LMFDB - Embedded newform 6025.2.a.g.1.10

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			1.10
Root			$0.582513$ 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)

$f(q)$	$=$	$q+2.13419 q^{2} +3.13727 q^{3} +2.55475 q^{4} +6.69551 q^{6} -1.41692 q^{7} +1.18395 q^{8} +6.84244 q^{9} +O(q^{10})$	\(q+2.13419 q^{2} +3.13727 q^{3} +2.55475 q^{4} +6.69551 q^{6} -1.41692 q^{7} +1.18395 q^{8} +6.84244 q^{9} -1.68982 q^{11} +8.01494 q^{12} +4.54068 q^{13} -3.02397 q^{14} -2.58274 q^{16} +3.25758 q^{17} +14.6030 q^{18} -0.0290193 q^{19} -4.44525 q^{21} -3.60639 q^{22} -2.28292 q^{23} +3.71436 q^{24} +9.69066 q^{26} +12.0548 q^{27} -3.61988 q^{28} +8.95147 q^{29} +4.17320 q^{31} -7.87995 q^{32} -5.30141 q^{33} +6.95229 q^{34} +17.4807 q^{36} -0.842329 q^{37} -0.0619326 q^{38} +14.2453 q^{39} +1.39974 q^{41} -9.48700 q^{42} +9.59930 q^{43} -4.31707 q^{44} -4.87217 q^{46} +4.29285 q^{47} -8.10275 q^{48} -4.99234 q^{49} +10.2199 q^{51} +11.6003 q^{52} -7.25448 q^{53} +25.7271 q^{54} -1.67756 q^{56} -0.0910413 q^{57} +19.1041 q^{58} -1.64417 q^{59} -2.40202 q^{61} +8.90640 q^{62} -9.69519 q^{63} -11.6518 q^{64} -11.3142 q^{66} -1.37406 q^{67} +8.32233 q^{68} -7.16212 q^{69} -12.3603 q^{71} +8.10109 q^{72} -11.3841 q^{73} -1.79769 q^{74} -0.0741372 q^{76} +2.39434 q^{77} +30.4022 q^{78} +1.36587 q^{79} +17.2917 q^{81} +2.98730 q^{82} -1.41517 q^{83} -11.3565 q^{84} +20.4867 q^{86} +28.0832 q^{87} -2.00065 q^{88} +16.0357 q^{89} -6.43378 q^{91} -5.83229 q^{92} +13.0925 q^{93} +9.16173 q^{94} -24.7215 q^{96} +13.8845 q^{97} -10.6546 q^{98} -11.5625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.13419	1.50910	0.754549	−	0.656244i	$-0.227856\pi$
$2$	2.13419	1.50910	0.754549	+	0.656244i	$0.227856\pi$
$3$	3.13727	1.81130	0.905651	−	0.424024i	$-0.139383\pi$
$3$	3.13727	1.81130	0.905651	+	0.424024i	$0.139383\pi$
$4$	2.55475	1.27738
$5$	0	0
$5$	0	0
$6$	6.69551	2.73343
$7$	−1.41692	−0.535545	−0.267773	−	0.963482i	$-0.586288\pi$
$7$	−1.41692	−0.535545	−0.267773	+	0.963482i	$0.586288\pi$
$8$	1.18395	0.418589
$9$	6.84244	2.28081
$10$	0	0
$11$	−1.68982	−0.509499	−0.254750	−	0.967007i	$-0.581993\pi$
$11$	−1.68982	−0.509499	−0.254750	+	0.967007i	$0.581993\pi$
$12$	8.01494	2.31371
$13$	4.54068	1.25936	0.629679	−	0.776855i	$-0.283186\pi$
$13$	4.54068	1.25936	0.629679	+	0.776855i	$0.283186\pi$
$14$	−3.02397	−0.808190
$15$	0	0
$16$	−2.58274	−0.645686
$17$	3.25758	0.790080	0.395040	−	0.918664i	$-0.370731\pi$
$17$	3.25758	0.790080	0.395040	+	0.918664i	$0.370731\pi$
$18$	14.6030	3.44197
$19$	−0.0290193	−0.00665749	−0.00332874	−	0.999994i	$-0.501060\pi$
$19$	−0.0290193	−0.00665749	−0.00332874	+	0.999994i	$0.501060\pi$
$20$	0	0
$21$	−4.44525	−0.970034
$22$	−3.60639	−0.768884
$23$	−2.28292	−0.476021	−0.238011	−	0.971263i	$-0.576495\pi$
$23$	−2.28292	−0.476021	−0.238011	+	0.971263i	$0.576495\pi$
$24$	3.71436	0.758190
$25$	0	0
$26$	9.69066	1.90049
$27$	12.0548	2.31994
$28$	−3.61988	−0.684093
$29$	8.95147	1.66225	0.831123	−	0.556088i	$-0.187698\pi$
$29$	8.95147	1.66225	0.831123	+	0.556088i	$0.187698\pi$
$30$	0	0
$31$	4.17320	0.749530	0.374765	−	0.927120i	$-0.377723\pi$
$31$	4.17320	0.749530	0.374765	+	0.927120i	$0.377723\pi$
$32$	−7.87995	−1.39299
$33$	−5.30141	−0.922857
$34$	6.95229	1.19231
$35$	0	0
$36$	17.4807	2.91346
$37$	−0.842329	−0.138478	−0.0692390	−	0.997600i	$-0.522057\pi$
$37$	−0.842329	−0.138478	−0.0692390	+	0.997600i	$0.522057\pi$
$38$	−0.0619326	−0.0100468
$39$	14.2453	2.28108
$40$	0	0
$41$	1.39974	0.218602	0.109301	−	0.994009i	$-0.465139\pi$
$41$	1.39974	0.218602	0.109301	+	0.994009i	$0.465139\pi$
$42$	−9.48700	−1.46388
$43$	9.59930	1.46388	0.731940	−	0.681369i	$-0.238615\pi$
$43$	9.59930	1.46388	0.731940	+	0.681369i	$0.238615\pi$
$44$	−4.31707	−0.650822
$45$	0	0
$46$	−4.87217	−0.718363
$47$	4.29285	0.626176	0.313088	−	0.949724i	$-0.398637\pi$
$47$	4.29285	0.626176	0.313088	+	0.949724i	$0.398637\pi$
$48$	−8.10275	−1.16953
$49$	−4.99234	−0.713191
$50$	0	0
$51$	10.2199	1.43107
$52$	11.6003	1.60867
$53$	−7.25448	−0.996480	−0.498240	−	0.867039i	$-0.666020\pi$
$53$	−7.25448	−0.996480	−0.498240	+	0.867039i	$0.666020\pi$
$54$	25.7271	3.50102
$55$	0	0
$56$	−1.67756	−0.224173
$57$	−0.0910413	−0.0120587
$58$	19.1041	2.50849
$59$	−1.64417	−0.214053	−0.107026	−	0.994256i	$-0.534133\pi$
$59$	−1.64417	−0.214053	−0.107026	+	0.994256i	$0.534133\pi$
$60$	0	0
$61$	−2.40202	−0.307547	−0.153774	−	0.988106i	$-0.549143\pi$
$61$	−2.40202	−0.307547	−0.153774	+	0.988106i	$0.549143\pi$
$62$	8.90640	1.13111
$63$	−9.69519	−1.22148
$64$	−11.6518	−1.45647
$65$	0	0
$66$	−11.3142	−1.39268
$67$	−1.37406	−0.167868	−0.0839340	−	0.996471i	$-0.526748\pi$
$67$	−1.37406	−0.167868	−0.0839340	+	0.996471i	$0.526748\pi$
$68$	8.32233	1.00923
$69$	−7.16212	−0.862218
$70$	0	0
$71$	−12.3603	−1.46690	−0.733450	−	0.679744i	$-0.762091\pi$
$71$	−12.3603	−1.46690	−0.733450	+	0.679744i	$0.762091\pi$
$72$	8.10109	0.954722
$73$	−11.3841	−1.33241	−0.666203	−	0.745771i	$-0.732081\pi$
$73$	−11.3841	−1.33241	−0.666203	+	0.745771i	$0.732081\pi$
$74$	−1.79769	−0.208977
$75$	0	0
$76$	−0.0741372	−0.00850412
