Properties

Label 1.54.a.a.1.3
Level $1$
Weight $54$
Character 1.1
Self dual yes
Analytic conductor $17.790$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 54 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.7903107608\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 2315873743412 x^{2} - 421178019174503472 x + 612167648493870378955584\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{27}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(447512.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.58420e7 q^{2} -2.97907e12 q^{3} -8.33939e15 q^{4} +5.38136e18 q^{5} -7.69850e19 q^{6} +2.33436e22 q^{7} -4.48271e23 q^{8} -1.05084e25 q^{9} +O(q^{10})\) \(q+2.58420e7 q^{2} -2.97907e12 q^{3} -8.33939e15 q^{4} +5.38136e18 q^{5} -7.69850e19 q^{6} +2.33436e22 q^{7} -4.48271e23 q^{8} -1.05084e25 q^{9} +1.39065e26 q^{10} -3.50807e27 q^{11} +2.48436e28 q^{12} -3.76599e28 q^{13} +6.03245e29 q^{14} -1.60314e31 q^{15} +6.35303e31 q^{16} -5.80067e32 q^{17} -2.71559e32 q^{18} -9.40144e33 q^{19} -4.48772e34 q^{20} -6.95421e34 q^{21} -9.06556e34 q^{22} -5.69353e35 q^{23} +1.33543e36 q^{24} +1.78568e37 q^{25} -9.73207e35 q^{26} +8.90492e37 q^{27} -1.94671e38 q^{28} -2.46957e38 q^{29} -4.14284e38 q^{30} -4.25695e39 q^{31} +5.67942e39 q^{32} +1.04508e40 q^{33} -1.49901e40 q^{34} +1.25620e41 q^{35} +8.76338e40 q^{36} -5.85991e41 q^{37} -2.42952e41 q^{38} +1.12191e41 q^{39} -2.41231e42 q^{40} +5.37725e42 q^{41} -1.79711e42 q^{42} +1.54488e43 q^{43} +2.92552e43 q^{44} -5.65495e43 q^{45} -1.47132e43 q^{46} -1.14085e44 q^{47} -1.89261e44 q^{48} -7.19501e43 q^{49} +4.61455e44 q^{50} +1.72806e45 q^{51} +3.14060e44 q^{52} +8.51129e44 q^{53} +2.30121e45 q^{54} -1.88782e46 q^{55} -1.04643e46 q^{56} +2.80075e46 q^{57} -6.38187e45 q^{58} -9.48774e46 q^{59} +1.33692e47 q^{60} +3.37366e47 q^{61} -1.10008e47 q^{62} -2.45304e47 q^{63} -4.25463e47 q^{64} -2.02661e47 q^{65} +2.70069e47 q^{66} -3.70994e48 q^{67} +4.83740e48 q^{68} +1.69614e48 q^{69} +3.24628e48 q^{70} +2.16582e48 q^{71} +4.71061e48 q^{72} -1.03616e49 q^{73} -1.51432e49 q^{74} -5.31966e49 q^{75} +7.84022e49 q^{76} -8.18910e49 q^{77} +2.89925e48 q^{78} +5.02034e49 q^{79} +3.41879e50 q^{80} -6.15963e49 q^{81} +1.38959e50 q^{82} -3.18305e50 q^{83} +5.79939e50 q^{84} -3.12155e51 q^{85} +3.99229e50 q^{86} +7.35702e50 q^{87} +1.57257e51 q^{88} +3.04162e51 q^{89} -1.46135e51 q^{90} -8.79117e50 q^{91} +4.74806e51 q^{92} +1.26817e52 q^{93} -2.94817e51 q^{94} -5.05925e52 q^{95} -1.69194e52 q^{96} +4.29374e52 q^{97} -1.85933e51 q^{98} +3.68643e52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + O(q^{10}) \) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + \)\(23\!\cdots\!00\)\(q^{10} + \)\(24\!\cdots\!28\)\(q^{11} - \)\(36\!\cdots\!40\)\(q^{12} + \)\(38\!\cdots\!40\)\(q^{13} - \)\(23\!\cdots\!24\)\(q^{14} + \)\(10\!\cdots\!00\)\(q^{15} - \)\(15\!\cdots\!36\)\(q^{16} - \)\(86\!\cdots\!60\)\(q^{17} - \)\(67\!\cdots\!80\)\(q^{18} - \)\(25\!\cdots\!60\)\(q^{19} - \)\(13\!\cdots\!00\)\(q^{20} - \)\(45\!\cdots\!32\)\(q^{21} - \)\(93\!\cdots\!40\)\(q^{22} + \)\(69\!\cdots\!60\)\(q^{23} + \)\(80\!\cdots\!20\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} + \)\(88\!\cdots\!88\)\(q^{26} + \)\(85\!\cdots\!40\)\(q^{27} - \)\(56\!\cdots\!60\)\(q^{28} - \)\(14\!\cdots\!40\)\(q^{29} - \)\(57\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!32\)\(q^{31} + \)\(34\!\cdots\!80\)\(q^{32} + \)\(26\!\cdots\!40\)\(q^{33} + \)\(14\!\cdots\!36\)\(q^{34} + \)\(61\!\cdots\!00\)\(q^{35} + \)\(74\!\cdots\!84\)\(q^{36} - \)\(28\!\cdots\!80\)\(q^{37} - \)\(21\!\cdots\!40\)\(q^{38} - \)\(36\!\cdots\!16\)\(q^{39} - \)\(53\!\cdots\!00\)\(q^{40} + \)\(81\!\cdots\!88\)\(q^{41} + \)\(34\!\cdots\!40\)\(q^{42} + \)\(45\!\cdots\!00\)\(q^{43} + \)\(36\!\cdots\!96\)\(q^{44} - \)\(52\!\cdots\!00\)\(q^{45} - \)\(28\!\cdots\!52\)\(q^{46} - \)\(45\!\cdots\!40\)\(q^{47} - \)\(30\!\cdots\!40\)\(q^{48} + \)\(61\!\cdots\!28\)\(q^{49} + \)\(52\!\cdots\!00\)\(q^{50} + \)\(48\!\cdots\!48\)\(q^{51} + \)\(64\!\cdots\!00\)\(q^{52} + \)\(38\!\cdots\!20\)\(q^{53} - \)\(90\!\cdots\!60\)\(q^{54} - \)\(25\!\cdots\!00\)\(q^{55} - \)\(41\!\cdots\!60\)\(q^{56} - \)\(78\!\cdots\!20\)\(q^{57} + \)\(23\!\cdots\!40\)\(q^{58} + \)\(16\!\cdots\!20\)\(q^{59} + \)\(40\!\cdots\!00\)\(q^{60} + \)\(65\!\cdots\!28\)\(q^{61} + \)\(39\!\cdots\!60\)\(q^{62} - \)\(30\!\cdots\!20\)\(q^{63} - \)\(10\!\cdots\!32\)\(q^{64} - \)\(34\!\cdots\!00\)\(q^{65} - \)\(65\!\cdots\!04\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} + \)\(28\!\cdots\!20\)\(q^{68} + \)\(77\!\cdots\!64\)\(q^{69} + \)\(33\!\cdots\!00\)\(q^{70} + \)\(35\!\cdots\!48\)\(q^{71} + \)\(26\!\cdots\!20\)\(q^{72} - \)\(70\!\cdots\!40\)\(q^{73} - \)\(24\!\cdots\!44\)\(q^{74} - \)\(21\!\cdots\!00\)\(q^{75} + \)\(45\!\cdots\!80\)\(q^{76} - \)\(16\!\cdots\!00\)\(q^{77} + \)\(51\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!40\)\(q^{79} + \)\(11\!\cdots\!00\)\(q^{80} - \)\(49\!\cdots\!56\)\(q^{81} + \)\(15\!\cdots\!60\)\(q^{82} - \)\(26\!\cdots\!20\)\(q^{83} - \)\(76\!\cdots\!24\)\(q^{84} - \)\(23\!\cdots\!00\)\(q^{85} - \)\(77\!\cdots\!32\)\(q^{86} - \)\(45\!\cdots\!80\)\(q^{87} + \)\(56\!\cdots\!80\)\(q^{88} - \)\(37\!\cdots\!20\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(12\!\cdots\!28\)\(q^{91} + \)\(89\!\cdots\!40\)\(q^{92} - \)\(99\!\cdots\!60\)\(q^{93} - \)\(37\!\cdots\!84\)\(q^{94} - \)\(17\!\cdots\!00\)\(q^{95} - \)\(11\!\cdots\!92\)\(q^{96} + \)\(10\!\cdots\!60\)\(q^{97} - \)\(88\!\cdots\!40\)\(q^{98} + \)\(20\!\cdots\!84\)\(q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58420e7 0.272290 0.136145 0.990689i \(-0.456529\pi\)
0.136145 + 0.990689i \(0.456529\pi\)
\(3\) −2.97907e12 −0.676654 −0.338327 0.941029i \(-0.609861\pi\)
−0.338327 + 0.941029i \(0.609861\pi\)
\(4\) −8.33939e15 −0.925858
\(5\) 5.38136e18 1.61505 0.807527 0.589831i \(-0.200806\pi\)
0.807527 + 0.589831i \(0.200806\pi\)
