−	0.291309i
$975$			5.27129i			0.168816i
$976$	27.3563	−	16.2320i	0.875655	−	0.519575i
$977$	41.8758			1.33973			0.669863	−	0.742484i	$-0.266353\pi$
$977$	41.8758			1.33973			0.669863	+	0.742484i	$0.266353\pi$
$978$	−24.8588	−	12.1670i	−0.794897	−	0.389059i
$979$	52.3776	−	52.3776i	1.67399	−	1.67399i
$980$	19.9676	−	31.9208i	0.637842	−	1.01967i
$981$	7.77089	+	7.77089i	0.248105	+	0.248105i
$982$	−12.2205	+	4.18895i	−0.389971	+	0.133675i
$983$			28.1376i			0.897450i	0.893670	+	0.448725i	$0.148122\pi$
$983$			28.1376i			0.897450i	−0.893670	+	0.448725i	$0.851878\pi$
$984$	−5.62339	−	3.68514i	−0.179267	−	0.117478i
$985$	22.2292			0.708281
$986$	24.5855	+	71.7237i	0.782963	+	2.28415i
$987$	0.313846	−	1.42337i	0.00998983	−	0.0453063i
$988$	12.7094	+	16.3604i	0.404340	+	0.520493i
$989$	−7.02917	+	7.02917i	−0.223515	+	0.223515i
$990$	−17.2213	−	8.42889i	−0.547329	−	0.267888i
$991$		−	57.5245i		−	1.82733i	−0.406473	−	0.913663i	$-0.633242\pi$
$991$		−	57.5245i		−	1.82733i	0.406473	−	0.913663i	$-0.366758\pi$
$992$	−3.32378	+	3.90595i	−0.105530	+	0.124014i
$993$			9.81186i			0.311370i
$994$	43.3913	−	4.93327i	1.37629	−	0.156474i
$995$	8.14606	+	8.14606i	0.258248	+	0.258248i
$996$	8.54602	−	6.63890i	0.270791	−	0.210361i
$997$	−31.2570	+	31.2570i	−0.989919	+	0.989919i	−0.999950	−	0.0100311i	$-0.996807\pi$
$997$	−31.2570	+	31.2570i	−0.989919	+	0.989919i	0.0100311	+	0.999950i	$0.496807\pi$
$998$	−0.0608033	−	0.177382i	−0.00192470	−	0.00561494i
$999$			3.55843i			0.112584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.3	✓	64
4.3	odd	2		1344.2.u.a.1231.19		64
7.6	odd	2	inner	336.2.u.a.139.4	yes	64
16.3	odd	4	inner	336.2.u.a.307.4	yes	64
16.13	even	4		1344.2.u.a.559.14		64
28.27	even	2		1344.2.u.a.1231.14		64
112.13	odd	4		1344.2.u.a.559.19		64
112.83	even	4	inner	336.2.u.a.307.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.3	✓	64	1.1	even	1	trivial
336.2.u.a.139.4	yes	64	7.6	odd	2	inner
336.2.u.a.307.3	yes	64	112.83	even	4	inner
336.2.u.a.307.4	yes	64	16.3	odd	4	inner
1344.2.u.a.559.14		64	16.13	even	4
1344.2.u.a.559.19		64	112.13	odd	4
1344.2.u.a.1231.14		64	28.27	even	2
1344.2.u.a.1231.19		64	4.3	odd	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27023 - 0.621708i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.22696 + 1.57942i) q^{4} +(1.90169 - 1.90169i) q^{5} +(1.33780 - 0.458573i) q^{6} +(2.22978 - 1.42411i) q^{7} +(-0.576579 - 2.76904i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.27023 - 0.621708i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.22696 + 1.57942i) q^{4} +(1.90169 - 1.90169i) q^{5} +(1.33780 - 