LMFDB - Embedded newform 289.10.a.f.1.1

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:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-38.1697 q^{2} -135.302 q^{3} +944.927 q^{4} +33.6875 q^{5} +5164.44 q^{6} -4816.06 q^{7} -16524.7 q^{8} -1376.34 q^{9} +O(q^{10})$	\(q-38.1697 q^{2} -135.302 q^{3} +944.927 q^{4} +33.6875 q^{5} +5164.44 q^{6} -4816.06 q^{7} -16524.7 q^{8} -1376.34 q^{9} -1285.84 q^{10} -5448.56 q^{11} -127851. q^{12} -84561.3 q^{13} +183827. q^{14} -4558.00 q^{15} +146941. q^{16} +52534.6 q^{18} +731833. q^{19} +31832.3 q^{20} +651622. q^{21} +207970. q^{22} +1.21270e6 q^{23} +2.23583e6 q^{24} -1.95199e6 q^{25} +3.22768e6 q^{26} +2.84937e6 q^{27} -4.55082e6 q^{28} -4.60499e6 q^{29} +173977. q^{30} -8.07173e6 q^{31} +2.85196e6 q^{32} +737202. q^{33} -162241. q^{35} -1.30054e6 q^{36} -9.10949e6 q^{37} -2.79339e7 q^{38} +1.14413e7 q^{39} -556677. q^{40} +2.46664e7 q^{41} -2.48722e7 q^{42} +1.54236e7 q^{43} -5.14849e6 q^{44} -46365.6 q^{45} -4.62883e7 q^{46} -3.04241e7 q^{47} -1.98814e7 q^{48} -1.71592e7 q^{49} +7.45069e7 q^{50} -7.99043e7 q^{52} +214544. q^{53} -1.08760e8 q^{54} -183549. q^{55} +7.95839e7 q^{56} -9.90186e7 q^{57} +1.75771e8 q^{58} -1.32098e8 q^{59} -4.30697e6 q^{60} +6.38202e7 q^{61} +3.08095e8 q^{62} +6.62854e6 q^{63} -1.84092e8 q^{64} -2.84866e6 q^{65} -2.81388e7 q^{66} -4.10480e6 q^{67} -1.64080e8 q^{69} +6.19270e6 q^{70} +1.30344e8 q^{71} +2.27437e7 q^{72} +1.18105e8 q^{73} +3.47707e8 q^{74} +2.64108e8 q^{75} +6.91529e8 q^{76} +2.62406e7 q^{77} -4.36712e8 q^{78} +2.79854e8 q^{79} +4.95007e6 q^{80} -3.58436e8 q^{81} -9.41509e8 q^{82} +4.27934e8 q^{83} +6.15736e8 q^{84} -5.88715e8 q^{86} +6.23065e8 q^{87} +9.00359e7 q^{88} +5.00841e8 q^{89} +1.76976e6 q^{90} +4.07252e8 q^{91} +1.14591e9 q^{92} +1.09212e9 q^{93} +1.16128e9 q^{94} +2.46537e7 q^{95} -3.85877e8 q^{96} +1.12142e9 q^{97} +6.54962e8 q^{98} +7.49908e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) $ 24 * q + 5124 * q^4 + 108368 * q^9	$ 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) $ 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * 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 $

$2$	−38.1697	−1.68688	−0.843440	−	0.537224i	$-0.819473\pi$
$2$	−38.1697	−1.68688	−0.843440	+	0.537224i	$0.819473\pi$
$3$	−135.302	−0.964404	−0.482202	−	0.876060i	$-0.660163\pi$
$3$	−135.302	−0.964404	−0.482202	+	0.876060i	$0.660163\pi$
$4$	944.927	1.84556
$5$	33.6875	0.0241048	0.0120524	−	0.999927i	$-0.496164\pi$
$5$	33.6875	0.0241048	0.0120524	+	0.999927i	$0.496164\pi$
$6$	5164.44	1.62683
$7$	−4816.06	−0.758142	−0.379071	−	0.925368i	$-0.623756\pi$
$7$	−4816.06	−0.758142	−0.379071	+	0.925368i	$0.623756\pi$
$8$	−16524.7	−1.42636
$9$	−1376.34	−0.0699254
$10$	−1285.84	−0.0406620
$11$	−5448.56	−0.112206	−0.0561028	−	0.998425i	$-0.517867\pi$
$11$	−5448.56	−0.112206	−0.0561028	+	0.998425i	$0.517867\pi$
$12$	−127851.	−1.77987
$13$	−84561.3	−0.821158	−0.410579	−	0.911825i	$-0.634673\pi$
$13$	−84561.3	−0.821158	−0.410579	+	0.911825i	$0.634673\pi$
$14$	183827.	1.27889
$15$	−4558.00	−0.0232468
$16$	146941.	0.560535
$17$	0	0
$17$	0	0
$18$	52534.6	0.117956
$19$	731833.	1.28831	0.644156	−	0.764894i	$-0.277209\pi$
$19$	731833.	1.28831	0.644156	+	0.764894i	$0.277209\pi$
$20$	31832.3	0.0444870
$21$	651622.	0.731155
$22$	207970.	0.189277
$23$	1.21270e6	0.903602	0.451801	−	0.892119i	$-0.350782\pi$
$23$	1.21270e6	0.903602	0.451801	+	0.892119i	$0.350782\pi$
$24$	2.23583e6	1.37559
$25$	−1.95199e6	−0.999419
$26$	3.22768e6	1.38519
$27$	2.84937e6	1.03184
$28$	−4.55082e6	−1.39920
$29$	−4.60499e6	−1.20903	−0.604516	−	0.796593i	$-0.706633\pi$
$29$	−4.60499e6	−1.20903	−0.604516	+	0.796593i	$0.706633\pi$
$30$	173977.	0.0392145
$31$	−8.07173e6	−1.56978	−0.784890	−	0.619635i	$-0.787281\pi$
$31$	−8.07173e6	−1.56978	−0.784890	+	0.619635i	$0.787281\pi$
$32$	2.85196e6	0.480805
$33$	737202.	0.108212
$34$	0	0
$35$	−162241.	−0.0182749
$36$	−1.30054e6	−0.129052
$37$	−9.10949e6	−0.799073	−0.399537	−	0.916717i	$-0.630829\pi$
$37$	−9.10949e6	−0.799073	−0.399537	+	0.916717i	$0.630829\pi$
$38$	−2.79339e7	−2.17323
$39$	1.14413e7	0.791928
$40$	−556677.	−0.0343822
$41$	2.46664e7	1.36326	0.681629	−	0.731698i	$-0.261272\pi$
$41$	2.46664e7	1.36326	0.681629	+	0.731698i	$0.261272\pi$
$42$	−2.48722e7	−1.23337
$43$	1.54236e7	0.687984	0.343992	−	0.938973i	$-0.388221\pi$
$43$	1.54236e7	0.687984	0.343992	+	0.938973i	$0.388221\pi$
$44$	−5.14849e6	−0.207082
$45$	−46365.6	−0.00168554
$46$	−4.62883e7	−1.52427
$47$	−3.04241e7	−0.909447	−0.454724	−	0.890633i	$-0.650262\pi$
$47$	−3.04241e7	−0.909447	−0.454724	+	0.890633i	$0.650262\pi$
$48$	−1.98814e7	−0.540582
$49$	−1.71592e7	−0.425221
$50$	7.45069e7	1.68590
$51$	0	0
$52$	−7.99043e7	−1.51550
$53$	214544.	0.00373487	0.00186744	−	0.999998i	$-0.499406\pi$
$53$	214544.	0.00373487	0.00186744	+	0.999998i	$0.499406\pi$
$54$	−1.08760e8	−1.74059
$55$	−183549.	−0.00270470
$56$	7.95839e7	1.08138
$57$	−9.90186e7	−1.24245
$58$	1.75771e8	2.03949
$59$	−1.32098e8	−1.41926	−0.709632	−	0.704573i	$-0.751139\pi$
$59$	−1.32098e8	−1.41926	−0.709632	+	0.704573i	$0.751139\pi$
$60$	−4.30697e6	−0.0429034
$61$	6.38202e7	0.590166	0.295083	−	0.955472i	$-0.404653\pi$
$61$	6.38202e7	0.590166	0.295083	+	0.955472i	$0.404653\pi$
$62$	3.08095e8	2.64803
$63$	6.62854e6	0.0530134
$64$	−1.84092e8	−1.37159
$65$	−2.84866e6	−0.0197939
$66$	−2.81388e7	−0.182540
$67$	−4.10480e6	−0.0248860	−0.0124430	−	0.999923i	$-0.503961\pi$
$67$	−4.10480e6	−0.0248860	−0.0124430	+	0.999923i	$0.503961\pi$
$68$	0	0
$69$	−1.64080e8	−0.871437
$70$	6.19270e6	0.0308275
$71$	1.30344e8	0.608734	0.304367	−	0.952555i	$-0.401555\pi$
$71$	1.30344e8	0.608734	0.304367	+	0.952555i	$0.401555\pi$
$72$	2.27437e7	0.0997388
$73$	1.18105e8	0.486760	0.243380	−	0.969931i	$-0.421744\pi$
$73$	1.18105e8	0.486760	0.243380	+	0.969931i	$0.421744\pi$
$74$	3.47707e8	1.34794
$75$	2.64108e8	0.963843
