LMFDB - Embedded newform 3525.2.a.bb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.6
Root			$1.49858$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.49858 q^{2} -1.00000 q^{3} +0.245756 q^{4} -1.49858 q^{6} +3.73400 q^{7} -2.62888 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.49858 q^{2} -1.00000 q^{3} +0.245756 q^{4} -1.49858 q^{6} +3.73400 q^{7} -2.62888 q^{8} +1.00000 q^{9} +4.52560 q^{11} -0.245756 q^{12} +6.66056 q^{13} +5.59572 q^{14} -4.43112 q^{16} +1.58935 q^{17} +1.49858 q^{18} -0.710075 q^{19} -3.73400 q^{21} +6.78199 q^{22} -8.96967 q^{23} +2.62888 q^{24} +9.98141 q^{26} -1.00000 q^{27} +0.917652 q^{28} +1.28529 q^{29} +6.01924 q^{31} -1.38263 q^{32} -4.52560 q^{33} +2.38177 q^{34} +0.245756 q^{36} +4.78781 q^{37} -1.06411 q^{38} -6.66056 q^{39} -7.22641 q^{41} -5.59572 q^{42} -4.67156 q^{43} +1.11219 q^{44} -13.4418 q^{46} -1.00000 q^{47} +4.43112 q^{48} +6.94276 q^{49} -1.58935 q^{51} +1.63687 q^{52} -2.17609 q^{53} -1.49858 q^{54} -9.81625 q^{56} +0.710075 q^{57} +1.92612 q^{58} +4.30262 q^{59} -14.0308 q^{61} +9.02033 q^{62} +3.73400 q^{63} +6.79024 q^{64} -6.78199 q^{66} +11.3846 q^{67} +0.390591 q^{68} +8.96967 q^{69} +13.9921 q^{71} -2.62888 q^{72} +9.91426 q^{73} +7.17493 q^{74} -0.174505 q^{76} +16.8986 q^{77} -9.98141 q^{78} +3.46097 q^{79} +1.00000 q^{81} -10.8294 q^{82} +7.73421 q^{83} -0.917652 q^{84} -7.00073 q^{86} -1.28529 q^{87} -11.8973 q^{88} -9.77201 q^{89} +24.8705 q^{91} -2.20435 q^{92} -6.01924 q^{93} -1.49858 q^{94} +1.38263 q^{96} +7.66774 q^{97} +10.4043 q^{98} +4.52560 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9} - 8 q^{11} - 5 q^{12} + 5 q^{13} - 3 q^{14} + 9 q^{16} + 10 q^{17} + q^{18} + 7 q^{19} - 11 q^{21} + 20 q^{22} + 4 q^{23} - 6 q^{24} - 7 q^{27} + 2 q^{28} - 11 q^{29} + 3 q^{31} + 28 q^{32} + 8 q^{33} + 8 q^{34} + 5 q^{36} + 11 q^{37} - 2 q^{38} - 5 q^{39} - 20 q^{41} + 3 q^{42} + 18 q^{43} + q^{44} - 19 q^{46} - 7 q^{47} - 9 q^{48} + 14 q^{49} - 10 q^{51} + 29 q^{52} + 12 q^{53} - q^{54} - 47 q^{56} - 7 q^{57} - 19 q^{58} + 18 q^{59} - 4 q^{61} + 12 q^{62} + 11 q^{63} + 42 q^{64} - 20 q^{66} + 22 q^{67} + 44 q^{68} - 4 q^{69} - 14 q^{71} + 6 q^{72} + 30 q^{73} + 31 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} + 7 q^{81} + 29 q^{82} + 54 q^{83} - 2 q^{84} - 29 q^{86} + 11 q^{87} - 22 q^{88} - 14 q^{89} + 20 q^{91} - 5 q^{92} - 3 q^{93} - q^{94} - 28 q^{96} + 24 q^{97} - 26 q^{98} - 8 q^{99}+O(q^{100}) $ 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9 - 8 * q^11 - 5 * q^12 + 5 * q^13 - 3 * q^14 + 9 * q^16 + 10 * q^17 + q^18 + 7 * q^19 - 11 * q^21 + 20 * q^22 + 4 * q^23 - 6 * q^24 - 7 * q^27 + 2 * q^28 - 11 * q^29 + 3 * q^31 + 28 * q^32 + 8 * q^33 + 8 * q^34 + 5 * q^36 + 11 * q^37 - 2 * q^38 - 5 * q^39 - 20 * q^41 + 3 * q^42 + 18 * q^43 + q^44 - 19 * q^46 - 7 * q^47 - 9 * q^48 + 14 * q^49 - 10 * q^51 + 29 * q^52 + 12 * q^53 - q^54 - 47 * q^56 - 7 * q^57 - 19 * q^58 + 18 * q^59 - 4 * q^61 + 12 * q^62 + 11 * q^63 + 42 * q^64 - 20 * q^66 + 22 * q^67 + 44 * q^68 - 4 * q^69 - 14 * q^71 + 6 * q^72 + 30 * q^73 + 31 * q^74 - 2 * q^76 - 8 * q^77 - q^79 + 7 * q^81 + 29 * q^82 + 54 * q^83 - 2 * q^84 - 29 * q^86 + 11 * q^87 - 22 * q^88 - 14 * q^89 + 20 * q^91 - 5 * q^92 - 3 * q^93 - q^94 - 28 * q^96 + 24 * q^97 - 26 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.49858	1.05966	0.529830	−	0.848104i	$-0.322256\pi$
$2$	1.49858	1.05966	0.529830	+	0.848104i	$0.322256\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.245756	0.122878
$5$	0	0
$5$	0	0
$6$	−1.49858	−0.611795
$7$	3.73400	1.41132	0.705660	−	0.708551i	$-0.250651\pi$
$7$	3.73400	1.41132	0.705660	+	0.708551i	$0.250651\pi$
$8$	−2.62888	−0.929451
$9$	1.00000	0.333333
$10$	0	0
$11$	4.52560	1.36452	0.682259	−	0.731110i	$-0.260998\pi$
$11$	4.52560	1.36452	0.682259	+	0.731110i	$0.260998\pi$
$12$	−0.245756	−0.0709435
$13$	6.66056	1.84731	0.923653	−	0.383230i	$-0.125188\pi$
$13$	6.66056	1.84731	0.923653	+	0.383230i	$0.125188\pi$
$14$	5.59572	1.49552
$15$	0	0
$16$	−4.43112	−1.10778
$17$	1.58935	0.385473	0.192737	−	0.981251i	$-0.438264\pi$
$17$	1.58935	0.385473	0.192737	+	0.981251i	$0.438264\pi$
$18$	1.49858	0.353220
$19$	−0.710075	−0.162902	−0.0814512	−	0.996677i	$-0.525955\pi$
$19$	−0.710075	−0.162902	−0.0814512	+	0.996677i	$0.525955\pi$
$20$	0	0
$21$	−3.73400	−0.814826
$22$	6.78199	1.44592
$23$	−8.96967	−1.87031	−0.935153	−	0.354244i	$-0.884738\pi$
$23$	−8.96967	−1.87031	−0.935153	+	0.354244i	$0.884738\pi$
$24$	2.62888	0.536619
$25$	0	0
$26$	9.98141	1.95751
$27$	−1.00000	−0.192450
$28$	0.917652	0.173420
$29$	1.28529	0.238673	0.119336	−	0.992854i	$-0.461923\pi$
$29$	1.28529	0.238673	0.119336	+	0.992854i	$0.461923\pi$
$30$	0	0
$31$	6.01924	1.08109	0.540543	−	0.841316i	$-0.318219\pi$
$31$	6.01924	1.08109	0.540543	+	0.841316i	$0.318219\pi$
$32$	−1.38263	−0.244417
$33$	−4.52560	−0.787805
$34$	2.38177	0.408470
$35$	0	0
$36$	0.245756	0.0409593
$37$	4.78781	0.787111	0.393555	−	0.919301i	$-0.371245\pi$
$37$	4.78781	0.787111	0.393555	+	0.919301i	$0.371245\pi$
$38$	−1.06411	−0.172621
$39$	−6.66056	−1.06654
$40$	0	0
$41$	−7.22641	−1.12858	−0.564288	−	0.825578i	$-0.690849\pi$
$41$	−7.22641	−1.12858	−0.564288	+	0.825578i	$0.690849\pi$
$42$	−5.59572	−0.863438
$43$	−4.67156	−0.712406	−0.356203	−	0.934409i	$-0.615929\pi$
$43$	−4.67156	−0.712406	−0.356203	+	0.934409i	$0.615929\pi$
$44$	1.11219	0.167669
$45$	0	0
$46$	−13.4418	−1.98189
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	4.43112	0.639576
$49$	6.94276	0.991823
