LMFDB - Embedded newform 8025.2.a.bc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, 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("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 26x^{7} + 51x^{6} - 101x^{5} - 65x^{4} + 126x^{3} + 5x^{2} - 10x + 1 $ x^10 - 2x^9 - 13x^8 + 26x^7 + 51x^6 - 101x^5 - 65x^4 + 126x^3 + 5x^2 - 10*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1605)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.148156$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.148156 q^{2} +1.00000 q^{3} -1.97805 q^{4} -0.148156 q^{6} +0.985585 q^{7} +0.589370 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.148156 q^{2} +1.00000 q^{3} -1.97805 q^{4} -0.148156 q^{6} +0.985585 q^{7} +0.589370 q^{8} +1.00000 q^{9} +4.10242 q^{11} -1.97805 q^{12} +3.39829 q^{13} -0.146020 q^{14} +3.86878 q^{16} -3.65722 q^{17} -0.148156 q^{18} +0.659579 q^{19} +0.985585 q^{21} -0.607796 q^{22} -8.49901 q^{23} +0.589370 q^{24} -0.503476 q^{26} +1.00000 q^{27} -1.94954 q^{28} -9.42182 q^{29} -3.49678 q^{31} -1.75192 q^{32} +4.10242 q^{33} +0.541837 q^{34} -1.97805 q^{36} +1.83999 q^{37} -0.0977203 q^{38} +3.39829 q^{39} -11.6916 q^{41} -0.146020 q^{42} +7.38803 q^{43} -8.11479 q^{44} +1.25918 q^{46} -9.66770 q^{47} +3.86878 q^{48} -6.02862 q^{49} -3.65722 q^{51} -6.72199 q^{52} +2.97703 q^{53} -0.148156 q^{54} +0.580874 q^{56} +0.659579 q^{57} +1.39590 q^{58} -11.0949 q^{59} +7.13927 q^{61} +0.518067 q^{62} +0.985585 q^{63} -7.47801 q^{64} -0.607796 q^{66} +6.22370 q^{67} +7.23416 q^{68} -8.49901 q^{69} +8.69116 q^{71} +0.589370 q^{72} -14.9790 q^{73} -0.272604 q^{74} -1.30468 q^{76} +4.04328 q^{77} -0.503476 q^{78} +3.29649 q^{79} +1.00000 q^{81} +1.73217 q^{82} +11.3141 q^{83} -1.94954 q^{84} -1.09458 q^{86} -9.42182 q^{87} +2.41784 q^{88} -1.84924 q^{89} +3.34930 q^{91} +16.8115 q^{92} -3.49678 q^{93} +1.43232 q^{94} -1.75192 q^{96} -3.60865 q^{97} +0.893174 q^{98} +4.10242 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9	$ 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9} - 14 q^{11} + 10 q^{12} + 3 q^{13} - 16 q^{14} + 10 q^{16} - 8 q^{17} - 2 q^{18} - 19 q^{19} - 5 q^{22} - 4 q^{23} - 22 q^{26} + 10 q^{27} - 25 q^{29} - 2 q^{31} + 13 q^{32} - 14 q^{33} - 37 q^{34} + 10 q^{36} + 10 q^{37} + 13 q^{38} + 3 q^{39} - 31 q^{41} - 16 q^{42} - 62 q^{44} + 2 q^{46} + q^{47} + 10 q^{48} + 26 q^{49} - 8 q^{51} + 30 q^{52} - 9 q^{53} - 2 q^{54} - 63 q^{56} - 19 q^{57} - 30 q^{58} - 65 q^{59} + 12 q^{61} + 39 q^{62} - 2 q^{64} - 5 q^{66} + 10 q^{67} - 22 q^{68} - 4 q^{69} - 45 q^{71} - q^{73} + 19 q^{74} - 39 q^{76} + q^{77} - 22 q^{78} - 47 q^{79} + 10 q^{81} + 23 q^{82} - q^{83} + 12 q^{86} - 25 q^{87} + 8 q^{88} - 34 q^{89} - 26 q^{91} - 14 q^{92} - 2 q^{93} - 64 q^{94} + 13 q^{96} - 5 q^{97} + 51 q^{98} - 14 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9 - 14 * q^11 + 10 * q^12 + 3 * q^13 - 16 * q^14 + 10 * q^16 - 8 * q^17 - 2 * q^18 - 19 * q^19 - 5 * q^22 - 4 * q^23 - 22 * q^26 + 10 * q^27 - 25 * q^29 - 2 * q^31 + 13 * q^32 - 14 * q^33 - 37 * q^34 + 10 * q^36 + 10 * q^37 + 13 * q^38 + 3 * q^39 - 31 * q^41 - 16 * q^42 - 62 * q^44 + 2 * q^46 + q^47 + 10 * q^48 + 26 * q^49 - 8 * q^51 + 30 * q^52 - 9 * q^53 - 2 * q^54 - 63 * q^56 - 19 * q^57 - 30 * q^58 - 65 * q^59 + 12 * q^61 + 39 * q^62 - 2 * q^64 - 5 * q^66 + 10 * q^67 - 22 * q^68 - 4 * q^69 - 45 * q^71 - q^73 + 19 * q^74 - 39 * q^76 + q^77 - 22 * q^78 - 47 * q^79 + 10 * q^81 + 23 * q^82 - q^83 + 12 * q^86 - 25 * q^87 + 8 * q^88 - 34 * q^89 - 26 * q^91 - 14 * q^92 - 2 * q^93 - 64 * q^94 + 13 * q^96 - 5 * q^97 + 51 * q^98 - 14 * 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 $

$2$	−0.148156	−0.104762	−0.0523809	−	0.998627i	$-0.516681\pi$
$2$	−0.148156	−0.104762	−0.0523809	+	0.998627i	$0.516681\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.97805	−0.989025
$5$	0	0
$5$	0	0
$6$	−0.148156	−0.0604842
$7$	0.985585	0.372516	0.186258	−	0.982501i	$-0.440364\pi$
$7$	0.985585	0.372516	0.186258	+	0.982501i	$0.440364\pi$
$8$	0.589370	0.208374
$9$	1.00000	0.333333
$10$	0	0
$11$	4.10242	1.23693	0.618463	−	0.785814i	$-0.287756\pi$
$11$	4.10242	1.23693	0.618463	+	0.785814i	$0.287756\pi$
$12$	−1.97805	−0.571014
$13$	3.39829	0.942517	0.471258	−	0.881995i	$-0.343800\pi$
$13$	3.39829	0.942517	0.471258	+	0.881995i	$0.343800\pi$
$14$	−0.146020	−0.0390254
$15$	0	0
$16$	3.86878	0.967195
$17$	−3.65722	−0.887006	−0.443503	−	0.896273i	$-0.646264\pi$
$17$	−3.65722	−0.887006	−0.443503	+	0.896273i	$0.646264\pi$
$18$	−0.148156	−0.0349206
$19$	0.659579	0.151318	0.0756589	−	0.997134i	$-0.475894\pi$
$19$	0.659579	0.151318	0.0756589	+	0.997134i	$0.475894\pi$
$20$	0	0
$21$	0.985585	0.215072
$22$	−0.607796	−0.129583
$23$	−8.49901	−1.77217	−0.886083	−	0.463526i	$-0.846584\pi$
$23$	−8.49901	−1.77217	−0.886083	+	0.463526i	$0.846584\pi$
$24$	0.589370	0.120305
$25$	0	0
$26$	−0.503476	−0.0987397
$27$	1.00000	0.192450
$28$	−1.94954	−0.368428
$29$	−9.42182	−1.74959	−0.874794	−	0.484494i	$-0.839004\pi$
$29$	−9.42182	−1.74959	−0.874794	+	0.484494i	$0.839004\pi$
$30$	0	0
$31$	−3.49678	−0.628040	−0.314020	−	0.949416i	$-0.601676\pi$
$31$	−3.49678	−0.628040	−0.314020	+	0.949416i	$0.601676\pi$
$32$	−1.75192	−0.309699
$33$	4.10242	0.714140
$34$	0.541837	0.0929243
$35$	0	0
$36$	−1.97805	−0.329675
$37$	1.83999	0.302492	0.151246	−	0.988496i	$-0.451671\pi$
$37$	1.83999	0.302492	0.151246	+	0.988496i	$0.451671\pi$
$38$	−0.0977203	−0.0158523
$39$	3.39829	0.544162
$40$	0	0
$41$	−11.6916	−1.82591	−0.912957	−	0.408055i	$-0.866207\pi$
$41$	−11.6916	−1.82591	−0.912957	+	0.408055i	$0.866207\pi$
$42$	−0.146020	−0.0225313
