LMFDB - Embedded newform 650.2.bd.b.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(47,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17, 5]))

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

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

chi := DirichletCharacter("650.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.bd (of order $20$, degree $8$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	650.47
Dual form			650.2.bd.b.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.89075 + 0.299466i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.55473 + 1.60711i) q^{5} +(1.89075 + 0.299466i) q^{6} +3.88967 q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.632103 - 0.205383i) q^{9} +(1.97526 - 1.04801i) q^{10} +(-1.85375 - 3.63818i) q^{11} +(-1.70567 - 0.869084i) q^{12} +(1.99669 - 3.00220i) q^{13} +(-3.69929 - 1.20197i) q^{14} +(2.45835 - 3.50424i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.106133 + 0.670099i) q^{17} -0.664633 q^{18} +(-0.892542 + 5.63529i) q^{19} +(-2.20244 + 0.386329i) q^{20} +(-7.35441 + 1.16482i) q^{21} +(0.638758 + 4.03296i) q^{22} +(2.17846 - 1.10998i) q^{23} +(1.35363 + 1.35363i) q^{24} +(-0.165604 - 4.99726i) q^{25} +(-2.82670 + 2.23825i) q^{26} +(3.98338 - 2.02963i) q^{27} +(3.14681 + 2.28629i) q^{28} +(-4.55237 + 6.26579i) q^{29} +(-3.42090 + 2.57306i) q^{30} +(3.45533 + 0.547270i) q^{31} -1.00000i q^{32} +(4.59449 + 6.32378i) q^{33} +(0.308011 - 0.604505i) q^{34} +(-6.04740 + 6.25112i) q^{35} +(0.632103 + 0.205383i) q^{36} +(2.72215 + 8.37791i) q^{37} +(2.59026 - 5.08367i) q^{38} +(-2.87619 + 6.27437i) q^{39} +(2.21403 + 0.313171i) q^{40} +(5.03785 - 9.88734i) q^{41} +(7.35441 + 1.16482i) q^{42} +(4.88202 + 4.88202i) q^{43} +(0.638758 - 4.03296i) q^{44} +(-0.652680 + 1.33517i) q^{45} +(-2.41484 + 0.382473i) q^{46} +(3.50504 + 2.54656i) q^{47} +(-0.869084 - 1.70567i) q^{48} +8.12952 q^{49} +(-1.38674 + 4.80385i) q^{50} -1.29878i q^{51} +(3.38001 - 1.25521i) q^{52} +(9.82624 - 1.55632i) q^{53} +(-4.41561 + 0.699363i) q^{54} +(8.72904 + 2.67723i) q^{55} +(-2.28629 - 3.14681i) q^{56} -10.9222i q^{57} +(6.26579 - 4.55237i) q^{58} +(-3.25785 + 6.39390i) q^{59} +(4.04858 - 1.39001i) q^{60} +(-0.840444 + 2.58662i) q^{61} +(-3.11710 - 1.58824i) q^{62} +(2.45867 - 0.798871i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.72055 + 7.87653i) q^{65} +(-2.41547 - 7.43405i) q^{66} +(0.740215 + 1.01882i) q^{67} +(-0.479738 + 0.479738i) q^{68} +(-3.78653 + 2.75108i) q^{69} +(7.68312 - 4.07642i) q^{70} +(2.52444 + 15.9387i) q^{71} +(-0.537699 - 0.390661i) q^{72} +(-0.143686 - 0.0466865i) q^{73} -8.80905i q^{74} +(1.80963 + 9.39899i) q^{75} +(-4.03442 + 4.03442i) q^{76} +(-7.21046 - 14.1513i) q^{77} +(4.67431 - 5.07849i) q^{78} +(-4.20678 + 5.79014i) q^{79} +(-2.00889 - 0.982016i) q^{80} +(-8.53688 + 6.20240i) q^{81} +(-7.84663 + 7.84663i) q^{82} +(-5.70478 + 4.14477i) q^{83} +(-6.63451 - 3.38045i) q^{84} +(-0.911914 - 1.21239i) q^{85} +(-3.13445 - 6.15171i) q^{86} +(6.73101 - 13.2104i) q^{87} +(-1.85375 + 3.63818i) q^{88} +(4.94900 - 2.52164i) q^{89} +(1.03333 - 1.06814i) q^{90} +(7.76647 - 11.6776i) q^{91} +(2.41484 + 0.382473i) q^{92} -6.69707 q^{93} +(-2.54656 - 3.50504i) q^{94} +(-7.66886 - 10.1958i) q^{95} +(0.299466 + 1.89075i) q^{96} +(3.89672 - 5.36337i) q^{97} +(-7.73164 - 2.51216i) q^{98} +(-1.91898 - 1.91898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} - 2 q^{5} - 20 q^{9} + 12 q^{13} - 26 q^{15} - 36 q^{16} + 6 q^{17} - 152 q^{18} - 20 q^{19} - 8 q^{20} - 6 q^{21} - 12 q^{23} - 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} - 12 q^{30}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 - 2 * q^5 - 20 * q^9 + 12 * q^13 - 26 * q^15 - 36 * q^16 + 6 * q^17 - 152 * q^18 - 20 * q^19 - 8 * q^20 - 6 * q^21 - 12 * q^23 - 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 - 12 * q^30 - 6 * q^31 + 30 * q^33 + 24 * q^34 + 40 * q^35 - 20 * q^36 - 6 * q^37 + 60 * q^39 - 8 * q^41 + 6 * q^42 + 12 * q^43 - 30 * q^45 - 12 * q^46 - 18 * q^47 + 160 * q^49 - 12 * q^52 + 20 * q^53 + 6 * q^54 - 32 * q^55 - 24 * q^58 + 16 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 40 * q^63 + 36 * q^64 - 54 * q^65 - 16 * q^66 - 6 * q^68 - 26 * q^69 + 2 * q^70 + 12 * q^71 - 48 * q^72 + 40 * q^73 - 32 * q^75 + 56 * q^77 + 16 * q^78 - 20 * q^79 - 2 * q^80 + 124 * q^81 + 22 * q^82 + 74 * q^83 - 24 * q^84 - 60 * q^85 + 12 * q^86 + 8 * q^87 - 58 * q^89 + 14 * q^90 - 16 * q^91 + 12 * q^92 - 16 * q^93 + 50 * q^94 + 46 * q^95 - 40 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−1.89075	+	0.299466i	−1.09163	+	0.172897i	−0.676192	−	0.736726i	$-0.736371\pi$
$3$	−1.89075	+	0.299466i	−1.09163	+	0.172897i	−0.415436	+	0.909622i	$0.636371\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.55473	+	1.60711i	−0.695298	+	0.718721i
$5$	−1.55473	+	1.60711i	−0.695298	+	0.718721i
$6$	1.89075	+	0.299466i	0.771897	+	0.122257i
$7$	3.88967			1.47016			0.735078	−	0.677982i	$-0.237145\pi$
$7$	3.88967			1.47016			0.735078	+	0.677982i	$0.237145\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.632103	−	0.205383i	0.210701	−	0.0684609i
$10$	1.97526	−	1.04801i	0.624633	−	0.331411i
$11$	−1.85375	−	3.63818i	−0.558926	−	1.09695i	−0.981649	−	0.190695i	$-0.938926\pi$
$11$	−1.85375	−	3.63818i	−0.558926	−	1.09695i	0.422724	−	0.906259i	$-0.361074\pi$
$12$	−1.70567	−	0.869084i	−0.492386	−	0.250883i
$13$	1.99669	−	3.00220i	0.553782	−	0.832661i
$13$	1.99669	−	3.00220i	0.553782	−	0.832661i
$14$	−3.69929	−	1.20197i	−0.988678	−	0.321241i
$15$	2.45835	−	3.50424i	0.634742	−	0.904791i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.106133	+	0.670099i	−0.0257411	+	0.162523i	−0.997210	−	0.0746427i	$-0.976218\pi$
$17$	−0.106133	+	0.670099i	−0.0257411	+	0.162523i	0.971469	+	0.237166i	$0.0762184\pi$
$18$	−0.664633			−0.156655
$19$	−0.892542	+	5.63529i	−0.204763	+	1.29282i	0.644398	+	0.764690i	$0.277108\pi$
$19$	−0.892542	+	5.63529i	−0.204763	+	1.29282i	−0.849161	+	0.528134i	$0.822892\pi$
$20$	−2.20244	+	0.386329i	−0.492481	+	0.0863859i
$21$	−7.35441	+	1.16482i	−1.60486	+	0.254185i
$22$	0.638758	+	4.03296i	0.136184	+	0.859829i
$23$	2.17846	−	1.10998i	0.454240	−	0.231447i	−0.211873	−	0.977297i	$-0.567956\pi$
$23$	2.17846	−	1.10998i	0.454240	−	0.231447i	0.666114	+	0.745850i	$0.267956\pi$
$24$	1.35363	+	1.35363i	0.276309	+	0.276309i
$25$	−0.165604	−	4.99726i	−0.0331208	−	0.999451i
$26$	−2.82670	+	2.23825i	−0.554361	+	0.438958i
$27$	3.98338	−	2.02963i	0.766601	−	0.390603i
$28$	3.14681	+	2.28629i	0.594691	+	0.432068i
$29$	−4.55237	+	6.26579i	−0.845353	+	1.16353i	0.139514	+	0.990220i	$0.455446\pi$
$29$	−4.55237	+	6.26579i	−0.845353	+	1.16353i	−0.984868	+	0.173309i	$0.944554\pi$
$30$	−3.42090	+	2.57306i	−0.624567	+	0.469774i
$31$	3.45533	+	0.547270i	0.620595	+	0.0982926i	0.458812	−	0.888534i	$-0.348275\pi$
$31$	3.45533	+	0.547270i	0.620595	+	0.0982926i	0.161784	+	0.986826i	$0.448275\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.59449	+	6.32378i	0.799799	+	1.10083i
$34$	0.308011	−	0.604505i	0.0528234	−	0.103672i
$35$	−6.04740	+	6.25112i	−1.02220	+	1.05663i
$36$	0.632103	+	0.205383i	0.105351	+	0.0342305i
$37$	2.72215	+	8.37791i	0.447518	+	1.37732i	0.879698	+	0.475532i	$0.157744\pi$
$37$	2.72215	+	8.37791i	0.447518	+	1.37732i	−0.432180	+	0.901787i	$0.642256\pi$
$38$	2.59026	−	5.08367i	0.420195	−	0.824680i
$39$	−2.87619	+	6.27437i	−0.460560	+	1.00470i
$40$	2.21403	+	0.313171i	0.350069	+	0.0495167i
$41$	5.03785	−	9.88734i	0.786780	−	1.54414i	−0.0513558	−	0.998680i	$-0.516354\pi$
$41$	5.03785	−	9.88734i	0.786780	−	1.54414i	0.838136	−	0.545462i	$-0.183646\pi$
$42$	7.35441	+	1.16482i	1.13481	+	0.179736i
$43$	4.88202	+	4.88202i	0.744502	+	0.744502i	0.973441	−	0.228939i	$-0.0735257\pi$
$43$	4.88202	+	4.88202i	0.744502	+	0.744502i	−0.228939	+	0.973441i	$0.573526\pi$
$44$	0.638758	−	4.03296i	0.0962963	−	0.607991i
$45$	−0.652680	+	1.33517i	−0.0972957	+	0.199036i
$46$	−2.41484	+	0.382473i	−0.356049	+	0.0563926i
$47$	3.50504	+	2.54656i	0.511263	+	0.371455i	0.813303	−	0.581841i	$-0.197667\pi$
$47$	3.50504	+	2.54656i	0.511263	+	0.371455i	−0.302039	+	0.953295i	$0.597667\pi$
$48$	−0.869084	−	1.70567i	−0.125442	−	0.246193i
$49$	8.12952			1.16136
$50$	−1.38674	+	4.80385i	−0.196114	+	0.679367i
$51$		−	1.29878i		−	0.181865i
$52$	3.38001	−	1.25521i	0.468723	−	0.174066i
$53$	9.82624	−	1.55632i	1.34974	−	0.213778i	0.560648	−	0.828055i	$-0.310552\pi$
$53$	9.82624	−	1.55632i	1.34974	−	0.213778i	0.789090	+	0.614277i	$0.210552\pi$
$54$	−4.41561	+	0.699363i	−0.600888	+	0.0951713i
$55$	8.72904	+	2.67723i	1.17702	+	0.360998i
$56$	−2.28629	−	3.14681i	−0.305518	−	0.420510i
$57$		−	10.9222i		−	1.44668i
$58$	6.26579	−	4.55237i	0.822739	−	0.597755i
$59$	−3.25785	+	6.39390i	−0.424136	+	0.832415i	0.575754	+	0.817623i	$0.304709\pi$
$59$	−3.25785	+	6.39390i	−0.424136	+	0.832415i	−0.999891	+	0.0147917i	$0.995291\pi$
$60$	4.04858	−	1.39001i	0.522670	−	0.179450i
$61$	−0.840444	+	2.58662i	−0.107608	+	0.331183i	−0.990334	−	0.138706i	$-0.955706\pi$
$61$	−0.840444	+	2.58662i	−0.107608	+	0.331183i	0.882726	+	0.469888i	$0.155706\pi$
$62$	−3.11710	−	1.58824i	−0.395872	−	0.201707i
$63$	2.45867	−	0.798871i	0.309764	−	0.100648i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	1.72055	+	7.87653i	0.213408	+	0.976963i
$66$	−2.41547	−	7.43405i	−0.297324	−	0.915068i
$67$	0.740215	+	1.01882i	0.0904316	+	0.124468i	0.851836	−	0.523809i	$-0.175490\pi$
