LMFDB - Embedded newform 575.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, 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("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 $ x^7 - x^6 - 12x^5 + 9x^4 + 43x^3 - 14x^2 - 49*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.07994$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.07994 q^{2} +1.06928 q^{3} -0.833738 q^{4} -1.15476 q^{6} -2.95289 q^{7} +3.06026 q^{8} -1.85663 q^{9} +O(q^{10})$	\(q-1.07994 q^{2} +1.06928 q^{3} -0.833738 q^{4} -1.15476 q^{6} -2.95289 q^{7} +3.06026 q^{8} -1.85663 q^{9} +5.89337 q^{11} -0.891503 q^{12} -3.64965 q^{13} +3.18893 q^{14} -1.63740 q^{16} +4.68638 q^{17} +2.00504 q^{18} +5.73350 q^{19} -3.15748 q^{21} -6.36446 q^{22} +1.00000 q^{23} +3.27228 q^{24} +3.94138 q^{26} -5.19312 q^{27} +2.46193 q^{28} +10.3864 q^{29} +7.29495 q^{31} -4.35222 q^{32} +6.30169 q^{33} -5.06099 q^{34} +1.54794 q^{36} -0.612908 q^{37} -6.19181 q^{38} -3.90251 q^{39} -9.10447 q^{41} +3.40987 q^{42} +1.58385 q^{43} -4.91353 q^{44} -1.07994 q^{46} +6.22567 q^{47} -1.75085 q^{48} +1.71954 q^{49} +5.01108 q^{51} +3.04285 q^{52} +3.17878 q^{53} +5.60824 q^{54} -9.03659 q^{56} +6.13074 q^{57} -11.2167 q^{58} +1.38576 q^{59} +6.02130 q^{61} -7.87808 q^{62} +5.48242 q^{63} +7.97493 q^{64} -6.80542 q^{66} +13.3807 q^{67} -3.90722 q^{68} +1.06928 q^{69} -6.22567 q^{71} -5.68177 q^{72} -4.48063 q^{73} +0.661901 q^{74} -4.78023 q^{76} -17.4024 q^{77} +4.21446 q^{78} -7.01303 q^{79} +0.0169706 q^{81} +9.83224 q^{82} +2.46049 q^{83} +2.63251 q^{84} -1.71046 q^{86} +11.1060 q^{87} +18.0352 q^{88} +2.15663 q^{89} +10.7770 q^{91} -0.833738 q^{92} +7.80038 q^{93} -6.72332 q^{94} -4.65376 q^{96} +17.7687 q^{97} -1.85699 q^{98} -10.9418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 11 q^{4} + 5 q^{6} - 3 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + q^2 + 11 * q^4 + 5 * q^6 - 3 * q^7 + 6 * q^8 + 15 * q^9	$ 7 q + q^{2} + 11 q^{4} + 5 q^{6} - 3 q^{7} + 6 q^{8} + 15 q^{9} - q^{11} - 6 q^{12} + 3 q^{13} + 7 q^{14} + 7 q^{16} - 10 q^{17} + 24 q^{18} + 15 q^{19} + 2 q^{21} - 21 q^{22} + 7 q^{23} + 18 q^{24} - 20 q^{26} + 11 q^{28} + 3 q^{29} + 14 q^{31} - 17 q^{32} - 6 q^{33} + 20 q^{34} + 10 q^{37} + 31 q^{38} - 8 q^{39} + 19 q^{41} - 44 q^{42} - 5 q^{43} - 3 q^{44} + q^{46} + 14 q^{47} + 27 q^{48} + 40 q^{49} + 2 q^{51} - 16 q^{52} - 4 q^{53} - q^{54} - 9 q^{56} + 4 q^{57} + 13 q^{58} - 16 q^{59} + 40 q^{61} + 12 q^{62} - 53 q^{63} - 4 q^{64} - 54 q^{66} + 4 q^{67} - 20 q^{68} - 14 q^{71} + 6 q^{72} + 3 q^{73} - 18 q^{74} + 35 q^{76} + 17 q^{77} - 23 q^{78} - q^{79} + 47 q^{81} + 22 q^{82} - 17 q^{83} - 60 q^{84} - 35 q^{86} + 56 q^{87} - 57 q^{88} + 16 q^{89} + 25 q^{91} + 11 q^{92} - 14 q^{93} + 7 q^{94} - 19 q^{96} + 24 q^{97} + 46 q^{98} - 53 q^{99}+O(q^{100}) $ 7 * q + q^2 + 11 * q^4 + 5 * q^6 - 3 * q^7 + 6 * q^8 + 15 * q^9 - q^11 - 6 * q^12 + 3 * q^13 + 7 * q^14 + 7 * q^16 - 10 * q^17 + 24 * q^18 + 15 * q^19 + 2 * q^21 - 21 * q^22 + 7 * q^23 + 18 * q^24 - 20 * q^26 + 11 * q^28 + 3 * q^29 + 14 * q^31 - 17 * q^32 - 6 * q^33 + 20 * q^34 + 10 * q^37 + 31 * q^38 - 8 * q^39 + 19 * q^41 - 44 * q^42 - 5 * q^43 - 3 * q^44 + q^46 + 14 * q^47 + 27 * q^48 + 40 * q^49 + 2 * q^51 - 16 * q^52 - 4 * q^53 - q^54 - 9 * q^56 + 4 * q^57 + 13 * q^58 - 16 * q^59 + 40 * q^61 + 12 * q^62 - 53 * q^63 - 4 * q^64 - 54 * q^66 + 4 * q^67 - 20 * q^68 - 14 * q^71 + 6 * q^72 + 3 * q^73 - 18 * q^74 + 35 * q^76 + 17 * q^77 - 23 * q^78 - q^79 + 47 * q^81 + 22 * q^82 - 17 * q^83 - 60 * q^84 - 35 * q^86 + 56 * q^87 - 57 * q^88 + 16 * q^89 + 25 * q^91 + 11 * q^92 - 14 * q^93 + 7 * q^94 - 19 * q^96 + 24 * q^97 + 46 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.07994	−0.763630	−0.381815	−	0.924239i	$-0.624701\pi$
$2$	−1.07994	−0.763630	−0.381815	+	0.924239i	$0.624701\pi$
$3$	1.06928	0.617352	0.308676	−	0.951167i	$-0.400114\pi$
$3$	1.06928	0.617352	0.308676	+	0.951167i	$0.400114\pi$
$4$	−0.833738	−0.416869
$5$	0	0
$5$	0	0
$6$	−1.15476	−0.471428
$7$	−2.95289	−1.11609	−0.558043	−	0.829812i	$-0.688448\pi$
$7$	−2.95289	−1.11609	−0.558043	+	0.829812i	$0.688448\pi$
$8$	3.06026	1.08196
$9$	−1.85663	−0.618877
$10$	0	0
$11$	5.89337	1.77692	0.888459	−	0.458956i	$-0.151777\pi$
$11$	5.89337	1.77692	0.888459	+	0.458956i	$0.151777\pi$
$12$	−0.891503	−0.257355
$13$	−3.64965	−1.01223	−0.506115	−	0.862466i	$-0.668919\pi$
$13$	−3.64965	−1.01223	−0.506115	+	0.862466i	$0.668919\pi$
$14$	3.18893	0.852277
$15$	0	0
$16$	−1.63740	−0.409351
$17$	4.68638	1.13661	0.568307	−	0.822816i	$-0.307598\pi$
$17$	4.68638	1.13661	0.568307	+	0.822816i	$0.307598\pi$
$18$	2.00504	0.472593
$19$	5.73350	1.31535	0.657677	−	0.753300i	$-0.271539\pi$
$19$	5.73350	1.31535	0.657677	+	0.753300i	$0.271539\pi$
$20$	0	0
$21$	−3.15748	−0.689018
$22$	−6.36446	−1.35691
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.27228	0.667952
$25$	0	0
$26$	3.94138	0.772969
$27$	−5.19312	−0.999416
$28$	2.46193	0.465262
$29$	10.3864	1.92871	0.964354	−	0.264617i	$-0.0852455\pi$
$29$	10.3864	1.92871	0.964354	+	0.264617i	$0.0852455\pi$
$30$	0	0
$31$	7.29495	1.31021	0.655106	−	0.755537i	$-0.272624\pi$
$31$	7.29495	1.31021	0.655106	+	0.755537i	$0.272624\pi$
$32$	−4.35222	−0.769371
$33$	6.30169	1.09698
$34$	−5.06099	−0.867953
$35$	0	0
$36$	1.54794	0.257991
$37$	−0.612908	−0.100761	−0.0503807	−	0.998730i	$-0.516043\pi$
$37$	−0.612908	−0.100761	−0.0503807	+	0.998730i	$0.516043\pi$
$38$	−6.19181	−1.00444
$39$	−3.90251	−0.624902
$40$	0	0
$41$	−9.10447	−1.42188	−0.710940	−	0.703253i	$-0.751730\pi$
$41$	−9.10447	−1.42188	−0.710940	+	0.703253i	$0.751730\pi$
$42$	3.40987	0.526155
