LMFDB - Embedded newform 4025.2.a.bb.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} + \cdots - 5 $ x^14 - x^13 - 22x^12 + 18x^11 + 187x^10 - 118x^9 - 772x^8 + 346x^7 + 1581x^6 - 443x^5 - 1429x^4 + 193x^3 + 386x^2 - 3x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.79074$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79074 q^{2} +2.29281 q^{3} +5.78823 q^{4} +6.39865 q^{6} +1.00000 q^{7} +10.5720 q^{8} +2.25700 q^{9} +O(q^{10})$	\(q+2.79074 q^{2} +2.29281 q^{3} +5.78823 q^{4} +6.39865 q^{6} +1.00000 q^{7} +10.5720 q^{8} +2.25700 q^{9} +0.340565 q^{11} +13.2713 q^{12} +1.30291 q^{13} +2.79074 q^{14} +17.9272 q^{16} -2.59659 q^{17} +6.29870 q^{18} -8.28544 q^{19} +2.29281 q^{21} +0.950428 q^{22} -1.00000 q^{23} +24.2396 q^{24} +3.63608 q^{26} -1.70356 q^{27} +5.78823 q^{28} +3.78448 q^{29} -9.08631 q^{31} +28.8861 q^{32} +0.780852 q^{33} -7.24642 q^{34} +13.0640 q^{36} -6.40257 q^{37} -23.1225 q^{38} +2.98733 q^{39} +0.841753 q^{41} +6.39865 q^{42} -9.17532 q^{43} +1.97127 q^{44} -2.79074 q^{46} -4.66829 q^{47} +41.1037 q^{48} +1.00000 q^{49} -5.95351 q^{51} +7.54155 q^{52} -3.49781 q^{53} -4.75420 q^{54} +10.5720 q^{56} -18.9970 q^{57} +10.5615 q^{58} -2.98127 q^{59} -3.00861 q^{61} -25.3575 q^{62} +2.25700 q^{63} +44.7594 q^{64} +2.17916 q^{66} +11.6183 q^{67} -15.0297 q^{68} -2.29281 q^{69} +5.87205 q^{71} +23.8610 q^{72} +7.81259 q^{73} -17.8679 q^{74} -47.9581 q^{76} +0.340565 q^{77} +8.33687 q^{78} +4.35387 q^{79} -10.6770 q^{81} +2.34912 q^{82} +9.31355 q^{83} +13.2713 q^{84} -25.6059 q^{86} +8.67710 q^{87} +3.60044 q^{88} +2.83424 q^{89} +1.30291 q^{91} -5.78823 q^{92} -20.8332 q^{93} -13.0280 q^{94} +66.2306 q^{96} -0.660946 q^{97} +2.79074 q^{98} +0.768655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9	$ 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9} - 3 q^{11} + 11 q^{12} + 15 q^{13} + q^{14} + 23 q^{16} + 9 q^{17} + 17 q^{18} - 4 q^{19} + 6 q^{21} + 9 q^{22} - 14 q^{23} + 10 q^{24} - 5 q^{26} + 33 q^{27} + 17 q^{28} + 11 q^{29} - q^{31} + 24 q^{32} + 26 q^{33} - 6 q^{34} + 13 q^{36} + 18 q^{37} - 6 q^{38} + 6 q^{39} - 7 q^{41} - 4 q^{42} + 18 q^{43} - 16 q^{44} - q^{46} + 10 q^{47} + 40 q^{48} + 14 q^{49} + 28 q^{51} + 46 q^{52} + 5 q^{53} - 24 q^{54} + 9 q^{56} - 26 q^{57} + 2 q^{58} - 24 q^{59} - 6 q^{61} - 16 q^{62} + 18 q^{63} + 29 q^{64} + 27 q^{66} + 61 q^{67} + 35 q^{68} - 6 q^{69} + 11 q^{71} + 12 q^{72} + 28 q^{73} - 49 q^{74} - 27 q^{76} - 3 q^{77} + 38 q^{78} + 6 q^{79} + 26 q^{81} - 14 q^{82} + 16 q^{83} + 11 q^{84} + 46 q^{86} + 61 q^{87} + 58 q^{88} - 39 q^{89} + 15 q^{91} - 17 q^{92} + 21 q^{93} - 74 q^{94} + 41 q^{96} + 19 q^{97} + q^{98} - 9 q^{99}+O(q^{100}) $ 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9 - 3 * q^11 + 11 * q^12 + 15 * q^13 + q^14 + 23 * q^16 + 9 * q^17 + 17 * q^18 - 4 * q^19 + 6 * q^21 + 9 * q^22 - 14 * q^23 + 10 * q^24 - 5 * q^26 + 33 * q^27 + 17 * q^28 + 11 * q^29 - q^31 + 24 * q^32 + 26 * q^33 - 6 * q^34 + 13 * q^36 + 18 * q^37 - 6 * q^38 + 6 * q^39 - 7 * q^41 - 4 * q^42 + 18 * q^43 - 16 * q^44 - q^46 + 10 * q^47 + 40 * q^48 + 14 * q^49 + 28 * q^51 + 46 * q^52 + 5 * q^53 - 24 * q^54 + 9 * q^56 - 26 * q^57 + 2 * q^58 - 24 * q^59 - 6 * q^61 - 16 * q^62 + 18 * q^63 + 29 * q^64 + 27 * q^66 + 61 * q^67 + 35 * q^68 - 6 * q^69 + 11 * q^71 + 12 * q^72 + 28 * q^73 - 49 * q^74 - 27 * q^76 - 3 * q^77 + 38 * q^78 + 6 * q^79 + 26 * q^81 - 14 * q^82 + 16 * q^83 + 11 * q^84 + 46 * q^86 + 61 * q^87 + 58 * q^88 - 39 * q^89 + 15 * q^91 - 17 * q^92 + 21 * q^93 - 74 * q^94 + 41 * q^96 + 19 * q^97 + q^98 - 9 * 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 $

$2$	2.79074	1.97335	0.986676	−	0.162699i	$-0.0520198\pi$
$2$	2.79074	1.97335	0.986676	+	0.162699i	$0.0520198\pi$
$3$	2.29281	1.32376	0.661879	−	0.749611i	$-0.269759\pi$
$3$	2.29281	1.32376	0.661879	+	0.749611i	$0.269759\pi$
$4$	5.78823	2.89412
$5$	0	0
$5$	0	0
$6$	6.39865	2.61224
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	10.5720	3.73776
$9$	2.25700	0.752333
$10$	0	0
$11$	0.340565	0.102684	0.0513421	−	0.998681i	$-0.483650\pi$
$11$	0.340565	0.102684	0.0513421	+	0.998681i	$0.483650\pi$
$12$	13.2713	3.83111
$13$	1.30291	0.361362	0.180681	−	0.983542i	$-0.442170\pi$
$13$	1.30291	0.361362	0.180681	+	0.983542i	$0.442170\pi$
$14$	2.79074	0.745857
$15$	0	0
$16$	17.9272	4.48179
$17$	−2.59659	−0.629767	−0.314883	−	0.949130i	$-0.601965\pi$
$17$	−2.59659	−0.629767	−0.314883	+	0.949130i	$0.601965\pi$
$18$	6.29870	1.48462
$19$	−8.28544	−1.90081	−0.950405	−	0.311015i	$-0.899331\pi$
$19$	−8.28544	−1.90081	−0.950405	+	0.311015i	$0.899331\pi$
$20$	0	0
$21$	2.29281	0.500333
$22$	0.950428	0.202632
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	24.2396	4.94788
$25$	0	0
$26$	3.63608	0.713095
$27$	−1.70356	−0.327851
$28$	5.78823	1.09387
$29$	3.78448	0.702760	0.351380	−	0.936233i	$-0.385713\pi$
$29$	3.78448	0.702760	0.351380	+	0.936233i	$0.385713\pi$
$30$	0	0
$31$	−9.08631	−1.63195	−0.815975	−	0.578088i	$-0.803799\pi$
$31$	−9.08631	−1.63195	−0.815975	+	0.578088i	$0.803799\pi$
$32$	28.8861	5.10640
$33$	0.780852	0.135929
$34$	−7.24642	−1.24275
$35$	0	0
$36$	13.0640	2.17734
$37$	−6.40257	−1.05258	−0.526288	−	0.850306i	$-0.676417\pi$
$37$	−6.40257	−1.05258	−0.526288	+	0.850306i	$0.676417\pi$
$38$	−23.1225	−3.75097
$39$	2.98733	0.478356
$40$	0	0
$41$	0.841753	0.131460	0.0657299	−	0.997837i	$-0.479062\pi$
$41$	0.841753	0.131460	0.0657299	+	0.997837i	$0.479062\pi$
$42$	6.39865	0.987333
$43$	−9.17532	−1.39922	−0.699612	−	0.714523i	$-0.746644\pi$
