LMFDB - Embedded newform 289.10.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-40.6100 q^{2} +102.962 q^{3} +1137.17 q^{4} +769.524 q^{5} -4181.30 q^{6} -1567.27 q^{7} -25388.3 q^{8} -9081.79 q^{9} +O(q^{10})$	\(q-40.6100 q^{2} +102.962 q^{3} +1137.17 q^{4} +769.524 q^{5} -4181.30 q^{6} -1567.27 q^{7} -25388.3 q^{8} -9081.79 q^{9} -31250.4 q^{10} +17032.6 q^{11} +117086. q^{12} +141996. q^{13} +63646.7 q^{14} +79231.9 q^{15} +448786. q^{16} +368812. q^{18} -743799. q^{19} +875082. q^{20} -161369. q^{21} -691694. q^{22} +1.55554e6 q^{23} -2.61403e6 q^{24} -1.36096e6 q^{25} -5.76647e6 q^{26} -2.96169e6 q^{27} -1.78225e6 q^{28} -5.73876e6 q^{29} -3.21761e6 q^{30} +4.58990e6 q^{31} -5.22641e6 q^{32} +1.75371e6 q^{33} -1.20605e6 q^{35} -1.03276e7 q^{36} +5.48318e6 q^{37} +3.02057e7 q^{38} +1.46203e7 q^{39} -1.95369e7 q^{40} -1.81160e7 q^{41} +6.55320e6 q^{42} +2.79841e7 q^{43} +1.93690e7 q^{44} -6.98865e6 q^{45} -6.31705e7 q^{46} +2.65154e7 q^{47} +4.62080e7 q^{48} -3.78973e7 q^{49} +5.52685e7 q^{50} +1.61474e8 q^{52} +7.58163e7 q^{53} +1.20274e8 q^{54} +1.31070e7 q^{55} +3.97902e7 q^{56} -7.65832e7 q^{57} +2.33051e8 q^{58} -4.75661e7 q^{59} +9.01004e7 q^{60} +1.40302e8 q^{61} -1.86396e8 q^{62} +1.42336e7 q^{63} -1.75339e7 q^{64} +1.09270e8 q^{65} -7.12184e7 q^{66} -7.10319e7 q^{67} +1.60162e8 q^{69} +4.89776e7 q^{70} +7.14261e7 q^{71} +2.30571e8 q^{72} +3.40249e8 q^{73} -2.22672e8 q^{74} -1.40127e8 q^{75} -8.45829e8 q^{76} -2.66946e7 q^{77} -5.93729e8 q^{78} -3.20837e8 q^{79} +3.45352e8 q^{80} -1.26185e8 q^{81} +7.35691e8 q^{82} +3.26635e8 q^{83} -1.83505e8 q^{84} -1.13644e9 q^{86} -5.90875e8 q^{87} -4.32429e8 q^{88} -2.75879e8 q^{89} +2.83809e8 q^{90} -2.22546e8 q^{91} +1.76892e9 q^{92} +4.72586e8 q^{93} -1.07679e9 q^{94} -5.72371e8 q^{95} -5.38123e8 q^{96} +6.65935e8 q^{97} +1.53901e9 q^{98} -1.54687e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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 $

$2$	−40.6100	−1.79473	−0.897363	−	0.441293i	$-0.854520\pi$
$2$	−40.6100	−1.79473	−0.897363	+	0.441293i	$0.854520\pi$
$3$	102.962	0.733892	0.366946	−	0.930242i	$-0.380403\pi$
$3$	102.962	0.733892	0.366946	+	0.930242i	$0.380403\pi$
$4$	1137.17	2.22104
$5$	769.524	0.550627	0.275313	−	0.961355i	$-0.411218\pi$
$5$	769.524	0.550627	0.275313	+	0.961355i	$0.411218\pi$
$6$	−4181.30	−1.31713
$7$	−1567.27	−0.246718	−0.123359	−	0.992362i	$-0.539367\pi$
$7$	−1567.27	−0.246718	−0.123359	+	0.992362i	$0.539367\pi$
$8$	−25388.3	−2.19144
$9$	−9081.79	−0.461403
$10$	−31250.4	−0.988224
$11$	17032.6	0.350763	0.175382	−	0.984501i	$-0.443884\pi$
$11$	17032.6	0.350763	0.175382	+	0.984501i	$0.443884\pi$
$12$	117086.	1.63000
$13$	141996.	1.37890	0.689449	−	0.724334i	$-0.257853\pi$
$13$	141996.	1.37890	0.689449	+	0.724334i	$0.257853\pi$
$14$	63646.7	0.442792
$15$	79231.9	0.404100
$16$	448786.	1.71198
$17$	0	0
$17$	0	0
$18$	368812.	0.828091
$19$	−743799.	−1.30938	−0.654688	−	0.755899i	$-0.727200\pi$
$19$	−743799.	−1.30938	−0.654688	+	0.755899i	$0.727200\pi$
$20$	875082.	1.22296
$21$	−161369.	−0.181065
$22$	−691694.	−0.629524
$23$	1.55554e6	1.15906	0.579530	−	0.814951i	$-0.303236\pi$
$23$	1.55554e6	1.15906	0.579530	+	0.814951i	$0.303236\pi$
$24$	−2.61403e6	−1.60828
$25$	−1.36096e6	−0.696810
$26$	−5.76647e6	−2.47474
$27$	−2.96169e6	−1.07251
$28$	−1.78225e6	−0.547972
$29$	−5.73876e6	−1.50670	−0.753350	−	0.657619i	$-0.771564\pi$
$29$	−5.73876e6	−1.50670	−0.753350	+	0.657619i	$0.771564\pi$
$30$	−3.21761e6	−0.725249
$31$	4.58990e6	0.892639	0.446320	−	0.894874i	$-0.352734\pi$
$31$	4.58990e6	0.892639	0.446320	+	0.894874i	$0.352734\pi$
$32$	−5.22641e6	−0.881107
$33$	1.75371e6	0.257422
$34$	0	0
$35$	−1.20605e6	−0.135850
$36$	−1.03276e7	−1.02479
$37$	5.48318e6	0.480977	0.240489	−	0.970652i	$-0.422692\pi$
$37$	5.48318e6	0.480977	0.240489	+	0.970652i	$0.422692\pi$
$38$	3.02057e7	2.34997
$39$	1.46203e7	1.01196
$40$	−1.95369e7	−1.20666
$41$	−1.81160e7	−1.00123	−0.500616	−	0.865669i	$-0.666893\pi$
$41$	−1.81160e7	−1.00123	−0.500616	+	0.865669i	$0.666893\pi$
$42$	6.55320e6	0.324961
$43$	2.79841e7	1.24826	0.624128	−	0.781322i	$-0.285454\pi$
$43$	2.79841e7	1.24826	0.624128	+	0.781322i	$0.285454\pi$
$44$	1.93690e7	0.779060
$45$	−6.98865e6	−0.254061
$46$	−6.31705e7	−2.08020
$47$	2.65154e7	0.792607	0.396304	−	0.918119i	$-0.370293\pi$
$47$	2.65154e7	0.792607	0.396304	+	0.918119i	$0.370293\pi$
$48$	4.62080e7	1.25641
$49$	−3.78973e7	−0.939130
$50$	5.52685e7	1.25058
$51$	0	0
$52$	1.61474e8	3.06259
$53$	7.58163e7	1.31984	0.659920	−	0.751336i	$-0.270590\pi$
$53$	7.58163e7	1.31984	0.659920	+	0.751336i	$0.270590\pi$
$54$	1.20274e8	1.92486
$55$	1.31070e7	0.193140
$56$	3.97902e7	0.540667
$57$	−7.65832e7	−0.960941
$58$	2.33051e8	2.70411
$59$	−4.75661e7	−0.511051	−0.255525	−	0.966802i	$-0.582248\pi$
$59$	−4.75661e7	−0.511051	−0.255525	+	0.966802i	$0.582248\pi$
$60$	9.01004e7	0.897524
$61$	1.40302e8	1.29742	0.648709	−	0.761036i	$-0.275309\pi$
$61$	1.40302e8	1.29742	0.648709	+	0.761036i	$0.275309\pi$
$62$	−1.86396e8	−1.60204
$63$	1.42336e7	0.113836
$64$	−1.75339e7	−0.130638
$65$	1.09270e8	0.759258
$66$	−7.12184e7	−0.462002
$67$	−7.10319e7	−0.430643	−0.215321	−	0.976543i	$-0.569080\pi$
$67$	−7.10319e7	−0.430643	−0.215321	+	0.976543i	$0.569080\pi$
$68$	0	0
$69$	1.60162e8	0.850625
$70$	4.89776e7	0.243813
$71$	7.14261e7	0.333576	0.166788	−	0.985993i	$-0.446661\pi$
$71$	7.14261e7	0.333576	0.166788	+	0.985993i	$0.446661\pi$
$72$	2.30571e8	1.01113
$73$	3.40249e8	1.40231	0.701154	−	0.713010i	$-0.252668\pi$
$73$	3.40249e8	1.40231	0.701154	+	0.713010i	$0.252668\pi$
$74$	−2.22672e8	−0.863222
$75$	−1.40127e8	−0.511384
$76$	−8.45829e8	−2.90818
$77$	−2.66946e7	−0.0865397
$78$	−5.93729e8	−1.81619
$79$	−3.20837e8	−0.926750	−0.463375	−	0.886162i	$-0.653362\pi$
$79$	−3.20837e8	−0.926750	−0.463375	+	0.886162i	$0.653362\pi$