$43$	1.58385	0.241535	0.120768	−	0.992681i	$-0.461464\pi$
$43$	1.58385	0.241535	0.120768	+	0.992681i	$0.461464\pi$
$44$	−4.91353	−0.740742
$45$	0	0
$46$	−1.07994	−0.159228
$47$	6.22567	0.908107	0.454053	−	0.890974i	$-0.349978\pi$
$47$	6.22567	0.908107	0.454053	+	0.890974i	$0.349978\pi$
$48$	−1.75085	−0.252714
$49$	1.71954	0.245648
$50$	0	0
$51$	5.01108	0.701691
$52$	3.04285	0.421967
$53$	3.17878	0.436639	0.218319	−	0.975877i	$-0.429943\pi$
$53$	3.17878	0.436639	0.218319	+	0.975877i	$0.429943\pi$
$54$	5.60824	0.763184
$55$	0	0
$56$	−9.03659	−1.20756
$57$	6.13074	0.812036
$58$	−11.2167	−1.47282
$59$	1.38576	0.180411	0.0902056	−	0.995923i	$-0.471248\pi$
$59$	1.38576	0.180411	0.0902056	+	0.995923i	$0.471248\pi$
$60$	0	0
$61$	6.02130	0.770949	0.385474	−	0.922719i	$-0.374038\pi$
$61$	6.02130	0.770949	0.385474	+	0.922719i	$0.374038\pi$
$62$	−7.87808	−1.00052
$63$	5.48242	0.690720
$64$	7.97493	0.996866
$65$	0	0
$66$	−6.80542	−0.837689
$67$	13.3807	1.63472	0.817359	−	0.576129i	$-0.195437\pi$
$67$	13.3807	1.63472	0.817359	+	0.576129i	$0.195437\pi$
$68$	−3.90722	−0.473820
$69$	1.06928	0.128727
$70$	0	0
$71$	−6.22567	−0.738851	−0.369425	−	0.929260i	$-0.620445\pi$
$71$	−6.22567	−0.738851	−0.369425	+	0.929260i	$0.620445\pi$
$72$	−5.68177	−0.669602
$73$	−4.48063	−0.524418	−0.262209	−	0.965011i	$-0.584451\pi$
$73$	−4.48063	−0.524418	−0.262209	+	0.965011i	$0.584451\pi$
$74$	0.661901	0.0769444
$75$	0	0
$76$	−4.78023	−0.548331
$77$	−17.4024	−1.98319
$78$	4.21446	0.477194
$79$	−7.01303	−0.789028	−0.394514	−	0.918890i	$-0.629087\pi$
$79$	−7.01303	−0.789028	−0.394514	+	0.918890i	$0.629087\pi$
$80$	0	0
$81$	0.0169706	0.00188563
$82$	9.83224	1.08579
$83$	2.46049	0.270074	0.135037	−	0.990841i	$-0.456885\pi$
$83$	2.46049	0.270074	0.135037	+	0.990841i	$0.456885\pi$
$84$	2.63251	0.287230
$85$	0	0
$86$	−1.71046	−0.184443
$87$	11.1060	1.19069
$88$	18.0352	1.92256
$89$	2.15663	0.228602	0.114301	−	0.993446i	$-0.463537\pi$
$89$	2.15663	0.228602	0.114301	+	0.993446i	$0.463537\pi$
$90$	0	0
$91$	10.7770	1.12974
$92$	−0.833738	−0.0869232
$93$	7.80038	0.808861
$94$	−6.72332	−0.693458
$95$	0	0
$96$	−4.65376	−0.474972
$97$	17.7687	1.80414	0.902068	−	0.431594i	$-0.142049\pi$
$97$	17.7687	1.80414	0.902068	+	0.431594i	$0.142049\pi$
$98$	−1.85699	−0.187585
$99$	−10.9418	−1.09969
$100$	0	0
$101$	3.18653	0.317072	0.158536	−	0.987353i	$-0.449323\pi$
$101$	3.18653	0.317072	0.158536	+	0.987353i	$0.449323\pi$
$102$	−5.41164	−0.535832
$103$	−12.6204	−1.24352	−0.621761	−	0.783207i	$-0.713582\pi$
$103$	−12.6204	−1.24352	−0.621761	+	0.783207i	$0.713582\pi$
$104$	−11.1688	−1.09520
$105$	0	0
$106$	−3.43288	−0.333431
$107$	1.68553	0.162947	0.0814733	−	0.996676i	$-0.474037\pi$
$107$	1.68553	0.162947	0.0814733	+	0.996676i	$0.474037\pi$
$108$	4.32970	0.416626
$109$	−5.80929	−0.556429	−0.278215	−	0.960519i	$-0.589743\pi$
$109$	−5.80929	−0.556429	−0.278215	+	0.960519i	$0.589743\pi$
$110$	0	0
$111$	−0.655373	−0.0622052
$112$	4.83507	0.456871
$113$	−9.40374	−0.884630	−0.442315	−	0.896860i	$-0.645843\pi$
$113$	−9.40374	−0.884630	−0.442315	+	0.896860i	$0.645843\pi$
$114$	−6.62081	−0.620095
$115$	0	0
$116$	−8.65954	−0.804018
$117$	6.77604	0.626446
$118$	−1.49654	−0.137767
$119$	−13.8384	−1.26856
$120$	0	0
$121$	23.7318	2.15744
$122$	−6.50262	−0.588720
$123$	−9.73527	−0.877799
$124$	−6.08208	−0.546187
$125$	0	0
$126$	−5.92066	−0.527455
$127$	−15.8267	−1.40440	−0.702198	−	0.711982i	$-0.747798\pi$
$127$	−15.8267	−1.40440	−0.702198	+	0.711982i	$0.747798\pi$
$128$	0.0920282	0.00813422
$129$	1.69359	0.149112
$130$	0	0
$131$	−6.97506	−0.609414	−0.304707	−	0.952446i	$-0.598558\pi$
$131$	−6.97506	−0.609414	−0.304707	+	0.952446i	$0.598558\pi$
$132$	−5.25396	−0.457298
$133$	−16.9304	−1.46805
$134$	−14.4503	−1.24832
$135$	0	0
$136$	14.3415	1.22978
$137$	−3.70809	−0.316803	−0.158402	−	0.987375i	$-0.550634\pi$
$137$	−3.70809	−0.316803	−0.158402	+	0.987375i	$0.550634\pi$
$138$	−1.15476	−0.0982996
$139$	−1.28393	−0.108902	−0.0544509	−	0.998516i	$-0.517341\pi$
$139$	−1.28393	−0.108902	−0.0544509	+	0.998516i	$0.517341\pi$
$140$	0	0
$141$	6.65701	0.560621
$142$	6.72332	0.564209
$143$	−21.5087	−1.79865
$144$	3.04006	0.253338
$145$	0	0
$146$	4.83880	0.400462
$147$	1.83868	0.151651
$148$	0.511004	0.0420043
$149$	−0.734825	−0.0601992	−0.0300996	−	0.999547i	$-0.509582\pi$
$149$	−0.734825	−0.0601992	−0.0300996	+	0.999547i	$0.509582\pi$
$150$	0	0
$151$	−12.8604	−1.04656	−0.523281	−	0.852160i	$-0.675292\pi$
$151$	−12.8604	−1.04656	−0.523281	+	0.852160i	$0.675292\pi$
$152$	17.5460	1.42317
$153$	−8.70088	−0.703425
$154$	18.7935	1.51443
$155$	0	0
$156$	3.25367	0.260502
$157$	−13.9303	−1.11176	−0.555878	−	0.831264i	$-0.687618\pi$
$157$	−13.9303	−1.11176	−0.555878	+	0.831264i	$0.687618\pi$
$158$	7.57362	0.602525
$159$	3.39902	0.269560
$160$	0	0
$161$	−2.95289	−0.232720
$162$	−0.0183272	−0.00143992
$163$	12.6677	0.992212	0.496106	−	0.868262i	$-0.334763\pi$
$163$	12.6677	0.992212	0.496106	+	0.868262i	$0.334763\pi$
$164$	7.59074	0.592737
$165$	0	0
$166$	−2.65717	−0.206237
$167$	−6.67811	−0.516768	−0.258384	−	0.966042i	$-0.583190\pi$
$167$	−6.67811	−0.516768	−0.258384	+	0.966042i	$0.583190\pi$
$168$	−9.66268	−0.745492
$169$	0.319911	0.0246085
$170$	0	0
$171$	−10.6450	−0.814042
$172$	−1.32052	−0.100688
$173$	15.7354	1.19634	0.598171	−	0.801369i	$-0.295894\pi$
$173$	15.7354	1.19634	0.598171	+	0.801369i	$0.295894\pi$
$174$	−11.9938	−0.909247
$175$	0	0
$176$	−9.64983	−0.727383
$177$	1.48178	0.111377
$178$	−2.32902	−0.174567
$179$	−7.77154	−0.580872	−0.290436	−	0.956894i	$-0.593800\pi$
$179$	−7.77154	−0.580872	−0.290436	+	0.956894i	$0.593800\pi$
$180$	0	0
$181$	−2.46939	−0.183548	−0.0917741	−	0.995780i	$-0.529254\pi$