$76$	6.91529e8	2.37766
$77$	2.62406e7	0.0850677
$78$	−4.36712e8	−1.33589
$79$	2.79854e8	0.808369	0.404185	−	0.914677i	$-0.367555\pi$
$79$	2.79854e8	0.808369	0.404185	+	0.914677i	$0.367555\pi$
$80$	4.95007e6	0.0135116
$81$	−3.58436e8	−0.925185
$82$	−9.41509e8	−2.29965
$83$	4.27934e8	0.989751	0.494875	−	0.868964i	$-0.335214\pi$
$83$	4.27934e8	0.989751	0.494875	+	0.868964i	$0.335214\pi$
$84$	6.15736e8	1.34939
$85$	0	0
$86$	−5.88715e8	−1.16055
$87$	6.23065e8	1.16599
$88$	9.00359e7	0.160046
$89$	5.00841e8	0.846145	0.423072	−	0.906096i	$-0.360952\pi$
$89$	5.00841e8	0.846145	0.423072	+	0.906096i	$0.360952\pi$
$90$	1.76976e6	0.00284331
$91$	4.07252e8	0.622554
$92$	1.14591e9	1.66765
$93$	1.09212e9	1.51390
$94$	1.16128e9	1.53413
$95$	2.46537e7	0.0310546
$96$	−3.85877e8	−0.463690
$97$	1.12142e9	1.28616	0.643079	−	0.765800i	$-0.277657\pi$
$97$	1.12142e9	1.28616	0.643079	+	0.765800i	$0.277657\pi$
$98$	6.54962e8	0.717297
$99$	7.49908e6	0.00784603
$100$	−1.84449e9	−1.84449
$101$	1.87960e9	1.79729	0.898647	−	0.438672i	$-0.144551\pi$
$101$	1.87960e9	1.79729	0.898647	+	0.438672i	$0.144551\pi$
$102$	0	0
$103$	8.90797e8	0.779850	0.389925	−	0.920847i	$-0.372501\pi$
$103$	8.90797e8	0.779850	0.389925	+	0.920847i	$0.372501\pi$
$104$	1.39735e9	1.17127
$105$	2.19516e7	0.0176244
$106$	−8.18910e6	−0.00630028
$107$	−1.44285e9	−1.06413	−0.532066	−	0.846703i	$-0.678584\pi$
$107$	−1.44285e9	−1.06413	−0.532066	+	0.846703i	$0.678584\pi$
$108$	2.69245e9	1.90432
$109$	−4.28115e8	−0.290497	−0.145248	−	0.989395i	$-0.546398\pi$
$109$	−4.28115e8	−0.290497	−0.145248	+	0.989395i	$0.546398\pi$
$110$	7.00600e6	0.00456250
$111$	1.23253e9	0.770629
$112$	−7.07675e8	−0.424965
$113$	−5.72053e7	−0.0330053	−0.0165026	−	0.999864i	$-0.505253\pi$
$113$	−5.72053e7	−0.0330053	−0.0165026	+	0.999864i	$0.505253\pi$
$114$	3.77951e9	2.09587
$115$	4.08528e7	0.0217812
$116$	−4.35138e9	−2.23134
$117$	1.16385e8	0.0574198
$118$	5.04215e9	2.39413
$119$	0	0
$120$	7.53196e7	0.0331583
$121$	−2.32826e9	−0.987410
$122$	−2.43600e9	−0.995539
$123$	−3.33741e9	−1.31473
$124$	−7.62719e9	−2.89712
$125$	−1.31554e8	−0.0481957
$126$	−2.53010e8	−0.0894272
$127$	3.89197e9	1.32756	0.663778	−	0.747929i	$-0.268952\pi$
$127$	3.89197e9	1.32756	0.663778	+	0.747929i	$0.268952\pi$
$128$	5.56655e9	1.83291
$129$	−2.08685e9	−0.663494
$130$	1.08733e8	0.0333899
$131$	4.26537e9	1.26542	0.632712	−	0.774387i	$-0.281942\pi$
$131$	4.26537e9	1.26542	0.632712	+	0.774387i	$0.281942\pi$
$132$	6.96602e8	0.199711
$133$	−3.52455e9	−0.976723
$134$	1.56679e8	0.0419797
$135$	9.59884e7	0.0248723
$136$	0	0
$137$	−5.82746e9	−1.41331	−0.706654	−	0.707560i	$-0.749796\pi$
$137$	−5.82746e9	−1.41331	−0.706654	+	0.707560i	$0.749796\pi$
$138$	6.26291e9	1.47001
$139$	4.27925e9	0.972301	0.486150	−	0.873875i	$-0.338401\pi$
$139$	4.27925e9	0.972301	0.486150	+	0.873875i	$0.338401\pi$
$140$	−1.53306e8	−0.0337274
$141$	4.11645e9	0.877074
$142$	−4.97519e9	−1.02686
$143$	4.60737e8	0.0921385
$144$	−2.02241e8	−0.0391956
$145$	−1.55131e8	−0.0291435
$146$	−4.50803e9	−0.821105
$147$	2.32168e9	0.410085
$148$	−8.60781e9	−1.47474
$149$	−9.06968e9	−1.50749	−0.753744	−	0.657168i	$-0.771754\pi$
$149$	−9.06968e9	−1.50749	−0.753744	+	0.657168i	$0.771754\pi$
$150$	−1.00809e10	−1.62589
$151$	9.99616e9	1.56472	0.782360	−	0.622826i	$-0.214016\pi$
$151$	9.99616e9	1.56472	0.782360	+	0.622826i	$0.214016\pi$
$152$	−1.20933e10	−1.83760
$153$	0	0
$154$	−1.00159e9	−0.143499
$155$	−2.71917e8	−0.0378393
$156$	1.08112e10	1.46155
$157$	1.14843e10	1.50854	0.754268	−	0.656567i	$-0.227992\pi$
$157$	1.14843e10	1.50854	0.754268	+	0.656567i	$0.227992\pi$
$158$	−1.06820e10	−1.36362
$159$	−2.90283e7	−0.00360193
$160$	9.60757e7	0.0115897
$161$	−5.84042e9	−0.685058
$162$	1.36814e10	1.56068
$163$	1.10311e10	1.22398	0.611989	−	0.790866i	$-0.290370\pi$
$163$	1.10311e10	1.22398	0.611989	+	0.790866i	$0.290370\pi$
$164$	2.33079e10	2.51598
$165$	2.48345e7	0.00260842
$166$	−1.63341e10	−1.66959
$167$	9.46762e9	0.941926	0.470963	−	0.882153i	$-0.343906\pi$
$167$	9.46762e9	0.941926	0.470963	+	0.882153i	$0.343906\pi$
$168$	−1.07679e10	−1.04289
$169$	−3.45388e9	−0.325700
$170$	0	0
$171$	−1.00725e9	−0.0900858
$172$	1.45742e10	1.26972
$173$	2.17323e9	0.184458	0.0922290	−	0.995738i	$-0.470601\pi$
$173$	2.17323e9	0.184458	0.0922290	+	0.995738i	$0.470601\pi$
$174$	−2.37822e10	−1.96689
$175$	9.40089e9	0.757701
$176$	−8.00616e8	−0.0628951
$177$	1.78732e10	1.36874
$178$	−1.91169e10	−1.42734
$179$	−3.30556e9	−0.240662	−0.120331	−	0.992734i	$-0.538396\pi$
$179$	−3.30556e9	−0.240662	−0.120331	+	0.992734i	$0.538396\pi$
$180$	−4.38121e7	−0.00311077
$181$	1.99217e9	0.137966	0.0689832	−	0.997618i	$-0.478025\pi$
$181$	1.99217e9	0.137966	0.0689832	+	0.997618i	$0.478025\pi$
$182$	−1.55447e10	−1.05017
$183$	−8.63501e9	−0.569158
$184$	−2.00395e10	−1.28886
$185$	−3.06876e8	−0.0192615
$186$	−4.16860e10	−2.55377
$187$	0	0
$188$	−2.87486e10	−1.67844
$189$	−1.37227e10	−0.782281
$190$	−9.41024e8	−0.0523853
$191$	−2.46723e10	−1.34141	−0.670703	−	0.741726i	$-0.734007\pi$
$191$	−2.46723e10	−1.34141	−0.670703	+	0.741726i	$0.734007\pi$
$192$	2.49081e10	1.32277
$193$	−2.70299e10	−1.40229	−0.701143	−	0.713020i	$-0.747327\pi$
$193$	−2.70299e10	−1.40229	−0.701143	+	0.713020i	$0.747327\pi$
$194$	−4.28041e10	−2.16959
$195$	3.85430e8	0.0190893
$196$	−1.62142e10	−0.784772
$197$	1.94743e10	0.921222	0.460611	−	0.887602i	$-0.347630\pi$
$197$	1.94743e10	0.921222	0.460611	+	0.887602i	$0.347630\pi$
$198$	−2.86238e8	−0.0132353
$199$	−1.30236e10	−0.588697	−0.294348	−	0.955698i	$-0.595103\pi$
$199$	−1.30236e10	−0.588697	−0.294348	+	0.955698i	$0.595103\pi$
$200$	3.22561e10	1.42553
$201$	5.55388e8	0.0240002
$202$	−7.17438e10	−3.03182
$203$	2.21779e10	0.916617
$204$	0	0
$205$	8.30950e8	0.0328611
$206$	−3.40015e10	−1.31551
$207$	−1.66909e9	−0.0631848
$208$	−1.24255e10	−0.460287
$209$	−3.98744e9	−0.144556
$210$	−8.37885e8	−0.0297302
