LMFDB - Embedded newform 4017.2.a.j.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.69069 q^{2} -1.00000 q^{3} +5.23983 q^{4} -3.39075 q^{5} -2.69069 q^{6} +3.55923 q^{7} +8.71737 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.69069 q^{2} -1.00000 q^{3} +5.23983 q^{4} -3.39075 q^{5} -2.69069 q^{6} +3.55923 q^{7} +8.71737 q^{8} +1.00000 q^{9} -9.12347 q^{10} +3.97019 q^{11} -5.23983 q^{12} +1.00000 q^{13} +9.57679 q^{14} +3.39075 q^{15} +12.9761 q^{16} -5.69126 q^{17} +2.69069 q^{18} -3.19194 q^{19} -17.7669 q^{20} -3.55923 q^{21} +10.6826 q^{22} +4.70654 q^{23} -8.71737 q^{24} +6.49719 q^{25} +2.69069 q^{26} -1.00000 q^{27} +18.6497 q^{28} +6.05116 q^{29} +9.12347 q^{30} +6.73805 q^{31} +17.4800 q^{32} -3.97019 q^{33} -15.3134 q^{34} -12.0685 q^{35} +5.23983 q^{36} -7.13584 q^{37} -8.58854 q^{38} -1.00000 q^{39} -29.5584 q^{40} +1.26699 q^{41} -9.57679 q^{42} -3.71867 q^{43} +20.8031 q^{44} -3.39075 q^{45} +12.6639 q^{46} -2.79607 q^{47} -12.9761 q^{48} +5.66810 q^{49} +17.4819 q^{50} +5.69126 q^{51} +5.23983 q^{52} +14.3686 q^{53} -2.69069 q^{54} -13.4619 q^{55} +31.0271 q^{56} +3.19194 q^{57} +16.2818 q^{58} +10.9643 q^{59} +17.7669 q^{60} -9.35699 q^{61} +18.1300 q^{62} +3.55923 q^{63} +21.0811 q^{64} -3.39075 q^{65} -10.6826 q^{66} -8.20608 q^{67} -29.8212 q^{68} -4.70654 q^{69} -32.4725 q^{70} -5.77396 q^{71} +8.71737 q^{72} -4.07053 q^{73} -19.2004 q^{74} -6.49719 q^{75} -16.7252 q^{76} +14.1308 q^{77} -2.69069 q^{78} +9.95930 q^{79} -43.9988 q^{80} +1.00000 q^{81} +3.40909 q^{82} +15.1402 q^{83} -18.6497 q^{84} +19.2976 q^{85} -10.0058 q^{86} -6.05116 q^{87} +34.6096 q^{88} +14.6677 q^{89} -9.12347 q^{90} +3.55923 q^{91} +24.6615 q^{92} -6.73805 q^{93} -7.52336 q^{94} +10.8231 q^{95} -17.4800 q^{96} +6.18570 q^{97} +15.2511 q^{98} +3.97019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	2.69069	1.90261	0.951303	−	0.308256i	$-0.0997454\pi$
$2$	2.69069	1.90261	0.951303	+	0.308256i	$0.0997454\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.23983	2.61991
$5$	−3.39075	−1.51639	−0.758195	−	0.652028i	$-0.773918\pi$
$5$	−3.39075	−1.51639	−0.758195	+	0.652028i	$0.773918\pi$
$6$	−2.69069	−1.09847
$7$	3.55923	1.34526	0.672631	−	0.739978i	$-0.265164\pi$
$7$	3.55923	1.34526	0.672631	+	0.739978i	$0.265164\pi$
$8$	8.71737	3.08206
$9$	1.00000	0.333333
$10$	−9.12347	−2.88509
$11$	3.97019	1.19706	0.598529	−	0.801101i	$-0.295752\pi$
$11$	3.97019	1.19706	0.598529	+	0.801101i	$0.295752\pi$
$12$	−5.23983	−1.51261
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	9.57679	2.55950
$15$	3.39075	0.875488
$16$	12.9761	3.24403
$17$	−5.69126	−1.38033	−0.690166	−	0.723651i	$-0.742463\pi$
$17$	−5.69126	−1.38033	−0.690166	+	0.723651i	$0.742463\pi$
$18$	2.69069	0.634202
$19$	−3.19194	−0.732282	−0.366141	−	0.930559i	$-0.619321\pi$
$19$	−3.19194	−0.732282	−0.366141	+	0.930559i	$0.619321\pi$
$20$	−17.7669	−3.97281
$21$	−3.55923	−0.776687
$22$	10.6826	2.27753
$23$	4.70654	0.981382	0.490691	−	0.871334i	$-0.336744\pi$
$23$	4.70654	0.981382	0.490691	+	0.871334i	$0.336744\pi$
$24$	−8.71737	−1.77943
$25$	6.49719	1.29944
$26$	2.69069	0.527688
$27$	−1.00000	−0.192450
$28$	18.6497	3.52447
$29$	6.05116	1.12367	0.561836	−	0.827249i	$-0.310095\pi$
$29$	6.05116	1.12367	0.561836	+	0.827249i	$0.310095\pi$
$30$	9.12347	1.66571
$31$	6.73805	1.21019	0.605095	−	0.796153i	$-0.293135\pi$
$31$	6.73805	1.21019	0.605095	+	0.796153i	$0.293135\pi$
$32$	17.4800	3.09006
$33$	−3.97019	−0.691122
$34$	−15.3134	−2.62623
$35$	−12.0685	−2.03994
$36$	5.23983	0.873304
$37$	−7.13584	−1.17313	−0.586563	−	0.809904i	$-0.699519\pi$
$37$	−7.13584	−1.17313	−0.586563	+	0.809904i	$0.699519\pi$
$38$	−8.58854	−1.39324
$39$	−1.00000	−0.160128
$40$	−29.5584	−4.67360
$41$	1.26699	0.197871	0.0989355	−	0.995094i	$-0.468456\pi$
$41$	1.26699	0.197871	0.0989355	+	0.995094i	$0.468456\pi$
$42$	−9.57679	−1.47773
$43$	−3.71867	−0.567091	−0.283546	−	0.958959i	$-0.591511\pi$
$43$	−3.71867	−0.567091	−0.283546	+	0.958959i	$0.591511\pi$
$44$	20.8031	3.13619
$45$	−3.39075	−0.505463
$46$	12.6639	1.86718
$47$	−2.79607	−0.407849	−0.203924	−	0.978987i	$-0.565370\pi$
$47$	−2.79607	−0.407849	−0.203924	+	0.978987i	$0.565370\pi$
$48$	−12.9761	−1.87294
$49$	5.66810	0.809729
$50$	17.4819	2.47232
$51$	5.69126	0.796936
$52$	5.23983	0.726633
$53$	14.3686	1.97368	0.986840	−	0.161702i	$-0.0516983\pi$
$53$	14.3686	1.97368	0.986840	+	0.161702i	$0.0516983\pi$
$54$	−2.69069	−0.366157
$55$	−13.4619	−1.81521
$56$	31.0271	4.14617
$57$	3.19194	0.422783
$58$	16.2818	2.13791
$59$	10.9643	1.42743	0.713715	−	0.700437i	$-0.247011\pi$
$59$	10.9643	1.42743	0.713715	+	0.700437i	$0.247011\pi$
$60$	17.7669	2.29370
$61$	−9.35699	−1.19804	−0.599020	−	0.800734i	$-0.704443\pi$
$61$	−9.35699	−1.19804	−0.599020	+	0.800734i	$0.704443\pi$
$62$	18.1300	2.30252
$63$	3.55923	0.448421
$64$	21.0811	2.63513
$65$	−3.39075	−0.420571
$66$	−10.6826	−1.31493
$67$	−8.20608	−1.00253	−0.501266	−	0.865293i	$-0.667132\pi$
$67$	−8.20608	−1.00253	−0.501266	+	0.865293i	$0.667132\pi$
$68$	−29.8212	−3.61635
$69$	−4.70654	−0.566601
$70$	−32.4725	−3.88120
$71$	−5.77396	−0.685243	−0.342622	−	0.939473i	$-0.611315\pi$
$71$	−5.77396	−0.685243	−0.342622	+	0.939473i	$0.611315\pi$
$72$	8.71737	1.02735
$73$	−4.07053	−0.476420	−0.238210	−	0.971214i	$-0.576561\pi$
$73$	−4.07053	−0.476420	−0.238210	+	0.971214i	$0.576561\pi$
$74$	−19.2004	−2.23200
$75$	−6.49719	−0.750230
$76$	−16.7252	−1.91851
$77$	14.1308	1.61036
