Properties

Label 2.82.a.a.1.1
Level 2
Weight 82
Character 2.1
Self dual yes
Analytic conductor 83.100
Analytic rank 1
Dimension 3
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 82 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(83.1002571076\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.86628e14\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.09951e12 q^{2} -2.10253e19 q^{3} +1.20893e24 q^{4} -2.29740e27 q^{5} +2.31176e31 q^{6} +2.01848e34 q^{7} -1.32923e36 q^{8} -1.36253e36 q^{9} +O(q^{10})\) \(q-1.09951e12 q^{2} -2.10253e19 q^{3} +1.20893e24 q^{4} -2.29740e27 q^{5} +2.31176e31 q^{6} +2.01848e34 q^{7} -1.32923e36 q^{8} -1.36253e36 q^{9} +2.52602e39 q^{10} -1.36227e40 q^{11} -2.54180e43 q^{12} -1.42413e45 q^{13} -2.21934e46 q^{14} +4.83036e46 q^{15} +1.46150e48 q^{16} -2.49146e49 q^{17} +1.49812e48 q^{18} +3.58251e51 q^{19} -2.77739e51 q^{20} -4.24392e53 q^{21} +1.49783e52 q^{22} -1.21454e54 q^{23} +2.79474e55 q^{24} -4.08312e56 q^{25} +1.56584e57 q^{26} +9.35183e57 q^{27} +2.44019e58 q^{28} +7.48499e58 q^{29} -5.31104e58 q^{30} +4.18685e60 q^{31} -1.60694e60 q^{32} +2.86422e59 q^{33} +2.73939e61 q^{34} -4.63726e61 q^{35} -1.64720e60 q^{36} -4.16471e63 q^{37} -3.93901e63 q^{38} +2.99427e64 q^{39} +3.05377e63 q^{40} +2.46558e65 q^{41} +4.66624e65 q^{42} +4.35471e65 q^{43} -1.64688e64 q^{44} +3.13028e63 q^{45} +1.33540e66 q^{46} +5.69163e67 q^{47} -3.07285e67 q^{48} +1.23673e68 q^{49} +4.48944e68 q^{50} +5.23838e68 q^{51} -1.72166e69 q^{52} -4.75793e69 q^{53} -1.02824e70 q^{54} +3.12969e67 q^{55} -2.68302e70 q^{56} -7.53234e70 q^{57} -8.22983e70 q^{58} +8.16342e71 q^{59} +5.83955e70 q^{60} +2.39995e72 q^{61} -4.60349e72 q^{62} -2.75024e70 q^{63} +1.76685e72 q^{64} +3.27179e72 q^{65} -3.14924e71 q^{66} -4.34245e72 q^{67} -3.01199e73 q^{68} +2.55360e73 q^{69} +5.09873e73 q^{70} -1.27087e75 q^{71} +1.81111e72 q^{72} -2.61921e75 q^{73} +4.57915e75 q^{74} +8.58489e75 q^{75} +4.33099e75 q^{76} -2.74972e74 q^{77} -3.29223e76 q^{78} -5.46168e76 q^{79} -3.35766e75 q^{80} -1.96021e77 q^{81} -2.71094e77 q^{82} -3.44153e77 q^{83} -5.13058e77 q^{84} +5.72390e76 q^{85} -4.78805e77 q^{86} -1.57374e78 q^{87} +1.81077e76 q^{88} -1.44681e79 q^{89} -3.44178e75 q^{90} -2.87457e79 q^{91} -1.46829e78 q^{92} -8.80299e79 q^{93} -6.25801e79 q^{94} -8.23047e78 q^{95} +3.37864e79 q^{96} -3.90900e80 q^{97} -1.35979e80 q^{98} +1.85614e76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3298534883328q^{2} + 12604360672390214988q^{3} + \)\(36\!\cdots\!28\)\(q^{4} - \)\(20\!\cdots\!50\)\(q^{5} - \)\(13\!\cdots\!88\)\(q^{6} - \)\(55\!\cdots\!24\)\(q^{7} - \)\(39\!\cdots\!28\)\(q^{8} - \)\(11\!\cdots\!61\)\(q^{9} + O(q^{10}) \) \( 3q - 3298534883328q^{2} + 12604360672390214988q^{3} + \)\(36\!\cdots\!28\)\(q^{4} - \)\(20\!\cdots\!50\)\(q^{5} - \)\(13\!\cdots\!88\)\(q^{6} - \)\(55\!\cdots\!24\)\(q^{7} - \)\(39\!\cdots\!28\)\(q^{8} - \)\(11\!\cdots\!61\)\(q^{9} + \)\(23\!\cdots\!00\)\(q^{10} + \)\(12\!\cdots\!36\)\(q^{11} + \)\(15\!\cdots\!88\)\(q^{12} - \)\(20\!\cdots\!42\)\(q^{13} + \)\(60\!\cdots\!24\)\(q^{14} + \)\(25\!\cdots\!00\)\(q^{15} + \)\(43\!\cdots\!28\)\(q^{16} + \)\(13\!\cdots\!46\)\(q^{17} + \)\(12\!\cdots\!36\)\(q^{18} + \)\(47\!\cdots\!60\)\(q^{19} - \)\(25\!\cdots\!00\)\(q^{20} - \)\(51\!\cdots\!04\)\(q^{21} - \)\(14\!\cdots\!36\)\(q^{22} - \)\(30\!\cdots\!72\)\(q^{23} - \)\(16\!\cdots\!88\)\(q^{24} + \)\(28\!\cdots\!25\)\(q^{25} + \)\(22\!\cdots\!92\)\(q^{26} - \)\(62\!\cdots\!20\)\(q^{27} - \)\(66\!\cdots\!24\)\(q^{28} + \)\(21\!\cdots\!90\)\(q^{29} - \)\(28\!\cdots\!00\)\(q^{30} - \)\(38\!\cdots\!04\)\(q^{31} - \)\(48\!\cdots\!28\)\(q^{32} + \)\(81\!\cdots\!56\)\(q^{33} - \)\(15\!\cdots\!96\)\(q^{34} + \)\(79\!\cdots\!00\)\(q^{35} - \)\(14\!\cdots\!36\)\(q^{36} - \)\(96\!\cdots\!14\)\(q^{37} - \)\(52\!\cdots\!60\)\(q^{38} + \)\(36\!\cdots\!68\)\(q^{39} + \)\(27\!\cdots\!00\)\(q^{40} + \)\(31\!\cdots\!26\)\(q^{41} + \)\(57\!\cdots\!04\)\(q^{42} + \)\(90\!\cdots\!68\)\(q^{43} + \)\(15\!\cdots\!36\)\(q^{44} + \)\(18\!\cdots\!50\)\(q^{45} + \)\(33\!\cdots\!72\)\(q^{46} + \)\(16\!\cdots\!56\)\(q^{47} + \)\(18\!\cdots\!88\)\(q^{48} + \)\(84\!\cdots\!71\)\(q^{49} - \)\(30\!\cdots\!00\)\(q^{50} - \)\(77\!\cdots\!84\)\(q^{51} - \)\(24\!\cdots\!92\)\(q^{52} - \)\(90\!\cdots\!62\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(47\!\cdots\!00\)\(q^{55} + \)\(73\!\cdots\!24\)\(q^{56} - \)\(21\!\cdots\!40\)\(q^{57} - \)\(23\!\cdots\!40\)\(q^{58} + \)\(17\!\cdots\!80\)\(q^{59} + \)\(31\!\cdots\!00\)\(q^{60} + \)\(36\!\cdots\!86\)\(q^{61} + \)\(42\!\cdots\!04\)\(q^{62} + \)\(97\!\cdots\!88\)\(q^{63} + \)\(53\!\cdots\!28\)\(q^{64} - \)\(44\!\cdots\!00\)\(q^{65} - \)\(89\!\cdots\!56\)\(q^{66} - \)\(45\!\cdots\!04\)\(q^{67} + \)\(16\!\cdots\!96\)\(q^{68} - \)\(38\!\cdots\!12\)\(q^{69} - \)\(87\!\cdots\!00\)\(q^{70} - \)\(66\!\cdots\!84\)\(q^{71} + \)\(15\!\cdots\!36\)\(q^{72} + \)\(28\!\cdots\!78\)\(q^{73} + \)\(10\!\cdots\!64\)\(q^{74} + \)\(10\!\cdots\!00\)\(q^{75} + \)\(57\!\cdots\!60\)\(q^{76} - \)\(30\!\cdots\!88\)\(q^{77} - \)\(40\!\cdots\!68\)\(q^{78} - \)\(16\!\cdots\!60\)\(q^{79} - \)\(30\!\cdots\!00\)\(q^{80} - \)\(29\!\cdots\!37\)\(q^{81} - \)\(34\!\cdots\!76\)\(q^{82} - \)\(15\!\cdots\!52\)\(q^{83} - \)\(62\!\cdots\!04\)\(q^{84} - \)\(52\!\cdots\!00\)\(q^{85} - \)\(10\!\cdots\!68\)\(q^{86} - \)\(55\!\cdots\!60\)\(q^{87} - \)\(17\!\cdots\!36\)\(q^{88} - \)\(86\!\cdots\!30\)\(q^{89} - \)\(20\!\cdots\!00\)\(q^{90} - \)\(58\!\cdots\!64\)\(q^{91} - \)\(36\!\cdots\!72\)\(q^{92} - \)\(24\!\cdots\!84\)\(q^{93} - \)\(17\!\cdots\!56\)\(q^{94} - \)\(43\!\cdots\!00\)\(q^{95} - \)\(20\!\cdots\!88\)\(q^{96} - \)\(53\!\cdots\!94\)\(q^{97} - \)\(93\!\cdots\!96\)\(q^{98} - \)\(54\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09951e12 −0.707107
\(3\) −2.10253e19 −0.998462 −0.499231 0.866469i \(-0.666384\pi\)
