Properties

Label 1.68.a.a.1.1
Level 1
Weight 68
Character 1.1
Self dual yes
Analytic conductor 28.429
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 68 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.4290351930\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 939384011925257456 x^{3} + 31046449413968483513911200 x^{2} + 156793504704482691874379743265203200 x + 20916736226052669578405116700517591609696000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(7.63188e8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.72055e10 q^{2} -1.09955e16 q^{3} +1.48456e20 q^{4} +4.93311e23 q^{5} +1.89183e26 q^{6} +1.79351e28 q^{7} -1.51842e28 q^{8} +2.81916e31 q^{9} +O(q^{10})\) \(q-1.72055e10 q^{2} -1.09955e16 q^{3} +1.48456e20 q^{4} +4.93311e23 q^{5} +1.89183e26 q^{6} +1.79351e28 q^{7} -1.51842e28 q^{8} +2.81916e31 q^{9} -8.48767e33 q^{10} +5.33040e34 q^{11} -1.63235e36 q^{12} +2.30226e37 q^{13} -3.08583e38 q^{14} -5.42420e39 q^{15} -2.16471e40 q^{16} -1.47145e40 q^{17} -4.85052e41 q^{18} +5.15198e42 q^{19} +7.32351e43 q^{20} -1.97206e44 q^{21} -9.17124e44 q^{22} -8.82286e44 q^{23} +1.66958e44 q^{24} +1.75593e47 q^{25} -3.96116e47 q^{26} +7.09406e47 q^{27} +2.66258e48 q^{28} -1.08736e49 q^{29} +9.33262e49 q^{30} +8.83737e49 q^{31} +3.74690e50 q^{32} -5.86105e50 q^{33} +2.53171e50 q^{34} +8.84758e51 q^{35} +4.18523e51 q^{36} -4.39811e52 q^{37} -8.86426e52 q^{38} -2.53145e53 q^{39} -7.49053e51 q^{40} -2.89577e53 q^{41} +3.39303e54 q^{42} -3.62794e54 q^{43} +7.91333e54 q^{44} +1.39072e55 q^{45} +1.51802e55 q^{46} -8.12174e54 q^{47} +2.38020e56 q^{48} -9.67096e55 q^{49} -3.02117e57 q^{50} +1.61793e56 q^{51} +3.41786e57 q^{52} +7.18898e57 q^{53} -1.22057e58 q^{54} +2.62954e58 q^{55} -2.72330e56 q^{56} -5.66486e58 q^{57} +1.87086e59 q^{58} +5.28583e58 q^{59} -8.05257e59 q^{60} +5.02401e59 q^{61} -1.52052e60 q^{62} +5.05620e59 q^{63} -3.25220e60 q^{64} +1.13573e61 q^{65} +1.00842e61 q^{66} -3.52159e60 q^{67} -2.18446e60 q^{68} +9.70118e60 q^{69} -1.52227e62 q^{70} +1.01640e62 q^{71} -4.28067e59 q^{72} -1.36139e62 q^{73} +7.56719e62 q^{74} -1.93073e63 q^{75} +7.64845e62 q^{76} +9.56014e62 q^{77} +4.35550e63 q^{78} +4.98511e63 q^{79} -1.06787e64 q^{80} -1.04139e64 q^{81} +4.98233e63 q^{82} -4.78696e63 q^{83} -2.92764e64 q^{84} -7.25882e63 q^{85} +6.24207e64 q^{86} +1.19560e65 q^{87} -8.09379e62 q^{88} -1.28002e64 q^{89} -2.39281e65 q^{90} +4.12913e65 q^{91} -1.30981e65 q^{92} -9.71713e65 q^{93} +1.39739e65 q^{94} +2.54153e66 q^{95} -4.11990e66 q^{96} -4.06660e66 q^{97} +1.66394e66 q^{98} +1.50273e66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} + O(q^{10}) \) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} - \)\(52\!\cdots\!00\)\(q^{10} + \)\(20\!\cdots\!60\)\(q^{11} - \)\(20\!\cdots\!24\)\(q^{12} + \)\(17\!\cdots\!02\)\(q^{13} + \)\(29\!\cdots\!80\)\(q^{14} - \)\(93\!\cdots\!00\)\(q^{15} + \)\(18\!\cdots\!80\)\(q^{16} + \)\(75\!\cdots\!06\)\(q^{17} - \)\(10\!\cdots\!68\)\(q^{18} + \)\(39\!\cdots\!00\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(17\!\cdots\!40\)\(q^{21} + \)\(18\!\cdots\!32\)\(q^{22} - \)\(41\!\cdots\!68\)\(q^{23} - \)\(13\!\cdots\!00\)\(q^{24} + \)\(17\!\cdots\!75\)\(q^{25} + \)\(21\!\cdots\!60\)\(q^{26} + \)\(18\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!48\)\(q^{28} + \)\(18\!\cdots\!50\)\(q^{29} + \)\(18\!\cdots\!00\)\(q^{30} + \)\(36\!\cdots\!60\)\(q^{31} + \)\(15\!\cdots\!96\)\(q^{32} + \)\(24\!\cdots\!84\)\(q^{33} + \)\(78\!\cdots\!80\)\(q^{34} + \)\(45\!\cdots\!00\)\(q^{35} - \)\(38\!\cdots\!20\)\(q^{36} - \)\(56\!\cdots\!94\)\(q^{37} - \)\(31\!\cdots\!80\)\(q^{38} - \)\(71\!\cdots\!80\)\(q^{39} - \)\(18\!\cdots\!00\)\(q^{40} + \)\(11\!\cdots\!10\)\(q^{41} + \)\(28\!\cdots\!92\)\(q^{42} + \)\(65\!\cdots\!92\)\(q^{43} + \)\(49\!\cdots\!80\)\(q^{44} + \)\(99\!\cdots\!50\)\(q^{45} + \)\(79\!\cdots\!60\)\(q^{46} - \)\(12\!\cdots\!44\)\(q^{47} - \)\(19\!\cdots\!68\)\(q^{48} - \)\(77\!\cdots\!35\)\(q^{49} - \)\(39\!\cdots\!00\)\(q^{50} - \)\(33\!\cdots\!40\)\(q^{51} + \)\(67\!\cdots\!16\)\(q^{52} + \)\(10\!\cdots\!22\)\(q^{53} + \)\(19\!\cdots\!00\)\(q^{54} + \)\(66\!\cdots\!00\)\(q^{55} + \)\(16\!\cdots\!00\)\(q^{56} - \)\(92\!\cdots\!60\)\(q^{57} - \)\(61\!\cdots\!20\)\(q^{58} - \)\(30\!\cdots\!00\)\(q^{59} - \)\(13\!\cdots\!00\)\(q^{60} - \)\(11\!\cdots\!90\)\(q^{61} - \)\(21\!\cdots\!28\)\(q^{62} - \)\(20\!\cdots\!68\)\(q^{63} + \)\(63\!\cdots\!40\)\(q^{64} + \)\(17\!\cdots\!00\)\(q^{65} + \)\(27\!\cdots\!20\)\(q^{66} - \)\(11\!\cdots\!44\)\(q^{67} + \)\(81\!\cdots\!48\)\(q^{68} + \)\(35\!\cdots\!20\)\(q^{69} - \)\(26\!\cdots\!00\)\(q^{70} - \)\(11\!\cdots\!40\)\(q^{71} - \)\(74\!\cdots\!40\)\(q^{72} - \)\(30\!\cdots\!18\)\(q^{73} + \)\(92\!\cdots\!80\)\(q^{74} + \)\(21\!\cdots\!00\)\(q^{75} + \)\(20\!\cdots\!00\)\(q^{76} + \)\(50\!\cdots\!32\)\(q^{77} + \)\(61\!\cdots\!64\)\(q^{78} + \)\(29\!\cdots\!00\)\(q^{79} - \)\(15\!\cdots\!00\)\(q^{80} - \)\(11\!\cdots\!95\)\(q^{81} - \)\(17\!\cdots\!08\)\(q^{82} - \)\(47\!\cdots\!88\)\(q^{83} - \)\(52\!\cdots\!20\)\(q^{84} - \)\(39\!\cdots\!00\)\(q^{85} + \)\(49\!\cdots\!60\)\(q^{86} + \)\(35\!\cdots\!60\)\(q^{87} + \)\(43\!\cdots\!60\)\(q^{88} - \)\(11\!\cdots\!50\)\(q^{89} + \)\(47\!\cdots\!00\)\(q^{90} + \)\(23\!\cdots\!60\)\(q^{91} - \)\(98\!\cdots\!44\)\(q^{92} - \)\(18\!\cdots\!36\)\(q^{93} - \)\(49\!\cdots\!20\)\(q^{94} - \)\(20\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!40\)\(q^{96} + \)\(28\!\cdots\!06\)\(q^{97} + \)\(12\!\cdots\!08\)\(q^{98} + \)\(16\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.72055e10 −1.41633 −0.708163 0.706049i \(-0.750476\pi\)
−0.708163 + 0.706049i \(0.750476\pi\)
\(3\) −1.09955e16 −1.14197 −0.570983 0.820962i \(-0.693438\pi\)
−0.570983 + 0.820962i \(0.693438\pi\)
\(4\) 1.48456e20 1.00598
\(5\) 4.93311e23 1.89507 0.947535 0.319652i \(-0.103566\pi\)
0.947535 + 0.319652i \(0.103566\pi\)
\(6\) 1.89183e26 1.61740
