LMFDB - Embedded newform 1190.2.a.k.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1190,2,Mod(1,1190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1190.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1190 = 2 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1190.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-3,-1,3,3,1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.50219784053$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.3229.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 4 $ x^3 - x^2 - 9*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.77016$ of defining polynomial
Character	$\chi$	$=$	1190.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +2.77016 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77016 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.67380 q^{9} -1.00000 q^{10} +1.67380 q^{11} +2.77016 q^{12} +4.00000 q^{13} -1.00000 q^{14} +2.77016 q^{15} +1.00000 q^{16} +1.00000 q^{17} -4.67380 q^{18} -1.67380 q^{19} +1.00000 q^{20} +2.77016 q^{21} -1.67380 q^{22} -6.77016 q^{23} -2.77016 q^{24} +1.00000 q^{25} -4.00000 q^{26} +4.63669 q^{27} +1.00000 q^{28} +1.22984 q^{29} -2.77016 q^{30} -5.21412 q^{31} -1.00000 q^{32} +4.63669 q^{33} -1.00000 q^{34} +1.00000 q^{35} +4.67380 q^{36} +5.54032 q^{37} +1.67380 q^{38} +11.0806 q^{39} -1.00000 q^{40} -1.67380 q^{41} -2.77016 q^{42} -8.31049 q^{43} +1.67380 q^{44} +4.67380 q^{45} +6.77016 q^{46} +8.31049 q^{47} +2.77016 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.77016 q^{51} +4.00000 q^{52} -4.77016 q^{53} -4.63669 q^{54} +1.67380 q^{55} -1.00000 q^{56} -4.63669 q^{57} -1.22984 q^{58} -4.77016 q^{59} +2.77016 q^{60} +10.0000 q^{61} +5.21412 q^{62} +4.67380 q^{63} +1.00000 q^{64} +4.00000 q^{65} -4.63669 q^{66} +10.7544 q^{67} +1.00000 q^{68} -18.7544 q^{69} -1.00000 q^{70} -12.8879 q^{71} -4.67380 q^{72} -9.08065 q^{73} -5.54032 q^{74} +2.77016 q^{75} -1.67380 q^{76} +1.67380 q^{77} -11.0806 q^{78} +12.8879 q^{79} +1.00000 q^{80} -1.17701 q^{81} +1.67380 q^{82} -13.0806 q^{83} +2.77016 q^{84} +1.00000 q^{85} +8.31049 q^{86} +3.40685 q^{87} -1.67380 q^{88} +8.19273 q^{89} -4.67380 q^{90} +4.00000 q^{91} -6.77016 q^{92} -14.4440 q^{93} -8.31049 q^{94} -1.67380 q^{95} -2.77016 q^{96} +6.00000 q^{97} -1.00000 q^{98} +7.82299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9} - 3 q^{10} + q^{11} - q^{12} + 12 q^{13} - 3 q^{14} - q^{15} + 3 q^{16} + 3 q^{17} - 10 q^{18} - q^{19} + 3 q^{20}+ \cdots + 66 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9 - 3 * q^10 + q^11 - q^12 + 12 * q^13 - 3 * q^14 - q^15 + 3 * q^16 + 3 * q^17 - 10 * q^18 - q^19 + 3 * q^20 - q^21 - q^22 - 11 * q^23 + q^24 + 3 * q^25 - 12 * q^26 - 10 * q^27 + 3 * q^28 + 13 * q^29 + q^30 + 7 * q^31 - 3 * q^32 - 10 * q^33 - 3 * q^34 + 3 * q^35 + 10 * q^36 - 2 * q^37 + q^38 - 4 * q^39 - 3 * q^40 - q^41 + q^42 + 3 * q^43 + q^44 + 10 * q^45 + 11 * q^46 - 3 * q^47 - q^48 + 3 * q^49 - 3 * q^50 - q^51 + 12 * q^52 - 5 * q^53 + 10 * q^54 + q^55 - 3 * q^56 + 10 * q^57 - 13 * q^58 - 5 * q^59 - q^60 + 30 * q^61 - 7 * q^62 + 10 * q^63 + 3 * q^64 + 12 * q^65 + 10 * q^66 - 9 * q^67 + 3 * q^68 - 15 * q^69 - 3 * q^70 - 12 * q^71 - 10 * q^72 + 10 * q^73 + 2 * q^74 - q^75 - q^76 + q^77 + 4 * q^78 + 12 * q^79 + 3 * q^80 + 39 * q^81 + q^82 - 2 * q^83 - q^84 + 3 * q^85 - 3 * q^86 - 23 * q^87 - q^88 + 14 * q^89 - 10 * q^90 + 12 * q^91 - 11 * q^92 - 30 * q^93 + 3 * q^94 - q^95 + q^96 + 18 * q^97 - 3 * q^98 + 66 * q^99

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.77016	1.59935	0.799677	−	0.600431i	$-0.205004\pi$
$3$	2.77016	1.59935	0.799677	+	0.600431i	$0.205004\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.77016	−1.13091
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	4.67380	1.55793
$10$	−1.00000	−0.316228
$11$	1.67380	0.504669	0.252334	−	0.967640i	$-0.418802\pi$
$11$	1.67380	0.504669	0.252334	+	0.967640i	$0.418802\pi$
$12$	2.77016	0.799677
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−1.00000	−0.267261
$15$	2.77016	0.715253
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−4.67380	−1.10162
$19$	−1.67380	−0.383995	−0.191998	−	0.981395i	$-0.561497\pi$
$19$	−1.67380	−0.383995	−0.191998	+	0.981395i	$0.561497\pi$
$20$	1.00000	0.223607
$21$	2.77016	0.604499
$22$	−1.67380	−0.356855
$23$	−6.77016	−1.41168	−0.705838	−	0.708373i	$-0.749429\pi$
$23$	−6.77016	−1.41168	−0.705838	+	0.708373i	$0.749429\pi$
$24$	−2.77016	−0.565457
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	4.63669	0.892331
$28$	1.00000	0.188982
$29$	1.22984	0.228375	0.114188	−	0.993459i	$-0.463574\pi$
$29$	1.22984	0.228375	0.114188	+	0.993459i	$0.463574\pi$
$30$	−2.77016	−0.505760
$31$	−5.21412	−0.936484	−0.468242	−	0.883600i	$-0.655112\pi$
$31$	−5.21412	−0.936484	−0.468242	+	0.883600i	$0.655112\pi$
$32$	−1.00000	−0.176777
$33$	4.63669	0.807144
$34$	−1.00000	−0.171499
$35$	1.00000	0.169031
$36$	4.67380	0.778966
$37$	5.54032	0.910824	0.455412	−	0.890281i	$-0.349492\pi$
$37$	5.54032	0.910824	0.455412	+	0.890281i	$0.349492\pi$
$38$	1.67380	0.271526
$39$	11.0806	1.77432
$40$	−1.00000	−0.158114
$41$	−1.67380	−0.261403	−0.130702	−	0.991422i	$-0.541723\pi$
$41$	−1.67380	−0.261403	−0.130702	+	0.991422i	$0.541723\pi$
$42$	−2.77016	−0.427445
$43$	−8.31049	−1.26734	−0.633669	−	0.773605i	$-0.718452\pi$
$43$	−8.31049	−1.26734	−0.633669	+	0.773605i	$0.718452\pi$
$44$	1.67380	0.252334
$45$	4.67380	0.696729
$46$	6.77016	0.998206
$47$	8.31049	1.21221	0.606104	−	0.795385i	$-0.292731\pi$
$47$	8.31049	1.21221	0.606104	+	0.795385i	$0.292731\pi$
$48$	2.77016	0.399838
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	2.77016	0.387900
$52$	4.00000	0.554700
$53$	−4.77016	−0.655232	−0.327616	−	0.944811i	$-0.606245\pi$
$53$	−4.77016	−0.655232	−0.327616	+	0.944811i	$0.606245\pi$
