LMFDB - Embedded newform 5290.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.61803 q^{6} +0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} -1.00000 q^{10} +2.85410 q^{11} +1.61803 q^{12} -7.09017 q^{13} +0.618034 q^{14} -1.61803 q^{15} +1.00000 q^{16} -6.09017 q^{17} -0.381966 q^{18} -1.85410 q^{19} -1.00000 q^{20} +1.00000 q^{21} +2.85410 q^{22} +1.61803 q^{24} +1.00000 q^{25} -7.09017 q^{26} -5.47214 q^{27} +0.618034 q^{28} -9.23607 q^{29} -1.61803 q^{30} +9.09017 q^{31} +1.00000 q^{32} +4.61803 q^{33} -6.09017 q^{34} -0.618034 q^{35} -0.381966 q^{36} -6.47214 q^{37} -1.85410 q^{38} -11.4721 q^{39} -1.00000 q^{40} +3.32624 q^{41} +1.00000 q^{42} +2.85410 q^{44} +0.381966 q^{45} -3.70820 q^{47} +1.61803 q^{48} -6.61803 q^{49} +1.00000 q^{50} -9.85410 q^{51} -7.09017 q^{52} -0.472136 q^{53} -5.47214 q^{54} -2.85410 q^{55} +0.618034 q^{56} -3.00000 q^{57} -9.23607 q^{58} +1.70820 q^{59} -1.61803 q^{60} +9.32624 q^{61} +9.09017 q^{62} -0.236068 q^{63} +1.00000 q^{64} +7.09017 q^{65} +4.61803 q^{66} -14.4721 q^{67} -6.09017 q^{68} -0.618034 q^{70} -4.09017 q^{71} -0.381966 q^{72} +3.23607 q^{73} -6.47214 q^{74} +1.61803 q^{75} -1.85410 q^{76} +1.76393 q^{77} -11.4721 q^{78} -1.52786 q^{79} -1.00000 q^{80} -7.70820 q^{81} +3.32624 q^{82} +6.94427 q^{83} +1.00000 q^{84} +6.09017 q^{85} -14.9443 q^{87} +2.85410 q^{88} +10.4721 q^{89} +0.381966 q^{90} -4.38197 q^{91} +14.7082 q^{93} -3.70820 q^{94} +1.85410 q^{95} +1.61803 q^{96} -12.3820 q^{97} -6.61803 q^{98} -1.09017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + q^{12} - 3 q^{13} - q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} + 3 q^{19} - 2 q^{20} + 2 q^{21}+ \cdots + 9 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + q^12 - 3 * q^13 - q^14 - q^15 + 2 * q^16 - q^17 - 3 * q^18 + 3 * q^19 - 2 * q^20 + 2 * q^21 - q^22 + q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - q^28 - 14 * q^29 - q^30 + 7 * q^31 + 2 * q^32 + 7 * q^33 - q^34 + q^35 - 3 * q^36 - 4 * q^37 + 3 * q^38 - 14 * q^39 - 2 * q^40 - 9 * q^41 + 2 * q^42 - q^44 + 3 * q^45 + 6 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 13 * q^51 - 3 * q^52 + 8 * q^53 - 2 * q^54 + q^55 - q^56 - 6 * q^57 - 14 * q^58 - 10 * q^59 - q^60 + 3 * q^61 + 7 * q^62 + 4 * q^63 + 2 * q^64 + 3 * q^65 + 7 * q^66 - 20 * q^67 - q^68 + q^70 + 3 * q^71 - 3 * q^72 + 2 * q^73 - 4 * q^74 + q^75 + 3 * q^76 + 8 * q^77 - 14 * q^78 - 12 * q^79 - 2 * q^80 - 2 * q^81 - 9 * q^82 - 4 * q^83 + 2 * q^84 + q^85 - 12 * q^87 - q^88 + 12 * q^89 + 3 * q^90 - 11 * q^91 + 16 * q^93 + 6 * q^94 - 3 * q^95 + q^96 - 27 * q^97 - 11 * q^98 + 9 * q^99

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
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.61803	0.660560
$7$	0.618034	0.233595	0.116797	−	0.993156i	$-0.462737\pi$
$7$	0.618034	0.233595	0.116797	+	0.993156i	$0.462737\pi$
$8$	1.00000	0.353553
$9$	−0.381966	−0.127322
$10$	−1.00000	−0.316228
$11$	2.85410	0.860544	0.430272	−	0.902699i	$-0.358418\pi$
$11$	2.85410	0.860544	0.430272	+	0.902699i	$0.358418\pi$
$12$	1.61803	0.467086
$13$	−7.09017	−1.96646	−0.983230	−	0.182372i	$-0.941623\pi$
$13$	−7.09017	−1.96646	−0.983230	+	0.182372i	$0.941623\pi$
$14$	0.618034	0.165177
$15$	−1.61803	−0.417775
$16$	1.00000	0.250000
$17$	−6.09017	−1.47708	−0.738542	−	0.674208i	$-0.764485\pi$
$17$	−6.09017	−1.47708	−0.738542	+	0.674208i	$0.764485\pi$
$18$	−0.381966	−0.0900303
$19$	−1.85410	−0.425360	−0.212680	−	0.977122i	$-0.568219\pi$
$19$	−1.85410	−0.425360	−0.212680	+	0.977122i	$0.568219\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	2.85410	0.608497
$23$	0	0
$23$	0	0
$24$	1.61803	0.330280
$25$	1.00000	0.200000
$26$	−7.09017	−1.39050
$27$	−5.47214	−1.05311
$28$	0.618034	0.116797
$29$	−9.23607	−1.71509	−0.857547	−	0.514405i	$-0.828013\pi$
$29$	−9.23607	−1.71509	−0.857547	+	0.514405i	$0.828013\pi$
$30$	−1.61803	−0.295411
$31$	9.09017	1.63264	0.816321	−	0.577598i	$-0.196010\pi$
$31$	9.09017	1.63264	0.816321	+	0.577598i	$0.196010\pi$
$32$	1.00000	0.176777
$33$	4.61803	0.803897
$34$	−6.09017	−1.04446
$35$	−0.618034	−0.104467
$36$	−0.381966	−0.0636610
$37$	−6.47214	−1.06401	−0.532006	−	0.846740i	$-0.678562\pi$
$37$	−6.47214	−1.06401	−0.532006	+	0.846740i	$0.678562\pi$
$38$	−1.85410	−0.300775
$39$	−11.4721	−1.83701
$40$	−1.00000	−0.158114
$41$	3.32624	0.519471	0.259736	−	0.965680i	$-0.416365\pi$
$41$	3.32624	0.519471	0.259736	+	0.965680i	$0.416365\pi$
$42$	1.00000	0.154303
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	2.85410	0.430272
$45$	0.381966	0.0569401
$46$	0	0
$47$	−3.70820	−0.540897	−0.270449	−	0.962734i	$-0.587172\pi$
$47$	−3.70820	−0.540897	−0.270449	+	0.962734i	$0.587172\pi$
$48$	1.61803	0.233543
$49$	−6.61803	−0.945433
$50$	1.00000	0.141421
$51$	−9.85410	−1.37985
$52$	−7.09017	−0.983230
$53$	−0.472136	−0.0648529	−0.0324264	−	0.999474i	$-0.510323\pi$
$53$	−0.472136	−0.0648529	−0.0324264	+	0.999474i	$0.510323\pi$
$54$	−5.47214	−0.744663
$55$	−2.85410	−0.384847
$56$	0.618034	0.0825883
$57$	−3.00000	−0.397360
$58$	−9.23607	−1.21276
$59$	1.70820	0.222389	0.111195	−	0.993799i	$-0.464532\pi$
$59$	1.70820	0.222389	0.111195	+	0.993799i	$0.464532\pi$
$60$	−1.61803	−0.208887
$61$	9.32624	1.19410	0.597051	−	0.802203i	$-0.296339\pi$
$61$	9.32624	1.19410	0.597051	+	0.802203i	$0.296339\pi$
$62$	9.09017	1.15445
$63$	−0.236068	−0.0297418
$64$	1.00000	0.125000
$65$	7.09017	0.879427
$66$	4.61803	0.568441
$67$	−14.4721	−1.76805	−0.884026	−	0.467437i	$-0.845177\pi$
$67$	−14.4721	−1.76805	−0.884026	+	0.467437i	$0.845177\pi$
$68$	−6.09017	−0.738542
$69$	0	0
$70$	−0.618034	−0.0738692