$211$	−5.01338e10	−1.74124	−0.870621	−	0.491954i	$-0.836283\pi$
$211$	−5.01338e10	−1.74124	−0.870621	+	0.491954i	$0.836283\pi$
$212$	2.02729e8	0.00689294
$213$	−1.76358e10	−0.587066
$214$	5.50733e10	1.79506
$215$	5.19584e8	0.0165837
$216$	−4.70851e10	−1.47177
$217$	3.88739e10	1.19012
$218$	1.63410e10	0.490033
$219$	−1.59798e10	−0.469433
$220$	−1.73440e8	−0.00499169
$221$	0	0
$222$	−4.70455e10	−1.29996
$223$	8.60424e9	0.232992	0.116496	−	0.993191i	$-0.462834\pi$
$223$	8.60424e9	0.232992	0.116496	+	0.993191i	$0.462834\pi$
$224$	−1.37352e10	−0.364518
$225$	2.68661e9	0.0698848
$226$	2.18351e9	0.0556759
$227$	7.76957e10	1.94214	0.971070	−	0.238794i	$-0.0767520\pi$
$227$	7.76957e10	1.94214	0.971070	+	0.238794i	$0.0767520\pi$
$228$	−9.35654e10	−2.29302
$229$	−4.32400e10	−1.03902	−0.519512	−	0.854463i	$-0.673886\pi$
$229$	−4.32400e10	−1.03902	−0.519512	+	0.854463i	$0.673886\pi$
$230$	−1.55934e9	−0.0367422
$231$	−3.55040e9	−0.0820397
$232$	7.60961e10	1.72451
$233$	5.30033e9	0.117815	0.0589076	−	0.998263i	$-0.481238\pi$
$233$	5.30033e9	0.117815	0.0589076	+	0.998263i	$0.481238\pi$
$234$	−4.44239e9	−0.0968603
$235$	−1.02491e9	−0.0219221
$236$	−1.24823e11	−2.61934
$237$	−3.78649e10	−0.779595
$238$	0	0
$239$	6.63919e10	1.31621	0.658104	−	0.752927i	$-0.271359\pi$
$239$	6.63919e10	1.31621	0.658104	+	0.752927i	$0.271359\pi$
$240$	−6.69755e8	−0.0130306
$241$	7.94084e10	1.51632	0.758158	−	0.652070i	$-0.226099\pi$
$241$	7.94084e10	1.51632	0.758158	+	0.652070i	$0.226099\pi$
$242$	8.88691e10	1.66564
$243$	−7.58712e9	−0.139588
$244$	6.03055e10	1.08919
$245$	−5.78052e8	−0.0102499
$246$	1.27388e11	2.21779
$247$	−6.18848e10	−1.05791
$248$	1.33383e11	2.23907
$249$	−5.79004e10	−0.954519
$250$	5.02137e9	0.0813003
$251$	2.43313e10	0.386932	0.193466	−	0.981107i	$-0.438027\pi$
$251$	2.43313e10	0.386932	0.193466	+	0.981107i	$0.438027\pi$
$252$	6.26349e9	0.0978394
$253$	−6.60745e9	−0.101389
$254$	−1.48555e11	−2.23943
$255$	0	0
$256$	−1.18218e11	−1.72030
$257$	−6.20805e10	−0.887679	−0.443839	−	0.896106i	$-0.646384\pi$
$257$	−6.20805e10	−0.887679	−0.443839	+	0.896106i	$0.646384\pi$
$258$	7.96544e10	1.11923
$259$	4.38718e10	0.605810
$260$	−2.69178e9	−0.0365308
$261$	6.33804e9	0.0845421
$262$	−1.62808e11	−2.13462
$263$	3.11356e10	0.401288	0.200644	−	0.979664i	$-0.435697\pi$
$263$	3.11356e10	0.401288	0.200644	+	0.979664i	$0.435697\pi$
$264$	−1.21820e10	−0.154349
$265$	7.22748e6	9.00286e−5 0
$266$	1.34531e11	1.64761
$267$	−6.77648e10	−0.816025
$268$	−3.87874e9	−0.0459287
$269$	−3.50438e10	−0.408062	−0.204031	−	0.978964i	$-0.565404\pi$
$269$	−3.50438e10	−0.408062	−0.204031	+	0.978964i	$0.565404\pi$
$270$	−3.66385e9	−0.0419566
$271$	−1.41065e10	−0.158876	−0.0794378	−	0.996840i	$-0.525313\pi$
$271$	−1.41065e10	−0.158876	−0.0794378	+	0.996840i	$0.525313\pi$
$272$	0	0
$273$	−5.51020e10	−0.600393
$274$	2.22432e11	2.38408
$275$	1.06355e10	0.112140
$276$	−1.55044e11	−1.60829
$277$	1.10070e11	1.12333	0.561667	−	0.827363i	$-0.310160\pi$
$277$	1.10070e11	1.12333	0.561667	+	0.827363i	$0.310160\pi$
$278$	−1.63338e11	−1.64015
$279$	1.11095e10	0.109768
$280$	2.68099e9	0.0260666
$281$	−3.69253e10	−0.353302	−0.176651	−	0.984274i	$-0.556526\pi$
$281$	−3.69253e10	−0.353302	−0.176651	+	0.984274i	$0.556526\pi$
$282$	−1.57124e11	−1.47952
$283$	−3.72888e10	−0.345573	−0.172786	−	0.984959i	$-0.555277\pi$
$283$	−3.72888e10	−0.345573	−0.172786	+	0.984959i	$0.555277\pi$
$284$	1.23165e11	1.12346
$285$	−3.33569e9	−0.0299491
$286$	−1.75862e10	−0.155427
$287$	−1.18795e11	−1.03354
$288$	−3.92528e9	−0.0336205
$289$	0	0
$290$	5.92130e9	0.0491616
$291$	−1.51730e11	−1.24037
$292$	1.11600e11	0.898345
$293$	−2.03656e11	−1.61433	−0.807166	−	0.590325i	$-0.799000\pi$
$293$	−2.03656e11	−1.61433	−0.807166	+	0.590325i	$0.799000\pi$
$294$	−8.86178e10	−0.691764
$295$	−4.45007e9	−0.0342111
$296$	1.50532e11	1.13977
$297$	−1.55250e10	−0.115778
$298$	3.46187e11	2.54295
$299$	−1.02547e11	−0.742000
$300$	2.49563e11	1.77883
$301$	−7.42810e10	−0.521589
$302$	−3.81550e11	−2.63949
$303$	−2.54314e11	−1.73332
$304$	1.07536e11	0.722143
$305$	2.14995e9	0.0142259
$306$	0	0
$307$	1.07324e11	0.689563	0.344781	−	0.938683i	$-0.387953\pi$
$307$	1.07324e11	0.689563	0.344781	+	0.938683i	$0.387953\pi$
$308$	2.47954e10	0.156998
$309$	−1.20527e11	−0.752091
$310$	1.03790e10	0.0638303
$311$	−5.18315e10	−0.314176	−0.157088	−	0.987585i	$-0.550211\pi$
$311$	−5.18315e10	−0.314176	−0.157088	+	0.987585i	$0.550211\pi$
$312$	−1.89065e11	−1.12957
$313$	2.92938e11	1.72515	0.862575	−	0.505930i	$-0.168851\pi$
$313$	2.92938e11	1.72515	0.862575	+	0.505930i	$0.168851\pi$
$314$	−4.38352e11	−2.54472
$315$	2.23299e8	0.00127788
$316$	2.64442e11	1.49190
$317$	9.61316e10	0.534687	0.267343	−	0.963601i	$-0.413854\pi$
$317$	9.61316e10	0.534687	0.267343	+	0.963601i	$0.413854\pi$
$318$	1.10800e9	0.00607601
$319$	2.50906e10	0.135660
$320$	−6.20162e9	−0.0330621
$321$	1.95221e11	1.02625
$322$	2.22927e11	1.15561
$323$	0	0
$324$	−3.38696e11	−1.70749
$325$	1.65063e11	0.820681
$326$	−4.21053e11	−2.06470
$327$	5.79249e10	0.280156
$328$	−4.07605e11	−1.94450
$329$	1.46524e11	0.689490
$330$	−9.47926e8	−0.00440009
$331$	−3.04918e11	−1.39623	−0.698116	−	0.715985i	$-0.745978\pi$
$331$	−3.04918e11	−1.39623	−0.698116	+	0.715985i	$0.745978\pi$
$332$	4.04367e11	1.82665
$333$	1.25378e10	0.0558755
$334$	−3.61377e11	−1.58892
$335$	−1.38281e8	−0.000599873 0
$336$	9.57499e10	0.409837
$337$	−1.69980e11	−0.717897	−0.358948	−	0.933357i	$-0.616865\pi$
$337$	−1.69980e11	−0.717897	−0.358948	+	0.933357i	$0.616865\pi$
$338$	1.31834e11	0.549416
$339$	7.74000e9	0.0318304
$340$	0	0
$341$	4.39793e10	0.176138
$342$	3.84466e10	0.151964
$343$	2.76985e11	1.08052
$344$	−2.54871e11	−0.981312
$345$	−5.52747e9	−0.0210059
$346$	−8.29514e10	−0.311158
$347$	2.00658e11	0.742975	0.371488	−	0.928438i	$-0.378848\pi$
$347$	2.00658e11	0.742975	0.371488	+	0.928438i	$0.378848\pi$
$348$	5.88751e11	2.15191