$67$	0.740215	+	1.01882i	0.0904316	+	0.124468i	−0.761404	+	0.648278i	$0.775490\pi$
$68$	−0.479738	+	0.479738i	−0.0581768	+	0.0581768i
$69$	−3.78653	+	2.75108i	−0.455845	+	0.331191i
$70$	7.68312	−	4.07642i	0.918309	−	0.487226i
$71$	2.52444	+	15.9387i	0.299596	+	1.89158i	0.434424	+	0.900709i	$0.356952\pi$
$71$	2.52444	+	15.9387i	0.299596	+	1.89158i	−0.134827	+	0.990869i	$0.543048\pi$
$72$	−0.537699	−	0.390661i	−0.0633684	−	0.0460399i
$73$	−0.143686	−	0.0466865i	−0.0168172	−	0.00546424i	0.300596	−	0.953751i	$-0.402814\pi$
$73$	−0.143686	−	0.0466865i	−0.0168172	−	0.00546424i	−0.317414	+	0.948287i	$0.602814\pi$
$74$		−	8.80905i		−	1.02403i
$75$	1.80963	+	9.39899i	0.208958	+	1.08530i
$76$	−4.03442	+	4.03442i	−0.462780	+	0.462780i
$77$	−7.21046	−	14.1513i	−0.821708	−	1.61269i
$78$	4.67431	−	5.07849i	0.529261	−	0.575026i
$79$	−4.20678	+	5.79014i	−0.473300	+	0.651442i	−0.977200	−	0.212320i	$-0.931898\pi$
$79$	−4.20678	+	5.79014i	−0.473300	+	0.651442i	0.503900	+	0.863762i	$0.331898\pi$
$80$	−2.00889	−	0.982016i	−0.224601	−	0.109793i
$81$	−8.53688	+	6.20240i	−0.948542	+	0.689156i
$82$	−7.84663	+	7.84663i	−0.866516	+	0.866516i
$83$	−5.70478	+	4.14477i	−0.626181	+	0.454947i	−0.855075	−	0.518504i	$-0.826489\pi$
$83$	−5.70478	+	4.14477i	−0.626181	+	0.454947i	0.228894	+	0.973451i	$0.426489\pi$
$84$	−6.63451	−	3.38045i	−0.723884	−	0.368837i
$85$	−0.911914	−	1.21239i	−0.0989109	−	0.131503i
$86$	−3.13445	−	6.15171i	−0.337997	−	0.663356i
$87$	6.73101	−	13.2104i	0.721640	−	1.41630i
$88$	−1.85375	+	3.63818i	−0.197610	+	0.387832i
$89$	4.94900	−	2.52164i	0.524593	−	0.267294i	−0.171577	−	0.985171i	$-0.554886\pi$
$89$	4.94900	−	2.52164i	0.524593	−	0.267294i	0.696170	+	0.717877i	$0.254886\pi$
$90$	1.03333	−	1.06814i	0.108922	−	0.112592i
$91$	7.76647	−	11.6776i	0.814147	−	1.22414i
$92$	2.41484	+	0.382473i	0.251765	+	0.0398756i
$93$	−6.69707			−0.694453
$94$	−2.54656	−	3.50504i	−0.262658	−	0.361518i
$95$	−7.66886	−	10.1958i	−0.786809	−	1.04607i
$96$	0.299466	+	1.89075i	0.0305641	+	0.192974i
$97$	3.89672	−	5.36337i	0.395652	−	0.544568i	−0.563994	−	0.825779i	$-0.690736\pi$
$97$	3.89672	−	5.36337i	0.395652	−	0.544568i	0.959646	+	0.281211i	$0.0907360\pi$
$98$	−7.73164	−	2.51216i	−0.781013	−	0.253767i
$99$	−1.91898	−	1.91898i	−0.192865	−	0.192865i
$100$	2.80334	−	4.14021i	0.280334	−	0.414021i
$101$			6.74105i			0.670760i	0.942083	+	0.335380i	$0.108865\pi$
$101$			6.74105i			0.670760i	−0.942083	+	0.335380i	$0.891135\pi$
$102$	−0.401344	+	1.23521i	−0.0397390	+	0.122304i
$103$	0.169564	+	1.07058i	0.0167076	+	0.105488i	0.994633	−	0.103467i	$-0.0329938\pi$
$103$	0.169564	+	1.07058i	0.0167076	+	0.105488i	−0.977925	+	0.208955i	$0.932994\pi$
$104$	−3.60246	+	0.149294i	−0.353250	+	0.0146395i
$105$	9.56215	−	13.6303i	0.933170	−	1.33018i
$106$	−9.82624	−	1.55632i	−0.954409	−	0.151164i
$107$	0.398717	+	0.398717i	0.0385454	+	0.0385454i	0.726117	−	0.687571i	$-0.241323\pi$
$107$	0.398717	+	0.398717i	0.0385454	+	0.0385454i	−0.687571	+	0.726117i	$0.741323\pi$
$108$	4.41561	+	0.699363i	0.424892	+	0.0672963i
$109$	−5.14569	−	2.62186i	−0.492868	−	0.251129i	0.189847	−	0.981814i	$-0.439201\pi$
$109$	−5.14569	−	2.62186i	−0.492868	−	0.251129i	−0.682715	+	0.730685i	$0.739201\pi$
$110$	−7.47450	−	5.24362i	−0.712666	−	0.499960i
$111$	−7.65581	−	15.0254i	−0.726657	−	1.42615i
$112$	1.20197	+	3.69929i	0.113576	+	0.349550i
$113$	14.4360	+	7.35551i	1.35802	+	0.691948i	0.972967	−	0.230944i	$-0.0741815\pi$
$113$	14.4360	+	7.35551i	1.35802	+	0.691948i	0.385058	+	0.922892i	$0.374181\pi$
$114$	−3.37516	+	10.3877i	−0.316112	+	0.972893i
$115$	−1.60307	+	5.22675i	−0.149487	+	0.487397i
$116$	−7.36588	+	2.39332i	−0.683905	+	0.222214i
$117$	0.645514	−	2.30779i	0.0596778	−	0.213355i
$118$	5.07423	−	5.07423i	0.467120	−	0.467120i
$119$	−0.412823	+	2.60646i	−0.0378434	+	0.238934i
$120$	−4.27997	+	0.0708974i	−0.390706	+	0.00647202i
$121$	−3.33436	+	4.58935i	−0.303124	+	0.417214i
$122$	1.59862	−	2.20031i	0.144732	−	0.199207i
$123$	−6.56441	+	20.2032i	−0.591893	+	1.82166i
$124$	2.47374	+	2.47374i	0.222149	+	0.222149i
$125$	8.28861	+	7.50326i	0.741356	+	0.671112i
$126$	−2.58520			−0.230308
$127$	−0.159680	−	0.313389i	−0.0141693	−	0.0278088i	0.883813	−	0.467840i	$-0.154968\pi$
$127$	−0.159680	−	0.313389i	−0.0141693	−	0.0278088i	−0.897983	+	0.440031i	$0.854968\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−10.6927	−	7.76871i	−0.941440	−	0.683997i
$130$	0.797644	−	8.02270i	0.0699580	−	0.703638i
$131$	9.89743	−	7.19091i	0.864743	−	0.628272i	−0.0644284	−	0.997922i	$-0.520522\pi$
$131$	9.89743	−	7.19091i	0.864743	−	0.628272i	0.929171	+	0.369650i	$0.120522\pi$
$132$			7.81662i			0.680349i
$133$	−3.47169	+	21.9194i	−0.301034	+	1.90065i
$134$	−0.389154	−	1.19769i	−0.0336178	−	0.103465i
$135$	−2.93125	+	9.55726i	−0.252282	+	0.822558i
$136$	0.604505	−	0.308011i	0.0518359	−	0.0264117i
$137$	−6.68244	−	20.5664i	−0.570919	−	1.75711i	−0.649672	−	0.760214i	$-0.725094\pi$
$137$	−6.68244	−	20.5664i	−0.570919	−	1.75711i	0.0787533	−	0.996894i	$-0.474906\pi$
$138$	4.45134	−	1.44633i	0.378923	−	0.123120i
$139$	8.98627	+	2.91982i	0.762206	+	0.247656i	0.664225	−	0.747533i	$-0.268762\pi$
$139$	8.98627	+	2.91982i	0.762206	+	0.247656i	0.0979807	+	0.995188i	$0.468762\pi$
$140$	−8.56677	+	1.50269i	−0.724024	+	0.127001i
$141$	−7.38979	−	3.76529i	−0.622332	−	0.317094i
$142$	2.52444	−	15.9387i	0.211847	−	1.33755i
$143$	−14.6239	−	1.69900i	−1.22291	−	0.142078i
$144$	0.390661	+	0.537699i	0.0325551	+	0.0448083i
$145$	−2.99210	−	17.0578i	−0.248480	−	1.41657i
$146$	0.122227	+	0.0888030i	0.0101156	+	0.00734938i
$147$	−15.3709	+	2.43452i	−1.26777	+	0.200796i
$148$	−2.72215	+	8.37791i	−0.223759	+	0.688660i
$149$	3.56297	−	3.56297i	0.291890	−	0.291890i	−0.545937	−	0.837826i	$-0.683826\pi$
$149$	3.56297	−	3.56297i	0.291890	−	0.291890i	0.837826	+	0.545937i	$0.183826\pi$
$150$	1.18339	−	9.49818i	0.0966236	−	0.775523i
$151$	0.937399	−	0.937399i	0.0762845	−	0.0762845i	−0.667935	−	0.744220i	$-0.732822\pi$
$151$	0.937399	−	0.937399i	0.0762845	−	0.0762845i	0.744220	+	0.667935i	$0.232822\pi$
$152$	5.08367	−	2.59026i	0.412340	−	0.210098i
$153$	0.0705396	+	0.445370i	0.00570279	+	0.0360060i
$154$	2.48456	+	15.6869i	0.200211	+	1.26408i
$155$	−6.25164	+	4.70223i	−0.502144	+	0.377692i
$156$	−6.01487	+	3.38549i	−0.481575	+	0.271056i
$157$	−3.93274	−	3.93274i	−0.313867	−	0.313867i	0.532539	−	0.846406i	$-0.321238\pi$
$157$	−3.93274	−	3.93274i	−0.313867	−	0.313867i	−0.846406	+	0.532539i	$0.821238\pi$
$158$	5.79014	−	4.20678i	0.460639	−	0.334674i
$159$	−18.1129	+	5.88525i	−1.43645	+	0.466731i
$160$	1.60711	+	1.55473i	0.127053	+	0.122913i
$161$	8.47349	−	4.31746i	0.667805	−	0.340263i
$162$	10.0357	−	3.26080i	0.788479	−	0.256192i
$163$	−5.73632	+	1.86384i	−0.449303	+	0.145988i	−0.524924	−	0.851149i	$-0.675906\pi$
$163$	−5.73632	+	1.86384i	−0.449303	+	0.145988i	0.0756205	+	0.997137i	$0.475906\pi$
$164$	9.88734	−	5.03785i	0.772071	−	0.393390i
$165$	−17.3062	−	2.44794i	−1.34729	−	0.190572i
$166$	6.70637	−	2.17903i	0.520516	−	0.169126i
$167$	−9.33556	+	6.78268i	−0.722407	+	0.524860i	−0.887152	−	0.461476i	$-0.847320\pi$
$167$	−9.33556	+	6.78268i	−0.722407	+	0.524860i	0.164745	+	0.986336i	$0.447320\pi$
$168$	5.26518	+	5.26518i	0.406217	+	0.406217i
$169$	−5.02645	−	11.9889i	−0.386650	−	0.922226i
$170$	0.492631	+	1.43485i	0.0377831	+	0.110048i
$171$	0.593212	+	3.74540i	0.0453641	+	0.286418i
$172$	1.08006	+	6.81922i	0.0823537	+	0.519961i
$173$	19.1220	−	9.74315i	1.45382	−	0.740758i	0.464371	−	0.885641i	$-0.346281\pi$
$173$	19.1220	−	9.74315i	1.45382	−	0.740758i	0.989449	+	0.144883i	$0.0462805\pi$
$174$	−10.4838	+	10.4838i	−0.794775	+	0.794775i
$175$	−0.644144	−	19.4377i	−0.0486927	−	1.46935i
$176$	2.88728	−	2.88728i	0.217637	−	0.217637i
$177$	4.24505	−	13.0649i	0.319077	−	0.982019i
$178$	−5.48601	+	0.868899i	−0.411194	+	0.0651267i
$179$	3.11468	+	2.26295i	0.232802	+	0.169140i	0.698070	−	0.716029i	$-0.254042\pi$
$179$	3.11468	+	2.26295i	0.232802	+	0.169140i	−0.465269	+	0.885170i	$0.654042\pi$
$180$	−1.31283	+	0.696544i	−0.0978522	+	0.0519173i
$181$	−12.4255	−	17.1023i	−0.923582	−	1.27120i	−0.962311	−	0.271952i	$-0.912331\pi$
$181$	−12.4255	−	17.1023i	−0.923582	−	1.27120i	0.0387282	−	0.999250i	$-0.487669\pi$
$182$	−10.9949	+	8.70607i	−0.814998	+	0.645337i
$183$	0.814468	−	5.14235i	0.0602072	−	0.380133i
$184$	−2.17846	−	1.10998i	−0.160598	−	0.0818289i
$185$	−17.6964	−	8.65063i	−1.30107	−	0.636007i
$186$	6.36929	+	2.06951i	0.467019	+	0.151744i
$187$	2.63469	−	0.856062i	0.192667	−	0.0626014i
$188$	1.33881	+	4.12043i	0.0976426	+	0.300513i
$189$	15.4940	−	7.89459i	1.12702	−	0.574247i
$190$	4.14285	+	12.0666i	0.300554	+	0.875402i
$191$	6.81727	+	20.9814i	0.493280	+	1.51816i	0.819619	+	0.572908i	$0.194185\pi$
$191$	6.81727	+	20.9814i	0.493280	+	1.51816i	−0.326339	+	0.945253i	$0.605815\pi$
$192$	0.299466	−	1.89075i	0.0216121	−	0.136453i
$193$		−	15.0524i		−	1.08350i	−0.840540	−	0.541749i	$-0.817762\pi$
$193$		−	15.0524i		−	1.08350i	0.840540	−	0.541749i	$-0.182238\pi$
$194$	−5.36337	+	3.89672i	−0.385068	+	0.279768i
$195$	−5.61189	−	14.3773i	−0.401876	−	1.02958i
$196$	6.57692	+	4.77841i	0.469780	+	0.341315i
$197$	−10.8255	+	14.9000i	−0.771286	+	1.06158i	0.224905	+	0.974381i	$0.427793\pi$
$197$	−10.8255	+	14.9000i	−0.771286	+	1.06158i	−0.996191	+	0.0872031i	$0.972207\pi$
$198$	1.23206	+	2.41806i	0.0875587	+	0.171844i
$199$	13.8673			0.983025			0.491512	−	0.870871i	$-0.336444\pi$
