Properties

Label 1.76.a.a.1.1
Level $1$
Weight $76$
Character 1.1
Self dual yes
Analytic conductor $35.623$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 76 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.6228392822\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 3 x^{5} - 38457853073924058692 x^{4} - 10276556354621685339901678086 x^{3} + 371187556674475060057870954681799784505 x^{2} + 52686123927652036687598761277591247931691204025 x - 675344021115865838575279495800656435684060652010336995750\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.40594e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.26741e11 q^{2} -1.51453e18 q^{3} +6.89808e22 q^{4} -4.33451e25 q^{5} +4.94860e29 q^{6} +4.24638e31 q^{7} -1.01949e34 q^{8} +1.68554e36 q^{9} +O(q^{10})\) \(q-3.26741e11 q^{2} -1.51453e18 q^{3} +6.89808e22 q^{4} -4.33451e25 q^{5} +4.94860e29 q^{6} +4.24638e31 q^{7} -1.01949e34 q^{8} +1.68554e36 q^{9} +1.41626e37 q^{10} +1.56603e38 q^{11} -1.04474e41 q^{12} -1.88327e41 q^{13} -1.38747e43 q^{14} +6.56475e43 q^{15} +7.25086e44 q^{16} +9.86838e45 q^{17} -5.50735e47 q^{18} -1.40944e47 q^{19} -2.98998e48 q^{20} -6.43128e49 q^{21} -5.11687e49 q^{22} +8.97012e50 q^{23} +1.54406e52 q^{24} -2.45910e52 q^{25} +6.15343e52 q^{26} -1.63156e54 q^{27} +2.92919e54 q^{28} +7.48449e54 q^{29} -2.14497e55 q^{30} +9.83848e55 q^{31} +1.48239e56 q^{32} -2.37180e56 q^{33} -3.22441e57 q^{34} -1.84060e57 q^{35} +1.16270e59 q^{36} -4.42368e58 q^{37} +4.60523e58 q^{38} +2.85228e59 q^{39} +4.41901e59 q^{40} +3.18294e60 q^{41} +2.10136e61 q^{42} -2.58944e61 q^{43} +1.08026e61 q^{44} -7.30598e61 q^{45} -2.93091e62 q^{46} -4.72886e61 q^{47} -1.09817e63 q^{48} -6.08688e62 q^{49} +8.03489e63 q^{50} -1.49460e64 q^{51} -1.29910e64 q^{52} -7.75824e64 q^{53} +5.33099e65 q^{54} -6.78797e63 q^{55} -4.32917e65 q^{56} +2.13465e65 q^{57} -2.44549e66 q^{58} -8.17255e64 q^{59} +4.52842e66 q^{60} -6.09863e66 q^{61} -3.21464e67 q^{62} +7.15745e67 q^{63} -7.58287e67 q^{64} +8.16306e66 q^{65} +7.74966e67 q^{66} +4.31126e68 q^{67} +6.80729e68 q^{68} -1.35855e69 q^{69} +6.01399e68 q^{70} +2.46110e69 q^{71} -1.71840e70 q^{72} -4.09634e69 q^{73} +1.44540e70 q^{74} +3.72438e70 q^{75} -9.72245e69 q^{76} +6.64997e69 q^{77} -9.31956e70 q^{78} +9.26377e69 q^{79} -3.14289e70 q^{80} +1.44580e72 q^{81} -1.04000e72 q^{82} -2.78206e69 q^{83} -4.43635e72 q^{84} -4.27746e71 q^{85} +8.46075e72 q^{86} -1.13355e73 q^{87} -1.59656e72 q^{88} +1.96684e73 q^{89} +2.38716e73 q^{90} -7.99710e72 q^{91} +6.18767e73 q^{92} -1.49007e74 q^{93} +1.54511e73 q^{94} +6.10924e72 q^{95} -2.24512e74 q^{96} +2.01886e74 q^{97} +1.98883e74 q^{98} +2.63961e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + O(q^{10}) \) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + \)\(13\!\cdots\!60\)\(q^{10} - \)\(94\!\cdots\!88\)\(q^{11} - \)\(11\!\cdots\!80\)\(q^{12} + \)\(53\!\cdots\!20\)\(q^{13} + \)\(82\!\cdots\!76\)\(q^{14} - \)\(30\!\cdots\!80\)\(q^{15} + \)\(26\!\cdots\!16\)\(q^{16} + \)\(18\!\cdots\!80\)\(q^{17} - \)\(43\!\cdots\!40\)\(q^{18} + \)\(10\!\cdots\!80\)\(q^{19} + \)\(92\!\cdots\!80\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(15\!\cdots\!20\)\(q^{22} + \)\(15\!\cdots\!80\)\(q^{23} - \)\(76\!\cdots\!60\)\(q^{24} + \)\(19\!\cdots\!50\)\(q^{25} + \)\(11\!\cdots\!52\)\(q^{26} - \)\(10\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!20\)\(q^{28} + \)\(14\!\cdots\!20\)\(q^{29} - \)\(25\!\cdots\!80\)\(q^{30} - \)\(41\!\cdots\!88\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(59\!\cdots\!20\)\(q^{33} + \)\(30\!\cdots\!56\)\(q^{34} + \)\(27\!\cdots\!60\)\(q^{35} + \)\(17\!\cdots\!16\)\(q^{36} + \)\(98\!\cdots\!40\)\(q^{37} + \)\(12\!\cdots\!80\)\(q^{38} + \)\(24\!\cdots\!44\)\(q^{39} + \)\(88\!\cdots\!00\)\(q^{40} + \)\(50\!\cdots\!12\)\(q^{41} + \)\(43\!\cdots\!80\)\(q^{42} + \)\(27\!\cdots\!00\)\(q^{43} - \)\(86\!\cdots\!44\)\(q^{44} - \)\(23\!\cdots\!80\)\(q^{45} - \)\(82\!\cdots\!88\)\(q^{46} - \)\(13\!\cdots\!80\)\(q^{47} - \)\(82\!\cdots\!20\)\(q^{48} - \)\(57\!\cdots\!42\)\(q^{49} + \)\(31\!\cdots\!00\)\(q^{50} + \)\(28\!\cdots\!32\)\(q^{51} + \)\(41\!\cdots\!00\)\(q^{52} + \)\(64\!\cdots\!60\)\(q^{53} + \)\(78\!\cdots\!80\)\(q^{54} + \)\(43\!\cdots\!20\)\(q^{55} + \)\(28\!\cdots\!20\)\(q^{56} - \)\(67\!\cdots\!40\)\(q^{57} - \)\(17\!\cdots\!80\)\(q^{58} - \)\(24\!\cdots\!60\)\(q^{59} - \)\(31\!\cdots\!40\)\(q^{60} - \)\(25\!\cdots\!88\)\(q^{61} - \)\(29\!\cdots\!80\)\(q^{62} + \)\(42\!\cdots\!40\)\(q^{63} + \)\(47\!\cdots\!48\)\(q^{64} + \)\(12\!\cdots\!20\)\(q^{65} + \)\(93\!\cdots\!84\)\(q^{66} + \)\(95\!\cdots\!80\)\(q^{67} + \)\(12\!\cdots\!60\)\(q^{68} - \)\(14\!\cdots\!36\)\(q^{69} - \)\(34\!\cdots\!40\)\(q^{70} - \)\(25\!\cdots\!88\)\(q^{71} - \)\(21\!\cdots\!60\)\(q^{72} - \)\(30\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!84\)\(q^{74} + \)\(19\!\cdots\!00\)\(q^{75} + \)\(10\!\cdots\!40\)\(q^{76} + \)\(15\!\cdots\!00\)\(q^{77} + \)\(13\!\cdots\!00\)\(q^{78} + \)\(11\!\cdots\!20\)\(q^{79} + \)\(12\!\cdots\!60\)\(q^{80} + \)\(29\!\cdots\!86\)\(q^{81} - \)\(25\!\cdots\!80\)\(q^{82} - \)\(79\!\cdots\!60\)\(q^{83} - \)\(91\!\cdots\!64\)\(q^{84} - \)\(36\!\cdots\!40\)\(q^{85} + \)\(72\!\cdots\!32\)\(q^{86} - \)\(14\!\cdots\!60\)\(q^{87} - \)\(48\!\cdots\!60\)\(q^{88} + \)\(53\!\cdots\!60\)\(q^{89} + \)\(85\!\cdots\!20\)\(q^{90} + \)\(34\!\cdots\!32\)\(q^{91} + \)\(18\!\cdots\!80\)\(q^{92} - \)\(16\!\cdots\!80\)\(q^{93} - \)\(29\!\cdots\!04\)\(q^{94} + \)\(19\!\cdots\!00\)\(q^{95} - \)\(89\!\cdots\!08\)\(q^{96} - \)\(74\!\cdots\!80\)\(q^{97} - \)\(16\!\cdots\!20\)\(q^{98} - \)\(18\!\cdots\!36\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.26741e11 −1.68104 −0.840522 0.541778i \(-0.817751\pi\)
−0.840522 + 0.541778i \(0.817751\pi\)
\(3\) −1.51453e18 −1.94192 −0.970960 0.239242i \(-0.923101\pi\)
−0.970960 + 0.239242i \(0.923101\pi\)
\(4\) 6.89808e22 1.82591
\(5\) −4.33451e25 −0.266419 −0.133209 0.991088i \(-0.542528\pi\)