$54$	−4.63669	−0.630973
$55$	1.67380	0.225695
$56$	−1.00000	−0.133631
$57$	−4.63669	−0.614144
$58$	−1.22984	−0.161486
$59$	−4.77016	−0.621022	−0.310511	−	0.950570i	$-0.600500\pi$
$59$	−4.77016	−0.621022	−0.310511	+	0.950570i	$0.600500\pi$
$60$	2.77016	0.357626
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	5.21412	0.662194
$63$	4.67380	0.588843
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	−4.63669	−0.570737
$67$	10.7544	1.31386	0.656932	−	0.753950i	$-0.271854\pi$
$67$	10.7544	1.31386	0.656932	+	0.753950i	$0.271854\pi$
$68$	1.00000	0.121268
$69$	−18.7544	−2.25777
$70$	−1.00000	−0.119523
$71$	−12.8879	−1.52951	−0.764757	−	0.644319i	$-0.777141\pi$
$71$	−12.8879	−1.52951	−0.764757	+	0.644319i	$0.777141\pi$
$72$	−4.67380	−0.550812
$73$	−9.08065	−1.06281	−0.531405	−	0.847118i	$-0.678336\pi$
$73$	−9.08065	−1.06281	−0.531405	+	0.847118i	$0.678336\pi$
$74$	−5.54032	−0.644050
$75$	2.77016	0.319871
$76$	−1.67380	−0.191998
$77$	1.67380	0.190747
$78$	−11.0806	−1.25464
$79$	12.8879	1.45000	0.725002	−	0.688747i	$-0.241839\pi$
$79$	12.8879	1.45000	0.725002	+	0.688747i	$0.241839\pi$
$80$	1.00000	0.111803
$81$	−1.17701	−0.130779
$82$	1.67380	0.184840
$83$	−13.0806	−1.43579	−0.717894	−	0.696153i	$-0.754894\pi$
$83$	−13.0806	−1.43579	−0.717894	+	0.696153i	$0.754894\pi$
$84$	2.77016	0.302249
$85$	1.00000	0.108465
$86$	8.31049	0.896143
$87$	3.40685	0.365253
$88$	−1.67380	−0.178427
$89$	8.19273	0.868428	0.434214	−	0.900810i	$-0.357026\pi$
$89$	8.19273	0.868428	0.434214	+	0.900810i	$0.357026\pi$
$90$	−4.67380	−0.492661
$91$	4.00000	0.419314
$92$	−6.77016	−0.705838
$93$	−14.4440	−1.49777
$94$	−8.31049	−0.857161
$95$	−1.67380	−0.171728
$96$	−2.77016	−0.282728
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	−1.00000	−0.101015
$99$	7.82299	0.786240
$100$	1.00000	0.100000
$101$	−9.21412	−0.916839	−0.458420	−	0.888736i	$-0.651584\pi$
$101$	−9.21412	−0.916839	−0.458420	+	0.888736i	$0.651584\pi$
$102$	−2.77016	−0.274287
$103$	−1.22984	−0.121180	−0.0605898	−	0.998163i	$-0.519298\pi$
$103$	−1.22984	−0.121180	−0.0605898	+	0.998163i	$0.519298\pi$
$104$	−4.00000	−0.392232
$105$	2.77016	0.270340
$106$	4.77016	0.463319
$107$	−6.88792	−0.665880	−0.332940	−	0.942948i	$-0.608041\pi$
$107$	−6.88792	−0.665880	−0.332940	+	0.942948i	$0.608041\pi$
$108$	4.63669	0.446166
$109$	−5.21412	−0.499422	−0.249711	−	0.968320i	$-0.580336\pi$
$109$	−5.21412	−0.499422	−0.249711	+	0.968320i	$0.580336\pi$
$110$	−1.67380	−0.159590
$111$	15.3476	1.45673
$112$	1.00000	0.0944911
$113$	11.2141	1.05494	0.527468	−	0.849575i	$-0.323142\pi$
$113$	11.2141	1.05494	0.527468	+	0.849575i	$0.323142\pi$
$114$	4.63669	0.434266
$115$	−6.77016	−0.631321
$116$	1.22984	0.114188
$117$	18.6952	1.72837
$118$	4.77016	0.439129
$119$	1.00000	0.0916698
$120$	−2.77016	−0.252880
$121$	−8.19840	−0.745309
$122$	−10.0000	−0.905357
$123$	−4.63669	−0.418076
$124$	−5.21412	−0.468242
$125$	1.00000	0.0894427
$126$	−4.67380	−0.416375
$127$	−10.4282	−0.925357	−0.462678	−	0.886526i	$-0.653112\pi$
$127$	−10.4282	−0.925357	−0.462678	+	0.886526i	$0.653112\pi$
$128$	−1.00000	−0.0883883
$129$	−23.0214	−2.02692
$130$	−4.00000	−0.350823
$131$	15.7331	1.37460	0.687302	−	0.726372i	$-0.258795\pi$
$131$	15.7331	1.37460	0.687302	+	0.726372i	$0.258795\pi$
$132$	4.63669	0.403572
$133$	−1.67380	−0.145137
$134$	−10.7544	−0.929043
$135$	4.63669	0.399063
$136$	−1.00000	−0.0857493
$137$	8.42824	0.720073	0.360037	−	0.932938i	$-0.382764\pi$
$137$	8.42824	0.720073	0.360037	+	0.932938i	$0.382764\pi$
$138$	18.7544	1.59648
$139$	−0.652406	−0.0553364	−0.0276682	−	0.999617i	$-0.508808\pi$
$139$	−0.652406	−0.0553364	−0.0276682	+	0.999617i	$0.508808\pi$
$140$	1.00000	0.0845154
$141$	23.0214	1.93875
$142$	12.8879	1.08153
$143$	6.69519	0.559880
$144$	4.67380	0.389483
$145$	1.22984	0.102132
$146$	9.08065	0.751520
$147$	2.77016	0.228479
$148$	5.54032	0.455412
$149$	−2.65241	−0.217294	−0.108647	−	0.994080i	$-0.534652\pi$
$149$	−2.65241	−0.217294	−0.108647	+	0.994080i	$0.534652\pi$
$150$	−2.77016	−0.226183
$151$	20.5617	1.67329	0.836644	−	0.547747i	$-0.184514\pi$
$151$	20.5617	1.67329	0.836644	+	0.547747i	$0.184514\pi$
$152$	1.67380	0.135763
$153$	4.67380	0.377854
$154$	−1.67380	−0.134878
$155$	−5.21412	−0.418808
$156$	11.0806	0.887162
$157$	−8.00000	−0.638470	−0.319235	−	0.947676i	$-0.603426\pi$
$157$	−8.00000	−0.638470	−0.319235	+	0.947676i	$0.603426\pi$
$158$	−12.8879	−1.02531
$159$	−13.2141	−1.04795
$160$	−1.00000	−0.0790569
$161$	−6.77016	−0.533564
$162$	1.17701	0.0924748
$163$	−9.73305	−0.762352	−0.381176	−	0.924503i	$-0.624481\pi$
$163$	−9.73305	−0.762352	−0.381176	+	0.924503i	$0.624481\pi$
$164$	−1.67380	−0.130702
$165$	4.63669	0.360966
$166$	13.0806	1.01526
$167$	−4.88792	−0.378238	−0.189119	−	0.981954i	$-0.560563\pi$
$167$	−4.88792	−0.378238	−0.189119	+	0.981954i	$0.560563\pi$
$168$	−2.77016	−0.213723
$169$	3.00000	0.230769
$170$	−1.00000	−0.0766965
$171$	−7.82299	−0.598239
$172$	−8.31049	−0.633669
$173$	4.13347	0.314262	0.157131	−	0.987578i	$-0.449775\pi$
$173$	4.13347	0.314262	0.157131	+	0.987578i	$0.449775\pi$
$174$	−3.40685	−0.258273
$175$	1.00000	0.0755929
$176$	1.67380	0.126167
$177$	−13.2141	−0.993234
$178$	−8.19273	−0.614071
$179$	−3.34759	−0.250211	−0.125105	−	0.992143i	$-0.539927\pi$
$179$	−3.34759	−0.250211	−0.125105	+	0.992143i	$0.539927\pi$
$180$	4.67380	0.348364
$181$	22.6210	1.68140	0.840702	−	0.541498i	$-0.182143\pi$
$181$	22.6210	1.68140	0.840702	+	0.541498i	$0.182143\pi$
$182$	−4.00000	−0.296500
$183$	27.7016	2.04776
$184$	6.77016	0.499103
$185$	5.54032	0.407333
$186$	14.4440	1.05908
$187$	1.67380	0.122400
$188$	8.31049	0.606104
$189$	4.63669	0.337269
$190$	1.67380	0.121430
$191$	−2.13347	−0.154373	−0.0771864	−	0.997017i	$-0.524594\pi$
$191$	−2.13347	−0.154373	−0.0771864	+	0.997017i	$0.524594\pi$
