LMFDB - Embedded newform 280.2.br.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.br (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	280.67
Dual form			280.2.br.a.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41382 - 0.0333641i) q^{2} +(0.388267 + 1.44903i) q^{3} +(1.99777 + 0.0943417i) q^{4} +(2.17362 - 0.524773i) q^{5} +(-0.500594 - 2.06162i) q^{6} +(2.60799 - 0.445401i) q^{7} +(-2.82134 - 0.200036i) q^{8} +(0.649136 - 0.374779i) q^{9} +O(q^{10})$	\(q+(-1.41382 - 0.0333641i) q^{2} +(0.388267 + 1.44903i) q^{3} +(1.99777 + 0.0943417i) q^{4} +(2.17362 - 0.524773i) q^{5} +(-0.500594 - 2.06162i) q^{6} +(2.60799 - 0.445401i) q^{7} +(-2.82134 - 0.200036i) q^{8} +(0.649136 - 0.374779i) q^{9} +(-3.09061 + 0.669413i) q^{10} +(1.03683 - 1.79585i) q^{11} +(0.638965 + 2.93147i) q^{12} +(-3.78195 - 3.78195i) q^{13} +(-3.70209 + 0.542703i) q^{14} +(1.60436 + 2.94589i) q^{15} +(3.98220 + 0.376947i) q^{16} +(-1.65553 + 0.443598i) q^{17} +(-0.930265 + 0.508212i) q^{18} +(1.96616 - 1.13516i) q^{19} +(4.39190 - 0.843314i) q^{20} +(1.65800 + 3.60613i) q^{21} +(-1.52581 + 2.50441i) q^{22} +(-1.79446 + 6.69701i) q^{23} +(-0.805576 - 4.16588i) q^{24} +(4.44923 - 2.28131i) q^{25} +(5.22082 + 5.47318i) q^{26} +(3.97740 + 3.97740i) q^{27} +(5.25220 - 0.643768i) q^{28} -8.01124 q^{29} +(-2.16998 - 4.21848i) q^{30} +(3.76977 + 2.17648i) q^{31} +(-5.61754 - 0.665798i) q^{32} +(3.00481 + 0.805136i) q^{33} +(2.35542 - 0.571932i) q^{34} +(5.43504 - 2.33673i) q^{35} +(1.33218 - 0.687482i) q^{36} +(3.81608 + 1.02252i) q^{37} +(-2.81766 + 1.53931i) q^{38} +(4.01176 - 6.94858i) q^{39} +(-6.23750 + 1.04576i) q^{40} -1.76232 q^{41} +(-2.22379 - 5.15373i) q^{42} +(-7.50054 + 7.50054i) q^{43} +(2.24078 - 3.48988i) q^{44} +(1.21430 - 1.15527i) q^{45} +(2.76048 - 9.40850i) q^{46} +(1.06992 + 0.286684i) q^{47} +(0.999948 + 5.91669i) q^{48} +(6.60324 - 2.32320i) q^{49} +(-6.36652 + 3.07692i) q^{50} +(-1.28557 - 2.22668i) q^{51} +(-7.19869 - 7.91228i) q^{52} +(-8.24761 + 2.20994i) q^{53} +(-5.49062 - 5.75603i) q^{54} +(1.31127 - 4.44759i) q^{55} +(-7.44714 + 0.734937i) q^{56} +(2.40828 + 2.40828i) q^{57} +(11.3265 + 0.267288i) q^{58} +(-8.33605 - 4.81282i) q^{59} +(2.92722 + 6.03658i) q^{60} +(-7.39983 + 4.27229i) q^{61} +(-5.25716 - 3.20292i) q^{62} +(1.52601 - 1.26655i) q^{63} +(7.91997 + 1.12874i) q^{64} +(-10.2052 - 6.23586i) q^{65} +(-4.22140 - 1.23857i) q^{66} +(-3.23533 + 0.866905i) q^{67} +(-3.34922 + 0.730022i) q^{68} -10.4009 q^{69} +(-7.76213 + 3.12238i) q^{70} +5.34585i q^{71} +(-1.90640 + 0.927529i) q^{72} +(-0.151531 - 0.565523i) q^{73} +(-5.36113 - 1.57297i) q^{74} +(5.03318 + 5.56131i) q^{75} +(4.03503 - 2.08230i) q^{76} +(1.90418 - 5.14536i) q^{77} +(-5.90374 + 9.69019i) q^{78} +(3.44100 + 5.95998i) q^{79} +(8.85359 - 1.27041i) q^{80} +(-3.09475 + 5.36026i) q^{81} +(2.49160 + 0.0587983i) q^{82} +(9.12181 - 9.12181i) q^{83} +(2.97209 + 7.36064i) q^{84} +(-3.36570 + 1.83299i) q^{85} +(10.8547 - 10.3542i) q^{86} +(-3.11050 - 11.6085i) q^{87} +(-3.28450 + 4.85930i) q^{88} +(-6.29757 + 3.63590i) q^{89} +(-1.75535 + 1.59284i) q^{90} +(-11.5478 - 8.17882i) q^{91} +(-4.21673 + 13.2098i) q^{92} +(-1.69011 + 6.30756i) q^{93} +(-1.50311 - 0.441017i) q^{94} +(3.67797 - 3.49919i) q^{95} +(-1.21634 - 8.39849i) q^{96} +(-10.7087 - 10.7087i) q^{97} +(-9.41330 + 3.06428i) q^{98} -1.55433i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.41382	−	0.0333641i	−0.999722	−	0.0235920i
$2$	−1.41382	−	0.0333641i	−0.999722	−	0.0235920i
$3$	0.388267	+	1.44903i	0.224166	+	0.836599i	0.982737	+	0.185008i	$0.0592312\pi$
$3$	0.388267	+	1.44903i	0.224166	+	0.836599i	−0.758571	+	0.651590i	$0.774102\pi$
$4$	1.99777	+	0.0943417i	0.998887	+	0.0471709i
$5$	2.17362	−	0.524773i	0.972071	−	0.234685i
$5$	2.17362	−	0.524773i	0.972071	−	0.234685i
$6$	−0.500594	−	2.06162i	−0.204366	−	0.841654i
$7$	2.60799	−	0.445401i	0.985728	−	0.168346i
$7$	2.60799	−	0.445401i	0.985728	−	0.168346i
$8$	−2.82134	−	0.200036i	−0.997496	−	0.0707235i
$9$	0.649136	−	0.374779i	0.216379	−	0.124926i
$10$	−3.09061	+	0.669413i	−0.977338	+	0.211687i
$11$	1.03683	−	1.79585i	0.312617	−	0.541469i	−0.666311	−	0.745674i	$-0.732128\pi$
$11$	1.03683	−	1.79585i	0.312617	−	0.541469i	0.978928	+	0.204205i	$0.0654610\pi$
$12$	0.638965	+	2.93147i	0.184453	+	0.846241i
$13$	−3.78195	−	3.78195i	−1.04893	−	1.04893i	−0.998740	−	0.0501853i	$-0.984019\pi$
$13$	−3.78195	−	3.78195i	−1.04893	−	1.04893i	−0.0501853	−	0.998740i	$-0.515981\pi$
$14$	−3.70209	+	0.542703i	−0.989425	+	0.145044i
$15$	1.60436	+	2.94589i	0.414243	+	0.760625i
$16$	3.98220	+	0.376947i	0.995550	+	0.0942367i
$17$	−1.65553	+	0.443598i	−0.401525	+	0.107588i	−0.453929	−	0.891038i	$-0.649978\pi$
$17$	−1.65553	+	0.443598i	−0.401525	+	0.107588i	0.0524045	+	0.998626i	$0.483311\pi$
$18$	−0.930265	+	0.508212i	−0.219266	+	0.119787i
$19$	1.96616	−	1.13516i	0.451067	−	0.260424i	−0.257214	−	0.966355i	$-0.582804\pi$
$19$	1.96616	−	1.13516i	0.451067	−	0.260424i	0.708281	+	0.705931i	$0.249471\pi$
$20$	4.39190	−	0.843314i	0.982060	−	0.188571i
$21$	1.65800	+	3.60613i	0.361804	+	0.786921i
$22$	−1.52581	+	2.50441i	−0.325304	+	0.533943i
$23$	−1.79446	+	6.69701i	−0.374170	+	1.39642i	0.480383	+	0.877059i	$0.340498\pi$
$23$	−1.79446	+	6.69701i	−0.374170	+	1.39642i	−0.854553	+	0.519364i	$0.826169\pi$
$24$	−0.805576	−	4.16588i	−0.164437	−	0.850358i
$25$	4.44923	−	2.28131i	0.889845	−	0.456262i
$26$	5.22082	+	5.47318i	1.02389	+	1.07338i
$27$	3.97740	+	3.97740i	0.765450	+	0.765450i
$28$	5.25220	−	0.643768i	0.992572	−	0.121661i
$29$	−8.01124			−1.48765			−0.743825	−	0.668375i	$-0.766990\pi$
$29$	−8.01124			−1.48765			−0.743825	+	0.668375i	$0.766990\pi$
$30$	−2.16998	−	4.21848i	−0.396183	−	0.770186i
$31$	3.76977	+	2.17648i	0.677070	+	0.390907i	0.798750	−	0.601663i	$-0.205495\pi$
$31$	3.76977	+	2.17648i	0.677070	+	0.390907i	−0.121680	+	0.992569i	$0.538828\pi$
$32$	−5.61754	−	0.665798i	−0.993049	−	0.117697i
$33$	3.00481	+	0.805136i	0.523070	+	0.140156i
$34$	2.35542	−	0.571932i	0.403951	−	0.0980855i
$35$	5.43504	−	2.33673i	0.918690	−	0.394980i
$36$	1.33218	−	0.687482i	0.222031	−	0.114580i
$37$	3.81608	+	1.02252i	0.627359	+	0.168100i	0.558471	−	0.829524i	$-0.311388\pi$
$37$	3.81608	+	1.02252i	0.627359	+	0.168100i	0.0688883	+	0.997624i	$0.478055\pi$
$38$	−2.81766	+	1.53931i	−0.457086	+	0.249710i
$39$	4.01176	−	6.94858i	0.642396	−	1.11266i
$40$	−6.23750	+	1.04576i	−0.986235	+	0.165350i
$41$	−1.76232			−0.275228			−0.137614	−	0.990486i	$-0.543943\pi$
$41$	−1.76232			−0.275228			−0.137614	+	0.990486i	$0.543943\pi$
$42$	−2.22379	−	5.15373i	−0.343139	−	0.795238i
$43$	−7.50054	+	7.50054i	−1.14382	+	1.14382i	−0.156077	+	0.987745i	$0.549885\pi$
$43$	−7.50054	+	7.50054i	−1.14382	+	1.14382i	−0.987745	+	0.156077i	$0.950115\pi$
$44$	2.24078	−	3.48988i	0.337811	−	0.526119i
$45$	1.21430	−	1.15527i	0.181017	−	0.172218i
$46$	2.76048	−	9.40850i	0.407011	−	1.38721i
$47$	1.06992	+	0.286684i	0.156064	+	0.0418172i	0.336005	−	0.941860i	$-0.390924\pi$
$47$	1.06992	+	0.286684i	0.156064	+	0.0418172i	−0.179941	+	0.983677i	$0.557591\pi$
$48$	0.999948	+	5.91669i	0.144330	+	0.854000i
$49$	6.60324	−	2.32320i	0.943319	−	0.331886i
$50$	−6.36652	+	3.07692i	−0.900362	+	0.435142i
$51$	−1.28557	−	2.22668i	−0.180016	−	0.311797i
$52$	−7.19869	−	7.91228i	−0.998279	−	1.09724i
$53$	−8.24761	+	2.20994i	−1.13290	+	0.303559i	−0.776091	−	0.630620i	$-0.782800\pi$
$53$	−8.24761	+	2.20994i	−1.13290	+	0.303559i	−0.356805	+	0.934179i	$0.616134\pi$
$54$	−5.49062	−	5.75603i	−0.747179	−	0.783296i
$55$	1.31127	−	4.44759i	0.176811	−	0.599713i
$56$	−7.44714	+	0.734937i	−0.995166	+	0.0982100i
$57$	2.40828	+	2.40828i	0.318984	+	0.318984i
$58$	11.3265	+	0.267288i	1.48724	+	0.0350966i
$59$	−8.33605	−	4.81282i	−1.08526	−	0.626576i	−0.152951	−	0.988234i	$-0.548878\pi$
$59$	−8.33605	−	4.81282i	−1.08526	−	0.626576i	−0.932311	+	0.361658i	$0.882211\pi$
$60$	2.92722	+	6.03658i	0.377902	+	0.779319i
$61$	−7.39983	+	4.27229i	−0.947451	+	0.547011i	−0.892288	−	0.451466i	$-0.850901\pi$
$61$	−7.39983	+	4.27229i	−0.947451	+	0.547011i	−0.0551627	+	0.998477i	$0.517568\pi$
$62$	−5.25716	−	3.20292i	−0.667660	−	0.406771i
$63$	1.52601	−	1.26655i	0.192260	−	0.159570i
$64$	7.91997	+	1.12874i	0.989996	+	0.141093i
$65$	−10.2052	−	6.23586i	−1.26580	−	0.773463i
$66$	−4.22140	−	1.23857i	−0.519618	−	0.152457i
$67$	−3.23533	+	0.866905i	−0.395259	+	0.105909i	−0.450973	−	0.892537i	$-0.648923\pi$
$67$	−3.23533	+	0.866905i	−0.395259	+	0.105909i	0.0557143	+	0.998447i	$0.482256\pi$
$68$	−3.34922	+	0.730022i	−0.406153	+	0.0885282i
$69$	−10.4009			−1.25212
$70$	−7.76213	+	3.12238i	−0.927752	+	0.373196i
$71$			5.34585i			0.634435i	0.948353	+	0.317218i	$0.102749\pi$
$71$			5.34585i			0.634435i	−0.948353	+	0.317218i	$0.897251\pi$
$72$	−1.90640	+	0.927529i	−0.224672	+	0.109310i
$73$	−0.151531	−	0.565523i	−0.0177354	−	0.0661894i	0.956491	−	0.291762i	$-0.0942415\pi$
$73$	−0.151531	−	0.565523i	−0.0177354	−	0.0661894i	−0.974226	+	0.225572i	$0.927575\pi$
$74$	−5.36113	−	1.57297i	−0.623219	−	0.182854i
$75$	5.03318	+	5.56131i	0.581181	+	0.642165i
$76$	4.03503	−	2.08230i	0.462849	−	0.238857i
$77$	1.90418	−	5.14536i	0.217001	−	0.586369i
$78$	−5.90374	+	9.69019i	−0.668467	+	1.09720i
