LMFDB - Embedded newform 1003.2.a.j.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.296053 q^{2} -0.947860 q^{3} -1.91235 q^{4} +1.42120 q^{5} -0.280617 q^{6} +3.81838 q^{7} -1.15826 q^{8} -2.10156 q^{9} +O(q^{10})$	\(q+0.296053 q^{2} -0.947860 q^{3} -1.91235 q^{4} +1.42120 q^{5} -0.280617 q^{6} +3.81838 q^{7} -1.15826 q^{8} -2.10156 q^{9} +0.420750 q^{10} -3.55592 q^{11} +1.81264 q^{12} +5.23855 q^{13} +1.13044 q^{14} -1.34710 q^{15} +3.48180 q^{16} -1.00000 q^{17} -0.622173 q^{18} -0.388534 q^{19} -2.71783 q^{20} -3.61929 q^{21} -1.05274 q^{22} +2.41064 q^{23} +1.09787 q^{24} -2.98020 q^{25} +1.55089 q^{26} +4.83557 q^{27} -7.30209 q^{28} +6.38404 q^{29} -0.398812 q^{30} -1.34241 q^{31} +3.34732 q^{32} +3.37051 q^{33} -0.296053 q^{34} +5.42667 q^{35} +4.01893 q^{36} -2.46164 q^{37} -0.115027 q^{38} -4.96542 q^{39} -1.64612 q^{40} +9.23475 q^{41} -1.07150 q^{42} -3.47368 q^{43} +6.80017 q^{44} -2.98673 q^{45} +0.713675 q^{46} +12.6147 q^{47} -3.30026 q^{48} +7.58002 q^{49} -0.882295 q^{50} +0.947860 q^{51} -10.0180 q^{52} +11.1597 q^{53} +1.43158 q^{54} -5.05366 q^{55} -4.42269 q^{56} +0.368276 q^{57} +1.89001 q^{58} +1.00000 q^{59} +2.57613 q^{60} +8.06140 q^{61} -0.397424 q^{62} -8.02456 q^{63} -5.97261 q^{64} +7.44502 q^{65} +0.997850 q^{66} -0.981593 q^{67} +1.91235 q^{68} -2.28495 q^{69} +1.60658 q^{70} +6.59321 q^{71} +2.43416 q^{72} -10.9997 q^{73} -0.728775 q^{74} +2.82481 q^{75} +0.743015 q^{76} -13.5778 q^{77} -1.47003 q^{78} +16.1125 q^{79} +4.94833 q^{80} +1.72124 q^{81} +2.73397 q^{82} -7.68913 q^{83} +6.92136 q^{84} -1.42120 q^{85} -1.02839 q^{86} -6.05117 q^{87} +4.11869 q^{88} -1.55143 q^{89} -0.884231 q^{90} +20.0028 q^{91} -4.60998 q^{92} +1.27242 q^{93} +3.73463 q^{94} -0.552184 q^{95} -3.17279 q^{96} +7.52247 q^{97} +2.24409 q^{98} +7.47298 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * 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 $

$2$	0.296053	0.209341	0.104670	−	0.994507i	$-0.466621\pi$
$2$	0.296053	0.209341	0.104670	+	0.994507i	$0.466621\pi$
$3$	−0.947860	−0.547247	−0.273624	−	0.961837i	$-0.588222\pi$
$3$	−0.947860	−0.547247	−0.273624	+	0.961837i	$0.588222\pi$
$4$	−1.91235	−0.956176
$5$	1.42120	0.635579	0.317790	−	0.948161i	$-0.397059\pi$
$5$	1.42120	0.635579	0.317790	+	0.948161i	$0.397059\pi$
$6$	−0.280617	−0.114561
$7$	3.81838	1.44321	0.721606	−	0.692304i	$-0.243404\pi$
$7$	3.81838	1.44321	0.721606	+	0.692304i	$0.243404\pi$
$8$	−1.15826	−0.409508
$9$	−2.10156	−0.700520
$10$	0.420750	0.133053
$11$	−3.55592	−1.07215	−0.536075	−	0.844171i	$-0.680093\pi$
$11$	−3.55592	−1.07215	−0.536075	+	0.844171i	$0.680093\pi$
$12$	1.81264	0.523265
$13$	5.23855	1.45291	0.726457	−	0.687212i	$-0.241166\pi$
$13$	5.23855	1.45291	0.726457	+	0.687212i	$0.241166\pi$
$14$	1.13044	0.302123
$15$	−1.34710	−0.347819
$16$	3.48180	0.870450
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.622173	−0.146648
$19$	−0.388534	−0.0891359	−0.0445679	−	0.999006i	$-0.514191\pi$
$19$	−0.388534	−0.0891359	−0.0445679	+	0.999006i	$0.514191\pi$
$20$	−2.71783	−0.607726
$21$	−3.61929	−0.789794
$22$	−1.05274	−0.224445
$23$	2.41064	0.502652	0.251326	−	0.967902i	$-0.419133\pi$
$23$	2.41064	0.502652	0.251326	+	0.967902i	$0.419133\pi$
$24$	1.09787	0.224102
$25$	−2.98020	−0.596039
$26$	1.55089	0.304154
$27$	4.83557	0.930605
$28$	−7.30209	−1.37997
$29$	6.38404	1.18549	0.592743	−	0.805392i	$-0.298045\pi$
$29$	6.38404	1.18549	0.592743	+	0.805392i	$0.298045\pi$
$30$	−0.398812	−0.0728128
$31$	−1.34241	−0.241104	−0.120552	−	0.992707i	$-0.538466\pi$
$31$	−1.34241	−0.241104	−0.120552	+	0.992707i	$0.538466\pi$
$32$	3.34732	0.591729
$33$	3.37051	0.586731
$34$	−0.296053	−0.0507726
$35$	5.42667	0.917275
$36$	4.01893	0.669821
$37$	−2.46164	−0.404691	−0.202345	−	0.979314i	$-0.564856\pi$
$37$	−2.46164	−0.404691	−0.202345	+	0.979314i	$0.564856\pi$
$38$	−0.115027	−0.0186598
$39$	−4.96542	−0.795103
$40$	−1.64612	−0.260275
$41$	9.23475	1.44223	0.721113	−	0.692818i	$-0.243631\pi$
$41$	9.23475	1.44223	0.721113	+	0.692818i	$0.243631\pi$
$42$	−1.07150	−0.165336
$43$	−3.47368	−0.529731	−0.264866	−	0.964285i	$-0.585328\pi$
$43$	−3.47368	−0.529731	−0.264866	+	0.964285i	$0.585328\pi$
$44$	6.80017	1.02516
$45$	−2.98673	−0.445236
$46$	0.713675	0.105226
$47$	12.6147	1.84005	0.920024	−	0.391861i	$-0.128169\pi$
$47$	12.6147	1.84005	0.920024	+	0.391861i	$0.128169\pi$
$48$	−3.30026	−0.476351
$49$	7.58002	1.08286
$50$	−0.882295	−0.124775
$51$	0.947860	0.132727
$52$	−10.0180	−1.38924
$53$	11.1597	1.53291	0.766454	−	0.642299i	$-0.222019\pi$
$53$	11.1597	1.53291	0.766454	+	0.642299i	$0.222019\pi$
$54$	1.43158	0.194814
$55$	−5.05366	−0.681436
$56$	−4.42269	−0.591006
$57$	0.368276	0.0487794
$58$	1.89001	0.248171
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.57613	0.332576
$61$	8.06140	1.03216	0.516078	−	0.856542i	$-0.327391\pi$
$61$	8.06140	1.03216	0.516078	+	0.856542i	$0.327391\pi$
$62$	−0.397424	−0.0504729
$63$	−8.02456	−1.01100
$64$	−5.97261	−0.746577
$65$	7.44502	0.923441
$66$	0.997850	0.122827
$67$	−0.981593	−0.119921	−0.0599603	−	0.998201i	$-0.519097\pi$
$67$	−0.981593	−0.119921	−0.0599603	+	0.998201i	$0.519097\pi$
$68$	1.91235	0.231907
$69$	−2.28495	−0.275075
$70$	1.60658	0.192023
$71$	6.59321	0.782470	0.391235	−	0.920291i	$-0.372048\pi$
$71$	6.59321	0.782470	0.391235	+	0.920291i	$0.372048\pi$
$72$	2.43416	0.286868
$73$	−10.9997	−1.28742	−0.643709	−	0.765270i	$-0.722605\pi$
$73$	−10.9997	−1.28742	−0.643709	+	0.765270i	$0.722605\pi$
$74$	−0.728775	−0.0847184
$75$	2.82481	0.326181
$76$	0.743015	0.0852296
