Properties

Label 1.48.a.a.1.3
Level $1$
Weight $48$
Character 1.1
Self dual yes
Analytic conductor $13.991$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 48 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.9907662655\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 832803191366 x^{2} + 3710135215485780 x + 13175318942671469337000\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{20}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(129356.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.55092e6 q^{2} -2.21918e11 q^{3} -1.20027e14 q^{4} -3.08341e16 q^{5} -1.00993e18 q^{6} +1.11073e20 q^{7} -1.18672e21 q^{8} +2.26588e22 q^{9} +O(q^{10})\) \(q+4.55092e6 q^{2} -2.21918e11 q^{3} -1.20027e14 q^{4} -3.08341e16 q^{5} -1.00993e18 q^{6} +1.11073e20 q^{7} -1.18672e21 q^{8} +2.26588e22 q^{9} -1.40324e23 q^{10} -1.19449e24 q^{11} +2.66361e25 q^{12} -2.71503e24 q^{13} +5.05485e26 q^{14} +6.84264e27 q^{15} +1.14916e28 q^{16} +1.17417e29 q^{17} +1.03118e29 q^{18} -1.65620e30 q^{19} +3.70091e30 q^{20} -2.46491e31 q^{21} -5.43602e30 q^{22} +5.41759e31 q^{23} +2.63354e32 q^{24} +2.40198e32 q^{25} -1.23559e31 q^{26} +8.72142e32 q^{27} -1.33317e34 q^{28} -1.03639e34 q^{29} +3.11403e34 q^{30} -3.80854e34 q^{31} +2.19313e35 q^{32} +2.65078e35 q^{33} +5.34356e35 q^{34} -3.42483e36 q^{35} -2.71966e36 q^{36} +8.41184e36 q^{37} -7.53724e36 q^{38} +6.02513e35 q^{39} +3.65913e37 q^{40} +7.68510e37 q^{41} -1.12176e38 q^{42} -2.17109e38 q^{43} +1.43370e38 q^{44} -6.98663e38 q^{45} +2.46550e38 q^{46} +2.73873e39 q^{47} -2.55019e39 q^{48} +7.09387e39 q^{49} +1.09312e39 q^{50} -2.60570e40 q^{51} +3.25875e38 q^{52} +8.29394e39 q^{53} +3.96905e39 q^{54} +3.68309e40 q^{55} -1.31812e41 q^{56} +3.67541e41 q^{57} -4.71655e40 q^{58} +7.09596e40 q^{59} -8.21298e41 q^{60} -6.43092e41 q^{61} -1.73324e41 q^{62} +2.51678e42 q^{63} -6.19220e41 q^{64} +8.37153e40 q^{65} +1.20635e42 q^{66} +1.19612e43 q^{67} -1.40932e43 q^{68} -1.20226e43 q^{69} -1.55862e43 q^{70} +2.64034e43 q^{71} -2.68896e43 q^{72} +3.87700e43 q^{73} +3.82817e43 q^{74} -5.33042e43 q^{75} +1.98788e44 q^{76} -1.32675e44 q^{77} +2.74199e42 q^{78} -1.22812e44 q^{79} -3.54332e44 q^{80} -7.96015e44 q^{81} +3.49743e44 q^{82} +1.65007e45 q^{83} +2.95855e45 q^{84} -3.62045e45 q^{85} -9.88045e44 q^{86} +2.29995e45 q^{87} +1.41752e45 q^{88} -6.00200e45 q^{89} -3.17956e45 q^{90} -3.01566e44 q^{91} -6.50255e45 q^{92} +8.45183e45 q^{93} +1.24637e46 q^{94} +5.10674e46 q^{95} -4.86695e46 q^{96} -1.75152e46 q^{97} +3.22837e46 q^{98} -2.70656e46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + 2392716988073784337920q^{8} - 17071972417358142200172q^{9} + O(q^{10}) \) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + \)\(23\!\cdots\!20\)\(q^{8} - \)\(17\!\cdots\!72\)\(q^{9} + \)\(16\!\cdots\!00\)\(q^{10} - \)\(19\!\cdots\!12\)\(q^{11} + \)\(50\!\cdots\!20\)\(q^{12} + \)\(12\!\cdots\!20\)\(q^{13} + \)\(34\!\cdots\!04\)\(q^{14} + \)\(12\!\cdots\!00\)\(q^{15} + \)\(12\!\cdots\!84\)\(q^{16} + \)\(21\!\cdots\!80\)\(q^{17} + \)\(40\!\cdots\!60\)\(q^{18} - \)\(10\!\cdots\!40\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(26\!\cdots\!12\)\(q^{21} - \)\(79\!\cdots\!80\)\(q^{22} + \)\(13\!\cdots\!80\)\(q^{23} + \)\(11\!\cdots\!80\)\(q^{24} + \)\(10\!\cdots\!00\)\(q^{25} + \)\(22\!\cdots\!88\)\(q^{26} - \)\(73\!\cdots\!20\)\(q^{27} - \)\(36\!\cdots\!80\)\(q^{28} - \)\(22\!\cdots\!60\)\(q^{29} - \)\(25\!\cdots\!00\)\(q^{30} + \)\(75\!\cdots\!48\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(26\!\cdots\!20\)\(q^{33} - \)\(12\!\cdots\!16\)\(q^{34} - \)\(13\!\cdots\!00\)\(q^{35} - \)\(13\!\cdots\!36\)\(q^{36} - \)\(11\!\cdots\!60\)\(q^{37} + \)\(29\!\cdots\!80\)\(q^{38} + \)\(39\!\cdots\!36\)\(q^{39} + \)\(70\!\cdots\!00\)\(q^{40} + \)\(13\!\cdots\!28\)\(q^{41} - \)\(10\!\cdots\!20\)\(q^{42} - \)\(44\!\cdots\!00\)\(q^{43} - \)\(15\!\cdots\!56\)\(q^{44} + \)\(86\!\cdots\!00\)\(q^{45} + \)\(12\!\cdots\!68\)\(q^{46} + \)\(20\!\cdots\!20\)\(q^{47} + \)\(10\!\cdots\!80\)\(q^{48} + \)\(91\!\cdots\!72\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(18\!\cdots\!52\)\(q^{51} - \)\(55\!\cdots\!00\)\(q^{52} + \)\(29\!\cdots\!60\)\(q^{53} - \)\(11\!\cdots\!40\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} + \)\(27\!\cdots\!40\)\(q^{56} + \)\(55\!\cdots\!60\)\(q^{57} - \)\(73\!\cdots\!80\)\(q^{58} + \)\(47\!\cdots\!80\)\(q^{59} - \)\(21\!\cdots\!00\)\(q^{60} + \)\(62\!\cdots\!88\)\(q^{61} - \)\(68\!\cdots\!80\)\(q^{62} + \)\(58\!\cdots\!40\)\(q^{63} + \)\(55\!\cdots\!72\)\(q^{64} + \)\(12\!\cdots\!00\)\(q^{65} - \)\(89\!\cdots\!24\)\(q^{66} + \)\(18\!\cdots\!80\)\(q^{67} - \)\(27\!\cdots\!40\)\(q^{68} - \)\(20\!\cdots\!04\)\(q^{69} - \)\(97\!\cdots\!00\)\(q^{70} + \)\(22\!\cdots\!68\)\(q^{71} - \)\(17\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!80\)\(q^{73} + \)\(18\!\cdots\!44\)\(q^{74} + \)\(32\!\cdots\!00\)\(q^{75} + \)\(35\!\cdots\!80\)\(q^{76} - \)\(26\!\cdots\!00\)\(q^{77} - \)\(49\!\cdots\!00\)\(q^{78} - \)\(13\!\cdots\!60\)\(q^{79} - \)\(94\!\cdots\!00\)\(q^{80} - \)\(10\!\cdots\!16\)\(q^{81} + \)\(38\!\cdots\!20\)\(q^{82} - \)\(14\!\cdots\!60\)\(q^{83} + \)\(52\!\cdots\!44\)\(q^{84} - \)\(10\!\cdots\!00\)\(q^{85} + \)\(95\!\cdots\!28\)\(q^{86} - \)\(43\!\cdots\!60\)\(q^{87} - \)\(15\!\cdots\!60\)\(q^{88} - \)\(79\!\cdots\!80\)\(q^{89} - \)\(16\!\cdots\!00\)\(q^{90} + \)\(53\!\cdots\!68\)\(q^{91} + \)\(13\!\cdots\!80\)\(q^{92} + \)\(10\!\cdots\!20\)\(q^{93} + \)\(34\!\cdots\!24\)\(q^{94} + \)\(75\!\cdots\!00\)\(q^{95} + \)\(64\!\cdots\!28\)\(q^{96} + \)\(95\!\cdots\!20\)\(q^{97} - \)\(29\!\cdots\!20\)\(q^{98} + \)\(53\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.55092e6 0.383614 0.191807 0.981433i \(-0.438565\pi\)
0.191807 + 0.981433i \(0.438565\pi\)
\(3\) −2.21918e11 −1.36095 −0.680476 0.732770i \(-0.738227\pi\)
−0.680476 + 0.732770i \(0.738227\pi\)
\(4\) −1.20027e14 −0.852840
