LMFDB - Embedded newform 6762.2.a.ci.1.4

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:	$1$
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			1.4
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	$-0.541814\pi$
$5$	−0.585786	−0.261972	−0.130986	+	0.991384i	$0.541814\pi$
$6$	−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	$-0.853094\pi$
$13$	−6.45666	−1.79075	−0.895377	+	0.445309i	$0.853094\pi$
$14$	0	0
$15$	0.585786	0.151249
$16$	1.00000	0.250000
$17$	0.371771	0.0901676	0.0450838	−	0.998983i	$-0.485645\pi$
$17$	0.371771	0.0901676	0.0450838	+	0.998983i	$0.485645\pi$
$18$	1.00000	0.235702
$19$	−3.26022	−0.747946	−0.373973	−	0.927440i	$-0.622005\pi$
$19$	−3.26022	−0.747946	−0.373973	+	0.927440i	$0.622005\pi$
$20$	−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	$-0.536101\pi$
$31$	−1.26022	−0.226342	−0.113171	+	0.993576i	$0.536101\pi$
$32$	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	$-0.196287\pi$
$41$	10.4476	1.63164	0.815818	+	0.578308i	$0.196287\pi$
$42$	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	$-0.781344\pi$
$47$	−10.6016	−1.54640	−0.773199	+	0.634164i	$0.781344\pi$
$48$	−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	$-0.521805\pi$
$59$	−1.05153	−0.136897	−0.0684485	+	0.997655i	$0.521805\pi$
$60$	0.585786	0.0756247
$61$	4.44757	0.569453	0.284727	−	0.958609i	$-0.408097\pi$
$61$	4.44757	0.569453	0.284727	+	0.958609i	$0.408097\pi$
$62$	−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	$-0.590019\pi$
$73$	−4.76840	−0.558099	−0.279050	+	0.960277i	$0.590019\pi$
$74$	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	$-0.544106\pi$
$83$	−2.51668	−0.276241	−0.138121	+	0.990415i	$0.544106\pi$
$84$	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	$-0.200938\pi$
$89$	15.2318	1.61456	0.807281	+	0.590167i	$0.200938\pi$
$90$	−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	$-0.648451\pi$
$97$	−8.85705	−0.899297	−0.449649	+	0.893205i	$0.648451\pi$
$98$	0	0
$99$	5.93089	0.596077
$100$	−4.65685	−0.465685
$101$	4.54154	0.451900	0.225950	−	0.974139i	$-0.427451\pi$
$101$	4.54154	0.451900	0.225950	+	0.974139i	$0.427451\pi$
$102$	−0.371771	−0.0368108
$103$	−5.77690	−0.569215	−0.284607	−	0.958644i	$-0.591863\pi$
$103$	−5.77690	−0.569215	−0.284607	+	0.958644i	$0.591863\pi$
$104$	−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	$-0.301821\pi$
$131$	13.3489	1.16630	0.583148	+	0.812366i	$0.301821\pi$
$132$	−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	$-0.651874\pi$
$139$	−10.8284	−0.918455	−0.459228	+	0.888319i	$0.651874\pi$
$140$	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	$-0.364865\pi$
$157$	10.3222	0.823802	0.411901	+	0.911229i	$0.364865\pi$
$158$	−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	$-0.452651\pi$
$167$	3.83039	0.296404	0.148202	+	0.988957i	$0.452651\pi$
$168$	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	$-0.462643\pi$
$173$	3.08015	0.234180	0.117090	+	0.993121i	$0.462643\pi$
$174$	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	$-0.668932\pi$
$181$	−13.6191	−1.01230	−0.506152	+	0.862445i	$0.668932\pi$
$182$	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	$-0.564048\pi$
$199$	−5.63869	−0.399716	−0.199858	+	0.979825i	$0.564048\pi$
$200$	−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	$-0.336700\pi$
$223$	14.6588	0.981627	0.490813	+	0.871265i	$0.336700\pi$
$224$	0	0
$225$	−4.65685	−0.310457
$226$	−10.5258	−0.700163
$227$	−8.36900	−0.555470	−0.277735	−	0.960658i	$-0.589584\pi$
$227$	−8.36900	−0.555470	−0.277735	+	0.960658i	$0.589584\pi$
$228$	3.26022	0.215913
$229$	−28.3666	−1.87452	−0.937259	−	0.348633i	$-0.886646\pi$
$229$	−28.3666	−1.87452	−0.937259	+	0.348633i	$0.886646\pi$
$230$	−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	$-0.556948\pi$
$241$	−5.52518	−0.355908	−0.177954	+	0.984039i	$0.556948\pi$
$242$	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	$-0.568589\pi$
$251$	−6.77494	−0.427630	−0.213815	+	0.976874i	$0.568589\pi$
$252$	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	$-0.552801\pi$
$257$	−5.29417	−0.330241	−0.165121	+	0.986273i	$0.552801\pi$
$258$	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	$-0.740687\pi$
