LMFDB - Embedded newform 8030.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.302776 q^{6} +1.00000 q^{8} -2.90833 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.302776 q^{6} +1.00000 q^{8} -2.90833 q^{9} +1.00000 q^{10} +1.00000 q^{11} +0.302776 q^{12} +1.69722 q^{13} +0.302776 q^{15} +1.00000 q^{16} -6.60555 q^{17} -2.90833 q^{18} -5.30278 q^{19} +1.00000 q^{20} +1.00000 q^{22} +2.60555 q^{23} +0.302776 q^{24} +1.00000 q^{25} +1.69722 q^{26} -1.78890 q^{27} +4.60555 q^{29} +0.302776 q^{30} -6.00000 q^{31} +1.00000 q^{32} +0.302776 q^{33} -6.60555 q^{34} -2.90833 q^{36} -6.00000 q^{37} -5.30278 q^{38} +0.513878 q^{39} +1.00000 q^{40} -1.39445 q^{41} -0.697224 q^{43} +1.00000 q^{44} -2.90833 q^{45} +2.60555 q^{46} +1.90833 q^{47} +0.302776 q^{48} -7.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} +1.69722 q^{52} +5.39445 q^{53} -1.78890 q^{54} +1.00000 q^{55} -1.60555 q^{57} +4.60555 q^{58} -2.30278 q^{59} +0.302776 q^{60} -8.90833 q^{61} -6.00000 q^{62} +1.00000 q^{64} +1.69722 q^{65} +0.302776 q^{66} +8.90833 q^{67} -6.60555 q^{68} +0.788897 q^{69} -14.5139 q^{71} -2.90833 q^{72} +1.00000 q^{73} -6.00000 q^{74} +0.302776 q^{75} -5.30278 q^{76} +0.513878 q^{78} -2.00000 q^{79} +1.00000 q^{80} +8.18335 q^{81} -1.39445 q^{82} -1.69722 q^{83} -6.60555 q^{85} -0.697224 q^{86} +1.39445 q^{87} +1.00000 q^{88} -12.9083 q^{89} -2.90833 q^{90} +2.60555 q^{92} -1.81665 q^{93} +1.90833 q^{94} -5.30278 q^{95} +0.302776 q^{96} -14.6056 q^{97} -7.00000 q^{98} -2.90833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} + 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 + 2 * q^8 + 5 * q^9	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} + 2 q^{8} + 5 q^{9} + 2 q^{10} + 2 q^{11} - 3 q^{12} + 7 q^{13} - 3 q^{15} + 2 q^{16} - 6 q^{17} + 5 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{22} - 2 q^{23} - 3 q^{24} + 2 q^{25} + 7 q^{26} - 18 q^{27} + 2 q^{29} - 3 q^{30} - 12 q^{31} + 2 q^{32} - 3 q^{33} - 6 q^{34} + 5 q^{36} - 12 q^{37} - 7 q^{38} - 17 q^{39} + 2 q^{40} - 10 q^{41} - 5 q^{43} + 2 q^{44} + 5 q^{45} - 2 q^{46} - 7 q^{47} - 3 q^{48} - 14 q^{49} + 2 q^{50} - 4 q^{51} + 7 q^{52} + 18 q^{53} - 18 q^{54} + 2 q^{55} + 4 q^{57} + 2 q^{58} - q^{59} - 3 q^{60} - 7 q^{61} - 12 q^{62} + 2 q^{64} + 7 q^{65} - 3 q^{66} + 7 q^{67} - 6 q^{68} + 16 q^{69} - 11 q^{71} + 5 q^{72} + 2 q^{73} - 12 q^{74} - 3 q^{75} - 7 q^{76} - 17 q^{78} - 4 q^{79} + 2 q^{80} + 38 q^{81} - 10 q^{82} - 7 q^{83} - 6 q^{85} - 5 q^{86} + 10 q^{87} + 2 q^{88} - 15 q^{89} + 5 q^{90} - 2 q^{92} + 18 q^{93} - 7 q^{94} - 7 q^{95} - 3 q^{96} - 22 q^{97} - 14 q^{98} + 5 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 + 2 * q^8 + 5 * q^9 + 2 * q^10 + 2 * q^11 - 3 * q^12 + 7 * q^13 - 3 * q^15 + 2 * q^16 - 6 * q^17 + 5 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^22 - 2 * q^23 - 3 * q^24 + 2 * q^25 + 7 * q^26 - 18 * q^27 + 2 * q^29 - 3 * q^30 - 12 * q^31 + 2 * q^32 - 3 * q^33 - 6 * q^34 + 5 * q^36 - 12 * q^37 - 7 * q^38 - 17 * q^39 + 2 * q^40 - 10 * q^41 - 5 * q^43 + 2 * q^44 + 5 * q^45 - 2 * q^46 - 7 * q^47 - 3 * q^48 - 14 * q^49 + 2 * q^50 - 4 * q^51 + 7 * q^52 + 18 * q^53 - 18 * q^54 + 2 * q^55 + 4 * q^57 + 2 * q^58 - q^59 - 3 * q^60 - 7 * q^61 - 12 * q^62 + 2 * q^64 + 7 * q^65 - 3 * q^66 + 7 * q^67 - 6 * q^68 + 16 * q^69 - 11 * q^71 + 5 * q^72 + 2 * q^73 - 12 * q^74 - 3 * q^75 - 7 * q^76 - 17 * q^78 - 4 * q^79 + 2 * q^80 + 38 * q^81 - 10 * q^82 - 7 * q^83 - 6 * q^85 - 5 * q^86 + 10 * q^87 + 2 * q^88 - 15 * q^89 + 5 * q^90 - 2 * q^92 + 18 * q^93 - 7 * q^94 - 7 * q^95 - 3 * q^96 - 22 * q^97 - 14 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.302776	0.174808	0.0874038	−	0.996173i	$-0.472143\pi$
$3$	0.302776	0.174808	0.0874038	+	0.996173i	$0.472143\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.302776	0.123608
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	−2.90833	−0.969442
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.302776	0.0874038
$13$	1.69722	0.470725	0.235363	−	0.971908i	$-0.424372\pi$
$13$	1.69722	0.470725	0.235363	+	0.971908i	$0.424372\pi$
$14$	0	0
$15$	0.302776	0.0781763
$16$	1.00000	0.250000
$17$	−6.60555	−1.60208	−0.801041	−	0.598610i	$-0.795720\pi$
$17$	−6.60555	−1.60208	−0.801041	+	0.598610i	$0.795720\pi$
$18$	−2.90833	−0.685499
$19$	−5.30278	−1.21654	−0.608270	−	0.793730i	$-0.708136\pi$
$19$	−5.30278	−1.21654	−0.608270	+	0.793730i	$0.708136\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	2.60555	0.543295	0.271647	−	0.962397i	$-0.412432\pi$
$23$	2.60555	0.543295	0.271647	+	0.962397i	$0.412432\pi$
$24$	0.302776	0.0618038
$25$	1.00000	0.200000
$26$	1.69722	0.332853
$27$	−1.78890	−0.344273
$28$	0	0
$29$	4.60555	0.855229	0.427615	−	0.903961i	$-0.359354\pi$
$29$	4.60555	0.855229	0.427615	+	0.903961i	$0.359354\pi$
$30$	0.302776	0.0552790
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.00000	0.176777
$33$	0.302776	0.0527065
$34$	−6.60555	−1.13284
$35$	0	0
$36$	−2.90833	−0.484721
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−5.30278	−0.860224
$39$	0.513878	0.0822864
$40$	1.00000	0.158114
$41$	−1.39445	−0.217776	−0.108888	−	0.994054i	$-0.534729\pi$
$41$	−1.39445	−0.217776	−0.108888	+	0.994054i	$0.534729\pi$
$42$	0	0
$43$	−0.697224	−0.106326	−0.0531629	−	0.998586i	$-0.516930\pi$
$43$	−0.697224	−0.106326	−0.0531629	+	0.998586i	$0.516930\pi$
$44$	1.00000	0.150756
$45$	−2.90833	−0.433548
$46$	2.60555	0.384168
$47$	1.90833	0.278358	0.139179	−	0.990267i	$-0.455554\pi$
$47$	1.90833	0.278358	0.139179	+	0.990267i	$0.455554\pi$
$48$	0.302776	0.0437019
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	−2.00000	−0.280056
$52$	1.69722	0.235363
