LMFDB - Embedded newform 804.2.e.b.535.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.29
Character	$\chi$	$=$	804.535
Dual form			804.2.e.b.535.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31376 - 0.523490i) q^{2} +1.00000 q^{3} +(1.45192 - 1.37548i) q^{4} +1.71706i q^{5} +(1.31376 - 0.523490i) q^{6} +3.43662 q^{7} +(1.18741 - 2.56711i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.31376 - 0.523490i) q^{2} +1.00000 q^{3} +(1.45192 - 1.37548i) q^{4} +1.71706i q^{5} +(1.31376 - 0.523490i) q^{6} +3.43662 q^{7} +(1.18741 - 2.56711i) q^{8} +1.00000 q^{9} +(0.898862 + 2.25579i) q^{10} -1.17026 q^{11} +(1.45192 - 1.37548i) q^{12} +1.11142i q^{13} +(4.51489 - 1.79904i) q^{14} +1.71706i q^{15} +(0.216118 - 3.99416i) q^{16} -6.00763 q^{17} +(1.31376 - 0.523490i) q^{18} -1.61491i q^{19} +(2.36177 + 2.49302i) q^{20} +3.43662 q^{21} +(-1.53743 + 0.612619i) q^{22} +5.58871i q^{23} +(1.18741 - 2.56711i) q^{24} +2.05172 q^{25} +(0.581818 + 1.46014i) q^{26} +1.00000 q^{27} +(4.98969 - 4.72700i) q^{28} -2.67857 q^{29} +(0.898862 + 2.25579i) q^{30} -3.52610 q^{31} +(-1.80698 - 5.36049i) q^{32} -1.17026 q^{33} +(-7.89257 + 3.14494i) q^{34} +5.90087i q^{35} +(1.45192 - 1.37548i) q^{36} +4.31616 q^{37} +(-0.845389 - 2.12160i) q^{38} +1.11142i q^{39} +(4.40787 + 2.03886i) q^{40} -8.77192i q^{41} +(4.51489 - 1.79904i) q^{42} -1.55663 q^{43} +(-1.69912 + 1.60966i) q^{44} +1.71706i q^{45} +(2.92563 + 7.34220i) q^{46} +3.12725i q^{47} +(0.216118 - 3.99416i) q^{48} +4.81038 q^{49} +(2.69546 - 1.07406i) q^{50} -6.00763 q^{51} +(1.52873 + 1.61369i) q^{52} -9.63385i q^{53} +(1.31376 - 0.523490i) q^{54} -2.00940i q^{55} +(4.08070 - 8.82218i) q^{56} -1.61491i q^{57} +(-3.51899 + 1.40220i) q^{58} -5.48116i q^{59} +(2.36177 + 2.49302i) q^{60} -3.17038i q^{61} +(-4.63244 + 1.84588i) q^{62} +3.43662 q^{63} +(-5.18009 - 6.09644i) q^{64} -1.90837 q^{65} +(-1.53743 + 0.612619i) q^{66} +(3.55266 + 7.37419i) q^{67} +(-8.72257 + 8.26336i) q^{68} +5.58871i q^{69} +(3.08905 + 7.75231i) q^{70} +14.4279i q^{71} +(1.18741 - 2.56711i) q^{72} -7.90152 q^{73} +(5.67038 - 2.25947i) q^{74} +2.05172 q^{75} +(-2.22127 - 2.34471i) q^{76} -4.02173 q^{77} +(0.581818 + 1.46014i) q^{78} -7.48688 q^{79} +(6.85819 + 0.371086i) q^{80} +1.00000 q^{81} +(-4.59201 - 11.5242i) q^{82} -3.57916i q^{83} +(4.98969 - 4.72700i) q^{84} -10.3154i q^{85} +(-2.04503 + 0.814881i) q^{86} -2.67857 q^{87} +(-1.38958 + 3.00418i) q^{88} -13.9566 q^{89} +(0.898862 + 2.25579i) q^{90} +3.81953i q^{91} +(7.68715 + 8.11433i) q^{92} -3.52610 q^{93} +(1.63709 + 4.10845i) q^{94} +2.77289 q^{95} +(-1.80698 - 5.36049i) q^{96} -7.37562i q^{97} +(6.31967 - 2.51819i) q^{98} -1.17026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.31376	−	0.523490i	0.928967	−	0.370164i
$2$	1.31376	−	0.523490i	0.928967	−	0.370164i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.45192	−	1.37548i	0.725958	−	0.687739i
$5$			1.71706i			0.767891i	0.923356	+	0.383945i	$0.125435\pi$
$5$			1.71706i			0.767891i	−0.923356	+	0.383945i	$0.874565\pi$
$6$	1.31376	−	0.523490i	0.536339	−	0.213714i
$7$	3.43662			1.29892			0.649461	−	0.760395i	$-0.274995\pi$
$7$	3.43662			1.29892			0.649461	+	0.760395i	$0.274995\pi$
$8$	1.18741	−	2.56711i	0.419814	−	0.907610i
$9$	1.00000			0.333333
$10$	0.898862	+	2.25579i	0.284245	+	0.713345i
$11$	−1.17026			−0.352846			−0.176423	−	0.984314i	$-0.556453\pi$
$11$	−1.17026			−0.352846			−0.176423	+	0.984314i	$0.556453\pi$
$12$	1.45192	−	1.37548i	0.419132	−	0.397066i
$13$			1.11142i			0.308252i	0.988051	+	0.154126i	$0.0492562\pi$
$13$			1.11142i			0.308252i	−0.988051	+	0.154126i	$0.950744\pi$
$14$	4.51489	−	1.79904i	1.20665	−	0.480813i
$15$			1.71706i			0.443342i
$16$	0.216118	−	3.99416i	0.0540294	−	0.998539i
$17$	−6.00763			−1.45706			−0.728532	−	0.685012i	$-0.759797\pi$
$17$	−6.00763			−1.45706			−0.728532	+	0.685012i	$0.759797\pi$
$18$	1.31376	−	0.523490i	0.309656	−	0.123388i
$19$		−	1.61491i		−	0.370485i	−0.982693	−	0.185243i	$-0.940693\pi$
$19$		−	1.61491i		−	0.370485i	0.982693	−	0.185243i	$-0.0593071\pi$
$20$	2.36177	+	2.49302i	0.528109	+	0.557456i
$21$	3.43662			0.749933
$22$	−1.53743	+	0.612619i	−0.327782	+	0.130611i
$23$			5.58871i			1.16533i	0.812714	+	0.582663i	$0.197989\pi$
$23$			5.58871i			1.16533i	−0.812714	+	0.582663i	$0.802011\pi$
$24$	1.18741	−	2.56711i	0.242380	−	0.524009i
$25$	2.05172			0.410344
$26$	0.581818	+	1.46014i	0.114104	+	0.286356i
$27$	1.00000			0.192450
$28$	4.98969	−	4.72700i	0.942962	−	0.893319i
$29$	−2.67857			−0.497397			−0.248699	−	0.968581i	$-0.580003\pi$
$29$	−2.67857			−0.497397			−0.248699	+	0.968581i	$0.580003\pi$
$30$	0.898862	+	2.25579i	0.164109	+	0.411850i
$31$	−3.52610			−0.633307			−0.316653	−	0.948541i	$-0.602559\pi$
$31$	−3.52610			−0.633307			−0.316653	+	0.948541i	$0.602559\pi$
$32$	−1.80698	−	5.36049i	−0.319431	−	0.947609i
$33$	−1.17026			−0.203716
$34$	−7.89257	+	3.14494i	−1.35356	+	0.539352i
$35$			5.90087i			0.997430i
$36$	1.45192	−	1.37548i	0.241986	−	0.229246i
$37$	4.31616			0.709572			0.354786	−	0.934948i	$-0.384554\pi$
$37$	4.31616			0.709572			0.354786	+	0.934948i	$0.384554\pi$
$38$	−0.845389	−	2.12160i	−0.137140	−	0.344168i
$39$			1.11142i			0.177970i
$40$	4.40787	+	2.03886i	0.696945	+	0.322372i
$41$		−	8.77192i		−	1.36994i	−0.728570	−	0.684972i	$-0.759815\pi$
$41$		−	8.77192i		−	1.36994i	0.728570	−	0.684972i	$-0.240185\pi$
$42$	4.51489	−	1.79904i	0.696662	−	0.277598i
$43$	−1.55663			−0.237384			−0.118692	−	0.992931i	$-0.537870\pi$
$43$	−1.55663			−0.237384			−0.118692	+	0.992931i	$0.537870\pi$
$44$	−1.69912	+	1.60966i	−0.256151	+	0.242666i
$45$			1.71706i			0.255964i
$46$	2.92563	+	7.34220i	0.431361	+	1.08255i
$47$			3.12725i			0.456157i	0.973643	+	0.228078i	$0.0732442\pi$
$47$			3.12725i			0.456157i	−0.973643	+	0.228078i	$0.926756\pi$
$48$	0.216118	−	3.99416i	0.0311939	−	0.576507i
$49$	4.81038			0.687197
$50$	2.69546	−	1.07406i	0.381196	−	0.151894i
$51$	−6.00763			−0.841236
$52$	1.52873	+	1.61369i	0.211997	+	0.223778i
$53$		−	9.63385i		−	1.32331i	−0.749808	−	0.661655i	$-0.769854\pi$
$53$		−	9.63385i		−	1.32331i	0.749808	−	0.661655i	$-0.230146\pi$
$54$	1.31376	−	0.523490i	0.178780	−	0.0712380i
$55$		−	2.00940i		−	0.270947i
$56$	4.08070	−	8.82218i	0.545306	−	1.17891i
$57$		−	1.61491i		−	0.213900i
$58$	−3.51899	+	1.40220i	−0.462065	+	0.184118i
$59$		−	5.48116i		−	0.713586i	−0.934183	−	0.356793i	$-0.883870\pi$
$59$		−	5.48116i		−	0.713586i	0.934183	−	0.356793i	$-0.116130\pi$
$60$	2.36177	+	2.49302i	0.304904	+	0.321847i
$61$		−	3.17038i		−	0.405926i	−0.979186	−	0.202963i	$-0.934943\pi$
$61$		−	3.17038i		−	0.405926i	0.979186	−	0.202963i	$-0.0650571\pi$
$62$	−4.63244	+	1.84588i	−0.588321	+	0.234427i
$63$	3.43662			0.432974
$64$	−5.18009	−	6.09644i	−0.647512	−	0.762056i
$65$	−1.90837			−0.236704
$66$	−1.53743	+	0.612619i	−0.189245	+	0.0754081i
$67$	3.55266	+	7.37419i	0.434026	+	0.900900i
$67$	3.55266	+	7.37419i	0.434026	+	0.900900i
$68$	−8.72257	+	8.26336i	−1.05777	+	1.00208i
$69$			5.58871i			0.672801i
$70$	3.08905	+	7.75231i	0.369212	+	0.926579i
$71$			14.4279i			1.71228i	0.516748	+	0.856138i	$0.327143\pi$
$71$			14.4279i			1.71228i	−0.516748	+	0.856138i	$0.672857\pi$
$72$	1.18741	−	2.56711i	0.139938	−	0.302537i
$73$	−7.90152			−0.924803			−0.462402	−	0.886671i	$-0.653012\pi$
$73$	−7.90152			−0.924803			−0.462402	+	0.886671i	$0.653012\pi$
$74$	5.67038	−	2.25947i	0.659169	−	0.262658i
$75$	2.05172			0.236912
$76$	−2.22127	−	2.34471i	−0.254797	−	0.268957i
$77$	−4.02173			−0.458319
$78$	0.581818	+	1.46014i	0.0658779	+	0.165328i
$79$	−7.48688			−0.842340			−0.421170	−	0.906982i	$-0.638380\pi$
