LMFDB - Embedded newform 117.2.x.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(2,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("117.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86694 + 1.86694i) q^{2} +(0.154854 + 1.72511i) q^{3} -4.97091i q^{4} +(-2.60400 - 0.697740i) q^{5} +(-3.50978 - 2.93158i) q^{6} +(-2.18636 - 0.585835i) q^{7} +(5.54651 + 5.54651i) q^{8} +(-2.95204 + 0.534283i) q^{9} +(6.16415 - 3.55887i) q^{10} +(-1.09462 - 1.09462i) q^{11} +(8.57539 - 0.769767i) q^{12} +(0.615605 + 3.55261i) q^{13} +(5.17552 - 2.98809i) q^{14} +(0.800441 - 4.60025i) q^{15} -10.7681 q^{16} +(1.06695 - 1.84800i) q^{17} +(4.51380 - 6.50875i) q^{18} +(-3.84372 + 1.02992i) q^{19} +(-3.46841 + 12.9443i) q^{20} +(0.672064 - 3.86245i) q^{21} +4.08719 q^{22} +(-3.55589 + 6.15899i) q^{23} +(-8.70946 + 10.4273i) q^{24} +(1.96386 + 1.13384i) q^{25} +(-7.78180 - 5.48320i) q^{26} +(-1.37884 - 5.00987i) q^{27} +(-2.91213 + 10.8682i) q^{28} -0.234733i q^{29} +(7.09401 + 10.0828i) q^{30} +(-1.61398 + 6.02345i) q^{31} +(9.01044 - 9.01044i) q^{32} +(1.71884 - 2.05786i) q^{33} +(1.45819 + 5.44203i) q^{34} +(5.28454 + 3.05103i) q^{35} +(2.65587 + 14.6743i) q^{36} +(2.21625 + 0.593843i) q^{37} +(5.25318 - 9.09878i) q^{38} +(-6.03333 + 1.61213i) q^{39} +(-10.5731 - 18.3131i) q^{40} +(-2.19405 - 8.18830i) q^{41} +(5.95625 + 8.46565i) q^{42} +(-0.659047 + 0.380501i) q^{43} +(-5.44127 + 5.44127i) q^{44} +(8.05991 + 0.668484i) q^{45} +(-4.85981 - 18.1371i) q^{46} +(-2.39009 + 0.640422i) q^{47} +(-1.66749 - 18.5763i) q^{48} +(-1.62519 - 0.938303i) q^{49} +(-5.78321 + 1.54961i) q^{50} +(3.35324 + 1.55443i) q^{51} +(17.6597 - 3.06012i) q^{52} +3.34230i q^{53} +(11.9273 + 6.77892i) q^{54} +(2.08664 + 3.61416i) q^{55} +(-8.87735 - 15.3760i) q^{56} +(-2.37195 - 6.47136i) q^{57} +(0.438232 + 0.438232i) q^{58} +(8.76738 + 8.76738i) q^{59} +(-22.8674 - 3.97892i) q^{60} +(4.83804 + 8.37973i) q^{61} +(-8.23221 - 14.2586i) q^{62} +(6.76724 + 0.561271i) q^{63} +12.1076i q^{64} +(0.875762 - 9.68054i) q^{65} +(0.632918 + 7.05086i) q^{66} +(7.39553 - 1.98163i) q^{67} +(-9.18627 - 5.30369i) q^{68} +(-11.1756 - 5.18058i) q^{69} +(-15.5620 + 4.16982i) q^{70} +(0.833742 + 3.11157i) q^{71} +(-19.3369 - 13.4101i) q^{72} +(-0.706395 + 0.706395i) q^{73} +(-5.24627 + 3.02893i) q^{74} +(-1.65189 + 3.56347i) q^{75} +(5.11965 + 19.1068i) q^{76} +(1.75198 + 3.03451i) q^{77} +(8.25411 - 14.2736i) q^{78} +(4.39999 - 7.62101i) q^{79} +(28.0403 + 7.51337i) q^{80} +(8.42908 - 3.15445i) q^{81} +(19.3832 + 11.1909i) q^{82} +(1.02501 + 3.82540i) q^{83} +(-19.1999 - 3.34077i) q^{84} +(-4.06776 + 4.06776i) q^{85} +(0.520028 - 1.94077i) q^{86} +(0.404942 - 0.0363494i) q^{87} -12.1427i q^{88} +(-0.560753 + 2.09276i) q^{89} +(-16.2954 + 13.7993i) q^{90} +(0.735305 - 8.12794i) q^{91} +(30.6158 + 17.6760i) q^{92} +(-10.6411 - 1.85154i) q^{93} +(3.26652 - 5.65778i) q^{94} +10.7277 q^{95} +(16.9393 + 14.1487i) q^{96} +(-0.165197 + 0.616524i) q^{97} +(4.78588 - 1.28237i) q^{98} +(3.81621 + 2.64653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.86694	+	1.86694i	−1.32012	+	1.32012i	−0.406452	+	0.913672i	$0.633234\pi$
$2$	−1.86694	+	1.86694i	−1.32012	+	1.32012i	−0.913672	+	0.406452i	$0.866766\pi$
$3$	0.154854	+	1.72511i	0.0894052	+	0.995995i
$3$	0.154854	+	1.72511i	0.0894052	+	0.995995i
$4$		−	4.97091i		−	2.48546i
$5$	−2.60400	−	0.697740i	−1.16455	−	0.312039i	−0.375766	−	0.926715i	$-0.622620\pi$
$5$	−2.60400	−	0.697740i	−1.16455	−	0.312039i	−0.788780	+	0.614676i	$0.789287\pi$
$6$	−3.50978	−	2.93158i	−1.43286	−	1.19681i
$7$	−2.18636	−	0.585835i	−0.826368	−	0.221425i	−0.179240	−	0.983805i	$-0.557364\pi$
$7$	−2.18636	−	0.585835i	−0.826368	−	0.221425i	−0.647129	+	0.762381i	$0.724030\pi$
$8$	5.54651	+	5.54651i	1.96099	+	1.96099i
$9$	−2.95204	+	0.534283i	−0.984013	+	0.178094i
$10$	6.16415	−	3.55887i	1.94928	−	1.12541i
$11$	−1.09462	−	1.09462i	−0.330041	−	0.330041i	0.522561	−	0.852602i	$-0.324977\pi$
$11$	−1.09462	−	1.09462i	−0.330041	−	0.330041i	−0.852602	+	0.522561i	$0.824977\pi$
$12$	8.57539	−	0.769767i	2.47550	−	0.222213i
$13$	0.615605	+	3.55261i	0.170738	+	0.985316i
$13$	0.615605	+	3.55261i	0.170738	+	0.985316i
$14$	5.17552	−	2.98809i	1.38322	−	0.798601i
$15$	0.800441	−	4.60025i	0.206673	−	1.18778i
$16$	−10.7681			−2.69204
$17$	1.06695	−	1.84800i	0.258772	−	0.448207i	−0.707141	−	0.707073i	$-0.750015\pi$
$17$	1.06695	−	1.84800i	0.258772	−	0.448207i	0.965913	+	0.258866i	$0.0833487\pi$
$18$	4.51380	−	6.50875i	1.06391	−	1.53413i
$19$	−3.84372	+	1.02992i	−0.881809	+	0.236280i	−0.671187	−	0.741288i	$-0.734215\pi$
$19$	−3.84372	+	1.02992i	−0.881809	+	0.236280i	−0.210622	+	0.977568i	$0.567549\pi$
$20$	−3.46841	+	12.9443i	−0.775559	+	2.89443i
$21$	0.672064	−	3.86245i	0.146656	−	0.842855i
$22$	4.08719			0.871391
$23$	−3.55589	+	6.15899i	−0.741455	+	1.28424i	0.210378	+	0.977620i	$0.432530\pi$
$23$	−3.55589	+	6.15899i	−0.741455	+	1.28424i	−0.951833	+	0.306617i	$0.900803\pi$
$24$	−8.70946	+	10.4273i	−1.77781	+	2.12846i
$25$	1.96386	+	1.13384i	0.392773	+	0.226767i
$26$	−7.78180	−	5.48320i	−1.52614	−	1.07534i
$27$	−1.37884	−	5.00987i	−0.265357	−	0.964150i
$28$	−2.91213	+	10.8682i	−0.550341	+	2.05390i
$29$		−	0.234733i		−	0.0435889i	−0.999762	−	0.0217944i	$-0.993062\pi$
$29$		−	0.234733i		−	0.0435889i	0.999762	−	0.0217944i	$-0.00693793\pi$
$30$	7.09401	+	10.0828i	1.29518	+	1.84085i
$31$	−1.61398	+	6.02345i	−0.289879	+	1.08184i	0.655321	+	0.755351i	$0.272534\pi$
$31$	−1.61398	+	6.02345i	−0.289879	+	1.08184i	−0.945200	+	0.326493i	$0.894133\pi$
$32$	9.01044	−	9.01044i	1.59283	−	1.59283i
$33$	1.71884	−	2.05786i	0.299212	−	0.358227i
$34$	1.45819	+	5.44203i	0.250077	+	0.933300i
$35$	5.28454	+	3.05103i	0.893250	+	0.515718i
$36$	2.65587	+	14.6743i	0.442645	+	2.44572i
$37$	2.21625	+	0.593843i	0.364349	+	0.0976271i	0.436349	−	0.899778i	$-0.356271\pi$
$37$	2.21625	+	0.593843i	0.364349	+	0.0976271i	−0.0719995	+	0.997405i	$0.522938\pi$
$38$	5.25318	−	9.09878i	0.852178	−	1.47602i
$39$	−6.03333	+	1.61213i	−0.966106	+	0.258147i
$40$	−10.5731	−	18.3131i	−1.67175	−	2.89556i
$41$	−2.19405	−	8.18830i	−0.342653	−	1.27880i	−0.895331	−	0.445402i	$-0.853061\pi$
$41$	−2.19405	−	8.18830i	−0.342653	−	1.27880i	0.552678	−	0.833395i	$-0.313606\pi$
$42$	5.95625	+	8.46565i	0.919069	+	1.30628i
$43$	−0.659047	+	0.380501i	−0.100504	+	0.0580259i	−0.549409	−	0.835553i	$-0.685147\pi$
$43$	−0.659047	+	0.380501i	−0.100504	+	0.0580259i	0.448906	+	0.893579i	$0.351814\pi$
$44$	−5.44127	+	5.44127i	−0.820303	+	0.820303i
$45$	8.05991	+	0.668484i	1.20150	+	0.0996517i
$46$	−4.85981	−	18.1371i	−0.716540	−	2.67416i
$47$	−2.39009	+	0.640422i	−0.348630	+	0.0934152i	−0.428885	−	0.903359i	$-0.641093\pi$
$47$	−2.39009	+	0.640422i	−0.348630	+	0.0934152i	0.0802545	+	0.996774i	$0.474427\pi$
$48$	−1.66749	−	18.5763i	−0.240682	−	2.68125i
$49$	−1.62519	−	0.938303i	−0.232170	−	0.134043i
$50$	−5.78321	+	1.54961i	−0.817870	+	0.219147i
$51$	3.35324	+	1.55443i	0.469547	+	0.217664i
$52$	17.6597	−	3.06012i	2.44896	−	0.424362i
$53$			3.34230i			0.459100i	0.973297	+	0.229550i	$0.0737254\pi$
$53$			3.34230i			0.459100i	−0.973297	+	0.229550i	$0.926275\pi$
$54$	11.9273	+	6.77892i	1.62310	+	0.922494i
$55$	2.08664	+	3.61416i	0.281362	+	0.487334i
$56$	−8.87735	−	15.3760i	−1.18629	−	2.05471i
$57$	−2.37195	−	6.47136i	−0.314172	−	0.857153i
$58$	0.438232	+	0.438232i	0.0575427	+	0.0575427i
$59$	8.76738	+	8.76738i	1.14142	+	1.14142i	0.988191	+	0.153225i	$0.0489658\pi$
$59$	8.76738	+	8.76738i	1.14142	+	1.14142i	0.153225	+	0.988191i	$0.451034\pi$
$60$	−22.8674	−	3.97892i	−2.95217	−	0.513677i
$61$	4.83804	+	8.37973i	0.619447	+	1.07291i	0.989587	+	0.143938i	$0.0459766\pi$
$61$	4.83804	+	8.37973i	0.619447	+	1.07291i	−0.370139	+	0.928976i	$0.620690\pi$
$62$	−8.23221	−	14.2586i	−1.04549	−	1.81084i
$63$	6.76724	+	0.561271i	0.852592	+	0.0707134i
$64$			12.1076i			1.51344i
$65$	0.875762	−	9.68054i	0.108625	−	1.20072i
$66$	0.632918	+	7.05086i	0.0779068	+	0.867901i
$67$	7.39553	−	1.98163i	0.903508	−	0.242094i	0.222986	−	0.974822i	$-0.428420\pi$
$67$	7.39553	−	1.98163i	0.903508	−	0.242094i	0.680522	+	0.732728i	$0.261753\pi$
$68$	−9.18627	−	5.30369i	−1.11400	−	0.643167i
$69$	−11.1756	−	5.18058i	−1.34538	−	0.623668i
$70$	−15.5620	+	4.16982i	−1.86001	+	0.498389i
$71$	0.833742	+	3.11157i	0.0989469	+	0.369275i	0.997588	−	0.0694091i	$-0.0221114\pi$
$71$	0.833742	+	3.11157i	0.0989469	+	0.369275i	−0.898641	+	0.438684i	$0.855445\pi$
$72$	−19.3369	−	13.4101i	−2.27888	−	1.58040i
$73$	−0.706395	+	0.706395i	−0.0826773	+	0.0826773i	−0.747236	−	0.664559i	$-0.768620\pi$
$73$	−0.706395	+	0.706395i	−0.0826773	+	0.0826773i	0.664559	+	0.747236i	$0.268620\pi$
$74$	−5.24627	+	3.02893i	−0.609866	+	0.352106i
$75$	−1.65189	+	3.56347i	−0.190743	+	0.411474i
$76$	5.11965	+	19.1068i	0.587264	+	2.19170i
$77$	1.75198	+	3.03451i	0.199656	+	0.345815i
$78$	8.25411	−	14.2736i	0.934594	−	1.61617i
$79$	4.39999	−	7.62101i	0.495038	−	0.857430i	−0.504946	−	0.863151i	$-0.668488\pi$