$79$	3.44100	+	5.95998i	0.387143	+	0.670551i	0.992064	−	0.125735i	$-0.0401288\pi$
$79$	3.44100	+	5.95998i	0.387143	+	0.670551i	−0.604921	+	0.796285i	$0.706795\pi$
$80$	8.85359	−	1.27041i	0.989861	−	0.142036i
$81$	−3.09475	+	5.36026i	−0.343861	+	0.595584i
$82$	2.49160	+	0.0587983i	0.275152	+	0.00649319i
$83$	9.12181	−	9.12181i	1.00125	−	1.00125i	0.00124987	−	0.999999i	$-0.499602\pi$
$83$	9.12181	−	9.12181i	1.00125	−	1.00125i	0.999999	−	0.00124987i	$-0.000397847\pi$
$84$	2.97209	+	7.36064i	0.324282	+	0.803112i
$85$	−3.36570	+	1.83299i	−0.365061	+	0.198815i
$86$	10.8547	−	10.3542i	1.17049	−	1.11652i
$87$	−3.11050	−	11.6085i	−0.333480	−	1.24457i
$88$	−3.28450	+	4.85930i	−0.350129	+	0.518003i
$89$	−6.29757	+	3.63590i	−0.667541	+	0.385405i	−0.795144	−	0.606420i	$-0.792605\pi$
$89$	−6.29757	+	3.63590i	−0.667541	+	0.385405i	0.127603	+	0.991825i	$0.459272\pi$
$90$	−1.75535	+	1.59284i	−0.185030	+	0.167900i
$91$	−11.5478	−	8.17882i	−1.21054	−	0.857373i
$92$	−4.21673	+	13.2098i	−0.439624	+	1.37722i
$93$	−1.69011	+	6.30756i	−0.175256	+	0.654064i
$94$	−1.50311	−	0.441017i	−0.155034	−	0.0454874i
$95$	3.67797	−	3.49919i	0.377352	−	0.359009i
$96$	−1.21634	−	8.39849i	−0.124142	−	0.857168i
$97$	−10.7087	−	10.7087i	−1.08731	−	1.08731i	−0.995805	−	0.0915005i	$-0.970834\pi$
$97$	−10.7087	−	10.7087i	−1.08731	−	1.08731i	−0.0915005	−	0.995805i	$-0.529166\pi$
$98$	−9.41330	+	3.06428i	−0.950887	+	0.309539i
$99$		−	1.55433i		−	0.156216i
$100$	9.10377	−	4.13779i	0.910377	−	0.413779i
$101$	5.95456	+	3.43786i	0.592500	+	0.342080i	0.766086	−	0.642739i	$-0.222202\pi$
$101$	5.95456	+	3.43786i	0.592500	+	0.342080i	−0.173585	+	0.984819i	$0.555535\pi$
$102$	1.74328	+	3.19102i	0.172610	+	0.315958i
$103$	2.99987	−	11.1957i	0.295586	−	1.10314i	−0.645164	−	0.764044i	$-0.723211\pi$
$103$	2.99987	−	11.1957i	0.295586	−	1.10314i	0.940751	−	0.339099i	$-0.110122\pi$
$104$	9.91367	+	11.4267i	0.972115	+	1.12048i
$105$	5.49625	+	6.96827i	0.536379	+	0.680033i
$106$	11.7344	−	2.84928i	1.13974	−	0.276747i
$107$	−2.35888	+	8.80346i	−0.228042	+	0.851063i	0.753122	+	0.657881i	$0.228547\pi$
$107$	−2.35888	+	8.80346i	−0.228042	+	0.851063i	−0.981163	+	0.193181i	$0.938119\pi$
$108$	7.57071	+	8.32117i	0.728491	+	0.800705i
$109$	5.94516	−	10.2973i	0.569443	−	0.986304i	−0.427178	−	0.904167i	$-0.640492\pi$
$109$	5.94516	−	10.2973i	0.569443	−	0.986304i	0.996621	−	0.0821366i	$-0.0261744\pi$
$110$	−2.00229	+	6.24434i	−0.190910	+	0.595375i
$111$			5.92663i			0.562530i
$112$	10.5534	−	0.790601i	0.997206	−	0.0747048i
$113$	12.1159	−	12.1159i	1.13976	−	1.13976i	0.151272	−	0.988492i	$-0.451663\pi$
$113$	12.1159	−	12.1159i	1.13976	−	1.13976i	0.988492	−	0.151272i	$-0.0483369\pi$
$114$	−3.32452	−	3.48522i	−0.311370	−	0.326421i
$115$	−0.386059	+	15.4984i	−0.0360002	+	1.44524i
$116$	−16.0046	−	0.755794i	−1.48599	−	0.0701737i
$117$	−3.87240	−	1.03761i	−0.358003	−	0.0959267i
$118$	11.6251	+	7.08259i	1.07018	+	0.652005i
$119$	−4.12003	+	1.89427i	−0.377682	+	0.173648i
$120$	−3.93716	−	8.63229i	−0.359411	−	0.788017i
$121$	3.34995	+	5.80229i	0.304541	+	0.527481i
$122$	10.6046	−	5.79336i	0.960092	−	0.524506i
$123$	−0.684251	−	2.55366i	−0.0616968	−	0.230256i
$124$	7.32581	+	4.70375i	0.657877	+	0.422410i
$125$	8.47375	−	7.29353i	0.757915	−	0.652353i
$126$	−2.19977	+	1.73975i	−0.195971	+	0.154989i
$127$	3.12715	−	3.12715i	0.277490	−	0.277490i	−0.554616	−	0.832106i	$-0.687135\pi$
$127$	3.12715	−	3.12715i	0.277490	−	0.277490i	0.832106	+	0.554616i	$0.187135\pi$
$128$	−11.1598	−	1.86008i	−0.986392	−	0.164409i
$129$	−13.7807	−	7.95631i	−1.21333	−	0.700514i
$130$	14.2202	+	9.15686i	1.24720	+	0.803110i
$131$	−1.04516	−	1.81027i	−0.0913159	−	0.158164i	0.816749	−	0.576993i	$-0.195774\pi$
$131$	−1.04516	−	1.81027i	−0.0913159	−	0.158164i	−0.908065	+	0.418829i	$0.862441\pi$
$132$	5.92697	+	1.89196i	0.515876	+	0.164674i
$133$	4.62212	−	3.83622i	0.400788	−	0.332642i
$134$	4.60310	−	1.11770i	0.397648	−	0.0965549i
$135$	10.7326	+	6.55811i	0.923713	+	0.564432i
$136$	4.75955	−	0.920376i	0.408128	−	0.0789216i
$137$	−0.0139394	+	0.00373506i	−0.00119093	+	0.000319108i	−0.259414	−	0.965766i	$-0.583530\pi$
$137$	−0.0139394	+	0.00373506i	−0.00119093	+	0.000319108i	0.258224	+	0.966085i	$0.416863\pi$
$138$	14.7050	+	0.347017i	1.25177	+	0.0295401i
$139$		−	2.69071i		−	0.228223i	−0.993468	−	0.114112i	$-0.963598\pi$
$139$		−	2.69071i		−	0.228223i	0.993468	−	0.114112i	$-0.0364021\pi$
$140$	11.0784	−	4.15551i	0.936299	−	0.351205i
$141$			1.66166i			0.139937i
$142$	0.178360	−	7.55807i	0.0149676	−	0.634259i
$143$	−10.7131	+	2.87056i	−0.895872	+	0.240048i
$144$	2.72626	−	1.24775i	0.227188	−	0.103979i
$145$	−17.4134	+	4.20408i	−1.44610	+	0.349130i
$146$	0.195370	+	0.804603i	0.0161689	+	0.0665894i
$147$	5.93021	+	8.66627i	0.489116	+	0.714782i
$148$	7.52720	+	2.40277i	0.618732	+	0.197506i
$149$	6.00081	+	10.3937i	0.491605	+	0.851485i	0.999953	−	0.00966656i	$-0.00307701\pi$
$149$	6.00081	+	10.3937i	0.491605	+	0.851485i	−0.508348	+	0.861152i	$0.669744\pi$
$150$	−6.93046	−	8.03062i	−0.565869	−	0.655698i
$151$	0.148194	+	0.0855599i	0.0120599	+	0.00696277i	0.506018	−	0.862523i	$-0.331117\pi$
$151$	0.148194	+	0.0855599i	0.0120599	+	0.00696277i	−0.493958	+	0.869486i	$0.664450\pi$
$152$	−5.77428	+	2.80938i	−0.468356	+	0.227871i
$153$	−0.908412	+	0.908412i	−0.0734408	+	0.0734408i
$154$	−2.86384	+	7.21109i	−0.230775	+	0.581086i
$155$	9.33619	+	2.75256i	0.749901	+	0.221091i
$156$	8.67013	−	13.5032i	0.694166	−	1.08112i
$157$	−0.796329	−	2.97194i	−0.0635539	−	0.237187i	0.926841	−	0.375454i	$-0.122513\pi$
$157$	−0.796329	−	2.97194i	−0.0635539	−	0.237187i	−0.990395	+	0.138268i	$0.955847\pi$
$158$	−4.66610	−	8.54115i	−0.371215	−	0.679498i
$159$	−6.40454	−	11.0930i	−0.507913	−	0.879732i
$160$	−12.5598	+	1.50074i	−0.992937	+	0.118644i
$161$	−1.69708	+	18.2650i	−0.133748	+	1.43948i
$162$	4.55425	−	7.47518i	0.357816	−	0.587306i
$163$	0.838533	+	0.224684i	0.0656790	+	0.0175986i	0.291509	−	0.956568i	$-0.405843\pi$
$163$	0.838533	+	0.224684i	0.0656790	+	0.0175986i	−0.225830	+	0.974167i	$0.572509\pi$
$164$	−3.52072	−	0.166260i	−0.274922	−	0.0129828i
$165$	6.95382	+	0.173217i	0.541354	+	0.0134849i
$166$	−13.2009	+	12.5923i	−1.02459	+	0.977349i
$167$	−10.5373	+	10.5373i	−0.815405	+	0.815405i	−0.985438	−	0.170034i	$-0.945612\pi$
$167$	−10.5373	+	10.5373i	−0.815405	+	0.815405i	0.170034	+	0.985438i	$0.445612\pi$
$168$	−3.95642	−	10.5058i	−0.305245	−	0.810539i
$169$			15.6063i			1.20049i
$170$	4.81965	−	2.47922i	0.369650	−	0.190148i
$171$	0.850868	−	1.47375i	0.0650675	−	0.112700i
$172$	−15.6920	+	14.2768i	−1.19650	+	1.08859i
$173$	4.37676	−	16.3343i	0.332759	−	1.24187i	−0.573520	−	0.819192i	$-0.694422\pi$
$173$	4.37676	−	16.3343i	0.332759	−	1.24187i	0.906278	−	0.422681i	$-0.138911\pi$
$174$	4.01038	+	16.5162i	0.304026	+	1.25209i
$175$	10.5874	−	7.93133i	0.800336	−	0.599552i
$176$	4.80582	−	6.76059i	0.362252	−	0.509599i
$177$	3.73732	−	13.9479i	0.280914	−	1.04839i
$178$	9.02494	−	4.93040i	0.676448	−	0.369549i
$179$	−7.00502	−	4.04435i	−0.523579	−	0.302289i	0.214818	−	0.976654i	$-0.431084\pi$
$179$	−7.00502	−	4.04435i	−0.523579	−	0.302289i	−0.738398	+	0.674365i	$0.764417\pi$
$180$	2.53489	−	2.19342i	0.188939	−	0.163488i
$181$		−	8.36290i		−	0.621609i	−0.950474	−	0.310805i	$-0.899401\pi$
$181$		−	8.36290i		−	0.621609i	0.950474	−	0.310805i	$-0.100599\pi$
$182$	16.0536	+	11.9487i	1.18997	+	0.885693i
$183$	−9.06379	−	9.06379i	−0.670015	−	0.670015i
$184$	6.40243	−	18.5356i	0.471993	−	1.36646i
$185$	8.83128	+	0.219984i	0.649289	+	0.0161735i
$186$	2.59995	−	8.86137i	0.190638	−	0.649747i
$187$	−0.919874	+	3.43302i	−0.0672678	+	0.251047i
$188$	2.11041	+	0.673668i	0.153918	+	0.0491323i
$189$	12.1446	+	8.60148i	0.883386	+	0.625666i
$190$	−5.31674	+	4.82451i	−0.385717	+	0.350007i
$191$	−1.50699	+	0.870062i	−0.109042	+	0.0629555i	−0.553529	−	0.832830i	$-0.686719\pi$
$191$	−1.50699	+	0.870062i	−0.109042	+	0.0629555i	0.444487	+	0.895785i	$0.353386\pi$
$192$	1.43948	+	11.9145i	0.103885	+	0.859858i
$193$	6.38935	+	23.8454i	0.459916	+	1.71643i	0.673220	+	0.739443i	$0.264911\pi$
$193$	6.38935	+	23.8454i	0.459916	+	1.71643i	−0.213304	+	0.976986i	$0.568423\pi$
$194$	14.7829	+	15.4975i	1.06135	+	1.11265i
$195$	5.07362	−	17.2088i	0.363329	−	1.23235i
$196$	13.4109	−	4.01827i	0.957925	−	0.287019i
$197$	4.28848	−	4.28848i	0.305542	−	0.305542i	−0.537636	−	0.843177i	$-0.680682\pi$
$197$	4.28848	−	4.28848i	0.305542	−	0.305542i	0.843177	+	0.537636i	$0.180682\pi$
$198$	−0.0518589	+	2.19755i	−0.00368545	+	0.156173i
$199$	−10.1676	+	17.6107i	−0.720760	+	1.24839i	0.239936	+	0.970789i	$0.422874\pi$
$199$	−10.1676	+	17.6107i	−0.720760	+	1.24839i	−0.960696	+	0.277604i	$0.910460\pi$
$200$	−13.0091	+	5.54636i	−0.919886	+	0.392187i
$201$	−2.51235	−	4.35151i	−0.177207	−	0.306932i
$202$	−8.30397	−	5.05919i	−0.584265	−	0.355963i
$203$	−20.8932	+	3.56821i	−1.46642	+	0.250439i
$204$	−2.35822	−	4.56968i	−0.165108	−	0.319942i
$205$	−3.83061	+	0.924818i	−0.267542	+	0.0645921i
$206$	−4.61481	+	15.7286i	−0.321529	+	1.09586i
$207$	1.34505	+	5.01979i	0.0934874	+	0.348900i
$208$	−13.6349	−	16.4861i	−0.945410	−	1.14310i
$209$		−	4.70789i		−	0.325652i
$210$	−7.53821	−	10.0353i	−0.520186	−	0.692498i
$211$	−14.9290			−1.02775			−0.513877	−	0.857864i	$-0.671791\pi$