\(5\) −3.08341e16 −1.15674 −0.578370 0.815774i \(-0.696311\pi\)
−0.578370 + 0.815774i \(0.696311\pi\)
\(6\) −1.00993e18 −0.522081
\(7\) 1.11073e20 1.53393 0.766963 0.641691i \(-0.221767\pi\)
0.766963 + 0.641691i \(0.221767\pi\)
\(8\) −1.18672e21 −0.710776
\(9\) 2.26588e22 0.852193
\(10\) −1.40324e23 −0.443742
\(11\) −1.19449e24 −0.402210 −0.201105 0.979570i \(-0.564453\pi\)
−0.201105 + 0.979570i \(0.564453\pi\)
\(12\) 2.66361e25 1.16068
\(13\) −2.71503e24 −0.0180345 −0.00901727 0.999959i \(-0.502870\pi\)
−0.00901727 + 0.999959i \(0.502870\pi\)
\(14\) 5.05485e26 0.588436
\(15\) 6.84264e27 1.57427
\(16\) 1.14916e28 0.580177
\(17\) 1.17417e29 1.42620 0.713102 0.701060i \(-0.247289\pi\)
0.713102 + 0.701060i \(0.247289\pi\)
\(18\) 1.03118e29 0.326913
\(19\) −1.65620e30 −1.47368 −0.736840 0.676067i \(-0.763683\pi\)
−0.736840 + 0.676067i \(0.763683\pi\)
\(20\) 3.70091e30 0.986515
\(21\) −2.46491e31 −2.08760
\(22\) −5.43602e30 −0.154294
\(23\) 5.41759e31 0.541006 0.270503 0.962719i \(-0.412810\pi\)
0.270503 + 0.962719i \(0.412810\pi\)
\(24\) 2.63354e32 0.967332
\(25\) 2.40198e32 0.338048
\(26\) −1.23559e31 −0.00691831
\(27\) 8.72142e32 0.201159
\(28\) −1.33317e34 −1.30819
\(29\) −1.03639e34 −0.445833 −0.222916 0.974838i \(-0.571558\pi\)
−0.222916 + 0.974838i \(0.571558\pi\)
\(30\) 3.11403e34 0.603912
\(31\) −3.80854e34 −0.341789 −0.170895 0.985289i \(-0.554666\pi\)
−0.170895 + 0.985289i \(0.554666\pi\)
\(32\) 2.19313e35 0.933340
\(33\) 2.65078e35 0.547389
\(34\) 5.34356e35 0.547112
\(35\) −3.42483e36 −1.77435
\(36\) −2.71966e36 −0.726784
\(37\) 8.41184e36 1.18073 0.590365 0.807136i \(-0.298984\pi\)
0.590365 + 0.807136i \(0.298984\pi\)
\(38\) −7.53724e36 −0.565324
\(39\) 6.02513e35 0.0245442
\(40\) 3.65913e37 0.822183
\(41\) 7.68510e37 0.966560 0.483280 0.875466i \(-0.339445\pi\)
0.483280 + 0.875466i \(0.339445\pi\)
\(42\) −1.12176e38 −0.800834
\(43\) −2.17109e38 −0.891597 −0.445799 0.895133i \(-0.647080\pi\)
−0.445799 + 0.895133i \(0.647080\pi\)
\(44\) 1.43370e38 0.343021
\(45\) −6.98663e38 −0.985766
\(46\) 2.46550e38 0.207537
\(47\) 2.73873e39 1.39075 0.695375 0.718647i \(-0.255238\pi\)
0.695375 + 0.718647i \(0.255238\pi\)
\(48\) −2.55019e39 −0.789593
\(49\) 7.09387e39 1.35293
\(50\) 1.09312e39 0.129680
\(51\) −2.60570e40 −1.94100
\(52\) 3.25875e38 0.0153806
\(53\) 8.29394e39 0.250195 0.125097 0.992144i \(-0.460076\pi\)
0.125097 + 0.992144i \(0.460076\pi\)
\(54\) 3.96905e39 0.0771673
\(55\) 3.68309e40 0.465253
\(56\) −1.31812e41 −1.09028
\(57\) 3.67541e41 2.00561
\(58\) −4.71655e40 −0.171028
\(59\) 7.09596e40 0.172182 0.0860912 0.996287i \(-0.472562\pi\)
0.0860912 + 0.996287i \(0.472562\pi\)
\(60\) −8.21298e41 −1.34260
\(61\) −6.43092e41 −0.712889 −0.356444 0.934317i \(-0.616011\pi\)
−0.356444 + 0.934317i \(0.616011\pi\)
\(62\) −1.73324e41 −0.131115
\(63\) 2.51678e42 1.30720
\(64\) −6.19220e41 −0.222134
\(65\) 8.37153e40 0.0208613
\(66\) 1.20635e42 0.209986
\(67\) 1.19612e43 1.46223 0.731114 0.682255i \(-0.239001\pi\)
0.731114 + 0.682255i \(0.239001\pi\)
\(68\) −1.40932e43 −1.21632
\(69\) −1.20226e43 −0.736283
\(70\) −1.55862e43 −0.680668
\(71\) 2.64034e43 0.826205 0.413103 0.910684i \(-0.364445\pi\)
0.413103 + 0.910684i \(0.364445\pi\)
\(72\) −2.68896e43 −0.605718
\(73\) 3.87700e43 0.631552 0.315776 0.948834i \(-0.397735\pi\)
0.315776 + 0.948834i \(0.397735\pi\)
\(74\) 3.82817e43 0.452945
\(75\) −5.33042e43 −0.460068
\(76\) 1.98788e44 1.25681
\(77\) −1.32675e44 −0.616961
\(78\) 2.74199e42 0.00941549
\(79\) −1.22812e44 −0.312612 −0.156306 0.987709i \(-0.549959\pi\)
−0.156306 + 0.987709i \(0.549959\pi\)
\(80\) −3.54332e44 −0.671114
\(81\) −7.96015e44 −1.12596
\(82\) 3.49743e44 0.370786
\(83\) 1.65007e45 1.31573 0.657867 0.753134i \(-0.271459\pi\)
0.657867 + 0.753134i \(0.271459\pi\)
\(84\) 2.95855e45 1.78039
\(85\) −3.62045e45 −1.64975
\(86\) −9.88045e44 −0.342029
\(87\) 2.29995e45 0.606757
\(88\) 1.41752e45 0.285881
\(89\) −6.00200e45 −0.928177 −0.464089 0.885789i \(-0.653618\pi\)
−0.464089 + 0.885789i \(0.653618\pi\)
\(90\) −3.17956e45 −0.378154
\(91\) −3.01566e44 −0.0276637
\(92\) −6.50255e45 −0.461391
\(93\) 8.45183e45 0.465159
\(94\) 1.24637e46 0.533512
\(95\) 5.10674e46 1.70466
\(96\) −4.86695e46 −1.27023
\(97\) −1.75152e46 −0.358328 −0.179164 0.983819i \(-0.557339\pi\)
−0.179164 + 0.983819i \(0.557339\pi\)
\(98\) 3.22837e46 0.519003
\(99\) −2.70656e46 −0.342761
\(100\) −2.88301e46 −0.288301
\(101\) −2.93699e46 −0.232461 −0.116231 0.993222i \(-0.537081\pi\)
−0.116231 + 0.993222i \(0.537081\pi\)
\(102\) −1.18583e47 −0.744594
\(103\) −2.42094e46 −0.120868 −0.0604338 0.998172i \(-0.519248\pi\)
−0.0604338 + 0.998172i \(0.519248\pi\)
\(104\) 3.22197e45 0.0128185
\(105\) 7.60032e47 2.41481
\(106\) 3.77451e46 0.0959782
\(107\) −3.58808e47 −0.731718 −0.365859 0.930670i \(-0.619225\pi\)
−0.365859 + 0.930670i \(0.619225\pi\)
\(108\) −1.04680e47 −0.171556
\(109\) −2.00272e47 −0.264301 −0.132150 0.991230i \(-0.542188\pi\)
−0.132150 + 0.991230i \(0.542188\pi\)
\(110\) 1.67615e47 0.178478
\(111\) −1.86674e48 −1.60692
\(112\) 1.27640e48 0.889948
\(113\) −4.99882e47 −0.282829 −0.141414 0.989950i \(-0.545165\pi\)
−0.141414 + 0.989950i \(0.545165\pi\)
\(114\) 1.67265e48 0.769380
\(115\) −1.67046e48 −0.625803
\(116\) 1.24395e48 0.380224
\(117\) −6.15192e46 −0.0153689
\(118\) 3.22932e47 0.0660516
\(119\) 1.30419e49 2.18769
\(120\) −8.12028e48 −1.11895
\(121\) −7.39295e48 −0.838227
\(122\) −2.92666e48 −0.273474
\(123\) −1.70546e49 −1.31544
\(124\) 4.57126e48 0.291492
\(125\) 1.45027e49 0.765706
\(126\) 1.14537e49 0.501461
\(127\) 8.93451e47 0.0324850 0.0162425 0.999868i \(-0.494830\pi\)
0.0162425 + 0.999868i \(0.494830\pi\)
\(128\) −3.36836e49 −1.01855
\(129\) 4.81804e49 1.21342
\(130\) 3.80982e47 0.00800269
\(131\) 8.86188e49 1.55471 0.777357 0.629060i \(-0.216560\pi\)
0.777357 + 0.629060i \(0.216560\pi\)
\(132\) −3.18164e49 −0.466836
\(133\) −1.83959e50 −2.26052
\(134\) 5.44343e49 0.560932
\(135\) −2.68917e49 −0.232688