$79$	4.39999	−	7.62101i	0.495038	−	0.857430i	0.999984	+	0.00572053i	$0.00182091\pi$
$80$	28.0403	+	7.51337i	3.13500	+	0.840020i
$81$	8.42908	−	3.15445i	0.936565	−	0.350494i
$82$	19.3832	+	11.1909i	2.14052	+	1.23583i
$83$	1.02501	+	3.82540i	0.112510	+	0.419892i	0.999089	−	0.0426854i	$-0.0135913\pi$
$83$	1.02501	+	3.82540i	0.112510	+	0.419892i	−0.886579	+	0.462578i	$0.846925\pi$
$84$	−19.1999	−	3.34077i	−2.09488	−	0.364508i
$85$	−4.06776	+	4.06776i	−0.441210	+	0.441210i
$86$	0.520028	−	1.94077i	0.0560761	−	0.209279i
$87$	0.404942	−	0.0363494i	0.0434143	−	0.00389707i
$88$		−	12.1427i		−	1.29441i
$89$	−0.560753	+	2.09276i	−0.0594397	+	0.221832i	−0.989256	−	0.146191i	$-0.953299\pi$
$89$	−0.560753	+	2.09276i	−0.0594397	+	0.221832i	0.929817	+	0.368023i	$0.119965\pi$
$90$	−16.2954	+	13.7993i	−1.71768	+	1.45458i
$91$	0.735305	−	8.12794i	0.0770809	−	0.852040i
$92$	30.6158	+	17.6760i	3.19192	+	1.84285i
$93$	−10.6411	−	1.85154i	−1.10343	−	0.191996i
$94$	3.26652	−	5.65778i	0.336916	−	0.583555i
$95$	10.7277			1.10064
$96$	16.9393	+	14.1487i	1.72886	+	1.44405i
$97$	−0.165197	+	0.616524i	−0.0167732	+	0.0625985i	−0.973805	−	0.227384i	$-0.926983\pi$
$97$	−0.165197	+	0.616524i	−0.0167732	+	0.0625985i	0.957032	+	0.289982i	$0.0936495\pi$
$98$	4.78588	−	1.28237i	0.483447	−	0.129539i
$99$	3.81621	+	2.64653i	0.383543	+	0.265987i
$100$	5.63620	−	9.76219i	0.563620	−	0.976219i
$101$	−5.84016			−0.581117			−0.290559	−	0.956857i	$-0.593841\pi$
$101$	−5.84016			−0.581117			−0.290559	+	0.956857i	$0.593841\pi$
$102$	−9.16232	+	3.35826i	−0.907205	+	0.332517i
$103$	−16.9587	+	9.79113i	−1.67099	+	0.964749i	−0.703911	+	0.710288i	$0.748565\pi$
$103$	−16.9587	+	9.79113i	−1.67099	+	0.964749i	−0.967083	+	0.254461i	$0.918102\pi$
$104$	−16.2901	+	23.1190i	−1.59738	+	2.26701i
$105$	−4.44504	+	9.58890i	−0.433792	+	0.935781i
$106$	−6.23986	−	6.23986i	−0.606068	−	0.606068i
$107$	−3.36744	+	1.94419i	−0.325543	+	0.187952i	−0.653861	−	0.756615i	$-0.726852\pi$
$107$	−3.36744	+	1.94419i	−0.325543	+	0.187952i	0.328318	+	0.944567i	$0.393518\pi$
$108$	−24.9036	+	6.85407i	−2.39635	+	0.659533i
$109$	−9.18667	−	9.18667i	−0.879924	−	0.879924i	0.113602	−	0.993526i	$-0.463761\pi$
$109$	−9.18667	−	9.18667i	−0.879924	−	0.879924i	−0.993526	+	0.113602i	$0.963761\pi$
$110$	−10.6430	−	2.85179i	−1.01477	−	0.271908i
$111$	−0.681251	+	3.91525i	−0.0646614	+	0.371619i
$112$	23.5431	+	6.30835i	2.22461	+	0.596083i
$113$		−	13.9105i		−	1.30859i	−0.756240	−	0.654294i	$-0.772966\pi$
$113$		−	13.9105i		−	1.30859i	0.756240	−	0.654294i	$-0.227034\pi$
$114$	16.5099	+	7.65335i	1.54629	+	0.716802i
$115$	13.5569	−	13.5569i	1.26419	−	1.26419i
$116$	−1.16684			−0.108338
$117$	−3.71539	−	10.1585i	−0.343488	−	0.939157i
$118$	−32.7363			−3.01362
$119$	−3.41536	+	3.41536i	−0.313085	+	0.313085i
$120$	29.9550	−	21.0757i	2.73450	−	1.92394i
$121$		−	8.60360i		−	0.782146i
$122$	−24.6767	−	6.61211i	−2.23413	−	0.598633i
$123$	13.7860	−	5.05298i	1.24304	−	0.455612i
$124$	29.9420	+	8.02295i	2.68887	+	0.720482i
$125$	5.20853	+	5.20853i	0.465865	+	0.465865i
$126$	−13.6819	+	11.5862i	−1.21888	+	1.03218i
$127$	−16.7201	+	9.65336i	−1.48367	+	0.856597i	−0.999828	−	0.0185590i	$-0.994092\pi$
$127$	−16.7201	+	9.65336i	−1.48367	+	0.856597i	−0.483841	+	0.875156i	$0.660759\pi$
$128$	−4.58318	−	4.58318i	−0.405100	−	0.405100i
$129$	−0.758464	−	1.07801i	−0.0667790	−	0.0949134i
$130$	16.4380	+	19.7080i	1.44170	+	1.72850i
$131$	0.0772661	−	0.0446096i	0.00675077	−	0.00389756i	−0.496621	−	0.867968i	$-0.665426\pi$
$131$	0.0772661	−	0.0446096i	0.00675077	−	0.00389756i	0.503372	+	0.864070i	$0.332093\pi$
$132$	−10.2294	−	8.54422i	−0.890357	−	0.743679i
$133$	9.00713			0.781017
$134$	−10.1074	+	17.5066i	−0.873148	+	1.51234i
$135$	0.0949004	+	14.0078i	0.00816772	+	1.20560i
$136$	16.1678	−	4.33215i	1.38638	−	0.371478i
$137$	0.366549	−	1.36798i	0.0313164	−	0.116874i	−0.948498	−	0.316782i	$-0.897398\pi$
$137$	0.366549	−	1.36798i	0.0313164	−	0.116874i	0.979815	+	0.199908i	$0.0640643\pi$
$138$	30.5360	−	11.1923i	2.59939	−	0.952755i
$139$	−7.95095			−0.674391			−0.337196	−	0.941435i	$-0.609478\pi$
$139$	−7.95095			−0.674391			−0.337196	+	0.941435i	$0.609478\pi$
$140$	15.1664	−	26.2690i	1.28180	−	2.22013i
$141$	−1.47492	−	4.02401i	−0.124210	−	0.338882i
$142$	−7.36564	−	4.25256i	−0.618111	−	0.356867i
$143$	3.21491	−	4.56262i	0.268844	−	0.381546i
$144$	31.7880	−	5.75323i	2.64900	−	0.479436i
$145$	−0.163783	+	0.611246i	−0.0136014	+	0.0507612i
$146$		−	2.63759i		−	0.218288i
$147$	1.36701	−	2.94894i	0.112749	−	0.243224i
$148$	2.95194	−	11.0168i	0.242648	−	0.905574i
$149$	11.6791	−	11.6791i	0.956786	−	0.956786i	−0.0423180	−	0.999104i	$-0.513474\pi$
$149$	11.6791	−	11.6791i	0.956786	−	0.956786i	0.999104	+	0.0423180i	$0.0134743\pi$
$150$	−3.56880	−	9.73674i	−0.291392	−	0.795001i
$151$	−2.25779	−	8.42619i	−0.183736	−	0.685714i	−0.994897	−	0.100891i	$-0.967831\pi$
$151$	−2.25779	−	8.42619i	−0.183736	−	0.685714i	0.811161	−	0.584823i	$-0.198836\pi$
$152$	−27.0317	−	15.6067i	−2.19256	−	1.26587i
$153$	−2.16231	+	6.02543i	−0.174812	+	0.487127i
$154$	−8.93608	−	2.39442i	−0.720090	−	0.192947i
$155$	8.40561	−	14.5589i	0.675155	−	1.16940i
$156$	8.01373	+	29.9911i	0.641612	+	2.40121i
$157$	−0.854259	−	1.47962i	−0.0681773	−	0.118087i	0.829922	−	0.557880i	$-0.188385\pi$
$157$	−0.854259	−	1.47962i	−0.0681773	−	0.118087i	−0.898099	+	0.439793i	$0.855052\pi$
$158$	6.01344	+	22.4425i	0.478403	+	1.78543i
$159$	−5.76584	+	0.517569i	−0.457261	+	0.0410459i
$160$	−29.7501	+	17.1763i	−2.35196	+	1.35790i
$161$	11.3826	−	11.3826i	0.897076	−	0.897076i
$162$	−9.84741	+	21.6257i	−0.773686	+	1.69908i
$163$	0.929365	+	3.46844i	0.0727935	+	0.271669i	0.992724	−	0.120413i	$-0.0384217\pi$
$163$	0.929365	+	3.46844i	0.0727935	+	0.271669i	−0.919930	+	0.392082i	$0.871755\pi$
$164$	−40.7033	+	10.9064i	−3.17839	+	0.851648i
$165$	−5.91172	+	4.15936i	−0.460227	+	0.323806i
$166$	−9.05542	−	5.22815i	−0.702837	−	0.405783i
$167$	1.89626	−	0.508102i	0.146737	−	0.0393181i	−0.184703	−	0.982794i	$-0.559132\pi$
$167$	1.89626	−	0.508102i	0.146737	−	0.0393181i	0.331440	+	0.943476i	$0.392466\pi$
$168$	25.1507	−	17.6955i	1.94042	−	1.36524i
$169$	−12.2421	+	4.37401i	−0.941697	+	0.336462i
$170$		−	15.1885i		−	1.16490i
$171$	10.7965	−	5.09400i	0.825632	−	0.389548i
$172$	1.89144	+	3.27606i	0.144221	+	0.249798i
$173$	8.81239	+	15.2635i	0.669994	+	1.16046i	0.977905	+	0.209048i	$0.0670366\pi$
$173$	8.81239	+	15.2635i	0.669994	+	1.16046i	−0.307911	+	0.951415i	$0.599630\pi$
$174$	−0.688139	+	0.823863i	−0.0521677	+	0.0624569i
$175$	−3.62948	−	3.62948i	−0.274363	−	0.274363i
$176$	11.7871	+	11.7871i	0.888483	+	0.888483i
$177$	−13.7671	+	16.4824i	−1.03480	+	1.23889i
$178$	−2.86016	−	4.95394i	−0.214378	−	0.371314i
$179$	5.11814	+	8.86487i	0.382548	+	0.662592i	0.991426	−	0.130672i	$-0.0417135\pi$
$179$	5.11814	+	8.86487i	0.382548	+	0.662592i	−0.608878	+	0.793264i	$0.708380\pi$
$180$	3.32298	−	40.0651i	0.247680	−	2.98628i
$181$		−	16.0613i		−	1.19382i	−0.802306	−	0.596912i	$-0.796394\pi$
$181$		−	16.0613i		−	1.19382i	0.802306	−	0.596912i	$-0.203606\pi$
$182$	13.8016	+	16.5471i	1.02304	+	1.22655i
$183$	−13.7068	+	9.64381i	−1.01324	+	0.712891i
$184$	−53.8836	+	14.4381i	−3.97235	+	1.06439i
$185$	−5.35678	−	3.09274i	−0.393838	−	0.227382i
$186$	23.3229	−	16.4095i	1.71012	−	1.20320i
$187$	−3.19077	+	0.854964i	−0.233332	+	0.0625212i
$188$	3.18348	+	11.8809i	0.232179	+	0.866505i
$189$	0.0796800	+	11.7612i	0.00579586	+	0.855500i
$190$	−20.0279	+	20.0279i	−1.45298	+	1.45298i
$191$	−5.17313	+	2.98671i	−0.374314	+	0.216111i	−0.675342	−	0.737505i	$-0.736004\pi$
$191$	−5.17313	+	2.98671i	−0.374314	+	0.216111i	0.301027	+	0.953616i	$0.402670\pi$
$192$	−20.8869	+	1.87491i	−1.50738	+	0.135310i
$193$	0.484108	+	1.80671i	0.0348468	+	0.130050i	0.981158	−	0.193207i	$-0.0618888\pi$
$193$	0.484108	+	1.80671i	0.0348468	+	0.130050i	−0.946311	+	0.323257i	$0.895222\pi$
$194$	−0.842599	−	1.45942i	−0.0604951	−	0.104781i
$195$	16.8357	+	0.0117176i	1.20563	+	0.000839116i
$196$	−4.66422	+	8.07867i	−0.333159	+	0.577048i
$197$	−20.1278	−	5.39323i	−1.43405	−	0.384252i	−0.543603	−	0.839343i	$-0.682940\pi$
$197$	−20.1278	−	5.39323i	−1.43405	−	0.384252i	−0.890445	+	0.455091i	$0.849607\pi$
$198$	−12.0655	+	2.18371i	−0.857460	+	0.155190i
$199$	6.00336	+	3.46604i	0.425567	+	0.245701i	0.697456	−	0.716627i	$-0.254315\pi$
$199$	6.00336	+	3.46604i	0.425567	+	0.245701i	−0.271889	+	0.962329i	$0.587648\pi$
$200$	4.60375	+	17.1814i	0.325534	+	1.21491i
$201$	4.56376	+	12.4513i	0.321903	+	0.878245i
$202$	10.9032	−	10.9032i	0.767147	−	0.767147i
$203$	−0.137515	+	0.513212i	−0.00965165	+	0.0360205i
$204$	7.72695	−	16.6687i	0.540994	−	1.16704i
$205$			22.8532i			1.59614i
$206$	13.3815	−	49.9403i	0.932332	−	3.47951i
$207$	7.20650	−	20.0814i	0.500886	−	1.39576i
$208$	−6.62892	−	38.2550i	−0.459633	−	2.65251i
$209$	5.33479	+	3.08005i	0.369015	+	0.213051i
$210$	−9.60326	−	26.2005i	−0.662688	−	1.80801i
$211$	1.23067	−	2.13158i	0.0847226	−	0.146744i	−0.820550	−	0.571574i	$-0.806333\pi$
