LMFDB - Embedded newform 3525.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 6x^{4} + 20x^{3} - 9x^{2} - 12x + 3 $ x^7 - x^6 - 9x^5 + 6x^4 + 20x^3 - 9x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.36884$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36884 q^{2} -1.00000 q^{3} -0.126278 q^{4} +1.36884 q^{6} -0.111162 q^{7} +2.91053 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.36884 q^{2} -1.00000 q^{3} -0.126278 q^{4} +1.36884 q^{6} -0.111162 q^{7} +2.91053 q^{8} +1.00000 q^{9} -5.40939 q^{11} +0.126278 q^{12} -2.91290 q^{13} +0.152163 q^{14} -3.73150 q^{16} -3.61860 q^{17} -1.36884 q^{18} -7.58593 q^{19} +0.111162 q^{21} +7.40459 q^{22} -2.06538 q^{23} -2.91053 q^{24} +3.98729 q^{26} -1.00000 q^{27} +0.0140374 q^{28} +0.581793 q^{29} +2.96278 q^{31} -0.713246 q^{32} +5.40939 q^{33} +4.95329 q^{34} -0.126278 q^{36} -3.06772 q^{37} +10.3839 q^{38} +2.91290 q^{39} -7.43965 q^{41} -0.152163 q^{42} +11.3099 q^{43} +0.683089 q^{44} +2.82717 q^{46} -1.00000 q^{47} +3.73150 q^{48} -6.98764 q^{49} +3.61860 q^{51} +0.367835 q^{52} +12.3113 q^{53} +1.36884 q^{54} -0.323541 q^{56} +7.58593 q^{57} -0.796381 q^{58} -5.63221 q^{59} -12.8089 q^{61} -4.05557 q^{62} -0.111162 q^{63} +8.43931 q^{64} -7.40459 q^{66} +6.95597 q^{67} +0.456951 q^{68} +2.06538 q^{69} -15.6148 q^{71} +2.91053 q^{72} -0.886754 q^{73} +4.19922 q^{74} +0.957938 q^{76} +0.601319 q^{77} -3.98729 q^{78} +0.266116 q^{79} +1.00000 q^{81} +10.1837 q^{82} +6.49929 q^{83} -0.0140374 q^{84} -15.4814 q^{86} -0.581793 q^{87} -15.7442 q^{88} +7.54867 q^{89} +0.323804 q^{91} +0.260812 q^{92} -2.96278 q^{93} +1.36884 q^{94} +0.713246 q^{96} -19.2853 q^{97} +9.56496 q^{98} -5.40939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9} - 8 q^{11} - 5 q^{12} + 5 q^{13} - 3 q^{14} + 9 q^{16} + 10 q^{17} + q^{18} + 7 q^{19} - 11 q^{21} + 20 q^{22} + 4 q^{23} - 6 q^{24} - 7 q^{27} + 2 q^{28} - 11 q^{29} + 3 q^{31} + 28 q^{32} + 8 q^{33} + 8 q^{34} + 5 q^{36} + 11 q^{37} - 2 q^{38} - 5 q^{39} - 20 q^{41} + 3 q^{42} + 18 q^{43} + q^{44} - 19 q^{46} - 7 q^{47} - 9 q^{48} + 14 q^{49} - 10 q^{51} + 29 q^{52} + 12 q^{53} - q^{54} - 47 q^{56} - 7 q^{57} - 19 q^{58} + 18 q^{59} - 4 q^{61} + 12 q^{62} + 11 q^{63} + 42 q^{64} - 20 q^{66} + 22 q^{67} + 44 q^{68} - 4 q^{69} - 14 q^{71} + 6 q^{72} + 30 q^{73} + 31 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} + 7 q^{81} + 29 q^{82} + 54 q^{83} - 2 q^{84} - 29 q^{86} + 11 q^{87} - 22 q^{88} - 14 q^{89} + 20 q^{91} - 5 q^{92} - 3 q^{93} - q^{94} - 28 q^{96} + 24 q^{97} - 26 q^{98} - 8 q^{99}+O(q^{100}) $ 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9 - 8 * q^11 - 5 * q^12 + 5 * q^13 - 3 * q^14 + 9 * q^16 + 10 * q^17 + q^18 + 7 * q^19 - 11 * q^21 + 20 * q^22 + 4 * q^23 - 6 * q^24 - 7 * q^27 + 2 * q^28 - 11 * q^29 + 3 * q^31 + 28 * q^32 + 8 * q^33 + 8 * q^34 + 5 * q^36 + 11 * q^37 - 2 * q^38 - 5 * q^39 - 20 * q^41 + 3 * q^42 + 18 * q^43 + q^44 - 19 * q^46 - 7 * q^47 - 9 * q^48 + 14 * q^49 - 10 * q^51 + 29 * q^52 + 12 * q^53 - q^54 - 47 * q^56 - 7 * q^57 - 19 * q^58 + 18 * q^59 - 4 * q^61 + 12 * q^62 + 11 * q^63 + 42 * q^64 - 20 * q^66 + 22 * q^67 + 44 * q^68 - 4 * q^69 - 14 * q^71 + 6 * q^72 + 30 * q^73 + 31 * q^74 - 2 * q^76 - 8 * q^77 - q^79 + 7 * q^81 + 29 * q^82 + 54 * q^83 - 2 * q^84 - 29 * q^86 + 11 * q^87 - 22 * q^88 - 14 * q^89 + 20 * q^91 - 5 * q^92 - 3 * q^93 - q^94 - 28 * q^96 + 24 * q^97 - 26 * q^98 - 8 * 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 $

$2$	−1.36884	−0.967916	−0.483958	−	0.875091i	$-0.660801\pi$
$2$	−1.36884	−0.967916	−0.483958	+	0.875091i	$0.660801\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.126278	−0.0631391
$5$	0	0
$5$	0	0
$6$	1.36884	0.558826
$7$	−0.111162	−0.0420153	−0.0210077	−	0.999779i	$-0.506687\pi$
$7$	−0.111162	−0.0420153	−0.0210077	+	0.999779i	$0.506687\pi$
$8$	2.91053	1.02903
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.40939	−1.63099	−0.815497	−	0.578762i	$-0.803536\pi$
$11$	−5.40939	−1.63099	−0.815497	+	0.578762i	$0.803536\pi$
$12$	0.126278	0.0364534
$13$	−2.91290	−0.807892	−0.403946	−	0.914783i	$-0.632362\pi$
$13$	−2.91290	−0.807892	−0.403946	+	0.914783i	$0.632362\pi$
$14$	0.152163	0.0406673
$15$	0	0
$16$	−3.73150	−0.932874
$17$	−3.61860	−0.877641	−0.438820	−	0.898575i	$-0.644604\pi$
$17$	−3.61860	−0.877641	−0.438820	+	0.898575i	$0.644604\pi$
$18$	−1.36884	−0.322639
$19$	−7.58593	−1.74033	−0.870166	−	0.492759i	$-0.835989\pi$
$19$	−7.58593	−1.74033	−0.870166	+	0.492759i	$0.835989\pi$
$20$	0	0
$21$	0.111162	0.0242576
$22$	7.40459	1.57866
$23$	−2.06538	−0.430661	−0.215330	−	0.976541i	$-0.569083\pi$
$23$	−2.06538	−0.430661	−0.215330	+	0.976541i	$0.569083\pi$
$24$	−2.91053	−0.594110
$25$	0	0
$26$	3.98729	0.781971
$27$	−1.00000	−0.192450
$28$	0.0140374	0.00265281
$29$	0.581793	0.108036	0.0540181	−	0.998540i	$-0.482797\pi$
$29$	0.581793	0.108036	0.0540181	+	0.998540i	$0.482797\pi$
$30$	0	0
$31$	2.96278	0.532131	0.266066	−	0.963955i	$-0.414276\pi$
$31$	2.96278	0.532131	0.266066	+	0.963955i	$0.414276\pi$
$32$	−0.713246	−0.126085
$33$	5.40939	0.941654
$34$	4.95329	0.849482
$35$	0	0
$36$	−0.126278	−0.0210464
$37$	−3.06772	−0.504330	−0.252165	−	0.967684i	$-0.581143\pi$
$37$	−3.06772	−0.504330	−0.252165	+	0.967684i	$0.581143\pi$
$38$	10.3839	1.68449
$39$	2.91290	0.466437
$40$	0	0
$41$	−7.43965	−1.16188	−0.580939	−	0.813947i	$-0.697314\pi$
$41$	−7.43965	−1.16188	−0.580939	+	0.813947i	$0.697314\pi$
$42$	−0.152163	−0.0234793
$43$	11.3099	1.72474	0.862368	−	0.506282i	$-0.168980\pi$
$43$	11.3099	1.72474	0.862368	+	0.506282i	$0.168980\pi$
$44$	0.683089	0.102979
