LMFDB - Embedded newform 507.2.s.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.320681 + 1.74990i) q^{2} +(-1.48788 + 0.886686i) q^{3} +(-1.08928 - 0.413111i) q^{4} +(-3.06762 - 0.185557i) q^{5} +(-1.07448 - 2.88799i) q^{6} +(1.60183 + 0.968339i) q^{7} +(-0.768515 + 1.27128i) q^{8} +(1.42758 - 2.63857i) q^{9} +(1.30844 - 5.30853i) q^{10} +(-0.489805 - 2.67278i) q^{11} +(1.98702 - 0.351193i) q^{12} +(-3.00548 - 1.99176i) q^{13} +(-2.20817 + 2.49251i) q^{14} +(4.72879 - 2.44393i) q^{15} +(-3.72218 - 3.29756i) q^{16} +(-5.24683 + 1.29323i) q^{17} +(4.15943 + 3.34425i) q^{18} +(2.04029 - 2.04029i) q^{19} +(3.26486 + 1.46939i) q^{20} +(-3.24194 - 0.0204534i) q^{21} +4.83417 q^{22} +5.44964 q^{23} +(0.0162327 - 2.57294i) q^{24} +(4.41234 + 0.535755i) q^{25} +(4.44918 - 4.62056i) q^{26} +(0.215519 + 5.19168i) q^{27} +(-1.34481 - 1.71653i) q^{28} +(6.93027 - 4.78362i) q^{29} +(2.76021 + 9.05863i) q^{30} +(4.70087 + 3.68290i) q^{31} +(4.62529 - 3.62368i) q^{32} +(3.09868 + 3.54247i) q^{33} +(-0.580460 - 9.59615i) q^{34} +(-4.73412 - 3.26773i) q^{35} +(-2.64505 + 2.28440i) q^{36} +(-2.62988 + 3.35680i) q^{37} +(2.91602 + 4.22458i) q^{38} +(6.23786 + 0.298589i) q^{39} +(2.59341 - 3.75720i) q^{40} +(0.489819 + 1.57188i) q^{41} +(1.07542 - 5.66652i) q^{42} +(-8.99765 - 1.09251i) q^{43} +(-0.570617 + 3.11376i) q^{44} +(-4.86887 + 7.82923i) q^{45} +(-1.74760 + 9.53633i) q^{46} +(-7.98296 - 3.59284i) q^{47} +(8.46206 + 1.60597i) q^{48} +(-1.62489 - 3.09597i) q^{49} +(-2.35247 + 7.54935i) q^{50} +(6.65997 - 6.57646i) q^{51} +(2.45100 + 3.41119i) q^{52} +(-2.51797 - 10.2158i) q^{53} +(-9.15404 - 1.28774i) q^{54} +(1.00658 + 8.28996i) q^{55} +(-2.46206 + 1.29219i) q^{56} +(-1.22661 + 4.84479i) q^{57} +(6.14845 + 13.6613i) q^{58} +(0.447660 - 7.40070i) q^{59} +(-6.16060 + 0.708623i) q^{60} +(-5.35610 - 1.32016i) q^{61} +(-7.95219 + 7.04502i) q^{62} +(4.84176 - 2.84415i) q^{63} +(0.235907 + 0.449483i) q^{64} +(8.85008 + 6.66766i) q^{65} +(-7.19266 + 4.28639i) q^{66} +(6.29386 + 2.83264i) q^{67} +(6.24953 + 0.758831i) q^{68} +(-8.10842 + 4.83212i) q^{69} +(7.23635 - 7.23635i) q^{70} +(0.610121 + 1.95795i) q^{71} +(2.25724 + 3.84263i) q^{72} +(1.59902 - 0.293031i) q^{73} +(-5.03071 - 5.67849i) q^{74} +(-7.04008 + 3.11522i) q^{75} +(-3.06531 + 1.37959i) q^{76} +(1.80357 - 4.75563i) q^{77} +(-2.52286 + 10.8199i) q^{78} +(-4.86508 - 12.8282i) q^{79} +(10.8064 + 10.8064i) q^{80} +(-4.92406 - 7.53350i) q^{81} +(-2.90772 + 0.353061i) q^{82} +(-11.9532 - 3.72477i) q^{83} +(3.52294 + 1.36156i) q^{84} +(16.3353 - 2.99355i) q^{85} +(4.79716 - 15.3946i) q^{86} +(-6.06984 + 13.2624i) q^{87} +(3.77427 + 1.43139i) q^{88} +(-0.600027 + 0.600027i) q^{89} +(-12.1390 - 11.0307i) q^{90} +(-2.88556 - 6.10078i) q^{91} +(-5.93621 - 2.25131i) q^{92} +(-10.2599 - 1.31151i) q^{93} +(8.84709 - 12.8172i) q^{94} +(-6.63742 + 5.88024i) q^{95} +(-3.66880 + 9.49278i) q^{96} +(-9.08250 + 0.549390i) q^{97} +(5.93870 - 1.85057i) q^{98} +(-7.75153 - 2.52321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−0.320681	+	1.74990i	−0.226756	+	1.23737i	0.651304	+	0.758817i	$0.274222\pi$
$2$	−0.320681	+	1.74990i	−0.226756	+	1.23737i	−0.878060	+	0.478550i	$0.841163\pi$
$3$	−1.48788	+	0.886686i	−0.859028	+	0.511928i
$3$	−1.48788	+	0.886686i	−0.859028	+	0.511928i
$4$	−1.08928	−	0.413111i	−0.544642	−	0.206555i
$5$	−3.06762	−	0.185557i	−1.37188	−	0.0829836i	−0.642078	−	0.766639i	$-0.721928\pi$
$5$	−3.06762	−	0.185557i	−1.37188	−	0.0829836i	−0.729805	+	0.683656i	$0.760389\pi$
$6$	−1.07448	−	2.88799i	−0.438654	−	1.17902i
$7$	1.60183	+	0.968339i	0.605434	+	0.365998i	0.786607	−	0.617453i	$-0.211836\pi$
$7$	1.60183	+	0.968339i	0.605434	+	0.365998i	−0.181173	+	0.983451i	$0.557989\pi$
$8$	−0.768515	+	1.27128i	−0.271711	+	0.449465i
$9$	1.42758	−	2.63857i	0.475858	−	0.879522i
$10$	1.30844	−	5.30853i	0.413764	−	1.67871i
$11$	−0.489805	−	2.67278i	−0.147682	−	0.805873i	−0.971143	−	0.238500i	$-0.923344\pi$
$11$	−0.489805	−	2.67278i	−0.147682	−	0.805873i	0.823461	−	0.567373i	$-0.192040\pi$
$12$	1.98702	−	0.351193i	0.573604	−	0.101381i
$13$	−3.00548	−	1.99176i	−0.833569	−	0.552415i
$13$	−3.00548	−	1.99176i	−0.833569	−	0.552415i
$14$	−2.20817	+	2.49251i	−0.590159	+	0.666152i
$15$	4.72879	−	2.44393i	1.22097	−	0.631021i
$16$	−3.72218	−	3.29756i	−0.930545	−	0.824391i
$17$	−5.24683	+	1.29323i	−1.27254	+	0.313654i	−0.817041	−	0.576580i	$-0.804387\pi$
$17$	−5.24683	+	1.29323i	−1.27254	+	0.313654i	−0.455503	+	0.890234i	$0.650541\pi$
$18$	4.15943	+	3.34425i	0.980387	+	0.788248i
$19$	2.04029	−	2.04029i	0.468074	−	0.468074i	−0.433216	−	0.901290i	$-0.642621\pi$
$19$	2.04029	−	2.04029i	0.468074	−	0.468074i	0.901290	+	0.433216i	$0.142621\pi$
$20$	3.26486	+	1.46939i	0.730044	+	0.328566i
$21$	−3.24194	−	0.0204534i	−0.707450	−	0.00446330i
$22$	4.83417			1.03065
$23$	5.44964			1.13633			0.568165	−	0.822915i	$-0.307654\pi$
$23$	5.44964			1.13633			0.568165	+	0.822915i	$0.307654\pi$
$24$	0.0162327	−	2.57294i	0.00331349	−	0.525200i
$25$	4.41234	+	0.535755i	0.882468	+	0.107151i
$26$	4.44918	−	4.62056i	0.872557	−	0.906167i
$27$	0.215519	+	5.19168i	0.0414766	+	0.999139i
$28$	−1.34481	−	1.71653i	−0.254146	−	0.324393i
$29$	6.93027	−	4.78362i	1.28692	−	0.888295i	0.289298	−	0.957239i	$-0.406578\pi$
$29$	6.93027	−	4.78362i	1.28692	−	0.888295i	0.997621	+	0.0689438i	$0.0219629\pi$
$30$	2.76021	+	9.05863i	0.503942	+	1.65387i
$31$	4.70087	+	3.68290i	0.844302	+	0.661468i	0.942686	−	0.333680i	$-0.108291\pi$
$31$	4.70087	+	3.68290i	0.844302	+	0.661468i	−0.0983847	+	0.995148i	$0.531368\pi$
$32$	4.62529	−	3.62368i	0.817643	−	0.640582i
$33$	3.09868	+	3.54247i	0.539412	+	0.616665i
$34$	−0.580460	−	9.59615i	−0.0995481	−	1.64573i
$35$	−4.73412	−	3.26773i	−0.800213	−	0.552347i
$36$	−2.64505	+	2.28440i	−0.440842	+	0.380733i
$37$	−2.62988	+	3.35680i	−0.432350	+	0.551854i	−0.953415	−	0.301663i	$-0.902458\pi$
$37$	−2.62988	+	3.35680i	−0.432350	+	0.551854i	0.521065	+	0.853517i	$0.325535\pi$
$38$	2.91602	+	4.22458i	0.473040	+	0.685317i
$39$	6.23786	+	0.298589i	0.998856	+	0.0478125i
$40$	2.59341	−	3.75720i	0.410054	−	0.594066i
$41$	0.489819	+	1.57188i	0.0764969	+	0.245487i	0.985046	−	0.172291i	$-0.0551168\pi$
$41$	0.489819	+	1.57188i	0.0764969	+	0.245487i	−0.908549	+	0.417778i	$0.862809\pi$
$42$	1.07542	−	5.66652i	0.165941	−	0.874363i
$43$	−8.99765	−	1.09251i	−1.37213	−	0.166607i	−0.598946	−	0.800790i	$-0.704413\pi$
$43$	−8.99765	−	1.09251i	−1.37213	−	0.166607i	−0.773183	+	0.634183i	$0.781337\pi$
$44$	−0.570617	+	3.11376i	−0.0860237	+	0.469416i
$45$	−4.86887	+	7.82923i	−0.725808	+	1.16711i
$46$	−1.74760	+	9.53633i	−0.257669	+	1.40606i
$47$	−7.98296	−	3.59284i	−1.16443	−	0.524069i	−0.266343	−	0.963878i	$-0.585815\pi$
$47$	−7.98296	−	3.59284i	−1.16443	−	0.524069i	−0.898091	+	0.439809i	$0.855046\pi$
$48$	8.46206	+	1.60597i	1.22139	+	0.231802i
$49$	−1.62489	−	3.09597i	−0.232127	−	0.442281i
$50$	−2.35247	+	7.54935i	−0.332690	+	1.06764i
$51$	6.65997	−	6.57646i	0.932582	−	0.920889i
$52$	2.45100	+	3.41119i	0.339892	+	0.473047i
$53$	−2.51797	−	10.2158i	−0.345870	−	1.40325i	−0.844092	−	0.536199i	$-0.819860\pi$
$53$	−2.51797	−	10.2158i	−0.345870	−	1.40325i	0.498222	−	0.867049i	$-0.333986\pi$
$54$	−9.15404	−	1.28774i	−1.24571	−	0.175239i
$55$	1.00658	+	8.28996i	0.135728	+	1.11782i
$56$	−2.46206	+	1.29219i	−0.329007	+	0.172676i