$349$	3.31661e10	0.119669	0.0598343	−	0.998208i	$-0.480943\pi$
$349$	3.31661e10	0.119669	0.0598343	+	0.998208i	$0.480943\pi$
$350$	−3.58829e11	−1.27815
$351$	−2.40947e11	−0.847303
$352$	−1.55391e10	−0.0539490
$353$	−3.10706e11	−1.06504	−0.532518	−	0.846419i	$-0.678754\pi$
$353$	−3.10706e11	−1.06504	−0.532518	+	0.846419i	$0.678754\pi$
$354$	−6.82214e11	−2.30890
$355$	4.39096e9	0.0146735
$356$	4.73258e11	1.56161
$357$	0	0
$358$	1.26172e11	0.405967
$359$	−2.82979e10	−0.0899142	−0.0449571	−	0.998989i	$-0.514315\pi$
$359$	−2.82979e10	−0.0899142	−0.0449571	+	0.998989i	$0.514315\pi$
$360$	7.66178e8	0.00240419
$361$	2.12892e11	0.659747
$362$	−7.60407e10	−0.232733
$363$	3.15019e11	0.952262
$364$	3.84823e11	1.14896
$365$	3.97866e9	0.0117333
$366$	3.29596e11	0.960101
$367$	−1.96246e11	−0.564680	−0.282340	−	0.959314i	$-0.591111\pi$
$367$	−1.96246e11	−0.564680	−0.282340	+	0.959314i	$0.591111\pi$
$368$	1.78195e11	0.506500
$369$	−3.39494e10	−0.0953265
$370$	1.17134e10	0.0324919
$371$	−1.03326e9	−0.00283156
$372$	1.03198e12	2.79400
$373$	2.86863e11	0.767335	0.383667	−	0.923471i	$-0.374661\pi$
$373$	2.86863e11	0.767335	0.383667	+	0.923471i	$0.374661\pi$
$374$	0	0
$375$	1.77995e10	0.0464801
$376$	5.02750e11	1.29720
$377$	3.89404e11	0.992806
$378$	5.23793e11	1.31961
$379$	5.50796e10	0.137124	0.0685621	−	0.997647i	$-0.478159\pi$
$379$	5.50796e10	0.137124	0.0685621	+	0.997647i	$0.478159\pi$
$380$	2.32959e10	0.0573131
$381$	−5.26592e11	−1.28030
$382$	9.41736e11	2.26279
$383$	−4.27720e11	−1.01570	−0.507849	−	0.861446i	$-0.669559\pi$
$383$	−4.27720e11	−1.01570	−0.507849	+	0.861446i	$0.669559\pi$
$384$	−7.53165e11	−1.76766
$385$	8.83980e8	0.00205054
$386$	1.03172e12	2.36549
$387$	−2.12282e10	−0.0481075
$388$	1.05966e12	2.37368
$389$	−6.41336e11	−1.42008	−0.710039	−	0.704162i	$-0.751323\pi$
$389$	−6.41336e11	−1.42008	−0.710039	+	0.704162i	$0.751323\pi$
$390$	−1.47118e10	−0.0322013
$391$	0	0
$392$	2.83551e11	0.606518
$393$	−5.77114e11	−1.22038
$394$	−7.43329e11	−1.55399
$395$	9.42760e9	0.0194856
$396$	7.08609e9	0.0144803
$397$	5.30146e11	1.07112	0.535561	−	0.844497i	$-0.320100\pi$
$397$	5.30146e11	1.07112	0.535561	+	0.844497i	$0.320100\pi$
$398$	4.97106e11	0.993060
$399$	4.76879e11	0.941955
$400$	−2.86827e11	−0.560209
$401$	4.65580e11	0.899176	0.449588	−	0.893236i	$-0.351571\pi$
$401$	4.65580e11	0.899176	0.449588	+	0.893236i	$0.351571\pi$
$402$	−2.11990e10	−0.0404854
$403$	6.82556e11	1.28904
$404$	1.77609e12	3.31702
$405$	−1.20748e10	−0.0223014
$406$	−8.46524e11	−1.54622
$407$	4.96336e10	0.0896605
$408$	0	0
$409$	7.09692e11	1.25405	0.627025	−	0.778999i	$-0.284272\pi$
$409$	7.09692e11	1.25405	0.627025	+	0.778999i	$0.284272\pi$
$410$	−3.17171e10	−0.0554328
$411$	7.88467e11	1.36300
$412$	8.41738e11	1.43926
$413$	6.36193e11	1.07600
$414$	6.37086e10	0.106585
$415$	1.44161e10	0.0238578
$416$	−2.41166e11	−0.394817
$417$	−5.78991e11	−0.937690
$418$	1.52199e11	0.243848
$419$	−3.09506e11	−0.490576	−0.245288	−	0.969450i	$-0.578883\pi$
$419$	−3.09506e11	−0.490576	−0.245288	+	0.969450i	$0.578883\pi$
$420$	2.07426e10	0.0325268
$421$	−1.13495e12	−1.76080	−0.880398	−	0.474235i	$-0.842725\pi$
$421$	−1.13495e12	−1.76080	−0.880398	+	0.474235i	$0.842725\pi$
$422$	1.91359e12	2.93727
$423$	4.18740e10	0.0635935
$424$	−3.54529e9	−0.00532727
$425$	0	0
$426$	6.73153e11	0.990309
$427$	−3.07362e11	−0.447429
$428$	−1.36339e12	−1.96392
$429$	−6.23387e10	−0.0888587
$430$	−1.98324e10	−0.0279748
$431$	−6.87197e11	−0.959254	−0.479627	−	0.877472i	$-0.659228\pi$
$431$	−6.87197e11	−0.959254	−0.479627	+	0.877472i	$0.659228\pi$
$432$	4.18689e11	0.578382
$433$	1.31231e11	0.179407	0.0897036	−	0.995969i	$-0.471408\pi$
$433$	1.31231e11	0.179407	0.0897036	+	0.995969i	$0.471408\pi$
$434$	−1.48380e12	−2.00758
$435$	2.09895e10	0.0281061
$436$	−4.04538e11	−0.536130
$437$	8.87492e11	1.16412
$438$	6.09945e11	0.791876
$439$	−6.12833e11	−0.787502	−0.393751	−	0.919217i	$-0.628823\pi$
$439$	−6.12833e11	−0.787502	−0.393751	+	0.919217i	$0.628823\pi$
$440$	3.03309e9	0.00385787
$441$	2.36170e10	0.0297338
$442$	0	0
$443$	−4.51857e11	−0.557422	−0.278711	−	0.960375i	$-0.589907\pi$
$443$	−4.51857e11	−0.557422	−0.278711	+	0.960375i	$0.589907\pi$
$444$	1.16465e12	1.42224
$445$	1.68721e10	0.0203962
$446$	−3.28422e11	−0.393029
$447$	1.22715e12	1.45383
$448$	8.86599e11	1.03986
$449$	−1.02961e12	−1.19554	−0.597770	−	0.801668i	$-0.703946\pi$
$449$	−1.02961e12	−1.19554	−0.597770	+	0.801668i	$0.703946\pi$
$450$	−1.02547e11	−0.117887
$451$	−1.34396e11	−0.152965
$452$	−5.40549e10	−0.0609133
$453$	−1.35250e12	−1.50902
$454$	−2.96562e12	−3.27616
$455$	1.37193e10	0.0150066
$456$	1.63625e12	1.77218
$457$	1.58775e12	1.70278	0.851389	−	0.524535i	$-0.175761\pi$
$457$	1.58775e12	1.70278	0.851389	+	0.524535i	$0.175761\pi$
$458$	1.65046e12	1.75271
$459$	0	0
$460$	3.86029e10	0.0401985
$461$	−1.72351e12	−1.77730	−0.888649	−	0.458588i	$-0.848355\pi$
$461$	−1.72351e12	−1.77730	−0.888649	+	0.458588i	$0.848355\pi$
$462$	1.35518e11	0.138391
$463$	8.31463e10	0.0840869	0.0420435	−	0.999116i	$-0.486613\pi$
$463$	8.31463e10	0.0840869	0.0420435	+	0.999116i	$0.486613\pi$
$464$	−6.76661e11	−0.677704
$465$	3.67909e10	0.0364924
$466$	−2.02312e11	−0.198740
$467$	−1.30167e12	−1.26641	−0.633206	−	0.773984i	$-0.718261\pi$
$467$	−1.30167e12	−1.26641	−0.633206	+	0.773984i	$0.718261\pi$
$468$	1.09976e11	0.105972
$469$	1.97689e10	0.0188671
$470$	3.91207e10	0.0369799
$471$	−1.55385e12	−1.45484
$472$	2.18289e12	2.02438
$473$	−8.40365e10	−0.0771956
$474$	1.44529e12	1.31508
$475$	−1.42853e12	−1.28756
$476$	0	0
$477$	−2.95287e8	−0.000261163 0
$478$	−2.53416e12	−2.22028
$479$	−1.53959e12	−1.33628	−0.668138	−	0.744037i	$-0.732909\pi$
$479$	−1.53959e12	−1.33628	−0.668138	+	0.744037i	$0.732909\pi$
$480$	−1.29992e10	−0.0111772
$481$	7.70311e11	0.656165
$482$	−3.03100e12	−2.55784
$483$	7.90221e11	0.660673
$484$	−2.20004e12	−1.82233
$485$	3.77778e10	0.0310026
$486$	2.89598e11	0.235468
