Properties

Label 1.74.a.a.1.5
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 1.5
Root \(-3.13124e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.31882e11 q^{2} +7.82937e15 q^{3} +7.94807e21 q^{4} -7.75470e24 q^{5} +1.03255e27 q^{6} +1.05974e30 q^{7} -1.97383e32 q^{8} -6.75239e34 q^{9} +O(q^{10})\) \(q+1.31882e11 q^{2} +7.82937e15 q^{3} +7.94807e21 q^{4} -7.75470e24 q^{5} +1.03255e27 q^{6} +1.05974e30 q^{7} -1.97383e32 q^{8} -6.75239e34 q^{9} -1.02270e36 q^{10} +5.33872e37 q^{11} +6.22283e37 q^{12} -2.33841e40 q^{13} +1.39761e41 q^{14} -6.07144e40 q^{15} -1.01099e44 q^{16} -3.97117e44 q^{17} -8.90517e45 q^{18} -7.99880e46 q^{19} -6.16349e46 q^{20} +8.29711e45 q^{21} +7.04080e48 q^{22} +6.65108e49 q^{23} -1.54539e48 q^{24} -9.98656e50 q^{25} -3.08393e51 q^{26} -1.05782e51 q^{27} +8.42290e51 q^{28} +2.50436e53 q^{29} -8.00713e51 q^{30} -3.03546e54 q^{31} -1.14688e55 q^{32} +4.17988e53 q^{33} -5.23725e55 q^{34} -8.21799e54 q^{35} -5.36684e56 q^{36} -2.59488e57 q^{37} -1.05490e58 q^{38} -1.83082e56 q^{39} +1.53065e57 q^{40} +1.11326e58 q^{41} +1.09424e57 q^{42} -1.82489e58 q^{43} +4.24325e59 q^{44} +5.23628e59 q^{45} +8.77155e60 q^{46} +1.00933e61 q^{47} -7.91538e59 q^{48} -4.80987e61 q^{49} -1.31704e62 q^{50} -3.10917e60 q^{51} -1.85858e62 q^{52} +9.84119e60 q^{53} -1.39507e62 q^{54} -4.14002e62 q^{55} -2.09175e62 q^{56} -6.26256e62 q^{57} +3.30280e64 q^{58} +5.71932e64 q^{59} -4.82562e62 q^{60} -7.84734e64 q^{61} -4.00322e65 q^{62} -7.15579e64 q^{63} -5.57680e65 q^{64} +1.81336e65 q^{65} +5.51250e64 q^{66} +5.03632e66 q^{67} -3.15631e66 q^{68} +5.20737e65 q^{69} -1.08380e66 q^{70} +4.24341e67 q^{71} +1.33281e67 q^{72} +9.03815e67 q^{73} -3.42218e68 q^{74} -7.81884e66 q^{75} -6.35750e68 q^{76} +5.65767e67 q^{77} -2.41452e67 q^{78} +2.30814e69 q^{79} +7.83990e68 q^{80} +4.55533e69 q^{81} +1.46819e69 q^{82} -1.28517e70 q^{83} +6.59460e67 q^{84} +3.07952e69 q^{85} -2.40669e69 q^{86} +1.96076e69 q^{87} -1.05377e70 q^{88} -2.21881e71 q^{89} +6.90570e70 q^{90} -2.47811e70 q^{91} +5.28632e71 q^{92} -2.37658e70 q^{93} +1.33113e72 q^{94} +6.20284e71 q^{95} -8.97937e70 q^{96} -2.42972e72 q^{97} -6.34334e72 q^{98} -3.60491e72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} + O(q^{10}) \) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} - \)\(10\!\cdots\!00\)\(q^{10} + \)\(50\!\cdots\!60\)\(q^{11} + \)\(13\!\cdots\!92\)\(q^{12} + \)\(47\!\cdots\!86\)\(q^{13} + \)\(26\!\cdots\!20\)\(q^{14} - \)\(50\!\cdots\!00\)\(q^{15} + \)\(57\!\cdots\!80\)\(q^{16} + \)\(66\!\cdots\!02\)\(q^{17} + \)\(69\!\cdots\!16\)\(q^{18} + \)\(31\!\cdots\!00\)\(q^{19} + \)\(68\!\cdots\!00\)\(q^{20} + \)\(87\!\cdots\!60\)\(q^{21} - \)\(94\!\cdots\!16\)\(q^{22} - \)\(41\!\cdots\!24\)\(q^{23} + \)\(16\!\cdots\!00\)\(q^{24} + \)\(32\!\cdots\!75\)\(q^{25} + \)\(44\!\cdots\!60\)\(q^{26} - \)\(12\!\cdots\!80\)\(q^{27} - \)\(37\!\cdots\!16\)\(q^{28} - \)\(21\!\cdots\!50\)\(q^{29} - \)\(80\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!40\)\(q^{31} - \)\(94\!\cdots\!68\)\(q^{32} - \)\(73\!\cdots\!28\)\(q^{33} - \)\(32\!\cdots\!80\)\(q^{34} - \)\(10\!\cdots\!00\)\(q^{35} - \)\(34\!\cdots\!20\)\(q^{36} - \)\(67\!\cdots\!78\)\(q^{37} - \)\(20\!\cdots\!20\)\(q^{38} - \)\(53\!\cdots\!20\)\(q^{39} - \)\(87\!\cdots\!00\)\(q^{40} - \)\(89\!\cdots\!90\)\(q^{41} + \)\(15\!\cdots\!84\)\(q^{42} + \)\(11\!\cdots\!56\)\(q^{43} + \)\(36\!\cdots\!20\)\(q^{44} + \)\(86\!\cdots\!50\)\(q^{45} + \)\(13\!\cdots\!60\)\(q^{46} + \)\(26\!\cdots\!32\)\(q^{47} - \)\(30\!\cdots\!24\)\(q^{48} - \)\(47\!\cdots\!15\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(66\!\cdots\!40\)\(q^{51} - \)\(18\!\cdots\!28\)\(q^{52} - \)\(22\!\cdots\!54\)\(q^{53} - \)\(98\!\cdots\!00\)\(q^{54} + \)\(52\!\cdots\!00\)\(q^{55} + \)\(17\!\cdots\!00\)\(q^{56} + \)\(39\!\cdots\!40\)\(q^{57} + \)\(63\!\cdots\!20\)\(q^{58} + \)\(49\!\cdots\!00\)\(q^{59} + \)\(91\!\cdots\!00\)\(q^{60} - \)\(20\!\cdots\!90\)\(q^{61} - \)\(45\!\cdots\!96\)\(q^{62} - \)\(14\!\cdots\!44\)\(q^{63} - \)\(26\!\cdots\!40\)\(q^{64} - \)\(22\!\cdots\!00\)\(q^{65} - \)\(79\!\cdots\!80\)\(q^{66} + \)\(17\!\cdots\!52\)\(q^{67} + \)\(25\!\cdots\!04\)\(q^{68} + \)\(43\!\cdots\!80\)\(q^{69} + \)\(60\!\cdots\!00\)\(q^{70} + \)\(29\!\cdots\!60\)\(q^{71} + \)\(59\!\cdots\!60\)\(q^{72} - \)\(23\!\cdots\!74\)\(q^{73} - \)\(38\!\cdots\!80\)\(q^{74} - \)\(78\!\cdots\!00\)\(q^{75} - \)\(40\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!56\)\(q^{77} + \)\(33\!\cdots\!72\)\(q^{78} + \)\(12\!\cdots\!00\)\(q^{79} + \)\(76\!\cdots\!00\)\(q^{80} + \)\(12\!\cdots\!05\)\(q^{81} + \)\(19\!\cdots\!64\)\(q^{82} + \)\(10\!\cdots\!16\)\(q^{83} - \)\(17\!\cdots\!80\)\(q^{84} - \)\(28\!\cdots\!00\)\(q^{85} - \)\(13\!\cdots\!40\)\(q^{86} - \)\(15\!\cdots\!40\)\(q^{87} - \)\(22\!\cdots\!60\)\(q^{88} - \)\(44\!\cdots\!50\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(50\!\cdots\!60\)\(q^{91} + \)\(10\!\cdots\!52\)\(q^{92} + \)\(20\!\cdots\!32\)\(q^{93} + \)\(12\!\cdots\!20\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} - \)\(12\!\cdots\!40\)\(q^{96} - \)\(47\!\cdots\!18\)\(q^{97} - \)\(76\!\cdots\!16\)\(q^{98} - \)\(15\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31882e11 1.35703 0.678516 0.734586i \(-0.262624\pi\)
0.678516 + 0.734586i \(0.262624\pi\)
\(3\) 7.82937e15 0.0301163 0.0150581 0.999887i \(-0.495207\pi\)
0.0150581 + 0.999887i \(0.495207\pi\)
\(4\) 7.94807e21 0.841534
\(5\) −7.75470e24 −0.238320 −0.119160 0.992875i \(-0.538020\pi\)
−0.119160 + 0.992875i \(0.538020\pi\)
\(6\) 1.03255e27 0.0408687
\(7\) 1.05974e30 0.151050 0.0755252 0.997144i \(-0.475937\pi\)
0.0755252 + 0.997144i \(0.475937\pi\)
\(8\) −1.97383e32 −0.215043
\(9\) −6.75239e34 −0.999093
\(10\) −1.02270e36 −0.323407
\(11\) 5.33872e37 0.520720 0.260360 0.965512i \(-0.416159\pi\)
0.260360 + 0.965512i \(0.416159\pi\)
\(12\) 6.22283e37 0.0253439
\(13\) −2.33841e40 −0.512847 −0.256423 0.966565i \(-0.582544\pi\)
−0.256423 + 0.966565i \(0.582544\pi\)
