LMFDB - Embedded newform 41.2.g.a.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.3
Character	$\chi$	$=$	41.33
Dual form			41.2.g.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42655 - 1.96347i) q^{2} +(-2.02366 + 2.02366i) q^{3} +(-1.20216 - 3.69986i) q^{4} +(0.110420 - 0.0358775i) q^{5} +(1.08656 + 6.86025i) q^{6} +(-0.422339 + 2.66654i) q^{7} +(-4.36309 - 1.41766i) q^{8} -5.19040i q^{9} +O(q^{10})$	\(q+(1.42655 - 1.96347i) q^{2} +(-2.02366 + 2.02366i) q^{3} +(-1.20216 - 3.69986i) q^{4} +(0.110420 - 0.0358775i) q^{5} +(1.08656 + 6.86025i) q^{6} +(-0.422339 + 2.66654i) q^{7} +(-4.36309 - 1.41766i) q^{8} -5.19040i q^{9} +(0.0870742 - 0.267987i) q^{10} +(-1.53663 - 3.01580i) q^{11} +(9.92000 + 5.05449i) q^{12} +(-1.03889 + 0.164544i) q^{13} +(4.63320 + 4.63320i) q^{14} +(-0.150848 + 0.296056i) q^{15} +(-2.71311 + 1.97119i) q^{16} +(3.25831 - 1.66019i) q^{17} +(-10.1912 - 7.40435i) q^{18} +(-2.25168 - 0.356630i) q^{19} +(-0.265483 - 0.365406i) q^{20} +(-4.54151 - 6.25085i) q^{21} +(-8.11352 - 1.28505i) q^{22} +(6.06568 + 4.40698i) q^{23} +(11.6983 - 5.96057i) q^{24} +(-4.03418 + 2.93100i) q^{25} +(-1.15895 + 2.27456i) q^{26} +(4.43263 + 4.43263i) q^{27} +(10.3735 - 1.64301i) q^{28} +(1.31408 + 0.669558i) q^{29} +(0.366106 + 0.718523i) q^{30} +(-0.964816 + 2.96940i) q^{31} -1.03614i q^{32} +(9.21257 + 2.99335i) q^{33} +(1.38839 - 8.76594i) q^{34} +(0.0490344 + 0.309591i) q^{35} +(-19.2037 + 6.23967i) q^{36} +(-0.348766 - 1.07339i) q^{37} +(-3.91235 + 3.91235i) q^{38} +(1.76938 - 2.43534i) q^{39} -0.532633 q^{40} +(-1.32339 + 6.26487i) q^{41} -18.7520 q^{42} +(0.583672 - 0.803355i) q^{43} +(-9.31076 + 9.31076i) q^{44} +(-0.186219 - 0.573122i) q^{45} +(17.3060 - 5.62305i) q^{46} +(-1.73020 - 10.9241i) q^{47} +(1.50140 - 9.47944i) q^{48} +(-0.274693 - 0.0892531i) q^{49} +12.1022i q^{50} +(-3.23405 + 9.95337i) q^{51} +(1.85769 + 3.64593i) q^{52} +(0.482987 + 0.246094i) q^{53} +(15.0267 - 2.37999i) q^{54} +(-0.277873 - 0.277873i) q^{55} +(5.62295 - 11.0357i) q^{56} +(5.27833 - 3.83493i) q^{57} +(3.18926 - 1.62501i) q^{58} +(-1.57246 - 1.14246i) q^{59} +(1.27671 + 0.202210i) q^{60} +(-5.95937 - 8.20238i) q^{61} +(4.45398 + 6.13037i) q^{62} +(13.8404 + 2.19211i) q^{63} +(-7.46066 - 5.42048i) q^{64} +(-0.108810 + 0.0554416i) q^{65} +(19.0195 - 13.8185i) q^{66} +(-6.02949 + 11.8335i) q^{67} +(-10.0595 - 10.0595i) q^{68} +(-21.1931 + 3.35666i) q^{69} +(0.677824 + 0.345368i) q^{70} +(-4.28484 - 8.40947i) q^{71} +(-7.35820 + 22.6462i) q^{72} +10.9108i q^{73} +(-2.60511 - 0.846450i) q^{74} +(2.23245 - 14.0952i) q^{75} +(1.38738 + 8.75960i) q^{76} +(8.69075 - 2.82380i) q^{77} +(-2.25762 - 6.94824i) q^{78} +(7.58864 - 7.58864i) q^{79} +(-0.228859 + 0.314998i) q^{80} -2.36906 q^{81} +(10.4130 + 11.5356i) q^{82} -0.635212 q^{83} +(-17.6676 + 24.3174i) q^{84} +(0.300218 - 0.300218i) q^{85} +(-0.744731 - 2.29205i) q^{86} +(-4.01421 + 1.30430i) q^{87} +(2.42908 + 15.3366i) q^{88} +(0.753161 - 4.75527i) q^{89} +(-1.39096 - 0.451950i) q^{90} -2.83974i q^{91} +(9.01328 - 27.7400i) q^{92} +(-4.05659 - 7.96151i) q^{93} +(-23.9173 - 12.1865i) q^{94} +(-0.261424 + 0.0414055i) q^{95} +(2.09680 + 2.09680i) q^{96} +(-1.25412 + 2.46135i) q^{97} +(-0.567108 + 0.412028i) q^{98} +(-15.6532 + 7.97572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{9}{20}\right)$

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 $

$2$	1.42655	−	1.96347i	1.00872	−	1.38838i	0.0889021	−	0.996040i	$-0.471664\pi$
$2$	1.42655	−	1.96347i	1.00872	−	1.38838i	0.919818	−	0.392344i	$-0.128336\pi$
$3$	−2.02366	+	2.02366i	−1.16836	+	1.16836i	−0.185767	+	0.982594i	$0.559477\pi$
$3$	−2.02366	+	2.02366i	−1.16836	+	1.16836i	−0.982594	+	0.185767i	$0.940523\pi$
$4$	−1.20216	−	3.69986i	−0.601078	−	1.84993i
$5$	0.110420	−	0.0358775i	0.0493811	−	0.0160449i	−0.284222	−	0.958758i	$-0.591735\pi$
$5$	0.110420	−	0.0358775i	0.0493811	−	0.0160449i	0.333603	+	0.942714i	$0.391735\pi$
$6$	1.08656	+	6.86025i	0.443585	+	2.80068i
$7$	−0.422339	+	2.66654i	−0.159629	+	1.00786i	0.769646	+	0.638471i	$0.220433\pi$
$7$	−0.422339	+	2.66654i	−0.159629	+	1.00786i	−0.929275	+	0.369388i	$0.879567\pi$
$8$	−4.36309	−	1.41766i	−1.54259	−	0.501217i
$9$		−	5.19040i		−	1.73013i
$10$	0.0870742	−	0.267987i	0.0275353	−	0.0847449i
$11$	−1.53663	−	3.01580i	−0.463311	−	0.909299i	−0.997936	−	0.0642096i	$-0.979547\pi$
$11$	−1.53663	−	3.01580i	−0.463311	−	0.909299i	0.534626	−	0.845089i	$-0.320453\pi$
$12$	9.92000	+	5.05449i	2.86366	+	1.45911i
$13$	−1.03889	+	0.164544i	−0.288136	+	0.0456362i	−0.298829	−	0.954307i	$-0.596596\pi$
$13$	−1.03889	+	0.164544i	−0.288136	+	0.0456362i	0.0106934	+	0.999943i	$0.496596\pi$
$14$	4.63320	+	4.63320i	1.23827	+	1.23827i
$15$	−0.150848	+	0.296056i	−0.0389488	+	0.0764412i
$16$	−2.71311	+	1.97119i	−0.678278	+	0.492798i
$17$	3.25831	−	1.66019i	0.790256	−	0.402655i	−0.0117807	−	0.999931i	$-0.503750\pi$
$17$	3.25831	−	1.66019i	0.790256	−	0.402655i	0.802036	+	0.597275i	$0.203750\pi$
$18$	−10.1912	−	7.40435i	−2.40209	−	1.74522i
$19$	−2.25168	−	0.356630i	−0.516570	−	0.0818166i	−0.107294	−	0.994227i	$-0.534219\pi$
$19$	−2.25168	−	0.356630i	−0.516570	−	0.0818166i	−0.409276	+	0.912411i	$0.634219\pi$
$20$	−0.265483	−	0.365406i	−0.0593638	−	0.0817073i
$21$	−4.54151	−	6.25085i	−0.991038	−	1.36405i
$22$	−8.11352	−	1.28505i	−1.72981	−	0.273975i
$23$	6.06568	+	4.40698i	1.26478	+	0.918918i	0.998982	−	0.0451098i	$-0.0143638\pi$
$23$	6.06568	+	4.40698i	1.26478	+	0.918918i	0.265800	+	0.964028i	$0.414364\pi$
$24$	11.6983	−	5.96057i	2.38790	−	1.21670i
$25$	−4.03418	+	2.93100i	−0.806836	+	0.586201i
$26$	−1.15895	+	2.27456i	−0.227288	+	0.446078i
$27$	4.43263	+	4.43263i	0.853060	+	0.853060i
$28$	10.3735	−	1.64301i	1.96042	−	0.310499i
$29$	1.31408	+	0.669558i	0.244019	+	0.124334i	0.571723	−	0.820446i	$-0.306275\pi$
$29$	1.31408	+	0.669558i	0.244019	+	0.124334i	−0.327705	+	0.944780i	$0.606275\pi$
$30$	0.366106	+	0.718523i	0.0668414	+	0.131184i
$31$	−0.964816	+	2.96940i	−0.173286	+	0.533320i	−0.999551	−	0.0299620i	$-0.990461\pi$
$31$	−0.964816	+	2.96940i	−0.173286	+	0.533320i	0.826265	+	0.563282i	$0.190461\pi$
$32$		−	1.03614i		−	0.183165i
$33$	9.21257	+	2.99335i	1.60370	+	0.521075i
$34$	1.38839	−	8.76594i	0.238107	−	1.50335i
$35$	0.0490344	+	0.309591i	0.00828833	+	0.0523305i
$36$	−19.2037	+	6.23967i	−3.20062	+	1.03995i
$37$	−0.348766	−	1.07339i	−0.0573368	−	0.176465i	0.918286	−	0.395917i	$-0.129573\pi$
$37$	−0.348766	−	1.07339i	−0.0573368	−	0.176465i	−0.975623	+	0.219452i	$0.929573\pi$
$38$	−3.91235	+	3.91235i	−0.634668	+	0.634668i
$39$	1.76938	−	2.43534i	0.283327	−	0.389966i
$40$	−0.532633			−0.0842167
$41$	−1.32339	+	6.26487i	−0.206678	+	0.978409i
$41$	−1.32339	+	6.26487i	−0.206678	+	0.978409i
$42$	−18.7520			−2.89350
$43$	0.583672	−	0.803355i	0.0890091	−	0.122511i	−0.762190	−	0.647353i	$-0.775876\pi$
$43$	0.583672	−	0.803355i	0.0890091	−	0.122511i	0.851199	+	0.524843i	$0.175876\pi$
$44$	−9.31076	+	9.31076i	−1.40365	+	1.40365i
$45$	−0.186219	−	0.573122i	−0.0277598	−	0.0854360i
$46$	17.3060	−	5.62305i	2.55162	−	0.829073i
$47$	−1.73020	−	10.9241i	−0.252376	−	1.59344i	−0.709939	−	0.704263i	$-0.751278\pi$
$47$	−1.73020	−	10.9241i	−0.252376	−	1.59344i	0.457563	−	0.889177i	$-0.348722\pi$
$48$	1.50140	−	9.47944i	0.216708	−	1.36824i
$49$	−0.274693	−	0.0892531i	−0.0392418	−	0.0127504i
$50$			12.1022i			1.71151i
$51$	−3.23405	+	9.95337i	−0.452857	+	1.39375i
$52$	1.85769	+	3.64593i	0.257616	+	0.505599i
$53$	0.482987	+	0.246094i	0.0663434	+	0.0338036i	0.486847	−	0.873487i	$-0.338147\pi$
$53$	0.482987	+	0.246094i	0.0663434	+	0.0338036i	−0.420504	+	0.907291i	$0.638147\pi$
$54$	15.0267	−	2.37999i	2.04487	−	0.323876i
$55$	−0.277873	−	0.277873i	−0.0374684	−	0.0374684i
$56$	5.62295	−	11.0357i	0.751398	−	1.47470i
$57$	5.27833	−	3.83493i	0.699131	−	0.507949i
$58$	3.18926	−	1.62501i	0.418770	−	0.213374i
$59$	−1.57246	−	1.14246i	−0.204717	−	0.148735i	0.480703	−	0.876883i	$-0.340381\pi$
$59$	−1.57246	−	1.14246i	−0.204717	−	0.148735i	−0.685420	+	0.728148i	$0.740381\pi$
$60$	1.27671	+	0.202210i	0.164822	+	0.0261052i
$61$	−5.95937	−	8.20238i	−0.763020	−	1.05021i	−0.996957	−	0.0779548i	$-0.975161\pi$
$61$	−5.95937	−	8.20238i	−0.763020	−	1.05021i	0.233937	−	0.972252i	$-0.424839\pi$
$62$	4.45398	+	6.13037i	0.565656	+	0.778558i
$63$	13.8404	+	2.19211i	1.74373	+	0.276180i
$64$	−7.46066	−	5.42048i	−0.932582	−	0.677561i
$65$	−0.108810	+	0.0554416i	−0.0134962	+	0.00687668i
$66$	19.0195	−	13.8185i	2.34114	−	1.70094i
$67$	−6.02949	+	11.8335i	−0.736619	+	1.44570i	0.152635	+	0.988283i	$0.451224\pi$
$67$	−6.02949	+	11.8335i	−0.736619	+	1.44570i	−0.889254	+	0.457414i	$0.848776\pi$
$68$	−10.0595	−	10.0595i	−1.21989	−	1.21989i
$69$	−21.1931	+	3.35666i	−2.55135	+	0.404094i
$70$	0.677824	+	0.345368i	0.0810154	+	0.0412794i
$71$	−4.28484	−	8.40947i	−0.508517	−	0.998021i	−0.992419	−	0.122899i	$-0.960781\pi$
$71$	−4.28484	−	8.40947i	−0.508517	−	0.998021i	0.483902	−	0.875122i	$-0.339219\pi$
$72$	−7.35820	+	22.6462i	−0.867172	+	2.66888i
$73$			10.9108i			1.27702i	0.769615	+	0.638508i	$0.220448\pi$
$73$			10.9108i			1.27702i	−0.769615	+	0.638508i	$0.779552\pi$
$74$	−2.60511	−	0.846450i	−0.302837	−	0.0983978i
