LMFDB - Embedded newform 6025.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.52552$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12957 q^{2} +1.80145 q^{3} -0.724078 q^{4} -2.03485 q^{6} -2.49744 q^{7} +3.07703 q^{8} +0.245209 q^{9} +O(q^{10})$	\(q-1.12957 q^{2} +1.80145 q^{3} -0.724078 q^{4} -2.03485 q^{6} -2.49744 q^{7} +3.07703 q^{8} +0.245209 q^{9} +2.59172 q^{11} -1.30439 q^{12} +4.85251 q^{13} +2.82102 q^{14} -2.02755 q^{16} +5.82204 q^{17} -0.276980 q^{18} +5.02847 q^{19} -4.49900 q^{21} -2.92752 q^{22} +2.75564 q^{23} +5.54310 q^{24} -5.48124 q^{26} -4.96261 q^{27} +1.80834 q^{28} +1.43438 q^{29} -7.81420 q^{31} -3.86380 q^{32} +4.66884 q^{33} -6.57639 q^{34} -0.177550 q^{36} +5.58469 q^{37} -5.68000 q^{38} +8.74154 q^{39} -1.96086 q^{41} +5.08192 q^{42} +4.02400 q^{43} -1.87661 q^{44} -3.11268 q^{46} +7.30467 q^{47} -3.65253 q^{48} -0.762807 q^{49} +10.4881 q^{51} -3.51360 q^{52} +1.72672 q^{53} +5.60560 q^{54} -7.68469 q^{56} +9.05852 q^{57} -1.62022 q^{58} -11.6101 q^{59} -6.49108 q^{61} +8.82666 q^{62} -0.612394 q^{63} +8.41953 q^{64} -5.27377 q^{66} +10.6614 q^{67} -4.21561 q^{68} +4.96414 q^{69} -1.43272 q^{71} +0.754515 q^{72} +7.21929 q^{73} -6.30829 q^{74} -3.64101 q^{76} -6.47265 q^{77} -9.87416 q^{78} +1.66021 q^{79} -9.67550 q^{81} +2.21493 q^{82} +2.17263 q^{83} +3.25763 q^{84} -4.54537 q^{86} +2.58395 q^{87} +7.97479 q^{88} +4.81967 q^{89} -12.1188 q^{91} -1.99530 q^{92} -14.0769 q^{93} -8.25112 q^{94} -6.96043 q^{96} -16.0991 q^{97} +0.861641 q^{98} +0.635512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * 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 $

$2$	−1.12957	−0.798725	−0.399362	−	0.916793i	$-0.630768\pi$
$2$	−1.12957	−0.798725	−0.399362	+	0.916793i	$0.630768\pi$
$3$	1.80145	1.04007	0.520033	−	0.854146i	$-0.325920\pi$
$3$	1.80145	1.04007	0.520033	+	0.854146i	$0.325920\pi$
$4$	−0.724078	−0.362039
$5$	0	0
$5$	0	0
$6$	−2.03485	−0.830726
$7$	−2.49744	−0.943943	−0.471971	−	0.881614i	$-0.656457\pi$
$7$	−2.49744	−0.943943	−0.471971	+	0.881614i	$0.656457\pi$
$8$	3.07703	1.08789
$9$	0.245209	0.0817363
$10$	0	0
$11$	2.59172	0.781433	0.390716	−	0.920511i	$-0.372227\pi$
$11$	2.59172	0.781433	0.390716	+	0.920511i	$0.372227\pi$
$12$	−1.30439	−0.376544
$13$	4.85251	1.34584	0.672922	−	0.739713i	$-0.265039\pi$
$13$	4.85251	1.34584	0.672922	+	0.739713i	$0.265039\pi$
$14$	2.82102	0.753950
$15$	0	0
$16$	−2.02755	−0.506889
$17$	5.82204	1.41205	0.706026	−	0.708185i	$-0.250486\pi$
$17$	5.82204	1.41205	0.706026	+	0.708185i	$0.250486\pi$
$18$	−0.276980	−0.0652848
$19$	5.02847	1.15361	0.576805	−	0.816882i	$-0.304299\pi$
$19$	5.02847	1.15361	0.576805	+	0.816882i	$0.304299\pi$
$20$	0	0
$21$	−4.49900	−0.981762
$22$	−2.92752	−0.624149
$23$	2.75564	0.574591	0.287295	−	0.957842i	$-0.407244\pi$
$23$	2.75564	0.574591	0.287295	+	0.957842i	$0.407244\pi$
$24$	5.54310	1.13148
$25$	0	0
$26$	−5.48124	−1.07496
$27$	−4.96261	−0.955054
$28$	1.80834	0.341744
$29$	1.43438	0.266357	0.133178	−	0.991092i	$-0.457482\pi$
$29$	1.43438	0.266357	0.133178	+	0.991092i	$0.457482\pi$
$30$	0	0
$31$	−7.81420	−1.40347	−0.701736	−	0.712437i	$-0.747591\pi$
$31$	−7.81420	−1.40347	−0.701736	+	0.712437i	$0.747591\pi$
$32$	−3.86380	−0.683030
$33$	4.66884	0.812741
$34$	−6.57639	−1.12784
$35$	0	0
$36$	−0.177550	−0.0295917
$37$	5.58469	0.918118	0.459059	−	0.888406i	$-0.348187\pi$
$37$	5.58469	0.918118	0.459059	+	0.888406i	$0.348187\pi$
$38$	−5.68000	−0.921417
$39$	8.74154	1.39977
$40$	0	0
$41$	−1.96086	−0.306236	−0.153118	−	0.988208i	$-0.548931\pi$
$41$	−1.96086	−0.306236	−0.153118	+	0.988208i	$0.548931\pi$
$42$	5.08192	0.784158
$43$	4.02400	0.613654	0.306827	−	0.951765i	$-0.400733\pi$
$43$	4.02400	0.613654	0.306827	+	0.951765i	$0.400733\pi$
$44$	−1.87661	−0.282909
$45$	0	0
$46$	−3.11268	−0.458940
$47$	7.30467	1.06550	0.532748	−	0.846274i	$-0.321159\pi$
$47$	7.30467	1.06550	0.532748	+	0.846274i	$0.321159\pi$
$48$	−3.65253	−0.527197
$49$	−0.762807	−0.108972
$50$	0	0
$51$	10.4881	1.46863
$52$	−3.51360	−0.487248
$53$	1.72672	0.237184	0.118592	−	0.992943i	$-0.462162\pi$
$53$	1.72672	0.237184	0.118592	+	0.992943i	$0.462162\pi$
$54$	5.60560	0.762825
$55$	0	0
$56$	−7.68469	−1.02691
$57$	9.05852	1.19983
$58$	−1.62022	−0.212746
$59$	−11.6101	−1.51151	−0.755754	−	0.654855i	$-0.772730\pi$
$59$	−11.6101	−1.51151	−0.755754	+	0.654855i	$0.772730\pi$
$60$	0	0
$61$	−6.49108	−0.831098	−0.415549	−	0.909571i	$-0.636410\pi$
$61$	−6.49108	−0.831098	−0.415549	+	0.909571i	$0.636410\pi$
$62$	8.82666	1.12099
$63$	−0.612394	−0.0771543
$64$	8.41953	1.05244
$65$	0	0
$66$	−5.27377	−0.649156
$67$	10.6614	1.30249	0.651246	−	0.758867i	$-0.274247\pi$
$67$	10.6614	1.30249	0.651246	+	0.758867i	$0.274247\pi$
$68$	−4.21561	−0.511218
$69$	4.96414	0.597612
$70$	0	0
$71$	−1.43272	−0.170033	−0.0850165	−	0.996380i	$-0.527094\pi$
$71$	−1.43272	−0.170033	−0.0850165	+	0.996380i	$0.527094\pi$
$72$	0.754515	0.0889204
$73$	7.21929	0.844954	0.422477	−	0.906374i	$-0.361161\pi$
$73$	7.21929	0.844954	0.422477	+	0.906374i	$0.361161\pi$
$74$	−6.30829	−0.733323
$75$	0	0
$76$	−3.64101	−0.417652
