LMFDB - Embedded newform 6762.2.a.ct.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:	$0$
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			1.4
Root			$2.77462$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.41421 q^{10} +2.29857 q^{11} +1.00000 q^{12} -1.54925 q^{13} +3.41421 q^{15} +1.00000 q^{16} -2.72082 q^{17} +1.00000 q^{18} +7.15442 q^{19} +3.41421 q^{20} +2.29857 q^{22} +1.00000 q^{23} +1.00000 q^{24} +6.65685 q^{25} -1.54925 q^{26} +1.00000 q^{27} -9.69564 q^{29} +3.41421 q^{30} +5.15442 q^{31} +1.00000 q^{32} +2.29857 q^{33} -2.72082 q^{34} +1.00000 q^{36} +2.72082 q^{37} +7.15442 q^{38} -1.54925 q^{39} +3.41421 q^{40} -6.01136 q^{41} +11.8193 q^{43} +2.29857 q^{44} +3.41421 q^{45} +1.00000 q^{46} -0.557278 q^{47} +1.00000 q^{48} +6.65685 q^{50} -2.72082 q^{51} -1.54925 q^{52} -3.31796 q^{53} +1.00000 q^{54} +7.84782 q^{55} +7.15442 q^{57} -9.69564 q^{58} -7.69564 q^{59} +3.41421 q^{60} -0.0113593 q^{61} +5.15442 q^{62} +1.00000 q^{64} -5.28946 q^{65} +2.29857 q^{66} +8.93604 q^{67} -2.72082 q^{68} +1.00000 q^{69} -9.25067 q^{71} +1.00000 q^{72} -8.09046 q^{73} +2.72082 q^{74} +6.65685 q^{75} +7.15442 q^{76} -1.54925 q^{78} -10.4062 q^{79} +3.41421 q^{80} +1.00000 q^{81} -6.01136 q^{82} +1.71279 q^{83} -9.28946 q^{85} +11.8193 q^{86} -9.69564 q^{87} +2.29857 q^{88} +16.0506 q^{89} +3.41421 q^{90} +1.00000 q^{92} +5.15442 q^{93} -0.557278 q^{94} +24.4267 q^{95} +1.00000 q^{96} -5.76446 q^{97} +2.29857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.41421	1.52688	0.763441	−	0.645877i	$-0.223508\pi$
$5$	3.41421	1.52688	0.763441	+	0.645877i	$0.223508\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.41421	1.07967
$11$	2.29857	0.693046	0.346523	−	0.938042i	$-0.387362\pi$
$11$	2.29857	0.693046	0.346523	+	0.938042i	$0.387362\pi$
$12$	1.00000	0.288675
$13$	−1.54925	−0.429683	−0.214842	−	0.976649i	$-0.568924\pi$
$13$	−1.54925	−0.429683	−0.214842	+	0.976649i	$0.568924\pi$
$14$	0	0
$15$	3.41421	0.881546
$16$	1.00000	0.250000
$17$	−2.72082	−0.659895	−0.329948	−	0.943999i	$-0.607031\pi$
$17$	−2.72082	−0.659895	−0.329948	+	0.943999i	$0.607031\pi$
$18$	1.00000	0.235702
$19$	7.15442	1.64134	0.820669	−	0.571404i	$-0.193601\pi$
$19$	7.15442	1.64134	0.820669	+	0.571404i	$0.193601\pi$
$20$	3.41421	0.763441
$21$	0	0
$22$	2.29857	0.490057
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	6.65685	1.33137
$26$	−1.54925	−0.303832
$27$	1.00000	0.192450
$28$	0	0
$29$	−9.69564	−1.80043	−0.900217	−	0.435441i	$-0.856592\pi$
$29$	−9.69564	−1.80043	−0.900217	+	0.435441i	$0.856592\pi$
$30$	3.41421	0.623347
$31$	5.15442	0.925762	0.462881	−	0.886420i	$-0.346816\pi$
$31$	5.15442	0.925762	0.462881	+	0.886420i	$0.346816\pi$
$32$	1.00000	0.176777
$33$	2.29857	0.400130
$34$	−2.72082	−0.466617
$35$	0	0
$36$	1.00000	0.166667
$37$	2.72082	0.447300	0.223650	−	0.974670i	$-0.428203\pi$
$37$	2.72082	0.447300	0.223650	+	0.974670i	$0.428203\pi$
$38$	7.15442	1.16060
$39$	−1.54925	−0.248078
$40$	3.41421	0.539835
$41$	−6.01136	−0.938817	−0.469408	−	0.882981i	$-0.655533\pi$
$41$	−6.01136	−0.938817	−0.469408	+	0.882981i	$0.655533\pi$
$42$	0	0
$43$	11.8193	1.80243	0.901214	−	0.433374i	$-0.142677\pi$
$43$	11.8193	1.80243	0.901214	+	0.433374i	$0.142677\pi$
$44$	2.29857	0.346523
$45$	3.41421	0.508961
$46$	1.00000	0.147442
$47$	−0.557278	−0.0812874	−0.0406437	−	0.999174i	$-0.512941\pi$
$47$	−0.557278	−0.0812874	−0.0406437	+	0.999174i	$0.512941\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	6.65685	0.941421
$51$	−2.72082	−0.380991
$52$	−1.54925	−0.214842
$53$	−3.31796	−0.455757	−0.227879	−	0.973690i	$-0.573179\pi$
$53$	−3.31796	−0.455757	−0.227879	+	0.973690i	$0.573179\pi$
$54$	1.00000	0.136083
$55$	7.84782	1.05820
$56$	0	0
$57$	7.15442	0.947627
$58$	−9.69564	−1.27310
$59$	−7.69564	−1.00189	−0.500943	−	0.865480i	$-0.667013\pi$
$59$	−7.69564	−1.00189	−0.500943	+	0.865480i	$0.667013\pi$
$60$	3.41421	0.440773
$61$	−0.0113593	−0.00145441	−0.000727205	−	1.00000i	$-0.500231\pi$
$61$	−0.0113593	−0.00145441	−0.000727205		1.00000i	$0.500231\pi$
$62$	5.15442	0.654612
$63$	0	0
$64$	1.00000	0.125000
$65$	−5.28946	−0.656076
$66$	2.29857	0.282935
$67$	8.93604	1.09171	0.545855	−	0.837879i	$-0.316205\pi$
$67$	8.93604	1.09171	0.545855	+	0.837879i	$0.316205\pi$
$68$	−2.72082	−0.329948
$69$	1.00000	0.120386
$70$	0	0
$71$	−9.25067	−1.09785	−0.548926	−	0.835871i	$-0.684963\pi$
$71$	−9.25067	−1.09785	−0.548926	+	0.835871i	$0.684963\pi$
$72$	1.00000	0.117851
$73$	−8.09046	−0.946917	−0.473458	−	0.880816i	$-0.656995\pi$
$73$	−8.09046	−0.946917	−0.473458	+	0.880816i	$0.656995\pi$
$74$	2.72082	0.316289
$75$	6.65685	0.768667
$76$	7.15442	0.820669
$77$	0	0
$78$	−1.54925	−0.175418
$79$	−10.4062	−1.17079	−0.585393	−	0.810749i	$-0.699060\pi$
$79$	−10.4062	−1.17079	−0.585393	+	0.810749i	$0.699060\pi$
$80$	3.41421	0.381721
$81$	1.00000	0.111111
$82$	−6.01136	−0.663844
$83$	1.71279	0.188003	0.0940014	−	0.995572i	$-0.470034\pi$
$83$	1.71279	0.188003	0.0940014	+	0.995572i	$0.470034\pi$
$84$	0	0
$85$	−9.28946	−1.00758
$86$	11.8193	1.27451
$87$	−9.69564	−1.03948
$88$	2.29857	0.245029
$89$	16.0506	1.70136	0.850680	−	0.525684i	$-0.176191\pi$
