LMFDB - Embedded newform 289.10.a.i.1.32

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			1.32
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)

$f(q)$	$=$	$q+16.1001 q^{2} +264.510 q^{3} -252.785 q^{4} +601.950 q^{5} +4258.66 q^{6} +1062.18 q^{7} -12313.2 q^{8} +50282.7 q^{9} +O(q^{10})$	\(q+16.1001 q^{2} +264.510 q^{3} -252.785 q^{4} +601.950 q^{5} +4258.66 q^{6} +1062.18 q^{7} -12313.2 q^{8} +50282.7 q^{9} +9691.49 q^{10} -17851.5 q^{11} -66864.3 q^{12} +37747.5 q^{13} +17101.2 q^{14} +159222. q^{15} -68817.6 q^{16} +809559. q^{18} -172185. q^{19} -152164. q^{20} +280957. q^{21} -287412. q^{22} +2.52174e6 q^{23} -3.25696e6 q^{24} -1.59078e6 q^{25} +607740. q^{26} +8.09394e6 q^{27} -268503. q^{28} -3.17554e6 q^{29} +2.56350e6 q^{30} +6.69446e6 q^{31} +5.19636e6 q^{32} -4.72191e6 q^{33} +639379. q^{35} -1.27107e7 q^{36} +1.35947e7 q^{37} -2.77221e6 q^{38} +9.98459e6 q^{39} -7.41191e6 q^{40} +2.57272e7 q^{41} +4.52346e6 q^{42} +1.63134e7 q^{43} +4.51260e6 q^{44} +3.02677e7 q^{45} +4.06004e7 q^{46} +4.00867e6 q^{47} -1.82030e7 q^{48} -3.92254e7 q^{49} -2.56118e7 q^{50} -9.54200e6 q^{52} -9.84470e7 q^{53} +1.30314e8 q^{54} -1.07457e7 q^{55} -1.30788e7 q^{56} -4.55447e7 q^{57} -5.11266e7 q^{58} +8.11001e7 q^{59} -4.02490e7 q^{60} -8.72141e7 q^{61} +1.07782e8 q^{62} +5.34092e7 q^{63} +1.18897e8 q^{64} +2.27221e7 q^{65} -7.60235e7 q^{66} +1.58490e8 q^{67} +6.67026e8 q^{69} +1.02941e7 q^{70} +2.43352e8 q^{71} -6.19139e8 q^{72} +3.71102e8 q^{73} +2.18877e8 q^{74} -4.20778e8 q^{75} +4.35258e7 q^{76} -1.89615e7 q^{77} +1.60753e8 q^{78} -1.68370e8 q^{79} -4.14248e7 q^{80} +1.15122e9 q^{81} +4.14211e8 q^{82} -5.49931e8 q^{83} -7.10219e7 q^{84} +2.62648e8 q^{86} -8.39962e8 q^{87} +2.19809e8 q^{88} +1.54695e8 q^{89} +4.87314e8 q^{90} +4.00946e7 q^{91} -6.37458e8 q^{92} +1.77075e9 q^{93} +6.45401e7 q^{94} -1.03647e8 q^{95} +1.37449e9 q^{96} +7.78794e8 q^{97} -6.31535e8 q^{98} -8.97623e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	16.1001	0.711533	0.355766	−	0.934575i	$-0.384220\pi$
$2$	16.1001	0.711533	0.355766	+	0.934575i	$0.384220\pi$
$3$	264.510	1.88537	0.942686	−	0.333682i	$-0.108291\pi$
$3$	264.510	1.88537	0.942686	+	0.333682i	$0.108291\pi$
$4$	−252.785	−0.493721
$5$	601.950	0.430721	0.215360	−	0.976535i	$-0.430907\pi$
$5$	601.950	0.430721	0.215360	+	0.976535i	$0.430907\pi$
$6$	4258.66	1.34150
$7$	1062.18	0.167208	0.0836039	−	0.996499i	$-0.473357\pi$
$7$	1062.18	0.167208	0.0836039	+	0.996499i	$0.473357\pi$
$8$	−12313.2	−1.06283
$9$	50282.7	2.55463
$10$	9691.49	0.306472
$11$	−17851.5	−0.367628	−0.183814	−	0.982961i	$-0.558844\pi$
$11$	−17851.5	−0.367628	−0.183814	+	0.982961i	$0.558844\pi$
$12$	−66864.3	−0.930848
$13$	37747.5	0.366558	0.183279	−	0.983061i	$-0.441329\pi$
$13$	37747.5	0.366558	0.183279	+	0.983061i	$0.441329\pi$
$14$	17101.2	0.118974
$15$	159222.	0.812069
$16$	−68817.6	−0.262518
$17$	0	0
$17$	0	0
$18$	809559.	1.81770
$19$	−172185.	−0.303113	−0.151556	−	0.988449i	$-0.548429\pi$
$19$	−172185.	−0.303113	−0.151556	+	0.988449i	$0.548429\pi$
$20$	−152164.	−0.212656
$21$	280957.	0.315249
$22$	−287412.	−0.261579
$23$	2.52174e6	1.87899	0.939496	−	0.342560i	$-0.111294\pi$
$23$	2.52174e6	1.87899	0.939496	+	0.342560i	$0.111294\pi$
$24$	−3.25696e6	−2.00383
$25$	−1.59078e6	−0.814480
$26$	607740.	0.260818
$27$	8.09394e6	2.93105
$28$	−268503.	−0.0825540
$29$	−3.17554e6	−0.833731	−0.416866	−	0.908968i	$-0.636871\pi$
$29$	−3.17554e6	−0.833731	−0.416866	+	0.908968i	$0.636871\pi$
$30$	2.56350e6	0.577813
$31$	6.69446e6	1.30193	0.650966	−	0.759107i	$-0.274364\pi$
$31$	6.69446e6	1.30193	0.650966	+	0.759107i	$0.274364\pi$
$32$	5.19636e6	0.876041
$33$	−4.72191e6	−0.693115
$34$	0	0
$35$	639379.	0.0720199
$36$	−1.27107e7	−1.26127
$37$	1.35947e7	1.19251	0.596257	−	0.802794i	$-0.296654\pi$
$37$	1.35947e7	1.19251	0.596257	+	0.802794i	$0.296654\pi$
$38$	−2.77221e6	−0.215675
$39$	9.98459e6	0.691098
$40$	−7.41191e6	−0.457784
$41$	2.57272e7	1.42189	0.710943	−	0.703250i	$-0.248269\pi$
$41$	2.57272e7	1.42189	0.710943	+	0.703250i	$0.248269\pi$
$42$	4.52346e6	0.224310
$43$	1.63134e7	0.727672	0.363836	−	0.931463i	$-0.381467\pi$
$43$	1.63134e7	0.727672	0.363836	+	0.931463i	$0.381467\pi$
$44$	4.51260e6	0.181506
$45$	3.02677e7	1.10033
$46$	4.06004e7	1.33696
$47$	4.00867e6	0.119828	0.0599142	−	0.998204i	$-0.480917\pi$
$47$	4.00867e6	0.119828	0.0599142	+	0.998204i	$0.480917\pi$
$48$	−1.82030e7	−0.494945
$49$	−3.92254e7	−0.972042
$50$	−2.56118e7	−0.579529
$51$	0	0
$52$	−9.54200e6	−0.180977
$53$	−9.84470e7	−1.71380	−0.856902	−	0.515480i	$-0.827614\pi$
$53$	−9.84470e7	−1.71380	−0.856902	+	0.515480i	$0.827614\pi$
$54$	1.30314e8	2.08554
$55$	−1.07457e7	−0.158345
$56$	−1.30788e7	−0.177714
$57$	−4.55447e7	−0.571480
$58$	−5.11266e7	−0.593227
$59$	8.11001e7	0.871339	0.435670	−	0.900107i	$-0.356512\pi$
$59$	8.11001e7	0.871339	0.435670	+	0.900107i	$0.356512\pi$
$60$	−4.02490e7	−0.400935
$61$	−8.72141e7	−0.806496	−0.403248	−	0.915091i	$-0.632119\pi$
$61$	−8.72141e7	−0.806496	−0.403248	+	0.915091i	$0.632119\pi$
$62$	1.07782e8	0.926367
$63$	5.34092e7	0.427154
$64$	1.18897e8	0.885850
$65$	2.27221e7	0.157884
$66$	−7.60235e7	−0.493174
$67$	1.58490e8	0.960872	0.480436	−	0.877030i	$-0.340478\pi$
$67$	1.58490e8	0.960872	0.480436	+	0.877030i	$0.340478\pi$
$68$	0	0
$69$	6.67026e8	3.54260
$70$	1.02941e7	0.0512445
$71$	2.43352e8	1.13651	0.568255	−	0.822853i	$-0.307619\pi$
$71$	2.43352e8	1.13651	0.568255	+	0.822853i	$0.307619\pi$
$72$	−6.19139e8	−2.71514
$73$	3.71102e8	1.52947	0.764734	−	0.644347i	$-0.222871\pi$
$73$	3.71102e8	1.52947	0.764734	+	0.644347i	$0.222871\pi$
$74$	2.18877e8	0.848512
$75$	−4.20778e8	−1.53560
$76$	4.35258e7	0.149653
$77$	−1.89615e7	−0.0614703
$78$	1.60753e8	0.491739
$79$	−1.68370e8	−0.486345	−0.243172	−	0.969983i	$-0.578188\pi$
$79$	−1.68370e8	−0.486345	−0.243172	+	0.969983i	$0.578188\pi$
