LMFDB - Embedded newform 107.2.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [107,2,Mod(1,107)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("107.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(107, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	107.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$0.854399301628$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 7x^{4} + 29x^{3} - 12x^{2} - 20x + 8 $ x^7 - x^6 - 10x^5 + 7x^4 + 29x^3 - 12x^2 - 20*x + 8
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			$0.896638$ of defining polynomial
Character	$\chi$	$=$	107.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.896638 q^{2} -2.53177 q^{3} -1.19604 q^{4} +4.31985 q^{5} +2.27008 q^{6} +1.44247 q^{7} +2.86569 q^{8} +3.40988 q^{9} -3.87334 q^{10} -0.651115 q^{11} +3.02810 q^{12} +5.15000 q^{13} -1.29338 q^{14} -10.9369 q^{15} -0.177405 q^{16} -3.87334 q^{17} -3.05742 q^{18} -2.26078 q^{19} -5.16672 q^{20} -3.65202 q^{21} +0.583814 q^{22} +6.98883 q^{23} -7.25528 q^{24} +13.6611 q^{25} -4.61769 q^{26} -1.03771 q^{27} -1.72526 q^{28} -7.86266 q^{29} +9.80643 q^{30} +1.22536 q^{31} -5.57231 q^{32} +1.64848 q^{33} +3.47299 q^{34} +6.23128 q^{35} -4.07835 q^{36} +1.35721 q^{37} +2.02710 q^{38} -13.0386 q^{39} +12.3794 q^{40} -3.51233 q^{41} +3.27454 q^{42} +4.41556 q^{43} +0.778760 q^{44} +14.7302 q^{45} -6.26645 q^{46} -8.03524 q^{47} +0.449149 q^{48} -4.91927 q^{49} -12.2491 q^{50} +9.80643 q^{51} -6.15961 q^{52} -4.30569 q^{53} +0.930453 q^{54} -2.81272 q^{55} +4.13369 q^{56} +5.72378 q^{57} +7.04996 q^{58} -1.14529 q^{59} +13.0810 q^{60} +5.53570 q^{61} -1.09870 q^{62} +4.91866 q^{63} +5.35116 q^{64} +22.2473 q^{65} -1.47809 q^{66} +1.12895 q^{67} +4.63268 q^{68} -17.6941 q^{69} -5.58720 q^{70} -5.09850 q^{71} +9.77165 q^{72} -4.57323 q^{73} -1.21693 q^{74} -34.5869 q^{75} +2.70398 q^{76} -0.939217 q^{77} +11.6909 q^{78} -7.67658 q^{79} -0.766364 q^{80} -7.60237 q^{81} +3.14929 q^{82} +8.24057 q^{83} +4.36796 q^{84} -16.7323 q^{85} -3.95916 q^{86} +19.9065 q^{87} -1.86589 q^{88} +1.42814 q^{89} -13.2076 q^{90} +7.42875 q^{91} -8.35893 q^{92} -3.10233 q^{93} +7.20470 q^{94} -9.76623 q^{95} +14.1078 q^{96} +1.54202 q^{97} +4.41080 q^{98} -2.22022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 3 q^{3} + 7 q^{4} + 5 q^{5} - 5 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} - q^{10} - 2 q^{11} + 6 q^{12} + 18 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - q^{17} - 17 q^{18} - 4 q^{19} - 10 q^{20}+ \cdots - 52 q^{99}+O(q^{100}) $ 7 * q - q^2 + 3 * q^3 + 7 * q^4 + 5 * q^5 - 5 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 - q^10 - 2 * q^11 + 6 * q^12 + 18 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - q^17 - 17 * q^18 - 4 * q^19 - 10 * q^20 - 11 * q^21 - 5 * q^22 - 31 * q^24 + 8 * q^25 - 22 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 8 * q^30 + 4 * q^31 - 13 * q^32 - 6 * q^33 - 19 * q^35 + 14 * q^36 + 25 * q^37 + 18 * q^38 + 5 * q^39 + 13 * q^40 + 17 * q^42 + 11 * q^43 - 17 * q^44 + 25 * q^45 + q^46 - 9 * q^47 + 19 * q^48 + 13 * q^49 + 7 * q^50 - 8 * q^51 + 44 * q^52 + 8 * q^53 - 35 * q^54 - 13 * q^55 + 26 * q^56 - 3 * q^57 + 35 * q^58 - 19 * q^59 + 9 * q^60 + 25 * q^61 + 23 * q^62 - 11 * q^63 - 18 * q^64 + 8 * q^65 + 63 * q^66 - 24 * q^67 + 11 * q^68 - 5 * q^70 - 19 * q^71 - 15 * q^72 + 30 * q^73 - 17 * q^74 - 41 * q^75 + 4 * q^76 + 6 * q^77 - 18 * q^78 - 21 * q^79 + 19 * q^80 - 17 * q^81 + 6 * q^82 + 12 * q^83 - 36 * q^84 + 2 * q^85 + 31 * q^86 - 15 * q^87 - 8 * q^88 - 22 * q^89 - 36 * q^90 - 2 * q^91 - 7 * q^92 + 9 * q^93 + 16 * q^94 - 44 * q^95 + 2 * q^96 - 4 * q^97 - 22 * q^98 - 52 * 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 $

$2$	−0.896638	−0.634019	−0.317009	−	0.948422i	$-0.602679\pi$
$2$	−0.896638	−0.634019	−0.317009	+	0.948422i	$0.602679\pi$
$3$	−2.53177	−1.46172	−0.730860	−	0.682527i	$-0.760881\pi$
$3$	−2.53177	−1.46172	−0.730860	+	0.682527i	$0.760881\pi$
$4$	−1.19604	−0.598020
$5$	4.31985	1.93190	0.965949	−	0.258734i	$-0.0833052\pi$
$5$	4.31985	1.93190	0.965949	+	0.258734i	$0.0833052\pi$
$6$	2.27008	0.926758
$7$	1.44247	0.545204	0.272602	−	0.962127i	$-0.412116\pi$
$7$	1.44247	0.545204	0.272602	+	0.962127i	$0.412116\pi$
$8$	2.86569	1.01317
$9$	3.40988	1.13663
$10$	−3.87334	−1.22486
$11$	−0.651115	−0.196319	−0.0981593	−	0.995171i	$-0.531295\pi$
$11$	−0.651115	−0.196319	−0.0981593	+	0.995171i	$0.531295\pi$
$12$	3.02810	0.874138
$13$	5.15000	1.42835	0.714177	−	0.699965i	$-0.246801\pi$
$13$	5.15000	1.42835	0.714177	+	0.699965i	$0.246801\pi$
$14$	−1.29338	−0.345670
$15$	−10.9369	−2.82389
$16$	−0.177405	−0.0443513
$17$	−3.87334	−0.939424	−0.469712	−	0.882820i	$-0.655642\pi$
$17$	−3.87334	−0.939424	−0.469712	+	0.882820i	$0.655642\pi$
$18$	−3.05742	−0.720642
$19$	−2.26078	−0.518658	−0.259329	−	0.965789i	$-0.583501\pi$
$19$	−2.26078	−0.518658	−0.259329	+	0.965789i	$0.583501\pi$
$20$	−5.16672	−1.15531
$21$	−3.65202	−0.796936
$22$	0.583814	0.124470
$23$	6.98883	1.45727	0.728636	−	0.684901i	$-0.240155\pi$
$23$	6.98883	1.45727	0.728636	+	0.684901i	$0.240155\pi$
$24$	−7.25528	−1.48098
$25$	13.6611	2.73223
$26$	−4.61769	−0.905603
$27$	−1.03771	−0.199708
$28$	−1.72526	−0.326043
$29$	−7.86266	−1.46006	−0.730030	−	0.683415i	$-0.760494\pi$
$29$	−7.86266	−1.46006	−0.730030	+	0.683415i	$0.760494\pi$
$30$	9.80643	1.79040
$31$	1.22536	0.220081	0.110041	−	0.993927i	$-0.464902\pi$
$31$	1.22536	0.220081	0.110041	+	0.993927i	$0.464902\pi$
$32$	−5.57231	−0.985055
$33$	1.64848	0.286963
$34$	3.47299	0.595612
$35$	6.23128	1.05328
$36$	−4.07835	−0.679725
$37$	1.35721	0.223124	0.111562	−	0.993757i	$-0.464415\pi$
$37$	1.35721	0.223124	0.111562	+	0.993757i	$0.464415\pi$
$38$	2.02710	0.328839
$39$	−13.0386	−2.08785
$40$	12.3794	1.95735
$41$	−3.51233	−0.548533	−0.274267	−	0.961654i	$-0.588435\pi$
$41$	−3.51233	−0.548533	−0.274267	+	0.961654i	$0.588435\pi$
$42$	3.27454	0.505272
$43$	4.41556	0.673367	0.336684	−	0.941618i	$-0.390695\pi$
