Properties

Label 1.32.a.a.1.2
Level $1$
Weight $32$
Character 1.1
Self dual yes
Analytic conductor $6.088$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 32 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.08771328190\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
Defining polynomial: \(x^{2} - x - 4573872\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2138.16\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+71307.9 q^{2} +3.08552e7 q^{3} +2.93733e9 q^{4} -8.25073e10 q^{5} +2.20022e12 q^{6} +1.14368e13 q^{7} +5.63222e13 q^{8} +3.34371e14 q^{9} +O(q^{10})\) \(q+71307.9 q^{2} +3.08552e7 q^{3} +2.93733e9 q^{4} -8.25073e10 q^{5} +2.20022e12 q^{6} +1.14368e13 q^{7} +5.63222e13 q^{8} +3.34371e14 q^{9} -5.88342e15 q^{10} -2.40262e15 q^{11} +9.06319e16 q^{12} -2.01886e17 q^{13} +8.15534e17 q^{14} -2.54578e18 q^{15} -2.29165e18 q^{16} +1.09264e19 q^{17} +2.38433e19 q^{18} -1.42851e19 q^{19} -2.42351e20 q^{20} +3.52885e20 q^{21} -1.71326e20 q^{22} -3.85062e18 q^{23} +1.73783e21 q^{24} +2.15084e21 q^{25} -1.43960e22 q^{26} -8.74135e21 q^{27} +3.35937e22 q^{28} +7.63087e22 q^{29} -1.81534e23 q^{30} +1.86701e23 q^{31} -2.84364e23 q^{32} -7.41334e22 q^{33} +7.79141e23 q^{34} -9.43620e23 q^{35} +9.82158e23 q^{36} +1.23709e24 q^{37} -1.01864e24 q^{38} -6.22922e24 q^{39} -4.64699e24 q^{40} +1.38199e25 q^{41} +2.51635e25 q^{42} -2.67871e25 q^{43} -7.05729e24 q^{44} -2.75881e25 q^{45} -2.74580e23 q^{46} +7.40922e25 q^{47} -7.07094e25 q^{48} -2.69748e25 q^{49} +1.53372e26 q^{50} +3.37138e26 q^{51} -5.93004e26 q^{52} +3.56092e25 q^{53} -6.23327e26 q^{54} +1.98234e26 q^{55} +6.44146e26 q^{56} -4.40770e26 q^{57} +5.44141e27 q^{58} -2.36122e27 q^{59} -7.47779e27 q^{60} -5.44842e27 q^{61} +1.33133e28 q^{62} +3.82414e27 q^{63} -1.53561e28 q^{64} +1.66570e28 q^{65} -5.28630e27 q^{66} -9.41082e27 q^{67} +3.20945e28 q^{68} -1.18812e26 q^{69} -6.72875e28 q^{70} -2.10678e28 q^{71} +1.88325e28 q^{72} +3.92731e28 q^{73} +8.82146e28 q^{74} +6.63646e28 q^{75} -4.19601e28 q^{76} -2.74783e28 q^{77} -4.44193e29 q^{78} +1.79850e29 q^{79} +1.89078e29 q^{80} -4.76249e29 q^{81} +9.85468e29 q^{82} -4.54329e29 q^{83} +1.03654e30 q^{84} -9.01511e29 q^{85} -1.91013e30 q^{86} +2.35452e30 q^{87} -1.35321e29 q^{88} +2.60812e29 q^{89} -1.96725e30 q^{90} -2.30893e30 q^{91} -1.13106e28 q^{92} +5.76072e30 q^{93} +5.28336e30 q^{94} +1.17863e30 q^{95} -8.77410e30 q^{96} -5.38067e30 q^{97} -1.92352e30 q^{98} -8.03368e29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 39960q^{2} + 17363160q^{3} + 1772534336q^{4} - 19391218020q^{5} + 2623167496224q^{6} + 30257527577200q^{7} + 160155058705920q^{8} - 101266456303926q^{9} + O(q^{10}) \) \( 2q + 39960q^{2} + 17363160q^{3} + 1772534336q^{4} - 19391218020q^{5} + 2623167496224q^{6} + 30257527577200q^{7} + 160155058705920q^{8} - 101266456303926q^{9} - 7861972212281520q^{10} - 7782353745118776q^{11} + 106347410955313920q^{12} + 74708953050260620q^{13} + 225544963845241152q^{14} - 3397345822674581040q^{15} - 3045212913684901888q^{16} + 17224607828987089380q^{17} + 37499616229575978360q^{18} - 12370563328022164040q^{19} - \)\(31\!\cdots\!60\)\(q^{20} + 98954957416071161664q^{21} - 2682713032996690080q^{22} + \)\(18\!\cdots\!80\)\(q^{23} + \)\(33\!\cdots\!80\)\(q^{24} + \)\(14\!\cdots\!50\)\(q^{25} - \)\(23\!\cdots\!16\)\(q^{26} + \)\(54\!\cdots\!80\)\(q^{27} + \)\(11\!\cdots\!20\)\(q^{28} + \)\(12\!\cdots\!40\)\(q^{29} - \)\(15\!\cdots\!40\)\(q^{30} + \)\(12\!\cdots\!64\)\(q^{31} - \)\(48\!\cdots\!40\)\(q^{32} - \)\(15\!\cdots\!80\)\(q^{33} + \)\(58\!\cdots\!92\)\(q^{34} + \)\(24\!\cdots\!80\)\(q^{35} + \)\(14\!\cdots\!32\)\(q^{36} - \)\(83\!\cdots\!60\)\(q^{37} - \)\(10\!\cdots\!20\)\(q^{38} - \)\(99\!\cdots\!12\)\(q^{39} + \)\(19\!\cdots\!00\)\(q^{40} + \)\(87\!\cdots\!84\)\(q^{41} + \)\(33\!\cdots\!80\)\(q^{42} - \)\(18\!\cdots\!00\)\(q^{43} - \)\(79\!\cdots\!68\)\(q^{44} - \)\(55\!\cdots\!40\)\(q^{45} - \)\(59\!\cdots\!56\)\(q^{46} + \)\(95\!\cdots\!20\)\(q^{47} - \)\(60\!\cdots\!20\)\(q^{48} + \)\(16\!\cdots\!86\)\(q^{49} + \)\(17\!\cdots\!00\)\(q^{50} + \)\(25\!\cdots\!44\)\(q^{51} - \)\(91\!\cdots\!00\)\(q^{52} + \)\(19\!\cdots\!60\)\(q^{53} - \)\(10\!\cdots\!40\)\(q^{54} - \)\(14\!\cdots\!40\)\(q^{55} + \)\(25\!\cdots\!40\)\(q^{56} - \)\(46\!\cdots\!40\)\(q^{57} + \)\(38\!\cdots\!20\)\(q^{58} - \)\(19\!\cdots\!20\)\(q^{59} - \)\(64\!\cdots\!20\)\(q^{60} - \)\(12\!\cdots\!76\)\(q^{61} + \)\(15\!\cdots\!20\)\(q^{62} - \)\(43\!\cdots\!60\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} + \)\(34\!\cdots\!60\)\(q^{65} - \)\(75\!\cdots\!12\)\(q^{66} - \)\(96\!\cdots\!20\)\(q^{67} + \)\(24\!\cdots\!60\)\(q^{68} - \)\(25\!\cdots\!92\)\(q^{69} - \)\(10\!\cdots\!20\)\(q^{70} + \)\(55\!\cdots\!44\)\(q^{71} - \)\(26\!\cdots\!60\)\(q^{72} + \)\(62\!\cdots\!80\)\(q^{73} + \)\(15\!\cdots\!72\)\(q^{74} + \)\(75\!\cdots\!00\)\(q^{75} - \)\(44\!\cdots\!20\)\(q^{76} - \)\(12\!\cdots\!00\)\(q^{77} - \)\(32\!\cdots\!00\)\(q^{78} - \)\(11\!\cdots\!60\)\(q^{79} + \)\(14\!\cdots\!80\)\(q^{80} - \)\(39\!\cdots\!58\)\(q^{81} + \)\(11\!\cdots\!20\)\(q^{82} - \)\(26\!\cdots\!60\)\(q^{83} + \)\(13\!\cdots\!52\)\(q^{84} - \)\(50\!\cdots\!20\)\(q^{85} - \)\(21\!\cdots\!36\)\(q^{86} + \)\(16\!\cdots\!40\)\(q^{87} - \)\(69\!\cdots\!60\)\(q^{88} - \)\(21\!\cdots\!80\)\(q^{89} - \)\(11\!\cdots\!40\)\(q^{90} + \)\(28\!\cdots\!24\)\(q^{91} - \)\(22\!\cdots\!20\)\(q^{92} + \)\(65\!\cdots\!20\)\(q^{93} + \)\(46\!\cdots\!12\)\(q^{94} + \)\(12\!\cdots\!00\)\(q^{95} - \)\(60\!\cdots\!96\)\(q^{96} - \)\(90\!\cdots\!80\)\(q^{97} - \)\(80\!\cdots\!20\)\(q^{98} + \)\(15\!\cdots\!88\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 71307.9 1.53877 0.769383 0.638788i \(-0.220564\pi\)
0.769383 + 0.638788i \(0.220564\pi\)
\(3\) 3.08552e7 1.24151 0.620754 0.784006i \(-0.286827\pi\)
0.620754 + 0.784006i \(0.286827\pi\)
\(4\) 2.93733e9 1.36780
\(5\) −8.25073e10 −1.20909 −0.604543 0.796573i \(-0.706644\pi\)