−0.499231 + 0.866469i \(0.666384\pi\)
\(4\) 1.20893e24 0.500000
\(5\) −2.29740e27 −0.112967 −0.0564836 0.998404i \(-0.517989\pi\)
−0.0564836 + 0.998404i \(0.517989\pi\)
\(6\) 2.31176e31 0.706020
\(7\) 2.01848e34 1.19827 0.599134 0.800649i \(-0.295512\pi\)
0.599134 + 0.800649i \(0.295512\pi\)
\(8\) −1.32923e36 −0.353553
\(9\) −1.36253e36 −0.00307273
\(10\) 2.52602e39 0.0798798
\(11\) −1.36227e40 −0.00907527 −0.00453764 0.999990i \(-0.501444\pi\)
−0.00453764 + 0.999990i \(0.501444\pi\)
\(12\) −2.54180e43 −0.499231
\(13\) −1.42413e45 −1.09356 −0.546780 0.837277i \(-0.684146\pi\)
−0.546780 + 0.837277i \(0.684146\pi\)
\(14\) −2.21934e46 −0.847303
\(15\) 4.83036e46 0.112793
\(16\) 1.46150e48 0.250000
\(17\) −2.49146e49 −0.365825 −0.182912 0.983129i \(-0.558552\pi\)
−0.182912 + 0.983129i \(0.558552\pi\)
\(18\) 1.49812e48 0.00217275
\(19\) 3.58251e51 0.581657 0.290828 0.956775i \(-0.406069\pi\)
0.290828 + 0.956775i \(0.406069\pi\)
\(20\) −2.77739e51 −0.0564836
\(21\) −4.24392e53 −1.19643
\(22\) 1.49783e52 0.00641719
\(23\) −1.21454e54 −0.0859871 −0.0429936 0.999075i \(-0.513689\pi\)
−0.0429936 + 0.999075i \(0.513689\pi\)
\(24\) 2.79474e55 0.353010
\(25\) −4.08312e56 −0.987238
\(26\) 1.56584e57 0.773263
\(27\) 9.35183e57 1.00153
\(28\) 2.44019e58 0.599134
\(29\) 7.48499e58 0.443683 0.221841 0.975083i \(-0.428793\pi\)
0.221841 + 0.975083i \(0.428793\pi\)
\(30\) −5.31104e58 −0.0797570
\(31\) 4.18685e60 1.66625 0.833123 0.553088i \(-0.186551\pi\)
0.833123 + 0.553088i \(0.186551\pi\)
\(32\) −1.60694e60 −0.176777
\(33\) 2.86422e59 0.00906132
\(34\) 2.73939e61 0.258677
\(35\) −4.63726e61 −0.135365
\(36\) −1.64720e60 −0.00153637
\(37\) −4.16471e63 −1.28061 −0.640303 0.768123i \(-0.721191\pi\)
−0.640303 + 0.768123i \(0.721191\pi\)
\(38\) −3.93901e63 −0.411293
\(39\) 2.99427e64 1.09188
\(40\) 3.05377e63 0.0399399
\(41\) 2.46558e65 1.18624 0.593121 0.805113i \(-0.297895\pi\)
0.593121 + 0.805113i \(0.297895\pi\)
\(42\) 4.66624e65 0.846000
\(43\) 4.35471e65 0.304429 0.152215 0.988347i \(-0.451359\pi\)
0.152215 + 0.988347i \(0.451359\pi\)
\(44\) −1.64688e64 −0.00453764
\(45\) 3.13028e63 0.000347118 0
\(46\) 1.33540e66 0.0608021
\(47\) 5.69163e67 1.08461 0.542305 0.840182i \(-0.317552\pi\)
0.542305 + 0.840182i \(0.317552\pi\)
\(48\) −3.07285e67 −0.249616
\(49\) 1.23673e68 0.435845
\(50\) 4.48944e68 0.698083
\(51\) 5.23838e68 0.365262
\(52\) −1.72166e69 −0.546780
\(53\) −4.75793e69 −0.698626 −0.349313 0.937006i \(-0.613585\pi\)
−0.349313 + 0.937006i \(0.613585\pi\)
\(54\) −1.02824e70 −0.708189
\(55\) 3.12969e67 0.00102521
\(56\) −2.68302e70 −0.423652
\(57\) −7.53234e70 −0.580762
\(58\) −8.22983e70 −0.313731
\(59\) 8.16342e71 1.55728 0.778638 0.627473i \(-0.215911\pi\)
0.778638 + 0.627473i \(0.215911\pi\)
\(60\) 5.83955e70 0.0563967
\(61\) 2.39995e72 1.18671 0.593355 0.804941i \(-0.297803\pi\)
0.593355 + 0.804941i \(0.297803\pi\)
\(62\) −4.60349e72 −1.17821
\(63\) −2.75024e70 −0.00368195
\(64\) 1.76685e72 0.125000
\(65\) 3.27179e72 0.123536
\(66\) −3.14924e71 −0.00640732
\(67\) −4.34245e72 −0.0480513 −0.0240256 0.999711i \(-0.507648\pi\)
−0.0240256 + 0.999711i \(0.507648\pi\)
\(68\) −3.01199e73 −0.182912
\(69\) 2.55360e73 0.0858549
\(70\) 5.09873e73 0.0957174
\(71\) −1.27087e75 −1.34319 −0.671597 0.740916i \(-0.734391\pi\)
−0.671597 + 0.740916i \(0.734391\pi\)
\(72\) 1.81111e72 0.00108637
\(73\) −2.61921e75 −0.898660 −0.449330 0.893366i \(-0.648337\pi\)
−0.449330 + 0.893366i \(0.648337\pi\)
\(74\) 4.57915e75 0.905525
\(75\) 8.58489e75 0.985720
\(76\) 4.33099e75 0.290828
\(77\) −2.74972e74 −0.0108746
\(78\) −3.29223e76 −0.772074
\(79\) −5.46168e76 −0.764591 −0.382296 0.924040i \(-0.624866\pi\)
−0.382296 + 0.924040i \(0.624866\pi\)
\(80\) −3.35766e75 −0.0282418
\(81\) −1.96021e77 −0.996918
\(82\) −2.71094e77 −0.838800
\(83\) −3.44153e77 −0.651761 −0.325881 0.945411i \(-0.605661\pi\)
−0.325881 + 0.945411i \(0.605661\pi\)
\(84\) −5.13058e77 −0.598213
\(85\) 5.72390e76 0.0413262
\(86\) −4.78805e77 −0.215264
\(87\) −1.57374e78 −0.443000
\(88\) 1.81077e76 0.00320859
\(89\) −1.44681e79 −1.62225 −0.811123 0.584875i \(-0.801143\pi\)
−0.811123 + 0.584875i \(0.801143\pi\)
\(90\) −3.44178e75 −0.000245449 0
\(91\) −2.87457e79 −1.31038
\(92\) −1.46829e78 −0.0429936
\(93\) −8.80299e79 −1.66368
\(94\) −6.25801e79 −0.766935
\(95\) −8.23047e78 −0.0657081
\(96\) 3.37864e79 0.176505
\(97\) −3.90900e80 −1.34218 −0.671090 0.741376i \(-0.734173\pi\)
−0.671090 + 0.741376i \(0.734173\pi\)
\(98\) −1.35979e80 −0.308189
\(99\) 1.85614e76 2.78859e−5 0
\(100\) −4.93619e80 −0.493619
\(101\) 7.67011e80 0.512609 0.256304 0.966596i \(-0.417495\pi\)
0.256304 + 0.966596i \(0.417495\pi\)
\(102\) −5.75966e80 −0.258280
\(103\) 4.13492e81 1.24899 0.624496 0.781028i \(-0.285305\pi\)
0.624496 + 0.781028i \(0.285305\pi\)
\(104\) 1.89299e81 0.386632
\(105\) 9.74999e80 0.135157
\(106\) 5.23139e81 0.494003
\(107\) 1.35023e82 0.871697 0.435848 0.900020i \(-0.356448\pi\)
0.435848 + 0.900020i \(0.356448\pi\)
\(108\) 1.13057e82 0.500765
\(109\) −5.08267e82 −1.54995 −0.774977 0.631990i \(-0.782239\pi\)
−0.774977 + 0.631990i \(0.782239\pi\)
\(110\) −3.44113e79 −0.000724931 0
\(111\) 8.75644e82 1.27864
\(112\) 2.95001e82 0.299567
\(113\) 2.71916e83 1.92645 0.963227 0.268690i \(-0.0865906\pi\)
0.963227 + 0.268690i \(0.0865906\pi\)
\(114\) 8.28190e82 0.410661
\(115\) 2.79028e81 0.00971372
\(116\) 9.04880e82 0.221841
\(117\) 1.94041e81 0.00336021
\(118\) −8.97577e83 −1.10116
\(119\) −5.02897e83 −0.438356
\(120\) −6.42066e82 −0.0398785
\(121\) −2.25305e84 −0.999918
\(122\) −2.63878e84 −0.839131
\(123\) −5.18397e84 −1.18442
\(124\) 5.06159e84 0.833123
\(125\) 1.88824e84 0.224493
\(126\) 3.02392e82 0.00260354
\(127\) −1.79031e85 −1.11912 −0.559561 0.828789i \(-0.689030\pi\)
−0.559561 + 0.828789i \(0.689030\pi\)
\(128\) −1.94267e84 −0.0883883