$43$	4.41556	0.673367	0.336684	+	0.941618i	$0.390695\pi$
$44$	0.778760	0.117403
$45$	14.7302	2.19584
$46$	−6.26645	−0.923938
$47$	−8.03524	−1.17206	−0.586030	−	0.810289i	$-0.699310\pi$
$47$	−8.03524	−1.17206	−0.586030	+	0.810289i	$0.699310\pi$
$48$	0.449149	0.0648291
$49$	−4.91927	−0.702752
$50$	−12.2491	−1.73228
$51$	9.80643	1.37317
$52$	−6.15961	−0.854184
$53$	−4.30569	−0.591432	−0.295716	−	0.955276i	$-0.595558\pi$
$53$	−4.30569	−0.591432	−0.295716	+	0.955276i	$0.595558\pi$
$54$	0.930453	0.126619
$55$	−2.81272	−0.379267
$56$	4.13369	0.552387
$57$	5.72378	0.758133
$58$	7.04996	0.925705
$59$	−1.14529	−0.149104	−0.0745521	−	0.997217i	$-0.523753\pi$
$59$	−1.14529	−0.149104	−0.0745521	+	0.997217i	$0.523753\pi$
$60$	13.0810	1.68875
$61$	5.53570	0.708773	0.354387	−	0.935099i	$-0.384690\pi$
$61$	5.53570	0.708773	0.354387	+	0.935099i	$0.384690\pi$
$62$	−1.09870	−0.139536
$63$	4.91866	0.619693
$64$	5.35116	0.668895
$65$	22.2473	2.75943
$66$	−1.47809	−0.181940
$67$	1.12895	0.137923	0.0689613	−	0.997619i	$-0.478031\pi$
$67$	1.12895	0.137923	0.0689613	+	0.997619i	$0.478031\pi$
$68$	4.63268	0.561795
$69$	−17.6941	−2.13012
$70$	−5.58720	−0.667798
$71$	−5.09850	−0.605081	−0.302540	−	0.953137i	$-0.597835\pi$
$71$	−5.09850	−0.605081	−0.302540	+	0.953137i	$0.597835\pi$
$72$	9.77165	1.15160
$73$	−4.57323	−0.535256	−0.267628	−	0.963522i	$-0.586240\pi$
$73$	−4.57323	−0.535256	−0.267628	+	0.963522i	$0.586240\pi$
$74$	−1.21693	−0.141465
$75$	−34.5869	−3.99375
$76$	2.70398	0.310168
$77$	−0.939217	−0.107034
$78$	11.6909	1.32374
$79$	−7.67658	−0.863683	−0.431841	−	0.901950i	$-0.642136\pi$
$79$	−7.67658	−0.863683	−0.431841	+	0.901950i	$0.642136\pi$
$80$	−0.766364	−0.0856821
$81$	−7.60237	−0.844708
$82$	3.14929	0.347780
$83$	8.24057	0.904520	0.452260	−	0.891886i	$-0.350618\pi$
$83$	8.24057	0.904520	0.452260	+	0.891886i	$0.350618\pi$
$84$	4.36796	0.476584
$85$	−16.7323	−1.81487
$86$	−3.95916	−0.426927
$87$	19.9065	2.13420
$88$	−1.86589	−0.198905
$89$	1.42814	0.151383	0.0756914	−	0.997131i	$-0.475884\pi$
$89$	1.42814	0.151383	0.0756914	+	0.997131i	$0.475884\pi$
$90$	−13.2076	−1.39221
$91$	7.42875	0.778744
$92$	−8.35893	−0.871478
$93$	−3.10233	−0.321697
$94$	7.20470	0.743108
$95$	−9.76623	−1.00199
$96$	14.1078	1.43987
$97$	1.54202	0.156568	0.0782840	−	0.996931i	$-0.475056\pi$
$97$	1.54202	0.156568	0.0782840	+	0.996931i	$0.475056\pi$
$98$	4.41080	0.445558
$99$	−2.22022	−0.223141
$100$	−16.3393	−1.63393
$101$	−4.28734	−0.426606	−0.213303	−	0.976986i	$-0.568422\pi$
$101$	−4.28734	−0.426606	−0.213303	+	0.976986i	$0.568422\pi$
$102$	−8.79281	−0.870618
$103$	−10.7265	−1.05692	−0.528458	−	0.848959i	$-0.677230\pi$
$103$	−10.7265	−1.05692	−0.528458	+	0.848959i	$0.677230\pi$
$104$	14.7583	1.44717
$105$	−15.7762	−1.53960
$106$	3.86064	0.374979
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	1.24115	0.119429
$109$	0.00784083	0.000751016 0	0.000375508	−	1.00000i	$-0.499880\pi$
$109$	0.00784083	0.000751016 0	0.000375508		1.00000i	$0.499880\pi$
$110$	2.52199	0.240463
$111$	−3.43615	−0.326145
$112$	−0.255902	−0.0241805
$113$	−14.0663	−1.32325	−0.661625	−	0.749835i	$-0.730133\pi$
$113$	−14.0663	−1.32325	−0.661625	+	0.749835i	$0.730133\pi$
$114$	−5.13216	−0.480670
$115$	30.1907	2.81530
$116$	9.40406	0.873145
$117$	17.5609	1.62350
$118$	1.02691	0.0945349
$119$	−5.58720	−0.512178
$120$	−31.3417	−2.86110
$121$	−10.5760	−0.961459
$122$	−4.96351	−0.449375
$123$	8.89242	0.801802
$124$	−1.46558	−0.131613
$125$	37.4148	3.34649
$126$	−4.41026	−0.392897
$127$	−3.61215	−0.320526	−0.160263	−	0.987074i	$-0.551234\pi$
$127$	−3.61215	−0.320526	−0.160263	+	0.987074i	$0.551234\pi$
$128$	6.34658	0.560964
$129$	−11.1792	−0.984274
$130$	−19.9477	−1.74953
$131$	4.60038	0.401937	0.200969	−	0.979598i	$-0.435591\pi$
$131$	4.60038	0.401937	0.200969	+	0.979598i	$0.435591\pi$
$132$	−1.97164	−0.171610
$133$	−3.26112	−0.282775
$134$	−1.01226	−0.0874455
$135$	−4.48277	−0.385815
$136$	−11.0998	−0.951801
$137$	20.3604	1.73951	0.869753	−	0.493487i	$-0.164278\pi$
$137$	20.3604	1.73951	0.869753	+	0.493487i	$0.164278\pi$
$138$	15.8652	1.35054
$139$	22.1595	1.87954	0.939772	−	0.341803i	$-0.111038\pi$
$139$	22.1595	1.87954	0.939772	+	0.341803i	$0.111038\pi$
$140$	−7.45286	−0.629882
$141$	20.3434	1.71322
$142$	4.57151	0.383633
$143$	−3.35324	−0.280412
$144$	−0.604929	−0.0504108
$145$	−33.9655	−2.82068
$146$	4.10053	0.339362
$147$	12.4545	1.02723
$148$	−1.62328	−0.133433
$149$	−14.2392	−1.16652	−0.583260	−	0.812286i	$-0.698223\pi$
$149$	−14.2392	−1.16652	−0.583260	+	0.812286i	$0.698223\pi$
$150$	31.0119	2.53211
$151$	−2.08950	−0.170041	−0.0850206	−	0.996379i	$-0.527096\pi$
$151$	−2.08950	−0.170041	−0.0850206	+	0.996379i	$0.527096\pi$
$152$	−6.47869	−0.525491
$153$	−13.2076	−1.06777
$154$	0.842137	0.0678614
$155$	5.29338	0.425174
$156$	15.5947	1.24858
$157$	15.2311	1.21557	0.607787	−	0.794100i	$-0.292057\pi$
$157$	15.2311	1.21557	0.607787	+	0.794100i	$0.292057\pi$
$158$	6.88311	0.547591
$159$	10.9010	0.864508
$160$	−24.0716	−1.90303
$161$	10.0812	0.794511
$162$	6.81658	0.535561
$163$	−1.67593	−0.131269	−0.0656345	−	0.997844i	$-0.520907\pi$
$163$	−1.67593	−0.131269	−0.0656345	+	0.997844i	$0.520907\pi$
$164$	4.20089	0.328034
$165$	7.12117	0.554383
$166$	−7.38881	−0.573483
$167$	−24.2178	−1.87403	−0.937016	−	0.349287i	$-0.886424\pi$
$167$	−24.2178	−1.87403	−0.937016	+	0.349287i	$0.886424\pi$
$168$	−10.4656	−0.807435
$169$	13.5225	1.04019
$170$	15.0028	1.15066
$171$	−7.70897	−0.589520
$172$	−5.28119	−0.402687
$173$	−2.85964	−0.217415	−0.108707	−	0.994074i	$-0.534671\pi$
$173$	−2.85964	−0.217415	−0.108707	+	0.994074i	$0.534671\pi$
$174$	−17.8489	−1.35312
$175$	19.7058	1.48962
$176$	0.115511	0.00870697
$177$	2.89962	0.217949
$178$	−1.28053	−0.0959796
$179$	−10.0545	−0.751508	−0.375754	−	0.926719i	$-0.622616\pi$
$179$	−10.0545	−0.751508	−0.375754	+	0.926719i	$0.622616\pi$
$180$	−17.6179	−1.31316
$181$	18.2712	1.35809	0.679043	−	0.734099i	$-0.262395\pi$