\(136\) −1.39341e50 −1.01371
\(137\) 1.56850e50 0.960619 0.480310 0.877099i \(-0.340524\pi\)
0.480310 + 0.877099i \(0.340524\pi\)
\(138\) −5.47140e49 −0.282449
\(139\) 2.09943e50 0.914648 0.457324 0.889300i \(-0.348808\pi\)
0.457324 + 0.889300i \(0.348808\pi\)
\(140\) 4.11071e50 1.51324
\(141\) −6.07773e50 −1.89275
\(142\) 1.20160e50 0.316944
\(143\) 3.24306e48 0.00725368
\(144\) 2.60385e50 0.494422
\(145\) 3.19563e50 0.515713
\(146\) 1.76440e50 0.242272
\(147\) −1.57426e51 −1.84128
\(148\) −1.00964e51 −1.00697
\(149\) 1.17929e51 1.00402 0.502009 0.864862i \(-0.332594\pi\)
0.502009 + 0.864862i \(0.332594\pi\)
\(150\) −2.42583e50 −0.176489
\(151\) −1.05626e51 −0.657377 −0.328689 0.944438i \(-0.606607\pi\)
−0.328689 + 0.944438i \(0.606607\pi\)
\(152\) 1.96544e51 1.04746
\(153\) 2.66053e51 1.21540
\(154\) −6.03795e50 −0.236675
\(155\) 1.17433e51 0.395361
\(156\) −7.23176e49 −0.0209323
\(157\) −2.43063e51 −0.605447 −0.302724 0.953078i \(-0.597896\pi\)
−0.302724 + 0.953078i \(0.597896\pi\)
\(158\) −5.58909e50 −0.119922
\(159\) −1.84057e51 −0.340503
\(160\) −6.76231e51 −1.07963
\(161\) 6.01748e51 0.829863
\(162\) −3.62260e51 −0.431934
\(163\) 8.76362e51 0.904222 0.452111 0.891962i \(-0.350671\pi\)
0.452111 + 0.891962i \(0.350671\pi\)
\(164\) −9.22416e51 −0.824321
\(165\) −8.17344e51 −0.633187
\(166\) 7.50936e51 0.504734
\(167\) 2.63045e52 1.53530 0.767648 0.640871i \(-0.221427\pi\)
0.767648 + 0.640871i \(0.221427\pi\)
\(168\) 2.92515e52 1.48382
\(169\) −2.26567e52 −0.999675
\(170\) −1.64764e52 −0.632867
\(171\) −3.75275e52 −1.25586
\(172\) 2.60588e52 0.760390
\(173\) −3.14535e52 −0.800913 −0.400456 0.916316i \(-0.631148\pi\)
−0.400456 + 0.916316i \(0.631148\pi\)
\(174\) 1.04669e52 0.232761
\(175\) 2.66795e52 0.518541
\(176\) −1.37265e52 −0.233353
\(177\) −1.57472e52 −0.234332
\(178\) −2.73146e52 −0.356062
\(179\) −5.75744e52 −0.657935 −0.328968 0.944341i \(-0.606701\pi\)
−0.328968 + 0.944341i \(0.606701\pi\)
\(180\) 8.38581e52 0.840701
\(181\) 1.66382e53 1.46440 0.732199 0.681091i \(-0.238494\pi\)
0.732199 + 0.681091i \(0.238494\pi\)
\(182\) −1.37240e51 −0.0106122
\(183\) 1.42714e53 0.970208
\(184\) −6.42915e52 −0.384534
\(185\) −2.59371e53 −1.36580
\(186\) 3.84636e52 0.178442
\(187\) −1.40253e53 −0.573634
\(188\) −3.28720e53 −1.18609
\(189\) 9.68714e52 0.308563
\(190\) 2.32404e53 0.653934
\(191\) −1.33768e53 −0.332713 −0.166356 0.986066i \(-0.553200\pi\)
−0.166356 + 0.986066i \(0.553200\pi\)
\(192\) 1.37416e53 0.302314
\(193\) 6.53394e53 1.27227 0.636134 0.771579i \(-0.280533\pi\)
0.636134 + 0.771579i \(0.280533\pi\)
\(194\) −7.97105e52 −0.137460
\(195\) −1.85779e52 −0.0283912
\(196\) −8.51453e53 −1.15383
\(197\) 9.89833e53 1.19016 0.595081 0.803666i \(-0.297120\pi\)
0.595081 + 0.803666i \(0.297120\pi\)
\(198\) −1.23174e53 −0.131488
\(199\) 1.17074e54 1.11023 0.555117 0.831772i \(-0.312673\pi\)
0.555117 + 0.831772i \(0.312673\pi\)
\(200\) −2.85047e53 −0.240277
\(201\) −2.65440e54 −1.99002
\(202\) −1.33660e53 −0.0891754
\(203\) −1.15115e54 −0.683875
\(204\) 3.12753e54 1.65536
\(205\) −2.36963e54 −1.11806
\(206\) −1.10175e53 −0.0463665
\(207\) 1.22756e54 0.461041
\(208\) −3.11999e52 −0.0104632
\(209\) 1.97831e54 0.592729
\(210\) 3.45885e54 0.926357
\(211\) 1.13707e54 0.272364 0.136182 0.990684i \(-0.456517\pi\)
0.136182 + 0.990684i \(0.456517\pi\)
\(212\) −9.95493e53 −0.213376
\(213\) −5.85938e54 −1.12443
\(214\) −1.63291e54 −0.280697
\(215\) 6.69435e54 1.03135
\(216\) −1.03499e54 −0.142979
\(217\) −4.23026e54 −0.524280
\(218\) −9.11424e53 −0.101389
\(219\) −8.60377e54 −0.859512
\(220\) −4.42069e54 −0.396786
\(221\) −3.18791e53 −0.0257210
\(222\) −8.49539e54 −0.616437
\(223\) 2.34179e55 1.52892 0.764459 0.644672i \(-0.223006\pi\)
0.764459 + 0.644672i \(0.223006\pi\)
\(224\) 2.43597e55 1.43167
\(225\) 5.44259e54 0.288082
\(226\) −2.27492e54 −0.108497
\(227\) 3.06780e55 1.31892 0.659462 0.751738i \(-0.270784\pi\)
0.659462 + 0.751738i \(0.270784\pi\)
\(228\) −4.41146e55 −1.71046
\(229\) −4.77257e55 −1.66962 −0.834811 0.550536i \(-0.814423\pi\)
−0.834811 + 0.550536i \(0.814423\pi\)
\(230\) −7.60215e54 −0.240067
\(231\) 2.94430e55 0.839655
\(232\) 1.22991e55 0.316887
\(233\) 1.85272e55 0.431464 0.215732 0.976453i \(-0.430786\pi\)
0.215732 + 0.976453i \(0.430786\pi\)
\(234\) −2.79969e53 −0.00589573
\(235\) −8.44462e55 −1.60874
\(236\) −8.51704e54 −0.146844
\(237\) 2.72543e55 0.425450
\(238\) 5.93526e55 0.839230
\(239\) −6.05119e55 −0.775336 −0.387668 0.921799i \(-0.626719\pi\)
−0.387668 + 0.921799i \(0.626719\pi\)
\(240\) 7.86327e55 0.913354
\(241\) 3.35331e55 0.353242 0.176621 0.984279i \(-0.443483\pi\)
0.176621 + 0.984279i \(0.443483\pi\)
\(242\) −3.36447e55 −0.321556
\(243\) 1.53461e56 1.33122
\(244\) 7.71881e55 0.607980
\(245\) −2.18733e56 −1.56499
\(246\) −7.76143e55 −0.504622
\(247\) 4.49663e54 0.0265771
\(248\) 4.51966e55 0.242936
\(249\) −3.66181e56 −1.79065
\(250\) 6.60005e55 0.293736
\(251\) 3.39203e56 1.37444 0.687222 0.726448i \(-0.258830\pi\)
0.687222 + 0.726448i \(0.258830\pi\)
\(252\) −3.02081e56 −1.11483
\(253\) −6.47124e55 −0.217598
\(254\) 4.06603e54 0.0124617
\(255\) 8.03443e56 2.24523
\(256\) −6.61439e55 −0.168597
\(257\) −7.45663e56 −1.73426 −0.867130 0.498082i \(-0.834038\pi\)
−0.867130 + 0.498082i \(0.834038\pi\)
\(258\) 2.19265e56 0.465486
\(259\) 9.34329e56 1.81115
\(260\) −1.00481e55 −0.0177913
\(261\) −2.34834e56 −0.379935
\(262\) 4.03298e56 0.596410
\(263\) −1.28505e57 −1.73764 −0.868819 0.495129i \(-0.835121\pi\)
−0.868819 + 0.495129i \(0.835121\pi\)
\(264\) −3.14573e56 −0.389071
\(265\) −2.55736e56 −0.289410
\(266\) −8.37184e56 −0.867166
\(267\) 1.33195e57 1.26321
\(268\) −1.43566e57 −1.24705
\(269\) 1.52143e57 1.21081 0.605403 0.795919i \(-0.293012\pi\)
0.605403 + 0.795919i \(0.293012\pi\)
\(270\) −1.22382e56 −0.0892625
\(271\) 2.08539e56 0.139447 0.0697235 0.997566i \(-0.477788\pi\)
0.0697235 + 0.997566i \(0.477788\pi\)
\(272\) 1.34931e57 0.827450