\(6\) −7.69850e19 −0.184246
\(7\) 2.33436e22 0.939874 0.469937 0.882700i \(-0.344277\pi\)
0.469937 + 0.882700i \(0.344277\pi\)
\(8\) −4.48271e23 −0.524392
\(9\) −1.05084e25 −0.542139
\(10\) 1.39065e26 0.439763
\(11\) −3.50807e27 −0.887487 −0.443744 0.896154i \(-0.646350\pi\)
−0.443744 + 0.896154i \(0.646350\pi\)
\(12\) 2.48436e28 0.626486
\(13\) −3.76599e28 −0.113862 −0.0569312 0.998378i \(-0.518132\pi\)
−0.0569312 + 0.998378i \(0.518132\pi\)
\(14\) 6.03245e29 0.255918
\(15\) −1.60314e31 −1.09283
\(16\) 6.35303e31 0.783072
\(17\) −5.80067e32 −1.43411 −0.717053 0.697018i \(-0.754510\pi\)
−0.717053 + 0.697018i \(0.754510\pi\)
\(18\) −2.71559e32 −0.147619
\(19\) −9.40144e33 −1.21962 −0.609809 0.792548i \(-0.708754\pi\)
−0.609809 + 0.792548i \(0.708754\pi\)
\(20\) −4.48772e34 −1.49531
\(21\) −6.95421e34 −0.635970
\(22\) −9.06556e34 −0.241654
\(23\) −5.69353e35 −0.467298 −0.233649 0.972321i \(-0.575067\pi\)
−0.233649 + 0.972321i \(0.575067\pi\)
\(24\) 1.33543e36 0.354832
\(25\) 1.78568e37 1.60840
\(26\) −9.73207e35 −0.0310035
\(27\) 8.90492e37 1.04349
\(28\) −1.94671e38 −0.870190
\(29\) −2.46957e38 −0.435587 −0.217794 0.975995i \(-0.569886\pi\)
−0.217794 + 0.975995i \(0.569886\pi\)
\(30\) −4.14284e38 −0.297567
\(31\) −4.25695e39 −1.28237 −0.641185 0.767386i \(-0.721557\pi\)
−0.641185 + 0.767386i \(0.721557\pi\)
\(32\) 5.67942e39 0.737614
\(33\) 1.04508e40 0.600522
\(34\) −1.49901e40 −0.390493
\(35\) 1.25620e41 1.51795
\(36\) 8.76338e40 0.501944
\(37\) −5.85991e41 −1.62385 −0.811924 0.583764i \(-0.801580\pi\)
−0.811924 + 0.583764i \(0.801580\pi\)
\(38\) −2.42952e41 −0.332090
\(39\) 1.12191e41 0.0770454
\(40\) −2.41231e42 −0.846920
\(41\) 5.37725e42 0.981269 0.490634 0.871366i \(-0.336765\pi\)
0.490634 + 0.871366i \(0.336765\pi\)
\(42\) −1.79711e42 −0.173168
\(43\) 1.54488e43 0.797961 0.398981 0.916959i \(-0.369364\pi\)
0.398981 + 0.916959i \(0.369364\pi\)
\(44\) 2.92552e43 0.821687
\(45\) −5.65495e43 −0.875583
\(46\) −1.47132e43 −0.127241
\(47\) −1.14085e44 −0.557999 −0.279000 0.960291i \(-0.590003\pi\)
−0.279000 + 0.960291i \(0.590003\pi\)
\(48\) −1.89261e44 −0.529869
\(49\) −7.19501e43 −0.116637
\(50\) 4.61455e44 0.437950
\(51\) 1.72806e45 0.970395
\(52\) 3.14060e44 0.105420
\(53\) 8.51129e44 0.172459 0.0862293 0.996275i \(-0.472518\pi\)
0.0862293 + 0.996275i \(0.472518\pi\)
\(54\) 2.30121e45 0.284133
\(55\) −1.88782e46 −1.43334
\(56\) −1.04643e46 −0.492862
\(57\) 2.80075e46 0.825260
\(58\) −6.38187e45 −0.118606
\(59\) −9.48774e46 −1.12095 −0.560473 0.828173i \(-0.689380\pi\)
−0.560473 + 0.828173i \(0.689380\pi\)
\(60\) 1.33692e47 1.01181
\(61\) 3.37366e47 1.64764 0.823818 0.566854i \(-0.191840\pi\)
0.823818 + 0.566854i \(0.191840\pi\)
\(62\) −1.10008e47 −0.349176
\(63\) −2.45304e47 −0.509542
\(64\) −4.25463e47 −0.582227
\(65\) −2.02661e47 −0.183894
\(66\) 2.70069e47 0.163516
\(67\) −3.70994e48 −1.50794 −0.753971 0.656908i \(-0.771864\pi\)
−0.753971 + 0.656908i \(0.771864\pi\)
\(68\) 4.83740e48 1.32778
\(69\) 1.69614e48 0.316199
\(70\) 3.24628e48 0.413321
\(71\) 2.16582e48 0.189355 0.0946774 0.995508i \(-0.469818\pi\)
0.0946774 + 0.995508i \(0.469818\pi\)
\(72\) 4.71061e48 0.284293
\(73\) −1.03616e49 −0.433882 −0.216941 0.976185i \(-0.569608\pi\)
−0.216941 + 0.976185i \(0.569608\pi\)
\(74\) −1.51432e49 −0.442157
\(75\) −5.31966e49 −1.08833
\(76\) 7.84022e49 1.12919
\(77\) −8.18910e49 −0.834126
\(78\) 2.89925e48 0.0209787
\(79\) 5.02034e49 0.259188 0.129594 0.991567i \(-0.458633\pi\)
0.129594 + 0.991567i \(0.458633\pi\)
\(80\) 3.41879e50 1.26470
\(81\) −6.15963e49 −0.163946
\(82\) 1.38959e50 0.267189
\(83\) −3.18305e50 −0.443889 −0.221944 0.975059i \(-0.571240\pi\)
−0.221944 + 0.975059i \(0.571240\pi\)
\(84\) 5.79939e50 0.588818
\(85\) −3.12155e51 −2.31616
\(86\) 3.99229e50 0.217277
\(87\) 7.35702e50 0.294742
\(88\) 1.57257e51 0.465391
\(89\) 3.04162e51 0.667222 0.333611 0.942711i \(-0.391733\pi\)
0.333611 + 0.942711i \(0.391733\pi\)
\(90\) −1.46135e51 −0.238412
\(91\) −8.79117e50 −0.107016
\(92\) 4.74806e51 0.432652
\(93\) 1.26817e52 0.867721
\(94\) −2.94817e51 −0.151938
\(95\) −5.05925e52 −1.96975
\(96\) −1.69194e52 −0.499110
\(97\) 4.29374e52 0.962465 0.481232 0.876593i \(-0.340189\pi\)
0.481232 + 0.876593i \(0.340189\pi\)
\(98\) −1.85933e51 −0.0317590
\(99\) 3.68643e52 0.481141
\(100\) −1.48915e53 −1.48915
\(101\) 2.40879e53 1.85047 0.925236 0.379392i \(-0.123867\pi\)
0.925236 + 0.379392i \(0.123867\pi\)
\(102\) 4.46565e52 0.264229
\(103\) 5.77425e52 0.263821 0.131910 0.991262i \(-0.457889\pi\)
0.131910 + 0.991262i \(0.457889\pi\)
\(104\) 1.68818e52 0.0597084
\(105\) −3.74231e53 −1.02713
\(106\) 2.19949e52 0.0469587
\(107\) −2.30554e53 −0.383797 −0.191899 0.981415i \(-0.561465\pi\)
−0.191899 + 0.981415i \(0.561465\pi\)
\(108\) −7.42616e53 −0.966128
\(109\) 5.84013e53 0.595142 0.297571 0.954700i \(-0.403824\pi\)
0.297571 + 0.954700i \(0.403824\pi\)
\(110\) −4.87850e53 −0.390284
\(111\) 1.74571e54 1.09878
\(112\) 1.48303e54 0.735989
\(113\) −4.64679e53 −0.182211 −0.0911055 0.995841i \(-0.529040\pi\)
−0.0911055 + 0.995841i \(0.529040\pi\)
\(114\) 7.23770e53 0.224710
\(115\) −3.06389e54 −0.754711
\(116\) 2.05947e54 0.403292
\(117\) 3.95745e53 0.0617292
\(118\) −2.45182e54 −0.305222
\(119\) −1.35408e55 −1.34788
\(120\) 7.18642e54 0.573072
\(121\) −3.31816e54 −0.212366
\(122\) 8.71823e54 0.448634
\(123\) −1.60192e55 −0.663980
\(124\) 3.55003e55 1.18729
\(125\) 3.63487e55 0.982593
\(126\) −6.33915e54 −0.138743
\(127\) 1.05751e54 0.0187709 0.00938545 0.999956i \(-0.497012\pi\)
0.00938545 + 0.999956i \(0.497012\pi\)
\(128\) −6.21504e55 −0.896149
\(129\) −4.60231e55 −0.539944
\(130\) −5.23717e54 −0.0500724
\(131\) 9.48285e55 0.740031 0.370015 0.929026i \(-0.379352\pi\)
0.370015 + 0.929026i \(0.379352\pi\)
\(132\) −8.71531e55 −0.555998
\(133\) −2.19463e56 −1.14629
\(134\) −9.58722e55 −0.410597
\(135\) 4.79206e56 1.68530
\(136\) 2.60027e56 0.752034
\(137\) 1.67624e56 0.399248 0.199624 0.979873i \(-0.436028\pi\)