$80$	3.45352e8	0.942664
$81$	−1.26185e8	−0.325705
$82$	7.35691e8	1.79694
$83$	3.26635e8	0.755459	0.377729	−	0.925916i	$-0.376705\pi$
$83$	3.26635e8	0.755459	0.377729	+	0.925916i	$0.376705\pi$
$84$	−1.83505e8	−0.402152
$85$	0	0
$86$	−1.13644e9	−2.24028
$87$	−5.90875e8	−1.10576
$88$	−4.32429e8	−0.768675
$89$	−2.75879e8	−0.466084	−0.233042	−	0.972467i	$-0.574868\pi$
$89$	−2.75879e8	−0.466084	−0.233042	+	0.972467i	$0.574868\pi$
$90$	2.83809e8	0.455969
$91$	−2.22546e8	−0.340199
$92$	1.76892e9	2.57432
$93$	4.72586e8	0.655101
$94$	−1.07679e9	−1.42251
$95$	−5.72371e8	−0.720977
$96$	−5.38123e8	−0.646637
$97$	6.65935e8	0.763764	0.381882	−	0.924211i	$-0.375276\pi$
$97$	6.65935e8	0.763764	0.381882	+	0.924211i	$0.375276\pi$
$98$	1.53901e9	1.68548
$99$	−1.54687e8	−0.161843
$100$	−1.54764e9	−1.54764
$101$	6.92506e8	0.662182	0.331091	−	0.943599i	$-0.392583\pi$
$101$	6.92506e8	0.662182	0.331091	+	0.943599i	$0.392583\pi$
$102$	0	0
$103$	−1.77196e9	−1.55127	−0.775633	−	0.631184i	$-0.782569\pi$
$103$	−1.77196e9	−1.55127	−0.775633	+	0.631184i	$0.782569\pi$
$104$	−3.60505e9	−3.02177
$105$	−1.24177e8	−0.0996989
$106$	−3.07890e9	−2.36875
$107$	7.73032e8	0.570126	0.285063	−	0.958509i	$-0.407986\pi$
$107$	7.73032e8	0.570126	0.285063	+	0.958509i	$0.407986\pi$
$108$	−3.36795e9	−2.38209
$109$	2.12026e9	1.43870	0.719350	−	0.694648i	$-0.244440\pi$
$109$	2.12026e9	1.43870	0.719350	+	0.694648i	$0.244440\pi$
$110$	−5.32275e8	−0.346633
$111$	5.64560e8	0.352985
$112$	−7.03367e8	−0.422378
$113$	2.21312e9	1.27688	0.638442	−	0.769670i	$-0.279579\pi$
$113$	2.21312e9	1.27688	0.638442	+	0.769670i	$0.279579\pi$
$114$	3.11004e9	1.72463
$115$	1.19703e9	0.638210
$116$	−6.52596e9	−3.34644
$117$	−1.28958e9	−0.636227
$118$	1.93166e9	0.917196
$119$	0	0
$120$	−2.01156e9	−0.885560
$121$	−2.06784e9	−0.876965
$122$	−5.69767e9	−2.32851
$123$	−1.86526e9	−0.734797
$124$	5.21952e9	1.98259
$125$	−2.55027e9	−0.934309
$126$	−5.78026e8	−0.204305
$127$	3.54124e8	0.120792	0.0603960	−	0.998174i	$-0.480764\pi$
$127$	3.54124e8	0.120792	0.0603960	+	0.998174i	$0.480764\pi$
$128$	3.38798e9	1.11557
$129$	2.88131e9	0.916085
$130$	−4.43744e9	−1.36266
$131$	−2.62702e9	−0.779368	−0.389684	−	0.920949i	$-0.627416\pi$
$131$	−2.62702e9	−0.779368	−0.389684	+	0.920949i	$0.627416\pi$
$132$	1.99428e9	0.571746
$133$	1.16573e9	0.323047
$134$	2.88461e9	0.772885
$135$	−2.27909e9	−0.590553
$136$	0	0
$137$	−3.91153e9	−0.948646	−0.474323	−	0.880351i	$-0.657307\pi$
$137$	−3.91153e9	−0.948646	−0.474323	+	0.880351i	$0.657307\pi$
$138$	−6.50418e9	−1.52664
$139$	3.69492e9	0.839534	0.419767	−	0.907632i	$-0.362112\pi$
$139$	3.69492e9	0.839534	0.419767	+	0.907632i	$0.362112\pi$
$140$	−1.37149e9	−0.301728
$141$	2.73009e9	0.581688
$142$	−2.90061e9	−0.598677
$143$	2.41857e9	0.483667
$144$	−4.07578e9	−0.789914
$145$	−4.41611e9	−0.829629
$146$	−1.38175e10	−2.51676
$147$	−3.90199e9	−0.689220
$148$	6.23532e9	1.06827
$149$	−6.36801e9	−1.05844	−0.529219	−	0.848485i	$-0.677515\pi$
$149$	−6.36801e9	−1.05844	−0.529219	+	0.848485i	$0.677515\pi$
$150$	5.69057e9	0.917793
$151$	−8.92054e9	−1.39635	−0.698176	−	0.715926i	$-0.746005\pi$
$151$	−8.92054e9	−1.39635	−0.698176	+	0.715926i	$0.746005\pi$
$152$	1.88838e10	2.86941
$153$	0	0
$154$	1.08407e9	0.155315
$155$	3.53204e9	0.491511
$156$	1.66258e10	2.24761
$157$	4.57442e9	0.600879	0.300440	−	0.953801i	$-0.402867\pi$
$157$	4.57442e9	0.600879	0.300440	+	0.953801i	$0.402867\pi$
$158$	1.30292e10	1.66326
$159$	7.80622e9	0.968620
$160$	−4.02185e9	−0.485161
$161$	−2.43795e9	−0.285961
$162$	5.12436e9	0.584551
$163$	−6.61139e9	−0.733582	−0.366791	−	0.930303i	$-0.619544\pi$
$163$	−6.61139e9	−0.733582	−0.366791	+	0.930303i	$0.619544\pi$
$164$	−2.06010e10	−2.22378
$165$	1.34953e9	0.141744
$166$	−1.32646e10	−1.35584
$167$	1.30049e10	1.29384	0.646922	−	0.762556i	$-0.276056\pi$
$167$	1.30049e10	1.29384	0.646922	+	0.762556i	$0.276056\pi$
$168$	4.09689e9	0.396791
$169$	9.55847e9	0.901359
$170$	0	0
$171$	6.75503e9	0.604150
$172$	3.18228e10	2.77243
$173$	−4.07288e9	−0.345696	−0.172848	−	0.984949i	$-0.555297\pi$
$173$	−4.07288e9	−0.345696	−0.172848	+	0.984949i	$0.555297\pi$
$174$	2.39954e10	1.98453
$175$	2.13298e9	0.171916
$176$	7.64400e9	0.600501
$177$	−4.89751e9	−0.375056
$178$	1.12035e10	0.836492
$179$	2.47219e10	1.79988	0.899938	−	0.436017i	$-0.143611\pi$
$179$	2.47219e10	1.79988	0.899938	+	0.436017i	$0.143611\pi$
$180$	−7.94731e9	−0.564279
$181$	3.57700e9	0.247722	0.123861	−	0.992300i	$-0.460472\pi$
$181$	3.57700e9	0.247722	0.123861	+	0.992300i	$0.460472\pi$
$182$	9.03759e9	0.610565
$183$	1.44458e10	0.952165
$184$	−3.94925e10	−2.54001
$185$	4.21943e9	0.264839
$186$	−1.91917e10	−1.17573
$187$	0	0
$188$	3.01526e10	1.76041
$189$	4.64175e9	0.264608
$190$	2.32440e10	1.29396
$191$	1.56335e10	0.849975	0.424988	−	0.905199i	$-0.360278\pi$
$191$	1.56335e10	0.849975	0.424988	+	0.905199i	$0.360278\pi$
$192$	−1.80533e9	−0.0958742
$193$	−7.93673e9	−0.411750	−0.205875	−	0.978578i	$-0.566004\pi$
$193$	−7.93673e9	−0.411750	−0.205875	+	0.978578i	$0.566004\pi$
$194$	−2.70436e10	−1.37075
$195$	1.12506e10	0.557213
$196$	−4.30958e10	−2.08585
$197$	2.65269e10	1.25484	0.627421	−	0.778680i	$-0.284111\pi$
$197$	2.65269e10	1.25484	0.627421	+	0.778680i	$0.284111\pi$
$198$	6.28182e9	0.290464
$199$	−4.18654e10	−1.89241	−0.946206	−	0.323563i	$-0.895119\pi$
$199$	−4.18654e10	−1.89241	−0.946206	+	0.323563i	$0.895119\pi$
$200$	3.45524e10	1.52701
$201$	−7.31360e9	−0.316045
$202$	−2.81227e10	−1.18844
$203$	8.99416e9	0.371731
$204$	0	0
$205$	−1.39407e10	−0.551305
$206$	7.19593e10	2.78410
$207$	−1.41271e10	−0.534794
$208$	6.37260e10	2.36065
$209$	−1.26688e10	−0.459281
$210$	5.04284e9	0.178932
$211$	2.51533e10	0.873623	0.436812	−	0.899553i	$-0.356108\pi$
$211$	2.51533e10	0.873623	0.436812	+	0.899553i	$0.356108\pi$