\(14\) 1.39761e41 0.204980
\(15\) −6.07144e40 −0.00717730
\(16\) −1.01099e44 −1.13335
\(17\) −3.97117e44 −0.487004 −0.243502 0.969900i \(-0.578296\pi\)
−0.243502 + 0.969900i \(0.578296\pi\)
\(18\) −8.90517e45 −1.35580
\(19\) −7.99880e46 −1.69246 −0.846230 0.532817i \(-0.821133\pi\)
−0.846230 + 0.532817i \(0.821133\pi\)
\(20\) −6.16349e46 −0.200554
\(21\) 8.29711e45 0.00454907
\(22\) 7.04080e48 0.706633
\(23\) 6.65108e49 1.31773 0.658864 0.752262i \(-0.271037\pi\)
0.658864 + 0.752262i \(0.271037\pi\)
\(24\) −1.54539e48 −0.00647629
\(25\) −9.98656e50 −0.943204
\(26\) −3.08393e51 −0.695949
\(27\) −1.05782e51 −0.0602052
\(28\) 8.42290e51 0.127114
\(29\) 2.50436e53 1.04995 0.524977 0.851117i \(-0.324074\pi\)
0.524977 + 0.851117i \(0.324074\pi\)
\(30\) −8.00713e51 −0.00973982
\(31\) −3.03546e54 −1.11564 −0.557819 0.829963i \(-0.688362\pi\)
−0.557819 + 0.829963i \(0.688362\pi\)
\(32\) −1.14688e55 −1.32295
\(33\) 4.17988e53 0.0156821
\(34\) −5.23725e55 −0.660880
\(35\) −8.21799e54 −0.0359983
\(36\) −5.36684e56 −0.840771
\(37\) −2.59488e57 −1.49539 −0.747696 0.664042i \(-0.768840\pi\)
−0.747696 + 0.664042i \(0.768840\pi\)
\(38\) −1.05490e58 −2.29672
\(39\) −1.83082e56 −0.0154450
\(40\) 1.53065e57 0.0512490
\(41\) 1.11326e58 0.151352 0.0756759 0.997132i \(-0.475889\pi\)
0.0756759 + 0.997132i \(0.475889\pi\)
\(42\) 1.09424e57 0.00617323
\(43\) −1.82489e58 −0.0436152 −0.0218076 0.999762i \(-0.506942\pi\)
−0.0218076 + 0.999762i \(0.506942\pi\)
\(44\) 4.24325e59 0.438204
\(45\) 5.23628e59 0.238104
\(46\) 8.77155e60 1.78820
\(47\) 1.00933e61 0.938562 0.469281 0.883049i \(-0.344513\pi\)
0.469281 + 0.883049i \(0.344513\pi\)
\(48\) −7.91538e59 −0.0341324
\(49\) −4.80987e61 −0.977184
\(50\) −1.31704e62 −1.27996
\(51\) −3.10917e60 −0.0146667
\(52\) −1.85858e62 −0.431578
\(53\) 9.84119e60 0.0114019 0.00570096 0.999984i \(-0.498185\pi\)
0.00570096 + 0.999984i \(0.498185\pi\)
\(54\) −1.39507e62 −0.0817003
\(55\) −4.14002e62 −0.124098
\(56\) −2.09175e62 −0.0324823
\(57\) −6.26256e62 −0.0509706
\(58\) 3.30280e64 1.42482
\(59\) 5.71932e64 1.32205 0.661023 0.750366i \(-0.270123\pi\)
0.661023 + 0.750366i \(0.270123\pi\)
\(60\) −4.82562e62 −0.00603994
\(61\) −7.84734e64 −0.537259 −0.268629 0.963244i \(-0.586571\pi\)
−0.268629 + 0.963244i \(0.586571\pi\)
\(62\) −4.00322e65 −1.51396
\(63\) −7.15579e64 −0.150913
\(64\) −5.57680e65 −0.661936
\(65\) 1.81336e65 0.122221
\(66\) 5.51250e64 0.0212811
\(67\) 5.03632e66 1.12301 0.561505 0.827474i \(-0.310223\pi\)
0.561505 + 0.827474i \(0.310223\pi\)
\(68\) −3.15631e66 −0.409831
\(69\) 5.20737e65 0.0396850
\(70\) −1.08380e66 −0.0488508
\(71\) 4.24341e67 1.13969 0.569843 0.821753i \(-0.307004\pi\)
0.569843 + 0.821753i \(0.307004\pi\)
\(72\) 1.33281e67 0.214848
\(73\) 9.03815e67 0.880633 0.440317 0.897843i \(-0.354866\pi\)
0.440317 + 0.897843i \(0.354866\pi\)
\(74\) −3.42218e68 −2.02929
\(75\) −7.81884e66 −0.0284058
\(76\) −6.35750e68 −1.42426
\(77\) 5.65767e67 0.0786549
\(78\) −2.41452e67 −0.0209594
\(79\) 2.30814e69 1.25856 0.629279 0.777180i \(-0.283350\pi\)
0.629279 + 0.777180i \(0.283350\pi\)
\(80\) 7.83990e68 0.270101
\(81\) 4.55533e69 0.997280
\(82\) 1.46819e69 0.205389
\(83\) −1.28517e70 −1.15507 −0.577536 0.816365i \(-0.695986\pi\)
−0.577536 + 0.816365i \(0.695986\pi\)
\(84\) 6.59460e67 0.00382820
\(85\) 3.07952e69 0.116063
\(86\) −2.40669e69 −0.0591871
\(87\) 1.96076e69 0.0316207
\(88\) −1.05377e70 −0.111977
\(89\) −2.21881e71 −1.56093 −0.780466 0.625198i \(-0.785018\pi\)
−0.780466 + 0.625198i \(0.785018\pi\)
\(90\) 6.90570e70 0.323114
\(91\) −2.47811e70 −0.0774657
\(92\) 5.28632e71 1.10891
\(93\) −2.37658e70 −0.0335988
\(94\) 1.33113e72 1.27366
\(95\) 6.20284e71 0.403347
\(96\) −8.97937e70 −0.0398424
\(97\) −2.42972e72 −0.738564 −0.369282 0.929317i \(-0.620396\pi\)
−0.369282 + 0.929317i \(0.620396\pi\)
\(98\) −6.34334e72 −1.32607
\(99\) −3.60491e72 −0.520248
\(100\) −7.93738e72 −0.793738
\(101\) 2.33656e73 1.62497 0.812486 0.582980i \(-0.198114\pi\)
0.812486 + 0.582980i \(0.198114\pi\)
\(102\) −4.10043e71 −0.0199032
\(103\) 5.10135e72 0.173431 0.0867155 0.996233i \(-0.472363\pi\)
0.0867155 + 0.996233i \(0.472363\pi\)
\(104\) 4.61562e72 0.110284
\(105\) −6.43416e70 −0.00108413
\(106\) 1.29787e72 0.0154728
\(107\) 7.28757e73 0.616701 0.308351 0.951273i \(-0.400223\pi\)
0.308351 + 0.951273i \(0.400223\pi\)
\(108\) −8.40761e72 −0.0506647
\(109\) 1.98778e73 0.0855662 0.0427831 0.999084i \(-0.486378\pi\)
0.0427831 + 0.999084i \(0.486378\pi\)
\(110\) −5.45993e73 −0.168405
\(111\) −2.03163e73 −0.0450356
\(112\) −1.07138e74 −0.171194
\(113\) −1.41242e75 −1.63155 −0.815773 0.578372i \(-0.803688\pi\)
−0.815773 + 0.578372i \(0.803688\pi\)
\(114\) −8.25917e73 −0.0691687
\(115\) −5.15771e74 −0.314041
\(116\) 1.99048e75 0.883572
\(117\) 1.57898e75 0.512381
\(118\) 7.54275e75 1.79406
\(119\) −4.20842e74 −0.0735622
\(120\) 1.19840e73 0.00154343
\(121\) −7.66134e75 −0.728851
\(122\) −1.03492e76 −0.729077
\(123\) 8.71616e73 0.00455815
\(124\) −2.41261e76 −0.938848
\(125\) 1.59549e76 0.463104
\(126\) −9.43718e75 −0.204794
\(127\) 8.09414e75 0.131624 0.0658120 0.997832i \(-0.479036\pi\)
0.0658120 + 0.997832i \(0.479036\pi\)
\(128\) 3.47722e76 0.424686
\(129\) −1.42877e74 −0.00131353
\(130\) 2.39150e76 0.165858
\(131\) −1.61076e75 −0.00844554 −0.00422277 0.999991i \(-0.501344\pi\)
−0.00422277 + 0.999991i \(0.501344\pi\)
\(132\) 3.32220e75 0.0131971
\(133\) −8.47667e76 −0.255647
\(134\) 6.64199e77 1.52396
\(135\) 8.20307e75 0.0143481
\(136\) 7.83842e76 0.104727
\(137\) −1.35087e78 −1.38138 −0.690690 0.723151i \(-0.742693\pi\)
−0.690690 + 0.723151i \(0.742693\pi\)
\(138\) 6.86757e76 0.0538538
\(139\) −2.90894e78 −1.75265 −0.876324 0.481722i \(-0.840011\pi\)
−0.876324 + 0.481722i \(0.840011\pi\)
\(140\) −6.53171e76 −0.0302938
\(141\) 7.90244e76 0.0282660
\(142\) 5.59629e78 1.54659
\(143\) −1.24841e78 −0.267049
\(144\) 6.82657e78 1.13233
\(145\) −1.94206e78 −0.250225
\(146\) 1.19197e79 1.19505