$79$	−7.48688			−0.842340			−0.421170	+	0.906982i	$0.638380\pi$
$80$	6.85819	+	0.371086i	0.766769	+	0.0414887i
$81$	1.00000			0.111111
$82$	−4.59201	−	11.5242i	−0.507103	−	1.27263i
$83$		−	3.57916i		−	0.392863i	−0.980518	−	0.196432i	$-0.937065\pi$
$83$		−	3.57916i		−	0.392863i	0.980518	−	0.196432i	$-0.0629354\pi$
$84$	4.98969	−	4.72700i	0.544419	−	0.515758i
$85$		−	10.3154i		−	1.11887i
$86$	−2.04503	+	0.814881i	−0.220522	+	0.0878709i
$87$	−2.67857			−0.287172
$88$	−1.38958	+	3.00418i	−0.148130	+	0.320247i
$89$	−13.9566			−1.47939			−0.739696	−	0.672941i	$-0.765031\pi$
$89$	−13.9566			−1.47939			−0.739696	+	0.672941i	$0.765031\pi$
$90$	0.898862	+	2.25579i	0.0947484	+	0.237782i
$91$			3.81953i			0.400396i
$92$	7.68715	+	8.11433i	0.801440	+	0.845977i
$93$	−3.52610			−0.365640
$94$	1.63709	+	4.10845i	0.168853	+	0.423754i
$95$	2.77289			0.284492
$96$	−1.80698	−	5.36049i	−0.184424	−	0.547103i
$97$		−	7.37562i		−	0.748880i	−0.927251	−	0.374440i	$-0.877835\pi$
$97$		−	7.37562i		−	0.748880i	0.927251	−	0.374440i	$-0.122165\pi$
$98$	6.31967	−	2.51819i	0.638383	−	0.254375i
$99$	−1.17026			−0.117615
$100$	2.97892	−	2.82210i	0.297892	−	0.282210i
$101$		−	11.4184i		−	1.13617i	−0.822968	−	0.568087i	$-0.807684\pi$
$101$		−	11.4184i		−	1.13617i	0.822968	−	0.568087i	$-0.192316\pi$
$102$	−7.89257	+	3.14494i	−0.781480	+	0.311395i
$103$			12.6926i			1.25064i	0.780368	+	0.625320i	$0.215032\pi$
$103$			12.6926i			1.25064i	−0.780368	+	0.625320i	$0.784968\pi$
$104$	2.85314	+	1.31972i	0.279773	+	0.129409i
$105$			5.90087i			0.575866i
$106$	−5.04323	−	12.6565i	−0.489841	−	1.22931i
$107$			15.0145i			1.45151i	0.687955	+	0.725753i	$0.258509\pi$
$107$			15.0145i			1.45151i	−0.687955	+	0.725753i	$0.741491\pi$
$108$	1.45192	−	1.37548i	0.139711	−	0.132355i
$109$			0.414438i			0.0396959i	0.999803	+	0.0198480i	$0.00631822\pi$
$109$			0.414438i			0.0396959i	−0.999803	+	0.0198480i	$0.993682\pi$
$110$	−1.05190	−	2.63986i	−0.100295	−	0.251701i
$111$	4.31616			0.409672
$112$	0.742714	−	13.7264i	0.0701799	−	1.29702i
$113$			8.28821i			0.779689i	0.920881	+	0.389844i	$0.127471\pi$
$113$			8.28821i			0.779689i	−0.920881	+	0.389844i	$0.872529\pi$
$114$	−0.845389	−	2.12160i	−0.0791779	−	0.198706i
$115$	−9.59612			−0.894843
$116$	−3.88905	+	3.68431i	−0.361089	+	0.342080i
$117$			1.11142i			0.102751i
$118$	−2.86933	−	7.20091i	−0.264144	−	0.662898i
$119$	−20.6460			−1.89261
$120$	4.40787	+	2.03886i	0.402382	+	0.186121i
$121$	−9.63050			−0.875500
$122$	−1.65967	−	4.16511i	−0.150259	−	0.377092i
$123$		−	8.77192i		−	0.790937i
$124$	−5.11960	+	4.85008i	−0.459754	+	0.435550i
$125$			12.1082i			1.08299i
$126$	4.51489	−	1.79904i	0.402218	−	0.160271i
$127$		−	10.2190i		−	0.906792i	−0.891309	−	0.453396i	$-0.850212\pi$
$127$		−	10.2190i		−	0.906792i	0.891309	−	0.453396i	$-0.149788\pi$
$128$	−9.99681	−	5.29752i	−0.883602	−	0.468239i
$129$	−1.55663			−0.137054
$130$	−2.50713	+	0.999013i	−0.219890	+	0.0876193i
$131$		−	5.16804i		−	0.451534i	−0.974181	−	0.225767i	$-0.927511\pi$
$131$		−	5.16804i		−	0.451534i	0.974181	−	0.225767i	$-0.0724888\pi$
$132$	−1.69912	+	1.60966i	−0.147889	+	0.140103i
$133$		−	5.54983i		−	0.481231i
$134$	8.52765	+	7.82811i	0.736676	+	0.676245i
$135$			1.71706i			0.147781i
$136$	−7.13355	+	15.4222i	−0.611697	+	1.32245i
$137$			21.9540i			1.87566i	0.347097	+	0.937829i	$0.387167\pi$
$137$			21.9540i			1.87566i	−0.347097	+	0.937829i	$0.612833\pi$
$138$	2.92563	+	7.34220i	0.249047	+	0.625010i
$139$	9.91101			0.840641			0.420320	−	0.907376i	$-0.361918\pi$
$139$	9.91101			0.840641			0.420320	+	0.907376i	$0.361918\pi$
$140$	8.11652	+	8.56757i	0.685972	+	0.724092i
$141$			3.12725i			0.263362i
$142$	7.55286	+	18.9547i	0.633822	+	1.59065i
$143$		−	1.30065i		−	0.108766i
$144$	0.216118	−	3.99416i	0.0180098	−	0.332846i
$145$		−	4.59925i		−	0.381947i
$146$	−10.3807	+	4.13637i	−0.859111	+	0.342329i
$147$	4.81038			0.396753
$148$	6.26670	−	5.93678i	0.515119	−	0.488001i
$149$	17.2963			1.41697			0.708483	−	0.705728i	$-0.249380\pi$
$149$	17.2963			1.41697			0.708483	+	0.705728i	$0.249380\pi$
$150$	2.69546	−	1.07406i	0.220083	−	0.0876963i
$151$			1.72171i			0.140111i	0.997543	+	0.0700553i	$0.0223176\pi$
$151$			1.72171i			0.140111i	−0.997543	+	0.0700553i	$0.977682\pi$
$152$	−4.14564	−	1.91756i	−0.336256	−	0.155535i
$153$	−6.00763			−0.485688
$154$	−5.28358	+	2.10534i	−0.425763	+	0.169653i
$155$		−	6.05452i		−	0.486310i
$156$	1.52873	+	1.61369i	0.122397	+	0.129198i
$157$	20.4651			1.63329			0.816645	−	0.577141i	$-0.195832\pi$
$157$	20.4651			1.63329			0.816645	+	0.577141i	$0.195832\pi$
$158$	−9.83595	+	3.91931i	−0.782506	+	0.311804i
$159$		−	9.63385i		−	0.764014i
$160$	9.20426	−	3.10268i	0.727660	−	0.245288i
$161$			19.2063i			1.51367i
$162$	1.31376	−	0.523490i	0.103219	−	0.0411293i
$163$			4.88761i			0.382827i	0.981509	+	0.191414i	$0.0613072\pi$
$163$			4.88761i			0.382827i	−0.981509	+	0.191414i	$0.938693\pi$
$164$	−12.0656	−	12.7361i	−0.942164	−	0.994521i
$165$		−	2.00940i		−	0.156431i
$166$	−1.87365	−	4.70214i	−0.145424	−	0.364957i
$167$		−	2.32807i		−	0.180151i	−0.995935	−	0.0900756i	$-0.971289\pi$
$167$		−	2.32807i		−	0.180151i	0.995935	−	0.0900756i	$-0.0287109\pi$
$168$	4.08070	−	8.82218i	0.314833	−	0.680646i
$169$	11.7647			0.904980
$170$	−5.40003	−	13.5520i	−0.414163	−	1.03939i
$171$		−	1.61491i		−	0.123495i
$172$	−2.26010	+	2.14111i	−0.172331	+	0.163258i
$173$	−5.54784			−0.421794			−0.210897	−	0.977508i	$-0.567639\pi$
$173$	−5.54784			−0.421794			−0.210897	+	0.977508i	$0.567639\pi$
$174$	−3.51899	+	1.40220i	−0.266774	+	0.106301i
$175$	7.05099			0.533004
$176$	−0.252913	+	4.67419i	−0.0190641	+	0.352331i
$177$		−	5.48116i		−	0.411989i
$178$	−18.3355	+	7.30612i	−1.37431	+	0.547617i
$179$	7.50648			0.561061			0.280530	−	0.959845i	$-0.409490\pi$
$179$	7.50648			0.561061			0.280530	+	0.959845i	$0.409490\pi$
$180$	2.36177	+	2.49302i	0.176036	+	0.185819i
$181$	−6.75725			−0.502263			−0.251131	−	0.967953i	$-0.580803\pi$
$181$	−6.75725			−0.502263			−0.251131	+	0.967953i	$0.580803\pi$
$182$	1.99949	+	5.01794i	0.148212	+	0.371954i
$183$		−	3.17038i		−	0.234362i
$184$	14.3468	+	6.63611i	1.05766	+	0.489221i
$185$			7.41109i			0.544874i
$186$	−4.63244	+	1.84588i	−0.339667	+	0.135347i
$187$	7.03047			0.514119
$188$	4.30147	+	4.54051i	0.313717	+	0.331150i
$189$	3.43662			0.249978
$190$	3.64290	−	1.45158i	0.264284	−	0.105309i
$191$	−14.3393			−1.03755			−0.518776	−	0.854910i	$-0.673612\pi$
$191$	−14.3393			−1.03755			−0.518776	+	0.854910i	$0.673612\pi$
$192$	−5.18009	−	6.09644i	−0.373841	−	0.439973i
$193$	−6.63609			−0.477677			−0.238838	−	0.971059i	$-0.576767\pi$
$193$	−6.63609			−0.477677			−0.238838	+	0.971059i	$0.576767\pi$
$194$	−3.86106	−	9.68977i	−0.277208	−	0.695685i
$195$	−1.90837			−0.136661
$196$	6.98426	−	6.61657i	0.498876	−	0.472612i
$197$		−	10.9332i		−	0.778955i	−0.921036	−	0.389478i	$-0.872656\pi$
$197$		−	10.9332i		−	0.778955i	0.921036	−	0.389478i	$-0.127344\pi$
$198$	−1.53743	+	0.612619i	−0.109261	+	0.0435369i
$199$		−	21.7663i		−	1.54297i	−0.636247	−	0.771485i	$-0.719514\pi$
$199$		−	21.7663i		−	1.54297i	0.636247	−	0.771485i	$-0.280486\pi$
$200$	2.43624	−	5.26699i	0.172268	−	0.372432i
$201$	3.55266	+	7.37419i	0.250585	+	0.520135i
$202$	−5.97743	−	15.0010i	−0.420570	−	1.05547i
$203$	−9.20522			−0.646080
$204$	−8.72257	+	8.26336i	−0.610702	+	0.578551i
$205$	15.0619			1.05197
$206$	6.64446	+	16.6750i	0.462942	+	1.16180i
$207$			5.58871i			0.388442i
$208$	4.43919	+	0.240197i	0.307802	+	0.0166547i
$209$			1.88986i			0.130724i
$210$	3.08905	+	7.75231i	0.213165	+	0.534961i
$211$			24.8456i			1.71044i	0.518263	+	0.855221i	$0.326579\pi$