−0.133209 + 0.991088i \(0.542528\pi\)
\(6\) 4.94860e29 3.26445
\(7\) 4.24638e31 0.864655 0.432327 0.901717i \(-0.357692\pi\)
0.432327 + 0.901717i \(0.357692\pi\)
\(8\) −1.01949e34 −1.38839
\(9\) 1.68554e36 2.77105
\(10\) 1.41626e37 0.447861
\(11\) 1.56603e38 0.138859 0.0694296 0.997587i \(-0.477882\pi\)
0.0694296 + 0.997587i \(0.477882\pi\)
\(12\) −1.04474e41 −3.54577
\(13\) −1.88327e41 −0.317715 −0.158857 0.987302i \(-0.550781\pi\)
−0.158857 + 0.987302i \(0.550781\pi\)
\(14\) −1.38747e43 −1.45352
\(15\) 6.56475e43 0.517364
\(16\) 7.25086e44 0.508031
\(17\) 9.86838e45 0.711888 0.355944 0.934507i \(-0.384159\pi\)
0.355944 + 0.934507i \(0.384159\pi\)
\(18\) −5.50735e47 −4.65826
\(19\) −1.40944e47 −0.156959 −0.0784797 0.996916i \(-0.525007\pi\)
−0.0784797 + 0.996916i \(0.525007\pi\)
\(20\) −2.98998e48 −0.486456
\(21\) −6.43128e49 −1.67909
\(22\) −5.11687e49 −0.233428
\(23\) 8.97012e50 0.772689 0.386344 0.922355i \(-0.373738\pi\)
0.386344 + 0.922355i \(0.373738\pi\)
\(24\) 1.54406e52 2.69614
\(25\) −2.45910e52 −0.929021
\(26\) 6.15343e52 0.534093
\(27\) −1.63156e54 −3.43924
\(28\) 2.92919e54 1.57878
\(29\) 7.48449e54 1.08202 0.541012 0.841015i \(-0.318041\pi\)
0.541012 + 0.841015i \(0.318041\pi\)
\(30\) −2.14497e55 −0.869711
\(31\) 9.83848e55 1.16645 0.583223 0.812312i \(-0.301791\pi\)
0.583223 + 0.812312i \(0.301791\pi\)
\(32\) 1.48239e56 0.534365
\(33\) −2.37180e56 −0.269653
\(34\) −3.22441e57 −1.19671
\(35\) −1.84060e57 −0.230360
\(36\) 1.16270e59 5.05969
\(37\) −4.42368e58 −0.689000 −0.344500 0.938786i \(-0.611952\pi\)
−0.344500 + 0.938786i \(0.611952\pi\)
\(38\) 4.60523e58 0.263856
\(39\) 2.85228e59 0.616977
\(40\) 4.41901e59 0.369892
\(41\) 3.18294e60 1.05544 0.527721 0.849418i \(-0.323047\pi\)
0.527721 + 0.849418i \(0.323047\pi\)
\(42\) 2.10136e61 2.82262
\(43\) −2.58944e61 −1.43926 −0.719628 0.694360i \(-0.755688\pi\)
−0.719628 + 0.694360i \(0.755688\pi\)
\(44\) 1.08026e61 0.253544
\(45\) −7.30598e61 −0.738260
\(46\) −2.93091e62 −1.29892
\(47\) −4.72886e61 −0.0935593 −0.0467797 0.998905i \(-0.514896\pi\)
−0.0467797 + 0.998905i \(0.514896\pi\)
\(48\) −1.09817e63 −0.986555
\(49\) −6.08688e62 −0.252372
\(50\) 8.03489e63 1.56173
\(51\) −1.49460e64 −1.38243
\(52\) −1.29910e64 −0.580118
\(53\) −7.75824e64 −1.69597 −0.847985 0.530020i \(-0.822184\pi\)
−0.847985 + 0.530020i \(0.822184\pi\)
\(54\) 5.33099e65 5.78152
\(55\) −6.78797e63 −0.0369947
\(56\) −4.32917e65 −1.20048
\(57\) 2.13465e65 0.304803
\(58\) −2.44549e66 −1.81893
\(59\) −8.17255e64 −0.0320190 −0.0160095 0.999872i \(-0.505096\pi\)
−0.0160095 + 0.999872i \(0.505096\pi\)
\(60\) 4.52842e66 0.944658
\(61\) −6.09863e66 −0.684484 −0.342242 0.939612i \(-0.611186\pi\)
−0.342242 + 0.939612i \(0.611186\pi\)
\(62\) −3.21464e67 −1.96085
\(63\) 7.15745e67 2.39600
\(64\) −7.58287e67 −1.40632
\(65\) 8.16306e66 0.0846451
\(66\) 7.74966e67 0.453299
\(67\) 4.31126e68 1.43483 0.717413 0.696648i \(-0.245326\pi\)
0.717413 + 0.696648i \(0.245326\pi\)
\(68\) 6.80729e68 1.29984
\(69\) −1.35855e69 −1.50050
\(70\) 6.01399e68 0.387245
\(71\) 2.46110e69 0.930981 0.465491 0.885053i \(-0.345878\pi\)
0.465491 + 0.885053i \(0.345878\pi\)
\(72\) −1.71840e70 −3.84729
\(73\) −4.09634e69 −0.546749 −0.273375 0.961908i \(-0.588140\pi\)
−0.273375 + 0.961908i \(0.588140\pi\)
\(74\) 1.44540e70 1.15824
\(75\) 3.72438e70 1.80408
\(76\) −9.72245e69 −0.286593
\(77\) 6.64997e69 0.120065
\(78\) −9.31956e70 −1.03716
\(79\) 9.26377e69 0.0639399 0.0319699 0.999489i \(-0.489822\pi\)
0.0319699 + 0.999489i \(0.489822\pi\)
\(80\) −3.14289e70 −0.135349
\(81\) 1.44580e72 3.90768
\(82\) −1.04000e72 −1.77424
\(83\) −2.78206e69 −0.00301257 −0.00150629 0.999999i \(-0.500479\pi\)
−0.00150629 + 0.999999i \(0.500479\pi\)
\(84\) −4.43635e72 −3.06586
\(85\) −4.27746e71 −0.189660
\(86\) 8.46075e72 2.41945
\(87\) −1.13355e73 −2.10121
\(88\) −1.59656e72 −0.192790
\(89\) 1.96684e73 1.55469 0.777346 0.629073i \(-0.216565\pi\)
0.777346 + 0.629073i \(0.216565\pi\)
\(90\) 2.38716e73 1.24105
\(91\) −7.99710e72 −0.274714
\(92\) 6.18767e73 1.41086
\(93\) −1.49007e74 −2.26514
\(94\) 1.54511e73 0.157277
\(95\) 6.10924e72 0.0418169
\(96\) −2.24512e74 −1.03769
\(97\) 2.01886e74 0.632653 0.316326 0.948650i \(-0.397551\pi\)
0.316326 + 0.948650i \(0.397551\pi\)
\(98\) 1.98883e74 0.424249
\(99\) 2.63961e74 0.384786
\(100\) −1.69631e75 −1.69631
\(101\) −1.56337e75 −1.07649 −0.538247 0.842787i \(-0.680913\pi\)
−0.538247 + 0.842787i \(0.680913\pi\)
\(102\) 4.88347e75 2.32392
\(103\) −5.07128e74 −0.167387 −0.0836935 0.996492i \(-0.526672\pi\)
−0.0836935 + 0.996492i \(0.526672\pi\)
\(104\) 1.91999e75 0.441111
\(105\) 2.78764e75 0.447341
\(106\) 2.53494e76 2.85100
\(107\) −8.29288e75 −0.655864 −0.327932 0.944701i \(-0.606352\pi\)
−0.327932 + 0.944701i \(0.606352\pi\)
\(108\) −1.12547e77 −6.27974
\(109\) 4.14553e76 1.63714 0.818570 0.574406i \(-0.194767\pi\)
0.818570 + 0.574406i \(0.194767\pi\)
\(110\) 2.21791e75 0.0621897
\(111\) 6.69980e76 1.33798
\(112\) 3.07899e76 0.439271
\(113\) −1.53804e76 −0.157227 −0.0786134 0.996905i \(-0.525049\pi\)
−0.0786134 + 0.996905i \(0.525049\pi\)
\(114\) −6.97476e76 −0.512386
\(115\) −3.88811e76 −0.205859
\(116\) 5.16286e77 1.97568
\(117\) −3.17433e77 −0.880405
\(118\) 2.67031e76 0.0538253
\(119\) 4.19049e77 0.615537
\(120\) −6.69272e77 −0.718301
\(121\) −1.24737e78 −0.980718
\(122\) 1.99267e78 1.15065
\(123\) −4.82067e78 −2.04958
\(124\) 6.78667e78 2.12982
\(125\) 2.21323e78 0.513927
\(126\) −2.33863e79 −4.02779
\(127\) 1.95181e78 0.249918 0.124959 0.992162i \(-0.460120\pi\)
0.124959 + 0.992162i \(0.460120\pi\)
\(128\) 1.91760e79 1.82972
\(129\) 3.92178e79 2.79492
\(130\) −2.66721e78 −0.142292
\(131\) −2.48929e78 −0.0996328 −0.0498164 0.998758i \(-0.515864\pi\)
−0.0498164 + 0.998758i \(0.515864\pi\)
\(132\) −1.63609e79 −0.492362
\(133\) −5.98503e78 −0.135716
\(134\) −1.40867e80 −2.41201
\(135\) 7.07202e79 0.916278
\(136\) −1.00608e80 −0.988375
\(137\) −1.62508e80 −1.21298 −0.606491 0.795090i \(-0.707423\pi\)