$45$	0	0
$46$	2.82717	0.416843
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	3.73150	0.538595
$49$	−6.98764	−0.998235
$50$	0	0
$51$	3.61860	0.506706
$52$	0.367835	0.0510096
$53$	12.3113	1.69109	0.845543	−	0.533908i	$-0.179277\pi$
$53$	12.3113	1.69109	0.845543	+	0.533908i	$0.179277\pi$
$54$	1.36884	0.186275
$55$	0	0
$56$	−0.323541	−0.0432350
$57$	7.58593	1.00478
$58$	−0.796381	−0.104570
$59$	−5.63221	−0.733252	−0.366626	−	0.930368i	$-0.619487\pi$
$59$	−5.63221	−0.733252	−0.366626	+	0.930368i	$0.619487\pi$
$60$	0	0
$61$	−12.8089	−1.64001	−0.820006	−	0.572355i	$-0.806030\pi$
$61$	−12.8089	−1.64001	−0.820006	+	0.572355i	$0.806030\pi$
$62$	−4.05557	−0.515058
$63$	−0.111162	−0.0140051
$64$	8.43931	1.05491
$65$	0	0
$66$	−7.40459	−0.911442
$67$	6.95597	0.849807	0.424903	−	0.905239i	$-0.360308\pi$
$67$	6.95597	0.849807	0.424903	+	0.905239i	$0.360308\pi$
$68$	0.456951	0.0554135
$69$	2.06538	0.248642
$70$	0	0
$71$	−15.6148	−1.85313	−0.926567	−	0.376129i	$-0.877255\pi$
$71$	−15.6148	−1.85313	−0.926567	+	0.376129i	$0.877255\pi$
$72$	2.91053	0.343010
$73$	−0.886754	−0.103787	−0.0518934	−	0.998653i	$-0.516526\pi$
$73$	−0.886754	−0.103787	−0.0518934	+	0.998653i	$0.516526\pi$
$74$	4.19922	0.488149
$75$	0	0
$76$	0.957938	0.109883
$77$	0.601319	0.0685267
$78$	−3.98729	−0.451471
$79$	0.266116	0.0299404	0.0149702	−	0.999888i	$-0.495235\pi$
$79$	0.266116	0.0299404	0.0149702	+	0.999888i	$0.495235\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.1837	1.12460
$83$	6.49929	0.713390	0.356695	−	0.934221i	$-0.383904\pi$
$83$	6.49929	0.713390	0.356695	+	0.934221i	$0.383904\pi$
$84$	−0.0140374	−0.00153160
$85$	0	0
$86$	−15.4814	−1.66940
$87$	−0.581793	−0.0623747
$88$	−15.7442	−1.67834
$89$	7.54867	0.800158	0.400079	−	0.916481i	$-0.368983\pi$
$89$	7.54867	0.800158	0.400079	+	0.916481i	$0.368983\pi$
$90$	0	0
$91$	0.323804	0.0339438
$92$	0.260812	0.0271916
$93$	−2.96278	−0.307226
$94$	1.36884	0.141185
$95$	0	0
$96$	0.713246	0.0727954
$97$	−19.2853	−1.95812	−0.979061	−	0.203569i	$-0.934746\pi$
$97$	−19.2853	−1.95812	−0.979061	+	0.203569i	$0.934746\pi$
$98$	9.56496	0.966207
$99$	−5.40939	−0.543664
$100$	0	0
$101$	−14.5594	−1.44872	−0.724359	−	0.689423i	$-0.757864\pi$
$101$	−14.5594	−1.44872	−0.724359	+	0.689423i	$0.757864\pi$
$102$	−4.95329	−0.490449
$103$	10.9510	1.07903	0.539517	−	0.841974i	$-0.318607\pi$
$103$	10.9510	1.07903	0.539517	+	0.841974i	$0.318607\pi$
$104$	−8.47808	−0.831344
$105$	0	0
$106$	−16.8522	−1.63683
$107$	−13.9499	−1.34859	−0.674293	−	0.738464i	$-0.735551\pi$
$107$	−13.9499	−1.34859	−0.674293	+	0.738464i	$0.735551\pi$
$108$	0.126278	0.0121511
$109$	7.43610	0.712249	0.356125	−	0.934438i	$-0.384098\pi$
$109$	7.43610	0.712249	0.356125	+	0.934438i	$0.384098\pi$
$110$	0	0
$111$	3.06772	0.291175
$112$	0.414801	0.0391950
$113$	−13.4230	−1.26273	−0.631363	−	0.775487i	$-0.717504\pi$
$113$	−13.4230	−1.26273	−0.631363	+	0.775487i	$0.717504\pi$
$114$	−10.3839	−0.972544
$115$	0	0
$116$	−0.0734678	−0.00682131
$117$	−2.91290	−0.269297
$118$	7.70960	0.709726
$119$	0.402252	0.0368744
$120$	0	0
$121$	18.2615	1.66014
$122$	17.5333	1.58739
$123$	7.43965	0.670810
$124$	−0.374135	−0.0335983
$125$	0	0
$126$	0.152163	0.0135558
$127$	−6.80800	−0.604113	−0.302056	−	0.953290i	$-0.597673\pi$
$127$	−6.80800	−0.604113	−0.302056	+	0.953290i	$0.597673\pi$
$128$	−10.1256	−0.894983
$129$	−11.3099	−0.995777
$130$	0	0
$131$	11.9807	1.04675	0.523377	−	0.852101i	$-0.324672\pi$
$131$	11.9807	1.04675	0.523377	+	0.852101i	$0.324672\pi$
$132$	−0.683089	−0.0594552
$133$	0.843268	0.0731206
$134$	−9.52161	−0.822542
$135$	0	0
$136$	−10.5321	−0.903118
$137$	5.56697	0.475618	0.237809	−	0.971312i	$-0.423571\pi$
$137$	5.56697	0.475618	0.237809	+	0.971312i	$0.423571\pi$
$138$	−2.82717	−0.240665
$139$	17.2048	1.45930	0.729648	−	0.683823i	$-0.239684\pi$
$139$	17.2048	1.45930	0.729648	+	0.683823i	$0.239684\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	21.3741	1.79368
$143$	15.7570	1.31767
$144$	−3.73150	−0.310958
$145$	0	0
$146$	1.21382	0.100457
$147$	6.98764	0.576331
$148$	0.387386	0.0318430
$149$	−15.1994	−1.24518	−0.622590	−	0.782548i	$-0.713920\pi$
$149$	−15.1994	−1.24518	−0.622590	+	0.782548i	$0.713920\pi$
$150$	0	0
$151$	15.4616	1.25825	0.629125	−	0.777304i	$-0.283413\pi$
$151$	15.4616	1.25825	0.629125	+	0.777304i	$0.283413\pi$
$152$	−22.0791	−1.79085
$153$	−3.61860	−0.292547
$154$	−0.823110	−0.0663281
$155$	0	0
$156$	−0.367835	−0.0294504
$157$	−7.22877	−0.576919	−0.288459	−	0.957492i	$-0.593143\pi$
$157$	−7.22877	−0.576919	−0.288459	+	0.957492i	$0.593143\pi$
$158$	−0.364270	−0.0289798
$159$	−12.3113	−0.976348
$160$	0	0
$161$	0.229592	0.0180944
$162$	−1.36884	−0.107546
$163$	6.14311	0.481165	0.240583	−	0.970629i	$-0.422662\pi$
$163$	6.14311	0.481165	0.240583	+	0.970629i	$0.422662\pi$
$164$	0.939466	0.0733599
$165$	0	0
$166$	−8.89648	−0.690501
$167$	5.98485	0.463121	0.231561	−	0.972820i	$-0.425617\pi$
$167$	5.98485	0.463121	0.231561	+	0.972820i	$0.425617\pi$
$168$	0.323541	0.0249617
$169$	−4.51504	−0.347311
$170$	0	0
$171$	−7.58593	−0.580111
$172$	−1.42819	−0.108898
$173$	10.8639	0.825970	0.412985	−	0.910738i	$-0.364486\pi$
$173$	10.8639	0.825970	0.412985	+	0.910738i	$0.364486\pi$
$174$	0.796381	0.0603735
$175$	0	0
$176$	20.1851	1.52151
$177$	5.63221	0.423343
$178$	−10.3329	−0.774485
$179$	−7.45268	−0.557040	−0.278520	−	0.960430i	$-0.589844\pi$
$179$	−7.45268	−0.557040	−0.278520	+	0.960430i	$0.589844\pi$
$180$	0	0
$181$	24.5435	1.82430	0.912150	−	0.409856i	$-0.134421\pi$
$181$	24.5435	1.82430	0.912150	+	0.409856i	$0.134421\pi$
$182$	−0.443235	−0.0328548
