Properties

Label 1.74.a.a.1.4
Level 1
Weight 74
Character 1.1
Self dual yes
Analytic conductor 33.748
Analytic rank 1
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 74 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.7483973737\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 10073499617947743056 x^{3} + 1429272143092482488433869600 x^{2} + 7661214288514935343595600445215756800 x + 1722510836040319301450745177697157900206688000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-6.50494e8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.28059e10 q^{2} -4.48831e17 q^{3} -9.28074e21 q^{4} +4.05981e25 q^{5} -5.74767e27 q^{6} -7.12492e30 q^{7} -2.39796e32 q^{8} +1.33864e35 q^{9} +O(q^{10})\) \(q+1.28059e10 q^{2} -4.48831e17 q^{3} -9.28074e21 q^{4} +4.05981e25 q^{5} -5.74767e27 q^{6} -7.12492e30 q^{7} -2.39796e32 q^{8} +1.33864e35 q^{9} +5.19894e35 q^{10} +5.42440e37 q^{11} +4.16549e39 q^{12} +7.16246e40 q^{13} -9.12407e40 q^{14} -1.82217e43 q^{15} +8.45834e43 q^{16} +1.30590e44 q^{17} +1.71425e45 q^{18} -2.65578e46 q^{19} -3.76781e47 q^{20} +3.19789e48 q^{21} +6.94640e47 q^{22} -6.34296e49 q^{23} +1.07628e50 q^{24} +5.89418e50 q^{25} +9.17214e50 q^{26} -2.97482e52 q^{27} +6.61246e52 q^{28} +8.00076e52 q^{29} -2.33345e53 q^{30} -3.53071e54 q^{31} +3.34797e54 q^{32} -2.43464e55 q^{33} +1.67231e54 q^{34} -2.89259e56 q^{35} -1.24236e57 q^{36} +1.61097e56 q^{37} -3.40096e56 q^{38} -3.21474e58 q^{39} -9.73526e57 q^{40} +6.62324e58 q^{41} +4.09517e58 q^{42} +5.13946e57 q^{43} -5.03424e59 q^{44} +5.43465e60 q^{45} -8.12270e59 q^{46} +1.87105e61 q^{47} -3.79637e61 q^{48} +1.54278e60 q^{49} +7.54801e60 q^{50} -5.86128e61 q^{51} -6.64729e62 q^{52} -2.36299e62 q^{53} -3.80951e62 q^{54} +2.20220e63 q^{55} +1.70853e63 q^{56} +1.19200e64 q^{57} +1.02457e63 q^{58} -2.19113e64 q^{59} +1.69111e65 q^{60} -1.30217e65 q^{61} -4.52138e64 q^{62} -9.53773e65 q^{63} -7.55994e65 q^{64} +2.90783e66 q^{65} -3.11776e65 q^{66} -5.38484e66 q^{67} -1.21197e66 q^{68} +2.84692e67 q^{69} -3.70420e66 q^{70} +3.88431e67 q^{71} -3.21001e67 q^{72} -9.28505e67 q^{73} +2.06298e66 q^{74} -2.64549e68 q^{75} +2.46476e68 q^{76} -3.86484e68 q^{77} -4.11674e68 q^{78} -4.44441e68 q^{79} +3.43393e69 q^{80} +4.30467e69 q^{81} +8.48163e68 q^{82} +9.20761e69 q^{83} -2.96788e70 q^{84} +5.30170e69 q^{85} +6.58152e67 q^{86} -3.59099e70 q^{87} -1.30075e70 q^{88} -3.27546e70 q^{89} +6.95953e70 q^{90} -5.10320e71 q^{91} +5.88674e71 q^{92} +1.58469e72 q^{93} +2.39603e71 q^{94} -1.07820e72 q^{95} -1.50267e72 q^{96} -2.09156e72 q^{97} +1.97567e70 q^{98} +7.26133e72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} + O(q^{10}) \) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} - \)\(10\!\cdots\!00\)\(q^{10} + \)\(50\!\cdots\!60\)\(q^{11} + \)\(13\!\cdots\!92\)\(q^{12} + \)\(47\!\cdots\!86\)\(q^{13} + \)\(26\!\cdots\!20\)\(q^{14} - \)\(50\!\cdots\!00\)\(q^{15} + \)\(57\!\cdots\!80\)\(q^{16} + \)\(66\!\cdots\!02\)\(q^{17} + \)\(69\!\cdots\!16\)\(q^{18} + \)\(31\!\cdots\!00\)\(q^{19} + \)\(68\!\cdots\!00\)\(q^{20} + \)\(87\!\cdots\!60\)\(q^{21} - \)\(94\!\cdots\!16\)\(q^{22} - \)\(41\!\cdots\!24\)\(q^{23} + \)\(16\!\cdots\!00\)\(q^{24} + \)\(32\!\cdots\!75\)\(q^{25} + \)\(44\!\cdots\!60\)\(q^{26} - \)\(12\!\cdots\!80\)\(q^{27} - \)\(37\!\cdots\!16\)\(q^{28} - \)\(21\!\cdots\!50\)\(q^{29} - \)\(80\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!40\)\(q^{31} - \)\(94\!\cdots\!68\)\(q^{32} - \)\(73\!\cdots\!28\)\(q^{33} - \)\(32\!\cdots\!80\)\(q^{34} - \)\(10\!\cdots\!00\)\(q^{35} - \)\(34\!\cdots\!20\)\(q^{36} - \)\(67\!\cdots\!78\)\(q^{37} - \)\(20\!\cdots\!20\)\(q^{38} - \)\(53\!\cdots\!20\)\(q^{39} - \)\(87\!\cdots\!00\)\(q^{40} - \)\(89\!\cdots\!90\)\(q^{41} + \)\(15\!\cdots\!84\)\(q^{42} + \)\(11\!\cdots\!56\)\(q^{43} + \)\(36\!\cdots\!20\)\(q^{44} + \)\(86\!\cdots\!50\)\(q^{45} + \)\(13\!\cdots\!60\)\(q^{46} + \)\(26\!\cdots\!32\)\(q^{47} - \)\(30\!\cdots\!24\)\(q^{48} - \)\(47\!\cdots\!15\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(66\!\cdots\!40\)\(q^{51} - \)\(18\!\cdots\!28\)\(q^{52} - \)\(22\!\cdots\!54\)\(q^{53} - \)\(98\!\cdots\!00\)\(q^{54} + \)\(52\!\cdots\!00\)\(q^{55} + \)\(17\!\cdots\!00\)\(q^{56} + \)\(39\!\cdots\!40\)\(q^{57} + \)\(63\!\cdots\!20\)\(q^{58} + \)\(49\!\cdots\!00\)\(q^{59} + \)\(91\!\cdots\!00\)\(q^{60} - \)\(20\!\cdots\!90\)\(q^{61} - \)\(45\!\cdots\!96\)\(q^{62} - \)\(14\!\cdots\!44\)\(q^{63} - \)\(26\!\cdots\!40\)\(q^{64} - \)\(22\!\cdots\!00\)\(q^{65} - \)\(79\!\cdots\!80\)\(q^{66} + \)\(17\!\cdots\!52\)\(q^{67} + \)\(25\!\cdots\!04\)\(q^{68} + \)\(43\!\cdots\!80\)\(q^{69} + \)\(60\!\cdots\!00\)\(q^{70} + \)\(29\!\cdots\!60\)\(q^{71} + \)\(59\!\cdots\!60\)\(q^{72} - \)\(23\!\cdots\!74\)\(q^{73} - \)\(38\!\cdots\!80\)\(q^{74} - \)\(78\!\cdots\!00\)\(q^{75} - \)\(40\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!56\)\(q^{77} + \)\(33\!\cdots\!72\)\(q^{78} + \)\(12\!\cdots\!00\)\(q^{79} + \)\(76\!\cdots\!00\)\(q^{80} + \)\(12\!\cdots\!05\)\(q^{81} + \)\(19\!\cdots\!64\)\(q^{82} + \)\(10\!\cdots\!16\)\(q^{83} - \)\(17\!\cdots\!80\)\(q^{84} - \)\(28\!\cdots\!00\)\(q^{85} - \)\(13\!\cdots\!40\)\(q^{86} - \)\(15\!\cdots\!40\)\(q^{87} - \)\(22\!\cdots\!60\)\(q^{88} - \)\(44\!\cdots\!50\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(50\!\cdots\!60\)\(q^{91} + \)\(10\!\cdots\!52\)\(q^{92} + \)\(20\!\cdots\!32\)\(q^{93} + \)\(12\!\cdots\!20\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} - \)\(12\!\cdots\!40\)\(q^{96} - \)\(47\!\cdots\!18\)\(q^{97} - \)\(76\!\cdots\!16\)\(q^{98} - \)\(15\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28059e10 0.131769 0.0658846 0.997827i \(-0.479013\pi\)
0.0658846 + 0.997827i \(0.479013\pi\)
\(3\) −4.48831e17 −1.72646 −0.863232 0.504808i \(-0.831563\pi\)
−0.863232 + 0.504808i \(0.831563\pi\)
\(4\) −9.28074e21 −0.982637
\(5\) 4.05981e25 1.24767 0.623837 0.781555i \(-0.285573\pi\)
0.623837 + 0.781555i \(0.285573\pi\)
\(6\) −5.74767e27 −0.227495
