LMFDB - Embedded newform 6762.2.a.ct.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.22833$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.585786 q^{10} +5.93089 q^{11} +1.00000 q^{12} +6.45666 q^{13} +0.585786 q^{15} +1.00000 q^{16} -0.371771 q^{17} +1.00000 q^{18} +3.26022 q^{19} +0.585786 q^{20} +5.93089 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.65685 q^{25} +6.45666 q^{26} +1.00000 q^{27} -0.948474 q^{29} +0.585786 q^{30} +1.26022 q^{31} +1.00000 q^{32} +5.93089 q^{33} -0.371771 q^{34} +1.00000 q^{36} +0.371771 q^{37} +3.26022 q^{38} +6.45666 q^{39} +0.585786 q^{40} -10.4476 q^{41} -6.54154 q^{43} +5.93089 q^{44} +0.585786 q^{45} +1.00000 q^{46} +10.6016 q^{47} +1.00000 q^{48} -4.65685 q^{50} -0.371771 q^{51} +6.45666 q^{52} -8.23356 q^{53} +1.00000 q^{54} +3.47424 q^{55} +3.26022 q^{57} -0.948474 q^{58} +1.05153 q^{59} +0.585786 q^{60} -4.44757 q^{61} +1.26022 q^{62} +1.00000 q^{64} +3.78222 q^{65} +5.93089 q^{66} -0.0286249 q^{67} -0.371771 q^{68} +1.00000 q^{69} +2.38755 q^{71} +1.00000 q^{72} +4.76840 q^{73} +0.371771 q^{74} -4.65685 q^{75} +3.26022 q^{76} +6.45666 q^{78} -10.7307 q^{79} +0.585786 q^{80} +1.00000 q^{81} -10.4476 q^{82} +2.51668 q^{83} -0.217778 q^{85} -6.54154 q^{86} -0.948474 q^{87} +5.93089 q^{88} -15.2318 q^{89} +0.585786 q^{90} +1.00000 q^{92} +1.26022 q^{93} +10.6016 q^{94} +1.90979 q^{95} +1.00000 q^{96} +8.85705 q^{97} +5.93089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 8 q^{10} + 4 q^{11} + 4 q^{12} + 12 q^{13} + 8 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 12 q^{26} + 4 q^{27} + 8 q^{29} + 8 q^{30} - 4 q^{31} + 4 q^{32} + 4 q^{33} - 4 q^{34} + 4 q^{36} + 4 q^{37} + 4 q^{38} + 12 q^{39} + 8 q^{40} - 8 q^{41} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 4 q^{46} + 12 q^{47} + 4 q^{48} + 4 q^{50} - 4 q^{51} + 12 q^{52} + 4 q^{53} + 4 q^{54} + 8 q^{55} + 4 q^{57} + 8 q^{58} + 16 q^{59} + 8 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{65} + 4 q^{66} + 20 q^{67} - 4 q^{68} + 4 q^{69} - 24 q^{71} + 4 q^{72} + 8 q^{73} + 4 q^{74} + 4 q^{75} + 4 q^{76} + 12 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} - 4 q^{83} + 4 q^{86} + 8 q^{87} + 4 q^{88} + 20 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} + 12 q^{94} + 4 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 8 * q^10 + 4 * q^11 + 4 * q^12 + 12 * q^13 + 8 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 + 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 12 * q^26 + 4 * q^27 + 8 * q^29 + 8 * q^30 - 4 * q^31 + 4 * q^32 + 4 * q^33 - 4 * q^34 + 4 * q^36 + 4 * q^37 + 4 * q^38 + 12 * q^39 + 8 * q^40 - 8 * q^41 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 4 * q^46 + 12 * q^47 + 4 * q^48 + 4 * q^50 - 4 * q^51 + 12 * q^52 + 4 * q^53 + 4 * q^54 + 8 * q^55 + 4 * q^57 + 8 * q^58 + 16 * q^59 + 8 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^65 + 4 * q^66 + 20 * q^67 - 4 * q^68 + 4 * q^69 - 24 * q^71 + 4 * q^72 + 8 * q^73 + 4 * q^74 + 4 * q^75 + 4 * q^76 + 12 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 - 4 * q^83 + 4 * q^86 + 8 * q^87 + 4 * q^88 + 20 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 + 12 * q^94 + 4 * q^96 + 4 * q^97 + 4 * q^99

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.585786	0.261972	0.130986	−	0.991384i	$-0.458186\pi$
$5$	0.585786	0.261972	0.130986	+	0.991384i	$0.458186\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.585786	0.185242
$11$	5.93089	1.78823	0.894116	−	0.447836i	$-0.147805\pi$
$11$	5.93089	1.78823	0.894116	+	0.447836i	$0.147805\pi$
$12$	1.00000	0.288675
$13$	6.45666	1.79075	0.895377	−	0.445309i	$-0.146906\pi$
$13$	6.45666	1.79075	0.895377	+	0.445309i	$0.146906\pi$
$14$	0	0
$15$	0.585786	0.151249
$16$	1.00000	0.250000
$17$	−0.371771	−0.0901676	−0.0450838	−	0.998983i	$-0.514355\pi$
$17$	−0.371771	−0.0901676	−0.0450838	+	0.998983i	$0.514355\pi$
$18$	1.00000	0.235702
$19$	3.26022	0.747946	0.373973	−	0.927440i	$-0.377995\pi$
$19$	3.26022	0.747946	0.373973	+	0.927440i	$0.377995\pi$
$20$	0.585786	0.130986
$21$	0	0
$22$	5.93089	1.26447
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−4.65685	−0.931371
$26$	6.45666	1.26625
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.948474	−0.176127	−0.0880636	−	0.996115i	$-0.528068\pi$
$29$	−0.948474	−0.176127	−0.0880636	+	0.996115i	$0.528068\pi$
$30$	0.585786	0.106949
$31$	1.26022	0.226342	0.113171	−	0.993576i	$-0.463899\pi$
$31$	1.26022	0.226342	0.113171	+	0.993576i	$0.463899\pi$
$32$	1.00000	0.176777
$33$	5.93089	1.03244
$34$	−0.371771	−0.0637581
$35$	0	0
$36$	1.00000	0.166667
$37$	0.371771	0.0611187	0.0305594	−	0.999533i	$-0.490271\pi$
$37$	0.371771	0.0611187	0.0305594	+	0.999533i	$0.490271\pi$
$38$	3.26022	0.528878
$39$	6.45666	1.03389
$40$	0.585786	0.0926210
$41$	−10.4476	−1.63164	−0.815818	−	0.578308i	$-0.803713\pi$
$41$	−10.4476	−1.63164	−0.815818	+	0.578308i	$0.803713\pi$
$42$	0	0
$43$	−6.54154	−0.997576	−0.498788	−	0.866724i	$-0.666221\pi$
$43$	−6.54154	−0.997576	−0.498788	+	0.866724i	$0.666221\pi$
$44$	5.93089	0.894116
$45$	0.585786	0.0873239
$46$	1.00000	0.147442
$47$	10.6016	1.54640	0.773199	−	0.634164i	$-0.218656\pi$
$47$	10.6016	1.54640	0.773199	+	0.634164i	$0.218656\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−4.65685	−0.658579
$51$	−0.371771	−0.0520583
$52$	6.45666	0.895377
$53$	−8.23356	−1.13097	−0.565483	−	0.824760i	$-0.691310\pi$
$53$	−8.23356	−1.13097	−0.565483	+	0.824760i	$0.691310\pi$
$54$	1.00000	0.136083
$55$	3.47424	0.468466
$56$	0	0
$57$	3.26022	0.431827
$58$	−0.948474	−0.124541
$59$	1.05153	0.136897	0.0684485	−	0.997655i	$-0.478195\pi$
