LMFDB - Embedded newform 117.2.x.a.32.1

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			32.1
Character	$\chi$	$=$	117.32
Dual form			117.2.x.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86694 - 1.86694i) q^{2} +(0.154854 - 1.72511i) q^{3} +4.97091i q^{4} +(-2.60400 + 0.697740i) q^{5} +(-3.50978 + 2.93158i) q^{6} +(-2.18636 + 0.585835i) q^{7} +(5.54651 - 5.54651i) q^{8} +(-2.95204 - 0.534283i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	−0.913672	−	0.406452i	$-0.866766\pi$
$2$	−1.86694	−	1.86694i	−1.32012	−	1.32012i	−0.406452	−	0.913672i	$-0.633234\pi$
$3$	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	−0.788780	−	0.614676i	$-0.789287\pi$
$5$	−2.60400	+	0.697740i	−1.16455	+	0.312039i	−0.375766	+	0.926715i	$0.622620\pi$
$6$	−3.50978	+	2.93158i	−1.43286	+	1.19681i
$7$	−2.18636	+	0.585835i	−0.826368	+	0.221425i	−0.647129	−	0.762381i	$-0.724030\pi$
$7$	−2.18636	+	0.585835i	−0.826368	+	0.221425i	−0.179240	+	0.983805i	$0.557364\pi$
$8$	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	−0.852602	−	0.522561i	$-0.824977\pi$
$11$	−1.09462	+	1.09462i	−0.330041	+	0.330041i	0.522561	+	0.852602i	$0.324977\pi$
$12$	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	0.965913	−	0.258866i	$-0.0833487\pi$
$17$	1.06695	+	1.84800i	0.258772	+	0.448207i	−0.707141	+	0.707073i	$0.750015\pi$
$18$	4.51380	+	6.50875i	1.06391	+	1.53413i
$19$	−3.84372	−	1.02992i	−0.881809	−	0.236280i	−0.210622	−	0.977568i	$-0.567549\pi$
$19$	−3.84372	−	1.02992i	−0.881809	−	0.236280i	−0.671187	+	0.741288i	$0.734215\pi$
$20$	−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	−0.951833	−	0.306617i	$-0.900803\pi$
$23$	−3.55589	−	6.15899i	−0.741455	−	1.28424i	0.210378	−	0.977620i	$-0.432530\pi$
$24$	−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	$0.00693793\pi$
$29$			0.234733i			0.0435889i	−0.999762	+	0.0217944i	$0.993062\pi$
$30$	7.09401	−	10.0828i	1.29518	−	1.84085i
$31$	−1.61398	−	6.02345i	−0.289879	−	1.08184i	−0.945200	−	0.326493i	$-0.894133\pi$
$31$	−1.61398	−	6.02345i	−0.289879	−	1.08184i	0.655321	−	0.755351i	$-0.272534\pi$
$32$	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	−0.0719995	−	0.997405i	$-0.522938\pi$
$37$	2.21625	−	0.593843i	0.364349	−	0.0976271i	0.436349	+	0.899778i	$0.356271\pi$
$38$	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	0.552678	+	0.833395i	$0.313606\pi$
$41$	−2.19405	+	8.18830i	−0.342653	+	1.27880i	−0.895331	+	0.445402i	$0.853061\pi$
$42$	5.95625	−	8.46565i	0.919069	−	1.30628i
$43$	−0.659047	−	0.380501i	−0.100504	−	0.0580259i	0.448906	−	0.893579i	$-0.351814\pi$
$43$	−0.659047	−	0.380501i	−0.100504	−	0.0580259i	−0.549409	+	0.835553i	$0.685147\pi$
$44$	−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	0.0802545	−	0.996774i	$-0.474427\pi$
$47$	−2.39009	−	0.640422i	−0.348630	−	0.0934152i	−0.428885	+	0.903359i	$0.641093\pi$
$48$	−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	$-0.926275\pi$
$53$		−	3.34230i		−	0.459100i	0.973297	−	0.229550i	$-0.0737254\pi$
$54$	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	0.153225	−	0.988191i	$-0.451034\pi$
$59$	8.76738	−	8.76738i	1.14142	−	1.14142i	0.988191	−	0.153225i	$-0.0489658\pi$
$60$	−22.8674	+	3.97892i	−2.95217	+	0.513677i
$61$	4.83804	−	8.37973i	0.619447	−	1.07291i	−0.370139	−	0.928976i	$-0.620690\pi$
$61$	4.83804	−	8.37973i	0.619447	−	1.07291i	0.989587	−	0.143938i	$-0.0459766\pi$
$62$	−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	0.680522	−	0.732728i	$-0.261753\pi$
$67$	7.39553	+	1.98163i	0.903508	+	0.242094i	0.222986	+	0.974822i	$0.428420\pi$
$68$	−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	−0.898641	−	0.438684i	$-0.855445\pi$
$71$	0.833742	−	3.11157i	0.0989469	−	0.369275i	0.997588	+	0.0694091i	$0.0221114\pi$
