LMFDB - Embedded newform 30.3.b.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,3,Mod(29,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("30.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	30.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.817440793081$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 16x^{2} + 81 $ x^4 + 16*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.2
Root			$0.707107 - 2.91548i$ of defining polynomial
Character	$\chi$	$=$	30.29
Dual form			30.3.b.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(0.707107 + 2.91548i) q^{3} +2.00000 q^{4} +(2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} -5.83095i q^{7} -2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(0.707107 + 2.91548i) q^{3} +2.00000 q^{4} +(2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} -5.83095i q^{7} -2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +(-4.00000 - 5.83095i) q^{10} -16.4924i q^{11} +(1.41421 + 5.83095i) q^{12} +8.24621i q^{14} +(-10.0208 + 11.1617i) q^{15} +4.00000 q^{16} +11.3137 q^{17} +(11.3137 - 5.83095i) q^{18} +12.0000 q^{19} +(5.65685 + 8.24621i) q^{20} +(17.0000 - 4.12311i) q^{21} +23.3238i q^{22} -24.0416 q^{23} +(-2.00000 - 8.24621i) q^{24} +(-9.00000 + 23.3238i) q^{25} +(-17.6777 - 20.4083i) q^{27} -11.6619i q^{28} +(14.1716 - 15.7850i) q^{30} -32.0000 q^{31} -5.65685 q^{32} +(48.0833 - 11.6619i) q^{33} -16.0000 q^{34} +(24.0416 - 16.4924i) q^{35} +(-16.0000 + 8.24621i) q^{36} -23.3238i q^{37} -16.9706 q^{38} +(-8.00000 - 11.6619i) q^{40} +57.7235i q^{41} +(-24.0416 + 5.83095i) q^{42} +40.8167i q^{43} -32.9848i q^{44} +(-39.6274 - 21.3229i) q^{45} +34.0000 q^{46} +35.3553 q^{47} +(2.82843 + 11.6619i) q^{48} +15.0000 q^{49} +(12.7279 - 32.9848i) q^{50} +(8.00000 + 32.9848i) q^{51} -67.8823 q^{53} +(25.0000 + 28.8617i) q^{54} +(68.0000 - 46.6476i) q^{55} +16.4924i q^{56} +(8.48528 + 34.9857i) q^{57} -16.4924i q^{59} +(-20.0416 + 22.3234i) q^{60} -16.0000 q^{61} +45.2548 q^{62} +(24.0416 + 46.6476i) q^{63} +8.00000 q^{64} +(-68.0000 + 16.4924i) q^{66} +5.83095i q^{67} +22.6274 q^{68} +(-17.0000 - 70.0928i) q^{69} +(-34.0000 + 23.3238i) q^{70} +(22.6274 - 11.6619i) q^{72} -116.619i q^{73} +32.9848i q^{74} +(-74.3640 - 9.74686i) q^{75} +24.0000 q^{76} -96.1665 q^{77} -72.0000 q^{79} +(11.3137 + 16.4924i) q^{80} +(47.0000 - 65.9697i) q^{81} -81.6333i q^{82} +43.8406 q^{83} +(34.0000 - 8.24621i) q^{84} +(32.0000 + 46.6476i) q^{85} -57.7235i q^{86} +46.6476i q^{88} +65.9697i q^{89} +(56.0416 + 30.1552i) q^{90} -48.0833 q^{92} +(-22.6274 - 93.2952i) q^{93} -50.0000 q^{94} +(33.9411 + 49.4773i) q^{95} +(-4.00000 - 16.4924i) q^{96} +163.267i q^{97} -21.2132 q^{98} +(68.0000 + 131.939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9	$ 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9} - 16 q^{10} + 8 q^{15} + 16 q^{16} + 48 q^{19} + 68 q^{21} - 8 q^{24} - 36 q^{25} + 68 q^{30} - 128 q^{31} - 64 q^{34} - 64 q^{36} - 32 q^{40} - 68 q^{45} + 136 q^{46} + 60 q^{49} + 32 q^{51} + 100 q^{54} + 272 q^{55} + 16 q^{60} - 64 q^{61} + 32 q^{64} - 272 q^{66} - 68 q^{69} - 136 q^{70} - 272 q^{75} + 96 q^{76} - 288 q^{79} + 188 q^{81} + 136 q^{84} + 128 q^{85} + 128 q^{90} - 200 q^{94} - 16 q^{96} + 272 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9 - 16 * q^10 + 8 * q^15 + 16 * q^16 + 48 * q^19 + 68 * q^21 - 8 * q^24 - 36 * q^25 + 68 * q^30 - 128 * q^31 - 64 * q^34 - 64 * q^36 - 32 * q^40 - 68 * q^45 + 136 * q^46 + 60 * q^49 + 32 * q^51 + 100 * q^54 + 272 * q^55 + 16 * q^60 - 64 * q^61 + 32 * q^64 - 272 * q^66 - 68 * q^69 - 136 * q^70 - 272 * q^75 + 96 * q^76 - 288 * q^79 + 188 * q^81 + 136 * q^84 + 128 * q^85 + 128 * q^90 - 200 * q^94 - 16 * q^96 + 272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	0.707107	+	2.91548i	0.235702	+	0.971825i
$3$	0.707107	+	2.91548i	0.235702	+	0.971825i
$4$	2.00000			0.500000
$5$	2.82843	+	4.12311i	0.565685	+	0.824621i
$5$	2.82843	+	4.12311i	0.565685	+	0.824621i
$6$	−1.00000	−	4.12311i	−0.166667	−	0.687184i
$7$		−	5.83095i		−	0.832993i	−0.909137	−	0.416497i	$-0.863258\pi$
$7$		−	5.83095i		−	0.832993i	0.909137	−	0.416497i	$-0.136742\pi$
$8$	−2.82843			−0.353553
$9$	−8.00000	+	4.12311i	−0.888889	+	0.458123i
$10$	−4.00000	−	5.83095i	−0.400000	−	0.583095i
$11$		−	16.4924i		−	1.49931i	−0.661828	−	0.749656i	$-0.730219\pi$
$11$		−	16.4924i		−	1.49931i	0.661828	−	0.749656i	$-0.269781\pi$
$12$	1.41421	+	5.83095i	0.117851	+	0.485913i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$			8.24621i			0.589015i
$15$	−10.0208	+	11.1617i	−0.668054	+	0.744112i
$16$	4.00000			0.250000
$17$	11.3137			0.665512			0.332756	−	0.943013i	$-0.392021\pi$
$17$	11.3137			0.665512			0.332756	+	0.943013i	$0.392021\pi$
$18$	11.3137	−	5.83095i	0.628539	−	0.323942i
$19$	12.0000			0.631579			0.315789	−	0.948829i	$-0.397731\pi$
$19$	12.0000			0.631579			0.315789	+	0.948829i	$0.397731\pi$
$20$	5.65685	+	8.24621i	0.282843	+	0.412311i
$21$	17.0000	−	4.12311i	0.809524	−	0.196338i
$22$			23.3238i			1.06017i
$23$	−24.0416			−1.04529			−0.522644	−	0.852551i	$-0.675054\pi$
$23$	−24.0416			−1.04529			−0.522644	+	0.852551i	$0.675054\pi$
$24$	−2.00000	−	8.24621i	−0.0833333	−	0.343592i
$25$	−9.00000	+	23.3238i	−0.360000	+	0.932952i
$26$		0			0
$27$	−17.6777	−	20.4083i	−0.654729	−	0.755864i
$28$		−	11.6619i		−	0.416497i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	14.1716	−	15.7850i	0.472386	−	0.526167i
$31$	−32.0000			−1.03226			−0.516129	−	0.856511i	$-0.672628\pi$
$31$	−32.0000			−1.03226			−0.516129	+	0.856511i	$0.672628\pi$
$32$	−5.65685			−0.176777
$33$	48.0833	−	11.6619i	1.45707	−	0.353391i
$34$	−16.0000			−0.470588
$35$	24.0416	−	16.4924i	0.686904	−	0.471212i
$36$	−16.0000	+	8.24621i	−0.444444	+	0.229061i
$37$		−	23.3238i		−	0.630373i	−0.949030	−	0.315187i	$-0.897933\pi$
$37$		−	23.3238i		−	0.630373i	0.949030	−	0.315187i	$-0.102067\pi$
$38$	−16.9706			−0.446594
$39$		0			0