$59$	1.05153	0.136897	0.0684485	+	0.997655i	$0.478195\pi$
$60$	0.585786	0.0756247
$61$	−4.44757	−0.569453	−0.284727	−	0.958609i	$-0.591903\pi$
$61$	−4.44757	−0.569453	−0.284727	+	0.958609i	$0.591903\pi$
$62$	1.26022	0.160048
$63$	0	0
$64$	1.00000	0.125000
$65$	3.78222	0.469127
$66$	5.93089	0.730042
$67$	−0.0286249	−0.00349709	−0.00174855	−	0.999998i	$-0.500557\pi$
$67$	−0.0286249	−0.00349709	−0.00174855	+	0.999998i	$0.500557\pi$
$68$	−0.371771	−0.0450838
$69$	1.00000	0.120386
$70$	0	0
$71$	2.38755	0.283350	0.141675	−	0.989913i	$-0.454751\pi$
$71$	2.38755	0.283350	0.141675	+	0.989913i	$0.454751\pi$
$72$	1.00000	0.117851
$73$	4.76840	0.558099	0.279050	−	0.960277i	$-0.409981\pi$
$73$	4.76840	0.558099	0.279050	+	0.960277i	$0.409981\pi$
$74$	0.371771	0.0432175
$75$	−4.65685	−0.537727
$76$	3.26022	0.373973
$77$	0	0
$78$	6.45666	0.731072
$79$	−10.7307	−1.20730	−0.603649	−	0.797250i	$-0.706287\pi$
$79$	−10.7307	−1.20730	−0.603649	+	0.797250i	$0.706287\pi$
$80$	0.585786	0.0654929
$81$	1.00000	0.111111
$82$	−10.4476	−1.15374
$83$	2.51668	0.276241	0.138121	−	0.990415i	$-0.455894\pi$
$83$	2.51668	0.276241	0.138121	+	0.990415i	$0.455894\pi$
$84$	0	0
$85$	−0.217778	−0.0236214
$86$	−6.54154	−0.705393
$87$	−0.948474	−0.101687
$88$	5.93089	0.632235
$89$	−15.2318	−1.61456	−0.807281	−	0.590167i	$-0.799062\pi$
$89$	−15.2318	−1.61456	−0.807281	+	0.590167i	$0.799062\pi$
$90$	0.585786	0.0617473
$91$	0	0
$92$	1.00000	0.104257
$93$	1.26022	0.130679
$94$	10.6016	1.09347
$95$	1.90979	0.195941
$96$	1.00000	0.102062
$97$	8.85705	0.899297	0.449649	−	0.893205i	$-0.351549\pi$
$97$	8.85705	0.899297	0.449649	+	0.893205i	$0.351549\pi$
$98$	0	0
$99$	5.93089	0.596077
$100$	−4.65685	−0.465685
$101$	−4.54154	−0.451900	−0.225950	−	0.974139i	$-0.572549\pi$
$101$	−4.54154	−0.451900	−0.225950	+	0.974139i	$0.572549\pi$
$102$	−0.371771	−0.0368108
$103$	5.77690	0.569215	0.284607	−	0.958644i	$-0.408137\pi$
$103$	5.77690	0.569215	0.284607	+	0.958644i	$0.408137\pi$
$104$	6.45666	0.633127
$105$	0	0
$106$	−8.23356	−0.799714
$107$	7.41798	0.717123	0.358561	−	0.933506i	$-0.383267\pi$
$107$	7.41798	0.717123	0.358561	+	0.933506i	$0.383267\pi$
$108$	1.00000	0.0962250
$109$	−10.8571	−1.03992	−0.519958	−	0.854192i	$-0.674053\pi$
$109$	−10.8571	−1.03992	−0.519958	+	0.854192i	$0.674053\pi$
$110$	3.47424	0.331255
$111$	0.371771	0.0352869
$112$	0	0
$113$	−10.5258	−0.990181	−0.495090	−	0.868842i	$-0.664865\pi$
$113$	−10.5258	−0.990181	−0.495090	+	0.868842i	$0.664865\pi$
$114$	3.26022	0.305348
$115$	0.585786	0.0546249
$116$	−0.948474	−0.0880636
$117$	6.45666	0.596918
$118$	1.05153	0.0968008
$119$	0	0
$120$	0.585786	0.0534747
$121$	24.1755	2.19777
$122$	−4.44757	−0.402664
$123$	−10.4476	−0.942026
$124$	1.26022	0.113171
$125$	−5.65685	−0.505964
$126$	0	0
$127$	−20.5925	−1.82729	−0.913644	−	0.406516i	$-0.866744\pi$
$127$	−20.5925	−1.82729	−0.913644	+	0.406516i	$0.866744\pi$
$128$	1.00000	0.0883883
$129$	−6.54154	−0.575951
$130$	3.78222	0.331723
$131$	−13.3489	−1.16630	−0.583148	−	0.812366i	$-0.698179\pi$
$131$	−13.3489	−1.16630	−0.583148	+	0.812366i	$0.698179\pi$
$132$	5.93089	0.516218
$133$	0	0
$134$	−0.0286249	−0.00247282
$135$	0.585786	0.0504165
$136$	−0.371771	−0.0318791
$137$	−10.7435	−0.917883	−0.458941	−	0.888467i	$-0.651771\pi$
$137$	−10.7435	−0.917883	−0.458941	+	0.888467i	$0.651771\pi$
$138$	1.00000	0.0851257
$139$	10.8284	0.918455	0.459228	−	0.888319i	$-0.348126\pi$
$139$	10.8284	0.918455	0.459228	+	0.888319i	$0.348126\pi$
$140$	0	0
$141$	10.6016	0.892813
$142$	2.38755	0.200359
$143$	38.2937	3.20228
$144$	1.00000	0.0833333
$145$	−0.555603	−0.0461403
$146$	4.76840	0.394636
$147$	0	0
$148$	0.371771	0.0305594
$149$	10.6616	0.873431	0.436716	−	0.899600i	$-0.356142\pi$
$149$	10.6616	0.873431	0.436716	+	0.899600i	$0.356142\pi$
$150$	−4.65685	−0.380231
$151$	−12.9005	−1.04983	−0.524913	−	0.851156i	$-0.675902\pi$
$151$	−12.9005	−1.04983	−0.524913	+	0.851156i	$0.675902\pi$
$152$	3.26022	0.264439
$153$	−0.371771	−0.0300559
$154$	0	0
$155$	0.738220	0.0592953
$156$	6.45666	0.516946
$157$	−10.3222	−0.823802	−0.411901	−	0.911229i	$-0.635135\pi$
$157$	−10.3222	−0.823802	−0.411901	+	0.911229i	$0.635135\pi$
$158$	−10.7307	−0.853688
$159$	−8.23356	−0.652964
$160$	0.585786	0.0463105
$161$	0	0
$162$	1.00000	0.0785674
$163$	2.18262	0.170956	0.0854779	−	0.996340i	$-0.472758\pi$
$163$	2.18262	0.170956	0.0854779	+	0.996340i	$0.472758\pi$
$164$	−10.4476	−0.815818
$165$	3.47424	0.270469
$166$	2.51668	0.195332
$167$	−3.83039	−0.296404	−0.148202	−	0.988957i	$-0.547349\pi$
$167$	−3.83039	−0.296404	−0.148202	+	0.988957i	$0.547349\pi$
$168$	0	0
$169$	28.6884	2.20680
$170$	−0.217778	−0.0167028
$171$	3.26022	0.249315
$172$	−6.54154	−0.498788
$173$	−3.08015	−0.234180	−0.117090	−	0.993121i	$-0.537357\pi$
$173$	−3.08015	−0.234180	−0.117090	+	0.993121i	$0.537357\pi$
$174$	−0.948474	−0.0719036
$175$	0	0
$176$	5.93089	0.447058
$177$	1.05153	0.0790376
$178$	−15.2318	−1.14167
$179$	10.3747	0.775442	0.387721	−	0.921777i	$-0.373262\pi$
$179$	10.3747	0.775442	0.387721	+	0.921777i	$0.373262\pi$
$180$	0.585786	0.0436619
$181$	13.6191	1.01230	0.506152	−	0.862445i	$-0.331068\pi$
$181$	13.6191	1.01230	0.506152	+	0.862445i	$0.331068\pi$
$182$	0	0
$183$	−4.44757	−0.328774
$184$	1.00000	0.0737210
$185$	0.217778	0.0160114
$186$	1.26022	0.0924039
$187$	−2.20493	−0.161241
$188$	10.6016	0.773199
$189$	0	0
$190$	1.90979	0.138551
$191$	9.30086	0.672987	0.336493	−	0.941686i	$-0.390759\pi$
$191$	9.30086	0.672987	0.336493	+	0.941686i	$0.390759\pi$
$192$	1.00000	0.0721688
$193$	−22.1240	−1.59252	−0.796259	−	0.604956i	$-0.793191\pi$