−0.606491 + 0.795090i \(0.707423\pi\)
\(138\) 4.43895e80 2.52240
\(139\) 2.33640e80 1.01273 0.506364 0.862320i \(-0.330989\pi\)
0.506364 + 0.862320i \(0.330989\pi\)
\(140\) −1.26966e80 −0.420616
\(141\) 7.16201e79 0.181685
\(142\) −8.04142e80 −1.56502
\(143\) −2.94926e79 −0.0441176
\(144\) 1.22216e81 1.40778
\(145\) −3.24416e80 −0.288272
\(146\) 1.33844e81 0.919110
\(147\) 9.21877e80 0.490087
\(148\) −3.05149e81 −1.25805
\(149\) 3.44890e81 1.10457 0.552287 0.833654i \(-0.313755\pi\)
0.552287 + 0.833654i \(0.313755\pi\)
\(150\) −1.21691e82 −3.03274
\(151\) −2.98374e81 −0.579597 −0.289798 0.957088i \(-0.593588\pi\)
−0.289798 + 0.957088i \(0.593588\pi\)
\(152\) 1.43692e81 0.217920
\(153\) 1.66335e82 1.97268
\(154\) −2.17282e81 −0.201835
\(155\) −4.26450e81 −0.310763
\(156\) 1.96752e82 1.12654
\(157\) −2.36792e82 −1.06692 −0.533458 0.845826i \(-0.679108\pi\)
−0.533458 + 0.845826i \(0.679108\pi\)
\(158\) −3.02685e81 −0.107486
\(159\) 1.17501e83 3.29344
\(160\) −6.42542e81 −0.142365
\(161\) 3.80906e82 0.668109
\(162\) −4.72401e83 −6.56898
\(163\) 5.73833e82 0.633506 0.316753 0.948508i \(-0.397407\pi\)
0.316753 + 0.948508i \(0.397407\pi\)
\(164\) 2.19562e83 1.92714
\(165\) 1.02806e82 0.0718407
\(166\) 9.09012e80 0.00506426
\(167\) −7.47244e82 −0.332349 −0.166175 0.986096i \(-0.553142\pi\)
−0.166175 + 0.986096i \(0.553142\pi\)
\(168\) 6.55666e83 2.33123
\(169\) −3.15892e83 −0.899057
\(170\) 1.39762e83 0.318827
\(171\) −2.37567e83 −0.434943
\(172\) −1.78621e84 −2.62795
\(173\) 7.78810e83 0.921940 0.460970 0.887416i \(-0.347502\pi\)
0.460970 + 0.887416i \(0.347502\pi\)
\(174\) 3.70377e84 3.53222
\(175\) −1.04423e84 −0.803283
\(176\) 1.13551e83 0.0705448
\(177\) 1.23776e83 0.0621782
\(178\) −6.42648e84 −2.61351
\(179\) 3.91485e84 1.29041 0.645203 0.764011i \(-0.276773\pi\)
0.645203 + 0.764011i \(0.276773\pi\)
\(180\) −5.03973e84 −1.34799
\(181\) −4.40838e84 −0.957928 −0.478964 0.877835i \(-0.658987\pi\)
−0.478964 + 0.877835i \(0.658987\pi\)
\(182\) 2.61298e84 0.461806
\(183\) 9.23657e84 1.32921
\(184\) −9.14499e84 −1.07279
\(185\) 1.91745e84 0.183562
\(186\) 4.86867e85 3.80781
\(187\) 1.54542e84 0.0988521
\(188\) −3.26201e84 −0.170831
\(189\) −6.92824e85 −2.97376
\(190\) −1.99614e84 −0.0702960
\(191\) −2.54828e85 −0.737047 −0.368524 0.929618i \(-0.620137\pi\)
−0.368524 + 0.929618i \(0.620137\pi\)
\(192\) 1.14845e86 2.73096
\(193\) −6.92114e85 −1.35450 −0.677250 0.735753i \(-0.736828\pi\)
−0.677250 + 0.735753i \(0.736828\pi\)
\(194\) −6.59643e85 −1.06352
\(195\) −1.23632e85 −0.164374
\(196\) −4.19878e85 −0.460808
\(197\) 1.15851e86 1.05055 0.525276 0.850932i \(-0.323962\pi\)
0.525276 + 0.850932i \(0.323962\pi\)
\(198\) −8.62468e85 −0.646842
\(199\) 2.78135e86 1.72689 0.863445 0.504444i \(-0.168302\pi\)
0.863445 + 0.504444i \(0.168302\pi\)
\(200\) 2.50704e86 1.28984
\(201\) −6.52955e86 −2.78632
\(202\) 5.10818e86 1.80963
\(203\) 3.17820e86 0.935578
\(204\) −1.03099e87 −2.52419
\(205\) −1.37965e86 −0.281189
\(206\) 1.65700e86 0.281385
\(207\) 1.51195e87 2.14116
\(208\) −1.36553e86 −0.161409
\(209\) −2.20723e85 −0.0217953
\(210\) −9.10838e86 −0.751999
\(211\) 6.21488e86 0.429379 0.214689 0.976682i \(-0.431126\pi\)
0.214689 + 0.976682i \(0.431126\pi\)
\(212\) −5.35170e87 −3.09668
\(213\) −3.72741e87 −1.80789
\(214\) 2.70963e87 1.10254
\(215\) 1.12239e87 0.383445
\(216\) 1.66337e88 4.77500
\(217\) 4.17780e87 1.00857
\(218\) −1.35451e88 −2.75211
\(219\) 6.20403e87 1.06174
\(220\) −4.68240e86 −0.0675489
\(221\) −1.85849e87 −0.226177
\(222\) −2.18910e88 −2.24921
\(223\) 1.14012e88 0.989737 0.494869 0.868968i \(-0.335216\pi\)
0.494869 + 0.868968i \(0.335216\pi\)
\(224\) 6.29479e87 0.462041
\(225\) −4.14491e88 −2.57437
\(226\) 5.02541e87 0.264305
\(227\) 2.58517e88 1.15218 0.576090 0.817386i \(-0.304578\pi\)
0.576090 + 0.817386i \(0.304578\pi\)
\(228\) 1.47250e88 0.556541
\(229\) 6.20331e87 0.198973 0.0994863 0.995039i \(-0.468280\pi\)
0.0994863 + 0.995039i \(0.468280\pi\)
\(230\) 1.27040e88 0.346057
\(231\) −1.00716e88 −0.233157
\(232\) −7.63040e88 −1.50227
\(233\) 4.08817e88 0.684986 0.342493 0.939520i \(-0.388729\pi\)
0.342493 + 0.939520i \(0.388729\pi\)
\(234\) 1.03718e89 1.48000
\(235\) 2.04973e87 0.0249259
\(236\) −5.63749e87 −0.0584637
\(237\) −1.40303e88 −0.124166
\(238\) −1.36921e89 −1.03474
\(239\) 5.69769e88 0.367941 0.183970 0.982932i \(-0.441105\pi\)
0.183970 + 0.982932i \(0.441105\pi\)
\(240\) 4.76001e88 0.262837
\(241\) 1.40344e89 0.663064 0.331532 0.943444i \(-0.392435\pi\)
0.331532 + 0.943444i \(0.392435\pi\)
\(242\) 4.07567e89 1.64863
\(243\) −1.19728e90 −4.14916
\(244\) −4.20688e89 −1.24980
\(245\) 2.63836e88 0.0672366
\(246\) 1.57511e90 3.44544
\(247\) 2.65436e88 0.0498683
\(248\) −1.00303e90 −1.61948
\(249\) 4.21351e87 0.00585017
\(250\) −7.23154e89 −0.863934
\(251\) −1.01537e89 −0.104439 −0.0522193 0.998636i \(-0.516629\pi\)
−0.0522193 + 0.998636i \(0.516629\pi\)
\(252\) 4.93727e90 4.37488
\(253\) 1.40475e89 0.107295
\(254\) −6.37736e89 −0.420123
\(255\) 6.47834e89 0.368305
\(256\) −3.40088e90 −1.66952
\(257\) 1.81313e90 0.769018 0.384509 0.923121i \(-0.374371\pi\)
0.384509 + 0.923121i \(0.374371\pi\)
\(258\) −1.28141e91 −4.69838
\(259\) −1.87846e90 −0.595747
\(260\) 5.63095e89 0.154554
\(261\) 1.26154e91 2.99835
\(262\) 8.13354e89 0.167487
\(263\) 3.47473e90 0.620270 0.310135 0.950693i \(-0.399626\pi\)
0.310135 + 0.950693i \(0.399626\pi\)
\(264\) 2.41804e90 0.374383
\(265\) 3.36281e90 0.451838
\(266\) 1.95556e90 0.228144
\(267\) −2.97885e91 −3.01909
\(268\) 2.97395e91 2.61986
\(269\) −1.34158e91 −1.02779 −0.513897 0.857852i \(-0.671799\pi\)
−0.513897 + 0.857852i \(0.671799\pi\)
\(270\) −2.31072e91 −1.54030
\(271\) 2.32034e91 1.34649 0.673246 0.739418i \(-0.264899\pi\)
0.673246 + 0.739418i \(0.264899\pi\)
\(272\) 7.15542e90 0.361661
\(273\) 1.21119e91 0.533472
\(274\) 5.30982e91 2.03908
\(275\) −3.85102e90 −0.129003
\(276\) −9.37142e91 −2.73977
\(277\) −5.73199e91 −1.46324 −0.731618 0.681715i \(-0.761235\pi\)