$43$	7.38803	1.12666	0.563332	−	0.826231i	$-0.309519\pi$
$43$	7.38803	1.12666	0.563332	+	0.826231i	$0.309519\pi$
$44$	−8.11479	−1.22335
$45$	0	0
$46$	1.25918	0.185655
$47$	−9.66770	−1.41018	−0.705090	−	0.709118i	$-0.749093\pi$
$47$	−9.66770	−1.41018	−0.705090	+	0.709118i	$0.749093\pi$
$48$	3.86878	0.558411
$49$	−6.02862	−0.861232
$50$	0	0
$51$	−3.65722	−0.512113
$52$	−6.72199	−0.932173
$53$	2.97703	0.408927	0.204464	−	0.978874i	$-0.434455\pi$
$53$	2.97703	0.408927	0.204464	+	0.978874i	$0.434455\pi$
$54$	−0.148156	−0.0201614
$55$	0	0
$56$	0.580874	0.0776226
$57$	0.659579	0.0873634
$58$	1.39590	0.183290
$59$	−11.0949	−1.44443	−0.722216	−	0.691667i	$-0.756877\pi$
$59$	−11.0949	−1.44443	−0.722216	+	0.691667i	$0.756877\pi$
$60$	0	0
$61$	7.13927	0.914090	0.457045	−	0.889444i	$-0.348908\pi$
$61$	7.13927	0.914090	0.457045	+	0.889444i	$0.348908\pi$
$62$	0.518067	0.0657945
$63$	0.985585	0.124172
$64$	−7.47801	−0.934751
$65$	0	0
$66$	−0.607796	−0.0748146
$67$	6.22370	0.760346	0.380173	−	0.924915i	$-0.375864\pi$
$67$	6.22370	0.760346	0.380173	+	0.924915i	$0.375864\pi$
$68$	7.23416	0.877271
$69$	−8.49901	−1.02316
$70$	0	0
$71$	8.69116	1.03145	0.515725	−	0.856754i	$-0.327523\pi$
$71$	8.69116	1.03145	0.515725	+	0.856754i	$0.327523\pi$
$72$	0.589370	0.0694579
$73$	−14.9790	−1.75316	−0.876578	−	0.481260i	$-0.840179\pi$
$73$	−14.9790	−1.75316	−0.876578	+	0.481260i	$0.840179\pi$
$74$	−0.272604	−0.0316896
$75$	0	0
$76$	−1.30468	−0.149657
$77$	4.04328	0.460775
$78$	−0.503476	−0.0570074
$79$	3.29649	0.370884	0.185442	−	0.982655i	$-0.440628\pi$
$79$	3.29649	0.370884	0.185442	+	0.982655i	$0.440628\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.73217	0.191286
$83$	11.3141	1.24189	0.620943	−	0.783856i	$-0.286750\pi$
$83$	11.3141	1.24189	0.620943	+	0.783856i	$0.286750\pi$
$84$	−1.94954	−0.212712
$85$	0	0
$86$	−1.09458	−0.118031
$87$	−9.42182	−1.01013
$88$	2.41784	0.257743
$89$	−1.84924	−0.196019	−0.0980094	−	0.995185i	$-0.531248\pi$
$89$	−1.84924	−0.196019	−0.0980094	+	0.995185i	$0.531248\pi$
$90$	0	0
$91$	3.34930	0.351103
$92$	16.8115	1.75272
$93$	−3.49678	−0.362599
$94$	1.43232	0.147733
$95$	0	0
$96$	−1.75192	−0.178805
$97$	−3.60865	−0.366403	−0.183201	−	0.983075i	$-0.558646\pi$
$97$	−3.60865	−0.366403	−0.183201	+	0.983075i	$0.558646\pi$
$98$	0.893174	0.0902242
$99$	4.10242	0.412309
$100$	0	0
$101$	−19.9290	−1.98301	−0.991504	−	0.130077i	$-0.958477\pi$
$101$	−19.9290	−1.98301	−0.991504	+	0.130077i	$0.958477\pi$
$102$	0.541837	0.0536499
$103$	10.3334	1.01818	0.509089	−	0.860714i	$-0.329982\pi$
$103$	10.3334	1.01818	0.509089	+	0.860714i	$0.329982\pi$
$104$	2.00285	0.196396
$105$	0	0
$106$	−0.441064	−0.0428399
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	−1.97805	−0.190338
$109$	−11.0345	−1.05691	−0.528456	−	0.848961i	$-0.677229\pi$
$109$	−11.0345	−1.05691	−0.528456	+	0.848961i	$0.677229\pi$
$110$	0	0
$111$	1.83999	0.174644
$112$	3.81301	0.360296
$113$	−0.729507	−0.0686262	−0.0343131	−	0.999411i	$-0.510924\pi$
$113$	−0.729507	−0.0686262	−0.0343131	+	0.999411i	$0.510924\pi$
$114$	−0.0977203	−0.00915234
$115$	0	0
$116$	18.6368	1.73039
$117$	3.39829	0.314172
$118$	1.64377	0.151321
$119$	−3.60450	−0.330424
$120$	0	0
$121$	5.82986	0.529987
$122$	−1.05772	−0.0957616
$123$	−11.6916	−1.05419
$124$	6.91680	0.621147
$125$	0	0
$126$	−0.146020	−0.0130085
$127$	9.67571	0.858580	0.429290	−	0.903167i	$-0.358764\pi$
$127$	9.67571	0.858580	0.429290	+	0.903167i	$0.358764\pi$
$128$	4.61175	0.407625
$129$	7.38803	0.650480
$130$	0	0
$131$	−9.67233	−0.845075	−0.422538	−	0.906345i	$-0.638861\pi$
$131$	−9.67233	−0.845075	−0.422538	+	0.906345i	$0.638861\pi$
$132$	−8.11479	−0.706302
$133$	0.650071	0.0563683
$134$	−0.922076	−0.0796552
$135$	0	0
$136$	−2.15545	−0.184829
$137$	0.00629373	0.000537710 0	0.000268855	−	1.00000i	$-0.499914\pi$
$137$	0.00629373	0.000537710 0	0.000268855		1.00000i	$0.499914\pi$
$138$	1.25918	0.107188
$139$	−2.23175	−0.189295	−0.0946474	−	0.995511i	$-0.530172\pi$
$139$	−2.23175	−0.189295	−0.0946474	+	0.995511i	$0.530172\pi$
$140$	0	0
$141$	−9.66770	−0.814167
$142$	−1.28764	−0.108057
$143$	13.9412	1.16582
$144$	3.86878	0.322398
$145$	0	0
$146$	2.21922	0.183664
$147$	−6.02862	−0.497232
$148$	−3.63959	−0.299172
$149$	13.6101	1.11498	0.557492	−	0.830182i	$-0.311764\pi$
$149$	13.6101	1.11498	0.557492	+	0.830182i	$0.311764\pi$
$150$	0	0
$151$	−0.719800	−0.0585765	−0.0292883	−	0.999571i	$-0.509324\pi$
$151$	−0.719800	−0.0585765	−0.0292883	+	0.999571i	$0.509324\pi$
$152$	0.388736	0.0315307
$153$	−3.65722	−0.295669
$154$	−0.599035	−0.0482716
$155$	0	0
$156$	−6.72199	−0.538190
$157$	−13.9627	−1.11434	−0.557171	−	0.830398i	$-0.688113\pi$
$157$	−13.9627	−1.11434	−0.557171	+	0.830398i	$0.688113\pi$
$158$	−0.488393	−0.0388544
$159$	2.97703	0.236094
$160$	0	0
$161$	−8.37650	−0.660160
$162$	−0.148156	−0.0116402
$163$	−1.94566	−0.152396	−0.0761981	−	0.997093i	$-0.524278\pi$
$163$	−1.94566	−0.152396	−0.0761981	+	0.997093i	$0.524278\pi$
$164$	23.1265	1.80588
$165$	0	0
$166$	−1.67625	−0.130102
$167$	8.85103	0.684914	0.342457	−	0.939534i	$-0.388741\pi$
$167$	8.85103	0.684914	0.342457	+	0.939534i	$0.388741\pi$
$168$	0.580874	0.0448154
$169$	−1.45161	−0.111662
$170$	0	0
$171$	0.659579	0.0504393
$172$	−14.6139	−1.11430
$173$	12.8444	0.976542	0.488271	−	0.872692i	$-0.337628\pi$
$173$	12.8444	0.976542	0.488271	+	0.872692i	$0.337628\pi$
$174$	1.39590	0.105823
$175$	0	0
$176$	15.8714	1.19635
$177$	−11.0949	−0.833944
$178$	0.273975	0.0205353
$179$	−4.93894	−0.369154	−0.184577	−	0.982818i	$-0.559091\pi$
$179$	−4.93894	−0.369154	−0.184577	+	0.982818i	$0.559091\pi$
$180$	0	0
$181$	12.0869	0.898410	0.449205	−	0.893429i	$-0.351707\pi$
