LMFDB - Embedded newform 6171.2.a.bk.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6171,2,Mod(1,6171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6171, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6171.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6171 = 3 \cdot 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6171.a (trivial)

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:	yes
Analytic conductor:	$49.2756830873$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 16 x^{10} + 15 x^{9} + 89 x^{8} - 78 x^{7} - 201 x^{6} + 157 x^{5} + 159 x^{4} + \cdots - 1 $ x^12 - x^11 - 16x^10 + 15x^9 + 89x^8 - 78x^7 - 201x^6 + 157x^5 + 159x^4 - 92x^3 - 29x^2 + 17x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 561)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.859524$ of defining polynomial
Character	$\chi$	$=$	6171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.859524 q^{2} +1.00000 q^{3} -1.26122 q^{4} +2.41916 q^{5} +0.859524 q^{6} +1.04339 q^{7} -2.80310 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.859524 q^{2} +1.00000 q^{3} -1.26122 q^{4} +2.41916 q^{5} +0.859524 q^{6} +1.04339 q^{7} -2.80310 q^{8} +1.00000 q^{9} +2.07932 q^{10} -1.26122 q^{12} -3.92892 q^{13} +0.896815 q^{14} +2.41916 q^{15} +0.113107 q^{16} +1.00000 q^{17} +0.859524 q^{18} -5.31125 q^{19} -3.05108 q^{20} +1.04339 q^{21} -6.52689 q^{23} -2.80310 q^{24} +0.852319 q^{25} -3.37701 q^{26} +1.00000 q^{27} -1.31594 q^{28} +8.28105 q^{29} +2.07932 q^{30} -9.79704 q^{31} +5.70341 q^{32} +0.859524 q^{34} +2.52411 q^{35} -1.26122 q^{36} -6.71473 q^{37} -4.56515 q^{38} -3.92892 q^{39} -6.78113 q^{40} +3.78144 q^{41} +0.896815 q^{42} +0.286986 q^{43} +2.41916 q^{45} -5.61002 q^{46} -3.94938 q^{47} +0.113107 q^{48} -5.91135 q^{49} +0.732589 q^{50} +1.00000 q^{51} +4.95523 q^{52} -8.17291 q^{53} +0.859524 q^{54} -2.92471 q^{56} -5.31125 q^{57} +7.11776 q^{58} +1.54661 q^{59} -3.05108 q^{60} +7.77647 q^{61} -8.42079 q^{62} +1.04339 q^{63} +4.67601 q^{64} -9.50468 q^{65} -15.5035 q^{67} -1.26122 q^{68} -6.52689 q^{69} +2.16954 q^{70} +14.0250 q^{71} -2.80310 q^{72} -10.5274 q^{73} -5.77147 q^{74} +0.852319 q^{75} +6.69864 q^{76} -3.37701 q^{78} -1.02636 q^{79} +0.273623 q^{80} +1.00000 q^{81} +3.25024 q^{82} +4.86718 q^{83} -1.31594 q^{84} +2.41916 q^{85} +0.246671 q^{86} +8.28105 q^{87} -12.6811 q^{89} +2.07932 q^{90} -4.09938 q^{91} +8.23183 q^{92} -9.79704 q^{93} -3.39459 q^{94} -12.8487 q^{95} +5.70341 q^{96} -3.29613 q^{97} -5.08095 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 12 q^{3} + 9 q^{4} - 14 q^{5} - q^{6} - 5 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - q^2 + 12 * q^3 + 9 * q^4 - 14 * q^5 - q^6 - 5 * q^7 + 12 * q^9	$ 12 q - q^{2} + 12 q^{3} + 9 q^{4} - 14 q^{5} - q^{6} - 5 q^{7} + 12 q^{9} + 8 q^{10} + 9 q^{12} - 7 q^{13} - 13 q^{14} - 14 q^{15} + 11 q^{16} + 12 q^{17} - q^{18} + 3 q^{19} - 36 q^{20} - 5 q^{21} - 39 q^{23} + 8 q^{25} - 25 q^{26} + 12 q^{27} - 9 q^{28} + 10 q^{29} + 8 q^{30} - 25 q^{31} - 11 q^{32} - q^{34} + 12 q^{35} + 9 q^{36} - 10 q^{37} - 34 q^{38} - 7 q^{39} - 13 q^{40} + 17 q^{41} - 13 q^{42} - 18 q^{43} - 14 q^{45} + 19 q^{46} - 38 q^{47} + 11 q^{48} - 15 q^{49} - 18 q^{50} + 12 q^{51} + 32 q^{52} - 40 q^{53} - q^{54} - 25 q^{56} + 3 q^{57} + 3 q^{58} - 18 q^{59} - 36 q^{60} - 22 q^{61} + 3 q^{62} - 5 q^{63} - 20 q^{64} + 3 q^{65} - 9 q^{67} + 9 q^{68} - 39 q^{69} + 13 q^{70} - 24 q^{71} + q^{73} - 4 q^{74} + 8 q^{75} + 29 q^{76} - 25 q^{78} - 3 q^{79} - 43 q^{80} + 12 q^{81} + q^{82} + 4 q^{83} - 9 q^{84} - 14 q^{85} - 4 q^{86} + 10 q^{87} - 62 q^{89} + 8 q^{90} - 5 q^{91} - 52 q^{92} - 25 q^{93} - 16 q^{94} - 4 q^{95} - 11 q^{96} - 5 q^{97} - 7 q^{98}+O(q^{100}) $ 12 * q - q^2 + 12 * q^3 + 9 * q^4 - 14 * q^5 - q^6 - 5 * q^7 + 12 * q^9 + 8 * q^10 + 9 * q^12 - 7 * q^13 - 13 * q^14 - 14 * q^15 + 11 * q^16 + 12 * q^17 - q^18 + 3 * q^19 - 36 * q^20 - 5 * q^21 - 39 * q^23 + 8 * q^25 - 25 * q^26 + 12 * q^27 - 9 * q^28 + 10 * q^29 + 8 * q^30 - 25 * q^31 - 11 * q^32 - q^34 + 12 * q^35 + 9 * q^36 - 10 * q^37 - 34 * q^38 - 7 * q^39 - 13 * q^40 + 17 * q^41 - 13 * q^42 - 18 * q^43 - 14 * q^45 + 19 * q^46 - 38 * q^47 + 11 * q^48 - 15 * q^49 - 18 * q^50 + 12 * q^51 + 32 * q^52 - 40 * q^53 - q^54 - 25 * q^56 + 3 * q^57 + 3 * q^58 - 18 * q^59 - 36 * q^60 - 22 * q^61 + 3 * q^62 - 5 * q^63 - 20 * q^64 + 3 * q^65 - 9 * q^67 + 9 * q^68 - 39 * q^69 + 13 * q^70 - 24 * q^71 + q^73 - 4 * q^74 + 8 * q^75 + 29 * q^76 - 25 * q^78 - 3 * q^79 - 43 * q^80 + 12 * q^81 + q^82 + 4 * q^83 - 9 * q^84 - 14 * q^85 - 4 * q^86 + 10 * q^87 - 62 * q^89 + 8 * q^90 - 5 * q^91 - 52 * q^92 - 25 * q^93 - 16 * q^94 - 4 * q^95 - 11 * q^96 - 5 * q^97 - 7 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	0.859524	0.607775	0.303888	−	0.952708i	$-0.401715\pi$
$2$	0.859524	0.607775	0.303888	+	0.952708i	$0.401715\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.26122	−0.630609
$5$	2.41916	1.08188	0.540940	−	0.841061i	$-0.318069\pi$
$5$	2.41916	1.08188	0.540940	+	0.841061i	$0.318069\pi$
$6$	0.859524	0.350899
$7$	1.04339	0.394362	0.197181	−	0.980367i	$-0.436821\pi$
$7$	1.04339	0.394362	0.197181	+	0.980367i	$0.436821\pi$
$8$	−2.80310	−0.991044
$9$	1.00000	0.333333
$10$	2.07932	0.657540
$11$	0	0
$11$	0	0
$12$	−1.26122	−0.364082
$13$	−3.92892	−1.08969	−0.544844	−	0.838538i	$-0.683411\pi$
$13$	−3.92892	−1.08969	−0.544844	+	0.838538i	$0.683411\pi$
$14$	0.896815	0.239684
$15$	2.41916	0.624624
$16$	0.113107	0.0282767
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.859524	0.202592
$19$	−5.31125	−1.21848	−0.609242	−	0.792984i	$-0.708526\pi$
$19$	−5.31125	−1.21848	−0.609242	+	0.792984i	$0.708526\pi$
$20$	−3.05108	−0.682243
$21$	1.04339	0.227685
$22$	0	0
$23$	−6.52689	−1.36095	−0.680475	−	0.732771i	$-0.738227\pi$
$23$	−6.52689	−1.36095	−0.680475	+	0.732771i	$0.738227\pi$
$24$	−2.80310	−0.572180
$25$	0.852319	0.170464
$26$	−3.37701	−0.662285
$27$	1.00000	0.192450
$28$	−1.31594	−0.248689
$29$	8.28105	1.53775	0.768876	−	0.639398i	$-0.220816\pi$