$181$	−2.46939	−0.183548	−0.0917741	+	0.995780i	$0.529254\pi$
$182$	−11.6385	−0.862700
$183$	6.43849	0.475947
$184$	3.06026	0.225605
$185$	0	0
$186$	−8.42391	−0.617671
$187$	27.6186	2.01967
$188$	−5.19058	−0.378562
$189$	15.3347	1.11543
$190$	0	0
$191$	−9.74202	−0.704908	−0.352454	−	0.935829i	$-0.614653\pi$
$191$	−9.74202	−0.704908	−0.352454	+	0.935829i	$0.614653\pi$
$192$	8.52747	0.615417
$193$	−1.54038	−0.110879	−0.0554394	−	0.998462i	$-0.517656\pi$
$193$	−1.54038	−0.110879	−0.0554394	+	0.998462i	$0.517656\pi$
$194$	−19.1890	−1.37769
$195$	0	0
$196$	−1.43365	−0.102403
$197$	−14.7266	−1.04923	−0.524614	−	0.851340i	$-0.675790\pi$
$197$	−14.7266	−1.04923	−0.524614	+	0.851340i	$0.675790\pi$
$198$	11.8165	0.839759
$199$	−19.3914	−1.37462	−0.687309	−	0.726365i	$-0.741208\pi$
$199$	−19.3914	−1.37462	−0.687309	+	0.726365i	$0.741208\pi$
$200$	0	0
$201$	14.3078	1.00920
$202$	−3.44125	−0.242126
$203$	−30.6699	−2.15260
$204$	−4.17793	−0.292513
$205$	0	0
$206$	13.6292	0.949590
$207$	−1.85663	−0.129045
$208$	5.97594	0.414357
$209$	33.7896	2.33728
$210$	0	0
$211$	23.0986	1.59017	0.795086	−	0.606497i	$-0.207426\pi$
$211$	23.0986	1.59017	0.795086	+	0.606497i	$0.207426\pi$
$212$	−2.65027	−0.182021
$213$	−6.65701	−0.456131
$214$	−1.82027	−0.124431
$215$	0	0
$216$	−15.8923	−1.08133
$217$	−21.5412	−1.46231
$218$	6.27366	0.424906
$219$	−4.79107	−0.323751
$220$	0	0
$221$	−17.1036	−1.15052
$222$	0.707760	0.0475018
$223$	2.17546	0.145679	0.0728396	−	0.997344i	$-0.476794\pi$
$223$	2.17546	0.145679	0.0728396	+	0.997344i	$0.476794\pi$
$224$	12.8516	0.858684
$225$	0	0
$226$	10.1554	0.675530
$227$	13.4985	0.895928	0.447964	−	0.894051i	$-0.352149\pi$
$227$	13.4985	0.895928	0.447964	+	0.894051i	$0.352149\pi$
$228$	−5.11143	−0.338513
$229$	9.00063	0.594778	0.297389	−	0.954756i	$-0.403884\pi$
$229$	9.00063	0.594778	0.297389	+	0.954756i	$0.403884\pi$
$230$	0	0
$231$	−18.6082	−1.22433
$232$	31.7851	2.08679
$233$	19.1523	1.25471	0.627354	−	0.778734i	$-0.284138\pi$
$233$	19.1523	1.25471	0.627354	+	0.778734i	$0.284138\pi$
$234$	−7.31769	−0.478373
$235$	0	0
$236$	−1.15536	−0.0752078
$237$	−7.49892	−0.487107
$238$	14.9445	0.968711
$239$	11.4712	0.742009	0.371005	−	0.928631i	$-0.379013\pi$
$239$	11.4712	0.742009	0.371005	+	0.928631i	$0.379013\pi$
$240$	0	0
$241$	26.4633	1.70465	0.852325	−	0.523012i	$-0.175192\pi$
$241$	26.4633	1.70465	0.852325	+	0.523012i	$0.175192\pi$
$242$	−25.6288	−1.64748
$243$	15.5975	1.00058
$244$	−5.02019	−0.321385
$245$	0	0
$246$	10.5135	0.670314
$247$	−20.9252	−1.33144
$248$	22.3244	1.41760
$249$	2.63096	0.166731
$250$	0	0
$251$	19.3419	1.22085	0.610426	−	0.792073i	$-0.290998\pi$
$251$	19.3419	1.22085	0.610426	+	0.792073i	$0.290998\pi$
$252$	−4.57090	−0.287940
$253$	5.89337	0.370513
$254$	17.0919	1.07244
$255$	0	0
$256$	−16.0492	−1.00308
$257$	10.7563	0.670959	0.335480	−	0.942047i	$-0.391102\pi$
$257$	10.7563	0.670959	0.335480	+	0.942047i	$0.391102\pi$
$258$	−1.82897	−0.113866
$259$	1.80985	0.112458
$260$	0	0
$261$	−19.2837	−1.19363
$262$	7.53262	0.465367
$263$	−14.9372	−0.921069	−0.460535	−	0.887642i	$-0.652342\pi$
$263$	−14.9372	−0.921069	−0.460535	+	0.887642i	$0.652342\pi$
$264$	19.2848	1.18690
$265$	0	0
$266$	18.2837	1.12105
$267$	2.30605	0.141128
$268$	−11.1560	−0.681463
$269$	14.1731	0.864146	0.432073	−	0.901839i	$-0.357782\pi$
$269$	14.1731	0.864146	0.432073	+	0.901839i	$0.357782\pi$
$270$	0	0
$271$	−6.12384	−0.371996	−0.185998	−	0.982550i	$-0.559552\pi$
$271$	−6.12384	−0.371996	−0.185998	+	0.982550i	$0.559552\pi$
$272$	−7.67350	−0.465275
$273$	11.5237	0.697444
$274$	4.00450	0.241921
$275$	0	0
$276$	−0.891503	−0.0536622
$277$	2.95941	0.177814	0.0889068	−	0.996040i	$-0.471663\pi$
$277$	2.95941	0.177814	0.0889068	+	0.996040i	$0.471663\pi$
$278$	1.38657	0.0831607
$279$	−13.5440	−0.810860
$280$	0	0
$281$	−27.1304	−1.61846	−0.809231	−	0.587490i	$-0.800116\pi$
$281$	−27.1304	−1.61846	−0.809231	+	0.587490i	$0.800116\pi$
$282$	−7.18914	−0.428107
$283$	−3.50760	−0.208505	−0.104253	−	0.994551i	$-0.533245\pi$
$283$	−3.50760	−0.208505	−0.104253	+	0.994551i	$0.533245\pi$
$284$	5.19058	0.308004
$285$	0	0
$286$	23.2280	1.37350
$287$	26.8845	1.58694
$288$	8.08047	0.476146
$289$	4.96219	0.291893
$290$	0	0
$291$	18.9998	1.11379
$292$	3.73567	0.218614
$293$	1.47172	0.0859787	0.0429894	−	0.999076i	$-0.486312\pi$
$293$	1.47172	0.0859787	0.0429894	+	0.999076i	$0.486312\pi$
$294$	−1.98565	−0.115806
$295$	0	0
$296$	−1.87565	−0.109020
$297$	−30.6050	−1.77588
$298$	0.793564	0.0459699
$299$	−3.64965	−0.211064
$300$	0	0
$301$	−4.67693	−0.269574
$302$	13.8884	0.799186
$303$	3.40731	0.195745
$304$	−9.38805	−0.538442
$305$	0	0
$306$	9.39640	0.537156
$307$	18.4258	1.05162	0.525808	−	0.850604i	$-0.323763\pi$
$307$	18.4258	1.05162	0.525808	+	0.850604i	$0.323763\pi$
$308$	14.5091	0.826732
$309$	−13.4948	−0.767690
$310$	0	0
$311$	−14.0373	−0.795985	−0.397992	−	0.917389i	$-0.630293\pi$
$311$	−14.0373	−0.795985	−0.397992	+	0.917389i	$0.630293\pi$
$312$	−11.9427	−0.676121
$313$	−4.85733	−0.274553	−0.137276	−	0.990533i	$-0.543835\pi$
$313$	−4.85733	−0.274553	−0.137276	+	0.990533i	$0.543835\pi$
$314$	15.0438	0.848970
$315$	0	0
$316$	5.84703	0.328921
$317$	20.5571	1.15460	0.577302	−	0.816531i	$-0.304105\pi$
$317$	20.5571	1.15460	0.577302	+	0.816531i	$0.304105\pi$
$318$	−3.67072	−0.205844
$319$	61.2109	3.42715
$320$	0	0
$321$	1.80231	0.100595
$322$	3.18893	0.177712
$323$	26.8694	1.49505
$324$	−0.0141491	−0.000786059 0
$325$	0	0
$326$	−13.6803	−0.757683
$327$	−6.21178	−0.343512
$328$	−27.8620	−1.53842
$329$	−18.3837	−1.01353
$330$	0	0
$331$	−28.5828	−1.57105	−0.785525	−	0.618830i	$-0.787607\pi$