\(7\) −7.12492e30 −1.01555 −0.507775 0.861489i \(-0.669532\pi\)
−0.507775 + 0.861489i \(0.669532\pi\)
\(8\) −2.39796e32 −0.261250
\(9\) 1.33864e35 1.98068
\(10\) 5.19894e35 0.164405
\(11\) 5.42440e37 0.529076 0.264538 0.964375i \(-0.414780\pi\)
0.264538 + 0.964375i \(0.414780\pi\)
\(12\) 4.16549e39 1.69649
\(13\) 7.16246e40 1.57083 0.785416 0.618968i \(-0.212449\pi\)
0.785416 + 0.618968i \(0.212449\pi\)
\(14\) −9.12407e40 −0.133818
\(15\) −1.82217e43 −2.15406
\(16\) 8.45834e43 0.948212
\(17\) 1.30590e44 0.160149 0.0800744 0.996789i \(-0.474484\pi\)
0.0800744 + 0.996789i \(0.474484\pi\)
\(18\) 1.71425e45 0.260992
\(19\) −2.65578e46 −0.561935 −0.280968 0.959717i \(-0.590655\pi\)
−0.280968 + 0.959717i \(0.590655\pi\)
\(20\) −3.76781e47 −1.22601
\(21\) 3.19789e48 1.75331
\(22\) 6.94640e47 0.0697159
\(23\) −6.34296e49 −1.25668 −0.628342 0.777937i \(-0.716266\pi\)
−0.628342 + 0.777937i \(0.716266\pi\)
\(24\) 1.07628e50 0.451039
\(25\) 5.89418e50 0.556690
\(26\) 9.17214e50 0.206987
\(27\) −2.97482e52 −1.69310
\(28\) 6.61246e52 0.997918
\(29\) 8.00076e52 0.335432 0.167716 0.985835i \(-0.446361\pi\)
0.167716 + 0.985835i \(0.446361\pi\)
\(30\) −2.33345e53 −0.283839
\(31\) −3.53071e54 −1.29766 −0.648829 0.760934i \(-0.724741\pi\)
−0.648829 + 0.760934i \(0.724741\pi\)
\(32\) 3.34797e54 0.386195
\(33\) −2.43464e55 −0.913431
\(34\) 1.67231e54 0.0211027
\(35\) −2.89259e56 −1.26708
\(36\) −1.24236e57 −1.94629
\(37\) 1.61097e56 0.0928376 0.0464188 0.998922i \(-0.485219\pi\)
0.0464188 + 0.998922i \(0.485219\pi\)
\(38\) −3.40096e56 −0.0740457
\(39\) −3.21474e58 −2.71198
\(40\) −9.73526e57 −0.325955
\(41\) 6.62324e58 0.900450 0.450225 0.892915i \(-0.351344\pi\)
0.450225 + 0.892915i \(0.351344\pi\)
\(42\) 4.09517e58 0.231032
\(43\) 5.13946e57 0.0122834 0.00614171 0.999981i \(-0.498045\pi\)
0.00614171 + 0.999981i \(0.498045\pi\)
\(44\) −5.03424e59 −0.519890
\(45\) 5.43465e60 2.47124
\(46\) −8.12270e59 −0.165592
\(47\) 1.87105e61 1.73985 0.869927 0.493181i \(-0.164166\pi\)
0.869927 + 0.493181i \(0.164166\pi\)
\(48\) −3.79637e61 −1.63705
\(49\) 1.54278e60 0.0313436
\(50\) 7.54801e60 0.0733545
\(51\) −5.86128e61 −0.276491
\(52\) −6.64729e62 −1.54356
\(53\) −2.36299e62 −0.273774 −0.136887 0.990587i \(-0.543710\pi\)
−0.136887 + 0.990587i \(0.543710\pi\)
\(54\) −3.80951e62 −0.223099
\(55\) 2.20220e63 0.660115
\(56\) 1.70853e63 0.265313
\(57\) 1.19200e64 0.970160
\(58\) 1.02457e63 0.0441996
\(59\) −2.19113e64 −0.506489 −0.253244 0.967402i \(-0.581498\pi\)
−0.253244 + 0.967402i \(0.581498\pi\)
\(60\) 1.69111e65 2.11666
\(61\) −1.30217e65 −0.891513 −0.445756 0.895154i \(-0.647065\pi\)
−0.445756 + 0.895154i \(0.647065\pi\)
\(62\) −4.52138e64 −0.170991
\(63\) −9.53773e65 −2.01148
\(64\) −7.55994e65 −0.897324
\(65\) 2.90783e66 1.95989
\(66\) −3.11776e65 −0.120362
\(67\) −5.38484e66 −1.20072 −0.600361 0.799729i \(-0.704977\pi\)
−0.600361 + 0.799729i \(0.704977\pi\)
\(68\) −1.21197e66 −0.157368
\(69\) 2.84692e67 2.16962
\(70\) −3.70420e66 −0.166962
\(71\) 3.88431e67 1.04324 0.521620 0.853178i \(-0.325328\pi\)
0.521620 + 0.853178i \(0.325328\pi\)
\(72\) −3.21001e67 −0.517452
\(73\) −9.28505e67 −0.904690 −0.452345 0.891843i \(-0.649412\pi\)
−0.452345 + 0.891843i \(0.649412\pi\)
\(74\) 2.06298e66 0.0122331
\(75\) −2.64549e68 −0.961105
\(76\) 2.46476e68 0.552178
\(77\) −3.86484e68 −0.537304
\(78\) −4.11674e68 −0.357356
\(79\) −4.44441e68 −0.242340 −0.121170 0.992632i \(-0.538665\pi\)
−0.121170 + 0.992632i \(0.538665\pi\)
\(80\) 3.43393e69 1.18306
\(81\) 4.30467e69 0.942402
\(82\) 8.48163e68 0.118652
\(83\) 9.20761e69 0.827555 0.413777 0.910378i \(-0.364209\pi\)
0.413777 + 0.910378i \(0.364209\pi\)
\(84\) −2.96788e70 −1.72287
\(85\) 5.30170e69 0.199813
\(86\) 6.58152e67 0.00161858
\(87\) −3.59099e70 −0.579111
\(88\) −1.30075e70 −0.138221
\(89\) −3.27546e70 −0.230429 −0.115214 0.993341i \(-0.536755\pi\)
−0.115214 + 0.993341i \(0.536755\pi\)
\(90\) 6.95953e70 0.325633
\(91\) −5.10320e71 −1.59526
\(92\) 5.88674e71 1.23486
\(93\) 1.58469e72 2.24036
\(94\) 2.39603e71 0.229259
\(95\) −1.07820e72 −0.701112
\(96\) −1.50267e72 −0.666752
\(97\) −2.09156e72 −0.635773 −0.317886 0.948129i \(-0.602973\pi\)
−0.317886 + 0.948129i \(0.602973\pi\)
\(98\) 1.97567e70 0.00413011
\(99\) 7.26133e72 1.04793
\(100\) −5.47024e72 −0.547024
\(101\) −2.75339e73 −1.91486 −0.957430 0.288664i \(-0.906789\pi\)
−0.957430 + 0.288664i \(0.906789\pi\)
\(102\) −7.50587e71 −0.0364330
\(103\) 4.01406e73 1.36466 0.682332 0.731043i \(-0.260966\pi\)
0.682332 + 0.731043i \(0.260966\pi\)
\(104\) −1.71753e73 −0.410380
\(105\) 1.29828e74 2.18756
\(106\) −3.02601e72 −0.0360750
\(107\) −1.95235e74 −1.65215 −0.826077 0.563557i \(-0.809432\pi\)
−0.826077 + 0.563557i \(0.809432\pi\)
\(108\) 2.76085e74 1.66370
\(109\) −2.72452e74 −1.17280 −0.586398 0.810023i \(-0.699454\pi\)
−0.586398 + 0.810023i \(0.699454\pi\)
\(110\) 2.82011e73 0.0869827
\(111\) −7.23053e73 −0.160281
\(112\) −6.02650e74 −0.962958
\(113\) 4.60081e74 0.531461 0.265730 0.964047i \(-0.414387\pi\)
0.265730 + 0.964047i \(0.414387\pi\)
\(114\) 1.52646e74 0.127837
\(115\) −2.57512e75 −1.56793
\(116\) −7.42530e74 −0.329608
\(117\) 9.58798e75 3.11131
\(118\) −2.80593e74 −0.0667396
\(119\) −9.30442e74 −0.162639
\(120\) 4.36949e75 0.562750
\(121\) −7.56913e75 −0.720078
\(122\) −1.66754e75 −0.117474
\(123\) −2.97272e76 −1.55459
\(124\) 3.27676e76 1.27513
\(125\) −1.90557e76 −0.553106
\(126\) −1.22139e76 −0.265051
\(127\) 5.34262e75 0.0868798 0.0434399 0.999056i \(-0.486168\pi\)
0.0434399 + 0.999056i \(0.486168\pi\)
\(128\) −4.13018e76 −0.504435
\(129\) −2.30675e75 −0.0212069
\(130\) 3.72372e76 0.258252
\(131\) 2.08365e77 1.09250 0.546252 0.837621i \(-0.316054\pi\)
0.546252 + 0.837621i \(0.316054\pi\)
\(132\) 2.25953e77 0.897571
\(133\) 1.89222e77 0.570674
\(134\) −6.89575e76 −0.158218
\(135\) −1.20772e78 −2.11244
\(136\) −3.13149e76 −0.0418389
\(137\) 1.66251e76 0.0170006 0.00850030 0.999964i \(-0.497294\pi\)
0.00850030 + 0.999964i \(0.497294\pi\)
\(138\) 3.64572e77 0.285889