$78$	−2.69069	−0.304661
$79$	9.95930	1.12051	0.560254	−	0.828321i	$-0.310703\pi$
$79$	9.95930	1.12051	0.560254	+	0.828321i	$0.310703\pi$
$80$	−43.9988	−4.91921
$81$	1.00000	0.111111
$82$	3.40909	0.376471
$83$	15.1402	1.66185	0.830925	−	0.556385i	$-0.187812\pi$
$83$	15.1402	1.66185	0.830925	+	0.556385i	$0.187812\pi$
$84$	−18.6497	−2.03485
$85$	19.2976	2.09312
$86$	−10.0058	−1.07895
$87$	−6.05116	−0.648752
$88$	34.6096	3.68940
$89$	14.6677	1.55477	0.777384	−	0.629026i	$-0.216546\pi$
$89$	14.6677	1.55477	0.777384	+	0.629026i	$0.216546\pi$
$90$	−9.12347	−0.961698
$91$	3.55923	0.373108
$92$	24.6615	2.57114
$93$	−6.73805	−0.698704
$94$	−7.52336	−0.775975
$95$	10.8231	1.11042
$96$	−17.4800	−1.78404
$97$	6.18570	0.628063	0.314032	−	0.949413i	$-0.398320\pi$
$97$	6.18570	0.628063	0.314032	+	0.949413i	$0.398320\pi$
$98$	15.2511	1.54060
$99$	3.97019	0.399019
$100$	34.0441	3.40441
$101$	−8.78051	−0.873693	−0.436847	−	0.899536i	$-0.643905\pi$
$101$	−8.78051	−0.873693	−0.436847	+	0.899536i	$0.643905\pi$
$102$	15.3134	1.51625
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	8.71737	0.854809
$105$	12.0685	1.17776
$106$	38.6615	3.75514
$107$	−3.81774	−0.369074	−0.184537	−	0.982826i	$-0.559079\pi$
$107$	−3.81774	−0.369074	−0.184537	+	0.982826i	$0.559079\pi$
$108$	−5.23983	−0.504202
$109$	−7.48563	−0.716994	−0.358497	−	0.933531i	$-0.616711\pi$
$109$	−7.48563	−0.716994	−0.358497	+	0.933531i	$0.616711\pi$
$110$	−36.2219	−3.45362
$111$	7.13584	0.677304
$112$	46.1850	4.36407
$113$	8.98479	0.845218	0.422609	−	0.906312i	$-0.361114\pi$
$113$	8.98479	0.845218	0.422609	+	0.906312i	$0.361114\pi$
$114$	8.58854	0.804390
$115$	−15.9587	−1.48816
$116$	31.7070	2.94392
$117$	1.00000	0.0924500
$118$	29.5015	2.71584
$119$	−20.2565	−1.85691
$120$	29.5584	2.69830
$121$	4.76242	0.432947
$122$	−25.1768	−2.27940
$123$	−1.26699	−0.114241
$124$	35.3062	3.17059
$125$	−5.07658	−0.454063
$126$	9.57679	0.853168
$127$	−0.0565956	−0.00502204	−0.00251102	−	0.999997i	$-0.500799\pi$
$127$	−0.0565956	−0.00502204	−0.00251102	+	0.999997i	$0.500799\pi$
$128$	21.7626	1.92356
$129$	3.71867	0.327410
$130$	−9.12347	−0.800181
$131$	14.0234	1.22523	0.612616	−	0.790381i	$-0.290117\pi$
$131$	14.0234	1.22523	0.612616	+	0.790381i	$0.290117\pi$
$132$	−20.8031	−1.81068
$133$	−11.3608	−0.985111
$134$	−22.0800	−1.90742
$135$	3.39075	0.291829
$136$	−49.6128	−4.25426
$137$	−0.460919	−0.0393790	−0.0196895	−	0.999806i	$-0.506268\pi$
$137$	−0.460919	−0.0393790	−0.0196895	+	0.999806i	$0.506268\pi$
$138$	−12.6639	−1.07802
$139$	−1.08724	−0.0922185	−0.0461092	−	0.998936i	$-0.514682\pi$
$139$	−1.08724	−0.0922185	−0.0461092	+	0.998936i	$0.514682\pi$
$140$	−63.2366	−5.34447
$141$	2.79607	0.235471
$142$	−15.5360	−1.30375
$143$	3.97019	0.332004
$144$	12.9761	1.08134
$145$	−20.5180	−1.70392
$146$	−10.9525	−0.906439
$147$	−5.66810	−0.467497
$148$	−37.3906	−3.07349
$149$	−12.0840	−0.989960	−0.494980	−	0.868904i	$-0.664825\pi$
$149$	−12.0840	−0.989960	−0.494980	+	0.868904i	$0.664825\pi$
$150$	−17.4819	−1.42739
$151$	−2.12941	−0.173289	−0.0866446	−	0.996239i	$-0.527614\pi$
$151$	−2.12941	−0.173289	−0.0866446	+	0.996239i	$0.527614\pi$
$152$	−27.8254	−2.25693
$153$	−5.69126	−0.460111
$154$	38.0217	3.06387
$155$	−22.8471	−1.83512
$156$	−5.23983	−0.419522
$157$	11.1255	0.887912	0.443956	−	0.896048i	$-0.353575\pi$
$157$	11.1255	0.887912	0.443956	+	0.896048i	$0.353575\pi$
$158$	26.7974	2.13189
$159$	−14.3686	−1.13950
$160$	−59.2703	−4.68573
$161$	16.7517	1.32022
$162$	2.69069	0.211401
$163$	0.480373	0.0376257	0.0188128	−	0.999823i	$-0.494011\pi$
$163$	0.480373	0.0376257	0.0188128	+	0.999823i	$0.494011\pi$
$164$	6.63882	0.518405
$165$	13.4619	1.04801
$166$	40.7375	3.16185
$167$	1.79007	0.138520	0.0692598	−	0.997599i	$-0.477936\pi$
$167$	1.79007	0.138520	0.0692598	+	0.997599i	$0.477936\pi$
$168$	−31.0271	−2.39379
$169$	1.00000	0.0769231
$170$	51.9240	3.98239
$171$	−3.19194	−0.244094
$172$	−19.4852	−1.48573
$173$	−3.45807	−0.262912	−0.131456	−	0.991322i	$-0.541965\pi$
$173$	−3.45807	−0.262912	−0.131456	+	0.991322i	$0.541965\pi$
$174$	−16.2818	−1.23432
$175$	23.1250	1.74808
$176$	51.5177	3.88329
$177$	−10.9643	−0.824127
$178$	39.4662	2.95811
$179$	−22.9901	−1.71836	−0.859181	−	0.511672i	$-0.829026\pi$
$179$	−22.9901	−1.71836	−0.859181	+	0.511672i	$0.829026\pi$
$180$	−17.7669	−1.32427
$181$	−2.48918	−0.185019	−0.0925096	−	0.995712i	$-0.529489\pi$
$181$	−2.48918	−0.185019	−0.0925096	+	0.995712i	$0.529489\pi$
$182$	9.57679	0.709879
$183$	9.35699	0.691689
$184$	41.0287	3.02468
$185$	24.1959	1.77891
$186$	−18.1300	−1.32936
$187$	−22.5954	−1.65234
$188$	−14.6509	−1.06853
$189$	−3.55923	−0.258896
$190$	29.1216	2.11270
$191$	−5.22992	−0.378423	−0.189212	−	0.981936i	$-0.560593\pi$
$191$	−5.22992	−0.378423	−0.189212	+	0.981936i	$0.560593\pi$
$192$	−21.0811	−1.52139
$193$	−18.7320	−1.34836	−0.674178	−	0.738569i	$-0.735502\pi$
$193$	−18.7320	−1.34836	−0.674178	+	0.738569i	$0.735502\pi$
$194$	16.6438	1.19496
$195$	3.39075	0.242817
$196$	29.6999	2.12142
$197$	3.47184	0.247358	0.123679	−	0.992322i	$-0.460531\pi$
$197$	3.47184	0.247358	0.123679	+	0.992322i	$0.460531\pi$
$198$	10.6826	0.759177
$199$	−27.6483	−1.95994	−0.979968	−	0.199156i	$-0.936180\pi$
$199$	−27.6483	−1.95994	−0.979968	+	0.199156i	$0.936180\pi$
$200$	56.6384	4.00494
$201$	8.20608	0.578812
$202$	−23.6256	−1.66229
$203$	21.5374	1.51163
$204$	29.8212	2.08790
$205$	−4.29606	−0.300050
$206$	−2.69069	−0.187469
$207$	4.70654	0.327127