$53$	5.39445	0.740985	0.370492	−	0.928836i	$-0.379189\pi$
$53$	5.39445	0.740985	0.370492	+	0.928836i	$0.379189\pi$
$54$	−1.78890	−0.243438
$55$	1.00000	0.134840
$56$	0	0
$57$	−1.60555	−0.212660
$58$	4.60555	0.604739
$59$	−2.30278	−0.299796	−0.149898	−	0.988701i	$-0.547895\pi$
$59$	−2.30278	−0.299796	−0.149898	+	0.988701i	$0.547895\pi$
$60$	0.302776	0.0390882
$61$	−8.90833	−1.14059	−0.570297	−	0.821438i	$-0.693172\pi$
$61$	−8.90833	−1.14059	−0.570297	+	0.821438i	$0.693172\pi$
$62$	−6.00000	−0.762001
$63$	0	0
$64$	1.00000	0.125000
$65$	1.69722	0.210515
$66$	0.302776	0.0372691
$67$	8.90833	1.08833	0.544163	−	0.838980i	$-0.316847\pi$
$67$	8.90833	1.08833	0.544163	+	0.838980i	$0.316847\pi$
$68$	−6.60555	−0.801041
$69$	0.788897	0.0949721
$70$	0	0
$71$	−14.5139	−1.72248	−0.861240	−	0.508198i	$-0.830312\pi$
$71$	−14.5139	−1.72248	−0.861240	+	0.508198i	$0.830312\pi$
$72$	−2.90833	−0.342750
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−6.00000	−0.697486
$75$	0.302776	0.0349615
$76$	−5.30278	−0.608270
$77$	0	0
$78$	0.513878	0.0581852
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	1.00000	0.111803
$81$	8.18335	0.909261
$82$	−1.39445	−0.153991
$83$	−1.69722	−0.186295	−0.0931473	−	0.995652i	$-0.529693\pi$
$83$	−1.69722	−0.186295	−0.0931473	+	0.995652i	$0.529693\pi$
$84$	0	0
$85$	−6.60555	−0.716473
$86$	−0.697224	−0.0751836
$87$	1.39445	0.149501
$88$	1.00000	0.106600
$89$	−12.9083	−1.36828	−0.684140	−	0.729351i	$-0.739822\pi$
$89$	−12.9083	−1.36828	−0.684140	+	0.729351i	$0.739822\pi$
$90$	−2.90833	−0.306565
$91$	0	0
$92$	2.60555	0.271647
$93$	−1.81665	−0.188378
$94$	1.90833	0.196829
$95$	−5.30278	−0.544053
$96$	0.302776	0.0309019
$97$	−14.6056	−1.48297	−0.741485	−	0.670970i	$-0.765878\pi$
$97$	−14.6056	−1.48297	−0.741485	+	0.670970i	$0.765878\pi$
$98$	−7.00000	−0.707107
$99$	−2.90833	−0.292298
$100$	1.00000	0.100000
$101$	−0.605551	−0.0602546	−0.0301273	−	0.999546i	$-0.509591\pi$
$101$	−0.605551	−0.0602546	−0.0301273	+	0.999546i	$0.509591\pi$
$102$	−2.00000	−0.198030
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	1.69722	0.166427
$105$	0	0
$106$	5.39445	0.523955
$107$	−11.3028	−1.09268	−0.546340	−	0.837563i	$-0.683979\pi$
$107$	−11.3028	−1.09268	−0.546340	+	0.837563i	$0.683979\pi$
$108$	−1.78890	−0.172137
$109$	19.2111	1.84009	0.920045	−	0.391813i	$-0.128152\pi$
$109$	19.2111	1.84009	0.920045	+	0.391813i	$0.128152\pi$
$110$	1.00000	0.0953463
$111$	−1.81665	−0.172429
$112$	0	0
$113$	5.11943	0.481595	0.240798	−	0.970575i	$-0.422591\pi$
$113$	5.11943	0.481595	0.240798	+	0.970575i	$0.422591\pi$
$114$	−1.60555	−0.150374
$115$	2.60555	0.242969
$116$	4.60555	0.427615
$117$	−4.93608	−0.456341
$118$	−2.30278	−0.211988
$119$	0	0
$120$	0.302776	0.0276395
$121$	1.00000	0.0909091
$122$	−8.90833	−0.806522
$123$	−0.422205	−0.0380690
$124$	−6.00000	−0.538816
$125$	1.00000	0.0894427
$126$	0	0
$127$	−4.90833	−0.435544	−0.217772	−	0.976000i	$-0.569879\pi$
$127$	−4.90833	−0.435544	−0.217772	+	0.976000i	$0.569879\pi$
$128$	1.00000	0.0883883
$129$	−0.211103	−0.0185865
$130$	1.69722	0.148856
$131$	−16.0000	−1.39793	−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000	−1.39793	−0.698963	+	0.715158i	$0.746355\pi$
$132$	0.302776	0.0263532
$133$	0	0
$134$	8.90833	0.769562
$135$	−1.78890	−0.153964
$136$	−6.60555	−0.566421
$137$	−8.60555	−0.735222	−0.367611	−	0.929980i	$-0.619824\pi$
$137$	−8.60555	−0.735222	−0.367611	+	0.929980i	$0.619824\pi$
$138$	0.788897	0.0671554
$139$	17.8167	1.51119	0.755594	−	0.655040i	$-0.227348\pi$
$139$	17.8167	1.51119	0.755594	+	0.655040i	$0.227348\pi$
$140$	0	0
$141$	0.577795	0.0486591
$142$	−14.5139	−1.21798
$143$	1.69722	0.141929
$144$	−2.90833	−0.242361
$145$	4.60555	0.382470
$146$	1.00000	0.0827606
$147$	−2.11943	−0.174808
$148$	−6.00000	−0.493197
$149$	−17.7250	−1.45209	−0.726044	−	0.687649i	$-0.758643\pi$
$149$	−17.7250	−1.45209	−0.726044	+	0.687649i	$0.758643\pi$
$150$	0.302776	0.0247215
$151$	9.69722	0.789149	0.394574	−	0.918864i	$-0.370892\pi$
$151$	9.69722	0.789149	0.394574	+	0.918864i	$0.370892\pi$
$152$	−5.30278	−0.430112
$153$	19.2111	1.55313
$154$	0	0
$155$	−6.00000	−0.481932
$156$	0.513878	0.0411432
$157$	−0.788897	−0.0629609	−0.0314804	−	0.999504i	$-0.510022\pi$
$157$	−0.788897	−0.0629609	−0.0314804	+	0.999504i	$0.510022\pi$
$158$	−2.00000	−0.159111
$159$	1.63331	0.129530
$160$	1.00000	0.0790569
$161$	0	0
$162$	8.18335	0.642944
$163$	8.42221	0.659678	0.329839	−	0.944037i	$-0.393006\pi$
$163$	8.42221	0.659678	0.329839	+	0.944037i	$0.393006\pi$
$164$	−1.39445	−0.108888
$165$	0.302776	0.0235711
$166$	−1.69722	−0.131730
$167$	−11.2111	−0.867541	−0.433771	−	0.901023i	$-0.642817\pi$
$167$	−11.2111	−0.867541	−0.433771	+	0.901023i	$0.642817\pi$
$168$	0	0
$169$	−10.1194	−0.778418
$170$	−6.60555	−0.506623
$171$	15.4222	1.17937
$172$	−0.697224	−0.0531629
$173$	−16.0000	−1.21646	−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000	−1.21646	−0.608229	+	0.793762i	$0.708120\pi$
$174$	1.39445	0.105713
$175$	0	0
$176$	1.00000	0.0753778
$177$	−0.697224	−0.0524066
$178$	−12.9083	−0.967520
$179$	7.30278	0.545835	0.272918	−	0.962037i	$-0.412011\pi$
$179$	7.30278	0.545835	0.272918	+	0.962037i	$0.412011\pi$
$180$	−2.90833	−0.216774
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	0	0
$183$	−2.69722	−0.199385
$184$	2.60555	0.192084
$185$	−6.00000	−0.441129
$186$	−1.81665	−0.133204
$187$	−6.60555	−0.483046
$188$	1.90833	0.139179
$189$	0	0
$190$	−5.30278	−0.384704
$191$	0.788897	0.0570826	0.0285413	−	0.999593i	$-0.490914\pi$
$191$	0.788897	0.0570826	0.0285413	+	0.999593i	$0.490914\pi$
$192$	0.302776	0.0218509
$193$	−11.3944	−0.820190	−0.410095	−	0.912043i	$-0.634505\pi$
