LMFDB - Embedded newform 289.10.a.i.1.22

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			1.22
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)

$f(q)$	$=$	$q-5.88080 q^{2} +265.157 q^{3} -477.416 q^{4} +2555.35 q^{5} -1559.33 q^{6} +3878.05 q^{7} +5818.56 q^{8} +50625.0 q^{9} +O(q^{10})$	\(q-5.88080 q^{2} +265.157 q^{3} -477.416 q^{4} +2555.35 q^{5} -1559.33 q^{6} +3878.05 q^{7} +5818.56 q^{8} +50625.0 q^{9} -15027.5 q^{10} +23484.5 q^{11} -126590. q^{12} +24364.7 q^{13} -22806.0 q^{14} +677567. q^{15} +210219. q^{16} -297715. q^{18} -304687. q^{19} -1.21996e6 q^{20} +1.02829e6 q^{21} -138107. q^{22} -39332.8 q^{23} +1.54283e6 q^{24} +4.57668e6 q^{25} -143284. q^{26} +8.20448e6 q^{27} -1.85145e6 q^{28} +3.15588e6 q^{29} -3.98464e6 q^{30} -1.64822e6 q^{31} -4.21536e6 q^{32} +6.22706e6 q^{33} +9.90977e6 q^{35} -2.41692e7 q^{36} -4.07050e6 q^{37} +1.79180e6 q^{38} +6.46045e6 q^{39} +1.48684e7 q^{40} +6.50885e6 q^{41} -6.04717e6 q^{42} -1.38073e7 q^{43} -1.12119e7 q^{44} +1.29365e8 q^{45} +231308. q^{46} +3.32251e7 q^{47} +5.57410e7 q^{48} -2.53143e7 q^{49} -2.69145e7 q^{50} -1.16321e7 q^{52} -3.63186e7 q^{53} -4.82489e7 q^{54} +6.00110e7 q^{55} +2.25647e7 q^{56} -8.07896e7 q^{57} -1.85591e7 q^{58} -5.20434e7 q^{59} -3.23482e8 q^{60} +1.27903e8 q^{61} +9.69286e6 q^{62} +1.96326e8 q^{63} -8.28426e7 q^{64} +6.22602e7 q^{65} -3.66201e7 q^{66} -1.60278e8 q^{67} -1.04293e7 q^{69} -5.82774e7 q^{70} -3.22336e8 q^{71} +2.94564e8 q^{72} -2.08495e8 q^{73} +2.39378e7 q^{74} +1.21354e9 q^{75} +1.45462e8 q^{76} +9.10740e7 q^{77} -3.79926e7 q^{78} +2.67098e8 q^{79} +5.37184e8 q^{80} +1.17902e9 q^{81} -3.82772e7 q^{82} +5.15358e8 q^{83} -4.90923e8 q^{84} +8.11977e7 q^{86} +8.36802e8 q^{87} +1.36646e8 q^{88} +4.25947e8 q^{89} -7.60767e8 q^{90} +9.44874e7 q^{91} +1.87781e7 q^{92} -4.37037e8 q^{93} -1.95390e8 q^{94} -7.78580e8 q^{95} -1.11773e9 q^{96} -2.18297e8 q^{97} +1.48868e8 q^{98} +1.18890e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.88080	−0.259897	−0.129948	−	0.991521i	$-0.541481\pi$
$2$	−5.88080	−0.259897	−0.129948	+	0.991521i	$0.541481\pi$
$3$	265.157	1.88998	0.944989	−	0.327102i	$-0.106072\pi$
$3$	265.157	1.88998	0.944989	+	0.327102i	$0.106072\pi$
$4$	−477.416	−0.932454
$5$	2555.35	1.82846	0.914229	−	0.405198i	$-0.132797\pi$
$5$	2555.35	1.82846	0.914229	+	0.405198i	$0.132797\pi$
$6$	−1559.33	−0.491200
$7$	3878.05	0.610481	0.305241	−	0.952275i	$-0.401263\pi$
$7$	3878.05	0.610481	0.305241	+	0.952275i	$0.401263\pi$
$8$	5818.56	0.502239
$9$	50625.0	2.57202
$10$	−15027.5	−0.475211
$11$	23484.5	0.483631	0.241815	−	0.970322i	$-0.422257\pi$
$11$	23484.5	0.483631	0.241815	+	0.970322i	$0.422257\pi$
$12$	−126590.	−1.76232
$13$	24364.7	0.236600	0.118300	−	0.992978i	$-0.462256\pi$
$13$	24364.7	0.236600	0.118300	+	0.992978i	$0.462256\pi$
$14$	−22806.0	−0.158662
$15$	677567.	3.45575
$16$	210219.	0.801923
$17$	0	0
$17$	0	0
$18$	−297715.	−0.668459
$19$	−304687.	−0.536367	−0.268184	−	0.963368i	$-0.586423\pi$
$19$	−304687.	−0.536367	−0.268184	+	0.963368i	$0.586423\pi$
$20$	−1.21996e6	−1.70495
$21$	1.02829e6	1.15380
$22$	−138107.	−0.125694
$23$	−39332.8	−0.0293075	−0.0146538	−	0.999893i	$-0.504665\pi$
$23$	−39332.8	−0.0293075	−0.0146538	+	0.999893i	$0.504665\pi$
$24$	1.54283e6	0.949220
$25$	4.57668e6	2.34326
$26$	−143284.	−0.0614917
$27$	8.20448e6	2.97108
$28$	−1.85145e6	−0.569246
$29$	3.15588e6	0.828570	0.414285	−	0.910147i	$-0.364032\pi$
$29$	3.15588e6	0.828570	0.414285	+	0.910147i	$0.364032\pi$
$30$	−3.98464e6	−0.898138
$31$	−1.64822e6	−0.320544	−0.160272	−	0.987073i	$-0.551237\pi$
$31$	−1.64822e6	−0.320544	−0.160272	+	0.987073i	$0.551237\pi$
$32$	−4.21536e6	−0.710656
$33$	6.22706e6	0.914051
$34$	0	0
$35$	9.90977e6	1.11624
$36$	−2.41692e7	−2.39829
$37$	−4.07050e6	−0.357059	−0.178530	−	0.983935i	$-0.557134\pi$
$37$	−4.07050e6	−0.357059	−0.178530	+	0.983935i	$0.557134\pi$
$38$	1.79180e6	0.139400
$39$	6.46045e6	0.447169
$40$	1.48684e7	0.918323
$41$	6.50885e6	0.359730	0.179865	−	0.983691i	$-0.442434\pi$
$41$	6.50885e6	0.359730	0.179865	+	0.983691i	$0.442434\pi$
$42$	−6.04717e6	−0.299868
$43$	−1.38073e7	−0.615884	−0.307942	−	0.951405i	$-0.599640\pi$
$43$	−1.38073e7	−0.615884	−0.307942	+	0.951405i	$0.599640\pi$
$44$	−1.12119e7	−0.450963
$45$	1.29365e8	4.70283
$46$	231308.	0.00761694
$47$	3.32251e7	0.993177	0.496588	−	0.867986i	$-0.334586\pi$
$47$	3.32251e7	0.993177	0.496588	+	0.867986i	$0.334586\pi$
$48$	5.57410e7	1.51562
$49$	−2.53143e7	−0.627312
$50$	−2.69145e7	−0.609006
$51$	0	0
$52$	−1.16321e7	−0.220619
$53$	−3.63186e7	−0.632249	−0.316124	−	0.948718i	$-0.602382\pi$
$53$	−3.63186e7	−0.632249	−0.316124	+	0.948718i	$0.602382\pi$
$54$	−4.82489e7	−0.772174
$55$	6.00110e7	0.884298
$56$	2.25647e7	0.306608
$57$	−8.07896e7	−1.01372
$58$	−1.85591e7	−0.215343
$59$	−5.20434e7	−0.559154	−0.279577	−	0.960123i	$-0.590194\pi$
$59$	−5.20434e7	−0.559154	−0.279577	+	0.960123i	$0.590194\pi$
$60$	−3.23482e8	−3.22232
$61$	1.27903e8	1.18276	0.591378	−	0.806394i	$-0.298584\pi$
$61$	1.27903e8	1.18276	0.591378	+	0.806394i	$0.298584\pi$
$62$	9.69286e6	0.0833085
$63$	1.96326e8	1.57017
$64$	−8.28426e7	−0.617226
$65$	6.22602e7	0.432614
$66$	−3.66201e7	−0.237559
$67$	−1.60278e8	−0.971710	−0.485855	−	0.874039i	$-0.661492\pi$
$67$	−1.60278e8	−0.971710	−0.485855	+	0.874039i	$0.661492\pi$
$68$	0	0
$69$	−1.04293e7	−0.0553906
$70$	−5.82774e7	−0.290107
$71$	−3.22336e8	−1.50538	−0.752689	−	0.658376i	$-0.771244\pi$
$71$	−3.22336e8	−1.50538	−0.752689	+	0.658376i	$0.771244\pi$
$72$	2.94564e8	1.29177
$73$	−2.08495e8	−0.859295	−0.429648	−	0.902997i	$-0.641362\pi$
$73$	−2.08495e8	−0.859295	−0.429648	+	0.902997i	$0.641362\pi$
$74$	2.39378e7	0.0927986
$75$	1.21354e9	4.42871
$76$	1.45462e8	0.500137
$77$	9.10740e7	0.295248
$78$	−3.79926e7	−0.116218
$79$	2.67098e8	0.771524	0.385762	−	0.922598i	$-0.373939\pi$