−0.731618 + 0.681715i \(0.761235\pi\)
\(278\) −7.63398e91 −1.70244
\(279\) 1.65831e92 3.23228
\(280\) 1.87648e91 0.319829
\(281\) −6.46798e91 −0.964454 −0.482227 0.876046i \(-0.660172\pi\)
−0.482227 + 0.876046i \(0.660172\pi\)
\(282\) −2.34012e91 −0.305420
\(283\) −7.40884e91 −0.846757 −0.423379 0.905953i \(-0.639156\pi\)
−0.423379 + 0.905953i \(0.639156\pi\)
\(284\) 1.69769e92 1.69989
\(285\) −9.25263e90 −0.0812051
\(286\) 9.63646e90 0.0741637
\(287\) 1.35160e92 0.912593
\(288\) 2.49862e92 1.48075
\(289\) −9.47777e91 −0.493216
\(290\) 1.06000e92 0.484597
\(291\) −3.05762e92 −1.22856
\(292\) −2.82569e92 −0.998314
\(293\) −1.11299e92 −0.345903 −0.172951 0.984930i \(-0.555330\pi\)
−0.172951 + 0.984930i \(0.555330\pi\)
\(294\) −3.01215e92 −0.823857
\(295\) 3.54240e90 0.00853045
\(296\) 4.50992e92 0.956598
\(297\) −2.55508e92 −0.477570
\(298\) −1.12690e93 −1.85684
\(299\) −1.68932e92 −0.245495
\(300\) 2.56911e93 3.29409
\(301\) −1.09957e93 −1.24446
\(302\) 9.74911e92 0.974327
\(303\) 2.36778e93 2.09046
\(304\) −1.02197e92 −0.0797402
\(305\) 2.64345e92 0.182359
\(306\) −5.43486e93 −3.31616
\(307\) 5.54198e92 0.299210 0.149605 0.988746i \(-0.452200\pi\)
0.149605 + 0.988746i \(0.452200\pi\)
\(308\) 4.58720e92 0.219228
\(309\) 7.68062e92 0.325052
\(310\) 1.39339e93 0.522406
\(311\) −2.52122e93 −0.837715 −0.418858 0.908052i \(-0.637569\pi\)
−0.418858 + 0.908052i \(0.637569\pi\)
\(312\) −2.90788e93 −0.856602
\(313\) 2.94579e93 0.769643 0.384822 0.922991i \(-0.374263\pi\)
0.384822 + 0.922991i \(0.374263\pi\)
\(314\) 7.73697e93 1.79353
\(315\) −3.10240e93 −0.638340
\(316\) 6.39022e92 0.116748
\(317\) 1.03547e94 1.68041 0.840203 0.542272i \(-0.182436\pi\)
0.840203 + 0.542272i \(0.182436\pi\)
\(318\) −3.83924e94 −5.53641
\(319\) 1.17209e93 0.150249
\(320\) 3.28680e93 0.374670
\(321\) 1.25598e94 1.27364
\(322\) −1.24458e94 −1.12312
\(323\) −1.39089e93 −0.111737
\(324\) 9.97323e94 7.13506
\(325\) 4.63115e93 0.295164
\(326\) −1.87495e94 −1.06495
\(327\) −6.27853e94 −3.17920
\(328\) −3.24499e94 −1.46536
\(329\) −2.00806e93 −0.0808965
\(330\) −3.35909e93 −0.120767
\(331\) 4.31190e94 1.38395 0.691973 0.721924i \(-0.256742\pi\)
0.691973 + 0.721924i \(0.256742\pi\)
\(332\) −1.91908e92 −0.00550068
\(333\) −7.45629e94 −1.90925
\(334\) 2.44155e94 0.558694
\(335\) −1.86872e94 −0.382265
\(336\) −4.66323e94 −0.853030
\(337\) 4.32493e94 0.707714 0.353857 0.935300i \(-0.384870\pi\)
0.353857 + 0.935300i \(0.384870\pi\)
\(338\) 1.03215e95 1.51135
\(339\) 2.32941e94 0.305322
\(340\) −2.95063e94 −0.346302
\(341\) 1.54074e94 0.161972
\(342\) 7.76229e94 0.731158
\(343\) −1.28264e95 −1.08287
\(344\) 2.63992e95 1.99824
\(345\) 5.88866e94 0.399761
\(346\) −2.54469e95 −1.54982
\(347\) 3.28354e95 1.79468 0.897339 0.441343i \(-0.145498\pi\)
0.897339 + 0.441343i \(0.145498\pi\)
\(348\) −7.81932e95 −3.83661
\(349\) −2.28464e95 −1.00662 −0.503309 0.864106i \(-0.667884\pi\)
−0.503309 + 0.864106i \(0.667884\pi\)
\(350\) 3.41192e95 1.35035
\(351\) 3.07268e95 1.09270
\(352\) 2.32147e94 0.0742014
\(353\) −2.28907e95 −0.657820 −0.328910 0.944361i \(-0.606681\pi\)
−0.328910 + 0.944361i \(0.606681\pi\)
\(354\) −4.04427e94 −0.104524
\(355\) −1.06676e95 −0.248031
\(356\) 1.35674e96 2.83872
\(357\) −6.34664e95 −1.19532
\(358\) −1.27914e96 −2.16923
\(359\) −3.43961e95 −0.525372 −0.262686 0.964881i \(-0.584608\pi\)
−0.262686 + 0.964881i \(0.584608\pi\)
\(360\) 7.44841e95 1.02499
\(361\) −7.86478e95 −0.975364
\(362\) 1.44040e96 1.61032
\(363\) 1.88918e96 1.90448
\(364\) −5.51647e95 −0.501602
\(365\) 1.77556e95 0.145664
\(366\) −3.01797e96 −2.23447
\(367\) 1.95272e96 1.30516 0.652579 0.757720i \(-0.273687\pi\)
0.652579 + 0.757720i \(0.273687\pi\)
\(368\) 6.50411e95 0.392550
\(369\) 5.36498e96 2.92469
\(370\) −6.26509e95 −0.308576
\(371\) −3.29445e96 −1.46643
\(372\) −1.02786e97 −4.13594
\(373\) −3.14216e94 −0.0114326 −0.00571632 0.999984i \(-0.501820\pi\)
−0.00571632 + 0.999984i \(0.501820\pi\)
\(374\) −5.04952e95 −0.166175
\(375\) −3.35201e96 −0.998005
\(376\) 4.82105e95 0.129896
\(377\) −1.40953e96 −0.343775
\(378\) 2.26374e97 4.99902
\(379\) −1.17713e96 −0.235427 −0.117713 0.993048i \(-0.537556\pi\)
−0.117713 + 0.993048i \(0.537556\pi\)
\(380\) 4.21420e95 0.0763538
\(381\) −2.95608e96 −0.485321
\(382\) 8.32627e96 1.23901
\(383\) 1.08925e97 1.46951 0.734755 0.678333i \(-0.237297\pi\)
0.734755 + 0.678333i \(0.237297\pi\)
\(384\) −2.90427e97 −3.55317
\(385\) −2.88243e95 −0.0319876
\(386\) 2.26142e97 2.27697
\(387\) −4.36460e97 −3.98825
\(388\) 1.39262e97 1.15517
\(389\) 1.78980e96 0.134801 0.0674007 0.997726i \(-0.478529\pi\)
0.0674007 + 0.997726i \(0.478529\pi\)
\(390\) 4.03957e96 0.276320
\(391\) 8.85206e96 0.550067
\(392\) 6.20554e96 0.350390
\(393\) 3.77011e96 0.193479
\(394\) −3.78534e97 −1.76602
\(395\) −4.01539e95 −0.0170348
\(396\) 1.82082e97 0.702584
\(397\) 2.74242e97 0.962698 0.481349 0.876529i \(-0.340147\pi\)
0.481349 + 0.876529i \(0.340147\pi\)
\(398\) −9.08780e97 −2.90298
\(399\) 9.06452e96 0.263549
\(400\) −1.78306e97 −0.471971
\(401\) 5.08366e97 1.22536 0.612678 0.790333i \(-0.290092\pi\)
0.612678 + 0.790333i \(0.290092\pi\)
\(402\) 2.13347e98 4.68392
\(403\) −1.85285e97 −0.370597
\(404\) −1.07843e98 −1.96558
\(405\) −6.26682e97 −1.04108
\(406\) −1.03845e98 −1.57275
\(407\) −6.92762e96 −0.0956740
\(408\) 1.52373e98 1.91935
\(409\) −3.24764e97 −0.373201 −0.186601 0.982436i \(-0.559747\pi\)
−0.186601 + 0.982436i \(0.559747\pi\)
\(410\) 4.50788e97 0.472692
\(411\) 2.46124e98 2.35551
\(412\) −3.49821e97 −0.305633
\(413\) −3.47038e96 −0.0276853
\(414\) −4.94016e98 −3.59938
\(415\) 1.20588e95 0.000802605 0
\(416\) −2.79174e97 −0.169776
\(417\) −3.53855e98 −1.96663
\(418\) 7.21193e96 0.0366388
\(419\) 3.50672e98 1.62883 0.814413 0.580286i \(-0.197059\pi\)
0.814413 + 0.580286i \(0.197059\pi\)
\(420\) 1.92294e98 0.816803
\(421\) 1.68894e98 0.656199 0.328099 0.944643i \(-0.393592\pi\)
0.328099 + 0.944643i \(0.393592\pi\)
\(422\) −2.03066e98 −0.721804
\(423\) −7.97068e97 −0.259258