$208$	12.9761	0.899732
$209$	−12.6726	−0.876584
$210$	32.4725	2.24081
$211$	−15.6447	−1.07703	−0.538513	−	0.842617i	$-0.681014\pi$
$211$	−15.6447	−1.07703	−0.538513	+	0.842617i	$0.681014\pi$
$212$	75.2890	5.17087
$213$	5.77396	0.395625
$214$	−10.2724	−0.702204
$215$	12.6091	0.859931
$216$	−8.71737	−0.593142
$217$	23.9823	1.62802
$218$	−20.1415	−1.36416
$219$	4.07053	0.275061
$220$	−70.5381	−4.75568
$221$	−5.69126	−0.382835
$222$	19.2004	1.28864
$223$	5.29312	0.354454	0.177227	−	0.984170i	$-0.443287\pi$
$223$	5.29312	0.354454	0.177227	+	0.984170i	$0.443287\pi$
$224$	62.2153	4.15693
$225$	6.49719	0.433146
$226$	24.1753	1.60812
$227$	−1.22433	−0.0812614	−0.0406307	−	0.999174i	$-0.512937\pi$
$227$	−1.22433	−0.0812614	−0.0406307	+	0.999174i	$0.512937\pi$
$228$	16.7252	1.10765
$229$	4.67193	0.308730	0.154365	−	0.988014i	$-0.450667\pi$
$229$	4.67193	0.308730	0.154365	+	0.988014i	$0.450667\pi$
$230$	−42.9400	−2.83138
$231$	−14.1308	−0.929739
$232$	52.7502	3.46322
$233$	17.6410	1.15570	0.577851	−	0.816142i	$-0.303892\pi$
$233$	17.6410	1.15570	0.577851	+	0.816142i	$0.303892\pi$
$234$	2.69069	0.175896
$235$	9.48077	0.618457
$236$	57.4510	3.73974
$237$	−9.95930	−0.646926
$238$	−54.5040	−3.53297
$239$	−9.35839	−0.605344	−0.302672	−	0.953095i	$-0.597879\pi$
$239$	−9.35839	−0.605344	−0.302672	+	0.953095i	$0.597879\pi$
$240$	43.9988	2.84011
$241$	−6.45712	−0.415940	−0.207970	−	0.978135i	$-0.566686\pi$
$241$	−6.45712	−0.415940	−0.207970	+	0.978135i	$0.566686\pi$
$242$	12.8142	0.823728
$243$	−1.00000	−0.0641500
$244$	−49.0290	−3.13876
$245$	−19.2191	−1.22786
$246$	−3.40909	−0.217356
$247$	−3.19194	−0.203098
$248$	58.7381	3.72987
$249$	−15.1402	−0.959469
$250$	−13.6595	−0.863904
$251$	−30.1157	−1.90088	−0.950442	−	0.310903i	$-0.899368\pi$
$251$	−30.1157	−1.90088	−0.950442	+	0.310903i	$0.899368\pi$
$252$	18.6497	1.17482
$253$	18.6859	1.17477
$254$	−0.152281	−0.00955498
$255$	−19.2976	−1.20846
$256$	16.3945	1.02465
$257$	30.2724	1.88834	0.944169	−	0.329461i	$-0.106867\pi$
$257$	30.2724	1.88834	0.944169	+	0.329461i	$0.106867\pi$
$258$	10.0058	0.622933
$259$	−25.3981	−1.57816
$260$	−17.7669	−1.10186
$261$	6.05116	0.374557
$262$	37.7327	2.33113
$263$	−20.4793	−1.26281	−0.631404	−	0.775454i	$-0.717521\pi$
$263$	−20.4793	−1.26281	−0.631404	+	0.775454i	$0.717521\pi$
$264$	−34.6096	−2.13008
$265$	−48.7203	−2.99287
$266$	−30.5686	−1.87428
$267$	−14.6677	−0.897646
$268$	−42.9984	−2.62655
$269$	−1.59398	−0.0971869	−0.0485935	−	0.998819i	$-0.515474\pi$
$269$	−1.59398	−0.0971869	−0.0485935	+	0.998819i	$0.515474\pi$
$270$	9.12347	0.555236
$271$	3.86498	0.234781	0.117390	−	0.993086i	$-0.462547\pi$
$271$	3.86498	0.234781	0.117390	+	0.993086i	$0.462547\pi$
$272$	−73.8504	−4.47784
$273$	−3.55923	−0.215414
$274$	−1.24019	−0.0749227
$275$	25.7951	1.55550
$276$	−24.6615	−1.48445
$277$	1.88019	0.112970	0.0564849	−	0.998403i	$-0.482011\pi$
$277$	1.88019	0.112970	0.0564849	+	0.998403i	$0.482011\pi$
$278$	−2.92543	−0.175455
$279$	6.73805	0.403397
$280$	−105.205	−6.28721
$281$	20.1209	1.20031	0.600156	−	0.799883i	$-0.295105\pi$
$281$	20.1209	1.20031	0.600156	+	0.799883i	$0.295105\pi$
$282$	7.52336	0.448010
$283$	−31.4850	−1.87159	−0.935796	−	0.352543i	$-0.885317\pi$
$283$	−31.4850	−1.87159	−0.935796	+	0.352543i	$0.885317\pi$
$284$	−30.2546	−1.79528
$285$	−10.8231	−0.641104
$286$	10.6826	0.631673
$287$	4.50952	0.266188
$288$	17.4800	1.03002
$289$	15.3904	0.905319
$290$	−55.2075	−3.24190
$291$	−6.18570	−0.362612
$292$	−21.3289	−1.24818
$293$	24.8054	1.44915	0.724573	−	0.689198i	$-0.242037\pi$
$293$	24.8054	1.44915	0.724573	+	0.689198i	$0.242037\pi$
$294$	−15.2511	−0.889463
$295$	−37.1772	−2.16454
$296$	−62.2058	−3.61564
$297$	−3.97019	−0.230374
$298$	−32.5143	−1.88350
$299$	4.70654	0.272186
$300$	−34.0441	−1.96554
$301$	−13.2356	−0.762886
$302$	−5.72960	−0.329701
$303$	8.78051	0.504427
$304$	−41.4190	−2.37554
$305$	31.7272	1.81670
$306$	−15.3134	−0.875410
$307$	11.8603	0.676905	0.338453	−	0.940983i	$-0.390097\pi$
$307$	11.8603	0.676905	0.338453	+	0.940983i	$0.390097\pi$
$308$	74.0430	4.21899
$309$	1.00000	0.0568880
$310$	−61.4744	−3.49151
$311$	−5.91420	−0.335364	−0.167682	−	0.985841i	$-0.553628\pi$
$311$	−5.91420	−0.335364	−0.167682	+	0.985841i	$0.553628\pi$
$312$	−8.71737	−0.493524
$313$	−26.7960	−1.51460	−0.757301	−	0.653066i	$-0.773482\pi$
$313$	−26.7960	−1.51460	−0.757301	+	0.653066i	$0.773482\pi$
$314$	29.9353	1.68935
$315$	−12.0685	−0.679980
$316$	52.1850	2.93563
$317$	0.676898	0.0380184	0.0190092	−	0.999819i	$-0.493949\pi$
$317$	0.676898	0.0380184	0.0190092	+	0.999819i	$0.493949\pi$
$318$	−38.6615	−2.16803
$319$	24.0243	1.34510
$320$	−71.4806	−3.99589
$321$	3.81774	0.213085
$322$	45.0736	2.51185
$323$	18.1662	1.01079
$324$	5.23983	0.291101
$325$	6.49719	0.360399
$326$	1.29253	0.0715869
$327$	7.48563	0.413957
$328$	11.0448	0.609850
$329$	−9.95185	−0.548663
$330$	36.2219	1.99395
$331$	−36.1015	−1.98432	−0.992159	−	0.124984i	$-0.960112\pi$
$331$	−36.1015	−1.98432	−0.992159	+	0.124984i	$0.960112\pi$
$332$	79.3318	4.35390
$333$	−7.13584	−0.391042
$334$	4.81652	0.263548
$335$	27.8248	1.52023
$336$	−46.1850	−2.51960
$337$	17.8760	0.973765	0.486883	−	0.873467i	$-0.338134\pi$
$337$	17.8760	0.973765	0.486883	+	0.873467i	$0.338134\pi$
$338$	2.69069	0.146354
$339$	−8.98479	−0.487987
$340$	101.116	5.48380
$341$	26.7514	1.44867
$342$	−8.58854	−0.464415
$343$	−4.74053	−0.255965
$344$	−32.4170	−1.74781
$345$	15.9587	0.859188