$181$	18.2712	1.35809	0.679043	+	0.734099i	$0.262395\pi$
$182$	−6.66089	−0.493738
$183$	−14.0151	−1.03603
$184$	20.0278	1.47647
$185$	5.86295	0.431053
$186$	2.78167	0.203962
$187$	2.52199	0.184426
$188$	9.61047	0.700916
$189$	−1.49688	−0.108882
$190$	8.75677	0.635283
$191$	−17.6438	−1.27666	−0.638330	−	0.769762i	$-0.720375\pi$
$191$	−17.6438	−1.27666	−0.638330	+	0.769762i	$0.720375\pi$
$192$	−13.5479	−0.977737
$193$	−4.76885	−0.343269	−0.171635	−	0.985161i	$-0.554905\pi$
$193$	−4.76885	−0.343269	−0.171635	+	0.985161i	$0.554905\pi$
$194$	−1.38263	−0.0992670
$195$	−56.3250	−4.03352
$196$	5.88364	0.420260
$197$	−7.64460	−0.544655	−0.272328	−	0.962205i	$-0.587793\pi$
$197$	−7.64460	−0.544655	−0.272328	+	0.962205i	$0.587793\pi$
$198$	1.99073	0.141475
$199$	−12.1554	−0.861676	−0.430838	−	0.902429i	$-0.641782\pi$
$199$	−12.1554	−0.861676	−0.430838	+	0.902429i	$0.641782\pi$
$200$	39.1486	2.76822
$201$	−2.85823	−0.201604
$202$	3.84419	0.270476
$203$	−11.3417	−0.796030
$204$	−11.7289	−0.821186
$205$	−15.1727	−1.05971
$206$	9.61782	0.670105
$207$	23.8310	1.65637
$208$	−0.913636	−0.0633493
$209$	1.47203	0.101822
$210$	14.1455	0.976134
$211$	6.19282	0.426331	0.213166	−	0.977016i	$-0.431623\pi$
$211$	6.19282	0.426331	0.213166	+	0.977016i	$0.431623\pi$
$212$	5.14978	0.353688
$213$	12.9083	0.884459
$214$	−0.896638	−0.0612929
$215$	19.0746	1.30088
$216$	−2.97377	−0.202339
$217$	1.76755	0.119989
$218$	−0.00703039	−0.000476158 0
$219$	11.5784	0.782394
$220$	3.36413	0.226810
$221$	−19.9477	−1.34183
$222$	3.08098	0.206782
$223$	20.7796	1.39150	0.695752	−	0.718282i	$-0.255071\pi$
$223$	20.7796	1.39150	0.695752	+	0.718282i	$0.255071\pi$
$224$	−8.03792	−0.537056
$225$	46.5828	3.10552
$226$	12.6124	0.838965
$227$	−15.0782	−1.00078	−0.500388	−	0.865801i	$-0.666809\pi$
$227$	−15.0782	−1.00078	−0.500388	+	0.865801i	$0.666809\pi$
$228$	−6.84587	−0.453379
$229$	9.24710	0.611065	0.305533	−	0.952182i	$-0.401165\pi$
$229$	9.24710	0.611065	0.305533	+	0.952182i	$0.401165\pi$
$230$	−27.0701	−1.78495
$231$	2.37788	0.156453
$232$	−22.5320	−1.47930
$233$	−20.9405	−1.37186	−0.685928	−	0.727670i	$-0.740603\pi$
$233$	−20.9405	−1.37186	−0.685928	+	0.727670i	$0.740603\pi$
$234$	−15.7457	−1.02933
$235$	−34.7111	−2.26430
$236$	1.36982	0.0891674
$237$	19.4354	1.26246
$238$	5.00969	0.324730
$239$	−8.27819	−0.535472	−0.267736	−	0.963492i	$-0.586275\pi$
$239$	−8.27819	−0.535472	−0.267736	+	0.963492i	$0.586275\pi$
$240$	1.94026	0.125243
$241$	15.7066	1.01175	0.505875	−	0.862607i	$-0.331170\pi$
$241$	15.7066	1.01175	0.505875	+	0.862607i	$0.331170\pi$
$242$	9.48288	0.609583
$243$	22.3606	1.43443
$244$	−6.62092	−0.423861
$245$	−21.2505	−1.35765
$246$	−7.97328	−0.508357
$247$	−11.6430	−0.740827
$248$	3.51150	0.222981
$249$	−20.8633	−1.32216
$250$	−33.5476	−2.12173
$251$	10.7933	0.681270	0.340635	−	0.940196i	$-0.389358\pi$
$251$	10.7933	0.681270	0.340635	+	0.940196i	$0.389358\pi$
$252$	−5.88292	−0.370589
$253$	−4.55053	−0.286090
$254$	3.23879	0.203220
$255$	42.3623	2.65283
$256$	−16.3929	−1.02456
$257$	2.03604	0.127005	0.0635023	−	0.997982i	$-0.479773\pi$
$257$	2.03604	0.127005	0.0635023	+	0.997982i	$0.479773\pi$
$258$	10.0237	0.624048
$259$	1.95774	0.121648
$260$	−26.6086	−1.65020
$261$	−26.8107	−1.65954
$262$	−4.12488	−0.254836
$263$	24.0914	1.48554	0.742769	−	0.669548i	$-0.233512\pi$
$263$	24.0914	1.48554	0.742769	+	0.669548i	$0.233512\pi$
$264$	4.72402	0.290743
$265$	−18.5999	−1.14259
$266$	2.92404	0.179284
$267$	−3.61573	−0.221279
$268$	−1.35026	−0.0824805
$269$	−25.1077	−1.53084	−0.765422	−	0.643529i	$-0.777470\pi$
$269$	−25.1077	−1.53084	−0.765422	+	0.643529i	$0.777470\pi$
$270$	4.01942	0.244614
$271$	2.73725	0.166276	0.0831380	−	0.996538i	$-0.473506\pi$
$271$	2.73725	0.166276	0.0831380	+	0.996538i	$0.473506\pi$
$272$	0.687151	0.0416646
$273$	−18.8079	−1.13831
$274$	−18.2559	−1.10288
$275$	−8.89497	−0.536387
$276$	21.1629	1.27386
$277$	1.22283	0.0734725	0.0367363	−	0.999325i	$-0.488304\pi$
$277$	1.22283	0.0734725	0.0367363	+	0.999325i	$0.488304\pi$
$278$	−19.8690	−1.19167
$279$	4.17833	0.250150
$280$	17.8569	1.06716
$281$	5.85779	0.349447	0.174723	−	0.984618i	$-0.444097\pi$
$281$	5.85779	0.349447	0.174723	+	0.984618i	$0.444097\pi$
$282$	−18.2407	−1.08622
$283$	−16.4973	−0.980665	−0.490333	−	0.871535i	$-0.663125\pi$
$283$	−16.4973	−0.980665	−0.490333	+	0.871535i	$0.663125\pi$
$284$	6.09802	0.361851
$285$	24.7259	1.46464
$286$	3.00664	0.177787
$287$	−5.06644	−0.299063
$288$	−19.0009	−1.11964
$289$	−1.99721	−0.117483
$290$	30.4548	1.78837
$291$	−3.90403	−0.228858
$292$	5.46977	0.320094
$293$	17.0149	0.994019	0.497010	−	0.867745i	$-0.334431\pi$
$293$	17.0149	0.994019	0.497010	+	0.867745i	$0.334431\pi$
$294$	−11.1671	−0.651281
$295$	−4.94749	−0.288054
$296$	3.88935	0.226064
$297$	0.675671	0.0392064
$298$	12.7674	0.739595
$299$	35.9925	2.08150
$300$	41.3673	2.38834
$301$	6.36934	0.367123
$302$	1.87353	0.107809
$303$	10.8546	0.623579
$304$	0.401073	0.0230031
$305$	23.9134	1.36928
$306$	11.8425	0.676988
$307$	−26.0663	−1.48768	−0.743840	−	0.668357i	$-0.766998\pi$
$307$	−26.0663	−1.48768	−0.743840	+	0.668357i	$0.766998\pi$
$308$	1.12334	0.0640083
$309$	27.1572	1.54492
$310$	−4.74624	−0.269568
$311$	23.6386	1.34042	0.670210	−	0.742171i	$-0.266204\pi$
$311$	23.6386	1.34042	0.670210	+	0.742171i	$0.266204\pi$
$312$	−37.3647	−2.11536
$313$	−11.3385	−0.640891	−0.320445	−	0.947267i	$-0.603833\pi$
$313$	−11.3385	−0.640891	−0.320445	+	0.947267i	$0.603833\pi$
$314$	−13.6568	−0.770697
$315$	21.2479	1.19718
$316$	9.18150	0.516500
$317$	18.1908	1.02170	0.510849	−	0.859670i	$-0.329331\pi$
$317$	18.1908	1.02170	0.510849	+	0.859670i	$0.329331\pi$
$318$	−9.77427	−0.548114
$319$	5.11950	0.286637
$320$	23.1162	1.29224
$321$	−2.53177	−0.141310
$322$	−9.03919	−0.503735
$323$	8.75677	0.487240
$324$	9.09275	0.505153
$325$	70.3549	3.90259
$326$	1.50270	0.0832270
$327$	−0.0198512	−0.00109777
$328$	−10.0652	−0.555760
$329$	−11.5906	−0.639012
$330$	−6.38511	−0.351489
$331$	−14.8356	−0.815438	−0.407719	−	0.913108i	$-0.633676\pi$