$211$	−14.9290			−1.02775			−0.513877	+	0.857864i	$0.671791\pi$
$212$	−16.6853	+	3.63687i	−1.14595	+	0.249781i
$213$	−7.74630	+	2.07562i	−0.530768	+	0.142219i
$214$	3.62875	−	12.3678i	0.248056	−	0.845446i
$215$	−12.3672	+	20.2394i	−0.843438	+	1.38032i
$216$	−10.4260	−	12.0172i	−0.709398	−	0.817669i
$217$	10.8009	+	3.99717i	0.733215	+	0.271346i
$218$	−8.74894	+	14.3602i	−0.592553	+	0.972595i
$219$	0.760626	−	0.439147i	0.0513983	−	0.0296748i
$220$	3.03921	−	8.76157i	0.204903	−	0.590705i
$221$	7.93880	+	4.58347i	0.534022	+	0.308317i
$222$	0.197737	−	8.37918i	0.0132712	−	0.562374i
$223$	−15.3643	−	15.3643i	−1.02887	−	1.02887i	−0.999571	−	0.0292986i	$-0.990673\pi$
$223$	−15.3643	−	15.3643i	−1.02887	−	1.02887i	−0.0292986	−	0.999571i	$-0.509327\pi$
$224$	−14.9470	+	0.765661i	−0.998691	+	0.0511579i
$225$	2.03317	−	3.14836i	0.135544	−	0.209890i
$226$	−17.5339	+	16.7254i	−1.16634	+	1.11256i
$227$	−2.20153	+	0.589897i	−0.146120	+	0.0391528i	−0.331138	−	0.943582i	$-0.607433\pi$
$227$	−2.20153	+	0.589897i	−0.146120	+	0.0391528i	0.185017	+	0.982735i	$0.440766\pi$
$228$	4.58399	+	5.03839i	0.303582	+	0.333676i
$229$	−2.58512	−	4.47756i	−0.170830	−	0.295886i	0.767881	−	0.640593i	$-0.221311\pi$
$229$	−2.58512	−	4.47756i	−0.170830	−	0.295886i	−0.938710	+	0.344707i	$0.887978\pi$
$230$	1.06291	−	21.8991i	0.0700862	−	1.44398i
$231$	8.19512	+	0.761443i	0.539199	+	0.0500993i
$232$	22.6025	+	1.60254i	1.48392	+	0.105212i
$233$	−2.09898	−	0.562420i	−0.137509	−	0.0368454i	0.189408	−	0.981898i	$-0.439343\pi$
$233$	−2.09898	−	0.562420i	−0.137509	−	0.0368454i	−0.326917	+	0.945053i	$0.606010\pi$
$234$	5.44025	+	1.59619i	0.355640	+	0.104346i
$235$	2.47604	+	0.0616771i	0.161519	+	0.00402337i
$236$	−16.1995	−	10.4014i	−1.05450	−	0.677071i
$237$	−7.30018	+	7.30018i	−0.474198	+	0.474198i
$238$	5.88818	−	2.54070i	0.381674	−	0.164689i
$239$	−11.9844			−0.775206			−0.387603	−	0.921826i	$-0.626697\pi$
$239$	−11.9844			−0.775206			−0.387603	+	0.921826i	$0.626697\pi$
$240$	5.27842	+	12.3359i	0.340721	+	0.796277i
$241$	7.04995	−	12.2109i	0.454127	−	0.786571i	−0.544510	−	0.838754i	$-0.683285\pi$
$241$	7.04995	−	12.2109i	0.454127	−	0.786571i	0.998638	+	0.0521828i	$0.0166179\pi$
$242$	−4.54264	−	8.31516i	−0.292012	−	0.534519i
$243$	7.33091	+	1.96431i	0.470278	+	0.126011i
$244$	−15.1862	+	7.83696i	−0.972199	+	0.501710i
$245$	13.1338	−	8.51495i	0.839085	−	0.544000i
$246$	0.882207	+	3.63324i	0.0562474	+	0.231647i
$247$	−11.7290	−	3.14279i	−0.746301	−	0.199971i
$248$	−10.2004	−	6.89468i	−0.647729	−	0.437813i
$249$	16.7595	+	9.67610i	1.06209	+	0.613198i
$250$	−12.2237	+	10.0290i	−0.773095	+	0.634291i
$251$	−2.13569			−0.134804			−0.0674019	−	0.997726i	$-0.521471\pi$
$251$	−2.13569			−0.134804			−0.0674019	+	0.997726i	$0.521471\pi$
$252$	3.16812	−	2.38630i	0.199573	−	0.150323i
$253$	10.1663	+	10.1663i	0.639147	+	0.639147i
$254$	−4.52556	+	4.31689i	−0.283959	+	0.270866i
$255$	−3.96285	−	4.16532i	−0.248163	−	0.260842i
$256$	15.7158	+	3.00215i	0.982239	+	0.187635i
$257$	7.23890	−	27.0159i	0.451550	−	1.68521i	−0.246487	−	0.969146i	$-0.579276\pi$
$257$	7.23890	−	27.0159i	0.451550	−	1.68521i	0.698037	−	0.716062i	$-0.254057\pi$
$258$	19.2180	+	11.7086i	1.19646	+	0.728944i
$259$	10.4077	+	0.967026i	0.646705	+	0.0600881i
$260$	−19.7994	−	13.4206i	−1.22790	−	0.832311i
$261$	−5.20038	+	3.00244i	−0.321896	+	0.185846i
$262$	1.41727	+	2.59426i	0.0875591	+	0.160274i
$263$	15.5334	−	4.16216i	0.957831	−	0.256650i	0.254149	−	0.967165i	$-0.418205\pi$
$263$	15.5334	−	4.16216i	0.957831	−	0.256650i	0.703682	+	0.710515i	$0.251538\pi$
$264$	−8.31654	−	2.87264i	−0.511848	−	0.176799i
$265$	−16.7674	+	9.13168i	−1.03002	+	0.560955i
$266$	−6.66283	+	5.26951i	−0.408524	+	0.323094i
$267$	−7.71367	−	7.71367i	−0.472069	−	0.472069i
$268$	−6.54525	+	1.42665i	−0.399815	+	0.0871467i
$269$	−2.62803	+	4.55187i	−0.160234	+	0.277533i	−0.934952	−	0.354773i	$-0.884558\pi$
$269$	−2.62803	+	4.55187i	−0.160234	+	0.277533i	0.774719	+	0.632306i	$0.217891\pi$
$270$	−14.9551	−	9.63007i	−0.910139	−	0.586068i
$271$	−5.39299	+	3.11364i	−0.327601	+	0.189140i	−0.654775	−	0.755823i	$-0.727237\pi$
$271$	−5.39299	+	3.11364i	−0.327601	+	0.189140i	0.327175	+	0.944964i	$0.393903\pi$
$272$	−6.75986	+	1.14245i	−0.409877	+	0.0692711i
$273$	7.36774	−	19.9087i	0.445916	−	1.20493i
$274$	0.0198325	−	0.00481563i	0.00119812	−	0.000290923i
$275$	0.516221	−	10.3555i	0.0311293	−	0.624459i
$276$	−20.7787	−	0.981239i	−1.25073	−	0.0590637i
$277$	−1.39658	−	5.21209i	−0.0839121	−	0.313164i	0.911194	−	0.411978i	$-0.135162\pi$
$277$	−1.39658	−	5.21209i	−0.0839121	−	0.313164i	−0.995106	+	0.0988136i	$0.968495\pi$
$278$	−0.0897732	+	3.80418i	−0.00538424	+	0.228160i
$279$	3.26279			0.195338
$280$	−15.8016	+	5.50553i	−0.944324	+	0.329018i
$281$	28.1583			1.67978			0.839892	−	0.542753i	$-0.182618\pi$
$281$	28.1583			1.67978			0.839892	+	0.542753i	$0.182618\pi$
$282$	0.0554397	−	2.34928i	0.00330139	−	0.139898i
$283$	−5.84252	−	21.8046i	−0.347302	−	1.29615i	−0.889900	−	0.456156i	$-0.849226\pi$
$283$	−5.84252	−	21.8046i	−0.347302	−	1.29615i	0.542598	−	0.839992i	$-0.317441\pi$
$284$	−0.504337	+	10.6798i	−0.0299269	+	0.633729i
$285$	6.49847	+	3.97087i	0.384936	+	0.235214i
$286$	15.2421	−	3.70102i	0.901286	−	0.218846i
$287$	−4.59612	+	0.784939i	−0.271300	+	0.0463335i
$288$	−3.89607	+	1.67314i	−0.229578	+	0.0985907i
$289$	−12.1784	+	7.03122i	−0.716378	+	0.413601i
$290$	24.7596	−	5.36283i	1.45394	−	0.314916i
$291$	11.3594	−	19.6751i	0.665901	−	1.15338i
$292$	−0.249373	−	1.14408i	−0.0145935	−	0.0669524i
$293$	20.5621	+	20.5621i	1.20125	+	1.20125i	0.973786	+	0.227467i	$0.0730443\pi$
$293$	20.5621	+	20.5621i	1.20125	+	1.20125i	0.227467	+	0.973786i	$0.426956\pi$
$294$	−8.09511	−	12.4504i	−0.472116	−	0.726122i
$295$	−20.6450	−	6.08670i	−1.20200	−	0.354382i
$296$	−10.5619	−	3.64822i	−0.613900	−	0.212049i
$297$	11.2667	−	3.01890i	0.653760	−	0.175175i
$298$	−8.13728	−	14.8950i	−0.471380	−	0.862846i
$299$	32.1143	−	18.5412i	1.85722	−	1.07227i
$300$	9.53048	+	11.5851i	0.550243	+	0.668865i
$301$	−16.2206	+	22.9021i	−0.934940	+	1.32005i
$302$	−0.206665	−	0.125911i	−0.0118922	−	0.00724535i
$303$	−2.66962	+	9.96315i	−0.153365	+	0.572368i
$304$	8.25752	−	3.77930i	0.473601	−	0.216758i
$305$	−13.8424	+	13.1696i	−0.792614	+	0.754087i
$306$	1.31464	−	1.25402i	0.0751529	−	0.0716877i
$307$	15.5640	+	15.5640i	0.888287	+	0.888287i	0.994358	−	0.106072i	$-0.0338273\pi$
$307$	15.5640	+	15.5640i	0.888287	+	0.888287i	−0.106072	+	0.994358i	$0.533827\pi$
$308$	4.28954	−	10.0996i	0.244419	−	0.575480i
$309$	17.3876			0.989148
$310$	−13.1079	−	4.20311i	−0.744476	−	0.238721i
$311$	8.37017	+	4.83252i	0.474629	+	0.274027i	0.718175	−	0.695862i	$-0.244978\pi$
$311$	8.37017	+	4.83252i	0.474629	+	0.274027i	−0.243547	+	0.969889i	$0.578311\pi$
$312$	−12.7085	+	18.8018i	−0.719479	+	1.06444i
$313$	1.37739	+	0.369070i	0.0778546	+	0.0208611i	0.297536	−	0.954711i	$-0.403835\pi$
$313$	1.37739	+	0.369070i	0.0778546	+	0.0208611i	−0.219681	+	0.975572i	$0.570502\pi$
$314$	1.02671	+	4.22836i	0.0579406	+	0.238620i
$315$	2.65232	−	3.55379i	0.149441	−	0.200234i
$316$	6.31206	+	12.2313i	0.355081	+	0.688066i
$317$	29.0824	+	7.79260i	1.63343	+	0.437676i	0.954907	−	0.296904i	$-0.0959542\pi$
$317$	29.0824	+	7.79260i	1.63343	+	0.437676i	0.678522	+	0.734580i	$0.262621\pi$
$318$	8.68476	+	15.8972i	0.487017	+	0.891470i
$319$	−8.30632	+	14.3870i	−0.465065	+	0.805516i
$320$	17.8073	−	1.70273i	0.995460	−	0.0951855i
$321$	−13.6724			−0.763117
$322$	3.00876	−	25.7668i	0.167672	−	1.43593i
$323$	−2.75147	+	2.75147i	−0.153096	+	0.153096i
$324$	−6.68830	+	10.4166i	−0.371572	+	0.578701i
$325$	−25.4546	−	8.19896i	−1.41197	−	0.454797i
$326$	−1.17804	−	0.345640i	−0.0652455	−	0.0191432i
$327$	17.2294	+	4.61662i	0.952790	+	0.255299i
$328$	4.97211	+	0.352528i	0.274539	+	0.0194651i
$329$	2.91803	+	0.271126i	0.160876	+	0.0149477i
$330$	−9.82567	−	0.476905i	−0.540885	−	0.0262528i
$331$	10.5349	+	18.2469i	0.579048	+	1.00294i	0.995589	+	0.0938236i	$0.0299090\pi$
$331$	10.5349	+	18.2469i	0.579048	+	1.00294i	−0.416541	+	0.909117i	$0.636758\pi$
$332$	19.0839	−	17.3628i	1.04736	−	0.952905i
$333$	2.86037	−	0.766434i	0.156747	−	0.0420003i
$334$	15.2495	−	14.5463i	0.834415	−	0.795941i
$335$	−6.57745	+	3.58214i	−0.359365	+	0.195713i
$336$	5.24315	+	14.9853i	0.286037	+	0.817515i
$337$	−23.3527	−	23.3527i	−1.27210	−	1.27210i	−0.944982	−	0.327122i	$-0.893921\pi$
$337$	−23.3527	−	23.3527i	−1.27210	−	1.27210i	−0.327122	−	0.944982i	$-0.606079\pi$
$338$	0.520692	−	22.0646i	0.0283219	−	1.20015i
$339$	22.2604	+	12.8521i	1.20902	+	0.698029i
$340$	−6.89683	+	3.34437i	−0.374033	+	0.181374i
$341$	7.81724	−	4.51329i	0.423327	−	0.244408i
$342$	−1.25214	+	2.05522i	−0.0677082	+	0.111134i
$343$	16.1864	−	8.99998i	0.873985	−	0.485953i
$344$	22.6620	−	19.6612i	1.22185	−	1.06006i
$345$	−22.6076	+	5.45811i	−1.21715	+	0.293855i
$346$	−6.73293	+	22.9477i	−0.361965	+	1.23368i
$347$	8.65562	−	2.31927i	0.464658	−	0.124505i	−0.0188919	−	0.999822i	$-0.506014\pi$
$347$	8.65562	−	2.31927i	0.464658	−	0.124505i	0.483550	+	0.875317i	$0.339347\pi$
$348$	−5.11890	−	23.4847i	−0.274402	−	1.25891i
$349$	−24.0045			−1.28493			−0.642465	−	0.766315i	$-0.722088\pi$
$349$	−24.0045			−1.28493			−0.642465	+	0.766315i	$0.722088\pi$