$71$	−4.09017	−0.485414	−0.242707	−	0.970100i	$-0.578035\pi$
$71$	−4.09017	−0.485414	−0.242707	+	0.970100i	$0.578035\pi$
$72$	−0.381966	−0.0450151
$73$	3.23607	0.378753	0.189377	−	0.981905i	$-0.439353\pi$
$73$	3.23607	0.378753	0.189377	+	0.981905i	$0.439353\pi$
$74$	−6.47214	−0.752371
$75$	1.61803	0.186834
$76$	−1.85410	−0.212680
$77$	1.76393	0.201019
$78$	−11.4721	−1.29896
$79$	−1.52786	−0.171898	−0.0859491	−	0.996300i	$-0.527392\pi$
$79$	−1.52786	−0.171898	−0.0859491	+	0.996300i	$0.527392\pi$
$80$	−1.00000	−0.111803
$81$	−7.70820	−0.856467
$82$	3.32624	0.367322
$83$	6.94427	0.762233	0.381116	−	0.924527i	$-0.375540\pi$
$83$	6.94427	0.762233	0.381116	+	0.924527i	$0.375540\pi$
$84$	1.00000	0.109109
$85$	6.09017	0.660572
$86$	0	0
$87$	−14.9443	−1.60219
$88$	2.85410	0.304248
$89$	10.4721	1.11004	0.555022	−	0.831836i	$-0.312710\pi$
$89$	10.4721	1.11004	0.555022	+	0.831836i	$0.312710\pi$
$90$	0.381966	0.0402628
$91$	−4.38197	−0.459355
$92$	0	0
$93$	14.7082	1.52517
$94$	−3.70820	−0.382472
$95$	1.85410	0.190227
$96$	1.61803	0.165140
$97$	−12.3820	−1.25720	−0.628599	−	0.777730i	$-0.716371\pi$
$97$	−12.3820	−1.25720	−0.628599	+	0.777730i	$0.716371\pi$
$98$	−6.61803	−0.668522
$99$	−1.09017	−0.109566
$100$	1.00000	0.100000
$101$	−0.291796	−0.0290348	−0.0145174	−	0.999895i	$-0.504621\pi$
$101$	−0.291796	−0.0290348	−0.0145174	+	0.999895i	$0.504621\pi$
$102$	−9.85410	−0.975701
$103$	−16.5623	−1.63193	−0.815966	−	0.578100i	$-0.803795\pi$
$103$	−16.5623	−1.63193	−0.815966	+	0.578100i	$0.803795\pi$
$104$	−7.09017	−0.695248
$105$	−1.00000	−0.0975900
$106$	−0.472136	−0.0458579
$107$	−18.1803	−1.75756	−0.878780	−	0.477227i	$-0.841642\pi$
$107$	−18.1803	−1.75756	−0.878780	+	0.477227i	$0.841642\pi$
$108$	−5.47214	−0.526557
$109$	11.5623	1.10747	0.553734	−	0.832694i	$-0.313202\pi$
$109$	11.5623	1.10747	0.553734	+	0.832694i	$0.313202\pi$
$110$	−2.85410	−0.272128
$111$	−10.4721	−0.993971
$112$	0.618034	0.0583987
$113$	−1.05573	−0.0993145	−0.0496573	−	0.998766i	$-0.515813\pi$
$113$	−1.05573	−0.0993145	−0.0496573	+	0.998766i	$0.515813\pi$
$114$	−3.00000	−0.280976
$115$	0	0
$116$	−9.23607	−0.857547
$117$	2.70820	0.250374
$118$	1.70820	0.157253
$119$	−3.76393	−0.345039
$120$	−1.61803	−0.147706
$121$	−2.85410	−0.259464
$122$	9.32624	0.844358
$123$	5.38197	0.485276
$124$	9.09017	0.816321
$125$	−1.00000	−0.0894427
$126$	−0.236068	−0.0210306
$127$	16.1803	1.43577	0.717886	−	0.696160i	$-0.245110\pi$
$127$	16.1803	1.43577	0.717886	+	0.696160i	$0.245110\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	7.09017	0.621849
$131$	2.94427	0.257242	0.128621	−	0.991694i	$-0.458945\pi$
$131$	2.94427	0.257242	0.128621	+	0.991694i	$0.458945\pi$
$132$	4.61803	0.401948
$133$	−1.14590	−0.0993620
$134$	−14.4721	−1.25020
$135$	5.47214	0.470966
$136$	−6.09017	−0.522228
$137$	10.3262	0.882230	0.441115	−	0.897451i	$-0.354583\pi$
$137$	10.3262	0.882230	0.441115	+	0.897451i	$0.354583\pi$
$138$	0	0
$139$	12.7639	1.08262	0.541311	−	0.840822i	$-0.317928\pi$
$139$	12.7639	1.08262	0.541311	+	0.840822i	$0.317928\pi$
$140$	−0.618034	−0.0522334
$141$	−6.00000	−0.505291
$142$	−4.09017	−0.343239
$143$	−20.2361	−1.69223
$144$	−0.381966	−0.0318305
$145$	9.23607	0.767014
$146$	3.23607	0.267819
$147$	−10.7082	−0.883198
$148$	−6.47214	−0.532006
$149$	7.85410	0.643433	0.321717	−	0.946836i	$-0.395740\pi$
$149$	7.85410	0.643433	0.321717	+	0.946836i	$0.395740\pi$
$150$	1.61803	0.132112
$151$	−2.56231	−0.208517	−0.104259	−	0.994550i	$-0.533247\pi$
$151$	−2.56231	−0.208517	−0.104259	+	0.994550i	$0.533247\pi$
$152$	−1.85410	−0.150388
$153$	2.32624	0.188065
$154$	1.76393	0.142142
$155$	−9.09017	−0.730140
$156$	−11.4721	−0.918506
$157$	3.70820	0.295947	0.147973	−	0.988991i	$-0.452725\pi$
$157$	3.70820	0.295947	0.147973	+	0.988991i	$0.452725\pi$
$158$	−1.52786	−0.121550
$159$	−0.763932	−0.0605838
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−7.70820	−0.605614
$163$	1.38197	0.108244	0.0541220	−	0.998534i	$-0.482764\pi$
$163$	1.38197	0.108244	0.0541220	+	0.998534i	$0.482764\pi$
$164$	3.32624	0.259736
$165$	−4.61803	−0.359513
$166$	6.94427	0.538980
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	1.00000	0.0771517
$169$	37.2705	2.86696
$170$	6.09017	0.467095
$171$	0.708204	0.0541577
$172$	0	0
$173$	−1.43769	−0.109306	−0.0546529	−	0.998505i	$-0.517405\pi$
$173$	−1.43769	−0.109306	−0.0546529	+	0.998505i	$0.517405\pi$
$174$	−14.9443	−1.13292
$175$	0.618034	0.0467190
$176$	2.85410	0.215136
$177$	2.76393	0.207750
$178$	10.4721	0.784920
$179$	2.18034	0.162966	0.0814831	−	0.996675i	$-0.474034\pi$
$179$	2.18034	0.162966	0.0814831	+	0.996675i	$0.474034\pi$
$180$	0.381966	0.0284701
$181$	12.1459	0.902797	0.451399	−	0.892322i	$-0.350925\pi$
$181$	12.1459	0.902797	0.451399	+	0.892322i	$0.350925\pi$
$182$	−4.38197	−0.324813
$183$	15.0902	1.11550
$184$	0	0
$185$	6.47214	0.475841
$186$	14.7082	1.07846
$187$	−17.3820	−1.27110
$188$	−3.70820	−0.270449
$189$	−3.38197	−0.246002
$190$	1.85410	0.134511
$191$	13.7082	0.991891	0.495945	−	0.868354i	$-0.334822\pi$
$191$	13.7082	0.991891	0.495945	+	0.868354i	$0.334822\pi$
$192$	1.61803	0.116772
$193$	0.763932	0.0549890	0.0274945	−	0.999622i	$-0.491247\pi$
$193$	0.763932	0.0549890	0.0274945	+	0.999622i	$0.491247\pi$
$194$	−12.3820	−0.888973
$195$	11.4721	0.821537
$196$	−6.61803	−0.472717
$197$	−22.5623	−1.60750	−0.803749	−	0.594969i	$-0.797164\pi$
$197$	−22.5623	−1.60750	−0.803749	+	0.594969i	$0.797164\pi$
$198$	−1.09017	−0.0774750
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	1.00000	0.0707107
$201$	−23.4164	−1.65167
