LMFDB - Embedded newform 4017.2.a.i.1.16

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			1.16
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)

$f(q)$	$=$	$q+0.831544 q^{2} -1.00000 q^{3} -1.30853 q^{4} -3.33918 q^{5} -0.831544 q^{6} -4.05766 q^{7} -2.75119 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.831544 q^{2} -1.00000 q^{3} -1.30853 q^{4} -3.33918 q^{5} -0.831544 q^{6} -4.05766 q^{7} -2.75119 q^{8} +1.00000 q^{9} -2.77667 q^{10} +3.72947 q^{11} +1.30853 q^{12} -1.00000 q^{13} -3.37412 q^{14} +3.33918 q^{15} +0.329332 q^{16} +3.27954 q^{17} +0.831544 q^{18} +7.29823 q^{19} +4.36943 q^{20} +4.05766 q^{21} +3.10122 q^{22} +4.91836 q^{23} +2.75119 q^{24} +6.15012 q^{25} -0.831544 q^{26} -1.00000 q^{27} +5.30958 q^{28} -6.72214 q^{29} +2.77667 q^{30} -5.68560 q^{31} +5.77624 q^{32} -3.72947 q^{33} +2.72708 q^{34} +13.5492 q^{35} -1.30853 q^{36} -7.20903 q^{37} +6.06880 q^{38} +1.00000 q^{39} +9.18672 q^{40} -0.0208201 q^{41} +3.37412 q^{42} +4.99440 q^{43} -4.88014 q^{44} -3.33918 q^{45} +4.08983 q^{46} -1.22992 q^{47} -0.329332 q^{48} +9.46458 q^{49} +5.11410 q^{50} -3.27954 q^{51} +1.30853 q^{52} -13.3609 q^{53} -0.831544 q^{54} -12.4534 q^{55} +11.1634 q^{56} -7.29823 q^{57} -5.58975 q^{58} +14.2888 q^{59} -4.36943 q^{60} +11.0814 q^{61} -4.72783 q^{62} -4.05766 q^{63} +4.14453 q^{64} +3.33918 q^{65} -3.10122 q^{66} +8.89766 q^{67} -4.29139 q^{68} -4.91836 q^{69} +11.2668 q^{70} +13.4933 q^{71} -2.75119 q^{72} -16.0820 q^{73} -5.99463 q^{74} -6.15012 q^{75} -9.54999 q^{76} -15.1329 q^{77} +0.831544 q^{78} -6.20800 q^{79} -1.09970 q^{80} +1.00000 q^{81} -0.0173128 q^{82} -0.393688 q^{83} -5.30958 q^{84} -10.9510 q^{85} +4.15306 q^{86} +6.72214 q^{87} -10.2605 q^{88} +17.7614 q^{89} -2.77667 q^{90} +4.05766 q^{91} -6.43585 q^{92} +5.68560 q^{93} -1.02274 q^{94} -24.3701 q^{95} -5.77624 q^{96} -16.9225 q^{97} +7.87021 q^{98} +3.72947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.831544	0.587990	0.293995	−	0.955807i	$-0.405015\pi$
$2$	0.831544	0.587990	0.293995	+	0.955807i	$0.405015\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.30853	−0.654267
$5$	−3.33918	−1.49333	−0.746663	−	0.665202i	$-0.768345\pi$
$5$	−3.33918	−1.49333	−0.746663	+	0.665202i	$0.768345\pi$
$6$	−0.831544	−0.339476
$7$	−4.05766	−1.53365	−0.766825	−	0.641856i	$-0.778165\pi$
$7$	−4.05766	−1.53365	−0.766825	+	0.641856i	$0.778165\pi$
$8$	−2.75119	−0.972693
$9$	1.00000	0.333333
$10$	−2.77667	−0.878062
$11$	3.72947	1.12448	0.562239	−	0.826975i	$-0.309940\pi$
$11$	3.72947	1.12448	0.562239	+	0.826975i	$0.309940\pi$
$12$	1.30853	0.377741
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.37412	−0.901771
$15$	3.33918	0.862173
$16$	0.329332	0.0823331
$17$	3.27954	0.795405	0.397702	−	0.917514i	$-0.369808\pi$
$17$	3.27954	0.795405	0.397702	+	0.917514i	$0.369808\pi$
$18$	0.831544	0.195997
$19$	7.29823	1.67433	0.837164	−	0.546951i	$-0.184212\pi$
$19$	7.29823	1.67433	0.837164	+	0.546951i	$0.184212\pi$
$20$	4.36943	0.977035
$21$	4.05766	0.885453
$22$	3.10122	0.661182
$23$	4.91836	1.02555	0.512775	−	0.858523i	$-0.328618\pi$
$23$	4.91836	1.02555	0.512775	+	0.858523i	$0.328618\pi$
$24$	2.75119	0.561585
$25$	6.15012	1.23002
$26$	−0.831544	−0.163079
$27$	−1.00000	−0.192450
$28$	5.30958	1.00342
$29$	−6.72214	−1.24827	−0.624135	−	0.781317i	$-0.714548\pi$
$29$	−6.72214	−1.24827	−0.624135	+	0.781317i	$0.714548\pi$
$30$	2.77667	0.506949
$31$	−5.68560	−1.02116	−0.510582	−	0.859829i	$-0.670570\pi$
$31$	−5.68560	−1.02116	−0.510582	+	0.859829i	$0.670570\pi$
$32$	5.77624	1.02110
$33$	−3.72947	−0.649217
$34$	2.72708	0.467690
$35$	13.5492	2.29024
$36$	−1.30853	−0.218089
$37$	−7.20903	−1.18516	−0.592579	−	0.805513i	$-0.701890\pi$
$37$	−7.20903	−1.18516	−0.592579	+	0.805513i	$0.701890\pi$
$38$	6.06880	0.984489
$39$	1.00000	0.160128
$40$	9.18672	1.45255
$41$	−0.0208201	−0.00325155	−0.00162578	−	0.999999i	$-0.500518\pi$
$41$	−0.0208201	−0.00325155	−0.00162578	+	0.999999i	$0.500518\pi$
$42$	3.37412	0.520638
$43$	4.99440	0.761639	0.380820	−	0.924649i	$-0.375642\pi$
$43$	4.99440	0.761639	0.380820	+	0.924649i	$0.375642\pi$
$44$	−4.88014	−0.735709
$45$	−3.33918	−0.497776
$46$	4.08983	0.603013
$47$	−1.22992	−0.179403	−0.0897014	−	0.995969i	$-0.528591\pi$
$47$	−1.22992	−0.179403	−0.0897014	+	0.995969i	$0.528591\pi$
$48$	−0.329332	−0.0475350
$49$	9.46458	1.35208
$50$	5.11410	0.723242
$51$	−3.27954	−0.459227
$52$	1.30853	0.181461
$53$	−13.3609	−1.83527	−0.917633	−	0.397428i	$-0.869903\pi$
$53$	−13.3609	−1.83527	−0.917633	+	0.397428i	$0.869903\pi$
$54$	−0.831544	−0.113159
$55$	−12.4534	−1.67921
$56$	11.1634	1.49177
$57$	−7.29823	−0.966674
$58$	−5.58975	−0.733970
$59$	14.2888	1.86025	0.930123	−	0.367249i	$-0.119700\pi$
$59$	14.2888	1.86025	0.930123	+	0.367249i	$0.119700\pi$
$60$	−4.36943	−0.564091
$61$	11.0814	1.41882	0.709412	−	0.704794i	$-0.248960\pi$
$61$	11.0814	1.41882	0.709412	+	0.704794i	$0.248960\pi$
$62$	−4.72783	−0.600435
$63$	−4.05766	−0.511217
$64$	4.14453	0.518066
$65$	3.33918	0.414174
$66$	−3.10122	−0.381733
$67$	8.89766	1.08702	0.543511	−	0.839402i	$-0.317095\pi$
$67$	8.89766	1.08702	0.543511	+	0.839402i	$0.317095\pi$
$68$	−4.29139	−0.520407
$69$	−4.91836	−0.592101
$70$	11.2668	1.34664
$71$	13.4933	1.60136	0.800679	−	0.599094i	$-0.204472\pi$
$71$	13.4933	1.60136	0.800679	+	0.599094i	$0.204472\pi$
$72$	−2.75119	−0.324231
$73$	−16.0820	−1.88225	−0.941127	−	0.338052i	$-0.890232\pi$
$73$	−16.0820	−1.88225	−0.941127	+	0.338052i	$0.890232\pi$
$74$	−5.99463	−0.696861
$75$	−6.15012	−0.710155