$89$	16.0506	1.70136	0.850680	+	0.525684i	$0.176191\pi$
$90$	3.41421	0.359890
$91$	0	0
$92$	1.00000	0.104257
$93$	5.15442	0.534489
$94$	−0.557278	−0.0574788
$95$	24.4267	2.50613
$96$	1.00000	0.102062
$97$	−5.76446	−0.585293	−0.292646	−	0.956221i	$-0.594536\pi$
$97$	−5.76446	−0.585293	−0.292646	+	0.956221i	$0.594536\pi$
$98$	0	0
$99$	2.29857	0.231015
$100$	6.65685	0.665685
$101$	13.8193	1.37507	0.687536	−	0.726150i	$-0.258692\pi$
$101$	13.8193	1.37507	0.687536	+	0.726150i	$0.258692\pi$
$102$	−2.72082	−0.269401
$103$	8.86721	0.873712	0.436856	−	0.899531i	$-0.356092\pi$
$103$	8.86721	0.873712	0.436856	+	0.899531i	$0.356092\pi$
$104$	−1.54925	−0.151916
$105$	0	0
$106$	−3.31796	−0.322269
$107$	13.1818	1.27434	0.637169	−	0.770724i	$-0.280105\pi$
$107$	13.1818	1.27434	0.637169	+	0.770724i	$0.280105\pi$
$108$	1.00000	0.0962250
$109$	3.76446	0.360570	0.180285	−	0.983614i	$-0.442298\pi$
$109$	3.76446	0.360570	0.180285	+	0.983614i	$0.442298\pi$
$110$	7.84782	0.748260
$111$	2.72082	0.258249
$112$	0	0
$113$	−6.15218	−0.578749	−0.289374	−	0.957216i	$-0.593447\pi$
$113$	−6.15218	−0.578749	−0.289374	+	0.957216i	$0.593447\pi$
$114$	7.15442	0.670073
$115$	3.41421	0.318377
$116$	−9.69564	−0.900217
$117$	−1.54925	−0.143228
$118$	−7.69564	−0.708441
$119$	0	0
$120$	3.41421	0.311674
$121$	−5.71656	−0.519688
$122$	−0.0113593	−0.00102842
$123$	−6.01136	−0.542026
$124$	5.15442	0.462881
$125$	5.65685	0.505964
$126$	0	0
$127$	−13.0033	−1.15386	−0.576929	−	0.816794i	$-0.695749\pi$
$127$	−13.0033	−1.15386	−0.576929	+	0.816794i	$0.695749\pi$
$128$	1.00000	0.0883883
$129$	11.8193	1.04063
$130$	−5.28946	−0.463916
$131$	−15.4804	−1.35253	−0.676265	−	0.736658i	$-0.736403\pi$
$131$	−15.4804	−1.35253	−0.676265	+	0.736658i	$0.736403\pi$
$132$	2.29857	0.200065
$133$	0	0
$134$	8.93604	0.771956
$135$	3.41421	0.293849
$136$	−2.72082	−0.233308
$137$	−15.4416	−1.31927	−0.659634	−	0.751587i	$-0.729289\pi$
$137$	−15.4416	−1.31927	−0.659634	+	0.751587i	$0.729289\pi$
$138$	1.00000	0.0851257
$139$	5.17157	0.438647	0.219324	−	0.975652i	$-0.429615\pi$
$139$	5.17157	0.438647	0.219324	+	0.975652i	$0.429615\pi$
$140$	0	0
$141$	−0.557278	−0.0469313
$142$	−9.25067	−0.776299
$143$	−3.56105	−0.297790
$144$	1.00000	0.0833333
$145$	−33.1030	−2.74905
$146$	−8.09046	−0.669571
$147$	0	0
$148$	2.72082	0.223650
$149$	6.70475	0.549275	0.274637	−	0.961548i	$-0.411442\pi$
$149$	6.70475	0.549275	0.274637	+	0.961548i	$0.411442\pi$
$150$	6.65685	0.543530
$151$	8.13395	0.661931	0.330966	−	0.943643i	$-0.392626\pi$
$151$	8.13395	0.661931	0.330966	+	0.943643i	$0.392626\pi$
$152$	7.15442	0.580300
$153$	−2.72082	−0.219965
$154$	0	0
$155$	17.5983	1.41353
$156$	−1.54925	−0.124039
$157$	−3.64396	−0.290820	−0.145410	−	0.989372i	$-0.546450\pi$
$157$	−3.64396	−0.290820	−0.145410	+	0.989372i	$0.546450\pi$
$158$	−10.4062	−0.827871
$159$	−3.31796	−0.263132
$160$	3.41421	0.269917
$161$	0	0
$162$	1.00000	0.0785674
$163$	−13.5047	−1.05777	−0.528884	−	0.848694i	$-0.677389\pi$
$163$	−13.5047	−1.05777	−0.528884	+	0.848694i	$0.677389\pi$
$164$	−6.01136	−0.469408
$165$	7.84782	0.610952
$166$	1.71279	0.132938
$167$	19.6009	1.51676	0.758382	−	0.651810i	$-0.225990\pi$
$167$	19.6009	1.51676	0.758382	+	0.651810i	$0.225990\pi$
$168$	0	0
$169$	−10.5998	−0.815372
$170$	−9.28946	−0.712469
$171$	7.15442	0.547112
$172$	11.8193	0.901214
$173$	14.6317	1.11243	0.556213	−	0.831040i	$-0.312254\pi$
$173$	14.6317	1.11243	0.556213	+	0.831040i	$0.312254\pi$
$174$	−9.69564	−0.735024
$175$	0	0
$176$	2.29857	0.173261
$177$	−7.69564	−0.578440
$178$	16.0506	1.20304
$179$	−6.28613	−0.469847	−0.234924	−	0.972014i	$-0.575484\pi$
$179$	−6.28613	−0.469847	−0.234924	+	0.972014i	$0.575484\pi$
$180$	3.41421	0.254480
$181$	14.8398	1.10303	0.551516	−	0.834164i	$-0.314049\pi$
$181$	14.8398	1.10303	0.551516	+	0.834164i	$0.314049\pi$
$182$	0	0
$183$	−0.0113593	−0.000839704 0
$184$	1.00000	0.0737210
$185$	9.28946	0.682974
$186$	5.15442	0.377941
$187$	−6.25400	−0.457338
$188$	−0.557278	−0.0406437
$189$	0	0
$190$	24.4267	1.77210
$191$	−18.3492	−1.32770	−0.663849	−	0.747866i	$-0.731078\pi$
$191$	−18.3492	−1.32770	−0.663849	+	0.747866i	$0.731078\pi$
$192$	1.00000	0.0721688
$193$	−0.979075	−0.0704753	−0.0352377	−	0.999379i	$-0.511219\pi$
$193$	−0.979075	−0.0704753	−0.0352377	+	0.999379i	$0.511219\pi$
$194$	−5.76446	−0.413864
$195$	−5.28946	−0.378786
$196$	0	0
$197$	4.65353	0.331550	0.165775	−	0.986164i	$-0.446987\pi$
$197$	4.65353	0.331550	0.165775	+	0.986164i	$0.446987\pi$
$198$	2.29857	0.163352
$199$	1.46436	0.103805	0.0519027	−	0.998652i	$-0.483471\pi$
$199$	1.46436	0.103805	0.0519027	+	0.998652i	$0.483471\pi$
$200$	6.65685	0.470711
$201$	8.93604	0.630299
$202$	13.8193	0.972323
$203$	0	0
$204$	−2.72082	−0.190495
$205$	−20.5241	−1.43346
$206$	8.86721	0.617808
$207$	1.00000	0.0695048
$208$	−1.54925	−0.107421
$209$	16.4450	1.13752
$210$	0	0
$211$	−12.9075	−0.888591	−0.444295	−	0.895880i	$-0.646546\pi$
$211$	−12.9075	−0.888591	−0.444295	+	0.895880i	$0.646546\pi$
$212$	−3.31796	−0.227879
$213$	−9.25067	−0.633846
$214$	13.1818	0.901093
$215$	40.3536	2.75210
$216$	1.00000	0.0680414
$217$	0	0
$218$	3.76446	0.254962