$77$	−13.5778	−1.54734
$78$	−1.47003	−0.166448
$79$	16.1125	1.81280	0.906398	−	0.422425i	$-0.138821\pi$
$79$	16.1125	1.81280	0.906398	+	0.422425i	$0.138821\pi$
$80$	4.94833	0.553240
$81$	1.72124	0.191249
$82$	2.73397	0.301917
$83$	−7.68913	−0.843991	−0.421996	−	0.906598i	$-0.638670\pi$
$83$	−7.68913	−0.843991	−0.421996	+	0.906598i	$0.638670\pi$
$84$	6.92136	0.755182
$85$	−1.42120	−0.154151
$86$	−1.02839	−0.110894
$87$	−6.05117	−0.648754
$88$	4.11869	0.439053
$89$	−1.55143	−0.164451	−0.0822257	−	0.996614i	$-0.526203\pi$
$89$	−1.55143	−0.164451	−0.0822257	+	0.996614i	$0.526203\pi$
$90$	−0.884231	−0.0932061
$91$	20.0028	2.09686
$92$	−4.60998	−0.480624
$93$	1.27242	0.131943
$94$	3.73463	0.385197
$95$	−0.552184	−0.0566529
$96$	−3.17279	−0.323822
$97$	7.52247	0.763791	0.381895	−	0.924206i	$-0.375271\pi$
$97$	7.52247	0.763791	0.381895	+	0.924206i	$0.375271\pi$
$98$	2.24409	0.226687
$99$	7.47298	0.751062
$100$	5.69919	0.569919
$101$	6.11666	0.608630	0.304315	−	0.952571i	$-0.401572\pi$
$101$	6.11666	0.608630	0.304315	+	0.952571i	$0.401572\pi$
$102$	0.280617	0.0277852
$103$	−17.7968	−1.75357	−0.876787	−	0.480878i	$-0.840318\pi$
$103$	−17.7968	−1.75357	−0.876787	+	0.480878i	$0.840318\pi$
$104$	−6.06762	−0.594979
$105$	−5.14373	−0.501977
$106$	3.30387	0.320900
$107$	14.6193	1.41330	0.706650	−	0.707564i	$-0.250206\pi$
$107$	14.6193	1.41330	0.706650	+	0.707564i	$0.250206\pi$
$108$	−9.24731	−0.889823
$109$	5.76998	0.552664	0.276332	−	0.961062i	$-0.410881\pi$
$109$	5.76998	0.552664	0.276332	+	0.961062i	$0.410881\pi$
$110$	−1.49615	−0.142652
$111$	2.33329	0.221466
$112$	13.2948	1.25624
$113$	7.07250	0.665325	0.332662	−	0.943046i	$-0.392053\pi$
$113$	7.07250	0.665325	0.332662	+	0.943046i	$0.392053\pi$
$114$	0.109029	0.0102115
$115$	3.42599	0.319475
$116$	−12.2085	−1.13353
$117$	−11.0091	−1.01780
$118$	0.296053	0.0272539
$119$	−3.81838	−0.350030
$120$	1.56029	0.142435
$121$	1.64454	0.149504
$122$	2.38660	0.216073
$123$	−8.75325	−0.789254
$124$	2.56716	0.230538
$125$	−11.3414	−1.01441
$126$	−2.37569	−0.211643
$127$	−8.53079	−0.756985	−0.378493	−	0.925604i	$-0.623557\pi$
$127$	−8.53079	−0.756985	−0.378493	+	0.925604i	$0.623557\pi$
$128$	−8.46285	−0.748018
$129$	3.29256	0.289894
$130$	2.20412	0.193314
$131$	−16.0888	−1.40568	−0.702841	−	0.711347i	$-0.748086\pi$
$131$	−16.0888	−1.40568	−0.702841	+	0.711347i	$0.748086\pi$
$132$	−6.44561	−0.561018
$133$	−1.48357	−0.128642
$134$	−0.290603	−0.0251043
$135$	6.87230	0.591473
$136$	1.15826	0.0993202
$137$	3.71700	0.317565	0.158782	−	0.987314i	$-0.449243\pi$
$137$	3.71700	0.317565	0.158782	+	0.987314i	$0.449243\pi$
$138$	−0.676464	−0.0575845
$139$	−5.82166	−0.493787	−0.246893	−	0.969043i	$-0.579410\pi$
$139$	−5.82166	−0.493787	−0.246893	+	0.969043i	$0.579410\pi$
$140$	−10.3777	−0.877077
$141$	−11.9570	−1.00696
$142$	1.95194	0.163803
$143$	−18.6279	−1.55774
$144$	−7.31721	−0.609768
$145$	9.07298	0.753470
$146$	−3.25649	−0.269509
$147$	−7.18480	−0.592593
$148$	4.70752	0.386956
$149$	−12.0405	−0.986400	−0.493200	−	0.869916i	$-0.664173\pi$
$149$	−12.0405	−0.986400	−0.493200	+	0.869916i	$0.664173\pi$
$150$	0.836293	0.0682830
$151$	−11.6734	−0.949964	−0.474982	−	0.879996i	$-0.657545\pi$
$151$	−11.6734	−0.949964	−0.474982	+	0.879996i	$0.657545\pi$
$152$	0.450025	0.0365018
$153$	2.10156	0.169901
$154$	−4.01976	−0.323921
$155$	−1.90783	−0.153241
$156$	9.49563	0.760259
$157$	−5.56664	−0.444266	−0.222133	−	0.975016i	$-0.571302\pi$
$157$	−5.56664	−0.444266	−0.222133	+	0.975016i	$0.571302\pi$
$158$	4.77015	0.379492
$159$	−10.5779	−0.838880
$160$	4.75721	0.376090
$161$	9.20472	0.725434
$162$	0.509578	0.0400362
$163$	−21.9040	−1.71566	−0.857828	−	0.513937i	$-0.828187\pi$
$163$	−21.9040	−1.71566	−0.857828	+	0.513937i	$0.828187\pi$
$164$	−17.6601	−1.37902
$165$	4.79017	0.372914
$166$	−2.27639	−0.176682
$167$	−16.1813	−1.25214	−0.626072	−	0.779765i	$-0.715339\pi$
$167$	−16.1813	−1.25214	−0.626072	+	0.779765i	$0.715339\pi$
$168$	4.19209	0.323427
$169$	14.4424	1.11096
$170$	−0.420750	−0.0322700
$171$	0.816529	0.0624415
$172$	6.64290	0.506517
$173$	9.83560	0.747787	0.373893	−	0.927472i	$-0.378023\pi$
$173$	9.83560	0.747787	0.373893	+	0.927472i	$0.378023\pi$
$174$	−1.79147	−0.135811
$175$	−11.3795	−0.860211
$176$	−12.3810	−0.933252
$177$	−0.947860	−0.0712455
$178$	−0.459305	−0.0344264
$179$	−7.64698	−0.571562	−0.285781	−	0.958295i	$-0.592253\pi$
$179$	−7.64698	−0.571562	−0.285781	+	0.958295i	$0.592253\pi$
$180$	5.71169	0.425724
$181$	−21.9309	−1.63011	−0.815056	−	0.579382i	$-0.803294\pi$
$181$	−21.9309	−1.63011	−0.815056	+	0.579382i	$0.803294\pi$
$182$	5.92188	0.438959
$183$	−7.64108	−0.564845
$184$	−2.79215	−0.205840
$185$	−3.49848	−0.257213
$186$	0.376702	0.0276212
$187$	3.55592	0.260034
$188$	−24.1238	−1.75941
$189$	18.4640	1.34306
$190$	−0.163476	−0.0118598
$191$	15.7257	1.13787	0.568934	−	0.822383i	$-0.307356\pi$
$191$	15.7257	1.13787	0.568934	+	0.822383i	$0.307356\pi$
$192$	5.66120	0.408562
$193$	−11.1353	−0.801537	−0.400768	−	0.916179i	$-0.631257\pi$
$193$	−11.1353	−0.801537	−0.400768	+	0.916179i	$0.631257\pi$
$194$	2.22705	0.159893
$195$	−7.05684	−0.505351
$196$	−14.4957	−1.03541
$197$	13.9133	0.991281	0.495640	−	0.868528i	$-0.334933\pi$
$197$	13.9133	0.991281	0.495640	+	0.868528i	$0.334933\pi$
$198$	2.21240	0.157228
$199$	12.3544	0.875781	0.437890	−	0.899028i	$-0.355726\pi$
$199$	12.3544	0.875781	0.437890	+	0.899028i	$0.355726\pi$
$200$	3.45185	0.244083
$201$	0.930413	0.0656263
$202$	1.81085	0.127411
$203$	24.3767	1.71091
$204$	−1.81264	−0.126910
$205$	13.1244	0.916649