\(424\) 7.90948e98 2.35466
\(425\) −2.42673e98 −0.661359
\(426\) 1.21790e99 3.03914
\(427\) −2.58971e98 −0.591842
\(428\) −5.72050e98 −1.19755
\(429\) 4.46675e97 0.0856729
\(430\) −3.66732e98 −0.644587
\(431\) −9.95538e98 −1.60384 −0.801919 0.597433i \(-0.796187\pi\)
−0.801919 + 0.597433i \(0.796187\pi\)
\(432\) −1.18302e99 −1.74724
\(433\) 6.16347e98 0.834698 0.417349 0.908746i \(-0.362959\pi\)
0.417349 + 0.908746i \(0.362959\pi\)
\(434\) −1.36506e99 −1.69545
\(435\) 4.91338e98 0.559800
\(436\) 2.85962e99 2.98927
\(437\) −1.26429e98 −0.121281
\(438\) −2.02711e99 −1.78484
\(439\) 1.65566e99 1.33829 0.669147 0.743130i \(-0.266660\pi\)
0.669147 + 0.743130i \(0.266660\pi\)
\(440\) 6.92030e97 0.0513629
\(441\) −1.02597e99 −0.699337
\(442\) 6.07244e98 0.380214
\(443\) −6.77161e97 −0.0389540 −0.0194770 0.999810i \(-0.506200\pi\)
−0.0194770 + 0.999810i \(0.506200\pi\)
\(444\) 4.62158e99 2.44303
\(445\) −8.52529e98 −0.414199
\(446\) −3.72526e99 −1.66379
\(447\) −5.22346e99 −2.14500
\(448\) −3.21998e99 −1.21598
\(449\) 2.65101e99 0.920819 0.460409 0.887707i \(-0.347703\pi\)
0.460409 + 0.887707i \(0.347703\pi\)
\(450\) 1.35431e100 4.32762
\(451\) 4.98459e98 0.146558
\(452\) −1.06095e99 −0.287081
\(453\) 4.51897e99 1.12553
\(454\) −8.44683e99 −1.93686
\(455\) 3.46635e98 0.0731888
\(456\) −2.17626e99 −0.423184
\(457\) −4.84378e99 −0.867615 −0.433807 0.901006i \(-0.642830\pi\)
−0.433807 + 0.901006i \(0.642830\pi\)
\(458\) −2.02688e99 −0.334482
\(459\) −1.61009e100 −2.44835
\(460\) −2.68205e99 −0.375879
\(461\) 1.31364e100 1.69704 0.848521 0.529162i \(-0.177493\pi\)
0.848521 + 0.529162i \(0.177493\pi\)
\(462\) 3.29080e99 0.391947
\(463\) 7.77164e99 0.853543 0.426772 0.904359i \(-0.359651\pi\)
0.426772 + 0.904359i \(0.359651\pi\)
\(464\) 5.42690e99 0.549702
\(465\) 6.45871e99 0.603476
\(466\) −1.33577e100 −1.15149
\(467\) 7.55574e99 0.601027 0.300513 0.953778i \(-0.402842\pi\)
0.300513 + 0.953778i \(0.402842\pi\)
\(468\) −2.18968e100 −1.60754
\(469\) 1.83073e100 1.24063
\(470\) −6.69731e98 −0.0419016
\(471\) 3.58629e100 2.07187
\(472\) 8.33187e98 0.0444547
\(473\) −4.05514e99 −0.199854
\(474\) 4.58427e99 0.208729
\(475\) 3.46596e99 0.145819
\(476\) 2.89064e100 1.12391
\(477\) −1.30768e101 −4.69962
\(478\) −1.86167e100 −0.618524
\(479\) 3.90184e100 1.19864 0.599319 0.800510i \(-0.295438\pi\)
0.599319 + 0.800510i \(0.295438\pi\)
\(480\) 9.73150e99 0.276461
\(481\) 8.33100e99 0.218905
\(482\) −4.58562e100 −1.11464
\(483\) −5.76894e100 −1.29741
\(484\) −8.60447e100 −1.79070
\(485\) −8.75075e99 −0.168550
\(486\) 3.91200e101 6.97492
\(487\) 1.26161e100 0.208251 0.104126 0.994564i \(-0.466796\pi\)
0.104126 + 0.994564i \(0.466796\pi\)
\(488\) 6.21752e100 0.950328
\(489\) −8.69089e100 −1.23022
\(490\) −8.62061e99 −0.113028
\(491\) 6.80665e99 0.0826756 0.0413378 0.999145i \(-0.486838\pi\)
0.0413378 + 0.999145i \(0.486838\pi\)
\(492\) −3.32534e101 −3.74235
\(493\) 7.38598e100 0.770280
\(494\) −8.67290e99 −0.0838308
\(495\) −1.14414e100 −0.102514
\(496\) 7.13374e100 0.592590
\(497\) 1.04508e101 0.804977
\(498\) −1.37673e99 −0.00983439
\(499\) −2.15058e100 −0.142490 −0.0712451 0.997459i \(-0.522697\pi\)
−0.0712451 + 0.997459i \(0.522697\pi\)
\(500\) 1.52671e101 0.938383
\(501\) 1.13172e101 0.645396
\(502\) 3.31764e100 0.175566
\(503\) −1.06452e101 −0.522824 −0.261412 0.965227i \(-0.584188\pi\)
−0.261412 + 0.965227i \(0.584188\pi\)
\(504\) −7.29698e101 −3.32658
\(505\) 6.77645e100 0.286798
\(506\) −4.58989e100 −0.180367
\(507\) 4.78429e101 1.74590
\(508\) 1.34637e101 0.456327
\(509\) −4.78996e101 −1.50805 −0.754023 0.656848i \(-0.771889\pi\)
−0.754023 + 0.656848i \(0.771889\pi\)
\(510\) −2.11674e101 −0.619136
\(511\) −1.73946e101 −0.472749
\(512\) 3.86756e101 0.976817
\(513\) 2.29959e101 0.539821
\(514\) −5.92423e101 −1.29275
\(515\) 2.19815e100 0.0445950
\(516\) 2.70528e102 5.10327
\(517\) −7.40554e99 −0.0129916
\(518\) 6.13772e101 1.00148
\(519\) −1.17953e102 −1.79033
\(520\) −8.32219e100 −0.117520
\(521\) 8.84088e101 1.16166 0.580832 0.814023i \(-0.302727\pi\)
0.580832 + 0.814023i \(0.302727\pi\)
\(522\) −4.12197e102 −5.04035
\(523\) −1.09779e100 −0.0124942 −0.00624709 0.999980i \(-0.501989\pi\)
−0.00624709 + 0.999980i \(0.501989\pi\)
\(524\) −1.71713e101 −0.181920
\(525\) 1.58152e102 1.55991
\(526\) −1.13534e102 −1.04270
\(527\) 9.70899e101 0.830378
\(528\) −1.71976e101 −0.136992
\(529\) −5.43052e101 −0.402952
\(530\) −1.09877e102 −0.759559
\(531\) −1.37752e101 −0.0887262
\(532\) −4.12853e101 −0.247804
\(533\) −5.99435e101 −0.335330
\(534\) 9.73311e102 5.07522
\(535\) 3.59456e101 0.174734
\(536\) −4.39531e102 −1.99209
\(537\) −5.92916e102 −2.50586
\(538\) 4.38350e102 1.72777
\(539\) −9.53224e100 −0.0350442
\(540\) 4.87834e102 1.67304
\(541\) 4.54819e101 0.145526 0.0727632 0.997349i \(-0.476818\pi\)
0.0727632 + 0.997349i \(0.476818\pi\)
\(542\) −7.58152e102 −2.26351
\(543\) 6.67663e102 1.86022
\(544\) 1.46288e102 0.380408
\(545\) −1.79688e102 −0.436165
\(546\) −3.95744e102 −0.896790
\(547\) 3.65619e102 0.773577 0.386789 0.922168i \(-0.373584\pi\)
0.386789 + 0.922168i \(0.373584\pi\)
\(548\) −1.12100e103 −2.21479
\(549\) −1.02795e103 −1.89674
\(550\) 1.25829e102 0.216860
\(551\) −1.05490e102 −0.169834
\(552\) 1.38504e103 2.08327
\(553\) 3.93375e101 0.0552859
\(554\) 1.87288e103 2.45976
\(555\) −2.90403e102 −0.356463
\(556\) 1.61167e103 1.84915
\(557\) −4.10459e102 −0.440251 −0.220126 0.975472i \(-0.570647\pi\)
−0.220126 + 0.975472i \(0.570647\pi\)
\(558\) −5.41840e103 −5.43361
\(559\) 4.87661e102 0.457273
\(560\) −1.33459e102 −0.117030
\(561\) −2.34059e102 −0.191963
\(562\) 2.11335e103 1.62129
\(563\) −2.03919e102 −0.146350 −0.0731751 0.997319i \(-0.523313\pi\)
−0.0731751 + 0.997319i \(0.523313\pi\)
\(564\) 4.94042e102 0.331739
\(565\) 6.66665e101 0.0418881
\(566\) 2.42077e103 1.42344
\(567\) 6.13941e103 3.37879
\(568\) −2.50908e103 −1.29256
\(569\) −1.21675e103 −0.586803 −0.293401 0.955989i \(-0.594787\pi\)