\(7\) 1.79351e28 0.876839 0.438419 0.898771i \(-0.355538\pi\)
0.438419 + 0.898771i \(0.355538\pi\)
\(8\) −1.51842e28 −0.00846988
\(9\) 2.81916e31 0.304086
\(10\) −8.48767e33 −2.68404
\(11\) 5.33040e34 0.691998 0.345999 0.938235i \(-0.387540\pi\)
0.345999 + 0.938235i \(0.387540\pi\)
\(12\) −1.63235e36 −1.14879
\(13\) 2.30226e37 1.10931 0.554654 0.832081i \(-0.312851\pi\)
0.554654 + 0.832081i \(0.312851\pi\)
\(14\) −3.08583e38 −1.24189
\(15\) −5.42420e39 −2.16410
\(16\) −2.16471e40 −0.993984
\(17\) −1.47145e40 −0.0886557 −0.0443279 0.999017i \(-0.514115\pi\)
−0.0443279 + 0.999017i \(0.514115\pi\)
\(18\) −4.85052e41 −0.430684
\(19\) 5.15198e42 0.747702 0.373851 0.927489i \(-0.378037\pi\)
0.373851 + 0.927489i \(0.378037\pi\)
\(20\) 7.32351e43 1.90640
\(21\) −1.97206e44 −1.00132
\(22\) −9.17124e44 −0.980096
\(23\) −8.82286e44 −0.212680 −0.106340 0.994330i \(-0.533913\pi\)
−0.106340 + 0.994330i \(0.533913\pi\)
\(24\) 1.66958e44 0.00967232
\(25\) 1.75593e47 2.59129
\(26\) −3.96116e47 −1.57114
\(27\) 7.09406e47 0.794710
\(28\) 2.66258e48 0.882082
\(29\) −1.08736e49 −1.11183 −0.555916 0.831238i \(-0.687633\pi\)
−0.555916 + 0.831238i \(0.687633\pi\)
\(30\) 9.33262e49 3.06508
\(31\) 8.83737e49 0.967623 0.483812 0.875172i \(-0.339252\pi\)
0.483812 + 0.875172i \(0.339252\pi\)
\(32\) 3.74690e50 1.41628
\(33\) −5.86105e50 −0.790238
\(34\) 2.53171e50 0.125565
\(35\) 8.84758e51 1.66167
\(36\) 4.18523e51 0.305904
\(37\) −4.39811e52 −1.28383 −0.641917 0.766774i \(-0.721860\pi\)
−0.641917 + 0.766774i \(0.721860\pi\)
\(38\) −8.86426e52 −1.05899
\(39\) −2.53145e53 −1.26679
\(40\) −7.49053e51 −0.0160510
\(41\) −2.89577e53 −0.271335 −0.135667 0.990754i \(-0.543318\pi\)
−0.135667 + 0.990754i \(0.543318\pi\)
\(42\) 3.39303e54 1.41820
\(43\) −3.62794e54 −0.689393 −0.344697 0.938714i \(-0.612018\pi\)
−0.344697 + 0.938714i \(0.612018\pi\)
\(44\) 7.91333e54 0.696137
\(45\) 1.39072e55 0.576263
\(46\) 1.51802e55 0.301224
\(47\) −8.12174e54 −0.0784099 −0.0392049 0.999231i \(-0.512483\pi\)
−0.0392049 + 0.999231i \(0.512483\pi\)
\(48\) 2.38020e56 1.13510
\(49\) −9.67096e55 −0.231154
\(50\) −3.02117e57 −3.67011
\(51\) 1.61793e56 0.101242
\(52\) 3.41786e57 1.11594
\(53\) 7.18898e57 1.24001 0.620005 0.784598i \(-0.287130\pi\)
0.620005 + 0.784598i \(0.287130\pi\)
\(54\) −1.22057e58 −1.12557
\(55\) 2.62954e58 1.31139
\(56\) −2.72330e56 −0.00742672
\(57\) −5.66486e58 −0.853850
\(58\) 1.87086e59 1.57472
\(59\) 5.28583e58 0.250941 0.125470 0.992097i \(-0.459956\pi\)
0.125470 + 0.992097i \(0.459956\pi\)
\(60\) −8.05257e59 −2.17705
\(61\) 5.02401e59 0.780731 0.390366 0.920660i \(-0.372349\pi\)
0.390366 + 0.920660i \(0.372349\pi\)
\(62\) −1.52052e60 −1.37047
\(63\) 5.05620e59 0.266634
\(64\) −3.25220e60 −1.01192
\(65\) 1.13573e61 2.10222
\(66\) 1.00842e61 1.11924
\(67\) −3.52159e60 −0.236174 −0.118087 0.993003i \(-0.537676\pi\)
−0.118087 + 0.993003i \(0.537676\pi\)
\(68\) −2.18446e60 −0.0891859
\(69\) 9.70118e60 0.242873
\(70\) −1.52227e62 −2.35347
\(71\) 1.01640e62 0.977033 0.488516 0.872555i \(-0.337538\pi\)
0.488516 + 0.872555i \(0.337538\pi\)
\(72\) −4.28067e59 −0.00257557
\(73\) −1.36139e62 −0.516019 −0.258010 0.966142i \(-0.583067\pi\)
−0.258010 + 0.966142i \(0.583067\pi\)
\(74\) 7.56719e62 1.81833
\(75\) −1.93073e63 −2.95916
\(76\) 7.64845e62 0.752173
\(77\) 9.56014e62 0.606771
\(78\) 4.35550e63 1.79419
\(79\) 4.98511e63 1.34019 0.670096 0.742274i \(-0.266253\pi\)
0.670096 + 0.742274i \(0.266253\pi\)
\(80\) −1.06787e64 −1.88367
\(81\) −1.04139e64 −1.21162
\(82\) 4.98233e63 0.384298
\(83\) −4.78696e63 −0.246005 −0.123002 0.992406i \(-0.539252\pi\)
−0.123002 + 0.992406i \(0.539252\pi\)
\(84\) −2.92764e64 −1.00731
\(85\) −7.25882e63 −0.168009
\(86\) 6.24207e64 0.976406
\(87\) 1.19560e65 1.26967
\(88\) −8.09379e62 −0.00586115
\(89\) −1.28002e64 −0.0634823 −0.0317411 0.999496i \(-0.510105\pi\)
−0.0317411 + 0.999496i \(0.510105\pi\)
\(90\) −2.39281e65 −0.816177
\(91\) 4.12913e65 0.972684
\(92\) −1.30981e65 −0.213952
\(93\) −9.71713e65 −1.10499
\(94\) 1.39739e65 0.111054
\(95\) 2.54153e66 1.41695
\(96\) −4.11990e66 −1.61734
\(97\) −4.06660e66 −1.12818 −0.564090 0.825713i \(-0.690773\pi\)
−0.564090 + 0.825713i \(0.690773\pi\)
\(98\) 1.66394e66 0.327389
\(99\) 1.50273e66 0.210427
\(100\) 2.60679e67 2.60679
\(101\) −1.05153e66 −0.0753450 −0.0376725 0.999290i \(-0.511994\pi\)
−0.0376725 + 0.999290i \(0.511994\pi\)
\(102\) −2.78374e66 −0.143391
\(103\) −2.37836e66 −0.0883548 −0.0441774 0.999024i \(-0.514067\pi\)
−0.0441774 + 0.999024i \(0.514067\pi\)
\(104\) −3.49580e65 −0.00939571
\(105\) −9.72836e67 −1.89757
\(106\) −1.23690e68 −1.75626
\(107\) 1.67319e68 1.73455 0.867277 0.497827i \(-0.165868\pi\)
0.867277 + 0.497827i \(0.165868\pi\)
\(108\) 1.05316e68 0.799463
\(109\) 1.41616e68 0.789450 0.394725 0.918799i \(-0.370840\pi\)
0.394725 + 0.918799i \(0.370840\pi\)
\(110\) −4.52427e68 −1.85735
\(111\) 4.83595e68 1.46609
\(112\) −3.88242e68 −0.871564
\(113\) 4.00544e68 0.667609 0.333804 0.942642i \(-0.391668\pi\)
0.333804 + 0.942642i \(0.391668\pi\)
\(114\) 9.74670e68 1.20933
\(115\) −4.35241e68 −0.403044
\(116\) −1.61425e69 −1.11848
\(117\) 6.49044e68 0.337325
\(118\) −9.09456e68 −0.355414
\(119\) −2.63906e68 −0.0777368
\(120\) 8.23621e67 0.0183297
\(121\) −3.09217e69 −0.521138
\(122\) −8.64409e69 −1.10577
\(123\) 3.18405e69 0.309855
\(124\) 1.31196e70 0.973410
\(125\) 5.31937e70 3.01561
\(126\) −8.69946e69 −0.377641
\(127\) −4.86585e70 −1.62082 −0.810408 0.585866i \(-0.800754\pi\)
−0.810408 + 0.585866i \(0.800754\pi\)
\(128\) 6.61353e68 0.0169395
\(129\) 3.98910e70 0.787263
\(130\) −1.95408e71 −2.97742
\(131\) 8.62495e70 1.01664 0.508321 0.861168i \(-0.330266\pi\)
0.508321 + 0.861168i \(0.330266\pi\)
\(132\) −8.70110e70 −0.794964
\(133\) 9.24013e70 0.655614
\(134\) 6.05908e70 0.334500
\(135\) 3.49958e71 1.50603
\(136\) 2.23428e68 0.000750903 0
\(137\) −6.03931e71 −1.58799 −0.793997 0.607922i \(-0.792003\pi\)
