LMFDB - Embedded newform 4017.2.a.j.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+0.940078 q^{2} -1.00000 q^{3} -1.11625 q^{4} -1.95082 q^{5} -0.940078 q^{6} -0.363346 q^{7} -2.92952 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.940078 q^{2} -1.00000 q^{3} -1.11625 q^{4} -1.95082 q^{5} -0.940078 q^{6} -0.363346 q^{7} -2.92952 q^{8} +1.00000 q^{9} -1.83392 q^{10} +1.99973 q^{11} +1.11625 q^{12} +1.00000 q^{13} -0.341574 q^{14} +1.95082 q^{15} -0.521471 q^{16} -2.22976 q^{17} +0.940078 q^{18} -5.96553 q^{19} +2.17761 q^{20} +0.363346 q^{21} +1.87990 q^{22} -1.97893 q^{23} +2.92952 q^{24} -1.19429 q^{25} +0.940078 q^{26} -1.00000 q^{27} +0.405586 q^{28} -1.52189 q^{29} +1.83392 q^{30} -6.18222 q^{31} +5.36882 q^{32} -1.99973 q^{33} -2.09614 q^{34} +0.708823 q^{35} -1.11625 q^{36} +2.13653 q^{37} -5.60807 q^{38} -1.00000 q^{39} +5.71497 q^{40} -0.409818 q^{41} +0.341574 q^{42} +10.8205 q^{43} -2.23220 q^{44} -1.95082 q^{45} -1.86035 q^{46} -11.1414 q^{47} +0.521471 q^{48} -6.86798 q^{49} -1.12273 q^{50} +2.22976 q^{51} -1.11625 q^{52} +1.45789 q^{53} -0.940078 q^{54} -3.90111 q^{55} +1.06443 q^{56} +5.96553 q^{57} -1.43069 q^{58} -2.75815 q^{59} -2.17761 q^{60} -2.43812 q^{61} -5.81177 q^{62} -0.363346 q^{63} +6.09005 q^{64} -1.95082 q^{65} -1.87990 q^{66} +0.0721191 q^{67} +2.48897 q^{68} +1.97893 q^{69} +0.666349 q^{70} +11.4933 q^{71} -2.92952 q^{72} +10.7686 q^{73} +2.00851 q^{74} +1.19429 q^{75} +6.65905 q^{76} -0.726592 q^{77} -0.940078 q^{78} +8.03620 q^{79} +1.01730 q^{80} +1.00000 q^{81} -0.385261 q^{82} +10.8876 q^{83} -0.405586 q^{84} +4.34986 q^{85} +10.1721 q^{86} +1.52189 q^{87} -5.85824 q^{88} +8.54917 q^{89} -1.83392 q^{90} -0.363346 q^{91} +2.20898 q^{92} +6.18222 q^{93} -10.4738 q^{94} +11.6377 q^{95} -5.36882 q^{96} -13.4153 q^{97} -6.45644 q^{98} +1.99973 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.940078	0.664735	0.332368	−	0.943150i	$-0.392152\pi$
$2$	0.940078	0.664735	0.332368	+	0.943150i	$0.392152\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.11625	−0.558127
$5$	−1.95082	−0.872434	−0.436217	−	0.899841i	$-0.643682\pi$
$5$	−1.95082	−0.872434	−0.436217	+	0.899841i	$0.643682\pi$
$6$	−0.940078	−0.383785
$7$	−0.363346	−0.137332	−0.0686659	−	0.997640i	$-0.521874\pi$
$7$	−0.363346	−0.137332	−0.0686659	+	0.997640i	$0.521874\pi$
$8$	−2.92952	−1.03574
$9$	1.00000	0.333333
$10$	−1.83392	−0.579938
$11$	1.99973	0.602940	0.301470	−	0.953476i	$-0.402523\pi$
$11$	1.99973	0.602940	0.301470	+	0.953476i	$0.402523\pi$
$12$	1.11625	0.322235
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.341574	−0.0912894
$15$	1.95082	0.503700
$16$	−0.521471	−0.130368
$17$	−2.22976	−0.540795	−0.270398	−	0.962749i	$-0.587155\pi$
$17$	−2.22976	−0.540795	−0.270398	+	0.962749i	$0.587155\pi$
$18$	0.940078	0.221578
$19$	−5.96553	−1.36859	−0.684294	−	0.729206i	$-0.739889\pi$
$19$	−5.96553	−1.36859	−0.684294	+	0.729206i	$0.739889\pi$
$20$	2.17761	0.486929
$21$	0.363346	0.0792886
$22$	1.87990	0.400796
$23$	−1.97893	−0.412635	−0.206317	−	0.978485i	$-0.566148\pi$
$23$	−1.97893	−0.412635	−0.206317	+	0.978485i	$0.566148\pi$
$24$	2.92952	0.597986
$25$	−1.19429	−0.238859
$26$	0.940078	0.184364
$27$	−1.00000	−0.192450
$28$	0.405586	0.0766486
$29$	−1.52189	−0.282607	−0.141304	−	0.989966i	$-0.545129\pi$
$29$	−1.52189	−0.282607	−0.141304	+	0.989966i	$0.545129\pi$
$30$	1.83392	0.334827
$31$	−6.18222	−1.11036	−0.555180	−	0.831730i	$-0.687351\pi$
$31$	−6.18222	−1.11036	−0.555180	+	0.831730i	$0.687351\pi$
$32$	5.36882	0.949082
$33$	−1.99973	−0.348108
$34$	−2.09614	−0.359486
$35$	0.708823	0.119813
$36$	−1.11625	−0.186042
$37$	2.13653	0.351244	0.175622	−	0.984458i	$-0.443806\pi$
$37$	2.13653	0.351244	0.175622	+	0.984458i	$0.443806\pi$
$38$	−5.60807	−0.909749
$39$	−1.00000	−0.160128
$40$	5.71497	0.903617
$41$	−0.409818	−0.0640028	−0.0320014	−	0.999488i	$-0.510188\pi$
$41$	−0.409818	−0.0640028	−0.0320014	+	0.999488i	$0.510188\pi$
$42$	0.341574	0.0527059
$43$	10.8205	1.65011	0.825057	−	0.565049i	$-0.191143\pi$
$43$	10.8205	1.65011	0.825057	+	0.565049i	$0.191143\pi$
$44$	−2.23220	−0.336517
$45$	−1.95082	−0.290811
$46$	−1.86035	−0.274293
$47$	−11.1414	−1.62514	−0.812568	−	0.582866i	$-0.801931\pi$
$47$	−11.1414	−1.62514	−0.812568	+	0.582866i	$0.801931\pi$
$48$	0.521471	0.0752679
$49$	−6.86798	−0.981140
$50$	−1.12273	−0.158778
$51$	2.22976	0.312228
$52$	−1.11625	−0.154797
$53$	1.45789	0.200256	0.100128	−	0.994975i	$-0.468075\pi$
$53$	1.45789	0.200256	0.100128	+	0.994975i	$0.468075\pi$
$54$	−0.940078	−0.127928
$55$	−3.90111	−0.526025
$56$	1.06443	0.142240
$57$	5.96553	0.790154
$58$	−1.43069	−0.187859
$59$	−2.75815	−0.359081	−0.179540	−	0.983751i	$-0.557461\pi$
$59$	−2.75815	−0.359081	−0.179540	+	0.983751i	$0.557461\pi$
$60$	−2.17761	−0.281128
$61$	−2.43812	−0.312170	−0.156085	−	0.987744i	$-0.549887\pi$
$61$	−2.43812	−0.312170	−0.156085	+	0.987744i	$0.549887\pi$
$62$	−5.81177	−0.738096
$63$	−0.363346	−0.0457773
$64$	6.09005	0.761256
$65$	−1.95082	−0.241970
$66$	−1.87990	−0.231399
$67$	0.0721191	0.00881075	0.00440538	−	0.999990i	$-0.498598\pi$
$67$	0.0721191	0.00881075	0.00440538	+	0.999990i	$0.498598\pi$
$68$	2.48897	0.301832
$69$	1.97893	0.238235
$70$	0.666349	0.0796440
$71$	11.4933	1.36400	0.682001	−	0.731351i	$-0.261110\pi$
$71$	11.4933	1.36400	0.682001	+	0.731351i	$0.261110\pi$
$72$	−2.92952	−0.345247
$73$	10.7686	1.26036	0.630182	−	0.776448i	$-0.282980\pi$
$73$	10.7686	1.26036	0.630182	+	0.776448i	$0.282980\pi$
$74$	2.00851	0.233484
$75$	1.19429	0.137905
$76$	6.65905	0.763845
