LMFDB - Embedded newform 345.2.m.c.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	345.16
Dual form			345.2.m.c.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71238 + 1.97619i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.688461 - 4.78835i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.372136 + 2.58826i) q^{6} +(-3.22191 + 0.946039i) q^{7} +(6.24206 + 4.01153i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.71238 + 1.97619i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.688461 - 4.78835i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.372136 + 2.58826i) q^{6} +(-3.22191 + 0.946039i) q^{7} +(6.24206 + 4.01153i) q^{8} +(0.415415 - 0.909632i) q^{9} +(2.50896 + 0.736696i) q^{10} +(2.97536 + 3.43375i) q^{11} +(-3.16795 - 3.65601i) q^{12} +(-4.24933 - 1.24772i) q^{13} +(3.64759 - 7.98710i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-9.33308 + 2.74044i) q^{16} +(-0.923869 + 6.42565i) q^{17} +(1.08626 + 2.37858i) q^{18} +(1.07871 + 7.50260i) q^{19} +(-4.06964 + 2.61540i) q^{20} +(-2.19898 + 2.53776i) q^{21} -11.8807 q^{22} +(-3.08438 + 3.67241i) q^{23} +7.41995 q^{24} +(-0.654861 + 0.755750i) q^{25} +(9.74221 - 6.26094i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(6.74813 + 14.7763i) q^{28} +(0.103326 - 0.718648i) q^{29} +(2.50896 - 0.736696i) q^{30} +(-2.89757 - 1.86215i) q^{31} +(4.40143 - 9.63779i) q^{32} +(4.35946 + 1.28005i) q^{33} +(-11.1163 - 12.8289i) q^{34} +(2.19898 + 2.53776i) q^{35} +(-4.64163 - 1.36291i) q^{36} +(1.61577 - 3.53805i) q^{37} +(-16.6737 - 10.7156i) q^{38} +(-4.24933 + 1.24772i) q^{39} +(1.05597 - 7.34443i) q^{40} +(0.199578 + 0.437015i) q^{41} +(-1.24961 - 8.69121i) q^{42} +(2.82894 - 1.81805i) q^{43} +(14.3936 - 16.6111i) q^{44} -1.00000 q^{45} +(-1.97576 - 12.3839i) q^{46} +10.8226 q^{47} +(-6.36989 + 7.35125i) q^{48} +(3.59696 - 2.31162i) q^{49} +(-0.372136 - 2.58826i) q^{50} +(2.69676 + 5.90508i) q^{51} +(-3.04901 + 21.2063i) q^{52} +(-10.9100 + 3.20346i) q^{53} +(2.19978 + 1.41371i) q^{54} +(1.88744 - 4.13292i) q^{55} +(-23.9064 - 7.01956i) q^{56} +(4.96368 + 5.72839i) q^{57} +(1.24325 + 1.43479i) q^{58} +(-5.83162 - 1.71232i) q^{59} +(-2.00961 + 4.40043i) q^{60} +(-1.15240 - 0.740602i) q^{61} +(8.64172 - 2.53744i) q^{62} +(-0.477884 + 3.32375i) q^{63} +(3.42765 + 7.50550i) q^{64} +(0.630274 + 4.38365i) q^{65} +(-9.99470 + 6.42320i) q^{66} +(5.68458 - 6.56035i) q^{67} +31.4043 q^{68} +(-0.609290 + 4.75697i) q^{69} -8.78059 q^{70} +(-3.41996 + 3.94685i) q^{71} +(6.24206 - 4.01153i) q^{72} +(0.691195 + 4.80736i) q^{73} +(4.22505 + 9.25157i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(35.1824 - 10.3305i) q^{76} +(-12.8348 - 8.24844i) q^{77} +(4.81075 - 10.5341i) q^{78} +(-4.55729 - 1.33814i) q^{79} +(6.36989 + 7.35125i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.20538 - 0.353932i) q^{82} +(0.0538928 - 0.118009i) q^{83} +(13.6656 + 8.78233i) q^{84} +(6.22876 - 1.82893i) q^{85} +(-1.25141 + 8.70372i) q^{86} +(-0.301607 - 0.660428i) q^{87} +(4.79780 + 33.3695i) q^{88} +(-1.88276 + 1.20997i) q^{89} +(1.71238 - 1.97619i) q^{90} +14.8714 q^{91} +(19.7083 + 12.2408i) q^{92} -3.44435 q^{93} +(-18.5325 + 21.3876i) q^{94} +(6.37649 - 4.09792i) q^{95} +(-1.50786 - 10.4874i) q^{96} +(2.93361 + 6.42370i) q^{97} +(-1.59115 + 11.0667i) q^{98} +(4.35946 - 1.28005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) $ 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.71238	+	1.97619i	−1.21084	+	1.39738i	−0.317338	+	0.948312i	$0.602789\pi$
$2$	−1.71238	+	1.97619i	−1.21084	+	1.39738i	−0.893498	+	0.449067i	$0.851756\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.688461	−	4.78835i	−0.344230	−	2.39417i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	−0.372136	+	2.58826i	−0.151924	+	1.05665i
$7$	−3.22191	+	0.946039i	−1.21777	+	0.357569i	−0.826621	−	0.562759i	$-0.809740\pi$
$7$	−3.22191	+	0.946039i	−1.21777	+	0.357569i	−0.391147	+	0.920328i	$0.627922\pi$
$8$	6.24206	+	4.01153i	2.20690	+	1.41829i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	2.50896	+	0.736696i	0.793402	+	0.232964i
$11$	2.97536	+	3.43375i	0.897106	+	1.03532i	0.999178	+	0.0405385i	$0.0129074\pi$
$11$	2.97536	+	3.43375i	0.897106	+	1.03532i	−0.102072	+	0.994777i	$0.532547\pi$
$12$	−3.16795	−	3.65601i	−0.914508	−	1.05540i
$13$	−4.24933	−	1.24772i	−1.17855	−	0.346055i	−0.366937	−	0.930246i	$-0.619594\pi$
$13$	−4.24933	−	1.24772i	−1.17855	−	0.346055i	−0.811616	+	0.584191i	$0.801412\pi$
$14$	3.64759	−	7.98710i	0.974859	−	2.13464i
$15$	−0.841254	−	0.540641i	−0.217211	−	0.139593i
$16$	−9.33308	+	2.74044i	−2.33327	+	0.685110i
$17$	−0.923869	+	6.42565i	−0.224071	+	1.55845i	0.498338	+	0.866983i	$0.333944\pi$
$17$	−0.923869	+	6.42565i	−0.224071	+	1.55845i	−0.722409	+	0.691466i	$0.756965\pi$
$18$	1.08626	+	2.37858i	0.256034	+	0.560636i
$19$	1.07871	+	7.50260i	0.247473	+	1.72121i	0.612717	+	0.790302i	$0.290076\pi$
$19$	1.07871	+	7.50260i	0.247473	+	1.72121i	−0.365244	+	0.930912i	$0.619015\pi$
$20$	−4.06964	+	2.61540i	−0.909999	+	0.584821i
$21$	−2.19898	+	2.53776i	−0.479856	+	0.553784i
$22$	−11.8807			−2.53298
$23$	−3.08438	+	3.67241i	−0.643138	+	0.765751i
$23$	−3.08438	+	3.67241i	−0.643138	+	0.765751i
$24$	7.41995			1.51459
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	9.74221	−	6.26094i	1.91061	−	1.22787i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	6.74813	+	14.7763i	1.27528	+	2.79246i
$29$	0.103326	−	0.718648i	0.0191872	−	0.133450i	−0.977976	−	0.208716i	$-0.933072\pi$
$29$	0.103326	−	0.718648i	0.0191872	−	0.133450i	0.997163	+	0.0752663i	$0.0239807\pi$
$30$	2.50896	−	0.736696i	0.458071	−	0.134502i
$31$	−2.89757	−	1.86215i	−0.520419	−	0.334453i	0.253919	−	0.967226i	$-0.418280\pi$
$31$	−2.89757	−	1.86215i	−0.520419	−	0.334453i	−0.774338	+	0.632773i	$0.781917\pi$
$32$	4.40143	−	9.63779i	0.778071	−	1.70374i
$33$	4.35946	+	1.28005i	0.758885	+	0.222829i
$34$	−11.1163	−	12.8289i	−1.90643	−	2.20014i
$35$	2.19898	+	2.53776i	0.371695	+	0.428959i
$36$	−4.64163	−	1.36291i	−0.773606	−	0.227151i
$37$	1.61577	−	3.53805i	0.265631	−	0.581652i	−0.729072	−	0.684437i	$-0.760048\pi$
$37$	1.61577	−	3.53805i	0.265631	−	0.581652i	0.994704	+	0.102785i	$0.0327754\pi$
$38$	−16.6737	−	10.7156i	−2.70484	−	1.73829i
$39$	−4.24933	+	1.24772i	−0.680438	+	0.199795i
$40$	1.05597	−	7.34443i	0.166963	−	1.16126i
$41$	0.199578	+	0.437015i	0.0311689	+	0.0682503i	0.924576	−	0.380997i	$-0.124419\pi$
$41$	0.199578	+	0.437015i	0.0311689	+	0.0682503i	−0.893407	+	0.449248i	$0.851692\pi$
$42$	−1.24961	−	8.69121i	−0.192819	−	1.34108i
$43$	2.82894	−	1.81805i	0.431409	−	0.277250i	−0.306862	−	0.951754i	$-0.599279\pi$
$43$	2.82894	−	1.81805i	0.431409	−	0.277250i	0.738271	+	0.674504i	$0.235643\pi$
$44$	14.3936	−	16.6111i	2.16992	−	2.50422i
$45$	−1.00000			−0.149071
$46$	−1.97576	−	12.3839i	−0.291310	−	1.82591i
$47$	10.8226			1.57864			0.789321	−	0.613981i	$-0.210433\pi$
$47$	10.8226			1.57864			0.789321	+	0.613981i	$0.210433\pi$
$48$	−6.36989	+	7.35125i	−0.919415	+	1.06106i
$49$	3.59696	−	2.31162i	0.513851	−	0.330232i
$50$	−0.372136	−	2.58826i	−0.0526280	−	0.366036i
$51$	2.69676	+	5.90508i	0.377622	+	0.826877i
$52$	−3.04901	+	21.2063i	−0.422821	+	2.94079i
$53$	−10.9100	+	3.20346i	−1.49860	+	0.440029i	−0.925274	−	0.379298i	$-0.876165\pi$
$53$	−10.9100	+	3.20346i	−1.49860	+	0.440029i	−0.573326	+	0.819327i	$0.694347\pi$
$54$	2.19978	+	1.41371i	0.299352	+	0.192382i
$55$	1.88744	−	4.13292i	0.254502	−	0.557283i
$56$	−23.9064	−	7.01956i	−3.19463	−	0.938029i
$57$	4.96368	+	5.72839i	0.657455	+	0.758744i
$58$	1.24325	+	1.43479i	0.163247	+	0.188397i
$59$	−5.83162	−	1.71232i	−0.759213	−	0.222925i	−0.120861	−	0.992669i	$-0.538565\pi$
$59$	−5.83162	−	1.71232i	−0.759213	−	0.222925i	−0.638352	+	0.769744i	$0.720384\pi$
$60$	−2.00961	+	4.40043i	−0.259439	+	0.568093i
$61$	−1.15240	−	0.740602i	−0.147550	−	0.0948244i	0.464783	−	0.885425i	$-0.346132\pi$
$61$	−1.15240	−	0.740602i	−0.147550	−	0.0948244i	−0.612333	+	0.790600i	$0.709769\pi$
$62$	8.64172	−	2.53744i	1.09750	−	0.322255i
$63$	−0.477884	+	3.32375i	−0.0602077	+	0.418754i
$64$	3.42765	+	7.50550i	0.428456	+	0.938188i
$65$	0.630274	+	4.38365i	0.0781759	+	0.543725i
$66$	−9.99470	+	6.42320i	−1.23026	+	0.790641i
$67$	5.68458	−	6.56035i	0.694482	−	0.801474i	−0.293514	−	0.955955i	$-0.594825\pi$
$67$	5.68458	−	6.56035i	0.694482	−	0.801474i	0.987996	+	0.154480i	$0.0493703\pi$
$68$	31.4043			3.80833
$69$	−0.609290	+	4.75697i	−0.0733499	+	0.572672i
$70$	−8.78059			−1.04948
$71$	−3.41996	+	3.94685i	−0.405875	+	0.468405i	−0.921482	−	0.388420i	$-0.873021\pi$
$71$	−3.41996	+	3.94685i	−0.405875	+	0.468405i	0.515607	+	0.856825i	$0.327566\pi$
$72$	6.24206	−	4.01153i	0.735634	−	0.472763i
$73$	0.691195	+	4.80736i	0.0808982	+	0.562659i	0.989449	+	0.144884i	$0.0462810\pi$
$73$	0.691195	+	4.80736i	0.0808982	+	0.562659i	−0.908550	+	0.417775i	$0.862810\pi$
$74$	4.22505	+	9.25157i	0.491152	+	1.07547i
$75$	−0.142315	+	0.989821i	−0.0164331	+	0.114295i
$76$	35.1824	−	10.3305i	4.03570	−	1.18499i
$77$	−12.8348	−	8.24844i	−1.46266	−	0.939997i