$350$	−15.2334	+	10.8602i	−0.814258	+	0.580503i
$351$		−	30.0847i		−	1.60580i
$352$	−7.02012	+	9.39792i	−0.374174	+	0.500911i
$353$	−2.75717	−	10.2899i	−0.146749	−	0.547675i	−0.999671	−	0.0256371i	$-0.991839\pi$
$353$	−2.75717	−	10.2899i	−0.146749	−	0.547675i	0.852922	−	0.522038i	$-0.174828\pi$
$354$	−5.74925	+	19.5951i	−0.305569	+	1.04147i
$355$	2.80535	+	11.6198i	0.148893	+	0.616717i
$356$	−12.9241	+	6.66959i	−0.684978	+	0.353487i
$357$	−4.34453	−	5.23456i	−0.229937	−	0.277043i
$358$	9.76890	+	5.95170i	0.516302	+	0.314557i
$359$	−4.51889	−	7.82694i	−0.238498	−	0.413090i	0.721786	−	0.692117i	$-0.243322\pi$
$359$	−4.51889	−	7.82694i	−0.238498	−	0.413090i	−0.960283	+	0.279026i	$0.909988\pi$
$360$	−3.65705	+	3.01652i	−0.192744	+	0.158985i
$361$	−6.92282	+	11.9907i	−0.364359	+	0.631088i
$362$	−0.279021	+	11.8236i	−0.0146650	+	0.621436i
$363$	−7.10702	+	7.10702i	−0.373022	+	0.373022i
$364$	−22.2983	−	17.4289i	−1.16875	−	0.913521i
$365$	−0.626142	−	1.14971i	−0.0327738	−	0.0601786i
$366$	12.5122	+	13.1170i	0.654021	+	0.685635i
$367$	3.43987	+	12.8378i	0.179560	+	0.670126i	0.995730	+	0.0923143i	$0.0294265\pi$
$367$	3.43987	+	12.8378i	0.179560	+	0.670126i	−0.816170	+	0.577811i	$0.803907\pi$
$368$	−9.67031	+	25.9924i	−0.504100	+	1.35495i
$369$	−1.14399	+	0.660480i	−0.0595535	+	0.0343832i
$370$	−12.4785	−	0.605665i	−0.648727	−	0.0314870i
$371$	−20.5254	+	9.43700i	−1.06562	+	0.489944i
$372$	−3.97152	+	12.4416i	−0.205914	+	0.645069i
$373$	0.414727	−	1.54778i	0.0214737	−	0.0801411i	−0.954357	−	0.298667i	$-0.903458\pi$
$373$	0.414727	−	1.54778i	0.0214737	−	0.0801411i	0.975831	+	0.218526i	$0.0701248\pi$
$374$	1.41508	−	4.82298i	0.0731718	−	0.249390i
$375$	13.8586	+	9.44689i	0.715656	+	0.487836i
$376$	−2.96126	−	1.02286i	−0.152716	−	0.0527498i
$377$	30.2981	+	30.2981i	1.56043	+	1.56043i
$378$	−16.8832	−	12.5661i	−0.868380	−	0.646332i
$379$			24.3327i			1.24989i	0.780669	+	0.624944i	$0.214878\pi$
$379$			24.3327i			1.24989i	−0.780669	+	0.624944i	$0.785122\pi$
$380$	7.67787	−	6.64360i	0.393867	−	0.340810i
$381$	5.74551	+	3.31717i	0.294351	+	0.169944i
$382$	2.15964	−	1.17983i	0.110497	−	0.0603655i
$383$	−1.11065	+	4.14500i	−0.0567515	+	0.211800i	−0.988479	−	0.151359i	$-0.951635\pi$
$383$	−1.11065	+	4.14500i	−0.0567515	+	0.211800i	0.931727	+	0.363159i	$0.118302\pi$
$384$	−1.63765	−	16.8930i	−0.0835708	−	0.862069i
$385$	1.43881	−	12.1833i	0.0733288	−	0.620919i
$386$	−8.23781	−	33.9263i	−0.419294	−	1.72680i
$387$	−2.05783	+	7.67991i	−0.104605	+	0.390392i
$388$	−20.3833	−	22.4039i	−1.03481	−	1.13738i
$389$	7.07499	−	12.2542i	0.358716	−	0.621315i	−0.629030	−	0.777381i	$-0.716548\pi$
$389$	7.07499	−	12.2542i	0.358716	−	0.621315i	0.987747	+	0.156066i	$0.0498812\pi$
$390$	−7.74734	+	24.1609i	−0.392302	+	1.22343i
$391$		−	11.8831i		−	0.600955i
$392$	−19.0947	+	5.23367i	−0.964429	+	0.264340i
$393$	2.21733	−	2.21733i	0.111850	−	0.111850i
$394$	−6.20622	+	5.92006i	−0.312665	+	0.298248i
$395$	10.6071	+	11.1490i	0.533699	+	0.560966i
$396$	0.146638	−	3.10520i	0.00736886	−	0.156042i
$397$	13.6314	+	3.65251i	0.684139	+	0.183314i	0.584115	−	0.811671i	$-0.301442\pi$
$397$	13.6314	+	3.65251i	0.684139	+	0.183314i	0.100023	+	0.994985i	$0.468108\pi$
$398$	14.9627	−	24.5592i	0.750011	−	1.23104i
$399$	7.35341	+	5.20812i	0.368131	+	0.260732i
$400$	18.5776	−	7.40751i	0.928882	−	0.370375i
$401$	12.1951	+	21.1225i	0.608993	+	1.05481i	0.991407	+	0.130815i	$0.0417595\pi$
$401$	12.1951	+	21.1225i	0.608993	+	1.05481i	−0.382414	+	0.923991i	$0.624907\pi$
$402$	3.40682	+	6.23608i	0.169917	+	0.311027i
$403$	−6.02575	−	22.4884i	−0.300164	−	1.12023i
$404$	11.5715	+	7.42984i	0.575705	+	0.369648i
$405$	−3.91388	+	13.2752i	−0.194482	+	0.659649i
$406$	29.6583	−	4.34773i	1.47192	−	0.215774i
$407$	5.79292	−	5.79292i	0.287144	−	0.287144i
$408$	3.18163	+	6.53939i	0.157514	+	0.323748i
$409$	−2.36852	−	1.36747i	−0.117116	−	0.0676168i	0.440298	−	0.897852i	$-0.354873\pi$
$409$	−2.36852	−	1.36747i	−0.117116	−	0.0676168i	−0.557414	+	0.830235i	$0.688206\pi$
$410$	5.44665	−	1.17972i	0.268991	−	0.0582623i
$411$	−0.0108244	−	0.0187485i	−0.000533930	−	0.000924794i
$412$	7.04929	−	22.0834i	0.347293	−	1.08797i
$413$	−23.8840	−	8.83891i	−1.17525	−	0.434934i
$414$	−1.73418	−	7.14196i	−0.0852301	−	0.351008i
$415$	15.0405	−	24.6142i	0.738307	−	1.20826i
$416$	18.7272	+	23.7633i	0.918179	+	1.16509i
$417$	3.89892	−	1.04471i	0.190931	−	0.0511598i
$418$	−0.157075	+	6.65611i	−0.00768277	+	0.325561i
$419$		−	9.10424i		−	0.444771i	−0.974959	−	0.222386i	$-0.928616\pi$
$419$		−	9.10424i		−	0.444771i	0.974959	−	0.222386i	$-0.0713844\pi$
$420$	10.3229	+	14.4396i	0.503704	+	0.704578i
$421$		−	7.13111i		−	0.347549i	−0.984785	−	0.173775i	$-0.944404\pi$
$421$		−	7.13111i		−	0.347549i	0.984785	−	0.173775i	$-0.0555964\pi$
$422$	21.1069	+	0.498093i	1.02747	+	0.0242468i
$423$	0.801966	−	0.214886i	0.0389929	−	0.0104481i
$424$	23.7114	−	4.58518i	1.15153	−	0.222676i
$425$	−6.35384	+	5.75044i	−0.308207	+	0.278937i
$426$	11.0211	−	2.67610i	0.533975	−	0.129657i
$427$	−17.3958	+	14.4380i	−0.841842	+	0.698703i
$428$	−5.54304	+	17.3648i	−0.267933	+	0.839358i
$429$	−8.31906	−	14.4090i	−0.401648	−	0.695675i
$430$	18.1603	−	28.2022i	0.875768	−	1.36003i
$431$	−18.0479	−	10.4200i	−0.869339	−	0.501913i	−0.00221040	−	0.999998i	$-0.500704\pi$
$431$	−18.0479	−	10.4200i	−0.869339	−	0.501913i	−0.867128	+	0.498085i	$0.834037\pi$
$432$	14.3395	+	17.3381i	0.689911	+	0.834178i
$433$	−7.47538	+	7.47538i	−0.359244	+	0.359244i	−0.863534	−	0.504290i	$-0.831754\pi$
$433$	−7.47538	+	7.47538i	−0.359244	+	0.359244i	0.504290	+	0.863534i	$0.331754\pi$
$434$	−15.1372	−	6.01165i	−0.726609	−	0.288568i
$435$	−12.8529	−	23.6002i	−0.616248	−	1.13154i
$436$	12.8485	−	20.0108i	0.615334	−	0.958345i
$437$	4.07400	+	15.2044i	0.194886	+	0.727324i
$438$	−1.09004	+	0.595498i	−0.0520841	+	0.0284540i
$439$	7.40260	+	12.8217i	0.353307	+	0.611945i	0.986827	−	0.161781i	$-0.0517239\pi$
$439$	7.40260	+	12.8217i	0.353307	+	0.611945i	−0.633520	+	0.773726i	$0.718391\pi$
$440$	−4.58922	+	12.2859i	−0.218782	+	0.585706i
$441$	3.41571	−	3.98283i	0.162653	−	0.189658i
$442$	−11.0711	−	6.74507i	−0.526599	−	0.320830i
$443$	−15.0133	−	4.02280i	−0.713303	−	0.191129i	−0.116121	−	0.993235i	$-0.537046\pi$
$443$	−15.0133	−	4.02280i	−0.713303	−	0.191129i	−0.597182	+	0.802106i	$0.703713\pi$
$444$	−0.559128	+	11.8401i	−0.0265350	+	0.561904i
$445$	−11.7805	+	11.2079i	−0.558448	+	0.531303i
$446$	21.2097	+	22.2350i	1.00431	+	1.05286i
$447$	−12.7309	+	12.7309i	−0.602150	+	0.602150i
$448$	21.1580	−	0.583812i	0.999620	−	0.0275825i
$449$		−	20.0367i		−	0.945588i	−0.881173	−	0.472794i	$-0.843245\pi$
$449$		−	20.0367i		−	0.945588i	0.881173	−	0.472794i	$-0.156755\pi$
$450$	−2.97957	+	4.38337i	−0.140458	+	0.206634i
$451$	−1.82723	+	3.16486i	−0.0860411	+	0.149027i
$452$	25.3478	−	23.0617i	1.19226	−	1.08473i
$453$	−0.0664402	+	0.247958i	−0.00312163	+	0.0116501i
$454$	3.13224	−	0.760556i	0.147003	−	0.0356947i
$455$	−29.3925	−	11.7177i	−1.37794	−	0.549332i
$456$	−6.31284	−	7.27632i	−0.295626	−	0.340745i
$457$	2.62323	−	9.79003i	0.122710	−	0.457958i	−0.877038	−	0.480421i	$-0.840484\pi$
$457$	2.62323	−	9.79003i	0.122710	−	0.457958i	0.999748	+	0.0224625i	$0.00715063\pi$
$458$	3.50551	+	6.41672i	0.163802	+	0.299833i
$459$	−8.34906	−	4.82033i	−0.389701	−	0.224994i
$460$	−2.23341	+	30.9259i	−0.104133	+	1.44193i
$461$		−	30.2196i		−	1.40747i	−0.710463	−	0.703735i	$-0.751514\pi$
$461$		−	30.2196i		−	1.40747i	0.710463	−	0.703735i	$-0.248486\pi$
$462$	−11.5610	−	1.34997i	−0.537867	−	0.0628061i
$463$	24.0778	+	24.0778i	1.11899	+	1.11899i	0.991890	+	0.127101i	$0.0405671\pi$
$463$	24.0778	+	24.0778i	1.11899	+	1.11899i	0.127101	+	0.991890i	$0.459433\pi$
$464$	−31.9024	−	3.01981i	−1.48103	−	0.140191i
$465$	−0.363609	+	14.5972i	−0.0168620	+	0.676927i
$466$	2.94881	+	0.865191i	0.136601	+	0.0400792i
$467$	−8.25570	+	30.8107i	−0.382028	+	1.42575i	0.460770	+	0.887519i	$0.347573\pi$
$467$	−8.25570	+	30.8107i	−0.382028	+	1.42575i	−0.842799	+	0.538229i	$0.819094\pi$
$468$	−7.63828	−	2.43823i	−0.353080	−	0.112707i
$469$	−8.05160	+	3.70190i	−0.371789	+	0.170938i
$470$	−3.49862	−	0.169811i	−0.161379	−	0.00783281i
$471$	3.99724	−	2.30781i	0.184183	−	0.106338i
$472$	22.5561	+	15.2461i	1.03823	+	0.701761i
$473$	5.69302	+	21.2467i	0.261765	+	0.976922i
$474$	10.5647	−	10.0776i	0.485253	−	0.462878i
$475$	6.15822	−	9.53600i	0.282559	−	0.437542i
$476$	−8.40959	+	3.39564i	−0.385453	+	0.155639i
$477$	−4.52558	+	4.52558i	−0.207212	+	0.207212i
$478$	16.9438	+	0.399849i	0.774990	+	0.0182887i
$479$	16.9392	−	29.3395i	0.773971	−	1.34056i	−0.161399	−	0.986889i	$-0.551601\pi$
$479$	16.9392	−	29.3395i	0.773971	−	1.34056i	0.935371	−	0.353669i	$-0.115066\pi$
$480$	−7.05116	−	17.6168i	−0.321840	−	0.804094i
$481$	−10.5651	−	18.2993i	−0.481728	−	0.834378i
$482$	−10.3748	+	17.0288i	−0.472558	+	0.775639i
$483$	−27.1255	+	4.63257i	−1.23425	+	0.210789i
$484$	6.14505	+	11.9077i	0.279320	+	0.541259i
$485$	−28.8963	−	17.6570i	−1.31211	−	0.801764i
$486$	−10.2990	−	3.02177i	−0.467174	−	0.137070i
$487$	−7.15944	−	26.7194i	−0.324425	−	1.21077i	−0.914888	−	0.403707i	$-0.867721\pi$
$487$	−7.15944	−	26.7194i	−0.324425	−	1.21077i	0.590463	−	0.807065i	$-0.298945\pi$