$77$	−6.47265	−0.737627
$78$	−9.87416	−1.11803
$79$	1.66021	0.186788	0.0933939	−	0.995629i	$-0.470228\pi$
$79$	1.66021	0.186788	0.0933939	+	0.995629i	$0.470228\pi$
$80$	0	0
$81$	−9.67550	−1.07506
$82$	2.21493	0.244598
$83$	2.17263	0.238477	0.119238	−	0.992866i	$-0.461955\pi$
$83$	2.17263	0.238477	0.119238	+	0.992866i	$0.461955\pi$
$84$	3.25763	0.355436
$85$	0	0
$86$	−4.54537	−0.490140
$87$	2.58395	0.277029
$88$	7.97479	0.850116
$89$	4.81967	0.510884	0.255442	−	0.966824i	$-0.417779\pi$
$89$	4.81967	0.510884	0.255442	+	0.966824i	$0.417779\pi$
$90$	0	0
$91$	−12.1188	−1.27040
$92$	−1.99530	−0.208024
$93$	−14.0769	−1.45970
$94$	−8.25112	−0.851038
$95$	0	0
$96$	−6.96043	−0.710396
$97$	−16.0991	−1.63461	−0.817307	−	0.576202i	$-0.804534\pi$
$97$	−16.0991	−1.63461	−0.817307	+	0.576202i	$0.804534\pi$
$98$	0.861641	0.0870389
$99$	0.635512	0.0638714
$100$	0	0
$101$	4.06729	0.404710	0.202355	−	0.979312i	$-0.435140\pi$
$101$	4.06729	0.404710	0.202355	+	0.979312i	$0.435140\pi$
$102$	−11.8470	−1.17303
$103$	−2.35662	−0.232205	−0.116102	−	0.993237i	$-0.537040\pi$
$103$	−2.35662	−0.232205	−0.116102	+	0.993237i	$0.537040\pi$
$104$	14.9313	1.46414
$105$	0	0
$106$	−1.95045	−0.189445
$107$	−17.8377	−1.72443	−0.862216	−	0.506540i	$-0.830924\pi$
$107$	−17.8377	−1.72443	−0.862216	+	0.506540i	$0.830924\pi$
$108$	3.59332	0.345767
$109$	7.09185	0.679276	0.339638	−	0.940556i	$-0.389695\pi$
$109$	7.09185	0.679276	0.339638	+	0.940556i	$0.389695\pi$
$110$	0	0
$111$	10.0605	0.954903
$112$	5.06369	0.478474
$113$	−1.39114	−0.130867	−0.0654337	−	0.997857i	$-0.520843\pi$
$113$	−1.39114	−0.130867	−0.0654337	+	0.997857i	$0.520843\pi$
$114$	−10.2322	−0.958334
$115$	0	0
$116$	−1.03860	−0.0964316
$117$	1.18988	0.110004
$118$	13.1144	1.20728
$119$	−14.5402	−1.33290
$120$	0	0
$121$	−4.28300	−0.389363
$122$	7.33211	0.663818
$123$	−3.53239	−0.318505
$124$	5.65809	0.508112
$125$	0	0
$126$	0.691740	0.0616251
$127$	4.66298	0.413772	0.206886	−	0.978365i	$-0.433667\pi$
$127$	4.66298	0.413772	0.206886	+	0.978365i	$0.433667\pi$
$128$	−1.78283	−0.157581
$129$	7.24901	0.638240
$130$	0	0
$131$	−1.81924	−0.158948	−0.0794739	−	0.996837i	$-0.525324\pi$
$131$	−1.81924	−0.158948	−0.0794739	+	0.996837i	$0.525324\pi$
$132$	−3.38061	−0.294244
$133$	−12.5583	−1.08894
$134$	−12.0427	−1.04033
$135$	0	0
$136$	17.9146	1.53616
$137$	−10.1801	−0.869747	−0.434874	−	0.900492i	$-0.643207\pi$
$137$	−10.1801	−0.869747	−0.434874	+	0.900492i	$0.643207\pi$
$138$	−5.60733	−0.477328
$139$	15.5975	1.32296	0.661482	−	0.749961i	$-0.269928\pi$
$139$	15.5975	1.32296	0.661482	+	0.749961i	$0.269928\pi$
$140$	0	0
$141$	13.1590	1.10819
$142$	1.61836	0.135810
$143$	12.5763	1.05169
$144$	−0.497174	−0.0414312
$145$	0	0
$146$	−8.15467	−0.674885
$147$	−1.37416	−0.113338
$148$	−4.04375	−0.332395
$149$	−0.170901	−0.0140008	−0.00700038	−	0.999975i	$-0.502228\pi$
$149$	−0.170901	−0.0140008	−0.00700038	+	0.999975i	$0.502228\pi$
$150$	0	0
$151$	11.9265	0.970565	0.485283	−	0.874357i	$-0.338717\pi$
$151$	11.9265	0.970565	0.485283	+	0.874357i	$0.338717\pi$
$152$	15.4728	1.25501
$153$	1.42762	0.115416
$154$	7.31130	0.589161
$155$	0	0
$156$	−6.32956	−0.506770
$157$	6.79472	0.542278	0.271139	−	0.962540i	$-0.412600\pi$
$157$	6.79472	0.542278	0.271139	+	0.962540i	$0.412600\pi$
$158$	−1.87531	−0.149192
$159$	3.11060	0.246687
$160$	0	0
$161$	−6.88204	−0.542381
$162$	10.9291	0.858673
$163$	10.7422	0.841393	0.420696	−	0.907202i	$-0.361786\pi$
$163$	10.7422	0.841393	0.420696	+	0.907202i	$0.361786\pi$
$164$	1.41982	0.110869
$165$	0	0
$166$	−2.45413	−0.190477
$167$	6.95437	0.538145	0.269073	−	0.963120i	$-0.413283\pi$
$167$	6.95437	0.538145	0.269073	+	0.963120i	$0.413283\pi$
$168$	−13.8436	−1.06805
$169$	10.5469	0.811299
$170$	0	0
$171$	1.23303	0.0942918
$172$	−2.91369	−0.222167
$173$	10.2833	0.781823	0.390911	−	0.920428i	$-0.372160\pi$
$173$	10.2833	0.781823	0.390911	+	0.920428i	$0.372160\pi$
$174$	−2.91875	−0.221270
$175$	0	0
$176$	−5.25485	−0.396099
$177$	−20.9150	−1.57207
$178$	−5.44414	−0.408056
$179$	−8.52237	−0.636991	−0.318496	−	0.947924i	$-0.603178\pi$
$179$	−8.52237	−0.636991	−0.318496	+	0.947924i	$0.603178\pi$
$180$	0	0
$181$	20.5360	1.52643	0.763216	−	0.646144i	$-0.223619\pi$
$181$	20.5360	1.52643	0.763216	+	0.646144i	$0.223619\pi$
$182$	13.6891	1.01470
$183$	−11.6933	−0.864396
$184$	8.47919	0.625094
$185$	0	0
$186$	15.9008	1.16590
$187$	15.0891	1.10342
$188$	−5.28915	−0.385751
$189$	12.3938	0.901517
$190$	0	0
$191$	20.3929	1.47558	0.737788	−	0.675032i	$-0.235870\pi$
$191$	20.3929	1.47558	0.737788	+	0.675032i	$0.235870\pi$
$192$	15.1673	1.09461
$193$	11.5417	0.830792	0.415396	−	0.909641i	$-0.363643\pi$
$193$	11.5417	0.830792	0.415396	+	0.909641i	$0.363643\pi$
$194$	18.1850	1.30561
$195$	0	0
$196$	0.552332	0.0394523
$197$	−21.8054	−1.55357	−0.776784	−	0.629767i	$-0.783151\pi$
$197$	−21.8054	−1.55357	−0.776784	+	0.629767i	$0.783151\pi$
$198$	−0.717854	−0.0510156
$199$	−17.3355	−1.22888	−0.614441	−	0.788963i	$-0.710618\pi$
$199$	−17.3355	−1.22888	−0.614441	+	0.788963i	$0.710618\pi$
$200$	0	0
$201$	19.2059	1.35468
$202$	−4.59428	−0.323252