$193$	−11.3944	−0.820190	−0.410095	+	0.912043i	$0.634505\pi$
$194$	−14.6056	−1.04862
$195$	0.513878	0.0367996
$196$	−7.00000	−0.500000
$197$	21.1194	1.50470	0.752349	−	0.658765i	$-0.228921\pi$
$197$	21.1194	1.50470	0.752349	+	0.658765i	$0.228921\pi$
$198$	−2.90833	−0.206686
$199$	−8.42221	−0.597034	−0.298517	−	0.954404i	$-0.596492\pi$
$199$	−8.42221	−0.597034	−0.298517	+	0.954404i	$0.596492\pi$
$200$	1.00000	0.0707107
$201$	2.69722	0.190248
$202$	−0.605551	−0.0426064
$203$	0	0
$204$	−2.00000	−0.140028
$205$	−1.39445	−0.0973925
$206$	4.00000	0.278693
$207$	−7.57779	−0.526693
$208$	1.69722	0.117681
$209$	−5.30278	−0.366801
$210$	0	0
$211$	−9.30278	−0.640429	−0.320215	−	0.947345i	$-0.603755\pi$
$211$	−9.30278	−0.640429	−0.320215	+	0.947345i	$0.603755\pi$
$212$	5.39445	0.370492
$213$	−4.39445	−0.301103
$214$	−11.3028	−0.772642
$215$	−0.697224	−0.0475503
$216$	−1.78890	−0.121719
$217$	0	0
$218$	19.2111	1.30114
$219$	0.302776	0.0204597
$220$	1.00000	0.0674200
$221$	−11.2111	−0.754140
$222$	−1.81665	−0.121926
$223$	1.81665	0.121652	0.0608261	−	0.998148i	$-0.480627\pi$
$223$	1.81665	0.121652	0.0608261	+	0.998148i	$0.480627\pi$
$224$	0	0
$225$	−2.90833	−0.193888
$226$	5.11943	0.340539
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	−1.60555	−0.106330
$229$	17.3028	1.14340	0.571700	−	0.820463i	$-0.306284\pi$
$229$	17.3028	1.14340	0.571700	+	0.820463i	$0.306284\pi$
$230$	2.60555	0.171805
$231$	0	0
$232$	4.60555	0.302369
$233$	−23.2111	−1.52061	−0.760305	−	0.649566i	$-0.774950\pi$
$233$	−23.2111	−1.52061	−0.760305	+	0.649566i	$0.774950\pi$
$234$	−4.93608	−0.322682
$235$	1.90833	0.124486
$236$	−2.30278	−0.149898
$237$	−0.605551	−0.0393348
$238$	0	0
$239$	14.3028	0.925170	0.462585	−	0.886575i	$-0.346922\pi$
$239$	14.3028	0.925170	0.462585	+	0.886575i	$0.346922\pi$
$240$	0.302776	0.0195441
$241$	−0.788897	−0.0508174	−0.0254087	−	0.999677i	$-0.508089\pi$
$241$	−0.788897	−0.0508174	−0.0254087	+	0.999677i	$0.508089\pi$
$242$	1.00000	0.0642824
$243$	7.84441	0.503219
$244$	−8.90833	−0.570297
$245$	−7.00000	−0.447214
$246$	−0.422205	−0.0269188
$247$	−9.00000	−0.572656
$248$	−6.00000	−0.381000
$249$	−0.513878	−0.0325657
$250$	1.00000	0.0632456
$251$	−17.8167	−1.12458	−0.562289	−	0.826941i	$-0.690079\pi$
$251$	−17.8167	−1.12458	−0.562289	+	0.826941i	$0.690079\pi$
$252$	0	0
$253$	2.60555	0.163810
$254$	−4.90833	−0.307976
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	2.18335	0.136193	0.0680967	−	0.997679i	$-0.478307\pi$
$257$	2.18335	0.136193	0.0680967	+	0.997679i	$0.478307\pi$
$258$	−0.211103	−0.0131427
$259$	0	0
$260$	1.69722	0.105257
$261$	−13.3944	−0.829096
$262$	−16.0000	−0.988483
$263$	31.0278	1.91325	0.956627	−	0.291317i	$-0.0940933\pi$
$263$	31.0278	1.91325	0.956627	+	0.291317i	$0.0940933\pi$
$264$	0.302776	0.0186346
$265$	5.39445	0.331378
$266$	0	0
$267$	−3.90833	−0.239186
$268$	8.90833	0.544163
$269$	23.0278	1.40403	0.702014	−	0.712164i	$-0.252285\pi$
$269$	23.0278	1.40403	0.702014	+	0.712164i	$0.252285\pi$
$270$	−1.78890	−0.108869
$271$	−13.3305	−0.809772	−0.404886	−	0.914367i	$-0.632689\pi$
$271$	−13.3305	−0.809772	−0.404886	+	0.914367i	$0.632689\pi$
$272$	−6.60555	−0.400520
$273$	0	0
$274$	−8.60555	−0.519880
$275$	1.00000	0.0603023
$276$	0.788897	0.0474860
$277$	16.9361	1.01759	0.508795	−	0.860888i	$-0.330091\pi$
$277$	16.9361	1.01759	0.508795	+	0.860888i	$0.330091\pi$
$278$	17.8167	1.06857
$279$	17.4500	1.04470
$280$	0	0
$281$	17.3305	1.03385	0.516926	−	0.856030i	$-0.327076\pi$
$281$	17.3305	1.03385	0.516926	+	0.856030i	$0.327076\pi$
$282$	0.577795	0.0344072
$283$	15.6333	0.929304	0.464652	−	0.885493i	$-0.346179\pi$
$283$	15.6333	0.929304	0.464652	+	0.885493i	$0.346179\pi$
$284$	−14.5139	−0.861240
$285$	−1.60555	−0.0951046
$286$	1.69722	0.100359
$287$	0	0
$288$	−2.90833	−0.171375
$289$	26.6333	1.56667
$290$	4.60555	0.270447
$291$	−4.42221	−0.259234
$292$	1.00000	0.0585206
$293$	−17.2111	−1.00548	−0.502742	−	0.864437i	$-0.667675\pi$
$293$	−17.2111	−1.00548	−0.502742	+	0.864437i	$0.667675\pi$
$294$	−2.11943	−0.123608
$295$	−2.30278	−0.134073
$296$	−6.00000	−0.348743
$297$	−1.78890	−0.103802
$298$	−17.7250	−1.02678
$299$	4.42221	0.255743
$300$	0.302776	0.0174808
$301$	0	0
$302$	9.69722	0.558013
$303$	−0.183346	−0.0105330
$304$	−5.30278	−0.304135
$305$	−8.90833	−0.510089
$306$	19.2111	1.09823
$307$	−20.5139	−1.17079	−0.585394	−	0.810749i	$-0.699060\pi$
$307$	−20.5139	−1.17079	−0.585394	+	0.810749i	$0.699060\pi$
$308$	0	0
$309$	1.21110	0.0688972
$310$	−6.00000	−0.340777
$311$	−21.5139	−1.21994	−0.609970	−	0.792424i	$-0.708819\pi$
$311$	−21.5139	−1.21994	−0.609970	+	0.792424i	$0.708819\pi$
$312$	0.513878	0.0290926
$313$	−13.3028	−0.751917	−0.375959	−	0.926636i	$-0.622687\pi$
$313$	−13.3028	−0.751917	−0.375959	+	0.926636i	$0.622687\pi$
$314$	−0.788897	−0.0445201
$315$	0	0
$316$	−2.00000	−0.112509
$317$	24.6972	1.38713	0.693567	−	0.720392i	$-0.256038\pi$
$317$	24.6972	1.38713	0.693567	+	0.720392i	$0.256038\pi$
$318$	1.63331	0.0915913
$319$	4.60555	0.257861
$320$	1.00000	0.0559017
$321$	−3.42221	−0.191009
$322$	0	0
$323$	35.0278	1.94900
$324$	8.18335	0.454630
$325$	1.69722	0.0941451
$326$	8.42221	0.466463
$327$	5.81665	0.321662
$328$	−1.39445	−0.0769956
$329$	0	0
$330$	0.302776	0.0166673
$331$	−34.9083	−1.91874	−0.959368	−	0.282159i	$-0.908949\pi$
$331$	−34.9083	−1.91874	−0.959368	+	0.282159i	$0.908949\pi$
$332$	−1.69722	−0.0931473
$333$	17.4500	0.956252
$334$	−11.2111	−0.613444
$335$	8.90833	0.486714
$336$	0	0
$337$	13.3944	0.729642	0.364821	−	0.931078i	$-0.381130\pi$
$337$	13.3944	0.729642	0.364821	+	0.931078i	$0.381130\pi$
$338$	−10.1194	−0.550424
$339$	1.55004	0.0841865
$340$	−6.60555	−0.358236
$341$	−6.00000	−0.324918