$80$	−4.14248e7	−0.113072
$81$	1.15122e9	2.97149
$82$	4.14211e8	1.01172
$83$	−5.49931e8	−1.27191	−0.635955	−	0.771726i	$-0.719394\pi$
$83$	−5.49931e8	−1.27191	−0.635955	+	0.771726i	$0.719394\pi$
$84$	−7.10219e7	−0.155645
$85$	0	0
$86$	2.62648e8	0.517762
$87$	−8.39962e8	−1.57189
$88$	2.19809e8	0.390726
$89$	1.54695e8	0.261349	0.130675	−	0.991425i	$-0.458286\pi$
$89$	1.54695e8	0.261349	0.130675	+	0.991425i	$0.458286\pi$
$90$	4.87314e8	0.782921
$91$	4.00946e7	0.0612914
$92$	−6.37458e8	−0.927698
$93$	1.77075e9	2.45462
$94$	6.45401e7	0.0852618
$95$	−1.03647e8	−0.130557
$96$	1.37449e9	1.65166
$97$	7.78794e8	0.893202	0.446601	−	0.894733i	$-0.352634\pi$
$97$	7.78794e8	0.893202	0.446601	+	0.894733i	$0.352634\pi$
$98$	−6.31535e8	−0.691639
$99$	−8.97623e8	−0.939152
$100$	4.02126e8	0.402126
$101$	−6.39144e7	−0.0611157	−0.0305578	−	0.999533i	$-0.509728\pi$
$101$	−6.39144e7	−0.0611157	−0.0305578	+	0.999533i	$0.509728\pi$
$102$	0	0
$103$	−6.02387e8	−0.527361	−0.263681	−	0.964610i	$-0.584936\pi$
$103$	−6.02387e8	−0.527361	−0.263681	+	0.964610i	$0.584936\pi$
$104$	−4.64790e8	−0.389589
$105$	1.69122e8	0.135784
$106$	−1.58501e9	−1.21943
$107$	5.82772e8	0.429805	0.214903	−	0.976635i	$-0.431057\pi$
$107$	5.82772e8	0.429805	0.214903	+	0.976635i	$0.431057\pi$
$108$	−2.04603e9	−1.44712
$109$	2.18065e9	1.47968	0.739840	−	0.672783i	$-0.234901\pi$
$109$	2.18065e9	1.47968	0.739840	+	0.672783i	$0.234901\pi$
$110$	−1.73008e8	−0.112668
$111$	3.59595e9	2.24833
$112$	−7.30967e7	−0.0438951
$113$	9.45637e8	0.545596	0.272798	−	0.962071i	$-0.412051\pi$
$113$	9.45637e8	0.545596	0.272798	+	0.962071i	$0.412051\pi$
$114$	−7.33277e8	−0.406627
$115$	1.51796e9	0.809320
$116$	8.02729e8	0.411631
$117$	1.89804e9	0.936419
$118$	1.30572e9	0.619987
$119$	0	0
$120$	−1.96053e9	−0.863092
$121$	−2.03927e9	−0.864850
$122$	−1.40416e9	−0.573849
$123$	6.80510e9	2.68078
$124$	−1.69226e9	−0.642791
$125$	−2.13326e9	−0.781534
$126$	8.59897e8	0.303934
$127$	−1.41525e9	−0.482744	−0.241372	−	0.970433i	$-0.577597\pi$
$127$	−1.41525e9	−0.482744	−0.241372	+	0.970433i	$0.577597\pi$
$128$	−7.46280e8	−0.245729
$129$	4.31505e9	1.37193
$130$	3.65829e8	0.112340
$131$	−1.25596e9	−0.372611	−0.186305	−	0.982492i	$-0.559651\pi$
$131$	−1.25596e9	−0.372611	−0.186305	+	0.982492i	$0.559651\pi$
$132$	1.19363e9	0.342206
$133$	−1.82891e8	−0.0506828
$134$	2.55172e9	0.683692
$135$	4.87215e9	1.26246
$136$	0	0
$137$	3.60544e9	0.874410	0.437205	−	0.899362i	$-0.355968\pi$
$137$	3.60544e9	0.874410	0.437205	+	0.899362i	$0.355968\pi$
$138$	1.07392e10	2.52067
$139$	−5.60113e9	−1.27265	−0.636325	−	0.771421i	$-0.719546\pi$
$139$	−5.60113e9	−1.27265	−0.636325	+	0.771421i	$0.719546\pi$
$140$	−1.61626e8	−0.0355577
$141$	1.06033e9	0.225921
$142$	3.91801e9	0.808664
$143$	−6.73850e8	−0.134757
$144$	−3.46034e9	−0.670637
$145$	−1.91152e9	−0.359105
$146$	5.97479e9	1.08827
$147$	−1.03755e10	−1.83266
$148$	−3.43655e9	−0.588769
$149$	−4.65102e9	−0.773054	−0.386527	−	0.922278i	$-0.626325\pi$
$149$	−4.65102e9	−0.773054	−0.386527	+	0.922278i	$0.626325\pi$
$150$	−6.77459e9	−1.09263
$151$	1.46924e9	0.229983	0.114991	−	0.993366i	$-0.463316\pi$
$151$	1.46924e9	0.229983	0.114991	+	0.993366i	$0.463316\pi$
$152$	2.12014e9	0.322158
$153$	0	0
$154$	−3.05283e8	−0.0437381
$155$	4.02973e9	0.560769
$156$	−2.52396e9	−0.341210
$157$	1.92308e9	0.252608	0.126304	−	0.991992i	$-0.459688\pi$
$157$	1.92308e9	0.252608	0.126304	+	0.991992i	$0.459688\pi$
$158$	−2.71079e9	−0.346050
$159$	−2.60402e10	−3.23116
$160$	3.12795e9	0.377329
$161$	2.67854e9	0.314182
$162$	1.85347e10	2.11431
$163$	−8.41963e9	−0.934220	−0.467110	−	0.884199i	$-0.654705\pi$
$163$	−8.41963e9	−0.934220	−0.467110	+	0.884199i	$0.654705\pi$
$164$	−6.50345e9	−0.702015
$165$	−2.84236e9	−0.298539
$166$	−8.85396e9	−0.905006
$167$	−1.73094e9	−0.172210	−0.0861048	−	0.996286i	$-0.527442\pi$
$167$	−1.73094e9	−0.172210	−0.0861048	+	0.996286i	$0.527442\pi$
$168$	−3.45947e9	−0.335056
$169$	−9.17963e9	−0.865635
$170$	0	0
$171$	−8.65793e9	−0.774340
$172$	−4.12378e9	−0.359267
$173$	2.54070e9	0.215648	0.107824	−	0.994170i	$-0.465612\pi$
$173$	2.54070e9	0.215648	0.107824	+	0.994170i	$0.465612\pi$
$174$	−1.35235e10	−1.11845
$175$	−1.68969e9	−0.136187
$176$	1.22850e9	0.0965091
$177$	2.14518e10	1.64280
$178$	2.49061e9	0.185958
$179$	−3.75621e9	−0.273471	−0.136736	−	0.990608i	$-0.543661\pi$
$179$	−3.75621e9	−0.273471	−0.136736	+	0.990608i	$0.543661\pi$
$180$	−7.65123e9	−0.543256
$181$	1.16028e10	0.803543	0.401771	−	0.915740i	$-0.368395\pi$
$181$	1.16028e10	0.803543	0.401771	+	0.915740i	$0.368395\pi$
$182$	6.45529e8	0.0436108
$183$	−2.30690e10	−1.52055
$184$	−3.10506e10	−1.99705
$185$	8.18336e9	0.513640
$186$	2.85094e10	1.74655
$187$	0	0
$188$	−1.01333e9	−0.0591618
$189$	8.59721e9	0.490094
$190$	−1.66873e9	−0.0928955
$191$	−6.16084e9	−0.334958	−0.167479	−	0.985876i	$-0.553563\pi$
$191$	−6.16084e9	−0.334958	−0.167479	+	0.985876i	$0.553563\pi$
$192$	3.14494e10	1.67016
$193$	−5.55132e9	−0.287998	−0.143999	−	0.989578i	$-0.545996\pi$
$193$	−5.55132e9	−0.287998	−0.143999	+	0.989578i	$0.545996\pi$
$194$	1.25387e10	0.635543
$195$	6.01023e9	0.297670
$196$	9.91560e9	0.479917
$197$	1.91364e9	0.0905236	0.0452618	−	0.998975i	$-0.485588\pi$
$197$	1.91364e9	0.0905236	0.0452618	+	0.998975i	$0.485588\pi$
$198$	−1.44519e10	−0.668237
$199$	−2.33997e10	−1.05772	−0.528862	−	0.848708i	$-0.677381\pi$
$199$	−2.33997e10	−1.05772	−0.528862	+	0.848708i	$0.677381\pi$
$200$	1.95875e10	0.865655
$201$	4.19223e10	1.81160
$202$	−1.02903e9	−0.0434858
$203$	−3.37299e9	−0.139406
$204$	0	0
$205$	1.54865e10	0.612435
$206$	−9.69852e9	−0.375235
$207$	1.26800e11	4.80012
$208$	−2.59769e9	−0.0962282
$209$	3.07377e9	0.111433
$210$	2.72290e9	0.0966149
$211$	−1.60793e10	−0.558464	−0.279232	−	0.960224i	$-0.590080\pi$
$211$	−1.60793e10	−0.558464	−0.279232	+	0.960224i	$0.590080\pi$
$212$	2.48859e10	0.846141
