LMFDB - Embedded newform 4017.2.a.i.1.14

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+0.444143 q^{2} -1.00000 q^{3} -1.80274 q^{4} +0.495430 q^{5} -0.444143 q^{6} +2.63750 q^{7} -1.68896 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.444143 q^{2} -1.00000 q^{3} -1.80274 q^{4} +0.495430 q^{5} -0.444143 q^{6} +2.63750 q^{7} -1.68896 q^{8} +1.00000 q^{9} +0.220041 q^{10} +4.65298 q^{11} +1.80274 q^{12} -1.00000 q^{13} +1.17142 q^{14} -0.495430 q^{15} +2.85534 q^{16} -8.19646 q^{17} +0.444143 q^{18} -0.642267 q^{19} -0.893129 q^{20} -2.63750 q^{21} +2.06659 q^{22} -4.89432 q^{23} +1.68896 q^{24} -4.75455 q^{25} -0.444143 q^{26} -1.00000 q^{27} -4.75471 q^{28} -6.98572 q^{29} -0.220041 q^{30} +5.25616 q^{31} +4.64609 q^{32} -4.65298 q^{33} -3.64040 q^{34} +1.30669 q^{35} -1.80274 q^{36} +6.45839 q^{37} -0.285258 q^{38} +1.00000 q^{39} -0.836760 q^{40} +0.00128922 q^{41} -1.17142 q^{42} +3.72446 q^{43} -8.38810 q^{44} +0.495430 q^{45} -2.17378 q^{46} +12.9544 q^{47} -2.85534 q^{48} -0.0436133 q^{49} -2.11170 q^{50} +8.19646 q^{51} +1.80274 q^{52} -7.76304 q^{53} -0.444143 q^{54} +2.30522 q^{55} -4.45462 q^{56} +0.642267 q^{57} -3.10266 q^{58} -4.72487 q^{59} +0.893129 q^{60} -1.19936 q^{61} +2.33448 q^{62} +2.63750 q^{63} -3.64714 q^{64} -0.495430 q^{65} -2.06659 q^{66} -2.43230 q^{67} +14.7761 q^{68} +4.89432 q^{69} +0.580359 q^{70} -15.0614 q^{71} -1.68896 q^{72} -15.7247 q^{73} +2.86845 q^{74} +4.75455 q^{75} +1.15784 q^{76} +12.2722 q^{77} +0.444143 q^{78} +13.0027 q^{79} +1.41462 q^{80} +1.00000 q^{81} +0.000572596 q^{82} +17.8562 q^{83} +4.75471 q^{84} -4.06077 q^{85} +1.65419 q^{86} +6.98572 q^{87} -7.85869 q^{88} -3.73637 q^{89} +0.220041 q^{90} -2.63750 q^{91} +8.82318 q^{92} -5.25616 q^{93} +5.75361 q^{94} -0.318198 q^{95} -4.64609 q^{96} -2.19985 q^{97} -0.0193705 q^{98} +4.65298 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	0.444143	0.314056	0.157028	−	0.987594i	$-0.449809\pi$
$2$	0.444143	0.314056	0.157028	+	0.987594i	$0.449809\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.80274	−0.901369
$5$	0.495430	0.221563	0.110781	−	0.993845i	$-0.464665\pi$
$5$	0.495430	0.221563	0.110781	+	0.993845i	$0.464665\pi$
$6$	−0.444143	−0.181321
$7$	2.63750	0.996880	0.498440	−	0.866924i	$-0.333906\pi$
$7$	2.63750	0.996880	0.498440	+	0.866924i	$0.333906\pi$
$8$	−1.68896	−0.597137
$9$	1.00000	0.333333
$10$	0.220041	0.0695832
$11$	4.65298	1.40293	0.701463	−	0.712706i	$-0.252530\pi$
$11$	4.65298	1.40293	0.701463	+	0.712706i	$0.252530\pi$
$12$	1.80274	0.520405
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.17142	0.313076
$15$	−0.495430	−0.127919
$16$	2.85534	0.713834
$17$	−8.19646	−1.98793	−0.993967	−	0.109684i	$-0.965016\pi$
$17$	−8.19646	−1.98793	−0.993967	+	0.109684i	$0.965016\pi$
$18$	0.444143	0.104685
$19$	−0.642267	−0.147346	−0.0736731	−	0.997282i	$-0.523472\pi$
$19$	−0.642267	−0.147346	−0.0736731	+	0.997282i	$0.523472\pi$
$20$	−0.893129	−0.199710
$21$	−2.63750	−0.575549
$22$	2.06659	0.440598
$23$	−4.89432	−1.02054	−0.510269	−	0.860015i	$-0.670454\pi$
$23$	−4.89432	−1.02054	−0.510269	+	0.860015i	$0.670454\pi$
$24$	1.68896	0.344757
$25$	−4.75455	−0.950910
$26$	−0.444143	−0.0871036
$27$	−1.00000	−0.192450
$28$	−4.75471	−0.898556
$29$	−6.98572	−1.29722	−0.648608	−	0.761123i	$-0.724648\pi$
$29$	−6.98572	−1.29722	−0.648608	+	0.761123i	$0.724648\pi$
$30$	−0.220041	−0.0401739
$31$	5.25616	0.944034	0.472017	−	0.881590i	$-0.343526\pi$
$31$	5.25616	0.944034	0.472017	+	0.881590i	$0.343526\pi$
$32$	4.64609	0.821321
$33$	−4.65298	−0.809980
$34$	−3.64040	−0.624323
$35$	1.30669	0.220872
$36$	−1.80274	−0.300456
$37$	6.45839	1.06175	0.530876	−	0.847449i	$-0.321863\pi$
$37$	6.45839	1.06175	0.530876	+	0.847449i	$0.321863\pi$
$38$	−0.285258	−0.0462750
$39$	1.00000	0.160128
$40$	−0.836760	−0.132303
$41$	0.00128922	0.000201342 0	0.000100671	−	1.00000i	$-0.499968\pi$
$41$	0.00128922	0.000201342 0	0.000100671		1.00000i	$0.499968\pi$
$42$	−1.17142	−0.180755
$43$	3.72446	0.567975	0.283987	−	0.958828i	$-0.408343\pi$
$43$	3.72446	0.567975	0.283987	+	0.958828i	$0.408343\pi$
$44$	−8.38810	−1.26455
$45$	0.495430	0.0738543
$46$	−2.17378	−0.320506
$47$	12.9544	1.88960	0.944798	−	0.327654i	$-0.106258\pi$
$47$	12.9544	1.88960	0.944798	+	0.327654i	$0.106258\pi$
$48$	−2.85534	−0.412132
$49$	−0.0436133	−0.00623047
$50$	−2.11170	−0.298639
$51$	8.19646	1.14773
$52$	1.80274	0.249995
$53$	−7.76304	−1.06634	−0.533168	−	0.846010i	$-0.678999\pi$
$53$	−7.76304	−1.06634	−0.533168	+	0.846010i	$0.678999\pi$
$54$	−0.444143	−0.0604402
$55$	2.30522	0.310836
$56$	−4.45462	−0.595274
$57$	0.642267	0.0850703
$58$	−3.10266	−0.407399
$59$	−4.72487	−0.615125	−0.307563	−	0.951528i	$-0.599513\pi$
$59$	−4.72487	−0.615125	−0.307563	+	0.951528i	$0.599513\pi$
$60$	0.893129	0.115303
$61$	−1.19936	−0.153563	−0.0767813	−	0.997048i	$-0.524464\pi$
$61$	−1.19936	−0.153563	−0.0767813	+	0.997048i	$0.524464\pi$
$62$	2.33448	0.296480
$63$	2.63750	0.332293
$64$	−3.64714	−0.455893
$65$	−0.495430	−0.0614505
$66$	−2.06659	−0.254379
$67$	−2.43230	−0.297152	−0.148576	−	0.988901i	$-0.547469\pi$
$67$	−2.43230	−0.297152	−0.148576	+	0.988901i	$0.547469\pi$
$68$	14.7761	1.79186
$69$	4.89432	0.589207
$70$	0.580359	0.0693661
$71$	−15.0614	−1.78745	−0.893727	−	0.448611i	$-0.851919\pi$
$71$	−15.0614	−1.78745	−0.893727	+	0.448611i	$0.851919\pi$
$72$	−1.68896	−0.199046
$73$	−15.7247	−1.84044	−0.920221	−	0.391399i	$-0.871991\pi$
$73$	−15.7247	−1.84044	−0.920221	+	0.391399i	$0.871991\pi$
$74$	2.86845	0.333450
$75$	4.75455	0.549008