$40$	−8.00000	−	11.6619i	−0.200000	−	0.291548i
$41$			57.7235i			1.40789i	0.710255	+	0.703945i	$0.248580\pi$
$41$			57.7235i			1.40789i	−0.710255	+	0.703945i	$0.751420\pi$
$42$	−24.0416	+	5.83095i	−0.572420	+	0.138832i
$43$			40.8167i			0.949225i	0.880195	+	0.474612i	$0.157412\pi$
$43$			40.8167i			0.949225i	−0.880195	+	0.474612i	$0.842588\pi$
$44$		−	32.9848i		−	0.749656i
$45$	−39.6274	−	21.3229i	−0.880609	−	0.473843i
$46$	34.0000			0.739130
$47$	35.3553			0.752241			0.376121	−	0.926571i	$-0.377258\pi$
$47$	35.3553			0.752241			0.376121	+	0.926571i	$0.377258\pi$
$48$	2.82843	+	11.6619i	0.0589256	+	0.242956i
$49$	15.0000			0.306122
$50$	12.7279	−	32.9848i	0.254558	−	0.659697i
$51$	8.00000	+	32.9848i	0.156863	+	0.646762i
$52$		0			0
$53$	−67.8823			−1.28080			−0.640399	−	0.768043i	$-0.721231\pi$
$53$	−67.8823			−1.28080			−0.640399	+	0.768043i	$0.721231\pi$
$54$	25.0000	+	28.8617i	0.462963	+	0.534477i
$55$	68.0000	−	46.6476i	1.23636	−	0.848138i
$56$			16.4924i			0.294508i
$57$	8.48528	+	34.9857i	0.148865	+	0.613784i
$58$		0			0
$59$		−	16.4924i		−	0.279533i	−0.990185	−	0.139766i	$-0.955365\pi$
$59$		−	16.4924i		−	0.279533i	0.990185	−	0.139766i	$-0.0446351\pi$
$60$	−20.0416	+	22.3234i	−0.334027	+	0.372056i
$61$	−16.0000			−0.262295			−0.131148	−	0.991363i	$-0.541866\pi$
$61$	−16.0000			−0.262295			−0.131148	+	0.991363i	$0.541866\pi$
$62$	45.2548			0.729917
$63$	24.0416	+	46.6476i	0.381613	+	0.740438i
$64$	8.00000			0.125000
$65$		0			0
$66$	−68.0000	+	16.4924i	−1.03030	+	0.249885i
$67$			5.83095i			0.0870291i	0.999053	+	0.0435146i	$0.0138555\pi$
$67$			5.83095i			0.0870291i	−0.999053	+	0.0435146i	$0.986145\pi$
$68$	22.6274			0.332756
$69$	−17.0000	−	70.0928i	−0.246377	−	1.01584i
$70$	−34.0000	+	23.3238i	−0.485714	+	0.333197i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	22.6274	−	11.6619i	0.314270	−	0.161971i
$73$		−	116.619i		−	1.59752i	−0.601649	−	0.798761i	$-0.705489\pi$
$73$		−	116.619i		−	1.59752i	0.601649	−	0.798761i	$-0.294511\pi$
$74$			32.9848i			0.445741i
$75$	−74.3640	−	9.74686i	−0.991519	−	0.129958i
$76$	24.0000			0.315789
$77$	−96.1665			−1.24892
$78$		0			0
$79$	−72.0000			−0.911392			−0.455696	−	0.890135i	$-0.650610\pi$
$79$	−72.0000			−0.911392			−0.455696	+	0.890135i	$0.650610\pi$
$80$	11.3137	+	16.4924i	0.141421	+	0.206155i
$81$	47.0000	−	65.9697i	0.580247	−	0.814441i
$82$		−	81.6333i		−	0.995528i
$83$	43.8406			0.528200			0.264100	−	0.964495i	$-0.414925\pi$
$83$	43.8406			0.528200			0.264100	+	0.964495i	$0.414925\pi$
$84$	34.0000	−	8.24621i	0.404762	−	0.0981692i
$85$	32.0000	+	46.6476i	0.376471	+	0.548795i
$86$		−	57.7235i		−	0.671203i
$87$		0			0
$88$			46.6476i			0.530087i
$89$			65.9697i			0.741232i	0.928786	+	0.370616i	$0.120853\pi$
$89$			65.9697i			0.741232i	−0.928786	+	0.370616i	$0.879147\pi$
$90$	56.0416	+	30.1552i	0.622685	+	0.335058i
$91$		0			0
$92$	−48.0833			−0.522644
$93$	−22.6274	−	93.2952i	−0.243306	−	1.00317i
$94$	−50.0000			−0.531915
$95$	33.9411	+	49.4773i	0.357275	+	0.520813i
$96$	−4.00000	−	16.4924i	−0.0416667	−	0.171796i
$97$			163.267i			1.68316i	0.540131	+	0.841581i	$0.318375\pi$
$97$			163.267i			1.68316i	−0.540131	+	0.841581i	$0.681625\pi$
$98$	−21.2132			−0.216461
$99$	68.0000	+	131.939i	0.686869	+	1.33272i
$100$	−18.0000	+	46.6476i	−0.180000	+	0.466476i
$101$		−	131.939i		−	1.30633i	−0.757215	−	0.653165i	$-0.773441\pi$
$101$		−	131.939i		−	1.30633i	0.757215	−	0.653165i	$-0.226559\pi$
$102$	−11.3137	−	46.6476i	−0.110919	−	0.457330i
$103$			99.1262i			0.962390i	0.876614	+	0.481195i	$0.159797\pi$
$103$			99.1262i			0.962390i	−0.876614	+	0.481195i	$0.840203\pi$
$104$		0			0
$105$	65.0833	+	58.4309i	0.619841	+	0.556485i
$106$	96.0000			0.905660
$107$	55.1543			0.515461			0.257731	−	0.966217i	$-0.417025\pi$
$107$	55.1543			0.515461			0.257731	+	0.966217i	$0.417025\pi$
$108$	−35.3553	−	40.8167i	−0.327364	−	0.377932i
$109$	80.0000			0.733945			0.366972	−	0.930232i	$-0.380394\pi$
$109$	80.0000			0.733945			0.366972	+	0.930232i	$0.380394\pi$
$110$	−96.1665	+	65.9697i	−0.874241	+	0.599724i
$111$	68.0000	−	16.4924i	0.612613	−	0.148580i
$112$		−	23.3238i		−	0.208248i
$113$	152.735			1.35164			0.675819	−	0.737068i	$-0.263790\pi$
$113$	152.735			1.35164			0.675819	+	0.737068i	$0.263790\pi$
$114$	−12.0000	−	49.4773i	−0.105263	−	0.434011i
$115$	−68.0000	−	99.1262i	−0.591304	−	0.861967i
$116$		0			0
$117$		0			0
$118$			23.3238i			0.197659i
$119$		−	65.9697i		−	0.554367i
$120$	28.3431	−	31.5700i	0.236193	−	0.263083i
$121$	−151.000			−1.24793
$122$	22.6274			0.185471
$123$	−168.291	+	40.8167i	−1.36822	+	0.331843i
$124$	−64.0000			−0.516129
$125$	−121.622	+	28.8617i	−0.972979	+	0.230894i
$126$	−34.0000	−	65.9697i	−0.269841	−	0.523569i
$127$		−	40.8167i		−	0.321391i	−0.987004	−	0.160696i	$-0.948626\pi$
$127$		−	40.8167i		−	0.321391i	0.987004	−	0.160696i	$-0.0513737\pi$
$128$	−11.3137			−0.0883883
$129$	−119.000	+	28.8617i	−0.922481	+	0.223734i
$130$		0			0
$131$		−	49.4773i		−	0.377689i	−0.982007	−	0.188845i	$-0.939526\pi$
$131$		−	49.4773i		−	0.377689i	0.982007	−	0.188845i	$-0.0604742\pi$
$132$	96.1665	−	23.3238i	0.728534	−	0.176696i
$133$		−	69.9714i		−	0.526101i
$134$		−	8.24621i		−	0.0615389i
$135$	34.1457	−	130.610i	0.252931	−	0.967484i
$136$	−32.0000			−0.235294
$137$	50.9117			0.371618			0.185809	−	0.982586i	$-0.440509\pi$
$137$	50.9117			0.371618			0.185809	+	0.982586i	$0.440509\pi$
$138$	24.0416	+	99.1262i	0.174215	+	0.718306i
$139$	44.0000			0.316547			0.158273	−	0.987395i	$-0.449407\pi$
$139$	44.0000			0.316547			0.158273	+	0.987395i	$0.449407\pi$
$140$	48.0833	−	32.9848i	0.343452	−	0.235606i
$141$	25.0000	+	103.078i	0.177305	+	0.731047i
$142$		0			0
$143$		0			0
$144$	−32.0000	+	16.4924i	−0.222222	+	0.114531i
$145$		0			0
$146$			164.924i			1.12962i
$147$	10.6066	+	43.7321i	0.0721538	+	0.297498i
$148$		−	46.6476i		−	0.315187i
$149$			8.24621i			0.0553437i	0.999617	+	0.0276718i	$0.00880935\pi$