$213$	6.43692e10	2.14274
$214$	9.38272e9	0.305821
$215$	9.81983e9	0.313423
$216$	−9.96619e10	−3.11521
$217$	7.11072e9	0.217693
$218$	3.51089e10	1.05284
$219$	9.81602e10	2.88361
$220$	2.71636e9	0.0781782
$221$	0	0
$222$	5.78953e10	1.59976
$223$	−8.88288e9	−0.240537	−0.120269	−	0.992741i	$-0.538376\pi$
$223$	−8.88288e9	−0.240537	−0.120269	+	0.992741i	$0.538376\pi$
$224$	5.51947e9	0.146481
$225$	−7.99888e10	−2.08069
$226$	1.52249e10	0.388210
$227$	3.98841e10	0.996973	0.498486	−	0.866898i	$-0.333889\pi$
$227$	3.98841e10	0.996973	0.498486	+	0.866898i	$0.333889\pi$
$228$	1.15130e10	0.282152
$229$	−2.76693e10	−0.664872	−0.332436	−	0.943126i	$-0.607871\pi$
$229$	−2.76693e10	−0.664872	−0.332436	+	0.943126i	$0.607871\pi$
$230$	2.44394e10	0.575858
$231$	−5.01552e9	−0.115894
$232$	3.91009e10	0.886116
$233$	4.58467e10	1.01908	0.509538	−	0.860448i	$-0.329816\pi$
$233$	4.58467e10	1.01908	0.509538	+	0.860448i	$0.329816\pi$
$234$	3.05588e10	0.666293
$235$	2.41302e9	0.0516125
$236$	−2.05009e10	−0.430199
$237$	−4.45357e10	−0.916940
$238$	0	0
$239$	7.50699e10	1.48825	0.744124	−	0.668041i	$-0.232867\pi$
$239$	7.50699e10	1.48825	0.744124	+	0.668041i	$0.232867\pi$
$240$	−1.09573e10	−0.213183
$241$	6.11555e10	1.16777	0.583887	−	0.811835i	$-0.301531\pi$
$241$	6.11555e10	1.16777	0.583887	+	0.811835i	$0.301531\pi$
$242$	−3.28326e10	−0.615369
$243$	1.45195e11	2.67131
$244$	2.20464e10	0.398184
$245$	−2.36117e10	−0.418678
$246$	1.09563e11	1.90746
$247$	−6.49955e9	−0.111108
$248$	−8.24299e10	−1.38373
$249$	−1.45462e11	−2.39802
$250$	−3.43457e10	−0.556087
$251$	−8.75084e10	−1.39161	−0.695806	−	0.718230i	$-0.744953\pi$
$251$	−8.75084e10	−1.39161	−0.695806	+	0.718230i	$0.744953\pi$
$252$	−1.35011e10	−0.210895
$253$	−4.50169e10	−0.690770
$254$	−2.27857e10	−0.343488
$255$	0	0
$256$	−7.28904e10	−1.06069
$257$	−2.72027e10	−0.388967	−0.194484	−	0.980906i	$-0.562303\pi$
$257$	−2.72027e10	−0.388967	−0.194484	+	0.980906i	$0.562303\pi$
$258$	6.94730e10	0.976174
$259$	1.44401e10	0.199398
$260$	−5.74381e9	−0.0779507
$261$	−1.59675e11	−2.12987
$262$	−2.02212e10	−0.265125
$263$	2.70118e10	0.348139	0.174070	−	0.984733i	$-0.444308\pi$
$263$	2.70118e10	0.348139	0.174070	+	0.984733i	$0.444308\pi$
$264$	5.81417e10	0.736665
$265$	−5.92602e10	−0.738171
$266$	−2.94458e9	−0.0360625
$267$	4.09184e10	0.492740
$268$	−4.00640e10	−0.474403
$269$	−8.99473e10	−1.04738	−0.523688	−	0.851910i	$-0.675444\pi$
$269$	−8.99473e10	−1.04738	−0.523688	+	0.851910i	$0.675444\pi$
$270$	7.84423e10	0.898284
$271$	8.44887e9	0.0951561	0.0475781	−	0.998868i	$-0.484850\pi$
$271$	8.44887e9	0.0951561	0.0475781	+	0.998868i	$0.484850\pi$
$272$	0	0
$273$	1.06054e10	0.115557
$274$	5.80481e10	0.622172
$275$	2.83979e10	0.299425
$276$	−1.68614e11	−1.74905
$277$	1.54944e11	1.58131	0.790655	−	0.612262i	$-0.209740\pi$
$277$	1.54944e11	1.58131	0.790655	+	0.612262i	$0.209740\pi$
$278$	−9.01791e10	−0.905533
$279$	3.36616e11	3.32595
$280$	−7.87278e9	−0.0765450
$281$	1.02854e11	0.984105	0.492052	−	0.870566i	$-0.336247\pi$
$281$	1.02854e11	0.984105	0.492052	+	0.870566i	$0.336247\pi$
$282$	1.70715e10	0.160750
$283$	2.54432e10	0.235794	0.117897	−	0.993026i	$-0.462385\pi$
$283$	2.54432e10	0.235794	0.117897	+	0.993026i	$0.462385\pi$
$284$	−6.15159e10	−0.561119
$285$	−2.74157e10	−0.246148
$286$	−1.08491e10	−0.0958840
$287$	2.73269e10	0.237750
$288$	2.61287e11	2.23796
$289$	0	0
$290$	−3.07757e10	−0.255515
$291$	2.05999e11	1.68402
$292$	−9.38090e10	−0.755130
$293$	1.48532e11	1.17737	0.588687	−	0.808361i	$-0.299645\pi$
$293$	1.48532e11	1.17737	0.588687	+	0.808361i	$0.299645\pi$
$294$	−1.67047e11	−1.30400
$295$	4.88182e10	0.375304
$296$	−1.67394e11	−1.26744
$297$	−1.44489e11	−1.07754
$298$	−7.48821e10	−0.550053
$299$	9.51892e10	0.688759
$300$	1.06366e11	0.758157
$301$	1.73277e10	0.121672
$302$	2.36549e10	0.163640
$303$	−1.69060e10	−0.115226
$304$	1.18494e10	0.0795727
$305$	−5.24986e10	−0.347375
$306$	0	0
$307$	1.71702e11	1.10320	0.551599	−	0.834110i	$-0.314018\pi$
$307$	1.71702e11	1.10320	0.551599	+	0.834110i	$0.314018\pi$
$308$	4.79319e9	0.0303492
$309$	−1.59338e11	−0.994272
$310$	6.48793e10	0.399005
$311$	−2.78688e11	−1.68926	−0.844629	−	0.535353i	$-0.820179\pi$
$311$	−2.78688e11	−1.68926	−0.844629	+	0.535353i	$0.820179\pi$
$312$	−1.22942e11	−0.734521
$313$	1.11843e10	0.0658660	0.0329330	−	0.999458i	$-0.489515\pi$
$313$	1.11843e10	0.0658660	0.0329330	+	0.999458i	$0.489515\pi$
$314$	3.09618e10	0.179739
$315$	3.21497e10	0.183984
$316$	4.25616e10	0.240119
$317$	−1.71493e11	−0.953849	−0.476924	−	0.878944i	$-0.658248\pi$
$317$	−1.71493e11	−0.953849	−0.476924	+	0.878944i	$0.658248\pi$
$318$	−4.19252e11	−2.29907
$319$	5.66882e10	0.306503
$320$	7.15700e10	0.381554
$321$	1.54149e11	0.810343
$322$	4.31249e10	0.223551
$323$	0	0
$324$	−2.91010e11	−1.46709
$325$	−6.00479e10	−0.298554
$326$	−1.35557e11	−0.664728
$327$	5.76806e11	2.78975
$328$	−3.16783e11	−1.51122
$329$	4.25792e9	0.0200362
$330$	−4.57624e10	−0.212420
$331$	−2.80771e11	−1.28566	−0.642831	−	0.766008i	$-0.722240\pi$
$331$	−2.80771e11	−1.28566	−0.642831	+	0.766008i	$0.722240\pi$
$332$	1.39014e11	0.627969
$333$	6.83581e11	3.04643
$334$	−2.78684e10	−0.122533
$335$	9.54032e10	0.413868
$336$	−1.93348e10	−0.0827587
$337$	−4.17137e11	−1.76175	−0.880874	−	0.473351i	$-0.843044\pi$
$337$	−4.17137e11	−1.76175	−0.880874	+	0.473351i	$0.843044\pi$
$338$	−1.47793e11	−0.615928
$339$	2.50131e11	1.02865
$340$	0	0
$341$	−1.19506e11	−0.478626
$342$	−1.39394e11	−0.550968
$343$	−8.45271e10	−0.329741
$344$	−2.00869e11	−0.773392
$345$	4.01517e11	1.52587
$346$	4.09056e10	0.153441
$347$	2.57242e11	0.952486	0.476243	−	0.879314i	$-0.341998\pi$
$347$	2.57242e11	0.952486	0.476243	+	0.879314i	$0.341998\pi$
$348$	2.12330e11	0.776077
$349$	3.55969e11	1.28439	0.642197	−	0.766540i	$-0.278023\pi$
$349$	3.55969e11	1.28439	0.642197	+	0.766540i	$0.278023\pi$