$211$	1.23067	−	2.13158i	0.0847226	−	0.146744i	0.905273	+	0.424830i	$0.139666\pi$
$212$	16.6143			1.14107
$213$	−5.23870	+	1.92014i	−0.358950	+	0.131566i
$214$	2.65712	−	9.91650i	0.181637	−	0.677878i
$215$	1.98165	−	0.530982i	0.135148	−	0.0362127i
$216$	20.1396	−	35.4350i	1.37032	−	2.41105i
$217$	7.05749	−	12.2239i	0.479094	−	0.829815i
$218$	34.3019			2.32322
$219$	−1.32800	−	1.10922i	−0.0897379	−	0.0749544i
$220$	17.9657	−	10.3725i	1.21125	−	0.699314i
$221$	7.22205	+	2.65280i	0.485808	+	0.178447i
$222$	−6.03767	−	8.58137i	−0.405222	−	0.575944i
$223$	14.2743	+	14.2743i	0.955877	+	0.955877i	0.999067	−	0.0431901i	$-0.0137521\pi$
$223$	14.2743	+	14.2743i	0.955877	+	0.955877i	−0.0431901	+	0.999067i	$0.513752\pi$
$224$	−24.9787	+	14.4215i	−1.66896	+	0.963575i
$225$	−6.40319	−	2.29787i	−0.426879	−	0.153192i
$226$	25.9700	+	25.9700i	1.72750	+	1.72750i
$227$	−19.2317	−	5.15313i	−1.27646	−	0.342025i	−0.443955	−	0.896049i	$-0.646425\pi$
$227$	−19.2317	−	5.15313i	−1.27646	−	0.342025i	−0.832501	+	0.554024i	$0.813092\pi$
$228$	−32.1686	+	11.7907i	−2.13042	+	0.780861i
$229$	23.4382	+	6.28023i	1.54884	+	0.415010i	0.929109	−	0.369807i	$-0.120576\pi$
$229$	23.4382	+	6.28023i	1.54884	+	0.415010i	0.619728	+	0.784817i	$0.287243\pi$
$230$			50.6199i			3.33778i
$231$	−4.96358	+	3.49227i	−0.326580	+	0.229774i
$232$	1.30195	−	1.30195i	0.0854772	−	0.0854772i
$233$	−18.4755			−1.21037			−0.605184	−	0.796085i	$-0.706901\pi$
$233$	−18.4755			−1.21037			−0.605184	+	0.796085i	$0.706901\pi$
$234$	25.9018	+	12.0290i	1.69325	+	0.786358i
$235$	6.67065			0.435145
$236$	43.5819	−	43.5819i	2.83694	−	2.83694i
$237$	13.8285	+	6.41034i	0.898256	+	0.416397i
$238$		−	12.7525i		−	0.826623i
$239$	−12.4741	−	3.34242i	−0.806882	−	0.216203i	−0.168278	−	0.985740i	$-0.553821\pi$
$239$	−12.4741	−	3.34242i	−0.806882	−	0.216203i	−0.638603	+	0.769536i	$0.720487\pi$
$240$	−8.61927	+	49.5362i	−0.556371	+	3.19755i
$241$	−3.67070	−	0.983562i	−0.236451	−	0.0633568i	0.138648	−	0.990342i	$-0.455724\pi$
$241$	−3.67070	−	0.983562i	−0.236451	−	0.0633568i	−0.375099	+	0.926985i	$0.622391\pi$
$242$	16.0624	+	16.0624i	1.03253	+	1.03253i
$243$	6.74706	+	14.0527i	0.432824	+	0.901478i
$244$	41.6549	−	24.0495i	2.66668	−	1.53961i
$245$	3.57730	+	3.57730i	0.228546	+	0.228546i
$246$	−16.3040	+	35.1712i	−1.03950	+	2.24243i
$247$	−6.02512	−	13.0212i	−0.383369	−	0.828519i
$248$	−42.3611	+	24.4572i	−2.68993	+	1.55303i
$249$	−6.44053	+	2.36064i	−0.408152	+	0.149600i
$250$	−19.4480			−1.23000
$251$	−9.87750	+	17.1083i	−0.623462	+	1.07987i	0.365374	+	0.930861i	$0.380941\pi$
$251$	−9.87750	+	17.1083i	−0.623462	+	1.07987i	−0.988836	+	0.149007i	$0.952392\pi$
$252$	2.79003	−	33.6393i	0.175755	−	2.11908i
$253$	10.6341	−	2.84941i	0.668562	−	0.179141i
$254$	13.1932	−	49.2376i	0.827813	−	3.08944i
$255$	−7.64726	−	6.38744i	−0.478890	−	0.399997i
$256$	−7.10209			−0.443880
$257$	−6.57131	+	11.3818i	−0.409907	+	0.709980i	−0.994879	−	0.101074i	$-0.967772\pi$
$257$	−6.57131	+	11.3818i	−0.409907	+	0.709980i	0.584972	+	0.811054i	$0.301106\pi$
$258$	3.42858	+	0.596571i	0.213454	+	0.0371409i
$259$	−4.49764	−	2.59671i	−0.279470	−	0.161352i
$260$	−48.1211	−	4.35334i	−2.98434	−	0.269983i
$261$	0.125414	+	0.692942i	0.00776293	+	0.0428920i
$262$	−0.0609676	+	0.227534i	−0.00376659	+	0.0140571i
$263$			13.7858i			0.850069i	0.905177	+	0.425035i	$0.139738\pi$
$263$			13.7858i			0.850069i	−0.905177	+	0.425035i	$0.860262\pi$
$264$	20.9475	−	1.88034i	1.28923	−	0.115727i
$265$	2.33205	−	8.70335i	0.143257	−	0.534642i
$266$	−16.8157	+	16.8157i	−1.03104	+	1.03104i
$267$	−3.69709	−	0.643291i	−0.226258	−	0.0393688i
$268$	−9.85049	−	36.7625i	−0.601714	−	2.24563i
$269$	21.8626	+	12.6224i	1.33299	+	0.769599i	0.985756	−	0.168181i	$-0.0537893\pi$
$269$	21.8626	+	12.6224i	1.33299	+	0.769599i	0.347229	+	0.937780i	$0.387123\pi$
$270$	−26.3288	−	25.9745i	−1.60232	−	1.58076i
$271$	−18.4487	−	4.94331i	−1.12068	−	0.300285i	−0.349520	−	0.936929i	$-0.613655\pi$
$271$	−18.4487	−	4.94331i	−1.12068	−	0.300285i	−0.771158	+	0.636644i	$0.780322\pi$
$272$	−11.4890	+	19.8996i	−0.696624	+	1.20659i
$273$	14.1355	+	0.00983831i	0.855519	+	0.000595442i
$274$	1.86961	+	3.23826i	0.112947	+	0.195630i
$275$	−0.908565	−	3.39081i	−0.0547886	−	0.204474i
$276$	−25.7522	+	55.5529i	−1.55010	+	3.34389i
$277$	−0.160642	+	0.0927467i	−0.00965204	+	0.00557261i	−0.504818	−	0.863226i	$-0.668440\pi$
$277$	−0.160642	+	0.0927467i	−0.00965204	+	0.00557261i	0.495166	+	0.868798i	$0.335107\pi$
$278$	14.8439	−	14.8439i	0.890280	−	0.890280i
$279$	1.54630	−	18.6438i	0.0925748	−	1.11617i
$280$	12.3882	+	46.2333i	0.740335	+	2.76297i
$281$	9.00672	−	2.41334i	0.537296	−	0.143968i	0.0200406	−	0.999799i	$-0.493620\pi$
$281$	9.00672	−	2.41334i	0.537296	−	0.143968i	0.517255	+	0.855831i	$0.326954\pi$
$282$	10.2661	+	4.75899i	0.611340	+	0.283394i
$283$	9.97030	+	5.75636i	0.592673	+	0.342180i	0.766154	−	0.642657i	$-0.222168\pi$
$283$	9.97030	+	5.75636i	0.592673	+	0.342180i	−0.173481	+	0.984837i	$0.555501\pi$
$284$	15.4673	−	4.14446i	0.917817	−	0.245928i
$285$	1.66123	+	18.5065i	0.0984025	+	1.09623i
$286$	2.51609	+	14.5202i	0.148780	+	0.858596i
$287$			19.1880i			1.13263i
$288$	−21.7850	+	31.4133i	−1.28370	+	1.85105i
$289$	6.22325	+	10.7790i	0.366074	+	0.634058i
$290$	−0.835386	−	1.44693i	−0.0490555	−	0.0849667i
$291$	−1.08916	−	0.189512i	−0.0638474	−	0.0111094i
$292$	3.51143	+	3.51143i	0.205491	+	0.205491i
$293$	−7.55565	−	7.55565i	−0.441406	−	0.441406i	0.451078	−	0.892484i	$-0.351039\pi$
$293$	−7.55565	−	7.55565i	−0.441406	−	0.441406i	−0.892484	+	0.451078i	$0.851039\pi$
$294$	2.95335	+	8.05761i	0.172243	+	0.469929i
$295$	−16.7129	−	28.9476i	−0.973065	−	1.68540i
$296$	8.99870	+	15.5862i	0.523039	+	0.905930i
$297$	−3.97462	+	6.99322i	−0.230631	+	0.405788i
$298$			43.6082i			2.52615i
$299$	−24.0695	−	8.84119i	−1.39197	−	0.511299i
$300$	17.7137	+	8.21138i	1.02270	+	0.474084i
$301$	1.66383	−	0.445821i	0.0959015	−	0.0256967i
$302$	19.9463	+	11.5160i	1.14778	+	0.662673i
$303$	−0.904374	−	10.0749i	−0.0519549	−	0.578790i
$304$	41.3897	−	11.0903i	2.37386	−	0.636074i
$305$	−6.75139	−	25.1965i	−0.386584	−	1.44275i
$306$	−7.21221	−	15.2860i	−0.412295	−	0.873843i
$307$	11.2905	−	11.2905i	0.644384	−	0.644384i	−0.307246	−	0.951630i	$-0.599407\pi$
$307$	11.2905	−	11.2905i	0.644384	−	0.644384i	0.951630	+	0.307246i	$0.0994075\pi$
$308$	15.0843	−	8.70892i	0.859508	−	0.496237i
$309$	−19.5170	−	27.7396i	−1.11028	−	1.57805i
$310$	11.4879	+	42.8734i	0.652468	+	2.43504i
$311$	−3.28642	−	5.69225i	−0.186356	−	0.322778i	0.757677	−	0.652630i	$-0.226334\pi$
$311$	−3.28642	−	5.69225i	−0.186356	−	0.322778i	−0.944033	+	0.329852i	$0.893001\pi$
$312$	−42.4056	−	24.5222i	−2.40074	−	1.38830i
$313$	10.7965	−	18.7000i	0.610253	−	1.05699i	−0.380945	−	0.924598i	$-0.624401\pi$
$313$	10.7965	−	18.7000i	0.610253	−	1.05699i	0.991198	−	0.132391i	$-0.0422654\pi$
$314$	4.35721	+	1.16751i	0.245891	+	0.0658864i
$315$	−17.2303	−	6.18333i	−0.970817	−	0.348391i
$316$	−37.8834	−	21.8720i	−2.13111	−	1.23039i
$317$	−1.59156	−	5.93980i	−0.0893912	−	0.333612i	0.906718	−	0.421737i	$-0.138579\pi$
$317$	−1.59156	−	5.93980i	−0.0893912	−	0.333612i	−0.996109	+	0.0881244i	$0.971913\pi$
$318$	9.79820	−	11.7307i	0.549456	−	0.657827i
$319$	−0.256944	+	0.256944i	−0.0143861	+	0.0143861i
$320$	8.44793	−	31.5281i	0.472254	−	1.76248i
$321$	−3.87542	−	5.50816i	−0.216305	−	0.307436i
$322$			42.5013i			2.36850i
$323$	−2.19774	+	8.20207i	−0.122285	+	0.456376i
$324$	−15.6805	−	41.9002i	−0.871138	−	2.32779i
$325$	−2.81911	+	7.67483i	−0.156376	+	0.425723i
$326$	−8.21043	−	4.74029i	−0.454733	−	0.262540i
$327$	14.4255	−	17.2707i	0.797730	−	0.955070i
$328$	33.2472	−	57.5858i	1.83577	−	3.17964i
$329$	5.60079			0.308781
$330$	3.27155	−	18.8021i	0.180093	−	1.03502i
$331$	−9.14621	+	34.1341i	−0.502721	+	1.87618i	−0.0211475	+	0.999776i	$0.506732\pi$
$331$	−9.14621	+	34.1341i	−0.502721	+	1.87618i	−0.481574	+	0.876405i	$0.659935\pi$
$332$	19.0157	−	5.09525i	1.04362	−	0.279638i
$333$	−6.85974	−	0.568943i	−0.375911	−	0.0311779i
$334$	−2.59161	+	4.48880i	−0.141807	+	0.245616i
$335$	−20.6406			−1.12772
$336$	−7.23688	+	41.5914i	−0.394804	+	2.26900i
$337$	−7.02186	+	4.05407i	−0.382505	+	0.220839i	−0.678908	−	0.734224i	$-0.737546\pi$
$337$	−7.02186	+	4.05407i	−0.382505	+	0.220839i	0.296403	+	0.955063i	$0.404213\pi$
$338$	14.6892	−	31.0212i	0.798985	−	1.68733i
$339$	23.9972	−	2.15410i	1.30335	−	0.116995i
$340$	20.2205	+	20.2205i	1.09661	+	1.09661i
$341$	8.36010	−	4.82671i	0.452725	−	0.261381i
$342$	−10.6463	+	29.6666i	−0.575685	+	1.60419i
$343$	14.2073	+	14.2073i	0.767121	+	0.767121i
$344$	−5.76586	−	1.54496i	−0.310874	−	0.0832985i
$345$	25.4866	+	21.2879i	1.37215	+	1.14610i
$346$	−44.9482	−	12.0438i	−2.41643	−	0.647481i
$347$		−	14.1322i		−	0.758656i	−0.925262	−	0.379328i	$-0.876155\pi$
$347$		−	14.1322i		−	0.758656i	0.925262	−	0.379328i	$-0.123845\pi$
$348$	−0.180690	−	2.01293i	−0.00968600	−	0.107904i