$29$	8.28105	1.53775	0.768876	+	0.639398i	$0.220816\pi$
$30$	2.07932	0.379631
$31$	−9.79704	−1.75960	−0.879800	−	0.475344i	$-0.842324\pi$
$31$	−9.79704	−1.75960	−0.879800	+	0.475344i	$0.842324\pi$
$32$	5.70341	1.00823
$33$	0	0
$34$	0.859524	0.147407
$35$	2.52411	0.426653
$36$	−1.26122	−0.210203
$37$	−6.71473	−1.10389	−0.551947	−	0.833879i	$-0.686115\pi$
$37$	−6.71473	−1.10389	−0.551947	+	0.833879i	$0.686115\pi$
$38$	−4.56515	−0.740564
$39$	−3.92892	−0.629131
$40$	−6.78113	−1.07219
$41$	3.78144	0.590562	0.295281	−	0.955410i	$-0.404587\pi$
$41$	3.78144	0.590562	0.295281	+	0.955410i	$0.404587\pi$
$42$	0.896815	0.138382
$43$	0.286986	0.0437649	0.0218825	−	0.999761i	$-0.493034\pi$
$43$	0.286986	0.0437649	0.0218825	+	0.999761i	$0.493034\pi$
$44$	0	0
$45$	2.41916	0.360627
$46$	−5.61002	−0.827152
$47$	−3.94938	−0.576077	−0.288038	−	0.957619i	$-0.593003\pi$
$47$	−3.94938	−0.576077	−0.288038	+	0.957619i	$0.593003\pi$
$48$	0.113107	0.0163256
$49$	−5.91135	−0.844478
$50$	0.732589	0.103604
$51$	1.00000	0.140028
$52$	4.95523	0.687167
$53$	−8.17291	−1.12264	−0.561318	−	0.827600i	$-0.689706\pi$
$53$	−8.17291	−1.12264	−0.561318	+	0.827600i	$0.689706\pi$
$54$	0.859524	0.116966
$55$	0	0
$56$	−2.92471	−0.390831
$57$	−5.31125	−0.703492
$58$	7.11776	0.934608
$59$	1.54661	0.201351	0.100675	−	0.994919i	$-0.467900\pi$
$59$	1.54661	0.201351	0.100675	+	0.994919i	$0.467900\pi$
$60$	−3.05108	−0.393893
$61$	7.77647	0.995675	0.497837	−	0.867270i	$-0.334128\pi$
$61$	7.77647	0.995675	0.497837	+	0.867270i	$0.334128\pi$
$62$	−8.42079	−1.06944
$63$	1.04339	0.131454
$64$	4.67601	0.584501
$65$	−9.50468	−1.17891
$66$	0	0
$67$	−15.5035	−1.89406	−0.947029	−	0.321149i	$-0.895931\pi$
$67$	−15.5035	−1.89406	−0.947029	+	0.321149i	$0.895931\pi$
$68$	−1.26122	−0.152945
$69$	−6.52689	−0.785745
$70$	2.16954	0.259309
$71$	14.0250	1.66446	0.832230	−	0.554431i	$-0.187064\pi$
$71$	14.0250	1.66446	0.832230	+	0.554431i	$0.187064\pi$
$72$	−2.80310	−0.330348
$73$	−10.5274	−1.23214	−0.616070	−	0.787691i	$-0.711276\pi$
$73$	−10.5274	−1.23214	−0.616070	+	0.787691i	$0.711276\pi$
$74$	−5.77147	−0.670920
$75$	0.852319	0.0984173
$76$	6.69864	0.768387
$77$	0	0
$78$	−3.37701	−0.382371
$79$	−1.02636	−0.115475	−0.0577374	−	0.998332i	$-0.518389\pi$
$79$	−1.02636	−0.115475	−0.0577374	+	0.998332i	$0.518389\pi$
$80$	0.273623	0.0305920
$81$	1.00000	0.111111
$82$	3.25024	0.358929
$83$	4.86718	0.534242	0.267121	−	0.963663i	$-0.413928\pi$
$83$	4.86718	0.534242	0.267121	+	0.963663i	$0.413928\pi$
$84$	−1.31594	−0.143580
$85$	2.41916	0.262394
$86$	0.246671	0.0265992
$87$	8.28105	0.887822
$88$	0	0
$89$	−12.6811	−1.34419	−0.672097	−	0.740464i	$-0.734606\pi$
$89$	−12.6811	−1.34419	−0.672097	+	0.740464i	$0.734606\pi$
$90$	2.07932	0.219180
$91$	−4.09938	−0.429732
$92$	8.23183	0.858227
$93$	−9.79704	−1.01591
$94$	−3.39459	−0.350125
$95$	−12.8487	−1.31825
$96$	5.70341	0.582102
$97$	−3.29613	−0.334671	−0.167335	−	0.985900i	$-0.553516\pi$
$97$	−3.29613	−0.334671	−0.167335	+	0.985900i	$0.553516\pi$
$98$	−5.08095	−0.513253
$99$	0	0
$100$	−1.07496	−0.107496
$101$	−0.580200	−0.0577321	−0.0288660	−	0.999583i	$-0.509190\pi$
$101$	−0.580200	−0.0577321	−0.0288660	+	0.999583i	$0.509190\pi$
$102$	0.859524	0.0851056
$103$	13.8650	1.36616	0.683080	−	0.730344i	$-0.260640\pi$
$103$	13.8650	1.36616	0.683080	+	0.730344i	$0.260640\pi$
$104$	11.0132	1.07993
$105$	2.52411	0.246328
$106$	−7.02482	−0.682311
$107$	−13.5829	−1.31311	−0.656555	−	0.754278i	$-0.727987\pi$
$107$	−13.5829	−1.31311	−0.656555	+	0.754278i	$0.727987\pi$
$108$	−1.26122	−0.121361
$109$	−14.4308	−1.38222	−0.691109	−	0.722750i	$-0.742878\pi$
$109$	−14.4308	−1.38222	−0.691109	+	0.722750i	$0.742878\pi$
$110$	0	0
$111$	−6.71473	−0.637334
$112$	0.118014	0.0111513
$113$	13.4467	1.26496	0.632478	−	0.774578i	$-0.282038\pi$
$113$	13.4467	1.26496	0.632478	+	0.774578i	$0.282038\pi$
$114$	−4.56515	−0.427565
$115$	−15.7896	−1.47238
$116$	−10.4442	−0.969721
$117$	−3.92892	−0.363229
$118$	1.32935	0.122376
$119$	1.04339	0.0956469
$120$	−6.78113	−0.619030
$121$	0	0
$122$	6.68406	0.605147
$123$	3.78144	0.340961
$124$	12.3562	1.10962
$125$	−10.0339	−0.897458
$126$	0.896815	0.0798946
$127$	12.1942	1.08206	0.541031	−	0.841003i	$-0.318034\pi$
$127$	12.1942	1.08206	0.541031	+	0.841003i	$0.318034\pi$
$128$	−7.38768	−0.652985
$129$	0.286986	0.0252677
$130$	−8.16951	−0.716513
$131$	20.5675	1.79699	0.898497	−	0.438980i	$-0.144660\pi$
$131$	20.5675	1.79699	0.898497	+	0.438980i	$0.144660\pi$
$132$	0	0
$133$	−5.54168	−0.480524
$134$	−13.3257	−1.15116
$135$	2.41916	0.208208
$136$	−2.80310	−0.240364
$137$	10.2854	0.878737	0.439369	−	0.898307i	$-0.355202\pi$
$137$	10.2854	0.878737	0.439369	+	0.898307i	$0.355202\pi$
$138$	−5.61002	−0.477556
$139$	−6.99689	−0.593468	−0.296734	−	0.954960i	$-0.595897\pi$
$139$	−6.99689	−0.593468	−0.296734	+	0.954960i	$0.595897\pi$
$140$	−3.18346	−0.269051
$141$	−3.94938	−0.332598
$142$	12.0548	1.01162
$143$	0	0
$144$	0.113107	0.00942557
$145$	20.0332	1.66366
$146$	−9.04857	−0.748865
$147$	−5.91135	−0.487560
$148$	8.46873	0.696126
$149$	−18.2326	−1.49367	−0.746835	−	0.665009i	$-0.768428\pi$
$149$	−18.2326	−1.49367	−0.746835	+	0.665009i	$0.768428\pi$
$150$	0.732589	0.0598156
$151$	9.43728	0.767995	0.383997	−	0.923334i	$-0.374547\pi$
$151$	9.43728	0.767995	0.383997	+	0.923334i	$0.374547\pi$
$152$	14.8879	1.20757
$153$	1.00000	0.0808452
$154$	0	0
$155$	−23.7006	−1.90368
$156$	4.95523	0.396736
$157$	−19.8256	−1.58225	−0.791127	−	0.611651i	$-0.790506\pi$
$157$	−19.8256	−1.58225	−0.791127	+	0.611651i	$0.790506\pi$
$158$	−0.882184	−0.0701828
$159$	−8.17291	−0.648154
$160$	13.7974	1.09078
$161$	−6.81006	−0.536708
$162$	0.859524	0.0675306
$163$	9.67800	0.758039	0.379020	−	0.925389i	$-0.376261\pi$
$163$	9.67800	0.758039	0.379020	+	0.925389i	$0.376261\pi$
$164$	−4.76922	−0.372414
$165$	0	0
$166$	4.18346	0.324699
$167$	12.3141	0.952895	0.476448	−	0.879203i	$-0.341924\pi$
$167$	12.3141	0.952895	0.476448	+	0.879203i	$0.341924\pi$
$168$	−2.92471	−0.225646
$169$	2.43644	0.187419