$181$	12.0869	0.898410	0.449205	+	0.893429i	$0.351707\pi$
$182$	−0.496218	−0.0367821
$183$	7.13927	0.527750
$184$	−5.00906	−0.369273
$185$	0	0
$186$	0.518067	0.0379865
$187$	−15.0034	−1.09716
$188$	19.1232	1.39470
$189$	0.985585	0.0716907
$190$	0	0
$191$	−1.74460	−0.126235	−0.0631175	−	0.998006i	$-0.520104\pi$
$191$	−1.74460	−0.126235	−0.0631175	+	0.998006i	$0.520104\pi$
$192$	−7.47801	−0.539679
$193$	−1.36466	−0.0982307	−0.0491154	−	0.998793i	$-0.515640\pi$
$193$	−1.36466	−0.0982307	−0.0491154	+	0.998793i	$0.515640\pi$
$194$	0.534641	0.0383850
$195$	0	0
$196$	11.9249	0.851780
$197$	−7.93810	−0.565566	−0.282783	−	0.959184i	$-0.591258\pi$
$197$	−7.93810	−0.565566	−0.282783	+	0.959184i	$0.591258\pi$
$198$	−0.607796	−0.0431942
$199$	−19.4757	−1.38059	−0.690296	−	0.723527i	$-0.742520\pi$
$199$	−19.4757	−1.38059	−0.690296	+	0.723527i	$0.742520\pi$
$200$	0	0
$201$	6.22370	0.438986
$202$	2.95259	0.207743
$203$	−9.28601	−0.651750
$204$	7.23416	0.506492
$205$	0	0
$206$	−1.53095	−0.106666
$207$	−8.49901	−0.590722
$208$	13.1473	0.911598
$209$	2.70587	0.187169
$210$	0	0
$211$	−3.96206	−0.272760	−0.136380	−	0.990657i	$-0.543547\pi$
$211$	−3.96206	−0.272760	−0.136380	+	0.990657i	$0.543547\pi$
$212$	−5.88872	−0.404439
$213$	8.69116	0.595508
$214$	−0.148156	−0.0101277
$215$	0	0
$216$	0.589370	0.0401016
$217$	−3.44637	−0.233955
$218$	1.63482	0.110724
$219$	−14.9790	−1.01219
$220$	0	0
$221$	−12.4283	−0.836018
$222$	−0.272604	−0.0182960
$223$	0.928481	0.0621757	0.0310879	−	0.999517i	$-0.490103\pi$
$223$	0.928481	0.0621757	0.0310879	+	0.999517i	$0.490103\pi$
$224$	−1.72667	−0.115368
$225$	0	0
$226$	0.108080	0.00718940
$227$	23.1559	1.53691	0.768456	−	0.639902i	$-0.221025\pi$
$227$	23.1559	1.53691	0.768456	+	0.639902i	$0.221025\pi$
$228$	−1.30468	−0.0864045
$229$	−12.4857	−0.825080	−0.412540	−	0.910940i	$-0.635358\pi$
$229$	−12.4857	−0.825080	−0.412540	+	0.910940i	$0.635358\pi$
$230$	0	0
$231$	4.04328	0.266029
$232$	−5.55294	−0.364568
$233$	−2.09427	−0.137200	−0.0686002	−	0.997644i	$-0.521853\pi$
$233$	−2.09427	−0.137200	−0.0686002	+	0.997644i	$0.521853\pi$
$234$	−0.503476	−0.0329132
$235$	0	0
$236$	21.9463	1.42858
$237$	3.29649	0.214130
$238$	0.534026	0.0346158
$239$	−19.5775	−1.26637	−0.633183	−	0.774002i	$-0.718252\pi$
$239$	−19.5775	−1.26637	−0.633183	+	0.774002i	$0.718252\pi$
$240$	0	0
$241$	14.4500	0.930806	0.465403	−	0.885099i	$-0.345909\pi$
$241$	14.4500	0.930806	0.465403	+	0.885099i	$0.345909\pi$
$242$	−0.863726	−0.0555224
$243$	1.00000	0.0641500
$244$	−14.1218	−0.904057
$245$	0	0
$246$	1.73217	0.110439
$247$	2.24144	0.142620
$248$	−2.06090	−0.130867
$249$	11.3141	0.717003
$250$	0	0
$251$	−20.4904	−1.29334	−0.646670	−	0.762770i	$-0.723839\pi$
$251$	−20.4904	−1.29334	−0.646670	+	0.762770i	$0.723839\pi$
$252$	−1.94954	−0.122809
$253$	−34.8665	−2.19204
$254$	−1.43351	−0.0899464
$255$	0	0
$256$	14.2728	0.892047
$257$	13.1238	0.818638	0.409319	−	0.912391i	$-0.365766\pi$
$257$	13.1238	0.818638	0.409319	+	0.912391i	$0.365766\pi$
$258$	−1.09458	−0.0681454
$259$	1.81346	0.112683
$260$	0	0
$261$	−9.42182	−0.583196
$262$	1.43301	0.0885316
$263$	−23.0038	−1.41848	−0.709239	−	0.704969i	$-0.750961\pi$
$263$	−23.0038	−1.41848	−0.709239	+	0.704969i	$0.750961\pi$
$264$	2.41784	0.148808
$265$	0	0
$266$	−0.0963116	−0.00590524
$267$	−1.84924	−0.113172
$268$	−12.3108	−0.752001
$269$	16.3649	0.997785	0.498892	−	0.866664i	$-0.333740\pi$
$269$	16.3649	0.997785	0.498892	+	0.866664i	$0.333740\pi$
$270$	0	0
$271$	23.8497	1.44877	0.724383	−	0.689398i	$-0.242125\pi$
$271$	23.8497	1.44877	0.724383	+	0.689398i	$0.242125\pi$
$272$	−14.1490	−0.857908
$273$	3.34930	0.202709
$274$	−0.000932451 0	−5.63315e−5 0
$275$	0	0
$276$	16.8115	1.01193
$277$	−12.6118	−0.757772	−0.378886	−	0.925443i	$-0.623693\pi$
$277$	−12.6118	−0.757772	−0.378886	+	0.925443i	$0.623693\pi$
$278$	0.330647	0.0198309
$279$	−3.49678	−0.209347
$280$	0	0
$281$	−6.52932	−0.389507	−0.194753	−	0.980852i	$-0.562391\pi$
$281$	−6.52932	−0.389507	−0.194753	+	0.980852i	$0.562391\pi$
$282$	1.43232	0.0852936
$283$	−7.29502	−0.433644	−0.216822	−	0.976211i	$-0.569569\pi$
$283$	−7.29502	−0.433644	−0.216822	+	0.976211i	$0.569569\pi$
$284$	−17.1915	−1.02013
$285$	0	0
$286$	−2.06547	−0.122134
$287$	−11.5230	−0.680182
$288$	−1.75192	−0.103233
$289$	−3.62476	−0.213221
$290$	0	0
$291$	−3.60865	−0.211543
$292$	29.6292	1.73392
$293$	−8.74594	−0.510943	−0.255472	−	0.966817i	$-0.582231\pi$
$293$	−8.74594	−0.510943	−0.255472	+	0.966817i	$0.582231\pi$
$294$	0.893174	0.0520909
$295$	0	0
$296$	1.08443	0.0630315
$297$	4.10242	0.238047
$298$	−2.01641	−0.116808
$299$	−28.8821	−1.67030
$300$	0	0
$301$	7.28153	0.419700
$302$	0.106642	0.00613658
$303$	−19.9290	−1.14489
$304$	2.55177	0.146354
$305$	0	0
$306$	0.541837	0.0309748
$307$	−14.5442	−0.830079	−0.415039	−	0.909803i	$-0.636232\pi$
$307$	−14.5442	−0.830079	−0.415039	+	0.909803i	$0.636232\pi$
$308$	−7.99782	−0.455718
$309$	10.3334	0.587845
$310$	0	0
$311$	−21.5973	−1.22467	−0.612335	−	0.790598i	$-0.709770\pi$
$311$	−21.5973	−1.22467	−0.612335	+	0.790598i	$0.709770\pi$
$312$	2.00285	0.113389
$313$	28.5818	1.61554	0.807769	−	0.589499i	$-0.200675\pi$
$313$	28.5818	1.61554	0.807769	+	0.589499i	$0.200675\pi$
$314$	2.06864	0.116740
$315$	0	0
$316$	−6.52062	−0.366813
$317$	−28.7407	−1.61424	−0.807118	−	0.590390i	$-0.798974\pi$
$317$	−28.7407	−1.61424	−0.807118	+	0.590390i	$0.798974\pi$
$318$	−0.441064	−0.0247336
$319$	−38.6523	−2.16411
$320$	0	0
$321$	1.00000	0.0558146
$322$	1.24102	0.0691596
$323$	−2.41222	−0.134220
$324$	−1.97805	−0.109892
$325$	0	0
$326$	0.288261	0.0159653
$327$	−11.0345	−0.610208