$487$	−1.99461e12	−1.60686	−0.803428	−	0.595402i	$-0.796993\pi$
$487$	−1.99461e12	−1.60686	−0.803428	+	0.595402i	$0.796993\pi$
$488$	−1.05461e12	−0.841789
$489$	−1.49253e12	−1.18041
$490$	2.20641e10	0.0172903
$491$	−1.52090e12	−1.18096	−0.590480	−	0.807053i	$-0.701061\pi$
$491$	−1.52090e12	−1.18096	−0.590480	+	0.807053i	$0.701061\pi$
$492$	−3.15361e12	−2.42642
$493$	0	0
$494$	2.36212e12	1.78456
$495$	2.52626e8	0.000189127 0
$496$	−1.18607e12	−0.879916
$497$	−6.27743e11	−0.461507
$498$	2.21004e12	1.61016
$499$	1.82903e12	1.32059	0.660294	−	0.751007i	$-0.270432\pi$
$499$	1.82903e12	1.32059	0.660294	+	0.751007i	$0.270432\pi$
$500$	−1.24309e11	−0.0889481
$501$	−1.28099e12	−0.908397
$502$	−9.28720e11	−0.652707
$503$	1.46281e12	1.01890	0.509450	−	0.860500i	$-0.329849\pi$
$503$	1.46281e12	1.01890	0.509450	+	0.860500i	$0.329849\pi$
$504$	−1.09535e11	−0.0756161
$505$	6.33191e10	0.0433235
$506$	2.52205e11	0.171031
$507$	4.67318e11	0.314106
$508$	3.67763e12	2.45009
$509$	4.28087e11	0.282685	0.141342	−	0.989961i	$-0.454858\pi$
$509$	4.28087e11	0.282685	0.141342	+	0.989961i	$0.454858\pi$
$510$	0	0
$511$	−5.68799e11	−0.369033
$512$	1.66228e12	1.06903
$513$	2.08527e12	1.32933
$514$	2.36959e12	1.49741
$515$	3.00088e10	0.0187982
$516$	−1.97192e12	−1.22452
$517$	1.65768e11	0.102045
$518$	−1.67458e12	−1.02193
$519$	−2.94042e11	−0.177892
$520$	4.70733e10	0.0282332
$521$	8.10781e11	0.482096	0.241048	−	0.970513i	$-0.422509\pi$
$521$	8.10781e11	0.482096	0.241048	+	0.970513i	$0.422509\pi$
$522$	−2.41921e11	−0.142612
$523$	−2.06333e12	−1.20590	−0.602949	−	0.797779i	$-0.706008\pi$
$523$	−2.06333e12	−1.20590	−0.602949	+	0.797779i	$0.706008\pi$
$524$	4.03047e12	2.33542
$525$	−1.27196e12	−0.730730
$526$	−1.18844e12	−0.676924
$527$	0	0
$528$	1.08325e11	0.0606563
$529$	−3.30518e11	−0.183504
$530$	−2.75871e8	−0.000151867 0
$531$	1.81812e11	0.0992426
$532$	−3.33044e12	−1.80260
$533$	−2.08582e12	−1.11945
$534$	2.58656e12	1.37654
$535$	−4.86062e10	−0.0256507
$536$	6.78306e10	0.0354964
$537$	4.47249e11	0.232095
$538$	1.33761e12	0.688351
$539$	9.34930e10	0.0477122
$540$	9.07021e10	0.0459034
$541$	5.86856e10	0.0294539	0.0147270	−	0.999892i	$-0.495312\pi$
$541$	5.86856e10	0.0294539	0.0147270	+	0.999892i	$0.495312\pi$
$542$	5.38441e11	0.268004
$543$	−2.69545e11	−0.133055
$544$	0	0
$545$	−1.44221e10	−0.00700238
$546$	2.10323e12	1.01279
$547$	−7.82148e11	−0.373547	−0.186774	−	0.982403i	$-0.559803\pi$
$547$	−7.82148e11	−0.373547	−0.186774	+	0.982403i	$0.559803\pi$
$548$	−5.50652e12	−2.60835
$549$	−8.78385e10	−0.0412676
$550$	−4.05955e11	−0.189167
$551$	−3.37009e12	−1.55761
$552$	2.71138e12	1.24298
$553$	−1.34779e12	−0.612859
$554$	−4.20133e12	−1.89493
$555$	4.15210e10	0.0185759
$556$	4.04358e12	1.79444
$557$	−1.21784e12	−0.536096	−0.268048	−	0.963406i	$-0.586379\pi$
$557$	−1.21784e12	−0.536096	−0.268048	+	0.963406i	$0.586379\pi$
$558$	−4.24045e11	−0.185165
$559$	−1.30424e12	−0.564943
$560$	−2.38398e10	−0.0102437
$561$	0	0
$562$	1.40943e12	0.595977
$563$	−7.08396e11	−0.297159	−0.148579	−	0.988900i	$-0.547470\pi$
$563$	−7.08396e11	−0.297159	−0.148579	+	0.988900i	$0.547470\pi$
$564$	3.88974e12	1.61869
$565$	−1.92711e9	−0.000795587 0
$566$	1.42330e12	0.582939
$567$	1.72625e12	0.701421
$568$	−2.15389e12	−0.868274
$569$	6.19769e11	0.247870	0.123935	−	0.992290i	$-0.460449\pi$
$569$	6.19769e11	0.247870	0.123935	+	0.992290i	$0.460449\pi$
$570$	1.27322e11	0.0505206
$571$	−2.87595e12	−1.13219	−0.566095	−	0.824340i	$-0.691547\pi$
$571$	−2.87595e12	−1.13219	−0.566095	+	0.824340i	$0.691547\pi$
$572$	4.35363e11	0.170047
$573$	3.33822e12	1.29366
$574$	4.53436e12	1.74346
$575$	−2.36717e12	−0.903077
$576$	2.53374e11	0.0959094
$577$	−1.62060e11	−0.0608673	−0.0304336	−	0.999537i	$-0.509689\pi$
$577$	−1.62060e11	−0.0608673	−0.0304336	+	0.999537i	$0.509689\pi$
$578$	0	0
$579$	3.65720e12	1.35237
$580$	−1.46587e11	−0.0537862
$581$	−2.06096e12	−0.750371
$582$	5.79149e12	2.09236
$583$	−1.16896e9	−0.000419074 0
$584$	−1.95165e12	−0.694294
$585$	3.92074e9	0.00138410
$586$	7.77349e12	2.72318
$587$	−4.89722e11	−0.170247	−0.0851233	−	0.996370i	$-0.527128\pi$
$587$	−4.89722e11	−0.170247	−0.0851233	+	0.996370i	$0.527128\pi$
$588$	2.19382e12	0.756837
$589$	−5.90716e12	−2.02237
$590$	1.69858e11	0.0577100
$591$	−2.63492e12	−0.888430
$592$	−1.33856e12	−0.447908
$593$	−1.30014e12	−0.431762	−0.215881	−	0.976420i	$-0.569262\pi$
$593$	−1.30014e12	−0.431762	−0.215881	+	0.976420i	$0.569262\pi$
$594$	5.92584e11	0.195304
$595$	0	0
$596$	−8.57019e12	−2.78216
$597$	1.76212e12	0.567741
$598$	3.91420e12	1.25166
$599$	−1.04261e12	−0.330903	−0.165451	−	0.986218i	$-0.552908\pi$
$599$	−1.04261e12	−0.330903	−0.165451	+	0.986218i	$0.552908\pi$
$600$	−4.36431e12	−1.37479
$601$	6.03209e12	1.88596	0.942980	−	0.332850i	$-0.108010\pi$
$601$	6.03209e12	1.88596	0.942980	+	0.332850i	$0.108010\pi$
$602$	2.83528e12	0.879857
$603$	5.64961e9	0.00174016
$604$	9.44564e12	2.88779
$605$	−7.84334e10	−0.0238014
$606$	9.70709e12	2.92390
$607$	6.30500e11	0.188511	0.0942554	−	0.995548i	$-0.469953\pi$
$607$	6.30500e11	0.188511	0.0942554	+	0.995548i	$0.469953\pi$
$608$	2.08716e12	0.619427
$609$	−3.00072e12	−0.883989
$610$	−8.20629e10	−0.0239973
$611$	2.57270e12	0.746800
$612$	0	0
$613$	5.77576e11	0.165210	0.0826052	−	0.996582i	$-0.473676\pi$
$613$	5.77576e11	0.165210	0.0826052	+	0.996582i	$0.473676\pi$
$614$	−4.09652e12	−1.16321
$615$	−1.12429e11	−0.0316914
$616$	−4.33618e11	−0.121337
$617$	−2.35566e12	−0.654380	−0.327190	−	0.944959i	$-0.606102\pi$
$617$	−2.35566e12	−0.654380	−0.327190	+	0.944959i	$0.606102\pi$
$618$	4.60047e12	1.26869
$619$	−1.61444e12	−0.441991	−0.220996	−	0.975275i	$-0.570931\pi$
$619$	−1.61444e12	−0.441991	−0.220996	+	0.975275i	$0.570931\pi$
$620$	−2.56941e11	−0.0698347
$621$	3.45543e12	0.932373
$622$	1.97840e12	0.529976
$623$	−2.41208e12	−0.641497
$624$	1.68120e12	0.443903
$625$	3.80805e12	0.998257