$79$	2.67098e8	0.771524	0.385762	+	0.922598i	$0.373939\pi$
$80$	5.37184e8	1.46628
$81$	1.17902e9	3.04325
$82$	−3.82772e7	−0.0934927
$83$	5.15358e8	1.19195	0.595975	−	0.803003i	$-0.296766\pi$
$83$	5.15358e8	1.19195	0.595975	+	0.803003i	$0.296766\pi$
$84$	−4.90923e8	−1.07586
$85$	0	0
$86$	8.11977e7	0.160067
$87$	8.36802e8	1.56598
$88$	1.36646e8	0.242898
$89$	4.25947e8	0.719616	0.359808	−	0.933026i	$-0.382842\pi$
$89$	4.25947e8	0.719616	0.359808	+	0.933026i	$0.382842\pi$
$90$	−7.60767e8	−1.22225
$91$	9.44874e7	0.144440
$92$	1.87781e7	0.0273279
$93$	−4.37037e8	−0.605822
$94$	−1.95390e8	−0.258124
$95$	−7.78580e8	−0.980725
$96$	−1.11773e9	−1.34312
$97$	−2.18297e8	−0.250366	−0.125183	−	0.992134i	$-0.539952\pi$
$97$	−2.18297e8	−0.250366	−0.125183	+	0.992134i	$0.539952\pi$
$98$	1.48868e8	0.163037
$99$	1.18890e9	1.24391
$100$	−2.18498e9	−2.18498
$101$	−1.62316e9	−1.55208	−0.776042	−	0.630682i	$-0.782775\pi$
$101$	−1.62316e9	−1.55208	−0.776042	+	0.630682i	$0.782775\pi$
$102$	0	0
$103$	−1.06758e9	−0.934615	−0.467307	−	0.884095i	$-0.654776\pi$
$103$	−1.06758e9	−0.934615	−0.467307	+	0.884095i	$0.654776\pi$
$104$	1.41767e8	0.118830
$105$	2.62764e9	2.10967
$106$	2.13582e8	0.164320
$107$	1.91006e9	1.40871	0.704353	−	0.709850i	$-0.251237\pi$
$107$	1.91006e9	1.40871	0.704353	+	0.709850i	$0.251237\pi$
$108$	−3.91695e9	−2.77039
$109$	−1.59734e9	−1.08387	−0.541936	−	0.840420i	$-0.682308\pi$
$109$	−1.59734e9	−1.08387	−0.541936	+	0.840420i	$0.682308\pi$
$110$	−3.52913e8	−0.229827
$111$	−1.07932e9	−0.674834
$112$	8.15242e8	0.489559
$113$	4.74662e8	0.273862	0.136931	−	0.990581i	$-0.456276\pi$
$113$	4.74662e8	0.273862	0.136931	+	0.990581i	$0.456276\pi$
$114$	4.75108e8	0.263463
$115$	−1.00509e8	−0.0535876
$116$	−1.50667e9	−0.772603
$117$	1.23346e9	0.608540
$118$	3.06057e8	0.145323
$119$	0	0
$120$	3.94246e9	1.73561
$121$	−1.80643e9	−0.766101
$122$	−7.52170e8	−0.307395
$123$	1.72586e9	0.679882
$124$	7.86888e8	0.298893
$125$	6.70409e9	2.45609
$126$	−1.15456e9	−0.408082
$127$	−7.50829e8	−0.256109	−0.128054	−	0.991767i	$-0.540873\pi$
$127$	−7.50829e8	−0.256109	−0.128054	+	0.991767i	$0.540873\pi$
$128$	2.64544e9	0.871071
$129$	−3.66108e9	−1.16401
$130$	−3.66139e8	−0.112435
$131$	−3.74842e9	−1.11206	−0.556029	−	0.831163i	$-0.687676\pi$
$131$	−3.74842e9	−1.11206	−0.556029	+	0.831163i	$0.687676\pi$
$132$	−2.97290e9	−0.852310
$133$	−1.18159e9	−0.327442
$134$	9.42561e8	0.252544
$135$	2.09653e10	5.43249
$136$	0	0
$137$	−3.55732e9	−0.862740	−0.431370	−	0.902175i	$-0.641970\pi$
$137$	−3.55732e9	−0.862740	−0.431370	+	0.902175i	$0.641970\pi$
$138$	6.13328e7	0.0143958
$139$	−3.74104e9	−0.850014	−0.425007	−	0.905190i	$-0.639728\pi$
$139$	−3.74104e9	−0.850014	−0.425007	+	0.905190i	$0.639728\pi$
$140$	−4.73109e9	−1.04084
$141$	8.80986e9	1.87708
$142$	1.89559e9	0.391243
$143$	5.72191e8	0.114427
$144$	1.06424e10	2.06256
$145$	8.06436e9	1.51501
$146$	1.22612e9	0.223328
$147$	−6.71226e9	−1.18561
$148$	1.94332e9	0.332941
$149$	−9.71745e9	−1.61515	−0.807577	−	0.589762i	$-0.799222\pi$
$149$	−9.71745e9	−1.61515	−0.807577	+	0.589762i	$0.799222\pi$
$150$	−7.13656e9	−1.15101
$151$	−4.12798e9	−0.646161	−0.323081	−	0.946371i	$-0.604719\pi$
$151$	−4.12798e9	−0.646161	−0.323081	+	0.946371i	$0.604719\pi$
$152$	−1.77284e9	−0.269384
$153$	0	0
$154$	−5.35588e8	−0.0767340
$155$	−4.21178e9	−0.586102
$156$	−3.08432e9	−0.416965
$157$	2.20794e9	0.290027	0.145014	−	0.989430i	$-0.453677\pi$
$157$	2.20794e9	0.290027	0.145014	+	0.989430i	$0.453677\pi$
$158$	−1.57075e9	−0.200517
$159$	−9.63012e9	−1.19494
$160$	−1.07717e10	−1.29941
$161$	−1.52535e8	−0.0178917
$162$	−6.93357e9	−0.790933
$163$	6.13644e9	0.680883	0.340441	−	0.940266i	$-0.389423\pi$
$163$	6.13644e9	0.680883	0.340441	+	0.940266i	$0.389423\pi$
$164$	−3.10743e9	−0.335431
$165$	1.59123e10	1.67130
$166$	−3.03072e9	−0.309784
$167$	−1.61045e10	−1.60222	−0.801110	−	0.598517i	$-0.795757\pi$
$167$	−1.61045e10	−1.60222	−0.801110	+	0.598517i	$0.795757\pi$
$168$	5.98317e9	0.579481
$169$	−1.00109e10	−0.944020
$170$	0	0
$171$	−1.54248e10	−1.37955
$172$	6.59181e9	0.574284
$173$	1.92562e10	1.63442	0.817209	−	0.576342i	$-0.195520\pi$
$173$	1.92562e10	1.63442	0.817209	+	0.576342i	$0.195520\pi$
$174$	−4.92106e9	−0.406993
$175$	1.77486e10	1.43052
$176$	4.93689e9	0.387835
$177$	−1.37997e10	−1.05679
$178$	−2.50491e9	−0.187026
$179$	4.00219e9	0.291379	0.145690	−	0.989330i	$-0.453460\pi$
$179$	4.00219e9	0.291379	0.145690	+	0.989330i	$0.453460\pi$
$180$	−6.17607e10	−4.38517
$181$	1.09621e10	0.759174	0.379587	−	0.925156i	$-0.376066\pi$
$181$	1.09621e10	0.759174	0.379587	+	0.925156i	$0.376066\pi$
$182$	−5.55661e8	−0.0375395
$183$	3.39142e10	2.23538
$184$	−2.28860e8	−0.0147194
$185$	−1.04016e10	−0.652868
$186$	2.57013e9	0.157451
$187$	0	0
$188$	−1.58622e10	−0.926091
$189$	3.18174e10	1.81379
$190$	4.57867e9	0.254887
$191$	9.93341e9	0.540068	0.270034	−	0.962851i	$-0.412965\pi$
$191$	9.93341e9	0.540068	0.270034	+	0.962851i	$0.412965\pi$
$192$	−2.19663e10	−1.16654
$193$	2.18731e10	1.13475	0.567377	−	0.823458i	$-0.307958\pi$
$193$	2.18731e10	1.13475	0.567377	+	0.823458i	$0.307958\pi$
$194$	1.28376e9	0.0650693
$195$	1.65087e10	0.817630
$196$	1.20855e10	0.584940
$197$	1.75687e10	0.831079	0.415540	−	0.909575i	$-0.363593\pi$
$197$	1.75687e10	0.831079	0.415540	+	0.909575i	$0.363593\pi$
$198$	−6.99169e9	−0.323288
$199$	3.17134e10	1.43352	0.716760	−	0.697320i	$-0.245624\pi$
$199$	3.17134e10	1.43352	0.716760	+	0.697320i	$0.245624\pi$
$200$	2.66297e10	1.17688
$201$	−4.24987e10	−1.83651
$202$	9.54547e9	0.403382
$203$	1.22387e10	0.505826
$204$	0	0
$205$	1.66324e10	0.657751
$206$	6.27822e9	0.242904
$207$	−1.99122e9	−0.0753795
$208$	5.12192e9	0.189735
$209$	−7.15541e9	−0.259404
$210$	−1.54526e10	−0.548297
$211$	5.37408e10	1.86652	0.933260	−	0.359201i	$-0.116951\pi$
$211$	5.37408e10	1.86652	0.933260	+	0.359201i	$0.116951\pi$