$212$	8.62163e10	2.93142
$213$	7.35419e9	0.244808
$214$	−3.13928e10	−1.02322
$215$	2.15344e10	0.687323
$216$	7.51921e10	2.35034
$217$	−7.19360e9	−0.220230
$218$	−8.61038e10	−2.58207
$219$	3.50327e10	1.02914
$220$	1.49049e10	0.428971
$221$	0	0
$222$	−2.29268e10	−0.633512
$223$	−3.42839e10	−0.928365	−0.464182	−	0.885740i	$-0.653652\pi$
$223$	−3.42839e10	−0.928365	−0.464182	+	0.885740i	$0.653652\pi$
$224$	8.19117e9	0.217385
$225$	1.23599e10	0.321510
$226$	−8.98748e10	−2.29166
$227$	3.92494e10	0.981107	0.490553	−	0.871411i	$-0.336795\pi$
$227$	3.92494e10	0.981107	0.490553	+	0.871411i	$0.336795\pi$
$228$	−8.70884e10	−2.13429
$229$	3.19695e10	0.768203	0.384102	−	0.923291i	$-0.374511\pi$
$229$	3.19695e10	0.768203	0.384102	+	0.923291i	$0.374511\pi$
$230$	−4.86112e10	−1.14541
$231$	−2.74854e9	−0.0635108
$232$	1.45697e11	3.30184
$233$	8.59764e10	1.91107	0.955537	−	0.294872i	$-0.0952771\pi$
$233$	8.59764e10	1.91107	0.955537	+	0.294872i	$0.0952771\pi$
$234$	5.23699e10	1.14185
$235$	2.04042e10	0.436431
$236$	−5.40909e10	−1.13506
$237$	−3.30341e10	−0.680135
$238$	0	0
$239$	3.27519e10	0.649300	0.324650	−	0.945834i	$-0.394753\pi$
$239$	3.27519e10	0.649300	0.324650	+	0.945834i	$0.394753\pi$
$240$	3.55582e10	0.691813
$241$	−2.29656e9	−0.0438533	−0.0219266	−	0.999760i	$-0.506980\pi$
$241$	−2.29656e9	−0.0438533	−0.0219266	+	0.999760i	$0.506980\pi$
$242$	8.39749e10	1.57391
$243$	4.53026e10	0.833479
$244$	1.59548e11	2.88162
$245$	−2.91629e10	−0.517110
$246$	7.57484e10	1.31876
$247$	−1.05617e11	−1.80550
$248$	−1.16530e11	−1.95616
$249$	3.36310e10	0.554425
$250$	1.03566e11	1.67683
$251$	−4.29930e10	−0.683700	−0.341850	−	0.939755i	$-0.611053\pi$
$251$	−4.29930e10	−0.683700	−0.341850	+	0.939755i	$0.611053\pi$
$252$	1.61860e10	0.252836
$253$	2.64949e10	0.406556
$254$	−1.43810e10	−0.216789
$255$	0	0
$256$	−1.28608e11	−1.87150
$257$	−1.68780e10	−0.241336	−0.120668	−	0.992693i	$-0.538504\pi$
$257$	−1.68780e10	−0.241336	−0.120668	+	0.992693i	$0.538504\pi$
$258$	−1.17010e11	−1.64412
$259$	−8.59359e9	−0.118666
$260$	1.24258e11	1.68634
$261$	5.21182e10	0.695196
$262$	1.06683e11	1.39875
$263$	−1.88404e10	−0.242823	−0.121412	−	0.992602i	$-0.538742\pi$
$263$	−1.88404e10	−0.242823	−0.121412	+	0.992602i	$0.538742\pi$
$264$	−4.45238e10	−0.564124
$265$	5.83425e10	0.726739
$266$	−4.73403e10	−0.579781
$267$	−2.84051e10	−0.342055
$268$	−8.07756e10	−0.956475
$269$	−9.27652e10	−1.08019	−0.540094	−	0.841604i	$-0.681612\pi$
$269$	−9.27652e10	−1.08019	−0.540094	+	0.841604i	$0.681612\pi$
$270$	9.25538e10	1.05988
$271$	1.11257e11	1.25304	0.626519	−	0.779406i	$-0.284479\pi$
$271$	1.11257e11	1.25304	0.626519	+	0.779406i	$0.284479\pi$
$272$	0	0
$273$	−2.29138e10	−0.249670
$274$	1.58847e11	1.70256
$275$	−2.31807e10	−0.244415
$276$	1.82132e11	1.88927
$277$	−1.24749e11	−1.27314	−0.636572	−	0.771217i	$-0.719648\pi$
$277$	−1.24749e11	−1.27314	−0.636572	+	0.771217i	$0.719648\pi$
$278$	−1.50051e11	−1.50673
$279$	−4.16845e10	−0.411866
$280$	3.06195e10	0.297706
$281$	8.65210e10	0.827834	0.413917	−	0.910315i	$-0.364160\pi$
$281$	8.65210e10	0.827834	0.413917	+	0.910315i	$0.364160\pi$
$282$	−1.10869e11	−1.04397
$283$	−1.35344e11	−1.25429	−0.627146	−	0.778901i	$-0.715777\pi$
$283$	−1.35344e11	−1.25429	−0.627146	+	0.778901i	$0.715777\pi$
$284$	8.12238e10	0.740885
$285$	−5.89326e10	−0.529119
$286$	−9.82181e10	−0.868049
$287$	2.83926e10	0.247022
$288$	4.74652e10	0.406545
$289$	0	0
$290$	1.79338e11	1.48896
$291$	6.85661e10	0.560520
$292$	3.86922e11	3.11458
$293$	−8.66175e10	−0.686596	−0.343298	−	0.939227i	$-0.611544\pi$
$293$	−8.66175e10	−0.686596	−0.343298	+	0.939227i	$0.611544\pi$
$294$	1.58460e11	1.23696
$295$	−3.66033e10	−0.281398
$296$	−1.39208e11	−1.05403
$297$	−5.04452e10	−0.376198
$298$	2.58605e11	1.89961
$299$	2.20881e11	1.59823
$300$	−1.59349e11	−1.13580
$301$	−4.38585e10	−0.307968
$302$	3.62263e11	2.50607
$303$	7.13019e10	0.485970
$304$	−3.33807e11	−2.24163
$305$	1.07966e11	0.714393
$306$	0	0
$307$	1.77951e11	1.14335	0.571674	−	0.820481i	$-0.306294\pi$
$307$	1.77951e11	1.14335	0.571674	+	0.820481i	$0.306294\pi$
$308$	−3.03564e10	−0.192208
$309$	−1.82445e11	−1.13846
$310$	−1.43436e11	−0.882127
$311$	7.17574e10	0.434956	0.217478	−	0.976065i	$-0.430217\pi$
$311$	7.17574e10	0.434956	0.217478	+	0.976065i	$0.430217\pi$
$312$	−3.71183e11	−2.21765
$313$	2.65394e11	1.56294	0.781469	−	0.623944i	$-0.214471\pi$
$313$	2.65394e11	1.56294	0.781469	+	0.623944i	$0.214471\pi$
$314$	−1.85767e11	−1.07841
$315$	1.09531e10	0.0626814
$316$	−3.64847e11	−2.05835
$317$	−7.54472e9	−0.0419640	−0.0209820	−	0.999780i	$-0.506679\pi$
$317$	−7.54472e9	−0.0419640	−0.0209820	+	0.999780i	$0.506679\pi$
$318$	−3.17011e11	−1.73841
$319$	−9.77460e10	−0.528495
$320$	−1.34928e10	−0.0719328
$321$	7.95931e10	0.418411
$322$	9.90050e10	0.513222
$323$	0	0
$324$	−1.43494e11	−0.723404
$325$	−1.93251e11	−0.960830
$326$	2.68489e11	1.31658
$327$	2.18307e11	1.05585
$328$	4.59934e11	2.19414
$329$	−4.15567e10	−0.195551
$330$	−5.48042e10	−0.254391
$331$	2.63533e11	1.20673	0.603365	−	0.797466i	$-0.293826\pi$
$331$	2.63533e11	1.20673	0.603365	+	0.797466i	$0.293826\pi$
$332$	3.71440e11	1.67790
$333$	−4.97970e10	−0.221924
$334$	−5.28128e11	−2.32210
$335$	−5.46608e10	−0.237123
$336$	−7.24202e10	−0.309980
$337$	9.26802e10	0.391429	0.195714	−	0.980661i	$-0.437297\pi$
$337$	9.26802e10	0.391429	0.195714	+	0.980661i	$0.437297\pi$
$338$	−3.88169e11	−1.61769
$339$	2.27867e11	0.937095
$340$	0	0
$341$	7.81780e10	0.313105
$342$	−2.74322e11	−1.08428
$343$	1.22640e11	0.478419
$344$	−7.10469e11	−2.73547
$345$	1.23248e11	0.468377
$346$	1.65400e11	0.620429
$347$	1.66519e11	0.616568	0.308284	−	0.951294i	$-0.400245\pi$
$347$	1.66519e11	0.616568	0.308284	+	0.951294i	$0.400245\pi$
$348$	−6.71927e11	−2.45593
$349$	−2.48718e11	−0.897413	−0.448707	−	0.893679i	$-0.648115\pi$