$202$	−0.291796	−0.0205307
$203$	−5.70820	−0.400637
$204$	−9.85410	−0.689925
$205$	−3.32624	−0.232315
$206$	−16.5623	−1.15395
$207$	0	0
$208$	−7.09017	−0.491615
$209$	−5.29180	−0.366041
$210$	−1.00000	−0.0690066
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	−0.472136	−0.0324264
$213$	−6.61803	−0.453460
$214$	−18.1803	−1.24278
$215$	0	0
$216$	−5.47214	−0.372332
$217$	5.61803	0.381377
$218$	11.5623	0.783098
$219$	5.23607	0.353821
$220$	−2.85410	−0.192424
$221$	43.1803	2.90462
$222$	−10.4721	−0.702844
$223$	−20.9443	−1.40253	−0.701266	−	0.712900i	$-0.747382\pi$
$223$	−20.9443	−1.40253	−0.701266	+	0.712900i	$0.747382\pi$
$224$	0.618034	0.0412941
$225$	−0.381966	−0.0254644
$226$	−1.05573	−0.0702260
$227$	18.7639	1.24541	0.622703	−	0.782458i	$-0.286035\pi$
$227$	18.7639	1.24541	0.622703	+	0.782458i	$0.286035\pi$
$228$	−3.00000	−0.198680
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	2.85410	0.187786
$232$	−9.23607	−0.606378
$233$	6.29180	0.412189	0.206095	−	0.978532i	$-0.433925\pi$
$233$	6.29180	0.412189	0.206095	+	0.978532i	$0.433925\pi$
$234$	2.70820	0.177041
$235$	3.70820	0.241897
$236$	1.70820	0.111195
$237$	−2.47214	−0.160582
$238$	−3.76393	−0.243979
$239$	−20.3607	−1.31702	−0.658511	−	0.752571i	$-0.728814\pi$
$239$	−20.3607	−1.31702	−0.658511	+	0.752571i	$0.728814\pi$
$240$	−1.61803	−0.104444
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	−2.85410	−0.183469
$243$	3.94427	0.253025
$244$	9.32624	0.597051
$245$	6.61803	0.422811
$246$	5.38197	0.343142
$247$	13.1459	0.836453
$248$	9.09017	0.577226
$249$	11.2361	0.712057
$250$	−1.00000	−0.0632456
$251$	−6.14590	−0.387926	−0.193963	−	0.981009i	$-0.562134\pi$
$251$	−6.14590	−0.387926	−0.193963	+	0.981009i	$0.562134\pi$
$252$	−0.236068	−0.0148709
$253$	0	0
$254$	16.1803	1.01524
$255$	9.85410	0.617088
$256$	1.00000	0.0625000
$257$	−7.81966	−0.487777	−0.243888	−	0.969803i	$-0.578423\pi$
$257$	−7.81966	−0.487777	−0.243888	+	0.969803i	$0.578423\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	7.09017	0.439714
$261$	3.52786	0.218369
$262$	2.94427	0.181898
$263$	−20.7426	−1.27905	−0.639523	−	0.768772i	$-0.720868\pi$
$263$	−20.7426	−1.27905	−0.639523	+	0.768772i	$0.720868\pi$
$264$	4.61803	0.284220
$265$	0.472136	0.0290031
$266$	−1.14590	−0.0702595
$267$	16.9443	1.03697
$268$	−14.4721	−0.884026
$269$	−14.1803	−0.864591	−0.432295	−	0.901732i	$-0.642296\pi$
$269$	−14.1803	−0.864591	−0.432295	+	0.901732i	$0.642296\pi$
$270$	5.47214	0.333024
$271$	−30.3262	−1.84219	−0.921094	−	0.389341i	$-0.872703\pi$
$271$	−30.3262	−1.84219	−0.921094	+	0.389341i	$0.872703\pi$
$272$	−6.09017	−0.369271
$273$	−7.09017	−0.429117
$274$	10.3262	0.623831
$275$	2.85410	0.172109
$276$	0	0
$277$	29.4164	1.76746	0.883730	−	0.467996i	$-0.155024\pi$
$277$	29.4164	1.76746	0.883730	+	0.467996i	$0.155024\pi$
$278$	12.7639	0.765530
$279$	−3.47214	−0.207871
$280$	−0.618034	−0.0369346
$281$	−22.7639	−1.35798	−0.678991	−	0.734146i	$-0.737583\pi$
$281$	−22.7639	−1.35798	−0.678991	+	0.734146i	$0.737583\pi$
$282$	−6.00000	−0.357295
$283$	26.9443	1.60167	0.800835	−	0.598885i	$-0.204389\pi$
$283$	26.9443	1.60167	0.800835	+	0.598885i	$0.204389\pi$
$284$	−4.09017	−0.242707
$285$	3.00000	0.177705
$286$	−20.2361	−1.19658
$287$	2.05573	0.121346
$288$	−0.381966	−0.0225076
$289$	20.0902	1.18177
$290$	9.23607	0.542361
$291$	−20.0344	−1.17444
$292$	3.23607	0.189377
$293$	19.8885	1.16190	0.580951	−	0.813939i	$-0.302681\pi$
$293$	19.8885	1.16190	0.580951	+	0.813939i	$0.302681\pi$
$294$	−10.7082	−0.624515
$295$	−1.70820	−0.0994555
$296$	−6.47214	−0.376185
$297$	−15.6180	−0.906250
$298$	7.85410	0.454976
$299$	0	0
$300$	1.61803	0.0934172
$301$	0	0
$302$	−2.56231	−0.147444
$303$	−0.472136	−0.0271235
$304$	−1.85410	−0.106340
$305$	−9.32624	−0.534019
$306$	2.32624	0.132982
$307$	−28.4508	−1.62378	−0.811888	−	0.583813i	$-0.801560\pi$
$307$	−28.4508	−1.62378	−0.811888	+	0.583813i	$0.801560\pi$
$308$	1.76393	0.100509
$309$	−26.7984	−1.52451
$310$	−9.09017	−0.516287
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	−11.4721	−0.649482
$313$	−12.7984	−0.723407	−0.361703	−	0.932293i	$-0.617805\pi$
$313$	−12.7984	−0.723407	−0.361703	+	0.932293i	$0.617805\pi$
$314$	3.70820	0.209266
$315$	0.236068	0.0133009
$316$	−1.52786	−0.0859491
$317$	−11.0902	−0.622886	−0.311443	−	0.950265i	$-0.600812\pi$
$317$	−11.0902	−0.622886	−0.311443	+	0.950265i	$0.600812\pi$
$318$	−0.763932	−0.0428392
$319$	−26.3607	−1.47591
$320$	−1.00000	−0.0559017
$321$	−29.4164	−1.64186
$322$	0	0
$323$	11.2918	0.628292
$324$	−7.70820	−0.428234
$325$	−7.09017	−0.393292
$326$	1.38197	0.0765400
$327$	18.7082	1.03457
$328$	3.32624	0.183661
$329$	−2.29180	−0.126351
$330$	−4.61803	−0.254214
$331$	19.2361	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$331$	19.2361	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$332$	6.94427	0.381116
$333$	2.47214	0.135472
$334$	−8.00000	−0.437741
$335$	14.4721	0.790697
$336$	1.00000	0.0545545
$337$	−13.6738	−0.744857	−0.372429	−	0.928061i	$-0.621475\pi$
$337$	−13.6738	−0.744857	−0.372429	+	0.928061i	$0.621475\pi$
$338$	37.2705	2.02725
$339$	−1.70820	−0.0927769
$340$	6.09017	0.330286
$341$	25.9443	1.40496
$342$	0.708204	0.0382953
$343$	−8.41641	−0.454443
$344$	0	0
$345$	0	0
$346$	−1.43769	−0.0772909
$347$	−6.38197	−0.342602	−0.171301	−	0.985219i	$-0.554797\pi$
$347$	−6.38197	−0.342602	−0.171301	+	0.985219i	$0.554797\pi$
$348$	−14.9443	−0.801097
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0.618034	0.0330353
$351$	38.7984	2.07090
$352$	2.85410	0.152124
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	2.76393	0.146901
