LMFDB - Embedded newform 841.2.e.j.236.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			236.2
Character	$\chi$	$=$	841.236
Dual form			841.2.e.j.196.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.602539 - 0.137526i) q^{2} +(0.268155 + 0.556829i) q^{3} +(-1.45780 - 0.702039i) q^{4} +(0.857618 - 3.75747i) q^{5} +(-0.0849954 - 0.372389i) q^{6} +(2.01463 - 0.970194i) q^{7} +(1.74823 + 1.39417i) q^{8} +(1.63232 - 2.04686i) q^{9} +O(q^{10})$	\(q+(-0.602539 - 0.137526i) q^{2} +(0.268155 + 0.556829i) q^{3} +(-1.45780 - 0.702039i) q^{4} +(0.857618 - 3.75747i) q^{5} +(-0.0849954 - 0.372389i) q^{6} +(2.01463 - 0.970194i) q^{7} +(1.74823 + 1.39417i) q^{8} +(1.63232 - 2.04686i) q^{9} +(-1.03350 + 2.14608i) q^{10} +(1.08046 - 0.861642i) q^{11} -1.00000i q^{12} +(0.147186 + 0.184565i) q^{13} +(-1.34732 + 0.307516i) q^{14} +(2.32225 - 0.530037i) q^{15} +(1.15601 + 1.44960i) q^{16} -4.38197i q^{17} +(-1.26503 + 1.00883i) q^{18} +(-2.10612 + 4.37339i) q^{19} +(-3.88812 + 4.87555i) q^{20} +(1.08046 + 0.861642i) q^{21} +(-0.769519 + 0.370581i) q^{22} +(0.275051 + 1.20508i) q^{23} +(-0.307516 + 1.34732i) q^{24} +(-8.87824 - 4.27553i) q^{25} +(-0.0633028 - 0.131450i) q^{26} +(3.38508 + 0.772623i) q^{27} -3.61803 q^{28} -1.47214 q^{30} +(9.83719 + 2.24527i) q^{31} +(-2.43757 - 5.06167i) q^{32} +(0.769519 + 0.370581i) q^{33} +(-0.602632 + 2.64030i) q^{34} +(-1.91769 - 8.40196i) q^{35} +(-3.81657 + 1.83796i) q^{36} +(-3.68102 - 2.93552i) q^{37} +(1.87047 - 2.34549i) q^{38} +(-0.0633028 + 0.131450i) q^{39} +(6.73785 - 5.37326i) q^{40} -3.85410i q^{41} +(-0.532524 - 0.667764i) q^{42} +(-7.05464 + 1.61018i) q^{43} +(-2.18001 + 0.497572i) q^{44} +(-6.29112 - 7.88881i) q^{45} -0.763932i q^{46} +(-5.47282 + 4.36443i) q^{47} +(-0.497187 + 1.03242i) q^{48} +(-1.24698 + 1.56366i) q^{49} +(4.76149 + 3.79716i) q^{50} +(2.44001 - 1.17505i) q^{51} +(-0.0849954 - 0.372389i) q^{52} +(0.445042 - 1.94986i) q^{53} +(-1.93339 - 0.931070i) q^{54} +(-2.31097 - 4.79877i) q^{55} +(4.87464 + 1.11260i) q^{56} -3.00000 q^{57} +6.09017 q^{59} +(-3.75747 - 0.857618i) q^{60} +(0.268155 + 0.556829i) q^{61} +(-5.61850 - 2.70573i) q^{62} +(1.30266 - 5.70733i) q^{63} +(-0.0525301 - 0.230149i) q^{64} +(0.819729 - 0.394760i) q^{65} +(-0.412701 - 0.329118i) q^{66} +(0.952608 - 1.19453i) q^{67} +(-3.07631 + 6.38802i) q^{68} +(-0.597266 + 0.476304i) q^{69} +5.32624i q^{70} +(-6.52927 - 8.18745i) q^{71} +(5.70733 - 1.30266i) q^{72} +(13.3645 - 3.05036i) q^{73} +(1.81425 + 2.27500i) q^{74} -6.09017i q^{75} +(6.14058 - 4.89695i) q^{76} +(1.34077 - 2.78415i) q^{77} +(0.0562200 - 0.0704977i) q^{78} +(-4.76149 - 3.79716i) q^{79} +(6.43823 - 3.10049i) q^{80} +(-1.27019 - 5.56509i) q^{81} +(-0.530037 + 2.32225i) q^{82} +(8.95948 + 4.31466i) q^{83} +(-0.970194 - 2.01463i) q^{84} +(-16.4651 - 3.75805i) q^{85} +4.47214 q^{86} +3.09017 q^{88} +(-4.59016 - 1.04767i) q^{89} +(2.70573 + 5.61850i) q^{90} +(0.475589 + 0.229032i) q^{91} +(0.445042 - 1.94986i) q^{92} +(1.38766 + 6.07972i) q^{93} +(3.89781 - 1.87708i) q^{94} +(14.6267 + 11.6644i) q^{95} +(2.16484 - 2.71463i) q^{96} +(-1.54563 + 3.20953i) q^{97} +(0.966397 - 0.770676i) q^{98} -3.61803i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−0.602539	−	0.137526i	−0.426059	−	0.0972452i	0.00411419	−	0.999992i	$-0.498690\pi$
$2$	−0.602539	−	0.137526i	−0.426059	−	0.0972452i	−0.430173	+	0.902746i	$0.641548\pi$
$3$	0.268155	+	0.556829i	0.154819	+	0.321486i	0.963923	−	0.266180i	$-0.0857615\pi$
$3$	0.268155	+	0.556829i	0.154819	+	0.321486i	−0.809104	+	0.587665i	$0.800047\pi$
$4$	−1.45780	−	0.702039i	−0.728899	−	0.351019i
$5$	0.857618	−	3.75747i	0.383539	−	1.68039i	−0.302756	−	0.953068i	$-0.597907\pi$
$5$	0.857618	−	3.75747i	0.383539	−	1.68039i	0.686294	−	0.727324i	$-0.259236\pi$
$6$	−0.0849954	−	0.372389i	−0.0346992	−	0.152027i
$7$	2.01463	−	0.970194i	0.761458	−	0.366699i	−0.0125117	−	0.999922i	$-0.503983\pi$
$7$	2.01463	−	0.970194i	0.761458	−	0.366699i	0.773969	+	0.633223i	$0.218268\pi$
$8$	1.74823	+	1.39417i	0.618092	+	0.492912i
$9$	1.63232	−	2.04686i	0.544106	−	0.682287i
$10$	−1.03350	+	2.14608i	−0.326820	+	0.678649i
$11$	1.08046	−	0.861642i	0.325772	−	0.259795i	−0.446922	−	0.894573i	$-0.647480\pi$
$11$	1.08046	−	0.861642i	0.325772	−	0.259795i	0.772694	+	0.634778i	$0.218908\pi$
$12$		−	1.00000i		−	0.288675i
$13$	0.147186	+	0.184565i	0.0408220	+	0.0511892i	0.801823	−	0.597561i	$-0.203863\pi$
$13$	0.147186	+	0.184565i	0.0408220	+	0.0511892i	−0.761001	+	0.648750i	$0.775292\pi$
$14$	−1.34732	+	0.307516i	−0.360086	+	0.0821872i
$15$	2.32225	−	0.530037i	0.599601	−	0.136855i
$16$	1.15601	+	1.44960i	0.289003	+	0.362399i
$17$		−	4.38197i		−	1.06278i	−0.847126	−	0.531391i	$-0.821669\pi$
$17$		−	4.38197i		−	1.06278i	0.847126	−	0.531391i	$-0.178331\pi$
$18$	−1.26503	+	1.00883i	−0.298170	+	0.237783i
$19$	−2.10612	+	4.37339i	−0.483176	+	1.00333i	0.506796	+	0.862066i	$0.330830\pi$
$19$	−2.10612	+	4.37339i	−0.483176	+	1.00333i	−0.989973	+	0.141260i	$0.954885\pi$
$20$	−3.88812	+	4.87555i	−0.869411	+	1.09021i
$21$	1.08046	+	0.861642i	0.235777	+	0.188026i
$22$	−0.769519	+	0.370581i	−0.164062	+	0.0790081i
$23$	0.275051	+	1.20508i	0.0573521	+	0.251276i	0.995475	−	0.0950275i	$-0.0302939\pi$
$23$	0.275051	+	1.20508i	0.0573521	+	0.251276i	−0.938123	+	0.346303i	$0.887437\pi$
$24$	−0.307516	+	1.34732i	−0.0627715	+	0.275020i
$25$	−8.87824	−	4.27553i	−1.77565	−	0.855107i
$26$	−0.0633028	−	0.131450i	−0.0124147	−	0.0257794i
$27$	3.38508	+	0.772623i	0.651459	+	0.148691i
$28$	−3.61803			−0.683744
$29$		0			0
$29$		0			0
$30$	−1.47214			−0.268774
$31$	9.83719	+	2.24527i	1.76681	+	0.403263i	0.977535	−	0.210775i	$-0.0675987\pi$
$31$	9.83719	+	2.24527i	1.76681	+	0.403263i	0.789277	+	0.614038i	$0.210456\pi$
$32$	−2.43757	−	5.06167i	−0.430906	−	0.894786i
$33$	0.769519	+	0.370581i	0.133956	+	0.0645099i
$34$	−0.602632	+	2.64030i	−0.103351	+	0.452808i
$35$	−1.91769	−	8.40196i	−0.324149	−	1.42019i
$36$	−3.81657	+	1.83796i	−0.636094	+	0.306327i
$37$	−3.68102	−	2.93552i	−0.605156	−	0.482596i	0.272326	−	0.962205i	$-0.412207\pi$
$37$	−3.68102	−	2.93552i	−0.605156	−	0.482596i	−0.877482	+	0.479609i	$0.840779\pi$
$38$	1.87047	−	2.34549i	0.303430	−	0.380489i
$39$	−0.0633028	+	0.131450i	−0.0101366	+	0.0210488i
$40$	6.73785	−	5.37326i	1.06535	−	0.849586i
$41$		−	3.85410i		−	0.601910i	−0.953638	−	0.300955i	$-0.902695\pi$
$41$		−	3.85410i		−	0.601910i	0.953638	−	0.300955i	$-0.0973053\pi$
$42$	−0.532524	−	0.667764i	−0.0821702	−	0.103038i
$43$	−7.05464	+	1.61018i	−1.07582	+	0.245550i	−0.723497	−	0.690328i	$-0.757466\pi$
$43$	−7.05464	+	1.61018i	−1.07582	+	0.245550i	−0.352326	+	0.935877i	$0.614609\pi$
$44$	−2.18001	+	0.497572i	−0.328648	+	0.0750118i
$45$	−6.29112	−	7.88881i	−0.937825	−	1.17599i
$46$		−	0.763932i		−	0.112636i
$47$	−5.47282	+	4.36443i	−0.798293	+	0.636617i	−0.935261	−	0.353958i	$-0.884836\pi$
$47$	−5.47282	+	4.36443i	−0.798293	+	0.636617i	0.136968	+	0.990575i	$0.456264\pi$
$48$	−0.497187	+	1.03242i	−0.0717627	+	0.149017i
$49$	−1.24698	+	1.56366i	−0.178140	+	0.223380i
$50$	4.76149	+	3.79716i	0.673376	+	0.536999i