$206$	−5.26880	−0.367095
$207$	−5.06610	−0.352118
$208$	18.2396	1.26469
$209$	1.38160	0.0955670
$210$	−1.52282	−0.105084
$211$	0.450450	0.0310103	0.0155051	−	0.999880i	$-0.495064\pi$
$211$	0.450450	0.0310103	0.0155051	+	0.999880i	$0.495064\pi$
$212$	−21.3414	−1.46573
$213$	−6.24945	−0.428205
$214$	4.32808	0.295861
$215$	−4.93679	−0.336686
$216$	−5.60086	−0.381090
$217$	−5.12583	−0.347964
$218$	1.70822	0.115695
$219$	10.4262	0.704537
$220$	9.66439	0.651573
$221$	−5.23855	−0.352383
$222$	0.690777	0.0463619
$223$	−5.75777	−0.385569	−0.192784	−	0.981241i	$-0.561752\pi$
$223$	−5.75777	−0.385569	−0.192784	+	0.981241i	$0.561752\pi$
$224$	12.7813	0.853990
$225$	6.26306	0.417538
$226$	2.09383	0.139280
$227$	28.0315	1.86051	0.930257	−	0.366910i	$-0.119584\pi$
$227$	28.0315	1.86051	0.930257	+	0.366910i	$0.119584\pi$
$228$	−0.704274	−0.0466417
$229$	27.1620	1.79491	0.897457	−	0.441102i	$-0.145412\pi$
$229$	27.1620	1.79491	0.897457	+	0.441102i	$0.145412\pi$
$230$	1.01427	0.0668792
$231$	12.8699	0.846777
$232$	−7.39439	−0.485466
$233$	−8.16910	−0.535176	−0.267588	−	0.963533i	$-0.586227\pi$
$233$	−8.16910	−0.535176	−0.267588	+	0.963533i	$0.586227\pi$
$234$	−3.25929	−0.213066
$235$	17.9280	1.16950
$236$	−1.91235	−0.124484
$237$	−15.2724	−0.992048
$238$	−1.13044	−0.0732757
$239$	−1.61570	−0.104511	−0.0522554	−	0.998634i	$-0.516641\pi$
$239$	−1.61570	−0.104511	−0.0522554	+	0.998634i	$0.516641\pi$
$240$	−4.69032	−0.302759
$241$	−2.24437	−0.144573	−0.0722863	−	0.997384i	$-0.523030\pi$
$241$	−2.24437	−0.144573	−0.0722863	+	0.997384i	$0.523030\pi$
$242$	0.486872	0.0312973
$243$	−16.1382	−1.03527
$244$	−15.4162	−0.986923
$245$	10.7727	0.688243
$246$	−2.59143	−0.165223
$247$	−2.03536	−0.129507
$248$	1.55486	0.0987339
$249$	7.28822	0.461872
$250$	−3.35766	−0.212357
$251$	4.58070	0.289131	0.144566	−	0.989495i	$-0.453822\pi$
$251$	4.58070	0.289131	0.144566	+	0.989495i	$0.453822\pi$
$252$	15.3458	0.966693
$253$	−8.57202	−0.538918
$254$	−2.52556	−0.158468
$255$	1.34710	0.0843585
$256$	9.43978	0.589986
$257$	2.51429	0.156837	0.0784185	−	0.996921i	$-0.475013\pi$
$257$	2.51429	0.156837	0.0784185	+	0.996921i	$0.475013\pi$
$258$	0.974773	0.0606867
$259$	−9.39947	−0.584055
$260$	−14.2375	−0.882973
$261$	−13.4164	−0.830457
$262$	−4.76313	−0.294267
$263$	−13.4994	−0.832407	−0.416204	−	0.909271i	$-0.636640\pi$
$263$	−13.4994	−0.832407	−0.416204	+	0.909271i	$0.636640\pi$
$264$	−3.90394	−0.240271
$265$	15.8602	0.974284
$266$	−0.439216	−0.0269300
$267$	1.47054	0.0899956
$268$	1.87715	0.114665
$269$	−4.89750	−0.298606	−0.149303	−	0.988791i	$-0.547703\pi$
$269$	−4.89750	−0.298606	−0.149303	+	0.988791i	$0.547703\pi$
$270$	2.03456	0.123820
$271$	−8.96041	−0.544306	−0.272153	−	0.962254i	$-0.587736\pi$
$271$	−8.96041	−0.544306	−0.272153	+	0.962254i	$0.587736\pi$
$272$	−3.48180	−0.211115
$273$	−18.9598	−1.14750
$274$	1.10043	0.0664793
$275$	10.5973	0.639043
$276$	4.36962	0.263020
$277$	−8.83610	−0.530910	−0.265455	−	0.964123i	$-0.585522\pi$
$277$	−8.83610	−0.530910	−0.265455	+	0.964123i	$0.585522\pi$
$278$	−1.72352	−0.103370
$279$	2.82115	0.168898
$280$	−6.28552	−0.375631
$281$	29.1872	1.74116	0.870582	−	0.492024i	$-0.163743\pi$
$281$	29.1872	1.74116	0.870582	+	0.492024i	$0.163743\pi$
$282$	−3.53991	−0.210798
$283$	−16.7481	−0.995569	−0.497784	−	0.867301i	$-0.665853\pi$
$283$	−16.7481	−0.995569	−0.497784	+	0.867301i	$0.665853\pi$
$284$	−12.6085	−0.748180
$285$	0.523394	0.0310032
$286$	−5.51483	−0.326099
$287$	35.2618	2.08144
$288$	−7.03460	−0.414518
$289$	1.00000	0.0588235
$290$	2.68608	0.157732
$291$	−7.13025	−0.417983
$292$	21.0353	1.23100
$293$	9.44930	0.552034	0.276017	−	0.961153i	$-0.410985\pi$
$293$	9.44930	0.552034	0.276017	+	0.961153i	$0.410985\pi$
$294$	−2.12708	−0.124054
$295$	1.42120	0.0827454
$296$	2.85122	0.165724
$297$	−17.1949	−0.997748
$298$	−3.56464	−0.206494
$299$	12.6282	0.730310
$300$	−5.40203	−0.311886
$301$	−13.2638	−0.764515
$302$	−3.45593	−0.198866
$303$	−5.79774	−0.333071
$304$	−1.35280	−0.0775883
$305$	11.4568	0.656017
$306$	0.622173	0.0355673
$307$	28.0772	1.60245	0.801225	−	0.598363i	$-0.204182\pi$
$307$	28.0772	1.60245	0.801225	+	0.598363i	$0.204182\pi$
$308$	25.9656	1.47953
$309$	16.8689	0.959639
$310$	−0.564818	−0.0320795
$311$	−6.22922	−0.353227	−0.176613	−	0.984280i	$-0.556514\pi$
$311$	−6.22922	−0.353227	−0.176613	+	0.984280i	$0.556514\pi$
$312$	5.75126	0.325601
$313$	−25.0927	−1.41832	−0.709161	−	0.705047i	$-0.750926\pi$
$313$	−25.0927	−1.41832	−0.709161	+	0.705047i	$0.750926\pi$
$314$	−1.64802	−0.0930031
$315$	−11.4045	−0.642570
$316$	−30.8128	−1.73335
$317$	−8.99180	−0.505030	−0.252515	−	0.967593i	$-0.581258\pi$
$317$	−8.99180	−0.505030	−0.252515	+	0.967593i	$0.581258\pi$
$318$	−3.13161	−0.175612
$319$	−22.7011	−1.27102
$320$	−8.48827	−0.474509
$321$	−13.8570	−0.773424
$322$	2.72508	0.151863
$323$	0.388534	0.0216186
$324$	−3.29162	−0.182868
$325$	−15.6119	−0.865993
$326$	−6.48475	−0.359157
$327$	−5.46914	−0.302444
$328$	−10.6963	−0.590603
$329$	48.1679	2.65558
$330$	1.41814	0.0780662
$331$	8.28485	0.455377	0.227688	−	0.973734i	$-0.426883\pi$
$331$	8.28485	0.455377	0.227688	+	0.973734i	$0.426883\pi$
$332$	14.7043	0.807004
$333$	5.17328	0.283494
$334$	−4.79051	−0.262125
$335$	−1.39504	−0.0762191
$336$	−12.6016	−0.687476
$337$	36.3195	1.97845	0.989224	−	0.146408i	$-0.0467713\pi$
$337$	36.3195	1.97845	0.989224	+	0.146408i	$0.0467713\pi$
$338$	4.27573	0.232569
$339$	−6.70374	−0.364097
$340$	2.71783	0.147395
$341$	4.77349	0.258499
$342$	0.241736	0.0130716
$343$	2.21475	0.119585