\(139\) −9.14130e76 −0.0550767 −0.0275383 0.999621i \(-0.508767\pi\)
−0.0275383 + 0.999621i \(0.508767\pi\)
\(140\) 2.68454e78 1.24508
\(141\) −8.39784e78 −3.00379
\(142\) 4.97419e77 0.137467
\(143\) 3.88520e78 0.831090
\(144\) 1.13227e79 1.87810
\(145\) 3.24816e78 0.418510
\(146\) −1.18903e78 −0.119210
\(147\) −6.92450e77 −0.0541135
\(148\) −1.49510e78 −0.0912257
\(149\) −1.98294e79 −0.946260 −0.473130 0.880993i \(-0.656876\pi\)
−0.473130 + 0.880993i \(0.656876\pi\)
\(150\) −3.38778e78 −0.126644
\(151\) −2.17790e79 −0.638821 −0.319410 0.947617i \(-0.603485\pi\)
−0.319410 + 0.947617i \(0.603485\pi\)
\(152\) 6.36845e78 0.146806
\(153\) 1.74813e79 0.317203
\(154\) −4.94926e78 −0.0708001
\(155\) −1.43340e80 −1.61905
\(156\) 2.98351e80 2.66490
\(157\) −1.69128e80 −1.19641 −0.598204 0.801344i \(-0.704119\pi\)
−0.598204 + 0.801344i \(0.704119\pi\)
\(158\) −5.69145e78 −0.0319330
\(159\) 1.06058e80 0.472661
\(160\) 1.35921e80 0.481846
\(161\) 4.51931e80 1.27623
\(162\) 5.51249e79 0.124180
\(163\) −4.96403e80 −0.893279 −0.446640 0.894714i \(-0.647379\pi\)
−0.446640 + 0.894714i \(0.647379\pi\)
\(164\) −6.14686e80 −0.884816
\(165\) −9.88418e80 −1.13966
\(166\) 1.17911e80 0.109046
\(167\) 1.76051e80 0.130764 0.0653818 0.997860i \(-0.479173\pi\)
0.0653818 + 0.997860i \(0.479173\pi\)
\(168\) −7.66840e80 −0.458053
\(169\) 3.05103e81 1.46751
\(170\) 6.78928e79 0.0263292
\(171\) −3.55515e81 −1.11301
\(172\) −4.76981e79 −0.0120701
\(173\) 8.57658e81 1.75643 0.878216 0.478265i \(-0.158734\pi\)
0.878216 + 0.478265i \(0.158734\pi\)
\(174\) −4.59857e80 −0.0763090
\(175\) −4.19956e81 −0.565347
\(176\) 4.58814e81 0.501677
\(177\) 9.83449e81 0.874435
\(178\) −4.19450e80 −0.0303634
\(179\) −1.04344e82 −0.615646 −0.307823 0.951444i \(-0.599600\pi\)
−0.307823 + 0.951444i \(0.599600\pi\)
\(180\) −5.04376e82 −2.42833
\(181\) −5.37748e81 −0.211500 −0.105750 0.994393i \(-0.533724\pi\)
−0.105750 + 0.994393i \(0.533724\pi\)
\(182\) −6.53508e81 −0.210206
\(183\) 5.84453e82 1.53916
\(184\) 1.52101e82 0.328309
\(185\) 6.54023e81 0.115831
\(186\) 2.02934e82 0.295210
\(187\) 7.08371e81 0.0847309
\(188\) −1.73647e83 −1.70964
\(189\) 2.11954e83 1.71943
\(190\) −1.38073e82 −0.0923849
\(191\) 2.08649e82 0.115265 0.0576325 0.998338i \(-0.481645\pi\)
0.0576325 + 0.998338i \(0.481645\pi\)
\(192\) 3.39314e83 1.54920
\(193\) −1.09262e83 −0.412693 −0.206347 0.978479i \(-0.566157\pi\)
−0.206347 + 0.978479i \(0.566157\pi\)
\(194\) −2.67842e82 −0.0837752
\(195\) −1.30512e84 −3.38367
\(196\) −1.43182e82 −0.0307993
\(197\) 7.56333e83 1.35113 0.675563 0.737302i \(-0.263901\pi\)
0.675563 + 0.737302i \(0.263901\pi\)
\(198\) 9.29876e82 0.138085
\(199\) −7.27551e83 −0.898930 −0.449465 0.893298i \(-0.648385\pi\)
−0.449465 + 0.893298i \(0.648385\pi\)
\(200\) −1.41340e83 −0.145435
\(201\) 2.41689e84 2.07300
\(202\) −3.52595e83 −0.252320
\(203\) −5.70048e83 −0.340648
\(204\) 5.43970e83 0.271690
\(205\) 2.68891e84 1.12347
\(206\) 5.14035e83 0.179820
\(207\) −8.49097e84 −2.48908
\(208\) 6.05825e84 1.48948
\(209\) −1.44060e84 −0.297307
\(210\) 1.66256e84 0.288253
\(211\) −3.42639e84 −0.499491 −0.249745 0.968312i \(-0.580347\pi\)
−0.249745 + 0.968312i \(0.580347\pi\)
\(212\) 2.19303e84 0.269021
\(213\) −1.74340e85 −1.80112
\(214\) −2.50015e84 −0.217703
\(215\) 2.08653e83 0.0153257
\(216\) 7.13349e84 0.442323
\(217\) 2.51560e85 1.31784
\(218\) −3.48898e84 −0.154538
\(219\) 4.16742e85 1.56191
\(220\) −2.04381e85 −0.648653
\(221\) 9.35344e84 0.251567
\(222\) −9.25931e83 −0.0211201
\(223\) −7.17475e85 −1.38893 −0.694463 0.719528i \(-0.744358\pi\)
−0.694463 + 0.719528i \(0.744358\pi\)
\(224\) −2.38540e85 −0.392201
\(225\) 7.89021e85 1.10262
\(226\) 5.89173e84 0.0700301
\(227\) 5.26645e85 0.532813 0.266406 0.963861i \(-0.414164\pi\)
0.266406 + 0.963861i \(0.414164\pi\)
\(228\) −1.10626e86 −0.953315
\(229\) −1.96927e86 −1.44648 −0.723238 0.690599i \(-0.757347\pi\)
−0.723238 + 0.690599i \(0.757347\pi\)
\(230\) −3.29767e85 −0.206605
\(231\) 1.73466e86 0.927636
\(232\) −1.91855e85 −0.0876317
\(233\) −2.47311e86 −0.965499 −0.482750 0.875758i \(-0.660362\pi\)
−0.482750 + 0.875758i \(0.660362\pi\)
\(234\) 1.22782e86 0.409975
\(235\) 7.59610e86 2.17077
\(236\) 2.03353e86 0.497695
\(237\) 1.99479e86 0.418392
\(238\) −1.19151e85 −0.0214308
\(239\) −9.15532e85 −0.141303 −0.0706513 0.997501i \(-0.522508\pi\)
−0.0706513 + 0.997501i \(0.522508\pi\)
\(240\) −1.54125e87 −2.04251
\(241\) −1.90452e86 −0.216852 −0.108426 0.994104i \(-0.534581\pi\)
−0.108426 + 0.994104i \(0.534581\pi\)
\(242\) −9.69291e85 −0.0948841
\(243\) 7.84674e85 0.0660786
\(244\) 1.20851e87 0.876033
\(245\) 6.26342e85 0.0391065
\(246\) −3.80682e86 −0.204848
\(247\) −1.90219e87 −0.882706
\(248\) 8.46649e86 0.339014
\(249\) −4.13267e87 −1.42874
\(250\) −2.44024e86 −0.0728823
\(251\) 6.30464e87 1.62768 0.813841 0.581087i \(-0.197373\pi\)
0.813841 + 0.581087i \(0.197373\pi\)
\(252\) 8.85173e87 1.97655
\(253\) −3.44067e87 −0.664882
\(254\) 6.84168e85 0.0114481
\(255\) −2.37957e87 −0.344971
\(256\) 6.61125e87 0.830855
\(257\) −6.84443e87 −0.746068 −0.373034 0.927818i \(-0.621683\pi\)
−0.373034 + 0.927818i \(0.621683\pi\)
\(258\) −2.95399e85 −0.00279441
\(259\) −1.14780e87 −0.0942814
\(260\) −2.69868e88 −1.92586
\(261\) 1.07102e88 0.664382
\(262\) 2.66829e87 0.143958
\(263\) −7.68237e87 −0.360670 −0.180335 0.983605i \(-0.557718\pi\)
−0.180335 + 0.983605i \(0.557718\pi\)
\(264\) 5.83816e87 0.238634
\(265\) −9.59330e87 −0.341581
\(266\) 2.42316e87 0.0751972
\(267\) 1.47013e88 0.397827
\(268\) 4.99753e88 1.17987
\(269\) −6.48183e87 −0.133579 −0.0667897 0.997767i \(-0.521276\pi\)
−0.0667897 + 0.997767i \(0.521276\pi\)
\(270\) −1.54659e88 −0.278354
\(271\) −7.02783e88 −1.10520 −0.552602 0.833445i \(-0.686365\pi\)
−0.552602 + 0.833445i \(0.686365\pi\)
\(272\) 1.10457e88 0.151855
\(273\) 2.29047e89 2.75416
\(274\) 2.12899e86 0.00224016
\(275\) 3.19724e88 0.294531
\(276\) −2.64215e89 −2.13195
\(277\) −2.35295e88 −0.166380 −0.0831901 0.996534i \(-0.526511\pi\)