$57$	−1.22661	+	4.84479i	−0.162468	+	0.641709i
$58$	6.14845	+	13.6613i	0.807331	+	1.79382i
$59$	0.447660	−	7.40070i	0.0582804	−	0.963489i	−0.845089	−	0.534626i	$-0.820453\pi$
$59$	0.447660	−	7.40070i	0.0582804	−	0.963489i	0.903369	−	0.428863i	$-0.141086\pi$
$60$	−6.16060	+	0.708623i	−0.795331	+	0.0914828i
$61$	−5.35610	−	1.32016i	−0.685778	−	0.169029i	−0.118993	−	0.992895i	$-0.537967\pi$
$61$	−5.35610	−	1.32016i	−0.685778	−	0.169029i	−0.566785	+	0.823866i	$0.691813\pi$
$62$	−7.95219	+	7.04502i	−1.00993	+	0.894719i
$63$	4.84176	−	2.84415i	0.610004	−	0.358330i
$64$	0.235907	+	0.449483i	0.0294884	+	0.0561854i
$65$	8.85008	+	6.66766i	1.09772	+	0.827022i
$66$	−7.19266	+	4.28639i	−0.885355	+	0.527618i
$67$	6.29386	+	2.83264i	0.768918	+	0.346062i	0.756613	−	0.653863i	$-0.226853\pi$
$67$	6.29386	+	2.83264i	0.768918	+	0.346062i	0.0123043	+	0.999924i	$0.496083\pi$
$68$	6.24953	+	0.758831i	0.757867	+	0.0920218i
$69$	−8.10842	+	4.83212i	−0.976139	+	0.581719i
$70$	7.23635	−	7.23635i	0.864909	−	0.864909i
$71$	0.610121	+	1.95795i	0.0724080	+	0.232365i	0.983829	−	0.179109i	$-0.0573216\pi$
$71$	0.610121	+	1.95795i	0.0724080	+	0.232365i	−0.911421	+	0.411475i	$0.865014\pi$
$72$	2.25724	+	3.84263i	0.266018	+	0.452858i
$73$	1.59902	−	0.293031i	0.187151	−	0.0342967i	−0.0858620	−	0.996307i	$-0.527364\pi$
$73$	1.59902	−	0.293031i	0.187151	−	0.0342967i	0.273013	+	0.962010i	$0.411980\pi$
$74$	−5.03071	−	5.67849i	−0.584808	−	0.660112i
$75$	−7.04008	+	3.11522i	−0.812918	+	0.359715i
$76$	−3.06531	+	1.37959i	−0.351616	+	0.158249i
$77$	1.80357	−	4.75563i	0.205536	−	0.541954i
$78$	−2.52286	+	10.8199i	−0.285658	+	1.22511i
$79$	−4.86508	−	12.8282i	−0.547365	−	1.44328i	−0.868232	−	0.496158i	$-0.834744\pi$
$79$	−4.86508	−	12.8282i	−0.547365	−	1.44328i	0.320867	−	0.947124i	$-0.396026\pi$
$80$	10.8064	+	10.8064i	1.20819	+	1.20819i
$81$	−4.92406	−	7.53350i	−0.547118	−	0.837056i
$82$	−2.90772	+	0.353061i	−0.321104	+	0.0389890i
$83$	−11.9532	−	3.72477i	−1.31203	−	0.408846i	−0.439871	−	0.898061i	$-0.644976\pi$
$83$	−11.9532	−	3.72477i	−1.31203	−	0.408846i	−0.872163	+	0.489215i	$0.837283\pi$
$84$	3.52294	+	1.36156i	0.384385	+	0.148558i
$85$	16.3353	−	2.99355i	1.77181	−	0.324696i
$86$	4.79716	−	15.3946i	0.517292	−	1.66005i
$87$	−6.06984	+	13.2624i	−0.650755	+	1.42188i
$88$	3.77427	+	1.43139i	0.402339	+	0.152587i
$89$	−0.600027	+	0.600027i	−0.0636027	+	0.0636027i	−0.738193	−	0.674590i	$-0.764320\pi$
$89$	−0.600027	+	0.600027i	−0.0636027	+	0.0636027i	0.674590	+	0.738193i	$0.264320\pi$
$90$	−12.1390	−	11.0307i	−1.27956	−	1.16274i
$91$	−2.88556	−	6.10078i	−0.302488	−	0.639536i
$92$	−5.93621	−	2.25131i	−0.618892	−	0.234715i
$93$	−10.2599	−	1.31151i	−1.06390	−	0.135998i
$94$	8.84709	−	12.8172i	0.912508	−	1.32200i
$95$	−6.63742	+	5.88024i	−0.680985	+	0.603300i
$96$	−3.66880	+	9.49278i	−0.374446	+	0.968853i
$97$	−9.08250	+	0.549390i	−0.922188	+	0.0557821i	−0.514644	−	0.857404i	$-0.672076\pi$
$97$	−9.08250	+	0.549390i	−0.922188	+	0.0557821i	−0.407543	+	0.913186i	$0.633615\pi$
$98$	5.93870	−	1.85057i	0.599900	−	0.186936i
$99$	−7.75153	−	2.52321i	−0.779058	−	0.253592i
$100$	−4.58496	−	2.40637i	−0.458496	−	0.240637i
$101$	−1.26871	+	10.4488i	−0.126242	+	1.03969i	0.782592	+	0.622535i	$0.213897\pi$
$101$	−1.26871	+	10.4488i	−0.126242	+	1.03969i	−0.908834	+	0.417158i	$0.863026\pi$
$102$	9.37243	+	13.7632i	0.928009	+	1.36276i
$103$	1.73636	−	3.30835i	0.171088	−	0.325982i	−0.784781	−	0.619773i	$-0.787225\pi$
$103$	1.73636	−	3.30835i	0.171088	−	0.325982i	0.955870	+	0.293791i	$0.0949171\pi$
$104$	4.84184	−	2.29010i	0.474782	−	0.224563i
$105$	9.94126	+	0.664309i	0.970168	+	0.0648299i
$106$	18.6841	−	1.13018i	1.81476	−	0.109773i
$107$	−12.1742	−	13.7418i	−1.17692	−	1.32847i	−0.933511	−	0.358548i	$-0.883272\pi$
$107$	−12.1742	−	13.7418i	−1.17692	−	1.32847i	−0.243411	−	0.969923i	$-0.578266\pi$
$108$	1.90998	−	5.74425i	0.183788	−	0.552740i
$109$	−2.11592	−	2.70077i	−0.202668	−	0.258687i	0.675150	−	0.737680i	$-0.264079\pi$
$109$	−2.11592	−	2.70077i	−0.202668	−	0.258687i	−0.877819	+	0.478993i	$0.841002\pi$
$110$	−14.8294	−	0.897013i	−1.41393	−	0.0855269i
$111$	0.936525	−	7.32639i	0.0888910	−	0.695390i
$112$	−2.76913	−	8.88646i	−0.261658	−	0.839692i
$113$	0.658479	+	1.25463i	0.0619445	+	0.118025i	0.914460	−	0.404677i	$-0.132616\pi$
$113$	0.658479	+	1.25463i	0.0619445	+	0.118025i	−0.852515	+	0.522703i	$0.824924\pi$
$114$	−8.08456	−	3.70008i	−0.757188	−	0.346544i
$115$	−16.7175	−	1.01122i	−1.55891	−	0.0942967i
$116$	−9.52519	+	2.34775i	−0.884392	+	0.217983i
$117$	−9.54594	+	5.08676i	−0.882522	+	0.470271i
$118$	12.8069	+	3.15663i	1.17897	+	0.290591i
$119$	−9.65681	−	3.00918i	−0.885238	−	0.275851i
$120$	−0.527224	+	7.88981i	−0.0481287	+	0.720238i
$121$	3.38135	−	1.28238i	0.307395	−	0.116580i
$122$	4.02775	−	8.94929i	0.364655	−	0.810231i
$123$	−2.12256	−	1.90446i	−0.191385	−	0.171719i
$124$	−3.59914	−	5.95370i	−0.323212	−	0.534658i
$125$	1.67847	+	0.307592i	0.150127	+	0.0275119i
$126$	3.42432	+	9.38466i	0.305063	+	0.836052i
$127$	−1.56031	+	0.591747i	−0.138455	+	0.0525091i	−0.422859	−	0.906195i	$-0.638973\pi$
$127$	−1.56031	+	0.591747i	−0.138455	+	0.0525091i	0.284404	+	0.958704i	$0.408204\pi$
$128$	10.3572	−	3.22743i	0.915454	−	0.285267i
$129$	14.3561	−	6.35256i	1.26399	−	0.559312i
$130$	−14.5058	+	13.3486i	−1.27224	+	1.17075i
$131$	−0.766150	+	0.528835i	−0.0669389	+	0.0462046i	−0.601064	−	0.799201i	$-0.705256\pi$
$131$	−0.766150	+	0.528835i	−0.0669389	+	0.0462046i	0.534125	+	0.845405i	$0.320641\pi$
$132$	−1.91191	−	5.13885i	−0.166411	−	0.447280i
$133$	5.24388	−	1.29250i	0.454702	−	0.112074i
$134$	−6.97516	+	10.1053i	−0.602562	+	0.872962i
$135$	0.302223	−	15.9661i	0.0260112	−	1.37414i
$136$	2.38822	−	7.66406i	0.204788	−	0.657188i
$137$	11.5584	+	14.7532i	0.987500	+	1.26045i	0.965422	+	0.260694i	$0.0839513\pi$
$137$	11.5584	+	14.7532i	0.987500	+	1.26045i	0.0220780	+	0.999756i	$0.492972\pi$
$138$	−5.85552	−	15.7385i	−0.498455	−	1.33975i
$139$	6.46500	+	5.72749i	0.548354	+	0.485799i	0.891211	−	0.453588i	$-0.149856\pi$
$139$	6.46500	+	5.72749i	0.548354	+	0.485799i	−0.342857	+	0.939388i	$0.611395\pi$
$140$	3.80687	+	5.51520i	0.321739	+	0.466120i
$141$	15.0634	−	1.73267i	1.26857	−	0.145917i
$142$	−3.62187	+	0.439774i	−0.303940	+	0.0369050i
$143$	−3.85144	+	9.00854i	−0.322074	+	0.753332i
$144$	−14.0145	+	5.11369i	−1.16788	+	0.426141i
$145$	−22.1471	+	13.3884i	−1.83921	+	1.11184i
$146$			2.89209i			0.239351i
$147$	5.16279	+	3.16566i	0.425820	+	0.261099i
$148$	4.25142	−	2.57007i	0.349464	−	0.211259i
$149$	−9.64912	+	21.4395i	−0.790487	+	1.75639i	−0.149610	+	0.988745i	$0.547802\pi$
$149$	−9.64912	+	21.4395i	−0.790487	+	1.75639i	−0.640876	+	0.767644i	$0.721429\pi$
$150$	−3.19371	−	13.3184i	−0.260765	−	1.08745i
$151$	−18.4071	+	8.28437i	−1.49795	+	0.674172i	−0.983094	−	0.183104i	$-0.941385\pi$
$151$	−18.4071	+	8.28437i	−1.49795	+	0.674172i	−0.514856	+	0.857277i	$0.672155\pi$
$152$	1.02578	+	4.16176i	0.0832020	+	0.337564i
$153$	−4.07798	+	15.6903i	−0.329685	+	1.26848i
$154$	7.74350	+	4.68111i	0.623989	+	0.377215i
$155$	−13.7371	−	12.1700i	−1.10339	−	0.977520i
$156$	−6.67144	−	2.90217i	−0.534143	−	0.232360i
$157$	5.01929	−	4.44670i	0.400583	−	0.354886i	−0.438650	−	0.898658i	$-0.644543\pi$
$157$	5.01929	−	4.44670i	0.400583	−	0.354886i	0.839233	+	0.543773i	$0.183005\pi$