$183$	12.8089	0.946861
$184$	−6.01135	−0.443163
$185$	0	0
$186$	4.05557	0.297369
$187$	19.5745	1.43143
$188$	0.126278	0.00920979
$189$	0.111162	0.00808585
$190$	0	0
$191$	−19.6509	−1.42189	−0.710944	−	0.703248i	$-0.751732\pi$
$191$	−19.6509	−1.42189	−0.710944	+	0.703248i	$0.751732\pi$
$192$	−8.43931	−0.609055
$193$	3.78234	0.272259	0.136129	−	0.990691i	$-0.456534\pi$
$193$	3.78234	0.272259	0.136129	+	0.990691i	$0.456534\pi$
$194$	26.3984	1.89530
$195$	0	0
$196$	0.882387	0.0630277
$197$	−0.864109	−0.0615652	−0.0307826	−	0.999526i	$-0.509800\pi$
$197$	−0.864109	−0.0615652	−0.0307826	+	0.999526i	$0.509800\pi$
$198$	7.40459	0.526221
$199$	24.4936	1.73631	0.868154	−	0.496294i	$-0.165306\pi$
$199$	24.4936	1.73631	0.868154	+	0.496294i	$0.165306\pi$
$200$	0	0
$201$	−6.95597	−0.490636
$202$	19.9295	1.40224
$203$	−0.0646733	−0.00453918
$204$	−0.456951	−0.0319930
$205$	0	0
$206$	−14.9902	−1.04441
$207$	−2.06538	−0.143554
$208$	10.8695	0.753661
$209$	41.0353	2.83847
$210$	0	0
$211$	−18.3628	−1.26415	−0.632073	−	0.774909i	$-0.717796\pi$
$211$	−18.3628	−1.26415	−0.632073	+	0.774909i	$0.717796\pi$
$212$	−1.55465	−0.106774
$213$	15.6148	1.06991
$214$	19.0951	1.30532
$215$	0	0
$216$	−2.91053	−0.198037
$217$	−0.329349	−0.0223577
$218$	−10.1788	−0.689397
$219$	0.886754	0.0599213
$220$	0	0
$221$	10.5406	0.709039
$222$	−4.19922	−0.281833
$223$	23.6047	1.58069	0.790345	−	0.612662i	$-0.209901\pi$
$223$	23.6047	1.58069	0.790345	+	0.612662i	$0.209901\pi$
$224$	0.0792860	0.00529752
$225$	0	0
$226$	18.3739	1.22221
$227$	1.49141	0.0989883	0.0494941	−	0.998774i	$-0.484239\pi$
$227$	1.49141	0.0989883	0.0494941	+	0.998774i	$0.484239\pi$
$228$	−0.957938	−0.0634410
$229$	−6.90415	−0.456239	−0.228120	−	0.973633i	$-0.573258\pi$
$229$	−6.90415	−0.456239	−0.228120	+	0.973633i	$0.573258\pi$
$230$	0	0
$231$	−0.601319	−0.0395639
$232$	1.69333	0.111172
$233$	−23.6480	−1.54923	−0.774616	−	0.632432i	$-0.782057\pi$
$233$	−23.6480	−1.54923	−0.774616	+	0.632432i	$0.782057\pi$
$234$	3.98729	0.260657
$235$	0	0
$236$	0.711226	0.0462969
$237$	−0.266116	−0.0172861
$238$	−0.550618	−0.0356913
$239$	1.80705	0.116888	0.0584442	−	0.998291i	$-0.481386\pi$
$239$	1.80705	0.116888	0.0584442	+	0.998291i	$0.481386\pi$
$240$	0	0
$241$	16.1360	1.03941	0.519704	−	0.854346i	$-0.326042\pi$
$241$	16.1360	1.03941	0.519704	+	0.854346i	$0.326042\pi$
$242$	−24.9971	−1.60687
$243$	−1.00000	−0.0641500
$244$	1.61749	0.103549
$245$	0	0
$246$	−10.1837	−0.649288
$247$	22.0970	1.40600
$248$	8.62327	0.547578
$249$	−6.49929	−0.411876
$250$	0	0
$251$	31.5934	1.99416	0.997079	−	0.0763798i	$-0.0243361\pi$
$251$	31.5934	1.99416	0.997079	+	0.0763798i	$0.0243361\pi$
$252$	0.0140374	0.000884270 0
$253$	11.1724	0.702405
$254$	9.31906	0.584730
$255$	0	0
$256$	−3.01834	−0.188646
$257$	−19.2297	−1.19952	−0.599759	−	0.800181i	$-0.704737\pi$
$257$	−19.2297	−1.19952	−0.599759	+	0.800181i	$0.704737\pi$
$258$	15.4814	0.963828
$259$	0.341014	0.0211896
$260$	0	0
$261$	0.581793	0.0360121
$262$	−16.3996	−1.01317
$263$	−4.53929	−0.279904	−0.139952	−	0.990158i	$-0.544695\pi$
$263$	−4.53929	−0.279904	−0.139952	+	0.990158i	$0.544695\pi$
$264$	15.7442	0.968990
$265$	0	0
$266$	−1.15430	−0.0707746
$267$	−7.54867	−0.461971
$268$	−0.878388	−0.0536561
$269$	10.5589	0.643787	0.321893	−	0.946776i	$-0.395681\pi$
$269$	10.5589	0.643787	0.321893	+	0.946776i	$0.395681\pi$
$270$	0	0
$271$	−0.756622	−0.0459615	−0.0229808	−	0.999736i	$-0.507316\pi$
$271$	−0.756622	−0.0459615	−0.0229808	+	0.999736i	$0.507316\pi$
$272$	13.5028	0.818728
$273$	−0.323804	−0.0195975
$274$	−7.62029	−0.460358
$275$	0	0
$276$	−0.260812	−0.0156990
$277$	9.77008	0.587027	0.293514	−	0.955955i	$-0.405175\pi$
$277$	9.77008	0.587027	0.293514	+	0.955955i	$0.405175\pi$
$278$	−23.5507	−1.41248
$279$	2.96278	0.177377
$280$	0	0
$281$	6.36902	0.379944	0.189972	−	0.981790i	$-0.439160\pi$
$281$	6.36902	0.379944	0.189972	+	0.981790i	$0.439160\pi$
$282$	−1.36884	−0.0815132
$283$	5.71171	0.339526	0.169763	−	0.985485i	$-0.445700\pi$
$283$	5.71171	0.339526	0.169763	+	0.985485i	$0.445700\pi$
$284$	1.97181	0.117005
$285$	0	0
$286$	−21.5688	−1.27539
$287$	0.827007	0.0488167
$288$	−0.713246	−0.0420284
$289$	−3.90570	−0.229747
$290$	0	0
$291$	19.2853	1.13052
$292$	0.111978	0.00655300
$293$	8.34879	0.487741	0.243871	−	0.969808i	$-0.421583\pi$
$293$	8.34879	0.487741	0.243871	+	0.969808i	$0.421583\pi$
$294$	−9.56496	−0.557840
$295$	0	0
$296$	−8.92870	−0.518970
$297$	5.40939	0.313885
$298$	20.8055	1.20523
$299$	6.01623	0.347927
$300$	0	0
$301$	−1.25723	−0.0724653
$302$	−21.1645	−1.21788
$303$	14.5594	0.836418
$304$	28.3069	1.62351
$305$	0	0
$306$	4.95329	0.283161
$307$	31.7089	1.80972	0.904861	−	0.425708i	$-0.139975\pi$
$307$	31.7089	1.80972	0.904861	+	0.425708i	$0.139975\pi$
$308$	−0.0759336	−0.00432672
$309$	−10.9510	−0.622981
$310$	0	0
$311$	−9.16353	−0.519616	−0.259808	−	0.965660i	$-0.583659\pi$
$311$	−9.16353	−0.519616	−0.259808	+	0.965660i	$0.583659\pi$
$312$	8.47808	0.479977
$313$	−21.7723	−1.23064	−0.615321	−	0.788276i	$-0.710974\pi$
$313$	−21.7723	−1.23064	−0.615321	+	0.788276i	$0.710974\pi$
$314$	9.89502	0.558409
$315$	0	0
$316$	−0.0336047	−0.00189041
$317$	−7.65975	−0.430214	−0.215107	−	0.976590i	$-0.569010\pi$
$317$	−7.65975	−0.430214	−0.215107	+	0.976590i	$0.569010\pi$
$318$	16.8522	0.945023
$319$	−3.14715	−0.176206
$320$	0	0
$321$	13.9499	0.778606
$322$	−0.314274	−0.0175138
$323$	27.4505	1.52739
$324$	−0.126278	−0.00701546
$325$	0	0
$326$	−8.40893	−0.465727
$327$	−7.43610	−0.411217
$328$	−21.6533	−1.19561
$329$	0.111162	0.00612856
$330$	0	0
$331$	−23.1684	−1.27345	−0.636726	−	0.771090i	$-0.719712\pi$