$203$	−3.58226	−0.251426
$204$	−7.59420	−0.531701
$205$	0	0
$206$	2.66196	0.185467
$207$	0.675708	0.0469649
$208$	−9.83873	−0.682194
$209$	13.0324	0.901469
$210$	0	0
$211$	−5.46546	−0.376258	−0.188129	−	0.982144i	$-0.560242\pi$
$211$	−5.46546	−0.376258	−0.188129	+	0.982144i	$0.560242\pi$
$212$	−1.25028	−0.0858698
$213$	−2.58097	−0.176845
$214$	20.1488	1.37735
$215$	0	0
$216$	−15.2701	−1.03900
$217$	19.5155	1.32480
$218$	−8.01072	−0.542554
$219$	13.0052	0.878807
$220$	0	0
$221$	28.2515	1.90040
$222$	−11.3640	−0.762704
$223$	−23.3432	−1.56318	−0.781589	−	0.623793i	$-0.785591\pi$
$223$	−23.3432	−1.56318	−0.781589	+	0.623793i	$0.785591\pi$
$224$	9.64960	0.644741
$225$	0	0
$226$	1.57139	0.104527
$227$	20.7099	1.37457	0.687283	−	0.726390i	$-0.258803\pi$
$227$	20.7099	1.37457	0.687283	+	0.726390i	$0.258803\pi$
$228$	−6.55908	−0.434386
$229$	−12.2647	−0.810477	−0.405239	−	0.914211i	$-0.632812\pi$
$229$	−12.2647	−0.810477	−0.405239	+	0.914211i	$0.632812\pi$
$230$	0	0
$231$	−11.6601	−0.767181
$232$	4.41362	0.289768
$233$	7.91104	0.518270	0.259135	−	0.965841i	$-0.416563\pi$
$233$	7.91104	0.518270	0.259135	+	0.965841i	$0.416563\pi$
$234$	−1.34405	−0.0878632
$235$	0	0
$236$	8.40663	0.547225
$237$	2.99077	0.194272
$238$	16.4241	1.06462
$239$	18.8637	1.22019	0.610094	−	0.792329i	$-0.291132\pi$
$239$	18.8637	1.22019	0.610094	+	0.792329i	$0.291132\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	4.83793	0.310994
$243$	−2.54207	−0.163074
$244$	4.70005	0.300890
$245$	0	0
$246$	3.99007	0.254398
$247$	24.4007	1.55258
$248$	−24.0445	−1.52683
$249$	3.91387	0.248032
$250$	0	0
$251$	2.41147	0.152211	0.0761053	−	0.997100i	$-0.475751\pi$
$251$	2.41147	0.152211	0.0761053	+	0.997100i	$0.475751\pi$
$252$	0.443421	0.0279329
$253$	7.14185	0.449004
$254$	−5.26714	−0.330490
$255$	0	0
$256$	−14.8252	−0.926577
$257$	11.2995	0.704844	0.352422	−	0.935841i	$-0.385358\pi$
$257$	11.2995	0.704844	0.352422	+	0.935841i	$0.385358\pi$
$258$	−8.18825	−0.509778
$259$	−13.9474	−0.866651
$260$	0	0
$261$	0.351722	0.0217710
$262$	2.05495	0.126956
$263$	23.9022	1.47387	0.736935	−	0.675964i	$-0.236272\pi$
$263$	23.9022	1.47387	0.736935	+	0.675964i	$0.236272\pi$
$264$	14.3662	0.884176
$265$	0	0
$266$	14.1854	0.869765
$267$	8.68238	0.531353
$268$	−7.71965	−0.471553
$269$	8.80582	0.536900	0.268450	−	0.963294i	$-0.413489\pi$
$269$	8.80582	0.536900	0.268450	+	0.963294i	$0.413489\pi$
$270$	0	0
$271$	21.7081	1.31867	0.659337	−	0.751848i	$-0.270837\pi$
$271$	21.7081	1.31867	0.659337	+	0.751848i	$0.270837\pi$
$272$	−11.8045	−0.715754
$273$	−21.8315	−1.32130
$274$	11.4991	0.694688
$275$	0	0
$276$	−3.59443	−0.216359
$277$	−16.7556	−1.00674	−0.503372	−	0.864070i	$-0.667907\pi$
$277$	−16.7556	−1.00674	−0.503372	+	0.864070i	$0.667907\pi$
$278$	−17.6184	−1.05668
$279$	−1.91611	−0.114715
$280$	0	0
$281$	−14.0236	−0.836579	−0.418290	−	0.908314i	$-0.637370\pi$
$281$	−14.0236	−0.836579	−0.418290	+	0.908314i	$0.637370\pi$
$282$	−14.8639	−0.885135
$283$	29.5858	1.75869	0.879347	−	0.476182i	$-0.157980\pi$
$283$	29.5858	1.75869	0.879347	+	0.476182i	$0.157980\pi$
$284$	1.03740	0.0615586
$285$	0	0
$286$	−14.2058	−0.840008
$287$	4.89714	0.289069
$288$	−0.947438	−0.0558283
$289$	16.8962	0.993894
$290$	0	0
$291$	−29.0016	−1.70011
$292$	−5.22733	−0.305906
$293$	−11.1102	−0.649065	−0.324533	−	0.945875i	$-0.605207\pi$
$293$	−11.1102	−0.649065	−0.324533	+	0.945875i	$0.605207\pi$
$294$	1.55220	0.0905262
$295$	0	0
$296$	17.1843	0.998815
$297$	−12.8617	−0.746311
$298$	0.193044	0.0111827
$299$	13.3718	0.773310
$300$	0	0
$301$	−10.0497	−0.579254
$302$	−13.4718	−0.775214
$303$	7.32700	0.420925
$304$	−10.1955	−0.584752
$305$	0	0
$306$	−1.61259	−0.0921855
$307$	25.7003	1.46679	0.733397	−	0.679801i	$-0.237934\pi$
$307$	25.7003	1.46679	0.733397	+	0.679801i	$0.237934\pi$
$308$	4.68671	0.267050
$309$	−4.24532	−0.241508
$310$	0	0
$311$	−17.5020	−0.992445	−0.496223	−	0.868195i	$-0.665280\pi$
$311$	−17.5020	−0.992445	−0.496223	+	0.868195i	$0.665280\pi$
$312$	26.8980	1.52280
$313$	−12.8010	−0.723558	−0.361779	−	0.932264i	$-0.617831\pi$
$313$	−12.8010	−0.723558	−0.361779	+	0.932264i	$0.617831\pi$
$314$	−7.67509	−0.433131
$315$	0	0
$316$	−1.20212	−0.0676245
$317$	−21.6381	−1.21532	−0.607659	−	0.794198i	$-0.707891\pi$
$317$	−21.6381	−1.21532	−0.607659	+	0.794198i	$0.707891\pi$
$318$	−3.51363	−0.197035
$319$	3.71750	0.208140
$320$	0	0
$321$	−32.1336	−1.79352
$322$	7.77373	0.433213
$323$	29.2760	1.62896
$324$	7.00582	0.389212
$325$	0	0
$326$	−12.1340	−0.672041
$327$	12.7756	0.706491
$328$	−6.03364	−0.333152
$329$	−18.2430	−1.00577
$330$	0	0
$331$	22.3102	1.22628	0.613139	−	0.789975i	$-0.289907\pi$
$331$	22.3102	1.22628	0.613139	+	0.789975i	$0.289907\pi$
$332$	−1.57315	−0.0863379
$333$	1.36942	0.0750435
$334$	−7.85542	−0.429830
$335$	0	0
$336$	9.12197	0.497644
$337$	24.1944	1.31795	0.658977	−	0.752163i	$-0.270989\pi$
$337$	24.1944	1.31795	0.658977	+	0.752163i	$0.270989\pi$
$338$	−11.9134	−0.648004
$339$	−2.50606	−0.136111
$340$	0	0
$341$	−20.2522	−1.09672
$342$	−1.39279	−0.0753132
$343$	19.3871	1.04681
$344$	12.3820	0.667590