$328$	−6.89065	−0.380473
$329$	−9.52834	−0.525314
$330$	0	0
$331$	4.74307	0.260703	0.130351	−	0.991468i	$-0.458389\pi$
$331$	4.74307	0.260703	0.130351	+	0.991468i	$0.458389\pi$
$332$	−22.3799	−1.22826
$333$	1.83999	0.100831
$334$	−1.31133	−0.0717528
$335$	0	0
$336$	3.81301	0.208017
$337$	−8.19859	−0.446606	−0.223303	−	0.974749i	$-0.571684\pi$
$337$	−8.19859	−0.446606	−0.223303	+	0.974749i	$0.571684\pi$
$338$	0.215064	0.0116979
$339$	−0.729507	−0.0396214
$340$	0	0
$341$	−14.3452	−0.776839
$342$	−0.0977203	−0.00528411
$343$	−12.8408	−0.693339
$344$	4.35428	0.234767
$345$	0	0
$346$	−1.90297	−0.102304
$347$	7.30217	0.392001	0.196001	−	0.980604i	$-0.437205\pi$
$347$	7.30217	0.392001	0.196001	+	0.980604i	$0.437205\pi$
$348$	18.6368	0.999039
$349$	19.8957	1.06499	0.532495	−	0.846433i	$-0.321254\pi$
$349$	19.8957	1.06499	0.532495	+	0.846433i	$0.321254\pi$
$350$	0	0
$351$	3.39829	0.181387
$352$	−7.18712	−0.383075
$353$	32.2123	1.71449	0.857244	−	0.514911i	$-0.172175\pi$
$353$	32.2123	1.71449	0.857244	+	0.514911i	$0.172175\pi$
$354$	1.64377	0.0873654
$355$	0	0
$356$	3.65789	0.193868
$357$	−3.60450	−0.190770
$358$	0.731731	0.0386732
$359$	−18.4751	−0.975080	−0.487540	−	0.873101i	$-0.662106\pi$
$359$	−18.4751	−0.975080	−0.487540	+	0.873101i	$0.662106\pi$
$360$	0	0
$361$	−18.5650	−0.977103
$362$	−1.79074	−0.0941190
$363$	5.82986	0.305988
$364$	−6.62509	−0.347249
$365$	0	0
$366$	−1.05772	−0.0552880
$367$	−28.6625	−1.49617	−0.748086	−	0.663602i	$-0.769027\pi$
$367$	−28.6625	−1.49617	−0.748086	+	0.663602i	$0.769027\pi$
$368$	−32.8808	−1.71403
$369$	−11.6916	−0.608638
$370$	0	0
$371$	2.93412	0.152332
$372$	6.91680	0.358619
$373$	−33.3224	−1.72537	−0.862685	−	0.505742i	$-0.831219\pi$
$373$	−33.3224	−1.72537	−0.862685	+	0.505742i	$0.831219\pi$
$374$	2.22284	0.114940
$375$	0	0
$376$	−5.69785	−0.293844
$377$	−32.0181	−1.64902
$378$	−0.146020	−0.00751045
$379$	22.0731	1.13382	0.566908	−	0.823781i	$-0.308139\pi$
$379$	22.0731	1.13382	0.566908	+	0.823781i	$0.308139\pi$
$380$	0	0
$381$	9.67571	0.495701
$382$	0.258473	0.0132246
$383$	30.0257	1.53424	0.767122	−	0.641501i	$-0.221688\pi$
$383$	30.0257	1.53424	0.767122	+	0.641501i	$0.221688\pi$
$384$	4.61175	0.235342
$385$	0	0
$386$	0.202183	0.0102908
$387$	7.38803	0.375555
$388$	7.13809	0.362381
$389$	−4.91703	−0.249303	−0.124652	−	0.992201i	$-0.539781\pi$
$389$	−4.91703	−0.249303	−0.124652	+	0.992201i	$0.539781\pi$
$390$	0	0
$391$	31.0827	1.57192
$392$	−3.55309	−0.179458
$393$	−9.67233	−0.487904
$394$	1.17607	0.0592497
$395$	0	0
$396$	−8.11479	−0.407784
$397$	25.1589	1.26269	0.631344	−	0.775503i	$-0.282503\pi$
$397$	25.1589	1.26269	0.631344	+	0.775503i	$0.282503\pi$
$398$	2.88543	0.144633
$399$	0.650071	0.0325442
$400$	0	0
$401$	−37.8723	−1.89125	−0.945626	−	0.325257i	$-0.894549\pi$
$401$	−37.8723	−1.89125	−0.945626	+	0.325257i	$0.894549\pi$
$402$	−0.922076	−0.0459890
$403$	−11.8831	−0.591938
$404$	39.4205	1.96124
$405$	0	0
$406$	1.37577	0.0682785
$407$	7.54841	0.374161
$408$	−2.15545	−0.106711
$409$	−29.3448	−1.45101	−0.725503	−	0.688219i	$-0.758393\pi$
$409$	−29.3448	−1.45101	−0.725503	+	0.688219i	$0.758393\pi$
$410$	0	0
$411$	0.00629373	0.000310447 0
$412$	−20.4399	−1.00700
$413$	−10.9350	−0.538074
$414$	1.25918	0.0618851
$415$	0	0
$416$	−5.95354	−0.291896
$417$	−2.23175	−0.109289
$418$	−0.400890	−0.0196082
$419$	−21.6284	−1.05662	−0.528309	−	0.849052i	$-0.677174\pi$
$419$	−21.6284	−1.05662	−0.528309	+	0.849052i	$0.677174\pi$
$420$	0	0
$421$	7.59315	0.370068	0.185034	−	0.982732i	$-0.440761\pi$
$421$	7.59315	0.370068	0.185034	+	0.982732i	$0.440761\pi$
$422$	0.587002	0.0285748
$423$	−9.66770	−0.470060
$424$	1.75457	0.0852097
$425$	0	0
$426$	−1.28764	−0.0623865
$427$	7.03635	0.340513
$428$	−1.97805	−0.0956127
$429$	13.9412	0.673089
$430$	0	0
$431$	35.3969	1.70501	0.852505	−	0.522719i	$-0.175082\pi$
$431$	35.3969	1.70501	0.852505	+	0.522719i	$0.175082\pi$
$432$	3.86878	0.186137
$433$	28.3405	1.36196	0.680979	−	0.732303i	$-0.261555\pi$
$433$	28.3405	1.36196	0.680979	+	0.732303i	$0.261555\pi$
$434$	0.510599	0.0245095
$435$	0	0
$436$	21.8268	1.04531
$437$	−5.60577	−0.268160
$438$	2.21922	0.106038
$439$	−7.54092	−0.359909	−0.179954	−	0.983675i	$-0.557595\pi$
$439$	−7.54092	−0.359909	−0.179954	+	0.983675i	$0.557595\pi$
$440$	0	0
$441$	−6.02862	−0.287077
$442$	1.84132	0.0875827
$443$	15.8148	0.751382	0.375691	−	0.926745i	$-0.377405\pi$
$443$	15.8148	0.751382	0.375691	+	0.926745i	$0.377405\pi$
$444$	−3.63959	−0.172727
$445$	0	0
$446$	−0.137560	−0.00651364
$447$	13.6101	0.643736
$448$	−7.37021	−0.348210
$449$	0.196509	0.00927384	0.00463692	−	0.999989i	$-0.498524\pi$
$449$	0.196509	0.00927384	0.00463692	+	0.999989i	$0.498524\pi$
$450$	0	0
$451$	−47.9637	−2.25852
$452$	1.44300	0.0678730
$453$	−0.719800	−0.0338192
$454$	−3.43068	−0.161010
$455$	0	0
$456$	0.388736	0.0182042
$457$	−22.9427	−1.07321	−0.536607	−	0.843832i	$-0.680294\pi$
$457$	−22.9427	−1.07321	−0.536607	+	0.843832i	$0.680294\pi$
$458$	1.84983	0.0864368
$459$	−3.65722	−0.170704
$460$	0	0
$461$	−34.5330	−1.60836	−0.804181	−	0.594385i	$-0.797396\pi$
$461$	−34.5330	−1.60836	−0.804181	+	0.594385i	$0.797396\pi$
$462$	−0.599035	−0.0278696
$463$	18.7791	0.872738	0.436369	−	0.899768i	$-0.356264\pi$
$463$	18.7791	0.872738	0.436369	+	0.899768i	$0.356264\pi$
$464$	−36.4510	−1.69219
$465$	0	0
$466$	0.310278	0.0143734
$467$	11.0087	0.509424	0.254712	−	0.967017i	$-0.418019\pi$
$467$	11.0087	0.509424	0.254712	+	0.967017i	$0.418019\pi$
$468$	−6.72199	−0.310724
$469$	6.13399	0.283241
$470$	0	0
$471$	−13.9627	−0.643365
$472$	−6.53900	−0.300982
$473$	30.3088	1.39360
$474$	−0.488393	−0.0224326
$475$	0	0