\(273\) 6.69230e55 0.0376490
\(274\) 7.13813e56 0.368507
\(275\) −2.86913e56 −0.135967
\(276\) 1.44303e57 0.627932
\(277\) −4.91573e57 −1.96478 −0.982388 0.186853i \(-0.940171\pi\)
−0.982388 + 0.186853i \(0.940171\pi\)
\(278\) 9.55436e56 0.350872
\(279\) −8.62969e56 −0.291270
\(280\) 4.06431e57 1.26117
\(281\) 2.99077e57 0.853462 0.426731 0.904379i \(-0.359665\pi\)
0.426731 + 0.904379i \(0.359665\pi\)
\(282\) −2.76593e57 −0.726084
\(283\) −2.40523e57 −0.580999 −0.290499 0.956875i \(-0.593821\pi\)
−0.290499 + 0.956875i \(0.593821\pi\)
\(284\) −3.16910e57 −0.704621
\(285\) −1.13328e58 −2.31997
\(286\) 1.47589e55 0.00278261
\(287\) 8.53607e57 1.48263
\(288\) 4.96937e57 0.795385
\(289\) 7.00882e57 1.03406
\(290\) 1.45430e57 0.197835
\(291\) 3.88695e57 0.487667
\(292\) −4.65344e57 −0.538613
\(293\) 7.67134e57 0.819374 0.409687 0.912226i \(-0.365638\pi\)
0.409687 + 0.912226i \(0.365638\pi\)
\(294\) −7.16433e57 −0.706339
\(295\) −2.18797e57 −0.199170
\(296\) −9.98248e57 −0.839235
\(297\) −1.04176e57 −0.0809081
\(298\) 5.36684e57 0.385156
\(299\) −1.47089e56 −0.00975679
\(300\) 6.39792e57 0.392364
\(301\) −2.41149e58 −1.36764
\(302\) −4.80698e57 −0.252179
\(303\) 6.51772e57 0.316369
\(304\) −1.90324e58 −0.854994
\(305\) 1.98291e58 0.824627
\(306\) 1.21079e58 0.466245
\(307\) 1.66078e58 0.592325 0.296162 0.955138i \(-0.404293\pi\)
0.296162 + 0.955138i \(0.404293\pi\)
\(308\) 1.59246e58 0.526169
\(309\) 5.37251e57 0.164495
\(310\) 5.34427e57 0.151666
\(311\) −2.17917e58 −0.573352 −0.286676 0.958028i \(-0.592550\pi\)
−0.286676 + 0.958028i \(0.592550\pi\)
\(312\) −7.15013e56 −0.0174454
\(313\) 4.52774e58 1.02468 0.512342 0.858782i \(-0.328778\pi\)
0.512342 + 0.858782i \(0.328778\pi\)
\(314\) −1.10616e58 −0.232258
\(315\) −7.76026e58 −1.51209
\(316\) 1.47407e58 0.266608
\(317\) −6.03868e58 −1.01403 −0.507014 0.861938i \(-0.669251\pi\)
−0.507014 + 0.861938i \(0.669251\pi\)
\(318\) −8.37631e57 −0.130622
\(319\) 1.23796e58 0.179319
\(320\) 1.90931e58 0.256952
\(321\) 7.96260e58 0.995833
\(322\) 2.73851e58 0.318347
\(323\) −1.94466e59 −2.10177
\(324\) 9.55429e58 0.960264
\(325\) −6.52143e56 −0.00609655
\(326\) 3.98826e58 0.346872
\(327\) 4.44440e58 0.359701
\(328\) −9.12004e58 −0.687007
\(329\) 3.04199e59 2.13331
\(330\) −3.71967e58 −0.242900
\(331\) −2.03088e57 −0.0123517 −0.00617585 0.999981i \(-0.501966\pi\)
−0.00617585 + 0.999981i \(0.501966\pi\)
\(332\) −1.98053e59 −1.12211
\(333\) 1.90602e59 1.00621
\(334\) 1.19710e59 0.588962
\(335\) −3.68811e59 −1.69142
\(336\) −2.83257e59 −1.21118
\(337\) −1.81636e59 −0.724268 −0.362134 0.932126i \(-0.617952\pi\)
−0.362134 + 0.932126i \(0.617952\pi\)
\(338\) −1.03109e59 −0.383489
\(339\) 1.10933e59 0.384917
\(340\) 4.34550e59 1.40697
\(341\) 4.54925e58 0.137471
\(342\) −1.70785e59 −0.481765
\(343\) 2.05545e59 0.541370
\(344\) 2.57647e59 0.633726
\(345\) 3.70706e59 0.851689
\(346\) −1.43142e59 −0.307241
\(347\) 1.01600e59 0.203776 0.101888 0.994796i \(-0.467512\pi\)
0.101888 + 0.994796i \(0.467512\pi\)
\(348\) −2.76055e59 −0.517467
\(349\) −4.81199e59 −0.843193 −0.421596 0.906784i \(-0.638530\pi\)
−0.421596 + 0.906784i \(0.638530\pi\)
\(350\) 1.21416e59 0.198920
\(351\) −2.36789e57 −0.00362781
\(352\) −2.61966e59 −0.375399
\(353\) 1.19790e60 1.60588 0.802941 0.596059i \(-0.203268\pi\)
0.802941 + 0.596059i \(0.203268\pi\)
\(354\) −7.16644e58 −0.0898932
\(355\) −8.14123e59 −0.955705
\(356\) 7.20400e59 0.791587
\(357\) −2.89423e60 −2.97735
\(358\) −2.62017e59 −0.252393
\(359\) −8.62063e58 −0.0777713 −0.0388857 0.999244i \(-0.512381\pi\)
−0.0388857 + 0.999244i \(0.512381\pi\)
\(360\) 8.29116e59 0.700658
\(361\) 1.47995e60 1.17173
\(362\) 7.57190e59 0.561764
\(363\) 1.64063e60 1.14079
\(364\) 3.61959e58 0.0235927
\(365\) −1.19544e60 −0.730542
\(366\) 6.49479e59 0.372185
\(367\) −2.19138e60 −1.17778 −0.588892 0.808212i \(-0.700435\pi\)
−0.588892 + 0.808212i \(0.700435\pi\)
\(368\) 6.22566e59 0.313879
\(369\) 1.74135e60 0.823696
\(370\) −1.18038e60 −0.523940
\(371\) 9.21233e59 0.383780
\(372\) −1.01444e60 −0.396706
\(373\) 1.32206e60 0.485393 0.242696 0.970102i \(-0.421968\pi\)
0.242696 + 0.970102i \(0.421968\pi\)
\(374\) −6.38282e59 −0.220054
\(375\) −3.21840e60 −1.04209
\(376\) −3.25010e60 −0.988512
\(377\) 2.81384e58 0.00804039
\(378\) 4.40854e59 0.118369
\(379\) 6.08671e60 1.53589 0.767947 0.640513i \(-0.221278\pi\)
0.767947 + 0.640513i \(0.221278\pi\)
\(380\) −6.12944e60 −1.45381
\(381\) −1.98273e59 −0.0442106
\(382\) −6.08770e59 −0.127633
\(383\) 3.42858e60 0.675995 0.337997 0.941147i \(-0.390250\pi\)
0.337997 + 0.941147i \(0.390250\pi\)
\(384\) 7.47499e60 1.38620
\(385\) 4.09092e60 0.713664
\(386\) 2.97355e60 0.488060
\(387\) −4.91942e60 −0.759813
\(388\) 2.10229e60 0.305596
\(389\) −5.62159e60 −0.769208 −0.384604 0.923082i \(-0.625662\pi\)
−0.384604 + 0.923082i \(0.625662\pi\)
\(390\) −8.45468e58 −0.0108913
\(391\) 6.36118e60 0.771585
\(392\) −8.41842e60 −0.961630
\(393\) −1.96661e61 −2.11589
\(394\) 4.50466e60 0.456563
\(395\) 3.78680e60 0.361611
\(396\) 3.24860e60 0.292320
\(397\) −1.94362e61 −1.64829 −0.824146 0.566377i \(-0.808345\pi\)
−0.824146 + 0.566377i \(0.808345\pi\)
\(398\) 5.32797e60 0.425902
\(399\) 4.08238e61 3.07646
\(400\) 2.76025e60 0.196128
\(401\) −2.48633e61 −1.66597 −0.832984 0.553296i \(-0.813370\pi\)
−0.832984 + 0.553296i \(0.813370\pi\)
\(402\) −1.20800e61 −0.763402
\(403\) 1.03403e59 0.00616401
\(404\) 3.52517e60 0.198252
\(405\) 2.45444e61 1.30244
\(406\) −5.23881e60 −0.262344
\(407\) −1.00478e61 −0.474902
\(408\) 3.09223e61 1.37961
\(409\) 1.77202e61 0.746397 0.373199 0.927751i \(-0.378261\pi\)
0.373199 + 0.927751i \(0.378261\pi\)
\(410\) −1.07840e61 −0.428903
\(411\) −3.48079e61 −1.30736
\(412\) 2.90578e60 0.103081
\(413\) 7.88170e60 0.264115
\(414\) 5.58653e60 0.176862
\(415\) −5.08785e61 −1.52196
\(416\) −5.95440e59 −0.0168324
\(417\) −4.65902e61 −1.24479
\(418\) 9.00313e60 0.227379
\(419\) 6.32251e61 1.50959 0.754797 0.655958i \(-0.227735\pi\)