$51$	2.44001	−	1.17505i	0.341669	−	0.164539i
$52$	−0.0849954	−	0.372389i	−0.0117867	−	0.0516411i
$53$	0.445042	−	1.94986i	0.0611312	−	0.267833i	−0.935121	−	0.354328i	$-0.884710\pi$
$53$	0.445042	−	1.94986i	0.0611312	−	0.267833i	0.996252	+	0.0864950i	$0.0275667\pi$
$54$	−1.93339	−	0.931070i	−0.263101	−	0.126703i
$55$	−2.31097	−	4.79877i	−0.311611	−	0.647067i
$56$	4.87464	+	1.11260i	0.651401	+	0.148678i
$57$	−3.00000			−0.397360
$58$		0			0
$59$	6.09017			0.792873			0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017			0.792873			0.396436	+	0.918062i	$0.370247\pi$
$60$	−3.75747	−	0.857618i	−0.485087	−	0.110718i
$61$	0.268155	+	0.556829i	0.0343337	+	0.0712947i	0.917430	−	0.397897i	$-0.130260\pi$
$61$	0.268155	+	0.556829i	0.0343337	+	0.0712947i	−0.883097	+	0.469191i	$0.844545\pi$
$62$	−5.61850	−	2.70573i	−0.713551	−	0.343628i
$63$	1.30266	−	5.70733i	0.164120	−	0.719056i
$64$	−0.0525301	−	0.230149i	−0.00656626	−	0.0287687i
$65$	0.819729	−	0.394760i	0.101675	−	0.0489640i
$66$	−0.412701	−	0.329118i	−0.0507999	−	0.0405116i
$67$	0.952608	−	1.19453i	0.116380	−	0.145935i	−0.720229	−	0.693736i	$-0.755963\pi$
$67$	0.952608	−	1.19453i	0.116380	−	0.145935i	0.836609	+	0.547801i	$0.184535\pi$
$68$	−3.07631	+	6.38802i	−0.373057	+	0.774662i
$69$	−0.597266	+	0.476304i	−0.0719024	+	0.0573402i
$70$			5.32624i			0.636607i
$71$	−6.52927	−	8.18745i	−0.774882	−	0.971671i	0.225115	−	0.974332i	$-0.427724\pi$
$71$	−6.52927	−	8.18745i	−0.774882	−	0.971671i	−0.999996	+	0.00266125i	$0.999153\pi$
$72$	5.70733	−	1.30266i	0.672615	−	0.153520i
$73$	13.3645	−	3.05036i	1.56420	−	0.357018i	0.649245	−	0.760579i	$-0.275085\pi$
$73$	13.3645	−	3.05036i	1.56420	−	0.357018i	0.914953	+	0.403561i	$0.132228\pi$
$74$	1.81425	+	2.27500i	0.210902	+	0.264463i
$75$		−	6.09017i		−	0.703232i
$76$	6.14058	−	4.89695i	0.704373	−	0.561719i
$77$	1.34077	−	2.78415i	0.152795	−	0.317283i
$78$	0.0562200	−	0.0704977i	0.00636567	−	0.00798229i
$79$	−4.76149	−	3.79716i	−0.535709	−	0.427214i	0.317903	−	0.948123i	$-0.397021\pi$
$79$	−4.76149	−	3.79716i	−0.535709	−	0.427214i	−0.853612	+	0.520910i	$0.825593\pi$
$80$	6.43823	−	3.10049i	0.719816	−	0.346645i
$81$	−1.27019	−	5.56509i	−0.141133	−	0.618343i
$82$	−0.530037	+	2.32225i	−0.0585328	+	0.256449i
$83$	8.95948	+	4.31466i	0.983431	+	0.473595i	0.855284	−	0.518160i	$-0.173383\pi$
$83$	8.95948	+	4.31466i	0.983431	+	0.473595i	0.128147	+	0.991755i	$0.459097\pi$
$84$	−0.970194	−	2.01463i	−0.105857	−	0.219814i
$85$	−16.4651	−	3.75805i	−1.78589	−	0.407618i
$86$	4.47214			0.482243
$87$		0			0
$88$	3.09017			0.329413
$89$	−4.59016	−	1.04767i	−0.486556	−	0.111053i	−0.0277963	−	0.999614i	$-0.508849\pi$
$89$	−4.59016	−	1.04767i	−0.486556	−	0.111053i	−0.458760	+	0.888560i	$0.651706\pi$
$90$	2.70573	+	5.61850i	0.285209	+	0.592242i
$91$	0.475589	+	0.229032i	0.0498553	+	0.0240090i
$92$	0.445042	−	1.94986i	0.0463988	−	0.203287i
$93$	1.38766	+	6.07972i	0.143893	+	0.630437i
$94$	3.89781	−	1.87708i	0.402028	−	0.193606i
$95$	14.6267	+	11.6644i	1.50066	+	1.19674i
$96$	2.16484	−	2.71463i	0.220948	−	0.277060i
$97$	−1.54563	+	3.20953i	−0.156935	+	0.325878i	−0.964580	−	0.263790i	$-0.915027\pi$
$97$	−1.54563	+	3.20953i	−0.156935	+	0.325878i	0.807645	+	0.589668i	$0.200742\pi$
$98$	0.966397	−	0.770676i	0.0976208	−	0.0778500i
$99$		−	3.61803i		−	0.363626i
$100$	9.94109	+	12.4657i	0.994109	+	1.24657i
$101$	−0.602539	+	0.137526i	−0.0599548	+	0.0136843i	−0.252393	−	0.967625i	$-0.581218\pi$
$101$	−0.602539	+	0.137526i	−0.0599548	+	0.0136843i	0.192438	+	0.981309i	$0.438360\pi$
$102$	−1.63180	+	0.372447i	−0.161572	+	0.0368778i
$103$	5.72385	+	7.17748i	0.563988	+	0.707218i	0.979289	−	0.202466i	$-0.0648955\pi$
$103$	5.72385	+	7.17748i	0.563988	+	0.707218i	−0.415302	+	0.909684i	$0.636324\pi$
$104$			0.527864i			0.0517613i
$105$	4.16422	−	3.32086i	0.406386	−	0.324082i
$106$	−0.536310	+	1.11366i	−0.0520910	+	0.108168i
$107$	4.21724	−	5.28826i	0.407696	−	0.511235i	−0.535016	−	0.844842i	$-0.679694\pi$
$107$	4.21724	−	5.28826i	0.407696	−	0.511235i	0.942712	+	0.333607i	$0.108266\pi$
$108$	−4.39236	−	3.50279i	−0.422655	−	0.337056i
$109$	−12.9577	+	6.24010i	−1.24112	+	0.597693i	−0.935118	−	0.354337i	$-0.884707\pi$
$109$	−12.9577	+	6.24010i	−1.24112	+	0.597693i	−0.306005	+	0.952030i	$0.598992\pi$
$110$	0.732494	+	3.20926i	0.0698405	+	0.305991i
$111$	0.647498	−	2.83687i	0.0614578	−	0.269264i
$112$	3.73533	+	1.79884i	0.352955	+	0.169974i
$113$	3.44689	+	7.15754i	0.324256	+	0.673325i	0.997833	−	0.0657920i	$-0.0209574\pi$
$113$	3.44689	+	7.15754i	0.324256	+	0.673325i	−0.673577	+	0.739117i	$0.735243\pi$
$114$	1.80762	+	0.412577i	0.169299	+	0.0386413i
$115$	4.76393			0.444239
$116$		0			0
$117$	0.618034			0.0571373
$118$	−3.66956	−	0.837554i	−0.337811	−	0.0771031i
$119$	−4.25136	−	8.82803i	−0.389721	−	0.809264i
$120$	4.79877	+	2.31097i	0.438066	+	0.210962i
$121$	−2.02275	+	8.86226i	−0.183887	+	0.805660i
$122$	−0.0849954	−	0.372389i	−0.00769512	−	0.0337145i
$123$	2.14608	−	1.03350i	0.193505	−	0.0931872i
$124$	−12.7644	−	10.1792i	−1.14627	−	0.914123i
$125$	−11.6644	+	14.6267i	−1.04329	+	1.30825i
$126$	−1.56981	+	3.25974i	−0.139849	+	0.290400i
$127$	−12.4657	+	9.94109i	−1.10615	+	0.882129i	−0.993761	−	0.111534i	$-0.964423\pi$
$127$	−12.4657	+	9.94109i	−1.10615	+	0.882129i	−0.112394	+	0.993664i	$0.535852\pi$
$128$			11.3820i			1.00603i
$129$	−2.78833	−	3.49646i	−0.245499	−	0.307846i
$130$	−0.548208	+	0.125125i	−0.0480810	+	0.0109742i
$131$	−13.9670	+	3.18789i	−1.22031	+	0.278527i	−0.783708	−	0.621129i	$-0.786674\pi$
$131$	−13.9670	+	3.18789i	−1.22031	+	0.278527i	−0.436599	+	0.899656i	$0.643817\pi$
$132$	−0.861642	−	1.08046i	−0.0749963	−	0.0940424i
$133$			10.8541i			0.941170i
$134$	−0.738262	+	0.588744i	−0.0637761	+	0.0508597i
$135$	5.80622	−	12.0567i	0.499720	−	1.03768i
$136$	6.10919	−	7.66068i	0.523858	−	0.656898i
$137$	5.58689	+	4.45539i	0.477320	+	0.380650i	0.832391	−	0.554189i	$-0.186972\pi$
$137$	5.58689	+	4.45539i	0.477320	+	0.380650i	−0.355070	+	0.934840i	$0.615543\pi$
$138$	0.425380	−	0.204852i	0.0362107	−	0.0174382i
$139$	−0.287452	−	1.25941i	−0.0243813	−	0.106822i	0.961273	−	0.275598i	$-0.0888757\pi$
$139$	−0.287452	−	1.25941i	−0.0243813	−	0.106822i	−0.985654	+	0.168776i	$0.946019\pi$
$140$	−3.10289	+	13.5947i	−0.262242	+	1.14896i
$141$	−3.89781	−	1.87708i	−0.328254	−	0.158079i
$142$	2.80815	+	5.83119i	0.235655	+	0.489343i
$143$	0.318058	+	0.0725948i	0.0265974	+	0.00607068i
$144$	4.85410			0.404508
$145$		0			0
$146$	−8.47214			−0.701159
$147$	−1.20508	−	0.275051i	−0.0993931	−	0.0226858i
$148$	3.30534	+	6.86361i	0.271697	+	0.564185i
$149$	8.66555	+	4.17311i	0.709909	+	0.341874i	0.753747	−	0.657164i	$-0.228244\pi$
$149$	8.66555	+	4.17311i	0.709909	+	0.341874i	−0.0438379	+	0.999039i	$0.513959\pi$
$150$	−0.837554	+	3.66956i	−0.0683860	+	0.299619i
$151$	0.594968	+	2.60673i	0.0484178	+	0.212132i	0.993350	−	0.115134i	$-0.0367297\pi$
$151$	0.594968	+	2.60673i	0.0484178	+	0.212132i	−0.944932	+	0.327266i	$0.893873\pi$
$152$	−9.77921	+	4.70942i	−0.793199	+	0.381984i
$153$	−8.96928	−	7.15276i	−0.725123	−	0.578266i