$75$	2.23245	−	14.0952i	0.257782	−	1.62757i
$76$	1.38738	+	8.75960i	0.159144	+	1.00480i
$77$	8.69075	−	2.82380i	0.990403	−	0.321801i
$78$	−2.25762	−	6.94824i	−0.255625	−	0.786734i
$79$	7.58864	−	7.58864i	0.853789	−	0.853789i	−0.136809	−	0.990597i	$-0.543685\pi$
$79$	7.58864	−	7.58864i	0.853789	−	0.853789i	0.990597	+	0.136809i	$0.0436846\pi$
$80$	−0.228859	+	0.314998i	−0.0255873	+	0.0352178i
$81$	−2.36906			−0.263229
$82$	10.4130	+	11.5356i	1.14993	+	1.27389i
$83$	−0.635212			−0.0697236			−0.0348618	−	0.999392i	$-0.511099\pi$
$83$	−0.635212			−0.0697236			−0.0348618	+	0.999392i	$0.511099\pi$
$84$	−17.6676	+	24.3174i	−1.92770	+	2.65325i
$85$	0.300218	−	0.300218i	0.0325632	−	0.0325632i
$86$	−0.744731	−	2.29205i	−0.0803064	−	0.247158i
$87$	−4.01421	+	1.30430i	−0.430369	+	0.139835i
$88$	2.42908	+	15.3366i	0.258941	+	1.63489i
$89$	0.753161	−	4.75527i	0.0798350	−	0.504058i	−0.915074	−	0.403285i	$-0.867868\pi$
$89$	0.753161	−	4.75527i	0.0798350	−	0.504058i	0.994909	−	0.100773i	$-0.0321316\pi$
$90$	−1.39096	−	0.451950i	−0.146620	−	0.0476397i
$91$		−	2.83974i		−	0.297685i
$92$	9.01328	−	27.7400i	0.939699	−	2.89210i
$93$	−4.05659	−	7.96151i	−0.420649	−	0.825570i
$94$	−23.9173	−	12.1865i	−2.46689	−	1.25694i
$95$	−0.261424	+	0.0414055i	−0.0268216	+	0.00424812i
$96$	2.09680	+	2.09680i	0.214003	+	0.214003i
$97$	−1.25412	+	2.46135i	−0.127337	+	0.249913i	−0.945869	−	0.324548i	$-0.894788\pi$
$97$	−1.25412	+	2.46135i	−0.127337	+	0.249913i	0.818533	+	0.574460i	$0.194788\pi$
$98$	−0.567108	+	0.412028i	−0.0572866	+	0.0416211i
$99$	−15.6532	+	7.97572i	−1.57321	+	0.801590i
$100$	15.6940	+	11.4024i	1.56940	+	1.14024i
$101$	9.34392	+	1.47993i	0.929755	+	0.147259i	0.602901	−	0.797816i	$-0.294012\pi$
$101$	9.34392	+	1.47993i	0.929755	+	0.147259i	0.326854	+	0.945075i	$0.394012\pi$
$102$	14.9296	+	20.5489i	1.47826	+	2.03464i
$103$	3.69313	+	5.08316i	0.363895	+	0.500858i	0.951229	−	0.308486i	$-0.0998225\pi$
$103$	3.69313	+	5.08316i	0.363895	+	0.500858i	−0.587334	+	0.809345i	$0.699822\pi$
$104$	4.76603	+	0.754866i	0.467348	+	0.0740207i
$105$	−0.725737	−	0.527278i	−0.0708246	−	0.0514571i
$106$	1.17220	−	0.597267i	0.113854	−	0.0580117i
$107$	−11.1143	+	8.07504i	−1.07446	+	0.780644i	−0.976709	−	0.214567i	$-0.931166\pi$
$107$	−11.1143	+	8.07504i	−1.07446	+	0.780644i	−0.0977545	+	0.995211i	$0.531166\pi$
$108$	11.0714	−	21.7288i	1.06534	−	2.09085i
$109$	10.4978	+	10.4978i	1.00551	+	1.00551i	0.999985	+	0.00552465i	$0.00175856\pi$
$109$	10.4978	+	10.4978i	1.00551	+	1.00551i	0.00552465	+	0.999985i	$0.498241\pi$
$110$	−0.941996	+	0.149197i	−0.0898158	+	0.0142254i
$111$	2.87796	+	1.46640i	0.273164	+	0.139184i
$112$	−4.11042	−	8.06715i	−0.388398	−	0.762274i
$113$	2.45600	−	7.55880i	0.231041	−	0.711073i	−0.766580	−	0.642148i	$-0.778043\pi$
$113$	2.45600	−	7.55880i	0.231041	−	0.711073i	0.997622	−	0.0689242i	$-0.0219567\pi$
$114$		−	15.8345i		−	1.48304i
$115$	0.827882	+	0.268995i	0.0772004	+	0.0250839i
$116$	0.897537	−	5.66683i	0.0833342	−	0.526151i
$117$	0.854048	+	5.39225i	0.0789568	+	0.498514i
$118$	−4.48637	+	1.45771i	−0.413004	+	0.134193i
$119$	3.05086	+	9.38959i	0.279672	+	0.860742i
$120$	1.07787	−	1.07787i	0.0983955	−	0.0983955i
$121$	−0.268199	+	0.369145i	−0.0243818	+	0.0335586i
$122$	−24.6065			−2.22776
$123$	−9.99989	−	15.3561i	−0.901660	−	1.38461i
$124$	12.1462			1.09076
$125$	−0.681511	+	0.938019i	−0.0609562	+	0.0838990i
$126$	24.0482	−	24.0482i	2.14238	−	2.14238i
$127$	−2.50455	−	7.70820i	−0.222243	−	0.683993i	−0.998560	−	0.0536500i	$-0.982914\pi$
$127$	−2.50455	−	7.70820i	−0.222243	−	0.683993i	0.776317	−	0.630343i	$-0.217086\pi$
$128$	−19.3151	+	6.27585i	−1.70723	+	0.554712i
$129$	0.444565	+	2.80687i	0.0391417	+	0.247131i
$130$	−0.0463648	+	0.292736i	−0.00406646	+	0.0256746i
$131$	−10.8285	−	3.51838i	−0.946087	−	0.307402i	−0.204962	−	0.978770i	$-0.565707\pi$
$131$	−10.8285	−	3.51838i	−0.946087	−	0.307402i	−0.741125	+	0.671368i	$0.765707\pi$
$132$		−	37.6836i		−	3.27994i
$133$	1.90194	−	5.85357i	0.164919	−	0.507569i
$134$	14.6335	+	28.7198i	1.26414	+	2.48101i
$135$	0.648481	+	0.330417i	0.0558123	+	0.0284378i
$136$	−16.5699	+	2.62441i	−1.42086	+	0.225041i
$137$	4.26765	+	4.26765i	0.364610	+	0.364610i	0.865507	−	0.500897i	$-0.166996\pi$
$137$	4.26765	+	4.26765i	0.364610	+	0.364610i	−0.500897	+	0.865507i	$0.666996\pi$
$138$	−23.6422	+	46.4005i	−2.01256	+	3.94987i
$139$	14.2798	−	10.3749i	1.21120	−	0.879987i	0.215860	−	0.976424i	$-0.430745\pi$
$139$	14.2798	−	10.3749i	1.21120	−	0.879987i	0.995339	+	0.0964369i	$0.0307446\pi$
$140$	1.08650	−	0.553597i	0.0918257	−	0.0467875i
$141$	25.6080	+	18.6053i	2.15658	+	1.56685i
$142$	−22.6243	−	3.58334i	−1.89859	−	0.300707i
$143$	2.09262	+	2.88024i	0.174993	+	0.240858i
$144$	10.2313	+	14.0821i	0.852606	+	1.17351i
$145$	0.169122	+	0.0267864i	0.0140449	+	0.00222449i
$146$	21.4231	+	15.5648i	1.77299	+	1.28815i
$147$	0.736503	−	0.375267i	0.0607458	−	0.0309515i
$148$	−3.55212	+	2.58077i	−0.291983	+	0.212138i
$149$	0.491547	−	0.964715i	0.0402691	−	0.0790326i	−0.869995	−	0.493060i	$-0.835878\pi$
$149$	0.491547	−	0.964715i	0.0402691	−	0.0790326i	0.910264	+	0.414028i	$0.135878\pi$
$150$	−24.4908	−	24.4908i	−1.99966	−	1.99966i
$151$	12.9796	−	2.05577i	1.05626	−	0.167296i	0.395940	−	0.918276i	$-0.370419\pi$
$151$	12.9796	−	2.05577i	1.05626	−	0.167296i	0.660324	+	0.750980i	$0.270419\pi$
$152$	9.31869	+	4.74811i	0.755846	+	0.385123i
$153$	−8.61706	−	16.9119i	−0.696648	−	1.36725i
$154$	6.85331	−	21.0923i	0.552255	−	1.69967i
$155$			0.362495i			0.0291163i
$156$	−11.1375	−	3.61878i	−0.891711	−	0.289734i
$157$	−2.56436	+	16.1907i	−0.204658	+	1.29216i	0.644737	+	0.764404i	$0.276967\pi$
$157$	−2.56436	+	16.1907i	−0.204658	+	1.29216i	−0.849396	+	0.527757i	$0.823033\pi$
$158$	−4.07454	−	25.7256i	−0.324153	−	2.04662i
$159$	−1.47541	+	0.479391i	−0.117008	+	0.0380181i
$160$	−0.0371741	−	0.114410i	−0.00293887	−	0.00904492i
$161$	−14.3132	+	14.3132i	−1.12804	+	1.12804i
$162$	−3.37958	+	4.65159i	−0.265525	+	0.365463i
$163$	14.6327			1.14612			0.573059	−	0.819514i	$-0.305757\pi$
$163$	14.6327			1.14612			0.573059	+	0.819514i	$0.305757\pi$
$164$	24.7700	−	2.63502i	1.93422	−	0.205761i
$165$	1.12464			0.0875533
$166$	−0.906159	+	1.24722i	−0.0703316	+	0.0968032i
$167$	−8.21554	+	8.21554i	−0.635738	+	0.635738i	−0.949501	−	0.313764i	$-0.898410\pi$
$167$	−8.21554	+	8.21554i	−0.635738	+	0.635738i	0.313764	+	0.949501i	$0.398410\pi$
$168$	10.9535	+	33.7113i	0.845079	+	2.60089i
$169$	−11.3115	+	3.67534i	−0.870117	+	0.282718i
$170$	−0.161195	−	1.01774i	−0.0123631	−	0.0780573i
$171$	−1.85106	+	11.6871i	−0.141554	+	0.893735i
$172$	−3.67396	−	1.19374i	−0.280137	−	0.0910220i
$173$		−	2.01872i		−	0.153480i	−0.997051	−	0.0767400i	$-0.975549\pi$
$173$		−	2.01872i		−	0.153480i	0.997051	−	0.0767400i	$-0.0244512\pi$
$174$	−3.16551	+	9.74244i	−0.239977	+	0.738572i
$175$	−6.11186	−	11.9952i	−0.462013	−	0.906752i
$176$	10.1138	+	5.15322i	0.762354	+	0.388439i
$177$	5.49407	−	0.870175i	0.412960	−	0.0654064i
$178$	−8.26243	−	8.26243i	−0.619295	−	0.619295i
$179$	8.10933	−	15.9155i	0.606120	−	1.18958i	−0.360355	−	0.932815i	$-0.617344\pi$
$179$	8.10933	−	15.9155i	0.606120	−	1.18958i	0.966475	−	0.256762i	$-0.0826555\pi$
$180$	−1.89660	+	1.37796i	−0.141365	+	0.102707i
$181$	−1.57724	+	0.803644i	−0.117235	+	0.0597344i	−0.511625	−	0.859209i	$-0.670956\pi$
$181$	−1.57724	+	0.803644i	−0.117235	+	0.0597344i	0.394389	+	0.918943i	$0.370956\pi$
$182$	−5.57574	−	4.05101i	−0.413302	−	0.300281i
$183$	28.6586	+	4.53907i	2.11850	+	0.335538i
$184$	−20.2176	−	27.8271i	−1.49046	−	2.05144i
$185$	−0.0770212	−	0.106011i	−0.00566271	−	0.00779406i
$186$	−21.4191	−	3.39246i	−1.57053	−	0.248747i
$187$	−10.0136	−	7.27532i	−0.732268	−	0.532024i
$188$	−38.3375	+	19.5339i	−2.79605	+	1.42466i
$189$	−13.6919	+	9.94773i	−0.995937	+	0.723591i
$190$	−0.291635	+	0.572366i	−0.0211574	+	0.0415238i
$191$	−3.86040	−	3.86040i	−0.279329	−	0.279329i	0.553512	−	0.832841i	$-0.313287\pi$
$191$	−3.86040	−	3.86040i	−0.279329	−	0.279329i	−0.832841	+	0.553512i	$0.813287\pi$
$192$	26.0671	−	4.12862i	1.88123	−	0.297957i
$193$	−5.84374	−	2.97753i	−0.420641	−	0.214328i	0.230841	−	0.972992i	$-0.425852\pi$
$193$	−5.84374	−	2.97753i	−0.420641	−	0.214328i	−0.651482	+	0.758664i	$0.725852\pi$
$194$	3.04374	+	5.97367i	0.218527	+	0.428884i
$195$	0.108000	−	0.332390i	0.00773404	−	0.0238029i
$196$			1.12362i			0.0802586i
$197$	−4.06150	−	1.31966i	−0.289370	−	0.0940220i	0.160735	−	0.986998i	$-0.448613\pi$
$197$	−4.06150	−	1.31966i	−0.289370	−	0.0940220i	−0.450105	+	0.892976i	$0.648613\pi$
$198$	−6.66995	+	42.1124i	−0.474013	+	2.99280i
$199$	−2.50210	−	15.7976i	−0.177369	−	1.11986i	−0.902321	−	0.431064i	$-0.858138\pi$
$199$	−2.50210	−	15.7976i	−0.177369	−	1.11986i	0.724952	−	0.688799i	$-0.241862\pi$
$200$	21.7567	−	7.06917i	1.53843	−	0.499866i
$201$	−11.7454	−	36.1487i	−0.828458	−	2.54973i
$202$	16.2353	−	16.2353i	1.14231	−	1.14231i
$203$	−2.34039	+	3.22128i	−0.164263	+	0.226089i
$204$	40.7139			2.85054
$205$	0.0786403	+	0.739245i	0.00549248	+	0.0516311i
$206$	15.2491			1.06245
$207$	22.8740	−	31.4833i	1.58985	−	2.18824i
$208$	2.49427	−	2.49427i	0.172947	−	0.172947i