$626$	−1.11814e13	−2.91012
$627$	5.39509e11	0.139410
$628$	1.08518e13	2.78409
$629$	0	0
$630$	−8.52327e9	−0.00215563
$631$	5.47382e12	1.37454	0.687272	−	0.726400i	$-0.258808\pi$
$631$	5.47382e12	1.37454	0.687272	+	0.726400i	$0.258808\pi$
$632$	−4.62451e12	−1.15303
$633$	6.78320e12	1.67926
$634$	−3.66932e12	−0.901952
$635$	1.31111e11	0.0320005
$636$	−2.74296e10	−0.00664757
$637$	1.45101e12	0.349174
$638$	−9.57700e11	−0.228842
$639$	−1.79398e11	−0.0425660
$640$	1.87523e11	0.0441820
$641$	1.09654e12	0.256544	0.128272	−	0.991739i	$-0.459057\pi$
$641$	1.09654e12	0.256544	0.128272	+	0.991739i	$0.459057\pi$
$642$	−7.45153e12	−1.73116
$643$	−3.67614e12	−0.848093	−0.424046	−	0.905641i	$-0.639391\pi$
$643$	−3.67614e12	−0.848093	−0.424046	+	0.905641i	$0.639391\pi$
$644$	−5.51877e12	−1.26432
$645$	−7.03008e10	−0.0159934
$646$	0	0
$647$	−3.35720e11	−0.0753196	−0.0376598	−	0.999291i	$-0.511990\pi$
$647$	−3.35720e11	−0.0753196	−0.0376598	+	0.999291i	$0.511990\pi$
$648$	5.92305e12	1.31965
$649$	7.19745e11	0.159249
$650$	−6.30040e12	−1.38439
$651$	−5.25972e12	−1.14775
$652$	1.04236e13	2.25893
$653$	3.92344e12	0.844417	0.422209	−	0.906499i	$-0.361255\pi$
$653$	3.92344e12	0.844417	0.422209	+	0.906499i	$0.361255\pi$
$654$	−2.21098e12	−0.472590
$655$	1.43690e11	0.0305028
$656$	3.62450e12	0.764154
$657$	−1.62553e11	−0.0340369
$658$	−5.59279e12	−1.16309
$659$	−3.63105e12	−0.749977	−0.374989	−	0.927029i	$-0.622353\pi$
$659$	−3.63105e12	−0.749977	−0.374989	+	0.927029i	$0.622353\pi$
$660$	2.34668e10	0.00481400
$661$	−6.68704e12	−1.36247	−0.681235	−	0.732064i	$-0.738557\pi$
$661$	−6.68704e12	−1.36247	−0.681235	+	0.732064i	$0.738557\pi$
$662$	1.16386e13	2.35527
$663$	0	0
$664$	−7.07149e12	−1.41174
$665$	−1.18733e11	−0.0235438
$666$	−4.78564e11	−0.0942553
$667$	−5.58446e12	−1.09248
$668$	8.94622e12	1.73838
$669$	−1.16417e12	−0.224698
$670$	5.27813e9	0.00101191
$671$	−3.47728e11	−0.0662199
$672$	1.85840e12	0.351543
$673$	2.18963e12	0.411436	0.205718	−	0.978611i	$-0.434047\pi$
$673$	2.18963e12	0.411436	0.205718	+	0.978611i	$0.434047\pi$
$674$	6.48807e12	1.21101
$675$	−5.56195e12	−1.03124
$676$	−3.26367e12	−0.601099
$677$	9.59093e11	0.175474	0.0877368	−	0.996144i	$-0.472037\pi$
$677$	9.59093e11	0.175474	0.0877368	+	0.996144i	$0.472037\pi$
$678$	−2.95434e11	−0.0536941
$679$	−5.40080e12	−0.975089
$680$	0	0
$681$	−1.05124e13	−1.87301
$682$	−1.67868e12	−0.297124
$683$	−2.11023e12	−0.371053	−0.185527	−	0.982639i	$-0.559399\pi$
$683$	−2.11023e12	−0.371053	−0.185527	+	0.982639i	$0.559399\pi$
$684$	−9.51781e11	−0.166259
$685$	−1.96313e11	−0.0340676
$686$	−1.05724e13	−1.82271
$687$	5.85046e12	1.00204
$688$	2.26636e12	0.385639
$689$	−1.81422e10	−0.00306692
$690$	2.10982e11	0.0354343
$691$	1.70994e12	0.285319	0.142659	−	0.989772i	$-0.454435\pi$
$691$	1.70994e12	0.285319	0.142659	+	0.989772i	$0.454435\pi$
$692$	2.05354e12	0.340428
$693$	−3.61160e10	−0.00594840
$694$	−7.65907e12	−1.25331
$695$	1.44157e11	0.0234372
$696$	−1.02960e13	−1.66313
$697$	0	0
$698$	−1.26594e12	−0.201866
$699$	−7.17146e11	−0.113621
$700$	8.88316e12	1.39838
$701$	−1.01887e13	−1.59363	−0.796816	−	0.604222i	$-0.793484\pi$
$701$	−1.01887e13	−1.59363	−0.796816	+	0.604222i	$0.793484\pi$
$702$	9.19687e12	1.42930
$703$	−6.66663e12	−1.02946
$704$	1.00304e12	0.153901
$705$	1.38673e11	0.0211417
$706$	1.18596e13	1.79659
$707$	−9.05226e12	−1.36260
$708$	1.68888e13	2.52610
$709$	9.56818e12	1.42207	0.711036	−	0.703156i	$-0.248226\pi$
$709$	9.56818e12	1.42207	0.711036	+	0.703156i	$0.248226\pi$
$710$	−1.67602e11	−0.0247523
$711$	−3.85175e11	−0.0565256
$712$	−8.27625e12	−1.20691
$713$	−9.78856e12	−1.41846
$714$	0	0
$715$	1.55211e10	0.00222098
$716$	−3.12352e12	−0.444155
$717$	−8.98296e12	−1.26936
$718$	1.08012e12	0.151674
$719$	2.41940e12	0.337619	0.168810	−	0.985649i	$-0.446008\pi$
$719$	2.41940e12	0.337619	0.168810	+	0.985649i	$0.446008\pi$
$720$	−6.81300e9	−0.000944805 0
$721$	−4.29013e12	−0.591237
$722$	−8.12604e12	−1.11291
$723$	−1.07441e13	−1.46234
$724$	1.88246e12	0.254625
$725$	8.98890e12	1.20833
$726$	−1.20242e13	−1.60635
$727$	5.62075e12	0.746259	0.373130	−	0.927779i	$-0.378285\pi$
$727$	5.62075e12	0.746259	0.373130	+	0.927779i	$0.378285\pi$
$728$	−6.72972e12	−0.887985
$729$	8.08164e12	1.05980
$730$	−1.51864e11	−0.0197926
$731$	0	0
$732$	−8.15946e12	−1.05042
$733$	5.95250e11	0.0761608	0.0380804	−	0.999275i	$-0.487876\pi$
$733$	5.95250e11	0.0761608	0.0380804	+	0.999275i	$0.487876\pi$
$734$	7.49064e12	0.952547
$735$	7.82116e10	0.00988504
$736$	3.45857e12	0.434457
$737$	2.23652e10	0.00279235
$738$	1.29584e12	0.160804
$739$	6.94825e12	0.856990	0.428495	−	0.903544i	$-0.359044\pi$
$739$	6.94825e12	0.856990	0.428495	+	0.903544i	$0.359044\pi$
$740$	−2.89976e11	−0.0355483
$741$	8.37314e12	1.02025
$742$	3.94392e10	0.00477650
$743$	−3.10384e12	−0.373637	−0.186818	−	0.982394i	$-0.559818\pi$
$743$	−3.10384e12	−0.373637	−0.186818	+	0.982394i	$0.559818\pi$
$744$	−1.80470e13	−2.15937
$745$	−3.05535e11	−0.0363378
$746$	−1.09495e13	−1.29440
$747$	−5.88984e11	−0.0692087
$748$	0	0
$749$	6.94886e12	0.806762
$750$	−6.79402e11	−0.0784063
$751$	7.49507e12	0.859797	0.429899	−	0.902877i	$-0.358549\pi$
$751$	7.49507e12	0.859797	0.429899	+	0.902877i	$0.358549\pi$
$752$	−4.47054e12	−0.509777
$753$	−3.29208e12	−0.373158
$754$	−1.48634e13	−1.67474
$755$	3.36746e11	0.0377173
$756$	−1.29670e13	−1.44375
$757$	−5.04488e12	−0.558366	−0.279183	−	0.960238i	$-0.590064\pi$
$757$	−5.04488e12	−0.558366	−0.279183	+	0.960238i	$0.590064\pi$
$758$	−2.10237e12	−0.231312
$759$	8.94002e11	0.0977801
$760$	−4.07395e11	−0.0442950
$761$	−1.46542e13	−1.58391	−0.791956	−	0.610578i	$-0.790937\pi$
$761$	−1.46542e13	−1.58391	−0.791956	+	0.610578i	$0.790937\pi$
$762$	2.00999e13	2.15971
$763$	2.06183e12	0.220238
$764$	−2.33136e13	−2.47565
$765$	0	0
$766$	1.63259e13	1.71336
$767$	1.11704e13	1.16544
$768$	1.59952e13	1.65907