\(147\) −3.76582e77 −0.0294291
\(148\) −2.06243e79 −1.25842
\(149\) −1.05138e79 −0.501717 −0.250859 0.968024i \(-0.580713\pi\)
−0.250859 + 0.968024i \(0.580713\pi\)
\(150\) −1.03116e78 −0.0385475
\(151\) −3.34668e79 −0.981646 −0.490823 0.871259i \(-0.663304\pi\)
−0.490823 + 0.871259i \(0.663304\pi\)
\(152\) 1.57883e79 0.363952
\(153\) 2.68149e79 0.486563
\(154\) 7.46143e78 0.106737
\(155\) 2.35391e79 0.265879
\(156\) −1.45515e78 −0.0129975
\(157\) −2.44529e80 −1.72979 −0.864894 0.501955i \(-0.832614\pi\)
−0.864894 + 0.501955i \(0.832614\pi\)
\(158\) 3.04401e80 1.70790
\(159\) 7.70503e76 0.000343383 0
\(160\) 8.89374e79 0.315286
\(161\) 7.04842e79 0.199043
\(162\) 6.00765e80 1.35334
\(163\) −7.33185e80 −1.31937 −0.659684 0.751543i \(-0.729310\pi\)
−0.659684 + 0.751543i \(0.729310\pi\)
\(164\) 8.84830e79 0.127368
\(165\) −3.24137e78 −0.00373736
\(166\) −1.69490e81 −1.56747
\(167\) −3.20208e80 −0.237838 −0.118919 0.992904i \(-0.537943\pi\)
−0.118919 + 0.992904i \(0.537943\pi\)
\(168\) −1.63771e78 −0.000978246 0
\(169\) −1.53223e81 −0.736988
\(170\) 4.06133e80 0.157501
\(171\) 5.40110e81 1.69093
\(172\) −1.45043e80 −0.0367037
\(173\) 7.26967e81 1.48878 0.744392 0.667743i \(-0.232739\pi\)
0.744392 + 0.667743i \(0.232739\pi\)
\(174\) 2.58588e80 0.0429102
\(175\) −1.05832e81 −0.142471
\(176\) −5.39737e81 −0.590160
\(177\) 4.47787e80 0.0398151
\(178\) −2.92620e82 −2.11824
\(179\) 1.31256e82 0.774431 0.387216 0.921989i \(-0.373437\pi\)
0.387216 + 0.921989i \(0.373437\pi\)
\(180\) 4.16183e81 0.200372
\(181\) 1.94546e81 0.0765166 0.0382583 0.999268i \(-0.487819\pi\)
0.0382583 + 0.999268i \(0.487819\pi\)
\(182\) −3.26817e81 −0.105123
\(183\) −6.14397e80 −0.0161802
\(184\) −1.31281e82 −0.283368
\(185\) 2.01225e82 0.356381
\(186\) −3.13427e81 −0.0455947
\(187\) −2.12010e82 −0.253593
\(188\) 8.02225e82 0.789832
\(189\) −1.12102e81 −0.00909402
\(190\) 8.18041e82 0.547354
\(191\) −2.93860e82 −0.162339 −0.0811695 0.996700i \(-0.525866\pi\)
−0.0811695 + 0.996700i \(0.525866\pi\)
\(192\) −4.36628e81 −0.0199350
\(193\) 2.95820e83 1.11734 0.558671 0.829389i \(-0.311311\pi\)
0.558671 + 0.829389i \(0.311311\pi\)
\(194\) −3.20436e83 −1.00225
\(195\) 1.41975e81 0.00368085
\(196\) −3.82291e83 −0.822334
\(197\) −7.95523e83 −1.42114 −0.710568 0.703628i \(-0.751562\pi\)
−0.710568 + 0.703628i \(0.751562\pi\)
\(198\) −4.75422e83 −0.705992
\(199\) 6.99041e83 0.863704 0.431852 0.901944i \(-0.357860\pi\)
0.431852 + 0.901944i \(0.357860\pi\)
\(200\) 1.97118e83 0.202829
\(201\) 3.94312e82 0.0338208
\(202\) 3.08149e84 2.20514
\(203\) 2.65398e83 0.158596
\(204\) −2.47119e82 −0.0123426
\(205\) −8.63304e82 −0.0360701
\(206\) 6.72775e83 0.235351
\(207\) −4.49107e84 −1.31653
\(208\) 2.36410e84 0.581237
\(209\) −4.27034e84 −0.881298
\(210\) −8.48549e81 −0.00147120
\(211\) −5.03036e84 −0.733313 −0.366657 0.930356i \(-0.619498\pi\)
−0.366657 + 0.930356i \(0.619498\pi\)
\(212\) 7.82184e82 0.00959511
\(213\) 3.32232e83 0.0343231
\(214\) 9.61098e84 0.836883
\(215\) 1.41515e83 0.0103944
\(216\) 2.08796e83 0.0129467
\(217\) −3.21681e84 −0.168518
\(218\) 2.62153e84 0.116116
\(219\) 7.07630e83 0.0265214
\(220\) −3.29052e84 −0.104433
\(221\) 9.28621e84 0.249759
\(222\) −2.67935e84 −0.0611147
\(223\) 7.49686e85 1.45128 0.725641 0.688073i \(-0.241543\pi\)
0.725641 + 0.688073i \(0.241543\pi\)
\(224\) −1.21540e85 −0.199833
\(225\) 6.74331e85 0.942348
\(226\) −1.86272e86 −2.21406
\(227\) −2.61202e85 −0.264261 −0.132131 0.991232i \(-0.542182\pi\)
−0.132131 + 0.991232i \(0.542182\pi\)
\(228\) −4.97752e84 −0.0428935
\(229\) −1.16589e86 −0.856369 −0.428185 0.903691i \(-0.640847\pi\)
−0.428185 + 0.903691i \(0.640847\pi\)
\(230\) −6.80208e85 −0.426163
\(231\) 4.42960e83 0.00236879
\(232\) −4.94319e85 −0.225785
\(233\) 3.91796e86 1.52957 0.764783 0.644288i \(-0.222846\pi\)
0.764783 + 0.644288i \(0.222846\pi\)
\(234\) 2.08239e86 0.695318
\(235\) −7.82708e85 −0.223678
\(236\) 4.54576e86 1.11255
\(237\) 1.80713e85 0.0379030
\(238\) −5.55013e85 −0.0998262
\(239\) 1.13004e86 0.174409 0.0872046 0.996190i \(-0.472207\pi\)
0.0872046 + 0.996190i \(0.472207\pi\)
\(240\) 6.13814e84 0.00813442
\(241\) −1.12975e87 −1.28635 −0.643175 0.765719i \(-0.722383\pi\)
−0.643175 + 0.765719i \(0.722383\pi\)
\(242\) −1.01039e87 −0.989073
\(243\) 1.07158e86 0.0902395
\(244\) −6.23712e86 −0.452121
\(245\) 3.72991e86 0.232882
\(246\) 1.14950e85 0.00618555
\(247\) 1.87045e87 0.867973
\(248\) 5.99150e86 0.239910
\(249\) −1.00620e86 −0.0347864
\(250\) 2.10416e87 0.628446
\(251\) −4.85688e87 −1.25391 −0.626955 0.779055i \(-0.715699\pi\)
−0.626955 + 0.779055i \(0.715699\pi\)
\(252\) −5.68747e86 −0.126999
\(253\) 3.55082e87 0.686167
\(254\) 1.06747e87 0.178618
\(255\) 2.41107e85 0.00349538
\(256\) 9.85296e87 1.23825
\(257\) −5.12068e87 −0.558173 −0.279087 0.960266i \(-0.590032\pi\)
−0.279087 + 0.960266i \(0.590032\pi\)
\(258\) −1.88429e85 −0.00178250
\(259\) −2.74991e87 −0.225879
\(260\) 1.44127e87 0.102854
\(261\) −1.69104e88 −1.04900
\(262\) −2.12429e86 −0.0114609
\(263\) −1.76095e88 −0.826727 −0.413364 0.910566i \(-0.635646\pi\)
−0.413364 + 0.910566i \(0.635646\pi\)
\(264\) −8.25038e85 −0.00337234
\(265\) −7.63155e85 −0.00271730
\(266\) −1.11792e88 −0.346921
\(267\) −1.73719e87 −0.0470095
\(268\) 4.00290e88 0.945051
\(269\) 4.34069e88 0.894541 0.447271 0.894399i \(-0.352396\pi\)
0.447271 + 0.894399i \(0.352396\pi\)
\(270\) 1.08184e87 0.0194708
\(271\) 9.76535e88 1.53571 0.767854 0.640625i \(-0.221325\pi\)
0.767854 + 0.640625i \(0.221325\pi\)
\(272\) 4.01480e88 0.551948
\(273\) −1.94020e86 −0.00233298
\(274\) −1.78155e89 −1.87458
\(275\) −5.33154e88 −0.491145
\(276\) 4.13885e87 0.0333963
\(277\) 1.10474e88 0.0781172 0.0390586 0.999237i \(-0.487564\pi\)
0.0390586 + 0.999237i \(0.487564\pi\)
\(278\) −3.83636e89 −2.37840
\(279\) 2.04966e89 1.11463
\(280\) 1.62209e87 0.00774118
\(281\) 1.93794e89 0.812006 0.406003 0.913872i \(-0.366922\pi\)
0.406003 + 0.913872i \(0.366922\pi\)
\(282\) 1.04219e88 0.0383578