$345$	0	0
$346$	−11.6156	−0.624461
$347$	30.5848	1.64188	0.820939	−	0.571016i	$-0.193451\pi$
$347$	30.5848	1.64188	0.820939	+	0.571016i	$0.193451\pi$
$348$	−1.87098	−0.100295
$349$	3.95746	0.211838	0.105919	−	0.994375i	$-0.466222\pi$
$349$	3.95746	0.211838	0.105919	+	0.994375i	$0.466222\pi$
$350$	0	0
$351$	−24.0811	−1.28536
$352$	−10.0139	−0.533742
$353$	−28.6485	−1.52481	−0.762404	−	0.647101i	$-0.775981\pi$
$353$	−28.6485	−1.52481	−0.762404	+	0.647101i	$0.775981\pi$
$354$	23.6249	1.25565
$355$	0	0
$356$	−3.48982	−0.184960
$357$	−26.1934	−1.38630
$358$	9.62658	0.508781
$359$	−11.2078	−0.591524	−0.295762	−	0.955262i	$-0.595574\pi$
$359$	−11.2078	−0.591524	−0.295762	+	0.955262i	$0.595574\pi$
$360$	0	0
$361$	6.28553	0.330817
$362$	−23.1968	−1.21920
$363$	−7.71559	−0.404963
$364$	8.77499	0.459935
$365$	0	0
$366$	13.2084	0.690414
$367$	−9.74228	−0.508543	−0.254271	−	0.967133i	$-0.581836\pi$
$367$	−9.74228	−0.508543	−0.254271	+	0.967133i	$0.581836\pi$
$368$	−5.58721	−0.291254
$369$	−0.480821	−0.0250306
$370$	0	0
$371$	−4.31239	−0.223888
$372$	10.1927	0.528469
$373$	17.5075	0.906503	0.453251	−	0.891383i	$-0.350264\pi$
$373$	17.5075	0.906503	0.453251	+	0.891383i	$0.350264\pi$
$374$	−17.0441	−0.881332
$375$	0	0
$376$	22.4767	1.15915
$377$	6.96033	0.358475
$378$	−13.9996	−0.720063
$379$	−16.5101	−0.848067	−0.424033	−	0.905647i	$-0.639386\pi$
$379$	−16.5101	−0.848067	−0.424033	+	0.905647i	$0.639386\pi$
$380$	0	0
$381$	8.40010	0.430350
$382$	−23.0351	−1.17858
$383$	−4.58870	−0.234471	−0.117236	−	0.993104i	$-0.537403\pi$
$383$	−4.58870	−0.234471	−0.117236	+	0.993104i	$0.537403\pi$
$384$	−3.21166	−0.163895
$385$	0	0
$386$	−13.0372	−0.663574
$387$	0.986719	0.0501578
$388$	11.6570	0.591794
$389$	13.6901	0.694114	0.347057	−	0.937844i	$-0.387181\pi$
$389$	13.6901	0.694114	0.347057	+	0.937844i	$0.387181\pi$
$390$	0	0
$391$	16.0435	0.811353
$392$	−2.34718	−0.118550
$393$	−3.27726	−0.165316
$394$	24.6306	1.24087
$395$	0	0
$396$	−0.460161	−0.0231239
$397$	7.67841	0.385368	0.192684	−	0.981261i	$-0.438281\pi$
$397$	7.67841	0.385368	0.192684	+	0.981261i	$0.438281\pi$
$398$	19.5816	0.981538
$399$	−22.6231	−1.13257
$400$	0	0
$401$	25.6876	1.28278	0.641390	−	0.767215i	$-0.278358\pi$
$401$	25.6876	1.28278	0.641390	+	0.767215i	$0.278358\pi$
$402$	−21.6943	−1.08201
$403$	−37.9185	−1.88886
$404$	−2.94504	−0.146521
$405$	0	0
$406$	4.04641	0.200820
$407$	14.4740	0.717447
$408$	32.2722	1.59771
$409$	11.8642	0.586646	0.293323	−	0.956013i	$-0.405239\pi$
$409$	11.8642	0.586646	0.293323	+	0.956013i	$0.405239\pi$
$410$	0	0
$411$	−18.3390	−0.904594
$412$	1.70638	0.0840671
$413$	28.9955	1.42678
$414$	−0.763257	−0.0375120
$415$	0	0
$416$	−18.7491	−0.919252
$417$	28.0981	1.37597
$418$	−14.7210	−0.720025
$419$	−20.9788	−1.02488	−0.512442	−	0.858722i	$-0.671259\pi$
$419$	−20.9788	−1.02488	−0.512442	+	0.858722i	$0.671259\pi$
$420$	0	0
$421$	1.19031	0.0580121	0.0290060	−	0.999579i	$-0.490766\pi$
$421$	1.19031	0.0580121	0.0290060	+	0.999579i	$0.490766\pi$
$422$	6.17361	0.300527
$423$	1.79117	0.0870897
$424$	5.31318	0.258031
$425$	0	0
$426$	2.91538	0.141251
$427$	16.2111	0.784509
$428$	12.9159	0.624312
$429$	22.6556	1.09382
$430$	0	0
$431$	26.9371	1.29752	0.648758	−	0.760995i	$-0.275289\pi$
$431$	26.9371	1.29752	0.648758	+	0.760995i	$0.275289\pi$
$432$	10.0620	0.484106
$433$	−9.15624	−0.440021	−0.220010	−	0.975498i	$-0.570609\pi$
$433$	−9.15624	−0.440021	−0.220010	+	0.975498i	$0.570609\pi$
$434$	−22.0440	−1.05815
$435$	0	0
$436$	−5.13505	−0.245924
$437$	13.8567	0.662854
$438$	−14.6902	−0.701925
$439$	−5.42244	−0.258799	−0.129399	−	0.991593i	$-0.541305\pi$
$439$	−5.42244	−0.258799	−0.129399	+	0.991593i	$0.541305\pi$
$440$	0	0
$441$	−0.187047	−0.00890700
$442$	−31.9120	−1.51790
$443$	−16.5230	−0.785030	−0.392515	−	0.919746i	$-0.628395\pi$
$443$	−16.5230	−0.785030	−0.392515	+	0.919746i	$0.628395\pi$
$444$	−7.28461	−0.345712
$445$	0	0
$446$	26.3678	1.24855
$447$	−0.307869	−0.0145617
$448$	−21.0272	−0.993444
$449$	30.1881	1.42466	0.712332	−	0.701842i	$-0.247639\pi$
$449$	30.1881	1.42466	0.712332	+	0.701842i	$0.247639\pi$
$450$	0	0
$451$	−5.08201	−0.239302
$452$	1.00729	0.0473791
$453$	21.4850	1.00945
$454$	−23.3932	−1.09790
$455$	0	0
$456$	27.8733	1.30529
$457$	−14.5636	−0.681255	−0.340627	−	0.940198i	$-0.610639\pi$
$457$	−14.5636	−0.681255	−0.340627	+	0.940198i	$0.610639\pi$
$458$	13.8539	0.647348
$459$	−28.8925	−1.34859
$460$	0	0
$461$	−16.8681	−0.785628	−0.392814	−	0.919618i	$-0.628498\pi$
$461$	−16.8681	−0.785628	−0.392814	+	0.919618i	$0.628498\pi$
$462$	13.1709	0.612766
$463$	2.62284	0.121894	0.0609468	−	0.998141i	$-0.480588\pi$
$463$	2.62284	0.121894	0.0609468	+	0.998141i	$0.480588\pi$
$464$	−2.90827	−0.135013
$465$	0	0
$466$	−8.93606	−0.413955
$467$	−9.98247	−0.461934	−0.230967	−	0.972962i	$-0.574189\pi$
$467$	−9.98247	−0.461934	−0.230967	+	0.972962i	$0.574189\pi$
$468$	−0.861565	−0.0398259
$469$	−26.6261	−1.22948
$470$	0	0
$471$	12.2403	0.564004
$472$	−35.7247	−1.64436
$473$	10.4291	0.479529
$474$	−3.37828	−0.155169
$475$	0	0
$476$	10.5282	0.482561
$477$	0.423408	0.0193865