$769$	2.31369e12	0.238581	0.119291	−	0.992859i	$-0.461938\pi$
$769$	2.31369e12	0.238581	0.119291	+	0.992859i	$0.461938\pi$
$770$	−3.37413e10	−0.00345902
$771$	8.39962e12	0.856081
$772$	−2.55413e13	−2.58801
$773$	−3.66057e12	−0.368757	−0.184379	−	0.982855i	$-0.559027\pi$
$773$	−3.66057e12	−0.368757	−0.184379	+	0.982855i	$0.559027\pi$
$774$	8.10273e11	0.0811516
$775$	1.57559e13	1.56887
$776$	−1.85311e13	−1.83452
$777$	−5.93595e12	−0.584246
$778$	2.44796e13	2.39550
$779$	1.80517e13	1.75630
$780$	3.64203e11	0.0352305
$781$	−7.10186e11	−0.0683034
$782$	0	0
$783$	−1.31213e13	−1.24753
$784$	−2.52139e12	−0.238351
$785$	3.86877e11	0.0363630
$786$	2.20283e13	2.05863
$787$	−1.49355e13	−1.38782	−0.693909	−	0.720063i	$-0.744113\pi$
$787$	−1.49355e13	−1.38782	−0.693909	+	0.720063i	$0.744113\pi$
$788$	1.84018e13	1.70017
$789$	−4.21271e12	−0.387004
$790$	−3.59849e11	−0.0328699
$791$	2.75504e11	0.0250227
$792$	−1.23920e11	−0.0111913
$793$	−5.39672e12	−0.484619
$794$	−2.02355e13	−1.80685
$795$	−9.77893e8	−8.68239e−5 0
$796$	−1.23063e13	−1.08648
$797$	1.44395e13	1.26762	0.633809	−	0.773490i	$-0.281490\pi$
$797$	1.44395e13	1.26762	0.633809	+	0.773490i	$0.281490\pi$
$798$	−1.82023e13	−1.58896
$799$	0	0
$800$	−5.56701e12	−0.480526
$801$	−6.89328e11	−0.0591670
$802$	−1.77711e13	−1.51680
$803$	−6.43501e11	−0.0546172
$804$	5.24801e11	0.0442938
$805$	−1.96749e11	−0.0165132
$806$	−2.60530e13	−2.17445
$807$	4.74150e12	0.393536
$808$	−3.10599e13	−2.56359
$809$	1.92836e13	1.58278	0.791390	−	0.611312i	$-0.209358\pi$
$809$	1.92836e13	1.58278	0.791390	+	0.611312i	$0.209358\pi$
$810$	4.60892e11	0.0376198
$811$	1.12909e13	0.916506	0.458253	−	0.888822i	$-0.348475\pi$
$811$	1.12909e13	0.916506	0.458253	+	0.888822i	$0.348475\pi$
$812$	2.09565e13	1.69167
$813$	1.90864e12	0.153220
$814$	−1.89450e12	−0.151246
$815$	3.71610e11	0.0295038
$816$	0	0
$817$	1.12875e13	0.886337
$818$	−2.70887e13	−2.11543
$819$	−5.60518e11	−0.0435323
$820$	7.85188e11	0.0606472
$821$	−1.25114e13	−0.961087	−0.480544	−	0.876971i	$-0.659561\pi$
$821$	−1.25114e13	−0.961087	−0.480544	+	0.876971i	$0.659561\pi$
$822$	−3.00956e13	−2.29921
$823$	−7.18780e12	−0.546131	−0.273065	−	0.961995i	$-0.588038\pi$
$823$	−7.18780e12	−0.546131	−0.273065	+	0.961995i	$0.588038\pi$
$824$	−1.47202e13	−1.11235
$825$	−1.43901e12	−0.108149
$826$	−2.42833e13	−1.81509
$827$	−1.28988e13	−0.958905	−0.479453	−	0.877568i	$-0.659165\pi$
$827$	−1.28988e13	−0.958905	−0.479453	+	0.877568i	$0.659165\pi$
$828$	−1.57717e12	−0.116611
$829$	1.20539e13	0.886406	0.443203	−	0.896421i	$-0.353842\pi$
$829$	1.20539e13	0.886406	0.443203	+	0.896421i	$0.353842\pi$
$830$	−5.50257e11	−0.0402452
$831$	−1.48927e13	−1.08335
$832$	1.55671e13	1.12630
$833$	0	0
$834$	2.20999e13	1.58177
$835$	3.18941e11	0.0227050
$836$	−3.76784e12	−0.266787
$837$	−2.29994e13	−1.61976
$838$	1.18138e13	0.827543
$839$	9.09787e11	0.0633886	0.0316943	−	0.999498i	$-0.489910\pi$
$839$	9.09787e11	0.0633886	0.0316943	+	0.999498i	$0.489910\pi$
$840$	−3.62743e11	−0.0251387
$841$	6.69879e12	0.461758
$842$	4.33209e13	2.97025
$843$	4.99607e12	0.340725
$844$	−4.73728e13	−3.21357
$845$	−1.16353e11	−0.00785095
$846$	−1.59832e12	−0.107275
$847$	1.12130e13	0.748596
$848$	3.15253e10	0.00209353
$849$	5.04525e12	0.333272
$850$	0	0
$851$	−1.10471e13	−0.722044
$852$	−1.66645e13	−1.08347
$853$	9.67484e12	0.625710	0.312855	−	0.949801i	$-0.398715\pi$
$853$	9.67484e12	0.625710	0.312855	+	0.949801i	$0.398715\pi$
$854$	1.17319e13	0.754759
$855$	−3.39319e10	−0.00217150
$856$	2.38427e13	1.51783
$857$	9.99648e12	0.633043	0.316522	−	0.948585i	$-0.397485\pi$
$857$	9.99648e12	0.633043	0.316522	+	0.948585i	$0.397485\pi$
$858$	2.37945e12	0.149894
$859$	−1.80838e13	−1.13323	−0.566617	−	0.823981i	$-0.691748\pi$
$859$	−1.80838e13	−1.13323	−0.566617	+	0.823981i	$0.691748\pi$
$860$	4.90969e11	0.0306063
$861$	1.60732e13	0.996753
$862$	2.62301e13	1.61815
$863$	2.81134e13	1.72530	0.862652	−	0.505799i	$-0.168802\pi$
$863$	2.81134e13	1.72530	0.862652	+	0.505799i	$0.168802\pi$
$864$	8.12631e12	0.496114
$865$	7.32106e10	0.00444633
$866$	−5.00904e12	−0.302638
$867$	0	0
$868$	3.67330e13	2.19643
$869$	−1.52480e12	−0.0907036
$870$	−8.01164e11	−0.0474116
$871$	3.47107e11	0.0204353
$872$	7.07448e12	0.414353
$873$	−1.54345e12	−0.0899351
$874$	−3.38753e13	−1.96373
$875$	6.33570e11	0.0365392
$876$	−1.50998e13	−0.866367
$877$	3.97361e12	0.226823	0.113411	−	0.993548i	$-0.463822\pi$
$877$	3.97361e12	0.226823	0.113411	+	0.993548i	$0.463822\pi$
$878$	2.33917e13	1.32842
$879$	2.75551e13	1.55687
$880$	−2.69708e10	−0.00151608
$881$	−1.26317e12	−0.0706431	−0.0353215	−	0.999376i	$-0.511246\pi$
$881$	−1.26317e12	−0.0706431	−0.0353215	+	0.999376i	$0.511246\pi$
$882$	−9.01452e11	−0.0501573
$883$	1.87841e13	1.03984	0.519922	−	0.854214i	$-0.325961\pi$
$883$	1.87841e13	1.03984	0.519922	+	0.854214i	$0.325961\pi$
$884$	0	0
$885$	6.02103e11	0.0329933
$886$	1.72472e13	0.940303
$887$	−1.92573e13	−1.04457	−0.522286	−	0.852771i	$-0.674920\pi$
$887$	−1.92573e13	−1.04457	−0.522286	+	0.852771i	$0.674920\pi$
$888$	−2.03673e13	−1.09919
$889$	−1.87440e13	−1.00648
$890$	−6.44003e11	−0.0344059
$891$	1.95296e12	0.103811
$892$	8.13038e12	0.430001
$893$	−2.22654e13	−1.17165
$894$	−4.68398e13	−2.45243
$895$	−1.11356e11	−0.00580111
$896$	−2.68088e13	−1.38960
$897$	1.38749e13	0.715587
$898$	3.92999e13	2.01673
$899$	3.71702e13	1.89791
$900$	2.53865e12	0.128977
$901$	0	0
$902$	5.12987e12	0.258034
$903$	1.00504e13	0.503022
$904$	9.45302e11	0.0470774
$905$	6.71114e10	0.00332566
$906$	5.16246e13	2.54554
$907$	−1.89564e13	−0.930086	−0.465043	−	0.885288i	$-0.653961\pi$
$907$	−1.89564e13	−0.930086	−0.465043	+	0.885288i	$0.653961\pi$
$908$	7.34168e13	3.58434
$909$	−2.58697e12	−0.125677
$910$	−5.23663e11	−0.0253143
$911$	3.63923e13	1.75056	0.875281	−	0.483615i	$-0.160677\pi$
$911$	3.63923e13	1.75056	0.875281	+	0.483615i	$0.160677\pi$
$912$	−1.45499e13	−0.696438
$913$	−2.33163e12	−0.111056