0.199624 + 0.979873i \(0.436028\pi\)
\(138\) 4.38317e55 0.0860978
\(139\) −6.36794e55 −0.103301 −0.0516507 0.998665i \(-0.516448\pi\)
−0.0516507 + 0.998665i \(0.516448\pi\)
\(140\) −1.04760e57 −1.40540
\(141\) 3.39865e56 0.377573
\(142\) 5.59692e55 0.0515594
\(143\) 1.32113e56 0.101051
\(144\) −6.67603e56 −0.424534
\(145\) −1.32897e57 −0.703496
\(146\) −2.67765e56 −0.118142
\(147\) 2.14344e56 0.0789227
\(148\) 4.88681e57 1.50345
\(149\) 5.30162e55 0.0136450 0.00682249 0.999977i \(-0.497828\pi\)
0.00682249 + 0.999977i \(0.497828\pi\)
\(150\) −1.37471e57 −0.296341
\(151\) −3.81438e56 −0.0689500 −0.0344750 0.999406i \(-0.510976\pi\)
−0.0344750 + 0.999406i \(0.510976\pi\)
\(152\) 4.21439e57 0.639557
\(153\) 6.09558e57 0.777485
\(154\) −2.11623e57 −0.227124
\(155\) −2.29082e58 −2.07110
\(156\) −9.35606e56 −0.0713331
\(157\) −2.25055e57 −0.144860 −0.0724298 0.997374i \(-0.523075\pi\)
−0.0724298 + 0.997374i \(0.523075\pi\)
\(158\) 1.29736e57 0.0705744
\(159\) −2.53557e57 −0.116695
\(160\) 3.05630e58 1.19129
\(161\) −1.32907e58 −0.439201
\(162\) −1.59177e57 −0.0446409
\(163\) 5.68137e58 1.35357 0.676786 0.736180i \(-0.263372\pi\)
0.676786 + 0.736180i \(0.263372\pi\)
\(164\) −4.48430e58 −0.908516
\(165\) 5.62394e58 0.969875
\(166\) −8.22564e57 −0.120866
\(167\) −5.90727e58 −0.740288 −0.370144 0.928974i \(-0.620692\pi\)
−0.370144 + 0.928974i \(0.620692\pi\)
\(168\) 3.11737e58 0.333497
\(169\) −1.07977e59 −0.987035
\(170\) −8.06670e58 −0.630666
\(171\) 9.87942e58 0.661202
\(172\) −1.28834e59 −0.738799
\(173\) 5.53658e58 0.272282 0.136141 0.990689i \(-0.456530\pi\)
0.136141 + 0.990689i \(0.456530\pi\)
\(174\) 1.90120e58 0.0802552
\(175\) 4.16842e59 1.51169
\(176\) −2.22869e59 −0.694966
\(177\) 2.82646e59 0.758492
\(178\) 7.86016e58 0.181678
\(179\) −7.91775e59 −1.57760 −0.788799 0.614651i \(-0.789297\pi\)
−0.788799 + 0.614651i \(0.789297\pi\)
\(180\) 4.71589e59 0.810666
\(181\) 6.76480e59 1.00409 0.502045 0.864841i \(-0.332581\pi\)
0.502045 + 0.864841i \(0.332581\pi\)
\(182\) −2.27181e58 −0.0291394
\(183\) −1.00504e60 −1.11488
\(184\) 2.55224e59 0.245047
\(185\) −3.15343e60 −2.62260
\(186\) 3.27721e59 0.236272
\(187\) 2.03491e60 1.27275
\(188\) 9.51396e59 0.516628
\(189\) 2.07873e60 0.980754
\(190\) −1.30741e60 −0.536342
\(191\) 5.29979e59 0.189180 0.0945899 0.995516i \(-0.469846\pi\)
0.0945899 + 0.995516i \(0.469846\pi\)
\(192\) 1.26748e60 0.393966
\(193\) −9.36608e59 −0.253682 −0.126841 0.991923i \(-0.540484\pi\)
−0.126841 + 0.991923i \(0.540484\pi\)
\(194\) 1.10959e60 0.262069
\(195\) 6.03741e59 0.124432
\(196\) 6.00020e59 0.107989
\(197\) −1.14277e61 −1.79723 −0.898615 0.438737i \(-0.855426\pi\)
−0.898615 + 0.438737i \(0.855426\pi\)
\(198\) 9.52646e59 0.131010
\(199\) 7.32212e59 0.0881110 0.0440555 0.999029i \(-0.485972\pi\)
0.0440555 + 0.999029i \(0.485972\pi\)
\(200\) −8.00468e60 −0.843430
\(201\) 1.10521e61 1.02035
\(202\) 6.22480e60 0.503865
\(203\) −5.76487e60 −0.409397
\(204\) −1.44109e61 −0.898448
\(205\) 2.89369e61 1.58480
\(206\) 1.49218e60 0.0718357
\(207\) 5.98300e60 0.253341
\(208\) −2.39254e60 −0.0891624
\(209\) 3.29809e61 1.08240
\(210\) −9.67088e60 −0.279676
\(211\) −7.50377e61 −1.91335 −0.956676 0.291156i \(-0.905960\pi\)
−0.956676 + 0.291156i \(0.905960\pi\)
\(212\) −7.09790e60 −0.159672
\(213\) −6.45212e60 −0.128128
\(214\) −5.95797e60 −0.104504
\(215\) 8.31358e61 1.28875
\(216\) −3.99182e61 −0.547200
\(217\) −9.93724e61 −1.20527
\(218\) 1.50921e61 0.162051
\(219\) 3.08679e61 0.293588
\(220\) 1.57433e62 1.32707
\(221\) 2.18452e61 0.163291
\(222\) 4.51125e61 0.299188
\(223\) −1.22197e61 −0.0719419 −0.0359710 0.999353i \(-0.511452\pi\)
−0.0359710 + 0.999353i \(0.511452\pi\)
\(224\) 1.32578e62 0.693264
\(225\) −1.87647e62 −0.871975
\(226\) −1.20082e61 −0.0496142
\(227\) −5.02981e61 −0.184870 −0.0924350 0.995719i \(-0.529465\pi\)
−0.0924350 + 0.995719i \(0.529465\pi\)
\(228\) −2.33565e62 −0.764073
\(229\) −3.41310e62 −0.994281 −0.497140 0.867670i \(-0.665617\pi\)
−0.497140 + 0.867670i \(0.665617\pi\)
\(230\) −7.91771e61 −0.205500
\(231\) 2.43959e62 0.564415
\(232\) 1.10704e62 0.228418
\(233\) 5.82407e62 1.07225 0.536123 0.844140i \(-0.319888\pi\)
0.536123 + 0.844140i \(0.319888\pi\)
\(234\) 1.02269e61 0.0168082
\(235\) −6.13930e62 −0.901198
\(236\) 7.91219e62 1.03784
\(237\) −1.49559e62 −0.175381
\(238\) −3.49923e62 −0.367014
\(239\) 1.01634e63 0.953879 0.476939 0.878936i \(-0.341746\pi\)
0.476939 + 0.878936i \(0.341746\pi\)
\(240\) −1.01848e63 −0.855766
\(241\) 2.10470e63 1.58394 0.791970 0.610560i \(-0.209056\pi\)
0.791970 + 0.610560i \(0.209056\pi\)
\(242\) −8.57480e61 −0.0578252
\(243\) −1.54256e63 −0.932560
\(244\) −2.81343e63 −1.52548
\(245\) −3.87189e62 −0.188374
\(246\) −4.13968e62 −0.180795
\(247\) 3.54057e62 0.138868
\(248\) 1.90826e63 0.672464
\(249\) 9.48252e62 0.300359
\(250\) 9.39324e62 0.267550
\(251\) −3.46671e63 −0.888309 −0.444154 0.895950i \(-0.646496\pi\)
−0.444154 + 0.895950i \(0.646496\pi\)
\(252\) 2.04569e63 0.471764
\(253\) 1.99733e63 0.414721
\(254\) 2.73281e61 0.00511113
\(255\) 9.29929e63 1.56724
\(256\) 2.22614e63 0.338215
\(257\) −7.98120e63 −1.09355 −0.546777 0.837278i \(-0.684146\pi\)
−0.546777 + 0.837278i \(0.684146\pi\)
\(258\) −1.18933e63 −0.147021
\(259\) −1.36791e64 −1.52621
\(260\) 1.69007e63 0.170259
\(261\) 2.59513e63 0.236149
\(262\) 2.45056e63 0.201503
\(263\) −6.73466e63 −0.500597 −0.250299 0.968169i \(-0.580529\pi\)
−0.250299 + 0.968169i \(0.580529\pi\)
\(264\) −4.68478e63 −0.314909
\(265\) 4.58023e63 0.278530
\(266\) −5.67137e63 −0.312122
\(267\) −9.06119e63 −0.451478
\(268\) 3.09386e64 1.39614
\(269\) 1.44464e64 0.590640 0.295320 0.955398i \(-0.404574\pi\)
0.295320 + 0.955398i \(0.404574\pi\)
\(270\) 1.23836e64 0.458890
\(271\) 2.71685e64 0.912810 0.456405 0.889772i \(-0.349137\pi\)
0.456405 + 0.889772i \(0.349137\pi\)
\(272\) −3.68518e64 −1.12301
\(273\) 2.61895e63 0.0724130
\(274\) 4.33175e63 0.108711