$76$	1.15784	0.132813
$77$	12.2722	1.39855
$78$	0.444143	0.0502893
$79$	13.0027	1.46292	0.731458	−	0.681887i	$-0.238840\pi$
$79$	13.0027	1.46292	0.731458	+	0.681887i	$0.238840\pi$
$80$	1.41462	0.158159
$81$	1.00000	0.111111
$82$	0.000572596 0	6.32326e−5 0
$83$	17.8562	1.95997	0.979984	−	0.199076i	$-0.0637941\pi$
$83$	17.8562	1.95997	0.979984	+	0.199076i	$0.0637941\pi$
$84$	4.75471	0.518782
$85$	−4.06077	−0.440452
$86$	1.65419	0.178376
$87$	6.98572	0.748948
$88$	−7.85869	−0.837739
$89$	−3.73637	−0.396054	−0.198027	−	0.980197i	$-0.563453\pi$
$89$	−3.73637	−0.396054	−0.198027	+	0.980197i	$0.563453\pi$
$90$	0.220041	0.0231944
$91$	−2.63750	−0.276485
$92$	8.82318	0.919880
$93$	−5.25616	−0.545038
$94$	5.75361	0.593440
$95$	−0.318198	−0.0326464
$96$	−4.64609	−0.474190
$97$	−2.19985	−0.223361	−0.111680	−	0.993744i	$-0.535623\pi$
$97$	−2.19985	−0.223361	−0.111680	+	0.993744i	$0.535623\pi$
$98$	−0.0193705	−0.00195672
$99$	4.65298	0.467642
$100$	8.57120	0.857120
$101$	−12.5559	−1.24936	−0.624678	−	0.780882i	$-0.714770\pi$
$101$	−12.5559	−1.24936	−0.624678	+	0.780882i	$0.714770\pi$
$102$	3.64040	0.360453
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.68896	0.165616
$105$	−1.30669	−0.127520
$106$	−3.44790	−0.334889
$107$	9.01144	0.871169	0.435584	−	0.900148i	$-0.356542\pi$
$107$	9.01144	0.871169	0.435584	+	0.900148i	$0.356542\pi$
$108$	1.80274	0.173468
$109$	−4.47672	−0.428792	−0.214396	−	0.976747i	$-0.568778\pi$
$109$	−4.47672	−0.428792	−0.214396	+	0.976747i	$0.568778\pi$
$110$	1.02385	0.0976201
$111$	−6.45839	−0.613003
$112$	7.53094	0.711607
$113$	14.5187	1.36581	0.682904	−	0.730508i	$-0.260717\pi$
$113$	14.5187	1.36581	0.682904	+	0.730508i	$0.260717\pi$
$114$	0.285258	0.0267169
$115$	−2.42479	−0.226113
$116$	12.5934	1.16927
$117$	−1.00000	−0.0924500
$118$	−2.09852	−0.193184
$119$	−21.6181	−1.98173
$120$	0.836760	0.0763854
$121$	10.6502	0.968202
$122$	−0.532688	−0.0482273
$123$	−0.00128922	−0.000116245 0
$124$	−9.47547	−0.850922
$125$	−4.83269	−0.432249
$126$	1.17142	0.104359
$127$	−8.64494	−0.767114	−0.383557	−	0.923517i	$-0.625301\pi$
$127$	−8.64494	−0.767114	−0.383557	+	0.923517i	$0.625301\pi$
$128$	−10.9120	−0.964497
$129$	−3.72446	−0.327921
$130$	−0.220041	−0.0192989
$131$	−19.6524	−1.71704	−0.858518	−	0.512784i	$-0.828614\pi$
$131$	−19.6524	−1.71704	−0.858518	+	0.512784i	$0.828614\pi$
$132$	8.38810	0.730090
$133$	−1.69398	−0.146886
$134$	−1.08029	−0.0933225
$135$	−0.495430	−0.0426398
$136$	13.8435	1.18707
$137$	−18.2632	−1.56033	−0.780167	−	0.625571i	$-0.784866\pi$
$137$	−18.2632	−1.56033	−0.780167	+	0.625571i	$0.784866\pi$
$138$	2.17378	0.185044
$139$	−1.15079	−0.0976089	−0.0488044	−	0.998808i	$-0.515541\pi$
$139$	−1.15079	−0.0976089	−0.0488044	+	0.998808i	$0.515541\pi$
$140$	−2.35563	−0.199087
$141$	−12.9544	−1.09096
$142$	−6.68939	−0.561361
$143$	−4.65298	−0.389102
$144$	2.85534	0.237945
$145$	−3.46093	−0.287415
$146$	−6.98403	−0.578002
$147$	0.0436133	0.00359716
$148$	−11.6428	−0.957030
$149$	−5.71549	−0.468231	−0.234115	−	0.972209i	$-0.575219\pi$
$149$	−5.71549	−0.468231	−0.234115	+	0.972209i	$0.575219\pi$
$150$	2.11170	0.172419
$151$	1.69636	0.138048	0.0690241	−	0.997615i	$-0.478011\pi$
$151$	1.69636	0.138048	0.0690241	+	0.997615i	$0.478011\pi$
$152$	1.08476	0.0879858
$153$	−8.19646	−0.662644
$154$	5.45062	0.439223
$155$	2.60406	0.209163
$156$	−1.80274	−0.144334
$157$	−4.05069	−0.323280	−0.161640	−	0.986850i	$-0.551678\pi$
$157$	−4.05069	−0.323280	−0.161640	+	0.986850i	$0.551678\pi$
$158$	5.77505	0.459438
$159$	7.76304	0.615649
$160$	2.30181	0.181974
$161$	−12.9088	−1.01735
$162$	0.444143	0.0348951
$163$	−18.9483	−1.48415	−0.742073	−	0.670319i	$-0.766157\pi$
$163$	−18.9483	−1.48415	−0.742073	+	0.670319i	$0.766157\pi$
$164$	−0.00232412	−0.000181483 0
$165$	−2.30522	−0.179461
$166$	7.93068	0.615540
$167$	16.0530	1.24222	0.621109	−	0.783724i	$-0.286682\pi$
$167$	16.0530	1.24222	0.621109	+	0.783724i	$0.286682\pi$
$168$	4.45462	0.343681
$169$	1.00000	0.0769231
$170$	−1.80356	−0.138327
$171$	−0.642267	−0.0491154
$172$	−6.71422	−0.511955
$173$	−19.0057	−1.44498	−0.722488	−	0.691383i	$-0.757002\pi$
$173$	−19.0057	−1.44498	−0.722488	+	0.691383i	$0.757002\pi$
$174$	3.10266	0.235212
$175$	−12.5401	−0.947943
$176$	13.2858	1.00146
$177$	4.72487	0.355143
$178$	−1.65948	−0.124383
$179$	−23.2866	−1.74052	−0.870262	−	0.492589i	$-0.836051\pi$
$179$	−23.2866	−1.74052	−0.870262	+	0.492589i	$0.836051\pi$
$180$	−0.893129	−0.0665699
$181$	−10.5353	−0.783086	−0.391543	−	0.920160i	$-0.628059\pi$
$181$	−10.5353	−0.783086	−0.391543	+	0.920160i	$0.628059\pi$
$182$	−1.17142	−0.0868318
$183$	1.19936	0.0886594
$184$	8.26631	0.609400
$185$	3.19968	0.235245
$186$	−2.33448	−0.171173
$187$	−38.1380	−2.78892
$188$	−23.3534	−1.70322
$189$	−2.63750	−0.191850
$190$	−0.141325	−0.0102528
$191$	24.0138	1.73757	0.868787	−	0.495186i	$-0.164900\pi$
$191$	24.0138	1.73757	0.868787	+	0.495186i	$0.164900\pi$
$192$	3.64714	0.263210
$193$	−18.7133	−1.34701	−0.673505	−	0.739183i	$-0.735212\pi$
$193$	−18.7133	−1.34701	−0.673505	+	0.739183i	$0.735212\pi$
$194$	−0.977046	−0.0701478
$195$	0.495430	0.0354785
$196$	0.0786232	0.00561595
$197$	−0.510917	−0.0364013	−0.0182006	−	0.999834i	$-0.505794\pi$
$197$	−0.510917	−0.0364013	−0.0182006	+	0.999834i	$0.505794\pi$
$198$	2.06659	0.146866
$199$	14.5488	1.03133	0.515667	−	0.856789i	$-0.327544\pi$
$199$	14.5488	1.03133	0.515667	+	0.856789i	$0.327544\pi$
$200$	8.03023	0.567823
$201$	2.43230	0.171561
$202$	−5.57660	−0.392368
$203$	−18.4248	−1.29317
$204$	−14.7761	−1.03453
$205$	0.000638716 0	4.46098e−5 0