$77$	2.39434	0.272860
$78$	30.4022	3.44237
$79$	1.36587	0.153673	0.0768365	−	0.997044i	$-0.475518\pi$
$79$	1.36587	0.153673	0.0768365	+	0.997044i	$0.475518\pi$
$80$	0	0
$81$	17.2917	1.92130
$82$	2.98730	0.329893
$83$	−1.41517	−0.155335	−0.0776677	−	0.996979i	$-0.524747\pi$
$83$	−1.41517	−0.155335	−0.0776677	+	0.996979i	$0.524747\pi$
$84$	−11.3565	−1.23910
$85$	0	0
$86$	20.4867	2.20914
$87$	28.0832	3.01083
$88$	−2.00065	−0.213271
$89$	16.0357	1.69978	0.849890	−	0.526960i	$-0.176668\pi$
$89$	16.0357	1.69978	0.849890	+	0.526960i	$0.176668\pi$
$90$	0	0
$91$	−6.43378	−0.674443
$92$	−5.83229	−0.608059
$93$	13.0925	1.35762
$94$	9.16173	0.944961
$95$	0	0
$96$	−24.7215	−2.52313
$97$	13.8845	1.40976	0.704878	−	0.709329i	$-0.251002\pi$
$97$	13.8845	1.40976	0.704878	+	0.709329i	$0.251002\pi$
$98$	−10.6546	−1.07628
$99$	−11.5625	−1.16207
$100$	0	0
$101$	13.0057	1.29411	0.647057	−	0.762441i	$-0.275999\pi$
$101$	13.0057	1.29411	0.647057	+	0.762441i	$0.275999\pi$
$102$	21.8112	2.15963
$103$	4.36747	0.430339	0.215170	−	0.976577i	$-0.430970\pi$
$103$	4.36747	0.430339	0.215170	+	0.976577i	$0.430970\pi$
$104$	5.37592	0.527153
$105$	0	0
$106$	−15.4824	−1.50379
$107$	−0.147506	−0.0142600	−0.00712998	−	0.999975i	$-0.502270\pi$
$107$	−0.147506	−0.0142600	−0.00712998	+	0.999975i	$0.502270\pi$
$108$	30.7969	2.96344
$109$	−8.77329	−0.840329	−0.420164	−	0.907448i	$-0.638028\pi$
$109$	−8.77329	−0.840329	−0.420164	+	0.907448i	$0.638028\pi$
$110$	0	0
$111$	−2.64261	−0.250825
$112$	3.65954	0.345794
$113$	−19.2572	−1.81156	−0.905782	−	0.423744i	$-0.860716\pi$
$113$	−19.2572	−1.81156	−0.905782	+	0.423744i	$0.860716\pi$
$114$	−0.194299	−0.0181978
$115$	0	0
$116$	22.8688	2.12332
$117$	31.0693	2.87236
$118$	−3.50897	−0.323027
$119$	−4.61574	−0.423124
$120$	0	0
$121$	−8.14452	−0.740411
$122$	−5.12636	−0.464119
$123$	4.39135	0.395955
$124$	10.6615	0.957432
$125$	0	0
$126$	−20.6913	−1.84333
$127$	−2.11479	−0.187657	−0.0938285	−	0.995588i	$-0.529911\pi$
$127$	−2.11479	−0.187657	−0.0938285	+	0.995588i	$0.529911\pi$
$128$	−9.10722	−0.804972
$129$	30.1156	2.65153
$130$	0	0
$131$	−14.7741	−1.29082	−0.645411	−	0.763835i	$-0.723314\pi$
$131$	−14.7741	−1.29082	−0.645411	+	0.763835i	$0.723314\pi$
$132$	−13.5438	−1.17884
$133$	0.0411180	0.00356539
$134$	−2.93250	−0.253329
$135$	0	0
$136$	3.85681	0.330719
$137$	1.02554	0.0876181	0.0438090	−	0.999040i	$-0.486051\pi$
$137$	1.02554	0.0876181	0.0438090	+	0.999040i	$0.486051\pi$
$138$	−15.2853	−1.30117
$139$	−22.5840	−1.91555	−0.957774	−	0.287523i	$-0.907168\pi$
$139$	−22.5840	−1.91555	−0.957774	+	0.287523i	$0.907168\pi$
$140$	0	0
$141$	13.4678	1.13419
$142$	−26.3792	−2.21369
$143$	−7.67292	−0.641642
$144$	−17.6723	−1.47269
$145$	0	0
$146$	−24.2957	−2.01073
$147$	−15.6623	−1.29180
$148$	−2.15194	−0.176889
$149$	−23.3333	−1.91154	−0.955771	−	0.294113i	$-0.904976\pi$
$149$	−23.3333	−1.91154	−0.955771	+	0.294113i	$0.904976\pi$
$150$	0	0
$151$	4.93814	0.401860	0.200930	−	0.979606i	$-0.435604\pi$
$151$	4.93814	0.401860	0.200930	+	0.979606i	$0.435604\pi$
$152$	−0.0343573	−0.00278675
$153$	22.2898	1.80203
$154$	5.10996	0.411772
$155$	0	0
$156$	36.3933	2.91379
$157$	−5.60129	−0.447031	−0.223516	−	0.974700i	$-0.571753\pi$
$157$	−5.60129	−0.447031	−0.223516	+	0.974700i	$0.571753\pi$
$158$	2.91503	0.231907
$159$	−22.7592	−1.80493
$160$	0	0
$161$	3.23471	0.254931
$162$	36.9036	2.89942
$163$	3.31371	0.259550	0.129775	−	0.991543i	$-0.458575\pi$
$163$	3.31371	0.259550	0.129775	+	0.991543i	$0.458575\pi$
$164$	3.57599	0.279238
$165$	0	0
$166$	−3.02024	−0.234416
$167$	15.9618	1.23516	0.617580	−	0.786508i	$-0.288113\pi$
$167$	15.9618	1.23516	0.617580	+	0.786508i	$0.288113\pi$
$168$	−5.26294	−0.406045
$169$	7.61777	0.585983
$170$	0	0
$171$	−0.198563	−0.0151845
$172$	24.5238	1.86993
$173$	4.91042	0.373333	0.186666	−	0.982423i	$-0.440232\pi$
$173$	4.91042	0.373333	0.186666	+	0.982423i	$0.440232\pi$
$174$	59.9347	4.54364
$175$	0	0
$176$	4.36436	0.328976
$177$	−5.15820	−0.387714
$178$	34.2232	2.56513
$179$	−9.12327	−0.681905	−0.340953	−	0.940081i	$-0.610750\pi$
$179$	−9.12327	−0.681905	−0.340953	+	0.940081i	$0.610750\pi$
$180$	0	0
$181$	−20.5517	−1.52759	−0.763796	−	0.645457i	$-0.776667\pi$
$181$	−20.5517	−1.52759	−0.763796	+	0.645457i	$0.776667\pi$
$182$	−13.7309	−1.01780
$183$	−7.53578	−0.557061
$184$	−2.70285	−0.199257
$185$	0	0
$186$	27.9417	2.04879
$187$	−5.50472	−0.402545
$188$	10.9672	0.799862
$189$	−17.0806	−1.24243
$190$	0	0
$191$	−1.77616	−0.128518	−0.0642592	−	0.997933i	$-0.520468\pi$
$191$	−1.77616	−0.128518	−0.0642592	+	0.997933i	$0.520468\pi$
$192$	−36.5548	−2.63811
$193$	−7.62661	−0.548976	−0.274488	−	0.961591i	$-0.588508\pi$
$193$	−7.62661	−0.548976	−0.274488	+	0.961591i	$0.588508\pi$
$194$	29.6321	2.12746
$195$	0	0
$196$	−12.7542	−0.911014
$197$	10.3385	0.736588	0.368294	−	0.929709i	$-0.379942\pi$
$197$	10.3385	0.736588	0.368294	+	0.929709i	$0.379942\pi$
$198$	−24.6765	−1.75368
$199$	−12.2216	−0.866363	−0.433181	−	0.901307i	$-0.642609\pi$
$199$	−12.2216	−0.866363	−0.433181	+	0.901307i	$0.642609\pi$
$200$	0	0
$201$	−4.31079	−0.304059