$219$	−8.09046	−0.546703
$220$	7.84782	0.529100
$221$	4.21522	0.283546
$222$	2.72082	0.182609
$223$	14.4293	0.966261	0.483130	−	0.875548i	$-0.339500\pi$
$223$	14.4293	0.966261	0.483130	+	0.875548i	$0.339500\pi$
$224$	0	0
$225$	6.65685	0.443790
$226$	−6.15218	−0.409237
$227$	−14.4133	−0.956643	−0.478322	−	0.878185i	$-0.658755\pi$
$227$	−14.4133	−0.956643	−0.478322	+	0.878185i	$0.658755\pi$
$228$	7.15442	0.473813
$229$	−1.26357	−0.0834988	−0.0417494	−	0.999128i	$-0.513293\pi$
$229$	−1.26357	−0.0834988	−0.0417494	+	0.999128i	$0.513293\pi$
$230$	3.41421	0.225127
$231$	0	0
$232$	−9.69564	−0.636550
$233$	−16.7166	−1.09514	−0.547569	−	0.836760i	$-0.684447\pi$
$233$	−16.7166	−1.09514	−0.547569	+	0.836760i	$0.684447\pi$
$234$	−1.54925	−0.101277
$235$	−1.90267	−0.124116
$236$	−7.69564	−0.500943
$237$	−10.4062	−0.675954
$238$	0	0
$239$	−22.6923	−1.46784	−0.733922	−	0.679234i	$-0.762312\pi$
$239$	−22.6923	−1.46784	−0.733922	+	0.679234i	$0.762312\pi$
$240$	3.41421	0.220387
$241$	20.6705	1.33150	0.665751	−	0.746174i	$-0.268111\pi$
$241$	20.6705	1.33150	0.665751	+	0.746174i	$0.268111\pi$
$242$	−5.71656	−0.367475
$243$	1.00000	0.0641500
$244$	−0.0113593	−0.000727205 0
$245$	0	0
$246$	−6.01136	−0.383270
$247$	−11.0840	−0.705256
$248$	5.15442	0.327306
$249$	1.71279	0.108543
$250$	5.65685	0.357771
$251$	27.6397	1.74460	0.872301	−	0.488969i	$-0.162627\pi$
$251$	27.6397	1.74460	0.872301	+	0.488969i	$0.162627\pi$
$252$	0	0
$253$	2.29857	0.144510
$254$	−13.0033	−0.815901
$255$	−9.28946	−0.581728
$256$	1.00000	0.0625000
$257$	−11.9383	−0.744689	−0.372345	−	0.928095i	$-0.621446\pi$
$257$	−11.9383	−0.744689	−0.372345	+	0.928095i	$0.621446\pi$
$258$	11.8193	0.735838
$259$	0	0
$260$	−5.28946	−0.328038
$261$	−9.69564	−0.600145
$262$	−15.4804	−0.956384
$263$	−8.68629	−0.535620	−0.267810	−	0.963472i	$-0.586300\pi$
$263$	−8.68629	−0.535620	−0.267810	+	0.963472i	$0.586300\pi$
$264$	2.29857	0.141467
$265$	−11.3282	−0.695888
$266$	0	0
$267$	16.0506	0.982280
$268$	8.93604	0.545855
$269$	−20.6134	−1.25682	−0.628412	−	0.777881i	$-0.716295\pi$
$269$	−20.6134	−1.25682	−0.628412	+	0.777881i	$0.716295\pi$
$270$	3.41421	0.207782
$271$	−3.53789	−0.214911	−0.107456	−	0.994210i	$-0.534270\pi$
$271$	−3.53789	−0.214911	−0.107456	+	0.994210i	$0.534270\pi$
$272$	−2.72082	−0.164974
$273$	0	0
$274$	−15.4416	−0.932863
$275$	15.3013	0.922701
$276$	1.00000	0.0601929
$277$	24.4898	1.47145	0.735724	−	0.677282i	$-0.236842\pi$
$277$	24.4898	1.47145	0.735724	+	0.677282i	$0.236842\pi$
$278$	5.17157	0.310170
$279$	5.15442	0.308587
$280$	0	0
$281$	−10.1582	−0.605987	−0.302994	−	0.952993i	$-0.597986\pi$
$281$	−10.1582	−0.605987	−0.302994	+	0.952993i	$0.597986\pi$
$282$	−0.557278	−0.0331854
$283$	−16.6042	−0.987020	−0.493510	−	0.869740i	$-0.664286\pi$
$283$	−16.6042	−0.987020	−0.493510	+	0.869740i	$0.664286\pi$
$284$	−9.25067	−0.548926
$285$	24.4267	1.44691
$286$	−3.56105	−0.210570
$287$	0	0
$288$	1.00000	0.0589256
$289$	−9.59715	−0.564538
$290$	−33.1030	−1.94387
$291$	−5.76446	−0.337919
$292$	−8.09046	−0.473458
$293$	24.9737	1.45898	0.729491	−	0.683991i	$-0.239757\pi$
$293$	24.9737	1.45898	0.729491	+	0.683991i	$0.239757\pi$
$294$	0	0
$295$	−26.2745	−1.52976
$296$	2.72082	0.158144
$297$	2.29857	0.133377
$298$	6.70475	0.388396
$299$	−1.54925	−0.0895952
$300$	6.65685	0.384334
$301$	0	0
$302$	8.13395	0.468056
$303$	13.8193	0.793899
$304$	7.15442	0.410334
$305$	−0.0387831	−0.00222071
$306$	−2.72082	−0.155539
$307$	−32.1239	−1.83341	−0.916704	−	0.399567i	$-0.869160\pi$
$307$	−32.1239	−1.83341	−0.916704	+	0.399567i	$0.869160\pi$
$308$	0	0
$309$	8.86721	0.504438
$310$	17.5983	0.999516
$311$	29.0571	1.64768	0.823838	−	0.566825i	$-0.191828\pi$
$311$	29.0571	1.64768	0.823838	+	0.566825i	$0.191828\pi$
$312$	−1.54925	−0.0877088
$313$	−1.74174	−0.0984492	−0.0492246	−	0.998788i	$-0.515675\pi$
$313$	−1.74174	−0.0984492	−0.0492246	+	0.998788i	$0.515675\pi$
$314$	−3.64396	−0.205641
$315$	0	0
$316$	−10.4062	−0.585393
$317$	−12.7796	−0.717774	−0.358887	−	0.933381i	$-0.616844\pi$
$317$	−12.7796	−0.717774	−0.358887	+	0.933381i	$0.616844\pi$
$318$	−3.31796	−0.186062
$319$	−22.2861	−1.24778
$320$	3.41421	0.190860
$321$	13.1818	0.735739
$322$	0	0
$323$	−19.4659	−1.08311
$324$	1.00000	0.0555556
$325$	−10.3131	−0.572068
$326$	−13.5047	−0.747955
$327$	3.76446	0.208175
$328$	−6.01136	−0.331922
$329$	0	0
$330$	7.84782	0.432008
$331$	6.34315	0.348651	0.174325	−	0.984688i	$-0.444226\pi$
$331$	6.34315	0.348651	0.174325	+	0.984688i	$0.444226\pi$
$332$	1.71279	0.0940014
$333$	2.72082	0.149100
$334$	19.6009	1.07251
$335$	30.5095	1.66691
$336$	0	0
$337$	15.8866	0.865398	0.432699	−	0.901538i	$-0.357561\pi$
$337$	15.8866	0.865398	0.432699	+	0.901538i	$0.357561\pi$
$338$	−10.5998	−0.576555
$339$	−6.15218	−0.334141
$340$	−9.28946	−0.503791
$341$	11.8478	0.641595
$342$	7.15442	0.386867
$343$	0	0
$344$	11.8193	0.637255
$345$	3.41421	0.183815
$346$	14.6317	0.786604
$347$	−28.7699	−1.54445	−0.772224	−	0.635350i	$-0.780856\pi$
$347$	−28.7699	−1.54445	−0.772224	+	0.635350i	$0.780856\pi$
$348$	−9.69564	−0.519741
$349$	14.6638	0.784935	0.392468	−	0.919766i	$-0.371621\pi$
$349$	14.6638	0.784935	0.392468	+	0.919766i	$0.371621\pi$