$192$	2.77016	0.199919
$193$	−22.5460	−1.62290	−0.811448	−	0.584424i	$-0.801320\pi$
$193$	−22.5460	−1.62290	−0.811448	+	0.584424i	$0.801320\pi$
$194$	−6.00000	−0.430775
$195$	11.0806	0.793502
$196$	1.00000	0.0714286
$197$	−12.6210	−0.899207	−0.449603	−	0.893228i	$-0.648435\pi$
$197$	−12.6210	−0.899207	−0.449603	+	0.893228i	$0.648435\pi$
$198$	−7.82299	−0.555956
$199$	14.7387	1.04480	0.522400	−	0.852700i	$-0.325037\pi$
$199$	14.7387	1.04480	0.522400	+	0.852700i	$0.325037\pi$
$200$	−1.00000	−0.0707107
$201$	29.7916	2.10133
$202$	9.21412	0.648303
$203$	1.22984	0.0863177
$204$	2.77016	0.193950
$205$	−1.67380	−0.116903
$206$	1.22984	0.0856869
$207$	−31.6424	−2.19930
$208$	4.00000	0.277350
$209$	−2.80160	−0.193790
$210$	−2.77016	−0.191159
$211$	1.11208	0.0765589	0.0382794	−	0.999267i	$-0.487812\pi$
$211$	1.11208	0.0765589	0.0382794	+	0.999267i	$0.487812\pi$
$212$	−4.77016	−0.327616
$213$	−35.7016	−2.44623
$214$	6.88792	0.470848
$215$	−8.31049	−0.566770
$216$	−4.63669	−0.315487
$217$	−5.21412	−0.353958
$218$	5.21412	0.353145
$219$	−25.1549	−1.69981
$220$	1.67380	0.112847
$221$	4.00000	0.269069
$222$	−15.3476	−1.03006
$223$	25.7758	1.72608	0.863039	−	0.505138i	$-0.168558\pi$
$223$	25.7758	1.72608	0.863039	+	0.505138i	$0.168558\pi$
$224$	−1.00000	−0.0668153
$225$	4.67380	0.311586
$226$	−11.2141	−0.745952
$227$	−8.05926	−0.534912	−0.267456	−	0.963570i	$-0.586183\pi$
$227$	−8.05926	−0.534912	−0.267456	+	0.963570i	$0.586183\pi$
$228$	−4.63669	−0.307072
$229$	15.0057	0.991603	0.495801	−	0.868436i	$-0.334874\pi$
$229$	15.0057	0.991603	0.495801	+	0.868436i	$0.334874\pi$
$230$	6.77016	0.446411
$231$	4.63669	0.305072
$232$	−1.22984	−0.0807428
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	−18.6952	−1.22214
$235$	8.31049	0.542116
$236$	−4.77016	−0.310511
$237$	35.7016	2.31907
$238$	−1.00000	−0.0648204
$239$	−2.78588	−0.180204	−0.0901018	−	0.995933i	$-0.528719\pi$
$239$	−2.78588	−0.180204	−0.0901018	+	0.995933i	$0.528719\pi$
$240$	2.77016	0.178813
$241$	−6.57743	−0.423690	−0.211845	−	0.977303i	$-0.567947\pi$
$241$	−6.57743	−0.423690	−0.211845	+	0.977303i	$0.567947\pi$
$242$	8.19840	0.527013
$243$	−17.1706	−1.10149
$244$	10.0000	0.640184
$245$	1.00000	0.0638877
$246$	4.63669	0.295624
$247$	−6.69519	−0.426005
$248$	5.21412	0.331097
$249$	−36.2355	−2.29633
$250$	−1.00000	−0.0632456
$251$	−12.7544	−0.805053	−0.402527	−	0.915408i	$-0.631868\pi$
$251$	−12.7544	−0.805053	−0.402527	+	0.915408i	$0.631868\pi$
$252$	4.67380	0.294422
$253$	−11.3319	−0.712429
$254$	10.4282	0.654326
$255$	2.77016	0.173474
$256$	1.00000	0.0625000
$257$	−7.46535	−0.465676	−0.232838	−	0.972516i	$-0.574801\pi$
$257$	−7.46535	−0.465676	−0.232838	+	0.972516i	$0.574801\pi$
$258$	23.0214	1.43325
$259$	5.54032	0.344259
$260$	4.00000	0.248069
$261$	5.74801	0.355793
$262$	−15.7331	−0.971991
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−4.63669	−0.285368
$265$	−4.77016	−0.293029
$266$	1.67380	0.102627
$267$	22.6952	1.38892
$268$	10.7544	0.656932
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	−4.63669	−0.282180
$271$	22.4282	1.36242	0.681209	−	0.732089i	$-0.261454\pi$
$271$	22.4282	1.36242	0.681209	+	0.732089i	$0.261454\pi$
$272$	1.00000	0.0606339
$273$	11.0806	0.670631
$274$	−8.42824	−0.509169
$275$	1.67380	0.100934
$276$	−18.7544	−1.12888
$277$	9.80727	0.589262	0.294631	−	0.955611i	$-0.404803\pi$
$277$	9.80727	0.589262	0.294631	+	0.955611i	$0.404803\pi$
$278$	0.652406	0.0391287
$279$	−24.3697	−1.45898
$280$	−1.00000	−0.0597614
$281$	−32.7387	−1.95303	−0.976514	−	0.215452i	$-0.930877\pi$
$281$	−32.7387	−1.95303	−0.976514	+	0.215452i	$0.930877\pi$
$282$	−23.0214	−1.37090
$283$	−25.7758	−1.53221	−0.766107	−	0.642713i	$-0.777809\pi$
$283$	−25.7758	−1.53221	−0.766107	+	0.642713i	$0.777809\pi$
$284$	−12.8879	−0.764757
$285$	−4.63669	−0.274654
$286$	−6.69519	−0.395895
$287$	−1.67380	−0.0988011
$288$	−4.67380	−0.275406
$289$	1.00000	0.0588235
$290$	−1.22984	−0.0722186
$291$	16.6210	0.974339
$292$	−9.08065	−0.531405
$293$	−11.3476	−0.662934	−0.331467	−	0.943467i	$-0.607543\pi$
$293$	−11.3476	−0.662934	−0.331467	+	0.943467i	$0.607543\pi$
$294$	−2.77016	−0.161559
$295$	−4.77016	−0.277730
$296$	−5.54032	−0.322025
$297$	7.76088	0.450332
$298$	2.65241	0.153650
$299$	−27.0806	−1.56611
$300$	2.77016	0.159935
$301$	−8.31049	−0.479008
$302$	−20.5617	−1.18319
$303$	−25.5246	−1.46635
$304$	−1.67380	−0.0959988
$305$	10.0000	0.572598
$306$	−4.67380	−0.267183
$307$	−29.3162	−1.67316	−0.836581	−	0.547844i	$-0.815449\pi$
$307$	−29.3162	−1.67316	−0.836581	+	0.547844i	$0.815449\pi$
$308$	1.67380	0.0953734
$309$	−3.40685	−0.193809
$310$	5.21412	0.296142
$311$	0.577432	0.0327432	0.0163716	−	0.999866i	$-0.494789\pi$
$311$	0.577432	0.0327432	0.0163716	+	0.999866i	$0.494789\pi$
$312$	−11.0806	−0.627318
$313$	−4.45968	−0.252076	−0.126038	−	0.992025i	$-0.540226\pi$
$313$	−4.45968	−0.252076	−0.126038	+	0.992025i	$0.540226\pi$
$314$	8.00000	0.451466
$315$	4.67380	0.263339
$316$	12.8879	0.725002
$317$	−12.6524	−0.710630	−0.355315	−	0.934747i	$-0.615626\pi$
$317$	−12.6524	−0.710630	−0.355315	+	0.934747i	$0.615626\pi$
$318$	13.2141	0.741011
$319$	2.05850	0.115254
$320$	1.00000	0.0559017
$321$	−19.0806	−1.06498
$322$	6.77016	0.377286
$323$	−1.67380	−0.0931326
$324$	−1.17701	−0.0653896
$325$	4.00000	0.221880
$326$	9.73305	0.539064
$327$	−14.4440	−0.798753
$328$	1.67380	0.0924200
$329$	8.31049	0.458172
$330$	−4.63669	−0.255241
$331$	18.6952	1.02758	0.513790	−	0.857916i	$-0.328241\pi$
$331$	18.6952	1.02758	0.513790	+	0.857916i	$0.328241\pi$
$332$	−13.0806	−0.717894
$333$	25.8943	1.41900
$334$	4.88792	0.267455
$335$	10.7544	0.587578
$336$	2.77016	0.151125
$337$	11.4653	0.624557	0.312279	−	0.949991i	$-0.398908\pi$
$337$	11.4653	0.624557	0.312279	+	0.949991i	$0.398908\pi$