\(275\) −6.26429e64 −1.42743
\(276\) −1.41448e64 −0.292756
\(277\) 2.80661e64 0.527798 0.263899 0.964550i \(-0.414991\pi\)
0.263899 + 0.964550i \(0.414991\pi\)
\(278\) −1.64560e63 −0.0281279
\(279\) 4.47338e64 0.695223
\(280\) −5.63119e64 −0.795998
\(281\) −2.78031e64 −0.357582 −0.178791 0.983887i \(-0.557219\pi\)
−0.178791 + 0.983887i \(0.557219\pi\)
\(282\) 8.78280e63 0.102809
\(283\) −6.35233e64 −0.677006 −0.338503 0.940965i \(-0.609920\pi\)
−0.338503 + 0.940965i \(0.609920\pi\)
\(284\) −1.80616e64 −0.175316
\(285\) 1.50718e65 1.33284
\(286\) 3.41408e63 0.0275153
\(287\) 1.25524e65 0.922269
\(288\) −5.96816e64 −0.399889
\(289\) 1.72874e65 1.05666
\(290\) −3.43432e64 −0.191555
\(291\) −1.27913e65 −0.651256
\(292\) 8.64095e64 0.401713
\(293\) −1.18763e65 −0.504300 −0.252150 0.967688i \(-0.581138\pi\)
−0.252150 + 0.967688i \(0.581138\pi\)
\(294\) 5.53908e63 0.0214899
\(295\) −5.10569e65 −1.81039
\(296\) 2.62683e65 0.851532
\(297\) −3.12391e65 −0.926089
\(298\) 1.37005e63 0.00371539
\(299\) 2.14418e64 0.0532076
\(300\) 4.43627e65 1.00764
\(301\) 3.60632e65 0.749983
\(302\) −9.85711e63 −0.0187744
\(303\) −7.17594e65 −1.25213
\(304\) −5.97276e65 −0.955048
\(305\) 1.81549e66 2.66102
\(306\) 1.57522e65 0.211701
\(307\) −1.02441e65 −0.126271 −0.0631357 0.998005i \(-0.520110\pi\)
−0.0631357 + 0.998005i \(0.520110\pi\)
\(308\) 6.82921e65 0.772283
\(309\) −1.72019e65 −0.178515
\(310\) −5.91993e65 −0.563938
\(311\) −2.08869e66 −1.82694 −0.913469 0.406909i \(-0.866607\pi\)
−0.913469 + 0.406909i \(0.866607\pi\)
\(312\) −5.02920e64 −0.0404020
\(313\) 8.41675e65 0.621183 0.310591 0.950543i \(-0.399473\pi\)
0.310591 + 0.950543i \(0.399473\pi\)
\(314\) −5.81587e64 −0.0394438
\(315\) −1.32007e66 −0.822938
\(316\) −4.18666e65 −0.239972
\(317\) 1.89204e66 0.997378 0.498689 0.866781i \(-0.333815\pi\)
0.498689 + 0.866781i \(0.333815\pi\)
\(318\) −6.55242e64 −0.0317748
\(319\) 8.66344e65 0.386578
\(320\) −2.28957e66 −0.940328
\(321\) 6.86835e65 0.259698
\(322\) −3.43460e65 −0.119590
\(323\) 5.45346e66 1.74906
\(324\) 5.13676e65 0.151791
\(325\) −6.72484e65 −0.183136
\(326\) 1.46818e66 0.368564
\(327\) −1.73981e66 −0.402705
\(328\) −2.41046e66 −0.514569
\(329\) −2.66314e66 −0.524449
\(330\) 1.45334e66 0.264087
\(331\) −3.72579e66 −0.624850 −0.312425 0.949942i \(-0.601141\pi\)
−0.312425 + 0.949942i \(0.601141\pi\)
\(332\) 2.65447e66 0.410978
\(333\) 6.15784e66 0.880351
\(334\) −1.52656e66 −0.201573
\(335\) −1.99645e67 −2.43540
\(336\) −4.41803e66 −0.498010
\(337\) 9.36606e66 0.975808 0.487904 0.872897i \(-0.337762\pi\)
0.487904 + 0.872897i \(0.337762\pi\)
\(338\) −2.79034e66 −0.268760
\(339\) 1.38431e66 0.123294
\(340\) 2.60318e67 2.14443
\(341\) 1.49337e67 1.13809
\(342\) 2.55304e66 0.180039
\(343\) −1.60796e67 −1.04950
\(344\) −6.92526e66 −0.418444
\(345\) 9.12754e66 0.510679
\(346\) 1.43076e66 0.0741397
\(347\) −2.74862e67 −1.31942 −0.659711 0.751520i \(-0.729321\pi\)
−0.659711 + 0.751520i \(0.729321\pi\)
\(348\) −6.13531e66 −0.272889
\(349\) 1.18632e67 0.489024 0.244512 0.969646i \(-0.421372\pi\)
0.244512 + 0.969646i \(0.421372\pi\)
\(350\) 1.07720e67 0.411618
\(351\) −3.35358e66 −0.118815
\(352\) −1.99238e67 −0.654623
\(353\) −2.74837e67 −0.837618 −0.418809 0.908074i \(-0.637552\pi\)
−0.418809 + 0.908074i \(0.637552\pi\)
\(354\) 7.30414e66 0.206530
\(355\) 1.16551e67 0.305818
\(356\) −2.53653e67 −0.617753
\(357\) 4.03391e67 0.912049
\(358\) −2.04610e67 −0.429564
\(359\) 3.20694e67 0.625299 0.312649 0.949869i \(-0.398784\pi\)
0.312649 + 0.949869i \(0.398784\pi\)
\(360\) 2.53495e67 0.459149
\(361\) 2.89659e67 0.487468
\(362\) 1.74816e67 0.273404
\(363\) 9.88503e66 0.143699
\(364\) 7.33130e66 0.0990819
\(365\) −5.57595e67 −0.700742
\(366\) −2.59722e67 −0.303570
\(367\) 6.14979e67 0.668666 0.334333 0.942455i \(-0.391489\pi\)
0.334333 + 0.942455i \(0.391489\pi\)
\(368\) −3.61712e67 −0.365928
\(369\) −5.65063e67 −0.531984
\(370\) −8.14909e67 −0.714107
\(371\) 1.98684e67 0.162089
\(372\) −1.05758e68 −0.803387
\(373\) 1.08656e68 0.768723 0.384362 0.923183i \(-0.374422\pi\)
0.384362 + 0.923183i \(0.374422\pi\)
\(374\) 5.25863e67 0.346557
\(375\) −1.08285e68 −0.664876
\(376\) 5.11408e67 0.292610
\(377\) 9.30038e66 0.0495970
\(378\) 5.37185e67 0.267049
\(379\) −2.80807e68 −1.30158 −0.650788 0.759259i \(-0.725561\pi\)
−0.650788 + 0.759259i \(0.725561\pi\)
\(380\) 4.21911e68 1.82371
\(381\) −3.15039e66 −0.0127014
\(382\) 1.36957e67 0.0515117
\(383\) 4.61965e68 1.62122 0.810610 0.585586i \(-0.199136\pi\)
0.810610 + 0.585586i \(0.199136\pi\)
\(384\) 1.85150e68 0.606383
\(385\) −4.40685e68 −1.34716
\(386\) −2.42038e67 −0.0690749
\(387\) −1.62343e68 −0.432606
\(388\) −3.58072e68 −0.891106
\(389\) −3.34377e68 −0.777271 −0.388636 0.921392i \(-0.627053\pi\)
−0.388636 + 0.921392i \(0.627053\pi\)
\(390\) 1.56019e67 0.0338817
\(391\) 3.30263e68 0.670155
\(392\) 3.22531e67 0.0611633
\(393\) −2.82500e68 −0.500745
\(394\) −2.95315e68 −0.489368
\(395\) 2.70163e68 0.418603
\(396\) −3.07425e68 −0.445469
\(397\) 2.89097e68 0.391827 0.195914 0.980621i \(-0.437233\pi\)
0.195914 + 0.980621i \(0.437233\pi\)
\(398\) 1.89218e67 0.0239917
\(399\) 6.53796e68 0.775640
\(400\) 1.13445e69 1.25949
\(401\) 4.66806e67 0.0485077 0.0242538 0.999706i \(-0.492279\pi\)
0.0242538 + 0.999706i \(0.492279\pi\)
\(402\) 2.85610e68 0.277832
\(403\) 1.60316e68 0.146014
\(404\) −2.00878e69 −1.71327
\(405\) −3.31472e68 −0.264782
\(406\) −1.48976e68 −0.111475
\(407\) 2.05570e69 1.44114
\(408\) −7.74637e68 −0.508867
\(409\) −5.42643e68 −0.334077 −0.167039 0.985950i \(-0.553420\pi\)
−0.167039 + 0.985950i \(0.553420\pi\)
\(410\) 7.47788e68 0.431525
\(411\) −4.99364e68 −0.270153
\(412\) −4.81537e68 −0.244261
\(413\) −2.21478e69 −1.05355
\(414\) 1.54613e68 0.0689820
\(415\) −1.71291e69 −0.716904
\(416\) −2.13886e68 −0.0839864
\(417\) 1.89705e68 0.0698994
\(418\) 8.52293e68 0.294725
\(419\) 2.80482e69 0.910403 0.455202 0.890388i \(-0.349567\pi\)