$149$			8.24621i			0.0553437i	−0.999617	+	0.0276718i	$0.991191\pi$
$150$	105.167	+	13.7841i	0.701110	+	0.0918943i
$151$	136.000			0.900662			0.450331	−	0.892862i	$-0.351306\pi$
$151$	136.000			0.900662			0.450331	+	0.892862i	$0.351306\pi$
$152$	−33.9411			−0.223297
$153$	−90.5097	+	46.6476i	−0.591566	+	0.304886i
$154$	136.000			0.883117
$155$	−90.5097	−	131.939i	−0.583933	−	0.851222i
$156$		0			0
$157$		−	116.619i		−	0.742796i	−0.928474	−	0.371398i	$-0.878878\pi$
$157$		−	116.619i		−	0.742796i	0.928474	−	0.371398i	$-0.121122\pi$
$158$	101.823			0.644452
$159$	−48.0000	−	197.909i	−0.301887	−	1.24471i
$160$	−16.0000	−	23.3238i	−0.100000	−	0.145774i
$161$			140.186i			0.870718i
$162$	−66.4680	+	93.2952i	−0.410297	+	0.575896i
$163$			99.1262i			0.608136i	0.952650	+	0.304068i	$0.0983450\pi$
$163$			99.1262i			0.608136i	−0.952650	+	0.304068i	$0.901655\pi$
$164$			115.447i			0.703945i
$165$	184.083	+	165.268i	1.11566	+	1.00162i
$166$	−62.0000			−0.373494
$167$	−292.742			−1.75295			−0.876474	−	0.481450i	$-0.840110\pi$
$167$	−292.742			−1.75295			−0.876474	+	0.481450i	$0.840110\pi$
$168$	−48.0833	+	11.6619i	−0.286210	+	0.0694161i
$169$	169.000			1.00000
$170$	−45.2548	−	65.9697i	−0.266205	−	0.388057i
$171$	−96.0000	+	49.4773i	−0.561404	+	0.289341i
$172$			81.6333i			0.474612i
$173$	164.049			0.948259			0.474129	−	0.880455i	$-0.342763\pi$
$173$	164.049			0.948259			0.474129	+	0.880455i	$0.342763\pi$
$174$		0			0
$175$	136.000	+	52.4786i	0.777143	+	0.299878i
$176$		−	65.9697i		−	0.374828i
$177$	48.0833	−	11.6619i	0.271657	−	0.0658865i
$178$		−	93.2952i		−	0.524131i
$179$		−	16.4924i		−	0.0921364i	−0.998938	−	0.0460682i	$-0.985331\pi$
$179$		−	16.4924i		−	0.0921364i	0.998938	−	0.0460682i	$-0.0146692\pi$
$180$	−79.2548	−	42.6459i	−0.440305	−	0.236922i
$181$	−82.0000			−0.453039			−0.226519	−	0.974007i	$-0.572735\pi$
$181$	−82.0000			−0.453039			−0.226519	+	0.974007i	$0.572735\pi$
$182$		0			0
$183$	−11.3137	−	46.6476i	−0.0618235	−	0.254905i
$184$	68.0000			0.369565
$185$	96.1665	−	65.9697i	0.519819	−	0.356593i
$186$	32.0000	+	131.939i	0.172043	+	0.709352i
$187$		−	186.590i		−	0.997810i
$188$	70.7107			0.376121
$189$	−119.000	+	103.078i	−0.629630	+	0.545384i
$190$	−48.0000	−	69.9714i	−0.252632	−	0.368271i
$191$			296.864i			1.55426i	0.629340	+	0.777130i	$0.283325\pi$
$191$			296.864i			1.55426i	−0.629340	+	0.777130i	$0.716675\pi$
$192$	5.65685	+	23.3238i	0.0294628	+	0.121478i
$193$		−	116.619i		−	0.604244i	−0.953269	−	0.302122i	$-0.902305\pi$
$193$		−	116.619i		−	0.604244i	0.953269	−	0.302122i	$-0.0976950\pi$
$194$		−	230.894i		−	1.19017i
$195$		0			0
$196$	30.0000			0.153061
$197$	192.333			0.976310			0.488155	−	0.872757i	$-0.337670\pi$
$197$	192.333			0.976310			0.488155	+	0.872757i	$0.337670\pi$
$198$	−96.1665	−	186.590i	−0.485690	−	0.942376i
$199$	−312.000			−1.56784			−0.783920	−	0.620862i	$-0.786783\pi$
$199$	−312.000			−1.56784			−0.783920	+	0.620862i	$0.786783\pi$
$200$	25.4558	−	65.9697i	0.127279	−	0.329848i
$201$	−17.0000	+	4.12311i	−0.0845771	+	0.0205130i
$202$			186.590i			0.923715i
$203$		0			0
$204$	16.0000	+	65.9697i	0.0784314	+	0.323381i
$205$	−238.000	+	163.267i	−1.16098	+	0.796423i
$206$		−	140.186i		−	0.680513i
$207$	192.333	−	99.1262i	0.929145	−	0.478870i
$208$		0			0
$209$		−	197.909i		−	0.946933i
$210$	−92.0416	−	82.6338i	−0.438293	−	0.393494i
$211$	−12.0000			−0.0568720			−0.0284360	−	0.999596i	$-0.509053\pi$
$211$	−12.0000			−0.0568720			−0.0284360	+	0.999596i	$0.509053\pi$
$212$	−135.765			−0.640399
$213$		0			0
$214$	−78.0000			−0.364486
$215$	−168.291	+	115.447i	−0.782751	+	0.536963i
$216$	50.0000	+	57.7235i	0.231481	+	0.267238i
$217$			186.590i			0.859864i
$218$	−113.137			−0.518977
$219$	340.000	−	82.4621i	1.55251	−	0.376539i
$220$	136.000	−	93.2952i	0.618182	−	0.424069i
$221$		0			0
$222$	−96.1665	+	23.3238i	−0.433183	+	0.105062i
$223$			40.8167i			0.183034i	0.995803	+	0.0915172i	$0.0291716\pi$
$223$			40.8167i			0.183034i	−0.995803	+	0.0915172i	$0.970828\pi$
$224$			32.9848i			0.147254i
$225$	−24.1665	−	223.698i	−0.107407	−	0.994215i
$226$	−216.000			−0.955752
$227$	159.806			0.703992			0.351996	−	0.936002i	$-0.385503\pi$
$227$	159.806			0.703992			0.351996	+	0.936002i	$0.385503\pi$
$228$	16.9706	+	69.9714i	0.0744323	+	0.306892i
$229$	82.0000			0.358079			0.179039	−	0.983842i	$-0.442701\pi$
$229$	82.0000			0.358079			0.179039	+	0.983842i	$0.442701\pi$
$230$	96.1665	+	140.186i	0.418115	+	0.609503i
$231$	−68.0000	−	280.371i	−0.294372	−	1.21373i
$232$		0			0
$233$	−192.333			−0.825464			−0.412732	−	0.910853i	$-0.635425\pi$
$233$	−192.333			−0.825464			−0.412732	+	0.910853i	$0.635425\pi$
$234$		0			0
$235$	100.000	+	145.774i	0.425532	+	0.620314i
$236$		−	32.9848i		−	0.139766i
$237$	−50.9117	−	209.914i	−0.214817	−	0.885714i
$238$			93.2952i			0.391997i
$239$			461.788i			1.93217i	0.258231	+	0.966083i	$0.416861\pi$
$239$			461.788i			1.93217i	−0.258231	+	0.966083i	$0.583139\pi$
$240$	−40.0833	+	44.6467i	−0.167014	+	0.186028i
$241$	304.000			1.26141			0.630705	−	0.776022i	$-0.282766\pi$
$241$	304.000			1.26141			0.630705	+	0.776022i	$0.282766\pi$
$242$	213.546			0.882423
$243$	225.567	+	90.3798i	0.928260	+	0.371933i
$244$	−32.0000			−0.131148
$245$	42.4264	+	61.8466i	0.173169	+	0.252435i
$246$	238.000	−	57.7235i	0.967480	−	0.234648i
$247$		0			0
$248$	90.5097			0.364958
$249$	31.0000	+	127.816i	0.124498	+	0.513318i
$250$	172.000	−	40.8167i	0.688000	−	0.163267i
$251$		−	346.341i		−	1.37984i	−0.723884	−	0.689922i	$-0.757645\pi$
$251$		−	346.341i		−	1.37984i	0.723884	−	0.689922i	$-0.242355\pi$
$252$	48.0833	+	93.2952i	0.190807	+	0.370219i
$253$			396.505i			1.56721i
$254$			57.7235i			0.227258i
$255$	−113.373	+	126.280i	−0.444598	+	0.495216i
$256$	16.0000			0.0625000
$257$	−390.323			−1.51877			−0.759383	−	0.650644i	$-0.774499\pi$
$257$	−390.323			−1.51877			−0.759383	+	0.650644i	$0.774499\pi$
$258$	168.291	−	40.8167i	0.652292	−	0.158204i
$259$	−136.000			−0.525097