$170$	2.07932	0.159477
$171$	−5.31125	−0.406161
$172$	−0.361952	−0.0275986
$173$	22.6973	1.72565	0.862824	−	0.505505i	$-0.168694\pi$
$173$	22.6973	1.72565	0.862824	+	0.505505i	$0.168694\pi$
$174$	7.11776	0.539596
$175$	0.889297	0.0672245
$176$	0	0
$177$	1.54661	0.116250
$178$	−10.8997	−0.816968
$179$	−8.72084	−0.651826	−0.325913	−	0.945400i	$-0.605672\pi$
$179$	−8.72084	−0.651826	−0.325913	+	0.945400i	$0.605672\pi$
$180$	−3.05108	−0.227414
$181$	−10.0962	−0.750443	−0.375221	−	0.926935i	$-0.622433\pi$
$181$	−10.0962	−0.750443	−0.375221	+	0.926935i	$0.622433\pi$
$182$	−3.52352	−0.261180
$183$	7.77647	0.574853
$184$	18.2955	1.34876
$185$	−16.2440	−1.19428
$186$	−8.42079	−0.617443
$187$	0	0
$188$	4.98103	0.363279
$189$	1.04339	0.0758951
$190$	−11.0438	−0.801202
$191$	12.7687	0.923908	0.461954	−	0.886904i	$-0.347149\pi$
$191$	12.7687	0.923908	0.461954	+	0.886904i	$0.347149\pi$
$192$	4.67601	0.337462
$193$	−5.79515	−0.417144	−0.208572	−	0.978007i	$-0.566882\pi$
$193$	−5.79515	−0.417144	−0.208572	+	0.978007i	$0.566882\pi$
$194$	−2.83310	−0.203405
$195$	−9.50468	−0.680644
$196$	7.45550	0.532536
$197$	−6.13474	−0.437082	−0.218541	−	0.975828i	$-0.570130\pi$
$197$	−6.13474	−0.437082	−0.218541	+	0.975828i	$0.570130\pi$
$198$	0	0
$199$	4.77430	0.338441	0.169221	−	0.985578i	$-0.445875\pi$
$199$	4.77430	0.338441	0.169221	+	0.985578i	$0.445875\pi$
$200$	−2.38913	−0.168937
$201$	−15.5035	−1.09353
$202$	−0.498696	−0.0350881
$203$	8.64032	0.606432
$204$	−1.26122	−0.0883029
$205$	9.14790	0.638917
$206$	11.9173	0.830318
$207$	−6.52689	−0.453650
$208$	−0.444388	−0.0308128
$209$	0	0
$210$	2.16954	0.149712
$211$	−3.16984	−0.218221	−0.109110	−	0.994030i	$-0.534800\pi$
$211$	−3.16984	−0.218221	−0.109110	+	0.994030i	$0.534800\pi$
$212$	10.3078	0.707944
$213$	14.0250	0.960976
$214$	−11.6749	−0.798076
$215$	0.694264	0.0473484
$216$	−2.80310	−0.190727
$217$	−10.2221	−0.693920
$218$	−12.4036	−0.840078
$219$	−10.5274	−0.711377
$220$	0	0
$221$	−3.92892	−0.264288
$222$	−5.77147	−0.387356
$223$	8.40394	0.562770	0.281385	−	0.959595i	$-0.409206\pi$
$223$	8.40394	0.562770	0.281385	+	0.959595i	$0.409206\pi$
$224$	5.95085	0.397608
$225$	0.852319	0.0568213
$226$	11.5577	0.768810
$227$	9.94254	0.659910	0.329955	−	0.943997i	$-0.392966\pi$
$227$	9.94254	0.659910	0.329955	+	0.943997i	$0.392966\pi$
$228$	6.69864	0.443628
$229$	−24.3077	−1.60630	−0.803149	−	0.595779i	$-0.796844\pi$
$229$	−24.3077	−1.60630	−0.803149	+	0.595779i	$0.796844\pi$
$230$	−13.5715	−0.894879
$231$	0	0
$232$	−23.2126	−1.52398
$233$	−9.31830	−0.610462	−0.305231	−	0.952278i	$-0.598734\pi$
$233$	−9.31830	−0.610462	−0.305231	+	0.952278i	$0.598734\pi$
$234$	−3.37701	−0.220762
$235$	−9.55417	−0.623246
$236$	−1.95061	−0.126974
$237$	−1.02636	−0.0666694
$238$	0.896815	0.0581319
$239$	17.4862	1.13109	0.565545	−	0.824717i	$-0.308666\pi$
$239$	17.4862	1.13109	0.565545	+	0.824717i	$0.308666\pi$
$240$	0.273623	0.0176623
$241$	2.49718	0.160858	0.0804288	−	0.996760i	$-0.474371\pi$
$241$	2.49718	0.160858	0.0804288	+	0.996760i	$0.474371\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−9.80782	−0.627881
$245$	−14.3005	−0.913624
$246$	3.25024	0.207228
$247$	20.8675	1.32777
$248$	27.4620	1.74384
$249$	4.86718	0.308445
$250$	−8.62437	−0.545453
$251$	−4.39891	−0.277657	−0.138828	−	0.990316i	$-0.544334\pi$
$251$	−4.39891	−0.277657	−0.138828	+	0.990316i	$0.544334\pi$
$252$	−1.31594	−0.0828962
$253$	0	0
$254$	10.4812	0.657651
$255$	2.41916	0.151493
$256$	−15.7019	−0.981369
$257$	13.1481	0.820155	0.410077	−	0.912051i	$-0.365502\pi$
$257$	13.1481	0.820155	0.410077	+	0.912051i	$0.365502\pi$
$258$	0.246671	0.0153571
$259$	−7.00605	−0.435334
$260$	11.9875	0.743432
$261$	8.28105	0.512584
$262$	17.6783	1.09217
$263$	3.56223	0.219657	0.109828	−	0.993951i	$-0.464970\pi$
$263$	3.56223	0.219657	0.109828	+	0.993951i	$0.464970\pi$
$264$	0	0
$265$	−19.7716	−1.21456
$266$	−4.76321	−0.292051
$267$	−12.6811	−0.776070
$268$	19.5533	1.19441
$269$	−13.3848	−0.816086	−0.408043	−	0.912963i	$-0.633789\pi$
$269$	−13.3848	−0.816086	−0.408043	+	0.912963i	$0.633789\pi$
$270$	2.07932	0.126544
$271$	−12.2154	−0.742031	−0.371016	−	0.928627i	$-0.620990\pi$
$271$	−12.2154	−0.742031	−0.371016	+	0.928627i	$0.620990\pi$
$272$	0.113107	0.00685811
$273$	−4.09938	−0.248106
$274$	8.84051	0.534075
$275$	0	0
$276$	8.23183	0.495498
$277$	−18.4436	−1.10817	−0.554084	−	0.832461i	$-0.686931\pi$
$277$	−18.4436	−1.10817	−0.554084	+	0.832461i	$0.686931\pi$
$278$	−6.01399	−0.360695
$279$	−9.79704	−0.586534
$280$	−7.07533	−0.422832
$281$	−27.1649	−1.62052	−0.810261	−	0.586069i	$-0.800675\pi$
$281$	−27.1649	−1.62052	−0.810261	+	0.586069i	$0.800675\pi$
$282$	−3.39459	−0.202145
$283$	−16.5549	−0.984089	−0.492044	−	0.870570i	$-0.663750\pi$
$283$	−16.5549	−0.984089	−0.492044	+	0.870570i	$0.663750\pi$
$284$	−17.6886	−1.04962
$285$	−12.8487	−0.761094
$286$	0	0
$287$	3.94550	0.232895
$288$	5.70341	0.336077
$289$	1.00000	0.0588235
$290$	17.2190	1.01113
$291$	−3.29613	−0.193222
$292$	13.2774	0.776999
$293$	23.7909	1.38988	0.694939	−	0.719068i	$-0.255431\pi$
$293$	23.7909	1.38988	0.694939	+	0.719068i	$0.255431\pi$
$294$	−5.08095	−0.296327
$295$	3.74148	0.217838
$296$	18.8220	1.09401
$297$	0	0
$298$	−15.6713	−0.907816
$299$	25.6436	1.48301
$300$	−1.07496	−0.0620629
$301$	0.299437	0.0172592
$302$	8.11157	0.466768
$303$	−0.580200	−0.0333316
$304$	−0.600738	−0.0344547
$305$	18.8125	1.07720
$306$	0.859524	0.0491357
$307$	−5.36749	−0.306339	−0.153169	−	0.988200i	$-0.548948\pi$
$307$	−5.36749	−0.306339	−0.153169	+	0.988200i	$0.548948\pi$
$308$	0	0
$309$	13.8650	0.788753
$310$	−20.3712	−1.15701
$311$	2.97244	0.168552	0.0842759	−	0.996442i	$-0.473142\pi$
$311$	2.97244	0.168552	0.0842759	+	0.996442i	$0.473142\pi$
$312$	11.0132	0.623497
$313$	5.54538	0.313443	0.156722	−	0.987643i	$-0.449907\pi$
$313$	5.54538	0.313443	0.156722	+	0.987643i	$0.449907\pi$
$314$	−17.0406	−0.961656
$315$	2.52411	0.142218
$316$	1.29447	0.0728195
$317$	−7.40663	−0.415998	−0.207999	−	0.978129i	$-0.566695\pi$
