LMFDB - Embedded newform 9025.2.a.cf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.22274$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} -2.30498 q^{6} +2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} +O(q^{10})$	\(q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} -2.30498 q^{6} +2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} +0.0848155 q^{11} +3.04938 q^{12} +5.72097 q^{13} -4.50122 q^{14} -1.23419 q^{16} +2.53072 q^{17} +4.27795 q^{18} +2.10001 q^{21} -0.188523 q^{22} +0.309088 q^{23} -2.16800 q^{24} -12.7162 q^{26} -5.10685 q^{27} +5.95489 q^{28} -2.62414 q^{29} -8.07278 q^{31} +6.92456 q^{32} +0.0879538 q^{33} -5.62513 q^{34} -5.65951 q^{36} -5.01303 q^{37} +5.93265 q^{39} +5.88035 q^{41} -4.66777 q^{42} -0.650519 q^{43} +0.249406 q^{44} -0.687021 q^{46} -6.90277 q^{47} -1.27985 q^{48} -2.89906 q^{49} +2.62436 q^{51} +16.8229 q^{52} +14.5544 q^{53} +11.3512 q^{54} -4.23372 q^{56} +5.83278 q^{58} -7.47335 q^{59} +13.3170 q^{61} +17.9437 q^{62} -3.89752 q^{63} -12.9231 q^{64} -0.195498 q^{66} +8.88244 q^{67} +7.44175 q^{68} +0.320524 q^{69} +14.3366 q^{71} +4.02371 q^{72} -10.8548 q^{73} +11.1426 q^{74} +0.171758 q^{77} -13.1867 q^{78} -0.115898 q^{79} +0.478079 q^{81} -13.0705 q^{82} +2.97552 q^{83} +6.17523 q^{84} +1.44593 q^{86} -2.72124 q^{87} -0.177319 q^{88} +11.1259 q^{89} +11.5854 q^{91} +0.908894 q^{92} -8.37148 q^{93} +15.3431 q^{94} +7.18078 q^{96} -0.225903 q^{97} +6.44385 q^{98} -0.163238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9	$ 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9} + 18 q^{12} + 9 q^{13} + 12 q^{16} + 9 q^{17} + 24 q^{18} - 12 q^{21} + 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} + 24 q^{27} + 15 q^{28} - 9 q^{29} - 18 q^{31} + 3 q^{32} - 9 q^{33} + 24 q^{34} + 18 q^{36} + 18 q^{37} + 18 q^{39} - 6 q^{41} + 12 q^{43} + 48 q^{44} + 9 q^{46} - 15 q^{47} - 21 q^{48} - 9 q^{49} + 6 q^{51} + 33 q^{52} + 15 q^{53} + 63 q^{54} - 6 q^{58} - 21 q^{59} - 12 q^{61} + 36 q^{62} - 21 q^{63} - 36 q^{64} + 3 q^{66} + 60 q^{67} + 51 q^{68} + 15 q^{69} + 18 q^{71} - 27 q^{73} + 27 q^{74} + 30 q^{77} - 6 q^{78} - 15 q^{79} + 33 q^{81} - 24 q^{82} + 48 q^{84} + 39 q^{86} - 15 q^{87} + 27 q^{88} + 39 q^{89} - 21 q^{91} + 6 q^{92} - 15 q^{93} - 15 q^{94} - 33 q^{96} + 15 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9 + 18 * q^12 + 9 * q^13 + 12 * q^16 + 9 * q^17 + 24 * q^18 - 12 * q^21 + 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 + 24 * q^27 + 15 * q^28 - 9 * q^29 - 18 * q^31 + 3 * q^32 - 9 * q^33 + 24 * q^34 + 18 * q^36 + 18 * q^37 + 18 * q^39 - 6 * q^41 + 12 * q^43 + 48 * q^44 + 9 * q^46 - 15 * q^47 - 21 * q^48 - 9 * q^49 + 6 * q^51 + 33 * q^52 + 15 * q^53 + 63 * q^54 - 6 * q^58 - 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 + 60 * q^67 + 51 * q^68 + 15 * q^69 + 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 - 6 * q^78 - 15 * q^79 + 33 * q^81 - 24 * q^82 + 48 * q^84 + 39 * q^86 - 15 * q^87 + 27 * q^88 + 39 * q^89 - 21 * q^91 + 6 * q^92 - 15 * q^93 - 15 * q^94 - 33 * q^96 + 15 * q^97 - 15 * q^98 - 36 * 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 $

$2$	−2.22274	−1.57171	−0.785857	−	0.618408i	$-0.787778\pi$
$2$	−2.22274	−1.57171	−0.785857	+	0.618408i	$0.787778\pi$
$3$	1.03700	0.598713	0.299356	−	0.954141i	$-0.403228\pi$
$3$	1.03700	0.598713	0.299356	+	0.954141i	$0.403228\pi$
$4$	2.94057	1.47029
$5$	0	0
$5$	0	0
$6$	−2.30498	−0.941006
$7$	2.02508	0.765408	0.382704	−	0.923871i	$-0.374993\pi$
$7$	2.02508	0.765408	0.382704	+	0.923871i	$0.374993\pi$
$8$	−2.09064	−0.739154
$9$	−1.92463	−0.641543
$10$	0	0
$11$	0.0848155	0.0255728	0.0127864	−	0.999918i	$-0.495930\pi$
$11$	0.0848155	0.0255728	0.0127864	+	0.999918i	$0.495930\pi$
$12$	3.04938	0.880279
$13$	5.72097	1.58671	0.793356	−	0.608758i	$-0.208332\pi$
$13$	5.72097	1.58671	0.793356	+	0.608758i	$0.208332\pi$
$14$	−4.50122	−1.20300
$15$	0	0
$16$	−1.23419	−0.308546
$17$	2.53072	0.613789	0.306895	−	0.951743i	$-0.400710\pi$
$17$	2.53072	0.613789	0.306895	+	0.951743i	$0.400710\pi$
$18$	4.27795	1.00832
$19$	0	0
$19$	0	0
$20$	0	0
$21$	2.10001	0.458260
$22$	−0.188523	−0.0401932
$23$	0.309088	0.0644492	0.0322246	−	0.999481i	$-0.489741\pi$
$23$	0.309088	0.0644492	0.0322246	+	0.999481i	$0.489741\pi$
$24$	−2.16800	−0.442541
$25$	0	0
$26$	−12.7162	−2.49386
$27$	−5.10685	−0.982813
$28$	5.95489	1.12537
$29$	−2.62414	−0.487291	−0.243646	−	0.969864i	$-0.578343\pi$
$29$	−2.62414	−0.487291	−0.243646	+	0.969864i	$0.578343\pi$
$30$	0	0
$31$	−8.07278	−1.44991	−0.724957	−	0.688795i	$-0.758140\pi$
$31$	−8.07278	−1.44991	−0.724957	+	0.688795i	$0.758140\pi$
$32$	6.92456	1.22410
$33$	0.0879538	0.0153108
$34$	−5.62513	−0.964701
$35$	0	0
$36$	−5.65951	−0.943251
$37$	−5.01303	−0.824136	−0.412068	−	0.911153i	$-0.635193\pi$
$37$	−5.01303	−0.824136	−0.412068	+	0.911153i	$0.635193\pi$
$38$	0	0
$39$	5.93265	0.949985
$40$	0	0
$41$	5.88035	0.918357	0.459179	−	0.888344i	$-0.348144\pi$
$41$	5.88035	0.918357	0.459179	+	0.888344i	$0.348144\pi$
$42$	−4.66777	−0.720253
$43$	−0.650519	−0.0992032	−0.0496016	−	0.998769i	$-0.515795\pi$
$43$	−0.650519	−0.0992032	−0.0496016	+	0.998769i	$0.515795\pi$
$44$	0.249406	0.0375994
$45$	0	0
$46$	−0.687021	−0.101296
$47$	−6.90277	−1.00687	−0.503437	−	0.864032i	$-0.667931\pi$
$47$	−6.90277	−1.00687	−0.503437	+	0.864032i	$0.667931\pi$
$48$	−1.27985	−0.184731
$49$	−2.89906	−0.414151
$50$	0	0
$51$	2.62436	0.367484
$52$	16.8229	2.33292
$53$	14.5544	1.99920	0.999601	−	0.0282415i	$-0.00899075\pi$