0.754797 + 0.655958i \(0.227735\pi\)
\(420\) −9.12241e61 −2.05945
\(421\) 8.68512e61 1.85416 0.927078 0.374868i \(-0.122312\pi\)
0.927078 + 0.374868i \(0.122312\pi\)
\(422\) 5.17472e60 0.104483
\(423\) 6.20563e61 1.18519
\(424\) −9.84256e60 −0.177832
\(425\) 2.82033e61 0.482126
\(426\) −2.66656e61 −0.431346
\(427\) −7.14301e61 −1.09352
\(428\) 4.30665e61 0.624038
\(429\) −7.19694e59 −0.00987192
\(430\) 3.04655e61 0.395639
\(431\) 6.27735e61 0.771898 0.385949 0.922520i \(-0.373874\pi\)
0.385949 + 0.922520i \(0.373874\pi\)
\(432\) 1.00223e61 0.116708
\(433\) −6.16297e61 −0.679711 −0.339855 0.940478i \(-0.610378\pi\)
−0.339855 + 0.940478i \(0.610378\pi\)
\(434\) −1.92516e61 −0.201121
\(435\) −7.09167e61 −0.701861
\(436\) 2.40380e61 0.225406
\(437\) −8.97261e61 −0.797269
\(438\) −3.91551e61 −0.329721
\(439\) −1.66474e62 −1.32871 −0.664353 0.747419i \(-0.731293\pi\)
−0.664353 + 0.747419i \(0.731293\pi\)
\(440\) −4.37079e61 −0.330691
\(441\) 1.60739e62 1.15296
\(442\) −1.45079e60 −0.00986692
\(443\) 1.29305e62 0.833929 0.416965 0.908923i \(-0.363094\pi\)
0.416965 + 0.908923i \(0.363094\pi\)
\(444\) 2.24058e62 1.37044
\(445\) 1.85066e62 1.07366
\(446\) 1.06573e62 0.586515
\(447\) −2.61705e62 −1.36642
\(448\) −6.87786e61 −0.340738
\(449\) −1.47587e62 −0.693839 −0.346920 0.937895i \(-0.612772\pi\)
−0.346920 + 0.937895i \(0.612772\pi\)
\(450\) 2.47688e61 0.110512
\(451\) −9.17975e61 −0.388760
\(452\) 5.99991e61 0.241208
\(453\) 2.34404e62 0.894659
\(454\) 1.39613e62 0.505958
\(455\) 9.29851e60 0.0319997
\(456\) −4.36167e62 −1.42554
\(457\) −1.90700e62 −0.591998 −0.295999 0.955188i \(-0.595653\pi\)
−0.295999 + 0.955188i \(0.595653\pi\)
\(458\) −2.17196e62 −0.640491
\(459\) 1.02404e62 0.286893
\(460\) 2.00500e62 0.533710
\(461\) 2.19785e61 0.0555939 0.0277970 0.999614i \(-0.491151\pi\)
0.0277970 + 0.999614i \(0.491151\pi\)
\(462\) 1.33993e62 0.322104
\(463\) −1.68005e62 −0.383857 −0.191929 0.981409i \(-0.561474\pi\)
−0.191929 + 0.981409i \(0.561474\pi\)
\(464\) −1.19098e62 −0.258662
\(465\) −2.60604e62 −0.538068
\(466\) 8.43157e61 0.165516
\(467\) 1.37225e62 0.256145 0.128073 0.991765i \(-0.459121\pi\)
0.128073 + 0.991765i \(0.459121\pi\)
\(468\) 7.38394e60 0.0131072
\(469\) 1.32856e63 2.24295
\(470\) −3.84308e62 −0.617134
\(471\) 5.39400e62 0.823985
\(472\) −8.42090e61 −0.122383
\(473\) 2.59334e62 0.358610
\(474\) 1.24032e62 0.163209
\(475\) −3.97815e62 −0.498175
\(476\) −1.56537e63 −1.86575
\(477\) 1.87931e62 0.213214
\(478\) −2.75385e62 −0.297430
\(479\) −1.62356e63 −1.66949 −0.834745 0.550637i \(-0.814385\pi\)
−0.834745 + 0.550637i \(0.814385\pi\)
\(480\) 1.50068e63 1.46933
\(481\) −2.28384e61 −0.0212939
\(482\) 1.52606e62 0.135509
\(483\) −1.33539e63 −1.12940
\(484\) 8.87351e62 0.714874
\(485\) 5.40066e62 0.414492
\(486\) 6.98388e62 0.510675
\(487\) 1.09889e62 0.0765640 0.0382820 0.999267i \(-0.487811\pi\)
0.0382820 + 0.999267i \(0.487811\pi\)
\(488\) 7.63168e62 0.506704
\(489\) −1.94481e63 −1.23060
\(490\) −9.95438e62 −0.600352
\(491\) 2.66145e63 1.53004 0.765020 0.644007i \(-0.222729\pi\)
0.765020 + 0.644007i \(0.222729\pi\)
\(492\) 2.04701e63 1.12186
\(493\) −1.21690e63 −0.635849
\(494\) 2.04638e61 0.0101954
\(495\) 8.34544e62 0.396485
\(496\) −4.37661e62 −0.198298
\(497\) 2.93270e63 1.26734
\(498\) −1.66646e63 −0.686919
\(499\) −2.22266e63 −0.873997 −0.436999 0.899462i \(-0.643959\pi\)
−0.436999 + 0.899462i \(0.643959\pi\)
\(500\) −1.74070e63 −0.653025
\(501\) −5.83743e63 −2.08947
\(502\) 1.54369e63 0.527256
\(503\) 3.07975e63 1.00385 0.501924 0.864912i \(-0.332626\pi\)
0.501924 + 0.864912i \(0.332626\pi\)
\(504\) −2.98671e63 −0.929127
\(505\) 9.05595e62 0.268897
\(506\) −2.94501e62 −0.0834737
\(507\) 5.02793e63 1.36051
\(508\) −1.07238e62 −0.0277046
\(509\) −5.72771e63 −1.41291 −0.706453 0.707760i \(-0.749706\pi\)
−0.706453 + 0.707760i \(0.749706\pi\)
\(510\) 3.65641e63 0.861302
\(511\) 4.30631e63 0.968754
\(512\) 4.43953e63 0.953877
\(513\) −1.44444e63 −0.296443
\(514\) −3.39346e63 −0.665287
\(515\) 7.46476e62 0.139812
\(516\) −5.78292e63 −1.03485
\(517\) −3.27137e63 −0.559374
\(518\) 4.25206e63 0.694784
\(519\) 6.98009e63 1.09000
\(520\) −9.93464e61 −0.0148277
\(521\) 1.17638e64 1.67826 0.839132 0.543928i \(-0.183064\pi\)
0.839132 + 0.543928i \(0.183064\pi\)
\(522\) −1.06871e63 −0.145749
\(523\) −6.38331e63 −0.832254 −0.416127 0.909306i \(-0.636613\pi\)
−0.416127 + 0.909306i \(0.636613\pi\)
\(524\) −1.06366e64 −1.32592
\(525\) −5.92066e63 −0.705710
\(526\) −5.84816e63 −0.666583
\(527\) −4.47188e63 −0.487461
\(528\) 3.04617e63 0.317582
\(529\) −7.09283e63 −0.707313
\(530\) −1.16383e63 −0.111022
\(531\) 1.60786e63 0.146733
\(532\) 2.20800e64 1.92786
\(533\) −2.08652e62 −0.0174315
\(534\) 6.06161e63 0.484583
\(535\) 1.10635e64 0.846408
\(536\) −1.41945e64 −1.03932
\(537\) 1.27768e64 0.895419
\(538\) 6.92393e63 0.464483
\(539\) −8.47354e63 −0.544163
\(540\) 3.22772e63 0.198446
\(541\) −7.64596e62 −0.0450087 −0.0225043 0.999747i \(-0.507164\pi\)
−0.0225043 + 0.999747i \(0.507164\pi\)
\(542\) 9.49045e62 0.0534938
\(543\) −3.69231e64 −1.99298
\(544\) 2.57511e64 1.33113
\(545\) 6.17521e63 0.305727
\(546\) 3.04561e62 0.0144427
\(547\) −1.77108e64 −0.804519 −0.402259 0.915526i \(-0.631775\pi\)
−0.402259 + 0.915526i \(0.631775\pi\)
\(548\) −1.88262e64 −0.819255
\(549\) −1.45717e64 −0.607519
\(550\) −1.30572e63 −0.0521587
\(551\) 1.71648e64 0.657015
\(552\) 1.42674e64 0.523332
\(553\) −1.36411e64 −0.479523
\(554\) −2.23711e64 −0.753716
\(555\) 5.75592e64 1.85879
\(556\) −2.51988e64 −0.780049
\(557\) 1.48786e64 0.441535 0.220767 0.975327i \(-0.429144\pi\)
0.220767 + 0.975327i \(0.429144\pi\)
\(558\) −3.92730e63 −0.111735
\(559\) 5.89456e62 0.0160795
\(560\) −3.93568e64 −1.02944
\(561\) 3.11247e64 0.780689
\(562\) 1.36108e64 0.327400
\(563\) 4.11252e64 0.948770 0.474385 0.880317i \(-0.342670\pi\)
0.474385 + 0.880317i \(0.342670\pi\)
\(564\) 7.29489e64 1.61421