$317$	−7.40663	−0.415998	−0.207999	+	0.978129i	$0.566695\pi$
$318$	−7.02482	−0.393932
$319$	0	0
$320$	11.3120	0.632360
$321$	−13.5829	−0.758125
$322$	−5.85341	−0.326198
$323$	−5.31125	−0.295526
$324$	−1.26122	−0.0700677
$325$	−3.34870	−0.185752
$326$	8.31847	0.460718
$327$	−14.4308	−0.798024
$328$	−10.5997	−0.585273
$329$	−4.12073	−0.227183
$330$	0	0
$331$	1.05159	0.0578007	0.0289004	−	0.999582i	$-0.490799\pi$
$331$	1.05159	0.0578007	0.0289004	+	0.999582i	$0.490799\pi$
$332$	−6.13857	−0.336898
$333$	−6.71473	−0.367965
$334$	10.5843	0.579146
$335$	−37.5055	−2.04914
$336$	0.118014	0.00643819
$337$	−14.3667	−0.782604	−0.391302	−	0.920262i	$-0.627975\pi$
$337$	−14.3667	−0.782604	−0.391302	+	0.920262i	$0.627975\pi$
$338$	2.09418	0.113908
$339$	13.4467	0.730323
$340$	−3.05108	−0.165468
$341$	0	0
$342$	−4.56515	−0.246855
$343$	−13.4715	−0.727393
$344$	−0.804449	−0.0433730
$345$	−15.7896	−0.850081
$346$	19.5089	1.04881
$347$	4.38846	0.235585	0.117792	−	0.993038i	$-0.462418\pi$
$347$	4.38846	0.235585	0.117792	+	0.993038i	$0.462418\pi$
$348$	−10.4442	−0.559868
$349$	−1.48206	−0.0793330	−0.0396665	−	0.999213i	$-0.512630\pi$
$349$	−1.48206	−0.0793330	−0.0396665	+	0.999213i	$0.512630\pi$
$350$	0.764372	0.0408574
$351$	−3.92892	−0.209710
$352$	0	0
$353$	−2.68618	−0.142971	−0.0714856	−	0.997442i	$-0.522774\pi$
$353$	−2.68618	−0.142971	−0.0714856	+	0.997442i	$0.522774\pi$
$354$	1.32935	0.0706539
$355$	33.9286	1.80075
$356$	15.9936	0.847660
$357$	1.04339	0.0552218
$358$	−7.49578	−0.396164
$359$	−7.50759	−0.396235	−0.198118	−	0.980178i	$-0.563483\pi$
$359$	−7.50759	−0.396235	−0.198118	+	0.980178i	$0.563483\pi$
$360$	−6.78113	−0.357397
$361$	9.20935	0.484703
$362$	−8.67791	−0.456101
$363$	0	0
$364$	5.17021	0.270993
$365$	−25.4675	−1.33303
$366$	6.68406	0.349382
$367$	−32.7469	−1.70938	−0.854688	−	0.519141i	$-0.826252\pi$
$367$	−32.7469	−1.70938	−0.854688	+	0.519141i	$0.826252\pi$
$368$	−0.738235	−0.0384832
$369$	3.78144	0.196854
$370$	−13.9621	−0.725855
$371$	−8.52749	−0.442725
$372$	12.3562	0.640639
$373$	18.1238	0.938413	0.469206	−	0.883089i	$-0.344540\pi$
$373$	18.1238	0.938413	0.469206	+	0.883089i	$0.344540\pi$
$374$	0	0
$375$	−10.0339	−0.518148
$376$	11.0705	0.570917
$377$	−32.5356	−1.67567
$378$	0.896815	0.0461272
$379$	30.5401	1.56874	0.784371	−	0.620292i	$-0.212986\pi$
$379$	30.5401	1.56874	0.784371	+	0.620292i	$0.212986\pi$
$380$	16.2051	0.831302
$381$	12.1942	0.624729
$382$	10.9750	0.561528
$383$	7.56076	0.386337	0.193168	−	0.981166i	$-0.438124\pi$
$383$	7.56076	0.386337	0.193168	+	0.981166i	$0.438124\pi$
$384$	−7.38768	−0.377001
$385$	0	0
$386$	−4.98107	−0.253530
$387$	0.286986	0.0145883
$388$	4.15713	0.211047
$389$	17.2791	0.876085	0.438042	−	0.898954i	$-0.355672\pi$
$389$	17.2791	0.876085	0.438042	+	0.898954i	$0.355672\pi$
$390$	−8.16951	−0.413679
$391$	−6.52689	−0.330079
$392$	16.5701	0.836915
$393$	20.5675	1.03750
$394$	−5.27296	−0.265648
$395$	−2.48293	−0.124930
$396$	0	0
$397$	−25.8435	−1.29705	−0.648523	−	0.761195i	$-0.724613\pi$
$397$	−25.8435	−1.29705	−0.648523	+	0.761195i	$0.724613\pi$
$398$	4.10363	0.205696
$399$	−5.54168	−0.277431
$400$	0.0964031	0.00482016
$401$	−3.36113	−0.167847	−0.0839234	−	0.996472i	$-0.526745\pi$
$401$	−3.36113	−0.167847	−0.0839234	+	0.996472i	$0.526745\pi$
$402$	−13.3257	−0.664623
$403$	38.4918	1.91741
$404$	0.731759	0.0364064
$405$	2.41916	0.120209
$406$	7.42657	0.368574
$407$	0	0
$408$	−2.80310	−0.138774
$409$	−5.76438	−0.285030	−0.142515	−	0.989793i	$-0.545519\pi$
$409$	−5.76438	−0.285030	−0.142515	+	0.989793i	$0.545519\pi$
$410$	7.86284	0.388318
$411$	10.2854	0.507339
$412$	−17.4868	−0.861512
$413$	1.61371	0.0794053
$414$	−5.61002	−0.275717
$415$	11.7745	0.577986
$416$	−22.4083	−1.09866
$417$	−6.99689	−0.342639
$418$	0	0
$419$	−2.35826	−0.115208	−0.0576042	−	0.998339i	$-0.518346\pi$
$419$	−2.35826	−0.115208	−0.0576042	+	0.998339i	$0.518346\pi$
$420$	−3.18346	−0.155337
$421$	26.6104	1.29691	0.648455	−	0.761253i	$-0.275415\pi$
$421$	26.6104	1.29691	0.648455	+	0.761253i	$0.275415\pi$
$422$	−2.72456	−0.132629
$423$	−3.94938	−0.192026
$424$	22.9095	1.11258
$425$	0.852319	0.0413436
$426$	12.0548	0.584058
$427$	8.11385	0.392657
$428$	17.1310	0.828059
$429$	0	0
$430$	0.596736	0.0287772
$431$	30.0635	1.44811	0.724055	−	0.689742i	$-0.242276\pi$
$431$	30.0635	1.44811	0.724055	+	0.689742i	$0.242276\pi$
$432$	0.113107	0.00544185
$433$	3.79287	0.182274	0.0911369	−	0.995838i	$-0.470950\pi$
$433$	3.79287	0.182274	0.0911369	+	0.995838i	$0.470950\pi$
$434$	−8.78613	−0.421748
$435$	20.0332	0.960517
$436$	18.2004	0.871639
$437$	34.6659	1.65830
$438$	−9.04857	−0.432357
$439$	−39.8376	−1.90135	−0.950673	−	0.310195i	$-0.899606\pi$
$439$	−39.8376	−1.90135	−0.950673	+	0.310195i	$0.899606\pi$
$440$	0	0
$441$	−5.91135	−0.281493
$442$	−3.37701	−0.160628
$443$	9.46280	0.449591	0.224796	−	0.974406i	$-0.427829\pi$
$443$	9.46280	0.449591	0.224796	+	0.974406i	$0.427829\pi$
$444$	8.46873	0.401908
$445$	−30.6775	−1.45426
$446$	7.22339	0.342038
$447$	−18.2326	−0.862371
$448$	4.87887	0.230505
$449$	−24.3248	−1.14796	−0.573978	−	0.818871i	$-0.694601\pi$
$449$	−24.3248	−1.14796	−0.573978	+	0.818871i	$0.694601\pi$
$450$	0.732589	0.0345346
$451$	0	0
$452$	−16.9592	−0.797693
$453$	9.43728	0.443402
$454$	8.54586	0.401077
$455$	−9.91704	−0.464918
$456$	14.8879	0.697192
$457$	18.2670	0.854493	0.427246	−	0.904135i	$-0.359484\pi$
$457$	18.2670	0.854493	0.427246	+	0.904135i	$0.359484\pi$
$458$	−20.8931	−0.976268
$459$	1.00000	0.0466760
$460$	19.9141	0.928499
$461$	16.5412	0.770399	0.385199	−	0.922833i	$-0.374133\pi$
$461$	16.5412	0.770399	0.385199	+	0.922833i	$0.374133\pi$
$462$	0	0
$463$	16.3714	0.760842	0.380421	−	0.924813i	$-0.375779\pi$
$463$	16.3714	0.760842	0.380421	+	0.924813i	$0.375779\pi$
$464$	0.936643	0.0434826
$465$	−23.7006	−1.09909
$466$	−8.00931	−0.371024
$467$	24.2712	1.12314	0.561570	−	0.827430i	$-0.310198\pi$
$467$	24.2712	1.12314	0.561570	+	0.827430i	$0.310198\pi$
$468$	4.95523	0.229056
$469$	−16.1761	−0.746945
$470$	−8.21204	−0.378793