$193$	−22.1240	−1.59252	−0.796259	+	0.604956i	$0.793191\pi$
$194$	8.85705	0.635899
$195$	3.78222	0.270851
$196$	0	0
$197$	−14.2493	−1.01522	−0.507612	−	0.861586i	$-0.669471\pi$
$197$	−14.2493	−1.01522	−0.507612	+	0.861586i	$0.669471\pi$
$198$	5.93089	0.421490
$199$	5.63869	0.399716	0.199858	−	0.979825i	$-0.435952\pi$
$199$	5.63869	0.399716	0.199858	+	0.979825i	$0.435952\pi$
$200$	−4.65685	−0.329289
$201$	−0.0286249	−0.00201905
$202$	−4.54154	−0.319542
$203$	0	0
$204$	−0.371771	−0.0260292
$205$	−6.12005	−0.427443
$206$	5.77690	0.402496
$207$	1.00000	0.0695048
$208$	6.45666	0.447689
$209$	19.3360	1.33750
$210$	0	0
$211$	10.0444	0.691485	0.345743	−	0.938329i	$-0.387627\pi$
$211$	10.0444	0.691485	0.345743	+	0.938329i	$0.387627\pi$
$212$	−8.23356	−0.565483
$213$	2.38755	0.163592
$214$	7.41798	0.507082
$215$	−3.83195	−0.261337
$216$	1.00000	0.0680414
$217$	0	0
$218$	−10.8571	−0.735332
$219$	4.76840	0.322219
$220$	3.47424	0.234233
$221$	−2.40040	−0.161468
$222$	0.371771	0.0249516
$223$	−14.6588	−0.981627	−0.490813	−	0.871265i	$-0.663300\pi$
$223$	−14.6588	−0.981627	−0.490813	+	0.871265i	$0.663300\pi$
$224$	0	0
$225$	−4.65685	−0.310457
$226$	−10.5258	−0.700163
$227$	8.36900	0.555470	0.277735	−	0.960658i	$-0.410416\pi$
$227$	8.36900	0.555470	0.277735	+	0.960658i	$0.410416\pi$
$228$	3.26022	0.215913
$229$	28.3666	1.87452	0.937259	−	0.348633i	$-0.113354\pi$
$229$	28.3666	1.87452	0.937259	+	0.348633i	$0.113354\pi$
$230$	0.585786	0.0386256
$231$	0	0
$232$	−0.948474	−0.0622703
$233$	13.1755	0.863155	0.431578	−	0.902076i	$-0.357957\pi$
$233$	13.1755	0.863155	0.431578	+	0.902076i	$0.357957\pi$
$234$	6.45666	0.422085
$235$	6.21025	0.405112
$236$	1.05153	0.0684485
$237$	−10.7307	−0.697034
$238$	0	0
$239$	−6.35599	−0.411135	−0.205567	−	0.978643i	$-0.565904\pi$
$239$	−6.35599	−0.411135	−0.205567	+	0.978643i	$0.565904\pi$
$240$	0.585786	0.0378124
$241$	5.52518	0.355908	0.177954	−	0.984039i	$-0.443052\pi$
$241$	5.52518	0.355908	0.177954	+	0.984039i	$0.443052\pi$
$242$	24.1755	1.55406
$243$	1.00000	0.0641500
$244$	−4.44757	−0.284727
$245$	0	0
$246$	−10.4476	−0.666113
$247$	21.0501	1.33939
$248$	1.26022	0.0800241
$249$	2.51668	0.159488
$250$	−5.65685	−0.357771
$251$	6.77494	0.427630	0.213815	−	0.976874i	$-0.431411\pi$
$251$	6.77494	0.427630	0.213815	+	0.976874i	$0.431411\pi$
$252$	0	0
$253$	5.93089	0.372872
$254$	−20.5925	−1.29209
$255$	−0.217778	−0.0136378
$256$	1.00000	0.0625000
$257$	5.29417	0.330241	0.165121	−	0.986273i	$-0.447199\pi$
$257$	5.29417	0.330241	0.165121	+	0.986273i	$0.447199\pi$
$258$	−6.54154	−0.407259
$259$	0	0
$260$	3.78222	0.234563
$261$	−0.948474	−0.0587090
$262$	−13.3489	−0.824696
$263$	−31.3137	−1.93089	−0.965443	−	0.260614i	$-0.916075\pi$
$263$	−31.3137	−1.93089	−0.965443	+	0.260614i	$0.916075\pi$
$264$	5.93089	0.365021
$265$	−4.82311	−0.296281
$266$	0	0
$267$	−15.2318	−0.932168
$268$	−0.0286249	−0.00174855
$269$	22.5064	1.37224	0.686119	−	0.727489i	$-0.259313\pi$
$269$	22.5064	1.37224	0.686119	+	0.727489i	$0.259313\pi$
$270$	0.585786	0.0356498
$271$	8.90423	0.540893	0.270447	−	0.962735i	$-0.412829\pi$
$271$	8.90423	0.540893	0.270447	+	0.962735i	$0.412829\pi$
$272$	−0.371771	−0.0225419
$273$	0	0
$274$	−10.7435	−0.649041
$275$	−27.6193	−1.66551
$276$	1.00000	0.0601929
$277$	−9.01637	−0.541741	−0.270870	−	0.962616i	$-0.587312\pi$
$277$	−9.01637	−0.541741	−0.270870	+	0.962616i	$0.587312\pi$
$278$	10.8284	0.649446
$279$	1.26022	0.0754475
$280$	0	0
$281$	24.4320	1.45749	0.728744	−	0.684786i	$-0.240104\pi$
$281$	24.4320	1.45749	0.728744	+	0.684786i	$0.240104\pi$
$282$	10.6016	0.631314
$283$	−0.762094	−0.0453018	−0.0226509	−	0.999743i	$-0.507211\pi$
$283$	−0.762094	−0.0453018	−0.0226509	+	0.999743i	$0.507211\pi$
$284$	2.38755	0.141675
$285$	1.90979	0.113126
$286$	38.2937	2.26436
$287$	0	0
$288$	1.00000	0.0589256
$289$	−16.8618	−0.991870
$290$	−0.555603	−0.0326261
$291$	8.85705	0.519210
$292$	4.76840	0.279050
$293$	2.71868	0.158827	0.0794135	−	0.996842i	$-0.474695\pi$
$293$	2.71868	0.158827	0.0794135	+	0.996842i	$0.474695\pi$
$294$	0	0
$295$	0.615970	0.0358632
$296$	0.371771	0.0216087
$297$	5.93089	0.344145
$298$	10.6616	0.617609
$299$	6.45666	0.373398
$300$	−4.65685	−0.268864
$301$	0	0
$302$	−12.9005	−0.742338
$303$	−4.54154	−0.260905
$304$	3.26022	0.186987
$305$	−2.60533	−0.149181
$306$	−0.371771	−0.0212527
$307$	21.5684	1.23097	0.615486	−	0.788148i	$-0.288960\pi$
$307$	21.5684	1.23097	0.615486	+	0.788148i	$0.288960\pi$
$308$	0	0
$309$	5.77690	0.328636
$310$	0.738220	0.0419281
$311$	17.0500	0.966815	0.483407	−	0.875395i	$-0.339399\pi$
$311$	17.0500	0.966815	0.483407	+	0.875395i	$0.339399\pi$
$312$	6.45666	0.365536
$313$	21.7522	1.22951	0.614753	−	0.788719i	$-0.289256\pi$
$313$	21.7522	1.22951	0.614753	+	0.788719i	$0.289256\pi$
$314$	−10.3222	−0.582516
$315$	0	0
$316$	−10.7307	−0.603649
$317$	28.1017	1.57835	0.789173	−	0.614171i	$-0.210509\pi$
$317$	28.1017	1.57835	0.789173	+	0.614171i	$0.210509\pi$
$318$	−8.23356	−0.461715
$319$	−5.62530	−0.314956
$320$	0.585786	0.0327465
$321$	7.41798	0.414031
$322$	0	0
$323$	−1.21205	−0.0674405
$324$	1.00000	0.0555556
$325$	−30.0677	−1.66786
$326$	2.18262	0.120884
$327$	−10.8571	−0.600396
$328$	−10.4476	−0.576871
$329$	0	0
$330$	3.47424	0.191250
$331$	17.6569	0.970508	0.485254	−	0.874373i	$-0.338727\pi$
$331$	17.6569	0.970508	0.485254	+	0.874373i	$0.338727\pi$
$332$	2.51668	0.138121
$333$	0.371771	0.0203729
$334$	−3.83039	−0.209590
$335$	−0.0167681	−0.000916139 0
$336$	0	0
$337$	14.0796	0.766963	0.383481	−	0.923549i	$-0.374725\pi$
$337$	14.0796	0.766963	0.383481	+	0.923549i	$0.374725\pi$