$78$	4.81075	−	10.5341i	0.544710	−	1.19275i
$79$	−4.55729	−	1.33814i	−0.512735	−	0.150552i	0.0151225	−	0.999886i	$-0.495186\pi$
$79$	−4.55729	−	1.33814i	−0.512735	−	0.150552i	−0.527857	+	0.849333i	$0.677004\pi$
$80$	6.36989	+	7.35125i	0.712176	+	0.821894i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−1.20538	−	0.353932i	−0.133112	−	0.0390852i
$83$	0.0538928	−	0.118009i	0.00591550	−	0.0129531i	−0.906651	−	0.421881i	$-0.861370\pi$
$83$	0.0538928	−	0.118009i	0.00591550	−	0.0129531i	0.912567	+	0.408928i	$0.134097\pi$
$84$	13.6656	+	8.78233i	1.49104	+	0.958231i
$85$	6.22876	−	1.82893i	0.675604	−	0.198375i
$86$	−1.25141	+	8.70372i	−0.134943	+	0.938546i
$87$	−0.301607	−	0.660428i	−0.0323357	−	0.0708053i
$88$	4.79780	+	33.3695i	0.511448	+	3.55720i
$89$	−1.88276	+	1.20997i	−0.199572	+	0.128257i	−0.636610	−	0.771186i	$-0.719664\pi$
$89$	−1.88276	+	1.20997i	−0.199572	+	0.128257i	0.437038	+	0.899443i	$0.356027\pi$
$90$	1.71238	−	1.97619i	0.180501	−	0.208309i
$91$	14.8714			1.55894
$92$	19.7083	+	12.2408i	2.05473	+	1.27619i
$93$	−3.44435			−0.357162
$94$	−18.5325	+	21.3876i	−1.91148	+	2.20596i
$95$	6.37649	−	4.09792i	0.654214	−	0.420438i
$96$	−1.50786	−	10.4874i	−0.153896	−	1.07037i
$97$	2.93361	+	6.42370i	0.297863	+	0.652228i	0.998096	−	0.0616863i	$-0.0196478\pi$
$97$	2.93361	+	6.42370i	0.297863	+	0.652228i	−0.700233	+	0.713914i	$0.746921\pi$
$98$	−1.59115	+	11.0667i	−0.160730	+	1.11790i
$99$	4.35946	−	1.28005i	0.438142	−	0.128650i
$100$	4.06964	+	2.61540i	0.406964	+	0.261540i
$101$	−3.92121	+	8.58626i	−0.390175	+	0.854365i	0.607997	+	0.793939i	$0.291973\pi$
$101$	−3.92121	+	8.58626i	−0.390175	+	0.854365i	−0.998173	+	0.0604259i	$0.980754\pi$
$102$	−16.2875	−	4.78243i	−1.61270	−	0.473531i
$103$	9.65374	+	11.1410i	0.951211	+	1.09776i	0.995115	+	0.0987204i	$0.0314749\pi$
$103$	9.65374	+	11.1410i	0.951211	+	1.09776i	−0.0439041	+	0.999036i	$0.513980\pi$
$104$	−21.5194	−	24.8347i	−2.11015	−	2.43524i
$105$	3.22191	+	0.946039i	0.314426	+	0.0923239i
$106$	12.3514	−	27.0458i	1.19967	−	2.62692i
$107$	−9.15159	−	5.88137i	−0.884717	−	0.568573i	0.0175039	−	0.999847i	$-0.494428\pi$
$107$	−9.15159	−	5.88137i	−0.884717	−	0.568573i	−0.902221	+	0.431274i	$0.858064\pi$
$108$	−4.64163	+	1.36291i	−0.446641	+	0.131146i
$109$	1.00558	−	6.99397i	0.0963172	−	0.669901i	−0.883268	−	0.468869i	$-0.844662\pi$
$109$	1.00558	−	6.99397i	0.0963172	−	0.669901i	0.979585	−	0.201031i	$-0.0644293\pi$
$110$	4.93543	+	10.8071i	0.470575	+	1.03041i
$111$	−0.553539	−	3.84995i	−0.0525396	−	0.365421i
$112$	27.4778	−	17.6589i	2.59641	−	1.66861i
$113$	−3.38846	+	3.91049i	−0.318759	+	0.367868i	−0.892405	−	0.451236i	$-0.850983\pi$
$113$	−3.38846	+	3.91049i	−0.318759	+	0.367868i	0.573646	+	0.819104i	$0.305529\pi$
$114$	−19.8201			−1.85632
$115$	4.62184	+	1.28008i	0.430989	+	0.119368i
$116$	−3.51228			−0.326107
$117$	−2.90020	+	3.34701i	−0.268124	+	0.309431i
$118$	13.3698	−	8.59227i	1.23079	−	0.790983i
$119$	−3.10229	−	21.5769i	−0.284386	−	1.97795i
$120$	−3.08236	−	6.74943i	−0.281380	−	0.616135i
$121$	−1.37241	+	9.54530i	−0.124764	+	0.867754i
$122$	3.43692	−	1.00917i	0.311164	−	0.0913661i
$123$	0.404164	+	0.259740i	0.0364422	+	0.0234200i
$124$	−6.92179	+	15.1566i	−0.621595	+	1.36110i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	−5.75006	−	6.63592i	−0.512256	−	0.591175i
$127$	−5.38458	−	6.21413i	−0.477804	−	0.551415i	0.464762	−	0.885436i	$-0.346140\pi$
$127$	−5.38458	−	6.21413i	−0.477804	−	0.551415i	−0.942566	+	0.334021i	$0.891594\pi$
$128$	−0.369601	−	0.108525i	−0.0326684	−	0.00959232i
$129$	1.39694	−	3.05888i	0.122994	−	0.269319i
$130$	−9.74221	−	6.26094i	−0.854449	−	0.549121i
$131$	15.6290	−	4.58909i	1.36551	−	0.400950i	0.484809	−	0.874620i	$-0.338889\pi$
$131$	15.6290	−	4.58909i	1.36551	−	0.400950i	0.880703	+	0.473670i	$0.157071\pi$
$132$	3.12803	−	21.7559i	0.272260	−	1.89361i
$133$	−10.5733	−	23.1522i	−0.916818	−	2.00755i
$134$	3.23036	+	22.4676i	0.279061	+	1.94091i
$135$	−0.841254	+	0.540641i	−0.0724036	+	0.0465310i
$136$	−31.5435	+	36.4032i	−2.70483	+	3.12155i
$137$	−0.756822			−0.0646596			−0.0323298	−	0.999477i	$-0.510293\pi$
$137$	−0.756822			−0.0646596			−0.0323298	+	0.999477i	$0.510293\pi$
$138$	−8.35736	−	9.34982i	−0.711425	−	0.795910i
$139$	−18.5056			−1.56962			−0.784810	−	0.619736i	$-0.787240\pi$
$139$	−18.5056			−1.56962			−0.784810	+	0.619736i	$0.787240\pi$
$140$	10.6378	−	12.2766i	0.899054	−	1.03756i
$141$	9.10457	−	5.85115i	0.766743	−	0.492756i
$142$	−1.94345	−	13.5170i	−0.163091	−	1.13432i
$143$	−8.35897	−	18.3036i	−0.699012	−	1.53062i
$144$	−1.38431	+	9.62809i	−0.115359	+	0.802341i
$145$	−0.696629	+	0.204549i	−0.0578519	+	0.0169868i
$146$	−10.6839	−	6.86611i	−0.884203	−	0.568243i
$147$	1.77619	−	3.88932i	0.146498	−	0.320786i
$148$	−18.0538	−	5.30108i	−1.48401	−	0.435746i
$149$	12.7972	+	14.7687i	1.04838	+	1.20990i	0.977174	+	0.212439i	$0.0681407\pi$
$149$	12.7972	+	14.7687i	1.04838	+	1.20990i	0.0712104	+	0.997461i	$0.477314\pi$
$150$	−1.71238	−	1.97619i	−0.139815	−	0.161356i
$151$	−3.87449	−	1.13765i	−0.315302	−	0.0925810i	0.120253	−	0.992743i	$-0.461630\pi$
$151$	−3.87449	−	1.13765i	−0.315302	−	0.0925810i	−0.435555	+	0.900162i	$0.643448\pi$
$152$	−23.3635	+	51.1589i	−1.89503	+	4.14954i
$153$	5.46119	+	3.50969i	0.441511	+	0.283742i
$154$	38.2786	−	11.2396i	3.08458	−	0.905715i
$155$	−0.490182	+	3.40929i	−0.0393723	+	0.273841i
$156$	8.90001	+	19.4883i	0.712571	+	1.56031i
$157$	−1.31099	−	9.11812i	−0.104628	−	0.727705i	−0.972835	−	0.231502i	$-0.925636\pi$
$157$	−1.31099	−	9.11812i	−0.104628	−	0.727705i	0.868206	−	0.496203i	$-0.165273\pi$
$158$	10.4482	−	6.71467i	0.831217	−	0.534191i
$159$	−7.44614	+	8.59330i	−0.590517	+	0.681493i
$160$	−10.5953			−0.837629
$161$	6.46336	−	14.7501i	0.509384	−	1.16247i
$162$	2.61488			0.205444
$163$	10.4016	−	12.0041i	0.814717	−	0.940233i	−0.184374	−	0.982856i	$-0.559026\pi$
$163$	10.4016	−	12.0041i	0.814717	−	0.940233i	0.999091	+	0.0426227i	$0.0135713\pi$
$164$	1.95518	−	1.25652i	0.152674	−	0.0981176i
$165$	−0.646608	−	4.49726i	−0.0503384	−	0.350111i
$166$	0.140923	+	0.308579i	0.0109378	+	0.0239503i
$167$	−0.185381	+	1.28935i	−0.0143452	+	0.0997732i	−0.995736	−	0.0922474i	$-0.970595\pi$
$167$	−0.185381	+	1.28935i	−0.0143452	+	0.0997732i	0.981391	+	0.192021i	$0.0615040\pi$
$168$	−23.9064	+	7.01956i	−1.84442	+	0.541571i
$169$	5.56375	+	3.57561i	0.427981	+	0.275047i
$170$	−7.05170	+	15.4411i	−0.540841	+	1.18428i
$171$	7.27271	+	2.13546i	0.556158	+	0.163303i
$172$	−10.6531	−	12.2943i	−0.812288	−	0.937430i
$173$	8.36790	+	9.65708i	0.636200	+	0.734214i	0.978698	−	0.205305i	$-0.0658185\pi$
$173$	8.36790	+	9.65708i	0.636200	+	0.734214i	−0.342498	+	0.939518i	$0.611273\pi$
$174$	1.82160	+	0.534870i	0.138095	+	0.0405484i
$175$	1.39494	−	3.05448i	0.105447	−	0.230897i
$176$	−37.1793	−	23.8937i	−2.80250	−	1.80105i
$177$	−5.83162	+	1.71232i	−0.438332	+	0.128706i
$178$	0.832854	−	5.79263i	0.0624251	−	0.434176i
$179$	0.0461786	+	0.101117i	0.00345155	+	0.00755783i	0.911350	−	0.411633i	$-0.135041\pi$
$179$	0.0461786	+	0.101117i	0.00345155	+	0.00755783i	−0.907898	+	0.419190i	$0.862314\pi$
$180$	0.688461	+	4.78835i	0.0513148	+	0.356903i
$181$	3.80972	−	2.44836i	0.283175	−	0.181985i	−0.391341	−	0.920246i	$-0.627989\pi$
$181$	3.80972	−	2.44836i	0.283175	−	0.181985i	0.674516	+	0.738260i	$0.264352\pi$
$182$	−25.4655	+	29.3887i	−1.88763	+	2.17844i
$183$	−1.36986			−0.101263
$184$	−33.9849	+	10.5503i	−2.50540	+	0.777781i
$185$	−3.88954			−0.285965
$186$	5.89804	−	6.80670i	0.432465	−	0.499091i
$187$	−24.8129	+	15.9463i	−1.81450	+	1.16611i
$188$	−7.45095	−	51.8225i	−0.543416	−	3.77954i
$189$	1.39494	+	3.05448i	0.101467	+	0.222181i
$190$	−2.82070	+	19.6184i	−0.204635	+	1.42327i
$191$	11.0462	−	3.24347i	0.799278	−	0.234689i	0.143507	−	0.989649i	$-0.454162\pi$
$191$	11.0462	−	3.24347i	0.799278	−	0.234689i	0.655771	+	0.754960i	$0.272344\pi$
$192$	6.94130	+	4.46090i	0.500945	+	0.321938i
$193$	1.81295	−	3.96980i	0.130499	−	0.285752i	−0.833092	−	0.553135i	$-0.813431\pi$
$193$	1.81295	−	3.96980i	0.130499	−	0.285752i	0.963590	+	0.267382i	$0.0861587\pi$
$194$	−17.7179	−	5.20245i	−1.27207	−	0.373514i
$195$	2.90020	+	3.34701i	0.207688	+	0.239684i
$196$	−13.5452	−	15.6320i	−0.967516	−	1.11657i
$197$	5.55720	+	1.63174i	0.395934	+	0.116257i	0.473638	−	0.880720i	$-0.342941\pi$
$197$	5.55720	+	1.63174i	0.395934	+	0.116257i	−0.0777036	+	0.996977i	$0.524759\pi$
$198$	−4.93543	+	10.8071i	−0.350746	+	0.768026i
$199$	11.8347	+	7.60572i	0.838942	+	0.539155i	0.888108	−	0.459636i	$-0.152020\pi$
$199$	11.8347	+	7.60572i	0.838942	+	0.539155i	−0.0491660	+	0.998791i	$0.515656\pi$
$200$	−7.11939	+	2.09044i	−0.503417	+	0.147817i
$201$	1.23538	−	8.59223i	0.0871367	−	0.606049i
$202$	−10.2535	−	22.4520i	−0.721434	−	1.57972i
$203$	0.346962	+	2.41317i	0.0243520	+	0.169372i
$204$	26.4190	−	16.9784i	1.84970	−	1.18873i
$205$	0.314615	−	0.363085i	0.0219737	−	0.0253590i
$206$	−38.5477			−2.68574
$207$	2.05925	+	4.33122i	0.143127	+	0.301041i
$208$	43.0787			2.98697
$209$	−22.5525	+	26.0270i	−1.55999	+	1.80032i
$210$	−7.38670	+	4.74714i	−0.509731	+	0.327584i