$76$	−9.54999	−1.09546
$77$	−15.1329	−1.72455
$78$	0.831544	0.0941538
$79$	−6.20800	−0.698454	−0.349227	−	0.937038i	$-0.613556\pi$
$79$	−6.20800	−0.698454	−0.349227	+	0.937038i	$0.613556\pi$
$80$	−1.09970	−0.122950
$81$	1.00000	0.111111
$82$	−0.0173128	−0.00191188
$83$	−0.393688	−0.0432128	−0.0216064	−	0.999767i	$-0.506878\pi$
$83$	−0.393688	−0.0432128	−0.0216064	+	0.999767i	$0.506878\pi$
$84$	−5.30958	−0.579323
$85$	−10.9510	−1.18780
$86$	4.15306	0.447836
$87$	6.72214	0.720689
$88$	−10.2605	−1.09377
$89$	17.7614	1.88270	0.941351	−	0.337428i	$-0.109557\pi$
$89$	17.7614	1.88270	0.941351	+	0.337428i	$0.109557\pi$
$90$	−2.77667	−0.292687
$91$	4.05766	0.425358
$92$	−6.43585	−0.670984
$93$	5.68560	0.589569
$94$	−1.02274	−0.105487
$95$	−24.3701	−2.50032
$96$	−5.77624	−0.589535
$97$	−16.9225	−1.71822	−0.859112	−	0.511788i	$-0.828983\pi$
$97$	−16.9225	−1.71822	−0.859112	+	0.511788i	$0.828983\pi$
$98$	7.87021	0.795012
$99$	3.72947	0.374826
$100$	−8.04765	−0.804765
$101$	−9.24041	−0.919455	−0.459728	−	0.888060i	$-0.652053\pi$
$101$	−9.24041	−0.919455	−0.459728	+	0.888060i	$0.652053\pi$
$102$	−2.72708	−0.270021
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.75119	0.269777
$105$	−13.5492	−1.32227
$106$	−11.1102	−1.07912
$107$	−18.9180	−1.82887	−0.914437	−	0.404728i	$-0.867366\pi$
$107$	−18.9180	−1.82887	−0.914437	+	0.404728i	$0.867366\pi$
$108$	1.30853	0.125914
$109$	3.05422	0.292541	0.146271	−	0.989245i	$-0.453273\pi$
$109$	3.05422	0.292541	0.146271	+	0.989245i	$0.453273\pi$
$110$	−10.3555	−0.987360
$111$	7.20903	0.684251
$112$	−1.33632	−0.126270
$113$	9.13352	0.859209	0.429604	−	0.903017i	$-0.358653\pi$
$113$	9.13352	0.859209	0.429604	+	0.903017i	$0.358653\pi$
$114$	−6.06880	−0.568395
$115$	−16.4233	−1.53148
$116$	8.79615	0.816702
$117$	−1.00000	−0.0924500
$118$	11.8818	1.09381
$119$	−13.3072	−1.21987
$120$	−9.18672	−0.838629
$121$	2.90894	0.264449
$122$	9.21465	0.834255
$123$	0.0208201	0.00187728
$124$	7.43981	0.668114
$125$	−3.84046	−0.343501
$126$	−3.37412	−0.300590
$127$	7.41243	0.657746	0.328873	−	0.944374i	$-0.393331\pi$
$127$	7.41243	0.657746	0.328873	+	0.944374i	$0.393331\pi$
$128$	−8.10612	−0.716486
$129$	−4.99440	−0.439733
$130$	2.77667	0.243530
$131$	−15.1466	−1.32337	−0.661684	−	0.749783i	$-0.730158\pi$
$131$	−15.1466	−1.32337	−0.661684	+	0.749783i	$0.730158\pi$
$132$	4.88014	0.424762
$133$	−29.6137	−2.56783
$134$	7.39879	0.639158
$135$	3.33918	0.287391
$136$	−9.02264	−0.773685
$137$	−18.8420	−1.60978	−0.804891	−	0.593422i	$-0.797777\pi$
$137$	−18.8420	−1.60978	−0.804891	+	0.593422i	$0.797777\pi$
$138$	−4.08983	−0.348150
$139$	−4.59855	−0.390044	−0.195022	−	0.980799i	$-0.562478\pi$
$139$	−4.59855	−0.390044	−0.195022	+	0.980799i	$0.562478\pi$
$140$	−17.7297	−1.49843
$141$	1.22992	0.103578
$142$	11.2203	0.941583
$143$	−3.72947	−0.311874
$144$	0.329332	0.0274444
$145$	22.4464	1.86407
$146$	−13.3729	−1.10675
$147$	−9.46458	−0.780625
$148$	9.43327	0.775410
$149$	2.72397	0.223156	0.111578	−	0.993756i	$-0.464410\pi$
$149$	2.72397	0.223156	0.111578	+	0.993756i	$0.464410\pi$
$150$	−5.11410	−0.417564
$151$	3.87447	0.315300	0.157650	−	0.987495i	$-0.449608\pi$
$151$	3.87447	0.315300	0.157650	+	0.987495i	$0.449608\pi$
$152$	−20.0788	−1.62861
$153$	3.27954	0.265135
$154$	−12.5837	−1.01402
$155$	18.9852	1.52493
$156$	−1.30853	−0.104767
$157$	16.3949	1.30846	0.654230	−	0.756296i	$-0.272993\pi$
$157$	16.3949	1.30846	0.654230	+	0.756296i	$0.272993\pi$
$158$	−5.16222	−0.410684
$159$	13.3609	1.05959
$160$	−19.2879	−1.52484
$161$	−19.9570	−1.57283
$162$	0.831544	0.0653323
$163$	−7.50769	−0.588047	−0.294024	−	0.955798i	$-0.594994\pi$
$163$	−7.50769	−0.588047	−0.294024	+	0.955798i	$0.594994\pi$
$164$	0.0272438	0.00212738
$165$	12.4534	0.969493
$166$	−0.327369	−0.0254087
$167$	21.5416	1.66694	0.833471	−	0.552563i	$-0.186350\pi$
$167$	21.5416	1.66694	0.833471	+	0.552563i	$0.186350\pi$
$168$	−11.1634	−0.861274
$169$	1.00000	0.0769231
$170$	−9.10621	−0.698414
$171$	7.29823	0.558110
$172$	−6.53535	−0.498316
$173$	−7.86962	−0.598316	−0.299158	−	0.954204i	$-0.596706\pi$
$173$	−7.86962	−0.598316	−0.299158	+	0.954204i	$0.596706\pi$
$174$	5.58975	0.423758
$175$	−24.9551	−1.88643
$176$	1.22824	0.0925817
$177$	−14.2888	−1.07401
$178$	14.7694	1.10701
$179$	−0.960157	−0.0717655	−0.0358828	−	0.999356i	$-0.511424\pi$
$179$	−0.960157	−0.0717655	−0.0358828	+	0.999356i	$0.511424\pi$
$180$	4.36943	0.325678
$181$	−4.66825	−0.346989	−0.173494	−	0.984835i	$-0.555506\pi$
$181$	−4.66825	−0.346989	−0.173494	+	0.984835i	$0.555506\pi$
$182$	3.37412	0.250106
$183$	−11.0814	−0.819159
$184$	−13.5314	−0.997545
$185$	24.0722	1.76983
$186$	4.72783	0.346661
$187$	12.2309	0.894415
$188$	1.60940	0.117377
$189$	4.05766	0.295151
$190$	−20.2648	−1.47016
$191$	11.5661	0.836891	0.418446	−	0.908242i	$-0.362575\pi$
$191$	11.5661	0.836891	0.418446	+	0.908242i	$0.362575\pi$
$192$	−4.14453	−0.299106
$193$	2.94340	0.211870	0.105935	−	0.994373i	$-0.466216\pi$
$193$	2.94340	0.211870	0.105935	+	0.994373i	$0.466216\pi$
$194$	−14.0718	−1.01030
$195$	−3.33918	−0.239124
$196$	−12.3847	−0.884624
$197$	20.7155	1.47592	0.737959	−	0.674846i	$-0.235790\pi$
$197$	20.7155	1.47592	0.737959	+	0.674846i	$0.235790\pi$
$198$	3.10122	0.220394
$199$	−11.8248	−0.838235	−0.419117	−	0.907932i	$-0.637660\pi$
$199$	−11.8248	−0.838235	−0.419117	+	0.907932i	$0.637660\pi$
$200$	−16.9202	−1.19644
$201$	−8.89766	−0.627592
$202$	−7.68381	−0.540631
$203$	27.2761	1.91441
$204$	4.29139	0.300457
$205$	0.0695220	0.00485563