$338$	−3.00000	−0.163178
$339$	31.0649	1.68722
$340$	1.00000	0.0542326
$341$	−8.72738	−0.472614
$342$	7.82299	0.423019
$343$	1.00000	0.0539949
$344$	8.31049	0.448071
$345$	−18.7544	−1.00971
$346$	−4.13347	−0.222217
$347$	−23.9258	−1.28440	−0.642202	−	0.766536i	$-0.721979\pi$
$347$	−23.9258	−1.28440	−0.642202	+	0.766536i	$0.721979\pi$
$348$	3.40685	0.182626
$349$	−7.96857	−0.426548	−0.213274	−	0.976992i	$-0.568413\pi$
$349$	−7.96857	−0.426548	−0.213274	+	0.976992i	$0.568413\pi$
$350$	−1.00000	−0.0534522
$351$	18.5468	0.989953
$352$	−1.67380	−0.0892137
$353$	−2.29477	−0.122138	−0.0610691	−	0.998134i	$-0.519451\pi$
$353$	−2.29477	−0.122138	−0.0610691	+	0.998134i	$0.519451\pi$
$354$	13.2141	0.702323
$355$	−12.8879	−0.684020
$356$	8.19273	0.434214
$357$	2.77016	0.146613
$358$	3.34759	0.176926
$359$	1.19840	0.0632493	0.0316247	−	0.999500i	$-0.489932\pi$
$359$	1.19840	0.0632493	0.0316247	+	0.999500i	$0.489932\pi$
$360$	−4.67380	−0.246331
$361$	−16.1984	−0.852548
$362$	−22.6210	−1.18893
$363$	−22.7109	−1.19201
$364$	4.00000	0.209657
$365$	−9.08065	−0.475303
$366$	−27.7016	−1.44799
$367$	−31.4661	−1.64252	−0.821259	−	0.570556i	$-0.806728\pi$
$367$	−31.4661	−1.64252	−0.821259	+	0.570556i	$0.806728\pi$
$368$	−6.77016	−0.352919
$369$	−7.82299	−0.407248
$370$	−5.54032	−0.288028
$371$	−4.77016	−0.247654
$372$	−14.4440	−0.748884
$373$	10.0750	0.521662	0.260831	−	0.965384i	$-0.416003\pi$
$373$	10.0750	0.521662	0.260831	+	0.965384i	$0.416003\pi$
$374$	−1.67380	−0.0865500
$375$	2.77016	0.143051
$376$	−8.31049	−0.428581
$377$	4.91935	0.253360
$378$	−4.63669	−0.238486
$379$	34.5460	1.77451	0.887254	−	0.461281i	$-0.152610\pi$
$379$	34.5460	1.77451	0.887254	+	0.461281i	$0.152610\pi$
$380$	−1.67380	−0.0858640
$381$	−28.8879	−1.47997
$382$	2.13347	0.109158
$383$	−8.32620	−0.425449	−0.212725	−	0.977112i	$-0.568234\pi$
$383$	−8.32620	−0.425449	−0.212725	+	0.977112i	$0.568234\pi$
$384$	−2.77016	−0.141364
$385$	1.67380	0.0853046
$386$	22.5460	1.14756
$387$	−38.8415	−1.97443
$388$	6.00000	0.304604
$389$	7.54032	0.382310	0.191155	−	0.981560i	$-0.438777\pi$
$389$	7.54032	0.382310	0.191155	+	0.981560i	$0.438777\pi$
$390$	−11.0806	−0.561090
$391$	−6.77016	−0.342382
$392$	−1.00000	−0.0505076
$393$	43.5831	2.19848
$394$	12.6210	0.635835
$395$	12.8879	0.648462
$396$	7.82299	0.393120
$397$	−11.8508	−0.594775	−0.297388	−	0.954757i	$-0.596115\pi$
$397$	−11.8508	−0.594775	−0.297388	+	0.954757i	$0.596115\pi$
$398$	−14.7387	−0.738786
$399$	−4.63669	−0.232125
$400$	1.00000	0.0500000
$401$	13.3476	0.666547	0.333274	−	0.942830i	$-0.391847\pi$
$401$	13.3476	0.666547	0.333274	+	0.942830i	$0.391847\pi$
$402$	−29.7916	−1.48587
$403$	−20.8565	−1.03894
$404$	−9.21412	−0.458420
$405$	−1.17701	−0.0584862
$406$	−1.22984	−0.0610358
$407$	9.27338	0.459664
$408$	−2.77016	−0.137143
$409$	16.4282	0.812324	0.406162	−	0.913801i	$-0.366867\pi$
$409$	16.4282	0.812324	0.406162	+	0.913801i	$0.366867\pi$
$410$	1.67380	0.0826629
$411$	23.3476	1.15165
$412$	−1.22984	−0.0605898
$413$	−4.77016	−0.234724
$414$	31.6424	1.55514
$415$	−13.0806	−0.642104
$416$	−4.00000	−0.196116
$417$	−1.80727	−0.0885024
$418$	2.80160	0.137031
$419$	3.11208	0.152035	0.0760176	−	0.997106i	$-0.475779\pi$
$419$	3.11208	0.152035	0.0760176	+	0.997106i	$0.475779\pi$
$420$	2.77016	0.135170
$421$	−18.2355	−0.888744	−0.444372	−	0.895842i	$-0.646573\pi$
$421$	−18.2355	−0.888744	−0.444372	+	0.895842i	$0.646573\pi$
$422$	−1.11208	−0.0541353
$423$	38.8415	1.88854
$424$	4.77016	0.231660
$425$	1.00000	0.0485071
$426$	35.7016	1.72975
$427$	10.0000	0.483934
$428$	−6.88792	−0.332940
$429$	18.5468	0.895446
$430$	8.31049	0.400767
$431$	20.0000	0.963366	0.481683	−	0.876346i	$-0.340026\pi$
$431$	20.0000	0.963366	0.481683	+	0.876346i	$0.340026\pi$
$432$	4.63669	0.223083
$433$	21.0806	1.01307	0.506536	−	0.862219i	$-0.330926\pi$
$433$	21.0806	1.01307	0.506536	+	0.862219i	$0.330926\pi$
$434$	5.21412	0.250286
$435$	3.40685	0.163346
$436$	−5.21412	−0.249711
$437$	11.3319	0.542077
$438$	25.1549	1.20195
$439$	−39.3597	−1.87854	−0.939268	−	0.343185i	$-0.888494\pi$
$439$	−39.3597	−1.87854	−0.939268	+	0.343185i	$0.888494\pi$
$440$	−1.67380	−0.0797951
$441$	4.67380	0.222562
$442$	−4.00000	−0.190261
$443$	−13.6153	−0.646882	−0.323441	−	0.946248i	$-0.604840\pi$
$443$	−13.6153	−0.646882	−0.323441	+	0.946248i	$0.604840\pi$
$444$	15.3476	0.728365
$445$	8.19273	0.388373
$446$	−25.7758	−1.22052
$447$	−7.34759	−0.347529
$448$	1.00000	0.0472456
$449$	33.0806	1.56117	0.780586	−	0.625048i	$-0.214921\pi$
$449$	33.0806	1.56117	0.780586	+	0.625048i	$0.214921\pi$
$450$	−4.67380	−0.220325
$451$	−2.80160	−0.131922
$452$	11.2141	0.527468
$453$	56.9593	2.67618
$454$	8.05926	0.378240
$455$	4.00000	0.187523
$456$	4.63669	0.217133
$457$	24.4282	1.14270	0.571352	−	0.820705i	$-0.306419\pi$
$457$	24.4282	1.14270	0.571352	+	0.820705i	$0.306419\pi$
$458$	−15.0057	−0.701169
$459$	4.63669	0.216422
$460$	−6.77016	−0.315660
$461$	17.5996	0.819694	0.409847	−	0.912154i	$-0.365582\pi$
$461$	17.5996	0.819694	0.409847	+	0.912154i	$0.365582\pi$
$462$	−4.63669	−0.215718
$463$	14.0428	0.652623	0.326312	−	0.945262i	$-0.394194\pi$
$463$	14.0428	0.652623	0.326312	+	0.945262i	$0.394194\pi$
$464$	1.22984	0.0570938
$465$	−14.4440	−0.669823
$466$	10.0000	0.463241
$467$	−15.8073	−0.731473	−0.365737	−	0.930718i	$-0.619183\pi$
$467$	−15.8073	−0.731473	−0.365737	+	0.930718i	$0.619183\pi$
$468$	18.6952	0.864185
$469$	10.7544	0.496594
$470$	−8.31049	−0.383334
$471$	−22.1613	−1.02114
$472$	4.77016	0.219564
$473$	−13.9101	−0.639586
$474$	−35.7016	−1.63983
$475$	−1.67380	−0.0767991
$476$	1.00000	0.0458349
$477$	−22.2948	−1.02081
$478$	2.78588	0.127423
$479$	30.1613	1.37810	0.689052	−	0.724712i	$-0.258027\pi$
$479$	30.1613	1.37810	0.689052	+	0.724712i	$0.258027\pi$