$50$	0	0
$51$	−1.58935	−0.222553
$52$	1.63687	0.226993
$53$	−2.17609	−0.298909	−0.149454	−	0.988769i	$-0.547752\pi$
$53$	−2.17609	−0.298909	−0.149454	+	0.988769i	$0.547752\pi$
$54$	−1.49858	−0.203932
$55$	0	0
$56$	−9.81625	−1.31175
$57$	0.710075	0.0940518
$58$	1.92612	0.252912
$59$	4.30262	0.560153	0.280077	−	0.959978i	$-0.409640\pi$
$59$	4.30262	0.560153	0.280077	+	0.959978i	$0.409640\pi$
$60$	0	0
$61$	−14.0308	−1.79646	−0.898229	−	0.439527i	$-0.855146\pi$
$61$	−14.0308	−1.79646	−0.898229	+	0.439527i	$0.855146\pi$
$62$	9.02033	1.14558
$63$	3.73400	0.470440
$64$	6.79024	0.848780
$65$	0	0
$66$	−6.78199	−0.834805
$67$	11.3846	1.39085	0.695426	−	0.718598i	$-0.255216\pi$
$67$	11.3846	1.39085	0.695426	+	0.718598i	$0.255216\pi$
$68$	0.390591	0.0473661
$69$	8.96967	1.07982
$70$	0	0
$71$	13.9921	1.66055	0.830276	−	0.557352i	$-0.188183\pi$
$71$	13.9921	1.66055	0.830276	+	0.557352i	$0.188183\pi$
$72$	−2.62888	−0.309817
$73$	9.91426	1.16038	0.580188	−	0.814483i	$-0.302979\pi$
$73$	9.91426	1.16038	0.580188	+	0.814483i	$0.302979\pi$
$74$	7.17493	0.834069
$75$	0	0
$76$	−0.174505	−0.0200171
$77$	16.8986	1.92577
$78$	−9.98141	−1.13017
$79$	3.46097	0.389389	0.194695	−	0.980864i	$-0.437628\pi$
$79$	3.46097	0.389389	0.194695	+	0.980864i	$0.437628\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−10.8294	−1.19591
$83$	7.73421	0.848940	0.424470	−	0.905442i	$-0.360460\pi$
$83$	7.73421	0.848940	0.424470	+	0.905442i	$0.360460\pi$
$84$	−0.917652	−0.100124
$85$	0	0
$86$	−7.00073	−0.754908
$87$	−1.28529	−0.137798
$88$	−11.8973	−1.26825
$89$	−9.77201	−1.03583	−0.517916	−	0.855432i	$-0.673292\pi$
$89$	−9.77201	−1.03583	−0.517916	+	0.855432i	$0.673292\pi$
$90$	0	0
$91$	24.8705	2.60714
$92$	−2.20435	−0.229819
$93$	−6.01924	−0.624166
$94$	−1.49858	−0.154567
$95$	0	0
$96$	1.38263	0.141115
$97$	7.66774	0.778541	0.389271	−	0.921123i	$-0.372727\pi$
$97$	7.66774	0.778541	0.389271	+	0.921123i	$0.372727\pi$
$98$	10.4043	1.05099
$99$	4.52560	0.454840
$100$	0	0
$101$	0.418788	0.0416710	0.0208355	−	0.999783i	$-0.493367\pi$
$101$	0.418788	0.0416710	0.0208355	+	0.999783i	$0.493367\pi$
$102$	−2.38177	−0.235830
$103$	−0.411656	−0.0405617	−0.0202808	−	0.999794i	$-0.506456\pi$
$103$	−0.411656	−0.0405617	−0.0202808	+	0.999794i	$0.506456\pi$
$104$	−17.5098	−1.71698
$105$	0	0
$106$	−3.26105	−0.316742
$107$	−4.03751	−0.390321	−0.195160	−	0.980771i	$-0.562523\pi$
$107$	−4.03751	−0.390321	−0.195160	+	0.980771i	$0.562523\pi$
$108$	−0.245756	−0.0236478
$109$	10.4742	1.00325	0.501625	−	0.865085i	$-0.332736\pi$
$109$	10.4742	1.00325	0.501625	+	0.865085i	$0.332736\pi$
$110$	0	0
$111$	−4.78781	−0.454438
$112$	−16.5458	−1.56343
$113$	−5.55641	−0.522703	−0.261352	−	0.965244i	$-0.584168\pi$
$113$	−5.55641	−0.522703	−0.261352	+	0.965244i	$0.584168\pi$
$114$	1.06411	0.0996628
$115$	0	0
$116$	0.315868	0.0293276
$117$	6.66056	0.615769
$118$	6.44784	0.593571
$119$	5.93462	0.544026
$120$	0	0
$121$	9.48102	0.861911
$122$	−21.0263	−1.90363
$123$	7.22641	0.651584
$124$	1.47926	0.132842
$125$	0	0
$126$	5.59572	0.498506
$127$	0.519263	0.0460771	0.0230385	−	0.999735i	$-0.492666\pi$
$127$	0.519263	0.0460771	0.0230385	+	0.999735i	$0.492666\pi$
$128$	12.9410	1.14383
$129$	4.67156	0.411308
$130$	0	0
$131$	−10.7961	−0.943258	−0.471629	−	0.881797i	$-0.656334\pi$
$131$	−10.7961	−0.943258	−0.471629	+	0.881797i	$0.656334\pi$
$132$	−1.11219	−0.0968038
$133$	−2.65142	−0.229907
$134$	17.0608	1.47383
$135$	0	0
$136$	−4.17821	−0.358278
$137$	14.3741	1.22806	0.614030	−	0.789283i	$-0.289547\pi$
$137$	14.3741	1.22806	0.614030	+	0.789283i	$0.289547\pi$
$138$	13.4418	1.14424
$139$	−13.4196	−1.13824	−0.569118	−	0.822256i	$-0.692715\pi$
$139$	−13.4196	−1.13824	−0.569118	+	0.822256i	$0.692715\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	20.9683	1.75962
$143$	30.1430	2.52068
$144$	−4.43112	−0.369260
$145$	0	0
$146$	14.8574	1.22960
$147$	−6.94276	−0.572630
$148$	1.17663	0.0967184
$149$	−16.3399	−1.33861	−0.669307	−	0.742986i	$-0.733409\pi$
$149$	−16.3399	−1.33861	−0.669307	+	0.742986i	$0.733409\pi$
$150$	0	0
$151$	16.7585	1.36378	0.681892	−	0.731453i	$-0.261158\pi$
$151$	16.7585	1.36378	0.681892	+	0.731453i	$0.261158\pi$
$152$	1.86670	0.151410
$153$	1.58935	0.128491
$154$	25.3240	2.04066
$155$	0	0
$156$	−1.63687	−0.131054
$157$	−8.15798	−0.651078	−0.325539	−	0.945529i	$-0.605546\pi$
$157$	−8.15798	−0.651078	−0.325539	+	0.945529i	$0.605546\pi$
$158$	5.18655	0.412620
$159$	2.17609	0.172575
$160$	0	0
$161$	−33.4928	−2.63960
$162$	1.49858	0.117740
$163$	8.27115	0.647846	0.323923	−	0.946083i	$-0.394998\pi$
$163$	8.27115	0.647846	0.323923	+	0.946083i	$0.394998\pi$
$164$	−1.77593	−0.138677
$165$	0	0
$166$	11.5904	0.899587
$167$	−1.59173	−0.123172	−0.0615858	−	0.998102i	$-0.519616\pi$
$167$	−1.59173	−0.123172	−0.0615858	+	0.998102i	$0.519616\pi$
$168$	9.81625	0.757340
$169$	31.3630	2.41254
$170$	0	0
$171$	−0.710075	−0.0543008
$172$	−1.14806	−0.0875389
$173$	22.2782	1.69378	0.846889	−	0.531770i	$-0.178473\pi$
$173$	22.2782	1.69378	0.846889	+	0.531770i	$0.178473\pi$
$174$	−1.92612	−0.146019
$175$	0	0
$176$	−20.0534	−1.51158
$177$	−4.30262	−0.323405
$178$	−14.6442	−1.09763
$179$	−16.3905	−1.22509	−0.612543	−	0.790437i	$-0.709853\pi$
$179$	−16.3905	−1.22509	−0.612543	+	0.790437i	$0.709853\pi$
$180$	0	0
$181$	−3.32595	−0.247216	−0.123608	−	0.992331i	$-0.539446\pi$
$181$	−3.32595	−0.247216	−0.123608	+	0.992331i	$0.539446\pi$
$182$	37.2706	2.76268
$183$	14.0308	1.03719
$184$	23.5802	1.73836
$185$	0	0
$186$	−9.02033	−0.661403