$478$	−21.3078	−0.974594
$479$	−12.7859	−0.584205	−0.292102	−	0.956387i	$-0.594355\pi$
$479$	−12.7859	−0.584205	−0.292102	+	0.956387i	$0.594355\pi$
$480$	0	0
$481$	27.0998	1.23564
$482$	−1.12957	−0.0514504
$483$	−12.3976	−0.564112
$484$	3.10122	0.140965
$485$	0	0
$486$	2.87144	0.130251
$487$	10.0941	0.457408	0.228704	−	0.973496i	$-0.426551\pi$
$487$	10.0941	0.457408	0.228704	+	0.973496i	$0.426551\pi$
$488$	−19.9732	−0.904146
$489$	19.3515	0.875103
$490$	0	0
$491$	23.8057	1.07434	0.537169	−	0.843475i	$-0.319494\pi$
$491$	23.8057	1.07434	0.537169	+	0.843475i	$0.319494\pi$
$492$	2.55773	0.115311
$493$	8.35100	0.376110
$494$	−27.5623	−1.24008
$495$	0	0
$496$	15.8437	0.711404
$497$	3.57814	0.160501
$498$	−4.42098	−0.198109
$499$	−38.0774	−1.70458	−0.852289	−	0.523071i	$-0.824786\pi$
$499$	−38.0774	−1.70458	−0.852289	+	0.523071i	$0.824786\pi$
$500$	0	0
$501$	12.5279	0.559706
$502$	−2.72392	−0.121574
$503$	38.6805	1.72468	0.862339	−	0.506331i	$-0.168999\pi$
$503$	38.6805	1.72468	0.862339	+	0.506331i	$0.168999\pi$
$504$	−1.88435	−0.0839358
$505$	0	0
$506$	−8.06720	−0.358631
$507$	18.9996	0.843804
$508$	−3.37636	−0.149802
$509$	−20.6444	−0.915045	−0.457523	−	0.889198i	$-0.651263\pi$
$509$	−20.6444	−0.915045	−0.457523	+	0.889198i	$0.651263\pi$
$510$	0	0
$511$	−18.0297	−0.797588
$512$	20.3118	0.897661
$513$	−24.9543	−1.10176
$514$	−12.7635	−0.562976
$515$	0	0
$516$	−5.24885	−0.231068
$517$	18.9317	0.832613
$518$	15.7545	0.692215
$519$	18.5248	0.813147
$520$	0	0
$521$	−26.8787	−1.17758	−0.588788	−	0.808287i	$-0.700395\pi$
$521$	−26.8787	−1.17758	−0.588788	+	0.808287i	$0.700395\pi$
$522$	−0.397293	−0.0173890
$523$	−27.7585	−1.21379	−0.606897	−	0.794780i	$-0.707586\pi$
$523$	−27.7585	−1.21379	−0.606897	+	0.794780i	$0.707586\pi$
$524$	1.31727	0.0575453
$525$	0	0
$526$	−26.9991	−1.17722
$527$	−45.4946	−1.98178
$528$	−9.46633	−0.411969
$529$	−15.4064	−0.669845
$530$	0	0
$531$	−2.84690	−0.123545
$532$	9.09319	0.394240
$533$	−9.51512	−0.412146
$534$	−9.80733	−0.424404
$535$	0	0
$536$	32.8053	1.41697
$537$	−15.3526	−0.662513
$538$	−9.94676	−0.428835
$539$	−1.97698	−0.0851546
$540$	0	0
$541$	18.1138	0.778775	0.389388	−	0.921074i	$-0.372687\pi$
$541$	18.1138	0.778775	0.389388	+	0.921074i	$0.372687\pi$
$542$	−24.5208	−1.05326
$543$	36.9946	1.58759
$544$	−22.4952	−0.964474
$545$	0	0
$546$	24.6601	1.05535
$547$	12.3306	0.527219	0.263609	−	0.964630i	$-0.415087\pi$
$547$	12.3306	0.527219	0.263609	+	0.964630i	$0.415087\pi$
$548$	7.37121	0.314882
$549$	−1.59167	−0.0679308
$550$	0	0
$551$	7.21272	0.307272
$552$	15.2748	0.650139
$553$	−4.14626	−0.176317
$554$	18.9265	0.804111
$555$	0	0
$556$	−11.2938	−0.478964
$557$	32.9393	1.39568	0.697842	−	0.716251i	$-0.254144\pi$
$557$	32.9393	1.39568	0.697842	+	0.716251i	$0.254144\pi$
$558$	2.16438	0.0916253
$559$	19.5265	0.825883
$560$	0	0
$561$	27.1822	1.14763
$562$	15.8406	0.668196
$563$	−23.5290	−0.991627	−0.495814	−	0.868429i	$-0.665130\pi$
$563$	−23.5290	−0.991627	−0.495814	+	0.868429i	$0.665130\pi$
$564$	−9.52813	−0.401207
$565$	0	0
$566$	−33.4192	−1.40471
$567$	24.1640	1.01479
$568$	−4.40853	−0.184978
$569$	37.5874	1.57574	0.787872	−	0.615839i	$-0.211183\pi$
$569$	37.5874	1.57574	0.787872	+	0.615839i	$0.211183\pi$
$570$	0	0
$571$	−5.14164	−0.215171	−0.107586	−	0.994196i	$-0.534312\pi$
$571$	−5.14164	−0.215171	−0.107586	+	0.994196i	$0.534312\pi$
$572$	−9.10626	−0.380752
$573$	36.7367	1.53470
$574$	−5.53164	−0.230886
$575$	0	0
$576$	2.06454	0.0860226
$577$	−18.8736	−0.785717	−0.392859	−	0.919599i	$-0.628514\pi$
$577$	−18.8736	−0.785717	−0.392859	+	0.919599i	$0.628514\pi$
$578$	−19.0854	−0.793847
$579$	20.7918	0.864078
$580$	0	0
$581$	−5.42600	−0.225108
$582$	32.7593	1.35792
$583$	4.47518	0.185343
$584$	22.2140	0.919220
$585$	0	0
$586$	12.5497	0.518424
$587$	−25.5645	−1.05516	−0.527581	−	0.849505i	$-0.676901\pi$
$587$	−25.5645	−1.05516	−0.527581	+	0.849505i	$0.676901\pi$
$588$	0.994996	0.0410329
$589$	−39.2935	−1.61906
$590$	0	0
$591$	−39.2812	−1.61581
$592$	−11.3233	−0.465383
$593$	−18.2020	−0.747467	−0.373734	−	0.927536i	$-0.621923\pi$
$593$	−18.2020	−0.747467	−0.373734	+	0.927536i	$0.621923\pi$
$594$	14.5281	0.596097
$595$	0	0
$596$	0.123746	0.00506882
$597$	−31.2290	−1.27812
$598$	−15.1043	−0.617662
$599$	16.1275	0.658952	0.329476	−	0.944164i	$-0.393128\pi$
$599$	16.1275	0.658952	0.329476	+	0.944164i	$0.393128\pi$
$600$	0	0
$601$	−40.2909	−1.64350	−0.821750	−	0.569849i	$-0.807002\pi$
$601$	−40.2909	−1.64350	−0.821750	+	0.569849i	$0.807002\pi$
$602$	11.3518	0.462664
$603$	2.61426	0.106461
$604$	−8.63572	−0.351383
$605$	0	0
$606$	−8.27634	−0.336203
$607$	−8.89385	−0.360990	−0.180495	−	0.983576i	$-0.557770\pi$
$607$	−8.89385	−0.360990	−0.180495	+	0.983576i	$0.557770\pi$
$608$	−19.4290	−0.787950
$609$	−6.45325	−0.261499
$610$	0	0
$611$	35.4460	1.43399
$612$	−1.03371	−0.0417851
$613$	20.8869	0.843615	0.421808	−	0.906685i	$-0.361396\pi$
$613$	20.8869	0.843615	0.421808	+	0.906685i	$0.361396\pi$
$614$	−29.0302	−1.17156
$615$	0	0
$616$	−19.9165	−0.802461
$617$	−32.4979	−1.30832	−0.654158	−	0.756358i	$-0.726977\pi$