$350$	−2.72043e10	−0.0969018
$351$	3.05526e11	1.07440
$352$	−9.27630e10	−0.322057
$353$	−2.14539e11	−0.735394	−0.367697	−	0.929946i	$-0.619854\pi$
$353$	−2.14539e11	−0.735394	−0.367697	+	0.929946i	$0.619854\pi$
$354$	3.45377e11	1.16891
$355$	1.46486e11	0.489518
$356$	−3.91046e10	−0.129034
$357$	0	0
$358$	−6.04756e10	−0.194584
$359$	2.01465e10	0.0640140	0.0320070	−	0.999488i	$-0.489810\pi$
$359$	2.01465e10	0.0640140	0.0320070	+	0.999488i	$0.489810\pi$
$360$	−3.72691e11	−1.16947
$361$	−2.93040e11	−0.908123
$362$	1.86807e11	0.571747
$363$	−5.39408e11	−1.63056
$364$	−1.01353e10	−0.0302608
$365$	2.23385e11	0.658773
$366$	−3.71415e11	−1.08192
$367$	−5.49651e11	−1.58157	−0.790787	−	0.612091i	$-0.790328\pi$
$367$	−5.49651e11	−1.58157	−0.790787	+	0.612091i	$0.790328\pi$
$368$	−1.73540e11	−0.493270
$369$	1.29363e12	3.63239
$370$	1.31753e11	0.365472
$371$	−1.04568e11	−0.286561
$372$	−4.47620e11	−1.21190
$373$	−6.64556e11	−1.77763	−0.888816	−	0.458264i	$-0.848472\pi$
$373$	−6.64556e11	−1.77763	−0.888816	+	0.458264i	$0.848472\pi$
$374$	0	0
$375$	−5.64268e11	−1.47348
$376$	−4.93593e10	−0.127357
$377$	−1.19868e11	−0.305611
$378$	1.38416e11	0.348718
$379$	−3.20321e11	−0.797459	−0.398730	−	0.917068i	$-0.630549\pi$
$379$	−3.20321e11	−0.797459	−0.398730	+	0.917068i	$0.630549\pi$
$380$	2.62004e10	0.0644587
$381$	−3.74348e11	−0.910151
$382$	−9.91905e10	−0.238333
$383$	−5.75973e11	−1.36775	−0.683877	−	0.729597i	$-0.739707\pi$
$383$	−5.75973e11	−1.36775	−0.683877	+	0.729597i	$0.739707\pi$
$384$	−1.97399e11	−0.463291
$385$	−1.14139e10	−0.0264765
$386$	−8.93772e10	−0.204920
$387$	8.20280e11	1.85893
$388$	−1.96868e11	−0.440993
$389$	−4.01657e11	−0.889369	−0.444684	−	0.895687i	$-0.646684\pi$
$389$	−4.01657e11	−0.889369	−0.444684	+	0.895687i	$0.646684\pi$
$390$	9.67656e10	0.211802
$391$	0	0
$392$	4.82988e11	1.03312
$393$	−3.32215e11	−0.702510
$394$	3.08099e10	0.0644105
$395$	−1.01351e11	−0.209479
$396$	2.26906e11	0.463679
$397$	4.71055e11	0.951732	0.475866	−	0.879518i	$-0.342135\pi$
$397$	4.71055e11	0.951732	0.475866	+	0.879518i	$0.342135\pi$
$398$	−3.76739e11	−0.752605
$399$	−4.83767e10	−0.0955560
$400$	1.09474e11	0.213816
$401$	−1.54828e11	−0.299020	−0.149510	−	0.988760i	$-0.547770\pi$
$401$	−1.54828e11	−0.299020	−0.149510	+	0.988760i	$0.547770\pi$
$402$	6.74955e11	1.28901
$403$	2.52699e11	0.477233
$404$	1.61566e10	0.0301741
$405$	6.92975e11	1.27988
$406$	−5.43056e10	−0.0991923
$407$	−2.42687e11	−0.438401
$408$	0	0
$409$	1.00784e12	1.78089	0.890445	−	0.455091i	$-0.150393\pi$
$409$	1.00784e12	1.78089	0.890445	+	0.455091i	$0.150393\pi$
$410$	2.49335e11	0.435768
$411$	9.53675e11	1.64859
$412$	1.52275e11	0.260369
$413$	8.61428e10	0.145695
$414$	2.04150e12	3.41544
$415$	−3.31031e11	−0.547838
$416$	1.96149e11	0.321120
$417$	−1.48156e12	−2.39942
$418$	4.94881e10	0.0792880
$419$	2.54771e11	0.403820	0.201910	−	0.979404i	$-0.435285\pi$
$419$	2.54771e11	0.403820	0.201910	+	0.979404i	$0.435285\pi$
$420$	−4.27516e10	−0.0670395
$421$	−2.87619e11	−0.446219	−0.223109	−	0.974793i	$-0.571621\pi$
$421$	−2.87619e11	−0.446219	−0.223109	+	0.974793i	$0.571621\pi$
$422$	−2.58878e11	−0.397365
$423$	2.01567e11	0.306117
$424$	1.21219e12	1.82148
$425$	0	0
$426$	1.03635e12	1.52463
$427$	−9.26370e10	−0.134853
$428$	−1.47316e11	−0.212204
$429$	−1.78240e11	−0.254067
$430$	1.58101e11	0.223011
$431$	−3.92035e11	−0.547238	−0.273619	−	0.961838i	$-0.588221\pi$
$431$	−3.92035e11	−0.547238	−0.273619	+	0.961838i	$0.588221\pi$
$432$	−5.57006e11	−0.769454
$433$	8.36210e11	1.14319	0.571597	−	0.820534i	$-0.306324\pi$
$433$	8.36210e11	1.14319	0.571597	+	0.820534i	$0.306324\pi$
$434$	1.14484e11	0.154896
$435$	−5.05616e11	−0.677047
$436$	−5.51237e11	−0.730549
$437$	−4.34206e11	−0.569546
$438$	1.58039e12	2.05179
$439$	1.26776e12	1.62910	0.814548	−	0.580096i	$-0.196985\pi$
$439$	1.26776e12	1.62910	0.814548	+	0.580096i	$0.196985\pi$
$440$	1.32314e11	0.168294
$441$	−1.97236e12	−2.48320
$442$	0	0
$443$	1.06154e11	0.130954	0.0654769	−	0.997854i	$-0.479143\pi$
$443$	1.06154e11	0.130954	0.0654769	+	0.997854i	$0.479143\pi$
$444$	−9.09003e11	−1.11005
$445$	9.31187e10	0.112568
$446$	−1.43016e11	−0.171150
$447$	−1.23024e12	−1.45749
$448$	1.26290e11	0.148121
$449$	−1.29833e12	−1.50756	−0.753781	−	0.657126i	$-0.771772\pi$
$449$	−1.29833e12	−1.50756	−0.753781	+	0.657126i	$0.771772\pi$
$450$	−1.28783e12	−1.48048
$451$	−4.59269e11	−0.522725
$452$	−2.39043e11	−0.269372
$453$	3.88628e11	0.433603
$454$	6.42140e11	0.709379
$455$	2.41349e10	0.0263995
$456$	5.60799e11	0.607387
$457$	−9.65248e11	−1.03518	−0.517590	−	0.855629i	$-0.673171\pi$
$457$	−9.65248e11	−1.03518	−0.517590	+	0.855629i	$0.673171\pi$
$458$	−4.45479e11	−0.473078
$459$	0	0
$460$	−3.83718e11	−0.399579
$461$	−1.04141e12	−1.07391	−0.536957	−	0.843610i	$-0.680426\pi$
$461$	−1.04141e12	−1.07391	−0.536957	+	0.843610i	$0.680426\pi$
$462$	−8.07506e10	−0.0824626
$463$	−5.45530e11	−0.551701	−0.275851	−	0.961201i	$-0.588960\pi$
$463$	−5.45530e11	−0.551701	−0.275851	+	0.961201i	$0.588960\pi$
$464$	2.18533e11	0.218870
$465$	1.06591e12	1.05726
$466$	7.38139e11	0.725106
$467$	−1.14323e12	−1.11226	−0.556131	−	0.831095i	$-0.687715\pi$
$467$	−1.14323e12	−1.11226	−0.556131	+	0.831095i	$0.687715\pi$
$468$	−4.79798e11	−0.462330
$469$	1.68345e11	0.160665
$470$	3.88500e10	0.0367240
$471$	5.08673e11	0.476261
$472$	−9.98598e11	−0.926087
$473$	−2.91218e11	−0.267512
$474$	−7.17032e11	−0.652433
$475$	2.73909e11	0.246879
$476$	0	0
$477$	−4.95018e12	−4.37813
$478$	1.20864e12	1.05894
$479$	−3.95842e11	−0.343567	−0.171784	−	0.985135i	$-0.554953\pi$
$479$	−3.95842e11	−0.343567	−0.171784	+	0.985135i	$0.554953\pi$
$480$	8.27376e11	0.711405
$481$	5.13167e11	0.437125
$482$	9.84612e11	0.830909
$483$	7.08501e11	0.592350
$484$	5.15497e11	0.426995
$485$	4.68795e11	0.384721
$486$	2.33767e12	1.90073
$487$	1.07081e12	0.862642	0.431321	−	0.902198i	$-0.358048\pi$
