LMFDB - Embedded newform 289.10.a.i.1.17

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			1.17
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)

$f(q)$	$=$	$q-14.8865 q^{2} -140.613 q^{3} -290.392 q^{4} +1537.70 q^{5} +2093.24 q^{6} +2138.55 q^{7} +11944.8 q^{8} +89.0110 q^{9} +O(q^{10})$	\(q-14.8865 q^{2} -140.613 q^{3} -290.392 q^{4} +1537.70 q^{5} +2093.24 q^{6} +2138.55 q^{7} +11944.8 q^{8} +89.0110 q^{9} -22891.0 q^{10} -84061.4 q^{11} +40832.8 q^{12} +12765.7 q^{13} -31835.6 q^{14} -216220. q^{15} -29136.1 q^{16} -1325.06 q^{18} +781004. q^{19} -446535. q^{20} -300708. q^{21} +1.25138e6 q^{22} -1.32503e6 q^{23} -1.67960e6 q^{24} +411393. q^{25} -190037. q^{26} +2.75517e6 q^{27} -621018. q^{28} +2.18670e6 q^{29} +3.21877e6 q^{30} +2.91345e6 q^{31} -5.68201e6 q^{32} +1.18201e7 q^{33} +3.28845e6 q^{35} -25848.0 q^{36} +962092. q^{37} -1.16264e7 q^{38} -1.79502e6 q^{39} +1.83675e7 q^{40} +2.92396e7 q^{41} +4.47650e6 q^{42} -9.73937e6 q^{43} +2.44107e7 q^{44} +136872. q^{45} +1.97251e7 q^{46} -1.22741e7 q^{47} +4.09692e6 q^{48} -3.57802e7 q^{49} -6.12420e6 q^{50} -3.70706e6 q^{52} -5.42576e7 q^{53} -4.10149e7 q^{54} -1.29261e8 q^{55} +2.55446e7 q^{56} -1.09819e8 q^{57} -3.25523e7 q^{58} +1.10830e8 q^{59} +6.27886e7 q^{60} -8.49900e7 q^{61} -4.33711e7 q^{62} +190355. q^{63} +9.95030e7 q^{64} +1.96298e7 q^{65} -1.75960e8 q^{66} -1.27439e8 q^{67} +1.86317e8 q^{69} -4.89536e7 q^{70} -3.50617e8 q^{71} +1.06322e6 q^{72} -2.51809e8 q^{73} -1.43222e7 q^{74} -5.78472e7 q^{75} -2.26797e8 q^{76} -1.79770e8 q^{77} +2.67217e7 q^{78} -1.63817e8 q^{79} -4.48026e7 q^{80} -3.89165e8 q^{81} -4.35276e8 q^{82} +7.86881e8 q^{83} +8.73232e7 q^{84} +1.44985e8 q^{86} -3.07478e8 q^{87} -1.00410e9 q^{88} -2.83737e8 q^{89} -2.03755e6 q^{90} +2.73002e7 q^{91} +3.84778e8 q^{92} -4.09669e8 q^{93} +1.82719e8 q^{94} +1.20095e9 q^{95} +7.98964e8 q^{96} -2.62185e8 q^{97} +5.32642e8 q^{98} -7.48239e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−14.8865	−0.657897	−0.328949	−	0.944348i	$-0.606694\pi$
$2$	−14.8865	−0.657897	−0.328949	+	0.944348i	$0.606694\pi$
$3$	−140.613	−1.00226	−0.501129	−	0.865372i	$-0.667082\pi$
$3$	−140.613	−1.00226	−0.501129	+	0.865372i	$0.667082\pi$
$4$	−290.392	−0.567171
$5$	1537.70	1.10029	0.550144	−	0.835070i	$-0.314573\pi$
$5$	1537.70	1.10029	0.550144	+	0.835070i	$0.314573\pi$
$6$	2093.24	0.659383
$7$	2138.55	0.336650	0.168325	−	0.985732i	$-0.446164\pi$
$7$	2138.55	0.336650	0.168325	+	0.985732i	$0.446164\pi$
$8$	11944.8	1.03104
$9$	89.0110	0.00452223
$10$	−22891.0	−0.723876
$11$	−84061.4	−1.73113	−0.865565	−	0.500797i	$-0.833040\pi$
$11$	−84061.4	−1.73113	−0.865565	+	0.500797i	$0.833040\pi$
$12$	40832.8	0.568452
$13$	12765.7	0.123965	0.0619826	−	0.998077i	$-0.480258\pi$
$13$	12765.7	0.123965	0.0619826	+	0.998077i	$0.480258\pi$
$14$	−31835.6	−0.221481
$15$	−216220.	−1.10277
$16$	−29136.1	−0.111146
$17$	0	0
$17$	0	0
$18$	−1325.06	−0.00297516
$19$	781004.	1.37487	0.687436	−	0.726245i	$-0.258736\pi$
$19$	781004.	1.37487	0.687436	+	0.726245i	$0.258736\pi$
$20$	−446535.	−0.624052
$21$	−300708.	−0.337411
$22$	1.25138e6	1.13891
$23$	−1.32503e6	−0.987303	−0.493652	−	0.869660i	$-0.664338\pi$
$23$	−1.32503e6	−0.987303	−0.493652	+	0.869660i	$0.664338\pi$
$24$	−1.67960e6	−1.03337
$25$	411393.	0.210633
$26$	−190037.	−0.0815564
$27$	2.75517e6	0.997726
$28$	−621018.	−0.190938
$29$	2.18670e6	0.574114	0.287057	−	0.957914i	$-0.407323\pi$
$29$	2.18670e6	0.574114	0.287057	+	0.957914i	$0.407323\pi$
$30$	3.21877e6	0.725511
$31$	2.91345e6	0.566605	0.283302	−	0.959031i	$-0.408570\pi$
$31$	2.91345e6	0.566605	0.283302	+	0.959031i	$0.408570\pi$
$32$	−5.68201e6	−0.957915
$33$	1.18201e7	1.73504
$34$	0	0
$35$	3.28845e6	0.370412
$36$	−25848.0	−0.00256488
$37$	962092.	0.0843935	0.0421968	−	0.999109i	$-0.486564\pi$
$37$	962092.	0.0843935	0.0421968	+	0.999109i	$0.486564\pi$
$38$	−1.16264e7	−0.904524
$39$	−1.79502e6	−0.124245
$40$	1.83675e7	1.13444
$41$	2.92396e7	1.61601	0.808005	−	0.589176i	$-0.200547\pi$
$41$	2.92396e7	1.61601	0.808005	+	0.589176i	$0.200547\pi$
$42$	4.47650e6	0.221982
$43$	−9.73937e6	−0.434433	−0.217216	−	0.976123i	$-0.569698\pi$
$43$	−9.73937e6	−0.434433	−0.217216	+	0.976123i	$0.569698\pi$
$44$	2.44107e7	0.981847
$45$	136872.	0.00497575
$46$	1.97251e7	0.649544
$47$	−1.22741e7	−0.366902	−0.183451	−	0.983029i	$-0.558727\pi$
$47$	−1.22741e7	−0.366902	−0.183451	+	0.983029i	$0.558727\pi$
$48$	4.09692e6	0.111397
$49$	−3.57802e7	−0.886667
$50$	−6.12420e6	−0.138575
$51$	0	0
$52$	−3.70706e6	−0.0703095
$53$	−5.42576e7	−0.944537	−0.472268	−	0.881455i	$-0.656565\pi$
$53$	−5.42576e7	−0.944537	−0.472268	+	0.881455i	$0.656565\pi$
$54$	−4.10149e7	−0.656401
$55$	−1.29261e8	−1.90474
$56$	2.55446e7	0.347099
$57$	−1.09819e8	−1.37798
$58$	−3.25523e7	−0.377708
$59$	1.10830e8	1.19076	0.595380	−	0.803444i	$-0.297001\pi$
$59$	1.10830e8	1.19076	0.595380	+	0.803444i	$0.297001\pi$
$60$	6.27886e7	0.625461
$61$	−8.49900e7	−0.785930	−0.392965	−	0.919553i	$-0.628551\pi$
$61$	−8.49900e7	−0.785930	−0.392965	+	0.919553i	$0.628551\pi$
$62$	−4.33711e7	−0.372768
$63$	190355.	0.00152241
$64$	9.95030e7	0.741355
$65$	1.96298e7	0.136397
$66$	−1.75960e8	−1.14148
$67$	−1.27439e8	−0.772619	−0.386310	−	0.922369i	$-0.626250\pi$
$67$	−1.27439e8	−0.772619	−0.386310	+	0.922369i	$0.626250\pi$
$68$	0	0
$69$	1.86317e8	0.989533
$70$	−4.89536e7	−0.243693
$71$	−3.50617e8	−1.63746	−0.818730	−	0.574179i	$-0.805321\pi$
$71$	−3.50617e8	−1.63746	−0.818730	+	0.574179i	$0.805321\pi$
$72$	1.06322e6	0.00466259
$73$	−2.51809e8	−1.03781	−0.518905	−	0.854832i	$-0.673660\pi$
$73$	−2.51809e8	−1.03781	−0.518905	+	0.854832i	$0.673660\pi$
$74$	−1.43222e7	−0.0555223
$75$	−5.78472e7	−0.211109
$76$	−2.26797e8	−0.779787
$77$	−1.79770e8	−0.582785
$78$	2.67217e7	0.0817406
$79$	−1.63817e8	−0.473192	−0.236596	−	0.971608i	$-0.576032\pi$
$79$	−1.63817e8	−0.473192	−0.236596	+	0.971608i	$0.576032\pi$