$344$	4.02344	0.216929
$345$	−3.24736	−0.174832
$346$	2.91186	0.156542
$347$	−22.0171	−1.18194	−0.590970	−	0.806693i	$-0.701255\pi$
$347$	−22.0171	−1.18194	−0.590970	+	0.806693i	$0.701255\pi$
$348$	11.5720	0.620323
$349$	−13.2291	−0.708135	−0.354068	−	0.935220i	$-0.615202\pi$
$349$	−13.2291	−0.708135	−0.354068	+	0.935220i	$0.615202\pi$
$350$	−3.36894	−0.180077
$351$	25.3314	1.35209
$352$	−11.9028	−0.634421
$353$	−24.6644	−1.31275	−0.656376	−	0.754434i	$-0.727911\pi$
$353$	−24.6644	−1.31275	−0.656376	+	0.754434i	$0.727911\pi$
$354$	−0.280617	−0.0149146
$355$	9.37026	0.497322
$356$	2.96688	0.157244
$357$	3.61929	0.191553
$358$	−2.26391	−0.119651
$359$	−4.51263	−0.238167	−0.119084	−	0.992884i	$-0.537996\pi$
$359$	−4.51263	−0.238167	−0.119084	+	0.992884i	$0.537996\pi$
$360$	3.45942	0.182328
$361$	−18.8490	−0.992055
$362$	−6.49271	−0.341249
$363$	−1.55880	−0.0818157
$364$	−38.2524	−2.00497
$365$	−15.6328	−0.818256
$366$	−2.26216	−0.118245
$367$	−14.4477	−0.754162	−0.377081	−	0.926180i	$-0.623072\pi$
$367$	−14.4477	−0.754162	−0.377081	+	0.926180i	$0.623072\pi$
$368$	8.39335	0.437533
$369$	−19.4074	−1.01031
$370$	−1.03573	−0.0538452
$371$	42.6121	2.21231
$372$	−2.43331	−0.126161
$373$	38.2946	1.98282	0.991411	−	0.130786i	$-0.0417500\pi$
$373$	38.2946	1.98282	0.991411	+	0.130786i	$0.0417500\pi$
$374$	1.05274	0.0544358
$375$	10.7501	0.555133
$376$	−14.6112	−0.753514
$377$	33.4431	1.72241
$378$	5.46633	0.281158
$379$	5.23823	0.269070	0.134535	−	0.990909i	$-0.457046\pi$
$379$	5.23823	0.269070	0.134535	+	0.990909i	$0.457046\pi$
$380$	1.05597	0.0541702
$381$	8.08600	0.414258
$382$	4.65563	0.238203
$383$	−12.2986	−0.628430	−0.314215	−	0.949352i	$-0.601741\pi$
$383$	−12.2986	−0.628430	−0.314215	+	0.949352i	$0.601741\pi$
$384$	8.02160	0.409351
$385$	−19.2968	−0.983456
$386$	−3.29664	−0.167794
$387$	7.30015	0.371088
$388$	−14.3856	−0.730319
$389$	−9.01051	−0.456851	−0.228425	−	0.973561i	$-0.573358\pi$
$389$	−9.01051	−0.456851	−0.228425	+	0.973561i	$0.573358\pi$
$390$	−2.08920	−0.105791
$391$	−2.41064	−0.121911
$392$	−8.77966	−0.443440
$393$	15.2499	0.769256
$394$	4.11907	0.207516
$395$	22.8990	1.15218
$396$	−14.2910	−0.718148
$397$	20.1455	1.01107	0.505536	−	0.862805i	$-0.331295\pi$
$397$	20.1455	1.01107	0.505536	+	0.862805i	$0.331295\pi$
$398$	3.65756	0.183337
$399$	1.40622	0.0703990
$400$	−10.3764	−0.518822
$401$	20.4530	1.02138	0.510688	−	0.859766i	$-0.329391\pi$
$401$	20.4530	1.02138	0.510688	+	0.859766i	$0.329391\pi$
$402$	0.275451	0.0137383
$403$	−7.03228	−0.350303
$404$	−11.6972	−0.581958
$405$	2.44622	0.121554
$406$	7.21678	0.358163
$407$	8.75338	0.433889
$408$	−1.09787	−0.0543527
$409$	34.9782	1.72956	0.864780	−	0.502151i	$-0.167458\pi$
$409$	34.9782	1.72956	0.864780	+	0.502151i	$0.167458\pi$
$410$	3.88552	0.191892
$411$	−3.52319	−0.173786
$412$	34.0338	1.67673
$413$	3.81838	0.187890
$414$	−1.49983	−0.0737127
$415$	−10.9278	−0.536423
$416$	17.5351	0.859730
$417$	5.51812	0.270223
$418$	0.409025	0.0200061
$419$	−23.6687	−1.15629	−0.578146	−	0.815933i	$-0.696224\pi$
$419$	−23.6687	−1.15629	−0.578146	+	0.815933i	$0.696224\pi$
$420$	9.83662	0.479978
$421$	−21.4059	−1.04326	−0.521631	−	0.853171i	$-0.674676\pi$
$421$	−21.4059	−1.04326	−0.521631	+	0.853171i	$0.674676\pi$
$422$	0.133357	0.00649172
$423$	−26.5106	−1.28899
$424$	−12.9259	−0.627738
$425$	2.98020	0.144561
$426$	−1.85017	−0.0896408
$427$	30.7815	1.48962
$428$	−27.9572	−1.35136
$429$	17.6566	0.852469
$430$	−1.46155	−0.0704822
$431$	−17.7515	−0.855059	−0.427529	−	0.904001i	$-0.640616\pi$
$431$	−17.7515	−0.855059	−0.427529	+	0.904001i	$0.640616\pi$
$432$	16.8365	0.810045
$433$	32.0246	1.53900	0.769501	−	0.638645i	$-0.220505\pi$
$433$	32.0246	1.53900	0.769501	+	0.638645i	$0.220505\pi$
$434$	−1.51752	−0.0728431
$435$	−8.59992	−0.412334
$436$	−11.0342	−0.528444
$437$	−0.936615	−0.0448043
$438$	3.08670	0.147488
$439$	−14.9020	−0.711232	−0.355616	−	0.934632i	$-0.615729\pi$
$439$	−14.9020	−0.711232	−0.355616	+	0.934632i	$0.615729\pi$
$440$	5.85347	0.279053
$441$	−15.9299	−0.758566
$442$	−1.55089	−0.0737682
$443$	13.9905	0.664706	0.332353	−	0.943155i	$-0.392157\pi$
$443$	13.9905	0.664706	0.332353	+	0.943155i	$0.392157\pi$
$444$	−4.46207	−0.211761
$445$	−2.20489	−0.104522
$446$	−1.70460	−0.0807153
$447$	11.4128	0.539805
$448$	−22.8057	−1.07747
$449$	14.9546	0.705753	0.352876	−	0.935670i	$-0.385204\pi$
$449$	14.9546	0.705753	0.352876	+	0.935670i	$0.385204\pi$
$450$	1.85420	0.0874077
$451$	−32.8380	−1.54628
$452$	−13.5251	−0.636168
$453$	11.0647	0.519865
$454$	8.29879	0.389482
$455$	28.4279	1.33272
$456$	−0.426561	−0.0199755
$457$	23.8240	1.11444	0.557220	−	0.830365i	$-0.311868\pi$
$457$	23.8240	1.11444	0.557220	+	0.830365i	$0.311868\pi$
$458$	8.04138	0.375749
$459$	−4.83557	−0.225705
$460$	−6.55170	−0.305475
$461$	−2.48351	−0.115668	−0.0578342	−	0.998326i	$-0.518419\pi$
$461$	−2.48351	−0.115668	−0.0578342	+	0.998326i	$0.518419\pi$
$462$	3.81017	0.177265
$463$	−32.0561	−1.48977	−0.744886	−	0.667192i	$-0.767496\pi$
$463$	−32.0561	−1.48977	−0.744886	+	0.667192i	$0.767496\pi$
$464$	22.2279	1.03191
$465$	1.80836	0.0838605
$466$	−2.41849	−0.112034
$467$	7.32665	0.339037	0.169518	−	0.985527i	$-0.445779\pi$
$467$	7.32665	0.339037	0.169518	+	0.985527i	$0.445779\pi$
$468$	21.0534	0.973192
$469$	−3.74810	−0.173071
$470$	5.30765	0.244823
$471$	5.27640	0.243124
$472$	−1.15826	−0.0533134
$473$	12.3521	0.567951
$474$	−4.52143	−0.207676
$475$	1.15791	0.0531285
$476$	7.30209	0.334691
$477$	−23.4529	−1.07383
$478$	−0.478332	−0.0218784
