LMFDB - Embedded newform 6017.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52748 q^{2} -3.01490 q^{3} +4.38814 q^{4} +1.64213 q^{5} +7.62008 q^{6} +3.19622 q^{7} -6.03597 q^{8} +6.08959 q^{9} +O(q^{10})$	\(q-2.52748 q^{2} -3.01490 q^{3} +4.38814 q^{4} +1.64213 q^{5} +7.62008 q^{6} +3.19622 q^{7} -6.03597 q^{8} +6.08959 q^{9} -4.15044 q^{10} -1.00000 q^{11} -13.2298 q^{12} -0.382053 q^{13} -8.07836 q^{14} -4.95084 q^{15} +6.47949 q^{16} -4.00010 q^{17} -15.3913 q^{18} -6.54968 q^{19} +7.20588 q^{20} -9.63625 q^{21} +2.52748 q^{22} +7.73601 q^{23} +18.1978 q^{24} -2.30342 q^{25} +0.965630 q^{26} -9.31480 q^{27} +14.0254 q^{28} +8.77340 q^{29} +12.5131 q^{30} -1.42767 q^{31} -4.30482 q^{32} +3.01490 q^{33} +10.1102 q^{34} +5.24859 q^{35} +26.7220 q^{36} +9.27786 q^{37} +16.5542 q^{38} +1.15185 q^{39} -9.91183 q^{40} +4.92019 q^{41} +24.3554 q^{42} -1.65433 q^{43} -4.38814 q^{44} +9.99989 q^{45} -19.5526 q^{46} -11.9117 q^{47} -19.5350 q^{48} +3.21579 q^{49} +5.82183 q^{50} +12.0599 q^{51} -1.67650 q^{52} -9.31240 q^{53} +23.5429 q^{54} -1.64213 q^{55} -19.2922 q^{56} +19.7466 q^{57} -22.1746 q^{58} +5.27658 q^{59} -21.7250 q^{60} -0.255834 q^{61} +3.60839 q^{62} +19.4637 q^{63} -2.07865 q^{64} -0.627380 q^{65} -7.62008 q^{66} -11.0516 q^{67} -17.5530 q^{68} -23.3232 q^{69} -13.2657 q^{70} -4.45019 q^{71} -36.7566 q^{72} -6.73588 q^{73} -23.4496 q^{74} +6.94456 q^{75} -28.7409 q^{76} -3.19622 q^{77} -2.91127 q^{78} +7.59552 q^{79} +10.6401 q^{80} +9.81437 q^{81} -12.4357 q^{82} -9.75736 q^{83} -42.2852 q^{84} -6.56868 q^{85} +4.18128 q^{86} -26.4509 q^{87} +6.03597 q^{88} +0.00887236 q^{89} -25.2745 q^{90} -1.22112 q^{91} +33.9467 q^{92} +4.30426 q^{93} +30.1067 q^{94} -10.7554 q^{95} +12.9786 q^{96} +6.78487 q^{97} -8.12784 q^{98} -6.08959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.52748	−1.78720	−0.893598	−	0.448868i	$-0.851827\pi$
$2$	−2.52748	−1.78720	−0.893598	+	0.448868i	$0.851827\pi$
$3$	−3.01490	−1.74065	−0.870325	−	0.492477i	$-0.836091\pi$
$3$	−3.01490	−1.74065	−0.870325	+	0.492477i	$0.836091\pi$
$4$	4.38814	2.19407
$5$	1.64213	0.734382	0.367191	−	0.930146i	$-0.380320\pi$
$5$	1.64213	0.734382	0.367191	+	0.930146i	$0.380320\pi$
$6$	7.62008	3.11088
$7$	3.19622	1.20806	0.604028	−	0.796963i	$-0.293562\pi$
$7$	3.19622	1.20806	0.604028	+	0.796963i	$0.293562\pi$
$8$	−6.03597	−2.13404
$9$	6.08959	2.02986
$10$	−4.15044	−1.31248
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−13.2298	−3.81911
$13$	−0.382053	−0.105962	−0.0529812	−	0.998596i	$-0.516872\pi$
$13$	−0.382053	−0.105962	−0.0529812	+	0.998596i	$0.516872\pi$
$14$	−8.07836	−2.15903
$15$	−4.95084	−1.27830
$16$	6.47949	1.61987
$17$	−4.00010	−0.970167	−0.485084	−	0.874468i	$-0.661211\pi$
$17$	−4.00010	−0.970167	−0.485084	+	0.874468i	$0.661211\pi$
$18$	−15.3913	−3.62777
$19$	−6.54968	−1.50260	−0.751300	−	0.659961i	$-0.770573\pi$
$19$	−6.54968	−1.50260	−0.751300	+	0.659961i	$0.770573\pi$
$20$	7.20588	1.61128
$21$	−9.63625	−2.10280
$22$	2.52748	0.538860
$23$	7.73601	1.61307	0.806534	−	0.591187i	$-0.201341\pi$
$23$	7.73601	1.61307	0.806534	+	0.591187i	$0.201341\pi$
$24$	18.1978	3.71461
$25$	−2.30342	−0.460683
$26$	0.965630	0.189376
$27$	−9.31480	−1.79263
$28$	14.0254	2.65056
$29$	8.77340	1.62918	0.814590	−	0.580038i	$-0.196962\pi$
$29$	8.77340	1.62918	0.814590	+	0.580038i	$0.196962\pi$
$30$	12.5131	2.28458
$31$	−1.42767	−0.256416	−0.128208	−	0.991747i	$-0.540923\pi$
$31$	−1.42767	−0.256416	−0.128208	+	0.991747i	$0.540923\pi$
$32$	−4.30482	−0.760991
$33$	3.01490	0.524826
$34$	10.1102	1.73388
$35$	5.24859	0.887174
$36$	26.7220	4.45366
$37$	9.27786	1.52527	0.762636	−	0.646828i	$-0.223905\pi$
$37$	9.27786	1.52527	0.762636	+	0.646828i	$0.223905\pi$
$38$	16.5542	2.68544
$39$	1.15185	0.184444
$40$	−9.91183	−1.56720
$41$	4.92019	0.768404	0.384202	−	0.923249i	$-0.374477\pi$
$41$	4.92019	0.768404	0.384202	+	0.923249i	$0.374477\pi$
$42$	24.3554	3.75812
$43$	−1.65433	−0.252283	−0.126141	−	0.992012i	$-0.540259\pi$
$43$	−1.65433	−0.252283	−0.126141	+	0.992012i	$0.540259\pi$
$44$	−4.38814	−0.661537
$45$	9.99989	1.49070
$46$	−19.5526	−2.88287
$47$	−11.9117	−1.73751	−0.868753	−	0.495245i	$-0.835078\pi$
$47$	−11.9117	−1.73751	−0.868753	+	0.495245i	$0.835078\pi$
$48$	−19.5350	−2.81963
$49$	3.21579	0.459399
$50$	5.82183	0.823332
$51$	12.0599	1.68872
$52$	−1.67650	−0.232489
$53$	−9.31240	−1.27916	−0.639578	−	0.768726i	$-0.720891\pi$
$53$	−9.31240	−1.27916	−0.639578	+	0.768726i	$0.720891\pi$
$54$	23.5429	3.20379
$55$	−1.64213	−0.221424
$56$	−19.2922	−2.57803
$57$	19.7466	2.61550
$58$	−22.1746	−2.91166
$59$	5.27658	0.686953	0.343476	−	0.939161i	$-0.388395\pi$
$59$	5.27658	0.686953	0.343476	+	0.939161i	$0.388395\pi$
$60$	−21.7250	−2.80468
$61$	−0.255834	−0.0327562	−0.0163781	−	0.999866i	$-0.505214\pi$
$61$	−0.255834	−0.0327562	−0.0163781	+	0.999866i	$0.505214\pi$
$62$	3.60839	0.458266
$63$	19.4637	2.45219
$64$	−2.07865	−0.259831
$65$	−0.627380	−0.0778168
$66$	−7.62008	−0.937967
$67$	−11.0516	−1.35017	−0.675084	−	0.737741i	$-0.735893\pi$
$67$	−11.0516	−1.35017	−0.675084	+	0.737741i	$0.735893\pi$
$68$	−17.5530	−2.12861
$69$	−23.3232	−2.80779
$70$	−13.2657	−1.58555
$71$	−4.45019	−0.528140	−0.264070	−	0.964504i	$-0.585065\pi$
$71$	−4.45019	−0.528140	−0.264070	+	0.964504i	$0.585065\pi$
$72$	−36.7566	−4.33180
$73$	−6.73588	−0.788375	−0.394188	−	0.919030i	$-0.628974\pi$
$73$	−6.73588	−0.788375	−0.394188	+	0.919030i	$0.628974\pi$
$74$	−23.4496	−2.72596