$187$	7.19274	0.525985
$188$	−0.245756	−0.0179236
$189$	−3.73400	−0.271609
$190$	0	0
$191$	0.836332	0.0605149	0.0302574	−	0.999542i	$-0.490367\pi$
$191$	0.836332	0.0605149	0.0302574	+	0.999542i	$0.490367\pi$
$192$	−6.79024	−0.490043
$193$	21.6412	1.55777	0.778884	−	0.627168i	$-0.215786\pi$
$193$	21.6412	1.55777	0.778884	+	0.627168i	$0.215786\pi$
$194$	11.4908	0.824988
$195$	0	0
$196$	1.70622	0.121873
$197$	−2.85481	−0.203397	−0.101698	−	0.994815i	$-0.532428\pi$
$197$	−2.85481	−0.203397	−0.101698	+	0.994815i	$0.532428\pi$
$198$	6.78199	0.481975
$199$	10.3423	0.733150	0.366575	−	0.930389i	$-0.380530\pi$
$199$	10.3423	0.733150	0.366575	+	0.930389i	$0.380530\pi$
$200$	0	0
$201$	−11.3846	−0.803008
$202$	0.627590	0.0441570
$203$	4.79929	0.336844
$204$	−0.390591	−0.0273468
$205$	0	0
$206$	−0.616902	−0.0429816
$207$	−8.96967	−0.623435
$208$	−29.5137	−2.04641
$209$	−3.21351	−0.222283
$210$	0	0
$211$	−24.0535	−1.65591	−0.827955	−	0.560794i	$-0.810496\pi$
$211$	−24.0535	−1.65591	−0.827955	+	0.560794i	$0.810496\pi$
$212$	−0.534786	−0.0367293
$213$	−13.9921	−0.958721
$214$	−6.05055	−0.413607
$215$	0	0
$216$	2.62888	0.178873
$217$	22.4758	1.52576
$218$	15.6965	1.06310
$219$	−9.91426	−0.669943
$220$	0	0
$221$	10.5859	0.712087
$222$	−7.17493	−0.481550
$223$	1.55319	0.104010	0.0520048	−	0.998647i	$-0.483439\pi$
$223$	1.55319	0.104010	0.0520048	+	0.998647i	$0.483439\pi$
$224$	−5.16276	−0.344951
$225$	0	0
$226$	−8.32675	−0.553887
$227$	11.4618	0.760746	0.380373	−	0.924833i	$-0.375796\pi$
$227$	11.4618	0.760746	0.380373	+	0.924833i	$0.375796\pi$
$228$	0.174505	0.0115569
$229$	−21.3821	−1.41297	−0.706484	−	0.707729i	$-0.749720\pi$
$229$	−21.3821	−1.41297	−0.706484	+	0.707729i	$0.749720\pi$
$230$	0	0
$231$	−16.8986	−1.11185
$232$	−3.37889	−0.221835
$233$	−7.62257	−0.499371	−0.249686	−	0.968327i	$-0.580327\pi$
$233$	−7.62257	−0.499371	−0.249686	+	0.968327i	$0.580327\pi$
$234$	9.98141	0.652505
$235$	0	0
$236$	1.05739	0.0688304
$237$	−3.46097	−0.224814
$238$	8.89353	0.576482
$239$	16.0814	1.04022	0.520110	−	0.854099i	$-0.325891\pi$
$239$	16.0814	1.04022	0.520110	+	0.854099i	$0.325891\pi$
$240$	0	0
$241$	−24.9643	−1.60809	−0.804045	−	0.594568i	$-0.797323\pi$
$241$	−24.9643	−1.60809	−0.804045	+	0.594568i	$0.797323\pi$
$242$	14.2081	0.913332
$243$	−1.00000	−0.0641500
$244$	−3.44815	−0.220745
$245$	0	0
$246$	10.8294	0.690457
$247$	−4.72950	−0.300931
$248$	−15.8239	−1.00482
$249$	−7.73421	−0.490136
$250$	0	0
$251$	23.7133	1.49677	0.748385	−	0.663265i	$-0.230830\pi$
$251$	23.7133	1.49677	0.748385	+	0.663265i	$0.230830\pi$
$252$	0.917652	0.0578066
$253$	−40.5931	−2.55207
$254$	0.778159	0.0488260
$255$	0	0
$256$	5.81273	0.363295
$257$	−3.96876	−0.247565	−0.123782	−	0.992309i	$-0.539502\pi$
$257$	−3.96876	−0.247565	−0.123782	+	0.992309i	$0.539502\pi$
$258$	7.00073	0.435846
$259$	17.8777	1.11086
$260$	0	0
$261$	1.28529	0.0795576
$262$	−16.1788	−0.999532
$263$	−26.9272	−1.66041	−0.830203	−	0.557462i	$-0.811775\pi$
$263$	−26.9272	−1.66041	−0.830203	+	0.557462i	$0.811775\pi$
$264$	11.8973	0.732226
$265$	0	0
$266$	−3.97338	−0.243624
$267$	9.77201	0.598038
$268$	2.79783	0.170905
$269$	−2.80319	−0.170913	−0.0854567	−	0.996342i	$-0.527235\pi$
$269$	−2.80319	−0.170913	−0.0854567	+	0.996342i	$0.527235\pi$
$270$	0	0
$271$	−15.7365	−0.955925	−0.477962	−	0.878380i	$-0.658624\pi$
$271$	−15.7365	−0.955925	−0.477962	+	0.878380i	$0.658624\pi$
$272$	−7.04258	−0.427019
$273$	−24.8705	−1.50523
$274$	21.5408	1.30132
$275$	0	0
$276$	2.20435	0.132686
$277$	−0.434626	−0.0261141	−0.0130571	−	0.999915i	$-0.504156\pi$
$277$	−0.434626	−0.0261141	−0.0130571	+	0.999915i	$0.504156\pi$
$278$	−20.1104	−1.20614
$279$	6.01924	0.360362
$280$	0	0
$281$	15.1677	0.904827	0.452414	−	0.891808i	$-0.350563\pi$
$281$	15.1677	0.904827	0.452414	+	0.891808i	$0.350563\pi$
$282$	1.49858	0.0892394
$283$	14.9367	0.887897	0.443949	−	0.896052i	$-0.353577\pi$
$283$	14.9367	0.887897	0.443949	+	0.896052i	$0.353577\pi$
$284$	3.43863	0.204045
$285$	0	0
$286$	45.1718	2.67107
$287$	−26.9834	−1.59278
$288$	−1.38263	−0.0814725
$289$	−14.4740	−0.851411
$290$	0	0
$291$	−7.66774	−0.449491
$292$	2.43648	0.142584
$293$	16.5848	0.968892	0.484446	−	0.874821i	$-0.339021\pi$
$293$	16.5848	0.968892	0.484446	+	0.874821i	$0.339021\pi$
$294$	−10.4043	−0.606792
$295$	0	0
$296$	−12.5866	−0.731580
$297$	−4.52560	−0.262602
$298$	−24.4867	−1.41847
$299$	−59.7430	−3.45503
$300$	0	0
$301$	−17.4436	−1.00543
$302$	25.1140	1.44515
$303$	−0.418788	−0.0240588
$304$	3.14643	0.180460
$305$	0	0
$306$	2.38177	0.136157
$307$	−21.1677	−1.20811	−0.604053	−	0.796944i	$-0.706448\pi$
$307$	−21.1677	−1.20811	−0.604053	+	0.796944i	$0.706448\pi$
$308$	4.15292	0.236635
$309$	0.411656	0.0234183
$310$	0	0
$311$	−14.5903	−0.827343	−0.413671	−	0.910426i	$-0.635754\pi$
$311$	−14.5903	−0.827343	−0.413671	+	0.910426i	$0.635754\pi$
$312$	17.5098	0.991299
$313$	−9.48837	−0.536314	−0.268157	−	0.963375i	$-0.586415\pi$
$313$	−9.48837	−0.536314	−0.268157	+	0.963375i	$0.586415\pi$
$314$	−12.2254	−0.689921
$315$	0	0
$316$	0.850552	0.0478473
$317$	−9.90530	−0.556337	−0.278168	−	0.960532i	$-0.589727\pi$
$317$	−9.90530	−0.556337	−0.278168	+	0.960532i	$0.589727\pi$
$318$	3.26105	0.182871
$319$	5.81672	0.325674
$320$	0	0
$321$	4.03751	0.225352
$322$	−50.1917	−2.79708
$323$	−1.12856	−0.0627945
$324$	0.245756	0.0136531
$325$	0	0
$326$	12.3950	0.686496
$327$	−10.4742	−0.579227
$328$	18.9974	1.04896
$329$	−3.73400	−0.205862
$330$	0	0
$331$	−0.637031	−0.0350144	−0.0175072	−	0.999847i	$-0.505573\pi$