$53$	14.5544	1.99920	0.999601	+	0.0282415i	$0.00899075\pi$
$54$	11.3512	1.54470
$55$	0	0
$56$	−4.23372	−0.565754
$57$	0	0
$58$	5.83278	0.765882
$59$	−7.47335	−0.972947	−0.486474	−	0.873695i	$-0.661717\pi$
$59$	−7.47335	−0.972947	−0.486474	+	0.873695i	$0.661717\pi$
$60$	0	0
$61$	13.3170	1.70507	0.852534	−	0.522672i	$-0.175065\pi$
$61$	13.3170	1.70507	0.852534	+	0.522672i	$0.175065\pi$
$62$	17.9437	2.27885
$63$	−3.89752	−0.491042
$64$	−12.9231	−1.61539
$65$	0	0
$66$	−0.195498	−0.0240642
$67$	8.88244	1.08516	0.542582	−	0.840003i	$-0.317447\pi$
$67$	8.88244	1.08516	0.542582	+	0.840003i	$0.317447\pi$
$68$	7.44175	0.902445
$69$	0.320524	0.0385866
$70$	0	0
$71$	14.3366	1.70144	0.850719	−	0.525620i	$-0.176167\pi$
$71$	14.3366	1.70144	0.850719	+	0.525620i	$0.176167\pi$
$72$	4.02371	0.474199
$73$	−10.8548	−1.27046	−0.635229	−	0.772324i	$-0.719094\pi$
$73$	−10.8548	−1.27046	−0.635229	+	0.772324i	$0.719094\pi$
$74$	11.1426	1.29531
$75$	0	0
$76$	0	0
$77$	0.171758	0.0195737
$78$	−13.1867	−1.49310
$79$	−0.115898	−0.0130395	−0.00651976	−	0.999979i	$-0.502075\pi$
$79$	−0.115898	−0.0130395	−0.00651976	+	0.999979i	$0.502075\pi$
$80$	0	0
$81$	0.478079	0.0531198
$82$	−13.0705	−1.44339
$83$	2.97552	0.326606	0.163303	−	0.986576i	$-0.447785\pi$
$83$	2.97552	0.326606	0.163303	+	0.986576i	$0.447785\pi$
$84$	6.17523	0.673772
$85$	0	0
$86$	1.44593	0.155919
$87$	−2.72124	−0.291747
$88$	−0.177319	−0.0189023
$89$	11.1259	1.17934	0.589670	−	0.807644i	$-0.299258\pi$
$89$	11.1259	1.17934	0.589670	+	0.807644i	$0.299258\pi$
$90$	0	0
$91$	11.5854	1.21448
$92$	0.908894	0.0947587
$93$	−8.37148	−0.868082
$94$	15.3431	1.58252
$95$	0	0
$96$	7.18078	0.732885
$97$	−0.225903	−0.0229370	−0.0114685	−	0.999934i	$-0.503651\pi$
$97$	−0.225903	−0.0229370	−0.0114685	+	0.999934i	$0.503651\pi$
$98$	6.44385	0.650927
$99$	−0.163238	−0.0164061
$100$	0	0
$101$	−12.6014	−1.25388	−0.626942	−	0.779066i	$-0.715694\pi$
$101$	−12.6014	−1.25388	−0.626942	+	0.779066i	$0.715694\pi$
$102$	−5.83326	−0.577579
$103$	17.7230	1.74630	0.873152	−	0.487448i	$-0.162072\pi$
$103$	17.7230	1.74630	0.873152	+	0.487448i	$0.162072\pi$
$104$	−11.9605	−1.17282
$105$	0	0
$106$	−32.3507	−3.14217
$107$	5.09612	0.492661	0.246330	−	0.969186i	$-0.420775\pi$
$107$	5.09612	0.492661	0.246330	+	0.969186i	$0.420775\pi$
$108$	−15.0170	−1.44502
$109$	6.13513	0.587639	0.293819	−	0.955861i	$-0.405074\pi$
$109$	6.13513	0.587639	0.293819	+	0.955861i	$0.405074\pi$
$110$	0	0
$111$	−5.19851	−0.493421
$112$	−2.49932	−0.236164
$113$	11.4316	1.07539	0.537697	−	0.843138i	$-0.319294\pi$
$113$	11.4316	1.07539	0.537697	+	0.843138i	$0.319294\pi$
$114$	0	0
$115$	0	0
$116$	−7.71648	−0.716457
$117$	−11.0107	−1.01794
$118$	16.6113	1.52919
$119$	5.12490	0.469799
$120$	0	0
$121$	−10.9928	−0.999346
$122$	−29.6002	−2.67988
$123$	6.09794	0.549832
$124$	−23.7386	−2.13179
$125$	0	0
$126$	8.66318	0.771777
$127$	−1.43978	−0.127760	−0.0638799	−	0.997958i	$-0.520347\pi$
$127$	−1.43978	−0.127760	−0.0638799	+	0.997958i	$0.520347\pi$
$128$	14.8756	1.31483
$129$	−0.674589	−0.0593942
$130$	0	0
$131$	−1.00345	−0.0876720	−0.0438360	−	0.999039i	$-0.513958\pi$
$131$	−1.00345	−0.0876720	−0.0438360	+	0.999039i	$0.513958\pi$
$132$	0.258634	0.0225112
$133$	0	0
$134$	−19.7434	−1.70557
$135$	0	0
$136$	−5.29083	−0.453685
$137$	10.4468	0.892530	0.446265	−	0.894901i	$-0.352754\pi$
$137$	10.4468	0.892530	0.446265	+	0.894901i	$0.352754\pi$
$138$	−0.712442	−0.0606471
$139$	10.6846	0.906256	0.453128	−	0.891445i	$-0.350308\pi$
$139$	10.6846	0.906256	0.453128	+	0.891445i	$0.350308\pi$
$140$	0	0
$141$	−7.15819	−0.602828
$142$	−31.8665	−2.67417
$143$	0.485227	0.0405767
$144$	2.37535	0.197946
$145$	0	0
$146$	24.1274	1.99680
$147$	−3.00632	−0.247957
$148$	−14.7412	−1.21172
$149$	−5.04462	−0.413271	−0.206636	−	0.978418i	$-0.566251\pi$
$149$	−5.04462	−0.413271	−0.206636	+	0.978418i	$0.566251\pi$
$150$	0	0
$151$	−20.8114	−1.69360	−0.846802	−	0.531909i	$-0.821475\pi$
$151$	−20.8114	−1.69360	−0.846802	+	0.531909i	$0.821475\pi$
$152$	0	0
$153$	−4.87069	−0.393772
$154$	−0.381774	−0.0307642
$155$	0	0
$156$	17.4454	1.39675
$157$	−23.6158	−1.88475	−0.942374	−	0.334561i	$-0.891412\pi$
$157$	−23.6158	−1.88475	−0.942374	+	0.334561i	$0.891412\pi$
$158$	0.257611	0.0204944
$159$	15.0929	1.19695
$160$	0	0
$161$	0.625927	0.0493299
$162$	−1.06264	−0.0834892
$163$	0.213533	0.0167252	0.00836258	−	0.999965i	$-0.497338\pi$
$163$	0.213533	0.0167252	0.00836258	+	0.999965i	$0.497338\pi$
$164$	17.2916	1.35025
$165$	0	0
$166$	−6.61382	−0.513332
$167$	19.7249	1.52636	0.763178	−	0.646188i	$-0.223638\pi$
$167$	19.7249	1.52636	0.763178	+	0.646188i	$0.223638\pi$
$168$	−4.39037	−0.338724
$169$	19.7295	1.51765
$170$	0	0
$171$	0	0
$172$	−1.91290	−0.145857
$173$	12.5749	0.956051	0.478026	−	0.878346i	$-0.341353\pi$
$173$	12.5749	0.956051	0.478026	+	0.878346i	$0.341353\pi$
$174$	6.04861	0.458544
$175$	0	0
$176$	−0.104678	−0.00789041
$177$	−7.74987	−0.582516
$178$	−24.7299	−1.85358
$179$	10.8183	0.808596	0.404298	−	0.914627i	$-0.367516\pi$
$179$	10.8183	0.808596	0.404298	+	0.914627i	$0.367516\pi$
$180$	0	0
$181$	5.41191	0.402264	0.201132	−	0.979564i	$-0.435538\pi$
$181$	5.41191	0.402264	0.201132	+	0.979564i	$0.435538\pi$
$182$	−25.7514	−1.90882
$183$	13.8098	1.02085
$184$	−0.646192	−0.0476379
$185$	0	0
$186$	18.6076	1.36438
$187$	0.214644	0.0156963
$188$	−20.2981	−1.48039
$189$	−10.3418	−0.752253
$190$	0	0
$191$	4.87144	0.352485	0.176243	−	0.984347i	$-0.443606\pi$
$191$	4.87144	0.352485	0.176243	+	0.984347i	$0.443606\pi$
$192$	−13.4013	−0.967155