\(129\) −9.15591e84 −0.303961
\(130\) −3.59737e84 −0.0873533
\(131\) 3.80860e85 0.678075 0.339038 0.940773i \(-0.389899\pi\)
0.339038 + 0.940773i \(0.389899\pi\)
\(132\) 3.46263e83 0.00453066
\(133\) 7.23123e85 0.696980
\(134\) 4.77457e84 0.0339774
\(135\) −2.14849e85 −0.113140
\(136\) 3.31172e85 0.129339
\(137\) 2.38833e86 0.693284 0.346642 0.937997i \(-0.387322\pi\)
0.346642 + 0.937997i \(0.387322\pi\)
\(138\) −2.80772e85 −0.0607086
\(139\) 1.17088e87 1.88979 0.944894 0.327376i \(-0.106164\pi\)
0.944894 + 0.327376i \(0.106164\pi\)
\(140\) −5.60611e85 −0.0676824
\(141\) −1.19668e87 −1.08294
\(142\) 1.39734e87 0.949782
\(143\) 1.94004e85 0.00992435
\(144\) −1.99134e84 −0.000768183 0
\(145\) −1.71960e86 −0.0501216
\(146\) 2.87986e87 0.635448
\(147\) −2.60026e87 −0.435175
\(148\) −5.03483e87 −0.640303
\(149\) −1.06584e88 −1.03192 −0.515961 0.856612i \(-0.672565\pi\)
−0.515961 + 0.856612i \(0.672565\pi\)
\(150\) −9.43919e87 −0.697010
\(151\) −2.18402e88 −1.23222 −0.616112 0.787658i \(-0.711293\pi\)
−0.616112 + 0.787658i \(0.711293\pi\)
\(152\) −4.76197e87 −0.205647
\(153\) 3.39470e85 0.00112408
\(154\) 3.02334e86 0.00768951
\(155\) −9.61889e87 −0.188231
\(156\) 3.61985e88 0.545939
\(157\) 4.25616e88 0.495544 0.247772 0.968818i \(-0.420302\pi\)
0.247772 + 0.968818i \(0.420302\pi\)
\(158\) 6.00518e88 0.540648
\(159\) 1.00037e89 0.697552
\(160\) 3.69179e87 0.0199700
\(161\) −2.45152e88 −0.103036
\(162\) 2.15527e89 0.704927
\(163\) −5.87911e89 −1.49870 −0.749348 0.662177i \(-0.769633\pi\)
−0.749348 + 0.662177i \(0.769633\pi\)
\(164\) 2.98071e89 0.593121
\(165\) −6.58026e86 −0.00102363
\(166\) 3.78400e89 0.460865
\(167\) 1.05962e90 1.01189 0.505943 0.862567i \(-0.331144\pi\)
0.505943 + 0.862567i \(0.331144\pi\)
\(168\) 5.64113e89 0.423000
\(169\) 3.32188e89 0.195872
\(170\) −6.29349e88 −0.0292220
\(171\) −4.88128e87 −0.00178727
\(172\) 5.26452e89 0.152215
\(173\) −6.31304e90 −1.44335 −0.721674 0.692233i \(-0.756627\pi\)
−0.721674 + 0.692233i \(0.756627\pi\)
\(174\) 1.73035e90 0.313249
\(175\) −8.24170e90 −1.18298
\(176\) −1.99096e88 −0.00226882
\(177\) −1.71638e91 −1.55488
\(178\) 1.59079e91 1.14710
\(179\) −1.38933e91 −0.798470 −0.399235 0.916849i \(-0.630724\pi\)
−0.399235 + 0.916849i \(0.630724\pi\)
\(180\) 3.78428e87 0.000173559 0
\(181\) −3.93299e90 −0.144125 −0.0720626 0.997400i \(-0.522958\pi\)
−0.0720626 + 0.997400i \(0.522958\pi\)
\(182\) 3.16062e91 0.926576
\(183\) −5.04598e91 −1.18489
\(184\) 1.61440e90 0.0304010
\(185\) 9.56803e90 0.144666
\(186\) 9.67899e91 1.17640
\(187\) 3.39405e89 0.00331996
\(188\) 6.88076e91 0.542305
\(189\) 1.88765e92 1.20010
\(190\) 9.04950e90 0.0464626
\(191\) 8.49770e91 0.352736 0.176368 0.984324i \(-0.443565\pi\)
0.176368 + 0.984324i \(0.443565\pi\)
\(192\) −3.71485e91 −0.124808
\(193\) −2.29054e92 −0.623545 −0.311772 0.950157i \(-0.600923\pi\)
−0.311772 + 0.950157i \(0.600923\pi\)
\(194\) 4.29799e92 0.949064
\(195\) −6.87904e91 −0.123346
\(196\) 1.49511e92 0.217923
\(197\) −1.06527e93 −1.26351 −0.631753 0.775170i \(-0.717664\pi\)
−0.631753 + 0.775170i \(0.717664\pi\)
\(198\) −2.04084e88 −1.97183e−5 0
\(199\) −1.73716e93 −1.36865 −0.684323 0.729179i \(-0.739902\pi\)
−0.684323 + 0.729179i \(0.739902\pi\)
\(200\) 5.42740e92 0.349041
\(201\) 9.13014e91 0.0479774
\(202\) −8.43338e92 −0.362469
\(203\) 1.51083e93 0.531650
\(204\) 6.33281e92 0.182631
\(205\) −5.66444e92 −0.134006
\(206\) −4.54639e93 −0.883170
\(207\) 1.65484e90 0.000264215 0
\(208\) −2.08136e93 −0.273390
\(209\) −4.88035e91 −0.00527869
\(210\) −1.07202e93 −0.0955703
\(211\) 2.25856e93 0.166108 0.0830542 0.996545i \(-0.473533\pi\)
0.0830542 + 0.996545i \(0.473533\pi\)
\(212\) −5.75198e93 −0.349313
\(213\) 2.67205e94 1.34113
\(214\) −1.48460e94 −0.616383
\(215\) −1.00045e93 −0.0343905
\(216\) −1.24307e94 −0.354094
\(217\) 8.45108e94 1.99661
\(218\) 5.58845e94 1.09598
\(219\) 5.50698e94 0.897278
\(220\) 3.78356e91 0.000512604 0
\(221\) 3.54816e94 0.400051
\(222\) −9.62781e94 −0.904132
\(223\) −1.81229e95 −1.41867 −0.709333 0.704874i \(-0.751004\pi\)
−0.709333 + 0.704874i \(0.751004\pi\)
\(224\) −3.24357e94 −0.211826
\(225\) 5.56338e92 0.00303352
\(226\) −2.98975e95 −1.36221
\(227\) 2.52463e93 0.00961947 0.00480973 0.999988i \(-0.498469\pi\)
0.00480973 + 0.999988i \(0.498469\pi\)
\(228\) −9.10604e94 −0.290381
\(229\) 1.08894e95 0.290848 0.145424 0.989369i \(-0.453545\pi\)
0.145424 + 0.989369i \(0.453545\pi\)
\(230\) −3.06795e93 −0.00686864
\(231\) 5.78136e93 0.0108579
\(232\) −9.94926e94 −0.156865
\(233\) −5.10521e95 −0.676237 −0.338118 0.941104i \(-0.609790\pi\)
−0.338118 + 0.941104i \(0.609790\pi\)
\(234\) −2.13351e93 −0.00237603
\(235\) −1.30760e95 −0.122525
\(236\) 9.86897e95 0.778638
\(237\) 1.14834e96 0.763416
\(238\) 5.52941e95 0.309965
\(239\) −3.29411e96 −1.55820 −0.779100 0.626900i \(-0.784323\pi\)
−0.779100 + 0.626900i \(0.784323\pi\)
\(240\) 7.05959e94 0.0281984
\(241\) 3.74739e96 1.26485 0.632424 0.774622i \(-0.282060\pi\)
0.632424 + 0.774622i \(0.282060\pi\)
\(242\) 2.47726e96 0.707049
\(243\) −2.54453e94 −0.00614544
\(244\) 2.90137e96 0.593355
\(245\) −2.84126e95 −0.0492362
\(246\) 5.69983e96 0.837510
\(247\) −5.10194e96 −0.636076
\(248\) −5.56528e96 −0.589107
\(249\) 7.23592e96 0.650759
\(250\) −2.07614e96 −0.158740
\(251\) −2.15478e97 −1.40157 −0.700787 0.713370i \(-0.747168\pi\)
−0.700787 + 0.713370i \(0.747168\pi\)
\(252\) −3.32484e94 −0.00184098
\(253\) 1.65453e94 0.000780357 0
\(254\) 1.96847e97 0.791339
\(255\) −1.20347e96 −0.0412627
\(256\) 2.13599e96 0.0625000
\(257\) −2.91463e97 −0.728270 −0.364135 0.931346i \(-0.618635\pi\)
−0.364135 + 0.931346i \(0.618635\pi\)
\(258\) 1.00670e97 0.214933
\(259\) −8.40639e97 −1.53451
\(260\) 3.95535e96 0.0617681
\(261\) −1.01985e95 −0.00136332
\(262\) −4.18760e97 −0.479471
\(263\) 3.04469e94 0.000298769 0 0.000149384 1.00000i \(-0.499952\pi\)