$260$		0			0
$261$		0			0
$262$			69.9714i			0.267066i
$263$	−295.571			−1.12384			−0.561921	−	0.827191i	$-0.689938\pi$
$263$	−295.571			−1.12384			−0.561921	+	0.827191i	$0.689938\pi$
$264$	−136.000	+	32.9848i	−0.515152	+	0.124943i
$265$	−192.000	−	279.886i	−0.724528	−	1.05617i
$266$			98.9545i			0.372010i
$267$	−192.333	+	46.6476i	−0.720348	+	0.174710i
$268$			11.6619i			0.0435146i
$269$		−	74.2159i		−	0.275896i	−0.990440	−	0.137948i	$-0.955949\pi$
$269$		−	74.2159i		−	0.275896i	0.990440	−	0.137948i	$-0.0440506\pi$
$270$	−48.2893	+	184.711i	−0.178849	+	0.684115i
$271$	40.0000			0.147601			0.0738007	−	0.997273i	$-0.476487\pi$
$271$	40.0000			0.147601			0.0738007	+	0.997273i	$0.476487\pi$
$272$	45.2548			0.166378
$273$		0			0
$274$	−72.0000			−0.262774
$275$	384.666	+	148.432i	1.39879	+	0.539752i
$276$	−34.0000	−	140.186i	−0.123188	−	0.507919i
$277$		−	443.152i		−	1.59983i	−0.600115	−	0.799914i	$-0.704878\pi$
$277$		−	443.152i		−	1.59983i	0.600115	−	0.799914i	$-0.295122\pi$
$278$	−62.2254			−0.223832
$279$	256.000	−	131.939i	0.917563	−	0.472901i
$280$	−68.0000	+	46.6476i	−0.242857	+	0.166599i
$281$		−	519.511i		−	1.84879i	−0.381431	−	0.924397i	$-0.624569\pi$
$281$		−	519.511i		−	1.84879i	0.381431	−	0.924397i	$-0.375431\pi$
$282$	−35.3553	−	145.774i	−0.125374	−	0.516928i
$283$		−	320.702i		−	1.13322i	−0.823985	−	0.566612i	$-0.808254\pi$
$283$		−	320.702i		−	1.13322i	0.823985	−	0.566612i	$-0.191746\pi$
$284$		0			0
$285$	−120.250	+	133.940i	−0.421929	+	0.469966i
$286$		0			0
$287$	336.583			1.17276
$288$	45.2548	−	23.3238i	0.157135	−	0.0809854i
$289$	−161.000			−0.557093
$290$		0			0
$291$	−476.000	+	115.447i	−1.63574	+	0.396725i
$292$		−	233.238i		−	0.798761i
$293$	−84.8528			−0.289600			−0.144800	−	0.989461i	$-0.546254\pi$
$293$	−84.8528			−0.289600			−0.144800	+	0.989461i	$0.546254\pi$
$294$	−15.0000	−	61.8466i	−0.0510204	−	0.210363i
$295$	68.0000	−	46.6476i	0.230508	−	0.158128i
$296$			65.9697i			0.222871i
$297$	−336.583	+	291.548i	−1.13328	+	0.981642i
$298$		−	11.6619i		−	0.0391339i
$299$		0			0
$300$	−148.728	−	19.4937i	−0.495760	−	0.0649791i
$301$	238.000			0.790698
$302$	−192.333			−0.636864
$303$	384.666	−	93.2952i	1.26953	−	0.307905i
$304$	48.0000			0.157895
$305$	−45.2548	−	65.9697i	−0.148377	−	0.216294i
$306$	128.000	−	65.9697i	0.418301	−	0.215587i
$307$			367.350i			1.19658i	0.801280	+	0.598290i	$0.204153\pi$
$307$			367.350i			1.19658i	−0.801280	+	0.598290i	$0.795847\pi$
$308$	−192.333			−0.624458
$309$	−289.000	+	70.0928i	−0.935275	+	0.226838i
$310$	128.000	+	186.590i	0.412903	+	0.601905i
$311$			98.9545i			0.318182i	0.987264	+	0.159091i	$0.0508563\pi$
$311$			98.9545i			0.318182i	−0.987264	+	0.159091i	$0.949144\pi$
$312$		0			0
$313$		−	186.590i		−	0.596136i	−0.954545	−	0.298068i	$-0.903658\pi$
$313$		−	186.590i		−	0.596136i	0.954545	−	0.298068i	$-0.0963422\pi$
$314$			164.924i			0.525236i
$315$	−124.333	+	231.066i	−0.394708	+	0.733541i
$316$	−144.000			−0.455696
$317$	520.431			1.64174			0.820868	−	0.571117i	$-0.193490\pi$
$317$	520.431			1.64174			0.820868	+	0.571117i	$0.193490\pi$
$318$	67.8823	+	279.886i	0.213466	+	0.880144i
$319$		0			0
$320$	22.6274	+	32.9848i	0.0707107	+	0.103078i
$321$	39.0000	+	160.801i	0.121495	+	0.500938i
$322$		−	198.252i		−	0.615691i
$323$	135.765			0.420324
$324$	94.0000	−	131.939i	0.290123	−	0.407220i
$325$		0			0
$326$		−	140.186i		−	0.430017i
$327$	56.5685	+	233.238i	0.172992	+	0.713266i
$328$		−	163.267i		−	0.497764i
$329$		−	206.155i		−	0.626612i
$330$	−260.333	−	233.724i	−0.788888	−	0.708253i
$331$	292.000			0.882175			0.441088	−	0.897464i	$-0.354593\pi$
$331$	292.000			0.882175			0.441088	+	0.897464i	$0.354593\pi$
$332$	87.6812			0.264100
$333$	96.1665	+	186.590i	0.288788	+	0.560332i
$334$	414.000			1.23952
$335$	−24.0416	+	16.4924i	−0.0717661	+	0.0492311i
$336$	68.0000	−	16.4924i	0.202381	−	0.0490846i
$337$			326.533i			0.968942i	0.874807	+	0.484471i	$0.160988\pi$
$337$			326.533i			0.968942i	−0.874807	+	0.484471i	$0.839012\pi$
$338$	−239.002			−0.707107
$339$	108.000	+	445.295i	0.318584	+	1.31356i
$340$	64.0000	+	93.2952i	0.188235	+	0.274398i
$341$			527.758i			1.54768i
$342$	135.765	−	69.9714i	0.396972	−	0.204595i
$343$		−	373.181i		−	1.08799i
$344$		−	115.447i		−	0.335602i
$345$	240.917	−	268.345i	0.698309	−	0.777812i
$346$	−232.000			−0.670520
$347$	−394.566			−1.13708			−0.568538	−	0.822657i	$-0.692491\pi$
$347$	−394.566			−1.13708			−0.568538	+	0.822657i	$0.692491\pi$
$348$		0			0
$349$	254.000			0.727794			0.363897	−	0.931439i	$-0.381446\pi$
$349$	254.000			0.727794			0.363897	+	0.931439i	$0.381446\pi$
$350$	−192.333	−	74.2159i	−0.549523	−	0.212045i
$351$		0			0
$352$			93.2952i			0.265043i
$353$	−345.068			−0.977530			−0.488765	−	0.872415i	$-0.662552\pi$
$353$	−345.068			−0.977530			−0.488765	+	0.872415i	$0.662552\pi$
$354$	−68.0000	+	16.4924i	−0.192090	+	0.0465888i
$355$		0			0
$356$			131.939i			0.370616i
$357$	192.333	−	46.6476i	0.538748	−	0.130666i
$358$			23.3238i			0.0651503i
$359$		−	395.818i		−	1.10256i	−0.834321	−	0.551279i	$-0.814140\pi$
$359$		−	395.818i		−	1.10256i	0.834321	−	0.551279i	$-0.185860\pi$
$360$	112.083	+	60.3104i	0.311342	+	0.167529i
$361$	−217.000			−0.601108
$362$	115.966			0.320347
$363$	−106.773	−	440.237i	−0.294141	−	1.21277i
$364$		0			0
$365$	480.833	−	329.848i	1.31735	−	0.903694i
$366$	16.0000	+	65.9697i	0.0437158	+	0.180245i
$367$			413.998i			1.12806i	0.825755	+	0.564029i	$0.190750\pi$
$367$			413.998i			1.12806i	−0.825755	+	0.564029i	$0.809250\pi$
$368$	−96.1665			−0.261322
$369$	−238.000	−	461.788i	−0.644986	−	1.25146i
$370$	−136.000	+	93.2952i	−0.367568	+	0.252149i
$371$			395.818i			1.06690i
$372$	−45.2548	−	186.590i	−0.121653	−	0.501587i
$373$			629.743i			1.68832i	0.536092	+	0.844159i	$0.319900\pi$
$373$			629.743i			1.68832i	−0.536092	+	0.844159i	$0.680100\pi$
$374$			263.879i			0.705558i
$375$	−170.146	−	334.179i	−0.453722	−	0.891143i
$376$	−100.000			−0.265957