$331$	−0.637031	−0.0350144	−0.0175072	+	0.999847i	$0.505573\pi$
$332$	1.90073	0.104316
$333$	4.78781	0.262370
$334$	−2.38534	−0.130520
$335$	0	0
$336$	16.5458	0.902647
$337$	27.2002	1.48169	0.740844	−	0.671677i	$-0.234426\pi$
$337$	27.2002	1.48169	0.740844	+	0.671677i	$0.234426\pi$
$338$	47.0001	2.55647
$339$	5.55641	0.301783
$340$	0	0
$341$	27.2406	1.47516
$342$	−1.06411	−0.0575404
$343$	−0.213720	−0.0115398
$344$	12.2810	0.662146
$345$	0	0
$346$	33.3857	1.79483
$347$	−3.08846	−0.165797	−0.0828986	−	0.996558i	$-0.526418\pi$
$347$	−3.08846	−0.165797	−0.0828986	+	0.996558i	$0.526418\pi$
$348$	−0.315868	−0.0169323
$349$	3.85704	0.206463	0.103231	−	0.994657i	$-0.467082\pi$
$349$	3.85704	0.206463	0.103231	+	0.994657i	$0.467082\pi$
$350$	0	0
$351$	−6.66056	−0.355514
$352$	−6.25724	−0.333512
$353$	21.8923	1.16521	0.582603	−	0.812757i	$-0.302034\pi$
$353$	21.8923	1.16521	0.582603	+	0.812757i	$0.302034\pi$
$354$	−6.44784	−0.342699
$355$	0	0
$356$	−2.40153	−0.127281
$357$	−5.93462	−0.314093
$358$	−24.5626	−1.29817
$359$	−15.1238	−0.798203	−0.399101	−	0.916907i	$-0.630678\pi$
$359$	−15.1238	−0.798203	−0.399101	+	0.916907i	$0.630678\pi$
$360$	0	0
$361$	−18.4958	−0.973463
$362$	−4.98421	−0.261964
$363$	−9.48102	−0.497625
$364$	6.11207	0.320360
$365$	0	0
$366$	21.0263	1.09906
$367$	−0.306762	−0.0160129	−0.00800643	−	0.999968i	$-0.502549\pi$
$367$	−0.306762	−0.0160129	−0.00800643	+	0.999968i	$0.502549\pi$
$368$	39.7457	2.07189
$369$	−7.22641	−0.376192
$370$	0	0
$371$	−8.12552	−0.421856
$372$	−1.47926	−0.0766961
$373$	17.1073	0.885784	0.442892	−	0.896575i	$-0.353953\pi$
$373$	17.1073	0.885784	0.442892	+	0.896575i	$0.353953\pi$
$374$	10.7789	0.557365
$375$	0	0
$376$	2.62888	0.135574
$377$	8.56077	0.440902
$378$	−5.59572	−0.287813
$379$	−27.2346	−1.39895	−0.699474	−	0.714658i	$-0.746582\pi$
$379$	−27.2346	−1.39895	−0.699474	+	0.714658i	$0.746582\pi$
$380$	0	0
$381$	−0.519263	−0.0266026
$382$	1.25331	0.0641251
$383$	17.9918	0.919338	0.459669	−	0.888090i	$-0.347968\pi$
$383$	17.9918	0.919338	0.459669	+	0.888090i	$0.347968\pi$
$384$	−12.9410	−0.660393
$385$	0	0
$386$	32.4312	1.65070
$387$	−4.67156	−0.237469
$388$	1.88439	0.0956654
$389$	−31.6333	−1.60387	−0.801936	−	0.597410i	$-0.796197\pi$
$389$	−31.6333	−1.60387	−0.801936	+	0.597410i	$0.796197\pi$
$390$	0	0
$391$	−14.2559	−0.720953
$392$	−18.2517	−0.921851
$393$	10.7961	0.544590
$394$	−4.27818	−0.215531
$395$	0	0
$396$	1.11219	0.0558897
$397$	14.2794	0.716660	0.358330	−	0.933595i	$-0.383346\pi$
$397$	14.2794	0.716660	0.358330	+	0.933595i	$0.383346\pi$
$398$	15.4989	0.776889
$399$	2.65142	0.132737
$400$	0	0
$401$	6.21781	0.310503	0.155251	−	0.987875i	$-0.450381\pi$
$401$	6.21781	0.310503	0.155251	+	0.987875i	$0.450381\pi$
$402$	−17.0608	−0.850915
$403$	40.0915	1.99710
$404$	0.102920	0.00512044
$405$	0	0
$406$	7.19214	0.356940
$407$	21.6677	1.07403
$408$	4.17821	0.206852
$409$	22.3214	1.10372	0.551862	−	0.833936i	$-0.313918\pi$
$409$	22.3214	1.10372	0.551862	+	0.833936i	$0.313918\pi$
$410$	0	0
$411$	−14.3741	−0.709020
$412$	−0.101167	−0.00498413
$413$	16.0660	0.790555
$414$	−13.4418	−0.660629
$415$	0	0
$416$	−9.20911	−0.451514
$417$	13.4196	0.657161
$418$	−4.81572	−0.235545
$419$	−9.12192	−0.445635	−0.222817	−	0.974860i	$-0.571525\pi$
$419$	−9.12192	−0.445635	−0.222817	+	0.974860i	$0.571525\pi$
$420$	0	0
$421$	−32.8234	−1.59972	−0.799858	−	0.600189i	$-0.795092\pi$
$421$	−32.8234	−1.59972	−0.799858	+	0.600189i	$0.795092\pi$
$422$	−36.0462	−1.75470
$423$	−1.00000	−0.0486217
$424$	5.72068	0.277821
$425$	0	0
$426$	−20.9683	−1.01592
$427$	−52.3910	−2.53538
$428$	−0.992241	−0.0479618
$429$	−30.1430	−1.45532
$430$	0	0
$431$	39.0997	1.88336	0.941682	−	0.336504i	$-0.109245\pi$
$431$	39.0997	1.88336	0.941682	+	0.336504i	$0.109245\pi$
$432$	4.43112	0.213192
$433$	−38.3963	−1.84521	−0.922604	−	0.385748i	$-0.873944\pi$
$433$	−38.3963	−1.84521	−0.922604	+	0.385748i	$0.873944\pi$
$434$	33.6819	1.61678
$435$	0	0
$436$	2.57410	0.123277
$437$	6.36914	0.304677
$438$	−14.8574	−0.709912
$439$	−12.1327	−0.579061	−0.289531	−	0.957169i	$-0.593499\pi$
$439$	−12.1327	−0.579061	−0.289531	+	0.957169i	$0.593499\pi$
$440$	0	0
$441$	6.94276	0.330608
$442$	15.8639	0.754569
$443$	−5.85177	−0.278026	−0.139013	−	0.990291i	$-0.544393\pi$
$443$	−5.85177	−0.278026	−0.139013	+	0.990291i	$0.544393\pi$
$444$	−1.17663	−0.0558404
$445$	0	0
$446$	2.32759	0.110215
$447$	16.3399	0.772849
$448$	25.3548	1.19790
$449$	−37.0067	−1.74646	−0.873228	−	0.487312i	$-0.837977\pi$
$449$	−37.0067	−1.74646	−0.873228	+	0.487312i	$0.837977\pi$
$450$	0	0
$451$	−32.7038	−1.53996
$452$	−1.36552	−0.0642286
$453$	−16.7585	−0.787381
$454$	17.1765	0.806132
$455$	0	0
$456$	−1.86670	−0.0874165
$457$	−12.4517	−0.582465	−0.291232	−	0.956652i	$-0.594065\pi$
$457$	−12.4517	−0.582465	−0.291232	+	0.956652i	$0.594065\pi$
$458$	−32.0429	−1.49727
$459$	−1.58935	−0.0741843
$460$	0	0
$461$	−28.1483	−1.31100	−0.655499	−	0.755196i	$-0.727541\pi$
$461$	−28.1483	−1.31100	−0.655499	+	0.755196i	$0.727541\pi$
$462$	−25.3240	−1.17818
$463$	−6.79272	−0.315684	−0.157842	−	0.987464i	$-0.550454\pi$
$463$	−6.79272	−0.315684	−0.157842	+	0.987464i	$0.550454\pi$
$464$	−5.69528	−0.264397
$465$	0	0
$466$	−11.4231	−0.529163
$467$	21.1689	0.979578	0.489789	−	0.871841i	$-0.337074\pi$
$467$	21.1689	0.979578	0.489789	+	0.871841i	$0.337074\pi$
$468$	1.63687	0.0756643
$469$	42.5101	1.96294
$470$	0	0
$471$	8.15798	0.375900
$472$	−11.3111	−0.520635
$473$	−21.1416	−0.972091
$474$	−5.18655	−0.238226
$475$	0	0
$476$	1.45847	0.0668487