$199$	13.8673			0.983025			0.491512	+	0.870871i	$0.336444\pi$
$200$	−3.94553	+	3.07129i	−0.278991	+	0.217173i
$201$	−1.70467	−	1.70467i	−0.120238	−	0.120238i
$202$	2.08310	−	6.41112i	0.146566	−	0.451085i
$203$	−17.7072	+	24.3719i	−1.24280	+	1.71057i
$204$	0.763401	−	1.05073i	0.0534488	−	0.0735660i
$205$	8.05752	+	23.4686i	0.562761	+	1.63911i
$206$	0.169564	−	1.07058i	0.0118141	−	0.0745910i
$207$	1.14904	−	1.14904i	0.0798639	−	0.0798639i
$208$	3.47228	+	0.971234i	0.240759	+	0.0673430i
$209$	22.1568	−	7.19917i	1.53261	−	0.497977i
$210$	−13.3061	+	10.0084i	−0.918212	+	0.690642i
$211$	5.30682	−	16.3327i	0.365337	−	1.12439i	−0.584433	−	0.811442i	$-0.698683\pi$
$211$	5.30682	−	16.3327i	0.365337	−	1.12439i	0.949770	−	0.312949i	$-0.101317\pi$
$212$	8.86438	+	4.51663i	0.608808	+	0.310203i
$213$	−9.54621	−	29.3802i	−0.654096	−	2.01310i
$214$	−0.255992	−	0.502413i	−0.0174993	−	0.0343442i
$215$	−15.4362	+	0.255700i	−1.05274	+	0.0174386i
$216$	−3.98338	−	2.02963i	−0.271034	−	0.138099i
$217$	13.4401	+	2.12870i	0.912372	+	0.144506i
$218$	4.08364	+	4.08364i	0.276579	+	0.276579i
$219$	0.285656	+	0.0452435i	0.0193029	+	0.00305727i
$220$	5.48831	+	7.29673i	0.370022	+	0.491945i
$221$	1.79986	+	1.65661i	0.121072	+	0.111436i
$222$	2.63801	+	16.6558i	0.177052	+	1.11786i
$223$	0.157217	−	0.483863i	0.0105280	−	0.0324019i	−0.945655	−	0.325173i	$-0.894577\pi$
$223$	0.157217	−	0.483863i	0.0105280	−	0.0324019i	0.956183	+	0.292771i	$0.0945774\pi$
$224$		−	3.88967i		−	0.259889i
$225$	−1.13103	−	3.12477i	−0.0754019	−	0.208318i
$226$	−11.4565	−	11.4565i	−0.762074	−	0.762074i
$227$	−12.4004	−	4.02914i	−0.823044	−	0.267423i	−0.132931	−	0.991125i	$-0.542439\pi$
$227$	−12.4004	−	4.02914i	−0.823044	−	0.267423i	−0.690112	+	0.723702i	$0.742439\pi$
$228$	6.41993	−	8.83627i	0.425170	−	0.585196i
$229$	−1.89918	−	11.9909i	−0.125501	−	0.792383i	−0.967494	−	0.252894i	$-0.918617\pi$
$229$	−1.89918	−	11.9909i	−0.125501	−	0.792383i	0.841993	−	0.539489i	$-0.181383\pi$
$230$	3.13976	−	4.47556i	0.207030	−	0.295110i
$231$	17.8711	+	24.5974i	1.17583	+	1.61839i
$232$	7.74495			0.508481
$233$	−11.5577	−	1.83056i	−0.757168	−	0.119924i	−0.234098	−	0.972213i	$-0.575214\pi$
$233$	−11.5577	−	1.83056i	−0.757168	−	0.119924i	−0.523071	+	0.852289i	$0.675214\pi$
$234$	−1.32707	+	1.99536i	−0.0867530	+	0.130441i
$235$	−9.54202	+	1.67376i	−0.622453	+	0.109184i
$236$	−6.39390	+	3.25785i	−0.416207	+	0.212068i
$237$	6.22004	−	12.2075i	0.404035	−	0.792964i
$238$	1.19806	−	2.35132i	0.0776587	−	0.152414i
$239$	11.9701	+	23.4926i	0.774280	+	1.51961i	0.852531	+	0.522676i	$0.175066\pi$
$239$	11.9701	+	23.4926i	0.774280	+	1.51961i	−0.0782511	+	0.996934i	$0.524934\pi$
$240$	4.09240	+	1.25516i	0.264163	+	0.0810200i
$241$	−20.2123	−	10.2987i	−1.30199	−	0.663397i	−0.341021	−	0.940056i	$-0.610773\pi$
$241$	−20.2123	−	10.2987i	−1.30199	−	0.663397i	−0.960968	+	0.276659i	$0.910773\pi$
$242$	4.58935	−	3.33436i	0.295015	−	0.214341i
$243$	4.80005	−	4.80005i	0.307924	−	0.307924i
$244$	−2.20031	+	1.59862i	−0.140860	+	0.102341i
$245$	−12.6392	+	13.0650i	−0.807492	+	0.834694i
$246$	12.4863	−	17.1859i	0.796095	−	1.09573i
$247$	15.1362	+	13.9315i	0.963090	+	0.886441i
$248$	−1.58824	−	3.11710i	−0.100853	−	0.197936i
$249$	9.54513	−	9.54513i	0.604898	−	0.604898i
$250$	−5.56430	−	9.69735i	−0.351917	−	0.613314i
$251$		−	19.5864i		−	1.23629i	−0.786066	−	0.618143i	$-0.787885\pi$
$251$		−	19.5864i		−	1.23629i	0.786066	−	0.618143i	$-0.212115\pi$
$252$	2.45867	+	0.798871i	0.154882	+	0.0503241i
$253$	−8.07663	−	5.86802i	−0.507773	−	0.368919i
$254$	0.0550219	+	0.347395i	0.00345238	+	0.0217975i
$255$	2.08728	+	2.01925i	0.130710	+	0.126450i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	12.5497	−	12.5497i	0.782827	−	0.782827i	−0.197480	−	0.980307i	$-0.563276\pi$
$257$	12.5497	−	12.5497i	0.782827	−	0.782827i	0.980307	+	0.197480i	$0.0632758\pi$
$258$	7.76871	+	10.6927i	0.483659	+	0.665699i
$259$	10.5882	+	32.5873i	0.657922	+	2.02487i
$260$	−3.23776	+	7.38356i	−0.200797	+	0.457909i
$261$	−1.59068	+	4.89561i	−0.0984606	+	0.303030i
$262$	−11.6351	+	3.78048i	−0.718821	+	0.233559i
$263$	11.4540	+	5.83610i	0.706283	+	0.359869i	0.769952	−	0.638102i	$-0.220280\pi$
$263$	11.4540	+	5.83610i	0.706283	+	0.359869i	−0.0636689	+	0.997971i	$0.520280\pi$
$264$	2.41547	−	7.43405i	0.148662	−	0.457534i
$265$	−12.7760	+	18.2115i	−0.784824	+	1.11872i
$266$	10.0752	−	19.7738i	0.617753	−	1.21241i
$267$	−8.60220	+	6.24987i	−0.526446	+	0.382486i
$268$			1.25933i			0.0769258i
$269$	−3.81965	−	5.25729i	−0.232888	−	0.320543i	0.676539	−	0.736407i	$-0.263479\pi$
$269$	−3.81965	−	5.25729i	−0.232888	−	0.320543i	−0.909427	+	0.415864i	$0.863479\pi$
$270$	5.74114	−	8.18369i	0.349395	−	0.498043i
$271$	24.1871	−	3.83086i	1.46926	−	0.232708i	0.630068	−	0.776540i	$-0.283027\pi$
$271$	24.1871	−	3.83086i	1.46926	−	0.232708i	0.839195	+	0.543831i	$0.183027\pi$
$272$	−0.670099	+	0.106133i	−0.0406307	+	0.00643527i
$273$	−11.1874	+	24.4052i	−0.677095	+	1.47707i
$274$			21.6248i			1.30640i
$275$	−17.8739	+	9.86615i	−1.07784	+	0.594951i
$276$	−4.68041			−0.281728
$277$	11.1948	+	21.9710i	0.672629	+	1.32011i	0.934830	+	0.355096i	$0.115552\pi$
$277$	11.1948	+	21.9710i	0.672629	+	1.32011i	−0.262200	+	0.965013i	$0.584448\pi$
$278$	−7.64418	−	5.55382i	−0.458467	−	0.333096i
$279$	2.29652	−	0.363734i	0.137489	−	0.0217762i
$280$	8.61184	+	1.21813i	0.514656	+	0.0727972i
$281$	−1.25793	+	7.94226i	−0.0750418	+	0.473796i	0.921337	+	0.388766i	$0.127098\pi$
$281$	−1.25793	+	7.94226i	−0.0750418	+	0.473796i	−0.996378	+	0.0850296i	$0.972902\pi$
$282$	5.86457	+	5.86457i	0.349230	+	0.349230i
$283$	29.0509	+	4.60121i	1.72690	+	0.273513i	0.939404	−	0.342812i	$-0.111379\pi$
$283$	29.0509	+	4.60121i	1.72690	+	0.273513i	0.787492	+	0.616325i	$0.211379\pi$
$284$	−7.32622	+	14.3785i	−0.434731	+	0.853208i
$285$	17.5532	+	16.9812i	1.03976	+	1.00588i
$286$	13.3832	+	6.13489i	0.791363	+	0.362764i
$287$	19.5956	−	38.4585i	1.15669	−	2.27013i
$288$	−0.205383	−	0.632103i	−0.0121023	−	0.0372470i
$289$	15.7302	+	5.11105i	0.925305	+	0.300650i
$290$	−2.42549	+	17.1475i	−0.142430	+	1.00694i
$291$	−5.76159	+	11.3078i	−0.337750	+	0.662872i
$292$	−0.0888030	−	0.122227i	−0.00519680	−	0.00715278i
$293$			7.86912i			0.459719i	0.973224	+	0.229859i	$0.0738266\pi$
$293$			7.86912i			0.459719i	−0.973224	+	0.229859i	$0.926173\pi$
$294$	15.3709	+	2.43452i	0.896451	+	0.141984i
$295$	−5.21060	−	15.1765i	−0.303373	−	0.883612i
$296$	5.17783	−	7.12667i	0.300955	−	0.414229i
$297$	−14.7683	−	10.7298i	−0.856946	−	0.622608i
$298$	−4.48960	+	2.28757i	−0.260076	+	0.132515i
$299$	1.01732	−	8.75647i	0.0588333	−	0.506400i
$300$	−4.06057	+	8.66762i	−0.234437	+	0.500425i
$301$	18.9895	+	18.9895i	1.09453	+	1.09453i
$302$	−1.18119	+	0.601847i	−0.0679700	+	0.0346324i
$303$	−2.01872	−	12.7457i	−0.115972	−	0.732220i
$304$	−5.63529	+	0.892542i	−0.323206	+	0.0511908i
$305$	−2.85032	−	5.37219i	−0.163209	−	0.307611i
$306$	0.0705396	−	0.445370i	0.00403248	−	0.0254601i
$307$	−26.5283			−1.51405			−0.757026	−	0.653385i	$-0.773348\pi$
$307$	−26.5283			−1.51405			−0.757026	+	0.653385i	$0.773348\pi$
$308$	2.48456	−	15.6869i	0.141571	−	0.893842i
$309$	−0.641206	−	1.97343i	−0.0364770	−	0.112265i
$310$	7.39873	−	2.54023i	0.420220	−	0.144275i
$311$	−17.0123	−	5.52763i	−0.964679	−	0.313443i	−0.216013	−	0.976391i	$-0.569305\pi$
$311$	−17.0123	−	5.52763i	−0.964679	−	0.313443i	−0.748666	+	0.662948i	$0.769305\pi$
$312$	6.76666	−	1.36109i	0.383087	−	0.0770567i
$313$	15.8187	+	8.06003i	0.894125	+	0.455580i	0.839770	−	0.542942i	$-0.182690\pi$
$313$	15.8187	+	8.06003i	0.894125	+	0.455580i	0.0543551	+	0.998522i	$0.482690\pi$
$314$	2.52497	+	4.95554i	0.142493	+	0.279657i
$315$	−2.53871	+	5.19339i	−0.143040	+	0.292614i
$316$	−6.80672	+	2.21164i	−0.382908	+	0.124414i
$317$	−14.7757	−	20.3369i	−0.829884	−	1.14224i	−0.987945	−	0.154807i	$-0.950524\pi$
$317$	−14.7757	−	20.3369i	−0.829884	−	1.14224i	0.158061	−	0.987429i	$-0.449476\pi$
$318$	19.0451			1.06799
$319$	31.2350	+	4.94714i	1.74883	+	0.276987i
$320$	−1.04801	−	1.97526i	−0.0585857	−	0.110421i
$321$	−0.873279	−	0.634474i	−0.0487417	−	0.0354129i
$322$	−9.39294	+	1.48770i	−0.523448	+	0.0829060i
$323$	−3.68147	−	1.19618i	−0.204843	−	0.0665574i
$324$	−10.5522			−0.586231
$325$	−15.3334	−	9.48080i	−0.850546	−	0.525900i
$326$	6.03153			0.334055
$327$	10.5144	+	3.41633i	0.581447	+	0.188924i
$328$	−10.9602	+	1.73592i	−0.605176	+	0.0958504i
$329$	13.6335	+	9.90529i	0.751637	+	0.546096i
$330$	15.7027	+	7.67604i	0.864407	+	0.422552i
$331$	3.20696	+	0.507932i	0.176270	+	0.0279185i	0.243946	−	0.969789i	$-0.421558\pi$
$331$	3.20696	+	0.507932i	0.176270	+	0.0279185i	−0.0676753	+	0.997707i	$0.521558\pi$
$332$	−7.05150			−0.387001
$333$	3.44136	+	4.73662i	0.188585	+	0.259565i
$334$	10.9746	−	3.56587i	0.600504	−	0.195116i
$335$	−2.78819	−	0.394385i	−0.152335	−	0.0215476i
$336$	−3.38045	−	6.63451i	−0.184419	−	0.361942i
$337$	19.8223	+	10.0999i	1.07979	+	0.550179i	0.901049	−	0.433718i	$-0.142798\pi$
$337$	19.8223	+	10.0999i	1.07979	+	0.550179i	0.178738	+	0.983897i	$0.442798\pi$
$338$	1.07565	+	12.9554i	0.0585077	+	0.704682i
$339$	−29.4977	−	9.58437i	−1.60209	−	0.520552i
$340$	−0.0251266	−	1.51686i	−0.00136268	−	0.0822631i
$341$	−4.41423	−	13.5856i	−0.239044	−	0.735702i
$342$	0.593212	−	3.74540i	0.0320773	−	0.202528i
$343$	4.39347			0.237225
$344$	1.08006	−	6.81922i	0.0582329	−	0.367668i
$345$	1.46577	−	10.3626i	0.0789143	−	0.557902i