$211$			24.8456i			1.71044i	−0.518263	+	0.855221i	$0.673421\pi$
$212$	−13.2511	−	13.9875i	−0.910093	−	0.960668i
$213$			14.4279i			0.988583i
$214$	7.85995	+	19.7254i	0.537295	+	1.34840i
$215$		−	2.67282i		−	0.182285i
$216$	1.18741	−	2.56711i	0.0807933	−	0.174670i
$217$	−12.1179			−0.822616
$218$	0.216954	+	0.544470i	0.0146940	+	0.0368762i
$219$	−7.90152			−0.533936
$220$	−2.76388	−	2.91748i	−0.186341	−	0.196696i
$221$		−	6.67700i		−	0.449144i
$222$	5.67038	−	2.25947i	0.380571	−	0.151646i
$223$		−	10.3441i		−	0.692695i	−0.938106	−	0.346348i	$-0.887422\pi$
$223$		−	10.3441i		−	0.692695i	0.938106	−	0.346348i	$-0.112578\pi$
$224$	−6.20990	−	18.4220i	−0.414916	−	1.23087i
$225$	2.05172			0.136781
$226$	4.33880	+	10.8887i	0.288612	+	0.724305i
$227$		−	6.48668i		−	0.430536i	−0.976555	−	0.215268i	$-0.930937\pi$
$227$		−	6.48668i		−	0.430536i	0.976555	−	0.215268i	$-0.0690625\pi$
$228$	−2.22127	−	2.34471i	−0.147107	−	0.155282i
$229$		−	17.8420i		−	1.17903i	−0.807756	−	0.589516i	$-0.799318\pi$
$229$		−	17.8420i		−	1.17903i	0.807756	−	0.589516i	$-0.200682\pi$
$230$	−12.6070	+	5.02348i	−0.831279	+	0.331238i
$231$	−4.02173			−0.264611
$232$	−3.18057	+	6.87617i	−0.208815	+	0.451443i
$233$		−	0.250483i		−	0.0164097i	−0.999966	−	0.00820483i	$-0.997388\pi$
$233$		−	0.250483i		−	0.0164097i	0.999966	−	0.00820483i	$-0.00261171\pi$
$234$	0.581818	+	1.46014i	0.0380346	+	0.0954521i
$235$	−5.36967			−0.350278
$236$	−7.53922	−	7.95818i	−0.490761	−	0.518033i
$237$	−7.48688			−0.486325
$238$	−27.1238	+	10.8080i	−1.75817	+	0.700576i
$239$	18.6682			1.20754			0.603772	−	0.797157i	$-0.293664\pi$
$239$	18.6682			1.20754			0.603772	+	0.797157i	$0.293664\pi$
$240$	6.85819	+	0.371086i	0.442694	+	0.0239535i
$241$	0.761920			0.0490796			0.0245398	−	0.999699i	$-0.492188\pi$
$241$	0.761920			0.0490796			0.0245398	+	0.999699i	$0.492188\pi$
$242$	−12.6521	+	5.04147i	−0.813310	+	0.324078i
$243$	1.00000			0.0641500
$244$	−4.36079	−	4.60313i	−0.279171	−	0.294685i
$245$			8.25969i			0.527692i
$246$	−4.59201	−	11.5242i	−0.292776	−	0.734754i
$247$	1.79484			0.114203
$248$	−4.18695	+	9.05189i	−0.265871	+	0.574796i
$249$		−	3.57916i		−	0.226820i
$250$	6.33852	+	15.9072i	0.400883	+	1.00606i
$251$	−16.0512			−1.01314			−0.506570	−	0.862199i	$-0.669087\pi$
$251$	−16.0512			−1.01314			−0.506570	+	0.862199i	$0.669087\pi$
$252$	4.98969	−	4.72700i	0.314321	−	0.297773i
$253$		−	6.54023i		−	0.411181i
$254$	−5.34956	−	13.4253i	−0.335662	−	0.842380i
$255$		−	10.3154i		−	0.645978i
$256$	−15.9066	−	1.72641i	−0.994162	−	0.107901i
$257$	−21.7232			−1.35506			−0.677528	−	0.735497i	$-0.736949\pi$
$257$	−21.7232			−1.35506			−0.677528	+	0.735497i	$0.736949\pi$
$258$	−2.04503	+	0.814881i	−0.127318	+	0.0507323i
$259$	14.8330			0.921678
$260$	−2.77079	+	2.62492i	−0.171837	+	0.162791i
$261$	−2.67857			−0.165799
$262$	−2.70542	−	6.78955i	−0.167142	−	0.419460i
$263$		−	2.29514i		−	0.141524i	−0.997493	−	0.0707621i	$-0.977457\pi$
$263$		−	2.29514i		−	0.141524i	0.997493	−	0.0707621i	$-0.0225431\pi$
$264$	−1.38958	+	3.00418i	−0.0855228	+	0.184894i
$265$	16.5419			1.01616
$266$	−2.90528	−	7.29113i	−0.178134	−	0.447048i
$267$	−13.9566			−0.854127
$268$	15.3012	+	5.82009i	0.934669	+	0.355518i
$269$	2.80644			0.171112			0.0855559	−	0.996333i	$-0.472733\pi$
$269$	2.80644			0.171112			0.0855559	+	0.996333i	$0.472733\pi$
$270$	0.898862	+	2.25579i	0.0547030	+	0.137283i
$271$	25.8915			1.57279			0.786397	−	0.617722i	$-0.211944\pi$
$271$	25.8915			1.57279			0.786397	+	0.617722i	$0.211944\pi$
$272$	−1.29835	+	23.9954i	−0.0787243	+	1.45494i
$273$			3.81953i			0.231169i
$274$	11.4927	+	28.8422i	0.694300	+	1.74242i
$275$	−2.40104			−0.144788
$276$	7.68715	+	8.11433i	0.462712	+	0.488425i
$277$	−19.8880			−1.19495			−0.597477	−	0.801886i	$-0.703830\pi$
$277$	−19.8880			−1.19495			−0.597477	+	0.801886i	$0.703830\pi$
$278$	13.0207	−	5.18832i	0.780927	−	0.311175i
$279$	−3.52610			−0.211102
$280$	15.1482	+	7.00678i	0.905277	+	0.418735i
$281$		−	5.26843i		−	0.314288i	−0.987576	−	0.157144i	$-0.949771\pi$
$281$		−	5.26843i		−	0.314288i	0.987576	−	0.157144i	$-0.0502287\pi$
$282$	1.63709	+	4.10845i	0.0974871	+	0.244655i
$283$		−	4.08352i		−	0.242740i	−0.992607	−	0.121370i	$-0.961271\pi$
$283$		−	4.08352i		−	0.242740i	0.992607	−	0.121370i	$-0.0387288\pi$
$284$	19.8453	+	20.9481i	1.17760	+	1.24304i
$285$	2.77289			0.164252
$286$	−0.680877	−	1.70874i	−0.0402611	−	0.101040i
$287$		−	30.1458i		−	1.77945i
$288$	−1.80698	−	5.36049i	−0.106477	−	0.315870i
$289$	19.0916			1.12304
$290$	−2.40766	−	6.04229i	−0.141383	−	0.354816i
$291$		−	7.37562i		−	0.432366i
$292$	−11.4723	+	10.8684i	−0.671368	+	0.636024i
$293$	9.95443			0.581544			0.290772	−	0.956792i	$-0.406088\pi$
$293$	9.95443			0.581544			0.290772	+	0.956792i	$0.406088\pi$
$294$	6.31967	−	2.51819i	0.368571	−	0.146864i
$295$	9.41145			0.547956
$296$	5.12507	−	11.0800i	0.297889	−	0.644015i
$297$	−1.17026			−0.0679052
$298$	22.7231	−	9.05443i	1.31631	−	0.524509i
$299$	−6.21140			−0.359215
$300$	2.97892	−	2.82210i	0.171988	−	0.162934i
$301$	−5.34955			−0.308343
$302$	0.901298	+	2.26191i	0.0518639	+	0.130158i
$303$		−	11.4184i		−	0.655971i
$304$	−6.45019	−	0.349010i	−0.369944	−	0.0200171i
$305$	5.44373			0.311707
$306$	−7.89257	+	3.14494i	−0.451188	+	0.179784i
$307$		−	9.48993i		−	0.541619i	−0.962633	−	0.270809i	$-0.912709\pi$
$307$		−	9.48993i		−	0.541619i	0.962633	−	0.270809i	$-0.0872913\pi$
$308$	−5.83922	+	5.53181i	−0.332720	+	0.315204i
$309$			12.6926i			0.722058i
$310$	−3.16948	−	7.95416i	−0.180014	−	0.451766i
$311$	10.6476			0.603770			0.301885	−	0.953344i	$-0.402384\pi$
$311$	10.6476			0.603770			0.301885	+	0.953344i	$0.402384\pi$
$312$	2.85314	+	1.31972i	0.161527	+	0.0747142i
$313$			5.82795i			0.329415i	0.986342	+	0.164707i	$0.0526680\pi$
$313$			5.82795i			0.329415i	−0.986342	+	0.164707i	$0.947332\pi$
$314$	26.8861	−	10.7133i	1.51727	−	0.604584i
$315$			5.90087i			0.332477i
$316$	−10.8703	+	10.2980i	−0.611503	+	0.579310i
$317$	15.2367			0.855779			0.427890	−	0.903831i	$-0.359257\pi$
$317$	15.2367			0.855779			0.427890	+	0.903831i	$0.359257\pi$
$318$	−5.04323	−	12.6565i	−0.282810	−	0.709743i
$319$	3.13461			0.175505
$320$	10.4679	−	8.89451i	0.585175	−	0.497218i
$321$			15.0145i			0.838028i
$322$	10.0543	+	25.2324i	0.560304	+	1.40615i
$323$			9.70176i			0.539821i
$324$	1.45192	−	1.37548i	0.0806620	−	0.0764155i
$325$			2.28032i			0.126490i
$326$	2.55862	+	6.42113i	0.141709	+	0.355634i
$327$			0.414438i			0.0229184i
$328$	−22.5185	−	10.4159i	−1.24337	−	0.575122i
$329$			10.7472i			0.592512i
$330$	−1.05190	−	2.63986i	−0.0579052	−	0.145320i
$331$	8.30227			0.456334			0.228167	−	0.973622i	$-0.426727\pi$
$331$	8.30227			0.456334			0.228167	+	0.973622i	$0.426727\pi$
$332$	−4.92305	−	5.19663i	−0.270188	−	0.285202i
$333$	4.31616			0.236524
$334$	−1.21872	−	3.05851i	−0.0666854	−	0.167354i
$335$	−12.6619	+	6.10011i	−0.691793	+	0.333285i
$336$	0.742714	−	13.7264i	0.0405184	−	0.748837i
$337$			22.6621i			1.23448i	0.786774	+	0.617241i	$0.211750\pi$
$337$			22.6621i			1.23448i	−0.786774	+	0.617241i	$0.788250\pi$
$338$	15.4560	−	6.15873i	0.840697	−	0.334991i
$339$			8.28821i			0.450154i
$340$	−14.1887	−	14.9771i	−0.769488	−	0.812249i
$341$	4.12645			0.223460
$342$	−0.845389	−	2.12160i	−0.0457134	−	0.114723i
$343$	−7.52491			−0.406307
$344$	−1.84837	+	3.99604i	−0.0996572	+	0.215452i
$345$	−9.59612			−0.516638
$346$	−7.28851	+	2.90424i	−0.391833	+	0.156133i
$347$	0.960707			0.0515734			0.0257867	−	0.999667i	$-0.491791\pi$
$347$	0.960707			0.0515734			0.0257867	+	0.999667i	$0.491791\pi$
$348$	−3.88905	+	3.68431i	−0.208475	+	0.197500i