$476$	7.12988	0.326797
$477$	2.97703	0.136309
$478$	2.90052	0.132667
$479$	39.3332	1.79718	0.898590	−	0.438790i	$-0.144593\pi$
$479$	39.3332	1.79718	0.898590	+	0.438790i	$0.144593\pi$
$480$	0	0
$481$	6.25282	0.285104
$482$	−2.14085	−0.0975129
$483$	−8.37650	−0.381144
$484$	−11.5318	−0.524171
$485$	0	0
$486$	−0.148156	−0.00672047
$487$	−2.64421	−0.119821	−0.0599103	−	0.998204i	$-0.519081\pi$
$487$	−2.64421	−0.119821	−0.0599103	+	0.998204i	$0.519081\pi$
$488$	4.20767	0.190472
$489$	−1.94566	−0.0879860
$490$	0	0
$491$	−11.0579	−0.499037	−0.249519	−	0.968370i	$-0.580272\pi$
$491$	−11.0579	−0.499037	−0.249519	+	0.968370i	$0.580272\pi$
$492$	23.1265	1.04262
$493$	34.4577	1.55190
$494$	−0.332082	−0.0149411
$495$	0	0
$496$	−13.5283	−0.607437
$497$	8.56587	0.384232
$498$	−1.67625	−0.0751145
$499$	−37.3944	−1.67400	−0.837001	−	0.547202i	$-0.815693\pi$
$499$	−37.3944	−1.67400	−0.837001	+	0.547202i	$0.815693\pi$
$500$	0	0
$501$	8.85103	0.395435
$502$	3.03576	0.135493
$503$	8.07638	0.360108	0.180054	−	0.983657i	$-0.442373\pi$
$503$	8.07638	0.360108	0.180054	+	0.983657i	$0.442373\pi$
$504$	0.580874	0.0258742
$505$	0	0
$506$	5.16567	0.229642
$507$	−1.45161	−0.0644682
$508$	−19.1390	−0.849157
$509$	18.7364	0.830477	0.415239	−	0.909713i	$-0.363698\pi$
$509$	18.7364	0.830477	0.415239	+	0.909713i	$0.363698\pi$
$510$	0	0
$511$	−14.7630	−0.653079
$512$	−11.3381	−0.501077
$513$	0.659579	0.0291211
$514$	−1.94436	−0.0857620
$515$	0	0
$516$	−14.6139	−0.643341
$517$	−39.6610	−1.74429
$518$	−0.268675	−0.0118049
$519$	12.8444	0.563807
$520$	0	0
$521$	−6.36777	−0.278977	−0.139488	−	0.990224i	$-0.544546\pi$
$521$	−6.36777	−0.278977	−0.139488	+	0.990224i	$0.544546\pi$
$522$	1.39590	0.0610967
$523$	−15.9873	−0.699074	−0.349537	−	0.936923i	$-0.613661\pi$
$523$	−15.9873	−0.699074	−0.349537	+	0.936923i	$0.613661\pi$
$524$	19.1323	0.835801
$525$	0	0
$526$	3.40814	0.148602
$527$	12.7885	0.557075
$528$	15.8714	0.690713
$529$	49.2332	2.14057
$530$	0	0
$531$	−11.0949	−0.481478
$532$	−1.28587	−0.0557497
$533$	−39.7313	−1.72096
$534$	0.273975	0.0118560
$535$	0	0
$536$	3.66806	0.158436
$537$	−4.93894	−0.213131
$538$	−2.42455	−0.104530
$539$	−24.7319	−1.06528
$540$	0	0
$541$	−3.98511	−0.171333	−0.0856667	−	0.996324i	$-0.527302\pi$
$541$	−3.98511	−0.171333	−0.0856667	+	0.996324i	$0.527302\pi$
$542$	−3.53346	−0.151775
$543$	12.0869	0.518697
$544$	6.40716	0.274705
$545$	0	0
$546$	−0.496218	−0.0212362
$547$	33.0881	1.41475	0.707373	−	0.706841i	$-0.249880\pi$
$547$	33.0881	1.41475	0.707373	+	0.706841i	$0.249880\pi$
$548$	−0.0124493	−0.000531809 0
$549$	7.13927	0.304697
$550$	0	0
$551$	−6.21444	−0.264744
$552$	−5.00906	−0.213200
$553$	3.24897	0.138160
$554$	1.86851	0.0793856
$555$	0	0
$556$	4.41452	0.187217
$557$	−8.38915	−0.355460	−0.177730	−	0.984079i	$-0.556875\pi$
$557$	−8.38915	−0.355460	−0.177730	+	0.984079i	$0.556875\pi$
$558$	0.518067	0.0219315
$559$	25.1067	1.06190
$560$	0	0
$561$	−15.0034	−0.633446
$562$	0.967355	0.0408054
$563$	−13.1664	−0.554896	−0.277448	−	0.960741i	$-0.589489\pi$
$563$	−13.1664	−0.554896	−0.277448	+	0.960741i	$0.589489\pi$
$564$	19.1232	0.805232
$565$	0	0
$566$	1.08080	0.0454293
$567$	0.985585	0.0413907
$568$	5.12231	0.214927
$569$	24.4543	1.02518	0.512590	−	0.858634i	$-0.328686\pi$
$569$	24.4543	1.02518	0.512590	+	0.858634i	$0.328686\pi$
$570$	0	0
$571$	14.4337	0.604030	0.302015	−	0.953303i	$-0.402341\pi$
$571$	14.4337	0.604030	0.302015	+	0.953303i	$0.402341\pi$
$572$	−27.5764	−1.15303
$573$	−1.74460	−0.0728818
$574$	1.70720	0.0712571
$575$	0	0
$576$	−7.47801	−0.311584
$577$	41.4750	1.72663	0.863313	−	0.504669i	$-0.168385\pi$
$577$	41.4750	1.72663	0.863313	+	0.504669i	$0.168385\pi$
$578$	0.537028	0.0223374
$579$	−1.36466	−0.0567135
$580$	0	0
$581$	11.1510	0.462622
$582$	0.534641	0.0221616
$583$	12.2130	0.505813
$584$	−8.82816	−0.365312
$585$	0	0
$586$	1.29576	0.0535273
$587$	1.78624	0.0737259	0.0368630	−	0.999320i	$-0.488263\pi$
$587$	1.78624	0.0737259	0.0368630	+	0.999320i	$0.488263\pi$
$588$	11.9249	0.491775
$589$	−2.30640	−0.0950336
$590$	0	0
$591$	−7.93810	−0.326530
$592$	7.11851	0.292569
$593$	−41.2548	−1.69413	−0.847067	−	0.531487i	$-0.821633\pi$
$593$	−41.2548	−1.69413	−0.847067	+	0.531487i	$0.821633\pi$
$594$	−0.607796	−0.0249382
$595$	0	0
$596$	−26.9215	−1.10275
$597$	−19.4757	−0.797086
$598$	4.27905	0.174983
$599$	14.0674	0.574779	0.287390	−	0.957814i	$-0.407213\pi$
$599$	14.0674	0.574779	0.287390	+	0.957814i	$0.407213\pi$
$600$	0	0
$601$	40.9040	1.66851	0.834254	−	0.551380i	$-0.185899\pi$
$601$	40.9040	1.66851	0.834254	+	0.551380i	$0.185899\pi$
$602$	−1.07880	−0.0439685
$603$	6.22370	0.253449
$604$	1.42380	0.0579336
$605$	0	0
$606$	2.95259	0.119941
$607$	−2.47869	−0.100607	−0.0503034	−	0.998734i	$-0.516019\pi$
$607$	−2.47869	−0.100607	−0.0503034	+	0.998734i	$0.516019\pi$
$608$	−1.15553	−0.0468629
$609$	−9.28601	−0.376288
$610$	0	0
$611$	−32.8537	−1.32912
$612$	7.23416	0.292424
$613$	−18.1780	−0.734204	−0.367102	−	0.930181i	$-0.619650\pi$
$613$	−18.1780	−0.734204	−0.367102	+	0.930181i	$0.619650\pi$
$614$	2.15480	0.0869605
$615$	0	0
$616$	2.38299	0.0960134
$617$	−46.6424	−1.87775	−0.938876	−	0.344257i	$-0.888131\pi$
$617$	−46.6424	−1.87775	−0.938876	+	0.344257i	$0.888131\pi$
$618$	−1.53095	−0.0615837
$619$	−4.86202	−0.195421	−0.0977105	−	0.995215i	$-0.531152\pi$
$619$	−4.86202	−0.195421	−0.0977105	+	0.995215i	$0.531152\pi$
$620$	0	0
$621$	−8.49901	−0.341054
$622$	3.19976	0.128299
$623$	−1.82258	−0.0730202
$624$	13.1473	0.526311
$625$	0	0
$626$	−4.23455	−0.169247
$627$	2.70587	0.108062
$628$	27.6188	1.10211
$629$	−6.72924	−0.268312
$630$	0	0