$72$	−19.3369	+	13.4101i	−2.27888	+	1.58040i
$73$	−0.706395	−	0.706395i	−0.0826773	−	0.0826773i	0.664559	−	0.747236i	$-0.268620\pi$
$73$	−0.706395	−	0.706395i	−0.0826773	−	0.0826773i	−0.747236	+	0.664559i	$0.768620\pi$
$74$	−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	0.999984	−	0.00572053i	$-0.00182091\pi$
$79$	4.39999	+	7.62101i	0.495038	+	0.857430i	−0.504946	+	0.863151i	$0.668488\pi$
$80$	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	−0.886579	−	0.462578i	$-0.846925\pi$
$83$	1.02501	−	3.82540i	0.112510	−	0.419892i	0.999089	+	0.0426854i	$0.0135913\pi$
$84$	−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	0.929817	−	0.368023i	$-0.119965\pi$
$89$	−0.560753	−	2.09276i	−0.0594397	−	0.221832i	−0.989256	+	0.146191i	$0.953299\pi$
$90$	−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	0.957032	−	0.289982i	$-0.0936495\pi$
$97$	−0.165197	−	0.616524i	−0.0167732	−	0.0625985i	−0.973805	+	0.227384i	$0.926983\pi$
$98$	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	−0.967083	−	0.254461i	$-0.918102\pi$
$103$	−16.9587	−	9.79113i	−1.67099	−	0.964749i	−0.703911	−	0.710288i	$-0.748565\pi$
$104$	−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	0.328318	−	0.944567i	$-0.393518\pi$
$107$	−3.36744	−	1.94419i	−0.325543	−	0.187952i	−0.653861	+	0.756615i	$0.726852\pi$
$108$	−24.9036	−	6.85407i	−2.39635	−	0.659533i
$109$	−9.18667	+	9.18667i	−0.879924	+	0.879924i	−0.993526	−	0.113602i	$-0.963761\pi$
$109$	−9.18667	+	9.18667i	−0.879924	+	0.879924i	0.113602	+	0.993526i	$0.463761\pi$
$110$	−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	$0.227034\pi$
$113$			13.9105i			1.30859i	−0.756240	+	0.654294i	$0.772966\pi$
$114$	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	−0.483841	−	0.875156i	$-0.660759\pi$
$127$	−16.7201	−	9.65336i	−1.48367	−	0.856597i	−0.999828	+	0.0185590i	$0.994092\pi$
$128$	−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	0.503372	−	0.864070i	$-0.332093\pi$
$131$	0.0772661	+	0.0446096i	0.00675077	+	0.00389756i	−0.496621	+	0.867968i	$0.665426\pi$
$132$	−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	0.979815	−	0.199908i	$-0.0640643\pi$
$137$	0.366549	+	1.36798i	0.0313164	+	0.116874i	−0.948498	+	0.316782i	$0.897398\pi$
$138$	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	0.999104	−	0.0423180i	$-0.0134743\pi$
$149$	11.6791	+	11.6791i	0.956786	+	0.956786i	−0.0423180	+	0.999104i	$0.513474\pi$
$150$	−3.56880	+	9.73674i	−0.291392	+	0.795001i
$151$	−2.25779	+	8.42619i	−0.183736	+	0.685714i	0.811161	+	0.584823i	$0.198836\pi$
$151$	−2.25779	+	8.42619i	−0.183736	+	0.685714i	−0.994897	+	0.100891i	$0.967831\pi$
$152$	−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	−0.898099	−	0.439793i	$-0.855052\pi$
$157$	−0.854259	+	1.47962i	−0.0681773	+	0.118087i	0.829922	+	0.557880i	$0.188385\pi$
$158$	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	−0.919930	−	0.392082i	$-0.871755\pi$
$163$	0.929365	−	3.46844i	0.0727935	−	0.271669i	0.992724	+	0.120413i	$0.0384217\pi$
$164$	−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	0.331440	−	0.943476i	$-0.392466\pi$
$167$	1.89626	+	0.508102i	0.146737	+	0.0393181i	−0.184703	+	0.982794i	$0.559132\pi$
$168$	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	−0.307911	−	0.951415i	$-0.599630\pi$
$173$	8.81239	−	15.2635i	0.669994	−	1.16046i	0.977905	−	0.209048i	$-0.0670366\pi$
$174$	−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	−0.608878	−	0.793264i	$-0.708380\pi$
$179$	5.11814	−	8.86487i	0.382548	−	0.662592i	0.991426	+	0.130672i	$0.0417135\pi$
$180$	3.32298	+	40.0651i	0.247680	+	2.98628i
$181$			16.0613i			1.19382i	0.802306	+	0.596912i	$0.203606\pi$
$181$			16.0613i			1.19382i	−0.802306	+	0.596912i	$0.796394\pi$
