Properties

Label 1.52.a.a.1.2
Level $1$
Weight $52$
Character 1.1
Self dual yes
Analytic conductor $16.473$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 52 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.4731353414\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 2 x^{3} - 495735060514 x^{2} - 23954614981416598 x + 48979992255622025570313\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(644100.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.27049e7 q^{2} -5.15198e11 q^{3} -2.09038e15 q^{4} -3.83602e17 q^{5} +6.54557e18 q^{6} -2.02239e21 q^{7} +5.51672e22 q^{8} -1.88826e24 q^{9} +O(q^{10})\) \(q-1.27049e7 q^{2} -5.15198e11 q^{3} -2.09038e15 q^{4} -3.83602e17 q^{5} +6.54557e18 q^{6} -2.02239e21 q^{7} +5.51672e22 q^{8} -1.88826e24 q^{9} +4.87365e24 q^{10} -2.47031e25 q^{11} +1.07696e27 q^{12} -1.34161e27 q^{13} +2.56944e28 q^{14} +1.97631e29 q^{15} +4.00623e30 q^{16} +3.03892e31 q^{17} +2.39903e31 q^{18} +7.39260e32 q^{19} +8.01876e32 q^{20} +1.04193e33 q^{21} +3.13851e32 q^{22} -7.84569e34 q^{23} -2.84221e34 q^{24} -2.96939e35 q^{25} +1.70450e34 q^{26} +2.08241e36 q^{27} +4.22758e36 q^{28} +1.79754e37 q^{29} -2.51089e36 q^{30} -9.27311e37 q^{31} -1.75124e38 q^{32} +1.27270e37 q^{33} -3.86093e38 q^{34} +7.75794e38 q^{35} +3.94720e39 q^{36} +6.86089e39 q^{37} -9.39226e39 q^{38} +6.91193e38 q^{39} -2.11623e40 q^{40} -1.74971e41 q^{41} -1.32377e40 q^{42} +5.07001e41 q^{43} +5.16389e40 q^{44} +7.24343e41 q^{45} +9.96791e41 q^{46} -2.50083e42 q^{47} -2.06400e42 q^{48} -8.49918e42 q^{49} +3.77259e42 q^{50} -1.56564e43 q^{51} +2.80447e42 q^{52} +1.56292e44 q^{53} -2.64569e43 q^{54} +9.47615e42 q^{55} -1.11570e44 q^{56} -3.80866e44 q^{57} -2.28376e44 q^{58} -5.63890e44 q^{59} -4.13125e44 q^{60} +3.98784e45 q^{61} +1.17814e45 q^{62} +3.81881e45 q^{63} -6.79628e45 q^{64} +5.14643e44 q^{65} -1.61696e44 q^{66} -1.33985e46 q^{67} -6.35251e46 q^{68} +4.04208e46 q^{69} -9.85643e45 q^{70} +2.44343e47 q^{71} -1.04170e47 q^{72} +1.85599e47 q^{73} -8.71673e46 q^{74} +1.52982e47 q^{75} -1.54534e48 q^{76} +4.99593e46 q^{77} -8.78157e45 q^{78} +1.63316e48 q^{79} -1.53680e48 q^{80} +2.99389e48 q^{81} +2.22300e48 q^{82} +5.04167e48 q^{83} -2.17804e48 q^{84} -1.16574e49 q^{85} -6.44142e48 q^{86} -9.26087e48 q^{87} -1.36280e48 q^{88} +1.69379e48 q^{89} -9.20274e48 q^{90} +2.71326e48 q^{91} +1.64005e50 q^{92} +4.77749e49 q^{93} +3.17729e49 q^{94} -2.83582e50 q^{95} +9.02238e49 q^{96} -6.10891e50 q^{97} +1.07982e50 q^{98} +4.66459e49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} + O(q^{10}) \) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} - \)\(26\!\cdots\!20\)\(q^{10} + \)\(35\!\cdots\!48\)\(q^{11} - \)\(49\!\cdots\!20\)\(q^{12} + \)\(30\!\cdots\!80\)\(q^{13} + \)\(11\!\cdots\!24\)\(q^{14} + \)\(14\!\cdots\!60\)\(q^{15} + \)\(13\!\cdots\!44\)\(q^{16} + \)\(48\!\cdots\!20\)\(q^{17} + \)\(73\!\cdots\!40\)\(q^{18} + \)\(81\!\cdots\!80\)\(q^{19} + \)\(66\!\cdots\!40\)\(q^{20} + \)\(31\!\cdots\!48\)\(q^{21} - \)\(34\!\cdots\!20\)\(q^{22} - \)\(54\!\cdots\!80\)\(q^{23} - \)\(87\!\cdots\!60\)\(q^{24} - \)\(57\!\cdots\!00\)\(q^{25} + \)\(15\!\cdots\!48\)\(q^{26} + \)\(36\!\cdots\!20\)\(q^{27} + \)\(34\!\cdots\!80\)\(q^{28} + \)\(24\!\cdots\!20\)\(q^{29} - \)\(32\!\cdots\!40\)\(q^{30} - \)\(74\!\cdots\!72\)\(q^{31} - \)\(69\!\cdots\!60\)\(q^{32} - \)\(17\!\cdots\!20\)\(q^{33} + \)\(59\!\cdots\!64\)\(q^{34} + \)\(54\!\cdots\!80\)\(q^{35} + \)\(12\!\cdots\!84\)\(q^{36} + \)\(92\!\cdots\!60\)\(q^{37} + \)\(42\!\cdots\!20\)\(q^{38} - \)\(11\!\cdots\!04\)\(q^{39} - \)\(26\!\cdots\!00\)\(q^{40} + \)\(14\!\cdots\!68\)\(q^{41} - \)\(39\!\cdots\!80\)\(q^{42} - \)\(38\!\cdots\!00\)\(q^{43} + \)\(39\!\cdots\!44\)\(q^{44} + \)\(25\!\cdots\!60\)\(q^{45} - \)\(68\!\cdots\!12\)\(q^{46} + \)\(70\!\cdots\!80\)\(q^{47} - \)\(19\!\cdots\!80\)\(q^{48} - \)\(21\!\cdots\!28\)\(q^{49} - \)\(65\!\cdots\!00\)\(q^{50} + \)\(69\!\cdots\!28\)\(q^{51} + \)\(20\!\cdots\!00\)\(q^{52} - \)\(46\!\cdots\!60\)\(q^{53} + \)\(29\!\cdots\!80\)\(q^{54} + \)\(28\!\cdots\!60\)\(q^{55} - \)\(71\!\cdots\!80\)\(q^{56} - \)\(88\!\cdots\!60\)\(q^{57} - \)\(32\!\cdots\!20\)\(q^{58} + \)\(11\!\cdots\!40\)\(q^{59} + \)\(55\!\cdots\!80\)\(q^{60} + \)\(34\!\cdots\!48\)\(q^{61} + \)\(96\!\cdots\!80\)\(q^{62} + \)\(21\!\cdots\!60\)\(q^{63} - \)\(34\!\cdots\!28\)\(q^{64} + \)\(10\!\cdots\!60\)\(q^{65} - \)\(15\!\cdots\!04\)\(q^{66} + \)\(30\!\cdots\!20\)\(q^{67} - \)\(92\!\cdots\!60\)\(q^{68} + \)\(15\!\cdots\!76\)\(q^{69} - \)\(12\!\cdots\!20\)\(q^{70} + \)\(39\!\cdots\!88\)\(q^{71} + \)\(50\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!56\)\(q^{74} + \)\(72\!\cdots\!00\)\(q^{75} - \)\(19\!\cdots\!60\)\(q^{76} + \)\(13\!\cdots\!00\)\(q^{77} - \)\(96\!\cdots\!00\)\(q^{78} + \)\(40\!\cdots\!20\)\(q^{79} + \)\(65\!\cdots\!80\)\(q^{80} + \)\(15\!\cdots\!44\)\(q^{81} + \)\(26\!\cdots\!80\)\(q^{82} + \)\(10\!\cdots\!60\)\(q^{83} - \)\(18\!\cdots\!56\)\(q^{84} - \)\(22\!\cdots\!20\)\(q^{85} - \)\(43\!\cdots\!32\)\(q^{86} - \)\(62\!\cdots\!40\)\(q^{87} - \)\(25\!\cdots\!40\)\(q^{88} - \)\(90\!\cdots\!40\)\(q^{89} + \)\(31\!\cdots\!60\)\(q^{90} + \)\(10\!\cdots\!88\)\(q^{91} + \)\(19\!\cdots\!20\)\(q^{92} - \)\(31\!\cdots\!20\)\(q^{93} + \)\(63\!\cdots\!84\)\(q^{94} - \)\(41\!\cdots\!00\)\(q^{95} - \)\(24\!\cdots\!32\)\(q^{96} - \)\(13\!\cdots\!20\)\(q^{97} - \)\(31\!\cdots\!80\)\(q^{98} - \)\(17\!\cdots\!64\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27049e7 −0.267737 −0.133868 0.990999i \(-0.542740\pi\)
−0.133868 + 0.990999i \(0.542740\pi\)
\(3\) −5.15198e11 −0.351061 −0.175530 0.984474i \(-0.556164\pi\)
−0.175530 + 0.984474i \(0.556164\pi\)
\(4\) −2.09038e15 −0.928317
\(5\) −3.83602e17 −0.575633 −0.287817 0.957686i \(-0.592929\pi\)
−0.287817 + 0.957686i \(0.592929\pi\)
\(6\) 6.54557e18 0.0939919
\(7\) −2.02239e21 −0.569988 −0.284994 0.958529i \(-0.591992\pi\)
−0.284994 + 0.958529i \(0.591992\pi\)