$75$	6.94456	0.801889
$76$	−28.7409	−3.29681
$77$	−3.19622	−0.364243
$78$	−2.91127	−0.329637
$79$	7.59552	0.854563	0.427282	−	0.904119i	$-0.359471\pi$
$79$	7.59552	0.854563	0.427282	+	0.904119i	$0.359471\pi$
$80$	10.6401	1.18960
$81$	9.81437	1.09049
$82$	−12.4357	−1.37329
$83$	−9.75736	−1.07101	−0.535505	−	0.844532i	$-0.679879\pi$
$83$	−9.75736	−1.07101	−0.535505	+	0.844532i	$0.679879\pi$
$84$	−42.2852	−4.61370
$85$	−6.56868	−0.712473
$86$	4.18128	0.450879
$87$	−26.4509	−2.83583
$88$	6.03597	0.643436
$89$	0.00887236	0.000940468 0	0.000470234	−	1.00000i	$-0.499850\pi$
$89$	0.00887236	0.000940468 0	0.000470234		1.00000i	$0.499850\pi$
$90$	−25.2745	−2.66416
$91$	−1.22112	−0.128008
$92$	33.9467	3.53918
$93$	4.30426	0.446331
$94$	30.1067	3.10526
$95$	−10.7554	−1.10348
$96$	12.9786	1.32462
$97$	6.78487	0.688899	0.344450	−	0.938805i	$-0.388066\pi$
$97$	6.78487	0.688899	0.344450	+	0.938805i	$0.388066\pi$
$98$	−8.12784	−0.821036
$99$	−6.08959	−0.612027
$100$	−10.1077	−1.01077
$101$	15.2176	1.51421	0.757103	−	0.653295i	$-0.226614\pi$
$101$	15.2176	1.51421	0.757103	+	0.653295i	$0.226614\pi$
$102$	−30.4811	−3.01808
$103$	−1.99590	−0.196662	−0.0983310	−	0.995154i	$-0.531350\pi$
$103$	−1.99590	−0.196662	−0.0983310	+	0.995154i	$0.531350\pi$
$104$	2.30606	0.226128
$105$	−15.8240	−1.54426
$106$	23.5369	2.28610
$107$	15.6583	1.51375	0.756873	−	0.653562i	$-0.226726\pi$
$107$	15.6583	1.51375	0.756873	+	0.653562i	$0.226726\pi$
$108$	−40.8746	−3.93316
$109$	−1.20455	−0.115375	−0.0576875	−	0.998335i	$-0.518373\pi$
$109$	−1.20455	−0.115375	−0.0576875	+	0.998335i	$0.518373\pi$
$110$	4.15044	0.395729
$111$	−27.9718	−2.65496
$112$	20.7098	1.95690
$113$	−3.32369	−0.312666	−0.156333	−	0.987704i	$-0.549967\pi$
$113$	−3.32369	−0.312666	−0.156333	+	0.987704i	$0.549967\pi$
$114$	−49.9091	−4.67441
$115$	12.7035	1.18461
$116$	38.4989	3.57453
$117$	−2.32655	−0.215089
$118$	−13.3364	−1.22772
$119$	−12.7852	−1.17202
$120$	29.8831	2.72794
$121$	1.00000	0.0909091
$122$	0.646616	0.0585418
$123$	−14.8338	−1.33752
$124$	−6.26479	−0.562595
$125$	−11.9931	−1.07270
$126$	−49.1939	−4.38254
$127$	−17.8581	−1.58465	−0.792323	−	0.610101i	$-0.791129\pi$
$127$	−17.8581	−1.58465	−0.792323	+	0.610101i	$0.791129\pi$
$128$	13.8634	1.22536
$129$	4.98763	0.439136
$130$	1.58569	0.139074
$131$	−5.37094	−0.469261	−0.234631	−	0.972085i	$-0.575388\pi$
$131$	−5.37094	−0.469261	−0.234631	+	0.972085i	$0.575388\pi$
$132$	13.2298	1.15150
$133$	−20.9342	−1.81523
$134$	27.9327	2.41301
$135$	−15.2961	−1.31648
$136$	24.1445	2.07037
$137$	−3.96240	−0.338531	−0.169266	−	0.985570i	$-0.554140\pi$
$137$	−3.96240	−0.338531	−0.169266	+	0.985570i	$0.554140\pi$
$138$	58.9490	5.01807
$139$	4.07016	0.345226	0.172613	−	0.984990i	$-0.444779\pi$
$139$	4.07016	0.345226	0.172613	+	0.984990i	$0.444779\pi$
$140$	23.0316	1.94652
$141$	35.9127	3.02439
$142$	11.2477	0.943889
$143$	0.382053	0.0319489
$144$	39.4574	3.28812
$145$	14.4070	1.19644
$146$	17.0248	1.40898
$147$	−9.69528	−0.799653
$148$	40.7125	3.34655
$149$	5.35726	0.438883	0.219442	−	0.975626i	$-0.429576\pi$
$149$	5.35726	0.438883	0.219442	+	0.975626i	$0.429576\pi$
$150$	−17.5522	−1.43313
$151$	3.89448	0.316929	0.158464	−	0.987365i	$-0.449346\pi$
$151$	3.89448	0.316929	0.158464	+	0.987365i	$0.449346\pi$
$152$	39.5337	3.20660
$153$	−24.3590	−1.96931
$154$	8.07836	0.650973
$155$	−2.34441	−0.188307
$156$	5.05447	0.404682
$157$	−15.0485	−1.20100	−0.600500	−	0.799625i	$-0.705032\pi$
$157$	−15.0485	−1.20100	−0.600500	+	0.799625i	$0.705032\pi$
$158$	−19.1975	−1.52727
$159$	28.0759	2.22656
$160$	−7.06906	−0.558858
$161$	24.7259	1.94868
$162$	−24.8056	−1.94891
$163$	−5.39036	−0.422205	−0.211103	−	0.977464i	$-0.567705\pi$
$163$	−5.39036	−0.422205	−0.211103	+	0.977464i	$0.567705\pi$
$164$	21.5905	1.68593
$165$	4.95084	0.385423
$166$	24.6615	1.91410
$167$	6.46125	0.499987	0.249993	−	0.968248i	$-0.419572\pi$
$167$	6.46125	0.499987	0.249993	+	0.968248i	$0.419572\pi$
$168$	58.1641	4.48746
$169$	−12.8540	−0.988772
$170$	16.6022	1.27333
$171$	−39.8849	−3.05007
$172$	−7.25943	−0.553526
$173$	2.83895	0.215841	0.107921	−	0.994160i	$-0.465581\pi$
$173$	2.83895	0.215841	0.107921	+	0.994160i	$0.465581\pi$
$174$	66.8540	5.06819
$175$	−7.36222	−0.556531
$176$	−6.47949	−0.488410
$177$	−15.9083	−1.19574
$178$	−0.0224247	−0.00168080
$179$	14.5712	1.08910	0.544551	−	0.838728i	$-0.316700\pi$
$179$	14.5712	1.08910	0.544551	+	0.838728i	$0.316700\pi$
$180$	43.8809	3.27069
$181$	4.34769	0.323161	0.161581	−	0.986860i	$-0.448341\pi$
$181$	4.34769	0.323161	0.161581	+	0.986860i	$0.448341\pi$
$182$	3.08636	0.228776
$183$	0.771314	0.0570172
$184$	−46.6943	−3.44235
$185$	15.2354	1.12013
$186$	−10.8789	−0.797681
$187$	4.00010	0.292516
$188$	−52.2704	−3.81221
$189$	−29.7721	−2.16560
$190$	27.1841	1.97214
$191$	−20.4303	−1.47829	−0.739143	−	0.673548i	$-0.764769\pi$
$191$	−20.4303	−1.47829	−0.739143	+	0.673548i	$0.764769\pi$
$192$	6.26690	0.452274
$193$	−22.8496	−1.64475	−0.822375	−	0.568946i	$-0.807351\pi$
$193$	−22.8496	−1.64475	−0.822375	+	0.568946i	$0.807351\pi$
$194$	−17.1486	−1.23120
$195$	1.89148	0.135452
$196$	14.1113	1.00795
$197$	−11.0892	−0.790076	−0.395038	−	0.918665i	$-0.629269\pi$
$197$	−11.0892	−0.790076	−0.395038	+	0.918665i	$0.629269\pi$
$198$	15.3913	1.09381
$199$	−7.04418	−0.499349	−0.249674	−	0.968330i	$-0.580324\pi$
$199$	−7.04418	−0.499349	−0.249674	+	0.968330i	$0.580324\pi$
$200$	13.9033	0.983115
$201$	33.3194	2.35017
$202$	−38.4621	−2.70618
$203$	28.0417	1.96814