$193$	−1.38414	−0.0996323	−0.0498162	−	0.998758i	$-0.515864\pi$
$193$	−1.38414	−0.0996323	−0.0498162	+	0.998758i	$0.515864\pi$
$194$	0.502123	0.0360503
$195$	0	0
$196$	−8.52488	−0.608920
$197$	−6.40750	−0.456515	−0.228258	−	0.973601i	$-0.573303\pi$
$197$	−6.40750	−0.456515	−0.228258	+	0.973601i	$0.573303\pi$
$198$	0.362836	0.0257857
$199$	15.6405	1.10873	0.554363	−	0.832275i	$-0.312962\pi$
$199$	15.6405	1.10873	0.554363	+	0.832275i	$0.312962\pi$
$200$	0	0
$201$	9.21111	0.649701
$202$	28.0096	1.97075
$203$	−5.31410	−0.372976
$204$	7.71711	0.540306
$205$	0	0
$206$	−39.3937	−2.74469
$207$	−0.594879	−0.0413469
$208$	−7.06074	−0.489574
$209$	0	0
$210$	0	0
$211$	−7.68384	−0.528978	−0.264489	−	0.964389i	$-0.585203\pi$
$211$	−7.68384	−0.528978	−0.264489	+	0.964389i	$0.585203\pi$
$212$	42.7983	2.93940
$213$	14.8670	1.01867
$214$	−11.3274	−0.774322
$215$	0	0
$216$	10.6766	0.726450
$217$	−16.3480	−1.10977
$218$	−13.6368	−0.923600
$219$	−11.2564	−0.760640
$220$	0	0
$221$	14.4782	0.973906
$222$	11.5549	0.775517
$223$	2.47996	0.166070	0.0830351	−	0.996547i	$-0.473539\pi$
$223$	2.47996	0.166070	0.0830351	+	0.996547i	$0.473539\pi$
$224$	14.0228	0.936936
$225$	0	0
$226$	−25.4095	−1.69021
$227$	−0.453554	−0.0301034	−0.0150517	−	0.999887i	$-0.504791\pi$
$227$	−0.453554	−0.0301034	−0.0150517	+	0.999887i	$0.504791\pi$
$228$	0	0
$229$	0.993282	0.0656379	0.0328190	−	0.999461i	$-0.489552\pi$
$229$	0.993282	0.0656379	0.0328190	+	0.999461i	$0.489552\pi$
$230$	0	0
$231$	0.178113	0.0117190
$232$	5.48615	0.360183
$233$	4.26321	0.279292	0.139646	−	0.990201i	$-0.455403\pi$
$233$	4.26321	0.279292	0.139646	+	0.990201i	$0.455403\pi$
$234$	24.4740	1.59992
$235$	0	0
$236$	−21.9759	−1.43051
$237$	−0.120186	−0.00780693
$238$	−11.3913	−0.738390
$239$	24.4583	1.58207	0.791037	−	0.611768i	$-0.209541\pi$
$239$	24.4583	1.58207	0.791037	+	0.611768i	$0.209541\pi$
$240$	0	0
$241$	−4.39485	−0.283097	−0.141548	−	0.989931i	$-0.545208\pi$
$241$	−4.39485	−0.283097	−0.141548	+	0.989931i	$0.545208\pi$
$242$	24.4341	1.57069
$243$	15.8163	1.01462
$244$	39.1596	2.50694
$245$	0	0
$246$	−13.5541	−0.864179
$247$	0	0
$248$	16.8773	1.07171
$249$	3.08562	0.195543
$250$	0	0
$251$	−0.387468	−0.0244568	−0.0122284	−	0.999925i	$-0.503893\pi$
$251$	−0.387468	−0.0244568	−0.0122284	+	0.999925i	$0.503893\pi$
$252$	−11.4609	−0.721972
$253$	0.0262154	0.00164815
$254$	3.20025	0.200802
$255$	0	0
$256$	−7.21836	−0.451148
$257$	−2.85296	−0.177963	−0.0889814	−	0.996033i	$-0.528361\pi$
$257$	−2.85296	−0.177963	−0.0889814	+	0.996033i	$0.528361\pi$
$258$	1.49944	0.0933508
$259$	−10.1518	−0.630800
$260$	0	0
$261$	5.05050	0.312618
$262$	2.23041	0.137795
$263$	10.8075	0.666417	0.333209	−	0.942853i	$-0.391869\pi$
$263$	10.8075	0.666417	0.333209	+	0.942853i	$0.391869\pi$
$264$	−0.183880	−0.0113170
$265$	0	0
$266$	0	0
$267$	11.5375	0.706086
$268$	26.1195	1.59550
$269$	−2.77764	−0.169356	−0.0846780	−	0.996408i	$-0.526986\pi$
$269$	−2.77764	−0.169356	−0.0846780	+	0.996408i	$0.526986\pi$
$270$	0	0
$271$	14.8624	0.902828	0.451414	−	0.892315i	$-0.350920\pi$
$271$	14.8624	0.902828	0.451414	+	0.892315i	$0.350920\pi$
$272$	−3.12338	−0.189382
$273$	12.0141	0.727126
$274$	−23.2205	−1.40280
$275$	0	0
$276$	0.942524	0.0567333
$277$	−18.0876	−1.08678	−0.543389	−	0.839481i	$-0.682859\pi$
$277$	−18.0876	−1.08678	−0.543389	+	0.839481i	$0.682859\pi$
$278$	−23.7491	−1.42438
$279$	15.5371	0.930181
$280$	0	0
$281$	3.88426	0.231716	0.115858	−	0.993266i	$-0.463038\pi$
$281$	3.88426	0.231716	0.115858	+	0.993266i	$0.463038\pi$
$282$	15.9108	0.947473
$283$	22.2860	1.32477	0.662383	−	0.749165i	$-0.269545\pi$
$283$	22.2860	1.32477	0.662383	+	0.749165i	$0.269545\pi$
$284$	42.1577	2.50160
$285$	0	0
$286$	−1.07853	−0.0637750
$287$	11.9082	0.702918
$288$	−13.3272	−0.785313
$289$	−10.5955	−0.623263
$290$	0	0
$291$	−0.234262	−0.0137327
$292$	−31.9193	−1.86794
$293$	−24.4514	−1.42846	−0.714232	−	0.699909i	$-0.753224\pi$
$293$	−24.4514	−1.42846	−0.714232	+	0.699909i	$0.753224\pi$
$294$	6.68228	0.389718
$295$	0	0
$296$	10.4804	0.609164
$297$	−0.433140	−0.0251333
$298$	11.2129	0.649544
$299$	1.76828	0.102262
$300$	0	0
$301$	−1.31735	−0.0759309
$302$	46.2582	2.66186
$303$	−13.0676	−0.750717
$304$	0	0
$305$	0	0
$306$	10.8263	0.618897
$307$	6.42519	0.366705	0.183353	−	0.983047i	$-0.441305\pi$
$307$	6.42519	0.366705	0.183353	+	0.983047i	$0.441305\pi$
$308$	0.505067	0.0287789
$309$	18.3788	1.04553
$310$	0	0
$311$	−17.5640	−0.995963	−0.497982	−	0.867188i	$-0.665925\pi$
$311$	−17.5640	−0.995963	−0.497982	+	0.867188i	$0.665925\pi$
$312$	−12.4031	−0.702185
$313$	3.64359	0.205948	0.102974	−	0.994684i	$-0.467164\pi$
$313$	3.64359	0.205948	0.102974	+	0.994684i	$0.467164\pi$
$314$	52.4918	2.96228
$315$	0	0
$316$	−0.340806	−0.0191718
$317$	4.49901	0.252689	0.126345	−	0.991986i	$-0.459675\pi$
$317$	4.49901	0.252689	0.126345	+	0.991986i	$0.459675\pi$
$318$	−33.5477	−1.88126
$319$	−0.222568	−0.0124614
$320$	0	0
$321$	5.28469	0.294962
$322$	−1.39127	−0.0775325
$323$	0	0
$324$	1.40582	0.0781013
$325$	0	0
$326$	−0.474627	−0.0262872
$327$	6.36214	0.351827
$328$	−12.2937	−0.678807
$329$	−13.9787	−0.770669
$330$	0	0
$331$	−34.1003	−1.87432	−0.937161	−	0.348898i	$-0.886556\pi$
$331$	−34.1003	−1.87432	−0.937161	+	0.348898i	$0.886556\pi$
$332$	8.74974	0.480204
$333$	9.64821	0.528719
$334$	−43.8433	−2.39900
$335$	0	0
$336$	−2.59180	−0.141394
$337$	−0.968932	−0.0527811	−0.0263905	−	0.999652i	$-0.508401\pi$
$337$	−0.968932	−0.0527811	−0.0263905	+	0.999652i	$0.508401\pi$
$338$	−43.8535	−2.38532
$339$	11.8546	0.643852