$487$	1.07081e12	0.862642	0.431321	+	0.902198i	$0.358048\pi$
$488$	1.07388e12	0.857170
$489$	−2.22708e12	−1.76135
$490$	−3.80152e11	−0.297903
$491$	−4.82796e11	−0.374884	−0.187442	−	0.982276i	$-0.560020\pi$
$491$	−4.82796e11	−0.374884	−0.187442	+	0.982276i	$0.560020\pi$
$492$	−1.72023e12	−1.32356
$493$	0	0
$494$	−1.04644e11	−0.0790573
$495$	−5.40325e11	−0.404512
$496$	−4.60697e11	−0.341781
$497$	2.58484e11	0.190033
$498$	−2.34196e12	−1.70627
$499$	−8.29184e11	−0.598685	−0.299342	−	0.954146i	$-0.596767\pi$
$499$	−8.29184e11	−0.598685	−0.299342	+	0.954146i	$0.596767\pi$
$500$	5.39255e11	0.385860
$501$	−4.57851e11	−0.324679
$502$	−1.40890e12	−0.990177
$503$	−2.10379e12	−1.46537	−0.732684	−	0.680569i	$-0.761733\pi$
$503$	−2.10379e12	−1.46537	−0.732684	+	0.680569i	$0.761733\pi$
$504$	−6.57636e11	−0.453992
$505$	−3.84733e10	−0.0263238
$506$	−7.24779e11	−0.491505
$507$	−2.42811e12	−1.63204
$508$	3.57754e11	0.238341
$509$	−2.53218e11	−0.167211	−0.0836054	−	0.996499i	$-0.526644\pi$
$509$	−2.53218e11	−0.167211	−0.0836054	+	0.996499i	$0.526644\pi$
$510$	0	0
$511$	3.94177e11	0.255739
$512$	−7.91451e11	−0.508990
$513$	−1.39366e12	−0.888438
$514$	−4.37968e11	−0.276763
$515$	−3.62607e11	−0.227145
$516$	−1.09078e12	−0.677351
$517$	−7.15608e10	−0.0440522
$518$	2.32487e11	0.141878
$519$	6.72040e11	0.406576
$520$	−2.79781e11	−0.167804
$521$	−2.66221e12	−1.58297	−0.791484	−	0.611189i	$-0.790691\pi$
$521$	−2.66221e12	−1.58297	−0.791484	+	0.611189i	$0.790691\pi$
$522$	−2.57079e12	−1.51547
$523$	−1.91077e11	−0.111674	−0.0558369	−	0.998440i	$-0.517783\pi$
$523$	−1.91077e11	−0.111674	−0.0558369	+	0.998440i	$0.517783\pi$
$524$	3.17489e11	0.183966
$525$	−4.46942e11	−0.256764
$526$	4.34895e11	0.247713
$527$	0	0
$528$	3.24951e11	0.181956
$529$	4.55801e12	2.53061
$530$	−9.54098e11	−0.525233
$531$	4.07793e12	2.22595
$532$	4.62322e10	0.0250232
$533$	9.71135e11	0.521203
$534$	6.58792e11	0.350601
$535$	3.50800e11	0.185126
$536$	−1.95151e12	−1.02125
$537$	−9.93557e11	−0.515595
$538$	−1.44816e12	−0.745242
$539$	7.00233e11	0.357350
$540$	−1.23161e12	−0.623305
$541$	−6.91395e11	−0.347007	−0.173504	−	0.984833i	$-0.555509\pi$
$541$	−6.91395e11	−0.347007	−0.173504	+	0.984833i	$0.555509\pi$
$542$	1.36028e11	0.0677067
$543$	3.06906e12	1.51498
$544$	0	0
$545$	1.31265e12	0.637328
$546$	1.70749e11	0.0822226
$547$	−2.93282e12	−1.40069	−0.700345	−	0.713805i	$-0.746970\pi$
$547$	−2.93282e12	−1.40069	−0.700345	+	0.713805i	$0.746970\pi$
$548$	−9.11401e11	−0.431715
$549$	−4.38536e12	−2.06030
$550$	4.57210e11	0.213051
$551$	5.46780e11	0.252715
$552$	−8.21319e12	−3.76518
$553$	−1.78840e11	−0.0813206
$554$	2.49463e12	1.12515
$555$	2.16458e12	0.968403
$556$	1.41588e12	0.628334
$557$	2.09071e12	0.920334	0.460167	−	0.887832i	$-0.347790\pi$
$557$	2.09071e12	0.920334	0.460167	+	0.887832i	$0.347790\pi$
$558$	5.41956e12	2.36652
$559$	6.15788e11	0.266734
$560$	−4.40006e10	−0.0189065
$561$	0	0
$562$	1.65596e12	0.700223
$563$	3.29291e12	1.38131	0.690657	−	0.723182i	$-0.257321\pi$
$563$	3.29291e12	1.38131	0.690657	+	0.723182i	$0.257321\pi$
$564$	−2.68037e11	−0.111542
$565$	5.69226e11	0.235000
$566$	4.09639e11	0.167775
$567$	1.22280e12	0.496856
$568$	−2.99644e12	−1.20792
$569$	2.28192e12	0.912632	0.456316	−	0.889818i	$-0.349169\pi$
$569$	2.28192e12	0.912632	0.456316	+	0.889818i	$0.349169\pi$
$570$	−4.41396e11	−0.175143
$571$	−2.02874e12	−0.798663	−0.399332	−	0.916807i	$-0.630758\pi$
$571$	−2.02874e12	−0.798663	−0.399332	+	0.916807i	$0.630758\pi$
$572$	1.70339e11	0.0665323
$573$	−1.62961e12	−0.631520
$574$	4.39966e11	0.169167
$575$	−4.01153e12	−1.53040
$576$	5.97845e12	2.26302
$577$	1.89658e12	0.712329	0.356165	−	0.934423i	$-0.384084\pi$
$577$	1.89658e12	0.712329	0.356165	+	0.934423i	$0.384084\pi$
$578$	0	0
$579$	−1.46838e12	−0.542982
$580$	4.83203e11	0.177298
$581$	−5.84125e11	−0.212673
$582$	3.31662e12	1.19823
$583$	1.75743e12	0.630042
$584$	−4.56943e12	−1.62557
$585$	1.14253e12	0.403335
$586$	2.39138e12	0.837740
$587$	−2.98552e12	−1.03788	−0.518942	−	0.854810i	$-0.673674\pi$
$587$	−2.98552e12	−1.03788	−0.518942	+	0.854810i	$0.673674\pi$
$588$	2.62278e12	0.904823
$589$	−1.15269e12	−0.394632
$590$	7.85981e11	0.267041
$591$	5.06177e11	0.170671
$592$	−9.35558e11	−0.313057
$593$	−3.78410e12	−1.25666	−0.628329	−	0.777948i	$-0.716261\pi$
$593$	−3.78410e12	−1.25666	−0.628329	+	0.777948i	$0.716261\pi$
$594$	−2.32630e12	−0.766702
$595$	0	0
$596$	1.17571e12	0.381673
$597$	−6.18947e12	−1.99420
$598$	1.53256e12	0.490075
$599$	−4.66663e12	−1.48109	−0.740546	−	0.672005i	$-0.765433\pi$
$599$	−4.66663e12	−1.48109	−0.740546	+	0.672005i	$0.765433\pi$
$600$	5.18110e12	1.63208
$601$	−1.08947e12	−0.340627	−0.170313	−	0.985390i	$-0.554478\pi$
$601$	−1.08947e12	−0.340627	−0.170313	+	0.985390i	$0.554478\pi$
$602$	2.78979e11	0.0865739
$603$	7.96931e12	2.45467
$604$	−3.71401e11	−0.113547
$605$	−1.22754e12	−0.372509
$606$	−2.72190e11	−0.0819869
$607$	−1.05916e11	−0.0316675	−0.0158338	−	0.999875i	$-0.505040\pi$
$607$	−1.05916e11	−0.0316675	−0.0158338	+	0.999875i	$0.505040\pi$
$608$	−8.94736e11	−0.265539
$609$	−8.92191e11	−0.262833
$610$	−8.45235e11	−0.247168
$611$	1.51317e11	0.0439240
$612$	0	0
$613$	−3.00944e12	−0.860821	−0.430411	−	0.902633i	$-0.641631\pi$
$613$	−3.00944e12	−0.860821	−0.430411	+	0.902633i	$0.641631\pi$
$614$	2.76443e12	0.784961
$615$	4.09633e12	1.15467
$616$	2.33476e11	0.0653325
$617$	6.70329e12	1.86211	0.931054	−	0.364881i	$-0.118890\pi$
$617$	6.70329e12	1.86211	0.931054	+	0.364881i	$0.118890\pi$
$618$	−2.56536e12	−0.707457
$619$	7.63678e11	0.209075	0.104537	−	0.994521i	$-0.466664\pi$
$619$	7.63678e11	0.209075	0.104537	+	0.994521i	$0.466664\pi$
$620$	−1.01866e12	−0.276863
$621$	2.04108e13	5.50742
$622$	−4.48691e12	−1.20196
$623$	1.64314e11	0.0436996
$624$	−6.87116e11	−0.181426
$625$	1.82288e12	0.477857