−0.604543 + 0.796573i \(0.706644\pi\)
\(6\) 2.20022e12 1.91039
\(7\) 1.14368e13 0.910511 0.455256 0.890361i \(-0.349548\pi\)
0.455256 + 0.890361i \(0.349548\pi\)
\(8\) 5.63222e13 0.565959
\(9\) 3.34371e14 0.541340
\(10\) −5.88342e15 −1.86050
\(11\) −2.40262e15 −0.173420 −0.0867099 0.996234i \(-0.527635\pi\)
−0.0867099 + 0.996234i \(0.527635\pi\)
\(12\) 9.06319e16 1.69813
\(13\) −2.01886e17 −1.09391 −0.546957 0.837161i \(-0.684214\pi\)
−0.546957 + 0.837161i \(0.684214\pi\)
\(14\) 8.15534e17 1.40106
\(15\) −2.54578e18 −1.50109
\(16\) −2.29165e18 −0.496923
\(17\) 1.09264e19 0.925807 0.462903 0.886409i \(-0.346808\pi\)
0.462903 + 0.886409i \(0.346808\pi\)
\(18\) 2.38433e19 0.832995
\(19\) −1.42851e19 −0.215875 −0.107938 0.994158i \(-0.534425\pi\)
−0.107938 + 0.994158i \(0.534425\pi\)
\(20\) −2.42351e20 −1.65379
\(21\) 3.52885e20 1.13041
\(22\) −1.71326e20 −0.266853
\(23\) −3.85062e18 −0.00301127 −0.00150564 0.999999i \(-0.500479\pi\)
−0.00150564 + 0.999999i \(0.500479\pi\)
\(24\) 1.73783e21 0.702642
\(25\) 2.15084e21 0.461889
\(26\) −1.43960e22 −1.68328
\(27\) −8.74135e21 −0.569430
\(28\) 3.35937e22 1.24540
\(29\) 7.63087e22 1.64212 0.821060 0.570842i \(-0.193383\pi\)
0.821060 + 0.570842i \(0.193383\pi\)
\(30\) −1.81534e23 −2.30982
\(31\) 1.86701e23 1.42903 0.714515 0.699620i \(-0.246647\pi\)
0.714515 + 0.699620i \(0.246647\pi\)
\(32\) −2.84364e23 −1.33061
\(33\) −7.41334e22 −0.215302
\(34\) 7.79141e23 1.42460
\(35\) −9.43620e23 −1.10089
\(36\) 9.82158e23 0.740445
\(37\) 1.23709e24 0.609924 0.304962 0.952364i \(-0.401356\pi\)
0.304962 + 0.952364i \(0.401356\pi\)
\(38\) −1.01864e24 −0.332182
\(39\) −6.22922e24 −1.35810
\(40\) −4.64699e24 −0.684293
\(41\) 1.38199e25 1.38789 0.693945 0.720028i \(-0.255871\pi\)
0.693945 + 0.720028i \(0.255871\pi\)
\(42\) 2.51635e25 1.73943
\(43\) −2.67871e25 −1.28578 −0.642888 0.765960i \(-0.722264\pi\)
−0.642888 + 0.765960i \(0.722264\pi\)
\(44\) −7.05729e24 −0.237204
\(45\) −2.75881e25 −0.654526
\(46\) −2.74580e23 −0.00463364
\(47\) 7.40922e25 0.895892 0.447946 0.894061i \(-0.352156\pi\)
0.447946 + 0.894061i \(0.352156\pi\)
\(48\) −7.07094e25 −0.616933
\(49\) −2.69748e25 −0.170970
\(50\) 1.53372e26 0.710739
\(51\) 3.37138e26 1.14940
\(52\) −5.93004e26 −1.49626
\(53\) 3.56092e25 0.0668784 0.0334392 0.999441i \(-0.489354\pi\)
0.0334392 + 0.999441i \(0.489354\pi\)
\(54\) −6.23327e26 −0.876219
\(55\) 1.98234e26 0.209680
\(56\) 6.44146e26 0.515312
\(57\) −4.40770e26 −0.268011
\(58\) 5.44141e27 2.52684
\(59\) −2.36122e27 −0.841260 −0.420630 0.907232i \(-0.638191\pi\)
−0.420630 + 0.907232i \(0.638191\pi\)
\(60\) −7.47779e27 −2.05319
\(61\) −5.44842e27 −1.15786 −0.578932 0.815376i \(-0.696530\pi\)
−0.578932 + 0.815376i \(0.696530\pi\)
\(62\) 1.33133e28 2.19894
\(63\) 3.82414e27 0.492896
\(64\) −1.53561e28 −1.55057
\(65\) 1.66570e28 1.32264
\(66\) −5.28630e27 −0.331299
\(67\) −9.41082e27 −0.467163 −0.233581 0.972337i \(-0.575044\pi\)
−0.233581 + 0.972337i \(0.575044\pi\)
\(68\) 3.20945e28 1.26632
\(69\) −1.18812e26 −0.00373851
\(70\) −6.72875e28 −1.69401
\(71\) −2.10678e28 −0.425712 −0.212856 0.977084i \(-0.568276\pi\)
−0.212856 + 0.977084i \(0.568276\pi\)
\(72\) 1.88325e28 0.306376
\(73\) 3.92731e28 0.515929 0.257965 0.966154i \(-0.416948\pi\)
0.257965 + 0.966154i \(0.416948\pi\)
\(74\) 8.82146e28 0.938531
\(75\) 6.63646e28 0.573438
\(76\) −4.19601e28 −0.295274
\(77\) −2.74783e28 −0.157901
\(78\) −4.44193e29 −2.08980
\(79\) 1.79850e29 0.694529 0.347264 0.937767i \(-0.387111\pi\)
0.347264 + 0.937767i \(0.387111\pi\)
\(80\) 1.89078e29 0.600822
\(81\) −4.76249e29 −1.24829
\(82\) 9.85468e29 2.13564
\(83\) −4.54329e29 −0.815944 −0.407972 0.912995i \(-0.633764\pi\)
−0.407972 + 0.912995i \(0.633764\pi\)
\(84\) 1.03654e30 1.54617
\(85\) −9.01511e29 −1.11938
\(86\) −1.91013e30 −1.97851
\(87\) 2.35452e30 2.03870
\(88\) −1.35321e29 −0.0981485
\(89\) 2.60812e29 0.158775 0.0793875 0.996844i \(-0.474704\pi\)
0.0793875 + 0.996844i \(0.474704\pi\)
\(90\) −1.96725e30 −1.00716
\(91\) −2.30893e30 −0.996021
\(92\) −1.13106e28 −0.00411882
\(93\) 5.76072e30 1.77415
\(94\) 5.28336e30 1.37857
\(95\) 1.17863e30 0.261012
\(96\) −8.77410e30 −1.65196
\(97\) −5.38067e30 −0.862729 −0.431365 0.902178i \(-0.641968\pi\)
−0.431365 + 0.902178i \(0.641968\pi\)
\(98\) −1.92352e30 −0.263082
\(99\) −8.03368e29 −0.0938791
\(100\) 6.31772e30 0.631772
\(101\) −1.28863e31 −1.10445 −0.552225 0.833695i \(-0.686221\pi\)
−0.552225 + 0.833695i \(0.686221\pi\)
\(102\) 2.40406e31 1.76865
\(103\) 1.91208e31 1.20928 0.604642 0.796497i \(-0.293316\pi\)
0.604642 + 0.796497i \(0.293316\pi\)
\(104\) −1.13706e31 −0.619110
\(105\) −2.91156e31 −1.36676
\(106\) 2.53922e30 0.102910
\(107\) 3.15334e31 1.10490 0.552449 0.833547i \(-0.313693\pi\)
0.552449 + 0.833547i \(0.313693\pi\)
\(108\) −2.56762e31 −0.778866
\(109\) −3.61029e31 −0.949360 −0.474680 0.880158i \(-0.657436\pi\)
−0.474680 + 0.880158i \(0.657436\pi\)
\(110\) 1.41356e31 0.322648
\(111\) 3.81708e31 0.757226
\(112\) −2.62092e31 −0.452453
\(113\) 1.52549e31 0.229454 0.114727 0.993397i \(-0.463401\pi\)
0.114727 + 0.993397i \(0.463401\pi\)
\(114\) −3.14304e31 −0.412406
\(115\) 3.17705e29 0.00364088
\(116\) 2.24144e32 2.24609
\(117\) −6.75047e31 −0.592179
\(118\) −1.68374e32 −1.29450
\(119\) 1.24964e32 0.842957
\(120\) −1.43384e32 −0.849554
\(121\) −1.86171e32 −0.969926
\(122\) −3.88515e32 −1.78168
\(123\) 4.26416e32 1.72308
\(124\) 5.48404e32 1.95463
\(125\) 2.06745e32 0.650623
\(126\) 2.72691e32 0.758451
\(127\) −5.69060e32 −1.40023 −0.700116 0.714029i \(-0.746869\pi\)
−0.700116 + 0.714029i \(0.746869\pi\)
\(128\) −4.84344e32 −1.05536
\(129\) −8.26523e32 −1.59630
\(130\) 1.18778e33 2.03523
\(131\) 1.80373e31 0.0274452 0.0137226 0.999906i \(-0.495632\pi\)
0.0137226 + 0.999906i \(0.495632\pi\)
\(132\) −2.17754e32 −0.294490
\(133\) −1.63376e32 −0.196557
\(134\) −6.71065e32 −0.718854
\(135\) 7.21225e32 0.688490
\(136\) 6.15401e32 0.523968