$338$	28.6884	1.56044
$339$	−10.5258	−0.571681
$340$	−0.217778	−0.0118107
$341$	7.47424	0.404753
$342$	3.26022	0.176293
$343$	0	0
$344$	−6.54154	−0.352696
$345$	0.585786	0.0315377
$346$	−3.08015	−0.165590
$347$	−17.5666	−0.943027	−0.471514	−	0.881859i	$-0.656292\pi$
$347$	−17.5666	−0.943027	−0.471514	+	0.881859i	$0.656292\pi$
$348$	−0.948474	−0.0508435
$349$	−15.6598	−0.838249	−0.419125	−	0.907929i	$-0.637663\pi$
$349$	−15.6598	−0.838249	−0.419125	+	0.907929i	$0.637663\pi$
$350$	0	0
$351$	6.45666	0.344631
$352$	5.93089	0.316118
$353$	29.8333	1.58787	0.793934	−	0.608004i	$-0.208030\pi$
$353$	29.8333	1.58787	0.793934	+	0.608004i	$0.208030\pi$
$354$	1.05153	0.0558880
$355$	1.39859	0.0742297
$356$	−15.2318	−0.807281
$357$	0	0
$358$	10.3747	0.548320
$359$	2.18262	0.115194	0.0575971	−	0.998340i	$-0.481656\pi$
$359$	2.18262	0.115194	0.0575971	+	0.998340i	$0.481656\pi$
$360$	0.585786	0.0308737
$361$	−8.37096	−0.440577
$362$	13.6191	0.715806
$363$	24.1755	1.26888
$364$	0	0
$365$	2.79327	0.146206
$366$	−4.44757	−0.232478
$367$	−9.22882	−0.481741	−0.240870	−	0.970557i	$-0.577433\pi$
$367$	−9.22882	−0.481741	−0.240870	+	0.970557i	$0.577433\pi$
$368$	1.00000	0.0521286
$369$	−10.4476	−0.543879
$370$	0.217778	0.0113218
$371$	0	0
$372$	1.26022	0.0653394
$373$	31.9974	1.65676	0.828381	−	0.560165i	$-0.189262\pi$
$373$	31.9974	1.65676	0.828381	+	0.560165i	$0.189262\pi$
$374$	−2.20493	−0.114014
$375$	−5.65685	−0.292119
$376$	10.6016	0.546734
$377$	−6.12397	−0.315400
$378$	0	0
$379$	−14.9015	−0.765436	−0.382718	−	0.923865i	$-0.625012\pi$
$379$	−14.9015	−0.765436	−0.382718	+	0.923865i	$0.625012\pi$
$380$	1.90979	0.0979703
$381$	−20.5925	−1.05498
$382$	9.30086	0.475874
$383$	9.63116	0.492129	0.246065	−	0.969253i	$-0.420862\pi$
$383$	9.63116	0.492129	0.246065	+	0.969253i	$0.420862\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−22.1240	−1.12608
$387$	−6.54154	−0.332525
$388$	8.85705	0.449649
$389$	−28.4882	−1.44441	−0.722205	−	0.691679i	$-0.756871\pi$
$389$	−28.4882	−1.44441	−0.722205	+	0.691679i	$0.756871\pi$
$390$	3.78222	0.191520
$391$	−0.371771	−0.0188013
$392$	0	0
$393$	−13.3489	−0.673361
$394$	−14.2493	−0.717871
$395$	−6.28590	−0.316278
$396$	5.93089	0.298039
$397$	−15.0047	−0.753066	−0.376533	−	0.926403i	$-0.622884\pi$
$397$	−15.0047	−0.753066	−0.376533	+	0.926403i	$0.622884\pi$
$398$	5.63869	0.282642
$399$	0	0
$400$	−4.65685	−0.232843
$401$	−34.6369	−1.72968	−0.864842	−	0.502045i	$-0.832581\pi$
$401$	−34.6369	−1.72968	−0.864842	+	0.502045i	$0.832581\pi$
$402$	−0.0286249	−0.00142768
$403$	8.13681	0.405324
$404$	−4.54154	−0.225950
$405$	0.585786	0.0291080
$406$	0	0
$407$	2.20493	0.109294
$408$	−0.371771	−0.0184054
$409$	−20.4515	−1.01126	−0.505631	−	0.862750i	$-0.668740\pi$
$409$	−20.4515	−1.01126	−0.505631	+	0.862750i	$0.668740\pi$
$410$	−6.12005	−0.302248
$411$	−10.7435	−0.529940
$412$	5.77690	0.284607
$413$	0	0
$414$	1.00000	0.0491473
$415$	1.47424	0.0723674
$416$	6.45666	0.316564
$417$	10.8284	0.530270
$418$	19.3360	0.945756
$419$	15.1145	0.738391	0.369195	−	0.929352i	$-0.379633\pi$
$419$	15.1145	0.738391	0.369195	+	0.929352i	$0.379633\pi$
$420$	0	0
$421$	10.4069	0.507203	0.253601	−	0.967309i	$-0.418385\pi$
$421$	10.4069	0.507203	0.253601	+	0.967309i	$0.418385\pi$
$422$	10.0444	0.488954
$423$	10.6016	0.515466
$424$	−8.23356	−0.399857
$425$	1.73128	0.0839795
$426$	2.38755	0.115677
$427$	0	0
$428$	7.41798	0.358561
$429$	38.2937	1.84884
$430$	−3.83195	−0.184793
$431$	−34.4892	−1.66129	−0.830643	−	0.556805i	$-0.812027\pi$
$431$	−34.4892	−1.66129	−0.830643	+	0.556805i	$0.812027\pi$
$432$	1.00000	0.0481125
$433$	25.9401	1.24660	0.623302	−	0.781981i	$-0.285791\pi$
$433$	25.9401	1.24660	0.623302	+	0.781981i	$0.285791\pi$
$434$	0	0
$435$	−0.555603	−0.0266391
$436$	−10.8571	−0.519958
$437$	3.26022	0.155958
$438$	4.76840	0.227843
$439$	−26.9891	−1.28812	−0.644060	−	0.764975i	$-0.722751\pi$
$439$	−26.9891	−1.28812	−0.644060	+	0.764975i	$0.722751\pi$
$440$	3.47424	0.165628
$441$	0	0
$442$	−2.40040	−0.114175
$443$	9.74706	0.463097	0.231548	−	0.972823i	$-0.425621\pi$
$443$	9.74706	0.463097	0.231548	+	0.972823i	$0.425621\pi$
$444$	0.371771	0.0176435
$445$	−8.92256	−0.422970
$446$	−14.6588	−0.694115
$447$	10.6616	0.504276
$448$	0	0
$449$	−34.8782	−1.64600	−0.823001	−	0.568040i	$-0.807702\pi$
$449$	−34.8782	−1.64600	−0.823001	+	0.568040i	$0.807702\pi$
$450$	−4.65685	−0.219526
$451$	−61.9634	−2.91774
$452$	−10.5258	−0.495090
$453$	−12.9005	−0.606117
$454$	8.36900	0.392777
$455$	0	0
$456$	3.26022	0.152674
$457$	−2.13821	−0.100021	−0.0500107	−	0.998749i	$-0.515926\pi$
$457$	−2.13821	−0.100021	−0.0500107	+	0.998749i	$0.515926\pi$
$458$	28.3666	1.32548
$459$	−0.371771	−0.0173528
$460$	0.585786	0.0273124
$461$	14.4385	0.672468	0.336234	−	0.941779i	$-0.390847\pi$
$461$	14.4385	0.672468	0.336234	+	0.941779i	$0.390847\pi$
$462$	0	0
$463$	−17.3911	−0.808232	−0.404116	−	0.914708i	$-0.632421\pi$
$463$	−17.3911	−0.808232	−0.404116	+	0.914708i	$0.632421\pi$
$464$	−0.948474	−0.0440318
$465$	0.738220	0.0342342
$466$	13.1755	0.610343
$467$	−10.9042	−0.504588	−0.252294	−	0.967651i	$-0.581185\pi$
$467$	−10.9042	−0.504588	−0.252294	+	0.967651i	$0.581185\pi$
$468$	6.45666	0.298459
$469$	0	0
$470$	6.21025	0.286458
$471$	−10.3222	−0.475622
$472$	1.05153	0.0484004
$473$	−38.7972	−1.78390
$474$	−10.7307	−0.492877
$475$	−15.1824	−0.696615
$476$	0	0
$477$	−8.23356	−0.376989
$478$	−6.35599	−0.290716
$479$	17.3729	0.793788	0.396894	−	0.917864i	$-0.370088\pi$
$479$	17.3729	0.793788	0.396894	+	0.917864i	$0.370088\pi$
$480$	0.585786	0.0267374
$481$	2.40040	0.109449
$482$	5.52518	0.251665