$631$	−4.19604	−0.167042	−0.0835209	−	0.996506i	$-0.526617\pi$
$631$	−4.19604	−0.167042	−0.0835209	+	0.996506i	$0.526617\pi$
$632$	1.94285	0.0772825
$633$	−3.96206	−0.157478
$634$	4.25809	0.169110
$635$	0	0
$636$	−5.88872	−0.233503
$637$	−20.4870	−0.811725
$638$	5.72655	0.226716
$639$	8.69116	0.343817
$640$	0	0
$641$	35.1190	1.38712	0.693559	−	0.720400i	$-0.256042\pi$
$641$	35.1190	1.38712	0.693559	+	0.720400i	$0.256042\pi$
$642$	−0.148156	−0.00584723
$643$	−26.8516	−1.05892	−0.529462	−	0.848333i	$-0.677606\pi$
$643$	−26.8516	−1.05892	−0.529462	+	0.848333i	$0.677606\pi$
$644$	16.5691	0.652915
$645$	0	0
$646$	0.357384	0.0140611
$647$	−25.6745	−1.00937	−0.504684	−	0.863304i	$-0.668391\pi$
$647$	−25.6745	−1.00937	−0.504684	+	0.863304i	$0.668391\pi$
$648$	0.589370	0.0231526
$649$	−45.5160	−1.78666
$650$	0	0
$651$	−3.44637	−0.135074
$652$	3.84862	0.150724
$653$	−30.4415	−1.19127	−0.595634	−	0.803256i	$-0.703099\pi$
$653$	−30.4415	−1.19127	−0.595634	+	0.803256i	$0.703099\pi$
$654$	1.63482	0.0639265
$655$	0	0
$656$	−45.2321	−1.76602
$657$	−14.9790	−0.584385
$658$	1.41168	0.0550329
$659$	10.9760	0.427565	0.213783	−	0.976881i	$-0.431422\pi$
$659$	10.9760	0.427565	0.213783	+	0.976881i	$0.431422\pi$
$660$	0	0
$661$	−37.8482	−1.47212	−0.736062	−	0.676914i	$-0.763317\pi$
$661$	−37.8482	−1.47212	−0.736062	+	0.676914i	$0.763317\pi$
$662$	−0.702712	−0.0273117
$663$	−12.4283	−0.482675
$664$	6.66820	0.258776
$665$	0	0
$666$	−0.272604	−0.0105632
$667$	80.0762	3.10056
$668$	−17.5078	−0.677397
$669$	0.928481	0.0358972
$670$	0	0
$671$	29.2883	1.13066
$672$	−1.72667	−0.0666076
$673$	−29.7951	−1.14852	−0.574259	−	0.818674i	$-0.694710\pi$
$673$	−29.7951	−1.14852	−0.574259	+	0.818674i	$0.694710\pi$
$674$	1.21467	0.0467872
$675$	0	0
$676$	2.87136	0.110437
$677$	22.8755	0.879177	0.439589	−	0.898199i	$-0.355124\pi$
$677$	22.8755	0.879177	0.439589	+	0.898199i	$0.355124\pi$
$678$	0.108080	0.00415080
$679$	−3.55663	−0.136491
$680$	0	0
$681$	23.1559	0.887337
$682$	2.12533	0.0813830
$683$	39.7350	1.52042	0.760209	−	0.649679i	$-0.225097\pi$
$683$	39.7350	1.52042	0.760209	+	0.649679i	$0.225097\pi$
$684$	−1.30468	−0.0498857
$685$	0	0
$686$	1.90244	0.0726354
$687$	−12.4857	−0.476360
$688$	28.5827	1.08970
$689$	10.1168	0.385421
$690$	0	0
$691$	−10.4687	−0.398250	−0.199125	−	0.979974i	$-0.563810\pi$
$691$	−10.4687	−0.398250	−0.199125	+	0.979974i	$0.563810\pi$
$692$	−25.4069	−0.965824
$693$	4.04328	0.153592
$694$	−1.08186	−0.0410667
$695$	0	0
$696$	−5.55294	−0.210484
$697$	42.7586	1.61960
$698$	−2.94765	−0.111570
$699$	−2.09427	−0.0792127
$700$	0	0
$701$	−51.0938	−1.92979	−0.964893	−	0.262642i	$-0.915406\pi$
$701$	−51.0938	−1.92979	−0.964893	+	0.262642i	$0.915406\pi$
$702$	−0.503476	−0.0190025
$703$	1.21362	0.0457725
$704$	−30.6779	−1.15622
$705$	0	0
$706$	−4.77243	−0.179613
$707$	−19.6417	−0.738702
$708$	21.9463	0.824791
$709$	−21.7181	−0.815642	−0.407821	−	0.913062i	$-0.633711\pi$
$709$	−21.7181	−0.815642	−0.407821	+	0.913062i	$0.633711\pi$
$710$	0	0
$711$	3.29649	0.123628
$712$	−1.08989	−0.0408452
$713$	29.7191	1.11299
$714$	0.534026	0.0199854
$715$	0	0
$716$	9.76947	0.365102
$717$	−19.5775	−0.731137
$718$	2.73719	0.102151
$719$	11.0238	0.411119	0.205559	−	0.978645i	$-0.434099\pi$
$719$	11.0238	0.411119	0.205559	+	0.978645i	$0.434099\pi$
$720$	0	0
$721$	10.1844	0.379288
$722$	2.75050	0.102363
$723$	14.4500	0.537401
$724$	−23.9084	−0.888550
$725$	0	0
$726$	−0.863726	−0.0320559
$727$	32.0197	1.18755	0.593773	−	0.804633i	$-0.297638\pi$
$727$	32.0197	1.18755	0.593773	+	0.804633i	$0.297638\pi$
$728$	1.97398	0.0731606
$729$	1.00000	0.0370370
$730$	0	0
$731$	−27.0196	−0.999357
$732$	−14.1218	−0.521958
$733$	−0.551343	−0.0203643	−0.0101822	−	0.999948i	$-0.503241\pi$
$733$	−0.551343	−0.0203643	−0.0101822	+	0.999948i	$0.503241\pi$
$734$	4.24651	0.156742
$735$	0	0
$736$	14.8896	0.548838
$737$	25.5322	0.940492
$738$	1.73217	0.0637620
$739$	−41.0082	−1.50851	−0.754255	−	0.656582i	$-0.772002\pi$
$739$	−41.0082	−1.50851	−0.754255	+	0.656582i	$0.772002\pi$
$740$	0	0
$741$	2.24144	0.0823414
$742$	−0.434706	−0.0159586
$743$	18.1387	0.665443	0.332721	−	0.943025i	$-0.392033\pi$
$743$	18.1387	0.665443	0.332721	+	0.943025i	$0.392033\pi$
$744$	−2.06090	−0.0755561
$745$	0	0
$746$	4.93690	0.180753
$747$	11.3141	0.413962
$748$	29.6776	1.08512
$749$	0.985585	0.0360125
$750$	0	0
$751$	−25.2857	−0.922687	−0.461344	−	0.887222i	$-0.652632\pi$
$751$	−25.2857	−0.922687	−0.461344	+	0.887222i	$0.652632\pi$
$752$	−37.4022	−1.36392
$753$	−20.4904	−0.746711
$754$	4.74366	0.172754
$755$	0	0
$756$	−1.94954	−0.0709039
$757$	31.6370	1.14987	0.574933	−	0.818201i	$-0.305028\pi$
$757$	31.6370	1.14987	0.574933	+	0.818201i	$0.305028\pi$
$758$	−3.27025	−0.118781
$759$	−34.8665	−1.26557
$760$	0	0
$761$	53.3856	1.93523	0.967614	−	0.252434i	$-0.0812311\pi$
$761$	53.3856	1.93523	0.967614	+	0.252434i	$0.0812311\pi$
$762$	−1.43351	−0.0519306
$763$	−10.8754	−0.393717
$764$	3.45091	0.124850
$765$	0	0
$766$	−4.44848	−0.160730
$767$	−37.7037	−1.36140
$768$	14.2728	0.515024
$769$	4.18380	0.150872	0.0754358	−	0.997151i	$-0.475965\pi$
$769$	4.18380	0.150872	0.0754358	+	0.997151i	$0.475965\pi$
$770$	0	0
$771$	13.1238	0.472641
$772$	2.69938	0.0971526
$773$	24.7962	0.891856	0.445928	−	0.895069i	$-0.352874\pi$
$773$	24.7962	0.891856	0.445928	+	0.895069i	$0.352874\pi$
$774$	−1.09458	−0.0393438
$775$	0	0
$776$	−2.12683	−0.0763487
$777$	1.81346	0.0650577
$778$	0.728484	0.0261174
$779$	−7.71151	−0.276293
$780$	0	0
$781$	35.6548	1.27583
$782$	−4.60508	−0.164677
$783$	−9.42182	−0.336709
$784$	−23.3234	−0.832979
$785$	0	0
$786$	1.43301	0.0511137
$787$	42.2600	1.50641	0.753203	−	0.657788i	$-0.228508\pi$
