LMFDB - Embedded newform 6025.2.a.f.1.6

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:	$1$
Dimension:	$7$
Coefficient field:	7.7.31056073.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 $ x^7 - 3x^6 - 3x^5 + 11x^4 + x^3 - 9x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.911223$ 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)

$f(q)$	$=$	$q+1.91122 q^{2} +0.186202 q^{3} +1.65278 q^{4} +0.355874 q^{6} -3.52970 q^{7} -0.663624 q^{8} -2.96533 q^{9} +O(q^{10})$	\(q+1.91122 q^{2} +0.186202 q^{3} +1.65278 q^{4} +0.355874 q^{6} -3.52970 q^{7} -0.663624 q^{8} -2.96533 q^{9} +0.515564 q^{11} +0.307750 q^{12} +5.38098 q^{13} -6.74604 q^{14} -4.57388 q^{16} +4.16566 q^{17} -5.66741 q^{18} +4.92935 q^{19} -0.657237 q^{21} +0.985358 q^{22} +7.69193 q^{23} -0.123568 q^{24} +10.2843 q^{26} -1.11076 q^{27} -5.83379 q^{28} -8.93755 q^{29} -4.43182 q^{31} -7.41447 q^{32} +0.0959992 q^{33} +7.96151 q^{34} -4.90102 q^{36} -5.99816 q^{37} +9.42110 q^{38} +1.00195 q^{39} -8.99946 q^{41} -1.25613 q^{42} +1.66336 q^{43} +0.852112 q^{44} +14.7010 q^{46} -8.55484 q^{47} -0.851668 q^{48} +5.45876 q^{49} +0.775656 q^{51} +8.89356 q^{52} -13.1736 q^{53} -2.12291 q^{54} +2.34239 q^{56} +0.917857 q^{57} -17.0817 q^{58} +9.25521 q^{59} -10.4203 q^{61} -8.47019 q^{62} +10.4667 q^{63} -5.02293 q^{64} +0.183476 q^{66} +3.91715 q^{67} +6.88490 q^{68} +1.43226 q^{69} -13.6724 q^{71} +1.96786 q^{72} -11.5529 q^{73} -11.4638 q^{74} +8.14711 q^{76} -1.81979 q^{77} +1.91495 q^{78} -1.43448 q^{79} +8.68916 q^{81} -17.2000 q^{82} -1.73047 q^{83} -1.08627 q^{84} +3.17906 q^{86} -1.66419 q^{87} -0.342141 q^{88} -1.07999 q^{89} -18.9932 q^{91} +12.7130 q^{92} -0.825214 q^{93} -16.3502 q^{94} -1.38059 q^{96} +16.0883 q^{97} +10.4329 q^{98} -1.52882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * 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 $

$2$	1.91122	1.35144	0.675720	−	0.737159i	$-0.263833\pi$
$2$	1.91122	1.35144	0.675720	+	0.737159i	$0.263833\pi$
$3$	0.186202	0.107504	0.0537520	−	0.998554i	$-0.482882\pi$
$3$	0.186202	0.107504	0.0537520	+	0.998554i	$0.482882\pi$
$4$	1.65278	0.826388
$5$	0	0
$5$	0	0
$6$	0.355874	0.145285
$7$	−3.52970	−1.33410	−0.667050	−	0.745013i	$-0.732443\pi$
$7$	−3.52970	−1.33410	−0.667050	+	0.745013i	$0.732443\pi$
$8$	−0.663624	−0.234627
$9$	−2.96533	−0.988443
$10$	0	0
$11$	0.515564	0.155448	0.0777242	−	0.996975i	$-0.475235\pi$
$11$	0.515564	0.155448	0.0777242	+	0.996975i	$0.475235\pi$
$12$	0.307750	0.0888399
$13$	5.38098	1.49242	0.746208	−	0.665712i	$-0.231872\pi$
$13$	5.38098	1.49242	0.746208	+	0.665712i	$0.231872\pi$
$14$	−6.74604	−1.80295
$15$	0	0
$16$	−4.57388	−1.14347
$17$	4.16566	1.01032	0.505161	−	0.863025i	$-0.331433\pi$
$17$	4.16566	1.01032	0.505161	+	0.863025i	$0.331433\pi$
$18$	−5.66741	−1.33582
$19$	4.92935	1.13087	0.565436	−	0.824792i	$-0.308708\pi$
$19$	4.92935	1.13087	0.565436	+	0.824792i	$0.308708\pi$
$20$	0	0
$21$	−0.657237	−0.143421
$22$	0.985358	0.210079
$23$	7.69193	1.60388	0.801940	−	0.597405i	$-0.203802\pi$
$23$	7.69193	1.60388	0.801940	+	0.597405i	$0.203802\pi$
$24$	−0.123568	−0.0252233
$25$	0	0
$26$	10.2843	2.01691
$27$	−1.11076	−0.213765
$28$	−5.83379	−1.10248
$29$	−8.93755	−1.65966	−0.829831	−	0.558015i	$-0.811563\pi$
$29$	−8.93755	−1.65966	−0.829831	+	0.558015i	$0.811563\pi$
$30$	0	0
$31$	−4.43182	−0.795978	−0.397989	−	0.917390i	$-0.630292\pi$
$31$	−4.43182	−0.795978	−0.397989	+	0.917390i	$0.630292\pi$
$32$	−7.41447	−1.31070
$33$	0.0959992	0.0167113
$34$	7.96151	1.36539
$35$	0	0
$36$	−4.90102	−0.816837
$37$	−5.99816	−0.986091	−0.493046	−	0.870003i	$-0.664116\pi$
$37$	−5.99816	−0.986091	−0.493046	+	0.870003i	$0.664116\pi$
$38$	9.42110	1.52830
$39$	1.00195	0.160441
$40$	0	0
$41$	−8.99946	−1.40548	−0.702740	−	0.711447i	$-0.748040\pi$
$41$	−8.99946	−1.40548	−0.702740	+	0.711447i	$0.748040\pi$
$42$	−1.25613	−0.193825
$43$	1.66336	0.253660	0.126830	−	0.991924i	$-0.459520\pi$
$43$	1.66336	0.253660	0.126830	+	0.991924i	$0.459520\pi$
$44$	0.852112	0.128461
$45$	0	0
$46$	14.7010	2.16754
$47$	−8.55484	−1.24785	−0.623926	−	0.781483i	$-0.714463\pi$
$47$	−8.55484	−1.24785	−0.623926	+	0.781483i	$0.714463\pi$
$48$	−0.851668	−0.122928
$49$	5.45876	0.779823
$50$	0	0
$51$	0.775656	0.108614
$52$	8.89356	1.23331
$53$	−13.1736	−1.80954	−0.904769	−	0.425903i	$-0.859957\pi$
$53$	−13.1736	−1.80954	−0.904769	+	0.425903i	$0.859957\pi$
$54$	−2.12291	−0.288891
$55$	0	0
$56$	2.34239	0.313015
$57$	0.917857	0.121573
$58$	−17.0817	−2.24293
$59$	9.25521	1.20493	0.602463	−	0.798147i	$-0.294186\pi$
$59$	9.25521	1.20493	0.602463	+	0.798147i	$0.294186\pi$
$60$	0	0
$61$	−10.4203	−1.33418	−0.667090	−	0.744978i	$-0.732460\pi$
$61$	−10.4203	−1.33418	−0.667090	+	0.744978i	$0.732460\pi$
$62$	−8.47019	−1.07572
$63$	10.4667	1.31868
$64$	−5.02293	−0.627867
$65$	0	0
$66$	0.183476	0.0225843
$67$	3.91715	0.478555	0.239278	−	0.970951i	$-0.423089\pi$
$67$	3.91715	0.478555	0.239278	+	0.970951i	$0.423089\pi$
$68$	6.88490	0.834917
$69$	1.43226	0.172423
$70$	0	0
$71$	−13.6724	−1.62262	−0.811308	−	0.584619i	$-0.801244\pi$
$71$	−13.6724	−1.62262	−0.811308	+	0.584619i	$0.801244\pi$
$72$	1.96786	0.231915