$77$	−0.726592	−0.0828029
$78$	−0.940078	−0.106443
$79$	8.03620	0.904143	0.452072	−	0.891982i	$-0.350685\pi$
$79$	8.03620	0.904143	0.452072	+	0.891982i	$0.350685\pi$
$80$	1.01730	0.113737
$81$	1.00000	0.111111
$82$	−0.385261	−0.0425449
$83$	10.8876	1.19507	0.597535	−	0.801843i	$-0.296147\pi$
$83$	10.8876	1.19507	0.597535	+	0.801843i	$0.296147\pi$
$84$	−0.405586	−0.0442531
$85$	4.34986	0.471808
$86$	10.1721	1.09689
$87$	1.52189	0.163163
$88$	−5.85824	−0.624490
$89$	8.54917	0.906211	0.453105	−	0.891457i	$-0.350316\pi$
$89$	8.54917	0.906211	0.453105	+	0.891457i	$0.350316\pi$
$90$	−1.83392	−0.193313
$91$	−0.363346	−0.0380890
$92$	2.20898	0.230302
$93$	6.18222	0.641067
$94$	−10.4738	−1.08029
$95$	11.6377	1.19400
$96$	−5.36882	−0.547953
$97$	−13.4153	−1.36211	−0.681057	−	0.732230i	$-0.738480\pi$
$97$	−13.4153	−1.36211	−0.681057	+	0.732230i	$0.738480\pi$
$98$	−6.45644	−0.652199
$99$	1.99973	0.200980
$100$	1.33313	0.133313
$101$	−6.35586	−0.632431	−0.316216	−	0.948687i	$-0.602412\pi$
$101$	−6.35586	−0.632431	−0.316216	+	0.948687i	$0.602412\pi$
$102$	2.09614	0.207549
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.92952	−0.287263
$105$	−0.708823	−0.0691741
$106$	1.37053	0.133117
$107$	3.80533	0.367875	0.183938	−	0.982938i	$-0.441116\pi$
$107$	3.80533	0.367875	0.183938	+	0.982938i	$0.441116\pi$
$108$	1.11625	0.107412
$109$	3.96810	0.380075	0.190038	−	0.981777i	$-0.439139\pi$
$109$	3.96810	0.380075	0.190038	+	0.981777i	$0.439139\pi$
$110$	−3.66735	−0.349668
$111$	−2.13653	−0.202791
$112$	0.189474	0.0179037
$113$	−1.14996	−0.108179	−0.0540893	−	0.998536i	$-0.517226\pi$
$113$	−1.14996	−0.108179	−0.0540893	+	0.998536i	$0.517226\pi$
$114$	5.60807	0.525244
$115$	3.86053	0.359997
$116$	1.69881	0.157731
$117$	1.00000	0.0924500
$118$	−2.59288	−0.238694
$119$	0.810173	0.0742684
$120$	−5.71497	−0.521703
$121$	−7.00110	−0.636463
$122$	−2.29203	−0.207510
$123$	0.409818	0.0369520
$124$	6.90093	0.619722
$125$	12.0840	1.08082
$126$	−0.341574	−0.0304298
$127$	−4.69610	−0.416711	−0.208356	−	0.978053i	$-0.566811\pi$
$127$	−4.69610	−0.416711	−0.208356	+	0.978053i	$0.566811\pi$
$128$	−5.01252	−0.443048
$129$	−10.8205	−0.952694
$130$	−1.83392	−0.160846
$131$	4.34589	0.379702	0.189851	−	0.981813i	$-0.439199\pi$
$131$	4.34589	0.379702	0.189851	+	0.981813i	$0.439199\pi$
$132$	2.23220	0.194288
$133$	2.16755	0.187951
$134$	0.0677976	0.00585682
$135$	1.95082	0.167900
$136$	6.53212	0.560124
$137$	20.9667	1.79131	0.895655	−	0.444750i	$-0.146708\pi$
$137$	20.9667	1.79131	0.895655	+	0.444750i	$0.146708\pi$
$138$	1.86035	0.158363
$139$	21.8389	1.85235	0.926174	−	0.377096i	$-0.123077\pi$
$139$	21.8389	1.85235	0.926174	+	0.377096i	$0.123077\pi$
$140$	−0.791227	−0.0668708
$141$	11.1414	0.938273
$142$	10.8046	0.906700
$143$	1.99973	0.167225
$144$	−0.521471	−0.0434559
$145$	2.96893	0.246556
$146$	10.1233	0.837808
$147$	6.86798	0.566461
$148$	−2.38491	−0.196039
$149$	18.1511	1.48700	0.743498	−	0.668738i	$-0.233165\pi$
$149$	18.1511	1.48700	0.743498	+	0.668738i	$0.233165\pi$
$150$	1.12273	0.0916704
$151$	8.10513	0.659586	0.329793	−	0.944053i	$-0.393021\pi$
$151$	8.10513	0.659586	0.329793	+	0.944053i	$0.393021\pi$
$152$	17.4762	1.41750
$153$	−2.22976	−0.180265
$154$	−0.683053	−0.0550420
$155$	12.0604	0.968716
$156$	1.11625	0.0893718
$157$	−4.49931	−0.359084	−0.179542	−	0.983750i	$-0.557462\pi$
$157$	−4.49931	−0.359084	−0.179542	+	0.983750i	$0.557462\pi$
$158$	7.55465	0.601016
$159$	−1.45789	−0.115618
$160$	−10.4736	−0.828012
$161$	0.719035	0.0566679
$162$	0.940078	0.0738595
$163$	−13.5433	−1.06080	−0.530398	−	0.847749i	$-0.677958\pi$
$163$	−13.5433	−1.06080	−0.530398	+	0.847749i	$0.677958\pi$
$164$	0.457461	0.0357217
$165$	3.90111	0.303701
$166$	10.2352	0.794406
$167$	−5.80573	−0.449261	−0.224630	−	0.974444i	$-0.572117\pi$
$167$	−5.80573	−0.449261	−0.224630	+	0.974444i	$0.572117\pi$
$168$	−1.06443	−0.0821225
$169$	1.00000	0.0769231
$170$	4.08920	0.313628
$171$	−5.96553	−0.456196
$172$	−12.0784	−0.920973
$173$	−9.85387	−0.749176	−0.374588	−	0.927191i	$-0.622216\pi$
$173$	−9.85387	−0.749176	−0.374588	+	0.927191i	$0.622216\pi$
$174$	1.43069	0.108460
$175$	0.433942	0.0328029
$176$	−1.04280	−0.0786040
$177$	2.75815	0.207315
$178$	8.03689	0.602390
$179$	−3.97070	−0.296784	−0.148392	−	0.988929i	$-0.547410\pi$
$179$	−3.97070	−0.296784	−0.148392	+	0.988929i	$0.547410\pi$
$180$	2.17761	0.162310
$181$	11.3750	0.845497	0.422749	−	0.906247i	$-0.361065\pi$
$181$	11.3750	0.845497	0.422749	+	0.906247i	$0.361065\pi$
$182$	−0.341574	−0.0253191
$183$	2.43812	0.180231
$184$	5.79731	0.427383
$185$	−4.16799	−0.306437
$186$	5.81177	0.426140
$187$	−4.45890	−0.326067
$188$	12.4366	0.907032
$189$	0.363346	0.0264295
$190$	10.9403	0.793696
$191$	15.8544	1.14719	0.573593	−	0.819140i	$-0.305549\pi$
$191$	15.8544	1.14719	0.573593	+	0.819140i	$0.305549\pi$
$192$	−6.09005	−0.439512
$193$	−14.6916	−1.05753	−0.528763	−	0.848770i	$-0.677344\pi$
$193$	−14.6916	−1.05753	−0.528763	+	0.848770i	$0.677344\pi$
$194$	−12.6114	−0.905446
$195$	1.95082	0.139701
$196$	7.66641	0.547600
$197$	9.75438	0.694971	0.347485	−	0.937685i	$-0.387036\pi$
$197$	9.75438	0.694971	0.347485	+	0.937685i	$0.387036\pi$
$198$	1.87990	0.133599
$199$	22.2546	1.57758	0.788792	−	0.614660i	$-0.210707\pi$
$199$	22.2546	1.57758	0.788792	+	0.614660i	$0.210707\pi$
$200$	3.49871	0.247396
$201$	−0.0721191	−0.00508689
$202$	−5.97500	−0.420400
$203$	0.552971	0.0388110
$204$	−2.48897	−0.174263
$205$	0.799482	0.0558382
$206$	−0.940078	−0.0654983
$207$	−1.97893	−0.137545
$208$	−0.521471	−0.0361575