$377$		0			0
$378$	168.291	−	145.774i	0.445215	−	0.385645i
$379$	−572.000			−1.50923			−0.754617	−	0.656165i	$-0.772178\pi$
$379$	−572.000			−1.50923			−0.754617	+	0.656165i	$0.772178\pi$
$380$	67.8823	+	98.9545i	0.178638	+	0.260407i
$381$	119.000	−	28.8617i	0.312336	−	0.0757526i
$382$		−	419.829i		−	1.09903i
$383$	193.747			0.505868			0.252934	−	0.967484i	$-0.418605\pi$
$383$	193.747			0.505868			0.252934	+	0.967484i	$0.418605\pi$
$384$	−8.00000	−	32.9848i	−0.0208333	−	0.0858980i
$385$	−272.000	−	396.505i	−0.706494	−	1.02988i
$386$			164.924i			0.427265i
$387$	−168.291	−	326.533i	−0.434862	−	0.843755i
$388$			326.533i			0.841581i
$389$			387.572i			0.996329i	0.867083	+	0.498164i	$0.165992\pi$
$389$			387.572i			0.996329i	−0.867083	+	0.498164i	$0.834008\pi$
$390$		0			0
$391$	−272.000			−0.695652
$392$	−42.4264			−0.108231
$393$	144.250	−	34.9857i	0.367048	−	0.0890222i
$394$	−272.000			−0.690355
$395$	−203.647	−	296.864i	−0.515561	−	0.751553i
$396$	136.000	+	263.879i	0.343434	+	0.666361i
$397$		−	513.124i		−	1.29250i	−0.763124	−	0.646252i	$-0.776336\pi$
$397$		−	513.124i		−	1.29250i	0.763124	−	0.646252i	$-0.223664\pi$
$398$	441.235			1.10863
$399$	204.000	−	49.4773i	0.511278	−	0.124003i
$400$	−36.0000	+	93.2952i	−0.0900000	+	0.233238i
$401$			65.9697i			0.164513i	0.996611	+	0.0822565i	$0.0262127\pi$
$401$			65.9697i			0.164513i	−0.996611	+	0.0822565i	$0.973787\pi$
$402$	24.0416	−	5.83095i	0.0598051	−	0.0145049i
$403$		0			0
$404$		−	263.879i		−	0.653165i
$405$	404.936	+	7.19550i	0.999842	+	0.0177667i
$406$		0			0
$407$	−384.666			−0.945126
$408$	−22.6274	−	93.2952i	−0.0554594	−	0.228665i
$409$	640.000			1.56479			0.782396	−	0.622781i	$-0.213997\pi$
$409$	640.000			1.56479			0.782396	+	0.622781i	$0.213997\pi$
$410$	336.583	−	230.894i	0.820934	−	0.563156i
$411$	36.0000	+	148.432i	0.0875912	+	0.361148i
$412$			198.252i			0.481195i
$413$	−96.1665			−0.232849
$414$	−272.000	+	140.186i	−0.657005	+	0.338613i
$415$	124.000	+	180.760i	0.298795	+	0.435565i
$416$		0			0
$417$	31.1127	+	128.281i	0.0746108	+	0.307628i
$418$			279.886i			0.669583i
$419$		−	577.235i		−	1.37765i	−0.724928	−	0.688824i	$-0.758127\pi$
$419$		−	577.235i		−	1.37765i	0.724928	−	0.688824i	$-0.241873\pi$
$420$	130.167	+	116.862i	0.309920	+	0.278242i
$421$	−656.000			−1.55819			−0.779097	−	0.626903i	$-0.784322\pi$
$421$	−656.000			−1.55819			−0.779097	+	0.626903i	$0.784322\pi$
$422$	16.9706			0.0402146
$423$	−282.843	+	145.774i	−0.668659	+	0.344619i
$424$	192.000			0.452830
$425$	−101.823	+	263.879i	−0.239584	+	0.620891i
$426$		0			0
$427$			93.2952i			0.218490i
$428$	110.309			0.257731
$429$		0			0
$430$	238.000	−	163.267i	0.553488	−	0.379690i
$431$		−	362.833i		−	0.841841i	−0.907098	−	0.420920i	$-0.861707\pi$
$431$		−	362.833i		−	0.841841i	0.907098	−	0.420920i	$-0.138293\pi$
$432$	−70.7107	−	81.6333i	−0.163682	−	0.188966i
$433$			163.267i			0.377059i	0.982068	+	0.188530i	$0.0603722\pi$
$433$			163.267i			0.377059i	−0.982068	+	0.188530i	$0.939628\pi$
$434$		−	263.879i		−	0.608016i
$435$		0			0
$436$	160.000			0.366972
$437$	−288.500			−0.660182
$438$	−480.833	+	116.619i	−1.09779	+	0.266254i
$439$	432.000			0.984055			0.492027	−	0.870580i	$-0.336256\pi$
$439$	432.000			0.984055			0.492027	+	0.870580i	$0.336256\pi$
$440$	−192.333	+	131.939i	−0.437121	+	0.299862i
$441$	−120.000	+	61.8466i	−0.272109	+	0.140242i
$442$		0			0
$443$	−123.037			−0.277735			−0.138867	−	0.990311i	$-0.544346\pi$
$443$	−123.037			−0.277735			−0.138867	+	0.990311i	$0.544346\pi$
$444$	136.000	−	32.9848i	0.306306	−	0.0742902i
$445$	−272.000	+	186.590i	−0.611236	+	0.419304i
$446$		−	57.7235i		−	0.129425i
$447$	−24.0416	+	5.83095i	−0.0537844	+	0.0130446i
$448$		−	46.6476i		−	0.104124i
$449$			865.852i			1.92840i	0.265174	+	0.964201i	$0.414571\pi$
$449$			865.852i			1.92840i	−0.265174	+	0.964201i	$0.585429\pi$
$450$	34.1766	+	316.357i	0.0759481	+	0.703016i
$451$	952.000			2.11086
$452$	305.470			0.675819
$453$	96.1665	+	396.505i	0.212288	+	0.875286i
$454$	−226.000			−0.497797
$455$		0			0
$456$	−24.0000	−	98.9545i	−0.0526316	−	0.217006i
$457$			466.476i			1.02074i	0.859956	+	0.510368i	$0.170491\pi$
$457$			466.476i			1.02074i	−0.859956	+	0.510368i	$0.829509\pi$
$458$	−115.966			−0.253200
$459$	−200.000	−	230.894i	−0.435730	−	0.503037i
$460$	−136.000	−	198.252i	−0.295652	−	0.430983i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$	96.1665	+	396.505i	0.208153	+	0.858235i
$463$		−	612.250i		−	1.32235i	−0.750230	−	0.661177i	$-0.770057\pi$
$463$		−	612.250i		−	1.32235i	0.750230	−	0.661177i	$-0.229943\pi$
$464$		0			0
$465$	320.666	−	357.174i	0.689604	−	0.768116i
$466$	272.000			0.583691
$467$	767.918			1.64436			0.822182	−	0.569225i	$-0.192757\pi$
$467$	767.918			1.64436			0.822182	+	0.569225i	$0.192757\pi$
$468$		0			0
$469$	34.0000			0.0724947
$470$	−141.421	−	206.155i	−0.300897	−	0.438628i
$471$	340.000	−	82.4621i	0.721868	−	0.175079i
$472$			46.6476i			0.0988297i
$473$	673.166			1.42318
$474$	72.0000	+	296.864i	0.151899	+	0.626295i
$475$	−108.000	+	279.886i	−0.227368	+	0.589233i
$476$		−	131.939i		−	0.277184i
$477$	543.058	−	279.886i	1.13849	−	0.586762i
$478$		−	653.067i		−	1.36625i
$479$			560.742i			1.17065i	0.810798	+	0.585326i	$0.199033\pi$
$479$			560.742i			1.17065i	−0.810798	+	0.585326i	$0.800967\pi$
$480$	56.6863	−	63.1400i	0.118096	−	0.131542i
$481$		0			0
$482$	−429.921			−0.891952
$483$	−408.708	+	99.1262i	−0.846186	+	0.205230i
$484$	−302.000			−0.623967
$485$	−673.166	+	461.788i	−1.38797	+	0.952140i
$486$	−319.000	−	127.816i	−0.656379	−	0.262996i
$487$		−	647.236i		−	1.32903i	−0.747277	−	0.664513i	$-0.768639\pi$
$487$		−	647.236i		−	1.32903i	0.747277	−	0.664513i	$-0.231361\pi$
$488$	45.2548			0.0927353
$489$	−289.000	+	70.0928i	−0.591002	+	0.143339i
$490$	−60.0000	−	87.4643i	−0.122449	−	0.178499i
$491$		−	346.341i		−	0.705379i	−0.935740	−	0.352689i	$-0.885267\pi$
$491$		−	346.341i		−	0.705379i	0.935740	−	0.352689i	$-0.114733\pi$