$73$	−11.5529	−1.35217	−0.676083	−	0.736825i	$-0.736324\pi$
$73$	−11.5529	−1.35217	−0.676083	+	0.736825i	$0.736324\pi$
$74$	−11.4638	−1.33264
$75$	0	0
$76$	8.14711	0.934538
$77$	−1.81979	−0.207384
$78$	1.91495	0.216826
$79$	−1.43448	−0.161391	−0.0806956	−	0.996739i	$-0.525714\pi$
$79$	−1.43448	−0.161391	−0.0806956	+	0.996739i	$0.525714\pi$
$80$	0	0
$81$	8.68916	0.965462
$82$	−17.2000	−1.89942
$83$	−1.73047	−0.189944	−0.0949720	−	0.995480i	$-0.530276\pi$
$83$	−1.73047	−0.189944	−0.0949720	+	0.995480i	$0.530276\pi$
$84$	−1.08627	−0.118521
$85$	0	0
$86$	3.17906	0.342807
$87$	−1.66419	−0.178420
$88$	−0.342141	−0.0364724
$89$	−1.07999	−0.114478	−0.0572392	−	0.998360i	$-0.518230\pi$
$89$	−1.07999	−0.114478	−0.0572392	+	0.998360i	$0.518230\pi$
$90$	0	0
$91$	−18.9932	−1.99103
$92$	12.7130	1.32543
$93$	−0.825214	−0.0855707
$94$	−16.3502	−1.68640
$95$	0	0
$96$	−1.38059	−0.140906
$97$	16.0883	1.63352	0.816759	−	0.576979i	$-0.195769\pi$
$97$	16.0883	1.63352	0.816759	+	0.576979i	$0.195769\pi$
$98$	10.4329	1.05388
$99$	−1.52882	−0.153652
$100$	0	0
$101$	−1.23922	−0.123307	−0.0616536	−	0.998098i	$-0.519637\pi$
$101$	−1.23922	−0.123307	−0.0616536	+	0.998098i	$0.519637\pi$
$102$	1.48245	0.146785
$103$	−5.27633	−0.519892	−0.259946	−	0.965623i	$-0.583705\pi$
$103$	−5.27633	−0.519892	−0.259946	+	0.965623i	$0.583705\pi$
$104$	−3.57095	−0.350161
$105$	0	0
$106$	−25.1778	−2.44548
$107$	−10.7822	−1.04236	−0.521178	−	0.853448i	$-0.674507\pi$
$107$	−10.7822	−1.04236	−0.521178	+	0.853448i	$0.674507\pi$
$108$	−1.83583	−0.176653
$109$	−1.15255	−0.110394	−0.0551972	−	0.998475i	$-0.517579\pi$
$109$	−1.15255	−0.110394	−0.0551972	+	0.998475i	$0.517579\pi$
$110$	0	0
$111$	−1.11687	−0.106009
$112$	16.1444	1.52550
$113$	8.70999	0.819367	0.409684	−	0.912228i	$-0.365639\pi$
$113$	8.70999	0.819367	0.409684	+	0.912228i	$0.365639\pi$
$114$	1.75423	0.164299
$115$	0	0
$116$	−14.7718	−1.37152
$117$	−15.9564	−1.47517
$118$	17.6888	1.62838
$119$	−14.7035	−1.34787
$120$	0	0
$121$	−10.7342	−0.975836
$122$	−19.9155	−1.80306
$123$	−1.67572	−0.151095
$124$	−7.32480	−0.657786
$125$	0	0
$126$	20.0042	1.78212
$127$	8.22063	0.729463	0.364732	−	0.931113i	$-0.381161\pi$
$127$	8.22063	0.729463	0.364732	+	0.931113i	$0.381161\pi$
$128$	5.22899	0.462181
$129$	0.309722	0.0272695
$130$	0	0
$131$	−7.30323	−0.638086	−0.319043	−	0.947740i	$-0.603362\pi$
$131$	−7.30323	−0.638086	−0.319043	+	0.947740i	$0.603362\pi$
$132$	0.158665	0.0138100
$133$	−17.3991	−1.50870
$134$	7.48654	0.646739
$135$	0	0
$136$	−2.76444	−0.237048
$137$	−5.95317	−0.508614	−0.254307	−	0.967124i	$-0.581847\pi$
$137$	−5.95317	−0.508614	−0.254307	+	0.967124i	$0.581847\pi$
$138$	2.73736	0.233020
$139$	14.9650	1.26931	0.634656	−	0.772795i	$-0.281142\pi$
$139$	14.9650	1.26931	0.634656	+	0.772795i	$0.281142\pi$
$140$	0	0
$141$	−1.59293	−0.134149
$142$	−26.1310	−2.19287
$143$	2.77424	0.231994
$144$	13.5631	1.13026
$145$	0	0
$146$	−22.0802	−1.82737
$147$	1.01643	0.0838340
$148$	−9.91361	−0.814894
$149$	−0.130576	−0.0106972	−0.00534860	−	0.999986i	$-0.501703\pi$
$149$	−0.130576	−0.0106972	−0.00534860	+	0.999986i	$0.501703\pi$
$150$	0	0
$151$	0.276102	0.0224688	0.0112344	−	0.999937i	$-0.496424\pi$
$151$	0.276102	0.0224688	0.0112344	+	0.999937i	$0.496424\pi$
$152$	−3.27124	−0.265333
$153$	−12.3526	−0.998645
$154$	−3.47802	−0.280267
$155$	0	0
$156$	1.65600	0.132586
$157$	−16.1044	−1.28527	−0.642636	−	0.766172i	$-0.722159\pi$
$157$	−16.1044	−1.28527	−0.642636	+	0.766172i	$0.722159\pi$
$158$	−2.74160	−0.218110
$159$	−2.45296	−0.194532
$160$	0	0
$161$	−27.1502	−2.13973
$162$	16.6069	1.30476
$163$	18.5215	1.45071	0.725357	−	0.688373i	$-0.241675\pi$
$163$	18.5215	1.45071	0.725357	+	0.688373i	$0.241675\pi$
$164$	−14.8741	−1.16147
$165$	0	0
$166$	−3.30732	−0.256698
$167$	−15.5017	−1.19956	−0.599779	−	0.800166i	$-0.704745\pi$
$167$	−15.5017	−1.19956	−0.599779	+	0.800166i	$0.704745\pi$
$168$	0.436159	0.0336504
$169$	15.9550	1.22731
$170$	0	0
$171$	−14.6172	−1.11780
$172$	2.74916	0.209622
$173$	0.366438	0.0278597	0.0139299	−	0.999903i	$-0.495566\pi$
$173$	0.366438	0.0278597	0.0139299	+	0.999903i	$0.495566\pi$
$174$	−3.18064	−0.241124
$175$	0	0
$176$	−2.35813	−0.177751
$177$	1.72334	0.129534
$178$	−2.06410	−0.154711
$179$	12.8719	0.962090	0.481045	−	0.876696i	$-0.340257\pi$
$179$	12.8719	0.962090	0.481045	+	0.876696i	$0.340257\pi$
$180$	0	0
$181$	−12.2125	−0.907746	−0.453873	−	0.891066i	$-0.649958\pi$
$181$	−12.2125	−0.907746	−0.453873	+	0.891066i	$0.649958\pi$
$182$	−36.3003	−2.69076
$183$	−1.94028	−0.143429
$184$	−5.10456	−0.376313
$185$	0	0
$186$	−1.57717	−0.115644
$187$	2.14767	0.157053
$188$	−14.1392	−1.03121
$189$	3.92064	0.285184
$190$	0	0
$191$	−3.92400	−0.283930	−0.141965	−	0.989872i	$-0.545342\pi$
$191$	−3.92400	−0.283930	−0.141965	+	0.989872i	$0.545342\pi$
$192$	−0.935281	−0.0674981
$193$	1.69319	0.121879	0.0609393	−	0.998141i	$-0.480590\pi$
$193$	1.69319	0.121879	0.0609393	+	0.998141i	$0.480590\pi$
$194$	30.7483	2.20760
$195$	0	0
$196$	9.02210	0.644436
$197$	2.20382	0.157016	0.0785080	−	0.996913i	$-0.474984\pi$
$197$	2.20382	0.157016	0.0785080	+	0.996913i	$0.474984\pi$
$198$	−2.92191	−0.207651