$342$	15.4222	0.833937
$343$	0	0
$344$	−0.697224	−0.0375918
$345$	0.788897	0.0424728
$346$	−16.0000	−0.860165
$347$	10.1833	0.546671	0.273335	−	0.961919i	$-0.411873\pi$
$347$	10.1833	0.546671	0.273335	+	0.961919i	$0.411873\pi$
$348$	1.39445	0.0747503
$349$	4.69722	0.251437	0.125718	−	0.992066i	$-0.459876\pi$
$349$	4.69722	0.251437	0.125718	+	0.992066i	$0.459876\pi$
$350$	0	0
$351$	−3.03616	−0.162058
$352$	1.00000	0.0533002
$353$	−22.6056	−1.20317	−0.601586	−	0.798808i	$-0.705464\pi$
$353$	−22.6056	−1.20317	−0.601586	+	0.798808i	$0.705464\pi$
$354$	−0.697224	−0.0370571
$355$	−14.5139	−0.770317
$356$	−12.9083	−0.684140
$357$	0	0
$358$	7.30278	0.385964
$359$	−1.21110	−0.0639195	−0.0319598	−	0.999489i	$-0.510175\pi$
$359$	−1.21110	−0.0639195	−0.0319598	+	0.999489i	$0.510175\pi$
$360$	−2.90833	−0.153282
$361$	9.11943	0.479970
$362$	14.0000	0.735824
$363$	0.302776	0.0158916
$364$	0	0
$365$	1.00000	0.0523424
$366$	−2.69722	−0.140986
$367$	−4.60555	−0.240408	−0.120204	−	0.992749i	$-0.538355\pi$
$367$	−4.60555	−0.240408	−0.120204	+	0.992749i	$0.538355\pi$
$368$	2.60555	0.135824
$369$	4.05551	0.211122
$370$	−6.00000	−0.311925
$371$	0	0
$372$	−1.81665	−0.0941891
$373$	19.8167	1.02607	0.513034	−	0.858368i	$-0.328522\pi$
$373$	19.8167	1.02607	0.513034	+	0.858368i	$0.328522\pi$
$374$	−6.60555	−0.341565
$375$	0.302776	0.0156353
$376$	1.90833	0.0984144
$377$	7.81665	0.402578
$378$	0	0
$379$	−15.1194	−0.776633	−0.388316	−	0.921526i	$-0.626943\pi$
$379$	−15.1194	−0.776633	−0.388316	+	0.921526i	$0.626943\pi$
$380$	−5.30278	−0.272027
$381$	−1.48612	−0.0761363
$382$	0.788897	0.0403635
$383$	19.3944	0.991010	0.495505	−	0.868605i	$-0.334983\pi$
$383$	19.3944	0.991010	0.495505	+	0.868605i	$0.334983\pi$
$384$	0.302776	0.0154510
$385$	0	0
$386$	−11.3944	−0.579962
$387$	2.02776	0.103077
$388$	−14.6056	−0.741485
$389$	−9.63331	−0.488428	−0.244214	−	0.969721i	$-0.578530\pi$
$389$	−9.63331	−0.488428	−0.244214	+	0.969721i	$0.578530\pi$
$390$	0.513878	0.0260212
$391$	−17.2111	−0.870403
$392$	−7.00000	−0.353553
$393$	−4.84441	−0.244368
$394$	21.1194	1.06398
$395$	−2.00000	−0.100631
$396$	−2.90833	−0.146149
$397$	−33.5416	−1.68341	−0.841703	−	0.539940i	$-0.818447\pi$
$397$	−33.5416	−1.68341	−0.841703	+	0.539940i	$0.818447\pi$
$398$	−8.42221	−0.422167
$399$	0	0
$400$	1.00000	0.0500000
$401$	−15.3305	−0.765570	−0.382785	−	0.923837i	$-0.625035\pi$
$401$	−15.3305	−0.765570	−0.382785	+	0.923837i	$0.625035\pi$
$402$	2.69722	0.134525
$403$	−10.1833	−0.507269
$404$	−0.605551	−0.0301273
$405$	8.18335	0.406634
$406$	0	0
$407$	−6.00000	−0.297409
$408$	−2.00000	−0.0990148
$409$	−9.30278	−0.459993	−0.229996	−	0.973191i	$-0.573871\pi$
$409$	−9.30278	−0.459993	−0.229996	+	0.973191i	$0.573871\pi$
$410$	−1.39445	−0.0688669
$411$	−2.60555	−0.128522
$412$	4.00000	0.197066
$413$	0	0
$414$	−7.57779	−0.372428
$415$	−1.69722	−0.0833135
$416$	1.69722	0.0832133
$417$	5.39445	0.264167
$418$	−5.30278	−0.259367
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	26.9083	1.31143	0.655716	−	0.755008i	$-0.272367\pi$
$421$	26.9083	1.31143	0.655716	+	0.755008i	$0.272367\pi$
$422$	−9.30278	−0.452852
$423$	−5.55004	−0.269852
$424$	5.39445	0.261978
$425$	−6.60555	−0.320416
$426$	−4.39445	−0.212912
$427$	0	0
$428$	−11.3028	−0.546340
$429$	0.513878	0.0248103
$430$	−0.697224	−0.0336231
$431$	34.9083	1.68147	0.840737	−	0.541443i	$-0.182122\pi$
$431$	34.9083	1.68147	0.840737	+	0.541443i	$0.182122\pi$
$432$	−1.78890	−0.0860684
$433$	−27.7250	−1.33238	−0.666189	−	0.745783i	$-0.732075\pi$
$433$	−27.7250	−1.33238	−0.666189	+	0.745783i	$0.732075\pi$
$434$	0	0
$435$	1.39445	0.0668587
$436$	19.2111	0.920045
$437$	−13.8167	−0.660940
$438$	0.302776	0.0144672
$439$	18.4222	0.879244	0.439622	−	0.898183i	$-0.355112\pi$
$439$	18.4222	0.879244	0.439622	+	0.898183i	$0.355112\pi$
$440$	1.00000	0.0476731
$441$	20.3583	0.969442
$442$	−11.2111	−0.533258
$443$	15.2111	0.722701	0.361351	−	0.932430i	$-0.382316\pi$
$443$	15.2111	0.722701	0.361351	+	0.932430i	$0.382316\pi$
$444$	−1.81665	−0.0862146
$445$	−12.9083	−0.611913
$446$	1.81665	0.0860211
$447$	−5.36669	−0.253836
$448$	0	0
$449$	−33.6333	−1.58725	−0.793627	−	0.608405i	$-0.791810\pi$
$449$	−33.6333	−1.58725	−0.793627	+	0.608405i	$0.791810\pi$
$450$	−2.90833	−0.137100
$451$	−1.39445	−0.0656620
$452$	5.11943	0.240798
$453$	2.93608	0.137949
$454$	−8.00000	−0.375459
$455$	0	0
$456$	−1.60555	−0.0751868
$457$	7.30278	0.341609	0.170805	−	0.985305i	$-0.445363\pi$
$457$	7.30278	0.341609	0.170805	+	0.985305i	$0.445363\pi$
$458$	17.3028	0.808506
$459$	11.8167	0.551554
$460$	2.60555	0.121484
$461$	10.9361	0.509344	0.254672	−	0.967027i	$-0.418032\pi$
$461$	10.9361	0.509344	0.254672	+	0.967027i	$0.418032\pi$
$462$	0	0
$463$	−8.78890	−0.408455	−0.204227	−	0.978923i	$-0.565468\pi$
$463$	−8.78890	−0.408455	−0.204227	+	0.978923i	$0.565468\pi$
$464$	4.60555	0.213807
$465$	−1.81665	−0.0842453
$466$	−23.2111	−1.07523
$467$	13.2111	0.611337	0.305668	−	0.952138i	$-0.401120\pi$
$467$	13.2111	0.611337	0.305668	+	0.952138i	$0.401120\pi$
$468$	−4.93608	−0.228171
$469$	0	0
$470$	1.90833	0.0880246
$471$	−0.238859	−0.0110060
$472$	−2.30278	−0.105994
$473$	−0.697224	−0.0320584
$474$	−0.605551	−0.0278139
$475$	−5.30278	−0.243308
$476$	0	0
$477$	−15.6888	−0.718342
$478$	14.3028	0.654194
$479$	−13.8167	−0.631299	−0.315650	−	0.948876i	$-0.602222\pi$
$479$	−13.8167	−0.631299	−0.315650	+	0.948876i	$0.602222\pi$
$480$	0.302776	0.0138198
$481$	−10.1833	−0.464321
$482$	−0.788897	−0.0359333
$483$	0	0
$484$	1.00000	0.0454545
$485$	−14.6056	−0.663204
$486$	7.84441	0.355830
$487$	13.8167	0.626092	0.313046	−	0.949738i	$-0.398651\pi$
$487$	13.8167	0.626092	0.313046	+	0.949738i	$0.398651\pi$