$492$	−336.583	+	81.6333i	−0.684111	+	0.165921i
$493$		0			0
$494$		0			0
$495$	−351.667	+	653.552i	−0.710438	+	1.32031i
$496$	−128.000			−0.258065
$497$		0			0
$498$	−43.8406	−	180.760i	−0.0880334	−	0.362971i
$499$	−660.000			−1.32265			−0.661323	−	0.750102i	$-0.730005\pi$
$499$	−660.000			−1.32265			−0.661323	+	0.750102i	$0.730005\pi$
$500$	−243.245	+	57.7235i	−0.486489	+	0.115447i
$501$	−207.000	−	853.483i	−0.413174	−	1.70356i
$502$			489.800i			0.975697i
$503$	182.434			0.362691			0.181345	−	0.983419i	$-0.441955\pi$
$503$	182.434			0.362691			0.181345	+	0.983419i	$0.441955\pi$
$504$	−68.0000	−	131.939i	−0.134921	−	0.261784i
$505$	544.000	−	373.181i	1.07723	−	0.738972i
$506$		−	560.742i		−	1.10819i
$507$	119.501	+	492.715i	0.235702	+	0.971825i
$508$		−	81.6333i		−	0.160696i
$509$		−	395.818i		−	0.777639i	−0.921314	−	0.388819i	$-0.872883\pi$
$509$		−	395.818i		−	0.777639i	0.921314	−	0.388819i	$-0.127117\pi$
$510$	160.333	−	178.587i	0.314379	−	0.350171i
$511$	−680.000			−1.33072
$512$	−22.6274			−0.0441942
$513$	−212.132	−	244.900i	−0.413513	−	0.477388i
$514$	552.000			1.07393
$515$	−408.708	+	280.371i	−0.793607	+	0.544410i
$516$	−238.000	+	57.7235i	−0.461240	+	0.111867i
$517$		−	583.095i		−	1.12784i
$518$	192.333			0.371299
$519$	116.000	+	478.280i	0.223507	+	0.921542i
$520$		0			0
$521$		−	131.939i		−	0.253243i	−0.991951	−	0.126621i	$-0.959587\pi$
$521$		−	131.939i		−	0.253243i	0.991951	−	0.126621i	$-0.0404133\pi$
$522$		0			0
$523$		−	145.774i		−	0.278726i	−0.990241	−	0.139363i	$-0.955494\pi$
$523$		−	145.774i		−	0.278726i	0.990241	−	0.139363i	$-0.0445055\pi$
$524$		−	98.9545i		−	0.188845i
$525$	−56.8335	+	433.613i	−0.108254	+	0.825929i
$526$	418.000			0.794677
$527$	−362.039			−0.686980
$528$	192.333	−	46.6476i	0.364267	−	0.0883478i
$529$	49.0000			0.0926276
$530$	271.529	+	395.818i	0.512319	+	0.746827i
$531$	68.0000	+	131.939i	0.128060	+	0.248473i
$532$		−	139.943i		−	0.263050i
$533$		0			0
$534$	272.000	−	65.9697i	0.509363	−	0.123539i
$535$	156.000	+	227.407i	0.291589	+	0.425060i
$536$		−	16.4924i		−	0.0307694i
$537$	48.0833	−	11.6619i	0.0895405	−	0.0217168i
$538$			104.957i			0.195088i
$539$		−	247.386i		−	0.458973i
$540$	68.2914	−	261.221i	0.126466	−	0.483742i
$541$	418.000			0.772643			0.386322	−	0.922364i	$-0.373745\pi$
$541$	418.000			0.772643			0.386322	+	0.922364i	$0.373745\pi$
$542$	−56.5685			−0.104370
$543$	−57.9828	−	239.069i	−0.106782	−	0.440274i
$544$	−64.0000			−0.117647
$545$	226.274	+	329.848i	0.415182	+	0.605227i
$546$		0			0
$547$		−	285.717i		−	0.522334i	−0.965294	−	0.261167i	$-0.915893\pi$
$547$		−	285.717i		−	0.522334i	0.965294	−	0.261167i	$-0.0841073\pi$
$548$	101.823			0.185809
$549$	128.000	−	65.9697i	0.233151	−	0.120163i
$550$	−544.000	−	209.914i	−0.989091	−	0.381662i
$551$		0			0
$552$	48.0833	+	198.252i	0.0871074	+	0.359153i
$553$			419.829i			0.759184i
$554$			626.712i			1.13125i
$555$	260.333	+	233.724i	0.469069	+	0.421124i
$556$	88.0000			0.158273
$557$	−424.264			−0.761695			−0.380847	−	0.924638i	$-0.624368\pi$
$557$	−424.264			−0.761695			−0.380847	+	0.924638i	$0.624368\pi$
$558$	−362.039	+	186.590i	−0.648815	+	0.334392i
$559$		0			0
$560$	96.1665	−	65.9697i	0.171726	−	0.117803i
$561$	544.000	−	131.939i	0.969697	−	0.235186i
$562$			734.700i			1.30730i
$563$	813.173			1.44436			0.722178	−	0.691707i	$-0.243141\pi$
$563$	813.173			1.44436			0.722178	+	0.691707i	$0.243141\pi$
$564$	50.0000	+	206.155i	0.0886525	+	0.365524i
$565$	432.000	+	629.743i	0.764602	+	1.11459i
$566$			453.542i			0.801310i
$567$	−384.666	−	274.055i	−0.678423	−	0.483342i
$568$		0			0
$569$		−	453.542i		−	0.797085i	−0.917150	−	0.398543i	$-0.869516\pi$
$569$		−	453.542i		−	0.797085i	0.917150	−	0.398543i	$-0.130484\pi$
$570$	170.059	−	189.420i	0.298349	−	0.332316i
$571$	220.000			0.385289			0.192644	−	0.981269i	$-0.438294\pi$
$571$	220.000			0.385289			0.192644	+	0.981269i	$0.438294\pi$
$572$		0			0
$573$	−865.499	+	209.914i	−1.51047	+	0.366343i
$574$	−476.000			−0.829268
$575$	216.375	−	560.742i	0.376304	−	0.975204i
$576$	−64.0000	+	32.9848i	−0.111111	+	0.0572654i
$577$			46.6476i			0.0808451i	0.999183	+	0.0404225i	$0.0128704\pi$
$577$			46.6476i			0.0808451i	−0.999183	+	0.0404225i	$0.987130\pi$
$578$	227.688			0.393925
$579$	340.000	−	82.4621i	0.587219	−	0.142422i
$580$		0			0
$581$		−	255.633i		−	0.439987i
$582$	673.166	−	163.267i	1.15664	−	0.280527i
$583$			1119.54i			1.92031i
$584$			329.848i			0.564809i
$585$		0			0
$586$	120.000			0.204778
$587$	−55.1543			−0.0939597			−0.0469798	−	0.998896i	$-0.514960\pi$
$587$	−55.1543			−0.0939597			−0.0469798	+	0.998896i	$0.514960\pi$
$588$	21.2132	+	87.4643i	0.0360769	+	0.148749i
$589$	−384.000			−0.651952
$590$	−96.1665	+	65.9697i	−0.162994	+	0.111813i
$591$	136.000	+	560.742i	0.230118	+	0.948803i
$592$		−	93.2952i		−	0.157593i
$593$	−390.323			−0.658217			−0.329109	−	0.944292i	$-0.606748\pi$
$593$	−390.323			−0.658217			−0.329109	+	0.944292i	$0.606748\pi$
$594$	476.000	−	412.311i	0.801347	−	0.694126i
$595$	272.000	−	186.590i	0.457143	−	0.313597i
$596$			16.4924i			0.0276718i
$597$	−220.617	−	909.628i	−0.369543	−	1.52367i
$598$		0			0
$599$			98.9545i			0.165200i	0.996583	+	0.0825998i	$0.0263223\pi$
$599$			98.9545i			0.165200i	−0.996583	+	0.0825998i	$0.973678\pi$
$600$	210.333	+	27.5683i	0.350555	+	0.0459471i
$601$	−880.000			−1.46423			−0.732113	−	0.681183i	$-0.761466\pi$
$601$	−880.000			−1.46423			−0.732113	+	0.681183i	$0.761466\pi$
$602$	−336.583			−0.559108
$603$	−24.0416	−	46.6476i	−0.0398700	−	0.0773592i
$604$	272.000			0.450331
$605$	−427.092	−	622.589i	−0.705938	−	1.02907i
$606$	−544.000	+	131.939i	−0.897690	+	0.217722i
$607$			425.659i			0.701251i	0.936516	+	0.350626i	$0.114031\pi$
$607$			425.659i			0.701251i	−0.936516	+	0.350626i	$0.885969\pi$
$608$	−67.8823			−0.111648
$609$		0			0
$610$	64.0000	+	93.2952i	0.104918	+	0.152943i
$611$		0			0