\(283\) −1.60337e89 −0.518597 −0.259298 0.965797i \(-0.583491\pi\)
−0.259298 + 0.965797i \(0.583491\pi\)
\(284\) 3.37269e89 0.959085
\(285\) 4.85643e87 0.0121473
\(286\) −1.64642e89 −0.362395
\(287\) 1.17977e88 0.0228617
\(288\) 7.74420e89 1.32175
\(289\) −5.07221e89 −0.762827
\(290\) −2.56122e89 −0.339563
\(291\) −1.90232e88 −0.0222428
\(292\) 7.18358e89 0.741083
\(293\) −2.60962e89 −0.237635 −0.118817 0.992916i \(-0.537910\pi\)
−0.118817 + 0.992916i \(0.537910\pi\)
\(294\) −4.96643e88 −0.0399362
\(295\) −4.43517e89 −0.315070
\(296\) 5.12186e89 0.321574
\(297\) −5.64740e88 −0.0313500
\(298\) −1.38657e90 −0.680846
\(299\) −1.55529e90 −0.675792
\(300\) −6.21447e88 −0.0239044
\(301\) −1.93391e88 −0.00658809
\(302\) −4.41365e90 −1.33212
\(303\) 1.82938e89 0.0489381
\(304\) 8.08668e90 1.91816
\(305\) 6.08538e89 0.128039
\(306\) 3.53639e90 0.660281
\(307\) 6.88569e90 1.14129 0.570646 0.821196i \(-0.306693\pi\)
0.570646 + 0.821196i \(0.306693\pi\)
\(308\) 4.49675e89 0.0661908
\(309\) 3.99404e88 0.00522309
\(310\) 3.10438e90 0.360806
\(311\) −1.52167e91 −1.57242 −0.786208 0.617962i \(-0.787958\pi\)
−0.786208 + 0.617962i \(0.787958\pi\)
\(312\) 3.61374e88 0.00332135
\(313\) 2.24817e90 0.183849 0.0919245 0.995766i \(-0.470698\pi\)
0.0919245 + 0.995766i \(0.470698\pi\)
\(314\) −3.22489e91 −2.34738
\(315\) 5.54911e89 0.0359656
\(316\) 1.83452e91 1.05912
\(317\) −1.42898e91 −0.735129 −0.367564 0.929998i \(-0.619808\pi\)
−0.367564 + 0.929998i \(0.619808\pi\)
\(318\) 1.01615e88 0.000465982 0
\(319\) 1.33701e91 0.546732
\(320\) 4.32464e90 0.157752
\(321\) 5.70571e89 0.0185727
\(322\) 9.29559e90 0.270108
\(323\) 3.17646e91 0.824236
\(324\) 3.62061e91 0.839245
\(325\) 2.33526e91 0.483719
\(326\) −9.66938e91 −1.79042
\(327\) 1.55631e89 0.00257693
\(328\) −2.19740e90 −0.0325472
\(329\) 1.06963e91 0.141770
\(330\) −4.27478e89 −0.00507172
\(331\) 1.73204e91 0.184007 0.0920036 0.995759i \(-0.470673\pi\)
0.0920036 + 0.995759i \(0.470673\pi\)
\(332\) −1.02146e92 −0.972032
\(333\) 1.75217e92 1.49403
\(334\) −4.22296e91 −0.322754
\(335\) −3.90552e91 −0.267635
\(336\) −8.38826e89 −0.00515571
\(337\) −1.40454e92 −0.774538 −0.387269 0.921967i \(-0.626582\pi\)
−0.387269 + 0.921967i \(0.626582\pi\)
\(338\) −2.02074e92 −1.00012
\(339\) −1.10583e91 −0.0491361
\(340\) 2.44763e91 0.0976708
\(341\) −1.62055e92 −0.580935
\(342\) 7.12307e92 2.29464
\(343\) −1.03135e92 −0.298654
\(344\) 3.60202e90 0.00937914
\(345\) −4.03816e90 −0.00945773
\(346\) 9.58736e92 2.02033
\(347\) −2.50690e92 −0.475457 −0.237728 0.971332i \(-0.576403\pi\)
−0.237728 + 0.971332i \(0.576403\pi\)
\(348\) 1.55842e91 0.0266099
\(349\) −2.05783e92 −0.316433 −0.158216 0.987404i \(-0.550574\pi\)
−0.158216 + 0.987404i \(0.550574\pi\)
\(350\) −1.39573e92 −0.193338
\(351\) 2.47361e91 0.0308760
\(352\) −6.12289e92 −0.688889
\(353\) −1.17187e93 −1.18879 −0.594393 0.804174i \(-0.702608\pi\)
−0.594393 + 0.804174i \(0.702608\pi\)
\(354\) 5.90549e91 0.0540303
\(355\) −3.29064e92 −0.271610
\(356\) −1.76352e93 −1.31358
\(357\) −3.29492e90 −0.00221542
\(358\) 1.73102e93 1.05093
\(359\) 9.08675e92 0.498266 0.249133 0.968469i \(-0.419854\pi\)
0.249133 + 0.968469i \(0.419854\pi\)
\(360\) −1.03355e92 −0.0512025
\(361\) 4.16445e93 1.86442
\(362\) 2.56571e92 0.103835
\(363\) −5.99834e91 −0.0219503
\(364\) −1.96962e92 −0.0651900
\(365\) −7.00882e92 −0.209872
\(366\) −8.10278e91 −0.0219571
\(367\) 1.48899e93 0.365242 0.182621 0.983183i \(-0.441542\pi\)
0.182621 + 0.983183i \(0.441542\pi\)
\(368\) −6.72414e93 −1.49345
\(369\) −7.51720e92 −0.151215
\(370\) 2.65380e93 0.483621
\(371\) 1.04291e91 0.00172227
\(372\) −1.88892e92 −0.0282746
\(373\) 2.51509e93 0.341336 0.170668 0.985329i \(-0.445408\pi\)
0.170668 + 0.985329i \(0.445408\pi\)
\(374\) −2.79602e93 −0.344133
\(375\) 1.24917e92 0.0139470
\(376\) −1.99225e93 −0.201831
\(377\) −5.85621e93 −0.538465
\(378\) −1.47841e92 −0.0123409
\(379\) −2.99096e93 −0.226714 −0.113357 0.993554i \(-0.536160\pi\)
−0.113357 + 0.993554i \(0.536160\pi\)
\(380\) 4.93005e93 0.339430
\(381\) 6.33720e91 0.00396402
\(382\) −3.87548e93 −0.220299
\(383\) 1.08200e94 0.559078 0.279539 0.960134i \(-0.409818\pi\)
0.279539 + 0.960134i \(0.409818\pi\)
\(384\) 2.72244e92 0.0127900
\(385\) −4.38735e92 −0.0187450
\(386\) 3.90133e94 1.51627
\(387\) 1.23224e93 0.0435756
\(388\) −1.93116e94 −0.621527
\(389\) 3.46532e94 1.01527 0.507636 0.861572i \(-0.330519\pi\)
0.507636 + 0.861572i \(0.330519\pi\)
\(390\) 1.87239e92 0.00499503
\(391\) −2.64125e94 −0.641739
\(392\) 9.49387e93 0.210137
\(393\) −1.26112e91 −0.000254348 0
\(394\) −1.04915e95 −1.92853
\(395\) −1.78989e94 −0.299939
\(396\) −2.86521e94 −0.437806
\(397\) −1.15711e95 −1.61258 −0.806288 0.591523i \(-0.798527\pi\)
−0.806288 + 0.591523i \(0.798527\pi\)
\(398\) 9.21907e94 1.17207
\(399\) −6.63670e92 −0.00769912
\(400\) 1.00963e95 1.06898
\(401\) 5.61950e94 0.543160 0.271580 0.962416i \(-0.412454\pi\)
0.271580 + 0.962416i \(0.412454\pi\)
\(402\) 5.20026e93 0.0458959
\(403\) 7.09815e94 0.572151
\(404\) 1.85711e95 1.36747
\(405\) −3.53253e94 −0.237672
\(406\) 3.50011e94 0.215220
\(407\) −1.38534e95 −0.778680
\(408\) 6.13699e92 0.00315398
\(409\) −1.31996e95 −0.620385 −0.310192 0.950674i \(-0.600393\pi\)
−0.310192 + 0.950674i \(0.600393\pi\)
\(410\) −1.13854e94 −0.0489483
\(411\) −1.05765e94 −0.0416020
\(412\) 4.05459e94 0.145948
\(413\) 6.06101e94 0.199695
\(414\) −5.92290e95 −1.78658
\(415\) 9.96608e94 0.275276
\(416\) 2.68188e95 0.678473
\(417\) −2.27752e94 −0.0527832
\(418\) −5.63180e95 −1.19595
\(419\) 5.03533e95 0.979978 0.489989 0.871729i \(-0.337001\pi\)
0.489989 + 0.871729i \(0.337001\pi\)
\(420\) −5.11392e92 −0.000912335 0
\(421\) 1.06657e96 1.74458 0.872292 0.488984i \(-0.162633\pi\)
0.872292 + 0.488984i \(0.162633\pi\)
\(422\) −6.63413e95 −0.995129
\(423\) −6.81541e95 −0.937710
\(424\) −1.94248e93 −0.00245191
\(425\) 3.96583e95 0.459344
\(426\) 4.38154e94 0.0465775
\(427\) −8.31615e94 −0.0811531
\(428\) 5.79221e95 0.518975
\(429\) −9.77426e93 −0.00804253