$346$	−9.30459	−0.500218
$347$	−13.2962	−0.713776	−0.356888	−	0.934147i	$-0.616162\pi$
$347$	−13.2962	−0.713776	−0.356888	+	0.934147i	$0.616162\pi$
$348$	−31.7070	−1.69967
$349$	−14.7753	−0.790905	−0.395453	−	0.918486i	$-0.629412\pi$
$349$	−14.7753	−0.790905	−0.395453	+	0.918486i	$0.629412\pi$
$350$	62.2222	3.32591
$351$	−1.00000	−0.0533761
$352$	69.3989	3.69898
$353$	−24.9011	−1.32535	−0.662675	−	0.748907i	$-0.730579\pi$
$353$	−24.9011	−1.32535	−0.662675	+	0.748907i	$0.730579\pi$
$354$	−29.5015	−1.56799
$355$	19.5781	1.03910
$356$	76.8560	4.07336
$357$	20.2565	1.07209
$358$	−61.8593	−3.26937
$359$	−15.6686	−0.826958	−0.413479	−	0.910514i	$-0.635686\pi$
$359$	−15.6686	−0.826958	−0.413479	+	0.910514i	$0.635686\pi$
$360$	−29.5584	−1.55787
$361$	−8.81150	−0.463763
$362$	−6.69761	−0.352019
$363$	−4.76242	−0.249962
$364$	18.6497	0.977512
$365$	13.8022	0.722438
$366$	25.1768	1.31601
$367$	24.8164	1.29540	0.647702	−	0.761893i	$-0.275730\pi$
$367$	24.8164	1.29540	0.647702	+	0.761893i	$0.275730\pi$
$368$	61.0727	3.18363
$369$	1.26699	0.0659570
$370$	65.1036	3.38457
$371$	51.1411	2.65511
$372$	−35.3062	−1.83054
$373$	6.40834	0.331812	0.165906	−	0.986142i	$-0.446945\pi$
$373$	6.40834	0.331812	0.165906	+	0.986142i	$0.446945\pi$
$374$	−60.7972	−3.14375
$375$	5.07658	0.262154
$376$	−24.3744	−1.25701
$377$	6.05116	0.311650
$378$	−9.57679	−0.492577
$379$	22.9273	1.17769	0.588847	−	0.808244i	$-0.299582\pi$
$379$	22.9273	1.17769	0.588847	+	0.808244i	$0.299582\pi$
$380$	56.7110	2.90922
$381$	0.0565956	0.00289948
$382$	−14.0721	−0.719991
$383$	−25.1672	−1.28598	−0.642992	−	0.765873i	$-0.722307\pi$
$383$	−25.1672	−1.28598	−0.642992	+	0.765873i	$0.722307\pi$
$384$	−21.7626	−1.11057
$385$	−47.9141	−2.44193
$386$	−50.4019	−2.56539
$387$	−3.71867	−0.189030
$388$	32.4120	1.64547
$389$	−35.7493	−1.81256	−0.906281	−	0.422675i	$-0.861091\pi$
$389$	−35.7493	−1.81256	−0.906281	+	0.422675i	$0.861091\pi$
$390$	9.12347	0.461985
$391$	−26.7862	−1.35463
$392$	49.4110	2.49563
$393$	−14.0234	−0.707388
$394$	9.34165	0.470626
$395$	−33.7695	−1.69913
$396$	20.8031	1.04540
$397$	−25.1766	−1.26358	−0.631788	−	0.775142i	$-0.717679\pi$
$397$	−25.1766	−1.26358	−0.631788	+	0.775142i	$0.717679\pi$
$398$	−74.3931	−3.72899
$399$	11.3608	0.568754
$400$	84.3083	4.21541
$401$	1.50056	0.0749342	0.0374671	−	0.999298i	$-0.488071\pi$
$401$	1.50056	0.0749342	0.0374671	+	0.999298i	$0.488071\pi$
$402$	22.0800	1.10125
$403$	6.73805	0.335646
$404$	−46.0083	−2.28900
$405$	−3.39075	−0.168488
$406$	57.9506	2.87604
$407$	−28.3307	−1.40430
$408$	49.6128	2.45620
$409$	11.9081	0.588817	0.294409	−	0.955680i	$-0.404877\pi$
$409$	11.9081	0.588817	0.294409	+	0.955680i	$0.404877\pi$
$410$	−11.5594	−0.570876
$411$	0.460919	0.0227355
$412$	−5.23983	−0.258148
$413$	39.0244	1.92027
$414$	12.6639	0.622395
$415$	−51.3365	−2.52001
$416$	17.4800	0.857027
$417$	1.08724	0.0532424
$418$	−34.0981	−1.66779
$419$	26.3736	1.28844	0.644219	−	0.764841i	$-0.277183\pi$
$419$	26.3736	1.28844	0.644219	+	0.764841i	$0.277183\pi$
$420$	63.2366	3.08563
$421$	−28.8430	−1.40572	−0.702861	−	0.711328i	$-0.748094\pi$
$421$	−28.8430	−1.40572	−0.702861	+	0.711328i	$0.748094\pi$
$422$	−42.0951	−2.04916
$423$	−2.79607	−0.135950
$424$	125.256	6.08299
$425$	−36.9772	−1.79366
$426$	15.5360	0.752719
$427$	−33.3037	−1.61168
$428$	−20.0043	−0.966943
$429$	−3.97019	−0.191683
$430$	33.9271	1.63611
$431$	−32.0033	−1.54154	−0.770771	−	0.637112i	$-0.780129\pi$
$431$	−32.0033	−1.54154	−0.770771	+	0.637112i	$0.780129\pi$
$432$	−12.9761	−0.624314
$433$	39.4532	1.89600	0.947999	−	0.318272i	$-0.103103\pi$
$433$	39.4532	1.89600	0.947999	+	0.318272i	$0.103103\pi$
$434$	64.5289	3.09749
$435$	20.5180	0.983761
$436$	−39.2234	−1.87846
$437$	−15.0230	−0.718648
$438$	10.9525	0.523333
$439$	2.96596	0.141558	0.0707788	−	0.997492i	$-0.477452\pi$
$439$	2.96596	0.141558	0.0707788	+	0.997492i	$0.477452\pi$
$440$	−117.353	−5.59457
$441$	5.66810	0.269910
$442$	−15.3134	−0.728385
$443$	19.6265	0.932485	0.466242	−	0.884657i	$-0.345607\pi$
$443$	19.6265	0.932485	0.466242	+	0.884657i	$0.345607\pi$
$444$	37.3906	1.77448
$445$	−49.7344	−2.35764
$446$	14.2422	0.674386
$447$	12.0840	0.571554
$448$	75.0323	3.54494
$449$	−21.9477	−1.03577	−0.517887	−	0.855449i	$-0.673281\pi$
$449$	−21.9477	−1.03577	−0.517887	+	0.855449i	$0.673281\pi$
$450$	17.4819	0.824106
$451$	5.03020	0.236863
$452$	47.0787	2.21440
$453$	2.12941	0.100049
$454$	−3.29428	−0.154608
$455$	−12.0685	−0.565778
$456$	27.8254	1.30304
$457$	8.34457	0.390342	0.195171	−	0.980769i	$-0.437474\pi$
$457$	8.34457	0.390342	0.195171	+	0.980769i	$0.437474\pi$
$458$	12.5707	0.587392
$459$	5.69126	0.265645
$460$	−83.6209	−3.89884
$461$	4.64128	0.216166	0.108083	−	0.994142i	$-0.465529\pi$
$461$	4.64128	0.216166	0.108083	+	0.994142i	$0.465529\pi$
$462$	−38.0217	−1.76893
$463$	−31.7309	−1.47466	−0.737329	−	0.675534i	$-0.763913\pi$
$463$	−31.7309	−1.47466	−0.737329	+	0.675534i	$0.763913\pi$
$464$	78.5205	3.64522
$465$	22.8471	1.05951
$466$	47.4666	2.19885
$467$	−39.6191	−1.83335	−0.916677	−	0.399628i	$-0.869139\pi$
$467$	−39.6191	−1.83335	−0.916677	+	0.399628i	$0.869139\pi$
$468$	5.23983	0.242211
$469$	−29.2073	−1.34867
$470$	25.5098	1.17668
$471$	−11.1255	−0.512636
$472$	95.5798	4.39942
$473$	−14.7638	−0.678841
$474$	−26.7974	−1.23085
$475$	−20.7386	−0.951554
$476$	−106.140	−4.86494
$477$	14.3686	0.657893
$478$	−25.1805	−1.15173
$479$	3.23975	0.148028	0.0740141	−	0.997257i	$-0.476419\pi$