$182$	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	0.301027	−	0.953616i	$-0.402670\pi$
$191$	−5.17313	−	2.98671i	−0.374314	−	0.216111i	−0.675342	+	0.737505i	$0.736004\pi$
$192$	−20.8869	−	1.87491i	−1.50738	−	0.135310i
$193$	0.484108	−	1.80671i	0.0348468	−	0.130050i	−0.946311	−	0.323257i	$-0.895222\pi$
$193$	0.484108	−	1.80671i	0.0348468	−	0.130050i	0.981158	+	0.193207i	$0.0618888\pi$
$194$	−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	−0.890445	−	0.455091i	$-0.849607\pi$
$197$	−20.1278	+	5.39323i	−1.43405	+	0.384252i	−0.543603	+	0.839343i	$0.682940\pi$
$198$	−12.0655	−	2.18371i	−0.857460	−	0.155190i
$199$	6.00336	−	3.46604i	0.425567	−	0.245701i	−0.271889	−	0.962329i	$-0.587648\pi$
$199$	6.00336	−	3.46604i	0.425567	−	0.245701i	0.697456	+	0.716627i	$0.254315\pi$
$200$	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	0.905273	−	0.424830i	$-0.139666\pi$
$211$	1.23067	+	2.13158i	0.0847226	+	0.146744i	−0.820550	+	0.571574i	$0.806333\pi$
$212$	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	−0.0431901	−	0.999067i	$-0.513752\pi$
$223$	14.2743	−	14.2743i	0.955877	−	0.955877i	0.999067	+	0.0431901i	$0.0137521\pi$
$224$	−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	−0.832501	−	0.554024i	$-0.813092\pi$
$227$	−19.2317	+	5.15313i	−1.27646	+	0.342025i	−0.443955	+	0.896049i	$0.646425\pi$
$228$	−32.1686	−	11.7907i	−2.13042	−	0.780861i
$229$	23.4382	−	6.28023i	1.54884	−	0.415010i	0.619728	−	0.784817i	$-0.287243\pi$
$229$	23.4382	−	6.28023i	1.54884	−	0.415010i	0.929109	+	0.369807i	$0.120576\pi$
$230$		−	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	−0.638603	−	0.769536i	$-0.720487\pi$
$239$	−12.4741	+	3.34242i	−0.806882	+	0.216203i	−0.168278	+	0.985740i	$0.553821\pi$
$240$	−8.61927	−	49.5362i	−0.556371	−	3.19755i
$241$	−3.67070	+	0.983562i	−0.236451	+	0.0633568i	−0.375099	−	0.926985i	$-0.622391\pi$
$241$	−3.67070	+	0.983562i	−0.236451	+	0.0633568i	0.138648	+	0.990342i	$0.455724\pi$
$242$	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	−0.988836	−	0.149007i	$-0.952392\pi$
$251$	−9.87750	−	17.1083i	−0.623462	−	1.07987i	0.365374	−	0.930861i	$-0.380941\pi$
$252$	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	0.584972	−	0.811054i	$-0.301106\pi$
$257$	−6.57131	−	11.3818i	−0.409907	−	0.709980i	−0.994879	+	0.101074i	$0.967772\pi$
$258$	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	$-0.860262\pi$
$263$		−	13.7858i		−	0.850069i	0.905177	−	0.425035i	$-0.139738\pi$
$264$	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	0.347229	−	0.937780i	$-0.387123\pi$
$269$	21.8626	−	12.6224i	1.33299	−	0.769599i	0.985756	+	0.168181i	$0.0537893\pi$
$270$	−26.3288	+	25.9745i	−1.60232	+	1.58076i
$271$	−18.4487	+	4.94331i	−1.12068	+	0.300285i	−0.771158	−	0.636644i	$-0.780322\pi$
$271$	−18.4487	+	4.94331i	−1.12068	+	0.300285i	−0.349520	+	0.936929i	$0.613655\pi$
$272$	−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	0.495166	−	0.868798i	$-0.335107\pi$
$277$	−0.160642	−	0.0927467i	−0.00965204	−	0.00557261i	−0.504818	+	0.863226i	$0.668440\pi$
$278$	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	0.517255	−	0.855831i	$-0.326954\pi$
$281$	9.00672	+	2.41334i	0.537296	+	0.143968i	0.0200406	+	0.999799i	$0.493620\pi$
$282$	10.2661	−	4.75899i	0.611340	−	0.283394i
$283$	9.97030	−	5.75636i	0.592673	−	0.342180i	−0.173481	−	0.984837i	$-0.555501\pi$
$283$	9.97030	−	5.75636i	0.592673	−	0.342180i	0.766154	+	0.642657i	$0.222168\pi$
$284$	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	−0.892484	−	0.451078i	$-0.851039\pi$
$293$	−7.55565	+	7.55565i	−0.441406	+	0.441406i	0.451078	+	0.892484i	$0.351039\pi$
$294$	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	0.951630	−	0.307246i	$-0.0994075\pi$