$479$	−13.4422	−0.614188	−0.307094	−	0.951679i	$-0.599357\pi$
$479$	−13.4422	−0.614188	−0.307094	+	0.951679i	$0.599357\pi$
$480$	−4.50917	−0.205814
$481$	−12.8954	−0.587981
$482$	−0.664452	−0.0302649
$483$	−8.72479	−0.396992
$484$	−3.14495	−0.142952
$485$	10.6909	0.485450
$486$	−4.77776	−0.216724
$487$	−17.1106	−0.775355	−0.387677	−	0.921795i	$-0.626723\pi$
$487$	−17.1106	−0.775355	−0.387677	+	0.921795i	$0.626723\pi$
$488$	−9.33722	−0.422676
$489$	20.7620	0.938889
$490$	3.18929	0.144078
$491$	−20.8748	−0.942069	−0.471034	−	0.882115i	$-0.656119\pi$
$491$	−20.8748	−0.942069	−0.471034	+	0.882115i	$0.656119\pi$
$492$	16.7393	0.754666
$493$	−6.38404	−0.287522
$494$	−0.602573	−0.0271111
$495$	10.6206	0.477360
$496$	−4.67400	−0.209869
$497$	25.1754	1.12927
$498$	2.15770	0.0966887
$499$	26.8854	1.20356	0.601778	−	0.798663i	$-0.294459\pi$
$499$	26.8854	1.20356	0.601778	+	0.798663i	$0.294459\pi$
$500$	21.6888	0.969954
$501$	15.3376	0.685233
$502$	1.35613	0.0605270
$503$	−31.9972	−1.42669	−0.713343	−	0.700815i	$-0.752820\pi$
$503$	−31.9972	−1.42669	−0.713343	+	0.700815i	$0.752820\pi$
$504$	9.29455	0.414012
$505$	8.69298	0.386833
$506$	−2.53777	−0.112818
$507$	−13.6894	−0.607968
$508$	16.3139	0.723811
$509$	−10.9584	−0.485725	−0.242862	−	0.970061i	$-0.578086\pi$
$509$	−10.9584	−0.485725	−0.242862	+	0.970061i	$0.578086\pi$
$510$	0.398812	0.0176597
$511$	−42.0011	−1.85802
$512$	19.7204	0.871526
$513$	−1.87878	−0.0829503
$514$	0.744362	0.0328324
$515$	−25.2928	−1.11454
$516$	−6.29654	−0.277190
$517$	−44.8570	−1.97281
$518$	−2.78274	−0.122267
$519$	−9.32277	−0.409224
$520$	−8.62329	−0.378156
$521$	−19.4389	−0.851633	−0.425817	−	0.904809i	$-0.640013\pi$
$521$	−19.4389	−0.851633	−0.425817	+	0.904809i	$0.640013\pi$
$522$	−3.97197	−0.173849
$523$	15.2032	0.664790	0.332395	−	0.943140i	$-0.392143\pi$
$523$	15.2032	0.664790	0.332395	+	0.943140i	$0.392143\pi$
$524$	30.7674	1.34408
$525$	10.7862	0.470748
$526$	−3.99653	−0.174257
$527$	1.34241	0.0584763
$528$	11.7354	0.510720
$529$	−17.1888	−0.747341
$530$	4.69546	0.203958
$531$	−2.10156	−0.0912000
$532$	2.83711	0.123004
$533$	48.3767	2.09543
$534$	0.435357	0.0188398
$535$	20.7769	0.898263
$536$	1.13694	0.0491085
$537$	7.24827	0.312786
$538$	−1.44992	−0.0625105
$539$	−26.9539	−1.16099
$540$	−13.1423	−0.565553
$541$	8.15313	0.350530	0.175265	−	0.984521i	$-0.443922\pi$
$541$	8.15313	0.350530	0.175265	+	0.984521i	$0.443922\pi$
$542$	−2.65275	−0.113946
$543$	20.7874	0.892075
$544$	−3.34732	−0.143515
$545$	8.20029	0.351262
$546$	−5.61312	−0.240219
$547$	−13.8775	−0.593358	−0.296679	−	0.954977i	$-0.595879\pi$
$547$	−13.8775	−0.593358	−0.296679	+	0.954977i	$0.595879\pi$
$548$	−7.10821	−0.303648
$549$	−16.9415	−0.723046
$550$	3.13737	0.133778
$551$	−2.48042	−0.105669
$552$	2.64657	0.112645
$553$	61.5236	2.61625
$554$	−2.61595	−0.111141
$555$	3.31607	0.140759
$556$	11.1331	0.472147
$557$	41.3513	1.75211	0.876056	−	0.482210i	$-0.160166\pi$
$557$	41.3513	1.75211	0.876056	+	0.482210i	$0.160166\pi$
$558$	0.835211	0.0353573
$559$	−18.1971	−0.769654
$560$	18.8946	0.798442
$561$	−3.37051	−0.142303
$562$	8.64096	0.364497
$563$	36.0410	1.51895	0.759474	−	0.650538i	$-0.225456\pi$
$563$	36.0410	1.51895	0.759474	+	0.650538i	$0.225456\pi$
$564$	22.8660	0.962833
$565$	10.0514	0.422866
$566$	−4.95831	−0.208413
$567$	6.57235	0.276013
$568$	−7.63667	−0.320428
$569$	−37.2124	−1.56003	−0.780013	−	0.625763i	$-0.784788\pi$
$569$	−37.2124	−1.56003	−0.780013	+	0.625763i	$0.784788\pi$
$570$	0.154952	0.00649023
$571$	21.1004	0.883022	0.441511	−	0.897256i	$-0.354443\pi$
$571$	21.1004	0.883022	0.441511	+	0.897256i	$0.354443\pi$
$572$	35.6230	1.48947
$573$	−14.9057	−0.622696
$574$	10.4393	0.435730
$575$	−7.18416	−0.299600
$576$	12.5518	0.522992
$577$	−29.8552	−1.24289	−0.621443	−	0.783459i	$-0.713453\pi$
$577$	−29.8552	−1.24289	−0.621443	+	0.783459i	$0.713453\pi$
$578$	0.296053	0.0123142
$579$	10.5547	0.438639
$580$	−17.3507	−0.720450
$581$	−29.3600	−1.21806
$582$	−2.11093	−0.0875009
$583$	−39.6831	−1.64351
$584$	12.7406	0.527208
$585$	−15.6462	−0.646889
$586$	2.79749	0.115563
$587$	8.87040	0.366120	0.183060	−	0.983102i	$-0.441400\pi$
$587$	8.87040	0.366120	0.183060	+	0.983102i	$0.441400\pi$
$588$	13.7399	0.566623
$589$	0.521572	0.0214910
$590$	0.420750	0.0173220
$591$	−13.1879	−0.542476
$592$	−8.57093	−0.352263
$593$	−20.3183	−0.834371	−0.417185	−	0.908821i	$-0.636983\pi$
$593$	−20.3183	−0.834371	−0.417185	+	0.908821i	$0.636983\pi$
$594$	−5.09059	−0.208869
$595$	−5.42667	−0.222472
$596$	23.0258	0.943172
$597$	−11.7103	−0.479269
$598$	3.73863	0.152884
$599$	21.1941	0.865968	0.432984	−	0.901402i	$-0.357461\pi$
$599$	21.1941	0.865968	0.432984	+	0.901402i	$0.357461\pi$
$600$	−3.27187	−0.133574
$601$	27.1581	1.10780	0.553901	−	0.832583i	$-0.313139\pi$
$601$	27.1581	1.10780	0.553901	+	0.832583i	$0.313139\pi$
$602$	−3.92679	−0.160044
$603$	2.06288	0.0840069
$604$	22.3236	0.908333
$605$	2.33722	0.0950217
$606$	−1.71644	−0.0697255
$607$	−30.2598	−1.22821	−0.614103	−	0.789226i	$-0.710482\pi$
$607$	−30.2598	−1.22821	−0.614103	+	0.789226i	$0.710482\pi$
$608$	−1.30055	−0.0527442
$609$	−23.1057	−0.936289
$610$	3.39183	0.137331
$611$	66.0830	2.67343
$612$	−4.01893	−0.162455
$613$	23.6822	0.956515	0.478258	−	0.878220i	$-0.341269\pi$
$613$	23.6822	0.956515	0.478258	+	0.878220i	$0.341269\pi$
$614$	8.31234	0.335459
$615$	−12.4401	−0.501634
$616$	15.7267	0.633647
$617$	−6.50661	−0.261946	−0.130973	−	0.991386i	$-0.541810\pi$
$617$	−6.50661	−0.261946	−0.130973	+	0.991386i	$0.541810\pi$
$618$	4.99409	0.200892