$43$	−9.17532	−1.39922	−0.699612	+	0.714523i	$0.746644\pi$
$44$	1.97127	0.297180
$45$	0	0
$46$	−2.79074	−0.411472
$47$	−4.66829	−0.680940	−0.340470	−	0.940255i	$-0.610586\pi$
$47$	−4.66829	−0.680940	−0.340470	+	0.940255i	$0.610586\pi$
$48$	41.1037	5.93281
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.95351	−0.833658
$52$	7.54155	1.04582
$53$	−3.49781	−0.480461	−0.240230	−	0.970716i	$-0.577223\pi$
$53$	−3.49781	−0.480461	−0.240230	+	0.970716i	$0.577223\pi$
$54$	−4.75420	−0.646964
$55$	0	0
$56$	10.5720	1.41274
$57$	−18.9970	−2.51621
$58$	10.5615	1.38679
$59$	−2.98127	−0.388128	−0.194064	−	0.980989i	$-0.562167\pi$
$59$	−2.98127	−0.388128	−0.194064	+	0.980989i	$0.562167\pi$
$60$	0	0
$61$	−3.00861	−0.385213	−0.192607	−	0.981276i	$-0.561694\pi$
$61$	−3.00861	−0.385213	−0.192607	+	0.981276i	$0.561694\pi$
$62$	−25.3575	−3.22041
$63$	2.25700	0.284355
$64$	44.7594	5.59492
$65$	0	0
$66$	2.17916	0.268236
$67$	11.6183	1.41940	0.709701	−	0.704503i	$-0.248830\pi$
$67$	11.6183	1.41940	0.709701	+	0.704503i	$0.248830\pi$
$68$	−15.0297	−1.82262
$69$	−2.29281	−0.276022
$70$	0	0
$71$	5.87205	0.696884	0.348442	−	0.937330i	$-0.386711\pi$
$71$	5.87205	0.696884	0.348442	+	0.937330i	$0.386711\pi$
$72$	23.8610	2.81204
$73$	7.81259	0.914395	0.457197	−	0.889365i	$-0.348853\pi$
$73$	7.81259	0.914395	0.457197	+	0.889365i	$0.348853\pi$
$74$	−17.8679	−2.07710
$75$	0	0
$76$	−47.9581	−5.50117
$77$	0.340565	0.0388110
$78$	8.33687	0.943964
$79$	4.35387	0.489848	0.244924	−	0.969542i	$-0.421237\pi$
$79$	4.35387	0.489848	0.244924	+	0.969542i	$0.421237\pi$
$80$	0	0
$81$	−10.6770	−1.18633
$82$	2.34912	0.259416
$83$	9.31355	1.02229	0.511147	−	0.859493i	$-0.329221\pi$
$83$	9.31355	1.02229	0.511147	+	0.859493i	$0.329221\pi$
$84$	13.2713	1.44802
$85$	0	0
$86$	−25.6059	−2.76116
$87$	8.67710	0.930283
$88$	3.60044	0.383809
$89$	2.83424	0.300429	0.150214	−	0.988653i	$-0.452004\pi$
$89$	2.83424	0.300429	0.150214	+	0.988653i	$0.452004\pi$
$90$	0	0
$91$	1.30291	0.136582
$92$	−5.78823	−0.603465
$93$	−20.8332	−2.16031
$94$	−13.0280	−1.34373
$95$	0	0
$96$	66.2306	6.75963
$97$	−0.660946	−0.0671089	−0.0335545	−	0.999437i	$-0.510683\pi$
$97$	−0.660946	−0.0671089	−0.0335545	+	0.999437i	$0.510683\pi$
$98$	2.79074	0.281907
$99$	0.768655	0.0772527
$100$	0	0
$101$	12.7434	1.26802	0.634010	−	0.773325i	$-0.281408\pi$
$101$	12.7434	1.26802	0.634010	+	0.773325i	$0.281408\pi$
$102$	−16.6147	−1.64510
$103$	12.2329	1.20534	0.602670	−	0.797991i	$-0.294104\pi$
$103$	12.2329	1.20534	0.602670	+	0.797991i	$0.294104\pi$
$104$	13.7743	1.35068
$105$	0	0
$106$	−9.76148	−0.948118
$107$	15.1269	1.46237	0.731186	−	0.682179i	$-0.238967\pi$
$107$	15.1269	1.46237	0.731186	+	0.682179i	$0.238967\pi$
$108$	−9.86061	−0.948838
$109$	9.13756	0.875219	0.437610	−	0.899165i	$-0.355825\pi$
$109$	9.13756	0.875219	0.437610	+	0.899165i	$0.355825\pi$
$110$	0	0
$111$	−14.6799	−1.39336
$112$	17.9272	1.69396
$113$	5.87183	0.552375	0.276188	−	0.961104i	$-0.410929\pi$
$113$	5.87183	0.552375	0.276188	+	0.961104i	$0.410929\pi$
$114$	−53.0156	−4.96537
$115$	0	0
$116$	21.9054	2.03387
$117$	2.94067	0.271865
$118$	−8.31994	−0.765913
$119$	−2.59659	−0.238029
$120$	0	0
$121$	−10.8840	−0.989456
$122$	−8.39625	−0.760161
$123$	1.92998	0.174021
$124$	−52.5937	−4.72305
$125$	0	0
$126$	6.29870	0.561133
$127$	−16.8289	−1.49332	−0.746662	−	0.665204i	$-0.768345\pi$
$127$	−16.8289	−1.49332	−0.746662	+	0.665204i	$0.768345\pi$
$128$	67.1396	5.93435
$129$	−21.0373	−1.85223
$130$	0	0
$131$	20.5076	1.79175	0.895877	−	0.444302i	$-0.146548\pi$
$131$	20.5076	1.79175	0.895877	+	0.444302i	$0.146548\pi$
$132$	4.51976	0.393394
$133$	−8.28544	−0.718439
$134$	32.4237	2.80098
$135$	0	0
$136$	−27.4511	−2.35392
$137$	−19.2523	−1.64484	−0.822418	−	0.568883i	$-0.807376\pi$
$137$	−19.2523	−1.64484	−0.822418	+	0.568883i	$0.807376\pi$
$138$	−6.39865	−0.544689
$139$	5.86865	0.497772	0.248886	−	0.968533i	$-0.419935\pi$
$139$	5.86865	0.497772	0.248886	+	0.968533i	$0.419935\pi$
$140$	0	0
$141$	−10.7035	−0.901399
$142$	16.3874	1.37520
$143$	0.443725	0.0371062
$144$	40.4616	3.37180
$145$	0	0
$146$	21.8029	1.80442
$147$	2.29281	0.189108
$148$	−37.0596	−3.04628
$149$	21.2884	1.74401	0.872006	−	0.489495i	$-0.162819\pi$
$149$	21.2884	1.74401	0.872006	+	0.489495i	$0.162819\pi$
$150$	0	0
$151$	8.74934	0.712011	0.356006	−	0.934484i	$-0.384138\pi$
$151$	8.74934	0.712011	0.356006	+	0.934484i	$0.384138\pi$
$152$	−87.5935	−7.10477
$153$	−5.86051	−0.473794
$154$	0.950428	0.0765877
$155$	0	0
$156$	17.2914	1.38442
$157$	−17.6262	−1.40672	−0.703360	−	0.710833i	$-0.748318\pi$
$157$	−17.6262	−1.40672	−0.703360	+	0.710833i	$0.748318\pi$
$158$	12.1505	0.966643
$159$	−8.01983	−0.636014
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−29.7966	−2.34104
$163$	19.4546	1.52380	0.761900	−	0.647695i	$-0.224267\pi$
$163$	19.4546	1.52380	0.761900	+	0.647695i	$0.224267\pi$
$164$	4.87226	0.380460
$165$	0	0
$166$	25.9917	2.01735
$167$	−23.2552	−1.79954	−0.899769	−	0.436367i	$-0.856265\pi$
$167$	−23.2552	−1.79954	−0.899769	+	0.436367i	$0.856265\pi$
$168$	24.2396	1.87012
$169$	−11.3024	−0.869417
$170$	0	0
$171$	−18.7002	−1.43004
$172$	−53.1089	−4.04952
$173$	11.4043	0.867055	0.433528	−	0.901140i	$-0.357269\pi$
$173$	11.4043	0.867055	0.433528	+	0.901140i	$0.357269\pi$
$174$	24.2155	1.83578
$175$	0	0
$176$	6.10537	0.460209
$177$	−6.83549	−0.513787
$178$	7.90963	0.592852
$179$	−2.41652	−0.180619	−0.0903096	−	0.995914i	$-0.528786\pi$
$179$	−2.41652	−0.180619	−0.0903096	+	0.995914i	$0.528786\pi$
$180$	0	0
$181$	−3.54238	−0.263303	−0.131651	−	0.991296i	$-0.542028\pi$