$331$	−23.1684	−1.27345	−0.636726	+	0.771090i	$0.719712\pi$
$332$	−0.820719	−0.0450428
$333$	−3.06772	−0.168110
$334$	−8.19230	−0.448262
$335$	0	0
$336$	−0.414801	−0.0226293
$337$	−2.56081	−0.139496	−0.0697481	−	0.997565i	$-0.522220\pi$
$337$	−2.56081	−0.139496	−0.0697481	+	0.997565i	$0.522220\pi$
$338$	6.18037	0.336168
$339$	13.4230	0.729035
$340$	0	0
$341$	−16.0268	−0.867902
$342$	10.3839	0.561498
$343$	1.55490	0.0839565
$344$	32.9177	1.77480
$345$	0	0
$346$	−14.8710	−0.799470
$347$	20.9239	1.12325	0.561626	−	0.827391i	$-0.310176\pi$
$347$	20.9239	1.12325	0.561626	+	0.827391i	$0.310176\pi$
$348$	0.0734678	0.00393829
$349$	18.7939	1.00601	0.503007	−	0.864282i	$-0.332227\pi$
$349$	18.7939	1.00601	0.503007	+	0.864282i	$0.332227\pi$
$350$	0	0
$351$	2.91290	0.155479
$352$	3.85823	0.205644
$353$	9.58087	0.509939	0.254969	−	0.966949i	$-0.417935\pi$
$353$	9.58087	0.509939	0.254969	+	0.966949i	$0.417935\pi$
$354$	−7.70960	−0.409760
$355$	0	0
$356$	−0.953233	−0.0505213
$357$	−0.402252	−0.0212894
$358$	10.2015	0.539168
$359$	−28.4889	−1.50359	−0.751794	−	0.659398i	$-0.770811\pi$
$359$	−28.4889	−1.50359	−0.751794	+	0.659398i	$0.770811\pi$
$360$	0	0
$361$	38.5464	2.02876
$362$	−33.5961	−1.76577
$363$	−18.2615	−0.958482
$364$	−0.0408893	−0.00214318
$365$	0	0
$366$	−17.5333	−0.916482
$367$	−0.969345	−0.0505994	−0.0252997	−	0.999680i	$-0.508054\pi$
$367$	−0.969345	−0.0505994	−0.0252997	+	0.999680i	$0.508054\pi$
$368$	7.70695	0.401752
$369$	−7.43965	−0.387293
$370$	0	0
$371$	−1.36855	−0.0710515
$372$	0.374135	0.0193980
$373$	−26.7073	−1.38285	−0.691427	−	0.722447i	$-0.743017\pi$
$373$	−26.7073	−1.38285	−0.691427	+	0.722447i	$0.743017\pi$
$374$	−26.7943	−1.38550
$375$	0	0
$376$	−2.91053	−0.150099
$377$	−1.69470	−0.0872816
$378$	−0.152163	−0.00782642
$379$	11.3275	0.581854	0.290927	−	0.956745i	$-0.406036\pi$
$379$	11.3275	0.581854	0.290927	+	0.956745i	$0.406036\pi$
$380$	0	0
$381$	6.80800	0.348785
$382$	26.8989	1.37627
$383$	17.9449	0.916944	0.458472	−	0.888709i	$-0.348397\pi$
$383$	17.9449	0.916944	0.458472	+	0.888709i	$0.348397\pi$
$384$	10.1256	0.516719
$385$	0	0
$386$	−5.17742	−0.263524
$387$	11.3099	0.574912
$388$	2.43531	0.123634
$389$	−21.7265	−1.10158	−0.550788	−	0.834645i	$-0.685673\pi$
$389$	−21.7265	−1.10158	−0.550788	+	0.834645i	$0.685673\pi$
$390$	0	0
$391$	7.47378	0.377965
$392$	−20.3378	−1.02721
$393$	−11.9807	−0.604344
$394$	1.18283	0.0595899
$395$	0	0
$396$	0.683089	0.0343265
$397$	27.9559	1.40306	0.701532	−	0.712638i	$-0.252500\pi$
$397$	27.9559	1.40306	0.701532	+	0.712638i	$0.252500\pi$
$398$	−33.5279	−1.68060
$399$	−0.843268	−0.0422162
$400$	0	0
$401$	−15.4213	−0.770103	−0.385051	−	0.922895i	$-0.625816\pi$
$401$	−15.4213	−0.770103	−0.385051	+	0.922895i	$0.625816\pi$
$402$	9.52161	0.474895
$403$	−8.63027	−0.429904
$404$	1.83854	0.0914708
$405$	0	0
$406$	0.0885274	0.00439354
$407$	16.5945	0.822559
$408$	10.5321	0.521415
$409$	0.763429	0.0377491	0.0188746	−	0.999822i	$-0.493992\pi$
$409$	0.763429	0.0377491	0.0188746	+	0.999822i	$0.493992\pi$
$410$	0	0
$411$	−5.56697	−0.274598
$412$	−1.38287	−0.0681293
$413$	0.626089	0.0308078
$414$	2.82717	0.138948
$415$	0	0
$416$	2.07761	0.101863
$417$	−17.2048	−0.842525
$418$	−56.1707	−2.74740
$419$	−15.9825	−0.780796	−0.390398	−	0.920646i	$-0.627663\pi$
$419$	−15.9825	−0.780796	−0.390398	+	0.920646i	$0.627663\pi$
$420$	0	0
$421$	−5.41198	−0.263764	−0.131882	−	0.991265i	$-0.542102\pi$
$421$	−5.41198	−0.263764	−0.131882	+	0.991265i	$0.542102\pi$
$422$	25.1357	1.22359
$423$	−1.00000	−0.0486217
$424$	35.8324	1.74018
$425$	0	0
$426$	−21.3741	−1.03558
$427$	1.42386	0.0689056
$428$	1.76157	0.0851485
$429$	−15.7570	−0.760755
$430$	0	0
$431$	33.0034	1.58972	0.794859	−	0.606794i	$-0.207545\pi$
$431$	33.0034	1.58972	0.794859	+	0.606794i	$0.207545\pi$
$432$	3.73150	0.179532
$433$	−23.8507	−1.14619	−0.573095	−	0.819489i	$-0.694258\pi$
$433$	−23.8507	−1.14619	−0.573095	+	0.819489i	$0.694258\pi$
$434$	0.450826	0.0216403
$435$	0	0
$436$	−0.939018	−0.0449708
$437$	15.6678	0.749493
$438$	−1.21382	−0.0579988
$439$	23.7540	1.13372	0.566858	−	0.823816i	$-0.308159\pi$
$439$	23.7540	1.13372	0.566858	+	0.823816i	$0.308159\pi$
$440$	0	0
$441$	−6.98764	−0.332745
$442$	−14.4284	−0.686290
$443$	−6.83125	−0.324563	−0.162281	−	0.986745i	$-0.551885\pi$
$443$	−6.83125	−0.324563	−0.162281	+	0.986745i	$0.551885\pi$
$444$	−0.387386	−0.0183845
$445$	0	0
$446$	−32.3111	−1.52998
$447$	15.1994	0.718905
$448$	−0.938132	−0.0443226
$449$	−5.10727	−0.241027	−0.120513	−	0.992712i	$-0.538454\pi$
$449$	−5.10727	−0.241027	−0.120513	+	0.992712i	$0.538454\pi$
$450$	0	0
$451$	40.2440	1.89501
$452$	1.69503	0.0797274
$453$	−15.4616	−0.726451
$454$	−2.04150	−0.0958123
$455$	0	0
$456$	22.0791	1.03395
$457$	11.9323	0.558167	0.279084	−	0.960267i	$-0.409969\pi$
$457$	11.9323	0.558167	0.279084	+	0.960267i	$0.409969\pi$
$458$	9.45068	0.441601
$459$	3.61860	0.168902
$460$	0	0
$461$	24.8937	1.15942	0.579708	−	0.814824i	$-0.303167\pi$
$461$	24.8937	1.15942	0.579708	+	0.814824i	$0.303167\pi$
$462$	0.823110	0.0382945
$463$	−8.33125	−0.387186	−0.193593	−	0.981082i	$-0.562014\pi$
$463$	−8.33125	−0.387186	−0.193593	+	0.981082i	$0.562014\pi$
$464$	−2.17096	−0.100784
$465$	0	0
$466$	32.3703	1.49953
$467$	−15.7408	−0.728397	−0.364198	−	0.931321i	$-0.618657\pi$
$467$	−15.7408	−0.728397	−0.364198	+	0.931321i	$0.618657\pi$
$468$	0.367835	0.0170032
$469$	−0.773240	−0.0357049
$470$	0	0
$471$	7.22877	0.333084
$472$	−16.3927	−0.754537
$473$	−61.1794	−2.81303
$474$	0.364270	0.0167315
$475$	0	0
$476$	−0.0507956	−0.00232821
$477$	12.3113	0.563695