$483$	0	0
$484$	24.1755	1.09889
$485$	5.18834	0.235590
$486$	1.00000	0.0453609
$487$	28.0888	1.27283	0.636413	−	0.771349i	$-0.280418\pi$
$487$	28.0888	1.27283	0.636413	+	0.771349i	$0.280418\pi$
$488$	−4.44757	−0.201332
$489$	2.18262	0.0987014
$490$	0	0
$491$	17.0608	0.769942	0.384971	−	0.922929i	$-0.374211\pi$
$491$	17.0608	0.769942	0.384971	+	0.922929i	$0.374211\pi$
$492$	−10.4476	−0.471013
$493$	0.352615	0.0158810
$494$	21.0501	0.947090
$495$	3.47424	0.156155
$496$	1.26022	0.0565856
$497$	0	0
$498$	2.51668	0.112775
$499$	29.7364	1.33118	0.665592	−	0.746315i	$-0.268179\pi$
$499$	29.7364	1.33118	0.665592	+	0.746315i	$0.268179\pi$
$500$	−5.65685	−0.252982
$501$	−3.83039	−0.171129
$502$	6.77494	0.302380
$503$	−34.1240	−1.52151	−0.760756	−	0.649038i	$-0.775172\pi$
$503$	−34.1240	−1.52151	−0.760756	+	0.649038i	$0.775172\pi$
$504$	0	0
$505$	−2.66037	−0.118385
$506$	5.93089	0.263660
$507$	28.6884	1.27410
$508$	−20.5925	−0.913644
$509$	28.0953	1.24530	0.622652	−	0.782499i	$-0.286055\pi$
$509$	28.0953	1.24530	0.622652	+	0.782499i	$0.286055\pi$
$510$	−0.217778	−0.00964338
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.26022	0.143942
$514$	5.29417	0.233516
$515$	3.38403	0.149118
$516$	−6.54154	−0.287975
$517$	62.8768	2.76532
$518$	0	0
$519$	−3.08015	−0.135204
$520$	3.78222	0.165861
$521$	−20.7188	−0.907709	−0.453854	−	0.891076i	$-0.649951\pi$
$521$	−20.7188	−0.907709	−0.453854	+	0.891076i	$0.649951\pi$
$522$	−0.948474	−0.0415136
$523$	11.6883	0.511092	0.255546	−	0.966797i	$-0.417745\pi$
$523$	11.6883	0.511092	0.255546	+	0.966797i	$0.417745\pi$
$524$	−13.3489	−0.583148
$525$	0	0
$526$	−31.3137	−1.36534
$527$	−0.468513	−0.0204088
$528$	5.93089	0.258109
$529$	1.00000	0.0434783
$530$	−4.82311	−0.209502
$531$	1.05153	0.0456324
$532$	0	0
$533$	−67.4564	−2.92186
$534$	−15.2318	−0.659143
$535$	4.34535	0.187866
$536$	−0.0286249	−0.00123641
$537$	10.3747	0.447702
$538$	22.5064	0.970319
$539$	0	0
$540$	0.585786	0.0252082
$541$	27.8582	1.19772	0.598858	−	0.800855i	$-0.295621\pi$
$541$	27.8582	1.19772	0.598858	+	0.800855i	$0.295621\pi$
$542$	8.90423	0.382469
$543$	13.6191	0.584453
$544$	−0.371771	−0.0159395
$545$	−6.35991	−0.272429
$546$	0	0
$547$	−13.9964	−0.598443	−0.299221	−	0.954184i	$-0.596727\pi$
$547$	−13.9964	−0.598443	−0.299221	+	0.954184i	$0.596727\pi$
$548$	−10.7435	−0.458941
$549$	−4.44757	−0.189818
$550$	−27.6193	−1.17769
$551$	−3.09223	−0.131734
$552$	1.00000	0.0425628
$553$	0	0
$554$	−9.01637	−0.383069
$555$	0.217778	0.00924417
$556$	10.8284	0.459228
$557$	−25.5397	−1.08215	−0.541077	−	0.840973i	$-0.681983\pi$
$557$	−25.5397	−1.08215	−0.541077	+	0.840973i	$0.681983\pi$
$558$	1.26022	0.0533494
$559$	−42.2365	−1.78641
$560$	0	0
$561$	−2.20493	−0.0930923
$562$	24.4320	1.03060
$563$	−42.5468	−1.79314	−0.896568	−	0.442907i	$-0.853947\pi$
$563$	−42.5468	−1.79314	−0.896568	+	0.442907i	$0.853947\pi$
$564$	10.6016	0.446406
$565$	−6.16585	−0.259399
$566$	−0.762094	−0.0320332
$567$	0	0
$568$	2.38755	0.100179
$569$	−38.0316	−1.59437	−0.797183	−	0.603738i	$-0.793677\pi$
$569$	−38.0316	−1.59437	−0.797183	+	0.603738i	$0.793677\pi$
$570$	1.90979	0.0799924
$571$	−5.92557	−0.247977	−0.123989	−	0.992284i	$-0.539569\pi$
$571$	−5.92557	−0.247977	−0.123989	+	0.992284i	$0.539569\pi$
$572$	38.2937	1.60114
$573$	9.30086	0.388549
$574$	0	0
$575$	−4.65685	−0.194204
$576$	1.00000	0.0416667
$577$	−45.0270	−1.87450	−0.937249	−	0.348661i	$-0.886636\pi$
$577$	−45.0270	−1.87450	−0.937249	+	0.348661i	$0.886636\pi$
$578$	−16.8618	−0.701358
$579$	−22.1240	−0.919441
$580$	−0.555603	−0.0230702
$581$	0	0
$582$	8.85705	0.367137
$583$	−48.8323	−2.02243
$584$	4.76840	0.197318
$585$	3.78222	0.156376
$586$	2.71868	0.112308
$587$	−43.3271	−1.78830	−0.894150	−	0.447767i	$-0.852219\pi$
$587$	−43.3271	−1.78830	−0.894150	+	0.447767i	$0.852219\pi$
$588$	0	0
$589$	4.10860	0.169292
$590$	0.615970	0.0253591
$591$	−14.2493	−0.586139
$592$	0.371771	0.0152797
$593$	−36.3058	−1.49090	−0.745449	−	0.666562i	$-0.767765\pi$
$593$	−36.3058	−1.49090	−0.745449	+	0.666562i	$0.767765\pi$
$594$	5.93089	0.243347
$595$	0	0
$596$	10.6616	0.436716
$597$	5.63869	0.230776
$598$	6.45666	0.264032
$599$	−30.2365	−1.23543	−0.617715	−	0.786402i	$-0.711941\pi$
$599$	−30.2365	−1.23543	−0.617715	+	0.786402i	$0.711941\pi$
$600$	−4.65685	−0.190115
$601$	13.4491	0.548602	0.274301	−	0.961644i	$-0.411554\pi$
$601$	13.4491	0.548602	0.274301	+	0.961644i	$0.411554\pi$
$602$	0	0
$603$	−0.0286249	−0.00116570
$604$	−12.9005	−0.524913
$605$	14.1617	0.575754
$606$	−4.54154	−0.184488
$607$	9.63610	0.391117	0.195559	−	0.980692i	$-0.437348\pi$
$607$	9.63610	0.391117	0.195559	+	0.980692i	$0.437348\pi$
$608$	3.26022	0.132219
$609$	0	0
$610$	−2.60533	−0.105487
$611$	68.4507	2.76922
$612$	−0.371771	−0.0150279
$613$	9.03043	0.364735	0.182368	−	0.983230i	$-0.441624\pi$
$613$	9.03043	0.364735	0.182368	+	0.983230i	$0.441624\pi$
$614$	21.5684	0.870428
$615$	−6.12005	−0.246784
$616$	0	0
$617$	−15.4871	−0.623486	−0.311743	−	0.950166i	$-0.600913\pi$
$617$	−15.4871	−0.623486	−0.311743	+	0.950166i	$0.600913\pi$
$618$	5.77690	0.232381
$619$	−45.0944	−1.81250	−0.906248	−	0.422747i	$-0.861066\pi$
$619$	−45.0944	−1.81250	−0.906248	+	0.422747i	$0.861066\pi$
$620$	0.738220	0.0296476
$621$	1.00000	0.0401286
$622$	17.0500	0.683641
$623$	0	0
$624$	6.45666	0.258473
$625$	19.9706	0.798823
$626$	21.7522	0.869393
$627$	19.3360	0.772206
$628$	−10.3222	−0.411901
$629$	−0.138213	−0.00551093
$630$	0	0
$631$	47.7071	1.89919	0.949595	−	0.313478i	$-0.101494\pi$
$631$	47.7071	1.89919	0.949595	+	0.313478i	$0.101494\pi$
$632$	−10.7307	−0.426844