$202$	27.7566	1.95295
$203$	−12.6835	−0.890208
$204$	26.1094	1.82802
$205$	0	0
$206$	9.32099	0.649424
$207$	−15.6207	−1.08572
$208$	−11.7274	−0.813149
$209$	0.0490374	0.00339198
$210$	0	0
$211$	3.70984	0.255396	0.127698	−	0.991813i	$-0.459241\pi$
$211$	3.70984	0.255396	0.127698	+	0.991813i	$0.459241\pi$
$212$	−18.5334	−1.27288
$213$	−38.7776	−2.65700
$214$	−0.314806	−0.0215197
$215$	0	0
$216$	14.2722	0.971100
$217$	−5.91309	−0.401407
$218$	−18.7238	−1.26814
$219$	−35.7149	−2.41339
$220$	0	0
$221$	14.7916	0.994994
$222$	−5.63982	−0.378520
$223$	26.6367	1.78373	0.891864	−	0.452303i	$-0.149398\pi$
$223$	26.6367	1.78373	0.891864	+	0.452303i	$0.149398\pi$
$224$	11.1653	0.746010
$225$	0	0
$226$	−41.0984	−2.73383
$227$	13.0135	0.863734	0.431867	−	0.901937i	$-0.357855\pi$
$227$	13.0135	0.863734	0.431867	+	0.901937i	$0.357855\pi$
$228$	−0.232588	−0.0154035
$229$	−27.4396	−1.81326	−0.906631	−	0.421924i	$-0.861355\pi$
$229$	−27.4396	−1.81326	−0.906631	+	0.421924i	$0.861355\pi$
$230$	0	0
$231$	7.51167	0.494232
$232$	10.5981	0.695797
$233$	−15.1309	−0.991257	−0.495629	−	0.868535i	$-0.665062\pi$
$233$	−15.1309	−0.991257	−0.495629	+	0.868535i	$0.665062\pi$
$234$	66.3077	4.33467
$235$	0	0
$236$	−4.20045	−0.273426
$237$	4.28511	0.278348
$238$	−9.85084	−0.638535
$239$	4.36373	0.282266	0.141133	−	0.989991i	$-0.454925\pi$
$239$	4.36373	0.282266	0.141133	+	0.989991i	$0.454925\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−17.3819	−1.11735
$243$	18.0843	1.16011
$244$	−6.13657	−0.392854
$245$	0	0
$246$	9.37197	0.597535
$247$	−0.131767	−0.00838416
$248$	4.94085	0.313744
$249$	−4.43978	−0.281359
$250$	0	0
$251$	−19.0199	−1.20053	−0.600263	−	0.799803i	$-0.704937\pi$
$251$	−19.0199	−1.20053	−0.600263	+	0.799803i	$0.704937\pi$
$252$	−24.7688	−1.56029
$253$	3.85772	0.242533
$254$	−4.51335	−0.283193
$255$	0	0
$256$	3.86710	0.241694
$257$	11.3876	0.710337	0.355168	−	0.934802i	$-0.384424\pi$
$257$	11.3876	0.710337	0.355168	+	0.934802i	$0.384424\pi$
$258$	64.2722	4.00141
$259$	1.19351	0.0741612
$260$	0	0
$261$	61.2499	3.79127
$262$	−31.5308	−1.94798
$263$	−23.6544	−1.45859	−0.729297	−	0.684198i	$-0.760153\pi$
$263$	−23.6544	−1.45859	−0.729297	+	0.684198i	$0.760153\pi$
$264$	−6.27659	−0.386297
$265$	0	0
$266$	0.0877536	0.00538052
$267$	50.3082	3.07881
$268$	−3.51038	−0.214431
$269$	−7.25723	−0.442481	−0.221241	−	0.975219i	$-0.571011\pi$
$269$	−7.25723	−0.442481	−0.221241	+	0.975219i	$0.571011\pi$
$270$	0	0
$271$	32.1081	1.95043	0.975214	−	0.221263i	$-0.0710180\pi$
$271$	32.1081	1.95043	0.975214	+	0.221263i	$0.0710180\pi$
$272$	−8.41350	−0.510143
$273$	−20.1845	−1.22162
$274$	2.18870	0.132224
$275$	0	0
$276$	−18.2975	−1.10138
$277$	10.1379	0.609129	0.304564	−	0.952492i	$-0.401489\pi$
$277$	10.1379	0.609129	0.304564	+	0.952492i	$0.401489\pi$
$278$	−48.1984	−2.89075
$279$	28.5549	1.70954
$280$	0	0
$281$	18.0463	1.07655	0.538277	−	0.842768i	$-0.319075\pi$
$281$	18.0463	1.07655	0.538277	+	0.842768i	$0.319075\pi$
$282$	28.7428	1.71161
$283$	21.0113	1.24899	0.624497	−	0.781027i	$-0.285304\pi$
$283$	21.0113	1.24899	0.624497	+	0.781027i	$0.285304\pi$
$284$	−31.5775	−1.87378
$285$	0	0
$286$	−16.3754	−0.968301
$287$	−1.98332	−0.117072
$288$	−53.9181	−3.17715
$289$	−6.38814	−0.375773
$290$	0	0
$291$	43.5593	2.55349
$292$	−29.0835	−1.70198
$293$	−8.72888	−0.509947	−0.254973	−	0.966948i	$-0.582067\pi$
$293$	−8.72888	−0.509947	−0.254973	+	0.966948i	$0.582067\pi$
$294$	−33.4263	−1.94946
$295$	0	0
$296$	−0.997273	−0.0579653
$297$	−20.3703	−1.18201
$298$	−49.7977	−2.88470
$299$	−10.3660	−0.599481
$300$	0	0
$301$	−13.6014	−0.783974
$302$	10.5389	0.606446
$303$	40.8023	2.34403
$304$	0.0749494	0.00429864
$305$	0	0
$306$	47.5707	2.71943
$307$	5.92354	0.338075	0.169037	−	0.985610i	$-0.445934\pi$
$307$	5.92354	0.338075	0.169037	+	0.985610i	$0.445934\pi$
$308$	6.11694	0.348545
$309$	13.7019	0.779475
$310$	0	0
$311$	−19.8778	−1.12716	−0.563582	−	0.826060i	$-0.690577\pi$
$311$	−19.8778	−1.12716	−0.563582	+	0.826060i	$0.690577\pi$
$312$	16.8657	0.954833
$313$	1.96825	0.111252	0.0556262	−	0.998452i	$-0.482285\pi$
$313$	1.96825	0.111252	0.0556262	+	0.998452i	$0.482285\pi$
$314$	−11.9542	−0.674614
$315$	0	0
$316$	3.48947	0.196298
$317$	−0.249169	−0.0139947	−0.00699736	−	0.999976i	$-0.502227\pi$
$317$	−0.249169	−0.0139947	−0.00699736	+	0.999976i	$0.502227\pi$
$318$	−48.5725	−2.72381
$319$	−15.1264	−0.846914
$320$	0	0
$321$	−0.462766	−0.0258291
$322$	6.90348	0.384716
$323$	−0.0945329	−0.00525995
$324$	44.1759	2.45422
$325$	0	0
$326$	7.07208	0.391686
$327$	−27.5241	−1.52209
$328$	1.65722	0.0915045
$329$	−6.08262	−0.335345
$330$	0	0
$331$	1.37786	0.0757338	0.0378669	−	0.999283i	$-0.487944\pi$
$331$	1.37786	0.0757338	0.0378669	+	0.999283i	$0.487944\pi$
$332$	−3.61542	−0.198422
$333$	−5.76358	−0.315842
$334$	34.0654	1.86398
$335$	0	0
$336$	11.4809	0.626337
$337$	−7.81509	−0.425715	−0.212858	−	0.977083i	$-0.568277\pi$
$337$	−7.81509	−0.425715	−0.212858	+	0.977083i	$0.568277\pi$
$338$	16.2578	0.884305
$339$	−60.4149	−3.28129
$340$	0	0
$341$	−7.05195	−0.381885
$342$	−0.423770	−0.0229149
$343$	16.9922	0.917491