$471$	−19.8256	−0.913515
$472$	−4.33529	−0.199548
$473$	0	0
$474$	−0.882184	−0.0405200
$475$	−4.52688	−0.207707
$476$	−1.31594	−0.0603158
$477$	−8.17291	−0.374212
$478$	15.0298	0.687449
$479$	−31.4636	−1.43761	−0.718805	−	0.695212i	$-0.755311\pi$
$479$	−31.4636	−1.43761	−0.718805	+	0.695212i	$0.755311\pi$
$480$	13.7974	0.629764
$481$	26.3816	1.20290
$482$	2.14639	0.0977653
$483$	−6.81006	−0.309868
$484$	0	0
$485$	−7.97385	−0.362074
$486$	0.859524	0.0389888
$487$	7.74873	0.351128	0.175564	−	0.984468i	$-0.443825\pi$
$487$	7.74873	0.351128	0.175564	+	0.984468i	$0.443825\pi$
$488$	−21.7982	−0.986758
$489$	9.67800	0.437654
$490$	−12.2916	−0.555278
$491$	7.62742	0.344220	0.172110	−	0.985078i	$-0.444941\pi$
$491$	7.62742	0.344220	0.172110	+	0.985078i	$0.444941\pi$
$492$	−4.76922	−0.215013
$493$	8.28105	0.372960
$494$	17.9361	0.806984
$495$	0	0
$496$	−1.10811	−0.0497557
$497$	14.6335	0.656401
$498$	4.18346	0.187465
$499$	19.8955	0.890643	0.445321	−	0.895371i	$-0.353089\pi$
$499$	19.8955	0.890643	0.445321	+	0.895371i	$0.353089\pi$
$500$	12.6549	0.565945
$501$	12.3141	0.550154
$502$	−3.78097	−0.168753
$503$	2.47357	0.110291	0.0551456	−	0.998478i	$-0.482438\pi$
$503$	2.47357	0.110291	0.0551456	+	0.998478i	$0.482438\pi$
$504$	−2.92471	−0.130277
$505$	−1.40359	−0.0624591
$506$	0	0
$507$	2.43644	0.108206
$508$	−15.3796	−0.682358
$509$	−25.0467	−1.11018	−0.555088	−	0.831792i	$-0.687315\pi$
$509$	−25.0467	−1.11018	−0.555088	+	0.831792i	$0.687315\pi$
$510$	2.07932	0.0920740
$511$	−10.9841	−0.485910
$512$	1.27919	0.0565329
$513$	−5.31125	−0.234497
$514$	11.3011	0.498470
$515$	33.5416	1.47802
$516$	−0.361952	−0.0159340
$517$	0	0
$518$	−6.02187	−0.264586
$519$	22.6973	0.996303
$520$	26.6425	1.16835
$521$	−22.7523	−0.996798	−0.498399	−	0.866948i	$-0.666079\pi$
$521$	−22.7523	−0.996798	−0.498399	+	0.866948i	$0.666079\pi$
$522$	7.11776	0.311536
$523$	−11.2009	−0.489782	−0.244891	−	0.969551i	$-0.578752\pi$
$523$	−11.2009	−0.489782	−0.244891	+	0.969551i	$0.578752\pi$
$524$	−25.9401	−1.13320
$525$	0.889297	0.0388121
$526$	3.06183	0.133502
$527$	−9.79704	−0.426766
$528$	0	0
$529$	19.6003	0.852185
$530$	−16.9941	−0.738178
$531$	1.54661	0.0671170
$532$	6.98926	0.303023
$533$	−14.8570	−0.643528
$534$	−10.8997	−0.471676
$535$	−32.8592	−1.42063
$536$	43.4579	1.87709
$537$	−8.72084	−0.376332
$538$	−11.5046	−0.495997
$539$	0	0
$540$	−3.05108	−0.131298
$541$	−45.2500	−1.94545	−0.972726	−	0.231959i	$-0.925487\pi$
$541$	−45.2500	−1.94545	−0.972726	+	0.231959i	$0.925487\pi$
$542$	−10.4994	−0.450988
$543$	−10.0962	−0.433268
$544$	5.70341	0.244532
$545$	−34.9103	−1.49539
$546$	−3.52352	−0.150793
$547$	−16.7034	−0.714186	−0.357093	−	0.934069i	$-0.616232\pi$
$547$	−16.7034	−0.714186	−0.357093	+	0.934069i	$0.616232\pi$
$548$	−12.9721	−0.554140
$549$	7.77647	0.331892
$550$	0	0
$551$	−43.9827	−1.87373
$552$	18.2955	0.778708
$553$	−1.07089	−0.0455389
$554$	−15.8527	−0.673518
$555$	−16.2440	−0.689518
$556$	8.82460	0.374246
$557$	24.3755	1.03282	0.516412	−	0.856340i	$-0.327267\pi$
$557$	24.3755	1.03282	0.516412	+	0.856340i	$0.327267\pi$
$558$	−8.42079	−0.356481
$559$	−1.12755	−0.0476901
$560$	0.285494	0.0120643
$561$	0	0
$562$	−23.3489	−0.984914
$563$	−16.1434	−0.680365	−0.340182	−	0.940360i	$-0.610489\pi$
$563$	−16.1434	−0.680365	−0.340182	+	0.940360i	$0.610489\pi$
$564$	4.98103	0.209739
$565$	32.5296	1.36853
$566$	−14.2294	−0.598105
$567$	1.04339	0.0438181
$568$	−39.3134	−1.64955
$569$	−30.0324	−1.25902	−0.629511	−	0.776992i	$-0.716745\pi$
$569$	−30.0324	−1.25902	−0.629511	+	0.776992i	$0.716745\pi$
$570$	−11.0438	−0.462574
$571$	42.7393	1.78858	0.894292	−	0.447484i	$-0.147680\pi$
$571$	42.7393	1.78858	0.894292	+	0.447484i	$0.147680\pi$
$572$	0	0
$573$	12.7687	0.533418
$574$	3.39125	0.141548
$575$	−5.56299	−0.231993
$576$	4.67601	0.194834
$577$	25.7744	1.07300	0.536501	−	0.843900i	$-0.319746\pi$
$577$	25.7744	1.07300	0.536501	+	0.843900i	$0.319746\pi$
$578$	0.859524	0.0357515
$579$	−5.79515	−0.240838
$580$	−25.2662	−1.04912
$581$	5.07834	0.210685
$582$	−2.83310	−0.117436
$583$	0	0
$584$	29.5094	1.22111
$585$	−9.50468	−0.392970
$586$	20.4488	0.844734
$587$	−7.02461	−0.289937	−0.144968	−	0.989436i	$-0.546308\pi$
$587$	−7.02461	−0.289937	−0.144968	+	0.989436i	$0.546308\pi$
$588$	7.45550	0.307460
$589$	52.0345	2.14404
$590$	3.21590	0.132396
$591$	−6.13474	−0.252349
$592$	−0.759481	−0.0312145
$593$	30.7916	1.26446	0.632230	−	0.774780i	$-0.282140\pi$
$593$	30.7916	1.26446	0.632230	+	0.774780i	$0.282140\pi$
$594$	0	0
$595$	2.52411	0.103478
$596$	22.9953	0.941922
$597$	4.77430	0.195399
$598$	22.0413	0.901337
$599$	−46.4471	−1.89778	−0.948889	−	0.315611i	$-0.897790\pi$
$599$	−46.4471	−1.89778	−0.948889	+	0.315611i	$0.897790\pi$
$600$	−2.38913	−0.0975359
$601$	8.64869	0.352787	0.176394	−	0.984320i	$-0.443557\pi$
$601$	8.64869	0.352787	0.176394	+	0.984320i	$0.443557\pi$
$602$	0.257373	0.0104897
$603$	−15.5035	−0.631352
$604$	−11.9025	−0.484305
$605$	0	0
$606$	−0.498696	−0.0202581
$607$	−18.0272	−0.731700	−0.365850	−	0.930674i	$-0.619222\pi$
$607$	−18.0272	−0.731700	−0.365850	+	0.930674i	$0.619222\pi$
$608$	−30.2922	−1.22851
$609$	8.64032	0.350124
$610$	16.1698	0.654696
$611$	15.5168	0.627743
$612$	−1.26122	−0.0509817
$613$	−30.2101	−1.22017	−0.610087	−	0.792334i	$-0.708866\pi$
$613$	−30.2101	−1.22017	−0.610087	+	0.792334i	$0.708866\pi$
$614$	−4.61349	−0.186185
$615$	9.14790	0.368879
$616$	0	0
$617$	3.32104	0.133700	0.0668501	−	0.997763i	$-0.478705\pi$
$617$	3.32104	0.133700	0.0668501	+	0.997763i	$0.478705\pi$
$618$	11.9173	0.479384
$619$	−30.0554	−1.20803	−0.604014	−	0.796974i	$-0.706433\pi$
$619$	−30.0554	−1.20803	−0.604014	+	0.796974i	$0.706433\pi$
$620$	29.8916	1.20048
$621$	−6.52689	−0.261915
$622$	2.55489	0.102442
$623$	−13.2313	−0.530099
$624$	−0.444388	−0.0177898
$625$	−28.5351	−1.14141
$626$	4.76639	0.190503
$627$	0	0
$628$	25.0044	0.997784
$629$	−6.71473	−0.267734
$630$	2.16954	0.0864364
$631$	−43.3111	−1.72419	−0.862093	−	0.506750i	$-0.830847\pi$
$631$	−43.3111	−1.72419	−0.862093	+	0.506750i	$0.830847\pi$