$331$	−14.8356	−0.815438	−0.407719	+	0.913108i	$0.633676\pi$
$332$	−9.85606	−0.540922
$333$	4.62792	0.253609
$334$	21.7146	1.18817
$335$	4.87688	0.266452
$336$	0.647886	0.0353451
$337$	−25.3391	−1.38031	−0.690153	−	0.723663i	$-0.742457\pi$
$337$	−25.3391	−1.38031	−0.690153	+	0.723663i	$0.742457\pi$
$338$	−12.1248	−0.659502
$339$	35.6128	1.93422
$340$	20.0125	1.08533
$341$	−0.797850	−0.0432060
$342$	6.91216	0.373767
$343$	−17.1932	−0.928348
$344$	12.6536	0.682238
$345$	−76.4361	−4.11518
$346$	2.56406	0.137845
$347$	−23.3898	−1.25563	−0.627814	−	0.778363i	$-0.716050\pi$
$347$	−23.3898	−1.25563	−0.627814	+	0.778363i	$0.716050\pi$
$348$	−23.8090	−1.27629
$349$	−2.14001	−0.114552	−0.0572761	−	0.998358i	$-0.518242\pi$
$349$	−2.14001	−0.114552	−0.0572761	+	0.998358i	$0.518242\pi$
$350$	−17.6690	−0.944448
$351$	−5.34422	−0.285254
$352$	3.62822	0.193385
$353$	4.27743	0.227665	0.113832	−	0.993500i	$-0.463687\pi$
$353$	4.27743	0.227665	0.113832	+	0.993500i	$0.463687\pi$
$354$	−2.59991	−0.138184
$355$	−22.0248	−1.16895
$356$	−1.70812	−0.0905300
$357$	14.1455	0.748661
$358$	9.01524	0.476470
$359$	12.1223	0.639790	0.319895	−	0.947453i	$-0.396352\pi$
$359$	12.1223	0.639790	0.319895	+	0.947453i	$0.396352\pi$
$360$	42.2121	2.22477
$361$	−13.8889	−0.730994
$362$	−16.3826	−0.861051
$363$	26.7762	1.40538
$364$	−8.88508	−0.465705
$365$	−19.7557	−1.03406
$366$	12.5665	0.656861
$367$	37.4441	1.95456	0.977282	−	0.211944i	$-0.0679795\pi$
$367$	37.4441	1.95456	0.977282	+	0.211944i	$0.0679795\pi$
$368$	−1.23985	−0.0646318
$369$	−11.9766	−0.623477
$370$	−5.25695	−0.273296
$371$	−6.21085	−0.322451
$372$	3.71052	0.192381
$373$	−4.06976	−0.210724	−0.105362	−	0.994434i	$-0.533600\pi$
$373$	−4.06976	−0.210724	−0.105362	+	0.994434i	$0.533600\pi$
$374$	−2.26131	−0.116930
$375$	−94.7259	−4.89162
$376$	−23.0265	−1.18750
$377$	−40.4927	−2.08548
$378$	1.34215	0.0690330
$379$	19.3304	0.992938	0.496469	−	0.868055i	$-0.334630\pi$
$379$	19.3304	0.992938	0.496469	+	0.868055i	$0.334630\pi$
$380$	11.6808	0.599213
$381$	9.14514	0.468520
$382$	15.8201	0.809427
$383$	18.0773	0.923709	0.461854	−	0.886956i	$-0.347184\pi$
$383$	18.0773	0.923709	0.461854	+	0.886956i	$0.347184\pi$
$384$	−16.0681	−0.819972
$385$	−4.05728	−0.206778
$386$	4.27593	0.217639
$387$	15.0565	0.765366
$388$	−1.84431	−0.0936308
$389$	−1.61758	−0.0820146	−0.0410073	−	0.999159i	$-0.513057\pi$
$389$	−1.61758	−0.0820146	−0.0410073	+	0.999159i	$0.513057\pi$
$390$	50.5031	2.55732
$391$	−27.0701	−1.36900
$392$	−14.0971	−0.712011
$393$	−11.6471	−0.587520
$394$	6.85444	0.345322
$395$	−33.1617	−1.66855
$396$	2.65548	0.133443
$397$	38.9265	1.95366	0.976832	−	0.214008i	$-0.0686518\pi$
$397$	38.9265	1.95366	0.976832	+	0.214008i	$0.0686518\pi$
$398$	10.8990	0.546319
$399$	8.25641	0.413337
$400$	−2.42355	−0.121178
$401$	5.26025	0.262684	0.131342	−	0.991337i	$-0.458071\pi$
$401$	5.26025	0.262684	0.131342	+	0.991337i	$0.458071\pi$
$402$	2.56280	0.127821
$403$	6.31061	0.314354
$404$	5.12784	0.255119
$405$	−32.8411	−1.63189
$406$	10.1694	0.504698
$407$	−0.883701	−0.0438034
$408$	28.1022	1.39127
$409$	13.1709	0.651258	0.325629	−	0.945498i	$-0.394424\pi$
$409$	13.1709	0.651258	0.325629	+	0.945498i	$0.394424\pi$
$410$	13.6045	0.671876
$411$	−51.5479	−2.54267
$412$	12.8294	0.632058
$413$	−1.65205	−0.0812923
$414$	−21.3678	−1.05017
$415$	35.5981	1.74744
$416$	−28.6974	−1.40701
$417$	−56.1028	−2.74737
$418$	−1.31987	−0.0645572
$419$	9.23413	0.451117	0.225558	−	0.974230i	$-0.427579\pi$
$419$	9.23413	0.451117	0.225558	+	0.974230i	$0.427579\pi$
$420$	18.8690	0.920711
$421$	−24.1530	−1.17714	−0.588572	−	0.808445i	$-0.700310\pi$
$421$	−24.1530	−1.17714	−0.588572	+	0.808445i	$0.700310\pi$
$422$	−5.55272	−0.270302
$423$	−27.3992	−1.33219
$424$	−12.3388	−0.599224
$425$	−52.9143	−2.56672
$426$	−11.5740	−0.560763
$427$	7.98510	0.386426
$428$	−1.19604	−0.0578128
$429$	8.48965	0.409884
$430$	−17.1030	−0.824780
$431$	0.198678	0.00957000	0.00478500	−	0.999989i	$-0.498477\pi$
$431$	0.198678	0.00957000	0.00478500	+	0.999989i	$0.498477\pi$
$432$	0.184096	0.00885730
$433$	13.0932	0.629218	0.314609	−	0.949221i	$-0.398127\pi$
$433$	13.0932	0.629218	0.314609	+	0.949221i	$0.398127\pi$
$434$	−1.58485	−0.0760754
$435$	85.9931	4.12305
$436$	−0.00937796	−0.000449123 0
$437$	−15.8002	−0.755826
$438$	−10.3816	−0.496052
$439$	−9.35726	−0.446598	−0.223299	−	0.974750i	$-0.571683\pi$
$439$	−9.35726	−0.446598	−0.223299	+	0.974750i	$0.571683\pi$
$440$	−8.06039	−0.384264
$441$	−16.7741	−0.798766
$442$	17.8859	0.850745
$443$	29.5624	1.40455	0.702276	−	0.711905i	$-0.252167\pi$
$443$	29.5624	1.40455	0.702276	+	0.711905i	$0.252167\pi$
$444$	4.10978	0.195041
$445$	6.16937	0.292456
$446$	−18.6318	−0.882239
$447$	36.0504	1.70513
$448$	7.71891	0.364684
$449$	36.5054	1.72280	0.861399	−	0.507930i	$-0.169589\pi$
$449$	36.5054	1.72280	0.861399	+	0.507930i	$0.169589\pi$
$450$	−41.7679	−1.96896
$451$	2.28693	0.107687
$452$	16.8239	0.791330
$453$	5.29015	0.248553
$454$	13.5197	0.634511
$455$	32.0911	1.50445
$456$	16.4026	0.768121
$457$	25.5324	1.19435	0.597177	−	0.802110i	$-0.296289\pi$
$457$	25.5324	1.19435	0.597177	+	0.802110i	$0.296289\pi$
$458$	−8.29130	−0.387427
$459$	4.01942	0.187610
$460$	−36.1093	−1.68361
$461$	−26.3068	−1.22523	−0.612614	−	0.790382i	$-0.709882\pi$
$461$	−26.3068	−1.22523	−0.612614	+	0.790382i	$0.709882\pi$
$462$	−2.13210	−0.0991943
$463$	−25.4315	−1.18190	−0.590951	−	0.806707i	$-0.701247\pi$
$463$	−25.4315	−1.18190	−0.590951	+	0.806707i	$0.701247\pi$
$464$	1.39488	0.0647555
$465$	−13.4016	−0.621486
$466$	18.7760	0.869782
$467$	12.6952	0.587464	0.293732	−	0.955888i	$-0.405103\pi$
$467$	12.6952	0.587464	0.293732	+	0.955888i	$0.405103\pi$
$468$	−21.0035	−0.970888
$469$	1.62848	0.0751960
$470$	31.1232	1.43561
$471$	−38.5617	−1.77683
$472$	−3.28205	−0.151069
$473$	−2.87504	−0.132194
$474$	−17.4265	−0.800425
$475$	−30.8848	−1.41709
$476$	6.68252	0.306293
$477$	−14.6819	−0.672237
$478$	7.42254	0.339499