$212$	1.73391e10	0.589543
$213$	−8.54694e10	−2.84513
$214$	−1.12327e10	−0.366118
$215$	−3.52823e10	−1.12612
$216$	4.77382e10	1.49219
$217$	−6.39189e9	−0.195686
$218$	9.39363e9	0.281695
$219$	−5.52838e10	−1.62405
$220$	−2.86502e10	−0.824567
$221$	0	0
$222$	6.34727e9	0.175387
$223$	−3.22100e10	−0.872207	−0.436103	−	0.899897i	$-0.643642\pi$
$223$	−3.22100e10	−0.872207	−0.436103	+	0.899897i	$0.643642\pi$
$224$	−1.63474e10	−0.433842
$225$	2.31694e11	6.02690
$226$	−2.79139e9	−0.0711759
$227$	−1.19903e10	−0.299718	−0.149859	−	0.988707i	$-0.547882\pi$
$227$	−1.19903e10	−0.299718	−0.149859	+	0.988707i	$0.547882\pi$
$228$	3.85703e10	0.945249
$229$	7.32712e10	1.76065	0.880327	−	0.474368i	$-0.157323\pi$
$229$	7.32712e10	1.76065	0.880327	+	0.474368i	$0.157323\pi$
$230$	5.91072e8	0.0139273
$231$	2.41489e10	0.558011
$232$	1.83626e10	0.416140
$233$	9.41182e9	0.209205	0.104602	−	0.994514i	$-0.466643\pi$
$233$	9.41182e9	0.209205	0.104602	+	0.994514i	$0.466643\pi$
$234$	−7.25373e9	−0.158158
$235$	8.49018e10	1.81598
$236$	2.48464e10	0.521386
$237$	7.08229e10	1.45816
$238$	0	0
$239$	5.20522e10	1.03192	0.515962	−	0.856611i	$-0.327434\pi$
$239$	5.20522e10	1.03192	0.515962	+	0.856611i	$0.327434\pi$
$240$	1.42438e11	2.77124
$241$	1.20904e10	0.230868	0.115434	−	0.993315i	$-0.463174\pi$
$241$	1.20904e10	0.230868	0.115434	+	0.993315i	$0.463174\pi$
$242$	1.06232e10	0.199107
$243$	1.51136e11	2.78061
$244$	−6.10628e10	−1.10287
$245$	−6.46869e10	−1.14701
$246$	−1.01495e10	−0.176699
$247$	−7.42358e9	−0.126905
$248$	−9.59027e9	−0.160990
$249$	1.36651e11	2.25276
$250$	−3.94254e10	−0.638331
$251$	3.61787e10	0.575336	0.287668	−	0.957730i	$-0.407120\pi$
$251$	3.61787e10	0.575336	0.287668	+	0.957730i	$0.407120\pi$
$252$	−9.37294e10	−1.46411
$253$	−9.23710e8	−0.0141740
$254$	4.41547e9	0.0665618
$255$	0	0
$256$	2.68581e10	0.390837
$257$	−4.62612e10	−0.661482	−0.330741	−	0.943722i	$-0.607299\pi$
$257$	−4.62612e10	−0.661482	−0.330741	+	0.943722i	$0.607299\pi$
$258$	2.15301e10	0.302522
$259$	−1.57856e10	−0.217978
$260$	−2.97240e10	−0.403392
$261$	1.59766e11	2.13110
$262$	2.20437e10	0.289021
$263$	−9.50558e10	−1.22512	−0.612558	−	0.790425i	$-0.709860\pi$
$263$	−9.50558e10	−1.22512	−0.612558	+	0.790425i	$0.709860\pi$
$264$	3.62325e10	0.459072
$265$	−9.28067e10	−1.15604
$266$	6.94869e9	0.0851012
$267$	1.12943e11	1.36006
$268$	7.65192e10	0.906074
$269$	5.22538e10	0.608461	0.304230	−	0.952599i	$-0.401601\pi$
$269$	5.22538e10	0.608461	0.304230	+	0.952599i	$0.401601\pi$
$270$	−1.23293e11	−1.41189
$271$	1.37092e11	1.54401	0.772005	−	0.635617i	$-0.219254\pi$
$271$	1.37092e11	1.54401	0.772005	+	0.635617i	$0.219254\pi$
$272$	0	0
$273$	2.50540e10	0.272989
$274$	2.09199e10	0.224224
$275$	1.07481e11	1.13327
$276$	4.97914e9	0.0516492
$277$	4.20601e10	0.429251	0.214625	−	0.976696i	$-0.431147\pi$
$277$	4.20601e10	0.429251	0.214625	+	0.976696i	$0.431147\pi$
$278$	2.20003e10	0.220916
$279$	−8.34412e10	−0.824445
$280$	5.76606e10	0.560619
$281$	−1.38821e11	−1.32824	−0.664120	−	0.747626i	$-0.731194\pi$
$281$	−1.38821e11	−1.32824	−0.664120	+	0.747626i	$0.731194\pi$
$282$	−5.18090e10	−0.487848
$283$	1.05455e11	0.977300	0.488650	−	0.872480i	$-0.337489\pi$
$283$	1.05455e11	0.977300	0.488650	+	0.872480i	$0.337489\pi$
$284$	1.53888e11	1.40370
$285$	−2.06446e11	−1.85355
$286$	−3.36494e9	−0.0297393
$287$	2.52416e10	0.219608
$288$	−2.13403e11	−1.82782
$289$	0	0
$290$	−4.74249e10	−0.393745
$291$	−5.78829e10	−0.473186
$292$	9.95388e10	0.801253
$293$	−2.29957e10	−0.182281	−0.0911405	−	0.995838i	$-0.529051\pi$
$293$	−2.29957e10	−0.182281	−0.0911405	+	0.995838i	$0.529051\pi$
$294$	3.94734e10	0.308136
$295$	−1.32989e11	−1.02239
$296$	−2.36845e10	−0.179329
$297$	1.92678e11	1.43690
$298$	5.71464e10	0.419774
$299$	−9.58329e8	−0.00693417
$300$	−5.79362e11	−4.12956
$301$	−5.35452e10	−0.375986
$302$	2.42758e10	0.167935
$303$	−4.30391e11	−2.93340
$304$	−6.40510e10	−0.430125
$305$	3.26836e11	2.16262
$306$	0	0
$307$	−1.45579e11	−0.935353	−0.467677	−	0.883900i	$-0.654909\pi$
$307$	−1.45579e11	−0.935353	−0.467677	+	0.883900i	$0.654909\pi$
$308$	−4.34802e10	−0.275305
$309$	−2.83076e11	−1.76640
$310$	2.47686e10	0.152326
$311$	−7.23128e10	−0.438322	−0.219161	−	0.975689i	$-0.570332\pi$
$311$	−7.23128e10	−0.438322	−0.219161	+	0.975689i	$0.570332\pi$
$312$	3.75905e10	0.224586
$313$	−1.05034e11	−0.618559	−0.309280	−	0.950971i	$-0.600088\pi$
$313$	−1.05034e11	−0.618559	−0.309280	+	0.950971i	$0.600088\pi$
$314$	−1.29844e10	−0.0753772
$315$	5.01682e11	2.87099
$316$	−1.27517e11	−0.719410
$317$	−1.27022e11	−0.706502	−0.353251	−	0.935529i	$-0.614924\pi$
$317$	−1.27022e11	−0.706502	−0.353251	+	0.935529i	$0.614924\pi$
$318$	5.66328e10	0.310560
$319$	7.41141e10	0.400722
$320$	−2.11692e11	−1.12857
$321$	5.06465e11	2.66242
$322$	8.97025e8	0.00465000
$323$	0	0
$324$	−5.62883e11	−2.83769
$325$	1.11509e11	0.554416
$326$	−3.60872e10	−0.176959
$327$	−4.23545e11	−2.04849
$328$	3.78721e10	0.180670
$329$	1.28849e11	0.606316
$330$	−9.35771e10	−0.434367
$331$	3.75153e11	1.71784	0.858921	−	0.512109i	$-0.171136\pi$
$331$	3.75153e11	1.71784	0.858921	+	0.512109i	$0.171136\pi$
$332$	−2.46040e11	−1.11144
$333$	−2.06069e11	−0.918363
$334$	9.47071e10	0.416412
$335$	−4.09565e11	−1.77673
$336$	2.16167e11	0.925256
$337$	1.32412e11	0.559234	0.279617	−	0.960112i	$-0.409792\pi$
$337$	1.32412e11	0.559234	0.279617	+	0.960112i	$0.409792\pi$
$338$	5.88719e10	0.245348
$339$	1.25860e11	0.517593
$340$	0	0
$341$	−3.87076e10	−0.155025
$342$	9.07099e10	0.358540
$343$	−2.54664e11	−0.993444
$344$	−8.03383e10	−0.309321
$345$	−2.66506e10	−0.101279
$346$	−1.13242e11	−0.424780
$347$	1.60350e11	0.593725	0.296862	−	0.954920i	$-0.404060\pi$
$347$	1.60350e11	0.593725	0.296862	+	0.954920i	$0.404060\pi$
$348$	−3.99503e11	−1.46020
$349$	2.17403e11	0.784425	0.392213	−	0.919875i	$-0.371710\pi$
$349$	2.17403e11	0.784425	0.392213	+	0.919875i	$0.371710\pi$