$80$	−4.48026e7	−0.122292
$81$	−3.89165e8	−1.00450
$82$	−4.35276e8	−1.06317
$83$	7.86881e8	1.81994	0.909972	−	0.414671i	$-0.136103\pi$
$83$	7.86881e8	1.81994	0.909972	+	0.414671i	$0.136103\pi$
$84$	8.73232e7	0.191370
$85$	0	0
$86$	1.44985e8	0.285812
$87$	−3.07478e8	−0.575411
$88$	−1.00410e9	−1.78486
$89$	−2.83737e8	−0.479360	−0.239680	−	0.970852i	$-0.577042\pi$
$89$	−2.83737e8	−0.479360	−0.239680	+	0.970852i	$0.577042\pi$
$90$	−2.03755e6	−0.00327353
$91$	2.73002e7	0.0417329
$92$	3.84778e8	0.559970
$93$	−4.09669e8	−0.567884
$94$	1.82719e8	0.241384
$95$	1.20095e9	1.51275
$96$	7.98964e8	0.960079
$97$	−2.62185e8	−0.300701	−0.150350	−	0.988633i	$-0.548040\pi$
$97$	−2.62185e8	−0.300701	−0.150350	+	0.988633i	$0.548040\pi$
$98$	5.32642e8	0.583335
$99$	−7.48239e6	−0.00782856
$100$	−1.19465e8	−0.119465
$101$	−1.01701e9	−0.972477	−0.486238	−	0.873826i	$-0.661631\pi$
$101$	−1.01701e9	−0.972477	−0.486238	+	0.873826i	$0.661631\pi$
$102$	0	0
$103$	1.11236e9	0.973814	0.486907	−	0.873454i	$-0.338125\pi$
$103$	1.11236e9	0.973814	0.486907	+	0.873454i	$0.338125\pi$
$104$	1.52484e8	0.127813
$105$	−4.62399e8	−0.371249
$106$	8.07706e8	0.621408
$107$	−1.17459e9	−0.866284	−0.433142	−	0.901326i	$-0.642595\pi$
$107$	−1.17459e9	−0.866284	−0.433142	+	0.901326i	$0.642595\pi$
$108$	−8.00078e8	−0.565882
$109$	−1.13422e9	−0.769625	−0.384813	−	0.922995i	$-0.625734\pi$
$109$	−1.13422e9	−0.769625	−0.384813	+	0.922995i	$0.625734\pi$
$110$	1.92425e9	1.25312
$111$	−1.35283e8	−0.0845841
$112$	−6.23092e7	−0.0374172
$113$	1.37503e9	0.793337	0.396668	−	0.917962i	$-0.370166\pi$
$113$	1.37503e9	0.793337	0.396668	+	0.917962i	$0.370166\pi$
$114$	1.63483e9	0.906567
$115$	−2.03750e9	−1.08632
$116$	−6.34999e8	−0.325621
$117$	1.13629e6	0.000560599 0
$118$	−1.64988e9	−0.783398
$119$	0	0
$120$	−2.58271e9	−1.13700
$121$	4.70837e9	1.99681
$122$	1.26521e9	0.517061
$123$	−4.11147e9	−1.61966
$124$	−8.46042e8	−0.321362
$125$	−2.37072e9	−0.868531
$126$	−2.83372e6	−0.00100159
$127$	−1.63757e9	−0.558577	−0.279289	−	0.960207i	$-0.590099\pi$
$127$	−1.63757e9	−0.558577	−0.279289	+	0.960207i	$0.590099\pi$
$128$	1.42794e9	0.470180
$129$	1.36948e9	0.435414
$130$	−2.92220e8	−0.0897355
$131$	4.89940e9	1.45352	0.726762	−	0.686890i	$-0.241024\pi$
$131$	4.89940e9	1.45352	0.726762	+	0.686890i	$0.241024\pi$
$132$	−3.43247e9	−0.984064
$133$	1.67022e9	0.462851
$134$	1.89712e9	0.508304
$135$	4.23662e9	1.09779
$136$	0	0
$137$	−3.10441e9	−0.752899	−0.376449	−	0.926437i	$-0.622855\pi$
$137$	−3.10441e9	−0.752899	−0.376449	+	0.926437i	$0.622855\pi$
$138$	−2.77360e9	−0.651011
$139$	2.82102e8	0.0640972	0.0320486	−	0.999486i	$-0.489797\pi$
$139$	2.82102e8	0.0640972	0.0320486	+	0.999486i	$0.489797\pi$
$140$	−9.54939e8	−0.210087
$141$	1.72590e9	0.367730
$142$	5.21947e9	1.07728
$143$	−1.07310e9	−0.214600
$144$	−2.59344e6	−0.000502625 0
$145$	3.36249e9	0.631691
$146$	3.74855e9	0.682772
$147$	5.03116e9	0.888669
$148$	−2.79384e8	−0.0478656
$149$	−1.55842e9	−0.259028	−0.129514	−	0.991578i	$-0.541342\pi$
$149$	−1.55842e9	−0.259028	−0.129514	+	0.991578i	$0.541342\pi$
$150$	8.61142e8	0.138888
$151$	8.38462e9	1.31246	0.656231	−	0.754560i	$-0.272150\pi$
$151$	8.38462e9	1.31246	0.656231	+	0.754560i	$0.272150\pi$
$152$	9.32895e9	1.41754
$153$	0	0
$154$	2.67615e9	0.383413
$155$	4.48001e9	0.623428
$156$	5.21260e8	0.0704683
$157$	8.18273e9	1.07486	0.537428	−	0.843310i	$-0.319396\pi$
$157$	8.18273e9	1.07486	0.537428	+	0.843310i	$0.319396\pi$
$158$	2.43867e9	0.311312
$159$	7.62932e9	0.946670
$160$	−8.73722e9	−1.05398
$161$	−2.83365e9	−0.332376
$162$	5.79330e9	0.660859
$163$	−9.23855e9	−1.02508	−0.512542	−	0.858662i	$-0.671296\pi$
$163$	−9.23855e9	−1.02508	−0.512542	+	0.858662i	$0.671296\pi$
$164$	−8.49093e9	−0.916554
$165$	1.81758e10	1.90904
$166$	−1.17139e10	−1.19734
$167$	1.07606e10	1.07056	0.535279	−	0.844675i	$-0.320206\pi$
$167$	1.07606e10	1.07056	0.535279	+	0.844675i	$0.320206\pi$
$168$	−3.59191e9	−0.347883
$169$	−1.04415e10	−0.984633
$170$	0	0
$171$	6.95179e7	0.00621748
$172$	2.82823e9	0.246398
$173$	−1.65396e10	−1.40384	−0.701921	−	0.712255i	$-0.747674\pi$
$173$	−1.65396e10	−1.40384	−0.701921	+	0.712255i	$0.747674\pi$
$174$	4.57728e9	0.378561
$175$	8.79785e8	0.0709097
$176$	2.44922e9	0.192407
$177$	−1.55842e10	−1.19345
$178$	4.22386e9	0.315369
$179$	1.20555e10	0.877699	0.438849	−	0.898561i	$-0.355386\pi$
$179$	1.20555e10	0.877699	0.438849	+	0.898561i	$0.355386\pi$
$180$	−3.97465e7	−0.00282210
$181$	2.05478e10	1.42302	0.711511	−	0.702675i	$-0.248011\pi$
$181$	2.05478e10	1.42302	0.711511	+	0.702675i	$0.248011\pi$
$182$	−4.06404e8	−0.0274560
$183$	1.19507e10	0.787705
$184$	−1.58272e10	−1.01795
$185$	1.47941e9	0.0928571
$186$	6.09854e9	0.373610
$187$	0	0
$188$	3.56430e9	0.208096
$189$	5.89208e9	0.335885
$190$	−1.78779e10	−0.995236
$191$	−3.26529e10	−1.77530	−0.887651	−	0.460517i	$-0.847664\pi$
$191$	−3.26529e10	−1.77530	−0.887651	+	0.460517i	$0.847664\pi$
$192$	−1.39914e10	−0.743030
$193$	2.78185e10	1.44320	0.721600	−	0.692310i	$-0.243407\pi$
$193$	2.78185e10	1.44320	0.721600	+	0.692310i	$0.243407\pi$
$194$	3.90302e9	0.197830
$195$	−2.76021e9	−0.136705
$196$	1.03903e10	0.502892
$197$	−2.76208e10	−1.30659	−0.653293	−	0.757105i	$-0.726613\pi$
$197$	−2.76208e10	−1.30659	−0.653293	+	0.757105i	$0.726613\pi$
$198$	1.11387e8	0.00515039
$199$	−3.75699e10	−1.69825	−0.849123	−	0.528195i	$-0.822869\pi$
$199$	−3.75699e10	−1.69825	−0.849123	+	0.528195i	$0.822869\pi$
$200$	4.91401e9	0.217171
$201$	1.79196e10	0.774364
$202$	1.51397e10	0.639790
$203$	4.67638e9	0.193276
$204$	0	0
$205$	4.49617e10	1.77808
$206$	−1.65591e10	−0.640670
$207$	−1.17942e8	−0.00446481
$208$	−3.71943e8	−0.0137782
$209$	−6.56523e10	−2.38008
$210$	6.88351e9	0.244244
$211$	−3.68658e9	−0.128042	−0.0640211	−	0.997949i	$-0.520392\pi$
$211$	−3.68658e9	−0.128042	−0.0640211	+	0.997949i	$0.520392\pi$