$349$	12.3546			0.661327			0.330663	−	0.943749i	$-0.392727\pi$
$349$	12.3546			0.661327			0.330663	+	0.943749i	$0.392727\pi$
$350$	9.26328	−	3.69112i	0.495143	−	0.197299i
$351$			1.11142i			0.0593232i
$352$	2.11463	+	6.27315i	0.112710	+	0.334360i
$353$			12.0578i			0.641771i	0.947118	+	0.320885i	$0.103980\pi$
$353$			12.0578i			0.641771i	−0.947118	+	0.320885i	$0.896020\pi$
$354$	−2.86933	−	7.20091i	−0.152503	−	0.382724i
$355$	−24.7735			−1.31484
$356$	−20.2637	+	19.1969i	−1.07398	+	1.01744i
$357$	−20.6460			−1.09270
$358$	9.86169	−	3.92957i	0.521206	−	0.207684i
$359$			23.1026i			1.21931i	0.792667	+	0.609654i	$0.208692\pi$
$359$			23.1026i			1.21931i	−0.792667	+	0.609654i	$0.791308\pi$
$360$	4.40787	+	2.03886i	0.232315	+	0.107457i
$361$	16.3921			0.862741
$362$	−8.87739	+	3.53736i	−0.466585	+	0.185919i
$363$	−9.63050			−0.505470
$364$	5.25368	+	5.54564i	0.275368	+	0.290670i
$365$		−	13.5674i		−	0.710148i
$366$	−1.65967	−	4.16511i	−0.0867521	−	0.217714i
$367$	9.00548			0.470082			0.235041	−	0.971985i	$-0.424478\pi$
$367$	9.00548			0.470082			0.235041	+	0.971985i	$0.424478\pi$
$368$	22.3222	+	1.20782i	1.16362	+	0.0629618i
$369$		−	8.77192i		−	0.456648i
$370$	3.87963	+	9.73637i	0.201692	+	0.506170i
$371$		−	33.1079i		−	1.71888i
$372$	−5.11960	+	4.85008i	−0.265439	+	0.251465i
$373$		−	11.5801i		−	0.599597i	−0.954003	−	0.299798i	$-0.903081\pi$
$373$		−	11.5801i		−	0.599597i	0.954003	−	0.299798i	$-0.0969194\pi$
$374$	9.23634	−	3.68039i	0.477600	−	0.190308i
$375$			12.1082i			0.625265i
$376$	8.02800	+	3.71335i	0.414012	+	0.191501i
$377$		−	2.97701i		−	0.153324i
$378$	4.51489	−	1.79904i	0.232221	−	0.0925326i
$379$	36.2809			1.86362			0.931812	−	0.362941i	$-0.118227\pi$
$379$	36.2809			1.86362			0.931812	+	0.362941i	$0.118227\pi$
$380$	4.02600	−	3.81405i	0.206529	−	0.195656i
$381$		−	10.2190i		−	0.523537i
$382$	−18.8383	+	7.50646i	−0.963851	+	0.384064i
$383$	32.8451			1.67831			0.839153	−	0.543895i	$-0.183051\pi$
$383$	32.8451			1.67831			0.839153	+	0.543895i	$0.183051\pi$
$384$	−9.99681	−	5.29752i	−0.510148	−	0.270338i
$385$		−	6.90554i		−	0.351939i
$386$	−8.71822	+	3.47393i	−0.443746	+	0.176818i
$387$	−1.55663			−0.0791280
$388$	−10.1450	−	10.7088i	−0.515034	−	0.543655i
$389$	−31.1926			−1.58153			−0.790764	−	0.612122i	$-0.790316\pi$
$389$	−31.1926			−1.58153			−0.790764	+	0.612122i	$0.790316\pi$
$390$	−2.50713	+	0.999013i	−0.126954	+	0.0505870i
$391$		−	33.5749i		−	1.69795i
$392$	5.71191	−	12.3488i	0.288495	−	0.623707i
$393$		−	5.16804i		−	0.260693i
$394$	−5.72340	−	14.3635i	−0.288341	−	0.723623i
$395$		−	12.8554i		−	0.646825i
$396$	−1.69912	+	1.60966i	−0.0853838	+	0.0808887i
$397$	10.3801			0.520962			0.260481	−	0.965479i	$-0.416119\pi$
$397$	10.3801			0.520962			0.260481	+	0.965479i	$0.416119\pi$
$398$	−11.3944	−	28.5956i	−0.571151	−	1.43337i
$399$		−	5.54983i		−	0.277839i
$400$	0.443413	−	8.19489i	0.0221706	−	0.409745i
$401$			3.19079i			0.159340i	0.996821	+	0.0796702i	$0.0253867\pi$
$401$			3.19079i			0.159340i	−0.996821	+	0.0796702i	$0.974613\pi$
$402$	8.52765	+	7.82811i	0.425320	+	0.390430i
$403$		−	3.91898i		−	0.195218i
$404$	−15.7058	−	16.5786i	−0.781392	−	0.824815i
$405$			1.71706i			0.0853212i
$406$	−12.0934	+	4.81885i	−0.600187	+	0.239155i
$407$	−5.05102			−0.250370
$408$	−7.13355	+	15.4222i	−0.353163	+	0.763514i
$409$		−	23.3932i		−	1.15672i	−0.815782	−	0.578359i	$-0.803693\pi$
$409$		−	23.3932i		−	1.15672i	0.815782	−	0.578359i	$-0.196307\pi$
$410$	19.7876	−	7.88474i	0.977242	−	0.389400i
$411$			21.9540i			1.08291i
$412$	17.4584	+	18.4286i	0.860115	+	0.907912i
$413$		−	18.8367i		−	0.926892i
$414$	2.92563	+	7.34220i	0.143787	+	0.360850i
$415$	6.14561			0.301676
$416$	5.95775	−	2.00831i	0.292103	−	0.0984655i
$417$	9.91101			0.485344
$418$	0.989323	+	2.48281i	0.0483893	+	0.121438i
$419$			5.86519i			0.286534i	0.989684	+	0.143267i	$0.0457607\pi$
$419$			5.86519i			0.286534i	−0.989684	+	0.143267i	$0.954239\pi$
$420$	8.11652	+	8.56757i	0.396046	+	0.418055i
$421$	0.631708			0.0307876			0.0153938	−	0.999882i	$-0.495100\pi$
$421$	0.631708			0.0307876			0.0153938	+	0.999882i	$0.495100\pi$
$422$	13.0064	+	32.6411i	0.633144	+	1.58894i
$423$			3.12725i			0.152052i
$424$	−24.7311	−	11.4394i	−1.20105	−	0.555545i
$425$	−12.3260			−0.597897
$426$	7.55286	+	18.9547i	0.365937	+	0.918360i
$427$		−	10.8954i		−	0.527266i
$428$	20.6521	+	21.7998i	0.998258	+	1.05373i
$429$		−	1.30065i		−	0.0627959i
$430$	−1.39920	−	3.51144i	−0.0674752	−	0.169337i
$431$		−	15.9423i		−	0.767911i	−0.923351	−	0.383956i	$-0.874562\pi$
$431$		−	15.9423i		−	0.767911i	0.923351	−	0.383956i	$-0.125438\pi$
$432$	0.216118	−	3.99416i	0.0103980	−	0.192169i
$433$		−	36.7027i		−	1.76382i	−0.471420	−	0.881909i	$-0.656259\pi$
$433$		−	36.7027i		−	1.76382i	0.471420	−	0.881909i	$-0.343741\pi$
$434$	−15.9200	+	6.34360i	−0.764183	+	0.304502i
$435$		−	4.59925i		−	0.220517i
$436$	0.570050	+	0.601728i	0.0273004	+	0.0288176i
$437$	9.02524			0.431736
$438$	−10.3807	+	4.13637i	−0.496008	+	0.197644i
$439$			16.3559i			0.780624i	0.920683	+	0.390312i	$0.127633\pi$
$439$			16.3559i			0.780624i	−0.920683	+	0.390312i	$0.872367\pi$
$440$	−5.15834	−	2.38599i	−0.245914	−	0.113748i
$441$	4.81038			0.229066
$442$	−3.49534	−	8.77195i	−0.166257	−	0.417239i
$443$	39.5681			1.87993			0.939967	−	0.341264i	$-0.110855\pi$
$443$	39.5681			1.87993			0.939967	+	0.341264i	$0.110855\pi$
$444$	6.26670	−	5.93678i	0.297404	−	0.281747i
$445$		−	23.9642i		−	1.13601i
$446$	−5.41506	−	13.5897i	−0.256411	−	0.643491i
$447$	17.2963			0.818085
$448$	−17.8020	−	20.9512i	−0.841067	−	0.989850i
$449$	16.4326			0.775502			0.387751	−	0.921764i	$-0.373252\pi$
$449$	16.4326			0.775502			0.387751	+	0.921764i	$0.373252\pi$
$450$	2.69546	−	1.07406i	0.127065	−	0.0506315i
$451$			10.2654i			0.483379i
$452$	11.4003	+	12.0338i	0.536223	+	0.566021i
$453$			1.72171i			0.0808929i
$454$	−3.39572	−	8.52192i	−0.159369	−	0.399954i
$455$	−6.55835			−0.307460
$456$	−4.14564	−	1.91756i	−0.194138	−	0.0897982i
$457$	−25.4258			−1.18937			−0.594685	−	0.803959i	$-0.702723\pi$
$457$	−25.4258			−1.18937			−0.594685	+	0.803959i	$0.702723\pi$
$458$	−9.34012	−	23.4401i	−0.436435	−	1.09528i
$459$	−6.00763			−0.280412
$460$	−13.9328	+	13.1993i	−0.649618	+	0.615419i
$461$	−15.3459			−0.714730			−0.357365	−	0.933965i	$-0.616325\pi$
$461$	−15.3459			−0.714730			−0.357365	+	0.933965i	$0.616325\pi$
$462$	−5.28358	+	2.10534i	−0.245814	+	0.0979493i
$463$	−7.90078			−0.367181			−0.183590	−	0.983003i	$-0.558772\pi$
$463$	−7.90078			−0.367181			−0.183590	+	0.983003i	$0.558772\pi$
$464$	−0.578885	+	10.6986i	−0.0268741	+	0.496671i
$465$		−	6.05452i		−	0.280771i
$466$	−0.131125	−	0.329073i	−0.00607426	−	0.0152440i
$467$			8.56126i			0.396168i	0.980185	+	0.198084i	$0.0634718\pi$
$467$			8.56126i			0.396168i	−0.980185	+	0.198084i	$0.936528\pi$
$468$	1.52873	+	1.61369i	0.0706658	+	0.0745928i
$469$	12.2092	+	25.3423i	0.563766	+	1.17020i
$470$	−7.05444	+	2.81097i	−0.325397	+	0.129660i
$471$	20.4651			0.942980
$472$	−14.0707	−	6.50841i	−0.647658	−	0.299574i
$473$	1.82166			0.0837599
$474$	−9.83595	+	3.91931i	−0.451780	+	0.180020i
$475$		−	3.31334i		−	0.152026i
$476$	−29.9762	+	28.3981i	−1.37396	+	1.30162i
$477$		−	9.63385i		−	0.441104i
$478$	24.5255	−	9.77261i	1.12177	−	0.446989i
$479$		−	29.1248i		−	1.33075i	−0.746510	−	0.665374i	$-0.768272\pi$
$479$		−	29.1248i		−	1.33075i	0.746510	−	0.665374i	$-0.231728\pi$
$480$	9.20426	−	3.10268i	0.420115	−	0.141617i
$481$			4.79707i			0.218727i
$482$	1.00098	−	0.398858i	0.0455933	−	0.0181675i
$483$			19.2063i			0.873916i
$484$	−13.9827	+	13.2465i	−0.635576	+	0.602116i