$617$	−32.4979	−1.30832	−0.654158	+	0.756358i	$0.726977\pi$
$618$	4.79538	0.192898
$619$	−6.02566	−0.242192	−0.121096	−	0.992641i	$-0.538641\pi$
$619$	−6.02566	−0.242192	−0.121096	+	0.992641i	$0.538641\pi$
$620$	0	0
$621$	−13.6752	−0.548766
$622$	19.7696	0.792691
$623$	−12.0368	−0.482245
$624$	−17.7240	−0.709526
$625$	0	0
$626$	14.4596	0.577924
$627$	23.4771	0.937587
$628$	−4.91991	−0.196326
$629$	32.5143	1.29643
$630$	0	0
$631$	43.8659	1.74627	0.873137	−	0.487475i	$-0.162082\pi$
$631$	43.8659	1.74627	0.873137	+	0.487475i	$0.162082\pi$
$632$	5.10850	0.203205
$633$	−9.84574	−0.391333
$634$	24.4417	0.970704
$635$	0	0
$636$	−2.25232	−0.0893102
$637$	−3.70153	−0.146660
$638$	−4.19916	−0.166246
$639$	−0.351316	−0.0138979
$640$	0	0
$641$	17.4074	0.687553	0.343776	−	0.939052i	$-0.388294\pi$
$641$	17.4074	0.687553	0.343776	+	0.939052i	$0.388294\pi$
$642$	36.2971	1.43253
$643$	18.0816	0.713071	0.356535	−	0.934282i	$-0.383958\pi$
$643$	18.0816	0.713071	0.356535	+	0.934282i	$0.383958\pi$
$644$	4.98314	0.196363
$645$	0	0
$646$	−33.0692	−1.30109
$647$	−44.2567	−1.73991	−0.869954	−	0.493132i	$-0.835852\pi$
$647$	−44.2567	−1.73991	−0.869954	+	0.493132i	$0.835852\pi$
$648$	−29.7718	−1.16955
$649$	−30.0902	−1.18114
$650$	0	0
$651$	35.1561	1.37788
$652$	−7.77818	−0.304617
$653$	9.17268	0.358955	0.179477	−	0.983762i	$-0.442559\pi$
$653$	9.17268	0.358955	0.179477	+	0.983762i	$0.442559\pi$
$654$	−14.4309	−0.564292
$655$	0	0
$656$	3.97576	0.155227
$657$	1.77023	0.0690634
$658$	20.6067	0.803331
$659$	−7.64799	−0.297923	−0.148962	−	0.988843i	$-0.547593\pi$
$659$	−7.64799	−0.297923	−0.148962	+	0.988843i	$0.547593\pi$
$660$	0	0
$661$	−26.5608	−1.03309	−0.516547	−	0.856259i	$-0.672783\pi$
$661$	−26.5608	−1.03309	−0.516547	+	0.856259i	$0.672783\pi$
$662$	−25.2008	−0.979458
$663$	50.8936	1.97655
$664$	6.68524	0.259438
$665$	0	0
$666$	−1.54685	−0.0599391
$667$	3.95262	0.153046
$668$	−5.03551	−0.194830
$669$	−42.0516	−1.62581
$670$	0	0
$671$	−16.8231	−0.649447
$672$	17.3832	0.670573
$673$	−28.7298	−1.10745	−0.553726	−	0.832699i	$-0.686794\pi$
$673$	−28.7298	−1.10745	−0.553726	+	0.832699i	$0.686794\pi$
$674$	−27.3292	−1.05268
$675$	0	0
$676$	−7.63677	−0.293722
$677$	−7.16539	−0.275388	−0.137694	−	0.990475i	$-0.543969\pi$
$677$	−7.16539	−0.275388	−0.137694	+	0.990475i	$0.543969\pi$
$678$	2.83077	0.108715
$679$	40.2065	1.54298
$680$	0	0
$681$	37.3078	1.42964
$682$	22.8762	0.875976
$683$	38.9311	1.48966	0.744828	−	0.667256i	$-0.232531\pi$
$683$	38.9311	1.48966	0.744828	+	0.667256i	$0.232531\pi$
$684$	−0.892807	−0.0341373
$685$	0	0
$686$	−21.8991	−0.836110
$687$	−22.0943	−0.842949
$688$	−8.15887	−0.311054
$689$	8.37895	0.319213
$690$	0	0
$691$	−8.87056	−0.337452	−0.168726	−	0.985663i	$-0.553965\pi$
$691$	−8.87056	−0.337452	−0.168726	+	0.985663i	$0.553965\pi$
$692$	−7.44589	−0.283050
$693$	−1.58715	−0.0602909
$694$	−34.5476	−1.31141
$695$	0	0
$696$	7.95089	0.301378
$697$	−11.4162	−0.432421
$698$	−4.47022	−0.169200
$699$	14.2513	0.539034
$700$	0	0
$701$	36.5265	1.37959	0.689794	−	0.724006i	$-0.257701\pi$
$701$	36.5265	1.37959	0.689794	+	0.724006i	$0.257701\pi$
$702$	27.2012	1.02664
$703$	28.0825	1.05915
$704$	21.8211	0.822412
$705$	0	0
$706$	32.3605	1.21790
$707$	−10.1578	−0.382023
$708$	15.1441	0.569150
$709$	−39.6672	−1.48973	−0.744866	−	0.667214i	$-0.767487\pi$
$709$	−39.6672	−1.48973	−0.744866	+	0.667214i	$0.767487\pi$
$710$	0	0
$711$	0.407097	0.0152673
$712$	14.8303	0.555788
$713$	−21.5331	−0.806422
$714$	29.5872	1.10727
$715$	0	0
$716$	6.17086	0.230616
$717$	33.9819	1.26908
$718$	12.6599	0.472465
$719$	−0.334936	−0.0124910	−0.00624551	−	0.999980i	$-0.501988\pi$
$719$	−0.334936	−0.0124910	−0.00624551	+	0.999980i	$0.501988\pi$
$720$	0	0
$721$	5.88551	0.219188
$722$	−7.09992	−0.264232
$723$	1.80145	0.0669965
$724$	−14.8697	−0.552628
$725$	0	0
$726$	8.71527	0.323454
$727$	50.9742	1.89053	0.945264	−	0.326306i	$-0.105804\pi$
$727$	50.9742	1.89053	0.945264	+	0.326306i	$0.105804\pi$
$728$	−37.2900	−1.38206
$729$	24.4471	0.905448
$730$	0	0
$731$	23.4279	0.866512
$732$	8.46689	0.312945
$733$	2.33663	0.0863052	0.0431526	−	0.999068i	$-0.486260\pi$
$733$	2.33663	0.0863052	0.0431526	+	0.999068i	$0.486260\pi$
$734$	11.0046	0.406186
$735$	0	0
$736$	−10.6472	−0.392463
$737$	27.6312	1.01781
$738$	0.543120	0.0199925
$739$	7.17939	0.264098	0.132049	−	0.991243i	$-0.457844\pi$
$739$	7.17939	0.264098	0.132049	+	0.991243i	$0.457844\pi$
$740$	0	0
$741$	43.9566	1.61479
$742$	4.87113	0.178825
$743$	39.6881	1.45601	0.728007	−	0.685569i	$-0.240447\pi$
$743$	39.6881	1.45601	0.728007	+	0.685569i	$0.240447\pi$
$744$	−43.3149	−1.58800
$745$	0	0
$746$	−19.7759	−0.724046
$747$	0.532747	0.0194922
$748$	−10.9257	−0.399483
$749$	44.5485	1.62777
$750$	0	0
$751$	−29.7269	−1.08475	−0.542375	−	0.840136i	$-0.682475\pi$
$751$	−29.7269	−1.08475	−0.542375	+	0.840136i	$0.682475\pi$
$752$	−14.8106	−0.540088
$753$	4.34413	0.158309
$754$	−7.86216	−0.286323
$755$	0	0
$756$	−8.97408	−0.326384
$757$	8.10497	0.294580	0.147290	−	0.989093i	$-0.452945\pi$
$757$	8.10497	0.294580	0.147290	+	0.989093i	$0.452945\pi$