$350$	0	0
$351$	−1.54925	−0.0826926
$352$	2.29857	0.122514
$353$	−12.6079	−0.671049	−0.335525	−	0.942031i	$-0.608914\pi$
$353$	−12.6079	−0.671049	−0.335525	+	0.942031i	$0.608914\pi$
$354$	−7.69564	−0.409019
$355$	−31.5838	−1.67629
$356$	16.0506	0.850680
$357$	0	0
$358$	−6.28613	−0.332232
$359$	−13.5047	−0.712749	−0.356375	−	0.934343i	$-0.615987\pi$
$359$	−13.5047	−0.712749	−0.356375	+	0.934343i	$0.615987\pi$
$360$	3.41421	0.179945
$361$	32.1858	1.69399
$362$	14.8398	0.779962
$363$	−5.71656	−0.300042
$364$	0	0
$365$	−27.6226	−1.44583
$366$	−0.0113593	−0.000593760 0
$367$	3.04364	0.158877	0.0794385	−	0.996840i	$-0.474687\pi$
$367$	3.04364	0.158877	0.0794385	+	0.996840i	$0.474687\pi$
$368$	1.00000	0.0521286
$369$	−6.01136	−0.312939
$370$	9.28946	0.482936
$371$	0	0
$372$	5.15442	0.267244
$373$	−37.2752	−1.93003	−0.965017	−	0.262187i	$-0.915556\pi$
$373$	−37.2752	−1.93003	−0.965017	+	0.262187i	$0.915556\pi$
$374$	−6.25400	−0.323387
$375$	5.65685	0.292119
$376$	−0.557278	−0.0287394
$377$	15.0209	0.773617
$378$	0	0
$379$	22.6720	1.16458	0.582291	−	0.812980i	$-0.302156\pi$
$379$	22.6720	1.16458	0.582291	+	0.812980i	$0.302156\pi$
$380$	24.4267	1.25306
$381$	−13.0033	−0.666181
$382$	−18.3492	−0.938825
$383$	−11.7278	−0.599261	−0.299630	−	0.954055i	$-0.596863\pi$
$383$	−11.7278	−0.599261	−0.299630	+	0.954055i	$0.596863\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−0.979075	−0.0498336
$387$	11.8193	0.600809
$388$	−5.76446	−0.292646
$389$	7.49223	0.379871	0.189936	−	0.981797i	$-0.439172\pi$
$389$	7.49223	0.379871	0.189936	+	0.981797i	$0.439172\pi$
$390$	−5.28946	−0.267842
$391$	−2.72082	−0.137598
$392$	0	0
$393$	−15.4804	−0.780884
$394$	4.65353	0.234441
$395$	−35.5289	−1.78765
$396$	2.29857	0.115508
$397$	−22.3616	−1.12230	−0.561148	−	0.827715i	$-0.689640\pi$
$397$	−22.3616	−1.12230	−0.561148	+	0.827715i	$0.689640\pi$
$398$	1.46436	0.0734015
$399$	0	0
$400$	6.65685	0.332843
$401$	−4.09580	−0.204534	−0.102267	−	0.994757i	$-0.532610\pi$
$401$	−4.09580	−0.204534	−0.102267	+	0.994757i	$0.532610\pi$
$402$	8.93604	0.445689
$403$	−7.98547	−0.397785
$404$	13.8193	0.687536
$405$	3.41421	0.169654
$406$	0	0
$407$	6.25400	0.309999
$408$	−2.72082	−0.134701
$409$	19.5336	0.965876	0.482938	−	0.875655i	$-0.339570\pi$
$409$	19.5336	0.965876	0.482938	+	0.875655i	$0.339570\pi$
$410$	−20.5241	−1.01361
$411$	−15.4416	−0.761680
$412$	8.86721	0.436856
$413$	0	0
$414$	1.00000	0.0491473
$415$	5.84782	0.287058
$416$	−1.54925	−0.0759580
$417$	5.17157	0.253253
$418$	16.4450	0.804350
$419$	−5.44055	−0.265788	−0.132894	−	0.991130i	$-0.542427\pi$
$419$	−5.44055	−0.265788	−0.132894	+	0.991130i	$0.542427\pi$
$420$	0	0
$421$	37.5149	1.82837	0.914183	−	0.405301i	$-0.132833\pi$
$421$	37.5149	1.82837	0.914183	+	0.405301i	$0.132833\pi$
$422$	−12.9075	−0.628329
$423$	−0.557278	−0.0270958
$424$	−3.31796	−0.161135
$425$	−18.1121	−0.878566
$426$	−9.25067	−0.448197
$427$	0	0
$428$	13.1818	0.637169
$429$	−3.56105	−0.171929
$430$	40.3536	1.94603
$431$	18.0303	0.868488	0.434244	−	0.900795i	$-0.357016\pi$
$431$	18.0303	0.868488	0.434244	+	0.900795i	$0.357016\pi$
$432$	1.00000	0.0481125
$433$	−25.4031	−1.22079	−0.610397	−	0.792096i	$-0.708990\pi$
$433$	−25.4031	−1.22079	−0.610397	+	0.792096i	$0.708990\pi$
$434$	0	0
$435$	−33.1030	−1.58717
$436$	3.76446	0.180285
$437$	7.15442	0.342243
$438$	−8.09046	−0.386577
$439$	−4.19205	−0.200076	−0.100038	−	0.994984i	$-0.531896\pi$
$439$	−4.19205	−0.200076	−0.100038	+	0.994984i	$0.531896\pi$
$440$	7.84782	0.374130
$441$	0	0
$442$	4.21522	0.200497
$443$	−24.0836	−1.14425	−0.572123	−	0.820168i	$-0.693880\pi$
$443$	−24.0836	−1.14425	−0.572123	+	0.820168i	$0.693880\pi$
$444$	2.72082	0.129124
$445$	54.8001	2.59778
$446$	14.4293	0.683249
$447$	6.70475	0.317124
$448$	0	0
$449$	5.89262	0.278090	0.139045	−	0.990286i	$-0.455597\pi$
$449$	5.89262	0.278090	0.139045	+	0.990286i	$0.455597\pi$
$450$	6.65685	0.313807
$451$	−13.8175	−0.650643
$452$	−6.15218	−0.289374
$453$	8.13395	0.382166
$454$	−14.4133	−0.676449
$455$	0	0
$456$	7.15442	0.335037
$457$	−9.40285	−0.439847	−0.219923	−	0.975517i	$-0.570581\pi$
$457$	−9.40285	−0.439847	−0.219923	+	0.975517i	$0.570581\pi$
$458$	−1.26357	−0.0590426
$459$	−2.72082	−0.126997
$460$	3.41421	0.159189
$461$	13.5720	0.632109	0.316055	−	0.948741i	$-0.397642\pi$
$461$	13.5720	0.632109	0.316055	+	0.948741i	$0.397642\pi$
$462$	0	0
$463$	32.7759	1.52323	0.761613	−	0.648033i	$-0.224408\pi$
$463$	32.7759	1.52323	0.761613	+	0.648033i	$0.224408\pi$
$464$	−9.69564	−0.450109
$465$	17.5983	0.816102
$466$	−16.7166	−0.774380
$467$	1.53789	0.0711649	0.0355824	−	0.999367i	$-0.488671\pi$
$467$	1.53789	0.0711649	0.0355824	+	0.999367i	$0.488671\pi$
$468$	−1.54925	−0.0716139
$469$	0	0
$470$	−1.90267	−0.0877634
$471$	−3.64396	−0.167905
$472$	−7.69564	−0.354220
$473$	27.1675	1.24917
$474$	−10.4062	−0.477972
$475$	47.6260	2.18523
$476$	0	0
$477$	−3.31796	−0.151919
$478$	−22.6923	−1.03792
$479$	−25.6547	−1.17219	−0.586096	−	0.810241i	$-0.699336\pi$
$479$	−25.6547	−1.17219	−0.586096	+	0.810241i	$0.699336\pi$
$480$	3.41421	0.155837
$481$	−4.21522	−0.192197
$482$	20.6705	0.941513