$485$	12.6643			0.575058
$486$	1.31376	−	0.523490i	0.0595932	−	0.0237460i
$487$	−2.54391			−0.115276			−0.0576378	−	0.998338i	$-0.518357\pi$
$487$	−2.54391			−0.115276			−0.0576378	+	0.998338i	$0.518357\pi$
$488$	−8.13872	−	3.76456i	−0.368423	−	0.170414i
$489$			4.88761i			0.221025i
$490$	4.32387	+	10.8512i	0.195332	+	0.490208i
$491$		−	16.6449i		−	0.751172i	−0.926788	−	0.375586i	$-0.877441\pi$
$491$		−	16.6449i		−	0.751172i	0.926788	−	0.375586i	$-0.122559\pi$
$492$	−12.0656	−	12.7361i	−0.543959	−	0.574187i
$493$	16.0918			0.724740
$494$	2.35798	−	0.939582i	0.106091	−	0.0422738i
$495$		−	2.00940i		−	0.0903157i
$496$	−0.762053	+	14.0838i	−0.0342172	+	0.632382i
$497$			49.5832i			2.22411i
$498$	−1.87365	−	4.70214i	−0.0839605	−	0.210708i
$499$	−4.08382			−0.182817			−0.0914085	−	0.995813i	$-0.529137\pi$
$499$	−4.08382			−0.182817			−0.0914085	+	0.995813i	$0.529137\pi$
$500$	16.6546	+	17.5801i	0.744815	+	0.786205i
$501$		−	2.32807i		−	0.104010i
$502$	−21.0873	+	8.40263i	−0.941174	+	0.375028i
$503$	35.4800			1.58197			0.790987	−	0.611833i	$-0.209568\pi$
$503$	35.4800			1.58197			0.790987	+	0.611833i	$0.209568\pi$
$504$	4.08070	−	8.82218i	0.181769	−	0.392971i
$505$	19.6061			0.872458
$506$	−3.42375	−	8.59227i	−0.152204	−	0.381973i
$507$	11.7647			0.522491
$508$	−14.0561	−	14.8372i	−0.623637	−	0.658293i
$509$	28.8834			1.28023			0.640117	−	0.768277i	$-0.278886\pi$
$509$	28.8834			1.28023			0.640117	+	0.768277i	$0.278886\pi$
$510$	−5.40003	−	13.5520i	−0.239117	−	0.600092i
$511$	−27.1546			−1.20125
$512$	−21.8012	+	6.05886i	−0.963484	+	0.267766i
$513$		−	1.61491i		−	0.0712999i
$514$	−28.5390	+	11.3719i	−1.25880	+	0.501593i
$515$	−21.7939			−0.960355
$516$	−2.26010	+	2.14111i	−0.0994952	+	0.0942572i
$517$		−	3.65969i		−	0.160953i
$518$	19.4870	−	7.76494i	0.856208	−	0.341172i
$519$	−5.54784			−0.243523
$520$	−2.26603	+	4.89899i	−0.0993718	+	0.214835i
$521$		−	28.2902i		−	1.23942i	−0.784832	−	0.619709i	$-0.787251\pi$
$521$		−	28.2902i		−	1.23942i	0.784832	−	0.619709i	$-0.212749\pi$
$522$	−3.51899	+	1.40220i	−0.154022	+	0.0613728i
$523$			31.8548i			1.39292i	0.717598	+	0.696458i	$0.245242\pi$
$523$			31.8548i			1.39292i	−0.717598	+	0.696458i	$0.754758\pi$
$524$	−7.10853	−	7.50356i	−0.310538	−	0.327795i
$525$	7.05099			0.307730
$526$	−1.20148	−	3.01525i	−0.0523871	−	0.131471i
$527$	21.1835			0.922769
$528$	−0.252913	+	4.67419i	−0.0110066	+	0.203418i
$529$	−8.23364			−0.357984
$530$	21.7320	−	8.65950i	0.943977	−	0.376145i
$531$		−	5.48116i		−	0.237862i
$532$	−7.63367	−	8.05788i	−0.330962	−	0.349353i
$533$	9.74928			0.422288
$534$	−18.3355	+	7.30612i	−0.793455	+	0.316167i
$535$	−25.7807			−1.11460
$536$	23.1488	−	0.363847i	0.999876	−	0.0157158i
$537$	7.50648			0.323928
$538$	3.68698	−	1.46915i	0.158957	−	0.0633393i
$539$	−5.62938			−0.242475
$540$	2.36177	+	2.49302i	0.101635	+	0.107282i
$541$		−	27.5286i		−	1.18355i	−0.806104	−	0.591774i	$-0.798428\pi$
$541$		−	27.5286i		−	1.18355i	0.806104	−	0.591774i	$-0.201572\pi$
$542$	34.0151	−	13.5539i	1.46107	−	0.582191i
$543$	−6.75725			−0.289982
$544$	10.8556	+	32.2038i	0.465432	+	1.38073i
$545$	−0.711612			−0.0304821
$546$	1.99949	+	5.01794i	0.0855702	+	0.214748i
$547$	8.24041			0.352334			0.176167	−	0.984360i	$-0.443630\pi$
$547$	8.24041			0.352334			0.176167	+	0.984360i	$0.443630\pi$
$548$	30.1973	+	31.8754i	1.28996	+	1.36165i
$549$		−	3.17038i		−	0.135309i
$550$	−3.15438	+	1.25692i	−0.134503	+	0.0535953i
$551$			4.32564i			0.184278i
$552$	14.3468	+	6.63611i	0.610641	+	0.282452i
$553$	−25.7296			−1.09413
$554$	−26.1280	+	10.4112i	−1.11007	+	0.442328i
$555$			7.41109i			0.314583i
$556$	14.3899	−	13.6324i	0.610270	−	0.578142i
$557$	16.4605			0.697453			0.348726	−	0.937225i	$-0.386614\pi$
$557$	16.4605			0.697453			0.348726	+	0.937225i	$0.386614\pi$
$558$	−4.63244	+	1.84588i	−0.196107	+	0.0781424i
$559$		−	1.73007i		−	0.0731742i
$560$	23.5690	+	1.27528i	0.995973	+	0.0538905i
$561$	7.03047			0.296827
$562$	−2.75797	−	6.92144i	−0.116338	−	0.291963i
$563$	39.4200			1.66136			0.830678	−	0.556753i	$-0.187953\pi$
$563$	39.4200			1.66136			0.830678	+	0.556753i	$0.187953\pi$
$564$	4.30147	+	4.54051i	0.181125	+	0.191190i
$565$	−14.2313			−0.598716
$566$	−2.13769	−	5.36476i	−0.0898537	−	0.225498i
$567$	3.43662			0.144325
$568$	37.0380	+	17.1319i	1.55408	+	0.718838i
$569$	17.5843			0.737173			0.368586	−	0.929593i	$-0.379842\pi$
$569$	17.5843			0.737173			0.368586	+	0.929593i	$0.379842\pi$
$570$	3.64290	−	1.45158i	0.152584	−	0.0608000i
$571$			29.6052i			1.23894i	0.785020	+	0.619470i	$0.212652\pi$
$571$			29.6052i			1.23894i	−0.785020	+	0.619470i	$0.787348\pi$
$572$	−1.78901	−	1.88843i	−0.0748024	−	0.0789593i
$573$	−14.3393			−0.599031
$574$	−15.7810	−	39.6042i	−0.658687	−	1.65305i
$575$			11.4665i			0.478184i
$576$	−5.18009	−	6.09644i	−0.215837	−	0.254019i
$577$			24.8946i			1.03638i	0.855267	+	0.518188i	$0.173393\pi$
$577$			24.8946i			1.03638i	−0.855267	+	0.518188i	$0.826607\pi$
$578$	25.0817	−	9.99427i	1.04326	−	0.415707i
$579$	−6.63609			−0.275787
$580$	−6.32617	−	6.67772i	−0.262680	−	0.277277i
$581$		−	12.3002i		−	0.510299i
$582$	−3.86106	−	9.68977i	−0.160046	−	0.401654i
$583$			11.2741i			0.466925i
$584$	−9.38238	+	20.2841i	−0.388246	+	0.839361i
$585$	−1.90837			−0.0789014
$586$	13.0777	−	5.21105i	0.540235	−	0.215266i
$587$	8.76986			0.361971			0.180985	−	0.983486i	$-0.442071\pi$
$587$	8.76986			0.361971			0.180985	+	0.983486i	$0.442071\pi$
$588$	6.98426	−	6.61657i	0.288026	−	0.272863i
$589$			5.69433i			0.234631i
$590$	12.3644	−	4.92681i	0.509033	−	0.202833i
$591$		−	10.9332i		−	0.449730i
$592$	0.932798	−	17.2394i	0.0383377	−	0.708536i
$593$			13.1468i			0.539875i	0.962878	+	0.269938i	$0.0870031\pi$
$593$			13.1468i			0.539875i	−0.962878	+	0.269938i	$0.912997\pi$
$594$	−1.53743	+	0.612619i	−0.0630817	+	0.0251360i
$595$		−	35.4503i		−	1.45332i
$596$	25.1127	−	23.7906i	1.02866	−	0.974503i
$597$		−	21.7663i		−	0.890834i
$598$	−8.16027	+	3.25161i	−0.333698	+	0.132968i
$599$	1.49884			0.0612408			0.0306204	−	0.999531i	$-0.490252\pi$
$599$	1.49884			0.0612408			0.0306204	+	0.999531i	$0.490252\pi$
$600$	2.43624	−	5.26699i	0.0994591	−	0.215024i
$601$	−35.0733			−1.43067			−0.715336	−	0.698781i	$-0.753726\pi$
$601$	−35.0733			−1.43067			−0.715336	+	0.698781i	$0.753726\pi$
$602$	−7.02801	+	2.80044i	−0.286440	+	0.114137i
$603$	3.55266	+	7.37419i	0.144675	+	0.300300i
$604$	2.36817	+	2.49977i	0.0963596	+	0.101714i
$605$		−	16.5361i		−	0.672288i
$606$	−5.97743	−	15.0010i	−0.242816	−	0.609375i
$607$			27.4233i			1.11308i	0.830822	+	0.556538i	$0.187871\pi$
$607$			27.4233i			1.11308i	−0.830822	+	0.556538i	$0.812129\pi$
$608$	−8.65669	+	2.91810i	−0.351075	+	0.118345i
$609$	−9.20522			−0.373014
$610$	7.15173	−	2.84974i	0.289565	−	0.115383i
$611$	−3.47569			−0.140611
$612$	−8.72257	+	8.26336i	−0.352589	+	0.334027i
$613$	8.13038			0.328383			0.164192	−	0.986428i	$-0.447498\pi$
$613$	8.13038			0.328383			0.164192	+	0.986428i	$0.447498\pi$
$614$	−4.96788	−	12.4675i	−0.200488	−	0.503146i
$615$	15.0619			0.607353
$616$	−4.77547	+	10.3242i	−0.192409	+	0.415975i
$617$	34.0281			1.36992			0.684961	−	0.728580i	$-0.259819\pi$
$617$	34.0281			1.36992			0.684961	+	0.728580i	$0.259819\pi$
$618$	6.64446	+	16.6750i	0.267280	+	0.670768i
$619$		−	14.2214i		−	0.571608i	−0.958288	−	0.285804i	$-0.907739\pi$
$619$		−	14.2214i		−	0.571608i	0.958288	−	0.285804i	$-0.0922607\pi$
$620$	−8.32786	−	8.79065i	−0.334455	−	0.353041i
$621$			5.58871i			0.224267i
$622$	13.9884	−	5.57392i	0.560882	−	0.223494i
$623$	−47.9634			−1.92161
$624$	4.43919	+	0.240197i	0.177710	+	0.00961559i
$625$	−10.5318			−0.421274