$488$	−8.90833	−0.403261
$489$	2.55004	0.115317
$490$	−7.00000	−0.316228
$491$	20.8444	0.940695	0.470348	−	0.882481i	$-0.344129\pi$
$491$	20.8444	0.940695	0.470348	+	0.882481i	$0.344129\pi$
$492$	−0.422205	−0.0190345
$493$	−30.4222	−1.37015
$494$	−9.00000	−0.404929
$495$	−2.90833	−0.130720
$496$	−6.00000	−0.269408
$497$	0	0
$498$	−0.513878	−0.0230274
$499$	−24.6056	−1.10150	−0.550748	−	0.834672i	$-0.685657\pi$
$499$	−24.6056	−1.10150	−0.550748	+	0.834672i	$0.685657\pi$
$500$	1.00000	0.0447214
$501$	−3.39445	−0.151653
$502$	−17.8167	−0.795196
$503$	−33.1194	−1.47672	−0.738361	−	0.674405i	$-0.764400\pi$
$503$	−33.1194	−1.47672	−0.738361	+	0.674405i	$0.764400\pi$
$504$	0	0
$505$	−0.605551	−0.0269467
$506$	2.60555	0.115831
$507$	−3.06392	−0.136073
$508$	−4.90833	−0.217772
$509$	28.8444	1.27851	0.639253	−	0.768996i	$-0.279244\pi$
$509$	28.8444	1.27851	0.639253	+	0.768996i	$0.279244\pi$
$510$	−2.00000	−0.0885615
$511$	0	0
$512$	1.00000	0.0441942
$513$	9.48612	0.418823
$514$	2.18335	0.0963033
$515$	4.00000	0.176261
$516$	−0.211103	−0.00929327
$517$	1.90833	0.0839281
$518$	0	0
$519$	−4.84441	−0.212646
$520$	1.69722	0.0744282
$521$	−37.4500	−1.64071	−0.820356	−	0.571853i	$-0.806225\pi$
$521$	−37.4500	−1.64071	−0.820356	+	0.571853i	$0.806225\pi$
$522$	−13.3944	−0.586259
$523$	−31.6333	−1.38323	−0.691614	−	0.722267i	$-0.743100\pi$
$523$	−31.6333	−1.38323	−0.691614	+	0.722267i	$0.743100\pi$
$524$	−16.0000	−0.698963
$525$	0	0
$526$	31.0278	1.35287
$527$	39.6333	1.72645
$528$	0.302776	0.0131766
$529$	−16.2111	−0.704831
$530$	5.39445	0.234320
$531$	6.69722	0.290635
$532$	0	0
$533$	−2.36669	−0.102513
$534$	−3.90833	−0.169130
$535$	−11.3028	−0.488662
$536$	8.90833	0.384781
$537$	2.21110	0.0954161
$538$	23.0278	0.992797
$539$	−7.00000	−0.301511
$540$	−1.78890	−0.0769819
$541$	−27.0278	−1.16201	−0.581007	−	0.813899i	$-0.697341\pi$
$541$	−27.0278	−1.16201	−0.581007	+	0.813899i	$0.697341\pi$
$542$	−13.3305	−0.572595
$543$	4.23886	0.181907
$544$	−6.60555	−0.283211
$545$	19.2111	0.822913
$546$	0	0
$547$	−2.42221	−0.103566	−0.0517830	−	0.998658i	$-0.516490\pi$
$547$	−2.42221	−0.103566	−0.0517830	+	0.998658i	$0.516490\pi$
$548$	−8.60555	−0.367611
$549$	25.9083	1.10574
$550$	1.00000	0.0426401
$551$	−24.4222	−1.04042
$552$	0.788897	0.0335777
$553$	0	0
$554$	16.9361	0.719545
$555$	−1.81665	−0.0771127
$556$	17.8167	0.755594
$557$	26.8444	1.13743	0.568717	−	0.822533i	$-0.307440\pi$
$557$	26.8444	1.13743	0.568717	+	0.822533i	$0.307440\pi$
$558$	17.4500	0.738716
$559$	−1.18335	−0.0500502
$560$	0	0
$561$	−2.00000	−0.0844401
$562$	17.3305	0.731044
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0.577795	0.0243296
$565$	5.11943	0.215376
$566$	15.6333	0.657117
$567$	0	0
$568$	−14.5139	−0.608989
$569$	33.6333	1.40998	0.704991	−	0.709216i	$-0.250951\pi$
$569$	33.6333	1.40998	0.704991	+	0.709216i	$0.250951\pi$
$570$	−1.60555	−0.0672491
$571$	−21.6333	−0.905326	−0.452663	−	0.891682i	$-0.649526\pi$
$571$	−21.6333	−0.905326	−0.452663	+	0.891682i	$0.649526\pi$
$572$	1.69722	0.0709645
$573$	0.238859	0.00997847
$574$	0	0
$575$	2.60555	0.108659
$576$	−2.90833	−0.121180
$577$	−35.1472	−1.46320	−0.731598	−	0.681736i	$-0.761225\pi$
$577$	−35.1472	−1.46320	−0.731598	+	0.681736i	$0.761225\pi$
$578$	26.6333	1.10780
$579$	−3.44996	−0.143376
$580$	4.60555	0.191235
$581$	0	0
$582$	−4.42221	−0.183306
$583$	5.39445	0.223415
$584$	1.00000	0.0413803
$585$	−4.93608	−0.204082
$586$	−17.2111	−0.710984
$587$	43.2666	1.78580	0.892902	−	0.450251i	$-0.148665\pi$
$587$	43.2666	1.78580	0.892902	+	0.450251i	$0.148665\pi$
$588$	−2.11943	−0.0874038
$589$	31.8167	1.31098
$590$	−2.30278	−0.0948038
$591$	6.39445	0.263032
$592$	−6.00000	−0.246598
$593$	24.6972	1.01419	0.507097	−	0.861889i	$-0.330719\pi$
$593$	24.6972	1.01419	0.507097	+	0.861889i	$0.330719\pi$
$594$	−1.78890	−0.0733994
$595$	0	0
$596$	−17.7250	−0.726044
$597$	−2.55004	−0.104366
$598$	4.42221	0.180837
$599$	18.0000	0.735460	0.367730	−	0.929933i	$-0.380135\pi$
$599$	18.0000	0.735460	0.367730	+	0.929933i	$0.380135\pi$
$600$	0.302776	0.0123608
$601$	17.3305	0.706927	0.353464	−	0.935448i	$-0.385004\pi$
$601$	17.3305	0.706927	0.353464	+	0.935448i	$0.385004\pi$
$602$	0	0
$603$	−25.9083	−1.05507
$604$	9.69722	0.394574
$605$	1.00000	0.0406558
$606$	−0.183346	−0.00744793
$607$	35.5416	1.44259	0.721295	−	0.692628i	$-0.243547\pi$
$607$	35.5416	1.44259	0.721295	+	0.692628i	$0.243547\pi$
$608$	−5.30278	−0.215056
$609$	0	0
$610$	−8.90833	−0.360688
$611$	3.23886	0.131030
$612$	19.2111	0.776563
$613$	43.7527	1.76716	0.883578	−	0.468284i	$-0.155127\pi$
$613$	43.7527	1.76716	0.883578	+	0.468284i	$0.155127\pi$
$614$	−20.5139	−0.827873
$615$	−0.422205	−0.0170250
$616$	0	0
$617$	−4.11943	−0.165842	−0.0829210	−	0.996556i	$-0.526425\pi$
$617$	−4.11943	−0.165842	−0.0829210	+	0.996556i	$0.526425\pi$
$618$	1.21110	0.0487177
$619$	45.2666	1.81942	0.909709	−	0.415245i	$-0.136304\pi$
$619$	45.2666	1.81942	0.909709	+	0.415245i	$0.136304\pi$
$620$	−6.00000	−0.240966
$621$	−4.66106	−0.187042
$622$	−21.5139	−0.862628
$623$	0	0
$624$	0.513878	0.0205716
$625$	1.00000	0.0400000
$626$	−13.3028	−0.531686
$627$	−1.60555	−0.0641195
$628$	−0.788897	−0.0314804
$629$	39.6333	1.58028
$630$	0	0
$631$	12.7889	0.509118	0.254559	−	0.967057i	$-0.418070\pi$
$631$	12.7889	0.509118	0.254559	+	0.967057i	$0.418070\pi$
$632$	−2.00000	−0.0795557
$633$	−2.81665	−0.111952
$634$	24.6972	0.980852
$635$	−4.90833	−0.194781
$636$	1.63331	0.0647649
$637$	−11.8806	−0.470725
$638$	4.60555	0.182336
$639$	42.2111	1.66985
$640$	1.00000	0.0395285
$641$	9.63331	0.380493	0.190246	−	0.981736i	$-0.439071\pi$
$641$	9.63331	0.380493	0.190246	+	0.981736i	$0.439071\pi$