$483$	0	0
$484$	−5.71656	−0.259844
$485$	−19.6811	−0.893673
$486$	1.00000	0.0453609
$487$	−17.8151	−0.807277	−0.403639	−	0.914919i	$-0.632255\pi$
$487$	−17.8151	−0.807277	−0.403639	+	0.914919i	$0.632255\pi$
$488$	−0.0113593	−0.000514212 0
$489$	−13.5047	−0.610702
$490$	0	0
$491$	−39.3973	−1.77797	−0.888987	−	0.457931i	$-0.848590\pi$
$491$	−39.3973	−1.77797	−0.888987	+	0.457931i	$0.848590\pi$
$492$	−6.01136	−0.271013
$493$	26.3801	1.18810
$494$	−11.0840	−0.498691
$495$	7.84782	0.352733
$496$	5.15442	0.231440
$497$	0	0
$498$	1.71279	0.0767518
$499$	20.2297	0.905608	0.452804	−	0.891610i	$-0.350424\pi$
$499$	20.2297	0.905608	0.452804	+	0.891610i	$0.350424\pi$
$500$	5.65685	0.252982
$501$	19.6009	0.875705
$502$	27.6397	1.23362
$503$	−12.9791	−0.578708	−0.289354	−	0.957222i	$-0.593441\pi$
$503$	−12.9791	−0.578708	−0.289354	+	0.957222i	$0.593441\pi$
$504$	0	0
$505$	47.1821	2.09957
$506$	2.29857	0.102184
$507$	−10.5998	−0.470755
$508$	−13.0033	−0.576929
$509$	15.9151	0.705425	0.352712	−	0.935732i	$-0.385259\pi$
$509$	15.9151	0.705425	0.352712	+	0.935732i	$0.385259\pi$
$510$	−9.28946	−0.411344
$511$	0	0
$512$	1.00000	0.0441942
$513$	7.15442	0.315876
$514$	−11.9383	−0.526575
$515$	30.2745	1.33406
$516$	11.8193	0.520316
$517$	−1.28094	−0.0563359
$518$	0	0
$519$	14.6317	0.642259
$520$	−5.28946	−0.231958
$521$	1.16732	0.0511411	0.0255705	−	0.999673i	$-0.491860\pi$
$521$	1.16732	0.0511411	0.0255705	+	0.999673i	$0.491860\pi$
$522$	−9.69564	−0.424367
$523$	16.5412	0.723297	0.361648	−	0.932315i	$-0.382214\pi$
$523$	16.5412	0.723297	0.361648	+	0.932315i	$0.382214\pi$
$524$	−15.4804	−0.676265
$525$	0	0
$526$	−8.68629	−0.378740
$527$	−14.0243	−0.610906
$528$	2.29857	0.100033
$529$	1.00000	0.0434783
$530$	−11.3282	−0.492067
$531$	−7.69564	−0.333962
$532$	0	0
$533$	9.31307	0.403394
$534$	16.0506	0.694577
$535$	45.0056	1.94576
$536$	8.93604	0.385978
$537$	−6.28613	−0.271266
$538$	−20.6134	−0.888708
$539$	0	0
$540$	3.41421	0.146924
$541$	−32.1400	−1.38181	−0.690903	−	0.722948i	$-0.742787\pi$
$541$	−32.1400	−1.38181	−0.690903	+	0.722948i	$0.742787\pi$
$542$	−3.53789	−0.151965
$543$	14.8398	0.636836
$544$	−2.72082	−0.116654
$545$	12.8527	0.550548
$546$	0	0
$547$	38.7371	1.65628	0.828140	−	0.560522i	$-0.189399\pi$
$547$	38.7371	1.65628	0.828140	+	0.560522i	$0.189399\pi$
$548$	−15.4416	−0.659634
$549$	−0.0113593	−0.000484803 0
$550$	15.3013	0.652448
$551$	−69.3667	−2.95512
$552$	1.00000	0.0425628
$553$	0	0
$554$	24.4898	1.04047
$555$	9.28946	0.394315
$556$	5.17157	0.219324
$557$	19.1879	0.813016	0.406508	−	0.913647i	$-0.366746\pi$
$557$	19.1879	0.813016	0.406508	+	0.913647i	$0.366746\pi$
$558$	5.15442	0.218204
$559$	−18.3110	−0.774473
$560$	0	0
$561$	−6.25400	−0.264044
$562$	−10.1582	−0.428498
$563$	9.61852	0.405372	0.202686	−	0.979244i	$-0.435033\pi$
$563$	9.61852	0.405372	0.202686	+	0.979244i	$0.435033\pi$
$564$	−0.557278	−0.0234656
$565$	−21.0049	−0.883681
$566$	−16.6042	−0.697929
$567$	0	0
$568$	−9.25067	−0.388150
$569$	−10.0570	−0.421612	−0.210806	−	0.977528i	$-0.567609\pi$
$569$	−10.0570	−0.421612	−0.210806	+	0.977528i	$0.567609\pi$
$570$	24.4267	1.02312
$571$	−14.4552	−0.604933	−0.302466	−	0.953160i	$-0.597810\pi$
$571$	−14.4552	−0.604933	−0.302466	+	0.953160i	$0.597810\pi$
$572$	−3.56105	−0.148895
$573$	−18.3492	−0.766547
$574$	0	0
$575$	6.65685	0.277610
$576$	1.00000	0.0416667
$577$	34.4456	1.43399	0.716995	−	0.697078i	$-0.245517\pi$
$577$	34.4456	1.43399	0.716995	+	0.697078i	$0.245517\pi$
$578$	−9.59715	−0.399189
$579$	−0.979075	−0.0406890
$580$	−33.1030	−1.37453
$581$	0	0
$582$	−5.76446	−0.238945
$583$	−7.62658	−0.315861
$584$	−8.09046	−0.334786
$585$	−5.28946	−0.218692
$586$	24.9737	1.03166
$587$	0.135481	0.00559192	0.00279596	−	0.999996i	$-0.499110\pi$
$587$	0.135481	0.00559192	0.00279596	+	0.999996i	$0.499110\pi$
$588$	0	0
$589$	36.8769	1.51949
$590$	−26.2745	−1.08171
$591$	4.65353	0.191421
$592$	2.72082	0.111825
$593$	28.1286	1.15510	0.577552	−	0.816354i	$-0.304008\pi$
$593$	28.1286	1.15510	0.577552	+	0.816354i	$0.304008\pi$
$594$	2.29857	0.0943116
$595$	0	0
$596$	6.70475	0.274637
$597$	1.46436	0.0599321
$598$	−1.54925	−0.0633534
$599$	−6.31102	−0.257861	−0.128931	−	0.991654i	$-0.541154\pi$
$599$	−6.31102	−0.257861	−0.128931	+	0.991654i	$0.541154\pi$
$600$	6.65685	0.271765
$601$	−27.0450	−1.10319	−0.551593	−	0.834113i	$-0.685980\pi$
$601$	−27.0450	−1.10319	−0.551593	+	0.834113i	$0.685980\pi$
$602$	0	0
$603$	8.93604	0.363904
$604$	8.13395	0.330966
$605$	−19.5176	−0.793502
$606$	13.8193	0.561371
$607$	−42.1683	−1.71156	−0.855778	−	0.517343i	$-0.826921\pi$
$607$	−42.1683	−1.71156	−0.855778	+	0.517343i	$0.826921\pi$
$608$	7.15442	0.290150
$609$	0	0
$610$	−0.0387831	−0.00157028
$611$	0.863361	0.0349278
$612$	−2.72082	−0.109983
$613$	26.4325	1.06760	0.533800	−	0.845611i	$-0.320764\pi$
$613$	26.4325	1.06760	0.533800	+	0.845611i	$0.320764\pi$
$614$	−32.1239	−1.29642
$615$	−20.5241	−0.827610
$616$	0	0
$617$	−24.8833	−1.00176	−0.500881	−	0.865516i	$-0.666991\pi$
$617$	−24.8833	−1.00176	−0.500881	+	0.865516i	$0.666991\pi$
$618$	8.86721	0.356692
$619$	−34.1496	−1.37259	−0.686293	−	0.727325i	$-0.740763\pi$