$209$	−11.9294	−0.825176
$210$	−0.666349	−0.0459825
$211$	15.3333	1.05559	0.527793	−	0.849373i	$-0.323020\pi$
$211$	15.3333	1.05559	0.527793	+	0.849373i	$0.323020\pi$
$212$	−1.62737	−0.111768
$213$	−11.4933	−0.787507
$214$	3.57731	0.244540
$215$	−21.1089	−1.43962
$216$	2.92952	0.199329
$217$	2.24629	0.152488
$218$	3.73033	0.252650
$219$	−10.7686	−0.727671
$220$	4.35463	0.293589
$221$	−2.22976	−0.149990
$222$	−2.00851	−0.134802
$223$	11.1131	0.744191	0.372095	−	0.928194i	$-0.378639\pi$
$223$	11.1131	0.744191	0.372095	+	0.928194i	$0.378639\pi$
$224$	−1.95074	−0.130339
$225$	−1.19429	−0.0796195
$226$	−1.08105	−0.0719102
$227$	1.68257	0.111676	0.0558380	−	0.998440i	$-0.482217\pi$
$227$	1.68257	0.111676	0.0558380	+	0.998440i	$0.482217\pi$
$228$	−6.65905	−0.441006
$229$	21.7690	1.43853	0.719267	−	0.694734i	$-0.244478\pi$
$229$	21.7690	1.43853	0.719267	+	0.694734i	$0.244478\pi$
$230$	3.62920	0.239303
$231$	0.726592	0.0478063
$232$	4.45840	0.292708
$233$	27.7588	1.81854	0.909270	−	0.416206i	$-0.136641\pi$
$233$	27.7588	1.81854	0.909270	+	0.416206i	$0.136641\pi$
$234$	0.940078	0.0614548
$235$	21.7348	1.41782
$236$	3.07880	0.200413
$237$	−8.03620	−0.522007
$238$	0.761625	0.0493688
$239$	−16.5132	−1.06815	−0.534076	−	0.845436i	$-0.679340\pi$
$239$	−16.5132	−1.06815	−0.534076	+	0.845436i	$0.679340\pi$
$240$	−1.01730	−0.0656663
$241$	−16.5745	−1.06766	−0.533828	−	0.845593i	$-0.679247\pi$
$241$	−16.5745	−1.06766	−0.533828	+	0.845593i	$0.679247\pi$
$242$	−6.58158	−0.423080
$243$	−1.00000	−0.0641500
$244$	2.72156	0.174230
$245$	13.3982	0.855980
$246$	0.385261	0.0245633
$247$	−5.96553	−0.379578
$248$	18.1110	1.15005
$249$	−10.8876	−0.689974
$250$	11.3599	0.718461
$251$	−17.0792	−1.07803	−0.539014	−	0.842297i	$-0.681203\pi$
$251$	−17.0792	−1.07803	−0.539014	+	0.842297i	$0.681203\pi$
$252$	0.405586	0.0255495
$253$	−3.95731	−0.248794
$254$	−4.41470	−0.277003
$255$	−4.34986	−0.272399
$256$	−16.8923	−1.05577
$257$	−14.9303	−0.931324	−0.465662	−	0.884963i	$-0.654184\pi$
$257$	−14.9303	−0.931324	−0.465662	+	0.884963i	$0.654184\pi$
$258$	−10.1721	−0.633290
$259$	−0.776300	−0.0482370
$260$	2.17761	0.135050
$261$	−1.52189	−0.0942024
$262$	4.08548	0.252402
$263$	24.9300	1.53725	0.768626	−	0.639699i	$-0.220941\pi$
$263$	24.9300	1.53725	0.768626	+	0.639699i	$0.220941\pi$
$264$	5.85824	0.360550
$265$	−2.84408	−0.174710
$266$	2.03767	0.124937
$267$	−8.54917	−0.523201
$268$	−0.0805032	−0.00491752
$269$	−5.86892	−0.357834	−0.178917	−	0.983864i	$-0.557259\pi$
$269$	−5.86892	−0.357834	−0.178917	+	0.983864i	$0.557259\pi$
$270$	1.83392	0.111609
$271$	17.2185	1.04595	0.522975	−	0.852348i	$-0.324822\pi$
$271$	17.2185	1.04595	0.522975	+	0.852348i	$0.324822\pi$
$272$	1.16275	0.0705023
$273$	0.363346	0.0219907
$274$	19.7104	1.19075
$275$	−2.38826	−0.144017
$276$	−2.20898	−0.132965
$277$	−10.4297	−0.626662	−0.313331	−	0.949644i	$-0.601445\pi$
$277$	−10.4297	−0.626662	−0.313331	+	0.949644i	$0.601445\pi$
$278$	20.5302	1.23132
$279$	−6.18222	−0.370120
$280$	−2.07651	−0.124095
$281$	19.2605	1.14898	0.574492	−	0.818510i	$-0.305200\pi$
$281$	19.2605	1.14898	0.574492	+	0.818510i	$0.305200\pi$
$282$	10.4738	0.623703
$283$	−14.3040	−0.850287	−0.425143	−	0.905126i	$-0.639776\pi$
$283$	−14.3040	−0.850287	−0.425143	+	0.905126i	$0.639776\pi$
$284$	−12.8294	−0.761286
$285$	−11.6377	−0.689358
$286$	1.87990	0.111161
$287$	0.148906	0.00878962
$288$	5.36882	0.316361
$289$	−12.0282	−0.707541
$290$	2.79102	0.163895
$291$	13.4153	0.786417
$292$	−12.0204	−0.703443
$293$	12.3450	0.721203	0.360601	−	0.932720i	$-0.382571\pi$
$293$	12.3450	0.721203	0.360601	+	0.932720i	$0.382571\pi$
$294$	6.45644	0.376547
$295$	5.38066	0.313274
$296$	−6.25902	−0.363798
$297$	−1.99973	−0.116036
$298$	17.0635	0.988459
$299$	−1.97893	−0.114444
$300$	−1.33313	−0.0769685
$301$	−3.93159	−0.226613
$302$	7.61946	0.438451
$303$	6.35586	0.365134
$304$	3.11085	0.178420
$305$	4.75634	0.272347
$306$	−2.09614	−0.119829
$307$	−27.0107	−1.54158	−0.770792	−	0.637087i	$-0.780139\pi$
$307$	−27.0107	−1.54158	−0.770792	+	0.637087i	$0.780139\pi$
$308$	0.811061	0.0462145
$309$	1.00000	0.0568880
$310$	11.3377	0.643940
$311$	−30.3100	−1.71872	−0.859361	−	0.511369i	$-0.829139\pi$
$311$	−30.3100	−1.71872	−0.859361	+	0.511369i	$0.829139\pi$
$312$	2.92952	0.165851
$313$	0.581827	0.0328868	0.0164434	−	0.999865i	$-0.494766\pi$
$313$	0.581827	0.0328868	0.0164434	+	0.999865i	$0.494766\pi$
$314$	−4.22970	−0.238696
$315$	0.708823	0.0399377
$316$	−8.97044	−0.504626
$317$	−10.0796	−0.566128	−0.283064	−	0.959101i	$-0.591351\pi$
$317$	−10.0796	−0.566128	−0.283064	+	0.959101i	$0.591351\pi$
$318$	−1.37053	−0.0768553
$319$	−3.04335	−0.170395
$320$	−11.8806	−0.664146
$321$	−3.80533	−0.212393
$322$	0.675949	0.0376692
$323$	13.3017	0.740125
$324$	−1.11625	−0.0620141
$325$	−1.19429	−0.0662475
$326$	−12.7318	−0.705149
$327$	−3.96810	−0.219437
$328$	1.20057	0.0662904
$329$	4.04817	0.223183
$330$	3.66735	0.201881
$331$	−18.8863	−1.03808	−0.519042	−	0.854749i	$-0.673711\pi$
$331$	−18.8863	−1.03808	−0.519042	+	0.854749i	$0.673711\pi$
$332$	−12.1533	−0.667001
$333$	2.13653	0.117081
$334$	−5.45783	−0.298639
$335$	−0.140692	−0.00768680
$336$	−0.189474	−0.0103367
$337$	−6.62308	−0.360782	−0.180391	−	0.983595i	$-0.557736\pi$
$337$	−6.62308	−0.360782	−0.180391	+	0.983595i	$0.557736\pi$
$338$	0.940078	0.0511335
$339$	1.14996	0.0624570
$340$	−4.85554	−0.263329
$341$	−12.3628	−0.669481
$342$	−5.60807	−0.303250
$343$	5.03887	0.272074
$344$	−31.6990	−1.70909
$345$	−3.86053	−0.207844
$346$	−9.26340	−0.498004