$204$	52.9205	3.70517
$205$	8.07957	0.564302
$206$	5.04459	0.351474
$207$	47.1091	3.27431
$208$	−2.47551	−0.171645
$209$	6.54968	0.453051
$210$	39.9947	2.75990
$211$	6.62321	0.455960	0.227980	−	0.973666i	$-0.426788\pi$
$211$	6.62321	0.455960	0.227980	+	0.973666i	$0.426788\pi$
$212$	−40.8641	−2.80656
$213$	13.4168	0.919307
$214$	−39.5760	−2.70536
$215$	−2.71662	−0.185272
$216$	56.2238	3.82555
$217$	−4.56313	−0.309765
$218$	3.04447	0.206198
$219$	20.3080	1.37229
$220$	−7.20588	−0.485821
$221$	1.52825	0.102801
$222$	70.6980	4.74494
$223$	−23.0051	−1.54054	−0.770268	−	0.637720i	$-0.779878\pi$
$223$	−23.0051	−1.54054	−0.770268	+	0.637720i	$0.779878\pi$
$224$	−13.7591	−0.919320
$225$	−14.0269	−0.935125
$226$	8.40055	0.558796
$227$	−6.19822	−0.411390	−0.205695	−	0.978616i	$-0.565946\pi$
$227$	−6.19822	−0.411390	−0.205695	+	0.978616i	$0.565946\pi$
$228$	86.6509	5.73859
$229$	−26.6391	−1.76036	−0.880179	−	0.474641i	$-0.842578\pi$
$229$	−26.6391	−1.76036	−0.880179	+	0.474641i	$0.842578\pi$
$230$	−32.1078	−2.11713
$231$	9.63625	0.634019
$232$	−52.9559	−3.47673
$233$	19.7637	1.29476	0.647381	−	0.762167i	$-0.275864\pi$
$233$	19.7637	1.29476	0.647381	+	0.762167i	$0.275864\pi$
$234$	5.88029	0.384407
$235$	−19.5606	−1.27599
$236$	23.1544	1.50722
$237$	−22.8997	−1.48750
$238$	32.3143	2.09462
$239$	−13.9684	−0.903541	−0.451770	−	0.892134i	$-0.649207\pi$
$239$	−13.9684	−0.903541	−0.451770	+	0.892134i	$0.649207\pi$
$240$	−32.0789	−2.07068
$241$	−9.14051	−0.588792	−0.294396	−	0.955684i	$-0.595118\pi$
$241$	−9.14051	−0.588792	−0.294396	+	0.955684i	$0.595118\pi$
$242$	−2.52748	−0.162472
$243$	−1.64489	−0.105520
$244$	−1.12264	−0.0718695
$245$	5.28074	0.337374
$246$	37.4922	2.39042
$247$	2.50232	0.159219
$248$	8.61734	0.547202
$249$	29.4174	1.86425
$250$	30.3124	1.91712
$251$	23.0817	1.45690	0.728452	−	0.685097i	$-0.240240\pi$
$251$	23.0817	1.45690	0.728452	+	0.685097i	$0.240240\pi$
$252$	85.4092	5.38027
$253$	−7.73601	−0.486359
$254$	45.1358	2.83207
$255$	19.8039	1.24017
$256$	−30.8820	−1.93013
$257$	18.2928	1.14107	0.570536	−	0.821273i	$-0.306736\pi$
$257$	18.2928	1.14107	0.570536	+	0.821273i	$0.306736\pi$
$258$	−12.6061	−0.784823
$259$	29.6540	1.84261
$260$	−2.75303	−0.170736
$261$	53.4264	3.30701
$262$	13.5749	0.838662
$263$	−18.7335	−1.15516	−0.577578	−	0.816336i	$-0.696002\pi$
$263$	−18.7335	−1.15516	−0.577578	+	0.816336i	$0.696002\pi$
$264$	−18.1978	−1.12000
$265$	−15.2921	−0.939389
$266$	52.9107	3.24416
$267$	−0.0267492	−0.00163703
$268$	−48.4960	−2.96236
$269$	−2.01011	−0.122559	−0.0612794	−	0.998121i	$-0.519518\pi$
$269$	−2.01011	−0.122559	−0.0612794	+	0.998121i	$0.519518\pi$
$270$	38.6605	2.35280
$271$	3.82442	0.232317	0.116159	−	0.993231i	$-0.462942\pi$
$271$	3.82442	0.232317	0.116159	+	0.993231i	$0.462942\pi$
$272$	−25.9186	−1.57155
$273$	3.68156	0.222818
$274$	10.0149	0.605021
$275$	2.30342	0.138901
$276$	−102.346	−6.16048
$277$	7.64065	0.459082	0.229541	−	0.973299i	$-0.426278\pi$
$277$	7.64065	0.459082	0.229541	+	0.973299i	$0.426278\pi$
$278$	−10.2872	−0.616987
$279$	−8.69390	−0.520490
$280$	−31.6803	−1.89326
$281$	20.8290	1.24256	0.621278	−	0.783590i	$-0.286614\pi$
$281$	20.8290	1.24256	0.621278	+	0.783590i	$0.286614\pi$
$282$	−90.7684	−5.40518
$283$	3.23442	0.192266	0.0961332	−	0.995368i	$-0.469353\pi$
$283$	3.23442	0.192266	0.0961332	+	0.995368i	$0.469353\pi$
$284$	−19.5280	−1.15878
$285$	32.4264	1.92078
$286$	−0.965630	−0.0570989
$287$	15.7260	0.928275
$288$	−26.2146	−1.54471
$289$	−0.999181	−0.0587753
$290$	−36.4135	−2.13827
$291$	−20.4557	−1.19913
$292$	−29.5580	−1.72975
$293$	15.7205	0.918403	0.459201	−	0.888332i	$-0.348136\pi$
$293$	15.7205	0.918403	0.459201	+	0.888332i	$0.348136\pi$
$294$	24.5046	1.42914
$295$	8.66482	0.504485
$296$	−56.0009	−3.25498
$297$	9.31480	0.540500
$298$	−13.5403	−0.784371
$299$	−2.95556	−0.170925
$300$	30.4737	1.75940
$301$	−5.28759	−0.304772
$302$	−9.84322	−0.566414
$303$	−45.8794	−2.63570
$304$	−42.4386	−2.43402
$305$	−0.420113	−0.0240556
$306$	61.5668	3.51954
$307$	−17.5585	−1.00212	−0.501059	−	0.865413i	$-0.667056\pi$
$307$	−17.5585	−1.00212	−0.501059	+	0.865413i	$0.667056\pi$
$308$	−14.0254	−0.799173
$309$	6.01743	0.342320
$310$	5.92544	0.336542
$311$	−1.80211	−0.102188	−0.0510942	−	0.998694i	$-0.516271\pi$
$311$	−1.80211	−0.102188	−0.0510942	+	0.998694i	$0.516271\pi$
$312$	−6.95252	−0.393609
$313$	7.93793	0.448679	0.224339	−	0.974511i	$-0.427978\pi$
$313$	7.93793	0.448679	0.224339	+	0.974511i	$0.427978\pi$
$314$	38.0347	2.14642
$315$	31.9618	1.80084
$316$	33.3302	1.87497
$317$	−20.3475	−1.14283	−0.571415	−	0.820661i	$-0.693605\pi$
$317$	−20.3475	−1.14283	−0.571415	+	0.820661i	$0.693605\pi$
$318$	−70.9612	−3.97931
$319$	−8.77340	−0.491216
$320$	−3.41340	−0.190815
$321$	−47.2081	−2.63490
$322$	−62.4942	−3.48267
$323$	26.1994	1.45777
$324$	43.0668	2.39260
$325$	0.880027	0.0488151
$326$	13.6240	0.754564
$327$	3.63159	0.200827
$328$	−29.6981	−1.63980
$329$	−38.0725	−2.09900
$330$	−12.5131	−0.688826
$331$	15.6006	0.857489	0.428744	−	0.903426i	$-0.358956\pi$
$331$	15.6006	0.857489	0.428744	+	0.903426i	$0.358956\pi$
$332$	−42.8167	−2.34987
$333$	56.4984	3.09609
$334$	−16.3307	−0.893574
$335$	−18.1481	−0.991539
$336$	−62.4380	−3.40627
$337$	−20.0599	−1.09273	−0.546365	−	0.837547i	$-0.683989\pi$
$337$	−20.0599	−1.09273	−0.546365	+	0.837547i	$0.683989\pi$
$338$	32.4883	1.76713
$339$	10.0206	0.544243
$340$	−28.8243	−1.56322
$341$	1.42767	0.0773124
$342$	100.808	5.45108