$199$	−15.5533	−1.10255	−0.551274	−	0.834324i	$-0.685858\pi$
$199$	−15.5533	−1.10255	−0.551274	+	0.834324i	$0.685858\pi$
$200$	0	0
$201$	0.729381	0.0514466
$202$	−2.36843	−0.166642
$203$	31.5468	2.21415
$204$	1.28198	0.0897569
$205$	0	0
$206$	−10.0842	−0.702603
$207$	−22.8091	−1.58534
$208$	−24.6120	−1.70654
$209$	2.54140	0.175792
$210$	0	0
$211$	6.55996	0.451606	0.225803	−	0.974173i	$-0.427499\pi$
$211$	6.55996	0.451606	0.225803	+	0.974173i	$0.427499\pi$
$212$	−21.7731	−1.49538
$213$	−2.54583	−0.174438
$214$	−20.6072	−1.40868
$215$	0	0
$216$	0.737126	0.0501551
$217$	15.6430	1.06191
$218$	−2.20278	−0.149191
$219$	−2.15118	−0.145363
$220$	0	0
$221$	22.4154	1.50782
$222$	−2.13459	−0.143264
$223$	−6.53800	−0.437817	−0.218908	−	0.975745i	$-0.570250\pi$
$223$	−6.53800	−0.437817	−0.218908	+	0.975745i	$0.570250\pi$
$224$	26.1708	1.74861
$225$	0	0
$226$	16.6467	1.10732
$227$	−16.1673	−1.07306	−0.536530	−	0.843881i	$-0.680265\pi$
$227$	−16.1673	−1.07306	−0.536530	+	0.843881i	$0.680265\pi$
$228$	1.51701	0.100466
$229$	0.0208412	0.00137722	0.000688612	−	1.00000i	$-0.499781\pi$
$229$	0.0208412	0.00137722	0.000688612		1.00000i	$0.499781\pi$
$230$	0	0
$231$	−0.338848	−0.0222946
$232$	5.93118	0.389401
$233$	0.651845	0.0427038	0.0213519	−	0.999772i	$-0.493203\pi$
$233$	0.651845	0.0427038	0.0213519	+	0.999772i	$0.493203\pi$
$234$	−30.4962	−1.99360
$235$	0	0
$236$	15.2968	0.995736
$237$	−0.267103	−0.0173502
$238$	−28.1017	−1.82156
$239$	−8.99997	−0.582160	−0.291080	−	0.956699i	$-0.594015\pi$
$239$	−8.99997	−0.582160	−0.291080	+	0.956699i	$0.594015\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−20.5154	−1.31878
$243$	4.95021	0.317556
$244$	−17.2224	−1.10255
$245$	0	0
$246$	−3.20268	−0.204195
$247$	26.5248	1.68773
$248$	2.94106	0.186758
$249$	−0.322218	−0.0204197
$250$	0	0
$251$	16.4986	1.04138	0.520691	−	0.853745i	$-0.325674\pi$
$251$	16.4986	1.04138	0.520691	+	0.853745i	$0.325674\pi$
$252$	17.2991	1.08974
$253$	3.96569	0.249321
$254$	15.7115	0.985825
$255$	0	0
$256$	20.0396	1.25248
$257$	−7.99029	−0.498420	−0.249210	−	0.968449i	$-0.580171\pi$
$257$	−7.99029	−0.498420	−0.249210	+	0.968449i	$0.580171\pi$
$258$	0.591948	0.0368530
$259$	21.1717	1.31554
$260$	0	0
$261$	26.5028	1.64048
$262$	−13.9581	−0.862335
$263$	5.47488	0.337595	0.168798	−	0.985651i	$-0.446012\pi$
$263$	5.47488	0.337595	0.168798	+	0.985651i	$0.446012\pi$
$264$	−0.0637074	−0.00392092
$265$	0	0
$266$	−33.2536	−2.03891
$267$	−0.201096	−0.0123069
$268$	6.47416	0.395472
$269$	−2.34697	−0.143097	−0.0715486	−	0.997437i	$-0.522794\pi$
$269$	−2.34697	−0.143097	−0.0715486	+	0.997437i	$0.522794\pi$
$270$	0	0
$271$	1.60301	0.0973758	0.0486879	−	0.998814i	$-0.484496\pi$
$271$	1.60301	0.0973758	0.0486879	+	0.998814i	$0.484496\pi$
$272$	−19.0533	−1.15527
$273$	−3.53658	−0.214044
$274$	−11.3778	−0.687360
$275$	0	0
$276$	2.36720	0.142488
$277$	21.6775	1.30247	0.651237	−	0.758875i	$-0.274250\pi$
$277$	21.6775	1.30247	0.651237	+	0.758875i	$0.274250\pi$
$278$	28.6014	1.71540
$279$	13.1418	0.786779
$280$	0	0
$281$	26.9010	1.60478	0.802388	−	0.596802i	$-0.203562\pi$
$281$	26.9010	1.60478	0.802388	+	0.596802i	$0.203562\pi$
$282$	−3.04445	−0.181294
$283$	−3.89230	−0.231373	−0.115687	−	0.993286i	$-0.536907\pi$
$283$	−3.89230	−0.231373	−0.115687	+	0.993286i	$0.536907\pi$
$284$	−22.5974	−1.34091
$285$	0	0
$286$	5.30220	0.313526
$287$	31.7654	1.87505
$288$	21.9863	1.29556
$289$	0.352752	0.0207501
$290$	0	0
$291$	2.99567	0.175610
$292$	−19.0944	−1.11741
$293$	5.57389	0.325630	0.162815	−	0.986657i	$-0.447943\pi$
$293$	5.57389	0.325630	0.162815	+	0.986657i	$0.447943\pi$
$294$	1.94263	0.113297
$295$	0	0
$296$	3.98053	0.231363
$297$	−0.572667	−0.0332295
$298$	−0.249560	−0.0144566
$299$	41.3902	2.39366
$300$	0	0
$301$	−5.87116	−0.338408
$302$	0.527692	0.0303652
$303$	−0.230746	−0.0132560
$304$	−22.5463	−1.29312
$305$	0	0
$306$	−23.6085	−1.34961
$307$	−23.0795	−1.31722	−0.658608	−	0.752486i	$-0.728854\pi$
$307$	−23.0795	−1.31722	−0.658608	+	0.752486i	$0.728854\pi$
$308$	−3.00770	−0.171379
$309$	−0.982465	−0.0558905
$310$	0	0
$311$	−14.9884	−0.849916	−0.424958	−	0.905213i	$-0.639711\pi$
$311$	−14.9884	−0.849916	−0.424958	+	0.905213i	$0.639711\pi$
$312$	−0.664919	−0.0376437
$313$	2.31082	0.130615	0.0653076	−	0.997865i	$-0.479197\pi$
$313$	2.31082	0.130615	0.0653076	+	0.997865i	$0.479197\pi$
$314$	−30.7791	−1.73697
$315$	0	0
$316$	−2.37087	−0.133372
$317$	18.3630	1.03137	0.515684	−	0.856779i	$-0.327538\pi$
$317$	18.3630	1.03137	0.515684	+	0.856779i	$0.327538\pi$
$318$	−4.68816	−0.262899
$319$	−4.60788	−0.257992
$320$	0	0
$321$	−2.00767	−0.112057
$322$	−51.8901	−2.89172
$323$	20.5340	1.14254
$324$	14.3612	0.797846
$325$	0	0
$326$	35.3987	1.96055
$327$	−0.214608	−0.0118678
$328$	5.97226	0.329763
$329$	30.1960	1.66476
$330$	0	0
$331$	−6.47933	−0.356136	−0.178068	−	0.984018i	$-0.556985\pi$
$331$	−6.47933	−0.356136	−0.178068	+	0.984018i	$0.556985\pi$
$332$	−2.86008	−0.156967
$333$	17.7865	0.974695
$334$	−29.6272	−1.62113
$335$	0	0
$336$	3.00613	0.163998
$337$	3.54257	0.192976	0.0964880	−	0.995334i	$-0.469239\pi$
$337$	3.54257	0.192976	0.0964880	+	0.995334i	$0.469239\pi$