$206$	−0.444143	−0.0309449
$207$	−4.89432	−0.340179
$208$	−2.85534	−0.197982
$209$	−2.98846	−0.206716
$210$	−0.580359	−0.0400485
$211$	−0.898104	−0.0618280	−0.0309140	−	0.999522i	$-0.509842\pi$
$211$	−0.898104	−0.0618280	−0.0309140	+	0.999522i	$0.509842\pi$
$212$	13.9947	0.961161
$213$	15.0614	1.03199
$214$	4.00237	0.273596
$215$	1.84521	0.125842
$216$	1.68896	0.114919
$217$	13.8631	0.941088
$218$	−1.98830	−0.134665
$219$	15.7247	1.06258
$220$	−4.15571	−0.280178
$221$	8.19646	0.551353
$222$	−2.86845	−0.192518
$223$	−20.4231	−1.36763	−0.683815	−	0.729655i	$-0.739681\pi$
$223$	−20.4231	−1.36763	−0.683815	+	0.729655i	$0.739681\pi$
$224$	12.2541	0.818758
$225$	−4.75455	−0.316970
$226$	6.44840	0.428941
$227$	−7.77168	−0.515825	−0.257912	−	0.966168i	$-0.583035\pi$
$227$	−7.77168	−0.515825	−0.257912	+	0.966168i	$0.583035\pi$
$228$	−1.15784	−0.0766797
$229$	5.98182	0.395289	0.197645	−	0.980274i	$-0.436671\pi$
$229$	5.98182	0.395289	0.197645	+	0.980274i	$0.436671\pi$
$230$	−1.07695	−0.0710123
$231$	−12.2722	−0.807453
$232$	11.7986	0.774615
$233$	−23.8201	−1.56051	−0.780255	−	0.625462i	$-0.784911\pi$
$233$	−23.8201	−1.56051	−0.780255	+	0.625462i	$0.784911\pi$
$234$	−0.444143	−0.0290345
$235$	6.41800	0.418664
$236$	8.51770	0.554455
$237$	−13.0027	−0.844615
$238$	−9.60153	−0.622375
$239$	4.96338	0.321055	0.160527	−	0.987031i	$-0.448681\pi$
$239$	4.96338	0.321055	0.160527	+	0.987031i	$0.448681\pi$
$240$	−1.41462	−0.0913132
$241$	−4.16841	−0.268511	−0.134256	−	0.990947i	$-0.542864\pi$
$241$	−4.16841	−0.268511	−0.134256	+	0.990947i	$0.542864\pi$
$242$	4.73022	0.304070
$243$	−1.00000	−0.0641500
$244$	2.16213	0.138416
$245$	−0.0216073	−0.00138044
$246$	−0.000572596 0	−3.65074e−5 0
$247$	0.642267	0.0408665
$248$	−8.87743	−0.563717
$249$	−17.8562	−1.13159
$250$	−2.14641	−0.135751
$251$	−23.6530	−1.49296	−0.746481	−	0.665407i	$-0.768258\pi$
$251$	−23.6530	−1.49296	−0.746481	+	0.665407i	$0.768258\pi$
$252$	−4.75471	−0.299519
$253$	−22.7732	−1.43174
$254$	−3.83959	−0.240917
$255$	4.06077	0.254295
$256$	2.44779	0.152987
$257$	−4.00647	−0.249917	−0.124958	−	0.992162i	$-0.539880\pi$
$257$	−4.00647	−0.249917	−0.124958	+	0.992162i	$0.539880\pi$
$258$	−1.65419	−0.102986
$259$	17.0340	1.05844
$260$	0.893129	0.0553895
$261$	−6.98572	−0.432405
$262$	−8.72846	−0.539246
$263$	−10.2157	−0.629928	−0.314964	−	0.949104i	$-0.601993\pi$
$263$	−10.2157	−0.629928	−0.314964	+	0.949104i	$0.601993\pi$
$264$	7.85869	0.483669
$265$	−3.84604	−0.236260
$266$	−0.752368	−0.0461306
$267$	3.73637	0.228662
$268$	4.38479	0.267844
$269$	12.1232	0.739162	0.369581	−	0.929199i	$-0.379501\pi$
$269$	12.1232	0.739162	0.369581	+	0.929199i	$0.379501\pi$
$270$	−0.220041	−0.0133913
$271$	−6.59369	−0.400538	−0.200269	−	0.979741i	$-0.564182\pi$
$271$	−6.59369	−0.400538	−0.200269	+	0.979741i	$0.564182\pi$
$272$	−23.4036	−1.41905
$273$	2.63750	0.159629
$274$	−8.11149	−0.490033
$275$	−22.1228	−1.33406
$276$	−8.82318	−0.531093
$277$	−18.2559	−1.09689	−0.548444	−	0.836187i	$-0.684780\pi$
$277$	−18.2559	−1.09689	−0.548444	+	0.836187i	$0.684780\pi$
$278$	−0.511116	−0.0306547
$279$	5.25616	0.314678
$280$	−2.20695	−0.131891
$281$	23.8186	1.42090	0.710450	−	0.703748i	$-0.248492\pi$
$281$	23.8186	1.42090	0.710450	+	0.703748i	$0.248492\pi$
$282$	−5.75361	−0.342622
$283$	16.0174	0.952138	0.476069	−	0.879408i	$-0.342061\pi$
$283$	16.0174	0.952138	0.476069	+	0.879408i	$0.342061\pi$
$284$	27.1517	1.61116
$285$	0.318198	0.0188484
$286$	−2.06659	−0.122200
$287$	0.00340030	0.000200714 0
$288$	4.64609	0.273774
$289$	50.1819	2.95188
$290$	−1.53715	−0.0902644
$291$	2.19985	0.128957
$292$	28.3476	1.65892
$293$	−7.83818	−0.457911	−0.228956	−	0.973437i	$-0.573531\pi$
$293$	−7.83818	−0.457911	−0.228956	+	0.973437i	$0.573531\pi$
$294$	0.0193705	0.00112971
$295$	−2.34084	−0.136289
$296$	−10.9079	−0.634012
$297$	−4.65298	−0.269993
$298$	−2.53849	−0.147051
$299$	4.89432	0.283046
$300$	−8.57120	−0.494859
$301$	9.82325	0.566203
$302$	0.753428	0.0433549
$303$	12.5559	0.721316
$304$	−1.83389	−0.105181
$305$	−0.594199	−0.0340237
$306$	−3.64040	−0.208108
$307$	18.0462	1.02995	0.514975	−	0.857205i	$-0.327801\pi$
$307$	18.0462	1.02995	0.514975	+	0.857205i	$0.327801\pi$
$308$	−22.1236	−1.26061
$309$	1.00000	0.0568880
$310$	1.15657	0.0656889
$311$	10.4263	0.591222	0.295611	−	0.955308i	$-0.404477\pi$
$311$	10.4263	0.591222	0.295611	+	0.955308i	$0.404477\pi$
$312$	−1.68896	−0.0956184
$313$	20.0747	1.13469	0.567346	−	0.823480i	$-0.307970\pi$
$313$	20.0747	1.13469	0.567346	+	0.823480i	$0.307970\pi$
$314$	−1.79908	−0.101528
$315$	1.30669	0.0736239
$316$	−23.4404	−1.31863
$317$	−1.62622	−0.0913374	−0.0456687	−	0.998957i	$-0.514542\pi$
$317$	−1.62622	−0.0913374	−0.0456687	+	0.998957i	$0.514542\pi$
$318$	3.44790	0.193348
$319$	−32.5044	−1.81990
$320$	−1.80690	−0.101009
$321$	−9.01144	−0.502970
$322$	−5.73333	−0.319506
$323$	5.26431	0.292914
$324$	−1.80274	−0.100152
$325$	4.75455	0.263735
$326$	−8.41575	−0.466105
$327$	4.47672	0.247563
$328$	−0.00217743	−0.000120229 0
$329$	34.1672	1.88370
$330$	−1.02385	−0.0563610
$331$	21.1896	1.16469	0.582343	−	0.812943i	$-0.302136\pi$
$331$	21.1896	1.16469	0.582343	+	0.812943i	$0.302136\pi$
$332$	−32.1900	−1.76665
$333$	6.45839	0.353917
$334$	7.12982	0.390126
$335$	−1.20503	−0.0658379
$336$	−7.53094	−0.410846
$337$	16.0206	0.872699	0.436349	−	0.899777i	$-0.356271\pi$
$337$	16.0206	0.872699	0.436349	+	0.899777i	$0.356271\pi$
$338$	0.444143	0.0241582
$339$	−14.5187	−0.788550
$340$	7.32050	0.397010
$341$	24.4568	1.32441
$342$	−0.285258	−0.0154250