$343$	−12.0951	−0.653076
$344$	9.98547	0.538381
$345$	−38.2997	−2.06199
$346$	−7.17538	−0.385751
$347$	31.5376	1.69303	0.846513	−	0.532368i	$-0.178698\pi$
$347$	31.5376	1.69303	0.846513	+	0.532368i	$0.178698\pi$
$348$	−116.070	−6.22201
$349$	16.2130	0.867860	0.433930	−	0.900947i	$-0.357127\pi$
$349$	16.2130	0.867860	0.433930	+	0.900947i	$0.357127\pi$
$350$	18.6078	0.994631
$351$	3.55875	0.189952
$352$	4.30482	0.229448
$353$	0.975875	0.0519406	0.0259703	−	0.999663i	$-0.491732\pi$
$353$	0.975875	0.0519406	0.0259703	+	0.999663i	$0.491732\pi$
$354$	40.2080	2.13703
$355$	−7.30777	−0.387856
$356$	0.0389331	0.00206345
$357$	38.5460	2.04007
$358$	−36.8284	−1.94644
$359$	−13.7514	−0.725771	−0.362885	−	0.931834i	$-0.618208\pi$
$359$	−13.7514	−0.725771	−0.362885	+	0.931834i	$0.618208\pi$
$360$	−60.3590	−3.18120
$361$	23.8983	1.25781
$362$	−10.9887	−0.577553
$363$	−3.01490	−0.158241
$364$	−5.35846	−0.280860
$365$	−11.0612	−0.578968
$366$	−1.94948	−0.101901
$367$	−17.7340	−0.925707	−0.462854	−	0.886435i	$-0.653174\pi$
$367$	−17.7340	−0.925707	−0.462854	+	0.886435i	$0.653174\pi$
$368$	50.1253	2.61296
$369$	29.9619	1.55976
$370$	−38.5072	−2.00189
$371$	−29.7644	−1.54529
$372$	18.8877	0.979281
$373$	29.7225	1.53897	0.769487	−	0.638663i	$-0.220512\pi$
$373$	29.7225	1.53897	0.769487	+	0.638663i	$0.220512\pi$
$374$	−10.1102	−0.522784
$375$	36.1581	1.86719
$376$	71.8989	3.70790
$377$	−3.35190	−0.172632
$378$	75.2483	3.87036
$379$	6.32284	0.324783	0.162391	−	0.986726i	$-0.448079\pi$
$379$	6.32284	0.324783	0.162391	+	0.986726i	$0.448079\pi$
$380$	−47.1963	−2.42112
$381$	53.8402	2.75832
$382$	51.6372	2.64199
$383$	−6.76790	−0.345823	−0.172912	−	0.984937i	$-0.555318\pi$
$383$	−6.76790	−0.345823	−0.172912	+	0.984937i	$0.555318\pi$
$384$	−41.7966	−2.13292
$385$	−5.24859	−0.267493
$386$	57.7518	2.93949
$387$	−10.0742	−0.512100
$388$	29.7729	1.51149
$389$	19.3988	0.983557	0.491778	−	0.870720i	$-0.336347\pi$
$389$	19.3988	0.983557	0.491778	+	0.870720i	$0.336347\pi$
$390$	−4.78068	−0.242079
$391$	−30.9448	−1.56495
$392$	−19.4104	−0.980374
$393$	16.1928	0.816820
$394$	28.0278	1.41202
$395$	12.4728	0.627576
$396$	−26.7220	−1.34283
$397$	22.7966	1.14413	0.572064	−	0.820209i	$-0.306143\pi$
$397$	22.7966	1.14413	0.572064	+	0.820209i	$0.306143\pi$
$398$	17.8040	0.892434
$399$	63.1144	3.15967
$400$	−14.9250	−0.746248
$401$	11.1721	0.557910	0.278955	−	0.960304i	$-0.410012\pi$
$401$	11.1721	0.557910	0.278955	+	0.960304i	$0.410012\pi$
$402$	−84.2141	−4.20022
$403$	0.545444	0.0271705
$404$	66.7769	3.32227
$405$	16.1164	0.800833
$406$	−70.8747	−3.51745
$407$	−9.27786	−0.459887
$408$	−72.7931	−3.60379
$409$	−22.3420	−1.10474	−0.552371	−	0.833598i	$-0.686277\pi$
$409$	−22.3420	−1.10474	−0.552371	+	0.833598i	$0.686277\pi$
$410$	−20.4209	−1.00852
$411$	11.9462	0.589264
$412$	−8.75829	−0.431490
$413$	16.8651	0.829877
$414$	−119.067	−5.85184
$415$	−16.0228	−0.786530
$416$	1.64467	0.0806365
$417$	−12.2711	−0.600919
$418$	−16.5542	−0.809691
$419$	−15.5639	−0.760344	−0.380172	−	0.924916i	$-0.624135\pi$
$419$	−15.5639	−0.760344	−0.380172	+	0.924916i	$0.624135\pi$
$420$	−69.4377	−3.38821
$421$	37.5427	1.82972	0.914860	−	0.403771i	$-0.132301\pi$
$421$	37.5427	1.82972	0.914860	+	0.403771i	$0.132301\pi$
$422$	−16.7400	−0.814890
$423$	−72.5377	−3.52690
$424$	56.2093	2.72977
$425$	9.21390	0.446940
$426$	−33.9108	−1.64298
$427$	−0.817702	−0.0395714
$428$	68.7108	3.32126
$429$	−1.15185	−0.0556118
$430$	6.86619	0.331117
$431$	−1.62014	−0.0780392	−0.0390196	−	0.999238i	$-0.512423\pi$
$431$	−1.62014	−0.0780392	−0.0390196	+	0.999238i	$0.512423\pi$
$432$	−60.3551	−2.90384
$433$	−26.3986	−1.26863	−0.634317	−	0.773073i	$-0.718719\pi$
$433$	−26.3986	−1.26863	−0.634317	+	0.773073i	$0.718719\pi$
$434$	11.5332	0.553611
$435$	−43.4357	−2.08258
$436$	−5.28573	−0.253141
$437$	−50.6684	−2.42380
$438$	−51.3279	−2.45254
$439$	0.753583	0.0359666	0.0179833	−	0.999838i	$-0.494275\pi$
$439$	0.753583	0.0359666	0.0179833	+	0.999838i	$0.494275\pi$
$440$	9.91183	0.472528
$441$	19.5829	0.932518
$442$	−3.86262	−0.183726
$443$	7.99632	0.379917	0.189958	−	0.981792i	$-0.439165\pi$
$443$	7.99632	0.379917	0.189958	+	0.981792i	$0.439165\pi$
$444$	−122.744	−5.82518
$445$	0.0145695	0.000690662 0
$446$	58.1449	2.75324
$447$	−16.1516	−0.763943
$448$	−6.64380	−0.313890
$449$	−0.603222	−0.0284678	−0.0142339	−	0.999899i	$-0.504531\pi$
$449$	−0.603222	−0.0284678	−0.0142339	+	0.999899i	$0.504531\pi$
$450$	35.4526	1.67125
$451$	−4.92019	−0.231683
$452$	−14.5848	−0.686012
$453$	−11.7415	−0.551662
$454$	15.6659	0.735235
$455$	−2.00524	−0.0940071
$456$	−119.190	−5.58158
$457$	8.72370	0.408078	0.204039	−	0.978963i	$-0.434593\pi$
$457$	8.72370	0.408078	0.204039	+	0.978963i	$0.434593\pi$
$458$	67.3296	3.14611
$459$	37.2602	1.73916
$460$	55.7448	2.59911
$461$	−10.1252	−0.471577	−0.235788	−	0.971804i	$-0.575767\pi$
$461$	−10.1252	−0.471577	−0.235788	+	0.971804i	$0.575767\pi$
$462$	−24.3554	−1.13312
$463$	22.6589	1.05305	0.526524	−	0.850160i	$-0.323495\pi$
$463$	22.6589	1.05305	0.526524	+	0.850160i	$0.323495\pi$
$464$	56.8471	2.63906
$465$	7.06815	0.327777
$466$	−49.9522	−2.31399
$467$	−31.0270	−1.43576	−0.717879	−	0.696168i	$-0.754887\pi$
$467$	−31.0270	−1.43576	−0.717879	+	0.696168i	$0.754887\pi$
$468$	−10.2092	−0.471921
$469$	−35.3233	−1.63108
$470$	49.4390	2.28045
$471$	45.3696	2.09052
$472$	−31.8493	−1.46598
$473$	1.65433	0.0760661
$474$	57.8785	2.65845
$475$	15.0867	0.692223
$476$	−56.1032	−2.57149