\(137\) −1.53340e32 −0.116543 −0.0582716 0.998301i \(-0.518559\pi\)
−0.0582716 + 0.998301i \(0.518559\pi\)
\(138\) −8.47222e30 −0.00575270
\(139\) 1.88034e33 1.14158 0.570791 0.821095i \(-0.306636\pi\)
0.570791 + 0.821095i \(0.306636\pi\)
\(140\) −2.77172e33 −1.50579
\(141\) 2.28613e33 1.11226
\(142\) −1.50230e33 −0.655070
\(143\) 4.85055e32 0.189706
\(144\) −7.66262e32 −0.269004
\(145\) −6.29602e33 −1.98546
\(146\) 2.80048e33 0.793895
\(147\) −8.32313e32 −0.212260
\(148\) 3.63375e33 0.834255
\(149\) 6.64703e33 1.37480 0.687401 0.726278i \(-0.258751\pi\)
0.687401 + 0.726278i \(0.258751\pi\)
\(150\) 4.73232e33 0.882387
\(151\) −6.58887e33 −1.10833 −0.554164 0.832408i \(-0.686962\pi\)
−0.554164 + 0.832408i \(0.686962\pi\)
\(152\) −8.04569e32 −0.122177
\(153\) 3.65349e33 0.501176
\(154\) −1.95942e33 −0.242972
\(155\) −1.54042e34 −1.72782
\(156\) −1.82973e34 −1.85761
\(157\) 1.60319e34 1.47414 0.737072 0.675814i \(-0.236208\pi\)
0.737072 + 0.675814i \(0.236208\pi\)
\(158\) 1.28247e34 1.06872
\(159\) 1.09873e33 0.0830300
\(160\) 2.34621e34 1.60882
\(161\) −4.40389e31 −0.00274179
\(162\) −3.39603e34 −1.92083
\(163\) −1.63484e34 −0.840555 −0.420277 0.907396i \(-0.638067\pi\)
−0.420277 + 0.907396i \(0.638067\pi\)
\(164\) 4.05936e34 1.89836
\(165\) 6.11655e33 0.260319
\(166\) −3.23972e34 −1.25555
\(167\) 1.68065e34 0.593433 0.296717 0.954966i \(-0.404108\pi\)
0.296717 + 0.954966i \(0.404108\pi\)
\(168\) 1.98753e34 0.639763
\(169\) 6.69784e33 0.196649
\(170\) −6.42848e34 −1.72246
\(171\) −4.77653e33 −0.116862
\(172\) −7.86826e34 −1.75868
\(173\) 1.67734e34 0.342695 0.171347 0.985211i \(-0.445188\pi\)
0.171347 + 0.985211i \(0.445188\pi\)
\(174\) 1.67896e35 3.13709
\(175\) 2.45987e34 0.420555
\(176\) 5.50597e33 0.0861762
\(177\) −7.28560e34 −1.04443
\(178\) 1.85979e34 0.244318
\(179\) 5.67856e33 0.0683937 0.0341968 0.999415i \(-0.489113\pi\)
0.0341968 + 0.999415i \(0.489113\pi\)
\(180\) −8.10352e34 −0.895262
\(181\) 1.47595e35 1.49642 0.748210 0.663462i \(-0.230914\pi\)
0.748210 + 0.663462i \(0.230914\pi\)
\(182\) −1.64645e35 −1.53264
\(183\) −1.68112e35 −1.43750
\(184\) −2.16876e32 −0.00170425
\(185\) −1.02069e35 −0.737451
\(186\) 4.10784e35 2.73000
\(187\) −2.62521e34 −0.160553
\(188\) 2.17633e35 1.22540
\(189\) −9.99731e34 −0.518472
\(190\) 8.40453e34 0.401636
\(191\) −4.38203e34 −0.193045 −0.0965224 0.995331i \(-0.530772\pi\)
−0.0965224 + 0.995331i \(0.530772\pi\)
\(192\) −4.73815e35 −1.92504
\(193\) 2.63656e35 0.988323 0.494161 0.869370i \(-0.335475\pi\)
0.494161 + 0.869370i \(0.335475\pi\)
\(194\) −3.83684e35 −1.32754
\(195\) 5.13956e35 1.64206
\(196\) −7.92339e34 −0.233852
\(197\) −2.72680e35 −0.743749 −0.371875 0.928283i \(-0.621285\pi\)
−0.371875 + 0.928283i \(0.621285\pi\)
\(198\) −5.72864e34 −0.144458
\(199\) 3.17714e35 0.740991 0.370496 0.928834i \(-0.379188\pi\)
0.370496 + 0.928834i \(0.379188\pi\)
\(200\) 1.21140e35 0.261410
\(201\) −2.90373e35 −0.579986
\(202\) −9.18893e35 −1.69949
\(203\) 8.72728e35 1.49517
\(204\) 9.90284e35 1.57214
\(205\) −1.14024e36 −1.67808
\(206\) 1.36346e36 1.86081
\(207\) −1.28754e33 −0.00163012
\(208\) 4.62651e35 0.543591
\(209\) 3.43217e34 0.0374371
\(210\) −2.07617e36 −2.10312
\(211\) −2.10102e36 −1.97721 −0.988604 0.150541i \(-0.951898\pi\)
−0.988604 + 0.150541i \(0.951898\pi\)
\(212\) 1.04596e35 0.0914763
\(213\) −6.50053e35 −0.528524
\(214\) 2.24858e36 1.70018
\(215\) 2.21013e36 1.55461
\(216\) −4.92332e35 −0.322274
\(217\) 2.13527e36 1.30115
\(218\) −2.57442e36 −1.46084
\(219\) 1.21178e36 0.640530
\(220\) 5.82278e35 0.286800
\(221\) −2.20589e36 −1.01275
\(222\) 2.72188e36 1.16519
\(223\) −2.62490e36 −1.04806 −0.524032 0.851699i \(-0.675573\pi\)
−0.524032 + 0.851699i \(0.675573\pi\)
\(224\) −3.25221e36 −1.21153
\(225\) 7.19178e35 0.250039
\(226\) 1.08780e36 0.353075
\(227\) 1.16088e35 0.0351874 0.0175937 0.999845i \(-0.494399\pi\)
0.0175937 + 0.999845i \(0.494399\pi\)
\(228\) −1.29469e36 −0.366585
\(229\) 1.39980e36 0.370353 0.185177 0.982705i \(-0.440714\pi\)
0.185177 + 0.982705i \(0.440714\pi\)
\(230\) 2.26548e34 0.00560247
\(231\) −8.47850e35 −0.196035
\(232\) 4.29787e36 0.929372
\(233\) 7.15120e36 1.44665 0.723323 0.690510i \(-0.242614\pi\)
0.723323 + 0.690510i \(0.242614\pi\)
\(234\) −4.81362e36 −0.911226
\(235\) −6.11315e36 −1.08321
\(236\) −6.93568e36 −1.15068
\(237\) 5.54931e36 0.862262
\(238\) 8.91089e36 1.29711
\(239\) 2.96558e36 0.404522 0.202261 0.979332i \(-0.435171\pi\)
0.202261 + 0.979332i \(0.435171\pi\)
\(240\) 5.83404e36 0.745925
\(241\) −7.20536e36 −0.863757 −0.431879 0.901932i \(-0.642149\pi\)
−0.431879 + 0.901932i \(0.642149\pi\)
\(242\) −1.32754e37 −1.49249
\(243\) −9.29545e36 −0.980332
\(244\) −1.60038e37 −1.58373
\(245\) 2.22562e36 0.206717
\(246\) 3.04068e37 2.65141
\(247\) 2.88396e36 0.236149
\(248\) 1.05154e37 0.808772
\(249\) −1.40184e37 −1.01300
\(250\) 1.47425e37 1.00116
\(251\) 9.47842e36 0.605053 0.302526 0.953141i \(-0.402170\pi\)
0.302526 + 0.953141i \(0.402170\pi\)
\(252\) 1.12328e37 0.674183
\(253\) 9.25159e33 0.000522214 0
\(254\) −4.05784e37 −2.15463
\(255\) −2.78163e37 −1.38972
\(256\) −1.56056e36 −0.0733772
\(257\) 3.15504e37 1.39650 0.698252 0.715852i \(-0.253962\pi\)
0.698252 + 0.715852i \(0.253962\pi\)
\(258\) −5.89376e37 −2.45633
\(259\) 1.41484e37 0.555343
\(260\) 4.89272e37 1.80910
\(261\) 2.55154e37 0.888945
\(262\) 1.28620e36 0.0422318
\(263\) −1.25731e37 −0.389159 −0.194580 0.980887i \(-0.562334\pi\)
−0.194580 + 0.980887i \(0.562334\pi\)
\(264\) −4.17536e36 −0.121852
\(265\) −2.93802e36 −0.0808618
\(266\) −1.16500e37 −0.302455
\(267\) 8.04741e36 0.197120
\(268\) −2.76427e37 −0.638985
\(269\) 3.34018e37 0.728801 0.364401 0.931242i \(-0.381274\pi\)
0.364401 + 0.931242i \(0.381274\pi\)
\(270\) 5.14290e37 1.05942
\(271\) −4.00526e36 −0.0779125 −0.0389562 0.999241i \(-0.512403\pi\)
−0.0389562 + 0.999241i \(0.512403\pi\)
\(272\) −2.50396e37 −0.460054
\(273\) −7.12424e37 −1.23657
\(274\) −1.09344e37 −0.179333