$346$	−21.1969	+	3.35726i	−1.13955	+	0.180487i
$347$	1.53923	+	9.71833i	0.0826303	+	0.521707i	0.993935	+	0.109973i	$0.0350766\pi$
$347$	1.53923	+	9.71833i	0.0826303	+	0.521707i	−0.911304	+	0.411734i	$0.864923\pi$
$348$	13.2104	−	6.73101i	0.708150	−	0.360820i
$349$	17.3121	+	17.3121i	0.926696	+	0.926696i	0.997491	−	0.0707944i	$-0.0225534\pi$
$349$	17.3121	+	17.3121i	0.926696	+	0.926696i	−0.0707944	+	0.997491i	$0.522553\pi$
$350$	−5.39395	+	18.6854i	−0.288319	+	0.998775i
$351$	1.86020	−	16.0115i	0.0992903	−	0.854628i
$352$	−3.63818	+	1.85375i	−0.193916	+	0.0988050i
$353$	11.3776	+	8.26631i	0.605569	+	0.439971i	0.847851	−	0.530234i	$-0.177896\pi$
$353$	11.3776	+	8.26631i	0.605569	+	0.439971i	−0.242282	+	0.970206i	$0.577896\pi$
$354$	−8.07456	+	11.1137i	−0.429158	+	0.590685i
$355$	−29.5401	−	20.7234i	−1.56783	−	1.09988i
$356$	5.48601	+	0.868899i	0.290758	+	0.0460516i
$357$		−	5.05181i		−	0.267370i
$358$	−2.26295	−	3.11468i	−0.119600	−	0.164616i
$359$	2.22821	−	4.37312i	0.117601	−	0.230804i	−0.824701	−	0.565569i	$-0.808657\pi$
$359$	2.22821	−	4.37312i	0.117601	−	0.230804i	0.942302	+	0.334764i	$0.108657\pi$
$360$	1.46381	−	0.256767i	0.0771498	−	0.0135328i
$361$	−12.8898	−	4.18814i	−0.678409	−	0.220428i
$362$	6.53249	+	20.1049i	0.343340	+	1.05669i
$363$	4.93010	−	9.67587i	0.258763	−	0.507851i
$364$	13.1471	−	4.88234i	0.689096	−	0.255904i
$365$	0.298424	−	0.158334i	0.0156202	−	0.00828760i
$366$	−2.36368	+	4.63898i	−0.123551	+	0.242483i
$367$	−10.1485	−	1.60737i	−0.529748	−	0.0839038i	−0.114170	−	0.993461i	$-0.536421\pi$
$367$	−10.1485	−	1.60737i	−0.529748	−	0.0839038i	−0.415578	+	0.909557i	$0.636421\pi$
$368$	1.72884	+	1.72884i	0.0901218	+	0.0901218i
$369$	1.15375	−	7.28450i	0.0600619	−	0.379216i
$370$	14.1571	+	13.6957i	0.735993	+	0.712007i
$371$	38.2208	−	6.05358i	1.98433	−	0.314286i
$372$	−5.41804	−	3.93644i	−0.280912	−	0.204095i
$373$	−12.4856	−	24.5044i	−0.646480	−	1.26879i	−0.948889	−	0.315609i	$-0.897791\pi$
$373$	−12.4856	−	24.5044i	−0.646480	−	1.26879i	0.302410	−	0.953178i	$-0.402209\pi$
$374$	−2.77027			−0.143247
$375$	−17.9187	−	11.7047i	−0.925318	−	0.604426i
$376$		−	4.33247i		−	0.223430i
$377$	9.72152	+	26.1780i	0.500684	+	1.34823i
$378$	−17.1752	+	2.72029i	−0.883399	+	0.139917i
$379$	−37.2473	+	5.89939i	−1.91327	+	0.303031i	−0.995552	−	0.0942117i	$-0.969967\pi$
$379$	−37.2473	+	5.89939i	−1.91327	+	0.303031i	−0.917713	+	0.397243i	$0.869967\pi$
$380$	−0.211306	−	12.7562i	−0.0108398	−	0.654380i
$381$	0.395765	+	0.544723i	0.0202756	+	0.0279070i
$382$		−	22.0612i		−	1.12875i
$383$	−19.4954	+	14.1642i	−0.996167	+	0.723758i	−0.961263	−	0.275633i	$-0.911113\pi$
$383$	−19.4954	+	14.1642i	−0.996167	+	0.723758i	−0.0349041	+	0.999391i	$0.511113\pi$
$384$	−0.869084	+	1.70567i	−0.0443503	+	0.0870423i
$385$	33.9531	+	10.4135i	1.73041	+	0.530723i
$386$	−4.65146	+	14.3157i	−0.236753	+	0.728651i
$387$	4.08863	+	2.08326i	0.207837	+	0.105898i
$388$	6.30502	−	2.04863i	0.320089	−	0.104003i
$389$	0.960723	−	2.95680i	0.0487106	−	0.149916i	−0.923743	−	0.383014i	$-0.874886\pi$
$389$	0.960723	−	2.95680i	0.0487106	−	0.149916i	0.972453	+	0.233098i	$0.0748862\pi$
$390$	0.894379	+	15.4078i	0.0452886	+	0.780206i
$391$	0.512590	+	1.57759i	0.0259228	+	0.0797822i
$392$	−4.77841	−	6.57692i	−0.241346	−	0.332185i
$393$	−16.5602	+	16.5602i	−0.835351	+	0.835351i
$394$	14.9000	−	10.8255i	0.750653	−	0.545381i
$395$	−2.76496	−	15.7629i	−0.139120	−	0.793117i
$396$	−0.424539	−	2.68043i	−0.0213339	−	0.134697i
$397$	7.64938	+	5.55760i	0.383911	+	0.278928i	0.762956	−	0.646450i	$-0.223747\pi$
$397$	7.64938	+	5.55760i	0.383911	+	0.278928i	−0.379045	+	0.925378i	$0.623747\pi$
$398$	−13.1886	−	4.28522i	−0.661083	−	0.214799i
$399$		−	42.4839i		−	2.12685i
$400$	4.70150	−	1.70174i	0.235075	−	0.0850868i
$401$	−9.82060	+	9.82060i	−0.490417	+	0.490417i	−0.908438	−	0.418020i	$-0.862724\pi$
$401$	−9.82060	+	9.82060i	−0.490417	+	0.490417i	0.418020	+	0.908438i	$0.362724\pi$
$402$	1.09446	+	2.14800i	0.0545869	+	0.107133i
$403$	8.54224	−	9.28087i	0.425519	−	0.462313i
$404$	−3.96229	+	5.45362i	−0.197131	+	0.271328i
$405$	3.30463	−	23.3628i	0.164208	−	1.16091i
$406$	24.3719	−	17.7072i	1.20956	−	0.878793i
$407$	25.4342	−	25.4342i	1.26073	−	1.26073i
$408$	−1.05073	+	0.763401i	−0.0520190	+	0.0377940i
$409$	−25.4043	−	12.9442i	−1.25616	−	0.640047i	−0.306069	−	0.952009i	$-0.599014\pi$
$409$	−25.4043	−	12.9442i	−1.25616	−	0.640047i	−0.950095	+	0.311962i	$0.899014\pi$
$410$	−0.410973	−	24.8098i	−0.0202965	−	1.22527i
$411$	18.7938	+	36.8849i	0.927030	+	1.81940i
$412$	−0.492093	+	0.965787i	−0.0242437	+	0.0475809i
$413$	−12.6720	+	24.8701i	−0.623547	+	1.22378i
$414$	−1.44788	+	0.737730i	−0.0711592	+	0.0362574i
$415$	2.20832	−	15.6122i	0.108402	−	0.766374i
$416$	−3.00220	−	1.99669i	−0.147195	−	0.0978958i
$417$	−17.8652	−	2.82957i	−0.874864	−	0.138565i
$418$	−23.2970			−1.13949
$419$	−0.526979	−	0.725324i	−0.0257446	−	0.0354344i	0.795951	−	0.605361i	$-0.206971\pi$
$419$	−0.526979	−	0.725324i	−0.0257446	−	0.0354344i	−0.821695	+	0.569927i	$0.806971\pi$
$420$	15.7477	−	5.40668i	0.768407	−	0.263819i
$421$	2.22292	+	14.0350i	0.108339	+	0.684024i	0.980752	+	0.195256i	$0.0625536\pi$
$421$	2.22292	+	14.0350i	0.108339	+	0.684024i	−0.872414	+	0.488768i	$0.837446\pi$
$422$	−10.0942	+	13.8934i	−0.491377	+	0.676322i
$423$	2.73857	+	0.889815i	0.133154	+	0.0432643i
$424$	−7.03481	−	7.03481i	−0.341641	−	0.341641i
$425$	3.36623	+	0.419404i	0.163286	+	0.0203441i
$426$			30.8922i			1.49673i
$427$	−3.26905	+	10.0611i	−0.158200	+	0.486891i
$428$	0.0882089	+	0.556929i	0.00426374	+	0.0269202i
$429$	28.1590	−	1.16697i	1.35953	−	0.0563421i
$430$	14.7597	+	4.52686i	0.711776	+	0.218305i
$431$	8.76048	+	1.38752i	0.421978	+	0.0668347i	0.363812	−	0.931472i	$-0.381475\pi$
$431$	8.76048	+	1.38752i	0.421978	+	0.0668347i	0.0581653	+	0.998307i	$0.481475\pi$
$432$	3.16123	+	3.16123i	0.152095	+	0.152095i
$433$	−21.0492	−	3.33387i	−1.01156	−	0.160215i	−0.371413	−	0.928468i	$-0.621127\pi$
$433$	−21.0492	−	3.33387i	−1.01156	−	0.160215i	−0.640147	+	0.768252i	$0.721127\pi$
$434$	−12.1245	−	6.17773i	−0.581993	−	0.296540i
$435$	10.7656	+	31.3561i	0.516169	+	1.50341i
$436$	−2.62186	−	5.14569i	−0.125564	−	0.246434i
$437$	4.31070	+	13.2670i	0.206209	+	0.634645i
$438$	−0.257694	−	0.131302i	−0.0123131	−	0.00627384i
$439$	−5.69517	+	17.5279i	−0.271816	+	0.836563i	0.718229	+	0.695807i	$0.244953\pi$
$439$	−5.69517	+	17.5279i	−0.271816	+	0.836563i	−0.990044	+	0.140755i	$0.955047\pi$
$440$	−2.96488	−	8.63558i	−0.141345	−	0.411685i
$441$	5.13870	−	1.66966i	0.244700	−	0.0795078i
$442$	−1.19985	−	2.13172i	−0.0570708	−	0.101396i
$443$	13.2539	−	13.2539i	0.629713	−	0.629713i	−0.318283	−	0.947996i	$-0.603106\pi$
$443$	13.2539	−	13.2539i	0.629713	−	0.629713i	0.947996	+	0.318283i	$0.103106\pi$
$444$	2.63801	−	16.6558i	0.125195	−	0.790447i
$445$	−3.64183	+	11.8741i	−0.172639	+	0.562885i
$446$	−0.299044	+	0.411598i	−0.0141601	+	0.0194898i
$447$	−5.66971	+	7.80369i	−0.268168	+	0.369102i
$448$	−1.20197	+	3.69929i	−0.0567879	+	0.174775i
$449$	−12.6619	−	12.6619i	−0.597552	−	0.597552i	0.342109	−	0.939660i	$-0.388859\pi$
$449$	−12.6619	−	12.6619i	−0.597552	−	0.597552i	−0.939660	+	0.342109i	$0.888859\pi$
$450$	0.110066	+	3.32134i	0.00518855	+	0.156569i
$451$	−45.3108			−2.13360
$452$	7.35551	+	14.4360i	0.345974	+	0.679012i
$453$	−1.49167	+	2.05311i	−0.0700849	+	0.0964636i
$454$	10.5484	+	7.66387i	0.495062	+	0.359683i
$455$	6.69236	+	30.6371i	0.313743	+	1.43629i
$456$	−8.83627	+	6.41993i	−0.413796	+	0.300641i
$457$			13.8927i			0.649872i	0.945736	+	0.324936i	$0.105343\pi$
$457$			13.8927i			0.649872i	−0.945736	+	0.324936i	$0.894657\pi$
$458$	−1.89918	+	11.9909i	−0.0887427	+	0.560300i
$459$	0.937285	+	2.88467i	0.0437487	+	0.134645i
$460$	−4.36911	+	3.28627i	−0.203711	+	0.153223i
$461$	−36.1814	+	18.4353i	−1.68514	+	0.858620i	−0.694918	+	0.719089i	$0.744559\pi$
$461$	−36.1814	+	18.4353i	−1.68514	+	0.858620i	−0.990218	+	0.139531i	$0.955441\pi$
$462$	−9.39537	−	28.9160i	−0.437112	−	1.34529i
$463$	16.1061	−	5.23317i	0.748512	−	0.243206i	0.0901710	−	0.995926i	$-0.471259\pi$
$463$	16.1061	−	5.23317i	0.748512	−	0.243206i	0.658341	+	0.752720i	$0.271259\pi$
$464$	−7.36588	−	2.39332i	−0.341953	−	0.111107i
$465$	10.4122	−	10.7629i	0.482852	−	0.499118i
$466$	10.4263	+	5.31248i	0.482990	+	0.246096i
$467$	1.06486	−	6.72323i	0.0492756	−	0.311114i	−0.950724	−	0.310039i	$-0.899658\pi$
$467$	1.06486	−	6.72323i	0.0492756	−	0.311114i	0.999999	−	0.00107500i	$-0.000342184\pi$
$468$	1.87872	−	1.48762i	0.0868437	−	0.0687651i
$469$	2.87919	+	3.96287i	0.132949	+	0.182988i
$470$	9.59222	+	1.35680i	0.442456	+	0.0625847i
$471$	8.61357	+	6.25812i	0.396892	+	0.288359i
$472$	7.08769	−	1.12258i	0.326237	−	0.0516709i
$473$	8.71166	−	26.8117i	0.400563	−	1.23280i
$474$	−9.68794	+	9.68794i	−0.444982	+	0.444982i
$475$	28.3088	+	3.52704i	1.29890	+	0.161831i
$476$	−1.86602	+	1.86602i	−0.0855290	+	0.0855290i
$477$	5.89156	−	3.00190i	0.269756	−	0.137447i
$478$	−4.12461	−	26.0418i	−0.188655	−	1.19112i
$479$	−4.98097	−	31.4486i	−0.227586	−	1.43692i	−0.791540	−	0.611118i	$-0.790720\pi$
$479$	−4.98097	−	31.4486i	−0.227586	−	1.43692i	0.563953	−	0.825807i	$-0.309280\pi$
$480$	−3.50424	−	2.45835i	−0.159946	−	0.112208i
$481$	30.5875	+	8.55565i	1.39467	+	0.390104i
$482$	16.0406	+	16.0406i	0.730628	+	0.730628i
$483$	−14.7284	+	10.7008i	−0.670164	+	0.486902i
$484$	−5.39511	+	1.75298i	−0.245232	+	0.0796808i
$485$	2.56117	+	14.6011i	0.116297	+	0.663001i