$343$	−18.5775	−1.00309
$344$	−6.29046	−0.339159
$345$	2.42479	0.130546
$346$	−8.44124	−0.453804
$347$	−11.2139	−0.601992	−0.300996	−	0.953625i	$-0.597319\pi$
$347$	−11.2139	−0.601992	−0.300996	+	0.953625i	$0.597319\pi$
$348$	−12.5934	−0.675078
$349$	16.2079	0.867590	0.433795	−	0.901012i	$-0.357174\pi$
$349$	16.2079	0.867590	0.433795	+	0.901012i	$0.357174\pi$
$350$	−5.56960	−0.297707
$351$	1.00000	0.0533761
$352$	21.6182	1.15225
$353$	6.72359	0.357860	0.178930	−	0.983862i	$-0.442736\pi$
$353$	6.72359	0.357860	0.178930	+	0.983862i	$0.442736\pi$
$354$	2.09852	0.111535
$355$	−7.46184	−0.396034
$356$	6.73569	0.356991
$357$	21.6181	1.14415
$358$	−10.3426	−0.546623
$359$	15.5739	0.821958	0.410979	−	0.911645i	$-0.365187\pi$
$359$	15.5739	0.821958	0.410979	+	0.911645i	$0.365187\pi$
$360$	−0.836760	−0.0441011
$361$	−18.5875	−0.978289
$362$	−4.67920	−0.245933
$363$	−10.6502	−0.558992
$364$	4.75471	0.249215
$365$	−7.79050	−0.407774
$366$	0.532688	0.0278440
$367$	−16.0771	−0.839216	−0.419608	−	0.907705i	$-0.637832\pi$
$367$	−16.0771	−0.839216	−0.419608	+	0.907705i	$0.637832\pi$
$368$	−13.9749	−0.728494
$369$	0.00128922	6.71139e−5 0
$370$	1.42111	0.0738802
$371$	−20.4750	−1.06301
$372$	9.47547	0.491280
$373$	−17.0162	−0.881064	−0.440532	−	0.897737i	$-0.645210\pi$
$373$	−17.0162	−0.881064	−0.440532	+	0.897737i	$0.645210\pi$
$374$	−16.9387	−0.875879
$375$	4.83269	0.249559
$376$	−21.8795	−1.12835
$377$	6.98572	0.359783
$378$	−1.17142	−0.0602516
$379$	19.5243	1.00290	0.501448	−	0.865188i	$-0.332801\pi$
$379$	19.5243	1.00290	0.501448	+	0.865188i	$0.332801\pi$
$380$	0.573628	0.0294265
$381$	8.64494	0.442894
$382$	10.6655	0.545696
$383$	1.36374	0.0696841	0.0348420	−	0.999393i	$-0.488907\pi$
$383$	1.36374	0.0696841	0.0348420	+	0.999393i	$0.488907\pi$
$384$	10.9120	0.556853
$385$	6.08002	0.309867
$386$	−8.31135	−0.423037
$387$	3.72446	0.189325
$388$	3.96574	0.201330
$389$	−24.4804	−1.24120	−0.620602	−	0.784126i	$-0.713112\pi$
$389$	−24.4804	−1.24120	−0.620602	+	0.784126i	$0.713112\pi$
$390$	0.220041	0.0111422
$391$	40.1161	2.02876
$392$	0.0736610	0.00372044
$393$	19.6524	0.991331
$394$	−0.226920	−0.0114321
$395$	6.44191	0.324128
$396$	−8.38810	−0.421518
$397$	14.4582	0.725639	0.362819	−	0.931859i	$-0.381814\pi$
$397$	14.4582	0.725639	0.362819	+	0.931859i	$0.381814\pi$
$398$	6.46173	0.323897
$399$	1.69398	0.0848049
$400$	−13.5758	−0.678792
$401$	−26.4188	−1.31929	−0.659647	−	0.751575i	$-0.729294\pi$
$401$	−26.4188	−1.31929	−0.659647	+	0.751575i	$0.729294\pi$
$402$	1.08029	0.0538798
$403$	−5.25616	−0.261828
$404$	22.6349	1.12613
$405$	0.495430	0.0246181
$406$	−8.18324	−0.406128
$407$	30.0508	1.48956
$408$	−13.8435	−0.685354
$409$	−23.8185	−1.17775	−0.588874	−	0.808225i	$-0.700429\pi$
$409$	−23.8185	−1.17775	−0.588874	+	0.808225i	$0.700429\pi$
$410$	0.000283681 0	1.40100e−5 0
$411$	18.2632	0.900859
$412$	1.80274	0.0888145
$413$	−12.4618	−0.613206
$414$	−2.17378	−0.106835
$415$	8.84647	0.434256
$416$	−4.64609	−0.227793
$417$	1.15079	0.0563545
$418$	−1.32730	−0.0649204
$419$	−31.5109	−1.53941	−0.769703	−	0.638402i	$-0.779596\pi$
$419$	−31.5109	−1.53941	−0.769703	+	0.638402i	$0.779596\pi$
$420$	2.35563	0.114943
$421$	0.534025	0.0260268	0.0130134	−	0.999915i	$-0.495858\pi$
$421$	0.534025	0.0260268	0.0130134	+	0.999915i	$0.495858\pi$
$422$	−0.398886	−0.0194175
$423$	12.9544	0.629865
$424$	13.1114	0.636748
$425$	38.9705	1.89035
$426$	6.68939	0.324102
$427$	−3.16331	−0.153083
$428$	−16.2453	−0.785244
$429$	4.65298	0.224648
$430$	0.819536	0.0395215
$431$	14.3155	0.689553	0.344776	−	0.938685i	$-0.387955\pi$
$431$	14.3155	0.689553	0.344776	+	0.938685i	$0.387955\pi$
$432$	−2.85534	−0.137377
$433$	23.7616	1.14191	0.570955	−	0.820981i	$-0.306573\pi$
$433$	23.7616	1.14191	0.570955	+	0.820981i	$0.306573\pi$
$434$	6.15719	0.295555
$435$	3.46093	0.165939
$436$	8.07034	0.386499
$437$	3.14346	0.150372
$438$	6.98403	0.333710
$439$	30.9278	1.47610	0.738052	−	0.674743i	$-0.235746\pi$
$439$	30.9278	1.47610	0.738052	+	0.674743i	$0.235746\pi$
$440$	−3.89343	−0.185612
$441$	−0.0436133	−0.00207682
$442$	3.64040	0.173156
$443$	5.11685	0.243109	0.121554	−	0.992585i	$-0.461212\pi$
$443$	5.11685	0.243109	0.121554	+	0.992585i	$0.461212\pi$
$444$	11.6428	0.552542
$445$	−1.85111	−0.0877509
$446$	−9.07076	−0.429513
$447$	5.71549	0.270333
$448$	−9.61933	−0.454471
$449$	−27.8323	−1.31349	−0.656745	−	0.754113i	$-0.728067\pi$
$449$	−27.8323	−1.31349	−0.656745	+	0.754113i	$0.728067\pi$
$450$	−2.11170	−0.0995464
$451$	0.00599870	0.000282468 0
$452$	−26.1735	−1.23110
$453$	−1.69636	−0.0797022
$454$	−3.45174	−0.161998
$455$	−1.30669	−0.0612587
$456$	−1.08476	−0.0507986
$457$	−30.6104	−1.43189	−0.715946	−	0.698155i	$-0.754004\pi$
$457$	−30.6104	−1.43189	−0.715946	+	0.698155i	$0.754004\pi$
$458$	2.65678	0.124143
$459$	8.19646	0.382578
$460$	4.37126	0.203811
$461$	22.5838	1.05183	0.525916	−	0.850536i	$-0.323723\pi$
$461$	22.5838	1.05183	0.525916	+	0.850536i	$0.323723\pi$
$462$	−5.45062	−0.253586
$463$	4.22556	0.196378	0.0981892	−	0.995168i	$-0.468695\pi$
$463$	4.22556	0.196378	0.0981892	+	0.995168i	$0.468695\pi$
$464$	−19.9466	−0.925996
$465$	−2.60406	−0.120760
$466$	−10.5795	−0.490088
$467$	23.5472	1.08964	0.544818	−	0.838554i	$-0.316599\pi$
$467$	23.5472	1.08964	0.544818	+	0.838554i	$0.316599\pi$
$468$	1.80274	0.0833316
$469$	−6.41517	−0.296225
$470$	2.85051	0.131484
$471$	4.05069	0.186646
$472$	7.98010	0.367314
$473$	17.3298	0.796827
$474$	−5.77505	−0.265257
$475$	3.05369	0.140113
$476$	38.9718	1.78627
$477$	−7.76304	−0.355445
$478$	2.20445	0.100829