$347$	−12.9059	−0.692824	−0.346412	−	0.938083i	$-0.612600\pi$
$347$	−12.9059	−0.692824	−0.346412	+	0.938083i	$0.612600\pi$
$348$	−1.69881	−0.0910658
$349$	−7.35854	−0.393894	−0.196947	−	0.980414i	$-0.563103\pi$
$349$	−7.35854	−0.393894	−0.196947	+	0.980414i	$0.563103\pi$
$350$	0.407939	0.0218053
$351$	−1.00000	−0.0533761
$352$	10.7362	0.572240
$353$	22.9517	1.22160	0.610799	−	0.791786i	$-0.290848\pi$
$353$	22.9517	1.22160	0.610799	+	0.791786i	$0.290848\pi$
$354$	2.59288	0.137810
$355$	−22.4213	−1.19000
$356$	−9.54304	−0.505780
$357$	−0.810173	−0.0428789
$358$	−3.73276	−0.197283
$359$	35.4244	1.86963	0.934814	−	0.355138i	$-0.115566\pi$
$359$	35.4244	1.86963	0.934814	+	0.355138i	$0.115566\pi$
$360$	5.71497	0.301206
$361$	16.5876	0.873032
$362$	10.6934	0.562032
$363$	7.00110	0.367462
$364$	0.405586	0.0212585
$365$	−21.0075	−1.09958
$366$	2.29203	0.119806
$367$	−32.6938	−1.70660	−0.853301	−	0.521418i	$-0.825403\pi$
$367$	−32.6938	−1.70660	−0.853301	+	0.521418i	$0.825403\pi$
$368$	1.03195	0.0537943
$369$	−0.409818	−0.0213343
$370$	−3.91824	−0.203700
$371$	−0.529717	−0.0275015
$372$	−6.90093	−0.357797
$373$	2.27042	0.117558	0.0587789	−	0.998271i	$-0.481279\pi$
$373$	2.27042	0.117558	0.0587789	+	0.998271i	$0.481279\pi$
$374$	−4.19171	−0.216748
$375$	−12.0840	−0.624013
$376$	32.6389	1.68322
$377$	−1.52189	−0.0783811
$378$	0.341574	0.0175686
$379$	16.7685	0.861340	0.430670	−	0.902509i	$-0.358277\pi$
$379$	16.7685	0.861340	0.430670	+	0.902509i	$0.358277\pi$
$380$	−12.9906	−0.666405
$381$	4.69610	0.240588
$382$	14.9044	0.762576
$383$	−6.32751	−0.323321	−0.161660	−	0.986846i	$-0.551685\pi$
$383$	−6.32751	−0.323321	−0.161660	+	0.986846i	$0.551685\pi$
$384$	5.01252	0.255794
$385$	1.41745	0.0722401
$386$	−13.8113	−0.702975
$387$	10.8205	0.550038
$388$	14.9748	0.760233
$389$	17.5492	0.889782	0.444891	−	0.895585i	$-0.353242\pi$
$389$	17.5492	0.889782	0.444891	+	0.895585i	$0.353242\pi$
$390$	1.83392	0.0928644
$391$	4.41252	0.223151
$392$	20.1199	1.01621
$393$	−4.34589	−0.219221
$394$	9.16988	0.461972
$395$	−15.6772	−0.788805
$396$	−2.23220	−0.112172
$397$	12.9479	0.649836	0.324918	−	0.945742i	$-0.394663\pi$
$397$	12.9479	0.649836	0.324918	+	0.945742i	$0.394663\pi$
$398$	20.9210	1.04868
$399$	−2.16755	−0.108513
$400$	0.622789	0.0311395
$401$	−25.5064	−1.27373	−0.636864	−	0.770976i	$-0.719769\pi$
$401$	−25.5064	−1.27373	−0.636864	+	0.770976i	$0.719769\pi$
$402$	−0.0677976	−0.00338144
$403$	−6.18222	−0.307959
$404$	7.09475	0.352977
$405$	−1.95082	−0.0969371
$406$	0.519836	0.0257990
$407$	4.27248	0.211779
$408$	−6.53212	−0.323388
$409$	−16.8621	−0.833776	−0.416888	−	0.908958i	$-0.636879\pi$
$409$	−16.8621	−0.833776	−0.416888	+	0.908958i	$0.636879\pi$
$410$	0.751575	0.0371176
$411$	−20.9667	−1.03421
$412$	1.11625	0.0549939
$413$	1.00216	0.0493132
$414$	−1.86035	−0.0914310
$415$	−21.2398	−1.04262
$416$	5.36882	0.263228
$417$	−21.8389	−1.06945
$418$	−11.2146	−0.548524
$419$	4.01833	0.196308	0.0981542	−	0.995171i	$-0.468706\pi$
$419$	4.01833	0.196308	0.0981542	+	0.995171i	$0.468706\pi$
$420$	0.791227	0.0386079
$421$	−15.3640	−0.748794	−0.374397	−	0.927268i	$-0.622150\pi$
$421$	−15.3640	−0.748794	−0.374397	+	0.927268i	$0.622150\pi$
$422$	14.4145	0.701686
$423$	−11.1414	−0.541712
$424$	−4.27091	−0.207414
$425$	2.66298	0.129174
$426$	−10.8046	−0.523484
$427$	0.885882	0.0428708
$428$	−4.24771	−0.205321
$429$	−1.99973	−0.0965477
$430$	−19.8440	−0.956964
$431$	−21.3395	−1.02789	−0.513945	−	0.857823i	$-0.671816\pi$
$431$	−21.3395	−1.02789	−0.513945	+	0.857823i	$0.671816\pi$
$432$	0.521471	0.0250893
$433$	−4.61830	−0.221941	−0.110971	−	0.993824i	$-0.535396\pi$
$433$	−4.61830	−0.221941	−0.110971	+	0.993824i	$0.535396\pi$
$434$	2.11168	0.101364
$435$	−2.96893	−0.142349
$436$	−4.42941	−0.212130
$437$	11.8054	0.564727
$438$	−10.1233	−0.483709
$439$	11.8407	0.565125	0.282562	−	0.959249i	$-0.408816\pi$
$439$	11.8407	0.565125	0.282562	+	0.959249i	$0.408816\pi$
$440$	11.4284	0.544827
$441$	−6.86798	−0.327047
$442$	−2.09614	−0.0997034
$443$	−11.7872	−0.560028	−0.280014	−	0.959996i	$-0.590339\pi$
$443$	−11.7872	−0.560028	−0.280014	+	0.959996i	$0.590339\pi$
$444$	2.38491	0.113183
$445$	−16.6779	−0.790609
$446$	10.4472	0.494690
$447$	−18.1511	−0.858518
$448$	−2.21280	−0.104545
$449$	1.56138	0.0736862	0.0368431	−	0.999321i	$-0.488270\pi$
$449$	1.56138	0.0736862	0.0368431	+	0.999321i	$0.488270\pi$
$450$	−1.12273	−0.0529259
$451$	−0.819523	−0.0385898
$452$	1.28364	0.0603774
$453$	−8.10513	−0.380812
$454$	1.58175	0.0742350
$455$	0.708823	0.0332302
$456$	−17.4762	−0.818396
$457$	8.20490	0.383809	0.191905	−	0.981414i	$-0.438534\pi$
$457$	8.20490	0.383809	0.191905	+	0.981414i	$0.438534\pi$
$458$	20.4645	0.956244
$459$	2.22976	0.104076
$460$	−4.30933	−0.200924
$461$	11.6349	0.541890	0.270945	−	0.962595i	$-0.412664\pi$
$461$	11.6349	0.541890	0.270945	+	0.962595i	$0.412664\pi$
$462$	0.683053	0.0317785
$463$	30.4947	1.41721	0.708605	−	0.705605i	$-0.249325\pi$
$463$	30.4947	1.41721	0.708605	+	0.705605i	$0.249325\pi$
$464$	0.793619	0.0368429
$465$	−12.0604	−0.559289
$466$	26.0955	1.20885
$467$	−24.8221	−1.14863	−0.574315	−	0.818634i	$-0.694732\pi$
$467$	−24.8221	−1.14863	−0.574315	+	0.818634i	$0.694732\pi$
$468$	−1.11625	−0.0515988
$469$	−0.0262042	−0.00121000
$470$	20.4324	0.942478
$471$	4.49931	0.207317
$472$	8.08007	0.371915
$473$	21.6381	0.994920
$474$	−7.55465	−0.346997
$475$	7.12460	0.326899
$476$	−0.904358	−0.0414512
$477$	1.45789	0.0667520
$478$	−15.5237	−0.710039
$479$	33.8138	1.54499	0.772496	−	0.635019i	$-0.219008\pi$