$340$	0	0
$341$	−0.684697	−0.0370784
$342$	0	0
$343$	−20.0464	−1.08240
$344$	1.36000	0.0733264
$345$	0	0
$346$	−27.9507	−1.50264
$347$	23.5064	1.26189	0.630945	−	0.775827i	$-0.282667\pi$
$347$	23.5064	1.26189	0.630945	+	0.775827i	$0.282667\pi$
$348$	−8.00200	−0.428952
$349$	19.4375	1.04047	0.520234	−	0.854024i	$-0.325845\pi$
$349$	19.4375	1.04047	0.520234	+	0.854024i	$0.325845\pi$
$350$	0	0
$351$	−29.2161	−1.55944
$352$	0.587310	0.0313037
$353$	11.9646	0.636814	0.318407	−	0.947954i	$-0.396852\pi$
$353$	11.9646	0.636814	0.318407	+	0.947954i	$0.396852\pi$
$354$	17.2259	0.915549
$355$	0	0
$356$	32.7164	1.73397
$357$	5.31453	0.281275
$358$	−24.0462	−1.27088
$359$	17.1901	0.907256	0.453628	−	0.891191i	$-0.350129\pi$
$359$	17.1901	0.907256	0.453628	+	0.891191i	$0.350129\pi$
$360$	0	0
$361$	0	0
$362$	−12.0293	−0.632244
$363$	−11.3996	−0.598321
$364$	34.0677	1.78563
$365$	0	0
$366$	−30.6955	−1.60448
$367$	17.6232	0.919924	0.459962	−	0.887938i	$-0.347863\pi$
$367$	17.6232	0.919924	0.459962	+	0.887938i	$0.347863\pi$
$368$	−0.381471	−0.0198856
$369$	−11.3175	−0.589165
$370$	0	0
$371$	29.4738	1.53021
$372$	−24.6169	−1.27633
$373$	−2.65476	−0.137458	−0.0687292	−	0.997635i	$-0.521894\pi$
$373$	−2.65476	−0.137458	−0.0687292	+	0.997635i	$0.521894\pi$
$374$	−0.477098	−0.0246701
$375$	0	0
$376$	14.4312	0.744234
$377$	−15.0126	−0.773190
$378$	22.9871	1.18233
$379$	18.9795	0.974909	0.487455	−	0.873148i	$-0.337925\pi$
$379$	18.9795	0.974909	0.487455	+	0.873148i	$0.337925\pi$
$380$	0	0
$381$	−1.49305	−0.0764914
$382$	−10.8279	−0.554006
$383$	−11.9285	−0.609519	−0.304759	−	0.952429i	$-0.598576\pi$
$383$	−11.9285	−0.609519	−0.304759	+	0.952429i	$0.598576\pi$
$384$	15.4260	0.787206
$385$	0	0
$386$	3.07657	0.156594
$387$	1.25201	0.0636431
$388$	−0.664283	−0.0337239
$389$	−9.76564	−0.495138	−0.247569	−	0.968870i	$-0.579632\pi$
$389$	−9.76564	−0.495138	−0.247569	+	0.968870i	$0.579632\pi$
$390$	0	0
$391$	0.782213	0.0395582
$392$	6.06089	0.306121
$393$	−1.04058	−0.0524903
$394$	14.2422	0.717512
$395$	0	0
$396$	−0.480014	−0.0241216
$397$	−28.8426	−1.44757	−0.723784	−	0.690026i	$-0.757599\pi$
$397$	−28.8426	−1.44757	−0.723784	+	0.690026i	$0.757599\pi$
$398$	−34.7648	−1.74260
$399$	0	0
$400$	0	0
$401$	−6.27130	−0.313174	−0.156587	−	0.987664i	$-0.550049\pi$
$401$	−6.27130	−0.313174	−0.156587	+	0.987664i	$0.550049\pi$
$402$	−20.4739	−1.02114
$403$	−46.1841	−2.30059
$404$	−37.0552	−1.84357
$405$	0	0
$406$	11.8118	0.586212
$407$	−0.425182	−0.0210755
$408$	−5.48660	−0.271627
$409$	−11.2239	−0.554988	−0.277494	−	0.960727i	$-0.589504\pi$
$409$	−11.2239	−0.554988	−0.277494	+	0.960727i	$0.589504\pi$
$410$	0	0
$411$	10.8333	0.534369
$412$	52.1159	2.56756
$413$	−15.1341	−0.744701
$414$	1.32226	0.0649855
$415$	0	0
$416$	39.6152	1.94229
$417$	11.0800	0.542588
$418$	0	0
$419$	−26.0754	−1.27387	−0.636934	−	0.770918i	$-0.719798\pi$
$419$	−26.0754	−1.27387	−0.636934	+	0.770918i	$0.719798\pi$
$420$	0	0
$421$	25.2605	1.23112	0.615562	−	0.788089i	$-0.288929\pi$
$421$	25.2605	1.23112	0.615562	+	0.788089i	$0.288929\pi$
$422$	17.0792	0.831401
$423$	13.2853	0.645952
$424$	−30.4281	−1.47772
$425$	0	0
$426$	−33.0456	−1.60106
$427$	26.9680	1.30507
$428$	14.9855	0.724352
$429$	0.503181	0.0242938
$430$	0	0
$431$	−38.1890	−1.83950	−0.919749	−	0.392508i	$-0.871608\pi$
$431$	−38.1890	−1.83950	−0.919749	+	0.392508i	$0.871608\pi$
$432$	6.30280	0.303243
$433$	2.62102	0.125958	0.0629792	−	0.998015i	$-0.479940\pi$
$433$	2.62102	0.125958	0.0629792	+	0.998015i	$0.479940\pi$
$434$	36.3374	1.74425
$435$	0	0
$436$	18.0408	0.863997
$437$	0	0
$438$	25.0201	1.19551
$439$	−6.71666	−0.320569	−0.160284	−	0.987071i	$-0.551241\pi$
$439$	−6.71666	−0.320569	−0.160284	+	0.987071i	$0.551241\pi$
$440$	0	0
$441$	5.57960	0.265695
$442$	−32.1812	−1.53070
$443$	26.0060	1.23558	0.617791	−	0.786342i	$-0.288028\pi$
$443$	26.0060	1.23558	0.617791	+	0.786342i	$0.288028\pi$
$444$	−15.2866	−0.725470
$445$	0	0
$446$	−5.51230	−0.261015
$447$	−5.23127	−0.247431
$448$	−26.1703	−1.23643
$449$	27.5720	1.30120	0.650602	−	0.759419i	$-0.274517\pi$
$449$	27.5720	1.30120	0.650602	+	0.759419i	$0.274517\pi$
$450$	0	0
$451$	0.498745	0.0234850
$452$	33.6154	1.58114
$453$	−21.5814	−1.01398
$454$	1.00813	0.0473139
$455$	0	0
$456$	0	0
$457$	−2.22524	−0.104092	−0.0520462	−	0.998645i	$-0.516574\pi$
$457$	−2.22524	−0.104092	−0.0520462	+	0.998645i	$0.516574\pi$
$458$	−2.20781	−0.103164
$459$	−12.9240	−0.603240
$460$	0	0
$461$	20.4553	0.952698	0.476349	−	0.879256i	$-0.341960\pi$
$461$	20.4553	0.952698	0.476349	+	0.879256i	$0.341960\pi$
$462$	−0.395900	−0.0184189
$463$	32.4300	1.50715	0.753575	−	0.657362i	$-0.228328\pi$
$463$	32.4300	1.50715	0.753575	+	0.657362i	$0.228328\pi$
$464$	3.23868	0.150352
$465$	0	0
$466$	−9.47601	−0.438968
$467$	6.92098	0.320265	0.160132	−	0.987096i	$-0.448808\pi$
$467$	6.92098	0.320265	0.160132	+	0.987096i	$0.448808\pi$
$468$	−32.3779	−1.49667
$469$	17.9876	0.830592
$470$	0	0
$471$	−24.4896	−1.12842
$472$	15.6241	0.719158
$473$	−0.0551741	−0.00253691
$474$	0.267143	0.0122703
$475$	0	0
$476$	15.0701	0.690739
$477$	−28.0118	−1.28257
$478$	−54.3644	−2.48657
$479$	−20.0438	−0.915825	−0.457913	−	0.888997i	$-0.651403\pi$
$479$	−20.0438	−0.915825	−0.457913	+	0.888997i	$0.651403\pi$
$480$	0	0
$481$	−28.6794	−1.30767
$482$	9.76860	0.444947
$483$	0.649087	0.0295345
$484$	−32.3251	−1.46932
$485$	0	0
$486$	−35.1555	−1.59469
$487$	7.12927	0.323058	0.161529	−	0.986868i	$-0.448357\pi$
$487$	7.12927	0.323058	0.161529	+	0.986868i	$0.448357\pi$
$488$	−27.8411	−1.26031