$477$	−56.7087	−2.59651
$478$	35.3048	1.61480
$479$	43.3028	1.97856	0.989278	−	0.146042i	$-0.0466536\pi$
$479$	43.3028	1.97856	0.989278	+	0.146042i	$0.0466536\pi$
$480$	21.3125	0.972777
$481$	−3.54463	−0.161621
$482$	23.1024	1.05229
$483$	−74.5461	−3.39197
$484$	4.38814	0.199461
$485$	11.1416	0.505915
$486$	4.15742	0.188584
$487$	−28.9829	−1.31334	−0.656669	−	0.754178i	$-0.728035\pi$
$487$	−28.9829	−1.31334	−0.656669	+	0.754178i	$0.728035\pi$
$488$	1.54421	0.0699030
$489$	16.2514	0.734912
$490$	−13.3470	−0.602954
$491$	−26.0383	−1.17509	−0.587547	−	0.809190i	$-0.699906\pi$
$491$	−26.0383	−1.17509	−0.587547	+	0.809190i	$0.699906\pi$
$492$	−65.0930	−2.93462
$493$	−35.0945	−1.58058
$494$	−6.32457	−0.284556
$495$	−9.99989	−0.449462
$496$	−9.25054	−0.415361
$497$	−14.2238	−0.638023
$498$	−74.3519	−3.33179
$499$	32.1747	1.44034	0.720168	−	0.693800i	$-0.244065\pi$
$499$	32.1747	1.44034	0.720168	+	0.693800i	$0.244065\pi$
$500$	−52.6276	−2.35358
$501$	−19.4800	−0.870302
$502$	−58.3384	−2.60377
$503$	−1.18596	−0.0528791	−0.0264396	−	0.999650i	$-0.508417\pi$
$503$	−1.18596	−0.0528791	−0.0264396	+	0.999650i	$0.508417\pi$
$504$	−117.482	−5.23306
$505$	24.9892	1.11201
$506$	19.5526	0.869218
$507$	38.7536	1.72111
$508$	−78.3636	−3.47682
$509$	−24.5801	−1.08950	−0.544748	−	0.838600i	$-0.683375\pi$
$509$	−24.5801	−1.08950	−0.544748	+	0.838600i	$0.683375\pi$
$510$	−50.0538	−2.21642
$511$	−21.5293	−0.952401
$512$	50.3269	2.22416
$513$	61.0090	2.69361
$514$	−46.2345	−2.03932
$515$	−3.27752	−0.144425
$516$	21.8864	0.963496
$517$	11.9117	0.523878
$518$	−74.9499	−3.29311
$519$	−8.55914	−0.375705
$520$	3.78684	0.166064
$521$	8.23523	0.360792	0.180396	−	0.983594i	$-0.442262\pi$
$521$	8.23523	0.360792	0.180396	+	0.983594i	$0.442262\pi$
$522$	−135.034	−5.91028
$523$	−3.30790	−0.144645	−0.0723223	−	0.997381i	$-0.523041\pi$
$523$	−3.30790	−0.144645	−0.0723223	+	0.997381i	$0.523041\pi$
$524$	−23.5684	−1.02959
$525$	22.1963	0.968727
$526$	47.3484	2.06449
$527$	5.71081	0.248767
$528$	19.5350	0.850150
$529$	36.8458	1.60199
$530$	38.6506	1.67887
$531$	32.1322	1.39442
$532$	−91.8622	−3.98273
$533$	−1.87977	−0.0814219
$534$	0.0676080	0.00292569
$535$	25.7129	1.11167
$536$	66.7071	2.88131
$537$	−43.9306	−1.89575
$538$	5.08051	0.219036
$539$	−3.21579	−0.138514
$540$	−67.1214	−2.88844
$541$	22.5718	0.970437	0.485219	−	0.874393i	$-0.338740\pi$
$541$	22.5718	0.970437	0.485219	+	0.874393i	$0.338740\pi$
$542$	−9.66614	−0.415196
$543$	−13.1078	−0.562511
$544$	17.2197	0.738289
$545$	−1.97802	−0.0847293
$546$	−9.30505	−0.398220
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−17.3876	−0.742761
$549$	−1.55793	−0.0664907
$550$	−5.82183	−0.248244
$551$	−57.4630	−2.44801
$552$	140.778	5.99192
$553$	24.2769	1.03236
$554$	−19.3116	−0.820469
$555$	−45.9332	−1.94976
$556$	17.8604	0.757451
$557$	19.3877	0.821483	0.410741	−	0.911752i	$-0.365270\pi$
$557$	19.3877	0.821483	0.410741	+	0.911752i	$0.365270\pi$
$558$	21.9736	0.930218
$559$	0.632041	0.0267325
$560$	34.0082	1.43711
$561$	−12.0599	−0.509169
$562$	−52.6449	−2.22069
$563$	−35.4838	−1.49546	−0.747732	−	0.664000i	$-0.768857\pi$
$563$	−35.4838	−1.49546	−0.747732	+	0.664000i	$0.768857\pi$
$564$	157.590	6.63572
$565$	−5.45792	−0.229616
$566$	−8.17492	−0.343618
$567$	31.3688	1.31737
$568$	26.8612	1.12707
$569$	−45.2915	−1.89872	−0.949358	−	0.314196i	$-0.898265\pi$
$569$	−45.2915	−1.89872	−0.949358	+	0.314196i	$0.898265\pi$
$570$	−81.9571	−3.43281
$571$	−42.5864	−1.78218	−0.891092	−	0.453822i	$-0.850060\pi$
$571$	−42.5864	−1.78218	−0.891092	+	0.453822i	$0.850060\pi$
$572$	1.67650	0.0700980
$573$	61.5953	2.57318
$574$	−39.7470	−1.65901
$575$	−17.8192	−0.743114
$576$	−12.6581	−0.527421
$577$	25.0751	1.04389	0.521945	−	0.852979i	$-0.325206\pi$
$577$	25.0751	1.04389	0.521945	+	0.852979i	$0.325206\pi$
$578$	2.52541	0.105043
$579$	68.8892	2.86294
$580$	63.2201	2.62507
$581$	−31.1866	−1.29384
$582$	51.7012	2.14308
$583$	9.31240	0.385680
$584$	40.6575	1.68242
$585$	−3.82049	−0.157958
$586$	−39.7333	−1.64137
$587$	−27.1666	−1.12129	−0.560643	−	0.828057i	$-0.689446\pi$
$587$	−27.1666	−1.12129	−0.560643	+	0.828057i	$0.689446\pi$
$588$	−42.5442	−1.75449
$589$	9.35076	0.385291
$590$	−21.9001	−0.901614
$591$	33.4329	1.37525
$592$	60.1158	2.47074
$593$	33.2293	1.36456	0.682281	−	0.731090i	$-0.260988\pi$
$593$	33.2293	1.36456	0.682281	+	0.731090i	$0.260988\pi$
$594$	−23.5429	−0.965979
$595$	−20.9949	−0.860707
$596$	23.5084	0.962941
$597$	21.2375	0.869192
$598$	7.47012	0.305476
$599$	6.34747	0.259350	0.129675	−	0.991557i	$-0.458607\pi$
$599$	6.34747	0.259350	0.129675	+	0.991557i	$0.458607\pi$
$600$	−41.9171	−1.71126
$601$	16.5653	0.675712	0.337856	−	0.941198i	$-0.390298\pi$
$601$	16.5653	0.675712	0.337856	+	0.941198i	$0.390298\pi$
$602$	13.3643	0.544687
$603$	−67.2998	−2.74066
$604$	17.0895	0.695363
$605$	1.64213	0.0667620
$606$	115.959	4.71052
$607$	−2.20835	−0.0896343	−0.0448171	−	0.998995i	$-0.514271\pi$
$607$	−2.20835	−0.0896343	−0.0448171	+	0.998995i	$0.514271\pi$
$608$	28.1952	1.14347
$609$	−84.5427	−3.42584
$610$	1.06183	0.0429921
$611$	4.55092	0.184110
$612$	−106.891	−4.32080
$613$	−29.7805	−1.20282	−0.601412	−	0.798939i	$-0.705395\pi$
$613$	−29.7805	−1.20282	−0.601412	+	0.798939i	$0.705395\pi$
$614$	44.3787	1.79098
$615$	−24.3591	−0.982253
$616$	19.2922	0.777307
$617$	−5.20274	−0.209455	−0.104727	−	0.994501i	$-0.533397\pi$
$617$	−5.20274	−0.209455	−0.104727	+	0.994501i	$0.533397\pi$
$618$	−15.2089	−0.611793