$479$	33.8138	1.54499	0.772496	+	0.635019i	$0.219008\pi$
$480$	10.4736	0.478053
$481$	2.13653	0.0974175
$482$	−15.5813	−0.709709
$483$	−0.719035	−0.0327172
$484$	7.81500	0.355227
$485$	26.1708	1.18836
$486$	−0.940078	−0.0426428
$487$	−14.2467	−0.645580	−0.322790	−	0.946471i	$-0.604621\pi$
$487$	−14.2467	−0.645580	−0.322790	+	0.946471i	$0.604621\pi$
$488$	7.14253	0.323327
$489$	13.5433	0.612451
$490$	12.5954	0.569000
$491$	14.4413	0.651727	0.325864	−	0.945417i	$-0.394345\pi$
$491$	14.4413	0.651727	0.325864	+	0.945417i	$0.394345\pi$
$492$	−0.457461	−0.0206239
$493$	3.39343	0.152833
$494$	−5.60807	−0.252319
$495$	−3.90111	−0.175342
$496$	3.22385	0.144755
$497$	−4.17604	−0.187321
$498$	−10.2352	−0.458650
$499$	−8.54587	−0.382565	−0.191283	−	0.981535i	$-0.561265\pi$
$499$	−8.54587	−0.382565	−0.191283	+	0.981535i	$0.561265\pi$
$500$	−13.4888	−0.603236
$501$	5.80573	0.259381
$502$	−16.0557	−0.716603
$503$	39.4044	1.75696	0.878478	−	0.477783i	$-0.158559\pi$
$503$	39.4044	1.75696	0.878478	+	0.477783i	$0.158559\pi$
$504$	1.06443	0.0474135
$505$	12.3991	0.551755
$506$	−3.72018	−0.165382
$507$	−1.00000	−0.0444116
$508$	5.24204	0.232578
$509$	−37.1959	−1.64868	−0.824340	−	0.566096i	$-0.808453\pi$
$509$	−37.1959	−1.64868	−0.824340	+	0.566096i	$0.808453\pi$
$510$	−4.08920	−0.181073
$511$	−3.91271	−0.173088
$512$	−5.85501	−0.258757
$513$	5.96553	0.263385
$514$	−14.0356	−0.619084
$515$	1.95082	0.0859635
$516$	12.0784	0.531724
$517$	−22.2797	−0.979860
$518$	−0.729783	−0.0320648
$519$	9.85387	0.432537
$520$	5.71497	0.250618
$521$	13.2940	0.582420	0.291210	−	0.956659i	$-0.405942\pi$
$521$	13.2940	0.582420	0.291210	+	0.956659i	$0.405942\pi$
$522$	−1.43069	−0.0626196
$523$	9.08576	0.397292	0.198646	−	0.980071i	$-0.436346\pi$
$523$	9.08576	0.397292	0.198646	+	0.980071i	$0.436346\pi$
$524$	−4.85112	−0.211922
$525$	−0.433942	−0.0189388
$526$	23.4362	1.02187
$527$	13.7848	0.600477
$528$	1.04280	0.0453820
$529$	−19.0838	−0.829733
$530$	−2.67365	−0.116136
$531$	−2.75815	−0.119694
$532$	−2.41954	−0.104900
$533$	−0.409818	−0.0177512
$534$	−8.03689	−0.347790
$535$	−7.42352	−0.320947
$536$	−0.211274	−0.00912567
$537$	3.97070	0.171348
$538$	−5.51724	−0.237865
$539$	−13.7341	−0.591569
$540$	−2.17761	−0.0937095
$541$	−1.58666	−0.0682157	−0.0341078	−	0.999418i	$-0.510859\pi$
$541$	−1.58666	−0.0682157	−0.0341078	+	0.999418i	$0.510859\pi$
$542$	16.1867	0.695280
$543$	−11.3750	−0.488148
$544$	−11.9712	−0.513259
$545$	−7.74106	−0.331591
$546$	0.341574	0.0146180
$547$	−3.55748	−0.152107	−0.0760534	−	0.997104i	$-0.524232\pi$
$547$	−3.55748	−0.152107	−0.0760534	+	0.997104i	$0.524232\pi$
$548$	−23.4042	−0.999778
$549$	−2.43812	−0.104057
$550$	−2.24515	−0.0957335
$551$	9.07886	0.386772
$552$	−5.79731	−0.246750
$553$	−2.91992	−0.124168
$554$	−9.80477	−0.416565
$555$	4.16799	0.176922
$556$	−24.3777	−1.03385
$557$	29.0416	1.23053	0.615265	−	0.788320i	$-0.289049\pi$
$557$	29.0416	1.23053	0.615265	+	0.788320i	$0.289049\pi$
$558$	−5.81177	−0.246032
$559$	10.8205	0.457659
$560$	−0.369631	−0.0156198
$561$	4.45890	0.188255
$562$	18.1064	0.763771
$563$	−4.84002	−0.203983	−0.101991	−	0.994785i	$-0.532521\pi$
$563$	−4.84002	−0.203983	−0.101991	+	0.994785i	$0.532521\pi$
$564$	−12.4366	−0.523675
$565$	2.24336	0.0943788
$566$	−13.4469	−0.565216
$567$	−0.363346	−0.0152591
$568$	−33.6698	−1.41275
$569$	2.20459	0.0924213	0.0462106	−	0.998932i	$-0.485285\pi$
$569$	2.20459	0.0924213	0.0462106	+	0.998932i	$0.485285\pi$
$570$	−10.9403	−0.458240
$571$	−15.0088	−0.628100	−0.314050	−	0.949407i	$-0.601686\pi$
$571$	−15.0088	−0.628100	−0.314050	+	0.949407i	$0.601686\pi$
$572$	−2.23220	−0.0933330
$573$	−15.8544	−0.662329
$574$	0.139983	0.00584277
$575$	2.36342	0.0985614
$576$	6.09005	0.253752
$577$	26.0752	1.08553	0.542763	−	0.839886i	$-0.317378\pi$
$577$	26.0752	1.08553	0.542763	+	0.839886i	$0.317378\pi$
$578$	−11.3074	−0.470327
$579$	14.6916	0.610563
$580$	−3.31408	−0.137610
$581$	−3.95597	−0.164121
$582$	12.6114	0.522759
$583$	2.91537	0.120742
$584$	−31.5467	−1.30541
$585$	−1.95082	−0.0806566
$586$	11.6053	0.479409
$587$	24.5676	1.01401	0.507006	−	0.861943i	$-0.330752\pi$
$587$	24.5676	1.01401	0.507006	+	0.861943i	$0.330752\pi$
$588$	−7.66641	−0.316157
$589$	36.8803	1.51963
$590$	5.05824	0.208245
$591$	−9.75438	−0.401242
$592$	−1.11414	−0.0457909
$593$	24.1549	0.991921	0.495961	−	0.868345i	$-0.334816\pi$
$593$	24.1549	0.991921	0.495961	+	0.868345i	$0.334816\pi$
$594$	−1.87990	−0.0771332
$595$	−1.58050	−0.0647943
$596$	−20.2612	−0.829932
$597$	−22.2546	−0.910819
$598$	−1.86035	−0.0760752
$599$	−19.7524	−0.807061	−0.403530	−	0.914966i	$-0.632217\pi$
$599$	−19.7524	−0.807061	−0.403530	+	0.914966i	$0.632217\pi$
$600$	−3.49871	−0.142834
$601$	−36.9777	−1.50835	−0.754175	−	0.656673i	$-0.771963\pi$
$601$	−36.9777	−1.50835	−0.754175	+	0.656673i	$0.771963\pi$
$602$	−3.69601	−0.150638
$603$	0.0721191	0.00293692
$604$	−9.04738	−0.368133
$605$	13.6579	0.555272
$606$	5.97500	0.242718
$607$	25.8702	1.05004	0.525020	−	0.851090i	$-0.324058\pi$
$607$	25.8702	1.05004	0.525020	+	0.851090i	$0.324058\pi$
$608$	−32.0279	−1.29890
$609$	−0.552971	−0.0224075
$610$	4.47133	0.181039
$611$	−11.1414	−0.450732
$612$	2.48897	0.100611
$613$	4.23254	0.170951	0.0854754	−	0.996340i	$-0.472759\pi$
$613$	4.23254	0.170951	0.0854754	+	0.996340i	$0.472759\pi$
$614$	−25.3922	−1.02475
$615$	−0.799482	−0.0322382
$616$	2.12857	0.0857624
$617$	−27.6785	−1.11429	−0.557147	−	0.830414i	$-0.688104\pi$
$617$	−27.6785	−1.11429	−0.557147	+	0.830414i	$0.688104\pi$
$618$	0.940078	0.0378155