$479$	−4.45305	−0.203465	−0.101732	−	0.994812i	$-0.532439\pi$
$479$	−4.45305	−0.203465	−0.101732	+	0.994812i	$0.532439\pi$
$480$	−2.30181	−0.105063
$481$	−6.45839	−0.294477
$482$	−1.85137	−0.0843276
$483$	12.9088	0.587369
$484$	−19.1996	−0.872707
$485$	−1.08987	−0.0494884
$486$	−0.444143	−0.0201467
$487$	−35.1877	−1.59451	−0.797254	−	0.603645i	$-0.793715\pi$
$487$	−35.1877	−1.59451	−0.797254	+	0.603645i	$0.793715\pi$
$488$	2.02567	0.0916978
$489$	18.9483	0.856872
$490$	−0.00959673	−0.000433536 0
$491$	41.0462	1.85239	0.926194	−	0.377048i	$-0.123061\pi$
$491$	41.0462	1.85239	0.926194	+	0.377048i	$0.123061\pi$
$492$	0.00232412	0.000104779 0
$493$	57.2581	2.57878
$494$	0.285258	0.0128344
$495$	2.30522	0.103612
$496$	15.0081	0.673883
$497$	−39.7243	−1.78188
$498$	−7.93068	−0.355382
$499$	−30.5740	−1.36868	−0.684340	−	0.729163i	$-0.739910\pi$
$499$	−30.5740	−1.36868	−0.684340	+	0.729163i	$0.739910\pi$
$500$	8.71208	0.389616
$501$	−16.0530	−0.717195
$502$	−10.5053	−0.468874
$503$	−21.5697	−0.961746	−0.480873	−	0.876790i	$-0.659680\pi$
$503$	−21.5697	−0.961746	−0.480873	+	0.876790i	$0.659680\pi$
$504$	−4.45462	−0.198425
$505$	−6.22055	−0.276811
$506$	−10.1145	−0.449647
$507$	−1.00000	−0.0444116
$508$	15.5846	0.691453
$509$	2.41756	0.107157	0.0535783	−	0.998564i	$-0.482937\pi$
$509$	2.41756	0.107157	0.0535783	+	0.998564i	$0.482937\pi$
$510$	1.80356	0.0798630
$511$	−41.4740	−1.83470
$512$	22.9112	1.01254
$513$	0.642267	0.0283568
$514$	−1.77944	−0.0784879
$515$	−0.495430	−0.0218312
$516$	6.71422	0.295577
$517$	60.2766	2.65096
$518$	7.56552	0.332410
$519$	19.0057	0.834258
$520$	0.836760	0.0366943
$521$	−42.8932	−1.87919	−0.939593	−	0.342294i	$-0.888796\pi$
$521$	−42.8932	−1.87919	−0.939593	+	0.342294i	$0.888796\pi$
$522$	−3.10266	−0.135800
$523$	−24.6603	−1.07832	−0.539160	−	0.842203i	$-0.681258\pi$
$523$	−24.6603	−1.07832	−0.539160	+	0.842203i	$0.681258\pi$
$524$	35.4281	1.54768
$525$	12.5401	0.547295
$526$	−4.53724	−0.197833
$527$	−43.0819	−1.87668
$528$	−13.2858	−0.578191
$529$	0.954410	0.0414961
$530$	−1.70819	−0.0741991
$531$	−4.72487	−0.205042
$532$	3.05380	0.132399
$533$	−0.00128922	−5.58421e−5 0
$534$	1.65948	0.0718128
$535$	4.46453	0.193019
$536$	4.10805	0.177441
$537$	23.2866	1.00489
$538$	5.38441	0.232138
$539$	−0.202932	−0.00874088
$540$	0.893129	0.0384342
$541$	−35.1187	−1.50987	−0.754935	−	0.655799i	$-0.772332\pi$
$541$	−35.1187	−1.50987	−0.754935	+	0.655799i	$0.772332\pi$
$542$	−2.92854	−0.125792
$543$	10.5353	0.452115
$544$	−38.0815	−1.63273
$545$	−2.21790	−0.0950043
$546$	1.17142	0.0501324
$547$	−20.5259	−0.877626	−0.438813	−	0.898578i	$-0.644601\pi$
$547$	−20.5259	−0.877626	−0.438813	+	0.898578i	$0.644601\pi$
$548$	32.9238	1.40644
$549$	−1.19936	−0.0511875
$550$	−9.82569	−0.418969
$551$	4.48670	0.191140
$552$	−8.26631	−0.351837
$553$	34.2945	1.45835
$554$	−8.10820	−0.344485
$555$	−3.19968	−0.135819
$556$	2.07458	0.0879816
$557$	−39.2493	−1.66305	−0.831523	−	0.555490i	$-0.812531\pi$
$557$	−39.2493	−1.66305	−0.831523	+	0.555490i	$0.812531\pi$
$558$	2.33448	0.0988266
$559$	−3.72446	−0.157528
$560$	3.73105	0.157666
$561$	38.1380	1.61019
$562$	10.5789	0.446243
$563$	−27.2953	−1.15036	−0.575179	−	0.818027i	$-0.695068\pi$
$563$	−27.2953	−1.15036	−0.575179	+	0.818027i	$0.695068\pi$
$564$	23.3534	0.983356
$565$	7.19302	0.302613
$566$	7.11403	0.299025
$567$	2.63750	0.110764
$568$	25.4380	1.06736
$569$	−9.45956	−0.396565	−0.198283	−	0.980145i	$-0.563536\pi$
$569$	−9.45956	−0.396565	−0.198283	+	0.980145i	$0.563536\pi$
$570$	0.141325	0.00591947
$571$	8.47167	0.354528	0.177264	−	0.984163i	$-0.443275\pi$
$571$	8.47167	0.354528	0.177264	+	0.984163i	$0.443275\pi$
$572$	8.38810	0.350724
$573$	−24.0138	−1.00319
$574$	0.00151022	6.30353e−5 0
$575$	23.2703	0.970439
$576$	−3.64714	−0.151964
$577$	27.7292	1.15438	0.577192	−	0.816609i	$-0.304148\pi$
$577$	27.7292	1.15438	0.577192	+	0.816609i	$0.304148\pi$
$578$	22.2879	0.927056
$579$	18.7133	0.777696
$580$	6.23915	0.259067
$581$	47.0956	1.95385
$582$	0.977046	0.0404998
$583$	−36.1213	−1.49599
$584$	26.5584	1.09900
$585$	−0.495430	−0.0204835
$586$	−3.48127	−0.143810
$587$	−13.8273	−0.570712	−0.285356	−	0.958422i	$-0.592112\pi$
$587$	−13.8273	−0.570712	−0.285356	+	0.958422i	$0.592112\pi$
$588$	−0.0786232	−0.00324237
$589$	−3.37586	−0.139100
$590$	−1.03967	−0.0428024
$591$	0.510917	0.0210163
$592$	18.4409	0.757915
$593$	−30.5585	−1.25489	−0.627443	−	0.778663i	$-0.715898\pi$
$593$	−30.5585	−1.25489	−0.627443	+	0.778663i	$0.715898\pi$
$594$	−2.06659	−0.0847931
$595$	−10.7103	−0.439078
$596$	10.3035	0.422049
$597$	−14.5488	−0.595441
$598$	2.17378	0.0888924
$599$	13.9834	0.571347	0.285673	−	0.958327i	$-0.407783\pi$
$599$	13.9834	0.571347	0.285673	+	0.958327i	$0.407783\pi$
$600$	−8.03023	−0.327833
$601$	25.2646	1.03056	0.515282	−	0.857021i	$-0.327687\pi$
$601$	25.2646	1.03056	0.515282	+	0.857021i	$0.327687\pi$
$602$	4.36293	0.177820
$603$	−2.43230	−0.0990507
$604$	−3.05810	−0.124432
$605$	5.27644	0.214518
$606$	5.57660	0.226534
$607$	−17.6471	−0.716274	−0.358137	−	0.933669i	$-0.616588\pi$
$607$	−17.6471	−0.716274	−0.358137	+	0.933669i	$0.616588\pi$
$608$	−2.98403	−0.121018
$609$	18.4248	0.746611
$610$	−0.263909	−0.0106854
$611$	−12.9544	−0.524080
$612$	14.7761	0.597287
$613$	43.1038	1.74094	0.870472	−	0.492217i	$-0.163813\pi$
$613$	43.1038	1.74094	0.870472	+	0.492217i	$0.163813\pi$
$614$	8.01508	0.323462
$615$	−0.000638716 0	−2.57555e−5 0
$616$	−20.7273	−0.835125
$617$	−32.1824	−1.29561	−0.647807	−	0.761805i	$-0.724314\pi$