$488$	21.7321	−	10.5734i	0.983765	−	0.478634i
$489$			1.30230i			0.0588919i
$490$	−18.8529	+	11.6004i	−0.851686	+	0.524053i
$491$	0.136113			0.00614271			0.00307136	−	0.999995i	$-0.499022\pi$
$491$	0.136113			0.00614271			0.00307136	+	0.999995i	$0.499022\pi$
$492$	−1.12606	−	5.16618i	−0.0507668	−	0.232910i
$493$	13.2628	−	3.55377i	0.597328	−	0.160054i
$494$	16.4779	+	4.83466i	0.741375	+	0.217522i
$495$	−0.815671	−	3.37852i	−0.0366617	−	0.151853i
$496$	14.1916	+	10.0882i	0.637219	+	0.452972i
$497$	2.38105	+	13.9419i	0.106804	+	0.625381i
$498$	−23.3721	−	14.2394i	−1.04733	−	0.638084i
$499$	−0.423881	+	0.244728i	−0.0189755	+	0.0109555i	−0.509458	−	0.860496i	$-0.670154\pi$
$499$	−0.423881	+	0.244728i	−0.0189755	+	0.0109555i	0.490482	+	0.871451i	$0.336821\pi$
$500$	17.6167	−	13.7714i	0.787844	−	0.615875i
$501$	−19.3603	−	11.1776i	−0.864952	−	0.499380i
$502$	3.01949	+	0.0712556i	0.134766	+	0.00318029i
$503$	12.8130	+	12.8130i	0.571302	+	0.571302i	0.932492	−	0.361190i	$-0.117629\pi$
$503$	12.8130	+	12.8130i	0.571302	+	0.571302i	−0.361190	+	0.932492i	$0.617629\pi$
$504$	−4.55876	+	3.26810i	−0.203064	+	0.145573i
$505$	14.7470	+	4.34781i	0.656234	+	0.193475i
$506$	−14.0341	−	14.7124i	−0.623891	−	0.654048i
$507$	−22.6141	+	6.05943i	−1.00433	+	0.269109i
$508$	6.54236	−	5.95232i	0.290270	−	0.264091i
$509$	−3.81518	−	6.60809i	−0.169105	−	0.292899i	0.769000	−	0.639248i	$-0.220754\pi$
$509$	−3.81518	−	6.60809i	−0.169105	−	0.292899i	−0.938105	+	0.346350i	$0.887421\pi$
$510$	5.46378	+	6.02122i	0.241940	+	0.266624i
$511$	−0.647077	−	1.40739i	−0.0286250	−	0.0622591i
$512$	−22.1192	−	4.76885i	−0.977539	−	0.210755i
$513$	12.3352	+	3.30520i	0.544611	+	0.145928i
$514$	−11.1359	+	37.9542i	−0.491182	+	1.67409i
$515$	0.645392	−	25.9094i	0.0284394	−	1.14170i
$516$	−26.7802	−	17.1950i	−1.17893	−	0.756968i
$517$	1.62417	−	1.62417i	0.0714309	−	0.0714309i
$518$	−14.6824	−	1.71445i	−0.645107	−	0.0753284i
$519$	25.3682			1.11354
$520$	27.5450	+	19.6349i	1.20793	+	0.861048i
$521$	4.44274	−	7.69505i	0.194640	−	0.337126i	−0.752143	−	0.659000i	$-0.770980\pi$
$521$	4.44274	−	7.69505i	0.194640	−	0.337126i	0.946782	+	0.321874i	$0.104313\pi$
$522$	7.45258	−	4.07141i	0.326190	−	0.178201i
$523$	35.9915	+	9.64389i	1.57380	+	0.421698i	0.936999	−	0.349333i	$-0.113592\pi$
$523$	35.9915	+	9.64389i	1.57380	+	0.421698i	0.636798	+	0.771030i	$0.280258\pi$
$524$	−1.91721	−	3.71510i	−0.0837535	−	0.162295i
$525$	15.6035	+	12.2621i	0.680992	+	0.535161i
$526$	−22.1003	+	5.36629i	−0.963619	+	0.233981i
$527$	−7.20644	−	1.93096i	−0.313917	−	0.0841139i
$528$	11.6623	+	4.33886i	0.507534	+	0.188825i
$529$	−21.7113	−	12.5350i	−0.943969	−	0.545001i
$530$	24.0108	−	12.3511i	1.04296	−	0.536499i
$531$	−7.21497			−0.313103
$532$	9.59586	−	7.22783i	0.416033	−	0.313366i
$533$	6.66502	+	6.66502i	0.288694	+	0.288694i
$534$	10.6484	+	11.1631i	0.460801	+	0.483075i
$535$	−0.507489	+	20.3732i	−0.0219407	+	0.880812i
$536$	9.30141	−	1.79865i	0.401760	−	0.0776901i
$537$	3.14057	−	11.7208i	0.135526	−	0.505789i
$538$	3.86742	−	6.34785i	0.166737	−	0.273675i
$539$	2.67434	−	14.2672i	0.115192	−	0.614531i
$540$	20.8225	+	14.1142i	0.896060	+	0.607376i
$541$	−7.84446	+	4.52900i	−0.337260	+	0.194717i	−0.659060	−	0.752091i	$-0.729046\pi$
$541$	−7.84446	+	4.52900i	−0.337260	+	0.194717i	0.321800	+	0.946808i	$0.395712\pi$
$542$	7.72860	−	4.22220i	0.331972	−	0.181359i
$543$	12.1181	−	3.24704i	0.520038	−	0.139344i
$544$	9.59534	−	1.38968i	0.411397	−	0.0595820i
$545$	7.51875	−	25.5023i	0.322068	−	1.09240i
$546$	−11.0809	+	27.9015i	−0.474218	+	1.19407i
$547$	−16.2455	−	16.2455i	−0.694608	−	0.694608i	0.268634	−	0.963242i	$-0.413428\pi$
$547$	−16.2455	−	16.2455i	−0.694608	−	0.694608i	−0.963242	+	0.268634i	$0.913428\pi$
$548$	−0.0282002	+	0.00614673i	−0.00120465	+	0.000262575i
$549$	−3.20233	+	5.54659i	−0.136672	+	0.236723i
$550$	−1.07535	+	14.6236i	−0.0458529	+	0.623550i
$551$	−15.7513	+	9.09405i	−0.671030	+	0.387419i
$552$	29.3445	+	2.08056i	1.24899	+	0.0885544i
$553$	11.6287	+	14.0110i	0.494502	+	0.595807i
$554$	1.80061	+	7.41556i	0.0765006	+	0.315057i
$555$	3.11013	+	12.8822i	0.132018	+	0.546820i
$556$	0.253846	−	5.37543i	0.0107655	−	0.227969i
$557$	5.86959	+	21.9056i	0.248702	+	0.928170i	0.971486	+	0.237096i	$0.0761955\pi$
$557$	5.86959	+	21.9056i	0.248702	+	0.928170i	−0.722784	+	0.691074i	$0.757138\pi$
$558$	−4.61299	−	0.108860i	−0.195284	−	0.00460841i
$559$	56.7334			2.39957
$560$	22.5242	−	7.25662i	0.951823	−	0.306648i
$561$	−5.33170			−0.225105
$562$	−39.8108	−	0.939478i	−1.67932	−	0.0396295i
$563$	1.30927	+	4.88628i	0.0551793	+	0.205932i	0.988012	−	0.154378i	$-0.0493375\pi$
$563$	1.30927	+	4.88628i	0.0551793	+	0.205932i	−0.932832	+	0.360310i	$0.882671\pi$
$564$	−0.156764	+	3.31961i	−0.00660094	+	0.139781i
$565$	19.9772	−	32.6933i	0.840446	−	1.37542i
$566$	7.53278	+	31.0227i	0.316626	+	1.30398i
$567$	−5.68361	+	15.3579i	−0.238689	+	0.644971i
$568$	1.06936	−	15.0825i	0.0448695	−	0.632847i
$569$	−23.8336	+	13.7604i	−0.999158	+	0.576864i	−0.907999	−	0.418972i	$-0.862390\pi$
$569$	−23.8336	+	13.7604i	−0.999158	+	0.576864i	−0.0911588	+	0.995836i	$0.529057\pi$
$570$	−9.05518	−	5.83092i	−0.379280	−	0.244230i
$571$	18.0810	−	31.3172i	0.756667	−	1.31059i	−0.187874	−	0.982193i	$-0.560160\pi$
$571$	18.0810	−	31.3172i	0.756667	−	1.31059i	0.944541	−	0.328393i	$-0.106507\pi$
$572$	−21.6731	+	4.72404i	−0.906198	+	0.197522i
$573$	−1.84586	−	1.84586i	−0.0771120	−	0.0771120i
$574$	6.52427	−	0.956417i	0.272318	−	0.0399201i
$575$	7.29400	+	33.8902i	0.304181	+	1.41332i
$576$	5.56416	−	2.23553i	0.231840	−	0.0931471i
$577$	−38.1212	+	10.2146i	−1.58701	+	0.425237i	−0.941086	−	0.338167i	$-0.890193\pi$
$577$	−38.1212	+	10.2146i	−1.58701	+	0.425237i	−0.645921	+	0.763404i	$0.723526\pi$
$578$	17.4527	−	9.53456i	0.725937	−	0.396585i
$579$	−32.0719	+	18.5167i	−1.33286	+	0.769529i
$580$	−35.1846	+	6.75599i	−1.46096	+	0.280527i
$581$	19.7267	−	27.8525i	0.818403	−	1.15552i
$582$	−16.7166	+	27.4381i	−0.692927	+	1.13734i
$583$	−4.58268	+	17.1028i	−0.189795	+	0.708325i
$584$	0.314397	+	1.62585i	0.0130099	+	0.0672780i
$585$	−8.96162	−	0.223230i	−0.370517	−	0.00922943i
$586$	−28.3851	−	29.7572i	−1.17258	−	1.22926i
$587$	−1.67036	−	1.67036i	−0.0689431	−	0.0689431i	0.671794	−	0.740738i	$-0.265524\pi$
$587$	−1.67036	−	1.67036i	−0.0689431	−	0.0689431i	−0.740738	+	0.671794i	$0.765524\pi$
$588$	11.0296	+	17.8727i	0.454854	+	0.737058i
$589$	9.88260			0.407206
$590$	28.9853	+	9.29431i	1.19330	+	0.382640i
$591$	7.87922	+	4.54907i	0.324108	+	0.187124i
$592$	14.8110	+	5.51032i	0.608726	+	0.226473i
$593$	−14.7654	−	3.95638i	−0.606343	−	0.162469i	−0.0574312	−	0.998349i	$-0.518291\pi$
$593$	−14.7654	−	3.95638i	−0.606343	−	0.162469i	−0.548912	+	0.835880i	$0.684958\pi$
$594$	−16.0298	+	3.89228i	−0.657711	+	0.159702i
$595$	−7.96130	+	6.27950i	−0.326381	+	0.257435i
$596$	11.0077	+	21.3304i	0.450893	+	0.873727i
$597$	−29.4663	−	7.89546i	−1.20597	−	0.323140i
$598$	−46.0225	+	25.1425i	−1.88200	+	1.02815i
$599$	−4.61537	+	7.99405i	−0.188579	+	0.326628i	−0.944777	−	0.327715i	$-0.893721\pi$
$599$	−4.61537	+	7.99405i	−0.188579	+	0.326628i	0.756198	+	0.654343i	$0.227055\pi$
$600$	−13.0879	−	16.6972i	−0.534310	−	0.681660i
$601$	36.4347			1.48620			0.743101	−	0.669179i	$-0.233354\pi$
$601$	36.4347			1.48620			0.743101	+	0.669179i	$0.233354\pi$
$602$	23.6971	−	31.8383i	0.965822	−	1.29763i
$603$	−1.77527	+	1.77527i	−0.0722947	+	0.0722947i
$604$	0.287986	+	0.184910i	0.0117180	+	0.00752389i
$605$	10.3264	+	10.8540i	0.419828	+	0.441278i
$606$	4.10677	−	13.9970i	0.166826	−	0.568590i
$607$	17.8396	+	4.78010i	0.724087	+	0.194018i	0.601994	−	0.798500i	$-0.294373\pi$
$607$	17.8396	+	4.78010i	0.724087	+	0.194018i	0.122092	+	0.992519i	$0.461040\pi$
$608$	−11.8007	+	5.06774i	−0.478583	+	0.205524i
$609$	−13.2826	−	28.8895i	−0.538238	−	1.17066i
$610$	20.0101	−	18.1575i	0.810184	−	0.735177i
$611$	−2.96216	−	5.13061i	−0.119836	−	0.207562i
$612$	−1.90050	+	1.72910i	−0.0768233	+	0.0698948i
$613$	−46.2248	+	12.3859i	−1.86700	+	0.500261i	−0.867003	+	0.498304i	$0.833956\pi$
$613$	−46.2248	+	12.3859i	−1.86700	+	0.500261i	−0.999998	+	0.00195771i	$0.999377\pi$
$614$	−21.4855	−	22.5240i	−0.867083	−	0.908996i
$615$	−2.82739	−	5.19160i	−0.114011	−	0.209346i
$616$	−6.40161	+	14.1359i	−0.257928	+	0.569553i
$617$	−28.1867	−	28.1867i	−1.13476	−	1.13476i	−0.989376	−	0.145379i	$-0.953560\pi$
$617$	−28.1867	−	28.1867i	−1.13476	−	1.13476i	−0.145379	−	0.989376i	$-0.546440\pi$
$618$	−24.5830	−	0.580123i	−0.988873	−	0.0233360i
$619$	5.94805	+	3.43411i	0.239072	+	0.138028i	0.614750	−	0.788722i	$-0.289257\pi$
$619$	5.94805	+	3.43411i	0.239072	+	0.138028i	−0.375678	+	0.926750i	$0.622590\pi$
$620$	18.3919	+	6.37978i	0.738637	+	0.256218i
$621$	−33.7739	+	19.4994i	−1.35530	+	0.782484i
$622$	−11.6727	−	7.11157i	−0.468032	−	0.285148i
$623$	−14.8046	+	12.2873i	−0.593133	+	0.492282i
$624$	18.5949	−	26.1584i	0.744391	−	1.04717i
$625$	14.5912	−	20.3001i	0.583650	−	0.812005i
$626$	−1.93506	−	0.567754i	−0.0773407	−	0.0226920i
$627$	6.82188	−	1.82792i	0.272440	−	0.0730000i
$628$	−1.31051	−	6.01239i	−0.0522949	−	0.239920i
$629$	−6.77121			−0.269986
$630$	−3.86847	+	4.93593i	−0.154124	+	0.196652i
$631$		−	7.46410i		−	0.297141i	−0.988902	−	0.148571i	$-0.952533\pi$