−0.793997 + 0.607922i \(0.792003\pi\)
\(138\) −1.66914e71 −0.343988
\(139\) 3.74979e71 0.606752 0.303376 0.952871i \(-0.401886\pi\)
0.303376 + 0.952871i \(0.401886\pi\)
\(140\) 1.31348e72 1.67161
\(141\) 8.93026e70 0.0895414
\(142\) −1.74877e72 −1.38380
\(143\) 1.22720e72 0.767639
\(144\) −6.10265e71 −0.302256
\(145\) −5.36405e72 −2.10700
\(146\) 2.34234e72 0.730851
\(147\) 1.06337e72 0.263970
\(148\) −6.52928e72 −1.29151
\(149\) −1.44128e72 −0.227514 −0.113757 0.993509i \(-0.536289\pi\)
−0.113757 + 0.993509i \(0.536289\pi\)
\(150\) 3.32192e73 4.19114
\(151\) −1.20935e73 −1.22130 −0.610651 0.791900i \(-0.709092\pi\)
−0.610651 + 0.791900i \(0.709092\pi\)
\(152\) −7.82287e70 −0.00633295
\(153\) −4.14826e71 −0.0269589
\(154\) −1.64487e73 −0.859386
\(155\) 4.35957e73 1.83371
\(156\) −3.75810e73 −1.27437
\(157\) −1.14455e73 −0.313327 −0.156664 0.987652i \(-0.550074\pi\)
−0.156664 + 0.987652i \(0.550074\pi\)
\(158\) −8.57714e73 −1.89815
\(159\) −7.90464e73 −1.41605
\(160\) 1.84839e74 2.68394
\(161\) −1.58239e73 −0.186486
\(162\) 1.79177e74 1.71605
\(163\) −2.51517e73 −0.196012 −0.0980061 0.995186i \(-0.531246\pi\)
−0.0980061 + 0.995186i \(0.531246\pi\)
\(164\) −4.29896e73 −0.272957
\(165\) −2.89132e74 −1.49756
\(166\) 8.23621e73 0.348423
\(167\) 2.64467e74 0.914893 0.457446 0.889237i \(-0.348764\pi\)
0.457446 + 0.889237i \(0.348764\pi\)
\(168\) 2.99441e72 0.00848106
\(169\) 9.93110e73 0.230565
\(170\) 1.24892e74 0.237955
\(171\) 1.45243e74 0.227365
\(172\) −5.38591e74 −0.693516
\(173\) −1.12766e75 −1.19573 −0.597864 0.801598i \(-0.703984\pi\)
−0.597864 + 0.801598i \(0.703984\pi\)
\(174\) −2.05710e75 −1.79827
\(175\) 3.14927e75 2.27214
\(176\) −1.15388e75 −0.687835
\(177\) −5.81204e74 −0.286566
\(178\) 2.20235e74 0.0899116
\(179\) 5.82360e75 1.97068 0.985338 0.170612i \(-0.0545746\pi\)
0.985338 + 0.170612i \(0.0545746\pi\)
\(180\) 2.06462e75 0.579710
\(181\) 5.77923e75 1.34784 0.673919 0.738805i \(-0.264609\pi\)
0.673919 + 0.738805i \(0.264609\pi\)
\(182\) −7.10439e75 −1.37764
\(183\) −5.52416e75 −0.891568
\(184\) 1.33968e73 0.00180138
\(185\) −2.16964e76 −2.43295
\(186\) 1.67188e76 1.56503
\(187\) −7.84342e74 −0.0613496
\(188\) −1.20572e75 −0.0788788
\(189\) 1.27233e76 0.696833
\(190\) −4.37283e76 −2.00686
\(191\) 2.42687e76 0.934177 0.467089 0.884210i \(-0.345303\pi\)
0.467089 + 0.884210i \(0.345303\pi\)
\(192\) 3.57596e76 1.15558
\(193\) 1.12591e76 0.305726 0.152863 0.988247i \(-0.451151\pi\)
0.152863 + 0.988247i \(0.451151\pi\)
\(194\) 6.99680e76 1.59787
\(195\) −1.24879e77 −2.40066
\(196\) −1.43572e76 −0.232536
\(197\) 9.92756e76 1.35589 0.677944 0.735113i \(-0.262871\pi\)
0.677944 + 0.735113i \(0.262871\pi\)
\(198\) −2.58552e76 −0.298033
\(199\) −4.94327e76 −0.481323 −0.240661 0.970609i \(-0.577364\pi\)
−0.240661 + 0.970609i \(0.577364\pi\)
\(200\) −2.66623e75 −0.0219479
\(201\) 3.87216e76 0.269703
\(202\) 1.80921e76 0.106713
\(203\) −1.95019e77 −0.974898
\(204\) 2.40193e76 0.101847
\(205\) −1.42852e77 −0.514198
\(206\) 4.09209e76 0.125139
\(207\) −2.48731e76 −0.0646730
\(208\) −4.98372e77 −1.10263
\(209\) 2.74621e77 0.517409
\(210\) 1.67382e78 2.68758
\(211\) 7.97263e77 1.09179 0.545895 0.837853i \(-0.316190\pi\)
0.545895 + 0.837853i \(0.316190\pi\)
\(212\) 1.06725e78 1.24743
\(213\) −1.11758e78 −1.11574
\(214\) −2.87881e78 −2.45669
\(215\) −1.78970e78 −1.30645
\(216\) −1.07718e76 −0.00673110
\(217\) 1.58499e78 0.848450
\(218\) −2.43658e78 −1.11812
\(219\) 1.49691e78 0.589276
\(220\) 3.90373e78 1.31923
\(221\) −3.38766e77 −0.0983465
\(222\) −8.32050e78 −2.07647
\(223\) 7.26198e78 1.55899 0.779493 0.626411i \(-0.215477\pi\)
0.779493 + 0.626411i \(0.215477\pi\)
\(224\) 6.72011e78 1.24185
\(225\) 4.95024e78 0.787974
\(226\) −6.89157e78 −0.945552
\(227\) −6.69941e78 −0.792812 −0.396406 0.918075i \(-0.629743\pi\)
−0.396406 + 0.918075i \(0.629743\pi\)
\(228\) −8.40985e78 −0.858956
\(229\) 1.52622e79 1.34626 0.673131 0.739523i \(-0.264949\pi\)
0.673131 + 0.739523i \(0.264949\pi\)
\(230\) 7.48856e78 0.570841
\(231\) −1.05119e79 −0.692912
\(232\) 1.65107e77 0.00941709
\(233\) −3.84717e78 −0.189985 −0.0949923 0.995478i \(-0.530283\pi\)
−0.0949923 + 0.995478i \(0.530283\pi\)
\(234\) −1.11672e79 −0.477762
\(235\) −4.00654e78 −0.148592
\(236\) 7.84716e78 0.252441
\(237\) −5.48138e79 −1.53045
\(238\) 4.54065e78 0.110101
\(239\) 3.15386e79 0.664526 0.332263 0.943187i \(-0.392188\pi\)
0.332263 + 0.943187i \(0.392188\pi\)
\(240\) 1.17418e80 2.15109
\(241\) −1.13954e80 −1.81618 −0.908091 0.418773i \(-0.862460\pi\)
−0.908091 + 0.418773i \(0.862460\pi\)
\(242\) 5.32024e79 0.738102
\(243\) 4.87375e79 0.588915
\(244\) 7.45848e79 0.785400
\(245\) −4.77079e79 −0.438052
\(246\) −5.47832e79 −0.438856
\(247\) 1.18612e80 0.829432
\(248\) −1.34188e78 −0.00819566
\(249\) 5.26350e79 0.280929
\(250\) −9.15226e80 −4.27108
\(251\) 8.37200e78 0.0341790 0.0170895 0.999854i \(-0.494560\pi\)
0.0170895 + 0.999854i \(0.494560\pi\)
\(252\) 7.50625e79 0.268229
\(253\) −4.70294e79 −0.147174
\(254\) 8.37195e80 2.29560
\(255\) 7.98144e79 0.191860
\(256\) 4.68561e80 0.987933
\(257\) 3.71814e80 0.687964 0.343982 0.938976i \(-0.388224\pi\)
0.343982 + 0.938976i \(0.388224\pi\)
\(258\) −6.86347e80 −1.11502
\(259\) −7.88806e80 −1.12571
\(260\) 1.68606e81 2.11479
\(261\) −3.06544e80 −0.338092
\(262\) −1.48397e81 −1.43990
\(263\) −1.23154e81 −1.05179 −0.525897 0.850548i \(-0.676270\pi\)
−0.525897 + 0.850548i \(0.676270\pi\)
\(264\) 8.89953e78 0.00669323
\(265\) 3.54640e81 2.34991
\(266\) −1.58981e81 −0.928564
\(267\) 1.40745e80 0.0724946
\(268\) −5.22803e80 −0.237587
\(269\) 2.94340e81 1.18072 0.590361 0.807139i \(-0.298985\pi\)
0.590361 + 0.807139i \(0.298985\pi\)
\(270\) −6.02121e81 −2.13303
\(271\) −2.56265e81 −0.802081 −0.401041 0.916060i \(-0.631351\pi\)
−0.401041 + 0.916060i \(0.631351\pi\)
\(272\) 3.18526e80 0.0881224
\(273\) −4.54019e81 −1.11077
\(274\) 1.03910e82 2.24912
\(275\) 9.35980e81 1.79317