$619$	−34.1496	−1.37259	−0.686293	+	0.727325i	$0.740763\pi$
$620$	17.5983	0.706765
$621$	1.00000	0.0401286
$622$	29.0571	1.16508
$623$	0	0
$624$	−1.54925	−0.0620195
$625$	−13.9706	−0.558823
$626$	−1.74174	−0.0696141
$627$	16.4450	0.656749
$628$	−3.64396	−0.145410
$629$	−7.40285	−0.295171
$630$	0	0
$631$	−24.5783	−0.978446	−0.489223	−	0.872159i	$-0.662720\pi$
$631$	−24.5783	−0.978446	−0.489223	+	0.872159i	$0.662720\pi$
$632$	−10.4062	−0.413936
$633$	−12.9075	−0.513028
$634$	−12.7796	−0.507543
$635$	−44.3961	−1.76181
$636$	−3.31796	−0.131566
$637$	0	0
$638$	−22.2861	−0.882316
$639$	−9.25067	−0.365951
$640$	3.41421	0.134959
$641$	−27.5998	−1.09013	−0.545064	−	0.838394i	$-0.683495\pi$
$641$	−27.5998	−1.09013	−0.545064	+	0.838394i	$0.683495\pi$
$642$	13.1818	0.520246
$643$	4.81128	0.189738	0.0948691	−	0.995490i	$-0.469757\pi$
$643$	4.81128	0.189738	0.0948691	+	0.995490i	$0.469757\pi$
$644$	0	0
$645$	40.3536	1.58892
$646$	−19.4659	−0.765875
$647$	32.4514	1.27580	0.637899	−	0.770120i	$-0.279804\pi$
$647$	32.4514	1.27580	0.637899	+	0.770120i	$0.279804\pi$
$648$	1.00000	0.0392837
$649$	−17.6890	−0.694353
$650$	−10.3131	−0.404513
$651$	0	0
$652$	−13.5047	−0.528884
$653$	11.5192	0.450781	0.225391	−	0.974268i	$-0.427634\pi$
$653$	11.5192	0.450781	0.225391	+	0.974268i	$0.427634\pi$
$654$	3.76446	0.147202
$655$	−52.8535	−2.06516
$656$	−6.01136	−0.234704
$657$	−8.09046	−0.315639
$658$	0	0
$659$	33.2288	1.29441	0.647205	−	0.762316i	$-0.275938\pi$
$659$	33.2288	1.29441	0.647205	+	0.762316i	$0.275938\pi$
$660$	7.84782	0.305476
$661$	−11.6358	−0.452579	−0.226290	−	0.974060i	$-0.572660\pi$
$661$	−11.6358	−0.452579	−0.226290	+	0.974060i	$0.572660\pi$
$662$	6.34315	0.246533
$663$	4.21522	0.163705
$664$	1.71279	0.0664690
$665$	0	0
$666$	2.72082	0.105430
$667$	−9.69564	−0.375417
$668$	19.6009	0.758382
$669$	14.4293	0.557871
$670$	30.5095	1.17869
$671$	−0.0261102	−0.00100797
$672$	0	0
$673$	−20.2745	−0.781526	−0.390763	−	0.920491i	$-0.627789\pi$
$673$	−20.2745	−0.781526	−0.390763	+	0.920491i	$0.627789\pi$
$674$	15.8866	0.611929
$675$	6.65685	0.256222
$676$	−10.5998	−0.407686
$677$	−2.87408	−0.110460	−0.0552300	−	0.998474i	$-0.517589\pi$
$677$	−2.87408	−0.110460	−0.0552300	+	0.998474i	$0.517589\pi$
$678$	−6.15218	−0.236273
$679$	0	0
$680$	−9.28946	−0.356234
$681$	−14.4133	−0.552318
$682$	11.8478	0.453676
$683$	32.5710	1.24630	0.623148	−	0.782104i	$-0.285853\pi$
$683$	32.5710	1.24630	0.623148	+	0.782104i	$0.285853\pi$
$684$	7.15442	0.273556
$685$	−52.7210	−2.01437
$686$	0	0
$687$	−1.26357	−0.0482081
$688$	11.8193	0.450607
$689$	5.14034	0.195831
$690$	3.41421	0.129977
$691$	11.8966	0.452570	0.226285	−	0.974061i	$-0.427342\pi$
$691$	11.8966	0.452570	0.226285	+	0.974061i	$0.427342\pi$
$692$	14.6317	0.556213
$693$	0	0
$694$	−28.7699	−1.09209
$695$	17.6569	0.669763
$696$	−9.69564	−0.367512
$697$	16.3558	0.619521
$698$	14.6638	0.555033
$699$	−16.7166	−0.632278
$700$	0	0
$701$	49.0439	1.85236	0.926181	−	0.377080i	$-0.123072\pi$
$701$	49.0439	1.85236	0.926181	+	0.377080i	$0.123072\pi$
$702$	−1.54925	−0.0584725
$703$	19.4659	0.734170
$704$	2.29857	0.0866307
$705$	−1.90267	−0.0716586
$706$	−12.6079	−0.474503
$707$	0	0
$708$	−7.69564	−0.289220
$709$	40.4789	1.52022	0.760108	−	0.649797i	$-0.225146\pi$
$709$	40.4789	1.52022	0.760108	+	0.649797i	$0.225146\pi$
$710$	−31.5838	−1.18532
$711$	−10.4062	−0.390262
$712$	16.0506	0.601521
$713$	5.15442	0.193035
$714$	0	0
$715$	−12.1582	−0.454691
$716$	−6.28613	−0.234924
$717$	−22.6923	−0.847460
$718$	−13.5047	−0.503990
$719$	−8.70946	−0.324808	−0.162404	−	0.986724i	$-0.551925\pi$
$719$	−8.70946	−0.324808	−0.162404	+	0.986724i	$0.551925\pi$
$720$	3.41421	0.127240
$721$	0	0
$722$	32.1858	1.19783
$723$	20.6705	0.768743
$724$	14.8398	0.551516
$725$	−64.5424	−2.39705
$726$	−5.71656	−0.212162
$727$	3.88814	0.144203	0.0721015	−	0.997397i	$-0.477029\pi$
$727$	3.88814	0.144203	0.0721015	+	0.997397i	$0.477029\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−27.6226	−1.02236
$731$	−32.1582	−1.18941
$732$	−0.0113593	−0.000419852 0
$733$	−14.0158	−0.517687	−0.258844	−	0.965919i	$-0.583341\pi$
$733$	−14.0158	−0.517687	−0.258844	+	0.965919i	$0.583341\pi$
$734$	3.04364	0.112343
$735$	0	0
$736$	1.00000	0.0368605
$737$	20.5401	0.756605
$738$	−6.01136	−0.221281
$739$	−38.5528	−1.41819	−0.709094	−	0.705114i	$-0.750896\pi$
$739$	−38.5528	−1.41819	−0.709094	+	0.705114i	$0.750896\pi$
$740$	9.28946	0.341487
$741$	−11.0840	−0.407179
$742$	0	0
$743$	−1.86605	−0.0684588	−0.0342294	−	0.999414i	$-0.510898\pi$
$743$	−1.86605	−0.0684588	−0.0342294	+	0.999414i	$0.510898\pi$
$744$	5.15442	0.188970
$745$	22.8915	0.838678
$746$	−37.2752	−1.36474
$747$	1.71279	0.0626676
$748$	−6.25400	−0.228669
$749$	0	0
$750$	5.65685	0.206559
$751$	9.90420	0.361409	0.180705	−	0.983537i	$-0.442162\pi$
$751$	9.90420	0.361409	0.180705	+	0.983537i	$0.442162\pi$
$752$	−0.557278	−0.0203218
$753$	27.6397	1.00725
$754$	15.0209	0.547030
$755$	27.7710	1.01069
$756$	0	0
$757$	32.6059	1.18508	0.592541	−	0.805541i	$-0.298125\pi$
$757$	32.6059	1.18508	0.592541	+	0.805541i	$0.298125\pi$
$758$	22.6720	0.823484
$759$	2.29857	0.0834329
$760$	24.4267	0.886051