$489$	0.221434	0.0100136
$490$	0	0
$491$	16.5051	0.744865	0.372433	−	0.928059i	$-0.378524\pi$
$491$	16.5051	0.744865	0.372433	+	0.928059i	$0.378524\pi$
$492$	17.9314	0.808410
$493$	−6.64096	−0.299094
$494$	0	0
$495$	0	0
$496$	9.96330	0.447366
$497$	29.0327	1.30229
$498$	−6.85854	−0.307338
$499$	−30.3605	−1.35912	−0.679562	−	0.733618i	$-0.737830\pi$
$499$	−30.3605	−1.35912	−0.679562	+	0.733618i	$0.737830\pi$
$500$	0	0
$501$	20.4547	0.913850
$502$	0.861241	0.0384390
$503$	5.76940	0.257245	0.128622	−	0.991694i	$-0.458944\pi$
$503$	5.76940	0.257245	0.128622	+	0.991694i	$0.458944\pi$
$504$	8.14833	0.362956
$505$	0	0
$506$	−0.0582700	−0.00259042
$507$	20.4595	0.908639
$508$	−4.23377	−0.187843
$509$	38.8654	1.72268	0.861340	−	0.508029i	$-0.169626\pi$
$509$	38.8654	1.72268	0.861340	+	0.508029i	$0.169626\pi$
$510$	0	0
$511$	−21.9818	−0.972418
$512$	−13.7067	−0.605755
$513$	0	0
$514$	6.34139	0.279707
$515$	0	0
$516$	−1.98368	−0.0873265
$517$	−0.585462	−0.0257486
$518$	22.5647	0.991438
$519$	13.0402	0.572400
$520$	0	0
$521$	36.5105	1.59956	0.799778	−	0.600296i	$-0.204951\pi$
$521$	36.5105	1.59956	0.799778	+	0.600296i	$0.204951\pi$
$522$	−11.2259	−0.491346
$523$	27.8101	1.21605	0.608025	−	0.793918i	$-0.291962\pi$
$523$	27.8101	1.21605	0.608025	+	0.793918i	$0.291962\pi$
$524$	−2.95072	−0.128903
$525$	0	0
$526$	−24.0222	−1.04742
$527$	−20.4299	−0.889941
$528$	−0.108551	−0.00472409
$529$	−22.9045	−0.995846
$530$	0	0
$531$	14.3834	0.624187
$532$	0	0
$533$	33.6413	1.45717
$534$	−25.6449	−1.10977
$535$	0	0
$536$	−18.5700	−0.802103
$537$	11.2186	0.484117
$538$	6.17398	0.266179
$539$	−0.245885	−0.0105910
$540$	0	0
$541$	−24.2484	−1.04252	−0.521261	−	0.853398i	$-0.674538\pi$
$541$	−24.2484	−1.04252	−0.521261	+	0.853398i	$0.674538\pi$
$542$	−33.0353	−1.41899
$543$	5.61216	0.240841
$544$	17.5241	0.751340
$545$	0	0
$546$	−26.7042	−1.14283
$547$	−0.591692	−0.0252989	−0.0126495	−	0.999920i	$-0.504027\pi$
$547$	−0.591692	−0.0252989	−0.0126495	+	0.999920i	$0.504027\pi$
$548$	30.7195	1.31227
$549$	−25.6303	−1.09387
$550$	0	0
$551$	0	0
$552$	−0.670102	−0.0285214
$553$	−0.234702	−0.00998056
$554$	40.2040	1.70810
$555$	0	0
$556$	31.4188	1.33246
$557$	24.7130	1.04712	0.523561	−	0.851988i	$-0.324603\pi$
$557$	24.7130	1.04712	0.523561	+	0.851988i	$0.324603\pi$
$558$	−34.5349	−1.46198
$559$	−3.72160	−0.157407
$560$	0	0
$561$	0.222586	0.00939760
$562$	−8.63370	−0.364191
$563$	11.9955	0.505550	0.252775	−	0.967525i	$-0.418657\pi$
$563$	11.9955	0.505550	0.252775	+	0.967525i	$0.418657\pi$
$564$	−21.0492	−0.886329
$565$	0	0
$566$	−49.5360	−2.08215
$567$	0.968147	0.0406583
$568$	−29.9727	−1.25763
$569$	−33.9446	−1.42303	−0.711517	−	0.702669i	$-0.751991\pi$
$569$	−33.9446	−1.42303	−0.711517	+	0.702669i	$0.751991\pi$
$570$	0	0
$571$	−3.81177	−0.159518	−0.0797588	−	0.996814i	$-0.525415\pi$
$571$	−3.81177	−0.159518	−0.0797588	+	0.996814i	$0.525415\pi$
$572$	1.42684	0.0596594
$573$	5.05169	0.211038
$574$	−26.4688	−1.10479
$575$	0	0
$576$	24.8722	1.03634
$577$	−1.65440	−0.0688734	−0.0344367	−	0.999407i	$-0.510964\pi$
$577$	−1.65440	−0.0688734	−0.0344367	+	0.999407i	$0.510964\pi$
$578$	23.5510	0.979591
$579$	−1.43535	−0.0596512
$580$	0	0
$581$	6.02567	0.249987
$582$	0.520702	0.0215838
$583$	1.23444	0.0511253
$584$	22.6935	0.939064
$585$	0	0
$586$	54.3490	2.24514
$587$	29.4152	1.21409	0.607047	−	0.794666i	$-0.292354\pi$
$587$	29.4152	1.21409	0.607047	+	0.794666i	$0.292354\pi$
$588$	−8.84031	−0.364568
$589$	0	0
$590$	0	0
$591$	−6.64458	−0.273322
$592$	6.18700	0.254284
$593$	−46.8254	−1.92289	−0.961445	−	0.274998i	$-0.911323\pi$
$593$	−46.8254	−1.92289	−0.961445	+	0.274998i	$0.911323\pi$
$594$	0.962757	0.0395024
$595$	0	0
$596$	−14.8340	−0.607626
$597$	16.2192	0.663808
$598$	−3.93043	−0.160727
$599$	−12.1717	−0.497321	−0.248660	−	0.968591i	$-0.579990\pi$
$599$	−12.1717	−0.497321	−0.248660	+	0.968591i	$0.579990\pi$
$600$	0	0
$601$	−10.0391	−0.409504	−0.204752	−	0.978814i	$-0.565639\pi$
$601$	−10.0391	−0.409504	−0.204752	+	0.978814i	$0.565639\pi$
$602$	2.92813	0.119342
$603$	−17.0954	−0.696179
$604$	−61.1972	−2.49008
$605$	0	0
$606$	29.0460	1.17991
$607$	20.5318	0.833358	0.416679	−	0.909054i	$-0.363194\pi$
$607$	20.5318	0.833358	0.416679	+	0.909054i	$0.363194\pi$
$608$	0	0
$609$	−5.51072	−0.223306
$610$	0	0
$611$	−39.4906	−1.59762
$612$	−14.3226	−0.578957
$613$	36.4730	1.47313	0.736565	−	0.676367i	$-0.236447\pi$
$613$	36.4730	1.47313	0.736565	+	0.676367i	$0.236447\pi$
$614$	−14.2815	−0.576356
$615$	0	0
$616$	−0.359085	−0.0144679
$617$	−21.4068	−0.861805	−0.430903	−	0.902398i	$-0.641805\pi$
$617$	−21.4068	−0.861805	−0.430903	+	0.902398i	$0.641805\pi$
$618$	−40.8513	−1.64328
$619$	−15.3752	−0.617981	−0.308991	−	0.951065i	$-0.599991\pi$
$619$	−15.3752	−0.617981	−0.308991	+	0.951065i	$0.599991\pi$
$620$	0	0
$621$	−1.57846	−0.0633415
$622$	39.0402	1.56537
$623$	22.5308	0.902676
$624$	−7.32200	−0.293114
$625$	0	0
$626$	−8.09876	−0.323691
$627$	0	0
$628$	−69.4440	−2.77112
$629$	−12.6866	−0.505846
$630$	0	0
$631$	−29.7129	−1.18285	−0.591426	−	0.806359i	$-0.701435\pi$
$631$	−29.7129	−1.18285	−0.591426	+	0.806359i	$0.701435\pi$
$632$	0.242301	0.00963822
$633$	−7.96816	−0.316706
$634$	−10.0001	−0.397156
$635$	0	0
$636$	44.3819	1.75986
$637$	−16.5854	−0.657138
$638$	0.494711	0.0195858
$639$	−27.5926	−1.09155
$640$	0	0
$641$	−19.1099	−0.754795	−0.377398	−	0.926051i	$-0.623181\pi$
$641$	−19.1099	−0.754795	−0.377398	+	0.926051i	$0.623181\pi$
$642$	−11.7465	−0.463597
$643$	−16.2284	−0.639984	−0.319992	−	0.947420i	$-0.603680\pi$