\(276\) 1.44020e81 0.244326
\(277\) −3.12521e81 −0.469686 −0.234843 0.972033i \(-0.575458\pi\)
−0.234843 + 0.972033i \(0.575458\pi\)
\(278\) −6.45171e81 −0.859359
\(279\) 2.49140e81 0.294240
\(280\) −1.34343e80 −0.0140742
\(281\) 1.11908e82 1.04040 0.520199 0.854045i \(-0.325858\pi\)
0.520199 + 0.854045i \(0.325858\pi\)
\(282\) −1.53650e81 −0.126820
\(283\) −2.21997e82 −1.62743 −0.813713 0.581267i \(-0.802557\pi\)
−0.813713 + 0.581267i \(0.802557\pi\)
\(284\) 1.50891e82 0.982876
\(285\) −2.79454e82 −1.61811
\(286\) −2.11146e82 −1.08723
\(287\) −5.19360e81 −0.237917
\(288\) 1.05631e82 0.430669
\(289\) −2.73307e82 −0.992140
\(290\) 9.22913e82 2.98420
\(291\) 4.47143e82 1.28834
\(292\) −2.02107e82 −0.519105
\(293\) −1.80269e82 −0.412909 −0.206455 0.978456i \(-0.566193\pi\)
−0.206455 + 0.978456i \(0.566193\pi\)
\(294\) −1.82959e82 −0.373867
\(295\) 2.60756e82 0.475550
\(296\) 6.67818e80 0.0108739
\(297\) 3.78142e82 0.549938
\(298\) 2.47980e82 0.322234
\(299\) −2.03125e82 −0.235928
\(300\) −2.86629e83 −2.97686
\(301\) −6.50675e82 −0.604487
\(302\) 2.08075e83 1.72976
\(303\) 1.15621e82 0.0860414
\(304\) −1.11525e83 −0.743204
\(305\) 2.47840e83 1.47954
\(306\) 7.13729e81 0.0381826
\(307\) −1.00209e83 −0.480587 −0.240294 0.970700i \(-0.577244\pi\)
−0.240294 + 0.970700i \(0.577244\pi\)
\(308\) 1.41926e83 0.610400
\(309\) 2.61512e82 0.100898
\(310\) −7.50087e83 −2.59714
\(311\) 2.45800e83 0.764028 0.382014 0.924157i \(-0.375231\pi\)
0.382014 + 0.924157i \(0.375231\pi\)
\(312\) 3.84381e81 0.0107296
\(313\) 5.45376e83 1.36761 0.683803 0.729667i \(-0.260325\pi\)
0.683803 + 0.729667i \(0.260325\pi\)
\(314\) 1.96927e83 0.443774
\(315\) 2.49428e83 0.505290
\(316\) 7.40072e83 1.34821
\(317\) −1.09174e84 −1.78910 −0.894550 0.446969i \(-0.852503\pi\)
−0.894550 + 0.446969i \(0.852503\pi\)
\(318\) 1.36004e84 2.00559
\(319\) −5.79605e83 −0.769386
\(320\) −1.60434e84 −1.91767
\(321\) −1.83975e84 −1.98080
\(322\) 2.72259e83 0.264125
\(323\) −7.58088e82 −0.0662880
\(324\) −1.54601e84 −1.21886
\(325\) 4.04260e84 2.87454
\(326\) 4.32749e83 0.277617
\(327\) −1.55714e84 −0.901524
\(328\) 4.39700e81 0.00229817
\(329\) −1.45664e83 −0.0687528
\(330\) 4.97466e84 2.12103
\(331\) 2.14161e84 0.825093 0.412547 0.910937i \(-0.364639\pi\)
0.412547 + 0.910937i \(0.364639\pi\)
\(332\) −7.10655e83 −0.247476
\(333\) −1.23990e84 −0.390395
\(334\) −4.55030e84 −1.29579
\(335\) −1.73724e84 −0.447567
\(336\) 4.26892e84 0.995296
\(337\) −1.76405e84 −0.372313 −0.186157 0.982520i \(-0.559603\pi\)
−0.186157 + 0.982520i \(0.559603\pi\)
\(338\) −1.70870e84 −0.326555
\(339\) −4.40418e84 −0.762386
\(340\) −1.07762e84 −0.169013
\(341\) 4.71067e84 0.669594
\(342\) −2.49898e84 −0.322024
\(343\) −9.23815e84 −1.07952
\(344\) 5.50874e82 0.00583908
\(345\) 4.78569e84 0.460262
\(346\) 1.94019e85 1.69354
\(347\) 5.12606e84 0.406206 0.203103 0.979157i \(-0.434897\pi\)
0.203103 + 0.979157i \(0.434897\pi\)
\(348\) 1.77495e85 1.27727
\(349\) −1.40759e85 −0.920078 −0.460039 0.887899i \(-0.652165\pi\)
−0.460039 + 0.887899i \(0.652165\pi\)
\(350\) −5.41849e85 −3.21810
\(351\) 1.63324e85 0.881579
\(352\) 1.99725e85 0.980060
\(353\) −4.27961e84 −0.190964 −0.0954820 0.995431i \(-0.530439\pi\)
−0.0954820 + 0.995431i \(0.530439\pi\)
\(354\) 9.99992e84 0.405870
\(355\) 5.01400e85 1.85155
\(356\) −1.90028e84 −0.0638619
\(357\) 2.90178e84 0.0887727
\(358\) −1.00198e86 −2.79112
\(359\) 3.75174e85 0.951849 0.475925 0.879486i \(-0.342114\pi\)
0.475925 + 0.879486i \(0.342114\pi\)
\(360\) −2.11170e83 −0.00488088
\(361\) −2.09350e85 −0.440942
\(362\) −9.94348e85 −1.90898
\(363\) 3.39999e85 0.595122
\(364\) 6.12996e85 0.978501
\(365\) −6.71587e85 −0.977892
\(366\) 9.50461e85 1.26275
\(367\) −1.08913e86 −1.32058 −0.660291 0.751010i \(-0.729567\pi\)
−0.660291 + 0.751010i \(0.729567\pi\)
\(368\) 1.90989e85 0.211401
\(369\) −8.16365e84 −0.0825090
\(370\) 3.73297e86 3.44586
\(371\) 1.28935e86 1.08729
\(372\) −1.44257e86 −1.11160
\(373\) 1.78512e86 1.25725 0.628625 0.777708i \(-0.283618\pi\)
0.628625 + 0.777708i \(0.283618\pi\)
\(374\) 1.34950e85 0.0868911
\(375\) −5.84891e86 −3.44372
\(376\) 1.23322e83 0.000664123 0
\(377\) −2.50338e86 −1.23337
\(378\) −2.18911e86 −0.986943
\(379\) −7.64909e83 −0.00315643 −0.00157821 0.999999i \(-0.500502\pi\)
−0.00157821 + 0.999999i \(0.500502\pi\)
\(380\) 3.77306e86 1.42542
\(381\) 5.35024e86 1.85092
\(382\) −4.17557e86 −1.32310
\(383\) −2.98598e85 −0.0866817 −0.0433409 0.999060i \(-0.513800\pi\)
−0.0433409 + 0.999060i \(0.513800\pi\)
\(384\) −7.27191e84 −0.0193443
\(385\) 4.71612e86 1.14987
\(386\) −1.93718e86 −0.433008
\(387\) −1.02278e86 −0.209635
\(388\) −6.03713e86 −1.13493
\(389\) −3.82483e86 −0.659631 −0.329815 0.944045i \(-0.606987\pi\)
−0.329815 + 0.944045i \(0.606987\pi\)
\(390\) 2.14861e87 3.40012
\(391\) 1.29824e85 0.0188553
\(392\) 1.46846e84 0.00195784
\(393\) −9.48356e86 −1.16097
\(394\) −1.70809e87 −1.92038
\(395\) 2.45921e87 2.53976
\(396\) 2.23089e86 0.211685
\(397\) −8.84606e86 −0.771380 −0.385690 0.922629i \(-0.626036\pi\)
−0.385690 + 0.922629i \(0.626036\pi\)
\(398\) 8.50516e86 0.681710
\(399\) −1.01600e87 −0.748689
\(400\) −3.80106e87 −2.57570
\(401\) 3.03362e87 1.89071 0.945356 0.326041i \(-0.105715\pi\)
0.945356 + 0.326041i \(0.105715\pi\)
\(402\) −6.66227e86 −0.381987
\(403\) 2.03459e87 1.07339
\(404\) −1.56106e86 −0.0757955
\(405\) −5.13729e87 −2.29610
\(406\) 3.35540e87 1.38077
\(407\) −2.34437e87 −0.888410
\(408\) −2.45670e84 −0.000857506 0
\(409\) 5.25302e86 0.168919 0.0844594 0.996427i \(-0.473084\pi\)
0.0844594 + 0.996427i \(0.473084\pi\)
\(410\) 2.45784e87 0.728272
\(411\) 6.64053e87 1.81343
\(412\) −3.53082e86 −0.0888831
\(413\) 9.48020e86 0.220034
\(414\) 4.27954e86 0.0915980
\(415\) −2.36146e87 −0.466196
\(416\) 8.62634e87 1.57109
\(417\) −4.12308e87 −0.692890
\(418\) −4.72501e87 −0.732819
\(419\) −5.17945e87 −0.741504 −0.370752 0.928732i \(-0.620900\pi\)