$344$	11.3651	0.612763
$345$	0	0
$346$	10.4798	0.563396
$347$	11.3046	0.606863	0.303432	−	0.952853i	$-0.401868\pi$
$347$	11.3046	0.606863	0.303432	+	0.952853i	$0.401868\pi$
$348$	71.7455	3.84596
$349$	8.21132	0.439542	0.219771	−	0.975551i	$-0.429469\pi$
$349$	8.21132	0.439542	0.219771	+	0.975551i	$0.429469\pi$
$350$	0	0
$351$	54.7368	2.92163
$352$	13.3157	0.709728
$353$	−10.5958	−0.563955	−0.281978	−	0.959421i	$-0.590990\pi$
$353$	−10.5958	−0.563955	−0.281978	+	0.959421i	$0.590990\pi$
$354$	−11.0086	−0.585099
$355$	0	0
$356$	40.9672	2.17126
$357$	−14.4808	−0.766405
$358$	−19.4708	−1.02906
$359$	2.78283	0.146872	0.0734361	−	0.997300i	$-0.476604\pi$
$359$	2.78283	0.146872	0.0734361	+	0.997300i	$0.476604\pi$
$360$	0	0
$361$	−18.9992	−0.999956
$362$	−43.8611	−2.30529
$363$	−25.5515	−1.34111
$364$	−16.4367	−0.861518
$365$	0	0
$366$	−16.0828	−0.840660
$367$	22.8715	1.19388	0.596940	−	0.802286i	$-0.296383\pi$
$367$	22.8715	1.19388	0.596940	+	0.802286i	$0.296383\pi$
$368$	5.89619	0.307360
$369$	9.57763	0.498591
$370$	0	0
$371$	10.2790	0.533660
$372$	33.4480	1.73420
$373$	−19.6760	−1.01879	−0.509393	−	0.860534i	$-0.670130\pi$
$373$	−19.6760	−1.01879	−0.509393	+	0.860534i	$0.670130\pi$
$374$	−11.7481	−0.607480
$375$	0	0
$376$	5.08250	0.262110
$377$	40.6458	2.09336
$378$	−36.4532	−1.87495
$379$	−19.9282	−1.02364	−0.511821	−	0.859092i	$-0.671029\pi$
$379$	−19.9282	−1.02364	−0.511821	+	0.859092i	$0.671029\pi$
$380$	0	0
$381$	−6.63465	−0.339903
$382$	−3.79066	−0.193947
$383$	19.3611	0.989304	0.494652	−	0.869091i	$-0.335296\pi$
$383$	19.3611	0.989304	0.494652	+	0.869091i	$0.335296\pi$
$384$	−28.5718	−1.45805
$385$	0	0
$386$	−16.2766	−0.828458
$387$	65.6826	3.33884
$388$	35.4714	1.80079
$389$	19.3887	0.983048	0.491524	−	0.870864i	$-0.336440\pi$
$389$	19.3887	0.983048	0.491524	+	0.870864i	$0.336440\pi$
$390$	0	0
$391$	−7.43680	−0.376095
$392$	−5.91067	−0.298534
$393$	−46.3504	−2.33807
$394$	22.0643	1.11158
$395$	0	0
$396$	−29.5393	−1.48440
$397$	32.3248	1.62233	0.811167	−	0.584815i	$-0.198833\pi$
$397$	32.3248	1.62233	0.811167	+	0.584815i	$0.198833\pi$
$398$	−26.0831	−1.30743
$399$	0.128998	0.00645799
$400$	0	0
$401$	−25.0648	−1.25168	−0.625839	−	0.779952i	$-0.715243\pi$
$401$	−25.0648	−1.25168	−0.625839	+	0.779952i	$0.715243\pi$
$402$	−9.20002	−0.458856
$403$	18.9492	0.943926
$404$	33.2263	1.65307
$405$	0	0
$406$	−27.0690	−1.34341
$407$	1.42338	0.0705544
$408$	12.0998	0.599031
$409$	−16.2463	−0.803327	−0.401664	−	0.915787i	$-0.631568\pi$
$409$	−16.2463	−0.803327	−0.401664	+	0.915787i	$0.631568\pi$
$410$	0	0
$411$	3.21740	0.158703
$412$	11.1578	0.549706
$413$	2.32966	0.114635
$414$	−33.3376	−1.63845
$415$	0	0
$416$	−35.7803	−1.75427
$417$	−70.8519	−3.46963
$418$	0.104655	0.00511884
$419$	28.6252	1.39843	0.699217	−	0.714909i	$-0.253532\pi$
$419$	28.6252	1.39843	0.699217	+	0.714909i	$0.253532\pi$
$420$	0	0
$421$	−20.1263	−0.980897	−0.490448	−	0.871470i	$-0.663167\pi$
$421$	−20.1263	−0.980897	−0.490448	+	0.871470i	$0.663167\pi$
$422$	7.91749	0.385417
$423$	29.3735	1.42819
$424$	−8.58892	−0.417115
$425$	0	0
$426$	−82.7586	−4.00967
$427$	3.40347	0.164706
$428$	−0.376842	−0.0182153
$429$	−24.0720	−1.16221
$430$	0	0
$431$	4.76674	0.229606	0.114803	−	0.993388i	$-0.463376\pi$
$431$	4.76674	0.229606	0.114803	+	0.993388i	$0.463376\pi$
$432$	−31.1343	−1.49795
$433$	−41.2831	−1.98394	−0.991970	−	0.126470i	$-0.959635\pi$
$433$	−41.2831	−1.98394	−0.991970	+	0.126470i	$0.959635\pi$
$434$	−12.6196	−0.605762
$435$	0	0
$436$	−22.4136	−1.07342
$437$	0.0662487	0.00316911
$438$	−76.2222	−3.64204
$439$	24.9365	1.19015	0.595076	−	0.803669i	$-0.297122\pi$
$439$	24.9365	1.19015	0.595076	+	0.803669i	$0.297122\pi$
$440$	0	0
$441$	−34.1598	−1.62666
$442$	31.5681	1.50154
$443$	29.4802	1.40065	0.700323	−	0.713826i	$-0.253039\pi$
$443$	29.4802	1.40065	0.700323	+	0.713826i	$0.253039\pi$
$444$	−6.75122	−0.320399
$445$	0	0
$446$	56.8478	2.69182
$447$	−73.2029	−3.46238
$448$	16.5097	0.780008
$449$	8.83623	0.417008	0.208504	−	0.978022i	$-0.433141\pi$
$449$	8.83623	0.417008	0.208504	+	0.978022i	$0.433141\pi$
$450$	0	0
$451$	−2.36530	−0.111378
$452$	−49.1974	−2.31405
$453$	15.4922	0.727889
$454$	27.7732	1.30346
$455$	0	0
$456$	−0.107788	−0.00504764
$457$	10.5965	0.495685	0.247842	−	0.968800i	$-0.420278\pi$
$457$	10.5965	0.495685	0.247842	+	0.968800i	$0.420278\pi$
$458$	−58.5613	−2.73639
$459$	39.2694	1.83294
$460$	0	0
$461$	−42.1466	−1.96296	−0.981481	−	0.191558i	$-0.938646\pi$
$461$	−42.1466	−1.96296	−0.981481	+	0.191558i	$0.938646\pi$
$462$	16.0313	0.745844
$463$	−34.1355	−1.58641	−0.793205	−	0.608955i	$-0.791589\pi$
$463$	−34.1355	−1.58641	−0.793205	+	0.608955i	$0.791589\pi$
$464$	−23.1193	−1.07329
$465$	0	0
$466$	−32.2921	−1.49590
$467$	−10.8416	−0.501687	−0.250844	−	0.968028i	$-0.580708\pi$
$467$	−10.8416	−0.501687	−0.250844	+	0.968028i	$0.580708\pi$
$468$	79.3745	3.66909
$469$	1.94693	0.0899009
$470$	0	0
$471$	−17.5727	−0.809709
$472$	−1.94661	−0.0896000
$473$	−16.2211	−0.745846
$474$	9.14523	0.420054
$475$	0	0
$476$	−11.7921	−0.540488
$477$	−49.6384	−2.27278