$349$	−10.3603	+	10.3603i	−0.554576	+	0.554576i	−0.927758	−	0.373182i	$-0.878267\pi$
$349$	−10.3603	+	10.3603i	−0.554576	+	0.554576i	0.373182	+	0.927758i	$0.378267\pi$
$350$	13.5520			0.724386
$351$	16.9493	−	7.98256i	0.904687	−	0.426078i
$352$	−19.7261			−1.05140
$353$	−22.4349	+	22.4349i	−1.19409	+	1.19409i	−0.218178	+	0.975909i	$0.570011\pi$
$353$	−22.4349	+	22.4349i	−1.19409	+	1.19409i	−0.975909	+	0.218178i	$0.929989\pi$
$354$	−5.06936	−	56.4739i	−0.269433	−	3.00155i
$355$		−	8.68426i		−	0.460913i
$356$	10.4029	+	2.78746i	0.551354	+	0.147735i
$357$	−6.42077	−	5.36300i	−0.339823	−	0.283840i
$358$	−26.1054	−	6.99492i	−1.37971	−	0.369693i
$359$	−12.5293	−	12.5293i	−0.661270	−	0.661270i	0.294409	−	0.955679i	$-0.404877\pi$
$359$	−12.5293	−	12.5293i	−0.661270	−	0.661270i	−0.955679	+	0.294409i	$0.904877\pi$
$360$	40.9966	+	48.4121i	2.16071	+	2.55154i
$361$	−2.74106	+	1.58255i	−0.144267	+	0.0832923i
$362$	29.9854	+	29.9854i	1.57600	+	1.57600i
$363$	14.8422	−	1.33230i	0.779013	−	0.0699279i
$364$	−40.4033	−	3.65514i	−2.11771	−	0.191581i
$365$	2.33233	−	1.34657i	0.122080	−	0.0704829i
$366$	7.58535	−	43.5941i	0.396493	−	2.27870i
$367$	−19.9467			−1.04121			−0.520604	−	0.853799i	$-0.674293\pi$
$367$	−19.9467			−1.04121			−0.520604	+	0.853799i	$0.674293\pi$
$368$	38.2903	−	66.3208i	1.99602	−	3.45721i
$369$	10.8518	+	22.9999i	0.564921	+	1.19733i
$370$	15.7747	−	4.22682i	0.820088	−	0.219742i
$371$	1.95803	−	7.30748i	0.101656	−	0.379385i
$372$	−9.20385	+	52.8958i	−0.477197	+	2.74252i
$373$	23.8683			1.23586			0.617928	−	0.786235i	$-0.287972\pi$
$373$	23.8683			1.23586			0.617928	+	0.786235i	$0.287972\pi$
$374$	4.36080	−	7.55313i	0.225492	−	0.390563i
$375$	−8.17875	+	9.79188i	−0.422349	+	0.505650i
$376$	−16.8088	−	9.70454i	−0.866845	−	0.500473i
$377$	0.833915	−	0.144503i	0.0429488	−	0.00744228i
$378$	−22.1061	−	21.8086i	−1.13702	−	1.12171i
$379$	3.76589	−	14.0545i	0.193441	−	0.721931i	−0.799224	−	0.601033i	$-0.794756\pi$
$379$	3.76589	−	14.0545i	0.193441	−	0.721931i	0.992665	−	0.120898i	$-0.0385773\pi$
$380$		−	53.3263i		−	2.73558i
$381$	−19.2423	−	27.3492i	−0.985814	−	1.40114i
$382$	4.08191	−	15.2339i	0.208849	−	0.779434i
$383$	2.94400	−	2.94400i	0.150432	−	0.150432i	−0.627879	−	0.778311i	$-0.716077\pi$
$383$	2.94400	−	2.94400i	0.150432	−	0.150432i	0.778311	+	0.627879i	$0.216077\pi$
$384$	7.19679	−	8.61624i	0.367259	−	0.439696i
$385$	−2.44485	−	9.12431i	−0.124601	−	0.465018i
$386$	−4.27682	−	2.46922i	−0.217684	−	0.125680i
$387$	1.74224	−	1.47537i	0.0885629	−	0.0749974i
$388$	3.06468	+	0.821180i	0.155586	+	0.0416891i
$389$	−0.190514	+	0.329980i	−0.00965945	+	0.0167307i	−0.870815	−	0.491611i	$-0.836408\pi$
$389$	−0.190514	+	0.329980i	−0.00965945	+	0.0167307i	0.861155	+	0.508342i	$0.169741\pi$
$390$	−31.4530	+	31.4092i	−1.59268	+	1.59047i
$391$	7.58789	+	13.1426i	0.383736	+	0.664650i
$392$	−3.80982	−	14.2184i	−0.192425	−	0.718139i
$393$	0.0889217	+	0.126385i	0.00448550	+	0.00637527i
$394$	47.6462	−	27.5086i	2.40038	−	1.38586i
$395$	−16.7751	+	16.7751i	−0.844046	+	0.844046i
$396$	13.1557	−	18.9700i	0.661098	−	0.953280i
$397$	4.01733	+	14.9929i	0.201624	+	0.752471i	0.990452	+	0.137857i	$0.0440214\pi$
$397$	4.01733	+	14.9929i	0.201624	+	0.752471i	−0.788828	+	0.614614i	$0.789312\pi$
$398$	−17.6788	+	4.73702i	−0.886158	+	0.237445i
$399$	1.39479	+	15.5383i	0.0698270	+	0.777890i
$400$	−21.1472	−	12.2093i	−1.05736	−	0.610466i
$401$	−32.4338	+	8.69060i	−1.61967	+	0.433988i	−0.950903	−	0.309488i	$-0.899842\pi$
$401$	−32.4338	+	8.69060i	−1.61967	+	0.433988i	−0.668762	+	0.743476i	$0.733176\pi$
$402$	−31.7660	−	14.7255i	−1.58434	−	0.734441i
$403$	−22.3925	−	2.02577i	−1.11545	−	0.100911i
$404$			29.0309i			1.44434i
$405$	−24.1503	+	2.33288i	−1.20004	+	0.115922i
$406$	−0.701404	−	1.21487i	−0.0348101	−	0.0602929i
$407$	−1.77592	−	3.07599i	−0.0880293	−	0.152471i
$408$	9.97710	+	27.2204i	0.493940	+	1.34761i
$409$	15.3477	+	15.3477i	0.758895	+	0.758895i	0.976121	−	0.217226i	$-0.0697008\pi$
$409$	15.3477	+	15.3477i	0.758895	+	0.758895i	−0.217226	+	0.976121i	$0.569701\pi$
$410$	−42.6655	−	42.6655i	−2.10710	−	2.10710i
$411$	2.41668	+	0.420502i	0.119206	+	0.0207418i
$412$	48.6709	+	84.3004i	2.39784	+	4.15318i
$413$	−14.0325	−	24.3049i	−0.690492	−	1.19597i
$414$	24.0367	+	50.9448i	1.18134	+	2.50380i
$415$		−	10.6765i		−	0.524091i
$416$	37.5574	+	26.4637i	1.84140	+	1.29749i
$417$	−1.23124	−	13.7163i	−0.0602941	−	0.671690i
$418$	−15.7100	+	4.20948i	−0.768400	+	0.205892i
$419$	27.3849	+	15.8107i	1.33784	+	0.772402i	0.986487	−	0.163842i	$-0.0523886\pi$
$419$	27.3849	+	15.8107i	1.33784	+	0.772402i	0.351352	+	0.936243i	$0.385722\pi$
$420$	47.6656	+	22.0959i	2.32584	+	1.07817i
$421$	6.47108	−	1.73392i	0.315381	−	0.0845062i	−0.0976561	−	0.995220i	$-0.531135\pi$
$421$	6.47108	−	1.73392i	0.315381	−	0.0845062i	0.413037	+	0.910714i	$0.364468\pi$
$422$	1.68194	+	6.27710i	0.0818757	+	0.305564i
$423$	6.71347	−	3.16754i	0.326420	−	0.154011i
$424$	−18.5381	+	18.5381i	−0.900288	+	0.900288i
$425$	4.19067	−	2.41948i	0.203277	−	0.117362i
$426$	6.19555	−	13.3651i	0.300175	−	0.647542i
$427$	−5.66858	−	21.1554i	−0.274322	−	1.02378i
$428$	9.66442	+	16.7393i	0.467147	+	0.809123i
$429$	8.36889	+	4.83955i	0.404054	+	0.233656i
$430$	−2.70831	+	4.69093i	−0.130606	+	0.226217i
$431$	6.56998	+	1.76042i	0.316465	+	0.0847965i	0.413555	−	0.910479i	$-0.364287\pi$
$431$	6.56998	+	1.76042i	0.316465	+	0.0847965i	−0.0970903	+	0.995276i	$0.530954\pi$
$432$	14.8475	+	53.9470i	0.714350	+	2.59553i
$433$	21.3766	+	12.3418i	1.02729	+	0.593108i	0.916208	−	0.400703i	$-0.131234\pi$
$433$	21.3766	+	12.3418i	1.02729	+	0.593108i	0.111085	+	0.993811i	$0.464567\pi$
$434$	9.64543	+	35.9972i	0.462995	+	1.72792i
$435$	−1.07983	−	0.187890i	−0.0517740	−	0.00900864i
$436$	−45.6662	+	45.6662i	−2.18701	+	2.18701i
$437$	7.32457	−	27.3357i	0.350382	−	1.30764i
$438$	4.55014	−	0.408442i	0.217414	−	0.0195161i
$439$		−	23.1471i		−	1.10475i	−0.833596	−	0.552374i	$-0.813722\pi$
$439$		−	23.1471i		−	1.10475i	0.833596	−	0.552374i	$-0.186278\pi$
$440$	−8.47243	+	31.6195i	−0.403907	+	1.50740i
$441$	5.29894	+	1.90160i	0.252331	+	0.0905523i
$442$	−18.4357	+	8.53051i	−0.876898	+	0.405755i
$443$	−20.9912	−	12.1193i	−0.997323	−	0.575805i	−0.0898679	−	0.995954i	$-0.528644\pi$
$443$	−20.9912	−	12.1193i	−0.997323	−	0.575805i	−0.907455	+	0.420149i	$0.861978\pi$
$444$	19.4623	+	3.38644i	0.923642	+	0.160713i
$445$	2.92041	−	5.05829i	0.138441	−	0.239786i
$446$	−53.2984			−2.52375
$447$	21.9563	+	18.3392i	1.03850	+	0.867413i
$448$	7.09303	−	26.4715i	0.335114	−	1.25066i
$449$	5.97900	−	1.60207i	0.282166	−	0.0756063i	−0.114960	−	0.993370i	$-0.536674\pi$
$449$	5.97900	−	1.60207i	0.282166	−	0.0756063i	0.397127	+	0.917764i	$0.370007\pi$
$450$	16.2443	−	7.66437i	0.765766	−	0.361302i
$451$	−6.56144	+	11.3648i	−0.308966	+	0.535145i
$452$	−69.1478			−3.25244
$453$	14.1865	−	5.19978i	0.666541	−	0.244307i
$454$	45.5251	−	26.2839i	2.13660	−	1.23356i
$455$	−7.58593	+	20.6521i	−0.355634	+	0.968187i
$456$	22.7374	−	49.0495i	1.06478	−	2.29695i
$457$	24.1719	+	24.1719i	1.13072	+	1.13072i	0.990058	+	0.140657i	$0.0449214\pi$
$457$	24.1719	+	24.1719i	1.13072	+	1.13072i	0.140657	+	0.990058i	$0.455079\pi$
$458$	−55.4824	+	32.0328i	−2.59252	+	1.49679i
$459$	−10.7294	−	2.79717i	−0.500806	−	0.130561i
$460$	−67.3903	−	67.3903i	−3.14209	−	3.14209i
$461$	9.41855	+	2.52369i	0.438666	+	0.117540i	0.471391	−	0.881924i	$-0.343752\pi$
$461$	9.41855	+	2.52369i	0.438666	+	0.117540i	−0.0327254	+	0.999464i	$0.510419\pi$
$462$	2.74685	−	15.7865i	0.127795	−	0.734457i
$463$	25.2403	+	6.76311i	1.17301	+	0.314308i	0.792152	−	0.610324i	$-0.208961\pi$
$463$	25.2403	+	6.76311i	1.17301	+	0.314308i	0.380862	+	0.924632i	$0.375627\pi$
$464$			2.52764i			0.117343i
$465$	26.4175	+	12.2461i	1.22508	+	0.567900i
$466$	34.4926	−	34.4926i	1.59784	−	1.59784i
$467$	39.3270			1.81984			0.909918	−	0.414789i	$-0.136144\pi$
$467$	39.3270			1.81984			0.909918	+	0.414789i	$0.136144\pi$
$468$	−50.4972	+	18.4689i	−2.33423	+	0.853724i
$469$	−17.3302			−0.800236
$470$	−12.4537	+	12.4537i	−0.574446	+	0.574446i
$471$	2.42023	−	1.70282i	0.111518	−	0.0784618i
$472$			97.2567i			4.47660i
$473$	1.13791	+	0.304903i	0.0523213	+	0.0140194i
$474$	−37.7846	+	13.8492i	−1.73550	+	0.636114i
$475$	−8.71629	−	2.33552i	−0.399931	−	0.107161i
$476$	16.9774	+	16.9774i	0.778160	+	0.778160i
$477$	−1.78573	−	9.86659i	−0.0817630	−	0.451760i
$478$	29.5284	−	17.0482i	1.35060	−	0.779769i
$479$	−4.47931	−	4.47931i	−0.204665	−	0.204665i	0.597330	−	0.801995i	$-0.296228\pi$
$479$	−4.47931	−	4.47931i	−0.204665	−	0.204665i	−0.801995	+	0.597330i	$0.796228\pi$
$480$	−34.2379	−	48.6626i	−1.56274	−	2.22113i
$481$	−0.745356	+	8.23904i	−0.0339853	+	0.375668i
$482$	8.68923	−	5.01673i	0.395783	−	0.228506i
$483$	21.3990	+	17.8737i	0.973687	+	0.813281i
$484$	−42.7677			−1.94399
$485$	0.860347	−	1.49016i	0.0390663	−	0.0676649i
$486$	−38.8318	−	13.6391i	−1.76145	−	0.618681i
$487$	−0.371552	+	0.0995570i	−0.0168366	+	0.00451136i	−0.267228	−	0.963633i	$-0.586108\pi$