$642$	−3.42221	−0.135064
$643$	6.60555	0.260498	0.130249	−	0.991481i	$-0.458422\pi$
$643$	6.60555	0.260498	0.130249	+	0.991481i	$0.458422\pi$
$644$	0	0
$645$	−0.211103	−0.00831215
$646$	35.0278	1.37815
$647$	0.513878	0.0202026	0.0101013	−	0.999949i	$-0.496785\pi$
$647$	0.513878	0.0202026	0.0101013	+	0.999949i	$0.496785\pi$
$648$	8.18335	0.321472
$649$	−2.30278	−0.0903919
$650$	1.69722	0.0665706
$651$	0	0
$652$	8.42221	0.329839
$653$	−8.30278	−0.324913	−0.162456	−	0.986716i	$-0.551942\pi$
$653$	−8.30278	−0.324913	−0.162456	+	0.986716i	$0.551942\pi$
$654$	5.81665	0.227449
$655$	−16.0000	−0.625172
$656$	−1.39445	−0.0544441
$657$	−2.90833	−0.113465
$658$	0	0
$659$	−11.7250	−0.456740	−0.228370	−	0.973574i	$-0.573340\pi$
$659$	−11.7250	−0.456740	−0.228370	+	0.973574i	$0.573340\pi$
$660$	0.302776	0.0117855
$661$	−6.36669	−0.247636	−0.123818	−	0.992305i	$-0.539514\pi$
$661$	−6.36669	−0.247636	−0.123818	+	0.992305i	$0.539514\pi$
$662$	−34.9083	−1.35675
$663$	−3.39445	−0.131829
$664$	−1.69722	−0.0658651
$665$	0	0
$666$	17.4500	0.676172
$667$	12.0000	0.464642
$668$	−11.2111	−0.433771
$669$	0.550039	0.0212657
$670$	8.90833	0.344159
$671$	−8.90833	−0.343902
$672$	0	0
$673$	−39.3305	−1.51608	−0.758040	−	0.652208i	$-0.773843\pi$
$673$	−39.3305	−1.51608	−0.758040	+	0.652208i	$0.773843\pi$
$674$	13.3944	0.515935
$675$	−1.78890	−0.0688547
$676$	−10.1194	−0.389209
$677$	25.1194	0.965418	0.482709	−	0.875781i	$-0.339653\pi$
$677$	25.1194	0.965418	0.482709	+	0.875781i	$0.339653\pi$
$678$	1.55004	0.0595289
$679$	0	0
$680$	−6.60555	−0.253311
$681$	−2.42221	−0.0928191
$682$	−6.00000	−0.229752
$683$	40.0555	1.53268	0.766341	−	0.642434i	$-0.222075\pi$
$683$	40.0555	1.53268	0.766341	+	0.642434i	$0.222075\pi$
$684$	15.4222	0.589683
$685$	−8.60555	−0.328801
$686$	0	0
$687$	5.23886	0.199875
$688$	−0.697224	−0.0265814
$689$	9.15559	0.348800
$690$	0.788897	0.0300328
$691$	21.3305	0.811452	0.405726	−	0.913995i	$-0.367019\pi$
$691$	21.3305	0.811452	0.405726	+	0.913995i	$0.367019\pi$
$692$	−16.0000	−0.608229
$693$	0	0
$694$	10.1833	0.386555
$695$	17.8167	0.675824
$696$	1.39445	0.0528564
$697$	9.21110	0.348895
$698$	4.69722	0.177793
$699$	−7.02776	−0.265814
$700$	0	0
$701$	1.39445	0.0526676	0.0263338	−	0.999653i	$-0.491617\pi$
$701$	1.39445	0.0526676	0.0263338	+	0.999653i	$0.491617\pi$
$702$	−3.03616	−0.114592
$703$	31.8167	1.19999
$704$	1.00000	0.0376889
$705$	0.577795	0.0217610
$706$	−22.6056	−0.850771
$707$	0	0
$708$	−0.697224	−0.0262033
$709$	35.5139	1.33375	0.666876	−	0.745169i	$-0.267631\pi$
$709$	35.5139	1.33375	0.666876	+	0.745169i	$0.267631\pi$
$710$	−14.5139	−0.544696
$711$	5.81665	0.218142
$712$	−12.9083	−0.483760
$713$	−15.6333	−0.585472
$714$	0	0
$715$	1.69722	0.0634726
$716$	7.30278	0.272918
$717$	4.33053	0.161727
$718$	−1.21110	−0.0451979
$719$	−43.4500	−1.62041	−0.810205	−	0.586147i	$-0.800644\pi$
$719$	−43.4500	−1.62041	−0.810205	+	0.586147i	$0.800644\pi$
$720$	−2.90833	−0.108387
$721$	0	0
$722$	9.11943	0.339390
$723$	−0.238859	−0.00888326
$724$	14.0000	0.520306
$725$	4.60555	0.171046
$726$	0.302776	0.0112371
$727$	26.2389	0.973145	0.486573	−	0.873640i	$-0.338247\pi$
$727$	26.2389	0.973145	0.486573	+	0.873640i	$0.338247\pi$
$728$	0	0
$729$	−22.1749	−0.821294
$730$	1.00000	0.0370117
$731$	4.60555	0.170342
$732$	−2.69722	−0.0996923
$733$	25.0278	0.924421	0.462211	−	0.886770i	$-0.347056\pi$
$733$	25.0278	0.924421	0.462211	+	0.886770i	$0.347056\pi$
$734$	−4.60555	−0.169994
$735$	−2.11943	−0.0781763
$736$	2.60555	0.0960419
$737$	8.90833	0.328142
$738$	4.05551	0.149285
$739$	12.8444	0.472489	0.236245	−	0.971694i	$-0.424083\pi$
$739$	12.8444	0.472489	0.236245	+	0.971694i	$0.424083\pi$
$740$	−6.00000	−0.220564
$741$	−2.72498	−0.100105
$742$	0	0
$743$	−14.6056	−0.535826	−0.267913	−	0.963443i	$-0.586334\pi$
$743$	−14.6056	−0.535826	−0.267913	+	0.963443i	$0.586334\pi$
$744$	−1.81665	−0.0666018
$745$	−17.7250	−0.649393
$746$	19.8167	0.725539
$747$	4.93608	0.180602
$748$	−6.60555	−0.241523
$749$	0	0
$750$	0.302776	0.0110558
$751$	−26.4222	−0.964160	−0.482080	−	0.876127i	$-0.660119\pi$
$751$	−26.4222	−0.964160	−0.482080	+	0.876127i	$0.660119\pi$
$752$	1.90833	0.0695895
$753$	−5.39445	−0.196585
$754$	7.81665	0.284666
$755$	9.69722	0.352918
$756$	0	0
$757$	−32.1472	−1.16841	−0.584205	−	0.811606i	$-0.698593\pi$
$757$	−32.1472	−1.16841	−0.584205	+	0.811606i	$0.698593\pi$
$758$	−15.1194	−0.549162
$759$	0.788897	0.0286352
$760$	−5.30278	−0.192352
$761$	27.3583	0.991737	0.495869	−	0.868398i	$-0.334850\pi$
$761$	27.3583	0.991737	0.495869	+	0.868398i	$0.334850\pi$
$762$	−1.48612	−0.0538365
$763$	0	0
$764$	0.788897	0.0285413
$765$	19.2111	0.694579
$766$	19.3944	0.700750
$767$	−3.90833	−0.141122
$768$	0.302776	0.0109255
$769$	−12.0917	−0.436037	−0.218018	−	0.975945i	$-0.569959\pi$
$769$	−12.0917	−0.436037	−0.218018	+	0.975945i	$0.569959\pi$
$770$	0	0
$771$	0.661064	0.0238076
$772$	−11.3944	−0.410095
$773$	−25.2111	−0.906780	−0.453390	−	0.891312i	$-0.649786\pi$
$773$	−25.2111	−0.906780	−0.453390	+	0.891312i	$0.649786\pi$
$774$	2.02776	0.0728862
$775$	−6.00000	−0.215526
$776$	−14.6056	−0.524309
$777$	0	0
$778$	−9.63331	−0.345371
$779$	7.39445	0.264934
$780$	0.513878	0.0183998
$781$	−14.5139	−0.519347
$782$	−17.2111	−0.615468
$783$	−8.23886	−0.294433
$784$	−7.00000	−0.250000
$785$	−0.788897	−0.0281570
$786$	−4.84441	−0.172794
$787$	−5.63331	−0.200806	−0.100403	−	0.994947i	$-0.532013\pi$
$787$	−5.63331	−0.200806	−0.100403	+	0.994947i	$0.532013\pi$
$788$	21.1194	0.752349
$789$	9.39445	0.334451
$790$	−2.00000	−0.0711568
$791$	0	0
$792$	−2.90833	−0.103343
$793$	−15.1194	−0.536907
$794$	−33.5416	−1.19035
$795$	1.63331	0.0579275