$349$	−2.48718e11	−0.897413	−0.448707	+	0.893679i	$0.648115\pi$
$350$	−8.66204e10	−0.308542
$351$	−4.20549e11	−1.47888
$352$	−8.90194e10	−0.309060
$353$	−2.22039e10	−0.0761102	−0.0380551	−	0.999276i	$-0.512116\pi$
$353$	−2.22039e10	−0.0761102	−0.0380551	+	0.999276i	$0.512116\pi$
$354$	1.98888e11	0.673123
$355$	5.49641e10	0.183676
$356$	−3.13722e11	−1.03519
$357$	0	0
$358$	−1.00396e12	−3.23029
$359$	−3.21561e11	−1.02174	−0.510868	−	0.859659i	$-0.670676\pi$
$359$	−3.21561e11	−1.02174	−0.510868	+	0.859659i	$0.670676\pi$
$360$	1.77430e11	0.556757
$361$	2.30550e11	0.714467
$362$	−1.45262e11	−0.444594
$363$	−2.12909e11	−0.643598
$364$	−2.53073e11	−0.755597
$365$	2.61829e11	0.772148
$366$	−5.86645e11	−1.70888
$367$	−3.84324e10	−0.110586	−0.0552931	−	0.998470i	$-0.517609\pi$
$367$	−3.84324e10	−0.110586	−0.0552931	+	0.998470i	$0.517609\pi$
$368$	6.98105e11	1.98429
$369$	1.64526e11	0.461972
$370$	−1.71351e11	−0.475313
$371$	−1.18824e11	−0.325629
$372$	5.37413e11	1.45501
$373$	2.79837e11	0.748540	0.374270	−	0.927320i	$-0.377893\pi$
$373$	2.79837e11	0.748540	0.374270	+	0.927320i	$0.377893\pi$
$374$	0	0
$375$	−2.62581e11	−0.685682
$376$	−6.73181e11	−1.73695
$377$	−8.14883e11	−2.07759
$378$	−1.88501e11	−0.474899
$379$	−2.19767e11	−0.547125	−0.273563	−	0.961854i	$-0.588202\pi$
$379$	−2.19767e11	−0.547125	−0.273563	+	0.961854i	$0.588202\pi$
$380$	−6.50885e11	−1.60132
$381$	3.64613e10	0.0886483
$382$	−6.34877e11	−1.52547
$383$	5.65339e11	1.34250	0.671250	−	0.741231i	$-0.265758\pi$
$383$	5.65339e11	1.34250	0.671250	+	0.741231i	$0.265758\pi$
$384$	3.48833e11	0.818705
$385$	−2.05421e10	−0.0476511
$386$	3.22311e11	0.738978
$387$	−2.54146e11	−0.575949
$388$	7.57283e11	1.69635
$389$	5.16400e11	1.14344	0.571719	−	0.820449i	$-0.306277\pi$
$389$	5.16400e11	1.14344	0.571719	+	0.820449i	$0.306277\pi$
$390$	−4.56888e11	−1.00004
$391$	0	0
$392$	9.62148e11	2.05804
$393$	−2.70484e11	−0.571972
$394$	−1.07726e12	−2.25210
$395$	−2.46892e11	−0.510293
$396$	−1.75905e11	−0.359460
$397$	2.44886e11	0.494774	0.247387	−	0.968917i	$-0.420428\pi$
$397$	2.44886e11	0.494774	0.247387	+	0.968917i	$0.420428\pi$
$398$	1.70015e12	3.39636
$399$	1.20026e11	0.237082
$400$	−6.10779e11	−1.19293
$401$	5.01628e11	0.968796	0.484398	−	0.874848i	$-0.339039\pi$
$401$	5.01628e11	0.968796	0.484398	+	0.874848i	$0.339039\pi$
$402$	2.97005e11	0.567214
$403$	6.51750e11	1.23086
$404$	7.87499e11	1.47073
$405$	−9.71022e10	−0.179342
$406$	−3.65253e11	−0.667155
$407$	9.33928e10	0.168709
$408$	0	0
$409$	1.25612e11	0.221960	0.110980	−	0.993823i	$-0.464601\pi$
$409$	1.25612e11	0.221960	0.110980	+	0.993823i	$0.464601\pi$
$410$	5.66132e11	0.989442
$411$	−4.02740e11	−0.696203
$412$	−2.01503e12	−3.44543
$413$	7.45488e10	0.126086
$414$	5.73702e11	0.959808
$415$	2.51353e11	0.415976
$416$	−7.42131e11	−1.21496
$417$	3.80437e11	0.616127
$418$	5.14482e11	0.824284
$419$	6.58138e11	1.04317	0.521584	−	0.853200i	$-0.325341\pi$
$419$	6.58138e11	1.04317	0.521584	+	0.853200i	$0.325341\pi$
$420$	−1.41211e11	−0.221435
$421$	2.88370e11	0.447384	0.223692	−	0.974660i	$-0.428189\pi$
$421$	2.88370e11	0.447384	0.223692	+	0.974660i	$0.428189\pi$
$422$	−1.02148e12	−1.56791
$423$	−2.40807e11	−0.365711
$424$	−1.92485e12	−2.89234
$425$	0	0
$426$	−2.98654e11	−0.439364
$427$	−2.19891e11	−0.320097
$428$	8.79072e11	1.26627
$429$	2.49021e11	0.354959
$430$	−8.74514e11	−1.23356
$431$	3.20484e11	0.447362	0.223681	−	0.974662i	$-0.428193\pi$
$431$	3.20484e11	0.447362	0.223681	+	0.974662i	$0.428193\pi$
$432$	−1.32916e12	−1.83612
$433$	1.13300e12	1.54894	0.774470	−	0.632610i	$-0.218016\pi$
$433$	1.13300e12	1.54894	0.774470	+	0.632610i	$0.218016\pi$
$434$	2.92132e11	0.395253
$435$	−4.54693e11	−0.608858
$436$	2.41110e12	3.19541
$437$	−1.15701e12	−1.51765
$438$	−1.42268e12	−1.84703
$439$	2.56493e11	0.329599	0.164799	−	0.986327i	$-0.447302\pi$
$439$	2.56493e11	0.329599	0.164799	+	0.986327i	$0.447302\pi$
$440$	−3.32764e11	−0.423253
$441$	3.44175e11	0.433317
$442$	0	0
$443$	−3.11296e11	−0.384023	−0.192011	−	0.981393i	$-0.561501\pi$
$443$	−3.11296e11	−0.384023	−0.192011	+	0.981393i	$0.561501\pi$
$444$	6.42002e11	0.783995
$445$	−2.12296e11	−0.256638
$446$	1.39227e12	1.66616
$447$	−6.55665e11	−0.776780
$448$	2.74803e10	0.0322308
$449$	1.40238e12	1.62838	0.814190	−	0.580598i	$-0.197181\pi$
$449$	1.40238e12	1.62838	0.814190	+	0.580598i	$0.197181\pi$
$450$	−5.01937e11	−0.577023
$451$	−3.08563e11	−0.351196
$452$	2.51670e12	2.83601
$453$	−9.18479e11	−1.02477
$454$	−1.59392e12	−1.76082
$455$	−1.71254e11	−0.187323
$456$	1.94432e12	2.10584
$457$	8.60205e11	0.922527	0.461263	−	0.887263i	$-0.347396\pi$
$457$	8.60205e11	0.922527	0.461263	+	0.887263i	$0.347396\pi$
$458$	−1.29828e12	−1.37871
$459$	0	0
$460$	1.36123e12	1.41749
$461$	1.43574e12	1.48054	0.740272	−	0.672307i	$-0.234697\pi$
$461$	1.43574e12	1.48054	0.740272	+	0.672307i	$0.234697\pi$
$462$	1.11618e11	0.113984
$463$	1.35035e12	1.36563	0.682814	−	0.730592i	$-0.260756\pi$
$463$	1.35035e12	1.36563	0.682814	+	0.730592i	$0.260756\pi$
$464$	−2.57548e12	−2.57945
$465$	3.63667e11	0.360716
$466$	−3.49150e12	−3.42985
$467$	1.64014e12	1.59571	0.797857	−	0.602847i	$-0.205967\pi$
$467$	1.64014e12	1.59571	0.797857	+	0.602847i	$0.205967\pi$
$468$	−1.46648e12	−1.41309
$469$	1.11326e11	0.106247
$470$	−8.28617e11	−0.783273
$471$	4.70992e11	0.440981
$472$	1.20762e12	1.11993
$473$	4.76643e11	0.437842
$474$	1.34151e12	1.22066
$475$	1.01228e12	0.912387
$476$	0	0
$477$	−6.88548e11	−0.608978
$478$	−1.33005e12	−1.16532
$479$	2.75788e11	0.239368	0.119684	−	0.992812i	$-0.461812\pi$
$479$	2.75788e11	0.239368	0.119684	+	0.992812i	$0.461812\pi$
$480$	−4.14098e11	−0.356056
$481$	7.78591e11	0.663218
$482$	9.32635e10	0.0787046
$483$	−2.51016e11	−0.209865
$484$	−2.35149e12	−1.94778
$485$	5.12453e11	0.420548
$486$	−1.83974e12	−1.49587