$617$	−32.1824	−1.29561	−0.647807	+	0.761805i	$0.724314\pi$
$618$	0.444143	0.0178660
$619$	−17.9734	−0.722411	−0.361205	−	0.932486i	$-0.617635\pi$
$619$	−17.9734	−0.722411	−0.361205	+	0.932486i	$0.617635\pi$
$620$	−4.69443	−0.188533
$621$	4.89432	0.196402
$622$	4.63077	0.185677
$623$	−9.85466	−0.394819
$624$	2.85534	0.114305
$625$	21.3785	0.855140
$626$	8.91605	0.356357
$627$	2.98846	0.119347
$628$	7.30233	0.291395
$629$	−52.9359	−2.11069
$630$	0.580359	0.0231220
$631$	27.6405	1.10035	0.550175	−	0.835050i	$-0.314561\pi$
$631$	27.6405	1.10035	0.550175	+	0.835050i	$0.314561\pi$
$632$	−21.9610	−0.873561
$633$	0.898104	0.0356964
$634$	−0.722272	−0.0286851
$635$	−4.28296	−0.169964
$636$	−13.9947	−0.554927
$637$	0.0436133	0.00172802
$638$	−14.4366	−0.571550
$639$	−15.0614	−0.595818
$640$	−5.40615	−0.213697
$641$	10.3585	0.409135	0.204568	−	0.978852i	$-0.434421\pi$
$641$	10.3585	0.409135	0.204568	+	0.978852i	$0.434421\pi$
$642$	−4.00237	−0.157961
$643$	12.5949	0.496693	0.248347	−	0.968671i	$-0.420113\pi$
$643$	12.5949	0.496693	0.248347	+	0.968671i	$0.420113\pi$
$644$	23.2711	0.917010
$645$	−1.84521	−0.0726550
$646$	2.33811	0.0919916
$647$	29.3730	1.15477	0.577386	−	0.816471i	$-0.304073\pi$
$647$	29.3730	1.15477	0.577386	+	0.816471i	$0.304073\pi$
$648$	−1.68896	−0.0663485
$649$	−21.9847	−0.862976
$650$	2.11170	0.0828276
$651$	−13.8631	−0.543338
$652$	34.1588	1.33776
$653$	43.9388	1.71946	0.859728	−	0.510751i	$-0.170633\pi$
$653$	43.9388	1.71946	0.859728	+	0.510751i	$0.170633\pi$
$654$	1.98830	0.0777487
$655$	−9.73637	−0.380431
$656$	0.00368114	0.000143725 0
$657$	−15.7247	−0.613481
$658$	15.1751	0.591588
$659$	9.58952	0.373555	0.186777	−	0.982402i	$-0.440196\pi$
$659$	9.58952	0.373555	0.186777	+	0.982402i	$0.440196\pi$
$660$	4.15571	0.161761
$661$	40.8834	1.59018	0.795091	−	0.606490i	$-0.207423\pi$
$661$	40.8834	1.59018	0.795091	+	0.606490i	$0.207423\pi$
$662$	9.41121	0.365777
$663$	−8.19646	−0.318324
$664$	−30.1583	−1.17037
$665$	−0.839246	−0.0325446
$666$	2.86845	0.111150
$667$	34.1904	1.32386
$668$	−28.9393	−1.11970
$669$	20.4231	0.789602
$670$	−0.535206	−0.0206768
$671$	−5.58061	−0.215437
$672$	−12.2541	−0.472710
$673$	−12.9969	−0.500992	−0.250496	−	0.968118i	$-0.580594\pi$
$673$	−12.9969	−0.500992	−0.250496	+	0.968118i	$0.580594\pi$
$674$	7.11544	0.274076
$675$	4.75455	0.183003
$676$	−1.80274	−0.0693360
$677$	16.3772	0.629428	0.314714	−	0.949187i	$-0.398091\pi$
$677$	16.3772	0.629428	0.314714	+	0.949187i	$0.398091\pi$
$678$	−6.44840	−0.247649
$679$	−5.80209	−0.222664
$680$	6.85847	0.263010
$681$	7.77168	0.297811
$682$	10.8623	0.415939
$683$	−20.2921	−0.776456	−0.388228	−	0.921563i	$-0.626913\pi$
$683$	−20.2921	−0.776456	−0.388228	+	0.921563i	$0.626913\pi$
$684$	1.15784	0.0442711
$685$	−9.04815	−0.345712
$686$	−8.25106	−0.315027
$687$	−5.98182	−0.228220
$688$	10.6346	0.405440
$689$	7.76304	0.295748
$690$	1.07695	0.0409989
$691$	27.0472	1.02892	0.514462	−	0.857513i	$-0.327992\pi$
$691$	27.0472	1.02892	0.514462	+	0.857513i	$0.327992\pi$
$692$	34.2623	1.30246
$693$	12.2722	0.466183
$694$	−4.98056	−0.189059
$695$	−0.570136	−0.0216265
$696$	−11.7986	−0.447224
$697$	−0.0105670	−0.000400254 0
$698$	7.19863	0.272472
$699$	23.8201	0.900960
$700$	22.6065	0.854446
$701$	0.327439	0.0123672	0.00618360	−	0.999981i	$-0.498032\pi$
$701$	0.327439	0.0123672	0.00618360	+	0.999981i	$0.498032\pi$
$702$	0.444143	0.0167631
$703$	−4.14801	−0.156445
$704$	−16.9701	−0.639584
$705$	−6.41800	−0.241716
$706$	2.98623	0.112388
$707$	−33.1161	−1.24546
$708$	−8.51770	−0.320115
$709$	−7.73459	−0.290479	−0.145239	−	0.989397i	$-0.546395\pi$
$709$	−7.73459	−0.290479	−0.145239	+	0.989397i	$0.546395\pi$
$710$	−3.31412	−0.124377
$711$	13.0027	0.487639
$712$	6.31057	0.236499
$713$	−25.7253	−0.963422
$714$	9.60153	0.359328
$715$	−2.30522	−0.0862105
$716$	41.9797	1.56885
$717$	−4.96338	−0.185361
$718$	6.91703	0.258141
$719$	18.1753	0.677824	0.338912	−	0.940818i	$-0.389941\pi$
$719$	18.1753	0.677824	0.338912	+	0.940818i	$0.389941\pi$
$720$	1.41462	0.0527197
$721$	−2.63750	−0.0982255
$722$	−8.25550	−0.307238
$723$	4.16841	0.155025
$724$	18.9925	0.705849
$725$	33.2139	1.23353
$726$	−4.73022	−0.175555
$727$	23.9833	0.889493	0.444747	−	0.895656i	$-0.353294\pi$
$727$	23.9833	0.889493	0.444747	+	0.895656i	$0.353294\pi$
$728$	4.45462	0.165099
$729$	1.00000	0.0370370
$730$	−3.46010	−0.128064
$731$	−30.5274	−1.12910
$732$	−2.16213	−0.0799148
$733$	−9.12211	−0.336933	−0.168466	−	0.985707i	$-0.553881\pi$
$733$	−9.12211	−0.336933	−0.168466	+	0.985707i	$0.553881\pi$
$734$	−7.14051	−0.263561
$735$	0.0216073	0.000796997 0
$736$	−22.7395	−0.838189
$737$	−11.3174	−0.416883
$738$	0.000572596 0	2.10775e−5 0
$739$	34.7701	1.27904	0.639519	−	0.768775i	$-0.279134\pi$
$739$	34.7701	1.27904	0.639519	+	0.768775i	$0.279134\pi$
$740$	−5.76818	−0.212042
$741$	−0.642267	−0.0235943
$742$	−9.09382	−0.333845
$743$	9.35166	0.343079	0.171540	−	0.985177i	$-0.445126\pi$
$743$	9.35166	0.343079	0.171540	+	0.985177i	$0.445126\pi$
$744$	8.87743	0.325462
$745$	−2.83162	−0.103743
$746$	−7.55761	−0.276704
$747$	17.8562	0.653323
$748$	68.7527	2.51385
$749$	23.7676	0.868451
$750$	2.14641	0.0783756
$751$	33.5581	1.22455	0.612277	−	0.790644i	$-0.290254\pi$
$751$	33.5581	1.22455	0.612277	+	0.790644i	$0.290254\pi$
$752$	36.9892	1.34886
$753$	23.6530	0.861962
$754$	3.10266	0.112992
$755$	0.840429	0.0305864
$756$	4.75471	0.172927
$757$	41.2078	1.49772	0.748862	−	0.662726i	$-0.230601\pi$
$757$	41.2078	1.49772	0.748862	+	0.662726i	$0.230601\pi$
$758$	8.67157	0.314966
$759$	22.7732	0.826615