\(430\) 1.86632e94 0.0141055
\(431\) 2.15593e96 1.49697 0.748487 0.663150i \(-0.230781\pi\)
0.748487 + 0.663150i \(0.230781\pi\)
\(432\) 1.06944e95 0.0682338
\(433\) −5.70080e95 −0.334293 −0.167147 0.985932i \(-0.553455\pi\)
−0.167147 + 0.985932i \(0.553455\pi\)
\(434\) −4.24238e95 −0.228684
\(435\) −1.52051e94 −0.00753583
\(436\) 1.57990e95 0.0720069
\(437\) −5.32006e96 −2.23020
\(438\) 9.33235e94 0.0359903
\(439\) −3.84665e96 −1.36498 −0.682492 0.730893i \(-0.739104\pi\)
−0.682492 + 0.730893i \(0.739104\pi\)
\(440\) 8.17170e94 0.0266864
\(441\) 3.24781e96 0.976297
\(442\) 1.22468e96 0.338930
\(443\) −1.87246e96 −0.477173 −0.238586 0.971121i \(-0.576684\pi\)
−0.238586 + 0.971121i \(0.576684\pi\)
\(444\) −1.61475e95 −0.0378990
\(445\) 1.72062e96 0.372001
\(446\) 9.88699e96 1.96944
\(447\) −8.23161e94 −0.0151098
\(448\) −5.90997e95 −0.0999857
\(449\) 1.04927e96 0.163642 0.0818211 0.996647i \(-0.473926\pi\)
0.0818211 + 0.996647i \(0.473926\pi\)
\(450\) 8.89320e96 1.27880
\(451\) 5.94341e95 0.0788119
\(452\) −1.12260e97 −1.37300
\(453\) −2.62024e95 −0.0295635
\(454\) −3.44478e96 −0.358611
\(455\) 1.92170e95 0.0184616
\(456\) 1.23612e95 0.0109609
\(457\) −1.31030e97 −1.07258 −0.536291 0.844033i \(-0.680175\pi\)
−0.536291 + 0.844033i \(0.680175\pi\)
\(458\) −1.53759e97 −1.16212
\(459\) 4.20078e95 0.0293202
\(460\) −4.09938e96 −0.264276
\(461\) 2.03230e97 1.21033 0.605166 0.796099i \(-0.293107\pi\)
0.605166 + 0.796099i \(0.293107\pi\)
\(462\) 5.84183e94 0.00321453
\(463\) 2.28467e97 1.16176 0.580881 0.813988i \(-0.302708\pi\)
0.580881 + 0.813988i \(0.302708\pi\)
\(464\) −2.53187e97 −1.18997
\(465\) 1.84297e95 0.00800727
\(466\) 5.16707e97 2.07567
\(467\) −4.33212e97 −1.60929 −0.804645 0.593756i \(-0.797645\pi\)
−0.804645 + 0.593756i \(0.797645\pi\)
\(468\) 1.25499e97 0.431187
\(469\) 5.33721e96 0.169631
\(470\) −1.03225e97 −0.303538
\(471\) −1.91451e96 −0.0520947
\(472\) −1.12890e97 −0.284297
\(473\) −9.74257e95 −0.0227113
\(474\) 2.38327e96 0.0514356
\(475\) 7.98805e97 1.59634
\(476\) −3.34488e96 −0.0619051
\(477\) −6.64515e95 −0.0113916
\(478\) 1.49031e97 0.236679
\(479\) −8.07458e97 −1.18816 −0.594078 0.804407i \(-0.702483\pi\)
−0.594078 + 0.804407i \(0.702483\pi\)
\(480\) 6.96324e95 0.00949524
\(481\) 6.06789e97 0.766906
\(482\) −1.48993e98 −1.74562
\(483\) 5.51847e95 0.00599444
\(484\) −6.08928e97 −0.613353
\(485\) 1.88418e97 0.176014
\(486\) 1.41322e97 0.122458
\(487\) −8.36643e97 −0.672563 −0.336282 0.941761i \(-0.609169\pi\)
−0.336282 + 0.941761i \(0.609169\pi\)
\(488\) 1.54893e97 0.115534
\(489\) −5.74038e96 −0.0397344
\(490\) 4.91907e97 0.316028
\(491\) 2.52751e98 1.50736 0.753681 0.657240i \(-0.228276\pi\)
0.753681 + 0.657240i \(0.228276\pi\)
\(492\) 6.92766e95 0.00383584
\(493\) −9.94524e97 −0.511332
\(494\) 2.46678e98 1.17787
\(495\) 2.79550e97 0.123985
\(496\) 3.06881e98 1.26441
\(497\) 4.49692e97 0.172150
\(498\) −1.32700e97 −0.0472063
\(499\) −4.63850e98 −1.53358 −0.766792 0.641896i \(-0.778148\pi\)
−0.766792 + 0.641896i \(0.778148\pi\)
\(500\) 1.26811e98 0.389718
\(501\) −2.50703e96 −0.00716279
\(502\) −6.40534e98 −1.70160
\(503\) −5.77546e98 −1.42677 −0.713387 0.700770i \(-0.752840\pi\)
−0.713387 + 0.700770i \(0.752840\pi\)
\(504\) 1.41243e97 0.0324529
\(505\) −1.81193e98 −0.387263
\(506\) 4.68289e98 0.931151
\(507\) −1.19964e97 −0.0221953
\(508\) 6.43328e97 0.110766
\(509\) 3.98850e98 0.639162 0.319581 0.947559i \(-0.396458\pi\)
0.319581 + 0.947559i \(0.396458\pi\)
\(510\) 3.17977e96 0.00474333
\(511\) 9.57811e97 0.133020
\(512\) 9.71011e98 1.25566
\(513\) 8.46129e97 0.101895
\(514\) −6.75325e98 −0.757458
\(515\) −3.95595e97 −0.0413320
\(516\) −1.13560e96 −0.00110538
\(517\) 5.38855e98 0.488728
\(518\) −3.62663e98 −0.306525
\(519\) 5.69169e97 0.0448366
\(520\) −3.57928e97 −0.0262829
\(521\) 1.51314e99 1.03586 0.517932 0.855422i \(-0.326702\pi\)
0.517932 + 0.855422i \(0.326702\pi\)
\(522\) −2.23018e99 −1.42353
\(523\) 8.82515e98 0.525303 0.262652 0.964891i \(-0.415403\pi\)
0.262652 + 0.964891i \(0.415403\pi\)
\(524\) −1.28024e97 −0.00710721
\(525\) −8.28596e96 −0.00429070
\(526\) −2.32237e99 −1.12189
\(527\) 1.20543e99 0.543321
\(528\) −4.22580e97 −0.0177734
\(529\) 1.87608e99 0.736408
\(530\) −1.00646e97 −0.00368747
\(531\) −3.86191e99 −1.32085
\(532\) −6.73731e98 −0.215136
\(533\) −2.60326e98 −0.0776203
\(534\) −2.29103e98 −0.0637933
\(535\) −5.65130e98 −0.146972
\(536\) −9.94086e98 −0.241495
\(537\) 1.02765e98 0.0233230
\(538\) 5.72458e99 1.21392
\(539\) −2.56785e99 −0.508839
\(540\) 6.51986e97 0.0120744
\(541\) 2.12211e99 0.367340 0.183670 0.982988i \(-0.441202\pi\)
0.183670 + 0.982988i \(0.441202\pi\)
\(542\) 1.28787e100 2.08400
\(543\) 1.52318e97 0.00230439
\(544\) 4.55447e99 0.644284
\(545\) −1.54147e98 −0.0203921
\(546\) −2.55877e97 −0.00316592
\(547\) −7.50110e99 −0.868136 −0.434068 0.900880i \(-0.642922\pi\)
−0.434068 + 0.900880i \(0.642922\pi\)
\(548\) −1.07368e100 −1.16248
\(549\) 5.29883e99 0.536771
\(550\) −7.03134e99 −0.666499
\(551\) −2.00319e100 −1.77701
\(552\) −1.02785e98 −0.00853399
\(553\) 2.44603e99 0.190105
\(554\) 1.45695e99 0.106008
\(555\) 1.57547e98 0.0107329
\(556\) −2.31205e100 −1.47491
\(557\) 1.56973e100 0.937801 0.468900 0.883251i \(-0.344650\pi\)
0.468900 + 0.883251i \(0.344650\pi\)
\(558\) 2.70313e100 1.51258
\(559\) 4.26733e98 0.0223679
\(560\) 8.30827e98 0.0407988
\(561\) −1.65990e98 −0.00763727
\(562\) 2.55579e100 1.10192
\(563\) 4.75620e99 0.192178 0.0960891 0.995373i \(-0.469367\pi\)
0.0960891 + 0.995373i \(0.469367\pi\)
\(564\) 6.28091e98 0.0237868
\(565\) 1.09529e100 0.388830
\(566\) −2.11456e100 −0.703752
\(567\) 4.82748e99 0.150639
\(568\) −8.37578e99 −0.245082
\(569\) 2.04030e100 0.559882 0.279941 0.960017i \(-0.409685\pi\)
0.279941 + 0.960017i \(0.409685\pi\)
\(570\) 6.40474e98 0.0164843
\(571\) −5.80730e100 −1.40203 −0.701013 0.713148i \(-0.747269\pi\)
−0.701013 + 0.713148i \(0.747269\pi\)
\(572\) −9.92244e99 −0.224731
\(573\) −2.30074e98 −0.00488904