$612$	−181.019	+	93.2952i	−0.295783	+	0.152443i
$613$		−	606.419i		−	0.989264i	−0.869102	−	0.494632i	$-0.835303\pi$
$613$		−	606.419i		−	0.989264i	0.869102	−	0.494632i	$-0.164697\pi$
$614$		−	519.511i		−	0.846110i
$615$	−644.291	−	578.436i	−1.04763	−	0.940547i
$616$	272.000			0.441558
$617$	113.137			0.183366			0.0916832	−	0.995788i	$-0.470775\pi$
$617$	113.137			0.183366			0.0916832	+	0.995788i	$0.470775\pi$
$618$	408.708	−	99.1262i	0.661339	−	0.160398i
$619$	52.0000			0.0840065			0.0420032	−	0.999117i	$-0.486626\pi$
$619$	52.0000			0.0840065			0.0420032	+	0.999117i	$0.486626\pi$
$620$	−181.019	−	263.879i	−0.291967	−	0.425611i
$621$	425.000	+	490.650i	0.684380	+	0.790096i
$622$		−	139.943i		−	0.224988i
$623$	384.666			0.617442
$624$		0			0
$625$	−463.000	−	419.829i	−0.740800	−	0.671726i
$626$			263.879i			0.421532i
$627$	576.999	−	139.943i	0.920254	−	0.223194i
$628$		−	233.238i		−	0.371398i
$629$		−	263.879i		−	0.419521i
$630$	175.833	−	326.776i	0.279101	−	0.518692i
$631$	−544.000			−0.862124			−0.431062	−	0.902322i	$-0.641861\pi$
$631$	−544.000			−0.862124			−0.431062	+	0.902322i	$0.641861\pi$
$632$	203.647			0.322226
$633$	−8.48528	−	34.9857i	−0.0134049	−	0.0552697i
$634$	−736.000			−1.16088
$635$	168.291	−	115.447i	0.265026	−	0.181806i
$636$	−96.0000	−	395.818i	−0.150943	−	0.622356i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−32.0000	−	46.6476i	−0.0500000	−	0.0728869i
$641$			849.360i			1.32505i	0.749038	+	0.662527i	$0.230516\pi$
$641$			849.360i			1.32505i	−0.749038	+	0.662527i	$0.769484\pi$
$642$	−55.1543	−	227.407i	−0.0859102	−	0.354217i
$643$			367.350i			0.571306i	0.958333	+	0.285653i	$0.0922105\pi$
$643$			367.350i			0.571306i	−0.958333	+	0.285653i	$0.907789\pi$
$644$			280.371i			0.435359i
$645$	−455.583	−	409.016i	−0.706330	−	0.634134i
$646$	−192.000			−0.297214
$647$	971.565			1.50165			0.750823	−	0.660504i	$-0.229657\pi$
$647$	971.565			1.50165			0.750823	+	0.660504i	$0.229657\pi$
$648$	−132.936	+	186.590i	−0.205148	+	0.287948i
$649$	−272.000			−0.419106
$650$		0			0
$651$	−544.000	+	131.939i	−0.835637	+	0.202672i
$652$			198.252i			0.304068i
$653$	−350.725			−0.537098			−0.268549	−	0.963266i	$-0.586544\pi$
$653$	−350.725			−0.537098			−0.268549	+	0.963266i	$0.586544\pi$
$654$	−80.0000	−	329.848i	−0.122324	−	0.504355i
$655$	204.000	−	139.943i	0.311450	−	0.213653i
$656$			230.894i			0.351972i
$657$	480.833	+	932.952i	0.731861	+	1.42002i
$658$			291.548i			0.443081i
$659$			577.235i			0.875925i	0.898993	+	0.437963i	$0.144300\pi$
$659$			577.235i			0.875925i	−0.898993	+	0.437963i	$0.855700\pi$
$660$	368.167	+	330.535i	0.557828	+	0.500811i
$661$	80.0000			0.121029			0.0605144	−	0.998167i	$-0.480726\pi$
$661$	80.0000			0.121029			0.0605144	+	0.998167i	$0.480726\pi$
$662$	−412.950			−0.623792
$663$		0			0
$664$	−124.000			−0.186747
$665$	288.500	−	197.909i	0.433834	−	0.297608i
$666$	−136.000	−	263.879i	−0.204204	−	0.396214i
$667$		0			0
$668$	−585.484			−0.876474
$669$	−119.000	+	28.8617i	−0.177877	+	0.0431416i
$670$	34.0000	−	23.3238i	0.0507463	−	0.0348117i
$671$			263.879i			0.393262i
$672$	−96.1665	+	23.3238i	−0.143105	+	0.0347080i
$673$		−	489.800i		−	0.727786i	−0.931441	−	0.363893i	$-0.881447\pi$
$673$		−	489.800i		−	0.727786i	0.931441	−	0.363893i	$-0.118553\pi$
$674$		−	461.788i		−	0.685145i
$675$	635.099	−	228.636i	0.940887	−	0.338719i
$676$	338.000			0.500000
$677$	−192.333			−0.284096			−0.142048	−	0.989860i	$-0.545369\pi$
$677$	−192.333			−0.284096			−0.142048	+	0.989860i	$0.545369\pi$
$678$	−152.735	−	629.743i	−0.225273	−	0.928824i
$679$	952.000			1.40206
$680$	−90.5097	−	131.939i	−0.133102	−	0.194029i
$681$	113.000	+	465.911i	0.165932	+	0.684157i
$682$		−	746.362i		−	1.09437i
$683$	−236.174			−0.345789			−0.172894	−	0.984940i	$-0.555312\pi$
$683$	−236.174			−0.345789			−0.172894	+	0.984940i	$0.555312\pi$
$684$	−192.000	+	98.9545i	−0.280702	+	0.144670i
$685$	144.000	+	209.914i	0.210219	+	0.306444i
$686$			527.758i			0.769326i
$687$	57.9828	+	239.069i	0.0843999	+	0.347990i
$688$			163.267i			0.237306i
$689$		0			0
$690$	−340.708	+	379.497i	−0.493779	+	0.549996i
$691$	−548.000			−0.793054			−0.396527	−	0.918023i	$-0.629785\pi$
$691$	−548.000			−0.793054			−0.396527	+	0.918023i	$0.629785\pi$
$692$	328.098			0.474129
$693$	769.332	−	396.505i	1.11015	−	0.572157i
$694$	558.000			0.804035
$695$	124.451	+	181.417i	0.179066	+	0.261031i
$696$		0			0
$697$			653.067i			0.936968i
$698$	−359.210			−0.514628
$699$	−136.000	−	560.742i	−0.194564	−	0.802207i
$700$	272.000	+	104.957i	0.388571	+	0.149939i
$701$			57.7235i			0.0823445i	0.999152	+	0.0411722i	$0.0131092\pi$
$701$			57.7235i			0.0823445i	−0.999152	+	0.0411722i	$0.986891\pi$
$702$		0			0
$703$		−	279.886i		−	0.398130i
$704$		−	131.939i		−	0.187414i
$705$	−354.289	+	394.625i	−0.502538	+	0.559752i
$706$	488.000			0.691218
$707$	−769.332			−1.08816
$708$	96.1665	−	23.3238i	0.135828	−	0.0329432i
$709$	1230.00			1.73484			0.867419	−	0.497579i	$-0.165777\pi$
$709$	1230.00			1.73484			0.867419	+	0.497579i	$0.165777\pi$
$710$		0			0
$711$	576.000	−	296.864i	0.810127	−	0.417530i
$712$		−	186.590i		−	0.262065i
$713$	769.332			1.07901
$714$	−272.000	+	65.9697i	−0.380952	+	0.0923945i
$715$		0			0
$716$		−	32.9848i		−	0.0460682i
$717$	−1346.33	+	326.533i	−1.87773	+	0.455416i
$718$			559.771i			0.779626i
$719$		−	626.712i		−	0.871644i	−0.900033	−	0.435822i	$-0.856458\pi$
$719$		−	626.712i		−	0.871644i	0.900033	−	0.435822i	$-0.143542\pi$
$720$	−158.510	−	85.2918i	−0.220152	−	0.118461i
$721$	578.000			0.801664
$722$	306.884			0.425048
$723$	214.960	+	886.305i	0.297317	+	1.22587i
$724$	−164.000			−0.226519
$725$		0			0
$726$	151.000	+	622.589i	0.207989	+	0.857561i
$727$		−	367.350i		−	0.505296i	−0.967558	−	0.252648i	$-0.918699\pi$
$727$		−	367.350i		−	0.505296i	0.967558	−	0.252648i	$-0.0813014\pi$
$728$		0			0
$729$	−104.000	+	721.543i	−0.142661	+	0.989772i
$730$	−680.000	+	466.476i	−0.931507	+	0.639008i
$731$			461.788i			0.631721i