$478$	−2.47356	−0.113138
$479$	1.57750	0.0720777	0.0360389	−	0.999350i	$-0.488526\pi$
$479$	1.57750	0.0720777	0.0360389	+	0.999350i	$0.488526\pi$
$480$	0	0
$481$	8.93595	0.407444
$482$	−22.0875	−1.00606
$483$	−0.229592	−0.0104468
$484$	−2.30603	−0.104820
$485$	0	0
$486$	1.36884	0.0620918
$487$	7.58266	0.343603	0.171802	−	0.985132i	$-0.445041\pi$
$487$	7.58266	0.343603	0.171802	+	0.985132i	$0.445041\pi$
$488$	−37.2807	−1.68762
$489$	−6.14311	−0.277801
$490$	0	0
$491$	−40.6843	−1.83606	−0.918028	−	0.396516i	$-0.870219\pi$
$491$	−40.6843	−1.83606	−0.918028	+	0.396516i	$0.870219\pi$
$492$	−0.939466	−0.0423544
$493$	−2.10528	−0.0948170
$494$	−30.2473	−1.36089
$495$	0	0
$496$	−11.0556	−0.496412
$497$	1.73577	0.0778601
$498$	8.89648	0.398661
$499$	36.0986	1.61600	0.807998	−	0.589185i	$-0.200551\pi$
$499$	36.0986	1.61600	0.807998	+	0.589185i	$0.200551\pi$
$500$	0	0
$501$	−5.98485	−0.267383
$502$	−43.2463	−1.93018
$503$	37.0321	1.65118	0.825590	−	0.564270i	$-0.190842\pi$
$503$	37.0321	1.65118	0.825590	+	0.564270i	$0.190842\pi$
$504$	−0.323541	−0.0144117
$505$	0	0
$506$	−15.2933	−0.679869
$507$	4.51504	0.200520
$508$	0.859703	0.0381431
$509$	−0.263082	−0.0116609	−0.00583046	−	0.999983i	$-0.501856\pi$
$509$	−0.263082	−0.0116609	−0.00583046	+	0.999983i	$0.501856\pi$
$510$	0	0
$511$	0.0985735	0.00436063
$512$	24.3828	1.07758
$513$	7.58593	0.334927
$514$	26.3224	1.16103
$515$	0	0
$516$	1.42819	0.0628725
$517$	5.40939	0.237905
$518$	−0.466794	−0.0205097
$519$	−10.8639	−0.476874
$520$	0	0
$521$	−2.52541	−0.110640	−0.0553201	−	0.998469i	$-0.517618\pi$
$521$	−2.52541	−0.110640	−0.0553201	+	0.998469i	$0.517618\pi$
$522$	−0.796381	−0.0348567
$523$	11.4926	0.502538	0.251269	−	0.967917i	$-0.419152\pi$
$523$	11.4926	0.502538	0.251269	+	0.967917i	$0.419152\pi$
$524$	−1.51290	−0.0660912
$525$	0	0
$526$	6.21355	0.270924
$527$	−10.7211	−0.467020
$528$	−20.1851	−0.878445
$529$	−18.7342	−0.814531
$530$	0	0
$531$	−5.63221	−0.244417
$532$	−0.106486	−0.00461677
$533$	21.6709	0.938671
$534$	10.3329	0.447149
$535$	0	0
$536$	20.2456	0.874476
$537$	7.45268	0.321607
$538$	−14.4534	−0.623131
$539$	37.7989	1.62811
$540$	0	0
$541$	40.2433	1.73020	0.865098	−	0.501603i	$-0.167256\pi$
$541$	40.2433	1.73020	0.865098	+	0.501603i	$0.167256\pi$
$542$	1.03569	0.0444869
$543$	−24.5435	−1.05326
$544$	2.58096	0.110658
$545$	0	0
$546$	0.443235	0.0189687
$547$	−22.6651	−0.969088	−0.484544	−	0.874767i	$-0.661014\pi$
$547$	−22.6651	−0.969088	−0.484544	+	0.874767i	$0.661014\pi$
$548$	−0.702987	−0.0300301
$549$	−12.8089	−0.546671
$550$	0	0
$551$	−4.41344	−0.188019
$552$	6.01135	0.255860
$553$	−0.0295820	−0.00125796
$554$	−13.3737	−0.568193
$555$	0	0
$556$	−2.17260	−0.0921386
$557$	37.7011	1.59745	0.798724	−	0.601697i	$-0.205509\pi$
$557$	37.7011	1.59745	0.798724	+	0.601697i	$0.205509\pi$
$558$	−4.05557	−0.171686
$559$	−32.9444	−1.39340
$560$	0	0
$561$	−19.5745	−0.826434
$562$	−8.71817	−0.367754
$563$	−13.3791	−0.563860	−0.281930	−	0.959435i	$-0.590975\pi$
$563$	−13.3791	−0.563860	−0.281930	+	0.959435i	$0.590975\pi$
$564$	−0.126278	−0.00531727
$565$	0	0
$566$	−7.81842	−0.328632
$567$	−0.111162	−0.00466837
$568$	−45.4474	−1.90693
$569$	−33.3933	−1.39992	−0.699959	−	0.714183i	$-0.746798\pi$
$569$	−33.3933	−1.39992	−0.699959	+	0.714183i	$0.746798\pi$
$570$	0	0
$571$	18.3389	0.767460	0.383730	−	0.923445i	$-0.374639\pi$
$571$	18.3389	0.767460	0.383730	+	0.923445i	$0.374639\pi$
$572$	−1.98977	−0.0831963
$573$	19.6509	0.820928
$574$	−1.13204	−0.0472504
$575$	0	0
$576$	8.43931	0.351638
$577$	3.44597	0.143457	0.0717287	−	0.997424i	$-0.477148\pi$
$577$	3.44597	0.143457	0.0717287	+	0.997424i	$0.477148\pi$
$578$	5.34627	0.222376
$579$	−3.78234	−0.157189
$580$	0	0
$581$	−0.722475	−0.0299733
$582$	−26.3984	−1.09425
$583$	−66.5966	−2.75815
$584$	−2.58093	−0.106800
$585$	0	0
$586$	−11.4281	−0.472092
$587$	−21.4061	−0.883523	−0.441762	−	0.897132i	$-0.645646\pi$
$587$	−21.4061	−0.883523	−0.441762	+	0.897132i	$0.645646\pi$
$588$	−0.882387	−0.0363890
$589$	−22.4755	−0.926085
$590$	0	0
$591$	0.864109	0.0355447
$592$	11.4472	0.470477
$593$	11.4281	0.469297	0.234648	−	0.972080i	$-0.424606\pi$
$593$	11.4281	0.469297	0.234648	+	0.972080i	$0.424606\pi$
$594$	−7.40459	−0.303814
$595$	0	0
$596$	1.91935	0.0786196
$597$	−24.4936	−1.00246
$598$	−8.23525	−0.336764
$599$	4.32160	0.176576	0.0882879	−	0.996095i	$-0.471860\pi$
$599$	4.32160	0.176576	0.0882879	+	0.996095i	$0.471860\pi$
$600$	0	0
$601$	37.8952	1.54578	0.772889	−	0.634542i	$-0.218811\pi$
$601$	37.8952	1.54578	0.772889	+	0.634542i	$0.218811\pi$
$602$	1.72094	0.0701403
$603$	6.95597	0.283269
$604$	−1.95247	−0.0794448
$605$	0	0
$606$	−19.9295	−0.809582
$607$	−16.0265	−0.650497	−0.325248	−	0.945629i	$-0.605448\pi$
$607$	−16.0265	−0.650497	−0.325248	+	0.945629i	$0.605448\pi$
$608$	5.41064	0.219430
$609$	0.0646733	0.00262070
$610$	0	0
$611$	2.91290	0.117843
$612$	0.456951	0.0184712
$613$	33.5924	1.35679	0.678393	−	0.734699i	$-0.262677\pi$
$613$	33.5924	1.35679	0.678393	+	0.734699i	$0.262677\pi$
$614$	−43.4044	−1.75166
$615$	0	0
$616$	1.75016	0.0705160
$617$	−41.9047	−1.68702	−0.843510	−	0.537114i	$-0.819515\pi$
$617$	−41.9047	−1.68702	−0.843510	+	0.537114i	$0.819515\pi$
$618$	14.9902	0.602993
$619$	0.940720	0.0378107	0.0189054	−	0.999821i	$-0.493982\pi$
$619$	0.940720	0.0378107	0.0189054	+	0.999821i	$0.493982\pi$
$620$	0	0
$621$	2.06538	0.0828807
$622$	12.5434	0.502945
$623$	−0.839126	−0.0336189
$624$	−10.8695	−0.435127
$625$	0	0
$626$	29.8028	1.19116
$627$	−41.0353	−1.63879
$628$	0.912836	0.0364261
$629$	11.1009	0.442621
$630$	0	0