$760$	0.537423	0.0194944
$761$	30.8408	1.11798	0.558989	−	0.829175i	$-0.311189\pi$
$761$	30.8408	1.11798	0.558989	+	0.829175i	$0.311189\pi$
$762$	3.83959	0.139094
$763$	−11.8073	−0.427454
$764$	−43.2905	−1.56620
$765$	−4.06077	−0.146817
$766$	0.605697	0.0218847
$767$	4.72487	0.170605
$768$	−2.44779	−0.0883268
$769$	22.7006	0.818604	0.409302	−	0.912399i	$-0.365772\pi$
$769$	22.7006	0.818604	0.409302	+	0.912399i	$0.365772\pi$
$770$	2.70040	0.0973155
$771$	4.00647	0.144289
$772$	33.7351	1.21415
$773$	−42.3285	−1.52245	−0.761226	−	0.648487i	$-0.775402\pi$
$773$	−42.3285	−1.52245	−0.761226	+	0.648487i	$0.775402\pi$
$774$	1.65419	0.0594587
$775$	−24.9907	−0.897691
$776$	3.71545	0.133377
$777$	−17.0340	−0.611090
$778$	−10.8728	−0.389808
$779$	−0.000828021 0	−2.96669e−5 0
$780$	−0.893129	−0.0319792
$781$	−70.0802	−2.50767
$782$	17.8173	0.637145
$783$	6.98572	0.249649
$784$	−0.124531	−0.00444752
$785$	−2.00683	−0.0716269
$786$	8.72846	0.311334
$787$	37.6581	1.34237	0.671184	−	0.741291i	$-0.265786\pi$
$787$	37.6581	1.34237	0.671184	+	0.741291i	$0.265786\pi$
$788$	0.921048	0.0328110
$789$	10.2157	0.363689
$790$	2.86113	0.101794
$791$	38.2931	1.36155
$792$	−7.85869	−0.279246
$793$	1.19936	0.0425906
$794$	6.42153	0.227891
$795$	3.84604	0.136405
$796$	−26.2276	−0.929613
$797$	32.9050	1.16556	0.582778	−	0.812631i	$-0.301966\pi$
$797$	32.9050	1.16556	0.582778	+	0.812631i	$0.301966\pi$
$798$	0.752368	0.0266335
$799$	−106.180	−3.75639
$800$	−22.0901	−0.781002
$801$	−3.73637	−0.132018
$802$	−11.7337	−0.414333
$803$	−73.1669	−2.58200
$804$	−4.38479	−0.154640
$805$	−6.39538	−0.225408
$806$	−2.33448	−0.0822287
$807$	−12.1232	−0.426755
$808$	21.2063	0.746037
$809$	−4.41376	−0.155179	−0.0775897	−	0.996985i	$-0.524722\pi$
$809$	−4.41376	−0.155179	−0.0775897	+	0.996985i	$0.524722\pi$
$810$	0.220041	0.00773147
$811$	18.6858	0.656148	0.328074	−	0.944652i	$-0.393600\pi$
$811$	18.6858	0.656148	0.328074	+	0.944652i	$0.393600\pi$
$812$	33.2151	1.16562
$813$	6.59369	0.231251
$814$	13.3468	0.467806
$815$	−9.38755	−0.328832
$816$	23.4036	0.819291
$817$	−2.39210	−0.0836889
$818$	−10.5788	−0.369879
$819$	−2.63750	−0.0921616
$820$	−0.00115144	−4.02099e−5 0
$821$	18.9467	0.661246	0.330623	−	0.943763i	$-0.392741\pi$
$821$	18.9467	0.661246	0.330623	+	0.943763i	$0.392741\pi$
$822$	8.11149	0.282921
$823$	−32.5044	−1.13303	−0.566517	−	0.824050i	$-0.691709\pi$
$823$	−32.5044	−1.13303	−0.566517	+	0.824050i	$0.691709\pi$
$824$	1.68896	0.0588376
$825$	22.1228	0.770218
$826$	−5.53483	−0.192581
$827$	−37.5197	−1.30469	−0.652344	−	0.757923i	$-0.726214\pi$
$827$	−37.5197	−1.30469	−0.652344	+	0.757923i	$0.726214\pi$
$828$	8.82318	0.306627
$829$	24.9280	0.865787	0.432893	−	0.901445i	$-0.357493\pi$
$829$	24.9280	0.865787	0.432893	+	0.901445i	$0.357493\pi$
$830$	3.92910	0.136381
$831$	18.2559	0.633289
$832$	3.64714	0.126442
$833$	0.357474	0.0123857
$834$	0.511116	0.0176985
$835$	7.95313	0.275229
$836$	5.38740	0.186327
$837$	−5.25616	−0.181679
$838$	−13.9953	−0.483460
$839$	9.76253	0.337040	0.168520	−	0.985698i	$-0.446101\pi$
$839$	9.76253	0.337040	0.168520	+	0.985698i	$0.446101\pi$
$840$	2.20695	0.0761470
$841$	19.8002	0.682767
$842$	0.237183	0.00817388
$843$	−23.8186	−0.820357
$844$	1.61905	0.0557298
$845$	0.495430	0.0170433
$846$	5.75361	0.197813
$847$	28.0899	0.965181
$848$	−22.1661	−0.761187
$849$	−16.0174	−0.549717
$850$	17.3084	0.593675
$851$	−31.6094	−1.08356
$852$	−27.1517	−0.930201
$853$	5.97806	0.204685	0.102342	−	0.994749i	$-0.467366\pi$
$853$	5.97806	0.204685	0.102342	+	0.994749i	$0.467366\pi$
$854$	−1.40496	−0.0480768
$855$	−0.318198	−0.0108821
$856$	−15.2199	−0.520207
$857$	−39.8413	−1.36095	−0.680476	−	0.732770i	$-0.738227\pi$
$857$	−39.8413	−1.36095	−0.680476	+	0.732770i	$0.738227\pi$
$858$	2.06659	0.0705521
$859$	36.1341	1.23288	0.616440	−	0.787402i	$-0.288574\pi$
$859$	36.1341	1.23288	0.616440	+	0.787402i	$0.288574\pi$
$860$	−3.32643	−0.113430
$861$	−0.00340030	−0.000115882 0
$862$	6.35812	0.216558
$863$	−51.1390	−1.74079	−0.870396	−	0.492352i	$-0.836137\pi$
$863$	−51.1390	−1.74079	−0.870396	+	0.492352i	$0.836137\pi$
$864$	−4.64609	−0.158063
$865$	−9.41599	−0.320153
$866$	10.5535	0.358624
$867$	−50.1819	−1.70427
$868$	−24.9915	−0.848267
$869$	60.5012	2.05236
$870$	1.53715	0.0521142
$871$	2.43230	0.0824152
$872$	7.56099	0.256047
$873$	−2.19985	−0.0744535
$874$	1.39615	0.0472254
$875$	−12.7462	−0.430901
$876$	−28.3476	−0.957776
$877$	13.5651	0.458062	0.229031	−	0.973419i	$-0.426444\pi$
$877$	13.5651	0.458062	0.229031	+	0.973419i	$0.426444\pi$
$878$	13.7364	0.463580
$879$	7.83818	0.264375
$880$	6.58219	0.221886
$881$	−41.5879	−1.40113	−0.700566	−	0.713587i	$-0.747069\pi$
$881$	−41.5879	−1.40113	−0.700566	+	0.713587i	$0.747069\pi$
$882$	−0.0193705	−0.000652239 0
$883$	10.1510	0.341607	0.170804	−	0.985305i	$-0.445364\pi$
$883$	10.1510	0.341607	0.170804	+	0.985305i	$0.445364\pi$
$884$	−14.7761	−0.496973
$885$	2.34084	0.0786865
$886$	2.27261	0.0763499
$887$	6.53964	0.219580	0.109790	−	0.993955i	$-0.464982\pi$
$887$	6.53964	0.219580	0.109790	+	0.993955i	$0.464982\pi$
$888$	10.9079	0.366047
$889$	−22.8010	−0.764721
$890$	−0.822156	−0.0275587
$891$	4.65298	0.155881
$892$	36.8175	1.23274
$893$	−8.32019	−0.278425
$894$	2.53849	0.0848998
$895$	−11.5369	−0.385635
$896$	−28.7805	−0.961488
$897$	−4.89432	−0.163417
$898$	−12.3615	−0.412510
$899$	−36.7180	−1.22461
$900$	8.57120	0.285707
$901$	63.6294	2.11980
$902$	0.00266428	8.87107e−5 0
$903$	−9.82325	−0.326897
$904$	−24.5216	−0.815575
$905$	−5.21952	−0.173503
$906$	−0.753428	−0.0250310