$480$	−2.77016	−0.126440
$481$	22.1613	1.01047
$482$	6.57743	0.299594
$483$	−18.7544	−0.853357
$484$	−8.19840	−0.372655
$485$	6.00000	0.272446
$486$	17.1706	0.778873
$487$	−5.24556	−0.237699	−0.118849	−	0.992912i	$-0.537921\pi$
$487$	−5.24556	−0.237699	−0.118849	+	0.992912i	$0.537921\pi$
$488$	−10.0000	−0.452679
$489$	−26.9621	−1.21927
$490$	−1.00000	−0.0451754
$491$	8.38546	0.378430	0.189215	−	0.981936i	$-0.439406\pi$
$491$	8.38546	0.378430	0.189215	+	0.981936i	$0.439406\pi$
$492$	−4.63669	−0.209038
$493$	1.22984	0.0553891
$494$	6.69519	0.301231
$495$	7.82299	0.351617
$496$	−5.21412	−0.234121
$497$	−12.8879	−0.578102
$498$	36.2355	1.62375
$499$	29.1399	1.30448	0.652241	−	0.758012i	$-0.273829\pi$
$499$	29.1399	1.30448	0.652241	+	0.758012i	$0.273829\pi$
$500$	1.00000	0.0447214
$501$	−13.5403	−0.604937
$502$	12.7544	0.569259
$503$	−42.4282	−1.89178	−0.945891	−	0.324485i	$-0.894809\pi$
$503$	−42.4282	−1.89178	−0.945891	+	0.324485i	$0.894809\pi$
$504$	−4.67380	−0.208187
$505$	−9.21412	−0.410023
$506$	11.3319	0.503763
$507$	8.31049	0.369082
$508$	−10.4282	−0.462678
$509$	−13.8508	−0.613926	−0.306963	−	0.951721i	$-0.599313\pi$
$509$	−13.8508	−0.613926	−0.306963	+	0.951721i	$0.599313\pi$
$510$	−2.77016	−0.122665
$511$	−9.08065	−0.401704
$512$	−1.00000	−0.0441942
$513$	−7.76088	−0.342651
$514$	7.46535	0.329282
$515$	−1.22984	−0.0541931
$516$	−23.0214	−1.01346
$517$	13.9101	0.611764
$518$	−5.54032	−0.243428
$519$	11.4504	0.502616
$520$	−4.00000	−0.175412
$521$	−2.96289	−0.129807	−0.0649033	−	0.997892i	$-0.520674\pi$
$521$	−2.96289	−0.129807	−0.0649033	+	0.997892i	$0.520674\pi$
$522$	−5.74801	−0.251584
$523$	15.1549	0.662676	0.331338	−	0.943512i	$-0.392500\pi$
$523$	15.1549	0.662676	0.331338	+	0.943512i	$0.392500\pi$
$524$	15.7331	0.687302
$525$	2.77016	0.120900
$526$	24.0000	1.04645
$527$	−5.21412	−0.227131
$528$	4.63669	0.201786
$529$	22.8351	0.992830
$530$	4.77016	0.207203
$531$	−22.2948	−0.967511
$532$	−1.67380	−0.0725683
$533$	−6.69519	−0.290001
$534$	−22.6952	−0.982117
$535$	−6.88792	−0.297791
$536$	−10.7544	−0.464521
$537$	−9.27338	−0.400176
$538$	−2.00000	−0.0862261
$539$	1.67380	0.0720955
$540$	4.63669	0.199531
$541$	40.9472	1.76046	0.880228	−	0.474551i	$-0.157389\pi$
$541$	40.9472	1.76046	0.880228	+	0.474551i	$0.157389\pi$
$542$	−22.4282	−0.963375
$543$	62.6638	2.68916
$544$	−1.00000	−0.0428746
$545$	−5.21412	−0.223348
$546$	−11.0806	−0.474208
$547$	−42.2355	−1.80586	−0.902930	−	0.429788i	$-0.858588\pi$
$547$	−42.2355	−1.80586	−0.902930	+	0.429788i	$0.858588\pi$
$548$	8.42824	0.360037
$549$	46.7380	1.99473
$550$	−1.67380	−0.0713709
$551$	−2.05850	−0.0876950
$552$	18.7544	0.798242
$553$	12.8879	0.548050
$554$	−9.80727	−0.416671
$555$	15.3476	0.651469
$556$	−0.652406	−0.0276682
$557$	30.6802	1.29996	0.649981	−	0.759950i	$-0.274777\pi$
$557$	30.6802	1.29996	0.649981	+	0.759950i	$0.274777\pi$
$558$	24.3697	1.03165
$559$	−33.2419	−1.40598
$560$	1.00000	0.0422577
$561$	4.63669	0.195761
$562$	32.7387	1.38100
$563$	−26.3855	−1.11201	−0.556007	−	0.831177i	$-0.687667\pi$
$563$	−26.3855	−1.11201	−0.556007	+	0.831177i	$0.687667\pi$
$564$	23.0214	0.969375
$565$	11.2141	0.471782
$566$	25.7758	1.08344
$567$	−1.17701	−0.0494299
$568$	12.8879	0.540765
$569$	−18.9786	−0.795625	−0.397812	−	0.917467i	$-0.630230\pi$
$569$	−18.9786	−0.795625	−0.397812	+	0.917467i	$0.630230\pi$
$570$	4.63669	0.194210
$571$	−31.8351	−1.33226	−0.666129	−	0.745837i	$-0.732050\pi$
$571$	−31.8351	−1.33226	−0.666129	+	0.745837i	$0.732050\pi$
$572$	6.69519	0.279940
$573$	−5.91007	−0.246897
$574$	1.67380	0.0698629
$575$	−6.77016	−0.282335
$576$	4.67380	0.194742
$577$	22.9472	0.955303	0.477652	−	0.878549i	$-0.341488\pi$
$577$	22.9472	0.955303	0.477652	+	0.878549i	$0.341488\pi$
$578$	−1.00000	−0.0415945
$579$	−62.4561	−2.59559
$580$	1.22984	0.0510662
$581$	−13.0806	−0.542677
$582$	−16.6210	−0.688961
$583$	−7.98428	−0.330675
$584$	9.08065	0.375760
$585$	18.6952	0.772951
$586$	11.3476	0.468765
$587$	39.1234	1.61480	0.807398	−	0.590007i	$-0.200875\pi$
$587$	39.1234	1.61480	0.807398	+	0.590007i	$0.200875\pi$
$588$	2.77016	0.114240
$589$	8.72738	0.359605
$590$	4.77016	0.196384
$591$	−34.9621	−1.43815
$592$	5.54032	0.227706
$593$	10.3105	0.423401	0.211700	−	0.977335i	$-0.432100\pi$
$593$	10.3105	0.423401	0.211700	+	0.977335i	$0.432100\pi$
$594$	−7.76088	−0.318433
$595$	1.00000	0.0409960
$596$	−2.65241	−0.108647
$597$	40.8287	1.67101
$598$	27.0806	1.10741
$599$	16.0435	0.655521	0.327761	−	0.944761i	$-0.393706\pi$
$599$	16.0435	0.655521	0.327761	+	0.944761i	$0.393706\pi$
$600$	−2.77016	−0.113091
$601$	−30.0593	−1.22614	−0.613071	−	0.790028i	$-0.710066\pi$
$601$	−30.0593	−1.22614	−0.613071	+	0.790028i	$0.710066\pi$
$602$	8.31049	0.338710
$603$	50.2641	2.04691
$604$	20.5617	0.836644
$605$	−8.19840	−0.333313
$606$	25.5246	1.03687
$607$	36.3540	1.47556	0.737782	−	0.675039i	$-0.235873\pi$
$607$	36.3540	1.47556	0.737782	+	0.675039i	$0.235873\pi$
$608$	1.67380	0.0678814
$609$	3.40685	0.138053
$610$	−10.0000	−0.404888
$611$	33.2419	1.34483
$612$	4.67380	0.188927
$613$	19.7758	0.798738	0.399369	−	0.916790i	$-0.369229\pi$
$613$	19.7758	0.798738	0.399369	+	0.916790i	$0.369229\pi$
$614$	29.3162	1.18310
$615$	−4.63669	−0.186969
$616$	−1.67380	−0.0674392
$617$	39.1670	1.57680	0.788401	−	0.615161i	$-0.210909\pi$
$617$	39.1670	1.57680	0.788401	+	0.615161i	$0.210909\pi$
$618$	3.40685	0.137044
$619$	−46.3968	−1.86485	−0.932423	−	0.361370i	$-0.882309\pi$
$619$	−46.3968	−1.86485	−0.932423	+	0.361370i	$0.882309\pi$
$620$	−5.21412	−0.209404
$621$	−31.3911	−1.25968
$622$	−0.577432	−0.0231529
$623$	8.19273	0.328235
$624$	11.0806	0.443581
$625$	1.00000	0.0400000
$626$	4.45968	0.178245
$627$	−7.76088	−0.309940
$628$	−8.00000	−0.319235
$629$	5.54032	0.220907
$630$	−4.67380	−0.186209