$158$	24.0082	−	4.39966i	1.90999	−	0.350018i
$159$	12.8046	+	12.9672i	1.01547	+	1.02837i
$160$	−14.8610	+	10.2578i	−1.17487	+	0.810953i
$161$	8.72939	+	5.27710i	0.687973	+	0.415894i
$162$	14.7619	−	6.20076i	1.15981	−	0.487178i
$163$	4.56059	−	5.82116i	0.357213	−	0.455948i	−0.574843	−	0.818264i	$-0.694937\pi$
$163$	4.56059	−	5.82116i	0.357213	−	0.455948i	0.932056	+	0.362316i	$0.118014\pi$
$164$	0.115811	−	1.91458i	0.00904329	−	0.149503i
$165$	−8.84827	−	11.4419i	−0.688837	−	0.890754i
$166$	10.3511	−	19.7225i	0.803404	−	1.53076i
$167$	−10.9386	−	2.00458i	−0.846456	−	0.155119i	−0.260512	−	0.965471i	$-0.583891\pi$
$167$	−10.9386	−	2.00458i	−0.846456	−	0.155119i	−0.585944	+	0.810352i	$0.699276\pi$
$168$	2.51748	−	4.10570i	0.194228	−	0.316761i
$169$	5.06577	+	11.9724i	0.389675	+	0.920953i
$170$			29.5451i			2.26600i
$171$	−2.47077	−	8.29609i	−0.188944	−	0.634418i
$172$	9.34966	+	4.90708i	0.712905	+	0.374161i
$173$	6.65562	−	17.5494i	0.506018	−	1.33426i	−0.402120	−	0.915587i	$-0.631727\pi$
$173$	6.65562	−	17.5494i	0.506018	−	1.33426i	0.908138	−	0.418672i	$-0.137504\pi$
$174$	−21.2614	−	14.8746i	−1.61183	−	1.12764i
$175$	6.54902	+	5.13083i	0.495059	+	0.387854i
$176$	−6.99051	+	11.5637i	−0.526929	+	0.871648i
$177$	5.89603	+	11.4083i	0.443173	+	0.857499i
$178$	−0.857570	−	1.24240i	−0.0642776	−	0.0931222i
$179$	−6.35959	−	1.56750i	−0.475338	−	0.117160i	−0.00563399	−	0.999984i	$-0.501793\pi$
$179$	−6.35959	−	1.56750i	−0.475338	−	0.117160i	−0.469704	+	0.882824i	$0.655640\pi$
$180$	8.53792	−	6.51687i	0.636379	−	0.485739i
$181$	−13.6468	−	15.4040i	−1.01436	−	1.14497i	−0.989390	−	0.145282i	$-0.953591\pi$
$181$	−13.6468	−	15.4040i	−1.01436	−	1.14497i	−0.0249648	−	0.999688i	$-0.507947\pi$
$182$	11.6011	−	3.09303i	0.859931	−	0.229271i
$183$	9.13980	−	2.78494i	0.675634	−	0.205869i
$184$	−4.18814	+	6.92802i	−0.308753	+	0.510741i
$185$	8.69037	−	9.80940i	0.638928	−	0.721201i
$186$	5.58518	−	17.5332i	0.409525	−	1.28560i
$187$	6.02643	+	13.3902i	0.440696	+	0.979187i
$188$	7.21146	+	7.21146i	0.525950	+	0.525950i
$189$	−4.68208	+	8.52488i	−0.340571	+	0.620094i
$190$	−8.16134	−	13.5005i	−0.592086	−	0.979429i
$191$		−	21.2794i		−	1.53972i	−0.638213	−	0.769860i	$-0.720326\pi$
$191$		−	21.2794i		−	1.53972i	0.638213	−	0.769860i	$-0.279674\pi$
$192$	−0.749552	−	0.459602i	−0.0540943	−	0.0331689i
$193$	−1.65480	−	2.73738i	−0.119115	−	0.197041i	0.790534	−	0.612419i	$-0.209803\pi$
$193$	−1.65480	−	2.73738i	−0.119115	−	0.197041i	−0.909649	+	0.415378i	$0.863649\pi$
$194$	1.95121	−	16.0696i	0.140089	−	1.15373i
$195$	−19.0800	−	2.07344i	−1.36635	−	0.148482i
$196$	0.490987	+	4.04364i	0.0350705	+	0.288832i
$197$	5.41923	−	4.24569i	0.386104	−	0.302493i	−0.404833	−	0.914391i	$-0.632670\pi$
$197$	5.41923	−	4.24569i	0.386104	−	0.302493i	0.790937	+	0.611897i	$0.209593\pi$
$198$	6.90114	−	12.7553i	0.490442	−	0.906477i
$199$	−10.5413	+	11.8986i	−0.747251	+	0.843473i	−0.992016	−	0.126110i	$-0.959751\pi$
$199$	−10.5413	+	11.8986i	−0.747251	+	0.843473i	0.244765	+	0.969582i	$0.421289\pi$
$200$	−4.07204	+	5.19758i	−0.287937	+	0.367524i
$201$	−11.8762	+	1.36606i	−0.837681	+	0.0963541i
$202$	−17.8775	−	5.57085i	−1.25786	−	0.391964i
$203$	15.7333	−	0.951687i	1.10426	−	0.0667953i
$204$	−9.97140	+	4.41233i	−0.698138	+	0.308925i
$205$	−1.21091	−	4.91284i	−0.0845734	−	0.343128i
$206$	5.23247	+	4.09938i	0.364563	+	0.285617i
$207$	7.77978	−	14.3792i	0.540732	−	0.999426i
$208$	4.61896	+	17.3244i	0.320267	+	1.20123i
$209$	−6.45257	−	4.45389i	−0.446334	−	0.308082i
$210$	−4.35045	+	17.1832i	−0.300210	+	1.18575i
$211$	3.64352	+	9.60718i	0.250830	+	0.661385i	1.00000		0.000993397i	$-0.000316208\pi$
$211$	3.64352	+	9.60718i	0.250830	+	0.661385i	−0.749169	+	0.662379i	$0.769547\pi$
$212$	−1.47748	+	12.1681i	−0.101473	+	0.835709i
$213$	−2.64387	−	2.37220i	−0.181155	−	0.162541i
$214$	27.9508	−	16.8969i	1.91068	−	1.15505i
$215$	27.3987	+	5.02099i	1.86857	+	0.342429i
$216$	−6.76571	−	3.71590i	−0.460348	−	0.252835i
$217$	3.96370	+	10.4514i	0.269073	+	0.709488i
$218$	5.40461	−	2.83656i	0.366047	−	0.192116i
$219$	−2.11932	+	1.85382i	−0.143211	+	0.125270i
$220$	2.32822	−	9.44595i	0.156968	−	0.636846i
$221$	18.3450	+	6.56367i	1.23402	+	0.441521i
$222$	12.5201	+	3.98826i	0.840296	+	0.267675i
$223$	−1.14452	+	18.9211i	−0.0766425	+	1.26705i	0.733041	+	0.680184i	$0.238100\pi$
$223$	−1.14452	+	18.9211i	−0.0766425	+	1.26705i	−0.809684	+	0.586867i	$0.800361\pi$
$224$	10.9179	−	1.32567i	0.729481	−	0.0885750i
$225$	7.71257	−	10.8774i	0.514171	−	0.725161i
$226$	−2.40664	+	0.749938i	−0.160087	+	0.0498851i
$227$	−10.8799	+	4.89667i	−0.722128	+	0.325003i	−0.737935	−	0.674872i	$-0.764199\pi$
$227$	−10.8799	+	4.89667i	−0.722128	+	0.325003i	0.0158074	+	0.999875i	$0.494968\pi$
$228$	3.33756	−	4.77063i	0.221035	−	0.315943i
$229$	−0.208058	+	0.163003i	−0.0137489	+	0.0107715i	−0.623570	−	0.781768i	$-0.714318\pi$
$229$	−0.208058	+	0.163003i	−0.0137489	+	0.0107715i	0.609821	+	0.792539i	$0.291241\pi$
$230$	7.13051	−	28.9296i	0.470172	−	1.90756i
$231$	1.53325	+	8.67501i	0.100880	+	0.570773i
$232$	0.755300	+	12.4866i	0.0495879	+	0.819785i
$233$	−6.50927	+	3.41633i	−0.426437	+	0.223811i	−0.664267	−	0.747496i	$-0.731256\pi$
$233$	−6.50927	+	3.41633i	−0.426437	+	0.223811i	0.237830	+	0.971307i	$0.423564\pi$
$234$	−5.84011	−	18.3357i	−0.381780	−	1.19864i
$235$	23.8220	+	12.5028i	1.55398	+	0.815591i
$236$	−3.54494	+	7.87653i	−0.230756	+	0.512718i
$237$	18.6132	+	14.7730i	1.20906	+	0.959608i
$238$	8.36253	−	15.9335i	0.542062	−	1.03281i
$239$	−3.44854	−	3.44854i	−0.223067	−	0.223067i	0.586722	−	0.809789i	$-0.300418\pi$
$239$	−3.44854	−	3.44854i	−0.223067	−	0.223067i	−0.809789	+	0.586722i	$0.800418\pi$
$240$	−25.6604	−	6.49672i	−1.65637	−	0.419361i
$241$	−0.285521	−	4.72023i	−0.0183920	−	0.304057i	−0.995726	−	0.0923543i	$-0.970561\pi$
$241$	−0.285521	−	4.72023i	−0.0183920	−	0.304057i	0.977334	−	0.211702i	$-0.0679008\pi$
$242$	1.15970	+	6.32826i	0.0745481	+	0.406796i
$243$	14.0063	+	6.84286i	0.898502	+	0.438969i
$244$	5.28894	+	3.65069i	0.338590	+	0.233712i
$245$	4.41007	+	9.79877i	0.281749	+	0.626020i
$246$	4.01328	−	3.10355i	0.255877	−	0.197875i
$247$	−10.1958	+	2.06827i	−0.648743	+	0.131601i
$248$	−8.29469	+	3.14576i	−0.526713	+	0.199756i
$249$	21.0876	−	5.05673i	1.33637	−	0.320457i
$250$	−1.07651	+	2.83853i	−0.0680845	+	0.179524i
$251$	1.36704	+	11.2586i	0.0862867	+	0.710635i	0.970085	+	0.242766i	$0.0780549\pi$
$251$	1.36704	+	11.2586i	0.0862867	+	0.710635i	−0.883798	+	0.467869i	$0.845022\pi$
$252$	−6.44900	+	1.09791i	−0.406249	+	0.0691616i
$253$	−2.66926	−	14.5657i	−0.167815	−	0.915737i
$254$	−0.535137	−	2.92015i	−0.0335775	−	0.183226i
$255$	−21.6506	+	18.9383i	−1.35581	+	1.18596i
$256$	2.44870	+	20.1669i	0.153044	+	1.26043i
$257$	0.882808	−	2.32777i	0.0550680	−	0.145203i	−0.904659	−	0.426136i	$-0.859875\pi$
$257$	0.882808	−	2.32777i	0.0550680	−	0.145203i	0.959727	+	0.280933i	$0.0906439\pi$
$258$	6.51261	+	27.1590i	0.405457	+	1.69084i
$259$	−7.46314	+	2.83039i	−0.463737	+	0.175872i
$260$	−6.88577	−	10.9190i	−0.427037	−	0.677170i
$261$	−2.72841	−	25.1149i	−0.168884	−	1.55458i
$262$	−0.679719	−	1.51027i	−0.0419932	−	0.0933051i
$263$	8.64844	+	5.96959i	0.533286	+	0.368101i	0.804065	−	0.594541i	$-0.202666\pi$
$263$	8.64844	+	5.96959i	0.533286	+	0.368101i	−0.270780	+	0.962641i	$0.587282\pi$