−0.0831901 + 0.996534i \(0.526511\pi\)
\(278\) −1.17062e87 −0.00725740
\(279\) −4.72637e89 −2.57024
\(280\) 6.93630e88 0.331024
\(281\) 3.29283e89 1.37971 0.689856 0.723947i \(-0.257674\pi\)
0.689856 + 0.723947i \(0.257674\pi\)
\(282\) −1.07542e89 −0.395807
\(283\) 5.00752e89 1.61964 0.809819 0.586680i \(-0.199565\pi\)
0.809819 + 0.586680i \(0.199565\pi\)
\(284\) −3.60493e89 −1.02513
\(285\) 4.83929e89 1.21044
\(286\) 4.97533e88 0.109512
\(287\) −4.71901e89 −0.914453
\(288\) 4.48174e89 0.764928
\(289\) −6.47869e89 −0.974352
\(290\) 4.15955e88 0.0551467
\(291\) 9.38757e89 1.09764
\(292\) 8.61722e89 0.888982
\(293\) −6.16045e89 −0.560976 −0.280488 0.959858i \(-0.590496\pi\)
−0.280488 + 0.959858i \(0.590496\pi\)
\(294\) −8.86741e87 −0.00713049
\(295\) −8.89559e89 −0.631933
\(296\) −3.86303e88 −0.0242539
\(297\) −1.61366e90 −0.895780
\(298\) −2.53932e89 −0.124688
\(299\) −4.54312e90 −1.97404
\(300\) 2.45522e90 0.944417
\(301\) −3.66183e88 −0.0124744
\(302\) −2.78898e89 −0.0841768
\(303\) 1.23581e91 3.30594
\(304\) −2.24635e90 −0.532834
\(305\) −5.28656e90 −1.11232
\(306\) 2.23863e89 0.0417975
\(307\) 9.29015e90 1.53983 0.769914 0.638148i \(-0.220299\pi\)
0.769914 + 0.638148i \(0.220299\pi\)
\(308\) 3.58686e90 0.527975
\(309\) −1.80164e91 −2.35604
\(310\) −1.83560e90 −0.213341
\(311\) 2.50281e90 0.258627 0.129314 0.991604i \(-0.458723\pi\)
0.129314 + 0.991604i \(0.458723\pi\)
\(312\) 7.70880e90 0.708507
\(313\) 1.82125e91 1.48937 0.744684 0.667417i \(-0.232600\pi\)
0.744684 + 0.667417i \(0.232600\pi\)
\(314\) −2.16583e90 −0.157650
\(315\) −3.87214e91 −2.50967
\(316\) 4.12475e90 0.238133
\(317\) −2.15612e91 −1.10920 −0.554601 0.832117i \(-0.687129\pi\)
−0.554601 + 0.832117i \(0.687129\pi\)
\(318\) 1.35817e90 0.0622821
\(319\) 4.33993e90 0.177469
\(320\) −3.06919e91 −1.11957
\(321\) 8.76277e91 2.85238
\(322\) 5.78736e90 0.168167
\(323\) −3.46818e90 −0.0899932
\(324\) −3.99505e91 −0.926039
\(325\) 4.22168e91 0.874466
\(326\) −6.35687e90 −0.117707
\(327\) 1.22285e92 2.02479
\(328\) −1.58822e91 −0.235243
\(329\) −1.33311e92 −1.76691
\(330\) −1.26575e91 −0.150173
\(331\) 2.31408e91 0.245842 0.122921 0.992416i \(-0.460774\pi\)
0.122921 + 0.992416i \(0.460774\pi\)
\(332\) −8.54535e91 −0.813186
\(333\) 2.15651e91 0.183881
\(334\) 2.25448e90 0.0172306
\(335\) −2.18615e92 −1.49811
\(336\) 2.70488e92 1.66251
\(337\) 2.57115e91 0.141787 0.0708935 0.997484i \(-0.477415\pi\)
0.0708935 + 0.997484i \(0.477415\pi\)
\(338\) 3.90710e91 0.193373
\(339\) −2.06499e92 −0.917548
\(340\) −4.92037e91 −0.196344
\(341\) −1.91520e92 −0.686560
\(342\) −4.55267e91 −0.146661
\(343\) 3.39709e92 0.983720
\(344\) −1.23242e90 −0.00320905
\(345\) 1.15580e93 2.70698
\(346\) 1.09830e92 0.231443
\(347\) −5.43093e92 −1.03003 −0.515013 0.857182i \(-0.672213\pi\)
−0.515013 + 0.857182i \(0.672213\pi\)
\(348\) 3.33271e92 0.569056
\(349\) −1.29977e90 −0.00199866 −0.000999328 1.00000i \(-0.500318\pi\)
−0.000999328 1.00000i \(0.500318\pi\)
\(350\) −5.37790e91 −0.0744953
\(351\) −2.13070e93 −2.65958
\(352\) 1.81607e92 0.204327
\(353\) −1.12268e93 −1.13888 −0.569442 0.822032i \(-0.692841\pi\)
−0.569442 + 0.822032i \(0.692841\pi\)
\(354\) 1.25939e92 0.115224
\(355\) 1.57696e93 1.30162
\(356\) 3.03987e92 0.226428
\(357\) 4.17612e92 0.280791
\(358\) −1.33621e92 −0.0811231
\(359\) 8.79228e91 0.0482119 0.0241059 0.999709i \(-0.492326\pi\)
0.0241059 + 0.999709i \(0.492326\pi\)
\(360\) −1.30320e93 −0.645612
\(361\) −1.52832e93 −0.684229
\(362\) −6.88633e91 −0.0278692
\(363\) 3.39726e93 1.24319
\(364\) 4.73614e93 1.56756
\(365\) −3.76956e93 −1.12876
\(366\) 7.48442e92 0.202814
\(367\) 3.02870e93 0.742925 0.371462 0.928448i \(-0.378856\pi\)
0.371462 + 0.928448i \(0.378856\pi\)
\(368\) −5.36509e93 −1.19160
\(369\) 8.86616e93 1.78350
\(370\) 8.37533e91 0.0152630
\(371\) 1.68361e93 0.278032
\(372\) −1.47071e94 −2.20146
\(373\) −1.41066e94 −1.91448 −0.957239 0.289297i \(-0.906579\pi\)
−0.957239 + 0.289297i \(0.906579\pi\)
\(374\) 9.07129e91 0.0111649
\(375\) 8.55278e93 0.954918
\(376\) −4.48669e93 −0.454537
\(377\) 5.73051e93 0.526907
\(378\) 2.71425e93 0.226568
\(379\) 3.09449e93 0.234562 0.117281 0.993099i \(-0.462582\pi\)
0.117281 + 0.993099i \(0.462582\pi\)
\(380\) 1.00065e94 0.688938
\(381\) −2.39794e93 −0.149995
\(382\) 2.67192e92 0.0151884
\(383\) −5.62498e93 −0.290647 −0.145323 0.989384i \(-0.546422\pi\)
−0.145323 + 0.989384i \(0.546422\pi\)
\(384\) 1.85375e94 0.870889
\(385\) −1.56905e94 −0.670380
\(386\) −1.39919e93 −0.0543802
\(387\) 6.87991e92 0.0243295
\(388\) 1.94112e94 0.624734
\(389\) 4.55175e94 1.33358 0.666789 0.745247i \(-0.267668\pi\)
0.666789 + 0.745247i \(0.267668\pi\)
\(390\) −1.67132e94 −0.445863
\(391\) −8.28326e93 −0.201256
\(392\) −3.69953e92 −0.00818852
\(393\) −9.35208e94 −1.88617
\(394\) 9.68549e93 0.178037
\(395\) −1.80435e94 −0.302362
\(396\) −6.73906e94 −1.02973
\(397\) 6.04038e94 0.841804 0.420902 0.907106i \(-0.361714\pi\)
0.420902 + 0.907106i \(0.361714\pi\)
\(398\) −9.31691e93 −0.118451
\(399\) −8.49290e94 −0.985247
\(400\) 4.98550e94 0.527860
\(401\) 1.81150e95 1.75093 0.875465 0.483281i \(-0.160555\pi\)
0.875465 + 0.483281i \(0.160555\pi\)
\(402\) 3.09503e94 0.273158
\(403\) −2.52886e95 −2.03840
\(404\) 2.55535e95 1.88161
\(405\) 1.74762e95 1.17581
\(406\) −7.29995e93 −0.0448869
\(407\) 8.73853e93 0.0491182
\(408\) 1.40551e94 0.0722334
\(409\) −2.92901e95 −1.37664 −0.688318 0.725409i \(-0.741651\pi\)
−0.688318 + 0.725409i \(0.741651\pi\)
\(410\) 3.44338e94 0.148038
\(411\) −7.46188e93 −0.0293509
\(412\) −3.72535e95 −1.34097
\(413\) 1.56116e95 0.514365
\(414\) −1.08734e95 −0.327984
\(415\) 3.73812e95 1.03252
\(416\) 2.39797e95 0.606648
\(417\) 4.10290e94 0.0950878
\(418\) −1.84481e94 −0.0391758
\(419\) −8.12273e95 −1.58085 −0.790424 0.612560i \(-0.790140\pi\)
−0.790424 + 0.612560i \(0.790140\pi\)
\(420\) −1.20490e96 −2.14958
\(421\) −1.37700e95 −0.225236 −0.112618 0.993638i \(-0.535924\pi\)
−0.112618 + 0.993638i \(0.535924\pi\)