$796$	−8.42221	−0.298517
$797$	36.9083	1.30736	0.653680	−	0.756771i	$-0.273224\pi$
$797$	36.9083	1.30736	0.653680	+	0.756771i	$0.273224\pi$
$798$	0	0
$799$	−12.6056	−0.445952
$800$	1.00000	0.0353553
$801$	37.5416	1.32647
$802$	−15.3305	−0.541340
$803$	1.00000	0.0352892
$804$	2.69722	0.0951238
$805$	0	0
$806$	−10.1833	−0.358693
$807$	6.97224	0.245435
$808$	−0.605551	−0.0213032
$809$	−21.3944	−0.752189	−0.376094	−	0.926581i	$-0.622733\pi$
$809$	−21.3944	−0.752189	−0.376094	+	0.926581i	$0.622733\pi$
$810$	8.18335	0.287533
$811$	−39.2666	−1.37884	−0.689419	−	0.724363i	$-0.742134\pi$
$811$	−39.2666	−1.37884	−0.689419	+	0.724363i	$0.742134\pi$
$812$	0	0
$813$	−4.03616	−0.141554
$814$	−6.00000	−0.210300
$815$	8.42221	0.295017
$816$	−2.00000	−0.0700140
$817$	3.69722	0.129350
$818$	−9.30278	−0.325264
$819$	0	0
$820$	−1.39445	−0.0486963
$821$	−8.33053	−0.290738	−0.145369	−	0.989378i	$-0.546437\pi$
$821$	−8.33053	−0.290738	−0.145369	+	0.989378i	$0.546437\pi$
$822$	−2.60555	−0.0908790
$823$	−0.330532	−0.0115216	−0.00576081	−	0.999983i	$-0.501834\pi$
$823$	−0.330532	−0.0115216	−0.00576081	+	0.999983i	$0.501834\pi$
$824$	4.00000	0.139347
$825$	0.302776	0.0105413
$826$	0	0
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	−7.57779	−0.263347
$829$	20.4222	0.709293	0.354646	−	0.935001i	$-0.384601\pi$
$829$	20.4222	0.709293	0.354646	+	0.935001i	$0.384601\pi$
$830$	−1.69722	−0.0589115
$831$	5.12783	0.177883
$832$	1.69722	0.0588407
$833$	46.2389	1.60208
$834$	5.39445	0.186794
$835$	−11.2111	−0.387976
$836$	−5.30278	−0.183400
$837$	10.7334	0.371000
$838$	−6.00000	−0.207267
$839$	−7.69722	−0.265738	−0.132869	−	0.991134i	$-0.542419\pi$
$839$	−7.69722	−0.265738	−0.132869	+	0.991134i	$0.542419\pi$
$840$	0	0
$841$	−7.78890	−0.268583
$842$	26.9083	0.927322
$843$	5.24726	0.180725
$844$	−9.30278	−0.320215
$845$	−10.1194	−0.348119
$846$	−5.55004	−0.190814
$847$	0	0
$848$	5.39445	0.185246
$849$	4.73338	0.162449
$850$	−6.60555	−0.226569
$851$	−15.6333	−0.535903
$852$	−4.39445	−0.150551
$853$	−3.02776	−0.103668	−0.0518342	−	0.998656i	$-0.516507\pi$
$853$	−3.02776	−0.103668	−0.0518342	+	0.998656i	$0.516507\pi$
$854$	0	0
$855$	15.4222	0.527428
$856$	−11.3028	−0.386321
$857$	44.5139	1.52057	0.760283	−	0.649593i	$-0.225060\pi$
$857$	44.5139	1.52057	0.760283	+	0.649593i	$0.225060\pi$
$858$	0.513878	0.0175435
$859$	−38.5694	−1.31597	−0.657985	−	0.753031i	$-0.728591\pi$
$859$	−38.5694	−1.31597	−0.657985	+	0.753031i	$0.728591\pi$
$860$	−0.697224	−0.0237752
$861$	0	0
$862$	34.9083	1.18898
$863$	−41.5694	−1.41504	−0.707519	−	0.706694i	$-0.750186\pi$
$863$	−41.5694	−1.41504	−0.707519	+	0.706694i	$0.750186\pi$
$864$	−1.78890	−0.0608595
$865$	−16.0000	−0.544016
$866$	−27.7250	−0.942133
$867$	8.06392	0.273865
$868$	0	0
$869$	−2.00000	−0.0678454
$870$	1.39445	0.0472762
$871$	15.1194	0.512302
$872$	19.2111	0.650570
$873$	42.4777	1.43765
$874$	−13.8167	−0.467355
$875$	0	0
$876$	0.302776	0.0102298
$877$	39.0278	1.31787	0.658937	−	0.752198i	$-0.271006\pi$
$877$	39.0278	1.31787	0.658937	+	0.752198i	$0.271006\pi$
$878$	18.4222	0.621719
$879$	−5.21110	−0.175766
$880$	1.00000	0.0337100
$881$	30.4222	1.02495	0.512475	−	0.858702i	$-0.328729\pi$
$881$	30.4222	1.02495	0.512475	+	0.858702i	$0.328729\pi$
$882$	20.3583	0.685499
$883$	−10.9722	−0.369245	−0.184623	−	0.982809i	$-0.559106\pi$
$883$	−10.9722	−0.369245	−0.184623	+	0.982809i	$0.559106\pi$
$884$	−11.2111	−0.377070
$885$	−0.697224	−0.0234369
$886$	15.2111	0.511027
$887$	−29.8167	−1.00115	−0.500573	−	0.865695i	$-0.666877\pi$
$887$	−29.8167	−1.00115	−0.500573	+	0.865695i	$0.666877\pi$
$888$	−1.81665	−0.0609629
$889$	0	0
$890$	−12.9083	−0.432688
$891$	8.18335	0.274152
$892$	1.81665	0.0608261
$893$	−10.1194	−0.338634
$894$	−5.36669	−0.179489
$895$	7.30278	0.244105
$896$	0	0
$897$	1.33894	0.0447058
$898$	−33.6333	−1.12236
$899$	−27.6333	−0.921622
$900$	−2.90833	−0.0969442
$901$	−35.6333	−1.18712
$902$	−1.39445	−0.0464301
$903$	0	0
$904$	5.11943	0.170270
$905$	14.0000	0.465376
$906$	2.93608	0.0975448
$907$	−26.8444	−0.891354	−0.445677	−	0.895194i	$-0.647037\pi$
$907$	−26.8444	−0.891354	−0.445677	+	0.895194i	$0.647037\pi$
$908$	−8.00000	−0.265489
$909$	1.76114	0.0584134
$910$	0	0
$911$	−6.51388	−0.215814	−0.107907	−	0.994161i	$-0.534415\pi$
$911$	−6.51388	−0.215814	−0.107907	+	0.994161i	$0.534415\pi$
$912$	−1.60555	−0.0531651
$913$	−1.69722	−0.0561699
$914$	7.30278	0.241554
$915$	−2.69722	−0.0891675
$916$	17.3028	0.571700
$917$	0	0
$918$	11.8167	0.390008
$919$	51.9638	1.71413	0.857064	−	0.515209i	$-0.172286\pi$
$919$	51.9638	1.71413	0.857064	+	0.515209i	$0.172286\pi$
$920$	2.60555	0.0859025
$921$	−6.21110	−0.204663
$922$	10.9361	0.360161
$923$	−24.6333	−0.810815
$924$	0	0
$925$	−6.00000	−0.197279
$926$	−8.78890	−0.288821
$927$	−11.6333	−0.382088
$928$	4.60555	0.151185
$929$	−7.39445	−0.242604	−0.121302	−	0.992616i	$-0.538707\pi$
$929$	−7.39445	−0.242604	−0.121302	+	0.992616i	$0.538707\pi$
$930$	−1.81665	−0.0595704
$931$	37.1194	1.21654
$932$	−23.2111	−0.760305
$933$	−6.51388	−0.213255
$934$	13.2111	0.432280
$935$	−6.60555	−0.216025
$936$	−4.93608	−0.161341
$937$	−45.7250	−1.49377	−0.746885	−	0.664953i	$-0.768451\pi$
$937$	−45.7250	−1.49377	−0.746885	+	0.664953i	$0.768451\pi$
$938$	0	0
$939$	−4.02776	−0.131441
$940$	1.90833	0.0622428
$941$	−18.4861	−0.602630	−0.301315	−	0.953525i	$-0.597426\pi$
$941$	−18.4861	−0.602630	−0.301315	+	0.953525i	$0.597426\pi$
$942$	−0.238859	−0.00778244
$943$	−3.63331	−0.118317
$944$	−2.30278	−0.0749490
$945$	0	0
$946$	−0.697224	−0.0226687
$947$	−31.6972	−1.03002	−0.515011	−	0.857184i	$-0.672212\pi$
$947$	−31.6972	−1.03002	−0.515011	+	0.857184i	$0.672212\pi$
$948$	−0.605551	−0.0196674