$619$	40.0909	1.61139	0.805695	−	0.592331i	$-0.201792\pi$
$619$	40.0909	1.61139	0.805695	+	0.592331i	$0.201792\pi$
$620$	3.64844	0.146525
$621$	11.6568	0.467771
$622$	−1.84418	−0.0739448
$623$	−5.92395	−0.237338
$624$	−17.2886	−0.692097
$625$	−1.21745	−0.0486981
$626$	−7.42876	−0.296913
$627$	−1.30956	−0.0522988
$628$	10.6454	0.424797
$629$	2.46164	0.0981520
$630$	−3.37633	−0.134516
$631$	−8.87116	−0.353155	−0.176578	−	0.984287i	$-0.556503\pi$
$631$	−8.87116	−0.353155	−0.176578	+	0.984287i	$0.556503\pi$
$632$	−18.6625	−0.742354
$633$	−0.426964	−0.0169703
$634$	−2.66205	−0.105723
$635$	−12.1239	−0.481124
$636$	20.2286	0.802117
$637$	39.7084	1.57330
$638$	−6.72072	−0.266076
$639$	−13.8560	−0.548136
$640$	−12.0274	−0.475424
$641$	−35.0318	−1.38367	−0.691837	−	0.722054i	$-0.743198\pi$
$641$	−35.0318	−1.38367	−0.691837	+	0.722054i	$0.743198\pi$
$642$	−4.10241	−0.161909
$643$	−22.9879	−0.906554	−0.453277	−	0.891370i	$-0.649745\pi$
$643$	−22.9879	−0.906554	−0.453277	+	0.891370i	$0.649745\pi$
$644$	−17.6027	−0.693642
$645$	4.67939	0.184251
$646$	0.115027	0.00452566
$647$	8.14319	0.320142	0.160071	−	0.987106i	$-0.448828\pi$
$647$	8.14319	0.320142	0.160071	+	0.987106i	$0.448828\pi$
$648$	−1.99365	−0.0783179
$649$	−3.55592	−0.139582
$650$	−4.62195	−0.181288
$651$	4.85857	0.190422
$652$	41.8882	1.64047
$653$	33.9399	1.32817	0.664085	−	0.747657i	$-0.268821\pi$
$653$	33.9399	1.32817	0.664085	+	0.747657i	$0.268821\pi$
$654$	−1.61915	−0.0633139
$655$	−22.8653	−0.893423
$656$	32.1535	1.25538
$657$	23.1166	0.901863
$658$	14.2602	0.555922
$659$	−27.8959	−1.08667	−0.543335	−	0.839516i	$-0.682839\pi$
$659$	−27.8959	−1.08667	−0.543335	+	0.839516i	$0.682839\pi$
$660$	−9.16049	−0.356571
$661$	28.3149	1.10132	0.550662	−	0.834728i	$-0.314375\pi$
$661$	28.3149	1.10132	0.550662	+	0.834728i	$0.314375\pi$
$662$	2.45275	0.0953290
$663$	4.96542	0.192841
$664$	8.90603	0.345621
$665$	−2.10845	−0.0817622
$666$	1.53156	0.0593469
$667$	15.3896	0.595887
$668$	30.9443	1.19727
$669$	5.45756	0.211001
$670$	−0.413005	−0.0159558
$671$	−28.6657	−1.10663
$672$	−12.1149	−0.467344
$673$	−11.9888	−0.462136	−0.231068	−	0.972938i	$-0.574222\pi$
$673$	−11.9888	−0.462136	−0.231068	+	0.972938i	$0.574222\pi$
$674$	10.7525	0.414170
$675$	−14.4109	−0.554677
$676$	−27.6190	−1.06227
$677$	−14.5240	−0.558205	−0.279102	−	0.960261i	$-0.590037\pi$
$677$	−14.5240	−0.558205	−0.279102	+	0.960261i	$0.590037\pi$
$678$	−1.98466	−0.0762205
$679$	28.7236	1.10231
$680$	1.64612	0.0631259
$681$	−26.5699	−1.01816
$682$	1.41321	0.0541145
$683$	−19.8332	−0.758897	−0.379448	−	0.925213i	$-0.623886\pi$
$683$	−19.8332	−0.758897	−0.379448	+	0.925213i	$0.623886\pi$
$684$	−1.56149	−0.0597051
$685$	5.28259	0.201837
$686$	0.655682	0.0250341
$687$	−25.7458	−0.982262
$688$	−12.0947	−0.461104
$689$	58.4609	2.22718
$690$	−0.961390	−0.0365995
$691$	−42.4151	−1.61355	−0.806773	−	0.590862i	$-0.798788\pi$
$691$	−42.4151	−1.61355	−0.806773	+	0.590862i	$0.798788\pi$
$692$	−18.8091	−0.715016
$693$	28.5347	1.08394
$694$	−6.51823	−0.247428
$695$	−8.27373	−0.313840
$696$	7.00885	0.265670
$697$	−9.23475	−0.349791
$698$	−3.91650	−0.148242
$699$	7.74317	0.292874
$700$	21.7617	0.822513
$701$	15.8444	0.598433	0.299216	−	0.954185i	$-0.403275\pi$
$701$	15.8444	0.598433	0.299216	+	0.954185i	$0.403275\pi$
$702$	7.49942	0.283048
$703$	0.956431	0.0360725
$704$	21.2381	0.800442
$705$	−16.9933	−0.640004
$706$	−7.30195	−0.274813
$707$	23.3557	0.878382
$708$	1.81264	0.0681233
$709$	−39.5829	−1.48657	−0.743283	−	0.668977i	$-0.766732\pi$
$709$	−39.5829	−1.48657	−0.743283	+	0.668977i	$0.766732\pi$
$710$	2.77409	0.104110
$711$	−33.8614	−1.26990
$712$	1.79696	0.0673441
$713$	−3.23606	−0.121191
$714$	1.07150	0.0400999
$715$	−26.4739	−0.990067
$716$	14.6237	0.546514
$717$	1.53146	0.0571932
$718$	−1.33598	−0.0498582
$719$	−4.60801	−0.171850	−0.0859248	−	0.996302i	$-0.527384\pi$
$719$	−4.60801	−0.171850	−0.0859248	+	0.996302i	$0.527384\pi$
$720$	−10.3992	−0.387556
$721$	−67.9551	−2.53078
$722$	−5.58031	−0.207678
$723$	2.12735	0.0791169
$724$	41.9396	1.55867
$725$	−19.0257	−0.706596
$726$	−0.461487	−0.0171274
$727$	−35.8314	−1.32891	−0.664456	−	0.747327i	$-0.731337\pi$
$727$	−35.8314	−1.32891	−0.664456	+	0.747327i	$0.731337\pi$
$728$	−23.1685	−0.858681
$729$	10.1330	0.375298
$730$	−4.62812	−0.171295
$731$	3.47368	0.128479
$732$	14.6124	0.540091
$733$	33.8744	1.25118	0.625590	−	0.780152i	$-0.284858\pi$
$733$	33.8744	1.25118	0.625590	+	0.780152i	$0.284858\pi$
$734$	−4.27727	−0.157877
$735$	−10.2110	−0.376639
$736$	8.06917	0.297434
$737$	3.49046	0.128573
$738$	−5.74561	−0.211499
$739$	−25.6051	−0.941900	−0.470950	−	0.882160i	$-0.656089\pi$
$739$	−25.6051	−0.941900	−0.470950	+	0.882160i	$0.656089\pi$
$740$	6.69032	0.245941
$741$	1.92924	0.0708722
$742$	12.6154	0.463127
$743$	15.7889	0.579240	0.289620	−	0.957142i	$-0.406471\pi$
$743$	15.7889	0.579240	0.289620	+	0.957142i	$0.406471\pi$
$744$	−1.47379	−0.0540319
$745$	−17.1120	−0.626935
$746$	11.3372	0.415086
$747$	16.1592	0.591233
$748$	−6.80017	−0.248639
$749$	55.8220	2.03969
$750$	3.18260	0.116212
$751$	−9.28882	−0.338954	−0.169477	−	0.985534i	$-0.554208\pi$
$751$	−9.28882	−0.338954	−0.169477	+	0.985534i	$0.554208\pi$
$752$	43.9220	1.60167
$753$	−4.34186	−0.158226
$754$	9.90093	0.360570
$755$	−16.5901	−0.603777
$756$	−35.3097	−1.28420
$757$	23.6533	0.859695	0.429848	−	0.902901i	$-0.358567\pi$
$757$	23.6533	0.859695	0.429848	+	0.902901i	$0.358567\pi$
$758$	1.55079	0.0563273
$759$	8.12508	0.294922
$760$	0.639575	0.0231998
$761$	22.2841	0.807799	0.403900	−	0.914803i	$-0.367655\pi$