$264$	−6.88486	+	1.21685i	−0.423734	+	0.0748922i
$265$	5.82857	+	31.8055i	0.358046	+	1.95379i
$266$	0.580133	+	9.59074i	0.0355702	+	0.588046i
$267$	0.360733	−	1.42480i	0.0220765	−	0.0871965i
$268$	−5.68561	−	5.68561i	−0.347304	−	0.347304i
$269$	−10.5159	+	20.0364i	−0.641167	+	1.22164i	0.320455	+	0.947264i	$0.396164\pi$
$269$	−10.5159	+	20.0364i	−0.641167	+	1.22164i	−0.961622	+	0.274378i	$0.911528\pi$
$270$	27.8422	+	5.64889i	1.69442	+	0.343781i
$271$	9.08932	−	20.1956i	0.552137	−	1.22680i	−0.398693	−	0.917085i	$-0.630536\pi$
$271$	9.08932	−	20.1956i	0.552137	−	1.22680i	0.950830	−	0.309714i	$-0.100233\pi$
$272$	23.7941	+	12.4881i	1.44273	+	0.757204i
$273$	9.70284	+	6.51865i	0.587243	+	0.394527i
$274$	−29.5232	+	15.4950i	−1.78356	+	0.936085i
$275$	−0.729230	−	12.0556i	−0.0439742	−	0.726981i
$276$	10.8286	−	1.91388i	0.651803	−	0.115202i
$277$	1.04729	−	4.24902i	0.0629255	−	0.255299i	−0.931051	−	0.364888i	$-0.881107\pi$
$277$	1.04729	−	4.24902i	0.0629255	−	0.255299i	0.993977	+	0.109589i	$0.0349535\pi$
$278$	−12.0957	+	9.47641i	−0.725455	+	0.568357i
$279$	16.4284	−	7.14595i	0.983544	−	0.427817i
$280$	7.79245	−	3.50710i	0.465688	−	0.209589i
$281$	23.2962	−	7.25939i	1.38973	−	0.433059i	0.490850	−	0.871244i	$-0.336686\pi$
$281$	23.2962	−	7.25939i	1.38973	−	0.433059i	0.898885	+	0.438185i	$0.144379\pi$
$282$	−1.79856	+	26.9151i	−0.107103	+	1.60277i
$283$	10.2856	−	1.24890i	0.611417	−	0.0742394i	0.191030	−	0.981584i	$-0.438817\pi$
$283$	10.2856	−	1.24890i	0.611417	−	0.0742394i	0.420387	+	0.907345i	$0.361894\pi$
$284$	0.144254	−	2.38481i	0.00855991	−	0.141512i
$285$	4.66176	−	14.6344i	0.276139	−	0.866867i
$286$	−14.5290	−	9.62851i	−0.859116	−	0.569346i
$287$	−0.737511	+	2.99220i	−0.0435339	+	0.176624i
$288$	−2.95837	−	17.3772i	−0.174324	−	1.02396i
$289$	10.8041	−	5.67041i	0.635533	−	0.333553i
$290$	−16.3262	−	43.0486i	−0.958706	−	2.52790i
$291$	13.0265	−	8.87075i	0.763629	−	0.520013i
$292$	−1.86284	−	0.341378i	−0.109014	−	0.0199776i
$293$	3.38395	−	2.04567i	0.197692	−	0.119509i	−0.415029	−	0.909808i	$-0.636229\pi$
$293$	3.38395	−	2.04567i	0.197692	−	0.119509i	0.612721	+	0.790299i	$0.290075\pi$
$294$	−7.19520	+	8.01920i	−0.419633	+	0.467689i
$295$	−2.74650	+	22.6195i	−0.159908	+	1.31696i
$296$	−2.24632	−	5.92307i	−0.130565	−	0.344271i
$297$	13.7706	−	3.11894i	0.799054	−	0.180979i
$298$	−34.4226	−	23.7602i	−1.99405	−	1.37639i
$299$	−16.3788	−	10.8544i	−0.947209	−	0.627726i
$300$	8.95557	−	0.485026i	0.517050	−	0.0280030i
$301$	−13.3548	−	10.4628i	−0.769756	−	0.603065i
$302$	−8.59401	−	34.8673i	−0.494530	−	2.00639i
$303$	−7.37710	−	16.6715i	−0.423803	−	0.957752i
$304$	−14.3223	+	0.866338i	−0.821439	+	0.0496879i
$305$	16.1855	+	5.04362i	0.926781	+	0.288797i
$306$	−26.1487	−	12.1676i	−1.49482	−	0.695578i
$307$	−9.16175	+	11.6941i	−0.522889	+	0.667418i	−0.974393	−	0.224851i	$-0.927811\pi$
$307$	−9.16175	+	11.6941i	−0.522889	+	0.667418i	0.451504	+	0.892269i	$0.350888\pi$
$308$	−3.92920	+	4.43515i	−0.223887	+	0.252716i
$309$	0.349978	+	6.46203i	0.0199096	+	0.367612i
$310$	25.7016	−	20.1359i	1.45975	−	1.14364i
$311$	2.36019	+	19.4379i	0.133834	+	1.10222i	0.892596	+	0.450857i	$0.148881\pi$
$311$	2.36019	+	19.4379i	0.133834	+	1.10222i	−0.758762	+	0.651368i	$0.774196\pi$
$312$	−5.17348	+	7.70059i	−0.292891	+	0.435960i
$313$	0.507570	−	4.18022i	0.0286896	−	0.236280i	−0.971309	−	0.237820i	$-0.923567\pi$
$313$	0.507570	−	4.18022i	0.0286896	−	0.236280i	0.999999	+	0.00154010i	$0.000490229\pi$
$314$	6.17170	+	10.2092i	0.348289	+	0.576140i
$315$	−15.3804	+	7.82637i	−0.866590	+	0.440966i
$316$			15.9833i			0.899133i
$317$	−7.65716	−	12.6665i	−0.430069	−	0.711421i	0.563318	−	0.826241i	$-0.309525\pi$
$317$	−7.65716	−	12.6665i	−0.430069	−	0.711421i	−0.993386	+	0.114820i	$0.963371\pi$
$318$	−26.7976	+	18.2485i	−1.50273	+	1.02333i
$319$	−16.1800	−	16.1800i	−0.905907	−	0.905907i
$320$	−0.640269	−	1.42262i	−0.0357921	−	0.0795269i
$321$	30.2984	+	9.65149i	1.69109	+	0.538694i
$322$	−12.0338	+	13.5833i	−0.670615	+	0.756968i
$323$	−8.06648	+	13.3436i	−0.448831	+	0.742457i
$324$	2.25152	+	10.2403i	0.125085	+	0.568906i
$325$	−12.1941	−	10.3985i	−0.676406	−	0.576806i
$326$	8.72396	+	9.84731i	0.483175	+	0.545392i
$327$	5.54297	+	2.14227i	0.306527	+	0.118468i
$328$	−2.37474	−	0.585321i	−0.131123	−	0.0323189i
$329$	−9.30824	−	13.4853i	−0.513180	−	0.743470i
$330$	22.8597	−	11.8144i	1.25839	−	0.650360i
$331$	2.68775	−	4.44608i	0.147732	−	0.244378i	−0.773147	−	0.634227i	$-0.781319\pi$
$331$	2.68775	−	4.44608i	0.147732	−	0.244378i	0.920879	+	0.389848i	$0.127472\pi$
$332$	11.4817	+	8.99532i	0.630139	+	0.493683i
$333$	5.10277	+	11.7312i	0.279630	+	0.642866i
$334$	7.01562	−	18.4987i	0.383878	−	1.01220i
$335$	−18.7816	−	9.85734i	−1.02615	−	0.538564i
$336$	11.9996	+	10.7666i	0.654634	+	0.587368i
$337$			12.5033i			0.681099i	0.940227	+	0.340550i	$0.110613\pi$
$337$			12.5033i			0.681099i	−0.940227	+	0.340550i	$0.889387\pi$
$338$	−22.5750	+	5.02528i	−1.22792	+	0.273339i
$339$	−2.09220	−	1.28287i	−0.113633	−	0.0696760i
$340$	−19.0304	−	3.48745i	−1.03207	−	0.189134i
$341$	7.54106	−	14.3683i	0.408371	−	0.778086i
$342$	15.3097	−	1.66320i	0.827852	−	0.0899353i
$343$	1.18626	−	19.6112i	0.0640518	−	1.05890i
$344$	8.30372	−	10.5989i	0.447707	−	0.571455i
$345$	25.7702	−	13.3186i	1.38742	−	0.717047i
$346$	28.5754	+	17.2745i	1.53622	+	0.928680i
$347$	4.35921	−	3.00895i	0.234015	−	0.161529i	−0.445287	−	0.895388i	$-0.646898\pi$
$347$	4.35921	−	3.00895i	0.234015	−	0.161529i	0.679302	+	0.733859i	$0.262283\pi$
$348$	12.0906	−	11.9390i	0.648125	−	0.639999i
$349$	−16.0014	+	2.93237i	−0.856538	+	0.156966i	−0.590541	−	0.807008i	$-0.701086\pi$
$349$	−16.0014	+	2.93237i	−0.856538	+	0.156966i	−0.265997	+	0.963974i	$0.585701\pi$
$350$	−11.0786	+	9.81477i	−0.592175	+	0.524621i
$351$	9.69286	−	16.0327i	0.517366	−	0.855764i
$352$	−11.9508	−	10.5875i	−0.636978	−	0.564314i
$353$	28.5506	+	17.2594i	1.51959	+	0.918627i	0.997851	+	0.0655239i	$0.0208719\pi$
$353$	28.5506	+	17.2594i	1.51959	+	0.918627i	0.521743	+	0.853103i	$0.325282\pi$
$354$	−21.8541	+	6.65905i	−1.16153	+	0.353925i
$355$	−1.50831	−	6.11945i	−0.0800528	−	0.324787i
$356$	0.901477	−	0.405722i	0.0477782	−	0.0215032i
$357$	17.0364	−	4.08525i	0.901661	−	0.216215i
$358$	4.78237	−	10.6260i	0.252756	−	0.561601i
$359$	4.19656	−	2.53691i	0.221486	−	0.133893i	−0.402245	−	0.915532i	$-0.631770\pi$
$359$	4.19656	−	2.53691i	0.221486	−	0.133893i	0.623731	+	0.781639i	$0.285616\pi$
$360$	−6.21134	−	12.2066i	−0.327366	−	0.643343i
$361$			10.6745i			0.561814i
$362$	31.3317	−	18.9407i	1.64676	−	0.995500i
$363$	−3.89398	+	4.90622i	−0.204381	+	0.257510i
$364$	0.622891	+	7.83753i	0.0326483	+	0.410798i
$365$	−4.95956	+	0.602200i	−0.259595	+	0.0315206i
$366$	1.94240	+	16.8868i	0.101531	+	0.882688i
$367$	−20.4172	−	29.5794i	−1.06577	−	1.54403i	−0.818003	−	0.575214i	$-0.804919\pi$
$367$	−20.4172	−	29.5794i	−1.06577	−	1.54403i	−0.247767	−	0.968820i	$-0.579697\pi$
$368$	−20.2845	−	17.9705i	−1.05741	−	0.936779i
$369$	4.84677	+	0.951564i	0.252313	+	0.0495364i
$370$	14.3786	+	18.3530i	0.747509	+	0.954125i
$371$	5.85901	−	18.8022i	0.304184	−	0.976162i
$372$	10.6341	+	5.66709i	0.551355	+	0.293825i
$373$	12.5077	−	18.1206i	0.647625	−	0.938247i	−0.352372	−	0.935860i	$-0.614625\pi$
$373$	12.5077	−	18.1206i	0.647625	−	0.938247i	0.999997	−	0.00238680i	$-0.000759742\pi$