$338$	30.4936	1.65863
$339$	1.62182	0.0880852
$340$	0	0
$341$	−2.28489	−0.123734
$342$	−27.9366	−1.51064
$343$	5.44011	0.293739
$344$	−1.10385	−0.0595155
$345$	0	0
$346$	0.700344	0.0376507
$347$	14.4844	0.777566	0.388783	−	0.921329i	$-0.372896\pi$
$347$	14.4844	0.777566	0.388783	+	0.921329i	$0.372896\pi$
$348$	−2.75053	−0.147444
$349$	−23.6287	−1.26482	−0.632408	−	0.774636i	$-0.717933\pi$
$349$	−23.6287	−1.26482	−0.632408	+	0.774636i	$0.717933\pi$
$350$	0	0
$351$	−5.97697	−0.319027
$352$	−3.82263	−0.203747
$353$	18.2662	0.972209	0.486105	−	0.873901i	$-0.338417\pi$
$353$	18.2662	0.972209	0.486105	+	0.873901i	$0.338417\pi$
$354$	3.29369	0.175058
$355$	0	0
$356$	−1.78498	−0.0946036
$357$	−2.73783	−0.144901
$358$	24.6010	1.30021
$359$	−20.3758	−1.07539	−0.537697	−	0.843138i	$-0.680706\pi$
$359$	−20.3758	−1.07539	−0.537697	+	0.843138i	$0.680706\pi$
$360$	0	0
$361$	5.29852	0.278870
$362$	−23.3408	−1.22676
$363$	−1.99873	−0.104906
$364$	−31.3916	−1.64536
$365$	0	0
$366$	−3.70830	−0.193836
$367$	1.76412	0.0920862	0.0460431	−	0.998939i	$-0.485339\pi$
$367$	1.76412	0.0920862	0.0460431	+	0.998939i	$0.485339\pi$
$368$	−35.1820	−1.83399
$369$	26.6864	1.38924
$370$	0	0
$371$	46.4989	2.41410
$372$	−1.36389	−0.0707146
$373$	32.1736	1.66589	0.832943	−	0.553359i	$-0.186654\pi$
$373$	32.1736	1.66589	0.832943	+	0.553359i	$0.186654\pi$
$374$	4.10467	0.212247
$375$	0	0
$376$	5.67720	0.292779
$377$	−48.0928	−2.47691
$378$	7.49321	0.385409
$379$	−31.3680	−1.61126	−0.805632	−	0.592416i	$-0.798174\pi$
$379$	−31.3680	−1.61126	−0.805632	+	0.592416i	$0.798174\pi$
$380$	0	0
$381$	1.53070	0.0784201
$382$	−7.49963	−0.383715
$383$	−16.8623	−0.861624	−0.430812	−	0.902442i	$-0.641773\pi$
$383$	−16.8623	−0.861624	−0.430812	+	0.902442i	$0.641773\pi$
$384$	0.973649	0.0496863
$385$	0	0
$386$	3.23607	0.164712
$387$	−4.93242	−0.250729
$388$	26.5903	1.34992
$389$	−0.816001	−0.0413729	−0.0206864	−	0.999786i	$-0.506585\pi$
$389$	−0.816001	−0.0413729	−0.0206864	+	0.999786i	$0.506585\pi$
$390$	0	0
$391$	32.0420	1.62043
$392$	−3.62257	−0.182967
$393$	−1.35988	−0.0685968
$394$	4.21200	0.212198
$395$	0	0
$396$	−2.52679	−0.126976
$397$	21.8279	1.09551	0.547755	−	0.836639i	$-0.315483\pi$
$397$	21.8279	1.09551	0.547755	+	0.836639i	$0.315483\pi$
$398$	−29.7259	−1.49003
$399$	−3.23976	−0.162191
$400$	0	0
$401$	−15.4857	−0.773321	−0.386661	−	0.922222i	$-0.626372\pi$
$401$	−15.4857	−0.773321	−0.386661	+	0.922222i	$0.626372\pi$
$402$	1.39401	0.0695269
$403$	−23.8475	−1.18793
$404$	−2.04816	−0.101900
$405$	0	0
$406$	60.2931	2.99229
$407$	−3.09244	−0.153286
$408$	−0.514744	−0.0254836
$409$	26.0377	1.28748	0.643740	−	0.765245i	$-0.277382\pi$
$409$	26.0377	1.28748	0.643740	+	0.765245i	$0.277382\pi$
$410$	0	0
$411$	−1.10849	−0.0546780
$412$	−8.72059	−0.429633
$413$	−32.6681	−1.60749
$414$	−43.5933	−2.14249
$415$	0	0
$416$	−39.8971	−1.95612
$417$	2.78651	0.136456
$418$	4.85718	0.237572
$419$	−33.2204	−1.62292	−0.811462	−	0.584406i	$-0.801328\pi$
$419$	−33.2204	−1.62292	−0.811462	+	0.584406i	$0.801328\pi$
$420$	0	0
$421$	2.90586	0.141623	0.0708115	−	0.997490i	$-0.477441\pi$
$421$	2.90586	0.141623	0.0708115	+	0.997490i	$0.477441\pi$
$422$	12.5375	0.610318
$423$	25.3679	1.23343
$424$	8.74235	0.424566
$425$	0	0
$426$	−4.86565	−0.235742
$427$	36.7804	1.77993
$428$	−17.8206	−0.861390
$429$	0.516570	0.0249402
$430$	0	0
$431$	−28.4892	−1.37228	−0.686139	−	0.727471i	$-0.740696\pi$
$431$	−28.4892	−1.37228	−0.686139	+	0.727471i	$0.740696\pi$
$432$	5.08048	0.244435
$433$	28.9311	1.39034	0.695169	−	0.718846i	$-0.255329\pi$
$433$	28.9311	1.39034	0.695169	+	0.718846i	$0.255329\pi$
$434$	29.8972	1.43511
$435$	0	0
$436$	−1.90491	−0.0912286
$437$	37.9163	1.81378
$438$	−4.11138	−0.196449
$439$	−8.92156	−0.425803	−0.212901	−	0.977074i	$-0.568291\pi$
$439$	−8.92156	−0.425803	−0.212901	+	0.977074i	$0.568291\pi$
$440$	0	0
$441$	−16.1870	−0.770810
$442$	42.8408	2.03773
$443$	−24.8216	−1.17931	−0.589656	−	0.807655i	$-0.700736\pi$
$443$	−24.8216	−1.17931	−0.589656	+	0.807655i	$0.700736\pi$
$444$	−1.84594	−0.0876042
$445$	0	0
$446$	−12.4956	−0.591683
$447$	−0.0243136	−0.00114999
$448$	17.7294	0.837637
$449$	11.9254	0.562793	0.281397	−	0.959592i	$-0.409202\pi$
$449$	11.9254	0.562793	0.281397	+	0.959592i	$0.409202\pi$
$450$	0	0
$451$	−4.63980	−0.218480
$452$	14.3957	0.677115
$453$	0.0514107	0.00241549
$454$	−30.8993	−1.45018
$455$	0	0
$456$	−0.609112	−0.0285243
$457$	−8.44205	−0.394902	−0.197451	−	0.980313i	$-0.563266\pi$
$457$	−8.44205	−0.394902	−0.197451	+	0.980313i	$0.563266\pi$
$458$	0.0398321	0.00186123
$459$	−4.62704	−0.215972
$460$	0	0
$461$	23.2925	1.08484	0.542419	−	0.840108i	$-0.317509\pi$
$461$	23.2925	1.08484	0.542419	+	0.840108i	$0.317509\pi$
$462$	−0.647614	−0.0301297
$463$	−1.66578	−0.0774152	−0.0387076	−	0.999251i	$-0.512324\pi$
$463$	−1.66578	−0.0774152	−0.0387076	+	0.999251i	$0.512324\pi$
$464$	40.8793	1.89777
$465$	0	0
$466$	1.24582	0.0577116
$467$	6.66428	0.308386	0.154193	−	0.988041i	$-0.450722\pi$
$467$	6.66428	0.308386	0.154193	+	0.988041i	$0.450722\pi$
$468$	−26.3723	−1.21906
$469$	−13.8263	−0.638441
$470$	0	0
$471$	−2.99868	−0.138172
$472$	−6.14198	−0.282708