$355$	4.09017	0.217084
$356$	10.4721	0.555022
$357$	−6.09017	−0.322326
$358$	2.18034	0.115235
$359$	−26.3607	−1.39126	−0.695632	−	0.718399i	$-0.744875\pi$
$359$	−26.3607	−1.39126	−0.695632	+	0.718399i	$0.744875\pi$
$360$	0.381966	0.0201314
$361$	−15.5623	−0.819069
$362$	12.1459	0.638374
$363$	−4.61803	−0.242384
$364$	−4.38197	−0.229677
$365$	−3.23607	−0.169384
$366$	15.0902	0.788776
$367$	−6.47214	−0.337843	−0.168921	−	0.985630i	$-0.554028\pi$
$367$	−6.47214	−0.337843	−0.168921	+	0.985630i	$0.554028\pi$
$368$	0	0
$369$	−1.27051	−0.0661401
$370$	6.47214	0.336470
$371$	−0.291796	−0.0151493
$372$	14.7082	0.762585
$373$	−20.1803	−1.04490	−0.522449	−	0.852670i	$-0.674982\pi$
$373$	−20.1803	−1.04490	−0.522449	+	0.852670i	$0.674982\pi$
$374$	−17.3820	−0.898800
$375$	−1.61803	−0.0835549
$376$	−3.70820	−0.191236
$377$	65.4853	3.37266
$378$	−3.38197	−0.173950
$379$	22.4508	1.15322	0.576611	−	0.817019i	$-0.304375\pi$
$379$	22.4508	1.15322	0.576611	+	0.817019i	$0.304375\pi$
$380$	1.85410	0.0951134
$381$	26.1803	1.34126
$382$	13.7082	0.701373
$383$	17.8885	0.914062	0.457031	−	0.889451i	$-0.348913\pi$
$383$	17.8885	0.914062	0.457031	+	0.889451i	$0.348913\pi$
$384$	1.61803	0.0825700
$385$	−1.76393	−0.0898983
$386$	0.763932	0.0388831
$387$	0	0
$388$	−12.3820	−0.628599
$389$	−21.3262	−1.08128	−0.540642	−	0.841253i	$-0.681818\pi$
$389$	−21.3262	−1.08128	−0.540642	+	0.841253i	$0.681818\pi$
$390$	11.4721	0.580914
$391$	0	0
$392$	−6.61803	−0.334261
$393$	4.76393	0.240309
$394$	−22.5623	−1.13667
$395$	1.52786	0.0768752
$396$	−1.09017	−0.0547831
$397$	7.32624	0.367693	0.183847	−	0.982955i	$-0.441145\pi$
$397$	7.32624	0.367693	0.183847	+	0.982955i	$0.441145\pi$
$398$	−2.00000	−0.100251
$399$	−1.85410	−0.0928212
$400$	1.00000	0.0500000
$401$	1.70820	0.0853036	0.0426518	−	0.999090i	$-0.486419\pi$
$401$	1.70820	0.0853036	0.0426518	+	0.999090i	$0.486419\pi$
$402$	−23.4164	−1.16790
$403$	−64.4508	−3.21053
$404$	−0.291796	−0.0145174
$405$	7.70820	0.383024
$406$	−5.70820	−0.283293
$407$	−18.4721	−0.915630
$408$	−9.85410	−0.487851
$409$	−30.2148	−1.49402	−0.747012	−	0.664810i	$-0.768512\pi$
$409$	−30.2148	−1.49402	−0.747012	+	0.664810i	$0.768512\pi$
$410$	−3.32624	−0.164271
$411$	16.7082	0.824155
$412$	−16.5623	−0.815966
$413$	1.05573	0.0519490
$414$	0	0
$415$	−6.94427	−0.340881
$416$	−7.09017	−0.347624
$417$	20.6525	1.01136
$418$	−5.29180	−0.258830
$419$	−14.4721	−0.707010	−0.353505	−	0.935433i	$-0.615010\pi$
$419$	−14.4721	−0.707010	−0.353505	+	0.935433i	$0.615010\pi$
$420$	−1.00000	−0.0487950
$421$	−13.7426	−0.669776	−0.334888	−	0.942258i	$-0.608698\pi$
$421$	−13.7426	−0.669776	−0.334888	+	0.942258i	$0.608698\pi$
$422$	14.0000	0.681509
$423$	1.41641	0.0688681
$424$	−0.472136	−0.0229289
$425$	−6.09017	−0.295417
$426$	−6.61803	−0.320645
$427$	5.76393	0.278936
$428$	−18.1803	−0.878780
$429$	−32.7426	−1.58083
$430$	0	0
$431$	−3.34752	−0.161245	−0.0806223	−	0.996745i	$-0.525691\pi$
$431$	−3.34752	−0.161245	−0.0806223	+	0.996745i	$0.525691\pi$
$432$	−5.47214	−0.263278
$433$	−8.50658	−0.408800	−0.204400	−	0.978887i	$-0.565524\pi$
$433$	−8.50658	−0.408800	−0.204400	+	0.978887i	$0.565524\pi$
$434$	5.61803	0.269674
$435$	14.9443	0.716523
$436$	11.5623	0.553734
$437$	0	0
$438$	5.23607	0.250189
$439$	−13.3820	−0.638686	−0.319343	−	0.947639i	$-0.603462\pi$
$439$	−13.3820	−0.638686	−0.319343	+	0.947639i	$0.603462\pi$
$440$	−2.85410	−0.136064
$441$	2.52786	0.120374
$442$	43.1803	2.05388
$443$	25.0902	1.19207	0.596035	−	0.802958i	$-0.296742\pi$
$443$	25.0902	1.19207	0.596035	+	0.802958i	$0.296742\pi$
$444$	−10.4721	−0.496986
$445$	−10.4721	−0.496427
$446$	−20.9443	−0.991740
$447$	12.7082	0.601077
$448$	0.618034	0.0291994
$449$	−1.56231	−0.0737298	−0.0368649	−	0.999320i	$-0.511737\pi$
$449$	−1.56231	−0.0737298	−0.0368649	+	0.999320i	$0.511737\pi$
$450$	−0.381966	−0.0180061
$451$	9.49342	0.447028
$452$	−1.05573	−0.0496573
$453$	−4.14590	−0.194791
$454$	18.7639	0.880635
$455$	4.38197	0.205430
$456$	−3.00000	−0.140488
$457$	37.7771	1.76714	0.883569	−	0.468301i	$-0.155134\pi$
$457$	37.7771	1.76714	0.883569	+	0.468301i	$0.155134\pi$
$458$	−10.0000	−0.467269
$459$	33.3262	1.55554
$460$	0	0
$461$	−39.2361	−1.82741	−0.913703	−	0.406383i	$-0.866790\pi$
$461$	−39.2361	−1.82741	−0.913703	+	0.406383i	$0.866790\pi$
$462$	2.85410	0.132785
$463$	2.00000	0.0929479	0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000	0.0929479	0.0464739	+	0.998920i	$0.485202\pi$
$464$	−9.23607	−0.428774
$465$	−14.7082	−0.682077
$466$	6.29180	0.291462
$467$	17.1246	0.792433	0.396216	−	0.918157i	$-0.370323\pi$
$467$	17.1246	0.792433	0.396216	+	0.918157i	$0.370323\pi$
$468$	2.70820	0.125187
$469$	−8.94427	−0.413008
$470$	3.70820	0.171047
$471$	6.00000	0.276465
$472$	1.70820	0.0786265
$473$	0	0
$474$	−2.47214	−0.113549
$475$	−1.85410	−0.0850720
$476$	−3.76393	−0.172520
$477$	0.180340	0.00825720
$478$	−20.3607	−0.931276
$479$	31.8885	1.45702	0.728512	−	0.685033i	$-0.240212\pi$
$479$	31.8885	1.45702	0.728512	+	0.685033i	$0.240212\pi$
$480$	−1.61803	−0.0738528
$481$	45.8885	2.09234
$482$	0	0
$483$	0	0
$484$	−2.85410	−0.129732
$485$	12.3820	0.562236
$486$	3.94427	0.178916
$487$	−19.8197	−0.898115	−0.449057	−	0.893503i	$-0.648240\pi$
$487$	−19.8197	−0.898115	−0.449057	+	0.893503i	$0.648240\pi$
$488$	9.32624	0.422179
$489$	2.23607	0.101118
$490$	6.61803	0.298972
$491$	6.18034	0.278915	0.139457	−	0.990228i	$-0.455464\pi$
$491$	6.18034	0.278915	0.139457	+	0.990228i	$0.455464\pi$
$492$	5.38197	0.242638
$493$	56.2492	2.53334
$494$	13.1459	0.591462
$495$	1.09017	0.0489995
$496$	9.09017	0.408161