\(8\) 5.51672e22 0.516281
\(9\) −1.88826e24 −0.876756
\(10\) 4.87365e24 0.154118
\(11\) −2.47031e25 −0.0687444 −0.0343722 0.999409i \(-0.510943\pi\)
−0.0343722 + 0.999409i \(0.510943\pi\)
\(12\) 1.07696e27 0.325896
\(13\) −1.34161e27 −0.0527314 −0.0263657 0.999652i \(-0.508393\pi\)
−0.0263657 + 0.999652i \(0.508393\pi\)
\(14\) 2.56944e28 0.152607
\(15\) 1.97631e29 0.202082
\(16\) 4.00623e30 0.790090
\(17\) 3.03892e31 1.27724 0.638618 0.769524i \(-0.279506\pi\)
0.638618 + 0.769524i \(0.279506\pi\)
\(18\) 2.39903e31 0.234740
\(19\) 7.39260e32 1.82214 0.911068 0.412257i \(-0.135259\pi\)
0.911068 + 0.412257i \(0.135259\pi\)
\(20\) 8.01876e32 0.534370
\(21\) 1.04193e33 0.200100
\(22\) 3.13851e32 0.0184054
\(23\) −7.84569e34 −1.48106 −0.740528 0.672026i \(-0.765424\pi\)
−0.740528 + 0.672026i \(0.765424\pi\)
\(24\) −2.84221e34 −0.181246
\(25\) −2.96939e35 −0.668646
\(26\) 1.70450e34 0.0141181
\(27\) 2.08241e36 0.658856
\(28\) 4.22758e36 0.529129
\(29\) 1.79754e37 0.919451 0.459726 0.888061i \(-0.347948\pi\)
0.459726 + 0.888061i \(0.347948\pi\)
\(30\) −2.51089e36 −0.0541049
\(31\) −9.27311e37 −0.865969 −0.432984 0.901401i \(-0.642539\pi\)
−0.432984 + 0.901401i \(0.642539\pi\)
\(32\) −1.75124e38 −0.727817
\(33\) 1.27270e37 0.0241335
\(34\) −3.86093e38 −0.341963
\(35\) 7.75794e38 0.328104
\(36\) 3.94720e39 0.813908
\(37\) 6.86089e39 0.703456 0.351728 0.936102i \(-0.385594\pi\)
0.351728 + 0.936102i \(0.385594\pi\)
\(38\) −9.39226e39 −0.487853
\(39\) 6.91193e38 0.0185119
\(40\) −2.11623e40 −0.297189
\(41\) −1.74971e41 −1.30912 −0.654559 0.756011i \(-0.727146\pi\)
−0.654559 + 0.756011i \(0.727146\pi\)
\(42\) −1.32377e40 −0.0535742
\(43\) 5.07001e41 1.12606 0.563032 0.826435i \(-0.309635\pi\)
0.563032 + 0.826435i \(0.309635\pi\)
\(44\) 5.16389e40 0.0638166
\(45\) 7.24343e41 0.504690
\(46\) 9.96791e41 0.396533
\(47\) −2.50083e42 −0.574895 −0.287448 0.957796i \(-0.592807\pi\)
−0.287448 + 0.957796i \(0.592807\pi\)
\(48\) −2.06400e42 −0.277369
\(49\) −8.49918e42 −0.675114
\(50\) 3.77259e42 0.179021
\(51\) −1.56564e43 −0.448388
\(52\) 2.80447e42 0.0489515
\(53\) 1.56292e44 1.67843 0.839215 0.543800i \(-0.183015\pi\)
0.839215 + 0.543800i \(0.183015\pi\)
\(54\) −2.64569e43 −0.176400
\(55\) 9.47615e42 0.0395716
\(56\) −1.11570e44 −0.294274
\(57\) −3.80866e44 −0.639680
\(58\) −2.28376e44 −0.246171
\(59\) −5.63890e44 −0.393068 −0.196534 0.980497i \(-0.562969\pi\)
−0.196534 + 0.980497i \(0.562969\pi\)
\(60\) −4.13125e44 −0.187596
\(61\) 3.98784e45 1.18803 0.594014 0.804454i \(-0.297542\pi\)
0.594014 + 0.804454i \(0.297542\pi\)
\(62\) 1.17814e45 0.231852
\(63\) 3.81881e45 0.499740
\(64\) −6.79628e45 −0.595226
\(65\) 5.14643e44 0.0303540
\(66\) −1.61696e44 −0.00646141
\(67\) −1.33985e46 −0.364879 −0.182439 0.983217i \(-0.558399\pi\)
−0.182439 + 0.983217i \(0.558399\pi\)
\(68\) −6.35251e46 −1.18568
\(69\) 4.04208e46 0.519940
\(70\) −9.85643e45 −0.0878455
\(71\) 2.44343e47 1.51674 0.758370 0.651824i \(-0.225996\pi\)
0.758370 + 0.651824i \(0.225996\pi\)
\(72\) −1.04170e47 −0.452653
\(73\) 1.85599e47 0.567339 0.283669 0.958922i \(-0.408448\pi\)
0.283669 + 0.958922i \(0.408448\pi\)
\(74\) −8.71673e46 −0.188341
\(75\) 1.52982e47 0.234735
\(76\) −1.54534e48 −1.69152
\(77\) 4.99593e46 0.0391835
\(78\) −8.78157e45 −0.00495633
\(79\) 1.63316e48 0.666097 0.333048 0.942910i \(-0.391923\pi\)
0.333048 + 0.942910i \(0.391923\pi\)
\(80\) −1.53680e48 −0.454802
\(81\) 2.99389e48 0.645458
\(82\) 2.22300e48 0.350499
\(83\) 5.04167e48 0.583556 0.291778 0.956486i \(-0.405753\pi\)
0.291778 + 0.956486i \(0.405753\pi\)
\(84\) −2.17804e48 −0.185757
\(85\) −1.16574e49 −0.735220
\(86\) −6.44142e48 −0.301489
\(87\) −9.26087e48 −0.322783
\(88\) −1.36280e48 −0.0354915
\(89\) 1.69379e48 0.0330685 0.0165342 0.999863i \(-0.494737\pi\)
0.0165342 + 0.999863i \(0.494737\pi\)
\(90\) −9.20274e48 −0.135124
\(91\) 2.71326e48 0.0300563
\(92\) 1.64005e50 1.37489
\(93\) 4.77749e49 0.304008
\(94\) 3.17729e49 0.153921
\(95\) −2.83582e50 −1.04888
\(96\) 9.02238e49 0.255508
\(97\) −6.10891e50 −1.32826 −0.664132 0.747615i \(-0.731199\pi\)
−0.664132 + 0.747615i \(0.731199\pi\)
\(98\) 1.07982e50 0.180753
\(99\) 4.66459e49 0.0602721
\(100\) 6.20716e50 0.620716
\(101\) −6.28480e50 −0.487636 −0.243818 0.969821i \(-0.578400\pi\)
−0.243818 + 0.969821i \(0.578400\pi\)
\(102\) 1.98914e50 0.120050
\(103\) 2.80053e51 1.31793 0.658963 0.752175i \(-0.270995\pi\)
0.658963 + 0.752175i \(0.270995\pi\)
\(104\) −7.40127e49 −0.0272243
\(105\) −3.99688e50 −0.115184
\(106\) −1.98569e51 −0.449377
\(107\) −1.63322e50 −0.0290910 −0.0145455 0.999894i \(-0.504630\pi\)
−0.0145455 + 0.999894i \(0.504630\pi\)
\(108\) −4.35304e51 −0.611627
\(109\) −1.58683e51 −0.176260 −0.0881302 0.996109i \(-0.528089\pi\)
−0.0881302 + 0.996109i \(0.528089\pi\)
\(110\) −1.20394e50 −0.0105948
\(111\) −3.53472e51 −0.246956
\(112\) −8.10217e51 −0.450341
\(113\) 3.37912e52 1.49728 0.748640 0.662977i \(-0.230707\pi\)
0.748640 + 0.662977i \(0.230707\pi\)
\(114\) 4.83888e51 0.171266
\(115\) 3.00962e52 0.852545
\(116\) −3.75754e52 −0.853542
\(117\) 2.53331e51 0.0462326
\(118\) 7.16419e51 0.105239
\(119\) −6.14589e52 −0.728009
\(120\) 1.09028e52 0.104331
\(121\) −1.28520e53 −0.995274
\(122\) −5.06653e52 −0.318079
\(123\) 9.01450e52 0.459580
\(124\) 1.93844e53 0.803893
\(125\) 2.84260e53 0.960529
\(126\) −4.85178e52 −0.133799
\(127\) −3.62929e53 −0.818137 −0.409069 0.912504i \(-0.634146\pi\)
−0.409069 + 0.912504i \(0.634146\pi\)
\(128\) 4.80692e53 0.887181
\(129\) −2.61206e53 −0.395317
\(130\) −6.53852e51 −0.00812688
\(131\) −2.78824e53 −0.285044 −0.142522 0.989792i \(-0.545521\pi\)
−0.142522 + 0.989792i \(0.545521\pi\)
\(132\) −2.66043e52 −0.0224035
\(133\) −1.49507e54 −1.03859
\(134\) 1.70227e53 0.0976914
\(135\) −7.98817e53 −0.379259
\(136\) 1.67649e54 0.659414
\(137\) 2.86306e54 0.934236 0.467118 0.884195i \(-0.345292\pi\)
0.467118 + 0.884195i \(0.345292\pi\)
\(138\) −5.13545e53 −0.139207