\(275\) −5.16765e36 −0.0801007
\(276\) −3.48990e35 −0.00511354
\(277\) −7.94796e37 −1.10108 −0.550541 0.834808i \(-0.685578\pi\)
−0.550541 + 0.834808i \(0.685578\pi\)
\(278\) 1.34083e38 1.75663
\(279\) 6.24276e37 0.773591
\(280\) −5.31467e37 −0.623056
\(281\) −1.69314e38 −1.87822 −0.939108 0.343621i \(-0.888346\pi\)
−0.939108 + 0.343621i \(0.888346\pi\)
\(282\) 1.63019e38 1.71150
\(283\) 1.18735e38 1.18002 0.590008 0.807397i \(-0.299125\pi\)
0.590008 + 0.807397i \(0.299125\pi\)
\(284\) −6.18832e37 −0.582288
\(285\) 3.63668e37 0.324048
\(286\) 3.45882e37 0.291914
\(287\) 1.58056e38 1.26369
\(288\) −9.50830e37 −0.720310
\(289\) −1.99019e37 −0.142882
\(290\) −4.48956e38 −3.05516
\(291\) −1.66022e38 −1.07108
\(292\) 1.15358e38 0.705689
\(293\) 9.32191e37 0.540825 0.270413 0.962745i \(-0.412840\pi\)
0.270413 + 0.962745i \(0.412840\pi\)
\(294\) −5.93505e37 −0.326618
\(295\) 1.94818e38 1.01716
\(296\) 6.96759e37 0.345192
\(297\) 2.10022e37 0.0987504
\(298\) 4.73985e38 2.11550
\(299\) 7.77386e35 0.00329407
\(300\) 1.94935e38 0.784349
\(301\) −3.06359e38 −1.17071
\(302\) −4.69838e38 −1.70546
\(303\) −3.97609e38 −1.37118
\(304\) 3.27365e37 0.107273
\(305\) 4.49534e38 1.39996
\(306\) 2.60522e38 0.771193
\(307\) −2.10829e38 −0.593314 −0.296657 0.954984i \(-0.595872\pi\)
−0.296657 + 0.954984i \(0.595872\pi\)
\(308\) −8.07129e37 −0.215977
\(309\) 5.89976e38 1.50134
\(310\) −1.09844e39 −2.65871
\(311\) 4.24765e38 0.978053 0.489027 0.872269i \(-0.337352\pi\)
0.489027 + 0.872269i \(0.337352\pi\)
\(312\) −3.50844e38 −0.768630
\(313\) −3.07637e38 −0.641360 −0.320680 0.947188i \(-0.603911\pi\)
−0.320680 + 0.947188i \(0.603911\pi\)
\(314\) 1.14320e39 2.26836
\(315\) −3.15519e38 −0.595954
\(316\) 5.28278e38 0.949976
\(317\) −9.76522e38 −1.67210 −0.836052 0.548650i \(-0.815142\pi\)
−0.836052 + 0.548650i \(0.815142\pi\)
\(318\) 7.83480e37 0.127764
\(319\) −1.83341e38 −0.284776
\(320\) 1.26699e39 1.87477
\(321\) 9.72970e38 1.37174
\(322\) −3.14032e36 −0.00421898
\(323\) −1.56085e38 −0.199859
\(324\) −1.39890e39 −1.70741
\(325\) −4.34223e38 −0.505267
\(326\) −1.16577e39 −1.29342
\(327\) −1.11396e39 −1.17864
\(328\) 7.78367e38 0.785489
\(329\) 8.47379e38 0.815720
\(330\) 4.36158e38 0.400569
\(331\) 8.30576e38 0.727856 0.363928 0.931427i \(-0.381435\pi\)
0.363928 + 0.931427i \(0.381435\pi\)
\(332\) −1.33451e39 −1.11605
\(333\) 4.13649e38 0.330176
\(334\) 1.19844e39 0.913155
\(335\) 7.76461e38 0.564840
\(336\) −8.08690e38 −0.561724
\(337\) 1.84495e39 1.22383 0.611916 0.790923i \(-0.290399\pi\)
0.611916 + 0.790923i \(0.290399\pi\)
\(338\) 4.77609e38 0.302596
\(339\) 4.70695e38 0.284868
\(340\) −2.64803e39 −1.53109
\(341\) −4.48573e38 −0.247822
\(342\) −3.40604e38 −0.179823
\(343\) −2.11295e39 −1.06618
\(344\) −1.50871e39 −0.727696
\(345\) 9.80284e36 0.00452018
\(346\) 1.19608e39 0.527327
\(347\) −3.59852e39 −1.51711 −0.758555 0.651609i \(-0.774094\pi\)
−0.758555 + 0.651609i \(0.774094\pi\)
\(348\) 6.91600e39 2.78854
\(349\) 4.09325e38 0.157861 0.0789303 0.996880i \(-0.474850\pi\)
0.0789303 + 0.996880i \(0.474850\pi\)
\(350\) 1.75408e39 0.647136
\(351\) 1.76475e39 0.622907
\(352\) 6.83218e38 0.230754
\(353\) −5.32510e39 −1.72116 −0.860578 0.509319i \(-0.829897\pi\)
−0.860578 + 0.509319i \(0.829897\pi\)
\(354\) −5.19520e39 −1.60713
\(355\) 1.73825e39 0.514722
\(356\) 7.66090e38 0.217173
\(357\) 3.85578e39 1.04654
\(358\) 4.04926e38 0.105242
\(359\) 4.10824e39 1.02257 0.511283 0.859412i \(-0.329170\pi\)
0.511283 + 0.859412i \(0.329170\pi\)
\(360\) −1.55382e39 −0.370435
\(361\) −4.17480e39 −0.953398
\(362\) 1.05247e40 2.30264
\(363\) −5.74434e39 −1.20417
\(364\) −6.78208e39 −1.36236
\(365\) −3.24031e39 −0.623803
\(366\) −1.19877e40 −2.21197
\(367\) 9.50139e39 1.68060 0.840298 0.542125i \(-0.182380\pi\)
0.840298 + 0.542125i \(0.182380\pi\)
\(368\) 8.82429e36 0.00149637
\(369\) 4.62098e39 0.751320
\(370\) −7.27834e39 −1.13476
\(371\) 4.07255e38 0.0608935
\(372\) 1.69211e40 2.42669
\(373\) 5.31105e39 0.730624 0.365312 0.930885i \(-0.380962\pi\)
0.365312 + 0.930885i \(0.380962\pi\)
\(374\) −1.87198e39 −0.247054
\(375\) 6.37915e39 0.807753
\(376\) 4.17304e39 0.507038
\(377\) −1.54056e40 −1.79634
\(378\) −7.12887e39 −0.797807
\(379\) 6.56433e39 0.705152 0.352576 0.935783i \(-0.385306\pi\)
0.352576 + 0.935783i \(0.385306\pi\)
\(380\) 3.46201e39 0.357012
\(381\) −1.75585e40 −1.73840
\(382\) −3.12473e39 −0.297051
\(383\) 4.90622e39 0.447884 0.223942 0.974602i \(-0.428107\pi\)
0.223942 + 0.974602i \(0.428107\pi\)
\(384\) −1.49445e40 −1.31023
\(385\) 2.26716e39 0.190916
\(386\) 1.88007e40 1.52080
\(387\) −8.95685e39 −0.696041
\(388\) −1.58048e40 −1.18004
\(389\) 1.47786e40 1.06026 0.530132 0.847915i \(-0.322142\pi\)
0.530132 + 0.847915i \(0.322142\pi\)
\(390\) 3.66491e40 2.52675
\(391\) −4.20736e37 −0.00278785
\(392\) −1.51928e39 −0.0967617
\(393\) 5.56545e38 0.0340734
\(394\) −1.94442e40 −1.14446
\(395\) −1.48389e40 −0.839745
\(396\) −2.35976e39 −0.128408
\(397\) 9.79733e39 0.512690 0.256345 0.966585i \(-0.417482\pi\)
0.256345 + 0.966585i \(0.417482\pi\)
\(398\) 2.26555e40 1.14021
\(399\) −5.04101e39 −0.244027
\(400\) −4.92897e39 −0.229523
\(401\) 1.11974e40 0.501624 0.250812 0.968036i \(-0.419302\pi\)
0.250812 + 0.968036i \(0.419302\pi\)
\(402\) −2.07059e40 −0.892462
\(403\) −3.76923e40 −1.56324
\(404\) −3.78513e40 −1.51067
\(405\) 3.92940e40 1.50929
\(406\) 6.22323e40 2.30071
\(407\) −2.97227e39 −0.105773
\(408\) 1.89883e40 0.650510
\(409\) −2.34914e40 −0.774815 −0.387408 0.921909i \(-0.626629\pi\)
−0.387408 + 0.921909i \(0.626629\pi\)
\(410\) −8.13083e40 −2.58217
\(411\) −4.73134e39 −0.144689
\(412\) 5.61640e40 1.65406
\(413\) −2.70048e40 −0.765977
\(414\) −9.18116e37 −0.00250837
\(415\) 3.74855e40 0.986546
\(416\) 5.74089e40 1.45557
\(417\) 5.80184e40 1.41728
\(418\) 2.44741e39 0.0576069
\(419\) 4.42578e40 1.00386 0.501929 0.864909i \(-0.332624\pi\)
0.501929 + 0.864909i \(0.332624\pi\)
\(420\) −8.55221e40 −1.86945