$486$	−6.04842	+	3.08182i	−0.274362	+	0.139794i
$487$	13.8681	−	4.50602i	0.628424	−	0.204187i	0.0225471	−	0.999746i	$-0.492822\pi$
$487$	13.8681	−	4.50602i	0.628424	−	0.204187i	0.605877	+	0.795558i	$0.292822\pi$
$488$	2.58662	−	0.840444i	0.117091	−	0.0380451i
$489$	10.2878	−	5.24191i	0.465231	−	0.237047i
$490$	16.0580	−	8.51985i	0.725424	−	0.384887i
$491$	−1.36023	+	0.441967i	−0.0613865	+	0.0199457i	−0.339549	−	0.940588i	$-0.610275\pi$
$491$	−1.36023	+	0.441967i	−0.0613865	+	0.0199457i	0.278163	+	0.960534i	$0.410275\pi$
$492$	−17.1859	+	12.4863i	−0.774798	+	0.562924i
$493$	−3.71555	−	3.71555i	−0.167340	−	0.167340i
$494$	−10.0903	−	17.9270i	−0.453982	−	0.806573i
$495$	6.06751	−	0.100508i	0.272714	−	0.00451750i
$496$	0.547270	+	3.45533i	0.0245732	+	0.155149i
$497$	9.81925	+	61.9963i	0.440454	+	2.78092i
$498$	−12.0276	+	6.12835i	−0.538968	+	0.274618i
$499$	11.2486	−	11.2486i	0.503557	−	0.503557i	−0.408984	−	0.912541i	$-0.634117\pi$
$499$	11.2486	−	11.2486i	0.503557	−	0.503557i	0.912541	+	0.408984i	$0.134117\pi$
$500$	2.29532	+	10.9422i	0.102650	+	0.489350i
$501$	15.6201	−	15.6201i	0.697853	−	0.697853i
$502$	−6.05254	+	18.6278i	−0.270138	+	0.831400i
$503$	37.8822	−	5.99996i	1.68909	−	0.267525i	0.763430	−	0.645891i	$-0.223514\pi$
$503$	37.8822	−	5.99996i	1.68909	−	0.267525i	0.925656	+	0.378366i	$0.123514\pi$
$504$	−2.09147	−	1.51954i	−0.0931615	−	0.0676858i
$505$	−10.8336	−	10.4805i	−0.482089	−	0.466378i
$506$	5.86802	+	8.07663i	0.260865	+	0.359050i
$507$	13.0941	+	21.1629i	0.581528	+	0.939877i
$508$	0.0550219	−	0.347395i	0.00244120	−	0.0154131i
$509$	−30.8560	−	15.7219i	−1.36767	−	0.696863i	−0.392797	−	0.919625i	$-0.628493\pi$
$509$	−30.8560	−	15.7219i	−1.36767	−	0.696863i	−0.974873	+	0.222763i	$0.928493\pi$
$510$	−1.36113	−	2.56543i	−0.0602720	−	0.113599i
$511$	−0.558892	−	0.181595i	−0.0247239	−	0.00803329i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	7.88223	+	24.2590i	0.348009	+	1.07106i
$514$	−15.8135	+	8.05738i	−0.697504	+	0.355396i
$515$	−1.98417	−	1.39196i	−0.0874330	−	0.0613373i
$516$	−4.08425	−	12.5700i	−0.179799	−	0.553365i
$517$	2.76740	−	17.4727i	0.121710	−	0.768448i
$518$		−	34.2643i		−	1.50549i
$519$	−33.2373	+	24.1483i	−1.45895	+	1.05999i
$520$	5.36093	−	6.02166i	0.235093	−	0.264067i
$521$	27.6680	+	20.1020i	1.21216	+	0.880683i	0.995425	−	0.0955488i	$-0.0304606\pi$
$521$	27.6680	+	20.1020i	1.21216	+	0.880683i	0.216731	+	0.976231i	$0.430461\pi$
$522$	3.02565	−	4.16445i	0.132429	−	0.182273i
$523$	−11.8866	−	23.3287i	−0.519764	−	1.02009i	−0.990460	−	0.137799i	$-0.955997\pi$
$523$	−11.8866	−	23.3287i	−0.519764	−	1.02009i	0.470696	−	0.882296i	$-0.344003\pi$
$524$	12.2339			0.534440
$525$	7.03884	+	36.5590i	0.307200	+	1.59556i
$526$	−9.08994	−	9.08994i	−0.396340	−	0.396340i
$527$	−0.733451	+	2.25733i	−0.0319496	+	0.0983308i
$528$	−4.59449	+	6.32378i	−0.199950	+	0.275207i
$529$	−10.0054	+	13.7713i	−0.435019	+	0.598752i
$530$	17.7784	−	13.3722i	0.772243	−	0.580850i
$531$	−0.746103	+	4.71071i	−0.0323781	+	0.204427i
$532$	−15.6926	+	15.6926i	−0.680359	+	0.680359i
$533$	−19.6248	−	34.8666i	−0.850043	−	1.51024i
$534$	10.1125	−	3.28575i	0.437611	−	0.142188i
$535$	−1.26068	+	0.0208831i	−0.0545040	+	0.000902855i
$536$	0.389154	−	1.19769i	0.0168089	−	0.0517325i
$537$	−6.56677	−	3.34593i	−0.283377	−	0.144388i
$538$	2.00811	+	6.18032i	0.0865756	+	0.266452i
$539$	−15.0701	−	29.5767i	−0.649114	−	1.27396i
$540$	−7.98905	+	6.00904i	−0.343794	+	0.258588i
$541$	5.71604	+	2.91247i	0.245752	+	0.125217i	0.572529	−	0.819885i	$-0.305963\pi$
$541$	5.71604	+	2.91247i	0.245752	+	0.125217i	−0.326777	+	0.945102i	$0.605963\pi$
$542$	−24.1871	−	3.83086i	−1.03893	−	0.164550i
$543$	28.6152	+	28.6152i	1.22799	+	1.22799i
$544$	0.670099	+	0.106133i	0.0287303	+	0.00455043i
$545$	12.2138	−	4.19339i	0.523182	−	0.179625i
$546$	18.1815	−	19.7536i	0.778097	−	0.845378i
$547$	−2.84708	−	17.9758i	−0.121733	−	0.768589i	−0.970727	−	0.240187i	$-0.922791\pi$
$547$	−2.84708	−	17.9758i	−0.121733	−	0.768589i	0.848994	−	0.528402i	$-0.177209\pi$
$548$	6.68244	−	20.5664i	0.285460	−	0.878554i
$549$			1.80762i			0.0771475i
$550$	20.0479	−	3.85991i	0.854847	−	0.164587i
$551$	−31.2464	−	31.2464i	−1.33114	−	1.33114i
$552$	4.45134	+	1.44633i	0.189461	+	0.0615598i
$553$	−16.3630	+	22.5217i	−0.695825	+	0.957721i
$554$	−3.85746	−	24.3550i	−0.163888	−	1.03475i
$555$	36.0502	+	11.0567i	1.53024	+	0.469332i
$556$	5.55382	+	7.64418i	0.235535	+	0.324185i
$557$	−6.95857			−0.294844			−0.147422	−	0.989074i	$-0.547098\pi$
$557$	−6.95857			−0.294844			−0.147422	+	0.989074i	$0.547098\pi$
$558$	−2.29652	−	0.363734i	−0.0972196	−	0.0153981i
$559$	24.4047	−	4.90894i	1.03221	−	0.207626i
$560$	−7.81392	−	3.81972i	−0.330198	−	0.161412i
$561$	−4.72519	+	2.40760i	−0.199497	+	0.101649i
$562$	3.65066	−	7.16482i	0.153994	−	0.302230i
$563$	−6.82574	+	13.3963i	−0.287671	+	0.564585i	−0.988941	−	0.148310i	$-0.952617\pi$
$563$	−6.82574	+	13.3963i	−0.287671	+	0.564585i	0.701270	+	0.712895i	$0.252617\pi$
$564$	−3.76529	−	7.38979i	−0.158547	−	0.311166i
$565$	−34.2653	+	11.7644i	−1.44155	+	0.494931i
$566$	−26.2072	−	13.3532i	−1.10157	−	0.561278i
$567$	−33.2056	+	24.1253i	−1.39451	+	1.01317i
$568$	11.4109	−	11.4109i	0.478789	−	0.478789i
$569$	−20.4965	+	14.8916i	−0.859259	+	0.624288i	−0.927683	−	0.373368i	$-0.878203\pi$
$569$	−20.4965	+	14.8916i	−0.859259	+	0.624288i	0.0684244	+	0.997656i	$0.478203\pi$
$570$	−11.4466	−	21.5743i	−0.479447	−	0.903648i
$571$	−6.55592	+	9.02345i	−0.274357	+	0.377620i	−0.923855	−	0.382744i	$-0.874979\pi$
$571$	−6.55592	+	9.02345i	−0.274357	+	0.377620i	0.649498	+	0.760364i	$0.274979\pi$
$572$	−10.8324	−	9.97025i	−0.452924	−	0.416877i
$573$	−19.1730	−	37.6291i	−0.800964	−	1.57198i
$574$	−30.5208	+	30.5208i	−1.27391	+	1.27391i
$575$	−5.90762	−	10.7025i	−0.246365	−	0.446326i
$576$			0.664633i			0.0276930i
$577$	−15.5914	−	5.06596i	−0.649079	−	0.210899i	−0.0340710	−	0.999419i	$-0.510847\pi$
$577$	−15.5914	−	5.06596i	−0.649079	−	0.210899i	−0.615008	+	0.788521i	$0.710847\pi$
$578$	−13.3809	−	9.72179i	−0.556572	−	0.404373i
$579$	4.50770	+	28.4605i	0.187333	+	1.18278i
$580$	7.60566	−	15.5588i	0.315808	−	0.646042i
$581$	−22.1897	+	16.1218i	−0.920585	+	0.668844i
$582$	8.97389	−	8.97389i	0.371980	−	0.371980i
$583$	−23.8776	−	32.8646i	−0.988907	−	1.36111i
$584$	0.0466865	+	0.143686i	0.00193190	+	0.00594578i
$585$	2.70527	+	4.62541i	0.111849	+	0.191237i
$586$	2.43169	−	7.48397i	0.100452	−	0.309160i
$587$	13.8544	−	4.50158i	0.571834	−	0.185800i	−0.00880497	−	0.999961i	$-0.502803\pi$
$587$	13.8544	−	4.50158i	0.571834	−	0.185800i	0.580639	+	0.814161i	$0.302803\pi$
$588$	−13.8663	−	7.06524i	−0.571837	−	0.291366i
$589$	−6.16805	+	18.9833i	−0.254150	+	0.782194i
$590$	0.265766	+	16.0439i	0.0109414	+	0.660517i
$591$	16.0063	−	31.4142i	0.658412	−	1.29221i
$592$	−7.12667	+	5.17783i	−0.292904	+	0.212808i
$593$		−	28.7290i		−	1.17976i	−0.807492	−	0.589879i	$-0.799176\pi$
$593$		−	28.7290i		−	1.17976i	0.807492	−	0.589879i	$-0.200824\pi$
$594$	10.7298	+	14.7683i	0.440250	+	0.605952i
$595$	−3.54704	−	4.71581i	−0.145415	−	0.193329i
$596$	4.97677	−	0.788242i	0.203856	−	0.0322877i
$597$	−26.2196	+	4.15278i	−1.07310	+	0.169962i
$598$	−3.67343	+	8.01353i	−0.150218	+	0.327698i
$599$		−	7.24455i		−	0.296004i	−0.988987	−	0.148002i	$-0.952716\pi$
$599$		−	7.24455i		−	0.296004i	0.988987	−	0.148002i	$-0.0472843\pi$
$600$	6.54027	−	6.98861i	0.267006	−	0.285309i
$601$	−11.7289			−0.478432			−0.239216	−	0.970966i	$-0.576890\pi$
$601$	−11.7289			−0.478432			−0.239216	+	0.970966i	$0.576890\pi$
$602$	−12.1920	−	23.9281i	−0.496908	−	0.975237i
$603$	0.677140	+	0.491971i	0.0275753	+	0.0200346i
$604$	1.30936	−	0.207382i	0.0532772	−	0.00843827i
$605$	−2.19155	−	12.4939i	−0.0890992	−	0.507950i
$606$	−2.01872	+	12.7457i	−0.0820047	+	0.517757i
$607$	2.49552	+	2.49552i	0.101290	+	0.101290i	0.755936	−	0.654646i	$-0.227182\pi$
$607$	2.49552	+	2.49552i	0.101290	+	0.101290i	−0.654646	+	0.755936i	$0.727182\pi$
$608$	5.63529	+	0.892542i	0.228541	+	0.0361974i
$609$	26.1814	−	51.3839i	1.06092	−	2.08218i
$610$	1.05071	+	5.99005i	0.0425421	+	0.242530i
$611$	14.6438	−	5.43816i	0.592424	−	0.220004i
$612$	−0.204714	+	0.401774i	−0.00827507	+	0.0162407i
$613$	−6.95283	−	21.3986i	−0.280822	−	0.864282i	−0.987620	−	0.156866i	$-0.949861\pi$
$613$	−6.95283	−	21.3986i	−0.280822	−	0.864282i	0.706798	−	0.707416i	$-0.250139\pi$
$614$	25.2299	+	8.19771i	1.01820	+	0.330833i
$615$	−22.2628	−	41.9603i	−0.897724	−	1.69200i
$616$	−7.21046	+	14.1513i	−0.290518	+	0.570173i
$617$	1.13165	+	1.55758i	0.0455583	+	0.0627057i	0.831188	−	0.555991i	$-0.187661\pi$
$617$	1.13165	+	1.55758i	0.0455583	+	0.0627057i	−0.785630	+	0.618697i	$0.787661\pi$
$618$			2.07499i			0.0834682i
$619$	−36.9288	−	5.84895i	−1.48429	−	0.235089i	−0.638924	−	0.769270i	$-0.720620\pi$
$619$	−36.9288	−	5.84895i	−1.48429	−	0.235089i	−0.845370	+	0.534181i	$0.820620\pi$
$620$	−7.82159	+	0.129564i	−0.314122	+	0.00520342i
$621$	6.42478	−	8.84295i	0.257817	−	0.354855i
$622$	14.4715	+	10.5142i	0.580255	+	0.421580i
$623$	19.2500	−	9.80836i	0.771234	−	0.392963i
$624$	−6.85607	−	0.796536i	−0.274463	−	0.0318870i
$625$	−24.9452	+	1.65513i	−0.997806	+	0.0662052i
$626$	−12.5538	−	12.5538i	−0.501750	−	0.501750i
$627$	−39.7371	+	20.2471i	−1.58695	+	0.808589i
$628$	−0.870047	−	5.49326i	−0.0347186	−	0.219205i
$629$	−5.90294	+	0.934933i	−0.235366	+	0.0372782i
$630$	4.01930	−	4.15470i	0.160133	−	0.165527i