$497$	−2.52786	−0.113390
$498$	11.2361	0.503500
$499$	12.3607	0.553340	0.276670	−	0.960965i	$-0.410769\pi$
$499$	12.3607	0.553340	0.276670	+	0.960965i	$0.410769\pi$
$500$	−1.00000	−0.0447214
$501$	−12.9443	−0.578307
$502$	−6.14590	−0.274305
$503$	−36.3262	−1.61971	−0.809853	−	0.586632i	$-0.800453\pi$
$503$	−36.3262	−1.61971	−0.809853	+	0.586632i	$0.800453\pi$
$504$	−0.236068	−0.0105153
$505$	0.291796	0.0129848
$506$	0	0
$507$	60.3050	2.67824
$508$	16.1803	0.717886
$509$	36.6525	1.62459	0.812296	−	0.583245i	$-0.198217\pi$
$509$	36.6525	1.62459	0.812296	+	0.583245i	$0.198217\pi$
$510$	9.85410	0.436347
$511$	2.00000	0.0884748
$512$	1.00000	0.0441942
$513$	10.1459	0.447952
$514$	−7.81966	−0.344910
$515$	16.5623	0.729822
$516$	0	0
$517$	−10.5836	−0.465466
$518$	−4.00000	−0.175750
$519$	−2.32624	−0.102111
$520$	7.09017	0.310925
$521$	15.5279	0.680288	0.340144	−	0.940373i	$-0.389524\pi$
$521$	15.5279	0.680288	0.340144	+	0.940373i	$0.389524\pi$
$522$	3.52786	0.154410
$523$	26.0000	1.13690	0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000	1.13690	0.568450	+	0.822718i	$0.307543\pi$
$524$	2.94427	0.128621
$525$	1.00000	0.0436436
$526$	−20.7426	−0.904422
$527$	−55.3607	−2.41155
$528$	4.61803	0.200974
$529$	0	0
$530$	0.472136	0.0205083
$531$	−0.652476	−0.0283150
$532$	−1.14590	−0.0496810
$533$	−23.5836	−1.02152
$534$	16.9443	0.733250
$535$	18.1803	0.786005
$536$	−14.4721	−0.625101
$537$	3.52786	0.152239
$538$	−14.1803	−0.611358
$539$	−18.8885	−0.813587
$540$	5.47214	0.235483
$541$	22.8328	0.981659	0.490830	−	0.871256i	$-0.336694\pi$
$541$	22.8328	0.981659	0.490830	+	0.871256i	$0.336694\pi$
$542$	−30.3262	−1.30262
$543$	19.6525	0.843368
$544$	−6.09017	−0.261114
$545$	−11.5623	−0.495275
$546$	−7.09017	−0.303431
$547$	27.9230	1.19390	0.596950	−	0.802278i	$-0.296379\pi$
$547$	27.9230	1.19390	0.596950	+	0.802278i	$0.296379\pi$
$548$	10.3262	0.441115
$549$	−3.56231	−0.152036
$550$	2.85410	0.121699
$551$	17.1246	0.729533
$552$	0	0
$553$	−0.944272	−0.0401545
$554$	29.4164	1.24978
$555$	10.4721	0.444517
$556$	12.7639	0.541311
$557$	22.8328	0.967457	0.483729	−	0.875218i	$-0.339282\pi$
$557$	22.8328	0.967457	0.483729	+	0.875218i	$0.339282\pi$
$558$	−3.47214	−0.146987
$559$	0	0
$560$	−0.618034	−0.0261167
$561$	−28.1246	−1.18742
$562$	−22.7639	−0.960239
$563$	13.8885	0.585332	0.292666	−	0.956215i	$-0.405458\pi$
$563$	13.8885	0.585332	0.292666	+	0.956215i	$0.405458\pi$
$564$	−6.00000	−0.252646
$565$	1.05573	0.0444148
$566$	26.9443	1.13255
$567$	−4.76393	−0.200066
$568$	−4.09017	−0.171620
$569$	2.00000	0.0838444	0.0419222	−	0.999121i	$-0.486652\pi$
$569$	2.00000	0.0838444	0.0419222	+	0.999121i	$0.486652\pi$
$570$	3.00000	0.125656
$571$	−15.9787	−0.668688	−0.334344	−	0.942451i	$-0.608515\pi$
$571$	−15.9787	−0.668688	−0.334344	+	0.942451i	$0.608515\pi$
$572$	−20.2361	−0.846113
$573$	22.1803	0.926597
$574$	2.05573	0.0858044
$575$	0	0
$576$	−0.381966	−0.0159153
$577$	−3.52786	−0.146867	−0.0734335	−	0.997300i	$-0.523396\pi$
$577$	−3.52786	−0.146867	−0.0734335	+	0.997300i	$0.523396\pi$
$578$	20.0902	0.835641
$579$	1.23607	0.0513692
$580$	9.23607	0.383507
$581$	4.29180	0.178054
$582$	−20.0344	−0.830454
$583$	−1.34752	−0.0558087
$584$	3.23607	0.133909
$585$	−2.70820	−0.111970
$586$	19.8885	0.821588
$587$	13.6180	0.562076	0.281038	−	0.959697i	$-0.409321\pi$
$587$	13.6180	0.562076	0.281038	+	0.959697i	$0.409321\pi$
$588$	−10.7082	−0.441599
$589$	−16.8541	−0.694461
$590$	−1.70820	−0.0703256
$591$	−36.5066	−1.50168
$592$	−6.47214	−0.266003
$593$	39.2361	1.61123	0.805616	−	0.592438i	$-0.201834\pi$
$593$	39.2361	1.61123	0.805616	+	0.592438i	$0.201834\pi$
$594$	−15.6180	−0.640816
$595$	3.76393	0.154306
$596$	7.85410	0.321717
$597$	−3.23607	−0.132443
$598$	0	0
$599$	−18.3820	−0.751067	−0.375533	−	0.926809i	$-0.622540\pi$
$599$	−18.3820	−0.751067	−0.375533	+	0.926809i	$0.622540\pi$
$600$	1.61803	0.0660560
$601$	−33.2705	−1.35713	−0.678566	−	0.734539i	$-0.737398\pi$
$601$	−33.2705	−1.35713	−0.678566	+	0.734539i	$0.737398\pi$
$602$	0	0
$603$	5.52786	0.225112
$604$	−2.56231	−0.104259
$605$	2.85410	0.116036
$606$	−0.472136	−0.0191792
$607$	26.4721	1.07447	0.537235	−	0.843432i	$-0.319469\pi$
$607$	26.4721	1.07447	0.537235	+	0.843432i	$0.319469\pi$
$608$	−1.85410	−0.0751938
$609$	−9.23607	−0.374264
$610$	−9.32624	−0.377608
$611$	26.2918	1.06365
$612$	2.32624	0.0940326
$613$	−19.3050	−0.779720	−0.389860	−	0.920874i	$-0.627477\pi$
$613$	−19.3050	−0.779720	−0.389860	+	0.920874i	$0.627477\pi$
$614$	−28.4508	−1.14818
$615$	−5.38197	−0.217022
$616$	1.76393	0.0710708
$617$	−34.0902	−1.37242	−0.686209	−	0.727404i	$-0.740727\pi$
$617$	−34.0902	−1.37242	−0.686209	+	0.727404i	$0.740727\pi$
$618$	−26.7984	−1.07799
$619$	2.79837	0.112476	0.0562381	−	0.998417i	$-0.482089\pi$
$619$	2.79837	0.112476	0.0562381	+	0.998417i	$0.482089\pi$
$620$	−9.09017	−0.365070
$621$	0	0
$622$	4.00000	0.160385
$623$	6.47214	0.259301
$624$	−11.4721	−0.459253
$625$	1.00000	0.0400000
$626$	−12.7984	−0.511526
$627$	−8.56231	−0.341946
$628$	3.70820	0.147973
$629$	39.4164	1.57164
$630$	0.236068	0.00940517
$631$	−42.0689	−1.67474	−0.837368	−	0.546640i	$-0.815907\pi$
$631$	−42.0689	−1.67474	−0.837368	+	0.546640i	$0.815907\pi$
$632$	−1.52786	−0.0607752
$633$	22.6525	0.900355
$634$	−11.0902	−0.440447
$635$	−16.1803	−0.642097
$636$	−0.763932	−0.0302919
$637$	46.9230	1.85916
$638$	−26.3607	−1.04363
$639$	1.56231	0.0618039
$640$	−1.00000	−0.0395285
$641$	−0.360680	−0.0142460	−0.00712300	−	0.999975i	$-0.502267\pi$
$641$	−0.360680	−0.0142460	−0.00712300	+	0.999975i	$0.502267\pi$