0.000149384 1.00000i \(0.499952\pi\)
\(264\) −3.80720e95 −0.00320366
\(265\) 1.09309e97 0.0789218
\(266\) −7.95082e97 −0.492839
\(267\) 3.04197e98 1.61975
\(268\) −5.24970e96 −0.0240256
\(269\) 2.83028e98 1.11394 0.556969 0.830533i \(-0.311964\pi\)
0.556969 + 0.830533i \(0.311964\pi\)
\(270\) 2.36229e97 0.0800021
\(271\) 2.67907e98 0.781138 0.390569 0.920574i \(-0.372278\pi\)
0.390569 + 0.920574i \(0.372278\pi\)
\(272\) −3.64128e97 −0.0914562
\(273\) 6.04387e98 1.30836
\(274\) −2.62600e98 −0.490226
\(275\) 5.56232e96 0.00895946
\(276\) 3.08712e97 0.0429275
\(277\) −3.99686e98 −0.480052 −0.240026 0.970766i \(-0.577156\pi\)
−0.240026 + 0.970766i \(0.577156\pi\)
\(278\) −1.28740e99 −1.33628
\(279\) −5.70472e96 −0.00511993
\(280\) 6.16398e97 0.0478587
\(281\) −1.29279e99 −0.868807 −0.434403 0.900718i \(-0.643041\pi\)
−0.434403 + 0.900718i \(0.643041\pi\)
\(282\) 1.31577e99 0.765756
\(283\) −2.45187e99 −1.23637 −0.618184 0.786034i \(-0.712131\pi\)
−0.618184 + 0.786034i \(0.712131\pi\)
\(284\) −1.53639e99 −0.671597
\(285\) 1.73048e98 0.0656071
\(286\) −2.13310e97 −0.00701757
\(287\) 4.97673e99 1.42144
\(288\) 2.18950e96 0.000543187 0
\(289\) −4.01760e99 −0.866172
\(290\) 1.89073e98 0.0354413
\(291\) 8.21880e99 1.34012
\(292\) −3.16644e99 −0.449330
\(293\) −9.78470e99 −1.20895 −0.604476 0.796624i \(-0.706617\pi\)
−0.604476 + 0.796624i \(0.706617\pi\)
\(294\) 2.85901e99 0.307715
\(295\) −1.87547e99 −0.175921
\(296\) 5.53585e99 0.452762
\(297\) −1.27397e98 −0.00908916
\(298\) 1.17190e100 0.729679
\(299\) 1.72965e99 0.0940321
\(300\) 1.03785e100 0.492860
\(301\) 8.78989e99 0.364788
\(302\) 2.40135e100 0.871314
\(303\) −1.61267e100 −0.511821
\(304\) 5.23585e99 0.145414
\(305\) −5.51366e99 −0.134059
\(306\) −3.73251e97 −0.000794846 0
\(307\) 3.16645e100 0.590837 0.295419 0.955368i \(-0.404541\pi\)
0.295419 + 0.955368i \(0.404541\pi\)
\(308\) −3.32420e98 −0.00543730
\(309\) −8.69380e100 −1.24707
\(310\) 1.05761e100 0.133099
\(311\) −1.26423e101 −1.39646 −0.698230 0.715873i \(-0.746029\pi\)
−0.698230 + 0.715873i \(0.746029\pi\)
\(312\) −3.98007e100 −0.386037
\(313\) 3.25054e100 0.276955 0.138478 0.990366i \(-0.455779\pi\)
0.138478 + 0.990366i \(0.455779\pi\)
\(314\) −4.67970e100 −0.350403
\(315\) 6.31841e97 0.000415940 0
\(316\) −6.60277e100 −0.382296
\(317\) 2.17246e101 1.10676 0.553379 0.832930i \(-0.313338\pi\)
0.553379 + 0.832930i \(0.313338\pi\)
\(318\) −1.09992e101 −0.493244
\(319\) −1.01966e99 −0.00402654
\(320\) −4.05916e99 −0.0141209
\(321\) −2.83891e101 −0.870356
\(322\) 2.69547e100 0.0728572
\(323\) −8.92570e100 −0.212784
\(324\) −2.36975e101 −0.498459
\(325\) 5.81488e101 1.07960
\(326\) 6.46414e101 1.05974
\(327\) 1.06865e102 1.54757
\(328\) −3.27732e101 −0.419400
\(329\) 1.14884e102 1.29965
\(330\) 7.23508e98 0.000723817 0
\(331\) −5.29292e100 −0.0468448 −0.0234224 0.999726i \(-0.507456\pi\)
−0.0234224 + 0.999726i \(0.507456\pi\)
\(332\) −4.16055e101 −0.325881
\(333\) 5.67455e99 0.00393496
\(334\) −1.16506e102 −0.715512
\(335\) 9.97636e99 0.00542822
\(336\) −6.20249e101 −0.299106
\(337\) 9.19849e101 0.393283 0.196642 0.980475i \(-0.436996\pi\)
0.196642 + 0.980475i \(0.436996\pi\)
\(338\) −3.65245e101 −0.138503
\(339\) −5.71713e102 −1.92349
\(340\) 6.91977e100 0.0206631
\(341\) −5.70363e100 −0.0151216
\(342\) 5.36702e99 0.00126379
\(343\) −3.23120e102 −0.676008
\(344\) −5.78840e101 −0.107632
\(345\) −5.86666e100 −0.00969879
\(346\) 6.94126e102 1.02060
\(347\) 6.02129e102 0.787673 0.393836 0.919181i \(-0.371148\pi\)
0.393836 + 0.919181i \(0.371148\pi\)
\(348\) −1.90254e102 −0.221500
\(349\) −3.16693e102 −0.328253 −0.164127 0.986439i \(-0.552481\pi\)
−0.164127 + 0.986439i \(0.552481\pi\)
\(350\) 9.06185e102 0.836490
\(351\) −1.33182e103 −1.09523
\(352\) 2.18908e100 0.00160430
\(353\) −1.90508e103 −1.24462 −0.622311 0.782770i \(-0.713806\pi\)
−0.622311 + 0.782770i \(0.713806\pi\)
\(354\) 1.88718e103 1.09947
\(355\) 2.91971e102 0.151737
\(356\) −1.74909e103 −0.811123
\(357\) 1.05736e103 0.437682
\(358\) 1.52759e103 0.564604
\(359\) 5.50297e103 1.81665 0.908327 0.418262i \(-0.137360\pi\)
0.908327 + 0.418262i \(0.137360\pi\)
\(360\) −4.16086e99 −0.000122725 0
\(361\) −2.51008e103 −0.661676
\(362\) 4.32436e102 0.101912
\(363\) 4.73712e103 0.998380
\(364\) −3.47514e103 −0.655188
\(365\) 6.01739e102 0.101519
\(366\) 5.54811e103 0.837841
\(367\) −4.41306e103 −0.596711 −0.298356 0.954455i \(-0.596438\pi\)
−0.298356 + 0.954455i \(0.596438\pi\)
\(368\) −1.77505e102 −0.0214968
\(369\) −3.35943e101 −0.00364501
\(370\) −1.05202e103 −0.102295
\(371\) −9.60378e103 −0.837141
\(372\) −1.06422e104 −0.831842
\(373\) −1.06681e104 −0.747959 −0.373979 0.927437i \(-0.622007\pi\)
−0.373979 + 0.927437i \(0.622007\pi\)
\(374\) −3.73180e101 −0.00234757
\(375\) −3.97009e103 −0.224147
\(376\) −7.56547e103 −0.383467
\(377\) −1.06596e104 −0.485193
\(378\) −2.07549e104 −0.848600
\(379\) 3.29469e104 1.21039 0.605197 0.796076i \(-0.293094\pi\)
0.605197 + 0.796076i \(0.293094\pi\)
\(380\) −9.95003e102 −0.0328540
\(381\) 3.76418e104 1.11740
\(382\) −9.34332e103 −0.249422
\(383\) 2.22508e104 0.534312 0.267156 0.963653i \(-0.413916\pi\)
0.267156 + 0.963653i \(0.413916\pi\)
\(384\) 4.08452e103 0.0882524
\(385\) 6.31721e101 0.00122847
\(386\) 2.51848e104 0.440913
\(387\) −5.93342e101 −0.000935430 0
\(388\) −4.72569e104 −0.671090
\(389\) 1.38573e105 1.77305 0.886526 0.462679i \(-0.153112\pi\)
0.886526 + 0.462679i \(0.153112\pi\)
\(390\) 7.56359e103 0.0872190
\(391\) 3.02598e103 0.0314562
\(392\) −1.64389e104 −0.154095
\(393\) −8.00770e104 −0.677033
\(394\) 1.17128e105 0.893433
\(395\) 1.25477e104 0.0863737
\(396\) 2.24393e100 1.39429e−5 0
\(397\) −1.20081e105 −0.673689 −0.336844 0.941560i \(-0.609360\pi\)
−0.336844 + 0.941560i \(0.609360\pi\)
\(398\) 1.91003e105 0.967779
\(399\) −1.52039e105 −0.695909