$209$	2.38446	+	7.33862i	0.164937	+	0.507623i
$210$	−2.07059	+	0.672777i	−0.142885	+	0.0464260i
$211$	3.90790	+	24.6735i	0.269031	+	1.69859i	0.638722	+	0.769438i	$0.279464\pi$
$211$	3.90790	+	24.6735i	0.269031	+	1.69859i	−0.369691	+	0.929155i	$0.620536\pi$
$212$	0.329887	−	2.08283i	0.0226567	−	0.143049i
$213$	25.6890	+	8.34685i	1.76018	+	0.571917i
$214$			33.3421i			2.27922i
$215$	0.0356264	−	0.109647i	0.00242970	−	0.00747785i
$216$	−13.0560	−	25.6239i	−0.888351	−	1.74349i
$217$	−7.51055	−	3.82682i	−0.509849	−	0.259781i
$218$	35.5878	−	5.63656i	2.41031	−	0.381756i
$219$	−22.0798	−	22.0798i	−1.49202	−	1.49202i
$220$	−0.694044	+	1.36214i	−0.0467924	+	0.0918353i
$221$	−3.11184	+	2.26089i	−0.209325	+	0.152084i
$222$	6.98478	−	3.55892i	0.468788	−	0.238859i
$223$	−2.68513	−	1.95086i	−0.179809	−	0.130639i	0.494240	−	0.869326i	$-0.335446\pi$
$223$	−2.68513	−	1.95086i	−0.179809	−	0.130639i	−0.674049	+	0.738686i	$0.735446\pi$
$224$	2.76291	+	0.437603i	0.184605	+	0.0292386i
$225$	15.2131	+	20.9390i	1.01421	+	1.39593i
$226$	−11.3379	−	15.6053i	−0.754186	−	1.03805i
$227$	−7.61270	−	1.20573i	−0.505272	−	0.0800273i	−0.101406	−	0.994845i	$-0.532334\pi$
$227$	−7.61270	−	1.20573i	−0.505272	−	0.0800273i	−0.403867	+	0.914818i	$0.632334\pi$
$228$	−20.5340	−	14.9189i	−1.35990	−	0.988026i
$229$	4.43150	−	2.25796i	0.292842	−	0.149210i	−0.301398	−	0.953499i	$-0.597453\pi$
$229$	4.43150	−	2.25796i	0.292842	−	0.149210i	0.594240	+	0.804288i	$0.297453\pi$
$230$	1.70918	−	1.24179i	0.112700	−	0.0818811i
$231$	−11.8727	+	23.3015i	−0.781168	+	1.53313i
$232$	−4.78426	−	4.78426i	−0.314102	−	0.314102i
$233$	−10.5733	+	1.67465i	−0.692680	+	0.109710i	−0.492841	−	0.870119i	$-0.664042\pi$
$233$	−10.5733	+	1.67465i	−0.692680	+	0.109710i	−0.199838	+	0.979829i	$0.564042\pi$
$234$	11.8059	+	6.01539i	0.771774	+	0.393238i
$235$	−0.582977	−	1.14416i	−0.0380292	−	0.0746366i
$236$	−2.33659	+	7.19128i	−0.152099	+	0.468113i
$237$			30.7137i			1.99507i
$238$	22.7884	+	7.40440i	1.47715	+	0.479956i
$239$	−1.44605	+	9.13003i	−0.0935375	+	0.590572i	0.895746	+	0.444566i	$0.146642\pi$
$239$	−1.44605	+	9.13003i	−0.0935375	+	0.590572i	−0.989284	+	0.146006i	$0.953358\pi$
$240$	−0.174315	−	1.10058i	−0.0112520	−	0.0710423i
$241$	−26.9539	+	8.75786i	−1.73626	+	0.564144i	−0.994330	−	0.106339i	$-0.966087\pi$
$241$	−26.9539	+	8.75786i	−1.73626	+	0.564144i	−0.741925	+	0.670482i	$0.766087\pi$
$242$	0.342207	+	1.05320i	0.0219979	+	0.0677025i
$243$	−8.50371	+	8.50371i	−0.545513	+	0.545513i
$244$	−23.1835	+	31.9094i	−1.48417	+	2.04279i
$245$	−0.0335337			−0.00214239
$246$	−44.4165	−	2.27161i	−2.83189	−	0.144833i
$247$	2.39792			0.152576
$248$	8.41916	−	11.5880i	0.534617	−	0.735838i
$249$	1.28545	−	1.28545i	0.0814623	−	0.0814623i
$250$	0.869568	+	2.67626i	0.0549963	+	0.169261i
$251$	6.28383	−	2.04174i	0.396632	−	0.128874i	−0.103908	−	0.994587i	$-0.533135\pi$
$251$	6.28383	−	2.04174i	0.396632	−	0.128874i	0.500540	+	0.865713i	$0.333135\pi$
$252$	−8.52787	−	53.8429i	−0.537205	−	3.39178i
$253$	3.96987	−	25.0648i	0.249584	−	1.57581i
$254$	−18.7077	−	6.07850i	−1.17383	−	0.381399i
$255$			1.21508i			0.0760910i
$256$	−9.53197	+	29.3364i	−0.595748	+	1.83352i
$257$	−1.99593	−	3.91722i	−0.124502	−	0.244350i	0.820339	−	0.571877i	$-0.193785\pi$
$257$	−1.99593	−	3.91722i	−0.124502	−	0.244350i	−0.944842	+	0.327527i	$0.893785\pi$
$258$	6.14541	+	3.13124i	0.382596	+	0.194943i
$259$	3.00954	−	0.476665i	0.187004	−	0.0296185i
$260$	0.335933	+	0.335933i	0.0208337	+	0.0208337i
$261$	3.47528	−	6.82061i	0.215114	−	0.422185i
$262$	−22.3555	+	16.2422i	−1.38113	+	1.00345i
$263$	−11.1561	+	5.68432i	−0.687915	+	0.350510i	−0.762757	−	0.646685i	$-0.776155\pi$
$263$	−11.1561	+	5.68432i	−0.687915	+	0.350510i	0.0748417	+	0.997195i	$0.476155\pi$
$264$	−35.9518	−	26.1205i	−2.21268	−	1.60761i
$265$	0.0621605	+	0.00984525i	0.00381849	+	0.000604789i
$266$	−8.78012	−	12.0848i	−0.538344	−	0.740967i
$267$	8.09892	+	11.1472i	0.495646	+	0.682198i
$268$	51.0308	+	8.08248i	3.11720	+	0.493716i
$269$	−2.86327	−	2.08029i	−0.174577	−	0.126838i	0.497066	−	0.867713i	$-0.334411\pi$
$269$	−2.86327	−	2.08029i	−0.174577	−	0.126838i	−0.671642	+	0.740875i	$0.734411\pi$
$270$	1.57385	−	0.801918i	0.0957817	−	0.0488032i
$271$	3.09632	−	2.24961i	0.188088	−	0.136654i	−0.489756	−	0.871859i	$-0.662914\pi$
$271$	3.09632	−	2.24961i	0.188088	−	0.136654i	0.677845	+	0.735205i	$0.262914\pi$
$272$	−5.56760	+	10.9270i	−0.337585	+	0.662549i
$273$	5.74666	+	5.74666i	0.347804	+	0.347804i
$274$	14.4674	−	2.29141i	0.874009	−	0.138429i
$275$	15.0384	+	7.66243i	0.906847	+	0.462062i
$276$	37.8966	+	74.3762i	2.28111	+	4.47692i
$277$	9.27253	−	28.5379i	0.557132	−	1.71468i	−0.133112	−	0.991101i	$-0.542497\pi$
$277$	9.27253	−	28.5379i	0.557132	−	1.71468i	0.690244	−	0.723576i	$-0.257503\pi$
$278$		−	42.8383i		−	2.56927i
$279$	15.4124	+	5.00778i	0.922714	+	0.299808i
$280$	0.224952	−	1.42029i	0.0134434	−	0.0848785i
$281$	0.860451	+	5.43268i	0.0513302	+	0.324086i	0.999970	+	0.00772841i	$0.00246005\pi$
$281$	0.860451	+	5.43268i	0.0513302	+	0.324086i	−0.948640	+	0.316358i	$0.897540\pi$
$282$	73.0619	−	23.7392i	4.35077	−	1.41365i
$283$	9.37505	+	28.8534i	0.557289	+	1.71516i	0.689822	+	0.723979i	$0.257689\pi$
$283$	9.37505	+	28.8534i	0.557289	+	1.71516i	−0.132533	+	0.991179i	$0.542311\pi$
$284$	−25.9628	+	25.9628i	−1.54061	+	1.54061i
$285$	0.445243	−	0.612824i	0.0263739	−	0.0363006i
$286$	8.64049			0.510923
$287$	−16.1466	−	6.17477i	−0.953106	−	0.364485i
$288$	−5.37798			−0.316901
$289$	−2.13201	+	2.93447i	−0.125413	+	0.172616i
$290$	0.293855	−	0.293855i	0.0172558	−	0.0172558i
$291$	−2.44303	−	7.51886i	−0.143213	−	0.440763i
$292$	40.3685	−	13.1165i	2.36239	−	0.767587i
$293$	−3.14362	−	19.8480i	−0.183652	−	1.15953i	−0.891450	−	0.453119i	$-0.850311\pi$
$293$	−3.14362	−	19.8480i	−0.183652	−	1.15953i	0.707798	−	0.706415i	$-0.249689\pi$
$294$	0.313829	−	1.98144i	0.0183029	−	0.115560i
$295$	−0.214619	−	0.0697339i	−0.0124956	−	0.00406006i
$296$			5.17774i			0.300950i
$297$	6.55663	−	20.1792i	0.380454	−	1.17092i
$298$	−1.19298	−	2.34135i	−0.0691073	−	0.135631i
$299$	−7.02671	−	3.58029i	−0.406365	−	0.207053i
$300$	−54.8338	+	8.68482i	−3.16583	+	0.501419i
$301$	1.89568	+	1.89568i	0.109265	+	0.109265i
$302$	14.4796	−	28.4177i	0.833205	−	1.63526i
$303$	−21.9038	+	15.9140i	−1.25834	+	0.914237i
$304$	6.81204	−	3.47091i	0.390697	−	0.199070i
$305$	−0.952313	−	0.691896i	−0.0545293	−	0.0396178i
$306$	−45.4987	−	7.20629i	−2.60099	−	0.411956i
$307$	0.132775	+	0.182749i	0.00757787	+	0.0104300i	0.812789	−	0.582558i	$-0.197948\pi$
$307$	0.132775	+	0.182749i	0.00757787	+	0.0104300i	−0.805211	+	0.592988i	$0.797948\pi$
$308$	−20.8953	−	28.7599i	−1.19062	−	1.63875i
$309$	−17.7602	−	2.81294i	−1.01034	−	0.160023i
$310$	0.711749	+	0.517116i	0.0404246	+	0.0293702i
$311$	12.9469	−	6.59679i	0.734153	−	0.374070i	−0.0465963	−	0.998914i	$-0.514837\pi$
$311$	12.9469	−	6.59679i	0.734153	−	0.374070i	0.780750	+	0.624844i	$0.214837\pi$
$312$	−11.1724	+	8.11724i	−0.632514	+	0.459548i
$313$	3.71571	−	7.29249i	0.210024	−	0.412196i	−0.761831	−	0.647776i	$-0.775699\pi$
$313$	3.71571	−	7.29249i	0.210024	−	0.412196i	0.971855	+	0.235581i	$0.0756992\pi$
$314$	28.1319	+	28.1319i	1.58757	+	1.58757i
$315$	1.60690	−	0.254508i	0.0905387	−	0.0143399i
$316$	−37.1996	−	18.9541i	−2.09264	−	1.06625i
$317$	4.35992	+	8.55683i	0.244878	+	0.480600i	0.980430	−	0.196868i	$-0.0630772\pi$
$317$	4.35992	+	8.55683i	0.244878	+	0.480600i	−0.735552	+	0.677468i	$0.763077\pi$
$318$	−1.16347	+	3.58080i	−0.0652444	+	0.200802i
$319$		−	4.99187i		−	0.279491i
$320$	−1.01828	−	0.330858i	−0.0569234	−	0.0184955i
$321$	6.15051	−	38.8328i	0.343288	−	2.16743i
$322$	7.68512	+	48.5219i	0.428275	+	2.70402i
$323$	−7.92873	+	2.57620i	−0.441166	+	0.143344i
$324$	2.84798	+	8.76519i	0.158221	+	0.486955i
$325$	3.70878	−	3.70878i	0.205726	−	0.205726i
$326$	20.8742	−	28.7308i	1.15611	−	1.59125i
$327$	−42.4881			−2.34960
$328$	14.6555	−	25.4581i	0.809214	−	1.40569i
$329$	29.8603			1.64625
$330$	1.60435	−	2.20820i	0.0883168	−	0.121558i
$331$	3.24814	−	3.24814i	0.178534	−	0.178534i	−0.612183	−	0.790716i	$-0.709708\pi$
$331$	3.24814	−	3.24814i	0.178534	−	0.178534i	0.790716	+	0.612183i	$0.209708\pi$
$332$	0.763624	+	2.35019i	0.0419093	+	0.128984i
$333$	−5.57133	+	1.81024i	−0.305307	+	0.0992003i
$334$	4.41114	+	27.8508i	0.241367	+	1.52393i
$335$	−0.241216	+	1.52298i	−0.0131790	+	0.0832092i
$336$	24.6432	+	8.00708i	1.34440	+	0.436822i
$337$			17.7306i			0.965849i	0.875662	+	0.482924i	$0.160425\pi$
$337$			17.7306i			0.965849i	−0.875662	+	0.482924i	$0.839575\pi$
$338$	−8.91999	+	27.4529i	−0.485183	+	1.49324i
$339$	10.3263	+	20.2666i	0.560849	+	1.10073i
$340$	−1.47167	−	0.749853i	−0.0798125	−	0.0406665i
$341$	10.4377	−	1.65317i	0.565232	−	0.0895240i
$342$	20.3067	+	20.3067i	1.09806	+	1.09806i
$343$	−8.22572	+	16.1439i	−0.444147	+	0.871688i
$344$	−3.68550	+	2.67767i	−0.198709	+	0.144370i
$345$	−2.21971	+	1.13100i	−0.119505	+	0.0608908i
$346$	−3.96369	−	2.87979i	−0.213089	−	0.154819i
$347$	15.9671	+	2.52894i	0.857160	+	0.135761i	0.569520	−	0.821978i	$-0.307129\pi$
$347$	15.9671	+	2.52894i	0.857160	+	0.135761i	0.287640	+	0.957739i	$0.407129\pi$