$643$	−16.2284	−0.639984	−0.319992	+	0.947420i	$0.603680\pi$
$644$	1.84058	0.0725291
$645$	0	0
$646$	0	0
$647$	−26.6353	−1.04714	−0.523571	−	0.851982i	$-0.675400\pi$
$647$	−26.6353	−1.04714	−0.523571	+	0.851982i	$0.675400\pi$
$648$	−0.999492	−0.0392637
$649$	−0.633856	−0.0248810
$650$	0	0
$651$	−16.9529	−0.664437
$652$	0.627908	0.0245908
$653$	40.8476	1.59849	0.799245	−	0.601005i	$-0.205233\pi$
$653$	40.8476	1.59849	0.799245	+	0.601005i	$0.205233\pi$
$654$	−14.1414	−0.552972
$655$	0	0
$656$	−7.25745	−0.283356
$657$	20.8914	0.815053
$658$	31.0709	1.21127
$659$	18.3460	0.714658	0.357329	−	0.933979i	$-0.383688\pi$
$659$	18.3460	0.714658	0.357329	+	0.933979i	$0.383688\pi$
$660$	0	0
$661$	24.3103	0.945560	0.472780	−	0.881181i	$-0.343251\pi$
$661$	24.3103	0.945560	0.472780	+	0.881181i	$0.343251\pi$
$662$	75.7961	2.94590
$663$	15.0139	0.583090
$664$	−6.22076	−0.241412
$665$	0	0
$666$	−21.4455	−0.830995
$667$	−0.811090	−0.0314055
$668$	58.0024	2.24418
$669$	2.57172	0.0994283
$670$	0	0
$671$	1.12949	0.0436034
$672$	14.5416	0.560956
$673$	−31.5695	−1.21691	−0.608457	−	0.793587i	$-0.708211\pi$
$673$	−31.5695	−1.21691	−0.608457	+	0.793587i	$0.708211\pi$
$674$	2.15368	0.0829568
$675$	0	0
$676$	58.0160	2.23138
$677$	−12.4254	−0.477545	−0.238773	−	0.971076i	$-0.576745\pi$
$677$	−12.4254	−0.477545	−0.238773	+	0.971076i	$0.576745\pi$
$678$	−26.3496	−1.01195
$679$	−0.457471	−0.0175561
$680$	0	0
$681$	−0.470336	−0.0180233
$682$	1.52190	0.0582766
$683$	9.71494	0.371732	0.185866	−	0.982575i	$-0.440491\pi$
$683$	9.71494	0.371732	0.185866	+	0.982575i	$0.440491\pi$
$684$	0	0
$685$	0	0
$686$	44.5579	1.70123
$687$	1.03003	0.0392983
$688$	0.802861	0.0306088
$689$	83.2653	3.17216
$690$	0	0
$691$	38.5888	1.46799	0.733994	−	0.679156i	$-0.237654\pi$
$691$	38.5888	1.46799	0.733994	+	0.679156i	$0.237654\pi$
$692$	36.9774	1.40567
$693$	−0.330570	−0.0125573
$694$	−52.2486	−1.98333
$695$	0	0
$696$	5.68914	0.215646
$697$	14.8815	0.563678
$698$	−43.2046	−1.63532
$699$	4.42096	0.167216
$700$	0	0
$701$	−18.2907	−0.690832	−0.345416	−	0.938450i	$-0.612262\pi$
$701$	−18.2907	−0.690832	−0.345416	+	0.938450i	$0.612262\pi$
$702$	64.9398	2.45099
$703$	0	0
$704$	−1.09608	−0.0413101
$705$	0	0
$706$	−26.5943	−1.00089
$707$	−25.5188	−0.959733
$708$	−22.7890	−0.856465
$709$	−10.9453	−0.411060	−0.205530	−	0.978651i	$-0.565892\pi$
$709$	−10.9453	−0.411060	−0.205530	+	0.978651i	$0.565892\pi$
$710$	0	0
$711$	0.223060	0.00836541
$712$	−23.2602	−0.871714
$713$	−2.49519	−0.0934458
$714$	−11.8128	−0.442084
$715$	0	0
$716$	31.8119	1.18887
$717$	25.3633	0.947209
$718$	−38.2090	−1.42595
$719$	−7.98877	−0.297931	−0.148965	−	0.988842i	$-0.547594\pi$
$719$	−7.98877	−0.297931	−0.148965	+	0.988842i	$0.547594\pi$
$720$	0	0
$721$	35.8906	1.33663
$722$	0	0
$723$	−4.55746	−0.169494
$724$	15.9141	0.591443
$725$	0	0
$726$	25.3382	0.940390
$727$	13.5437	0.502309	0.251154	−	0.967947i	$-0.419190\pi$
$727$	13.5437	0.502309	0.251154	+	0.967947i	$0.419190\pi$
$728$	−24.2210	−0.897689
$729$	14.9673	0.554344
$730$	0	0
$731$	−1.64628	−0.0608898
$732$	40.6085	1.50094
$733$	−12.2354	−0.451925	−0.225962	−	0.974136i	$-0.572553\pi$
$733$	−12.2354	−0.451925	−0.225962	+	0.974136i	$0.572553\pi$
$734$	−39.1718	−1.44586
$735$	0	0
$736$	2.14030	0.0788923
$737$	0.753369	0.0277507
$738$	25.1558	0.926000
$739$	−5.42922	−0.199717	−0.0998586	−	0.995002i	$-0.531839\pi$
$739$	−5.42922	−0.199717	−0.0998586	+	0.995002i	$0.531839\pi$
$740$	0	0
$741$	0	0
$742$	−65.5126	−2.40505
$743$	−3.77234	−0.138394	−0.0691968	−	0.997603i	$-0.522044\pi$
$743$	−3.77234	−0.138394	−0.0691968	+	0.997603i	$0.522044\pi$
$744$	17.5018	0.641646
$745$	0	0
$746$	5.90084	0.216045
$747$	−5.72678	−0.209532
$748$	0.631176	0.0230781
$749$	10.3201	0.377086
$750$	0	0
$751$	6.28316	0.229276	0.114638	−	0.993407i	$-0.463429\pi$
$751$	6.28316	0.229276	0.114638	+	0.993407i	$0.463429\pi$
$752$	8.51931	0.310667
$753$	−0.401805	−0.0146426
$754$	33.3692	1.21523
$755$	0	0
$756$	−30.4107	−1.10603
$757$	50.8221	1.84716	0.923580	−	0.383406i	$-0.125249\pi$
$757$	50.8221	1.84716	0.923580	+	0.383406i	$0.125249\pi$
$758$	−42.1864	−1.53228
$759$	0.0271854	0.000986768 0
$760$	0	0
$761$	−10.2538	−0.371701	−0.185850	−	0.982578i	$-0.559504\pi$
$761$	−10.2538	−0.371701	−0.185850	+	0.982578i	$0.559504\pi$
$762$	3.31867	0.120223
$763$	12.4241	0.449783
$764$	14.3248	0.518254
$765$	0	0
$766$	26.5140	0.957989
$767$	−42.7548	−1.54379
$768$	−7.48545	−0.270108
$769$	−1.50423	−0.0542440	−0.0271220	−	0.999632i	$-0.508634\pi$
$769$	−1.50423	−0.0542440	−0.0271220	+	0.999632i	$0.508634\pi$
$770$	0	0
$771$	−2.95852	−0.106549
$772$	−4.07015	−0.146488
$773$	37.3223	1.34239	0.671195	−	0.741281i	$-0.265781\pi$
$773$	37.3223	1.34239	0.671195	+	0.741281i	$0.265781\pi$
$774$	−2.78288	−0.100029
$775$	0	0
$776$	0.472282	0.0169539
$777$	−10.5274	−0.377668
$778$	21.7065	0.778215
$779$	0	0
$780$	0	0
$781$	1.21596	0.0435106
$782$	−1.73866	−0.0621742
$783$	13.4011	0.478916
$784$	3.57797	0.127785
$785$	0	0
$786$	2.31294	0.0824998
$787$	32.9294	1.17381	0.586903	−	0.809657i	$-0.300347\pi$
$787$	32.9294	1.17381	0.586903	+	0.809657i	$0.300347\pi$
$788$	−18.8417	−0.671208
$789$	11.2074	0.398993
$790$	0	0
$791$	23.1499	0.823115
$792$	0.341273	0.0121266
$793$	76.1862	2.70545
$794$	64.1096	2.27516
$795$	0	0
$796$	45.9920	1.63014
$797$	−18.1078	−0.641410	−0.320705	−	0.947179i	$-0.603920\pi$
$797$	−18.1078	−0.641410	−0.320705	+	0.947179i	$0.603920\pi$
$798$	0	0
$799$	−17.4690	−0.618008
$800$	0	0
$801$	−21.4132	−0.756597