\(139\) 3.12773e54 0.705264 0.352632 0.935762i \(-0.385287\pi\)
0.352632 + 0.935762i \(0.385287\pi\)
\(140\) −1.62171e54 −0.304585
\(141\) 1.28842e54 0.201823
\(142\) −3.10436e54 −0.406087
\(143\) 3.31418e52 0.00362499
\(144\) −7.56482e54 −0.692716
\(145\) −6.89539e54 −0.529267
\(146\) −2.35802e54 −0.151897
\(147\) 4.37876e54 0.237006
\(148\) −1.43419e55 −0.653030
\(149\) 4.23740e55 1.62499 0.812493 0.582971i \(-0.198110\pi\)
0.812493 + 0.582971i \(0.198110\pi\)
\(150\) −1.94363e54 −0.0628473
\(151\) 7.71079e54 0.210468 0.105234 0.994447i \(-0.466441\pi\)
0.105234 + 0.994447i \(0.466441\pi\)
\(152\) 4.07829e55 0.940734
\(153\) −5.73828e55 −1.11983
\(154\) −6.34730e53 −0.0104909
\(155\) 3.55718e55 0.498480
\(156\) −1.44486e54 −0.0171849
\(157\) −1.17035e56 −1.18270 −0.591351 0.806414i \(-0.701405\pi\)
−0.591351 + 0.806414i \(0.701405\pi\)
\(158\) −2.07492e55 −0.178339
\(159\) −8.05215e55 −0.589231
\(160\) 6.71781e55 0.418956
\(161\) 1.58671e56 0.844183
\(162\) −3.80372e55 −0.172813
\(163\) −1.56667e56 −0.608405 −0.304203 0.952607i \(-0.598390\pi\)
−0.304203 + 0.952607i \(0.598390\pi\)
\(164\) 3.65757e56 1.21528
\(165\) −4.88209e54 −0.0138920
\(166\) −6.40541e55 −0.156239
\(167\) 4.64519e56 0.972150 0.486075 0.873917i \(-0.338428\pi\)
0.486075 + 0.873917i \(0.338428\pi\)
\(168\) 5.74806e55 0.103308
\(169\) −6.45508e56 −0.997219
\(170\) 1.48106e56 0.196846
\(171\) −1.39592e57 −1.59757
\(172\) −1.05983e57 −1.04534
\(173\) 1.75769e57 1.49543 0.747714 0.664021i \(-0.231151\pi\)
0.747714 + 0.664021i \(0.231151\pi\)
\(174\) 1.17659e56 0.0864209
\(175\) 6.00526e56 0.381120
\(176\) −9.89661e55 −0.0543142
\(177\) 2.90515e56 0.137991
\(178\) −2.15195e55 −0.00885364
\(179\) 3.24188e57 1.15623 0.578116 0.815955i \(-0.303788\pi\)
0.578116 + 0.815955i \(0.303788\pi\)
\(180\) −1.51415e57 −0.468513
\(181\) 8.53725e56 0.229358 0.114679 0.993403i \(-0.463416\pi\)
0.114679 + 0.993403i \(0.463416\pi\)
\(182\) −3.44718e55 −0.00804717
\(183\) −2.05453e57 −0.417070
\(184\) −4.32825e57 −0.764641
\(185\) −2.63185e57 −0.404933
\(186\) −6.06977e56 −0.0813940
\(187\) −7.50706e56 −0.0878029
\(188\) 5.22769e57 0.533685
\(189\) −4.21145e57 −0.375540
\(190\) 3.60289e57 0.280824
\(191\) 9.24442e57 0.630273 0.315136 0.949046i \(-0.397950\pi\)
0.315136 + 0.949046i \(0.397950\pi\)
\(192\) 3.50143e57 0.208961
\(193\) −2.11389e57 −0.110502 −0.0552512 0.998472i \(-0.517596\pi\)
−0.0552512 + 0.998472i \(0.517596\pi\)
\(194\) 7.76134e57 0.355625
\(195\) −2.65143e56 −0.0106561
\(196\) 1.77666e58 0.626720
\(197\) −2.03837e58 −0.631531 −0.315765 0.948837i \(-0.602261\pi\)
−0.315765 + 0.948837i \(0.602261\pi\)
\(198\) −5.92634e56 −0.0161371
\(199\) −4.89566e58 −1.17235 −0.586176 0.810184i \(-0.699367\pi\)
−0.586176 + 0.810184i \(0.699367\pi\)
\(200\) −1.63813e58 −0.345210
\(201\) 6.90288e57 0.128095
\(202\) 7.98480e57 0.130558
\(203\) −3.63532e58 −0.524076
\(204\) 3.27280e58 0.416246
\(205\) 6.71194e58 0.753572
\(206\) −3.55806e58 −0.352857
\(207\) 1.48147e59 1.29852
\(208\) −5.37478e57 −0.0416626
\(209\) −1.82620e58 −0.125262
\(210\) 5.07801e57 0.0308391
\(211\) 1.53613e59 0.826467 0.413234 0.910625i \(-0.364399\pi\)
0.413234 + 0.910625i \(0.364399\pi\)
\(212\) −3.26711e59 −1.55811
\(213\) −1.25885e59 −0.532468
\(214\) 2.07500e57 0.00778872
\(215\) −1.94487e59 −0.648200
\(216\) 1.14881e59 0.340155
\(217\) 1.87539e59 0.493591
\(218\) 2.01606e58 0.0471914
\(219\) −9.56202e58 −0.199170
\(220\) −1.98088e58 −0.0367350
\(221\) −4.07703e58 −0.0673505
\(222\) 4.49084e58 0.0661191
\(223\) 8.84276e59 1.16095 0.580475 0.814278i \(-0.302867\pi\)
0.580475 + 0.814278i \(0.302867\pi\)
\(224\) 3.54171e59 0.414847
\(225\) 5.60699e59 0.586240
\(226\) −4.29315e59 −0.400877
\(227\) −1.84839e60 −1.54218 −0.771090 0.636726i \(-0.780288\pi\)
−0.771090 + 0.636726i \(0.780288\pi\)
\(228\) 7.96155e59 0.593826
\(229\) −1.13494e60 −0.757126 −0.378563 0.925576i \(-0.623582\pi\)
−0.378563 + 0.925576i \(0.623582\pi\)
\(230\) −3.82371e59 −0.228258
\(231\) −2.57389e58 −0.0137558
\(232\) 9.91651e59 0.474696
\(233\) −1.75626e60 −0.753376 −0.376688 0.926340i \(-0.622937\pi\)
−0.376688 + 0.926340i \(0.622937\pi\)
\(234\) −3.21855e58 −0.0123782
\(235\) 9.59324e59 0.330929
\(236\) 1.17875e60 0.364892
\(237\) −8.41400e59 −0.233840
\(238\) 7.80832e59 0.194915
\(239\) 7.46779e60 1.67512 0.837560 0.546346i \(-0.183982\pi\)
0.837560 + 0.546346i \(0.183982\pi\)
\(240\) 7.91756e59 0.159663
\(241\) −2.67830e60 −0.485763 −0.242882 0.970056i \(-0.578093\pi\)
−0.242882 + 0.970056i \(0.578093\pi\)
\(242\) 1.63284e60 0.266471
\(243\) −6.02732e60 −0.885451
\(244\) −8.33612e60 −1.10287
\(245\) 3.26031e60 0.388618
\(246\) −1.14529e60 −0.123046
\(247\) −9.91796e59 −0.0960838
\(248\) −5.11572e60 −0.447083
\(249\) −2.59746e60 −0.204864
\(250\) −3.61151e60 −0.257169
\(251\) 2.75172e61 1.76980 0.884900 0.465782i \(-0.154227\pi\)
0.884900 + 0.465782i \(0.154227\pi\)
\(252\) −7.98279e60 −0.463917
\(253\) 1.93813e60 0.101814
\(254\) 4.61099e60 0.219045
\(255\) 6.00585e60 0.258107
\(256\) 9.19670e60 0.357695
\(257\) −4.92610e59 −0.0173464 −0.00867318 0.999962i \(-0.502761\pi\)
−0.00867318 + 0.999962i \(0.502761\pi\)
\(258\) 3.31861e60 0.105841
\(259\) −1.38754e61 −0.400961
\(260\) −1.07580e60 −0.0281781
\(261\) −3.39422e61 −0.806135
\(262\) 3.54245e60 0.0763169
\(263\) −1.45507e60 −0.0284454 −0.0142227 0.999899i \(-0.504527\pi\)
−0.0142227 + 0.999899i \(0.504527\pi\)
\(264\) 7.02112e59 0.0124597
\(265\) −5.99541e61 −0.966160
\(266\) 1.89948e61 0.278070
\(267\) −8.72636e59 −0.0116090
\(268\) 2.80080e61 0.338723
\(269\) 8.25887e60 0.0908318 0.0454159 0.998968i \(-0.485539\pi\)
0.0454159 + 0.998968i \(0.485539\pi\)
\(270\) 1.01489e61 0.101542
\(271\) 8.46290e61 0.770553 0.385276 0.922801i \(-0.374106\pi\)
0.385276 + 0.922801i \(0.374106\pi\)
\(272\) 1.21746e62 1.00913
\(273\) −1.39786e60 −0.0105516
\(274\) −3.63751e61 −0.250129
\(275\) 7.33529e60 0.0459657
\(276\) −8.44951e61 −0.482669