$732$	−22.6274	−	93.2952i	−0.0309118	−	0.127453i
$733$		−	1002.92i		−	1.36825i	−0.729367	−	0.684123i	$-0.760185\pi$
$733$		−	1002.92i		−	1.36825i	0.729367	−	0.684123i	$-0.239815\pi$
$734$		−	585.481i		−	0.797658i
$735$	−150.312	+	167.425i	−0.204506	+	0.227790i
$736$	136.000			0.184783
$737$	96.1665			0.130484
$738$	336.583	+	653.067i	0.456074	+	0.884914i
$739$	−340.000			−0.460081			−0.230041	−	0.973181i	$-0.573886\pi$
$739$	−340.000			−0.460081			−0.230041	+	0.973181i	$0.573886\pi$
$740$	192.333	−	131.939i	0.259910	−	0.178296i
$741$		0			0
$742$		−	559.771i		−	0.754409i
$743$	−1243.09			−1.67307			−0.836537	−	0.547911i	$-0.815423\pi$
$743$	−1243.09			−1.67307			−0.836537	+	0.547911i	$0.815423\pi$
$744$	64.0000	+	263.879i	0.0860215	+	0.354676i
$745$	−34.0000	+	23.3238i	−0.0456376	+	0.0313071i
$746$		−	890.591i		−	1.19382i
$747$	−350.725	+	180.760i	−0.469511	+	0.241981i
$748$		−	373.181i		−	0.498905i
$749$		−	321.602i		−	0.429375i
$750$	240.622	+	472.600i	0.320830	+	0.630133i
$751$	−520.000			−0.692410			−0.346205	−	0.938159i	$-0.612530\pi$
$751$	−520.000			−0.692410			−0.346205	+	0.938159i	$0.612530\pi$
$752$	141.421			0.188060
$753$	1009.75	−	244.900i	1.34097	−	0.325232i
$754$		0			0
$755$	384.666	+	560.742i	0.509492	+	0.742705i
$756$	−238.000	+	206.155i	−0.314815	+	0.272692i
$757$			816.333i			1.07838i	0.842184	+	0.539190i	$0.181269\pi$
$757$			816.333i			1.07838i	−0.842184	+	0.539190i	$0.818731\pi$
$758$	808.930			1.06719
$759$	−1156.00	+	280.371i	−1.52306	+	0.369395i
$760$	−96.0000	−	139.943i	−0.126316	−	0.184135i
$761$		−	395.818i		−	0.520129i	−0.965591	−	0.260064i	$-0.916256\pi$
$761$		−	395.818i		−	0.520129i	0.965591	−	0.260064i	$-0.0837438\pi$
$762$	−168.291	+	40.8167i	−0.220855	+	0.0535652i
$763$		−	466.476i		−	0.611371i
$764$			593.727i			0.777130i
$765$	−448.333	−	241.242i	−0.586056	−	0.315348i
$766$	−274.000			−0.357702
$767$		0			0
$768$	11.3137	+	46.6476i	0.0147314	+	0.0607391i
$769$	−306.000			−0.397919			−0.198960	−	0.980008i	$-0.563756\pi$
$769$	−306.000			−0.397919			−0.198960	+	0.980008i	$0.563756\pi$
$770$	384.666	+	560.742i	0.499566	+	0.728237i
$771$	−276.000	−	1137.98i	−0.357977	−	1.47598i
$772$		−	233.238i		−	0.302122i
$773$	−305.470			−0.395175			−0.197587	−	0.980285i	$-0.563311\pi$
$773$	−305.470			−0.395175			−0.197587	+	0.980285i	$0.563311\pi$
$774$	238.000	+	461.788i	0.307494	+	0.596625i
$775$	288.000	−	746.362i	0.371613	−	0.963048i
$776$		−	461.788i		−	0.595087i
$777$	−96.1665	−	396.505i	−0.123766	−	0.510302i
$778$		−	548.109i		−	0.704511i

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	30.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(0.707107 + 2.91548i) q^{3} +2.00000 q^{4} +(2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} -5.83095i q^{7} -2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(0.707107 + 2.91548i) q^{3} +2.00000 q^{4} +(2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} -5.83095i q^{7} -2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +(-4.00000 - 5.83095i) q^{10} -16.4924i q^{11} +(1.41421 + 5.83095i) q^{12} +8.24621i q^{14} +(-10.0208 + 11.1617i) q^{15} +4.00000 q^{16} +11.3137 q^{17} +(11.3137 - 5.83095i) q^{18} +12.0000 q^{19} +(5.65685 + 8.24621i) q^{20} +(17.0000 - 4.12311i) q^{21} +23.3238i q^{22} -24.0416 q^{23} +(-2.00000 - 8.24621i) q^{24} +(-9.00000 + 23.3238i) q^{25} +(-17.6777 - 20.4083i) q^{27} -11.6619i q^{28} +(14.1716 - 15.7850i) q^{30} -32.0000 q^{31} -5.65685 q^{32} +(48.0833 - 11.6619i) q^{33} -16.0000 q^{34} +(24.0416 - 16.4924i) q^{35} +(-16.0000 + 8.24621i) q^{36} -23.3238i q^{37} -16.9706 q^{38} +(-8.00000 - 11.6619i) q^{40} +57.7235i q^{41} +(-24.0416 + 5.83095i) q^{42} +40.8167i q^{43} -32.9848i q^{44} +(-39.6274 - 21.3229i) q^{45} +34.0000 q^{46} +35.3553 q^{47} +(2.82843 + 11.6619i) q^{48} +15.0000 q^{49} +(12.7279 - 32.9848i) q^{50} +(8.00000 + 32.9848i) q^{51} -67.8823 q^{53} +(25.0000 + 28.8617i) q^{54} +(68.0000 - 46.6476i) q^{55} +16.4924i q^{56} +(8.48528 + 34.9857i) q^{57} -16.4924i q^{59} +(-20.0416 + 22.3234i) q^{60} -16.0000 q^{61} +45.2548 q^{62} +(24.0416 + 46.6476i) q^{63} +8.00000 q^{64} +(-68.0000 + 16.4924i) q^{66} +5.83095i q^{67} +22.6274 q^{68} +(-17.0000 - 70.0928i) q^{69} +(-34.0000 + 23.3238i) q^{70} +(22.6274 - 11.6619i) q^{72} -116.619i q^{73} +32.9848i q^{74} +(-74.3640 - 9.74686i) q^{75} +24.0000 q^{76} -96.1665 q^{77} -72.0000 q^{79} +(11.3137 + 16.4924i) q^{80} +(47.0000 - 65.9697i) q^{81} -81.6333i q^{82} +43.8406 q^{83} +(34.0000 - 8.24621i) q^{84} +(32.0000 + 46.6476i) q^{85} -57.7235i q^{86} +46.6476i q^{88} +65.9697i q^{89} +(56.0416 + 30.1552i) q^{90} -48.0833 q^{92} +(-22.6274 - 93.2952i) q^{93} -50.0000 q^{94} +(33.9411 + 49.4773i) q^{95} +(-4.00000 - 16.4924i) q^{96} +163.267i q^{97} -21.2132 q^{98} +(68.0000 + 131.939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9	\( 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9} - 16 q^{10} + 8 q^{15} + 16 q^{16} + 48 q^{19} + 68 q^{21} - 8 q^{24} - 36 q^{25} + 68 q^{30} - 128 q^{31} - 64 q^{34} - 64 q^{36} - 32 q^{40} - 68 q^{45} + 136 q^{46} + 60 q^{49} + 32 q^{51} + 100 q^{54} + 272 q^{55} + 16 q^{60} - 64 q^{61} + 32 q^{64} - 272 q^{66} - 68 q^{69} - 136 q^{70} - 272 q^{75} + 96 q^{76} - 288 q^{79} + 188 q^{81} + 136 q^{84} + 128 q^{85} + 128 q^{90} - 200 q^{94} - 16 q^{96} + 272 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9 - 16 * q^10 + 8 * q^15 + 16 * q^16 + 48 * q^19 + 68 * q^21 - 8 * q^24 - 36 * q^25 + 68 * q^30 - 128 * q^31 - 64 * q^34 - 64 * q^36 - 32 * q^40 - 68 * q^45 + 136 * q^46 + 60 * q^49 + 32 * q^51 + 100 * q^54 + 272 * q^55 + 16 * q^60 - 64 * q^61 + 32 * q^64 - 272 * q^66 - 68 * q^69 - 136 * q^70 - 272 * q^75 + 96 * q^76 - 288 * q^79 + 188 * q^81 + 136 * q^84 + 128 * q^85 + 128 * q^90 - 200 * q^94 - 16 * q^96 + 272 * q^99

Introduction

L-functions

Modular forms

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