0.455202 + 0.890388i \(0.349567\pi\)
\(420\) 3.12086e69 0.950972
\(421\) 4.47945e69 1.28159 0.640795 0.767712i \(-0.278605\pi\)
0.640795 + 0.767712i \(0.278605\pi\)
\(422\) −1.93913e69 −0.520986
\(423\) 1.19885e69 0.302513
\(424\) −3.81536e68 −0.0904359
\(425\) −1.03581e70 −2.30661
\(426\) −1.66736e68 −0.0348879
\(427\) 7.87535e69 1.54857
\(428\) 1.92268e69 0.355342
\(429\) −3.93575e68 −0.0683768
\(430\) 2.14840e69 0.350914
\(431\) −1.07297e70 −1.64793 −0.823967 0.566638i \(-0.808244\pi\)
−0.823967 + 0.566638i \(0.808244\pi\)
\(432\) 5.65733e69 0.817131
\(433\) −1.28857e70 −1.75057 −0.875286 0.483606i \(-0.839327\pi\)
−0.875286 + 0.483606i \(0.839327\pi\)
\(434\) −2.56798e69 −0.328182
\(435\) 3.95908e69 0.476024
\(436\) −4.87031e69 −0.551017
\(437\) 5.35274e69 0.569925
\(438\) 7.97689e68 0.0799410
\(439\) 2.10965e69 0.199022 0.0995111 0.995036i \(-0.468272\pi\)
0.0995111 + 0.995036i \(0.468272\pi\)
\(440\) 8.46254e69 0.751631
\(441\) 7.56081e68 0.0632333
\(442\) 5.64525e68 0.0444624
\(443\) 1.77505e70 1.31678 0.658389 0.752678i \(-0.271238\pi\)
0.658389 + 0.752678i \(0.271238\pi\)
\(444\) −1.45581e70 −1.01732
\(445\) 1.63681e70 1.07760
\(446\) −3.15782e68 −0.0195891
\(447\) −1.57939e68 −0.00923293
\(448\) −9.93183e69 −0.547220
\(449\) −7.87557e69 −0.409029 −0.204515 0.978864i \(-0.565562\pi\)
−0.204515 + 0.978864i \(0.565562\pi\)
\(450\) −4.84916e69 −0.237430
\(451\) −1.88638e70 −0.870863
\(452\) 3.87514e69 0.168702
\(453\) 1.13633e69 0.0466553
\(454\) −1.29980e69 −0.0503382
\(455\) −4.73084e69 −0.172837
\(456\) −1.25549e70 −0.432759
\(457\) 3.48981e70 1.13507 0.567536 0.823349i \(-0.307897\pi\)
0.567536 + 0.823349i \(0.307897\pi\)
\(458\) −8.82014e69 −0.270733
\(459\) −5.16545e70 −1.49648
\(460\) 2.55510e70 0.698756
\(461\) 4.79728e70 1.23857 0.619286 0.785166i \(-0.287422\pi\)
0.619286 + 0.785166i \(0.287422\pi\)
\(462\) 6.30438e69 0.153684
\(463\) −5.09571e70 −1.17303 −0.586514 0.809939i \(-0.699500\pi\)
−0.586514 + 0.809939i \(0.699500\pi\)
\(464\) −1.56893e70 −0.341096
\(465\) 6.82449e70 1.40142
\(466\) 1.50506e70 0.291962
\(467\) 8.74085e70 1.60198 0.800989 0.598680i \(-0.204308\pi\)
0.800989 + 0.598680i \(0.204308\pi\)
\(468\) −3.30028e69 −0.0571525
\(469\) −8.66033e70 −1.41727
\(470\) −1.58652e70 −0.245387
\(471\) 6.70453e69 0.0980199
\(472\) 4.25307e70 0.587814
\(473\) −5.41956e70 −0.708181
\(474\) −3.86491e69 −0.0477544
\(475\) −1.67879e71 −1.96163
\(476\) 1.12922e71 1.24795
\(477\) −8.94402e69 −0.0934966
\(478\) 2.62642e70 0.259732
\(479\) −9.38882e70 −0.878455 −0.439228 0.898376i \(-0.644748\pi\)
−0.439228 + 0.898376i \(0.644748\pi\)
\(480\) −9.10491e70 −0.806089
\(481\) 2.20683e70 0.184895
\(482\) 5.43897e70 0.431291
\(483\) 3.95940e70 0.297187
\(484\) 2.76715e70 0.196621
\(485\) 2.31062e71 1.55443
\(486\) −3.98629e70 −0.253927
\(487\) 3.27176e71 1.97362 0.986810 0.161885i \(-0.0517573\pi\)
0.986810 + 0.161885i \(0.0517573\pi\)
\(488\) −1.51232e71 −0.864006
\(489\) −1.69252e71 −0.915900
\(490\) −1.00057e70 −0.0512924
\(491\) −2.76660e71 −1.34365 −0.671826 0.740709i \(-0.734490\pi\)
−0.671826 + 0.740709i \(0.734490\pi\)
\(492\) 1.33590e71 0.614751
\(493\) 1.43252e71 0.624679
\(494\) 9.14954e69 0.0378125
\(495\) 1.98380e71 0.777069
\(496\) −2.70445e71 −1.00419
\(497\) 5.05580e70 0.177970
\(498\) 2.45047e70 0.0817848
\(499\) −4.81364e71 −1.52338 −0.761692 0.647939i \(-0.775631\pi\)
−0.761692 + 0.647939i \(0.775631\pi\)
\(500\) −3.03126e71 −0.909742
\(501\) 1.75981e71 0.500919
\(502\) −8.95868e70 −0.241877
\(503\) −4.97279e71 −1.27364 −0.636822 0.771011i \(-0.719751\pi\)
−0.636822 + 0.771011i \(0.719751\pi\)
\(504\) 1.09963e71 0.267200
\(505\) 1.29626e72 2.98861
\(506\) 5.16150e70 0.112924
\(507\) 3.21670e71 0.667882
\(508\) −8.81898e69 −0.0173792
\(509\) −4.86664e71 −0.910349 −0.455174 0.890402i \(-0.650423\pi\)
−0.455174 + 0.890402i \(0.650423\pi\)
\(510\) 2.40312e71 0.426743
\(511\) −2.41877e71 −0.407794
\(512\) 6.17329e71 0.988241
\(513\) −8.37190e71 −1.27267
\(514\) −2.06250e71 −0.297764
\(515\) 3.10733e71 0.426084
\(516\) 3.83805e71 0.499912
\(517\) 4.00217e71 0.495217
\(518\) −3.53496e71 −0.415572
\(519\) −1.64938e71 −0.184241
\(520\) 9.08471e70 0.0964323
\(521\) −1.04553e72 −1.05472 −0.527358 0.849643i \(-0.676817\pi\)
−0.527358 + 0.849643i \(0.676817\pi\)
\(522\) 6.70634e70 0.0643009
\(523\) −2.01240e71 −0.183408 −0.0917042 0.995786i \(-0.529231\pi\)
−0.0917042 + 0.995786i \(0.529231\pi\)
\(524\) −7.90812e71 −0.685163
\(525\) −1.24180e72 −1.02289
\(526\) −1.74037e71 −0.136308
\(527\) 2.46931e72 1.83906
\(528\) 6.63941e71 0.470252
\(529\) −1.16032e72 −0.781633
\(530\) 1.18362e71 0.0758409
\(531\) 9.97011e71 0.607708
\(532\) 1.83019e72 1.06130
\(533\) −2.02506e71 −0.111730
\(534\) −2.34159e71 −0.122933
\(535\) −1.24069e72 −0.619853
\(536\) 1.66306e72 0.790752
\(537\) 2.35875e72 1.06749
\(538\) 3.73323e71 0.160825
\(539\) 2.52406e71 0.103514
\(540\) −3.99628e72 −1.56035
\(541\) −2.67923e72 −0.996053 −0.498026 0.867162i \(-0.665942\pi\)
−0.498026 + 0.867162i \(0.665942\pi\)
\(542\) 7.02090e71 0.248549
\(543\) −2.01528e72 −0.679422
\(544\) −3.29444e72 −1.05782
\(545\) 3.14278e72 0.961186
\(546\) 6.76788e70 0.0197173
\(547\) 3.99196e72 1.10795 0.553977 0.832532i \(-0.313110\pi\)
0.553977 + 0.832532i \(0.313110\pi\)
\(548\) −1.39789e72 −0.369647
\(549\) −3.54519e72 −0.893248
\(550\) −1.61882e72 −0.388675
\(551\) 2.32175e72 0.531250
\(552\) −7.60330e71 −0.165812
\(553\) 1.17193e72 0.243604
\(554\) 7.25284e71 0.143714
\(555\) 9.39427e72 1.77459
\(556\) 5.31047e71 0.0956425
\(557\) −4.75050e72 −0.815786 −0.407893 0.913030i \(-0.633736\pi\)
−0.407893 + 0.913030i \(0.633736\pi\)
\(558\) 1.15601e72 0.189302
\(559\) −5.81801e71 −0.0908577
\(560\) 7.98070e72 1.18866
\(561\) −6.06215e72 −0.861213
\(562\) −7.18488e71 −0.0973660
\(563\) 2.08122e72 0.269058 0.134529 0.990910i \(-0.457048\pi\)
0.134529 + 0.990910i \(0.457048\pi\)
\(564\) −2.83427e72 −0.349579