\(565\) 1.54134e64 0.327160
\(566\) −1.09460e64 −0.222879
\(567\) −8.84157e64 −1.72714
\(568\) −3.13333e64 −0.587247
\(569\) −5.04135e64 −0.906586 −0.453293 0.891362i \(-0.649751\pi\)
−0.453293 + 0.891362i \(0.649751\pi\)
\(570\) −5.15746e64 −0.889973
\(571\) 1.68666e64 0.279305 0.139652 0.990201i \(-0.455402\pi\)
0.139652 + 0.990201i \(0.455402\pi\)
\(572\) −3.89254e62 −0.00618623
\(573\) 2.96856e64 0.452806
\(574\) 3.88470e64 0.568759
\(575\) 1.30129e64 0.182886
\(576\) −1.40308e64 −0.189301
\(577\) −9.79059e63 −0.126817 −0.0634084 0.997988i \(-0.520197\pi\)
−0.0634084 + 0.997988i \(0.520197\pi\)
\(578\) 3.18966e64 0.396680
\(579\) −1.45000e65 −1.73150
\(580\) −3.83560e64 −0.439821
\(581\) 1.83279e65 2.01824
\(582\) 1.76892e64 0.187076
\(583\) −9.90700e63 −0.100631
\(584\) −4.60091e64 −0.448892
\(585\) 1.89689e63 0.0177778
\(586\) 3.49117e64 0.314323
\(587\) 2.78831e64 0.241183 0.120591 0.992702i \(-0.461521\pi\)
0.120591 + 0.992702i \(0.461521\pi\)
\(588\) 1.88953e65 1.57031
\(589\) 6.30770e64 0.503688
\(590\) −9.95730e63 −0.0764046
\(591\) −2.19662e65 −1.61975
\(592\) 9.66654e64 0.685032
\(593\) 1.49430e65 1.01778 0.508889 0.860832i \(-0.330056\pi\)
0.508889 + 0.860832i \(0.330056\pi\)
\(594\) −4.74098e63 −0.0310375
\(595\) −4.02134e65 −2.53059
\(596\) −1.41546e65 −0.856267
\(597\) −2.59809e65 −1.51098
\(598\) −6.69390e62 −0.00374284
\(599\) 2.99285e65 1.60899 0.804496 0.593957i \(-0.202435\pi\)
0.804496 + 0.593957i \(0.202435\pi\)
\(600\) 6.32570e64 0.327005
\(601\) −1.56472e65 −0.777831 −0.388916 0.921273i \(-0.627150\pi\)
−0.388916 + 0.921273i \(0.627150\pi\)
\(602\) −1.09745e65 −0.524648
\(603\) 2.71025e65 1.24610
\(604\) 1.26780e65 0.560638
\(605\) 2.27955e65 0.969611
\(606\) 2.96616e64 0.121364
\(607\) 8.61159e64 0.338961 0.169480 0.985534i \(-0.445791\pi\)
0.169480 + 0.985534i \(0.445791\pi\)
\(608\) −3.63226e65 −1.37544
\(609\) 2.55462e65 0.930721
\(610\) 9.02409e64 0.316339
\(611\) −7.43572e63 −0.0250816
\(612\) −3.19334e65 −1.03654
\(613\) −1.58806e65 −0.496072 −0.248036 0.968751i \(-0.579785\pi\)
−0.248036 + 0.968751i \(0.579785\pi\)
\(614\) 7.55808e64 0.227224
\(615\) 5.25864e65 1.52163
\(616\) 1.57448e65 0.438521
\(617\) −6.01082e65 −1.61151 −0.805753 0.592251i \(-0.798239\pi\)
−0.805753 + 0.592251i \(0.798239\pi\)
\(618\) 2.44499e64 0.0631026
\(619\) 3.62211e65 0.899978 0.449989 0.893034i \(-0.351428\pi\)
0.449989 + 0.893034i \(0.351428\pi\)
\(620\) −1.40950e65 −0.337180
\(621\) 4.72491e64 0.108828
\(622\) −9.91723e64 −0.219946
\(623\) −6.66660e65 −1.42376
\(624\) 6.92383e63 0.0142399
\(625\) −6.17847e65 −1.22377
\(626\) 2.06054e65 0.393083
\(627\) −4.39022e65 −0.806677
\(628\) 2.91740e65 0.516350
\(629\) 9.87695e65 1.68396
\(630\) −3.53164e65 −0.580060
\(631\) 9.92614e65 1.57069 0.785345 0.619059i \(-0.212486\pi\)
0.785345 + 0.619059i \(0.212486\pi\)
\(632\) 1.45743e65 0.222197
\(633\) −2.52336e65 −0.370675
\(634\) −2.74816e65 −0.388995
\(635\) −2.75487e64 −0.0375768
\(636\) 2.20918e65 0.290395
\(637\) −1.92601e64 −0.0243995
\(638\) 5.63386e64 0.0687891
\(639\) 5.98268e65 0.704086
\(640\) 1.03860e66 1.17820
\(641\) −1.70256e66 −1.86183 −0.930915 0.365236i \(-0.880988\pi\)
−0.930915 + 0.365236i \(0.880988\pi\)
\(642\) 3.62372e65 0.382016
\(643\) 8.06741e65 0.819929 0.409964 0.912102i \(-0.365541\pi\)
0.409964 + 0.912102i \(0.365541\pi\)
\(644\) −7.22257e65 −0.707740
\(645\) −1.48560e66 −1.40361
\(646\) −8.85001e65 −0.806268
\(647\) −2.90914e65 −0.255573 −0.127786 0.991802i \(-0.540787\pi\)
−0.127786 + 0.991802i \(0.540787\pi\)
\(648\) 9.44644e65 0.800305
\(649\) −8.47603e64 −0.0692536
\(650\) −2.96785e63 −0.00233872
\(651\) 9.38770e65 0.713520
\(652\) −1.05187e66 −0.771157
\(653\) 3.73213e65 0.263935 0.131967 0.991254i \(-0.457871\pi\)
0.131967 + 0.991254i \(0.457871\pi\)
\(654\) 2.02261e65 0.137986
\(655\) −2.73248e66 −1.79840
\(656\) 8.83139e65 0.560775
\(657\) 8.78482e65 0.538204
\(658\) 1.38439e66 0.818368
\(659\) 7.84754e65 0.447637 0.223819 0.974631i \(-0.428148\pi\)
0.223819 + 0.974631i \(0.428148\pi\)
\(660\) 9.81030e65 0.540008
\(661\) 5.69856e65 0.302713 0.151356 0.988479i \(-0.451636\pi\)
0.151356 + 0.988479i \(0.451636\pi\)
\(662\) −9.24239e63 −0.00473829
\(663\) 7.07454e64 0.0350050
\(664\) −1.95817e66 −0.935192
\(665\) 5.67221e66 2.61483
\(666\) 8.67416e65 0.385996
\(667\) −5.61476e65 −0.241198
\(668\) −3.15723e66 −1.30936
\(669\) −5.19686e66 −2.08079
\(670\) −1.67843e66 −0.648852
\(671\) 7.68164e65 0.286731
\(672\) −5.40587e66 −1.94844
\(673\) 4.43578e66 1.54389 0.771945 0.635689i \(-0.219284\pi\)
0.771945 + 0.635689i \(0.219284\pi\)
\(674\) −8.26612e65 −0.277840
\(675\) 2.09487e65 0.0680013
\(676\) 2.71940e66 0.852563
\(677\) 3.52339e66 1.06691 0.533454 0.845829i \(-0.320894\pi\)
0.533454 + 0.845829i \(0.320894\pi\)
\(678\) 5.04846e65 0.147660
\(679\) −1.94547e66 −0.549648
\(680\) 4.29645e66 1.17260
\(681\) −6.80801e66 −1.79499
\(682\) 2.07033e65 0.0527359
\(683\) −3.36076e66 −0.827087 −0.413543 0.910484i \(-0.635709\pi\)
−0.413543 + 0.910484i \(0.635709\pi\)
\(684\) 4.50430e66 1.07105
\(685\) −4.83633e66 −1.11119
\(686\) 9.35418e65 0.207677
\(687\) 1.05912e67 2.27228
\(688\) −2.49492e66 −0.517284
\(689\) −2.25183e64 −0.00451214
\(690\) 1.68705e66 0.326720
\(691\) 2.04623e66 0.383020 0.191510 0.981491i \(-0.438662\pi\)
0.191510 + 0.981491i \(0.438662\pi\)
\(692\) 3.77525e66 0.683050
\(693\) −3.00626e66 −0.525770
\(694\) 4.62376e65 0.0781714
\(695\) −6.47341e66 −1.05801
\(696\) −2.72939e66 −0.431268
\(697\) 9.02362e66 1.37851
\(698\) −2.18990e66 −0.323461
\(699\) −4.11151e66 −0.587203
\(700\) −3.20225e66 −0.442233
\(701\) −1.21798e67 −1.62655 −0.813275 0.581879i \(-0.802318\pi\)
−0.813275 + 0.581879i \(0.802318\pi\)
\(702\) −1.07761e64 −0.00139168
\(703\) −1.39317e67 −1.74002
\(704\) 7.39650e65 0.0893447
\(705\) 1.87401e67 2.18942
\(706\) 5.45153e66 0.616039
\(707\) −3.26221e66 −0.356578
\(708\) 1.89008e66 0.199848