$907$	−5.87245	−0.194991	−0.0974957	−	0.995236i	$-0.531083\pi$
$907$	−5.87245	−0.194991	−0.0974957	+	0.995236i	$0.531083\pi$
$908$	14.0103	0.464948
$909$	−12.5559	−0.416452
$910$	−0.580359	−0.0192387
$911$	−23.7269	−0.786107	−0.393054	−	0.919516i	$-0.628581\pi$
$911$	−23.7269	−0.786107	−0.393054	+	0.919516i	$0.628581\pi$
$912$	1.83389	0.0607261
$913$	83.0844	2.74969
$914$	−13.5954	−0.449695
$915$	0.594199	0.0196436
$916$	−10.7836	−0.356302
$917$	−51.8331	−1.71168
$918$	3.64040	0.120151
$919$	7.99171	0.263622	0.131811	−	0.991275i	$-0.457921\pi$
$919$	7.99171	0.263622	0.131811	+	0.991275i	$0.457921\pi$
$920$	4.09537	0.135020
$921$	−18.0462	−0.594642
$922$	10.0304	0.330335
$923$	15.0614	0.495751
$924$	22.1236	0.727813
$925$	−30.7067	−1.00963
$926$	1.87675	0.0616739
$927$	−1.00000	−0.0328443
$928$	−32.4563	−1.06543
$929$	5.59958	0.183716	0.0918581	−	0.995772i	$-0.470719\pi$
$929$	5.59958	0.183716	0.0918581	+	0.995772i	$0.470719\pi$
$930$	−1.15657	−0.0379255
$931$	0.0280114	0.000918035 0
$932$	42.9415	1.40659
$933$	−10.4263	−0.341342
$934$	10.4583	0.342207
$935$	−18.8947	−0.617922
$936$	1.68896	0.0552053
$937$	5.52666	0.180548	0.0902741	−	0.995917i	$-0.471226\pi$
$937$	5.52666	0.180548	0.0902741	+	0.995917i	$0.471226\pi$
$938$	−2.84925	−0.0930314
$939$	−20.0747	−0.655114
$940$	−11.5700	−0.377371
$941$	−27.6491	−0.901334	−0.450667	−	0.892692i	$-0.648814\pi$
$941$	−27.6491	−0.901334	−0.450667	+	0.892692i	$0.648814\pi$
$942$	1.79908	0.0586173
$943$	−0.00630984	−0.000205477 0
$944$	−13.4911	−0.439097
$945$	−1.30669	−0.0425068
$946$	7.69692	0.250249
$947$	−12.2668	−0.398617	−0.199309	−	0.979937i	$-0.563870\pi$
$947$	−12.2668	−0.398617	−0.199309	+	0.979937i	$0.563870\pi$
$948$	23.4404	0.761309
$949$	15.7247	0.510447
$950$	1.35627	0.0440034
$951$	1.62622	0.0527337
$952$	36.5121	1.18336
$953$	20.0367	0.649052	0.324526	−	0.945877i	$-0.394795\pi$
$953$	20.0367	0.649052	0.324526	+	0.945877i	$0.394795\pi$
$954$	−3.44790	−0.111630
$955$	11.8971	0.384982
$956$	−8.94768	−0.289389
$957$	32.5044	1.05072
$958$	−1.97779	−0.0638994
$959$	−48.1692	−1.55547
$960$	1.80690	0.0583175
$961$	−3.37281	−0.108800
$962$	−2.86845	−0.0924824
$963$	9.01144	0.290390
$964$	7.51455	0.242027
$965$	−9.27110	−0.298447
$966$	5.73333	0.184467
$967$	−45.1954	−1.45339	−0.726693	−	0.686962i	$-0.758944\pi$
$967$	−45.1954	−1.45339	−0.726693	+	0.686962i	$0.758944\pi$
$968$	−17.9878	−0.578149
$969$	−5.26431	−0.169114
$970$	−0.484057	−0.0155421
$971$	−35.4073	−1.13627	−0.568137	−	0.822934i	$-0.692335\pi$
$971$	−35.4073	−1.13627	−0.568137	+	0.822934i	$0.692335\pi$
$972$	1.80274	0.0578228
$973$	−3.03521	−0.0973043
$974$	−15.6284	−0.500765
$975$	−4.75455	−0.152267
$976$	−3.42458	−0.109618
$977$	−2.70143	−0.0864264	−0.0432132	−	0.999066i	$-0.513759\pi$
$977$	−2.70143	−0.0864264	−0.0432132	+	0.999066i	$0.513759\pi$
$978$	8.41575	0.269106
$979$	−17.3852	−0.555635
$980$	0.0389523	0.00124429
$981$	−4.47672	−0.142931
$982$	18.2304	0.581754
$983$	6.39895	0.204095	0.102047	−	0.994780i	$-0.467461\pi$
$983$	6.39895	0.204095	0.102047	+	0.994780i	$0.467461\pi$
$984$	0.00217743	6.94140e−5 0
$985$	−0.253123	−0.00806517
$986$	25.4308	0.809881
$987$	−34.1672	−1.08755
$988$	−1.15784	−0.0368358
$989$	−18.2287	−0.579640
$990$	1.02385	0.0325400
$991$	29.3348	0.931849	0.465925	−	0.884824i	$-0.345722\pi$
$991$	29.3348	0.931849	0.465925	+	0.884824i	$0.345722\pi$
$992$	24.4206	0.775355
$993$	−21.1896	−0.672432
$994$	−17.6433	−0.559610
$995$	7.20789	0.228505
$996$	32.1900	1.01998
$997$	17.8810	0.566297	0.283148	−	0.959076i	$-0.408621\pi$
$997$	17.8810	0.566297	0.283148	+	0.959076i	$0.408621\pi$
$998$	−13.5792	−0.429843
$999$	−6.45839	−0.204334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+0.444143 q^{2} -1.00000 q^{3} -1.80274 q^{4} +0.495430 q^{5} -0.444143 q^{6} +2.63750 q^{7} -1.68896 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.444143 q^{2} -1.00000 q^{3} -1.80274 q^{4} +0.495430 q^{5} -0.444143 q^{6} +2.63750 q^{7} -1.68896 q^{8} +1.00000 q^{9} +0.220041 q^{10} +4.65298 q^{11} +1.80274 q^{12} -1.00000 q^{13} +1.17142 q^{14} -0.495430 q^{15} +2.85534 q^{16} -8.19646 q^{17} +0.444143 q^{18} -0.642267 q^{19} -0.893129 q^{20} -2.63750 q^{21} +2.06659 q^{22} -4.89432 q^{23} +1.68896 q^{24} -4.75455 q^{25} -0.444143 q^{26} -1.00000 q^{27} -4.75471 q^{28} -6.98572 q^{29} -0.220041 q^{30} +5.25616 q^{31} +4.64609 q^{32} -4.65298 q^{33} -3.64040 q^{34} +1.30669 q^{35} -1.80274 q^{36} +6.45839 q^{37} -0.285258 q^{38} +1.00000 q^{39} -0.836760 q^{40} +0.00128922 q^{41} -1.17142 q^{42} +3.72446 q^{43} -8.38810 q^{44} +0.495430 q^{45} -2.17378 q^{46} +12.9544 q^{47} -2.85534 q^{48} -0.0436133 q^{49} -2.11170 q^{50} +8.19646 q^{51} +1.80274 q^{52} -7.76304 q^{53} -0.444143 q^{54} +2.30522 q^{55} -4.45462 q^{56} +0.642267 q^{57} -3.10266 q^{58} -4.72487 q^{59} +0.893129 q^{60} -1.19936 q^{61} +2.33448 q^{62} +2.63750 q^{63} -3.64714 q^{64} -0.495430 q^{65} -2.06659 q^{66} -2.43230 q^{67} +14.7761 q^{68} +4.89432 q^{69} +0.580359 q^{70} -15.0614 q^{71} -1.68896 q^{72} -15.7247 q^{73} +2.86845 q^{74} +4.75455 q^{75} +1.15784 q^{76} +12.2722 q^{77} +0.444143 q^{78} +13.0027 q^{79} +1.41462 q^{80} +1.00000 q^{81} +0.000572596 q^{82} +17.8562 q^{83} +4.75471 q^{84} -4.06077 q^{85} +1.65419 q^{86} +6.98572 q^{87} -7.85869 q^{88} -3.73637 q^{89} +0.220041 q^{90} -2.63750 q^{91} +8.82318 q^{92} -5.25616 q^{93} +5.75361 q^{94} -0.318198 q^{95} -4.64609 q^{96} -2.19985 q^{97} -0.0193705 q^{98} +4.65298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more