$478$	9.31300	0.425967
$479$	42.1123	1.92416	0.962079	−	0.272771i	$-0.0879401\pi$
$479$	42.1123	1.92416	0.962079	+	0.272771i	$0.0879401\pi$
$480$	0	0
$481$	−3.82475	−0.174393
$482$	2.13419	0.0972095
$483$	10.1482	0.461757
$484$	−20.8072	−0.945783
$485$	0	0
$486$	38.5952	1.75072
$487$	−22.7869	−1.03257	−0.516287	−	0.856416i	$-0.672686\pi$
$487$	−22.7869	−1.03257	−0.516287	+	0.856416i	$0.672686\pi$
$488$	−2.84387	−0.128736
$489$	10.3960	0.470123
$490$	0	0
$491$	10.4759	0.472771	0.236386	−	0.971659i	$-0.424037\pi$
$491$	10.4759	0.472771	0.236386	+	0.971659i	$0.424037\pi$
$492$	11.2188	0.505784
$493$	29.1602	1.31331
$494$	−0.281216	−0.0126525
$495$	0	0
$496$	−10.7783	−0.483960
$497$	17.5136	0.785591
$498$	−9.47531	−0.424599
$499$	19.1245	0.856129	0.428065	−	0.903748i	$-0.359196\pi$
$499$	19.1245	0.856129	0.428065	+	0.903748i	$0.359196\pi$
$500$	0	0
$501$	50.0764	2.23725
$502$	−40.5920	−1.81171
$503$	16.8341	0.750596	0.375298	−	0.926904i	$-0.377540\pi$
$503$	16.8341	0.750596	0.375298	+	0.926904i	$0.377540\pi$
$504$	−11.4786	−0.511297
$505$	0	0
$506$	8.23309	0.366005
$507$	23.8990	1.06139
$508$	−5.40276	−0.239709
$509$	18.3512	0.813403	0.406701	−	0.913561i	$-0.366679\pi$
$509$	18.3512	0.813403	0.406701	+	0.913561i	$0.366679\pi$
$510$	0	0
$511$	16.1303	0.713563
$512$	26.4675	1.16971
$513$	−0.349821	−0.0154450
$514$	24.3032	1.07197
$515$	0	0
$516$	76.9378	3.38700
$517$	−7.25413	−0.319036
$518$	2.54718	0.111917
$519$	15.4053	0.676218
$520$	0	0
$521$	−7.11176	−0.311572	−0.155786	−	0.987791i	$-0.549791\pi$
$521$	−7.11176	−0.311572	−0.155786	+	0.987791i	$0.549791\pi$
$522$	130.719	5.72141
$523$	−35.5818	−1.55588	−0.777941	−	0.628338i	$-0.783736\pi$
$523$	−35.5818	−1.55588	−0.777941	+	0.628338i	$0.783736\pi$
$524$	−37.7443	−1.64887
$525$	0	0
$526$	−50.4829	−2.20116
$527$	13.5946	0.592189
$528$	13.6922	0.595875
$529$	−17.7883	−0.773404
$530$	0	0
$531$	−11.2501	−0.488215
$532$	0.105046	0.00455434
$533$	6.35577	0.275299
$534$	107.367	4.64623
$535$	0	0
$536$	−1.62681	−0.0702676
$537$	−28.6221	−1.23514
$538$	−15.4883	−0.667748
$539$	8.43614	0.363370
$540$	0	0
$541$	−31.3913	−1.34962	−0.674809	−	0.737992i	$-0.735774\pi$
$541$	−31.3913	−1.34962	−0.674809	+	0.737992i	$0.735774\pi$
$542$	68.5247	2.94339
$543$	−64.4760	−2.76693
$544$	−25.6696	−1.10058
$545$	0	0
$546$	−43.0774	−1.84354
$547$	13.8925	0.593999	0.297000	−	0.954878i	$-0.404014\pi$
$547$	13.8925	0.593999	0.297000	+	0.954878i	$0.404014\pi$
$548$	2.62001	0.111921
$549$	−16.4357	−0.701458
$550$	0	0
$551$	−0.259766	−0.0110664
$552$	−8.47957	−0.360915
$553$	−1.93533	−0.0822988
$554$	21.6362	0.919235
$555$	0	0
$556$	−57.6965	−2.44688
$557$	−21.3096	−0.902919	−0.451459	−	0.892292i	$-0.649096\pi$
$557$	−21.3096	−0.902919	−0.451459	+	0.892292i	$0.649096\pi$
$558$	60.9415	2.57986
$559$	43.5873	1.84355
$560$	0	0
$561$	−17.2698	−0.729131
$562$	38.5142	1.62463
$563$	−4.43966	−0.187110	−0.0935548	−	0.995614i	$-0.529823\pi$
$563$	−4.43966	−0.187110	−0.0935548	+	0.995614i	$0.529823\pi$
$564$	34.4069	1.44879
$565$	0	0
$566$	44.8421	1.88485
$567$	−24.5009	−1.02894
$568$	−14.6340	−0.614027
$569$	−2.37135	−0.0994123	−0.0497061	−	0.998764i	$-0.515828\pi$
$569$	−2.37135	−0.0994123	−0.0497061	+	0.998764i	$0.515828\pi$
$570$	0	0
$571$	11.8257	0.494891	0.247446	−	0.968902i	$-0.420409\pi$
$571$	11.8257	0.494891	0.247446	+	0.968902i	$0.420409\pi$
$572$	−19.6024	−0.819618
$573$	−5.57228	−0.232786
$574$	−4.23277	−0.176672
$575$	0	0
$576$	−79.7267	−3.32195
$577$	−34.2099	−1.42418	−0.712089	−	0.702089i	$-0.752251\pi$
$577$	−34.2099	−1.42418	−0.712089	+	0.702089i	$0.752251\pi$
$578$	−13.6335	−0.567078
$579$	−23.9267	−0.994361
$580$	0	0
$581$	2.00519	0.0831892
$582$	92.9637	3.85347
$583$	12.2588	0.507706
$584$	−13.4781	−0.557730
$585$	0	0
$586$	−18.6291	−0.769560
$587$	22.9609	0.947698	0.473849	−	0.880606i	$-0.342864\pi$
$587$	22.9609	0.947698	0.473849	+	0.880606i	$0.342864\pi$
$588$	−40.0133	−1.65012
$589$	−0.121104	−0.00498998
$590$	0	0
$591$	32.4346	1.33418
$592$	2.17552	0.0894133
$593$	35.4912	1.45745	0.728724	−	0.684808i	$-0.240114\pi$
$593$	35.4912	1.45745	0.728724	+	0.684808i	$0.240114\pi$
$594$	−43.4741	−1.78376
$595$	0	0
$596$	−59.6109	−2.44176
$597$	−38.3423	−1.56924
$598$	−22.1230	−0.904676
$599$	−43.0139	−1.75750	−0.878751	−	0.477280i	$-0.841623\pi$
$599$	−43.0139	−1.75750	−0.878751	+	0.477280i	$0.841623\pi$
$600$	0	0
$601$	−11.3673	−0.463684	−0.231842	−	0.972754i	$-0.574475\pi$
$601$	−11.3673	−0.463684	−0.231842	+	0.972754i	$0.574475\pi$
$602$	−29.0280	−1.18309
$603$	−9.40191	−0.382875
$604$	12.6157	0.513326
$605$	0	0
$606$	87.0798	3.53737
$607$	30.7720	1.24900	0.624499	−	0.781025i	$-0.285303\pi$
$607$	30.7720	1.24900	0.624499	+	0.781025i	$0.285303\pi$
$608$	0.228671	0.00927382
$609$	−39.7916	−1.61244
$610$	0	0
$611$	19.4924	0.788580
$612$	56.9450	2.30187
$613$	12.5473	0.506781	0.253391	−	0.967364i	$-0.418454\pi$
$613$	12.5473	0.506781	0.253391	+	0.967364i	$0.418454\pi$
$614$	12.6419	0.510188
$615$	0	0
$616$	2.83477	0.114216
$617$	30.4582	1.22620	0.613101	−	0.790004i	$-0.289922\pi$
$617$	30.4582	1.22620	0.613101	+	0.790004i	$0.289922\pi$