$154$	−1.19076	+	1.49317i	−0.0959541	+	0.120323i
$155$	16.8731	−	35.0374i	1.35528	−	2.81427i
$156$	0.184565	−	0.147186i	0.0147771	−	0.0117843i
$157$		−	14.5623i		−	1.16220i	−0.813833	−	0.581099i	$-0.802623\pi$
$157$		−	14.5623i		−	1.16220i	0.813833	−	0.581099i	$-0.197377\pi$
$158$	2.34677	+	2.94276i	0.186699	+	0.234113i
$159$	1.20508	−	0.275051i	0.0955688	−	0.0218130i
$160$	−21.1096	+	4.81813i	−1.66886	+	0.380907i
$161$	1.72328	+	2.16093i	0.135814	+	0.170305i
$162$			3.52786i			0.277175i
$163$	−4.71792	+	3.76241i	−0.369536	+	0.294695i	−0.790596	−	0.612338i	$-0.790229\pi$
$163$	−4.71792	+	3.76241i	−0.369536	+	0.294695i	0.421061	+	0.907032i	$0.361658\pi$
$164$	−2.70573	+	5.61850i	−0.211282	+	0.438731i
$165$	2.05240	−	2.57363i	0.159779	−	0.200357i
$166$	−4.80506	−	3.83190i	−0.372945	−	0.297413i
$167$	9.48528	−	4.56787i	0.733993	−	0.353472i	−0.0292604	−	0.999572i	$-0.509315\pi$
$167$	9.48528	−	4.56787i	0.733993	−	0.353472i	0.763253	+	0.646100i	$0.223601\pi$
$168$	0.687628	+	3.01269i	0.0530516	+	0.232434i
$169$	2.88037	−	12.6197i	0.221567	−	0.970749i
$170$	9.40404	+	4.52875i	0.721257	+	0.347339i
$171$	5.51388	+	11.4497i	0.421657	+	0.875580i
$172$	11.4147	+	2.60532i	0.870359	+	0.198654i
$173$	−4.09017			−0.310970			−0.155485	−	0.987838i	$-0.549694\pi$
$173$	−4.09017			−0.310970			−0.155485	+	0.987838i	$0.549694\pi$
$174$		0			0
$175$	−22.0344			−1.66565
$176$	2.49806	+	0.570167i	0.188299	+	0.0429779i
$177$	1.63311	+	3.39119i	0.122752	+	0.254897i
$178$	2.62167	+	1.26253i	0.196502	+	0.0946305i
$179$	−3.56033	+	15.5988i	−0.266112	+	1.16591i	0.648383	+	0.761315i	$0.275446\pi$
$179$	−3.56033	+	15.5988i	−0.266112	+	1.16591i	−0.914495	+	0.404598i	$0.867411\pi$
$180$	3.63293	+	15.9169i	0.270783	+	1.18638i
$181$	−5.35560	+	2.57912i	−0.398079	+	0.191705i	−0.622203	−	0.782856i	$-0.713762\pi$
$181$	−5.35560	+	2.57912i	−0.398079	+	0.191705i	0.224124	+	0.974561i	$0.428048\pi$
$182$	−0.255063	−	0.203406i	−0.0189065	−	0.0150775i
$183$	−0.238152	+	0.298633i	−0.0176047	+	0.0220756i
$184$	−1.19923	+	2.49022i	−0.0884081	+	0.183581i
$185$	−14.1870	+	11.3138i	−1.04305	+	0.831806i
$186$		−	3.85410i		−	0.282596i
$187$	−3.77568	−	4.73456i	−0.276105	−	0.346225i
$188$	11.0423	−	2.52033i	0.805340	−	0.183814i
$189$	7.56927	−	1.72764i	0.550584	−	0.125667i
$190$	−7.20898	−	9.03977i	−0.522994	−	0.655814i
$191$			17.0344i			1.23257i	0.787524	+	0.616284i	$0.211363\pi$
$191$			17.0344i			1.23257i	−0.787524	+	0.616284i	$0.788637\pi$
$192$	0.114068	−	0.0909659i	0.00823213	−	0.00656490i
$193$	5.41146	−	11.2370i	0.389525	−	0.808857i	−0.610335	−	0.792143i	$-0.708965\pi$
$193$	5.41146	−	11.2370i	0.389525	−	0.808857i	0.999860	−	0.0167141i	$-0.00532050\pi$
$194$	1.37269	−	1.72130i	0.0985535	−	0.123582i
$195$	0.439628	+	0.350592i	0.0314824	+	0.0251064i
$196$	2.91560	−	1.40408i	0.208257	−	0.100291i
$197$	1.40006	+	6.13405i	0.0997499	+	0.437033i	0.999999	+	0.00165687i	$0.000527397\pi$
$197$	1.40006	+	6.13405i	0.0997499	+	0.437033i	−0.900249	+	0.435376i	$0.856615\pi$
$198$	−0.497572	+	2.18001i	−0.0353609	+	0.154926i
$199$	5.27436	+	2.54000i	0.373890	+	0.180056i	0.611386	−	0.791333i	$-0.290612\pi$
$199$	5.27436	+	2.54000i	0.373890	+	0.180056i	−0.237496	+	0.971389i	$0.576327\pi$
$200$	−9.56039	−	19.8523i	−0.676021	−	1.40377i
$201$	0.920597	+	0.210120i	0.0649339	+	0.0148207i
$202$	0.381966			0.0268750
$203$		0			0
$204$	−4.38197			−0.306799
$205$	−14.4817	−	3.30535i	−1.01144	−	0.230856i
$206$	−2.46175	−	5.11188i	−0.171518	−	0.356162i
$207$	2.91560	+	1.40408i	0.202648	+	0.0975901i
$208$	−0.0973961	+	0.426720i	−0.00675320	+	0.0295877i
$209$	1.49272	+	6.54002i	0.103253	+	0.452382i
$210$	−2.96581	+	1.42826i	−0.204660	+	0.0985591i
$211$	9.11027	+	7.26520i	0.627177	+	0.500157i	0.884728	−	0.466108i	$-0.154344\pi$
$211$	9.11027	+	7.26520i	0.627177	+	0.500157i	−0.257551	+	0.966265i	$0.582916\pi$
$212$	−2.01766	+	2.53006i	−0.138573	+	0.173765i
$213$	2.80815	−	5.83119i	0.192412	−	0.399547i
$214$	−3.26832	+	2.60640i	−0.223418	+	0.178170i
$215$			27.8885i			1.90198i
$216$	4.84073	+	6.07009i	0.329370	+	0.413017i
$217$	21.9966	−	5.02059i	1.49323	−	0.340820i
$218$	8.66569	−	1.97789i	0.586915	−	0.133959i
$219$	5.28229	+	6.62378i	0.356944	+	0.447594i
$220$			8.61803i			0.581028i
$221$	0.808759	−	0.644964i	0.0544030	−	0.0433850i
$222$	−0.780285	+	1.62028i	−0.0523693	+	0.108746i
$223$	1.66706	−	2.09043i	0.111635	−	0.139986i	−0.722875	−	0.690979i	$-0.757180\pi$
$223$	1.66706	−	2.09043i	0.111635	−	0.139986i	0.834510	+	0.550993i	$0.185751\pi$
$224$	−9.82161	−	7.83247i	−0.656234	−	0.523329i
$225$	−23.2435	+	11.1935i	−1.54957	+	0.746233i
$226$	−1.09254	−	4.78673i	−0.0726747	−	0.318409i
$227$	4.64814	−	20.3648i	0.308508	−	1.35166i	−0.548411	−	0.836209i	$-0.684767\pi$
$227$	4.64814	−	20.3648i	0.308508	−	1.35166i	0.856919	−	0.515452i	$-0.172376\pi$
$228$	4.37339	+	2.10612i	0.289635	+	0.139481i
$229$	0.994373	+	2.06484i	0.0657100	+	0.136448i	0.931237	−	0.364414i	$-0.118731\pi$
$229$	0.994373	+	2.06484i	0.0657100	+	0.136448i	−0.865527	+	0.500862i	$0.833016\pi$
$230$	−2.87045	−	0.655162i	−0.189272	−	0.0432001i
$231$	1.90983			0.125658
$232$		0			0
$233$	15.2361			0.998148			0.499074	−	0.866559i	$-0.333674\pi$
$233$	15.2361			0.998148			0.499074	+	0.866559i	$0.333674\pi$
$234$	−0.372389	−	0.0849954i	−0.0243439	−	0.00555633i
$235$	11.7056	+	24.3070i	0.763591	+	1.58561i
$236$	−8.87824	−	4.27553i	−0.577924	−	0.278314i
$237$	0.837554	−	3.66956i	0.0544050	−	0.238364i
$238$	1.34753	+	5.90390i	0.0873472	+	0.382693i
$239$	24.9953	−	12.0371i	1.61681	−	0.778614i	0.616845	−	0.787085i	$-0.288411\pi$
$239$	24.9953	−	12.0371i	1.61681	−	0.778614i	0.999964	+	0.00847060i	$0.00269631\pi$
$240$	3.45289	+	2.75359i	0.222883	+	0.177743i
$241$	2.90077	−	3.63745i	0.186855	−	0.234309i	−0.679577	−	0.733605i	$-0.737836\pi$
$241$	2.90077	−	3.63745i	0.186855	−	0.234309i	0.866432	+	0.499296i	$0.166408\pi$
$242$	2.43757	−	5.06167i	0.156693	−	0.325377i
$243$	10.9021	−	8.69411i	0.699368	−	0.557728i
$244$		−	1.00000i		−	0.0640184i
$245$	4.80599	+	6.02652i	0.307043	+	0.385020i
$246$	−1.43523	+	0.327581i	−0.0915067	+	0.0208858i
$247$	−1.11717	+	0.254986i	−0.0710837	+	0.0162244i
$248$	14.0674	+	17.6399i	0.893279	+	1.12014i
$249$			6.14590i			0.389480i
$250$	9.03977	−	7.20898i	0.571726	−	0.455936i
$251$	−8.52689	+	17.7063i	−0.538213	+	1.11761i	0.437634	+	0.899153i	$0.355817\pi$
$251$	−8.52689	+	17.7063i	−0.538213	+	1.11761i	−0.975847	+	0.218457i	$0.929898\pi$
$252$	−5.90578	+	7.40561i	−0.372029	+	0.466510i
$253$	1.33553	+	1.06505i	0.0839639	+	0.0669590i
$254$	8.87824	−	4.27553i	0.557070	−	0.268271i
$255$	−2.32261	−	10.1760i	−0.145447	−	0.637246i
$256$	1.46025	−	6.39778i	0.0912657	−	0.399861i
$257$	20.8848	+	10.0576i	1.30276	+	0.627374i	0.951137	−	0.308769i	$-0.0999170\pi$
$257$	20.8848	+	10.0576i	1.30276	+	0.627374i	0.351619	+	0.936143i	$0.385631\pi$
$258$	1.19923	+	2.49022i	0.0746605	+	0.155034i
$259$	−10.2639	−	2.34267i	−0.637768	−	0.145566i
$260$	−1.47214			−0.0912980
$261$		0			0
$262$	8.85410			0.547008
$263$	16.2893	+	3.71793i	1.00444	+	0.229257i	0.692945	−	0.720990i	$-0.256313\pi$