$949$	1.69722	0.0550942
$950$	−5.30278	−0.172045
$951$	7.47772	0.242482
$952$	0	0
$953$	−50.9638	−1.65088	−0.825440	−	0.564489i	$-0.809073\pi$
$953$	−50.9638	−1.65088	−0.825440	+	0.564489i	$0.809073\pi$
$954$	−15.6888	−0.507944
$955$	0.788897	0.0255281
$956$	14.3028	0.462585
$957$	1.39445	0.0450761
$958$	−13.8167	−0.446396
$959$	0	0
$960$	0.302776	0.00977204
$961$	5.00000	0.161290
$962$	−10.1833	−0.328324
$963$	32.8722	1.05929
$964$	−0.788897	−0.0254087
$965$	−11.3944	−0.366800
$966$	0	0
$967$	−43.6972	−1.40521	−0.702604	−	0.711581i	$-0.747979\pi$
$967$	−43.6972	−1.40521	−0.702604	+	0.711581i	$0.747979\pi$
$968$	1.00000	0.0321412
$969$	10.6056	0.340699
$970$	−14.6056	−0.468956
$971$	−4.69722	−0.150741	−0.0753706	−	0.997156i	$-0.524014\pi$
$971$	−4.69722	−0.150741	−0.0753706	+	0.997156i	$0.524014\pi$
$972$	7.84441	0.251610
$973$	0	0
$974$	13.8167	0.442714
$975$	0.513878	0.0164573
$976$	−8.90833	−0.285149
$977$	−19.1472	−0.612573	−0.306286	−	0.951939i	$-0.599087\pi$
$977$	−19.1472	−0.612573	−0.306286	+	0.951939i	$0.599087\pi$
$978$	2.55004	0.0815412
$979$	−12.9083	−0.412552
$980$	−7.00000	−0.223607
$981$	−55.8722	−1.78386
$982$	20.8444	0.665172
$983$	−54.7527	−1.74634	−0.873171	−	0.487415i	$-0.837940\pi$
$983$	−54.7527	−1.74634	−0.873171	+	0.487415i	$0.837940\pi$
$984$	−0.422205	−0.0134594
$985$	21.1194	0.672921
$986$	−30.4222	−0.968840
$987$	0	0
$988$	−9.00000	−0.286328
$989$	−1.81665	−0.0577662
$990$	−2.90833	−0.0924327
$991$	32.1833	1.02234	0.511169	−	0.859480i	$-0.329213\pi$
$991$	32.1833	1.02234	0.511169	+	0.859480i	$0.329213\pi$
$992$	−6.00000	−0.190500
$993$	−10.5694	−0.335409
$994$	0	0
$995$	−8.42221	−0.267002
$996$	−0.513878	−0.0162829
$997$	23.5778	0.746716	0.373358	−	0.927687i	$-0.378206\pi$
$997$	23.5778	0.746716	0.373358	+	0.927687i	$0.378206\pi$
$998$	−24.6056	−0.778875
$999$	10.7334	0.339589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.n.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.n.1.2	✓	2	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.302776 q^{6} +1.00000 q^{8} -2.90833 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.302776 q^{6} +1.00000 q^{8} -2.90833 q^{9} +1.00000 q^{10} +1.00000 q^{11} +0.302776 q^{12} +1.69722 q^{13} +0.302776 q^{15} +1.00000 q^{16} -6.60555 q^{17} -2.90833 q^{18} -5.30278 q^{19} +1.00000 q^{20} +1.00000 q^{22} +2.60555 q^{23} +0.302776 q^{24} +1.00000 q^{25} +1.69722 q^{26} -1.78890 q^{27} +4.60555 q^{29} +0.302776 q^{30} -6.00000 q^{31} +1.00000 q^{32} +0.302776 q^{33} -6.60555 q^{34} -2.90833 q^{36} -6.00000 q^{37} -5.30278 q^{38} +0.513878 q^{39} +1.00000 q^{40} -1.39445 q^{41} -0.697224 q^{43} +1.00000 q^{44} -2.90833 q^{45} +2.60555 q^{46} +1.90833 q^{47} +0.302776 q^{48} -7.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} +1.69722 q^{52} +5.39445 q^{53} -1.78890 q^{54} +1.00000 q^{55} -1.60555 q^{57} +4.60555 q^{58} -2.30278 q^{59} +0.302776 q^{60} -8.90833 q^{61} -6.00000 q^{62} +1.00000 q^{64} +1.69722 q^{65} +0.302776 q^{66} +8.90833 q^{67} -6.60555 q^{68} +0.788897 q^{69} -14.5139 q^{71} -2.90833 q^{72} +1.00000 q^{73} -6.00000 q^{74} +0.302776 q^{75} -5.30278 q^{76} +0.513878 q^{78} -2.00000 q^{79} +1.00000 q^{80} +8.18335 q^{81} -1.39445 q^{82} -1.69722 q^{83} -6.60555 q^{85} -0.697224 q^{86} +1.39445 q^{87} +1.00000 q^{88} -12.9083 q^{89} -2.90833 q^{90} +2.60555 q^{92} -1.81665 q^{93} +1.90833 q^{94} -5.30278 q^{95} +0.302776 q^{96} -14.6056 q^{97} -7.00000 q^{98} -2.90833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} + 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 + 2 * q^8 + 5 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} + 2 q^{8} + 5 q^{9} + 2 q^{10} + 2 q^{11} - 3 q^{12} + 7 q^{13} - 3 q^{15} + 2 q^{16} - 6 q^{17} + 5 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{22} - 2 q^{23} - 3 q^{24} + 2 q^{25} + 7 q^{26} - 18 q^{27} + 2 q^{29} - 3 q^{30} - 12 q^{31} + 2 q^{32} - 3 q^{33} - 6 q^{34} + 5 q^{36} - 12 q^{37} - 7 q^{38} - 17 q^{39} + 2 q^{40} - 10 q^{41} - 5 q^{43} + 2 q^{44} + 5 q^{45} - 2 q^{46} - 7 q^{47} - 3 q^{48} - 14 q^{49} + 2 q^{50} - 4 q^{51} + 7 q^{52} + 18 q^{53} - 18 q^{54} + 2 q^{55} + 4 q^{57} + 2 q^{58} - q^{59} - 3 q^{60} - 7 q^{61} - 12 q^{62} + 2 q^{64} + 7 q^{65} - 3 q^{66} + 7 q^{67} - 6 q^{68} + 16 q^{69} - 11 q^{71} + 5 q^{72} + 2 q^{73} - 12 q^{74} - 3 q^{75} - 7 q^{76} - 17 q^{78} - 4 q^{79} + 2 q^{80} + 38 q^{81} - 10 q^{82} - 7 q^{83} - 6 q^{85} - 5 q^{86} + 10 q^{87} + 2 q^{88} - 15 q^{89} + 5 q^{90} - 2 q^{92} + 18 q^{93} - 7 q^{94} - 7 q^{95} - 3 q^{96} - 22 q^{97} - 14 q^{98} + 5 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 + 2 * q^8 + 5 * q^9 + 2 * q^10 + 2 * q^11 - 3 * q^12 + 7 * q^13 - 3 * q^15 + 2 * q^16 - 6 * q^17 + 5 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^22 - 2 * q^23 - 3 * q^24 + 2 * q^25 + 7 * q^26 - 18 * q^27 + 2 * q^29 - 3 * q^30 - 12 * q^31 + 2 * q^32 - 3 * q^33 - 6 * q^34 + 5 * q^36 - 12 * q^37 - 7 * q^38 - 17 * q^39 + 2 * q^40 - 10 * q^41 - 5 * q^43 + 2 * q^44 + 5 * q^45 - 2 * q^46 - 7 * q^47 - 3 * q^48 - 14 * q^49 + 2 * q^50 - 4 * q^51 + 7 * q^52 + 18 * q^53 - 18 * q^54 + 2 * q^55 + 4 * q^57 + 2 * q^58 - q^59 - 3 * q^60 - 7 * q^61 - 12 * q^62 + 2 * q^64 + 7 * q^65 - 3 * q^66 + 7 * q^67 - 6 * q^68 + 16 * q^69 - 11 * q^71 + 5 * q^72 + 2 * q^73 - 12 * q^74 - 3 * q^75 - 7 * q^76 - 17 * q^78 - 4 * q^79 + 2 * q^80 + 38 * q^81 - 10 * q^82 - 7 * q^83 - 6 * q^85 - 5 * q^86 + 10 * q^87 + 2 * q^88 - 15 * q^89 + 5 * q^90 - 2 * q^92 + 18 * q^93 - 7 * q^94 - 7 * q^95 - 3 * q^96 - 22 * q^97 - 14 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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