$212$	1.57559e10	0.535714
$213$	4.93013e10	1.64116
$214$	1.74856e10	0.569926
$215$	−1.49762e10	−0.478001
$216$	3.29100e10	1.02869
$217$	6.23057e9	0.190748
$218$	1.68846e10	0.506334
$219$	3.54076e10	1.04015
$220$	3.75363e10	1.08031
$221$	0	0
$222$	2.01389e9	0.0556477
$223$	−1.26499e10	−0.342544	−0.171272	−	0.985224i	$-0.554788\pi$
$223$	−1.26499e10	−0.342544	−0.171272	+	0.985224i	$0.554788\pi$
$224$	−1.21513e10	−0.322483
$225$	3.66185e7	0.000952530 0
$226$	−2.04693e10	−0.521934
$227$	4.42724e10	1.10667	0.553333	−	0.832960i	$-0.313356\pi$
$227$	4.42724e10	1.10667	0.553333	+	0.832960i	$0.313356\pi$
$228$	3.18906e10	0.781549
$229$	6.67619e10	1.60424	0.802119	−	0.597164i	$-0.203706\pi$
$229$	6.67619e10	1.60424	0.802119	+	0.597164i	$0.203706\pi$
$230$	3.03312e10	0.714685
$231$	2.52780e10	0.584101
$232$	2.61197e10	0.591933
$233$	6.22710e10	1.38415	0.692076	−	0.721824i	$-0.256696\pi$
$233$	6.22710e10	1.38415	0.692076	+	0.721824i	$0.256696\pi$
$234$	−1.69154e7	−0.000368816 0
$235$	−1.88739e10	−0.403697
$236$	−3.21842e10	−0.675365
$237$	2.30348e10	0.474261
$238$	0	0
$239$	6.82772e10	1.35358	0.676792	−	0.736174i	$-0.263370\pi$
$239$	6.82772e10	1.35358	0.676792	+	0.736174i	$0.263370\pi$
$240$	6.29983e9	0.122568
$241$	−6.20183e10	−1.18425	−0.592125	−	0.805846i	$-0.701711\pi$
$241$	−6.20183e10	−1.18425	−0.592125	+	0.805846i	$0.701711\pi$
$242$	−7.00912e10	−1.31369
$243$	4.91595e8	0.00904438
$244$	2.46804e10	0.445757
$245$	−5.50192e10	−0.975588
$246$	6.12054e10	1.06557
$247$	9.97007e9	0.170436
$248$	3.48006e10	0.584191
$249$	−1.10646e11	−1.82405
$250$	3.52918e10	0.571404
$251$	8.72683e10	1.38779	0.693897	−	0.720074i	$-0.255892\pi$
$251$	8.72683e10	1.38779	0.693897	+	0.720074i	$0.255892\pi$
$252$	−5.52774e7	−0.000863467 0
$253$	1.11384e11	1.70915
$254$	2.43777e10	0.367486
$255$	0	0
$256$	−7.22025e10	−1.05069
$257$	−2.32433e10	−0.332353	−0.166176	−	0.986096i	$-0.553142\pi$
$257$	−2.32433e10	−0.332353	−0.166176	+	0.986096i	$0.553142\pi$
$258$	−2.03868e10	−0.286458
$259$	2.05749e9	0.0284111
$260$	−5.70033e9	−0.0773607
$261$	1.94640e8	0.00259627
$262$	−7.29350e10	−0.956269
$263$	2.54583e10	0.328117	0.164058	−	0.986451i	$-0.447541\pi$
$263$	2.54583e10	0.328117	0.164058	+	0.986451i	$0.447541\pi$
$264$	1.41189e11	1.78889
$265$	−8.34318e10	−1.03926
$266$	−2.48637e10	−0.304508
$267$	3.98972e10	0.480442
$268$	3.70072e10	0.438207
$269$	−1.66536e10	−0.193921	−0.0969603	−	0.995288i	$-0.530912\pi$
$269$	−1.66536e10	−0.193921	−0.0969603	+	0.995288i	$0.530912\pi$
$270$	−6.30685e10	−0.722230
$271$	7.55383e10	0.850756	0.425378	−	0.905016i	$-0.360141\pi$
$271$	7.55383e10	0.850756	0.425378	+	0.905016i	$0.360141\pi$
$272$	0	0
$273$	−3.83876e9	−0.0418272
$274$	4.62138e10	0.495330
$275$	−3.45822e10	−0.364633
$276$	−5.41048e10	−0.561235
$277$	−3.08726e10	−0.315076	−0.157538	−	0.987513i	$-0.550356\pi$
$277$	−3.08726e10	−0.315076	−0.157538	+	0.987513i	$0.550356\pi$
$278$	−4.19951e9	−0.0421694
$279$	2.59329e8	0.00256231
$280$	3.92800e10	0.381909
$281$	5.90092e10	0.564601	0.282300	−	0.959326i	$-0.408903\pi$
$281$	5.90092e10	0.564601	0.282300	+	0.959326i	$0.408903\pi$
$282$	−2.56926e10	−0.241929
$283$	1.83598e11	1.70149	0.850745	−	0.525579i	$-0.176151\pi$
$283$	1.83598e11	1.70149	0.850745	+	0.525579i	$0.176151\pi$
$284$	1.01816e11	0.928720
$285$	−1.68869e11	−1.51617
$286$	1.59748e10	0.141185
$287$	6.25304e10	0.544030
$288$	−5.05761e8	−0.00433191
$289$	0	0
$290$	−5.00557e10	−0.415587
$291$	3.68666e10	0.301380
$292$	7.31231e10	0.588616
$293$	8.80276e10	0.697774	0.348887	−	0.937165i	$-0.386560\pi$
$293$	8.80276e10	0.697774	0.348887	+	0.937165i	$0.386560\pi$
$294$	−7.48964e10	−0.584653
$295$	1.70424e11	1.31018
$296$	1.14920e10	0.0870129
$297$	−2.31603e11	−1.72719
$298$	2.31995e10	0.170414
$299$	−1.69150e10	−0.122391
$300$	1.67983e10	0.119735
$301$	−2.08282e10	−0.146252
$302$	−1.24818e11	−0.863465
$303$	1.43005e11	0.974673
$304$	−2.27554e10	−0.152811
$305$	−1.30689e11	−0.864749
$306$	0	0
$307$	1.25066e11	0.803558	0.401779	−	0.915737i	$-0.368392\pi$
$307$	1.25066e11	0.803558	0.401779	+	0.915737i	$0.368392\pi$
$308$	5.22037e10	0.330539
$309$	−1.56412e11	−0.976014
$310$	−6.66917e10	−0.410152
$311$	−1.23644e11	−0.749466	−0.374733	−	0.927133i	$-0.622266\pi$
$311$	−1.23644e11	−0.749466	−0.374733	+	0.927133i	$0.622266\pi$
$312$	−2.14412e10	−0.128101
$313$	4.92496e10	0.290037	0.145018	−	0.989429i	$-0.453676\pi$
$313$	4.92496e10	0.290037	0.145018	+	0.989429i	$0.453676\pi$
$314$	−1.21812e11	−0.707144
$315$	2.92708e8	0.00167509
$316$	4.75712e10	0.268381
$317$	2.94046e11	1.63549	0.817745	−	0.575580i	$-0.195224\pi$
$317$	2.94046e11	1.63549	0.817745	+	0.575580i	$0.195224\pi$
$318$	−1.13574e11	−0.622812
$319$	−1.83817e11	−0.993865
$320$	1.53006e11	0.815704
$321$	1.65163e11	0.868240
$322$	4.21832e10	0.218669
$323$	0	0
$324$	1.13010e11	0.569725
$325$	5.25172e9	0.0261112
$326$	1.37530e11	0.674400
$327$	1.59487e11	0.771363
$328$	3.49262e11	1.66617
$329$	−2.62488e10	−0.123518
$330$	−2.70574e11	−1.25595
$331$	3.07114e10	0.140629	0.0703143	−	0.997525i	$-0.477600\pi$
$331$	3.07114e10	0.140629	0.0703143	+	0.997525i	$0.477600\pi$
$332$	−2.28504e11	−1.03222
$333$	8.56368e7	0.000381646 0
$334$	−1.60187e11	−0.704318
$335$	−1.95963e11	−0.850104
$336$	8.76148e9	0.0375017
$337$	−4.27513e11	−1.80557	−0.902787	−	0.430088i	$-0.858482\pi$
$337$	−4.27513e11	−1.80557	−0.902787	+	0.430088i	$0.858482\pi$
$338$	1.55438e11	0.647787
$339$	−1.93346e11	−0.795129
$340$	0	0
$341$	−2.44909e11	−0.980866
$342$	−1.03488e9	−0.00409046
$343$	−1.62816e11	−0.635147
$344$	−1.16335e11	−0.447917
$345$	2.86499e11	1.08877
$346$	2.46217e11	0.923584
$347$	−1.31346e11	−0.486335	−0.243167	−	0.969984i	$-0.578186\pi$
$347$	−1.31346e11	−0.486335	−0.243167	+	0.969984i	$0.578186\pi$
$348$	8.92892e10	0.326356
$349$	−1.90494e11	−0.687333	−0.343666	−	0.939092i	$-0.611669\pi$
$349$	−1.90494e11	−0.687333	−0.343666	+	0.939092i	$0.611669\pi$