$263$	16.2893	+	3.71793i	1.00444	+	0.229257i	0.311496	+	0.950248i	$0.399170\pi$
$264$	0.828644	+	1.72070i	0.0509995	+	0.105902i
$265$	−6.94485	−	3.34446i	−0.426619	−	0.205449i
$266$	1.49272	−	6.54002i	0.0915243	−	0.400994i
$267$	−0.647498	−	2.83687i	−0.0396262	−	0.173614i
$268$	−2.22732	+	1.07262i	−0.136055	+	0.0655207i
$269$	4.69099	+	3.74094i	0.286015	+	0.228089i	0.755978	−	0.654597i	$-0.227162\pi$
$269$	4.69099	+	3.74094i	0.286015	+	0.228089i	−0.469964	+	0.882686i	$0.655733\pi$
$270$	−5.15658	+	6.46614i	−0.313819	+	0.393517i
$271$	−4.41708	+	9.17217i	−0.268319	+	0.557170i	−0.990976	−	0.134037i	$-0.957206\pi$
$271$	−4.41708	+	9.17217i	−0.268319	+	0.557170i	0.722658	+	0.691206i	$0.242920\pi$
$272$	6.35208	−	5.06561i	0.385151	−	0.307148i
$273$			0.326238i			0.0197448i
$274$	−2.75359	−	3.45289i	−0.166350	−	0.208597i
$275$	−13.2766	+	3.03030i	−0.800609	+	0.182734i
$276$	1.20508	−	0.275051i	0.0725371	−	0.0165561i
$277$	−13.3314	−	16.7171i	−0.801008	−	1.00443i	−0.999703	−	0.0243714i	$-0.992242\pi$
$277$	−13.3314	−	16.7171i	−0.801008	−	1.00443i	0.198695	−	0.980061i	$-0.436330\pi$
$278$			0.798374i			0.0478833i
$279$	20.6532	−	16.4704i	1.23647	−	0.986055i
$280$	8.36116	−	17.3621i	0.499675	−	1.03759i
$281$	14.4180	−	18.0795i	0.860103	−	1.07854i	−0.136032	−	0.990704i	$-0.543435\pi$
$281$	14.4180	−	18.0795i	0.860103	−	1.07854i	0.996135	−	0.0878311i	$-0.0279936\pi$
$282$	2.09043	+	1.66706i	0.124483	+	0.0992722i
$283$	−4.71753	+	2.27184i	−0.280428	+	0.135047i	−0.568811	−	0.822468i	$-0.692597\pi$
$283$	−4.71753	+	2.27184i	−0.280428	+	0.135047i	0.288383	+	0.957515i	$0.406882\pi$
$284$	3.77046	+	16.5194i	0.223735	+	0.980249i
$285$	−2.57286	+	11.2724i	−0.152403	+	0.667720i
$286$	−0.181659	−	0.0874823i	−0.0107417	−	0.00517294i
$287$	−3.73922	−	7.76458i	−0.220719	−	0.458329i
$288$	−14.3394	−	3.27288i	−0.844960	−	0.192856i
$289$	−2.20163			−0.129507
$290$		0			0
$291$	−2.20163			−0.129062
$292$	−21.6242	−	4.93559i	−1.26546	−	0.288834i
$293$	−3.70010	−	7.68334i	−0.216162	−	0.448866i	0.764487	−	0.644639i	$-0.222992\pi$
$293$	−3.70010	−	7.68334i	−0.216162	−	0.448866i	−0.980649	+	0.195774i	$0.937278\pi$
$294$	0.688279	+	0.331458i	0.0401412	+	0.0193310i
$295$	5.22304	−	22.8836i	0.304097	−	1.33234i
$296$	−2.34267	−	10.2639i	−0.136165	−	0.596578i
$297$	4.32319	−	2.08194i	0.250857	−	0.120806i
$298$	−4.64742	−	3.70619i	−0.269218	−	0.214694i
$299$	−0.181932	+	0.228135i	−0.0105214	+	0.0131934i
$300$	−4.27553	+	8.87824i	−0.246848	+	0.512585i
$301$	−12.6503	+	10.0883i	−0.729151	+	0.581479i
$302$		−	1.65248i		−	0.0950893i
$303$	−0.238152	−	0.298633i	−0.0136815	−	0.0171560i
$304$	−8.77435	+	2.00269i	−0.503244	+	0.114862i
$305$	2.32225	−	0.530037i	0.132971	−	0.0303498i
$306$	4.42065	+	5.54332i	0.252712	+	0.316890i
$307$		−	19.1803i		−	1.09468i	−0.836910	−	0.547340i	$-0.815640\pi$
$307$		−	19.1803i		−	1.09468i	0.836910	−	0.547340i	$-0.184360\pi$
$308$	−3.90916	+	3.11745i	−0.222745	+	0.177633i
$309$	−2.46175	+	5.11188i	−0.140044	+	0.290805i
$310$	−14.9852	+	18.7909i	−0.851104	+	1.06725i
$311$	1.63416	+	1.30320i	0.0926647	+	0.0738977i	0.668726	−	0.743509i	$-0.266840\pi$
$311$	1.63416	+	1.30320i	0.0926647	+	0.0738977i	−0.576062	+	0.817406i	$0.695411\pi$
$312$	−0.293930	+	0.141549i	−0.0166405	+	0.00801365i
$313$	2.87271	+	12.5862i	0.162375	+	0.711411i	0.988909	+	0.148524i	$0.0474523\pi$
$313$	2.87271	+	12.5862i	0.162375	+	0.711411i	−0.826534	+	0.562887i	$0.809691\pi$
$314$	−2.00269	+	8.77435i	−0.113018	+	0.495165i
$315$	−20.3279	−	9.78942i	−1.14535	−	0.551571i
$316$	4.27553	+	8.87824i	0.240518	+	0.499440i
$317$	27.0135	+	6.16566i	1.51723	+	0.346298i	0.898383	−	0.439214i	$-0.144743\pi$
$317$	27.0135	+	6.16566i	1.51723	+	0.346298i	0.618847	+	0.785512i	$0.287600\pi$
$318$	−0.763932			−0.0428392
$319$		0			0
$320$	−0.909830			−0.0508610
$321$	4.07553	+	0.930213i	0.227474	+	0.0519194i
$322$	−0.741162	−	1.53904i	−0.0413033	−	0.0857673i
$323$	19.1641	+	9.22893i	1.06632	+	0.513511i
$324$	−2.05522	+	9.00450i	−0.114179	+	0.500250i
$325$	−0.517637	−	2.26791i	−0.0287133	−	0.125801i
$326$	3.36015	−	1.61817i	0.186102	−	0.0896219i
$327$	−6.94934	−	5.54192i	−0.384300	−	0.306469i
$328$	5.37326	−	6.73785i	0.296688	−	0.372036i
$329$	−6.79135	+	14.1024i	−0.374420	+	0.777490i
$330$	−1.59059	+	1.26845i	−0.0875591	+	0.0698261i
$331$		−	21.1803i		−	1.16418i	−0.813126	−	0.582088i	$-0.802236\pi$
$331$		−	21.1803i		−	1.16418i	0.813126	−	0.582088i	$-0.197764\pi$
$332$	−10.0321	−	12.5798i	−0.550581	−	0.690406i
$333$	−12.0172	+	2.74285i	−0.658538	+	0.150307i
$334$	−6.34344	+	1.44785i	−0.347098	+	0.0792228i
$335$	−3.67145	−	4.60385i	−0.200593	−	0.251535i
$336$			2.56231i			0.139785i
$337$	−26.6361	+	21.2416i	−1.45096	+	1.15710i	−0.493065	+	0.869992i	$0.664124\pi$
$337$	−26.6361	+	21.2416i	−1.45096	+	1.15710i	−0.957897	+	0.287111i	$0.907305\pi$
$338$	−3.47107	+	7.20775i	−0.188801	+	0.392050i
$339$	−3.06123	+	3.83866i	−0.166263	+	0.208487i
$340$	21.3645	+	17.0376i	1.15865	+	0.923995i
$341$	12.5634	−	6.05019i	0.680344	−	0.327636i
$342$	−1.74770	−	7.65718i	−0.0945049	−	0.414053i
$343$	−4.47815	+	19.6200i	−0.241797	+	1.05938i
$344$	−14.5780	−	7.02039i	−0.785992	−	0.378514i
$345$	1.27747	+	2.65270i	0.0687768	+	0.142816i
$346$	2.46449	+	0.562503i	0.132492	+	0.0302403i
$347$	32.1246			1.72454			0.862270	−	0.506449i	$-0.169042\pi$
$347$	32.1246			1.72454			0.862270	+	0.506449i	$0.169042\pi$
$348$		0			0
$349$	4.52786			0.242371			0.121186	−	0.992630i	$-0.461330\pi$
$349$	4.52786			0.242371			0.121186	+	0.992630i	$0.461330\pi$
$350$	13.2766	+	3.03030i	0.709664	+	0.161976i
$351$	0.355637	+	0.738488i	0.0189825	+	0.0394176i
$352$	−6.99506	−	3.36864i	−0.372838	−	0.179549i
$353$	−4.25563	+	18.6451i	−0.226504	+	0.992379i	0.725962	+	0.687735i	$0.241395\pi$
$353$	−4.25563	+	18.6451i	−0.226504	+	0.992379i	−0.952466	+	0.304645i	$0.901462\pi$
$354$	−0.517637	−	2.26791i	−0.0275121	−	0.120538i
$355$	−36.3637	+	17.5118i	−1.92999	+	0.929432i
$356$	5.95602	+	4.74977i	0.315668	+	0.251737i
$357$	3.77568	−	4.73456i	0.199830	−	0.250579i
$358$	4.29048	−	8.90927i	0.226759	−	0.470870i
$359$	18.5794	−	14.8166i	0.980583	−	0.781989i	0.00463409	−	0.999989i	$-0.498525\pi$
$359$	18.5794	−	14.8166i	0.980583	−	0.781989i	0.975949	+	0.218001i	$0.0699535\pi$
$360$		−	22.5623i		−	1.18914i
$361$	−2.84455	−	3.56695i	−0.149713	−	0.187734i
$362$	3.58165	−	0.817489i	0.188248	−	0.0429663i
$363$	−5.47718	+	1.25013i	−0.287477	+	0.0656148i
$364$	−0.532524	−	0.667764i	−0.0279118	−	0.0350003i
$365$		−	52.8328i		−	2.76540i
$366$	0.184565	−	0.147186i	0.00964739	−	0.00769353i
$367$	11.8322	−	24.5699i	0.617637	−	1.28254i	−0.324047	−	0.946041i	$-0.605044\pi$
$367$	11.8322	−	24.5699i	0.617637	−	1.28254i	0.941685	−	0.336496i	$-0.109242\pi$
$368$	−1.42891	+	1.79180i	−0.0744872	+	0.0934039i
$369$	−7.88881	−	6.29112i	−0.410675	−	0.327503i
$370$	10.1042	−	4.86591i	0.525291	−	0.252967i
$371$	−0.995144	−	4.36001i	−0.0516653	−	0.226360i
$372$	2.24527	−	9.83719i	0.116412	−	0.510034i
$373$	−18.5762	−	8.94583i	−0.961840	−	0.463198i	−0.114018	−	0.993479i	$-0.536372\pi$