$479$	5.79820	0.264927	0.132463	−	0.991188i	$-0.457711\pi$
$479$	5.79820	0.264927	0.132463	+	0.991188i	$0.457711\pi$
$480$	60.9438	2.78169
$481$	6.98964	0.318700
$482$	−14.0831	−0.641469
$483$	−25.5233	−1.16135
$484$	12.6494	0.574972
$485$	6.66128	0.302473
$486$	−20.0494	−0.909458
$487$	12.1182	0.549127	0.274564	−	0.961569i	$-0.411467\pi$
$487$	12.1182	0.549127	0.274564	+	0.961569i	$0.411467\pi$
$488$	15.8636	0.718111
$489$	4.24307	0.191878
$490$	19.0540	0.860773
$491$	24.1156	1.08832	0.544161	−	0.838981i	$-0.316848\pi$
$491$	24.1156	1.08832	0.544161	+	0.838981i	$0.316848\pi$
$492$	−10.6357	−0.479494
$493$	30.4548	1.37161
$494$	10.4396	0.469698
$495$	−9.59103	−0.431085
$496$	−0.217385	−0.00976088
$497$	−7.35446	−0.329893
$498$	18.7068	0.838271
$499$	−33.0116	−1.47780	−0.738901	−	0.673814i	$-0.764655\pi$
$499$	−33.0116	−1.47780	−0.738901	+	0.673814i	$0.764655\pi$
$500$	−44.7497	−2.00127
$501$	61.3140	2.73931
$502$	−9.67772	−0.431938
$503$	19.3233	0.861584	0.430792	−	0.902451i	$-0.358234\pi$
$503$	19.3233	0.861584	0.430792	+	0.902451i	$0.358234\pi$
$504$	14.0954	0.627857
$505$	−18.5207	−0.824160
$506$	4.08018	0.181386
$507$	−34.2359	−1.52047
$508$	4.32028	0.191681
$509$	7.39712	0.327872	0.163936	−	0.986471i	$-0.447581\pi$
$509$	7.39712	0.327872	0.163936	+	0.986471i	$0.447581\pi$
$510$	−37.9837	−1.68195
$511$	−6.59677	−0.291824
$512$	2.00533	0.0886240
$513$	2.34604	0.103580
$514$	−1.82559	−0.0805232
$515$	−46.3371	−2.04186
$516$	13.3708	0.588616
$517$	5.23186	0.230097
$518$	−1.75539	−0.0771272
$519$	7.23996	0.317799
$520$	63.7537	2.79579
$521$	−8.13233	−0.356284	−0.178142	−	0.984005i	$-0.557009\pi$
$521$	−8.13233	−0.356284	−0.178142	+	0.984005i	$0.557009\pi$
$522$	24.0395	1.05218
$523$	27.7176	1.21201	0.606003	−	0.795462i	$-0.292772\pi$
$523$	27.7176	1.21201	0.606003	+	0.795462i	$0.292772\pi$
$524$	−5.50225	−0.240367
$525$	−49.8907	−2.17741
$526$	−21.6012	−0.941859
$527$	−4.74624	−0.206750
$528$	−0.292448	−0.0127272
$529$	25.8438	1.12364
$530$	16.6774	0.724421
$531$	−3.90530	−0.169476
$532$	3.90043	0.169105
$533$	−18.0885	−0.783499
$534$	3.24200	0.140295
$535$	4.31985	0.186764
$536$	3.23521	0.139740
$537$	25.4557	1.09849
$538$	22.5125	0.970584
$539$	3.20301	0.137963
$540$	5.36157	0.230725
$541$	−11.7411	−0.504788	−0.252394	−	0.967625i	$-0.581218\pi$
$541$	−11.7411	−0.504788	−0.252394	+	0.967625i	$0.581218\pi$
$542$	−2.45432	−0.105422
$543$	−46.2585	−1.98514
$544$	21.5835	0.925384
$545$	0.0338713	0.00145089
$546$	16.8639	0.721707
$547$	35.8262	1.53182	0.765909	−	0.642949i	$-0.222289\pi$
$547$	35.8262	1.53182	0.765909	+	0.642949i	$0.222289\pi$
$548$	−24.3519	−1.04026
$549$	18.8760	0.805610
$550$	7.97557	0.340079
$551$	17.7757	0.757272
$552$	−50.7059	−2.15819
$553$	−11.0733	−0.470883
$554$	−1.09643	−0.0465829
$555$	−14.8437	−0.630079
$556$	−26.5037	−1.12401
$557$	37.6819	1.59663	0.798316	−	0.602238i	$-0.205724\pi$
$557$	37.6819	1.59663	0.798316	+	0.602238i	$0.205724\pi$
$558$	−3.74645	−0.158600
$559$	22.7402	0.961806
$560$	−1.10546	−0.0467142
$561$	−6.38511	−0.269580
$562$	−5.25232	−0.221556
$563$	−17.2694	−0.727820	−0.363910	−	0.931434i	$-0.618558\pi$
$563$	−17.2694	−0.727820	−0.363910	+	0.931434i	$0.618558\pi$
$564$	−24.3315	−1.02454
$565$	−60.7645	−2.55638
$566$	14.7921	0.621760
$567$	−10.9662	−0.460538
$568$	−14.6107	−0.613053
$569$	2.75570	0.115525	0.0577624	−	0.998330i	$-0.481603\pi$
$569$	2.75570	0.115525	0.0577624	+	0.998330i	$0.481603\pi$
$570$	−22.1702	−0.928606
$571$	9.88304	0.413592	0.206796	−	0.978384i	$-0.433696\pi$
$571$	9.88304	0.413592	0.206796	+	0.978384i	$0.433696\pi$
$572$	4.01062	0.167692
$573$	44.6701	1.86612
$574$	4.54276	0.189611
$575$	95.4754	3.98160
$576$	18.2468	0.760283
$577$	−6.50457	−0.270789	−0.135394	−	0.990792i	$-0.543230\pi$
$577$	−6.50457	−0.270789	−0.135394	+	0.990792i	$0.543230\pi$
$578$	1.79077	0.0744862
$579$	12.0737	0.501764
$580$	40.6242	1.68683
$581$	11.8868	0.493148
$582$	3.50050	0.145101
$583$	2.80350	0.116109
$584$	−13.1055	−0.542308
$585$	75.8604	3.13644
$586$	−15.2562	−0.630227
$587$	30.5723	1.26185	0.630927	−	0.775842i	$-0.282675\pi$
$587$	30.5723	1.26185	0.630927	+	0.775842i	$0.282675\pi$
$588$	−14.8961	−0.614303
$589$	−2.77027	−0.114147
$590$	4.43611	0.182632
$591$	19.3544	0.796134
$592$	−0.240776	−0.00989583
$593$	−28.8451	−1.18453	−0.592263	−	0.805745i	$-0.701765\pi$
$593$	−28.8451	−1.18453	−0.592263	+	0.805745i	$0.701765\pi$
$594$	−0.605832	−0.0248576
$595$	−24.1359	−0.989475
$596$	17.0306	0.697603
$597$	30.7748	1.25953
$598$	−32.2722	−1.31971
$599$	−16.3274	−0.667120	−0.333560	−	0.942729i	$-0.608250\pi$
$599$	−16.3274	−0.667120	−0.333560	+	0.942729i	$0.608250\pi$
$600$	−99.1154	−4.04637
$601$	13.2880	0.542027	0.271014	−	0.962575i	$-0.412641\pi$
$601$	13.2880	0.542027	0.271014	+	0.962575i	$0.412641\pi$
$602$	−5.71099	−0.232763
$603$	3.84956	0.156766
$604$	2.49913	0.101688
$605$	−45.6870	−1.85744
$606$	−9.73262	−0.395361
$607$	3.04423	0.123561	0.0617806	−	0.998090i	$-0.480322\pi$
$607$	3.04423	0.123561	0.0617806	+	0.998090i	$0.480322\pi$
$608$	12.5978	0.510907
$609$	28.7146	1.16357
$610$	−21.4417	−0.868147
$611$	−41.3815	−1.67412
$612$	15.7969	0.638550
$613$	−36.0484	−1.45598	−0.727991	−	0.685586i	$-0.759546\pi$
$613$	−36.0484	−1.45598	−0.727991	+	0.685586i	$0.759546\pi$
$614$	23.3720	0.943217
$615$	38.4139	1.54900
$616$	−2.69151	−0.108444
$617$	25.9625	1.04521	0.522604	−	0.852575i	$-0.324960\pi$
$617$	25.9625	1.04521	0.522604	+	0.852575i	$0.324960\pi$
$618$	−24.3501	−0.979506
$619$	−13.0175	−0.523216	−0.261608	−	0.965174i	$-0.584253\pi$
$619$	−13.0175	−0.523216	−0.261608	+	0.965174i	$0.584253\pi$
$620$	−6.33109	−0.254263
$621$	−7.25240	−0.291029
$622$	−21.1952	−0.849851
$623$	2.06006	0.0825346
$624$	2.31312	0.0925989
$625$	93.3210	3.73284
$626$	10.1665	0.406337
$627$	−3.72684	−0.148836
$628$	−18.2170	−0.726938
$629$	−5.25695	−0.209608
$630$	−19.0517	−0.759036
$631$	−8.70729	−0.346632	−0.173316	−	0.984866i	$-0.555448\pi$