$631$	−4.90081	−0.195098	−0.0975492	−	0.995231i	$-0.531100\pi$
$631$	−4.90081	−0.195098	−0.0975492	+	0.995231i	$0.531100\pi$
$632$	0.774540	0.0308096
$633$	18.3628	0.729855
$634$	10.4850	0.416411
$635$	0	0
$636$	1.55465	0.0616458
$637$	20.3543	0.806466
$638$	4.30794	0.170553
$639$	−15.6148	−0.617712
$640$	0	0
$641$	−29.1853	−1.15275	−0.576375	−	0.817186i	$-0.695533\pi$
$641$	−29.1853	−1.15275	−0.576375	+	0.817186i	$0.695533\pi$
$642$	−19.0951	−0.753625
$643$	−5.01884	−0.197924	−0.0989619	−	0.995091i	$-0.531552\pi$
$643$	−5.01884	−0.197924	−0.0989619	+	0.995091i	$0.531552\pi$
$644$	−0.0289924	−0.00114246
$645$	0	0
$646$	−37.5753	−1.47838
$647$	−31.1186	−1.22340	−0.611699	−	0.791091i	$-0.709514\pi$
$647$	−31.1186	−1.22340	−0.611699	+	0.791091i	$0.709514\pi$
$648$	2.91053	0.114337
$649$	30.4668	1.19593
$650$	0	0
$651$	0.329349	0.0129082
$652$	−0.775741	−0.0303804
$653$	37.4084	1.46390	0.731952	−	0.681356i	$-0.238610\pi$
$653$	37.4084	1.46390	0.731952	+	0.681356i	$0.238610\pi$
$654$	10.1788	0.398024
$655$	0	0
$656$	27.7610	1.08389
$657$	−0.886754	−0.0345956
$658$	−0.152163	−0.00593193
$659$	−20.7758	−0.809308	−0.404654	−	0.914470i	$-0.632608\pi$
$659$	−20.7758	−0.809308	−0.404654	+	0.914470i	$0.632608\pi$
$660$	0	0
$661$	−13.9149	−0.541229	−0.270614	−	0.962688i	$-0.587227\pi$
$661$	−13.9149	−0.541229	−0.270614	+	0.962688i	$0.587227\pi$
$662$	31.7139	1.23259
$663$	−10.5406	−0.409364
$664$	18.9164	0.734099
$665$	0	0
$666$	4.19922	0.162716
$667$	−1.20162	−0.0465270
$668$	−0.755756	−0.0292411
$669$	−23.6047	−0.912612
$670$	0	0
$671$	69.2884	2.67485
$672$	−0.0792860	−0.00305852
$673$	28.1287	1.08428	0.542141	−	0.840288i	$-0.317614\pi$
$673$	28.1287	1.08428	0.542141	+	0.840288i	$0.317614\pi$
$674$	3.50534	0.135021
$675$	0	0
$676$	0.570152	0.0219289
$677$	30.2709	1.16340	0.581702	−	0.813402i	$-0.302387\pi$
$677$	30.2709	1.16340	0.581702	+	0.813402i	$0.302387\pi$
$678$	−18.3739	−0.705645
$679$	2.14379	0.0822711
$680$	0	0
$681$	−1.49141	−0.0571509
$682$	21.9382	0.840056
$683$	−4.79144	−0.183339	−0.0916696	−	0.995789i	$-0.529220\pi$
$683$	−4.79144	−0.183339	−0.0916696	+	0.995789i	$0.529220\pi$
$684$	0.957938	0.0366277
$685$	0	0
$686$	−2.12840	−0.0812628
$687$	6.90415	0.263410
$688$	−42.2027	−1.60896
$689$	−35.8615	−1.36621
$690$	0	0
$691$	11.6175	0.441952	0.220976	−	0.975279i	$-0.429076\pi$
$691$	11.6175	0.441952	0.220976	+	0.975279i	$0.429076\pi$
$692$	−1.37188	−0.0521510
$693$	0.601319	0.0228422
$694$	−28.6414	−1.08721
$695$	0	0
$696$	−1.69333	−0.0641854
$697$	26.9211	1.01971
$698$	−25.7258	−0.973737
$699$	23.6480	0.894449
$700$	0	0
$701$	10.4351	0.394127	0.197064	−	0.980391i	$-0.436859\pi$
$701$	10.4351	0.394127	0.197064	+	0.980391i	$0.436859\pi$
$702$	−3.98729	−0.150490
$703$	23.2715	0.877702
$704$	−45.6516	−1.72056
$705$	0	0
$706$	−13.1147	−0.493578
$707$	1.61846	0.0608684
$708$	−0.711226	−0.0267295
$709$	−9.12635	−0.342747	−0.171374	−	0.985206i	$-0.554821\pi$
$709$	−9.12635	−0.342747	−0.171374	+	0.985206i	$0.554821\pi$
$710$	0	0
$711$	0.266116	0.00998014
$712$	21.9707	0.823385
$713$	−6.11926	−0.229168
$714$	0.550618	0.0206064
$715$	0	0
$716$	0.941112	0.0351710
$717$	−1.80705	−0.0674856
$718$	38.9968	1.45535
$719$	20.7563	0.774080	0.387040	−	0.922063i	$-0.373497\pi$
$719$	20.7563	0.774080	0.387040	+	0.922063i	$0.373497\pi$
$720$	0	0
$721$	−1.21734	−0.0453360
$722$	−52.7638	−1.96366
$723$	−16.1360	−0.600103
$724$	−3.09930	−0.115185
$725$	0	0
$726$	24.9971	0.927730
$727$	−4.16244	−0.154376	−0.0771881	−	0.997017i	$-0.524594\pi$
$727$	−4.16244	−0.154376	−0.0771881	+	0.997017i	$0.524594\pi$
$728$	0.942441	0.0349292
$729$	1.00000	0.0370370
$730$	0	0
$731$	−40.9259	−1.51370
$732$	−1.61749	−0.0597840
$733$	−21.8466	−0.806922	−0.403461	−	0.914997i	$-0.632193\pi$
$733$	−21.8466	−0.806922	−0.403461	+	0.914997i	$0.632193\pi$
$734$	1.32688	0.0489759
$735$	0	0
$736$	1.47312	0.0543000
$737$	−37.6276	−1.38603
$738$	10.1837	0.374867
$739$	−16.3416	−0.601137	−0.300569	−	0.953760i	$-0.597176\pi$
$739$	−16.3416	−0.601137	−0.300569	+	0.953760i	$0.597176\pi$
$740$	0	0
$741$	−22.0970	−0.811754
$742$	1.87332	0.0687719
$743$	43.9154	1.61110	0.805549	−	0.592529i	$-0.201870\pi$
$743$	43.9154	1.61110	0.805549	+	0.592529i	$0.201870\pi$
$744$	−8.62327	−0.316145
$745$	0	0
$746$	36.5581	1.33849
$747$	6.49929	0.237797
$748$	−2.47183	−0.0903790
$749$	1.55070	0.0566612
$750$	0	0
$751$	−6.66585	−0.243240	−0.121620	−	0.992577i	$-0.538809\pi$
$751$	−6.66585	−0.243240	−0.121620	+	0.992577i	$0.538809\pi$
$752$	3.73150	0.136074
$753$	−31.5934	−1.15133
$754$	2.31977	0.0844812
$755$	0	0
$756$	−0.0140374	−0.000510534 0
$757$	38.1825	1.38777	0.693883	−	0.720088i	$-0.255899\pi$
$757$	38.1825	1.38777	0.693883	+	0.720088i	$0.255899\pi$
$758$	−15.5055	−0.563186
$759$	−11.1724	−0.405534
$760$	0	0
$761$	−47.5954	−1.72533	−0.862665	−	0.505775i	$-0.831207\pi$
$761$	−47.5954	−1.72533	−0.862665	+	0.505775i	$0.831207\pi$
$762$	−9.31906	−0.337594
$763$	−0.826612	−0.0299254
$764$	2.48148	0.0897768
$765$	0	0
$766$	−24.5637	−0.887524
$767$	16.4060	0.592388
$768$	3.01834	0.108915
$769$	8.31253	0.299757	0.149879	−	0.988704i	$-0.452112\pi$
$769$	8.31253	0.299757	0.149879	+	0.988704i	$0.452112\pi$
$770$	0	0
$771$	19.2297	0.692542
$772$	−0.477627	−0.0171902
$773$	−29.1290	−1.04770	−0.523848	−	0.851812i	$-0.675504\pi$
$773$	−29.1290	−1.04770	−0.523848	+	0.851812i	$0.675504\pi$
$774$	−15.4814	−0.556466
$775$	0	0
$776$	−56.1304	−2.01496
$777$	−0.341014	−0.0122338
$778$	29.7401	1.06623
$779$	56.4367	2.02205
$780$	0	0
$781$	84.4665	3.02245
$782$	−10.2304	−0.365839
$783$	−0.581793	−0.0207916
$784$	26.0744	0.931228