$373$	−18.5762	−	8.94583i	−0.961840	−	0.463198i	−0.847822	+	0.530281i	$0.822086\pi$
$374$	1.62387	+	3.37201i	0.0839685	+	0.174362i
$375$	−11.2724	−	2.57286i	−0.582105	−	0.132862i
$376$	−15.6525			−0.807215
$377$		0			0
$378$	−4.79837			−0.246802
$379$	23.6828	+	5.40543i	1.21650	+	0.277658i	0.782153	−	0.623087i	$-0.214122\pi$
$379$	23.6828	+	5.40543i	1.21650	+	0.277658i	0.434348	+	0.900745i	$0.356979\pi$
$380$	−13.1339	−	27.2728i	−0.673754	−	1.39906i
$381$	−8.87824	−	4.27553i	−0.454846	−	0.219042i
$382$	2.34267	−	10.2639i	0.119861	−	0.525147i
$383$	−6.42064	−	28.1307i	−0.328079	−	1.43741i	−0.822787	−	0.568350i	$-0.807582\pi$
$383$	−6.42064	−	28.1307i	−0.328079	−	1.43741i	0.494707	−	0.869060i	$-0.335275\pi$
$384$	−6.33781	+	3.05213i	−0.323425	+	0.155753i
$385$	−9.31148	−	7.42566i	−0.474557	−	0.378447i
$386$	−4.80599	+	6.02652i	−0.244618	+	0.306742i
$387$	−8.21961	+	17.0682i	−0.417826	+	0.867625i
$388$	4.50642	−	3.59375i	0.228779	−	0.182445i
$389$			19.1246i			0.969656i	0.874609	+	0.484828i	$0.161118\pi$
$389$			19.1246i			0.969656i	−0.874609	+	0.484828i	$0.838882\pi$
$390$	−0.216678	−	0.271705i	−0.0109719	−	0.0137583i
$391$	5.28061	−	1.20526i	0.267052	−	0.0609528i
$392$	−4.36001	+	0.995144i	−0.220214	+	0.0502624i
$393$	−5.52044	−	6.92242i	−0.278469	−	0.349190i
$394$		−	3.88854i		−	0.195902i
$395$	−18.3513	+	14.6346i	−0.923352	+	0.736349i
$396$	−2.54000	+	5.27436i	−0.127640	+	0.265047i
$397$	−8.76360	+	10.9892i	−0.439833	+	0.551533i	−0.951499	−	0.307651i	$-0.900457\pi$
$397$	−8.76360	+	10.9892i	−0.439833	+	0.551533i	0.511666	+	0.859184i	$0.329028\pi$
$398$	−2.82869	−	2.25581i	−0.141790	−	0.113073i
$399$	−6.04388	+	2.91058i	−0.302573	+	0.145711i
$400$	−4.06557	−	17.8124i	−0.203279	−	0.890622i
$401$	−5.57835	+	24.4404i	−0.278570	+	1.22049i	0.621033	+	0.783784i	$0.286713\pi$
$401$	−5.57835	+	24.4404i	−0.278570	+	1.22049i	−0.899603	+	0.436709i	$0.856144\pi$
$402$	−0.525798	−	0.253211i	−0.0262244	−	0.0126290i
$403$	1.03350	+	2.14608i	0.0514821	+	0.106904i
$404$	0.974928	+	0.222521i	0.0485045	+	0.0110708i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	−6.50658			−0.322519
$408$	5.90390	+	1.34753i	0.292287	+	0.0667125i
$409$	−11.8955	−	24.7013i	−0.588196	−	1.22140i	−0.956510	−	0.291700i	$-0.905779\pi$
$409$	−11.8955	−	24.7013i	−0.588196	−	1.22140i	0.368313	−	0.929702i	$-0.379935\pi$
$410$	8.27120	+	3.98320i	0.408485	+	0.196716i
$411$	−0.982743	+	4.30568i	−0.0484751	+	0.212383i
$412$	−3.30535	−	14.4817i	−0.162843	−	0.713461i
$413$	12.2694	−	5.90864i	0.603739	−	0.290745i
$414$	−1.56366	−	1.24698i	−0.0768498	−	0.0612857i
$415$	23.8960	−	29.9647i	1.17301	−	1.47091i
$416$	0.575433	−	1.19490i	0.0282129	−	0.0585847i
$417$	0.624194	−	0.497778i	0.0305669	−	0.0243763i
$418$		−	4.14590i		−	0.202783i
$419$	10.9499	+	13.7308i	0.534939	+	0.670792i	0.973706	−	0.227809i	$-0.0731562\pi$
$419$	10.9499	+	13.7308i	0.534939	+	0.670792i	−0.438767	+	0.898601i	$0.644585\pi$
$420$	−8.40196	+	1.91769i	−0.409974	+	0.0935738i
$421$	30.2563	−	6.90581i	1.47460	−	0.336569i	0.591714	−	0.806148i	$-0.298452\pi$
$421$	30.2563	−	6.90581i	1.47460	−	0.336569i	0.882890	+	0.469579i	$0.155594\pi$
$422$	−4.49014	−	5.63046i	−0.218577	−	0.274086i
$423$			18.3262i			0.891052i
$424$	3.49646	−	2.78833i	0.169803	−	0.135413i
$425$	−18.7352	+	38.9041i	−0.908793	+	1.88713i
$426$	−2.49396	+	3.12733i	−0.120833	+	0.151519i
$427$	1.08046	+	0.861642i	0.0522873	+	0.0416978i
$428$	−9.86045	+	4.74854i	−0.476623	+	0.229529i
$429$	0.0448660	+	0.196571i	0.00216615	+	0.00949053i
$430$	3.83539	−	16.8039i	0.184959	−	0.810357i
$431$	−13.1512	−	6.33329i	−0.633472	−	0.305064i	0.0894526	−	0.995991i	$-0.471488\pi$
$431$	−13.1512	−	6.33329i	−0.633472	−	0.305064i	−0.722924	+	0.690927i	$0.757203\pi$
$432$	2.79321	+	5.80016i	0.134388	+	0.279060i
$433$	10.1217	+	2.31020i	0.486416	+	0.111021i	0.458694	−	0.888594i	$-0.348317\pi$
$433$	10.1217	+	2.31020i	0.486416	+	0.111021i	0.0277224	+	0.999616i	$0.491175\pi$
$434$	−13.9443			−0.669346
$435$		0			0
$436$	23.2705			1.11446
$437$	−5.84957	−	1.33513i	−0.279823	−	0.0638677i
$438$	−2.27184	−	4.71753i	−0.108553	−	0.225413i
$439$	−18.8701	−	9.08738i	−0.900622	−	0.433717i	−0.0745088	−	0.997220i	$-0.523739\pi$
$439$	−18.8701	−	9.08738i	−0.900622	−	0.433717i	−0.826114	+	0.563503i	$0.809453\pi$
$440$	2.65019	−	11.6112i	0.126343	−	0.553543i
$441$	1.16513	+	5.10479i	0.0554826	+	0.243085i
$442$	−0.576008	+	0.277391i	−0.0273979	+	0.0131941i
$443$	1.49317	+	1.19076i	0.0709424	+	0.0565747i	0.658319	−	0.752739i	$-0.271268\pi$
$443$	1.49317	+	1.19076i	0.0709424	+	0.0565747i	−0.587377	+	0.809314i	$0.699839\pi$
$444$	−2.93552	+	3.68102i	−0.139313	+	0.174694i
$445$	−7.87321	+	16.3489i	−0.373226	+	0.775012i
$446$	−1.29196	+	1.03030i	−0.0611760	+	0.0487862i
$447$			5.94427i			0.281154i
$448$	−0.329118	−	0.412701i	−0.0155494	−	0.0194983i
$449$	−25.4696	+	5.81327i	−1.20199	+	0.274345i	−0.776205	−	0.630481i	$-0.782858\pi$
$449$	−25.4696	+	5.81327i	−1.20199	+	0.274345i	−0.425781	+	0.904826i	$0.640001\pi$
$450$	15.5445	−	3.54793i	0.732775	−	0.167251i
$451$	−3.32086	−	4.16422i	−0.156373	−	0.196085i
$452$		−	12.8541i		−	0.604606i
$453$	−1.29196	+	1.03030i	−0.0607015	+	0.0484078i
$454$	−5.60137	+	11.6314i	−0.262885	+	0.545887i
$455$	1.26845	−	1.59059i	0.0594660	−	0.0745680i
$456$	−5.24469	−	4.18250i	−0.245605	−	0.195863i
$457$	16.8555	−	8.11719i	0.788467	−	0.379706i	0.00409151	−	0.999992i	$-0.498698\pi$
$457$	16.8555	−	8.11719i	0.788467	−	0.379706i	0.784376	+	0.620286i	$0.212983\pi$
$458$	−0.315180	−	1.38090i	−0.0147274	−	0.0645250i
$459$	3.38561	−	14.8333i	0.158027	−	0.692360i
$460$	−6.94485	−	3.34446i	−0.323805	−	0.155936i
$461$	−16.9122	−	35.1186i	−0.787681	−	1.63564i	−0.771886	−	0.635761i	$-0.780686\pi$
$461$	−16.9122	−	35.1186i	−0.787681	−	1.63564i	−0.0157954	−	0.999875i	$-0.505028\pi$
$462$	−1.15075	−	0.262650i	−0.0535376	−	0.0122196i
$463$	−10.7082			−0.497652			−0.248826	−	0.968548i	$-0.580045\pi$
$463$	−10.7082			−0.497652			−0.248826	+	0.968548i	$0.580045\pi$
$464$		0			0
$465$	24.0344			1.11457
$466$	−9.18032	−	2.09535i	−0.425270	−	0.0970651i
$467$	7.78573	+	16.1672i	0.360281	+	0.748130i	0.999787	−	0.0206558i	$-0.00657541\pi$
$467$	7.78573	+	16.1672i	0.360281	+	0.748130i	−0.639506	+	0.768786i	$0.720861\pi$
$468$	−0.900969	−	0.433884i	−0.0416473	−	0.0200563i
$469$	0.760222	−	3.33075i	0.0351038	−	0.153800i
$470$	−3.71026	−	16.2557i	−0.171142	−	0.749820i
$471$	8.10872	−	3.90495i	0.373630	−	0.179931i
$472$	10.6470	+	8.49071i	0.490068	+	0.390816i
$473$	−6.23490	+	7.81831i	−0.286681	+	0.359486i
$474$	−1.00932	+	2.09587i	−0.0463595	+	0.0962664i
$475$	37.3972	−	29.8233i	1.71590	−	1.36839i
$476$			15.8541i			0.726672i
$477$	−3.26463	−	4.09372i	−0.149477	−	0.187439i
$478$	−16.7160	+	3.81532i	−0.764573	+	0.174509i
$479$	10.9000	−	2.48786i	0.498035	−	0.113673i	0.0338776	−	0.999426i	$-0.489214\pi$
$479$	10.9000	−	2.48786i	0.498035	−	0.113673i	0.464157	+	0.885753i	$0.346357\pi$
$480$	−8.34352	−	10.4624i	−0.380828	−	0.477543i
$481$		−	1.11146i		−	0.0506780i
$482$	−2.24807	+	1.79278i	−0.102397	+	0.0816587i