$211$	2.90082	+	20.1757i	0.199701	+	1.38895i	0.805152	+	0.593068i	$0.202083\pi$
$211$	2.90082	+	20.1757i	0.199701	+	1.38895i	−0.605452	+	0.795882i	$0.707007\pi$
$212$	22.8504	+	50.0353i	1.56937	+	3.43644i
$213$	−0.743229	+	5.16927i	−0.0509252	+	0.354193i
$214$	27.2937	−	8.01416i	1.86576	−	0.547837i
$215$	−2.82894	−	1.81805i	−0.192932	−	0.123990i
$216$	3.08236	−	6.74943i	0.209728	−	0.459240i
$217$	11.0974	+	3.25849i	0.753340	+	0.221200i
$218$	12.0995	+	13.9636i	0.819481	+	0.945732i
$219$	3.18053	+	3.67052i	0.214920	+	0.248031i
$220$	−21.0893	−	6.19237i	−1.42184	−	0.417490i
$221$	11.9432	−	26.1520i	0.803388	−	1.75917i
$222$	8.55611	+	5.49868i	0.574249	+	0.369047i
$223$	1.44121	−	0.423176i	0.0965102	−	0.0283380i	−0.233121	−	0.972448i	$-0.574894\pi$
$223$	1.44121	−	0.423176i	0.0965102	−	0.0283380i	0.329631	+	0.944110i	$0.393076\pi$
$224$	−5.06330	+	35.2160i	−0.338306	+	2.35297i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	−1.92555	−	13.3925i	−0.128086	−	0.890855i
$227$	12.6259	−	8.11414i	0.838007	−	0.538555i	−0.0498057	−	0.998759i	$-0.515860\pi$
$227$	12.6259	−	8.11414i	0.838007	−	0.538555i	0.887813	+	0.460204i	$0.152224\pi$
$228$	24.0122	−	27.7116i	1.59025	−	1.83525i
$229$	1.31445			0.0868616			0.0434308	−	0.999056i	$-0.486171\pi$
$229$	1.31445			0.0868616			0.0434308	+	0.999056i	$0.486171\pi$
$230$	−10.4440	+	6.94167i	−0.688659	+	0.457720i
$231$	−15.2568			−1.00382
$232$	3.52785	−	4.07135i	0.231614	−	0.267297i
$233$	−14.0181	+	9.00891i	−0.918359	+	0.590193i	−0.912181	−	0.409788i	$-0.865603\pi$
$233$	−14.0181	+	9.00891i	−0.918359	+	0.590193i	−0.00617763	+	0.999981i	$0.501966\pi$
$234$	−1.64809	−	11.4627i	−0.107739	−	0.749341i
$235$	−4.49588	−	9.84460i	−0.293279	−	0.642191i
$236$	−4.18434	+	29.1027i	−0.272377	+	1.89443i
$237$	−4.55729	+	1.33814i	−0.296028	+	0.0869215i
$238$	47.9524	+	30.8171i	3.10829	+	1.99758i
$239$	11.4371	−	25.0437i	0.739803	−	1.61994i	−0.0440752	−	0.999028i	$-0.514034\pi$
$239$	11.4371	−	25.0437i	0.739803	−	1.61994i	0.783878	−	0.620915i	$-0.213239\pi$
$240$	9.33308	+	2.74044i	0.602448	+	0.176895i
$241$	−5.76839	−	6.65708i	−0.371575	−	0.428820i	0.538910	−	0.842364i	$-0.318836\pi$
$241$	−5.76839	−	6.65708i	−0.371575	−	0.428820i	−0.910484	+	0.413543i	$0.864291\pi$
$242$	−16.5133	−	19.0573i	−1.06151	−	1.22505i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	−2.75288	+	6.02797i	−0.176235	+	0.385901i
$245$	−3.59696	−	2.31162i	−0.229801	−	0.147684i
$246$	−1.20538	+	0.353932i	−0.0768523	+	0.0225659i
$247$	4.77732	−	33.2270i	0.303973	−	2.11418i
$248$	−10.6167	−	23.2474i	−0.674162	−	1.47621i
$249$	−0.0184628	−	0.128412i	−0.00117004	−	0.00813777i
$250$	−2.19978	+	1.41371i	−0.139126	+	0.0894109i
$251$	7.68932	−	8.87395i	0.485345	−	0.560119i	−0.459270	−	0.888297i	$-0.651889\pi$
$251$	7.68932	−	8.87395i	0.485345	−	0.560119i	0.944616	+	0.328178i	$0.106435\pi$
$252$	16.2443			1.02329
$253$	−21.7873	+	0.335763i	−1.36976	+	0.0211092i
$254$	21.5008			1.34908
$255$	4.25118	−	4.90612i	0.266219	−	0.307233i
$256$	−13.0352	+	8.37724i	−0.814703	+	0.523578i
$257$	−1.87292	−	13.0265i	−0.116830	−	0.812568i	−0.961011	−	0.276510i	$-0.910822\pi$
$257$	−1.87292	−	13.0265i	−0.116830	−	0.812568i	0.844181	−	0.536058i	$-0.180087\pi$
$258$	3.65283	+	7.99859i	0.227416	+	0.497971i
$259$	−1.85875	+	12.9279i	−0.115497	+	0.803299i
$260$	20.5565	−	6.03594i	1.27486	−	0.374333i
$261$	−0.610782	−	0.392526i	−0.0378065	−	0.0242968i
$262$	−17.6939	+	38.7442i	−1.09313	+	2.39362i
$263$	−20.4860	−	6.01522i	−1.26322	−	0.370914i	−0.419527	−	0.907743i	$-0.637804\pi$
$263$	−20.4860	−	6.01522i	−1.26322	−	0.370914i	−0.843691	+	0.536829i	$0.819622\pi$
$264$	22.0771	+	25.4783i	1.35875	+	1.56808i
$265$	7.44614	+	8.59330i	0.457413	+	0.527882i
$266$	63.8587	+	18.7506i	3.91543	+	1.14967i
$267$	−0.929714	+	2.03579i	−0.0568976	+	0.124588i
$268$	−35.3269	−	22.7032i	−2.15793	−	1.38682i
$269$	−13.9019	+	4.08195i	−0.847611	+	0.248881i	−0.676566	−	0.736382i	$-0.736533\pi$
$269$	−13.9019	+	4.08195i	−0.847611	+	0.248881i	−0.171045	+	0.985263i	$0.554714\pi$
$270$	0.372136	−	2.58826i	0.0226475	−	0.157517i
$271$	10.6768	+	23.3790i	0.648571	+	1.42017i	0.892799	+	0.450455i	$0.148738\pi$
$271$	10.6768	+	23.3790i	0.648571	+	1.42017i	−0.244228	+	0.969718i	$0.578535\pi$
$272$	−8.98656	−	62.5029i	−0.544890	−	3.78979i
$273$	12.5106	−	8.04007i	0.757176	−	0.486607i
$274$	1.29597	−	1.49563i	0.0782923	−	0.0903541i
$275$	−4.54351			−0.273984
$276$	23.1975	−	0.357495i	1.39633	−	0.0215187i
$277$	−3.56368			−0.214121			−0.107060	−	0.994253i	$-0.534144\pi$
$277$	−3.56368			−0.214121			−0.107060	+	0.994253i	$0.534144\pi$
$278$	31.6886	−	36.5706i	1.90055	−	2.19336i
$279$	−2.89757	+	1.86215i	−0.173473	+	0.111484i
$280$	3.54587	+	24.6621i	0.211906	+	1.47384i
$281$	1.24465	+	2.72541i	0.0742497	+	0.162584i	0.943117	−	0.332461i	$-0.107879\pi$
$281$	1.24465	+	2.72541i	0.0742497	+	0.162584i	−0.868867	+	0.495045i	$0.835152\pi$
$282$	−4.02749	+	28.0118i	−0.239833	+	1.66808i
$283$	28.7283	−	8.43538i	1.70772	−	0.501431i	0.725349	−	0.688382i	$-0.241679\pi$
$283$	28.7283	−	8.43538i	1.70772	−	0.501431i	0.982369	+	0.186951i	$0.0598604\pi$
$284$	21.2534	+	13.6587i	1.26116	+	0.810497i
$285$	3.14874	−	6.89478i	0.186515	−	0.408412i
$286$	50.4852	+	14.8238i	2.98525	+	0.876548i
$287$	−1.05646	−	1.21922i	−0.0623607	−	0.0719681i
$288$	−6.93842	−	8.00737i	−0.408850	−	0.471839i
$289$	−24.1240	−	7.08346i	−1.41906	−	0.416674i
$290$	0.788666	−	1.72694i	0.0463121	−	0.101409i
$291$	5.94082	+	3.81793i	0.348257	+	0.223811i
$292$	22.5435	−	6.61936i	1.31926	−	0.387369i
$293$	−1.25273	+	8.71291i	−0.0731851	+	0.509013i	0.919950	+	0.392037i	$0.128229\pi$
$293$	−1.25273	+	8.71291i	−0.0731851	+	0.509013i	−0.993135	+	0.116977i	$0.962680\pi$
$294$	4.64453	+	10.1701i	0.270875	+	0.593133i
$295$	0.864964	+	6.01596i	0.0503601	+	0.350262i
$296$	24.2787	−	15.6030i	1.41117	−	0.906906i
$297$	2.97536	−	3.43375i	0.172648	−	0.199247i
$298$	−51.0995			−2.96011
$299$	17.6887	−	11.7569i	1.02296	−	0.679917i
$300$	4.83759			0.279298
$301$	−7.39464	+	8.53387i	−0.426220	+	0.491884i
$302$	8.88283	−	5.70865i	0.511150	−	0.328496i
$303$	1.34335	+	9.34319i	0.0771733	+	0.536752i
$304$	−30.6281	−	67.0662i	−1.75664	−	3.84651i
$305$	−0.194951	+	1.35592i	−0.0111629	+	0.0776396i
$306$	−16.2875	+	4.78243i	−0.931092	+	0.273393i
$307$	−7.33231	−	4.71219i	−0.418477	−	0.268939i	0.314413	−	0.949286i	$-0.398192\pi$
$307$	−7.33231	−	4.71219i	−0.418477	−	0.268939i	−0.732890	+	0.680348i	$0.761829\pi$
$308$	−30.6602	+	67.1364i	−1.74702	+	3.82545i
$309$	14.1445	+	4.15321i	0.804654	+	0.236268i
$310$	−5.89804	−	6.80670i	−0.334986	−	0.386594i
$311$	16.4972	+	19.0387i	0.935468	+	1.07959i	0.996676	+	0.0814622i	$0.0259590\pi$
$311$	16.4972	+	19.0387i	0.935468	+	1.07959i	−0.0612088	+	0.998125i	$0.519496\pi$
$312$	−31.5299	−	9.25800i	−1.78503	−	0.524131i
$313$	−2.92536	+	6.40564i	−0.165351	+	0.362068i	−0.974111	−	0.226071i	$-0.927412\pi$
$313$	−2.92536	+	6.40564i	−0.165351	+	0.362068i	0.808760	+	0.588139i	$0.200139\pi$
$314$	20.2641	+	13.0229i	1.14357	+	0.734926i
$315$	3.22191	−	0.946039i	0.181534	−	0.0533033i
$316$	−3.26997	+	22.7431i	−0.183950	+	1.27940i
$317$	3.66526	+	8.02580i	0.205861	+	0.450774i	0.984197	−	0.177074i	$-0.0566633\pi$
$317$	3.66526	+	8.02580i	0.205861	+	0.450774i	−0.778336	+	0.627848i	$0.783936\pi$
$318$	−4.23140	−	29.4300i	−0.237285	−	1.65035i
$319$	2.77509	−	1.78344i	0.155375	−	0.0998537i
$320$	5.40335	−	6.23580i	0.302056	−	0.348592i
$321$	−10.8785			−0.607179
$322$	18.0814	+	38.0307i	1.00764	+	2.11937i
$323$	−49.2056			−2.73787
$324$	−3.16795	+	3.65601i	−0.175997	+	0.203111i
$325$	3.72568	−	2.39435i	0.206664	−	0.132815i
$326$	5.91090	+	41.1112i	0.327374	+	2.27694i
$327$	−2.93528	−	6.42736i	−0.162321	−	0.355434i
$328$	−0.507320	+	3.52849i	−0.0280121	+	0.194828i
$329$	−34.8695	+	10.2386i	−1.92242	+	0.564474i
$330$	9.99470	+	6.42320i	0.550190	+	0.353586i
$331$	−8.72090	+	19.0961i	−0.479344	+	1.04962i	0.503300	+	0.864112i	$0.332119\pi$
$331$	−8.72090	+	19.0961i	−0.479344	+	1.04962i	−0.982643	+	0.185504i	$0.940608\pi$
$332$	−0.602170	−	0.176813i	−0.0330484	−	0.00970388i
$333$	−2.54711	−	2.93952i	−0.139581	−	0.161085i
$334$	−2.23057	−	2.57421i	−0.122051	−	0.140855i
$335$	−8.32896	−	2.44560i	−0.455060	−	0.133618i
$336$	13.5687	−	29.7112i	0.740232	−	1.62088i
$337$	−4.82059	−	3.09801i	−0.262594	−	0.168759i	0.402718	−	0.915324i	$-0.368065\pi$
$337$	−4.82059	−	3.09801i	−0.262594	−	0.168759i	−0.665313	+	0.746565i	$0.731702\pi$
$338$	−16.5934	+	4.87225i	−0.902560	+	0.265015i
$339$	−0.736382	+	5.12165i	−0.0399948	+	0.278170i
$340$	−13.0458	−	28.5664i	−0.707509	−	1.54923i
$341$	−2.22714	−	15.4901i	−0.120607	−	0.838837i
$342$	−16.6737	+	10.7156i	−0.901613	+	0.579431i
$343$	5.99065	−	6.91358i	0.323465	−	0.373298i
$344$	24.9515			1.34530
$345$	4.58020	−	1.42189i	0.246590	−	0.0765518i
$346$	−33.4133			−1.79631
$347$	−6.48284	+	7.48160i	−0.348017	+	0.401633i	−0.902589	−	0.430502i	$-0.858336\pi$
$347$	−6.48284	+	7.48160i	−0.348017	+	0.401633i	0.554572	+	0.832135i	$0.312882\pi$
$348$	−2.95471	+	1.89888i	−0.158389	+	0.101791i