$619$	−17.3478	−0.697266	−0.348633	−	0.937259i	$-0.613354\pi$
$619$	−17.3478	−0.697266	−0.348633	+	0.937259i	$0.613354\pi$
$620$	−10.2876	−0.413160
$621$	−72.0594	−2.89164
$622$	4.55480	0.182631
$623$	0.0283580	0.00113614
$624$	7.46339	0.298775
$625$	−8.17718	−0.327087
$626$	−20.0629	−0.801877
$627$	−19.7466	−0.788604
$628$	−66.0349	−2.63508
$629$	−37.1124	−1.47977
$630$	−80.7827	−3.21846
$631$	21.3185	0.848675	0.424337	−	0.905504i	$-0.360507\pi$
$631$	21.3185	0.848675	0.424337	+	0.905504i	$0.360507\pi$
$632$	−45.8463	−1.82367
$633$	−19.9683	−0.793668
$634$	51.4279	2.04246
$635$	−29.3252	−1.16374
$636$	123.201	4.88524
$637$	−1.22860	−0.0486790
$638$	22.1746	0.877899
$639$	−27.0998	−1.07205
$640$	22.7654	0.899882
$641$	14.1095	0.557293	0.278647	−	0.960394i	$-0.410114\pi$
$641$	14.1095	0.557293	0.278647	+	0.960394i	$0.410114\pi$
$642$	119.317	4.70909
$643$	−30.8100	−1.21503	−0.607514	−	0.794309i	$-0.707833\pi$
$643$	−30.8100	−1.21503	−0.607514	+	0.794309i	$0.707833\pi$
$644$	108.501	4.27553
$645$	8.19032	0.322494
$646$	−66.2184	−2.60533
$647$	−27.1728	−1.06827	−0.534137	−	0.845398i	$-0.679363\pi$
$647$	−27.1728	−1.06827	−0.534137	+	0.845398i	$0.679363\pi$
$648$	−59.2392	−2.32713
$649$	−5.27658	−0.207124
$650$	−2.22425	−0.0872422
$651$	13.7573	0.539193
$652$	−23.6536	−0.926348
$653$	−39.2047	−1.53420	−0.767100	−	0.641528i	$-0.778301\pi$
$653$	−39.2047	−1.53420	−0.767100	+	0.641528i	$0.778301\pi$
$654$	−9.17876	−0.358918
$655$	−8.81977	−0.344617
$656$	31.8803	1.24472
$657$	−41.0188	−1.60029
$658$	96.2274	3.75133
$659$	36.1256	1.40726	0.703628	−	0.710569i	$-0.251562\pi$
$659$	36.1256	1.40726	0.703628	+	0.710569i	$0.251562\pi$
$660$	21.7250	0.845644
$661$	−14.8694	−0.578352	−0.289176	−	0.957276i	$-0.593381\pi$
$661$	−14.8694	−0.578352	−0.289176	+	0.957276i	$0.593381\pi$
$662$	−39.4303	−1.53250
$663$	−4.60752	−0.178941
$664$	58.8951	2.28557
$665$	−34.3766	−1.33307
$666$	−142.798	−5.53333
$667$	67.8711	2.62798
$668$	28.3529	1.09701
$669$	69.3580	2.68154
$670$	45.8690	1.77207
$671$	0.255834	0.00987638
$672$	41.4823	1.60021
$673$	−46.5261	−1.79345	−0.896725	−	0.442589i	$-0.854060\pi$
$673$	−46.5261	−1.79345	−0.896725	+	0.442589i	$0.854060\pi$
$674$	50.7008	1.95292
$675$	21.4559	0.825837
$676$	−56.4053	−2.16943
$677$	25.4606	0.978529	0.489265	−	0.872135i	$-0.337265\pi$
$677$	25.4606	0.978529	0.489265	+	0.872135i	$0.337265\pi$
$678$	−25.3268	−0.972669
$679$	21.6859	0.832229
$680$	39.6483	1.52044
$681$	18.6870	0.716087
$682$	−3.60839	−0.138172
$683$	−15.2161	−0.582228	−0.291114	−	0.956688i	$-0.594026\pi$
$683$	−15.2161	−0.582228	−0.291114	+	0.956688i	$0.594026\pi$
$684$	−175.021	−6.69208
$685$	−6.50677	−0.248611
$686$	30.5702	1.16718
$687$	80.3140	3.06417
$688$	−10.7192	−0.408666
$689$	3.55783	0.135542
$690$	96.8017	3.68518
$691$	−17.1594	−0.652775	−0.326388	−	0.945236i	$-0.605832\pi$
$691$	−17.1594	−0.652775	−0.326388	+	0.945236i	$0.605832\pi$
$692$	12.4577	0.473571
$693$	−19.4637	−0.739363
$694$	−79.7105	−3.02577
$695$	6.68372	0.253528
$696$	159.657	6.05177
$697$	−19.6813	−0.745481
$698$	−40.9779	−1.55104
$699$	−59.5854	−2.25373
$700$	−32.3064	−1.22107
$701$	38.0105	1.43564	0.717819	−	0.696230i	$-0.245140\pi$
$701$	38.0105	1.43564	0.717819	+	0.696230i	$0.245140\pi$
$702$	−8.99465	−0.339481
$703$	−60.7671	−2.29187
$704$	2.07865	0.0783419
$705$	58.9732	2.22106
$706$	−2.46650	−0.0928280
$707$	48.6387	1.82925
$708$	−69.8080	−2.62355
$709$	−50.5900	−1.89995	−0.949973	−	0.312332i	$-0.898890\pi$
$709$	−50.5900	−1.89995	−0.949973	+	0.312332i	$0.898890\pi$
$710$	18.4702	0.693175
$711$	46.2537	1.73465
$712$	−0.0535532	−0.00200699
$713$	−11.0444	−0.413617
$714$	−97.4241	−3.64601
$715$	0.627380	0.0234627
$716$	63.9404	2.38957
$717$	42.1133	1.57275
$718$	34.7563	1.29709
$719$	20.1451	0.751287	0.375643	−	0.926764i	$-0.377422\pi$
$719$	20.1451	0.751287	0.375643	+	0.926764i	$0.377422\pi$
$720$	64.7941	2.41473
$721$	−6.37933	−0.237579
$722$	−60.4025	−2.24795
$723$	27.5577	1.02488
$724$	19.0783	0.709038
$725$	−20.2088	−0.750536
$726$	7.62008	0.282808
$727$	43.0535	1.59677	0.798383	−	0.602149i	$-0.205689\pi$
$727$	43.0535	1.59677	0.798383	+	0.602149i	$0.205689\pi$
$728$	7.37066	0.273175
$729$	−24.4839	−0.906812
$730$	27.9569	1.03473
$731$	6.61749	0.244757
$732$	3.38463	0.125100
$733$	−42.6316	−1.57463	−0.787317	−	0.616549i	$-0.788530\pi$
$733$	−42.6316	−1.57463	−0.787317	+	0.616549i	$0.788530\pi$
$734$	44.8223	1.65442
$735$	−15.9209	−0.587251
$736$	−33.3021	−1.22753
$737$	11.0516	0.407091
$738$	−75.7281	−2.78759
$739$	7.57072	0.278494	0.139247	−	0.990258i	$-0.455532\pi$
$739$	7.57072	0.278494	0.139247	+	0.990258i	$0.455532\pi$
$740$	66.8552	2.45765
$741$	−7.54425	−0.277145
$742$	75.2289	2.76174
$743$	20.6406	0.757229	0.378615	−	0.925554i	$-0.376401\pi$
$743$	20.6406	0.757229	0.378615	+	0.925554i	$0.376401\pi$
$744$	−25.9804	−0.952487
$745$	8.79730	0.322308
$746$	−75.1230	−2.75045
$747$	−59.4184	−2.17400
$748$	17.5530	0.641801
$749$	50.0473	1.82869
$750$	−91.3887	−3.33704
$751$	−17.8282	−0.650561	−0.325280	−	0.945618i	$-0.605459\pi$
$751$	−17.8282	−0.650561	−0.325280	+	0.945618i	$0.605459\pi$
$752$	−77.1820	−2.81454
$753$	−69.5889	−2.53596
$754$	8.47185	0.308527
$755$	6.39524	0.232747
$756$	−130.644	−4.75148
$757$	41.3061	1.50129	0.750647	−	0.660703i	$-0.229742\pi$
$757$	41.3061	1.50129	0.750647	+	0.660703i	$0.229742\pi$
$758$	−15.9808	−0.580450
$759$	23.3232	0.846580
$760$	64.9193	2.35487
$761$	−31.6255	−1.14642	−0.573211	−	0.819408i	$-0.694303\pi$