\(400\) −5.96749e104 −0.246810
\(401\) −8.56806e104 −0.320284 −0.160142 0.987094i \(-0.551195\pi\)
−0.160142 + 0.987094i \(0.551195\pi\)
\(402\) −1.00387e104 −0.0339252
\(403\) −5.96260e105 −1.82214
\(404\) 9.27259e104 0.256304
\(405\) 4.50339e104 0.112619
\(406\) −1.66118e105 −0.375934
\(407\) 5.67347e103 0.0116218
\(408\) −6.96300e104 −0.129140
\(409\) 3.81353e104 0.0640520 0.0320260 0.999487i \(-0.489804\pi\)
0.0320260 + 0.999487i \(0.489804\pi\)
\(410\) 6.22812e104 0.0947569
\(411\) −5.02154e105 −0.692218
\(412\) 4.99881e105 0.624496
\(413\) 1.64777e106 1.86603
\(414\) −1.81952e102 −0.000186829 0
\(415\) 7.90658e104 0.0736276
\(416\) 2.28848e105 0.193316
\(417\) −2.46181e106 −1.88688
\(418\) 5.36600e103 0.00373260
\(419\) 1.12635e106 0.711225 0.355613 0.934633i \(-0.384272\pi\)
0.355613 + 0.934633i \(0.384272\pi\)
\(420\) 1.17870e105 0.0675784
\(421\) 1.03233e106 0.537521 0.268760 0.963207i \(-0.413386\pi\)
0.268760 + 0.963207i \(0.413386\pi\)
\(422\) −2.48331e105 −0.117456
\(423\) −7.75502e103 −0.00333271
\(424\) 6.32437e105 0.247002
\(425\) 1.01730e106 0.361156
\(426\) −2.93795e106 −0.948322
\(427\) 4.84426e106 1.42200
\(428\) 1.63233e106 0.435848
\(429\) −4.07900e104 −0.00990909
\(430\) 1.10001e105 0.0243178
\(431\) 5.16918e106 1.04014 0.520070 0.854123i \(-0.325906\pi\)
0.520070 + 0.854123i \(0.325906\pi\)
\(432\) 1.36677e106 0.250383
\(433\) −5.31481e106 −0.886600 −0.443300 0.896373i \(-0.646192\pi\)
−0.443300 + 0.896373i \(0.646192\pi\)
\(434\) −9.29206e106 −1.41182
\(435\) 3.61552e105 0.0500445
\(436\) −6.14457e106 −0.774977
\(437\) −4.35109e105 −0.0500150
\(438\) −6.05499e106 −0.634471
\(439\) −1.64708e107 −1.57363 −0.786813 0.617191i \(-0.788270\pi\)
−0.786813 + 0.617191i \(0.788270\pi\)
\(440\) −4.16007e103 −0.000362466 0
\(441\) −1.68508e104 −0.00133924
\(442\) −3.90124e106 −0.282879
\(443\) −5.83215e105 −0.0385902 −0.0192951 0.999814i \(-0.506142\pi\)
−0.0192951 + 0.999814i \(0.506142\pi\)
\(444\) 1.05859e107 0.639318
\(445\) 3.32391e106 0.183261
\(446\) 1.99263e107 1.00315
\(447\) 2.24095e107 1.03033
\(448\) 3.56635e106 0.149783
\(449\) −2.70273e107 −1.03711 −0.518556 0.855044i \(-0.673530\pi\)
−0.518556 + 0.855044i \(0.673530\pi\)
\(450\) −6.11700e104 −0.00214502
\(451\) −3.35879e105 −0.0107655
\(452\) 3.28727e107 0.963227
\(453\) 4.59197e107 1.23033
\(454\) −2.77586e105 −0.00680199
\(455\) 6.60404e106 0.148030
\(456\) 1.00122e107 0.205330
\(457\) 2.99963e106 0.0562939 0.0281469 0.999604i \(-0.491039\pi\)
0.0281469 + 0.999604i \(0.491039\pi\)
\(458\) −1.19730e107 −0.205661
\(459\) −2.32997e107 −0.366385
\(460\) 3.37325e105 0.00485686
\(461\) −6.71187e107 −0.885027 −0.442513 0.896762i \(-0.645913\pi\)
−0.442513 + 0.896762i \(0.645913\pi\)
\(462\) −6.35668e105 −0.00767768
\(463\) −3.73565e107 −0.413367 −0.206683 0.978408i \(-0.566267\pi\)
−0.206683 + 0.978408i \(0.566267\pi\)
\(464\) 1.09393e107 0.110921
\(465\) 2.02240e107 0.187942
\(466\) 5.61324e107 0.478172
\(467\) −6.42362e107 −0.501702 −0.250851 0.968026i \(-0.580710\pi\)
−0.250851 + 0.968026i \(0.580710\pi\)
\(468\) 2.34582e105 0.00168011
\(469\) −8.76514e106 −0.0575783
\(470\) 1.43772e107 0.0866384
\(471\) −8.94872e107 −0.494782
\(472\) −1.08510e108 −0.550580
\(473\) −5.93229e105 −0.00276278
\(474\) −1.26261e108 −0.539816
\(475\) −1.46278e108 −0.574234
\(476\) −6.07965e107 −0.219178
\(477\) 6.48282e105 0.00214669
\(478\) 3.62191e108 1.10181
\(479\) 5.34560e107 0.149420 0.0747100 0.997205i \(-0.476197\pi\)
0.0747100 + 0.997205i \(0.476197\pi\)
\(480\) −7.76210e106 −0.0199393
\(481\) 5.93107e108 1.40042
\(482\) −4.12030e108 −0.894383
\(483\) 5.15440e107 0.102877
\(484\) −2.72378e108 −0.499959
\(485\) 8.98055e107 0.151622
\(486\) 2.79774e106 0.00434548
\(487\) 3.63856e108 0.520004 0.260002 0.965608i \(-0.416277\pi\)
0.260002 + 0.965608i \(0.416277\pi\)
\(488\) −3.19009e108 −0.419565
\(489\) 1.23610e109 1.49639
\(490\) 3.12400e107 0.0348152
\(491\) 8.51295e108 0.873534 0.436767 0.899575i \(-0.356123\pi\)
0.436767 + 0.899575i \(0.356123\pi\)
\(492\) −6.26703e108 −0.592209
\(493\) −1.86486e108 −0.162310
\(494\) 5.60965e108 0.449774
\(495\) −4.26429e103 −3.15019e−6 0
\(496\) 6.11909e108 0.416561
\(497\) −2.56523e109 −1.60951
\(498\) −7.95598e108 −0.460156
\(499\) 1.21907e109 0.650065 0.325033 0.945703i \(-0.394625\pi\)
0.325033 + 0.945703i \(0.394625\pi\)
\(500\) 2.28274e108 0.112246
\(501\) −2.22788e109 −1.01033
\(502\) 2.36920e109 0.991063
\(503\) −4.35706e108 −0.168147 −0.0840737 0.996460i \(-0.526793\pi\)
−0.0840737 + 0.996460i \(0.526793\pi\)
\(504\) 3.65570e106 0.00130177
\(505\) −1.76213e108 −0.0579079
\(506\) −1.81917e106 −0.000551796 0
\(507\) −6.98436e108 −0.195571
\(508\) −2.16435e109 −0.559561
\(509\) −6.58524e109 −1.57218 −0.786089 0.618114i \(-0.787897\pi\)
−0.786089 + 0.618114i \(0.787897\pi\)
\(510\) 1.32323e108 0.0291771
\(511\) −5.28683e109 −1.07683
\(512\) −2.34854e108 −0.0441942
\(513\) 3.35030e109 0.582547
\(514\) 3.20467e109 0.514964
\(515\) −9.49958e108 −0.141095
\(516\) −1.10688e109 −0.151981
\(517\) −7.75354e107 −0.00984313
\(518\) 9.24292e109 1.08506
\(519\) 1.32734e110 1.44113
\(520\) −4.34896e108 −0.0436767
\(521\) 1.28591e110 1.19476 0.597382 0.801957i \(-0.296208\pi\)
0.597382 + 0.801957i \(0.296208\pi\)
\(522\) 1.12134e107 0.000964011 0
\(523\) −3.50557e109 −0.278895 −0.139448 0.990229i \(-0.544533\pi\)
−0.139448 + 0.990229i \(0.544533\pi\)
\(524\) 4.60431e109 0.339038
\(525\) 1.73284e110 1.18116
\(526\) −3.34767e106 −0.000211261 0
\(527\) −1.04314e110 −0.609554
\(528\) 4.18606e107 0.00226533
\(529\) −1.98030e110 −0.992606
\(530\) −1.20186e109 −0.0558062
\(531\) −1.11229e108 −0.00478509
\(532\) 8.74202e109 0.348490
\(533\) −3.51130e110 −1.29723
\(534\) −3.34468e110 −1.14534
\(535\) −3.10203e109 −0.0984731
\(536\) 5.77210e108 0.0169887
\(537\) 2.92112e110 0.797242
\(538\) −3.11192e110 −0.787674