$348$	9.65142	+	13.2840i	0.517370	+	0.712099i
$349$	−6.28967	−	8.65699i	−0.336678	−	0.463398i	0.606789	−	0.794863i	$-0.292457\pi$
$349$	−6.28967	−	8.65699i	−0.336678	−	0.463398i	−0.943468	+	0.331465i	$0.892457\pi$
$350$	−32.2711	−	5.11124i	−1.72496	−	0.273207i
$351$	−5.33437	−	3.87565i	−0.284727	−	0.206867i
$352$	−3.12479	+	1.59216i	−0.166552	+	0.0848625i
$353$	21.0319	−	15.2806i	1.11942	−	0.813304i	0.135297	−	0.990805i	$-0.456801\pi$
$353$	21.0319	−	15.2806i	1.11942	−	0.813304i	0.984121	+	0.177501i	$0.0568012\pi$
$354$	6.12898	−	12.0288i	0.325752	−	0.639323i
$355$	−0.774841	−	0.774841i	−0.0411243	−	0.0411243i
$356$	−18.4992	+	2.92999i	−0.980458	+	0.155289i
$357$	−25.1752	−	12.8274i	−1.33241	−	0.678899i
$358$	−19.6812	−	38.6266i	−1.04018	−	2.04148i
$359$	−3.00578	+	9.25084i	−0.158639	+	0.488241i	−0.998511	−	0.0545433i	$-0.982630\pi$
$359$	−3.00578	+	9.25084i	−0.158639	+	0.488241i	0.839872	+	0.542784i	$0.182630\pi$
$360$			2.76458i			0.145706i
$361$	−13.1272	−	4.26529i	−0.690906	−	0.224489i
$362$	−0.672073	+	4.24330i	−0.0353234	+	0.223023i
$363$	−0.204279	−	1.28977i	−0.0107219	−	0.0676952i
$364$	−10.5066	+	3.41380i	−0.550696	+	0.178932i
$365$	0.391454	+	1.20477i	0.0204896	+	0.0630606i
$366$	49.7951	−	49.7951i	2.60283	−	2.60283i
$367$	13.2160	−	18.1902i	0.689868	−	0.949522i	−0.310131	−	0.950694i	$-0.600373\pi$
$367$	13.2160	−	18.1902i	0.689868	−	0.949522i	0.999999	+	0.00117139i	$0.000372866\pi$
$368$	−25.1439			−1.31072
$369$	32.5172	+	6.86890i	1.69278	+	0.357581i
$370$	−0.318023			−0.0165332
$371$	−0.860205	+	1.18397i	−0.0446596	+	0.0614687i
$372$	−24.5798	+	24.5798i	−1.27440	+	1.27440i
$373$	−0.994171	−	3.05974i	−0.0514762	−	0.158428i	0.922014	−	0.387157i	$-0.126543\pi$
$373$	−0.994171	−	3.05974i	−0.0514762	−	0.158428i	−0.973490	+	0.228730i	$0.926543\pi$
$374$	−28.5698	+	9.28288i	−1.47731	+	0.480006i
$375$	−0.519086	−	3.27738i	−0.0268055	−	0.169243i
$376$	−7.93753	+	50.1156i	−0.409347	+	2.58452i
$377$	−1.47536	−	0.479372i	−0.0759847	−	0.0246889i
$378$			41.0745i			2.11264i
$379$	−5.92193	+	18.2258i	−0.304189	+	0.936198i	0.675789	+	0.737095i	$0.263803\pi$
$379$	−5.92193	+	18.2258i	−0.304189	+	0.936198i	−0.979978	+	0.199103i	$0.936197\pi$
$380$	0.467467	+	0.917456i	0.0239806	+	0.0470645i
$381$	20.6671	+	10.5304i	1.05881	+	0.539490i
$382$	−13.0868	+	2.07275i	−0.669581	+	0.106051i
$383$	20.6909	+	20.6909i	1.05726	+	1.05726i	0.998258	+	0.0589972i	$0.0187903\pi$
$383$	20.6909	+	20.6909i	1.05726	+	1.05726i	0.0589972	+	0.998258i	$0.481210\pi$
$384$	26.3870	−	51.7874i	1.34656	−	2.64276i
$385$	0.858318	−	0.623605i	0.0437439	−	0.0317818i
$386$	−14.1827	+	7.22643i	−0.721879	+	0.367816i
$387$	−4.16974	−	3.02949i	−0.211960	−	0.153998i
$388$	10.6143	+	1.68114i	0.538859	+	0.0853470i
$389$	−5.16511	−	7.10917i	−0.261882	−	0.360449i	0.657746	−	0.753239i	$-0.271510\pi$
$389$	−5.16511	−	7.10917i	−0.261882	−	0.360449i	−0.919628	+	0.392790i	$0.871510\pi$
$390$	−0.498571	−	0.686225i	−0.0252461	−	0.0347483i
$391$	27.0803	+	4.28910i	1.36951	+	0.216909i
$392$	1.07198	+	0.778840i	0.0541432	+	0.0393373i
$393$	29.0331	−	14.7931i	1.46453	−	0.746214i
$394$	−8.38504	+	6.09209i	−0.422432	+	0.306915i
$395$	0.565673	−	1.11020i	0.0284621	−	0.0558600i
$396$	48.3266	+	48.3266i	2.42850	+	2.42850i
$397$	−24.8449	+	3.93505i	−1.24693	+	0.197495i	−0.744795	−	0.667294i	$-0.767453\pi$
$397$	−24.8449	+	3.93505i	−1.24693	+	0.197495i	−0.502137	+	0.864788i	$0.667453\pi$
$398$	−34.5875	−	17.6232i	−1.73372	−	0.883372i
$399$	7.99676	+	15.6945i	0.400339	+	0.785709i
$400$	5.16761	−	15.9043i	0.258381	−	0.795214i
$401$			28.1172i			1.40411i	0.712124	+	0.702054i	$0.247733\pi$
$401$			28.1172i			1.40411i	−0.712124	+	0.702054i	$0.752267\pi$
$402$	−87.7324	−	28.5060i	−4.37569	−	1.42175i
$403$	0.513740	−	3.24363i	0.0255912	−	0.161577i
$404$	−5.75731	−	36.3502i	−0.286437	−	1.80849i
$405$	−0.261591	+	0.0849960i	−0.0129986	+	0.00422349i
$406$	2.98621	+	9.19060i	0.148203	+	0.456122i
$407$	−2.70121	+	2.70121i	−0.133894	+	0.133894i
$408$	28.2209	−	38.8427i	1.39714	−	1.92300i
$409$	1.43475			0.0709440			0.0354720	−	0.999371i	$-0.488707\pi$
$409$	1.43475			0.0709440			0.0354720	+	0.999371i	$0.488707\pi$
$410$	1.56367	+	0.900159i	0.0772242	+	0.0444557i
$411$	−17.2726			−0.851992
$412$	14.3672	−	19.7748i	0.707822	−	0.974234i
$413$	3.71053	−	3.71053i	0.182583	−	0.182583i
$414$	−29.1859	−	89.8249i	−1.43441	−	4.41465i
$415$	−0.0701399	+	0.0227898i	−0.00344303	+	0.00111871i
$416$	0.170490	+	1.07643i	0.00835898	+	0.0527765i
$417$	−7.90224	+	49.8928i	−0.386974	+	2.44326i
$418$	17.8107	+	5.78705i	0.871151	+	0.283054i
$419$		−	15.5755i		−	0.760912i	−0.924799	−	0.380456i	$-0.875767\pi$
$419$		−	15.5755i		−	0.760912i	0.924799	−	0.380456i	$-0.124233\pi$
$420$	−1.07841	+	3.31899i	−0.0526208	+	0.161950i
$421$	−3.37083	−	6.61562i	−0.164284	−	0.322426i	0.794159	−	0.607710i	$-0.207912\pi$
$421$	−3.37083	−	6.61562i	−0.164284	−	0.322426i	−0.958443	+	0.285285i	$0.907912\pi$
$422$	54.0205	+	27.5248i	2.62968	+	1.33989i
$423$	−56.7003	+	8.98045i	−2.75687	+	0.436645i
$424$	−1.75844	−	1.75844i	−0.0853974	−	0.0853974i
$425$	−8.27857	+	16.2476i	−0.401570	+	0.788125i
$426$	53.0353	−	38.5324i	2.56957	−	1.86690i
$427$	24.3889	−	12.4268i	1.18026	−	0.601373i
$428$	43.2376	+	31.4140i	2.08997	+	1.51845i
$429$	−10.0634	−	1.59388i	−0.485864	−	0.0769533i
$430$	−0.164466	−	0.226368i	−0.00793125	−	0.0109164i
$431$	20.1133	+	27.6836i	0.968824	+	1.33347i	0.942639	+	0.333815i	$0.108336\pi$
$431$	20.1133	+	27.6836i	0.968824	+	1.33347i	0.0261853	+	0.999657i	$0.491664\pi$
$432$	−20.7638	−	3.28866i	−0.998998	−	0.158226i
$433$	−6.78471	−	4.92938i	−0.326053	−	0.236891i	0.412701	−	0.910866i	$-0.364585\pi$
$433$	−6.78471	−	4.92938i	−0.326053	−	0.236891i	−0.738754	+	0.673975i	$0.764585\pi$
$434$	−18.2280	+	9.28763i	−0.874972	+	0.445820i
$435$	−0.396453	+	0.288040i	−0.0190085	+	0.0138105i
$436$	26.2204	−	51.4605i	1.25573	−	2.46451i
$437$	−12.0863	−	12.0863i	−0.578166	−	0.578166i
$438$	−74.8510	+	11.8552i	−3.57652	+	0.566465i
$439$	21.8040	+	11.1097i	1.04065	+	0.530236i	0.888861	−	0.458178i	$-0.151498\pi$
$439$	21.8040	+	11.1097i	1.04065	+	0.530236i	0.151786	+	0.988413i	$0.451498\pi$
$440$	0.818459	+	1.60632i	0.0390185	+	0.0765781i
$441$	−0.463260	+	1.42577i	−0.0220600	+	0.0678936i
$442$			9.33528i			0.444034i
$443$	−13.1456	−	4.27126i	−0.624565	−	0.202933i	−0.0203990	−	0.999792i	$-0.506494\pi$
$443$	−13.1456	−	4.27126i	−0.624565	−	0.202933i	−0.604166	+	0.796858i	$0.706494\pi$
$444$	1.96569	−	12.4109i	0.0932876	−	0.588995i
$445$	−0.0874436	−	0.552097i	−0.00414522	−	0.0261719i
$446$	−7.66092	+	2.48918i	−0.362755	+	0.117866i
$447$	0.957532	+	2.94698i	0.0452897	+	0.139387i
$448$	17.6049	−	17.6049i	0.831753	−	0.831753i
$449$	0.627367	−	0.863496i	0.0296073	−	0.0407509i	−0.793957	−	0.607974i	$-0.791982\pi$
$449$	0.627367	−	0.863496i	0.0296073	−	0.0407509i	0.823564	+	0.567223i	$0.191982\pi$
$450$	62.8153			2.96114
$451$	20.9272	−	5.63571i	0.985422	−	0.265375i
$452$	−30.9190			−1.45431
$453$	−22.1061	+	30.4265i	−1.03864	+	1.42956i
$454$	−13.2273	+	13.2273i	−0.620787	+	0.620787i
$455$	−0.101883	−	0.313562i	−0.00477633	−	0.0147000i
$456$	−28.4664	+	9.24931i	−1.33306	+	0.433138i
$457$	−4.71510	−	29.7700i	−0.220563	−	1.39258i	−0.810787	−	0.585342i	$-0.800960\pi$
$457$	−4.71510	−	29.7700i	−0.220563	−	1.39258i	0.590223	−	0.807240i	$-0.299040\pi$
$458$	1.88829	−	11.9222i	0.0882342	−	0.557089i
$459$	21.8019	+	7.08386i	1.01762	+	0.330646i
$460$		−	3.38642i		−	0.157892i
$461$	0.963390	−	2.96501i	0.0448695	−	0.138094i	−0.926112	−	0.377249i	$-0.876870\pi$
$461$	0.963390	−	2.96501i	0.0448695	−	0.138094i	0.970982	+	0.239154i	$0.0768702\pi$
$462$	28.8149	+	56.5525i	1.34059	+	2.63106i
$463$	−6.30485	−	3.21248i	−0.293011	−	0.149297i	0.301306	−	0.953528i	$-0.402577\pi$
$463$	−6.30485	−	3.21248i	−0.293011	−	0.149297i	−0.594317	+	0.804231i	$0.702577\pi$
$464$	−4.88508	+	0.773720i	−0.226784	+	0.0359191i
$465$	−0.733567	−	0.733567i	−0.0340183	−	0.0340183i
$466$	−11.7952	+	23.1493i	−0.546401	+	1.07237i
$467$	31.9737	−	23.2303i	1.47957	−	1.07497i	0.501873	−	0.864941i	$-0.332644\pi$
$467$	31.9737	−	23.2303i	1.47957	−	1.07497i	0.977695	−	0.210028i	$-0.0673556\pi$
$468$	18.9238	−	9.64218i	0.874755	−	0.445710i
$469$	−29.0082	−	21.0757i	−1.33947	−	0.973184i
$470$	−3.07816	−	0.487533i	−0.141985	−	0.0224882i
$471$	−27.5751	−	37.9539i	−1.27060	−	1.74882i
$472$	5.24117	+	7.21386i	0.241245	+	0.332045i
$473$	−3.31965	−	0.525780i	−0.152638	−	0.0241754i
$474$	60.3054	+	43.8144i	2.76992	+	2.01246i
$475$	10.1289	−	5.16096i	0.464748	−	0.236801i
$476$	31.0725	−	22.5755i	1.42421	−	1.03475i
$477$	1.27733	−	2.50690i	0.0584848	−	0.114783i
$478$	15.8637	+	15.8637i	0.725588	+	0.725588i
$479$	11.5501	−	1.82935i	0.527737	−	0.0835853i	0.113120	−	0.993581i	$-0.463916\pi$
$479$	11.5501	−	1.82935i	0.527737	−	0.0835853i	0.414617	+	0.909996i	$0.363916\pi$
$480$	0.306755	+	0.156300i	0.0140014	+	0.00713407i
$481$	0.538949	+	1.05775i	0.0245740	+	0.0482291i
$482$	−21.2552	+	65.4168i	−0.968148	+	2.97965i
$483$		−	57.9300i		−	2.63591i
$484$	1.68820	+	0.548529i	0.0767363	+	0.0249331i
$485$	−0.0501725	+	0.316776i	−0.00227821	+	0.0143841i