$350$	−1.30969e10	−0.0466513
$351$	3.51717e10	0.123683
$352$	4.77638e11	1.65828
$353$	−5.20746e10	−0.178501	−0.0892503	−	0.996009i	$-0.528447\pi$
$353$	−5.20746e10	−0.178501	−0.0892503	+	0.996009i	$0.528447\pi$
$354$	2.31994e11	0.785167
$355$	−5.39144e11	−1.80168
$356$	8.23950e10	0.271879
$357$	0	0
$358$	−1.79464e11	−0.577435
$359$	6.15238e11	1.95487	0.977436	−	0.211232i	$-0.0677474\pi$
$359$	6.15238e11	1.95487	0.977436	+	0.211232i	$0.0677474\pi$
$360$	1.63491e9	0.00513019
$361$	2.87279e11	0.890271
$362$	−3.05885e11	−0.936202
$363$	−6.62058e11	−2.00132
$364$	−7.92774e9	−0.0236697
$365$	−3.87206e11	−1.14189
$366$	−1.77904e11	−0.518229
$367$	5.60031e11	1.61144	0.805721	−	0.592295i	$-0.201778\pi$
$367$	5.60031e11	1.61144	0.805721	+	0.592295i	$0.201778\pi$
$368$	3.86063e10	0.109734
$369$	2.60264e9	0.00730796
$370$	−2.20232e10	−0.0610904
$371$	−1.16033e11	−0.317979
$372$	1.18964e11	0.322088
$373$	−2.00817e10	−0.0537169	−0.0268585	−	0.999639i	$-0.508550\pi$
$373$	−2.00817e10	−0.0537169	−0.0268585	+	0.999639i	$0.508550\pi$
$374$	0	0
$375$	3.33354e11	0.870492
$376$	−1.46612e11	−0.378289
$377$	2.79148e10	0.0711702
$378$	−8.77125e10	−0.220978
$379$	−2.22361e10	−0.0553581	−0.0276791	−	0.999617i	$-0.508812\pi$
$379$	−2.22361e10	−0.0553581	−0.0276791	+	0.999617i	$0.508812\pi$
$380$	−3.48746e11	−0.857990
$381$	2.30264e11	0.559839
$382$	4.86089e11	1.16797
$383$	1.05889e11	0.251453	0.125726	−	0.992065i	$-0.459874\pi$
$383$	1.05889e11	0.251453	0.125726	+	0.992065i	$0.459874\pi$
$384$	−2.00786e11	−0.471242
$385$	−2.76432e11	−0.641231
$386$	−4.14121e11	−0.949477
$387$	−8.66911e8	−0.00196460
$388$	7.61363e10	0.170549
$389$	6.41740e10	0.142097	0.0710486	−	0.997473i	$-0.477365\pi$
$389$	6.41740e10	0.142097	0.0710486	+	0.997473i	$0.477365\pi$
$390$	4.10899e10	0.0899381
$391$	0	0
$392$	−4.27388e11	−0.914187
$393$	−6.88919e11	−1.45681
$394$	4.11177e11	0.859600
$395$	−2.51902e11	−0.520648
$396$	2.17282e9	0.00444013
$397$	−1.37059e11	−0.276917	−0.138458	−	0.990368i	$-0.544215\pi$
$397$	−1.37059e11	−0.276917	−0.138458	+	0.990368i	$0.544215\pi$
$398$	5.59284e11	1.11727
$399$	−2.34854e11	−0.463896
$400$	−1.19864e10	−0.0234109
$401$	−4.83309e11	−0.933415	−0.466708	−	0.884412i	$-0.654560\pi$
$401$	−4.83309e11	−0.933415	−0.466708	+	0.884412i	$0.654560\pi$
$402$	−2.66760e11	−0.509452
$403$	3.71923e10	0.0702393
$404$	2.95331e11	0.551561
$405$	−5.98418e11	−1.10524
$406$	−6.96149e10	−0.127156
$407$	−8.08748e10	−0.146096
$408$	0	0
$409$	−2.08768e11	−0.368900	−0.184450	−	0.982842i	$-0.559050\pi$
$409$	−2.08768e11	−0.368900	−0.184450	+	0.982842i	$0.559050\pi$
$410$	−6.69323e11	−1.16979
$411$	4.36520e11	0.754599
$412$	−3.23019e11	−0.552319
$413$	2.37016e11	0.400870
$414$	1.75575e9	0.00293739
$415$	1.20999e12	2.00246
$416$	−7.25349e10	−0.118748
$417$	−3.96672e10	−0.0642420
$418$	9.77333e11	1.56585
$419$	−1.79984e11	−0.285280	−0.142640	−	0.989775i	$-0.545559\pi$
$419$	−1.79984e11	−0.285280	−0.142640	+	0.989775i	$0.545559\pi$
$420$	1.34277e11	0.210562
$421$	1.24378e12	1.92963	0.964813	−	0.262937i	$-0.0846912\pi$
$421$	1.24378e12	1.92963	0.964813	+	0.262937i	$0.0846912\pi$
$422$	5.48804e10	0.0842386
$423$	−1.09253e9	−0.00165921
$424$	−6.48097e11	−0.973853
$425$	0	0
$426$	−7.33925e11	−1.07971
$427$	−1.81756e11	−0.264584
$428$	3.41092e11	0.491331
$429$	1.50892e11	0.215084
$430$	2.22944e11	0.314476
$431$	−8.50306e11	−1.18694	−0.593468	−	0.804857i	$-0.702242\pi$
$431$	−8.50306e11	−1.18694	−0.593468	+	0.804857i	$0.702242\pi$
$432$	−8.02750e10	−0.110893
$433$	6.91161e11	0.944895	0.472448	−	0.881359i	$-0.343371\pi$
$433$	6.91161e11	0.944895	0.472448	+	0.881359i	$0.343371\pi$
$434$	−9.27515e10	−0.125492
$435$	−4.72809e11	−0.633117
$436$	3.29369e11	0.436509
$437$	−1.03485e12	−1.35741
$438$	−5.27095e11	−0.684314
$439$	1.98550e11	0.255140	0.127570	−	0.991830i	$-0.459282\pi$
$439$	1.98550e11	0.255140	0.127570	+	0.991830i	$0.459282\pi$
$440$	−1.54400e12	−1.96386
$441$	−3.18483e9	−0.00400971
$442$	0	0
$443$	1.17901e12	1.45445	0.727227	−	0.686397i	$-0.240809\pi$
$443$	1.17901e12	1.45445	0.727227	+	0.686397i	$0.240809\pi$
$444$	3.92850e10	0.0479737
$445$	−4.36303e11	−0.527434
$446$	1.88313e11	0.225359
$447$	2.19134e11	0.259613
$448$	2.12793e11	0.249578
$449$	−7.72876e10	−0.0897432	−0.0448716	−	0.998993i	$-0.514288\pi$
$449$	−7.72876e10	−0.0897432	−0.0448716	+	0.998993i	$0.514288\pi$
$450$	−5.45121e8	−0.000626667 0
$451$	−2.45792e12	−2.79752
$452$	−3.99296e11	−0.449958
$453$	−1.17899e12	−1.31543
$454$	−6.59062e11	−0.728073
$455$	4.19794e10	0.0459182
$456$	−1.31177e12	−1.42075
$457$	−2.62124e11	−0.281115	−0.140558	−	0.990073i	$-0.544890\pi$
$457$	−2.62124e11	−0.281115	−0.140558	+	0.990073i	$0.544890\pi$
$458$	−9.93851e11	−1.05542
$459$	0	0
$460$	5.91672e11	0.616128
$461$	7.85754e11	0.810275	0.405138	−	0.914256i	$-0.367224\pi$
$461$	7.85754e11	0.810275	0.405138	+	0.914256i	$0.367224\pi$
$462$	−3.76301e11	−0.384279
$463$	1.23202e12	1.24596	0.622981	−	0.782237i	$-0.285921\pi$
$463$	1.23202e12	1.24596	0.622981	+	0.782237i	$0.285921\pi$
$464$	−6.37120e10	−0.0638102
$465$	−6.29948e11	−0.624836
$466$	−9.26998e11	−0.910630
$467$	5.56830e10	0.0541747	0.0270874	−	0.999633i	$-0.491377\pi$
$467$	5.56830e10	0.0541747	0.0270874	+	0.999633i	$0.491377\pi$
$468$	−3.29969e8	−0.000317955 0
$469$	−2.72535e11	−0.260103
$470$	2.80966e11	0.265591
$471$	−1.15060e12	−1.07728
$472$	1.32385e12	1.22772
$473$	8.18705e11	0.752059
$474$	−3.42908e11	−0.312015
$475$	3.21299e11	0.289593
$476$	0	0
$477$	−4.82952e9	−0.00427141
$478$	−1.01641e12	−0.890519
$479$	1.63312e12	1.41745	0.708726	−	0.705484i	$-0.249270\pi$
$479$	1.63312e12	1.41745	0.708726	+	0.705484i	$0.249270\pi$
$480$	1.22857e12	1.05636
$481$	1.22818e10	0.0104619
$482$	9.23237e11	0.779115
$483$	3.98448e11	0.333127
$484$	−1.36727e12	−1.13253
$485$	−4.03161e11	−0.330857
$486$	−7.31813e9	−0.00595027