$206$	−0.831544	−0.0579364
$207$	4.91836	0.341850
$208$	−0.329332	−0.0228351
$209$	27.2185	1.88274
$210$	−11.2668	−0.777483
$211$	8.84021	0.608585	0.304292	−	0.952579i	$-0.401580\pi$
$211$	8.84021	0.608585	0.304292	+	0.952579i	$0.401580\pi$
$212$	17.4833	1.20075
$213$	−13.4933	−0.924544
$214$	−15.7312	−1.07536
$215$	−16.6772	−1.13738
$216$	2.75119	0.187195
$217$	23.0702	1.56611
$218$	2.53972	0.172011
$219$	16.0820	1.08672
$220$	16.2957	1.09865
$221$	−3.27954	−0.220606
$222$	5.99463	0.402333
$223$	−11.7970	−0.789988	−0.394994	−	0.918684i	$-0.629253\pi$
$223$	−11.7970	−0.789988	−0.394994	+	0.918684i	$0.629253\pi$
$224$	−23.4380	−1.56602
$225$	6.15012	0.410008
$226$	7.59492	0.505206
$227$	−11.5738	−0.768182	−0.384091	−	0.923295i	$-0.625485\pi$
$227$	−11.5738	−0.768182	−0.384091	+	0.923295i	$0.625485\pi$
$228$	9.54999	0.632463
$229$	14.0767	0.930217	0.465109	−	0.885254i	$-0.346015\pi$
$229$	14.0767	0.930217	0.465109	+	0.885254i	$0.346015\pi$
$230$	−13.6567	−0.900496
$231$	15.1329	0.995672
$232$	18.4939	1.21418
$233$	−9.43033	−0.617802	−0.308901	−	0.951094i	$-0.599961\pi$
$233$	−9.43033	−0.617802	−0.308901	+	0.951094i	$0.599961\pi$
$234$	−0.831544	−0.0543597
$235$	4.10694	0.267907
$236$	−18.6974	−1.21710
$237$	6.20800	0.403253
$238$	−11.0656	−0.717273
$239$	−22.4904	−1.45478	−0.727390	−	0.686224i	$-0.759267\pi$
$239$	−22.4904	−1.45478	−0.727390	+	0.686224i	$0.759267\pi$
$240$	1.09970	0.0709853
$241$	12.8197	0.825789	0.412895	−	0.910779i	$-0.364518\pi$
$241$	12.8197	0.825789	0.412895	+	0.910779i	$0.364518\pi$
$242$	2.41891	0.155493
$243$	−1.00000	−0.0641500
$244$	−14.5004	−0.928291
$245$	−31.6039	−2.01910
$246$	0.0173128	0.00110383
$247$	−7.29823	−0.464375
$248$	15.6422	0.993279
$249$	0.393688	0.0249489
$250$	−3.19351	−0.201976
$251$	−9.02602	−0.569717	−0.284859	−	0.958570i	$-0.591947\pi$
$251$	−9.02602	−0.569717	−0.284859	+	0.958570i	$0.591947\pi$
$252$	5.30958	0.334472
$253$	18.3429	1.15321
$254$	6.16376	0.386749
$255$	10.9510	0.685776
$256$	−15.0297	−0.939353
$257$	0.745783	0.0465207	0.0232603	−	0.999729i	$-0.492595\pi$
$257$	0.745783	0.0465207	0.0232603	+	0.999729i	$0.492595\pi$
$258$	−4.15306	−0.258558
$259$	29.2518	1.81762
$260$	−4.36943	−0.270981
$261$	−6.72214	−0.416090
$262$	−12.5951	−0.778127
$263$	−17.4784	−1.07776	−0.538882	−	0.842381i	$-0.681153\pi$
$263$	−17.4784	−1.07776	−0.538882	+	0.842381i	$0.681153\pi$
$264$	10.2605	0.631489
$265$	44.6146	2.74065
$266$	−24.6251	−1.50986
$267$	−17.7614	−1.08698
$268$	−11.6429	−0.711203
$269$	−10.4497	−0.637131	−0.318565	−	0.947901i	$-0.603201\pi$
$269$	−10.4497	−0.637131	−0.318565	+	0.947901i	$0.603201\pi$
$270$	2.77667	0.168983
$271$	24.7885	1.50579	0.752897	−	0.658138i	$-0.228656\pi$
$271$	24.7885	1.50579	0.752897	+	0.658138i	$0.228656\pi$
$272$	1.08006	0.0654882
$273$	−4.05766	−0.245581
$274$	−15.6680	−0.946537
$275$	22.9367	1.38313
$276$	6.43585	0.387393
$277$	4.11333	0.247146	0.123573	−	0.992335i	$-0.460565\pi$
$277$	4.11333	0.247146	0.123573	+	0.992335i	$0.460565\pi$
$278$	−3.82390	−0.229342
$279$	−5.68560	−0.340388
$280$	−37.2766	−2.22770
$281$	−23.0385	−1.37436	−0.687180	−	0.726487i	$-0.741152\pi$
$281$	−23.0385	−1.37436	−0.687180	+	0.726487i	$0.741152\pi$
$282$	1.02274	0.0609030
$283$	−22.4518	−1.33462	−0.667310	−	0.744780i	$-0.732554\pi$
$283$	−22.4518	−1.33462	−0.667310	+	0.744780i	$0.732554\pi$
$284$	−17.6564	−1.04772
$285$	24.3701	1.44356
$286$	−3.10122	−0.183379
$287$	0.0844808	0.00498674
$288$	5.77624	0.340368
$289$	−6.24463	−0.367331
$290$	18.6652	1.09606
$291$	16.9225	0.992017
$292$	21.0438	1.23150
$293$	3.91720	0.228845	0.114423	−	0.993432i	$-0.463498\pi$
$293$	3.91720	0.228845	0.114423	+	0.993432i	$0.463498\pi$
$294$	−7.87021	−0.459000
$295$	−47.7129	−2.77795
$296$	19.8334	1.15279
$297$	−3.72947	−0.216406
$298$	2.26510	0.131214
$299$	−4.91836	−0.284436
$300$	8.04765	0.464631
$301$	−20.2656	−1.16809
$302$	3.22179	0.185393
$303$	9.24041	0.530848
$304$	2.40354	0.137853
$305$	−37.0027	−2.11877
$306$	2.72708	0.155897
$307$	9.09899	0.519307	0.259653	−	0.965702i	$-0.416392\pi$
$307$	9.09899	0.519307	0.259653	+	0.965702i	$0.416392\pi$
$308$	19.8019	1.12832
$309$	1.00000	0.0568880
$310$	15.7871	0.896645
$311$	−19.5503	−1.10859	−0.554297	−	0.832319i	$-0.687013\pi$
$311$	−19.5503	−1.10859	−0.554297	+	0.832319i	$0.687013\pi$
$312$	−2.75119	−0.155756
$313$	16.5409	0.934949	0.467475	−	0.884006i	$-0.345164\pi$
$313$	16.5409	0.934949	0.467475	+	0.884006i	$0.345164\pi$
$314$	13.6331	0.769361
$315$	13.5492	0.763413
$316$	8.12338	0.456976
$317$	−22.9713	−1.29020	−0.645098	−	0.764100i	$-0.723183\pi$
$317$	−22.9713	−1.29020	−0.645098	+	0.764100i	$0.723183\pi$
$318$	11.1102	0.623030
$319$	−25.0700	−1.40365
$320$	−13.8393	−0.773642
$321$	18.9180	1.05590
$322$	−16.5951	−0.924811
$323$	23.9348	1.33177
$324$	−1.30853	−0.0726964
$325$	−6.15012	−0.341147
$326$	−6.24297	−0.345766
$327$	−3.05422	−0.168899
$328$	0.0572801	0.00316276
$329$	4.99061	0.275141
$330$	10.3555	0.570053
$331$	−10.5441	−0.579557	−0.289778	−	0.957094i	$-0.593582\pi$
$331$	−10.5441	−0.579557	−0.289778	+	0.957094i	$0.593582\pi$
$332$	0.515154	0.0282727
$333$	−7.20903	−0.395052
$334$	17.9128	0.980146
$335$	−29.7109	−1.62328
$336$	1.33632	0.0729021
$337$	13.4926	0.734986	0.367493	−	0.930026i	$-0.380216\pi$
$337$	13.4926	0.734986	0.367493	+	0.930026i	$0.380216\pi$
$338$	0.831544	0.0452300
$339$	−9.13352	−0.496064
$340$	14.3297	0.777138
$341$	−21.2043	−1.14828
$342$	6.06880	0.328163
$343$	−10.0004	−0.539972
$344$	−13.7406	−0.740841
$345$	16.4233	0.884201