$307$	11.2905	+	11.2905i	0.644384	+	0.644384i	−0.307246	+	0.951630i	$0.599407\pi$
$308$	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	−0.944033	−	0.329852i	$-0.893001\pi$
$311$	−3.28642	+	5.69225i	−0.186356	+	0.322778i	0.757677	+	0.652630i	$0.226334\pi$
$312$	−42.4056	+	24.5222i	−2.40074	+	1.38830i
$313$	10.7965	+	18.7000i	0.610253	+	1.05699i	0.991198	+	0.132391i	$0.0422654\pi$
$313$	10.7965	+	18.7000i	0.610253	+	1.05699i	−0.380945	+	0.924598i	$0.624401\pi$
$314$	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	−0.996109	−	0.0881244i	$-0.971913\pi$
$317$	−1.59156	+	5.93980i	−0.0893912	+	0.333612i	0.906718	+	0.421737i	$0.138579\pi$
$318$	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	−0.481574	−	0.876405i	$-0.659935\pi$
$331$	−9.14621	−	34.1341i	−0.502721	−	1.87618i	−0.0211475	−	0.999776i	$-0.506732\pi$
$332$	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	0.296403	−	0.955063i	$-0.404213\pi$
$337$	−7.02186	−	4.05407i	−0.382505	−	0.220839i	−0.678908	+	0.734224i	$0.737546\pi$
$338$	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	$0.123845\pi$
$347$			14.1322i			0.758656i	−0.925262	+	0.379328i	$0.876155\pi$
$348$	−0.180690	+	2.01293i	−0.00968600	+	0.107904i
$349$	−10.3603	−	10.3603i	−0.554576	−	0.554576i	0.373182	−	0.927758i	$-0.378267\pi$
$349$	−10.3603	−	10.3603i	−0.554576	−	0.554576i	−0.927758	+	0.373182i	$0.878267\pi$
$350$	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	−0.975909	−	0.218178i	$-0.929989\pi$
$353$	−22.4349	−	22.4349i	−1.19409	−	1.19409i	−0.218178	−	0.975909i	$-0.570011\pi$
$354$	−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	−0.955679	−	0.294409i	$-0.904877\pi$
$359$	−12.5293	+	12.5293i	−0.661270	+	0.661270i	0.294409	+	0.955679i	$0.404877\pi$
$360$	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	0.992665	+	0.120898i	$0.0385773\pi$
$379$	3.76589	+	14.0545i	0.193441	+	0.721931i	−0.799224	+	0.601033i	$0.794756\pi$
$380$			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	0.778311	−	0.627879i	$-0.216077\pi$
$383$	2.94400	+	2.94400i	0.150432	+	0.150432i	−0.627879	+	0.778311i	$0.716077\pi$
$384$	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	0.861155	−	0.508342i	$-0.169741\pi$
$389$	−0.190514	−	0.329980i	−0.00965945	−	0.0167307i	−0.870815	+	0.491611i	$0.836408\pi$
$390$	−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	−0.788828	−	0.614614i	$-0.789312\pi$
$397$	4.01733	−	14.9929i	0.201624	−	0.752471i	0.990452	−	0.137857i	$-0.0440214\pi$
$398$	−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	−0.668762	−	0.743476i	$-0.733176\pi$
$401$	−32.4338	−	8.69060i	−1.61967	−	0.433988i	−0.950903	+	0.309488i	$0.899842\pi$
$402$	−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	−0.217226	−	0.976121i	$-0.569701\pi$
$409$	15.3477	−	15.3477i	0.758895	−	0.758895i	0.976121	+	0.217226i	$0.0697008\pi$
$410$	−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	0.351352	−	0.936243i	$-0.385722\pi$
$419$	27.3849	−	15.8107i	1.33784	−	0.772402i	0.986487	+	0.163842i	$0.0523886\pi$
$420$	47.6656	−	22.0959i	2.32584	−	1.07817i
$421$	6.47108	+	1.73392i	0.315381	+	0.0845062i	0.413037	−	0.910714i	$-0.364468\pi$
$421$	6.47108	+	1.73392i	0.315381	+	0.0845062i	−0.0976561	+	0.995220i	$0.531135\pi$
$422$	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	−0.0970903	−	0.995276i	$-0.530954\pi$
$431$	6.56998	−	1.76042i	0.316465	−	0.0847965i	0.413555	+	0.910479i	$0.364287\pi$
$432$	14.8475	−	53.9470i	0.714350	−	2.59553i
$433$	21.3766	−	12.3418i	1.02729	−	0.593108i	0.111085	−	0.993811i	$-0.464567\pi$
$433$	21.3766	−	12.3418i	1.02729	−	0.593108i	0.916208	+	0.400703i	$0.131234\pi$
$434$	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	$0.186278\pi$