$758$	18.6493	0.677372
$759$	12.8657	0.466994
$760$	0	0
$761$	−26.4657	−0.959379	−0.479690	−	0.877438i	$-0.659251\pi$
$761$	−26.4657	−0.959379	−0.479690	+	0.877438i	$0.659251\pi$
$762$	−9.48848	−0.343731
$763$	−17.7114	−0.641197
$764$	−14.7660	−0.534216
$765$	0	0
$766$	5.18324	0.187278
$767$	−56.3383	−2.03426
$768$	−26.7069	−0.963701
$769$	−41.1714	−1.48468	−0.742340	−	0.670023i	$-0.766284\pi$
$769$	−41.1714	−1.48468	−0.742340	+	0.670023i	$0.766284\pi$
$770$	0	0
$771$	20.3555	0.733084
$772$	−8.35711	−0.300779
$773$	39.4692	1.41961	0.709805	−	0.704398i	$-0.248783\pi$
$773$	39.4692	1.41961	0.709805	+	0.704398i	$0.248783\pi$
$774$	−1.11457	−0.0400622
$775$	0	0
$776$	−49.5374	−1.77829
$777$	−25.1255	−0.901373
$778$	−15.4639	−0.554406
$779$	−9.86015	−0.353277
$780$	0	0
$781$	−3.71322	−0.132869
$782$	−18.1222	−0.648047
$783$	−7.11824	−0.254385
$784$	1.54663	0.0552369
$785$	0	0
$786$	3.70189	0.132042
$787$	44.5916	1.58952	0.794759	−	0.606926i	$-0.207597\pi$
$787$	44.5916	1.58952	0.794759	+	0.606926i	$0.207597\pi$
$788$	15.7888	0.562453
$789$	43.0584	1.53292
$790$	0	0
$791$	3.47428	0.123531
$792$	1.95549	0.0694853
$793$	−31.4981	−1.11853
$794$	−8.67328	−0.307803
$795$	0	0
$796$	12.5523	0.444903
$797$	17.3363	0.614084	0.307042	−	0.951696i	$-0.400661\pi$
$797$	17.3363	0.614084	0.307042	+	0.951696i	$0.400661\pi$
$798$	25.5543	0.904612
$799$	42.5281	1.50454
$800$	0	0
$801$	1.18183	0.0417577
$802$	−29.0159	−1.02459
$803$	18.7104	0.660275
$804$	−13.9065	−0.490446
$805$	0	0
$806$	42.8315	1.50868
$807$	15.8632	0.558411
$808$	12.5152	0.440282
$809$	0.598182	0.0210310	0.0105155	−	0.999945i	$-0.496653\pi$
$809$	0.598182	0.0210310	0.0105155	+	0.999945i	$0.496653\pi$
$810$	0	0
$811$	−37.2416	−1.30773	−0.653864	−	0.756612i	$-0.726853\pi$
$811$	−37.2416	−1.30773	−0.653864	+	0.756612i	$0.726853\pi$
$812$	2.59384	0.0910259
$813$	39.1060	1.37151
$814$	−16.3493	−0.573043
$815$	0	0
$816$	−21.2652	−0.744431
$817$	20.2346	0.707917
$818$	−13.4014	−0.468568
$819$	−2.97165	−0.103838
$820$	0	0
$821$	8.45638	0.295130	0.147565	−	0.989052i	$-0.452856\pi$
$821$	8.45638	0.295130	0.147565	+	0.989052i	$0.452856\pi$
$822$	20.7151	0.722521
$823$	−37.0696	−1.29217	−0.646083	−	0.763267i	$-0.723594\pi$
$823$	−37.0696	−1.29217	−0.646083	+	0.763267i	$0.723594\pi$
$824$	−7.25139	−0.252614
$825$	0	0
$826$	−32.7524	−1.13960
$827$	−37.5141	−1.30449	−0.652247	−	0.758007i	$-0.726173\pi$
$827$	−37.5141	−1.30449	−0.652247	+	0.758007i	$0.726173\pi$
$828$	−0.489265	−0.0170031
$829$	−19.8735	−0.690236	−0.345118	−	0.938559i	$-0.612161\pi$
$829$	−19.8735	−0.690236	−0.345118	+	0.938559i	$0.612161\pi$
$830$	0	0
$831$	−30.1842	−1.04708
$832$	40.8559	1.41642
$833$	−4.44109	−0.153875
$834$	−31.7387	−1.09902
$835$	0	0
$836$	−9.43646	−0.326367
$837$	38.7788	1.34039
$838$	23.6970	0.818600
$839$	34.2009	1.18075	0.590373	−	0.807130i	$-0.298981\pi$
$839$	34.2009	1.18075	0.590373	+	0.807130i	$0.298981\pi$
$840$	0	0
$841$	−26.9426	−0.929054
$842$	−1.34453	−0.0463357
$843$	−25.2628	−0.870097
$844$	3.95742	0.136220
$845$	0	0
$846$	−2.02325	−0.0695607
$847$	10.6965	0.367537
$848$	−3.50103	−0.120226
$849$	53.2972	1.82916
$850$	0	0
$851$	15.3894	0.527542
$852$	1.86883	0.0640250
$853$	36.9931	1.26662	0.633310	−	0.773898i	$-0.281696\pi$
$853$	36.9931	1.26662	0.633310	+	0.773898i	$0.281696\pi$
$854$	−18.3115	−0.626606
$855$	0	0
$856$	−54.8870	−1.87600
$857$	−13.0250	−0.444927	−0.222463	−	0.974941i	$-0.571410\pi$
$857$	−13.0250	−0.444927	−0.222463	+	0.974941i	$0.571410\pi$
$858$	−25.5910	−0.873664
$859$	−37.2837	−1.27211	−0.636053	−	0.771646i	$-0.719434\pi$
$859$	−37.2837	−1.27211	−0.636053	+	0.771646i	$0.719434\pi$
$860$	0	0
$861$	8.82193	0.300650
$862$	−30.4273	−1.03636
$863$	−4.00745	−0.136415	−0.0682076	−	0.997671i	$-0.521728\pi$
$863$	−4.00745	−0.136415	−0.0682076	+	0.997671i	$0.521728\pi$
$864$	19.1745	0.652331
$865$	0	0
$866$	10.3426	0.351455
$867$	30.4376	1.03371
$868$	−14.1307	−0.479628
$869$	4.30279	0.145962
$870$	0	0
$871$	51.7344	1.75295
$872$	21.8218	0.738980
$873$	−3.94764	−0.133607
$874$	−15.6520	−0.529438
$875$	0	0
$876$	−9.41675	−0.318163
$877$	43.3980	1.46545	0.732723	−	0.680527i	$-0.238249\pi$
$877$	43.3980	1.46545	0.732723	+	0.680527i	$0.238249\pi$
$878$	6.12501	0.206709
$879$	−20.0144	−0.675070
$880$	0	0
$881$	−42.2889	−1.42475	−0.712375	−	0.701799i	$-0.752380\pi$
$881$	−42.2889	−1.42475	−0.712375	+	0.701799i	$0.752380\pi$
$882$	0.211282	0.00711424
$883$	38.9967	1.31234	0.656172	−	0.754611i	$-0.272174\pi$
$883$	38.9967	1.31234	0.656172	+	0.754611i	$0.272174\pi$
$884$	−20.4563	−0.688021
$885$	0	0
$886$	18.6638	0.627023
$887$	5.09100	0.170939	0.0854696	−	0.996341i	$-0.472761\pi$
$887$	5.09100	0.170939	0.0854696	+	0.996341i	$0.472761\pi$
$888$	30.9565	1.03883
$889$	−11.6455	−0.390577
$890$	0	0
$891$	−25.0762	−0.840083
$892$	16.9023	0.565932
$893$	36.7313	1.22917
$894$	0.347759	0.0116308
$895$	0	0
$896$	4.45249	0.148747
$897$	24.0886	0.804293
$898$	−34.0995	−1.13791
$899$	−11.2085	−0.373824
$900$	0	0
$901$	10.0531	0.334916
$902$	5.74047	0.191137
$903$	−18.1040	−0.602462
$904$	−4.28058	−0.142370
$905$	0	0