−0.370752 + 0.928732i \(0.620900\pi\)
\(420\) −1.44424e88 −1.90892
\(421\) 6.80858e87 0.831010 0.415505 0.909591i \(-0.363605\pi\)
0.415505 + 0.909591i \(0.363605\pi\)
\(422\) −1.37173e88 −1.54633
\(423\) −2.28965e86 −0.0238433
\(424\) −1.09159e86 −0.0105027
\(425\) −2.58376e87 −0.229733
\(426\) 1.92286e88 1.58025
\(427\) 9.01063e87 0.684575
\(428\) 2.48395e88 1.74493
\(429\) −1.34937e88 −0.876618
\(430\) 3.07928e88 1.85036
\(431\) −2.41768e88 −1.34404 −0.672018 0.740535i \(-0.734572\pi\)
−0.672018 + 0.740535i \(0.734572\pi\)
\(432\) −1.53566e88 −0.789929
\(433\) −1.54829e88 −0.737066 −0.368533 0.929615i \(-0.620140\pi\)
−0.368533 + 0.929615i \(0.620140\pi\)
\(434\) −2.72706e88 −1.20168
\(435\) 5.89804e88 2.40612
\(436\) 2.10238e88 0.794171
\(437\) −4.54552e87 −0.159021
\(438\) −2.57552e88 −0.834607
\(439\) −4.85118e88 −1.45642 −0.728208 0.685356i \(-0.759647\pi\)
−0.728208 + 0.685356i \(0.759647\pi\)
\(440\) −3.99275e86 −0.0111073
\(441\) −2.72640e87 −0.0702905
\(442\) 5.82865e87 0.139291
\(443\) 4.06798e88 0.901267 0.450634 0.892709i \(-0.351198\pi\)
0.450634 + 0.892709i \(0.351198\pi\)
\(444\) 7.17927e88 1.47486
\(445\) −6.31449e87 −0.120303
\(446\) −1.24946e89 −2.20803
\(447\) 1.58476e88 0.259813
\(448\) −5.83286e88 −0.887295
\(449\) 1.75617e88 0.247921 0.123961 0.992287i \(-0.460440\pi\)
0.123961 + 0.992287i \(0.460440\pi\)
\(450\) −8.51715e88 −1.11603
\(451\) −1.54356e88 −0.187763
\(452\) 5.94633e88 0.671601
\(453\) 1.32974e89 1.39469
\(454\) 1.15267e89 1.12288
\(455\) 2.03694e89 1.84331
\(456\) 8.60164e86 0.00723201
\(457\) 1.71391e88 0.133905 0.0669524 0.997756i \(-0.478672\pi\)
0.0669524 + 0.997756i \(0.478672\pi\)
\(458\) −2.62595e89 −1.90675
\(459\) −1.04386e88 −0.0704556
\(460\) −6.46144e88 −0.405454
\(461\) −2.85185e89 −1.66397 −0.831984 0.554799i \(-0.812795\pi\)
−0.831984 + 0.554799i \(0.812795\pi\)
\(462\) 1.80862e89 0.981389
\(463\) 1.68560e89 0.850731 0.425366 0.905022i \(-0.360145\pi\)
0.425366 + 0.905022i \(0.360145\pi\)
\(464\) 2.35381e89 1.10514
\(465\) −4.79356e89 −2.09404
\(466\) 6.61927e88 0.269080
\(467\) −4.95124e89 −1.87326 −0.936631 0.350317i \(-0.886074\pi\)
−0.936631 + 0.350317i \(0.886074\pi\)
\(468\) 9.63548e88 0.339342
\(469\) −6.31601e88 −0.207087
\(470\) 6.89347e88 0.210455
\(471\) 1.25850e89 0.357809
\(472\) −8.02611e86 −0.00212544
\(473\) −1.93384e89 −0.477059
\(474\) 9.43100e89 2.16762
\(475\) 9.04650e89 1.93751
\(476\) −3.91786e88 −0.0782016
\(477\) 2.02669e89 0.377069
\(478\) −5.42638e89 −0.941186
\(479\) 6.60213e89 1.06769 0.533844 0.845583i \(-0.320747\pi\)
0.533844 + 0.845583i \(0.320747\pi\)
\(480\) −2.03239e90 −3.06497
\(481\) −1.01256e90 −1.42417
\(482\) 1.96064e90 2.57231
\(483\) 1.73992e89 0.212961
\(484\) −4.59052e89 −0.524255
\(485\) −2.00610e90 −2.13798
\(486\) −8.38554e89 −0.834096
\(487\) 2.04394e90 1.89779 0.948896 0.315588i \(-0.102202\pi\)
0.948896 + 0.315588i \(0.102202\pi\)
\(488\) −7.62857e87 −0.00661270
\(489\) 2.76556e89 0.223839
\(490\) 8.20839e89 0.620425
\(491\) −1.82715e89 −0.128986 −0.0644932 0.997918i \(-0.520543\pi\)
−0.0644932 + 0.997918i \(0.520543\pi\)
\(492\) 4.72693e89 0.311708
\(493\) 1.59999e89 0.0985703
\(494\) −2.04078e90 −1.17475
\(495\) 7.41311e89 0.398773
\(496\) −1.91303e90 −0.961802
\(497\) 1.82292e90 0.856700
\(498\) −9.05613e89 −0.397887
\(499\) −2.98431e90 −1.22596 −0.612979 0.790100i \(-0.710029\pi\)
−0.612979 + 0.790100i \(0.710029\pi\)
\(500\) 7.89695e90 3.03364
\(501\) −2.90795e90 −1.04478
\(502\) −1.44045e89 −0.0484086
\(503\) 6.14610e90 1.93229 0.966145 0.258000i \(-0.0830634\pi\)
0.966145 + 0.258000i \(0.0830634\pi\)
\(504\) −7.67743e87 −0.00225836
\(505\) −5.18729e89 −0.142784
\(506\) 8.09166e89 0.208447
\(507\) −1.09197e90 −0.263297
\(508\) −7.22366e90 −1.63051
\(509\) 4.35588e89 0.0920515 0.0460257 0.998940i \(-0.485344\pi\)
0.0460257 + 0.998940i \(0.485344\pi\)
\(510\) −1.37325e90 −0.271737
\(511\) −2.44166e90 −0.452466
\(512\) −8.15944e90 −1.41617
\(513\) 3.65485e90 0.594207
\(514\) −6.39725e90 −0.974381
\(515\) −1.17327e90 −0.167438
\(516\) 5.92208e90 0.791971
\(517\) −4.32921e89 −0.0542595
\(518\) 1.35718e91 1.59438
\(519\) 1.23991e91 1.36548
\(520\) −1.72451e89 −0.0178055
\(521\) −1.44636e91 −1.40028 −0.700139 0.714007i \(-0.746878\pi\)
−0.700139 + 0.714007i \(0.746878\pi\)
\(522\) 5.27425e90 0.478849
\(523\) 1.71161e91 1.45747 0.728733 0.684798i \(-0.240110\pi\)
0.728733 + 0.684798i \(0.240110\pi\)
\(524\) 1.28043e91 1.02272
\(525\) −3.46278e91 −2.59471
\(526\) 2.11893e91 1.48968
\(527\) −1.30037e90 −0.0857853
\(528\) 1.26874e91 0.785484
\(529\) −1.64309e91 −0.954767
\(530\) −6.10177e91 −3.32824
\(531\) 1.49016e90 0.0763074
\(532\) 1.37176e91 0.659535
\(533\) −6.66682e90 −0.300994
\(534\) −2.42159e90 −0.102676
\(535\) 8.25400e91 3.28710
\(536\) 5.34725e88 0.00200037
\(537\) −6.40335e91 −2.25044
\(538\) −5.06427e91 −1.67229
\(539\) −5.15501e90 −0.159958
\(540\) 5.19535e91 1.51504
\(541\) 2.45133e91 0.671883 0.335941 0.941883i \(-0.390946\pi\)
0.335941 + 0.941883i \(0.390946\pi\)
\(542\) 4.40918e91 1.13601
\(543\) −6.35456e91 −1.53919
\(544\) −5.51338e90 −0.125561
\(545\) 6.98606e91 1.49606
\(546\) 7.81163e91 1.57322
\(547\) 2.28762e91 0.433319 0.216660 0.976247i \(-0.430484\pi\)
0.216660 + 0.976247i \(0.430484\pi\)
\(548\) −8.96575e91 −1.59749
\(549\) 1.41635e91 0.237409
\(550\) −1.61040e92 −2.53971
\(551\) −5.60204e91 −0.831320
\(552\) −1.47305e89 −0.00205711
\(553\) 8.94085e91 1.17513
\(554\) 5.37710e91 0.665229
\(555\) 2.38562e92 2.77835
\(556\) 5.56681e91 0.610380
\(557\) −1.43839e92 −1.48500 −0.742499 0.669847i \(-0.766360\pi\)
−0.742499 + 0.669847i \(0.766360\pi\)
\(558\) −4.28658e91 −0.416740
\(559\) −8.35247e91 −0.764750
\(560\) −1.91524e92 −1.65167
\(561\) 8.62424e90 0.0700591
\(562\) −1.92544e92 −1.47354
\(563\) −1.11672e92 −0.805216 −0.402608 0.915372i \(-0.631896\pi\)
−0.402608 + 0.915372i \(0.631896\pi\)
\(564\) 1.32576e91 0.0900769