$626$	3.05087	+	7.65650i	0.121937	+	0.306015i
$627$			1.88986i			0.0754737i
$628$	29.7135	−	28.1492i	1.18570	−	1.12328i
$629$	−25.9299			−1.03389
$630$	3.08905	+	7.75231i	0.123071	+	0.308860i
$631$	−23.8524			−0.949549			−0.474775	−	0.880107i	$-0.657470\pi$
$631$	−23.8524			−0.949549			−0.474775	+	0.880107i	$0.657470\pi$
$632$	−8.89003	+	19.2196i	−0.353627	+	0.764516i
$633$			24.8456i			0.987525i
$634$	20.0173	−	7.97627i	0.794990	−	0.316778i
$635$	17.5466			0.696317
$636$	−13.2511	−	13.9875i	−0.525442	−	0.554642i
$637$			5.34635i			0.211830i
$638$	4.11812	−	1.64094i	0.163038	−	0.0649654i
$639$			14.4279i			0.570759i
$640$	9.09613	−	17.1651i	0.359556	−	0.678510i
$641$			45.5542i			1.79928i	0.436628	+	0.899642i	$0.356172\pi$
$641$			45.5542i			1.79928i	−0.436628	+	0.899642i	$0.643828\pi$
$642$	7.85995	+	19.7254i	0.310207	+	0.778500i
$643$			25.3323i			0.999007i	0.866312	+	0.499504i	$0.166484\pi$
$643$			25.3323i			0.999007i	−0.866312	+	0.499504i	$0.833516\pi$
$644$	26.4178	+	27.8859i	1.04101	+	1.09886i
$645$		−	2.67282i		−	0.105242i
$646$	5.07878	+	12.7458i	0.199822	+	0.501475i
$647$	−21.7790			−0.856219			−0.428110	−	0.903727i	$-0.640820\pi$
$647$	−21.7790			−0.856219			−0.428110	+	0.903727i	$0.640820\pi$
$648$	1.18741	−	2.56711i	0.0466460	−	0.100846i
$649$			6.41437i			0.251786i
$650$	1.19373	+	2.99579i	0.0468218	+	0.117505i
$651$	−12.1179			−0.474937
$652$	6.72280	+	7.09640i	0.263285	+	0.277916i
$653$		−	35.5811i		−	1.39240i	−0.717850	−	0.696198i	$-0.754874\pi$
$653$		−	35.5811i		−	1.39240i	0.717850	−	0.696198i	$-0.245126\pi$
$654$	0.216954	+	0.544470i	0.00848358	+	0.0212905i
$655$	8.87382			0.346729
$656$	−35.0364	−	1.89577i	−1.36794	−	0.0740172i
$657$	−7.90152			−0.308268
$658$	5.62605	+	14.1192i	0.219326	+	0.550424i
$659$		−	16.1633i		−	0.629633i	−0.949153	−	0.314816i	$-0.898057\pi$
$659$		−	16.1633i		−	0.629633i	0.949153	−	0.314816i	$-0.101943\pi$
$660$	−2.76388	−	2.91748i	−0.107584	−	0.113563i
$661$			44.1823i			1.71849i	0.511562	+	0.859247i	$0.329067\pi$
$661$			44.1823i			1.71849i	−0.511562	+	0.859247i	$0.670933\pi$
$662$	10.9072	−	4.34616i	0.423919	−	0.168918i
$663$		−	6.67700i		−	0.259313i
$664$	−9.18808	−	4.24994i	−0.356567	−	0.164930i
$665$	9.52936			0.369533
$666$	5.67038	−	2.25947i	0.219723	−	0.0875526i
$667$		−	14.9697i		−	0.579630i
$668$	−3.20220	−	3.38016i	−0.123897	−	0.130782i
$669$		−	10.3441i		−	0.399928i
$670$	−13.4413	+	14.6424i	−0.519282	+	0.565687i
$671$			3.71017i			0.143229i
$672$	−6.20990	−	18.4220i	−0.239552	−	0.710643i
$673$			14.9441i			0.576054i	0.957622	+	0.288027i	$0.0929994\pi$
$673$			14.9441i			0.576054i	−0.957622	+	0.288027i	$0.907001\pi$
$674$	11.8634	+	29.7725i	0.456960	+	1.14679i
$675$	2.05172			0.0789707
$676$	17.0814	−	16.1822i	0.656978	−	0.622391i
$677$			6.35008i			0.244054i	0.992527	+	0.122027i	$0.0389394\pi$
$677$			6.35008i			0.244054i	−0.992527	+	0.122027i	$0.961061\pi$
$678$	4.33880	+	10.8887i	0.166630	+	0.418178i
$679$		−	25.3472i		−	0.972737i
$680$	−26.4808	−	12.2487i	−1.01549	−	0.469716i
$681$		−	6.48668i		−	0.248570i
$682$	5.42115	−	2.16016i	0.207587	−	0.0827167i
$683$	−44.9065			−1.71830			−0.859150	−	0.511724i	$-0.829007\pi$
$683$	−44.9065			−1.71830			−0.859150	+	0.511724i	$0.829007\pi$
$684$	−2.22127	−	2.34471i	−0.0849324	−	0.0896522i
$685$	−37.6963			−1.44030
$686$	−9.88590	+	3.93922i	−0.377445	+	0.150400i
$687$		−	17.8420i		−	0.680715i
$688$	−0.336415	+	6.21743i	−0.0128257	+	0.237037i
$689$	10.7072			0.407914
$690$	−12.6070	+	5.02348i	−0.479939	+	0.191241i
$691$			20.5238i			0.780764i	0.920653	+	0.390382i	$0.127657\pi$
$691$			20.5238i			0.780764i	−0.920653	+	0.390382i	$0.872343\pi$
$692$	−8.05500	+	7.63094i	−0.306205	+	0.290085i
$693$	−4.02173			−0.152773
$694$	1.26214	−	0.502921i	0.0479100	−	0.0190906i
$695$			17.0178i			0.645520i
$696$	−3.18057	+	6.87617i	−0.120559	+	0.260641i
$697$			52.6984i			1.99610i
$698$	16.2310	−	6.46752i	0.614351	−	0.244799i
$699$		−	0.250483i		−	0.00947412i
$700$	10.2374	−	9.69848i	0.386939	−	0.366568i
$701$		−	38.5142i		−	1.45466i	−0.686287	−	0.727331i	$-0.740760\pi$
$701$		−	38.5142i		−	1.45466i	0.686287	−	0.727331i	$-0.259240\pi$
$702$	0.581818	+	1.46014i	0.0219593	+	0.0551093i
$703$		−	6.97020i		−	0.262886i
$704$	6.06204	+	7.13441i	0.228472	+	0.268888i
$705$	−5.36967			−0.202233
$706$	6.31213	+	15.8410i	0.237560	+	0.596184i
$707$		−	39.2408i		−	1.47580i
$708$	−7.53922	−	7.95818i	−0.283341	−	0.299087i
$709$	8.41092			0.315879			0.157939	−	0.987449i	$-0.449515\pi$
$709$	8.41092			0.315879			0.157939	+	0.987449i	$0.449515\pi$
$710$	−32.5464	+	12.9687i	−1.22144	+	0.486706i
$711$	−7.48688			−0.280780
$712$	−16.5722	+	35.8280i	−0.621070	+	1.34271i
$713$		−	19.7064i		−	0.738009i
$714$	−27.1238	+	10.8080i	−1.01508	+	0.404478i
$715$	2.23328			0.0835201
$716$	10.8988	−	10.3250i	0.407306	−	0.385863i
$717$	18.6682			0.697176
$718$	12.0940	+	30.3512i	0.451344	+	1.13270i
$719$			26.0757i			0.972461i	0.873831	+	0.486230i	$0.161628\pi$
$719$			26.0757i			0.972461i	−0.873831	+	0.486230i	$0.838372\pi$
$720$	6.85819	+	0.371086i	0.255590	+	0.0138296i
$721$			43.6197i			1.62448i
$722$	21.5352	−	8.58109i	0.801457	−	0.319355i
$723$	0.761920			0.0283361
$724$	−9.81096	+	9.29446i	−0.364622	+	0.345426i
$725$	−5.49567			−0.204104
$726$	−12.6521	+	5.04147i	−0.469565	+	0.187107i
$727$	−47.8363			−1.77415			−0.887074	−	0.461627i	$-0.847266\pi$
$727$	−47.8363			−1.77415			−0.887074	+	0.461627i	$0.847266\pi$
$728$	9.80515	+	4.53537i	0.363403	+	0.168092i
$729$	1.00000			0.0370370
$730$	−7.10238	−	17.8242i	−0.262871	−	0.659704i
$731$	9.35166			0.345884
$732$	−4.36079	−	4.60313i	−0.161180	−	0.170137i
$733$		−	44.2327i		−	1.63377i	−0.576798	−	0.816887i	$-0.695698\pi$
$733$		−	44.2327i		−	1.63377i	0.576798	−	0.816887i	$-0.304302\pi$
$734$	11.8310	−	4.71428i	0.436691	−	0.174007i
$735$			8.25969i			0.304663i
$736$	29.9582	−	10.0987i	1.10427	−	0.372242i
$737$	−4.15753	−	8.62970i	−0.153144	−	0.317879i
$738$	−4.59201	−	11.5242i	−0.169034	−	0.424211i
$739$	−21.7388			−0.799673			−0.399837	−	0.916586i	$-0.630933\pi$
$739$	−21.7388			−0.799673			−0.399837	+	0.916586i	$0.630933\pi$
$740$	10.1938	+	10.7603i	0.374731	+	0.395555i
$741$	1.79484			0.0659351
$742$	−17.3317	−	43.4957i	−0.636266	−	1.59678i
$743$			5.66794i			0.207937i	0.994581	+	0.103968i	$0.0331541\pi$
$743$			5.66794i			0.207937i	−0.994581	+	0.103968i	$0.966846\pi$
$744$	−4.18695	+	9.05189i	−0.153501	+	0.331858i
$745$			29.6987i			1.08807i
$746$	−6.06209	−	15.2135i	−0.221949	−	0.557005i
$747$		−	3.57916i		−	0.130954i
$748$	10.2077	−	9.67027i	0.373229	−	0.353580i
$749$			51.5992i			1.88539i
$750$	6.33852	+	15.9072i	0.231450	+	0.580850i
$751$			29.4760i			1.07560i	0.843074	+	0.537798i	$0.180744\pi$
$751$			29.4760i			1.07560i	−0.843074	+	0.537798i	$0.819256\pi$
$752$	12.4907	+	0.675854i	0.455490	+	0.0246459i
$753$	−16.0512			−0.584937
$754$	−1.55844	−	3.91107i	−0.0567549	−	0.142433i
$755$	−2.95627			−0.107590
$756$	4.98969	−	4.72700i	0.181473	−	0.171919i
$757$		−	35.9361i		−	1.30612i	−0.757307	−	0.653060i	$-0.773485\pi$
$757$		−	35.9361i		−	1.30612i	0.757307	−	0.653060i	$-0.226515\pi$
$758$	47.6643	−	18.9927i	1.73124	−	0.689846i
$759$		−	6.54023i		−	0.237395i
$760$	3.29257	−	7.11830i	0.119434	−	0.258208i
$761$	−46.8165			−1.69710			−0.848548	−	0.529119i	$-0.822523\pi$
$761$	−46.8165			−1.69710			−0.848548	+	0.529119i	$0.822523\pi$
$762$	−5.34956	−	13.4253i	−0.193794	−	0.486348i
$763$			1.42427i			0.0515619i
$764$	−20.8194	+	19.7233i	−0.753219	+	0.713565i
$765$		−	10.3154i		−	0.372955i
$766$	43.1505	−	17.1941i	1.55909	−	0.621248i
$767$	6.09187			0.219965