\(421\) −4.58467e40 −0.965907 −0.482954 0.875646i \(-0.660436\pi\)
−0.482954 + 0.875646i \(0.660436\pi\)
\(422\) −1.49819e41 −3.04246
\(423\) 2.47743e40 0.484982
\(424\) 2.00559e39 0.0378504
\(425\) 2.35010e40 0.427620
\(426\) −4.63539e40 −0.813275
\(427\) −6.23125e40 −1.05425
\(428\) 9.26239e40 1.51128
\(429\) 1.49665e40 0.235522
\(430\) 1.57600e41 2.39219
\(431\) −1.63894e40 −0.239975 −0.119987 0.992775i \(-0.538285\pi\)
−0.119987 + 0.992775i \(0.538285\pi\)
\(432\) 2.00321e40 0.282962
\(433\) 7.21840e39 0.0983737 0.0491868 0.998790i \(-0.484337\pi\)
0.0491868 + 0.998790i \(0.484337\pi\)
\(434\) 1.52261e41 2.00216
\(435\) −1.94265e41 −2.46497
\(436\) −1.06046e41 −1.29854
\(437\) 5.50066e37 0.000650059 0
\(438\) 8.64094e40 0.985626
\(439\) 1.72040e40 0.189422 0.0947109 0.995505i \(-0.469807\pi\)
0.0947109 + 0.995505i \(0.469807\pi\)
\(440\) 1.11650e40 0.118670
\(441\) −9.01960e39 −0.0925527
\(442\) −1.57297e41 −1.55839
\(443\) −9.22567e39 −0.0882552 −0.0441276 0.999026i \(-0.514051\pi\)
−0.0441276 + 0.999026i \(0.514051\pi\)
\(444\) 1.12120e41 1.03573
\(445\) −2.15189e40 −0.191973
\(446\) −1.87176e41 −1.61272
\(447\) 2.05095e41 1.70683
\(448\) −1.75625e41 −1.41181
\(449\) 1.80147e41 1.39897 0.699484 0.714648i \(-0.253413\pi\)
0.699484 + 0.714648i \(0.253413\pi\)
\(450\) 5.12831e40 0.384751
\(451\) −3.32040e40 −0.240688
\(452\) 4.48088e40 0.313847
\(453\) −2.03301e41 −1.37600
\(454\) 8.27801e39 0.0541452
\(455\) 1.90503e41 1.20428
\(456\) −2.48252e40 −0.151683
\(457\) 7.03528e40 0.415509 0.207754 0.978181i \(-0.433385\pi\)
0.207754 + 0.978181i \(0.433385\pi\)
\(458\) 9.98168e40 0.569887
\(459\) −9.55118e40 −0.527182
\(460\) 9.33203e38 0.00498000
\(461\) −2.15013e40 −0.110943 −0.0554717 0.998460i \(-0.517666\pi\)
−0.0554717 + 0.998460i \(0.517666\pi\)
\(462\) −6.04584e40 −0.301652
\(463\) 3.68798e41 1.77944 0.889720 0.456506i \(-0.150899\pi\)
0.889720 + 0.456506i \(0.150899\pi\)
\(464\) −1.74873e41 −0.816006
\(465\) −4.75301e41 −2.14510
\(466\) 5.09937e41 2.22605
\(467\) −3.35225e41 −1.41555 −0.707775 0.706438i \(-0.750301\pi\)
−0.707775 + 0.706438i \(0.750301\pi\)
\(468\) −1.98284e41 −0.809983
\(469\) −1.07630e41 −0.425357
\(470\) −4.35916e41 −1.66681
\(471\) 4.94668e41 1.83016
\(472\) −1.32989e41 −0.476118
\(473\) 6.43593e40 0.222979
\(474\) 3.95709e41 1.32682
\(475\) −3.07250e40 −0.0997104
\(476\) 3.67059e41 1.15300
\(477\) 1.19067e40 0.0362040
\(478\) 2.11469e41 0.622464
\(479\) −1.78256e41 −0.507976 −0.253988 0.967207i \(-0.581742\pi\)
−0.253988 + 0.967207i \(0.581742\pi\)
\(480\) 7.23927e41 1.99736
\(481\) −2.49751e41 −0.667205
\(482\) −5.13799e41 −1.32912
\(483\) −1.35883e39 −0.00340396
\(484\) −5.46845e41 −1.32666
\(485\) 4.43944e41 1.04311
\(486\) −6.62839e41 −1.50850
\(487\) −2.96115e41 −0.652772 −0.326386 0.945237i \(-0.605831\pi\)
−0.326386 + 0.945237i \(0.605831\pi\)
\(488\) −3.06867e41 −0.655304
\(489\) −5.04432e41 −1.04355
\(490\) 1.58704e41 0.318089
\(491\) 2.87172e41 0.557671 0.278836 0.960339i \(-0.410052\pi\)
0.278836 + 0.960339i \(0.410052\pi\)
\(492\) 1.25252e42 2.35682
\(493\) 8.33782e41 1.52029
\(494\) 2.05649e41 0.363378
\(495\) 6.62837e40 0.113508
\(496\) −4.27855e41 −0.710117
\(497\) −2.40949e41 −0.387615
\(498\) −9.99624e41 −1.55877
\(499\) −1.19160e42 −1.80125 −0.900623 0.434601i \(-0.856889\pi\)
−0.900623 + 0.434601i \(0.856889\pi\)
\(500\) 6.07277e41 0.889922
\(501\) 5.18568e41 0.736752
\(502\) 6.75886e41 0.931035
\(503\) 1.92359e41 0.256926 0.128463 0.991714i \(-0.458996\pi\)
0.128463 + 0.991714i \(0.458996\pi\)
\(504\) 2.15384e41 0.278959
\(505\) 1.06321e42 1.33538
\(506\) 6.59712e38 0.000803565 0
\(507\) 2.06663e41 0.244141
\(508\) −1.67152e42 −1.91524
\(509\) −4.08219e41 −0.453699 −0.226849 0.973930i \(-0.572843\pi\)
−0.226849 + 0.973930i \(0.572843\pi\)
\(510\) −1.98352e42 −2.13845
\(511\) 4.49158e41 0.469759
\(512\) 9.28840e41 0.942446
\(513\) 1.24871e41 0.122926
\(514\) 2.24980e42 2.14889
\(515\) −1.57760e42 −1.46213
\(516\) −2.42777e42 −2.18342
\(517\) −1.78016e41 −0.155366
\(518\) 1.00889e42 0.854543
\(519\) 5.17548e41 0.425458
\(520\) 9.38160e41 0.748558
\(521\) 8.76030e41 0.678476 0.339238 0.940701i \(-0.389831\pi\)
0.339238 + 0.940701i \(0.389831\pi\)
\(522\) 1.81945e42 1.36788
\(523\) −1.52051e42 −1.10972 −0.554859 0.831944i \(-0.687228\pi\)
−0.554859 + 0.831944i \(0.687228\pi\)
\(524\) 5.29815e40 0.0375396
\(525\) 7.58999e41 0.522122
\(526\) −8.96559e41 −0.598825
\(527\) 2.03998e42 1.32301
\(528\) 1.69888e41 0.106988
\(529\) −1.63516e42 −0.999991
\(530\) −2.09504e41 −0.124427
\(531\) −7.89524e41 −0.455408
\(532\) −4.79889e41 −0.268851
\(533\) −2.79004e42 −1.51823
\(534\) 5.73844e41 0.303322
\(535\) −2.60173e42 −1.33592
\(536\) −5.30038e41 −0.264395
\(537\) 1.75213e41 0.0849113
\(538\) 2.38181e42 1.12145
\(539\) 6.48102e40 0.0296495
\(540\) 2.11848e42 0.941716
\(541\) 2.17683e42 0.940301 0.470150 0.882586i \(-0.344200\pi\)
0.470150 + 0.882586i \(0.344200\pi\)
\(542\) −2.85607e41 −0.119889
\(543\) 4.55407e42 1.85782
\(544\) −3.10708e42 −1.23188
\(545\) 2.97875e42 1.14786
\(546\) −5.08015e42 −1.90279
\(547\) 2.57006e42 0.935707 0.467854 0.883806i \(-0.345027\pi\)
0.467854 + 0.883806i \(0.345027\pi\)
\(548\) −4.50410e41 −0.159408
\(549\) −1.82179e42 −0.626798
\(550\) −3.68494e41 −0.123256
\(551\) −1.09008e42 −0.354493
\(552\) −6.69174e39 −0.00211584
\(553\) 2.05691e42 0.632376
\(554\) −5.66752e42 −1.69431
\(555\) −3.14937e42 −0.915551
\(556\) 5.52318e42 1.56146
\(557\) −2.88974e42 −0.794517 −0.397258 0.917707i \(-0.630038\pi\)
−0.397258 + 0.917707i \(0.630038\pi\)
\(558\) 4.45158e42 1.19038
\(559\) 5.40793e42 1.40653
\(560\) 2.16245e42 0.547055
\(561\) −8.10014e41 −0.199328
\(562\) −1.20734e43 −2.89014
\(563\) −5.57652e42 −1.29862 −0.649312 0.760522i \(-0.724943\pi\)
−0.649312 + 0.760522i \(0.724943\pi\)
\(564\) 6.71512e42 1.52135
\(565\) −1.25864e42 −0.277429
\(566\) 8.46672e42 1.81577
\(567\) −5.44676e42 −1.13658
\(568\) −1.18659e42 −0.240935