0.458573i) q^{6} +(2.22978 - 1.42411i) q^{7} +(-0.576579 - 2.76904i) q^{8} -1.00000i q^{9} +(-3.59788 + 1.23329i) q^{10} +(-3.56463 + 3.56463i) q^{11} +(-1.98441 - 0.249229i) q^{12} +(1.66932 + 1.66932i) q^{13} +(-3.71771 + 0.422676i) q^{14} +2.68940i q^{15} +(-0.989144 + 3.87577i) q^{16} -7.15496i q^{17} +(-0.621708 + 1.27023i) q^{18} +(3.10260 - 3.10260i) q^{19} +(5.33687 + 0.670275i) q^{20} +(-0.569692 + 2.58369i) q^{21} +(6.74404 - 2.31173i) q^{22} +3.63389 q^{23} +(2.36571 + 1.55030i) q^{24} -2.23286i q^{25} +(-1.08259 - 3.15825i) q^{26} +(0.707107 + 0.707107i) q^{27} +(4.98512 + 1.77443i) q^{28} +(5.29845 - 5.29845i) q^{29} +(1.67202 - 3.41615i) q^{30} -0.906641 q^{31} +(3.66604 - 4.30815i) q^{32} -5.04114i q^{33} +(-4.44830 + 9.08843i) q^{34} +(1.53213 - 6.94857i) q^{35} +(1.57942 - 1.22696i) q^{36} +(2.51619 + 2.51619i) q^{37} +(-5.86992 + 2.01210i) q^{38} -2.36078 q^{39} +(-6.36233 - 4.16938i) q^{40} -2.37705 q^{41} +(2.32994 - 2.92769i) q^{42} +(-1.93434 + 1.93434i) q^{43} +(-10.0037 - 1.25640i) q^{44} +(-1.90169 - 1.90169i) q^{45} +(-4.61587 - 2.25922i) q^{46} -0.550905 q^{47} +(-2.04115 - 3.44001i) q^{48} +(2.94382 - 6.35090i) q^{49} +(-1.38819 + 2.83624i) q^{50} +(5.05932 + 5.05932i) q^{51} +(-0.588373 + 4.68475i) q^{52} +(3.05130 + 3.05130i) q^{53} +(-0.458573 - 1.33780i) q^{54} +13.5576i q^{55} +(-5.22906 - 5.35322i) q^{56} +4.38774i q^{57} +(-10.0243 + 3.43615i) q^{58} +(9.17593 + 9.17593i) q^{59} +(-4.24769 + 3.29978i) q^{60} +(-5.62319 - 5.62319i) q^{61} +(1.15164 + 0.563666i) q^{62} +(-1.42411 - 2.22978i) q^{63} +(-7.33511 + 3.19313i) q^{64} +6.34907 q^{65} +(-3.13412 + 6.40340i) q^{66} +(1.68616 + 1.68616i) q^{67} +(11.3007 - 8.77884i) q^{68} +(-2.56955 + 2.56955i) q^{69} +(-6.26613 + 7.87373i) q^{70} -11.6715 q^{71} +(-2.76904 + 0.576579i) q^{72} +8.41083 q^{73} +(-1.63180 - 4.76048i) q^{74} +(1.57887 + 1.57887i) q^{75} +(8.70707 + 1.09355i) q^{76} +(-2.87190 + 13.0247i) q^{77} +(2.99872 + 1.46771i) q^{78} -12.6448i q^{79} +(5.48947 + 9.25157i) q^{80} -1.00000 q^{81} +(3.01939 + 1.47783i) q^{82} +(-3.82605 + 3.82605i) q^{83} +(-4.77972 + 2.27030i) q^{84} +(-13.6065 - 13.6065i) q^{85} +(3.65964 - 1.25446i) q^{86} +7.49314i q^{87} +(11.9259 + 7.81529i) q^{88} -14.6937 q^{89} +(1.23329 + 3.59788i) q^{90} +(6.09951 + 1.34492i) q^{91} +(4.45864 + 5.73945i) q^{92} +(0.641092 - 0.641092i) q^{93} +(0.699775 + 0.342502i) q^{94} -11.8004i q^{95} +(0.454046 + 5.63860i) q^{96} +6.22825i q^{97} +(-7.68772 + 6.23690i) q^{98} +(3.56463 + 3.56463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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