$761$	22.2841	0.807799	0.403900	+	0.914803i	$0.367655\pi$
$762$	2.39388	0.0867212
$763$	22.0320	0.797611
$764$	−30.0730	−1.08800
$765$	2.98673	0.107986
$766$	−3.64104	−0.131556
$767$	5.23855	0.189153
$768$	−8.94759	−0.322868
$769$	−47.3655	−1.70805	−0.854023	−	0.520236i	$-0.825844\pi$
$769$	−47.3655	−1.70805	−0.854023	+	0.520236i	$0.825844\pi$
$770$	−5.71287	−0.205878
$771$	−2.38319	−0.0858286
$772$	21.2946	0.766410
$773$	9.65078	0.347114	0.173557	−	0.984824i	$-0.444474\pi$
$773$	9.65078	0.347114	0.173557	+	0.984824i	$0.444474\pi$
$774$	2.16123	0.0776838
$775$	4.00064	0.143707
$776$	−8.71300	−0.312778
$777$	8.90939	0.319622
$778$	−2.66759	−0.0956376
$779$	−3.58802	−0.128554
$780$	13.4952	0.483205
$781$	−23.4449	−0.838925
$782$	−0.713675	−0.0255210
$783$	30.8704	1.10322
$784$	26.3921	0.942575
$785$	−7.91130	−0.282366
$786$	4.51478	0.161037
$787$	−47.1118	−1.67935	−0.839676	−	0.543087i	$-0.817255\pi$
$787$	−47.1118	−1.67935	−0.839676	+	0.543087i	$0.817255\pi$
$788$	−26.6071	−0.947839
$789$	12.7955	0.455533
$790$	6.77932	0.241197
$791$	27.0055	0.960204
$792$	−8.65567	−0.307566
$793$	42.2301	1.49963
$794$	5.96412	0.211659
$795$	−15.0333	−0.533175
$796$	−23.6260	−0.837401
$797$	−8.03423	−0.284587	−0.142294	−	0.989825i	$-0.545448\pi$
$797$	−8.03423	−0.284587	−0.142294	+	0.989825i	$0.545448\pi$
$798$	0.416315	0.0147374
$799$	−12.6147	−0.446277
$800$	−9.97568	−0.352693
$801$	3.26043	0.115201
$802$	6.05517	0.213816
$803$	39.1141	1.38031
$804$	−1.77928	−0.0627503
$805$	13.0817	0.461070
$806$	−2.08193	−0.0733327
$807$	4.64215	0.163411
$808$	−7.08470	−0.249239
$809$	3.65084	0.128357	0.0641784	−	0.997938i	$-0.479557\pi$
$809$	3.65084	0.128357	0.0641784	+	0.997938i	$0.479557\pi$
$810$	0.724211	0.0254462
$811$	19.9149	0.699307	0.349653	−	0.936879i	$-0.386299\pi$
$811$	19.9149	0.699307	0.349653	+	0.936879i	$0.386299\pi$
$812$	−46.6168	−1.63593
$813$	8.49322	0.297870
$814$	2.59146	0.0908307
$815$	−31.1300	−1.09044
$816$	3.30026	0.115532
$817$	1.34964	0.0472181
$818$	10.3554	0.362068
$819$	−42.0371	−1.46889
$820$	−25.0985	−0.876478
$821$	−24.4741	−0.854152	−0.427076	−	0.904216i	$-0.640456\pi$
$821$	−24.4741	−0.854152	−0.427076	+	0.904216i	$0.640456\pi$
$822$	−1.04305	−0.0363806
$823$	−11.3179	−0.394519	−0.197259	−	0.980351i	$-0.563204\pi$
$823$	−11.3179	−0.394519	−0.197259	+	0.980351i	$0.563204\pi$
$824$	20.6134	0.718103
$825$	−10.0448	−0.349715
$826$	1.13044	0.0393331
$827$	−38.9030	−1.35279	−0.676395	−	0.736539i	$-0.736459\pi$
$827$	−38.9030	−1.35279	−0.676395	+	0.736539i	$0.736459\pi$
$828$	9.68816	0.336687
$829$	−15.0174	−0.521576	−0.260788	−	0.965396i	$-0.583982\pi$
$829$	−15.0174	−0.521576	−0.260788	+	0.965396i	$0.583982\pi$
$830$	−3.23520	−0.112295
$831$	8.37539	0.290539
$832$	−31.2879	−1.08471
$833$	−7.58002	−0.262632
$834$	1.63365	0.0565688
$835$	−22.9968	−0.795837
$836$	−2.64210	−0.0913789
$837$	−6.49131	−0.224372
$838$	−7.00719	−0.242059
$839$	21.3507	0.737107	0.368553	−	0.929607i	$-0.379853\pi$
$839$	21.3507	0.737107	0.368553	+	0.929607i	$0.379853\pi$
$840$	5.95779	0.205563
$841$	11.7559	0.405376
$842$	−6.33729	−0.218397
$843$	−27.6654	−0.952847
$844$	−0.861420	−0.0296513
$845$	20.5256	0.706101
$846$	−7.84855	−0.269839
$847$	6.27950	0.215766
$848$	38.8560	1.33432
$849$	15.8748	0.544823
$850$	0.882295	0.0302625
$851$	−5.93411	−0.203419
$852$	11.9511	0.409439
$853$	33.2359	1.13797	0.568987	−	0.822346i	$-0.307335\pi$
$853$	33.2359	1.13797	0.568987	+	0.822346i	$0.307335\pi$
$854$	9.11294	0.311838
$855$	1.16045	0.0396865
$856$	−16.9330	−0.578757
$857$	−3.32260	−0.113498	−0.0567490	−	0.998388i	$-0.518073\pi$
$857$	−3.32260	−0.113498	−0.0567490	+	0.998388i	$0.518073\pi$
$858$	5.22729	0.178457
$859$	23.6694	0.807589	0.403794	−	0.914850i	$-0.367691\pi$
$859$	23.6694	0.807589	0.403794	+	0.914850i	$0.367691\pi$
$860$	9.44088	0.321931
$861$	−33.4232	−1.13906
$862$	−5.25538	−0.178999
$863$	12.5099	0.425840	0.212920	−	0.977070i	$-0.431703\pi$
$863$	12.5099	0.425840	0.212920	+	0.977070i	$0.431703\pi$
$864$	16.1862	0.550666
$865$	13.9783	0.475278
$866$	9.48096	0.322176
$867$	−0.947860	−0.0321910
$868$	9.80239	0.332715
$869$	−57.2947	−1.94359
$870$	−2.54603	−0.0863185
$871$	−5.14213	−0.174234
$872$	−6.68316	−0.226320
$873$	−15.8089	−0.535051
$874$	−0.277287	−0.00937938
$875$	−43.3059	−1.46401
$876$	−19.9386	−0.673661
$877$	39.7399	1.34192	0.670960	−	0.741493i	$-0.265882\pi$
$877$	39.7399	1.34192	0.670960	+	0.741493i	$0.265882\pi$
$878$	−4.41177	−0.148890
$879$	−8.95661	−0.302099
$880$	−17.5958	−0.593155
$881$	−4.50995	−0.151944	−0.0759720	−	0.997110i	$-0.524206\pi$
$881$	−4.50995	−0.151944	−0.0759720	+	0.997110i	$0.524206\pi$
$882$	−4.71608	−0.158799
$883$	−39.8647	−1.34155	−0.670777	−	0.741659i	$-0.734039\pi$
$883$	−39.8647	−1.34155	−0.670777	+	0.741659i	$0.734039\pi$
$884$	10.0180	0.336941
$885$	−1.34710	−0.0452822
$886$	4.14191	0.139150
$887$	−35.1629	−1.18066	−0.590328	−	0.807163i	$-0.701002\pi$
$887$	−35.1629	−1.18066	−0.590328	+	0.807163i	$0.701002\pi$
$888$	−2.70256	−0.0906921
$889$	−32.5738	−1.09249
$890$	−0.652764	−0.0218807
$891$	−6.12059	−0.205047
$892$	11.0109	0.368672
$893$	−4.90126	−0.164014
$894$	3.37878	0.113003
$895$	−10.8679	−0.363273
$896$	−32.3144	−1.07955
$897$	−11.9698	−0.399660
$898$	4.42736	0.147743
$899$	−8.56999	−0.285825
$900$	−11.9772	−0.399240
$901$	−11.1597	−0.371785
$902$	−9.72178	−0.323700
$903$	12.5723	0.418379
$904$	−8.19181	−0.272456
$905$	−31.1682	−1.03607
$906$	3.27574	0.108829
$907$	38.3198	1.27239	0.636194	−	0.771529i	$-0.280508\pi$