$631$	−8.70729	−0.346632	−0.173316	+	0.984866i	$0.555448\pi$
$632$	−21.9987	−0.875061
$633$	−15.6788	−0.623177
$634$	−16.3106	−0.647776
$635$	−15.6040	−0.619224
$636$	−13.0381	−0.516993
$637$	−25.3342	−1.00378
$638$	−4.59033	−0.181733
$639$	−17.3853	−0.687750
$640$	27.4163	1.08372
$641$	−0.643700	−0.0254246	−0.0127123	−	0.999919i	$-0.504047\pi$
$641$	−0.643700	−0.0254246	−0.0127123	+	0.999919i	$0.504047\pi$
$642$	2.27008	0.0895930
$643$	3.62279	0.142869	0.0714344	−	0.997445i	$-0.477242\pi$
$643$	3.62279	0.142869	0.0714344	+	0.997445i	$0.477242\pi$
$644$	−12.0575	−0.475134
$645$	−48.2925	−1.90152
$646$	−7.85165	−0.308919
$647$	−34.5269	−1.35739	−0.678696	−	0.734419i	$-0.737455\pi$
$647$	−34.5269	−1.35739	−0.678696	+	0.734419i	$0.737455\pi$
$648$	−21.7861	−0.855837
$649$	0.745717	0.0292719
$650$	−63.0828	−2.47431
$651$	−4.47504	−0.175391
$652$	2.00448	0.0785015
$653$	29.1020	1.13885	0.569425	−	0.822043i	$-0.307166\pi$
$653$	29.1020	1.13885	0.569425	+	0.822043i	$0.307166\pi$
$654$	0.0177993	0.000696010 0
$655$	19.8730	0.776502
$656$	0.623104	0.0243281
$657$	−15.5941	−0.608385
$658$	10.3926	0.405146
$659$	−8.51689	−0.331771	−0.165886	−	0.986145i	$-0.553048\pi$
$659$	−8.51689	−0.331771	−0.165886	+	0.986145i	$0.553048\pi$
$660$	−8.51721	−0.331532
$661$	−20.8966	−0.812784	−0.406392	−	0.913699i	$-0.633213\pi$
$661$	−20.8966	−0.812784	−0.406392	+	0.913699i	$0.633213\pi$
$662$	13.3021	0.517003
$663$	50.5031	1.96138
$664$	23.6149	0.916437
$665$	−14.0875	−0.546292
$666$	−4.14957	−0.160793
$667$	−54.9508	−2.12770
$668$	28.9655	1.12071
$669$	−52.6092	−2.03399
$670$	−4.37279	−0.168936
$671$	−3.60437	−0.139145
$672$	20.3502	0.785026
$673$	−8.61168	−0.331956	−0.165978	−	0.986129i	$-0.553078\pi$
$673$	−8.61168	−0.331956	−0.165978	+	0.986129i	$0.553078\pi$
$674$	22.7200	0.875140
$675$	−14.1763	−0.545648
$676$	−16.1735	−0.622057
$677$	−19.9462	−0.766596	−0.383298	−	0.923625i	$-0.625212\pi$
$677$	−19.9462	−0.766596	−0.383298	+	0.923625i	$0.625212\pi$
$678$	−31.9318	−1.22633
$679$	2.22432	0.0853615
$680$	−47.9495	−1.83878
$681$	38.1746	1.46285
$682$	0.715383	0.0273934
$683$	23.9704	0.917200	0.458600	−	0.888643i	$-0.348351\pi$
$683$	23.9704	0.917200	0.458600	+	0.888643i	$0.348351\pi$
$684$	9.22025	0.352545
$685$	87.9540	3.36055
$686$	15.4161	0.588590
$687$	−23.4116	−0.893206
$688$	−0.783343	−0.0298647
$689$	−22.1743	−0.844774
$690$	68.5355	2.60910
$691$	36.7573	1.39831	0.699157	−	0.714968i	$-0.253559\pi$
$691$	36.7573	1.39831	0.699157	+	0.714968i	$0.253559\pi$
$692$	3.42025	0.130018
$693$	−3.20261	−0.121657
$694$	20.9721	0.796092
$695$	95.7258	3.63108
$696$	57.0458	2.16232
$697$	13.6045	0.515305
$698$	1.91881	0.0726282
$699$	53.0165	2.00527
$700$	−23.5690	−0.890824
$701$	−46.2916	−1.74841	−0.874204	−	0.485558i	$-0.838616\pi$
$701$	−46.2916	−1.74841	−0.874204	+	0.485558i	$0.838616\pi$
$702$	4.79183	0.180856
$703$	−3.06835	−0.115725
$704$	−3.48422	−0.131316
$705$	87.8805	3.30977
$706$	−3.83531	−0.144344
$707$	−6.18438	−0.232588
$708$	−3.46806	−0.130338
$709$	33.2270	1.24787	0.623934	−	0.781477i	$-0.285533\pi$
$709$	33.2270	1.24787	0.623934	+	0.781477i	$0.285533\pi$
$710$	19.7483	0.741139
$711$	−26.1762	−0.981684
$712$	4.09262	0.153377
$713$	8.56384	0.320718
$714$	−12.6834	−0.474665
$715$	−14.4855	−0.541728
$716$	12.0256	0.449417
$717$	20.9585	0.782710
$718$	−10.8693	−0.405638
$719$	−20.6940	−0.771757	−0.385878	−	0.922550i	$-0.626102\pi$
$719$	−20.6940	−0.771757	−0.385878	+	0.922550i	$0.626102\pi$
$720$	−2.61321	−0.0973884
$721$	−15.4728	−0.576236
$722$	12.4533	0.463464
$723$	−39.7655	−1.47890
$724$	−21.8531	−0.812163
$725$	−107.413	−3.98921
$726$	−24.0085	−0.891040
$727$	−36.7600	−1.36335	−0.681676	−	0.731654i	$-0.738749\pi$
$727$	−36.7600	−1.36335	−0.681676	+	0.731654i	$0.738749\pi$
$728$	21.2885	0.789004
$729$	−33.8049	−1.25203
$730$	17.7137	0.655613
$731$	−17.1030	−0.632577
$732$	16.7627	0.619566
$733$	14.0414	0.518630	0.259315	−	0.965793i	$-0.416503\pi$
$733$	14.0414	0.518630	0.259315	+	0.965793i	$0.416503\pi$
$734$	−33.5737	−1.23923
$735$	53.8015	1.98450
$736$	−38.9440	−1.43549
$737$	−0.735073	−0.0270768
$738$	10.7387	0.395296
$739$	−32.3793	−1.19109	−0.595546	−	0.803321i	$-0.703064\pi$
$739$	−32.3793	−1.19109	−0.595546	+	0.803321i	$0.703064\pi$
$740$	−7.01233	−0.257778
$741$	29.4775	1.08288
$742$	5.56888	0.204440
$743$	−35.9295	−1.31813	−0.659064	−	0.752087i	$-0.729047\pi$
$743$	−35.9295	−1.31813	−0.659064	+	0.752087i	$0.729047\pi$
$744$	−8.89033	−0.325935
$745$	−61.5112	−2.25360
$746$	3.64910	0.133603
$747$	28.0993	1.02810
$748$	−3.01641	−0.110291
$749$	1.44247	0.0527069
$750$	84.9348	3.10138
$751$	−21.1224	−0.770769	−0.385384	−	0.922756i	$-0.625931\pi$
$751$	−21.1224	−0.770769	−0.385384	+	0.922756i	$0.625931\pi$
$752$	1.42549	0.0519823
$753$	−27.3263	−0.995826
$754$	36.3073	1.32223
$755$	−9.02634	−0.328502
$756$	1.79032	0.0651134
$757$	−0.953205	−0.0346448	−0.0173224	−	0.999850i	$-0.505514\pi$
$757$	−0.953205	−0.0346448	−0.0173224	+	0.999850i	$0.505514\pi$
$758$	−17.3324	−0.629541
$759$	11.5209	0.418183
$760$	−27.9870	−1.01520
$761$	4.01838	0.145666	0.0728331	−	0.997344i	$-0.476796\pi$
$761$	4.01838	0.145666	0.0728331	+	0.997344i	$0.476796\pi$
$762$	−8.19988	−0.297050
$763$	0.0113102	0.000409457 0
$764$	21.1027	0.763469
$765$	−57.0550	−2.06283
$766$	−16.2088	−0.585648
$767$	−5.89825	−0.212974
$768$	41.5031	1.49761
$769$	−26.1744	−0.943871	−0.471936	−	0.881633i	$-0.656445\pi$
$769$	−26.1744	−0.943871	−0.471936	+	0.881633i	$0.656445\pi$
$770$	3.63791	0.131101
$771$	−5.15478	−0.185645
$772$	5.70374	0.205282
$773$	−33.8328	−1.21688	−0.608440	−	0.793600i	$-0.708204\pi$
$773$	−33.8328	−1.21688	−0.608440	+	0.793600i	$0.708204\pi$
$774$	−13.5002	−0.485256
$775$	16.7398	0.601312
$776$	4.41894	0.158631
$777$	−4.95656	−0.177816
$778$	1.45038	0.0519988
$779$	7.94059	0.284501
$780$	67.3670	2.41213
$781$	3.31971	0.118789
$782$	24.2721	0.867969
$783$	8.15919	0.291586
$784$	0.872703	0.0311679
$785$	65.7962	2.34837
$786$	10.4433	0.372499