$768$	−15.9066	−	1.72641i	−0.573979	−	0.0622966i
$769$			50.4895i			1.82070i	0.413840	+	0.910350i	$0.364187\pi$
$769$			50.4895i			1.82070i	−0.413840	+	0.910350i	$0.635813\pi$
$770$	−3.61499	−	9.07221i	−0.130275	−	0.326940i
$771$	−21.7232			−0.782342
$772$	−9.63505	+	9.12781i	−0.346773	+	0.328517i
$773$	17.7120			0.637056			0.318528	−	0.947913i	$-0.396812\pi$
$773$	17.7120			0.637056			0.318528	+	0.947913i	$0.396812\pi$
$774$	−2.04503	+	0.814881i	−0.0735072	+	0.0292903i
$775$	−7.23457			−0.259874
$776$	−18.9340	−	8.75791i	−0.679691	−	0.314391i
$777$	14.8330			0.532131
$778$	−40.9795	+	16.3290i	−1.46919	+	0.585424i
$779$	−14.1658			−0.507544
$780$	−2.77079	+	2.62492i	−0.0992103	+	0.0939873i
$781$		−	16.8843i		−	0.604170i
$782$	−17.5761	−	44.1092i	−0.628521	−	1.57734i
$783$	−2.67857			−0.0957242
$784$	1.03961	−	19.2134i	0.0371288	−	0.686193i
$785$			35.1396i			1.25419i
$786$	−2.70542	−	6.78955i	−0.0964992	−	0.242175i
$787$	−49.2798			−1.75664			−0.878318	−	0.478078i	$-0.841334\pi$
$787$	−49.2798			−1.75664			−0.878318	+	0.478078i	$0.841334\pi$
$788$	−15.0383	−	15.8740i	−0.535718	−	0.565488i
$789$		−	2.29514i		−	0.0817090i
$790$	−6.72968	−	16.8889i	−0.239431	−	0.600879i
$791$			28.4834i			1.01275i
$792$	−1.38958	+	3.00418i	−0.0493766	+	0.106749i
$793$	3.52363			0.125128
$794$	13.6369	−	5.43388i	0.483957	−	0.192841i
$795$	16.5419			0.586679
$796$	−29.9390	−	31.6028i	−1.06116	−	1.12013i
$797$	8.35617			0.295991			0.147995	−	0.988988i	$-0.452718\pi$
$797$	8.35617			0.295991			0.147995	+	0.988988i	$0.452718\pi$
$798$	−2.90528	−	7.29113i	−0.102846	−	0.258103i
$799$		−	18.7874i		−	0.664649i
$800$	−3.70741	−	10.9982i	−0.131077	−	0.388846i
$801$	−13.9566			−0.493130
$802$	1.67035	+	4.19192i	0.0589820	+	0.148022i
$803$	9.24682			0.326313
$804$	15.3012	+	5.82009i	0.539632	+	0.205259i
$805$	−32.9782			−1.16233
$806$	−2.05155	−	5.14859i	−0.0722627	−	0.181351i
$807$	2.80644			0.0987914
$808$	−29.3123	−	13.5584i	−1.03120	−	0.476982i
$809$		−	50.3086i		−	1.76876i	−0.466772	−	0.884378i	$-0.654583\pi$
$809$		−	50.3086i		−	1.76876i	0.466772	−	0.884378i	$-0.345417\pi$
$810$	0.898862	+	2.25579i	0.0315828	+	0.0792605i
$811$	−33.5942			−1.17965			−0.589826	−	0.807530i	$-0.700804\pi$
$811$	−33.5942			−1.17965			−0.589826	+	0.807530i	$0.700804\pi$
$812$	−13.3652	+	12.6616i	−0.469027	+	0.444335i
$813$	25.8915			0.908053
$814$	−6.63581	+	2.64416i	−0.232585	+	0.0926777i
$815$	−8.39230			−0.293969
$816$	−1.29835	+	23.9954i	−0.0454515	+	0.840008i
$817$			2.51381i			0.0879472i
$818$	−12.2461	−	30.7330i	−0.428175	−	1.07455i
$819$			3.81953i			0.133465i
$820$	21.8686	−	20.7173i	0.763683	−	0.723479i
$821$	−18.3022			−0.638750			−0.319375	−	0.947628i	$-0.603473\pi$
$821$	−18.3022			−0.638750			−0.319375	+	0.947628i	$0.603473\pi$
$822$	11.4927	+	28.8422i	0.400855	+	1.00599i
$823$			35.5431i			1.23895i	0.785015	+	0.619477i	$0.212655\pi$
$823$			35.5431i			1.23895i	−0.785015	+	0.619477i	$0.787345\pi$
$824$	32.5833	+	15.0714i	1.13509	+	0.525037i
$825$	−2.40104			−0.0835935
$826$	−9.86082	−	24.7468i	−0.343102	−	0.861052i
$827$		−	48.9483i		−	1.70210i	−0.525085	−	0.851050i	$-0.675967\pi$
$827$		−	48.9483i		−	1.70210i	0.525085	−	0.851050i	$-0.324033\pi$
$828$	7.68715	+	8.11433i	0.267147	+	0.281992i
$829$	4.41929			0.153488			0.0767441	−	0.997051i	$-0.475548\pi$
$829$	4.41929			0.153488			0.0767441	+	0.997051i	$0.475548\pi$
$830$	8.07384	−	3.21717i	0.280247	−	0.111670i
$831$	−19.8880			−0.689907
$832$	6.77571	−	5.75726i	0.234905	−	0.199597i
$833$	−28.8990			−1.00129
$834$	13.0207	−	5.18832i	0.450869	−	0.179657i
$835$	3.99742			0.138336
$836$	2.59946	+	2.74391i	0.0899042	+	0.0949003i
$837$	−3.52610			−0.121880
$838$	3.07037	+	7.70544i	0.106064	+	0.266180i
$839$			46.7153i			1.61279i	0.591377	+	0.806395i	$0.298585\pi$
$839$			46.7153i			1.61279i	−0.591377	+	0.806395i	$0.701415\pi$
$840$	15.1482	+	7.00678i	0.522662	+	0.241757i
$841$	−21.8253			−0.752596
$842$	0.829911	−	0.330693i	0.0286006	−	0.0113964i
$843$		−	5.26843i		−	0.181454i
$844$	34.1746	+	36.0737i	1.17634	+	1.24171i
$845$			20.2007i			0.694926i
$846$	1.63709	+	4.10845i	0.0562842	+	0.141251i
$847$	−33.0964			−1.13721
$848$	−38.4791	−	2.08204i	−1.32138	−	0.0714977i
$849$		−	4.08352i		−	0.140146i
$850$	−16.1933	+	6.45253i	−0.555427	+	0.221320i
$851$			24.1217i			0.826883i
$852$	19.8453	+	20.9481i	0.679887	+	0.717669i
$853$	−34.4954			−1.18110			−0.590550	−	0.807001i	$-0.701089\pi$
$853$	−34.4954			−1.18110			−0.590550	+	0.807001i	$0.701089\pi$
$854$	−5.70364	−	14.3139i	−0.195175	−	0.489812i
$855$	2.77289			0.0948307
$856$	38.5438	+	17.8284i	1.31740	+	0.609363i
$857$			9.03924i			0.308775i	0.988010	+	0.154387i	$0.0493404\pi$
$857$			9.03924i			0.308775i	−0.988010	+	0.154387i	$0.950660\pi$
$858$	−0.680877	−	1.70874i	−0.0232447	−	0.0583353i
$859$		−	52.6776i		−	1.79734i	−0.438628	−	0.898669i	$-0.644535\pi$
$859$		−	52.6776i		−	1.79734i	0.438628	−	0.898669i	$-0.355465\pi$
$860$	−3.67641	−	3.88071i	−0.125364	−	0.132331i
$861$		−	30.1458i		−	1.02737i
$862$	−8.34562	−	20.9443i	−0.284253	−	0.713364i
$863$		−	35.0023i		−	1.19149i	−0.803173	−	0.595746i	$-0.796856\pi$
$863$		−	35.0023i		−	1.19149i	0.803173	−	0.595746i	$-0.203144\pi$
$864$	−1.80698	−	5.36049i	−0.0614746	−	0.182368i
$865$		−	9.52595i		−	0.323892i
$866$	−19.2135	−	48.2184i	−0.652901	−	1.63853i
$867$	19.0916			0.648385
$868$	−17.5941	+	16.6679i	−0.597184	+	0.565745i
$869$	8.76158			0.297216
$870$	−2.40766	−	6.04229i	−0.0816274	−	0.204853i
$871$	−8.19582	+	3.94850i	−0.277705	+	0.133790i
$872$	1.06391	+	0.492109i	0.0360284	+	0.0166649i
$873$		−	7.37562i		−	0.249627i
$874$	11.8570	−	4.72463i	0.401068	−	0.159813i
$875$			41.6113i			1.40672i
$876$	−11.4723	+	10.8684i	−0.387615	+	0.367208i
$877$	−40.7293			−1.37533			−0.687666	−	0.726027i	$-0.741365\pi$
$877$	−40.7293			−1.37533			−0.687666	+	0.726027i	$0.741365\pi$
$878$	8.56215	+	21.4877i	0.288959	+	0.725174i
$879$	9.95443			0.335755
$880$	−8.02585	−	0.434266i	−0.270551	−	0.0146391i
$881$	−12.1623			−0.409759			−0.204880	−	0.978787i	$-0.565680\pi$
$881$	−12.1623			−0.409759			−0.204880	+	0.978787i	$0.565680\pi$
$882$	6.31967	−	2.51819i	0.212794	−	0.0847918i
$883$	25.2022			0.848121			0.424061	−	0.905634i	$-0.360604\pi$
$883$	25.2022			0.848121			0.424061	+	0.905634i	$0.360604\pi$
$884$	−9.18407	−	9.69444i	−0.308894	−	0.326059i
$885$	9.41145			0.316363
$886$	51.9828	−	20.7135i	1.74640	−	0.695884i
$887$			20.0308i			0.672569i	0.941761	+	0.336284i	$0.109170\pi$
$887$			20.0308i			0.672569i	−0.941761	+	0.336284i	$0.890830\pi$
$888$	5.12507	−	11.0800i	0.171986	−	0.371822i
$889$		−	35.1190i		−	1.17785i
$890$	−12.5450	−	31.4831i	−0.420510	−	1.05532i
$891$	−1.17026			−0.0392051
$892$	−14.2282	−	15.0188i	−0.476394	−	0.502868i
$893$	5.05022			0.168999
$894$	22.7231	−	9.05443i	0.759974	−	0.302825i
$895$			12.8890i			0.430833i
$896$	−34.3553	−	18.2056i	−1.14773	−	0.608205i
$897$	−6.21140			−0.207393
$898$	21.5884	−	8.60231i	0.720416	−	0.287063i
$899$	9.44490			0.315005
$900$	2.97892	−	2.82210i	0.0992975	−	0.0940699i
$901$			57.8766i			1.92815i
$902$	5.37384	+	13.4862i	0.178929	+	0.449043i
$903$	−5.34955			−0.178022
$904$	21.2767	+	9.84154i	0.707653	+	0.327325i
$905$		−	11.6026i		−	0.385683i
$906$	0.901298	+	2.26191i	0.0299436	+	0.0751468i
$907$			34.9208i			1.15953i	0.814785	+	0.579763i	$0.196855\pi$
$907$			34.9208i			1.15953i	−0.814785	+	0.579763i	$0.803145\pi$
$908$	−8.92229	−	9.41811i	−0.296097	−	0.312551i
$909$		−	11.4184i		−	0.378725i
$910$	−8.61608	+	3.43323i	−0.285620	+	0.113811i
$911$			8.50206i			0.281686i	0.990032	+	0.140843i	$0.0449813\pi$
$911$			8.50206i			0.281686i	−0.990032	+	0.140843i	$0.955019\pi$