$477$	−2.17609	−0.0996363
$478$	24.0993	1.10228
$479$	−15.4658	−0.706649	−0.353324	−	0.935501i	$-0.614949\pi$
$479$	−15.4658	−0.706649	−0.353324	+	0.935501i	$0.614949\pi$
$480$	0	0
$481$	31.8895	1.45403
$482$	−37.4111	−1.70403
$483$	33.4928	1.52397
$484$	2.33001	0.105910
$485$	0	0
$486$	−1.49858	−0.0679772
$487$	25.6270	1.16127	0.580634	−	0.814165i	$-0.302805\pi$
$487$	25.6270	1.16127	0.580634	+	0.814165i	$0.302805\pi$
$488$	36.8853	1.66972
$489$	−8.27115	−0.374034
$490$	0	0
$491$	19.1862	0.865861	0.432930	−	0.901427i	$-0.357480\pi$
$491$	19.1862	0.865861	0.432930	+	0.901427i	$0.357480\pi$
$492$	1.77593	0.0800652
$493$	2.04278	0.0920020
$494$	−7.08755	−0.318884
$495$	0	0
$496$	−26.6719	−1.19760
$497$	52.2464	2.34357
$498$	−11.5904	−0.519377
$499$	−32.0852	−1.43633	−0.718166	−	0.695872i	$-0.755018\pi$
$499$	−32.0852	−1.43633	−0.718166	+	0.695872i	$0.755018\pi$
$500$	0	0
$501$	1.59173	0.0711131
$502$	35.5364	1.58607
$503$	−20.5931	−0.918201	−0.459101	−	0.888384i	$-0.651828\pi$
$503$	−20.5931	−0.918201	−0.459101	+	0.888384i	$0.651828\pi$
$504$	−9.81625	−0.437251
$505$	0	0
$506$	−60.8322	−2.70432
$507$	−31.3630	−1.39288
$508$	0.127612	0.00566185
$509$	31.5906	1.40023	0.700115	−	0.714030i	$-0.253132\pi$
$509$	31.5906	1.40023	0.700115	+	0.714030i	$0.253132\pi$
$510$	0	0
$511$	37.0198	1.63766
$512$	−17.1712	−0.758865
$513$	0.710075	0.0313506
$514$	−5.94753	−0.262334
$515$	0	0
$516$	1.14806	0.0505406
$517$	−4.52560	−0.199035
$518$	26.7912	1.17714
$519$	−22.2782	−0.977903
$520$	0	0
$521$	−2.18485	−0.0957202	−0.0478601	−	0.998854i	$-0.515240\pi$
$521$	−2.18485	−0.0957202	−0.0478601	+	0.998854i	$0.515240\pi$
$522$	1.92612	0.0843040
$523$	−0.985170	−0.0430785	−0.0215392	−	0.999768i	$-0.506857\pi$
$523$	−0.985170	−0.0430785	−0.0215392	+	0.999768i	$0.506857\pi$
$524$	−2.65320	−0.115906
$525$	0	0
$526$	−40.3528	−1.75946
$527$	9.56665	0.416730
$528$	20.0534	0.872714
$529$	57.4550	2.49804
$530$	0	0
$531$	4.30262	0.186718
$532$	−0.651602	−0.0282505
$533$	−48.1319	−2.08483
$534$	14.6442	0.633716
$535$	0	0
$536$	−29.9288	−1.29273
$537$	16.3905	0.707304
$538$	−4.20082	−0.181110
$539$	31.4201	1.35336
$540$	0	0
$541$	17.5996	0.756664	0.378332	−	0.925670i	$-0.376498\pi$
$541$	17.5996	0.756664	0.378332	+	0.925670i	$0.376498\pi$
$542$	−23.5825	−1.01295
$543$	3.32595	0.142730
$544$	−2.19748	−0.0942164
$545$	0	0
$546$	−37.2706	−1.59503
$547$	41.2363	1.76314	0.881568	−	0.472057i	$-0.156488\pi$
$547$	41.2363	1.76314	0.881568	+	0.472057i	$0.156488\pi$
$548$	3.53251	0.150901
$549$	−14.0308	−0.598820
$550$	0	0
$551$	−0.912655	−0.0388804
$552$	−23.5802	−1.00364
$553$	12.9232	0.549552
$554$	−0.651323	−0.0276721
$555$	0	0
$556$	−3.29794	−0.139864
$557$	−39.7205	−1.68301	−0.841506	−	0.540247i	$-0.818331\pi$
$557$	−39.7205	−1.68301	−0.841506	+	0.540247i	$0.818331\pi$
$558$	9.02033	0.381861
$559$	−31.1152	−1.31603
$560$	0	0
$561$	−7.19274	−0.303678
$562$	22.7300	0.958808
$563$	1.74288	0.0734536	0.0367268	−	0.999325i	$-0.488307\pi$
$563$	1.74288	0.0734536	0.0367268	+	0.999325i	$0.488307\pi$
$564$	0.245756	0.0103482
$565$	0	0
$566$	22.3840	0.940869
$567$	3.73400	0.156813
$568$	−36.7835	−1.54340
$569$	−41.6427	−1.74575	−0.872876	−	0.487942i	$-0.837748\pi$
$569$	−41.6427	−1.74575	−0.872876	+	0.487942i	$0.837748\pi$
$570$	0	0
$571$	−7.69957	−0.322217	−0.161109	−	0.986937i	$-0.551507\pi$
$571$	−7.69957	−0.322217	−0.161109	+	0.986937i	$0.551507\pi$
$572$	7.40781	0.309736
$573$	−0.836332	−0.0349383
$574$	−40.4370	−1.68781
$575$	0	0
$576$	6.79024	0.282927
$577$	−43.5280	−1.81210	−0.906048	−	0.423175i	$-0.860915\pi$
$577$	−43.5280	−1.81210	−0.906048	+	0.423175i	$0.860915\pi$
$578$	−21.6905	−0.902205
$579$	−21.6412	−0.899378
$580$	0	0
$581$	28.8795	1.19813
$582$	−11.4908	−0.476307
$583$	−9.84810	−0.407867
$584$	−26.0634	−1.07851
$585$	0	0
$586$	24.8537	1.02669
$587$	44.6329	1.84220	0.921099	−	0.389327i	$-0.127293\pi$
$587$	44.6329	1.84220	0.921099	+	0.389327i	$0.127293\pi$
$588$	−1.70622	−0.0703635
$589$	−4.27411	−0.176112
$590$	0	0
$591$	2.85481	0.117431
$592$	−21.2153	−0.871944
$593$	−26.4683	−1.08692	−0.543462	−	0.839434i	$-0.682887\pi$
$593$	−26.4683	−1.08692	−0.543462	+	0.839434i	$0.682887\pi$
$594$	−6.78199	−0.278268
$595$	0	0
$596$	−4.01561	−0.164486
$597$	−10.3423	−0.423284
$598$	−89.5300	−3.66115
$599$	−0.0161862	−0.000661349 0	−0.000330675	−	1.00000i	$-0.500105\pi$
$599$	−0.0161862	−0.000661349 0	−0.000330675		1.00000i	$0.500105\pi$
$600$	0	0
$601$	45.6165	1.86073	0.930367	−	0.366629i	$-0.119488\pi$
$601$	45.6165	1.86073	0.930367	+	0.366629i	$0.119488\pi$
$602$	−26.1407	−1.06542
$603$	11.3846	0.463617
$604$	4.11848	0.167579
$605$	0	0
$606$	−0.627590	−0.0254941
$607$	27.8964	1.13228	0.566140	−	0.824309i	$-0.308436\pi$
$607$	27.8964	1.13228	0.566140	+	0.824309i	$0.308436\pi$
$608$	0.981774	0.0398162
$609$	−4.79929	−0.194477
$610$	0	0
$611$	−6.66056	−0.269457
$612$	0.390591	0.0157887
$613$	14.5556	0.587897	0.293948	−	0.955821i	$-0.405031\pi$
$613$	14.5556	0.587897	0.293948	+	0.955821i	$0.405031\pi$
$614$	−31.7216	−1.28018
$615$	0	0
$616$	−44.4244	−1.78991
$617$	−15.0308	−0.605118	−0.302559	−	0.953131i	$-0.597841\pi$
$617$	−15.0308	−0.605118	−0.302559	+	0.953131i	$0.597841\pi$
$618$	0.616902	0.0248154
$619$	33.9734	1.36551	0.682754	−	0.730649i	$-0.260782\pi$
$619$	33.9734	1.36551	0.682754	+	0.730649i	$0.260782\pi$
$620$	0	0
$621$	8.96967	0.359941
$622$	−21.8649	−0.876701
$623$	−36.4887	−1.46189
$624$	29.5137	1.18149
$625$	0	0
$626$	−14.2191	−0.568311
$627$	3.21351	0.128335