$346$	−6.54394	−0.351804
$347$	20.9867	1.12662	0.563311	−	0.826245i	$-0.309527\pi$
$347$	20.9867	1.12662	0.563311	+	0.826245i	$0.309527\pi$
$348$	−8.79615	−0.471523
$349$	2.49591	0.133603	0.0668014	−	0.997766i	$-0.478721\pi$
$349$	2.49591	0.133603	0.0668014	+	0.997766i	$0.478721\pi$
$350$	−20.7512	−1.10920
$351$	1.00000	0.0533761
$352$	21.5423	1.14821
$353$	−21.0577	−1.12079	−0.560395	−	0.828226i	$-0.689351\pi$
$353$	−21.0577	−1.12079	−0.560395	+	0.828226i	$0.689351\pi$
$354$	−11.8818	−0.631509
$355$	−45.0565	−2.39135
$356$	−23.2414	−1.23179
$357$	13.3072	0.704294
$358$	−0.798413	−0.0421974
$359$	14.0445	0.741239	0.370620	−	0.928785i	$-0.379145\pi$
$359$	14.0445	0.741239	0.370620	+	0.928785i	$0.379145\pi$
$360$	9.18672	0.484183
$361$	34.2642	1.80338
$362$	−3.88186	−0.204026
$363$	−2.90894	−0.152680
$364$	−5.30958	−0.278298
$365$	53.7007	2.81082
$366$	−9.21465	−0.481658
$367$	12.2125	0.637485	0.318743	−	0.947841i	$-0.396739\pi$
$367$	12.2125	0.637485	0.318743	+	0.947841i	$0.396739\pi$
$368$	1.61978	0.0844367
$369$	−0.0208201	−0.00108385
$370$	20.0171	1.04064
$371$	54.2141	2.81466
$372$	−7.43981	−0.385736
$373$	−6.67236	−0.345481	−0.172741	−	0.984967i	$-0.555262\pi$
$373$	−6.67236	−0.345481	−0.172741	+	0.984967i	$0.555262\pi$
$374$	10.1706	0.525907
$375$	3.84046	0.198321
$376$	3.38376	0.174504
$377$	6.72214	0.346208
$378$	3.37412	0.173546
$379$	−7.19514	−0.369590	−0.184795	−	0.982777i	$-0.559162\pi$
$379$	−7.19514	−0.369590	−0.184795	+	0.982777i	$0.559162\pi$
$380$	31.8891	1.63588
$381$	−7.41243	−0.379750
$382$	9.61769	0.492084
$383$	13.8327	0.706820	0.353410	−	0.935469i	$-0.385022\pi$
$383$	13.8327	0.706820	0.353410	+	0.935469i	$0.385022\pi$
$384$	8.10612	0.413664
$385$	50.5315	2.57532
$386$	2.44756	0.124578
$387$	4.99440	0.253880
$388$	22.1437	1.12418
$389$	−9.89851	−0.501874	−0.250937	−	0.968003i	$-0.580739\pi$
$389$	−9.89851	−0.501874	−0.250937	+	0.968003i	$0.580739\pi$
$390$	−2.77667	−0.140602
$391$	16.1300	0.815727
$392$	−26.0389	−1.31516
$393$	15.1466	0.764047
$394$	17.2258	0.867826
$395$	20.7296	1.04302
$396$	−4.88014	−0.245236
$397$	−0.807826	−0.0405436	−0.0202718	−	0.999795i	$-0.506453\pi$
$397$	−0.807826	−0.0405436	−0.0202718	+	0.999795i	$0.506453\pi$
$398$	−9.83281	−0.492874
$399$	29.6137	1.48254
$400$	2.02543	0.101272
$401$	−25.4484	−1.27083	−0.635416	−	0.772170i	$-0.719171\pi$
$401$	−25.4484	−1.27083	−0.635416	+	0.772170i	$0.719171\pi$
$402$	−7.39879	−0.369018
$403$	5.68560	0.283220
$404$	12.0914	0.601570
$405$	−3.33918	−0.165925
$406$	22.6813	1.12565
$407$	−26.8859	−1.33268
$408$	9.02264	0.446687
$409$	27.1643	1.34319	0.671595	−	0.740918i	$-0.265609\pi$
$409$	27.1643	1.34319	0.671595	+	0.740918i	$0.265609\pi$
$410$	0.0578106	0.00285506
$411$	18.8420	0.929409
$412$	1.30853	0.0644669
$413$	−57.9791	−2.85297
$414$	4.08983	0.201004
$415$	1.31459	0.0645309
$416$	−5.77624	−0.283203
$417$	4.59855	0.225192
$418$	22.6334	1.10704
$419$	13.8363	0.675947	0.337973	−	0.941156i	$-0.390259\pi$
$419$	13.8363	0.675947	0.337973	+	0.941156i	$0.390259\pi$
$420$	17.7297	0.865119
$421$	−2.87249	−0.139996	−0.0699982	−	0.997547i	$-0.522299\pi$
$421$	−2.87249	−0.139996	−0.0699982	+	0.997547i	$0.522299\pi$
$422$	7.35102	0.357842
$423$	−1.22992	−0.0598009
$424$	36.7585	1.78515
$425$	20.1696	0.978367
$426$	−11.2203	−0.543623
$427$	−44.9644	−2.17598
$428$	24.7549	1.19657
$429$	3.72947	0.180060
$430$	−13.8678	−0.668766
$431$	−0.421533	−0.0203045	−0.0101523	−	0.999948i	$-0.503232\pi$
$431$	−0.421533	−0.0203045	−0.0101523	+	0.999948i	$0.503232\pi$
$432$	−0.329332	−0.0158450
$433$	14.6318	0.703162	0.351581	−	0.936158i	$-0.385644\pi$
$433$	14.6318	0.703162	0.351581	+	0.936158i	$0.385644\pi$
$434$	19.1839	0.920857
$435$	−22.4464	−1.07622
$436$	−3.99655	−0.191400
$437$	35.8953	1.71711
$438$	13.3729	0.638981
$439$	−36.4912	−1.74163	−0.870814	−	0.491613i	$-0.836408\pi$
$439$	−36.4912	−1.74163	−0.870814	+	0.491613i	$0.836408\pi$
$440$	34.2616	1.63336
$441$	9.46458	0.450694
$442$	−2.72708	−0.129714
$443$	−1.14912	−0.0545961	−0.0272981	−	0.999627i	$-0.508690\pi$
$443$	−1.14912	−0.0545961	−0.0272981	+	0.999627i	$0.508690\pi$
$444$	−9.43327	−0.447683
$445$	−59.3084	−2.81149
$446$	−9.80976	−0.464506
$447$	−2.72397	−0.128839
$448$	−16.8171	−0.794533
$449$	4.96218	0.234180	0.117090	−	0.993121i	$-0.462643\pi$
$449$	4.96218	0.234180	0.117090	+	0.993121i	$0.462643\pi$
$450$	5.11410	0.241081
$451$	−0.0776479	−0.00365630
$452$	−11.9515	−0.562152
$453$	−3.87447	−0.182038
$454$	−9.62415	−0.451684
$455$	−13.5492	−0.635198
$456$	20.0788	0.940277
$457$	21.5209	1.00670	0.503352	−	0.864082i	$-0.332100\pi$
$457$	21.5209	1.00670	0.503352	+	0.864082i	$0.332100\pi$
$458$	11.7054	0.546959
$459$	−3.27954	−0.153076
$460$	21.4905	1.00200
$461$	−13.8627	−0.645649	−0.322825	−	0.946459i	$-0.604632\pi$
$461$	−13.8627	−0.645649	−0.322825	+	0.946459i	$0.604632\pi$
$462$	12.5837	0.585446
$463$	−32.3816	−1.50490	−0.752450	−	0.658649i	$-0.771128\pi$
$463$	−32.3816	−1.50490	−0.752450	+	0.658649i	$0.771128\pi$
$464$	−2.21382	−0.102774
$465$	−18.9852	−0.880419
$466$	−7.84173	−0.363261
$467$	−15.7548	−0.729045	−0.364523	−	0.931195i	$-0.618768\pi$
$467$	−15.7548	−0.729045	−0.364523	+	0.931195i	$0.618768\pi$
$468$	1.30853	0.0604870
$469$	−36.1036	−1.66711
$470$	3.41510	0.157527
$471$	−16.3949	−0.755439
$472$	−39.3113	−1.80945
$473$	18.6265	0.856446
$474$	5.16222	0.237109
$475$	44.8850	2.05947
$476$	17.4130	0.798123
$477$	−13.3609	−0.611755
$478$	−18.7017	−0.855397
$479$	−9.54263	−0.436014	−0.218007	−	0.975947i	$-0.569956\pi$