$331$	−28.5828	−1.57105	−0.785525	+	0.618830i	$0.787607\pi$
$332$	−2.05141	−0.112585
$333$	1.13794	0.0623589
$334$	7.21193	0.394619
$335$	0	0
$336$	5.17006	0.282050
$337$	3.73357	0.203381	0.101690	−	0.994816i	$-0.467575\pi$
$337$	3.73357	0.203381	0.101690	+	0.994816i	$0.467575\pi$
$338$	−0.345484	−0.0187918
$339$	−10.0553	−0.546128
$340$	0	0
$341$	42.9918	2.32814
$342$	11.4959	0.621627
$343$	15.5926	0.841921
$344$	4.84699	0.261332
$345$	0	0
$346$	−16.9932	−0.913562
$347$	26.2237	1.40776	0.703880	−	0.710319i	$-0.251449\pi$
$347$	26.2237	1.40776	0.703880	+	0.710319i	$0.251449\pi$
$348$	−9.25951	−0.496362
$349$	28.6776	1.53507	0.767537	−	0.641004i	$-0.221482\pi$
$349$	28.6776	1.53507	0.767537	+	0.641004i	$0.221482\pi$
$350$	0	0
$351$	18.9530	1.01164
$352$	−25.6492	−1.36711
$353$	0.121347	0.00645865	0.00322933	−	0.999995i	$-0.498972\pi$
$353$	0.121347	0.00645865	0.00322933	+	0.999995i	$0.498972\pi$
$354$	−1.60022	−0.0850509
$355$	0	0
$356$	−1.79806	−0.0952971
$357$	−14.7971	−0.783148
$358$	8.39277	0.443572
$359$	−23.2795	−1.22865	−0.614324	−	0.789054i	$-0.710571\pi$
$359$	−23.2795	−1.22865	−0.614324	+	0.789054i	$0.710571\pi$
$360$	0	0
$361$	13.8730	0.730157
$362$	2.66678	0.140163
$363$	25.3760	1.33190
$364$	−8.98519	−0.470952
$365$	0	0
$366$	−6.95315	−0.363447
$367$	−28.8647	−1.50673	−0.753363	−	0.657605i	$-0.771570\pi$
$367$	−28.8647	−1.50673	−0.753363	+	0.657605i	$0.771570\pi$
$368$	−1.63740	−0.0853556
$369$	16.9036	0.879968
$370$	0	0
$371$	−9.38657	−0.487327
$372$	−6.50347	−0.337189
$373$	25.2116	1.30541	0.652703	−	0.757614i	$-0.273635\pi$
$373$	25.2116	1.30541	0.652703	+	0.757614i	$0.273635\pi$
$374$	−29.8263	−1.54228
$375$	0	0
$376$	19.0521	0.982539
$377$	−37.9067	−1.95229
$378$	−16.5605	−0.851780
$379$	7.32791	0.376409	0.188205	−	0.982130i	$-0.439733\pi$
$379$	7.32791	0.376409	0.188205	+	0.982130i	$0.439733\pi$
$380$	0	0
$381$	−16.9233	−0.867006
$382$	10.5208	0.538289
$383$	−4.37082	−0.223338	−0.111669	−	0.993745i	$-0.535620\pi$
$383$	−4.37082	−0.223338	−0.111669	+	0.993745i	$0.535620\pi$
$384$	0.0984043	0.00502168
$385$	0	0
$386$	1.66351	0.0846704
$387$	−2.94063	−0.149480
$388$	−14.8144	−0.752089
$389$	−16.6902	−0.846226	−0.423113	−	0.906077i	$-0.639063\pi$
$389$	−16.6902	−0.846226	−0.423113	+	0.906077i	$0.639063\pi$
$390$	0	0
$391$	4.68638	0.237001
$392$	5.26223	0.265783
$393$	−7.45832	−0.376222
$394$	15.9038	0.801222
$395$	0	0
$396$	9.12260	0.458428
$397$	−18.2264	−0.914754	−0.457377	−	0.889273i	$-0.651211\pi$
$397$	−18.2264	−0.914754	−0.457377	+	0.889273i	$0.651211\pi$
$398$	20.9414	1.04970
$399$	−18.1034	−0.906302
$400$	0	0
$401$	−23.9721	−1.19711	−0.598554	−	0.801082i	$-0.704258\pi$
$401$	−23.9721	−1.19711	−0.598554	+	0.801082i	$0.704258\pi$
$402$	−15.4515	−0.770652
$403$	−26.6240	−1.32624
$404$	−2.65673	−0.132177
$405$	0	0
$406$	33.1215	1.64379
$407$	−3.61209	−0.179045
$408$	15.3352	0.759204
$409$	33.7235	1.66752	0.833760	−	0.552127i	$-0.186184\pi$
$409$	33.7235	1.66752	0.833760	+	0.552127i	$0.186184\pi$
$410$	0	0
$411$	−3.96500	−0.195579
$412$	10.5221	0.518386
$413$	−4.09200	−0.201354
$414$	2.00504	0.0985425
$415$	0	0
$416$	15.8841	0.778780
$417$	−1.37289	−0.0672307
$418$	−36.4906	−1.78481
$419$	3.62819	0.177249	0.0886244	−	0.996065i	$-0.471753\pi$
$419$	3.62819	0.177249	0.0886244	+	0.996065i	$0.471753\pi$
$420$	0	0
$421$	15.3678	0.748982	0.374491	−	0.927231i	$-0.377818\pi$
$421$	15.3678	0.748982	0.374491	+	0.927231i	$0.377818\pi$
$422$	−24.9450	−1.21430
$423$	−11.5588	−0.562006
$424$	9.72788	0.472427
$425$	0	0
$426$	7.18914	0.348315
$427$	−17.7802	−0.860445
$428$	−1.40529	−0.0679274
$429$	−22.9989	−1.11040
$430$	0	0
$431$	−14.0199	−0.675313	−0.337656	−	0.941269i	$-0.609634\pi$
$431$	−14.0199	−0.675313	−0.337656	+	0.941269i	$0.609634\pi$
$432$	8.50324	0.409112
$433$	−22.9911	−1.10488	−0.552441	−	0.833552i	$-0.686303\pi$
$433$	−22.9911	−1.10488	−0.552441	+	0.833552i	$0.686303\pi$
$434$	23.2631	1.11666
$435$	0	0
$436$	4.84343	0.231958
$437$	5.73350	0.274270
$438$	5.17405	0.247226
$439$	3.54418	0.169154	0.0845772	−	0.996417i	$-0.473046\pi$
$439$	3.54418	0.169154	0.0845772	+	0.996417i	$0.473046\pi$
$440$	0	0
$441$	−3.19255	−0.152026
$442$	18.4708	0.878568
$443$	4.89648	0.232639	0.116319	−	0.993212i	$-0.462890\pi$
$443$	4.89648	0.232639	0.116319	+	0.993212i	$0.462890\pi$
$444$	0.546409	0.0259314
$445$	0	0
$446$	−2.34935	−0.111245
$447$	−0.785737	−0.0371641
$448$	−23.5491	−1.11259
$449$	−33.5702	−1.58427	−0.792137	−	0.610344i	$-0.791031\pi$
$449$	−33.5702	−1.58427	−0.792137	+	0.610344i	$0.791031\pi$
$450$	0	0
$451$	−53.6560	−2.52656
$452$	7.84026	0.368775
$453$	−13.7514	−0.646096
$454$	−14.5775	−0.684158
$455$	0	0
$456$	18.7616	0.878594
$457$	35.2502	1.64893	0.824467	−	0.565910i	$-0.191475\pi$
$457$	35.2502	1.64893	0.824467	+	0.565910i	$0.191475\pi$
$458$	−9.72010	−0.454190
$459$	−24.3369	−1.13595
$460$	0	0
$461$	−30.3269	−1.41247	−0.706233	−	0.707979i	$-0.749607\pi$
$461$	−30.3269	−1.41247	−0.706233	+	0.707979i	$0.749607\pi$
$462$	20.0956	0.934933
$463$	−21.7155	−1.00920	−0.504602	−	0.863352i	$-0.668361\pi$
$463$	−21.7155	−1.00920	−0.504602	+	0.863352i	$0.668361\pi$
$464$	−17.0067	−0.789518
$465$	0	0
$466$	−20.6833	−0.958133
$467$	−16.4780	−0.762511	−0.381255	−	0.924470i	$-0.624508\pi$
$467$	−16.4780	−0.762511	−0.381255	+	0.924470i	$0.624508\pi$
$468$	−5.64945	−0.261146
$469$	−39.5118	−1.82449
$470$	0	0
$471$	−14.8954	−0.686344
$472$	4.24079	0.195198
$473$	9.33422	0.429188
$474$	8.09836	0.371970
$475$	0	0
$476$	11.5376	0.528824
$477$	−5.90182	−0.270226
$478$	−12.3881	−0.566621
$479$	−33.3508	−1.52384	−0.761919	−	0.647672i	$-0.775743\pi$