$350$	−1.04376e11	−0.371787
$351$	1.99899e11	0.702958
$352$	−9.89955e10	−0.343695
$353$	−2.93201e11	−1.00503	−0.502515	−	0.864569i	$-0.667592\pi$
$353$	−2.93201e11	−1.00503	−0.502515	+	0.864569i	$0.667592\pi$
$354$	8.11530e10	0.274656
$355$	−8.23679e11	−2.75252
$356$	−2.03354e11	−0.671008
$357$	0	0
$358$	−2.35360e10	−0.0757286
$359$	−2.15290e11	−0.684067	−0.342034	−	0.939688i	$-0.611116\pi$
$359$	−2.15290e11	−0.684067	−0.342034	+	0.939688i	$0.611116\pi$
$360$	7.52715e11	2.36194
$361$	−2.29854e11	−0.712310
$362$	−6.44661e10	−0.197307
$363$	−4.78986e11	−1.44791
$364$	−4.51098e10	−0.134684
$365$	−5.32777e11	−1.57119
$366$	−1.99443e11	−0.580970
$367$	3.10408e11	0.893174	0.446587	−	0.894740i	$-0.352639\pi$
$367$	3.10408e11	0.893174	0.446587	+	0.894740i	$0.352639\pi$
$368$	−8.26851e9	−0.0235024
$369$	3.29510e11	0.925232
$370$	6.11694e10	0.169678
$371$	−1.40846e11	−0.385976
$372$	2.08648e11	0.564900
$373$	−1.67058e11	−0.446867	−0.223433	−	0.974719i	$-0.571727\pi$
$373$	−1.67058e11	−0.446867	−0.223433	+	0.974719i	$0.571727\pi$
$374$	0	0
$375$	1.77763e12	4.64196
$376$	1.93322e11	0.498812
$377$	7.68918e10	0.196040
$378$	−1.87112e11	−0.471398
$379$	5.19146e11	1.29245	0.646224	−	0.763148i	$-0.276347\pi$
$379$	5.19146e11	1.29245	0.646224	+	0.763148i	$0.276347\pi$
$380$	3.71707e11	0.914480
$381$	−1.99087e11	−0.484040
$382$	−5.84164e10	−0.140362
$383$	−5.57468e11	−1.32381	−0.661904	−	0.749589i	$-0.730251\pi$
$383$	−5.57468e11	−1.32381	−0.661904	+	0.749589i	$0.730251\pi$
$384$	7.01457e11	1.64631
$385$	2.32726e11	0.539848
$386$	−1.28631e11	−0.294919
$387$	−6.98992e11	−1.58407
$388$	1.04218e11	0.233454
$389$	−1.18240e11	−0.261813	−0.130907	−	0.991395i	$-0.541789\pi$
$389$	−1.18240e11	−0.261813	−0.130907	+	0.991395i	$0.541789\pi$
$390$	−9.70843e10	−0.212500
$391$	0	0
$392$	−1.47293e11	−0.315061
$393$	−9.93918e11	−2.10177
$394$	−1.03318e11	−0.215995
$395$	6.82529e11	1.41070
$396$	−5.67601e11	−1.15988
$397$	5.41094e10	0.109324	0.0546620	−	0.998505i	$-0.482592\pi$
$397$	5.41094e10	0.109324	0.0546620	+	0.998505i	$0.482592\pi$
$398$	−1.86500e11	−0.372568
$399$	−3.13306e11	−0.618858
$400$	9.62106e11	1.87911
$401$	1.56214e11	0.301696	0.150848	−	0.988557i	$-0.451800\pi$
$401$	1.56214e11	0.301696	0.150848	+	0.988557i	$0.451800\pi$
$402$	2.49926e11	0.477303
$403$	−4.01583e10	−0.0758408
$404$	7.74923e11	1.44725
$405$	3.01280e12	5.56446
$406$	−7.19731e10	−0.131463
$407$	−9.55936e10	−0.172685
$408$	0	0
$409$	−1.04863e12	−1.85296	−0.926481	−	0.376342i	$-0.877182\pi$
$409$	−1.04863e12	−1.85296	−0.926481	+	0.376342i	$0.877182\pi$
$410$	−9.78116e10	−0.170948
$411$	−9.43246e11	−1.63056
$412$	5.09680e11	0.871485
$413$	−2.01827e11	−0.341353
$414$	1.17100e10	0.0195909
$415$	1.31692e12	2.17943
$416$	−1.02706e11	−0.168141
$417$	−9.91962e11	−1.60651
$418$	4.20795e10	0.0674182
$419$	4.52773e11	0.717657	0.358829	−	0.933403i	$-0.383176\pi$
$419$	4.52773e11	0.717657	0.358829	+	0.933403i	$0.383176\pi$
$420$	−1.25448e12	−1.96717
$421$	−5.71478e11	−0.886605	−0.443303	−	0.896372i	$-0.646193\pi$
$421$	−5.71478e11	−0.886605	−0.443303	+	0.896372i	$0.646193\pi$
$422$	−3.16039e11	−0.485103
$423$	1.68202e12	2.55447
$424$	−2.11322e11	−0.317540
$425$	0	0
$426$	5.02628e11	0.739441
$427$	4.96013e11	0.722051
$428$	−9.11894e11	−1.31355
$429$	1.51720e11	0.216265
$430$	2.07488e11	0.292675
$431$	3.88291e11	0.542013	0.271007	−	0.962577i	$-0.412643\pi$
$431$	3.88291e11	0.542013	0.271007	+	0.962577i	$0.412643\pi$
$432$	1.72474e12	2.38258
$433$	8.11956e11	1.11004	0.555018	−	0.831839i	$-0.312712\pi$
$433$	8.11956e11	1.11004	0.555018	+	0.831839i	$0.312712\pi$
$434$	3.75894e10	0.0508583
$435$	2.13832e12	2.86333
$436$	7.62595e11	1.01066
$437$	1.19842e10	0.0157196
$438$	3.25113e11	0.422086
$439$	1.61742e11	0.207842	0.103921	−	0.994586i	$-0.466861\pi$
$439$	1.61742e11	0.207842	0.103921	+	0.994586i	$0.466861\pi$
$440$	3.49177e11	0.444129
$441$	−1.28154e12	−1.61346
$442$	0	0
$443$	1.27513e12	1.57304	0.786518	−	0.617568i	$-0.211882\pi$
$443$	1.27513e12	1.57304	0.786518	+	0.617568i	$0.211882\pi$
$444$	5.15285e11	0.629252
$445$	1.08844e12	1.31579
$446$	1.89421e11	0.226684
$447$	−2.57665e12	−3.05261
$448$	−3.21268e11	−0.376805
$449$	−8.62840e11	−1.00189	−0.500947	−	0.865478i	$-0.667015\pi$
$449$	−8.62840e11	−1.00189	−0.500947	+	0.865478i	$0.667015\pi$
$450$	−1.36255e12	−1.56637
$451$	1.52857e11	0.173976
$452$	−2.26612e11	−0.255364
$453$	−1.09456e12	−1.22123
$454$	7.05124e10	0.0778958
$455$	2.41448e11	0.264103
$456$	−4.70079e11	−0.509131
$457$	−1.82372e12	−1.95585	−0.977925	−	0.208958i	$-0.932993\pi$
$457$	−1.82372e12	−1.95585	−0.977925	+	0.208958i	$0.932993\pi$
$458$	−4.30893e11	−0.457589
$459$	0	0
$460$	4.79846e10	0.0499679
$461$	−1.35980e12	−1.40224	−0.701118	−	0.713046i	$-0.747315\pi$
$461$	−1.35980e12	−1.40224	−0.701118	+	0.713046i	$0.747315\pi$
$462$	−1.42015e11	−0.145025
$463$	−1.18118e12	−1.19455	−0.597273	−	0.802038i	$-0.703749\pi$
$463$	−1.18118e12	−1.19455	−0.597273	+	0.802038i	$0.703749\pi$
$464$	6.63426e11	0.664449
$465$	−1.11678e12	−1.10772
$466$	−5.53490e10	−0.0543717
$467$	1.10514e11	0.107521	0.0537603	−	0.998554i	$-0.482879\pi$
$467$	1.10514e11	0.107521	0.0537603	+	0.998554i	$0.482879\pi$
$468$	−5.88874e11	−0.567435
$469$	−6.21565e11	−0.593211
$470$	−4.99290e11	−0.471968
$471$	5.85450e11	0.548145
$472$	−3.02818e11	−0.280829
$473$	−3.24256e11	−0.297861
$474$	−4.16495e11	−0.378972
$475$	−1.39445e12	−1.25685
$476$	0	0
$477$	−1.83863e12	−1.62615
$478$	−3.06108e11	−0.268194
$479$	6.78705e11	0.589076	0.294538	−	0.955640i	$-0.404834\pi$
$479$	6.78705e11	0.589076	0.294538	+	0.955640i	$0.404834\pi$
$480$	−2.85619e12	−2.45585
$481$	−9.91764e10	−0.0844803
$482$	−7.11013e10	−0.0600020
$483$	−4.04455e10	−0.0338149
$484$	8.62418e11	0.714354
$485$	−5.57825e11	−0.457783
$486$	−8.88800e11	−0.722671