$479$	3.23975	0.148028	0.0740141	+	0.997257i	$0.476419\pi$
$480$	59.2703	2.70531
$481$	−7.13584	−0.325366
$482$	−17.3741	−0.791370
$483$	−16.7517	−0.762227
$484$	24.9542	1.13428
$485$	−20.9742	−0.952388
$486$	−2.69069	−0.122052
$487$	26.9052	1.21919	0.609596	−	0.792712i	$-0.291332\pi$
$487$	26.9052	1.21919	0.609596	+	0.792712i	$0.291332\pi$
$488$	−81.5684	−3.69243
$489$	−0.480373	−0.0217232
$490$	−51.7127	−2.33614
$491$	−24.2946	−1.09640	−0.548201	−	0.836347i	$-0.684687\pi$
$491$	−24.2946	−1.09640	−0.548201	+	0.836347i	$0.684687\pi$
$492$	−6.63882	−0.299301
$493$	−34.4387	−1.55104
$494$	−8.58854	−0.386416
$495$	−13.4619	−0.605069
$496$	87.4338	3.92589
$497$	−20.5508	−0.921831
$498$	−40.7375	−1.82549
$499$	−32.8172	−1.46910	−0.734551	−	0.678554i	$-0.762607\pi$
$499$	−32.8172	−1.46910	−0.734551	+	0.678554i	$0.762607\pi$
$500$	−26.6004	−1.18961
$501$	−1.79007	−0.0799743
$502$	−81.0320	−3.61663
$503$	4.80346	0.214176	0.107088	−	0.994250i	$-0.465847\pi$
$503$	4.80346	0.214176	0.107088	+	0.994250i	$0.465847\pi$
$504$	31.0271	1.38206
$505$	29.7725	1.32486
$506$	50.2780	2.23513
$507$	−1.00000	−0.0444116
$508$	−0.296551	−0.0131573
$509$	12.3488	0.547350	0.273675	−	0.961822i	$-0.411761\pi$
$509$	12.3488	0.547350	0.273675	+	0.961822i	$0.411761\pi$
$510$	−51.9240	−2.29923
$511$	−14.4879	−0.640909
$512$	0.587183	0.0259501
$513$	3.19194	0.140928
$514$	81.4536	3.59277
$515$	3.39075	0.149414
$516$	19.4852	0.857786
$517$	−11.1009	−0.488218
$518$	−68.3384	−3.00262
$519$	3.45807	0.151792
$520$	−29.5584	−1.29622
$521$	38.7317	1.69687	0.848434	−	0.529302i	$-0.177546\pi$
$521$	38.7317	1.69687	0.848434	+	0.529302i	$0.177546\pi$
$522$	16.2818	0.712635
$523$	−12.4507	−0.544431	−0.272216	−	0.962236i	$-0.587756\pi$
$523$	−12.4507	−0.544431	−0.272216	+	0.962236i	$0.587756\pi$
$524$	73.4802	3.21000
$525$	−23.1250	−1.00926
$526$	−55.1035	−2.40263
$527$	−38.3480	−1.67046
$528$	−51.5177	−2.24202
$529$	−0.848443	−0.0368888
$530$	−131.091	−5.69425
$531$	10.9643	0.475810
$532$	−59.5289	−2.58090
$533$	1.26699	0.0548796
$534$	−39.4662	−1.70787
$535$	12.9450	0.559661
$536$	−71.5354	−3.08986
$537$	22.9901	0.992097
$538$	−4.28892	−0.184909
$539$	22.5034	0.969292
$540$	17.7669	0.764567
$541$	28.1218	1.20905	0.604526	−	0.796585i	$-0.293363\pi$
$541$	28.1218	1.20905	0.604526	+	0.796585i	$0.293363\pi$
$542$	10.3995	0.446696
$543$	2.48918	0.106821
$544$	−99.4832	−4.26531
$545$	25.3819	1.08724
$546$	−9.57679	−0.409849
$547$	39.7301	1.69874	0.849369	−	0.527799i	$-0.176983\pi$
$547$	39.7301	1.69874	0.849369	+	0.527799i	$0.176983\pi$
$548$	−2.41513	−0.103169
$549$	−9.35699	−0.399347
$550$	69.4066	2.95951
$551$	−19.3149	−0.822844
$552$	−41.0287	−1.74630
$553$	35.4474	1.50738
$554$	5.05902	0.214937
$555$	−24.1959	−1.02706
$556$	−5.69695	−0.241604
$557$	−34.1735	−1.44798	−0.723989	−	0.689811i	$-0.757693\pi$
$557$	−34.1735	−1.44798	−0.723989	+	0.689811i	$0.757693\pi$
$558$	18.1300	0.767505
$559$	−3.71867	−0.157283
$560$	−156.602	−6.61763
$561$	22.5954	0.953978
$562$	54.1391	2.28372
$563$	−40.7054	−1.71553	−0.857764	−	0.514044i	$-0.828147\pi$
$563$	−40.7054	−1.71553	−0.857764	+	0.514044i	$0.828147\pi$
$564$	14.6509	0.616915
$565$	−30.4652	−1.28168
$566$	−84.7166	−3.56090
$567$	3.55923	0.149474
$568$	−50.3338	−2.11196
$569$	−2.06896	−0.0867353	−0.0433677	−	0.999059i	$-0.513809\pi$
$569$	−2.06896	−0.0867353	−0.0433677	+	0.999059i	$0.513809\pi$
$570$	−29.1216	−1.21977
$571$	22.3349	0.934685	0.467343	−	0.884076i	$-0.345211\pi$
$571$	22.3349	0.934685	0.467343	+	0.884076i	$0.345211\pi$
$572$	20.8031	0.869822
$573$	5.22992	0.218483
$574$	12.1337	0.506452
$575$	30.5793	1.27524
$576$	21.0811	0.878377
$577$	16.6712	0.694029	0.347015	−	0.937860i	$-0.387195\pi$
$577$	16.6712	0.694029	0.347015	+	0.937860i	$0.387195\pi$
$578$	41.4109	1.72247
$579$	18.7320	0.778473
$580$	−107.511	−4.46413
$581$	53.8873	2.23562
$582$	−16.6438	−0.689909
$583$	57.0461	2.36261
$584$	−35.4843	−1.46835
$585$	−3.39075	−0.140190
$586$	66.7436	2.75715
$587$	−36.3447	−1.50011	−0.750054	−	0.661377i	$-0.769972\pi$
$587$	−36.3447	−1.50011	−0.750054	+	0.661377i	$0.769972\pi$
$588$	−29.6999	−1.22480
$589$	−21.5075	−0.886200
$590$	−100.032	−4.11827
$591$	−3.47184	−0.142812
$592$	−92.5955	−3.80565
$593$	−14.5823	−0.598822	−0.299411	−	0.954124i	$-0.596790\pi$
$593$	−14.5823	−0.598822	−0.299411	+	0.954124i	$0.596790\pi$
$594$	−10.6826	−0.438311
$595$	68.6847	2.81580
$596$	−63.3181	−2.59361
$597$	27.6483	1.13157
$598$	12.6639	0.517864
$599$	45.3540	1.85311	0.926557	−	0.376155i	$-0.122754\pi$
$599$	45.3540	1.85311	0.926557	+	0.376155i	$0.122754\pi$
$600$	−56.6384	−2.31225
$601$	20.1306	0.821143	0.410572	−	0.911828i	$-0.365329\pi$
$601$	20.1306	0.821143	0.410572	+	0.911828i	$0.365329\pi$
$602$	−35.6129	−1.45147
$603$	−8.20608	−0.334177
$604$	−11.1578	−0.454003
$605$	−16.1482	−0.656517
$606$	23.6256	0.959726
$607$	35.9338	1.45851	0.729253	−	0.684244i	$-0.239868\pi$
$607$	35.9338	1.45851	0.729253	+	0.684244i	$0.239868\pi$
$608$	−55.7951	−2.26279
$609$	−21.5374	−0.872741
$610$	85.3682	3.45646
$611$	−2.79607	−0.113117
$612$	−29.8212	−1.20545
$613$	−13.3918	−0.540890	−0.270445	−	0.962735i	$-0.587171\pi$
$613$	−13.3918	−0.540890	−0.270445	+	0.962735i	$0.587171\pi$
$614$	31.9125	1.28788
$615$	4.29606	0.173234
$616$	123.184	4.96321
$617$	−17.0134	−0.684934	−0.342467	−	0.939530i	$-0.611263\pi$
$617$	−17.0134	−0.684934	−0.342467	+	0.939530i	$0.611263\pi$
$618$	2.69069	0.108236