$439$			23.1471i			1.10475i	−0.833596	+	0.552374i	$0.813722\pi$
$440$	−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	−0.907455	−	0.420149i	$-0.861978\pi$
$443$	−20.9912	+	12.1193i	−0.997323	+	0.575805i	−0.0898679	+	0.995954i	$0.528644\pi$
$444$	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	0.397127	−	0.917764i	$-0.370007\pi$
$449$	5.97900	+	1.60207i	0.282166	+	0.0756063i	−0.114960	+	0.993370i	$0.536674\pi$
$450$	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	0.140657	−	0.990058i	$-0.455079\pi$
$457$	24.1719	−	24.1719i	1.13072	−	1.13072i	0.990058	−	0.140657i	$-0.0449214\pi$
$458$	−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	−0.0327254	−	0.999464i	$-0.510419\pi$
$461$	9.41855	−	2.52369i	0.438666	−	0.117540i	0.471391	+	0.881924i	$0.343752\pi$
$462$	2.74685	+	15.7865i	0.127795	+	0.734457i
$463$	25.2403	−	6.76311i	1.17301	−	0.314308i	0.380862	−	0.924632i	$-0.375627\pi$
$463$	25.2403	−	6.76311i	1.17301	−	0.314308i	0.792152	+	0.610324i	$0.208961\pi$
$464$		−	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	−0.801995	−	0.597330i	$-0.796228\pi$
$479$	−4.47931	+	4.47931i	−0.204665	+	0.204665i	0.597330	+	0.801995i	$0.296228\pi$
$480$	−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	0.250391	−	0.968145i	$-0.419441\pi$
$487$	−0.371552	−	0.0995570i	−0.0168366	−	0.00451136i	−0.267228	+	0.963633i	$0.586108\pi$
$488$	−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	0.961904	−	0.273389i	$-0.0881446\pi$
$491$	5.41089	+	9.37193i	0.244190	+	0.422949i	−0.717714	+	0.696338i	$0.754811\pi$
$492$	−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	0.878575	+	0.477605i	$0.158495\pi$
$499$	7.96381	+	29.7213i	0.356509	+	1.33051i	−0.522066	+	0.852905i	$0.674838\pi$
$500$	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	−0.192657	−	0.981266i	$-0.561710\pi$
$503$	12.5778	−	7.26179i	0.560816	−	0.323787i	0.753473	+	0.657479i	$0.228377\pi$
$504$	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	−0.694485	−	0.719507i	$-0.744368\pi$
$509$	6.01726	−	22.4567i	0.266710	−	0.995376i	0.961195	−	0.275869i	$-0.0889655\pi$
$510$	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	$0.0246841\pi$
$521$			3.53656i			0.154940i	−0.996995	+	0.0774698i	$0.975316\pi$
$522$	−1.52782	+	1.05954i	−0.0668708	+	0.0463748i
$523$	3.21981	−	5.57688i	0.140793	−	0.243860i	−0.787003	−	0.616950i	$-0.788368\pi$
$523$	3.21981	−	5.57688i	0.140793	−	0.243860i	0.927795	+	0.373090i	$0.121702\pi$
$524$	−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	−0.880994	−	0.473127i	$-0.843125\pi$
$541$	−31.4961	−	31.4961i	−1.35412	−	1.35412i	−0.473127	−	0.880994i	$-0.656875\pi$
$542$	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	0.997540	−	0.0700942i	$-0.0223300\pi$
$547$	10.2455	+	17.7458i	0.438067	+	0.758754i	−0.559474	+	0.828848i	$0.688997\pi$
$548$	−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	−0.947385	−	0.320096i	$-0.896285\pi$
$557$	−6.77282	−	25.2765i	−0.286974	−	1.07100i	0.660411	−	0.750904i	$-0.270382\pi$
$558$	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	0.249597	−	0.968350i	$-0.419702\pi$
$571$	−11.0928	−	6.40445i	−0.464221	−	0.268018i	−0.713817	+	0.700332i	$0.753035\pi$
$572$	−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	−0.637402	−	0.770532i	$-0.719991\pi$
$577$	3.19790	−	3.19790i	0.133130	−	0.133130i	0.770532	+	0.637402i	$0.219991\pi$
$578$	−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	0.516148	−	0.856499i	$-0.327365\pi$
$587$	−8.24606	−	8.24606i	−0.340351	−	0.340351i	−0.856499	+	0.516148i	$0.827365\pi$
$588$	−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	−0.0379511	+	0.999280i	$0.512083\pi$
$593$	−25.2582	+	25.2582i	−1.03723	+	1.03723i	−0.999280	+	0.0379511i	$0.987917\pi$