$181$	−3.54238	−0.263303	−0.131651	+	0.991296i	$0.542028\pi$
$182$	3.63608	0.269524
$183$	−6.89819	−0.509929
$184$	−10.5720	−0.779376
$185$	0	0
$186$	−58.1401	−4.26304
$187$	−0.884309	−0.0646671
$188$	−27.0211	−1.97072
$189$	−1.70356	−0.123916
$190$	0	0
$191$	3.78907	0.274168	0.137084	−	0.990559i	$-0.456227\pi$
$191$	3.78907	0.274168	0.137084	+	0.990559i	$0.456227\pi$
$192$	102.625	7.40632
$193$	19.3042	1.38955	0.694774	−	0.719229i	$-0.255505\pi$
$193$	19.3042	1.38955	0.694774	+	0.719229i	$0.255505\pi$
$194$	−1.84453	−0.132429
$195$	0	0
$196$	5.78823	0.413445
$197$	−17.3149	−1.23364	−0.616818	−	0.787106i	$-0.711579\pi$
$197$	−17.3149	−1.23364	−0.616818	+	0.787106i	$0.711579\pi$
$198$	2.14512	0.152447
$199$	11.8403	0.839338	0.419669	−	0.907677i	$-0.362146\pi$
$199$	11.8403	0.839338	0.419669	+	0.907677i	$0.362146\pi$
$200$	0	0
$201$	26.6386	1.87894
$202$	35.5637	2.50225
$203$	3.78448	0.265618
$204$	−34.4603	−2.41270
$205$	0	0
$206$	34.1387	2.37856
$207$	−2.25700	−0.156872
$208$	23.3575	1.61955
$209$	−2.82173	−0.195183
$210$	0	0
$211$	10.7747	0.741760	0.370880	−	0.928681i	$-0.379056\pi$
$211$	10.7747	0.741760	0.370880	+	0.928681i	$0.379056\pi$
$212$	−20.2461	−1.39051
$213$	13.4635	0.922506
$214$	42.2152	2.88577
$215$	0	0
$216$	−18.0100	−1.22543
$217$	−9.08631	−0.616819
$218$	25.5006	1.72712
$219$	17.9128	1.21044
$220$	0	0
$221$	−3.38313	−0.227574
$222$	−40.9678	−2.74958
$223$	17.0655	1.14279	0.571395	−	0.820675i	$-0.306402\pi$
$223$	17.0655	1.14279	0.571395	+	0.820675i	$0.306402\pi$
$224$	28.8861	1.93004
$225$	0	0
$226$	16.3867	1.09003
$227$	15.7713	1.04678	0.523390	−	0.852093i	$-0.324667\pi$
$227$	15.7713	1.04678	0.523390	+	0.852093i	$0.324667\pi$
$228$	−109.959	−7.28221
$229$	−18.1881	−1.20191	−0.600953	−	0.799285i	$-0.705212\pi$
$229$	−18.1881	−1.20191	−0.600953	+	0.799285i	$0.705212\pi$
$230$	0	0
$231$	0.780852	0.0513763
$232$	40.0094	2.62675
$233$	−19.4957	−1.27721	−0.638604	−	0.769535i	$-0.720488\pi$
$233$	−19.4957	−1.27721	−0.638604	+	0.769535i	$0.720488\pi$
$234$	8.20664	0.536485
$235$	0	0
$236$	−17.2563	−1.12329
$237$	9.98261	0.648440
$238$	−7.24642	−0.469716
$239$	22.0911	1.42896	0.714478	−	0.699658i	$-0.246664\pi$
$239$	22.0911	1.42896	0.714478	+	0.699658i	$0.246664\pi$
$240$	0	0
$241$	9.30479	0.599374	0.299687	−	0.954038i	$-0.403118\pi$
$241$	9.30479	0.599374	0.299687	+	0.954038i	$0.403118\pi$
$242$	−30.3745	−1.95254
$243$	−19.3696	−1.24256
$244$	−17.4145	−1.11485
$245$	0	0
$246$	5.38609	0.343404
$247$	−10.7952	−0.686881
$248$	−96.0603	−6.09983
$249$	21.3542	1.35327
$250$	0	0
$251$	−17.4581	−1.10195	−0.550974	−	0.834522i	$-0.685744\pi$
$251$	−17.4581	−1.10195	−0.550974	+	0.834522i	$0.685744\pi$
$252$	13.0640	0.822957
$253$	−0.340565	−0.0214111
$254$	−46.9651	−2.94685
$255$	0	0
$256$	97.8503	6.11564
$257$	15.9658	0.995918	0.497959	−	0.867200i	$-0.334083\pi$
$257$	15.9658	0.995918	0.497959	+	0.867200i	$0.334083\pi$
$258$	−58.7097	−3.65510
$259$	−6.40257	−0.397836
$260$	0	0
$261$	8.54156	0.528709
$262$	57.2313	3.53576
$263$	14.5099	0.894722	0.447361	−	0.894354i	$-0.352364\pi$
$263$	14.5099	0.894722	0.447361	+	0.894354i	$0.352364\pi$
$264$	8.25515	0.508069
$265$	0	0
$266$	−23.1225	−1.41773
$267$	6.49839	0.397695
$268$	67.2495	4.10792
$269$	1.69801	0.103530	0.0517649	−	0.998659i	$-0.483515\pi$
$269$	1.69801	0.103530	0.0517649	+	0.998659i	$0.483515\pi$
$270$	0	0
$271$	−10.9797	−0.666970	−0.333485	−	0.942755i	$-0.608225\pi$
$271$	−10.9797	−0.666970	−0.333485	+	0.942755i	$0.608225\pi$
$272$	−46.5496	−2.82248
$273$	2.98733	0.180802
$274$	−53.7282	−3.24584
$275$	0	0
$276$	−13.2713	−0.798841
$277$	−2.28492	−0.137287	−0.0686437	−	0.997641i	$-0.521867\pi$
$277$	−2.28492	−0.137287	−0.0686437	+	0.997641i	$0.521867\pi$
$278$	16.3779	0.982280
$279$	−20.5078	−1.22777
$280$	0	0
$281$	−7.74870	−0.462249	−0.231124	−	0.972924i	$-0.574240\pi$
$281$	−7.74870	−0.462249	−0.231124	+	0.972924i	$0.574240\pi$
$282$	−29.8707	−1.77878
$283$	4.22375	0.251076	0.125538	−	0.992089i	$-0.459934\pi$
$283$	4.22375	0.251076	0.125538	+	0.992089i	$0.459934\pi$
$284$	33.9888	2.01686
$285$	0	0
$286$	1.23832	0.0732235
$287$	0.841753	0.0496871
$288$	65.1960	3.84171
$289$	−10.2577	−0.603394
$290$	0	0
$291$	−1.51543	−0.0888359
$292$	45.2211	2.64636
$293$	−20.7133	−1.21008	−0.605042	−	0.796193i	$-0.706844\pi$
$293$	−20.7133	−1.21008	−0.605042	+	0.796193i	$0.706844\pi$
$294$	6.39865	0.373177
$295$	0	0
$296$	−67.6878	−3.93428
$297$	−0.580173	−0.0336651
$298$	59.4104	3.44155
$299$	−1.30291	−0.0753492
$300$	0	0
$301$	−9.17532	−0.528857
$302$	24.4171	1.40505
$303$	29.2184	1.67855
$304$	−148.535	−8.51904
$305$	0	0
$306$	−16.3552	−0.934963
$307$	−25.5218	−1.45661	−0.728303	−	0.685255i	$-0.759691\pi$
$307$	−25.5218	−1.45661	−0.728303	+	0.685255i	$0.759691\pi$
$308$	1.97127	0.112323
$309$	28.0477	1.59558
$310$	0	0
$311$	−23.8893	−1.35464	−0.677320	−	0.735689i	$-0.736859\pi$
$311$	−23.8893	−1.35464	−0.677320	+	0.735689i	$0.736859\pi$
$312$	31.5820	1.78798
$313$	−20.1080	−1.13657	−0.568287	−	0.822831i	$-0.692394\pi$
$313$	−20.1080	−1.13657	−0.568287	+	0.822831i	$0.692394\pi$
$314$	−49.1900	−2.77596
$315$	0	0
$316$	25.2012	1.41768
$317$	5.99196	0.336542	0.168271	−	0.985741i	$-0.446182\pi$
$317$	5.99196	0.336542	0.168271	+	0.985741i	$0.446182\pi$
$318$	−22.3813	−1.25508
$319$	1.28886	0.0721623
$320$	0	0
$321$	34.6831	1.93582
$322$	−2.79074	−0.155522
$323$	21.5139	1.19707
$324$	−61.8007	−3.43337
$325$	0	0
$326$	54.2927	3.00699
$327$	20.9507	1.15858
$328$	8.89900	0.491365
$329$	−4.66829	−0.257371
$330$	0	0