$619$	−47.2728	−1.90006	−0.950028	−	0.312165i	$-0.898946\pi$
$619$	−47.2728	−1.90006	−0.950028	+	0.312165i	$0.898946\pi$
$620$	−119.715	−4.80785
$621$	−4.70654	−0.188867
$622$	−15.9133	−0.638065
$623$	52.2055	2.09157
$624$	−12.9761	−0.519460
$625$	−15.2725	−0.610900
$626$	−72.0999	−2.88169
$627$	12.6726	0.506096
$628$	58.2957	2.32625
$629$	40.6119	1.61930
$630$	−32.4725	−1.29373
$631$	−3.17379	−0.126347	−0.0631733	−	0.998003i	$-0.520122\pi$
$631$	−3.17379	−0.126347	−0.0631733	+	0.998003i	$0.520122\pi$
$632$	86.8189	3.45347
$633$	15.6447	0.621822
$634$	1.82132	0.0723340
$635$	0.191901	0.00761538
$636$	−75.2890	−2.98540
$637$	5.66810	0.224578
$638$	64.6419	2.55920
$639$	−5.77396	−0.228414
$640$	−73.7917	−2.91687
$641$	−41.2087	−1.62765	−0.813824	−	0.581112i	$-0.802618\pi$
$641$	−41.2087	−1.62765	−0.813824	+	0.581112i	$0.802618\pi$
$642$	10.2724	0.405417
$643$	44.1860	1.74252	0.871262	−	0.490818i	$-0.163302\pi$
$643$	44.1860	1.74252	0.871262	+	0.490818i	$0.163302\pi$
$644$	87.7758	3.45885
$645$	−12.6091	−0.496481
$646$	48.8796	1.92314
$647$	30.2881	1.19075	0.595374	−	0.803449i	$-0.297004\pi$
$647$	30.2881	1.19075	0.595374	+	0.803449i	$0.297004\pi$
$648$	8.71737	0.342451
$649$	43.5303	1.70872
$650$	17.4819	0.685698
$651$	−23.9823	−0.939939
$652$	2.51707	0.0985760
$653$	−18.6600	−0.730223	−0.365112	−	0.930964i	$-0.618969\pi$
$653$	−18.6600	−0.730223	−0.365112	+	0.930964i	$0.618969\pi$
$654$	20.1415	0.787597
$655$	−47.5499	−1.85793
$656$	16.4407	0.641900
$657$	−4.07053	−0.158807
$658$	−26.7774	−1.04389
$659$	27.0943	1.05545	0.527723	−	0.849417i	$-0.323046\pi$
$659$	27.0943	1.05545	0.527723	+	0.849417i	$0.323046\pi$
$660$	70.5381	2.74569
$661$	−43.8094	−1.70399	−0.851994	−	0.523552i	$-0.824607\pi$
$661$	−43.8094	−1.70399	−0.851994	+	0.523552i	$0.824607\pi$
$662$	−97.1380	−3.77538
$663$	5.69126	0.221030
$664$	131.982	5.12191
$665$	38.5218	1.49381
$666$	−19.2004	−0.743999
$667$	28.4800	1.10275
$668$	9.37964	0.362909
$669$	−5.29312	−0.204644
$670$	74.8679	2.89240
$671$	−37.1490	−1.43412
$672$	−62.2153	−2.40001
$673$	18.1591	0.699981	0.349991	−	0.936753i	$-0.386185\pi$
$673$	18.1591	0.699981	0.349991	+	0.936753i	$0.386185\pi$
$674$	48.0987	1.85269
$675$	−6.49719	−0.250077
$676$	5.23983	0.201532
$677$	−26.3658	−1.01332	−0.506659	−	0.862146i	$-0.669120\pi$
$677$	−26.3658	−1.01332	−0.506659	+	0.862146i	$0.669120\pi$
$678$	−24.1753	−0.928447
$679$	22.0163	0.844909
$680$	168.225	6.45112
$681$	1.22433	0.0469163
$682$	71.9797	2.75624
$683$	51.7241	1.97917	0.989584	−	0.143959i	$-0.0459834\pi$
$683$	51.7241	1.97917	0.989584	+	0.143959i	$0.0459834\pi$
$684$	−16.7252	−0.639505
$685$	1.56286	0.0597138
$686$	−12.7553	−0.487000
$687$	−4.67193	−0.178245
$688$	−48.2538	−1.83966
$689$	14.3686	0.547400
$690$	42.9400	1.63470
$691$	2.96484	0.112788	0.0563938	−	0.998409i	$-0.482040\pi$
$691$	2.96484	0.112788	0.0563938	+	0.998409i	$0.482040\pi$
$692$	−18.1197	−0.688806
$693$	14.1308	0.536785
$694$	−35.7759	−1.35803
$695$	3.68656	0.139839
$696$	−52.7502	−1.99949
$697$	−7.21078	−0.273128
$698$	−39.7559	−1.50478
$699$	−17.6410	−0.667245
$700$	121.171	4.57982
$701$	−14.6820	−0.554533	−0.277266	−	0.960793i	$-0.589428\pi$
$701$	−14.6820	−0.554533	−0.277266	+	0.960793i	$0.589428\pi$
$702$	−2.69069	−0.101554
$703$	22.7772	0.859058
$704$	83.6958	3.15441
$705$	−9.48077	−0.357066
$706$	−67.0011	−2.52162
$707$	−31.2518	−1.17535
$708$	−57.4510	−2.15914
$709$	7.49469	0.281469	0.140735	−	0.990047i	$-0.455054\pi$
$709$	7.49469	0.281469	0.140735	+	0.990047i	$0.455054\pi$
$710$	52.6785	1.97699
$711$	9.95930	0.373503
$712$	127.863	4.79189
$713$	31.7129	1.18766
$714$	54.5040	2.03976
$715$	−13.4619	−0.503447
$716$	−120.464	−4.50196
$717$	9.35839	0.349495
$718$	−42.1594	−1.57338
$719$	15.1168	0.563760	0.281880	−	0.959450i	$-0.409042\pi$
$719$	15.1168	0.563760	0.281880	+	0.959450i	$0.409042\pi$
$720$	−43.9988	−1.63974
$721$	−3.55923	−0.132553
$722$	−23.7090	−0.882359
$723$	6.45712	0.240143
$724$	−13.0429	−0.484734
$725$	39.3155	1.46014
$726$	−12.8142	−0.475580
$727$	−5.12143	−0.189943	−0.0949717	−	0.995480i	$-0.530276\pi$
$727$	−5.12143	−0.189943	−0.0949717	+	0.995480i	$0.530276\pi$
$728$	31.0271	1.14994
$729$	1.00000	0.0370370
$730$	37.1374	1.37452
$731$	21.1639	0.782775
$732$	49.0290	1.81216
$733$	−30.0695	−1.11064	−0.555321	−	0.831636i	$-0.687405\pi$
$733$	−30.0695	−1.11064	−0.555321	+	0.831636i	$0.687405\pi$
$734$	66.7733	2.46465
$735$	19.2191	0.708908
$736$	82.2704	3.03253
$737$	−32.5797	−1.20009
$738$	3.40909	0.125490
$739$	35.8412	1.31844	0.659220	−	0.751950i	$-0.270886\pi$
$739$	35.8412	1.31844	0.659220	+	0.751950i	$0.270886\pi$
$740$	126.782	4.66060
$741$	3.19194	0.117259
$742$	137.605	5.05164
$743$	0.491872	0.0180450	0.00902252	−	0.999959i	$-0.497128\pi$
$743$	0.491872	0.0180450	0.00902252	+	0.999959i	$0.497128\pi$
$744$	−58.7381	−2.15344
$745$	40.9738	1.50116
$746$	17.2429	0.631307
$747$	15.1402	0.553950
$748$	−118.396	−4.32898
$749$	−13.5882	−0.496502
$750$	13.6595	0.498775
$751$	−2.47358	−0.0902624	−0.0451312	−	0.998981i	$-0.514371\pi$
$751$	−2.47358	−0.0902624	−0.0451312	+	0.998981i	$0.514371\pi$
$752$	−36.2821	−1.32307
$753$	30.1157	1.09748
$754$	16.2818	0.592948
$755$	7.22031	0.262774
$756$	−18.6497	−0.678284
$757$	3.37719	0.122746	0.0613731	−	0.998115i	$-0.480452\pi$
$757$	3.37719	0.122746	0.0613731	+	0.998115i	$0.480452\pi$
$758$	61.6902	2.24069
$759$	−18.6859	−0.678254
$760$	94.3488	3.42239
$761$	37.6906	1.36628	0.683142	−	0.730286i	$-0.260613\pi$