$761$	−31.6255	−1.14642	−0.573211	+	0.819408i	$0.694303\pi$
$762$	−136.080	−4.92965
$763$	−3.85000	−0.139379
$764$	−89.6511	−3.24346
$765$	−40.0006	−1.44622
$766$	17.1057	0.618054
$767$	−2.01593	−0.0727911
$768$	93.1061	3.35968
$769$	−5.60842	−0.202245	−0.101122	−	0.994874i	$-0.532243\pi$
$769$	−5.60842	−0.202245	−0.101122	+	0.994874i	$0.532243\pi$
$770$	13.2657	0.478063
$771$	−55.1508	−1.98621
$772$	−100.267	−3.60870
$773$	−10.4517	−0.375920	−0.187960	−	0.982177i	$-0.560188\pi$
$773$	−10.4517	−0.375920	−0.187960	+	0.982177i	$0.560188\pi$
$774$	25.4623	0.915223
$775$	3.28851	0.118127
$776$	−40.9532	−1.47014
$777$	−89.4038	−3.20734
$778$	−49.0300	−1.75781
$779$	−32.2257	−1.15460
$780$	8.30009	0.297191
$781$	4.45019	0.159240
$782$	78.2123	2.79687
$783$	−81.7225	−2.92052
$784$	20.8367	0.744167
$785$	−24.7115	−0.881993
$786$	−40.9270	−1.45982
$787$	−42.6588	−1.52062	−0.760311	−	0.649559i	$-0.774954\pi$
$787$	−42.6588	−1.52062	−0.760311	+	0.649559i	$0.774954\pi$
$788$	−48.6611	−1.73348
$789$	56.4795	2.01072
$790$	−31.5248	−1.12160
$791$	−10.6232	−0.377718
$792$	36.7566	1.30609
$793$	0.0977423	0.00347093
$794$	−57.6178	−2.04478
$795$	46.1042	1.63515
$796$	−30.9108	−1.09561
$797$	30.0857	1.06569	0.532845	−	0.846213i	$-0.321123\pi$
$797$	30.0857	1.06569	0.532845	+	0.846213i	$0.321123\pi$
$798$	−159.520	−5.64695
$799$	47.6482	1.68567
$800$	9.91579	0.350576
$801$	0.0540290	0.00190902
$802$	−28.2373	−0.997095
$803$	6.73588	0.237704
$804$	146.210	5.15644
$805$	40.6032	1.43107
$806$	−1.37860	−0.0485590
$807$	6.06028	0.213332
$808$	−91.8528	−3.23137
$809$	41.4039	1.45568	0.727841	−	0.685746i	$-0.240524\pi$
$809$	41.4039	1.45568	0.727841	+	0.685746i	$0.240524\pi$
$810$	−40.7339	−1.43124
$811$	−19.3898	−0.680869	−0.340435	−	0.940268i	$-0.610574\pi$
$811$	−19.3898	−0.680869	−0.340435	+	0.940268i	$0.610574\pi$
$812$	123.051	4.31824
$813$	−11.5302	−0.404383
$814$	23.4496	0.821907
$815$	−8.85166	−0.310060
$816$	78.1419	2.73551
$817$	10.8353	0.379080
$818$	56.4690	1.97439
$819$	−7.43614	−0.259840
$820$	35.4543	1.23812
$821$	4.30805	0.150352	0.0751761	−	0.997170i	$-0.476048\pi$
$821$	4.30805	0.150352	0.0751761	+	0.997170i	$0.476048\pi$
$822$	−30.1938	−1.05313
$823$	−27.6559	−0.964023	−0.482011	−	0.876165i	$-0.660094\pi$
$823$	−27.6559	−0.964023	−0.482011	+	0.876165i	$0.660094\pi$
$824$	12.0472	0.419684
$825$	−6.94456	−0.241779
$826$	−42.6261	−1.48315
$827$	−23.9822	−0.833944	−0.416972	−	0.908919i	$-0.636909\pi$
$827$	−23.9822	−0.833944	−0.416972	+	0.908919i	$0.636909\pi$
$828$	206.721	7.18407
$829$	31.1828	1.08302	0.541512	−	0.840693i	$-0.317852\pi$
$829$	31.1828	1.08302	0.541512	+	0.840693i	$0.317852\pi$
$830$	40.4973	1.40568
$831$	−23.0357	−0.799101
$832$	0.794152	0.0275323
$833$	−12.8635	−0.445694
$834$	31.0149	1.07396
$835$	10.6102	0.367181
$836$	28.7409	0.994025
$837$	13.2984	0.459661
$838$	39.3373	1.35888
$839$	10.7652	0.371654	0.185827	−	0.982582i	$-0.440504\pi$
$839$	10.7652	0.371654	0.185827	+	0.982582i	$0.440504\pi$
$840$	95.5129	3.29551
$841$	47.9725	1.65423
$842$	−94.8884	−3.27007
$843$	−62.7974	−2.16286
$844$	29.0635	1.00041
$845$	−21.1080	−0.726136
$846$	183.337	6.30327
$847$	3.19622	0.109823
$848$	−60.3396	−2.07207
$849$	−9.75144	−0.334669
$850$	−23.2879	−0.798769
$851$	71.7736	2.46037
$852$	58.8750	2.01702
$853$	−28.6417	−0.980673	−0.490336	−	0.871533i	$-0.663126\pi$
$853$	−28.6417	−0.980673	−0.490336	+	0.871533i	$0.663126\pi$
$854$	2.06672	0.0707218
$855$	−65.4961	−2.23992
$856$	−94.5130	−3.23039
$857$	4.67197	0.159591	0.0797957	−	0.996811i	$-0.474573\pi$
$857$	4.67197	0.159591	0.0797957	+	0.996811i	$0.474573\pi$
$858$	2.91127	0.0993892
$859$	29.9296	1.02118	0.510592	−	0.859823i	$-0.329426\pi$
$859$	29.9296	1.02118	0.510592	+	0.859823i	$0.329426\pi$
$860$	−11.9209	−0.406499
$861$	−47.4122	−1.61580
$862$	4.09486	0.139471
$863$	−14.5872	−0.496553	−0.248276	−	0.968689i	$-0.579864\pi$
$863$	−14.5872	−0.496553	−0.248276	+	0.968689i	$0.579864\pi$
$864$	40.0985	1.36418
$865$	4.66192	0.158510
$866$	66.7218	2.26730
$867$	3.01243	0.102307
$868$	−20.0236	−0.679646
$869$	−7.59552	−0.257661
$870$	109.783	3.72198
$871$	4.22230	0.143067
$872$	7.27062	0.246214
$873$	41.3171	1.39837
$874$	128.063	4.33180
$875$	−38.3327	−1.29588
$876$	89.1142	3.01089
$877$	41.4005	1.39799	0.698997	−	0.715124i	$-0.253630\pi$
$877$	41.4005	1.39799	0.698997	+	0.715124i	$0.253630\pi$
$878$	−1.90466	−0.0642793
$879$	−47.3957	−1.59862
$880$	−10.6401	−0.358679
$881$	−58.5764	−1.97349	−0.986745	−	0.162277i	$-0.948116\pi$
$881$	−58.5764	−1.97349	−0.986745	+	0.162277i	$0.948116\pi$
$882$	−49.4953	−1.66659
$883$	38.8192	1.30637	0.653185	−	0.757198i	$-0.273432\pi$
$883$	38.8192	1.30637	0.653185	+	0.757198i	$0.273432\pi$
$884$	6.70618	0.225553
$885$	−26.1235	−0.878133
$886$	−20.2105	−0.678986
$887$	−35.5776	−1.19458	−0.597290	−	0.802025i	$-0.703756\pi$
$887$	−35.5776	−1.19458	−0.597290	+	0.802025i	$0.703756\pi$
$888$	168.837	5.66579
$889$	−57.0782	−1.91434
$890$	−0.0368242	−0.00123435
$891$	−9.81437	−0.328794
$892$	−100.950	−3.38004
$893$	78.0181	2.61078
$894$	40.8227	1.36532
$895$	23.9278	0.799817
$896$	44.3103	1.48030
$897$	8.91071	0.297520
$898$	1.52463	0.0508776
$899$	−12.5255	−0.417748
$900$	−61.5519	−2.05173
$901$	37.2506	1.24100
$902$	12.4357	0.414062
$903$	15.9415	0.530501
$904$	20.0617	0.667241
$905$	7.13946	0.237324
$906$	29.6763	0.985928
$907$	2.99318	0.0993870	0.0496935	−	0.998765i	$-0.484176\pi$