\(565\) −2.50061e72 −0.294280
\(566\) −1.64157e72 −0.184342
\(567\) −1.43788e72 −0.154089
\(568\) −9.70874e71 −0.0992961
\(569\) −8.16033e72 −0.796586 −0.398293 0.917258i \(-0.630397\pi\)
−0.398293 + 0.917258i \(0.630397\pi\)
\(570\) 3.89487e72 0.362918
\(571\) −5.30282e72 −0.471683 −0.235841 0.971792i \(-0.575785\pi\)
−0.235841 + 0.971792i \(0.575785\pi\)
\(572\) −1.10175e72 −0.0935592
\(573\) −1.57884e72 −0.128009
\(574\) 3.24380e72 0.251124
\(575\) −1.01668e73 −0.751601
\(576\) 4.47094e72 0.315648
\(577\) 2.14077e73 1.44348 0.721740 0.692164i \(-0.243343\pi\)
0.721740 + 0.692164i \(0.243343\pi\)
\(578\) 4.46741e72 0.287718
\(579\) 2.79022e72 0.171655
\(580\) 1.10828e73 0.651338
\(581\) −7.43039e72 −0.417200
\(582\) −3.30554e72 −0.177330
\(583\) −2.98582e72 −0.153055
\(584\) 4.64481e72 0.227524
\(585\) 2.12965e72 0.0996959
\(586\) −3.06907e72 −0.137316
\(587\) −1.26033e73 −0.538981 −0.269490 0.963003i \(-0.586855\pi\)
−0.269490 + 0.963003i \(0.586855\pi\)
\(588\) −1.78750e72 −0.0730713
\(589\) 4.00214e73 1.56400
\(590\) −1.31941e73 −0.492950
\(591\) 3.40439e73 1.21610
\(592\) −3.72282e73 −1.27159
\(593\) −3.38540e73 −1.10576 −0.552880 0.833261i \(-0.686471\pi\)
−0.552880 + 0.833261i \(0.686471\pi\)
\(594\) −8.07281e72 −0.252164
\(595\) −7.28681e73 −2.17690
\(596\) −4.42123e71 −0.0126333
\(597\) −2.18131e72 −0.0596207
\(598\) 5.54098e71 0.0144879
\(599\) 4.50976e73 1.12809 0.564043 0.825745i \(-0.309245\pi\)
0.564043 + 0.825745i \(0.309245\pi\)
\(600\) 2.38465e73 0.570710
\(601\) 5.21159e73 1.19343 0.596714 0.802454i \(-0.296473\pi\)
0.596714 + 0.802454i \(0.296473\pi\)
\(602\) 9.31944e72 0.204213
\(603\) 3.89856e73 0.817514
\(604\) 3.18096e72 0.0638379
\(605\) −1.78562e73 −0.342983
\(606\) −1.85441e73 −0.340942
\(607\) 1.40353e72 0.0247015 0.0123507 0.999924i \(-0.496069\pi\)
0.0123507 + 0.999924i \(0.496069\pi\)
\(608\) −5.33947e73 −0.899607
\(609\) 1.71739e73 0.277020
\(610\) 4.69159e73 0.724569
\(611\) 4.29641e72 0.0635351
\(612\) −5.08334e73 −0.719841
\(613\) 9.09089e73 1.23283 0.616416 0.787421i \(-0.288584\pi\)
0.616416 + 0.787421i \(0.288584\pi\)
\(614\) −2.64727e72 −0.0343824
\(615\) −8.62049e73 −1.07236
\(616\) 3.67093e73 0.437409
\(617\) −1.15906e74 −1.32297 −0.661486 0.749957i \(-0.730074\pi\)
−0.661486 + 0.749957i \(0.730074\pi\)
\(618\) −4.44531e72 −0.0486079
\(619\) −1.53802e74 −1.61124 −0.805621 0.592432i \(-0.798168\pi\)
−0.805621 + 0.592432i \(0.798168\pi\)
\(620\) 1.91040e74 1.91754
\(621\) −5.07004e73 −0.487623
\(622\) −5.39760e73 −0.497457
\(623\) 7.10024e73 0.627104
\(624\) 7.12755e72 0.0603321
\(625\) −2.64476e72 −0.0214568
\(626\) 2.17506e73 0.169142
\(627\) −9.82523e73 −0.732407
\(628\) 1.87682e73 0.134119
\(629\) 3.39914e74 2.32877
\(630\) −3.41133e73 −0.224078
\(631\) −1.90940e74 −1.20259 −0.601297 0.799025i \(-0.705349\pi\)
−0.601297 + 0.799025i \(0.705349\pi\)
\(632\) −2.25047e73 −0.135916
\(633\) 2.23542e74 1.29468
\(634\) 4.88941e73 0.271576
\(635\) 5.69083e72 0.0303160
\(636\) 2.11451e73 0.108043
\(637\) 2.70963e72 0.0132805
\(638\) 2.23881e73 0.105261
\(639\) −2.27593e73 −0.102657
\(640\) −3.34454e74 −1.44733
\(641\) −2.13596e74 −0.886860 −0.443430 0.896309i \(-0.646239\pi\)
−0.443430 + 0.896309i \(0.646239\pi\)
\(642\) 1.77492e73 0.0707132
\(643\) 1.06521e74 0.407235 0.203617 0.979051i \(-0.434730\pi\)
0.203617 + 0.979051i \(0.434730\pi\)
\(644\) 1.10837e74 0.406638
\(645\) −2.47667e74 −0.872038
\(646\) 1.40928e74 0.476252
\(647\) −3.74264e74 −1.21399 −0.606995 0.794706i \(-0.707625\pi\)
−0.606995 + 0.794706i \(0.707625\pi\)
\(648\) 2.76118e73 0.0859721
\(649\) 3.32836e74 0.994824
\(650\) −1.73783e73 −0.0498660
\(651\) 2.96037e74 0.815549
\(652\) −4.73791e74 −1.25322
\(653\) −5.40144e73 −0.137186 −0.0685930 0.997645i \(-0.521851\pi\)
−0.0685930 + 0.997645i \(0.521851\pi\)
\(654\) −4.49603e73 −0.109653
\(655\) 5.10306e74 1.19519
\(656\) 3.41618e74 0.768404
\(657\) 1.08884e74 0.235224
\(658\) −6.88210e73 −0.142802
\(659\) 7.60313e74 1.51541 0.757703 0.652599i \(-0.226322\pi\)
0.757703 + 0.652599i \(0.226322\pi\)
\(660\) −4.69002e74 −0.897967
\(661\) −2.63286e72 −0.00484272 −0.00242136 0.999997i \(-0.500771\pi\)
−0.00242136 + 0.999997i \(0.500771\pi\)
\(662\) −9.62818e73 −0.170140
\(663\) −6.50784e73 −0.110491
\(664\) 1.42687e74 0.232772
\(665\) −1.18101e75 −1.85131
\(666\) 1.59131e74 0.239711
\(667\) 1.40606e74 0.203549
\(668\) 4.92630e74 0.685401
\(669\) 3.64033e73 0.0486798
\(670\) −5.15923e74 −0.663136
\(671\) −1.18351e75 −1.46226
\(672\) −3.94958e74 −0.469100
\(673\) −6.59799e74 −0.753378 −0.376689 0.926340i \(-0.622937\pi\)
−0.376689 + 0.926340i \(0.622937\pi\)
\(674\) 2.42038e74 0.265703
\(675\) 1.59013e75 1.67835
\(676\) 9.00460e74 0.913855
\(677\) −9.68261e74 −0.944915 −0.472457 0.881354i \(-0.656633\pi\)
−0.472457 + 0.881354i \(0.656633\pi\)
\(678\) 3.57734e73 0.0335717
\(679\) 1.00231e75 0.904596
\(680\) 1.39930e75 1.21457
\(681\) 1.49841e74 0.125093
\(682\) 3.85916e74 0.309890
\(683\) −2.38917e75 −1.84543 −0.922715 0.385483i \(-0.874035\pi\)
−0.922715 + 0.385483i \(0.874035\pi\)
\(684\) −8.23883e74 −0.612180
\(685\) 9.02047e74 0.644806
\(686\) −4.15530e74 −0.285768
\(687\) 1.01679e75 0.672784
\(688\) 9.81470e74 0.624861
\(689\) −3.20534e73 −0.0196365
\(690\) 2.35874e74 0.139053
\(691\) −2.74982e74 −0.156004 −0.0780020 0.996953i \(-0.524854\pi\)
−0.0780020 + 0.996953i \(0.524854\pi\)
\(692\) −4.61717e74 −0.252095
\(693\) 8.60544e74 0.452212
\(694\) −7.10298e74 −0.359265
\(695\) −3.42681e74 −0.166837
\(696\) −3.29794e74 −0.154560
\(697\) −3.11916e75 −1.40724
\(698\) 3.06570e74 0.133156
\(699\) −1.73503e75 −0.725540
\(700\) −3.47621e75 −1.39961
\(701\) 5.35713e74 0.207685 0.103842 0.994594i \(-0.466886\pi\)
0.103842 + 0.994594i \(0.466886\pi\)
\(702\) −8.66633e73 −0.0323520
\(703\) 5.50916e75 1.98047
\(704\) 1.49255e75 0.516719
\(705\) 1.82894e75 0.609800
\(706\) −7.10235e74 −0.228075
\(707\) 5.62298e75 1.73921
\(708\) −2.35709e75 −0.702256