$642$	−29.4164	−1.16097
$643$	8.29180	0.326997	0.163498	−	0.986544i	$-0.447722\pi$
$643$	8.29180	0.326997	0.163498	+	0.986544i	$0.447722\pi$
$644$	0	0
$645$	0	0
$646$	11.2918	0.444270
$647$	−36.2492	−1.42510	−0.712552	−	0.701619i	$-0.752461\pi$
$647$	−36.2492	−1.42510	−0.712552	+	0.701619i	$0.752461\pi$
$648$	−7.70820	−0.302807
$649$	4.87539	0.191376
$650$	−7.09017	−0.278099
$651$	9.09017	0.356272
$652$	1.38197	0.0541220
$653$	−8.03444	−0.314412	−0.157206	−	0.987566i	$-0.550249\pi$
$653$	−8.03444	−0.314412	−0.157206	+	0.987566i	$0.550249\pi$
$654$	18.7082	0.731549
$655$	−2.94427	−0.115042
$656$	3.32624	0.129868
$657$	−1.23607	−0.0482236
$658$	−2.29180	−0.0893435
$659$	46.2492	1.80161	0.900807	−	0.434220i	$-0.142976\pi$
$659$	46.2492	1.80161	0.900807	+	0.434220i	$0.142976\pi$
$660$	−4.61803	−0.179757
$661$	−18.6738	−0.726325	−0.363163	−	0.931726i	$-0.618303\pi$
$661$	−18.6738	−0.726325	−0.363163	+	0.931726i	$0.618303\pi$
$662$	19.2361	0.747631
$663$	69.8673	2.71342
$664$	6.94427	0.269490
$665$	1.14590	0.0444360
$666$	2.47214	0.0957933
$667$	0	0
$668$	−8.00000	−0.309529
$669$	−33.8885	−1.31021
$670$	14.4721	0.559107
$671$	26.6180	1.02758
$672$	1.00000	0.0385758
$673$	−10.9443	−0.421871	−0.210935	−	0.977500i	$-0.567651\pi$
$673$	−10.9443	−0.421871	−0.210935	+	0.977500i	$0.567651\pi$
$674$	−13.6738	−0.526694
$675$	−5.47214	−0.210623
$676$	37.2705	1.43348
$677$	50.9443	1.95795	0.978974	−	0.203986i	$-0.0653899\pi$
$677$	50.9443	1.95795	0.978974	+	0.203986i	$0.0653899\pi$
$678$	−1.70820	−0.0656032
$679$	−7.65248	−0.293675
$680$	6.09017	0.233547
$681$	30.3607	1.16342
$682$	25.9443	0.993458
$683$	−31.5623	−1.20770	−0.603849	−	0.797099i	$-0.706367\pi$
$683$	−31.5623	−1.20770	−0.603849	+	0.797099i	$0.706367\pi$
$684$	0.708204	0.0270789
$685$	−10.3262	−0.394545
$686$	−8.41641	−0.321340
$687$	−16.1803	−0.617318
$688$	0	0
$689$	3.34752	0.127531
$690$	0	0
$691$	−29.2361	−1.11219	−0.556096	−	0.831118i	$-0.687701\pi$
$691$	−29.2361	−1.11219	−0.556096	+	0.831118i	$0.687701\pi$
$692$	−1.43769	−0.0546529
$693$	−0.673762	−0.0255941
$694$	−6.38197	−0.242256
$695$	−12.7639	−0.484164
$696$	−14.9443	−0.566461
$697$	−20.2574	−0.767302
$698$	−2.00000	−0.0757011
$699$	10.1803	0.385056
$700$	0.618034	0.0233595
$701$	−43.3394	−1.63691	−0.818453	−	0.574573i	$-0.805168\pi$
$701$	−43.3394	−1.63691	−0.818453	+	0.574573i	$0.805168\pi$
$702$	38.7984	1.46435
$703$	12.0000	0.452589
$704$	2.85410	0.107568
$705$	6.00000	0.225973
$706$	24.0000	0.903252
$707$	−0.180340	−0.00678238
$708$	2.76393	0.103875
$709$	26.0902	0.979837	0.489918	−	0.871768i	$-0.337027\pi$
$709$	26.0902	0.979837	0.489918	+	0.871768i	$0.337027\pi$
$710$	4.09017	0.153501
$711$	0.583592	0.0218864
$712$	10.4721	0.392460
$713$	0	0
$714$	−6.09017	−0.227919
$715$	20.2361	0.756786
$716$	2.18034	0.0814831
$717$	−32.9443	−1.23033
$718$	−26.3607	−0.983772
$719$	35.2705	1.31537	0.657684	−	0.753294i	$-0.271536\pi$
$719$	35.2705	1.31537	0.657684	+	0.753294i	$0.271536\pi$
$720$	0.381966	0.0142350
$721$	−10.2361	−0.381211
$722$	−15.5623	−0.579169
$723$	0	0
$724$	12.1459	0.451399
$725$	−9.23607	−0.343019
$726$	−4.61803	−0.171391
$727$	−28.2016	−1.04594	−0.522970	−	0.852351i	$-0.675176\pi$
$727$	−28.2016	−1.04594	−0.522970	+	0.852351i	$0.675176\pi$
$728$	−4.38197	−0.162406
$729$	29.5066	1.09284
$730$	−3.23607	−0.119772
$731$	0	0
$732$	15.0902	0.557749
$733$	29.4164	1.08652	0.543260	−	0.839565i	$-0.317190\pi$
$733$	29.4164	1.08652	0.543260	+	0.839565i	$0.317190\pi$
$734$	−6.47214	−0.238891
$735$	10.7082	0.394978
$736$	0	0
$737$	−41.3050	−1.52149
$738$	−1.27051	−0.0467681
$739$	−13.8885	−0.510898	−0.255449	−	0.966822i	$-0.582223\pi$
$739$	−13.8885	−0.510898	−0.255449	+	0.966822i	$0.582223\pi$
$740$	6.47214	0.237920
$741$	21.2705	0.781392
$742$	−0.291796	−0.0107122
$743$	−33.6312	−1.23381	−0.616904	−	0.787038i	$-0.711613\pi$
$743$	−33.6312	−1.23381	−0.616904	+	0.787038i	$0.711613\pi$
$744$	14.7082	0.539229
$745$	−7.85410	−0.287752
$746$	−20.1803	−0.738855
$747$	−2.65248	−0.0970490
$748$	−17.3820	−0.635548
$749$	−11.2361	−0.410557
$750$	−1.61803	−0.0590822
$751$	47.0132	1.71553	0.857767	−	0.514038i	$-0.171851\pi$
$751$	47.0132	1.71553	0.857767	+	0.514038i	$0.171851\pi$
$752$	−3.70820	−0.135224
$753$	−9.94427	−0.362389
$754$	65.4853	2.38483
$755$	2.56231	0.0932519
$756$	−3.38197	−0.123001
$757$	17.8885	0.650170	0.325085	−	0.945685i	$-0.394607\pi$
$757$	17.8885	0.650170	0.325085	+	0.945685i	$0.394607\pi$
$758$	22.4508	0.815452
$759$	0	0
$760$	1.85410	0.0672553
$761$	46.8673	1.69894	0.849468	−	0.527640i	$-0.176923\pi$
$761$	46.8673	1.69894	0.849468	+	0.527640i	$0.176923\pi$
$762$	26.1803	0.948414
$763$	7.14590	0.258699
$764$	13.7082	0.495945
$765$	−2.32624	−0.0841053
$766$	17.8885	0.646339
$767$	−12.1115	−0.437319
$768$	1.61803	0.0583858
$769$	6.58359	0.237410	0.118705	−	0.992930i	$-0.462126\pi$
$769$	6.58359	0.237410	0.118705	+	0.992930i	$0.462126\pi$
$770$	−1.76393	−0.0635677
$771$	−12.6525	−0.455668
$772$	0.763932	0.0274945
$773$	−28.9443	−1.04105	−0.520527	−	0.853845i	$-0.674264\pi$
$773$	−28.9443	−1.04105	−0.520527	+	0.853845i	$0.674264\pi$
$774$	0	0
$775$	9.09017	0.326529
$776$	−12.3820	−0.444487
$777$	−6.47214	−0.232187
$778$	−21.3262	−0.764583
$779$	−6.16718	−0.220962
$780$	11.4721	0.410768
$781$	−11.6738	−0.417720
$782$	0	0
$783$	50.5410	1.80619
$784$	−6.61803	−0.236358
$785$	−3.70820	−0.132351
$786$	4.76393	0.169924
$787$	2.87539	0.102497	0.0512483	−	0.998686i	$-0.483680\pi$
$787$	2.87539	0.102497	0.0512483	+	0.998686i	$0.483680\pi$
$788$	−22.5623	−0.803749
$789$	−33.5623	−1.19485
$790$	1.52786	0.0543590