\(565\) 1.97592e92 1.26517
\(566\) 3.81958e92 2.30497
\(567\) −1.86775e92 −1.06239
\(568\) −1.54332e90 −0.00827535
\(569\) −3.93668e91 −0.199007 −0.0995036 0.995037i \(-0.531725\pi\)
−0.0995036 + 0.995037i \(0.531725\pi\)
\(570\) 4.80815e92 2.29177
\(571\) 1.48833e92 0.668943 0.334471 0.942406i \(-0.391442\pi\)
0.334471 + 0.942406i \(0.391442\pi\)
\(572\) 1.82185e92 0.772230
\(573\) −2.66847e92 −1.06680
\(574\) 8.93587e91 0.336968
\(575\) −1.54923e92 −0.551116
\(576\) −9.16848e91 −0.307712
\(577\) −3.49967e92 −1.10825 −0.554124 0.832434i \(-0.686947\pi\)
−0.554124 + 0.832434i \(0.686947\pi\)
\(578\) 4.70239e92 1.40519
\(579\) −1.23799e92 −0.349129
\(580\) −7.96328e92 −2.11960
\(581\) −8.58546e91 −0.215706
\(582\) −7.69333e92 −1.82471
\(583\) 3.83201e92 0.858085
\(584\) 2.06716e90 0.00437062
\(585\) 3.20180e92 0.639254
\(586\) 3.10162e92 0.584814
\(587\) 4.67398e92 0.832359 0.416180 0.909282i \(-0.363369\pi\)
0.416180 + 0.909282i \(0.363369\pi\)
\(588\) 1.57864e92 0.265548
\(589\) 4.55300e92 0.723494
\(590\) −4.48644e92 −0.673534
\(591\) −1.09159e93 −1.54838
\(592\) 9.52062e92 1.27611
\(593\) 1.07249e93 1.35851 0.679253 0.733904i \(-0.262304\pi\)
0.679253 + 0.733904i \(0.262304\pi\)
\(594\) −6.50614e92 −0.778892
\(595\) −1.30188e92 −0.147317
\(596\) −2.13967e92 −0.228875
\(597\) 5.43538e92 0.549654
\(598\) 3.49488e92 0.334151
\(599\) −1.28809e93 −1.16452 −0.582259 0.813003i \(-0.697831\pi\)
−0.582259 + 0.813003i \(0.697831\pi\)
\(600\) 2.93166e91 0.0250638
\(601\) 7.69849e92 0.622459 0.311230 0.950335i \(-0.399259\pi\)
0.311230 + 0.950335i \(0.399259\pi\)
\(602\) 1.11952e93 0.856151
\(603\) −9.92793e91 −0.0718172
\(604\) −1.79535e93 −1.22861
\(605\) −1.52540e93 −0.987593
\(606\) −1.98931e92 −0.121863
\(607\) 5.65104e92 0.327572 0.163786 0.986496i \(-0.447629\pi\)
0.163786 + 0.986496i \(0.447629\pi\)
\(608\) 1.93040e93 1.05895
\(609\) 2.14433e93 1.11330
\(610\) −4.26422e93 −2.09551
\(611\) −1.86984e92 −0.0869807
\(612\) −6.15835e91 −0.0271201
\(613\) −3.50864e93 −1.46289 −0.731447 0.681898i \(-0.761155\pi\)
−0.731447 + 0.681898i \(0.761155\pi\)
\(614\) 1.72415e93 0.680669
\(615\) 1.57072e93 0.587197
\(616\) −1.45163e91 −0.00513928
\(617\) 2.70034e93 0.905451 0.452725 0.891650i \(-0.350452\pi\)
0.452725 + 0.891650i \(0.350452\pi\)
\(618\) −4.49946e92 −0.142905
\(619\) −2.68678e93 −0.808342 −0.404171 0.914683i \(-0.632440\pi\)
−0.404171 + 0.914683i \(0.632440\pi\)
\(620\) 6.47206e93 1.84468
\(621\) −6.25899e92 −0.169019
\(622\) −4.22912e93 −1.08211
\(623\) −2.29574e92 −0.0556637
\(624\) 5.47985e93 1.25917
\(625\) 1.43424e94 3.12349
\(626\) −9.38349e93 −1.93698
\(627\) −3.01960e93 −0.590863
\(628\) −1.69917e93 −0.315201
\(629\) 6.47160e92 0.113819
\(630\) −4.29153e93 −0.715656
\(631\) −3.83662e93 −0.606688 −0.303344 0.952881i \(-0.598103\pi\)
−0.303344 + 0.952881i \(0.598103\pi\)
\(632\) −7.56949e91 −0.0113513
\(633\) −8.76631e93 −1.24679
\(634\) 1.87840e94 2.53395
\(635\) −2.40037e94 −3.07156
\(636\) −1.17350e94 −1.42452
\(637\) −2.22651e93 −0.256421
\(638\) 9.97242e93 1.08970
\(639\) 2.86539e93 0.297102
\(640\) 3.26253e92 0.0321015
\(641\) 1.07467e94 1.00353 0.501765 0.865004i \(-0.332684\pi\)
0.501765 + 0.865004i \(0.332684\pi\)
\(642\) 3.16539e94 2.80546
\(643\) −4.05930e93 −0.341494 −0.170747 0.985315i \(-0.554618\pi\)
−0.170747 + 0.985315i \(0.554618\pi\)
\(644\) −2.34916e93 −0.187601
\(645\) 1.96787e94 1.49192
\(646\) 1.30433e93 0.0938855
\(647\) −1.63125e93 −0.111488 −0.0557438 0.998445i \(-0.517753\pi\)
−0.0557438 + 0.998445i \(0.517753\pi\)
\(648\) 1.58127e92 0.0102623
\(649\) 2.81756e93 0.173650
\(650\) −6.95551e94 −4.07129
\(651\) −1.74278e94 −0.968900
\(652\) −3.73394e93 −0.197184
\(653\) 5.05458e93 0.253568 0.126784 0.991930i \(-0.459535\pi\)
0.126784 + 0.991930i \(0.459535\pi\)
\(654\) 2.67914e94 1.27685
\(655\) 4.25478e94 1.92661
\(656\) 6.26850e93 0.269702
\(657\) −3.83797e93 −0.156914
\(658\) 2.50623e93 0.0973765
\(659\) 7.75623e93 0.286411 0.143205 0.989693i \(-0.454259\pi\)
0.143205 + 0.989693i \(0.454259\pi\)
\(660\) −4.29235e94 −1.50651
\(661\) −2.70603e94 −0.902784 −0.451392 0.892326i \(-0.649072\pi\)
−0.451392 + 0.892326i \(0.649072\pi\)
\(662\) −3.68476e94 −1.16860
\(663\) 3.72490e93 0.112308
\(664\) 7.26861e91 0.00208363
\(665\) 4.55826e94 1.24243
\(666\) 2.13331e94 0.552927
\(667\) 9.59361e93 0.236465
\(668\) 3.92619e94 0.920364
\(669\) −7.98491e94 −1.78031
\(670\) 2.98901e94 0.633901
\(671\) 2.67800e94 0.540265
\(672\) −7.38910e94 −1.41814
\(673\) −1.46662e94 −0.267801 −0.133900 0.990995i \(-0.542750\pi\)
−0.133900 + 0.990995i \(0.542750\pi\)
\(674\) 3.03514e94 0.527317
\(675\) 1.24567e95 2.05933
\(676\) 1.47434e94 0.231943
\(677\) −1.64408e94 −0.246152 −0.123076 0.992397i \(-0.539276\pi\)
−0.123076 + 0.992397i \(0.539276\pi\)
\(678\) 7.57762e94 1.07979
\(679\) −7.29349e94 −0.989232
\(680\) 1.10219e92 0.00142301
\(681\) 7.36634e94 0.905364
\(682\) −8.10497e94 −0.948363
\(683\) −9.12704e94 −1.01680 −0.508401 0.861120i \(-0.669763\pi\)
−0.508401 + 0.861120i \(0.669763\pi\)
\(684\) 2.15622e94 0.228725
\(685\) −2.97926e95 −3.00936
\(686\) 1.58947e95 1.52896
\(687\) −1.67816e95 −1.53739
\(688\) 7.85343e94 0.685246
\(689\) 1.65509e95 1.37555
\(690\) −8.23404e94 −0.651881
\(691\) 9.94852e94 0.750315 0.375158 0.926961i \(-0.377589\pi\)
0.375158 + 0.926961i \(0.377589\pi\)
\(692\) −1.67408e95 −1.20288
\(693\) 2.69516e94 0.184510
\(694\) −8.81965e94 −0.575320
\(695\) 1.84981e95 1.14984
\(696\) −1.81543e93 −0.0107540
\(697\) 4.26099e93 0.0240554
\(698\) 2.42183e95 1.30313
\(699\) 4.23016e94 0.216956
\(700\) 4.67530e95 2.28573
\(701\) 1.03900e95 0.484243 0.242121 0.970246i \(-0.422157\pi\)
0.242121 + 0.970246i \(0.422157\pi\)
\(702\) −2.81007e95 −1.24860
\(703\) −2.26590e95 −0.959925
\(704\) −1.73355e95 −0.700250
\(705\) 4.40539e94 0.169687
\(706\) 7.36329e94 0.270467
\(707\) −1.88592e94 −0.0660654
\(708\) −8.62835e94 −0.288279