$479$	−9.54263	−0.436014	−0.218007	+	0.975947i	$0.569956\pi$
$480$	19.2879	0.880368
$481$	7.20903	0.328703
$482$	10.6601	0.485556
$483$	19.9570	0.908076
$484$	−3.80645	−0.173020
$485$	56.5074	2.56587
$486$	−0.831544	−0.0377196
$487$	−7.69046	−0.348488	−0.174244	−	0.984703i	$-0.555748\pi$
$487$	−7.69046	−0.348488	−0.174244	+	0.984703i	$0.555748\pi$
$488$	−30.4870	−1.38008
$489$	7.50769	0.339509
$490$	−26.2801	−1.18721
$491$	−32.3012	−1.45773	−0.728866	−	0.684656i	$-0.759952\pi$
$491$	−32.3012	−1.45773	−0.728866	+	0.684656i	$0.759952\pi$
$492$	−0.0272438	−0.00122825
$493$	−22.0455	−0.992880
$494$	−6.06880	−0.273048
$495$	−12.4534	−0.559737
$496$	−1.87245	−0.0840756
$497$	−54.7511	−2.45592
$498$	0.327369	0.0146697
$499$	−28.7784	−1.28830	−0.644149	−	0.764900i	$-0.722788\pi$
$499$	−28.7784	−1.28830	−0.644149	+	0.764900i	$0.722788\pi$
$500$	5.02538	0.224742
$501$	−21.5416	−0.962410
$502$	−7.50553	−0.334988
$503$	−13.5398	−0.603711	−0.301856	−	0.953354i	$-0.597606\pi$
$503$	−13.5398	−0.603711	−0.301856	+	0.953354i	$0.597606\pi$
$504$	11.1634	0.497257
$505$	30.8554	1.37305
$506$	15.2529	0.678075
$507$	−1.00000	−0.0444116
$508$	−9.69942	−0.430342
$509$	−16.4823	−0.730566	−0.365283	−	0.930896i	$-0.619028\pi$
$509$	−16.4823	−0.730566	−0.365283	+	0.930896i	$0.619028\pi$
$510$	9.10621	0.403230
$511$	65.2552	2.88672
$512$	3.71442	0.164156
$513$	−7.29823	−0.322225
$514$	0.620151	0.0273537
$515$	3.33918	0.147142
$516$	6.53535	0.287703
$517$	−4.58696	−0.201734
$518$	24.3241	1.06874
$519$	7.86962	0.345438
$520$	−9.18672	−0.402865
$521$	−24.8477	−1.08860	−0.544299	−	0.838891i	$-0.683204\pi$
$521$	−24.8477	−1.08860	−0.544299	+	0.838891i	$0.683204\pi$
$522$	−5.58975	−0.244657
$523$	−21.2913	−0.931002	−0.465501	−	0.885047i	$-0.654126\pi$
$523$	−21.2913	−0.931002	−0.465501	+	0.885047i	$0.654126\pi$
$524$	19.8199	0.865836
$525$	24.9551	1.08913
$526$	−14.5341	−0.633715
$527$	−18.6461	−0.812239
$528$	−1.22824	−0.0534521
$529$	1.19029	0.0517516
$530$	37.0990	1.61148
$531$	14.2888	0.620082
$532$	38.7506	1.68005
$533$	0.0208201	0.000901818 0
$534$	−14.7694	−0.639133
$535$	63.1707	2.73111
$536$	−24.4792	−1.05734
$537$	0.960157	0.0414338
$538$	−8.68940	−0.374627
$539$	35.2978	1.52039
$540$	−4.36943	−0.188030
$541$	−3.06153	−0.131626	−0.0658128	−	0.997832i	$-0.520964\pi$
$541$	−3.06153	−0.131626	−0.0658128	+	0.997832i	$0.520964\pi$
$542$	20.6127	0.885392
$543$	4.66825	0.200334
$544$	18.9434	0.812191
$545$	−10.1986	−0.436860
$546$	−3.37412	−0.144399
$547$	35.1592	1.50330	0.751650	−	0.659562i	$-0.229258\pi$
$547$	35.1592	1.50330	0.751650	+	0.659562i	$0.229258\pi$
$548$	24.6554	1.05323
$549$	11.0814	0.472942
$550$	19.0729	0.813270
$551$	−49.0597	−2.09001
$552$	13.5314	0.575933
$553$	25.1899	1.07118
$554$	3.42042	0.145320
$555$	−24.0722	−1.02181
$556$	6.01737	0.255193
$557$	30.0066	1.27142	0.635710	−	0.771928i	$-0.280708\pi$
$557$	30.0066	1.27142	0.635710	+	0.771928i	$0.280708\pi$
$558$	−4.72783	−0.200145
$559$	−4.99440	−0.211241
$560$	4.46221	0.188563
$561$	−12.2309	−0.516391
$562$	−19.1575	−0.808111
$563$	−15.5192	−0.654055	−0.327027	−	0.945015i	$-0.606047\pi$
$563$	−15.5192	−0.654055	−0.327027	+	0.945015i	$0.606047\pi$
$564$	−1.60940	−0.0677679
$565$	−30.4984	−1.28308
$566$	−18.6696	−0.784744
$567$	−4.05766	−0.170406
$568$	−37.1226	−1.55763
$569$	−15.6235	−0.654969	−0.327485	−	0.944857i	$-0.606201\pi$
$569$	−15.6235	−0.654969	−0.327485	+	0.944857i	$0.606201\pi$
$570$	20.2648	0.848800
$571$	−37.5698	−1.57225	−0.786123	−	0.618071i	$-0.787915\pi$
$571$	−37.5698	−1.57225	−0.786123	+	0.618071i	$0.787915\pi$
$572$	4.88014	0.204049
$573$	−11.5661	−0.483179
$574$	0.0702495	0.00293216
$575$	30.2485	1.26145
$576$	4.14453	0.172689
$577$	−13.0864	−0.544792	−0.272396	−	0.962185i	$-0.587816\pi$
$577$	−13.0864	−0.544792	−0.272396	+	0.962185i	$0.587816\pi$
$578$	−5.19268	−0.215987
$579$	−2.94340	−0.122323
$580$	−29.3719	−1.21960
$581$	1.59745	0.0662734
$582$	14.0718	0.583297
$583$	−49.8292	−2.06372
$584$	44.2446	1.83086
$585$	3.33918	0.138058
$586$	3.25733	0.134559
$587$	23.2460	0.959464	0.479732	−	0.877415i	$-0.340734\pi$
$587$	23.2460	0.959464	0.479732	+	0.877415i	$0.340734\pi$
$588$	12.3847	0.510738
$589$	−41.4948	−1.70976
$590$	−39.6754	−1.63341
$591$	−20.7155	−0.852122
$592$	−2.37417	−0.0975777
$593$	21.8024	0.895317	0.447658	−	0.894205i	$-0.352258\pi$
$593$	21.8024	0.895317	0.447658	+	0.894205i	$0.352258\pi$
$594$	−3.10122	−0.127244
$595$	44.4353	1.82167
$596$	−3.56440	−0.146004
$597$	11.8248	0.483955
$598$	−4.08983	−0.167246
$599$	6.09410	0.248998	0.124499	−	0.992220i	$-0.460268\pi$
$599$	6.09410	0.248998	0.124499	+	0.992220i	$0.460268\pi$
$600$	16.9202	0.690763
$601$	24.4103	0.995715	0.497858	−	0.867259i	$-0.334120\pi$
$601$	24.4103	0.995715	0.497858	+	0.867259i	$0.334120\pi$
$602$	−16.8517	−0.686824
$603$	8.89766	0.362341
$604$	−5.06988	−0.206290
$605$	−9.71347	−0.394909
$606$	7.68381	0.312133
$607$	−38.9214	−1.57977	−0.789886	−	0.613254i	$-0.789860\pi$
$607$	−38.9214	−1.57977	−0.789886	+	0.613254i	$0.789860\pi$
$608$	42.1563	1.70966
$609$	−27.2761	−1.10528
$610$	−30.7694	−1.24582
$611$	1.22992	0.0497574
$612$	−4.29139	−0.173469
$613$	10.8812	0.439489	0.219744	−	0.975557i	$-0.429478\pi$
$613$	10.8812	0.439489	0.219744	+	0.975557i	$0.429478\pi$
$614$	7.56621	0.305347
$615$	−0.0695220	−0.00280340
$616$	41.6335	1.67746
$617$	−27.2693	−1.09782	−0.548910	−	0.835881i	$-0.684957\pi$
$617$	−27.2693	−1.09782	−0.548910	+	0.835881i	$0.684957\pi$
$618$	0.831544	0.0334496