$914$	−6.06038e13	−2.87238
$915$	−2.90892e11	−0.0137195
$916$	−4.08586e13	−1.91758
$917$	−2.05423e13	−0.959370
$918$	0	0
$919$	−3.39029e13	−1.56790	−0.783949	−	0.620826i	$-0.786797\pi$
$919$	−3.39029e13	−1.56790	−0.783949	+	0.620826i	$0.786797\pi$
$920$	−6.75081e11	−0.0310678
$921$	−1.45211e13	−0.665017
$922$	6.57860e13	2.99809
$923$	−1.10220e13	−0.499867
$924$	−3.35487e12	−0.151409
$925$	1.77816e13	0.798609
$926$	−3.17367e12	−0.141844
$927$	−1.22604e12	−0.0545314
$928$	−1.31333e13	−0.581309
$929$	5.56576e12	0.245162	0.122581	−	0.992458i	$-0.460883\pi$
$929$	5.56576e12	0.245162	0.122581	+	0.992458i	$0.460883\pi$
$930$	−1.40430e12	−0.0615582
$931$	−1.25577e13	−0.547818
$932$	5.00843e12	0.217435
$933$	7.01292e12	0.302992
$934$	4.96844e13	2.13628
$935$	0	0
$936$	−1.92323e12	−0.0819013
$937$	1.90936e13	0.809207	0.404603	−	0.914492i	$-0.367410\pi$
$937$	1.90936e13	0.809207	0.404603	+	0.914492i	$0.367410\pi$
$938$	−7.54575e11	−0.0318265
$939$	−3.96352e13	−1.66374
$940$	−9.68469e11	−0.0404586
$941$	2.33252e12	0.0969778	0.0484889	−	0.998824i	$-0.484559\pi$
$941$	2.33252e12	0.0969778	0.0484889	+	0.998824i	$0.484559\pi$
$942$	5.93099e13	2.45414
$943$	2.99129e13	1.23184
$944$	−1.94106e13	−0.795546
$945$	−4.62285e11	−0.0188568
$946$	3.20765e12	0.130220
$947$	−2.99883e13	−1.21165	−0.605824	−	0.795599i	$-0.707157\pi$
$947$	−2.99883e13	−1.21165	−0.605824	+	0.795599i	$0.707157\pi$
$948$	−3.57795e13	−1.43879
$949$	−9.98709e12	−0.399706
$950$	5.45266e13	2.17196
$951$	−1.30068e13	−0.515654
$952$	0	0
$953$	6.76956e12	0.265853	0.132927	−	0.991126i	$-0.457563\pi$
$953$	6.76956e12	0.265853	0.132927	+	0.991126i	$0.457563\pi$
$954$	1.12710e10	0.000440550 0
$955$	−8.31151e11	−0.0323344
$956$	6.27355e13	2.42914
$957$	−3.39481e12	−0.130831
$958$	5.87659e13	2.25414
$959$	2.80654e13	1.07149
$960$	8.39092e11	0.0318852
$961$	3.87131e13	1.46421
$962$	−2.94025e13	−1.10687
$963$	1.98586e12	0.0744098
$964$	7.50352e13	2.79846
$965$	−9.10571e11	−0.0338019
$966$	−3.01625e13	−1.11447
$967$	2.76210e13	1.01583	0.507915	−	0.861407i	$-0.330416\pi$
$967$	2.76210e13	1.01583	0.507915	+	0.861407i	$0.330416\pi$
$968$	3.84738e13	1.40840
$969$	0	0
$970$	−1.44197e12	−0.0522977
$971$	3.68276e13	1.32950	0.664748	−	0.747068i	$-0.268539\pi$
$971$	3.68276e13	1.32950	0.664748	+	0.747068i	$0.268539\pi$
$972$	−7.16928e12	−0.257619
$973$	−2.06091e13	−0.737142
$974$	7.61335e13	2.71057
$975$	−2.23333e13	−0.791467
$976$	9.37780e12	0.330808
$977$	−1.06932e13	−0.375477	−0.187739	−	0.982219i	$-0.560116\pi$
$977$	−1.06932e13	−0.375477	−0.187739	+	0.982219i	$0.560116\pi$
$978$	5.69694e13	1.99121
$979$	−2.72886e12	−0.0949422
$980$	−5.46217e11	−0.0189168
$981$	5.89233e11	0.0203131
$982$	5.80525e13	1.99214
$983$	−4.29588e13	−1.46744	−0.733722	−	0.679450i	$-0.762218\pi$
$983$	−4.29588e13	−1.46744	−0.733722	+	0.679450i	$0.762218\pi$
$984$	5.51498e13	1.87528
$985$	6.56042e11	0.0222059
$986$	0	0
$987$	−1.98250e13	−0.664947
$988$	−5.84766e13	−1.95243
$989$	1.87042e13	0.621663
$990$	−9.64265e9	−0.000319035 0
$991$	−5.14896e13	−1.69585	−0.847926	−	0.530114i	$-0.822149\pi$
$991$	−5.14896e13	−1.69585	−0.847926	+	0.530114i	$0.822149\pi$
$992$	−2.30203e13	−0.754758
$993$	4.12561e13	1.34653
$994$	2.39608e13	0.778506
$995$	−4.38732e11	−0.0141904
$996$	−5.47117e13	−1.76162
$997$	4.62725e13	1.48318	0.741592	−	0.670851i	$-0.234071\pi$
$997$	4.62725e13	1.48318	0.741592	+	0.670851i	$0.234071\pi$
$998$	−6.98134e13	−2.22767
$999$	−2.59563e13	−0.824516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.1		24
17.2	even	8		17.10.c.a.4.1	✓	24
17.9	even	8		17.10.c.a.13.12	yes	24
17.16	even	2	inner	289.10.a.f.1.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.1	✓	24	17.2	even	8
17.10.c.a.13.12	yes	24	17.9	even	8
289.10.a.f.1.1		24	1.1	even	1	trivial
289.10.a.f.1.2		24	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)

\(f(q)\)	\(=\)	\(q-38.1697 q^{2} -135.302 q^{3} +944.927 q^{4} +33.6875 q^{5} +5164.44 q^{6} -4816.06 q^{7} -16524.7 q^{8} -1376.34 q^{9} +O(q^{10})\)	\(q-38.1697 q^{2} -135.302 q^{3} +944.927 q^{4} +33.6875 q^{5} +5164.44 q^{6} -4816.06 q^{7} -16524.7 q^{8} -1376.34 q^{9} -1285.84 q^{10} -5448.56 q^{11} -127851. q^{12} -84561.3 q^{13} +183827. q^{14} -4558.00 q^{15} +146941. q^{16} +52534.6 q^{18} +731833. q^{19} +31832.3 q^{20} +651622. q^{21} +207970. q^{22} +1.21270e6 q^{23} +2.23583e6 q^{24} -1.95199e6 q^{25} +3.22768e6 q^{26} +2.84937e6 q^{27} -4.55082e6 q^{28} -4.60499e6 q^{29} +173977. q^{30} -8.07173e6 q^{31} +2.85196e6 q^{32} +737202. q^{33} -162241. q^{35} -1.30054e6 q^{36} -9.10949e6 q^{37} -2.79339e7 q^{38} +1.14413e7 q^{39} -556677. q^{40} +2.46664e7 q^{41} -2.48722e7 q^{42} +1.54236e7 q^{43} -5.14849e6 q^{44} -46365.6 q^{45} -4.62883e7 q^{46} -3.04241e7 q^{47} -1.98814e7 q^{48} -1.71592e7 q^{49} +7.45069e7 q^{50} -7.99043e7 q^{52} +214544. q^{53} -1.08760e8 q^{54} -183549. q^{55} +7.95839e7 q^{56} -9.90186e7 q^{57} +1.75771e8 q^{58} -1.32098e8 q^{59} -4.30697e6 q^{60} +6.38202e7 q^{61} +3.08095e8 q^{62} +6.62854e6 q^{63} -1.84092e8 q^{64} -2.84866e6 q^{65} -2.81388e7 q^{66} -4.10480e6 q^{67} -1.64080e8 q^{69} +6.19270e6 q^{70} +1.30344e8 q^{71} +2.27437e7 q^{72} +1.18105e8 q^{73} +3.47707e8 q^{74} +2.64108e8 q^{75} +6.91529e8 q^{76} +2.62406e7 q^{77} -4.36712e8 q^{78} +2.79854e8 q^{79} +4.95007e6 q^{80} -3.58436e8 q^{81} -9.41509e8 q^{82} +4.27934e8 q^{83} +6.15736e8 q^{84} -5.88715e8 q^{86} +6.23065e8 q^{87} +9.00359e7 q^{88} +5.00841e8 q^{89} +1.76976e6 q^{90} +4.07252e8 q^{91} +1.14591e9 q^{92} +1.09212e9 q^{93} +1.16128e9 q^{94} +2.46537e7 q^{95} -3.85877e8 q^{96} +1.12142e9 q^{97} +6.54962e8 q^{98} +7.49908e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) 24 * q + 5124 * q^4 + 108368 * q^9	\( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) \) 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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