$626$	1.80070e11	0.0468658
$627$	8.13043e11	0.210092
$628$	−4.86125e11	−0.124718
$629$	0	0
$630$	5.17615e11	0.130911
$631$	−1.10815e12	−0.278269	−0.139134	−	0.990273i	$-0.544432\pi$
$631$	−1.10815e12	−0.278269	−0.139134	+	0.990273i	$0.544432\pi$
$632$	2.07317e12	0.516902
$633$	−4.25313e12	−1.05291
$634$	−2.76106e12	−0.678695
$635$	−8.51911e11	−0.207928
$636$	6.58259e12	1.59529
$637$	−1.48066e12	−0.356310
$638$	9.12689e11	0.218087
$639$	1.22364e13	2.90336
$640$	−4.49224e11	−0.105841
$641$	2.97305e12	0.695571	0.347786	−	0.937574i	$-0.386934\pi$
$641$	2.97305e12	0.695571	0.347786	+	0.937574i	$0.386934\pi$
$642$	2.48183e12	0.576586
$643$	1.10850e12	0.255732	0.127866	−	0.991791i	$-0.459187\pi$
$643$	1.10850e12	0.255732	0.127866	+	0.991791i	$0.459187\pi$
$644$	−6.77095e11	−0.155118
$645$	2.59745e12	0.590919
$646$	0	0
$647$	−1.81314e12	−0.406782	−0.203391	−	0.979098i	$-0.565196\pi$
$647$	−1.81314e12	−0.406782	−0.203391	+	0.979098i	$0.565196\pi$
$648$	−1.41751e13	−3.15819
$649$	−1.44776e12	−0.320329
$650$	−9.66781e11	−0.212431
$651$	1.88086e12	0.410432
$652$	2.12836e12	0.461244
$653$	−4.21286e12	−0.906709	−0.453355	−	0.891330i	$-0.649773\pi$
$653$	−4.21286e12	−0.906709	−0.453355	+	0.891330i	$0.649773\pi$
$654$	9.28666e12	1.98500
$655$	−7.56027e11	−0.160491
$656$	−1.77048e12	−0.373271
$657$	1.86600e13	3.90722
$658$	6.85532e10	0.0142564
$659$	3.69466e12	0.763115	0.381558	−	0.924345i	$-0.375388\pi$
$659$	3.69466e12	0.763115	0.381558	+	0.924345i	$0.375388\pi$
$660$	7.18506e11	0.147395
$661$	2.05436e12	0.418572	0.209286	−	0.977855i	$-0.432886\pi$
$661$	2.05436e12	0.418572	0.209286	+	0.977855i	$0.432886\pi$
$662$	−4.52046e12	−0.914790
$663$	0	0
$664$	6.77138e12	1.35183
$665$	−1.10092e11	−0.0218301
$666$	1.10057e13	2.16763
$667$	−8.00788e12	−1.56657
$668$	4.37556e11	0.0850236
$669$	−2.34961e12	−0.453502
$670$	1.53601e12	0.294480
$671$	1.55691e12	0.296491
$672$	1.45996e12	0.276171
$673$	−7.61227e12	−1.43036	−0.715182	−	0.698939i	$-0.753656\pi$
$673$	−7.61227e12	−1.43036	−0.715182	+	0.698939i	$0.753656\pi$
$674$	−6.71596e12	−1.25354
$675$	−1.28757e13	−2.38728
$676$	2.32047e12	0.427382
$677$	2.51336e12	0.459839	0.229920	−	0.973210i	$-0.426154\pi$
$677$	2.51336e12	0.459839	0.229920	+	0.973210i	$0.426154\pi$
$678$	4.02714e12	0.731919
$679$	8.27219e11	0.149350
$680$	0	0
$681$	1.05497e13	1.87966
$682$	−1.92407e12	−0.340558
$683$	3.30149e12	0.580519	0.290259	−	0.956948i	$-0.406258\pi$
$683$	3.30149e12	0.580519	0.290259	+	0.956948i	$0.406258\pi$
$684$	2.18860e12	0.382308
$685$	2.17029e12	0.376627
$686$	−1.36090e12	−0.234621
$687$	−7.31881e12	−1.25353
$688$	−1.12265e12	−0.191027
$689$	−3.71612e12	−0.628208
$690$	6.46448e12	1.08571
$691$	−5.58149e12	−0.931321	−0.465660	−	0.884963i	$-0.654183\pi$
$691$	−5.58149e12	−0.931321	−0.465660	+	0.884963i	$0.654183\pi$
$692$	−6.42250e11	−0.106470
$693$	−9.53437e11	−0.157034
$694$	4.14163e12	0.677725
$695$	−3.37160e12	−0.548157
$696$	1.03426e13	1.67066
$697$	0	0
$698$	5.73116e12	0.913888
$699$	1.21269e13	1.92134
$700$	4.27130e11	0.0672386
$701$	−3.02645e12	−0.473372	−0.236686	−	0.971586i	$-0.576061\pi$
$701$	−3.02645e12	−0.473372	−0.236686	+	0.971586i	$0.576061\pi$
$702$	4.91901e12	0.764470
$703$	−2.34081e12	−0.361466
$704$	−2.12249e12	−0.325663
$705$	6.38268e11	0.0973088
$706$	−3.45411e12	−0.523257
$707$	−6.78886e10	−0.0102190
$708$	−5.42270e12	−0.811084
$709$	1.33974e12	0.199119	0.0995594	−	0.995032i	$-0.468257\pi$
$709$	1.33974e12	0.199119	0.0995594	+	0.995032i	$0.468257\pi$
$710$	2.35845e12	0.348308
$711$	−8.46612e12	−1.24243
$712$	−1.90478e12	−0.277770
$713$	1.68817e13	2.44632
$714$	0	0
$715$	−4.05624e11	−0.0580426
$716$	9.49515e11	0.135019
$717$	1.98568e13	2.80590
$718$	3.24362e11	0.0455481
$719$	3.42645e11	0.0478150	0.0239075	−	0.999714i	$-0.492389\pi$
$719$	3.42645e11	0.0478150	0.0239075	+	0.999714i	$0.492389\pi$
$720$	−2.08295e12	−0.288857
$721$	−6.39843e11	−0.0881789
$722$	−4.71799e12	−0.646159
$723$	1.61763e13	2.20169
$724$	−2.93301e12	−0.396726
$725$	5.05158e12	0.679057
$726$	−8.68455e12	−1.16020
$727$	1.10997e13	1.47369	0.736844	−	0.676063i	$-0.236315\pi$
$727$	1.10997e13	1.47369	0.736844	+	0.676063i	$0.236315\pi$
$728$	−4.93691e11	−0.0651424
$729$	1.57463e13	2.06493
$730$	3.59653e12	0.468739
$731$	0	0
$732$	5.83151e12	0.750725
$733$	1.20634e13	1.54348	0.771742	−	0.635936i	$-0.219386\pi$
$733$	1.20634e13	1.54348	0.771742	+	0.635936i	$0.219386\pi$
$734$	−8.84946e12	−1.12534
$735$	−6.24555e12	−0.789364
$736$	1.31039e13	1.64607
$737$	−2.82929e12	−0.353243
$738$	2.08277e13	2.58456
$739$	2.13547e12	0.263387	0.131693	−	0.991290i	$-0.457959\pi$
$739$	2.13547e12	0.263387	0.131693	+	0.991290i	$0.457959\pi$
$740$	−2.06863e12	−0.253595
$741$	−1.71920e12	−0.209481
$742$	−1.68357e12	−0.203898
$743$	4.31738e12	0.519721	0.259861	−	0.965646i	$-0.416323\pi$
$743$	4.31738e12	0.519721	0.259861	+	0.965646i	$0.416323\pi$
$744$	−2.18036e13	−2.60885
$745$	−2.79968e12	−0.332970
$746$	−1.06995e13	−1.26484
$747$	−2.76520e13	−3.24926
$748$	0	0
$749$	6.19009e11	0.0718668
$750$	−9.08480e12	−1.04843
$751$	−3.11231e12	−0.357029	−0.178514	−	0.983937i	$-0.557129\pi$
$751$	−3.11231e12	−0.357029	−0.178514	+	0.983937i	$0.557129\pi$
$752$	−2.75867e11	−0.0314572
$753$	−2.31469e13	−2.62370
$754$	−1.92990e12	−0.217452
$755$	8.84408e11	0.0990584
$756$	−2.17325e12	−0.241970
$757$	−1.32575e13	−1.46734	−0.733671	−	0.679505i	$-0.762195\pi$
$757$	−1.32575e13	−1.46734	−0.733671	+	0.679505i	$0.762195\pi$
$758$	−5.15721e12	−0.567419
$759$	−1.19074e13	−1.30236
$760$	1.27622e12	0.138760
$761$	−1.36854e13	−1.47920	−0.739601	−	0.673045i	$-0.764986\pi$
$761$	−1.36854e13	−1.47920	−0.739601	+	0.673045i	$0.764986\pi$
$762$	−6.02707e12	−0.647603
$763$	2.31625e12	0.247414
$764$	1.55737e12	0.165376
$765$	0	0
$766$	−9.27326e12	−0.973202
$767$	3.06132e12	0.319396
$768$	−1.92803e13	−1.99980