$486$	4.56586	+	28.8277i	0.207112	+	1.30765i
$487$	−23.9864	+	7.79365i	−1.08693	+	0.353164i	−0.797058	−	0.603903i	$-0.793612\pi$
$487$	−23.9864	+	7.79365i	−1.08693	+	0.353164i	−0.289869	+	0.957066i	$0.593612\pi$
$488$	14.3732	+	44.2361i	0.650643	+	2.00247i
$489$	−29.6115	+	29.6115i	−1.33908	+	1.33908i
$490$	−0.0478373	+	0.0658424i	−0.00216107	+	0.00297446i
$491$	−31.5085			−1.42196			−0.710980	−	0.703212i	$-0.751748\pi$
$491$	−31.5085			−1.42196			−0.710980	+	0.703212i	$0.751748\pi$
$492$	−44.7938	+	55.4585i	−2.01946	+	2.50026i
$493$	5.39328			0.242901
$494$	3.42075	−	4.70825i	0.153907	−	0.211834i
$495$	−1.44227	+	1.44227i	−0.0648254	+	0.0648254i
$496$	−3.23560	−	9.95815i	−0.145283	−	0.447134i
$497$	24.2339	−	7.87407i	1.08704	−	0.353200i
$498$	−0.690194	−	4.35771i	−0.0309283	−	0.195274i
$499$	0.773481	−	4.88356i	0.0346257	−	0.218618i	−0.964308	−	0.264783i	$-0.914700\pi$
$499$	0.773481	−	4.88356i	0.0346257	−	0.218618i	0.998934	+	0.0461643i	$0.0146998\pi$
$500$	4.28982	+	1.39385i	0.191846	+	0.0623347i
$501$		−	33.2509i		−	1.48554i
$502$	4.95528	−	15.2508i	0.221165	−	0.680675i
$503$	−11.0443	−	21.6756i	−0.492439	−	0.966466i	−0.994804	−	0.101810i	$-0.967537\pi$
$503$	−11.0443	−	21.6756i	−0.492439	−	0.966466i	0.502365	−	0.864656i	$-0.332463\pi$
$504$	−57.2795	−	29.1853i	−2.55143	−	1.30002i
$505$	1.08485	−	0.171823i	0.0482751	−	0.00764602i
$506$	−43.5508	−	43.5508i	−1.93607	−	1.93607i
$507$	15.4530	−	30.3283i	0.686294	−	1.34693i
$508$	−25.5084	+	18.5329i	−1.13175	+	0.822266i
$509$	29.2644	−	14.9110i	1.29712	−	0.660917i	0.337266	−	0.941409i	$-0.390498\pi$
$509$	29.2644	−	14.9110i	1.29712	−	0.660917i	0.959856	+	0.280493i	$0.0904978\pi$
$510$	2.38577	+	1.73336i	0.105644	+	0.0767546i
$511$	−29.0942	−	4.60807i	−1.28705	−	0.203849i
$512$	20.1286	+	27.7047i	0.889568	+	1.22438i
$513$	−8.40003	−	11.5617i	−0.370870	−	0.510459i
$514$	−10.5386	−	1.66916i	−0.464839	−	0.0736233i
$515$	0.590165	+	0.428780i	0.0260058	+	0.0188943i
$516$	9.85058	−	5.01912i	0.433648	−	0.220955i
$517$	−30.2862	+	22.0042i	−1.33198	+	0.967743i
$518$	3.35734	−	6.58914i	0.147513	−	0.289510i
$519$	4.08519	+	4.08519i	0.179320	+	0.179320i
$520$	0.553346	−	0.0876415i	0.0242658	−	0.00384333i
$521$	−37.3756	−	19.0438i	−1.63745	−	0.834325i	−0.997844	−	0.0656258i	$-0.979096\pi$
$521$	−37.3756	−	19.0438i	−1.63745	−	0.834325i	−0.639611	−	0.768699i	$-0.720904\pi$
$522$	−8.43444	−	16.5535i	−0.369165	−	0.724528i
$523$	−4.76782	+	14.6739i	−0.208482	+	0.641643i	0.791070	+	0.611726i	$0.209524\pi$
$523$	−4.76782	+	14.6739i	−0.208482	+	0.641643i	−0.999552	+	0.0299172i	$0.990476\pi$
$524$			44.2934i			1.93496i
$525$	36.6425	+	11.9059i	1.59921	+	0.519615i
$526$	−4.75370	+	30.0137i	−0.207271	+	1.30866i
$527$	1.78610	+	11.2770i	0.0778037	+	0.491233i
$528$	−30.8952	+	10.0385i	−1.34454	+	0.436868i
$529$	10.2637	+	31.5884i	0.446247	+	1.37341i
$530$	0.108006	−	0.108006i	0.00469147	−	0.00469147i
$531$	−5.92982	+	8.16169i	−0.257332	+	0.354187i
$532$	−23.9438			−1.03810
$533$	0.344004	−	6.72626i	0.0149005	−	0.291347i
$534$	33.4407			1.44712
$535$	−0.937529	+	1.29040i	−0.0405329	+	0.0557888i
$536$	43.0831	−	43.0831i	1.86091	−	1.86091i
$537$	15.7969	+	48.6180i	0.681688	+	2.09802i
$538$	−8.16919	+	2.65433i	−0.352199	+	0.114436i
$539$	0.152931	+	0.965568i	0.00658720	+	0.0415900i
$540$	0.442922	−	2.79650i	0.0190603	−	0.120342i
$541$	8.26506	+	2.68548i	0.355343	+	0.115458i	0.481248	−	0.876584i	$-0.340184\pi$
$541$	8.26506	+	2.68548i	0.355343	+	0.115458i	−0.125905	+	0.992042i	$0.540184\pi$
$542$		−	9.28872i		−	0.398985i
$543$	1.56550	−	4.81810i	0.0671819	−	0.206765i
$544$	−1.72019	−	3.37606i	−0.0737525	−	0.144748i
$545$	1.53580	+	0.782530i	0.0657865	+	0.0335199i
$546$	19.4813	−	3.08553i	0.833722	−	0.132049i
$547$	1.94269	+	1.94269i	0.0830635	+	0.0830635i	0.747418	−	0.664354i	$-0.231293\pi$
$547$	1.94269	+	1.94269i	0.0830635	+	0.0830635i	−0.664354	+	0.747418i	$0.731293\pi$
$548$	10.6593	−	20.9201i	0.455343	−	0.893661i
$549$	−42.5736	+	30.9315i	−1.81700	+	1.32013i
$550$	36.4979	−	18.5966i	1.55627	−	0.792962i
$551$	−2.72010	−	1.97627i	−0.115880	−	0.0841919i
$552$	97.2261	+	15.3991i	4.13822	+	0.655429i
$553$	17.0305	+	23.4404i	0.724209	+	0.996788i
$554$	−42.8057	−	58.9170i	−1.81864	−	2.50314i
$555$	0.370394	+	0.0586647i	0.0157224	+	0.00249018i
$556$	−55.5522	−	40.3610i	−2.35594	−	1.71169i
$557$	−29.7769	+	15.1721i	−1.26169	+	0.642862i	−0.951452	−	0.307797i	$-0.900408\pi$
$557$	−29.7769	+	15.1721i	−1.26169	+	0.642862i	−0.310236	+	0.950660i	$0.600408\pi$
$558$	31.8191	−	23.1179i	1.34701	−	0.978660i
$559$	−0.474183	+	0.930636i	−0.0200558	+	0.0393617i
$560$	−0.743300	−	0.743300i	−0.0314101	−	0.0314101i
$561$	34.9869	−	5.54138i	1.47715	−	0.233957i
$562$	11.8944	+	6.06049i	0.501734	+	0.255646i
$563$	7.71260	+	15.1368i	0.325047	+	0.637941i	0.994479	−	0.104932i	$-0.0334626\pi$
$563$	7.71260	+	15.1368i	0.325047	+	0.637941i	−0.669432	+	0.742873i	$0.733463\pi$
$564$	38.0521	−	117.112i	1.60228	−	4.93131i
$565$		−	0.922756i		−	0.0388206i
$566$	70.0268	+	22.7531i	2.94345	+	0.956384i
$567$	1.00055	−	6.31721i	0.0420191	−	0.265298i
$568$	6.77343	+	42.7657i	0.284207	+	1.79441i
$569$	24.8527	−	8.07512i	1.04188	−	0.338526i	0.262402	−	0.964959i	$-0.415486\pi$
$569$	24.8527	−	8.07512i	1.04188	−	0.338526i	0.779476	+	0.626432i	$0.215486\pi$
$570$	−0.568104	−	1.74844i	−0.0237953	−	0.0732343i
$571$	−1.00428	+	1.00428i	−0.0420278	+	0.0420278i	−0.727808	−	0.685781i	$-0.759461\pi$
$571$	−1.00428	+	1.00428i	−0.0420278	+	0.0420278i	0.685781	+	0.727808i	$0.259461\pi$
$572$	8.14082	−	11.2049i	0.340385	−	0.468499i
$573$	15.6243			0.652714
$574$	−35.1579	+	22.8949i	−1.46746	+	0.955615i
$575$	−37.3869			−1.55914
$576$	−28.1345	+	38.7238i	−1.17227	+	1.61349i
$577$	23.1743	−	23.1743i	0.964760	−	0.964760i	−0.0346401	−	0.999400i	$-0.511028\pi$
$577$	23.1743	−	23.1743i	0.964760	−	0.964760i	0.999400	+	0.0346401i	$0.0110285\pi$
$578$	2.72033	+	8.37230i	0.113151	+	0.348242i
$579$	17.8513	−	5.80022i	0.741873	−	0.241049i
$580$	−0.104206	−	0.657930i	−0.00432691	−	0.0273191i
$581$	0.268275	−	1.69382i	0.0111299	−	0.0702715i
$582$	−18.2482	−	5.92919i	−0.756411	−	0.245773i
$583$		−	1.83475i		−	0.0759875i
$584$	15.4678	−	47.6050i	0.640062	−	1.96991i
$585$	0.287764	+	0.564769i	0.0118976	+	0.0233503i
$586$	−43.4556	−	22.1417i	−1.79513	−	0.914667i
$587$	−7.53663	+	1.19368i	−0.311070	+	0.0492686i	−0.310018	−	0.950731i	$-0.600335\pi$
$587$	−7.53663	+	1.19368i	−0.311070	+	0.0492686i	−0.00105233	+	0.999999i	$0.500335\pi$
$588$	−2.27383	−	2.27383i	−0.0937710	−	0.0937710i
$589$	3.23143	−	6.34204i	0.133149	−	0.261319i
$590$	−0.443084	+	0.321920i	−0.0182415	+	0.0132532i
$591$	10.8896	−	5.54855i	0.447940	−	0.228237i
$592$	3.06210	+	2.22475i	0.125852	+	0.0914366i
$593$	−41.5892	−	6.58708i	−1.70786	−	0.270499i	−0.775322	−	0.631566i	$-0.782413\pi$
$593$	−41.5892	−	6.58708i	−1.70786	−	0.270499i	−0.932540	+	0.361067i	$0.882413\pi$
$594$	−30.2680	−	41.6604i	−1.24191	−	1.70935i
$595$	0.673750	+	0.927337i	0.0276210	+	0.0380171i
$596$	−4.16022	−	0.658915i	−0.170409	−	0.0269902i
$597$	37.0324	+	26.9056i	1.51563	+	1.10117i
$598$	−17.0537	+	8.68931i	−0.697379	+	0.355332i
$599$	37.0626	−	26.9276i	1.51434	−	1.10023i	0.550129	−	0.835079i	$-0.314578\pi$
$599$	37.0626	−	26.9276i	1.51434	−	1.10023i	0.964207	−	0.265151i	$-0.0854216\pi$
$600$	−29.7225	+	58.3337i	−1.21342	+	2.38146i
$601$	−8.39569	−	8.39569i	−0.342467	−	0.342467i	0.514827	−	0.857294i	$-0.327856\pi$
$601$	−8.39569	−	8.39569i	−0.342467	−	0.342467i	−0.857294	+	0.514827i	$0.827856\pi$
$602$	6.42637	−	1.01784i	0.261919	−	0.0414840i
$603$	61.4208	+	31.2955i	2.50125	+	1.27445i
$604$	−23.2095	−	45.5513i	−0.944383	−	1.85346i
$605$	−0.0163705	+	0.0503831i	−0.000665554	+	0.00204837i
$606$			65.7096i			2.66927i
$607$	−22.8222	−	7.41539i	−0.926325	−	0.300981i	−0.193266	−	0.981146i	$-0.561908\pi$
$607$	−22.8222	−	7.41539i	−0.926325	−	0.300981i	−0.733059	+	0.680165i	$0.761908\pi$
$608$	−0.369519	+	2.33305i	−0.0149860	+	0.0946177i
$609$	−1.78261	−	11.2549i	−0.0722348	−	0.456073i
$610$	−2.71704	+	0.882818i	−0.110010	+	0.0357443i
$611$	3.59498	+	11.0642i	0.145437	+	0.447610i
$612$	−52.2126	+	52.2126i	−2.11057	+	2.11057i
$613$	−10.8769	+	14.9708i	−0.439315	+	0.604665i	−0.970060	−	0.242867i	$-0.921912\pi$
$613$	−10.8769	+	14.9708i	−0.439315	+	0.604665i	0.530745	+	0.847532i	$0.321912\pi$
$614$	0.548233			0.0221249
$615$	−1.65512	−	1.33684i	−0.0667409	−	0.0539065i
$616$	−41.9217			−1.68907
$617$	−0.798604	+	1.09918i	−0.0321506	+	0.0442515i	−0.824790	−	0.565440i	$-0.808707\pi$
$617$	−0.798604	+	1.09918i	−0.0321506	+	0.0442515i	0.792639	+	0.609691i	$0.208707\pi$
$618$	−30.8589	+	30.8589i	−1.24133	+	1.24133i
$619$	12.9896	+	39.9780i	0.522097	+	1.60685i	0.769985	+	0.638062i	$0.220264\pi$
$619$	12.9896	+	39.9780i	0.522097	+	1.60685i	−0.247888	+	0.968789i	$0.579736\pi$
$620$	1.34118	−	0.435775i	0.0538630	−	0.0175012i
$621$	7.35243	+	46.4214i	0.295043	+	1.86283i
$622$	5.51678	−	34.8316i	0.221203	−	1.39662i
$623$	12.3621	+	4.01668i	0.495276	+	0.160925i
$624$			10.0951i			0.404128i
$625$	7.66300	−	23.5843i	0.306520	−	0.943371i
$626$	−9.01797	−	17.6988i	−0.360430	−	0.707385i
$627$	−19.6762	−	10.0255i	−0.785792	−	0.400381i