$374$	−25.3641	+	6.25168i	−1.31154	+	0.323267i
$375$	−2.77011	+	1.03062i	−0.143048	+	0.0532210i
$376$	10.7025	−	7.38742i	0.551941	−	0.380977i
$377$	−30.3566	+	0.573607i	−1.56344	+	0.0295423i
$378$	−13.4162	−	10.9269i	−0.690057	−	0.562022i
$379$	8.47980	−	2.64241i	0.435578	−	0.135732i	−0.0718698	−	0.997414i	$-0.522897\pi$
$379$	8.47980	−	2.64241i	0.435578	−	0.135732i	0.507448	+	0.861682i	$0.330589\pi$
$380$	9.65922	−	3.66326i	0.495507	−	0.187921i
$381$	1.79686	−	2.26395i	0.0920558	−	0.115986i
$382$	37.2367	+	6.82389i	1.90520	+	0.349140i
$383$	15.2855	+	25.2852i	0.781051	+	1.29202i	0.951806	+	0.306702i	$0.0992255\pi$
$383$	15.2855	+	25.2852i	0.781051	+	1.29202i	−0.170755	+	0.985314i	$0.554621\pi$
$384$	−12.5485	+	13.9856i	−0.640365	+	0.713700i
$385$	−6.41512	+	14.2538i	−0.326945	+	0.726441i
$386$	5.32080	−	2.01791i	0.270822	−	0.102709i
$387$	−15.7275	+	22.1812i	−0.799473	+	1.12754i
$388$	10.1204	+	3.15364i	0.513784	+	0.160102i
$389$	−26.6717	−	6.57399i	−1.35231	−	0.333314i	−0.504407	−	0.863466i	$-0.668289\pi$
$389$	−26.6717	−	6.57399i	−1.35231	−	0.333314i	−0.847903	+	0.530152i	$0.822135\pi$
$390$	9.74690	−	32.7232i	0.493554	−	1.65700i
$391$	−28.5934	+	7.04763i	−1.44603	+	0.356414i
$392$	5.18459	+	0.313610i	0.261861	+	0.0158397i
$393$	0.671029	−	1.46618i	0.0338489	−	0.0739589i
$394$	5.69170	+	10.8446i	0.286744	+	0.546344i
$395$	12.5439	+	40.2548i	0.631152	+	2.02544i
$396$	7.40125	+	5.95073i	0.371927	+	0.299035i
$397$	22.2783	+	1.34759i	1.11811	+	0.0676335i	0.609077	−	0.793111i	$-0.291540\pi$
$397$	22.2783	+	1.34759i	1.11811	+	0.0676335i	0.509037	+	0.860744i	$0.330002\pi$
$398$	−17.4411	−	22.2619i	−0.874241	−	1.11589i
$399$	−6.65622	+	6.57276i	−0.333228	+	0.329049i
$400$	−14.6568	−	16.5441i	−0.732841	−	0.827207i
$401$	−18.5085	+	1.11956i	−0.924270	+	0.0559080i	−0.515653	−	0.856798i	$-0.672450\pi$
$401$	−18.5085	+	1.11956i	−0.924270	+	0.0559080i	−0.408617	+	0.912706i	$0.633989\pi$
$402$	1.41800	−	21.2202i	0.0707236	−	1.05837i
$403$	−6.79290	−	20.4319i	−0.338379	−	1.01778i
$404$	5.69849	−	10.8576i	0.283511	−	0.540184i
$405$	13.7073	+	24.0236i	0.681119	+	1.19374i
$406$	−3.38000	+	27.8368i	−0.167747	+	1.38152i
$407$	10.2601	+	5.38491i	0.508574	+	0.266920i
$408$	3.24223	+	13.5208i	0.160514	+	0.669379i
$409$	2.71429	−	0.845807i	0.134213	−	0.0418225i	−0.229661	−	0.973271i	$-0.573762\pi$
$409$	2.71429	−	0.845807i	0.134213	−	0.0418225i	0.363874	+	0.931448i	$0.381454\pi$
$410$	8.98530	−	0.543510i	0.443752	−	0.0268421i
$411$	−30.2789	−	11.7023i	−1.49355	−	0.577233i
$412$	−3.25810	+	2.88642i	−0.160515	+	0.142204i
$413$	7.88346	−	11.4212i	0.387920	−	0.561999i
$414$	22.6674	+	18.2250i	1.11404	+	0.895709i
$415$	35.9768	+	13.6442i	1.76603	+	0.669767i
$416$	−21.1187	+	1.67842i	−1.03543	+	0.0822911i
$417$	−14.6976	−	2.78939i	−0.719746	−	0.136597i
$418$	9.86308	−	9.86308i	0.482419	−	0.482419i
$419$	−32.6785	−	12.3933i	−1.59645	−	0.605454i	−0.613560	−	0.789648i	$-0.710263\pi$
$419$	−32.6785	−	12.3933i	−1.59645	−	0.605454i	−0.982890	+	0.184194i	$0.941032\pi$
$420$	−10.5544	−	4.83046i	−0.515003	−	0.235702i
$421$	−10.4631	+	33.5773i	−0.509941	+	1.63646i	0.236958	+	0.971520i	$0.423850\pi$
$421$	−10.4631	+	33.5773i	−0.509941	+	1.63646i	−0.746899	+	0.664938i	$0.768458\pi$
$422$	−17.9800	+	3.29496i	−0.875253	+	0.160396i
$423$	−20.8762	+	15.9345i	−1.01504	+	0.774762i
$424$	14.9222	+	4.64996i	0.724688	+	0.225822i
$425$	−23.8437	+	2.89514i	−1.15659	+	0.140435i
$426$	4.99896	−	3.86579i	0.242200	−	0.187298i
$427$	−7.30119	−	7.30119i	−0.353329	−	0.353329i
$428$	7.58425	+	19.9980i	0.366598	+	0.966640i
$429$	−2.25727	−	16.8186i	−0.108982	−	0.812012i
$430$	−17.5725	+	46.3348i	−0.847420	+	2.23446i
$431$	−3.11370	+	1.40136i	−0.149981	+	0.0675012i	−0.484013	−	0.875061i	$-0.660821\pi$
$431$	−3.11370	+	1.40136i	−0.149981	+	0.0675012i	0.334032	+	0.942562i	$0.391591\pi$
$432$	16.3177	−	20.0350i	0.785085	−	0.963937i
$433$	9.40793	+	10.6194i	0.452116	+	0.510334i	0.929733	−	0.368235i	$-0.120038\pi$
$433$	9.40793	+	10.6194i	0.452116	+	0.510334i	−0.477617	+	0.878568i	$0.658499\pi$
$434$	−19.5600	+	3.58450i	−0.938911	+	0.172062i
$435$	21.0809	−	39.5578i	1.01075	−	1.89665i
$436$	1.18912	+	3.81601i	0.0569484	+	0.182754i
$437$	11.1188	−	11.1188i	0.531886	−	0.531886i
$438$	−2.56438	−	4.30309i	−0.122531	−	0.205610i
$439$	−12.5079	−	1.51874i	−0.596972	−	0.0724855i	−0.183527	−	0.983015i	$-0.558751\pi$
$439$	−12.5079	−	1.51874i	−0.596972	−	0.0724855i	−0.413445	+	0.910529i	$0.635675\pi$
$440$	−11.3124	−	5.09131i	−0.539299	−	0.242719i
$441$	−10.4886	−	0.132350i	−0.499455	−	0.00630238i
$442$	−17.3687	+	29.9971i	−0.826144	+	1.42682i
$443$	−12.1904	−	23.2268i	−0.579182	−	1.10354i	−0.982110	−	0.188308i	$-0.939700\pi$
$443$	−12.1904	−	23.2268i	−0.579182	−	1.10354i	0.402928	−	0.915232i	$-0.367992\pi$
$444$	−4.04675	+	7.59363i	−0.192050	+	0.360378i
$445$	1.95200	−	1.72932i	0.0925335	−	0.0819775i
$446$	−32.7430	−	8.07043i	−1.55043	−	0.382146i
$447$	−4.65334	−	40.4551i	−0.220096	−	1.91346i
$448$	−0.0573696	+	0.948433i	−0.00271046	+	0.0448093i
$449$	16.9381	+	37.6350i	0.799361	+	1.77611i	0.606858	+	0.794810i	$0.292430\pi$
$449$	16.9381	+	37.6350i	0.799361	+	1.77611i	0.192503	+	0.981296i	$0.438340\pi$
$450$	16.5611	+	16.9844i	0.780699	+	0.800653i
$451$	3.96138	−	2.07909i	0.186534	−	0.0979007i
$452$	−0.198971	−	1.63867i	−0.00935879	−	0.0770766i
$453$	20.0419	−	28.6475i	0.941653	−	1.34598i
$454$	−5.07969	−	20.6091i	−0.238401	−	0.967233i
$455$	7.71976	+	19.2503i	0.361908	+	0.902470i
$456$	−5.21642	−	5.28266i	−0.244281	−	0.247383i
$457$	−5.58215	+	17.9137i	−0.261122	+	0.837970i	0.727311	+	0.686308i	$0.240770\pi$
$457$	−5.58215	+	17.9137i	−0.261122	+	0.837970i	−0.988433	+	0.151661i	$0.951538\pi$
$458$	−0.218519	−	0.416353i	−0.0102107	−	0.0194549i
$459$	−7.84482	−	26.9612i	−0.366165	−	1.25844i
$460$	17.7923	+	8.00766i	0.829570	+	0.373359i
$461$	−3.05987	+	16.6972i	−0.142512	+	0.777665i	0.832247	+	0.554406i	$0.187054\pi$
$461$	−3.05987	+	16.6972i	−0.142512	+	0.777665i	−0.974759	+	0.223260i	$0.928330\pi$
$462$	−15.6721	−	0.0988752i	−0.729131	−	0.00460009i
$463$	3.77869	−	20.6197i	0.175611	−	0.958277i	−0.771226	−	0.636562i	$-0.780356\pi$
$463$	3.77869	−	20.6197i	0.175611	−	0.958277i	0.946836	−	0.321715i	$-0.104259\pi$
$464$	−41.5700	−	5.04751i	−1.92984	−	0.234325i
$465$	31.2302	+	5.92703i	1.44826	+	0.274859i
$466$	−3.89084	−	12.4861i	−0.180239	−	0.578409i
$467$	13.9557	−	20.2184i	0.645794	−	0.935594i	−0.354206	−	0.935167i	$-0.615249\pi$
$467$	13.9557	−	20.2184i	0.645794	−	0.935594i	1.00000		0.000426357i	$-0.000135714\pi$
$468$	12.4996	−	1.59739i	0.577795	−	0.0738394i
$469$	7.33873	+	10.6320i	0.338871	+	0.490940i
$470$	−29.5179	+	37.6768i	−1.36156	+	1.73790i
$471$	−3.52527	+	11.0667i	−0.162436	+	0.509927i
$472$	9.06433	+	6.25665i	0.417219	+	0.287986i
$473$	1.48705	+	24.5838i	0.0683745	+	1.13037i
$474$	−31.8202	+	27.8339i	−1.46155	+	1.27845i
$475$	10.0955	−	7.90934i	0.463214	−	0.362905i
$476$	9.27588	+	7.26718i	0.425159	+	0.333091i
$477$	−30.5497	−	7.94000i	−1.39877	−	0.363548i
$478$	7.14048	−	4.92871i	0.326598	−	0.225434i
$479$	−8.28094	−	10.5698i	−0.378366	−	0.482948i	0.560049	−	0.828460i	$-0.310782\pi$
$479$	−8.28094	−	10.5698i	−0.378366	−	0.482948i	−0.938415	+	0.345512i	$0.887705\pi$
$480$	13.0160	−	28.4395i	0.594095	−	1.29808i