$487$	1.37904e12	1.11095	0.555476	−	0.831532i	$-0.312536\pi$
$487$	1.37904e12	1.11095	0.555476	+	0.831532i	$0.312536\pi$
$488$	7.44209e11	0.594026
$489$	1.62712e12	1.28685
$490$	3.80411e11	0.298106
$491$	2.46933e11	0.191740	0.0958698	−	0.995394i	$-0.469437\pi$
$491$	2.46933e11	0.191740	0.0958698	+	0.995394i	$0.469437\pi$
$492$	−8.23955e11	−0.633958
$493$	0	0
$494$	4.36566e10	0.0329821
$495$	3.03806e12	2.27443
$496$	−3.46488e11	−0.257052
$497$	−1.25003e12	−0.919006
$498$	−8.03615e11	−0.585485
$499$	−5.15637e10	−0.0372298	−0.0186149	−	0.999827i	$-0.505926\pi$
$499$	−5.15637e10	−0.0372298	−0.0186149	+	0.999827i	$0.505926\pi$
$500$	−3.20064e12	−2.29019
$501$	−4.27020e12	−3.02816
$502$	−2.12760e11	−0.149528
$503$	−2.01930e11	−0.140652	−0.0703258	−	0.997524i	$-0.522404\pi$
$503$	−2.01930e11	−0.140652	−0.0703258	+	0.997524i	$0.522404\pi$
$504$	1.14234e12	0.788600
$505$	−4.14774e12	−2.83792
$506$	5.43215e9	0.00368379
$507$	−2.65445e12	−1.78418
$508$	3.58458e11	0.238809
$509$	5.30367e11	0.350224	0.175112	−	0.984548i	$-0.443971\pi$
$509$	5.30367e11	0.350224	0.175112	+	0.984548i	$0.443971\pi$
$510$	0	0
$511$	−8.08554e11	−0.524584
$512$	−1.51241e12	−0.972649
$513$	−2.49979e12	−1.59359
$514$	2.72053e11	0.171917
$515$	−2.72804e12	−1.70890
$516$	1.74786e12	1.08538
$517$	7.80275e11	0.480331
$518$	9.28321e10	0.0566518
$519$	5.10591e12	3.08901
$520$	3.62264e11	0.217275
$521$	−2.10426e12	−1.25121	−0.625605	−	0.780140i	$-0.715148\pi$
$521$	−2.10426e12	−1.25121	−0.625605	+	0.780140i	$0.715148\pi$
$522$	−9.39553e11	−0.553865
$523$	2.42426e12	1.41684	0.708421	−	0.705790i	$-0.249408\pi$
$523$	2.42426e12	1.41684	0.708421	+	0.705790i	$0.249408\pi$
$524$	1.78956e12	1.03694
$525$	4.70616e12	2.70364
$526$	5.59004e11	0.318404
$527$	0	0
$528$	1.30905e12	0.732999
$529$	−1.79961e12	−0.999141
$530$	5.45777e11	0.300451
$531$	−2.63470e12	−1.43815
$532$	5.64110e11	0.305325
$533$	1.58586e11	0.0851122
$534$	−6.64193e11	−0.353475
$535$	4.88087e12	2.57576
$536$	−9.32585e11	−0.488030
$537$	1.06121e12	0.550700
$538$	−3.07294e11	−0.158137
$539$	−5.94494e11	−0.303388
$540$	−1.00092e13	−5.06555
$541$	−5.52051e11	−0.277071	−0.138536	−	0.990357i	$-0.544240\pi$
$541$	−5.52051e11	−0.277071	−0.138536	+	0.990357i	$0.544240\pi$
$542$	−8.06210e11	−0.401283
$543$	2.90668e12	1.43482
$544$	0	0
$545$	−4.08176e12	−1.98181
$546$	−1.47337e11	−0.0709489
$547$	3.37993e12	1.61423	0.807113	−	0.590397i	$-0.201029\pi$
$547$	3.37993e12	1.61423	0.807113	+	0.590397i	$0.201029\pi$
$548$	1.69832e12	0.804465
$549$	6.47507e12	3.04207
$550$	−6.32073e11	−0.294534
$551$	−9.61553e11	−0.444418
$552$	−6.06837e10	−0.0278193
$553$	1.03582e12	0.471001
$554$	−2.47347e11	−0.111561
$555$	−2.75804e12	−1.23391
$556$	1.78603e12	0.792598
$557$	−2.62511e12	−1.15558	−0.577789	−	0.816186i	$-0.696085\pi$
$557$	−2.62511e12	−1.15558	−0.577789	+	0.816186i	$0.696085\pi$
$558$	4.90701e11	0.214271
$559$	−3.36409e11	−0.145718
$560$	2.08323e12	0.895139
$561$	0	0
$562$	8.16378e11	0.345205
$563$	−2.33325e12	−0.978754	−0.489377	−	0.872072i	$-0.662776\pi$
$563$	−2.33325e12	−0.978754	−0.489377	+	0.872072i	$0.662776\pi$
$564$	−4.20597e12	−1.75029
$565$	1.21293e12	0.500745
$566$	−6.20159e11	−0.253997
$567$	4.57230e12	1.85785
$568$	−1.87553e12	−0.756059
$569$	2.53499e12	1.01384	0.506922	−	0.861992i	$-0.330783\pi$
$569$	2.53499e12	1.01384	0.506922	+	0.861992i	$0.330783\pi$
$570$	1.21407e12	0.481732
$571$	1.77902e12	0.700357	0.350179	−	0.936683i	$-0.386121\pi$
$571$	1.77902e12	0.700357	0.350179	+	0.936683i	$0.386121\pi$
$572$	−2.73173e11	−0.106698
$573$	2.63391e12	1.02072
$574$	−1.48441e11	−0.0570756
$575$	−1.80013e11	−0.0686751
$576$	−4.19391e12	−1.58752
$577$	4.30248e12	1.61595	0.807975	−	0.589217i	$-0.200564\pi$
$577$	4.30248e12	1.61595	0.807975	+	0.589217i	$0.200564\pi$
$578$	0	0
$579$	5.79978e12	2.14466
$580$	−3.85006e12	−1.41267
$581$	1.99859e12	0.727663
$582$	3.40397e11	0.122980
$583$	−8.52924e11	−0.305775
$584$	−1.21314e12	−0.431572
$585$	3.15192e12	1.11269
$586$	1.35233e11	0.0473743
$587$	−3.69337e12	−1.28396	−0.641979	−	0.766722i	$-0.721886\pi$
$587$	−3.69337e12	−1.28396	−0.641979	+	0.766722i	$0.721886\pi$
$588$	3.20454e12	1.10552
$589$	5.02191e11	0.171929
$590$	7.82082e11	0.265716
$591$	4.65847e12	1.57072
$592$	−8.55699e11	−0.286334
$593$	1.56989e12	0.521342	0.260671	−	0.965428i	$-0.416056\pi$
$593$	1.56989e12	0.521342	0.260671	+	0.965428i	$0.416056\pi$
$594$	−1.13310e12	−0.373447
$595$	0	0
$596$	4.63927e12	1.50606
$597$	8.40902e12	2.70932
$598$	5.63574e9	0.00180217
$599$	−1.61609e12	−0.512913	−0.256457	−	0.966556i	$-0.582555\pi$
$599$	−1.61609e12	−0.512913	−0.256457	+	0.966556i	$0.582555\pi$
$600$	7.06103e12	2.22427
$601$	−4.21063e12	−1.31647	−0.658237	−	0.752811i	$-0.728698\pi$
$601$	−4.21063e12	−1.31647	−0.658237	+	0.752811i	$0.728698\pi$
$602$	3.14889e11	0.0977176
$603$	−8.11406e12	−2.49925
$604$	1.97076e12	0.602515
$605$	−4.61605e12	−1.40078
$606$	2.53104e12	0.762383
$607$	−3.33394e12	−0.996802	−0.498401	−	0.866947i	$-0.666079\pi$
$607$	−3.33394e12	−0.996802	−0.498401	+	0.866947i	$0.666079\pi$
$608$	1.28436e12	0.381173
$609$	3.24516e12	0.956001
$610$	−1.92206e12	−0.562059
$611$	8.09519e11	0.234986
$612$	0	0
$613$	−3.00176e12	−0.858627	−0.429313	−	0.903156i	$-0.641244\pi$
$613$	−3.00176e12	−0.858627	−0.429313	+	0.903156i	$0.641244\pi$
$614$	8.56120e11	0.243096
$615$	4.41018e12	1.24314
$616$	5.29919e11	0.148285
$617$	−6.25387e12	−1.73726	−0.868631	−	0.495459i	$-0.835000\pi$
$617$	−6.25387e12	−1.73726	−0.868631	+	0.495459i	$0.835000\pi$
$618$	1.66471e12	0.459082
$619$	−2.55283e12	−0.698900	−0.349450	−	0.936955i	$-0.613631\pi$
$619$	−2.55283e12	−0.698900	−0.349450	+	0.936955i	$0.613631\pi$
$620$	2.01077e12	0.546513
$621$	−3.22705e11	−0.0870749
$622$	4.25257e11	0.113919
$623$	1.65184e12	0.439312
$624$	1.35811e12	0.358595
$625$	8.19246e12	2.14760
$626$	6.17685e11	0.160762
$627$	−1.89730e12	−0.490267