$619$	14.3567	0.577044	0.288522	−	0.957473i	$-0.406836\pi$
$619$	14.3567	0.577044	0.288522	+	0.957473i	$0.406836\pi$
$620$	−13.4625	−0.540666
$621$	1.97893	0.0794116
$622$	−28.4938	−1.14250
$623$	−3.10631	−0.124452
$624$	0.521471	0.0208756
$625$	−17.6022	−0.704088
$626$	0.546963	0.0218610
$627$	11.9294	0.476416
$628$	5.02237	0.200414
$629$	−4.76394	−0.189951
$630$	0.666349	0.0265480
$631$	−3.90054	−0.155278	−0.0776391	−	0.996982i	$-0.524738\pi$
$631$	−3.90054	−0.155278	−0.0776391	+	0.996982i	$0.524738\pi$
$632$	−23.5422	−0.936459
$633$	−15.3333	−0.609443
$634$	−9.47563	−0.376325
$635$	9.16126	0.363553
$636$	1.62737	0.0645295
$637$	−6.86798	−0.272119
$638$	−2.86099	−0.113268
$639$	11.4933	0.454667
$640$	9.77853	0.386530
$641$	7.88596	0.311477	0.155738	−	0.987798i	$-0.450224\pi$
$641$	7.88596	0.311477	0.155738	+	0.987798i	$0.450224\pi$
$642$	−3.57731	−0.141185
$643$	18.0104	0.710261	0.355131	−	0.934817i	$-0.384436\pi$
$643$	18.0104	0.710261	0.355131	+	0.934817i	$0.384436\pi$
$644$	−0.802625	−0.0316279
$645$	21.1089	0.831163
$646$	12.5046	0.491988
$647$	−1.54626	−0.0607899	−0.0303950	−	0.999538i	$-0.509677\pi$
$647$	−1.54626	−0.0607899	−0.0303950	+	0.999538i	$0.509677\pi$
$648$	−2.92952	−0.115082
$649$	−5.51555	−0.216504
$650$	−1.12273	−0.0440370
$651$	−2.24629	−0.0880389
$652$	15.1178	0.592059
$653$	−30.6869	−1.20087	−0.600435	−	0.799674i	$-0.705006\pi$
$653$	−30.6869	−1.20087	−0.600435	+	0.799674i	$0.705006\pi$
$654$	−3.73033	−0.145867
$655$	−8.47807	−0.331265
$656$	0.213708	0.00834390
$657$	10.7686	0.420121
$658$	3.80560	0.148358
$659$	6.68165	0.260280	0.130140	−	0.991496i	$-0.458457\pi$
$659$	6.68165	0.260280	0.130140	+	0.991496i	$0.458457\pi$
$660$	−4.35463	−0.169504
$661$	−19.1587	−0.745185	−0.372593	−	0.927995i	$-0.621531\pi$
$661$	−19.1587	−0.745185	−0.372593	+	0.927995i	$0.621531\pi$
$662$	−17.7546	−0.690051
$663$	2.22976	0.0865965
$664$	−31.8955	−1.23778
$665$	−4.22851	−0.163975
$666$	2.00851	0.0778281
$667$	3.01170	0.116613
$668$	6.48066	0.250744
$669$	−11.1131	−0.429659
$670$	−0.132261	−0.00510969
$671$	−4.87558	−0.188220
$672$	1.95074	0.0752514
$673$	17.6735	0.681263	0.340632	−	0.940197i	$-0.389359\pi$
$673$	17.6735	0.681263	0.340632	+	0.940197i	$0.389359\pi$
$674$	−6.22621	−0.239825
$675$	1.19429	0.0459684
$676$	−1.11625	−0.0429328
$677$	37.0818	1.42517	0.712584	−	0.701587i	$-0.247525\pi$
$677$	37.0818	1.42517	0.712584	+	0.701587i	$0.247525\pi$
$678$	1.08105	0.0415174
$679$	4.87439	0.187062
$680$	−12.7430	−0.488672
$681$	−1.68257	−0.0644762
$682$	−11.6220	−0.445028
$683$	24.9633	0.955193	0.477597	−	0.878579i	$-0.341508\pi$
$683$	24.9633	0.955193	0.477597	+	0.878579i	$0.341508\pi$
$684$	6.65905	0.254615
$685$	−40.9024	−1.56280
$686$	4.73693	0.180857
$687$	−21.7690	−0.830538
$688$	−5.64259	−0.215122
$689$	1.45789	0.0555411
$690$	−3.62920	−0.138161
$691$	37.2090	1.41550	0.707748	−	0.706465i	$-0.249711\pi$
$691$	37.2090	1.41550	0.707748	+	0.706465i	$0.249711\pi$
$692$	10.9994	0.418135
$693$	−0.726592	−0.0276010
$694$	−12.1325	−0.460544
$695$	−42.6037	−1.61605
$696$	−4.45840	−0.168995
$697$	0.913793	0.0346124
$698$	−6.91760	−0.261835
$699$	−27.7588	−1.04993
$700$	−0.484389	−0.0183082
$701$	5.78338	0.218435	0.109218	−	0.994018i	$-0.465165\pi$
$701$	5.78338	0.218435	0.109218	+	0.994018i	$0.465165\pi$
$702$	−0.940078	−0.0354810
$703$	−12.7456	−0.480708
$704$	12.1784	0.458992
$705$	−21.7348	−0.818581
$706$	21.5764	0.812039
$707$	2.30938	0.0868530
$708$	−3.07880	−0.115708
$709$	−35.2990	−1.32568	−0.662841	−	0.748760i	$-0.730649\pi$
$709$	−35.2990	−1.32568	−0.662841	+	0.748760i	$0.730649\pi$
$710$	−21.0778	−0.791036
$711$	8.03620	0.301381
$712$	−25.0450	−0.938600
$713$	12.2342	0.458173
$714$	−0.761625	−0.0285031
$715$	−3.90111	−0.145893
$716$	4.43230	0.165643
$717$	16.5132	0.616698
$718$	33.3017	1.24281
$719$	28.8586	1.07624	0.538121	−	0.842867i	$-0.319134\pi$
$719$	28.8586	1.07624	0.538121	+	0.842867i	$0.319134\pi$
$720$	1.01730	0.0379124
$721$	0.363346	0.0135317
$722$	15.5936	0.580335
$723$	16.5745	0.616412
$724$	−12.6974	−0.471895
$725$	1.81758	0.0675031
$726$	6.58158	0.244265
$727$	22.4518	0.832693	0.416346	−	0.909206i	$-0.363310\pi$
$727$	22.4518	0.832693	0.416346	+	0.909206i	$0.363310\pi$
$728$	1.06443	0.0394504
$729$	1.00000	0.0370370
$730$	−19.7487	−0.730933
$731$	−24.1271	−0.892374
$732$	−2.72156	−0.100592
$733$	0.202654	0.00748521	0.00374261	−	0.999993i	$-0.498809\pi$
$733$	0.202654	0.00748521	0.00374261	+	0.999993i	$0.498809\pi$
$734$	−30.7347	−1.13444
$735$	−13.3982	−0.494200
$736$	−10.6245	−0.391624
$737$	0.144218	0.00531235
$738$	−0.385261	−0.0141816
$739$	−11.7675	−0.432873	−0.216437	−	0.976297i	$-0.569444\pi$
$739$	−11.7675	−0.432873	−0.216437	+	0.976297i	$0.569444\pi$
$740$	4.65254	0.171031
$741$	5.96553	0.219149
$742$	−0.497975	−0.0182813
$743$	6.90155	0.253193	0.126597	−	0.991954i	$-0.459595\pi$
$743$	6.90155	0.253193	0.126597	+	0.991954i	$0.459595\pi$
$744$	−18.1110	−0.663980
$745$	−35.4096	−1.29731
$746$	2.13437	0.0781448
$747$	10.8876	0.398357
$748$	4.97726	0.181987
$749$	−1.38265	−0.0505210
$750$	−11.3599	−0.414804
$751$	−43.7926	−1.59802	−0.799008	−	0.601320i	$-0.794642\pi$
$751$	−43.7926	−1.59802	−0.799008	+	0.601320i	$0.794642\pi$
$752$	5.80990	0.211865
$753$	17.0792	0.622399
$754$	−1.43069	−0.0521027
$755$	−15.8117	−0.575446
$756$	−0.405586	−0.0147510
$757$	0.472591	0.0171766	0.00858830	−	0.999963i	$-0.497266\pi$
$757$	0.472591	0.0171766	0.00858830	+	0.999963i	$0.497266\pi$
$758$	15.7637	0.572563
$759$	3.95731	0.143641
$760$	−34.0929	−1.23668