$769$	1.60424e13	1.65425	0.827123	−	0.562021i	$-0.189976\pi$
$769$	1.60424e13	1.65425	0.827123	+	0.562021i	$0.189976\pi$
$770$	−1.83765e11	−0.0188389
$771$	−7.19540e12	−0.733348
$772$	1.40329e12	0.142190
$773$	2.10861e12	0.212416	0.106208	−	0.994344i	$-0.466129\pi$
$773$	2.10861e12	0.212416	0.106208	+	0.994344i	$0.466129\pi$
$774$	1.32066e13	1.32269
$775$	−1.06494e13	−1.06040
$776$	−9.58941e12	−0.949324
$777$	3.81954e12	0.375939
$778$	−6.46673e12	−0.632815
$779$	−4.42983e12	−0.430992
$780$	−1.51930e12	−0.146966
$781$	−4.34421e12	−0.417813
$782$	0	0
$783$	−2.57026e13	−2.44371
$784$	2.69940e12	0.255179
$785$	1.15760e12	0.108804
$786$	−5.34871e12	−0.499859
$787$	1.48852e13	1.38315	0.691573	−	0.722306i	$-0.256918\pi$
$787$	1.48852e13	1.38315	0.691573	+	0.722306i	$0.256918\pi$
$788$	−4.83740e11	−0.0446934
$789$	7.14491e12	0.656372
$790$	−1.63176e12	−0.149051
$791$	1.00444e12	0.0912280
$792$	1.10526e13	0.998160
$793$	−3.29211e12	−0.295628
$794$	7.58406e12	0.677188
$795$	−1.56749e13	−1.39173
$796$	5.91511e12	0.522220
$797$	−9.98804e11	−0.0876835	−0.0438418	−	0.999038i	$-0.513960\pi$
$797$	−9.98804e11	−0.0876835	−0.0438418	+	0.999038i	$0.513960\pi$
$798$	−7.78871e11	−0.0679912
$799$	0	0
$800$	−8.26627e12	−0.713518
$801$	7.77848e12	0.667649
$802$	−2.49276e12	−0.212763
$803$	−6.62474e12	−0.562275
$804$	−1.05973e13	−0.894426
$805$	1.61235e12	0.135325
$806$	4.06849e12	0.339567
$807$	−2.37920e13	−1.97469
$808$	7.86988e11	0.0649557
$809$	−8.26332e11	−0.0678245	−0.0339122	−	0.999425i	$-0.510797\pi$
$809$	−8.26332e11	−0.0678245	−0.0339122	+	0.999425i	$0.510797\pi$
$810$	1.11570e13	0.910678
$811$	−6.85748e12	−0.556635	−0.278318	−	0.960489i	$-0.589777\pi$
$811$	−6.85748e12	−0.556635	−0.278318	+	0.960489i	$0.589777\pi$
$812$	8.52642e11	0.0688279
$813$	2.23481e12	0.179405
$814$	−3.90730e12	−0.311937
$815$	−5.06820e12	−0.402388
$816$	0	0
$817$	−2.80892e12	−0.220567
$818$	1.62264e13	1.26716
$819$	2.01606e12	0.156577
$820$	−3.91475e12	−0.302372
$821$	−5.66930e12	−0.435497	−0.217749	−	0.976005i	$-0.569871\pi$
$821$	−5.66930e12	−0.435497	−0.217749	+	0.976005i	$0.569871\pi$
$822$	1.53543e13	1.17302
$823$	−9.24298e12	−0.702284	−0.351142	−	0.936322i	$-0.614207\pi$
$823$	−9.24298e12	−0.702284	−0.351142	+	0.936322i	$0.614207\pi$
$824$	7.41729e12	0.560496
$825$	7.51153e12	0.564528
$826$	1.38691e12	0.103667
$827$	−1.93635e13	−1.43949	−0.719745	−	0.694238i	$-0.755741\pi$
$827$	−1.93635e13	−1.43949	−0.719745	+	0.694238i	$0.755741\pi$
$828$	−3.20531e13	−2.36992
$829$	−3.41186e12	−0.250897	−0.125449	−	0.992100i	$-0.540037\pi$
$829$	−3.41186e12	−0.250897	−0.125449	+	0.992100i	$0.540037\pi$
$830$	−5.32965e12	−0.389805
$831$	4.09844e13	2.98136
$832$	4.48805e12	0.324716
$833$	0	0
$834$	−2.38533e13	−1.70727
$835$	−1.04194e12	−0.0741743
$836$	−7.77003e11	−0.0550167
$837$	5.41846e13	3.81602
$838$	4.10186e12	0.287331
$839$	−1.53139e12	−0.106698	−0.0533492	−	0.998576i	$-0.516990\pi$
$839$	−1.53139e12	−0.106698	−0.0533492	+	0.998576i	$0.516990\pi$
$840$	−2.08243e12	−0.144316
$841$	−4.42311e12	−0.304892
$842$	−4.63071e12	−0.317499
$843$	2.72059e13	1.85540
$844$	4.06460e12	0.275725
$845$	−5.52568e12	−0.372847
$846$	3.24525e12	0.217812
$847$	−2.16607e12	−0.144610
$848$	6.77489e12	0.449905
$849$	6.72998e12	0.444558
$850$	0	0
$851$	3.42824e13	2.24072
$852$	−1.62716e13	−1.05792
$853$	−2.88573e12	−0.186631	−0.0933157	−	0.995637i	$-0.529747\pi$
$853$	−2.88573e12	−0.186631	−0.0933157	+	0.995637i	$0.529747\pi$
$854$	−1.49147e12	−0.0959520
$855$	−5.21165e12	−0.333524
$856$	−7.17576e12	−0.456811
$857$	7.26101e12	0.459815	0.229908	−	0.973212i	$-0.426158\pi$
$857$	7.26101e12	0.459815	0.229908	+	0.973212i	$0.426158\pi$
$858$	−2.86970e12	−0.180777
$859$	−1.38238e13	−0.866277	−0.433138	−	0.901327i	$-0.642594\pi$
$859$	−1.38238e13	−0.866277	−0.433138	+	0.901327i	$0.642594\pi$
$860$	−2.48231e12	−0.154744
$861$	7.22824e12	0.448248
$862$	−6.31182e12	−0.389378
$863$	2.32472e13	1.42666	0.713332	−	0.700826i	$-0.247185\pi$
$863$	2.32472e13	1.42666	0.713332	+	0.700826i	$0.247185\pi$
$864$	4.20590e13	2.56772
$865$	1.52937e12	0.0928840
$866$	1.34631e13	0.813420
$867$	0	0
$868$	−1.79748e12	−0.107480
$869$	3.00567e12	0.178794
$870$	−8.14049e12	−0.481741
$871$	5.98260e12	0.352215
$872$	−2.68507e13	−1.57265
$873$	3.91599e13	2.28180
$874$	−6.99078e12	−0.405251
$875$	−2.26590e12	−0.130679
$876$	−2.48135e13	−1.42370
$877$	−2.26911e13	−1.29526	−0.647630	−	0.761955i	$-0.724240\pi$
$877$	−2.26911e13	−1.29526	−0.647630	+	0.761955i	$0.724240\pi$
$878$	2.04111e13	1.15916
$879$	3.92881e13	2.21979
$880$	7.39496e11	0.0415685
$881$	7.26928e12	0.406537	0.203268	−	0.979123i	$-0.434844\pi$
$881$	7.26928e12	0.406537	0.203268	+	0.979123i	$0.434844\pi$
$882$	−3.17553e13	−1.76688
$883$	−2.86632e13	−1.58673	−0.793363	−	0.608749i	$-0.791672\pi$
$883$	−2.86632e13	−1.58673	−0.793363	+	0.608749i	$0.791672\pi$
$884$	0	0
$885$	1.29129e13	0.707587
$886$	1.70909e12	0.0931780
$887$	−1.36812e13	−0.742108	−0.371054	−	0.928611i	$-0.621004\pi$
$887$	−1.36812e13	−0.742108	−0.371054	+	0.928611i	$0.621004\pi$
$888$	−4.42775e13	−2.38960
$889$	−1.50325e12	−0.0807185
$890$	1.49922e12	0.0800961
$891$	−2.05510e13	−1.09240
$892$	2.24546e12	0.118758
$893$	−6.90232e11	−0.0363215
$894$	−1.98071e13	−1.03705
$895$	−2.26105e12	−0.117790
$896$	−7.92683e11	−0.0410879
$897$	2.51785e13	1.29857
$898$	−2.09032e13	−1.07268
$899$	−2.12585e13	−1.08546
$900$	2.02200e13	1.02728
$901$	0	0
$902$	−7.39430e12	−0.371936
$903$	4.58336e12	0.229398
$904$	−1.16438e13	−0.579877
$905$	6.98431e12	0.346103
$906$	6.25697e12	0.308523
$907$	1.73752e13	0.852504	0.426252	−	0.904604i	$-0.359834\pi$
$907$	1.73752e13	0.852504	0.426252	+	0.904604i	$0.359834\pi$
$908$	−1.00821e13	−0.492226
$909$	−3.21379e12	−0.156128
$910$	3.88576e11	0.0187841
$911$	6.58508e12	0.316759	0.158379	−	0.987378i	$-0.449373\pi$
$911$	6.58508e12	0.316759	0.158379	+	0.987378i	$0.449373\pi$