\(574\) 1.55591e99 0.0310241
\(575\) −6.64213e100 −1.24289
\(576\) 3.76567e100 0.661336
\(577\) 1.19206e101 1.96508 0.982539 0.186059i \(-0.0595714\pi\)
0.982539 + 0.186059i \(0.0595714\pi\)
\(578\) −6.68932e100 −1.03518
\(579\) 2.31609e99 0.0336502
\(580\) −1.54356e100 −0.210573
\(581\) −1.36194e100 −0.174474
\(582\) −2.50881e99 −0.0301841
\(583\) 5.25394e98 0.00593721
\(584\) −1.78398e100 −0.189374
\(585\) −1.22445e100 −0.122111
\(586\) −3.44162e100 −0.322478
\(587\) −6.02937e100 −0.530862 −0.265431 0.964130i \(-0.585514\pi\)
−0.265431 + 0.964130i \(0.585514\pi\)
\(588\) −2.99310e99 −0.0247656
\(589\) 2.42801e101 1.88817
\(590\) −5.84918e100 −0.427559
\(591\) −6.22845e99 −0.0427993
\(592\) 2.62339e101 1.69481
\(593\) 7.82421e100 0.475274 0.237637 0.971354i \(-0.423627\pi\)
0.237637 + 0.971354i \(0.423627\pi\)
\(594\) −7.44789e99 −0.0425430
\(595\) 3.26350e99 0.0175313
\(596\) −8.35640e100 −0.422212
\(597\) 5.47305e99 0.0260115
\(598\) −2.05115e101 −0.917072
\(599\) −1.98442e101 −0.834745 −0.417372 0.908736i \(-0.637049\pi\)
−0.417372 + 0.908736i \(0.637049\pi\)
\(600\) 1.54331e99 0.00610846
\(601\) 4.38699e100 0.163399 0.0816994 0.996657i \(-0.473965\pi\)
0.0816994 + 0.996657i \(0.473965\pi\)
\(602\) −2.55048e99 −0.00894024
\(603\) −3.40072e101 −1.12199
\(604\) −2.65996e101 −0.826089
\(605\) 5.94114e100 0.173700
\(606\) 2.41261e100 0.0664105
\(607\) −4.89694e101 −1.26922 −0.634611 0.772832i \(-0.718840\pi\)
−0.634611 + 0.772832i \(0.718840\pi\)
\(608\) 9.17369e101 2.23905
\(609\) 2.07790e99 0.00477631
\(610\) 8.02550e100 0.173753
\(611\) −2.36023e101 −0.481338
\(612\) 2.13126e101 0.409459
\(613\) 5.37584e101 0.973058 0.486529 0.873664i \(-0.338263\pi\)
0.486529 + 0.873664i \(0.338263\pi\)
\(614\) 9.08097e101 1.54877
\(615\) −6.75912e98 −0.00108630
\(616\) −1.11673e100 −0.0169142
\(617\) 3.31920e101 0.473833 0.236916 0.971530i \(-0.423863\pi\)
0.236916 + 0.971530i \(0.423863\pi\)
\(618\) 5.26740e99 0.00708790
\(619\) −1.13312e102 −1.43737 −0.718684 0.695337i \(-0.755255\pi\)
−0.718684 + 0.695337i \(0.755255\pi\)
\(620\) 1.87091e101 0.223746
\(621\) −7.03563e100 −0.0793341
\(622\) −2.00681e102 −2.13382
\(623\) −2.35136e101 −0.235779
\(624\) 1.85094e100 0.0175047
\(625\) 9.33642e101 0.832837
\(626\) 2.96493e101 0.249489
\(627\) −3.34341e100 −0.0265414
\(628\) −1.94353e102 −1.45567
\(629\) 1.03047e102 0.728262
\(630\) 7.31826e100 0.0488065
\(631\) 2.37031e102 1.49188 0.745938 0.666015i \(-0.232001\pi\)
0.745938 + 0.666015i \(0.232001\pi\)
\(632\) −4.55588e101 −0.270644
\(633\) −3.93845e100 −0.0220846
\(634\) −1.88457e102 −0.997593
\(635\) −6.27677e100 −0.0313686
\(636\) 6.12401e98 0.000288969 0
\(637\) 1.12474e102 0.501145
\(638\) 1.76327e102 0.741932
\(639\) −2.86532e102 −1.13865
\(640\) −2.69648e101 −0.101211
\(641\) 3.06386e102 1.08630 0.543152 0.839634i \(-0.317231\pi\)
0.543152 + 0.839634i \(0.317231\pi\)
\(642\) 7.52479e100 0.0252038
\(643\) 5.67273e101 0.179511 0.0897557 0.995964i \(-0.471391\pi\)
0.0897557 + 0.995964i \(0.471391\pi\)
\(644\) 5.60213e101 0.167502
\(645\) 1.10797e99 0.000313039 0
\(646\) 4.18917e102 1.11851
\(647\) −5.49944e102 −1.38775 −0.693876 0.720094i \(-0.744099\pi\)
−0.693876 + 0.720094i \(0.744099\pi\)
\(648\) −8.99146e101 −0.214458
\(649\) 3.05339e102 0.688415
\(650\) 3.07978e102 0.656422
\(651\) −2.51856e100 −0.00507512
\(652\) −5.82740e102 −1.11029
\(653\) −5.48029e102 −0.987353 −0.493676 0.869646i \(-0.664347\pi\)
−0.493676 + 0.869646i \(0.664347\pi\)
\(654\) 2.05249e100 0.00349698
\(655\) 1.24909e100 0.00201274
\(656\) −1.12549e102 −0.171535
\(657\) −6.10291e102 −0.879835
\(658\) 1.41065e102 0.192386
\(659\) −7.75339e102 −1.00040 −0.500200 0.865910i \(-0.666740\pi\)
−0.500200 + 0.865910i \(0.666740\pi\)
\(660\) −2.57627e100 −0.00314512
\(661\) 8.44451e102 0.975486 0.487743 0.872987i \(-0.337820\pi\)
0.487743 + 0.872987i \(0.337820\pi\)
\(662\) 2.28424e102 0.249704
\(663\) 7.27051e100 0.00752179
\(664\) 2.53670e102 0.248390
\(665\) 6.57341e101 0.0609257
\(666\) 2.31079e103 2.02745
\(667\) 1.66567e103 1.38355
\(668\) −2.54504e102 −0.200149
\(669\) 5.86957e101 0.0437072
\(670\) −5.15067e102 −0.363190
\(671\) −4.18948e102 −0.279761
\(672\) −9.51582e100 −0.00601821
\(673\) −8.74718e102 −0.523984 −0.261992 0.965070i \(-0.584379\pi\)
−0.261992 + 0.965070i \(0.584379\pi\)
\(674\) −1.85233e103 −1.05107
\(675\) 1.05640e102 0.0567858
\(676\) −1.21783e103 −0.620201
\(677\) −1.30620e103 −0.630263 −0.315132 0.949048i \(-0.602049\pi\)
−0.315132 + 0.949048i \(0.602049\pi\)
\(678\) −1.45839e102 −0.0666792
\(679\) −2.57488e102 −0.111560
\(680\) −6.07846e101 −0.0249585
\(681\) −2.04505e101 −0.00795856
\(682\) −2.13721e103 −0.788347
\(683\) 1.16711e103 0.408089 0.204045 0.978962i \(-0.434591\pi\)
0.204045 + 0.978962i \(0.434591\pi\)
\(684\) 4.29283e103 1.42297
\(685\) 1.04756e103 0.329210
\(686\) −1.36016e103 −0.405283
\(687\) −9.12815e101 −0.0257906
\(688\) 1.84494e102 0.0494314
\(689\) −2.30127e101 −0.00584744
\(690\) −5.32560e101 −0.0128344
\(691\) 4.35029e102 0.0994419 0.0497209 0.998763i \(-0.484167\pi\)
0.0497209 + 0.998763i \(0.484167\pi\)
\(692\) 5.77798e103 1.25286
\(693\) −3.82028e102 −0.0785836
\(694\) −3.30614e103 −0.645210
\(695\) 2.25580e103 0.417691
\(696\) −3.87020e101 −0.00679981
\(697\) −4.42096e102 −0.0737090
\(698\) −2.71390e103 −0.429409
\(699\) 3.06751e102 0.0460648
\(700\) −8.41158e102 −0.119894
\(701\) −8.51668e103 −1.15229 −0.576146 0.817347i \(-0.695444\pi\)
−0.576146 + 0.817347i \(0.695444\pi\)
\(702\) 3.26224e102 0.0418997
\(703\) 2.07560e104 2.53089
\(704\) −2.97730e103 −0.344683
\(705\) −6.12811e101 −0.00673634
\(706\) −1.54549e104 −1.61322
\(707\) 2.47615e103 0.245453
\(708\) 3.55904e102 0.0335057
\(709\) 6.19940e103 0.554322 0.277161 0.960824i \(-0.410607\pi\)
0.277161 + 0.960824i \(0.410607\pi\)
\(710\) −4.33975e103 −0.368583
\(711\) −1.55854e104 −1.25742
\(712\) 4.37955e103 0.335668
\(713\) −2.01891e104 −1.47011
\(714\) −4.34540e101 −0.00300639