−0.293401 + 0.955989i \(0.594787\pi\)
\(570\) 3.02322e102 0.136509
\(571\) −3.95470e103 −1.67209 −0.836044 0.548663i \(-0.815137\pi\)
−0.836044 + 0.548663i \(0.815137\pi\)
\(572\) −2.03443e102 −0.0805547
\(573\) 3.85944e103 1.43129
\(574\) −4.41623e103 −1.53411
\(575\) −2.20584e103 −0.717844
\(576\) −1.27812e104 −3.89699
\(577\) −2.30970e103 −0.659877 −0.329938 0.944002i \(-0.607028\pi\)
−0.329938 + 0.944002i \(0.607028\pi\)
\(578\) 3.09678e103 0.829118
\(579\) 1.04823e104 2.63033
\(580\) −2.23785e103 −0.526357
\(581\) −1.18137e101 −0.00260483
\(582\) 9.99051e103 2.06526
\(583\) −1.21496e103 −0.235501
\(584\) 4.17619e103 0.759099
\(585\) 1.37592e103 0.234556
\(586\) 3.63658e103 0.581478
\(587\) −4.27950e103 −0.641896 −0.320948 0.947097i \(-0.604001\pi\)
−0.320948 + 0.947097i \(0.604001\pi\)
\(588\) 6.35918e103 0.894853
\(589\) −1.38668e103 −0.183085
\(590\) −1.15745e102 −0.0143401
\(591\) −1.75460e104 −2.04009
\(592\) −3.20755e103 −0.350033
\(593\) 5.73284e103 0.587245 0.293622 0.955922i \(-0.405139\pi\)
0.293622 + 0.955922i \(0.405139\pi\)
\(594\) 8.34849e103 0.802817
\(595\) −1.81637e103 −0.163990
\(596\) 2.37908e104 2.01685
\(597\) −4.21244e104 −3.35348
\(598\) 5.51970e103 0.412687
\(599\) −8.09810e103 −0.568692 −0.284346 0.958722i \(-0.591776\pi\)
−0.284346 + 0.958722i \(0.591776\pi\)
\(600\) −3.79699e104 −2.50477
\(601\) 1.48364e103 0.0919469 0.0459735 0.998943i \(-0.485361\pi\)
0.0459735 + 0.998943i \(0.485361\pi\)
\(602\) 3.59276e104 2.09199
\(603\) 7.26681e104 3.97598
\(604\) −2.05821e104 −1.05829
\(605\) 5.40674e103 0.261282
\(606\) −7.73651e104 −3.51416
\(607\) 3.19159e104 1.36280 0.681400 0.731912i \(-0.261372\pi\)
0.681400 + 0.731912i \(0.261372\pi\)
\(608\) −2.08934e103 −0.0838735
\(609\) −4.81349e104 −1.81682
\(610\) −8.63725e103 −0.306554
\(611\) 8.90574e102 0.0297252
\(612\) 1.14740e105 3.60193
\(613\) 1.90887e104 0.563650 0.281825 0.959466i \(-0.409060\pi\)
0.281825 + 0.959466i \(0.409060\pi\)
\(614\) −1.81079e104 −0.502985
\(615\) 2.08952e104 0.546047
\(616\) −6.77961e103 −0.166697
\(617\) −4.16335e104 −0.963273 −0.481636 0.876371i \(-0.659957\pi\)
−0.481636 + 0.876371i \(0.659957\pi\)
\(618\) −2.50957e104 −0.546427
\(619\) 5.63359e104 1.15448 0.577239 0.816575i \(-0.304130\pi\)
0.577239 + 0.816575i \(0.304130\pi\)
\(620\) −2.94168e104 −0.567424
\(621\) −1.46353e105 −2.65746
\(622\) 8.23787e104 1.40824
\(623\) 8.35197e104 1.34427
\(624\) 2.06814e104 0.313443
\(625\) 5.54985e104 0.792101
\(626\) −9.62511e104 −1.29380
\(627\) 3.34292e103 0.0423246
\(628\) −1.63341e105 −1.94809
\(629\) −4.36546e104 −0.490490
\(630\) 1.01368e105 1.07308
\(631\) −4.77847e104 −0.476637 −0.238319 0.971187i \(-0.576596\pi\)
−0.238319 + 0.971187i \(0.576596\pi\)
\(632\) −9.44436e103 −0.0887733
\(633\) −9.41263e104 −0.833819
\(634\) −3.38330e105 −2.82484
\(635\) −8.46013e103 −0.0665828
\(636\) 8.10532e105 6.01351
\(637\) 1.14632e104 0.0801824
\(638\) −3.82971e104 −0.252575
\(639\) 4.14828e105 2.57980
\(640\) −8.31187e104 −0.487472
\(641\) −1.19877e104 −0.0663069 −0.0331534 0.999450i \(-0.510555\pi\)
−0.0331534 + 0.999450i \(0.510555\pi\)
\(642\) −4.10382e105 −2.14104
\(643\) 2.25954e105 1.11201 0.556006 0.831178i \(-0.312333\pi\)
0.556006 + 0.831178i \(0.312333\pi\)
\(644\) 2.62752e105 1.21991
\(645\) −1.69990e105 −0.744619
\(646\) 4.54462e104 0.187836
\(647\) 3.62715e103 0.0141467 0.00707334 0.999975i \(-0.497748\pi\)
0.00707334 + 0.999975i \(0.497748\pi\)
\(648\) −1.47398e106 −5.42537
\(649\) −1.27985e103 −0.00444613
\(650\) −1.51319e105 −0.496183
\(651\) −6.32740e105 −1.95857
\(652\) 3.95835e105 1.15672
\(653\) 3.74683e105 1.03376 0.516880 0.856058i \(-0.327093\pi\)
0.516880 + 0.856058i \(0.327093\pi\)
\(654\) 2.05145e106 5.34437
\(655\) 1.07899e104 0.0265440
\(656\) 2.30791e105 0.536197
\(657\) −6.90454e105 −1.51507
\(658\) 6.56115e104 0.135991
\(659\) −8.83130e105 −1.72911 −0.864553 0.502542i \(-0.832398\pi\)
−0.864553 + 0.502542i \(0.832398\pi\)
\(660\) 7.09164e104 0.131174
\(661\) 3.25607e105 0.569036 0.284518 0.958671i \(-0.408166\pi\)
0.284518 + 0.958671i \(0.408166\pi\)
\(662\) −1.40888e106 −2.32647
\(663\) 2.81474e105 0.439218
\(664\) 2.83629e103 0.00418261
\(665\) 2.59422e104 0.0361572
\(666\) 2.43628e106 3.20954
\(667\) 6.71368e105 0.836068
\(668\) −5.15455e105 −0.606839
\(669\) −1.72675e106 −1.92199
\(670\) 6.10588e105 0.642603
\(671\) −9.55064e104 −0.0950469
\(672\) −9.53366e105 −0.897246
\(673\) 1.25330e106 1.11555 0.557777 0.829991i \(-0.311654\pi\)
0.557777 + 0.829991i \(0.311654\pi\)
\(674\) −1.41313e106 −1.18970
\(675\) 4.01218e106 3.19513
\(676\) −2.17905e106 −1.64160
\(677\) −1.53726e106 −1.09565 −0.547824 0.836594i \(-0.684544\pi\)
−0.547824 + 0.836594i \(0.684544\pi\)
\(678\) −7.61115e105 −0.513259
\(679\) 8.57284e105 0.547026
\(680\) 4.36084e105 0.263322
\(681\) −3.91533e106 −2.23744
\(682\) −5.03422e105 −0.272281
\(683\) 1.70977e106 0.875311 0.437655 0.899143i \(-0.355809\pi\)
0.437655 + 0.899143i \(0.355809\pi\)
\(684\) −1.63876e106 −0.794165
\(685\) 7.04394e105 0.323161
\(686\) 4.19092e106 1.82035
\(687\) −9.39512e105 −0.386389
\(688\) −1.87756e106 −0.731186
\(689\) 1.46109e106 0.538835
\(690\) −1.92407e106 −0.672016
\(691\) 4.55165e106 1.50571 0.752856 0.658185i \(-0.228676\pi\)
0.752856 + 0.658185i \(0.228676\pi\)
\(692\) 5.37230e106 1.68338
\(693\) 1.12088e106 0.332707
\(694\) −1.07287e107 −3.01693
\(695\) −1.01271e106 −0.269809
\(696\) 1.15565e107 2.91729
\(697\) 3.14105e106 0.751356
\(698\) 7.46487e106 1.69217
\(699\) −6.19166e106 −1.33019
\(700\) −7.20317e106 −1.46672
\(701\) −6.86314e106 −1.32464 −0.662319 0.749222i \(-0.730427\pi\)
−0.662319 + 0.749222i \(0.730427\pi\)
\(702\) −1.00397e107 −1.83687
\(703\) 6.23492e105 0.108145
\(704\) −1.18750e106 −0.195281
\(705\) −3.10438e105 −0.0484042
\(706\) 7.47932e106 1.10582
\(707\) −6.63868e106 −0.930795
\(708\) 8.53816e105 0.113532
\(709\) −4.47111e105 −0.0563873 −0.0281936 0.999602i \(-0.508976\pi\)
−0.0281936 + 0.999602i \(0.508976\pi\)
\(710\) 3.48556e106 0.416950