$349$	−0.493785	−	3.43435i	−0.0264317	−	0.183837i	0.972328	−	0.233618i	$-0.0750566\pi$
$349$	−0.493785	−	3.43435i	−0.0264317	−	0.183837i	−0.998760	+	0.0497816i	$0.984147\pi$
$350$	3.64759	+	7.98710i	0.194972	+	0.426929i
$351$	−0.630274	+	4.38365i	−0.0336415	+	0.233982i
$352$	46.1897	−	13.5625i	2.46192	−	0.722884i
$353$	−4.17004	−	2.67992i	−0.221949	−	0.142638i	0.424942	−	0.905221i	$-0.360295\pi$
$353$	−4.17004	−	2.67992i	−0.221949	−	0.142638i	−0.646891	+	0.762583i	$0.723931\pi$
$354$	6.60209	−	14.4566i	0.350897	−	0.768358i
$355$	5.01089	+	1.47133i	0.265950	+	0.0780900i
$356$	7.08998	+	8.18228i	0.375768	+	0.433660i
$357$	−14.2752	−	16.4744i	−0.755522	−	0.871918i
$358$	−0.278902	−	0.0818930i	−0.0147404	−	0.00432818i
$359$	−4.04165	+	8.84999i	−0.213310	+	0.467084i	−0.985796	−	0.167948i	$-0.946286\pi$
$359$	−4.04165	+	8.84999i	−0.213310	+	0.467084i	0.772486	+	0.635032i	$0.219013\pi$
$360$	−6.24206	−	4.01153i	−0.328985	−	0.211426i
$361$	−36.8950	+	10.8333i	−1.94184	+	0.570176i
$362$	−1.68527	+	11.7213i	−0.0885756	+	0.616057i
$363$	4.00604	+	8.77199i	0.210262	+	0.460410i
$364$	−10.2384	−	71.2093i	−0.536636	−	3.73238i
$365$	4.08580	−	2.62578i	0.213861	−	0.137440i
$366$	2.34572	−	2.70711i	0.122613	−	0.141503i
$367$	22.2404			1.16094			0.580470	−	0.814282i	$-0.302869\pi$
$367$	22.2404			1.16094			0.580470	+	0.814282i	$0.302869\pi$
$368$	18.7227	−	42.7275i	0.975990	−	2.22732i
$369$	0.480431			0.0250102
$370$	6.66037	−	7.68648i	0.346256	−	0.399601i
$371$	32.1204	−	20.6425i	1.66761	−	1.07171i
$372$	2.37130	+	16.4927i	0.122946	+	0.855109i
$373$	3.71722	+	8.13958i	0.192470	+	0.421452i	0.981122	−	0.193389i	$-0.0619478\pi$
$373$	3.71722	+	8.13958i	0.192470	+	0.421452i	−0.788652	+	0.614840i	$0.789221\pi$
$374$	10.9762	−	76.3413i	0.567567	−	3.94752i
$375$	0.959493	−	0.281733i	0.0495480	−	0.0145486i
$376$	67.5555	+	43.4153i	3.48391	+	2.23897i
$377$	−1.33574	+	2.92486i	−0.0687940	+	0.150638i
$378$	−8.42491	−	2.47378i	−0.433331	−	0.127237i
$379$	−6.10544	−	7.04606i	−0.313615	−	0.361932i	0.576956	−	0.816775i	$-0.304241\pi$
$379$	−6.10544	−	7.04606i	−0.313615	−	0.361932i	−0.890571	+	0.454844i	$0.849695\pi$
$380$	−24.0122	−	27.7116i	−1.23180	−	1.42158i
$381$	−7.88941	−	2.31654i	−0.404187	−	0.118680i
$382$	−12.5057	+	27.3836i	−0.639845	+	1.40107i
$383$	29.2354	+	18.7884i	1.49386	+	0.960044i	0.995668	+	0.0929757i	$0.0296379\pi$
$383$	29.2354	+	18.7884i	1.49386	+	0.960044i	0.498189	+	0.867068i	$0.333998\pi$
$384$	−0.369601	+	0.108525i	−0.0188611	+	0.00553813i
$385$	−2.17127	+	15.1015i	−0.110658	+	0.769644i
$386$	4.74064	+	10.3805i	0.241292	+	0.528356i
$387$	−0.478571	−	3.32854i	−0.0243271	−	0.169199i
$388$	28.7393	−	18.4696i	1.45901	−	0.937652i
$389$	−23.0115	+	26.5567i	−1.16673	+	1.34648i	−0.239988	+	0.970776i	$0.577143\pi$
$389$	−23.0115	+	26.5567i	−1.16673	+	1.34648i	−0.926741	+	0.375701i	$0.877402\pi$
$390$	−11.5806			−0.586406
$391$	−20.7481	−	23.2120i	−1.04927	−	1.17388i
$392$	31.7256			1.60238
$393$	10.6669	−	12.3103i	0.538074	−	0.620970i
$394$	−12.7407	+	8.18794i	−0.641866	+	0.412502i
$395$	0.675950	+	4.70134i	0.0340107	+	0.236550i
$396$	−9.13066	−	19.9934i	−0.458833	−	1.00470i
$397$	4.07797	−	28.3629i	0.204668	−	1.42349i	−0.585534	−	0.810648i	$-0.699115\pi$
$397$	4.07797	−	28.3629i	0.204668	−	1.42349i	0.790202	−	0.612847i	$-0.209976\pi$
$398$	−35.2959	+	10.3638i	−1.76923	+	0.519491i
$399$	−21.4118	−	13.7605i	−1.07193	−	0.688889i
$400$	4.04078	−	8.84808i	0.202039	−	0.442404i
$401$	−20.3676	−	5.98046i	−1.01711	−	0.298650i	−0.269649	−	0.962959i	$-0.586908\pi$
$401$	−20.3676	−	5.98046i	−1.01711	−	0.298650i	−0.747458	+	0.664309i	$0.768726\pi$
$402$	14.8645	+	17.1545i	0.741373	+	0.855590i
$403$	9.98930	+	11.5283i	0.497603	+	0.574264i
$404$	43.8136	+	12.8648i	2.17981	+	0.640050i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	−5.36303	−	3.44661i	−0.266163	−	0.171052i
$407$	16.9563	−	4.97882i	0.840493	−	0.246791i
$408$	−6.85506	+	47.6780i	−0.339376	+	2.36041i
$409$	11.4827	+	25.1435i	0.567781	+	1.24327i	0.947970	+	0.318358i	$0.103132\pi$
$409$	11.4827	+	25.1435i	0.567781	+	1.24327i	−0.380189	+	0.924909i	$0.624141\pi$
$410$	0.178786	+	1.24348i	0.00882959	+	0.0614112i
$411$	−0.636679	+	0.409169i	−0.0314051	+	0.0201828i
$412$	46.7008	−	53.8956i	2.30078	−	2.65525i
$413$	20.4089			1.00426
$414$	−12.0856	−	3.34724i	−0.593972	−	0.164508i
$415$	−0.129732			−0.00636831
$416$	−30.7284	+	35.4625i	−1.50658	+	1.73869i
$417$	−15.5679	+	10.0049i	−0.762362	+	0.489940i
$418$	−12.8159	−	89.1362i	−0.626844	−	4.35980i
$419$	0.351352	+	0.769353i	0.0171646	+	0.0375853i	0.918020	−	0.396534i	$-0.129787\pi$
$419$	0.351352	+	0.769353i	0.0171646	+	0.0375853i	−0.900856	+	0.434119i	$0.857060\pi$
$420$	2.31180	−	16.0790i	0.112805	−	0.784573i
$421$	11.3957	−	3.34609i	0.555394	−	0.163079i	0.00802228	−	0.999968i	$-0.497446\pi$
$421$	11.3957	−	3.34609i	0.555394	−	0.163079i	0.547372	+	0.836889i	$0.315628\pi$
$422$	−44.8383	−	28.8158i	−2.18270	−	1.40273i
$423$	4.49588	−	9.84460i	0.218597	−	0.478661i
$424$	−80.9515	−	23.7695i	−3.93135	−	1.15435i
$425$	−4.25118	−	4.90612i	−0.206212	−	0.237982i
$426$	−8.94279	−	10.3205i	−0.433280	−	0.500031i
$427$	4.41357	+	1.29594i	0.213588	+	0.0627150i
$428$	−21.8615	+	47.8701i	−1.05672	+	2.31389i
$429$	−16.9277	−	10.8788i	−0.817276	−	0.525231i
$430$	8.43703	−	2.47734i	0.406870	−	0.119468i
$431$	−1.09964	+	7.64818i	−0.0529679	+	0.368400i	0.946047	+	0.324029i	$0.105037\pi$
$431$	−1.09964	+	7.64818i	−0.0529679	+	0.368400i	−0.999015	+	0.0443710i	$0.985872\pi$
$432$	4.04078	+	8.84808i	0.194412	+	0.425703i
$433$	5.56534	+	38.7078i	0.267453	+	1.86018i	0.472374	+	0.881398i	$0.343397\pi$
$433$	5.56534	+	38.7078i	0.267453	+	1.86018i	−0.204920	+	0.978779i	$0.565694\pi$
$434$	−25.4424	+	16.3508i	−1.22127	+	0.784864i
$435$	−0.475454	+	0.548703i	−0.0227963	+	0.0263083i
$436$	−34.1819			−1.63701
$437$	−30.8798	−	19.1794i	−1.47718	−	0.917474i
$438$	−12.6999			−0.606827
$439$	18.9321	−	21.8488i	0.903581	−	1.04279i	−0.0952984	−	0.995449i	$-0.530381\pi$
$439$	18.9321	−	21.8488i	0.903581	−	1.04279i	0.998879	−	0.0473388i	$-0.0150740\pi$
$440$	28.3608	−	18.2264i	1.35205	−	0.868910i
$441$	−0.608497	−	4.23219i	−0.0289761	−	0.201533i
$442$	31.2301	+	68.3843i	1.48546	+	3.25271i
$443$	−1.29179	+	8.98459i	−0.0613747	+	0.426871i	0.935849	+	0.352402i	$0.114635\pi$
$443$	−1.29179	+	8.98459i	−0.0613747	+	0.426871i	−0.997223	+	0.0744685i	$0.976274\pi$
$444$	−18.0538	+	5.30108i	−0.856796	+	0.251578i
$445$	1.88276	+	1.20997i	0.0892512	+	0.0573583i
$446$	−1.63162	+	3.57274i	−0.0772592	+	0.169174i
$447$	18.7502	+	5.50556i	0.886856	+	0.260404i
$448$	−18.1441	−	20.9394i	−0.857227	−	0.989293i
$449$	−7.38292	−	8.52034i	−0.348421	−	0.402100i	0.554306	−	0.832313i	$-0.312984\pi$
$449$	−7.38292	−	8.52034i	−0.348421	−	0.402100i	−0.902727	+	0.430213i	$0.858438\pi$
$450$	−2.50896	−	0.736696i	−0.118273	−	0.0347282i
$451$	−0.906785	+	1.98558i	−0.0426988	+	0.0934974i
$452$	21.0576	+	13.5329i	0.990466	+	0.636534i
$453$	−3.87449	+	1.13765i	−0.182040	+	0.0534516i
$454$	−5.58516	+	38.8456i	−0.262125	+	1.82312i
$455$	−6.17779	−	13.5275i	−0.289619	−	0.634178i
$456$	8.00398	+	55.6689i	0.374821	+	2.60694i
$457$	−11.0119	+	7.07692i	−0.515115	+	0.331044i	−0.772237	−	0.635335i	$-0.780862\pi$
$457$	−11.0119	+	7.07692i	−0.515115	+	0.331044i	0.257122	+	0.966379i	$0.417226\pi$
$458$	−2.25085	+	2.59762i	−0.105175	+	0.121379i
$459$	6.49172			0.303008
$460$	2.94749	−	23.0123i	0.137428	−	1.07295i
$461$	0.794029			0.0369816			0.0184908	−	0.999829i	$-0.494114\pi$
$461$	0.794029			0.0369816			0.0184908	+	0.999829i	$0.494114\pi$
$462$	26.1254	−	30.1504i	1.21547	−	1.40272i
$463$	−35.1181	+	22.5691i	−1.63208	+	1.04887i	−0.684667	+	0.728856i	$0.740052\pi$
$463$	−35.1181	+	22.5691i	−1.63208	+	1.04887i	−0.947412	+	0.320017i	$0.896311\pi$
$464$	1.00506	+	6.99036i	0.0466588	+	0.324519i
$465$	1.43083	+	3.13309i	0.0663533	+	0.145294i
$466$	6.20105	−	43.1292i	0.287258	−	1.99792i
$467$	36.9722	−	10.8560i	1.71087	−	0.502357i	0.727832	−	0.685755i	$-0.240528\pi$
$467$	36.9722	−	10.8560i	1.71087	−	0.502357i	0.983039	+	0.183398i	$0.0587097\pi$
$468$	18.0233	+	11.5829i	0.833129	+	0.535419i
$469$	−12.1089	+	26.5147i	−0.559135	+	1.22434i
$470$	27.1535	+	7.97299i	1.25250	+	0.367766i
$471$	−6.03250	−	6.96188i	−0.277963	−	0.320786i
$472$	−29.5323	−	34.0821i	−1.35934	−	1.56876i
$473$	14.6598	+	4.30452i	0.674060	+	0.197922i
$474$	5.15939	−	11.2975i	0.236979	−	0.518911i
$475$	−6.37649	−	4.09792i	−0.292573	−	0.188026i
$476$	−101.182	+	29.7097i	−4.63767	+	1.36174i
$477$	−1.61820	+	11.2548i	−0.0740923	+	0.515323i
$478$	29.9066	+	65.4863i	1.36789	+	2.99527i
$479$	0.364903	+	2.53796i	0.0166729	+	0.115962i	0.996458	−	0.0840893i	$-0.0267981\pi$
$479$	0.364903	+	2.53796i	0.0166729	+	0.115962i	−0.979785	+	0.200052i	$0.935889\pi$
$480$	−8.91330	+	5.72823i	−0.406835	+	0.261457i
$481$	−11.2804	+	13.0183i	−0.514344	+	0.593585i
$482$	23.0334			1.04914
$483$	−2.53720	−	15.9030i	−0.115447	−	0.723609i
$484$	46.6511			2.12050
$485$	4.62454	−	5.33700i	0.209990	−	0.242341i
$486$	2.19978	−	1.41371i	0.0997839	−	0.0641272i