$618$	29.2424	1.17630
$619$	15.9774	0.642188	0.321094	−	0.947047i	$-0.395949\pi$
$619$	15.9774	0.642188	0.321094	+	0.947047i	$0.395949\pi$
$620$	0	0
$621$	−27.5200	−1.10434
$622$	−42.4229	−1.70100
$623$	−22.7213	−0.910309
$624$	−36.7920	−1.47286
$625$	0	0
$626$	4.20062	0.167891
$627$	0.153843	0.00614391
$628$	−14.3099	−0.571027
$629$	−2.74396	−0.109409
$630$	0	0
$631$	−16.1624	−0.643413	−0.321707	−	0.946839i	$-0.604256\pi$
$631$	−16.1624	−0.643413	−0.321707	+	0.946839i	$0.604256\pi$
$632$	1.61712	0.0643257
$633$	11.6387	0.462599
$634$	−0.531773	−0.0211194
$635$	0	0
$636$	−58.1442	−2.30557
$637$	−22.6686	−0.898163
$638$	−32.2825	−1.27808
$639$	−84.5747	−3.34572
$640$	0	0
$641$	18.3274	0.723891	0.361945	−	0.932199i	$-0.382113\pi$
$641$	18.3274	0.723891	0.361945	+	0.932199i	$0.382113\pi$
$642$	−0.987629	−0.0389786
$643$	−26.2338	−1.03456	−0.517279	−	0.855817i	$-0.673055\pi$
$643$	−26.2338	−1.03456	−0.517279	+	0.855817i	$0.673055\pi$
$644$	8.26389	0.325643
$645$	0	0
$646$	−0.201751	−0.00793778
$647$	42.0543	1.65332	0.826662	−	0.562699i	$-0.190237\pi$
$647$	42.0543	1.65332	0.826662	+	0.562699i	$0.190237\pi$
$648$	20.4724	0.804232
$649$	2.77835	0.109060
$650$	0	0
$651$	−18.5509	−0.727069
$652$	8.46571	0.331543
$653$	31.0303	1.21431	0.607155	−	0.794583i	$-0.292311\pi$
$653$	31.0303	1.21431	0.607155	+	0.794583i	$0.292311\pi$
$654$	−58.7417	−2.29698
$655$	0	0
$656$	−3.61516	−0.141148
$657$	−77.8949	−3.03897
$658$	−12.9814	−0.506069
$659$	−2.55835	−0.0996591	−0.0498296	−	0.998758i	$-0.515868\pi$
$659$	−2.55835	−0.0996591	−0.0498296	+	0.998758i	$0.515868\pi$
$660$	0	0
$661$	38.7318	1.50649	0.753247	−	0.657738i	$-0.228487\pi$
$661$	38.7318	1.50649	0.753247	+	0.657738i	$0.228487\pi$
$662$	2.94060	0.114290
$663$	46.4053	1.80223
$664$	−1.67549	−0.0650216
$665$	0	0
$666$	−12.3006	−0.476637
$667$	−20.4355	−0.791265
$668$	40.7784	1.57776
$669$	83.5666	3.23087
$670$	0	0
$671$	4.05898	0.156695
$672$	35.0284	1.35125
$673$	16.5141	0.636573	0.318287	−	0.947995i	$-0.396893\pi$
$673$	16.5141	0.636573	0.318287	+	0.947995i	$0.396893\pi$
$674$	−16.6789	−0.642446
$675$	0	0
$676$	19.4615	0.748520
$677$	−15.8449	−0.608968	−0.304484	−	0.952517i	$-0.598484\pi$
$677$	−15.8449	−0.608968	−0.304484	+	0.952517i	$0.598484\pi$
$678$	−128.937	−4.95179
$679$	−19.6732	−0.754988
$680$	0	0
$681$	40.8267	1.56448
$682$	−15.0502	−0.576302
$683$	−23.4280	−0.896446	−0.448223	−	0.893922i	$-0.647943\pi$
$683$	−23.4280	−0.896446	−0.448223	+	0.893922i	$0.647943\pi$
$684$	−0.507279	−0.0193963
$685$	0	0
$686$	36.2645	1.38458
$687$	−86.0855	−3.28436
$688$	−24.7925	−0.945206
$689$	−32.9403	−1.25492
$690$	0	0
$691$	−19.6103	−0.746011	−0.373006	−	0.927829i	$-0.621673\pi$
$691$	−19.6103	−0.746011	−0.373006	+	0.927829i	$0.621673\pi$
$692$	12.5449	0.476886
$693$	16.3831	0.622342
$694$	24.1261	0.915816
$695$	0	0
$696$	33.2490	1.26030
$697$	4.55977	0.172714
$698$	17.5245	0.663312
$699$	−47.4696	−1.79547
$700$	0	0
$701$	−21.7449	−0.821293	−0.410647	−	0.911795i	$-0.634697\pi$
$701$	−21.7449	−0.821293	−0.410647	+	0.911795i	$0.634697\pi$
$702$	116.819	4.40903
$703$	0.0244438	0.000921916 0
$704$	19.6894	0.742073
$705$	0	0
$706$	−22.6133	−0.851063
$707$	−18.4280	−0.693057
$708$	−13.1779	−0.495257
$709$	5.87515	0.220646	0.110323	−	0.993896i	$-0.464811\pi$
$709$	5.87515	0.220646	0.110323	+	0.993896i	$0.464811\pi$
$710$	0	0
$711$	9.34592	0.350499
$712$	18.9854	0.711508
$713$	−9.52708	−0.356792
$714$	−30.9047	−1.15658
$715$	0	0
$716$	−23.3077	−0.871050
$717$	13.6902	0.511269
$718$	5.93908	0.221645
$719$	44.3942	1.65562	0.827812	−	0.561006i	$-0.189586\pi$
$719$	44.3942	1.65562	0.827812	+	0.561006i	$0.189586\pi$
$720$	0	0
$721$	−6.18835	−0.230466
$722$	−40.5478	−1.50903
$723$	3.13727	0.116676
$724$	−52.5044	−1.95131
$725$	0	0
$726$	−54.5317	−2.02386
$727$	2.54419	0.0943587	0.0471793	−	0.998886i	$-0.484977\pi$
$727$	2.54419	0.0943587	0.0471793	+	0.998886i	$0.484977\pi$
$728$	−7.61725	−0.282314
$729$	4.86022	0.180008
$730$	0	0
$731$	31.2705	1.15658
$732$	−19.2521	−0.711577
$733$	45.9580	1.69750	0.848750	−	0.528795i	$-0.177356\pi$
$733$	45.9580	1.69750	0.848750	+	0.528795i	$0.177356\pi$
$734$	48.8120	1.80168
$735$	0	0
$736$	17.9893	0.663094
$737$	2.32191	0.0855286
$738$	20.4404	0.752423
$739$	−1.63694	−0.0602158	−0.0301079	−	0.999547i	$-0.509585\pi$
$739$	−1.63694	−0.0602158	−0.0301079	+	0.999547i	$0.509585\pi$
$740$	0	0
$741$	−0.413389	−0.0151862
$742$	21.9373	0.805345
$743$	4.65465	0.170763	0.0853813	−	0.996348i	$-0.472789\pi$
$743$	4.65465	0.170763	0.0853813	+	0.996348i	$0.472789\pi$
$744$	15.5008	0.568286
$745$	0	0
$746$	−41.9923	−1.53745
$747$	−9.68324	−0.354291
$748$	−14.0632	−0.514202
$749$	0.209004	0.00763685
$750$	0	0
$751$	33.9509	1.23889	0.619443	−	0.785042i	$-0.287358\pi$
$751$	33.9509	1.23889	0.619443	+	0.785042i	$0.287358\pi$
$752$	−11.0873	−0.404313
$753$	−59.6705	−2.17451
$754$	86.7457	3.15909
$755$	0	0
$756$	−43.6368	−1.58705
$757$	−18.7173	−0.680293	−0.340147	−	0.940372i	$-0.610477\pi$
$757$	−18.7173	−0.680293	−0.340147	+	0.940372i	$0.610477\pi$
$758$	−42.5305	−1.54478