$907$	38.3198	1.27239	0.636194	+	0.771529i	$0.280508\pi$
$908$	−53.6060	−1.77898
$909$	−12.8545	−0.426358
$910$	8.41617	0.278993
$911$	−23.9677	−0.794085	−0.397043	−	0.917800i	$-0.629963\pi$
$911$	−23.9677	−0.794085	−0.397043	+	0.917800i	$0.629963\pi$
$912$	1.28226	0.0424600
$913$	27.3419	0.904884
$914$	7.05317	0.233298
$915$	−10.8595	−0.359004
$916$	−51.9433	−1.71625
$917$	−61.4331	−2.02870
$918$	−1.43158	−0.0472493
$919$	40.9352	1.35033	0.675164	−	0.737668i	$-0.264073\pi$
$919$	40.9352	1.35033	0.675164	+	0.737668i	$0.264073\pi$
$920$	−3.96820	−0.130828
$921$	−26.6133	−0.876937
$922$	−0.735249	−0.0242141
$923$	34.5389	1.13686
$924$	−24.6118	−0.809668
$925$	7.33617	0.241212
$926$	−9.49029	−0.311870
$927$	37.4011	1.22841
$928$	21.3694	0.701486
$929$	−35.3832	−1.16089	−0.580443	−	0.814301i	$-0.697121\pi$
$929$	−35.3832	−1.16089	−0.580443	+	0.814301i	$0.697121\pi$
$930$	0.535369	0.0175554
$931$	−2.94510	−0.0965217
$932$	15.6222	0.511722
$933$	5.90443	0.193302
$934$	2.16907	0.0709743
$935$	5.05366	0.165272
$936$	12.7515	0.416795
$937$	9.82552	0.320986	0.160493	−	0.987037i	$-0.448692\pi$
$937$	9.82552	0.320986	0.160493	+	0.987037i	$0.448692\pi$
$938$	−1.10963	−0.0362308
$939$	23.7844	0.776173
$940$	−34.2847	−1.11824
$941$	33.0132	1.07620	0.538099	−	0.842881i	$-0.319142\pi$
$941$	33.0132	1.07620	0.538099	+	0.842881i	$0.319142\pi$
$942$	1.56209	0.0508957
$943$	22.2616	0.724938
$944$	3.48180	0.113323
$945$	26.2410	0.853621
$946$	3.65688	0.118895
$947$	10.7624	0.349730	0.174865	−	0.984592i	$-0.444051\pi$
$947$	10.7624	0.349730	0.174865	+	0.984592i	$0.444051\pi$
$948$	29.2062	0.948573
$949$	−57.6226	−1.87051
$950$	0.342802	0.0111220
$951$	8.52297	0.276376
$952$	4.42269	0.143340
$953$	43.1494	1.39775	0.698873	−	0.715246i	$-0.253685\pi$
$953$	43.1494	1.39775	0.698873	+	0.715246i	$0.253685\pi$
$954$	−6.94329	−0.224797
$955$	22.3493	0.723206
$956$	3.08978	0.0999307
$957$	21.5175	0.695561
$958$	−3.97959	−0.128575
$959$	14.1929	0.458313
$960$	8.04569	0.259674
$961$	−29.1979	−0.941869
$962$	−3.81773	−0.123088
$963$	−30.7233	−0.990045
$964$	4.29203	0.138237
$965$	−15.8255	−0.509440
$966$	−2.58300	−0.0831066
$967$	−22.6875	−0.729582	−0.364791	−	0.931089i	$-0.618860\pi$
$967$	−22.6875	−0.729582	−0.364791	+	0.931089i	$0.618860\pi$
$968$	−1.90482	−0.0612231
$969$	−0.368276	−0.0118307
$970$	3.16508	0.101624
$971$	5.88926	0.188995	0.0944976	−	0.995525i	$-0.469876\pi$
$971$	5.88926	0.188995	0.0944976	+	0.995525i	$0.469876\pi$
$972$	30.8619	0.989897
$973$	−22.2293	−0.712639
$974$	−5.06564	−0.162313
$975$	14.7979	0.473913
$976$	28.0682	0.898440
$977$	−59.4002	−1.90038	−0.950191	−	0.311669i	$-0.899112\pi$
$977$	−59.4002	−1.90038	−0.950191	+	0.311669i	$0.899112\pi$
$978$	6.14664	0.196548
$979$	5.51676	0.176316
$980$	−20.6012	−0.658082
$981$	−12.1260	−0.387152
$982$	−6.18006	−0.197214
$983$	6.89986	0.220071	0.110036	−	0.993928i	$-0.464903\pi$
$983$	6.89986	0.220071	0.110036	+	0.993928i	$0.464903\pi$
$984$	10.1386	0.323206
$985$	19.7735	0.630037
$986$	−1.89001	−0.0601902
$987$	−45.6564	−1.45326
$988$	3.89232	0.123831
$989$	−8.37378	−0.266271
$990$	3.14425	0.0999309
$991$	22.5513	0.716366	0.358183	−	0.933651i	$-0.383396\pi$
$991$	22.5513	0.716366	0.358183	+	0.933651i	$0.383396\pi$
$992$	−4.49348	−0.142668
$993$	−7.85288	−0.249204
$994$	7.45324	0.236403
$995$	17.5581	0.556628
$996$	−13.9376	−0.441631
$997$	40.0880	1.26960	0.634800	−	0.772676i	$-0.281082\pi$
$997$	40.0880	1.26960	0.634800	+	0.772676i	$0.281082\pi$
$998$	7.95950	0.251954
$999$	−11.9034	−0.376607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.11	✓	22
3.2	odd	2		9027.2.a.s.1.12		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.11	✓	22	1.1	even	1	trivial
9027.2.a.s.1.12		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+0.296053 q^{2} -0.947860 q^{3} -1.91235 q^{4} +1.42120 q^{5} -0.280617 q^{6} +3.81838 q^{7} -1.15826 q^{8} -2.10156 q^{9} +O(q^{10})\)	\(q+0.296053 q^{2} -0.947860 q^{3} -1.91235 q^{4} +1.42120 q^{5} -0.280617 q^{6} +3.81838 q^{7} -1.15826 q^{8} -2.10156 q^{9} +0.420750 q^{10} -3.55592 q^{11} +1.81264 q^{12} +5.23855 q^{13} +1.13044 q^{14} -1.34710 q^{15} +3.48180 q^{16} -1.00000 q^{17} -0.622173 q^{18} -0.388534 q^{19} -2.71783 q^{20} -3.61929 q^{21} -1.05274 q^{22} +2.41064 q^{23} +1.09787 q^{24} -2.98020 q^{25} +1.55089 q^{26} +4.83557 q^{27} -7.30209 q^{28} +6.38404 q^{29} -0.398812 q^{30} -1.34241 q^{31} +3.34732 q^{32} +3.37051 q^{33} -0.296053 q^{34} +5.42667 q^{35} +4.01893 q^{36} -2.46164 q^{37} -0.115027 q^{38} -4.96542 q^{39} -1.64612 q^{40} +9.23475 q^{41} -1.07150 q^{42} -3.47368 q^{43} +6.80017 q^{44} -2.98673 q^{45} +0.713675 q^{46} +12.6147 q^{47} -3.30026 q^{48} +7.58002 q^{49} -0.882295 q^{50} +0.947860 q^{51} -10.0180 q^{52} +11.1597 q^{53} +1.43158 q^{54} -5.05366 q^{55} -4.42269 q^{56} +0.368276 q^{57} +1.89001 q^{58} +1.00000 q^{59} +2.57613 q^{60} +8.06140 q^{61} -0.397424 q^{62} -8.02456 q^{63} -5.97261 q^{64} +7.44502 q^{65} +0.997850 q^{66} -0.981593 q^{67} +1.91235 q^{68} -2.28495 q^{69} +1.60658 q^{70} +6.59321 q^{71} +2.43416 q^{72} -10.9997 q^{73} -0.728775 q^{74} +2.82481 q^{75} +0.743015 q^{76} -13.5778 q^{77} -1.47003 q^{78} +16.1125 q^{79} +4.94833 q^{80} +1.72124 q^{81} +2.73397 q^{82} -7.68913 q^{83} +6.92136 q^{84} -1.42120 q^{85} -1.02839 q^{86} -6.05117 q^{87} +4.11869 q^{88} -1.55143 q^{89} -0.884231 q^{90} +20.0028 q^{91} -4.60998 q^{92} +1.27242 q^{93} +3.73463 q^{94} -0.552184 q^{95} -3.17279 q^{96} +7.52247 q^{97} +2.24409 q^{98} +7.47298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more