$631$	−0.587195	+	3.70740i	−0.0233759	+	0.147589i	−0.996616	−	0.0822025i	$-0.973805\pi$
$631$	−0.587195	+	3.70740i	−0.0233759	+	0.147589i	0.973240	+	0.229792i	$0.0738046\pi$
$632$	7.15701			0.284690
$633$	−5.14280	+	32.4704i	−0.204408	+	1.29058i
$634$	7.76802	+	23.9075i	0.308508	+	0.949489i
$635$	0.751910	+	0.230614i	0.0298386	+	0.00915163i
$636$	−18.1129	−	5.88525i	−0.718225	−	0.233365i
$637$	16.2321	−	24.4065i	0.643141	−	0.967020i
$638$	−28.1775	−	14.3572i	−1.11556	−	0.568406i
$639$	4.86925	+	9.55644i	0.192624	+	0.378047i
$640$	0.386329	+	2.20244i	0.0152710	+	0.0870592i
$641$	−17.6506	+	5.73504i	−0.697158	+	0.226520i	−0.636092	−	0.771613i	$-0.719450\pi$
$641$	−17.6506	+	5.73504i	−0.697158	+	0.226520i	−0.0610664	+	0.998134i	$0.519450\pi$
$642$	0.634474	+	0.873279i	0.0250407	+	0.0344656i
$643$	−15.6297			−0.616376			−0.308188	−	0.951325i	$-0.599723\pi$
$643$	−15.6297			−0.616376			−0.308188	+	0.951325i	$0.599723\pi$
$644$	9.39294	+	1.48770i	0.370134	+	0.0586234i
$645$	29.1095	−	5.10608i	1.14618	−	0.201052i
$646$	3.13165	+	2.27528i	0.123213	+	0.0895195i
$647$	−3.98190	+	0.630671i	−0.156545	+	0.0247942i	−0.234215	−	0.972185i	$-0.575252\pi$
$647$	−3.98190	+	0.630671i	−0.156545	+	0.0247942i	0.0776702	+	0.996979i	$0.475252\pi$
$648$	10.0357	+	3.26080i	0.394240	+	0.128096i
$649$	29.3014			1.15018
$650$	11.6532	+	13.7551i	0.457078	+	0.539518i
$651$	−26.0494			−1.02096
$652$	−5.73632	−	1.86384i	−0.224652	−	0.0729938i
$653$	32.7342	−	5.18459i	1.28099	−	0.202889i	0.521411	−	0.853306i	$-0.325406\pi$
$653$	32.7342	−	5.18459i	1.28099	−	0.202889i	0.759577	+	0.650417i	$0.225406\pi$
$654$	−8.94408	−	6.49825i	−0.349741	−	0.254102i
$655$	−3.83130	+	27.0862i	−0.149701	+	1.05835i
$656$	10.9602	+	1.73592i	0.427924	+	0.0677765i
$657$	−0.100413			−0.00391749
$658$	−9.90529	−	13.6335i	−0.386148	−	0.531488i
$659$	32.3279	−	10.5040i	1.25932	−	0.409177i	0.398067	−	0.917357i	$-0.369681\pi$
$659$	32.3279	−	10.5040i	1.25932	−	0.409177i	0.861251	+	0.508179i	$0.169681\pi$
$660$	−12.5622	−	12.1528i	−0.488982	−	0.473046i
$661$	−16.6325	−	32.6431i	−0.646929	−	1.26967i	−0.948666	−	0.316279i	$-0.897566\pi$
$661$	−16.6325	−	32.6431i	−0.646929	−	1.26967i	0.301737	−	0.953391i	$-0.402434\pi$
$662$	−2.89304	−	1.47408i	−0.112441	−	0.0572916i
$663$	−3.89919	−	2.59325i	−0.151432	−	0.100714i
$664$	6.70637	+	2.17903i	0.260258	+	0.0845629i
$665$	−29.8293	−	39.6582i	−1.15673	−	1.53788i
$666$	−1.80923	−	5.56823i	−0.0701061	−	0.215765i
$667$	−2.96224	+	18.7028i	−0.114698	+	0.724176i
$668$	−11.5394			−0.446472
$669$	−0.152357	+	0.961947i	−0.00589048	+	0.0371910i
$670$	2.52986	+	1.23668i	0.0977368	+	0.0477771i
$671$	10.9686	−	1.73725i	0.423437	−	0.0670658i
$672$	1.16482	+	7.35441i	0.0449341	+	0.283702i
$673$	−30.3373	+	15.4576i	−1.16942	+	0.595848i	−0.927271	−	0.374392i	$-0.877851\pi$
$673$	−30.3373	+	15.4576i	−1.16942	+	0.595848i	−0.242146	+	0.970240i	$0.577851\pi$
$674$	−15.7310	−	15.7310i	−0.605937	−	0.605937i
$675$	−10.8023	−	19.5698i	−0.415779	−	0.753243i
$676$	2.98044	−	12.6537i	0.114632	−	0.486682i
$677$	0.724748	−	0.369278i	0.0278543	−	0.0141925i	−0.440008	−	0.897994i	$-0.645024\pi$
$677$	0.724748	−	0.369278i	0.0278543	−	0.0141925i	0.467862	+	0.883801i	$0.345024\pi$
$678$	25.0922	+	18.2306i	0.963661	+	0.700140i
$679$	15.1569	−	20.8617i	0.581670	−	0.800600i
$680$	−0.444838	+	1.45038i	−0.0170587	+	0.0556196i
$681$	24.6527	+	3.90461i	0.944694	+	0.149625i
$682$			14.2848i			0.546992i
$683$	−0.564313	−	0.776711i	−0.0215929	−	0.0297200i	0.798084	−	0.602546i	$-0.205847\pi$
$683$	−0.564313	−	0.776711i	−0.0215929	−	0.0297200i	−0.819677	+	0.572826i	$0.805847\pi$
$684$	−1.72157	+	3.37877i	−0.0658259	+	0.129191i
$685$	43.4419	+	21.2359i	1.65983	+	0.811383i
$686$	−4.17844	−	1.35766i	−0.159533	−	0.0518356i
$687$	7.18176	+	22.1032i	0.274001	+	0.843289i
$688$	−3.13445	+	6.15171i	−0.119500	+	0.234532i
$689$	14.9476	−	32.6079i	0.569457	−	1.24226i
$690$	−4.59624	+	9.40244i	−0.174976	+	0.357945i
$691$	−15.5342	+	30.4875i	−0.590948	+	1.15980i	0.380993	+	0.924578i	$0.375582\pi$
$691$	−15.5342	+	30.4875i	−0.590948	+	1.15980i	−0.971941	+	0.235223i	$0.924418\pi$
$692$	21.1969	+	3.35726i	0.805786	+	0.127624i
$693$	−7.46419	−	7.46419i	−0.283541	−	0.283541i
$694$	1.53923	−	9.71833i	0.0584284	−	0.368903i
$695$	−18.6637	+	9.90239i	−0.707956	+	0.375619i
$696$	−14.6438	+	2.31935i	−0.555072	+	0.0879147i
$697$	6.09081	+	4.42523i	0.230706	+	0.167618i
$698$	−11.1151	−	21.8145i	−0.420711	−	0.825693i
$699$	22.4009			0.847280
$700$	10.9041	−	16.1040i	0.412135	−	0.608675i
$701$			18.9933i			0.717365i	0.933460	+	0.358683i	$0.116774\pi$
$701$			18.9933i			0.717365i	−0.933460	+	0.358683i	$0.883226\pi$
$702$	−6.71697	+	14.6530i	−0.253516	+	0.553040i
$703$	−49.6415	+	7.86245i	−1.87227	+	0.296538i
$704$	4.03296	−	0.638758i	0.151998	−	0.0240741i
$705$	17.5404	−	6.02218i	0.660609	−	0.226809i
$706$	−8.26631	−	11.3776i	−0.311107	−	0.428202i
$707$			26.2205i			0.986122i
$708$	11.1137	−	8.07456i	0.417677	−	0.303460i
$709$	−0.217945	+	0.427742i	−0.00818511	+	0.0160642i	−0.895063	−	0.445940i	$-0.852869\pi$
$709$	−0.217945	+	0.427742i	−0.00818511	+	0.0160642i	0.886878	+	0.462004i	$0.152869\pi$
$710$	21.6904	+	28.8375i	0.814027	+	1.08225i
$711$	−1.46993	+	4.52397i	−0.0551265	+	0.169662i
$712$	−4.94900	−	2.52164i	−0.185472	−	0.0945026i
$713$	8.13476	−	2.64314i	0.304649	−	0.0989865i
$714$	−1.56109	+	4.80456i	−0.0584225	+	0.179806i
$715$	25.4668	−	20.8608i	0.952404	−	0.780148i
$716$	1.18970	+	3.66152i	0.0444612	+	0.136838i
$717$	−29.6677	−	40.8341i	−1.10796	−	1.52498i
$718$	−3.47053	+	3.47053i	−0.129519	+	0.129519i
$719$	−31.2418	+	22.6985i	−1.16512	+	0.846511i	−0.990417	−	0.138110i	$-0.955897\pi$
$719$	−31.2418	+	22.6985i	−1.16512	+	0.846511i	−0.174705	+	0.984621i	$0.555897\pi$
$720$	−1.47152	−	0.208144i	−0.0548402	−	0.00775705i
$721$	0.659546	+	4.16421i	0.0245628	+	0.155083i
$722$	10.9647	+	7.96631i	0.408063	+	0.296475i
$723$	41.3006	+	13.4194i	1.53599	+	0.499072i
$724$		−	21.1396i		−	0.785646i
$725$	32.0657	+	21.7117i	1.19089	+	0.806352i
$726$	−7.67881	+	7.67881i	−0.284987	+	0.284987i
$727$	−19.3657	−	38.0072i	−0.718232	−	1.40961i	−0.904224	−	0.427059i	$-0.859550\pi$
$727$	−19.3657	−	38.0072i	−0.718232	−	1.40961i	0.185991	−	0.982551i	$-0.440450\pi$
$728$	−14.0124	+	0.580705i	−0.519333	+	0.0215223i
$729$	10.9689	−	15.0975i	0.406257	−	0.559165i
$730$	−0.332746	+	0.0583669i	−0.0123155	+	0.00216026i
$731$	−3.78958	+	2.75329i	−0.140163	+	0.101834i
$732$	3.68152	−	3.68152i	0.136073	−	0.136073i
$733$	31.8055	−	23.1080i	1.17476	−	0.853515i	0.183191	−	0.983077i	$-0.441357\pi$
$733$	31.8055	−	23.1080i	1.17476	−	0.853515i	0.991571	+	0.129563i	$0.0413574\pi$
$734$	9.15510	+	4.66476i	0.337921	+	0.172179i
$735$	19.9852	−	28.4878i	0.737164	−	1.05079i
$736$	−1.10998	−	2.17846i	−0.0409145	−	0.0802991i
$737$	2.33448	−	4.58167i	0.0859916	−	0.168768i
$738$	−3.34832	+	6.57145i	−0.123253	+	0.241898i
$739$	18.7224	−	9.53955i	0.688716	−	0.350918i	−0.0743563	−	0.997232i	$-0.523690\pi$
$739$	18.7224	−	9.53955i	0.688716	−	0.350918i	0.763072	+	0.646314i	$0.223690\pi$
$740$	−9.23200	−	17.4002i	−0.339375	−	0.639644i
$741$	−32.7908	−	21.8083i	−1.20460	−	0.801149i
$742$	−38.2208	−	6.05358i	−1.40313	−	0.222234i
$743$	14.7474			0.541031			0.270516	−	0.962716i	$-0.412806\pi$
$743$	14.7474			0.541031			0.270516	+	0.962716i	$0.412806\pi$
$744$	3.93644	+	5.41804i	0.144317	+	0.198635i
$745$	0.186613	+	11.2656i	0.00683698	+	0.412738i
$746$	4.30224	+	27.1633i	0.157516	+	0.994519i
$747$	−2.75475	+	3.79159i	−0.100791	+	0.138727i
$748$	2.63469	+	0.856062i	0.0963337	+	0.0313007i
$749$	1.55088	+	1.55088i	0.0566678	+	0.0566678i
$750$	13.4248	+	16.6690i	0.490203	+	0.608665i
$751$			25.8314i			0.942602i	0.881972	+	0.471301i	$0.156215\pi$
$751$			25.8314i			0.942602i	−0.881972	+	0.471301i	$0.843785\pi$
$752$	−1.33881	+	4.12043i	−0.0488213	+	0.150257i
$753$	5.86547	+	37.0332i	0.213750	+	1.34956i
$754$	−1.15628	−	27.9009i	−0.0421091	−	1.01609i
$755$	0.0490970	+	2.96391i	0.00178682	+	0.107868i
$756$	17.1752	+	2.72029i	0.624658	+	0.0989361i
$757$	17.4682	+	17.4682i	0.634894	+	0.634894i	0.949291	−	0.314397i	$-0.101802\pi$
$757$	17.4682	+	17.4682i	0.634894	+	0.634894i	−0.314397	+	0.949291i	$0.601802\pi$
$758$	37.2473	+	5.89939i	1.35288	+	0.214276i
$759$	17.0282	+	8.67630i	0.618084	+	0.314930i
$760$	−3.74092	+	12.1972i	−0.135697	+	0.442438i
$761$	21.4915	+	42.1794i	0.779065	+	1.52900i	0.847169	+	0.531324i	$0.178305\pi$
$761$	21.4915	+	42.1794i	0.779065	+	1.52900i	−0.0681036	+	0.997678i	$0.521695\pi$
$762$	−0.208066	−	0.640361i	−0.00753743	−	0.0231978i
$763$	−20.0150	−	10.1982i	−0.724593	−	0.369198i
$764$	−6.81727	+	20.9814i	−0.246640	+	0.759081i
$765$	−0.825428	−	0.579067i	−0.0298434	−	0.0209362i
$766$	22.9182	−	7.44657i	0.828068	−	0.269056i
$767$	12.6909	+	22.5474i	0.458240	+	0.814139i
$768$	1.35363	−	1.35363i	0.0488449	−	0.0488449i
$769$	−2.34328	+	14.7949i	−0.0845009	+	0.533518i	0.908732	+	0.417380i	$0.137051\pi$
$769$	−2.34328	+	14.7949i	−0.0845009	+	0.533518i	−0.993233	+	0.116138i	$0.962949\pi$
$770$	−29.0733	−	20.3960i	−1.04773	−	0.735019i
$771$	−19.9701	+	27.4865i	−0.719207	+	0.989904i
$772$	8.84760	−	12.1777i	0.318432	−	0.438284i
$773$	4.92374	−	15.1537i	0.177095	−	0.545041i	−0.822628	−	0.568579i	$-0.807493\pi$
$773$	4.92374	−	15.1537i	0.177095	−	0.545041i	0.999723	+	0.0235383i	$0.00749317\pi$
$774$	−3.24475	−	3.24475i	−0.116630	−	0.116630i
$775$	2.16263	−	17.3578i	0.0776841	−	0.623510i