$487$	−6.65187e11	−0.535875	−0.267937	−	0.963436i	$-0.586342\pi$
$487$	−6.65187e11	−0.535875	−0.267937	+	0.963436i	$0.586342\pi$
$488$	−3.56203e12	−2.84321
$489$	−6.80723e11	−0.538370
$490$	1.18430e12	0.928071
$491$	1.08124e11	0.0839570	0.0419785	−	0.999119i	$-0.486634\pi$
$491$	1.08124e11	0.0839570	0.0419785	+	0.999119i	$0.486634\pi$
$492$	−2.12113e12	−1.63201
$493$	0	0
$494$	4.28910e12	3.24037
$495$	−1.19035e11	−0.0891151
$496$	2.05989e12	1.52818
$497$	−1.11944e11	−0.0822992
$498$	−1.36576e12	−0.995041
$499$	1.19150e12	0.860280	0.430140	−	0.902762i	$-0.358464\pi$
$499$	1.19150e12	0.860280	0.430140	+	0.902762i	$0.358464\pi$
$500$	−2.90009e12	−2.07514
$501$	1.33901e12	0.949542
$502$	1.74594e12	1.22705
$503$	2.63721e12	1.83692	0.918458	−	0.395518i	$-0.129435\pi$
$503$	2.63721e12	1.83692	0.918458	+	0.395518i	$0.129435\pi$
$504$	−3.61366e11	−0.249465
$505$	5.32900e11	0.364615
$506$	−1.07596e12	−0.729656
$507$	9.84160e11	0.661500
$508$	4.02700e11	0.268284
$509$	1.59065e12	1.05038	0.525189	−	0.850986i	$-0.323995\pi$
$509$	1.59065e12	1.05038	0.525189	+	0.850986i	$0.323995\pi$
$510$	0	0
$511$	−5.33260e11	−0.345975
$512$	3.48814e12	2.24326
$513$	2.20290e12	1.40432
$514$	6.85416e11	0.433132
$515$	−1.36357e12	−0.854169
$516$	3.27654e12	2.03466
$517$	4.51627e11	0.278018
$518$	3.48986e11	0.212973
$519$	−4.19352e11	−0.253703
$520$	−2.77417e12	−1.66386
$521$	−2.27882e12	−1.35500	−0.677501	−	0.735522i	$-0.736937\pi$
$521$	−2.27882e12	−1.35500	−0.677501	+	0.735522i	$0.736937\pi$
$522$	−2.11652e12	−1.24769
$523$	−4.41293e11	−0.257910	−0.128955	−	0.991650i	$-0.541162\pi$
$523$	−4.41293e11	−0.257910	−0.128955	+	0.991650i	$0.541162\pi$
$524$	−2.98738e12	−1.73101
$525$	2.19616e11	0.126168
$526$	7.65110e11	0.435801
$527$	0	0
$528$	7.87043e11	0.440703
$529$	6.18555e11	0.343422
$530$	−2.36929e12	−1.30430
$531$	4.31986e11	0.235800
$532$	1.32564e12	0.717501
$533$	−2.57241e12	−1.38060
$534$	1.15353e12	0.613895
$535$	5.94867e11	0.313926
$536$	1.80338e12	0.943725
$537$	2.54542e12	1.32091
$538$	3.76720e12	1.93864
$539$	−6.45490e11	−0.329412
$540$	−2.59172e12	−1.31164
$541$	−1.02615e12	−0.515018	−0.257509	−	0.966276i	$-0.582902\pi$
$541$	−1.02615e12	−0.515018	−0.257509	+	0.966276i	$0.582902\pi$
$542$	−4.51813e12	−2.24886
$543$	3.68296e11	0.181801
$544$	0	0
$545$	1.63159e12	0.792186
$546$	9.30530e11	0.448088
$547$	−3.05683e12	−1.45992	−0.729960	−	0.683490i	$-0.760461\pi$
$547$	−3.05683e12	−1.45992	−0.729960	+	0.683490i	$0.760461\pi$
$548$	−4.44809e12	−2.10698
$549$	−1.27419e12	−0.598633
$550$	9.41367e11	0.438659
$551$	4.26848e12	1.97284
$552$	−4.06624e12	−1.86409
$553$	5.02837e11	0.228646
$554$	5.06606e12	2.28495
$555$	4.34442e11	0.194363
$556$	4.20176e12	1.86464
$557$	1.36756e12	0.602002	0.301001	−	0.953624i	$-0.402679\pi$
$557$	1.36756e12	0.602002	0.301001	+	0.953624i	$0.402679\pi$
$558$	1.69281e12	0.739187
$559$	3.97364e12	1.72122
$560$	−5.41258e11	−0.232572
$561$	0	0
$562$	−3.51362e12	−1.48573
$563$	9.34193e11	0.391876	0.195938	−	0.980616i	$-0.437225\pi$
$563$	9.34193e11	0.391876	0.195938	+	0.980616i	$0.437225\pi$
$564$	3.10458e12	1.29195
$565$	1.70305e12	0.703087
$566$	5.49631e12	2.25111
$567$	1.97765e11	0.0803573
$568$	−1.81339e12	−0.731009
$569$	−3.19843e11	−0.127918	−0.0639589	−	0.997953i	$-0.520373\pi$
$569$	−3.19843e11	−0.127918	−0.0639589	+	0.997953i	$0.520373\pi$
$570$	2.39325e12	0.949624
$571$	−4.20176e12	−1.65413	−0.827064	−	0.562108i	$-0.809991\pi$
$571$	−4.20176e12	−1.65413	−0.827064	+	0.562108i	$0.809991\pi$
$572$	2.75033e12	1.07424
$573$	1.60966e12	0.623790
$574$	−1.15302e12	−0.443338
$575$	−2.11703e12	−0.807646
$576$	1.59240e11	0.0602767
$577$	−2.55609e12	−0.960029	−0.480014	−	0.877261i	$-0.659369\pi$
$577$	−2.55609e12	−0.960029	−0.480014	+	0.877261i	$0.659369\pi$
$578$	0	0
$579$	−8.17183e11	−0.302180
$580$	−5.02188e12	−1.84264
$581$	−5.11923e11	−0.186385
$582$	−2.78447e12	−1.00598
$583$	1.29135e12	0.462952
$584$	−8.63833e12	−3.07307
$585$	−9.92363e11	−0.350324
$586$	3.51754e12	1.23225
$587$	1.14636e12	0.398519	0.199259	−	0.979947i	$-0.436146\pi$
$587$	1.14636e12	0.398519	0.199259	+	0.979947i	$0.436146\pi$
$588$	−4.43724e12	−1.53079
$589$	−3.41397e12	−1.16880
$590$	1.48646e12	0.505032
$591$	2.73127e12	0.920918
$592$	2.46077e12	0.823425
$593$	3.04937e12	1.01266	0.506331	−	0.862339i	$-0.331002\pi$
$593$	3.04937e12	1.01266	0.506331	+	0.862339i	$0.331002\pi$
$594$	2.04858e12	0.675172
$595$	0	0
$596$	−7.24154e12	−2.35084
$597$	−4.31055e12	−1.38883
$598$	−8.96999e12	−2.86838
$599$	−3.29572e12	−1.04599	−0.522997	−	0.852334i	$-0.675186\pi$
$599$	−3.29572e12	−1.04599	−0.522997	+	0.852334i	$0.675186\pi$
$600$	3.55759e12	1.12066
$601$	−7.69804e11	−0.240683	−0.120341	−	0.992733i	$-0.538399\pi$
$601$	−7.69804e11	−0.240683	−0.120341	+	0.992733i	$0.538399\pi$
$602$	1.78110e12	0.552717
$603$	6.45097e11	0.198700
$604$	−1.01442e13	−3.10136
$605$	−1.59125e12	−0.482880
$606$	−2.89557e12	−0.872183
$607$	1.60628e12	0.480255	0.240127	−	0.970741i	$-0.422811\pi$
$607$	1.60628e12	0.480255	0.240127	+	0.970741i	$0.422811\pi$
$608$	3.88740e12	1.15370
$609$	9.26058e11	0.272810
$610$	−4.38450e12	−1.28214
$611$	3.76509e12	1.09292
$612$	0	0
$613$	−4.16207e12	−1.19052	−0.595261	−	0.803533i	$-0.702951\pi$
$613$	−4.16207e12	−1.19052	−0.595261	+	0.803533i	$0.702951\pi$
$614$	−7.22661e12	−2.05200
$615$	−1.43536e12	−0.404599
$616$	6.77731e11	0.189646
$617$	−3.92295e12	−1.08976	−0.544879	−	0.838515i	$-0.683424\pi$
$617$	−3.92295e12	−1.08976	−0.544879	+	0.838515i	$0.683424\pi$
$618$	7.40909e12	2.04323
$619$	1.03693e12	0.283885	0.141943	−	0.989875i	$-0.454665\pi$
$619$	1.03693e12	0.283885	0.141943	+	0.989875i	$0.454665\pi$
$620$	4.01654e12	1.09167
$621$	−4.60702e12	−1.24311
$622$	−2.91407e12	−0.780626
$623$	4.32376e11	0.114991
$624$	6.56137e12	1.73246
$625$	6.95630e11	0.182355