$907$	2.99318	0.0993870	0.0496935	+	0.998765i	$0.484176\pi$
$908$	−27.1986	−0.902619
$909$	92.6689	3.07363
$910$	5.06820	0.168009
$911$	−22.4423	−0.743546	−0.371773	−	0.928324i	$-0.621250\pi$
$911$	−22.4423	−0.743546	−0.371773	+	0.928324i	$0.621250\pi$
$912$	127.948	4.23678
$913$	9.75736	0.322922
$914$	−22.0490	−0.729315
$915$	1.26660	0.0418724
$916$	−116.896	−3.86235
$917$	−17.1667	−0.566894
$918$	−94.1742	−3.10821
$919$	−55.6189	−1.83470	−0.917350	−	0.398082i	$-0.869676\pi$
$919$	−55.6189	−1.83470	−0.917350	+	0.398082i	$0.869676\pi$
$920$	−76.6779	−2.52800
$921$	52.9371	1.74434
$922$	25.5912	0.842800
$923$	1.70021	0.0559630
$924$	42.2852	1.39108
$925$	−21.3708	−0.702667
$926$	−57.2698	−1.88200
$927$	−12.1542	−0.399197
$928$	−37.7679	−1.23979
$929$	−50.0799	−1.64307	−0.821535	−	0.570158i	$-0.806882\pi$
$929$	−50.0799	−1.64307	−0.821535	+	0.570158i	$0.806882\pi$
$930$	−17.8646	−0.585803
$931$	−21.0624	−0.690293
$932$	86.7258	2.84080
$933$	5.43318	0.177874
$934$	78.4200	2.56598
$935$	6.56868	0.214819
$936$	14.0430	0.459008
$937$	34.4729	1.12618	0.563090	−	0.826396i	$-0.309612\pi$
$937$	34.4729	1.12618	0.563090	+	0.826396i	$0.309612\pi$
$938$	89.2788	2.91506
$939$	−23.9320	−0.780993
$940$	−85.8346	−2.79962
$941$	−30.3816	−0.990411	−0.495205	−	0.868776i	$-0.664907\pi$
$941$	−30.3816	−0.990411	−0.495205	+	0.868776i	$0.664907\pi$
$942$	−114.671	−3.73617
$943$	38.0626	1.23949
$944$	34.1895	1.11277
$945$	−48.8896	−1.59038
$946$	−4.18128	−0.135945
$947$	20.5137	0.666606	0.333303	−	0.942820i	$-0.391837\pi$
$947$	20.5137	0.666606	0.333303	+	0.942820i	$0.391837\pi$
$948$	−100.487	−3.26367
$949$	2.57346	0.0835381
$950$	−38.1312	−1.23714
$951$	61.3457	1.98927
$952$	77.1710	2.50113
$953$	52.7787	1.70967	0.854836	−	0.518899i	$-0.173658\pi$
$953$	52.7787	1.70967	0.854836	+	0.518899i	$0.173658\pi$
$954$	143.330	4.64048
$955$	−33.5492	−1.08563
$956$	−61.2953	−1.98243
$957$	26.4509	0.855036
$958$	−109.447	−3.53607
$959$	−12.6647	−0.408964
$960$	10.2910	0.332142
$961$	−28.9618	−0.934251
$962$	8.95898	0.288849
$963$	95.3527	3.07270
$964$	−40.1098	−1.29185
$965$	−37.5220	−1.20787
$966$	188.414	6.06211
$967$	−59.1742	−1.90292	−0.951458	−	0.307780i	$-0.900414\pi$
$967$	−59.1742	−1.90292	−0.951458	+	0.307780i	$0.900414\pi$
$968$	−6.03597	−0.194003
$969$	−78.9885	−2.53747
$970$	−28.1602	−0.904169
$971$	−17.9098	−0.574752	−0.287376	−	0.957818i	$-0.592783\pi$
$971$	−17.9098	−0.574752	−0.287376	+	0.957818i	$0.592783\pi$
$972$	−7.21800	−0.231517
$973$	13.0091	0.417053
$974$	73.2535	2.34719
$975$	−2.65319	−0.0849701
$976$	−1.65768	−0.0530609
$977$	−7.73884	−0.247587	−0.123794	−	0.992308i	$-0.539506\pi$
$977$	−7.73884	−0.247587	−0.123794	+	0.992308i	$0.539506\pi$
$978$	−41.0749	−1.31343
$979$	−0.00887236	−0.000283562 0
$980$	23.1726	0.740223
$981$	−7.33522	−0.234196
$982$	65.8113	2.10012
$983$	−32.4336	−1.03447	−0.517236	−	0.855843i	$-0.673039\pi$
$983$	−32.4336	−1.03447	−0.517236	+	0.855843i	$0.673039\pi$
$984$	89.5366	2.85432
$985$	−18.2100	−0.580217
$986$	88.7005	2.82480
$987$	114.785	3.65363
$988$	10.9805	0.349338
$989$	−12.7979	−0.406950
$990$	25.2745	0.803276
$991$	−27.5154	−0.874056	−0.437028	−	0.899448i	$-0.643969\pi$
$991$	−27.5154	−0.874056	−0.437028	+	0.899448i	$0.643969\pi$
$992$	6.14584	0.195131
$993$	−47.0343	−1.49259
$994$	35.9502	1.14027
$995$	−11.5674	−0.366713
$996$	129.088	4.09030
$997$	50.4613	1.59813	0.799063	−	0.601248i	$-0.205329\pi$
$997$	50.4613	1.59813	0.799063	+	0.601248i	$0.205329\pi$
$998$	−81.3207	−2.57416
$999$	−86.4214	−2.73425

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.6	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.6	✓	107	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52748 q^{2} -3.01490 q^{3} +4.38814 q^{4} +1.64213 q^{5} +7.62008 q^{6} +3.19622 q^{7} -6.03597 q^{8} +6.08959 q^{9} +O(q^{10})\)	\(q-2.52748 q^{2} -3.01490 q^{3} +4.38814 q^{4} +1.64213 q^{5} +7.62008 q^{6} +3.19622 q^{7} -6.03597 q^{8} +6.08959 q^{9} -4.15044 q^{10} -1.00000 q^{11} -13.2298 q^{12} -0.382053 q^{13} -8.07836 q^{14} -4.95084 q^{15} +6.47949 q^{16} -4.00010 q^{17} -15.3913 q^{18} -6.54968 q^{19} +7.20588 q^{20} -9.63625 q^{21} +2.52748 q^{22} +7.73601 q^{23} +18.1978 q^{24} -2.30342 q^{25} +0.965630 q^{26} -9.31480 q^{27} +14.0254 q^{28} +8.77340 q^{29} +12.5131 q^{30} -1.42767 q^{31} -4.30482 q^{32} +3.01490 q^{33} +10.1102 q^{34} +5.24859 q^{35} +26.7220 q^{36} +9.27786 q^{37} +16.5542 q^{38} +1.15185 q^{39} -9.91183 q^{40} +4.92019 q^{41} +24.3554 q^{42} -1.65433 q^{43} -4.38814 q^{44} +9.99989 q^{45} -19.5526 q^{46} -11.9117 q^{47} -19.5350 q^{48} +3.21579 q^{49} +5.82183 q^{50} +12.0599 q^{51} -1.67650 q^{52} -9.31240 q^{53} +23.5429 q^{54} -1.64213 q^{55} -19.2922 q^{56} +19.7466 q^{57} -22.1746 q^{58} +5.27658 q^{59} -21.7250 q^{60} -0.255834 q^{61} +3.60839 q^{62} +19.4637 q^{63} -2.07865 q^{64} -0.627380 q^{65} -7.62008 q^{66} -11.0516 q^{67} -17.5530 q^{68} -23.3232 q^{69} -13.2657 q^{70} -4.45019 q^{71} -36.7566 q^{72} -6.73588 q^{73} -23.4496 q^{74} +6.94456 q^{75} -28.7409 q^{76} -3.19622 q^{77} -2.91127 q^{78} +7.59552 q^{79} +10.6401 q^{80} +9.81437 q^{81} -12.4357 q^{82} -9.75736 q^{83} -42.2852 q^{84} -6.56868 q^{85} +4.18128 q^{86} -26.4509 q^{87} +6.03597 q^{88} +0.00887236 q^{89} -25.2745 q^{90} -1.22112 q^{91} +33.9467 q^{92} +4.30426 q^{93} +30.1067 q^{94} -10.7554 q^{95} +12.9786 q^{96} +6.78487 q^{97} -8.12784 q^{98} -6.08959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more