$632$	2.87699	0.114441
$633$	−3.16984	−0.125990
$634$	−6.36618	−0.252833
$635$	29.4997	1.17066
$636$	10.3078	0.408732
$637$	23.2252	0.920217
$638$	0	0
$639$	14.0250	0.554820
$640$	−17.8720	−0.706451
$641$	7.52330	0.297153	0.148576	−	0.988901i	$-0.452531\pi$
$641$	7.52330	0.297153	0.148576	+	0.988901i	$0.452531\pi$
$642$	−11.6749	−0.460770
$643$	−20.7344	−0.817684	−0.408842	−	0.912605i	$-0.634067\pi$
$643$	−20.7344	−0.817684	−0.408842	+	0.912605i	$0.634067\pi$
$644$	8.58897	0.338453
$645$	0.694264	0.0273366
$646$	−4.56515	−0.179613
$647$	8.02158	0.315361	0.157680	−	0.987490i	$-0.449598\pi$
$647$	8.02158	0.315361	0.157680	+	0.987490i	$0.449598\pi$
$648$	−2.80310	−0.110116
$649$	0	0
$650$	−2.87829	−0.112896
$651$	−10.2221	−0.400635
$652$	−12.2061	−0.478026
$653$	−31.0206	−1.21393	−0.606965	−	0.794729i	$-0.707613\pi$
$653$	−31.0206	−1.21393	−0.606965	+	0.794729i	$0.707613\pi$
$654$	−12.4036	−0.485019
$655$	49.7561	1.94413
$656$	0.427707	0.0166991
$657$	−10.5274	−0.410714
$658$	−3.54186	−0.138076
$659$	−15.0982	−0.588143	−0.294071	−	0.955783i	$-0.595010\pi$
$659$	−15.0982	−0.588143	−0.294071	+	0.955783i	$0.595010\pi$
$660$	0	0
$661$	4.92861	0.191701	0.0958503	−	0.995396i	$-0.469443\pi$
$661$	4.92861	0.191701	0.0958503	+	0.995396i	$0.469443\pi$
$662$	0.903869	0.0351299
$663$	−3.92892	−0.152587
$664$	−13.6432	−0.529458
$665$	−13.4062	−0.519869
$666$	−5.77147	−0.223640
$667$	−54.0495	−2.09280
$668$	−15.5308	−0.600904
$669$	8.40394	0.324915
$670$	−32.2369	−1.24542
$671$	0	0
$672$	5.95085	0.229559
$673$	21.3657	0.823587	0.411793	−	0.911277i	$-0.364903\pi$
$673$	21.3657	0.823587	0.411793	+	0.911277i	$0.364903\pi$
$674$	−12.3485	−0.475648
$675$	0.852319	0.0328058
$676$	−3.07288	−0.118188
$677$	25.2982	0.972290	0.486145	−	0.873878i	$-0.338403\pi$
$677$	25.2982	0.972290	0.486145	+	0.873878i	$0.338403\pi$
$678$	11.5577	0.443872
$679$	−3.43913	−0.131982
$680$	−6.78113	−0.260044
$681$	9.94254	0.380999
$682$	0	0
$683$	28.0183	1.07209	0.536045	−	0.844190i	$-0.319918\pi$
$683$	28.0183	1.07209	0.536045	+	0.844190i	$0.319918\pi$
$684$	6.69864	0.256129
$685$	24.8819	0.950688
$686$	−11.5791	−0.442092
$687$	−24.3077	−0.927396
$688$	0.0324601	0.00123753
$689$	32.1108	1.22332
$690$	−13.5715	−0.516659
$691$	39.1524	1.48943	0.744715	−	0.667383i	$-0.232586\pi$
$691$	39.1524	1.48943	0.744715	+	0.667383i	$0.232586\pi$
$692$	−28.6263	−1.08821
$693$	0	0
$694$	3.77198	0.143183
$695$	−16.9266	−0.642061
$696$	−23.2126	−0.879871
$697$	3.78144	0.143232
$698$	−1.27387	−0.0482167
$699$	−9.31830	−0.352451
$700$	−1.12160	−0.0423924
$701$	19.4410	0.734278	0.367139	−	0.930166i	$-0.380337\pi$
$701$	19.4410	0.734278	0.367139	+	0.930166i	$0.380337\pi$
$702$	−3.37701	−0.127457
$703$	35.6636	1.34508
$704$	0	0
$705$	−9.55417	−0.359831
$706$	−2.30884	−0.0868944
$707$	−0.605372	−0.0227674
$708$	−1.95061	−0.0733083
$709$	22.6904	0.852154	0.426077	−	0.904687i	$-0.359895\pi$
$709$	22.6904	0.852154	0.426077	+	0.904687i	$0.359895\pi$
$710$	29.1625	1.09445
$711$	−1.02636	−0.0384916
$712$	35.5463	1.33215
$713$	63.9442	2.39473
$714$	0.896815	0.0335624
$715$	0	0
$716$	10.9989	0.411048
$717$	17.4862	0.653035
$718$	−6.45295	−0.240822
$719$	7.39412	0.275754	0.137877	−	0.990449i	$-0.455972\pi$
$719$	7.39412	0.275754	0.137877	+	0.990449i	$0.455972\pi$
$720$	0.273623	0.0101973
$721$	14.4665	0.538762
$722$	7.91566	0.294590
$723$	2.49718	0.0928712
$724$	12.7335	0.473236
$725$	7.05810	0.262131
$726$	0	0
$727$	48.0281	1.78126	0.890632	−	0.454724i	$-0.150262\pi$
$727$	48.0281	1.78126	0.890632	+	0.454724i	$0.150262\pi$
$728$	11.4910	0.425883
$729$	1.00000	0.0370370
$730$	−21.8899	−0.810182
$731$	0.286986	0.0106146
$732$	−9.80782	−0.362508
$733$	2.98453	0.110236	0.0551181	−	0.998480i	$-0.482446\pi$
$733$	2.98453	0.110236	0.0551181	+	0.998480i	$0.482446\pi$
$734$	−28.1468	−1.03892
$735$	−14.3005	−0.527481
$736$	−37.2255	−1.37215
$737$	0	0
$738$	3.25024	0.119643
$739$	−10.2521	−0.377130	−0.188565	−	0.982061i	$-0.560384\pi$
$739$	−10.2521	−0.377130	−0.188565	+	0.982061i	$0.560384\pi$
$740$	20.4872	0.753124
$741$	20.8675	0.766586
$742$	−7.32959	−0.269078
$743$	43.8323	1.60805	0.804026	−	0.594594i	$-0.202687\pi$
$743$	43.8323	1.60805	0.804026	+	0.594594i	$0.202687\pi$
$744$	27.4620	1.00681
$745$	−44.1075	−1.61597
$746$	15.5778	0.570344
$747$	4.86718	0.178081
$748$	0	0
$749$	−14.1722	−0.517842
$750$	−8.62437	−0.314918
$751$	−32.9728	−1.20319	−0.601597	−	0.798800i	$-0.705469\pi$
$751$	−32.9728	−1.20319	−0.601597	+	0.798800i	$0.705469\pi$
$752$	−0.446702	−0.0162895
$753$	−4.39891	−0.160305
$754$	−27.9652	−1.01843
$755$	22.8303	0.830878
$756$	−1.31594	−0.0478601
$757$	26.4188	0.960209	0.480105	−	0.877211i	$-0.340599\pi$
$757$	26.4188	0.960209	0.480105	+	0.877211i	$0.340599\pi$
$758$	26.2500	0.953443
$759$	0	0
$760$	36.0163	1.30645
$761$	17.0803	0.619162	0.309581	−	0.950873i	$-0.399811\pi$
$761$	17.0803	0.619162	0.309581	+	0.950873i	$0.399811\pi$
$762$	10.4812	0.379695
$763$	−15.0569	−0.545095
$764$	−16.1041	−0.582625
$765$	2.41916	0.0874648
$766$	6.49866	0.234806
$767$	−6.07650	−0.219410
$768$	−15.7019	−0.566594
$769$	34.1570	1.23173	0.615866	−	0.787851i	$-0.288806\pi$
$769$	34.1570	1.23173	0.615866	+	0.787851i	$0.288806\pi$
$770$	0	0
$771$	13.1481	0.473517
$772$	7.30895	0.263055
$773$	16.5196	0.594169	0.297085	−	0.954851i	$-0.403986\pi$
$773$	16.5196	0.594169	0.297085	+	0.954851i	$0.403986\pi$
$774$	0.246671	0.00886641
$775$	−8.35021	−0.299948
$776$	9.23936	0.331674
$777$	−7.00605	−0.251340
$778$	14.8518	0.532463
$779$	−20.0842	−0.719590
$780$	11.9875	0.429221
$781$	0	0
$782$	−5.61002	−0.200614
$783$	8.28105	0.295941
$784$	−0.668614	−0.0238791
$785$	−47.9612	−1.71181
$786$	17.6783	0.630564
$787$	19.4081	0.691824	0.345912	−	0.938267i	$-0.387570\pi$
$787$	19.4081	0.691824	0.345912	+	0.938267i	$0.387570\pi$
$788$	7.73724	0.275628
$789$	3.56223	0.126819
$790$	−2.13414	−0.0759293
$791$	14.0301	0.498851
$792$	0	0
$793$	−30.5532	−1.08497
$794$	−22.2131	−0.788313
$795$	−19.7716	−0.701225
$796$	−6.02144	−0.213424