$787$	2.91856	0.104036	0.0520178	−	0.998646i	$-0.483435\pi$
$787$	2.91856	0.104036	0.0520178	+	0.998646i	$0.483435\pi$
$788$	9.14326	0.325715
$789$	−60.9939	−2.17144
$790$	29.7340	1.05789
$791$	−20.2903	−0.721441
$792$	−6.36247	−0.226080
$793$	28.5088	1.01238
$794$	−34.9029	−1.23866
$795$	47.0909	1.67014
$796$	14.5384	0.515300
$797$	6.64902	0.235520	0.117760	−	0.993042i	$-0.462429\pi$
$797$	6.64902	0.235520	0.117760	+	0.993042i	$0.462429\pi$
$798$	−7.40301	−0.262064
$799$	31.1232	1.10106
$800$	−76.1241	−2.69139
$801$	4.86979	0.172066
$802$	−4.71654	−0.166547
$803$	2.97770	0.105081
$804$	3.41856	0.120563
$805$	43.5494	1.53491
$806$	−5.65833	−0.199306
$807$	63.5670	2.23767
$808$	−12.2862	−0.432227
$809$	27.5872	0.969915	0.484958	−	0.874538i	$-0.338835\pi$
$809$	27.5872	0.969915	0.484958	+	0.874538i	$0.338835\pi$
$810$	29.4466	1.03465
$811$	−41.1002	−1.44322	−0.721612	−	0.692297i	$-0.756599\pi$
$811$	−41.1002	−1.44322	−0.721612	+	0.692297i	$0.756599\pi$
$812$	13.5651	0.476042
$813$	−6.93009	−0.243049
$814$	0.792359	0.0277722
$815$	−7.23977	−0.253598
$816$	−1.73971	−0.0609020
$817$	−9.98261	−0.349247
$818$	−11.8095	−0.412910
$819$	25.3311	0.885140
$820$	18.1472	0.633728
$821$	−1.90523	−0.0664929	−0.0332464	−	0.999447i	$-0.510585\pi$
$821$	−1.90523	−0.0664929	−0.0332464	+	0.999447i	$0.510585\pi$
$822$	46.2198	1.61210
$823$	−50.6637	−1.76602	−0.883012	−	0.469350i	$-0.844488\pi$
$823$	−50.6637	−1.76602	−0.883012	+	0.469350i	$0.844488\pi$
$824$	−30.7389	−1.07084
$825$	22.5201	0.784048
$826$	1.48129	0.0515408
$827$	28.1005	0.977149	0.488575	−	0.872522i	$-0.337517\pi$
$827$	28.1005	0.977149	0.488575	+	0.872522i	$0.337517\pi$
$828$	−28.5029	−0.990544
$829$	7.56739	0.262826	0.131413	−	0.991328i	$-0.458049\pi$
$829$	7.56739	0.262826	0.131413	+	0.991328i	$0.458049\pi$
$830$	−31.9186	−1.10791
$831$	−3.09592	−0.107396
$832$	27.5585	0.955418
$833$	19.0540	0.660182
$834$	50.3039	1.74188
$835$	−104.617	−3.62044
$836$	−1.76060	−0.0608918
$837$	−1.27157	−0.0439520
$838$	−8.27967	−0.286016
$839$	1.84972	0.0638595	0.0319297	−	0.999490i	$-0.489835\pi$
$839$	1.84972	0.0638595	0.0319297	+	0.999490i	$0.489835\pi$
$840$	−45.2097	−1.55988
$841$	32.8214	1.13177
$842$	21.6565	0.746331
$843$	−14.8306	−0.510793
$844$	−7.40686	−0.254955
$845$	58.4153	2.00955
$846$	24.5671	0.844635
$847$	−15.2557	−0.524191
$848$	0.763851	0.0262307
$849$	41.7675	1.43346
$850$	47.4449	1.62735
$851$	9.48532	0.325153
$852$	−15.4388	−0.528924
$853$	29.4981	1.01000	0.504998	−	0.863121i	$-0.331493\pi$
$853$	29.4981	1.01000	0.504998	+	0.863121i	$0.331493\pi$
$854$	−7.15974	−0.245001
$855$	−33.3016	−1.13889
$856$	2.86569	0.0979473
$857$	−8.80077	−0.300628	−0.150314	−	0.988638i	$-0.548029\pi$
$857$	−8.80077	−0.300628	−0.150314	+	0.988638i	$0.548029\pi$
$858$	−7.61214	−0.259874
$859$	56.1648	1.91632	0.958160	−	0.286235i	$-0.0924037\pi$
$859$	56.1648	1.91632	0.958160	+	0.286235i	$0.0924037\pi$
$860$	−22.8140	−0.777950
$861$	12.8271	0.437146
$862$	−0.178142	−0.00606756
$863$	−19.2402	−0.654945	−0.327472	−	0.944861i	$-0.606197\pi$
$863$	−19.2402	−0.654945	−0.327472	+	0.944861i	$0.606197\pi$
$864$	5.78246	0.196723
$865$	−12.3532	−0.420023
$866$	−11.7398	−0.398936
$867$	5.05647	0.171727
$868$	−2.11406	−0.0717560
$869$	4.99834	0.169557
$870$	−77.1046	−2.61409
$871$	5.81407	0.197002
$872$	0.0224694	0.000760910 0
$873$	5.25808	0.177959
$874$	14.1671	0.479208
$875$	53.9700	1.82452
$876$	−13.8482	−0.467888
$877$	36.5806	1.23524	0.617619	−	0.786477i	$-0.288097\pi$
$877$	36.5806	1.23524	0.617619	+	0.786477i	$0.288097\pi$
$878$	8.39007	0.283151
$879$	−43.0778	−1.45298
$880$	0.498991	0.0168210
$881$	37.1530	1.25171	0.625857	−	0.779938i	$-0.284749\pi$
$881$	37.1530	1.25171	0.625857	+	0.779938i	$0.284749\pi$
$882$	15.0403	0.506433
$883$	−48.5321	−1.63324	−0.816618	−	0.577178i	$-0.804154\pi$
$883$	−48.5321	−1.63324	−0.816618	+	0.577178i	$0.804154\pi$
$884$	23.8583	0.802441
$885$	12.5259	0.421055
$886$	−26.5068	−0.890512
$887$	19.4240	0.652193	0.326096	−	0.945337i	$-0.394267\pi$
$887$	19.4240	0.652193	0.326096	+	0.945337i	$0.394267\pi$
$888$	−9.84695	−0.330442
$889$	−5.21043	−0.174752
$890$	−5.53169	−0.185423
$891$	4.95002	0.165832
$892$	−24.8532	−0.832148
$893$	18.1659	0.607899
$894$	−32.3241	−1.08108
$895$	−43.4339	−1.45184
$896$	9.15478	0.305840
$897$	−91.1248	−3.04257
$898$	−32.7321	−1.09229
$899$	−9.63459	−0.321332
$900$	−55.7149	−1.85716
$901$	16.6774	0.555605
$902$	−2.05055	−0.0682757
$903$	−16.1257	−0.536630
$904$	−40.3098	−1.34068
$905$	78.9288	2.62368
$906$	−4.74334	−0.157587
$907$	29.9083	0.993087	0.496544	−	0.868012i	$-0.334602\pi$
$907$	29.9083	0.993087	0.496544	+	0.868012i	$0.334602\pi$
$908$	18.0342	0.598484
$909$	−14.6193	−0.484892
$910$	−28.7741	−0.953852
$911$	−15.4875	−0.513125	−0.256563	−	0.966528i	$-0.582590\pi$
$911$	−15.4875	−0.513125	−0.256563	+	0.966528i	$0.582590\pi$
$912$	−1.01543	−0.0336241
$913$	−5.36556	−0.177574
$914$	−22.8933	−0.757242
$915$	−60.5433	−2.00150
$916$	−11.0599	−0.365429
$917$	6.63594	0.219138
$918$	−3.60396	−0.118949
$919$	−32.2465	−1.06372	−0.531858	−	0.846834i	$-0.678506\pi$
$919$	−32.2465	−1.06372	−0.531858	+	0.846834i	$0.678506\pi$
$920$	86.5173	2.85239
$921$	65.9939	2.17457
$922$	23.5876	0.776818
$923$	−26.2573	−0.864269
$924$	−2.84405	−0.0935623
$925$	18.5410	0.609626
$926$	22.8029	0.749348
$927$	−36.5762	−1.20132
$928$	43.8132	1.43824
$929$	11.5002	0.377308	0.188654	−	0.982044i	$-0.439588\pi$
$929$	11.5002	0.377308	0.188654	+	0.982044i	$0.439588\pi$
$930$	12.0164	0.394034
$931$	11.1214	0.364488
$932$	25.0456	0.820397
$933$	−59.8475	−1.95932
$934$	−11.3830	−0.372463
$935$	10.8946	0.356293
$936$	50.3240	1.64489
$937$	4.85543	0.158620	0.0793099	−	0.996850i	$-0.474728\pi$
$937$	4.85543	0.158620	0.0793099	+	0.996850i	$0.474728\pi$
$938$	−1.46015	−0.0476757
$939$	28.7065	0.936803
$940$	41.5158	1.35410
$941$	25.4887	0.830908	0.415454	−	0.909614i	$-0.363623\pi$
$941$	25.4887	0.830908	0.415454	+	0.909614i	$0.363623\pi$
$942$	34.5759	1.12654