$331$	−30.8960	−1.69820	−0.849098	−	0.528235i	$-0.822854\pi$
$331$	−30.8960	−1.69820	−0.849098	+	0.528235i	$0.822854\pi$
$332$	53.9090	2.95864
$333$	−14.4506	−0.791888
$334$	−64.8991	−3.55112
$335$	0	0
$336$	41.1037	2.24239
$337$	17.4157	0.948691	0.474346	−	0.880339i	$-0.342685\pi$
$337$	17.4157	0.948691	0.474346	+	0.880339i	$0.342685\pi$
$338$	−31.5421	−1.71567
$339$	13.4630	0.731210
$340$	0	0
$341$	−3.09448	−0.167575
$342$	−52.1875	−2.82198
$343$	1.00000	0.0539949
$344$	−97.0013	−5.22996
$345$	0	0
$346$	31.8265	1.71100
$347$	−3.91958	−0.210414	−0.105207	−	0.994450i	$-0.533551\pi$
$347$	−3.91958	−0.210414	−0.105207	+	0.994450i	$0.533551\pi$
$348$	50.2251	2.69235
$349$	−20.2285	−1.08281	−0.541404	−	0.840762i	$-0.682107\pi$
$349$	−20.2285	−1.08281	−0.541404	+	0.840762i	$0.682107\pi$
$350$	0	0
$351$	−2.21959	−0.118473
$352$	9.83761	0.524346
$353$	10.7111	0.570092	0.285046	−	0.958514i	$-0.407991\pi$
$353$	10.7111	0.570092	0.285046	+	0.958514i	$0.407991\pi$
$354$	−19.0761	−1.01388
$355$	0	0
$356$	16.4052	0.869476
$357$	−5.95351	−0.315093
$358$	−6.74388	−0.356425
$359$	−0.848230	−0.0447679	−0.0223839	−	0.999749i	$-0.507126\pi$
$359$	−0.848230	−0.0447679	−0.0223839	+	0.999749i	$0.507126\pi$
$360$	0	0
$361$	49.6485	2.61308
$362$	−9.88586	−0.519589
$363$	−24.9550	−1.30980
$364$	7.54155	0.395284
$365$	0	0
$366$	−19.2510	−1.00627
$367$	−7.32206	−0.382209	−0.191104	−	0.981570i	$-0.561207\pi$
$367$	−7.32206	−0.382209	−0.191104	+	0.981570i	$0.561207\pi$
$368$	−17.9272	−0.934519
$369$	1.89984	0.0989016
$370$	0	0
$371$	−3.49781	−0.181597
$372$	−120.588	−6.25217
$373$	−5.42327	−0.280806	−0.140403	−	0.990094i	$-0.544840\pi$
$373$	−5.42327	−0.280806	−0.140403	+	0.990094i	$0.544840\pi$
$374$	−2.46788	−0.127611
$375$	0	0
$376$	−49.3530	−2.54519
$377$	4.93083	0.253951
$378$	−4.75420	−0.244530
$379$	−4.81942	−0.247557	−0.123778	−	0.992310i	$-0.539501\pi$
$379$	−4.81942	−0.247557	−0.123778	+	0.992310i	$0.539501\pi$
$380$	0	0
$381$	−38.5855	−1.97680
$382$	10.5743	0.541029
$383$	−0.160218	−0.00818675	−0.00409338	−	0.999992i	$-0.501303\pi$
$383$	−0.160218	−0.00818675	−0.00409338	+	0.999992i	$0.501303\pi$
$384$	153.939	7.85565
$385$	0	0
$386$	53.8730	2.74207
$387$	−20.7087	−1.05268
$388$	−3.82571	−0.194221
$389$	15.6916	0.795597	0.397798	−	0.917473i	$-0.369774\pi$
$389$	15.6916	0.795597	0.397798	+	0.917473i	$0.369774\pi$
$390$	0	0
$391$	2.59659	0.131315
$392$	10.5720	0.533965
$393$	47.0201	2.37185
$394$	−48.3214	−2.43440
$395$	0	0
$396$	4.44915	0.223578
$397$	2.75070	0.138054	0.0690268	−	0.997615i	$-0.478011\pi$
$397$	2.75070	0.138054	0.0690268	+	0.997615i	$0.478011\pi$
$398$	33.0433	1.65631
$399$	−18.9970	−0.951038
$400$	0	0
$401$	−35.3053	−1.76306	−0.881532	−	0.472125i	$-0.843487\pi$
$401$	−35.3053	−1.76306	−0.881532	+	0.472125i	$0.843487\pi$
$402$	74.3415	3.70782
$403$	−11.8386	−0.589725
$404$	73.7620	3.66980
$405$	0	0
$406$	10.5615	0.524158
$407$	−2.18049	−0.108083
$408$	−62.9404	−3.11601
$409$	30.1715	1.49188	0.745942	−	0.666010i	$-0.231999\pi$
$409$	30.1715	1.49188	0.745942	+	0.666010i	$0.231999\pi$
$410$	0	0
$411$	−44.1420	−2.17736
$412$	70.8066	3.48839
$413$	−2.98127	−0.146699
$414$	−6.29870	−0.309564
$415$	0	0
$416$	37.6360	1.84526
$417$	13.4557	0.658930
$418$	−7.87472	−0.385165
$419$	−6.01345	−0.293776	−0.146888	−	0.989153i	$-0.546926\pi$
$419$	−6.01345	−0.293776	−0.146888	+	0.989153i	$0.546926\pi$
$420$	0	0
$421$	5.48581	0.267362	0.133681	−	0.991024i	$-0.457320\pi$
$421$	5.48581	0.267362	0.133681	+	0.991024i	$0.457320\pi$
$422$	30.0694	1.46375
$423$	−10.5363	−0.512294
$424$	−36.9787	−1.79585
$425$	0	0
$426$	37.5732	1.82043
$427$	−3.00861	−0.145597
$428$	87.5579	4.23227
$429$	1.01738	0.0491196
$430$	0	0
$431$	−16.1380	−0.777342	−0.388671	−	0.921377i	$-0.627066\pi$
$431$	−16.1380	−0.777342	−0.388671	+	0.921377i	$0.627066\pi$
$432$	−30.5400	−1.46936
$433$	−11.0995	−0.533406	−0.266703	−	0.963779i	$-0.585934\pi$
$433$	−11.0995	−0.533406	−0.266703	+	0.963779i	$0.585934\pi$
$434$	−25.3575	−1.21720
$435$	0	0
$436$	52.8903	2.53299
$437$	8.28544	0.396346
$438$	49.9900	2.38862
$439$	0.163841	0.00781971	0.00390986	−	0.999992i	$-0.498755\pi$
$439$	0.163841	0.00781971	0.00390986	+	0.999992i	$0.498755\pi$
$440$	0	0
$441$	2.25700	0.107476
$442$	−9.44143	−0.449083
$443$	−11.2602	−0.534991	−0.267495	−	0.963559i	$-0.586196\pi$
$443$	−11.2602	−0.534991	−0.267495	+	0.963559i	$0.586196\pi$
$444$	−84.9708	−4.03253
$445$	0	0
$446$	47.6254	2.25513
$447$	48.8103	2.30865
$448$	44.7594	2.11468
$449$	−10.9029	−0.514537	−0.257269	−	0.966340i	$-0.582823\pi$
$449$	−10.9029	−0.514537	−0.257269	+	0.966340i	$0.582823\pi$
$450$	0	0
$451$	0.286672	0.0134988
$452$	33.9875	1.59864
$453$	20.0606	0.942530
$454$	44.0137	2.06566
$455$	0	0
$456$	−200.836	−9.40499
$457$	25.0195	1.17036	0.585182	−	0.810902i	$-0.301023\pi$
$457$	25.0195	1.17036	0.585182	+	0.810902i	$0.301023\pi$
$458$	−50.7583	−2.37178
$459$	4.42346	0.206469
$460$	0	0
$461$	−10.0753	−0.469253	−0.234626	−	0.972086i	$-0.575387\pi$
$461$	−10.0753	−0.469253	−0.234626	+	0.972086i	$0.575387\pi$
$462$	2.17916	0.101384
$463$	42.3926	1.97015	0.985075	−	0.172123i	$-0.0550628\pi$
$463$	42.3926	1.97015	0.985075	+	0.172123i	$0.0550628\pi$
$464$	67.8450	3.14962
$465$	0	0
$466$	−54.4076	−2.52038
$467$	18.6945	0.865077	0.432539	−	0.901615i	$-0.357618\pi$
$467$	18.6945	0.865077	0.432539	+	0.901615i	$0.357618\pi$
$468$	17.0213	0.786808
$469$	11.6183	0.536484
$470$	0	0
$471$	−40.4135	−1.86216
$472$	−31.5179	−1.45073
$473$	−3.12479	−0.143678
$474$	27.8589	1.27960
$475$	0	0
$476$	−15.0297	−0.688885