$487$	2.55695	+	17.7840i	0.115866	+	0.805869i	0.962030	+	0.272945i	$0.0879977\pi$
$487$	2.55695	+	17.7840i	0.115866	+	0.805869i	−0.846163	+	0.532924i	$0.821093\pi$
$488$	−4.22240	−	9.24577i	−0.191139	−	0.418536i
$489$	2.26049	−	15.7220i	0.102223	−	0.710974i
$490$	10.7276	−	3.14990i	0.484623	−	0.142298i
$491$	−12.5103	−	8.03986i	−0.564580	−	0.362834i	0.227004	−	0.973894i	$-0.427107\pi$
$491$	−12.5103	−	8.03986i	−0.564580	−	0.362834i	−0.791584	+	0.611060i	$0.790743\pi$
$492$	0.965477	−	2.11410i	0.0435271	−	0.0953110i
$493$	4.52232	+	1.32787i	0.203675	+	0.0598044i
$494$	57.4823	+	66.3381i	2.58625	+	2.98469i
$495$	−2.97536	−	3.43375i	−0.133733	−	0.154336i
$496$	32.1464	+	9.43902i	1.44341	+	0.423825i
$497$	7.28495	−	15.9518i	0.326775	−	0.715537i
$498$	0.285382	+	0.183404i	0.0127883	+	0.00821853i
$499$	35.3172	−	10.3701i	1.58101	−	0.464228i	0.630831	−	0.775920i	$-0.282714\pi$
$499$	35.3172	−	10.3701i	1.58101	−	0.464228i	0.950183	+	0.311693i	$0.100896\pi$
$500$	0.688461	−	4.78835i	0.0307889	−	0.214142i
$501$	0.541125	+	1.18490i	0.0241757	+	0.0529373i
$502$	4.36959	+	30.3912i	0.195024	+	1.35642i
$503$	−1.60313	+	1.03027i	−0.0714802	+	0.0459375i	−0.575893	−	0.817525i	$-0.695345\pi$
$503$	−1.60313	+	1.03027i	−0.0714802	+	0.0459375i	0.504413	+	0.863463i	$0.331709\pi$
$504$	−16.3163	+	18.8300i	−0.726786	+	0.838756i
$505$	9.43927			0.420042
$506$	36.6446	−	43.6309i	1.62905	−	1.93963i
$507$	6.61365			0.293722
$508$	−26.0484	+	30.0614i	−1.15571	+	1.33376i
$509$	1.09149	−	0.701457i	0.0483793	−	0.0310915i	−0.516228	−	0.856451i	$-0.672664\pi$
$509$	1.09149	−	0.701457i	0.0483793	−	0.0310915i	0.564607	+	0.825360i	$0.309028\pi$
$510$	2.41580	+	16.8023i	0.106974	+	0.744018i
$511$	−6.77492	−	14.8350i	−0.299705	−	0.656262i
$512$	5.87590	−	40.8678i	0.259680	−	1.80612i
$513$	7.27271	−	2.13546i	0.321098	−	0.0942829i
$514$	28.9499	+	18.6050i	1.27693	+	0.820631i
$515$	6.12391	−	13.4095i	0.269852	−	0.590893i
$516$	−15.6087	−	4.58313i	−0.687135	−	0.201761i
$517$	32.2012	+	37.1622i	1.41621	+	1.63439i
$518$	−22.3651	−	25.8107i	−0.982665	−	1.13406i
$519$	12.2605	+	3.60002i	0.538178	+	0.158023i
$520$	−13.6509	+	29.8914i	−0.598633	+	1.31082i
$521$	−14.1235	−	9.07665i	−0.618763	−	0.397655i	0.193371	−	0.981126i	$-0.438058\pi$
$521$	−14.1235	−	9.07665i	−0.618763	−	0.397655i	−0.812134	+	0.583471i	$0.801694\pi$
$522$	1.82160	−	0.534870i	0.0797293	−	0.0234106i
$523$	1.25097	−	8.70067i	0.0547010	−	0.380454i	−0.944020	−	0.329889i	$-0.892989\pi$
$523$	1.25097	−	8.70067i	0.0547010	−	0.380454i	0.998721	−	0.0505649i	$-0.0161022\pi$
$524$	−32.7341	−	71.6777i	−1.43000	−	3.13125i
$525$	−0.477884	−	3.32375i	−0.0208566	−	0.145060i
$526$	46.9670	−	30.1839i	2.04786	−	1.31608i
$527$	14.6425	−	16.8984i	0.637838	−	0.736105i
$528$	−44.1951			−1.92335
$529$	−3.97321	−	22.6542i	−0.172748	−	0.984966i
$530$	−29.7326			−1.29150
$531$	−3.98013	+	4.59331i	−0.172723	+	0.199333i
$532$	−103.582	+	66.5679i	−4.49083	+	2.88608i
$533$	−0.302803	−	2.10604i	−0.0131159	−	0.0912228i
$534$	−2.43109	−	5.32334i	−0.105204	−	0.230364i
$535$	−1.54817	+	10.7678i	−0.0669334	+	0.465532i
$536$	61.8005	−	18.1463i	2.66938	−	0.783799i
$537$	0.0935158	+	0.0600990i	0.00403551	+	0.00259346i
$538$	15.7385	−	34.4626i	0.678537	−	1.48579i
$539$	18.6398	+	5.47314i	0.802873	+	0.235745i
$540$	3.16795	+	3.65601i	0.136327	+	0.157329i
$541$	−1.24363	−	1.43522i	−0.0534677	−	0.0617050i	0.728386	−	0.685167i	$-0.240271\pi$
$541$	−1.24363	−	1.43522i	−0.0534677	−	0.0617050i	−0.781853	+	0.623462i	$0.785725\pi$
$542$	−64.4842	−	18.9343i	−2.76983	−	0.813297i
$543$	1.88126	−	4.11938i	0.0807326	−	0.176780i
$544$	57.8627	+	37.1861i	2.48084	+	1.59434i
$545$	−6.77967	+	1.99069i	−0.290409	+	0.0852718i
$546$	−5.53417	+	38.4910i	−0.236841	+	1.64726i
$547$	9.17260	+	20.0852i	0.392192	+	0.858781i	0.998003	+	0.0631718i	$0.0201216\pi$
$547$	9.17260	+	20.0852i	0.392192	+	0.858781i	−0.605811	+	0.795609i	$0.707151\pi$
$548$	0.521042	+	3.62393i	0.0222578	+	0.154807i
$549$	−1.15240	+	0.740602i	−0.0491832	+	0.0316081i
$550$	7.78022	−	8.97885i	0.331750	−	0.382859i
$551$	5.50319			0.234444
$552$	−22.8859	+	27.2491i	−0.974091	+	1.15980i
$553$	15.9491			0.678225
$554$	6.10238	−	7.04252i	0.259265	−	0.299208i
$555$	−3.27209	+	2.10284i	−0.138892	+	0.0892607i
$556$	12.7403	+	88.6111i	0.540311	+	3.75795i
$557$	14.1141	+	30.9056i	0.598034	+	1.30951i	0.930464	+	0.366385i	$0.119405\pi$
$557$	14.1141	+	30.9056i	0.598034	+	1.30951i	−0.332429	+	0.943128i	$0.607868\pi$
$558$	1.28177	−	8.91488i	0.0542615	−	0.377397i
$559$	−14.2895	+	4.19578i	−0.604382	+	0.177463i
$560$	−27.4778	−	17.6589i	−1.16115	−	0.746225i
$561$	−12.2527	+	26.8298i	−0.517311	+	1.13275i
$562$	−7.51725	−	2.20726i	−0.317096	−	0.0931077i
$563$	−17.7579	−	20.4937i	−0.748407	−	0.863708i	0.246006	−	0.969268i	$-0.420882\pi$
$563$	−17.7579	−	20.4937i	−0.748407	−	0.863708i	−0.994413	+	0.105560i	$0.966336\pi$
$564$	−34.2855	−	39.5676i	−1.44368	−	1.66610i
$565$	4.96472	+	1.45777i	0.208867	+	0.0613290i
$566$	−32.5238	+	71.2172i	−1.36708	+	2.99348i
$567$	2.82487	+	1.81544i	0.118633	+	0.0762411i
$568$	−37.1805	+	10.9172i	−1.56006	+	0.458075i
$569$	5.10942	−	35.5368i	0.214198	−	1.48978i	−0.544733	−	0.838609i	$-0.683369\pi$
$569$	5.10942	−	35.5368i	0.214198	−	1.48978i	0.758931	−	0.651171i	$-0.225722\pi$
$570$	8.23358	+	18.0290i	0.344867	+	0.755152i
$571$	5.04869	+	35.1144i	0.211281	+	1.46949i	0.768887	+	0.639385i	$0.220811\pi$
$571$	5.04869	+	35.1144i	0.211281	+	1.46949i	−0.557606	+	0.830106i	$0.688280\pi$
$572$	−81.8891	+	52.6269i	−3.42396	+	2.20044i
$573$	7.53914	−	8.70063i	0.314952	−	0.363474i
$574$	4.21846			0.176075
$575$	−0.755584	−	4.73594i	−0.0315100	−	0.197502i
$576$	8.25114			0.343798
$577$	29.1366	−	33.6254i	1.21297	−	1.39984i	0.321411	−	0.946940i	$-0.395843\pi$
$577$	29.1366	−	33.6254i	1.21297	−	1.39984i	0.891560	−	0.452903i	$-0.149612\pi$
$578$	55.3078	−	35.5442i	2.30050	−	1.47844i
$579$	−0.621088	−	4.31976i	−0.0258115	−	0.179523i
$580$	1.45905	+	3.19488i	0.0605838	+	0.132660i
$581$	−0.0619970	+	0.431199i	−0.00257207	+	0.0178891i
$582$	−17.7179	+	5.20245i	−0.734432	+	0.215649i
$583$	−43.4610	−	27.9307i	−1.79997	−	1.15677i
$584$	−14.9704	+	32.7806i	−0.619480	+	1.35647i
$585$	4.24933	+	1.24772i	0.175688	+	0.0515868i
$586$	−15.0732	−	17.3954i	−0.622670	−	0.718599i
$587$	29.7011	+	34.2769i	1.22590	+	1.41476i	0.878975	+	0.476867i	$0.158228\pi$
$587$	29.7011	+	34.2769i	1.22590	+	1.41476i	0.346922	+	0.937894i	$0.387227\pi$
$588$	−19.8463	−	5.82739i	−0.818447	−	0.240318i
$589$	10.8454	−	23.7480i	0.446875	−	0.978520i
$590$	−13.3698	−	8.59227i	−0.550428	−	0.353738i
$591$	5.55720	−	1.63174i	0.228593	−	0.0671209i
$592$	−5.38433	+	37.4488i	−0.221294	+	1.53914i
$593$	1.53648	+	3.36443i	0.0630958	+	0.138161i	0.938553	−	0.345135i	$-0.112167\pi$
$593$	1.53648	+	3.36443i	0.0630958	+	0.138161i	−0.875457	+	0.483296i	$0.839440\pi$
$594$	1.69080	+	11.7598i	0.0693745	+	0.482510i
$595$	−18.3383	+	11.7853i	−0.751797	+	0.483150i
$596$	61.9074	−	71.4450i	2.53583	−	2.92650i
$597$	14.0680			0.575764
$598$	−7.05593	+	55.0885i	−0.288539	+	2.25274i
$599$	−15.2093			−0.621433			−0.310717	−	0.950503i	$-0.600569\pi$
$599$	−15.2093			−0.621433			−0.310717	+	0.950503i	$0.600569\pi$
$600$	−4.85904	+	5.60763i	−0.198369	+	0.228930i
$601$	15.5364	−	9.98462i	0.633742	−	0.407281i	−0.183952	−	0.982935i	$-0.558889\pi$
$601$	15.5364	−	9.98462i	0.633742	−	0.407281i	0.817693	+	0.575654i	$0.195253\pi$
$602$	−4.20213	−	29.2265i	−0.171266	−	1.19118i
$603$	−3.60605	−	7.89614i	−0.146850	−	0.321556i
$604$	−2.78005	+	19.3357i	−0.113119	+	0.786757i
$605$	9.25283	−	2.71687i	0.376181	−	0.110457i
$606$	−20.7643	−	13.3444i	−0.843491	−	0.542079i
$607$	13.4419	−	29.4338i	0.545592	−	1.19468i	−0.413218	−	0.910632i	$-0.635595\pi$
$607$	13.4419	−	29.4338i	0.545592	−	1.19468i	0.958810	−	0.284047i	$-0.0916773\pi$
$608$	77.0563	+	22.6258i	3.12505	+	0.917597i
$609$	1.59654	+	1.84251i	0.0646952	+	0.0746622i
$610$	−2.34572	−	2.70711i	−0.0949756	−	0.109608i
$611$	−45.9890	−	13.5036i	−1.86051	−	0.546296i
$612$	13.0458	−	28.5664i	0.527346	−	1.15473i
$613$	26.3364	+	16.9254i	1.06372	+	0.683609i	0.950740	−	0.309989i	$-0.100325\pi$
$613$	26.3364	+	16.9254i	1.06372	+	0.683609i	0.112976	+	0.993598i	$0.463962\pi$
$614$	21.8679	−	6.42099i	0.882516	−	0.259130i
$615$	0.0683724	−	0.475541i	0.00275704	−	0.0191757i
$616$	−47.0269	−	102.975i	−1.89477	−	4.14896i
$617$	−2.12999	−	14.8144i	−0.0857503	−	0.596407i	−0.986708	−	0.162501i	$-0.948044\pi$
$617$	−2.12999	−	14.8144i	−0.0857503	−	0.596407i	0.900958	−	0.433906i	$-0.142865\pi$
$618$	−32.4284	+	20.8404i	−1.30446	+	0.838326i
$619$	−10.4119	+	12.0159i	−0.418488	+	0.482961i	−0.925376	−	0.379051i	$-0.876251\pi$
$619$	−10.4119	+	12.0159i	−0.418488	+	0.482961i	0.506887	+	0.862012i	$0.330796\pi$
$620$	16.6623			0.669176
$621$	4.07398	+	2.53035i	0.163483	+	0.101539i
$622$	−65.8736			−2.64129
$623$	4.92140	−	5.67959i	0.197172	−	0.227548i
$624$	36.2401	−	23.2901i	1.45076	−	0.932350i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−7.64946	−	16.7500i	−0.305734	−	0.669464i