$479$	−33.3508	−1.52384	−0.761919	+	0.647672i	$0.775743\pi$
$480$	0	0
$481$	2.23690	0.101994
$482$	−28.5787	−1.30172
$483$	−3.15748	−0.143670
$484$	−19.7861	−0.899368
$485$	0	0
$486$	−16.8443	−0.764073
$487$	−19.9386	−0.903506	−0.451753	−	0.892143i	$-0.649201\pi$
$487$	−19.9386	−0.903506	−0.451753	+	0.892143i	$0.649201\pi$
$488$	18.4267	0.834139
$489$	13.5454	0.612544
$490$	0	0
$491$	−9.51846	−0.429562	−0.214781	−	0.976662i	$-0.568904\pi$
$491$	−9.51846	−0.429562	−0.214781	+	0.976662i	$0.568904\pi$
$492$	8.11666	0.365927
$493$	48.6747	2.19220
$494$	22.5979	1.01673
$495$	0	0
$496$	−11.9448	−0.536337
$497$	18.3837	0.824621
$498$	−2.84127	−0.127321
$499$	−27.6987	−1.23997	−0.619983	−	0.784616i	$-0.712860\pi$
$499$	−27.6987	−1.23997	−0.619983	+	0.784616i	$0.712860\pi$
$500$	0	0
$501$	−7.14080	−0.319027
$502$	−20.8880	−0.932279
$503$	−0.761780	−0.0339661	−0.0169831	−	0.999856i	$-0.505406\pi$
$503$	−0.761780	−0.0339661	−0.0169831	+	0.999856i	$0.505406\pi$
$504$	16.7776	0.747334
$505$	0	0
$506$	−6.36446	−0.282935
$507$	0.342076	0.0151921
$508$	13.1954	0.585449
$509$	10.2481	0.454239	0.227119	−	0.973867i	$-0.427069\pi$
$509$	10.2481	0.454239	0.227119	+	0.973867i	$0.427069\pi$
$510$	0	0
$511$	13.2308	0.585296
$512$	17.1481	0.757846
$513$	−29.7747	−1.31459
$514$	−11.6161	−0.512365
$515$	0	0
$516$	−1.41201	−0.0621602
$517$	36.6901	1.61363
$518$	−1.95452	−0.0858766
$519$	16.8256	0.738563
$520$	0	0
$521$	1.36360	0.0597405	0.0298702	−	0.999554i	$-0.490491\pi$
$521$	1.36360	0.0597405	0.0298702	+	0.999554i	$0.490491\pi$
$522$	20.8252	0.911494
$523$	−2.50258	−0.109430	−0.0547150	−	0.998502i	$-0.517425\pi$
$523$	−2.50258	−0.109430	−0.0547150	+	0.998502i	$0.517425\pi$
$524$	5.81537	0.254046
$525$	0	0
$526$	16.1313	0.703356
$527$	34.1869	1.48921
$528$	−10.3184	−0.449051
$529$	1.00000	0.0434783
$530$	0	0
$531$	−2.57285	−0.111652
$532$	14.1155	0.611984
$533$	33.2281	1.43927
$534$	−2.49038	−0.107769
$535$	0	0
$536$	40.9485	1.76871
$537$	−8.30999	−0.358603
$538$	−15.3060	−0.659888
$539$	10.1339	0.436497
$540$	0	0
$541$	14.4910	0.623019	0.311509	−	0.950243i	$-0.399166\pi$
$541$	14.4910	0.623019	0.311509	+	0.950243i	$0.399166\pi$
$542$	6.61335	0.284068
$543$	−2.64048	−0.113314
$544$	−20.3962	−0.874479
$545$	0	0
$546$	−12.4448	−0.532589
$547$	25.9898	1.11124	0.555622	−	0.831435i	$-0.312480\pi$
$547$	25.9898	1.11124	0.555622	+	0.831435i	$0.312480\pi$
$548$	3.09157	0.132066
$549$	−11.1793	−0.477122
$550$	0	0
$551$	59.5504	2.53693
$552$	3.27228	0.139278
$553$	20.7087	0.880623
$554$	−3.19597	−0.135784
$555$	0	0
$556$	1.07046	0.0453978
$557$	−6.12731	−0.259623	−0.129811	−	0.991539i	$-0.541437\pi$
$557$	−6.12731	−0.259623	−0.129811	+	0.991539i	$0.541437\pi$
$558$	14.6267	0.619197
$559$	−5.78049	−0.244489
$560$	0	0
$561$	29.5321	1.24685
$562$	29.2991	1.23591
$563$	22.2228	0.936579	0.468289	−	0.883575i	$-0.344870\pi$
$563$	22.2228	0.936579	0.468289	+	0.883575i	$0.344870\pi$
$564$	−5.55020	−0.233706
$565$	0	0
$566$	3.78799	0.159221
$567$	−0.0501123	−0.00210452
$568$	−19.0521	−0.799410
$569$	−2.78729	−0.116849	−0.0584247	−	0.998292i	$-0.518608\pi$
$569$	−2.78729	−0.116849	−0.0584247	+	0.998292i	$0.518608\pi$
$570$	0	0
$571$	−22.7888	−0.953683	−0.476842	−	0.878989i	$-0.658218\pi$
$571$	−22.7888	−0.953683	−0.476842	+	0.878989i	$0.658218\pi$
$572$	17.9326	0.749801
$573$	−10.4170	−0.435176
$574$	−29.0335	−1.21183
$575$	0	0
$576$	−14.8065	−0.616937
$577$	−24.8664	−1.03520	−0.517601	−	0.855622i	$-0.673175\pi$
$577$	−24.8664	−1.03520	−0.517601	+	0.855622i	$0.673175\pi$
$578$	−5.35884	−0.222899
$579$	−1.64710	−0.0684512
$580$	0	0
$581$	−7.26555	−0.301426
$582$	−20.5185	−0.850521
$583$	18.7337	0.775871
$584$	−13.7119	−0.567402
$585$	0	0
$586$	−1.58936	−0.0656559
$587$	−40.7204	−1.68071	−0.840356	−	0.542035i	$-0.817654\pi$
$587$	−40.7204	−1.68071	−0.840356	+	0.542035i	$0.817654\pi$
$588$	−1.53297	−0.0632188
$589$	41.8256	1.72339
$590$	0	0
$591$	−15.7469	−0.647742
$592$	1.00358	0.0412468
$593$	−10.8793	−0.446761	−0.223380	−	0.974731i	$-0.571709\pi$
$593$	−10.8793	−0.446761	−0.223380	+	0.974731i	$0.571709\pi$
$594$	33.0514	1.35612
$595$	0	0
$596$	0.612651	0.0250952
$597$	−20.7349	−0.848623
$598$	3.94138	0.161175
$599$	4.34005	0.177330	0.0886648	−	0.996062i	$-0.471740\pi$
$599$	4.34005	0.177330	0.0886648	+	0.996062i	$0.471740\pi$
$600$	0	0
$601$	2.35747	0.0961633	0.0480817	−	0.998843i	$-0.484689\pi$
$601$	2.35747	0.0961633	0.0480817	+	0.998843i	$0.484689\pi$
$602$	5.05079	0.205855
$603$	−24.8431	−1.01169
$604$	10.7222	0.436279
$605$	0	0
$606$	−3.67968	−0.149477
$607$	21.0552	0.854603	0.427301	−	0.904109i	$-0.359464\pi$
$607$	21.0552	0.854603	0.427301	+	0.904109i	$0.359464\pi$
$608$	−24.9534	−1.01200
$609$	−32.7948	−1.32891
$610$	0	0
$611$	−22.7215	−0.919212
$612$	7.25426	0.293236
$613$	−5.65525	−0.228414	−0.114207	−	0.993457i	$-0.536433\pi$
$613$	−5.65525	−0.228414	−0.114207	+	0.993457i	$0.536433\pi$
$614$	−19.8987	−0.803045
$615$	0	0
$616$	−53.2559	−2.14574
$617$	26.9891	1.08654	0.543270	−	0.839558i	$-0.317186\pi$
$617$	26.9891	1.08654	0.543270	+	0.839558i	$0.317186\pi$
$618$	14.5735	0.586231
$619$	−19.0549	−0.765883	−0.382941	−	0.923773i	$-0.625089\pi$
$619$	−19.0549	−0.765883	−0.382941	+	0.923773i	$0.625089\pi$
$620$	0	0
$621$	−5.19312	−0.208393
$622$	15.1594	0.607838
$623$	−6.36827	−0.255139
$624$	6.38998	0.255804
$625$	0	0
$626$	5.24561	0.209657
$627$	36.1307	1.44292
$628$	11.6142	0.463456
$629$	−2.87232	−0.114527
$630$	0	0
$631$	29.9572	1.19258	0.596288	−	0.802771i	$-0.296642\pi$
$631$	29.9572	1.19258	0.596288	+	0.802771i	$0.296642\pi$
$632$	−21.4617	−0.853699
$633$	24.6989	0.981695
$634$	−22.2004	−0.881691
$635$	0	0
$636$	−2.83389	−0.112371