\(539\) −1.68476e108 −0.00395541
\(540\) −2.59737e109 −0.0565700
\(541\) 7.10748e110 1.43624 0.718119 0.695920i \(-0.245003\pi\)
0.718119 + 0.695920i \(0.245003\pi\)
\(542\) −2.94567e110 −0.552348
\(543\) 8.26923e109 0.143904
\(544\) 4.00363e109 0.0646693
\(545\) 1.16769e110 0.175094
\(546\) −6.64531e110 −0.925152
\(547\) −4.39560e110 −0.568239 −0.284119 0.958789i \(-0.591701\pi\)
−0.284119 + 0.958789i \(0.591701\pi\)
\(548\) 2.88731e110 0.346642
\(549\) −3.27001e108 −0.00364644
\(550\) −6.11583e108 −0.00633529
\(551\) 2.68151e110 0.258071
\(552\) −3.39432e109 −0.0303543
\(553\) −1.10243e111 −0.916185
\(554\) 4.39460e110 0.339448
\(555\) −2.01171e110 −0.144444
\(556\) 1.41551e111 0.944894
\(557\) 2.19281e111 1.36102 0.680511 0.732738i \(-0.261758\pi\)
0.680511 + 0.732738i \(0.261758\pi\)
\(558\) 6.27240e108 0.00362033
\(559\) −6.20165e110 −0.332912
\(560\) −6.77737e109 −0.0338412
\(561\) −7.13609e108 −0.00331486
\(562\) 1.42144e111 0.614339
\(563\) 2.72175e111 1.09461 0.547303 0.836935i \(-0.315655\pi\)
0.547303 + 0.836935i \(0.315655\pi\)
\(564\) −1.44670e111 −0.541471
\(565\) −6.24702e110 −0.217626
\(566\) 2.69586e111 0.874244
\(567\) −3.95664e111 −1.19457
\(568\) 1.68928e111 0.474891
\(569\) −2.11741e111 −0.554316 −0.277158 0.960824i \(-0.589393\pi\)
−0.277158 + 0.960824i \(0.589393\pi\)
\(570\) −1.90269e110 −0.0463912
\(571\) 1.46222e110 0.0332086 0.0166043 0.999862i \(-0.494714\pi\)
0.0166043 + 0.999862i \(0.494714\pi\)
\(572\) 2.34537e109 0.00496217
\(573\) −1.78667e111 −0.352194
\(574\) −5.47197e111 −1.00511
\(575\) 4.95910e110 0.0848898
\(576\) −2.40738e108 −0.000384091 0
\(577\) −8.53416e111 −1.26923 −0.634615 0.772829i \(-0.718841\pi\)
−0.634615 + 0.772829i \(0.718841\pi\)
\(578\) 4.41740e111 0.612476
\(579\) 4.81594e111 0.622586
\(580\) −2.07887e110 −0.0250608
\(581\) −6.94665e111 −0.780984
\(582\) −9.03666e111 −0.947605
\(583\) 6.48158e109 0.00634022
\(584\) 3.48153e111 0.317724
\(585\) −4.45791e108 −0.000379594 0
\(586\) 1.07584e112 0.854858
\(587\) −1.30980e112 −0.971318 −0.485659 0.874148i \(-0.661420\pi\)
−0.485659 + 0.874148i \(0.661420\pi\)
\(588\) −3.14352e111 −0.217588
\(589\) 1.49994e112 0.969183
\(590\) 2.06210e111 0.124395
\(591\) 2.23976e112 1.26156
\(592\) −6.08674e111 −0.320151
\(593\) 1.34450e112 0.660459 0.330230 0.943901i \(-0.392874\pi\)
0.330230 + 0.943901i \(0.392874\pi\)
\(594\) 1.40075e110 0.00642701
\(595\) 1.15536e111 0.0495198
\(596\) −1.28852e112 −0.515961
\(597\) 3.65244e112 1.36654
\(598\) −1.90177e111 −0.0664907
\(599\) 3.09454e111 0.101114 0.0505568 0.998721i \(-0.483900\pi\)
0.0505568 + 0.998721i \(0.483900\pi\)
\(600\) −1.14113e112 −0.348505
\(601\) 4.06984e112 1.16188 0.580941 0.813946i \(-0.302685\pi\)
0.580941 + 0.813946i \(0.302685\pi\)
\(602\) −9.66459e111 −0.257944
\(603\) 5.91672e108 0.000147649 0
\(604\) −2.64032e112 −0.616112
\(605\) 5.17618e111 0.112958
\(606\) 1.77314e112 0.361912
\(607\) −5.43516e112 −1.03770 −0.518849 0.854866i \(-0.673639\pi\)
−0.518849 + 0.854866i \(0.673639\pi\)
\(608\) −5.75687e111 −0.102823
\(609\) −3.17657e112 −0.530833
\(610\) 6.06234e111 0.0947942
\(611\) −8.10559e112 −1.18608
\(612\) 4.10394e109 0.000562041 0
\(613\) −1.06775e113 −1.36874 −0.684372 0.729133i \(-0.739924\pi\)
−0.684372 + 0.729133i \(0.739924\pi\)
\(614\) −3.48155e112 −0.417785
\(615\) 1.19097e112 0.133800
\(616\) 3.65500e110 0.00384475
\(617\) 6.03780e112 0.594743 0.297372 0.954762i \(-0.403890\pi\)
0.297372 + 0.954762i \(0.403890\pi\)
\(618\) 9.55893e112 0.881812
\(619\) 8.14944e112 0.704136 0.352068 0.935974i \(-0.385479\pi\)
0.352068 + 0.935974i \(0.385479\pi\)
\(620\) −1.16285e112 −0.0941155
\(621\) −1.13581e112 −0.0861187
\(622\) 1.39003e113 0.987447
\(623\) −2.92036e113 −1.94389
\(624\) 4.37613e112 0.272969
\(625\) 1.64536e113 0.961878
\(626\) −3.57401e112 −0.195837
\(627\) 1.02611e111 0.00527058
\(628\) 5.14539e112 0.247772
\(629\) 1.03762e113 0.468477
\(630\) −6.94717e109 −0.000294114 0
\(631\) 5.50874e112 0.218707 0.109354 0.994003i \(-0.465122\pi\)
0.109354 + 0.994003i \(0.465122\pi\)
\(632\) 7.25982e112 0.270324
\(633\) −4.74869e112 −0.165853
\(634\) −2.38865e113 −0.782596
\(635\) 4.11307e112 0.126424
\(636\) 1.20937e113 0.348776
\(637\) −1.76125e113 −0.476623
\(638\) 1.12113e111 0.00284719
\(639\) 1.73160e111 0.00412728
\(640\) 4.46309e111 0.00998498
\(641\) 4.86842e113 1.02244 0.511220 0.859450i \(-0.329194\pi\)
0.511220 + 0.859450i \(0.329194\pi\)
\(642\) 3.12141e113 0.615435
\(643\) −8.15143e111 −0.0150900 −0.00754500 0.999972i \(-0.502402\pi\)
−0.00754500 + 0.999972i \(0.502402\pi\)
\(644\) −2.96371e112 −0.0515178
\(645\) 2.10348e112 0.0343377
\(646\) 9.81391e112 0.150461
\(647\) 4.95184e113 0.713088 0.356544 0.934279i \(-0.383955\pi\)
0.356544 + 0.934279i \(0.383955\pi\)
\(648\) 2.60557e113 0.352464
\(649\) −1.11208e112 −0.0141327
\(650\) −6.39353e113 −0.763395
\(651\) −1.77687e114 −1.99354
\(652\) −7.10740e113 −0.749348
\(653\) −8.70348e113 −0.862401 −0.431200 0.902256i \(-0.641910\pi\)
−0.431200 + 0.902256i \(0.641910\pi\)
\(654\) −1.17499e114 −1.09430
\(655\) −8.74989e112 −0.0766002
\(656\) 3.60345e113 0.296561
\(657\) 3.56876e111 0.00276134
\(658\) −1.26317e114 −0.918993
\(659\) 2.30030e114 1.57371 0.786857 0.617135i \(-0.211707\pi\)
0.786857 + 0.617135i \(0.211707\pi\)
\(660\) −7.95505e110 −0.000511816 0
\(661\) 1.94796e114 1.17875 0.589373 0.807861i \(-0.299375\pi\)
0.589373 + 0.807861i \(0.299375\pi\)
\(662\) 5.81962e112 0.0331243
\(663\) −7.46011e113 −0.399436
\(664\) 4.57457e113 0.230432
\(665\) −1.66130e113 −0.0787359
\(666\) −6.23923e111 −0.00278243
\(667\) −9.09080e112 −0.0381510
\(668\) 1.28100e114 0.505943
\(669\) 3.81039e114 1.41648
\(670\) −1.09691e112 −0.00383833
\(671\) −3.26939e112 −0.0107697
\(672\) 6.81971e113 0.211500
\(673\) 2.28004e114 0.665782 0.332891 0.942965i \(-0.391976\pi\)