$627$	−4.90113	+	34.0881i	−0.195732	+	1.36135i
$628$	−42.7582	+	12.5549i	−1.70624	+	0.500996i
$629$	21.2415	+	13.6511i	0.846954	+	0.544304i
$630$	−3.64759	+	7.98710i	−0.145323	+	0.318214i
$631$	9.95478	+	2.92299i	0.396294	+	0.116362i	0.473806	−	0.880629i	$-0.342880\pi$
$631$	9.95478	+	2.92299i	0.396294	+	0.116362i	−0.0775127	+	0.996991i	$0.524698\pi$
$632$	−23.0789	−	26.6344i	−0.918028	−	1.05946i
$633$	13.3481	+	15.4045i	0.530540	+	0.612276i
$634$	−22.1368	−	6.49996i	−0.879166	−	0.258147i
$635$	−3.41574	+	7.47943i	−0.135550	+	0.296812i
$636$	46.2741	+	29.7386i	1.83489	+	1.17921i
$637$	−18.1689	+	5.33488i	−0.719879	+	0.211376i
$638$	−1.22759	+	8.53806i	−0.0486007	+	0.338025i
$639$	2.16948	+	4.75049i	0.0858231	+	0.187926i
$640$	0.0548203	+	0.381284i	0.00216696	+	0.0150716i
$641$	−23.6870	+	15.2227i	−0.935581	+	0.601261i	−0.917138	−	0.398569i	$-0.869507\pi$
$641$	−23.6870	+	15.2227i	−0.935581	+	0.601261i	−0.0184423	+	0.999830i	$0.505871\pi$
$642$	18.6282	−	21.4980i	0.735195	−	0.848460i
$643$	−4.58049			−0.180637			−0.0903184	−	0.995913i	$-0.528788\pi$
$643$	−4.58049			−0.180637			−0.0903184	+	0.995913i	$0.528788\pi$
$644$	−75.0786	−	20.7939i	−2.95851	−	0.819396i
$645$	−3.36276			−0.132409
$646$	84.2588	−	97.2398i	3.31512	−	3.82585i
$647$	−28.8202	+	18.5216i	−1.13304	+	0.728159i	−0.966192	−	0.257823i	$-0.916995\pi$
$647$	−28.8202	+	18.5216i	−1.13304	+	0.728159i	−0.166846	+	0.985983i	$0.553358\pi$
$648$	−1.05597	−	7.34443i	−0.0414824	−	0.288516i
$649$	−11.4715	−	25.1191i	−0.450297	−	0.986012i
$650$	−1.64809	+	11.4627i	−0.0646434	+	0.449605i
$651$	11.0974	−	3.25849i	0.434941	−	0.127710i
$652$	−64.6409	−	41.5422i	−2.53153	−	1.62692i
$653$	−11.3567	+	24.8677i	−0.444422	+	0.973148i	0.546344	+	0.837561i	$0.316019\pi$
$653$	−11.3567	+	24.8677i	−0.444422	+	0.973148i	−0.990765	+	0.135587i	$0.956708\pi$
$654$	17.7280	+	5.20541i	0.693220	+	0.203548i
$655$	−10.6669	−	12.3103i	−0.416790	−	0.481002i
$656$	−3.06029	−	3.53177i	−0.119484	−	0.137892i
$657$	4.66006	+	1.36832i	0.181806	+	0.0533832i
$658$	39.4765	−	86.4414i	1.53895	−	3.36984i
$659$	20.2184	+	12.9936i	0.787598	+	0.506158i	0.871547	−	0.490312i	$-0.163117\pi$
$659$	20.2184	+	12.9936i	0.787598	+	0.506158i	−0.0839493	+	0.996470i	$0.526753\pi$
$660$	−21.0893	+	6.19237i	−0.820900	+	0.241038i
$661$	−0.806668	+	5.61050i	−0.0313757	+	0.218223i	−0.999477	−	0.0323360i	$-0.989705\pi$
$661$	−0.806668	+	5.61050i	−0.0313757	+	0.218223i	0.968101	+	0.250559i	$0.0806144\pi$
$662$	−22.8041	−	49.9340i	−0.886306	−	1.94074i
$663$	−4.09156	−	28.4575i	−0.158903	−	1.10520i
$664$	0.809798	−	0.520425i	0.0314262	−	0.0201964i
$665$	−16.6677	+	19.2356i	−0.646346	+	0.745923i
$666$	10.1707			0.394106
$667$	2.32048	+	2.59604i	0.0898492	+	0.100519i
$668$	6.30150			0.243812
$669$	0.983633	−	1.13517i	0.0380294	−	0.0438883i
$670$	19.0953	−	12.2718i	0.737718	−	0.474102i
$671$	−0.885763	−	6.16062i	−0.0341945	−	0.237828i
$672$	14.7797	+	32.3631i	0.570140	+	1.24843i
$673$	7.20771	−	50.1307i	0.277837	−	1.93240i	−0.0760377	−	0.997105i	$-0.524227\pi$
$673$	7.20771	−	50.1307i	0.277837	−	1.93240i	0.353875	−	0.935293i	$-0.384864\pi$
$674$	14.3770	−	4.22145i	0.553780	−	0.162604i
$675$	0.841254	+	0.540641i	0.0323799	+	0.0208093i
$676$	13.2908	−	29.1029i	0.511186	−	1.11934i
$677$	−13.8716	−	4.07306i	−0.533128	−	0.156541i	0.00407769	−	0.999992i	$-0.498702\pi$
$677$	−13.8716	−	4.07306i	−0.533128	−	0.156541i	−0.537206	+	0.843451i	$0.680520\pi$
$678$	−8.86040	−	10.2254i	−0.340282	−	0.392706i
$679$	−15.5289	−	17.9213i	−0.595944	−	0.687756i
$680$	46.2171	+	13.5706i	1.77235	+	0.520408i
$681$	6.23471	−	13.6521i	0.238914	−	0.523150i
$682$	34.4252	+	22.1237i	1.31821	+	0.847162i
$683$	8.33337	−	2.44690i	0.318867	−	0.0936279i	−0.118382	−	0.992968i	$-0.537771\pi$
$683$	8.33337	−	2.44690i	0.318867	−	0.0936279i	0.437250	+	0.899340i	$0.355953\pi$
$684$	5.21836	−	36.2945i	0.199529	−	1.38775i
$685$	0.314395	+	0.688429i	0.0120124	+	0.0263035i
$686$	3.40429	+	23.6774i	0.129977	+	0.904006i
$687$	1.10579	−	0.710648i	0.0421885	−	0.0271129i
$688$	−21.4204	+	24.7205i	−0.816647	+	0.942460i
$689$	50.3572			1.91845
$690$	−5.03312	+	11.4862i	−0.191608	+	0.437271i
$691$	44.7625			1.70284			0.851422	−	0.524481i	$-0.175741\pi$
$691$	44.7625			1.70284			0.851422	+	0.524481i	$0.175741\pi$
$692$	40.4805	−	46.7170i	1.53884	−	1.77591i
$693$	−12.8348	+	8.24844i	−0.487555	+	0.313332i
$694$	−3.68399	−	25.6227i	−0.139842	−	0.972624i
$695$	7.68749	+	16.8332i	0.291603	+	0.638521i
$696$	0.766674	−	5.33234i	0.0290607	−	0.202122i
$697$	−2.99249	+	0.878674i	−0.113349	+	0.0332822i
$698$	7.63249	+	4.90510i	0.288894	+	0.185661i
$699$	−6.92222	+	15.1576i	−0.261822	+	0.573311i
$700$	−15.5863	−	4.57655i	−0.589106	−	0.172977i
$701$	9.51336	+	10.9790i	0.359315	+	0.414671i	0.906410	−	0.422399i	$-0.138812\pi$
$701$	9.51336	+	10.9790i	0.359315	+	0.414671i	−0.547095	+	0.837070i	$0.684266\pi$
$702$	−7.58367	−	8.75203i	−0.286227	−	0.330324i
$703$	28.2875	+	8.30596i	1.06688	+	0.313265i
$704$	−15.5735	+	34.1013i	−0.586950	+	1.28524i
$705$	−9.10457	−	5.85115i	−0.342898	−	0.220367i
$706$	12.4368	−	3.65176i	0.468063	−	0.137436i
$707$	4.51087	−	31.3738i	0.169649	−	1.17993i
$708$	12.2140	+	26.7450i	0.459031	+	1.00514i
$709$	−0.430639	−	2.99516i	−0.0161730	−	0.112486i	0.980136	−	0.198328i	$-0.0635510\pi$
$709$	−0.430639	−	2.99516i	−0.0161730	−	0.112486i	−0.996309	+	0.0858422i	$0.972642\pi$
$710$	−11.4882	+	7.38300i	−0.431144	+	0.277079i
$711$	−3.11038	+	3.58957i	−0.116648	+	0.134619i
$712$	−16.6061			−0.622341
$713$	15.7758	−	4.89747i	0.590808	−	0.183412i
$714$	57.0011			2.13321
$715$	−13.1771	+	15.2072i	−0.492795	+	0.568716i
$716$	0.452391	−	0.290734i	0.0169067	−	0.0108652i
$717$	−3.91817	−	27.2515i	−0.146327	−	1.01772i
$718$	−10.5684	−	23.1416i	−0.394410	−	0.863638i
$719$	−4.54982	+	31.6447i	−0.169680	+	1.18015i	0.709867	+	0.704336i	$0.248755\pi$
$719$	−4.54982	+	31.6447i	−0.169680	+	1.18015i	−0.879547	+	0.475813i	$0.842154\pi$
$720$	9.33308	−	2.74044i	0.347823	−	0.102130i
$721$	−41.6433	−	26.7625i	−1.55088	−	0.996689i
$722$	41.7695	−	91.4624i	1.55450	−	3.40388i
$723$	−8.45177	−	2.48166i	−0.314325	−	0.0922941i
$724$	−14.3465	−	16.5567i	−0.533182	−	0.615325i
$725$	0.475454	+	0.548703i	0.0176579	+	0.0203783i
$726$	−24.1950	−	7.10430i	−0.897961	−	0.263665i
$727$	−6.88509	+	15.0762i	−0.255354	+	0.559147i	−0.993280	−	0.115734i	$-0.963078\pi$
$727$	−6.88509	+	15.0762i	−0.255354	+	0.559147i	0.737926	+	0.674881i	$0.235805\pi$
$728$	92.8280	+	59.6570i	3.44044	+	2.21103i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−1.80739	+	12.5707i	−0.0668945	+	0.465261i
$731$	9.06857	+	19.8574i	0.335413	+	0.734452i
$732$	0.943095	+	6.55937i	0.0348578	+	0.242441i
$733$	−5.08804	+	3.26989i	−0.187931	+	0.120776i	−0.631223	−	0.775601i	$-0.717447\pi$
$733$	−5.08804	+	3.26989i	−0.187931	+	0.120776i	0.443292	+	0.896377i	$0.353810\pi$
$734$	−38.0841	+	43.9514i	−1.40571	+	1.62227i
$735$	−4.27571			−0.157712
$736$	21.8182	+	45.8905i	0.804231	+	1.69155i
$737$	39.4403			1.45280
$738$	−0.822681	+	0.949424i	−0.0302833	+	0.0349488i
$739$	−37.5059	+	24.1036i	−1.37968	+	0.886665i	−0.999272	−	0.0381548i	$-0.987852\pi$
$739$	−37.5059	+	24.1036i	−1.37968	+	0.886665i	−0.380406	+	0.924820i	$0.624216\pi$
$740$	2.67780	+	18.6245i	0.0984377	+	0.684649i
$741$	−13.9449	−	30.5351i	−0.512280	−	1.12174i
$742$	−14.2087	+	98.8240i	−0.521619	+	3.62794i
$743$	−41.6727	+	12.2362i	−1.52882	+	0.448903i	−0.934691	−	0.355462i	$-0.884323\pi$
$743$	−41.6727	+	12.2362i	−1.52882	+	0.448903i	−0.594134	+	0.804366i	$0.702505\pi$
$744$	−21.4998	−	13.8171i	−0.788222	−	0.506559i
$745$	8.11796	−	17.7759i	0.297419	−	0.651257i
$746$	−22.4507	−	6.59212i	−0.821978	−	0.241355i
$747$	−0.0849567	−	0.0980452i	−0.00310840	−	0.00358729i
$748$	93.4392	+	107.835i	3.41648	+	3.94282i
$749$	35.0496	+	10.2915i	1.28069	+	0.376043i
$750$	−1.08626	+	2.37858i	−0.0396646	+	0.0868534i
$751$	−17.2615	−	11.0933i	−0.629881	−	0.404800i	0.186384	−	0.982477i	$-0.440323\pi$
$751$	−17.2615	−	11.0933i	−0.629881	−	0.404800i	−0.816266	+	0.577677i	$0.803959\pi$
$752$	−101.008	+	29.6587i	−3.68340	+	1.08154i
$753$	1.67105	−	11.6224i	0.0608964	−	0.423544i
$754$	−3.49279	−	7.64814i	−0.127200	−	0.278529i
$755$	0.574676	+	3.99696i	0.0209146	+	0.145464i
$756$	13.6656	−	8.78233i	0.497012	−	0.319410i
$757$	−13.0239	+	15.0304i	−0.473363	+	0.546290i	−0.941344	−	0.337449i	$-0.890436\pi$
$757$	−13.0239	+	15.0304i	−0.473363	+	0.546290i	0.467981	+	0.883738i	$0.344981\pi$
$758$	24.3792			0.885493
$759$	−18.1471	+	12.0616i	−0.658699	+	0.437807i
$760$	56.2414			2.04009
$761$	−10.8312	+	12.4999i	−0.392631	+	0.453120i	−0.917306	−	0.398182i	$-0.869641\pi$
$761$	−10.8312	+	12.4999i	−0.392631	+	0.453120i	0.524676	+	0.851302i	$0.324187\pi$
$762$	18.0876	−	11.6242i	0.655245	−	0.421100i
$763$	3.37667	+	23.4853i	0.122244	+	0.850224i
$764$	−23.1358	−	50.6603i	−0.837023	−	1.83282i
$765$	0.923869	−	6.42565i	0.0334025	−	0.232320i
$766$	−87.1917	+	25.6018i	−3.15036	+	0.925030i
$767$	22.6440	+	14.5524i	0.817629	+	0.525458i
$768$	−6.43686	+	14.0948i	−0.232270	+	0.508601i