$633$	10.0444	0.399229
$634$	28.1017	1.11606
$635$	−12.0628	−0.478697
$636$	−8.23356	−0.326482
$637$	0	0
$638$	−5.62530	−0.222708
$639$	2.38755	0.0944500
$640$	0.585786	0.0231552
$641$	11.6884	0.461665	0.230832	−	0.972994i	$-0.425855\pi$
$641$	11.6884	0.461665	0.230832	+	0.972994i	$0.425855\pi$
$642$	7.41798	0.292764
$643$	−10.3966	−0.410003	−0.205002	−	0.978762i	$-0.565720\pi$
$643$	−10.3966	−0.410003	−0.205002	+	0.978762i	$0.565720\pi$
$644$	0	0
$645$	−3.83195	−0.150883
$646$	−1.21205	−0.0476877
$647$	−41.9064	−1.64751	−0.823754	−	0.566947i	$-0.808124\pi$
$647$	−41.9064	−1.64751	−0.823754	+	0.566947i	$0.808124\pi$
$648$	1.00000	0.0392837
$649$	6.23649	0.244804
$650$	−30.0677	−1.17935
$651$	0	0
$652$	2.18262	0.0854779
$653$	11.9542	0.467804	0.233902	−	0.972260i	$-0.424851\pi$
$653$	11.9542	0.467804	0.233902	+	0.972260i	$0.424851\pi$
$654$	−10.8571	−0.424544
$655$	−7.81959	−0.305537
$656$	−10.4476	−0.407909
$657$	4.76840	0.186033
$658$	0	0
$659$	22.7816	0.887447	0.443723	−	0.896164i	$-0.353657\pi$
$659$	22.7816	0.887447	0.443723	+	0.896164i	$0.353657\pi$
$660$	3.47424	0.135234
$661$	−25.5639	−0.994319	−0.497160	−	0.867659i	$-0.665624\pi$
$661$	−25.5639	−0.994319	−0.497160	+	0.867659i	$0.665624\pi$
$662$	17.6569	0.686253
$663$	−2.40040	−0.0932236
$664$	2.51668	0.0976661
$665$	0	0
$666$	0.371771	0.0144058
$667$	−0.948474	−0.0367250
$668$	−3.83039	−0.148202
$669$	−14.6588	−0.566743
$670$	−0.0167681	−0.000647808 0
$671$	−26.3781	−1.01831
$672$	0	0
$673$	6.61597	0.255027	0.127513	−	0.991837i	$-0.459300\pi$
$673$	6.61597	0.255027	0.127513	+	0.991837i	$0.459300\pi$
$674$	14.0796	0.542325
$675$	−4.65685	−0.179242
$676$	28.6884	1.10340
$677$	−20.7556	−0.797701	−0.398850	−	0.917016i	$-0.630591\pi$
$677$	−20.7556	−0.797701	−0.398850	+	0.917016i	$0.630591\pi$
$678$	−10.5258	−0.404239
$679$	0	0
$680$	−0.217778	−0.00835141
$681$	8.36900	0.320701
$682$	7.47424	0.286203
$683$	13.4837	0.515940	0.257970	−	0.966153i	$-0.416946\pi$
$683$	13.4837	0.515940	0.257970	+	0.966153i	$0.416946\pi$
$684$	3.26022	0.124658
$685$	−6.29342	−0.240459
$686$	0	0
$687$	28.3666	1.08225
$688$	−6.54154	−0.249394
$689$	−53.1613	−2.02528
$690$	0.585786	0.0223005
$691$	42.7475	1.62619	0.813095	−	0.582131i	$-0.197781\pi$
$691$	42.7475	1.62619	0.813095	+	0.582131i	$0.197781\pi$
$692$	−3.08015	−0.117090
$693$	0	0
$694$	−17.5666	−0.666821
$695$	6.34315	0.240609
$696$	−0.948474	−0.0359518
$697$	3.88410	0.147121
$698$	−15.6598	−0.592732
$699$	13.1755	0.498343
$700$	0	0
$701$	−7.30717	−0.275988	−0.137994	−	0.990433i	$-0.544065\pi$
$701$	−7.30717	−0.275988	−0.137994	+	0.990433i	$0.544065\pi$
$702$	6.45666	0.243691
$703$	1.21205	0.0457135
$704$	5.93089	0.223529
$705$	6.21025	0.233892
$706$	29.8333	1.12279
$707$	0	0
$708$	1.05153	0.0395188
$709$	−35.7486	−1.34257	−0.671283	−	0.741201i	$-0.734257\pi$
$709$	−35.7486	−1.34257	−0.671283	+	0.741201i	$0.734257\pi$
$710$	1.39859	0.0524883
$711$	−10.7307	−0.402433
$712$	−15.2318	−0.570834
$713$	1.26022	0.0471957
$714$	0	0
$715$	22.4320	0.838908
$716$	10.3747	0.387721
$717$	−6.35599	−0.237369
$718$	2.18262	0.0814546
$719$	−1.92420	−0.0717605	−0.0358802	−	0.999356i	$-0.511423\pi$
$719$	−1.92420	−0.0717605	−0.0358802	+	0.999356i	$0.511423\pi$
$720$	0.585786	0.0218310
$721$	0	0
$722$	−8.37096	−0.311535
$723$	5.52518	0.205484
$724$	13.6191	0.506152
$725$	4.41690	0.164040
$726$	24.1755	0.897237
$727$	−20.3471	−0.754631	−0.377315	−	0.926085i	$-0.623153\pi$
$727$	−20.3471	−0.754631	−0.377315	+	0.926085i	$0.623153\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.79327	0.103383
$731$	2.43195	0.0899491
$732$	−4.44757	−0.164387
$733$	−1.91649	−0.0707871	−0.0353936	−	0.999373i	$-0.511268\pi$
$733$	−1.91649	−0.0707871	−0.0353936	+	0.999373i	$0.511268\pi$
$734$	−9.22882	−0.340642
$735$	0	0
$736$	1.00000	0.0368605
$737$	−0.169771	−0.00625361
$738$	−10.4476	−0.384580
$739$	5.94252	0.218599	0.109300	−	0.994009i	$-0.465139\pi$
$739$	5.94252	0.218599	0.109300	+	0.994009i	$0.465139\pi$
$740$	0.217778	0.00800569
$741$	21.0501	0.773296
$742$	0	0
$743$	−22.9005	−0.840137	−0.420068	−	0.907492i	$-0.637994\pi$
$743$	−22.9005	−0.840137	−0.420068	+	0.907492i	$0.637994\pi$
$744$	1.26022	0.0462019
$745$	6.24541	0.228814
$746$	31.9974	1.17151
$747$	2.51668	0.0920805
$748$	−2.20493	−0.0806203
$749$	0	0
$750$	−5.65685	−0.206559
$751$	−20.6369	−0.753051	−0.376525	−	0.926406i	$-0.622881\pi$
$751$	−20.6369	−0.753051	−0.376525	+	0.926406i	$0.622881\pi$
$752$	10.6016	0.386599
$753$	6.77494	0.246893
$754$	−6.12397	−0.223022
$755$	−7.55692	−0.275024
$756$	0	0
$757$	50.8780	1.84919	0.924596	−	0.380950i	$-0.124403\pi$
$757$	50.8780	1.84919	0.924596	+	0.380950i	$0.124403\pi$
$758$	−14.9015	−0.541245
$759$	5.93089	0.215278
$760$	1.90979	0.0692755
$761$	21.3165	0.772722	0.386361	−	0.922348i	$-0.373732\pi$
$761$	21.3165	0.772722	0.386361	+	0.922348i	$0.373732\pi$
$762$	−20.5925	−0.745987
$763$	0	0
$764$	9.30086	0.336493
$765$	−0.217778	−0.00787379
$766$	9.63116	0.347988
$767$	6.78934	0.245149
$768$	1.00000	0.0360844
$769$	−41.4864	−1.49604	−0.748019	−	0.663677i	$-0.768995\pi$
$769$	−41.4864	−1.49604	−0.748019	+	0.663677i	$0.768995\pi$
$770$	0	0
$771$	5.29417	0.190665
$772$	−22.1240	−0.796259
$773$	−11.1261	−0.400178	−0.200089	−	0.979778i	$-0.564123\pi$
$773$	−11.1261	−0.400178	−0.200089	+	0.979778i	$0.564123\pi$
$774$	−6.54154	−0.235131
$775$	−5.86867	−0.210809
$776$	8.85705	0.317950
$777$	0	0
$778$	−28.4882	−1.02135
$779$	−34.0614	−1.22038
$780$	3.78222	0.135425
$781$	14.1603	0.506695
$782$	−0.371771	−0.0132945
$783$	−0.948474	−0.0338957
$784$	0	0
$785$	−6.04661	−0.215813
$786$	−13.3489	−0.476138