$631$	37.2141	1.48147	0.740735	−	0.671797i	$-0.234477\pi$
$631$	37.2141	1.48147	0.740735	+	0.671797i	$0.234477\pi$
$632$	−12.8879	−0.512654
$633$	3.08065	0.122445
$634$	12.6524	0.502491
$635$	−10.4282	−0.413832
$636$	−13.2141	−0.523974
$637$	4.00000	0.158486
$638$	−2.05850	−0.0814968
$639$	−60.2355	−2.38288
$640$	−1.00000	−0.0395285
$641$	−30.2041	−1.19299	−0.596495	−	0.802617i	$-0.703440\pi$
$641$	−30.2041	−1.19299	−0.596495	+	0.802617i	$0.703440\pi$
$642$	19.0806	0.753053
$643$	−5.77584	−0.227777	−0.113888	−	0.993494i	$-0.536331\pi$
$643$	−5.77584	−0.227777	−0.113888	+	0.993494i	$0.536331\pi$
$644$	−6.77016	−0.266782
$645$	−23.0214	−0.906466
$646$	1.67380	0.0658547
$647$	8.91935	0.350656	0.175328	−	0.984510i	$-0.443901\pi$
$647$	8.91935	0.350656	0.175328	+	0.984510i	$0.443901\pi$
$648$	1.17701	0.0462374
$649$	−7.98428	−0.313411
$650$	−4.00000	−0.156893
$651$	−14.4440	−0.566103
$652$	−9.73305	−0.381176
$653$	31.7016	1.24058	0.620290	−	0.784372i	$-0.287015\pi$
$653$	31.7016	1.24058	0.620290	+	0.784372i	$0.287015\pi$
$654$	14.4440	0.564803
$655$	15.7331	0.614741
$656$	−1.67380	−0.0653508
$657$	−42.4411	−1.65579
$658$	−8.31049	−0.323976
$659$	−22.8137	−0.888696	−0.444348	−	0.895854i	$-0.646565\pi$
$659$	−22.8137	−0.888696	−0.444348	+	0.895854i	$0.646565\pi$
$660$	4.63669	0.180483
$661$	9.21412	0.358388	0.179194	−	0.983814i	$-0.442651\pi$
$661$	9.21412	0.358388	0.179194	+	0.983814i	$0.442651\pi$
$662$	−18.6952	−0.726609
$663$	11.0806	0.430337
$664$	13.0806	0.507628
$665$	−1.67380	−0.0649071
$666$	−25.8943	−1.00339
$667$	−8.32620	−0.322392
$668$	−4.88792	−0.189119
$669$	71.4032	2.76061
$670$	−10.7544	−0.415480
$671$	16.7380	0.646162
$672$	−2.77016	−0.106861
$673$	39.1513	1.50917	0.754585	−	0.656202i	$-0.227838\pi$
$673$	39.1513	1.50917	0.754585	+	0.656202i	$0.227838\pi$
$674$	−11.4653	−0.441629
$675$	4.63669	0.178466
$676$	3.00000	0.115385
$677$	25.1556	0.966809	0.483405	−	0.875397i	$-0.339400\pi$
$677$	25.1556	0.966809	0.483405	+	0.875397i	$0.339400\pi$
$678$	−31.0649	−1.19304
$679$	6.00000	0.230259
$680$	−1.00000	−0.0383482
$681$	−22.3254	−0.855513
$682$	8.72738	0.334189
$683$	27.7758	1.06281	0.531406	−	0.847117i	$-0.321664\pi$
$683$	27.7758	1.06281	0.531406	+	0.847117i	$0.321664\pi$
$684$	−7.82299	−0.299119
$685$	8.42824	0.322027
$686$	−1.00000	−0.0381802
$687$	41.5681	1.58592
$688$	−8.31049	−0.316834
$689$	−19.0806	−0.726915
$690$	18.7544	0.713970
$691$	−42.3968	−1.61285	−0.806425	−	0.591336i	$-0.798601\pi$
$691$	−42.3968	−1.61285	−0.806425	+	0.591336i	$0.798601\pi$
$692$	4.13347	0.157131
$693$	7.82299	0.297171
$694$	23.9258	0.908210
$695$	−0.652406	−0.0247472
$696$	−3.40685	−0.129136
$697$	−1.67380	−0.0633996
$698$	7.96857	0.301615
$699$	−27.7016	−1.04777
$700$	1.00000	0.0377964
$701$	−8.19273	−0.309435	−0.154718	−	0.987959i	$-0.549447\pi$
$701$	−8.19273	−0.309435	−0.154718	+	0.987959i	$0.549447\pi$
$702$	−18.5468	−0.700002
$703$	−9.27338	−0.349752
$704$	1.67380	0.0630836
$705$	23.0214	0.867036
$706$	2.29477	0.0863648
$707$	−9.21412	−0.346533
$708$	−13.2141	−0.496617
$709$	4.31049	0.161884	0.0809418	−	0.996719i	$-0.474207\pi$
$709$	4.31049	0.161884	0.0809418	+	0.996719i	$0.474207\pi$
$710$	12.8879	0.483675
$711$	60.2355	2.25901
$712$	−8.19273	−0.307036
$713$	35.3004	1.32201
$714$	−2.77016	−0.103671
$715$	6.69519	0.250386
$716$	−3.34759	−0.125105
$717$	−7.71734	−0.288209
$718$	−1.19840	−0.0447240
$719$	−38.3376	−1.42975	−0.714875	−	0.699253i	$-0.753516\pi$
$719$	−38.3376	−1.42975	−0.714875	+	0.699253i	$0.753516\pi$
$720$	4.67380	0.174182
$721$	−1.22984	−0.0458016
$722$	16.1984	0.602842
$723$	−18.2206	−0.677630
$724$	22.6210	0.840702
$725$	1.22984	0.0456750
$726$	22.7109	0.842881
$727$	26.0863	0.967488	0.483744	−	0.875210i	$-0.339277\pi$
$727$	26.0863	0.967488	0.483744	+	0.875210i	$0.339277\pi$
$728$	−4.00000	−0.148250
$729$	−44.0343	−1.63090
$730$	9.08065	0.336090
$731$	−8.31049	−0.307374
$732$	27.7016	1.02388
$733$	−14.0428	−0.518682	−0.259341	−	0.965786i	$-0.583505\pi$
$733$	−14.0428	−0.518682	−0.259341	+	0.965786i	$0.583505\pi$
$734$	31.4661	1.16144
$735$	2.77016	0.102179
$736$	6.77016	0.249551
$737$	18.0008	0.663066
$738$	7.82299	0.287968
$739$	28.3540	1.04302	0.521510	−	0.853245i	$-0.325369\pi$
$739$	28.3540	1.04302	0.521510	+	0.853245i	$0.325369\pi$
$740$	5.54032	0.203666
$741$	−18.5468	−0.681332
$742$	4.77016	0.175118
$743$	−43.9371	−1.61190	−0.805949	−	0.591986i	$-0.798344\pi$
$743$	−43.9371	−1.61190	−0.805949	+	0.591986i	$0.798344\pi$
$744$	14.4440	0.529541
$745$	−2.65241	−0.0971766
$746$	−10.0750	−0.368871
$747$	−61.1363	−2.23686
$748$	1.67380	0.0612001
$749$	−6.88792	−0.251679
$750$	−2.77016	−0.101152
$751$	29.2419	1.06705	0.533527	−	0.845783i	$-0.320866\pi$
$751$	29.2419	1.06705	0.533527	+	0.845783i	$0.320866\pi$
$752$	8.31049	0.303052
$753$	−35.3319	−1.28757
$754$	−4.91935	−0.179152
$755$	20.5617	0.748317
$756$	4.63669	0.168635
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−34.5460	−1.25477
$759$	−31.3911	−1.13943
$760$	1.67380	0.0607150
$761$	49.0178	1.77689	0.888447	−	0.458980i	$-0.151785\pi$
$761$	49.0178	1.77689	0.888447	+	0.458980i	$0.151785\pi$
$762$	28.8879	1.04650
$763$	−5.21412	−0.188764
$764$	−2.13347	−0.0771864
$765$	4.67380	0.168981
$766$	8.32620	0.300838
$767$	−19.0806	−0.688962
$768$	2.77016	0.0999596
$769$	−4.49111	−0.161954	−0.0809768	−	0.996716i	$-0.525804\pi$
$769$	−4.49111	−0.161954	−0.0809768	+	0.996716i	$0.525804\pi$
$770$	−1.67380	−0.0603195
$771$	−20.6802	−0.744780
$772$	−22.5460	−0.811448
$773$	−18.6952	−0.672419	−0.336210	−	0.941787i	$-0.609145\pi$
$773$	−18.6952	−0.672419	−0.336210	+	0.941787i	$0.609145\pi$
$774$	38.8415	1.39613
$775$	−5.21412	−0.187297
$776$	−6.00000	−0.215387
$777$	15.3476	0.550592
$778$	−7.54032	−0.270334
$779$	2.80160	0.100378
$780$	11.0806	0.396751