$626$	−1.07777e13	−2.80505
$627$	−1.30441e12	−0.337063
$628$	5.20190e12	1.33458
$629$	0	0
$630$	−4.44805e11	−0.112496
$631$	−4.47475e12	−1.12366	−0.561832	−	0.827251i	$-0.689903\pi$
$631$	−4.47475e12	−1.12366	−0.561832	+	0.827251i	$0.689903\pi$
$632$	8.14551e12	2.03091
$633$	2.58984e12	0.641145
$634$	3.06391e11	0.0753138
$635$	2.72507e11	0.0665113
$636$	8.87702e12	2.15135
$637$	−5.38128e12	−1.29496
$638$	3.96947e12	0.948504
$639$	−6.48677e11	−0.153913
$640$	2.60713e12	0.614261
$641$	7.27990e10	0.0170319	0.00851597	−	0.999964i	$-0.497289\pi$
$641$	7.27990e10	0.0170319	0.00851597	+	0.999964i	$0.497289\pi$
$642$	−3.23228e12	−0.750932
$643$	−1.86086e11	−0.0429303	−0.0214652	−	0.999770i	$-0.506833\pi$
$643$	−1.86086e11	−0.0429303	−0.0214652	+	0.999770i	$0.506833\pi$
$644$	−2.77237e12	−0.635132
$645$	2.21723e12	0.504421
$646$	0	0
$647$	2.89537e12	0.649583	0.324791	−	0.945786i	$-0.394706\pi$
$647$	2.89537e12	0.649583	0.324791	+	0.945786i	$0.394706\pi$
$648$	3.20361e12	0.713761
$649$	−8.10176e11	−0.179258
$650$	7.84793e12	1.72443
$651$	−7.40668e11	−0.161625
$652$	−7.51830e12	−1.62932
$653$	−4.46865e12	−0.961761	−0.480880	−	0.876786i	$-0.659683\pi$
$653$	−4.46865e12	−0.961761	−0.480880	+	0.876786i	$0.659683\pi$
$654$	−8.86544e12	−1.89496
$655$	−2.02156e12	−0.429141
$656$	−8.13022e12	−1.71409
$657$	−3.09007e12	−0.647029
$658$	1.68762e12	0.350960
$659$	4.32558e12	0.893429	0.446714	−	0.894677i	$-0.352594\pi$
$659$	4.32558e12	0.893429	0.446714	+	0.894677i	$0.352594\pi$
$660$	1.53464e12	0.314818
$661$	−3.49165e12	−0.711417	−0.355709	−	0.934597i	$-0.615760\pi$
$661$	−3.49165e12	−0.711417	−0.355709	+	0.934597i	$0.615760\pi$
$662$	−1.07021e13	−2.16575
$663$	0	0
$664$	−8.29269e12	−1.65554
$665$	8.97058e11	0.177878
$666$	2.02226e12	0.398293
$667$	−8.92687e12	−1.74636
$668$	1.47888e13	2.87368
$669$	−3.52995e12	−0.681319
$670$	2.21977e12	0.425571
$671$	2.38971e12	0.455087
$672$	8.43381e11	0.159537
$673$	7.03831e12	1.32251	0.661257	−	0.750159i	$-0.270023\pi$
$673$	7.03831e12	1.32251	0.661257	+	0.750159i	$0.270023\pi$
$674$	−3.76374e12	−0.702507
$675$	4.03073e12	0.747337
$676$	1.08696e13	2.00196
$677$	5.38586e12	0.985385	0.492692	−	0.870203i	$-0.336013\pi$
$677$	5.38586e12	0.985385	0.492692	+	0.870203i	$0.336013\pi$
$678$	−9.25370e12	−1.68183
$679$	−1.04370e12	−0.188434
$680$	0	0
$681$	4.04120e12	0.720026
$682$	−3.17481e12	−0.561938
$683$	3.57812e12	0.629162	0.314581	−	0.949231i	$-0.398136\pi$
$683$	3.57812e12	0.629162	0.314581	+	0.949231i	$0.398136\pi$
$684$	7.68164e12	1.34184
$685$	−3.01001e12	−0.522349
$686$	−4.98041e12	−0.858631
$687$	3.29165e12	0.563778
$688$	1.25589e13	2.13699
$689$	1.07656e13	1.81993
$690$	−5.00512e12	−0.840608
$691$	−9.36146e12	−1.56204	−0.781020	−	0.624505i	$-0.785301\pi$
$691$	−9.36146e12	−1.56204	−0.781020	+	0.624505i	$0.785301\pi$
$692$	−4.63157e12	−0.767804
$693$	2.42435e11	0.0399297
$694$	−6.76234e12	−1.10657
$695$	2.84333e12	0.462270
$696$	1.50013e13	2.42319
$697$	0	0
$698$	1.01004e13	1.61061
$699$	8.85231e12	1.40252
$700$	2.42557e12	0.381832
$701$	7.85905e12	1.22925	0.614624	−	0.788821i	$-0.289308\pi$
$701$	7.85905e12	1.22925	0.614624	+	0.788821i	$0.289308\pi$
$702$	1.70785e13	2.65419
$703$	−4.07838e12	−0.629780
$704$	−2.98649e11	−0.0458230
$705$	2.10087e12	0.320293
$706$	9.01701e11	0.136597
$707$	−1.08534e12	−0.163372
$708$	−5.56932e12	−0.833015
$709$	−7.23260e12	−1.07495	−0.537473	−	0.843281i	$-0.680621\pi$
$709$	−7.23260e12	−1.07495	−0.537473	+	0.843281i	$0.680621\pi$
$710$	−2.23209e12	−0.329647
$711$	2.91378e12	0.427605
$712$	7.00410e12	1.02139
$713$	7.13978e12	1.03462
$714$	0	0
$715$	1.86115e12	0.266320
$716$	2.81131e13	3.99760
$717$	3.37221e12	0.476516
$718$	1.30586e13	1.83374
$719$	−3.43266e12	−0.479016	−0.239508	−	0.970894i	$-0.576986\pi$
$719$	−3.43266e12	−0.479016	−0.239508	+	0.970894i	$0.576986\pi$
$720$	−3.13641e12	−0.434948
$721$	2.77713e12	0.382726
$722$	−9.36262e12	−1.28227
$723$	−2.36459e11	−0.0321836
$724$	4.06767e12	0.550202
$725$	7.81021e12	1.04988
$726$	8.64624e12	1.15508
$727$	−4.17490e12	−0.554295	−0.277148	−	0.960827i	$-0.589389\pi$
$727$	−4.17490e12	−0.554295	−0.277148	+	0.960827i	$0.589389\pi$
$728$	5.65006e12	0.745525
$729$	7.14815e12	0.937389
$730$	−1.06329e13	−1.38579
$731$	0	0
$732$	1.64274e13	2.11480
$733$	5.29693e11	0.0677729	0.0338865	−	0.999426i	$-0.489212\pi$
$733$	5.29693e11	0.0677729	0.0338865	+	0.999426i	$0.489212\pi$
$734$	1.56074e12	0.198472
$735$	−3.00267e12	−0.379503
$736$	−8.12990e12	−1.02126
$737$	−1.20986e12	−0.151054
$738$	−6.68139e12	−0.829112
$739$	4.99613e12	0.616217	0.308109	−	0.951351i	$-0.400304\pi$
$739$	4.99613e12	0.616217	0.308109	+	0.951351i	$0.400304\pi$
$740$	4.79823e12	0.588218
$741$	−1.08745e13	−1.32504
$742$	4.82546e12	0.584414
$743$	−4.24607e12	−0.511138	−0.255569	−	0.966791i	$-0.582263\pi$
$743$	−4.24607e12	−0.511138	−0.255569	+	0.966791i	$0.582263\pi$
$744$	−1.19982e13	−1.43561
$745$	−4.90034e12	−0.582805
$746$	−1.13642e13	−1.34342
$747$	−2.96643e12	−0.348571
$748$	0	0
$749$	−1.21155e12	−0.140660
$750$	1.06634e13	1.23061
$751$	1.61654e13	1.85441	0.927204	−	0.374556i	$-0.122205\pi$
$751$	1.61654e13	1.85441	0.927204	+	0.374556i	$0.122205\pi$
$752$	1.18998e13	1.35693
$753$	−4.42665e12	−0.501762
$754$	3.30924e13	3.72870
$755$	−6.86457e12	−0.768869
$756$	5.27847e12	0.587706
$757$	−1.65437e13	−1.83106	−0.915528	−	0.402254i	$-0.868227\pi$
$757$	−1.65437e13	−1.83106	−0.915528	+	0.402254i	$0.868227\pi$
$758$	8.92476e12	0.981940
$759$	2.72797e12	0.298368
$760$	1.45315e13	1.57998
$761$	4.75009e12	0.513418	0.256709	−	0.966489i	$-0.417362\pi$
$761$	4.75009e12	0.513418	0.256709	+	0.966489i	$0.417362\pi$
$762$	−1.48070e12	−0.159099
$763$	−3.32301e12	−0.354954
$764$	1.77780e13	1.88783
$765$	0	0
$766$	−2.29584e13	−2.40942
$767$	−6.75422e12	−0.704687
$768$	−1.32418e13	−1.37348