$628$	−2.00487	−0.0800031
$629$	7.60948	0.303410
$630$	0	0
$631$	−15.1270	−0.602198	−0.301099	−	0.953593i	$-0.597353\pi$
$631$	−15.1270	−0.602198	−0.301099	+	0.953593i	$0.597353\pi$
$632$	−9.09847	−0.361918
$633$	24.0535	0.956040
$634$	−14.8439	−0.589528
$635$	0	0
$636$	0.534786	0.0212057
$637$	46.2427	1.83220
$638$	8.71684	0.345103
$639$	13.9921	0.553518
$640$	0	0
$641$	−12.9449	−0.511292	−0.255646	−	0.966771i	$-0.582288\pi$
$641$	−12.9449	−0.511292	−0.255646	+	0.966771i	$0.582288\pi$
$642$	6.05055	0.238796
$643$	18.9485	0.747256	0.373628	−	0.927579i	$-0.378114\pi$
$643$	18.9485	0.747256	0.373628	+	0.927579i	$0.378114\pi$
$644$	−8.23104	−0.324348
$645$	0	0
$646$	−1.69124	−0.0665408
$647$	−22.1657	−0.871425	−0.435713	−	0.900086i	$-0.643504\pi$
$647$	−22.1657	−0.871425	−0.435713	+	0.900086i	$0.643504\pi$
$648$	−2.62888	−0.103272
$649$	19.4719	0.764339
$650$	0	0
$651$	−22.4758	−0.880897
$652$	2.03268	0.0796059
$653$	−36.1135	−1.41323	−0.706616	−	0.707597i	$-0.749779\pi$
$653$	−36.1135	−1.41323	−0.706616	+	0.707597i	$0.749779\pi$
$654$	−15.6965	−0.613783
$655$	0	0
$656$	32.0211	1.25021
$657$	9.91426	0.386792
$658$	−5.59572	−0.218144
$659$	0.277132	0.0107955	0.00539777	−	0.999985i	$-0.498282\pi$
$659$	0.277132	0.0107955	0.00539777	+	0.999985i	$0.498282\pi$
$660$	0	0
$661$	40.1895	1.56319	0.781596	−	0.623785i	$-0.214406\pi$
$661$	40.1895	1.56319	0.781596	+	0.623785i	$0.214406\pi$
$662$	−0.954645	−0.0371033
$663$	−10.5859	−0.411123
$664$	−20.3323	−0.789048
$665$	0	0
$666$	7.17493	0.278023
$667$	−11.5287	−0.446391
$668$	−0.391176	−0.0151351
$669$	−1.55319	−0.0600500
$670$	0	0
$671$	−63.4977	−2.45130
$672$	5.16276	0.199158
$673$	−29.1715	−1.12448	−0.562240	−	0.826974i	$-0.690060\pi$
$673$	−29.1715	−1.12448	−0.562240	+	0.826974i	$0.690060\pi$
$674$	40.7617	1.57008
$675$	0	0
$676$	7.70764	0.296448
$677$	23.7776	0.913849	0.456924	−	0.889506i	$-0.348951\pi$
$677$	23.7776	0.913849	0.456924	+	0.889506i	$0.348951\pi$
$678$	8.32675	0.319787
$679$	28.6313	1.09877
$680$	0	0
$681$	−11.4618	−0.439217
$682$	40.8224	1.56317
$683$	−25.2778	−0.967230	−0.483615	−	0.875281i	$-0.660676\pi$
$683$	−25.2778	−0.967230	−0.483615	+	0.875281i	$0.660676\pi$
$684$	−0.174505	−0.00667236
$685$	0	0
$686$	−0.320278	−0.0122283
$687$	21.3821	0.815778
$688$	20.7002	0.789188
$689$	−14.4940	−0.552176
$690$	0	0
$691$	6.83800	0.260130	0.130065	−	0.991505i	$-0.458481\pi$
$691$	6.83800	0.260130	0.130065	+	0.991505i	$0.458481\pi$
$692$	5.47498	0.208128
$693$	16.8986	0.641924
$694$	−4.62832	−0.175689
$695$	0	0
$696$	3.37889	0.128076
$697$	−11.4853	−0.435036
$698$	5.78010	0.218780
$699$	7.62257	0.288312
$700$	0	0
$701$	38.9700	1.47188	0.735939	−	0.677048i	$-0.236741\pi$
$701$	38.9700	1.47188	0.735939	+	0.677048i	$0.236741\pi$
$702$	−9.98141	−0.376724
$703$	−3.39970	−0.128222
$704$	30.7299	1.15818
$705$	0	0
$706$	32.8074	1.23472
$707$	1.56376	0.0588111
$708$	−1.05739	−0.0397392
$709$	−10.7868	−0.405105	−0.202553	−	0.979271i	$-0.564924\pi$
$709$	−10.7868	−0.405105	−0.202553	+	0.979271i	$0.564924\pi$
$710$	0	0
$711$	3.46097	0.129796
$712$	25.6895	0.962754
$713$	−53.9906	−2.02196
$714$	−8.89353	−0.332832
$715$	0	0
$716$	−4.02807	−0.150536
$717$	−16.0814	−0.600571
$718$	−22.6643	−0.845823
$719$	−12.2157	−0.455568	−0.227784	−	0.973712i	$-0.573148\pi$
$719$	−12.2157	−0.455568	−0.227784	+	0.973712i	$0.573148\pi$
$720$	0	0
$721$	−1.53712	−0.0572455
$722$	−27.7175	−1.03154
$723$	24.9643	0.928431
$724$	−0.817370	−0.0303773
$725$	0	0
$726$	−14.2081	−0.527313
$727$	39.9032	1.47993	0.739964	−	0.672646i	$-0.234842\pi$
$727$	39.9032	1.47993	0.739964	+	0.672646i	$0.234842\pi$
$728$	−65.3817	−2.42321
$729$	1.00000	0.0370370
$730$	0	0
$731$	−7.42472	−0.274613
$732$	3.44815	0.127447
$733$	6.12293	0.226156	0.113078	−	0.993586i	$-0.463929\pi$
$733$	6.12293	0.226156	0.113078	+	0.993586i	$0.463929\pi$
$734$	−0.459709	−0.0169682
$735$	0	0
$736$	12.4018	0.457136
$737$	51.5221	1.89784
$738$	−10.8294	−0.398635
$739$	−32.4517	−1.19375	−0.596877	−	0.802333i	$-0.703592\pi$
$739$	−32.4517	−1.19375	−0.596877	+	0.802333i	$0.703592\pi$
$740$	0	0
$741$	4.72950	0.173742
$742$	−12.1768	−0.447024
$743$	−30.8567	−1.13202	−0.566011	−	0.824397i	$-0.691514\pi$
$743$	−30.8567	−1.13202	−0.566011	+	0.824397i	$0.691514\pi$
$744$	15.8239	0.580131
$745$	0	0
$746$	25.6368	0.938629
$747$	7.73421	0.282980
$748$	1.76766	0.0646319
$749$	−15.0761	−0.550867
$750$	0	0
$751$	6.87869	0.251007	0.125504	−	0.992093i	$-0.459945\pi$
$751$	6.87869	0.251007	0.125504	+	0.992093i	$0.459945\pi$
$752$	4.43112	0.161586
$753$	−23.7133	−0.864160
$754$	12.8290	0.467206
$755$	0	0
$756$	−0.917652	−0.0333747
$757$	21.9661	0.798373	0.399186	−	0.916870i	$-0.369293\pi$
$757$	21.9661	0.798373	0.399186	+	0.916870i	$0.369293\pi$
$758$	−40.8134	−1.48241
$759$	40.5931	1.47344
$760$	0	0
$761$	18.7761	0.680634	0.340317	−	0.940311i	$-0.389466\pi$
$761$	18.7761	0.680634	0.340317	+	0.940311i	$0.389466\pi$
$762$	−0.778159	−0.0281897
$763$	39.1108	1.41591
$764$	0.205533	0.00743593
$765$	0	0
$766$	26.9622	0.974185
$767$	28.6578	1.03477
$768$	−5.81273	−0.209749
$769$	−48.5852	−1.75203	−0.876013	−	0.482287i	$-0.839806\pi$
$769$	−48.5852	−1.75203	−0.876013	+	0.482287i	$0.839806\pi$
$770$	0	0
$771$	3.96876	0.142931
$772$	5.31845	0.191415
$773$	−8.42278	−0.302946	−0.151473	−	0.988461i	$-0.548402\pi$
$773$	−8.42278	−0.302946	−0.151473	+	0.988461i	$0.548402\pi$
$774$	−7.00073	−0.251636
$775$	0	0
$776$	−20.1576	−0.723615
$777$	−17.8777	−0.641358
$778$	−47.4052	−1.69956
$779$	5.13130	0.183848