$477$	−7.89455	−0.361467
$478$	61.6506	2.81983
$479$	−8.00167	−0.365606	−0.182803	−	0.983150i	$-0.558517\pi$
$479$	−8.00167	−0.365606	−0.182803	+	0.983150i	$0.558517\pi$
$480$	0	0
$481$	−8.34198	−0.380361
$482$	25.9672	1.18278
$483$	−2.29281	−0.104327
$484$	−62.9992	−2.86360
$485$	0	0
$486$	−54.0555	−2.45201
$487$	7.34483	0.332826	0.166413	−	0.986056i	$-0.446781\pi$
$487$	7.34483	0.332826	0.166413	+	0.986056i	$0.446781\pi$
$488$	−31.8070	−1.43983
$489$	44.6057	2.01714
$490$	0	0
$491$	6.48742	0.292773	0.146387	−	0.989227i	$-0.453236\pi$
$491$	6.48742	0.292773	0.146387	+	0.989227i	$0.453236\pi$
$492$	11.1712	0.503637
$493$	−9.82675	−0.442575
$494$	−30.1266	−1.35546
$495$	0	0
$496$	−162.892	−7.31406
$497$	5.87205	0.263398
$498$	59.5942	2.67048
$499$	−16.9776	−0.760023	−0.380012	−	0.924982i	$-0.624080\pi$
$499$	−16.9776	−0.760023	−0.380012	+	0.924982i	$0.624080\pi$
$500$	0	0
$501$	−53.3198	−2.38215
$502$	−48.7212	−2.17453
$503$	−29.2073	−1.30229	−0.651145	−	0.758953i	$-0.725711\pi$
$503$	−29.2073	−1.30229	−0.651145	+	0.758953i	$0.725711\pi$
$504$	23.8610	1.06285
$505$	0	0
$506$	−0.950428	−0.0422517
$507$	−25.9144	−1.15090
$508$	−97.4096	−4.32185
$509$	−10.9500	−0.485351	−0.242675	−	0.970108i	$-0.578025\pi$
$509$	−10.9500	−0.485351	−0.242675	+	0.970108i	$0.578025\pi$
$510$	0	0
$511$	7.81259	0.345609
$512$	138.796	6.13396
$513$	14.1148	0.623182
$514$	44.5564	1.96530
$515$	0	0
$516$	−121.769	−5.36058
$517$	−1.58985	−0.0699217
$518$	−17.8679	−0.785071
$519$	26.1480	1.14777
$520$	0	0
$521$	−39.7639	−1.74209	−0.871043	−	0.491206i	$-0.836556\pi$
$521$	−39.7639	−1.74209	−0.871043	+	0.491206i	$0.836556\pi$
$522$	23.8373	1.04333
$523$	20.1830	0.882541	0.441271	−	0.897374i	$-0.354528\pi$
$523$	20.1830	0.882541	0.441271	+	0.897374i	$0.354528\pi$
$524$	118.703	5.18555
$525$	0	0
$526$	40.4935	1.76560
$527$	23.5935	1.02775
$528$	13.9985	0.609206
$529$	1.00000	0.0434783
$530$	0	0
$531$	−6.72872	−0.292001
$532$	−47.9581	−2.07925
$533$	1.09673	0.0475046
$534$	18.1353	0.784792
$535$	0	0
$536$	122.829	5.30538
$537$	−5.54063	−0.239096
$538$	4.73872	0.204301
$539$	0.340565	0.0146692
$540$	0	0
$541$	−22.0445	−0.947768	−0.473884	−	0.880587i	$-0.657148\pi$
$541$	−22.0445	−0.947768	−0.473884	+	0.880587i	$0.657148\pi$
$542$	−30.6415	−1.31617
$543$	−8.12202	−0.348549
$544$	−75.0056	−3.21584
$545$	0	0
$546$	8.33687	0.356785
$547$	−10.4538	−0.446972	−0.223486	−	0.974707i	$-0.571744\pi$
$547$	−10.4538	−0.446972	−0.223486	+	0.974707i	$0.571744\pi$
$548$	−111.437	−4.76035
$549$	−6.79043	−0.289809
$550$	0	0
$551$	−31.3561	−1.33581
$552$	−24.2396	−1.03171
$553$	4.35387	0.185145
$554$	−6.37661	−0.270916
$555$	0	0
$556$	33.9691	1.44061
$557$	10.0603	0.426270	0.213135	−	0.977023i	$-0.431633\pi$
$557$	10.0603	0.426270	0.213135	+	0.977023i	$0.431633\pi$
$558$	−57.2320	−2.42282
$559$	−11.9546	−0.505626
$560$	0	0
$561$	−2.02756	−0.0856035
$562$	−21.6246	−0.912179
$563$	5.15810	0.217388	0.108694	−	0.994075i	$-0.465333\pi$
$563$	5.15810	0.217388	0.108694	+	0.994075i	$0.465333\pi$
$564$	−61.9545	−2.60875
$565$	0	0
$566$	11.7874	0.495461
$567$	−10.6770	−0.448390
$568$	62.0792	2.60478
$569$	−31.4681	−1.31921	−0.659605	−	0.751612i	$-0.729277\pi$
$569$	−31.4681	−1.31921	−0.659605	+	0.751612i	$0.729277\pi$
$570$	0	0
$571$	−23.9799	−1.00353	−0.501763	−	0.865005i	$-0.667315\pi$
$571$	−23.9799	−1.00353	−0.501763	+	0.865005i	$0.667315\pi$
$572$	2.56839	0.107390
$573$	8.68764	0.362931
$574$	2.34912	0.0980502
$575$	0	0
$576$	101.022	4.20925
$577$	−22.1641	−0.922702	−0.461351	−	0.887218i	$-0.652635\pi$
$577$	−22.1641	−0.922702	−0.461351	+	0.887218i	$0.652635\pi$
$578$	−28.6266	−1.19071
$579$	44.2610	1.83942
$580$	0	0
$581$	9.31355	0.386391
$582$	−4.22916	−0.175304
$583$	−1.19123	−0.0493357
$584$	82.5945	3.41779
$585$	0	0
$586$	−57.8055	−2.38792
$587$	−32.9841	−1.36140	−0.680700	−	0.732562i	$-0.738324\pi$
$587$	−32.9841	−1.36140	−0.680700	+	0.732562i	$0.738324\pi$
$588$	13.2713	0.547301
$589$	75.2841	3.10203
$590$	0	0
$591$	−39.6999	−1.63303
$592$	−114.780	−4.71743
$593$	20.0061	0.821551	0.410776	−	0.911736i	$-0.365258\pi$
$593$	20.0061	0.821551	0.410776	+	0.911736i	$0.365258\pi$
$594$	−1.61911	−0.0664330
$595$	0	0
$596$	123.222	5.04737
$597$	27.1477	1.11108
$598$	−3.63608	−0.148691
$599$	−44.4511	−1.81622	−0.908111	−	0.418730i	$-0.862475\pi$
$599$	−44.4511	−1.81622	−0.908111	+	0.418730i	$0.862475\pi$
$600$	0	0
$601$	−37.7530	−1.53998	−0.769989	−	0.638057i	$-0.779738\pi$
$601$	−37.7530	−1.53998	−0.769989	+	0.638057i	$0.779738\pi$
$602$	−25.6059	−1.04362
$603$	26.2225	1.06786
$604$	50.6432	2.06064
$605$	0	0
$606$	81.5409	3.31237
$607$	29.5127	1.19788	0.598941	−	0.800793i	$-0.295588\pi$
$607$	29.5127	1.19788	0.598941	+	0.800793i	$0.295588\pi$
$608$	−239.334	−9.70629
$609$	8.67710	0.351614
$610$	0	0
$611$	−6.08236	−0.246066
$612$	−33.9220	−1.37122
$613$	24.5507	0.991593	0.495797	−	0.868439i	$-0.334876\pi$
$613$	24.5507	0.991593	0.495797	+	0.868439i	$0.334876\pi$
$614$	−71.2247	−2.87439
$615$	0	0
$616$	3.60044	0.145066
$617$	39.6302	1.59545	0.797727	−	0.603019i	$-0.206036\pi$
$617$	39.6302	1.59545	0.797727	+	0.603019i	$0.206036\pi$
$618$	78.2738	3.14863
$619$	15.5441	0.624770	0.312385	−	0.949956i	$-0.398872\pi$
$619$	15.5441	0.624770	0.312385	+	0.949956i	$0.398872\pi$
$620$	0	0
$621$	1.70356	0.0683616
$622$	−66.6689	−2.67318
$623$	2.83424	0.113551
$624$	53.5544	2.14389
$625$	0	0
$626$	−56.1163	−2.24286
$627$	−6.46970	−0.258375
$628$	−102.024	−4.07121
$629$	16.6249	0.662878
$630$	0	0
$631$	12.4320	0.494908	0.247454	−	0.968900i	$-0.420406\pi$