$487$	−0.371552	+	0.0995570i	−0.0168366	+	0.00451136i	0.250391	+	0.968145i	$0.419441\pi$
$488$	−19.6440	+	73.3124i	−0.889243	+	3.31870i
$489$	−5.83954	+	2.14036i	−0.264073	+	0.0967906i
$490$	−13.3572			−0.603417
$491$	5.41089	−	9.37193i	0.244190	−	0.422949i	−0.717714	−	0.696338i	$-0.754811\pi$
$491$	5.41089	−	9.37193i	0.244190	−	0.422949i	0.961904	+	0.273389i	$0.0881446\pi$
$492$	−25.1179	−	68.5290i	−1.13240	−	3.08952i
$493$	−0.433788	−	0.250448i	−0.0195368	−	0.0112796i
$494$	35.5583	+	13.0612i	1.59984	+	0.587653i
$495$	−8.09083	−	9.55430i	−0.363656	−	0.429434i
$496$	17.3796	−	64.8614i	0.780365	−	2.91236i
$497$		−	7.29145i		−	0.327066i
$498$	7.61689	−	16.4312i	0.341321	−	0.736301i
$499$	7.96381	−	29.7213i	0.356509	−	1.33051i	−0.522066	−	0.852905i	$-0.674838\pi$
$499$	7.96381	−	29.7213i	0.356509	−	1.33051i	0.878575	−	0.477605i	$-0.158495\pi$
$500$	25.8912	−	25.8912i	1.15789	−	1.15789i
$501$	1.17018	+	3.19259i	0.0522797	+	0.142634i
$502$	−13.4995	−	50.3808i	−0.602512	−	2.24861i
$503$	12.5778	+	7.26179i	0.560816	+	0.323787i	0.753473	−	0.657479i	$-0.228377\pi$
$503$	12.5778	+	7.26179i	0.560816	+	0.323787i	−0.192657	+	0.981266i	$0.561710\pi$
$504$	34.4214	+	40.6476i	1.53325	+	1.81059i
$505$	15.2078	+	4.07491i	0.676738	+	0.181331i
$506$	−14.5336	+	25.1729i	−0.646097	+	1.11907i
$507$	−9.44140	−	20.4416i	−0.419307	−	0.907844i
$508$	47.9860	+	83.1142i	2.12903	+	3.68759i
$509$	6.01726	+	22.4567i	0.266710	+	0.995376i	0.961195	+	0.275869i	$0.0889655\pi$
$509$	6.01726	+	22.4567i	0.266710	+	0.995376i	−0.694485	+	0.719507i	$0.744368\pi$
$510$	26.2019	−	2.35200i	1.16024	−	0.104148i
$511$	1.95827	−	1.13061i	0.0866286	−	0.0500151i
$512$	22.4255	−	22.4255i	0.991077	−	0.991077i
$513$	10.4596	+	17.8364i	0.461804	+	0.787498i
$514$	−8.98097	−	33.5174i	−0.396133	−	1.47839i
$515$	50.9923	−	13.6633i	2.24699	−	0.602079i
$516$	−5.35869	+	3.77026i	−0.235903	+	0.165976i
$517$	3.31727	+	1.91523i	0.145893	+	0.0842315i
$518$	13.2447	−	3.54891i	0.581939	−	0.155930i
$519$	−24.9667	+	17.5660i	−1.09592	+	0.771062i
$520$	58.5506	−	48.8357i	2.56761	−	2.14159i
$521$		−	3.53656i		−	0.154940i	−0.996995	−	0.0774698i	$-0.975316\pi$
$521$		−	3.53656i		−	0.154940i	0.996995	−	0.0774698i	$-0.0246841\pi$
$522$	−1.52782	−	1.05954i	−0.0668708	−	0.0463748i
$523$	3.21981	+	5.57688i	0.140793	+	0.243860i	0.927795	−	0.373090i	$-0.121702\pi$
$523$	3.21981	+	5.57688i	0.140793	+	0.243860i	−0.787003	+	0.616950i	$0.788368\pi$
$524$	−0.221750	−	0.384083i	−0.00968721	−	0.0167787i
$525$	5.69923	−	6.82331i	0.248735	−	0.297794i
$526$	−25.7372	−	25.7372i	−1.12220	−	1.12220i
$527$	9.40933	+	9.40933i	0.409877	+	0.409877i
$528$	−18.5087	+	22.1593i	−0.805490	+	0.964360i
$529$	−13.7887	−	23.8828i	−0.599510	−	1.03838i
$530$	11.8948	+	20.6024i	0.516677	+	0.894911i
$531$	−30.5659	−	21.1974i	−1.32645	−	0.919889i
$532$		−	44.7737i		−	1.94118i
$533$	27.7392	−	12.8353i	1.20152	−	0.555961i
$534$	8.10321	−	5.70124i	0.350660	−	0.246717i
$535$	10.1254	−	2.71309i	0.437758	−	0.117297i
$536$	52.0105	+	30.0283i	2.24651	+	1.29702i
$537$	−14.5004	+	10.2021i	−0.625737	+	0.440255i
$538$	−64.3812	+	17.2509i	−2.77567	+	0.743739i
$539$	0.751881	+	2.80606i	0.0323858	+	0.120865i
$540$	69.6315	−	0.471741i	2.99646	−	0.0203005i
$541$	−31.4961	+	31.4961i	−1.35412	+	1.35412i	−0.473127	+	0.880994i	$0.656875\pi$
$541$	−31.4961	+	31.4961i	−1.35412	+	1.35412i	−0.880994	+	0.473127i	$0.843125\pi$
$542$	43.6714	−	25.2137i	1.87585	−	1.08302i
$543$	27.7075	−	2.48716i	1.18904	−	0.106734i
$544$	−7.03768	−	26.2650i	−0.301738	−	1.12610i
$545$	17.5122	+	30.3320i	0.750141	+	1.29928i
$546$	−26.4085	+	26.3717i	−1.13018	+	1.12861i
$547$	10.2455	−	17.7458i	0.438067	−	0.758754i	−0.559474	−	0.828848i	$-0.688997\pi$
$547$	10.2455	−	17.7458i	0.438067	−	0.758754i	0.997540	+	0.0700942i	$0.0223300\pi$
$548$	−6.80011	−	1.82208i	−0.290486	−	0.0778355i
$549$	−18.7592	−	22.1524i	−0.800624	−	0.945442i
$550$	8.02667	+	4.63420i	0.342258	+	0.197603i
$551$	0.241757	+	0.902248i	0.0102992	+	0.0384371i
$552$	−33.2514	−	90.7196i	−1.41528	−	3.86128i
$553$	−14.0846	+	14.0846i	−0.598940	+	0.598940i
$554$	0.126756	−	0.473061i	0.00538536	−	0.0200984i
$555$	4.50580	−	9.71997i	0.191261	−	0.412590i
$556$			39.5235i			1.67617i
$557$	−6.77282	+	25.2765i	−0.286974	+	1.07100i	0.660411	+	0.750904i	$0.270382\pi$
$557$	−6.77282	+	25.2765i	−0.286974	+	1.07100i	−0.947385	+	0.320096i	$0.896285\pi$
$558$	31.9199	+	37.6936i	1.35128	+	1.59570i
$559$	−1.75748	−	2.10710i	−0.0743336	−	0.0891208i
$560$	−56.9047	−	32.8539i	−2.40466	−	1.38833i
$561$	−1.96902	−	5.37205i	−0.0831319	−	0.226808i
$562$	−12.3094	+	21.3205i	−0.519242	+	0.899353i
$563$	−27.1030			−1.14226			−0.571128	−	0.820861i	$-0.693494\pi$
$563$	−27.1030			−1.14226			−0.571128	+	0.820861i	$0.693494\pi$
$564$	−20.0030	+	7.33169i	−0.842277	+	0.308720i
$565$	−9.70591	+	36.2230i	−0.408331	+	1.52391i
$566$	−29.3607	+	7.86717i	−1.23412	+	0.330682i
$567$	−20.2770	+	1.95873i	−0.851556	+	0.0822588i
$568$	−12.6340	+	21.8827i	−0.530110	+	0.918177i
$569$	15.9876			0.670235			0.335118	−	0.942176i	$-0.391224\pi$
$569$	15.9876			0.670235			0.335118	+	0.942176i	$0.391224\pi$
$570$	−37.6518	−	31.4490i	−1.57706	−	1.31725i
$571$	−11.0928	+	6.40445i	−0.464221	+	0.268018i	−0.713817	−	0.700332i	$-0.753035\pi$
$571$	−11.0928	+	6.40445i	−0.464221	+	0.268018i	0.249597	+	0.968350i	$0.419702\pi$
$572$	−22.6804	−	15.9810i	−0.948315	−	0.668201i
$573$	−5.95349	−	8.46173i	−0.248711	−	0.353494i
$574$	−35.8227	−	35.8227i	−1.49521	−	1.49521i
$575$	−13.9666	+	8.06360i	−0.582446	+	0.336275i
$576$	−6.46886	−	35.7420i	−0.269536	−	1.48925i
$577$	3.19790	+	3.19790i	0.133130	+	0.133130i	0.770532	−	0.637402i	$-0.219991\pi$
$577$	3.19790	+	3.19790i	0.133130	+	0.133130i	−0.637402	+	0.770532i	$0.719991\pi$
$578$	−31.7421	−	8.50528i	−1.32030	−	0.353773i
$579$	−3.04182	+	1.11492i	−0.126414	+	0.0463344i
$580$	3.03845	+	0.814150i	0.126165	+	0.0338057i
$581$		−	8.96421i		−	0.371898i
$582$	2.38719	−	1.67958i	0.0989523	−	0.0696207i
$583$	3.65855	−	3.65855i	0.151522	−	0.151522i
$584$	−7.83605			−0.324258
$585$	2.58686	+	29.0452i	0.106953	+	1.20087i
$586$	28.2119			1.16542
$587$	−8.24606	+	8.24606i	−0.340351	+	0.340351i	−0.856499	−	0.516148i	$-0.827365\pi$
$587$	−8.24606	+	8.24606i	−0.340351	+	0.340351i	0.516148	+	0.856499i	$0.327365\pi$
$588$	−14.6589	−	6.79530i	−0.604523	−	0.280233i
$589$		−	24.8147i		−	1.02247i
$590$	85.2455	+	22.8415i	3.50950	+	0.940368i
$591$	6.18707	−	35.5580i	0.254502	−	1.46266i
$592$	−23.8649	−	6.39458i	−0.980841	−	0.262816i
$593$	−25.2582	−	25.2582i	−1.03723	−	1.03723i	−0.999280	−	0.0379511i	$-0.987917\pi$
$593$	−25.2582	−	25.2582i	−1.03723	−	1.03723i	−0.0379511	−	0.999280i	$-0.512083\pi$
$594$	−5.63555	−	20.4763i	−0.231230	−	0.840152i
$595$	11.2766	−	6.51057i	0.462297	−	0.266907i
$596$	−58.0556	−	58.0556i	−2.37805	−	2.37805i
$597$	−5.04968	+	10.8932i	−0.206669	+	0.445830i
$598$	61.4422	−	28.4303i	2.51256	−	1.16260i
$599$	−10.2097	+	5.89457i	−0.417157	+	0.240846i	−0.693860	−	0.720110i	$-0.744091\pi$
$599$	−10.2097	+	5.89457i	−0.417157	+	0.240846i	0.276703	+	0.960955i	$0.410758\pi$
$600$	−28.9270	+	10.6026i	−1.18094	+	0.432849i
$601$	25.8982			1.05641			0.528204	−	0.849117i	$-0.322866\pi$
$601$	25.8982			1.05641			0.528204	+	0.849117i	$0.322866\pi$
$602$	−2.27394	+	3.93858i	−0.0926790	+	0.160525i
$603$	−20.7732	+	9.80114i	−0.845948	+	0.399133i
$604$	−41.8859	+	11.2233i	−1.70431	+	0.456669i
$605$	−6.00308	+	22.4038i	−0.244060	+	0.910844i
$606$	20.4977	+	17.1209i	0.832662	+	0.695488i
$607$	−40.7117			−1.65244			−0.826218	−	0.563350i	$-0.809512\pi$
$607$	−40.7117			−1.65244			−0.826218	+	0.563350i	$0.809512\pi$
$608$	−25.3535	+	43.9136i	−1.02822	+	1.78093i
$609$	−0.906645	−	0.157756i	−0.0367391	−	0.00639259i
$610$	59.6448	+	34.4359i	2.41495	+	1.39427i
$611$	−3.74652	−	8.09680i	−0.151568	−	0.327562i
$612$	29.9519	+	10.7487i	1.21073	+	0.434488i
$613$	−8.59441	+	32.0748i	−0.347125	+	1.29549i	0.542985	+	0.839742i	$0.317294\pi$
$613$	−8.59441	+	32.0748i	−0.347125	+	1.29549i	−0.890110	+	0.455746i	$0.849373\pi$
$614$			42.1574i			1.70133i
$615$	−39.4244	+	3.53892i	−1.58975	+	0.142703i
$616$	−7.11360	+	26.5483i	−0.286615	+	1.06966i
$617$	−18.8503	+	18.8503i	−0.758883	+	0.758883i	−0.976119	−	0.217236i	$-0.930296\pi$
$617$	−18.8503	+	18.8503i	−0.758883	+	0.758883i	0.217236	+	0.976119i	$0.430296\pi$
$618$	88.2250	+	15.3511i	3.54893	+	0.617512i
$619$	7.34762	+	27.4217i	0.295326	+	1.10217i	0.940958	+	0.338523i	$0.109927\pi$
$619$	7.34762	+	27.4217i	0.295326	+	1.10217i	−0.645632	+	0.763648i	$0.723406\pi$
$620$	−72.3712	−	41.7835i	−2.90650	−	1.67807i
$621$	35.7587	+	9.32234i	1.43495	+	0.374092i
$622$	16.7626	+	4.49153i	0.672120	+	0.180094i
$623$	2.45202	−	4.24703i	0.0982382	−	0.170154i
$624$	64.9677	−	17.3596i	2.60079	−	0.694940i
$625$	−15.5980	−	27.0165i	−0.623920	−	1.08066i
$626$	14.7555	+	55.0681i	0.589747	+	2.20097i
$627$	−4.48731	+	9.68009i	−0.179206	+	0.386586i
$628$	−7.35506	+	4.24645i	−0.293499	+	0.169452i