$787$	26.5482	0.946342	0.473171	−	0.880970i	$-0.343109\pi$
$787$	26.5482	0.946342	0.473171	+	0.880970i	$0.343109\pi$
$788$	−14.2493	−0.507612
$789$	−31.3137	−1.11480
$790$	−6.28590	−0.223642
$791$	0	0
$792$	5.93089	0.210745
$793$	−28.7165	−1.01975
$794$	−15.0047	−0.532498
$795$	−4.82311	−0.171058
$796$	5.63869	0.199858
$797$	30.6436	1.08545	0.542726	−	0.839910i	$-0.317392\pi$
$797$	30.6436	1.08545	0.542726	+	0.839910i	$0.317392\pi$
$798$	0	0
$799$	−3.94135	−0.139435
$800$	−4.65685	−0.164645
$801$	−15.2318	−0.538188
$802$	−34.6369	−1.22307
$803$	28.2809	0.998011
$804$	−0.0286249	−0.00100952
$805$	0	0
$806$	8.13681	0.286607
$807$	22.5064	0.792262
$808$	−4.54154	−0.159771
$809$	24.6941	0.868200	0.434100	−	0.900865i	$-0.357067\pi$
$809$	24.6941	0.868200	0.434100	+	0.900865i	$0.357067\pi$
$810$	0.585786	0.0205824
$811$	40.6941	1.42896	0.714482	−	0.699654i	$-0.246662\pi$
$811$	40.6941	1.42896	0.714482	+	0.699654i	$0.246662\pi$
$812$	0	0
$813$	8.90423	0.312285
$814$	2.20493	0.0772828
$815$	1.27855	0.0447856
$816$	−0.371771	−0.0130146
$817$	−21.3269	−0.746133
$818$	−20.4515	−0.715070
$819$	0	0
$820$	−6.12005	−0.213721
$821$	19.8043	0.691175	0.345588	−	0.938386i	$-0.387680\pi$
$821$	19.8043	0.691175	0.345588	+	0.938386i	$0.387680\pi$
$822$	−10.7435	−0.374724
$823$	44.3287	1.54520	0.772600	−	0.634893i	$-0.218956\pi$
$823$	44.3287	1.54520	0.772600	+	0.634893i	$0.218956\pi$
$824$	5.77690	0.201248
$825$	−27.6193	−0.961581
$826$	0	0
$827$	13.9988	0.486785	0.243393	−	0.969928i	$-0.421740\pi$
$827$	13.9988	0.486785	0.243393	+	0.969928i	$0.421740\pi$
$828$	1.00000	0.0347524
$829$	53.1050	1.84441	0.922206	−	0.386698i	$-0.126385\pi$
$829$	53.1050	1.84441	0.922206	+	0.386698i	$0.126385\pi$
$830$	1.47424	0.0511715
$831$	−9.01637	−0.312774
$832$	6.45666	0.223844
$833$	0	0
$834$	10.8284	0.374958
$835$	−2.24379	−0.0776495
$836$	19.3360	0.668750
$837$	1.26022	0.0435596
$838$	15.1145	0.522121
$839$	−38.7399	−1.33745	−0.668726	−	0.743509i	$-0.733160\pi$
$839$	−38.7399	−1.33745	−0.668726	+	0.743509i	$0.733160\pi$
$840$	0	0
$841$	−28.1004	−0.968979
$842$	10.4069	0.358647
$843$	24.4320	0.841481
$844$	10.0444	0.345743
$845$	16.8053	0.578119
$846$	10.6016	0.364489
$847$	0	0
$848$	−8.23356	−0.282742
$849$	−0.762094	−0.0261550
$850$	1.73128	0.0593825
$851$	0.371771	0.0127441
$852$	2.38755	0.0817961
$853$	2.51391	0.0860745	0.0430373	−	0.999073i	$-0.486297\pi$
$853$	2.51391	0.0860745	0.0430373	+	0.999073i	$0.486297\pi$
$854$	0	0
$855$	1.90979	0.0653136
$856$	7.41798	0.253541
$857$	−25.2280	−0.861772	−0.430886	−	0.902406i	$-0.641799\pi$
$857$	−25.2280	−0.861772	−0.430886	+	0.902406i	$0.641799\pi$
$858$	38.2937	1.30733
$859$	−30.1994	−1.03039	−0.515195	−	0.857073i	$-0.672280\pi$
$859$	−30.1994	−1.03039	−0.515195	+	0.857073i	$0.672280\pi$
$860$	−3.83195	−0.130668
$861$	0	0
$862$	−34.4892	−1.17471
$863$	34.1427	1.16223	0.581115	−	0.813821i	$-0.302617\pi$
$863$	34.1427	1.16223	0.581115	+	0.813821i	$0.302617\pi$
$864$	1.00000	0.0340207
$865$	−1.80431	−0.0613484
$866$	25.9401	0.881482
$867$	−16.8618	−0.572656
$868$	0	0
$869$	−63.6426	−2.15893
$870$	−0.555603	−0.0188367
$871$	−0.184821	−0.00626243
$872$	−10.8571	−0.367666
$873$	8.85705	0.299766
$874$	3.26022	0.110279
$875$	0	0
$876$	4.76840	0.161109
$877$	31.1520	1.05193	0.525964	−	0.850507i	$-0.323705\pi$
$877$	31.1520	1.05193	0.525964	+	0.850507i	$0.323705\pi$
$878$	−26.9891	−0.910839
$879$	2.71868	0.0916988
$880$	3.47424	0.117117
$881$	−23.0380	−0.776168	−0.388084	−	0.921624i	$-0.626863\pi$
$881$	−23.0380	−0.776168	−0.388084	+	0.921624i	$0.626863\pi$
$882$	0	0
$883$	−31.4248	−1.05753	−0.528765	−	0.848768i	$-0.677345\pi$
$883$	−31.4248	−1.05753	−0.528765	+	0.848768i	$0.677345\pi$
$884$	−2.40040	−0.0807340
$885$	0.615970	0.0207056
$886$	9.74706	0.327459
$887$	36.5245	1.22637	0.613187	−	0.789938i	$-0.289887\pi$
$887$	36.5245	1.22637	0.613187	+	0.789938i	$0.289887\pi$
$888$	0.371771	0.0124758
$889$	0	0
$890$	−8.92256	−0.299085
$891$	5.93089	0.198692
$892$	−14.6588	−0.490813
$893$	34.5634	1.15662
$894$	10.6616	0.356577
$895$	6.07736	0.203144
$896$	0	0
$897$	6.45666	0.215581
$898$	−34.8782	−1.16390
$899$	−1.19529	−0.0398650
$900$	−4.65685	−0.155228
$901$	3.06100	0.101977
$902$	−61.9634	−2.06316
$903$	0	0
$904$	−10.5258	−0.350082
$905$	7.97791	0.265195
$906$	−12.9005	−0.428589
$907$	−19.4917	−0.647212	−0.323606	−	0.946192i	$-0.604895\pi$
$907$	−19.4917	−0.647212	−0.323606	+	0.946192i	$0.604895\pi$
$908$	8.36900	0.277735
$909$	−4.54154	−0.150633
$910$	0	0
$911$	−1.79169	−0.0593614	−0.0296807	−	0.999559i	$-0.509449\pi$
$911$	−1.79169	−0.0593614	−0.0296807	+	0.999559i	$0.509449\pi$
$912$	3.26022	0.107957
$913$	14.9262	0.493984
$914$	−2.13821	−0.0707258
$915$	−2.60533	−0.0861295
$916$	28.3666	0.937259
$917$	0	0
$918$	−0.371771	−0.0122703
$919$	−11.3617	−0.374788	−0.187394	−	0.982285i	$-0.560004\pi$
$919$	−11.3617	−0.374788	−0.187394	+	0.982285i	$0.560004\pi$
$920$	0.585786	0.0193128
$921$	21.5684	0.710702
$922$	14.4385	0.475506
$923$	15.4156	0.507410
$924$	0	0
$925$	−1.73128	−0.0569242
$926$	−17.3911	−0.571506
$927$	5.77690	0.189738
$928$	−0.948474	−0.0311352
$929$	−0.185391	−0.00608247	−0.00304124	−	0.999995i	$-0.500968\pi$
$929$	−0.185391	−0.00608247	−0.00304124	+	0.999995i	$0.500968\pi$
$930$	0.738220	0.0242072
$931$	0	0
$932$	13.1755	0.431578
$933$	17.0500	0.558191
$934$	−10.9042	−0.356797
$935$	−1.29162	−0.0422405
$936$	6.45666	0.211042
$937$	45.8410	1.49756	0.748780	−	0.662818i	$-0.230640\pi$
$937$	45.8410	1.49756	0.748780	+	0.662818i	$0.230640\pi$
$938$	0	0
$939$	21.7522	0.709856
$940$	6.21025	0.202556