$269$	−22.5064	−1.37224	−0.686119	+	0.727489i	$0.740687\pi$
$270$	0.585786	0.0356498
$271$	−8.90423	−0.540893	−0.270447	−	0.962735i	$-0.587171\pi$
$271$	−8.90423	−0.540893	−0.270447	+	0.962735i	$0.587171\pi$
$272$	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	$-0.492789\pi$
$283$	0.762094	0.0453018	0.0226509	+	0.999743i	$0.492789\pi$
$284$	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	$-0.525305\pi$
$293$	−2.71868	−0.158827	−0.0794135	+	0.996842i	$0.525305\pi$
$294$	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	$-0.711040\pi$
$307$	−21.5684	−1.23097	−0.615486	+	0.788148i	$0.711040\pi$
$308$	0	0
$309$	5.77690	0.328636
$310$	0.738220	0.0419281
$311$	−17.0500	−0.966815	−0.483407	−	0.875395i	$-0.660601\pi$
$311$	−17.0500	−0.966815	−0.483407	+	0.875395i	$0.660601\pi$
$312$	6.45666	0.365536
$313$	−21.7522	−1.22951	−0.614753	−	0.788719i	$-0.710744\pi$
$313$	−21.7522	−1.22951	−0.614753	+	0.788719i	$0.710744\pi$
$314$	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	$-0.362337\pi$
$349$	15.6598	0.838249	0.419125	+	0.907929i	$0.362337\pi$
$350$	0	0
$351$	6.45666	0.344631
$352$	5.93089	0.316118
$353$	−29.8333	−1.58787	−0.793934	−	0.608004i	$-0.791970\pi$
$353$	−29.8333	−1.58787	−0.793934	+	0.608004i	$0.791970\pi$
$354$	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	$-0.422567\pi$
$367$	9.22882	0.481741	0.240870	+	0.970557i	$0.422567\pi$
$368$	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	$-0.579138\pi$
$383$	−9.63116	−0.492129	−0.246065	+	0.969253i	$0.579138\pi$
$384$	−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	$-0.377116\pi$
$397$	15.0047	0.753066	0.376533	+	0.926403i	$0.377116\pi$
$398$	−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	$-0.331260\pi$
$409$	20.4515	1.01126	0.505631	+	0.862750i	$0.331260\pi$
$410$	−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	$-0.620367\pi$
$419$	−15.1145	−0.738391	−0.369195	+	0.929352i	$0.620367\pi$
$420$	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	$-0.714209\pi$
$433$	−25.9401	−1.24660	−0.623302	+	0.781981i	$0.714209\pi$
$434$	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	$-0.277249\pi$
$439$	26.9891	1.28812	0.644060	+	0.764975i	$0.277249\pi$
$440$	−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	$-0.609153\pi$
$461$	−14.4385	−0.672468	−0.336234	+	0.941779i	$0.609153\pi$
$462$	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	$-0.418815\pi$
$467$	10.9042	0.504588	0.252294	+	0.967651i	$0.418815\pi$
$468$	−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	$-0.629912\pi$
$479$	−17.3729	−0.793788	−0.396894	+	0.917864i	$0.629912\pi$
$480$	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	$-0.224828\pi$
$503$	34.1240	1.52151	0.760756	+	0.649038i	$0.224828\pi$
$504$	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	$-0.713945\pi$
$509$	−28.0953	−1.24530	−0.622652	+	0.782499i	$0.713945\pi$
$510$	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	$-0.350049\pi$
$521$	20.7188	0.907709	0.453854	+	0.891076i	$0.350049\pi$
$522$	−0.948474	−0.0415136
$523$	−11.6883	−0.511092	−0.255546	−	0.966797i	$-0.582255\pi$
$523$	−11.6883	−0.511092	−0.255546	+	0.966797i	$0.582255\pi$
$524$	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	$-0.146053\pi$
$563$	42.5468	1.79314	0.896568	+	0.442907i	$0.146053\pi$
$564$	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	$-0.113364\pi$
$577$	45.0270	1.87450	0.937249	+	0.348661i	$0.113364\pi$
$578$	−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	$-0.147781\pi$
$587$	43.3271	1.78830	0.894150	+	0.447767i	$0.147781\pi$
$588$	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	$-0.232235\pi$
$593$	36.3058	1.49090	0.745449	+	0.666562i	$0.232235\pi$
$594$	−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	$-0.588446\pi$
$601$	−13.4491	−0.548602	−0.274301	+	0.961644i	$0.588446\pi$
$602$	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	$-0.562652\pi$
$607$	−9.63610	−0.391117	−0.195559	+	0.980692i	$0.562652\pi$
$608$	−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	$-0.138934\pi$
$619$	45.0944	1.81250	0.906248	+	0.422747i	$0.138934\pi$
$620$	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	$-0.434280\pi$