\(569\) −3.00301e42 −0.593357 −0.296679 0.954977i \(-0.595879\pi\)
−0.296679 + 0.954977i \(0.595879\pi\)
\(570\) 2.59324e42 0.498634
\(571\) 1.00812e43 1.88649 0.943245 0.332099i \(-0.107757\pi\)
0.943245 + 0.332099i \(0.107757\pi\)
\(572\) 1.42477e42 0.259481
\(573\) −1.35208e42 −0.239666
\(574\) 1.12706e43 1.94452
\(575\) −8.28207e39 −0.00139087
\(576\) −5.13463e42 −0.839385
\(577\) −7.02075e42 −1.11727 −0.558635 0.829413i \(-0.688675\pi\)
−0.558635 + 0.829413i \(0.688675\pi\)
\(578\) −1.41916e42 −0.219862
\(579\) 8.13515e42 1.22701
\(580\) −1.84935e43 −2.71572
\(581\) −5.19607e42 −0.742926
\(582\) −1.18387e43 −1.64815
\(583\) −8.55554e40 −0.0115980
\(584\) 2.21194e42 0.291995
\(585\) 5.56963e42 0.715996
\(586\) 6.64726e42 0.832203
\(587\) 1.56627e43 1.90974 0.954872 0.297018i \(-0.0959922\pi\)
0.954872 + 0.297018i \(0.0959922\pi\)
\(588\) −2.44478e42 −0.290329
\(589\) −2.66705e42 −0.308492
\(590\) 1.38920e43 1.56516
\(591\) −8.41360e42 −0.923370
\(592\) −2.83499e42 −0.303085
\(593\) −1.51645e42 −0.157936 −0.0789678 0.996877i \(-0.525162\pi\)
−0.0789678 + 0.996877i \(0.525162\pi\)
\(594\) 1.49762e42 0.151954
\(595\) −1.03104e43 −1.01921
\(596\) 1.95245e43 1.88046
\(597\) 9.80312e42 0.919946
\(598\) 5.54337e40 0.00506880
\(599\) −8.56958e42 −0.763561 −0.381781 0.924253i \(-0.624689\pi\)
−0.381781 + 0.924253i \(0.624689\pi\)
\(600\) 3.73780e42 0.324542
\(601\) −2.71633e42 −0.229841 −0.114921 0.993375i \(-0.536661\pi\)
−0.114921 + 0.993375i \(0.536661\pi\)
\(602\) −2.18458e43 −1.80145
\(603\) −3.14671e42 −0.252894
\(604\) −1.93537e43 −1.51597
\(605\) 1.53604e43 1.17272
\(606\) −2.83527e43 −2.10993
\(607\) 5.39744e42 0.391528 0.195764 0.980651i \(-0.437281\pi\)
0.195764 + 0.980651i \(0.437281\pi\)
\(608\) 4.06217e42 0.287245
\(609\) 2.69282e43 1.85626
\(610\) 3.20553e43 2.15421
\(611\) −1.49582e43 −0.980030
\(612\) 1.07315e43 0.685509
\(613\) 6.77481e42 0.421949 0.210975 0.977492i \(-0.432336\pi\)
0.210975 + 0.977492i \(0.432336\pi\)
\(614\) −1.50337e43 −0.912972
\(615\) −3.51824e43 −2.08335
\(616\) −1.54764e42 −0.0893653
\(617\) −8.39156e41 −0.0472523 −0.0236261 0.999721i \(-0.507521\pi\)
−0.0236261 + 0.999721i \(0.507521\pi\)
\(618\) 4.20699e43 2.31020
\(619\) 1.34876e43 0.722318 0.361159 0.932504i \(-0.382381\pi\)
0.361159 + 0.932504i \(0.382381\pi\)
\(620\) −4.52473e43 −2.36331
\(621\) 3.36597e40 0.00171471
\(622\) 3.02891e43 1.50499
\(623\) 2.98286e42 0.144566
\(624\) 1.42752e43 0.674872
\(625\) −2.70736e43 −1.24855
\(626\) −2.19370e43 −0.986902
\(627\) 1.05900e42 0.0464784
\(628\) 4.70909e43 2.01634
\(629\) 1.35170e43 0.564672
\(630\) −2.24990e43 −0.917033
\(631\) −4.65263e42 −0.185031 −0.0925153 0.995711i \(-0.529491\pi\)
−0.0925153 + 0.995711i \(0.529491\pi\)
\(632\) 1.01295e43 0.393074
\(633\) −6.48274e43 −2.45472
\(634\) −6.96337e43 −2.57298
\(635\) 4.69516e43 1.69300
\(636\) 3.22733e42 0.113569
\(637\) 5.44582e42 0.187026
\(638\) −1.30736e43 −0.438204
\(639\) −7.04448e42 −0.230455
\(640\) 3.99619e43 1.27602
\(641\) 4.24972e43 1.32453 0.662263 0.749271i \(-0.269596\pi\)
0.662263 + 0.749271i \(0.269596\pi\)
\(642\) 6.93804e43 2.11078
\(643\) −5.33186e43 −1.58347 −0.791733 0.610868i \(-0.790821\pi\)
−0.791733 + 0.610868i \(0.790821\pi\)
\(644\) −1.29357e41 −0.00375023
\(645\) 6.81941e43 1.93006
\(646\) −1.11301e43 −0.307536
\(647\) −1.00492e43 −0.271092 −0.135546 0.990771i \(-0.543279\pi\)
−0.135546 + 0.990771i \(0.543279\pi\)
\(648\) −2.68234e43 −0.706481
\(649\) 5.67312e42 0.145891
\(650\) −3.09635e43 −0.777487
\(651\) 6.58842e43 1.61538
\(652\) −4.80205e43 −1.14971
\(653\) −7.98263e43 −1.86634 −0.933172 0.359430i \(-0.882971\pi\)
−0.933172 + 0.359430i \(0.882971\pi\)
\(654\) −7.94343e43 −1.81365
\(655\) −1.48821e42 −0.0331836
\(656\) −3.16704e43 −0.689674
\(657\) 1.31318e43 0.279293
\(658\) 6.04248e43 1.25520
\(659\) 7.54017e43 1.52988 0.764940 0.644102i \(-0.222769\pi\)
0.764940 + 0.644102i \(0.222769\pi\)
\(660\) 1.79663e43 0.356064
\(661\) −3.00409e42 −0.0581555 −0.0290777 0.999577i \(-0.509257\pi\)
−0.0290777 + 0.999577i \(0.509257\pi\)
\(662\) 5.92266e43 1.12000
\(663\) −6.80632e43 −1.25734
\(664\) −2.55888e43 −0.461790
\(665\) 1.34797e43 0.237654
\(666\) 2.94964e43 0.508064
\(667\) −2.93836e41 −0.00494487
\(668\) 4.93662e43 0.811698
\(669\) −8.09919e43 −1.30118
\(670\) 5.53678e43 0.869156
\(671\) 1.30905e43 0.200797
\(672\) −1.00348e44 −1.50412
\(673\) 2.05730e43 0.301346 0.150673 0.988584i \(-0.451856\pi\)
0.150673 + 0.988584i \(0.451856\pi\)
\(674\) 1.31560e44 1.88319
\(675\) −1.88012e43 −0.263013
\(676\) 1.96738e43 0.268976
\(677\) −1.03692e44 −1.38554 −0.692772 0.721157i \(-0.743611\pi\)
−0.692772 + 0.721157i \(0.743611\pi\)
\(678\) 3.35642e43 0.438345
\(679\) −6.15377e43 −0.785524
\(680\) −5.07751e43 −0.633523
\(681\) 3.58193e42 0.0436855
\(682\) −3.19868e43 −0.381340
\(683\) 1.01818e44 1.18660 0.593302 0.804980i \(-0.297824\pi\)
0.593302 + 0.804980i \(0.297824\pi\)
\(684\) −1.40302e43 −0.159844
\(685\) 1.26517e43 0.140911
\(686\) −1.50670e44 −1.64060
\(687\) 4.31911e43 0.459796
\(688\) 6.13867e43 0.638931
\(689\) −7.18898e42 −0.0731593
\(690\) 6.99020e41 0.00695550
\(691\) 1.12626e44 1.09579 0.547895 0.836547i \(-0.315429\pi\)
0.547895 + 0.836547i \(0.315429\pi\)
\(692\) 4.92691e43 0.468738
\(693\) −9.18796e42 −0.0854779
\(694\) −2.56603e44 −2.33448
\(695\) −1.55142e44 −1.38027
\(696\) 1.32612e44 1.15382
\(697\) 1.51002e44 1.28492
\(698\) 2.91881e43 0.242911
\(699\) 2.20652e44 1.79602
\(700\) 7.22545e43 0.575235
\(701\) 3.06210e43 0.238446 0.119223 0.992867i \(-0.461960\pi\)
0.119223 + 0.992867i \(0.461960\pi\)
\(702\) 1.25841e44 0.958509
\(703\) −1.76720e43 −0.131668
\(704\) 3.68949e43 0.268899
\(705\) −1.88623e44 −1.34481
\(706\) −3.79722e44 −2.64846
\(707\) −1.47378e44 −1.00561
\(708\) −2.14002e44 −1.42857
\(709\) −9.24433e43 −0.603752 −0.301876 0.953347i \(-0.597613\pi\)
−0.301876 + 0.953347i \(0.597613\pi\)
\(710\) 1.23951e44 0.792036