$631$		−	7.46410i		−	0.297141i	0.988902	−	0.148571i	$-0.0474672\pi$
$632$	−8.51603	−	17.5035i	−0.338750	−	0.696252i
$633$	−5.79643	−	21.6326i	−0.230387	−	0.859817i
$634$	−40.8573	−	11.9876i	−1.62265	−	0.476090i
$635$	5.15619	−	8.43827i	0.204617	−	0.334863i
$636$	−11.7483	−	22.7655i	−0.465850	−	0.902711i
$637$	−33.7594	−	16.1869i	−1.33760	−	0.641348i
$638$	12.2237	−	20.0635i	0.483939	−	0.794320i
$639$	2.00351	+	3.47018i	0.0792576	+	0.137278i
$640$	−25.2332	+	1.81323i	−0.997428	+	0.0716741i
$641$	−6.23519	+	10.7997i	−0.246275	+	0.426561i	−0.962489	−	0.271319i	$-0.912540\pi$
$641$	−6.23519	+	10.7997i	−0.246275	+	0.426561i	0.716214	+	0.697881i	$0.245873\pi$
$642$	19.3303	+	0.456166i	0.762905	+	0.0180035i
$643$	−20.0209	+	20.0209i	−0.789548	+	0.789548i	−0.981420	−	0.191872i	$-0.938544\pi$
$643$	−20.0209	+	20.0209i	−0.789548	+	0.789548i	0.191872	+	0.981420i	$0.438544\pi$
$644$	−5.11353	+	36.3292i	−0.201501	+	1.43157i
$645$	−34.1293	−	10.0622i	−1.34384	−	0.396200i
$646$	3.98189	−	3.79829i	0.156665	−	0.149442i
$647$	−11.0436	−	41.2153i	−0.434169	−	1.62034i	−0.743046	−	0.669240i	$-0.766620\pi$
$647$	−11.0436	−	41.2153i	−0.434169	−	1.62034i	0.308877	−	0.951102i	$-0.400047\pi$
$648$	9.80359	−	14.5041i	0.385121	−	0.569774i
$649$	−17.2862	+	9.98019i	−0.678543	+	0.391757i
$650$	35.7146	+	12.4411i	1.40084	+	0.487981i
$651$	−1.59839	+	17.2028i	−0.0626458	+	0.674233i
$652$	1.65400	+	0.527977i	0.0647757	+	0.0206772i
$653$	6.92000	−	25.8258i	0.270801	−	1.01064i	−0.687803	−	0.725897i	$-0.741425\pi$
$653$	6.92000	−	25.8258i	0.270801	−	1.01064i	0.958604	−	0.284744i	$-0.0919086\pi$
$654$	−24.2053	−	7.10191i	−0.946502	−	0.277707i
$655$	−3.22175	−	3.38636i	−0.125884	−	0.132316i
$656$	−7.01791	−	0.664301i	−0.274003	−	0.0259366i
$657$	−0.310310	−	0.310310i	−0.0121064	−	0.0121064i
$658$	−4.11652	−	0.480682i	−0.160479	−	0.0187389i
$659$			25.4132i			0.989959i	0.868905	+	0.494980i	$0.164824\pi$
$659$			25.4132i			0.989959i	−0.868905	+	0.494980i	$0.835176\pi$
$660$	13.8758	+	1.00208i	0.540115	+	0.0390060i
$661$	21.0064	+	12.1280i	0.817053	+	0.471726i	0.849399	−	0.527751i	$-0.176965\pi$
$661$	21.0064	+	12.1280i	0.817053	+	0.471726i	−0.0323461	+	0.999477i	$0.510298\pi$
$662$	−14.2856	−	26.1493i	−0.555226	−	1.01632i
$663$	−3.55922	+	13.2832i	−0.138229	+	0.515876i
$664$	−27.5605	+	23.9111i	−1.06955	+	0.927930i
$665$	8.03357	−	10.7640i	0.311529	−	0.417411i
$666$	−4.06962	+	0.988166i	−0.157695	+	0.0382906i
$667$	14.3758	−	53.6514i	0.556635	−	2.07739i
$668$	−22.0454	+	20.0571i	−0.852960	+	0.776034i
$669$	16.2979	−	28.2288i	0.630113	−	1.09139i
$670$	9.41885	−	4.84504i	0.363882	−	0.187180i
$671$			17.7186i			0.684020i
$672$	−6.91290	−	21.3614i	−0.266671	−	0.824035i
$673$	−7.27359	+	7.27359i	−0.280376	+	0.280376i	−0.833259	−	0.552883i	$-0.813528\pi$
$673$	−7.27359	+	7.27359i	−0.280376	+	0.280376i	0.552883	+	0.833259i	$0.313528\pi$
$674$	32.2374	+	33.7957i	1.24174	+	1.30176i
$675$	26.7700	+	8.62267i	1.03038	+	0.331887i
$676$	−1.47233	+	31.1780i	−0.0566281	+	1.19915i
$677$	−0.908708	−	0.243488i	−0.0349245	−	0.00935799i	0.241315	−	0.970447i	$-0.422421\pi$
$677$	−0.908708	−	0.243488i	−0.0349245	−	0.00935799i	−0.276239	+	0.961089i	$0.589088\pi$
$678$	−31.0435	−	18.9132i	−1.19222	−	0.726358i
$679$	−32.6979	−	23.1586i	−1.25483	−	0.888744i
$680$	9.86246	−	4.49823i	0.378208	−	0.172499i
$681$	−1.70956	−	2.96104i	−0.0655104	−	0.113467i
$682$	−11.2028	+	6.12016i	−0.428976	+	0.234353i
$683$	9.89135	+	36.9150i	0.378482	+	1.41251i	0.848190	+	0.529692i	$0.177692\pi$
$683$	9.89135	+	36.9150i	0.378482	+	1.41251i	−0.469708	+	0.882822i	$0.655641\pi$
$684$	1.83888	−	2.86394i	0.0703112	−	0.109505i
$685$	−0.0283389	+	0.0154336i	−0.00108278	+	0.000589689i
$686$	−23.1850	+	12.1843i	−0.885206	+	0.465199i
$687$	5.48441	−	5.48441i	0.209243	−	0.209243i
$688$	−32.6960	+	27.0414i	−1.24652	+	1.03094i
$689$	39.5500	+	22.8342i	1.50673	+	0.869913i
$690$	32.1452	−	6.96250i	1.22375	−	0.265058i
$691$	5.11739	+	8.86358i	0.194675	+	0.337187i	0.946794	−	0.321841i	$-0.104302\pi$
$691$	5.11739	+	8.86358i	0.194675	+	0.337187i	−0.752119	+	0.659027i	$0.770968\pi$
$692$	10.2848	−	32.2193i	0.390969	−	1.22479i
$693$	−0.692301	−	4.05368i	−0.0262983	−	0.153987i
$694$	−12.3149	+	2.99024i	−0.467466	+	0.113508i
$695$	−1.41201	−	5.84858i	−0.0535606	−	0.221849i
$696$	6.45366	+	33.3739i	0.244625	+	1.26503i
$697$	2.91757	−	0.781762i	0.110511	−	0.0296113i
$698$	33.9380	+	0.800889i	1.28457	+	0.0303141i
$699$		−	3.25986i		−	0.123299i
$700$	21.8996	−	14.8462i	0.827726	−	0.561132i
$701$		−	6.72080i		−	0.253841i	−0.991913	−	0.126920i	$-0.959491\pi$
$701$		−	6.72080i		−	0.253841i	0.991913	−	0.126920i	$-0.0405093\pi$
$702$	−1.00375	+	42.5343i	−0.0378840	+	1.60535i
$703$	8.66373	−	2.32144i	0.326759	−	0.0875547i
$704$	10.2387	−	13.0527i	0.385887	−	0.491944i
$705$	0.871992	+	3.61181i	0.0328411	+	0.136028i
$706$	3.55482	+	14.6400i	0.133788	+	0.550985i
$707$	17.0607	+	6.31376i	0.641632	+	0.237453i
$708$	8.78218	−	27.5121i	0.330055	−	1.03397i
$709$	14.8443	+	25.7111i	0.557489	+	0.965599i	0.997705	+	0.0677074i	$0.0215684\pi$
$709$	14.8443	+	25.7111i	0.557489	+	0.965599i	−0.440216	+	0.897892i	$0.645098\pi$
$710$	−3.57858	−	16.5219i	−0.134302	−	0.620058i
$711$	4.46735	+	2.57923i	0.167539	+	0.0967285i
$712$	18.4949	−	8.99839i	0.693127	−	0.337229i
$713$	−21.3406	+	21.3406i	−0.799211	+	0.799211i
$714$	5.96774	+	7.54568i	0.223337	+	0.282390i
$715$	−21.7797	+	11.8614i	−0.814516	+	0.443592i
$716$	−13.6129	−	8.74056i	−0.508737	−	0.326650i
$717$	−4.65314	−	17.3658i	−0.173775	−	0.648536i
$718$	6.12775	+	11.2167i	0.228686	+	0.418602i
$719$	−23.5433	−	40.7782i	−0.878017	−	1.52077i	−0.853513	−	0.521071i	$-0.825533\pi$
$719$	−23.5433	−	40.7782i	−0.878017	−	1.52077i	−0.0245039	−	0.999700i	$-0.507801\pi$
$720$	5.27106	−	4.14281i	0.196441	−	0.154393i
$721$	2.83708	−	30.5344i	0.105658	−	1.13716i
$722$	10.1877	−	16.7217i	0.379146	−	0.622317i
$723$	20.4312	+	5.47452i	0.759844	+	0.203600i
$724$	0.788970	−	16.7072i	0.0293219	−	0.620917i
$725$	−35.6438	+	18.2761i	−1.32378	+	0.678758i
$726$	10.2852	−	9.81093i	0.381718	−	0.364118i
$727$	18.1993	−	18.1993i	0.674976	−	0.674976i	−0.283883	−	0.958859i	$-0.591623\pi$
$727$	18.1993	−	18.1993i	0.674976	−	0.674976i	0.958859	+	0.283883i	$0.0916227\pi$
$728$	30.9442	+	25.3852i	1.14687	+	0.940839i
$729$			29.9539i			1.10940i
$730$	0.846893	+	1.64637i	0.0313449	+	0.0609351i
$731$	9.09014	−	15.7446i	0.336211	−	0.582335i
$732$	−17.2523	−	18.9625i	−0.637664	−	0.700874i
$733$	−5.27586	+	19.6898i	−0.194868	+	0.727259i	0.797432	+	0.603408i	$0.206191\pi$
$733$	−5.27586	+	19.6898i	−0.194868	+	0.727259i	−0.992301	+	0.123851i	$0.960476\pi$
$734$	−4.43503	−	18.2651i	−0.163700	−	0.674175i
$735$	17.4378	+	15.7252i	0.643204	+	0.580031i
$736$	14.5393	−	36.4260i	0.535925	−	1.34268i
$737$	−1.79767	+	6.70901i	−0.0662181	+	0.247129i
$738$	1.63943	−	0.895632i	0.0603481	−	0.0329687i
$739$	−6.17231	−	3.56359i	−0.227052	−	0.131089i	0.382159	−	0.924096i	$-0.375181\pi$
$739$	−6.17231	−	3.56359i	−0.227052	−	0.131089i	−0.609211	+	0.793008i	$0.708514\pi$
$740$	17.6222	+	1.27264i	0.647803	+	0.0467830i
$741$		−	18.2160i		−	0.669181i
$742$	29.3340	−	12.6574i	1.07689	−	0.464668i
$743$	1.82621	+	1.82621i	0.0669973	+	0.0669973i	0.739812	−	0.672814i	$-0.234915\pi$
$743$	1.82621	+	1.82621i	0.0669973	+	0.0669973i	−0.672814	+	0.739812i	$0.734915\pi$
$744$	6.03011	−	17.4577i	0.221075	−	0.640031i
$745$	18.4978	+	19.4429i	0.677706	+	0.712332i
$746$	−0.637989	+	2.17445i	−0.0233584	+	0.0796121i
$747$	2.50263	−	9.33996i	0.0915666	−	0.341731i
$748$	−2.16158	+	6.77161i	−0.0790351	+	0.247594i
$749$	−2.23087	+	24.0100i	−0.0815142	+	0.877306i
$750$	−19.2784	−	13.8186i	−0.703948	−	0.504584i
$751$	−14.7753	+	8.53052i	−0.539158	+	0.311283i	−0.744738	−	0.667357i	$-0.767425\pi$
$751$	−14.7753	+	8.53052i	−0.539158	+	0.311283i	0.205580	+	0.978640i	$0.434092\pi$
$752$	4.15257	+	1.54494i	0.151429	+	0.0563380i
$753$	−0.829219	−	3.09469i	−0.0302184	−	0.112777i
$754$	−41.8252	−	43.8470i	−1.52319	−	1.59681i
$755$	0.367017	+	0.108206i	0.0133571	+	0.00393803i
$756$	23.4506	+	18.3296i	0.852890	+	0.666639i
$757$	−19.9476	+	19.9476i	−0.725007	+	0.725007i	−0.969621	−	0.244614i	$-0.921339\pi$
$757$	−19.9476	+	19.9476i	−0.725007	+	0.725007i	0.244614	+	0.969621i	$0.421339\pi$
$758$	0.811840	−	34.4021i	0.0294874	−	1.24954i
$759$	−10.7840	+	18.6784i	−0.391435	+	0.677985i
$760$	−11.0768	+	9.13669i	−0.401797	+	0.331423i
$761$	−14.2802	−	24.7340i	−0.517656	−	0.896607i	−0.999790	−	0.0205088i	$-0.993471\pi$
$761$	−14.2802	−	24.7340i	−0.517656	−	0.896607i	0.482134	−	0.876098i	$-0.339862\pi$
$762$	−8.01244	−	4.88157i	−0.290260	−	0.176841i
$763$	10.9185	−	29.5033i	0.395276	−	1.06809i
$764$	−3.09271	+	1.59602i	−0.111890	+	0.0577418i
$765$	−1.49783	+	2.45125i	−0.0541542	+	0.0886251i
$766$	1.70855	−	5.82323i	0.0617325	−	0.210402i
$767$	13.3247	+	49.7284i	0.481127	+	1.79559i
$768$	1.75172	+	23.9384i	0.0632096	+	0.863801i
$769$			1.35549i			0.0488803i	0.999701	+	0.0244401i	$0.00778031\pi$
$769$			1.35549i			0.0488803i	−0.999701	+	0.0244401i	$0.992220\pi$
$770$	−2.44071	+	17.1770i	−0.0879571	+	0.619016i
$771$	41.9576			1.51106
$772$	10.5149	+	48.2405i	0.378438	+	1.73621i