$628$	−1.05411e12	−0.270437
$629$	0	0
$630$	−2.95029e12	−0.746161
$631$	1.19537e10	0.00300171	0.00150085	−	0.999999i	$-0.499522\pi$
$631$	1.19537e10	0.00300171	0.00150085	+	0.999999i	$0.499522\pi$
$632$	1.55413e12	0.387489
$633$	1.42497e13	3.52768
$634$	7.46993e11	0.183618
$635$	−1.91863e12	−0.468284
$636$	4.59758e12	1.11422
$637$	−6.16775e11	−0.148422
$638$	−4.35850e11	−0.104146
$639$	−1.63182e13	−3.87186
$640$	6.76003e12	1.59272
$641$	−4.71653e12	−1.10347	−0.551736	−	0.834019i	$-0.686034\pi$
$641$	−4.71653e12	−1.10347	−0.551736	+	0.834019i	$0.686034\pi$
$642$	−2.97842e12	−0.691956
$643$	−1.82349e12	−0.420683	−0.210341	−	0.977628i	$-0.567458\pi$
$643$	−1.82349e12	−0.420683	−0.210341	+	0.977628i	$0.567458\pi$
$644$	7.28225e10	0.0166832
$645$	−9.35534e12	−2.12834
$646$	0	0
$647$	−4.84793e12	−1.08765	−0.543823	−	0.839200i	$-0.683024\pi$
$647$	−4.84793e12	−1.08765	−0.543823	+	0.839200i	$0.683024\pi$
$648$	6.86019e12	1.52844
$649$	−1.22221e12	−0.270424
$650$	−6.55763e11	−0.144091
$651$	−1.69485e12	−0.369843
$652$	−2.92964e12	−0.634892
$653$	−3.05462e12	−0.657427	−0.328714	−	0.944430i	$-0.606615\pi$
$653$	−3.05462e12	−0.657427	−0.328714	+	0.944430i	$0.606615\pi$
$654$	2.49078e12	0.532397
$655$	−9.57852e12	−2.03335
$656$	1.36829e12	0.288476
$657$	−1.05551e13	−2.21012
$658$	−7.57734e11	−0.157580
$659$	4.89090e12	1.01019	0.505096	−	0.863063i	$-0.331457\pi$
$659$	4.89090e12	1.01019	0.505096	+	0.863063i	$0.331457\pi$
$660$	−7.59680e12	−1.55841
$661$	−4.99707e10	−0.0101814	−0.00509071	−	0.999987i	$-0.501620\pi$
$661$	−4.99707e10	−0.0101814	−0.00509071	+	0.999987i	$0.501620\pi$
$662$	−2.20620e12	−0.446462
$663$	0	0
$664$	2.99864e12	0.598643
$665$	−3.01937e12	−0.598714
$666$	1.21185e12	0.238680
$667$	−1.24129e11	−0.0242833
$668$	7.68853e12	1.49400
$669$	−8.54071e12	−1.64845
$670$	2.40857e12	0.461767
$671$	3.00373e12	0.572017
$672$	−4.33462e12	−0.819953
$673$	1.01628e13	1.90961	0.954803	−	0.297241i	$-0.0960664\pi$
$673$	1.01628e13	1.90961	0.954803	+	0.297241i	$0.0960664\pi$
$674$	−7.78690e11	−0.145343
$675$	3.75493e13	6.96200
$676$	4.77935e12	0.880255
$677$	−4.53222e12	−0.829204	−0.414602	−	0.910003i	$-0.636079\pi$
$677$	−4.53222e12	−0.829204	−0.414602	+	0.910003i	$0.636079\pi$
$678$	−7.40156e11	−0.134521
$679$	−8.46567e11	−0.152844
$680$	0	0
$681$	−3.17930e12	−0.566460
$682$	2.27632e11	0.0402905
$683$	−5.02714e12	−0.883950	−0.441975	−	0.897027i	$-0.645722\pi$
$683$	−5.02714e12	−0.883950	−0.441975	+	0.897027i	$0.645722\pi$
$684$	7.36403e12	1.28636
$685$	−9.09018e12	−1.57748
$686$	1.49763e12	0.258193
$687$	1.94284e13	3.32760
$688$	−2.90255e12	−0.493892
$689$	−8.84891e11	−0.149590
$690$	1.56727e11	0.0263222
$691$	−1.06579e13	−1.77836	−0.889181	−	0.457556i	$-0.848725\pi$
$691$	−1.06579e13	−1.77836	−0.889181	+	0.457556i	$0.848725\pi$
$692$	−9.19322e12	−1.52402
$693$	4.61062e12	0.759382
$694$	−9.42984e11	−0.154307
$695$	−9.55966e12	−1.55421
$696$	4.86898e12	0.786495
$697$	0	0
$698$	−1.27850e12	−0.203870
$699$	2.49560e12	0.395393
$700$	−8.47347e12	−1.33389
$701$	7.69046e12	1.20288	0.601438	−	0.798919i	$-0.294595\pi$
$701$	7.69046e12	1.20288	0.601438	+	0.798919i	$0.294595\pi$
$702$	−1.17557e12	−0.182697
$703$	1.24023e12	0.191515
$704$	−1.94552e12	−0.298509
$705$	2.25123e13	3.43217
$706$	1.72425e12	0.261204
$707$	−6.29470e12	−0.947518
$708$	6.58818e12	0.985407
$709$	5.13352e12	0.762970	0.381485	−	0.924375i	$-0.375413\pi$
$709$	5.13352e12	0.762970	0.381485	+	0.924375i	$0.375413\pi$
$710$	4.84389e12	0.715372
$711$	1.35219e13	1.98437
$712$	2.47840e12	0.361419
$713$	6.48291e10	0.00939436
$714$	0	0
$715$	1.46215e12	0.209225
$716$	−1.91071e12	−0.271698
$717$	1.38020e13	1.95032
$718$	1.26608e12	0.177787
$719$	8.41476e12	1.17425	0.587127	−	0.809495i	$-0.300259\pi$
$719$	8.41476e12	1.17425	0.587127	+	0.809495i	$0.300259\pi$
$720$	2.71949e13	3.77130
$721$	−4.14013e12	−0.570565
$722$	1.35172e12	0.185127
$723$	3.20585e12	0.436336
$724$	−5.23350e12	−0.707895
$725$	1.44434e13	1.94155
$726$	2.81682e12	0.376309
$727$	−1.19709e13	−1.58936	−0.794680	−	0.607029i	$-0.792361\pi$
$727$	−1.19709e13	−1.58936	−0.794680	+	0.607029i	$0.792361\pi$
$728$	5.49780e11	0.0725434
$729$	1.68681e13	2.21203
$730$	3.13315e12	0.408346
$731$	0	0
$732$	−1.61912e13	−2.08439
$733$	6.16092e12	0.788275	0.394138	−	0.919051i	$-0.371043\pi$
$733$	6.16092e12	0.788275	0.394138	+	0.919051i	$0.371043\pi$
$734$	−1.82545e12	−0.232133
$735$	−1.71522e13	−2.16783
$736$	1.65802e11	0.0208276
$737$	−3.76404e12	−0.469949
$738$	−1.93778e12	−0.240465
$739$	−5.87894e12	−0.725102	−0.362551	−	0.931964i	$-0.618094\pi$
$739$	−5.87894e12	−0.725102	−0.362551	+	0.931964i	$0.618094\pi$
$740$	4.96587e12	0.608769
$741$	−1.96841e12	−0.239847
$742$	8.28284e11	0.100314
$743$	−5.62235e12	−0.676812	−0.338406	−	0.941000i	$-0.609888\pi$
$743$	−5.62235e12	−0.676812	−0.338406	+	0.941000i	$0.609888\pi$
$744$	−2.54292e12	−0.304267
$745$	−2.48315e13	−2.95324
$746$	9.82436e11	0.116139
$747$	2.60900e13	3.06571
$748$	0	0
$749$	7.40732e12	0.859989
$750$	−1.04539e13	−1.20643
$751$	−8.50924e12	−0.976138	−0.488069	−	0.872805i	$-0.662299\pi$
$751$	−8.50924e12	−0.976138	−0.488069	+	0.872805i	$0.662299\pi$
$752$	6.98457e12	0.796451
$753$	9.59302e12	1.08737
$754$	−4.52185e11	−0.0509501
$755$	−1.05484e13	−1.18148
$756$	−1.51901e13	−1.69127
$757$	−3.76614e12	−0.416836	−0.208418	−	0.978040i	$-0.566831\pi$
$757$	−3.76614e12	−0.416836	−0.208418	+	0.978040i	$0.566831\pi$
$758$	−3.05299e12	−0.335903
$759$	−2.44928e11	−0.0267886
$760$	−4.53021e12	−0.492558
$761$	−4.70810e12	−0.508879	−0.254439	−	0.967089i	$-0.581891\pi$
$761$	−4.70810e12	−0.508879	−0.254439	+	0.967089i	$0.581891\pi$
$762$	1.17079e12	0.125800
$763$	−6.19456e12	−0.661683
$764$	−4.74237e12	−0.503588
$765$	0	0
$766$	3.27835e12	0.344054
$767$	−1.26802e12	−0.132296
$768$	7.12160e12	0.738673