$761$	37.6906	1.36628	0.683142	+	0.730286i	$0.260613\pi$
$762$	0.152281	0.00551657
$763$	−26.6431	−0.964544
$764$	−27.4038	−0.991436
$765$	19.2976	0.697707
$766$	−67.7172	−2.44672
$767$	10.9643	0.395898
$768$	−16.3945	−0.591584
$769$	5.57218	0.200938	0.100469	−	0.994940i	$-0.467966\pi$
$769$	5.57218	0.200938	0.100469	+	0.994940i	$0.467966\pi$
$770$	−128.922	−4.64603
$771$	−30.2724	−1.09023
$772$	−98.1522	−3.53257
$773$	7.56955	0.272258	0.136129	−	0.990691i	$-0.456534\pi$
$773$	7.56955	0.272258	0.136129	+	0.990691i	$0.456534\pi$
$774$	−10.0058	−0.359650
$775$	43.7784	1.57257
$776$	53.9231	1.93573
$777$	25.3981	0.911151
$778$	−96.1904	−3.44859
$779$	−4.04417	−0.144897
$780$	17.7669	0.636158
$781$	−22.9237	−0.820276
$782$	−72.0733	−2.57734
$783$	−6.05116	−0.216251
$784$	73.5500	2.62678
$785$	−37.7238	−1.34642
$786$	−37.7327	−1.34588
$787$	−27.3002	−0.973147	−0.486574	−	0.873640i	$-0.661753\pi$
$787$	−27.3002	−0.973147	−0.486574	+	0.873640i	$0.661753\pi$
$788$	18.1918	0.648057
$789$	20.4793	0.729083
$790$	−90.8633	−3.23277
$791$	31.9789	1.13704
$792$	34.6096	1.22980
$793$	−9.35699	−0.332277
$794$	−67.7424	−2.40409
$795$	48.7203	1.72793
$796$	−144.872	−5.13486
$797$	50.4628	1.78748	0.893741	−	0.448583i	$-0.148071\pi$
$797$	50.4628	1.78748	0.893741	+	0.448583i	$0.148071\pi$
$798$	30.5686	1.08211
$799$	15.9131	0.562967
$800$	113.571	4.01533
$801$	14.6677	0.518256
$802$	4.03754	0.142570
$803$	−16.1608	−0.570302
$804$	42.9984	1.51644
$805$	−56.8007	−2.00196
$806$	18.1300	0.638603
$807$	1.59398	0.0561109
$808$	−76.5430	−2.69277
$809$	−18.4900	−0.650075	−0.325037	−	0.945701i	$-0.605377\pi$
$809$	−18.4900	−0.650075	−0.325037	+	0.945701i	$0.605377\pi$
$810$	−9.12347	−0.320566
$811$	−2.17608	−0.0764124	−0.0382062	−	0.999270i	$-0.512164\pi$
$811$	−2.17608	−0.0764124	−0.0382062	+	0.999270i	$0.512164\pi$
$812$	112.852	3.96035
$813$	−3.86498	−0.135551
$814$	−76.2291	−2.67183
$815$	−1.62882	−0.0570552
$816$	73.8504	2.58528
$817$	11.8698	0.415271
$818$	32.0410	1.12029
$819$	3.55923	0.124369
$820$	−22.5106	−0.786104
$821$	−6.56440	−0.229099	−0.114550	−	0.993418i	$-0.536542\pi$
$821$	−6.56440	−0.229099	−0.114550	+	0.993418i	$0.536542\pi$
$822$	1.24019	0.0432566
$823$	40.2319	1.40239	0.701197	−	0.712967i	$-0.252649\pi$
$823$	40.2319	1.40239	0.701197	+	0.712967i	$0.252649\pi$
$824$	−8.71737	−0.303684
$825$	−25.7951	−0.898069
$826$	105.003	3.65351
$827$	38.9788	1.35542	0.677712	−	0.735327i	$-0.262971\pi$
$827$	38.9788	1.35542	0.677712	+	0.735327i	$0.262971\pi$
$828$	24.6615	0.857045
$829$	−35.8071	−1.24363	−0.621816	−	0.783164i	$-0.713605\pi$
$829$	−35.8071	−1.24363	−0.621816	+	0.783164i	$0.713605\pi$
$830$	−138.131	−4.79459
$831$	−1.88019	−0.0652232
$832$	21.0811	0.730854
$833$	−32.2586	−1.11770
$834$	2.92543	0.101299
$835$	−6.06967	−0.210050
$836$	−66.4023	−2.29657
$837$	−6.73805	−0.232901
$838$	70.9634	2.45139
$839$	3.01513	0.104094	0.0520470	−	0.998645i	$-0.483425\pi$
$839$	3.01513	0.104094	0.0520470	+	0.998645i	$0.483425\pi$
$840$	105.205	3.62992
$841$	7.61651	0.262638
$842$	−77.6076	−2.67453
$843$	−20.1209	−0.693001
$844$	−81.9756	−2.82172
$845$	−3.39075	−0.116645
$846$	−7.52336	−0.258658
$847$	16.9505	0.582427
$848$	186.449	6.40267
$849$	31.4850	1.08056
$850$	−99.4942	−3.41262
$851$	−33.5852	−1.15128
$852$	30.2546	1.03650
$853$	40.4998	1.38669	0.693343	−	0.720608i	$-0.256137\pi$
$853$	40.4998	1.38669	0.693343	+	0.720608i	$0.256137\pi$
$854$	−89.6099	−3.06639
$855$	10.8231	0.370141
$856$	−33.2806	−1.13751
$857$	39.2621	1.34117	0.670583	−	0.741834i	$-0.266044\pi$
$857$	39.2621	1.34117	0.670583	+	0.741834i	$0.266044\pi$
$858$	−10.6826	−0.364697
$859$	10.4351	0.356041	0.178020	−	0.984027i	$-0.443031\pi$
$859$	10.4351	0.356041	0.178020	+	0.984027i	$0.443031\pi$
$860$	66.0693	2.25294
$861$	−4.50952	−0.153684
$862$	−86.1109	−2.93295
$863$	−18.3631	−0.625087	−0.312543	−	0.949904i	$-0.601181\pi$
$863$	−18.3631	−0.625087	−0.312543	+	0.949904i	$0.601181\pi$
$864$	−17.4800	−0.594682
$865$	11.7254	0.398677
$866$	106.156	3.60734
$867$	−15.3904	−0.522686
$868$	125.663	4.26528
$869$	39.5403	1.34131
$870$	55.2075	1.87171
$871$	−8.20608	−0.278052
$872$	−65.2551	−2.20982
$873$	6.18570	0.209354
$874$	−40.4223	−1.36731
$875$	−18.0687	−0.610834
$876$	21.3289	0.720636
$877$	−8.53828	−0.288317	−0.144159	−	0.989555i	$-0.546048\pi$
$877$	−8.53828	−0.288317	−0.144159	+	0.989555i	$0.546048\pi$
$878$	7.98048	0.269328
$879$	−24.8054	−0.836665
$880$	−174.684	−5.88858
$881$	6.88497	0.231961	0.115980	−	0.993252i	$-0.462999\pi$
$881$	6.88497	0.231961	0.115980	+	0.993252i	$0.462999\pi$
$882$	15.2511	0.513532
$883$	12.1994	0.410542	0.205271	−	0.978705i	$-0.434192\pi$
$883$	12.1994	0.410542	0.205271	+	0.978705i	$0.434192\pi$
$884$	−29.8212	−1.00300
$885$	37.1772	1.24970
$886$	52.8090	1.77415
$887$	−8.27124	−0.277721	−0.138861	−	0.990312i	$-0.544344\pi$
$887$	−8.27124	−0.277721	−0.138861	+	0.990312i	$0.544344\pi$
$888$	62.2058	2.08749
$889$	−0.201437	−0.00675596
$890$	−133.820	−4.48565
$891$	3.97019	0.133006
$892$	27.7350	0.928638
$893$	8.92489	0.298660
$894$	32.5143	1.08744
$895$	77.9537	2.60571
$896$	77.4582	2.58770
$897$	−4.70654	−0.157147
$898$	−59.0544	−1.97067
$899$	40.7730	1.35986
$900$	34.0441	1.13480
$901$	−81.7754	−2.72433
$902$	13.5347	0.450657
$903$	13.2356	0.440452
$904$	78.3238	2.60501
$905$	8.44018	0.280561
$906$	5.72960	0.190353
$907$	54.4054	1.80650	0.903251	−	0.429114i	$-0.141174\pi$