\(709\) 1.52742e67 1.56233 0.781166 0.624323i \(-0.214625\pi\)
0.781166 + 0.624323i \(0.214625\pi\)
\(710\) −3.70501e66 −0.366622
\(711\) −2.78278e66 −0.266405
\(712\) 7.12268e66 0.659726
\(713\) −2.06331e66 −0.184910
\(714\) −1.31714e67 −1.14215
\(715\) −9.99969e64 −0.00839063
\(716\) 6.91046e66 0.561114
\(717\) 1.34287e67 1.05520
\(718\) −3.92318e65 −0.0298342
\(719\) 5.76158e66 0.424045 0.212023 0.977265i \(-0.431995\pi\)
0.212023 + 0.977265i \(0.431995\pi\)
\(720\) −8.02874e66 −0.571918
\(721\) −2.68901e66 −0.185402
\(722\) 6.73515e66 0.449493
\(723\) −7.44159e66 −0.480746
\(724\) −1.99702e67 −1.24890
\(725\) −2.48940e66 −0.150713
\(726\) 7.46638e66 0.437622
\(727\) −7.68143e65 −0.0435896 −0.0217948 0.999762i \(-0.506938\pi\)
−0.0217948 + 0.999762i \(0.506938\pi\)
\(728\) 3.57874e65 0.0196627
\(729\) −1.28906e67 −0.685768
\(730\) −5.44035e66 −0.280246
\(731\) −2.54923e67 −1.27160
\(732\) −1.71294e67 −0.827432
\(733\) 3.73856e67 1.74889 0.874443 0.485129i \(-0.161227\pi\)
0.874443 + 0.485129i \(0.161227\pi\)
\(734\) −9.97281e66 −0.451814
\(735\) 4.85408e67 2.12988
\(736\) 1.18815e67 0.504942
\(737\) −1.42874e67 −0.588124
\(738\) 7.92476e66 0.315981
\(739\) −1.50450e67 −0.581095 −0.290548 0.956861i \(-0.593837\pi\)
−0.290548 + 0.956861i \(0.593837\pi\)
\(740\) 3.11315e67 1.16481
\(741\) −9.97882e65 −0.0361702
\(742\) 4.19246e66 0.147223
\(743\) 5.97073e66 0.203138 0.101569 0.994829i \(-0.467614\pi\)
0.101569 + 0.994829i \(0.467614\pi\)
\(744\) −1.00299e67 −0.330624
\(745\) −3.63622e67 −1.16139
\(746\) 6.01659e66 0.186204
\(747\) 3.73887e67 1.12126
\(748\) 1.68341e67 0.489218
\(749\) −3.98539e67 −1.12240
\(750\) −1.46467e67 −0.399761
\(751\) −1.14848e67 −0.303797 −0.151898 0.988396i \(-0.548539\pi\)
−0.151898 + 0.988396i \(0.548539\pi\)
\(752\) 3.14723e67 0.806881
\(753\) −7.52752e67 −1.87055
\(754\) 1.28056e65 0.00308441
\(755\) 3.25690e67 0.760415
\(756\) −1.16271e67 −0.263155
\(757\) 3.51013e66 0.0770141 0.0385070 0.999258i \(-0.487740\pi\)
0.0385070 + 0.999258i \(0.487740\pi\)
\(758\) 2.77002e67 0.589191
\(759\) 1.43608e67 0.296141
\(760\) −6.06026e67 −1.21163
\(761\) 2.99687e67 0.580937 0.290468 0.956885i \(-0.406189\pi\)
0.290468 + 0.956885i \(0.406189\pi\)
\(762\) −9.02325e65 −0.0169598
\(763\) −2.22448e67 −0.405418
\(764\) 1.60558e67 0.283751
\(765\) −8.20350e67 −1.40590
\(766\) 1.56032e67 0.259321
\(767\) −1.92657e65 −0.00310523
\(768\) 1.46785e67 0.229453
\(769\) 1.28547e68 1.94892 0.974461 0.224557i \(-0.0720935\pi\)
0.974461 + 0.224557i \(0.0720935\pi\)
\(770\) 1.86175e67 0.273772
\(771\) 1.65476e68 2.36025
\(772\) −7.84247e67 −1.08504
\(773\) 6.24752e67 0.838474 0.419237 0.907877i \(-0.362298\pi\)
0.419237 + 0.907877i \(0.362298\pi\)
\(774\) −2.23879e67 −0.291475
\(775\) −9.14802e66 −0.115541
\(776\) 2.07856e67 0.254691
\(777\) −2.07344e68 −2.46489
\(778\) −2.55834e67 −0.295079
\(779\) −1.27281e68 −1.42440
\(780\) 2.22985e66 0.0242132
\(781\) −3.15385e67 −0.332308
\(782\) 2.89492e67 0.295991
\(783\) −9.03883e66 −0.0896831
\(784\) 8.15198e67 0.784939
\(785\) 7.49461e67 0.700345
\(786\) −8.94990e67 −0.811687
\(787\) −3.00261e67 −0.264297 −0.132149 0.991230i \(-0.542188\pi\)
−0.132149 + 0.991230i \(0.542188\pi\)
\(788\) −1.18806e68 −1.01502
\(789\) 2.85175e68 2.36484
\(790\) 1.72335e67 0.138719
\(791\) −5.55233e67 −0.433839
\(792\) 3.21193e67 0.243626
\(793\) 1.74601e66 0.0128566
\(794\) −8.84526e67 −0.632308
\(795\) 5.67524e67 0.393874
\(796\) −1.40520e68 −0.946852
\(797\) −2.46726e67 −0.161415 −0.0807077 0.996738i \(-0.525718\pi\)
−0.0807077 + 0.996738i \(0.525718\pi\)
\(798\) 1.85786e68 1.18017
\(799\) 3.21574e68 1.98349
\(800\) 5.26785e67 0.315514
\(801\) −1.35998e68 −0.790986
\(802\) −1.13151e68 −0.639089
\(803\) −4.63103e67 −0.254017
\(804\) 3.18598e68 1.69717
\(805\) −1.85543e68 −0.959936
\(806\) 4.70578e65 0.00236460
\(807\) −3.37634e68 −1.64785
\(808\) 3.48538e67 0.165228
\(809\) −2.87119e68 −1.32212 −0.661061 0.750332i \(-0.729894\pi\)
−0.661061 + 0.750332i \(0.729894\pi\)
\(810\) 1.11700e68 0.499636
\(811\) 4.03047e67 0.175132 0.0875661 0.996159i \(-0.472091\pi\)
0.0875661 + 0.996159i \(0.472091\pi\)
\(812\) 1.38169e68 0.583236
\(813\) −4.62786e67 −0.189781
\(814\) −4.57269e67 −0.182179
\(815\) −2.70218e68 −1.04595
\(816\) −2.99436e68 −1.12612
\(817\) 3.59575e68 1.31393
\(818\) 8.06431e67 0.286329
\(819\) −6.83312e66 −0.0235748
\(820\) 2.84419e68 0.953526
\(821\) 2.55050e68 0.830923 0.415462 0.909611i \(-0.363620\pi\)
0.415462 + 0.909611i \(0.363620\pi\)
\(822\) −1.58408e68 −0.501521
\(823\) 2.96708e68 0.912922 0.456461 0.889743i \(-0.349117\pi\)
0.456461 + 0.889743i \(0.349117\pi\)
\(824\) 2.87298e67 0.0859097
\(825\) 6.36712e67 0.185044
\(826\) 3.58690e67 0.101318
\(827\) −5.78282e68 −1.58767 −0.793835 0.608133i \(-0.791919\pi\)
−0.793835 + 0.608133i \(0.791919\pi\)
\(828\) −1.47340e68 −0.393194
\(829\) −1.50860e68 −0.391330 −0.195665 0.980671i \(-0.562687\pi\)
−0.195665 + 0.980671i \(0.562687\pi\)
\(830\) −2.31544e68 −0.583846
\(831\) 1.09089e69 2.67397
\(832\) 1.68120e66 0.00400609
\(833\) 8.32942e68 1.92956
\(834\) −2.12028e68 −0.477520
\(835\) −8.11074e68 −1.77594
\(836\) −2.37450e68 −0.505503
\(837\) −3.32159e67 −0.0687539
\(838\) 2.87733e68 0.579102
\(839\) 5.78467e67 0.113207 0.0566034 0.998397i \(-0.481973\pi\)
0.0566034 + 0.998397i \(0.481973\pi\)
\(840\) −9.01944e68 −1.71639
\(841\) −4.32977e68 −0.801233
\(842\) 3.95253e68 0.711281
\(843\) −6.63705e68 −1.16152
\(844\) −1.36479e68 −0.232283
\(845\) 6.98598e68 1.15636
\(846\) 2.82413e68 0.454655
\(847\) −8.21157e68 −1.28578
\(848\) 9.53104e67 0.145157
\(849\) 5.33764e68 0.790712
\(850\) 1.28351e68 0.184950
\(851\) 4.55719e68 0.638782
\(852\) 7.03281e68 0.958956
\(853\) −6.70885e68 −0.889910 −0.444955 0.895553i \(-0.646780\pi\)
−0.444955 + 0.895553i \(0.646780\pi\)
\(854\) −3.25073e68 −0.419489
\(855\) 1.15713e69 1.45270
\(856\) 4.25804e68 0.520087
\(857\) 1.18679e69 1.41034 0.705168 0.709040i \(-0.250871\pi\)