$785$	0	0
$786$	16.3996	0.584954
$787$	8.92292	0.318068	0.159034	−	0.987273i	$-0.449162\pi$
$787$	8.92292	0.318068	0.159034	+	0.987273i	$0.449162\pi$
$788$	0.109118	0.00388717
$789$	4.53929	0.161603
$790$	0	0
$791$	1.49213	0.0530539
$792$	−15.7442	−0.559447
$793$	37.3110	1.32495
$794$	−38.2671	−1.35805
$795$	0	0
$796$	−3.09302	−0.109629
$797$	31.1244	1.10248	0.551242	−	0.834345i	$-0.314154\pi$
$797$	31.1244	1.10248	0.551242	+	0.834345i	$0.314154\pi$
$798$	1.15430	0.0408617
$799$	3.61860	0.128017
$800$	0	0
$801$	7.54867	0.266719
$802$	21.1093	0.745394
$803$	4.79680	0.169275
$804$	0.878388	0.0309783
$805$	0	0
$806$	11.8135	0.416111
$807$	−10.5589	−0.371691
$808$	−42.3757	−1.49077
$809$	−10.5753	−0.371809	−0.185905	−	0.982568i	$-0.559522\pi$
$809$	−10.5753	−0.371809	−0.185905	+	0.982568i	$0.559522\pi$
$810$	0	0
$811$	−33.9256	−1.19129	−0.595645	−	0.803248i	$-0.703104\pi$
$811$	−33.9256	−1.19129	−0.595645	+	0.803248i	$0.703104\pi$
$812$	0.00816683	0.000286600 0
$813$	0.756622	0.0265359
$814$	−22.7152	−0.796168
$815$	0	0
$816$	−13.5028	−0.472693
$817$	−85.7958	−3.00161
$818$	−1.04501	−0.0365380
$819$	0.323804	0.0113146
$820$	0	0
$821$	33.0847	1.15466	0.577331	−	0.816510i	$-0.304094\pi$
$821$	33.0847	1.15466	0.577331	+	0.816510i	$0.304094\pi$
$822$	7.62029	0.265788
$823$	−31.4592	−1.09660	−0.548300	−	0.836282i	$-0.684725\pi$
$823$	−31.4592	−1.09660	−0.548300	+	0.836282i	$0.684725\pi$
$824$	31.8733	1.11036
$825$	0	0
$826$	−0.857015	−0.0298194
$827$	55.8365	1.94163	0.970813	−	0.239839i	$-0.0770948\pi$
$827$	55.8365	1.94163	0.970813	+	0.239839i	$0.0770948\pi$
$828$	0.260812	0.00906385
$829$	4.19408	0.145666	0.0728331	−	0.997344i	$-0.476796\pi$
$829$	4.19408	0.145666	0.0728331	+	0.997344i	$0.476796\pi$
$830$	0	0
$831$	−9.77008	−0.338920
$832$	−24.5828	−0.852257
$833$	25.2855	0.876091
$834$	23.5507	0.815493
$835$	0	0
$836$	−5.18186	−0.179219
$837$	−2.96278	−0.102409
$838$	21.8775	0.755745
$839$	−27.3634	−0.944689	−0.472344	−	0.881414i	$-0.656592\pi$
$839$	−27.3634	−0.944689	−0.472344	+	0.881414i	$0.656592\pi$
$840$	0	0
$841$	−28.6615	−0.988328
$842$	7.40813	0.255301
$843$	−6.36902	−0.219361
$844$	2.31882	0.0798171
$845$	0	0
$846$	1.36884	0.0470617
$847$	−2.02999	−0.0697513
$848$	−45.9395	−1.57757
$849$	−5.71171	−0.196025
$850$	0	0
$851$	6.33600	0.217195
$852$	−1.97181	−0.0675530
$853$	−44.6143	−1.52757	−0.763783	−	0.645474i	$-0.776660\pi$
$853$	−44.6143	−1.52757	−0.763783	+	0.645474i	$0.776660\pi$
$854$	−1.94904	−0.0666948
$855$	0	0
$856$	−40.6016	−1.38773
$857$	49.7199	1.69840	0.849199	−	0.528072i	$-0.177085\pi$
$857$	49.7199	1.69840	0.849199	+	0.528072i	$0.177085\pi$
$858$	21.5688	0.736347
$859$	−27.5925	−0.941445	−0.470722	−	0.882281i	$-0.656007\pi$
$859$	−27.5925	−0.941445	−0.470722	+	0.882281i	$0.656007\pi$
$860$	0	0
$861$	−0.827007	−0.0281843
$862$	−45.1764	−1.53871
$863$	15.0144	0.511096	0.255548	−	0.966796i	$-0.417744\pi$
$863$	15.0144	0.511096	0.255548	+	0.966796i	$0.417744\pi$
$864$	0.713246	0.0242651
$865$	0	0
$866$	32.6478	1.10942
$867$	3.90570	0.132644
$868$	0.0415896	0.00141164
$869$	−1.43953	−0.0488326
$870$	0	0
$871$	−20.2620	−0.686552
$872$	21.6430	0.732925
$873$	−19.2853	−0.652707
$874$	−21.4467	−0.725446
$875$	0	0
$876$	−0.111978	−0.00378338
$877$	15.3818	0.519405	0.259702	−	0.965689i	$-0.416376\pi$
$877$	15.3818	0.519405	0.259702	+	0.965689i	$0.416376\pi$
$878$	−32.5154	−1.09734
$879$	−8.34879	−0.281598
$880$	0	0
$881$	3.30692	0.111413	0.0557064	−	0.998447i	$-0.482259\pi$
$881$	3.30692	0.111413	0.0557064	+	0.998447i	$0.482259\pi$
$882$	9.56496	0.322069
$883$	−33.6728	−1.13318	−0.566591	−	0.823999i	$-0.691738\pi$
$883$	−33.6728	−1.13318	−0.566591	+	0.823999i	$0.691738\pi$
$884$	−1.33105	−0.0447681
$885$	0	0
$886$	9.35089	0.314149
$887$	−27.9305	−0.937815	−0.468908	−	0.883247i	$-0.655352\pi$
$887$	−27.9305	−0.937815	−0.468908	+	0.883247i	$0.655352\pi$
$888$	8.92870	0.299628
$889$	0.756792	0.0253820
$890$	0	0
$891$	−5.40939	−0.181221
$892$	−2.98077	−0.0998034
$893$	7.58593	0.253854
$894$	−20.8055	−0.695839
$895$	0	0
$896$	1.12558	0.0376030
$897$	−6.01623	−0.200876
$898$	6.99103	0.233294
$899$	1.72373	0.0574894
$900$	0	0
$901$	−44.5497	−1.48417
$902$	−55.0875	−1.83421
$903$	1.25723	0.0418379
$904$	−39.0680	−1.29938
$905$	0	0
$906$	21.1645	0.703143
$907$	1.95084	0.0647765	0.0323882	−	0.999475i	$-0.489689\pi$
$907$	1.95084	0.0647765	0.0323882	+	0.999475i	$0.489689\pi$
$908$	−0.188332	−0.00625003
$909$	−14.5594	−0.482906
$910$	0	0
$911$	−11.1699	−0.370074	−0.185037	−	0.982732i	$-0.559241\pi$
$911$	−11.1699	−0.370074	−0.185037	+	0.982732i	$0.559241\pi$
$912$	−28.3069	−0.937335
$913$	−35.1572	−1.16353
$914$	−16.3333	−0.540259
$915$	0	0
$916$	0.871844	0.0288065
$917$	−1.33179	−0.0439797
$918$	−4.95329	−0.163483
$919$	−25.3167	−0.835122	−0.417561	−	0.908649i	$-0.637115\pi$
$919$	−25.3167	−0.835122	−0.417561	+	0.908649i	$0.637115\pi$
$920$	0	0
$921$	−31.7089	−1.04484
$922$	−34.0755	−1.12222
$923$	45.4842	1.49713
$924$	0.0759336	0.00249803
$925$	0	0
$926$	11.4041	0.374763
$927$	10.9510	0.359678
$928$	−0.414962	−0.0136218
$929$	24.8483	0.815248	0.407624	−	0.913150i	$-0.366357\pi$
$929$	24.8483	0.815248	0.407624	+	0.913150i	$0.366357\pi$
$930$	0	0
$931$	53.0078	1.73726
$932$	2.98623	0.0978171
$933$	9.16353	0.300000
$934$	21.5466	0.705027
$935$	0	0
$936$	−8.47808	−0.277115
$937$	−49.4534	−1.61557	−0.807786	−	0.589475i	$-0.799334\pi$
$937$	−49.4534	−1.61557	−0.807786	+	0.589475i	$0.799334\pi$
$938$	1.05844	0.0345593
$939$	21.7723	0.710512
$940$	0	0
$941$	−2.23714	−0.0729286	−0.0364643	−	0.999335i	$-0.511610\pi$