$761$	31.2067	1.13124	0.565621	−	0.824665i	$-0.308636\pi$
$761$	31.2067	1.13124	0.565621	+	0.824665i	$0.308636\pi$
$762$	4.41470	0.159928
$763$	−1.44179	−0.0521965
$764$	−17.6976	−0.640276
$765$	4.34986	0.157269
$766$	−5.94836	−0.214923
$767$	−2.75815	−0.0995911
$768$	16.8923	0.609547
$769$	44.7549	1.61390	0.806951	−	0.590618i	$-0.201116\pi$
$769$	44.7549	1.61390	0.806951	+	0.590618i	$0.201116\pi$
$770$	1.33252	0.0480205
$771$	14.9303	0.537700
$772$	16.3996	0.590233
$773$	41.2095	1.48220	0.741101	−	0.671394i	$-0.234304\pi$
$773$	41.2095	1.48220	0.741101	+	0.671394i	$0.234304\pi$
$774$	10.1721	0.365630
$775$	7.38339	0.265219
$776$	39.3003	1.41080
$777$	0.776300	0.0278496
$778$	16.4977	0.591470
$779$	2.44478	0.0875934
$780$	−2.17761	−0.0779710
$781$	22.9834	0.822411
$782$	4.14811	0.148336
$783$	1.52189	0.0543878
$784$	3.58145	0.127909
$785$	8.77735	0.313277
$786$	−4.08548	−0.145724
$787$	24.8745	0.886680	0.443340	−	0.896354i	$-0.353794\pi$
$787$	24.8745	0.886680	0.443340	+	0.896354i	$0.353794\pi$
$788$	−10.8884	−0.387882
$789$	−24.9300	−0.887533
$790$	−14.7378	−0.524347
$791$	0.417832	0.0148564
$792$	−5.85824	−0.208163
$793$	−2.43812	−0.0865803
$794$	12.1720	0.431969
$795$	2.84408	0.100869
$796$	−24.8417	−0.880492
$797$	−9.33618	−0.330704	−0.165352	−	0.986235i	$-0.552876\pi$
$797$	−9.33618	−0.330704	−0.165352	+	0.986235i	$0.552876\pi$
$798$	−2.03767	−0.0721327
$799$	24.8425	0.878866
$800$	−6.41194	−0.226696
$801$	8.54917	0.302070
$802$	−23.9780	−0.846693
$803$	21.5341	0.759924
$804$	0.0805032	0.00283913
$805$	−1.40271	−0.0494390
$806$	−5.81177	−0.204711
$807$	5.86892	0.206596
$808$	18.6196	0.655036
$809$	37.5827	1.32134	0.660668	−	0.750678i	$-0.270273\pi$
$809$	37.5827	1.32134	0.660668	+	0.750678i	$0.270273\pi$
$810$	−1.83392	−0.0644375
$811$	−46.0354	−1.61652	−0.808260	−	0.588826i	$-0.799590\pi$
$811$	−46.0354	−1.61652	−0.808260	+	0.588826i	$0.799590\pi$
$812$	−0.617256	−0.0216614
$813$	−17.2185	−0.603880
$814$	4.01646	0.140777
$815$	26.4207	0.925475
$816$	−1.16275	−0.0407045
$817$	−64.5502	−2.25833
$818$	−15.8517	−0.554241
$819$	−0.363346	−0.0126963
$820$	−0.892424	−0.0311648
$821$	−3.55570	−0.124095	−0.0620473	−	0.998073i	$-0.519763\pi$
$821$	−3.55570	−0.124095	−0.0620473	+	0.998073i	$0.519763\pi$
$822$	−19.7104	−0.687478
$823$	4.62255	0.161132	0.0805660	−	0.996749i	$-0.474327\pi$
$823$	4.62255	0.161132	0.0805660	+	0.996749i	$0.474327\pi$
$824$	2.92952	0.102055
$825$	2.38826	0.0831485
$826$	0.942112	0.0327803
$827$	24.9504	0.867612	0.433806	−	0.901006i	$-0.357170\pi$
$827$	24.9504	0.867612	0.433806	+	0.901006i	$0.357170\pi$
$828$	2.20898	0.0767675
$829$	−18.3119	−0.636000	−0.318000	−	0.948091i	$-0.603011\pi$
$829$	−18.3119	−0.636000	−0.318000	+	0.948091i	$0.603011\pi$
$830$	−19.9671	−0.693067
$831$	10.4297	0.361804
$832$	6.09005	0.211135
$833$	15.3139	0.530596
$834$	−20.5302	−0.710904
$835$	11.3259	0.391950
$836$	13.3163	0.460553
$837$	6.18222	0.213689
$838$	3.77755	0.130493
$839$	19.2523	0.664663	0.332332	−	0.943163i	$-0.392165\pi$
$839$	19.2523	0.664663	0.332332	+	0.943163i	$0.392165\pi$
$840$	2.07651	0.0716465
$841$	−26.6839	−0.920133
$842$	−14.4433	−0.497750
$843$	−19.2605	−0.663366
$844$	−17.1158	−0.589151
$845$	−1.95082	−0.0671103
$846$	−10.4738	−0.360095
$847$	2.54382	0.0874067
$848$	−0.760246	−0.0261069
$849$	14.3040	0.490913
$850$	2.50341	0.0858663
$851$	−4.22804	−0.144935
$852$	12.8294	0.439529
$853$	−52.3913	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$853$	−52.3913	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$854$	0.832798	0.0284978
$855$	11.6377	0.398001
$856$	−11.1478	−0.381024
$857$	45.9744	1.57046	0.785228	−	0.619207i	$-0.212546\pi$
$857$	45.9744	1.57046	0.785228	+	0.619207i	$0.212546\pi$
$858$	−1.87990	−0.0641787
$859$	−13.0709	−0.445974	−0.222987	−	0.974821i	$-0.571581\pi$
$859$	−13.0709	−0.445974	−0.222987	+	0.974821i	$0.571581\pi$
$860$	23.5629	0.803488
$861$	−0.148906	−0.00507469
$862$	−20.0608	−0.683274
$863$	−41.9159	−1.42683	−0.713417	−	0.700740i	$-0.752853\pi$
$863$	−41.9159	−1.42683	−0.713417	+	0.700740i	$0.752853\pi$
$864$	−5.36882	−0.182651
$865$	19.2231	0.653606
$866$	−4.34156	−0.147532
$867$	12.0282	0.408499
$868$	−2.50743	−0.0851076
$869$	16.0702	0.545144
$870$	−2.79102	−0.0946246
$871$	0.0721191	0.00244366
$872$	−11.6246	−0.393660
$873$	−13.4153	−0.454038
$874$	11.0980	0.375394
$875$	−4.39066	−0.148431
$876$	12.0204	0.406133
$877$	−24.9212	−0.841531	−0.420765	−	0.907170i	$-0.638238\pi$
$877$	−24.9212	−0.841531	−0.420765	+	0.907170i	$0.638238\pi$
$878$	11.1312	0.375659
$879$	−12.3450	−0.416387
$880$	2.03432	0.0685768
$881$	−16.9630	−0.571497	−0.285749	−	0.958305i	$-0.592242\pi$
$881$	−16.9630	−0.571497	−0.285749	+	0.958305i	$0.592242\pi$
$882$	−6.45644	−0.217400
$883$	−9.83390	−0.330937	−0.165469	−	0.986215i	$-0.552914\pi$
$883$	−9.83390	−0.330937	−0.165469	+	0.986215i	$0.552914\pi$
$884$	2.48897	0.0837132
$885$	−5.38066	−0.180869
$886$	−11.0809	−0.372270
$887$	25.0602	0.841438	0.420719	−	0.907191i	$-0.361778\pi$
$887$	25.0602	0.841438	0.420719	+	0.907191i	$0.361778\pi$
$888$	6.25902	0.210039
$889$	1.70631	0.0572278
$890$	−15.6785	−0.525546
$891$	1.99973	0.0669933
$892$	−12.4051	−0.415353
$893$	66.4642	2.22414
$894$	−17.0635	−0.570687
$895$	7.74612	0.258924
$896$	1.82128	0.0608446
$897$	1.97893	0.0660744
$898$	1.46782	0.0489818
$899$	9.40864	0.313796
$900$	1.33313	0.0444378
$901$	−3.25073	−0.108298
$902$	−0.770416	−0.0256520
$903$	3.93159	0.130835
$904$	3.36882	0.112045
$905$	−22.1906	−0.737641
$906$	−7.61946	−0.253140