$787$	42.2600	1.50641	0.753203	+	0.657788i	$0.228508\pi$
$788$	15.7020	0.559359
$789$	−23.0038	−0.818958
$790$	0	0
$791$	−0.718990	−0.0255644
$792$	2.41784	0.0859143
$793$	24.2613	0.861545
$794$	−3.72743	−0.132282
$795$	0	0
$796$	38.5238	1.36544
$797$	−21.3908	−0.757701	−0.378851	−	0.925458i	$-0.623681\pi$
$797$	−21.3908	−0.757701	−0.378851	+	0.925458i	$0.623681\pi$
$798$	−0.0963116	−0.00340939
$799$	35.3569	1.25084
$800$	0	0
$801$	−1.84924	−0.0653396
$802$	5.61099	0.198131
$803$	−61.4500	−2.16853
$804$	−12.3108	−0.434168
$805$	0	0
$806$	1.76054	0.0620124
$807$	16.3649	0.576071
$808$	−11.7455	−0.413207
$809$	−6.93876	−0.243954	−0.121977	−	0.992533i	$-0.538923\pi$
$809$	−6.93876	−0.243954	−0.121977	+	0.992533i	$0.538923\pi$
$810$	0	0
$811$	22.5876	0.793157	0.396579	−	0.918001i	$-0.370197\pi$
$811$	22.5876	0.793157	0.396579	+	0.918001i	$0.370197\pi$
$812$	18.3682	0.644597
$813$	23.8497	0.836446
$814$	−1.11834	−0.0391977
$815$	0	0
$816$	−14.1490	−0.495313
$817$	4.87299	0.170484
$818$	4.34759	0.152010
$819$	3.34930	0.117034
$820$	0	0
$821$	−0.924354	−0.0322602	−0.0161301	−	0.999870i	$-0.505135\pi$
$821$	−0.924354	−0.0322602	−0.0161301	+	0.999870i	$0.505135\pi$
$822$	−0.000932451 0	−3.25230e−5 0
$823$	−0.427635	−0.0149064	−0.00745321	−	0.999972i	$-0.502372\pi$
$823$	−0.427635	−0.0149064	−0.00745321	+	0.999972i	$0.502372\pi$
$824$	6.09019	0.212162
$825$	0	0
$826$	1.62008	0.0563696
$827$	21.4570	0.746132	0.373066	−	0.927805i	$-0.378306\pi$
$827$	21.4570	0.746132	0.373066	+	0.927805i	$0.378306\pi$
$828$	16.8115	0.584239
$829$	46.3160	1.60862	0.804311	−	0.594208i	$-0.202534\pi$
$829$	46.3160	1.60862	0.804311	+	0.594208i	$0.202534\pi$
$830$	0	0
$831$	−12.6118	−0.437500
$832$	−25.4125	−0.881018
$833$	22.0480	0.763917
$834$	0.330647	0.0114494
$835$	0	0
$836$	−5.35235	−0.185115
$837$	−3.49678	−0.120866
$838$	3.20437	0.110693
$839$	−12.8325	−0.443028	−0.221514	−	0.975157i	$-0.571100\pi$
$839$	−12.8325	−0.443028	−0.221514	+	0.975157i	$0.571100\pi$
$840$	0	0
$841$	59.7708	2.06106
$842$	−1.12497	−0.0387689
$843$	−6.52932	−0.224882
$844$	7.83716	0.269766
$845$	0	0
$846$	1.43232	0.0492443
$847$	5.74582	0.197429
$848$	11.5175	0.395512
$849$	−7.29502	−0.250364
$850$	0	0
$851$	−15.6381	−0.536067
$852$	−17.1915	−0.588973
$853$	−30.7393	−1.05249	−0.526246	−	0.850332i	$-0.676401\pi$
$853$	−30.7393	−1.05249	−0.526246	+	0.850332i	$0.676401\pi$
$854$	−1.04247	−0.0356727
$855$	0	0
$856$	0.589370	0.0201443
$857$	44.3660	1.51551	0.757756	−	0.652537i	$-0.226296\pi$
$857$	44.3660	1.51551	0.757756	+	0.652537i	$0.226296\pi$
$858$	−2.06547	−0.0705140
$859$	8.73798	0.298136	0.149068	−	0.988827i	$-0.452373\pi$
$859$	8.73798	0.298136	0.149068	+	0.988827i	$0.452373\pi$
$860$	0	0
$861$	−11.5230	−0.392704
$862$	−5.24425	−0.178620
$863$	23.6968	0.806649	0.403325	−	0.915057i	$-0.367855\pi$
$863$	23.6968	0.806649	0.403325	+	0.915057i	$0.367855\pi$
$864$	−1.75192	−0.0596016
$865$	0	0
$866$	−4.19880	−0.142681
$867$	−3.62476	−0.123103
$868$	6.81709	0.231387
$869$	13.5236	0.458756
$870$	0	0
$871$	21.1500	0.716639
$872$	−6.50339	−0.220233
$873$	−3.60865	−0.122134
$874$	0.830526	0.0280929
$875$	0	0
$876$	29.6292	1.00108
$877$	1.61030	0.0543759	0.0271879	−	0.999630i	$-0.491345\pi$
$877$	1.61030	0.0543759	0.0271879	+	0.999630i	$0.491345\pi$
$878$	1.11723	0.0377047
$879$	−8.74594	−0.294993
$880$	0	0
$881$	−42.0904	−1.41806	−0.709031	−	0.705177i	$-0.750867\pi$
$881$	−42.0904	−1.41806	−0.709031	+	0.705177i	$0.750867\pi$
$882$	0.893174	0.0300747
$883$	16.1757	0.544355	0.272178	−	0.962247i	$-0.412256\pi$
$883$	16.1757	0.544355	0.272178	+	0.962247i	$0.412256\pi$
$884$	24.5838	0.826842
$885$	0	0
$886$	−2.34304	−0.0787161
$887$	−7.61213	−0.255590	−0.127795	−	0.991801i	$-0.540790\pi$
$887$	−7.61213	−0.255590	−0.127795	+	0.991801i	$0.540790\pi$
$888$	1.08443	0.0363912
$889$	9.53623	0.319835
$890$	0	0
$891$	4.10242	0.137436
$892$	−1.83658	−0.0614933
$893$	−6.37661	−0.213385
$894$	−2.01641	−0.0674390
$895$	0	0
$896$	4.54527	0.151847
$897$	−28.8821	−0.964346
$898$	−0.0291139	−0.000971544 0
$899$	32.9460	1.09881
$900$	0	0
$901$	−10.8877	−0.362721
$902$	7.10609	0.236607
$903$	7.28153	0.242314
$904$	−0.429949	−0.0142999
$905$	0	0
$906$	0.106642	0.00354295
$907$	−34.4539	−1.14402	−0.572012	−	0.820245i	$-0.693837\pi$
$907$	−34.4539	−1.14402	−0.572012	+	0.820245i	$0.693837\pi$
$908$	−45.8036	−1.52004
$909$	−19.9290	−0.661003
$910$	0	0
$911$	−14.7141	−0.487499	−0.243750	−	0.969838i	$-0.578377\pi$
$911$	−14.7141	−0.487499	−0.243750	+	0.969838i	$0.578377\pi$
$912$	2.55177	0.0844974
$913$	46.4153	1.53612
$914$	3.39909	0.112432
$915$	0	0
$916$	24.6974	0.816025
$917$	−9.53290	−0.314804
$918$	0.541837	0.0178833
$919$	37.1257	1.22466	0.612332	−	0.790600i	$-0.290231\pi$
$919$	37.1257	1.22466	0.612332	+	0.790600i	$0.290231\pi$
$920$	0	0
$921$	−14.5442	−0.479246
$922$	5.11625	0.168495
$923$	29.5351	0.972159
$924$	−7.99782	−0.263109
$925$	0	0
$926$	−2.78223	−0.0914296
$927$	10.3334	0.339393
$928$	16.5063	0.541846
$929$	−30.0398	−0.985575	−0.492788	−	0.870150i	$-0.664022\pi$
$929$	−30.0398	−0.985575	−0.492788	+	0.870150i	$0.664022\pi$
$930$	0	0
$931$	−3.97635	−0.130320
$932$	4.14258	0.135695
$933$	−21.5973	−0.707064
$934$	−1.63101	−0.0533681
$935$	0	0
$936$	2.00285	0.0654653
$937$	−14.1791	−0.463210	−0.231605	−	0.972810i	$-0.574398\pi$
$937$	−14.1791	−0.463210	−0.231605	+	0.972810i	$0.574398\pi$
$938$	−0.908784	−0.0296728
$939$	28.5818	0.932732
$940$	0	0
$941$	23.0969	0.752936	0.376468	−	0.926430i	$-0.377138\pi$
$941$	23.0969	0.752936	0.376468	+	0.926430i	$0.377138\pi$
$942$	2.06864	0.0674001
$943$	99.3667	3.23583
$944$	−42.9237	−1.39705