$619$	25.6794	1.03214	0.516071	−	0.856546i	$-0.327394\pi$
$619$	25.6794	1.03214	0.516071	+	0.856546i	$0.327394\pi$
$620$	−24.8428	−0.997713
$621$	−4.91836	−0.197367
$622$	−16.2569	−0.651843
$623$	−72.0696	−2.88741
$624$	0.329332	0.0131838
$625$	−17.9266	−0.717064
$626$	13.7545	0.549741
$627$	−27.2185	−1.08700
$628$	−21.4534	−0.856082
$629$	−23.6423	−0.942680
$630$	11.2668	0.448880
$631$	−7.44195	−0.296259	−0.148130	−	0.988968i	$-0.547325\pi$
$631$	−7.44195	−0.296259	−0.148130	+	0.988968i	$0.547325\pi$
$632$	17.0794	0.679382
$633$	−8.84021	−0.351367
$634$	−19.1016	−0.758623
$635$	−24.7514	−0.982230
$636$	−17.4833	−0.693256
$637$	−9.46458	−0.375000
$638$	−20.8468	−0.825333
$639$	13.4933	0.533786
$640$	27.0678	1.06995
$641$	−14.5251	−0.573706	−0.286853	−	0.957975i	$-0.592609\pi$
$641$	−14.5251	−0.573706	−0.286853	+	0.957975i	$0.592609\pi$
$642$	15.7312	0.620860
$643$	−15.9229	−0.627937	−0.313969	−	0.949433i	$-0.601659\pi$
$643$	−15.9229	−0.627937	−0.313969	+	0.949433i	$0.601659\pi$
$644$	26.1145	1.02905
$645$	16.6772	0.656664
$646$	19.9029	0.783068
$647$	10.6492	0.418661	0.209331	−	0.977845i	$-0.432871\pi$
$647$	10.6492	0.418661	0.209331	+	0.977845i	$0.432871\pi$
$648$	−2.75119	−0.108077
$649$	53.2897	2.09180
$650$	−5.11410	−0.200591
$651$	−23.0702	−0.904193
$652$	9.82407	0.384740
$653$	12.0571	0.471829	0.235915	−	0.971774i	$-0.424191\pi$
$653$	12.0571	0.471829	0.235915	+	0.971774i	$0.424191\pi$
$654$	−2.53972	−0.0993109
$655$	50.5773	1.97622
$656$	−0.00685673	−0.000267710 0
$657$	−16.0820	−0.627418
$658$	4.14991	0.161780
$659$	−23.0496	−0.897885	−0.448943	−	0.893561i	$-0.648199\pi$
$659$	−23.0496	−0.897885	−0.448943	+	0.893561i	$0.648199\pi$
$660$	−16.2957	−0.634308
$661$	26.3280	1.02404	0.512021	−	0.858973i	$-0.328897\pi$
$661$	26.3280	1.02404	0.512021	+	0.858973i	$0.328897\pi$
$662$	−8.76789	−0.340774
$663$	3.27954	0.127367
$664$	1.08311	0.0420328
$665$	98.8855	3.83462
$666$	−5.99463	−0.232287
$667$	−33.0619	−1.28016
$668$	−28.1880	−1.09063
$669$	11.7970	0.456100
$670$	−24.7059	−0.954472
$671$	41.3276	1.59544
$672$	23.4380	0.904140
$673$	−48.4862	−1.86900	−0.934502	−	0.355958i	$-0.884155\pi$
$673$	−48.4862	−1.86900	−0.934502	+	0.355958i	$0.884155\pi$
$674$	11.2197	0.432165
$675$	−6.15012	−0.236718
$676$	−1.30853	−0.0503283
$677$	−37.2064	−1.42996	−0.714979	−	0.699145i	$-0.753564\pi$
$677$	−37.2064	−1.42996	−0.714979	+	0.699145i	$0.753564\pi$
$678$	−7.59492	−0.291681
$679$	68.6659	2.63515
$680$	30.1282	1.15536
$681$	11.5738	0.443510
$682$	−17.6323	−0.675175
$683$	18.3138	0.700759	0.350380	−	0.936608i	$-0.386053\pi$
$683$	18.3138	0.700759	0.350380	+	0.936608i	$0.386053\pi$
$684$	−9.54999	−0.365153
$685$	62.9169	2.40393
$686$	−8.31578	−0.317498
$687$	−14.0767	−0.537061
$688$	1.64482	0.0627081
$689$	13.3609	0.509011
$690$	13.6567	0.519901
$691$	43.0546	1.63788	0.818938	−	0.573882i	$-0.194563\pi$
$691$	43.0546	1.63788	0.818938	+	0.573882i	$0.194563\pi$
$692$	10.2977	0.391459
$693$	−15.1329	−0.574852
$694$	17.4513	0.662443
$695$	15.3554	0.582463
$696$	−18.4939	−0.701009
$697$	−0.0682803	−0.00258630
$698$	2.07546	0.0785571
$699$	9.43033	0.356688
$700$	32.6546	1.23423
$701$	−47.3562	−1.78862	−0.894309	−	0.447451i	$-0.852332\pi$
$701$	−47.3562	−1.78862	−0.894309	+	0.447451i	$0.852332\pi$
$702$	0.831544	0.0313846
$703$	−52.6132	−1.98434
$704$	15.4569	0.582554
$705$	−4.10694	−0.154676
$706$	−17.5104	−0.659013
$707$	37.4944	1.41012
$708$	18.6974	0.702692
$709$	−7.84460	−0.294610	−0.147305	−	0.989091i	$-0.547060\pi$
$709$	−7.84460	−0.294610	−0.147305	+	0.989091i	$0.547060\pi$
$710$	−37.4665	−1.40609
$711$	−6.20800	−0.232818
$712$	−48.8650	−1.83129
$713$	−27.9638	−1.04725
$714$	11.0656	0.414118
$715$	12.4534	0.465730
$716$	1.25640	0.0469538
$717$	22.4904	0.839918
$718$	11.6786	0.435842
$719$	−0.393375	−0.0146704	−0.00733520	−	0.999973i	$-0.502335\pi$
$719$	−0.393375	−0.0146704	−0.00733520	+	0.999973i	$0.502335\pi$
$720$	−1.09970	−0.0409834
$721$	4.05766	0.151115
$722$	28.4922	1.06037
$723$	−12.8197	−0.476770
$724$	6.10857	0.227023
$725$	−41.3420	−1.53540
$726$	−2.41891	−0.0897742
$727$	−20.0399	−0.743239	−0.371620	−	0.928385i	$-0.621197\pi$
$727$	−20.0399	−0.743239	−0.371620	+	0.928385i	$0.621197\pi$
$728$	−11.1634	−0.413743
$729$	1.00000	0.0370370
$730$	44.6545	1.65274
$731$	16.3793	0.605811
$732$	14.5004	0.535949
$733$	−0.810164	−0.0299241	−0.0149620	−	0.999888i	$-0.504763\pi$
$733$	−0.810164	−0.0299241	−0.0149620	+	0.999888i	$0.504763\pi$
$734$	10.1552	0.374835
$735$	31.6039	1.16573
$736$	28.4096	1.04719
$737$	33.1835	1.22233
$738$	−0.0173128	−0.000637294 0
$739$	−0.849190	−0.0312380	−0.0156190	−	0.999878i	$-0.504972\pi$
$739$	−0.849190	−0.0312380	−0.0156190	+	0.999878i	$0.504972\pi$
$740$	−31.4994	−1.15794
$741$	7.29823	0.268107
$742$	45.0814	1.65499
$743$	6.25193	0.229361	0.114681	−	0.993402i	$-0.463416\pi$
$743$	6.25193	0.229361	0.114681	+	0.993402i	$0.463416\pi$
$744$	−15.6422	−0.573470
$745$	−9.09581	−0.333245
$746$	−5.54836	−0.203140
$747$	−0.393688	−0.0144043
$748$	−16.0046	−0.585186
$749$	76.7629	2.80485
$750$	3.19351	0.116611
$751$	23.8772	0.871293	0.435646	−	0.900118i	$-0.356520\pi$
$751$	23.8772	0.871293	0.435646	+	0.900118i	$0.356520\pi$
$752$	−0.405054	−0.0147708
$753$	9.02602	0.328927
$754$	5.58975	0.203567
$755$	−12.9375	−0.470846
$756$	−5.30958	−0.193108
$757$	−18.6373	−0.677383	−0.338692	−	0.940897i	$-0.609984\pi$
$757$	−18.6373	−0.677383	−0.338692	+	0.940897i	$0.609984\pi$
$758$	−5.98308	−0.217315
$759$	−18.3429	−0.665804
$760$	67.0468	2.43204