\(715\) 9.68105e102 0.0636432
\(716\) 1.04323e104 0.651710
\(717\) 8.84748e101 0.00525255
\(718\) 1.19838e104 0.676163
\(719\) 2.00289e104 1.07412 0.537060 0.843544i \(-0.319535\pi\)
0.537060 + 0.843544i \(0.319535\pi\)
\(720\) −5.29380e103 −0.269856
\(721\) 5.40612e102 0.0261968
\(722\) 5.49215e104 2.53008
\(723\) −8.84521e102 −0.0387400
\(724\) 1.54627e103 0.0643913
\(725\) −2.50099e104 −0.990320
\(726\) −7.91072e102 −0.0297872
\(727\) 2.41721e103 0.0865582 0.0432791 0.999063i \(-0.486220\pi\)
0.0432791 + 0.999063i \(0.486220\pi\)
\(728\) 4.89137e102 0.0166585
\(729\) −3.07034e104 −0.994562
\(730\) −9.24335e103 −0.284803
\(731\) 7.24694e102 0.0212408
\(732\) −4.88327e102 −0.0136162
\(733\) −6.29556e104 −1.67009 −0.835044 0.550183i \(-0.814558\pi\)
−0.835044 + 0.550183i \(0.814558\pi\)
\(734\) 1.96371e104 0.495645
\(735\) 2.92028e102 0.00701354
\(736\) −7.62800e104 −1.74329
\(737\) 2.68875e104 0.584774
\(738\) −9.91381e103 −0.205203
\(739\) 3.87280e104 0.762962 0.381481 0.924377i \(-0.375414\pi\)
0.381481 + 0.924377i \(0.375414\pi\)
\(740\) 1.59935e104 0.299907
\(741\) 1.46444e103 0.0261401
\(742\) 1.37541e102 0.00233717
\(743\) 7.35672e104 1.19012 0.595062 0.803680i \(-0.297127\pi\)
0.595062 + 0.803680i \(0.297127\pi\)
\(744\) 4.69096e102 0.00722520
\(745\) 8.15311e103 0.119569
\(746\) 3.31695e104 0.463203
\(747\) 8.67794e104 1.15402
\(748\) −1.68507e104 −0.213407
\(749\) 7.72295e103 0.0931530
\(750\) 1.64742e103 0.0189265
\(751\) −3.95530e104 −0.432834 −0.216417 0.976301i \(-0.569437\pi\)
−0.216417 + 0.976301i \(0.569437\pi\)
\(752\) −1.02042e105 −1.06372
\(753\) −3.80263e103 −0.0377631
\(754\) −7.72328e104 −0.730714
\(755\) 2.59525e104 0.233946
\(756\) −8.90990e102 −0.00765292
\(757\) 7.45337e104 0.610033 0.305016 0.952347i \(-0.401338\pi\)
0.305016 + 0.952347i \(0.401338\pi\)
\(758\) −3.94452e104 −0.307658
\(759\) 2.78007e103 0.0206648
\(760\) −1.22434e104 −0.0867370
\(761\) 3.87339e103 0.0261548 0.0130774 0.999914i \(-0.495837\pi\)
0.0130774 + 0.999914i \(0.495837\pi\)
\(762\) 8.35762e102 0.00537930
\(763\) 2.10654e103 0.0129248
\(764\) −2.33562e104 −0.136614
\(765\) −2.07941e104 −0.115957
\(766\) 1.42696e105 0.758686
\(767\) −1.33741e105 −0.678006
\(768\) 7.71424e103 0.0372914
\(769\) −3.13426e105 −1.44485 −0.722426 0.691449i \(-0.756973\pi\)
−0.722426 + 0.691449i \(0.756973\pi\)
\(770\) −5.78612e103 −0.0254376
\(771\) −4.00917e103 −0.0168101
\(772\) 2.35120e105 0.940282
\(773\) −1.54663e105 −0.589975 −0.294988 0.955501i \(-0.595316\pi\)
−0.294988 + 0.955501i \(0.595316\pi\)
\(774\) 1.62509e104 0.0591335
\(775\) 3.03138e105 1.05227
\(776\) 4.79586e104 0.158823
\(777\) −2.15300e103 −0.00680264
\(778\) 4.57012e105 1.37776
\(779\) −8.90478e104 −0.256157
\(780\) 1.12843e103 0.00309756
\(781\) 2.26544e105 0.593458
\(782\) −3.48333e105 −0.870860
\(783\) −2.64916e104 −0.0632126
\(784\) 4.86271e105 1.10750
\(785\) 1.89625e105 0.412242
\(786\) −1.66319e102 −0.000345158 0
\(787\) −6.10714e105 −1.20993 −0.604965 0.796252i \(-0.706813\pi\)
−0.604965 + 0.796252i \(0.706813\pi\)
\(788\) −6.32287e105 −1.19593
\(789\) −1.37871e104 −0.0248979
\(790\) −2.36054e105 −0.407027
\(791\) −1.49680e105 −0.246446
\(792\) 7.11549e104 0.111876
\(793\) 1.83503e105 0.275531
\(794\) −1.52601e106 −2.18832
\(795\) −5.97502e101 −8.18350e−5 0
\(796\) 5.55602e105 0.726837
\(797\) −1.83409e105 −0.229188 −0.114594 0.993412i \(-0.536557\pi\)
−0.114594 + 0.993412i \(0.536557\pi\)
\(798\) −8.75259e103 −0.0104480
\(799\) −4.00823e105 −0.457084
\(800\) 1.14534e106 1.24782
\(801\) 1.49822e106 1.55952
\(802\) 7.41110e105 0.737086
\(803\) 4.82522e105 0.458563
\(804\) 3.13402e104 0.0284614
\(805\) −5.46584e104 −0.0474360
\(806\) 9.36116e105 0.776427
\(807\) 3.39849e104 0.0269402
\(808\) −4.61197e105 −0.349439
\(809\) −2.14223e105 −0.155147 −0.0775737 0.996987i \(-0.524717\pi\)
−0.0775737 + 0.996987i \(0.524717\pi\)
\(810\) −4.65876e105 −0.322528
\(811\) −1.90972e106 −1.26389 −0.631943 0.775015i \(-0.717742\pi\)
−0.631943 + 0.775015i \(0.717742\pi\)
\(812\) 2.10940e105 0.133464
\(813\) 7.64565e104 0.0462498
\(814\) −1.82701e106 −1.05669
\(815\) 5.68563e105 0.314432
\(816\) 3.14333e104 0.0166226
\(817\) 1.45969e105 0.0738170
\(818\) −1.74079e106 −0.841882
\(819\) 1.67331e105 0.0773954
\(820\) −6.86159e104 −0.0303542
\(821\) 4.47743e106 1.89454 0.947269 0.320438i \(-0.103830\pi\)
0.947269 + 0.320438i \(0.103830\pi\)
\(822\) −1.39484e105 −0.0564552
\(823\) −3.95023e106 −1.52942 −0.764712 0.644372i \(-0.777119\pi\)
−0.764712 + 0.644372i \(0.777119\pi\)
\(824\) −1.00692e105 −0.0372951
\(825\) −4.17426e104 −0.0147914
\(826\) 7.99337e105 0.270993
\(827\) 2.04734e106 0.664108 0.332054 0.943260i \(-0.392258\pi\)
0.332054 + 0.943260i \(0.392258\pi\)
\(828\) −3.56953e106 −1.10791
\(829\) 1.25356e106 0.372310 0.186155 0.982520i \(-0.440397\pi\)
0.186155 + 0.982520i \(0.440397\pi\)
\(830\) 1.31434e106 0.373559
\(831\) 8.64938e103 0.00235260
\(832\) 1.30408e106 0.339472
\(833\) 1.91008e106 0.475893
\(834\) −3.00363e105 −0.0716285
\(835\) 2.48312e105 0.0566815
\(836\) −3.39409e106 −0.741643
\(837\) 3.21097e105 0.0671672
\(838\) 6.64069e106 1.32986
\(839\) −7.25075e106 −1.39018 −0.695090 0.718922i \(-0.744636\pi\)
−0.695090 + 0.718922i \(0.744636\pi\)
\(840\) 1.27000e103 0.000233135 0
\(841\) 5.82589e105 0.102402
\(842\) 1.40661e107 2.36746
\(843\) 1.51728e105 0.0244546
\(844\) −3.99816e106 −0.617108
\(845\) 1.18820e106 0.175639
\(846\) −8.98829e106 −1.27250
\(847\) −8.11904e105 −0.110093
\(848\) −9.94930e104 −0.0129224
\(849\) −1.25534e105 −0.0156182
\(850\) 5.23021e106 0.623345
\(851\) −1.72588e107 −1.97052
\(852\) 2.64060e105 0.0288841
\(853\) −1.20325e107 −1.26100 −0.630502 0.776187i \(-0.717151\pi\)
−0.630502 + 0.776187i \(0.717151\pi\)
\(854\) −1.09675e106 −0.110127
\(855\) −4.18840e106 −0.402981
\(856\) −1.43844e106 −0.132617
\(857\) 1.24387e107 1.09894 0.549469 0.835514i \(-0.314830\pi\)
0.549469 + 0.835514i \(0.314830\pi\)
\(858\) −1.28905e105 −0.0109140