$791$	−0.652476	−0.0231994
$792$	−1.09017	−0.0387375
$793$	−66.1246	−2.34815
$794$	7.32624	0.259998
$795$	0.763932	0.0270939
$796$	−2.00000	−0.0708881
$797$	−13.7082	−0.485569	−0.242785	−	0.970080i	$-0.578061\pi$
$797$	−13.7082	−0.485569	−0.242785	+	0.970080i	$0.578061\pi$
$798$	−1.85410	−0.0656345
$799$	22.5836	0.798950
$800$	1.00000	0.0353553
$801$	−4.00000	−0.141333
$802$	1.70820	0.0603188
$803$	9.23607	0.325934
$804$	−23.4164	−0.825833
$805$	0	0
$806$	−64.4508	−2.27018
$807$	−22.9443	−0.807677
$808$	−0.291796	−0.0102653
$809$	−46.7426	−1.64338	−0.821692	−	0.569932i	$-0.806970\pi$
$809$	−46.7426	−1.64338	−0.821692	+	0.569932i	$0.806970\pi$
$810$	7.70820	0.270839
$811$	21.8197	0.766192	0.383096	−	0.923709i	$-0.374858\pi$
$811$	21.8197	0.766192	0.383096	+	0.923709i	$0.374858\pi$
$812$	−5.70820	−0.200319
$813$	−49.0689	−1.72092
$814$	−18.4721	−0.647448
$815$	−1.38197	−0.0484082
$816$	−9.85410	−0.344963
$817$	0	0
$818$	−30.2148	−1.05644
$819$	1.67376	0.0584860
$820$	−3.32624	−0.116157
$821$	−33.0557	−1.15365	−0.576826	−	0.816867i	$-0.695709\pi$
$821$	−33.0557	−1.15365	−0.576826	+	0.816867i	$0.695709\pi$
$822$	16.7082	0.582766
$823$	25.4164	0.885960	0.442980	−	0.896531i	$-0.353921\pi$
$823$	25.4164	0.885960	0.442980	+	0.896531i	$0.353921\pi$
$824$	−16.5623	−0.576975
$825$	4.61803	0.160779
$826$	1.05573	0.0367335
$827$	−21.7082	−0.754868	−0.377434	−	0.926036i	$-0.623194\pi$
$827$	−21.7082	−0.754868	−0.377434	+	0.926036i	$0.623194\pi$
$828$	0	0
$829$	18.9443	0.657962	0.328981	−	0.944337i	$-0.393295\pi$
$829$	18.9443	0.657962	0.328981	+	0.944337i	$0.393295\pi$
$830$	−6.94427	−0.241039
$831$	47.5967	1.65111
$832$	−7.09017	−0.245807
$833$	40.3050	1.39648
$834$	20.6525	0.715137
$835$	8.00000	0.276851
$836$	−5.29180	−0.183021
$837$	−49.7426	−1.71936
$838$	−14.4721	−0.499932
$839$	−33.0132	−1.13974	−0.569870	−	0.821735i	$-0.693007\pi$
$839$	−33.0132	−1.13974	−0.569870	+	0.821735i	$0.693007\pi$
$840$	−1.00000	−0.0345033
$841$	56.3050	1.94155
$842$	−13.7426	−0.473603
$843$	−36.8328	−1.26859
$844$	14.0000	0.481900
$845$	−37.2705	−1.28214
$846$	1.41641	0.0486971
$847$	−1.76393	−0.0606094
$848$	−0.472136	−0.0162132
$849$	43.5967	1.49624
$850$	−6.09017	−0.208891
$851$	0	0
$852$	−6.61803	−0.226730
$853$	−10.7984	−0.369729	−0.184865	−	0.982764i	$-0.559185\pi$
$853$	−10.7984	−0.369729	−0.184865	+	0.982764i	$0.559185\pi$
$854$	5.76393	0.197238
$855$	−0.708204	−0.0242201
$856$	−18.1803	−0.621391
$857$	−6.58359	−0.224891	−0.112446	−	0.993658i	$-0.535868\pi$
$857$	−6.58359	−0.224891	−0.112446	+	0.993658i	$0.535868\pi$
$858$	−32.7426	−1.11782
$859$	−24.0689	−0.821220	−0.410610	−	0.911811i	$-0.634684\pi$
$859$	−24.0689	−0.821220	−0.410610	+	0.911811i	$0.634684\pi$
$860$	0	0
$861$	3.32624	0.113358
$862$	−3.34752	−0.114017
$863$	32.7639	1.11530	0.557649	−	0.830077i	$-0.311704\pi$
$863$	32.7639	1.11530	0.557649	+	0.830077i	$0.311704\pi$
$864$	−5.47214	−0.186166
$865$	1.43769	0.0488831
$866$	−8.50658	−0.289065
$867$	32.5066	1.10398
$868$	5.61803	0.190688
$869$	−4.36068	−0.147926
$870$	14.9443	0.506658
$871$	102.610	3.47680
$872$	11.5623	0.391549
$873$	4.72949	0.160069
$874$	0	0
$875$	−0.618034	−0.0208934
$876$	5.23607	0.176910
$877$	18.7426	0.632894	0.316447	−	0.948610i	$-0.397510\pi$
$877$	18.7426	0.632894	0.316447	+	0.948610i	$0.397510\pi$
$878$	−13.3820	−0.451619
$879$	32.1803	1.08542
$880$	−2.85410	−0.0962118
$881$	−8.58359	−0.289189	−0.144594	−	0.989491i	$-0.546188\pi$
$881$	−8.58359	−0.289189	−0.144594	+	0.989491i	$0.546188\pi$
$882$	2.52786	0.0851176
$883$	15.5623	0.523713	0.261857	−	0.965107i	$-0.415665\pi$
$883$	15.5623	0.523713	0.261857	+	0.965107i	$0.415665\pi$
$884$	43.1803	1.45231
$885$	−2.76393	−0.0929086
$886$	25.0902	0.842921
$887$	−5.16718	−0.173497	−0.0867485	−	0.996230i	$-0.527648\pi$
$887$	−5.16718	−0.173497	−0.0867485	+	0.996230i	$0.527648\pi$
$888$	−10.4721	−0.351422
$889$	10.0000	0.335389
$890$	−10.4721	−0.351027
$891$	−22.0000	−0.737028
$892$	−20.9443	−0.701266
$893$	6.87539	0.230076
$894$	12.7082	0.425026
$895$	−2.18034	−0.0728807
$896$	0.618034	0.0206471
$897$	0	0
$898$	−1.56231	−0.0521348
$899$	−83.9574	−2.80014
$900$	−0.381966	−0.0127322
$901$	2.87539	0.0957931
$902$	9.49342	0.316096
$903$	0	0
$904$	−1.05573	−0.0351130
$905$	−12.1459	−0.403743
$906$	−4.14590	−0.137738
$907$	−7.12461	−0.236569	−0.118284	−	0.992980i	$-0.537739\pi$
$907$	−7.12461	−0.236569	−0.118284	+	0.992980i	$0.537739\pi$
$908$	18.7639	0.622703
$909$	0.111456	0.00369677
$910$	4.38197	0.145261
$911$	−36.0689	−1.19502	−0.597508	−	0.801863i	$-0.703842\pi$
$911$	−36.0689	−1.19502	−0.597508	+	0.801863i	$0.703842\pi$
$912$	−3.00000	−0.0993399
$913$	19.8197	0.655935
$914$	37.7771	1.24955
$915$	−15.0902	−0.498866
$916$	−10.0000	−0.330409
$917$	1.81966	0.0600905
$918$	33.3262	1.09993
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	0	0
$921$	−46.0344	−1.51689
$922$	−39.2361	−1.29217
$923$	29.0000	0.954547
$924$	2.85410	0.0938931
$925$	−6.47214	−0.212803
$926$	2.00000	0.0657241
$927$	6.32624	0.207781
$928$	−9.23607	−0.303189
$929$	−3.52786	−0.115745	−0.0578727	−	0.998324i	$-0.518432\pi$
$929$	−3.52786	−0.115745	−0.0578727	+	0.998324i	$0.518432\pi$
$930$	−14.7082	−0.482301
$931$	12.2705	0.402150
$932$	6.29180	0.206095
$933$	6.47214	0.211888
$934$	17.1246	0.560334
$935$	17.3820	0.568451
$936$	2.70820	0.0885204
$937$	36.7984	1.20215	0.601075	−	0.799192i	$-0.294739\pi$
$937$	36.7984	1.20215	0.601075	+	0.799192i	$0.294739\pi$
$938$	−8.94427	−0.292041
$939$	−20.7082	−0.675787
$940$	3.70820	0.120948
$941$	22.4934	0.733265	0.366632	−	0.930366i	$-0.380511\pi$