\(277\) −2.17621e62 −1.13362 −0.566808 0.823850i \(-0.691822\pi\)
−0.566808 + 0.823850i \(0.691822\pi\)
\(278\) −3.97376e61 −0.188825
\(279\) 1.75101e62 0.759243
\(280\) 4.27984e61 0.169394
\(281\) −4.49759e62 −1.62543 −0.812715 0.582661i \(-0.802012\pi\)
−0.812715 + 0.582661i \(0.802012\pi\)
\(282\) −1.63693e61 −0.0540355
\(283\) 5.28631e62 1.59440 0.797202 0.603713i \(-0.206313\pi\)
0.797202 + 0.603713i \(0.206313\pi\)
\(284\) −5.10770e62 −1.40802
\(285\) 1.46101e62 0.368221
\(286\) −4.21065e59 −0.000970543 0
\(287\) 3.53861e62 0.746181
\(288\) 3.30681e62 0.638119
\(289\) 3.57400e62 0.631334
\(290\) 8.76056e61 0.141704
\(291\) 3.14730e62 0.466301
\(292\) −3.87973e62 −0.526670
\(293\) −1.35914e63 −1.69099 −0.845493 0.533987i \(-0.820693\pi\)
−0.845493 + 0.533987i \(0.820693\pi\)
\(294\) −5.56320e61 −0.0634552
\(295\) 2.16309e62 0.226263
\(296\) 3.78496e62 0.363181
\(297\) −5.14419e61 −0.0452926
\(298\) −5.38359e62 −0.435069
\(299\) 1.05258e62 0.0780982
\(300\) −3.19792e62 −0.217909
\(301\) −1.02535e63 −0.641843
\(302\) −9.79652e61 −0.0563501
\(303\) 3.23791e62 0.171190
\(304\) 2.96165e63 1.43965
\(305\) −1.52974e63 −0.683869
\(306\) 7.29046e62 0.299818
\(307\) 3.47883e63 1.31645 0.658226 0.752821i \(-0.271307\pi\)
0.658226 + 0.752821i \(0.271307\pi\)
\(308\) −1.04434e62 −0.0363747
\(309\) −1.44283e63 −0.462672
\(310\) −4.51939e62 −0.133462
\(311\) 9.88875e62 0.268999 0.134500 0.990914i \(-0.457057\pi\)
0.134500 + 0.990914i \(0.457057\pi\)
\(312\) 3.81312e61 0.00955737
\(313\) −5.32344e63 −1.22974 −0.614868 0.788630i \(-0.710791\pi\)
−0.614868 + 0.788630i \(0.710791\pi\)
\(314\) 1.48693e63 0.316653
\(315\) −1.46491e63 −0.287667
\(316\) −3.41393e63 −0.618349
\(317\) −2.07710e63 −0.347094 −0.173547 0.984826i \(-0.555523\pi\)
−0.173547 + 0.984826i \(0.555523\pi\)
\(318\) 1.02302e63 0.157759
\(319\) −4.44046e62 −0.0632071
\(320\) 2.60707e63 0.342632
\(321\) 8.41432e61 0.0102127
\(322\) −2.01590e63 −0.226019
\(323\) 2.24655e64 2.32730
\(324\) −6.25838e63 −0.599190
\(325\) 3.98375e62 0.0352587
\(326\) 1.99044e63 0.162892
\(327\) 8.17532e62 0.0618781
\(328\) −9.65269e63 −0.675873
\(329\) 5.05766e63 0.327683
\(330\) 6.20268e61 0.00371941
\(331\) −1.81346e63 −0.100669 −0.0503343 0.998732i \(-0.516029\pi\)
−0.0503343 + 0.998732i \(0.516029\pi\)
\(332\) −1.05390e64 −0.541725
\(333\) −1.29552e64 −0.616759
\(334\) −5.90169e63 −0.260280
\(335\) 5.13969e63 0.210036
\(336\) 4.17422e63 0.158097
\(337\) −1.27328e64 −0.447056 −0.223528 0.974698i \(-0.571757\pi\)
−0.223528 + 0.974698i \(0.571757\pi\)
\(338\) 8.20115e63 0.266992
\(339\) −1.74091e64 −0.525636
\(340\) 2.43684e64 0.682518
\(341\) 2.29074e63 0.0595305
\(342\) 1.77351e64 0.427728
\(343\) 4.26491e64 0.954794
\(344\) 2.79698e64 0.581366
\(345\) −1.55055e64 −0.299295
\(346\) −2.23313e64 −0.400381
\(347\) −4.50582e64 −0.750537 −0.375269 0.926916i \(-0.622450\pi\)
−0.375269 + 0.926916i \(0.622450\pi\)
\(348\) 1.93588e64 0.299645
\(349\) 6.10318e63 0.0878026 0.0439013 0.999036i \(-0.486021\pi\)
0.0439013 + 0.999036i \(0.486021\pi\)
\(350\) −7.62966e63 −0.102040
\(351\) −2.79377e63 −0.0347424
\(352\) 4.32611e63 0.0500334
\(353\) −6.21110e64 −0.668211 −0.334106 0.942536i \(-0.608434\pi\)
−0.334106 + 0.942536i \(0.608434\pi\)
\(354\) −3.69098e63 −0.0369452
\(355\) −9.37304e64 −0.873087
\(356\) −3.54067e63 −0.0306980
\(357\) 3.16635e64 0.255576
\(358\) −4.11879e64 −0.309566
\(359\) −2.08428e64 −0.145898 −0.0729488 0.997336i \(-0.523241\pi\)
−0.0729488 + 0.997336i \(0.523241\pi\)
\(360\) 3.99600e64 0.260562
\(361\) 3.81904e65 2.32018
\(362\) −1.08465e64 −0.0614076
\(363\) 6.62131e64 0.349402
\(364\) −5.67175e63 −0.0279017
\(365\) −7.11962e64 −0.326579
\(366\) 2.61027e64 0.111665
\(367\) −1.66429e65 −0.664118 −0.332059 0.943259i \(-0.607743\pi\)
−0.332059 + 0.943259i \(0.607743\pi\)
\(368\) −3.14316e65 −1.17017
\(369\) 3.30392e65 1.14778
\(370\) 3.34376e64 0.108415
\(371\) −3.16085e65 −0.956684
\(372\) −9.98678e64 −0.282215
\(373\) 3.79646e64 0.100185 0.0500925 0.998745i \(-0.484048\pi\)
0.0500925 + 0.998745i \(0.484048\pi\)
\(374\) 9.53768e63 0.0235081
\(375\) −1.46450e65 −0.337204
\(376\) −1.37964e65 −0.296808
\(377\) −2.41159e64 −0.0484840
\(378\) 5.35063e64 0.100546
\(379\) 3.34355e65 0.587364 0.293682 0.955903i \(-0.405119\pi\)
0.293682 + 0.955903i \(0.405119\pi\)
\(380\) 5.92795e65 0.973695
\(381\) 1.86980e65 0.287216
\(382\) −1.17450e65 −0.168747
\(383\) 3.02479e65 0.406561 0.203281 0.979121i \(-0.434840\pi\)
0.203281 + 0.979121i \(0.434840\pi\)
\(384\) −2.47651e65 −0.311455
\(385\) −1.91645e64 −0.0225553
\(386\) 2.68569e64 0.0295855
\(387\) −9.57352e65 −0.987284
\(388\) 1.27700e66 1.23305
\(389\) 3.96714e65 0.358726 0.179363 0.983783i \(-0.442596\pi\)
0.179363 + 0.983783i \(0.442596\pi\)
\(390\) 3.36863e63 0.00285303
\(391\) −2.38424e66 −1.89166
\(392\) −4.68876e65 −0.348549
\(393\) 1.43650e65 0.100068
\(394\) 2.58974e65 0.169084
\(395\) −6.26483e65 −0.383428
\(396\) −9.75079e64 −0.0559516
\(397\) 1.53914e65 0.0828174 0.0414087 0.999142i \(-0.486815\pi\)
0.0414087 + 0.999142i \(0.486815\pi\)
\(398\) 6.21992e65 0.313882
\(399\) 7.70260e65 0.364610
\(400\) −1.18960e66 −0.528290
\(401\) 3.72470e66 1.55207 0.776033 0.630693i \(-0.217229\pi\)
0.776033 + 0.630693i \(0.217229\pi\)
\(402\) −8.77007e64 −0.0342956
\(403\) 1.24409e65 0.0456638
\(404\) 1.31376e66 0.452681
\(405\) −1.14846e66 −0.371547
\(406\) 4.61866e65 0.140314
\(407\) −1.69485e65 −0.0483586
\(408\) −8.63723e65 −0.231494
\(409\) 1.18361e66 0.298033 0.149017 0.988835i \(-0.452389\pi\)
0.149017 + 0.988835i \(0.452389\pi\)
\(410\) −8.52749e65 −0.201759
\(411\) −1.47505e66 −0.327974
\(412\) −5.85419e66 −1.22345
\(413\) 1.14041e66 0.224044
\(414\) −1.88220e66 −0.347663
\(415\) −1.93399e66 −0.335915
\(416\) 2.34948e65 0.0383789
\(417\) −1.61140e66 −0.247591
\(418\) 2.32018e65 0.0335371
\(419\) 9.81782e66 1.33523 0.667617 0.744505i \(-0.267314\pi\)
0.667617 + 0.744505i \(0.267314\pi\)
\(420\) 8.35501e65 0.106928