$487$	−6.96278e11	−0.560922	−0.280461	−	0.959865i	$-0.590487\pi$
$487$	−6.96278e11	−0.560922	−0.280461	+	0.959865i	$0.590487\pi$
$488$	−1.01519e12	−0.810323
$489$	1.29906e12	1.02740
$490$	8.19044e11	0.641837
$491$	7.38660e10	0.0573559	0.0286779	−	0.999589i	$-0.490870\pi$
$491$	7.38660e10	0.0573559	0.0286779	+	0.999589i	$0.490870\pi$
$492$	1.19394e12	0.918624
$493$	0	0
$494$	−1.48420e11	−0.112129
$495$	−1.15057e10	−0.00861367
$496$	−8.48867e10	−0.0629756
$497$	−7.49814e11	−0.551251
$498$	1.64713e12	1.20004
$499$	4.42678e11	0.319621	0.159811	−	0.987148i	$-0.448912\pi$
$499$	4.42678e11	0.319621	0.159811	+	0.987148i	$0.448912\pi$
$500$	6.88437e11	0.492606
$501$	−1.51307e12	−1.07298
$502$	−1.29912e12	−0.913026
$503$	−7.67499e11	−0.534591	−0.267296	−	0.963615i	$-0.586130\pi$
$503$	−7.67499e11	−0.534591	−0.267296	+	0.963615i	$0.586130\pi$
$504$	2.27375e9	0.00156966
$505$	−1.56386e12	−1.07000
$506$	−1.65812e12	−1.12444
$507$	1.46822e12	0.986856
$508$	4.75537e11	0.316809
$509$	1.23640e12	0.816452	0.408226	−	0.912881i	$-0.366148\pi$
$509$	1.23640e12	0.816452	0.408226	+	0.912881i	$0.366148\pi$
$510$	0	0
$511$	−5.38506e11	−0.349379
$512$	3.43741e11	0.221063
$513$	2.15180e12	1.37174
$514$	3.46012e11	0.218654
$515$	1.71047e12	1.07148
$516$	−3.97686e11	−0.246954
$517$	1.03178e12	0.635154
$518$	−3.06288e10	−0.0186916
$519$	2.32569e12	1.40701
$520$	2.34474e11	0.140631
$521$	6.77564e11	0.402885	0.201442	−	0.979500i	$-0.435437\pi$
$521$	6.77564e11	0.402885	0.201442	+	0.979500i	$0.435437\pi$
$522$	−2.89751e9	−0.00170808
$523$	−1.65170e12	−0.965324	−0.482662	−	0.875807i	$-0.660330\pi$
$523$	−1.65170e12	−0.965324	−0.482662	+	0.875807i	$0.660330\pi$
$524$	−1.42274e12	−0.824397
$525$	−1.23709e11	−0.0710698
$526$	−3.78985e11	−0.215867
$527$	0	0
$528$	−3.44393e11	−0.192842
$529$	−4.54466e10	−0.0252320
$530$	1.24201e12	0.683728
$531$	9.86511e9	0.00538489
$532$	−4.85018e11	−0.262516
$533$	3.73264e11	0.200329
$534$	−5.93930e11	−0.316082
$535$	−1.80617e12	−0.953161
$536$	−1.52223e12	−0.796600
$537$	−1.69516e12	−0.879681
$538$	2.47915e11	0.127580
$539$	3.00773e12	1.53493
$540$	−1.23028e12	−0.622633
$541$	9.85219e10	0.0494476	0.0247238	−	0.999694i	$-0.492129\pi$
$541$	9.85219e10	0.0494476	0.0247238	+	0.999694i	$0.492129\pi$
$542$	−1.12450e12	−0.559710
$543$	−2.88929e12	−1.42624
$544$	0	0
$545$	−1.74409e12	−0.846809
$546$	5.71457e10	0.0275180
$547$	−1.58944e11	−0.0759102	−0.0379551	−	0.999279i	$-0.512084\pi$
$547$	−1.58944e11	−0.0759102	−0.0379551	+	0.999279i	$0.512084\pi$
$548$	9.01495e11	0.427022
$549$	−7.56505e9	−0.00355415
$550$	5.14809e11	0.239891
$551$	1.70782e12	0.789333
$552$	2.22552e12	1.02025
$553$	−3.50332e11	−0.159300
$554$	4.59586e11	0.207287
$555$	−2.08024e11	−0.0930669
$556$	−8.19200e10	−0.0363541
$557$	2.80868e12	1.23639	0.618194	−	0.786026i	$-0.287865\pi$
$557$	2.80868e12	1.23639	0.618194	+	0.786026i	$0.287865\pi$
$558$	−3.86051e9	−0.00168574
$559$	−1.24330e11	−0.0538546
$560$	−9.58128e10	−0.0411697
$561$	0	0
$562$	−8.78442e11	−0.371449
$563$	3.00188e11	0.125923	0.0629616	−	0.998016i	$-0.479945\pi$
$563$	3.00188e11	0.125923	0.0629616	+	0.998016i	$0.479945\pi$
$564$	−5.01187e11	−0.208566
$565$	2.11437e12	0.872899
$566$	−2.73314e12	−1.11940
$567$	−8.32249e11	−0.338166
$568$	−4.18806e12	−1.68828
$569$	4.28791e12	1.71491	0.857454	−	0.514561i	$-0.172045\pi$
$569$	4.28791e12	1.71491	0.857454	+	0.514561i	$0.172045\pi$
$570$	2.51387e12	0.997484
$571$	1.67794e11	0.0660562	0.0330281	−	0.999454i	$-0.489485\pi$
$571$	1.67794e11	0.0660562	0.0330281	+	0.999454i	$0.489485\pi$
$572$	3.11620e11	0.121715
$573$	4.59143e12	1.77931
$574$	−9.30860e11	−0.357916
$575$	−5.45108e11	−0.207959
$576$	8.85686e9	0.00335258
$577$	7.33555e11	0.275513	0.137756	−	0.990466i	$-0.456011\pi$
$577$	7.33555e11	0.275513	0.137756	+	0.990466i	$0.456011\pi$
$578$	0	0
$579$	−3.91165e12	−1.44646
$580$	−9.76438e11	−0.358277
$581$	1.68279e12	0.612684
$582$	−5.48815e11	−0.198277
$583$	4.56097e12	1.63512
$584$	−3.00781e12	−1.07002
$585$	1.74727e9	0.000616820 0
$586$	−1.31042e12	−0.459064
$587$	3.71592e12	1.29180	0.645899	−	0.763423i	$-0.276483\pi$
$587$	3.71592e12	1.29180	0.645899	+	0.763423i	$0.276483\pi$
$588$	−1.46101e12	−0.504028
$589$	2.27542e12	0.779008
$590$	−2.53701e12	−0.861963
$591$	3.88384e12	1.30954
$592$	−2.80316e10	−0.00937996
$593$	2.82729e11	0.0938910	0.0469455	−	0.998897i	$-0.485051\pi$
$593$	2.82729e11	0.0938910	0.0469455	+	0.998897i	$0.485051\pi$
$594$	3.44777e12	1.13632
$595$	0	0
$596$	4.52553e11	0.146913
$597$	5.28281e12	1.70208
$598$	2.51805e11	0.0805209
$599$	−5.50565e12	−1.74738	−0.873691	−	0.486482i	$-0.838280\pi$
$599$	−5.50565e12	−1.74738	−0.873691	+	0.486482i	$0.838280\pi$
$600$	−6.90974e11	−0.217661
$601$	1.54272e12	0.482338	0.241169	−	0.970483i	$-0.422469\pi$
$601$	1.54272e12	0.482338	0.241169	+	0.970483i	$0.422469\pi$
$602$	3.10059e11	0.0962188
$603$	−1.13435e10	−0.00349396
$604$	−2.43482e12	−0.744391
$605$	7.24005e12	2.19706
$606$	−2.12884e12	−0.641235
$607$	3.59153e12	1.07382	0.536909	−	0.843640i	$-0.319592\pi$
$607$	3.59153e12	1.07382	0.536909	+	0.843640i	$0.319592\pi$
$608$	−4.43767e12	−1.31701
$609$	−6.57559e11	−0.193712
$610$	1.94551e12	0.568916
$611$	−1.56688e11	−0.0454830
$612$	0	0
$613$	5.79969e12	1.65895	0.829474	−	0.558546i	$-0.188641\pi$
$613$	5.79969e12	1.65895	0.829474	+	0.558546i	$0.188641\pi$
$614$	−1.86180e12	−0.528658
$615$	−6.32220e12	−1.78209
$616$	−2.14732e12	−0.600873
$617$	−5.14222e12	−1.42846	−0.714229	−	0.699912i	$-0.753222\pi$
$617$	−5.14222e12	−1.42846	−0.714229	+	0.699912i	$0.753222\pi$
$618$	2.32842e12	0.642117
$619$	1.66025e11	0.0454534	0.0227267	−	0.999742i	$-0.492765\pi$
$619$	1.66025e11	0.0454534	0.0227267	+	0.999742i	$0.492765\pi$
$620$	−1.30096e12	−0.353591
$621$	−3.65068e12	−0.985058
$622$	1.84063e12	0.493071
$623$	−6.06788e11	−0.161377
$624$	5.23001e10	0.0138093
$625$	−4.44895e12	−1.16627