$761$	23.8204	0.863489	0.431744	−	0.901996i	$-0.357898\pi$
$761$	23.8204	0.863489	0.431744	+	0.901996i	$0.357898\pi$
$762$	−13.0033	−0.471061
$763$	0	0
$764$	−18.3492	−0.663849
$765$	−9.28946	−0.335861
$766$	−11.7278	−0.423741
$767$	11.9224	0.430494
$768$	1.00000	0.0360844
$769$	20.8608	0.752259	0.376130	−	0.926567i	$-0.377255\pi$
$769$	20.8608	0.752259	0.376130	+	0.926567i	$0.377255\pi$
$770$	0	0
$771$	−11.9383	−0.429947
$772$	−0.979075	−0.0352377
$773$	50.2919	1.80887	0.904437	−	0.426606i	$-0.140291\pi$
$773$	50.2919	1.80887	0.904437	+	0.426606i	$0.140291\pi$
$774$	11.8193	0.424836
$775$	34.3122	1.23253
$776$	−5.76446	−0.206932
$777$	0	0
$778$	7.49223	0.268609
$779$	−43.0078	−1.54091
$780$	−5.28946	−0.189393
$781$	−21.2633	−0.760862
$782$	−2.72082	−0.0972963
$783$	−9.69564	−0.346494
$784$	0	0
$785$	−12.4413	−0.444048
$786$	−15.4804	−0.552168
$787$	−2.23020	−0.0794979	−0.0397490	−	0.999210i	$-0.512656\pi$
$787$	−2.23020	−0.0794979	−0.0397490	+	0.999210i	$0.512656\pi$
$788$	4.65353	0.165775
$789$	−8.68629	−0.309240
$790$	−35.5289	−1.26406
$791$	0	0
$792$	2.29857	0.0816762
$793$	0.0175984	0.000624936 0
$794$	−22.3616	−0.793584
$795$	−11.3282	−0.401771
$796$	1.46436	0.0519027
$797$	−10.3151	−0.365379	−0.182690	−	0.983171i	$-0.558480\pi$
$797$	−10.3151	−0.365379	−0.182690	+	0.983171i	$0.558480\pi$
$798$	0	0
$799$	1.51625	0.0536412
$800$	6.65685	0.235355
$801$	16.0506	0.567120
$802$	−4.09580	−0.144628
$803$	−18.5965	−0.656257
$804$	8.93604	0.315150
$805$	0	0
$806$	−7.98547	−0.281276
$807$	−20.6134	−0.725627
$808$	13.8193	0.486162
$809$	−23.7763	−0.835929	−0.417965	−	0.908463i	$-0.637256\pi$
$809$	−23.7763	−0.835929	−0.417965	+	0.908463i	$0.637256\pi$
$810$	3.41421	0.119963
$811$	−7.77627	−0.273062	−0.136531	−	0.990636i	$-0.543595\pi$
$811$	−7.77627	−0.273062	−0.136531	+	0.990636i	$0.543595\pi$
$812$	0	0
$813$	−3.53789	−0.124079
$814$	6.25400	0.219203
$815$	−46.1078	−1.61509
$816$	−2.72082	−0.0952477
$817$	84.5604	2.95839
$818$	19.5336	0.682977
$819$	0	0
$820$	−20.5241	−0.716731
$821$	−31.9557	−1.11526	−0.557630	−	0.830090i	$-0.688289\pi$
$821$	−31.9557	−1.11526	−0.557630	+	0.830090i	$0.688289\pi$
$822$	−15.4416	−0.538589
$823$	−35.1918	−1.22671	−0.613354	−	0.789808i	$-0.710180\pi$
$823$	−35.1918	−1.22671	−0.613354	+	0.789808i	$0.710180\pi$
$824$	8.86721	0.308904
$825$	15.3013	0.532722
$826$	0	0
$827$	−31.8868	−1.10881	−0.554407	−	0.832246i	$-0.687055\pi$
$827$	−31.8868	−1.10881	−0.554407	+	0.832246i	$0.687055\pi$
$828$	1.00000	0.0347524
$829$	−3.80631	−0.132199	−0.0660994	−	0.997813i	$-0.521055\pi$
$829$	−3.80631	−0.132199	−0.0660994	+	0.997813i	$0.521055\pi$
$830$	5.84782	0.202981
$831$	24.4898	0.849541
$832$	−1.54925	−0.0537104
$833$	0	0
$834$	5.17157	0.179077
$835$	66.9217	2.31592
$836$	16.4450	0.568761
$837$	5.15442	0.178163
$838$	−5.44055	−0.187941
$839$	9.29547	0.320915	0.160458	−	0.987043i	$-0.448703\pi$
$839$	9.29547	0.320915	0.160458	+	0.987043i	$0.448703\pi$
$840$	0	0
$841$	65.0054	2.24156
$842$	37.5149	1.29285
$843$	−10.1582	−0.349867
$844$	−12.9075	−0.444295
$845$	−36.1901	−1.24498
$846$	−0.557278	−0.0191596
$847$	0	0
$848$	−3.31796	−0.113939
$849$	−16.6042	−0.569856
$850$	−18.1121	−0.621240
$851$	2.72082	0.0932685
$852$	−9.25067	−0.316923
$853$	−23.4213	−0.801931	−0.400965	−	0.916093i	$-0.631325\pi$
$853$	−23.4213	−0.801931	−0.400965	+	0.916093i	$0.631325\pi$
$854$	0	0
$855$	24.4267	0.835377
$856$	13.1818	0.450546
$857$	14.6467	0.500320	0.250160	−	0.968204i	$-0.419517\pi$
$857$	14.6467	0.500320	0.250160	+	0.968204i	$0.419517\pi$
$858$	−3.56105	−0.121572
$859$	16.0142	0.546398	0.273199	−	0.961958i	$-0.411918\pi$
$859$	16.0142	0.546398	0.273199	+	0.961958i	$0.411918\pi$
$860$	40.3536	1.37605
$861$	0	0
$862$	18.0303	0.614113
$863$	−19.9994	−0.680786	−0.340393	−	0.940283i	$-0.610560\pi$
$863$	−19.9994	−0.680786	−0.340393	+	0.940283i	$0.610560\pi$
$864$	1.00000	0.0340207
$865$	49.9557	1.69854
$866$	−25.4031	−0.863232
$867$	−9.59715	−0.325936
$868$	0	0
$869$	−23.9194	−0.811409
$870$	−33.1030	−1.12230
$871$	−13.8441	−0.469090
$872$	3.76446	0.127481
$873$	−5.76446	−0.195098
$874$	7.15442	0.242002
$875$	0	0
$876$	−8.09046	−0.273351
$877$	20.5613	0.694306	0.347153	−	0.937808i	$-0.387148\pi$
$877$	20.5613	0.694306	0.347153	+	0.937808i	$0.387148\pi$
$878$	−4.19205	−0.141475
$879$	24.9737	0.842343
$880$	7.84782	0.264550
$881$	−57.6246	−1.94142	−0.970712	−	0.240247i	$-0.922772\pi$
$881$	−57.6246	−1.94142	−0.970712	+	0.240247i	$0.922772\pi$
$882$	0	0
$883$	17.3701	0.584550	0.292275	−	0.956334i	$-0.405588\pi$
$883$	17.3701	0.584550	0.292275	+	0.956334i	$0.405588\pi$
$884$	4.21522	0.141773
$885$	−26.2745	−0.883209
$886$	−24.0836	−0.809104
$887$	−35.3772	−1.18785	−0.593925	−	0.804520i	$-0.702422\pi$
$887$	−35.3772	−1.18785	−0.593925	+	0.804520i	$0.702422\pi$
$888$	2.72082	0.0913047
$889$	0	0
$890$	54.8001	1.83691
$891$	2.29857	0.0770051
$892$	14.4293	0.483130
$893$	−3.98700	−0.133420
$894$	6.70475	0.224241
$895$	−21.4622	−0.717402
$896$	0	0
$897$	−1.54925	−0.0517278
$898$	5.89262	0.196639
$899$	−49.9754	−1.66677
$900$	6.65685	0.221895
$901$	9.02758	0.300752
$902$	−13.8175	−0.460074