\(421\) 4.41844e66 0.532201 0.266101 0.963945i \(-0.414265\pi\)
0.266101 + 0.963945i \(0.414265\pi\)
\(422\) −1.95165e66 −0.221276
\(423\) 4.72223e66 0.504043
\(424\) 8.62222e66 0.866542
\(425\) −9.02372e66 −0.854019
\(426\) 1.59936e66 0.142561
\(427\) −8.06498e66 −0.677162
\(428\) 3.41406e65 0.0270056
\(429\) −1.70746e64 −0.00127259
\(430\) 2.47094e66 0.173547
\(431\) −9.31273e66 −0.616463 −0.308231 0.951311i \(-0.599737\pi\)
−0.308231 + 0.951311i \(0.599737\pi\)
\(432\) 8.34261e66 0.520555
\(433\) −5.53636e66 −0.325674 −0.162837 0.986653i \(-0.552064\pi\)
−0.162837 + 0.986653i \(0.552064\pi\)
\(434\) −2.38267e66 −0.132153
\(435\) 3.55249e66 0.185805
\(436\) 3.31709e66 0.163626
\(437\) −5.80001e67 −2.69868
\(438\) 1.21485e66 0.0533252
\(439\) 3.50063e67 1.44978 0.724888 0.688867i \(-0.241891\pi\)
0.724888 + 0.688867i \(0.241891\pi\)
\(440\) 5.22773e65 0.0204301
\(441\) 1.60487e67 0.591910
\(442\) 5.17985e65 0.0180322
\(443\) 3.49460e67 1.14842 0.574211 0.818707i \(-0.305309\pi\)
0.574211 + 0.818707i \(0.305309\pi\)
\(444\) 7.38892e66 0.229253
\(445\) −6.49741e65 −0.0190353
\(446\) −1.12347e67 −0.310829
\(447\) −2.18310e67 −0.570469
\(448\) 1.37447e67 0.339272
\(449\) 3.38559e67 0.789501 0.394750 0.918788i \(-0.370831\pi\)
0.394750 + 0.918788i \(0.370831\pi\)
\(450\) −7.12365e66 −0.156958
\(451\) 4.32233e66 0.0899945
\(452\) −7.06365e67 −1.38995
\(453\) −3.97259e66 −0.0738872
\(454\) 2.34838e67 0.412899
\(455\) −1.04081e66 −0.0173014
\(456\) −2.10113e67 −0.330255
\(457\) −1.12417e68 −1.67096 −0.835482 0.549517i \(-0.814812\pi\)
−0.835482 + 0.549517i \(0.814812\pi\)
\(458\) 1.44194e67 0.202710
\(459\) 6.32827e67 0.841515
\(460\) −6.29127e67 −0.791432
\(461\) 3.19451e67 0.380216 0.190108 0.981763i \(-0.439116\pi\)
0.190108 + 0.981763i \(0.439116\pi\)
\(462\) 3.27012e65 0.00368293
\(463\) 1.31779e68 1.40453 0.702263 0.711918i \(-0.252173\pi\)
0.702263 + 0.711918i \(0.252173\pi\)
\(464\) 7.20134e67 0.726449
\(465\) −1.83266e67 −0.174997
\(466\) 2.23131e67 0.201706
\(467\) −4.26431e67 −0.364979 −0.182490 0.983208i \(-0.558416\pi\)
−0.182490 + 0.983208i \(0.558416\pi\)
\(468\) −5.29559e66 −0.0429185
\(469\) 2.70970e67 0.207976
\(470\) −1.21882e67 −0.0886018
\(471\) 6.02963e67 0.415200
\(472\) −3.11082e67 −0.202934
\(473\) −1.25245e67 −0.0774106
\(474\) 1.06899e67 0.0626077
\(475\) −2.19515e68 −1.21836
\(476\) 1.28473e68 0.675823
\(477\) −2.95121e68 −1.47157
\(478\) −9.48779e67 −0.448491
\(479\) 1.74665e68 0.782801 0.391401 0.920220i \(-0.371991\pi\)
0.391401 + 0.920220i \(0.371991\pi\)
\(480\) −3.46101e67 −0.147079
\(481\) −9.20462e66 −0.0370942
\(482\) 3.40277e67 0.130057
\(483\) −8.17468e67 −0.296360
\(484\) 2.68656e68 0.923930
\(485\) 2.34339e68 0.764593
\(486\) 7.65768e67 0.237068
\(487\) −3.99057e68 −1.17232 −0.586161 0.810195i \(-0.699361\pi\)
−0.586161 + 0.810195i \(0.699361\pi\)
\(488\) 2.19998e68 0.613357
\(489\) 8.07144e67 0.213587
\(490\) −4.14220e67 −0.104047
\(491\) 1.41320e68 0.336997 0.168499 0.985702i \(-0.446108\pi\)
0.168499 + 0.985702i \(0.446108\pi\)
\(492\) −1.88438e68 −0.426636
\(493\) 5.46256e68 1.17436
\(494\) 1.26007e67 0.0257252
\(495\) −1.78935e67 −0.0346946
\(496\) −3.71502e68 −0.684193
\(497\) −4.94157e68 −0.864523
\(498\) 3.30006e67 0.0548496
\(499\) 3.57937e68 0.565253 0.282626 0.959230i \(-0.408794\pi\)
0.282626 + 0.959230i \(0.408794\pi\)
\(500\) −5.94212e68 −0.891675
\(501\) −2.39319e68 −0.341284
\(502\) −3.49604e68 −0.473840
\(503\) −4.56639e68 −0.588287 −0.294143 0.955761i \(-0.595034\pi\)
−0.294143 + 0.955761i \(0.595034\pi\)
\(504\) 2.10673e68 0.258007
\(505\) 2.41086e68 0.280700
\(506\) −2.46238e67 −0.0272594
\(507\) 3.32565e68 0.350085
\(508\) 7.58660e68 0.759491
\(509\) 1.62918e69 1.55119 0.775596 0.631230i \(-0.217450\pi\)
0.775596 + 0.631230i \(0.217450\pi\)
\(510\) −7.63040e67 −0.0691047
\(511\) −3.75354e68 −0.323376
\(512\) −1.19926e69 −0.982949
\(513\) 1.53944e69 1.20052
\(514\) 6.25858e66 0.00464426
\(515\) −1.07429e69 −0.758643
\(516\) 5.46021e68 0.366979
\(517\) 6.17781e67 0.0395208
\(518\) 1.76287e68 0.107352
\(519\) −9.05557e68 −0.524986
\(520\) 2.83914e67 0.0156712
\(521\) −1.25774e69 −0.661040 −0.330520 0.943799i \(-0.607224\pi\)
−0.330520 + 0.943799i \(0.607224\pi\)
\(522\) 4.31234e68 0.215832
\(523\) −1.98441e69 −0.945883 −0.472941 0.881094i \(-0.656808\pi\)
−0.472941 + 0.881094i \(0.656808\pi\)
\(524\) 5.82850e68 0.264612
\(525\) −3.09390e68 −0.133796
\(526\) 1.84866e67 0.00761589
\(527\) −2.81802e69 −1.10605
\(528\) 5.09872e67 0.0190676
\(529\) 3.34927e69 1.19352
\(530\) 7.61714e68 0.258677
\(531\) 1.06477e69 0.344625
\(532\) 3.12528e69 0.964145
\(533\) 2.34743e68 0.0690317
\(534\) 1.10868e67 0.00310817
\(535\) 6.26507e67 0.0167457
\(536\) −7.39158e68 −0.188380
\(537\) −1.67021e69 −0.405908
\(538\) −1.04929e68 −0.0243190
\(539\) 2.09956e68 0.0464103
\(540\) 1.66983e69 0.352073
\(541\) 2.04153e69 0.410606 0.205303 0.978698i \(-0.434182\pi\)
0.205303 + 0.978698i \(0.434182\pi\)
\(542\) −1.07521e69 −0.206305
\(543\) −4.39837e68 −0.0805187
\(544\) −5.32189e69 −0.929595
\(545\) 6.08712e68 0.101461
\(546\) 1.77598e67 0.00282505
\(547\) −1.73926e69 −0.264050 −0.132025 0.991246i \(-0.542148\pi\)
−0.132025 + 0.991246i \(0.542148\pi\)
\(548\) −5.98490e69 −0.867267
\(549\) −7.53010e69 −1.04161
\(550\) −9.31945e67 −0.0123067
\(551\) 1.32885e70 1.67536
\(552\) 2.22991e69 0.268435
\(553\) −3.30289e69 −0.379667
\(554\) 2.76486e69 0.303511
\(555\) 1.35593e69 0.142156
\(556\) −6.53815e69 −0.654709
\(557\) 1.57782e70 1.50921 0.754604 0.656180i \(-0.227829\pi\)
0.754604 + 0.656180i \(0.227829\pi\)
\(558\) −2.22465e69 −0.203277
\(559\) −6.80195e68 −0.0593790
\(560\) 3.10801e69 0.259232
\(561\) 3.86762e68 0.0308241
\(562\) 5.71416e69 0.435188
\(563\) 1.07629e70 0.783370 0.391685 0.920099i \(-0.371892\pi\)
0.391685 + 0.920099i \(0.371892\pi\)
\(564\) −2.69330e69 −0.187356
\(565\) −1.29624e70 −0.861884
\(566\) −6.71623e69 −0.426881