$773$	21.8416	−	5.85244i	0.785588	−	0.210498i	0.156341	−	0.987703i	$-0.450030\pi$
$773$	21.8416	−	5.85244i	0.785588	−	0.210498i	0.629247	+	0.777205i	$0.283363\pi$
$774$	3.16563	−	10.7894i	0.113786	−	0.387815i
$775$	21.7378	+	1.08363i	0.780844	+	0.0389251i
$776$	28.0709	+	32.3551i	1.00768	+	1.16148i
$777$	2.63972	+	15.4566i	0.0946996	+	0.554502i
$778$	−10.4116	+	17.0893i	−0.373275	+	0.612679i
$779$	−3.46500	+	2.00052i	−0.124146	+	0.0716760i
$780$	11.7594	−	33.9007i	0.421056	−	1.21384i
$781$	9.60033	+	5.54275i	0.343527	+	0.198335i
$782$	−0.396470	+	16.8006i	−0.0141777	+	0.600788i
$783$	−31.8639	−	31.8639i	−1.13872	−	1.13872i
$784$	27.1711	−	6.76239i	0.970397	−	0.241514i
$785$	−3.29051	−	6.04197i	−0.117443	−	0.215647i
$786$	−3.20889	+	3.06093i	−0.114457	+	0.109180i
$787$	−13.5594	+	3.63323i	−0.483340	+	0.129511i	−0.492257	−	0.870450i	$-0.663828\pi$
$787$	−13.5594	+	3.63323i	−0.483340	+	0.129511i	0.00891736	+	0.999960i	$0.497161\pi$
$788$	8.97199	−	8.16283i	0.319614	−	0.290789i
$789$	12.0622	+	20.8924i	0.429426	+	0.743788i
$790$	−14.6245	−	16.1166i	−0.520316	−	0.573401i
$791$	26.2016	−	36.9945i	0.931623	−	1.31537i
$792$	−0.310923	+	4.38531i	−0.0110482	+	0.155825i
$793$	44.1434	+	11.8282i	1.56758	+	0.420031i
$794$	−19.1504	−	5.61880i	−0.679624	−	0.199404i
$795$	−19.7423	−	20.7510i	−0.700188	−	0.735962i
$796$	−21.9739	+	34.2231i	−0.778845	+	1.21300i
$797$	8.95615	−	8.95615i	0.317243	−	0.317243i	−0.530464	−	0.847707i	$-0.677982\pi$
$797$	8.95615	−	8.95615i	0.317243	−	0.317243i	0.847707	+	0.530464i	$0.177982\pi$
$798$	−10.2226	−	7.60868i	−0.361877	−	0.269344i
$799$	−1.89846			−0.0671625
$800$	−26.5126	+	9.85306i	−0.937362	+	0.348358i
$801$	−2.72532	+	4.72039i	−0.0962944	+	0.166787i
$802$	−16.5369	−	30.2703i	−0.583938	−	1.06888i
$803$	−1.17271	−	0.314226i	−0.0413839	−	0.0110888i
$804$	−4.60857	−	8.93035i	−0.162532	−	0.314949i
$805$	5.89617	+	40.5917i	0.207813	+	1.43067i
$806$	7.76902	+	31.9956i	0.273652	+	1.12700i
$807$	−7.61618	−	2.04075i	−0.268102	−	0.0718378i
$808$	−16.1122	−	10.8905i	−0.566824	−	0.383127i
$809$	28.0498	+	16.1946i	0.986178	+	0.569370i	0.904130	−	0.427258i	$-0.140520\pi$
$809$	28.0498	+	16.1946i	0.986178	+	0.569370i	0.0820487	+	0.996628i	$0.473854\pi$
$810$	5.97643	−	18.6381i	0.209990	−	0.654878i
$811$	−8.22841			−0.288938			−0.144469	−	0.989509i	$-0.546147\pi$
$811$	−8.22841			−0.288938			−0.144469	+	0.989509i	$0.546147\pi$
$812$	−42.0766	+	5.15738i	−1.47660	+	0.180988i
$813$	−6.60569	−	6.60569i	−0.231672	−	0.231672i
$814$	−8.38342	+	7.99687i	−0.293839	+	0.280290i
$815$	1.94056	+	0.0483385i	0.0679748	+	0.00169322i
$816$	−4.28007	−	9.35167i	−0.149832	−	0.327374i
$817$	−6.23292	+	23.2616i	−0.218062	+	0.813819i
$818$	3.30304	+	2.01237i	0.115488	+	0.0703610i
$819$	−10.5613	−	0.981298i	−0.369043	−	0.0342893i
$820$	−7.73994	+	1.48619i	−0.270291	+	0.0519000i
$821$	29.6787	−	17.1350i	1.03579	−	0.598016i	0.117155	−	0.993114i	$-0.462623\pi$
$821$	29.6787	−	17.1350i	1.03579	−	0.598016i	0.918639	+	0.395098i	$0.129289\pi$
$822$	0.0146783	+	0.0268681i	0.000511964	+	0.000937133i
$823$	35.1088	−	9.40737i	1.22382	−	0.327920i	0.411647	−	0.911343i	$-0.364954\pi$
$823$	35.1088	−	9.40737i	1.22382	−	0.327920i	0.812168	+	0.583423i	$0.198287\pi$
$824$	−10.7032	+	30.9868i	−0.372864	+	1.07948i
$825$	15.2058	−	3.27267i	0.529399	−	0.113940i
$826$	33.4728	+	13.2935i	1.16467	+	0.462540i
$827$	17.3030	+	17.3030i	0.601684	+	0.601684i	0.940759	−	0.339075i	$-0.110114\pi$
$827$	17.3030	+	17.3030i	0.601684	+	0.601684i	−0.339075	+	0.940759i	$0.610114\pi$
$828$	2.21353	+	10.1553i	0.0769254	+	0.352921i
$829$	3.29605	−	5.70893i	0.114477	−	0.198279i	−0.803094	−	0.595853i	$-0.796814\pi$
$829$	3.29605	−	5.70893i	0.114477	−	0.198279i	0.917570	+	0.397573i	$0.130148\pi$
$830$	−22.0857	+	34.2983i	−0.766607	+	1.19051i
$831$	7.01024	−	4.04736i	0.243183	−	0.140402i
$832$	−25.6841	−	34.2218i	−0.890436	−	1.18643i
$833$	−9.90128	+	6.77531i	−0.343059	+	0.234751i
$834$	−5.54723	+	1.34695i	−0.192085	+	0.0466411i
$835$	−17.3745	+	28.4339i	−0.601268	+	0.983995i
$836$	0.444151	−	9.40530i	0.0153613	−	0.325289i
$837$	6.33715	+	23.6506i	0.219044	+	0.817483i
$838$	−0.303755	+	12.8718i	−0.0104930	+	0.444648i
$839$	53.0081			1.83004			0.915022	−	0.403405i	$-0.132173\pi$
$839$	53.0081			1.83004			0.915022	+	0.403405i	$0.132173\pi$
$840$	−14.1129	−	20.7593i	−0.486941	−	0.716265i
$841$	35.1800			1.21310
$842$	−0.237923	+	10.0821i	−0.00819938	+	0.347452i
$843$	10.9329	+	40.8023i	0.376550	+	1.40531i
$844$	−29.8247	−	1.40843i	−1.02661	−	0.0484800i
$845$	8.18978	+	33.9222i	0.281737	+	1.16696i
$846$	−1.14100	+	0.277053i	−0.0392286	+	0.00952529i
$847$	11.3210	+	13.6402i	0.388994	+	0.468684i
$848$	−33.6766	+	5.69151i	−1.15646	+	0.195447i
$849$	29.3271	−	16.9320i	1.00650	−	0.581105i
$850$	9.17505	−	7.91810i	0.314702	−	0.271589i
$851$	−13.6956	+	23.7215i	−0.469479	+	0.813161i
$852$	−15.6712	+	3.41581i	−0.536886	+	0.117024i
$853$	35.4072	+	35.4072i	1.21232	+	1.21232i	0.970262	+	0.242056i	$0.0778218\pi$
$853$	35.4072	+	35.4072i	1.21232	+	1.21232i	0.242056	+	0.970262i	$0.422178\pi$
$854$	25.0762	−	19.8323i	0.858091	−	0.678648i
$855$	1.07608	−	3.64987i	0.0368012	−	0.124823i
$856$	8.41623	−	24.3657i	0.287661	−	0.832804i
$857$	5.23560	−	1.40287i	0.178845	−	0.0479213i	−0.168285	−	0.985738i	$-0.553823\pi$
$857$	5.23560	−	1.40287i	0.178845	−	0.0479213i	0.347130	+	0.937817i	$0.387156\pi$
$858$	11.2809	+	20.6493i	0.385124	+	0.704957i
$859$	−1.32568	+	0.765383i	−0.0452317	+	0.0261145i	−0.522445	−	0.852673i	$-0.674980\pi$
$859$	−1.32568	+	0.765383i	−0.0452317	+	0.0261145i	0.477214	+	0.878787i	$0.341647\pi$
$860$	−26.6164	+	39.2670i	−0.907610	+	1.33899i
$861$	−2.92192	−	6.35515i	−0.0995788	−	0.216583i
$862$	25.1689	+	15.3341i	0.857256	+	0.522283i
$863$	0.600608	−	2.24150i	0.0204449	−	0.0763016i	−0.954950	−	0.296768i	$-0.904091\pi$
$863$	0.600608	−	2.24150i	0.0204449	−	0.0763016i	0.975395	+	0.220466i	$0.0707579\pi$
$864$	−19.6950	−	24.9913i	−0.670039	−	0.850222i
$865$	0.941615	−	37.8013i	0.0320159	−	1.28528i
$866$	10.8183	−	10.3194i	0.367619	−	0.350669i
$867$	−14.9169	−	14.9169i	−0.506606	−	0.506606i
$868$	21.2007	+	9.00443i	0.719599	+	0.305630i
$869$	14.2710			0.484110
$870$	17.3843	+	33.7953i	0.589381	+	1.14577i
$871$	15.5145	+	8.95729i	0.525688	+	0.303506i
$872$	−18.8332	+	27.8630i	−0.637772	+	0.943561i
$873$	−10.9648	−	2.93801i	−0.371103	−	0.0994366i
$874$	−5.25262	−	21.6322i	−0.177672	−	0.731719i
$875$	18.8509	−	22.7957i	0.637278	−	0.770634i
$876$	1.56099	−	0.805558i	0.0527409	−	0.0272173i
$877$	26.7929	+	7.17913i	0.904731	+	0.242422i	0.681047	−	0.732240i	$-0.261525\pi$
$877$	26.7929	+	7.17913i	0.904731	+	0.242422i	0.223684	+	0.974662i	$0.428192\pi$
$878$	−10.0382	−	18.3745i	−0.338771	−	0.620110i
$879$	−21.8116	+	37.7788i	−0.735686	+	1.27425i
$880$	6.89823	−	17.2169i	0.232539	−	0.580382i
$881$	−12.2442			−0.412518			−0.206259	−	0.978497i	$-0.566129\pi$
$881$	−12.2442			−0.412518			−0.206259	+	0.978497i	$0.566129\pi$
$882$	−4.96208	+	5.51704i	−0.167082	+	0.185768i
$883$	16.6226	−	16.6226i	0.559395	−	0.559395i	−0.369740	−	0.929135i	$-0.620553\pi$
$883$	16.6226	−	16.6226i	0.559395	−	0.559395i	0.929135	+	0.369740i	$0.120553\pi$
$884$	15.4275	+	9.90569i	0.518883	+	0.333165i
$885$	0.804045	−	32.2786i	0.0270277	−	1.08503i
$886$	21.0919	+	6.18842i	0.708595	+	0.207904i
$887$	−17.2517	−	4.62259i	−0.579256	−	0.155211i	−0.0427179	−	0.999087i	$-0.513602\pi$
$887$	−17.2517	−	4.62259i	−0.579256	−	0.155211i	−0.536538	+	0.843876i	$0.680268\pi$
$888$	1.18554	−	16.7211i	0.0397841	−	0.561122i
$889$	6.76274	−	9.54842i	0.226815	−	0.320244i
$890$	17.0294	−	15.4528i	0.570828	−	0.517980i
$891$	6.41747	+	11.1154i	0.214993	+	0.372380i
$892$	−29.2449	−	32.1439i	−0.979191	−	1.07626i
$893$	2.42906	−	0.650865i	0.0812854	−	0.0217804i
$894$	18.4239	−	17.5744i	0.616188	−	0.587777i
$895$	−17.3486	−	5.11483i	−0.579899	−	0.170970i
$896$	−29.9330	+	0.119489i	−0.999992	+	0.00399184i
$897$	39.3357	+	39.3357i	1.31338	+	1.31338i
$898$	−0.668505	+	28.3282i	−0.0223083	+	0.945325i
$899$	−30.2005	−	17.4363i	−1.00724	−	0.581532i
$900$	4.35883	−	6.09789i	0.145294	−	0.203263i
$901$	12.6738	−	7.31724i	0.422227	−	0.243773i
$902$	2.68897	−	4.41358i	0.0895330	−	0.146956i
$903$	−39.4838	−	14.6120i	−1.31394	−	0.486258i
$904$	−36.6066	+	31.7594i	−1.21752	+	1.05630i
$905$	−4.38862	−	18.1777i	−0.145883	−	0.604249i
$906$	0.102207	−	0.348351i	0.00339561	−	0.0115732i
$907$	40.1471	−	10.7574i	1.33306	−	0.357193i	0.479206	−	0.877702i	$-0.340925\pi$
$907$	40.1471	−	10.7574i	1.33306	−	0.357193i	0.853856	+	0.520510i	$0.174258\pi$
$908$	−4.45380	+	0.970785i	−0.147805	+	0.0322166i
$909$	5.15375			0.170939
$910$	41.1647	+	17.5473i	1.36460	+	0.581688i
$911$		−	7.85892i		−	0.260378i	−0.991489	−	0.130189i	$-0.958442\pi$
$911$		−	7.85892i		−	0.260378i	0.991489	−	0.130189i	$-0.0415584\pi$
$912$	8.68244	+	10.4980i	0.287504	+	0.347624i
$913$	−6.92359	−	25.8392i	−0.229137	−	0.855152i
$914$	−4.03541	+	13.7538i	−0.133480	+	0.454936i
$915$	−24.4576	−	14.9448i	−0.808545	−	0.494059i
$916$	−4.74207	−	9.18904i	−0.156682	−	0.303614i
$917$	−3.53206	−	4.25565i	−0.116639	−	0.140534i
$918$	11.6432	+	7.09364i	0.384284	+	0.234125i
$919$	−5.33141	−	9.23428i	−0.175867	−	0.304611i	0.764594	−	0.644512i	$-0.222940\pi$