$776$	−6.62949			−0.237985
$777$	−29.7786	−	58.4437i	−1.06830	−	2.09666i
$778$	−1.82740	+	2.51521i	−0.0655156	+	0.0901745i
$779$	51.2215	+	37.2146i	1.83520	+	1.33335i
$780$	3.91068	−	14.9301i	0.140025	−	0.534583i
$781$	53.3083	−	38.7307i	1.90752	−	1.38589i
$782$		−	1.65878i		−	0.0593177i
$783$	−5.41653	+	34.1986i	−0.193571	+	1.22216i
$784$	2.51216	+	7.73164i	0.0897200	+	0.276130i
$785$	12.4347	−	0.205980i	0.443814	−	0.00735174i
$786$	20.8670	−	10.6323i	0.744303	−	0.379241i
$787$	12.3713	+	38.0749i	0.440989	+	1.35722i	0.886823	+	0.462109i	$0.152907\pi$
$787$	12.3713	+	38.0749i	0.440989	+	1.35722i	−0.445834	+	0.895116i	$0.647093\pi$
$788$	−17.5160	+	5.69131i	−0.623983	+	0.202744i
$789$	−23.4044	−	7.60455i	−0.833218	−	0.270729i
$790$	−2.24137	+	15.8458i	−0.0797442	+	0.563769i
$791$	56.1513	+	28.6105i	1.99651	+	1.01727i
$792$	−0.424539	+	2.68043i	−0.0150853	+	0.0952451i
$793$	6.08745	+	7.68786i	0.216172	+	0.273004i
$794$	−5.55760	−	7.64938i	−0.197232	−	0.271466i
$795$	18.7026	−	38.2595i	0.663312	−	1.35692i
$796$	11.2189	+	8.15098i	0.397642	+	0.288904i
$797$	−3.42447	+	0.542383i	−0.121301	+	0.0192122i	−0.216790	−	0.976218i	$-0.569559\pi$
$797$	−3.42447	+	0.542383i	−0.121301	+	0.0192122i	0.0954887	+	0.995431i	$0.469559\pi$
$798$	−13.1282	+	40.4046i	−0.464735	+	1.43031i
$799$	−2.07845	+	2.07845i	−0.0735303	+	0.0735303i
$800$	−4.99726	+	0.165604i	−0.176680	+	0.00585498i
$801$	2.61038	−	2.61038i	0.0922332	−	0.0922332i
$802$	12.3747	−	6.30521i	0.436965	−	0.222645i
$803$	0.0965039	+	0.609302i	0.00340555	+	0.0215018i
$804$	−0.377126	−	2.38108i	−0.0133002	−	0.0839743i
$805$	−6.23539	+	20.3303i	−0.219769	+	0.716550i
$806$	−10.9921	+	6.18693i	−0.387180	+	0.217925i
$807$	8.79639	+	8.79639i	0.309648	+	0.309648i
$808$	5.45362	−	3.96229i	0.191858	−	0.139393i
$809$	−30.5484	+	9.92578i	−1.07403	+	0.348972i	−0.792054	−	0.610451i	$-0.790988\pi$
$809$	−30.5484	+	9.92578i	−1.07403	+	0.348972i	−0.281971	+	0.959423i	$0.590988\pi$
$810$	−10.3624	+	21.1981i	−0.364097	+	0.744827i
$811$	13.9262	−	7.09577i	0.489016	−	0.249166i	−0.192054	−	0.981384i	$-0.561515\pi$
$811$	13.9262	−	7.09577i	0.489016	−	0.249166i	0.681070	+	0.732218i	$0.261515\pi$
$812$	−28.6508	+	9.30922i	−1.00545	+	0.326690i
$813$	−44.5847	+	14.4864i	−1.56365	+	0.508062i
$814$	−32.0489	+	16.3298i	−1.12331	+	0.572357i
$815$	5.92305	−	12.1167i	0.207476	−	0.424429i
$816$	1.23521	−	0.401344i	0.0432410	−	0.0140498i
$817$	−31.8690	+	23.1542i	−1.11496	+	0.810063i
$818$	20.1610	+	20.1610i	0.704913	+	0.704913i
$819$	2.51083	−	8.97653i	0.0877357	−	0.313665i
$820$	−7.27580	+	23.7225i	−0.254082	+	0.828427i
$821$	−0.439121	−	2.77250i	−0.0153254	−	0.0967610i	0.978840	−	0.204627i	$-0.0655982\pi$
$821$	−0.439121	−	2.77250i	−0.0153254	−	0.0967610i	−0.994165	+	0.107866i	$0.965598\pi$
$822$	−6.47590	−	40.8872i	−0.225873	−	1.42611i
$823$	−6.41600	+	3.26912i	−0.223648	+	0.113954i	−0.562225	−	0.826984i	$-0.690054\pi$
$823$	−6.41600	+	3.26912i	−0.223648	+	0.113954i	0.338577	+	0.940939i	$0.390054\pi$
$824$	0.766453	−	0.766453i	0.0267006	−	0.0267006i
$825$	30.8407	−	24.0071i	1.07373	−	0.835820i
$826$	19.7371	−	19.7371i	0.686740	−	0.686740i
$827$	−1.58965	+	4.89245i	−0.0552776	+	0.170127i	−0.974884	−	0.222715i	$-0.928508\pi$
$827$	−1.58965	+	4.89245i	−0.0552776	+	0.170127i	0.919606	+	0.392842i	$0.128508\pi$
$828$	1.60498	−	0.254204i	0.0557770	−	0.00883421i
$829$	−14.1320	−	10.2675i	−0.490825	−	0.356605i	0.314676	−	0.949199i	$-0.398104\pi$
$829$	−14.1320	−	10.2675i	−0.490825	−	0.356605i	−0.805502	+	0.592594i	$0.798104\pi$
$830$	−6.92468	+	14.1657i	−0.240359	+	0.491699i
$831$	−27.7462	−	38.1893i	−0.962504	−	1.32477i
$832$	2.23825	+	2.82670i	0.0775975	+	0.0979981i
$833$	−0.862813	+	5.44759i	−0.0298947	+	0.188748i
$834$	16.1164	+	8.21174i	0.558067	+	0.284349i
$835$	3.61380	−	25.5485i	0.125061	−	0.884144i
$836$	22.1568	+	7.19917i	0.766307	+	0.248988i
$837$	14.8746	−	4.83306i	0.514142	−	0.167055i
$838$	0.277049	+	0.852669i	0.00957050	+	0.0294550i
$839$	−31.7125	+	16.1583i	−1.09484	+	0.557847i	−0.905621	−	0.424088i	$-0.860595\pi$
$839$	−31.7125	+	16.1583i	−1.09484	+	0.557847i	−0.189216	+	0.981936i	$0.560595\pi$
$840$	−16.6477	+	0.275767i	−0.574399	+	0.00951488i
$841$	−9.57465	−	29.4678i	−0.330160	−	1.01613i
$842$	2.22292	−	14.0350i	0.0766071	−	0.483678i
$843$		−	15.3936i		−	0.530183i
$844$	13.8934	−	10.0942i	0.478232	−	0.347456i
$845$	27.0823	+	10.5616i	0.931661	+	0.363329i
$846$	−2.32957	−	1.69253i	−0.0800922	−	0.0581904i
$847$	−12.9696	+	17.8511i	−0.445639	+	0.613370i
$848$	4.51663	+	8.86438i	0.155102	+	0.304404i
$849$	−56.3060			−1.93242
$850$	−3.07188	−	1.43910i	−0.105364	−	0.0493607i
$851$	15.2294	+	15.2294i	0.522057	+	0.522057i
$852$	9.54621	−	29.3802i	0.327048	−	1.00655i
$853$	−13.9074	+	19.1419i	−0.476181	+	0.655407i	−0.977765	−	0.209701i	$-0.932751\pi$
$853$	−13.9074	+	19.1419i	−0.476181	+	0.655407i	0.501584	+	0.865109i	$0.332751\pi$
$854$	6.21810	−	8.55848i	0.212779	−	0.292865i
$855$	−6.94155	−	4.86974i	−0.237396	−	0.166542i
$856$	0.0882089	−	0.556929i	0.00301492	−	0.0190354i
$857$	13.4342	−	13.4342i	0.458905	−	0.458905i	−0.439391	−	0.898296i	$-0.644806\pi$
$857$	13.4342	−	13.4342i	0.458905	−	0.458905i	0.898296	+	0.439391i	$0.144806\pi$
$858$	−27.1415	−	7.59176i	−0.926594	−	0.259179i
$859$	3.83810	−	1.24708i	0.130954	−	0.0425497i	−0.242807	−	0.970075i	$-0.578068\pi$
$859$	3.83810	−	1.24708i	0.130954	−	0.0425497i	0.373761	+	0.927525i	$0.378068\pi$
$860$	−12.6384	−	8.86630i	−0.430967	−	0.302338i
$861$	−25.5334	+	78.5837i	−0.870176	+	2.67813i
$862$	−7.90295	−	4.02675i	−0.269175	−	0.137152i
$863$	−9.32901	−	28.7117i	−0.317563	−	0.977359i	−0.974686	−	0.223576i	$-0.928227\pi$
$863$	−9.32901	−	28.7117i	−0.317563	−	0.977359i	0.657123	−	0.753783i	$-0.271773\pi$
$864$	−2.02963	−	3.98338i	−0.0690495	−	0.135517i
$865$	−14.0713	+	45.8792i	−0.478440	+	1.55994i
$866$	18.9888	+	9.67525i	0.645264	+	0.328779i
$867$	−31.2725	−	4.95308i	−1.06207	−	0.168215i
$868$	9.62204	+	9.62204i	0.326593	+	0.326593i
$869$	28.8639	+	4.57159i	0.979141	+	0.155081i
$870$	−0.549097	−	33.1481i	−0.0186161	−	1.12383i
$871$	4.53668	−	0.188010i	0.153720	−	0.00637049i
$872$	0.903431	+	5.70404i	0.0305940	+	0.193163i
$873$	1.36158	−	4.19052i	0.0460826	−	0.141828i
$874$		−	13.9497i		−	0.471856i
$875$	32.2399	+	29.1852i	1.08991	+	0.986640i
$876$	0.204507	+	0.204507i	0.00690966	+	0.00690966i
$877$	27.9593	+	9.08454i	0.944120	+	0.306763i	0.740324	−	0.672250i	$-0.234672\pi$
$877$	27.9593	+	9.08454i	0.944120	+	0.306763i	0.203796	+	0.979013i	$0.434672\pi$
$878$	10.8329	−	14.9101i	0.365591	−	0.503193i
$879$	−2.35653	−	14.8786i	−0.0794839	−	0.501842i
$880$	0.151223	+	9.12912i	0.00509774	+	0.307743i
$881$	−14.9501	−	20.5770i	−0.503682	−	0.693258i	0.479156	−	0.877730i	$-0.340943\pi$
$881$	−14.9501	−	20.5770i	−0.503682	−	0.693258i	−0.982838	+	0.184471i	$0.940943\pi$
$882$	−5.40315			−0.181933
$883$	8.97825	+	1.42202i	0.302142	+	0.0478546i	0.305665	−	0.952139i	$-0.401121\pi$
$883$	8.97825	+	1.42202i	0.302142	+	0.0478546i	−0.00352267	+	0.999994i	$0.501121\pi$
$884$	0.482383	+	2.39816i	0.0162243	+	0.0806588i
$885$	14.3968	+	27.1347i	0.483944	+	0.912123i
$886$	−16.7009	+	8.50954i	−0.561078	+	0.285883i
$887$	9.12815	−	17.9150i	0.306493	−	0.601527i	−0.685463	−	0.728107i	$-0.740400\pi$
$887$	9.12815	−	17.9150i	0.306493	−	0.601527i	0.991956	+	0.126581i	$0.0404002\pi$
$888$	−7.65581	+	15.0254i	−0.256912	+	0.504218i
$889$	−0.621101	−	1.21898i	−0.0208311	−	0.0408833i
$890$	7.13287	−	10.1675i	0.239094	−	0.340816i
$891$	38.3907	+	19.5610i	1.28614	+	0.655319i
$892$	0.411598	−	0.299044i	0.0137813	−	0.0100127i
$893$	−17.4790	+	17.4790i	−0.584913	+	0.584913i
$894$	7.80369	−	5.66971i	0.260994	−	0.189624i
$895$	−8.47930	+	1.48735i	−0.283432	+	0.0497166i
$896$	2.28629	−	3.14681i	0.0763796	−	0.105127i
$897$	0.698758	+	16.8610i	0.0233308	+	0.562972i
$898$	8.12943	+	15.9549i	0.271283	+	0.532422i
$899$	−19.1590	+	19.1590i	−0.638989	+	0.638989i
$900$	0.921672	−	3.19279i	0.0307224	−	0.106426i
$901$			6.74973i			0.224866i
$902$	43.0932	+	14.0018i	1.43485	+	0.466210i
$903$	−41.5911	−	30.2177i	−1.38406	−	1.00558i
$904$	−2.53454	−	16.0024i	−0.0842974	−	0.532233i
$905$	46.8036	+	6.62030i	1.55581	+	0.220066i
$906$	2.05311	−	1.49167i	0.0682101	−	0.0495575i
$907$	0.620702	−	0.620702i	0.0206101	−	0.0206101i	−0.696727	−	0.717337i	$-0.745361\pi$
$907$	0.620702	−	0.620702i	0.0206101	−	0.0206101i	0.717337	+	0.696727i	$0.245361\pi$
$908$	−7.66387	−	10.5484i	−0.254334	−	0.350061i
$909$	1.38450	+	4.26104i	0.0459208	+	0.141330i
$910$	3.10257	−	31.2057i	0.102849	−	1.03446i
$911$	−14.8952	+	45.8426i	−0.493499	+	1.51883i	0.325784	+	0.945444i	$0.394372\pi$
$911$	−14.8952	+	45.8426i	−0.493499	+	1.51883i	−0.819283	+	0.573389i	$0.805628\pi$
$912$	10.3877	−	3.37516i	0.343970	−	0.111763i
$913$	25.6546	+	13.0717i	0.849045	+	0.432610i
$914$	4.29307	−	13.2127i	0.142002	−	0.437038i
$915$	6.99804	+	9.30392i	0.231348	+	0.307578i
$916$	5.51163	−	10.8172i	0.182109	−	0.357410i
$917$	38.4977	−	27.9702i	1.27131	−	0.923659i
$918$		−	3.03312i		−	0.100108i
$919$	10.3648	+	14.2659i	0.341902	+	0.470588i	0.944996	−	0.327082i	$-0.106065\pi$
$919$	10.3648	+	14.2659i	0.341902	+	0.470588i	−0.603093	+	0.797671i	$0.706065\pi$
$920$	5.17079	−	1.77530i	0.170476	−	0.0585299i
$921$	50.1586	−	7.94434i	1.65278	−	0.261775i
$922$	40.1074	−	6.35239i	1.32087	−	0.209205i
$923$	52.8918	+	24.2458i	1.74096	+	0.798060i
$924$			30.4041i			1.00022i