$594$	−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	0.276703	−	0.960955i	$-0.410758\pi$
$599$	−10.2097	−	5.89457i	−0.417157	−	0.240846i	−0.693860	+	0.720110i	$0.744091\pi$
$600$	−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	−0.890110	−	0.455746i	$-0.849373\pi$
$613$	−8.59441	−	32.0748i	−0.347125	−	1.29549i	0.542985	−	0.839742i	$-0.317294\pi$
$614$		−	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	0.217236	−	0.976119i	$-0.430296\pi$
$617$	−18.8503	−	18.8503i	−0.758883	−	0.758883i	−0.976119	+	0.217236i	$0.930296\pi$
$618$	88.2250	−	15.3511i	3.54893	−	0.617512i
$619$	7.34762	−	27.4217i	0.295326	−	1.10217i	−0.645632	−	0.763648i	$-0.723406\pi$
$619$	7.34762	−	27.4217i	0.295326	−	1.10217i	0.940958	−	0.338523i	$-0.109927\pi$
$620$	−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	0.830333	+	0.557268i	$0.188150\pi$
$631$	−4.20481	+	15.6925i	−0.167391	+	0.624710i	−0.997723	+	0.0674422i	$0.978516\pi$
$632$	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	−0.155570	−	0.987825i	$-0.549721\pi$
$641$	19.6897	−	34.1036i	0.777697	−	1.34701i	0.933266	−	0.359185i	$-0.116945\pi$
$642$	17.5186	−	3.04822i	0.691403	−	0.120304i
$643$	−22.8953	+	22.8953i	−0.902903	+	0.902903i	−0.995686	−	0.0927834i	$-0.970424\pi$
$643$	−22.8953	+	22.8953i	−0.902903	+	0.902903i	0.0927834	+	0.995686i	$0.470424\pi$
$644$	−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	0.258761	+	0.965941i	$0.416686\pi$
$647$	−17.9872	+	31.1547i	−0.707149	+	1.22482i	−0.965910	+	0.258877i	$0.916648\pi$
$648$	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	−0.722080	+	0.691810i	$0.756814\pi$
$653$	−42.9879	+	24.8190i	−1.68224	+	0.971244i	−0.960165	+	0.279435i	$0.909853\pi$
$654$	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	0.731089	−	0.682282i	$-0.239012\pi$
$659$	12.9834	+	7.49595i	0.505760	+	0.292001i	−0.225329	+	0.974283i	$0.572346\pi$
$660$	20.6758	−	29.3866i	0.804805	−	1.14387i
$661$	−1.73707	+	6.48283i	−0.0675641	+	0.252153i	−0.991445	−	0.130529i	$-0.958333\pi$
$661$	−1.73707	+	6.48283i	−0.0675641	+	0.252153i	0.923880	+	0.382681i	$0.124999\pi$
$662$	−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	$0.265206\pi$
$673$			38.3980i			1.48013i	−0.672534	+	0.740067i	$0.734794\pi$
$674$	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	0.125461	−	0.992099i	$-0.459959\pi$
$677$	27.2519	−	15.7339i	1.04737	−	0.604702i	0.921913	+	0.387397i	$0.126626\pi$
$678$	−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	0.900891	−	0.434045i	$-0.142914\pi$
$683$	38.2622	+	10.2523i	1.46406	+	0.392295i	0.563173	+	0.826339i	$0.309581\pi$
$684$	−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	−0.487519	−	0.873113i	$-0.662098\pi$
$691$	10.1361	−	10.1361i	0.385594	−	0.385594i	0.873113	+	0.487519i	$0.162098\pi$
$692$	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	−0.868401	+	0.495863i	$0.834852\pi$
$709$	−49.7497	+	13.3304i	−1.86839	+	0.500633i	−0.999989	+	0.00477057i	$0.998481\pi$
$710$	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	0.973120	−	0.230300i	$-0.0739708\pi$
$719$	7.69872	+	13.3346i	0.287114	+	0.497296i	−0.686006	+	0.727596i	$0.740638\pi$
$720$	−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	−0.508026	−	0.861342i	$-0.669625\pi$
$727$	−0.433980	+	0.250558i	−0.0160954	+	0.00929270i	0.491931	+	0.870634i	$0.336291\pi$
$728$	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	0.933388	−	0.358869i	$-0.116838\pi$
$733$	−1.47240	−	5.49507i	−0.0543844	−	0.202965i	−0.987772	+	0.155904i	$0.950171\pi$
$734$	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	−0.432827	−	0.901477i	$-0.642484\pi$
$739$	−9.70292	+	2.59989i	−0.356928	+	0.0956385i	0.0758992	+	0.997115i	$0.475817\pi$