$941$	59.9386	1.95394	0.976971	−	0.213373i	$-0.0684448\pi$
$941$	59.9386	1.95394	0.976971	+	0.213373i	$0.0684448\pi$
$942$	−10.3222	−0.336316
$943$	−10.4476	−0.340220
$944$	1.05153	0.0342243
$945$	0	0
$946$	−38.7972	−1.26141
$947$	−3.83947	−0.124766	−0.0623830	−	0.998052i	$-0.519870\pi$
$947$	−3.83947	−0.124766	−0.0623830	+	0.998052i	$0.519870\pi$
$948$	−10.7307	−0.348517
$949$	30.7879	0.999419
$950$	−15.1824	−0.492581
$951$	28.1017	0.911259
$952$	0	0
$953$	18.7974	0.608908	0.304454	−	0.952527i	$-0.401526\pi$
$953$	18.7974	0.608908	0.304454	+	0.952527i	$0.401526\pi$
$954$	−8.23356	−0.266571
$955$	5.44832	0.176303
$956$	−6.35599	−0.205567
$957$	−5.62530	−0.181840
$958$	17.3729	0.561293
$959$	0	0
$960$	0.585786	0.0189062
$961$	−29.4118	−0.948769
$962$	2.40040	0.0773919
$963$	7.41798	0.239041
$964$	5.52518	0.177954
$965$	−12.9599	−0.417195
$966$	0	0
$967$	31.4578	1.01161	0.505807	−	0.862647i	$-0.331195\pi$
$967$	31.4578	1.01161	0.505807	+	0.862647i	$0.331195\pi$
$968$	24.1755	0.777030
$969$	−1.21205	−0.0389368
$970$	5.18834	0.166588
$971$	−57.5241	−1.84604	−0.923018	−	0.384756i	$-0.874286\pi$
$971$	−57.5241	−1.84604	−0.923018	+	0.384756i	$0.874286\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	28.0888	0.900023
$975$	−30.0677	−0.962937
$976$	−4.44757	−0.142363
$977$	−4.54448	−0.145391	−0.0726953	−	0.997354i	$-0.523160\pi$
$977$	−4.54448	−0.145391	−0.0726953	+	0.997354i	$0.523160\pi$
$978$	2.18262	0.0697924
$979$	−90.3379	−2.88721
$980$	0	0
$981$	−10.8571	−0.346639
$982$	17.0608	0.544431
$983$	−36.3842	−1.16047	−0.580237	−	0.814447i	$-0.697040\pi$
$983$	−36.3842	−1.16047	−0.580237	+	0.814447i	$0.697040\pi$
$984$	−10.4476	−0.333056
$985$	−8.34707	−0.265960
$986$	0.352615	0.0112295
$987$	0	0
$988$	21.0501	0.669694
$989$	−6.54154	−0.208009
$990$	3.47424	0.110418
$991$	40.8089	1.29634	0.648168	−	0.761497i	$-0.275535\pi$
$991$	40.8089	1.29634	0.648168	+	0.761497i	$0.275535\pi$
$992$	1.26022	0.0400121
$993$	17.6569	0.560323
$994$	0	0
$995$	3.30307	0.104714
$996$	2.51668	0.0797440
$997$	−5.30325	−0.167956	−0.0839778	−	0.996468i	$-0.526762\pi$
$997$	−5.30325	−0.167956	−0.0839778	+	0.996468i	$0.526762\pi$
$998$	29.7364	0.941290
$999$	0.371771	0.0117623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.ct.1.2	yes	4
7.6	odd	2		6762.2.a.ci.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.ci.1.4	✓	4	7.6	odd	2
6762.2.a.ct.1.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.585786 q^{10} +5.93089 q^{11} +1.00000 q^{12} +6.45666 q^{13} +0.585786 q^{15} +1.00000 q^{16} -0.371771 q^{17} +1.00000 q^{18} +3.26022 q^{19} +0.585786 q^{20} +5.93089 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.65685 q^{25} +6.45666 q^{26} +1.00000 q^{27} -0.948474 q^{29} +0.585786 q^{30} +1.26022 q^{31} +1.00000 q^{32} +5.93089 q^{33} -0.371771 q^{34} +1.00000 q^{36} +0.371771 q^{37} +3.26022 q^{38} +6.45666 q^{39} +0.585786 q^{40} -10.4476 q^{41} -6.54154 q^{43} +5.93089 q^{44} +0.585786 q^{45} +1.00000 q^{46} +10.6016 q^{47} +1.00000 q^{48} -4.65685 q^{50} -0.371771 q^{51} +6.45666 q^{52} -8.23356 q^{53} +1.00000 q^{54} +3.47424 q^{55} +3.26022 q^{57} -0.948474 q^{58} +1.05153 q^{59} +0.585786 q^{60} -4.44757 q^{61} +1.26022 q^{62} +1.00000 q^{64} +3.78222 q^{65} +5.93089 q^{66} -0.0286249 q^{67} -0.371771 q^{68} +1.00000 q^{69} +2.38755 q^{71} +1.00000 q^{72} +4.76840 q^{73} +0.371771 q^{74} -4.65685 q^{75} +3.26022 q^{76} +6.45666 q^{78} -10.7307 q^{79} +0.585786 q^{80} +1.00000 q^{81} -10.4476 q^{82} +2.51668 q^{83} -0.217778 q^{85} -6.54154 q^{86} -0.948474 q^{87} +5.93089 q^{88} -15.2318 q^{89} +0.585786 q^{90} +1.00000 q^{92} +1.26022 q^{93} +10.6016 q^{94} +1.90979 q^{95} +1.00000 q^{96} +8.85705 q^{97} +5.93089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 8 q^{10} + 4 q^{11} + 4 q^{12} + 12 q^{13} + 8 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 12 q^{26} + 4 q^{27} + 8 q^{29} + 8 q^{30} - 4 q^{31} + 4 q^{32} + 4 q^{33} - 4 q^{34} + 4 q^{36} + 4 q^{37} + 4 q^{38} + 12 q^{39} + 8 q^{40} - 8 q^{41} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 4 q^{46} + 12 q^{47} + 4 q^{48} + 4 q^{50} - 4 q^{51} + 12 q^{52} + 4 q^{53} + 4 q^{54} + 8 q^{55} + 4 q^{57} + 8 q^{58} + 16 q^{59} + 8 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{65} + 4 q^{66} + 20 q^{67} - 4 q^{68} + 4 q^{69} - 24 q^{71} + 4 q^{72} + 8 q^{73} + 4 q^{74} + 4 q^{75} + 4 q^{76} + 12 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} - 4 q^{83} + 4 q^{86} + 8 q^{87} + 4 q^{88} + 20 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} + 12 q^{94} + 4 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 8 * q^10 + 4 * q^11 + 4 * q^12 + 12 * q^13 + 8 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 + 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 12 * q^26 + 4 * q^27 + 8 * q^29 + 8 * q^30 - 4 * q^31 + 4 * q^32 + 4 * q^33 - 4 * q^34 + 4 * q^36 + 4 * q^37 + 4 * q^38 + 12 * q^39 + 8 * q^40 - 8 * q^41 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 4 * q^46 + 12 * q^47 + 4 * q^48 + 4 * q^50 - 4 * q^51 + 12 * q^52 + 4 * q^53 + 4 * q^54 + 8 * q^55 + 4 * q^57 + 8 * q^58 + 16 * q^59 + 8 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^65 + 4 * q^66 + 20 * q^67 - 4 * q^68 + 4 * q^69 - 24 * q^71 + 4 * q^72 + 8 * q^73 + 4 * q^74 + 4 * q^75 + 4 * q^76 + 12 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 - 4 * q^83 + 4 * q^86 + 8 * q^87 + 4 * q^88 + 20 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 + 12 * q^94 + 4 * q^96 + 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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