$481$	14.5900	−	4.85067i	0.665246	−	0.221172i
$482$	8.35150	+	1.01406i	0.380400	+	0.0461889i
$483$	−17.6674	−	0.111464i	−0.803896	−	0.00507178i
$484$	−4.21301			−0.191501
$485$	27.9636			1.26976
$486$	−16.4659	+	22.3152i	−0.746907	+	1.01224i
$487$	−31.0284	−	13.9647i	−1.40603	−	0.632803i	−0.441618	−	0.897203i	$-0.645595\pi$
$487$	−31.0284	−	13.9647i	−1.40603	−	0.632803i	−0.964413	+	0.264400i	$0.914826\pi$
$488$	5.79454	−	5.79454i	0.262306	−	0.262306i
$489$	−1.62407	+	12.7050i	−0.0734428	+	0.574540i
$490$	−18.5611	+	4.57490i	−0.838505	+	0.206673i
$491$	11.0519	+	9.79110i	0.498764	+	0.441866i	0.874618	−	0.484813i	$-0.161112\pi$
$491$	11.0519	+	9.79110i	0.498764	+	0.441866i	−0.375854	+	0.926679i	$0.622651\pi$
$492$	1.52532	+	2.95135i	0.0687666	+	0.133057i
$493$	−30.1756	+	34.0613i	−1.35904	+	1.53404i
$494$	−0.349661	−	18.5049i	−0.0157320	−	0.832574i
$495$	23.3106	+	9.17861i	1.04773	+	0.412548i
$496$	−5.35290	−	29.2098i	−0.240352	−	1.31156i
$497$	−0.918647	+	3.72710i	−0.0412070	+	0.167183i
$498$	2.08637	+	38.5229i	0.0934923	+	1.72625i
$499$	0.775540	−	1.28290i	0.0347179	−	0.0574305i	−0.837940	−	0.545762i	$-0.816240\pi$
$499$	0.775540	−	1.28290i	0.0347179	−	0.0574305i	0.872658	+	0.488331i	$0.162394\pi$
$500$	−1.70127	−	1.02845i	−0.0760829	−	0.0459937i
$501$	18.0528	−	6.71655i	0.806539	−	0.300073i
$502$	−20.1398	−	1.21823i	−0.898882	−	0.0543723i
$503$	−0.255006	−	0.0967110i	−0.0113702	−	0.00431213i	0.348913	−	0.937155i	$-0.386551\pi$
$503$	−0.255006	−	0.0967110i	−0.0113702	−	0.00431213i	−0.360283	+	0.932843i	$0.617320\pi$
$504$	−0.105251	+	8.34100i	−0.00468825	+	0.371538i
$505$	5.83078	−	31.8175i	0.259466	−	1.41586i
$506$	26.3445			1.17115
$507$	−18.1530	−	13.3217i	−0.806203	−	0.591639i
$508$	1.94408			0.0862544
$509$	5.60320	−	30.5757i	0.248358	−	1.35524i	−0.588799	−	0.808280i	$-0.700399\pi$
$509$	5.60320	−	30.5757i	0.248358	−	1.35524i	0.837156	−	0.546964i	$-0.184216\pi$
$510$	−26.1972	−	43.9595i	−1.16003	−	1.94656i
$511$	2.84511	+	1.07901i	0.125860	+	0.0477325i
$512$	−14.4181	−	0.872133i	−0.637195	−	0.0385432i
$513$	11.0322	+	10.1528i	0.487085	+	0.448257i
$514$	3.79027	+	2.29130i	0.167182	+	0.101065i
$515$	−5.94038	+	9.82658i	−0.261764	+	0.433011i
$516$	−18.2622	+	0.989067i	−0.803949	+	0.0435412i
$517$	−5.69276	+	23.0965i	−0.250367	+	1.01578i
$518$	−2.55962	−	13.9674i	−0.112463	−	0.613693i
$519$	5.65807	+	32.0129i	0.248362	+	1.40521i
$520$	−15.2779	+	6.12673i	−0.669980	+	0.268675i
$521$	7.67203	−	8.65993i	0.336118	−	0.379399i	−0.556015	−	0.831172i	$-0.687670\pi$
$521$	7.67203	−	8.65993i	0.336118	−	0.379399i	0.892132	+	0.451774i	$0.149209\pi$
$522$	44.8236	+	3.27944i	1.96188	+	0.143537i
$523$	−19.2190	−	17.0266i	−0.840390	−	0.744520i	0.128580	−	0.991699i	$-0.458958\pi$
$523$	−19.2190	−	17.0266i	−0.840390	−	0.744520i	−0.968970	+	0.247179i	$0.920497\pi$
$524$	1.05302	−	0.259547i	0.0460015	−	0.0113384i
$525$	−14.2936	−	1.82713i	−0.623823	−	0.0797426i
$526$	−13.2196	+	13.2196i	−0.576401	+	0.576401i
$527$	−29.4275	−	13.2442i	−1.28188	−	0.576929i
$528$	0.147655	−	23.4038i	0.00642585	−	1.01852i
$529$	6.69861			0.291244
$530$	−57.5255			−2.49875
$531$	−18.8882	−	11.7462i	−0.819677	−	0.509743i
$532$	−6.24601	−	0.758403i	−0.270799	−	0.0328809i
$533$	1.65868	−	5.69986i	0.0718454	−	0.246889i
$534$	2.37758	+	1.08815i	0.102888	+	0.0470890i
$535$	34.7959	+	44.4137i	1.50436	+	1.92017i
$536$	−8.43801	+	5.82434i	−0.364466	+	0.251573i
$537$	10.8522	−	3.30671i	0.468307	−	0.142695i
$538$	−31.6895	−	24.8271i	−1.36623	−	1.07037i
$539$	−7.47895	+	5.85938i	−0.322141	+	0.252381i
$540$	−6.92498	+	17.2668i	−0.298004	+	0.743044i
$541$	−1.82399	−	30.1542i	−0.0784196	−	1.29643i	−0.798269	−	0.602301i	$-0.794251\pi$
$541$	−1.82399	−	30.1542i	−0.0784196	−	1.29643i	0.719850	−	0.694130i	$-0.244211\pi$
$542$	32.4256	+	22.3818i	1.39280	+	0.961380i
$543$	33.9632	+	10.8189i	1.45750	+	0.464284i
$544$	−19.5819	+	24.9944i	−0.839565	+	1.07163i
$545$	5.98969	+	8.67757i	0.256570	+	0.371706i
$546$	−14.5185	+	14.8886i	−0.621335	+	0.637173i
$547$	−3.73238	+	5.40728i	−0.159585	+	0.231199i	−0.894617	−	0.446833i	$-0.852552\pi$
$547$	−3.73238	+	5.40728i	−0.159585	+	0.231199i	0.735032	+	0.678032i	$0.237167\pi$
$548$	−6.49566	−	20.8453i	−0.277481	−	0.890467i
$549$	−11.1296	+	12.2478i	−0.474998	+	0.522723i
$550$	21.3300	+	2.58993i	0.909513	+	0.110435i
$551$	4.37978	−	23.8997i	0.186585	−	1.01816i
$552$	0.0884625	−	14.0216i	0.00376521	−	0.596800i
$553$	4.62899	−	25.2596i	0.196845	−	1.07415i
$554$	7.09952	+	3.19523i	0.301630	+	0.135752i
$555$	−4.23237	+	22.3008i	−0.179654	+	0.946618i
$556$	−4.67613	−	8.90962i	−0.198312	−	0.377852i
$557$	−5.14108	+	16.4983i	−0.217835	+	0.699056i	0.779521	+	0.626376i	$0.215463\pi$
$557$	−5.14108	+	16.4983i	−0.217835	+	0.699056i	−0.997355	+	0.0726794i	$0.976845\pi$
$558$	7.23641	+	31.0397i	0.306342	+	1.31401i
$559$	24.8662	+	21.2047i	1.05173	+	0.896863i
$560$	6.84571	+	27.7741i	0.289284	+	1.17367i
$561$	−20.8395	−	14.5794i	−0.879844	−	0.615544i
$562$	5.23256	+	43.0940i	0.220722	+	1.81781i
$563$	7.85101	−	4.12053i	0.330881	−	0.173660i	−0.291099	−	0.956693i	$-0.594021\pi$
$563$	7.85101	−	4.12053i	0.330881	−	0.173660i	0.621980	+	0.783033i	$0.286329\pi$
$564$	−17.1241	−	4.33549i	−0.721055	−	0.182557i
$565$	−1.78716	−	3.97091i	−0.0751865	−	0.167057i
$566$	−1.11295	+	18.3993i	−0.0467809	+	0.773381i
$567$	−0.592511	−	16.8355i	−0.0248831	−	0.707026i
$568$	−2.95798	−	0.729078i	−0.124114	−	0.0305914i
$569$	5.45359	−	4.83146i	0.228626	−	0.202545i	−0.541031	−	0.841003i	$-0.681966\pi$
$569$	5.45359	−	4.83146i	0.228626	−	0.202545i	0.769657	+	0.638458i	$0.220427\pi$
$570$	24.1138	+	12.8506i	1.01002	+	0.538252i
$571$	12.8860	+	24.5522i	0.539261	+	1.02748i	0.990814	+	0.135232i	$0.0431779\pi$
$571$	12.8860	+	24.5522i	0.539261	+	1.02748i	−0.451553	+	0.892244i	$0.649130\pi$
$572$	7.91683	−	8.22178i	0.331019	−	0.343770i
$573$	18.8681	+	31.6611i	0.788226	+	1.32266i
$574$	−4.99955	−	2.25011i	−0.208677	−	0.0939179i
$575$	24.0457	+	2.91967i	1.00277	+	0.121759i
$576$	1.52277	+	0.0192150i	0.0634486	+	0.000800627i
$577$	−19.2371	+	19.2371i	−0.800849	+	0.800849i	−0.983228	−	0.182379i	$-0.941620\pi$
$577$	−19.2371	+	19.2371i	−0.800849	+	0.800849i	0.182379	+	0.983228i	$0.441620\pi$
$578$	6.45799	+	20.7244i	0.268617	+	0.862022i
$579$	4.88934	+	2.60560i	0.203194	+	0.108285i
$580$	29.6553	−	5.43454i	1.23137	−	0.225657i
$581$	−15.5401	−	17.5412i	−0.644714	−	0.727731i
$582$	11.3456	+	25.6398i	0.470289	+	1.06280i
$583$	−26.0712	+	11.7337i	−1.07976	+	0.485961i
$584$	−0.856347	+	2.25800i	−0.0354359	+	0.0934367i
$585$	30.2272	−	13.8329i	1.24974	−	0.571921i
$586$	2.49455	+	6.57758i	0.103049	+	0.271717i
$587$	2.82722	+	2.82722i	0.116692	+	0.116692i	0.763042	−	0.646349i	$-0.223705\pi$
$587$	2.82722	+	2.82722i	0.116692	+	0.116692i	−0.646349	+	0.763042i	$0.723705\pi$
$588$	−4.31597	−	5.58111i	−0.177988	−	0.230161i
$589$	17.1053	−	2.07696i	0.704811	−	0.0855795i
$590$	−38.7011	−	12.0598i	−1.59330	−	0.496492i
$591$	−4.29856	+	11.1222i	−0.176819	+	0.457508i
$592$	20.8581	−	3.82240i	0.857264	−	0.157099i
$593$	10.5607	−	33.8904i	0.433675	−	1.39171i	−0.436826	−	0.899546i	$-0.643897\pi$
$593$	10.5607	−	33.8904i	0.433675	−	1.39171i	0.870501	−	0.492167i	$-0.163795\pi$
$594$	1.04185	+	25.0974i	0.0427477	+	1.02976i
$595$	29.0651	+	11.0229i	1.19155	+	0.451896i
$596$	19.3675	−	19.3675i	0.793324	−	0.793324i