\(422\) −4.38779e94 −0.0658175
\(423\) 2.50467e96 3.44609
\(424\) 5.66635e94 0.0715236
\(425\) 7.69720e94 0.0891532
\(426\) −2.23257e95 −0.237331
\(427\) 9.27784e95 0.905377
\(428\) 1.81193e96 1.62347
\(429\) −1.74380e96 −1.43485
\(430\) 2.67198e93 0.00201945
\(431\) 2.16300e95 0.150189 0.0750943 0.997176i \(-0.476074\pi\)
0.0750943 + 0.997176i \(0.476074\pi\)
\(432\) −2.51620e96 −1.60542
\(433\) −1.06805e96 −0.626299 −0.313149 0.949704i \(-0.601384\pi\)
−0.313149 + 0.949704i \(0.601384\pi\)
\(434\) 3.22145e95 0.173650
\(435\) −1.45788e96 −0.722542
\(436\) 2.52855e96 1.15243
\(437\) 1.68455e96 0.706175
\(438\) 5.33674e95 0.205812
\(439\) −4.18327e96 −1.48443 −0.742217 0.670160i \(-0.766225\pi\)
−0.742217 + 0.670160i \(0.766225\pi\)
\(440\) −5.28079e95 −0.172455
\(441\) 2.06524e95 0.0620814
\(442\) 1.19779e95 0.0331487
\(443\) −1.44956e96 −0.369403 −0.184701 0.982795i \(-0.559132\pi\)
−0.184701 + 0.982795i \(0.559132\pi\)
\(444\) 6.71047e95 0.157498
\(445\) −1.32977e96 −0.287500
\(446\) −9.18788e95 −0.183018
\(447\) 8.90005e96 1.63368
\(448\) 5.38640e96 0.911278
\(449\) −8.52316e95 −0.132926 −0.0664629 0.997789i \(-0.521171\pi\)
−0.0664629 + 0.997789i \(0.521171\pi\)
\(450\) 1.01041e96 0.145292
\(451\) 3.59271e96 0.476407
\(452\) −4.26990e96 −0.522233
\(453\) 9.77509e96 1.10290
\(454\) 6.74414e95 0.0702083
\(455\) −2.07180e97 −1.99036
\(456\) −2.85836e96 −0.253455
\(457\) −1.28421e97 −1.05122 −0.525610 0.850726i \(-0.676163\pi\)
−0.525610 + 0.850726i \(0.676163\pi\)
\(458\) −2.52182e96 −0.190601
\(459\) −3.88481e96 −0.271148
\(460\) 2.38991e97 1.54071
\(461\) −2.16592e97 −1.28991 −0.644954 0.764221i \(-0.723124\pi\)
−0.644954 + 0.764221i \(0.723124\pi\)
\(462\) 2.22138e96 0.122234
\(463\) −7.61030e96 −0.386986 −0.193493 0.981102i \(-0.561982\pi\)
−0.193493 + 0.981102i \(0.561982\pi\)
\(464\) 6.76731e96 0.318061
\(465\) 6.43356e97 2.79524
\(466\) −3.16703e96 −0.127223
\(467\) −2.32926e97 −0.865270 −0.432635 0.901569i \(-0.642416\pi\)
−0.432635 + 0.901569i \(0.642416\pi\)
\(468\) −8.89836e97 −3.05729
\(469\) 3.83666e97 1.21939
\(470\) 9.72746e96 0.286040
\(471\) 7.59101e97 2.06555
\(472\) 5.25424e96 0.132320
\(473\) 2.78785e95 0.00649887
\(474\) 2.55450e96 0.0551311
\(475\) −1.56537e97 −0.312824
\(476\) 8.63519e96 0.159815
\(477\) −3.16320e97 −0.542258
\(478\) −1.17242e96 −0.0186193
\(479\) 2.29746e97 0.338066 0.169033 0.985610i \(-0.445936\pi\)
0.169033 + 0.985610i \(0.445936\pi\)
\(480\) −6.10057e97 −0.831889
\(481\) 1.15385e97 0.145832
\(482\) −2.43890e96 −0.0285745
\(483\) −2.02841e98 −2.20336
\(484\) 7.02471e97 0.707575
\(485\) −8.49134e97 −0.793237
\(486\) 1.00484e96 0.00870711
\(487\) 9.83578e97 0.790682 0.395341 0.918534i \(-0.370626\pi\)
0.395341 + 0.918534i \(0.370626\pi\)
\(488\) 3.12254e97 0.232908
\(489\) 2.22801e98 1.54221
\(490\) 8.02084e95 0.00515303
\(491\) −1.73954e98 −1.03743 −0.518716 0.854947i \(-0.673590\pi\)
−0.518716 + 0.854947i \(0.673590\pi\)
\(492\) 2.75890e98 1.52760
\(493\) 1.04482e97 0.0537190
\(494\) −2.43592e97 −0.116313
\(495\) 2.94797e98 1.30747
\(496\) −2.98639e98 −1.23046
\(497\) −2.76754e98 −1.05946
\(498\) −5.29223e97 −0.188264
\(499\) −4.48498e97 −0.148283 −0.0741413 0.997248i \(-0.523622\pi\)
−0.0741413 + 0.997248i \(0.523622\pi\)
\(500\) 1.76851e98 0.543503
\(501\) −7.90172e97 −0.225759
\(502\) 8.07363e97 0.214478
\(503\) 7.59682e98 1.87672 0.938362 0.345655i \(-0.112343\pi\)
0.938362 + 0.345655i \(0.112343\pi\)
\(504\) 2.28711e98 0.525499
\(505\) −1.11782e99 −2.38912
\(506\) −4.40608e97 −0.0876109
\(507\) −1.36940e99 −2.53361
\(508\) −4.95835e97 −0.0853713
\(509\) 1.10612e98 0.177257 0.0886284 0.996065i \(-0.471752\pi\)
0.0886284 + 0.996065i \(0.471752\pi\)
\(510\) −3.04724e97 −0.0454565
\(511\) 6.61553e98 0.918759
\(512\) 4.74747e98 0.613916
\(513\) 7.90047e98 0.951413
\(514\) −8.76488e97 −0.0983087
\(515\) 1.62964e99 1.70265
\(516\) 2.14084e97 0.0208387
\(517\) 1.01493e99 0.920516
\(518\) −1.46986e97 −0.0124234
\(519\) −3.84944e99 −3.03242
\(520\) −6.97284e98 −0.512021
\(521\) 1.94380e99 1.33068 0.665341 0.746540i \(-0.268286\pi\)
0.665341 + 0.746540i \(0.268286\pi\)
\(522\) 1.37153e98 0.0875451
\(523\) 3.22586e98 0.192014 0.0960072 0.995381i \(-0.469393\pi\)
0.0960072 + 0.995381i \(0.469393\pi\)
\(524\) −1.93378e99 −1.07353
\(525\) 1.88489e99 0.976051
\(526\) −9.83793e97 −0.0475252
\(527\) −4.61075e98 −0.207818
\(528\) −2.05930e99 −0.866126
\(529\) 1.47571e99 0.579255
\(530\) −1.22850e98 −0.0450098
\(531\) −2.93315e99 −1.00319
\(532\) −1.75613e99 −0.560765
\(533\) 4.74387e99 1.41446
\(534\) 1.88262e98 0.0524213
\(535\) −7.92619e99 −2.06135
\(536\) 1.29126e99 0.313689
\(537\) 4.68327e99 1.06289
\(538\) −8.30054e97 −0.0176016
\(539\) 8.36867e97 0.0165831
\(540\) 1.12086e100 2.07576
\(541\) 2.75772e99 0.477364 0.238682 0.971098i \(-0.423285\pi\)
0.238682 + 0.971098i \(0.423285\pi\)
\(542\) −8.99974e98 −0.145632
\(543\) 2.41358e99 0.365148
\(544\) 4.37210e98 0.0618487
\(545\) −1.10610e100 −1.46327
\(546\) 2.93315e99 0.362913
\(547\) 2.20581e99 0.255288 0.127644 0.991820i \(-0.459258\pi\)
0.127644 + 0.991820i \(0.459258\pi\)
\(548\) −1.54294e98 −0.0167054
\(549\) −1.74314e100 −1.76580
\(550\) 4.09434e98 0.0388102
\(551\) −2.12483e99 −0.188491
\(552\) −6.82679e99 −0.566814
\(553\) 3.16661e99 0.246109
\(554\) −3.01316e98 −0.0219238
\(555\) −2.93546e99 −0.199978
\(556\) 8.48380e98 0.0541204
\(557\) 3.12775e100 1.86860 0.934302 0.356482i \(-0.116024\pi\)
0.934302 + 0.356482i \(0.116024\pi\)
\(558\) −6.05251e99 −0.338678
\(559\) 3.68112e98 0.0192952
\(560\) −2.44665e100 −1.20146
\(561\) −3.17939e99 −0.146285
\(562\) 4.21674e99 0.181803
\(563\) −3.06947e100 −1.24024 −0.620122 0.784505i \(-0.712917\pi\)
−0.620122 + 0.784505i \(0.712917\pi\)
\(564\) 7.79382e100 2.95164
\(565\) 1.86784e100 0.663090
\(566\) 6.41256e99 0.213418
\(567\) −3.06704e100 −0.957058
\(568\) −9.31441e99 −0.272547
\(569\) 5.43050e99 0.149019 0.0745095 0.997220i \(-0.476261\pi\)
0.0745095 + 0.997220i \(0.476261\pi\)
\(570\) 6.19713e99 0.159499