$769$	3.18611e11	0.0328543	0.0164271	−	0.999865i	$-0.494771\pi$
$769$	3.18611e11	0.0328543	0.0164271	+	0.999865i	$0.494771\pi$
$770$	−1.36861e12	−0.140305
$771$	−1.22665e13	−1.25019
$772$	−1.04426e13	−1.05810
$773$	8.76078e12	0.882541	0.441271	−	0.897374i	$-0.354528\pi$
$773$	8.76078e12	0.882541	0.441271	+	0.897374i	$0.354528\pi$
$774$	4.11063e12	0.411694
$775$	−7.54338e12	−0.751118
$776$	−1.27017e12	−0.125743
$777$	−4.18566e12	−0.411974
$778$	6.95346e11	0.0680444
$779$	−1.98316e12	−0.192947
$780$	−7.88152e12	−0.762402
$781$	−7.56988e12	−0.728047
$782$	0	0
$783$	2.58923e13	2.46174
$784$	−5.32156e12	−0.503056
$785$	5.64205e12	0.530302
$786$	5.84503e12	0.546243
$787$	3.83338e12	0.356201	0.178101	−	0.984012i	$-0.443005\pi$
$787$	3.83338e12	0.356201	0.178101	+	0.984012i	$0.443005\pi$
$788$	−8.38760e12	−0.774943
$789$	−2.52047e13	−2.31544
$790$	−4.01382e12	−0.366637
$791$	1.84077e12	0.167188
$792$	6.91769e12	0.624738
$793$	3.11630e12	0.279840
$794$	−3.18206e11	−0.0284130
$795$	−2.46083e13	−2.18489
$796$	−1.51405e13	−1.33669
$797$	−1.53815e13	−1.35032	−0.675160	−	0.737671i	$-0.735926\pi$
$797$	−1.53815e13	−1.35032	−0.675160	+	0.737671i	$0.735926\pi$
$798$	1.84249e12	0.160839
$799$	0	0
$800$	−1.92923e13	−1.66525
$801$	2.15636e13	1.85086
$802$	−9.18660e11	−0.0784098
$803$	−4.89639e12	−0.415582
$804$	2.02896e13	1.71246
$805$	−3.89779e11	−0.0327142
$806$	2.36163e11	0.0197108
$807$	1.38554e13	1.14998
$808$	−9.44444e12	−0.779516
$809$	2.15944e13	1.77245	0.886223	−	0.463258i	$-0.153320\pi$
$809$	2.15944e13	1.77245	0.886223	+	0.463258i	$0.153320\pi$
$810$	−1.77177e13	−1.44619
$811$	−9.95110e12	−0.807751	−0.403875	−	0.914814i	$-0.632337\pi$
$811$	−9.95110e12	−0.807751	−0.403875	+	0.914814i	$0.632337\pi$
$812$	−5.84293e12	−0.471660
$813$	3.63508e13	2.91814
$814$	5.62167e11	0.0448803
$815$	1.56807e13	1.24497
$816$	0	0
$817$	4.20688e12	0.330340
$818$	6.16677e12	0.481579
$819$	4.78343e12	0.371502
$820$	−7.94056e12	−0.613322
$821$	−2.87036e12	−0.220492	−0.110246	−	0.993904i	$-0.535164\pi$
$821$	−2.87036e12	−0.220492	−0.110246	+	0.993904i	$0.535164\pi$
$822$	5.54704e12	0.423778
$823$	−1.69215e13	−1.28570	−0.642849	−	0.765993i	$-0.722248\pi$
$823$	−1.69215e13	−1.28570	−0.642849	+	0.765993i	$0.722248\pi$
$824$	−6.21177e12	−0.469400
$825$	2.84993e13	2.14186
$826$	1.18690e12	0.0887167
$827$	4.66470e11	0.0346776	0.0173388	−	0.999850i	$-0.494481\pi$
$827$	4.66470e11	0.0346776	0.0173388	+	0.999850i	$0.494481\pi$
$828$	9.50642e11	0.0702878
$829$	2.22818e13	1.63853	0.819265	−	0.573416i	$-0.194382\pi$
$829$	2.22818e13	1.63853	0.819265	+	0.573416i	$0.194382\pi$
$830$	−7.74454e12	−0.566427
$831$	1.11525e13	0.811274
$832$	−2.01843e12	−0.146036
$833$	0	0
$834$	5.83353e12	0.417526
$835$	−4.11525e13	−2.92959
$836$	3.41611e12	0.241882
$837$	−1.35228e13	−0.952362
$838$	−2.66267e12	−0.186517
$839$	2.10552e13	1.46700	0.733502	−	0.679687i	$-0.237885\pi$
$839$	2.10552e13	1.46700	0.733502	+	0.679687i	$0.237885\pi$
$840$	1.52891e13	1.05956
$841$	−4.54759e12	−0.313472
$842$	3.36075e12	0.230426
$843$	−3.68093e13	−2.51034
$844$	−2.56567e13	−1.74044
$845$	−2.55812e13	−1.72610
$846$	−9.89164e12	−0.663898
$847$	−7.00542e12	−0.467691
$848$	−7.63488e12	−0.507015
$849$	2.79621e13	1.84708
$850$	0	0
$851$	1.60104e11	0.0104645
$852$	4.08045e13	2.65295
$853$	−1.26238e12	−0.0816433	−0.0408217	−	0.999166i	$-0.512998\pi$
$853$	−1.26238e12	−0.0816433	−0.0408217	+	0.999166i	$0.512998\pi$
$854$	−2.91695e12	−0.187659
$855$	−3.94156e13	−2.52244
$856$	1.11138e13	0.707507
$857$	2.57392e13	1.62998	0.814988	−	0.579478i	$-0.196744\pi$
$857$	2.57392e13	1.62998	0.814988	+	0.579478i	$0.196744\pi$
$858$	−8.92236e11	−0.0562066
$859$	−6.96775e12	−0.436640	−0.218320	−	0.975877i	$-0.570058\pi$
$859$	−6.96775e12	−0.436640	−0.218320	+	0.975877i	$0.570058\pi$
$860$	1.68444e13	1.05005
$861$	6.69299e12	0.415055
$862$	−2.28346e12	−0.140868
$863$	4.14183e12	0.254182	0.127091	−	0.991891i	$-0.459436\pi$
$863$	4.14183e12	0.254182	0.127091	+	0.991891i	$0.459436\pi$
$864$	−3.45848e13	−2.11141
$865$	4.92063e13	2.98846
$866$	−4.77495e12	−0.288495
$867$	0	0
$868$	3.05159e12	0.182468
$869$	6.27267e12	0.373133
$870$	−1.25750e13	−0.744170
$871$	−3.90511e12	−0.229907
$872$	−9.29421e12	−0.544362
$873$	−1.10513e13	−0.643945
$874$	−7.04765e10	−0.00408548
$875$	2.59988e13	1.49940
$876$	2.63934e13	1.51435
$877$	3.40242e12	0.194218	0.0971090	−	0.995274i	$-0.469040\pi$
$877$	3.40242e12	0.194218	0.0971090	+	0.995274i	$0.469040\pi$
$878$	−9.51174e11	−0.0540175
$879$	−6.09745e12	−0.344507
$880$	1.26155e13	0.709139
$881$	1.83410e13	1.02573	0.512863	−	0.858471i	$-0.328585\pi$
$881$	1.83410e13	1.02573	0.512863	+	0.858471i	$0.328585\pi$
$882$	7.53646e12	0.419333
$883$	1.16529e12	0.0645077	0.0322539	−	0.999480i	$-0.489731\pi$
$883$	1.16529e12	0.0645077	0.0322539	+	0.999480i	$0.489731\pi$
$884$	0	0
$885$	−3.52629e13	−1.93230
$886$	−7.49880e12	−0.408827
$887$	2.10781e13	1.14334	0.571669	−	0.820484i	$-0.306296\pi$
$887$	2.10781e13	1.14334	0.571669	+	0.820484i	$0.306296\pi$
$888$	−6.28009e12	−0.338928
$889$	−2.91175e12	−0.156350
$890$	−6.40091e12	−0.341969
$891$	2.76886e13	1.47181
$892$	1.53776e13	0.813292
$893$	−1.01233e13	−0.532707
$894$	1.51527e13	0.793363
$895$	1.02270e13	0.532775
$896$	1.02592e13	0.531773
$897$	−2.54107e11	−0.0131054
$898$	5.07419e12	0.260389
$899$	−5.20158e12	−0.265593
$900$	−1.10615e14	−5.61981
$901$	0	0
$902$	−8.98920e11	−0.0452160
$903$	−1.41979e13	−0.710605
$904$	2.76185e12	0.137544
$905$	2.80121e13	1.38812
$906$	6.43689e12	0.317394
$907$	−1.58198e13	−0.776192	−0.388096	−	0.921619i	$-0.626867\pi$
$907$	−1.58198e13	−0.776192	−0.388096	+	0.921619i	$0.626867\pi$
$908$	5.72435e12	0.279473
$909$	−8.21725e13	−3.99198
$910$	−1.41991e12	−0.0686395
$911$	−5.47531e12	−0.263376	−0.131688	−	0.991291i	$-0.542040\pi$
$911$	−5.47531e12	−0.263376	−0.131688	+	0.991291i	$0.542040\pi$