$628$	62.9861	−	9.97602i	2.51342	−	0.398087i
$629$	−2.91842	−	2.91842i	−0.116365	−	0.116365i
$630$	1.79260	−	3.51818i	0.0714189	−	0.140168i
$631$	29.2153	−	21.2262i	1.16304	−	0.845001i	0.172884	−	0.984942i	$-0.444691\pi$
$631$	29.2153	−	21.2262i	1.16304	−	0.845001i	0.990160	+	0.139941i	$0.0446914\pi$
$632$	−43.8680	+	22.3519i	−1.74498	+	0.889110i
$633$	−57.8390	−	42.0225i	−2.29889	−	1.67024i
$634$	23.0207	+	3.64613i	0.914270	+	0.144806i
$635$	−0.553102	−	0.761280i	−0.0219492	−	0.0302105i
$636$	3.54735	+	4.88251i	0.140662	+	0.193604i
$637$	0.300061	+	0.0475251i	0.0118889	+	0.00188301i
$638$	−9.80140	−	7.12114i	−0.388041	−	0.281928i
$639$	−43.6485	+	22.2400i	−1.72671	+	0.879802i
$640$	−1.90760	+	1.38595i	−0.0754046	+	0.0547847i
$641$	−20.0951	+	39.4388i	−0.793708	+	1.55774i	0.0358741	+	0.999356i	$0.488578\pi$
$641$	−20.0951	+	39.4388i	−0.793708	+	1.55774i	−0.829583	+	0.558384i	$0.811422\pi$
$642$	−67.4731	−	67.4731i	−2.66295	−	2.66295i
$643$	−12.3017	+	1.94839i	−0.485131	+	0.0768372i	−0.394209	−	0.919021i	$-0.628981\pi$
$643$	−12.3017	+	1.94839i	−0.485131	+	0.0768372i	−0.0909219	+	0.995858i	$0.528981\pi$
$644$	70.1633	+	35.7500i	2.76482	+	1.40875i
$645$	0.149792	+	0.293984i	0.00589806	+	0.0115756i
$646$	−6.25240	+	19.2429i	−0.245997	+	0.757102i
$647$		−	15.7465i		−	0.619061i	−0.950890	−	0.309530i	$-0.899828\pi$
$647$		−	15.7465i		−	0.619061i	0.950890	−	0.309530i	$-0.100172\pi$
$648$	10.3364	+	3.35851i	0.406054	+	0.131935i
$649$	−1.02914	+	6.49776i	−0.0403974	+	0.255059i
$650$	−1.99134	−	12.5728i	−0.0781069	−	0.493148i
$651$	22.9430	−	7.45463i	0.899206	−	0.292170i
$652$	−17.5907	−	54.1387i	−0.688906	−	2.12024i
$653$	13.7349	−	13.7349i	0.537489	−	0.537489i	−0.385301	−	0.922791i	$-0.625903\pi$
$653$	13.7349	−	13.7349i	0.537489	−	0.537489i	0.922791	+	0.385301i	$0.125903\pi$
$654$	−60.6112	+	83.4241i	−2.37009	+	3.26214i
$655$	−1.32190			−0.0516511
$656$	−8.75877	−	19.6060i	−0.341973	−	0.765484i
$657$	56.6316			2.20941
$658$	42.5971	−	58.6298i	1.66061	−	2.28563i
$659$	−8.94994	+	8.94994i	−0.348640	+	0.348640i	−0.859603	−	0.510963i	$-0.829289\pi$
$659$	−8.94994	+	8.94994i	−0.348640	+	0.348640i	0.510963	+	0.859603i	$0.329289\pi$
$660$	−1.35200	−	4.16101i	−0.0526263	−	0.161967i
$661$	35.5255	−	11.5429i	1.38178	−	0.448968i	0.478527	−	0.878073i	$-0.341171\pi$
$661$	35.5255	−	11.5429i	1.38178	−	0.448968i	0.903255	+	0.429105i	$0.141171\pi$
$662$	−1.74401	−	11.0112i	−0.0677829	−	0.427964i
$663$	1.72205	−	10.8726i	0.0668788	−	0.422256i
$664$	2.77149	+	0.900512i	0.107555	+	0.0349466i
$665$		−	0.714586i		−	0.0277105i
$666$	−4.39342	+	13.5215i	−0.170241	+	0.523949i
$667$	5.02008	+	9.85246i	0.194378	+	0.381489i
$668$	40.2727	+	20.5199i	1.55820	+	0.793941i
$669$	9.38166	−	1.48591i	0.362716	−	0.0574486i
$670$	2.64622	+	2.64622i	0.102232	+	0.102232i
$671$	−15.5794	+	30.5763i	−0.601436	+	1.18038i
$672$	−6.47676	+	4.70564i	−0.249846	+	0.181524i
$673$	−9.32618	+	4.75192i	−0.359498	+	0.183173i	−0.624405	−	0.781101i	$-0.714659\pi$
$673$	−9.32618	+	4.75192i	−0.359498	+	0.183173i	0.264908	+	0.964274i	$0.414659\pi$
$674$	34.8136	+	25.2936i	1.34097	+	0.974271i
$675$	−30.8741	−	4.88997i	−1.18834	−	0.188215i
$676$	27.1964	+	37.4327i	1.04602	+	1.43972i
$677$	9.95839	+	13.7066i	0.382732	+	0.526786i	0.956306	−	0.292368i	$-0.0944434\pi$
$677$	9.95839	+	13.7066i	0.382732	+	0.526786i	−0.573574	+	0.819154i	$0.694443\pi$
$678$	54.5238	+	8.63573i	2.09398	+	0.331653i
$679$	−6.03364	−	4.38370i	−0.231550	−	0.168231i
$680$	−1.73548	+	0.884272i	−0.0665527	+	0.0339103i
$681$	17.8455	−	12.9655i	0.683841	−	0.496840i
$682$	11.6439	−	22.8524i	0.445867	−	0.875064i
$683$	−14.4614	−	14.4614i	−0.553350	−	0.553350i	0.374056	−	0.927406i	$-0.377967\pi$
$683$	−14.4614	−	14.4614i	−0.553350	−	0.553350i	−0.927406	+	0.374056i	$0.877967\pi$
$684$	45.4658	−	7.20108i	1.73843	−	0.275340i
$685$	0.624345	+	0.318120i	0.0238550	+	0.0121547i
$686$	19.9637	+	39.1810i	0.762218	+	1.49594i
$687$	−4.39851	+	13.5372i	−0.167813	+	0.516477i
$688$			3.33012i			0.126960i
$689$	−0.542263	−	0.176192i	−0.0206586	−	0.00671238i
$690$	−0.945832	+	5.97175i	−0.0360072	+	0.227341i
$691$	−1.41031	−	8.90432i	−0.0536506	−	0.338736i	−0.999884	−	0.0152509i	$-0.995145\pi$
$691$	−1.41031	−	8.90432i	−0.0536506	−	0.338736i	0.946233	−	0.323486i	$-0.104855\pi$
$692$	−7.46895	+	2.42681i	−0.283927	+	0.0922535i
$693$	−14.6566	−	45.1085i	−0.556759	−	1.71353i
$694$	27.7433	−	27.7433i	1.05312	−	1.05312i
$695$	1.20455	−	1.65792i	0.0456911	−	0.0628884i
$696$	19.3634			0.733969
$697$	6.08889	+	22.6100i	0.230633	+	0.856413i
$698$	−25.9703			−0.982989
$699$	18.0078	−	24.7857i	0.681119	−	0.937480i
$700$	−37.0331	+	37.0331i	−1.39972	+	1.39972i
$701$	3.66441	+	11.2779i	0.138403	+	0.425960i	0.996104	−	0.0881889i	$-0.0281079\pi$
$701$	3.66441	+	11.2779i	0.138403	+	0.425960i	−0.857701	+	0.514149i	$0.828108\pi$
$702$	−15.2194	+	4.94510i	−0.574421	+	0.186641i
$703$	0.402504	+	2.54131i	0.0151807	+	0.0958474i
$704$	−4.88286	+	30.8291i	−0.184030	+	1.16192i
$705$	3.49513	+	1.13564i	0.131634	+	0.0427706i
$706$		−	63.0941i		−	2.37458i
$707$	−7.89260	+	24.2909i	−0.296832	+	0.913555i
$708$	−9.82425	−	19.2812i	−0.369218	−	0.724631i
$709$	36.6676	+	18.6831i	1.37708	+	0.701658i	0.976684	−	0.214683i	$-0.0688718\pi$
$709$	36.6676	+	18.6831i	1.37708	+	0.701658i	0.400398	+	0.916341i	$0.368872\pi$
$710$	−2.62673	+	0.416033i	−0.0985793	+	0.0156134i
$711$	−39.3881	−	39.3881i	−1.47717	−	1.47717i
$712$	−10.0275	+	19.6800i	−0.375795	+	0.737539i
$713$	−18.9383	+	13.7595i	−0.709246	+	0.515298i
$714$	−61.0999	+	31.1320i	−2.28661	+	1.16508i
$715$	0.334402	+	0.242957i	0.0125059	+	0.00908608i
$716$	−68.6336	−	10.8705i	−2.56496	−	0.406249i
$717$	−15.5498	−	21.4024i	−0.580716	−	0.799287i
$718$	13.8759	+	19.0985i	0.517843	+	0.712750i
$719$	−24.4544	−	3.87320i	−0.911996	−	0.144446i	−0.317233	−	0.948348i	$-0.602754\pi$
$719$	−24.4544	−	3.87320i	−0.911996	−	0.144446i	−0.594762	+	0.803902i	$0.702754\pi$
$720$	1.63497	+	1.18787i	0.0609316	+	0.0442694i
$721$	−15.1142	+	7.70108i	−0.562883	+	0.286803i
$722$	−27.1014	+	19.6903i	−1.00861	+	0.732797i
$723$	36.8227	−	72.2685i	1.36945	−	2.68770i
$724$	4.86946	+	4.86946i	0.180972	+	0.180972i
$725$	−7.26372	+	1.15046i	−0.269768	+	0.0427270i
$726$	−2.82384	−	1.43882i	−0.104802	−	0.0533995i
$727$	−0.177225	−	0.347823i	−0.00657290	−	0.0129000i	0.887697	−	0.460429i	$-0.152304\pi$
$727$	−0.177225	−	0.347823i	−0.00657290	−	0.0129000i	−0.894270	+	0.447529i	$0.852304\pi$
$728$	−4.02577	+	12.3900i	−0.149205	+	0.459205i
$729$		−	41.5244i		−	1.53794i
$730$	2.92396	+	0.950052i	0.108221	+	0.0351630i
$731$	0.568059	−	3.58659i	0.0210104	−	0.132655i
$732$	−17.6582	−	111.489i	−0.652664	−	4.12076i
$733$	−9.37877	+	3.04735i	−0.346413	+	0.112556i	−0.477055	−	0.878873i	$-0.658296\pi$
$733$	−9.37877	+	3.04735i	−0.346413	+	0.112556i	0.130643	+	0.991430i	$0.458296\pi$
$734$	−16.8628	−	51.8984i	−0.622418	−	1.91561i
$735$	0.0678607	−	0.0678607i	0.00250308	−	0.00250308i
$736$	4.56625	−	6.28490i	0.168314	−	0.231664i
$737$	44.9527			1.65585
$738$	59.8742	−	54.0478i	2.20400	−	1.98953i
$739$	13.8121			0.508087			0.254044	−	0.967193i	$-0.418239\pi$
$739$	13.8121			0.508087			0.254044	+	0.967193i	$0.418239\pi$
$740$	−0.299632	+	0.412409i	−0.0110147	+	0.0151604i
$741$	−4.85258	+	4.85258i	−0.178264	+	0.178264i
$742$	1.09757	+	3.37798i	0.0402931	+	0.124010i
$743$	−24.8949	+	8.08883i	−0.913304	+	0.296750i	−0.727717	−	0.685878i	$-0.759419\pi$
$743$	−24.8949	+	8.08883i	−0.913304	+	0.296750i	−0.185587	+	0.982628i	$0.559419\pi$
$744$	6.41262	+	40.4877i	0.235098	+	1.48435i
$745$	0.0196648	−	0.124159i	0.000720464	−	0.00454883i
$746$	−7.42595	−	2.41284i	−0.271883	−	0.0883403i
$747$			3.29701i			0.120631i
$748$	−14.8797	+	45.7950i	−0.544055	+	1.67443i
$749$	−16.8384	−	33.0473i	−0.615263	−	1.20752i
$750$	−7.17554	−	3.65612i	−0.262014	−	0.133503i
$751$	−20.6029	+	3.26318i	−0.751812	+	0.119075i	−0.520568	−	0.853820i	$-0.674280\pi$
$751$	−20.6029	+	3.26318i	−0.751812	+	0.119075i	−0.231244	+	0.972896i	$0.574280\pi$
$752$	26.2277	+	26.2277i	0.956425	+	0.956425i
$753$	−8.58455	+	16.8481i	−0.312839	+	0.613980i
$754$	−3.04590	+	2.21297i	−0.110925	+	0.0805918i
$755$	1.35945	−	0.692672i	0.0494753	−	0.0252089i
$756$	53.2649	+	38.6992i	1.93723	+	1.40748i
$757$	44.0377	+	6.97489i	1.60058	+	0.253507i	0.891970	−	0.452095i	$-0.149323\pi$
$757$	44.0377	+	6.97489i	1.60058	+	0.253507i	0.708609	+	0.705602i	$0.249323\pi$
$758$	27.3380	+	37.6275i	0.992961	+	1.36669i
$759$	42.6889	+	58.7563i	1.54951	+	2.13272i
$760$	1.19932	+	0.189953i	0.0435038	+	0.00689032i
$761$	−35.6363	−	25.8913i	−1.29182	−	0.938559i	−0.291976	−	0.956426i	$-0.594313\pi$
$761$	−35.6363	−	25.8913i	−1.29182	−	0.938559i	−0.999840	+	0.0178662i	$0.994313\pi$
$762$	50.1588	−	25.5572i	1.81706	−	0.925840i
$763$	−32.4266	+	23.5593i	−1.17392	+	0.852903i
$764$	−9.64213	+	18.9237i	−0.348840	+	0.684637i
$765$	−1.55825	−	1.55825i	−0.0563386	−	0.0563386i
$766$	70.1425	−	11.1095i	2.53435	−	0.401402i
$767$	1.82159	+	0.928148i	0.0657739	+	0.0335135i
$768$	−40.0774	−	78.6563i	−1.44617	−	2.83827i
$769$	−5.91420	+	18.2020i	−0.213272	+	0.656383i	0.786000	+	0.618226i	$0.212148\pi$