\(571\) 5.10752e100 1.23308 0.616541 0.787323i \(-0.288534\pi\)
0.616541 + 0.787323i \(0.288534\pi\)
\(572\) −3.60575e100 −0.816660
\(573\) −9.36481e99 −0.199001
\(574\) −6.04309e99 −0.120497
\(575\) −3.73866e100 −0.699583
\(576\) −1.01201e101 −1.77731
\(577\) 1.75584e100 0.289447 0.144723 0.989472i \(-0.453771\pi\)
0.144723 + 0.989472i \(0.453771\pi\)
\(578\) −8.29652e99 −0.128390
\(579\) 4.90402e100 0.712500
\(580\) −3.01454e100 −0.411243
\(581\) −6.56035e100 −0.840424
\(582\) 1.20216e100 0.144635
\(583\) −1.28178e100 −0.144847
\(584\) 2.22652e100 0.236351
\(585\) 3.89254e101 3.88190
\(586\) −7.88898e99 −0.0739193
\(587\) −1.85514e101 −1.63337 −0.816687 0.577081i \(-0.804192\pi\)
−0.816687 + 0.577081i \(0.804192\pi\)
\(588\) 6.42645e99 0.0531739
\(589\) 9.37680e100 0.729200
\(590\) −1.13916e100 −0.0832693
\(591\) −3.39466e101 −2.33267
\(592\) 1.36261e100 0.0880298
\(593\) 2.31200e101 1.40440 0.702202 0.711978i \(-0.252200\pi\)
0.702202 + 0.711978i \(0.252200\pi\)
\(594\) −2.06643e100 −0.118036
\(595\) −3.77742e100 −0.202921
\(596\) 1.84031e101 0.929830
\(597\) 3.26548e101 1.55197
\(598\) −5.81785e100 −0.260117
\(599\) −2.30638e101 −0.970178 −0.485089 0.874465i \(-0.661213\pi\)
−0.485089 + 0.874465i \(0.661213\pi\)
\(600\) 6.34378e100 0.251089
\(601\) −3.98037e101 −1.48254 −0.741269 0.671209i \(-0.765775\pi\)
−0.741269 + 0.671209i \(0.765775\pi\)
\(602\) −4.68928e98 −0.00164375
\(603\) −7.20839e101 −2.37824
\(604\) 2.02125e101 0.627729
\(605\) −3.07292e101 −0.898423
\(606\) 1.58256e101 0.435620
\(607\) 2.03446e101 0.527306 0.263653 0.964618i \(-0.415073\pi\)
0.263653 + 0.964618i \(0.415073\pi\)
\(608\) −8.89148e100 −0.217017
\(609\) 2.55856e101 0.588117
\(610\) −6.76989e100 −0.146569
\(611\) 1.34013e102 2.73302
\(612\) −1.62240e101 −0.311695
\(613\) 8.11549e101 1.46895 0.734476 0.678635i \(-0.237428\pi\)
0.734476 + 0.678635i \(0.237428\pi\)
\(614\) 1.18968e101 0.202902
\(615\) −1.20687e102 −1.93963
\(616\) 9.26772e100 0.140371
\(617\) −4.85215e101 −0.692669 −0.346335 0.938111i \(-0.612574\pi\)
−0.346335 + 0.938111i \(0.612574\pi\)
\(618\) −2.30715e101 −0.310453
\(619\) −1.16809e102 −1.48173 −0.740864 0.671655i \(-0.765584\pi\)
−0.740864 + 0.671655i \(0.765584\pi\)
\(620\) 1.33030e102 1.59094
\(621\) 1.88692e102 2.12769
\(622\) 3.20507e100 0.0340791
\(623\) 2.33374e101 0.234012
\(624\) −2.71913e102 −2.57154
\(625\) −1.39770e102 −1.24679
\(626\) 2.33227e101 0.196253
\(627\) 6.46587e101 0.513289
\(628\) 1.56964e102 1.17563
\(629\) 2.10376e100 0.0148678
\(630\) −4.95861e101 −0.330697
\(631\) −2.95061e102 −1.85712 −0.928559 0.371185i \(-0.878952\pi\)
−0.928559 + 0.371185i \(0.878952\pi\)
\(632\) 1.06575e101 0.0633115
\(633\) 1.53787e102 0.862353
\(634\) −2.76110e101 −0.146159
\(635\) 2.16901e101 0.108398
\(636\) −9.84300e101 −0.464454
\(637\) 1.10501e101 0.0492355
\(638\) 5.55765e100 0.0233850
\(639\) 5.19971e102 2.06632
\(640\) −1.67678e102 −0.629370
\(641\) 4.29395e102 1.52244 0.761218 0.648496i \(-0.224602\pi\)
0.761218 + 0.648496i \(0.224602\pi\)
\(642\) 1.12215e102 0.375856
\(643\) 1.03978e102 0.329034 0.164517 0.986374i \(-0.447393\pi\)
0.164517 + 0.986374i \(0.447393\pi\)
\(644\) −4.19426e102 −1.25407
\(645\) −9.36499e100 −0.0264593
\(646\) −4.44130e100 −0.0118583
\(647\) −9.92922e101 −0.250558 −0.125279 0.992122i \(-0.539983\pi\)
−0.125279 + 0.992122i \(0.539983\pi\)
\(648\) −1.03224e102 −0.246203
\(649\) −1.18856e102 −0.267971
\(650\) 5.40623e101 0.115228
\(651\) −1.12908e103 −2.27520
\(652\) 4.60699e102 0.877769
\(653\) −2.55572e102 −0.460450 −0.230225 0.973137i \(-0.573946\pi\)
−0.230225 + 0.973137i \(0.573946\pi\)
\(654\) 1.56596e102 0.266805
\(655\) 8.45924e102 1.36309
\(656\) 5.60216e102 0.853818
\(657\) −1.24294e103 −1.79190
\(658\) −1.70716e102 −0.232824
\(659\) −9.61531e102 −1.24064 −0.620320 0.784349i \(-0.712997\pi\)
−0.620320 + 0.784349i \(0.712997\pi\)
\(660\) 9.17326e102 1.11988
\(661\) 8.19473e102 0.946633 0.473316 0.880893i \(-0.343057\pi\)
0.473316 + 0.880893i \(0.343057\pi\)
\(662\) 2.96337e101 0.0323944
\(663\) −4.19812e102 −0.434321
\(664\) −2.20795e102 −0.216199
\(665\) 7.68208e102 0.712015
\(666\) 2.76160e101 0.0242299
\(667\) −5.07485e102 −0.421532
\(668\) −1.63388e102 −0.128493
\(669\) 3.22025e103 2.39793
\(670\) −2.79955e102 −0.197405
\(671\) −7.06347e102 −0.471678
\(672\) 1.07064e103 0.677121
\(673\) 9.08707e102 0.544344 0.272172 0.962249i \(-0.412258\pi\)
0.272172 + 0.962249i \(0.412258\pi\)
\(674\) 3.29258e101 0.0186831
\(675\) −1.75341e103 −0.942533
\(676\) −2.83158e103 −1.44203
\(677\) −2.19434e103 −1.05881 −0.529405 0.848369i \(-0.677585\pi\)
−0.529405 + 0.848369i \(0.677585\pi\)
\(678\) −2.64439e102 −0.120904
\(679\) 1.49022e103 0.645659
\(680\) −1.27133e102 −0.0522013
\(681\) −2.36375e103 −0.919882
\(682\) −2.45257e102 −0.0904675
\(683\) −3.52716e103 −1.23330 −0.616651 0.787236i \(-0.711511\pi\)
−0.616651 + 0.787236i \(0.711511\pi\)
\(684\) 3.29944e103 1.09369
\(685\) 6.74950e101 0.0212112
\(686\) 4.35026e102 0.129624
\(687\) 8.83872e103 2.49729
\(688\) 4.34713e101 0.0116473
\(689\) −1.69248e103 −0.430053
\(690\) 1.48010e103 0.356696
\(691\) 5.99882e103 1.37125 0.685626 0.727954i \(-0.259528\pi\)
0.685626 + 0.727954i \(0.259528\pi\)
\(692\) −7.95970e103 −1.72593
\(693\) −5.17364e103 −1.06423
\(694\) −6.95477e102 −0.135726
\(695\) −3.71120e102 −0.0687177
\(696\) 8.61105e102 0.151293
\(697\) 8.64928e102 0.144206
\(698\) −1.66446e100 −0.000263361 0
\(699\) 1.11001e104 1.66690
\(700\) 3.89750e103 0.555531
\(701\) 8.24063e103 1.11494 0.557472 0.830196i \(-0.311771\pi\)
0.557472 + 0.830196i \(0.311771\pi\)
\(702\) −2.72854e103 −0.350450
\(703\) −4.27838e102 −0.0521687
\(704\) −4.10081e103 −0.474753
\(705\) −3.40937e104 −3.74776
\(706\) −1.43769e103 −0.150070
\(707\) 1.96177e104 1.94464
\(708\) −9.12713e103 −0.859252
\(709\) −1.70430e104 −1.52391 −0.761953 0.647632i \(-0.775760\pi\)
−0.761953 + 0.647632i \(0.775760\pi\)
\(710\) 2.01943e103 0.171514
\(711\) −5.94949e103 −0.479998