$483$	−0.741162	+	1.53904i	−0.0337240	+	0.0700287i
$484$	9.17042	−	11.4993i	0.416837	−	0.522697i
$485$	10.7341	+	8.56020i	0.487413	+	0.388699i
$486$	−7.76458	+	3.73922i	−0.352209	+	0.169615i
$487$	−9.47100	−	41.4952i	−0.429172	−	1.88033i	−0.472613	−	0.881270i	$-0.656689\pi$
$487$	−9.47100	−	41.4952i	−0.429172	−	1.88033i	0.0434408	−	0.999056i	$-0.486168\pi$
$488$	−0.307516	+	1.34732i	−0.0139206	+	0.0609902i
$489$	−3.36015	−	1.61817i	−0.151951	−	0.0731760i
$490$	−2.06699	−	4.29215i	−0.0933772	−	0.193900i
$491$	−14.7454	−	3.36554i	−0.665451	−	0.151885i	−0.123564	−	0.992337i	$-0.539433\pi$
$491$	−14.7454	−	3.36554i	−0.665451	−	0.151885i	−0.541886	+	0.840452i	$0.682290\pi$
$492$	−3.85410			−0.173756
$493$		0			0
$494$	0.708204			0.0318636
$495$	−13.5947	−	3.10289i	−0.611035	−	0.139465i
$496$	8.11719	+	16.8555i	0.364472	+	0.756835i
$497$	−21.0975	−	10.1600i	−0.946350	−	0.455738i
$498$	0.845218	−	3.70314i	0.0378751	−	0.165942i
$499$	5.49336	+	24.0680i	0.245916	+	1.07743i	0.935529	+	0.353251i	$0.114924\pi$
$499$	5.49336	+	24.0680i	0.245916	+	1.07743i	−0.689612	+	0.724179i	$0.742219\pi$
$500$	27.2728	−	13.1339i	1.21968	−	0.587365i
$501$	5.08705	+	4.05678i	0.227273	+	0.181244i
$502$	7.57284	−	9.49605i	0.337993	−	0.423829i
$503$	−6.19174	+	12.8573i	−0.276076	+	0.573278i	−0.992194	−	0.124701i	$-0.960203\pi$
$503$	−6.19174	+	12.8573i	−0.276076	+	0.573278i	0.716118	+	0.697979i	$0.245917\pi$
$504$	10.2343	−	8.16159i	0.455872	−	0.363546i
$505$			2.38197i			0.105996i
$506$	−0.658236	−	0.825401i	−0.0292621	−	0.0366936i
$507$	7.79942	−	1.78017i	0.346385	−	0.0790600i
$508$	25.1516	−	5.74068i	1.11592	−	0.254701i
$509$	19.6788	+	24.6764i	0.872246	+	1.09376i	0.994855	+	0.101307i	$0.0323025\pi$
$509$	19.6788	+	24.6764i	0.872246	+	1.09376i	−0.122609	+	0.992455i	$0.539126\pi$
$510$			6.45085i			0.285648i
$511$	23.9651	−	19.1115i	1.06015	−	0.845443i
$512$	8.11719	−	16.8555i	0.358732	−	0.744915i
$513$	−10.5084	+	13.1771i	−0.463955	+	0.581782i
$514$	−11.2007	−	8.93226i	−0.494042	−	0.393985i
$515$	31.8780	−	15.3517i	1.40471	−	0.676475i
$516$	1.61018	+	7.05464i	0.0708841	+	0.310563i
$517$	−2.15261	+	9.43122i	−0.0946719	+	0.414785i
$518$	5.86222	+	2.82310i	0.257571	+	0.124040i
$519$	−1.09680	−	2.27753i	−0.0481441	−	0.0999723i
$520$	1.98343	+	0.452706i	0.0869793	+	0.0198525i
$521$	−4.09017			−0.179194			−0.0895968	−	0.995978i	$-0.528558\pi$
$521$	−4.09017			−0.179194			−0.0895968	+	0.995978i	$0.528558\pi$
$522$		0			0
$523$	−20.3820			−0.891241			−0.445621	−	0.895222i	$-0.647017\pi$
$523$	−20.3820			−0.891241			−0.445621	+	0.895222i	$0.647017\pi$
$524$	22.5992	+	5.15811i	0.987249	+	0.225333i
$525$	−5.90864	−	12.2694i	−0.257874	−	0.535482i
$526$	−9.30362	−	4.48039i	−0.405657	−	0.195354i
$527$	9.83871	−	43.1062i	0.428581	−	1.87774i
$528$	0.352382	+	1.54389i	0.0153355	+	0.0671891i
$529$	19.3457	−	9.31641i	0.841119	−	0.405061i
$530$	3.72459	+	2.97026i	0.161786	+	0.129020i
$531$	9.94109	−	12.4657i	0.431407	−	0.540967i
$532$	7.62000	−	15.8231i	0.330369	−	0.686018i
$533$	0.711334	−	0.567270i	0.0308113	−	0.0245712i
$534$			1.79837i			0.0778232i
$535$	−16.2537	−	20.3815i	−0.702708	−	0.881168i
$536$	3.33075	−	0.760222i	0.143867	−	0.0328366i
$537$	−9.64062	+	2.20041i	−0.416023	+	0.0949546i
$538$	−2.31203	−	2.89919i	−0.0996786	−	0.124993i
$539$			2.76393i			0.119051i
$540$	−16.9286	+	13.5001i	−0.728490	+	0.580952i
$541$	−6.33329	+	13.1512i	−0.272289	+	0.565415i	−0.991610	−	0.129263i	$-0.958739\pi$
$541$	−6.33329	+	13.1512i	−0.272289	+	0.565415i	0.719321	+	0.694678i	$0.244453\pi$
$542$	3.92287	−	4.91912i	0.168502	−	0.211294i
$543$	−2.87226	−	2.29055i	−0.123261	−	0.0982970i
$544$	−22.1801	+	10.6814i	−0.950963	+	0.457960i
$545$	12.3342	+	54.0398i	0.528341	+	2.31481i
$546$	0.0448660	−	0.196571i	0.00192009	−	0.00841246i
$547$	−6.65092	−	3.20292i	−0.284373	−	0.136947i	0.286260	−	0.958152i	$-0.407588\pi$
$547$	−6.65092	−	3.20292i	−0.284373	−	0.136947i	−0.570633	+	0.821205i	$0.693302\pi$
$548$	−5.01670	−	10.4173i	−0.214303	−	0.445004i
$549$	1.57747	+	0.360046i	0.0673246	+	0.0153664i
$550$	8.41641			0.358877
$551$		0			0
$552$	−1.70820			−0.0727060
$553$	−13.2766	−	3.03030i	−0.564579	−	0.128861i
$554$	5.73368	+	11.9061i	0.243601	+	0.505842i
$555$	−10.1042	−	4.86591i	−0.428898	−	0.206546i
$556$	−0.465107	+	2.03777i	−0.0197249	+	0.0864205i
$557$	−1.22533	−	5.36852i	−0.0519188	−	0.227471i	0.942312	−	0.334737i	$-0.108648\pi$
$557$	−1.22533	−	5.36852i	−0.0519188	−	0.227471i	−0.994230	+	0.107266i	$0.965790\pi$
$558$	−14.7094	+	7.08369i	−0.622700	+	0.299876i
$559$	−1.33553	−	1.06505i	−0.0564868	−	0.0450467i
$560$	9.96257	−	12.4927i	0.420995	−	0.527911i
$561$	1.62387	−	3.37201i	0.0685600	−	0.142366i
$562$	−11.1738	+	8.91079i	−0.471337	+	0.375879i
$563$		−	28.3951i		−	1.19671i	−0.801230	−	0.598356i	$-0.795821\pi$
$563$		−	28.3951i		−	1.19671i	0.801230	−	0.598356i	$-0.204179\pi$
$564$	4.36443	+	5.47282i	0.183776	+	0.230447i
$565$	29.8504	−	6.81315i	1.25581	−	0.286632i
$566$	3.15493	−	0.720093i	0.132612	−	0.0302678i
$567$	−7.95818	−	9.97924i	−0.334212	−	0.419089i
$568$		−	23.4164i		−	0.982531i
$569$	−1.52009	+	1.21223i	−0.0637256	+	0.0508195i	−0.654835	−	0.755772i	$-0.727262\pi$
$569$	−1.52009	+	1.21223i	−0.0637256	+	0.0508195i	0.591109	+	0.806592i	$0.298690\pi$
$570$	3.10049	−	6.43823i	0.129865	−	0.269668i
$571$	−21.5145	+	26.9783i	−0.900354	+	1.12901i	0.0907443	+	0.995874i	$0.471075\pi$
$571$	−21.5145	+	26.9783i	−0.900354	+	1.12901i	−0.991098	+	0.133134i	$0.957496\pi$
$572$	−0.412701	−	0.329118i	−0.0172559	−	0.0137611i
$573$	−9.48528	+	4.56787i	−0.396253	+	0.190825i
$574$	1.18520	+	5.19270i	0.0494693	+	0.216739i
$575$	2.71038	−	11.8750i	0.113031	−	0.495220i
$576$	−0.556829	−	0.268155i	−0.0232012	−	0.0111731i
$577$	−1.19923	−	2.49022i	−0.0499244	−	0.103669i	0.874514	−	0.485000i	$-0.161180\pi$
$577$	−1.19923	−	2.49022i	−0.0499244	−	0.103669i	−0.924439	+	0.381331i	$0.875466\pi$
$578$	1.32656	+	0.302780i	0.0551778	+	0.0125940i
$579$	7.70820			0.320342
$580$		0			0
$581$	22.2361			0.922508
$582$	1.32656	+	0.302780i	0.0549879	+	0.0125506i
$583$	−1.19923	−	2.49022i	−0.0496668	−	0.103134i
$584$	27.6169	+	13.2996i	1.14280	+	0.550342i
$585$	0.530037	−	2.32225i	0.0219143	−	0.0960130i
$586$	1.17280	+	5.13837i	0.0484479	+	0.212264i
$587$	−42.0014	+	20.2268i	−1.73358	+	0.834850i	−0.748421	+	0.663224i	$0.769188\pi$
$587$	−42.0014	+	20.2268i	−1.73358	+	0.834850i	−0.985162	+	0.171626i	$0.945098\pi$
$588$	1.56366	+	1.24698i	0.0644844	+	0.0514246i
$589$	−30.5377	+	38.2931i	−1.25829	+	1.57784i
$590$	−6.29417	+	13.0700i	−0.259127	+	0.538082i
$591$	−3.04019	+	2.42447i	−0.125057	+	0.0997293i
$592$		−	8.72949i		−	0.358780i
$593$	9.00176	+	11.2878i	0.369658	+	0.463536i	0.931518	−	0.363696i	$-0.118485\pi$
$593$	9.00176	+	11.2878i	0.369658	+	0.463536i	−0.561860	+	0.827232i	$0.689914\pi$
$594$	−2.89121	+	0.659899i	−0.118628	+	0.0270760i
$595$	−36.8171	+	8.40327i	−1.50935	+	0.344500i
$596$	−9.70294	−	12.1671i	−0.397448	−	0.498384i
$597$			3.61803i			0.148076i
$598$	0.140995	−	0.112440i	0.00576573	−	0.00459802i