$919$	−5.33141	−	9.23428i	−0.175867	−	0.304611i	−0.940461	+	0.339902i	$0.889606\pi$
$920$	4.18945	−	43.6492i	0.138122	−	1.43907i
$921$	−16.5098	+	28.5958i	−0.544016	+	0.942263i
$922$	−1.00825	+	42.7251i	−0.0332050	+	1.40708i
$923$	20.2177	−	20.2177i	0.665475	−	0.665475i
$924$	16.3002	+	2.29433i	0.536236	+	0.0754780i
$925$	19.3113	−	4.15626i	0.634951	−	0.136657i
$926$	−33.2383	−	34.8450i	−1.09228	−	1.14508i
$927$	−2.24858	−	8.39180i	−0.0738529	−	0.275623i
$928$	45.0034	+	5.33386i	1.47731	+	0.175093i
$929$	25.4869	−	14.7149i	0.836197	−	0.482779i	−0.0197726	−	0.999805i	$-0.506294\pi$
$929$	25.4869	−	14.7149i	0.836197	−	0.482779i	0.855970	+	0.517026i	$0.172961\pi$
$930$	1.00110	−	20.6256i	0.0328273	−	0.676341i
$931$	10.3458	−	12.0635i	0.339069	−	0.395366i
$932$	−4.14023	−	1.32161i	−0.135618	−	0.0432907i
$933$	−3.75261	+	14.0049i	−0.122855	+	0.458501i
$934$	12.7000	−	43.2853i	0.415558	−	1.41634i
$935$	−0.197901	+	7.94479i	−0.00647207	+	0.259822i
$936$	10.7178	+	3.70206i	0.350322	+	0.121006i
$937$	−8.44266	−	8.44266i	−0.275810	−	0.275810i	0.555624	−	0.831434i	$-0.312479\pi$
$937$	−8.44266	−	8.44266i	−0.275810	−	0.275810i	−0.831434	+	0.555624i	$0.812479\pi$
$938$	11.5070	−	4.96519i	0.375718	−	0.162119i
$939$			2.13918i			0.0698094i
$940$	4.94075	+	0.356811i	0.161149	+	0.0116379i
$941$	−22.7532	−	13.1366i	−0.741732	−	0.428239i	0.0809665	−	0.996717i	$-0.474199\pi$
$941$	−22.7532	−	13.1366i	−0.741732	−	0.428239i	−0.822699	+	0.568477i	$0.807533\pi$
$942$	−5.72838	+	3.12946i	−0.186641	+	0.101963i
$943$	3.16241	−	11.8023i	0.102982	−	0.384335i
$944$	−31.3816	−	22.3079i	−1.02139	−	0.726059i
$945$	30.9114	+	12.3232i	1.00555	+	0.400874i
$946$	−7.34003	−	30.2289i	−0.238645	−	0.982826i
$947$	14.9808	−	55.9090i	0.486810	−	1.81680i	−0.0849604	−	0.996384i	$-0.527076\pi$
$947$	14.9808	−	55.9090i	0.486810	−	1.81680i	0.571770	−	0.820414i	$-0.306257\pi$
$948$	−15.2728	+	13.8954i	−0.496038	+	0.451301i
$949$	−1.56570	+	2.71187i	−0.0508247	+	0.0880309i
$950$	−9.02478	+	13.2767i	−0.292802	+	0.430754i
$951$			45.1669i			1.46464i
$952$	12.0029	−	4.52024i	0.389017	−	0.146502i
$953$	−8.93166	+	8.93166i	−0.289325	+	0.289325i	−0.836813	−	0.547488i	$-0.815584\pi$
$953$	−8.93166	+	8.93166i	−0.289325	+	0.289325i	0.547488	+	0.836813i	$0.315584\pi$
$954$	6.54934	−	6.24736i	0.212043	−	0.202266i
$955$	−2.81904	+	2.68201i	−0.0912220	+	0.0867879i
$956$	−23.9421	−	1.13063i	−0.774343	−	0.0365671i
$957$	−24.0722	−	6.45014i	−0.778145	−	0.208503i
$958$	−24.9279	+	40.9157i	−0.805382	+	1.32193i
$959$	−0.0346903	+	0.0159496i	−0.00112021	+	0.000515041i
$960$	9.38130	+	25.1423i	0.302780	+	0.811463i
$961$	−6.02590	−	10.4372i	−0.194384	−	0.336683i
$962$	14.3266	+	26.2245i	0.461910	+	0.845511i
$963$	1.76812	+	6.59870i	0.0569767	+	0.212640i
$964$	15.2362	−	23.7294i	0.490725	−	0.764274i
$965$	26.4014	+	48.4778i	0.849892	+	1.56056i
$966$	38.5051	−	5.64461i	1.23888	−	0.181612i
$967$	−31.6291	+	31.6291i	−1.01712	+	1.01712i	−0.0172727	+	0.999851i	$0.505498\pi$
$967$	−31.6291	+	31.6291i	−1.01712	+	1.01712i	−0.999851	+	0.0172727i	$0.994502\pi$
$968$	−8.29070	−	17.0404i	−0.266473	−	0.547698i
$969$	−5.05528	−	2.91867i	−0.162399	−	0.0937611i
$970$	40.2651	+	25.9279i	1.29283	+	0.832496i
$971$	2.92796	+	5.07137i	0.0939626	+	0.162748i	0.909175	−	0.416414i	$-0.136713\pi$
$971$	2.92796	+	5.07137i	0.0939626	+	0.162748i	−0.815213	+	0.579162i	$0.803380\pi$
$972$	14.4602	+	4.61586i	0.463811	+	0.148054i
$973$	−1.19844	−	7.01735i	−0.0384204	−	0.224966i
$974$	9.23069	+	38.0153i	0.295771	+	1.21809i
$975$	1.99739	−	40.0679i	0.0639676	−	1.28320i
$976$	−31.0780	+	14.2238i	−0.994783	+	0.455292i
$977$	−24.6834	+	6.61390i	−0.789693	+	0.211597i	−0.631054	−	0.775739i	$-0.717377\pi$
$977$	−24.6834	+	6.61390i	−0.789693	+	0.211597i	−0.158639	+	0.987337i	$0.550711\pi$
$978$	0.0434500	−	1.84121i	0.00138938	−	0.0588755i
$979$			15.0793i			0.481937i
$980$	27.0416	−	15.7719i	0.863812	−	0.503814i
$981$		−	8.91247i		−	0.284553i
$982$	−0.192440	−	0.00454130i	−0.00614100	−	0.000144919i
$983$	−5.86808	+	1.57235i	−0.187163	+	0.0501501i	−0.351183	−	0.936307i	$-0.614220\pi$
$983$	−5.86808	+	1.57235i	−0.187163	+	0.0501501i	0.164020	+	0.986457i	$0.447554\pi$
$984$	1.41968	+	7.34162i	0.0452578	+	0.234042i
$985$	7.07104	−	11.5720i	0.225302	−	0.368714i
$986$	−18.8698	+	4.58188i	−0.600938	+	0.145917i
$987$	0.740103	+	4.33359i	0.0235577	+	0.137940i
$988$	−23.1355	−	7.38511i	−0.736037	−	0.234952i
$989$	−36.7718	−	63.6906i	−1.16928	−	2.02524i
$990$	1.04049	+	4.80384i	0.0330690	+	0.152676i
$991$	−52.1775	−	30.1247i	−1.65747	−	0.956943i	−0.973875	−	0.227084i	$-0.927081\pi$
$991$	−52.1775	−	30.1247i	−1.65747	−	0.956943i	−0.683598	−	0.729859i	$-0.739586\pi$
$992$	−19.7277	−	14.7363i	−0.626356	−	0.467879i
$993$	−22.3500	+	22.3500i	−0.709256	+	0.709256i
$994$	−2.90121	−	19.7908i	−0.0920208	−	0.627726i
$995$	−12.8588	+	43.6147i	−0.407650	+	1.38268i
$996$	32.5688	+	20.9118i	1.03198	+	0.662615i
$997$	−8.12658	−	30.3288i	−0.257371	−	0.960522i	−0.966756	−	0.255701i	$-0.917694\pi$
$997$	−8.12658	−	30.3288i	−0.257371	−	0.960522i	0.709385	−	0.704821i	$-0.248973\pi$
$998$	0.607456	−	0.331858i	0.0192287	−	0.0105048i
$999$	11.1111	+	19.2450i	0.351540	+	0.608885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.67.1	✓	176
5.3	odd	4	inner	280.2.br.a.123.23	yes	176
7.2	even	3	inner	280.2.br.a.107.30	yes	176
8.3	odd	2	inner	280.2.br.a.67.37	yes	176
35.23	odd	12	inner	280.2.br.a.163.37	yes	176
40.3	even	4	inner	280.2.br.a.123.30	yes	176
56.51	odd	6	inner	280.2.br.a.107.23	yes	176
280.163	even	12	inner	280.2.br.a.163.1	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.1	✓	176	1.1	even	1	trivial
280.2.br.a.67.37	yes	176	8.3	odd	2	inner
280.2.br.a.107.23	yes	176	56.51	odd	6	inner
280.2.br.a.107.30	yes	176	7.2	even	3	inner
280.2.br.a.123.23	yes	176	5.3	odd	4	inner
280.2.br.a.123.30	yes	176	40.3	even	4	inner
280.2.br.a.163.1	yes	176	280.163	even	12	inner
280.2.br.a.163.37	yes	176	35.23	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41382 - 0.0333641i) q^{2} +(0.388267 + 1.44903i) q^{3} +(1.99777 + 0.0943417i) q^{4} +(2.17362 - 0.524773i) q^{5} +(-0.500594 - 2.06162i) q^{6} +(2.60799 - 0.445401i) q^{7} +(-2.82134 - 0.200036i) q^{8} +(0.649136 - 0.374779i) q^{9} +O(q^{10})\)	\(q+(-1.41382 - 0.0333641i) q^{2} +(0.388267 + 1.44903i) q^{3} +(1.99777 + 0.0943417i) q^{4} +(2.17362 - 0.524773i) q^{5} +(-0.500594 - 2.06162i) q^{6} +(2.60799 - 0.445401i) q^{7} +(-2.82134 - 0.200036i) q^{8} +(0.649136 - 0.374779i) q^{9} +(-3.09061 + 0.669413i) q^{10} +(1.03683 - 1.79585i) q^{11} +(0.638965 + 2.93147i) q^{12} +(-3.78195 - 3.78195i) q^{13} +(-3.70209 + 0.542703i) q^{14} +(1.60436 + 2.94589i) q^{15} +(3.98220 + 0.376947i) q^{16} +(-1.65553 + 0.443598i) q^{17} +(-0.930265 + 0.508212i) q^{18} +(1.96616 - 1.13516i) q^{19} +(4.39190 - 0.843314i) q^{20} +(1.65800 + 3.60613i) q^{21} +(-1.52581 + 2.50441i) q^{22} +(-1.79446 + 6.69701i) q^{23} +(-0.805576 - 4.16588i) q^{24} +(4.44923 - 2.28131i) q^{25} +(5.22082 + 5.47318i) q^{26} +(3.97740 + 3.97740i) q^{27} +(5.25220 - 0.643768i) q^{28} -8.01124 q^{29} +(-2.16998 - 4.21848i) q^{30} +(3.76977 + 2.17648i) q^{31} +(-5.61754 - 0.665798i) q^{32} +(3.00481 + 0.805136i) q^{33} +(2.35542 - 0.571932i) q^{34} +(5.43504 - 2.33673i) q^{35} +(1.33218 - 0.687482i) q^{36} +(3.81608 + 1.02252i) q^{37} +(-2.81766 + 1.53931i) q^{38} +(4.01176 - 6.94858i) q^{39} +(-6.23750 + 1.04576i) q^{40} -1.76232 q^{41} +(-2.22379 - 5.15373i) q^{42} +(-7.50054 + 7.50054i) q^{43} +(2.24078 - 3.48988i) q^{44} +(1.21430 - 1.15527i) q^{45} +(2.76048 - 9.40850i) q^{46} +(1.06992 + 0.286684i) q^{47} +(0.999948 + 5.91669i) q^{48} +(6.60324 - 2.32320i) q^{49} +(-6.36652 + 3.07692i) q^{50} +(-1.28557 - 2.22668i) q^{51} +(-7.19869 - 7.91228i) q^{52} +(-8.24761 + 2.20994i) q^{53} +(-5.49062 - 5.75603i) q^{54} +(1.31127 - 4.44759i) q^{55} +(-7.44714 + 0.734937i) q^{56} +(2.40828 + 2.40828i) q^{57} +(11.3265 + 0.267288i) q^{58} +(-8.33605 - 4.81282i) q^{59} +(2.92722 + 6.03658i) q^{60} +(-7.39983 + 4.27229i) q^{61} +(-5.25716 - 3.20292i) q^{62} +(1.52601 - 1.26655i) q^{63} +(7.91997 + 1.12874i) q^{64} +(-10.2052 - 6.23586i) q^{65} +(-4.22140 - 1.23857i) q^{66} +(-3.23533 + 0.866905i) q^{67} +(-3.34922 + 0.730022i) q^{68} -10.4009 q^{69} +(-7.76213 + 3.12238i) q^{70} +5.34585i q^{71} +(-1.90640 + 0.927529i) q^{72} +(-0.151531 - 0.565523i) q^{73} +(-5.36113 - 1.57297i) q^{74} +(5.03318 + 5.56131i) q^{75} +(4.03503 - 2.08230i) q^{76} +(1.90418 - 5.14536i) q^{77} +(-5.90374 + 9.69019i) q^{78} +(3.44100 + 5.95998i) q^{79} +(8.85359 - 1.27041i) q^{80} +(-3.09475 + 5.36026i) q^{81} +(2.49160 + 0.0587983i) q^{82} +(9.12181 - 9.12181i) q^{83} +(2.97209 + 7.36064i) q^{84} +(-3.36570 + 1.83299i) q^{85} +(10.8547 - 10.3542i) q^{86} +(-3.11050 - 11.6085i) q^{87} +(-3.28450 + 4.85930i) q^{88} +(-6.29757 + 3.63590i) q^{89} +(-1.75535 + 1.59284i) q^{90} +(-11.5478 - 8.17882i) q^{91} +(-4.21673 + 13.2098i) q^{92} +(-1.69011 + 6.30756i) q^{93} +(-1.50311 - 0.441017i) q^{94} +(3.67797 - 3.49919i) q^{95} +(-1.21634 - 8.39849i) q^{96} +(-10.7087 - 10.7087i) q^{97} +(-9.41330 + 3.06428i) q^{98} -1.55433i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

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