$925$	41.4157	−	14.9907i	1.36174	−	0.492890i
$926$	−16.9349			−0.556515
$927$	0.327061	+	0.641893i	0.0107421	+	0.0210825i
$928$	6.26579	+	4.55237i	0.205685	+	0.149439i
$929$	40.2288	−	6.37161i	1.31986	−	0.209046i	0.543541	−	0.839382i	$-0.317083\pi$
$929$	40.2288	−	6.37161i	1.31986	−	0.209046i	0.776322	+	0.630336i	$0.217083\pi$
$930$	−13.2285	+	7.01861i	−0.433779	+	0.230149i
$931$	−7.25594	+	45.8122i	−0.237804	+	1.50143i
$932$	−8.27438	−	8.27438i	−0.271036	−	0.271036i
$933$	33.8214	+	5.35678i	1.10726	+	0.175373i
$934$	−3.09033	+	6.06512i	−0.101119	+	0.198457i
$935$	−2.72045	+	5.56518i	−0.0889683	+	0.182001i
$936$	−2.24646	+	0.834252i	−0.0734280	+	0.0272684i
$937$	−14.0153	+	27.5065i	−0.457859	+	0.898598i	0.540501	+	0.841343i	$0.318235\pi$
$937$	−14.0153	+	27.5065i	−0.457859	+	0.898598i	−0.998360	+	0.0572549i	$0.981765\pi$
$938$	−1.51368	−	4.65863i	−0.0494234	−	0.152110i
$939$	−32.3230	−	10.5024i	−1.05482	−	0.342732i
$940$	−8.70347	−	4.25456i	−0.283876	−	0.138768i
$941$	2.62791	−	5.15756i	0.0856674	−	0.168132i	−0.844198	−	0.536031i	$-0.819923\pi$
$941$	2.62791	−	5.15756i	0.0856674	−	0.168132i	0.929866	+	0.367899i	$0.119923\pi$
$942$	−6.25812	−	8.61357i	−0.203901	−	0.280645i
$943$		−	27.1311i		−	0.883510i
$944$	−7.08769	−	1.12258i	−0.230685	−	0.0365369i
$945$	−11.4016	+	37.1746i	−0.370894	+	1.20929i
$946$	−16.5706	+	22.8074i	−0.538755	+	0.741533i
$947$	31.8898	+	23.1693i	1.03628	+	0.752901i	0.969556	−	0.244870i	$-0.0787454\pi$
$947$	31.8898	+	23.1693i	1.03628	+	0.752901i	0.0667236	+	0.997771i	$0.478745\pi$
$948$	12.2075	−	6.22004i	0.396482	−	0.202018i
$949$	−0.427059	+	0.338157i	−0.0138629	+	0.0109770i
$950$	−25.8333	−	12.1023i	−0.838144	−	0.392651i
$951$	34.0274	+	34.0274i	1.10341	+	1.10341i
$952$	2.35132	−	1.19806i	0.0762069	−	0.0388293i
$953$	3.23344	+	20.4151i	0.104741	+	0.661310i	0.983067	+	0.183247i	$0.0586609\pi$
$953$	3.23344	+	20.4151i	0.104741	+	0.661310i	−0.878326	+	0.478063i	$0.841339\pi$
$954$	−6.53084	+	1.03438i	−0.211444	+	0.0334894i
$955$	−44.3185	−	21.6644i	−1.43411	−	0.701044i
$956$	−4.12461	+	26.0418i	−0.133399	+	0.842250i
$957$	−60.5393			−1.95696
$958$	−4.98097	+	31.4486i	−0.160928	+	1.01606i
$959$	−25.9925	−	79.9966i	−0.839341	−	2.58322i
$960$	2.57306	+	3.42090i	0.0830452	+	0.110409i
$961$	−17.8430	−	5.79753i	−0.575580	−	0.187017i
$962$	−26.4466	−	17.5890i	−0.852671	−	0.567091i
$963$	0.333920	+	0.170141i	0.0107604	+	0.00548271i
$964$	−10.2987	−	20.2123i	−0.331698	−	0.650995i
$965$	24.1909	+	23.4025i	0.778733	+	0.753354i
$966$	17.3142	−	5.62573i	0.557076	−	0.181005i
$967$	−21.6677	−	29.8230i	−0.696786	−	0.959044i	−0.999981	−	0.00611541i	$-0.998053\pi$
$967$	−21.6677	−	29.8230i	−0.696786	−	0.959044i	0.303195	−	0.952928i	$-0.401947\pi$
$968$	5.67275			0.182329
$969$	7.31898	+	1.15921i	0.235119	+	0.0372393i
$970$	2.07616	−	14.6779i	0.0666616	−	0.471279i
$971$	−22.0955	−	16.0533i	−0.709079	−	0.515176i	0.173797	−	0.984781i	$-0.444396\pi$
$971$	−22.0955	−	16.0533i	−0.709079	−	0.515176i	−0.882877	+	0.469605i	$0.844396\pi$
$972$	6.70473	−	1.06192i	0.215054	−	0.0340612i
$973$	34.9536	+	11.3571i	1.12056	+	0.364093i
$974$	−14.5818			−0.467231
$975$	31.8310	+	13.3340i	1.01941	+	0.427030i
$976$	−2.71973			−0.0870566
$977$	24.3498	+	7.91172i	0.779018	+	0.253118i	0.671421	−	0.741076i	$-0.265684\pi$
$977$	24.3498	+	7.91172i	0.779018	+	0.253118i	0.107597	+	0.994195i	$0.465684\pi$
$978$	−11.4041	+	1.80624i	−0.364664	+	0.0577571i
$979$	−18.3484	−	13.3309i	−0.586417	−	0.426057i
$980$	−17.9048	+	3.14067i	−0.571948	+	0.100325i
$981$	−3.79109	−	0.600450i	−0.121040	−	0.0191709i
$982$	1.43023			0.0456406
$983$	−13.9121	−	19.1484i	−0.443728	−	0.610739i	0.527308	−	0.849674i	$-0.323202\pi$
$983$	−13.9121	−	19.1484i	−0.443728	−	0.610739i	−0.971035	+	0.238936i	$0.923202\pi$
$984$	20.2032	−	6.56441i	0.644054	−	0.209266i
$985$	−7.11521	−	40.5634i	−0.226709	−	1.29246i
$986$	2.38553	+	4.68186i	0.0759707	+	0.149101i
$987$	−28.7438	−	14.6457i	−0.914926	−	0.466178i
$988$	4.05666	+	20.1676i	0.129060	+	0.641618i
$989$	16.0543	+	5.21634i	0.510496	+	0.165870i
$990$	−5.80161	−	1.77938i	−0.184387	−	0.0565523i
$991$	−16.2423	−	49.9886i	−0.515953	−	1.58794i	−0.781541	−	0.623853i	$-0.785566\pi$
$991$	−16.2423	−	49.9886i	−0.515953	−	1.58794i	0.265588	−	0.964087i	$-0.414434\pi$
$992$	0.547270	−	3.45533i	0.0173758	−	0.109707i
$993$	−6.21568			−0.197249
$994$	9.81925	−	61.9963i	0.311448	−	1.96640i
$995$	−21.5599	+	22.2862i	−0.683495	+	0.706521i
$996$	13.3327	−	2.11169i	0.422461	−	0.0669113i
$997$	−7.90923	−	49.9369i	−0.250488	−	1.58152i	−0.717045	−	0.697026i	$-0.754506\pi$
$997$	−7.90923	−	49.9369i	−0.250488	−	1.58152i	0.466558	−	0.884491i	$-0.345494\pi$
$998$	−14.1741	+	7.22206i	−0.448673	+	0.228610i
$999$	27.8474	+	27.8474i	0.881053	+	0.881053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.bd.b.47.5	yes	144
13.5	odd	4		650.2.ba.b.447.5	yes	144
25.8	odd	20		650.2.ba.b.333.5	✓	144
325.83	even	20	inner	650.2.bd.b.83.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.b.333.5	✓	144	25.8	odd	20
650.2.ba.b.447.5	yes	144	13.5	odd	4
650.2.bd.b.47.5	yes	144	1.1	even	1	trivial
650.2.bd.b.83.5	yes	144	325.83	even	20	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.bd (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.89075 + 0.299466i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.55473 + 1.60711i) q^{5} +(1.89075 + 0.299466i) q^{6} +3.88967 q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.632103 - 0.205383i) q^{9} +(1.97526 - 1.04801i) q^{10} +(-1.85375 - 3.63818i) q^{11} +(-1.70567 - 0.869084i) q^{12} +(1.99669 - 3.00220i) q^{13} +(-3.69929 - 1.20197i) q^{14} +(2.45835 - 3.50424i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.106133 + 0.670099i) q^{17} -0.664633 q^{18} +(-0.892542 + 5.63529i) q^{19} +(-2.20244 + 0.386329i) q^{20} +(-7.35441 + 1.16482i) q^{21} +(0.638758 + 4.03296i) q^{22} +(2.17846 - 1.10998i) q^{23} +(1.35363 + 1.35363i) q^{24} +(-0.165604 - 4.99726i) q^{25} +(-2.82670 + 2.23825i) q^{26} +(3.98338 - 2.02963i) q^{27} +(3.14681 + 2.28629i) q^{28} +(-4.55237 + 6.26579i) q^{29} +(-3.42090 + 2.57306i) q^{30} +(3.45533 + 0.547270i) q^{31} -1.00000i q^{32} +(4.59449 + 6.32378i) q^{33} +(0.308011 - 0.604505i) q^{34} +(-6.04740 + 6.25112i) q^{35} +(0.632103 + 0.205383i) q^{36} +(2.72215 + 8.37791i) q^{37} +(2.59026 - 5.08367i) q^{38} +(-2.87619 + 6.27437i) q^{39} +(2.21403 + 0.313171i) q^{40} +(5.03785 - 9.88734i) q^{41} +(7.35441 + 1.16482i) q^{42} +(4.88202 + 4.88202i) q^{43} +(0.638758 - 4.03296i) q^{44} +(-0.652680 + 1.33517i) q^{45} +(-2.41484 + 0.382473i) q^{46} +(3.50504 + 2.54656i) q^{47} +(-0.869084 - 1.70567i) q^{48} +8.12952 q^{49} +(-1.38674 + 4.80385i) q^{50} -1.29878i q^{51} +(3.38001 - 1.25521i) q^{52} +(9.82624 - 1.55632i) q^{53} +(-4.41561 + 0.699363i) q^{54} +(8.72904 + 2.67723i) q^{55} +(-2.28629 - 3.14681i) q^{56} -10.9222i q^{57} +(6.26579 - 4.55237i) q^{58} +(-3.25785 + 6.39390i) q^{59} +(4.04858 - 1.39001i) q^{60} +(-0.840444 + 2.58662i) q^{61} +(-3.11710 - 1.58824i) q^{62} +(2.45867 - 0.798871i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.72055 + 7.87653i) q^{65} +(-2.41547 - 7.43405i) q^{66} +(0.740215 + 1.01882i) q^{67} +(-0.479738 + 0.479738i) q^{68} +(-3.78653 + 2.75108i) q^{69} +(7.68312 - 4.07642i) q^{70} +(2.52444 + 15.9387i) q^{71} +(-0.537699 - 0.390661i) q^{72} +(-0.143686 - 0.0466865i) q^{73} -8.80905i q^{74} +(1.80963 + 9.39899i) q^{75} +(-4.03442 + 4.03442i) q^{76} +(-7.21046 - 14.1513i) q^{77} +(4.67431 - 5.07849i) q^{78} +(-4.20678 + 5.79014i) q^{79} +(-2.00889 - 0.982016i) q^{80} +(-8.53688 + 6.20240i) q^{81} +(-7.84663 + 7.84663i) q^{82} +(-5.70478 + 4.14477i) q^{83} +(-6.63451 - 3.38045i) q^{84} +(-0.911914 - 1.21239i) q^{85} +(-3.13445 - 6.15171i) q^{86} +(6.73101 - 13.2104i) q^{87} +(-1.85375 + 3.63818i) q^{88} +(4.94900 - 2.52164i) q^{89} +(1.03333 - 1.06814i) q^{90} +(7.76647 - 11.6776i) q^{91} +(2.41484 + 0.382473i) q^{92} -6.69707 q^{93} +(-2.54656 - 3.50504i) q^{94} +(-7.66886 - 10.1958i) q^{95} +(0.299466 + 1.89075i) q^{96} +(3.89672 - 5.36337i) q^{97} +(-7.73164 - 2.51216i) q^{98} +(-1.91898 - 1.91898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} - 2 q^{5} - 20 q^{9} + 12 q^{13} - 26 q^{15} - 36 q^{16} + 6 q^{17} - 152 q^{18} - 20 q^{19} - 8 q^{20} - 6 q^{21} - 12 q^{23} - 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} - 12 q^{30}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 - 2 * q^5 - 20 * q^9 + 12 * q^13 - 26 * q^15 - 36 * q^16 + 6 * q^17 - 152 * q^18 - 20 * q^19 - 8 * q^20 - 6 * q^21 - 12 * q^23 - 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 - 12 * q^30 - 6 * q^31 + 30 * q^33 + 24 * q^34 + 40 * q^35 - 20 * q^36 - 6 * q^37 + 60 * q^39 - 8 * q^41 + 6 * q^42 + 12 * q^43 - 30 * q^45 - 12 * q^46 - 18 * q^47 + 160 * q^49 - 12 * q^52 + 20 * q^53 + 6 * q^54 - 32 * q^55 - 24 * q^58 + 16 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 40 * q^63 + 36 * q^64 - 54 * q^65 - 16 * q^66 - 6 * q^68 - 26 * q^69 + 2 * q^70 + 12 * q^71 - 48 * q^72 + 40 * q^73 - 32 * q^75 + 56 * q^77 + 16 * q^78 - 20 * q^79 - 2 * q^80 + 124 * q^81 + 22 * q^82 + 74 * q^83 - 24 * q^84 - 60 * q^85 + 12 * q^86 + 8 * q^87 - 58 * q^89 + 14 * q^90 - 16 * q^91 + 12 * q^92 - 16 * q^93 + 50 * q^94 + 46 * q^95 - 40 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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Database

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