$769$	−9.86330e12	−1.01708	−0.508538	−	0.861039i	$-0.669814\pi$
$769$	−9.86330e12	−1.01708	−0.508538	+	0.861039i	$0.669814\pi$
$770$	8.34217e11	0.0855206
$771$	−1.73780e12	−0.177114
$772$	−9.02543e12	−0.914514
$773$	−3.02810e12	−0.305044	−0.152522	−	0.988300i	$-0.548740\pi$
$773$	−3.02810e12	−0.305044	−0.152522	+	0.988300i	$0.548740\pi$
$774$	1.03209e13	1.03367
$775$	−6.24667e12	−0.622000
$776$	−1.69069e13	−1.67374
$777$	−8.84815e11	−0.0870879
$778$	−2.09710e13	−2.05216
$779$	1.34747e13	1.31099
$780$	1.27939e13	1.23759
$781$	1.21657e12	0.117006
$782$	0	0
$783$	1.69964e13	1.61595
$784$	−1.70078e13	−1.60778
$785$	3.52012e12	0.330860
$786$	1.09844e13	1.02653
$787$	−1.11143e13	−1.03275	−0.516374	−	0.856363i	$-0.672719\pi$
$787$	−1.11143e13	−1.03275	−0.516374	+	0.856363i	$0.672719\pi$
$788$	3.01657e13	2.78706
$789$	−1.93985e12	−0.178206
$790$	1.00263e13	0.915837
$791$	−3.46854e12	−0.315031
$792$	3.92723e12	0.354669
$793$	1.99224e13	1.78901
$794$	−9.94483e12	−0.887984
$795$	6.00707e12	0.533348
$796$	−4.76082e13	−4.20313
$797$	8.24068e12	0.723437	0.361718	−	0.932287i	$-0.382190\pi$
$797$	8.24068e12	0.723437	0.361718	+	0.932287i	$0.382190\pi$
$798$	−4.87426e12	−0.425497
$799$	0	0
$800$	7.11293e12	0.613965
$801$	2.50548e12	0.215052
$802$	−2.03711e13	−1.73872
$803$	5.79532e12	0.491878
$804$	−8.31683e12	−0.701949
$805$	−1.87606e12	−0.157458
$806$	−2.64676e13	−2.20905
$807$	−9.55131e12	−0.792742
$808$	−1.75815e13	−1.45113
$809$	−6.01180e12	−0.493442	−0.246721	−	0.969087i	$-0.579353\pi$
$809$	−6.01180e12	−0.493442	−0.246721	+	0.969087i	$0.579353\pi$
$810$	3.94332e12	0.321869
$811$	1.46588e13	1.18989	0.594943	−	0.803768i	$-0.297175\pi$
$811$	1.46588e13	1.18989	0.594943	+	0.803768i	$0.297175\pi$
$812$	1.02279e13	0.825629
$813$	1.14552e13	0.919594
$814$	−3.79268e12	−0.302787
$815$	−5.08762e12	−0.403930
$816$	0	0
$817$	−2.08146e13	−1.63444
$818$	−5.10109e12	−0.398357
$819$	2.02112e12	0.156969
$820$	−1.58530e13	−1.22447
$821$	1.36762e13	1.05056	0.525280	−	0.850929i	$-0.323960\pi$
$821$	1.36762e13	1.05056	0.525280	+	0.850929i	$0.323960\pi$
$822$	1.63553e13	1.24949
$823$	−1.23214e13	−0.936180	−0.468090	−	0.883681i	$-0.655058\pi$
$823$	−1.23214e13	−0.936180	−0.468090	+	0.883681i	$0.655058\pi$
$824$	4.49871e13	3.39950
$825$	−2.38673e12	−0.179375
$826$	−3.02743e12	−0.226289
$827$	1.87511e13	1.39397	0.696983	−	0.717088i	$-0.254525\pi$
$827$	1.87511e13	1.39397	0.696983	+	0.717088i	$0.254525\pi$
$828$	−1.60650e13	−1.18780
$829$	6.45929e12	0.474995	0.237498	−	0.971388i	$-0.423673\pi$
$829$	6.45929e12	0.474995	0.237498	+	0.971388i	$0.423673\pi$
$830$	−1.02075e13	−0.746562
$831$	−1.28444e13	−0.934351
$832$	−2.48976e12	−0.180136
$833$	0	0
$834$	−1.54495e13	−1.10578
$835$	1.00076e13	0.712425
$836$	−1.44067e13	−1.02008
$837$	−1.35939e13	−0.957366
$838$	−2.67270e13	−1.87220
$839$	−2.06836e13	−1.44111	−0.720557	−	0.693396i	$-0.756114\pi$
$839$	−2.06836e13	−1.44111	−0.720557	+	0.693396i	$0.756114\pi$
$840$	3.15265e12	0.218484
$841$	1.84262e13	1.27015
$842$	−1.17107e13	−0.802931
$843$	8.90839e12	0.607541
$844$	2.86037e13	1.94035
$845$	7.35547e12	0.496312
$846$	9.77919e12	0.656351
$847$	3.24085e12	0.216363
$848$	3.40253e13	2.25955
$849$	−1.39353e13	−0.920515
$850$	0	0
$851$	8.52930e12	0.557482
$852$	8.36298e12	0.543730
$853$	2.64082e12	0.170793	0.0853963	−	0.996347i	$-0.472784\pi$
$853$	2.64082e12	0.170793	0.0853963	+	0.996347i	$0.472784\pi$
$854$	8.92977e12	0.574486
$855$	5.19816e12	0.332661
$856$	−1.96260e13	−1.24939
$857$	−1.71578e13	−1.08654	−0.543272	−	0.839557i	$-0.682815\pi$
$857$	−1.71578e13	−1.08654	−0.543272	+	0.839557i	$0.682815\pi$
$858$	−1.01127e13	−0.637054
$859$	8.08574e12	0.506700	0.253350	−	0.967375i	$-0.418468\pi$
$859$	8.08574e12	0.506700	0.253350	+	0.967375i	$0.418468\pi$
$860$	2.44884e13	1.52657
$861$	2.92336e12	0.181288
$862$	−1.30149e13	−0.802893
$863$	−1.72986e13	−1.06161	−0.530803	−	0.847495i	$-0.678109\pi$
$863$	−1.72986e13	−1.06161	−0.530803	+	0.847495i	$0.678109\pi$
$864$	1.54790e13	0.944998
$865$	−3.13418e12	−0.190349
$866$	−4.60112e13	−2.77992
$867$	0	0
$868$	−8.18037e12	−0.489141
$869$	−5.46469e12	−0.325070
$870$	1.84651e13	1.09273
$871$	−1.00863e13	−0.593812
$872$	−5.38298e13	−3.15282
$873$	−6.04788e12	−0.352403
$874$	4.69862e13	2.72376
$875$	3.99694e12	0.230511
$876$	3.98383e13	2.28577
$877$	−1.81609e12	−0.103666	−0.0518332	−	0.998656i	$-0.516506\pi$
$877$	−1.81609e12	−0.103666	−0.0518332	+	0.998656i	$0.516506\pi$
$878$	−1.04162e13	−0.591540
$879$	−8.91833e12	−0.503887
$880$	5.88224e12	0.330652
$881$	3.76167e12	0.210372	0.105186	−	0.994453i	$-0.466456\pi$
$881$	3.76167e12	0.210372	0.105186	+	0.994453i	$0.466456\pi$
$882$	−1.39770e13	−0.777686
$883$	3.03716e13	1.68130	0.840649	−	0.541581i	$-0.182174\pi$
$883$	3.03716e13	1.68130	0.840649	+	0.541581i	$0.182174\pi$
$884$	0	0
$885$	−3.76875e12	−0.206516
$886$	1.26417e13	0.689215
$887$	8.30135e12	0.450290	0.225145	−	0.974325i	$-0.427714\pi$
$887$	8.30135e12	0.450290	0.225145	+	0.974325i	$0.427714\pi$
$888$	−1.43332e13	−0.773544
$889$	−5.55006e11	−0.0298016
$890$	8.62133e12	0.460595
$891$	−2.14925e12	−0.114245
$892$	−3.89868e13	−2.06194
$893$	−1.97221e13	−1.03782
$894$	2.66266e13	1.39411
$895$	1.90241e13	0.991060
$896$	−5.30986e12	−0.275231
$897$	2.27424e13	1.17293
$898$	−5.69505e13	−2.92250
$899$	−2.63403e13	−1.34494
$900$	1.40554e13	0.714088
$901$	0	0
$902$	1.25307e13	0.630300
$903$	−4.51577e12	−0.226015
$904$	−5.61873e13	−2.79821
$905$	2.75259e12	0.136402
$906$	3.72994e13	1.83918
$907$	−1.31615e13	−0.645763	−0.322882	−	0.946439i	$-0.604652\pi$
$907$	−1.31615e13	−0.645763	−0.322882	+	0.946439i	$0.604652\pi$
$908$	4.46333e13	2.17908
$909$	−6.28919e12	−0.305533
$910$	6.95465e12	0.336193
$911$	−2.85075e13	−1.37128	−0.685641	−	0.727940i	$-0.740478\pi$