$597$	5.13380	−	27.0506i	0.210112	−	1.10711i
$598$	24.2465	−	25.1804i	0.991512	−	1.02970i
$599$	15.2721	+	5.79196i	0.624003	+	0.236653i	0.646282	−	0.763099i	$-0.276323\pi$
$599$	15.2721	+	5.79196i	0.624003	+	0.236653i	−0.0222792	+	0.999752i	$0.507092\pi$
$600$	1.45009	−	11.3440i	0.0591997	−	0.463117i
$601$	16.9634	−	24.5757i	0.691952	−	1.00247i	−0.306763	−	0.951786i	$-0.599246\pi$
$601$	16.9634	−	24.5757i	0.691952	−	1.00247i	0.998715	−	0.0506797i	$-0.0161388\pi$
$602$	22.5915	−	20.0143i	0.920760	−	0.815722i
$603$	16.4591	−	12.5630i	0.670265	−	0.511604i
$604$	23.4729	−	1.41985i	0.955100	−	0.0577729i
$605$	−10.6107	+	3.30642i	−0.431385	+	0.134425i
$606$	31.5391	−	7.56296i	1.28119	−	0.307224i
$607$	−19.7483	−	10.3647i	−0.801560	−	0.420691i	0.0136143	−	0.999907i	$-0.495666\pi$
$607$	−19.7483	−	10.3647i	−0.801560	−	0.420691i	−0.815174	+	0.579216i	$0.803359\pi$
$608$	2.04356	−	16.8302i	0.0828774	−	0.682557i
$609$	−22.5654	+	15.3665i	−0.914395	+	0.622680i
$610$	−14.0162	+	26.7057i	−0.567500	+	1.08128i
$611$	16.8365	+	26.6983i	0.681132	+	1.08010i
$612$	10.9239	−	15.4065i	0.441573	−	0.622772i
$613$	16.6277	−	1.00579i	0.671586	−	0.0406234i	0.278933	−	0.960310i	$-0.410019\pi$
$613$	16.6277	−	1.00579i	0.671586	−	0.0406234i	0.392652	+	0.919687i	$0.371558\pi$
$614$	−17.5255	−	19.7822i	−0.707273	−	0.798346i
$615$	6.15783	+	6.23602i	0.248308	+	0.251461i
$616$	4.65966	+	5.94762i	0.187743	+	0.239636i
$617$	13.9624	+	0.844568i	0.562104	+	0.0340010i	0.338988	−	0.940791i	$-0.389916\pi$
$617$	13.9624	+	0.844568i	0.562104	+	0.0340010i	0.223116	+	0.974792i	$0.428377\pi$
$618$	−11.4201	−	1.45983i	−0.459386	−	0.0587228i
$619$	0.127439	+	0.408966i	0.00512220	+	0.0164377i	0.957247	−	0.289273i	$-0.0934136\pi$
$619$	0.127439	+	0.408966i	0.00512220	+	0.0164377i	−0.952124	+	0.305711i	$0.901106\pi$
$620$	9.93605	+	18.9316i	0.399041	+	0.760310i
$621$	1.17450	+	28.2928i	0.0471311	+	1.13535i
$622$	−34.7713	−	2.10328i	−1.39420	−	0.0843338i
$623$	−1.54217	+	0.380111i	−0.0617857	+	0.0152288i
$624$	−22.2338	−	21.6811i	−0.890064	−	0.867939i
$625$	−26.6698	−	6.57351i	−1.06679	−	0.262941i
$626$	7.15220	+	2.22872i	0.285859	+	0.0890774i
$627$	13.5499	+	0.905447i	0.541129	+	0.0361601i
$628$	−7.30441	+	2.77020i	−0.291478	+	0.110543i
$629$	9.45745	−	21.0136i	0.377093	−	0.837867i
$630$	−8.76315	−	29.4240i	−0.349132	−	1.17228i
$631$	19.6680	+	32.5348i	0.782969	+	1.29519i	0.950933	+	0.309396i	$0.100127\pi$
$631$	19.6680	+	32.5348i	0.782969	+	1.29519i	−0.167964	+	0.985793i	$0.553719\pi$
$632$	20.0471	+	3.67377i	0.797430	+	0.146135i
$633$	−13.9397	−	11.0637i	−0.554052	−	0.439741i
$634$	24.6206	−	9.33736i	0.977809	−	0.370834i
$635$	4.89624	−	1.52573i	0.194301	−	0.0605468i
$636$	−8.59098	−	19.4147i	−0.340655	−	0.769844i
$637$	−1.28286	+	12.5412i	−0.0508289	+	0.496902i
$638$	33.5021	−	23.1248i	1.32636	−	0.915520i
$639$	6.03716	+	1.18527i	0.238826	+	0.0468886i
$640$	−32.3708	+	7.97869i	−1.27957	+	0.315385i
$641$	2.78479	−	4.03447i	0.109993	−	0.159352i	−0.764122	−	0.645072i	$-0.776827\pi$
$641$	2.78479	−	4.03447i	0.109993	−	0.159352i	0.874114	+	0.485720i	$0.161443\pi$
$642$	−26.6053	+	49.9241i	−1.05003	+	1.97035i
$643$	−4.49950	+	14.4394i	−0.177443	+	0.569435i	0.822557	+	0.568683i	$0.192547\pi$
$643$	−4.49950	+	14.4394i	−0.177443	+	0.569435i	−1.00000		0.000751476i	$0.999761\pi$
$644$	−7.32876	−	9.35447i	−0.288793	−	0.368618i
$645$	−45.2180	+	16.8234i	−1.78046	+	0.662420i
$646$	−20.7632	−	18.3946i	−0.816917	−	0.723725i
$647$	10.1658	+	14.7277i	0.399660	+	0.579007i	0.970213	−	0.242253i	$-0.0778865\pi$
$647$	10.1658	+	14.7277i	0.399660	+	0.579007i	−0.570553	+	0.821261i	$0.693271\pi$
$648$	13.3614	−	0.470242i	0.524886	−	0.0184729i
$649$	−19.9997	+	2.42840i	−0.785056	+	0.0953231i
$650$	22.1068	−	18.0038i	0.867100	−	0.706168i
$651$	−15.1646	−	12.0359i	−0.594349	−	0.471724i
$652$	−7.37256	+	4.45686i	−0.288732	+	0.174544i
$653$			42.5153i			1.66375i	0.554963	+	0.831875i	$0.312733\pi$
$653$			42.5153i			1.66375i	−0.554963	+	0.831875i	$0.687267\pi$
$654$	−5.52628	+	9.01266i	−0.216095	+	0.352423i
$655$	2.44839	−	1.48010i	0.0956665	−	0.0578324i
$656$	3.36019	−	7.46604i	0.131194	−	0.291500i
$657$	1.50954	−	4.63744i	0.0588927	−	0.180924i
$658$	26.5829	−	11.9640i	1.03631	−	0.466406i
$659$	2.74614	+	11.1415i	0.106975	+	0.434013i	0.999868	−	0.0162555i	$-0.00517451\pi$
$659$	2.74614	+	11.1415i	0.106975	+	0.434013i	−0.892893	+	0.450268i	$0.851328\pi$
$660$	4.91148	+	16.1188i	0.191179	+	0.627425i
$661$	−11.5825	−	7.00189i	−0.450508	−	0.272342i	0.273841	−	0.961775i	$-0.411706\pi$
$661$	−11.5825	−	7.00189i	−0.450508	−	0.272342i	−0.724349	+	0.689433i	$0.757860\pi$
$662$	6.91828	+	6.12906i	0.268887	+	0.238213i
$663$	−33.1151	+	6.50032i	−1.28608	+	0.252452i
$664$	13.9214	−	12.3333i	0.540257	−	0.478626i
$665$	−16.3261	+	2.99186i	−0.633098	+	0.116019i
$666$	−22.1648	+	5.16737i	−0.858868	+	0.200232i
$667$	37.7675	−	26.0690i	1.46236	−	1.00940i
$668$	11.0871	+	6.70241i	0.428975	+	0.259324i
$669$	−15.0742	−	29.1672i	−0.582802	−	1.12767i
$670$	23.2723	−	29.7048i	0.899086	−	1.14760i
$671$	−0.905051	+	14.9623i	−0.0349391	+	0.577612i
$672$	−15.0690	+	11.6532i	−0.581300	+	0.449530i
$673$	23.2918	−	44.3788i	0.897833	−	1.71068i	0.219947	−	0.975512i	$-0.429412\pi$
$673$	23.2918	−	44.3788i	0.897833	−	1.71068i	0.677887	−	0.735166i	$-0.262896\pi$
$674$	−21.8796	−	4.00958i	−0.842770	−	0.154443i
$675$	−1.83053	+	23.0229i	−0.0704570	+	0.886152i
$676$	−0.572139	−	15.1340i	−0.0220054	−	0.582079i
$677$		−	12.0964i		−	0.464903i	−0.972608	−	0.232451i	$-0.925325\pi$
$677$		−	12.0964i		−	0.464903i	0.972608	−	0.232451i	$-0.0746746\pi$
$678$	2.91583	−	3.24975i	0.111982	−	0.124806i
$679$	−15.0806	−	7.91491i	−0.578740	−	0.303746i
$680$	−8.74827	+	23.0673i	−0.335481	+	0.884590i
$681$	11.8463	−	16.9328i	0.453949	−	0.648865i
$682$	22.7248	+	17.8037i	0.870177	+	0.681740i
$683$	4.98505	−	8.24629i	0.190748	−	0.315535i	−0.745739	−	0.666238i	$-0.767903\pi$
$683$	4.98505	−	8.24629i	0.190748	−	0.315535i	0.936487	+	0.350703i	$0.114057\pi$
$684$	−0.735838	+	10.0575i	−0.0281355	+	0.384558i
$685$	−32.7192	−	47.4020i	−1.25014	−	1.81114i
$686$	33.9372	+	8.36476i	1.29573	+	0.319368i
$687$	0.165033	−	0.427011i	0.00629640	−	0.0162915i
$688$	29.8882	+	33.7368i	1.13948	+	1.28620i
$689$	−12.7797	+	35.7185i	−0.486870	+	1.36077i
$690$	15.0421	+	49.3663i	0.572644	+	1.87934i
$691$	22.2013	−	36.7254i	0.844577	−	1.39710i	−0.0720687	−	0.997400i	$-0.522960\pi$
$691$	22.2013	−	36.7254i	0.844577	−	1.39710i	0.916646	−	0.399701i	$-0.130886\pi$
$692$	−14.4997	+	16.3668i	−0.551197	+	0.622172i
$693$	−9.97330	−	11.5479i	−0.378854	−	0.438667i
$694$	3.86744	+	8.59311i	0.146806	+	0.326190i
$695$	−18.7694	−	18.7694i	−0.711964	−	0.711964i
$696$	−12.1955	−	17.9088i	−0.462269	−	0.678833i
$697$	−4.60280	−	7.61397i	−0.174344	−	0.288400i
$698$		−	28.9413i		−	1.09544i
$699$	6.65580	−	10.8548i	0.251746	−	0.410565i
$700$	−5.01414	−	8.29439i	−0.189517	−	0.313499i
$701$	−5.59219	+	46.0558i	−0.211214	+	1.73951i	0.372934	+	0.927858i	$0.378352\pi$
$701$	−5.59219	+	46.0558i	−0.211214	+	1.73951i	−0.584148	+	0.811647i	$0.698571\pi$
$702$	24.9474	+	22.1029i	0.941578	+	0.834221i
$703$	1.48311	+	12.2145i	0.0559367	+	0.460680i
$704$	1.08582	−	0.850686i	0.0409234	−	0.0320614i
$705$	−46.5304	+	2.52005i	−1.75243	+	0.0949104i