$769$	19.3738	+	5.68867i	0.698638	+	0.205139i	0.611717	−	0.791077i	$-0.290479\pi$
$769$	19.3738	+	5.68867i	0.698638	+	0.205139i	0.0869209	+	0.996215i	$0.472297\pi$
$770$	−26.1254	−	30.1504i	−0.941495	−	1.08654i
$771$	−8.61823	−	9.94597i	−0.310378	−	0.358195i
$772$	−20.2569	−	5.94797i	−0.729063	−	0.214072i
$773$	21.1971	−	46.4152i	0.762407	−	1.66944i	0.0197132	−	0.999806i	$-0.493725\pi$
$773$	21.1971	−	46.4152i	0.762407	−	1.66944i	0.742693	−	0.669632i	$-0.233548\pi$
$774$	7.39733	+	4.75397i	0.265891	+	0.170878i
$775$	3.30483	−	0.970385i	0.118713	−	0.0348573i
$776$	−7.45712	+	51.8654i	−0.267695	+	1.86186i
$777$	5.42566	+	11.8805i	0.194644	+	0.426212i
$778$	−13.0767	−	90.9503i	−0.468822	−	3.26073i
$779$	−3.06346	+	1.96877i	−0.109760	+	0.0705384i
$780$	14.0300	−	16.1915i	0.502354	−	0.579747i
$781$	−23.7281			−0.849060
$782$	81.3999	−	1.25445i	2.91086	−	0.0448590i
$783$	−0.726038			−0.0259465
$784$	−27.2358	+	31.4318i	−0.972708	+	1.12256i
$785$	−7.74953	+	4.98032i	−0.276592	+	0.177755i
$786$	6.06165	+	42.1597i	0.216212	+	1.50379i
$787$	−7.95983	−	17.4296i	−0.283737	−	0.621298i	0.713074	−	0.701088i	$-0.247302\pi$
$787$	−7.95983	−	17.4296i	−0.283737	−	0.621298i	−0.996812	+	0.0797906i	$0.974575\pi$
$788$	3.98743	−	27.7332i	0.142046	−	0.987955i
$789$	−20.4860	+	6.01522i	−0.729319	+	0.214147i
$790$	−10.4482	−	6.71467i	−0.371731	−	0.238897i
$791$	7.21784	−	15.8049i	0.256637	−	0.561956i
$792$	32.3470	+	9.49794i	1.14940	+	0.337495i
$793$	3.97287	+	4.58494i	0.141081	+	0.162816i
$794$	49.0676	+	56.6270i	1.74134	+	2.00962i
$795$	10.9100	+	3.20346i	0.386937	+	0.113615i
$796$	28.2711	−	61.9051i	1.00204	−	2.19417i
$797$	20.9816	+	13.4841i	0.743207	+	0.477630i	0.856639	−	0.515916i	$-0.172548\pi$
$797$	20.9816	+	13.4841i	0.743207	+	0.477630i	−0.113433	+	0.993546i	$0.536185\pi$
$798$	63.8587	−	18.7506i	2.26057	−	0.663764i
$799$	−9.99868	+	69.5424i	−0.353728	+	2.46023i
$800$	4.40143	+	9.63779i	0.155614	+	0.340747i
$801$	0.318506	+	2.21526i	0.0112539	+	0.0782723i
$802$	46.6956	−	30.0094i	1.64888	−	1.05967i
$803$	−14.4507	+	16.6771i	−0.509956	+	0.588520i
$804$	−41.9931			−1.48098
$805$	−16.1022	+	0.248150i	−0.567527	+	0.00874612i
$806$	−39.8876			−1.40498
$807$	−9.48811	+	10.9499i	−0.333997	+	0.385454i
$808$	−58.9205	+	37.8659i	−2.07282	+	1.33212i
$809$	−4.53881	−	31.5681i	−0.159576	−	1.10988i	−0.899416	−	0.437094i	$-0.856008\pi$
$809$	−4.53881	−	31.5681i	−0.159576	−	1.10988i	0.739840	−	0.672783i	$-0.234901\pi$
$810$	−1.08626	−	2.37858i	−0.0381673	−	0.0835747i
$811$	−5.13286	+	35.6998i	−0.180239	+	1.25359i	0.675957	+	0.736941i	$0.263730\pi$
$811$	−5.13286	+	35.6998i	−0.180239	+	1.25359i	−0.856197	+	0.516650i	$0.827179\pi$
$812$	11.3162	−	3.32275i	0.397122	−	0.116606i
$813$	21.6216	+	13.8953i	0.758301	+	0.487331i
$814$	−19.1965	+	42.0346i	−0.672838	+	1.47331i
$815$	−15.2403	−	4.47495i	−0.533844	−	0.156751i
$816$	−41.3516	−	47.7223i	−1.44759	−	1.67061i
$817$	16.6917	+	19.2632i	0.583968	+	0.673935i
$818$	−69.3511	−	20.3633i	−2.42481	−	0.711987i
$819$	6.17779	−	13.5275i	0.215870	−	0.472688i
$820$	−1.95518	−	1.25652i	−0.0682778	−	0.0438795i
$821$	23.0051	−	6.75490i	0.802883	−	0.235748i	0.145553	−	0.989350i	$-0.453504\pi$
$821$	23.0051	−	6.75490i	0.802883	−	0.235748i	0.657330	+	0.753603i	$0.271686\pi$
$822$	0.281641	−	1.95885i	0.00982335	−	0.0683229i
$823$	−20.8794	−	45.7196i	−0.727812	−	1.59369i	−0.802622	−	0.596488i	$-0.796563\pi$
$823$	−20.8794	−	45.7196i	−0.727812	−	1.59369i	0.0748107	−	0.997198i	$-0.476165\pi$
$824$	15.5667	+	108.269i	0.542293	+	3.77173i
$825$	−3.82224	+	2.45641i	−0.133073	+	0.0855211i
$826$	−34.9478	+	40.3319i	−1.21599	+	1.40333i
$827$	22.6627			0.788061			0.394030	−	0.919097i	$-0.371080\pi$
$827$	22.6627			0.788061			0.394030	+	0.919097i	$0.371080\pi$
$828$	19.3217	−	12.8423i	0.671476	−	0.446300i
$829$	0.357249			0.0124078			0.00620388	−	0.999981i	$-0.498025\pi$
$829$	0.357249			0.0124078			0.00620388	+	0.999981i	$0.498025\pi$
$830$	0.222151	−	0.256376i	0.00771099	−	0.00889895i
$831$	−2.99796	+	1.92667i	−0.103998	+	0.0668355i
$832$	−5.20048	−	36.1701i	−0.180294	−	1.25397i
$833$	11.5306	+	25.2484i	0.399510	+	0.874806i
$834$	6.88658	−	47.8972i	0.238463	−	1.65855i
$835$	1.24985	−	0.366988i	0.0432527	−	0.0127002i
$836$	140.153	+	90.0707i	4.84729	+	3.11516i
$837$	−1.43083	+	3.13309i	−0.0494568	+	0.108295i
$838$	−2.12204	−	0.623086i	−0.0733046	−	0.0215242i
$839$	2.46412	+	2.84375i	0.0850709	+	0.0981771i	0.796689	−	0.604389i	$-0.206583\pi$
$839$	2.46412	+	2.84375i	0.0850709	+	0.0981771i	−0.711618	+	0.702566i	$0.752037\pi$
$840$	16.3163	+	18.8300i	0.562966	+	0.649698i
$841$	27.3195	+	8.02173i	0.942052	+	0.276612i
$842$	−12.9013	+	28.2500i	−0.444609	+	0.973558i
$843$	2.52053	+	1.61985i	0.0868118	+	0.0557905i
$844$	94.6110	−	27.7803i	3.25665	−	0.956238i
$845$	0.941220	−	6.54633i	0.0323790	−	0.225201i
$846$	11.7562	+	25.7424i	0.404186	+	0.885043i
$847$	−4.60845	−	32.0525i	−0.158348	−	1.10134i
$848$	93.0448	−	59.7963i	3.19517	−	2.05341i
$849$	19.6072	−	22.6280i	0.672919	−	0.776590i
$850$	16.9751			0.582240
$851$	8.00951	+	16.8465i	0.274563	+	0.577490i
$852$	25.2640			0.865530
$853$	−30.1104	+	34.7493i	−1.03096	+	1.18979i	−0.0493728	+	0.998780i	$0.515722\pi$
$853$	−30.1104	+	34.7493i	−1.03096	+	1.18979i	−0.981588	+	0.191012i	$0.938823\pi$
$854$	−10.1187	+	6.50292i	−0.346256	+	0.222525i
$855$	−1.07871	−	7.50260i	−0.0368911	−	0.256583i
$856$	−33.5315	−	73.4237i	−1.14608	−	2.50957i
$857$	−6.34036	+	44.0982i	−0.216583	+	1.50636i	0.533942	+	0.845521i	$0.320710\pi$
$857$	−6.34036	+	44.0982i	−0.216583	+	1.50636i	−0.750524	+	0.660843i	$0.770199\pi$
$858$	50.4852	−	14.8238i	1.72353	−	0.506075i
$859$	10.1776	+	6.54075i	0.347255	+	0.223167i	0.702628	−	0.711557i	$-0.252010\pi$
$859$	10.1776	+	6.54075i	0.347255	+	0.223167i	−0.355373	+	0.934725i	$0.615646\pi$
$860$	−6.75783	+	14.7976i	−0.230440	+	0.504594i
$861$	−1.54791	−	0.454506i	−0.0527525	−	0.0154895i
$862$	−13.2313	−	15.2697i	−0.450659	−	0.520088i
$863$	−16.1653	−	18.6557i	−0.550273	−	0.635049i	0.410674	−	0.911782i	$-0.365294\pi$
$863$	−16.1653	−	18.6557i	−0.550273	−	0.635049i	−0.960947	+	0.276733i	$0.910748\pi$
$864$	−10.1661	−	2.98503i	−0.345857	−	0.101553i
$865$	5.30823	−	11.6234i	0.180485	−	0.395208i
$866$	−86.0240	−	55.2843i	−2.92322	−	1.87864i
$867$	−24.1240	+	7.08346i	−0.819295	+	0.240567i
$868$	7.96266	−	55.3815i	0.270270	−	1.87977i
$869$	−8.96474	−	19.6300i	−0.304108	−	0.665904i
$870$	−0.270185	−	1.87918i	−0.00916013	−	0.0637101i
$871$	−32.3411	+	20.7844i	−1.09584	+	0.704252i
$872$	34.3334	−	39.6229i	1.16268	−	1.34180i
$873$	7.06187			0.239008
$874$	90.7801	−	28.1820i	3.07068	−	0.953270i
$875$	−3.35793			−0.113519
$876$	15.3861	−	17.7565i	0.519848	−	0.599936i
$877$	20.8903	−	13.4254i	0.705416	−	0.453343i	−0.138120	−	0.990415i	$-0.544106\pi$
$877$	20.8903	−	13.4254i	0.705416	−	0.453343i	0.843536	+	0.537072i	$0.180470\pi$
$878$	10.7585	+	74.8270i	0.363082	+	2.52529i
$879$	3.65669	+	8.00704i	0.123337	+	0.270071i
$880$	−6.28962	+	43.7453i	−0.212023	+	1.47465i
$881$	37.6745	−	11.0622i	1.26928	−	0.372696i	0.423342	−	0.905970i	$-0.360857\pi$
$881$	37.6745	−	11.0622i	1.26928	−	0.372696i	0.845942	+	0.533274i	$0.179039\pi$
$882$	9.40560	+	6.04462i	0.316703	+	0.203533i
$883$	5.02867	−	11.0113i	0.169228	−	0.370558i	−0.805949	−	0.591985i	$-0.798344\pi$
$883$	5.02867	−	11.0113i	0.169228	−	0.370558i	0.975177	+	0.221427i	$0.0710716\pi$
$884$	−133.447	−	39.1837i	−4.48832	−	1.31789i
$885$	3.98013	+	4.59331i	0.133790	+	0.154402i
$886$	−15.5433	−	17.9379i	−0.522186	−	0.602634i
$887$	−18.9571	−	5.56632i	−0.636518	−	0.186899i	−0.0524763	−	0.998622i	$-0.516711\pi$
$887$	−18.9571	−	5.56632i	−0.636518	−	0.186899i	−0.584042	+	0.811724i	$0.698530\pi$
$888$	11.9890	−	26.2522i	0.402323	−	0.880965i
$889$	23.2274	+	14.9274i	0.779024	+	0.500648i
$890$	−5.61514	+	1.64875i	−0.188220	+	0.0552664i
$891$	0.646608	−	4.49726i	0.0216622	−	0.150664i
$892$	−3.01853	−	6.60966i	−0.101068	−	0.221308i
$893$	11.6745	+	81.1978i	0.390672	+	2.71718i
$894$	−42.9876	+	27.6265i	−1.43772	+	0.923967i
$895$	0.0727959	−	0.0840110i	0.00243330	−	0.00280818i
$896$	1.29349			0.0432125
$897$	8.52443	−	19.4537i	0.284622	−	0.649541i
$898$	29.4802			0.983767
$899$	−1.63763	+	1.88992i	−0.0546180	+	0.0630325i
$900$	4.06964	−	2.61540i	0.135655	−	0.0871799i
$901$	−10.5049	−	73.0632i	−0.349969	−	2.43409i
$902$	−2.37113	−	5.19205i	−0.0789501	−	0.172877i
$903$	−1.60701	+	11.1770i	−0.0534779	+	0.371947i
$904$	−36.8380	+	10.8166i	−1.22521	+	0.359755i
$905$	−3.80972	−	2.44836i	−0.126639	−	0.0813863i
$906$	4.38639	−	9.60485i	0.145728	−	0.319100i
$907$	18.3791	+	5.39660i	0.610269	+	0.179191i	0.572241	−	0.820086i	$-0.306074\pi$
$907$	18.3791	+	5.39660i	0.610269	+	0.179191i	0.0380278	+	0.999277i	$0.487892\pi$
$908$	−47.5458	−	54.8707i	−1.57786	−	1.82095i
$909$	6.18141	+	7.13372i	0.205024	+	0.236611i
$910$	37.3116	+	10.9557i	1.23687	+	0.363178i
$911$	7.36503	−	16.1272i	0.244014	−	0.534317i	−0.747508	−	0.664253i	$-0.768750\pi$
$911$	7.36503	−	16.1272i	0.244014	−	0.534317i	0.991522	+	0.129936i	$0.0414771\pi$
$912$	−62.0247	−	39.8609i	−2.05384	−	1.31993i