$945$	0	0
$946$	−4.49042	−0.145996
$947$	−3.67580	−0.119447	−0.0597237	−	0.998215i	$-0.519022\pi$
$947$	−3.67580	−0.119447	−0.0597237	+	0.998215i	$0.519022\pi$
$948$	−6.52062	−0.211780
$949$	−50.9029	−1.65238
$950$	0	0
$951$	−28.7407	−0.931980
$952$	−2.12438	−0.0688517
$953$	−31.2647	−1.01276	−0.506382	−	0.862309i	$-0.669018\pi$
$953$	−31.2647	−1.01276	−0.506382	+	0.862309i	$0.669018\pi$
$954$	−0.441064	−0.0142800
$955$	0	0
$956$	38.7254	1.25247
$957$	−38.6523	−1.24945
$958$	−5.82743	−0.188276
$959$	0.00620301	0.000200306 0
$960$	0	0
$961$	−18.7726	−0.605566
$962$	−0.926390	−0.0298680
$963$	1.00000	0.0322245
$964$	−28.5828	−0.920591
$965$	0	0
$966$	1.24102	0.0399293
$967$	−26.8657	−0.863943	−0.431972	−	0.901887i	$-0.642182\pi$
$967$	−26.8657	−0.863943	−0.431972	+	0.901887i	$0.642182\pi$
$968$	3.43594	0.110435
$969$	−2.41222	−0.0774918
$970$	0	0
$971$	40.1071	1.28710	0.643549	−	0.765405i	$-0.277461\pi$
$971$	40.1071	1.28710	0.643549	+	0.765405i	$0.277461\pi$
$972$	−1.97805	−0.0634460
$973$	−2.19958	−0.0705154
$974$	0.391754	0.0125526
$975$	0	0
$976$	27.6203	0.884103
$977$	40.3443	1.29073	0.645364	−	0.763875i	$-0.276706\pi$
$977$	40.3443	1.29073	0.645364	+	0.763875i	$0.276706\pi$
$978$	0.288261	0.00921756
$979$	−7.58635	−0.242461
$980$	0	0
$981$	−11.0345	−0.352304
$982$	1.63829	0.0522800
$983$	37.4270	1.19374	0.596868	−	0.802339i	$-0.296412\pi$
$983$	37.4270	1.19374	0.596868	+	0.802339i	$0.296412\pi$
$984$	−6.89065	−0.219666
$985$	0	0
$986$	−5.10509	−0.162579
$987$	−9.52834	−0.303290
$988$	−4.43368	−0.141054
$989$	−62.7909	−1.99664
$990$	0	0
$991$	−19.4198	−0.616889	−0.308445	−	0.951242i	$-0.599808\pi$
$991$	−19.4198	−0.616889	−0.308445	+	0.951242i	$0.599808\pi$
$992$	6.12608	0.194503
$993$	4.74307	0.150517
$994$	−1.26908	−0.0402528
$995$	0	0
$996$	−22.3799	−0.709134
$997$	−1.36966	−0.0433775	−0.0216887	−	0.999765i	$-0.506904\pi$
$997$	−1.36966	−0.0433775	−0.0216887	+	0.999765i	$0.506904\pi$
$998$	5.54018	0.175371
$999$	1.83999	0.0582147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.bc.1.6		10
5.4	even	2		1605.2.a.k.1.5	✓	10
15.14	odd	2		4815.2.a.p.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1605.2.a.k.1.5	✓	10	5.4	even	2
4815.2.a.p.1.6		10	15.14	odd	2
8025.2.a.bc.1.6		10	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:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.148156 q^{2} +1.00000 q^{3} -1.97805 q^{4} -0.148156 q^{6} +0.985585 q^{7} +0.589370 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.148156 q^{2} +1.00000 q^{3} -1.97805 q^{4} -0.148156 q^{6} +0.985585 q^{7} +0.589370 q^{8} +1.00000 q^{9} +4.10242 q^{11} -1.97805 q^{12} +3.39829 q^{13} -0.146020 q^{14} +3.86878 q^{16} -3.65722 q^{17} -0.148156 q^{18} +0.659579 q^{19} +0.985585 q^{21} -0.607796 q^{22} -8.49901 q^{23} +0.589370 q^{24} -0.503476 q^{26} +1.00000 q^{27} -1.94954 q^{28} -9.42182 q^{29} -3.49678 q^{31} -1.75192 q^{32} +4.10242 q^{33} +0.541837 q^{34} -1.97805 q^{36} +1.83999 q^{37} -0.0977203 q^{38} +3.39829 q^{39} -11.6916 q^{41} -0.146020 q^{42} +7.38803 q^{43} -8.11479 q^{44} +1.25918 q^{46} -9.66770 q^{47} +3.86878 q^{48} -6.02862 q^{49} -3.65722 q^{51} -6.72199 q^{52} +2.97703 q^{53} -0.148156 q^{54} +0.580874 q^{56} +0.659579 q^{57} +1.39590 q^{58} -11.0949 q^{59} +7.13927 q^{61} +0.518067 q^{62} +0.985585 q^{63} -7.47801 q^{64} -0.607796 q^{66} +6.22370 q^{67} +7.23416 q^{68} -8.49901 q^{69} +8.69116 q^{71} +0.589370 q^{72} -14.9790 q^{73} -0.272604 q^{74} -1.30468 q^{76} +4.04328 q^{77} -0.503476 q^{78} +3.29649 q^{79} +1.00000 q^{81} +1.73217 q^{82} +11.3141 q^{83} -1.94954 q^{84} -1.09458 q^{86} -9.42182 q^{87} +2.41784 q^{88} -1.84924 q^{89} +3.34930 q^{91} +16.8115 q^{92} -3.49678 q^{93} +1.43232 q^{94} -1.75192 q^{96} -3.60865 q^{97} +0.893174 q^{98} +4.10242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9	\( 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9} - 14 q^{11} + 10 q^{12} + 3 q^{13} - 16 q^{14} + 10 q^{16} - 8 q^{17} - 2 q^{18} - 19 q^{19} - 5 q^{22} - 4 q^{23} - 22 q^{26} + 10 q^{27} - 25 q^{29} - 2 q^{31} + 13 q^{32} - 14 q^{33} - 37 q^{34} + 10 q^{36} + 10 q^{37} + 13 q^{38} + 3 q^{39} - 31 q^{41} - 16 q^{42} - 62 q^{44} + 2 q^{46} + q^{47} + 10 q^{48} + 26 q^{49} - 8 q^{51} + 30 q^{52} - 9 q^{53} - 2 q^{54} - 63 q^{56} - 19 q^{57} - 30 q^{58} - 65 q^{59} + 12 q^{61} + 39 q^{62} - 2 q^{64} - 5 q^{66} + 10 q^{67} - 22 q^{68} - 4 q^{69} - 45 q^{71} - q^{73} + 19 q^{74} - 39 q^{76} + q^{77} - 22 q^{78} - 47 q^{79} + 10 q^{81} + 23 q^{82} - q^{83} + 12 q^{86} - 25 q^{87} + 8 q^{88} - 34 q^{89} - 26 q^{91} - 14 q^{92} - 2 q^{93} - 64 q^{94} + 13 q^{96} - 5 q^{97} + 51 q^{98} - 14 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9 - 14 * q^11 + 10 * q^12 + 3 * q^13 - 16 * q^14 + 10 * q^16 - 8 * q^17 - 2 * q^18 - 19 * q^19 - 5 * q^22 - 4 * q^23 - 22 * q^26 + 10 * q^27 - 25 * q^29 - 2 * q^31 + 13 * q^32 - 14 * q^33 - 37 * q^34 + 10 * q^36 + 10 * q^37 + 13 * q^38 + 3 * q^39 - 31 * q^41 - 16 * q^42 - 62 * q^44 + 2 * q^46 + q^47 + 10 * q^48 + 26 * q^49 - 8 * q^51 + 30 * q^52 - 9 * q^53 - 2 * q^54 - 63 * q^56 - 19 * q^57 - 30 * q^58 - 65 * q^59 + 12 * q^61 + 39 * q^62 - 2 * q^64 - 5 * q^66 + 10 * q^67 - 22 * q^68 - 4 * q^69 - 45 * q^71 - q^73 + 19 * q^74 - 39 * q^76 + q^77 - 22 * q^78 - 47 * q^79 + 10 * q^81 + 23 * q^82 - q^83 + 12 * q^86 - 25 * q^87 + 8 * q^88 - 34 * q^89 - 26 * q^91 - 14 * q^92 - 2 * q^93 - 64 * q^94 + 13 * q^96 - 5 * q^97 + 51 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

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Database

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