$906$	−24.2687	−0.806274
$907$	−2.37177	−0.0787533	−0.0393767	−	0.999224i	$-0.512537\pi$
$907$	−2.37177	−0.0787533	−0.0393767	+	0.999224i	$0.512537\pi$
$908$	−14.9956	−0.497646
$909$	0.997335	0.0330795
$910$	0	0
$911$	0.219248	0.00726400	0.00363200	−	0.999993i	$-0.498844\pi$
$911$	0.219248	0.00726400	0.00363200	+	0.999993i	$0.498844\pi$
$912$	−18.3666	−0.608180
$913$	5.63084	0.186354
$914$	16.4505	0.544135
$915$	0	0
$916$	8.88064	0.293424
$917$	4.54344	0.150038
$918$	32.6360	1.07715
$919$	−22.6503	−0.747164	−0.373582	−	0.927597i	$-0.621871\pi$
$919$	−22.6503	−0.747164	−0.373582	+	0.927597i	$0.621871\pi$
$920$	0	0
$921$	46.2977	1.52556
$922$	19.0537	0.627500
$923$	−6.95231	−0.228838
$924$	8.44285	0.277749
$925$	0	0
$926$	−2.96267	−0.0973593
$927$	−0.577864	−0.0189795
$928$	−5.54214	−0.181930
$929$	−12.9112	−0.423601	−0.211801	−	0.977313i	$-0.567933\pi$
$929$	−12.9112	−0.423601	−0.211801	+	0.977313i	$0.567933\pi$
$930$	0	0
$931$	−3.83575	−0.125712
$932$	−5.72821	−0.187634
$933$	−31.5289	−1.03221
$934$	11.2759	0.368958
$935$	0	0
$936$	3.66129	0.119673
$937$	53.8233	1.75833	0.879165	−	0.476517i	$-0.158101\pi$
$937$	53.8233	1.75833	0.879165	+	0.476517i	$0.158101\pi$
$938$	30.0759	0.982014
$939$	−23.0604	−0.752548
$940$	0	0
$941$	9.43438	0.307552	0.153776	−	0.988106i	$-0.450857\pi$
$941$	9.43438	0.307552	0.153776	+	0.988106i	$0.450857\pi$
$942$	−13.8263	−0.450484
$943$	−5.40344	−0.175960
$944$	23.5402	0.766167
$945$	0	0
$946$	−11.7803	−0.383012
$947$	28.6373	0.930588	0.465294	−	0.885156i	$-0.345949\pi$
$947$	28.6373	0.930588	0.465294	+	0.885156i	$0.345949\pi$
$948$	−2.16555	−0.0703339
$949$	35.0317	1.13718
$950$	0	0
$951$	−38.9799	−1.26401
$952$	−44.7406	−1.45005
$953$	−30.6400	−0.992526	−0.496263	−	0.868172i	$-0.665295\pi$
$953$	−30.6400	−0.992526	−0.496263	+	0.868172i	$0.665295\pi$
$954$	−0.478268	−0.0154845
$955$	0	0
$956$	−13.6588	−0.441756
$957$	6.69687	0.216479
$958$	14.4426	0.466619
$959$	25.4242	0.820991
$960$	0	0
$961$	30.0617	0.969733
$962$	−30.6110	−0.986939
$963$	−4.37395	−0.140949
$964$	−0.724078	−0.0233210
$965$	0	0
$966$	14.0040	0.450570
$967$	−35.6442	−1.14624	−0.573120	−	0.819471i	$-0.694267\pi$
$967$	−35.6442	−1.14624	−0.573120	+	0.819471i	$0.694267\pi$
$968$	−13.1789	−0.423586
$969$	52.7391	1.69422
$970$	0	0
$971$	19.3515	0.621020	0.310510	−	0.950570i	$-0.399500\pi$
$971$	19.3515	0.621020	0.310510	+	0.950570i	$0.399500\pi$
$972$	1.84066	0.0590390
$973$	−38.9538	−1.24880
$974$	−11.4020	−0.365343
$975$	0	0
$976$	13.1610	0.421274
$977$	−55.0858	−1.76235	−0.881176	−	0.472789i	$-0.843247\pi$
$977$	−55.0858	−1.76235	−0.881176	+	0.472789i	$0.843247\pi$
$978$	−21.8588	−0.698967
$979$	12.4912	0.399221
$980$	0	0
$981$	1.73898	0.0555215
$982$	−26.8902	−0.858100
$983$	32.6742	1.04214	0.521072	−	0.853513i	$-0.325532\pi$
$983$	32.6742	1.04214	0.521072	+	0.853513i	$0.325532\pi$
$984$	−10.8693	−0.346500
$985$	0	0
$986$	−9.43301	−0.300408
$987$	−32.8637	−1.04606
$988$	−17.6680	−0.562095
$989$	11.0887	0.352600
$990$	0	0
$991$	40.0719	1.27293	0.636464	−	0.771307i	$-0.280397\pi$
$991$	40.0719	1.27293	0.636464	+	0.771307i	$0.280397\pi$
$992$	30.1925	0.958613
$993$	40.1906	1.27541
$994$	−4.04175	−0.128196
$995$	0	0
$996$	−2.83395	−0.0897971
$997$	−32.8267	−1.03963	−0.519816	−	0.854279i	$-0.673999\pi$
$997$	−32.8267	−1.03963	−0.519816	+	0.854279i	$0.673999\pi$
$998$	43.0110	1.36149
$999$	−27.7146	−0.876852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.4		11
5.4	even	2		1205.2.a.b.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.8	✓	11	5.4	even	2
6025.2.a.g.1.4		11	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.12957 q^{2} +1.80145 q^{3} -0.724078 q^{4} -2.03485 q^{6} -2.49744 q^{7} +3.07703 q^{8} +0.245209 q^{9} +O(q^{10})\)	\(q-1.12957 q^{2} +1.80145 q^{3} -0.724078 q^{4} -2.03485 q^{6} -2.49744 q^{7} +3.07703 q^{8} +0.245209 q^{9} +2.59172 q^{11} -1.30439 q^{12} +4.85251 q^{13} +2.82102 q^{14} -2.02755 q^{16} +5.82204 q^{17} -0.276980 q^{18} +5.02847 q^{19} -4.49900 q^{21} -2.92752 q^{22} +2.75564 q^{23} +5.54310 q^{24} -5.48124 q^{26} -4.96261 q^{27} +1.80834 q^{28} +1.43438 q^{29} -7.81420 q^{31} -3.86380 q^{32} +4.66884 q^{33} -6.57639 q^{34} -0.177550 q^{36} +5.58469 q^{37} -5.68000 q^{38} +8.74154 q^{39} -1.96086 q^{41} +5.08192 q^{42} +4.02400 q^{43} -1.87661 q^{44} -3.11268 q^{46} +7.30467 q^{47} -3.65253 q^{48} -0.762807 q^{49} +10.4881 q^{51} -3.51360 q^{52} +1.72672 q^{53} +5.60560 q^{54} -7.68469 q^{56} +9.05852 q^{57} -1.62022 q^{58} -11.6101 q^{59} -6.49108 q^{61} +8.82666 q^{62} -0.612394 q^{63} +8.41953 q^{64} -5.27377 q^{66} +10.6614 q^{67} -4.21561 q^{68} +4.96414 q^{69} -1.43272 q^{71} +0.754515 q^{72} +7.21929 q^{73} -6.30829 q^{74} -3.64101 q^{76} -6.47265 q^{77} -9.87416 q^{78} +1.66021 q^{79} -9.67550 q^{81} +2.21493 q^{82} +2.17263 q^{83} +3.25763 q^{84} -4.54537 q^{86} +2.58395 q^{87} +7.97479 q^{88} +4.81967 q^{89} -12.1188 q^{91} -1.99530 q^{92} -14.0769 q^{93} -8.25112 q^{94} -6.96043 q^{96} -16.0991 q^{97} +0.861641 q^{98} +0.635512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more