$631$	12.4320	0.494908	0.247454	+	0.968900i	$0.420406\pi$
$632$	46.0290	1.83093
$633$	24.7044	0.981911
$634$	16.7220	0.664116
$635$	0	0
$636$	−46.4206	−1.84070
$637$	1.30291	0.0516232
$638$	3.59687	0.142402
$639$	13.2532	0.524289
$640$	0	0
$641$	31.6123	1.24861	0.624306	−	0.781180i	$-0.285382\pi$
$641$	31.6123	1.24861	0.624306	+	0.781180i	$0.285382\pi$
$642$	96.7917	3.82006
$643$	36.9408	1.45680	0.728401	−	0.685151i	$-0.240264\pi$
$643$	36.9408	1.45680	0.728401	+	0.685151i	$0.240264\pi$
$644$	−5.78823	−0.228088
$645$	0	0
$646$	60.0398	2.36223
$647$	9.98222	0.392441	0.196221	−	0.980560i	$-0.437133\pi$
$647$	9.98222	0.392441	0.196221	+	0.980560i	$0.437133\pi$
$648$	−112.876	−4.43421
$649$	−1.01531	−0.0398546
$650$	0	0
$651$	−20.8332	−0.816519
$652$	112.608	4.41005
$653$	10.6583	0.417091	0.208545	−	0.978013i	$-0.433127\pi$
$653$	10.6583	0.417091	0.208545	+	0.978013i	$0.433127\pi$
$654$	58.4680	2.28628
$655$	0	0
$656$	15.0903	0.589176
$657$	17.6330	0.687930
$658$	−13.0280	−0.507883
$659$	27.9875	1.09024	0.545119	−	0.838359i	$-0.316485\pi$
$659$	27.9875	1.09024	0.545119	+	0.838359i	$0.316485\pi$
$660$	0	0
$661$	48.0644	1.86949	0.934745	−	0.355319i	$-0.115628\pi$
$661$	48.0644	1.86949	0.934745	+	0.355319i	$0.115628\pi$
$662$	−86.2226	−3.35114
$663$	−7.75689	−0.301253
$664$	98.4626	3.82109
$665$	0	0
$666$	−40.3279	−1.56267
$667$	−3.78448	−0.146536
$668$	−134.606	−5.20807
$669$	39.1280	1.51278
$670$	0	0
$671$	−1.02463	−0.0395553
$672$	66.2306	2.55490
$673$	−35.1764	−1.35595	−0.677975	−	0.735085i	$-0.737142\pi$
$673$	−35.1764	−1.35595	−0.677975	+	0.735085i	$0.737142\pi$
$674$	48.6026	1.87210
$675$	0	0
$676$	−65.4211	−2.51620
$677$	−27.9596	−1.07457	−0.537287	−	0.843399i	$-0.680551\pi$
$677$	−27.9596	−1.07457	−0.537287	+	0.843399i	$0.680551\pi$
$678$	37.5718	1.44294
$679$	−0.660946	−0.0253648
$680$	0	0
$681$	36.1607	1.38568
$682$	−8.63589	−0.330685
$683$	2.93123	0.112161	0.0560803	−	0.998426i	$-0.482140\pi$
$683$	2.93123	0.112161	0.0560803	+	0.998426i	$0.482140\pi$
$684$	−108.241	−4.13871
$685$	0	0
$686$	2.79074	0.106551
$687$	−41.7020	−1.59103
$688$	−164.488	−6.27103
$689$	−4.55733	−0.173620
$690$	0	0
$691$	33.4627	1.27298	0.636490	−	0.771285i	$-0.280386\pi$
$691$	33.4627	1.27298	0.636490	+	0.771285i	$0.280386\pi$
$692$	66.0109	2.50936
$693$	0.768655	0.0291988
$694$	−10.9385	−0.415221
$695$	0	0
$696$	91.7341	3.47717
$697$	−2.18569	−0.0827890
$698$	−56.4526	−2.13676
$699$	−44.7001	−1.69071
$700$	0	0
$701$	21.1388	0.798402	0.399201	−	0.916864i	$-0.369288\pi$
$701$	21.1388	0.798402	0.399201	+	0.916864i	$0.369288\pi$
$702$	−6.19429	−0.233788
$703$	53.0481	2.00075
$704$	15.2435	0.574510
$705$	0	0
$706$	29.8918	1.12499
$707$	12.7434	0.479267
$708$	−39.5654	−1.48696
$709$	−41.7990	−1.56979	−0.784897	−	0.619627i	$-0.787284\pi$
$709$	−41.7990	−1.56979	−0.784897	+	0.619627i	$0.787284\pi$
$710$	0	0
$711$	9.82667	0.368529
$712$	29.9635	1.12293
$713$	9.08631	0.340285
$714$	−16.6147	−0.621790
$715$	0	0
$716$	−13.9874	−0.522733
$717$	50.6509	1.89159
$718$	−2.36719	−0.0883428
$719$	−35.8849	−1.33828	−0.669140	−	0.743136i	$-0.733338\pi$
$719$	−35.8849	−1.33828	−0.669140	+	0.743136i	$0.733338\pi$
$720$	0	0
$721$	12.2329	0.455575
$722$	138.556	5.15652
$723$	21.3342	0.793426
$724$	−20.5041	−0.762030
$725$	0	0
$726$	−69.6430	−2.58470
$727$	43.5701	1.61592	0.807962	−	0.589234i	$-0.200570\pi$
$727$	43.5701	1.61592	0.807962	+	0.589234i	$0.200570\pi$
$728$	13.7743	0.510511
$729$	−12.3800	−0.458519
$730$	0	0
$731$	23.8246	0.881184
$732$	−39.9283	−1.47579
$733$	−9.30801	−0.343799	−0.171900	−	0.985114i	$-0.554990\pi$
$733$	−9.30801	−0.343799	−0.171900	+	0.985114i	$0.554990\pi$
$734$	−20.4340	−0.754232
$735$	0	0
$736$	−28.8861	−1.06476
$737$	3.95679	0.145750
$738$	5.30195	0.195168
$739$	15.1965	0.559011	0.279505	−	0.960144i	$-0.409830\pi$
$739$	15.1965	0.559011	0.279505	+	0.960144i	$0.409830\pi$
$740$	0	0
$741$	−24.7514	−0.909264
$742$	−9.76148	−0.358355
$743$	−33.2864	−1.22116	−0.610579	−	0.791955i	$-0.709063\pi$
$743$	−33.2864	−1.22116	−0.610579	+	0.791955i	$0.709063\pi$
$744$	−220.248	−8.07470
$745$	0	0
$746$	−15.1349	−0.554129
$747$	21.0207	0.769107
$748$	−5.11859	−0.187154
$749$	15.1269	0.552724
$750$	0	0
$751$	27.4114	1.00026	0.500128	−	0.865952i	$-0.333286\pi$
$751$	27.4114	1.00026	0.500128	+	0.865952i	$0.333286\pi$
$752$	−83.6892	−3.05183
$753$	−40.0283	−1.45871
$754$	13.7607	0.501134
$755$	0	0
$756$	−9.86061	−0.358627
$757$	−40.1658	−1.45985	−0.729926	−	0.683526i	$-0.760445\pi$
$757$	−40.1658	−1.45985	−0.729926	+	0.683526i	$0.760445\pi$
$758$	−13.4497	−0.488517
$759$	−0.780852	−0.0283431
$760$	0	0
$761$	2.65834	0.0963646	0.0481823	−	0.998839i	$-0.484657\pi$
$761$	2.65834	0.0963646	0.0481823	+	0.998839i	$0.484657\pi$
$762$	−107.682	−3.90092
$763$	9.13756	0.330802
$764$	21.9320	0.793473
$765$	0	0
$766$	−0.447127	−0.0161553
$767$	−3.88432	−0.140255
$768$	224.353	8.09563
$769$	−53.4285	−1.92668	−0.963341	−	0.268281i	$-0.913544\pi$
$769$	−53.4285	−1.92668	−0.963341	+	0.268281i	$0.913544\pi$
$770$	0	0
$771$	36.6066	1.31835
$772$	111.737	4.02151
$773$	43.0461	1.54826	0.774130	−	0.633026i	$-0.218188\pi$
$773$	43.0461	1.54826	0.774130	+	0.633026i	$0.218188\pi$
$774$	−57.7926	−2.07731
$775$	0	0
$776$	−6.98751	−0.250837
$777$	−14.6799	−0.526639
$778$	43.7912	1.56999
$779$	−6.97430	−0.249880
$780$	0	0
$781$	1.99981	0.0715590
$782$	7.24642	0.259131
$783$	−6.44709	−0.230400
$784$	17.9272	0.640256
$785$	0	0
$786$	131.221	4.68049
$787$	−1.48807	−0.0530440	−0.0265220	−	0.999648i	$-0.508443\pi$