\(709\) −1.34893e95 −0.429874 −0.214937 0.976628i \(-0.568955\pi\)
−0.214937 + 0.976628i \(0.568955\pi\)
\(710\) −8.62685e95 −2.62239
\(711\) 1.40538e95 0.407533
\(712\) 1.94361e92 0.000537687 0
\(713\) −7.79709e94 −0.205794
\(714\) −4.99267e94 −0.125731
\(715\) 6.05390e95 1.45473
\(716\) 8.64552e95 1.98246
\(717\) −3.46782e95 −0.758866
\(718\) −6.45506e95 −1.34813
\(719\) 4.02663e95 0.802645 0.401322 0.915937i \(-0.368551\pi\)
0.401322 + 0.915937i \(0.368551\pi\)
\(720\) −3.01050e95 −0.572797
\(721\) −4.26561e94 −0.0774729
\(722\) 3.60197e95 0.624517
\(723\) 1.25298e96 2.07402
\(724\) 8.57965e95 1.35590
\(725\) −1.90932e96 −2.88108
\(726\) −5.84987e95 −0.842887
\(727\) −6.99986e95 −0.963133 −0.481567 0.876410i \(-0.659932\pi\)
−0.481567 + 0.876410i \(0.659932\pi\)
\(728\) −6.26976e93 −0.00823852
\(729\) 4.29575e95 0.539097
\(730\) 1.15550e96 1.38501
\(731\) 5.33834e94 0.0611186
\(732\) −8.20097e95 −0.896900
\(733\) 5.32830e94 0.0556679 0.0278340 0.999613i \(-0.491139\pi\)
0.0278340 + 0.999613i \(0.491139\pi\)
\(734\) 1.87390e96 1.87037
\(735\) 5.24572e95 0.500241
\(736\) −3.30584e95 −0.301214
\(737\) −1.87715e95 −0.163432
\(738\) 1.40460e95 0.116860
\(739\) 8.51506e95 0.677016 0.338508 0.940963i \(-0.390078\pi\)
0.338508 + 0.940963i \(0.390078\pi\)
\(740\) −3.22096e96 −2.44750
\(741\) −1.30420e96 −0.947183
\(742\) −2.21840e96 −1.53996
\(743\) 1.89590e96 1.25803 0.629013 0.777395i \(-0.283459\pi\)
0.629013 + 0.777395i \(0.283459\pi\)
\(744\) 1.47547e94 0.00935916
\(745\) −7.10998e95 −0.431155
\(746\) −3.07140e96 −1.78068
\(747\) −1.34952e95 −0.0748065
\(748\) −1.16441e95 −0.0617165
\(749\) 3.00088e96 1.52092
\(750\) 1.00634e97 4.87743
\(751\) −4.17131e96 −1.93346 −0.966728 0.255806i \(-0.917659\pi\)
−0.966728 + 0.255806i \(0.917659\pi\)
\(752\) 1.75812e95 0.0779382
\(753\) −9.20543e94 −0.0390312
\(754\) 4.30720e96 1.74685
\(755\) −5.96584e96 −2.31445
\(756\) 1.88885e96 0.701000
\(757\) 8.46751e95 0.300638 0.150319 0.988638i \(-0.451970\pi\)
0.150319 + 0.988638i \(0.451970\pi\)
\(758\) 1.31607e94 0.00447053
\(759\) 5.17112e95 0.168068
\(760\) −3.85910e94 −0.0120014
\(761\) 3.16557e95 0.0942033 0.0471016 0.998890i \(-0.485002\pi\)
0.0471016 + 0.998890i \(0.485002\pi\)
\(762\) −9.20538e96 −2.62150
\(763\) 2.53990e96 0.692220
\(764\) 3.60285e96 0.939764
\(765\) −2.04638e95 −0.0510890
\(766\) 5.13753e95 0.122770
\(767\) 1.21694e96 0.278370
\(768\) −5.15206e96 −1.12819
\(769\) −5.10943e96 −1.07113 −0.535563 0.844496i \(-0.679900\pi\)
−0.535563 + 0.844496i \(0.679900\pi\)
\(770\) −8.11433e96 −1.62860
\(771\) −4.08828e96 −0.785631
\(772\) 1.67148e96 0.307555
\(773\) 4.84034e96 0.852831 0.426416 0.904527i \(-0.359776\pi\)
0.426416 + 0.904527i \(0.359776\pi\)
\(774\) 1.75974e96 0.296911
\(775\) 1.55178e97 2.50739
\(776\) 6.17481e94 0.00955555
\(777\) 8.67332e96 1.28553
\(778\) 6.58083e96 0.934253
\(779\) −1.49190e96 −0.202877
\(780\) −1.85391e97 −2.41502
\(781\) 5.41781e96 0.676105
\(782\) −2.23369e95 −0.0267053
\(783\) −7.71378e96 −0.883585
\(784\) 2.09348e96 0.229763
\(785\) −5.64621e96 −0.593777
\(786\) 1.63170e97 1.64431
\(787\) −8.19889e96 −0.791775 −0.395887 0.918299i \(-0.629563\pi\)
−0.395887 + 0.918299i \(0.629563\pi\)
\(788\) 1.47381e97 1.36400
\(789\) 1.35414e97 1.20111
\(790\) −4.23120e97 −3.59713
\(791\) 7.18380e96 0.585385
\(792\) −2.28177e94 −0.00178229
\(793\) 1.15666e97 0.866071
\(794\) 1.52201e97 1.09253
\(795\) −3.89944e97 −2.68351
\(796\) −7.33861e96 −0.484201
\(797\) −1.17038e97 −0.740413 −0.370206 0.928949i \(-0.620713\pi\)
−0.370206 + 0.928949i \(0.620713\pi\)
\(798\) 1.74808e97 1.06039
\(799\) 1.19507e95 0.00695148
\(800\) 6.57928e97 3.66998
\(801\) −3.60859e95 −0.0193040
\(802\) −5.21951e97 −2.67786
\(803\) −7.25674e96 −0.357084
\(804\) 5.74848e96 0.271316
\(805\) −7.80610e96 −0.353404
\(806\) −3.50063e97 −1.52027
\(807\) −3.23641e97 −1.34834
\(808\) 1.59666e94 0.000638163 0
\(809\) 6.68432e96 0.256319 0.128160 0.991754i \(-0.459093\pi\)
0.128160 + 0.991754i \(0.459093\pi\)
\(810\) 8.83898e97 3.25203
\(811\) 4.48195e97 1.58223 0.791113 0.611670i \(-0.209502\pi\)
0.791113 + 0.611670i \(0.209502\pi\)
\(812\) −2.89518e97 −0.980728
\(813\) 2.81776e97 0.915949
\(814\) 4.03362e97 1.25828
\(815\) −1.24076e97 −0.371457
\(816\) −3.50235e96 −0.100633
\(817\) −1.86911e97 −0.515461
\(818\) −9.03810e96 −0.239244
\(819\) 1.16407e97 0.295779
\(820\) −2.12072e97 −0.517273
\(821\) 5.60928e97 1.31344 0.656721 0.754133i \(-0.271943\pi\)
0.656721 + 0.754133i \(0.271943\pi\)
\(822\) −1.14254e98 −2.56841
\(823\) −1.05963e97 −0.228696 −0.114348 0.993441i \(-0.536478\pi\)
−0.114348 + 0.993441i \(0.536478\pi\)
\(824\) 3.61134e94 0.000748354 0
\(825\) −1.02916e98 −2.04774
\(826\) −1.63112e97 −0.311641
\(827\) −1.39147e97 −0.255292 −0.127646 0.991820i \(-0.540742\pi\)
−0.127646 + 0.991820i \(0.540742\pi\)
\(828\) −3.69257e96 −0.0650597
\(829\) 4.21519e97 0.713247 0.356624 0.934248i \(-0.383928\pi\)
0.356624 + 0.934248i \(0.383928\pi\)
\(830\) 4.06301e97 0.660286
\(831\) 3.43633e97 0.536365
\(832\) −7.48741e97 −1.12254
\(833\) 1.42303e96 0.0204931
\(834\) 7.09398e97 0.981358
\(835\) 1.30465e98 1.73379
\(836\) 4.07693e97 0.520503
\(837\) 6.26928e97 0.768980
\(838\) 8.91151e97 1.05021
\(839\) −1.62194e98 −1.83657 −0.918287 0.395915i \(-0.870427\pi\)
−0.918287 + 0.395915i \(0.870427\pi\)
\(840\) 1.47717e96 0.0160722
\(841\) 2.25889e97 0.236172
\(842\) −1.17145e98 −1.17698
\(843\) −1.23048e98 −1.18810
\(844\) 1.18359e98 1.09832
\(845\) 4.89911e97 0.436936
\(846\) 3.93946e96 0.0337699
\(847\) −5.54584e97 −0.456954
\(848\) −1.55620e98 −1.23255
\(849\) 2.44097e98 1.85847
\(850\) 4.44549e97 0.325376
\(851\) 3.88039e97 0.273046
\(852\) −1.65912e98 −1.12241
\(853\) −5.59225e97 −0.363742 −0.181871 0.983322i \(-0.558215\pi\)
−0.181871 + 0.983322i \(0.558215\pi\)
\(854\) −1.55033e98 −0.969582
\(855\) 7.16497e97 0.430873
\(856\) −2.54060e96 −0.0146915
\(857\) −1.87727e98 −1.04393 −0.521963 0.852968i \(-0.674800\pi\)