$473$	0.857570	0.0394311
$474$	−0.510493	−0.0234477
$475$	0	0
$476$	−24.3016	−1.11386
$477$	39.0642	1.78863
$478$	−17.2010	−0.786753
$479$	−13.6902	−0.625523	−0.312762	−	0.949832i	$-0.601254\pi$
$479$	−13.6902	−0.625523	−0.312762	+	0.949832i	$0.601254\pi$
$480$	0	0
$481$	−32.2760	−1.47166
$482$	−1.91122	−0.0870538
$483$	−5.05543	−0.230030
$484$	−17.7412	−0.806419
$485$	0	0
$486$	9.46096	0.429158
$487$	−31.9634	−1.44840	−0.724200	−	0.689590i	$-0.757791\pi$
$487$	−31.9634	−1.44840	−0.724200	+	0.689590i	$0.757791\pi$
$488$	6.91515	0.313034
$489$	3.44874	0.155957
$490$	0	0
$491$	−10.0550	−0.453777	−0.226889	−	0.973921i	$-0.572855\pi$
$491$	−10.0550	−0.453777	−0.226889	+	0.973921i	$0.572855\pi$
$492$	−2.76959	−0.124863
$493$	−37.2308	−1.67679
$494$	50.6948	2.28087
$495$	0	0
$496$	20.2706	0.910178
$497$	48.2594	2.16473
$498$	−0.615830	−0.0275960
$499$	9.14295	0.409295	0.204647	−	0.978836i	$-0.434395\pi$
$499$	9.14295	0.409295	0.204647	+	0.978836i	$0.434395\pi$
$500$	0	0
$501$	−2.88645	−0.128957
$502$	31.5325	1.40736
$503$	27.2050	1.21301	0.606506	−	0.795079i	$-0.292571\pi$
$503$	27.2050	1.21301	0.606506	+	0.795079i	$0.292571\pi$
$504$	−6.94597	−0.309398
$505$	0	0
$506$	7.57931	0.336941
$507$	2.97086	0.131940
$508$	13.5869	0.602819
$509$	7.79598	0.345551	0.172775	−	0.984961i	$-0.444726\pi$
$509$	7.79598	0.345551	0.172775	+	0.984961i	$0.444726\pi$
$510$	0	0
$511$	40.7783	1.80392
$512$	27.8422	1.23046
$513$	−5.47532	−0.241741
$514$	−15.2712	−0.673585
$515$	0	0
$516$	0.511900	0.0225352
$517$	−4.41057	−0.193977
$518$	40.4638	1.77788
$519$	0.0682315	0.00299503
$520$	0	0
$521$	32.6959	1.43243	0.716216	−	0.697878i	$-0.245872\pi$
$521$	32.6959	1.43243	0.716216	+	0.697878i	$0.245872\pi$
$522$	50.6527	2.21701
$523$	7.80136	0.341129	0.170565	−	0.985346i	$-0.445441\pi$
$523$	7.80136	0.341129	0.170565	+	0.985346i	$0.445441\pi$
$524$	−12.0706	−0.527307
$525$	0	0
$526$	10.4637	0.456240
$527$	−18.4615	−0.804194
$528$	−0.439089	−0.0191089
$529$	36.1658	1.57243
$530$	0	0
$531$	−27.4447	−1.19100
$532$	−28.7568	−1.24677
$533$	−48.4260	−2.09756
$534$	−0.384340	−0.0166320
$535$	0	0
$536$	−2.59951	−0.112282
$537$	2.39677	0.103428
$538$	−4.48558	−0.193387
$539$	2.81434	0.121222
$540$	0	0
$541$	22.3971	0.962926	0.481463	−	0.876467i	$-0.340106\pi$
$541$	22.3971	0.962926	0.481463	+	0.876467i	$0.340106\pi$
$542$	3.06371	0.131597
$543$	−2.27399	−0.0975863
$544$	−30.8862	−1.32423
$545$	0	0
$546$	−6.75920	−0.289267
$547$	−37.2322	−1.59193	−0.795966	−	0.605341i	$-0.793037\pi$
$547$	−37.2322	−1.59193	−0.795966	+	0.605341i	$0.793037\pi$
$548$	−9.83925	−0.420312
$549$	30.8995	1.31876
$550$	0	0
$551$	−44.0563	−1.87686
$552$	−0.950480	−0.0404551
$553$	5.06326	0.215312
$554$	41.4305	1.76021
$555$	0	0
$556$	24.7337	1.04894
$557$	27.6457	1.17139	0.585693	−	0.810533i	$-0.300823\pi$
$557$	27.6457	1.17139	0.585693	+	0.810533i	$0.300823\pi$
$558$	25.1169	1.06328
$559$	8.95053	0.378567
$560$	0	0
$561$	0.399900	0.0168838
$562$	51.4138	2.16876
$563$	23.3454	0.983891	0.491945	−	0.870626i	$-0.336286\pi$
$563$	23.3454	0.983891	0.491945	+	0.870626i	$0.336286\pi$
$564$	−2.63276	−0.110859
$565$	0	0
$566$	−7.43905	−0.312687
$567$	−30.6701	−1.28802
$568$	9.07334	0.380709
$569$	2.61346	0.109562	0.0547811	−	0.998498i	$-0.482554\pi$
$569$	2.61346	0.109562	0.0547811	+	0.998498i	$0.482554\pi$
$570$	0	0
$571$	16.9259	0.708326	0.354163	−	0.935184i	$-0.384766\pi$
$571$	16.9259	0.708326	0.354163	+	0.935184i	$0.384766\pi$
$572$	4.58520	0.191717
$573$	−0.730657	−0.0305236
$574$	60.7107	2.53402
$575$	0	0
$576$	14.8946	0.620610
$577$	−4.67534	−0.194637	−0.0973185	−	0.995253i	$-0.531027\pi$
$577$	−4.67534	−0.194637	−0.0973185	+	0.995253i	$0.531027\pi$
$578$	0.674188	0.0280425
$579$	0.315276	0.0131024
$580$	0	0
$581$	6.10804	0.253404
$582$	5.72540	0.237326
$583$	−6.79185	−0.281290
$584$	7.66680	0.317254
$585$	0	0
$586$	10.6530	0.440069
$587$	3.78940	0.156405	0.0782027	−	0.996937i	$-0.475082\pi$
$587$	3.78940	0.156405	0.0782027	+	0.996937i	$0.475082\pi$
$588$	1.67994	0.0692794
$589$	−21.8460	−0.900148
$590$	0	0
$591$	0.410357	0.0168798
$592$	27.4349	1.12757
$593$	6.81434	0.279831	0.139916	−	0.990163i	$-0.455317\pi$
$593$	6.81434	0.279831	0.139916	+	0.990163i	$0.455317\pi$
$594$	−1.09449	−0.0449076
$595$	0	0
$596$	−0.215813	−0.00884004
$597$	−2.89607	−0.118528
$598$	79.1059	3.23488
$599$	−39.7739	−1.62512	−0.812559	−	0.582879i	$-0.801926\pi$
$599$	−39.7739	−1.62512	−0.812559	+	0.582879i	$0.801926\pi$
$600$	0	0
$601$	27.4256	1.11871	0.559356	−	0.828927i	$-0.311048\pi$
$601$	27.4256	1.11871	0.559356	+	0.828927i	$0.311048\pi$
$602$	−11.2211	−0.457338
$603$	−11.6156	−0.473025
$604$	0.456334	0.0185680
$605$	0	0
$606$	−0.441007	−0.0179147
$607$	−20.6168	−0.836811	−0.418405	−	0.908260i	$-0.637411\pi$
$607$	−20.6168	−0.836811	−0.418405	+	0.908260i	$0.637411\pi$
$608$	−36.5485	−1.48224
$609$	5.87409	0.238030
$610$	0	0
$611$	−46.0335	−1.86232
$612$	−20.4160	−0.825268
$613$	12.9127	0.521540	0.260770	−	0.965401i	$-0.416024\pi$
$613$	12.9127	0.521540	0.260770	+	0.965401i	$0.416024\pi$
$614$	−44.1100	−1.78014
$615$	0	0
$616$	1.20765	0.0486578
$617$	−26.3856	−1.06225	−0.531123	−	0.847295i	$-0.678230\pi$