$629$	3.46204	−	3.46204i	0.138041	−	0.138041i
$630$	43.7118	−	20.6240i	1.74152	−	0.821679i
$631$	−4.20481	−	15.6925i	−0.167391	−	0.624710i	−0.997723	−	0.0674422i	$-0.978516\pi$
$631$	−4.20481	−	15.6925i	−0.167391	−	0.624710i	0.830333	−	0.557268i	$-0.188150\pi$
$632$	66.6746	−	17.8654i	2.65217	−	0.710647i
$633$	3.86779	+	1.79296i	0.153731	+	0.0712636i
$634$	14.0606	+	8.11788i	0.558417	+	0.322402i
$635$	50.2747	−	13.4711i	1.99509	−	0.534583i
$636$	2.57279	+	28.6615i	0.102018	+	1.13650i
$637$	2.33295	−	6.35128i	0.0924348	−	0.251647i
$638$		−	0.959398i		−	0.0379829i
$639$	−4.12370	−	8.74002i	−0.163131	−	0.345750i
$640$	8.73675	+	15.1325i	0.345350	+	0.598164i
$641$	19.6897	+	34.1036i	0.777697	+	1.34701i	0.933266	+	0.359185i	$0.116945\pi$
$641$	19.6897	+	34.1036i	0.777697	+	1.34701i	−0.155570	+	0.987825i	$0.549721\pi$
$642$	17.5186	+	3.04822i	0.691403	+	0.120304i
$643$	−22.8953	−	22.8953i	−0.902903	−	0.902903i	0.0927834	−	0.995686i	$-0.470424\pi$
$643$	−22.8953	−	22.8953i	−0.902903	−	0.902903i	−0.995686	+	0.0927834i	$0.970424\pi$
$644$	−56.5820	−	56.5820i	−2.22964	−	2.22964i
$645$	1.22287	+	3.33635i	0.0481505	+	0.131369i
$646$	−11.2097	−	19.4158i	−0.441040	−	0.763904i
$647$	−17.9872	−	31.1547i	−0.707149	−	1.22482i	−0.965910	−	0.258877i	$-0.916648\pi$
$647$	−17.9872	−	31.1547i	−0.707149	−	1.22482i	0.258761	−	0.965941i	$-0.416686\pi$
$648$	64.2481	+	29.2558i	2.52391	+	1.14928i
$649$		−	19.1940i		−	0.753429i
$650$	−9.06532	−	19.5915i	−0.355571	−	0.768444i
$651$	22.1806	+	10.2821i	0.869325	+	0.402985i
$652$	17.2413	−	4.61979i	0.675222	−	0.180925i
$653$	−42.9879	−	24.8190i	−1.68224	−	0.971244i	−0.960165	−	0.279435i	$-0.909853\pi$
$653$	−42.9879	−	24.8190i	−1.68224	−	0.971244i	−0.722080	−	0.691810i	$-0.756814\pi$
$654$	5.31180	+	59.1747i	0.207708	+	2.31391i
$655$	−0.232327	+	0.0622519i	−0.00907777	+	0.00243238i
$656$	23.6258	+	88.1728i	0.922433	+	3.44257i
$657$	1.70789	−	2.46272i	0.0666312	−	0.0960799i
$658$	−10.4563	+	10.4563i	−0.407630	+	0.407630i
$659$	12.9834	−	7.49595i	0.505760	−	0.292001i	−0.225329	−	0.974283i	$-0.572346\pi$
$659$	12.9834	−	7.49595i	0.505760	−	0.292001i	0.731089	+	0.682282i	$0.239012\pi$
$660$	20.6758	+	29.3866i	0.804805	+	1.14387i
$661$	−1.73707	−	6.48283i	−0.0675641	−	0.252153i	0.923880	−	0.382681i	$-0.124999\pi$
$661$	−1.73707	−	6.48283i	−0.0675641	−	0.252153i	−0.991445	+	0.130529i	$0.958333\pi$
$662$	−46.6509	−	80.8017i	−1.81314	−	3.14045i
$663$	−3.45802	+	12.8697i	−0.134298	+	0.499816i
$664$	−15.5324	+	26.9029i	−0.602773	+	1.04403i
$665$	−23.4546	−	6.28464i	−0.909530	−	0.243708i
$666$	13.8689	−	11.7445i	0.537409	−	0.455091i
$667$	1.44572	+	0.834686i	0.0559784	+	0.0323192i
$668$	−2.52573	−	9.42616i	−0.0977235	−	0.364709i
$669$	−22.4143	+	26.8352i	−0.866588	+	1.03751i
$670$	38.5348	−	38.5348i	1.48873	−	1.48873i
$671$	3.87682	−	14.4685i	0.149663	−	0.558549i
$672$	−28.7468	−	40.8579i	−1.10893	−	1.57613i
$673$		−	38.3980i		−	1.48013i	−0.672534	−	0.740067i	$-0.734794\pi$
$673$		−	38.3980i		−	1.48013i	0.672534	−	0.740067i	$-0.265206\pi$
$674$	5.54067	−	20.6781i	0.213419	−	0.796490i
$675$	2.97253	−	11.4021i	0.114413	−	0.438866i
$676$	21.7428	+	60.8542i	0.836262	+	2.34055i
$677$	27.2519	+	15.7339i	1.04737	+	0.604702i	0.921913	−	0.387397i	$-0.126626\pi$
$677$	27.2519	+	15.7339i	1.04737	+	0.604702i	0.125461	+	0.992099i	$0.459959\pi$
$678$	−40.7797	+	48.8228i	−1.56613	+	1.87503i
$679$	0.722362	−	1.25117i	0.0277217	−	0.0480154i
$680$	−45.1237			−1.73041
$681$	5.91162	−	33.9750i	0.226534	−	1.30192i
$682$	−6.59663	+	24.6190i	−0.252598	+	0.942709i
$683$	38.2622	−	10.2523i	1.46406	−	0.392295i	0.563173	−	0.826339i	$-0.309581\pi$
$683$	38.2622	−	10.2523i	1.46406	−	0.392295i	0.900891	+	0.434045i	$0.142914\pi$
$684$	−25.3218	−	53.6686i	−0.968204	−	2.05207i
$685$	−1.90899	+	3.30647i	−0.0729387	+	0.126334i
$686$	−53.0482			−2.02539
$687$	−7.20462	+	41.4060i	−0.274874	+	1.57974i
$688$	7.09671	−	4.09729i	0.270560	−	0.156208i
$689$	−11.8739	+	2.05753i	−0.452358	+	0.0783858i
$690$	−87.3251	+	7.83870i	−3.32441	+	0.298414i
$691$	10.1361	+	10.1361i	0.385594	+	0.385594i	0.873113	−	0.487519i	$-0.162098\pi$
$691$	10.1361	+	10.1361i	0.385594	+	0.385594i	−0.487519	+	0.873113i	$0.662098\pi$
$692$	75.8736	−	43.8056i	2.88428	−	1.66524i
$693$	−6.79319	−	8.02195i	−0.258052	−	0.304729i
$694$	26.3839	+	26.3839i	1.00152	+	1.00152i
$695$	20.7043	+	5.54770i	0.785359	+	0.210436i
$696$	2.44762	+	2.04440i	0.0927770	+	0.0774928i
$697$	−17.4729	−	4.68186i	−0.661835	−	0.177338i
$698$		−	38.6842i		−	1.46422i
$699$	−2.86101	−	31.8723i	−0.108213	−	1.20552i
$700$	−18.0418	+	18.0418i	−0.681917	+	0.681917i
$701$	15.9193			0.601265			0.300633	−	0.953740i	$-0.402802\pi$
$701$	15.9193			0.601265			0.300633	+	0.953740i	$0.402802\pi$
$702$	−16.7403	+	46.5462i	−0.631823	+	1.75677i
$703$	−9.13025			−0.344354
$704$	13.2532	−	13.2532i	0.499499	−	0.499499i
$705$	1.03298	+	11.5076i	0.0389042	+	0.433402i
$706$		−	83.7690i		−	3.15269i
$707$	12.7687	+	3.42137i	0.480217	+	0.128674i
$708$	81.9326	+	68.4349i	3.07922	+	2.57194i
$709$	−49.7497	−	13.3304i	−1.86839	−	0.500633i	−0.999989	−	0.00477057i	$-0.998481\pi$
$709$	−49.7497	−	13.3304i	−1.86839	−	0.500633i	−0.868401	−	0.495863i	$-0.834852\pi$
$710$	16.2130	+	16.2130i	0.608462	+	0.608462i
$711$	−8.91718	+	24.8484i	−0.334420	+	0.931886i
$712$	−14.7177	+	8.49729i	−0.551570	+	0.318449i
$713$	−31.3592	−	31.3592i	−1.17441	−	1.17441i
$714$	21.9996	−	1.97478i	0.823313	−	0.0739044i
$715$	−11.5552	+	9.63791i	−0.432139	+	0.360437i
$716$	44.0665	−	25.4418i	1.64684	−	0.950805i
$717$	3.83439	−	22.0368i	0.143198	−	0.822980i
$718$	46.7828			1.74592
$719$	7.69872	−	13.3346i	0.287114	−	0.497296i	−0.686006	−	0.727596i	$-0.740638\pi$
$719$	7.69872	−	13.3346i	0.287114	−	0.497296i	0.973120	+	0.230300i	$0.0739708\pi$
$720$	−86.7903	−	7.19833i	−3.23448	−	0.268266i
$721$	42.8140	−	11.4720i	1.59448	−	0.427239i
$722$	2.16287	−	8.07192i	0.0804935	−	0.300406i
$723$	1.12833	−	6.48469i	0.0419632	−	0.241168i
$724$	−79.8392			−2.96720
$725$	0.266149	−	0.460984i	0.00988453	−	0.0171205i
$726$	−25.2221	+	30.1968i	−0.936081	+	1.12071i
$727$	−0.433980	−	0.250558i	−0.0160954	−	0.00929270i	0.491931	−	0.870634i	$-0.336291\pi$
$727$	−0.433980	−	0.250558i	−0.0160954	−	0.00929270i	−0.508026	+	0.861342i	$0.669625\pi$
$728$	49.1601	−	41.0033i	1.82199	−	1.51968i
$729$	−23.1976	+	13.8156i	−0.859171	+	0.511688i
$730$	−1.84035	+	6.86829i	−0.0681145	+	0.254207i
$731$			1.62390i			0.0600619i
$732$	47.9385	+	68.1353i	1.77186	+	2.51835i
$733$	−1.47240	+	5.49507i	−0.0543844	+	0.202965i	−0.987772	−	0.155904i	$-0.950171\pi$
$733$	−1.47240	+	5.49507i	−0.0543844	+	0.202965i	0.933388	+	0.358869i	$0.116838\pi$
$734$	37.2392	−	37.2392i	1.37452	−	1.37452i
$735$	−5.61730	+	6.72522i	−0.207197	+	0.248063i
$736$	23.4550	+	87.5353i	0.864563	+	3.22659i
$737$	−10.2644	−	5.92618i	−0.378096	−	0.218294i
$738$	−63.1991	−	22.6799i	−2.32639	−	0.834857i
$739$	−9.70292	−	2.59989i	−0.356928	−	0.0956385i	0.0758992	−	0.997115i	$-0.475817\pi$
$739$	−9.70292	−	2.59989i	−0.356928	−	0.0956385i	−0.432827	+	0.901477i	$0.642484\pi$
$740$	−15.3737	+	26.6281i	−0.565149	+	0.978867i
$741$	21.5300	−	12.4104i	0.790926	−	0.455908i
$742$	9.98708	+	17.2981i	0.366637	+	0.635034i
$743$	−7.54919	−	28.1739i	−0.276953	−	1.03360i	−0.954521	−	0.298142i	$-0.903633\pi$
$743$	−7.54919	−	28.1739i	−0.276953	−	1.03360i	0.677569	−	0.735460i	$-0.263034\pi$
$744$	−48.7512	−	69.2904i	−1.78731	−	2.54031i
$745$	−38.5613	+	22.2634i	−1.41278	+	0.815666i
$746$	−44.5607	+	44.5607i	−1.63148	+	1.63148i
$747$	−5.06973	−	10.7451i	−0.185492	−	0.393142i
$748$	4.24995	+	15.8610i	0.155394	+	0.579937i
$749$	8.50144	−	2.27795i	0.310636	−	0.0832346i
$750$	−3.01161	−	33.5500i	−0.109968	−	1.22507i
$751$	12.4527	+	7.18958i	0.454406	+	0.262351i	0.709689	−	0.704515i	$-0.248835\pi$
$751$	12.4527	+	7.18958i	0.454406	+	0.262351i	−0.255283	+	0.966866i	$0.582169\pi$
$752$	25.7368	−	6.89616i	0.938525	−	0.251477i
$753$	−31.0434	−	14.3905i	−1.13128	−	0.524420i
$754$	−1.28709	+	1.82665i	−0.0468731	+	0.0665225i
$755$			23.5172i			0.855878i
$756$	58.4638	−	0.396082i	2.12631	−	0.0144054i
$757$	−18.2836	−	31.6681i	−0.664529	−	1.15100i	−0.979413	−	0.201868i	$-0.935299\pi$
$757$	−18.2836	−	31.6681i	−0.664529	−	1.15100i	0.314883	−	0.949130i	$-0.398035\pi$
$758$	19.2082	+	33.2695i	0.697673	+	1.20840i
$759$	6.56229	+	17.9038i	0.238196	+	0.649868i
$760$	59.5011	+	59.5011i	2.15833	+	2.15833i
$761$	7.39684	+	7.39684i	0.268135	+	0.268135i	0.828348	−	0.560213i	$-0.189281\pi$
$761$	7.39684	+	7.39684i	0.268135	+	0.268135i	−0.560213	+	0.828348i	$0.689281\pi$
$762$	86.9835	+	15.1351i	3.15108	+	0.548286i
$763$	14.7036	+	25.4673i	0.532304	+	0.921978i
$764$	14.8467	+	25.7152i	0.537133	+	0.930342i
$765$	9.83485	−	14.1815i	0.355580	−	0.512734i
$766$			10.9925i			0.397177i
$767$	−25.7498	+	36.5443i	−0.929773	+	1.31954i
$768$	−1.09979	−	12.2519i	−0.0396852	−	0.442103i
$769$	6.08238	−	1.62977i	0.219336	−	0.0587710i	−0.147477	−	0.989065i	$-0.547115\pi$