$903$	0	0
$904$	−6.15218	−0.204619
$905$	50.6662	1.68420
$906$	8.13395	0.270232
$907$	55.0175	1.82682	0.913412	−	0.407036i	$-0.133438\pi$
$907$	55.0175	1.82682	0.913412	+	0.407036i	$0.133438\pi$
$908$	−14.4133	−0.478322
$909$	13.8193	0.458358
$910$	0	0
$911$	−7.43376	−0.246291	−0.123146	−	0.992389i	$-0.539298\pi$
$911$	−7.43376	−0.246291	−0.123146	+	0.992389i	$0.539298\pi$
$912$	7.15442	0.236907
$913$	3.93696	0.130295
$914$	−9.40285	−0.311019
$915$	−0.0387831	−0.00128213
$916$	−1.26357	−0.0417494
$917$	0	0
$918$	−2.72082	−0.0898004
$919$	−18.5159	−0.610782	−0.305391	−	0.952227i	$-0.598787\pi$
$919$	−18.5159	−0.610782	−0.305391	+	0.952227i	$0.598787\pi$
$920$	3.41421	0.112563
$921$	−32.1239	−1.05852
$922$	13.5720	0.446969
$923$	14.3316	0.471729
$924$	0	0
$925$	18.1121	0.595522
$926$	32.7759	1.07708
$927$	8.86721	0.291237
$928$	−9.69564	−0.318275
$929$	−9.62943	−0.315931	−0.157966	−	0.987445i	$-0.550494\pi$
$929$	−9.62943	−0.315931	−0.157966	+	0.987445i	$0.550494\pi$
$930$	17.5983	0.577071
$931$	0	0
$932$	−16.7166	−0.547569
$933$	29.0571	0.951286
$934$	1.53789	0.0503212
$935$	−21.3525	−0.698301
$936$	−1.54925	−0.0506387
$937$	−23.5568	−0.769567	−0.384784	−	0.923007i	$-0.625724\pi$
$937$	−23.5568	−0.769567	−0.384784	+	0.923007i	$0.625724\pi$
$938$	0	0
$939$	−1.74174	−0.0568397
$940$	−1.90267	−0.0620581
$941$	29.3496	0.956771	0.478386	−	0.878150i	$-0.341222\pi$
$941$	29.3496	0.956771	0.478386	+	0.878150i	$0.341222\pi$
$942$	−3.64396	−0.118727
$943$	−6.01136	−0.195757
$944$	−7.69564	−0.250472
$945$	0	0
$946$	27.1675	0.883293
$947$	23.1615	0.752649	0.376324	−	0.926488i	$-0.377188\pi$
$947$	23.1615	0.752649	0.376324	+	0.926488i	$0.377188\pi$
$948$	−10.4062	−0.337977
$949$	12.5341	0.406874
$950$	47.6260	1.54519
$951$	−12.7796	−0.414407
$952$	0	0
$953$	15.2573	0.494233	0.247117	−	0.968986i	$-0.420517\pi$
$953$	15.2573	0.494233	0.247117	+	0.968986i	$0.420517\pi$
$954$	−3.31796	−0.107423
$955$	−62.6480	−2.02724
$956$	−22.6923	−0.733922
$957$	−22.2861	−0.720408
$958$	−25.6547	−0.828865
$959$	0	0
$960$	3.41421	0.110193
$961$	−4.43192	−0.142965
$962$	−4.21522	−0.135904
$963$	13.1818	0.424779
$964$	20.6705	0.665751
$965$	−3.34277	−0.107608
$966$	0	0
$967$	−21.9247	−0.705052	−0.352526	−	0.935802i	$-0.614677\pi$
$967$	−21.9247	−0.705052	−0.352526	+	0.935802i	$0.614677\pi$
$968$	−5.71656	−0.183737
$969$	−19.4659	−0.625334
$970$	−19.6811	−0.631922
$971$	17.3574	0.557026	0.278513	−	0.960432i	$-0.410158\pi$
$971$	17.3574	0.557026	0.278513	+	0.960432i	$0.410158\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−17.8151	−0.570831
$975$	−10.3131	−0.330284
$976$	−0.0113593	−0.000363602 0
$977$	32.8263	1.05021	0.525103	−	0.851039i	$-0.324027\pi$
$977$	32.8263	1.05021	0.525103	+	0.851039i	$0.324027\pi$
$978$	−13.5047	−0.431832
$979$	36.8935	1.17912
$980$	0	0
$981$	3.76446	0.120190
$982$	−39.3973	−1.25722
$983$	−34.4371	−1.09837	−0.549186	−	0.835700i	$-0.685062\pi$
$983$	−34.4371	−1.09837	−0.549186	+	0.835700i	$0.685062\pi$
$984$	−6.01136	−0.191635
$985$	15.8881	0.506238
$986$	26.3801	0.840113
$987$	0	0
$988$	−11.0840	−0.352628
$989$	11.8193	0.375832
$990$	7.84782	0.249420
$991$	18.9045	0.600520	0.300260	−	0.953857i	$-0.402927\pi$
$991$	18.9045	0.600520	0.300260	+	0.953857i	$0.402927\pi$
$992$	5.15442	0.163653
$993$	6.34315	0.201294
$994$	0	0
$995$	4.99962	0.158499
$996$	1.71279	0.0542717
$997$	15.4989	0.490855	0.245427	−	0.969415i	$-0.421072\pi$
$997$	15.4989	0.490855	0.245427	+	0.969415i	$0.421072\pi$
$998$	20.2297	0.640361
$999$	2.72082	0.0860829

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.ci.1.2	✓	4	7.6	odd	2
6762.2.a.ct.1.4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.41421 q^{10} +2.29857 q^{11} +1.00000 q^{12} -1.54925 q^{13} +3.41421 q^{15} +1.00000 q^{16} -2.72082 q^{17} +1.00000 q^{18} +7.15442 q^{19} +3.41421 q^{20} +2.29857 q^{22} +1.00000 q^{23} +1.00000 q^{24} +6.65685 q^{25} -1.54925 q^{26} +1.00000 q^{27} -9.69564 q^{29} +3.41421 q^{30} +5.15442 q^{31} +1.00000 q^{32} +2.29857 q^{33} -2.72082 q^{34} +1.00000 q^{36} +2.72082 q^{37} +7.15442 q^{38} -1.54925 q^{39} +3.41421 q^{40} -6.01136 q^{41} +11.8193 q^{43} +2.29857 q^{44} +3.41421 q^{45} +1.00000 q^{46} -0.557278 q^{47} +1.00000 q^{48} +6.65685 q^{50} -2.72082 q^{51} -1.54925 q^{52} -3.31796 q^{53} +1.00000 q^{54} +7.84782 q^{55} +7.15442 q^{57} -9.69564 q^{58} -7.69564 q^{59} +3.41421 q^{60} -0.0113593 q^{61} +5.15442 q^{62} +1.00000 q^{64} -5.28946 q^{65} +2.29857 q^{66} +8.93604 q^{67} -2.72082 q^{68} +1.00000 q^{69} -9.25067 q^{71} +1.00000 q^{72} -8.09046 q^{73} +2.72082 q^{74} +6.65685 q^{75} +7.15442 q^{76} -1.54925 q^{78} -10.4062 q^{79} +3.41421 q^{80} +1.00000 q^{81} -6.01136 q^{82} +1.71279 q^{83} -9.28946 q^{85} +11.8193 q^{86} -9.69564 q^{87} +2.29857 q^{88} +16.0506 q^{89} +3.41421 q^{90} +1.00000 q^{92} +5.15442 q^{93} -0.557278 q^{94} +24.4267 q^{95} +1.00000 q^{96} -5.76446 q^{97} +2.29857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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

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Database

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