$797$	18.6580	0.660901	0.330451	−	0.943823i	$-0.392799\pi$
$797$	18.6580	0.660901	0.330451	+	0.943823i	$0.392799\pi$
$798$	−4.76321	−0.168616
$799$	−3.94938	−0.139719
$800$	4.86113	0.171867
$801$	−12.6811	−0.448064
$802$	−2.88897	−0.102013
$803$	0	0
$804$	19.5533	0.689593
$805$	−16.4746	−0.580653
$806$	33.0847	1.16536
$807$	−13.3848	−0.471168
$808$	1.62636	0.0572150
$809$	−4.19498	−0.147488	−0.0737438	−	0.997277i	$-0.523495\pi$
$809$	−4.19498	−0.147488	−0.0737438	+	0.997277i	$0.523495\pi$
$810$	2.07932	0.0730600
$811$	−38.6397	−1.35682	−0.678411	−	0.734683i	$-0.737331\pi$
$811$	−38.6397	−1.35682	−0.678411	+	0.734683i	$0.737331\pi$
$812$	−10.8973	−0.382421
$813$	−12.2154	−0.428412
$814$	0	0
$815$	23.4126	0.820107
$816$	0.113107	0.00395953
$817$	−1.52425	−0.0533268
$818$	−4.95463	−0.173234
$819$	−4.09938	−0.143244
$820$	−11.5375	−0.402907
$821$	21.7621	0.759504	0.379752	−	0.925088i	$-0.376009\pi$
$821$	21.7621	0.759504	0.379752	+	0.925088i	$0.376009\pi$
$822$	8.84051	0.308348
$823$	−34.7023	−1.20965	−0.604823	−	0.796360i	$-0.706756\pi$
$823$	−34.7023	−1.20965	−0.604823	+	0.796360i	$0.706756\pi$
$824$	−38.8649	−1.35392
$825$	0	0
$826$	1.38702	0.0482606
$827$	7.32400	0.254680	0.127340	−	0.991859i	$-0.459356\pi$
$827$	7.32400	0.254680	0.127340	+	0.991859i	$0.459356\pi$
$828$	8.23183	0.286076
$829$	−43.5911	−1.51398	−0.756990	−	0.653426i	$-0.773331\pi$
$829$	−43.5911	−1.51398	−0.756990	+	0.653426i	$0.773331\pi$
$830$	10.1204	0.351286
$831$	−18.4436	−0.639801
$832$	−18.3717	−0.636923
$833$	−5.91135	−0.204816
$834$	−6.01399	−0.208248
$835$	29.7898	1.03092
$836$	0	0
$837$	−9.79704	−0.338635
$838$	−2.02698	−0.0700209
$839$	30.7258	1.06077	0.530387	−	0.847756i	$-0.322047\pi$
$839$	30.7258	1.06077	0.530387	+	0.847756i	$0.322047\pi$
$840$	−7.07533	−0.244122
$841$	39.5758	1.36468
$842$	22.8723	0.788230
$843$	−27.1649	−0.935609
$844$	3.99786	0.137612
$845$	5.89413	0.202764
$846$	−3.39459	−0.116708
$847$	0	0
$848$	−0.924412	−0.0317444
$849$	−16.5549	−0.568164
$850$	0.732589	0.0251276
$851$	43.8263	1.50234
$852$	−17.6886	−0.606000
$853$	31.5178	1.07915	0.539575	−	0.841938i	$-0.318585\pi$
$853$	31.5178	1.07915	0.539575	+	0.841938i	$0.318585\pi$
$854$	6.97405	0.238647
$855$	−12.8487	−0.439418
$856$	38.0742	1.30135
$857$	−10.2943	−0.351646	−0.175823	−	0.984422i	$-0.556259\pi$
$857$	−10.2943	−0.351646	−0.175823	+	0.984422i	$0.556259\pi$
$858$	0	0
$859$	33.7093	1.15015	0.575073	−	0.818102i	$-0.304974\pi$
$859$	33.7093	1.15015	0.575073	+	0.818102i	$0.304974\pi$
$860$	−0.875618	−0.0298583
$861$	3.94550	0.134462
$862$	25.8403	0.880126
$863$	39.0603	1.32963	0.664814	−	0.747009i	$-0.268511\pi$
$863$	39.0603	1.32963	0.664814	+	0.747009i	$0.268511\pi$
$864$	5.70341	0.194034
$865$	54.9084	1.86694
$866$	3.26007	0.110782
$867$	1.00000	0.0339618
$868$	12.8923	0.437592
$869$	0	0
$870$	17.2190	0.583778
$871$	60.9122	2.06393
$872$	40.4509	1.36984
$873$	−3.29613	−0.111557
$874$	29.7962	1.00787
$875$	−10.4692	−0.353924
$876$	13.2774	0.448601
$877$	25.6342	0.865604	0.432802	−	0.901489i	$-0.357525\pi$
$877$	25.6342	0.865604	0.432802	+	0.901489i	$0.357525\pi$
$878$	−34.2414	−1.15559
$879$	23.7909	0.802447
$880$	0	0
$881$	−20.9147	−0.704635	−0.352317	−	0.935881i	$-0.614606\pi$
$881$	−20.9147	−0.704635	−0.352317	+	0.935881i	$0.614606\pi$
$882$	−5.08095	−0.171084
$883$	8.48737	0.285623	0.142811	−	0.989750i	$-0.454386\pi$
$883$	8.48737	0.285623	0.142811	+	0.989750i	$0.454386\pi$
$884$	4.95523	0.166662
$885$	3.74148	0.125769
$886$	8.13351	0.273251
$887$	−29.0070	−0.973959	−0.486979	−	0.873414i	$-0.661901\pi$
$887$	−29.0070	−0.973959	−0.486979	+	0.873414i	$0.661901\pi$
$888$	18.8220	0.631626
$889$	12.7233	0.426725
$890$	−26.3681	−0.883861
$891$	0	0
$892$	−10.5992	−0.354888
$893$	20.9761	0.701940
$894$	−15.6713	−0.524128
$895$	−21.0971	−0.705198
$896$	−7.70819	−0.257513
$897$	25.6436	0.856216
$898$	−20.9077	−0.697699
$899$	−81.1298	−2.70583
$900$	−1.07496	−0.0358320
$901$	−8.17291	−0.272279
$902$	0	0
$903$	0.299437	0.00996463
$904$	−37.6923	−1.25363
$905$	−24.4242	−0.811889
$906$	8.11157	0.269489
$907$	24.7822	0.822878	0.411439	−	0.911437i	$-0.365026\pi$
$907$	24.7822	0.822878	0.411439	+	0.911437i	$0.365026\pi$
$908$	−12.5397	−0.416145
$909$	−0.580200	−0.0192440
$910$	−8.52394	−0.282566
$911$	0.651349	0.0215801	0.0107901	−	0.999942i	$-0.496565\pi$
$911$	0.651349	0.0215801	0.0107901	+	0.999942i	$0.496565\pi$
$912$	−0.600738	−0.0198924
$913$	0	0
$914$	15.7009	0.519340
$915$	18.8125	0.621922
$916$	30.6573	1.01295
$917$	21.4599	0.708667
$918$	0.859524	0.0283685
$919$	−24.5981	−0.811417	−0.405709	−	0.914003i	$-0.632975\pi$
$919$	−24.5981	−0.811417	−0.405709	+	0.914003i	$0.632975\pi$
$920$	44.2597	1.45920
$921$	−5.36749	−0.176865
$922$	14.2175	0.468229
$923$	−55.1031	−1.81374
$924$	0	0
$925$	−5.72309	−0.188174
$926$	14.0716	0.462421
$927$	13.8650	0.455386
$928$	47.2302	1.55041
$929$	−28.3571	−0.930365	−0.465182	−	0.885215i	$-0.654011\pi$
$929$	−28.3571	−0.930365	−0.465182	+	0.885215i	$0.654011\pi$
$930$	−20.3712	−0.667999
$931$	31.3966	1.02898
$932$	11.7524	0.384963
$933$	2.97244	0.0973134
$934$	20.8617	0.682616
$935$	0	0
$936$	11.0132	0.359976
$937$	16.0838	0.525436	0.262718	−	0.964873i	$-0.415381\pi$
$937$	16.0838	0.525436	0.262718	+	0.964873i	$0.415381\pi$
$938$	−13.9038	−0.453975
$939$	5.54538	0.180967
$940$	12.0499	0.393024
$941$	−54.6515	−1.78159	−0.890794	−	0.454408i	$-0.849851\pi$
$941$	−54.6515	−1.78159	−0.890794	+	0.454408i	$0.849851\pi$
$942$	−17.0406	−0.555212
$943$	−24.6810	−0.803725
$944$	0.174932	0.00569354
$945$	2.52411	0.0821094
$946$	0	0
$947$	−8.99559	−0.292317	−0.146159	−	0.989261i	$-0.546691\pi$
$947$	−8.99559	−0.292317	−0.146159	+	0.989261i	$0.546691\pi$
$948$	1.29447	0.0420423
$949$	41.3614	1.34265
$950$	−3.89096	−0.126239
$951$	−7.40663	−0.240176
$952$	−2.92471	−0.0947903
$953$	−3.70112	−0.119891	−0.0599456	−	0.998202i	$-0.519093\pi$
$953$	−3.70112	−0.119891	−0.0599456	+	0.998202i	$0.519093\pi$
$954$	−7.02482	−0.227437
$955$	30.8894	0.999557
$956$	−22.0539	−0.713276