\(711\) 6.01366e43 0.375976
\(712\) 1.46895e43 0.0898601
\(713\) −7.18917e41 −0.00430320
\(714\) 2.74947e44 1.61038
\(715\) −4.00205e43 −0.229371
\(716\) 1.66798e43 0.0935489
\(717\) 9.15036e43 0.502217
\(718\) 2.92950e44 1.57349
\(719\) −9.29670e43 −0.488687 −0.244344 0.969689i \(-0.578572\pi\)
−0.244344 + 0.969689i \(0.578572\pi\)
\(720\) 6.32222e43 0.325249
\(721\) 2.18681e44 1.10107
\(722\) −2.97696e44 −1.46706
\(723\) −2.22323e44 −1.07236
\(724\) 4.33535e44 2.04680
\(725\) 1.64128e44 0.758477
\(726\) −4.09617e44 −1.85293
\(727\) 1.34756e44 0.596710 0.298355 0.954455i \(-0.403562\pi\)
0.298355 + 0.954455i \(0.403562\pi\)
\(728\) −1.30044e44 −0.563707
\(729\) 7.35277e42 0.0312014
\(730\) −2.31060e44 −0.959887
\(731\) −2.92688e44 −1.19038
\(732\) −4.93800e44 −1.96621
\(733\) 1.96770e44 0.767093 0.383546 0.923522i \(-0.374703\pi\)
0.383546 + 0.923522i \(0.374703\pi\)
\(734\) 6.77524e44 2.58604
\(735\) 6.86719e43 0.256641
\(736\) 1.09498e42 0.00400681
\(737\) 2.26106e43 0.0810153
\(738\) 3.29512e44 1.15611
\(739\) −3.41064e44 −1.17178 −0.585891 0.810390i \(-0.699255\pi\)
−0.585891 + 0.810390i \(0.699255\pi\)
\(740\) −2.99811e44 −1.00869
\(741\) 8.89852e43 0.293181
\(742\) 2.90405e43 0.0937009
\(743\) −2.64820e44 −0.836805 −0.418403 0.908262i \(-0.637410\pi\)
−0.418403 + 0.908262i \(0.637410\pi\)
\(744\) 3.24456e44 1.00410
\(745\) −5.48428e44 −1.66225
\(746\) 3.78720e44 1.12426
\(747\) −1.51915e44 −0.441703
\(748\) −7.71111e43 −0.219605
\(749\) 3.60641e44 1.00602
\(750\) 4.54884e44 1.24294
\(751\) 3.88190e44 1.03902 0.519511 0.854464i \(-0.326114\pi\)
0.519511 + 0.854464i \(0.326114\pi\)
\(752\) −1.69794e44 −0.445189
\(753\) 2.92459e44 0.751177
\(754\) −1.09854e45 −2.76414
\(755\) 5.43630e44 1.34006
\(756\) −2.93654e44 −0.709166
\(757\) 2.10907e44 0.499004 0.249502 0.968374i \(-0.419733\pi\)
0.249502 + 0.968374i \(0.419733\pi\)
\(758\) 4.68088e44 1.08506
\(759\) 2.85460e41 0.000648332 0
\(760\) 6.63828e43 0.147722
\(761\) 3.24151e43 0.0706782 0.0353391 0.999375i \(-0.488749\pi\)
0.0353391 + 0.999375i \(0.488749\pi\)
\(762\) −1.25206e45 −2.67499
\(763\) −4.12902e44 −0.864403
\(764\) −1.28715e44 −0.264047
\(765\) −3.01439e44 −0.605965
\(766\) 3.49852e44 0.689189
\(767\) 4.76696e44 0.920266
\(768\) −4.81514e43 −0.0910983
\(769\) −6.38736e44 −1.18430 −0.592152 0.805827i \(-0.701721\pi\)
−0.592152 + 0.805827i \(0.701721\pi\)
\(770\) 1.61666e44 0.293774
\(771\) 9.73496e44 1.73377
\(772\) 7.74443e44 1.35183
\(773\) −8.28645e44 −1.41771 −0.708853 0.705356i \(-0.750787\pi\)
−0.708853 + 0.705356i \(0.750787\pi\)
\(774\) −6.38694e44 −1.07104
\(775\) 4.01565e44 0.660053
\(776\) −3.03051e44 −0.488269
\(777\) 4.36552e44 0.689462
\(778\) 1.05383e45 1.63150
\(779\) −1.97419e44 −0.299611
\(780\) 1.50966e45 2.24601
\(781\) 5.06180e43 0.0738268
\(782\) −3.00018e42 −0.00428985
\(783\) −6.67041e44 −0.935072
\(784\) 6.18168e43 0.0849587
\(785\) −1.32275e45 −1.78237
\(786\) 3.96860e43 0.0524310
\(787\) −8.07362e44 −1.04583 −0.522913 0.852386i \(-0.675155\pi\)
−0.522913 + 0.852386i \(0.675155\pi\)
\(788\) −8.00950e44 −1.01730
\(789\) −3.87945e44 −0.483144
\(790\) −1.05813e45 −1.29217
\(791\) 1.74468e44 0.208920
\(792\) −4.52474e43 −0.0531317
\(793\) 1.09996e45 1.26660
\(794\) 6.98627e44 0.788910
\(795\) −9.06532e43 −0.100390
\(796\) 9.33229e44 1.01353
\(797\) 8.20375e44 0.873792 0.436896 0.899512i \(-0.356078\pi\)
0.436896 + 0.899512i \(0.356078\pi\)
\(798\) −3.59463e44 −0.375500
\(799\) 8.09564e44 0.829423
\(800\) −6.11620e44 −0.614592
\(801\) 8.72080e43 0.0859513
\(802\) 7.98461e44 0.771882
\(803\) −9.43583e43 −0.0894724
\(804\) −8.52921e44 −0.793304
\(805\) 3.63353e42 0.00331507
\(806\) −2.68776e45 −2.40546
\(807\) 1.03062e45 0.904812
\(808\) −7.25784e44 −0.625073
\(809\) −2.25872e44 −0.190836 −0.0954182 0.995437i \(-0.530419\pi\)
−0.0954182 + 0.995437i \(0.530419\pi\)
\(810\) 2.80197e45 2.32245
\(811\) −1.42546e45 −1.15913 −0.579565 0.814926i \(-0.696778\pi\)
−0.579565 + 0.814926i \(0.696778\pi\)
\(812\) 2.56349e45 2.04509
\(813\) −1.23583e44 −0.0967289
\(814\) −2.11946e44 −0.162760
\(815\) 1.34886e45 1.01630
\(816\) −7.72602e44 −0.571161
\(817\) 3.82657e44 0.277567
\(818\) −1.67512e45 −1.19226
\(819\) −7.72039e44 −0.539186
\(820\) −3.34927e45 −2.29528
\(821\) −2.34861e44 −0.157940 −0.0789699 0.996877i \(-0.525163\pi\)
−0.0789699 + 0.996877i \(0.525163\pi\)
\(822\) −3.37382e44 −0.222643
\(823\) 2.26372e45 1.46597 0.732984 0.680246i \(-0.238127\pi\)
0.732984 + 0.680246i \(0.238127\pi\)
\(824\) 1.07692e45 0.684405
\(825\) −1.59449e44 −0.0994456
\(826\) −1.92566e45 −1.17866
\(827\) 1.11856e45 0.671929 0.335965 0.941875i \(-0.390938\pi\)
0.335965 + 0.941875i \(0.390938\pi\)
\(828\) −3.78192e42 −0.00222968
\(829\) −2.19670e45 −1.27109 −0.635544 0.772064i \(-0.719224\pi\)
−0.635544 + 0.772064i \(0.719224\pi\)
\(830\) 2.67301e45 1.51806
\(831\) −2.45236e45 −1.36700
\(832\) 3.10017e45 1.69619
\(833\) −2.94738e44 −0.158285
\(834\) 4.13717e45 2.18087
\(835\) −1.38666e45 −0.717512
\(836\) 1.00814e44 0.0512064
\(837\) −1.63202e45 −0.813733
\(838\) 3.15593e45 1.54470
\(839\) 3.71878e45 1.78686 0.893429 0.449204i \(-0.148293\pi\)
0.893429 + 0.449204i \(0.148293\pi\)
\(840\) −1.63985e45 −0.773528
\(841\) 3.66359e45 1.69656
\(842\) −3.26923e45 −1.48631
\(843\) −5.22423e45 −2.33182
\(844\) −6.17139e45 −2.70442
\(845\) −5.52621e44 −0.237765
\(846\) 1.76660e45 0.746274
\(847\) −2.12920e45 −0.883128
\(848\) −8.16038e43 −0.0332334
\(849\) 3.66359e45 1.46500
\(850\) 1.67581e45 0.658007
\(851\) −4.76359e42 −0.00183665
\(852\) −1.90942e45 −0.722915
\(853\) 2.48938e45 0.925509 0.462754 0.886487i \(-0.346861\pi\)
0.462754 + 0.886487i \(0.346861\pi\)
\(854\) −4.44337e45 −1.62224
\(855\) 3.94099e44 0.141296
\(856\) 1.77603e45 0.625326
\(857\) −8.68133e44 −0.300181 −0.150091 0.988672i \(-0.547957\pi\)
−0.150091 + 0.988672i \(0.547957\pi\)
\(858\) 1.06723e45 0.362413
\(859\) −1.43587e45 −0.478875 −0.239437 0.970912i \(-0.576963\pi\)