\(712\) 7.85440e102 0.0601996
\(713\) 2.23952e104 1.63075
\(714\) 5.34787e102 0.0369995
\(715\) 1.57732e104 1.03693
\(716\) 9.68387e103 0.604956
\(717\) 4.10919e103 0.243954
\(718\) 1.12593e102 0.00635284
\(719\) −3.17489e104 −1.70265 −0.851323 0.524642i \(-0.824199\pi\)
−0.851323 + 0.524642i \(0.824199\pi\)
\(720\) 4.59681e104 2.34326
\(721\) −2.85999e104 −1.38588
\(722\) −1.95714e103 −0.0901602
\(723\) 8.54810e103 0.374388
\(724\) 4.99070e103 0.207828
\(725\) 4.71580e103 0.186732
\(726\) 4.35048e103 0.163814
\(727\) −2.53957e102 −0.00909398 −0.00454699 0.999990i \(-0.501447\pi\)
−0.00454699 + 0.999990i \(0.501447\pi\)
\(728\) 1.22372e104 0.416762
\(729\) −3.26150e104 −1.05648
\(730\) −4.82724e103 −0.148736
\(731\) 6.71162e101 0.00196717
\(732\) −5.42416e104 −1.51244
\(733\) 5.13601e104 1.36248 0.681242 0.732059i \(-0.261440\pi\)
0.681242 + 0.732059i \(0.261440\pi\)
\(734\) 3.87851e103 0.0978946
\(735\) −2.81122e103 −0.0675160
\(736\) −2.12360e104 −0.485326
\(737\) −2.92095e104 −0.635274
\(738\) 1.13539e104 0.235010
\(739\) −8.61961e104 −1.69811 −0.849054 0.528306i \(-0.822828\pi\)
−0.849054 + 0.528306i \(0.822828\pi\)
\(740\) −6.06982e103 −0.113820
\(741\) 8.53764e104 1.52396
\(742\) 2.15601e103 0.0366360
\(743\) 8.31834e104 1.34569 0.672845 0.739784i \(-0.265072\pi\)
0.672845 + 0.739784i \(0.265072\pi\)
\(744\) −3.80003e104 −0.585295
\(745\) −8.05036e104 −1.18062
\(746\) −1.80647e104 −0.252269
\(747\) 1.23257e105 1.63912
\(748\) −6.57421e103 −0.0832597
\(749\) 1.39104e105 1.67785
\(750\) 1.09526e104 0.125829
\(751\) 8.23505e104 0.901174 0.450587 0.892733i \(-0.351215\pi\)
0.450587 + 0.892733i \(0.351215\pi\)
\(752\) 1.58259e105 1.64975
\(753\) −2.82972e105 −2.81013
\(754\) 7.33841e103 0.0694301
\(755\) −8.84186e104 −0.797040
\(756\) −1.96709e105 −1.68958
\(757\) −2.18065e104 −0.178479 −0.0892394 0.996010i \(-0.528444\pi\)
−0.0892394 + 0.996010i \(0.528444\pi\)
\(758\) 3.96275e103 0.0309080
\(759\) 1.54428e105 1.14789
\(760\) 2.58547e104 0.183166
\(761\) −2.07078e105 −1.39828 −0.699140 0.714985i \(-0.746433\pi\)
−0.699140 + 0.714985i \(0.746433\pi\)
\(762\) −3.07076e103 −0.0197647
\(763\) 1.94120e105 1.19103
\(764\) −1.93641e104 −0.113264
\(765\) 7.09709e104 0.395766
\(766\) −7.20327e103 −0.0382983
\(767\) −1.56939e105 −0.795609
\(768\) −2.96734e105 −1.43444
\(769\) 1.22335e105 0.563947 0.281973 0.959422i \(-0.409011\pi\)
0.281973 + 0.959422i \(0.409011\pi\)
\(770\) −2.00931e104 −0.0883354
\(771\) 3.07200e105 1.28806
\(772\) 1.01403e105 0.405528
\(773\) −8.34378e104 −0.318281 −0.159141 0.987256i \(-0.550872\pi\)
−0.159141 + 0.987256i \(0.550872\pi\)
\(774\) 8.81032e102 0.00320587
\(775\) −2.08107e105 −0.722393
\(776\) 5.01547e104 0.166096
\(777\) 5.15170e104 0.162773
\(778\) 5.82891e104 0.175724
\(779\) −1.75899e105 −0.505995
\(780\) 1.21125e106 3.32492
\(781\) 2.10700e105 0.551953
\(782\) −1.06074e104 −0.0265194
\(783\) −2.38008e105 −0.567921
\(784\) 1.30494e104 0.0297203
\(785\) −6.86630e105 −1.49273
\(786\) −1.19761e105 −0.248539
\(787\) −2.99942e105 −0.594236 −0.297118 0.954841i \(-0.596026\pi\)
−0.297118 + 0.954841i \(0.596026\pi\)
\(788\) −7.01933e105 −1.32767
\(789\) 3.44809e105 0.622684
\(790\) −2.31062e104 −0.0398419
\(791\) −3.27804e105 −0.539726
\(792\) −1.74124e105 −0.273772
\(793\) −9.32671e105 −1.40042
\(794\) 7.73522e104 0.110924
\(795\) 4.30577e105 0.589727
\(796\) 6.75221e105 0.883322
\(797\) 1.44943e106 1.81121 0.905604 0.424124i \(-0.139418\pi\)
0.905604 + 0.424124i \(0.139418\pi\)
\(798\) −1.08759e105 −0.129825
\(799\) 2.44340e105 0.278635
\(800\) 1.97335e105 0.214991
\(801\) −4.38467e105 −0.456405
\(802\) 2.31978e105 0.230719
\(803\) −5.03658e105 −0.478650
\(804\) −2.24305e106 −2.03701
\(805\) 1.83476e106 1.59231
\(806\) −3.23842e105 −0.268599
\(807\) 2.90925e105 0.230620
\(808\) 6.60250e105 0.500258
\(809\) 1.25435e106 0.908442 0.454221 0.890889i \(-0.349918\pi\)
0.454221 + 0.890889i \(0.349918\pi\)
\(810\) 2.23797e105 0.154936
\(811\) −1.31775e106 −0.872112 −0.436056 0.899920i \(-0.643625\pi\)
−0.436056 + 0.899920i \(0.643625\pi\)
\(812\) 5.29047e105 0.334734
\(813\) 3.15431e106 1.90809
\(814\) 1.11904e104 0.00647226
\(815\) −2.01531e106 −1.11452
\(816\) −4.95767e105 −0.262172
\(817\) −1.36493e104 −0.00690248
\(818\) −3.75084e105 −0.181398
\(819\) −6.83136e106 −3.15969
\(820\) −2.49551e106 −1.10396
\(821\) 2.12804e106 0.900439 0.450219 0.892918i \(-0.351346\pi\)
0.450219 + 0.892918i \(0.351346\pi\)
\(822\) −9.55558e103 −0.00386755
\(823\) 2.97912e106 1.15344 0.576720 0.816942i \(-0.304333\pi\)
0.576720 + 0.816942i \(0.304333\pi\)
\(824\) −9.62555e105 −0.356519
\(825\) −1.43502e106 −0.508498
\(826\) 1.99920e105 0.0677775
\(827\) 3.05296e106 0.990306 0.495153 0.868806i \(-0.335112\pi\)
0.495153 + 0.868806i \(0.335112\pi\)
\(828\) 7.88025e106 2.44587
\(829\) −3.55563e106 −1.05603 −0.528015 0.849235i \(-0.677064\pi\)
−0.528015 + 0.849235i \(0.677064\pi\)
\(830\) 4.78698e105 0.136054
\(831\) 1.05608e106 0.287249
\(832\) −5.41477e106 −1.40954
\(833\) 2.01472e104 0.00501963
\(834\) 5.25411e104 0.0125296
\(835\) 7.14734e105 0.163150
\(836\) 1.33699e106 0.292144
\(837\) 1.05032e107 2.19707
\(838\) −1.04019e106 −0.208307
\(839\) 1.13258e106 0.217148 0.108574 0.994088i \(-0.465372\pi\)
0.108574 + 0.994088i \(0.465372\pi\)
\(840\) −3.11323e106 −0.571501
\(841\) −5.04911e106 −0.887485
\(842\) −1.76337e105 −0.0296792
\(843\) −1.47792e107 −2.38202
\(844\) 3.17995e106 0.490818
\(845\) 1.23866e107 1.83098
\(846\) 3.20744e106 0.454088
\(847\) 5.39294e106 0.731276
\(848\) −1.99870e106 −0.259596
\(849\) −2.24753e107 −2.79625
\(850\) 9.85692e104 0.0117476
\(851\) −1.02183e106 −0.116668
\(852\) 1.61800e107 1.76984
\(853\) −9.81188e106 −1.02828 −0.514141 0.857706i \(-0.671889\pi\)
−0.514141 + 0.857706i \(0.671889\pi\)
\(854\) 1.18811e106 0.119301
\(855\) −1.44332e107 −1.38868
\(856\) 4.68166e106 0.431626
\(857\) −7.41614e106 −0.655206 −0.327603 0.944815i \(-0.606241\pi\)
−0.327603 + 0.944815i \(0.606241\pi\)
\(858\) −2.23308e106 −0.189068