$912$	−6.45019	−	0.349010i	−0.213587	−	0.0115569i
$913$			4.18854i			0.138620i
$914$	−33.4034	+	13.3102i	−1.10489	+	0.440262i
$915$	5.44373			0.179964
$916$	−24.5413	−	25.9051i	−0.810867	−	0.855928i
$917$		−	17.7606i		−	0.586507i
$918$	−7.89257	+	3.14494i	−0.260493	+	0.103798i
$919$	36.1724			1.19322			0.596609	−	0.802532i	$-0.296514\pi$
$919$	36.1724			1.19322			0.596609	+	0.802532i	$0.296514\pi$
$920$	−11.3946	+	24.6343i	−0.375668	+	0.812168i
$921$		−	9.48993i		−	0.312704i
$922$	−20.1608	+	8.03344i	−0.663961	+	0.264567i
$923$	−16.0354			−0.527813
$924$	−5.83922	+	5.53181i	−0.192096	+	0.181983i
$925$	8.85555			0.291169
$926$	−10.3797	+	4.13598i	−0.341098	+	0.135917i
$927$			12.6926i			0.416880i
$928$	4.84011	+	14.3584i	0.158884	+	0.471338i
$929$		−	12.1272i		−	0.397879i	−0.980012	−	0.198940i	$-0.936250\pi$
$929$		−	12.1272i		−	0.397879i	0.980012	−	0.198940i	$-0.0637497\pi$
$930$	−3.16948	−	7.95416i	−0.103931	−	0.260827i
$931$		−	7.76831i		−	0.254596i
$932$	−0.344533	−	0.363680i	−0.0112856	−	0.0119127i
$933$	10.6476			0.348587
$934$	4.48174	+	11.2474i	0.146647	+	0.368027i
$935$			12.0717i			0.394787i
$936$	2.85314	+	1.31972i	0.0932577	+	0.0431363i
$937$		−	9.65964i		−	0.315567i	−0.987474	−	0.157783i	$-0.949565\pi$
$937$		−	9.65964i		−	0.315567i	0.987474	−	0.157783i	$-0.0504348\pi$
$938$	29.3063	+	26.9022i	0.956885	+	0.878390i
$939$			5.82795i			0.190188i
$940$	−7.79630	+	7.38586i	−0.254287	+	0.240900i
$941$			34.2385i			1.11614i	0.829793	+	0.558071i	$0.188458\pi$
$941$			34.2385i			1.11614i	−0.829793	+	0.558071i	$0.811542\pi$
$942$	26.8861	−	10.7133i	0.875997	−	0.349057i
$943$	49.0237			1.59643
$944$	−21.8926	−	1.18457i	−0.712544	−	0.0385546i
$945$			5.90087i			0.191955i
$946$	2.39322	−	0.953621i	0.0778102	−	0.0310049i
$947$		−	46.1972i		−	1.50121i	−0.660754	−	0.750603i	$-0.729763\pi$
$947$		−	46.1972i		−	1.50121i	0.660754	−	0.750603i	$-0.270237\pi$
$948$	−10.8703	+	10.2980i	−0.353052	+	0.334465i
$949$		−	8.78191i		−	0.285073i
$950$	−1.73450	−	4.35292i	−0.0562746	−	0.141227i
$951$	15.2367			0.494084
$952$	−24.5153	+	53.0004i	−0.794546	+	1.71775i
$953$	−16.5122			−0.534882			−0.267441	−	0.963574i	$-0.586178\pi$
$953$	−16.5122			−0.534882			−0.267441	+	0.963574i	$0.586178\pi$
$954$	−5.04323	−	12.6565i	−0.163280	−	0.409770i
$955$		−	24.6213i		−	0.796726i
$956$	27.1046	−	25.6777i	0.876626	−	0.830475i
$957$	3.13461			0.101328
$958$	−15.2466	−	38.2630i	−0.492594	−	1.23622i
$959$			75.4477i			2.43633i
$960$	10.4679	−	8.89451i	0.337851	−	0.287069i
$961$	−18.5666			−0.598922
$962$	2.51122	+	6.30218i	0.0809649	+	0.203190i
$963$			15.0145i			0.483835i
$964$	1.10624	−	1.04801i	0.0356297	−	0.0337540i
$965$		−	11.3945i		−	0.366803i
$966$	10.0543	+	25.2324i	0.323492	+	0.811839i
$967$			11.6189i			0.373639i	0.982394	+	0.186820i	$0.0598180\pi$
$967$			11.6189i			0.373639i	−0.982394	+	0.186820i	$0.940182\pi$
$968$	−11.4354	+	24.7225i	−0.367547	+	0.794612i
$969$			9.70176i			0.311666i
$970$	16.6379	−	6.62966i	0.534210	−	0.212866i
$971$			17.4663i			0.560520i	0.959924	+	0.280260i	$0.0904206\pi$
$971$			17.4663i			0.560520i	−0.959924	+	0.280260i	$0.909579\pi$
$972$	1.45192	−	1.37548i	0.0465702	−	0.0441185i
$973$	34.0604			1.09193
$974$	−3.34208	+	1.33171i	−0.107087	+	0.0426709i
$975$			2.28032i			0.0730288i
$976$	−12.6630	−	0.685175i	−0.405333	−	0.0219319i
$977$	−17.0470			−0.545381			−0.272690	−	0.962102i	$-0.587913\pi$
$977$	−17.0470			−0.545381			−0.272690	+	0.962102i	$0.587913\pi$
$978$	2.55862	+	6.42113i	0.0818155	+	0.205325i
$979$	16.3328			0.521997
$980$	11.3610	+	11.9924i	0.362915	+	0.383082i
$981$			0.414438i			0.0132320i
$982$	−8.71343	−	21.8673i	−0.278057	−	0.697814i
$983$	−36.1727			−1.15373			−0.576865	−	0.816839i	$-0.695724\pi$
$983$	−36.1727			−1.15373			−0.576865	+	0.816839i	$0.695724\pi$
$984$	−22.5185	−	10.4159i	−0.717862	−	0.332047i
$985$	18.7728			0.598152
$986$	21.1408	−	8.42392i	0.673259	−	0.268272i
$987$			10.7472i			0.342087i
$988$	2.60596	−	2.46876i	0.0829065	−	0.0785419i
$989$		−	8.69955i		−	0.276630i
$990$	−1.05190	−	2.63986i	−0.0334316	−	0.0839003i
$991$	2.72634			0.0866051			0.0433025	−	0.999062i	$-0.486212\pi$
$991$	2.72634			0.0866051			0.0433025	+	0.999062i	$0.486212\pi$
$992$	6.37159	+	18.9016i	0.202298	+	0.600127i
$993$	8.30227			0.263465
$994$	25.9563	+	65.1403i	0.823285	+	2.06613i
$995$	37.3739			1.18483
$996$	−4.92305	−	5.19663i	−0.155993	−	0.164662i
$997$	−0.407309			−0.0128996			−0.00644980	−	0.999979i	$-0.502053\pi$
$997$	−0.407309			−0.0128996			−0.00644980	+	0.999979i	$0.502053\pi$
$998$	−5.36515	+	2.13784i	−0.169831	+	0.0676722i
$999$	4.31616			0.136557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.b.535.29	yes	34
4.3	odd	2		804.2.e.a.535.5	✓	34
67.66	odd	2		804.2.e.a.535.6	yes	34
268.267	even	2	inner	804.2.e.b.535.30	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.5	✓	34	4.3	odd	2
804.2.e.a.535.6	yes	34	67.66	odd	2
804.2.e.b.535.29	yes	34	1.1	even	1	trivial
804.2.e.b.535.30	yes	34	268.267	even	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31376 - 0.523490i) q^{2} +1.00000 q^{3} +(1.45192 - 1.37548i) q^{4} +1.71706i q^{5} +(1.31376 - 0.523490i) q^{6} +3.43662 q^{7} +(1.18741 - 2.56711i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.31376 - 0.523490i) q^{2} +1.00000 q^{3} +(1.45192 - 1.37548i) q^{4} +1.71706i q^{5} +(1.31376 - 0.523490i) q^{6} +3.43662 q^{7} +(1.18741 - 2.56711i) q^{8} +1.00000 q^{9} +(0.898862 + 2.25579i) q^{10} -1.17026 q^{11} +(1.45192 - 1.37548i) q^{12} +1.11142i q^{13} +(4.51489 - 1.79904i) q^{14} +1.71706i q^{15} +(0.216118 - 3.99416i) q^{16} -6.00763 q^{17} +(1.31376 - 0.523490i) q^{18} -1.61491i q^{19} +(2.36177 + 2.49302i) q^{20} +3.43662 q^{21} +(-1.53743 + 0.612619i) q^{22} +5.58871i q^{23} +(1.18741 - 2.56711i) q^{24} +2.05172 q^{25} +(0.581818 + 1.46014i) q^{26} +1.00000 q^{27} +(4.98969 - 4.72700i) q^{28} -2.67857 q^{29} +(0.898862 + 2.25579i) q^{30} -3.52610 q^{31} +(-1.80698 - 5.36049i) q^{32} -1.17026 q^{33} +(-7.89257 + 3.14494i) q^{34} +5.90087i q^{35} +(1.45192 - 1.37548i) q^{36} +4.31616 q^{37} +(-0.845389 - 2.12160i) q^{38} +1.11142i q^{39} +(4.40787 + 2.03886i) q^{40} -8.77192i q^{41} +(4.51489 - 1.79904i) q^{42} -1.55663 q^{43} +(-1.69912 + 1.60966i) q^{44} +1.71706i q^{45} +(2.92563 + 7.34220i) q^{46} +3.12725i q^{47} +(0.216118 - 3.99416i) q^{48} +4.81038 q^{49} +(2.69546 - 1.07406i) q^{50} -6.00763 q^{51} +(1.52873 + 1.61369i) q^{52} -9.63385i q^{53} +(1.31376 - 0.523490i) q^{54} -2.00940i q^{55} +(4.08070 - 8.82218i) q^{56} -1.61491i q^{57} +(-3.51899 + 1.40220i) q^{58} -5.48116i q^{59} +(2.36177 + 2.49302i) q^{60} -3.17038i q^{61} +(-4.63244 + 1.84588i) q^{62} +3.43662 q^{63} +(-5.18009 - 6.09644i) q^{64} -1.90837 q^{65} +(-1.53743 + 0.612619i) q^{66} +(3.55266 + 7.37419i) q^{67} +(-8.72257 + 8.26336i) q^{68} +5.58871i q^{69} +(3.08905 + 7.75231i) q^{70} +14.4279i q^{71} +(1.18741 - 2.56711i) q^{72} -7.90152 q^{73} +(5.67038 - 2.25947i) q^{74} +2.05172 q^{75} +(-2.22127 - 2.34471i) q^{76} -4.02173 q^{77} +(0.581818 + 1.46014i) q^{78} -7.48688 q^{79} +(6.85819 + 0.371086i) q^{80} +1.00000 q^{81} +(-4.59201 - 11.5242i) q^{82} -3.57916i q^{83} +(4.98969 - 4.72700i) q^{84} -10.3154i q^{85} +(-2.04503 + 0.814881i) q^{86} -2.67857 q^{87} +(-1.38958 + 3.00418i) q^{88} -13.9566 q^{89} +(0.898862 + 2.25579i) q^{90} +3.81953i q^{91} +(7.68715 + 8.11433i) q^{92} -3.52610 q^{93} +(1.63709 + 4.10845i) q^{94} +2.77289 q^{95} +(-1.80698 - 5.36049i) q^{96} -7.37562i q^{97} +(6.31967 - 2.51819i) q^{98} -1.17026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more