\(709\) −3.32161e75 −0.953287 −0.476644 0.879097i \(-0.658147\pi\)
−0.476644 + 0.879097i \(0.658147\pi\)
\(710\) 3.01190e74 0.0832711
\(711\) −5.27559e74 −0.140516
\(712\) −1.36347e75 −0.349885
\(713\) 2.42371e75 0.599249
\(714\) 1.04244e75 0.248342
\(715\) 7.10950e74 0.163203
\(716\) 6.60292e75 1.46063
\(717\) −3.02773e75 −0.645446
\(718\) 8.28737e74 0.170262
\(719\) −6.15825e75 −1.21939 −0.609694 0.792637i \(-0.708708\pi\)
−0.609694 + 0.792637i \(0.708708\pi\)
\(720\) −3.59261e75 −0.685645
\(721\) 1.34792e75 0.247958
\(722\) 7.48536e74 0.132732
\(723\) −6.27004e75 −1.07178
\(724\) −5.64143e75 −0.929645
\(725\) −4.40987e75 −0.700597
\(726\) 2.55449e74 0.0391277
\(727\) 1.07750e76 1.59131 0.795657 0.605747i \(-0.207126\pi\)
0.795657 + 0.605747i \(0.207126\pi\)
\(728\) 3.94082e74 0.0561184
\(729\) 5.78933e75 0.794967
\(730\) −1.44094e75 −0.190805
\(731\) −8.96136e75 −1.14436
\(732\) 8.38139e75 1.03222
\(733\) −1.46870e75 −0.174453 −0.0872263 0.996189i \(-0.527800\pi\)
−0.0872263 + 0.996189i \(0.527800\pi\)
\(734\) 1.58923e75 0.182071
\(735\) 1.15346e75 0.127464
\(736\) −3.23359e75 −0.344686
\(737\) 1.30147e76 1.33828
\(738\) −1.46024e75 −0.144854
\(739\) −7.45777e75 −0.713726 −0.356863 0.934157i \(-0.616154\pi\)
−0.356863 + 0.934157i \(0.616154\pi\)
\(740\) 2.62977e76 2.42816
\(741\) −1.05476e75 −0.0939660
\(742\) 5.13440e74 0.0441353
\(743\) −2.17472e76 −1.80385 −0.901923 0.431897i \(-0.857845\pi\)
−0.901923 + 0.431897i \(0.857845\pi\)
\(744\) −5.68485e75 −0.455026
\(745\) 2.85299e74 0.0220374
\(746\) 2.80789e75 0.209316
\(747\) 3.34488e75 0.240649
\(748\) −1.69699e76 −1.17839
\(749\) −5.38195e75 −0.360721
\(750\) −2.79831e75 −0.181039
\(751\) 8.74960e75 0.546424 0.273212 0.961954i \(-0.411914\pi\)
0.273212 + 0.961954i \(0.411914\pi\)
\(752\) −7.24783e75 −0.436953
\(753\) 1.03276e76 0.601078
\(754\) 2.40341e74 0.0135047
\(755\) −2.05265e75 −0.111358
\(756\) −1.73353e76 −0.908039
\(757\) 2.13811e76 1.08141 0.540705 0.841212i \(-0.318158\pi\)
0.540705 + 0.841212i \(0.318158\pi\)
\(758\) −7.25663e75 −0.354406
\(759\) −5.95018e75 −0.280623
\(760\) 2.26791e76 1.03292
\(761\) −2.22724e76 −0.979658 −0.489829 0.871819i \(-0.662941\pi\)
−0.489829 + 0.871819i \(0.662941\pi\)
\(762\) −8.14123e73 −0.00345847
\(763\) 1.36330e76 0.559358
\(764\) −4.41970e75 −0.175154
\(765\) 3.28025e76 1.25568
\(766\) 1.19381e76 0.441442
\(767\) 3.57307e75 0.127633
\(768\) −6.63181e75 −0.228855
\(769\) −1.21344e75 −0.0404548 −0.0202274 0.999795i \(-0.506439\pi\)
−0.0202274 + 0.999795i \(0.506439\pi\)
\(770\) −1.13882e76 −0.366817
\(771\) 2.37765e76 0.739958
\(772\) 7.81074e75 0.234873
\(773\) 8.70709e75 0.252998 0.126499 0.991967i \(-0.459626\pi\)
0.126499 + 0.991967i \(0.459626\pi\)
\(774\) −4.19527e75 −0.117794
\(775\) −7.60154e76 −2.06256
\(776\) −1.92476e76 −0.504709
\(777\) 4.07510e76 1.03272
\(778\) −8.64098e75 −0.211643
\(779\) −5.05539e76 −1.19677
\(780\) −5.03483e75 −0.115207
\(781\) −7.59785e75 −0.168050
\(782\) 8.53465e75 0.182476
\(783\) −2.19914e76 −0.454533
\(784\) −4.57101e75 −0.0913349
\(785\) −1.21110e76 −0.233956
\(786\) −7.30038e75 −0.136348
\(787\) 7.21858e76 1.30353 0.651766 0.758420i \(-0.274029\pi\)
0.651766 + 0.758420i \(0.274029\pi\)
\(788\) 9.53000e76 1.66398
\(789\) 2.00630e76 0.338731
\(790\) 6.98155e75 0.113981
\(791\) −1.08473e76 −0.171255
\(792\) −1.65252e76 −0.252307
\(793\) −1.27052e76 −0.187604
\(794\) 7.47084e75 0.106691
\(795\) −1.36448e76 −0.188468
\(796\) −6.10620e75 −0.0815783
\(797\) −7.22104e76 −0.933155 −0.466578 0.884480i \(-0.654513\pi\)
−0.466578 + 0.884480i \(0.654513\pi\)
\(798\) 1.68954e76 0.211199
\(799\) 6.61767e76 0.800231
\(800\) 1.01416e77 1.18638
\(801\) −3.19626e76 −0.361727
\(802\) 1.20632e75 0.0132082
\(803\) 3.63493e76 0.385065
\(804\) −9.21682e76 −0.944704
\(805\) −7.15223e76 −0.709334
\(806\) 4.14289e75 0.0397580
\(807\) −4.30366e76 −0.399659
\(808\) −1.07979e77 −0.970372
\(809\) −1.58042e77 −1.37447 −0.687235 0.726435i \(-0.741176\pi\)
−0.687235 + 0.726435i \(0.741176\pi\)
\(810\) −8.56590e75 −0.0720974
\(811\) 1.16585e77 0.949707 0.474853 0.880065i \(-0.342501\pi\)
0.474853 + 0.880065i \(0.342501\pi\)
\(812\) 4.80755e76 0.379044
\(813\) −8.09369e76 −0.617656
\(814\) 5.31234e76 0.392409
\(815\) 3.05735e77 2.18609
\(816\) 1.09784e77 0.759889
\(817\) −1.45241e77 −0.973208
\(818\) −1.40230e76 −0.0909658
\(819\) 9.23812e75 0.0580177
\(820\) −2.41316e77 −1.46730
\(821\) 2.60575e77 1.53405 0.767023 0.641619i \(-0.221737\pi\)
0.767023 + 0.641619i \(0.221737\pi\)
\(822\) −1.29046e76 −0.0735598
\(823\) 3.34341e76 0.184541 0.0922707 0.995734i \(-0.470588\pi\)
0.0922707 + 0.995734i \(0.470588\pi\)
\(824\) −2.58843e76 −0.138345
\(825\) 1.86617e77 0.965878
\(826\) −5.72343e76 −0.286870
\(827\) −1.56452e77 −0.759426 −0.379713 0.925104i \(-0.623977\pi\)
−0.379713 + 0.925104i \(0.623977\pi\)
\(828\) −4.98945e76 −0.234557
\(829\) 2.97591e77 1.35495 0.677477 0.735544i \(-0.263073\pi\)
0.677477 + 0.735544i \(0.263073\pi\)
\(830\) −4.42651e76 −0.195206
\(831\) −8.36107e76 −0.357137
\(832\) 1.60229e76 0.0662937
\(833\) 4.17359e76 0.167269
\(834\) 4.90236e75 0.0190329
\(835\) −3.17891e77 −1.19560
\(836\) −2.75041e77 −1.00214
\(837\) −3.79078e77 −1.33815
\(838\) 7.24822e76 0.247893
\(839\) 2.75386e77 0.912535 0.456267 0.889843i \(-0.349186\pi\)
0.456267 + 0.889843i \(0.349186\pi\)
\(840\) 1.67757e77 0.538616
\(841\) −2.60448e77 −0.810264
\(842\) 1.15758e77 0.348964
\(843\) 8.28273e76 0.241959
\(844\) 6.25769e77 1.77149
\(845\) −5.81062e77 −1.59411
\(846\) 3.09806e76 0.0823713
\(847\) −7.74579e76 −0.199598
\(848\) 5.40725e76 0.135048
\(849\) 1.89240e77 0.458099
\(850\) −2.67675e77 −0.628067
\(851\) 3.33636e77 0.758821
\(852\) 5.38068e76 0.118628
\(853\) 6.83575e77 1.46096 0.730478 0.682936i \(-0.239297\pi\)
0.730478 + 0.682936i \(0.239297\pi\)
\(854\) 2.03515e77 0.421660
\(855\) 5.31647e77 1.06788
\(856\) 1.03350e77 0.201260