$637$	−6.27571	−0.248653
$638$	−66.1039	−2.61708
$639$	11.5588	0.457258
$640$	0	0
$641$	−21.3875	−0.844755	−0.422378	−	0.906420i	$-0.638804\pi$
$641$	−21.3875	−0.844755	−0.422378	+	0.906420i	$0.638804\pi$
$642$	−1.94638	−0.0768177
$643$	−47.7440	−1.88284	−0.941420	−	0.337236i	$-0.890508\pi$
$643$	−47.7440	−1.88284	−0.941420	+	0.337236i	$0.890508\pi$
$644$	2.46193	0.0970138
$645$	0	0
$646$	−29.0172	−1.14167
$647$	13.2144	0.519510	0.259755	−	0.965675i	$-0.416358\pi$
$647$	13.2144	0.519510	0.259755	+	0.965675i	$0.416358\pi$
$648$	0.0519345	0.00204018
$649$	8.16682	0.320576
$650$	0	0
$651$	−23.0336	−0.902759
$652$	−10.5616	−0.413623
$653$	24.5353	0.960142	0.480071	−	0.877230i	$-0.340611\pi$
$653$	24.5353	0.960142	0.480071	+	0.877230i	$0.340611\pi$
$654$	6.70833	0.262316
$655$	0	0
$656$	14.9077	0.582048
$657$	8.31888	0.324550
$658$	19.8532	0.773959
$659$	17.7100	0.689883	0.344941	−	0.938624i	$-0.387899\pi$
$659$	17.7100	0.689883	0.344941	+	0.938624i	$0.387899\pi$
$660$	0	0
$661$	−30.9074	−1.20216	−0.601078	−	0.799190i	$-0.705262\pi$
$661$	−30.9074	−1.20216	−0.601078	+	0.799190i	$0.705262\pi$
$662$	30.8675	1.19970
$663$	−18.2887	−0.710272
$664$	7.52973	0.292210
$665$	0	0
$666$	−1.22891	−0.0476191
$667$	10.3864	0.402163
$668$	5.56780	0.215424
$669$	2.32618	0.0899353
$670$	0	0
$671$	35.4858	1.36991
$672$	13.7420	0.530110
$673$	18.8356	0.726059	0.363029	−	0.931778i	$-0.381742\pi$
$673$	18.8356	0.726059	0.363029	+	0.931778i	$0.381742\pi$
$674$	−4.03202	−0.155308
$675$	0	0
$676$	−0.266722	−0.0102585
$677$	−9.47784	−0.364263	−0.182132	−	0.983274i	$-0.558300\pi$
$677$	−9.47784	−0.364263	−0.182132	+	0.983274i	$0.558300\pi$
$678$	10.8591	0.417040
$679$	−52.4689	−2.01357
$680$	0	0
$681$	14.4338	0.553103
$682$	−46.4284	−1.77784
$683$	14.0831	0.538874	0.269437	−	0.963018i	$-0.413162\pi$
$683$	14.0831	0.538874	0.269437	+	0.963018i	$0.413162\pi$
$684$	8.87513	0.339349
$685$	0	0
$686$	−16.8390	−0.642917
$687$	9.62423	0.367187
$688$	−2.59340	−0.0988726
$689$	−11.6014	−0.441979
$690$	0	0
$691$	−14.8398	−0.564531	−0.282265	−	0.959336i	$-0.591086\pi$
$691$	−14.8398	−0.564531	−0.282265	+	0.959336i	$0.591086\pi$
$692$	−13.1192	−0.498718
$693$	32.3099	1.22735
$694$	−28.3199	−1.07501
$695$	0	0
$696$	33.9873	1.28828
$697$	−42.6670	−1.61613
$698$	−30.9699	−1.17223
$699$	20.4793	0.774597
$700$	0	0
$701$	2.93446	0.110833	0.0554165	−	0.998463i	$-0.482351\pi$
$701$	2.93446	0.110833	0.0554165	+	0.998463i	$0.482351\pi$
$702$	−20.4681	−0.772518
$703$	−3.51410	−0.132537
$704$	46.9992	1.77135
$705$	0	0
$706$	−0.131047	−0.00493202
$707$	−9.40947	−0.353879
$708$	−1.23541	−0.0464297
$709$	25.8990	0.972656	0.486328	−	0.873776i	$-0.338336\pi$
$709$	25.8990	0.972656	0.486328	+	0.873776i	$0.338336\pi$
$710$	0	0
$711$	13.0206	0.488311
$712$	6.59983	0.247339
$713$	7.29495	0.273198
$714$	15.9800	0.598035
$715$	0	0
$716$	6.47943	0.242148
$717$	12.2660	0.458081
$718$	25.1404	0.938232
$719$	−26.5304	−0.989418	−0.494709	−	0.869059i	$-0.664725\pi$
$719$	−26.5304	−0.989418	−0.494709	+	0.869059i	$0.664725\pi$
$720$	0	0
$721$	37.2665	1.38788
$722$	−14.9819	−0.557570
$723$	28.2968	1.05237
$724$	2.05882	0.0765156
$725$	0	0
$726$	−27.4045	−1.01708
$727$	−15.6397	−0.580045	−0.290022	−	0.957020i	$-0.593663\pi$
$727$	−15.6397	−0.580045	−0.290022	+	0.957020i	$0.593663\pi$
$728$	32.9803	1.22233
$729$	16.6273	0.615824
$730$	0	0
$731$	7.42253	0.274532
$732$	−5.36801	−0.198407
$733$	42.0912	1.55468	0.777338	−	0.629084i	$-0.216570\pi$
$733$	42.0912	1.55468	0.777338	+	0.629084i	$0.216570\pi$
$734$	31.1721	1.15058
$735$	0	0
$736$	−4.35222	−0.160425
$737$	78.8576	2.90476
$738$	−18.2548	−0.671970
$739$	10.2699	0.377783	0.188892	−	0.981998i	$-0.439510\pi$
$739$	10.2699	0.377783	0.188892	+	0.981998i	$0.439510\pi$
$740$	0	0
$741$	−22.3750	−0.821967
$742$	10.1369	0.372137
$743$	−40.4417	−1.48366	−0.741832	−	0.670586i	$-0.766043\pi$
$743$	−40.4417	−1.48366	−0.741832	+	0.670586i	$0.766043\pi$
$744$	23.8712	0.875159
$745$	0	0
$746$	−27.2269	−0.996848
$747$	−4.56822	−0.167143
$748$	−23.0267	−0.841938
$749$	−4.97719	−0.181863
$750$	0	0
$751$	−15.3636	−0.560625	−0.280312	−	0.959909i	$-0.590438\pi$
$751$	−15.3636	−0.560625	−0.280312	+	0.959909i	$0.590438\pi$
$752$	−10.1939	−0.371734
$753$	20.6820	0.753695
$754$	40.9368	1.49083
$755$	0	0
$756$	−12.7851	−0.464990
$757$	2.10127	0.0763720	0.0381860	−	0.999271i	$-0.487842\pi$
$757$	2.10127	0.0763720	0.0381860	+	0.999271i	$0.487842\pi$
$758$	−7.91367	−0.287437
$759$	6.30169	0.228737
$760$	0	0
$761$	−5.01242	−0.181700	−0.0908501	−	0.995865i	$-0.528958\pi$
$761$	−5.01242	−0.181700	−0.0908501	+	0.995865i	$0.528958\pi$
$762$	18.2761	0.662072
$763$	17.1542	0.621023
$764$	8.12229	0.293854
$765$	0	0
$766$	4.72020	0.170548
$767$	−5.05755	−0.182617
$768$	−17.1612	−0.619252
$769$	−9.51281	−0.343041	−0.171520	−	0.985181i	$-0.554868\pi$
$769$	−9.51281	−0.343041	−0.171520	+	0.985181i	$0.554868\pi$
$770$	0	0
$771$	11.5015	0.414218
$772$	1.28427	0.0462219
$773$	19.0278	0.684384	0.342192	−	0.939630i	$-0.388831\pi$
$773$	19.0278	0.684384	0.342192	+	0.939630i	$0.388831\pi$
$774$	3.17569	0.114148
$775$	0	0
$776$	54.3767	1.95201
$777$	1.93524	0.0694264
$778$	18.0243	0.646203
$779$	−52.2004	−1.87027
$780$	0	0
$781$	−36.6901	−1.31288
$782$	−5.06099	−0.180981
$783$	−53.9378	−1.92758
$784$	−2.81558	−0.100556
$785$	0	0
$786$	8.05451	0.287295
$787$	−26.8205	−0.956048	−0.478024	−	0.878347i	$-0.658647\pi$
$787$	−26.8205	−0.956048	−0.478024	+	0.878347i	$0.658647\pi$
$788$	12.2781	0.437391
$789$	−15.9721	−0.568624
$790$	0	0
$791$	27.7682	0.987323
$792$	−33.4847	−1.18983
$793$	−21.9756	−0.780377
$794$	19.6833	0.698534
$795$	0	0