$941$	−2.23714	−0.0729286	−0.0364643	+	0.999335i	$0.511610\pi$
$942$	−9.89502	−0.322397
$943$	15.3657	0.500375
$944$	21.0166	0.684032
$945$	0	0
$946$	83.7448	2.72278
$947$	9.21716	0.299518	0.149759	−	0.988723i	$-0.452150\pi$
$947$	9.21716	0.299518	0.149759	+	0.988723i	$0.452150\pi$
$948$	0.0336047	0.00109143
$949$	2.58302	0.0838484
$950$	0	0
$951$	7.65975	0.248384
$952$	1.17077	0.0379448
$953$	−54.0768	−1.75172	−0.875859	−	0.482566i	$-0.839705\pi$
$953$	−54.0768	−1.75172	−0.875859	+	0.482566i	$0.839705\pi$
$954$	−16.8522	−0.545609
$955$	0	0
$956$	−0.228191	−0.00738023
$957$	3.14715	0.101733
$958$	−2.15934	−0.0697652
$959$	−0.618836	−0.0199832
$960$	0	0
$961$	−22.2219	−0.716836
$962$	−12.2319	−0.394372
$963$	−13.9499	−0.449528
$964$	−2.03762	−0.0656273
$965$	0	0
$966$	0.314274	0.0101116
$967$	−47.3534	−1.52278	−0.761391	−	0.648293i	$-0.775483\pi$
$967$	−47.3534	−1.52278	−0.761391	+	0.648293i	$0.775483\pi$
$968$	53.1508	1.70833
$969$	−27.4505	−0.881837
$970$	0	0
$971$	7.26250	0.233065	0.116532	−	0.993187i	$-0.462822\pi$
$971$	7.26250	0.233065	0.116532	+	0.993187i	$0.462822\pi$
$972$	0.126278	0.00405038
$973$	−1.91253	−0.0613128
$974$	−10.3794	−0.332579
$975$	0	0
$976$	47.7964	1.52993
$977$	1.37386	0.0439537	0.0219768	−	0.999758i	$-0.493004\pi$
$977$	1.37386	0.0439537	0.0219768	+	0.999758i	$0.493004\pi$
$978$	8.40893	0.268888
$979$	−40.8337	−1.30505
$980$	0	0
$981$	7.43610	0.237416
$982$	55.6903	1.77715
$983$	10.4271	0.332574	0.166287	−	0.986077i	$-0.446822\pi$
$983$	10.4271	0.332574	0.166287	+	0.986077i	$0.446822\pi$
$984$	21.6533	0.690283
$985$	0	0
$986$	2.88179	0.0917749
$987$	−0.111162	−0.00353833
$988$	−2.79037	−0.0887736
$989$	−23.3591	−0.742776
$990$	0	0
$991$	−30.5916	−0.971775	−0.485887	−	0.874021i	$-0.661504\pi$
$991$	−30.5916	−0.971775	−0.485887	+	0.874021i	$0.661504\pi$
$992$	−2.11319	−0.0670939
$993$	23.1684	0.735228
$994$	−2.37599	−0.0753620
$995$	0	0
$996$	0.820719	0.0260055
$997$	−6.34477	−0.200941	−0.100470	−	0.994940i	$-0.532035\pi$
$997$	−6.34477	−0.200941	−0.100470	+	0.994940i	$0.532035\pi$
$998$	−49.4132	−1.56415
$999$	3.06772	0.0970584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bb.1.2	yes	7
5.4	even	2		3525.2.a.y.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.y.1.6	✓	7	5.4	even	2
3525.2.a.bb.1.2	yes	7	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36884 q^{2} -1.00000 q^{3} -0.126278 q^{4} +1.36884 q^{6} -0.111162 q^{7} +2.91053 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.36884 q^{2} -1.00000 q^{3} -0.126278 q^{4} +1.36884 q^{6} -0.111162 q^{7} +2.91053 q^{8} +1.00000 q^{9} -5.40939 q^{11} +0.126278 q^{12} -2.91290 q^{13} +0.152163 q^{14} -3.73150 q^{16} -3.61860 q^{17} -1.36884 q^{18} -7.58593 q^{19} +0.111162 q^{21} +7.40459 q^{22} -2.06538 q^{23} -2.91053 q^{24} +3.98729 q^{26} -1.00000 q^{27} +0.0140374 q^{28} +0.581793 q^{29} +2.96278 q^{31} -0.713246 q^{32} +5.40939 q^{33} +4.95329 q^{34} -0.126278 q^{36} -3.06772 q^{37} +10.3839 q^{38} +2.91290 q^{39} -7.43965 q^{41} -0.152163 q^{42} +11.3099 q^{43} +0.683089 q^{44} +2.82717 q^{46} -1.00000 q^{47} +3.73150 q^{48} -6.98764 q^{49} +3.61860 q^{51} +0.367835 q^{52} +12.3113 q^{53} +1.36884 q^{54} -0.323541 q^{56} +7.58593 q^{57} -0.796381 q^{58} -5.63221 q^{59} -12.8089 q^{61} -4.05557 q^{62} -0.111162 q^{63} +8.43931 q^{64} -7.40459 q^{66} +6.95597 q^{67} +0.456951 q^{68} +2.06538 q^{69} -15.6148 q^{71} +2.91053 q^{72} -0.886754 q^{73} +4.19922 q^{74} +0.957938 q^{76} +0.601319 q^{77} -3.98729 q^{78} +0.266116 q^{79} +1.00000 q^{81} +10.1837 q^{82} +6.49929 q^{83} -0.0140374 q^{84} -15.4814 q^{86} -0.581793 q^{87} -15.7442 q^{88} +7.54867 q^{89} +0.323804 q^{91} +0.260812 q^{92} -2.96278 q^{93} +1.36884 q^{94} +0.713246 q^{96} -19.2853 q^{97} +9.56496 q^{98} -5.40939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9} - 8 q^{11} - 5 q^{12} + 5 q^{13} - 3 q^{14} + 9 q^{16} + 10 q^{17} + q^{18} + 7 q^{19} - 11 q^{21} + 20 q^{22} + 4 q^{23} - 6 q^{24} - 7 q^{27} + 2 q^{28} - 11 q^{29} + 3 q^{31} + 28 q^{32} + 8 q^{33} + 8 q^{34} + 5 q^{36} + 11 q^{37} - 2 q^{38} - 5 q^{39} - 20 q^{41} + 3 q^{42} + 18 q^{43} + q^{44} - 19 q^{46} - 7 q^{47} - 9 q^{48} + 14 q^{49} - 10 q^{51} + 29 q^{52} + 12 q^{53} - q^{54} - 47 q^{56} - 7 q^{57} - 19 q^{58} + 18 q^{59} - 4 q^{61} + 12 q^{62} + 11 q^{63} + 42 q^{64} - 20 q^{66} + 22 q^{67} + 44 q^{68} - 4 q^{69} - 14 q^{71} + 6 q^{72} + 30 q^{73} + 31 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} + 7 q^{81} + 29 q^{82} + 54 q^{83} - 2 q^{84} - 29 q^{86} + 11 q^{87} - 22 q^{88} - 14 q^{89} + 20 q^{91} - 5 q^{92} - 3 q^{93} - q^{94} - 28 q^{96} + 24 q^{97} - 26 q^{98} - 8 q^{99}+O(q^{100}) \) 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9 - 8 * q^11 - 5 * q^12 + 5 * q^13 - 3 * q^14 + 9 * q^16 + 10 * q^17 + q^18 + 7 * q^19 - 11 * q^21 + 20 * q^22 + 4 * q^23 - 6 * q^24 - 7 * q^27 + 2 * q^28 - 11 * q^29 + 3 * q^31 + 28 * q^32 + 8 * q^33 + 8 * q^34 + 5 * q^36 + 11 * q^37 - 2 * q^38 - 5 * q^39 - 20 * q^41 + 3 * q^42 + 18 * q^43 + q^44 - 19 * q^46 - 7 * q^47 - 9 * q^48 + 14 * q^49 - 10 * q^51 + 29 * q^52 + 12 * q^53 - q^54 - 47 * q^56 - 7 * q^57 - 19 * q^58 + 18 * q^59 - 4 * q^61 + 12 * q^62 + 11 * q^63 + 42 * q^64 - 20 * q^66 + 22 * q^67 + 44 * q^68 - 4 * q^69 - 14 * q^71 + 6 * q^72 + 30 * q^73 + 31 * q^74 - 2 * q^76 - 8 * q^77 - q^79 + 7 * q^81 + 29 * q^82 + 54 * q^83 - 2 * q^84 - 29 * q^86 + 11 * q^87 - 22 * q^88 - 14 * q^89 + 20 * q^91 - 5 * q^92 - 3 * q^93 - q^94 - 28 * q^96 + 24 * q^97 - 26 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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