$769$	6.08238	−	1.62977i	0.219336	−	0.0587710i	0.366814	+	0.930294i	$0.380449\pi$
$770$	21.5989	+	12.4701i	0.778370	+	0.449392i
$771$	−20.6526	−	9.57374i	−0.743785	−	0.344790i
$772$	8.98102	−	2.40646i	0.323234	−	0.0866103i
$773$	1.54426	+	5.76325i	0.0555431	+	0.207290i	0.988121	−	0.153680i	$-0.0491125\pi$
$773$	1.54426	+	5.76325i	0.0555431	+	0.207290i	−0.932578	+	0.360970i	$0.882446\pi$
$774$	−0.498223	+	6.00708i	−0.0179083	+	0.215920i
$775$	−9.99924	+	9.99924i	−0.359183	+	0.359183i
$776$	−4.33582	+	2.50329i	−0.155647	+	0.0898628i
$777$	3.78315	−	8.16105i	0.135720	−	0.292776i
$778$	−0.260374	−	0.971730i	−0.00933487	−	0.0348382i
$779$	16.8666	+	29.2138i	0.604308	+	1.04669i
$780$	0.0582473	−	83.6885i	0.00208559	−	2.99653i
$781$	2.49336	−	4.31862i	0.0892194	−	0.154533i
$782$	−38.7025	−	10.3703i	−1.38400	−	0.370842i
$783$	−1.17598	+	0.323658i	−0.0420262	+	0.0115666i
$784$	17.5003	+	10.1038i	0.625009	+	0.360849i
$785$	1.19210	+	4.44899i	0.0425480	+	0.158791i
$786$	−0.401964	−	0.0699415i	−0.0143376	−	0.00249473i
$787$	−11.5157	+	11.5157i	−0.410489	+	0.410489i	−0.881909	−	0.471420i	$-0.843742\pi$
$787$	−11.5157	+	11.5157i	−0.410489	+	0.410489i	0.471420	+	0.881909i	$0.343742\pi$
$788$	−26.8093	+	100.054i	−0.955041	+	3.56426i
$789$	−23.7821	+	2.13479i	−0.846665	+	0.0760006i
$790$		−	62.6360i		−	2.22849i
$791$	−8.14925	+	30.4134i	−0.289754	+	1.08138i
$792$	6.48762	+	35.8456i	0.230527	+	1.27372i
$793$	−26.7916	+	22.3463i	−0.951397	+	0.793539i
$794$	−35.4909	−	20.4907i	−1.25952	−	0.727186i
$795$	15.3754	+	2.67531i	0.545309	+	0.0948835i
$796$	17.2294	−	29.8422i	0.610680	−	1.05773i
$797$	24.0973			0.853569			0.426784	−	0.904353i	$-0.359646\pi$
$797$	24.0973			0.853569			0.426784	+	0.904353i	$0.359646\pi$
$798$	−31.6131	−	26.4051i	−1.11909	−	0.934731i
$799$	−1.36659	+	5.10019i	−0.0483465	+	0.180432i
$800$	27.9116	−	7.47890i	0.986825	−	0.264419i
$801$	0.537241	−	6.47751i	0.0189825	−	0.228872i
$802$	44.3270	−	76.7766i	1.56524	−	2.71108i
$803$	1.54647			0.0545738
$804$	61.8942	−	22.6861i	2.18284	−	0.800076i
$805$	−37.5825	+	21.6983i	−1.32461	+	0.764764i
$806$	45.5875	−	38.0235i	1.60575	−	1.33932i
$807$	−18.3895	+	39.6701i	−0.647342	+	1.39645i
$808$	−32.3925	−	32.3925i	−1.13956	−	1.13956i
$809$	34.9272	−	20.1652i	1.22797	−	0.708971i	0.261368	−	0.965239i	$-0.415826\pi$
$809$	34.9272	−	20.1652i	1.22797	−	0.708971i	0.966606	+	0.256268i	$0.0824931\pi$
$810$	40.7318	−	49.4425i	1.43117	−	1.73723i
$811$	30.0454	+	30.0454i	1.05504	+	1.05504i	0.998395	+	0.0566424i	$0.0180395\pi$
$811$	30.0454	+	30.0454i	1.05504	+	1.05504i	0.0566424	+	0.998395i	$0.481961\pi$
$812$	2.55113	+	0.683574i	0.0895273	+	0.0239888i
$813$	5.67092	−	32.5916i	0.198888	−	1.14304i
$814$	9.05823	+	2.42714i	0.317491	+	0.0850714i
$815$		−	9.68028i		−	0.339085i
$816$	−36.1082	−	16.7383i	−1.26404	−	0.585959i
$817$	2.14130	−	2.14130i	0.0749147	−	0.0749147i
$818$	−57.3064			−2.00367
$819$	2.17197	+	24.3869i	0.0758948	+	0.852146i
$820$	113.601			3.96713
$821$	19.6435	−	19.6435i	0.685563	−	0.685563i	−0.275685	−	0.961248i	$-0.588905\pi$
$821$	19.6435	−	19.6435i	0.685563	−	0.685563i	0.961248	+	0.275685i	$0.0889046\pi$
$822$	−5.29685	+	3.72675i	−0.184749	+	0.129985i
$823$			25.3342i			0.883093i	0.897238	+	0.441547i	$0.145570\pi$
$823$			25.3342i			0.883093i	−0.897238	+	0.441547i	$0.854430\pi$
$824$	−148.368	−	39.7552i	−5.16866	−	1.38494i
$825$	5.70884	−	2.09246i	0.198756	−	0.0728502i
$826$	71.5735	+	19.1781i	2.49036	+	0.667290i
$827$	6.21133	+	6.21133i	0.215989	+	0.215989i	0.806806	−	0.590817i	$-0.201194\pi$
$827$	6.21133	+	6.21133i	0.215989	+	0.215989i	−0.590817	+	0.806806i	$0.701194\pi$
$828$	−99.8230	−	35.8229i	−3.46909	−	1.24493i
$829$	−27.6454	+	15.9611i	−0.960166	+	0.554352i	−0.896224	−	0.443601i	$-0.853701\pi$
$829$	−27.6454	+	15.9611i	−0.960166	+	0.554352i	−0.0639420	+	0.997954i	$0.520367\pi$
$830$	19.9324	+	19.9324i	0.691865	+	0.691865i
$831$	−0.184875	−	0.262764i	−0.00641324	−	0.00911517i
$832$	−43.0134	+	7.45347i	−1.49122	+	0.258403i
$833$	−3.46798	+	2.00224i	−0.120158	+	0.0693734i
$834$	27.9061	+	23.3088i	0.966310	+	0.807119i
$835$	−5.29240			−0.183151
$836$	15.3106	−	26.5188i	0.529529	−	0.917172i
$837$	32.4021	−	0.219519i	1.11998	−	0.00758768i
$838$	−80.6434	+	21.6083i	−2.78578	+	0.746447i
$839$	5.79267	−	21.6185i	0.199985	−	0.746355i	−0.790935	−	0.611901i	$-0.790405\pi$
$839$	5.79267	−	21.6185i	0.199985	−	0.746355i	0.990920	−	0.134454i	$-0.0429281\pi$
$840$	−77.8394	+	28.5304i	−2.68571	+	0.984394i
$841$	28.9449			0.998100
$842$	−8.84399	+	15.3182i	−0.304784	+	0.527901i
$843$	5.55802	+	15.1639i	0.191428	+	0.522273i
$844$	−10.5959	−	6.11753i	−0.364725	−	0.210574i
$845$	34.9303	−	2.84814i	1.20164	−	0.0979791i
$846$	−6.62004	+	18.4472i	−0.227602	+	0.634229i
$847$	−5.04029	+	18.8106i	−0.173186	+	0.646340i
$848$		−	35.9903i		−	1.23591i
$849$	−8.38643	+	18.0913i	−0.287821	+	0.620892i
$850$	−3.30669	+	12.3407i	−0.113419	+	0.423284i
$851$	−11.5382	+	11.5382i	−0.395525	+	0.395525i
$852$	9.54484	+	26.0411i	0.327001	+	0.892154i
$853$	−7.89664	−	29.4707i	−0.270376	−	1.00906i	−0.958877	−	0.283822i	$-0.908398\pi$
$853$	−7.89664	−	29.4707i	−0.270376	−	1.00906i	0.688501	−	0.725235i	$-0.258269\pi$
$854$	50.0788	+	28.9130i	1.71366	+	0.989382i
$855$	−31.6685	+	5.73161i	−1.08304	+	0.196017i
$856$	−29.4610	−	7.89406i	−1.00696	−	0.269814i
$857$	−1.77173	+	3.06872i	−0.0605211	+	0.104826i	−0.894698	−	0.446671i	$-0.852610\pi$
$857$	−1.77173	+	3.06872i	−0.0605211	+	0.104826i	0.834177	+	0.551496i	$0.185943\pi$
$858$	−24.6593	+	6.58906i	−0.841856	+	0.224947i
$859$	17.6074	+	30.4970i	0.600758	+	1.04054i	0.992706	+	0.120557i	$0.0384679\pi$
$859$	17.6074	+	30.4970i	0.600758	+	1.04054i	−0.391948	+	0.919987i	$0.628199\pi$
$860$	−2.63946	−	9.85061i	−0.0900050	−	0.335903i
$861$	−33.1014	+	2.97134i	−1.12809	+	0.101263i
$862$	−15.5523	+	8.97915i	−0.529715	+	0.305831i
$863$	−5.22630	+	5.22630i	−0.177905	+	0.177905i	−0.790442	−	0.612537i	$-0.790149\pi$
$863$	−5.22630	+	5.22630i	−0.177905	+	0.177905i	0.612537	+	0.790442i	$0.290149\pi$
$864$	−57.5650	−	32.7172i	−1.95840	−	1.11306i
$865$	−12.2975	−	45.8950i	−0.418129	−	1.56048i
$866$	−62.9501	+	16.8674i	−2.13913	+	0.573178i
$867$	−17.6313	+	12.4050i	−0.598790	+	0.421296i
$868$	−60.7641	−	35.0822i	−2.06247	−	1.19077i
$869$	−13.1585	+	3.52580i	−0.446370	+	0.119605i
$870$	2.36676	−	1.66520i	0.0802406	−	0.0564555i
$871$	11.5927	+	25.0535i	0.392803	+	0.848906i
$872$		−	101.908i		−	3.45104i
$873$	0.158270	−	1.90826i	0.00535664	−	0.0645850i
$874$	37.3595	+	64.7085i	1.26370	+	2.18880i
$875$	−8.33641	−	14.4391i	−0.281822	−	0.488130i
$876$	−5.51385	+	6.60137i	−0.186296	+	0.223040i
$877$	−14.6210	−	14.6210i	−0.493717	−	0.493717i	0.415758	−	0.909475i	$-0.363516\pi$
$877$	−14.6210	−	14.6210i	−0.493717	−	0.493717i	−0.909475	+	0.415758i	$0.863516\pi$
$878$	43.2141	+	43.2141i	1.45841	+	1.45841i
$879$	11.8643	−	14.2044i	0.400174	−	0.479102i
$880$	−22.4692	−	38.9178i	−0.757437	−	1.31192i
$881$	22.9876	+	39.8157i	0.774472	+	1.34142i	0.935091	+	0.354408i	$0.115318\pi$
$881$	22.9876	+	39.8157i	0.774472	+	1.34142i	−0.160619	+	0.987016i	$0.551349\pi$
$882$	−13.4430	+	6.34263i	−0.452648	+	0.213567i
$883$			7.05482i			0.237414i	0.992929	+	0.118707i	$0.0378749\pi$
$883$			7.05482i			0.237414i	−0.992929	+	0.118707i	$0.962125\pi$
$884$	13.1868	−	35.9002i	0.443521	−	1.20745i
$885$	47.3499	−	33.3144i	1.59165	−	1.11985i
$886$	61.8153	−	16.5633i	2.07672	−	0.556457i
$887$	−18.0959	−	10.4477i	−0.607601	−	0.350798i	0.164425	−	0.986390i	$-0.447423\pi$
$887$	−18.0959	−	10.4477i	−0.607601	−	0.350798i	−0.772026	+	0.635591i	$0.780756\pi$
$888$	−25.4945	+	17.9374i	−0.855539	+	0.601939i
$889$	42.2115	−	11.3105i	1.41573	−	0.379343i
$890$	3.99130	+	14.8957i	0.133789	+	0.499306i
$891$	−12.6796	−	5.77374i	−0.424783	−	0.193427i
$892$	70.9562	−	70.9562i	2.37579	−	2.37579i
$893$	8.52724	−	4.92320i	0.285353	−	0.164749i
$894$	−75.2291	+	6.75291i	−2.51604	+	0.225851i
$895$	−7.14226	−	26.6553i	−0.238740	−	0.890988i
$896$	7.33552	+	12.7055i	0.245063	+	0.424461i
$897$	11.5248	−	42.8917i	0.384802	−	1.43211i
$898$	−8.17146	+	14.1534i	−0.272685	+	0.472304i
$899$	1.41390	+	0.378854i	0.0471563	+	0.0126355i
$900$	−11.4225	+	31.8297i	−0.380751	+	1.06099i
$901$	6.17657	+	3.56605i	0.205772	+	0.118802i
$902$	−8.96748	−	33.4671i	−0.298584	−	1.11433i
$903$	1.02674	+	2.80126i	0.0341679	+	0.0932200i
$904$	77.1546	−	77.1546i	2.56612	−	2.56612i
$905$	−11.2066	+	41.8236i	−0.372520	+	1.39026i
$906$	−16.7777	+	36.1930i	−0.557401	+	1.20243i
$907$		−	3.13870i		−	0.104219i	−0.998641	−	0.0521094i	$-0.983406\pi$
$907$		−	3.13870i		−	0.104219i	0.998641	−	0.0521094i	$-0.0165945\pi$
$908$	−25.6158	+	95.5993i	−0.850089	+	3.17258i
$909$	17.2404	−	3.12030i	0.571827	−	0.103494i
$910$	−24.3938	−	52.7187i	−0.808646	−	1.74761i
$911$	18.1814	+	10.4970i	0.602375	+	0.347782i	0.769975	−	0.638074i	$-0.220268\pi$
$911$	18.1814	+	10.4970i	0.602375	+	0.347782i	−0.167600	+	0.985855i	$0.553602\pi$
$912$	25.5415	+	69.6846i	0.845762	+	2.30749i