−0.521963 + 0.852968i \(0.674800\pi\)
\(858\) 2.32166e98 1.24158
\(859\) −7.06967e97 −0.363603 −0.181802 0.983335i \(-0.558193\pi\)
−0.181802 + 0.983335i \(0.558193\pi\)
\(860\) −2.65693e98 −1.31426
\(861\) 5.71063e97 0.271693
\(862\) 4.15975e98 1.90359
\(863\) −8.77573e97 −0.386297 −0.193149 0.981170i \(-0.561870\pi\)
−0.193149 + 0.981170i \(0.561870\pi\)
\(864\) 2.65807e98 1.12553
\(865\) −5.56285e98 −2.26599
\(866\) 2.66391e98 1.04393
\(867\) 3.00515e98 1.13299
\(868\) 2.35302e98 0.853523
\(869\) 2.65726e98 0.927411
\(870\) −1.01479e99 −3.40785
\(871\) −8.10762e97 −0.261990
\(872\) −2.15032e96 −0.00668655
\(873\) −1.14644e98 −0.343063
\(874\) 7.82081e97 0.225226
\(875\) 9.54035e98 2.64420
\(876\) 2.22226e98 0.592800
\(877\) −5.28961e98 −1.35812 −0.679058 0.734084i \(-0.737612\pi\)
−0.679058 + 0.734084i \(0.737612\pi\)
\(878\) 8.34671e98 2.06276
\(879\) 1.98214e98 0.471528
\(880\) −5.69219e98 −1.30350
\(881\) −4.98423e98 −1.09877 −0.549383 0.835571i \(-0.685137\pi\)
−0.549383 + 0.835571i \(0.685137\pi\)
\(882\) 4.69091e97 0.0995543
\(883\) 6.32680e97 0.129271 0.0646355 0.997909i \(-0.479412\pi\)
0.0646355 + 0.997909i \(0.479412\pi\)
\(884\) −5.02920e97 −0.0989346
\(885\) −2.86714e98 −0.543062
\(886\) −6.99917e98 −1.27649
\(887\) −3.93382e98 −0.690834 −0.345417 0.938449i \(-0.612263\pi\)
−0.345417 + 0.938449i \(0.612263\pi\)
\(888\) −7.34300e96 −0.0124176
\(889\) −8.72695e98 −1.42119
\(890\) 1.08644e98 0.170389
\(891\) −5.55103e98 −0.838437
\(892\) 1.07809e99 1.56831
\(893\) −4.18430e97 −0.0586272
\(894\) −2.72666e98 −0.367980
\(895\) 2.87285e99 3.73457
\(896\) 1.18614e97 0.0148532
\(897\) 2.23346e98 0.269421
\(898\) −3.02158e98 −0.351138
\(899\) −9.60938e98 −1.07584
\(900\) 7.34895e98 0.792686
\(901\) −1.05782e98 −0.109934
\(902\) 2.65578e98 0.265934
\(903\) 7.15450e98 0.690303
\(904\) −6.08194e96 −0.00565457
\(905\) 2.85096e99 2.55425
\(906\) −2.28789e99 −1.97533
\(907\) 2.18119e98 0.181488 0.0907442 0.995874i \(-0.471075\pi\)
0.0907442 + 0.995874i \(0.471075\pi\)
\(908\) −9.94571e98 −0.797553
\(909\) −2.96442e97 −0.0229113
\(910\) −3.50467e99 −2.61072
\(911\) −1.64375e99 −1.18024 −0.590120 0.807316i \(-0.700920\pi\)
−0.590120 + 0.807316i \(0.700920\pi\)
\(912\) 1.22628e99 0.848713
\(913\) −2.55164e98 −0.170235
\(914\) −2.94888e98 −0.189653
\(915\) −2.72512e99 −1.68958
\(916\) 2.26578e99 1.35431
\(917\) 1.54689e99 0.891431
\(918\) 1.79601e98 0.0997881
\(919\) 1.01573e99 0.544136 0.272068 0.962278i \(-0.412292\pi\)
0.272068 + 0.962278i \(0.412292\pi\)
\(920\) 6.60879e96 0.00341373
\(921\) 1.10185e99 0.548814
\(922\) 4.90675e99 2.35672
\(923\) 2.34001e99 1.08383
\(924\) −1.56055e99 −0.697055
\(925\) −7.72276e99 −3.32678
\(926\) −2.90017e99 −1.20491
\(927\) −6.70497e97 −0.0268674
\(928\) −4.07422e99 −1.57466
\(929\) 2.75267e99 1.02619 0.513095 0.858332i \(-0.328499\pi\)
0.513095 + 0.858332i \(0.328499\pi\)
\(930\) 8.24758e99 2.96584
\(931\) −4.98246e98 −0.172834
\(932\) −5.71138e98 −0.191121
\(933\) −2.70270e99 −0.872493
\(934\) 8.51888e99 2.65315
\(935\) −3.86924e98 −0.116262
\(936\) −9.85522e96 −0.00285710
\(937\) −2.08417e99 −0.582984 −0.291492 0.956573i \(-0.594152\pi\)
−0.291492 + 0.956573i \(0.594152\pi\)
\(938\) 1.08670e99 0.293303
\(939\) −5.99669e99 −1.56176
\(940\) −5.94797e98 −0.149481
\(941\) 2.96805e99 0.719812 0.359906 0.932989i \(-0.382809\pi\)
0.359906 + 0.932989i \(0.382809\pi\)
\(942\) −2.16531e99 −0.506774
\(943\) 2.55490e98 0.0577075
\(944\) −1.14423e99 −0.249431
\(945\) 6.27653e99 1.32055
\(946\) 3.32727e99 0.675671
\(947\) −4.39465e99 −0.861391 −0.430696 0.902497i \(-0.641732\pi\)
−0.430696 + 0.902497i \(0.641732\pi\)
\(948\) −8.13746e99 −1.53961
\(949\) −3.13427e99 −0.572424
\(950\) −1.55650e100 −2.74415
\(951\) 1.20042e100 2.04309
\(952\) 4.00721e96 0.000658421 0
\(953\) −2.21477e99 −0.351330 −0.175665 0.984450i \(-0.556208\pi\)
−0.175665 + 0.984450i \(0.556208\pi\)
\(954\) −3.48703e99 −0.534053
\(955\) 1.19720e100 1.77033
\(956\) 4.68210e99 0.668500
\(957\) 6.37305e99 0.878613
\(958\) −1.13593e100 −1.51219
\(959\) −1.08316e100 −1.39241
\(960\) 1.76406e100 2.18991
\(961\) −5.31385e98 −0.0637053
\(962\) 1.74216e100 2.01708
\(963\) 4.71698e99 0.527453
\(964\) −1.69172e100 −1.82704
\(965\) 5.55422e99 0.579373
\(966\) −2.99362e99 −0.301622
\(967\) −8.50453e99 −0.827681 −0.413841 0.910349i \(-0.635813\pi\)
−0.413841 + 0.910349i \(0.635813\pi\)
\(968\) 4.69521e97 0.00441398
\(969\) 8.33556e98 0.0756987
\(970\) 3.45160e100 3.02808
\(971\) −6.28247e98 −0.0532459 −0.0266229 0.999646i \(-0.508475\pi\)
−0.0266229 + 0.999646i \(0.508475\pi\)
\(972\) 7.23539e99 0.592437
\(973\) 6.72529e99 0.532024
\(974\) −3.51671e100 −2.68789
\(975\) −4.44504e100 −3.28263
\(976\) −1.08755e100 −0.776034
\(977\) 4.93122e99 0.340006 0.170003 0.985444i \(-0.445622\pi\)
0.170003 + 0.985444i \(0.445622\pi\)
\(978\) −4.75829e99 −0.317029
\(979\) −6.82304e98 −0.0439296
\(980\) −7.08254e99 −0.440672
\(981\) 3.99238e99 0.240060
\(982\) 3.14371e99 0.182687
\(983\) 3.40156e99 0.191045 0.0955223 0.995427i \(-0.469548\pi\)
0.0955223 + 0.995427i \(0.469548\pi\)
\(984\) −4.83472e97 −0.00262443
\(985\) 4.89737e100 2.56950
\(986\) −2.75287e99 −0.139608
\(987\) 1.60165e99 0.0785134
\(988\) 1.76087e100 0.834392
\(989\) 3.20088e99 0.146620
\(990\) −1.27546e100 −0.564793
\(991\) 2.76108e100 1.18198 0.590992 0.806678i \(-0.298737\pi\)
0.590992 + 0.806678i \(0.298737\pi\)
\(992\) 3.31127e100 1.37042
\(993\) −2.35481e100 −0.942228
\(994\) −3.13643e100 −1.21337
\(995\) −2.43857e100 −0.912140
\(996\) 7.81401e99 0.282609
\(997\) −5.66901e100 −1.98253 −0.991263 0.131897i \(-0.957893\pi\)
−0.991263 + 0.131897i \(0.957893\pi\)
\(998\) 5.13466e100 1.73636
\(999\) −3.12005e100 −1.02028
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 1.68.a.a.1.1 5
3.2 odd 2 9.68.a.a.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.68.a.a.1.1 5 1.1 even 1 trivial
9.68.a.a.1.5 5 3.2 odd 2