0.332891 + 0.942965i \(0.391976\pi\)
\(674\) −1.01138e114 −0.278093
\(675\) −3.81847e114 −0.988749
\(676\) 4.01591e113 0.0979361
\(677\) 4.46383e114 1.02534 0.512669 0.858587i \(-0.328657\pi\)
0.512669 + 0.858587i \(0.328657\pi\)
\(678\) 6.28605e114 1.36011
\(679\) −7.89024e114 −1.60829
\(680\) −7.60837e112 −0.0146110
\(681\) −5.30812e112 −0.00960468
\(682\) 6.27120e112 0.0106926
\(683\) −8.52083e114 −1.36913 −0.684563 0.728954i \(-0.740007\pi\)
−0.684563 + 0.728954i \(0.740007\pi\)
\(684\) −5.90111e111 −0.000893637 0
\(685\) −5.48696e113 −0.0783184
\(686\) 3.55274e114 0.478010
\(687\) −2.28953e114 −0.290401
\(688\) 6.36441e113 0.0761074
\(689\) 6.77588e114 0.763989
\(690\) 6.45046e112 0.00685808
\(691\) −1.69879e115 −1.70325 −0.851625 0.524152i \(-0.824382\pi\)
−0.851625 + 0.524152i \(0.824382\pi\)
\(692\) −7.63199e114 −0.721674
\(693\) 3.74657e110 3.34147e−5 0
\(694\) −6.62048e114 −0.556969
\(695\) −2.68999e114 −0.213484
\(696\) 2.09186e114 0.156624
\(697\) −6.14291e114 −0.433957
\(698\) 3.48208e114 0.232110
\(699\) 1.07339e115 0.675197
\(700\) −9.96360e114 −0.591488
\(701\) 2.67824e115 1.50062 0.750308 0.661088i \(-0.229905\pi\)
0.750308 + 0.661088i \(0.229905\pi\)
\(702\) 1.46435e115 0.774447
\(703\) −1.49201e115 −0.744873
\(704\) −2.40692e112 −0.00113441
\(705\) 2.74926e114 0.122337
\(706\) 2.09466e115 0.880081
\(707\) 1.54820e115 0.614242
\(708\) −2.07498e115 −0.777441
\(709\) 1.40926e115 0.498676 0.249338 0.968416i \(-0.419787\pi\)
0.249338 + 0.968416i \(0.419787\pi\)
\(710\) −3.21025e114 −0.107294
\(711\) 7.44171e112 0.00234938
\(712\) 1.92314e115 0.573551
\(713\) −5.08509e114 −0.143276
\(714\) −1.16258e115 −0.309488
\(715\) −4.45706e112 −0.00112113
\(716\) −1.67960e115 −0.399235
\(717\) 6.92597e115 1.55580
\(718\) −6.05058e115 −1.28457
\(719\) −2.84699e115 −0.571303 −0.285651 0.958334i \(-0.592210\pi\)
−0.285651 + 0.958334i \(0.592210\pi\)
\(720\) 4.57491e111 8.67794e−5 0
\(721\) 8.34625e115 1.49663
\(722\) 2.75986e115 0.467875
\(723\) −7.87900e115 −1.26290
\(724\) −4.75469e114 −0.0720626
\(725\) −3.05621e115 −0.438020
\(726\) −5.20852e115 −0.705961
\(727\) 4.59849e114 0.0589483 0.0294741 0.999566i \(-0.490617\pi\)
0.0294741 + 0.999566i \(0.490617\pi\)
\(728\) 3.82096e115 0.463288
\(729\) 8.74559e115 1.00305
\(730\) −6.61619e114 −0.0717848
\(731\) −1.08496e115 −0.111368
\(732\) −6.10022e115 −0.592443
\(733\) −1.40579e116 −1.29184 −0.645919 0.763406i \(-0.723526\pi\)
−0.645919 + 0.763406i \(0.723526\pi\)
\(734\) 4.85221e115 0.421939
\(735\) 5.97384e114 0.0491605
\(736\) 1.95169e114 0.0152005
\(737\) 5.91559e112 0.000436079 0
\(738\) 3.69374e113 0.00257741
\(739\) −2.87356e116 −1.89811 −0.949053 0.315117i \(-0.897956\pi\)
−0.949053 + 0.315117i \(0.897956\pi\)
\(740\) 1.15670e115 0.0723332
\(741\) 1.07270e116 0.635098
\(742\) 1.05595e116 0.591948
\(743\) −2.96299e116 −1.57284 −0.786418 0.617694i \(-0.788067\pi\)
−0.786418 + 0.617694i \(0.788067\pi\)
\(744\) 1.17012e116 0.588201
\(745\) 2.44866e115 0.116573
\(746\) 1.17297e116 0.528887
\(747\) 4.68919e113 0.00200269
\(748\) 4.10315e113 0.00165998
\(749\) 2.72542e116 1.04453
\(750\) 4.36516e115 0.158496
\(751\) 7.39906e115 0.254542 0.127271 0.991868i \(-0.459378\pi\)
0.127271 + 0.991868i \(0.459378\pi\)
\(752\) 8.31833e115 0.271152
\(753\) 4.53048e116 1.39942
\(754\) 1.17203e116 0.343083
\(755\) 5.01757e115 0.139201
\(756\) 2.28203e116 0.600051
\(757\) 1.13053e116 0.281774 0.140887 0.990026i \(-0.455005\pi\)
0.140887 + 0.990026i \(0.455005\pi\)
\(758\) −3.62255e116 −0.855878
\(759\) −3.47870e113 −0.000779157 0
\(760\) 1.09402e115 0.0232313
\(761\) 6.89950e116 1.38912 0.694559 0.719436i \(-0.255600\pi\)
0.694559 + 0.719436i \(0.255600\pi\)
\(762\) −4.13876e116 −0.790122
\(763\) −1.02593e117 −1.85726
\(764\) 1.02731e116 0.176368
\(765\) −7.79899e112 −0.000126984 0
\(766\) −2.44650e116 −0.377816
\(767\) −1.16257e117 −1.70297
\(768\) −4.49098e115 −0.0624039
\(769\) −7.77013e116 −1.02426 −0.512131 0.858907i \(-0.671144\pi\)
−0.512131 + 0.858907i \(0.671144\pi\)
\(770\) −6.94584e113 −0.000868662 0
\(771\) 6.12811e116 0.727150
\(772\) −2.76910e116 −0.311772
\(773\) 9.13803e116 0.976299 0.488150 0.872760i \(-0.337672\pi\)
0.488150 + 0.872760i \(0.337672\pi\)
\(774\) 6.52387e113 0.000661449 0
\(775\) −1.70954e117 −1.64498
\(776\) 5.19595e116 0.474532
\(777\) 1.76747e117 1.53215
\(778\) −1.52363e117 −1.25374
\(779\) 8.83298e116 0.689986
\(780\) −8.31625e115 −0.0616732
\(781\) 1.73127e115 0.0121899
\(782\) −3.32710e115 −0.0222429
\(783\) 6.99984e116 0.444362
\(784\) 1.80748e116 0.108961
\(785\) −9.77813e115 −0.0559802
\(786\) 8.80456e116 0.478734
\(787\) −7.44614e116 −0.384552 −0.192276 0.981341i \(-0.561587\pi\)
−0.192276 + 0.981341i \(0.561587\pi\)
\(788\) −1.28783e117 −0.631753
\(789\) −6.40156e113 −0.000298309 0
\(790\) −1.37963e116 −0.0610754
\(791\) 5.48858e117 2.30841
\(792\) −2.46723e112 −9.85915e−6 0
\(793\) −3.41784e117 −1.29774
\(794\) 1.32031e117 0.476370
\(795\) −2.29825e116 −0.0788005
\(796\) −2.10010e117 −0.684323
\(797\) 4.19634e117 1.29960 0.649799 0.760106i \(-0.274853\pi\)
0.649799 + 0.760106i \(0.274853\pi\)
\(798\) 1.67168e117 0.492082
\(799\) −1.41805e117 −0.396777
\(800\) 6.56132e116 0.174521
\(801\) 1.97133e115 0.00498473
\(802\) 9.42068e116 0.226475
\(803\) 3.56808e115 0.00815558
\(804\) 1.10377e116 0.0239887
\(805\) 5.63213e115 0.0116396
\(806\) 6.55595e117 1.28845
\(807\) −5.95074e117 −1.11223
\(808\) −1.01953e117 −0.181235
\(809\) −8.93791e117 −1.51120 −0.755598 0.655036i \(-0.772654\pi\)
−0.755598 + 0.655036i \(0.772654\pi\)
\(810\) −4.95153e116 −0.0796336
\(811\) −6.22876e117 −0.952922 −0.476461 0.879196i \(-0.658081\pi\)
−0.476461 + 0.879196i \(0.658081\pi\)
\(812\) 1.82648e117 0.265825
\(813\) −5.63283e117 −0.779937
\(814\) −6.23804e115 −0.00821788
\(815\) 1.35067e117 0.169303
\(816\) 7.65590e116 0.0913156
\(817\) 1.56008e117 0.177073