$626$	−7.33155e11	−0.190815
$627$	9.23156e12	2.38546
$628$	−2.37620e12	−0.609627
$629$	0	0
$630$	−4.35741e9	−0.00110204
$631$	2.14564e12	0.538796	0.269398	−	0.963029i	$-0.413175\pi$
$631$	2.14564e12	0.538796	0.269398	+	0.963029i	$0.413175\pi$
$632$	−1.95677e12	−0.487879
$633$	5.18382e11	0.128331
$634$	−4.37731e12	−1.07598
$635$	−2.51809e12	−0.614595
$636$	−2.21549e12	−0.536924
$637$	−4.56759e11	−0.109916
$638$	2.73639e12	0.653861
$639$	−3.12088e10	−0.00740496
$640$	2.19574e12	0.517333
$641$	−6.35807e11	−0.148752	−0.0743762	−	0.997230i	$-0.523697\pi$
$641$	−6.35807e11	−0.148752	−0.0743762	+	0.997230i	$0.523697\pi$
$642$	−2.45870e12	−0.571213
$643$	4.36286e12	1.00652	0.503259	−	0.864135i	$-0.332134\pi$
$643$	4.36286e12	1.00652	0.503259	+	0.864135i	$0.332134\pi$
$644$	8.22868e11	0.188514
$645$	2.10585e12	0.479081
$646$	0	0
$647$	5.37030e12	1.20484	0.602419	−	0.798180i	$-0.294204\pi$
$647$	5.37030e12	1.20484	0.602419	+	0.798180i	$0.294204\pi$
$648$	−4.64850e12	−1.03568
$649$	−9.31655e12	−2.06136
$650$	−7.81798e10	−0.0171785
$651$	−8.76099e11	−0.191178
$652$	2.68280e12	0.581399
$653$	1.91038e12	0.411160	0.205580	−	0.978640i	$-0.434092\pi$
$653$	1.91038e12	0.411160	0.205580	+	0.978640i	$0.434092\pi$
$654$	−2.37420e12	−0.507478
$655$	7.53380e12	1.59929
$656$	−8.51928e11	−0.179612
$657$	−2.24137e10	−0.00469321
$658$	3.90754e11	0.0812619
$659$	−4.74561e11	−0.0980184	−0.0490092	−	0.998798i	$-0.515606\pi$
$659$	−4.74561e11	−0.0980184	−0.0490092	+	0.998798i	$0.515606\pi$
$660$	−5.27810e12	−1.08275
$661$	−6.60336e12	−1.34542	−0.672710	−	0.739906i	$-0.734870\pi$
$661$	−6.60336e12	−1.34542	−0.672710	+	0.739906i	$0.734870\pi$
$662$	−4.57186e11	−0.0925192
$663$	0	0
$664$	9.39915e12	1.87643
$665$	2.56829e12	0.509269
$666$	−1.27483e9	−0.000251084 0
$667$	−2.89744e12	−0.566825
$668$	−3.12478e12	−0.607190
$669$	1.77874e12	0.343317
$670$	2.91720e12	0.559281
$671$	7.14438e12	1.36055
$672$	1.70863e12	0.323211
$673$	2.74504e12	0.515800	0.257900	−	0.966172i	$-0.416969\pi$
$673$	2.74504e12	0.515800	0.257900	+	0.966172i	$0.416969\pi$
$674$	6.36418e12	1.18788
$675$	1.13346e12	0.210154
$676$	3.03214e12	0.558455
$677$	1.15812e12	0.211887	0.105943	−	0.994372i	$-0.466214\pi$
$677$	1.15812e12	0.211887	0.105943	+	0.994372i	$0.466214\pi$
$678$	2.87825e12	0.523113
$679$	−5.60696e11	−0.101231
$680$	0	0
$681$	−6.22527e12	−1.10917
$682$	3.64584e12	0.645309
$683$	−6.11786e12	−1.07574	−0.537869	−	0.843029i	$-0.680770\pi$
$683$	−6.11786e12	−1.07574	−0.537869	+	0.843029i	$0.680770\pi$
$684$	−2.01874e10	−0.00352637
$685$	−4.77365e12	−0.828405
$686$	2.42377e12	0.417861
$687$	−9.38758e12	−1.60786
$688$	2.83767e11	0.0482853
$689$	−6.92636e11	−0.117090
$690$	−4.26497e12	−0.716300
$691$	−2.38401e12	−0.397793	−0.198897	−	0.980020i	$-0.563736\pi$
$691$	−2.38401e12	−0.397793	−0.198897	+	0.980020i	$0.563736\pi$
$692$	4.80297e12	0.796219
$693$	−1.60015e10	−0.00263549
$694$	1.95529e12	0.319958
$695$	4.33787e11	0.0705253
$696$	−3.67277e12	−0.593270
$697$	0	0
$698$	2.83579e12	0.452194
$699$	−8.75611e12	−1.38728
$700$	−2.55482e11	−0.0402179
$701$	−3.30170e12	−0.516424	−0.258212	−	0.966088i	$-0.583133\pi$
$701$	−3.30170e12	−0.516424	−0.258212	+	0.966088i	$0.583133\pi$
$702$	−5.23584e11	−0.0813709
$703$	7.51398e11	0.116030
$704$	−8.36436e12	−1.28338
$705$	2.65391e12	0.404609
$706$	7.75209e11	0.117435
$707$	−2.17493e12	−0.327385
$708$	4.52551e12	0.676890
$709$	−6.50115e12	−0.966234	−0.483117	−	0.875556i	$-0.660495\pi$
$709$	−6.50115e12	−0.966234	−0.483117	+	0.875556i	$0.660495\pi$
$710$	8.02597e12	1.18532
$711$	−1.45815e10	−0.00213988
$712$	−3.38919e12	−0.494238
$713$	−3.86041e12	−0.559411
$714$	0	0
$715$	−1.65011e12	−0.236122
$716$	−3.50081e12	−0.497805
$717$	−9.60066e12	−1.35664
$718$	−9.15875e12	−1.28610
$719$	2.37012e12	0.330742	0.165371	−	0.986231i	$-0.447118\pi$
$719$	2.37012e12	0.330742	0.165371	+	0.986231i	$0.447118\pi$
$720$	−3.98792e9	−0.000553032 0
$721$	2.37883e12	0.327835
$722$	−4.27659e12	−0.585706
$723$	8.72058e12	1.18692
$724$	−5.96691e12	−0.807097
$725$	8.99592e11	0.120927
$726$	9.85573e12	1.31666
$727$	−6.84668e12	−0.909023	−0.454512	−	0.890741i	$-0.650186\pi$
$727$	−6.84668e12	−0.909023	−0.454512	+	0.890741i	$0.650186\pi$
$728$	3.26095e11	0.0430282
$729$	7.59080e12	0.995437
$730$	5.76414e12	0.751246
$731$	0	0
$732$	−3.47039e12	−0.446764
$733$	1.22017e13	1.56118	0.780592	−	0.625041i	$-0.214918\pi$
$733$	1.22017e13	1.56118	0.780592	+	0.625041i	$0.214918\pi$
$734$	−8.33691e12	−1.06016
$735$	7.73641e12	0.977792
$736$	7.52884e12	0.945753
$737$	1.07127e13	1.33750
$738$	−3.87443e10	−0.00480789
$739$	6.41729e12	0.791501	0.395751	−	0.918358i	$-0.370484\pi$
$739$	6.41729e12	0.791501	0.395751	+	0.918358i	$0.370484\pi$
$740$	−4.29608e11	−0.0526659
$741$	−1.40192e12	−0.170821
$742$	1.72732e12	0.209197
$743$	1.87182e11	0.0225327	0.0112664	−	0.999937i	$-0.496414\pi$
$743$	1.87182e11	0.0225327	0.0112664	+	0.999937i	$0.496414\pi$
$744$	−4.89342e12	−0.585510
$745$	−2.39638e12	−0.285005
$746$	2.98947e11	0.0353402
$747$	7.00411e10	0.00823019
$748$	0	0
$749$	−2.51193e12	−0.291635
$750$	−4.96248e12	−0.572695
$751$	1.47873e13	1.69633	0.848163	−	0.529735i	$-0.177709\pi$
$751$	1.47873e13	1.69633	0.848163	+	0.529735i	$0.177709\pi$
$752$	3.57620e11	0.0407795
$753$	−1.22711e13	−1.39093
$754$	−4.15554e11	−0.0468226
$755$	1.28930e13	1.44409
$756$	−1.71101e12	−0.190504
$757$	1.41642e13	1.56770	0.783848	−	0.620952i	$-0.213254\pi$
$757$	1.41642e13	1.56770	0.783848	+	0.620952i	$0.213254\pi$
$758$	3.31017e11	0.0364200
$759$	−1.56620e13	−1.71301
$760$	1.43451e13	1.55971
$761$	−1.94664e12	−0.210404	−0.105202	−	0.994451i	$-0.533549\pi$
$761$	−1.94664e12	−0.210404	−0.105202	+	0.994451i	$0.533549\pi$
$762$	−3.42782e12	−0.368316
$763$	−2.42560e12	−0.259095
$764$	9.48215e12	1.00690
$765$	0	0
$766$	−1.57632e12	−0.165430
$767$	1.41483e12	0.147613
$768$	1.01526e13	1.05306