\(859\) 5.72297e106 0.464377 0.232189 0.972671i \(-0.425411\pi\)
0.232189 + 0.972671i \(0.425411\pi\)
\(860\) 1.12477e105 0.00874721
\(861\) 9.23688e103 0.000688510 0
\(862\) 2.84328e107 2.03144
\(863\) 2.04897e107 1.40327 0.701635 0.712537i \(-0.252454\pi\)
0.701635 + 0.712537i \(0.252454\pi\)
\(864\) 1.21319e106 0.0796487
\(865\) −5.63741e106 −0.354807
\(866\) −7.51831e106 −0.453646
\(867\) −3.97122e105 −0.0229735
\(868\) −2.55674e106 −0.141813
\(869\) 1.23225e107 0.655356
\(870\) −2.00527e105 −0.0102264
\(871\) −1.17770e107 −0.575932
\(872\) −3.92355e105 −0.0184004
\(873\) 1.64064e107 0.737894
\(874\) −7.01620e107 −3.02646
\(875\) 1.69081e106 0.0699520
\(876\) 5.62429e105 0.0223186
\(877\) 3.53292e107 1.34477 0.672386 0.740201i \(-0.265270\pi\)
0.672386 + 0.740201i \(0.265270\pi\)
\(878\) −5.07303e107 −1.85233
\(879\) −2.04317e105 −0.00715666
\(880\) 4.18550e106 0.140647
\(881\) −3.92634e107 −1.26581 −0.632903 0.774231i \(-0.718137\pi\)
−0.632903 + 0.774231i \(0.718137\pi\)
\(882\) 4.28327e107 1.32487
\(883\) 7.97346e106 0.236636 0.118318 0.992976i \(-0.462250\pi\)
0.118318 + 0.992976i \(0.462250\pi\)
\(884\) 7.38074e106 0.210180
\(885\) −3.47246e105 −0.00948871
\(886\) −2.46943e107 −0.647538
\(887\) 4.80107e107 1.20816 0.604082 0.796922i \(-0.293540\pi\)
0.604082 + 0.796922i \(0.293540\pi\)
\(888\) 4.01009e105 0.00968459
\(889\) 8.57771e105 0.0198819
\(890\) 2.26918e107 0.504817
\(891\) 2.43197e107 0.519304
\(892\) 5.95855e107 1.22130
\(893\) −8.07346e107 −1.58848
\(894\) −1.08560e106 −0.0205045
\(895\) −1.01785e107 −0.184562
\(896\) 3.68496e106 0.0641490
\(897\) −1.21769e106 −0.0203523
\(898\) 1.38379e107 0.222068
\(899\) −7.60190e107 −1.17137
\(900\) 5.35963e107 0.793018
\(901\) −3.90810e105 −0.00555279
\(902\) 7.83827e106 0.106950
\(903\) −1.51413e104 −0.000198408 0
\(904\) 2.78787e107 0.350853
\(905\) −1.50865e106 −0.0182354
\(906\) −3.45561e106 −0.0401186
\(907\) 9.97593e107 1.11247 0.556234 0.831026i \(-0.312246\pi\)
0.556234 + 0.831026i \(0.312246\pi\)
\(908\) −2.07605e107 −0.222385
\(909\) −1.57773e108 −1.62350
\(910\) 2.53437e106 0.0250530
\(911\) 6.39729e107 0.607541 0.303770 0.952745i \(-0.401754\pi\)
0.303770 + 0.952745i \(0.401754\pi\)
\(912\) 6.33136e106 0.0577677
\(913\) −6.86114e107 −0.601469
\(914\) −1.72805e108 −1.45553
\(915\) 4.76447e105 0.00385607
\(916\) −9.26654e107 −0.720664
\(917\) −1.70699e105 −0.00127570
\(918\) 5.54006e106 0.0397884
\(919\) 7.62885e107 0.526554 0.263277 0.964720i \(-0.415197\pi\)
0.263277 + 0.964720i \(0.415197\pi\)
\(920\) 1.01805e107 0.0675323
\(921\) 5.39106e106 0.0343714
\(922\) 2.68024e108 1.64246
\(923\) −9.92282e107 −0.584485
\(924\) 3.52067e105 0.00199342
\(925\) 2.59139e108 1.41046
\(926\) 3.01306e108 1.57655
\(927\) −3.44463e107 −0.173274
\(928\) −2.87221e108 −1.38904
\(929\) −1.19972e108 −0.557836 −0.278918 0.960315i \(-0.589976\pi\)
−0.278918 + 0.960315i \(0.589976\pi\)
\(930\) 2.43053e106 0.0108661
\(931\) 3.84732e108 1.65385
\(932\) 3.11402e108 1.28718
\(933\) −1.19137e107 −0.0473553
\(934\) −5.71328e108 −2.18386
\(935\) 1.64407e107 0.0604362
\(936\) −3.11665e107 −0.110184
\(937\) −4.93029e108 −1.67640 −0.838199 0.545364i \(-0.816392\pi\)
−0.838199 + 0.545364i \(0.816392\pi\)
\(938\) 7.03880e107 0.230195
\(939\) 1.76018e106 0.00553684
\(940\) −6.22102e107 −0.188233
\(941\) −2.57654e108 −0.749922 −0.374961 0.927041i \(-0.622344\pi\)
−0.374961 + 0.927041i \(0.622344\pi\)
\(942\) −2.52488e107 −0.0706942
\(943\) 7.40441e107 0.199441
\(944\) −5.78216e108 −1.49835
\(945\) 8.69314e105 0.00216728
\(946\) −1.28487e107 −0.0308199
\(947\) 5.94015e108 1.37095 0.685477 0.728094i \(-0.259594\pi\)
0.685477 + 0.728094i \(0.259594\pi\)
\(948\) 1.43632e107 0.0318967
\(949\) −2.11349e108 −0.451630
\(950\) 1.05348e109 2.16628
\(951\) −1.11880e107 −0.0221393
\(952\) 8.30670e106 0.0158190
\(953\) 7.40128e108 1.35649 0.678244 0.734837i \(-0.262741\pi\)
0.678244 + 0.734837i \(0.262741\pi\)
\(954\) −8.76375e106 −0.0154587
\(955\) 2.27880e107 0.0386886
\(956\) 8.98161e107 0.146771
\(957\) 1.04679e107 0.0164655
\(958\) −1.06489e109 −1.61237
\(959\) −1.43158e108 −0.208658
\(960\) 3.38592e106 0.00475091
\(961\) 1.81111e108 0.244648
\(962\) 8.00244e108 1.04072
\(963\) −4.92085e108 −0.616142
\(964\) −8.97930e108 −1.08251
\(965\) −2.29400e108 −0.266285
\(966\) 7.27786e106 0.00813464
\(967\) 6.04627e108 0.650761 0.325381 0.945583i \(-0.394508\pi\)
0.325381 + 0.945583i \(0.394508\pi\)
\(968\) 1.51222e108 0.156734
\(969\) 2.48697e107 0.0248229
\(970\) 2.48488e108 0.238857
\(971\) −1.02330e108 −0.0947325 −0.0473663 0.998878i \(-0.515083\pi\)
−0.0473663 + 0.998878i \(0.515083\pi\)
\(972\) 8.51701e107 0.0759396
\(973\) −3.08273e108 −0.264738
\(974\) −1.10338e109 −0.912690
\(975\) 1.82836e107 0.0145678
\(976\) 7.93355e108 0.608904
\(977\) −8.76474e108 −0.648019 −0.324009 0.946054i \(-0.605031\pi\)
−0.324009 + 0.946054i \(0.605031\pi\)
\(978\) −7.57051e107 −0.0539209
\(979\) −1.18456e109 −0.812809
\(980\) 2.96456e108 0.195978
\(981\) −1.34223e108 −0.0854886
\(982\) 3.33332e109 2.04554
\(983\) −1.92093e109 −1.13582 −0.567908 0.823092i \(-0.692247\pi\)
−0.567908 + 0.823092i \(0.692247\pi\)
\(984\) −1.72042e106 −0.000980199 0
\(985\) 6.16905e108 0.338685
\(986\) −1.31160e109 −0.693893
\(987\) 8.37455e106 0.00426958
\(988\) 1.48664e109 0.730429
\(989\) −1.21375e108 −0.0574729
\(990\) 3.68676e108 0.168252
\(991\) 4.65440e108 0.204727 0.102363 0.994747i \(-0.467360\pi\)
0.102363 + 0.994747i \(0.467360\pi\)
\(992\) 3.48132e109 1.47594
\(993\) 1.35607e107 0.00554161
\(994\) 5.93062e108 0.233613
\(995\) −5.42085e108 −0.205838
\(996\) −7.99737e107 −0.0292740
\(997\) 4.58521e109 1.61803 0.809015 0.587788i \(-0.200001\pi\)
0.809015 + 0.587788i \(0.200001\pi\)
\(998\) −6.11733e109 −2.08112
\(999\) 2.74492e108 0.0900303
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.1.5 5
3.2 odd 2 9.74.a.a.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.74.a.a.1.5 5 1.1 even 1 trivial
9.74.a.a.1.1 5 3.2 odd 2