−0.239437 + 0.970912i \(0.576963\pi\)
\(860\) 6.49189e45 2.12640
\(861\) 4.87684e45 1.56888
\(862\) −1.16869e45 −0.369265
\(863\) −3.91776e45 −1.21582 −0.607911 0.794005i \(-0.707992\pi\)
−0.607911 + 0.794005i \(0.707992\pi\)
\(864\) 2.48572e45 0.757687
\(865\) −1.38393e45 −0.414347
\(866\) 5.14729e44 0.151374
\(867\) −6.14076e44 −0.177389
\(868\) 6.27199e45 1.77971
\(869\) −4.32111e44 −0.120445
\(870\) −1.38526e46 −3.79301
\(871\) 1.89991e45 0.511036
\(872\) −2.03339e45 −0.537299
\(873\) −1.79914e45 −0.467030
\(874\) 3.92241e42 0.00100029
\(875\) 2.36450e45 0.592399
\(876\) 3.55939e45 0.876117
\(877\) −2.59910e45 −0.628535 −0.314267 0.949335i \(-0.601759\pi\)
−0.314267 + 0.949335i \(0.601759\pi\)
\(878\) 1.22678e45 0.291476
\(879\) 2.87630e45 0.671438
\(880\) −4.54283e44 −0.104194
\(881\) 1.04135e45 0.234676 0.117338 0.993092i \(-0.462564\pi\)
0.117338 + 0.993092i \(0.462564\pi\)
\(882\) −6.43168e44 −0.142417
\(883\) −9.31982e44 −0.202776 −0.101388 0.994847i \(-0.532328\pi\)
−0.101388 + 0.994847i \(0.532328\pi\)
\(884\) −6.47943e45 −1.38524
\(885\) 6.01115e45 1.26281
\(886\) −6.57863e44 −0.135804
\(887\) 1.93996e45 0.393529 0.196764 0.980451i \(-0.436957\pi\)
0.196764 + 0.980451i \(0.436957\pi\)
\(888\) 2.14986e45 0.428558
\(889\) −6.50823e45 −1.27493
\(890\) −1.53447e45 −0.295401
\(891\) 1.14425e45 0.216478
\(892\) −7.71020e45 −1.43354
\(893\) −1.05842e45 −0.193401
\(894\) 1.46249e46 2.62641
\(895\) −4.68522e44 −0.0826939
\(896\) −5.53934e45 −0.960913
\(897\) 2.39864e43 0.00408961
\(898\) 1.28459e46 2.15269
\(899\) 1.42469e46 2.34664
\(900\) 2.11246e45 0.342003
\(901\) 3.89082e44 0.0619165
\(902\) −2.36771e45 −0.370362
\(903\) −9.45278e45 −1.45345
\(904\) 8.59192e44 0.129861
\(905\) −1.21777e46 −1.80930
\(906\) −1.44970e46 −2.11734
\(907\) −8.10222e45 −1.16330 −0.581649 0.813440i \(-0.697592\pi\)
−0.581649 + 0.813440i \(0.697592\pi\)
\(908\) 3.40990e44 0.0481294
\(909\) −4.30880e45 −0.597883
\(910\) 1.35844e46 1.85310
\(911\) −1.13425e46 −1.52115 −0.760575 0.649250i \(-0.775083\pi\)
−0.760575 + 0.649250i \(0.775083\pi\)
\(912\) 1.01009e45 0.133181
\(913\) 1.09158e45 0.141501
\(914\) 5.01671e45 0.639370
\(915\) 1.38705e46 1.73806
\(916\) 4.11167e45 0.506569
\(917\) 2.06289e44 0.0249892
\(918\) −6.81075e45 −0.811210
\(919\) 1.39631e46 1.63527 0.817637 0.575734i \(-0.195283\pi\)
0.817637 + 0.575734i \(0.195283\pi\)
\(920\) 1.78938e43 0.00206059
\(921\) −6.50516e45 −0.736604
\(922\) −1.53322e45 −0.170716
\(923\) 4.25329e45 0.465692
\(924\) −2.49041e45 −0.268137
\(925\) 2.66079e45 0.281717
\(926\) 2.62982e46 2.73814
\(927\) 6.39344e45 0.654634
\(928\) −2.16994e46 −2.18501
\(929\) −3.21761e45 −0.318632 −0.159316 0.987228i \(-0.550929\pi\)
−0.159316 + 0.987228i \(0.550929\pi\)
\(930\) −3.38927e46 −3.30081
\(931\) 3.85338e44 0.0369081
\(932\) 2.10054e46 1.97872
\(933\) 1.31062e46 1.21426
\(934\) −2.39042e46 −2.17820
\(935\) 2.16599e45 0.194123
\(936\) −3.80201e45 −0.335149
\(937\) 1.44001e46 1.24853 0.624267 0.781211i \(-0.285398\pi\)
0.624267 + 0.781211i \(0.285398\pi\)
\(938\) −7.67485e45 −0.654524
\(939\) −9.49221e45 −0.796252
\(940\) −1.79563e46 −1.48162
\(941\) −1.38781e46 −1.12640 −0.563198 0.826322i \(-0.690429\pi\)
−0.563198 + 0.826322i \(0.690429\pi\)
\(942\) 3.52737e46 2.81619
\(943\) −5.32153e43 −0.00417931
\(944\) 5.41109e45 0.418041
\(945\) 8.24851e45 0.626877
\(946\) 4.58933e45 0.343112
\(947\) −3.58686e45 −0.263809 −0.131905 0.991262i \(-0.542109\pi\)
−0.131905 + 0.991262i \(0.542109\pi\)
\(948\) 1.63001e46 1.17940
\(949\) −7.92866e45 −0.564383
\(950\) −2.19093e45 −0.153431
\(951\) −3.01308e46 −2.07593
\(952\) 7.03822e45 0.477079
\(953\) 8.63539e45 0.575893 0.287947 0.957646i \(-0.407027\pi\)
0.287947 + 0.957646i \(0.407027\pi\)
\(954\) 8.49040e44 0.0557094
\(955\) 3.61549e45 0.233408
\(956\) 8.71088e45 0.553305
\(957\) −5.65702e45 −0.353552
\(958\) −1.27110e46 −0.781656
\(959\) −1.75372e45 −0.106114
\(960\) 3.90932e46 2.32754
\(961\) 1.77883e46 1.04213
\(962\) −1.78092e46 −1.02667
\(963\) 1.05439e46 0.598125
\(964\) −2.11645e46 −1.18145
\(965\) −2.17535e46 −1.19497
\(966\) −9.68952e43 −0.00523789
\(967\) −1.07239e46 −0.570481 −0.285241 0.958456i \(-0.592073\pi\)
−0.285241 + 0.958456i \(0.592073\pi\)
\(968\) −1.04855e46 −0.548938
\(969\) −4.81605e45 −0.248126
\(970\) 3.16567e46 1.60511
\(971\) 1.69197e46 0.844295 0.422148 0.906527i \(-0.361276\pi\)
0.422148 + 0.906527i \(0.361276\pi\)
\(972\) −2.73038e46 −1.34090
\(973\) 2.15051e46 1.03942
\(974\) −2.11153e46 −1.00446
\(975\) −1.33980e46 −0.627292
\(976\) 1.24859e46 0.575369
\(977\) −1.63831e46 −0.743069 −0.371534 0.928419i \(-0.621168\pi\)
−0.371534 + 0.928419i \(0.621168\pi\)
\(978\) −3.59700e46 −1.60579
\(979\) −6.26632e44 −0.0275347
\(980\) 6.53737e45 0.282748
\(981\) −1.20718e46 −0.513927
\(982\) 2.04776e46 0.858126
\(983\) 1.26750e46 0.522839 0.261419 0.965225i \(-0.415809\pi\)
0.261419 + 0.965225i \(0.415809\pi\)
\(984\) 2.40167e46 0.975190
\(985\) 2.24981e46 0.899257
\(986\) 5.94552e46 2.33936
\(987\) 2.61461e46 1.01272
\(988\) 8.47114e45 0.323005
\(989\) 1.03147e44 0.00387182
\(990\) 4.72655e45 0.174662
\(991\) −3.41939e46 −1.24396 −0.621980 0.783033i \(-0.713672\pi\)
−0.621980 + 0.783033i \(0.713672\pi\)
\(992\) −5.30911e46 −1.90148
\(993\) 2.56276e46 0.903638
\(994\) −1.71815e46 −0.596449
\(995\) −2.62137e46 −0.895922
\(996\) −4.11767e46 −1.38558
\(997\) 3.16608e46 1.04893 0.524466 0.851432i \(-0.324265\pi\)
0.524466 + 0.851432i \(0.324265\pi\)
\(998\) −8.49707e46 −2.77170
\(999\) −1.08139e46 −0.347309
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 1.32.a.a.1.2 2
3.2 odd 2 9.32.a.a.1.1 2
4.3 odd 2 16.32.a.b.1.1 2
5.2 odd 4 25.32.b.a.24.4 4
5.3 odd 4 25.32.b.a.24.1 4
5.4 even 2 25.32.a.a.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.32.a.a.1.2 2 1.1 even 1 trivial
9.32.a.a.1.1 2 3.2 odd 2
16.32.a.b.1.1 2 4.3 odd 2
25.32.a.a.1.1 2 5.4 even 2
25.32.b.a.24.1 4 5.3 odd 4
25.32.b.a.24.4 4 5.2 odd 4