$787$	−1.48807	−0.0530440	−0.0265220	+	0.999648i	$0.508443\pi$
$788$	−100.223	−3.57029
$789$	33.2686	1.18439
$790$	0	0
$791$	5.87183	0.208778
$792$	8.12620	0.288752
$793$	−3.91995	−0.139201
$794$	7.67648	0.272428
$795$	0	0
$796$	68.5346	2.42914
$797$	10.0121	0.354648	0.177324	−	0.984153i	$-0.443256\pi$
$797$	10.0121	0.354648	0.177324	+	0.984153i	$0.443256\pi$
$798$	−53.0156	−1.87673
$799$	12.1216	0.428833
$800$	0	0
$801$	6.39688	0.226023
$802$	−98.5280	−3.47914
$803$	2.66069	0.0938939
$804$	154.191	5.43789
$805$	0	0
$806$	−33.0386	−1.16373
$807$	3.89323	0.137048
$808$	134.723	4.73955
$809$	−11.4480	−0.402491	−0.201246	−	0.979541i	$-0.564499\pi$
$809$	−11.4480	−0.402491	−0.201246	+	0.979541i	$0.564499\pi$
$810$	0	0
$811$	−1.19686	−0.0420274	−0.0210137	−	0.999779i	$-0.506689\pi$
$811$	−1.19686	−0.0420274	−0.0210137	+	0.999779i	$0.506689\pi$
$812$	21.9054	0.768730
$813$	−25.1745	−0.882907
$814$	−6.08519	−0.213286
$815$	0	0
$816$	−106.730	−3.73628
$817$	76.0216	2.65966
$818$	84.2008	2.94401
$819$	2.94067	0.102755
$820$	0	0
$821$	−55.3711	−1.93246	−0.966232	−	0.257674i	$-0.917044\pi$
$821$	−55.3711	−1.93246	−0.966232	+	0.257674i	$0.917044\pi$
$822$	−123.189	−4.29671
$823$	29.2048	1.01802	0.509008	−	0.860762i	$-0.330012\pi$
$823$	29.2048	1.01802	0.509008	+	0.860762i	$0.330012\pi$
$824$	129.325	4.50527
$825$	0	0
$826$	−8.31994	−0.289488
$827$	−3.53535	−0.122936	−0.0614681	−	0.998109i	$-0.519578\pi$
$827$	−3.53535	−0.122936	−0.0614681	+	0.998109i	$0.519578\pi$
$828$	−13.0640	−0.454007
$829$	−9.17625	−0.318704	−0.159352	−	0.987222i	$-0.550941\pi$
$829$	−9.17625	−0.318704	−0.159352	+	0.987222i	$0.550941\pi$
$830$	0	0
$831$	−5.23889	−0.181735
$832$	58.3175	2.02179
$833$	−2.59659	−0.0899667
$834$	37.5514	1.30030
$835$	0	0
$836$	−16.3328	−0.564883
$837$	15.4791	0.535036
$838$	−16.7820	−0.579724
$839$	−9.35807	−0.323077	−0.161538	−	0.986866i	$-0.551646\pi$
$839$	−9.35807	−0.323077	−0.161538	+	0.986866i	$0.551646\pi$
$840$	0	0
$841$	−14.6777	−0.506129
$842$	15.3095	0.527599
$843$	−17.7663	−0.611905
$844$	62.3664	2.14674
$845$	0	0
$846$	−29.4041	−1.01094
$847$	−10.8840	−0.373979
$848$	−62.7058	−2.15333
$849$	9.68428	0.332364
$850$	0	0
$851$	6.40257	0.219477
$852$	77.9300	2.66984
$853$	−23.2096	−0.794681	−0.397340	−	0.917671i	$-0.630067\pi$
$853$	−23.2096	−0.794681	−0.397340	+	0.917671i	$0.630067\pi$
$854$	−8.39625	−0.287314
$855$	0	0
$856$	159.921	5.46599
$857$	52.8608	1.80569	0.902845	−	0.429965i	$-0.141474\pi$
$857$	52.8608	1.80569	0.902845	+	0.429965i	$0.141474\pi$
$858$	2.83924	0.0969302
$859$	−17.9744	−0.613278	−0.306639	−	0.951826i	$-0.599204\pi$
$859$	−17.9744	−0.613278	−0.306639	+	0.951826i	$0.599204\pi$
$860$	0	0
$861$	1.92998	0.0657737
$862$	−45.0371	−1.53397
$863$	50.2664	1.71109	0.855545	−	0.517729i	$-0.173222\pi$
$863$	50.2664	1.71109	0.855545	+	0.517729i	$0.173222\pi$
$864$	−49.2093	−1.67414
$865$	0	0
$866$	−30.9757	−1.05260
$867$	−23.5190	−0.798747
$868$	−52.5937	−1.78515
$869$	1.48277	0.0502997
$870$	0	0
$871$	15.1376	0.512919
$872$	96.6020	3.27136
$873$	−1.49176	−0.0504883
$874$	23.1225	0.782131
$875$	0	0
$876$	103.684	3.50314
$877$	−6.50538	−0.219671	−0.109836	−	0.993950i	$-0.535032\pi$
$877$	−6.50538	−0.219671	−0.109836	+	0.993950i	$0.535032\pi$
$878$	0.457238	0.0154310
$879$	−47.4918	−1.60186
$880$	0	0
$881$	−19.8310	−0.668122	−0.334061	−	0.942551i	$-0.608419\pi$
$881$	−19.8310	−0.668122	−0.334061	+	0.942551i	$0.608419\pi$
$882$	6.29870	0.212088
$883$	14.9867	0.504344	0.252172	−	0.967682i	$-0.418855\pi$
$883$	14.9867	0.504344	0.252172	+	0.967682i	$0.418855\pi$
$884$	−19.5823	−0.658625
$885$	0	0
$886$	−31.4244	−1.05572
$887$	3.22519	0.108291	0.0541457	−	0.998533i	$-0.482756\pi$
$887$	3.22519	0.108291	0.0541457	+	0.998533i	$0.482756\pi$
$888$	−155.196	−5.20803
$889$	−16.8289	−0.564423
$890$	0	0
$891$	−3.63619	−0.121817
$892$	98.7791	3.30737
$893$	38.6788	1.29434
$894$	136.217	4.55578
$895$	0	0
$896$	67.1396	2.24298
$897$	−2.98733	−0.0997441
$898$	−30.4270	−1.01536
$899$	−34.3869	−1.14687
$900$	0	0
$901$	9.08239	0.302578
$902$	0.800026	0.0266380
$903$	−21.0373	−0.700078
$904$	62.0768	2.06464
$905$	0	0
$906$	55.9840	1.85994
$907$	−7.88833	−0.261928	−0.130964	−	0.991387i	$-0.541807\pi$
$907$	−7.88833	−0.261928	−0.130964	+	0.991387i	$0.541807\pi$
$908$	91.2881	3.02950
$909$	28.7620	0.953974
$910$	0	0
$911$	8.60435	0.285075	0.142537	−	0.989789i	$-0.454474\pi$
$911$	8.60435	0.285075	0.142537	+	0.989789i	$0.454474\pi$
$912$	−340.562	−11.2771
$913$	3.17187	0.104974
$914$	69.8230	2.30954
$915$	0	0
$916$	−105.277	−3.47845
$917$	20.5076	0.677220
$918$	12.3447	0.407437
$919$	25.8091	0.851364	0.425682	−	0.904873i	$-0.360034\pi$
$919$	25.8091	0.851364	0.425682	+	0.904873i	$0.360034\pi$
$920$	0	0
$921$	−58.5167	−1.92819
$922$	−28.1175	−0.926000
$923$	7.65075	0.251828
$924$	4.51976	0.148689
$925$	0	0
$926$	118.307	3.88780
$927$	27.6096	0.906817
$928$	109.319	3.58857
$929$	22.4171	0.735483	0.367741	−	0.929928i	$-0.380131\pi$
$929$	22.4171	0.735483	0.367741	+	0.929928i	$0.380131\pi$
$930$	0	0
$931$	−8.28544	−0.271544
$932$	−112.846	−3.69639
$933$	−54.7738	−1.79321
$934$	52.1714	1.70710
$935$	0	0
$936$	31.0887	1.01616
$937$	−17.3093	−0.565470	−0.282735	−	0.959198i	$-0.591242\pi$
$937$	−17.3093	−0.565470	−0.282735	+	0.959198i	$0.591242\pi$
$938$	32.4237	1.05867
$939$	−46.1040	−1.50455
$940$	0	0
$941$	−35.9965	−1.17345	−0.586727	−	0.809785i	$-0.699584\pi$
$941$	−35.9965	−1.17345	−0.586727	+	0.809785i	$0.699584\pi$
$942$	−112.784	−3.67469
$943$	−0.841753	−0.0274113
$944$	−53.4457	−1.73951
$945$	0	0
$946$	−8.72048	−0.283527