$780$	0	0
$781$	63.3224	2.26586
$782$	−21.3637	−0.763964
$783$	−1.28529	−0.0459326
$784$	−30.7642	−1.09872
$785$	0	0
$786$	16.1788	0.577080
$787$	16.4726	0.587183	0.293592	−	0.955931i	$-0.405149\pi$
$787$	16.4726	0.587183	0.293592	+	0.955931i	$0.405149\pi$
$788$	−0.701586	−0.0249930
$789$	26.9272	0.958635
$790$	0	0
$791$	−20.7476	−0.737701
$792$	−11.8973	−0.422751
$793$	−93.4529	−3.31861
$794$	21.3988	0.759416
$795$	0	0
$796$	2.54169	0.0900878
$797$	−36.1402	−1.28015	−0.640076	−	0.768311i	$-0.721097\pi$
$797$	−36.1402	−1.28015	−0.640076	+	0.768311i	$0.721097\pi$
$798$	3.97338	0.140656
$799$	−1.58935	−0.0562270
$800$	0	0
$801$	−9.77201	−0.345277
$802$	9.31791	0.329027
$803$	44.8679	1.58335
$804$	−2.79783	−0.0986719
$805$	0	0
$806$	60.0804	2.11624
$807$	2.80319	0.0986770
$808$	−1.10095	−0.0387311
$809$	−2.65931	−0.0934962	−0.0467481	−	0.998907i	$-0.514886\pi$
$809$	−2.65931	−0.0934962	−0.0467481	+	0.998907i	$0.514886\pi$
$810$	0	0
$811$	53.3518	1.87343	0.936717	−	0.350088i	$-0.113848\pi$
$811$	53.3518	1.87343	0.936717	+	0.350088i	$0.113848\pi$
$812$	1.17945	0.0413906
$813$	15.7365	0.551903
$814$	32.4708	1.13810
$815$	0	0
$816$	7.04258	0.246539
$817$	3.31716	0.116053
$818$	33.4505	1.16957
$819$	24.8705	0.869046
$820$	0	0
$821$	15.8090	0.551740	0.275870	−	0.961195i	$-0.411034\pi$
$821$	15.8090	0.551740	0.275870	+	0.961195i	$0.411034\pi$
$822$	−21.5408	−0.751320
$823$	−31.0167	−1.08117	−0.540586	−	0.841288i	$-0.681798\pi$
$823$	−31.0167	−1.08117	−0.540586	+	0.841288i	$0.681798\pi$
$824$	1.08220	0.0377001
$825$	0	0
$826$	24.0762	0.837719
$827$	1.64620	0.0572440	0.0286220	−	0.999590i	$-0.490888\pi$
$827$	1.64620	0.0572440	0.0286220	+	0.999590i	$0.490888\pi$
$828$	−2.20435	−0.0766064
$829$	7.76442	0.269670	0.134835	−	0.990868i	$-0.456950\pi$
$829$	7.76442	0.269670	0.134835	+	0.990868i	$0.456950\pi$
$830$	0	0
$831$	0.434626	0.0150770
$832$	45.2268	1.56796
$833$	11.0345	0.382321
$834$	20.1104	0.696367
$835$	0	0
$836$	−0.789739	−0.0273137
$837$	−6.01924	−0.208055
$838$	−13.6700	−0.472221
$839$	42.3453	1.46192	0.730962	−	0.682419i	$-0.239072\pi$
$839$	42.3453	1.46192	0.730962	+	0.682419i	$0.239072\pi$
$840$	0	0
$841$	−27.3480	−0.943035
$842$	−49.1887	−1.69515
$843$	−15.1677	−0.522402
$844$	−5.91128	−0.203475
$845$	0	0
$846$	−1.49858	−0.0515224
$847$	35.4021	1.21643
$848$	9.64250	0.331125
$849$	−14.9367	−0.512628
$850$	0	0
$851$	−42.9451	−1.47214
$852$	−3.43863	−0.117806
$853$	34.9151	1.19547	0.597735	−	0.801694i	$-0.296068\pi$
$853$	34.9151	1.19547	0.597735	+	0.801694i	$0.296068\pi$
$854$	−78.5123	−2.68664
$855$	0	0
$856$	10.6141	0.362784
$857$	−30.9074	−1.05578	−0.527888	−	0.849314i	$-0.677016\pi$
$857$	−30.9074	−1.05578	−0.527888	+	0.849314i	$0.677016\pi$
$858$	−45.1718	−1.54214
$859$	9.24373	0.315392	0.157696	−	0.987488i	$-0.449593\pi$
$859$	9.24373	0.315392	0.157696	+	0.987488i	$0.449593\pi$
$860$	0	0
$861$	26.9834	0.919593
$862$	58.5941	1.99572
$863$	−17.5837	−0.598556	−0.299278	−	0.954166i	$-0.596746\pi$
$863$	−17.5837	−0.598556	−0.299278	+	0.954166i	$0.596746\pi$
$864$	1.38263	0.0470382
$865$	0	0
$866$	−57.5401	−1.95529
$867$	14.4740	0.491562
$868$	5.52356	0.187482
$869$	15.6629	0.531329
$870$	0	0
$871$	75.8278	2.56933
$872$	−27.5356	−0.932472
$873$	7.66774	0.259514
$874$	9.54470	0.322854
$875$	0	0
$876$	−2.43648	−0.0823212
$877$	−56.0479	−1.89260	−0.946302	−	0.323284i	$-0.895213\pi$
$877$	−56.0479	−1.89260	−0.946302	+	0.323284i	$0.895213\pi$
$878$	−18.1818	−0.613608
$879$	−16.5848	−0.559390
$880$	0	0
$881$	−56.8957	−1.91687	−0.958433	−	0.285317i	$-0.907901\pi$
$881$	−56.8957	−1.91687	−0.958433	+	0.285317i	$0.907901\pi$
$882$	10.4043	0.350332
$883$	−32.0922	−1.07999	−0.539994	−	0.841669i	$-0.681573\pi$
$883$	−32.0922	−1.07999	−0.539994	+	0.841669i	$0.681573\pi$
$884$	2.60155	0.0874997
$885$	0	0
$886$	−8.76938	−0.294613
$887$	−26.3122	−0.883476	−0.441738	−	0.897144i	$-0.645638\pi$
$887$	−26.3122	−0.883476	−0.441738	+	0.897144i	$0.645638\pi$
$888$	12.5866	0.422378
$889$	1.93893	0.0650295
$890$	0	0
$891$	4.52560	0.151613
$892$	0.381706	0.0127805
$893$	0.710075	0.0237618
$894$	24.4867	0.818956
$895$	0	0
$896$	48.3218	1.61432
$897$	59.7430	1.99476
$898$	−55.4577	−1.85065
$899$	7.73648	0.258026
$900$	0	0
$901$	−3.45856	−0.115221
$902$	−49.0095	−1.63184
$903$	17.4436	0.580487
$904$	14.6072	0.485827
$905$	0	0
$906$	−25.1140	−0.834355
$907$	−51.1953	−1.69991	−0.849955	−	0.526855i	$-0.823371\pi$
$907$	−51.1953	−1.69991	−0.849955	+	0.526855i	$0.823371\pi$
$908$	2.81680	0.0934789
$909$	0.418788	0.0138903
$910$	0	0
$911$	14.7923	0.490091	0.245046	−	0.969512i	$-0.421197\pi$
$911$	14.7923	0.490091	0.245046	+	0.969512i	$0.421197\pi$
$912$	−3.14643	−0.104189
$913$	35.0019	1.15839
$914$	−18.6599	−0.617214
$915$	0	0
$916$	−5.25477	−0.173623
$917$	−40.3126	−1.33124
$918$	−2.38177	−0.0786101
$919$	50.6500	1.67079	0.835395	−	0.549651i	$-0.185239\pi$
$919$	50.6500	1.67079	0.835395	+	0.549651i	$0.185239\pi$
$920$	0	0
$921$	21.1677	0.697500
$922$	−42.1826	−1.38921
$923$	93.1950	3.06755
$924$	−4.15292	−0.136621
$925$	0	0
$926$	−10.1795	−0.334518
$927$	−0.411656	−0.0135206
$928$	−1.77709	−0.0583358
$929$	−30.6827	−1.00667	−0.503334	−	0.864092i	$-0.667894\pi$
$929$	−30.6827	−1.00667	−0.503334	+	0.864092i	$0.667894\pi$
$930$	0	0
$931$	−4.92988	−0.161570
$932$	−1.87329	−0.0613616
$933$	14.5903	0.477666
$934$	31.7233	1.03802
$935$	0	0
$936$	−17.5098	−0.572327
$937$	−29.6864	−0.969813	−0.484906	−	0.874566i	$-0.661146\pi$
$937$	−29.6864	−0.969813	−0.484906	+	0.874566i	$0.661146\pi$