\(859\) 8.57042e106 0.695427 0.347714 0.937601i \(-0.386958\pi\)
0.347714 + 0.937601i \(0.386958\pi\)
\(860\) −1.93645e105 −0.0150596
\(861\) 2.11804e107 1.57877
\(862\) 2.76991e105 0.0197902
\(863\) 7.22821e106 0.495036 0.247518 0.968883i \(-0.420385\pi\)
0.247518 + 0.968883i \(0.420385\pi\)
\(864\) −9.95960e106 −0.653868
\(865\) 3.48193e107 2.19145
\(866\) −1.36772e106 −0.0825269
\(867\) 2.90784e107 1.68218
\(868\) −2.33467e107 −1.29496
\(869\) −2.41083e106 −0.128217
\(870\) −1.86694e106 −0.0952087
\(871\) −3.85687e107 −1.88613
\(872\) 6.53327e106 0.306393
\(873\) −2.79985e107 −1.25926
\(874\) 2.15721e106 0.0930520
\(875\) 1.35770e107 0.561708
\(876\) −3.86768e107 −1.53480
\(877\) 1.98341e107 0.754967 0.377483 0.926016i \(-0.376790\pi\)
0.377483 + 0.926016i \(0.376790\pi\)
\(878\) −5.35703e106 −0.195602
\(879\) 2.76500e107 0.968504
\(880\) 1.86270e107 0.625929
\(881\) −3.33655e107 −1.07567 −0.537833 0.843052i \(-0.680757\pi\)
−0.537833 + 0.843052i \(0.680757\pi\)
\(882\) 2.64471e105 0.00818042
\(883\) −4.17223e106 −0.123823 −0.0619116 0.998082i \(-0.519720\pi\)
−0.0619116 + 0.998082i \(0.519720\pi\)
\(884\) −8.68068e106 −0.247199
\(885\) 3.99262e107 1.09101
\(886\) −1.85628e106 −0.0486759
\(887\) −5.76985e107 −1.45195 −0.725976 0.687720i \(-0.758612\pi\)
−0.725976 + 0.687720i \(0.758612\pi\)
\(888\) 1.73385e106 0.0418734
\(889\) −3.80658e106 −0.0882308
\(890\) −1.70289e106 −0.0378836
\(891\) 2.33502e107 0.498603
\(892\) 6.65870e107 1.36481
\(893\) −4.96909e107 −0.977685
\(894\) 1.13973e107 0.215269
\(895\) −4.23616e107 −0.768125
\(896\) 2.94272e107 0.512279
\(897\) 2.03909e108 3.40811
\(898\) −1.09146e106 −0.0175155
\(899\) −2.82484e107 −0.435276
\(900\) −7.32270e107 −1.08348
\(901\) −3.08582e106 −0.0438446
\(902\) 4.60077e106 0.0627757
\(903\) 1.64354e106 0.0215367
\(904\) −1.10325e107 −0.138844
\(905\) −2.18316e107 −0.263883
\(906\) 1.25178e107 0.145328
\(907\) −1.62085e107 −0.180749 −0.0903746 0.995908i \(-0.528806\pi\)
−0.0903746 + 0.995908i \(0.528806\pi\)
\(908\) −4.88766e107 −0.523561
\(909\) −3.68581e108 −3.79272
\(910\) −2.65312e107 −0.262268
\(911\) 7.78998e107 0.739802 0.369901 0.929071i \(-0.379392\pi\)
0.369901 + 0.929071i \(0.379392\pi\)
\(912\) 1.00823e108 0.919918
\(913\) 4.99457e107 0.437840
\(914\) −1.64454e107 −0.138518
\(915\) 2.37277e108 1.92038
\(916\) 1.82763e108 1.42136
\(917\) −1.48459e108 −1.10949
\(918\) −4.97483e106 −0.0357290
\(919\) 1.01773e107 0.0702448 0.0351224 0.999383i \(-0.488818\pi\)
0.0351224 + 0.999383i \(0.488818\pi\)
\(920\) 6.17504e107 0.409623
\(921\) −4.16971e108 −2.65846
\(922\) −2.77365e107 −0.169970
\(923\) 2.78212e108 1.63875
\(924\) −1.60989e108 −0.911529
\(925\) 9.49534e106 0.0516818
\(926\) −9.74564e106 −0.0509929
\(927\) 5.37340e108 2.70296
\(928\) 2.67863e107 0.129542
\(929\) −1.93150e108 −0.898092 −0.449046 0.893509i \(-0.648236\pi\)
−0.449046 + 0.893509i \(0.648236\pi\)
\(930\) 8.23873e107 0.368326
\(931\) −4.09730e106 −0.0176130
\(932\) 2.29523e108 0.948735
\(933\) −1.12334e108 −0.446511
\(934\) −2.98281e107 −0.114016
\(935\) 2.87585e107 0.105717
\(936\) −2.29916e108 −0.812831
\(937\) 3.17605e108 1.07992 0.539960 0.841691i \(-0.318439\pi\)
0.539960 + 0.841691i \(0.318439\pi\)
\(938\) 4.91317e107 0.160679
\(939\) −8.17436e108 −2.57134
\(940\) −7.04975e108 −2.13308
\(941\) 2.32516e108 0.676756 0.338378 0.941010i \(-0.390122\pi\)
0.338378 + 0.941010i \(0.390122\pi\)
\(942\) 9.72094e107 0.272176
\(943\) −4.20110e108 −1.13158
\(944\) −1.85333e108 −0.480259
\(945\) 8.60492e108 2.14529
\(946\) 3.57008e105 0.000856350 0
\(947\) 6.27531e108 1.44831 0.724154 0.689638i \(-0.242230\pi\)
0.724154 + 0.689638i \(0.242230\pi\)
\(948\) −1.85132e108 −0.411127
\(949\) −6.65038e108 −1.42112
\(950\) −2.00459e107 −0.0412205
\(951\) 9.67736e108 1.91500
\(952\) 2.23116e107 0.0424895
\(953\) −1.78151e107 −0.0326511 −0.0163255 0.999867i \(-0.505197\pi\)
−0.0163255 + 0.999867i \(0.505197\pi\)
\(954\) −4.05075e107 −0.0714529
\(955\) 8.47075e107 0.143813
\(956\) 8.49682e107 0.138849
\(957\) −1.94790e108 −0.306394
\(958\) 2.94209e107 0.0445467
\(959\) −1.18453e107 −0.0172650
\(960\) 1.37755e109 1.93289
\(961\) 5.06299e108 0.683917
\(962\) 1.47760e107 0.0192162
\(963\) −2.61351e109 −3.27238
\(964\) 1.76754e108 0.213087
\(965\) −4.43584e108 −0.514907
\(966\) −2.59755e108 −0.290335
\(967\) 9.41056e108 1.01286 0.506430 0.862281i \(-0.330965\pi\)
0.506430 + 0.862281i \(0.330965\pi\)
\(968\) 1.81504e108 0.188121
\(969\) 1.55663e108 0.155370
\(970\) −1.08739e108 −0.104524
\(971\) 5.54960e107 0.0513759 0.0256879 0.999670i \(-0.491822\pi\)
0.0256879 + 0.999670i \(0.491822\pi\)
\(972\) −7.28236e107 −0.0649312
\(973\) 6.51310e107 0.0559331
\(974\) 1.25956e108 0.104187
\(975\) −1.89482e109 −1.50973
\(976\) −1.10142e109 −0.845343
\(977\) 1.67241e109 1.23649 0.618245 0.785985i \(-0.287844\pi\)
0.618245 + 0.785985i \(0.287844\pi\)
\(978\) 2.85316e108 0.203216
\(979\) −1.77674e108 −0.121914
\(980\) −5.81292e107 −0.0384275
\(981\) −3.64716e109 −2.32293
\(982\) −2.22763e108 −0.136701
\(983\) 2.14789e108 0.127002 0.0635008 0.997982i \(-0.479773\pi\)
0.0635008 + 0.997982i \(0.479773\pi\)
\(984\) 7.12845e108 0.406138
\(985\) 3.07057e109 1.68576
\(986\) 1.33798e107 0.00707851
\(987\) 5.98340e109 3.05051
\(988\) 1.76538e109 0.867379
\(989\) −3.25994e107 −0.0154364
\(990\) 3.77512e108 0.172285
\(991\) −2.88916e109 −1.27082 −0.635410 0.772175i \(-0.719169\pi\)
−0.635410 + 0.772175i \(0.719169\pi\)
\(992\) −1.18207e109 −0.501150
\(993\) −1.03863e109 −0.424437
\(994\) −3.54407e108 −0.139605
\(995\) −2.95372e109 −1.12157
\(996\) 3.83542e109 1.40394
\(997\) −2.76095e109 −0.974284 −0.487142 0.873323i \(-0.661961\pi\)
−0.487142 + 0.873323i \(0.661961\pi\)
\(998\) −5.74340e107 −0.0195391
\(999\) −4.79234e108 −0.157184
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 1.74.a.a.1.4 5
3.2 odd 2 9.74.a.a.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.74.a.a.1.4 5 1.1 even 1 trivial
9.74.a.a.1.2 5 3.2 odd 2