$759$	12.1027	0.439300
$760$	0	0
$761$	−18.0459	−0.654165	−0.327083	−	0.944996i	$-0.606066\pi$
$761$	−18.0459	−0.654165	−0.327083	+	0.944996i	$0.606066\pi$
$762$	−14.1596	−0.512948
$763$	12.4310	0.450034
$764$	−4.53765	−0.164166
$765$	0	0
$766$	41.3201	1.49296
$767$	−7.46565	−0.269569
$768$	12.1321	0.437780
$769$	−45.8935	−1.65496	−0.827482	−	0.561493i	$-0.810227\pi$
$769$	−45.8935	−1.65496	−0.827482	+	0.561493i	$0.810227\pi$
$770$	0	0
$771$	35.7258	1.28663
$772$	−19.4841	−0.701249
$773$	−50.4996	−1.81635	−0.908173	−	0.418595i	$-0.862523\pi$
$773$	−50.4996	−1.81635	−0.908173	+	0.418595i	$0.862523\pi$
$774$	140.179	5.03863
$775$	0	0
$776$	16.4385	0.590108
$777$	3.74437	0.134328
$778$	41.3792	1.48352
$779$	−0.0406195	−0.00145534
$780$	0	0
$781$	20.8867	0.747384
$782$	−15.8715	−0.567564
$783$	107.908	3.85631
$784$	12.8939	0.460497
$785$	0	0
$786$	−98.9204	−3.52838
$787$	32.5890	1.16167	0.580837	−	0.814020i	$-0.302725\pi$
$787$	32.5890	1.16167	0.580837	+	0.814020i	$0.302725\pi$
$788$	26.4123	0.940900
$789$	−74.2102	−2.64195
$790$	0	0
$791$	27.2859	0.970174
$792$	−13.6894	−0.486430
$793$	−10.9068	−0.387312
$794$	68.9871	2.44826
$795$	0	0
$796$	−31.2230	−1.10667
$797$	8.18770	0.290023	0.145012	−	0.989430i	$-0.453678\pi$
$797$	8.18770	0.290023	0.145012	+	0.989430i	$0.453678\pi$
$798$	0.275306	0.00974574
$799$	13.9843	0.494729
$800$	0	0
$801$	109.723	3.87688
$802$	−53.4930	−1.88890
$803$	19.2370	0.678859
$804$	−11.0130	−0.388398
$805$	0	0
$806$	40.4411	1.42448
$807$	−22.7679	−0.801467
$808$	15.3981	0.541702
$809$	8.91588	0.313465	0.156733	−	0.987641i	$-0.449904\pi$
$809$	8.91588	0.313465	0.156733	+	0.987641i	$0.449904\pi$
$810$	0	0
$811$	33.8174	1.18749	0.593744	−	0.804654i	$-0.297649\pi$
$811$	33.8174	1.18749	0.593744	+	0.804654i	$0.297649\pi$
$812$	−32.4033	−1.13713
$813$	100.732	3.53281
$814$	3.03776	0.106474
$815$	0	0
$816$	−26.3954	−0.924024
$817$	−0.278565	−0.00974576
$818$	−34.6726	−1.21230
$819$	−44.0227	−1.53828
$820$	0	0
$821$	−10.7451	−0.375005	−0.187503	−	0.982264i	$-0.560039\pi$
$821$	−10.7451	−0.375005	−0.187503	+	0.982264i	$0.560039\pi$
$822$	6.86654	0.239498
$823$	−9.35870	−0.326224	−0.163112	−	0.986608i	$-0.552153\pi$
$823$	−9.35870	−0.326224	−0.163112	+	0.986608i	$0.552153\pi$
$824$	5.17085	0.180135
$825$	0	0
$826$	4.97192	0.172995
$827$	−28.1688	−0.979526	−0.489763	−	0.871856i	$-0.662917\pi$
$827$	−28.1688	−0.979526	−0.489763	+	0.871856i	$0.662917\pi$
$828$	−39.9071	−1.38687
$829$	−3.86410	−0.134206	−0.0671028	−	0.997746i	$-0.521376\pi$
$829$	−3.86410	−0.134206	−0.0671028	+	0.997746i	$0.521376\pi$
$830$	0	0
$831$	31.8054	1.10332
$832$	−52.9071	−1.83422
$833$	−16.2630	−0.563478
$834$	−151.211	−5.23602
$835$	0	0
$836$	0.125278	0.00433284
$837$	50.3070	1.73886
$838$	61.0916	2.11037
$839$	−52.0851	−1.79818	−0.899089	−	0.437766i	$-0.855770\pi$
$839$	−52.0851	−1.79818	−0.899089	+	0.437766i	$0.855770\pi$
$840$	0	0
$841$	51.1289	1.76306
$842$	−42.9533	−1.48027
$843$	56.6162	1.94996
$844$	9.47772	0.326237
$845$	0	0
$846$	62.6886	2.15528
$847$	11.5401	0.396523
$848$	18.7365	0.643413
$849$	65.9182	2.26231
$850$	0	0
$851$	1.92297	0.0659185
$852$	−99.0672	−3.39399
$853$	40.9790	1.40309	0.701547	−	0.712623i	$-0.252493\pi$
$853$	40.9790	1.40309	0.701547	+	0.712623i	$0.252493\pi$
$854$	7.26364	0.248557
$855$	0	0
$856$	−0.174640	−0.00596906
$857$	1.91051	0.0652618	0.0326309	−	0.999467i	$-0.489611\pi$
$857$	1.91051	0.0652618	0.0326309	+	0.999467i	$0.489611\pi$
$858$	−51.3741	−1.75388
$859$	48.2469	1.64616	0.823081	−	0.567924i	$-0.192253\pi$
$859$	48.2469	1.64616	0.823081	+	0.567924i	$0.192253\pi$
$860$	0	0
$861$	−6.22219	−0.212052
$862$	10.1731	0.346497
$863$	52.0649	1.77231	0.886155	−	0.463388i	$-0.153366\pi$
$863$	52.0649	1.77231	0.886155	+	0.463388i	$0.153366\pi$
$864$	−94.9909	−3.23165
$865$	0	0
$866$	−88.1059	−2.99396
$867$	−20.0413	−0.680638
$868$	−15.1065	−0.512748
$869$	−2.30808	−0.0782962
$870$	0	0
$871$	−6.23916	−0.211406
$872$	−10.3871	−0.351752
$873$	95.0037	3.21539
$874$	0.141387	0.00478249
$875$	0	0
$876$	−91.2427	−3.08281
$877$	11.6765	0.394288	0.197144	−	0.980375i	$-0.436833\pi$
$877$	11.6765	0.394288	0.197144	+	0.980375i	$0.436833\pi$
$878$	53.2190	1.79606
$879$	−27.3848	−0.923667
$880$	0	0
$881$	−37.1884	−1.25291	−0.626455	−	0.779457i	$-0.715495\pi$
$881$	−37.1884	−1.25291	−0.626455	+	0.779457i	$0.715495\pi$
$882$	−72.9034	−2.45478
$883$	−24.6177	−0.828453	−0.414227	−	0.910174i	$-0.635948\pi$
$883$	−24.6177	−0.828453	−0.414227	+	0.910174i	$0.635948\pi$
$884$	37.7890	1.27098
$885$	0	0
$886$	62.9163	2.11371
$887$	38.9257	1.30700	0.653498	−	0.756928i	$-0.273301\pi$
$887$	38.9257	1.30700	0.653498	+	0.756928i	$0.273301\pi$
$888$	−3.12871	−0.104993
$889$	2.99648	0.100499
$890$	0	0
$891$	−29.2198	−0.978899
$892$	68.0503	2.27849
$893$	−0.124575	−0.00416876
$894$	−156.229	−5.22507
$895$	0	0
$896$	12.9042	0.431099
$897$	−32.5209	−1.08584
$898$	18.8582	0.629305
$899$	37.3563	1.24590
$900$	0	0
$901$	−23.6321	−0.787299
$902$	−5.04800	−0.168080
$903$	−42.6713	−1.42001
$904$	−22.7995	−0.758300
$905$	0	0
$906$	33.0633	1.09846