$706$	−39.3579	+	44.4259i	−1.48125	+	1.67199i
$707$	−12.1502	+	15.5086i	−0.456956	+	0.583262i
$708$	−1.70957	−	14.8626i	−0.0642494	−	0.558570i
$709$	−40.3094	−	12.5609i	−1.51385	−	0.471735i	−0.575613	−	0.817722i	$-0.695236\pi$
$709$	−40.3094	−	12.5609i	−1.51385	−	0.471735i	−0.938239	+	0.345987i	$0.887544\pi$
$710$	11.1921	−	0.676999i	0.420033	−	0.0254073i
$711$	−40.7933	−	5.47634i	−1.52987	−	0.205379i
$712$	−0.301672	−	1.22393i	−0.0113056	−	0.0458688i
$713$	25.6181	+	20.0705i	0.959404	+	0.751645i
$714$	1.68554	+	31.1220i	0.0630799	+	1.16471i
$715$	13.4864	−	26.9201i	0.504361	−	1.00676i
$716$	6.27985	+	4.33467i	0.234689	+	0.161994i
$717$	8.18878	+	2.07324i	0.305816	+	0.0774265i
$718$	3.09358	+	8.15711i	0.115452	+	0.304421i
$719$	2.29126	−	18.8702i	0.0854495	−	0.703740i	−0.885531	−	0.464581i	$-0.846205\pi$
$719$	2.29126	−	18.8702i	0.0854495	−	0.703740i	0.970980	−	0.239159i	$-0.0768718\pi$
$720$	43.9402	−	13.0864i	1.63755	−	0.487701i
$721$	5.98495	−	3.61803i	0.222891	−	0.134742i
$722$	−18.6793	−	3.42310i	−0.695170	−	0.127395i
$723$	4.61018	+	6.76997i	0.171455	+	0.251778i
$724$	8.50162	+	22.4169i	0.315960	+	0.833119i
$725$	33.1415	−	17.3940i	1.23085	−	0.645997i
$726$	−7.33667	−	8.38741i	−0.272289	−	0.311286i
$727$	8.65004	−	35.0946i	0.320812	−	1.30159i	−0.560146	−	0.828394i	$-0.689255\pi$
$727$	8.65004	−	35.0946i	0.320812	−	1.30159i	0.880959	−	0.473193i	$-0.156899\pi$
$728$	9.97339	+	1.02019i	0.369639	+	0.0378109i
$729$	−26.9071	+	2.23781i	−0.996559	+	0.0828818i
$730$	0.536649	−	8.87186i	0.0198623	−	0.328362i
$731$	48.6220	−	5.90378i	1.79835	−	0.218359i
$732$	−11.1063	−	0.742162i	−0.410502	−	0.0274311i
$733$	0.103373	−	0.0322125i	0.00381819	−	0.00118980i	−0.295593	−	0.955314i	$-0.595517\pi$
$733$	0.103373	−	0.0322125i	0.00381819	−	0.00118980i	0.299412	+	0.954124i	$0.403210\pi$
$734$	58.3085	−	26.2425i	2.15221	−	0.968629i
$735$	−15.2501	−	10.6690i	−0.562508	−	0.393534i
$736$	25.2062	−	19.7478i	0.929111	−	0.727912i
$737$	4.48825	−	18.2095i	0.165327	−	0.670757i
$738$	−3.21941	+	8.17622i	−0.118508	+	0.300971i
$739$	−2.38556	−	39.4380i	−0.0877543	−	1.45075i	−0.729577	−	0.683898i	$-0.760283\pi$
$739$	−2.38556	−	39.4380i	−0.0877543	−	1.45075i	0.641823	−	0.766853i	$-0.278178\pi$
$740$	−13.5186	+	7.09513i	−0.496955	+	0.260822i
$741$	13.3362	−	12.1178i	0.489918	−	0.445158i
$742$	31.0231	+	16.2822i	1.13889	+	0.597738i
$743$	8.94859	−	19.8830i	0.328292	−	0.729435i	−0.671643	−	0.740875i	$-0.734411\pi$
$743$	8.94859	−	19.8830i	0.328292	−	0.729435i	0.999935	+	0.0114406i	$0.00364172\pi$
$744$	9.55220	−	12.0353i	0.350201	−	0.441235i
$745$	33.5781	−	63.9777i	1.23021	−	2.34396i
$746$	27.6982	+	27.6982i	1.01410	+	1.01410i
$747$	−26.8921	+	26.2219i	−0.983932	+	0.959410i
$748$	−1.03286	−	17.0753i	−0.0377653	−	0.624334i
$749$	−6.19422	−	33.8008i	−0.226332	−	1.23505i
$750$	−0.915162	−	5.17791i	−0.0334170	−	0.189071i
$751$	−28.8589	−	19.9199i	−1.05308	−	0.726886i	−0.0899530	−	0.995946i	$-0.528672\pi$
$751$	−28.8589	−	19.9199i	−1.05308	−	0.726886i	−0.963123	+	0.269060i	$0.913287\pi$
$752$	17.8664	+	39.6975i	0.651520	+	1.44762i
$753$	−12.0168	−	15.5393i	−0.437917	−	0.566283i
$754$	8.73103	−	53.3049i	0.317965	−	1.94125i
$755$	58.0033	−	21.9978i	2.11096	−	0.800580i
$756$	8.62183	−	7.35179i	0.313573	−	0.267382i
$757$	−11.1359	+	29.3628i	−0.404739	+	1.06721i	0.565433	+	0.824794i	$0.308709\pi$
$757$	−11.1359	+	29.3628i	−0.404739	+	1.06721i	−0.970172	+	0.242416i	$0.922060\pi$
$758$	1.90465	+	15.6862i	0.0691799	+	0.569748i
$759$	16.8867	+	19.3052i	0.612949	+	0.700734i
$760$	−2.37447	−	12.9571i	−0.0861311	−	0.470002i
$761$	0.313032	+	1.70816i	0.0113474	+	0.0619207i	0.988806	−	0.149205i	$-0.0476716\pi$
$761$	0.313032	+	1.70816i	0.0113474	+	0.0619207i	−0.977459	+	0.211126i	$0.932287\pi$
$762$	3.38547	+	3.87033i	0.122643	+	0.140207i
$763$	−0.774077	−	6.37509i	−0.0280235	−	0.230794i
$764$	−8.79073	+	23.1792i	−0.318037	+	0.838596i
$765$	15.4212	−	47.3752i	0.557553	−	1.71285i
$766$	−49.1484	+	18.6395i	−1.77580	+	0.673474i
$767$	−16.0859	+	21.3510i	−0.580827	+	0.770940i
$768$	−21.5251	−	27.8347i	−0.776719	−	1.00440i
$769$	1.57936	+	3.50919i	0.0569532	+	0.126545i	0.938179	−	0.346151i	$-0.112512\pi$
$769$	1.57936	+	3.50919i	0.0569532	+	0.126545i	−0.881226

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.320681 + 1.74990i) q^{2} +(-1.48788 + 0.886686i) q^{3} +(-1.08928 - 0.413111i) q^{4} +(-3.06762 - 0.185557i) q^{5} +(-1.07448 - 2.88799i) q^{6} +(1.60183 + 0.968339i) q^{7} +(-0.768515 + 1.27128i) q^{8} +(1.42758 - 2.63857i) q^{9} +(1.30844 - 5.30853i) q^{10} +(-0.489805 - 2.67278i) q^{11} +(1.98702 - 0.351193i) q^{12} +(-3.00548 - 1.99176i) q^{13} +(-2.20817 + 2.49251i) q^{14} +(4.72879 - 2.44393i) q^{15} +(-3.72218 - 3.29756i) q^{16} +(-5.24683 + 1.29323i) q^{17} +(4.15943 + 3.34425i) q^{18} +(2.04029 - 2.04029i) q^{19} +(3.26486 + 1.46939i) q^{20} +(-3.24194 - 0.0204534i) q^{21} +4.83417 q^{22} +5.44964 q^{23} +(0.0162327 - 2.57294i) q^{24} +(4.41234 + 0.535755i) q^{25} +(4.44918 - 4.62056i) q^{26} +(0.215519 + 5.19168i) q^{27} +(-1.34481 - 1.71653i) q^{28} +(6.93027 - 4.78362i) q^{29} +(2.76021 + 9.05863i) q^{30} +(4.70087 + 3.68290i) q^{31} +(4.62529 - 3.62368i) q^{32} +(3.09868 + 3.54247i) q^{33} +(-0.580460 - 9.59615i) q^{34} +(-4.73412 - 3.26773i) q^{35} +(-2.64505 + 2.28440i) q^{36} +(-2.62988 + 3.35680i) q^{37} +(2.91602 + 4.22458i) q^{38} +(6.23786 + 0.298589i) q^{39} +(2.59341 - 3.75720i) q^{40} +(0.489819 + 1.57188i) q^{41} +(1.07542 - 5.66652i) q^{42} +(-8.99765 - 1.09251i) q^{43} +(-0.570617 + 3.11376i) q^{44} +(-4.86887 + 7.82923i) q^{45} +(-1.74760 + 9.53633i) q^{46} +(-7.98296 - 3.59284i) q^{47} +(8.46206 + 1.60597i) q^{48} +(-1.62489 - 3.09597i) q^{49} +(-2.35247 + 7.54935i) q^{50} +(6.65997 - 6.57646i) q^{51} +(2.45100 + 3.41119i) q^{52} +(-2.51797 - 10.2158i) q^{53} +(-9.15404 - 1.28774i) q^{54} +(1.00658 + 8.28996i) q^{55} +(-2.46206 + 1.29219i) q^{56} +(-1.22661 + 4.84479i) q^{57} +(6.14845 + 13.6613i) q^{58} +(0.447660 - 7.40070i) q^{59} +(-6.16060 + 0.708623i) q^{60} +(-5.35610 - 1.32016i) q^{61} +(-7.95219 + 7.04502i) q^{62} +(4.84176 - 2.84415i) q^{63} +(0.235907 + 0.449483i) q^{64} +(8.85008 + 6.66766i) q^{65} +(-7.19266 + 4.28639i) q^{66} +(6.29386 + 2.83264i) q^{67} +(6.24953 + 0.758831i) q^{68} +(-8.10842 + 4.83212i) q^{69} +(7.23635 - 7.23635i) q^{70} +(0.610121 + 1.95795i) q^{71} +(2.25724 + 3.84263i) q^{72} +(1.59902 - 0.293031i) q^{73} +(-5.03071 - 5.67849i) q^{74} +(-7.04008 + 3.11522i) q^{75} +(-3.06531 + 1.37959i) q^{76} +(1.80357 - 4.75563i) q^{77} +(-2.52286 + 10.8199i) q^{78} +(-4.86508 - 12.8282i) q^{79} +(10.8064 + 10.8064i) q^{80} +(-4.92406 - 7.53350i) q^{81} +(-2.90772 + 0.353061i) q^{82} +(-11.9532 - 3.72477i) q^{83} +(3.52294 + 1.36156i) q^{84} +(16.3353 - 2.99355i) q^{85} +(4.79716 - 15.3946i) q^{86} +(-6.06984 + 13.2624i) q^{87} +(3.77427 + 1.43139i) q^{88} +(-0.600027 + 0.600027i) q^{89} +(-12.1390 - 11.0307i) q^{90} +(-2.88556 - 6.10078i) q^{91} +(-5.93621 - 2.25131i) q^{92} +(-10.2599 - 1.31151i) q^{93} +(8.84709 - 12.8172i) q^{94} +(-6.63742 + 5.88024i) q^{95} +(-3.66880 + 9.49278i) q^{96} +(-9.08250 + 0.549390i) q^{97} +(5.93870 - 1.85057i) q^{98} +(-7.75153 - 2.52321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

L-functions

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