$912$	3.13428e12	0.150024
$913$	9.81710e12	0.467590
$914$	−1.55406e13	−0.736565
$915$	−1.38864e13	−0.654930
$916$	6.99438e12	0.328261
$917$	−1.33406e12	−0.0623035
$918$	0	0
$919$	2.27287e13	1.05112	0.525562	−	0.850755i	$-0.323855\pi$
$919$	2.27287e13	1.05112	0.525562	+	0.850755i	$0.323855\pi$
$920$	−1.86909e13	−0.860171
$921$	4.54170e13	2.07994
$922$	−1.67669e13	−0.764125
$923$	9.18594e12	0.416597
$924$	1.26785e12	0.0572194
$925$	−2.16263e13	−0.971278
$926$	−8.78311e12	−0.392554
$927$	−3.02897e13	−1.34721
$928$	−1.65012e13	−0.730383
$929$	1.78937e13	0.788189	0.394095	−	0.919070i	$-0.371058\pi$
$929$	1.78937e13	0.788189	0.394095	+	0.919070i	$0.371058\pi$
$930$	1.71612e13	0.752273
$931$	6.75402e12	0.294638
$932$	−1.15894e13	−0.503139
$933$	−7.37157e13	−3.18488
$934$	−1.84061e13	−0.791411
$935$	0	0
$936$	−2.33709e13	−0.995255
$937$	8.74280e11	0.0370529	0.0185265	−	0.999828i	$-0.494103\pi$
$937$	8.74280e11	0.0370529	0.0185265	+	0.999828i	$0.494103\pi$
$938$	2.71038e12	0.114319
$939$	2.95837e12	0.124182
$940$	−6.09975e11	−0.0254822
$941$	−2.82843e13	−1.17596	−0.587979	−	0.808876i	$-0.700076\pi$
$941$	−2.82843e13	−1.17596	−0.587979	+	0.808876i	$0.700076\pi$
$942$	8.18971e12	0.338875
$943$	6.48772e13	2.67171
$944$	−5.58112e12	−0.228743
$945$	5.17510e12	0.211094
$946$	−4.68866e12	−0.190344
$947$	3.84475e13	1.55343	0.776717	−	0.629849i	$-0.216883\pi$
$947$	3.84475e13	1.55343	0.776717	+	0.629849i	$0.216883\pi$
$948$	1.12580e13	0.452713
$949$	1.40082e13	0.560638
$950$	4.40997e12	0.175663
$951$	−4.53617e13	−1.79836
$952$	0	0
$953$	1.03626e13	0.406960	0.203480	−	0.979079i	$-0.434775\pi$
$953$	1.03626e13	0.406960	0.203480	+	0.979079i	$0.434775\pi$
$954$	−7.96987e13	−3.11518
$955$	−3.70852e12	−0.144273
$956$	−1.89766e13	−0.734779
$957$	1.49946e13	0.577872
$958$	−6.37311e12	−0.244459
$959$	3.82962e12	0.146208
$960$	1.89310e13	0.719371
$961$	1.83762e13	0.695024
$962$	8.26207e12	0.311029
$963$	2.93034e13	1.09799
$964$	−1.54592e13	−0.576554
$965$	−3.34162e12	−0.124046
$966$	1.14070e13	0.421476
$967$	3.39415e13	1.24828	0.624139	−	0.781313i	$-0.285450\pi$
$967$	3.39415e13	1.24828	0.624139	+	0.781313i	$0.285450\pi$
$968$	2.51099e13	0.919190
$969$	0	0
$970$	7.54768e12	0.273741
$971$	−2.32423e12	−0.0839059	−0.0419530	−	0.999120i	$-0.513358\pi$
$971$	−2.32423e12	−0.0839059	−0.0419530	+	0.999120i	$0.513358\pi$
$972$	−3.67033e13	−1.31888
$973$	−5.94941e12	−0.212797
$974$	1.72402e13	0.613798
$975$	−1.58833e13	−0.562885
$976$	6.00187e12	0.211720
$977$	−1.12122e13	−0.393701	−0.196850	−	0.980434i	$-0.563071\pi$
$977$	−1.12122e13	−0.393701	−0.196850	+	0.980434i	$0.563071\pi$
$978$	−3.58563e13	−1.25326
$979$	−2.76154e12	−0.0960792
$980$	5.96870e12	0.206710
$981$	1.09649e14	3.78003
$982$	−7.77308e12	−0.266742
$983$	−4.08695e13	−1.39607	−0.698037	−	0.716062i	$-0.745943\pi$
$983$	−4.08695e13	−1.39607	−0.698037	+	0.716062i	$0.745943\pi$
$984$	−8.37923e13	−2.84922
$985$	1.15192e12	0.0389904
$986$	0	0
$987$	1.12626e12	0.0377758
$988$	1.64299e12	0.0548566
$989$	4.11380e13	1.36729
$990$	−8.69931e12	−0.287824
$991$	−3.06869e12	−0.101070	−0.0505350	−	0.998722i	$-0.516093\pi$
$991$	−3.06869e12	−0.101070	−0.0505350	+	0.998722i	$0.516093\pi$
$992$	3.47868e13	1.14054
$993$	−7.42669e13	−2.42395
$994$	4.16163e12	0.135215
$995$	−1.40855e13	−0.455583
$996$	3.67707e13	1.18395
$997$	−1.08134e13	−0.346605	−0.173303	−	0.984869i	$-0.555444\pi$
$997$	−1.08134e13	−0.346605	−0.173303	+	0.984869i	$0.555444\pi$
$998$	−1.33500e13	−0.425984
$999$	1.10035e14	3.49531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.32		52
17.11	odd	16		17.10.d.a.2.8	✓	52
17.14	odd	16		17.10.d.a.9.8	yes	52
17.16	even	2	inner	289.10.a.i.1.31		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.8	✓	52	17.11	odd	16
17.10.d.a.9.8	yes	52	17.14	odd	16
289.10.a.i.1.31		52	17.16	even	2	inner
289.10.a.i.1.32		52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+16.1001 q^{2} +264.510 q^{3} -252.785 q^{4} +601.950 q^{5} +4258.66 q^{6} +1062.18 q^{7} -12313.2 q^{8} +50282.7 q^{9} +O(q^{10})\)	\(q+16.1001 q^{2} +264.510 q^{3} -252.785 q^{4} +601.950 q^{5} +4258.66 q^{6} +1062.18 q^{7} -12313.2 q^{8} +50282.7 q^{9} +9691.49 q^{10} -17851.5 q^{11} -66864.3 q^{12} +37747.5 q^{13} +17101.2 q^{14} +159222. q^{15} -68817.6 q^{16} +809559. q^{18} -172185. q^{19} -152164. q^{20} +280957. q^{21} -287412. q^{22} +2.52174e6 q^{23} -3.25696e6 q^{24} -1.59078e6 q^{25} +607740. q^{26} +8.09394e6 q^{27} -268503. q^{28} -3.17554e6 q^{29} +2.56350e6 q^{30} +6.69446e6 q^{31} +5.19636e6 q^{32} -4.72191e6 q^{33} +639379. q^{35} -1.27107e7 q^{36} +1.35947e7 q^{37} -2.77221e6 q^{38} +9.98459e6 q^{39} -7.41191e6 q^{40} +2.57272e7 q^{41} +4.52346e6 q^{42} +1.63134e7 q^{43} +4.51260e6 q^{44} +3.02677e7 q^{45} +4.06004e7 q^{46} +4.00867e6 q^{47} -1.82030e7 q^{48} -3.92254e7 q^{49} -2.56118e7 q^{50} -9.54200e6 q^{52} -9.84470e7 q^{53} +1.30314e8 q^{54} -1.07457e7 q^{55} -1.30788e7 q^{56} -4.55447e7 q^{57} -5.11266e7 q^{58} +8.11001e7 q^{59} -4.02490e7 q^{60} -8.72141e7 q^{61} +1.07782e8 q^{62} +5.34092e7 q^{63} +1.18897e8 q^{64} +2.27221e7 q^{65} -7.60235e7 q^{66} +1.58490e8 q^{67} +6.67026e8 q^{69} +1.02941e7 q^{70} +2.43352e8 q^{71} -6.19139e8 q^{72} +3.71102e8 q^{73} +2.18877e8 q^{74} -4.20778e8 q^{75} +4.35258e7 q^{76} -1.89615e7 q^{77} +1.60753e8 q^{78} -1.68370e8 q^{79} -4.14248e7 q^{80} +1.15122e9 q^{81} +4.14211e8 q^{82} -5.49931e8 q^{83} -7.10219e7 q^{84} +2.62648e8 q^{86} -8.39962e8 q^{87} +2.19809e8 q^{88} +1.54695e8 q^{89} +4.87314e8 q^{90} +4.00946e7 q^{91} -6.37458e8 q^{92} +1.77075e9 q^{93} +6.45401e7 q^{94} -1.03647e8 q^{95} +1.37449e9 q^{96} +7.78794e8 q^{97} -6.31535e8 q^{98} -8.97623e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 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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