$769$	−5.91420	+	18.2020i	−0.213272	+	0.656383i	−0.999272	+	0.0381563i	$0.987852\pi$
$770$		−	2.57489i		−	0.0927924i
$771$	11.9662	+	3.88806i	0.430952	+	0.140025i
$772$	−3.99136	+	25.2004i	−0.143652	+	0.906984i
$773$	4.60071	+	29.0477i	0.165476	+	1.04477i	0.920974	+	0.389624i	$0.127395\pi$
$773$	4.60071	+	29.0477i	0.165476	+	1.04477i	−0.755498	+	0.655151i	$0.772605\pi$
$774$	−11.8966	+	3.86545i	−0.427616	+	0.138941i
$775$	−4.81107	−	14.8070i	−0.172819	−	0.531882i
$776$	8.96120	−	8.96120i	0.321688	−	0.321688i
$777$	−5.12569	+	7.05490i	−0.183883	+	0.253093i
$778$	−21.3269			−0.764608
$779$	5.21408	−	13.6345i	0.186814	−	0.488507i
$780$	−1.35963			−0.0486825
$781$	−18.7771	+	25.8445i	−0.671897	+	0.924787i
$782$	47.0528	−	47.0528i	1.68260	−	1.68260i
$783$	2.85693	+	8.79274i	0.102098	+	0.314227i
$784$	0.921208	−	0.299319i	0.0329003	−	0.0106899i
$785$	0.297727	+	1.87978i	0.0106263	+	0.0670921i
$786$	12.3712	−	78.1088i	0.441267	−	2.78605i
$787$	−22.7158	−	7.38080i	−0.809730	−	0.263097i	−0.125246	−	0.992126i	$-0.539972\pi$
$787$	−22.7158	−	7.38080i	−0.809730	−	0.263097i	−0.684483	+	0.729028i	$0.739972\pi$
$788$			16.6134i			0.591828i
$789$	11.0730	−	34.0793i	0.394211	−	1.21326i
$790$	−1.37288	−	2.69443i	−0.0488449	−	0.0958635i
$791$	19.1186	+	9.74142i	0.679780	+	0.346365i
$792$	79.6033	−	12.6079i	2.82858	−	0.448003i
$793$	7.54078	+	7.54078i	0.267781	+	0.267781i
$794$	−27.7161	+	54.3959i	−0.983607	+	1.93044i
$795$	−0.145715	+	0.105868i	−0.00516798	+	0.00375476i
$796$	−55.4410	+	28.2486i	−1.96505	+	1.00124i
$797$	26.5246	+	19.2712i	0.939548	+	0.682622i	0.948312	−	0.317340i	$-0.102790\pi$
$797$	26.5246	+	19.2712i	0.939548	+	0.682622i	−0.00876372	+	0.999962i	$0.502790\pi$
$798$	42.2235	+	6.68755i	1.49470	+	0.236737i
$799$	−23.7736	−	32.7215i	−0.841049	−	1.15760i
$800$	3.03693	+	4.17998i	0.107372	+	0.147784i
$801$	−24.6818	−	3.90921i	−0.872088	−	0.138125i
$802$	55.2074	+	40.1105i	1.94944	+	1.41635i
$803$	32.9049	−	16.7659i	1.16119	−	0.591656i
$804$	−119.625	+	86.9127i	−4.21885	+	3.06518i
$805$	−1.06693	+	2.09398i	−0.0376045	+	0.0738030i
$806$	−5.63590	−	5.63590i	−0.198516	−	0.198516i
$807$	10.0041	−	1.58449i	0.352161	−	0.0557768i
$808$	−38.6704	−	19.7035i	−1.36042	−	0.693168i
$809$	−9.00467	−	17.6727i	−0.316587	−	0.621338i	0.676798	−	0.736169i	$-0.263367\pi$
$809$	−9.00467	−	17.6727i	−0.316587	−	0.621338i	−0.993385	+	0.114831i	$0.963367\pi$
$810$	−0.206284	+	0.634877i	−0.00724809	+	0.0223073i
$811$			12.6254i			0.443338i	0.975122	+	0.221669i	$0.0711505\pi$
$811$			12.6254i			0.443338i	−0.975122	+	0.221669i	$0.928850\pi$
$812$	14.7318	+	4.78664i	0.516984	+	0.167978i
$813$	−1.71346	+	10.8184i	−0.0600936	+	0.379416i
$814$	1.45035	+	9.15716i	0.0508348	+	0.320958i
$815$	1.61573	−	0.524983i	0.0565966	−	0.0183894i
$816$	−10.8457	−	33.3795i	−0.379674	−	1.16852i
$817$	−1.60074	+	1.60074i	−0.0560028	+	0.0560028i
$818$	2.04674	−	2.81710i	0.0715627	−	0.0984976i
$819$	−14.7394			−0.515035
$820$	2.64056	−	1.17965i	0.0922124	−	0.0411950i
$821$	−3.71560			−0.129675			−0.0648376	−	0.997896i	$-0.520653\pi$
$821$	−3.71560			−0.129675			−0.0648376	+	0.997896i	$0.520653\pi$
$822$	−24.6401	+	33.9142i	−0.859422	+	1.18289i
$823$	30.0144	−	30.0144i	1.04624	−	1.04624i	0.0473578	−	0.998878i	$-0.484920\pi$
$823$	30.0144	−	30.0144i	1.04624	−	1.04624i	0.998878	−	0.0473578i	$-0.0150801\pi$
$824$	−8.90731	−	27.4139i	−0.310301	−	0.955007i
$825$	−45.9387	+	14.9264i	−1.59938	+	0.519670i
$826$	−1.99228	−	12.5788i	−0.0693202	−	0.437671i
$827$	2.13027	−	13.4500i	0.0740766	−	0.467702i	−0.922567	−	0.385837i	$-0.873913\pi$
$827$	2.13027	−	13.4500i	0.0740766	−	0.467702i	0.996643	−	0.0818642i	$-0.0260874\pi$
$828$	−143.982	−	46.7825i	−5.00372	−	1.62581i
$829$			38.0361i			1.32105i	0.750805	+	0.660524i	$0.229666\pi$
$829$			38.0361i			1.32105i	−0.750805	+	0.660524i	$0.770334\pi$
$830$	−0.0553106	+	0.170228i	−0.00191986	+	0.00590872i
$831$	38.9866	+	76.5155i	1.35243	+	2.65429i
$832$	8.64270	+	4.40367i	0.299632	+	0.152670i
$833$	−1.04321	+	0.165228i	−0.0361451	+	0.00572483i
$834$	86.6902	+	86.6902i	3.00184	+	3.00184i
$835$	−0.612404	+	1.20191i	−0.0211931	+	0.0415938i
$836$	24.2853	−	17.6443i	0.839926	−	0.610242i
$837$	−17.4389	+	8.88557i	−0.602777	+	0.307130i
$838$	−30.5820	−	22.2191i	−1.05644	−	0.767547i
$839$	−7.44308	−	1.17887i	−0.256964	−	0.0406991i	0.0266234	−	0.999646i	$-0.491525\pi$
$839$	−7.44308	−	1.17887i	−0.256964	−	0.0406991i	−0.283587	+	0.958946i	$0.591525\pi$
$840$	2.41896	+	3.32941i	0.0834620	+	0.114876i
$841$	−15.7673	−	21.7018i	−0.543699	−	0.748337i
$842$	−17.7982	−	2.81896i	−0.613368	−	0.0971479i
$843$	−12.7352	−	9.25263i	−0.438622	−	0.318678i
$844$	86.5904	−	44.1200i	2.98057	−	1.51867i
$845$	−1.11715	+	0.811658i	−0.0384312	+	0.0279219i
$846$	−63.2528	+	124.141i	−2.17468	+	4.26804i
$847$	−0.871070	−	0.871070i	−0.0299303	−	0.0299303i
$848$	−1.79550	+	0.284379i	−0.0616576	+	0.00976561i
$849$	−77.3614	−	39.4176i	−2.65504	−	1.35281i
$850$	20.0920	+	39.4327i	0.689149	+	1.35253i
$851$	2.61491	−	8.04786i	0.0896379	−	0.275877i
$852$		−	105.080i		−	3.59997i
$853$	−44.7084	−	14.5266i	−1.53079	−	0.497383i	−0.581971	−	0.813210i	$-0.697718\pi$
$853$	−44.7084	−	14.5266i	−1.53079	−	0.497383i	−0.948817	+	0.315827i	$0.897718\pi$
$854$	10.3923	−	65.6142i	0.355616	−	2.24527i
$855$	0.214911	+	1.35690i	0.00734981	+	0.0464049i
$856$	59.9405	−	19.4759i	2.04873	−	0.665671i
$857$	6.41959	+	19.7575i	0.219289	+	0.674903i	0.998821	+	0.0485403i	$0.0154569\pi$
$857$	6.41959	+	19.7575i	0.219289	+	0.674903i	−0.779532	+	0.626362i	$0.784543\pi$
$858$	−17.4854	+	17.4854i	−0.596942	+	0.596942i
$859$	−7.73097	+	10.6408i	−0.263777	+	0.363058i	−0.920277	−	0.391268i	$-0.872036\pi$
$859$	−7.73097	+	10.6408i	−0.263777	+	0.363058i	0.656499	+	0.754327i	$0.272036\pi$
$860$	−0.448506			−0.0152939
$861$	45.1710	−	20.1797i	1.53942	−	0.687722i
$862$	83.0485			2.82864
$863$	−10.8301	+	14.9063i	−0.368661	+	0.507418i	−0.952536	−	0.304425i	$-0.901536\pi$
$863$	−10.8301	+	14.9063i	−0.368661	+	0.507418i	0.583876	+	0.811843i	$0.301536\pi$
$864$	4.59282	−	4.59282i	0.156251	−	0.156251i
$865$	−0.0724265	−	0.222906i	−0.00246257	−	0.00757902i
$866$	−19.3574	+	6.28961i	−0.657792	+	0.213729i
$867$	−1.62389	−	10.2528i	−0.0551502	−	0.348204i
$868$	−5.12982	+	32.3884i	−0.174117	+	1.09933i
$869$	−34.5468	−	11.2249i	−1.17192	−	0.380779i
$870$			1.18933i			0.0403219i
$871$	4.31683	−	13.2858i	0.146270	−	0.450174i
$872$	−30.9207	−	60.6853i	−1.04711	−	2.05506i
$873$	12.7754	+	6.50940i	0.432382	+	0.220310i
$874$	−40.9728	+	6.48945i	−1.38592	+	0.219509i
$875$	−2.21344	−	2.21344i	−0.0748280	−	0.0748280i
$876$	−55.1488	+	108.236i	−1.86330	+	3.65694i
$877$	−15.2047	+	11.0469i	−0.513426	+	0.373026i	−0.814122	−	0.580694i	$-0.802781\pi$
$877$	−15.2047	+	11.0469i	−0.513426	+	0.373026i	0.300696	+	0.953720i	$0.402781\pi$
$878$	52.9179	−	26.9630i	1.78589	−	0.909958i
$879$	46.5273	+	33.8041i	1.56933	+	1.14018i
$880$	1.30164	+	0.206160i	0.0438784	+	0.00694965i
$881$	6.74048	+	9.27748i	0.227093	+	0.312566i	0.907325	−	0.420431i	$-0.138121\pi$
$881$	6.74048	+	9.27748i	0.227093	+	0.312566i	−0.680232	+	0.732997i	$0.738121\pi$
$882$	2.13859	+	2.94352i	0.0720101	+	0.0991135i
$883$	36.1792	+	5.73023i	1.21753	+	0.192837i	0.731951	−	0.681357i	$-0.238610\pi$
$883$	36.1792	+	5.73023i	1.21753	+	0.192837i	0.485576	+	0.874194i	$0.338610\pi$
$884$	12.1059	+	8.79543i	0.407165	+	0.295822i
$885$	0.575433	−	0.293198i	0.0193430	−	0.00985574i
$886$	−27.1393	+	19.7178i	−0.911761	+	0.662433i
$887$	20.8224	−	40.8663i	0.699149	−	1.37216i	−0.218922	−	0.975742i	$-0.570254\pi$
$887$	20.8224	−	40.8663i	0.699149	−	1.37216i	0.918071	−	0.396415i	$-0.129746\pi$
$888$	−10.4780	−	10.4780i	−0.351618	−	0.351618i
$889$	21.6120	−	3.42301i	0.724844	−	0.114804i
$890$	−1.20877	−	0.615899i	−0.0405181	−	0.0206450i
$891$	3.64037	+	7.14462i	0.121957	+	0.239354i
$892$	−3.98995	+	12.2798i	−0.133594	+	0.411159i
$893$			25.2145i			0.843772i
$894$	7.15228	+	2.32392i	0.239208	+	0.0777234i
$895$	0.324422	−	2.04832i	0.0108442	−	0.0684678i
$896$	−8.57732	−	54.1551i	−0.286548	−	1.80919i
$897$	21.4650	−	6.97439i	0.716694	−	0.232868i
$898$	−0.800483	−	2.46363i	−0.0267125	−	0.0822125i
$899$	−3.25603	+	3.25603i	−0.108595	+	0.108595i
$900$	59.1828	−	81.4582i	1.97276	−	2.71527i
$901$	1.98228			0.0660394
$902$	18.7880	−	49.1295i	0.625572	−	1.63583i
$903$	−7.67240			−0.255322
$904$	−21.4316	+	29.4980i	−0.712803	+	0.981089i
$905$	−0.145326	+	0.145326i	−0.00483078	+	0.00483078i
$906$	28.2061	+	86.8095i	0.937086	+	2.88405i
$907$	−4.33501	+	1.40853i	−0.143942	+	0.0467695i	−0.380102	−	0.924945i	$-0.624111\pi$
$907$	−4.33501	+	1.40853i	−0.143942	+	0.0467695i	0.236160	+	0.971714i	$0.424111\pi$
$908$	4.69061	+	29.6153i	0.155663	+	0.982820i
$909$	7.68144	−	48.4987i	0.254777	−	1.60860i
$910$	−0.761012	−	0.247268i	−0.0252273	−	0.00819684i
$911$			0.497074i			0.0164688i	0.999966	+	0.00823439i	$0.00262112\pi$
$911$			0.497074i			0.0164688i	−0.999966	+	0.00823439i	$0.997379\pi$
$912$	−6.76131	+	20.8092i	−0.223889	+	0.689061i
$913$	0.976085	+	1.91567i	0.0323037	+	0.0633996i
$914$	−65.1789	−	33.2103i	−2.15593	−	1.09850i
$915$	3.32732	−	0.526995i	0.109998	−	0.0174219i