0.705168 + 0.709040i \(0.250871\pi\)
\(858\) −3.27527e66 −0.00378701
\(859\) −1.90685e67 −0.0214525 −0.0107262 0.999942i \(-0.503414\pi\)
−0.0107262 + 0.999942i \(0.503414\pi\)
\(860\) −8.03500e68 −0.879574
\(861\) −1.89431e69 −2.01779
\(862\) 2.85677e68 0.296111
\(863\) −8.52667e68 −0.860054 −0.430027 0.902816i \(-0.641496\pi\)
−0.430027 + 0.902816i \(0.641496\pi\)
\(864\) 1.91272e68 0.187749
\(865\) 9.69839e68 0.926448
\(866\) −2.80472e68 −0.260747
\(867\) −1.55538e69 −1.40731
\(868\) 5.07743e68 0.447127
\(869\) 1.46698e68 0.125736
\(870\) −3.22736e68 −0.269244
\(871\) −3.24749e67 −0.0263706
\(872\) 2.37667e68 0.187858
\(873\) −3.96874e68 −0.305364
\(874\) −4.08337e68 −0.305844
\(875\) 1.61085e69 1.17454
\(876\) 1.03268e69 0.733027
\(877\) 7.64441e67 0.0528267 0.0264134 0.999651i \(-0.491591\pi\)
0.0264134 + 0.999651i \(0.491591\pi\)
\(878\) −7.57608e68 −0.509711
\(879\) −1.70241e69 −1.11513
\(880\) 4.23245e68 0.269929
\(881\) −9.82470e68 −0.610078 −0.305039 0.952340i \(-0.598670\pi\)
−0.305039 + 0.952340i \(0.598670\pi\)
\(882\) 7.31509e68 0.442291
\(883\) −1.96558e68 −0.115722 −0.0578609 0.998325i \(-0.518428\pi\)
−0.0578609 + 0.998325i \(0.518428\pi\)
\(884\) 3.82633e67 0.0219359
\(885\) 4.85551e68 0.271062
\(886\) 5.88459e68 0.319907
\(887\) 3.52341e69 1.86534 0.932670 0.360731i \(-0.117473\pi\)
0.932670 + 0.360731i \(0.117473\pi\)
\(888\) 2.21529e69 1.14216
\(889\) 9.92383e67 0.0498297
\(890\) 8.42222e68 0.411871
\(891\) 9.50829e68 0.452873
\(892\) −2.81077e69 −1.30392
\(893\) −4.53588e69 −2.04952
\(894\) −1.19100e69 −0.524179
\(895\) 1.77525e69 0.761061
\(896\) −3.74134e69 −1.56239
\(897\) 3.26417e67 0.0132785
\(898\) −6.71657e68 −0.266167
\(899\) 3.94715e68 0.152381
\(900\) −6.53256e68 −0.245688
\(901\) 9.73850e68 0.356829
\(902\) −4.17763e68 −0.149134
\(903\) 5.35154e69 1.86130
\(904\) 5.93218e68 0.201028
\(905\) −5.13022e69 −1.69393
\(906\) 1.06676e69 0.343204
\(907\) 1.85786e69 0.582428 0.291214 0.956658i \(-0.405941\pi\)
0.291214 + 0.956658i \(0.405941\pi\)
\(908\) −3.68218e69 −1.12483
\(909\) −6.65487e68 −0.198102
\(910\) 4.23168e67 0.0122755
\(911\) 1.88130e69 0.531835 0.265918 0.963996i \(-0.414325\pi\)
0.265918 + 0.963996i \(0.414325\pi\)
\(912\) 4.22362e69 1.16361
\(913\) −1.97099e69 −0.529202
\(914\) −8.67862e68 −0.227099
\(915\) −4.40044e69 −1.12228
\(916\) 5.72835e69 1.42392
\(917\) 9.84316e69 2.38482
\(918\) 4.66035e68 0.110056
\(919\) −3.45864e69 −0.796143 −0.398071 0.917354i \(-0.630320\pi\)
−0.398071 + 0.917354i \(0.630320\pi\)
\(920\) 1.98237e69 0.444806
\(921\) −3.68557e69 −0.806126
\(922\) 1.00023e68 0.0213266
\(923\) −7.16858e67 −0.0149002
\(924\) −3.53395e69 −0.716092
\(925\) 2.02051e69 0.399144
\(926\) −7.64579e68 −0.147253
\(927\) −5.48557e68 −0.103002
\(928\) −2.27295e69 −0.416113
\(929\) −3.44629e69 −0.615153 −0.307576 0.951523i \(-0.599518\pi\)
−0.307576 + 0.951523i \(0.599518\pi\)
\(930\) −1.18599e69 −0.206411
\(931\) −1.17489e70 −1.99379
\(932\) −2.22375e69 −0.367970
\(933\) 4.83597e69 0.780306
\(934\) 6.24500e68 0.0982609
\(935\) 4.32458e69 0.663546
\(936\) 7.30059e67 0.0109238
\(937\) 2.88144e69 0.420464 0.210232 0.977652i \(-0.432578\pi\)
0.210232 + 0.977652i \(0.432578\pi\)
\(938\) 6.04618e69 0.860428
\(939\) −1.00479e70 −1.39455
\(940\) 1.01358e70 1.37200
\(941\) 3.65396e69 0.482400 0.241200 0.970475i \(-0.422459\pi\)
0.241200 + 0.970475i \(0.422459\pi\)
\(942\) 2.45477e69 0.316092
\(943\) 4.16347e69 0.522914
\(944\) 8.15438e68 0.0998962
\(945\) −2.98694e69 −0.356927
\(946\) 1.18021e69 0.137568
\(947\) −2.53356e69 −0.288075 −0.144038 0.989572i \(-0.546009\pi\)
−0.144038 + 0.989572i \(0.546009\pi\)
\(948\) −3.27124e69 −0.362841
\(949\) −1.05262e68 −0.0113898
\(950\) −1.81043e69 −0.191107
\(951\) 1.34009e70 1.38004
\(952\) −1.54770e70 −1.55496
\(953\) −4.10317e69 −0.402195 −0.201097 0.979571i \(-0.564451\pi\)
−0.201097 + 0.979571i \(0.564451\pi\)
\(954\) 8.55258e68 0.0817919
\(955\) 4.12463e69 0.384862
\(956\) 7.26304e69 0.661238
\(957\) −2.74725e69 −0.244044
\(958\) −7.38870e69 −0.640440
\(959\) 1.74218e70 1.47352
\(960\) −4.23710e69 −0.349699
\(961\) −1.09660e70 −0.883180
\(962\) −1.03936e68 −0.00816866
\(963\) −8.13016e69 −0.623565
\(964\) −4.02486e69 −0.301259
\(965\) −2.01468e70 −1.47168
\(966\) −6.07724e69 −0.433256
\(967\) −2.82974e69 −0.196890 −0.0984451 0.995142i \(-0.531387\pi\)
−0.0984451 + 0.995142i \(0.531387\pi\)
\(968\) 8.77334e69 0.595791
\(969\) 4.31556e70 2.86041
\(970\) 2.45780e69 0.159005
\(971\) −2.13025e70 −1.34517 −0.672587 0.740018i \(-0.734817\pi\)
−0.672587 + 0.740018i \(0.734817\pi\)
\(972\) −1.84194e70 −1.13532
\(973\) 2.33190e70 1.40300
\(974\) 5.00098e68 0.0293711
\(975\) 1.44722e68 0.00829711
\(976\) −7.39014e69 −0.413601
\(977\) 2.95878e70 1.61655 0.808277 0.588802i \(-0.200400\pi\)
0.808277 + 0.588802i \(0.200400\pi\)
\(978\) −8.85066e69 −0.472077
\(979\) 7.16931e69 0.373322
\(980\) 2.62538e70 1.33469
\(981\) −4.53793e69 −0.225235
\(982\) 1.21120e70 0.586945
\(983\) −5.99760e69 −0.283772 −0.141886 0.989883i \(-0.545317\pi\)
−0.141886 + 0.989883i \(0.545317\pi\)
\(984\) 2.02390e70 0.934985
\(985\) −3.05206e70 −1.37671
\(986\) −5.53804e69 −0.243921
\(987\) −6.75072e70 −2.90333
\(988\) −5.39715e68 −0.0226661
\(989\) −1.17621e70 −0.482359
\(990\) 3.79795e69 0.152097
\(991\) 3.56295e70 1.39341 0.696706 0.717357i \(-0.254648\pi\)
0.696706 + 0.717357i \(0.254648\pi\)
\(992\) −8.35261e69 −0.319005
\(993\) 4.50689e68 0.0168101
\(994\) 1.33465e70 0.486169
\(995\) −3.60988e70 −1.28425
\(996\) 4.39514e70 1.52714
\(997\) −8.80387e69 −0.298770 −0.149385 0.988779i \(-0.547729\pi\)
−0.149385 + 0.988779i \(0.547729\pi\)
\(998\) −1.01152e70 −0.335278
\(999\) 7.33632e69 0.237514
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 1.48.a.a.1.3 4
3.2 odd 2 9.48.a.c.1.2 4
4.3 odd 2 16.48.a.d.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.48.a.a.1.3 4 1.1 even 1 trivial
9.48.a.c.1.2 4 3.2 odd 2
16.48.a.d.1.4 4 4.3 odd 2