$947$	−17.0281	−0.553338	−0.276669	−	0.960965i	$-0.589231\pi$
$947$	−17.0281	−0.553338	−0.276669	+	0.960965i	$0.589231\pi$
$948$	57.7817	1.87666
$949$	10.1791	0.330428
$950$	0	0
$951$	13.7385	0.445500
$952$	−27.4511	−0.889696
$953$	1.95658	0.0633799	0.0316899	−	0.999498i	$-0.489911\pi$
$953$	1.95658	0.0633799	0.0316899	+	0.999498i	$0.489911\pi$
$954$	−22.0316	−0.713301
$955$	0	0
$956$	127.869	4.13557
$957$	2.95512	0.0955254
$958$	−22.3306	−0.721469
$959$	−19.2523	−0.621690
$960$	0	0
$961$	51.5610	1.66326
$962$	−23.2803	−0.750587
$963$	34.1414	1.10019
$964$	53.8583	1.73466
$965$	0	0
$966$	−6.39865	−0.205873
$967$	−11.5841	−0.372519	−0.186259	−	0.982501i	$-0.559636\pi$
$967$	−11.5841	−0.372519	−0.186259	+	0.982501i	$0.559636\pi$
$968$	−115.066	−3.69835
$969$	49.3274	1.58463
$970$	0	0
$971$	−43.0267	−1.38079	−0.690397	−	0.723431i	$-0.742564\pi$
$971$	−43.0267	−1.38079	−0.690397	+	0.723431i	$0.742564\pi$
$972$	−112.116	−3.59611
$973$	5.86865	0.188140
$974$	20.4975	0.656783
$975$	0	0
$976$	−53.9359	−1.72645
$977$	−46.6160	−1.49138	−0.745689	−	0.666294i	$-0.767879\pi$
$977$	−46.6160	−1.49138	−0.745689	+	0.666294i	$0.767879\pi$
$978$	124.483	3.98053
$979$	0.965243	0.0308493
$980$	0	0
$981$	20.6235	0.658457
$982$	18.1047	0.577745
$983$	−24.9615	−0.796147	−0.398073	−	0.917354i	$-0.630321\pi$
$983$	−24.9615	−0.796147	−0.398073	+	0.917354i	$0.630321\pi$
$984$	20.4037	0.650448
$985$	0	0
$986$	−27.4239	−0.873355
$987$	−10.7035	−0.340697
$988$	−62.4850	−1.98791
$989$	9.17532	0.291758
$990$	0	0
$991$	−0.548307	−0.0174175	−0.00870877	−	0.999962i	$-0.502772\pi$
$991$	−0.548307	−0.0174175	−0.00870877	+	0.999962i	$0.502772\pi$
$992$	−262.469	−8.33338
$993$	−70.8387	−2.24800
$994$	16.3874	0.519776
$995$	0	0
$996$	123.603	3.91652
$997$	−1.96623	−0.0622712	−0.0311356	−	0.999515i	$-0.509912\pi$
$997$	−1.96623	−0.0622712	−0.0311356	+	0.999515i	$0.509912\pi$
$998$	−47.3802	−1.49979
$999$	10.9072	0.345088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bb.1.14	yes	14
5.4	even	2		4025.2.a.ba.1.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.ba.1.1	✓	14	5.4	even	2
4025.2.a.bb.1.14	yes	14	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.79074 q^{2} +2.29281 q^{3} +5.78823 q^{4} +6.39865 q^{6} +1.00000 q^{7} +10.5720 q^{8} +2.25700 q^{9} +O(q^{10})\)	\(q+2.79074 q^{2} +2.29281 q^{3} +5.78823 q^{4} +6.39865 q^{6} +1.00000 q^{7} +10.5720 q^{8} +2.25700 q^{9} +0.340565 q^{11} +13.2713 q^{12} +1.30291 q^{13} +2.79074 q^{14} +17.9272 q^{16} -2.59659 q^{17} +6.29870 q^{18} -8.28544 q^{19} +2.29281 q^{21} +0.950428 q^{22} -1.00000 q^{23} +24.2396 q^{24} +3.63608 q^{26} -1.70356 q^{27} +5.78823 q^{28} +3.78448 q^{29} -9.08631 q^{31} +28.8861 q^{32} +0.780852 q^{33} -7.24642 q^{34} +13.0640 q^{36} -6.40257 q^{37} -23.1225 q^{38} +2.98733 q^{39} +0.841753 q^{41} +6.39865 q^{42} -9.17532 q^{43} +1.97127 q^{44} -2.79074 q^{46} -4.66829 q^{47} +41.1037 q^{48} +1.00000 q^{49} -5.95351 q^{51} +7.54155 q^{52} -3.49781 q^{53} -4.75420 q^{54} +10.5720 q^{56} -18.9970 q^{57} +10.5615 q^{58} -2.98127 q^{59} -3.00861 q^{61} -25.3575 q^{62} +2.25700 q^{63} +44.7594 q^{64} +2.17916 q^{66} +11.6183 q^{67} -15.0297 q^{68} -2.29281 q^{69} +5.87205 q^{71} +23.8610 q^{72} +7.81259 q^{73} -17.8679 q^{74} -47.9581 q^{76} +0.340565 q^{77} +8.33687 q^{78} +4.35387 q^{79} -10.6770 q^{81} +2.34912 q^{82} +9.31355 q^{83} +13.2713 q^{84} -25.6059 q^{86} +8.67710 q^{87} +3.60044 q^{88} +2.83424 q^{89} +1.30291 q^{91} -5.78823 q^{92} -20.8332 q^{93} -13.0280 q^{94} +66.2306 q^{96} -0.660946 q^{97} +2.79074 q^{98} +0.768655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9	\( 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9} - 3 q^{11} + 11 q^{12} + 15 q^{13} + q^{14} + 23 q^{16} + 9 q^{17} + 17 q^{18} - 4 q^{19} + 6 q^{21} + 9 q^{22} - 14 q^{23} + 10 q^{24} - 5 q^{26} + 33 q^{27} + 17 q^{28} + 11 q^{29} - q^{31} + 24 q^{32} + 26 q^{33} - 6 q^{34} + 13 q^{36} + 18 q^{37} - 6 q^{38} + 6 q^{39} - 7 q^{41} - 4 q^{42} + 18 q^{43} - 16 q^{44} - q^{46} + 10 q^{47} + 40 q^{48} + 14 q^{49} + 28 q^{51} + 46 q^{52} + 5 q^{53} - 24 q^{54} + 9 q^{56} - 26 q^{57} + 2 q^{58} - 24 q^{59} - 6 q^{61} - 16 q^{62} + 18 q^{63} + 29 q^{64} + 27 q^{66} + 61 q^{67} + 35 q^{68} - 6 q^{69} + 11 q^{71} + 12 q^{72} + 28 q^{73} - 49 q^{74} - 27 q^{76} - 3 q^{77} + 38 q^{78} + 6 q^{79} + 26 q^{81} - 14 q^{82} + 16 q^{83} + 11 q^{84} + 46 q^{86} + 61 q^{87} + 58 q^{88} - 39 q^{89} + 15 q^{91} - 17 q^{92} + 21 q^{93} - 74 q^{94} + 41 q^{96} + 19 q^{97} + q^{98} - 9 q^{99}+O(q^{100}) \) 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9 - 3 * q^11 + 11 * q^12 + 15 * q^13 + q^14 + 23 * q^16 + 9 * q^17 + 17 * q^18 - 4 * q^19 + 6 * q^21 + 9 * q^22 - 14 * q^23 + 10 * q^24 - 5 * q^26 + 33 * q^27 + 17 * q^28 + 11 * q^29 - q^31 + 24 * q^32 + 26 * q^33 - 6 * q^34 + 13 * q^36 + 18 * q^37 - 6 * q^38 + 6 * q^39 - 7 * q^41 - 4 * q^42 + 18 * q^43 - 16 * q^44 - q^46 + 10 * q^47 + 40 * q^48 + 14 * q^49 + 28 * q^51 + 46 * q^52 + 5 * q^53 - 24 * q^54 + 9 * q^56 - 26 * q^57 + 2 * q^58 - 24 * q^59 - 6 * q^61 - 16 * q^62 + 18 * q^63 + 29 * q^64 + 27 * q^66 + 61 * q^67 + 35 * q^68 - 6 * q^69 + 11 * q^71 + 12 * q^72 + 28 * q^73 - 49 * q^74 - 27 * q^76 - 3 * q^77 + 38 * q^78 + 6 * q^79 + 26 * q^81 - 14 * q^82 + 16 * q^83 + 11 * q^84 + 46 * q^86 + 61 * q^87 + 58 * q^88 - 39 * q^89 + 15 * q^91 - 17 * q^92 + 21 * q^93 - 74 * q^94 + 41 * q^96 + 19 * q^97 + q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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