$617$	−26.3856	−1.06225	−0.531123	+	0.847295i	$0.678230\pi$
$618$	−1.87771	−0.0755326
$619$	−2.30850	−0.0927866	−0.0463933	−	0.998923i	$-0.514773\pi$
$619$	−2.30850	−0.0927866	−0.0463933	+	0.998923i	$0.514773\pi$
$620$	0	0
$621$	−8.54387	−0.342854
$622$	−28.6462	−1.14861
$623$	3.81203	0.152726
$624$	−4.58281	−0.183459
$625$	0	0
$626$	4.41649	0.176519
$627$	0.473214	0.0188983
$628$	−26.6170	−1.06213
$629$	−24.9863	−0.996270
$630$	0	0
$631$	−8.60820	−0.342687	−0.171343	−	0.985211i	$-0.554811\pi$
$631$	−8.60820	−0.342687	−0.171343	+	0.985211i	$0.554811\pi$
$632$	0.951953	0.0378667
$633$	1.22148	0.0485494
$634$	35.0958	1.39383
$635$	0	0
$636$	−4.05419	−0.160759
$637$	29.3735	1.16382
$638$	−8.80669	−0.348660
$639$	40.5432	1.60386
$640$	0	0
$641$	−11.7479	−0.464014	−0.232007	−	0.972714i	$-0.574529\pi$
$641$	−11.7479	−0.464014	−0.232007	+	0.972714i	$0.574529\pi$
$642$	−3.83711	−0.151439
$643$	−15.0808	−0.594729	−0.297364	−	0.954764i	$-0.596108\pi$
$643$	−15.0808	−0.594729	−0.297364	+	0.954764i	$0.596108\pi$
$644$	−44.8732	−1.76825
$645$	0	0
$646$	39.2451	1.54408
$647$	5.68014	0.223309	0.111655	−	0.993747i	$-0.464385\pi$
$647$	5.68014	0.223309	0.111655	+	0.993747i	$0.464385\pi$
$648$	−5.76634	−0.226523
$649$	4.77166	0.187304
$650$	0	0
$651$	2.91276	0.114160
$652$	30.6118	1.19885
$653$	48.9941	1.91729	0.958644	−	0.284608i	$-0.0918633\pi$
$653$	48.9941	1.91729	0.958644	+	0.284608i	$0.0918633\pi$
$654$	−0.410163	−0.0160387
$655$	0	0
$656$	41.1625	1.60713
$657$	34.2582	1.33654
$658$	57.7113	2.24982
$659$	−23.5789	−0.918505	−0.459252	−	0.888306i	$-0.651883\pi$
$659$	−23.5789	−0.918505	−0.459252	+	0.888306i	$0.651883\pi$
$660$	0	0
$661$	−38.6322	−1.50262	−0.751310	−	0.659949i	$-0.770578\pi$
$661$	−38.6322	−1.50262	−0.751310	+	0.659949i	$0.770578\pi$
$662$	−12.3835	−0.481296
$663$	4.17379	0.162097
$664$	1.14838	0.0445659
$665$	0	0
$666$	33.9940	1.31724
$667$	−68.7470	−2.66190
$668$	−25.6208	−0.991300
$669$	−1.21739	−0.0470670
$670$	0	0
$671$	−5.37232	−0.207396
$672$	4.87306	0.187983
$673$	37.4530	1.44371	0.721853	−	0.692047i	$-0.243291\pi$
$673$	37.4530	1.44371	0.721853	+	0.692047i	$0.243291\pi$
$674$	6.77064	0.260795
$675$	0	0
$676$	26.3700	1.01423
$677$	−16.0616	−0.617297	−0.308649	−	0.951176i	$-0.599877\pi$
$677$	−16.0616	−0.617297	−0.308649	+	0.951176i	$0.599877\pi$
$678$	3.09966	0.119042
$679$	−56.7868	−2.17928
$680$	0	0
$681$	−3.01038	−0.115358
$682$	−4.36693	−0.167218
$683$	−13.5819	−0.519696	−0.259848	−	0.965649i	$-0.583673\pi$
$683$	−13.5819	−0.519696	−0.259848	+	0.965649i	$0.583673\pi$
$684$	−24.1589	−0.923737
$685$	0	0
$686$	10.3973	0.396970
$687$	0.00388067	0.000148057 0
$688$	−7.60803	−0.290053
$689$	−70.8871	−2.70058
$690$	0	0
$691$	−5.72328	−0.217724	−0.108862	−	0.994057i	$-0.534721\pi$
$691$	−5.72328	−0.217724	−0.108862	+	0.994057i	$0.534721\pi$
$692$	0.605639	0.0230229
$693$	5.39626	0.204987
$694$	27.6830	1.05083
$695$	0	0
$696$	1.10440	0.0418621
$697$	−37.4887	−1.41999
$698$	−45.1597	−1.70932
$699$	0.121375	0.00459083
$700$	0	0
$701$	−20.2921	−0.766421	−0.383211	−	0.923661i	$-0.625182\pi$
$701$	−20.2921	−0.766421	−0.383211	+	0.923661i	$0.625182\pi$
$702$	−11.4233	−0.431146
$703$	−29.5670	−1.11514
$704$	−2.58964	−0.0976009
$705$	0	0
$706$	34.9107	1.31388
$707$	4.37408	0.164504
$708$	2.84829	0.107045
$709$	−31.5398	−1.18450	−0.592251	−	0.805754i	$-0.701761\pi$
$709$	−31.5398	−1.18450	−0.592251	+	0.805754i	$0.701761\pi$
$710$	0	0
$711$	4.25369	0.159526
$712$	0.716706	0.0268597
$713$	−34.0892	−1.27665
$714$	−5.23260	−0.195825
$715$	0	0
$716$	21.2743	0.795059
$717$	−1.67581	−0.0625844
$718$	−38.9427	−1.45333
$719$	−11.0676	−0.412753	−0.206376	−	0.978473i	$-0.566167\pi$
$719$	−11.0676	−0.412753	−0.206376	+	0.978473i	$0.566167\pi$
$720$	0	0
$721$	18.6238	0.693588
$722$	10.1267	0.376875
$723$	−0.186202	−0.00692494
$724$	−20.1845	−0.750150
$725$	0	0
$726$	−3.82002	−0.141774
$727$	49.5631	1.83819	0.919096	−	0.394033i	$-0.128921\pi$
$727$	49.5631	1.83819	0.919096	+	0.394033i	$0.128921\pi$
$728$	12.6044	0.467149
$729$	−25.1457	−0.931324
$730$	0	0
$731$	6.92901	0.256279
$732$	−3.20684	−0.118528
$733$	2.44508	0.0903110	0.0451555	−	0.998980i	$-0.485622\pi$
$733$	2.44508	0.0903110	0.0451555	+	0.998980i	$0.485622\pi$
$734$	3.37162	0.124449
$735$	0	0
$736$	−57.0316	−2.10221
$737$	2.01954	0.0743907
$738$	51.0036	1.87747
$739$	36.9067	1.35764	0.678818	−	0.734307i	$-0.262492\pi$
$739$	36.9067	1.35764	0.678818	+	0.734307i	$0.262492\pi$
$740$	0	0
$741$	4.93897	0.181438
$742$	88.8699	3.26252
$743$	−40.6188	−1.49016	−0.745079	−	0.666976i	$-0.767588\pi$
$743$	−40.6188	−1.49016	−0.745079	+	0.666976i	$0.767588\pi$
$744$	0.547632	0.0200772
$745$	0	0
$746$	61.4909	2.25134
$747$	5.13142	0.187749
$748$	3.54961	0.129787
$749$	38.0579	1.39061
$750$	0	0
$751$	−14.0406	−0.512349	−0.256174	−	0.966631i	$-0.582462\pi$
$751$	−14.0406	−0.512349	−0.256174	+	0.966631i	$0.582462\pi$
$752$	39.1289	1.42688
$753$	3.07207	0.111953
$754$	−91.9161	−3.34739
$755$	0	0
$756$	6.47993	0.235673
$757$	−24.6936	−0.897505	−0.448752	−	0.893656i	$-0.648131\pi$
$757$	−24.6936	−0.897505	−0.448752	+	0.893656i	$0.648131\pi$