\(567\) −6.05482e69 −0.367903
\(568\) 1.34797e70 0.783065
\(569\) −2.42046e70 −1.34442 −0.672210 0.740361i \(-0.734655\pi\)
−0.672210 + 0.740361i \(0.734655\pi\)
\(570\) −1.85620e69 −0.0985864
\(571\) −2.02012e70 −1.02602 −0.513012 0.858382i \(-0.671470\pi\)
−0.513012 + 0.858382i \(0.671470\pi\)
\(572\) −6.92791e67 −0.00336514
\(573\) −4.76271e69 −0.221264
\(574\) −4.49579e69 −0.199780
\(575\) 2.32969e70 0.990302
\(576\) 1.28332e70 0.521868
\(577\) 2.07089e70 0.805699 0.402850 0.915266i \(-0.368020\pi\)
0.402850 + 0.915266i \(0.368020\pi\)
\(578\) −4.54075e69 −0.169031
\(579\) 1.08907e69 0.0387930
\(580\) 1.44140e70 0.491327
\(581\) −1.01962e70 −0.332620
\(582\) −3.99863e69 −0.124846
\(583\) −3.86090e69 −0.115383
\(584\) 1.02390e70 0.292906
\(585\) −9.71783e68 −0.0266130
\(586\) 1.72678e70 0.452739
\(587\) 4.82066e70 1.21014 0.605070 0.796173i \(-0.293145\pi\)
0.605070 + 0.796173i \(0.293145\pi\)
\(588\) −9.15330e69 −0.220017
\(589\) −6.85524e70 −1.57791
\(590\) −2.74820e69 −0.0605790
\(591\) 1.05017e70 0.221706
\(592\) 2.74863e70 0.555793
\(593\) −6.85044e70 −1.32686 −0.663428 0.748240i \(-0.730899\pi\)
−0.663428 + 0.748240i \(0.730899\pi\)
\(594\) 6.53567e68 0.0121265
\(595\) 2.35758e70 0.419067
\(596\) −8.85779e70 −1.50850
\(597\) 2.52224e70 0.411567
\(598\) −1.33730e69 −0.0209097
\(599\) −3.61715e70 −0.541979 −0.270990 0.962582i \(-0.587351\pi\)
−0.270990 + 0.962582i \(0.587351\pi\)
\(600\) 8.43960e69 0.121190
\(601\) 6.55680e70 0.902387 0.451193 0.892426i \(-0.350998\pi\)
0.451193 + 0.892426i \(0.350998\pi\)
\(602\) 1.30271e70 0.171845
\(603\) 2.52999e70 0.319910
\(604\) −1.61185e70 −0.195381
\(605\) 4.93004e70 0.572913
\(606\) −4.11375e69 −0.0458339
\(607\) 1.24140e71 1.32617 0.663086 0.748544i \(-0.269247\pi\)
0.663086 + 0.748544i \(0.269247\pi\)
\(608\) −1.29463e71 −1.32618
\(609\) 1.87291e70 0.183982
\(610\) 1.94353e70 0.183097
\(611\) 3.35513e69 0.0303151
\(612\) 1.19952e71 1.03955
\(613\) −7.66168e70 −0.636916 −0.318458 0.947937i \(-0.603165\pi\)
−0.318458 + 0.947937i \(0.603165\pi\)
\(614\) −4.41984e70 −0.352462
\(615\) −3.45798e70 −0.264550
\(616\) 2.75612e69 0.0202297
\(617\) 8.27703e70 0.582912 0.291456 0.956584i \(-0.405860\pi\)
0.291456 + 0.956584i \(0.405860\pi\)
\(618\) 1.83311e70 0.123874
\(619\) −1.97805e71 −1.28270 −0.641350 0.767248i \(-0.721625\pi\)
−0.641350 + 0.767248i \(0.721625\pi\)
\(620\) −7.43588e70 −0.462748
\(621\) −1.63379e71 −0.975801
\(622\) −1.25636e70 −0.0720210
\(623\) −3.42550e69 −0.0188486
\(624\) 2.76908e69 0.0146261
\(625\) 2.28244e70 0.115734
\(626\) 6.76341e70 0.329246
\(627\) 9.40854e69 0.0439744
\(628\) 2.44649e71 1.09792
\(629\) 2.08497e71 0.898480
\(630\) 1.86115e70 0.0770191
\(631\) −1.41814e71 −0.563598 −0.281799 0.959473i \(-0.590931\pi\)
−0.281799 + 0.959473i \(0.590931\pi\)
\(632\) 9.00968e70 0.343893
\(633\) −7.91412e70 −0.290140
\(634\) 2.63895e70 0.0929297
\(635\) 1.39220e71 0.470947
\(636\) 1.68321e71 0.546993
\(637\) 1.14026e70 0.0355997
\(638\) 5.64159e69 0.0169229
\(639\) −4.61384e71 −1.32981
\(640\) −1.84394e71 −0.510691
\(641\) 3.78805e71 1.00818 0.504088 0.863652i \(-0.331829\pi\)
0.504088 + 0.863652i \(0.331829\pi\)
\(642\) −1.06903e69 −0.00273432
\(643\) −2.33505e71 −0.574006 −0.287003 0.957930i \(-0.592659\pi\)
−0.287003 + 0.957930i \(0.592659\pi\)
\(644\) −3.31683e71 −0.783670
\(645\) 1.00199e71 0.227558
\(646\) −2.85423e71 −0.623103
\(647\) −2.29082e71 −0.480764 −0.240382 0.970678i \(-0.577273\pi\)
−0.240382 + 0.970678i \(0.577273\pi\)
\(648\) 1.65165e71 0.333238
\(649\) 1.39298e70 0.0270212
\(650\) −5.06133e69 −0.00944004
\(651\) −9.66196e70 −0.173281
\(652\) 3.27494e71 0.564793
\(653\) 8.77846e71 1.45590 0.727951 0.685629i \(-0.240473\pi\)
0.727951 + 0.685629i \(0.240473\pi\)
\(654\) −1.03867e70 −0.0165671
\(655\) 1.06958e71 0.164081
\(656\) −7.00976e71 −1.03432
\(657\) −3.50460e71 −0.497418
\(658\) −6.42573e70 −0.0877329
\(659\) 9.01191e71 1.18369 0.591846 0.806051i \(-0.298399\pi\)
0.591846 + 0.806051i \(0.298399\pi\)
\(660\) 1.02055e70 0.0128962
\(661\) 5.00776e71 0.608845 0.304422 0.952537i \(-0.401537\pi\)
0.304422 + 0.952537i \(0.401537\pi\)
\(662\) 2.30399e70 0.0269527
\(663\) 2.10048e70 0.0236441
\(664\) 2.78135e71 0.301279
\(665\) 5.73514e71 0.597850
\(666\) 1.64595e71 0.165129
\(667\) −1.41029e72 −1.36176
\(668\) −9.71022e71 −0.902463
\(669\) −4.55577e71 −0.407564
\(670\) −6.52995e70 −0.0562345
\(671\) −9.85118e70 −0.0816703
\(672\) −1.82468e71 −0.145636
\(673\) −8.23485e71 −0.632807 −0.316404 0.948625i \(-0.602475\pi\)
−0.316404 + 0.948625i \(0.602475\pi\)
\(674\) 1.61770e71 0.119693
\(675\) −6.18348e71 −0.440541
\(676\) 1.34936e72 0.925736
\(677\) −1.48471e71 −0.0980916 −0.0490458 0.998797i \(-0.515618\pi\)
−0.0490458 + 0.998797i \(0.515618\pi\)
\(678\) 2.21182e71 0.140732
\(679\) 1.23546e72 0.757094
\(680\) −6.43104e71 −0.379581
\(681\) 9.52289e71 0.541399
\(682\) −2.91038e70 −0.0159385
\(683\) −9.71690e71 −0.512625 −0.256313 0.966594i \(-0.582508\pi\)
−0.256313 + 0.966594i \(0.582508\pi\)
\(684\) 2.91801e72 1.48305
\(685\) −1.09828e72 −0.537778
\(686\) −5.41855e71 −0.255634
\(687\) 5.84719e71 0.265797
\(688\) 2.03116e72 0.889691
\(689\) −2.09683e71 −0.0885060
\(690\) 1.96997e71 0.0801323
\(691\) 1.49847e72 0.587431 0.293715 0.955893i \(-0.405108\pi\)
0.293715 + 0.955893i \(0.405108\pi\)
\(692\) −3.67424e72 −1.38823
\(693\) −9.43364e70 −0.0343543
\(694\) 5.72462e71 0.200946
\(695\) −1.19980e72 −0.405974
\(696\) −5.10897e71 −0.166647
\(697\) −5.31724e72 −1.67205
\(698\) −7.75405e70 −0.0235080
\(699\) 9.04820e71 0.264481
\(700\) −1.25533e72 −0.353800
\(701\) −4.77735e71 −0.129831 −0.0649153 0.997891i \(-0.520678\pi\)
−0.0649153 + 0.997891i \(0.520678\pi\)
\(702\) 3.54948e70 0.00930182
\(703\) 5.07199e72 1.28179
\(704\) 1.67889e71 0.0409185
\(705\) −4.94242e71 −0.116176
\(706\) 7.89117e71 0.178905
\(707\) 1.27103e72 0.277947
\(708\) −6.07288e71 −0.128099
\(709\) 3.39807e72 0.691439 0.345719 0.938338i \(-0.387635\pi\)