$913$	0.565564	−	0.166064i	0.0187174	−	0.00549593i
$914$	4.87121	−	33.8800i	0.161125	−	1.12065i
$915$	0.569061	+	1.24607i	0.0188126	+	0.0411938i
$916$	−0.904950	−	6.29407i	−0.0299004	−	0.207962i
$917$	−46.0138	+	29.5713i	−1.51951	+	0.976530i
$918$	−11.1163	+	12.8289i	−0.366893	+	0.423417i
$919$	9.04286			0.298296			0.149148	−	0.988815i	$-0.452347\pi$
$919$	9.04286			0.298296			0.149148	+	0.988815i	$0.452347\pi$
$920$	23.7147	+	26.5310i	0.781852	+	0.874700i
$921$	−8.71593			−0.287200
$922$	−1.35968	+	1.56916i	−0.0447787	+	0.0516774i
$923$	19.4571	−	12.5043i	0.640439	−	0.411585i
$924$	10.5037	+	73.0548i	0.345546	+	2.40333i
$925$	1.61577	+	3.53805i	0.0531263	+	0.116330i
$926$	15.5348	−	108.047i	0.510506	−	3.55065i
$927$	14.1445	−	4.15321i	0.464567	−	0.136409i
$928$	−6.47140	−	4.15892i	−0.212434	−	0.136523i
$929$	0.713917	−	1.56326i	0.0234229	−	0.0512889i	−0.897559	−	0.440894i	$-0.854661\pi$
$929$	0.713917	−	1.56326i	0.0234229	−	0.0512889i	0.920982	+	0.389605i	$0.127389\pi$
$930$	−8.64172	−	2.53744i	−0.283373	−	0.0832059i
$931$	21.2233	+	24.4929i	0.695564	+	0.802724i
$932$	52.7887	+	60.9215i	1.72915	+	1.99555i
$933$	24.1714	+	7.09736i	0.791336	+	0.232357i
$934$	−41.8570	+	91.6539i	−1.36960	+	2.99901i
$935$	24.8129	+	15.9463i	0.811470	+	0.521500i
$936$	−31.5299	+	9.25800i	−1.03059	+	0.302607i
$937$	6.23427	−	43.3603i	0.203665	−	1.41652i	−0.589626	−	0.807676i	$-0.700725\pi$
$937$	6.23427	−	43.3603i	0.203665	−	1.41652i	0.793291	−	0.608843i	$-0.208366\pi$
$938$	−31.6632	−	69.3327i	−1.03384	−	2.26379i
$939$	1.00218	+	6.97034i	0.0327050	+	0.227468i
$940$	−44.0442	+	28.3055i	−1.43656	+	0.923223i
$941$	−27.9470	+	32.2526i	−0.911048	+	1.05141i	0.0874258	+	0.996171i	$0.472136\pi$
$941$	−27.9470	+	32.2526i	−0.911048	+	1.05141i	−0.998473	+	0.0552340i	$0.982410\pi$
$942$	24.0879			0.784828
$943$	−2.22047	−	0.614988i	−0.0723086	−	0.0200268i
$944$	59.1195			1.92418
$945$	2.19898	−	2.53776i	0.0715328	−	0.0825532i
$946$	−33.6098	+	21.5997i	−1.09275	+	0.702267i
$947$	−0.866591	−	6.02727i	−0.0281604	−	0.195860i	0.970885	−	0.239547i	$-0.0769988\pi$
$947$	−0.866591	−	6.02727i	−0.0281604	−	0.195860i	−0.999045	+	0.0436866i	$0.986090\pi$
$948$	9.54499	+	20.9006i	0.310007	+	0.678821i
$949$	3.06111	−	21.2905i	0.0993680	−	0.691119i
$950$	19.0173	−	5.58397i	0.617002	−	0.181168i
$951$	7.42248	+	4.77014i	0.240691	+	0.154682i
$952$	67.1917	−	147.129i	2.17769	−	4.76848i
$953$	−48.0173	−	14.0991i	−1.55543	−	0.456716i	−0.612714	−	0.790305i	$-0.709922\pi$
$953$	−48.0173	−	14.0991i	−1.55543	−	0.456716i	−0.942719	+	0.333589i	$0.891740\pi$
$954$	−19.4707	−	22.4704i	−0.630389	−	0.727507i
$955$	−7.53914	−	8.70063i	−0.243961	−	0.281546i
$956$	−127.792	−	37.5231i	−4.13309	−	1.21358i
$957$	1.37035	−	3.00066i	0.0442973	−	0.0969975i
$958$	−5.64035	−	3.62483i	−0.182231	−	0.117113i
$959$	2.43841	−	0.715983i	0.0787405	−	0.0231203i
$960$	1.17426	−	8.16716i	0.0378991	−	0.263594i
$961$	−7.94958	−	17.4071i	−0.256438	−	0.561521i
$962$	−6.41031	−	44.5847i	−0.206677	−	1.43747i
$963$	−9.15159	+	5.88137i	−0.294906	+	0.189524i
$964$	−27.9051	+	32.2042i	−0.898763	+	1.03723i
$965$	−4.36418			−0.140488
$966$	35.7720	+	22.2179i	1.15094	+	0.714850i
$967$	−38.7437			−1.24591			−0.622956	−	0.782257i	$-0.714068\pi$
$967$	−38.7437			−1.24591			−0.622956	+	0.782257i	$0.714068\pi$
$968$	−46.8579	+	54.0769i	−1.50607	+	1.73810i
$969$	−41.3944	+	26.6026i	−1.32978	+	0.854598i
$970$	2.62798	+	18.2780i	0.0843792	+	0.586870i
$971$	−10.6638	−	23.3505i	−0.342218	−	0.749354i	0.657774	−	0.753215i	$-0.271498\pi$
$971$	−10.6638	−	23.3505i	−0.342218	−	0.749354i	−0.999993	+	0.00386144i	$0.998771\pi$
$972$	−0.688461	+	4.78835i	−0.0220824	+	0.153586i
$973$	59.6233	−	17.5070i	1.91143	−	0.561248i
$974$	−39.5230	−	25.3999i	−1.26640	−	0.813866i
$975$	1.83976	−	4.02851i	0.0589195	−	0.129016i
$976$	12.7850	+	3.75402i	0.409238	+	0.120163i
$977$	32.4951	+	37.5014i	1.03961	+	1.19977i	0.979471	+	0.201585i	$0.0646092\pi$
$977$	32.4951	+	37.5014i	1.03961	+	1.19977i	0.0601397	+	0.998190i	$0.480845\pi$
$978$	27.1989	+	31.3893i	0.869726	+	1.00372i
$979$	−9.75664	−	2.86481i	−0.311824	−	0.0915597i
$980$	−8.59250	+	18.8149i	−0.274477	+	0.601022i
$981$	−5.94420	−	3.82011i	−0.189784	−	0.121967i
$982$	37.3107	−	10.9554i	1.19063	−	0.349601i
$983$	1.48433	−	10.3237i	0.0473427	−	0.329276i	−0.952362	−	0.304970i	$-0.901353\pi$
$983$	1.48433	−	10.3237i	0.0473427	−	0.329276i	0.999705	−	0.0243054i	$-0.00773742\pi$
$984$	1.48086	+	3.24263i	0.0472081	+	0.103371i
$985$	−0.824260	−	5.73286i	−0.0262631	−	0.182664i
$986$	−10.3681	+	6.66316i	−0.330187	+	0.212198i
$987$	−23.7987	+	27.4652i	−0.757521	+	0.874226i
$988$	−162.391			−5.16636
$989$	−2.04890	+	15.9966i	−0.0651511	+	0.508661i
$990$	11.8807			0.377594
$991$	9.78359	−	11.2909i	0.310786	−	0.358666i	−0.578771	−	0.815490i	$-0.696468\pi$
$991$	9.78359	−	11.2909i	0.310786	−	0.358666i	0.889557	+	0.456824i	$0.151013\pi$
$992$	−30.7005	+	19.7300i	−0.974742	+	0.626429i
$993$	2.98765	+	20.7795i	0.0948101	+	0.659418i
$994$	19.0493	+	41.7121i	0.604206	+	1.32303i
$995$	2.00208	−	13.9248i	0.0634702	−	0.441445i
$996$	−0.602170	+	0.176813i	−0.0190805	+	0.00560254i
$997$	−26.6800	−	17.1462i	−0.844964	−	0.543025i	0.0450363	−	0.998985i	$-0.485660\pi$
$997$	−26.6800	−	17.1462i	−0.844964	−	0.543025i	−0.890000	+	0.455960i	$0.849296\pi$
$998$	−39.9832	+	87.5511i	−1.26565	+	2.77138i
$999$	−3.73199	−	1.09581i	−0.118075	−	0.0346699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.c.16.1	✓	50
23.6	even	11		7935.2.a.bv.1.23		25
23.13	even	11	inner	345.2.m.c.151.1	yes	50
23.17	odd	22		7935.2.a.bw.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.16.1	✓	50	1.1	even	1	trivial
345.2.m.c.151.1	yes	50	23.13	even	11	inner
7935.2.a.bv.1.23		25	23.6	even	11
7935.2.a.bw.1.23		25	23.17	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71238 + 1.97619i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.688461 - 4.78835i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.372136 + 2.58826i) q^{6} +(-3.22191 + 0.946039i) q^{7} +(6.24206 + 4.01153i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.71238 + 1.97619i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.688461 - 4.78835i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.372136 + 2.58826i) q^{6} +(-3.22191 + 0.946039i) q^{7} +(6.24206 + 4.01153i) q^{8} +(0.415415 - 0.909632i) q^{9} +(2.50896 + 0.736696i) q^{10} +(2.97536 + 3.43375i) q^{11} +(-3.16795 - 3.65601i) q^{12} +(-4.24933 - 1.24772i) q^{13} +(3.64759 - 7.98710i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-9.33308 + 2.74044i) q^{16} +(-0.923869 + 6.42565i) q^{17} +(1.08626 + 2.37858i) q^{18} +(1.07871 + 7.50260i) q^{19} +(-4.06964 + 2.61540i) q^{20} +(-2.19898 + 2.53776i) q^{21} -11.8807 q^{22} +(-3.08438 + 3.67241i) q^{23} +7.41995 q^{24} +(-0.654861 + 0.755750i) q^{25} +(9.74221 - 6.26094i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(6.74813 + 14.7763i) q^{28} +(0.103326 - 0.718648i) q^{29} +(2.50896 - 0.736696i) q^{30} +(-2.89757 - 1.86215i) q^{31} +(4.40143 - 9.63779i) q^{32} +(4.35946 + 1.28005i) q^{33} +(-11.1163 - 12.8289i) q^{34} +(2.19898 + 2.53776i) q^{35} +(-4.64163 - 1.36291i) q^{36} +(1.61577 - 3.53805i) q^{37} +(-16.6737 - 10.7156i) q^{38} +(-4.24933 + 1.24772i) q^{39} +(1.05597 - 7.34443i) q^{40} +(0.199578 + 0.437015i) q^{41} +(-1.24961 - 8.69121i) q^{42} +(2.82894 - 1.81805i) q^{43} +(14.3936 - 16.6111i) q^{44} -1.00000 q^{45} +(-1.97576 - 12.3839i) q^{46} +10.8226 q^{47} +(-6.36989 + 7.35125i) q^{48} +(3.59696 - 2.31162i) q^{49} +(-0.372136 - 2.58826i) q^{50} +(2.69676 + 5.90508i) q^{51} +(-3.04901 + 21.2063i) q^{52} +(-10.9100 + 3.20346i) q^{53} +(2.19978 + 1.41371i) q^{54} +(1.88744 - 4.13292i) q^{55} +(-23.9064 - 7.01956i) q^{56} +(4.96368 + 5.72839i) q^{57} +(1.24325 + 1.43479i) q^{58} +(-5.83162 - 1.71232i) q^{59} +(-2.00961 + 4.40043i) q^{60} +(-1.15240 - 0.740602i) q^{61} +(8.64172 - 2.53744i) q^{62} +(-0.477884 + 3.32375i) q^{63} +(3.42765 + 7.50550i) q^{64} +(0.630274 + 4.38365i) q^{65} +(-9.99470 + 6.42320i) q^{66} +(5.68458 - 6.56035i) q^{67} +31.4043 q^{68} +(-0.609290 + 4.75697i) q^{69} -8.78059 q^{70} +(-3.41996 + 3.94685i) q^{71} +(6.24206 - 4.01153i) q^{72} +(0.691195 + 4.80736i) q^{73} +(4.22505 + 9.25157i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(35.1824 - 10.3305i) q^{76} +(-12.8348 - 8.24844i) q^{77} +(4.81075 - 10.5341i) q^{78} +(-4.55729 - 1.33814i) q^{79} +(6.36989 + 7.35125i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.20538 - 0.353932i) q^{82} +(0.0538928 - 0.118009i) q^{83} +(13.6656 + 8.78233i) q^{84} +(6.22876 - 1.82893i) q^{85} +(-1.25141 + 8.70372i) q^{86} +(-0.301607 - 0.660428i) q^{87} +(4.79780 + 33.3695i) q^{88} +(-1.88276 + 1.20997i) q^{89} +(1.71238 - 1.97619i) q^{90} +14.8714 q^{91} +(19.7083 + 12.2408i) q^{92} -3.44435 q^{93} +(-18.5325 + 21.3876i) q^{94} +(6.37649 - 4.09792i) q^{95} +(-1.50786 - 10.4874i) q^{96} +(2.93361 + 6.42370i) q^{97} +(-1.59115 + 11.0667i) q^{98} +(4.35946 - 1.28005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more