$599$	5.67038	−	11.7747i	0.231685	−	0.481099i	−0.752420	−	0.658683i	$-0.771114\pi$
$599$	5.67038	−	11.7747i	0.231685	−	0.481099i	0.984106	+	0.177584i	$0.0568281\pi$
$600$	8.49071	−	10.6470i	0.346632	−	0.434662i
$601$	22.7975	+	18.1804i	0.929928	+	0.741593i	0.966212	−	0.257749i	$-0.0829807\pi$
$601$	22.7975	+	18.1804i	0.929928	+	0.741593i	−0.0362840	+	0.999342i	$0.511552\pi$
$602$	9.00969	−	4.33884i	0.367207	−	0.176838i
$603$	−0.890084	−	3.89971i	−0.0362470	−	0.158809i
$604$	0.962679	−	4.21777i	0.0391708	−	0.171619i
$605$	31.5649	+	15.2009i	1.28330	+	0.618003i
$606$	0.102426	+	0.212690i	0.00416077	+	0.00863994i
$607$	10.7035	+	2.44299i	0.434440	+	0.0991581i	0.434147	−	0.900842i	$-0.357050\pi$
$607$	10.7035	+	2.44299i	0.434440	+	0.0991581i	0.000292533		1.00000i	$0.499907\pi$
$608$	27.2705			1.10597
$609$		0			0
$610$	−1.47214			−0.0596050
$611$	−1.61104	−	0.367710i	−0.0651759	−	0.0148760i
$612$	8.05388	+	16.7241i	0.325559	+	0.676030i
$613$	24.8136	+	11.9496i	1.00221	+	0.482640i	0.861689	−	0.507438i	$-0.169407\pi$
$613$	24.8136	+	11.9496i	1.00221	+	0.482640i	0.140523	+	0.990077i	$0.455121\pi$
$614$	−2.63779	+	11.5569i	−0.106452	+	0.466398i
$615$	−2.04282	−	8.95017i	−0.0823744	−	0.360906i
$616$	6.22554	−	2.99806i	0.250834	−	0.120795i
$617$	11.0866	+	8.84130i	0.446331	+	0.355937i	0.820716	−	0.571336i	$-0.193575\pi$
$617$	11.0866	+	8.84130i	0.446331	+	0.355937i	−0.374385	+	0.927273i	$0.622146\pi$
$618$	2.18632	−	2.74155i	0.0879465	−	0.110281i
$619$	−3.06137	+	6.35699i	−0.123047	+	0.255509i	−0.953389	−	0.301745i	$-0.902431\pi$
$619$	−3.06137	+	6.35699i	−0.123047	+	0.255509i	0.830342	+	0.557254i	$0.188145\pi$
$620$	−49.1952	+	39.2318i	−1.97573	+	1.57559i
$621$			4.29180i			0.172224i
$622$	−0.805422	−	1.00997i	−0.0322945	−	0.0404960i
$623$	−10.2639	+	2.34267i	−0.411215	+	0.0938571i
$624$	−0.263728	+	0.0601941i	−0.0105576	+	0.00240969i
$625$	14.2360	+	17.8514i	0.569441	+	0.714057i
$626$		−	7.97871i		−	0.318894i
$627$	−3.24139	+	2.58493i	−0.129449	+	0.103232i
$628$	−10.2233	+	21.2289i	−0.407954	+	0.847125i
$629$	−12.8633	+	16.1301i	−0.512895	+	0.643150i
$630$	10.9021	+	8.69411i	0.434349	+	0.346382i
$631$	−25.4206	+	12.2419i	−1.01198	+	0.487344i	−0.864987	−	0.501794i	$-0.832674\pi$
$631$	−25.4206	+	12.2419i	−1.01198	+	0.487344i	−0.146992	+	0.989138i	$0.546959\pi$
$632$	−3.03030	−	13.2766i	−0.120539	−	0.528115i
$633$	−1.60251	+	7.02107i	−0.0636942	+	0.279062i
$634$	−15.4287	−	7.43009i	−0.612754	−	0.295087i
$635$	26.6625	+	55.3653i	1.05807	+	2.19711i
$636$	−1.94986	−	0.445042i	−0.0773168	−	0.0176471i
$637$	−0.472136			−0.0187067
$638$		0			0
$639$	−27.4164			−1.08458
$640$	42.7674	+	9.76138i	1.69053	+	0.385853i
$641$	−4.79690	−	9.96087i	−0.189466	−	0.393431i	0.784498	−	0.620131i	$-0.212921\pi$
$641$	−4.79690	−	9.96087i	−0.189466	−	0.393431i	−0.973965	+	0.226700i	$0.927206\pi$
$642$	−2.32774	−	1.12098i	−0.0918684	−	0.0442415i
$643$	−8.32593	+	36.4783i	−0.328343	+	1.43856i	0.493946	+	0.869493i	$0.335554\pi$
$643$	−8.32593	+	36.4783i	−0.328343	+	1.43856i	−0.822288	+	0.569071i	$0.807303\pi$
$644$	−0.995144	−	4.36001i	−0.0392142	−	0.171808i
$645$	−15.5292	+	7.47845i	−0.611460	+	0.294464i
$646$	−10.2779	−	8.19633i	−0.404378	−	0.322480i
$647$	19.0338	−	23.8676i	0.748296	−	0.938334i	−0.251266	−	0.967918i	$-0.580847\pi$
$647$	19.0338	−	23.8676i	0.748296	−	0.938334i	0.999562	+	0.0295841i	$0.00941830\pi$
$648$	5.53806	−	11.4999i	0.217556	−	0.451759i
$649$	6.58021	−	5.24754i	0.258296	−	0.205984i
$650$			1.43769i			0.0563910i
$651$	8.69411	+	10.9021i	0.340749	+	0.427286i
$652$	9.51913	−	2.17268i	0.372798	−	0.0850887i
$653$	−46.8094	+	10.6839i	−1.83179	+	0.418095i	−0.992151	−	0.125047i	$-0.960092\pi$
$653$	−46.8094	+	10.6839i	−1.83179	+	0.418095i	−0.839641	+	0.543141i	$0.817235\pi$
$654$	3.42509	+	4.29493i	0.133932	+	0.167945i
$655$			55.2148i			2.15742i
$656$	5.58689	−	4.45539i	0.218131	−	0.173954i
$657$	15.5715	−	32.3345i	0.607500	−	1.26149i
$658$	6.03149	−	7.56325i	0.235132	−	0.294846i
$659$	−5.51639	−	4.39917i	−0.214888	−	0.171368i	0.510130	−	0.860097i	$-0.329597\pi$
$659$	−5.51639	−	4.39917i	−0.214888	−	0.171368i	−0.725018	+	0.688730i	$0.758169\pi$
$660$	−4.79877	+	2.31097i	−0.186792	+	0.0899543i
$661$	8.33360	+	36.5119i	0.324139	+	1.42015i	0.830111	+	0.557598i	$0.188277\pi$
$661$	8.33360	+	36.5119i	0.324139	+	1.42015i	−0.505972	+	0.862550i	$0.668866\pi$
$662$	−2.91284	+	12.7620i	−0.113211	+	0.496008i
$663$	0.576008	+	0.277391i	0.0223703	+	0.0107730i
$664$	9.64787	+	20.0340i	0.374410	+	0.777470i
$665$	40.7840	+	9.30868i	1.58153	+	0.360975i
$666$	7.61803			0.295193
$667$		0			0
$668$	−17.0344			−0.659082
$669$	1.61104	+	0.367710i	0.0622866	+	0.0142165i
$670$	1.57904	+	3.27891i	0.0610037	+	0.126676i
$671$	0.769519	+	0.370581i	0.0297070	+	0.0143061i
$672$	1.72764	−	7.56927i	0.0666451	−	0.291991i
$673$	−1.44019	−	6.30987i	−0.0555151	−	0.243227i	0.939556	−	0.342397i	$-0.111239\pi$
$673$	−1.44019	−	6.30987i	−0.0555151	−	0.243227i	−0.995071	+	0.0991692i	$0.968382\pi$
$674$	18.9706	−	9.13574i	0.730718	−	0.351895i
$675$	−26.7502	−	21.3326i	−1.02962	−	0.821091i
$676$	−13.0585	+	16.3749i	−0.502252	+	0.629804i
$677$	17.7167	−	36.7891i	0.680908	−	1.41392i	−0.218073	−	0.975932i	$-0.569977\pi$
$677$	17.7167	−	36.7891i	0.680908	−	1.41392i	0.898981	−	0.437987i	$-0.144309\pi$
$678$	2.37242	−	1.89194i	0.0911123	−	0.0726597i
$679$			7.96556i			0.305690i
$680$	−23.5454	−	29.5250i	−0.902926	−	1.13223i
$681$	12.5862	−	2.87271i	0.482302	−	0.110082i
$682$	−8.40196	+	1.91769i	−0.321728	+	0.0734323i
$683$	13.0023	+	16.3044i	0.497520	+	0.623870i	0.965668	−	0.259780i	$-0.0836500\pi$
$683$	13.0023	+	16.3044i	0.497520	+	0.623870i	−0.468148	+	0.883650i	$0.655079\pi$
$684$		−	20.5623i		−	0.786219i
$685$	21.5324	−	17.1715i	0.822712	−	0.656091i
$686$	5.39651	−	11.2060i	0.206040	−	0.427846i
$687$	−0.883116	+	1.10739i	−0.0336930	+	0.0422496i
$688$	−10.4894	−	8.36499i	−0.399903	−	0.318912i
$689$	0.425380	−	0.204852i	0.0162057	−	0.00780424i
$690$	−0.404912	−	1.77404i	−0.0154148	−	0.0675365i
$691$	−2.63305	+	11.5361i	−0.100166	+	0.438856i	0.899831	+	0.436239i	$0.143690\pi$
$691$	−2.63305	+	11.5361i	−0.100166	+	0.438856i	−0.999997	+	0.00261618i	$0.999167\pi$
$692$	5.96264	+	2.87146i	0.226666	+	0.109156i
$693$	−3.51019	−	7.28899i	−0.133341	−	0.276886i
$694$	−19.3563	−	4.41795i	−0.734756	−	0.167703i
$695$	−4.97871			−0.188853
$696$		0			0
$697$	−16.8885			−0.639699
$698$	−2.72821	−	0.622697i	−0.103264	−	0.0235694i
$699$	4.08563	+	8.48389i	0.154533	+	0.320890i
$700$	32.1218	+	15.4690i	1.21409	+	0.584674i
$701$	−4.68534	+	20.5278i	−0.176963	+	0.775325i	0.806059	+	0.591835i	$0.201596\pi$
$701$	−4.68534	+	20.5278i	−0.176963	+	0.775325i	−0.983022	+	0.183490i	$0.941261\pi$
$702$	−0.112724	−	0.493877i	−0.00425450	−	0.0186402i
$703$	20.5908	−	9.91602i	0.776598	−	0.373990i
$704$	−0.255063	−	0.203406i	−0.00961305	−	0.00766615i
$705$	−10.3959	+	13.0361i	−0.391533	+	0.490967i
$706$	5.12836	−	10.6491i	0.193008	−	0.400786i
$707$	−1.08046	+	0.861642i	−0.0406351	+	0.0324054i
$708$		−	6.09017i		−	0.228883i