0.345719 + 0.938338i \(0.387635\pi\)
\(710\) 1.19084e72 0.233757
\(711\) −3.08383e72 −0.584004
\(712\) 9.34416e70 0.0170726
\(713\) 7.27539e72 1.28255
\(714\) −4.02283e71 −0.0684270
\(715\) −1.27133e70 −0.00208667
\(716\) −6.77678e72 −1.07335
\(717\) −3.84739e72 −0.588069
\(718\) 2.64807e71 0.0390621
\(719\) 9.45409e72 1.34596 0.672981 0.739659i \(-0.265013\pi\)
0.672981 + 0.739659i \(0.265013\pi\)
\(720\) 2.90188e72 0.398751
\(721\) −5.66378e72 −0.751202
\(722\) −4.85207e72 −0.621196
\(723\) 1.37985e72 0.170532
\(724\) −1.78461e72 −0.212917
\(725\) −5.33758e72 −0.614787
\(726\) −8.41234e71 −0.0935477
\(727\) −9.75134e72 −1.04698 −0.523488 0.852033i \(-0.675370\pi\)
−0.523488 + 0.852033i \(0.675370\pi\)
\(728\) 1.49683e71 0.0155175
\(729\) −3.34266e72 −0.334611
\(730\) 9.04544e71 0.0874373
\(731\) 1.54073e73 1.43825
\(732\) 4.29475e72 0.387173
\(733\) −7.22486e72 −0.629040 −0.314520 0.949251i \(-0.601843\pi\)
−0.314520 + 0.949251i \(0.601843\pi\)
\(734\) 2.11448e72 0.177809
\(735\) −1.67970e72 −0.136429
\(736\) 1.37397e73 1.07794
\(737\) 3.30984e71 0.0250834
\(738\) −4.19762e72 −0.307302
\(739\) 2.75849e72 0.195091 0.0975456 0.995231i \(-0.468901\pi\)
0.0975456 + 0.995231i \(0.468901\pi\)
\(740\) 5.50159e72 0.375906
\(741\) 5.10972e71 0.0337313
\(742\) 4.01584e72 0.256140
\(743\) 1.34405e73 0.828325 0.414162 0.910203i \(-0.364075\pi\)
0.414162 + 0.910203i \(0.364075\pi\)
\(744\) 2.63561e72 0.156953
\(745\) −1.62548e73 −0.935396
\(746\) −4.82338e71 −0.0268232
\(747\) −9.52000e72 −0.511637
\(748\) 1.56926e72 0.0815089
\(749\) 3.30301e71 0.0165815
\(750\) 1.86064e72 0.0902819
\(751\) −3.23615e73 −1.51778 −0.758892 0.651216i \(-0.774259\pi\)
−0.758892 + 0.651216i \(0.774259\pi\)
\(752\) −1.00189e73 −0.454219
\(753\) −1.41768e73 −0.621307
\(754\) 3.06391e71 0.0129809
\(755\) −2.95788e72 −0.121153
\(756\) 8.80355e72 0.348620
\(757\) 3.58779e73 1.37367 0.686834 0.726814i \(-0.259000\pi\)
0.686834 + 0.726814i \(0.259000\pi\)
\(758\) −4.24796e72 −0.157259
\(759\) −9.98518e71 −0.0357430
\(760\) −1.56444e73 −0.541518
\(761\) 3.58257e73 1.19918 0.599592 0.800306i \(-0.295330\pi\)
0.599592 + 0.800306i \(0.295330\pi\)
\(762\) −2.37557e72 −0.0768983
\(763\) 3.20920e72 0.100466
\(764\) −1.93244e73 −0.585093
\(765\) 2.20122e73 0.644609
\(766\) −3.84298e72 −0.108851
\(767\) 7.56518e71 0.0207271
\(768\) −4.73812e72 −0.125573
\(769\) 5.92781e73 1.51975 0.759876 0.650068i \(-0.225259\pi\)
0.759876 + 0.650068i \(0.225259\pi\)
\(770\) 2.43484e71 0.00603889
\(771\) 2.53792e71 0.00608963
\(772\) 4.41885e72 0.102581
\(773\) −5.75726e73 −1.29312 −0.646560 0.762863i \(-0.723793\pi\)
−0.646560 + 0.762863i \(0.723793\pi\)
\(774\) 1.21631e73 0.264332
\(775\) 2.75354e73 0.579026
\(776\) −3.37011e73 −0.685758
\(777\) 7.14859e72 0.140762
\(778\) −5.04023e72 −0.0960441
\(779\) −1.29349e74 −2.38539
\(780\) 5.54251e71 0.00989223
\(781\) −6.03601e72 −0.104267
\(782\) 3.02916e73 0.506466
\(783\) 3.74321e73 0.605785
\(784\) −3.40497e73 −0.533400
\(785\) 4.48950e73 0.680803
\(786\) −1.82506e72 −0.0267919
\(787\) 1.39652e73 0.198469 0.0992344 0.995064i \(-0.468361\pi\)
0.0992344 + 0.995064i \(0.468361\pi\)
\(788\) 4.26098e73 0.586261
\(789\) 7.49650e71 0.00998608
\(790\) 7.95943e72 0.102658
\(791\) −6.83390e73 −0.853431
\(792\) 2.57333e72 0.0311174
\(793\) −5.35011e72 −0.0626465
\(794\) −1.95548e72 −0.0221733
\(795\) 3.08882e73 0.339181
\(796\) 1.02338e74 1.08831
\(797\) 9.83821e73 1.01328 0.506640 0.862158i \(-0.330888\pi\)
0.506640 + 0.862158i \(0.330888\pi\)
\(798\) −9.78611e72 −0.0976195
\(799\) −7.59982e73 −0.734277
\(800\) 5.20012e73 0.486652
\(801\) −3.19832e72 −0.0289930
\(802\) −4.73222e73 −0.415545
\(803\) −4.58486e72 −0.0390014
\(804\) −1.44297e73 −0.118912
\(805\) −6.08664e73 −0.485940
\(806\) −1.58060e72 −0.0122259
\(807\) −4.25496e72 −0.0318875
\(808\) −3.46715e73 −0.251758
\(809\) −2.22779e74 −1.56742 −0.783712 0.621125i \(-0.786676\pi\)
−0.783712 + 0.621125i \(0.786676\pi\)
\(810\) 1.45912e73 0.0994769
\(811\) −7.69456e73 −0.508338 −0.254169 0.967160i \(-0.581802\pi\)
−0.254169 + 0.967160i \(0.581802\pi\)
\(812\) 7.59922e73 0.486509
\(813\) −4.36007e73 −0.270511
\(814\) 2.15330e72 0.0129474
\(815\) 6.00977e73 0.350218
\(816\) −6.27233e73 −0.354266
\(817\) 3.74806e74 2.05184
\(818\) −1.50377e73 −0.0797944
\(819\) −5.12334e72 −0.0263520
\(820\) −1.40305e74 −0.699554
\(821\) 1.32614e74 0.640971 0.320486 0.947253i \(-0.396154\pi\)
0.320486 + 0.947253i \(0.396154\pi\)
\(822\) 1.87404e73 0.0878106
\(823\) 1.51804e73 0.0689585 0.0344792 0.999405i \(-0.489023\pi\)
0.0344792 + 0.999405i \(0.489023\pi\)
\(824\) 1.54498e74 0.680421
\(825\) −3.77913e72 −0.0161367
\(826\) −1.44888e73 −0.0599848
\(827\) 3.58794e74 1.44031 0.720153 0.693815i \(-0.244072\pi\)
0.720153 + 0.693815i \(0.244072\pi\)
\(828\) −3.09685e74 −1.20544
\(829\) −1.78233e74 −0.672741 −0.336370 0.941730i \(-0.609199\pi\)
−0.336370 + 0.941730i \(0.609199\pi\)
\(830\) 2.45713e73 0.0899367
\(831\) 1.12118e74 0.397968
\(832\) 9.11793e72 0.0313871
\(833\) −2.58283e74 −0.862281
\(834\) 2.04728e73 0.0662891
\(835\) −1.78190e74 −0.559602
\(836\) 3.81746e73 0.116282
\(837\) −1.93104e74 −0.570548
\(838\) −1.24735e74 −0.357491
\(839\) 6.85470e73 0.190572 0.0952859 0.995450i \(-0.469623\pi\)
0.0952859 + 0.995450i \(0.469623\pi\)
\(840\) −2.20497e73 −0.0594676
\(841\) −5.90927e73 −0.154609
\(842\) −5.61361e73 −0.142490
\(843\) 2.31715e74 0.570625
\(844\) −3.21110e74 −0.767224
\(845\) 2.47618e74 0.574033
\(846\) −5.99957e73 −0.134951
\(847\) 2.59917e74 0.567294
\(848\) 6.26143e74 1.32611
\(849\) −2.72350e74 −0.559733
\(850\) 1.14646e74 0.228652
\(851\) −5.38284e74 −1.04186
\(852\) 2.63148e74 0.494299
\(853\) 2.78536e74 0.507787 0.253893 0.967232i \(-0.418289\pi\)
0.253893 + 0.967232i \(0.418289\pi\)
\(854\) 1.02465e74 0.181301
\(855\) 5.35478e74 0.919614
\(856\) −9.01002e72 −0.0150191
\(857\) −9.69175e74 −1.56816 −0.784082 0.620658i \(-0.786866\pi\)