$796$	16.1673	0.573036
$797$	−50.4220	−1.78604	−0.893019	−	0.450019i	$-0.851417\pi$
$797$	−50.4220	−1.78604	−0.893019	+	0.450019i	$0.851417\pi$
$798$	19.5505	0.692080
$799$	29.1759	1.03217
$800$	0	0
$801$	−4.00406	−0.141476
$802$	25.8883	0.914148
$803$	−26.4060	−0.931848
$804$	−11.9290	−0.420702
$805$	0	0
$806$	28.7522	1.01275
$807$	15.1550	0.533482
$808$	9.75160	0.343060
$809$	49.3793	1.73608	0.868042	−	0.496490i	$-0.165378\pi$
$809$	49.3793	1.73608	0.868042	+	0.496490i	$0.165378\pi$
$810$	0	0
$811$	−16.3987	−0.575835	−0.287918	−	0.957655i	$-0.592963\pi$
$811$	−16.3987	−0.575835	−0.287918	+	0.957655i	$0.592963\pi$
$812$	25.5706	0.897354
$813$	−6.54812	−0.229653
$814$	3.90083	0.136724
$815$	0	0
$816$	−8.20516	−0.287238
$817$	9.08100	0.317704
$818$	−36.4192	−1.27337
$819$	−20.0089	−0.699167
$820$	0	0
$821$	−1.68535	−0.0588190	−0.0294095	−	0.999567i	$-0.509363\pi$
$821$	−1.68535	−0.0588190	−0.0294095	+	0.999567i	$0.509363\pi$
$822$	4.28195	0.149350
$823$	16.2573	0.566693	0.283347	−	0.959018i	$-0.408555\pi$
$823$	16.2573	0.566693	0.283347	+	0.959018i	$0.408555\pi$
$824$	−38.6215	−1.34545
$825$	0	0
$826$	4.41910	0.153760
$827$	−53.9104	−1.87465	−0.937324	−	0.348460i	$-0.886705\pi$
$827$	−53.9104	−1.87465	−0.937324	+	0.348460i	$0.886705\pi$
$828$	1.54794	0.0537948
$829$	23.9588	0.832123	0.416062	−	0.909336i	$-0.363410\pi$
$829$	23.9588	0.832123	0.416062	+	0.909336i	$0.363410\pi$
$830$	0	0
$831$	3.16445	0.109773
$832$	−29.1057	−1.00906
$833$	8.05842	0.279208
$834$	1.48263	0.0513394
$835$	0	0
$836$	−28.1717	−0.974338
$837$	−37.8836	−1.30945
$838$	−3.91822	−0.135353
$839$	−4.56491	−0.157598	−0.0787991	−	0.996891i	$-0.525109\pi$
$839$	−4.56491	−0.157598	−0.0787991	+	0.996891i	$0.525109\pi$
$840$	0	0
$841$	78.8774	2.71991
$842$	−16.5963	−0.571945
$843$	−29.0101	−0.999160
$844$	−19.2582	−0.662893
$845$	0	0
$846$	12.4827	0.429165
$847$	−70.0773	−2.40788
$848$	−5.20495	−0.178739
$849$	−3.75063	−0.128721
$850$	0	0
$851$	−0.612908	−0.0210102
$852$	5.55020	0.190147
$853$	2.86000	0.0979244	0.0489622	−	0.998801i	$-0.484409\pi$
$853$	2.86000	0.0979244	0.0489622	+	0.998801i	$0.484409\pi$
$854$	19.2015	0.657062
$855$	0	0
$856$	5.15816	0.176302
$857$	−42.6985	−1.45855	−0.729276	−	0.684219i	$-0.760143\pi$
$857$	−42.6985	−1.45855	−0.729276	+	0.684219i	$0.760143\pi$
$858$	24.8374	0.847934
$859$	−16.7846	−0.572683	−0.286341	−	0.958128i	$-0.592439\pi$
$859$	−16.7846	−0.572683	−0.286341	+	0.958128i	$0.592439\pi$
$860$	0	0
$861$	28.7471	0.979700
$862$	15.1406	0.515689
$863$	21.0775	0.717487	0.358743	−	0.933436i	$-0.383205\pi$
$863$	21.0775	0.717487	0.358743	+	0.933436i	$0.383205\pi$
$864$	22.6016	0.768922
$865$	0	0
$866$	24.8289	0.843721
$867$	5.30599	0.180201
$868$	17.9597	0.609592
$869$	−41.3304	−1.40204
$870$	0	0
$871$	−48.8349	−1.65471
$872$	−17.7779	−0.602036
$873$	−32.9899	−1.11654
$874$	−6.19181	−0.209441
$875$	0	0
$876$	3.99450	0.134962
$877$	−45.1822	−1.52570	−0.762848	−	0.646578i	$-0.776200\pi$
$877$	−45.1822	−1.52570	−0.762848	+	0.646578i	$0.776200\pi$
$878$	−3.82749	−0.129171
$879$	1.57369	0.0530791
$880$	0	0
$881$	8.33503	0.280814	0.140407	−	0.990094i	$-0.455159\pi$
$881$	8.33503	0.280814	0.140407	+	0.990094i	$0.455159\pi$
$882$	3.44775	0.116092
$883$	12.6224	0.424779	0.212390	−	0.977185i	$-0.431875\pi$
$883$	12.6224	0.424779	0.212390	+	0.977185i	$0.431875\pi$
$884$	14.2600	0.479614
$885$	0	0
$886$	−5.28788	−0.177650
$887$	38.9112	1.30651	0.653256	−	0.757137i	$-0.273403\pi$
$887$	38.9112	1.30651	0.653256	+	0.757137i	$0.273403\pi$
$888$	−2.00561	−0.0673038
$889$	46.7346	1.56743
$890$	0	0
$891$	0.100014	0.00335060
$892$	−1.81376	−0.0607292
$893$	35.6948	1.19448
$894$	0.848545	0.0283796
$895$	0	0
$896$	−0.271749	−0.00907849
$897$	−3.90251	−0.130301
$898$	36.2536	1.20980
$899$	75.7683	2.52701
$900$	0	0
$901$	14.8970	0.496290
$902$	57.9450	1.92936
$903$	−5.00097	−0.166422
$904$	−28.7779	−0.957138
$905$	0	0
$906$	14.8506	0.493379
$907$	−46.5114	−1.54438	−0.772192	−	0.635389i	$-0.780840\pi$
$907$	−46.5114	−1.54438	−0.772192	+	0.635389i	$0.780840\pi$
$908$	−11.2542	−0.373485
$909$	−5.91621	−0.196228
$910$	0	0
$911$	1.59191	0.0527422	0.0263711	−	0.999652i	$-0.491605\pi$
$911$	1.59191	0.0527422	0.0263711	+	0.999652i	$0.491605\pi$
$912$	−10.0385	−0.332408
$913$	14.5006	0.479899
$914$	−38.0679	−1.25918
$915$	0	0
$916$	−7.50417	−0.247945
$917$	20.5966	0.680158
$918$	26.2823	0.867447
$919$	−10.4308	−0.344080	−0.172040	−	0.985090i	$-0.555036\pi$
$919$	−10.4308	−0.344080	−0.172040	+	0.985090i	$0.555036\pi$
$920$	0	0
$921$	19.7024	0.649216
$922$	32.7512	1.07860
$923$	22.7215	0.747886
$924$	15.5143	0.510384
$925$	0	0
$926$	23.4513	0.770658
$927$	23.4314	0.769587
$928$	−45.2039	−1.48389
$929$	36.7943	1.20718	0.603592	−	0.797294i	$-0.293736\pi$
$929$	36.7943	1.20718	0.603592	+	0.797294i	$0.293736\pi$
$930$	0	0
$931$	9.85897	0.323115
$932$	−15.9680	−0.523049
$933$	−15.0099	−0.491403
$934$	17.7952	0.582276
$935$	0	0
$936$	20.7364	0.677791
$937$	13.3700	0.436779	0.218389	−	0.975862i	$-0.429920\pi$
$937$	13.3700	0.436779	0.218389	+	0.975862i	$0.429920\pi$
$938$	42.6702	1.39323
$939$	−5.19387	−0.169496
$940$	0	0
$941$	−53.3116	−1.73791	−0.868955	−	0.494891i	$-0.835208\pi$
$941$	−53.3116	−1.73791	−0.868955	+	0.494891i	$0.835208\pi$
$942$	16.0861	0.524113
$943$	−9.10447	−0.296482
$944$	−2.26906	−0.0738515
$945$	0	0
$946$	−10.0804	−0.327741
$947$	−30.5958	−0.994230	−0.497115	−	0.867685i	$-0.665607\pi$
$947$	−30.5958	−0.994230	−0.497115	+	0.867685i	$0.665607\pi$
$948$	6.25214	0.203060
$949$	16.3527	0.530832
$950$	0	0
$951$	21.9814	0.712797
$952$	−42.3489	−1.37254
$953$	−40.5905	−1.31485	−0.657427	−	0.753518i	$-0.728355\pi$