$957$	0	0
$958$	−27.0438	−0.873744
$959$	10.7316	0.346541
$960$	11.3120	0.365093
$961$	64.9820	2.09619
$962$	22.6757	0.731093
$963$	−13.5829	−0.437704
$964$	−3.14949	−0.101438
$965$	−14.0194	−0.451300
$966$	−5.85341	−0.188330
$967$	29.0343	0.933681	0.466840	−	0.884342i	$-0.345392\pi$
$967$	29.0343	0.933681	0.466840	+	0.884342i	$0.345392\pi$
$968$	0	0
$969$	−5.31125	−0.170622
$970$	−6.85372	−0.220060
$971$	−25.1048	−0.805651	−0.402826	−	0.915277i	$-0.631972\pi$
$971$	−25.1048	−0.805651	−0.402826	+	0.915277i	$0.631972\pi$
$972$	−1.26122	−0.0404536
$973$	−7.30045	−0.234042
$974$	6.66022	0.213407
$975$	−3.34870	−0.107244
$976$	0.879572	0.0281544
$977$	0.505296	0.0161659	0.00808293	−	0.999967i	$-0.497427\pi$
$977$	0.505296	0.0161659	0.00808293	+	0.999967i	$0.497427\pi$
$978$	8.31847	0.265995
$979$	0	0
$980$	18.0360	0.576139
$981$	−14.4308	−0.460739
$982$	6.55595	0.209209
$983$	−14.9764	−0.477672	−0.238836	−	0.971060i	$-0.576766\pi$
$983$	−14.9764	−0.477672	−0.238836	+	0.971060i	$0.576766\pi$
$984$	−10.5997	−0.337907
$985$	−14.8409	−0.472870
$986$	7.11776	0.226676
$987$	−4.12073	−0.131164
$988$	−26.3184	−0.837301
$989$	−1.87312	−0.0595619
$990$	0	0
$991$	−12.0943	−0.384188	−0.192094	−	0.981377i	$-0.561528\pi$
$991$	−12.0943	−0.384188	−0.192094	+	0.981377i	$0.561528\pi$
$992$	−55.8765	−1.77408
$993$	1.05159	0.0333713
$994$	12.5778	0.398944
$995$	11.5498	0.366153
$996$	−6.13857	−0.194508
$997$	22.9537	0.726951	0.363476	−	0.931604i	$-0.381590\pi$
$997$	22.9537	0.726951	0.363476	+	0.931604i	$0.381590\pi$
$998$	17.1006	0.541311
$999$	−6.71473	−0.212445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6171.2.a.bk.1.9		12
11.5	even	5		561.2.m.d.256.2	yes	24
11.9	even	5		561.2.m.d.103.2	✓	24
11.10	odd	2		6171.2.a.bl.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.103.2	✓	24	11.9	even	5
561.2.m.d.256.2	yes	24	11.5	even	5
6171.2.a.bk.1.9		12	1.1	even	1	trivial
6171.2.a.bl.1.4		12	11.10	odd	2

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:	\( N \)	\(=\)	\( 6171 = 3 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6171.a (trivial)

\(f(q)\)	\(=\)	\(q+0.859524 q^{2} +1.00000 q^{3} -1.26122 q^{4} +2.41916 q^{5} +0.859524 q^{6} +1.04339 q^{7} -2.80310 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.859524 q^{2} +1.00000 q^{3} -1.26122 q^{4} +2.41916 q^{5} +0.859524 q^{6} +1.04339 q^{7} -2.80310 q^{8} +1.00000 q^{9} +2.07932 q^{10} -1.26122 q^{12} -3.92892 q^{13} +0.896815 q^{14} +2.41916 q^{15} +0.113107 q^{16} +1.00000 q^{17} +0.859524 q^{18} -5.31125 q^{19} -3.05108 q^{20} +1.04339 q^{21} -6.52689 q^{23} -2.80310 q^{24} +0.852319 q^{25} -3.37701 q^{26} +1.00000 q^{27} -1.31594 q^{28} +8.28105 q^{29} +2.07932 q^{30} -9.79704 q^{31} +5.70341 q^{32} +0.859524 q^{34} +2.52411 q^{35} -1.26122 q^{36} -6.71473 q^{37} -4.56515 q^{38} -3.92892 q^{39} -6.78113 q^{40} +3.78144 q^{41} +0.896815 q^{42} +0.286986 q^{43} +2.41916 q^{45} -5.61002 q^{46} -3.94938 q^{47} +0.113107 q^{48} -5.91135 q^{49} +0.732589 q^{50} +1.00000 q^{51} +4.95523 q^{52} -8.17291 q^{53} +0.859524 q^{54} -2.92471 q^{56} -5.31125 q^{57} +7.11776 q^{58} +1.54661 q^{59} -3.05108 q^{60} +7.77647 q^{61} -8.42079 q^{62} +1.04339 q^{63} +4.67601 q^{64} -9.50468 q^{65} -15.5035 q^{67} -1.26122 q^{68} -6.52689 q^{69} +2.16954 q^{70} +14.0250 q^{71} -2.80310 q^{72} -10.5274 q^{73} -5.77147 q^{74} +0.852319 q^{75} +6.69864 q^{76} -3.37701 q^{78} -1.02636 q^{79} +0.273623 q^{80} +1.00000 q^{81} +3.25024 q^{82} +4.86718 q^{83} -1.31594 q^{84} +2.41916 q^{85} +0.246671 q^{86} +8.28105 q^{87} -12.6811 q^{89} +2.07932 q^{90} -4.09938 q^{91} +8.23183 q^{92} -9.79704 q^{93} -3.39459 q^{94} -12.8487 q^{95} +5.70341 q^{96} -3.29613 q^{97} -5.08095 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 12 q^{3} + 9 q^{4} - 14 q^{5} - q^{6} - 5 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - q^2 + 12 * q^3 + 9 * q^4 - 14 * q^5 - q^6 - 5 * q^7 + 12 * q^9	\( 12 q - q^{2} + 12 q^{3} + 9 q^{4} - 14 q^{5} - q^{6} - 5 q^{7} + 12 q^{9} + 8 q^{10} + 9 q^{12} - 7 q^{13} - 13 q^{14} - 14 q^{15} + 11 q^{16} + 12 q^{17} - q^{18} + 3 q^{19} - 36 q^{20} - 5 q^{21} - 39 q^{23} + 8 q^{25} - 25 q^{26} + 12 q^{27} - 9 q^{28} + 10 q^{29} + 8 q^{30} - 25 q^{31} - 11 q^{32} - q^{34} + 12 q^{35} + 9 q^{36} - 10 q^{37} - 34 q^{38} - 7 q^{39} - 13 q^{40} + 17 q^{41} - 13 q^{42} - 18 q^{43} - 14 q^{45} + 19 q^{46} - 38 q^{47} + 11 q^{48} - 15 q^{49} - 18 q^{50} + 12 q^{51} + 32 q^{52} - 40 q^{53} - q^{54} - 25 q^{56} + 3 q^{57} + 3 q^{58} - 18 q^{59} - 36 q^{60} - 22 q^{61} + 3 q^{62} - 5 q^{63} - 20 q^{64} + 3 q^{65} - 9 q^{67} + 9 q^{68} - 39 q^{69} + 13 q^{70} - 24 q^{71} + q^{73} - 4 q^{74} + 8 q^{75} + 29 q^{76} - 25 q^{78} - 3 q^{79} - 43 q^{80} + 12 q^{81} + q^{82} + 4 q^{83} - 9 q^{84} - 14 q^{85} - 4 q^{86} + 10 q^{87} - 62 q^{89} + 8 q^{90} - 5 q^{91} - 52 q^{92} - 25 q^{93} - 16 q^{94} - 4 q^{95} - 11 q^{96} - 5 q^{97} - 7 q^{98}+O(q^{100}) \) 12 * q - q^2 + 12 * q^3 + 9 * q^4 - 14 * q^5 - q^6 - 5 * q^7 + 12 * q^9 + 8 * q^10 + 9 * q^12 - 7 * q^13 - 13 * q^14 - 14 * q^15 + 11 * q^16 + 12 * q^17 - q^18 + 3 * q^19 - 36 * q^20 - 5 * q^21 - 39 * q^23 + 8 * q^25 - 25 * q^26 + 12 * q^27 - 9 * q^28 + 10 * q^29 + 8 * q^30 - 25 * q^31 - 11 * q^32 - q^34 + 12 * q^35 + 9 * q^36 - 10 * q^37 - 34 * q^38 - 7 * q^39 - 13 * q^40 + 17 * q^41 - 13 * q^42 - 18 * q^43 - 14 * q^45 + 19 * q^46 - 38 * q^47 + 11 * q^48 - 15 * q^49 - 18 * q^50 + 12 * q^51 + 32 * q^52 - 40 * q^53 - q^54 - 25 * q^56 + 3 * q^57 + 3 * q^58 - 18 * q^59 - 36 * q^60 - 22 * q^61 + 3 * q^62 - 5 * q^63 - 20 * q^64 + 3 * q^65 - 9 * q^67 + 9 * q^68 - 39 * q^69 + 13 * q^70 - 24 * q^71 + q^73 - 4 * q^74 + 8 * q^75 + 29 * q^76 - 25 * q^78 - 3 * q^79 - 43 * q^80 + 12 * q^81 + q^82 + 4 * q^83 - 9 * q^84 - 14 * q^85 - 4 * q^86 + 10 * q^87 - 62 * q^89 + 8 * q^90 - 5 * q^91 - 52 * q^92 - 25 * q^93 - 16 * q^94 - 4 * q^95 - 11 * q^96 - 5 * q^97 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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