$802$	13.9395	0.492220
$803$	−0.920655	−0.0324892
$804$	27.0859	0.955246
$805$	0	0
$806$	102.655	3.61588
$807$	−2.88042	−0.101396
$808$	26.3450	0.926814
$809$	−7.85536	−0.276180	−0.138090	−	0.990420i	$-0.544096\pi$
$809$	−7.85536	−0.276180	−0.138090	+	0.990420i	$0.544096\pi$
$810$	0	0
$811$	19.5323	0.685873	0.342936	−	0.939359i	$-0.388578\pi$
$811$	19.5323	0.685873	0.342936	+	0.939359i	$0.388578\pi$
$812$	−15.6265	−0.548382
$813$	15.4124	0.540535
$814$	0.945069	0.0331247
$815$	0	0
$816$	−3.23895	−0.113386
$817$	0	0
$818$	24.9479	0.872282
$819$	−22.2976	−0.779142
$820$	0	0
$821$	−18.2498	−0.636922	−0.318461	−	0.947936i	$-0.603166\pi$
$821$	−18.2498	−0.636922	−0.318461	+	0.947936i	$0.603166\pi$
$822$	−24.0797	−0.839876
$823$	−16.5637	−0.577373	−0.288687	−	0.957424i	$-0.593219\pi$
$823$	−16.5637	−0.577373	−0.288687	+	0.957424i	$0.593219\pi$
$824$	−37.0526	−1.29079
$825$	0	0
$826$	33.6392	1.17046
$827$	16.7592	0.582774	0.291387	−	0.956605i	$-0.405883\pi$
$827$	16.7592	0.582774	0.291387	+	0.956605i	$0.405883\pi$
$828$	−1.74928	−0.0607918
$829$	9.99830	0.347255	0.173628	−	0.984811i	$-0.444451\pi$
$829$	9.99830	0.347255	0.173628	+	0.984811i	$0.444451\pi$
$830$	0	0
$831$	−18.7569	−0.650668
$832$	−73.9328	−2.56316
$833$	−7.33669	−0.254201
$834$	−24.6278	−0.852793
$835$	0	0
$836$	0	0
$837$	41.2264	1.42499
$838$	57.9589	2.00216
$839$	−45.5490	−1.57253	−0.786263	−	0.617892i	$-0.787987\pi$
$839$	−45.5490	−1.57253	−0.786263	+	0.617892i	$0.787987\pi$
$840$	0	0
$841$	−22.1139	−0.762547
$842$	−56.1476	−1.93497
$843$	4.02798	0.138731
$844$	−22.5949	−0.777748
$845$	0	0
$846$	−29.5297	−1.01525
$847$	−22.2613	−0.764907
$848$	−17.9628	−0.616847
$849$	23.1106	0.793155
$850$	0	0
$851$	−1.54946	−0.0531149
$852$	43.7176	1.49774
$853$	−25.5008	−0.873129	−0.436565	−	0.899673i	$-0.643805\pi$
$853$	−25.5008	−0.873129	−0.436565	+	0.899673i	$0.643805\pi$
$854$	−59.9428	−2.05120
$855$	0	0
$856$	−10.6542	−0.364152
$857$	−7.24518	−0.247491	−0.123745	−	0.992314i	$-0.539491\pi$
$857$	−7.24518	−0.247491	−0.123745	+	0.992314i	$0.539491\pi$
$858$	−1.11844	−0.0381829
$859$	−30.1074	−1.02725	−0.513625	−	0.858015i	$-0.671698\pi$
$859$	−30.1074	−1.02725	−0.513625	+	0.858015i	$0.671698\pi$
$860$	0	0
$861$	12.3488	0.420846
$862$	84.8841	2.89116
$863$	7.47961	0.254609	0.127305	−	0.991864i	$-0.459367\pi$
$863$	7.47961	0.254609	0.127305	+	0.991864i	$0.459367\pi$
$864$	−35.3627	−1.20306
$865$	0	0
$866$	−5.82585	−0.197971
$867$	−10.9875	−0.373156
$868$	−48.0725	−1.63169
$869$	−0.00982994	−0.000333458 0
$870$	0	0
$871$	50.8162	1.72184
$872$	−12.8264	−0.434356
$873$	0.434779	0.0147150
$874$	0	0
$875$	0	0
$876$	−33.1004	−1.11836
$877$	−24.6798	−0.833377	−0.416689	−	0.909049i	$-0.636809\pi$
$877$	−24.6798	−0.833377	−0.416689	+	0.909049i	$0.636809\pi$
$878$	14.9294	0.503843
$879$	−25.3561	−0.855240
$880$	0	0
$881$	7.30247	0.246026	0.123013	−	0.992405i	$-0.460744\pi$
$881$	7.30247	0.246026	0.123013	+	0.992405i	$0.460744\pi$
$882$	−12.4020	−0.417597
$883$	43.8146	1.47448	0.737239	−	0.675632i	$-0.236129\pi$
$883$	43.8146	1.47448	0.737239	+	0.675632i	$0.236129\pi$
$884$	42.5741	1.43192
$885$	0	0
$886$	−57.8046	−1.94198
$887$	−49.3920	−1.65842	−0.829211	−	0.558936i	$-0.811210\pi$
$887$	−49.3920	−1.65842	−0.829211	+	0.558936i	$0.811210\pi$
$888$	10.8682	0.364714
$889$	−2.91567	−0.0977883
$890$	0	0
$891$	0.0405485	0.00135843
$892$	7.29249	0.244170
$893$	0	0
$894$	11.6278	0.388890
$895$	0	0
$896$	30.1243	1.00638
$897$	1.83371	0.0612258
$898$	−61.2854	−2.04512
$899$	21.1841	0.706530
$900$	0	0
$901$	36.8331	1.22709
$902$	−1.10858	−0.0369117
$903$	−1.36610	−0.0454608
$904$	−23.8994	−0.794882
$905$	0	0
$906$	47.9698	1.59369
$907$	−10.6373	−0.353206	−0.176603	−	0.984282i	$-0.556511\pi$
$907$	−10.6373	−0.353206	−0.176603	+	0.984282i	$0.556511\pi$
$908$	−1.33371	−0.0442606
$909$	24.2530	0.804420
$910$	0	0
$911$	40.5583	1.34376	0.671878	−	0.740662i	$-0.265488\pi$
$911$	40.5583	1.34376	0.671878	+	0.740662i	$0.265488\pi$
$912$	0	0
$913$	0.252371	0.00835225
$914$	4.94613	0.163603
$915$	0	0
$916$	2.92082	0.0965065
$917$	−2.03207	−0.0671048
$918$	28.7267	0.948121
$919$	38.3456	1.26491	0.632453	−	0.774599i	$-0.282048\pi$
$919$	38.3456	1.26491	0.632453	+	0.774599i	$0.282048\pi$
$920$	0	0
$921$	6.66294	0.219551
$922$	−45.4668	−1.49737
$923$	82.0191	2.69969
$924$	0.523755	0.0172303
$925$	0	0
$926$	−72.0835	−2.36881
$927$	−34.1103	−1.12033
$928$	−18.1710	−0.596493
$929$	43.6424	1.43186	0.715931	−	0.698171i	$-0.246003\pi$
$929$	43.6424	1.43186	0.715931	+	0.698171i	$0.246003\pi$
$930$	0	0
$931$	0	0
$932$	12.5363	0.410639
$933$	−18.2139	−0.596296
$934$	−15.3835	−0.503365
$935$	0	0
$936$	23.0195	0.752417
$937$	35.9137	1.17325	0.586624	−	0.809859i	$-0.300457\pi$
$937$	35.9137	1.17325	0.586624	+	0.809859i	$0.300457\pi$
$938$	−39.9819	−1.30545
$939$	3.77841	0.123304
$940$	0	0
$941$	−30.9209	−1.00799	−0.503997	−	0.863706i	$-0.668138\pi$
$941$	−30.9209	−1.00799	−0.503997	+	0.863706i	$0.668138\pi$
$942$	54.4341	1.77356
$943$	1.81754	0.0591874
$944$	9.22350	0.300199
$945$	0	0
$946$	0.122638	0.00398729
$947$	−11.1663	−0.362856	−0.181428	−	0.983404i	$-0.558072\pi$
$947$	−11.1663	−0.362856	−0.181428	+	0.983404i	$0.558072\pi$
$948$	−0.353416	−0.0114784
$949$	−62.1000	−2.01585
$950$	0	0
$951$	4.66548	0.151288
$952$	−10.7143	−0.347254
$953$	−7.40383	−0.239834	−0.119917	−	0.992784i	$-0.538263\pi$
$953$	−7.40383	−0.239834	−0.119917	+	0.992784i	$0.538263\pi$
$954$	62.2630	2.01584
$955$	0	0
$956$	71.9213	2.32610
$957$	−0.230803	−0.00746081
$958$	44.5522	1.43942