$907$	−19.1516	−0.635919	−0.317959	−	0.948104i	$-0.602998\pi$
$907$	−19.1516	−0.635919	−0.317959	+	0.948104i	$0.602998\pi$
$908$	33.2462	1.10331
$909$	88.9907	2.95163
$910$	0	0
$911$	−24.8708	−0.824008	−0.412004	−	0.911182i	$-0.635171\pi$
$911$	−24.8708	−0.824008	−0.412004	+	0.911182i	$0.635171\pi$
$912$	0.235136	0.00778614
$913$	2.39138	0.0791433
$914$	22.6150	0.748037
$915$	0	0
$916$	−70.1015	−2.31622
$917$	20.9338	0.691294
$918$	83.8082	2.76608
$919$	15.1200	0.498762	0.249381	−	0.968405i	$-0.419773\pi$
$919$	15.1200	0.498762	0.249381	+	0.968405i	$0.419773\pi$
$920$	0	0
$921$	18.5837	0.612355
$922$	−89.9487	−2.96230
$923$	−56.1242	−1.84735
$924$	19.1905	0.631320
$925$	0	0
$926$	−72.8515	−2.39405
$927$	29.8841	0.981524
$928$	−70.5372	−2.31550
$929$	56.3040	1.84727	0.923637	−	0.383269i	$-0.125202\pi$
$929$	56.3040	1.84727	0.923637	+	0.383269i	$0.125202\pi$
$930$	0	0
$931$	0.144874	0.00474806
$932$	−38.6557	−1.26621
$933$	−62.3619	−2.04164
$934$	−23.1379	−0.757095
$935$	0	0
$936$	36.7844	1.20234
$937$	−38.3794	−1.25380	−0.626900	−	0.779100i	$-0.715676\pi$
$937$	−38.3794	−1.25380	−0.626900	+	0.779100i	$0.715676\pi$
$938$	4.15511	0.135669
$939$	6.17494	0.201511
$940$	0	0
$941$	47.1607	1.53740	0.768698	−	0.639612i	$-0.220905\pi$
$941$	47.1607	1.53740	0.768698	+	0.639612i	$0.220905\pi$
$942$	−37.5035	−1.22193
$943$	−3.19549	−0.104059
$944$	4.24647	0.138211
$945$	0	0
$946$	−34.6188	−1.12555
$947$	4.87531	0.158426	0.0792131	−	0.996858i	$-0.474759\pi$
$947$	4.87531	0.158426	0.0792131	+	0.996858i	$0.474759\pi$
$948$	10.9474	0.355555
$949$	−51.6914	−1.67798
$950$	0	0
$951$	−0.781709	−0.0253487
$952$	−5.46479	−0.177115
$953$	−8.20430	−0.265764	−0.132882	−	0.991132i	$-0.542423\pi$
$953$	−8.20430	−0.265764	−0.132882	+	0.991132i	$0.542423\pi$
$954$	−105.938	−3.42985
$955$	0	0
$956$	11.1482	0.360560
$957$	−47.4554	−1.53402
$958$	89.8754	2.90374
$959$	−1.45311	−0.0469235
$960$	0	0
$961$	−13.5844	−0.438205
$962$	−8.16272	−0.263177
$963$	−1.00930	−0.0325243
$964$	2.55475	0.0822831
$965$	0	0
$966$	21.6580	0.696836
$967$	−43.1483	−1.38756	−0.693778	−	0.720189i	$-0.744055\pi$
$967$	−43.1483	−1.38756	−0.693778	+	0.720189i	$0.744055\pi$
$968$	−9.64268	−0.309927
$969$	−0.296575	−0.00952736
$970$	0	0
$971$	1.33209	0.0427487	0.0213744	−	0.999772i	$-0.493196\pi$
$971$	1.33209	0.0427487	0.0213744	+	0.999772i	$0.493196\pi$
$972$	46.2009	1.48189
$973$	31.9997	1.02586
$974$	−48.6315	−1.55825
$975$	0	0
$976$	6.20380	0.198579
$977$	−33.1504	−1.06057	−0.530287	−	0.847818i	$-0.677916\pi$
$977$	−33.1504	−1.06057	−0.530287	+	0.847818i	$0.677916\pi$
$978$	22.1870	0.709462
$979$	−27.0974	−0.866037
$980$	0	0
$981$	−60.0307	−1.91663
$982$	22.3575	0.713458
$983$	13.6552	0.435533	0.217766	−	0.976001i	$-0.430123\pi$
$983$	13.6552	0.435533	0.217766	+	0.976001i	$0.430123\pi$
$984$	5.19913	0.165742
$985$	0	0
$986$	62.2333	1.98191
$987$	−19.0828	−0.607412
$988$	−0.336633	−0.0107097
$989$	−21.9144	−0.696838
$990$	0	0
$991$	32.5122	1.03278	0.516392	−	0.856352i	$-0.327275\pi$
$991$	32.5122	1.03278	0.516392	+	0.856352i	$0.327275\pi$
$992$	−32.8846	−1.04409
$993$	4.32270	0.137177
$994$	37.3772	1.18553
$995$	0	0
$996$	−11.3425	−0.359402
$997$	48.1685	1.52551	0.762756	−	0.646686i	$-0.223846\pi$
$997$	48.1685	1.52551	0.762756	+	0.646686i	$0.223846\pi$
$998$	40.8152	1.29198
$999$	−10.1541	−0.321261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.10		11
5.4	even	2		1205.2.a.b.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.2	✓	11	5.4	even	2
6025.2.a.g.1.10		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)

\(f(q)\)	\(=\)	\(q+2.13419 q^{2} +3.13727 q^{3} +2.55475 q^{4} +6.69551 q^{6} -1.41692 q^{7} +1.18395 q^{8} +6.84244 q^{9} +O(q^{10})\)	\(q+2.13419 q^{2} +3.13727 q^{3} +2.55475 q^{4} +6.69551 q^{6} -1.41692 q^{7} +1.18395 q^{8} +6.84244 q^{9} -1.68982 q^{11} +8.01494 q^{12} +4.54068 q^{13} -3.02397 q^{14} -2.58274 q^{16} +3.25758 q^{17} +14.6030 q^{18} -0.0290193 q^{19} -4.44525 q^{21} -3.60639 q^{22} -2.28292 q^{23} +3.71436 q^{24} +9.69066 q^{26} +12.0548 q^{27} -3.61988 q^{28} +8.95147 q^{29} +4.17320 q^{31} -7.87995 q^{32} -5.30141 q^{33} +6.95229 q^{34} +17.4807 q^{36} -0.842329 q^{37} -0.0619326 q^{38} +14.2453 q^{39} +1.39974 q^{41} -9.48700 q^{42} +9.59930 q^{43} -4.31707 q^{44} -4.87217 q^{46} +4.29285 q^{47} -8.10275 q^{48} -4.99234 q^{49} +10.2199 q^{51} +11.6003 q^{52} -7.25448 q^{53} +25.7271 q^{54} -1.67756 q^{56} -0.0910413 q^{57} +19.1041 q^{58} -1.64417 q^{59} -2.40202 q^{61} +8.90640 q^{62} -9.69519 q^{63} -11.6518 q^{64} -11.3142 q^{66} -1.37406 q^{67} +8.32233 q^{68} -7.16212 q^{69} -12.3603 q^{71} +8.10109 q^{72} -11.3841 q^{73} -1.79769 q^{74} -0.0741372 q^{76} +2.39434 q^{77} +30.4022 q^{78} +1.36587 q^{79} +17.2917 q^{81} +2.98730 q^{82} -1.41517 q^{83} -11.3565 q^{84} +20.4867 q^{86} +28.0832 q^{87} -2.00065 q^{88} +16.0357 q^{89} -6.43378 q^{91} -5.83229 q^{92} +13.0925 q^{93} +9.16173 q^{94} -24.7215 q^{96} +13.8845 q^{97} -10.6546 q^{98} -11.5625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 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