\(711\) 1.56144e106 0.177181
\(712\) −2.00519e107 −2.15851
\(713\) 8.82524e106 0.901299
\(714\) 2.07371e107 2.00939
\(715\) 1.27836e105 0.0117538
\(716\) 2.70049e107 2.35616
\(717\) −8.62933e106 −0.714511
\(718\) 1.12386e107 0.883174
\(719\) −4.46581e106 −0.333094 −0.166547 0.986034i \(-0.553262\pi\)
−0.166547 + 0.986034i \(0.553262\pi\)
\(720\) −5.29746e106 −0.375059
\(721\) −2.15346e106 −0.144732
\(722\) 2.56975e107 1.63963
\(723\) −2.12556e107 −1.28762
\(724\) −3.04094e107 −1.74909
\(725\) −1.84051e107 −1.00522
\(726\) −6.17274e107 −3.20151
\(727\) 7.07466e106 0.348470 0.174235 0.984704i \(-0.444255\pi\)
0.174235 + 0.984704i \(0.444255\pi\)
\(728\) 8.15300e106 0.381409
\(729\) 9.33887e107 4.14966
\(730\) −5.80148e106 −0.244868
\(731\) −2.55535e107 −1.02459
\(732\) 6.37146e107 2.42702
\(733\) 4.53195e107 1.64016 0.820080 0.572249i \(-0.193929\pi\)
0.820080 + 0.572249i \(0.193929\pi\)
\(734\) −6.38035e107 −2.19403
\(735\) −3.99588e106 −0.130568
\(736\) 1.32972e107 0.412897
\(737\) 6.75157e106 0.199239
\(738\) −1.75296e108 −4.91652
\(739\) −3.01848e107 −0.804679 −0.402339 0.915491i \(-0.631803\pi\)
−0.402339 + 0.915491i \(0.631803\pi\)
\(740\) 1.32267e107 0.335168
\(741\) −4.02012e106 −0.0968403
\(742\) 1.07643e108 2.46513
\(743\) −6.62438e107 −1.44233 −0.721165 0.692764i \(-0.756393\pi\)
−0.721165 + 0.692764i \(0.756393\pi\)
\(744\) 1.51912e108 3.14490
\(745\) −1.49493e107 −0.294279
\(746\) 1.02667e106 0.0192188
\(747\) −4.68926e105 −0.00834799
\(748\) 1.06604e107 0.180495
\(749\) −3.52148e107 −0.567096
\(750\) 1.09524e108 1.67769
\(751\) 1.02618e108 1.49529 0.747645 0.664099i \(-0.231185\pi\)
0.747645 + 0.664099i \(0.231185\pi\)
\(752\) −3.42883e106 −0.0475310
\(753\) 1.53781e107 0.202811
\(754\) 4.60553e107 0.577901
\(755\) 1.29331e107 0.154415
\(756\) −4.77916e108 −5.42981
\(757\) −8.55357e107 −0.924808 −0.462404 0.886669i \(-0.653013\pi\)
−0.462404 + 0.886669i \(0.653013\pi\)
\(758\) 3.84618e107 0.395762
\(759\) −2.12754e107 −0.208358
\(760\) −6.22833e106 −0.0580580
\(761\) 1.22517e108 1.08711 0.543553 0.839375i \(-0.317079\pi\)
0.543553 + 0.839375i \(0.317079\pi\)
\(762\) 9.65872e107 0.815846
\(763\) 1.76035e108 1.41556
\(764\) −1.75782e108 −1.34578
\(765\) −7.20982e107 −0.525558
\(766\) −3.55902e108 −2.47031
\(767\) 1.53911e106 0.0101729
\(768\) 5.15073e108 3.24208
\(769\) 1.12833e108 0.676393 0.338197 0.941075i \(-0.390183\pi\)
0.338197 + 0.941075i \(0.390183\pi\)
\(770\) 9.41810e106 0.0537726
\(771\) −2.74604e108 −1.49337
\(772\) −4.77426e108 −2.47319
\(773\) 2.94129e107 0.145147 0.0725734 0.997363i \(-0.476879\pi\)
0.0725734 + 0.997363i \(0.476879\pi\)
\(774\) 1.42609e109 6.70443
\(775\) −2.41938e108 −1.08365
\(776\) −2.05821e108 −0.878367
\(777\) 2.84499e108 1.15689
\(778\) −5.84801e107 −0.226607
\(779\) −4.48618e107 −0.165662
\(780\) −8.52825e107 −0.300132
\(781\) 3.85416e107 0.129275
\(782\) −2.89233e108 −0.924687
\(783\) −1.22114e109 −3.72135
\(784\) −4.41351e107 −0.128213
\(785\) 1.02638e108 0.284246
\(786\) −1.23185e108 −0.325246
\(787\) 7.86662e108 1.98032 0.990161 0.139936i \(-0.0446896\pi\)
0.990161 + 0.139936i \(0.0446896\pi\)
\(788\) 7.99152e108 1.91821
\(789\) −5.26259e108 −1.20451
\(790\) 1.31199e107 0.0286362
\(791\) −6.53111e107 −0.135947
\(792\) −2.69106e108 −0.534232
\(793\) 1.14854e108 0.217471
\(794\) −8.96061e108 −1.61834
\(795\) −5.09309e108 −0.877433
\(796\) 1.91860e109 3.15314
\(797\) 9.68204e107 0.151803 0.0759014 0.997115i \(-0.475817\pi\)
0.0759014 + 0.997115i \(0.475817\pi\)
\(798\) −2.96175e108 −0.443037
\(799\) −4.66662e107 −0.0666037
\(800\) −3.64534e108 −0.496436
\(801\) 3.31519e109 4.30813
\(802\) −1.66104e109 −2.05988
\(803\) −6.41499e107 −0.0759212
\(804\) −4.50414e109 −5.08756
\(805\) −1.65104e108 −0.177997
\(806\) 6.05404e108 0.622990
\(807\) 2.03187e109 1.99590
\(808\) 1.59385e109 1.49459
\(809\) 1.25823e109 1.12640 0.563199 0.826321i \(-0.309570\pi\)
0.563199 + 0.826321i \(0.309570\pi\)
\(810\) 2.04763e109 1.75010
\(811\) −1.83325e109 −1.49603 −0.748014 0.663683i \(-0.768992\pi\)
−0.748014 + 0.663683i \(0.768992\pi\)
\(812\) 2.19235e109 1.70828
\(813\) −3.51423e109 −2.61478
\(814\) 2.26354e108 0.160832
\(815\) −2.48728e108 −0.168778
\(816\) −1.08371e109 −0.702316
\(817\) 3.64966e108 0.225905
\(818\) 1.06114e109 0.627368
\(819\) −1.34794e109 −0.761246
\(820\) −9.51694e108 −0.513426
\(821\) 5.30578e108 0.273452 0.136726 0.990609i \(-0.456342\pi\)
0.136726 + 0.990609i \(0.456342\pi\)
\(822\) −8.04189e109 −3.95972
\(823\) −4.35738e107 −0.0204989 −0.0102495 0.999947i \(-0.503263\pi\)
−0.0102495 + 0.999947i \(0.503263\pi\)
\(824\) 5.17014e108 0.232398
\(825\) 5.83250e108 0.250514
\(826\) 1.13392e108 0.0465403
\(827\) 9.43799e107 0.0370188 0.0185094 0.999829i \(-0.494108\pi\)
0.0185094 + 0.999829i \(0.494108\pi\)
\(828\) 1.04296e110 3.90956
\(829\) −4.56308e109 −1.63480 −0.817398 0.576073i \(-0.804584\pi\)
−0.817398 + 0.576073i \(0.804584\pi\)
\(830\) −3.94012e106 −0.00134921
\(831\) 8.68129e109 2.84149
\(832\) 1.42806e109 0.446809
\(833\) −6.00676e108 −0.179661
\(834\) 1.15619e110 3.30600
\(835\) 3.23893e108 0.0885440
\(836\) −1.52257e108 −0.0397961
\(837\) −1.60521e110 −4.01169
\(838\) −1.14579e110 −2.73813
\(839\) 7.28934e108 0.166577 0.0832884 0.996525i \(-0.473458\pi\)
0.0832884 + 0.996525i \(0.473458\pi\)
\(840\) −2.84199e109 −0.621082
\(841\) 8.17112e108 0.170778
\(842\) −5.51846e109 −1.10310
\(843\) 9.79596e109 1.87289
\(844\) 4.28707e109 0.784006
\(845\) 1.36924e109 0.239526
\(846\) 2.60435e109 0.435824
\(847\) −5.29682e109 −0.847983
\(848\) −5.62539e109 −0.861605
\(849\) 1.12209e110 1.64433
\(850\) 7.92913e109 1.11177
\(851\) −3.96810e109 −0.532382
\(852\) −2.57120e110 −3.30104
\(853\) −1.01292e110 −1.24448 −0.622240 0.782827i \(-0.713777\pi\)
−0.622240 + 0.782827i \(0.713777\pi\)
\(854\) 8.46165e109 0.994913
\(855\) 1.02974e109 0.115877
\(856\) 8.45455e109 0.910593
\(857\) 1.65427e110 1.70540 0.852698 0.522405i \(-0.174965\pi\)
0.852698 + 0.522405i \(0.174965\pi\)