$913$	3.06537	−	5.30937i	0.101449	−	0.175715i
$914$	−90.2550			−2.98537
$915$	42.4214	−	15.5487i	1.40241	−	0.514025i
$916$	31.2185	−	116.509i	1.03149	−	3.84957i
$917$	−0.195066	+	0.0522677i	−0.00644164	+	0.00172603i
$918$	25.2533	−	14.8090i	0.833482	−	0.488770i
$919$	21.7742	−	37.7141i	0.718266	−	1.24407i	−0.243420	−	0.969921i	$-0.578269\pi$
$919$	21.7742	−	37.7141i	0.718266	−	1.24407i	0.961686	−	0.274153i	$-0.0883973\pi$
$920$	150.387			4.95812
$921$	21.2258	+	17.7291i	0.699415	+	0.584192i
$922$	−22.2954	+	12.8723i	−0.734261	+	0.423926i
$923$	−10.5409	+	4.87745i	−0.346959	+	0.160543i
$924$	17.3598	+	24.6735i	0.571094	+	0.811699i
$925$	3.67909	+	3.67909i	0.120968	+	0.120968i
$926$	−59.7483	+	34.4957i	−1.96345	+	1.13360i
$927$	44.8317	−	37.9646i	1.47246	−	1.24692i
$928$	−2.11505	−	2.11505i	−0.0694299	−	0.0694299i
$929$	−29.0496	−	7.78381i	−0.953086	−	0.255379i	−0.251415	−	0.967879i	$-0.580896\pi$
$929$	−29.0496	−	7.78381i	−0.953086	−	0.255379i	−0.701671	+	0.712501i	$0.747562\pi$
$930$	−72.1826	+	26.4571i	−2.36696	+	0.867561i
$931$	7.21314	+	1.93276i	0.236401	+	0.0633435i
$932$			91.8400i			3.00832i
$933$	9.31087	−	6.55093i	0.304824	−	0.214468i
$934$	−73.4210	+	73.4210i	−2.40241	+	2.40241i
$935$	8.90532			0.291235
$936$	35.7370	−	76.9518i	1.16810	−	2.51525i
$937$	−12.6407			−0.412955			−0.206478	−	0.978451i	$-0.566200\pi$
$937$	−12.6407			−0.412955			−0.206478	+	0.978451i	$0.566200\pi$
$938$	32.3545	−	32.3545i	1.05641	−	1.05641i
$939$	33.9316	+	15.7294i	1.10732	+	0.513308i
$940$		−	33.1592i		−	1.08153i
$941$	4.19656	+	1.12447i	0.136804	+	0.0366565i	0.326571	−	0.945173i	$-0.394107\pi$
$941$	4.19656	+	1.12447i	0.136804	+	0.0366565i	−0.189767	+	0.981829i	$0.560773\pi$
$942$	−1.33936	+	7.69748i	−0.0436386	+	0.250797i
$943$	58.2334	+	15.6036i	1.89634	+	0.508123i
$944$	−94.4084	−	94.4084i	−3.07273	−	3.07273i
$945$	7.99876	−	30.6817i	0.260200	−	0.998077i
$946$	−2.69365	+	1.55518i	−0.0875780	+	0.0505632i
$947$	−11.8871	−	11.8871i	−0.386277	−	0.386277i	0.487080	−	0.873357i	$-0.338062\pi$
$947$	−11.8871	−	11.8871i	−0.386277	−	0.386277i	−0.873357	+	0.487080i	$0.838062\pi$
$948$	31.8653	−	68.7401i	1.03494	−	2.23257i
$949$	−2.94440	−	2.07468i	−0.0955794	−	0.0673471i
$950$	20.6331	−	11.9125i	0.669425	−	0.386492i
$951$	10.0004	−	3.66543i	0.324284	−	0.118860i
$952$	−37.8866			−1.22791
$953$	14.1311	−	24.4758i	0.457751	−	0.792848i	−0.541091	−	0.840964i	$-0.681988\pi$
$953$	14.1311	−	24.4758i	0.457751	−	0.792848i	0.998842	+	0.0481162i	$0.0153218\pi$
$954$	21.7542	+	15.0865i	0.704317	+	0.488442i
$955$	15.5548	−	4.16789i	0.503341	−	0.134870i
$956$	−16.6149	+	62.0076i	−0.537364	+	2.00547i
$957$	−0.483047	−	0.403470i	−0.0156147	−	0.0130423i
$958$	16.7252			0.540366
$959$	−1.60282	+	2.77617i	−0.0517578	+	0.0896471i
$960$	55.6978	+	9.69139i	1.79764	+	0.312788i
$961$	−6.83023	−	3.94344i	−0.220330	−	0.127208i
$962$	−13.9902	−	16.7733i	−0.451064	−	0.540793i
$963$	8.90208	−	7.53851i	0.286866	−	0.242925i
$964$	−4.88920	+	18.2467i	−0.157471	+	0.587688i
$965$		−	5.04247i		−	0.162323i
$966$	−73.3196	+	6.58151i	−2.35902	+	0.211757i
$967$	−7.29613	+	27.2295i	−0.234628	+	0.875643i	0.743688	+	0.668526i	$0.233075\pi$
$967$	−7.29613	+	27.2295i	−0.234628	+	0.875643i	−0.978316	+	0.207117i	$0.933592\pi$
$968$	47.7199	−	47.7199i	1.53378	−	1.53378i
$969$	−14.4898	−	2.52122i	−0.465481	−	0.0809934i
$970$	1.17583	+	4.38826i	0.0377536	+	0.140899i
$971$	−48.3799	−	27.9321i	−1.55258	−	0.896385i	−0.997930	−	0.0643034i	$-0.979517\pi$
$971$	−48.3799	−	27.9321i	−1.55258	−	0.896385i	−0.554654	−	0.832081i	$-0.687149\pi$
$972$	69.8545	−	33.5391i	2.24058	−	1.07577i
$973$	17.3837	+	4.65794i	0.557295	+	0.149327i
$974$	0.507797	−	0.879530i	0.0162709	−	0.0281820i
$975$	−13.6765	−	3.67482i	−0.437999	−	0.117688i
$976$	−52.0967	−	90.2341i	−1.66757	−	2.88832i
$977$	−1.21070	−	4.51840i	−0.0387337	−	0.144556i	0.943851	−	0.330372i	$-0.107174\pi$
$977$	−1.21070	−	4.51840i	−0.0387337	−	0.144556i	−0.982585	+	0.185815i	$0.940507\pi$
$978$	6.90613	−	14.8980i	0.220834	−	0.476385i
$979$	2.90460	−	1.67697i	0.0928313	−	0.0535962i
$980$	17.7825	−	17.7825i	0.568040	−	0.568040i
$981$	32.0277	+	22.2112i	1.02257	+	0.709147i
$982$	7.39502	+	27.5986i	0.235985	+	0.880707i
$983$	−8.75529	+	2.34597i	−0.279250	+	0.0748249i	−0.395726	−	0.918369i	$-0.629507\pi$
$983$	−8.75529	+	2.34597i	−0.279250	+	0.0748249i	0.116476	+	0.993194i	$0.462840\pi$
$984$	104.490	+	48.4377i	3.33104	+	1.54414i
$985$	48.6498	+	28.0880i	1.55011	+	0.894958i
$986$	1.27743	−	0.342285i	0.0406815	−	0.0109006i
$987$	0.867306	+	9.66200i	0.0276067	+	0.307545i
$988$	−64.7272	+	29.9503i	−2.05925	+	0.952847i
$989$		−	5.41208i		−	0.172094i
$990$	32.9424	+	2.73222i	1.04698	+	0.0868356i
$991$	−17.0282	−	29.4937i	−0.540919	−	0.936899i	−0.998852	−	0.0479121i	$-0.984743\pi$
$991$	−17.0282	−	29.4937i	−0.540919	−	0.936899i	0.457933	−	0.888987i	$-0.348590\pi$
$992$	39.7313	+	68.8166i	1.26147	+	2.18493i
$993$	−60.3016	−	10.4924i	−1.91361	−	0.332968i
$994$	13.6127	+	13.6127i	0.431768	+	0.431768i
$995$	−13.2144	−	13.2144i	−0.418924	−	0.418924i
$996$	11.7346	+	32.0153i	0.371824	+	1.01444i
$997$	18.6485	+	32.3001i	0.590604	+	1.02296i	0.994151	+	0.107997i	$0.0344437\pi$
$997$	18.6485	+	32.3001i	0.590604	+	1.02296i	−0.403547	+	0.914959i	$0.632223\pi$
$998$	40.6200	+	70.3558i	1.28580	+	2.22708i
$999$	−0.0807691	−	11.9219i	−0.00255542	−	0.377194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.1	✓	48
3.2	odd	2		351.2.ba.a.89.12		48
9.4	even	3		351.2.bf.a.206.1		48
9.5	odd	6		117.2.bc.a.50.12	yes	48
13.6	odd	12		117.2.bc.a.110.12	yes	48
39.32	even	12		351.2.bf.a.305.1		48
117.32	even	12	inner	117.2.x.a.32.1	yes	48
117.58	odd	12		351.2.ba.a.71.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.1	✓	48	1.1	even	1	trivial
117.2.x.a.32.1	yes	48	117.32	even	12	inner
117.2.bc.a.50.12	yes	48	9.5	odd	6
117.2.bc.a.110.12	yes	48	13.6	odd	12
351.2.ba.a.71.12		48	117.58	odd	12
351.2.ba.a.89.12		48	3.2	odd	2
351.2.bf.a.206.1		48	9.4	even	3
351.2.bf.a.305.1		48	39.32	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86694 + 1.86694i) q^{2} +(0.154854 + 1.72511i) q^{3} -4.97091i q^{4} +(-2.60400 - 0.697740i) q^{5} +(-3.50978 - 2.93158i) q^{6} +(-2.18636 - 0.585835i) q^{7} +(5.54651 + 5.54651i) q^{8} +(-2.95204 + 0.534283i) q^{9} +(6.16415 - 3.55887i) q^{10} +(-1.09462 - 1.09462i) q^{11} +(8.57539 - 0.769767i) q^{12} +(0.615605 + 3.55261i) q^{13} +(5.17552 - 2.98809i) q^{14} +(0.800441 - 4.60025i) q^{15} -10.7681 q^{16} +(1.06695 - 1.84800i) q^{17} +(4.51380 - 6.50875i) q^{18} +(-3.84372 + 1.02992i) q^{19} +(-3.46841 + 12.9443i) q^{20} +(0.672064 - 3.86245i) q^{21} +4.08719 q^{22} +(-3.55589 + 6.15899i) q^{23} +(-8.70946 + 10.4273i) q^{24} +(1.96386 + 1.13384i) q^{25} +(-7.78180 - 5.48320i) q^{26} +(-1.37884 - 5.00987i) q^{27} +(-2.91213 + 10.8682i) q^{28} -0.234733i q^{29} +(7.09401 + 10.0828i) q^{30} +(-1.61398 + 6.02345i) q^{31} +(9.01044 - 9.01044i) q^{32} +(1.71884 - 2.05786i) q^{33} +(1.45819 + 5.44203i) q^{34} +(5.28454 + 3.05103i) q^{35} +(2.65587 + 14.6743i) q^{36} +(2.21625 + 0.593843i) q^{37} +(5.25318 - 9.09878i) q^{38} +(-6.03333 + 1.61213i) q^{39} +(-10.5731 - 18.3131i) q^{40} +(-2.19405 - 8.18830i) q^{41} +(5.95625 + 8.46565i) q^{42} +(-0.659047 + 0.380501i) q^{43} +(-5.44127 + 5.44127i) q^{44} +(8.05991 + 0.668484i) q^{45} +(-4.85981 - 18.1371i) q^{46} +(-2.39009 + 0.640422i) q^{47} +(-1.66749 - 18.5763i) q^{48} +(-1.62519 - 0.938303i) q^{49} +(-5.78321 + 1.54961i) q^{50} +(3.35324 + 1.55443i) q^{51} +(17.6597 - 3.06012i) q^{52} +3.34230i q^{53} +(11.9273 + 6.77892i) q^{54} +(2.08664 + 3.61416i) q^{55} +(-8.87735 - 15.3760i) q^{56} +(-2.37195 - 6.47136i) q^{57} +(0.438232 + 0.438232i) q^{58} +(8.76738 + 8.76738i) q^{59} +(-22.8674 - 3.97892i) q^{60} +(4.83804 + 8.37973i) q^{61} +(-8.23221 - 14.2586i) q^{62} +(6.76724 + 0.561271i) q^{63} +12.1076i q^{64} +(0.875762 - 9.68054i) q^{65} +(0.632918 + 7.05086i) q^{66} +(7.39553 - 1.98163i) q^{67} +(-9.18627 - 5.30369i) q^{68} +(-11.1756 - 5.18058i) q^{69} +(-15.5620 + 4.16982i) q^{70} +(0.833742 + 3.11157i) q^{71} +(-19.3369 - 13.4101i) q^{72} +(-0.706395 + 0.706395i) q^{73} +(-5.24627 + 3.02893i) q^{74} +(-1.65189 + 3.56347i) q^{75} +(5.11965 + 19.1068i) q^{76} +(1.75198 + 3.03451i) q^{77} +(8.25411 - 14.2736i) q^{78} +(4.39999 - 7.62101i) q^{79} +(28.0403 + 7.51337i) q^{80} +(8.42908 - 3.15445i) q^{81} +(19.3832 + 11.1909i) q^{82} +(1.02501 + 3.82540i) q^{83} +(-19.1999 - 3.34077i) q^{84} +(-4.06776 + 4.06776i) q^{85} +(0.520028 - 1.94077i) q^{86} +(0.404942 - 0.0363494i) q^{87} -12.1427i q^{88} +(-0.560753 + 2.09276i) q^{89} +(-16.2954 + 13.7993i) q^{90} +(0.735305 - 8.12794i) q^{91} +(30.6158 + 17.6760i) q^{92} +(-10.6411 - 1.85154i) q^{93} +(3.26652 - 5.65778i) q^{94} +10.7277 q^{95} +(16.9393 + 14.1487i) q^{96} +(-0.165197 + 0.616524i) q^{97} +(4.78588 - 1.28237i) q^{98} +(3.81621 + 2.64653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

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