$943$	−24.5471	−0.799362
$944$	0.203180	0.00661296
$945$	−6.46628	−0.210348
$946$	2.57787	0.0838137
$947$	−35.0546	−1.13912	−0.569560	−	0.821950i	$-0.692886\pi$
$947$	−35.0546	−1.13912	−0.569560	+	0.821950i	$0.692886\pi$
$948$	−23.2455	−0.754978
$949$	−23.5521	−0.764534
$950$	27.6925	0.898463
$951$	−46.0550	−1.49344
$952$	−16.0112	−0.518926
$953$	−0.848275	−0.0274783	−0.0137392	−	0.999906i	$-0.504373\pi$
$953$	−0.848275	−0.0274783	−0.0137392	+	0.999906i	$0.504373\pi$
$954$	13.1643	0.426210
$955$	−76.2187	−2.46638
$956$	9.90105	0.320223
$957$	−12.9614	−0.418983
$958$	−5.19888	−0.167968
$959$	29.3694	0.948386
$960$	−58.5250	−1.88889
$961$	−29.4985	−0.951564
$962$	−6.26717	−0.202062
$963$	3.40988	0.109882
$964$	−18.7857	−0.605047
$965$	−20.6007	−0.663161
$966$	22.8852	0.736319
$967$	−1.72151	−0.0553599	−0.0276800	−	0.999617i	$-0.508812\pi$
$967$	−1.72151	−0.0553599	−0.0276800	+	0.999617i	$0.508812\pi$
$968$	−30.3077	−0.974126
$969$	−22.1702	−0.712208
$970$	−5.97276	−0.191774
$971$	17.2771	0.554447	0.277224	−	0.960805i	$-0.410586\pi$
$971$	17.2771	0.554447	0.277224	+	0.960805i	$0.410586\pi$
$972$	−26.7442	−0.857821
$973$	31.9645	1.02473
$974$	−10.8656	−0.348157
$975$	−178.123	−5.70449
$976$	−0.982060	−0.0314350
$977$	58.9366	1.88555	0.942774	−	0.333433i	$-0.108207\pi$
$977$	58.9366	1.88555	0.942774	+	0.333433i	$0.108207\pi$
$978$	−3.80450	−0.121655
$979$	−0.929885	−0.0297193
$980$	25.4165	0.811900
$981$	0.0267363	0.000853624 0
$982$	−21.6229	−0.690016
$983$	−2.78745	−0.0889057	−0.0444529	−	0.999011i	$-0.514154\pi$
$983$	−2.78745	−0.0889057	−0.0444529	+	0.999011i	$0.514154\pi$
$984$	25.4829	0.812366
$985$	−33.0236	−1.05222
$986$	−27.3069	−0.869629
$987$	29.3448	0.934057
$988$	13.9255	0.443030
$989$	30.8596	0.981279
$990$	8.59968	0.273316
$991$	−47.3221	−1.50324	−0.751618	−	0.659599i	$-0.770726\pi$
$991$	−47.3221	−1.50324	−0.751618	+	0.659599i	$0.770726\pi$
$992$	−6.82809	−0.216792
$993$	37.5603	1.19194
$994$	6.59429	0.209158
$995$	−52.5097	−1.66467
$996$	24.9533	0.790676
$997$	4.54734	0.144016	0.0720079	−	0.997404i	$-0.477059\pi$
$997$	4.54734	0.144016	0.0720079	+	0.997404i	$0.477059\pi$
$998$	29.5994	0.936954
$999$	−1.40840	−0.0445597

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	107.2.a.b.1.3	✓	7
3.2	odd	2		963.2.a.f.1.5		7
4.3	odd	2		1712.2.a.t.1.7		7
5.4	even	2		2675.2.a.g.1.5		7
7.6	odd	2		5243.2.a.g.1.3		7
8.3	odd	2		6848.2.a.bv.1.1		7
8.5	even	2		6848.2.a.bu.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
107.2.a.b.1.3	✓	7	1.1	even	1	trivial
963.2.a.f.1.5		7	3.2	odd	2
1712.2.a.t.1.7		7	4.3	odd	2
2675.2.a.g.1.5		7	5.4	even	2
5243.2.a.g.1.3		7	7.6	odd	2
6848.2.a.bu.1.7		7	8.5	even	2
6848.2.a.bv.1.1		7	8.3	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:	\( N \)	\(=\)	\( 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	107.a (trivial)

\(f(q)\)	\(=\)	\(q-0.896638 q^{2} -2.53177 q^{3} -1.19604 q^{4} +4.31985 q^{5} +2.27008 q^{6} +1.44247 q^{7} +2.86569 q^{8} +3.40988 q^{9} -3.87334 q^{10} -0.651115 q^{11} +3.02810 q^{12} +5.15000 q^{13} -1.29338 q^{14} -10.9369 q^{15} -0.177405 q^{16} -3.87334 q^{17} -3.05742 q^{18} -2.26078 q^{19} -5.16672 q^{20} -3.65202 q^{21} +0.583814 q^{22} +6.98883 q^{23} -7.25528 q^{24} +13.6611 q^{25} -4.61769 q^{26} -1.03771 q^{27} -1.72526 q^{28} -7.86266 q^{29} +9.80643 q^{30} +1.22536 q^{31} -5.57231 q^{32} +1.64848 q^{33} +3.47299 q^{34} +6.23128 q^{35} -4.07835 q^{36} +1.35721 q^{37} +2.02710 q^{38} -13.0386 q^{39} +12.3794 q^{40} -3.51233 q^{41} +3.27454 q^{42} +4.41556 q^{43} +0.778760 q^{44} +14.7302 q^{45} -6.26645 q^{46} -8.03524 q^{47} +0.449149 q^{48} -4.91927 q^{49} -12.2491 q^{50} +9.80643 q^{51} -6.15961 q^{52} -4.30569 q^{53} +0.930453 q^{54} -2.81272 q^{55} +4.13369 q^{56} +5.72378 q^{57} +7.04996 q^{58} -1.14529 q^{59} +13.0810 q^{60} +5.53570 q^{61} -1.09870 q^{62} +4.91866 q^{63} +5.35116 q^{64} +22.2473 q^{65} -1.47809 q^{66} +1.12895 q^{67} +4.63268 q^{68} -17.6941 q^{69} -5.58720 q^{70} -5.09850 q^{71} +9.77165 q^{72} -4.57323 q^{73} -1.21693 q^{74} -34.5869 q^{75} +2.70398 q^{76} -0.939217 q^{77} +11.6909 q^{78} -7.67658 q^{79} -0.766364 q^{80} -7.60237 q^{81} +3.14929 q^{82} +8.24057 q^{83} +4.36796 q^{84} -16.7323 q^{85} -3.95916 q^{86} +19.9065 q^{87} -1.86589 q^{88} +1.42814 q^{89} -13.2076 q^{90} +7.42875 q^{91} -8.35893 q^{92} -3.10233 q^{93} +7.20470 q^{94} -9.76623 q^{95} +14.1078 q^{96} +1.54202 q^{97} +4.41080 q^{98} -2.22022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 3 q^{3} + 7 q^{4} + 5 q^{5} - 5 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} - q^{10} - 2 q^{11} + 6 q^{12} + 18 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - q^{17} - 17 q^{18} - 4 q^{19} - 10 q^{20}+ \cdots - 52 q^{99}+O(q^{100}) \) 7 * q - q^2 + 3 * q^3 + 7 * q^4 + 5 * q^5 - 5 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 - q^10 - 2 * q^11 + 6 * q^12 + 18 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - q^17 - 17 * q^18 - 4 * q^19 - 10 * q^20 - 11 * q^21 - 5 * q^22 - 31 * q^24 + 8 * q^25 - 22 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 8 * q^30 + 4 * q^31 - 13 * q^32 - 6 * q^33 - 19 * q^35 + 14 * q^36 + 25 * q^37 + 18 * q^38 + 5 * q^39 + 13 * q^40 + 17 * q^42 + 11 * q^43 - 17 * q^44 + 25 * q^45 + q^46 - 9 * q^47 + 19 * q^48 + 13 * q^49 + 7 * q^50 - 8 * q^51 + 44 * q^52 + 8 * q^53 - 35 * q^54 - 13 * q^55 + 26 * q^56 - 3 * q^57 + 35 * q^58 - 19 * q^59 + 9 * q^60 + 25 * q^61 + 23 * q^62 - 11 * q^63 - 18 * q^64 + 8 * q^65 + 63 * q^66 - 24 * q^67 + 11 * q^68 - 5 * q^70 - 19 * q^71 - 15 * q^72 + 30 * q^73 - 17 * q^74 - 41 * q^75 + 4 * q^76 + 6 * q^77 - 18 * q^78 - 21 * q^79 + 19 * q^80 - 17 * q^81 + 6 * q^82 + 12 * q^83 - 36 * q^84 + 2 * q^85 + 31 * q^86 - 15 * q^87 - 8 * q^88 - 22 * q^89 - 36 * q^90 - 2 * q^91 - 7 * q^92 + 9 * q^93 + 16 * q^94 - 44 * q^95 + 2 * q^96 - 4 * q^97 - 22 * q^98 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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