$916$	−13.6815	−	13.6815i	−0.452049	−	0.452049i
$917$	13.9552	−	27.3886i	0.460841	−	0.904452i
$918$	45.0103	−	32.7019i	1.48556	−	1.07932i
$919$	−19.8412	+	10.1096i	−0.654502	+	0.333485i	−0.749512	−	0.661991i	$-0.769712\pi$
$919$	−19.8412	+	10.1096i	−0.654502	+	0.333485i	0.0950101	+	0.995476i	$0.469712\pi$
$920$	−3.23078	−	2.34730i	−0.106516	−	0.0773882i
$921$	−0.638514	−	0.101131i	−0.0210397	−	0.00333237i
$922$	−4.44739	−	6.12131i	−0.146467	−	0.201595i
$923$	5.83520	+	8.03146i	0.192068	+	0.264359i
$924$	100.485	+	15.9153i	3.30572	+	0.523574i
$925$	4.55310	+	3.30802i	0.149705	+	0.108767i
$926$	−15.3018	+	7.79664i	−0.502847	+	0.256214i
$927$	26.3836	−	19.1688i	0.866552	−	0.629587i
$928$	0.693756	−	1.36157i	0.0227737	−	0.0446958i
$929$	−6.13292	−	6.13292i	−0.201215	−	0.201215i	0.599306	−	0.800520i	$-0.295443\pi$
$929$	−6.13292	−	6.13292i	−0.201215	−	0.201215i	−0.800520	+	0.599306i	$0.795443\pi$
$930$	−2.48680	+	0.393871i	−0.0815455	+	0.0129155i
$931$	0.586689	+	0.298933i	0.0192280	+	0.00979713i
$932$	18.9067	+	37.1065i	0.619310	+	1.21546i
$933$	−12.8505	+	39.5499i	−0.420707	+	1.29480i
$934$		−	95.9186i		−	3.13855i
$935$	−1.36672	−	0.444074i	−0.0446965	−	0.0145228i
$936$	3.91806	−	24.7376i	0.128066	−	0.808575i
$937$	−4.33799	−	27.3890i	−0.141716	−	0.894759i	−0.951415	−	0.307913i	$-0.900370\pi$
$937$	−4.33799	−	27.3890i	−0.141716	−	0.894759i	0.809699	−	0.586846i	$-0.199630\pi$
$938$	−82.7630	+	26.8913i	−2.70231	+	0.878033i
$939$	7.23819	+	22.2768i	0.236209	+	0.726977i
$940$	−3.53239	+	3.53239i	−0.115214	+	0.115214i
$941$	15.4910	−	21.3216i	0.504993	−	0.695063i	−0.478072	−	0.878321i	$-0.658664\pi$
$941$	15.4910	−	21.3216i	0.504993	−	0.695063i	0.983065	+	0.183257i	$0.0586642\pi$
$942$	−113.859			−3.70972
$943$	−35.6364	+	32.1686i	−1.16048	+	1.04755i
$944$	6.51826			0.212151
$945$	−1.15495	+	1.58965i	−0.0375706	+	0.0517115i
$946$	−5.76799	+	5.76799i	−0.187533	+	0.187533i
$947$	−17.4125	−	53.5901i	−0.565830	−	1.74144i	−0.665474	−	0.746421i	$-0.731770\pi$
$947$	−17.4125	−	53.5901i	−0.565830	−	1.74144i	0.0996438	−	0.995023i	$-0.468230\pi$
$948$	113.636	−	36.9226i	3.69073	−	1.19919i
$949$	−1.79531	−	11.3351i	−0.0582782	−	0.367954i
$950$	4.31602	−	27.2503i	0.140030	−	0.884115i
$951$	−26.1391	−	8.49312i	−0.847619	−	0.275408i
$952$		−	45.2927i		−	1.46795i
$953$	−9.02900	+	27.7884i	−0.292478	+	0.900154i	0.691579	+	0.722301i	$0.256915\pi$
$953$	−9.02900	+	27.7884i	−0.292478	+	0.900154i	−0.984057	+	0.177854i	$0.943085\pi$
$954$	−3.10006	−	6.08420i	−0.100368	−	0.196983i
$955$	−0.564766	−	0.287763i	−0.0182754	−	0.00931178i
$956$	35.5182	−	5.62552i	1.14874	−	0.181942i
$957$	10.1019	+	10.1019i	0.326547	+	0.326547i
$958$	12.8848	−	25.2879i	0.416291	−	0.817016i
$959$	−13.1823	+	9.57748i	−0.425678	+	0.309273i
$960$	2.73019	−	1.39110i	0.0881165	−	0.0448976i
$961$	17.1931	+	12.4915i	0.554615	+	0.402952i
$962$	2.84569	+	0.450713i	0.0917488	+	0.0145316i
$963$	41.9127	+	57.6879i	1.35062	+	1.85897i
$964$	64.8057	+	89.1973i	2.08725	+	2.87285i
$965$	−0.752090	−	0.119119i	−0.0242106	−	0.00383459i
$966$	−113.744	−	82.6398i	−3.65965	−	2.65889i
$967$	−17.8304	+	9.08505i	−0.573388	+	0.292156i	−0.716541	−	0.697545i	$-0.754276\pi$
$967$	−17.8304	+	9.08505i	−0.573388	+	0.292156i	0.143153	+	0.989701i	$0.454276\pi$
$968$	1.69350	−	1.23040i	0.0544311	−	0.0395465i
$969$	10.8317	−	21.2584i	0.347964	−	0.682918i
$970$	0.550408	+	0.550408i	0.0176725	+	0.0176725i
$971$	−3.43652	+	0.544291i	−0.110283	+	0.0174671i	−0.211332	−	0.977414i	$-0.567780\pi$
$971$	−3.43652	+	0.544291i	−0.110283	+	0.0174671i	0.101049	+	0.994881i	$0.467780\pi$
$972$	41.6853	+	21.2397i	1.33706	+	0.681264i
$973$	21.6342	+	42.4595i	0.693561	+	1.36119i
$974$	−18.9151	+	58.2146i	−0.606078	+	1.86532i
$975$			15.0106i			0.480725i
$976$	32.3369	+	10.5069i	1.03508	+	0.336318i
$977$	−0.933392	+	5.89321i	−0.0298619	+	0.188540i	−0.998110	−	0.0614501i	$-0.980428\pi$
$977$	−0.933392	+	5.89321i	−0.0298619	+	0.188540i	0.968248	+	0.249991i	$0.0804275\pi$
$978$	15.8992	+	100.384i	0.508400	+	3.20991i
$979$	−15.4983	+	5.03570i	−0.495328	+	0.160942i
$980$	0.0403127	+	0.124070i	0.00128774	+	0.00396326i
$981$	54.4879	−	54.4879i	1.73967	−	1.73967i
$982$	−44.9484	+	61.8661i	−1.43436	+	1.97423i
$983$	42.8287			1.36602			0.683011	−	0.730408i	$-0.260670\pi$
$983$	42.8287			1.36602			0.683011	+	0.730408i	$0.260670\pi$
$984$	21.8609	+	81.1763i	0.696899	+	2.58781i
$985$	−0.495816			−0.0157980
$986$	7.69376	−	10.5895i	0.245019	−	0.337240i
$987$	−60.4270	+	60.4270i	−1.92341	+	1.92341i
$988$	−2.88268	−	8.87196i	−0.0917101	−	0.282255i
$989$	7.08074	−	2.30067i	0.225154	−	0.0731571i
$990$	0.774395	+	4.88934i	0.0246119	+	0.155393i
$991$	4.88595	−	30.8487i	0.155207	−	0.979940i	−0.779985	−	0.625799i	$-0.784773\pi$
$991$	4.88595	−	30.8487i	0.155207	−	0.979940i	0.935192	−	0.354141i	$-0.115227\pi$
$992$	3.07671	+	0.999685i	0.0976857	+	0.0317400i
$993$			13.1463i			0.417184i
$994$	19.1102	−	58.8153i	0.606140	−	1.86551i
$995$	−0.843059	−	1.65460i	−0.0267268	−	0.0524542i
$996$	−6.30131	−	3.21068i	−0.199665	−	0.101734i
$997$	43.0807	−	6.82332i	1.36438	−	0.216097i	0.569065	−	0.822293i	$-0.307305\pi$
$997$	43.0807	−	6.82332i	1.36438	−	0.216097i	0.795315	+	0.606196i	$0.207305\pi$
$998$	−8.48534	−	8.48534i	−0.268599	−	0.268599i
$999$	3.21200	−	6.30390i	0.101623	−	0.199446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.33.3	yes	24
3.2	odd	2		369.2.u.a.361.1		24
4.3	odd	2		656.2.bs.d.33.3		24
41.5	even	20	inner	41.2.g.a.5.3	✓	24
41.13	odd	40		1681.2.a.m.1.22		24
41.28	odd	40		1681.2.a.m.1.21		24
123.5	odd	20		369.2.u.a.46.1		24
164.87	odd	20		656.2.bs.d.497.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.3	✓	24	41.5	even	20	inner
41.2.g.a.33.3	yes	24	1.1	even	1	trivial
369.2.u.a.46.1		24	123.5	odd	20
369.2.u.a.361.1		24	3.2	odd	2
656.2.bs.d.33.3		24	4.3	odd	2
656.2.bs.d.497.3		24	164.87	odd	20
1681.2.a.m.1.21		24	41.28	odd	40
1681.2.a.m.1.22		24	41.13	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42655 - 1.96347i) q^{2} +(-2.02366 + 2.02366i) q^{3} +(-1.20216 - 3.69986i) q^{4} +(0.110420 - 0.0358775i) q^{5} +(1.08656 + 6.86025i) q^{6} +(-0.422339 + 2.66654i) q^{7} +(-4.36309 - 1.41766i) q^{8} -5.19040i q^{9} +O(q^{10})\)	\(q+(1.42655 - 1.96347i) q^{2} +(-2.02366 + 2.02366i) q^{3} +(-1.20216 - 3.69986i) q^{4} +(0.110420 - 0.0358775i) q^{5} +(1.08656 + 6.86025i) q^{6} +(-0.422339 + 2.66654i) q^{7} +(-4.36309 - 1.41766i) q^{8} -5.19040i q^{9} +(0.0870742 - 0.267987i) q^{10} +(-1.53663 - 3.01580i) q^{11} +(9.92000 + 5.05449i) q^{12} +(-1.03889 + 0.164544i) q^{13} +(4.63320 + 4.63320i) q^{14} +(-0.150848 + 0.296056i) q^{15} +(-2.71311 + 1.97119i) q^{16} +(3.25831 - 1.66019i) q^{17} +(-10.1912 - 7.40435i) q^{18} +(-2.25168 - 0.356630i) q^{19} +(-0.265483 - 0.365406i) q^{20} +(-4.54151 - 6.25085i) q^{21} +(-8.11352 - 1.28505i) q^{22} +(6.06568 + 4.40698i) q^{23} +(11.6983 - 5.96057i) q^{24} +(-4.03418 + 2.93100i) q^{25} +(-1.15895 + 2.27456i) q^{26} +(4.43263 + 4.43263i) q^{27} +(10.3735 - 1.64301i) q^{28} +(1.31408 + 0.669558i) q^{29} +(0.366106 + 0.718523i) q^{30} +(-0.964816 + 2.96940i) q^{31} -1.03614i q^{32} +(9.21257 + 2.99335i) q^{33} +(1.38839 - 8.76594i) q^{34} +(0.0490344 + 0.309591i) q^{35} +(-19.2037 + 6.23967i) q^{36} +(-0.348766 - 1.07339i) q^{37} +(-3.91235 + 3.91235i) q^{38} +(1.76938 - 2.43534i) q^{39} -0.532633 q^{40} +(-1.32339 + 6.26487i) q^{41} -18.7520 q^{42} +(0.583672 - 0.803355i) q^{43} +(-9.31076 + 9.31076i) q^{44} +(-0.186219 - 0.573122i) q^{45} +(17.3060 - 5.62305i) q^{46} +(-1.73020 - 10.9241i) q^{47} +(1.50140 - 9.47944i) q^{48} +(-0.274693 - 0.0892531i) q^{49} +12.1022i q^{50} +(-3.23405 + 9.95337i) q^{51} +(1.85769 + 3.64593i) q^{52} +(0.482987 + 0.246094i) q^{53} +(15.0267 - 2.37999i) q^{54} +(-0.277873 - 0.277873i) q^{55} +(5.62295 - 11.0357i) q^{56} +(5.27833 - 3.83493i) q^{57} +(3.18926 - 1.62501i) q^{58} +(-1.57246 - 1.14246i) q^{59} +(1.27671 + 0.202210i) q^{60} +(-5.95937 - 8.20238i) q^{61} +(4.45398 + 6.13037i) q^{62} +(13.8404 + 2.19211i) q^{63} +(-7.46066 - 5.42048i) q^{64} +(-0.108810 + 0.0554416i) q^{65} +(19.0195 - 13.8185i) q^{66} +(-6.02949 + 11.8335i) q^{67} +(-10.0595 - 10.0595i) q^{68} +(-21.1931 + 3.35666i) q^{69} +(0.677824 + 0.345368i) q^{70} +(-4.28484 - 8.40947i) q^{71} +(-7.35820 + 22.6462i) q^{72} +10.9108i q^{73} +(-2.60511 - 0.846450i) q^{74} +(2.23245 - 14.0952i) q^{75} +(1.38738 + 8.75960i) q^{76} +(8.69075 - 2.82380i) q^{77} +(-2.25762 - 6.94824i) q^{78} +(7.58864 - 7.58864i) q^{79} +(-0.228859 + 0.314998i) q^{80} -2.36906 q^{81} +(10.4130 + 11.5356i) q^{82} -0.635212 q^{83} +(-17.6676 + 24.3174i) q^{84} +(0.300218 - 0.300218i) q^{85} +(-0.744731 - 2.29205i) q^{86} +(-4.01421 + 1.30430i) q^{87} +(2.42908 + 15.3366i) q^{88} +(0.753161 - 4.75527i) q^{89} +(-1.39096 - 0.451950i) q^{90} -2.83974i q^{91} +(9.01328 - 27.7400i) q^{92} +(-4.05659 - 7.96151i) q^{93} +(-23.9173 - 12.1865i) q^{94} +(-0.261424 + 0.0414055i) q^{95} +(2.09680 + 2.09680i) q^{96} +(-1.25412 + 2.46135i) q^{97} +(-0.567108 + 0.412028i) q^{98} +(-15.6532 + 7.97572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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