$761$	34.1723	1.23875	0.619373	−	0.785097i	$-0.287387\pi$
$761$	34.1723	1.23875	0.619373	+	0.785097i	$0.287387\pi$
$762$	−6.16376	−0.223289
$763$	−12.3930	−0.448656
$764$	−15.1346	−0.547550
$765$	−10.9510	−0.395933
$766$	11.5025	0.415603
$767$	−14.2888	−0.515939
$768$	15.0297	0.542336
$769$	1.70318	0.0614183	0.0307091	−	0.999528i	$-0.490223\pi$
$769$	1.70318	0.0614183	0.0307091	+	0.999528i	$0.490223\pi$
$770$	42.0192	1.51427
$771$	−0.745783	−0.0268587
$772$	−3.85154	−0.138620
$773$	−41.6348	−1.49750	−0.748750	−	0.662853i	$-0.769346\pi$
$773$	−41.6348	−1.49750	−0.748750	+	0.662853i	$0.769346\pi$
$774$	4.15306	0.149279
$775$	−34.9671	−1.25606
$776$	46.5572	1.67130
$777$	−29.2518	−1.04940
$778$	−8.23105	−0.295097
$779$	−0.151950	−0.00544417
$780$	4.36943	0.156451
$781$	50.3228	1.80069
$782$	13.4128	0.479640
$783$	6.72214	0.240230
$784$	3.11699	0.111321
$785$	−54.7457	−1.95396
$786$	12.5951	0.449252
$787$	31.1797	1.11144	0.555718	−	0.831371i	$-0.312443\pi$
$787$	31.1797	1.11144	0.555718	+	0.831371i	$0.312443\pi$
$788$	−27.1069	−0.965645
$789$	17.4784	0.622248
$790$	17.2376	0.613286
$791$	−37.0607	−1.31773
$792$	−10.2605	−0.364590
$793$	−11.0814	−0.393511
$794$	−0.671743	−0.0238393
$795$	−44.6146	−1.58232
$796$	15.4731	0.548430
$797$	−19.0001	−0.673019	−0.336510	−	0.941680i	$-0.609246\pi$
$797$	−19.0001	−0.673019	−0.336510	+	0.941680i	$0.609246\pi$
$798$	24.6251	0.871719
$799$	−4.03358	−0.142698
$800$	35.5246	1.25598
$801$	17.7614	0.627567
$802$	−21.1615	−0.747237
$803$	−59.9773	−2.11655
$804$	11.6429	0.410613
$805$	66.6401	2.34875
$806$	4.72783	0.166531
$807$	10.4497	0.367848
$808$	25.4222	0.894348
$809$	−46.5206	−1.63558	−0.817789	−	0.575518i	$-0.804800\pi$
$809$	−46.5206	−1.63558	−0.817789	+	0.575518i	$0.804800\pi$
$810$	−2.77667	−0.0975624
$811$	10.1436	0.356190	0.178095	−	0.984013i	$-0.443007\pi$
$811$	10.1436	0.356190	0.178095	+	0.984013i	$0.443007\pi$
$812$	−35.6918	−1.25254
$813$	−24.7885	−0.869371
$814$	−22.3568	−0.783604
$815$	25.0695	0.878147
$816$	−1.08006	−0.0378096
$817$	36.4503	1.27523
$818$	22.5883	0.789783
$819$	4.05766	0.141786
$820$	−0.0909720	−0.00317688
$821$	−19.4556	−0.679005	−0.339503	−	0.940605i	$-0.610259\pi$
$821$	−19.4556	−0.679005	−0.339503	+	0.940605i	$0.610259\pi$
$822$	15.6680	0.546483
$823$	−49.3830	−1.72138	−0.860691	−	0.509127i	$-0.829968\pi$
$823$	−49.3830	−1.72138	−0.860691	+	0.509127i	$0.829968\pi$
$824$	2.75119	0.0958423
$825$	−22.9367	−0.798553
$826$	−48.2122	−1.67752
$827$	6.31452	0.219577	0.109789	−	0.993955i	$-0.464983\pi$
$827$	6.31452	0.219577	0.109789	+	0.993955i	$0.464983\pi$
$828$	−6.43585	−0.223661
$829$	48.5878	1.68752	0.843761	−	0.536719i	$-0.180336\pi$
$829$	48.5878	1.68752	0.843761	+	0.536719i	$0.180336\pi$
$830$	1.09314	0.0379435
$831$	−4.11333	−0.142690
$832$	−4.14453	−0.143686
$833$	31.0394	1.07545
$834$	3.82390	0.132411
$835$	−71.9314	−2.48929
$836$	−35.6164	−1.23182
$837$	5.68560	0.196523
$838$	11.5055	0.397450
$839$	−28.0606	−0.968761	−0.484381	−	0.874857i	$-0.660955\pi$
$839$	−28.0606	−0.968761	−0.484381	+	0.874857i	$0.660955\pi$
$840$	37.2766	1.28616
$841$	16.1871	0.558177
$842$	−2.38860	−0.0823165
$843$	23.0385	0.793487
$844$	−11.5677	−0.398177
$845$	−3.33918	−0.114871
$846$	−1.02274	−0.0351624
$847$	−11.8035	−0.405572
$848$	−4.40019	−0.151103
$849$	22.4518	0.770543
$850$	16.7719	0.575271
$851$	−35.4566	−1.21544
$852$	17.6564	0.604899
$853$	31.2143	1.06876	0.534378	−	0.845246i	$-0.320546\pi$
$853$	31.2143	1.06876	0.534378	+	0.845246i	$0.320546\pi$
$854$	−37.3899	−1.27946
$855$	−24.3701	−0.833440
$856$	52.0471	1.77893
$857$	21.3782	0.730266	0.365133	−	0.930955i	$-0.381024\pi$
$857$	21.3782	0.730266	0.365133	+	0.930955i	$0.381024\pi$
$858$	3.10122	0.105874
$859$	18.6152	0.635142	0.317571	−	0.948234i	$-0.397133\pi$
$859$	18.6152	0.635142	0.317571	+	0.948234i	$0.397133\pi$
$860$	21.8227	0.744148
$861$	−0.0844808	−0.00287910
$862$	−0.350523	−0.0119389
$863$	−21.5415	−0.733281	−0.366640	−	0.930363i	$-0.619492\pi$
$863$	−21.5415	−0.733281	−0.366640	+	0.930363i	$0.619492\pi$
$864$	−5.77624	−0.196512
$865$	26.2781	0.893482
$866$	12.1670	0.413452
$867$	6.24463	0.212079
$868$	−30.1882	−1.02465
$869$	−23.1525	−0.785396
$870$	−18.6652	−0.632809
$871$	−8.89766	−0.301486
$872$	−8.40275	−0.284553
$873$	−16.9225	−0.572741
$874$	29.8486	1.00964
$875$	15.5833	0.526811
$876$	−21.0438	−0.711006
$877$	−14.7285	−0.497346	−0.248673	−	0.968588i	$-0.579994\pi$
$877$	−14.7285	−0.497346	−0.248673	+	0.968588i	$0.579994\pi$
$878$	−30.3440	−1.02406
$879$	−3.91720	−0.132124
$880$	−4.10130	−0.138255
$881$	−6.90928	−0.232779	−0.116390	−	0.993204i	$-0.537132\pi$
$881$	−6.90928	−0.232779	−0.116390	+	0.993204i	$0.537132\pi$
$882$	7.87021	0.265004
$883$	9.12412	0.307051	0.153526	−	0.988145i	$-0.450937\pi$
$883$	9.12412	0.307051	0.153526	+	0.988145i	$0.450937\pi$
$884$	4.29139	0.144335
$885$	47.7129	1.60385
$886$	−0.955540	−0.0321020
$887$	39.3266	1.32046	0.660229	−	0.751064i	$-0.270459\pi$
$887$	39.3266	1.32046	0.660229	+	0.751064i	$0.270459\pi$
$888$	−19.8334	−0.665566
$889$	−30.0771	−1.00875
$890$	−49.3176	−1.65313
$891$	3.72947	0.124942
$892$	15.4368	0.516864
$893$	−8.97627	−0.300379
$894$	−2.26510	−0.0757562
$895$	3.20614	0.107169
$896$	32.8918	1.09884
$897$	4.91836	0.164219
$898$	4.12627	0.137695
$899$	38.2194	1.27469
$900$	−8.04765	−0.268255
$901$	−43.8177	−1.45978
$902$	−0.0645676	−0.00214987
$903$	20.2656	0.674396
$904$	−25.1281	−0.835747
$905$	15.5881	0.518167
$906$	−3.22179	−0.107037
$907$	31.9291	1.06019	0.530094	−	0.847939i	$-0.322157\pi$