$740$	−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	0.677569	+	0.735460i	$0.263034\pi$
$743$	−7.54919	+	28.1739i	−0.276953	+	1.03360i	−0.954521	+	0.298142i	$0.903633\pi$
$744$	−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	−0.255283	−	0.966866i	$-0.582169\pi$
$751$	12.4527	−	7.18958i	0.454406	−	0.262351i	0.709689	+	0.704515i	$0.248835\pi$
$752$	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	0.314883	+	0.949130i	$0.398035\pi$
$757$	−18.2836	+	31.6681i	−0.664529	+	1.15100i	−0.979413	+	0.201868i	$0.935299\pi$
$758$	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	−0.560213	−	0.828348i	$-0.689281\pi$
$761$	7.39684	−	7.39684i	0.268135	−	0.268135i	0.828348	+	0.560213i	$0.189281\pi$
$762$	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	0.366814	−	0.930294i	$-0.380449\pi$
$769$	6.08238	+	1.62977i	0.219336	+	0.0587710i	−0.147477	+	0.989065i	$0.547115\pi$
$770$	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	−0.932578	−	0.360970i	$-0.882446\pi$
$773$	1.54426	−	5.76325i	0.0555431	−	0.207290i	0.988121	+	0.153680i	$0.0491125\pi$
$774$	−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	0.471420	−	0.881909i	$-0.343742\pi$
$787$	−11.5157	−	11.5157i	−0.410489	−	0.410489i	−0.881909	+	0.471420i	$0.843742\pi$
$788$	−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	0.966606	−	0.256268i	$-0.0824931\pi$
$809$	34.9272	+	20.1652i	1.22797	+	0.708971i	0.261368	+	0.965239i	$0.415826\pi$
$810$	40.7318	+	49.4425i	1.43117	+	1.73723i
$811$	30.0454	−	30.0454i	1.05504	−	1.05504i	0.0566424	−	0.998395i	$-0.481961\pi$
$811$	30.0454	−	30.0454i	1.05504	−	1.05504i	0.998395	−	0.0566424i	$-0.0180395\pi$
$812$	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	0.961248	−	0.275685i	$-0.0889046\pi$
$821$	19.6435	+	19.6435i	0.685563	+	0.685563i	−0.275685	+	0.961248i	$0.588905\pi$
$822$	−5.29685	−	3.72675i	−0.184749	−	0.129985i
$823$		−	25.3342i		−	0.883093i	−0.897238	−	0.441547i	$-0.854430\pi$
$823$		−	25.3342i		−	0.883093i	0.897238	−	0.441547i	$-0.145570\pi$
$824$	−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	−0.590817	−	0.806806i	$-0.701194\pi$
$827$	6.21133	−	6.21133i	0.215989	−	0.215989i	0.806806	+	0.590817i	$0.201194\pi$
$828$	−99.8230	+	35.8229i	−3.46909	+	1.24493i
$829$	−27.6454	−	15.9611i	−0.960166	−	0.554352i	−0.0639420	−	0.997954i	$-0.520367\pi$
$829$	−27.6454	−	15.9611i	−0.960166	−	0.554352i	−0.896224	+	0.443601i	$0.853701\pi$
$830$	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	0.990920	+	0.134454i	$0.0429281\pi$
$839$	5.79267	+	21.6185i	0.199985	+	0.746355i	−0.790935	+	0.611901i	$0.790405\pi$
$840$	−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	0.688501	+	0.725235i	$0.258269\pi$
$853$	−7.89664	+	29.4707i	−0.270376	+	1.00906i	−0.958877	+	0.283822i	$0.908398\pi$
$854$	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	0.834177	−	0.551496i	$-0.185943\pi$
$857$	−1.77173	−	3.06872i	−0.0605211	−	0.104826i	−0.894698	+	0.446671i	$0.852610\pi$
$858$	−24.6593	−	6.58906i	−0.841856	−	0.224947i
$859$	17.6074	−	30.4970i	0.600758	−	1.04054i	−0.391948	−	0.919987i	$-0.628199\pi$
$859$	17.6074	−	30.4970i	0.600758	−	1.04054i	0.992706	−	0.120557i	$-0.0384679\pi$
$860$	−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	0.612537	−	0.790442i	$-0.290149\pi$
$863$	−5.22630	−	5.22630i	−0.177905	−	0.177905i	−0.790442	+	0.612537i	$0.790149\pi$
$864$	−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	−0.909475	−	0.415758i	$-0.863516\pi$
$877$	−14.6210	+	14.6210i	−0.493717	+	0.493717i	0.415758	+	0.909475i	$0.363516\pi$
$878$	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	−0.160619	−	0.987016i	$-0.551349\pi$
$881$	22.9876	−	39.8157i	0.774472	−	1.34142i	0.935091	−	0.354408i	$-0.115318\pi$