$758$	−59.9512	−2.17753
$759$	0.738419	0.0268029
$760$	0	0
$761$	12.6083	0.457051	0.228525	−	0.973538i	$-0.426610\pi$
$761$	12.6083	0.457051	0.228525	+	0.973538i	$0.426610\pi$
$762$	2.92551	0.105980
$763$	4.06816	0.147277
$764$	−6.48548	−0.234636
$765$	0	0
$766$	−32.2276	−1.16443
$767$	49.8021	1.79825
$768$	3.73142	0.134646
$769$	42.1413	1.51965	0.759827	−	0.650125i	$-0.225283\pi$
$769$	42.1413	1.51965	0.759827	+	0.650125i	$0.225283\pi$
$770$	0	0
$771$	−1.48781	−0.0535821
$772$	2.79847	0.100719
$773$	9.62659	0.346244	0.173122	−	0.984900i	$-0.444614\pi$
$773$	9.62659	0.346244	0.173122	+	0.984900i	$0.444614\pi$
$774$	−9.42695	−0.338845
$775$	0	0
$776$	−10.6766	−0.383267
$777$	3.94221	0.141426
$778$	−1.55956	−0.0559129
$779$	−44.3615	−1.58942
$780$	0	0
$781$	−7.04900	−0.252233
$782$	61.2394	2.18992
$783$	9.92745	0.354778
$784$	−24.9677	−0.891705
$785$	0	0
$786$	−2.59903	−0.0927044
$787$	−50.4413	−1.79804	−0.899019	−	0.437909i	$-0.855719\pi$
$787$	−50.4413	−1.79804	−0.899019	+	0.437909i	$0.855719\pi$
$788$	3.64243	0.129756
$789$	1.01943	0.0362928
$790$	0	0
$791$	−30.7436	−1.09312
$792$	1.01456	0.0360508
$793$	−56.0713	−1.99115
$794$	41.7179	1.48051
$795$	0	0
$796$	−25.7062	−0.911131
$797$	−34.3043	−1.21512	−0.607561	−	0.794273i	$-0.707852\pi$
$797$	−34.3043	−1.21512	−0.607561	+	0.794273i	$0.707852\pi$
$798$	−6.19190	−0.219191
$799$	−35.6366	−1.26073
$800$	0	0
$801$	3.20252	0.113155
$802$	−29.5967	−1.04510
$803$	−5.95627	−0.210192
$804$	1.20550	0.0425148
$805$	0	0
$806$	−45.5780	−1.60542
$807$	−0.437011	−0.0153835
$808$	0.822378	0.0289312
$809$	−43.9886	−1.54656	−0.773279	−	0.634066i	$-0.781385\pi$
$809$	−43.9886	−1.54656	−0.773279	+	0.634066i	$0.781385\pi$
$810$	0	0
$811$	−43.0270	−1.51088	−0.755440	−	0.655217i	$-0.772577\pi$
$811$	−43.0270	−1.51088	−0.755440	+	0.655217i	$0.772577\pi$
$812$	52.1398	1.82975
$813$	0.298484	0.0104683
$814$	−5.91034	−0.207157
$815$	0	0
$816$	−3.54776	−0.124196
$817$	8.19930	0.286857
$818$	49.7638	1.73995
$819$	56.3212	1.96802
$820$	0	0
$821$	18.7704	0.655090	0.327545	−	0.944836i	$-0.393779\pi$
$821$	18.7704	0.655090	0.327545	+	0.944836i	$0.393779\pi$
$822$	−2.11858	−0.0738939
$823$	−27.1588	−0.946695	−0.473348	−	0.880876i	$-0.656955\pi$
$823$	−27.1588	−0.946695	−0.473348	+	0.880876i	$0.656955\pi$
$824$	3.50150	0.121981
$825$	0	0
$826$	−62.4360	−2.17243
$827$	−41.5157	−1.44364	−0.721821	−	0.692079i	$-0.756695\pi$
$827$	−41.5157	−1.44364	−0.721821	+	0.692079i	$0.756695\pi$
$828$	−37.6983	−1.31011
$829$	−30.6349	−1.06399	−0.531997	−	0.846746i	$-0.678558\pi$
$829$	−30.6349	−1.06399	−0.531997	+	0.846746i	$0.678558\pi$
$830$	0	0
$831$	4.03640	0.140021
$832$	−27.0283	−0.937039
$833$	22.7394	0.787872
$834$	5.32565	0.184412
$835$	0	0
$836$	4.20036	0.145272
$837$	4.92267	0.170153
$838$	−63.4916	−2.19328
$839$	30.2456	1.04419	0.522097	−	0.852886i	$-0.325150\pi$
$839$	30.2456	1.04419	0.522097	+	0.852886i	$0.325150\pi$
$840$	0	0
$841$	50.8798	1.75447
$842$	5.55375	0.191395
$843$	5.00902	0.172520
$844$	10.8421	0.373202
$845$	0	0
$846$	48.4838	1.66691
$847$	37.8884	1.30186
$848$	60.2547	2.06915
$849$	−0.724755	−0.0248735
$850$	0	0
$851$	−46.1374	−1.58157
$852$	−4.20769	−0.144153
$853$	−42.7734	−1.46453	−0.732267	−	0.681018i	$-0.761538\pi$
$853$	−42.7734	−1.46453	−0.732267	+	0.681018i	$0.761538\pi$
$854$	70.2956	2.40546
$855$	0	0
$856$	7.15534	0.244564
$857$	18.8048	0.642361	0.321181	−	0.947018i	$-0.395920\pi$
$857$	18.8048	0.642361	0.321181	+	0.947018i	$0.395920\pi$
$858$	0.987281	0.0337052
$859$	−8.22676	−0.280693	−0.140347	−	0.990102i	$-0.544822\pi$
$859$	−8.22676	−0.280693	−0.140347	+	0.990102i	$0.544822\pi$
$860$	0	0
$861$	5.91478	0.201575
$862$	−54.4493	−1.85455
$863$	41.8464	1.42447	0.712235	−	0.701941i	$-0.247683\pi$
$863$	41.8464	1.42447	0.712235	+	0.701941i	$0.247683\pi$
$864$	8.23567	0.280183
$865$	0	0
$866$	55.2937	1.87896
$867$	0.0656832	0.00223072
$868$	25.8543	0.877552
$869$	−0.739564	−0.0250880
$870$	0	0
$871$	21.0781	0.714204
$872$	0.764862	0.0259015
$873$	−47.7071	−1.61464
$874$	72.4664	2.45121
$875$	0	0
$876$	−3.55541	−0.120126
$877$	6.11483	0.206483	0.103242	−	0.994656i	$-0.467079\pi$
$877$	6.11483	0.206483	0.103242	+	0.994656i	$0.467079\pi$
$878$	−17.0511	−0.575446
$879$	1.03787	0.0350065
$880$	0	0
$881$	−13.5157	−0.455355	−0.227678	−	0.973737i	$-0.573113\pi$
$881$	−13.5157	−0.455355	−0.227678	+	0.973737i	$0.573113\pi$
$882$	−30.9370	−1.04170
$883$	−38.5489	−1.29727	−0.648637	−	0.761098i	$-0.724661\pi$
$883$	−38.5489	−1.29727	−0.648637	+	0.761098i	$0.724661\pi$
$884$	37.0476	1.24604
$885$	0	0
$886$	−47.4397	−1.59377
$887$	−40.8386	−1.37123	−0.685613	−	0.727966i	$-0.740466\pi$
$887$	−40.8386	−1.37123	−0.685613	+	0.727966i	$0.740466\pi$
$888$	0.741183	0.0248725
$889$	−29.0163	−0.973177
$890$	0	0
$891$	4.47982	0.150080
$892$	−10.8058	−0.361806
$893$	−42.1698	−1.41116
$894$	−0.0464686	−0.00155414
$895$	0	0
$896$	−18.4567	−0.616596
$897$	7.70694	0.257327
$898$	22.7921	0.760581
$899$	39.6096	1.32105
$900$	0	0
$901$	−54.8769	−1.82822
$902$	−8.86770	−0.295262
$903$	−1.09322	−0.0363802
$904$	−5.78016	−0.192245
$905$	0	0
$906$	0.0982574	0.00326438