$907$	31.9291	1.06019	0.530094	+	0.847939i	$0.322157\pi$
$908$	15.1448	0.502596
$909$	−9.24041	−0.306485
$910$	−11.2668	−0.373491
$911$	−51.8111	−1.71658	−0.858289	−	0.513166i	$-0.828473\pi$
$911$	−51.8111	−1.71658	−0.858289	+	0.513166i	$0.828473\pi$
$912$	−2.40354	−0.0795893
$913$	−1.46825	−0.0485919
$914$	17.8955	0.591932
$915$	37.0027	1.22327
$916$	−18.4199	−0.608611
$917$	61.4598	2.02958
$918$	−2.72708	−0.0900071
$919$	28.9165	0.953868	0.476934	−	0.878939i	$-0.341748\pi$
$919$	28.9165	0.953868	0.476934	+	0.878939i	$0.341748\pi$
$920$	45.1836	1.48966
$921$	−9.09899	−0.299822
$922$	−11.5274	−0.379636
$923$	−13.4933	−0.444137
$924$	−19.8019	−0.651436
$925$	−44.3364	−1.45777
$926$	−26.9267	−0.884867
$927$	−1.00000	−0.0328443
$928$	−38.8287	−1.27461
$929$	23.2311	0.762189	0.381094	−	0.924536i	$-0.375547\pi$
$929$	23.2311	0.762189	0.381094	+	0.924536i	$0.375547\pi$
$930$	−15.7871	−0.517678
$931$	69.0747	2.26383
$932$	12.3399	0.404207
$933$	19.5503	0.640047
$934$	−13.1008	−0.428671
$935$	−40.8413	−1.33565
$936$	2.75119	0.0899255
$937$	10.7057	0.349740	0.174870	−	0.984592i	$-0.444050\pi$
$937$	10.7057	0.349740	0.174870	+	0.984592i	$0.444050\pi$
$938$	−30.0218	−0.980245
$939$	−16.5409	−0.539793
$940$	−5.37407	−0.175283
$941$	27.8496	0.907871	0.453935	−	0.891035i	$-0.350020\pi$
$941$	27.8496	0.907871	0.453935	+	0.891035i	$0.350020\pi$
$942$	−13.6331	−0.444191
$943$	−0.102401	−0.00333463
$944$	4.70577	0.153160
$945$	−13.5492	−0.440757
$946$	15.4887	0.503582
$947$	−47.5666	−1.54571	−0.772854	−	0.634584i	$-0.781172\pi$
$947$	−47.5666	−1.54571	−0.772854	+	0.634584i	$0.781172\pi$
$948$	−8.12338	−0.263835
$949$	16.0820	0.522044
$950$	37.3239	1.21095
$951$	22.9713	0.744895
$952$	36.6108	1.18656
$953$	−32.8439	−1.06392	−0.531959	−	0.846770i	$-0.678544\pi$
$953$	−32.8439	−1.06392	−0.531959	+	0.846770i	$0.678544\pi$
$954$	−11.1102	−0.359706
$955$	−38.6212	−1.24975
$956$	29.4294	0.951815
$957$	25.0700	0.810398
$958$	−7.93512	−0.256372
$959$	76.4545	2.46884
$960$	13.8393	0.446663
$961$	1.32605	0.0427758
$962$	5.99463	0.193274
$963$	−18.9180	−0.609625
$964$	−16.7750	−0.540287
$965$	−9.82853	−0.316392
$966$	16.5951	0.533940
$967$	45.3407	1.45806	0.729030	−	0.684482i	$-0.239971\pi$
$967$	45.3407	1.45806	0.729030	+	0.684482i	$0.239971\pi$
$968$	−8.00305	−0.257228
$969$	−23.9348	−0.768897
$970$	46.9884	1.50871
$971$	0.391770	0.0125725	0.00628625	−	0.999980i	$-0.497999\pi$
$971$	0.391770	0.0125725	0.00628625	+	0.999980i	$0.497999\pi$
$972$	1.30853	0.0419713
$973$	18.6594	0.598191
$974$	−6.39495	−0.204908
$975$	6.15012	0.196962
$976$	3.64946	0.116816
$977$	−16.7787	−0.536800	−0.268400	−	0.963308i	$-0.586495\pi$
$977$	−16.7787	−0.536800	−0.268400	+	0.963308i	$0.586495\pi$
$978$	6.24297	0.199628
$979$	66.2405	2.11706
$980$	41.3548	1.32103
$981$	3.05422	0.0975138
$982$	−26.8598	−0.857132
$983$	−46.8573	−1.49451	−0.747257	−	0.664535i	$-0.768630\pi$
$983$	−46.8573	−1.49451	−0.747257	+	0.664535i	$0.768630\pi$
$984$	−0.0572801	−0.00182602
$985$	−69.1728	−2.20403
$986$	−18.3318	−0.583804
$987$	−4.99061	−0.158853
$988$	9.54999	0.303826
$989$	24.5643	0.781098
$990$	−10.3555	−0.329120
$991$	41.6638	1.32349	0.661746	−	0.749728i	$-0.269816\pi$
$991$	41.6638	1.32349	0.661746	+	0.749728i	$0.269816\pi$
$992$	−32.8414	−1.04271
$993$	10.5441	0.334607
$994$	−45.5279	−1.44406
$995$	39.4850	1.25176
$996$	−0.515154	−0.0163233
$997$	17.3680	0.550051	0.275025	−	0.961437i	$-0.411314\pi$
$997$	17.3680	0.550051	0.275025	+	0.961437i	$0.411314\pi$
$998$	−23.9305	−0.757507
$999$	7.20903	0.228084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.16	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+0.831544 q^{2} -1.00000 q^{3} -1.30853 q^{4} -3.33918 q^{5} -0.831544 q^{6} -4.05766 q^{7} -2.75119 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.831544 q^{2} -1.00000 q^{3} -1.30853 q^{4} -3.33918 q^{5} -0.831544 q^{6} -4.05766 q^{7} -2.75119 q^{8} +1.00000 q^{9} -2.77667 q^{10} +3.72947 q^{11} +1.30853 q^{12} -1.00000 q^{13} -3.37412 q^{14} +3.33918 q^{15} +0.329332 q^{16} +3.27954 q^{17} +0.831544 q^{18} +7.29823 q^{19} +4.36943 q^{20} +4.05766 q^{21} +3.10122 q^{22} +4.91836 q^{23} +2.75119 q^{24} +6.15012 q^{25} -0.831544 q^{26} -1.00000 q^{27} +5.30958 q^{28} -6.72214 q^{29} +2.77667 q^{30} -5.68560 q^{31} +5.77624 q^{32} -3.72947 q^{33} +2.72708 q^{34} +13.5492 q^{35} -1.30853 q^{36} -7.20903 q^{37} +6.06880 q^{38} +1.00000 q^{39} +9.18672 q^{40} -0.0208201 q^{41} +3.37412 q^{42} +4.99440 q^{43} -4.88014 q^{44} -3.33918 q^{45} +4.08983 q^{46} -1.22992 q^{47} -0.329332 q^{48} +9.46458 q^{49} +5.11410 q^{50} -3.27954 q^{51} +1.30853 q^{52} -13.3609 q^{53} -0.831544 q^{54} -12.4534 q^{55} +11.1634 q^{56} -7.29823 q^{57} -5.58975 q^{58} +14.2888 q^{59} -4.36943 q^{60} +11.0814 q^{61} -4.72783 q^{62} -4.05766 q^{63} +4.14453 q^{64} +3.33918 q^{65} -3.10122 q^{66} +8.89766 q^{67} -4.29139 q^{68} -4.91836 q^{69} +11.2668 q^{70} +13.4933 q^{71} -2.75119 q^{72} -16.0820 q^{73} -5.99463 q^{74} -6.15012 q^{75} -9.54999 q^{76} -15.1329 q^{77} +0.831544 q^{78} -6.20800 q^{79} -1.09970 q^{80} +1.00000 q^{81} -0.0173128 q^{82} -0.393688 q^{83} -5.30958 q^{84} -10.9510 q^{85} +4.15306 q^{86} +6.72214 q^{87} -10.2605 q^{88} +17.7614 q^{89} -2.77667 q^{90} +4.05766 q^{91} -6.43585 q^{92} +5.68560 q^{93} -1.02274 q^{94} -24.3701 q^{95} -5.77624 q^{96} -16.9225 q^{97} +7.87021 q^{98} +3.72947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 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