$781$	−21.5718	−0.771898
$782$	6.77016	0.242100
$783$	5.70238	0.203786
$784$	1.00000	0.0357143
$785$	−8.00000	−0.285532
$786$	−43.5831	−1.55456
$787$	−36.9157	−1.31590	−0.657952	−	0.753060i	$-0.728577\pi$
$787$	−36.9157	−1.31590	−0.657952	+	0.753060i	$0.728577\pi$
$788$	−12.6210	−0.449603
$789$	−66.4839	−2.36689
$790$	−12.8879	−0.458532
$791$	11.2141	0.398728
$792$	−7.82299	−0.277978
$793$	40.0000	1.42044
$794$	11.8508	0.420569
$795$	−13.2141	−0.468657
$796$	14.7387	0.522400
$797$	37.2419	1.31918	0.659589	−	0.751627i	$-0.270731\pi$
$797$	37.2419	1.31918	0.659589	+	0.751627i	$0.270731\pi$
$798$	4.63669	0.164137
$799$	8.31049	0.294004
$800$	−1.00000	−0.0353553
$801$	38.2912	1.35295
$802$	−13.3476	−0.471320
$803$	−15.1992	−0.536367
$804$	29.7916	1.05067
$805$	−6.77016	−0.238617
$806$	20.8565	0.734638
$807$	5.54032	0.195029
$808$	9.21412	0.324152
$809$	28.6638	1.00776	0.503882	−	0.863773i	$-0.331905\pi$
$809$	28.6638	1.00776	0.503882	+	0.863773i	$0.331905\pi$
$810$	1.17701	0.0413560
$811$	−39.9686	−1.40349	−0.701743	−	0.712430i	$-0.747595\pi$
$811$	−39.9686	−1.40349	−0.701743	+	0.712430i	$0.747595\pi$
$812$	1.22984	0.0431589
$813$	62.1299	2.17899
$814$	−9.27338	−0.325032
$815$	−9.73305	−0.340934
$816$	2.77016	0.0969751
$817$	13.9101	0.486652
$818$	−16.4282	−0.574400
$819$	18.6952	0.653263
$820$	−1.67380	−0.0584515
$821$	−3.58311	−0.125051	−0.0625256	−	0.998043i	$-0.519916\pi$
$821$	−3.58311	−0.125051	−0.0625256	+	0.998043i	$0.519916\pi$
$822$	−23.3476	−0.814341
$823$	52.9157	1.84453	0.922263	−	0.386562i	$-0.126338\pi$
$823$	52.9157	1.84453	0.922263	+	0.386562i	$0.126338\pi$
$824$	1.22984	0.0428434
$825$	4.63669	0.161429
$826$	4.77016	0.165975
$827$	49.2847	1.71380	0.856899	−	0.515484i	$-0.172388\pi$
$827$	49.2847	1.71380	0.856899	+	0.515484i	$0.172388\pi$
$828$	−31.6424	−1.09965
$829$	6.51893	0.226412	0.113206	−	0.993572i	$-0.463888\pi$
$829$	6.51893	0.226412	0.113206	+	0.993572i	$0.463888\pi$
$830$	13.0806	0.454036
$831$	27.1677	0.942438
$832$	4.00000	0.138675
$833$	1.00000	0.0346479
$834$	1.80727	0.0625806
$835$	−4.88792	−0.169153
$836$	−2.80160	−0.0968952
$837$	−24.1763	−0.835654
$838$	−3.11208	−0.107505
$839$	−9.81938	−0.339002	−0.169501	−	0.985530i	$-0.554216\pi$
$839$	−9.81938	−0.339002	−0.169501	+	0.985530i	$0.554216\pi$
$840$	−2.77016	−0.0955797
$841$	−27.4875	−0.947845
$842$	18.2355	0.628437
$843$	−90.6916	−3.12358
$844$	1.11208	0.0382794
$845$	3.00000	0.103203
$846$	−38.8415	−1.33540
$847$	−8.19840	−0.281700
$848$	−4.77016	−0.163808
$849$	−71.4032	−2.45055
$850$	−1.00000	−0.0342997
$851$	−37.5089	−1.28579
$852$	−35.7016	−1.22312
$853$	−4.92011	−0.168461	−0.0842307	−	0.996446i	$-0.526843\pi$
$853$	−4.92011	−0.168461	−0.0842307	+	0.996446i	$0.526843\pi$
$854$	−10.0000	−0.342193
$855$	−7.82299	−0.267541
$856$	6.88792	0.235424
$857$	7.95722	0.271813	0.135907	−	0.990722i	$-0.456605\pi$
$857$	7.95722	0.271813	0.135907	+	0.990722i	$0.456605\pi$
$858$	−18.5468	−0.633176
$859$	−20.5782	−0.702119	−0.351059	−	0.936353i	$-0.614178\pi$
$859$	−20.5782	−0.702119	−0.351059	+	0.936353i	$0.614178\pi$
$860$	−8.31049	−0.283385
$861$	−4.63669	−0.158018
$862$	−20.0000	−0.681203
$863$	−25.1549	−0.856282	−0.428141	−	0.903712i	$-0.640831\pi$
$863$	−25.1549	−0.856282	−0.428141	+	0.903712i	$0.640831\pi$
$864$	−4.63669	−0.157743
$865$	4.13347	0.140542
$866$	−21.0806	−0.716350
$867$	2.77016	0.0940796
$868$	−5.21412	−0.176979
$869$	21.5718	0.731772
$870$	−3.40685	−0.115503
$871$	43.0178	1.45760
$872$	5.21412	0.176572
$873$	28.0428	0.949104
$874$	−11.3319	−0.383306
$875$	1.00000	0.0338062
$876$	−25.1549	−0.849904
$877$	13.1234	0.443147	0.221573	−	0.975144i	$-0.428881\pi$
$877$	13.1234	0.443147	0.221573	+	0.975144i	$0.428881\pi$
$878$	39.3597	1.32833
$879$	−31.4347	−1.06027
$880$	1.67380	0.0564237
$881$	−9.27262	−0.312403	−0.156201	−	0.987725i	$-0.549925\pi$
$881$	−9.27262	−0.312403	−0.156201	+	0.987725i	$0.549925\pi$
$882$	−4.67380	−0.157375
$883$	3.14352	0.105788	0.0528939	−	0.998600i	$-0.483155\pi$
$883$	3.14352	0.105788	0.0528939	+	0.998600i	$0.483155\pi$
$884$	4.00000	0.134535
$885$	−13.2141	−0.444188
$886$	13.6153	0.457415
$887$	22.1927	0.745159	0.372579	−	0.928000i	$-0.378473\pi$
$887$	22.1927	0.745159	0.372579	+	0.928000i	$0.378473\pi$
$888$	−15.3476	−0.515032
$889$	−10.4282	−0.349752
$890$	−8.19273	−0.274621
$891$	−1.97008	−0.0660002
$892$	25.7758	0.863039
$893$	−13.9101	−0.465483
$894$	7.34759	0.245740
$895$	−3.34759	−0.111898
$896$	−1.00000	−0.0334077
$897$	−75.0178	−2.50477
$898$	−33.0806	−1.10392
$899$	−6.41252	−0.213870
$900$	4.67380	0.155793
$901$	−4.77016	−0.158917
$902$	2.80160	0.0932830
$903$	−23.0214	−0.766104
$904$	−11.2141	−0.372976
$905$	22.6210	0.751947
$906$	−56.9593	−1.89235
$907$	−2.26695	−0.0752727	−0.0376364	−	0.999292i	$-0.511983\pi$
$907$	−2.26695	−0.0752727	−0.0376364	+	0.999292i	$0.511983\pi$
$908$	−8.05926	−0.267456
$909$	−43.0649	−1.42837
$910$	−4.00000	−0.132599
$911$	46.1299	1.52835	0.764175	−	0.645009i	$-0.223146\pi$
$911$	46.1299	1.52835	0.764175	+	0.645009i	$0.223146\pi$
$912$	−4.63669	−0.153536
$913$	−21.8943	−0.724597
$914$	−24.4282	−0.808014
$915$	27.7016	0.915787
$916$	15.0057	0.495801
$917$	15.7331	0.519551
$918$	−4.63669	−0.153034
$919$	−37.4339	−1.23483	−0.617415	−	0.786637i	$-0.711820\pi$
$919$	−37.4339	−1.23483	−0.617415	+	0.786637i	$0.711820\pi$
$920$	6.77016	0.223206
$921$	−81.2105	−2.67598
$922$	−17.5996	−0.579611
$923$	−51.5517	−1.69684
$924$	4.63669	0.152536
$925$	5.54032	0.182165
$926$	−14.0428	−0.461474
$927$	−5.74801	−0.188790
$928$	−1.22984	−0.0403714
$929$	23.3904	0.767413	0.383707	−	0.923455i	$-0.374647\pi$
$929$	23.3904	0.767413	0.383707	+	0.923455i	$0.374647\pi$
$930$	14.4440	0.473636
$931$	−1.67380	−0.0548565
$932$	−10.0000	−0.327561
$933$	1.59958	0.0523679
$934$	15.8073	0.517230