\(857\) −6.22171e77 −1.17467 −0.587337 0.809342i \(-0.699824\pi\)
−0.587337 + 0.809342i \(0.699824\pi\)
\(858\) −1.01708e76 −0.0186183
\(859\) −4.11261e77 −0.729960 −0.364980 0.931015i \(-0.618924\pi\)
−0.364980 + 0.931015i \(0.618924\pi\)
\(860\) −6.93302e77 −1.19320
\(861\) −3.73945e77 −0.624057
\(862\) −2.77277e77 −0.448716
\(863\) −3.72761e77 −0.584984 −0.292492 0.956268i \(-0.594484\pi\)
−0.292492 + 0.956268i \(0.594484\pi\)
\(864\) 5.05747e77 0.769697
\(865\) 2.97943e77 0.439751
\(866\) −3.32993e77 −0.476663
\(867\) −5.15002e77 −0.714995
\(868\) 8.28706e77 1.11591
\(869\) −1.76117e77 −0.230026
\(870\) 1.02311e77 0.129616
\(871\) 1.39716e77 0.171698
\(872\) −2.61796e77 −0.312087
\(873\) −4.51204e77 −0.521790
\(874\) 1.38325e77 0.155185
\(875\) 8.48510e77 0.923514
\(876\) −2.57420e77 −0.271821
\(877\) 4.87970e77 0.499924 0.249962 0.968256i \(-0.419582\pi\)
0.249962 + 0.968256i \(0.419582\pi\)
\(878\) 5.45177e76 0.0541917
\(879\) 3.53803e77 0.341237
\(880\) −1.19934e78 −1.12241
\(881\) 1.30154e78 1.18194 0.590970 0.806693i \(-0.298745\pi\)
0.590970 + 0.806693i \(0.298745\pi\)
\(882\) 1.95387e76 0.0172178
\(883\) 3.47958e77 0.297556 0.148778 0.988871i \(-0.452466\pi\)
0.148778 + 0.988871i \(0.452466\pi\)
\(884\) −1.82176e77 −0.151184
\(885\) 1.52102e78 1.22501
\(886\) 4.58710e77 0.358545
\(887\) −1.85101e78 −1.40421 −0.702107 0.712071i \(-0.747757\pi\)
−0.702107 + 0.712071i \(0.747757\pi\)
\(888\) −7.82549e77 −0.576193
\(889\) 2.46861e76 0.0176423
\(890\) 4.22984e77 0.293419
\(891\) 2.16084e77 0.145500
\(892\) 1.01905e77 0.0666080
\(893\) 1.07256e78 0.680546
\(894\) −4.08146e75 −0.00251403
\(895\) −4.26082e78 −2.54790
\(896\) −1.45081e78 −0.842267
\(897\) −6.38764e76 −0.0360032
\(898\) −2.03521e77 −0.111374
\(899\) 1.05128e78 0.558584
\(900\) 1.56486e78 0.807325
\(901\) −4.93712e77 −0.247324
\(902\) −4.87478e77 −0.237127
\(903\) −1.07435e78 −0.507479
\(904\) 2.08302e77 0.0955499
\(905\) 3.64038e78 1.62166
\(906\) 2.93650e76 0.0127038
\(907\) 1.94140e78 0.815686 0.407843 0.913052i \(-0.366281\pi\)
0.407843 + 0.913052i \(0.366281\pi\)
\(908\) 4.19456e77 0.171163
\(909\) −2.53126e78 −1.00321
\(910\) −1.22254e77 −0.0470617
\(911\) 6.52188e75 0.00243857 0.00121929 0.999999i \(-0.499612\pi\)
0.00121929 + 0.999999i \(0.499612\pi\)
\(912\) 1.77933e78 0.646237
\(913\) 1.11664e78 0.393946
\(914\) 9.01838e77 0.309068
\(915\) −5.40846e78 −1.80059
\(916\) 2.84632e78 0.920563
\(917\) 2.21364e78 0.695536
\(918\) −1.33486e78 −0.407477
\(919\) 1.20106e78 0.356208 0.178104 0.984012i \(-0.443004\pi\)
0.178104 + 0.984012i \(0.443004\pi\)
\(920\) 1.37345e78 0.395764
\(921\) 3.05177e77 0.0854421
\(922\) 1.23971e78 0.337250
\(923\) −8.15645e76 −0.0215604
\(924\) −2.03447e78 −0.522568
\(925\) −1.04639e79 −2.61179
\(926\) −1.31683e78 −0.319404
\(927\) −6.06782e77 −0.143027
\(928\) −1.40257e78 −0.321295
\(929\) −1.35743e78 −0.302205 −0.151103 0.988518i \(-0.548282\pi\)
−0.151103 + 0.988518i \(0.548282\pi\)
\(930\) 1.76359e78 0.381591
\(931\) 6.76434e77 0.142252
\(932\) −4.85692e78 −0.992748
\(933\) 6.22235e78 1.23621
\(934\) 2.25881e78 0.436202
\(935\) 1.09506e79 2.05556
\(936\) −1.77401e77 −0.0323703
\(937\) −7.78543e77 −0.138097 −0.0690483 0.997613i \(-0.521996\pi\)
−0.0690483 + 0.997613i \(0.521996\pi\)
\(938\) −2.23800e78 −0.385909
\(939\) −2.50741e78 −0.420326
\(940\) 5.11980e78 0.834382
\(941\) −8.40474e77 −0.133168 −0.0665839 0.997781i \(-0.521210\pi\)
−0.0665839 + 0.997781i \(0.521210\pi\)
\(942\) 1.73259e77 0.0266898
\(943\) −3.06155e78 −0.458545
\(944\) −6.02759e78 −0.877780
\(945\) 1.11864e79 1.58397
\(946\) −1.40052e78 −0.192830
\(947\) 6.73558e78 0.901780 0.450890 0.892579i \(-0.351107\pi\)
0.450890 + 0.892579i \(0.351107\pi\)
\(948\) 1.24723e78 0.162378
\(949\) 3.90217e77 0.0494028
\(950\) −4.33834e78 −0.534132
\(951\) −5.63651e78 −0.674880
\(952\) 6.06996e78 0.706817
\(953\) −1.66845e79 −1.88952 −0.944758 0.327768i \(-0.893704\pi\)
−0.944758 + 0.327768i \(0.893704\pi\)
\(954\) −2.31131e77 −0.0254582
\(955\) 2.85201e78 0.305535
\(956\) −8.47563e78 −0.883157
\(957\) −2.58090e78 −0.261580
\(958\) −2.42626e78 −0.239194
\(959\) 3.91296e78 0.375242
\(960\) 6.82077e78 0.636277
\(961\) 7.10190e78 0.644473
\(962\) 5.70290e77 0.0503450
\(963\) 2.42275e78 0.208072
\(964\) −1.75519e79 −1.46650
\(965\) −5.04022e78 −0.409709
\(966\) 1.02319e78 0.0809211
\(967\) 2.07490e79 1.59660 0.798301 0.602259i \(-0.205733\pi\)
0.798301 + 0.602259i \(0.205733\pi\)
\(968\) 1.48744e78 0.111363
\(969\) −1.62462e79 −1.18351
\(970\) 5.97110e78 0.423256
\(971\) −7.04775e78 −0.486117 −0.243059 0.970012i \(-0.578151\pi\)
−0.243059 + 0.970012i \(0.578151\pi\)
\(972\) 1.28640e79 0.863418
\(973\) −1.48651e78 −0.0970904
\(974\) 8.45487e78 0.537396
\(975\) 2.00338e78 0.123920
\(976\) 2.14330e79 1.29022
\(977\) 1.67318e79 0.980247 0.490123 0.871653i \(-0.336952\pi\)
0.490123 + 0.871653i \(0.336952\pi\)
\(978\) −4.37380e78 −0.249390
\(979\) −1.06702e79 −0.592151
\(980\) 3.22892e78 0.174408
\(981\) −6.13705e78 −0.322650
\(982\) −7.14945e78 −0.365863
\(983\) −5.74735e78 −0.286286 −0.143143 0.989702i \(-0.545721\pi\)
−0.143143 + 0.989702i \(0.545721\pi\)
\(984\) 7.18093e78 0.348185
\(985\) −6.14966e79 −2.90262
\(986\) 3.70191e78 0.170094
\(987\) 7.93368e78 0.354871
\(988\) −2.95262e78 −0.128573
\(989\) −8.79585e78 −0.372886
\(990\) 5.12653e78 0.211588
\(991\) 2.54858e79 1.02411 0.512055 0.858953i \(-0.328885\pi\)
0.512055 + 0.858953i \(0.328885\pi\)
\(992\) −2.41770e79 −0.945894
\(993\) 1.10994e79 0.422808
\(994\) 1.30652e78 0.0484593
\(995\) 3.94029e78 0.142304
\(996\) −7.90784e78 −0.278090
\(997\) 4.70743e79 1.61199 0.805994 0.591924i \(-0.201631\pi\)
0.805994 + 0.591924i \(0.201631\pi\)
\(998\) −1.24394e79 −0.414802
\(999\) −5.21820e79 −1.69448
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.54.a.a.1.3 4
3.2 odd 2 9.54.a.b.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.54.a.a.1.3 4 1.1 even 1 trivial
9.54.a.b.1.2 4 3.2 odd 2