$882$	−13.4430	−	6.34263i	−0.452648	−	0.213567i
$883$		−	7.05482i		−	0.237414i	−0.992929	−	0.118707i	$-0.962125\pi$
$883$		−	7.05482i		−	0.237414i	0.992929	−	0.118707i	$-0.0378749\pi$
$884$	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	−0.772026	−	0.635591i	$-0.780756\pi$
$887$	−18.0959	+	10.4477i	−0.607601	+	0.350798i	0.164425	+	0.986390i	$0.447423\pi$
$888$	−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	$0.0165945\pi$
$907$			3.13870i			0.104219i	−0.998641	+	0.0521094i	$0.983406\pi$
$908$	−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	−0.167600	−	0.985855i	$-0.553602\pi$
$911$	18.1814	−	10.4970i	0.602375	−	0.347782i	0.769975	+	0.638074i	$0.220268\pi$
$912$	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	0.961686	+	0.274153i	$0.0883973\pi$
$919$	21.7742	+	37.7141i	0.718266	+	1.24407i	−0.243420	+	0.969921i	$0.578269\pi$
$920$	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	−0.701671	−	0.712501i	$-0.747562\pi$
$929$	−29.0496	+	7.78381i	−0.953086	+	0.255379i	−0.251415	+	0.967879i	$0.580896\pi$
$930$	−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	−0.189767	−	0.981829i	$-0.560773\pi$
$941$	4.19656	−	1.12447i	0.136804	−	0.0366565i	0.326571	+	0.945173i	$0.394107\pi$
$942$	−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	−0.873357	−	0.487080i	$-0.838062\pi$
$947$	−11.8871	+	11.8871i	−0.386277	+	0.386277i	0.487080	+	0.873357i	$0.338062\pi$
$948$	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	0.998842	−	0.0481162i	$-0.0153218\pi$
$953$	14.1311	+	24.4758i	0.457751	+	0.792848i	−0.541091	+	0.840964i	$0.681988\pi$
$954$	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	−0.978316	−	0.207117i	$-0.933592\pi$
$967$	−7.29613	−	27.2295i	−0.234628	−	0.875643i	0.743688	−	0.668526i	$-0.233075\pi$
$968$	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	−0.554654	+	0.832081i	$0.687149\pi$
$971$	−48.3799	+	27.9321i	−1.55258	+	0.896385i	−0.997930	+	0.0643034i	$0.979517\pi$
$972$	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	−0.982585	−	0.185815i	$-0.940507\pi$
$977$	−1.21070	+	4.51840i	−0.0387337	+	0.144556i	0.943851	+	0.330372i	$0.107174\pi$
$978$	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	0.116476	−	0.993194i	$-0.462840\pi$
$983$	−8.75529	−	2.34597i	−0.279250	−	0.0748249i	−0.395726	+	0.918369i	$0.629507\pi$
$984$	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	0.457933	+	0.888987i	$0.348590\pi$
$991$	−17.0282	+	29.4937i	−0.540919	+	0.936899i	−0.998852	+	0.0479121i	$0.984743\pi$
$992$	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	−0.403547	−	0.914959i	$-0.632223\pi$
$997$	18.6485	−	32.3001i	0.590604	−	1.02296i	0.994151	−	0.107997i	$-0.0344437\pi$
$998$	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.32.1	yes	48
3.2	odd	2		351.2.ba.a.71.12		48
9.2	odd	6		117.2.bc.a.110.12	yes	48
9.7	even	3		351.2.bf.a.305.1		48
13.11	odd	12		117.2.bc.a.50.12	yes	48
39.11	even	12		351.2.bf.a.206.1		48
117.11	even	12	inner	117.2.x.a.11.1	✓	48
117.115	odd	12		351.2.ba.a.89.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.1	✓	48	117.11	even	12	inner
117.2.x.a.32.1	yes	48	1.1	even	1	trivial
117.2.bc.a.50.12	yes	48	13.11	odd	12
117.2.bc.a.110.12	yes	48	9.2	odd	6
351.2.ba.a.71.12		48	3.2	odd	2
351.2.ba.a.89.12		48	117.115	odd	12
351.2.bf.a.206.1		48	39.11	even	12
351.2.bf.a.305.1		48	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.86694 - 1.86694i) q^{2} +(0.154854 - 1.72511i) q^{3} +4.97091i q^{4} +(-2.60400 + 0.697740i) q^{5} +(-3.50978 + 2.93158i) q^{6} +(-2.18636 + 0.585835i) q^{7} +(5.54651 - 5.54651i) q^{8} +(-2.95204 - 0.534283i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

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