$769$	−9.54772e12	−0.984535	−0.492267	−	0.870444i	$-0.663832\pi$
$769$	−9.54772e12	−0.984535	−0.492267	+	0.870444i	$0.663832\pi$
$770$	4.11511e12	0.421864
$771$	3.26831e12	0.333103
$772$	−8.07827e12	−0.818542
$773$	−6.14763e12	−0.619298	−0.309649	−	0.950851i	$-0.600212\pi$
$773$	−6.14763e12	−0.619298	−0.309649	+	0.950851i	$0.600212\pi$
$774$	1.29053e10	0.00129251
$775$	1.19857e12	0.119346
$776$	−3.13175e12	−0.310034
$777$	−2.89309e11	−0.0284753
$778$	−9.55327e11	−0.0934854
$779$	2.28362e13	2.22180
$780$	8.01541e11	0.0775354
$781$	2.94734e13	2.83465
$782$	0	0
$783$	6.02473e12	0.572808
$784$	1.04250e12	0.0985490
$785$	1.25826e13	1.18265
$786$	1.02556e13	0.958429
$787$	9.50792e12	0.883485	0.441742	−	0.897142i	$-0.354361\pi$
$787$	9.50792e12	0.883485	0.441742	+	0.897142i	$0.354361\pi$
$788$	8.02085e12	0.741058
$789$	−3.57977e12	−0.328858
$790$	3.74994e12	0.342533
$791$	2.94057e12	0.267077
$792$	−8.93757e10	−0.00807154
$793$	−1.08496e12	−0.0974280
$794$	2.04033e12	0.182183
$795$	1.17316e13	1.04161
$796$	1.09100e13	0.963196
$797$	4.57017e12	0.401208	0.200604	−	0.979672i	$-0.435710\pi$
$797$	4.57017e12	0.401208	0.200604	+	0.979672i	$0.435710\pi$
$798$	3.49616e12	0.305196
$799$	0	0
$800$	−2.33754e12	−0.201769
$801$	−2.52557e10	−0.00216777
$802$	7.19478e12	0.614091
$803$	2.11674e13	1.79658
$804$	−5.20369e12	−0.439197
$805$	−4.35730e12	−0.365709
$806$	−5.53663e11	−0.0462102
$807$	2.34172e12	0.194359
$808$	−1.21480e13	−1.00266
$809$	1.08135e13	0.887560	0.443780	−	0.896136i	$-0.353637\pi$
$809$	1.08135e13	0.887560	0.443780	+	0.896136i	$0.353637\pi$
$810$	8.90836e12	0.727135
$811$	−1.66684e13	−1.35301	−0.676504	−	0.736439i	$-0.736506\pi$
$811$	−1.66684e13	−1.35301	−0.676504	+	0.736439i	$0.736506\pi$
$812$	−1.35798e12	−0.109620
$813$	−1.06217e13	−0.852678
$814$	1.20394e12	0.0961162
$815$	−1.42061e13	−1.12789
$816$	0	0
$817$	−7.60648e12	−0.597289
$818$	3.10782e12	0.242698
$819$	2.43001e9	0.000188726 0
$820$	−1.30565e13	−1.00847
$821$	7.04533e12	0.541199	0.270600	−	0.962692i	$-0.412778\pi$
$821$	7.04533e12	0.541199	0.270600	+	0.962692i	$0.412778\pi$
$822$	−6.49827e12	−0.496449
$823$	−4.13230e12	−0.313973	−0.156986	−	0.987601i	$-0.550178\pi$
$823$	−4.13230e12	−0.313973	−0.156986	+	0.987601i	$0.550178\pi$
$824$	1.32869e13	1.00404
$825$	4.86271e12	0.365457
$826$	−3.52835e12	−0.263731
$827$	3.87796e12	0.288289	0.144145	−	0.989557i	$-0.453957\pi$
$827$	3.87796e12	0.288289	0.144145	+	0.989557i	$0.453957\pi$
$828$	3.42495e10	0.00253231
$829$	2.77616e12	0.204150	0.102075	−	0.994777i	$-0.467452\pi$
$829$	2.77616e12	0.204150	0.102075	+	0.994777i	$0.467452\pi$
$830$	−1.80125e13	−1.31741
$831$	4.34109e12	0.315787
$832$	1.27023e12	0.0919023
$833$	0	0
$834$	5.90506e11	0.0422646
$835$	1.65465e13	1.17792
$836$	1.90649e13	1.34991
$837$	8.02705e12	0.565316
$838$	2.67934e12	0.187685
$839$	1.10624e13	0.770760	0.385380	−	0.922758i	$-0.374070\pi$
$839$	1.10624e13	0.770760	0.385380	+	0.922758i	$0.374070\pi$
$840$	−5.52327e12	−0.382771
$841$	−9.72549e12	−0.670393
$842$	−1.85155e13	−1.26950
$843$	−8.29746e12	−0.565876
$844$	1.07055e12	0.0726218
$845$	−1.60559e13	−1.08338
$846$	1.62640e10	0.00109159
$847$	1.00691e13	0.672226
$848$	1.58086e12	0.104981
$849$	−2.58163e13	−1.70533
$850$	0	0
$851$	−1.27480e12	−0.0833220
$852$	−1.43167e13	−0.930818
$853$	−2.50474e13	−1.61992	−0.809958	−	0.586488i	$-0.800510\pi$
$853$	−2.50474e13	−1.61992	−0.809958	+	0.586488i	$0.800510\pi$
$854$	2.70571e12	0.174069
$855$	1.06898e11	0.00684101
$856$	−1.40303e13	−0.893171
$857$	2.13270e12	0.135057	0.0675284	−	0.997717i	$-0.478489\pi$
$857$	2.13270e12	0.135057	0.0675284	+	0.997717i	$0.478489\pi$
$858$	−2.24626e12	−0.141503
$859$	4.78118e11	0.0299617	0.0149808	−	0.999888i	$-0.495231\pi$
$859$	4.78118e11	0.0299617	0.0149808	+	0.999888i	$0.495231\pi$
$860$	4.34897e12	0.271109
$861$	−8.79259e12	−0.545259
$862$	1.26581e13	0.780882
$863$	8.51279e12	0.522424	0.261212	−	0.965281i	$-0.415878\pi$
$863$	8.51279e12	0.522424	0.261212	+	0.965281i	$0.415878\pi$
$864$	−1.56549e13	−0.955737
$865$	−2.54330e13	−1.54463
$866$	−1.02890e13	−0.621644
$867$	0	0
$868$	−1.80931e12	−0.108187
$869$	1.37707e13	0.819157
$870$	7.03848e12	0.416526
$871$	−1.62685e12	−0.0957779
$872$	−1.35481e13	−0.793512
$873$	−2.33373e10	−0.00135984
$874$	1.54054e13	0.893039
$875$	−5.06991e12	−0.292391
$876$	−1.02821e13	−0.589945
$877$	−1.88647e13	−1.07684	−0.538421	−	0.842676i	$-0.680979\pi$
$877$	−1.88647e13	−1.07684	−0.538421	+	0.842676i	$0.680979\pi$
$878$	−2.95571e12	−0.167856
$879$	−1.23778e13	−0.699350
$880$	3.76617e12	0.211703
$881$	−2.99720e12	−0.167619	−0.0838095	−	0.996482i	$-0.526709\pi$
$881$	−2.99720e12	−0.167619	−0.0838095	+	0.996482i	$0.526709\pi$
$882$	4.74110e10	0.00263797
$883$	−9.35302e12	−0.517760	−0.258880	−	0.965909i	$-0.583353\pi$
$883$	−9.35302e12	−0.517760	−0.258880	+	0.965909i	$0.583353\pi$
$884$	0	0
$885$	−2.39638e13	−1.31314
$886$	−1.75513e13	−0.956881
$887$	1.00237e13	0.543716	0.271858	−	0.962337i	$-0.412362\pi$
$887$	1.00237e13	0.543716	0.271858	+	0.962337i	$0.412362\pi$
$888$	−1.61593e12	−0.0872094
$889$	−3.50203e12	−0.188045
$890$	6.49502e12	0.346997
$891$	3.27137e13	1.73892
$892$	3.67343e12	0.194281
$893$	−9.58613e12	−0.504442
$894$	−3.26215e12	−0.170799
$895$	1.85377e13	0.965721
$896$	3.05372e12	0.158286
$897$	2.37846e12	0.122668
$898$	1.15054e12	0.0590418
$899$	6.37084e12	0.325296
$900$	−1.06337e10	−0.000540248 0
$901$	0	0
$902$	3.65899e13	1.84048
$903$	2.92871e12	0.146582
$904$	1.64244e13	0.817960
$905$	3.15963e13	1.56573
$906$	1.75510e13	0.865416
$907$	−9.97808e12	−0.489569	−0.244785	−	0.969577i	$-0.578717\pi$
$907$	−9.97808e12	−0.489569	−0.244785	+	0.969577i	$0.578717\pi$
$908$	−1.28563e13	−0.627669
$909$	−9.05251e10	−0.00439776
$910$	−6.24927e11	−0.0302095
$911$	2.06967e13	0.995562	0.497781	−	0.867303i	$-0.334148\pi$
$911$	2.06967e13	0.995562	0.497781	+	0.867303i	$0.334148\pi$