$959$	21.1556	0.683149
$960$	0	0
$961$	34.1697	1.10225
$962$	63.7468	2.05528
$963$	−9.80814	−0.316063
$964$	−12.9234	−0.416233
$965$	0	0
$966$	−1.44275	−0.0464197
$967$	17.5783	0.565279	0.282640	−	0.959226i	$-0.408790\pi$
$967$	17.5783	0.565279	0.282640	+	0.959226i	$0.408790\pi$
$968$	22.9820	0.738671
$969$	0	0
$970$	0	0
$971$	5.31430	0.170544	0.0852721	−	0.996358i	$-0.472824\pi$
$971$	5.31430	0.170544	0.0852721	+	0.996358i	$0.472824\pi$
$972$	46.5090	1.49178
$973$	21.6372	0.693656
$974$	−15.8465	−0.507755
$975$	0	0
$976$	−16.4357	−0.526093
$977$	13.6507	0.436723	0.218362	−	0.975868i	$-0.429929\pi$
$977$	13.6507	0.436723	0.218362	+	0.975868i	$0.429929\pi$
$978$	−0.492189	−0.0157385
$979$	0.943646	0.0301591
$980$	0	0
$981$	−11.8078	−0.376995
$982$	−36.6866	−1.17072
$983$	28.7597	0.917291	0.458646	−	0.888619i	$-0.348335\pi$
$983$	28.7597	0.917291	0.458646	+	0.888619i	$0.348335\pi$
$984$	−12.7486	−0.406411
$985$	0	0
$986$	14.7611	0.470090
$987$	−14.4959	−0.461409
$988$	0	0
$989$	−0.201067	−0.00639357
$990$	0	0
$991$	56.4946	1.79461	0.897306	−	0.441410i	$-0.145521\pi$
$991$	56.4946	1.79461	0.897306	+	0.441410i	$0.145521\pi$
$992$	−55.9004	−1.77484
$993$	−35.3621	−1.12218
$994$	−64.5321	−2.04683
$995$	0	0
$996$	9.07349	0.287505
$997$	14.1163	0.447066	0.223533	−	0.974696i	$-0.428241\pi$
$997$	14.1163	0.447066	0.223533	+	0.974696i	$0.428241\pi$
$998$	67.4835	2.13615
$999$	25.6007	0.809972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cf.1.1		9
5.4	even	2		1805.2.a.s.1.9		9
19.3	odd	18		475.2.l.c.351.3		18
19.13	odd	18		475.2.l.c.226.3		18
19.18	odd	2		9025.2.a.cc.1.9		9
95.3	even	36		475.2.u.b.199.6		36
95.13	even	36		475.2.u.b.74.1		36
95.22	even	36		475.2.u.b.199.1		36
95.32	even	36		475.2.u.b.74.6		36
95.79	odd	18		95.2.k.a.66.1	yes	18
95.89	odd	18		95.2.k.a.36.1	✓	18
95.94	odd	2		1805.2.a.v.1.1		9
285.89	even	18		855.2.bs.c.226.3		18
285.269	even	18		855.2.bs.c.541.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.1	✓	18	95.89	odd	18
95.2.k.a.66.1	yes	18	95.79	odd	18
475.2.l.c.226.3		18	19.13	odd	18
475.2.l.c.351.3		18	19.3	odd	18
475.2.u.b.74.1		36	95.13	even	36
475.2.u.b.74.6		36	95.32	even	36
475.2.u.b.199.1		36	95.22	even	36
475.2.u.b.199.6		36	95.3	even	36
855.2.bs.c.226.3		18	285.89	even	18
855.2.bs.c.541.3		18	285.269	even	18
1805.2.a.s.1.9		9	5.4	even	2
1805.2.a.v.1.1		9	95.94	odd	2
9025.2.a.cc.1.9		9	19.18	odd	2
9025.2.a.cf.1.1		9	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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} -2.30498 q^{6} +2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} +O(q^{10})\)	\(q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} -2.30498 q^{6} +2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} +0.0848155 q^{11} +3.04938 q^{12} +5.72097 q^{13} -4.50122 q^{14} -1.23419 q^{16} +2.53072 q^{17} +4.27795 q^{18} +2.10001 q^{21} -0.188523 q^{22} +0.309088 q^{23} -2.16800 q^{24} -12.7162 q^{26} -5.10685 q^{27} +5.95489 q^{28} -2.62414 q^{29} -8.07278 q^{31} +6.92456 q^{32} +0.0879538 q^{33} -5.62513 q^{34} -5.65951 q^{36} -5.01303 q^{37} +5.93265 q^{39} +5.88035 q^{41} -4.66777 q^{42} -0.650519 q^{43} +0.249406 q^{44} -0.687021 q^{46} -6.90277 q^{47} -1.27985 q^{48} -2.89906 q^{49} +2.62436 q^{51} +16.8229 q^{52} +14.5544 q^{53} +11.3512 q^{54} -4.23372 q^{56} +5.83278 q^{58} -7.47335 q^{59} +13.3170 q^{61} +17.9437 q^{62} -3.89752 q^{63} -12.9231 q^{64} -0.195498 q^{66} +8.88244 q^{67} +7.44175 q^{68} +0.320524 q^{69} +14.3366 q^{71} +4.02371 q^{72} -10.8548 q^{73} +11.1426 q^{74} +0.171758 q^{77} -13.1867 q^{78} -0.115898 q^{79} +0.478079 q^{81} -13.0705 q^{82} +2.97552 q^{83} +6.17523 q^{84} +1.44593 q^{86} -2.72124 q^{87} -0.177319 q^{88} +11.1259 q^{89} +11.5854 q^{91} +0.908894 q^{92} -8.37148 q^{93} +15.3431 q^{94} +7.18078 q^{96} -0.225903 q^{97} +6.44385 q^{98} -0.163238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9	\( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9} + 18 q^{12} + 9 q^{13} + 12 q^{16} + 9 q^{17} + 24 q^{18} - 12 q^{21} + 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} + 24 q^{27} + 15 q^{28} - 9 q^{29} - 18 q^{31} + 3 q^{32} - 9 q^{33} + 24 q^{34} + 18 q^{36} + 18 q^{37} + 18 q^{39} - 6 q^{41} + 12 q^{43} + 48 q^{44} + 9 q^{46} - 15 q^{47} - 21 q^{48} - 9 q^{49} + 6 q^{51} + 33 q^{52} + 15 q^{53} + 63 q^{54} - 6 q^{58} - 21 q^{59} - 12 q^{61} + 36 q^{62} - 21 q^{63} - 36 q^{64} + 3 q^{66} + 60 q^{67} + 51 q^{68} + 15 q^{69} + 18 q^{71} - 27 q^{73} + 27 q^{74} + 30 q^{77} - 6 q^{78} - 15 q^{79} + 33 q^{81} - 24 q^{82} + 48 q^{84} + 39 q^{86} - 15 q^{87} + 27 q^{88} + 39 q^{89} - 21 q^{91} + 6 q^{92} - 15 q^{93} - 15 q^{94} - 33 q^{96} + 15 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9 + 18 * q^12 + 9 * q^13 + 12 * q^16 + 9 * q^17 + 24 * q^18 - 12 * q^21 + 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 + 24 * q^27 + 15 * q^28 - 9 * q^29 - 18 * q^31 + 3 * q^32 - 9 * q^33 + 24 * q^34 + 18 * q^36 + 18 * q^37 + 18 * q^39 - 6 * q^41 + 12 * q^43 + 48 * q^44 + 9 * q^46 - 15 * q^47 - 21 * q^48 - 9 * q^49 + 6 * q^51 + 33 * q^52 + 15 * q^53 + 63 * q^54 - 6 * q^58 - 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 + 60 * q^67 + 51 * q^68 + 15 * q^69 + 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 - 6 * q^78 - 15 * q^79 + 33 * q^81 - 24 * q^82 + 48 * q^84 + 39 * q^86 - 15 * q^87 + 27 * q^88 + 39 * q^89 - 21 * q^91 + 6 * q^92 - 15 * q^93 - 15 * q^94 - 33 * q^96 + 15 * q^97 - 15 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more