$938$	63.7050	2.08004
$939$	9.48837	0.309641
$940$	0	0
$941$	−34.2075	−1.11513	−0.557567	−	0.830132i	$-0.688265\pi$
$941$	−34.2075	−1.11513	−0.557567	+	0.830132i	$0.688265\pi$
$942$	12.2254	0.398326
$943$	64.8186	2.11078
$944$	−19.0654	−0.620526
$945$	0	0
$946$	−31.6825	−1.03009
$947$	−61.4743	−1.99765	−0.998823	−	0.0485033i	$-0.984555\pi$
$947$	−61.4743	−1.99765	−0.998823	+	0.0485033i	$0.984555\pi$
$948$	−0.850552	−0.0276246
$949$	66.0345	2.14357
$950$	0	0
$951$	9.90530	0.321201
$952$	−15.6014	−0.505645
$953$	23.6217	0.765183	0.382592	−	0.923918i	$-0.375032\pi$
$953$	23.6217	0.765183	0.382592	+	0.923918i	$0.375032\pi$
$954$	−3.26105	−0.105581
$955$	0	0
$956$	3.95210	0.127820
$957$	−5.81672	−0.188028
$958$	−23.1767	−0.748807
$959$	53.6728	1.73318
$960$	0	0
$961$	5.23120	0.168748
$962$	47.7890	1.54078
$963$	−4.03751	−0.130107
$964$	−6.13511	−0.197599
$965$	0	0
$966$	50.1917	1.61489
$967$	−6.31649	−0.203125	−0.101562	−	0.994829i	$-0.532384\pi$
$967$	−6.31649	−0.203125	−0.101562	+	0.994829i	$0.532384\pi$
$968$	−24.9245	−0.801104
$969$	1.12856	0.0362544
$970$	0	0
$971$	12.7492	0.409143	0.204571	−	0.978852i	$-0.434420\pi$
$971$	12.7492	0.409143	0.204571	+	0.978852i	$0.434420\pi$
$972$	−0.245756	−0.00788262
$973$	−50.1088	−1.60642
$974$	38.4042	1.23055
$975$	0	0
$976$	62.1721	1.99008
$977$	23.8126	0.761833	0.380916	−	0.924609i	$-0.375609\pi$
$977$	23.8126	0.761833	0.380916	+	0.924609i	$0.375609\pi$
$978$	−12.3950	−0.396349
$979$	−44.2242	−1.41341
$980$	0	0
$981$	10.4742	0.334417
$982$	28.7521	0.917518
$983$	−39.2680	−1.25245	−0.626227	−	0.779641i	$-0.715402\pi$
$983$	−39.2680	−1.25245	−0.626227	+	0.779641i	$0.715402\pi$
$984$	−18.9974	−0.605615
$985$	0	0
$986$	3.06127	0.0974908
$987$	3.73400	0.118855
$988$	−1.16230	−0.0369777
$989$	41.9023	1.33242
$990$	0	0
$991$	8.63121	0.274180	0.137090	−	0.990559i	$-0.456225\pi$
$991$	8.63121	0.274180	0.137090	+	0.990559i	$0.456225\pi$
$992$	−8.32240	−0.264236
$993$	0.637031	0.0202156
$994$	78.2956	2.48339
$995$	0	0
$996$	−1.90073	−0.0602268
$997$	−1.35122	−0.0427937	−0.0213968	−	0.999771i	$-0.506811\pi$
$997$	−1.35122	−0.0427937	−0.0213968	+	0.999771i	$0.506811\pi$
$998$	−48.0824	−1.52202
$999$	−4.78781	−0.151479

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+1.49858 q^{2} -1.00000 q^{3} +0.245756 q^{4} -1.49858 q^{6} +3.73400 q^{7} -2.62888 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.49858 q^{2} -1.00000 q^{3} +0.245756 q^{4} -1.49858 q^{6} +3.73400 q^{7} -2.62888 q^{8} +1.00000 q^{9} +4.52560 q^{11} -0.245756 q^{12} +6.66056 q^{13} +5.59572 q^{14} -4.43112 q^{16} +1.58935 q^{17} +1.49858 q^{18} -0.710075 q^{19} -3.73400 q^{21} +6.78199 q^{22} -8.96967 q^{23} +2.62888 q^{24} +9.98141 q^{26} -1.00000 q^{27} +0.917652 q^{28} +1.28529 q^{29} +6.01924 q^{31} -1.38263 q^{32} -4.52560 q^{33} +2.38177 q^{34} +0.245756 q^{36} +4.78781 q^{37} -1.06411 q^{38} -6.66056 q^{39} -7.22641 q^{41} -5.59572 q^{42} -4.67156 q^{43} +1.11219 q^{44} -13.4418 q^{46} -1.00000 q^{47} +4.43112 q^{48} +6.94276 q^{49} -1.58935 q^{51} +1.63687 q^{52} -2.17609 q^{53} -1.49858 q^{54} -9.81625 q^{56} +0.710075 q^{57} +1.92612 q^{58} +4.30262 q^{59} -14.0308 q^{61} +9.02033 q^{62} +3.73400 q^{63} +6.79024 q^{64} -6.78199 q^{66} +11.3846 q^{67} +0.390591 q^{68} +8.96967 q^{69} +13.9921 q^{71} -2.62888 q^{72} +9.91426 q^{73} +7.17493 q^{74} -0.174505 q^{76} +16.8986 q^{77} -9.98141 q^{78} +3.46097 q^{79} +1.00000 q^{81} -10.8294 q^{82} +7.73421 q^{83} -0.917652 q^{84} -7.00073 q^{86} -1.28529 q^{87} -11.8973 q^{88} -9.77201 q^{89} +24.8705 q^{91} -2.20435 q^{92} -6.01924 q^{93} -1.49858 q^{94} +1.38263 q^{96} +7.66774 q^{97} +10.4043 q^{98} +4.52560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9} - 8 q^{11} - 5 q^{12} + 5 q^{13} - 3 q^{14} + 9 q^{16} + 10 q^{17} + q^{18} + 7 q^{19} - 11 q^{21} + 20 q^{22} + 4 q^{23} - 6 q^{24} - 7 q^{27} + 2 q^{28} - 11 q^{29} + 3 q^{31} + 28 q^{32} + 8 q^{33} + 8 q^{34} + 5 q^{36} + 11 q^{37} - 2 q^{38} - 5 q^{39} - 20 q^{41} + 3 q^{42} + 18 q^{43} + q^{44} - 19 q^{46} - 7 q^{47} - 9 q^{48} + 14 q^{49} - 10 q^{51} + 29 q^{52} + 12 q^{53} - q^{54} - 47 q^{56} - 7 q^{57} - 19 q^{58} + 18 q^{59} - 4 q^{61} + 12 q^{62} + 11 q^{63} + 42 q^{64} - 20 q^{66} + 22 q^{67} + 44 q^{68} - 4 q^{69} - 14 q^{71} + 6 q^{72} + 30 q^{73} + 31 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} + 7 q^{81} + 29 q^{82} + 54 q^{83} - 2 q^{84} - 29 q^{86} + 11 q^{87} - 22 q^{88} - 14 q^{89} + 20 q^{91} - 5 q^{92} - 3 q^{93} - q^{94} - 28 q^{96} + 24 q^{97} - 26 q^{98} - 8 q^{99}+O(q^{100}) \) 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9 - 8 * q^11 - 5 * q^12 + 5 * q^13 - 3 * q^14 + 9 * q^16 + 10 * q^17 + q^18 + 7 * q^19 - 11 * q^21 + 20 * q^22 + 4 * q^23 - 6 * q^24 - 7 * q^27 + 2 * q^28 - 11 * q^29 + 3 * q^31 + 28 * q^32 + 8 * q^33 + 8 * q^34 + 5 * q^36 + 11 * q^37 - 2 * q^38 - 5 * q^39 - 20 * q^41 + 3 * q^42 + 18 * q^43 + q^44 - 19 * q^46 - 7 * q^47 - 9 * q^48 + 14 * q^49 - 10 * q^51 + 29 * q^52 + 12 * q^53 - q^54 - 47 * q^56 - 7 * q^57 - 19 * q^58 + 18 * q^59 - 4 * q^61 + 12 * q^62 + 11 * q^63 + 42 * q^64 - 20 * q^66 + 22 * q^67 + 44 * q^68 - 4 * q^69 - 14 * q^71 + 6 * q^72 + 30 * q^73 + 31 * q^74 - 2 * q^76 - 8 * q^77 - q^79 + 7 * q^81 + 29 * q^82 + 54 * q^83 - 2 * q^84 - 29 * q^86 + 11 * q^87 - 22 * q^88 - 14 * q^89 + 20 * q^91 - 5 * q^92 - 3 * q^93 - q^94 - 28 * q^96 + 24 * q^97 - 26 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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