$912$	3.19971e12	0.153156
$913$	−6.61463e13	−3.15056
$914$	3.90212e12	0.184945
$915$	1.83766e13	0.866702
$916$	−1.93871e13	−0.909878
$917$	1.04776e13	0.489329
$918$	0	0
$919$	1.75832e13	0.813164	0.406582	−	0.913614i	$-0.366721\pi$
$919$	1.75832e13	0.813164	0.406582	+	0.913614i	$0.366721\pi$
$920$	−2.43375e13	−1.12003
$921$	−1.75859e13	−0.805373
$922$	−1.16971e13	−0.533078
$923$	−4.47588e12	−0.202988
$924$	−7.34051e12	−0.331286
$925$	3.95798e11	0.0177761
$926$	−1.83405e13	−0.819715
$927$	9.90119e10	0.00440381
$928$	−1.24248e13	−0.549953
$929$	−2.50697e13	−1.10428	−0.552138	−	0.833753i	$-0.686188\pi$
$929$	−2.50697e13	−1.10428	−0.552138	+	0.833753i	$0.686188\pi$
$930$	9.37772e12	0.411078
$931$	−2.79445e13	−1.21905
$932$	−1.80830e13	−0.785052
$933$	1.73860e13	0.751158
$934$	−8.28926e11	−0.0356414
$935$	0	0
$936$	1.35728e10	0.000577998 0
$937$	−3.59638e13	−1.52418	−0.762091	−	0.647470i	$-0.775827\pi$
$937$	−3.59638e13	−1.52418	−0.762091	+	0.647470i	$0.775827\pi$
$938$	4.05710e12	0.171121
$939$	−6.92514e12	−0.290692
$940$	5.48082e12	0.228966
$941$	−4.41801e13	−1.83685	−0.918425	−	0.395596i	$-0.870538\pi$
$941$	−4.41801e13	−1.83685	−0.918425	+	0.395596i	$0.870538\pi$
$942$	1.71284e13	0.708741
$943$	−3.87434e13	−1.59549
$944$	−3.22916e12	−0.132348
$945$	9.06024e12	0.369570
$946$	−1.21877e13	−0.494778
$947$	1.28335e13	0.518527	0.259263	−	0.965807i	$-0.416520\pi$
$947$	1.28335e13	0.518527	0.259263	+	0.965807i	$0.416520\pi$
$948$	−6.68912e12	−0.268987
$949$	−3.21451e12	−0.128652
$950$	−4.78303e12	−0.190523
$951$	−4.13466e13	−1.63918
$952$	0	0
$953$	−3.92880e13	−1.54291	−0.771457	−	0.636281i	$-0.780472\pi$
$953$	−3.92880e13	−1.54291	−0.771457	+	0.636281i	$0.780472\pi$
$954$	7.18947e10	0.00281015
$955$	−5.02104e13	−1.95334
$956$	−1.98271e13	−0.767714
$957$	2.58471e13	0.996110
$958$	−2.43115e13	−0.932537
$959$	−6.63895e12	−0.253464
$960$	−2.15146e13	−0.817546
$961$	−1.79514e13	−0.678959
$962$	−1.82833e11	−0.00688283
$963$	−1.04552e11	−0.00391753
$964$	1.80096e13	0.671673
$965$	4.27765e13	1.58794
$966$	−5.93150e12	−0.219163
$967$	−1.46165e13	−0.537556	−0.268778	−	0.963202i	$-0.586620\pi$
$967$	−1.46165e13	−0.537556	−0.268778	+	0.963202i	$0.586620\pi$
$968$	5.62406e13	2.05878
$969$	0	0
$970$	6.00167e12	0.217670
$971$	2.39472e13	0.864508	0.432254	−	0.901752i	$-0.357718\pi$
$971$	2.39472e13	0.864508	0.432254	+	0.901752i	$0.357718\pi$
$972$	−1.42755e11	−0.00512971
$973$	6.03290e11	0.0215783
$974$	1.03652e13	0.369029
$975$	−7.38460e11	−0.0261701
$976$	2.47628e12	0.0873526
$977$	4.54828e13	1.59706	0.798530	−	0.601954i	$-0.205611\pi$
$977$	4.54828e13	1.59706	0.798530	+	0.601954i	$0.205611\pi$
$978$	−1.93385e13	−0.675923
$979$	2.38514e13	0.829833
$980$	1.59771e13	0.553326
$981$	−1.00958e11	−0.00348042
$982$	−1.09961e12	−0.0377343
$983$	3.89910e12	0.133191	0.0665954	−	0.997780i	$-0.478786\pi$
$983$	3.89910e12	0.133191	0.0665954	+	0.997780i	$0.478786\pi$
$984$	−4.91107e13	−1.66993
$985$	−4.24725e13	−1.43762
$986$	0	0
$987$	3.69093e12	0.123797
$988$	−2.89522e12	−0.0966665
$989$	1.29050e13	0.428917
$990$	1.71279e11	0.00566691
$991$	1.86771e13	0.615147	0.307574	−	0.951524i	$-0.400483\pi$
$991$	1.86771e13	0.615147	0.307574	+	0.951524i	$0.400483\pi$
$992$	−1.65543e13	−0.542759
$993$	−4.31842e12	−0.140946
$994$	1.11621e13	0.362667
$995$	−5.77711e13	−1.86856
$996$	3.21306e13	1.03455
$997$	−4.71408e13	−1.51101	−0.755507	−	0.655140i	$-0.772610\pi$
$997$	−4.71408e13	−1.51101	−0.755507	+	0.655140i	$0.772610\pi$
$998$	−6.58993e12	−0.210278
$999$	2.65073e12	0.0842016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.17		52
17.3	odd	16		17.10.d.a.9.5	yes	52
17.6	odd	16		17.10.d.a.2.5	✓	52
17.16	even	2	inner	289.10.a.i.1.18		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.5	✓	52	17.6	odd	16
17.10.d.a.9.5	yes	52	17.3	odd	16
289.10.a.i.1.17		52	1.1	even	1	trivial
289.10.a.i.1.18		52	17.16	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-14.8865 q^{2} -140.613 q^{3} -290.392 q^{4} +1537.70 q^{5} +2093.24 q^{6} +2138.55 q^{7} +11944.8 q^{8} +89.0110 q^{9} +O(q^{10})\)	\(q-14.8865 q^{2} -140.613 q^{3} -290.392 q^{4} +1537.70 q^{5} +2093.24 q^{6} +2138.55 q^{7} +11944.8 q^{8} +89.0110 q^{9} -22891.0 q^{10} -84061.4 q^{11} +40832.8 q^{12} +12765.7 q^{13} -31835.6 q^{14} -216220. q^{15} -29136.1 q^{16} -1325.06 q^{18} +781004. q^{19} -446535. q^{20} -300708. q^{21} +1.25138e6 q^{22} -1.32503e6 q^{23} -1.67960e6 q^{24} +411393. q^{25} -190037. q^{26} +2.75517e6 q^{27} -621018. q^{28} +2.18670e6 q^{29} +3.21877e6 q^{30} +2.91345e6 q^{31} -5.68201e6 q^{32} +1.18201e7 q^{33} +3.28845e6 q^{35} -25848.0 q^{36} +962092. q^{37} -1.16264e7 q^{38} -1.79502e6 q^{39} +1.83675e7 q^{40} +2.92396e7 q^{41} +4.47650e6 q^{42} -9.73937e6 q^{43} +2.44107e7 q^{44} +136872. q^{45} +1.97251e7 q^{46} -1.22741e7 q^{47} +4.09692e6 q^{48} -3.57802e7 q^{49} -6.12420e6 q^{50} -3.70706e6 q^{52} -5.42576e7 q^{53} -4.10149e7 q^{54} -1.29261e8 q^{55} +2.55446e7 q^{56} -1.09819e8 q^{57} -3.25523e7 q^{58} +1.10830e8 q^{59} +6.27886e7 q^{60} -8.49900e7 q^{61} -4.33711e7 q^{62} +190355. q^{63} +9.95030e7 q^{64} +1.96298e7 q^{65} -1.75960e8 q^{66} -1.27439e8 q^{67} +1.86317e8 q^{69} -4.89536e7 q^{70} -3.50617e8 q^{71} +1.06322e6 q^{72} -2.51809e8 q^{73} -1.43222e7 q^{74} -5.78472e7 q^{75} -2.26797e8 q^{76} -1.79770e8 q^{77} +2.67217e7 q^{78} -1.63817e8 q^{79} -4.48026e7 q^{80} -3.89165e8 q^{81} -4.35276e8 q^{82} +7.86881e8 q^{83} +8.73232e7 q^{84} +1.44985e8 q^{86} -3.07478e8 q^{87} -1.00410e9 q^{88} -2.83737e8 q^{89} -2.03755e6 q^{90} +2.73002e7 q^{91} +3.84778e8 q^{92} -4.09669e8 q^{93} +1.82719e8 q^{94} +1.20095e9 q^{95} +7.98964e8 q^{96} -2.62185e8 q^{97} +5.32642e8 q^{98} -7.48239e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 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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