$912$	−1.69835e13	−0.812927
$913$	1.21029e13	0.576463
$914$	1.07249e13	0.508319
$915$	8.66627e13	4.08731
$916$	−3.49809e13	−1.64173
$917$	−1.45366e13	−0.678891
$918$	0	0
$919$	1.55403e13	0.718687	0.359344	−	0.933205i	$-0.383001\pi$
$919$	1.55403e13	0.718687	0.359344	+	0.933205i	$0.383001\pi$
$920$	−5.84817e11	−0.0269138
$921$	−3.86012e13	−1.76780
$922$	7.99671e12	0.364437
$923$	−7.85359e12	−0.356173
$924$	−1.15291e13	−0.520320
$925$	−1.86294e13	−0.836682
$926$	6.94630e12	0.310459
$927$	−5.40462e13	−2.40385
$928$	−1.33032e13	−0.588828
$929$	3.09798e12	0.136461	0.0682305	−	0.997670i	$-0.478265\pi$
$929$	3.09798e12	0.136461	0.0682305	+	0.997670i	$0.478265\pi$
$930$	6.56756e12	0.287893
$931$	7.71293e12	0.336470
$932$	−4.49335e12	−0.195074
$933$	−1.91742e13	−0.828419
$934$	−6.49911e11	−0.0279443
$935$	0	0
$936$	7.17696e12	0.305632
$937$	−2.75914e13	−1.16935	−0.584677	−	0.811266i	$-0.698779\pi$
$937$	−2.75914e13	−1.16935	−0.584677	+	0.811266i	$0.698779\pi$
$938$	3.65530e12	0.154174
$939$	−2.78505e13	−1.16906
$940$	−4.05335e13	−1.69332
$941$	−2.28417e13	−0.949673	−0.474837	−	0.880074i	$-0.657493\pi$
$941$	−2.28417e13	−0.949673	−0.474837	+	0.880074i	$0.657493\pi$
$942$	−3.44291e12	−0.142461
$943$	−2.56011e11	−0.0105428
$944$	−1.09405e13	−0.448399
$945$	8.13045e13	3.31643
$946$	1.90688e12	0.0774131
$947$	2.91716e13	1.17865	0.589325	−	0.807896i	$-0.299394\pi$
$947$	2.91716e13	1.17865	0.589325	+	0.807896i	$0.299394\pi$
$948$	−3.38120e13	−1.35967
$949$	−5.07990e12	−0.203309
$950$	8.20049e12	0.326651
$951$	−3.36808e13	−1.33527
$952$	0	0
$953$	1.74819e13	0.686549	0.343274	−	0.939235i	$-0.388464\pi$
$953$	1.74819e13	0.686549	0.343274	+	0.939235i	$0.388464\pi$
$954$	1.08126e13	0.422633
$955$	2.53833e13	0.987491
$956$	−2.48505e13	−0.962222
$957$	1.96518e13	0.757355
$958$	−3.99133e12	−0.153099
$959$	−1.37955e13	−0.526687
$960$	−5.61315e13	−2.13298
$961$	−2.37230e13	−0.897251
$962$	5.83236e11	0.0219562
$963$	9.66969e13	3.62322
$964$	−5.77216e12	−0.215274
$965$	5.58933e13	2.07485
$966$	2.37852e11	0.00878840
$967$	1.81112e13	0.666083	0.333041	−	0.942912i	$-0.391925\pi$
$967$	1.81112e13	0.666083	0.333041	+	0.942912i	$0.391925\pi$
$968$	−1.05108e13	−0.384766
$969$	0	0
$970$	3.28045e12	0.118976
$971$	3.68447e12	0.133011	0.0665056	−	0.997786i	$-0.478815\pi$
$971$	3.68447e12	0.133011	0.0665056	+	0.997786i	$0.478815\pi$
$972$	−7.21547e13	−2.59279
$973$	−1.45080e13	−0.518918
$974$	−8.10983e12	−0.288733
$975$	2.95674e13	1.04783
$976$	2.68876e13	0.948480
$977$	−8.61703e12	−0.302574	−0.151287	−	0.988490i	$-0.548342\pi$
$977$	−8.61703e12	−0.302574	−0.151287	+	0.988490i	$0.548342\pi$
$978$	−9.56875e12	−0.334449
$979$	1.00031e13	0.348028
$980$	3.08826e13	1.06954
$981$	−8.08653e13	−2.78774
$982$	−1.45216e12	−0.0498326
$983$	−8.44205e11	−0.0288375	−0.0144187	−	0.999896i	$-0.504590\pi$
$983$	−8.44205e11	−0.0288375	−0.0144187	+	0.999896i	$0.504590\pi$
$984$	1.00420e13	0.341463
$985$	4.48942e13	1.51959
$986$	0	0
$987$	3.41651e13	1.14592
$988$	3.54414e12	0.118333
$989$	5.43077e11	0.0180501
$990$	−1.78662e13	−0.591118
$991$	−2.73698e13	−0.901446	−0.450723	−	0.892664i	$-0.648834\pi$
$991$	−2.73698e13	−0.901446	−0.450723	+	0.892664i	$0.648834\pi$
$992$	6.94785e12	0.227797
$993$	9.94744e13	3.24668
$994$	7.35120e12	0.238847
$995$	8.10388e13	2.62113
$996$	−6.52392e13	−2.10059
$997$	3.06590e13	0.982720	0.491360	−	0.870956i	$-0.336500\pi$
$997$	3.06590e13	0.982720	0.491360	+	0.870956i	$0.336500\pi$
$998$	3.03235e11	0.00967593
$999$	−3.33964e13	−1.06085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.22		52
17.10	odd	16		17.10.d.a.15.8	yes	52
17.12	odd	16		17.10.d.a.8.8	✓	52
17.16	even	2	inner	289.10.a.i.1.21		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.8.8	✓	52	17.12	odd	16
17.10.d.a.15.8	yes	52	17.10	odd	16
289.10.a.i.1.21		52	17.16	even	2	inner
289.10.a.i.1.22		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)

\(f(q)\)	\(=\)	\(q-5.88080 q^{2} +265.157 q^{3} -477.416 q^{4} +2555.35 q^{5} -1559.33 q^{6} +3878.05 q^{7} +5818.56 q^{8} +50625.0 q^{9} +O(q^{10})\)	\(q-5.88080 q^{2} +265.157 q^{3} -477.416 q^{4} +2555.35 q^{5} -1559.33 q^{6} +3878.05 q^{7} +5818.56 q^{8} +50625.0 q^{9} -15027.5 q^{10} +23484.5 q^{11} -126590. q^{12} +24364.7 q^{13} -22806.0 q^{14} +677567. q^{15} +210219. q^{16} -297715. q^{18} -304687. q^{19} -1.21996e6 q^{20} +1.02829e6 q^{21} -138107. q^{22} -39332.8 q^{23} +1.54283e6 q^{24} +4.57668e6 q^{25} -143284. q^{26} +8.20448e6 q^{27} -1.85145e6 q^{28} +3.15588e6 q^{29} -3.98464e6 q^{30} -1.64822e6 q^{31} -4.21536e6 q^{32} +6.22706e6 q^{33} +9.90977e6 q^{35} -2.41692e7 q^{36} -4.07050e6 q^{37} +1.79180e6 q^{38} +6.46045e6 q^{39} +1.48684e7 q^{40} +6.50885e6 q^{41} -6.04717e6 q^{42} -1.38073e7 q^{43} -1.12119e7 q^{44} +1.29365e8 q^{45} +231308. q^{46} +3.32251e7 q^{47} +5.57410e7 q^{48} -2.53143e7 q^{49} -2.69145e7 q^{50} -1.16321e7 q^{52} -3.63186e7 q^{53} -4.82489e7 q^{54} +6.00110e7 q^{55} +2.25647e7 q^{56} -8.07896e7 q^{57} -1.85591e7 q^{58} -5.20434e7 q^{59} -3.23482e8 q^{60} +1.27903e8 q^{61} +9.69286e6 q^{62} +1.96326e8 q^{63} -8.28426e7 q^{64} +6.22602e7 q^{65} -3.66201e7 q^{66} -1.60278e8 q^{67} -1.04293e7 q^{69} -5.82774e7 q^{70} -3.22336e8 q^{71} +2.94564e8 q^{72} -2.08495e8 q^{73} +2.39378e7 q^{74} +1.21354e9 q^{75} +1.45462e8 q^{76} +9.10740e7 q^{77} -3.79926e7 q^{78} +2.67098e8 q^{79} +5.37184e8 q^{80} +1.17902e9 q^{81} -3.82772e7 q^{82} +5.15358e8 q^{83} -4.90923e8 q^{84} +8.11977e7 q^{86} +8.36802e8 q^{87} +1.36646e8 q^{88} +4.25947e8 q^{89} -7.60767e8 q^{90} +9.44874e7 q^{91} +1.87781e7 q^{92} -4.37037e8 q^{93} -1.95390e8 q^{94} -7.78580e8 q^{95} -1.11773e9 q^{96} -2.18297e8 q^{97} +1.48868e8 q^{98} +1.18890e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 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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