$907$	25.1854	0.836268	0.418134	−	0.908385i	$-0.362684\pi$
$907$	25.1854	0.836268	0.418134	+	0.908385i	$0.362684\pi$
$908$	−1.87817	−0.0623294
$909$	−6.35586	−0.210810
$910$	0.666349	0.0220893
$911$	16.1748	0.535896	0.267948	−	0.963433i	$-0.413655\pi$
$911$	16.1748	0.535896	0.267948	+	0.963433i	$0.413655\pi$
$912$	−3.11085	−0.103011
$913$	21.7722	0.720556
$914$	7.71325	0.255132
$915$	−4.75634	−0.157240
$916$	−24.2997	−0.802884
$917$	−1.57906	−0.0521453
$918$	2.09614	0.0691831
$919$	−46.6478	−1.53877	−0.769385	−	0.638786i	$-0.779437\pi$
$919$	−46.6478	−1.53877	−0.769385	+	0.638786i	$0.779437\pi$
$920$	−11.3095	−0.372864
$921$	27.0107	0.890033
$922$	10.9377	0.360214
$923$	11.4933	0.378306
$924$	−0.811061	−0.0266820
$925$	−2.55165	−0.0838976
$926$	28.6674	0.942070
$927$	−1.00000	−0.0328443
$928$	−8.17073	−0.268217
$929$	−41.9061	−1.37489	−0.687447	−	0.726235i	$-0.741269\pi$
$929$	−41.9061	−1.37489	−0.687447	+	0.726235i	$0.741269\pi$
$930$	−11.3377	−0.371779
$931$	40.9712	1.34278
$932$	−30.9859	−1.01498
$933$	30.3100	0.992305
$934$	−23.3347	−0.763535
$935$	8.69852	0.284472
$936$	−2.92952	−0.0957544
$937$	−19.0891	−0.623615	−0.311807	−	0.950145i	$-0.600934\pi$
$937$	−19.0891	−0.623615	−0.311807	+	0.950145i	$0.600934\pi$
$938$	−0.0246340	−0.000804328 0
$939$	−0.581827	−0.0189872
$940$	−24.2616	−0.791326
$941$	−48.5957	−1.58417	−0.792087	−	0.610408i	$-0.791006\pi$
$941$	−48.5957	−1.58417	−0.792087	+	0.610408i	$0.791006\pi$
$942$	4.22970	0.137811
$943$	0.810999	0.0264098
$944$	1.43830	0.0468126
$945$	−0.708823	−0.0230580
$946$	20.3415	0.661359
$947$	−24.1898	−0.786063	−0.393031	−	0.919525i	$-0.628574\pi$
$947$	−24.1898	−0.786063	−0.393031	+	0.919525i	$0.628574\pi$
$948$	8.97044	0.291346
$949$	10.7686	0.349562
$950$	6.69768	0.217301
$951$	10.0796	0.326854
$952$	−2.37342	−0.0769229
$953$	22.1662	0.718033	0.359017	−	0.933331i	$-0.383112\pi$
$953$	22.1662	0.718033	0.359017	+	0.933331i	$0.383112\pi$
$954$	1.37053	0.0443724
$955$	−30.9292	−1.00084
$956$	18.4330	0.596164
$957$	3.04335	0.0983777
$958$	31.7876	1.02701
$959$	−7.61818	−0.246004
$960$	11.8806	0.383445
$961$	7.21990	0.232900
$962$	2.00851	0.0647569
$963$	3.80533	0.122625
$964$	18.5013	0.595888
$965$	28.6607	0.922622
$966$	−0.675949	−0.0217483
$967$	10.2777	0.330510	0.165255	−	0.986251i	$-0.447155\pi$
$967$	10.2777	0.330510	0.165255	+	0.986251i	$0.447155\pi$
$968$	20.5099	0.659212
$969$	−13.3017	−0.427312
$970$	24.6026	0.789942
$971$	22.4892	0.721713	0.360856	−	0.932621i	$-0.382484\pi$
$971$	22.4892	0.721713	0.360856	+	0.932621i	$0.382484\pi$
$972$	1.11625	0.0358038
$973$	−7.93506	−0.254386
$974$	−13.3930	−0.429140
$975$	1.19429	0.0382480
$976$	1.27141	0.0406969
$977$	46.0872	1.47446	0.737231	−	0.675641i	$-0.236133\pi$
$977$	46.0872	1.47446	0.737231	+	0.675641i	$0.236133\pi$
$978$	12.7318	0.407118
$979$	17.0960	0.546391
$980$	−14.9558	−0.477745
$981$	3.96810	0.126692
$982$	13.5760	0.433226
$983$	−0.0339864	−0.00108400	−0.000541999	−	1.00000i	$-0.500173\pi$
$983$	−0.0339864	−0.00108400	−0.000541999		1.00000i	$0.500173\pi$
$984$	−1.20057	−0.0382728
$985$	−19.0291	−0.606316
$986$	3.19009	0.101593
$987$	−4.04817	−0.128855
$988$	6.65905	0.211853
$989$	−21.4130	−0.680895
$990$	−3.66735	−0.116556
$991$	−23.4112	−0.743681	−0.371841	−	0.928297i	$-0.621273\pi$
$991$	−23.4112	−0.743681	−0.371841	+	0.928297i	$0.621273\pi$
$992$	−33.1912	−1.05382
$993$	18.8863	0.599338
$994$	−3.92580	−0.124519
$995$	−43.4147	−1.37634
$996$	12.1533	0.385093
$997$	16.0225	0.507437	0.253718	−	0.967278i	$-0.418346\pi$
$997$	16.0225	0.507437	0.253718	+	0.967278i	$0.418346\pi$
$998$	−8.03378	−0.254305
$999$	−2.13653	−0.0675969

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.15	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+0.940078 q^{2} -1.00000 q^{3} -1.11625 q^{4} -1.95082 q^{5} -0.940078 q^{6} -0.363346 q^{7} -2.92952 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.940078 q^{2} -1.00000 q^{3} -1.11625 q^{4} -1.95082 q^{5} -0.940078 q^{6} -0.363346 q^{7} -2.92952 q^{8} +1.00000 q^{9} -1.83392 q^{10} +1.99973 q^{11} +1.11625 q^{12} +1.00000 q^{13} -0.341574 q^{14} +1.95082 q^{15} -0.521471 q^{16} -2.22976 q^{17} +0.940078 q^{18} -5.96553 q^{19} +2.17761 q^{20} +0.363346 q^{21} +1.87990 q^{22} -1.97893 q^{23} +2.92952 q^{24} -1.19429 q^{25} +0.940078 q^{26} -1.00000 q^{27} +0.405586 q^{28} -1.52189 q^{29} +1.83392 q^{30} -6.18222 q^{31} +5.36882 q^{32} -1.99973 q^{33} -2.09614 q^{34} +0.708823 q^{35} -1.11625 q^{36} +2.13653 q^{37} -5.60807 q^{38} -1.00000 q^{39} +5.71497 q^{40} -0.409818 q^{41} +0.341574 q^{42} +10.8205 q^{43} -2.23220 q^{44} -1.95082 q^{45} -1.86035 q^{46} -11.1414 q^{47} +0.521471 q^{48} -6.86798 q^{49} -1.12273 q^{50} +2.22976 q^{51} -1.11625 q^{52} +1.45789 q^{53} -0.940078 q^{54} -3.90111 q^{55} +1.06443 q^{56} +5.96553 q^{57} -1.43069 q^{58} -2.75815 q^{59} -2.17761 q^{60} -2.43812 q^{61} -5.81177 q^{62} -0.363346 q^{63} +6.09005 q^{64} -1.95082 q^{65} -1.87990 q^{66} +0.0721191 q^{67} +2.48897 q^{68} +1.97893 q^{69} +0.666349 q^{70} +11.4933 q^{71} -2.92952 q^{72} +10.7686 q^{73} +2.00851 q^{74} +1.19429 q^{75} +6.65905 q^{76} -0.726592 q^{77} -0.940078 q^{78} +8.03620 q^{79} +1.01730 q^{80} +1.00000 q^{81} -0.385261 q^{82} +10.8876 q^{83} -0.405586 q^{84} +4.34986 q^{85} +10.1721 q^{86} +1.52189 q^{87} -5.85824 q^{88} +8.54917 q^{89} -1.83392 q^{90} -0.363346 q^{91} +2.20898 q^{92} +6.18222 q^{93} -10.4738 q^{94} +11.6377 q^{95} -5.36882 q^{96} -13.4153 q^{97} -6.45644 q^{98} +1.99973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more