$907$	54.4054	1.80650	0.903251	+	0.429114i	$0.141174\pi$
$908$	−6.41525	−0.212898
$909$	−8.78051	−0.291231
$910$	−32.4725	−1.07645
$911$	1.33568	0.0442529	0.0221264	−	0.999755i	$-0.492956\pi$
$911$	1.33568	0.0442529	0.0221264	+	0.999755i	$0.492956\pi$
$912$	41.4190	1.37152
$913$	60.1094	1.98933
$914$	22.4527	0.742668
$915$	−31.7272	−1.04887
$916$	24.4801	0.808846
$917$	49.9125	1.64826
$918$	15.3134	0.505418
$919$	46.1937	1.52379	0.761895	−	0.647701i	$-0.224269\pi$
$919$	46.1937	1.52379	0.761895	+	0.647701i	$0.224269\pi$
$920$	−139.118	−4.58659
$921$	−11.8603	−0.390811
$922$	12.4882	0.411278
$923$	−5.77396	−0.190052
$924$	−74.0430	−2.43584
$925$	−46.3629	−1.52440
$926$	−85.3780	−2.80570
$927$	−1.00000	−0.0328443
$928$	105.774	3.47221
$929$	22.6032	0.741587	0.370793	−	0.928715i	$-0.379086\pi$
$929$	22.6032	0.741587	0.370793	+	0.928715i	$0.379086\pi$
$930$	61.4744	2.01582
$931$	−18.0923	−0.592950
$932$	92.4359	3.02784
$933$	5.91420	0.193622
$934$	−106.603	−3.48815
$935$	76.6153	2.50559
$936$	8.71737	0.284936
$937$	−25.3624	−0.828554	−0.414277	−	0.910151i	$-0.635965\pi$
$937$	−25.3624	−0.828554	−0.414277	+	0.910151i	$0.635965\pi$
$938$	−78.5878	−2.56598
$939$	26.7960	0.874456
$940$	49.6776	1.62030
$941$	−20.7246	−0.675604	−0.337802	−	0.941217i	$-0.609683\pi$
$941$	−20.7246	−0.675604	−0.337802	+	0.941217i	$0.609683\pi$
$942$	−29.9353	−0.975346
$943$	5.96316	0.194187
$944$	142.274	4.63062
$945$	12.0685	0.392587
$946$	−39.7249	−1.29157
$947$	8.01337	0.260399	0.130200	−	0.991488i	$-0.458438\pi$
$947$	8.01337	0.260399	0.130200	+	0.991488i	$0.458438\pi$
$948$	−52.1850	−1.69489
$949$	−4.07053	−0.132135
$950$	−55.8013	−1.81043
$951$	−0.676898	−0.0219499
$952$	−176.583	−5.72310
$953$	−50.2186	−1.62674	−0.813371	−	0.581746i	$-0.802370\pi$
$953$	−50.2186	−1.62674	−0.813371	+	0.581746i	$0.802370\pi$
$954$	38.6615	1.25171
$955$	17.7333	0.573837
$956$	−49.0363	−1.58595
$957$	−24.0243	−0.776594
$958$	8.71718	0.281639
$959$	−1.64052	−0.0529750
$960$	71.4806	2.30703
$961$	14.4014	0.464560
$962$	−19.2004	−0.619044
$963$	−3.81774	−0.123025
$964$	−33.8342	−1.08973
$965$	63.5154	2.04463
$966$	−45.0736	−1.45022
$967$	19.1682	0.616409	0.308205	−	0.951320i	$-0.400272\pi$
$967$	19.1682	0.616409	0.308205	+	0.951320i	$0.400272\pi$
$968$	41.5158	1.33437
$969$	−18.1662	−0.583581
$970$	−56.4351	−1.81202
$971$	−8.71813	−0.279778	−0.139889	−	0.990167i	$-0.544675\pi$
$971$	−8.71813	−0.279778	−0.139889	+	0.990167i	$0.544675\pi$
$972$	−5.23983	−0.168067
$973$	−3.86973	−0.124058
$974$	72.3937	2.31964
$975$	−6.49719	−0.208076
$976$	−121.417	−3.88648
$977$	−33.2068	−1.06238	−0.531190	−	0.847253i	$-0.678255\pi$
$977$	−33.2068	−1.06238	−0.531190	+	0.847253i	$0.678255\pi$
$978$	−1.29253	−0.0413307
$979$	58.2334	1.86115
$980$	−100.705	−3.21690
$981$	−7.48563	−0.238998
$982$	−65.3694	−2.08602
$983$	31.5305	1.00567	0.502834	−	0.864383i	$-0.332291\pi$
$983$	31.5305	1.00567	0.502834	+	0.864383i	$0.332291\pi$
$984$	−11.0448	−0.352097
$985$	−11.7721	−0.375092
$986$	−92.6639	−2.95102
$987$	9.95185	0.316771
$988$	−16.7252	−0.532100
$989$	−17.5021	−0.556533
$990$	−36.2219	−1.15121
$991$	14.2588	0.452945	0.226472	−	0.974018i	$-0.427281\pi$
$991$	14.2588	0.452945	0.226472	+	0.974018i	$0.427281\pi$
$992$	117.781	3.73956
$993$	36.1015	1.14565
$994$	−55.2960	−1.75388
$995$	93.7485	2.97203
$996$	−79.3318	−2.51373
$997$	25.8738	0.819432	0.409716	−	0.912213i	$-0.365628\pi$
$997$	25.8738	0.819432	0.409716	+	0.912213i	$0.365628\pi$
$998$	−88.3011	−2.79512
$999$	7.13584	0.225768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.24	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.24	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+2.69069 q^{2} -1.00000 q^{3} +5.23983 q^{4} -3.39075 q^{5} -2.69069 q^{6} +3.55923 q^{7} +8.71737 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.69069 q^{2} -1.00000 q^{3} +5.23983 q^{4} -3.39075 q^{5} -2.69069 q^{6} +3.55923 q^{7} +8.71737 q^{8} +1.00000 q^{9} -9.12347 q^{10} +3.97019 q^{11} -5.23983 q^{12} +1.00000 q^{13} +9.57679 q^{14} +3.39075 q^{15} +12.9761 q^{16} -5.69126 q^{17} +2.69069 q^{18} -3.19194 q^{19} -17.7669 q^{20} -3.55923 q^{21} +10.6826 q^{22} +4.70654 q^{23} -8.71737 q^{24} +6.49719 q^{25} +2.69069 q^{26} -1.00000 q^{27} +18.6497 q^{28} +6.05116 q^{29} +9.12347 q^{30} +6.73805 q^{31} +17.4800 q^{32} -3.97019 q^{33} -15.3134 q^{34} -12.0685 q^{35} +5.23983 q^{36} -7.13584 q^{37} -8.58854 q^{38} -1.00000 q^{39} -29.5584 q^{40} +1.26699 q^{41} -9.57679 q^{42} -3.71867 q^{43} +20.8031 q^{44} -3.39075 q^{45} +12.6639 q^{46} -2.79607 q^{47} -12.9761 q^{48} +5.66810 q^{49} +17.4819 q^{50} +5.69126 q^{51} +5.23983 q^{52} +14.3686 q^{53} -2.69069 q^{54} -13.4619 q^{55} +31.0271 q^{56} +3.19194 q^{57} +16.2818 q^{58} +10.9643 q^{59} +17.7669 q^{60} -9.35699 q^{61} +18.1300 q^{62} +3.55923 q^{63} +21.0811 q^{64} -3.39075 q^{65} -10.6826 q^{66} -8.20608 q^{67} -29.8212 q^{68} -4.70654 q^{69} -32.4725 q^{70} -5.77396 q^{71} +8.71737 q^{72} -4.07053 q^{73} -19.2004 q^{74} -6.49719 q^{75} -16.7252 q^{76} +14.1308 q^{77} -2.69069 q^{78} +9.95930 q^{79} -43.9988 q^{80} +1.00000 q^{81} +3.40909 q^{82} +15.1402 q^{83} -18.6497 q^{84} +19.2976 q^{85} -10.0058 q^{86} -6.05116 q^{87} +34.6096 q^{88} +14.6677 q^{89} -9.12347 q^{90} +3.55923 q^{91} +24.6615 q^{92} -6.73805 q^{93} -7.52336 q^{94} +10.8231 q^{95} -17.4800 q^{96} +6.18570 q^{97} +15.2511 q^{98} +3.97019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more