$935$	1.67380	0.0547390
$936$	−18.6952	−0.611071
$937$	1.15562	0.0377525	0.0188763	−	0.999822i	$-0.493991\pi$
$937$	1.15562	0.0377525	0.0188763	+	0.999822i	$0.493991\pi$
$938$	−10.7544	−0.351145
$939$	−12.3540	−0.403158
$940$	8.31049	0.271058
$941$	32.6952	1.06583	0.532916	−	0.846168i	$-0.321096\pi$
$941$	32.6952	1.06583	0.532916	+	0.846168i	$0.321096\pi$
$942$	22.1613	0.722054
$943$	11.3319	0.369017
$944$	−4.77016	−0.155256
$945$	4.63669	0.150831
$946$	13.9101	0.452255
$947$	5.11208	0.166120	0.0830602	−	0.996545i	$-0.473531\pi$
$947$	5.11208	0.166120	0.0830602	+	0.996545i	$0.473531\pi$
$948$	35.7016	1.15953
$949$	−36.3226	−1.17908
$950$	1.67380	0.0543051
$951$	−35.0492	−1.13655
$952$	−1.00000	−0.0324102
$953$	6.88792	0.223122	0.111561	−	0.993758i	$-0.464415\pi$
$953$	6.88792	0.223122	0.111561	+	0.993758i	$0.464415\pi$
$954$	22.2948	0.721820
$955$	−2.13347	−0.0690376
$956$	−2.78588	−0.0901018
$957$	5.70238	0.184332
$958$	−30.1613	−0.974467
$959$	8.42824	0.272162
$960$	2.77016	0.0894066
$961$	−3.81294	−0.122998
$962$	−22.1613	−0.714509
$963$	−32.1927	−1.03740
$964$	−6.57743	−0.211845
$965$	−22.5460	−0.725781
$966$	18.7544	0.603414
$967$	59.7016	1.91987	0.959937	−	0.280215i	$-0.0904057\pi$
$967$	59.7016	1.91987	0.959937	+	0.280215i	$0.0904057\pi$
$968$	8.19840	0.263507
$969$	−4.63669	−0.148952
$970$	−6.00000	−0.192648
$971$	−6.97861	−0.223954	−0.111977	−	0.993711i	$-0.535718\pi$
$971$	−6.97861	−0.223954	−0.111977	+	0.993711i	$0.535718\pi$
$972$	−17.1706	−0.550747
$973$	−0.652406	−0.0209152
$974$	5.24556	0.168078
$975$	11.0806	0.354865
$976$	10.0000	0.320092
$977$	−52.8137	−1.68966	−0.844830	−	0.535035i	$-0.820298\pi$
$977$	−52.8137	−1.68966	−0.844830	+	0.535035i	$0.820298\pi$
$978$	26.9621	0.862154
$979$	13.7130	0.438268
$980$	1.00000	0.0319438
$981$	−24.3697	−0.778066
$982$	−8.38546	−0.267591
$983$	3.76449	0.120069	0.0600343	−	0.998196i	$-0.480879\pi$
$983$	3.76449	0.120069	0.0600343	+	0.998196i	$0.480879\pi$
$984$	4.63669	0.147812
$985$	−12.6210	−0.402138
$986$	−1.22984	−0.0391660
$987$	23.0214	0.732779
$988$	−6.69519	−0.213002
$989$	56.2633	1.78907
$990$	−7.82299	−0.248631
$991$	1.30481	0.0414487	0.0207244	−	0.999785i	$-0.493403\pi$
$991$	1.30481	0.0414487	0.0207244	+	0.999785i	$0.493403\pi$
$992$	5.21412	0.165549
$993$	51.7887	1.64346
$994$	12.8879	0.408780
$995$	14.7387	0.467249
$996$	−36.2355	−1.14817
$997$	−58.8565	−1.86400	−0.932002	−	0.362454i	$-0.881939\pi$
$997$	−58.8565	−1.86400	−0.932002	+	0.362454i	$0.881939\pi$
$998$	−29.1399	−0.922408
$999$	25.6888	0.812756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1190.2.a.k.1.3	✓	3
4.3	odd	2		9520.2.a.y.1.1		3
5.4	even	2		5950.2.a.bl.1.1		3
7.6	odd	2		8330.2.a.bv.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.a.k.1.3	✓	3	1.1	even	1	trivial
5950.2.a.bl.1.1		3	5.4	even	2
8330.2.a.bv.1.1		3	7.6	odd	2
9520.2.a.y.1.1		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.77016 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77016 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.67380 q^{9} -1.00000 q^{10} +1.67380 q^{11} +2.77016 q^{12} +4.00000 q^{13} -1.00000 q^{14} +2.77016 q^{15} +1.00000 q^{16} +1.00000 q^{17} -4.67380 q^{18} -1.67380 q^{19} +1.00000 q^{20} +2.77016 q^{21} -1.67380 q^{22} -6.77016 q^{23} -2.77016 q^{24} +1.00000 q^{25} -4.00000 q^{26} +4.63669 q^{27} +1.00000 q^{28} +1.22984 q^{29} -2.77016 q^{30} -5.21412 q^{31} -1.00000 q^{32} +4.63669 q^{33} -1.00000 q^{34} +1.00000 q^{35} +4.67380 q^{36} +5.54032 q^{37} +1.67380 q^{38} +11.0806 q^{39} -1.00000 q^{40} -1.67380 q^{41} -2.77016 q^{42} -8.31049 q^{43} +1.67380 q^{44} +4.67380 q^{45} +6.77016 q^{46} +8.31049 q^{47} +2.77016 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.77016 q^{51} +4.00000 q^{52} -4.77016 q^{53} -4.63669 q^{54} +1.67380 q^{55} -1.00000 q^{56} -4.63669 q^{57} -1.22984 q^{58} -4.77016 q^{59} +2.77016 q^{60} +10.0000 q^{61} +5.21412 q^{62} +4.67380 q^{63} +1.00000 q^{64} +4.00000 q^{65} -4.63669 q^{66} +10.7544 q^{67} +1.00000 q^{68} -18.7544 q^{69} -1.00000 q^{70} -12.8879 q^{71} -4.67380 q^{72} -9.08065 q^{73} -5.54032 q^{74} +2.77016 q^{75} -1.67380 q^{76} +1.67380 q^{77} -11.0806 q^{78} +12.8879 q^{79} +1.00000 q^{80} -1.17701 q^{81} +1.67380 q^{82} -13.0806 q^{83} +2.77016 q^{84} +1.00000 q^{85} +8.31049 q^{86} +3.40685 q^{87} -1.67380 q^{88} +8.19273 q^{89} -4.67380 q^{90} +4.00000 q^{91} -6.77016 q^{92} -14.4440 q^{93} -8.31049 q^{94} -1.67380 q^{95} -2.77016 q^{96} +6.00000 q^{97} -1.00000 q^{98} +7.82299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9} - 3 q^{10} + q^{11} - q^{12} + 12 q^{13} - 3 q^{14} - q^{15} + 3 q^{16} + 3 q^{17} - 10 q^{18} - q^{19} + 3 q^{20}+ \cdots + 66 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9 - 3 * q^10 + q^11 - q^12 + 12 * q^13 - 3 * q^14 - q^15 + 3 * q^16 + 3 * q^17 - 10 * q^18 - q^19 + 3 * q^20 - q^21 - q^22 - 11 * q^23 + q^24 + 3 * q^25 - 12 * q^26 - 10 * q^27 + 3 * q^28 + 13 * q^29 + q^30 + 7 * q^31 - 3 * q^32 - 10 * q^33 - 3 * q^34 + 3 * q^35 + 10 * q^36 - 2 * q^37 + q^38 - 4 * q^39 - 3 * q^40 - q^41 + q^42 + 3 * q^43 + q^44 + 10 * q^45 + 11 * q^46 - 3 * q^47 - q^48 + 3 * q^49 - 3 * q^50 - q^51 + 12 * q^52 - 5 * q^53 + 10 * q^54 + q^55 - 3 * q^56 + 10 * q^57 - 13 * q^58 - 5 * q^59 - q^60 + 30 * q^61 - 7 * q^62 + 10 * q^63 + 3 * q^64 + 12 * q^65 + 10 * q^66 - 9 * q^67 + 3 * q^68 - 15 * q^69 - 3 * q^70 - 12 * q^71 - 10 * q^72 + 10 * q^73 + 2 * q^74 - q^75 - q^76 + q^77 + 4 * q^78 + 12 * q^79 + 3 * q^80 + 39 * q^81 + q^82 - 2 * q^83 - q^84 + 3 * q^85 - 3 * q^86 - 23 * q^87 - q^88 + 14 * q^89 - 10 * q^90 + 12 * q^91 - 11 * q^92 - 30 * q^93 + 3 * q^94 - q^95 + q^96 + 18 * q^97 - 3 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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