$907$	34.3321	1.13998	0.569989	−	0.821652i	$-0.306947\pi$
$907$	34.3321	1.13998	0.569989	+	0.821652i	$0.306947\pi$
$908$	−26.7209	−0.886763
$909$	3.67470	0.121882
$910$	0	0
$911$	49.0410	1.62480	0.812400	−	0.583100i	$-0.198160\pi$
$911$	49.0410	1.62480	0.812400	+	0.583100i	$0.198160\pi$
$912$	−4.19817	−0.139015
$913$	−0.892169	−0.0295265
$914$	−16.1346	−0.533686
$915$	0	0
$916$	0.0344458	0.00113812
$917$	25.7782	0.851271
$918$	−8.84331	−0.291873
$919$	48.7329	1.60755	0.803775	−	0.594934i	$-0.202822\pi$
$919$	48.7329	1.60755	0.803775	+	0.594934i	$0.202822\pi$
$920$	0	0
$921$	−4.29745	−0.141606
$922$	44.5171	1.46609
$923$	−73.5710	−2.42162
$924$	−0.560040	−0.0184240
$925$	0	0
$926$	−3.18367	−0.104622
$927$	15.6461	0.513884
$928$	66.2672	2.17533
$929$	52.9031	1.73569	0.867847	−	0.496832i	$-0.165504\pi$
$929$	52.9031	1.73569	0.867847	+	0.496832i	$0.165504\pi$
$930$	0	0
$931$	26.9081	0.881879
$932$	1.07735	0.0352899
$933$	−2.79088	−0.0913693
$934$	12.7369	0.416765
$935$	0	0
$936$	10.5891	0.346114
$937$	16.1310	0.526976	0.263488	−	0.964663i	$-0.415127\pi$
$937$	16.1310	0.526976	0.263488	+	0.964663i	$0.415127\pi$
$938$	−26.4252	−0.862814
$939$	0.430280	0.0140416
$940$	0	0
$941$	10.7225	0.349544	0.174772	−	0.984609i	$-0.444081\pi$
$941$	10.7225	0.349544	0.174772	+	0.984609i	$0.444081\pi$
$942$	−5.73114	−0.186731
$943$	−69.2233	−2.25422
$944$	−42.3323	−1.37780
$945$	0	0
$946$	1.63901	0.0532887
$947$	21.9984	0.714851	0.357426	−	0.933942i	$-0.383655\pi$
$947$	21.9984	0.714851	0.357426	+	0.933942i	$0.383655\pi$
$948$	−0.441460	−0.0143380
$949$	−62.1660	−2.01800
$950$	0	0
$951$	3.41923	0.110876
$952$	9.75762	0.316246
$953$	40.5214	1.31262	0.656309	−	0.754492i	$-0.272117\pi$
$953$	40.5214	1.31262	0.656309	+	0.754492i	$0.272117\pi$
$954$	74.6603	2.41722
$955$	0	0
$956$	−14.8749	−0.481090
$957$	−0.857998	−0.0277351
$958$	−26.1651	−0.845356
$959$	21.0129	0.678542
$960$	0	0
$961$	−11.3590	−0.366419
$962$	−61.6867	−1.98886
$963$	31.9728	1.03031
$964$	−1.65278	−0.0532323
$965$	0	0
$966$	−9.66205	−0.310871
$967$	46.5645	1.49741	0.748706	−	0.662902i	$-0.230676\pi$
$967$	46.5645	1.49741	0.748706	+	0.662902i	$0.230676\pi$
$968$	7.12347	0.228957
$969$	3.82348	0.122828
$970$	0	0
$971$	2.03099	0.0651775	0.0325887	−	0.999469i	$-0.489625\pi$
$971$	2.03099	0.0651775	0.0325887	+	0.999469i	$0.489625\pi$
$972$	8.18159	0.262425
$973$	−52.8218	−1.69339
$974$	−61.0892	−1.95743
$975$	0	0
$976$	47.6611	1.52560
$977$	45.7170	1.46262	0.731308	−	0.682047i	$-0.238910\pi$
$977$	45.7170	1.46262	0.731308	+	0.682047i	$0.238910\pi$
$978$	6.59131	0.210767
$979$	−0.556803	−0.0177955
$980$	0	0
$981$	3.41770	0.109119
$982$	−19.2174	−0.613252
$983$	47.0190	1.49967	0.749837	−	0.661623i	$-0.230132\pi$
$983$	47.0190	1.49967	0.749837	+	0.661623i	$0.230132\pi$
$984$	1.11205	0.0354508
$985$	0	0
$986$	−71.1564	−2.26608
$987$	5.62256	0.178968
$988$	43.8395	1.39472
$989$	12.7945	0.406841
$990$	0	0
$991$	54.4626	1.73006	0.865031	−	0.501718i	$-0.167298\pi$
$991$	54.4626	1.73006	0.865031	+	0.501718i	$0.167298\pi$
$992$	32.8596	1.04329
$993$	−1.20647	−0.0382860
$994$	92.2346	2.92550
$995$	0	0
$996$	−0.532553	−0.0168746
$997$	−13.5868	−0.430297	−0.215149	−	0.976581i	$-0.569024\pi$
$997$	−13.5868	−0.430297	−0.215149	+	0.976581i	$0.569024\pi$
$998$	17.4742	0.553137
$999$	6.66250	0.210792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.f.1.6		7
5.4	even	2		241.2.a.a.1.2	✓	7
15.14	odd	2		2169.2.a.e.1.6		7
20.19	odd	2		3856.2.a.j.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.2	✓	7	5.4	even	2
2169.2.a.e.1.6		7	15.14	odd	2
3856.2.a.j.1.3		7	20.19	odd	2
6025.2.a.f.1.6		7	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)

\(f(q)\)	\(=\)	\(q+1.91122 q^{2} +0.186202 q^{3} +1.65278 q^{4} +0.355874 q^{6} -3.52970 q^{7} -0.663624 q^{8} -2.96533 q^{9} +O(q^{10})\)	\(q+1.91122 q^{2} +0.186202 q^{3} +1.65278 q^{4} +0.355874 q^{6} -3.52970 q^{7} -0.663624 q^{8} -2.96533 q^{9} +0.515564 q^{11} +0.307750 q^{12} +5.38098 q^{13} -6.74604 q^{14} -4.57388 q^{16} +4.16566 q^{17} -5.66741 q^{18} +4.92935 q^{19} -0.657237 q^{21} +0.985358 q^{22} +7.69193 q^{23} -0.123568 q^{24} +10.2843 q^{26} -1.11076 q^{27} -5.83379 q^{28} -8.93755 q^{29} -4.43182 q^{31} -7.41447 q^{32} +0.0959992 q^{33} +7.96151 q^{34} -4.90102 q^{36} -5.99816 q^{37} +9.42110 q^{38} +1.00195 q^{39} -8.99946 q^{41} -1.25613 q^{42} +1.66336 q^{43} +0.852112 q^{44} +14.7010 q^{46} -8.55484 q^{47} -0.851668 q^{48} +5.45876 q^{49} +0.775656 q^{51} +8.89356 q^{52} -13.1736 q^{53} -2.12291 q^{54} +2.34239 q^{56} +0.917857 q^{57} -17.0817 q^{58} +9.25521 q^{59} -10.4203 q^{61} -8.47019 q^{62} +10.4667 q^{63} -5.02293 q^{64} +0.183476 q^{66} +3.91715 q^{67} +6.88490 q^{68} +1.43226 q^{69} -13.6724 q^{71} +1.96786 q^{72} -11.5529 q^{73} -11.4638 q^{74} +8.14711 q^{76} -1.81979 q^{77} +1.91495 q^{78} -1.43448 q^{79} +8.68916 q^{81} -17.2000 q^{82} -1.73047 q^{83} -1.08627 q^{84} +3.17906 q^{86} -1.66419 q^{87} -0.342141 q^{88} -1.07999 q^{89} -18.9932 q^{91} +12.7130 q^{92} -0.825214 q^{93} -16.3502 q^{94} -1.38059 q^{96} +16.0883 q^{97} +10.4329 q^{98} -1.52882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more