$953$	−40.5905	−1.31485	−0.657427	+	0.753518i	$0.728355\pi$
$954$	6.37359	0.206352
$955$	0	0
$956$	−9.56396	−0.309321
$957$	65.4519	2.11576
$958$	36.0168	1.16365
$959$	10.9496	0.353580
$960$	0	0
$961$	22.2163	0.716655
$962$	−2.41570	−0.0778854
$963$	−3.12941	−0.100844
$964$	−22.0635	−0.710616
$965$	0	0
$966$	3.40987	0.109711
$967$	12.0775	0.388387	0.194194	−	0.980963i	$-0.437791\pi$
$967$	12.0775	0.388387	0.194194	+	0.980963i	$0.437791\pi$
$968$	72.6254	2.33427
$969$	28.7310	0.922972
$970$	0	0
$971$	25.8205	0.828621	0.414310	−	0.910136i	$-0.364023\pi$
$971$	25.8205	0.828621	0.414310	+	0.910136i	$0.364023\pi$
$972$	−13.0042	−0.417111
$973$	3.79131	0.121544
$974$	21.5324	0.689944
$975$	0	0
$976$	−9.85931	−0.315589
$977$	−13.8713	−0.443783	−0.221892	−	0.975071i	$-0.571223\pi$
$977$	−13.8713	−0.443783	−0.221892	+	0.975071i	$0.571223\pi$
$978$	−14.6282	−0.467757
$979$	12.7098	0.406207
$980$	0	0
$981$	10.7857	0.344361
$982$	10.2793	0.328027
$983$	0.852788	0.0271997	0.0135999	−	0.999908i	$-0.495671\pi$
$983$	0.852788	0.0271997	0.0135999	+	0.999908i	$0.495671\pi$
$984$	−29.7924	−0.949747
$985$	0	0
$986$	−52.5655	−1.67403
$987$	−19.6574	−0.625702
$988$	17.4462	0.555036
$989$	1.58385	0.0503635
$990$	0	0
$991$	−57.0162	−1.81118	−0.905589	−	0.424156i	$-0.860571\pi$
$991$	−57.0162	−1.81118	−0.905589	+	0.424156i	$0.860571\pi$
$992$	−31.7492	−1.00804
$993$	−30.5631	−0.969891
$994$	−19.8532	−0.629705
$995$	0	0
$996$	−2.19354	−0.0695048
$997$	21.2745	0.673770	0.336885	−	0.941546i	$-0.390627\pi$
$997$	21.2745	0.673770	0.336885	+	0.941546i	$0.390627\pi$
$998$	29.9128	0.946875
$999$	3.18290	0.100703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.l.1.3	yes	7
3.2	odd	2		5175.2.a.cb.1.5		7
4.3	odd	2		9200.2.a.db.1.3		7
5.2	odd	4		575.2.b.f.24.6		14
5.3	odd	4		575.2.b.f.24.9		14
5.4	even	2		575.2.a.k.1.5	✓	7
15.14	odd	2		5175.2.a.cg.1.3		7
20.19	odd	2		9200.2.a.da.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.k.1.5	✓	7	5.4	even	2
575.2.a.l.1.3	yes	7	1.1	even	1	trivial
575.2.b.f.24.6		14	5.2	odd	4
575.2.b.f.24.9		14	5.3	odd	4
5175.2.a.cb.1.5		7	3.2	odd	2
5175.2.a.cg.1.3		7	15.14	odd	2
9200.2.a.da.1.5		7	20.19	odd	2
9200.2.a.db.1.3		7	4.3	odd	2

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q-1.07994 q^{2} +1.06928 q^{3} -0.833738 q^{4} -1.15476 q^{6} -2.95289 q^{7} +3.06026 q^{8} -1.85663 q^{9} +O(q^{10})\)	\(q-1.07994 q^{2} +1.06928 q^{3} -0.833738 q^{4} -1.15476 q^{6} -2.95289 q^{7} +3.06026 q^{8} -1.85663 q^{9} +5.89337 q^{11} -0.891503 q^{12} -3.64965 q^{13} +3.18893 q^{14} -1.63740 q^{16} +4.68638 q^{17} +2.00504 q^{18} +5.73350 q^{19} -3.15748 q^{21} -6.36446 q^{22} +1.00000 q^{23} +3.27228 q^{24} +3.94138 q^{26} -5.19312 q^{27} +2.46193 q^{28} +10.3864 q^{29} +7.29495 q^{31} -4.35222 q^{32} +6.30169 q^{33} -5.06099 q^{34} +1.54794 q^{36} -0.612908 q^{37} -6.19181 q^{38} -3.90251 q^{39} -9.10447 q^{41} +3.40987 q^{42} +1.58385 q^{43} -4.91353 q^{44} -1.07994 q^{46} +6.22567 q^{47} -1.75085 q^{48} +1.71954 q^{49} +5.01108 q^{51} +3.04285 q^{52} +3.17878 q^{53} +5.60824 q^{54} -9.03659 q^{56} +6.13074 q^{57} -11.2167 q^{58} +1.38576 q^{59} +6.02130 q^{61} -7.87808 q^{62} +5.48242 q^{63} +7.97493 q^{64} -6.80542 q^{66} +13.3807 q^{67} -3.90722 q^{68} +1.06928 q^{69} -6.22567 q^{71} -5.68177 q^{72} -4.48063 q^{73} +0.661901 q^{74} -4.78023 q^{76} -17.4024 q^{77} +4.21446 q^{78} -7.01303 q^{79} +0.0169706 q^{81} +9.83224 q^{82} +2.46049 q^{83} +2.63251 q^{84} -1.71046 q^{86} +11.1060 q^{87} +18.0352 q^{88} +2.15663 q^{89} +10.7770 q^{91} -0.833738 q^{92} +7.80038 q^{93} -6.72332 q^{94} -4.65376 q^{96} +17.7687 q^{97} -1.85699 q^{98} -10.9418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 11 q^{4} + 5 q^{6} - 3 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + q^2 + 11 * q^4 + 5 * q^6 - 3 * q^7 + 6 * q^8 + 15 * q^9	\( 7 q + q^{2} + 11 q^{4} + 5 q^{6} - 3 q^{7} + 6 q^{8} + 15 q^{9} - q^{11} - 6 q^{12} + 3 q^{13} + 7 q^{14} + 7 q^{16} - 10 q^{17} + 24 q^{18} + 15 q^{19} + 2 q^{21} - 21 q^{22} + 7 q^{23} + 18 q^{24} - 20 q^{26} + 11 q^{28} + 3 q^{29} + 14 q^{31} - 17 q^{32} - 6 q^{33} + 20 q^{34} + 10 q^{37} + 31 q^{38} - 8 q^{39} + 19 q^{41} - 44 q^{42} - 5 q^{43} - 3 q^{44} + q^{46} + 14 q^{47} + 27 q^{48} + 40 q^{49} + 2 q^{51} - 16 q^{52} - 4 q^{53} - q^{54} - 9 q^{56} + 4 q^{57} + 13 q^{58} - 16 q^{59} + 40 q^{61} + 12 q^{62} - 53 q^{63} - 4 q^{64} - 54 q^{66} + 4 q^{67} - 20 q^{68} - 14 q^{71} + 6 q^{72} + 3 q^{73} - 18 q^{74} + 35 q^{76} + 17 q^{77} - 23 q^{78} - q^{79} + 47 q^{81} + 22 q^{82} - 17 q^{83} - 60 q^{84} - 35 q^{86} + 56 q^{87} - 57 q^{88} + 16 q^{89} + 25 q^{91} + 11 q^{92} - 14 q^{93} + 7 q^{94} - 19 q^{96} + 24 q^{97} + 46 q^{98} - 53 q^{99}+O(q^{100}) \) 7 * q + q^2 + 11 * q^4 + 5 * q^6 - 3 * q^7 + 6 * q^8 + 15 * q^9 - q^11 - 6 * q^12 + 3 * q^13 + 7 * q^14 + 7 * q^16 - 10 * q^17 + 24 * q^18 + 15 * q^19 + 2 * q^21 - 21 * q^22 + 7 * q^23 + 18 * q^24 - 20 * q^26 + 11 * q^28 + 3 * q^29 + 14 * q^31 - 17 * q^32 - 6 * q^33 + 20 * q^34 + 10 * q^37 + 31 * q^38 - 8 * q^39 + 19 * q^41 - 44 * q^42 - 5 * q^43 - 3 * q^44 + q^46 + 14 * q^47 + 27 * q^48 + 40 * q^49 + 2 * q^51 - 16 * q^52 - 4 * q^53 - q^54 - 9 * q^56 + 4 * q^57 + 13 * q^58 - 16 * q^59 + 40 * q^61 + 12 * q^62 - 53 * q^63 - 4 * q^64 - 54 * q^66 + 4 * q^67 - 20 * q^68 - 14 * q^71 + 6 * q^72 + 3 * q^73 - 18 * q^74 + 35 * q^76 + 17 * q^77 - 23 * q^78 - q^79 + 47 * q^81 + 22 * q^82 - 17 * q^83 - 60 * q^84 - 35 * q^86 + 56 * q^87 - 57 * q^88 + 16 * q^89 + 25 * q^91 + 11 * q^92 - 14 * q^93 + 7 * q^94 - 19 * q^96 + 24 * q^97 + 46 * q^98 - 53 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more