$709$	25.8789	+	32.4511i	0.971904	+	1.21873i	0.975784	+	0.218736i	$0.0701934\pi$
$709$	25.8789	+	32.4511i	0.971904	+	1.21873i	−0.00388053	+	0.999992i	$0.501235\pi$
$710$	24.3189	−	5.55062i	0.912671	−	0.208311i
$711$	−15.5445	+	3.54793i	−0.582965	+	0.133058i
$712$	−6.56402	−	8.23102i	−0.245997	−	0.308470i
$713$			12.4721i			0.467085i
$714$	−2.92612	+	2.33350i	−0.109507	+	0.0873291i
$715$	0.545546	−	1.13284i	0.0204022	−	0.0423657i
$716$	16.1412	−	20.2405i	0.603227	−	0.756422i
$717$	13.4052	+	10.6903i	0.500626	+	0.399236i
$718$	−13.2325	+	6.37241i	−0.493831	+	0.237816i
$719$	−1.89289	−	8.29330i	−0.0705929	−	0.309288i	0.927288	−	0.374348i	$-0.122133\pi$
$719$	−1.89289	−	8.29330i	−0.0705929	−	0.309288i	−0.997881	+	0.0650598i	$0.979276\pi$
$720$	4.16297	−	18.2392i	0.155145	−	0.679733i
$721$	18.4950	+	8.90671i	0.688789	+	0.331703i
$722$	1.22340	+	2.54043i	0.0455304	+	0.0945449i
$723$	2.80330	+	0.639834i	0.104256	+	0.0237957i
$724$	9.61803			0.357451
$725$		0			0
$726$	3.47214			0.128863
$727$	−27.3523	−	6.24299i	−1.01444	−	0.231540i	−0.317187	−	0.948363i	$-0.602738\pi$
$727$	−27.3523	−	6.24299i	−1.01444	−	0.231540i	−0.697255	+	0.716824i	$0.745595\pi$
$728$	0.512130	+	1.06345i	0.0189808	+	0.0394141i
$729$	−7.66416	−	3.69087i	−0.283858	−	0.136699i
$730$	−7.26586	+	31.8338i	−0.268922	+	1.17822i
$731$	7.05574	+	30.9132i	0.260966	+	1.14337i
$732$	0.556829	−	0.268155i	0.0205810	−	0.00991129i
$733$	−11.5865	−	9.23991i	−0.427956	−	0.341284i	0.385706	−	0.922622i	$-0.373958\pi$
$733$	−11.5865	−	9.23991i	−0.427956	−	0.341284i	−0.813662	+	0.581338i	$0.802529\pi$
$734$	−10.5084	+	13.1771i	−0.387871	+	0.486374i
$735$	−2.06699	+	4.29215i	−0.0762422	+	0.158319i
$736$	5.42925	−	4.32968i	0.200125	−	0.159594i
$737$		−	2.11146i		−	0.0777765i
$738$	3.88812	+	4.87555i	0.143124	+	0.179472i
$739$	−48.8136	+	11.1414i	−1.79564	+	0.409842i	−0.984553	−	0.175089i	$-0.943979\pi$
$739$	−48.8136	+	11.1414i	−1.79564	+	0.409842i	−0.811083	+	0.584931i	$0.801122\pi$
$740$	28.6245	−	6.53337i	1.05226	−	0.240171i
$741$	−0.441558	−	0.553696i	−0.0162210	−	0.0203405i
$742$			2.76393i			0.101467i
$743$	27.5487	−	21.9693i	1.01066	−	0.805977i	0.0295793	−	0.999562i	$-0.490583\pi$
$743$	27.5487	−	21.9693i	1.01066	−	0.805977i	0.981083	+	0.193586i	$0.0620118\pi$
$744$	−6.05019	+	12.5634i	−0.221811	+	0.460595i
$745$	23.1121	−	28.9816i	0.846761	−	1.06180i
$746$	9.96260	+	7.94491i	0.364757	+	0.290884i
$747$	23.4562	−	11.2959i	0.858218	−	0.413296i
$748$	2.18034	+	9.55271i	0.0797212	+	0.349282i
$749$	3.36554	−	14.7454i	0.122974	−	0.538785i
$750$	6.43823	+	3.10049i	0.235091	+	0.113214i
$751$	−8.03894	−	16.6930i	−0.293345	−	0.609137i	0.701256	−	0.712910i	$-0.252623\pi$
$751$	−8.03894	−	16.6930i	−0.293345	−	0.609137i	−0.994601	+	0.103772i	$0.966909\pi$
$752$	−12.6533	−	2.88804i	−0.461419	−	0.105316i
$753$	−12.1459			−0.442621
$754$		0			0
$755$	10.3050			0.375036
$756$	−12.2473	−	2.79538i	−0.445432	−	0.101667i
$757$	0.00923575	+	0.0191782i	0.000335679	+	0.000697045i	0.901137	−	0.433535i	$-0.142734\pi$
$757$	0.00923575	+	0.0191782i	0.000335679	+	0.000697045i	−0.900801	+	0.434232i	$0.857020\pi$
$758$	−13.5264	−	6.51396i	−0.491300	−	0.236598i
$759$	−0.234922	+	1.02926i	−0.00852711	+	0.0373597i
$760$	9.30868	+	40.7840i	0.337661	+	1.47939i
$761$	−22.7059	+	10.9346i	−0.823088	+	0.396378i	−0.797518	−	0.603295i	$-0.793854\pi$
$761$	−22.7059	+	10.9346i	−0.823088	+	0.396378i	−0.0255694	+	0.999673i	$0.508140\pi$
$762$	4.76149	+	3.79716i	0.172490	+	0.137557i
$763$	−20.0508	+	25.1430i	−0.725889	+	0.910236i
$764$	11.9588	−	24.8328i	0.432656	−	0.898418i
$765$	−34.5685	+	27.5675i	−1.24983	+	0.996704i
$766$			17.8328i			0.644326i
$767$	0.896388	+	1.12403i	0.0323667	+	0.0405865i
$768$	3.95404	−	0.902484i	0.142679	−	0.0325656i
$769$	18.8753	−	4.30816i	0.680660	−	0.155356i	0.131807	−	0.991275i	$-0.457922\pi$
$769$	18.8753	−	4.30816i	0.680660	−	0.155356i	0.548852	+	0.835919i	$0.315065\pi$
$770$	4.58931	+	5.75481i

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.602539 - 0.137526i) q^{2} +(0.268155 + 0.556829i) q^{3} +(-1.45780 - 0.702039i) q^{4} +(0.857618 - 3.75747i) q^{5} +(-0.0849954 - 0.372389i) q^{6} +(2.01463 - 0.970194i) q^{7} +(1.74823 + 1.39417i) q^{8} +(1.63232 - 2.04686i) q^{9} +O(q^{10})\)	\(q+(-0.602539 - 0.137526i) q^{2} +(0.268155 + 0.556829i) q^{3} +(-1.45780 - 0.702039i) q^{4} +(0.857618 - 3.75747i) q^{5} +(-0.0849954 - 0.372389i) q^{6} +(2.01463 - 0.970194i) q^{7} +(1.74823 + 1.39417i) q^{8} +(1.63232 - 2.04686i) q^{9} +(-1.03350 + 2.14608i) q^{10} +(1.08046 - 0.861642i) q^{11} -1.00000i q^{12} +(0.147186 + 0.184565i) q^{13} +(-1.34732 + 0.307516i) q^{14} +(2.32225 - 0.530037i) q^{15} +(1.15601 + 1.44960i) q^{16} -4.38197i q^{17} +(-1.26503 + 1.00883i) q^{18} +(-2.10612 + 4.37339i) q^{19} +(-3.88812 + 4.87555i) q^{20} +(1.08046 + 0.861642i) q^{21} +(-0.769519 + 0.370581i) q^{22} +(0.275051 + 1.20508i) q^{23} +(-0.307516 + 1.34732i) q^{24} +(-8.87824 - 4.27553i) q^{25} +(-0.0633028 - 0.131450i) q^{26} +(3.38508 + 0.772623i) q^{27} -3.61803 q^{28} -1.47214 q^{30} +(9.83719 + 2.24527i) q^{31} +(-2.43757 - 5.06167i) q^{32} +(0.769519 + 0.370581i) q^{33} +(-0.602632 + 2.64030i) q^{34} +(-1.91769 - 8.40196i) q^{35} +(-3.81657 + 1.83796i) q^{36} +(-3.68102 - 2.93552i) q^{37} +(1.87047 - 2.34549i) q^{38} +(-0.0633028 + 0.131450i) q^{39} +(6.73785 - 5.37326i) q^{40} -3.85410i q^{41} +(-0.532524 - 0.667764i) q^{42} +(-7.05464 + 1.61018i) q^{43} +(-2.18001 + 0.497572i) q^{44} +(-6.29112 - 7.88881i) q^{45} -0.763932i q^{46} +(-5.47282 + 4.36443i) q^{47} +(-0.497187 + 1.03242i) q^{48} +(-1.24698 + 1.56366i) q^{49} +(4.76149 + 3.79716i) q^{50} +(2.44001 - 1.17505i) q^{51} +(-0.0849954 - 0.372389i) q^{52} +(0.445042 - 1.94986i) q^{53} +(-1.93339 - 0.931070i) q^{54} +(-2.31097 - 4.79877i) q^{55} +(4.87464 + 1.11260i) q^{56} -3.00000 q^{57} +6.09017 q^{59} +(-3.75747 - 0.857618i) q^{60} +(0.268155 + 0.556829i) q^{61} +(-5.61850 - 2.70573i) q^{62} +(1.30266 - 5.70733i) q^{63} +(-0.0525301 - 0.230149i) q^{64} +(0.819729 - 0.394760i) q^{65} +(-0.412701 - 0.329118i) q^{66} +(0.952608 - 1.19453i) q^{67} +(-3.07631 + 6.38802i) q^{68} +(-0.597266 + 0.476304i) q^{69} +5.32624i q^{70} +(-6.52927 - 8.18745i) q^{71} +(5.70733 - 1.30266i) q^{72} +(13.3645 - 3.05036i) q^{73} +(1.81425 + 2.27500i) q^{74} -6.09017i q^{75} +(6.14058 - 4.89695i) q^{76} +(1.34077 - 2.78415i) q^{77} +(0.0562200 - 0.0704977i) q^{78} +(-4.76149 - 3.79716i) q^{79} +(6.43823 - 3.10049i) q^{80} +(-1.27019 - 5.56509i) q^{81} +(-0.530037 + 2.32225i) q^{82} +(8.95948 + 4.31466i) q^{83} +(-0.970194 - 2.01463i) q^{84} +(-16.4651 - 3.75805i) q^{85} +4.47214 q^{86} +3.09017 q^{88} +(-4.59016 - 1.04767i) q^{89} +(2.70573 + 5.61850i) q^{90} +(0.475589 + 0.229032i) q^{91} +(0.445042 - 1.94986i) q^{92} +(1.38766 + 6.07972i) q^{93} +(3.89781 - 1.87708i) q^{94} +(14.6267 + 11.6644i) q^{95} +(2.16484 - 2.71463i) q^{96} +(-1.54563 + 3.20953i) q^{97} +(0.966397 - 0.770676i) q^{98} -3.61803i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

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