$643$	10.3966	0.410003	0.205002	+	0.978762i	$0.434280\pi$
$644$	0	0
$645$	−3.83195	−0.150883
$646$	−1.21205	−0.0476877
$647$	41.9064	1.64751	0.823754	−	0.566947i	$-0.191876\pi$
$647$	41.9064	1.64751	0.823754	+	0.566947i	$0.191876\pi$
$648$	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	$-0.334376\pi$
$661$	25.5639	0.994319	0.497160	+	0.867659i	$0.334376\pi$
$662$	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	$-0.369409\pi$
$677$	20.7556	0.797701	0.398850	+	0.917016i	$0.369409\pi$
$678$	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	$-0.802219\pi$
$691$	−42.7475	−1.62619	−0.813095	+	0.582131i	$0.802219\pi$
$692$	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	$-0.488577\pi$
$719$	1.92420	0.0717605	0.0358802	+	0.999356i	$0.488577\pi$
$720$	−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	$-0.376847\pi$
$727$	20.3471	0.754631	0.377315	+	0.926085i	$0.376847\pi$
$728$	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	$-0.488732\pi$
$733$	1.91649	0.0707871	0.0353936	+	0.999373i	$0.488732\pi$
$734$	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	$-0.626268\pi$
$761$	−21.3165	−0.772722	−0.386361	+	0.922348i	$0.626268\pi$
$762$	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	$-0.231005\pi$
$769$	41.4864	1.49604	0.748019	+	0.663677i	$0.231005\pi$
$770$	0	0
$771$	5.29417	0.190665
$772$	−22.1240	−0.796259
$773$	11.1261	0.400178	0.200089	−	0.979778i	$-0.435877\pi$
$773$	11.1261	0.400178	0.200089	+	0.979778i	$0.435877\pi$
$774$	−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	$-0.656891\pi$
$787$	−26.5482	−0.946342	−0.473171	+	0.880970i	$0.656891\pi$
$788$	−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	$-0.682608\pi$
$797$	−30.6436	−1.08545	−0.542726	+	0.839910i	$0.682608\pi$
$798$	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	$-0.753338\pi$
$811$	−40.6941	−1.42896	−0.714482	+	0.699654i	$0.753338\pi$
$812$	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	$-0.873615\pi$
$829$	−53.1050	−1.84441	−0.922206	+	0.386698i	$0.873615\pi$
$830$	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	$-0.266840\pi$
$839$	38.7399	1.33745	0.668726	+	0.743509i	$0.266840\pi$
$840$	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	$-0.513703\pi$
$853$	−2.51391	−0.0860745	−0.0430373	+	0.999073i	$0.513703\pi$
$854$	0	0
$855$	1.90979	0.0653136
$856$	7.41798	0.253541
$857$	25.2280	0.861772	0.430886	−	0.902406i	$-0.358201\pi$
$857$	25.2280	0.861772	0.430886	+	0.902406i	$0.358201\pi$
$858$	38.2937	1.30733
$859$	30.1994	1.03039	0.515195	−	0.857073i	$-0.327720\pi$
$859$	30.1994	1.03039	0.515195	+	0.857073i	$0.327720\pi$
$860$	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	$-0.373137\pi$
$881$	23.0380	0.776168	0.388084	+	0.921624i	$0.373137\pi$
$882$	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	$-0.710113\pi$
$887$	−36.5245	−1.22637	−0.613187	+	0.789938i	$0.710113\pi$
$888$	−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	$-0.499032\pi$
$929$	0.185391	0.00608247	0.00304124	+	0.999995i	$0.499032\pi$
$930$	−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	$-0.769360\pi$
$937$	−45.8410	−1.49756	−0.748780	+	0.662818i	$0.769360\pi$
$938$	0	0
$939$	21.7522	0.709856
$940$	6.21025	0.202556
$941$	−59.9386	−1.95394	−0.976971	−	0.213373i	$-0.931555\pi$
$941$	−59.9386	−1.95394	−0.976971	+	0.213373i	$0.931555\pi$
$942$	−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	$-0.125714\pi$
$971$	57.5241	1.84604	0.923018	+	0.384756i	$0.125714\pi$
$972$	−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	$-0.302960\pi$
$983$	36.3842	1.16047	0.580237	+	0.814447i	$0.302960\pi$
$984$	−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	$-0.473238\pi$
$997$	5.30325	0.167956	0.0839778	+	0.996468i	$0.473238\pi$
$998$	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.ci.1.4	✓	4
7.6	odd	2		6762.2.a.ct.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.ci.1.4	✓	4	1.1	even	1	trivial
6762.2.a.ct.1.2	yes	4	7.6	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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
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

Properties

Related objects

Downloads

Learn more