\(858\) −1.45947e109 −0.144020
\(859\) 5.68954e109 0.537444 0.268722 0.963218i \(-0.413399\pi\)
0.268722 + 0.963218i \(0.413399\pi\)
\(860\) 7.74236e109 0.700134
\(861\) −2.04704e110 −1.77218
\(862\) 3.25283e110 2.69612
\(863\) −9.44371e108 −0.0749442 −0.0374721 0.999298i \(-0.511931\pi\)
−0.0374721 + 0.999298i \(0.511931\pi\)
\(864\) −2.41861e110 −1.83781
\(865\) −3.37576e109 −0.245622
\(866\) −2.01386e110 −1.40316
\(867\) 1.43544e110 0.957786
\(868\) 2.88188e110 1.84156
\(869\) 1.45073e108 0.00887864
\(870\) −1.60540e110 −0.941049
\(871\) −8.11929e109 −0.455866
\(872\) −4.22634e110 −2.27298
\(873\) 3.40286e110 1.75311
\(874\) 4.13095e109 0.203878
\(875\) 9.39823e109 0.444370
\(876\) 4.27959e110 1.93865
\(877\) −1.65254e110 −0.717246 −0.358623 0.933482i \(-0.616754\pi\)
−0.358623 + 0.933482i \(0.616754\pi\)
\(878\) −5.40972e110 −2.24973
\(879\) 1.68565e110 0.671716
\(880\) −4.92186e108 −0.0187944
\(881\) −3.05928e110 −1.11950 −0.559748 0.828663i \(-0.689102\pi\)
−0.559748 + 0.828663i \(0.689102\pi\)
\(882\) 3.35226e110 1.17562
\(883\) −1.03341e110 −0.347334 −0.173667 0.984804i \(-0.555562\pi\)
−0.173667 + 0.984804i \(0.555562\pi\)
\(884\) −1.28200e110 −0.412979
\(885\) −5.36507e108 −0.0165654
\(886\) 2.21256e109 0.0654834
\(887\) −4.02103e110 −1.14078 −0.570390 0.821374i \(-0.693208\pi\)
−0.570390 + 0.821374i \(0.693208\pi\)
\(888\) −6.83041e110 −1.85764
\(889\) 8.28813e109 0.216093
\(890\) 2.78556e110 0.696286
\(891\) 2.26416e110 0.542617
\(892\) 7.86467e110 1.80717
\(893\) 6.66506e108 0.0146850
\(894\) 1.70672e111 3.60583
\(895\) −1.69689e110 −0.343788
\(896\) 8.14288e110 1.58208
\(897\) 2.55853e110 0.476731
\(898\) −8.66195e110 −1.54794
\(899\) 7.36360e110 1.26212
\(900\) −2.85919e111 −4.70056
\(901\) −7.65613e110 −1.20734
\(902\) −1.62867e110 −0.246370
\(903\) 1.66534e111 2.41664
\(904\) 1.56802e110 0.218291
\(905\) 1.91082e110 0.255210
\(906\) −1.47653e111 −1.89207
\(907\) −1.12894e111 −1.38803 −0.694013 0.719963i \(-0.744159\pi\)
−0.694013 + 0.719963i \(0.744159\pi\)
\(908\) 1.78328e111 2.10377
\(909\) −2.63513e111 −2.98302
\(910\) −1.13260e110 −0.123034
\(911\) −1.25185e110 −0.130501 −0.0652506 0.997869i \(-0.520785\pi\)
−0.0652506 + 0.997869i \(0.520785\pi\)
\(912\) 1.54780e110 0.154849
\(913\) −4.35678e107 −0.000418323 0
\(914\) 1.58266e111 1.45850
\(915\) −4.00360e110 −0.354127
\(916\) 4.27910e110 0.363306
\(917\) −1.05705e110 −0.0861480
\(918\) 5.26082e111 4.11579
\(919\) 1.73300e111 1.30157 0.650785 0.759262i \(-0.274440\pi\)
0.650785 + 0.759262i \(0.274440\pi\)
\(920\) 3.96390e110 0.285811
\(921\) −8.39351e110 −0.581042
\(922\) −4.29221e111 −2.85280
\(923\) −4.63492e110 −0.295787
\(924\) −6.94747e110 −0.425723
\(925\) 1.08783e111 0.640095
\(926\) −2.53932e111 −1.43484
\(927\) −8.54784e110 −0.463838
\(928\) 1.10949e111 0.578196
\(929\) 6.51740e110 0.326201 0.163100 0.986609i \(-0.447851\pi\)
0.163100 + 0.986609i \(0.447851\pi\)
\(930\) −2.11033e111 −1.01447
\(931\) 8.57910e109 0.0396122
\(932\) 2.82005e111 1.25072
\(933\) 3.81847e111 1.62678
\(934\) −2.46877e111 −1.01035
\(935\) −6.69863e109 −0.0263360
\(936\) 3.23621e111 1.22234
\(937\) 5.15863e111 1.87197 0.935987 0.352035i \(-0.114510\pi\)
0.935987 + 0.352035i \(0.114510\pi\)
\(938\) −5.98174e111 −2.08555
\(939\) −4.46149e111 −1.49459
\(940\) 1.41392e110 0.0455125
\(941\) 5.35193e110 0.165539 0.0827694 0.996569i \(-0.473624\pi\)
0.0827694 + 0.996569i \(0.473624\pi\)
\(942\) −1.17179e112 −3.48290
\(943\) 2.85514e111 0.815528
\(944\) −5.92580e109 −0.0162666
\(945\) 3.00305e111 0.792264
\(946\) 1.32498e111 0.335963
\(947\) 6.35901e111 1.54976 0.774881 0.632107i \(-0.217810\pi\)
0.774881 + 0.632107i \(0.217810\pi\)
\(948\) −9.67820e110 −0.226716
\(949\) 7.71452e110 0.173710
\(950\) −1.13247e111 −0.245127
\(951\) −1.56825e112 −3.26321
\(952\) −4.27219e111 −0.854603
\(953\) −2.74523e111 −0.527952 −0.263976 0.964529i \(-0.585034\pi\)
−0.263976 + 0.964529i \(0.585034\pi\)
\(954\) 4.27274e112 7.90027
\(955\) 1.10455e111 0.196363
\(956\) 3.93032e111 0.671825
\(957\) −1.77517e111 −0.291772
\(958\) −1.27489e112 −2.01496
\(959\) −6.90073e111 −1.04881
\(960\) −4.97796e111 −0.727579
\(961\) 2.56535e111 0.360595
\(962\) −2.72208e111 −0.367990
\(963\) −1.39780e112 −1.81743
\(964\) 9.68106e111 1.21069
\(965\) 2.99997e111 0.360864
\(966\) 1.88495e112 2.18101
\(967\) −6.60617e111 −0.735287 −0.367643 0.929967i \(-0.619835\pi\)
−0.367643 + 0.929967i \(0.619835\pi\)
\(968\) 1.27169e112 1.36162
\(969\) 2.10655e111 0.216985
\(970\) 2.85923e111 0.283341
\(971\) 1.03596e112 0.987695 0.493847 0.869549i \(-0.335590\pi\)
0.493847 + 0.869549i \(0.335590\pi\)
\(972\) −8.25893e112 −7.57598
\(973\) 9.92126e111 0.875659
\(974\) −4.12219e111 −0.350080
\(975\) −7.01403e111 −0.573184
\(976\) −4.42203e111 −0.347739
\(977\) −2.05932e112 −1.55839 −0.779197 0.626779i \(-0.784373\pi\)
−0.779197 + 0.626779i \(0.784373\pi\)
\(978\) 2.83967e112 2.06805
\(979\) 3.08014e111 0.215883
\(980\) 1.81996e111 0.122768
\(981\) 6.98745e112 4.53660
\(982\) −2.22401e111 −0.138981
\(983\) −9.74562e111 −0.586209 −0.293105 0.956080i \(-0.594688\pi\)
−0.293105 + 0.956080i \(0.594688\pi\)
\(984\) 4.91465e112 2.84561
\(985\) −5.02158e111 −0.279886
\(986\) −2.41330e112 −1.29487
\(987\) 3.04126e111 0.157095
\(988\) 1.83100e111 0.0910550
\(989\) −2.32276e112 −1.11210
\(990\) 3.73837e111 0.172331
\(991\) 2.65057e112 1.17646 0.588230 0.808694i \(-0.299825\pi\)
0.588230 + 0.808694i \(0.299825\pi\)
\(992\) 1.45844e112 0.623307
\(993\) −6.53051e112 −2.68751
\(994\) −3.41470e112 −1.35320
\(995\) −1.20558e112 −0.460075
\(996\) 2.90651e110 0.0106819
\(997\) −2.01612e112 −0.713587 −0.356793 0.934183i \(-0.616130\pi\)
−0.356793 + 0.934183i \(0.616130\pi\)
\(998\) 7.02683e111 0.239532
\(999\) 7.21752e112 2.36964
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 1.76.a.a.1.1 6
3.2 odd 2 9.76.a.c.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.76.a.a.1.1 6 1.1 even 1 trivial
9.76.a.c.1.6 6 3.2 odd 2