−0.784082 + 0.620658i \(0.786866\pi\)
\(858\) 2.16932e71 0.000340720 0
\(859\) 8.61964e74 1.31421 0.657103 0.753801i \(-0.271782\pi\)
0.657103 + 0.753801i \(0.271782\pi\)
\(860\) 4.06552e74 0.601735
\(861\) −1.82309e74 −0.261955
\(862\) 1.18318e74 0.165050
\(863\) −9.32304e74 −1.26265 −0.631324 0.775519i \(-0.717488\pi\)
−0.631324 + 0.775519i \(0.717488\pi\)
\(864\) −3.64681e74 −0.479526
\(865\) −6.74252e74 −0.860819
\(866\) 7.03392e73 0.0871949
\(867\) −1.84132e74 −0.221637
\(868\) −3.92028e74 −0.458209
\(869\) −4.03440e73 −0.0457904
\(870\) −4.51342e73 −0.0497468
\(871\) 1.79755e73 0.0192406
\(872\) −8.75410e73 −0.0910000
\(873\) 1.15352e75 1.16456
\(874\) 7.36888e74 0.722536
\(875\) −5.74885e74 −0.547489
\(876\) 1.99883e74 0.184893
\(877\) −9.43999e74 −0.848168 −0.424084 0.905623i \(-0.639404\pi\)
−0.424084 + 0.905623i \(0.639404\pi\)
\(878\) −4.44753e74 −0.388158
\(879\) 7.00226e74 0.593639
\(880\) 3.79636e73 0.0312651
\(881\) 5.77938e74 0.462376 0.231188 0.972909i \(-0.425739\pi\)
0.231188 + 0.972909i \(0.425739\pi\)
\(882\) −2.03898e74 −0.158476
\(883\) 2.23770e75 1.68968 0.844838 0.535022i \(-0.179697\pi\)
0.844838 + 0.535022i \(0.179697\pi\)
\(884\) 8.52256e73 0.0625227
\(885\) −1.11442e74 −0.0794322
\(886\) −4.43987e74 −0.307475
\(887\) 8.40500e74 0.565568 0.282784 0.959184i \(-0.408742\pi\)
0.282784 + 0.959184i \(0.408742\pi\)
\(888\) −1.95001e74 −0.127499
\(889\) 7.33984e74 0.466328
\(890\) 8.25492e72 0.00509645
\(891\) −7.39583e73 −0.0443716
\(892\) −1.84848e75 −1.07773
\(893\) −1.84876e75 −1.04754
\(894\) 2.77362e74 0.152735
\(895\) −1.24359e75 −0.665566
\(896\) −9.72147e74 −0.505682
\(897\) −5.42289e73 −0.0274172
\(898\) −4.30137e74 −0.211378
\(899\) −1.66687e75 −0.796216
\(900\) −1.17208e75 −0.544216
\(901\) 4.74960e75 2.14375
\(902\) −5.49150e73 −0.0240948
\(903\) 5.28261e74 0.225326
\(904\) 1.86416e75 0.773017
\(905\) −3.27491e74 −0.132026
\(906\) 5.04715e73 0.0197823
\(907\) −4.85471e75 −1.85002 −0.925012 0.379937i \(-0.875946\pi\)
−0.925012 + 0.379937i \(0.875946\pi\)
\(908\) 3.86385e75 1.43163
\(909\) 1.18674e75 0.427538
\(910\) 1.32234e73 0.00463222
\(911\) 1.08836e75 0.370727 0.185364 0.982670i \(-0.440654\pi\)
0.185364 + 0.982670i \(0.440654\pi\)
\(912\) −1.52583e75 −0.505405
\(913\) −1.24545e74 −0.0401162
\(914\) 1.42825e75 0.447379
\(915\) 7.88121e74 0.240080
\(916\) 2.37246e75 0.702853
\(917\) 5.63892e74 0.162472
\(918\) −8.04004e74 −0.225304
\(919\) −1.86949e75 −0.509538 −0.254769 0.967002i \(-0.581999\pi\)
−0.254769 + 0.967002i \(0.581999\pi\)
\(920\) 1.66033e75 0.440153
\(921\) −1.79229e75 −0.462154
\(922\) −4.05860e74 −0.101798
\(923\) −3.27812e74 −0.0799799
\(924\) 5.38043e73 0.0127697
\(925\) −2.03726e75 −0.470363
\(926\) −1.67424e75 −0.376043
\(927\) −5.28815e75 −1.15550
\(928\) −3.14793e75 −0.669193
\(929\) 7.68668e75 1.58978 0.794892 0.606751i \(-0.207527\pi\)
0.794892 + 0.606751i \(0.207527\pi\)
\(930\) 2.32838e74 0.0468531
\(931\) −6.28311e75 −1.23015
\(932\) 3.67125e75 0.699372
\(933\) −5.09466e74 −0.0944352
\(934\) 5.41778e74 0.0977184
\(935\) 2.87972e74 0.0505423
\(936\) 1.39756e74 0.0238690
\(937\) 5.84868e74 0.0972071 0.0486036 0.998818i \(-0.484523\pi\)
0.0486036 + 0.998818i \(0.484523\pi\)
\(938\) −3.44266e74 −0.0556829
\(939\) 2.74263e75 0.431712
\(940\) −2.00536e75 −0.307207
\(941\) 2.81919e75 0.420328 0.210164 0.977666i \(-0.432600\pi\)
0.210164 + 0.977666i \(0.432600\pi\)
\(942\) −7.66062e74 −0.111164
\(943\) 1.37277e76 1.93888
\(944\) −2.25907e75 −0.310559
\(945\) 1.61552e75 0.216173
\(946\) 1.59123e74 0.0207257
\(947\) −6.56754e75 −0.832680 −0.416340 0.909209i \(-0.636687\pi\)
−0.416340 + 0.909209i \(0.636687\pi\)
\(948\) 1.75885e75 0.217078
\(949\) −2.49001e74 −0.0299166
\(950\) 2.78892e75 0.326201
\(951\) 1.07012e75 0.121851
\(952\) −3.39051e75 −0.375858
\(953\) 4.31977e74 0.0466221 0.0233110 0.999728i \(-0.492579\pi\)
0.0233110 + 0.999728i \(0.492579\pi\)
\(954\) 3.74950e75 0.393994
\(955\) −3.54618e75 −0.362806
\(956\) −1.56106e76 −1.55504
\(957\) 2.28772e74 0.0221895
\(958\) −2.21912e75 −0.209585
\(959\) −5.79024e75 −0.532503
\(960\) −1.34316e75 −0.120285
\(961\) −2.86786e75 −0.250099
\(962\) 1.16944e74 0.00993149
\(963\) 3.08395e74 0.0255057
\(964\) 5.59867e75 0.450942
\(965\) 8.10894e74 0.0636089
\(966\) 1.03859e75 0.0793464
\(967\) 1.78694e76 1.32964 0.664820 0.747004i \(-0.268508\pi\)
0.664820 + 0.747004i \(0.268508\pi\)
\(968\) −7.09007e75 −0.513842
\(969\) −1.15742e76 −0.817023
\(970\) −2.97727e75 −0.204710
\(971\) 1.48969e76 0.997715 0.498857 0.866684i \(-0.333753\pi\)
0.498857 + 0.866684i \(0.333753\pi\)
\(972\) 1.25994e76 0.821979
\(973\) −6.32550e75 −0.401992
\(974\) 5.07000e75 0.313873
\(975\) −2.05242e74 −0.0123779
\(976\) 1.59762e76 0.938649
\(977\) 3.67383e75 0.210285 0.105142 0.994457i \(-0.466470\pi\)
0.105142 + 0.994457i \(0.466470\pi\)
\(978\) −1.02547e75 −0.0571851
\(979\) −4.18417e73 −0.00227327
\(980\) −6.81529e75 −0.360761
\(981\) 2.99636e75 0.154537
\(982\) −1.79547e75 −0.0902265
\(983\) −2.53462e76 −1.24108 −0.620538 0.784176i \(-0.713086\pi\)
−0.620538 + 0.784176i \(0.713086\pi\)
\(984\) 4.97305e75 0.237273
\(985\) 7.81924e75 0.363530
\(986\) −6.94016e75 −0.314419
\(987\) −2.60570e75 −0.115037
\(988\) 2.07324e75 0.0891962
\(989\) −3.97777e76 −1.66776
\(990\) 2.27336e74 0.00928903
\(991\) −1.78337e76 −0.710173 −0.355086 0.934834i \(-0.615549\pi\)
−0.355086 + 0.934834i \(0.615549\pi\)
\(992\) 1.62395e76 0.630267
\(993\) 9.34291e74 0.0353408
\(994\) 6.27824e75 0.231465
\(995\) 1.87799e76 0.674845
\(996\) 5.42968e75 0.190178
\(997\) −6.38902e75 −0.218126 −0.109063 0.994035i \(-0.534785\pi\)
−0.109063 + 0.994035i \(0.534785\pi\)
\(998\) −4.54757e75 −0.151339
\(999\) 1.42872e76 0.463476
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 1.52.a.a.1.2 4
3.2 odd 2 9.52.a.b.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.52.a.a.1.2 4 1.1 even 1 trivial
9.52.a.b.1.3 4 3.2 odd 2