$911$	−2.85075e13	−1.37128	−0.685641	+	0.727940i	$0.740478\pi$
$912$	−3.43695e13	−1.64512
$913$	5.56344e12	0.264987
$914$	−3.49329e13	−1.65568
$915$	1.11164e13	0.524287
$916$	3.63549e13	1.70621
$917$	4.11724e12	0.192284
$918$	0	0
$919$	2.80490e13	1.29717	0.648585	−	0.761142i	$-0.275361\pi$
$919$	2.80490e13	1.29717	0.648585	+	0.761142i	$0.275361\pi$
$920$	−3.03904e13	−1.39859
$921$	1.83223e13	0.839094
$922$	−5.83054e13	−2.65717
$923$	1.01422e13	0.459967
$924$	−3.12556e12	−0.141060
$925$	−7.46237e12	−0.335150
$926$	−5.48378e13	−2.45093
$927$	1.60926e13	0.715759
$928$	2.99931e13	1.32756
$929$	−3.51380e13	−1.54777	−0.773886	−	0.633325i	$-0.781690\pi$
$929$	−3.51380e13	−1.54777	−0.773886	+	0.633325i	$0.781690\pi$
$930$	−1.47685e13	−0.647386
$931$	2.81880e13	1.22967
$932$	9.77700e13	4.24457
$933$	7.38830e12	0.319210
$934$	−6.66061e13	−2.86387
$935$	0	0
$936$	3.27403e13	1.39425
$937$	−4.23191e12	−0.179353	−0.0896765	−	0.995971i	$-0.528583\pi$
$937$	−4.23191e12	−0.179353	−0.0896765	+	0.995971i	$0.528583\pi$
$938$	−4.52094e12	−0.190685
$939$	2.73256e13	1.14703
$940$	2.32032e13	0.969331
$941$	2.94937e13	1.22624	0.613121	−	0.789989i	$-0.289914\pi$
$941$	2.94937e13	1.22624	0.613121	+	0.789989i	$0.289914\pi$
$942$	−1.91270e13	−0.791439
$943$	−2.81802e13	−1.16049
$944$	−2.13470e13	−0.874910
$945$	3.57194e12	0.145700
$946$	−1.93565e13	−0.785807
$947$	4.70153e12	0.189961	0.0949805	−	0.995479i	$-0.469721\pi$
$947$	4.70153e12	0.189961	0.0949805	+	0.995479i	$0.469721\pi$
$948$	−3.75655e13	−1.51061
$949$	4.83141e13	1.93364
$950$	−4.11087e13	−1.63749
$951$	−7.76821e11	−0.0307970
$952$	0	0
$953$	8.96893e12	0.352227	0.176114	−	0.984370i	$-0.443647\pi$
$953$	8.96893e12	0.352227	0.176114	+	0.984370i	$0.443647\pi$
$954$	2.79619e13	1.09295
$955$	1.20304e13	0.468019
$956$	3.72446e13	1.44212
$957$	−1.00641e13	−0.387858
$958$	−1.11998e13	−0.429600
$959$	6.13040e12	0.234048
$960$	−1.38925e12	−0.0527909
$961$	−5.37241e12	−0.203195
$962$	−3.16186e13	−1.19030
$963$	−7.02052e12	−0.263058
$964$	−2.61159e12	−0.0973999
$965$	−6.10750e12	−0.226720
$966$	1.01938e13	0.376650
$967$	2.26056e13	0.831375	0.415688	−	0.909507i	$-0.363541\pi$
$967$	2.26056e13	0.831375	0.415688	+	0.909507i	$0.363541\pi$
$968$	5.24989e13	1.92181
$969$	0	0
$970$	−2.08107e13	−0.754769
$971$	−2.62758e12	−0.0948569	−0.0474284	−	0.998875i	$-0.515103\pi$
$971$	−2.62758e12	−0.0948569	−0.0474284	+	0.998875i	$0.515103\pi$
$972$	5.15169e13	1.85119
$973$	−5.79092e12	−0.207128
$974$	2.70132e13	0.961748
$975$	−1.98976e13	−0.705146
$976$	6.29657e13	2.22116
$977$	−4.61018e13	−1.61880	−0.809399	−	0.587260i	$-0.800207\pi$
$977$	−4.61018e13	−1.61880	−0.809399	+	0.587260i	$0.800207\pi$
$978$	2.76442e13	0.966226
$979$	−4.69894e12	−0.163485
$980$	−3.31632e13	−1.14852
$981$	−1.92558e13	−0.663820
$982$	−4.39093e12	−0.150680
$983$	3.21788e13	1.09921	0.549603	−	0.835426i	$-0.314779\pi$
$983$	3.21788e13	1.09921	0.549603	+	0.835426i	$0.314779\pi$
$984$	4.73559e13	1.61026
$985$	2.04131e13	0.690949
$986$	0	0
$987$	−4.27877e12	−0.143513
$988$	−1.20105e14	−4.01008
$989$	4.35304e13	1.44680
$990$	4.83401e12	0.159937
$991$	−4.93442e13	−1.62519	−0.812595	−	0.582828i	$-0.801946\pi$
$991$	−4.93442e13	−1.62519	−0.812595	+	0.582828i	$0.801946\pi$
$992$	−2.39887e13	−0.786511
$993$	2.71340e13	0.885609
$994$	4.54603e12	0.147705
$995$	−3.22164e13	−1.04201
$996$	3.82443e13	1.23140
$997$	3.09242e13	0.991222	0.495611	−	0.868545i	$-0.334944\pi$
$997$	3.09242e13	0.991222	0.495611	+	0.868545i	$0.334944\pi$
$998$	−4.83866e13	−1.54397
$999$	−1.62394e13	−0.515853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.4		52
17.10	odd	16		17.10.d.a.15.13	yes	52
17.12	odd	16		17.10.d.a.8.13	✓	52
17.16	even	2	inner	289.10.a.i.1.3		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.8.13	✓	52	17.12	odd	16
17.10.d.a.15.13	yes	52	17.10	odd	16
289.10.a.i.1.3		52	17.16	even	2	inner
289.10.a.i.1.4		52	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-40.6100 q^{2} +102.962 q^{3} +1137.17 q^{4} +769.524 q^{5} -4181.30 q^{6} -1567.27 q^{7} -25388.3 q^{8} -9081.79 q^{9} +O(q^{10})\)	\(q-40.6100 q^{2} +102.962 q^{3} +1137.17 q^{4} +769.524 q^{5} -4181.30 q^{6} -1567.27 q^{7} -25388.3 q^{8} -9081.79 q^{9} -31250.4 q^{10} +17032.6 q^{11} +117086. q^{12} +141996. q^{13} +63646.7 q^{14} +79231.9 q^{15} +448786. q^{16} +368812. q^{18} -743799. q^{19} +875082. q^{20} -161369. q^{21} -691694. q^{22} +1.55554e6 q^{23} -2.61403e6 q^{24} -1.36096e6 q^{25} -5.76647e6 q^{26} -2.96169e6 q^{27} -1.78225e6 q^{28} -5.73876e6 q^{29} -3.21761e6 q^{30} +4.58990e6 q^{31} -5.22641e6 q^{32} +1.75371e6 q^{33} -1.20605e6 q^{35} -1.03276e7 q^{36} +5.48318e6 q^{37} +3.02057e7 q^{38} +1.46203e7 q^{39} -1.95369e7 q^{40} -1.81160e7 q^{41} +6.55320e6 q^{42} +2.79841e7 q^{43} +1.93690e7 q^{44} -6.98865e6 q^{45} -6.31705e7 q^{46} +2.65154e7 q^{47} +4.62080e7 q^{48} -3.78973e7 q^{49} +5.52685e7 q^{50} +1.61474e8 q^{52} +7.58163e7 q^{53} +1.20274e8 q^{54} +1.31070e7 q^{55} +3.97902e7 q^{56} -7.65832e7 q^{57} +2.33051e8 q^{58} -4.75661e7 q^{59} +9.01004e7 q^{60} +1.40302e8 q^{61} -1.86396e8 q^{62} +1.42336e7 q^{63} -1.75339e7 q^{64} +1.09270e8 q^{65} -7.12184e7 q^{66} -7.10319e7 q^{67} +1.60162e8 q^{69} +4.89776e7 q^{70} +7.14261e7 q^{71} +2.30571e8 q^{72} +3.40249e8 q^{73} -2.22672e8 q^{74} -1.40127e8 q^{75} -8.45829e8 q^{76} -2.66946e7 q^{77} -5.93729e8 q^{78} -3.20837e8 q^{79} +3.45352e8 q^{80} -1.26185e8 q^{81} +7.35691e8 q^{82} +3.26635e8 q^{83} -1.83505e8 q^{84} -1.13644e9 q^{86} -5.90875e8 q^{87} -4.32429e8 q^{88} -2.75879e8 q^{89} +2.83809e8 q^{90} -2.22546e8 q^{91} +1.76892e9 q^{92} +4.72586e8 q^{93} -1.07679e9 q^{94} -5.72371e8 q^{95} -5.38123e8 q^{96} +6.65935e8 q^{97} +1.53901e9 q^{98} -1.54687e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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