$941$	22.4934	0.733265	0.366632	+	0.930366i	$0.380511\pi$
$942$	6.00000	0.195491
$943$	0	0
$944$	1.70820	0.0555973
$945$	3.38197	0.110015
$946$	0	0
$947$	−54.6869	−1.77709	−0.888543	−	0.458793i	$-0.848282\pi$
$947$	−54.6869	−1.77709	−0.888543	+	0.458793i	$0.848282\pi$
$948$	−2.47214	−0.0802912
$949$	−22.9443	−0.744803
$950$	−1.85410	−0.0601550
$951$	−17.9443	−0.581883
$952$	−3.76393	−0.121990
$953$	−3.79837	−0.123041	−0.0615207	−	0.998106i	$-0.519595\pi$
$953$	−3.79837	−0.123041	−0.0615207	+	0.998106i	$0.519595\pi$
$954$	0.180340	0.00583872
$955$	−13.7082	−0.443587
$956$	−20.3607	−0.658511
$957$	−42.6525	−1.37876
$958$	31.8885	1.03027
$959$	6.38197	0.206084
$960$	−1.61803	−0.0522218
$961$	51.6312	1.66552
$962$	45.8885	1.47951
$963$	6.94427	0.223776
$964$	0	0
$965$	−0.763932	−0.0245918
$966$	0	0
$967$	−16.5410	−0.531923	−0.265962	−	0.963984i	$-0.585689\pi$
$967$	−16.5410	−0.531923	−0.265962	+	0.963984i	$0.585689\pi$
$968$	−2.85410	−0.0917343
$969$	18.2705	0.586933
$970$	12.3820	0.397561
$971$	−34.2705	−1.09979	−0.549896	−	0.835233i	$-0.685333\pi$
$971$	−34.2705	−1.09979	−0.549896	+	0.835233i	$0.685333\pi$
$972$	3.94427	0.126513
$973$	7.88854	0.252895
$974$	−19.8197	−0.635063
$975$	−11.4721	−0.367402
$976$	9.32624	0.298526
$977$	23.5623	0.753825	0.376912	−	0.926249i	$-0.376986\pi$
$977$	23.5623	0.753825	0.376912	+	0.926249i	$0.376986\pi$
$978$	2.23607	0.0715016
$979$	29.8885	0.955242
$980$	6.61803	0.211405
$981$	−4.41641	−0.141005
$982$	6.18034	0.197223
$983$	14.2705	0.455159	0.227579	−	0.973760i	$-0.426919\pi$
$983$	14.2705	0.455159	0.227579	+	0.973760i	$0.426919\pi$
$984$	5.38197	0.171571
$985$	22.5623	0.718895
$986$	56.2492	1.79134
$987$	−3.70820	−0.118033
$988$	13.1459	0.418227
$989$	0	0
$990$	1.09017	0.0346479
$991$	27.5066	0.873775	0.436888	−	0.899516i	$-0.356081\pi$
$991$	27.5066	0.873775	0.436888	+	0.899516i	$0.356081\pi$
$992$	9.09017	0.288613
$993$	31.1246	0.987710
$994$	−2.52786	−0.0801790
$995$	2.00000	0.0634043
$996$	11.2361	0.356028
$997$	57.1935	1.81134	0.905668	−	0.423987i	$-0.139370\pi$
$997$	57.1935	1.81134	0.905668	+	0.423987i	$0.139370\pi$
$998$	12.3607	0.391270
$999$	35.4164	1.12053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.o.1.2		2
23.22	odd	2		230.2.a.c.1.2	✓	2
69.68	even	2		2070.2.a.u.1.1		2
92.91	even	2		1840.2.a.l.1.1		2
115.22	even	4		1150.2.b.i.599.3		4
115.68	even	4		1150.2.b.i.599.2		4
115.114	odd	2		1150.2.a.j.1.1		2
184.45	odd	2		7360.2.a.bh.1.1		2
184.91	even	2		7360.2.a.bn.1.2		2
460.459	even	2		9200.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.c.1.2	✓	2	23.22	odd	2
1150.2.a.j.1.1		2	115.114	odd	2
1150.2.b.i.599.2		4	115.68	even	4
1150.2.b.i.599.3		4	115.22	even	4
1840.2.a.l.1.1		2	92.91	even	2
2070.2.a.u.1.1		2	69.68	even	2
5290.2.a.o.1.2		2	1.1	even	1	trivial
7360.2.a.bh.1.1		2	184.45	odd	2
7360.2.a.bn.1.2		2	184.91	even	2
9200.2.a.bu.1.2		2	460.459	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.61803 q^{6} +0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} -1.00000 q^{10} +2.85410 q^{11} +1.61803 q^{12} -7.09017 q^{13} +0.618034 q^{14} -1.61803 q^{15} +1.00000 q^{16} -6.09017 q^{17} -0.381966 q^{18} -1.85410 q^{19} -1.00000 q^{20} +1.00000 q^{21} +2.85410 q^{22} +1.61803 q^{24} +1.00000 q^{25} -7.09017 q^{26} -5.47214 q^{27} +0.618034 q^{28} -9.23607 q^{29} -1.61803 q^{30} +9.09017 q^{31} +1.00000 q^{32} +4.61803 q^{33} -6.09017 q^{34} -0.618034 q^{35} -0.381966 q^{36} -6.47214 q^{37} -1.85410 q^{38} -11.4721 q^{39} -1.00000 q^{40} +3.32624 q^{41} +1.00000 q^{42} +2.85410 q^{44} +0.381966 q^{45} -3.70820 q^{47} +1.61803 q^{48} -6.61803 q^{49} +1.00000 q^{50} -9.85410 q^{51} -7.09017 q^{52} -0.472136 q^{53} -5.47214 q^{54} -2.85410 q^{55} +0.618034 q^{56} -3.00000 q^{57} -9.23607 q^{58} +1.70820 q^{59} -1.61803 q^{60} +9.32624 q^{61} +9.09017 q^{62} -0.236068 q^{63} +1.00000 q^{64} +7.09017 q^{65} +4.61803 q^{66} -14.4721 q^{67} -6.09017 q^{68} -0.618034 q^{70} -4.09017 q^{71} -0.381966 q^{72} +3.23607 q^{73} -6.47214 q^{74} +1.61803 q^{75} -1.85410 q^{76} +1.76393 q^{77} -11.4721 q^{78} -1.52786 q^{79} -1.00000 q^{80} -7.70820 q^{81} +3.32624 q^{82} +6.94427 q^{83} +1.00000 q^{84} +6.09017 q^{85} -14.9443 q^{87} +2.85410 q^{88} +10.4721 q^{89} +0.381966 q^{90} -4.38197 q^{91} +14.7082 q^{93} -3.70820 q^{94} +1.85410 q^{95} +1.61803 q^{96} -12.3820 q^{97} -6.61803 q^{98} -1.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + q^{12} - 3 q^{13} - q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} + 3 q^{19} - 2 q^{20} + 2 q^{21}+ \cdots + 9 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + q^12 - 3 * q^13 - q^14 - q^15 + 2 * q^16 - q^17 - 3 * q^18 + 3 * q^19 - 2 * q^20 + 2 * q^21 - q^22 + q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - q^28 - 14 * q^29 - q^30 + 7 * q^31 + 2 * q^32 + 7 * q^33 - q^34 + q^35 - 3 * q^36 - 4 * q^37 + 3 * q^38 - 14 * q^39 - 2 * q^40 - 9 * q^41 + 2 * q^42 - q^44 + 3 * q^45 + 6 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 13 * q^51 - 3 * q^52 + 8 * q^53 - 2 * q^54 + q^55 - q^56 - 6 * q^57 - 14 * q^58 - 10 * q^59 - q^60 + 3 * q^61 + 7 * q^62 + 4 * q^63 + 2 * q^64 + 3 * q^65 + 7 * q^66 - 20 * q^67 - q^68 + q^70 + 3 * q^71 - 3 * q^72 + 2 * q^73 - 4 * q^74 + q^75 + 3 * q^76 + 8 * q^77 - 14 * q^78 - 12 * q^79 - 2 * q^80 - 2 * q^81 - 9 * q^82 - 4 * q^83 + 2 * q^84 + q^85 - 12 * q^87 - q^88 + 12 * q^89 + 3 * q^90 - 11 * q^91 + 16 * q^93 + 6 * q^94 - 3 * q^95 + q^96 - 27 * q^97 - 11 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

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