\(818\) −4.19302e116 −0.0452916
\(819\) 3.91669e115 0.00402644
\(820\) −6.84789e116 −0.0670032
\(821\) 1.39025e118 1.29478 0.647388 0.762160i \(-0.275861\pi\)
0.647388 + 0.762160i \(0.275861\pi\)
\(822\) 5.52124e117 0.489472
\(823\) −6.86081e117 −0.579005 −0.289503 0.957177i \(-0.593490\pi\)
−0.289503 + 0.957177i \(0.593490\pi\)
\(824\) −5.49625e117 −0.441585
\(825\) −1.16949e116 −0.00894568
\(826\) −1.81174e118 −1.31948
\(827\) 1.35166e118 0.937337 0.468668 0.883374i \(-0.344734\pi\)
0.468668 + 0.883374i \(0.344734\pi\)
\(828\) 2.00058e114 0.000132108 0
\(829\) −1.58897e118 −0.999212 −0.499606 0.866253i \(-0.666522\pi\)
−0.499606 + 0.866253i \(0.666522\pi\)
\(830\) −8.69337e116 −0.0520626
\(831\) 8.40353e117 0.479314
\(832\) −2.51621e117 −0.136695
\(833\) −3.08126e117 −0.159443
\(834\) 2.70679e118 1.33423
\(835\) −2.43437e117 −0.114310
\(836\) −5.89998e115 −0.00263935
\(837\) 3.91547e118 1.66880
\(838\) −1.23844e118 −0.502912
\(839\) 4.38951e118 1.69847 0.849233 0.528018i \(-0.177064\pi\)
0.849233 + 0.528018i \(0.177064\pi\)
\(840\) −1.29600e117 −0.0477851
\(841\) −2.28577e118 −0.803146
\(842\) −1.13506e118 −0.380085
\(843\) 2.71814e118 0.867471
\(844\) 2.73043e117 0.0830542
\(845\) −7.63170e116 −0.0221271
\(846\) 8.52673e115 0.00235658
\(847\) −4.54775e118 −1.19817
\(848\) −6.95372e117 −0.174657
\(849\) 5.15514e118 1.23447
\(850\) −1.11853e118 −0.255376
\(851\) 5.05820e117 0.110116
\(852\) 3.23031e118 0.670565
\(853\) −4.99213e118 −0.988212 −0.494106 0.869402i \(-0.664505\pi\)
−0.494106 + 0.869402i \(0.664505\pi\)
\(854\) −5.32632e118 −1.00550
\(855\) 1.12143e115 0.000201903 0
\(856\) −1.79477e118 −0.308191
\(857\) −1.12173e119 −1.83723 −0.918617 0.395148i \(-0.870693\pi\)
−0.918617 + 0.395148i \(0.870693\pi\)
\(858\) 4.48491e116 0.00700678
\(859\) −2.93029e117 −0.0436704 −0.0218352 0.999762i \(-0.506951\pi\)
−0.0218352 + 0.999762i \(0.506951\pi\)
\(860\) −1.20947e117 −0.0171953
\(861\) −1.04637e119 −1.41925
\(862\) −5.68357e118 −0.735491
\(863\) 7.85476e118 0.969831 0.484915 0.874561i \(-0.338850\pi\)
0.484915 + 0.874561i \(0.338850\pi\)
\(864\) −1.50278e118 −0.177047
\(865\) 1.45036e118 0.163051
\(866\) 5.84370e118 0.626921
\(867\) 8.44713e118 0.864840
\(868\) 1.02167e119 0.998304
\(869\) 7.44029e116 0.00693887
\(870\) −3.97531e117 −0.0353868
\(871\) 6.18419e117 0.0525470
\(872\) 6.75603e118 0.547991
\(873\) 5.32613e116 0.00412416
\(874\) 4.78408e117 0.0353659
\(875\) 3.81138e118 0.269002
\(876\) 6.65753e118 0.448639
\(877\) −1.42582e119 −0.917446 −0.458723 0.888579i \(-0.651693\pi\)
−0.458723 + 0.888579i \(0.651693\pi\)
\(878\) 1.81098e119 1.11272
\(879\) 2.05726e119 1.20709
\(880\) 4.57404e115 0.000256302 0
\(881\) −3.24461e119 −1.73635 −0.868176 0.496256i \(-0.834708\pi\)
−0.868176 + 0.496256i \(0.834708\pi\)
\(882\) 1.85276e116 0.000946983 0
\(883\) 4.20170e118 0.205124 0.102562 0.994727i \(-0.467296\pi\)
0.102562 + 0.994727i \(0.467296\pi\)
\(884\) 4.28946e118 0.200026
\(885\) 3.94323e118 0.175651
\(886\) 6.41251e117 0.0272874
\(887\) 2.61237e119 1.06201 0.531003 0.847370i \(-0.321815\pi\)
0.531003 + 0.847370i \(0.321815\pi\)
\(888\) −1.16393e119 −0.452066
\(889\) −3.61371e119 −1.34101
\(890\) −3.65468e118 −0.129585
\(891\) 2.67034e117 0.00904730
\(892\) −2.19092e119 −0.709333
\(893\) 2.03903e119 0.630870
\(894\) −2.46396e119 −0.728557
\(895\) 3.19186e118 0.0902009
\(896\) −3.92124e118 −0.105913
\(897\) −3.63665e118 −0.0938875
\(898\) 2.97168e119 0.733348
\(899\) 3.13386e119 0.739284
\(900\) 6.72571e116 0.00151676
\(901\) 1.18542e119 0.255575
\(902\) 3.69303e117 0.00761234
\(903\) −1.84810e119 −0.364227
\(904\) −3.61439e119 −0.681104
\(905\) 9.03566e117 0.0162814
\(906\) −5.04892e119 −0.869974
\(907\) −5.39721e119 −0.889353 −0.444677 0.895691i \(-0.646681\pi\)
−0.444677 + 0.895691i \(0.646681\pi\)
\(908\) 3.05209e117 0.00480973
\(909\) −1.04508e117 −0.00157511
\(910\) −7.26122e118 −0.104673
\(911\) −7.60146e118 −0.104810 −0.0524050 0.998626i \(-0.516689\pi\)
−0.0524050 + 0.998626i \(0.516689\pi\)
\(912\) −1.10085e119 −0.145191
\(913\) 4.68829e117 0.00591491
\(914\) −3.29812e118 −0.0398058
\(915\) 1.15927e119 0.133853
\(916\) 1.31645e119 0.145424
\(917\) 7.68758e119 0.812515
\(918\) 2.56183e119 0.259073
\(919\) −4.88999e118 −0.0473184 −0.0236592 0.999720i \(-0.507532\pi\)
−0.0236592 + 0.999720i \(0.507532\pi\)
\(920\) −3.70892e117 −0.00343432
\(921\) −6.65755e119 −0.589929
\(922\) 7.37978e119 0.625808
\(923\) 1.80988e120 1.46886
\(924\) 6.98924e117 0.00542894
\(925\) 1.70050e120 1.26426
\(926\) 4.10739e119 0.292294
\(927\) −5.63395e117 −0.00383782
\(928\) −1.20279e119 −0.0784327
\(929\) −2.32066e120 −1.44869 −0.724344 0.689439i \(-0.757857\pi\)
−0.724344 + 0.689439i \(0.757857\pi\)
\(930\) −2.22366e119 −0.132895
\(931\) 4.43058e119 0.253512
\(932\) −6.17182e119 −0.338118
\(933\) 2.65807e120 1.39431
\(934\) 7.06284e119 0.354757
\(935\) −7.79750e116 −0.000375046 0
\(936\) −2.57925e117 −0.00118802
\(937\) −3.61543e120 −1.59480 −0.797401 0.603450i \(-0.793792\pi\)
−0.797401 + 0.603450i \(0.793792\pi\)
\(938\) 9.63738e118 0.0407140
\(939\) −6.83437e119 −0.276530
\(940\) −1.58079e119 −0.0612626
\(941\) −1.90331e120 −0.706530 −0.353265 0.935523i \(-0.614929\pi\)
−0.353265 + 0.935523i \(0.614929\pi\)
\(942\) 9.83922e119 0.349864
\(943\) −2.99454e119 −0.102002
\(944\) 1.19308e120 0.389319
\(945\) −4.33669e119 −0.135572
\(946\) 6.52262e117 0.00195358
\(947\) −5.83517e120 −1.67448 −0.837239 0.546837i \(-0.815832\pi\)
−0.837239 + 0.546837i \(0.815832\pi\)
\(948\) 1.38825e120 0.381708
\(949\) 3.73009e120 0.982738
\(950\) 1.60835e120 0.406045
\(951\) −4.56767e120 −1.10506
\(952\) 6.68465e119 0.154982
\(953\) −6.39494e120 −1.42093 −0.710467 0.703730i \(-0.751516\pi\)
−0.710467 + 0.703730i \(0.751516\pi\)
\(954\) −7.12794e117 −0.00151794
\(955\) −1.95227e119 −0.0398476
\(956\) −3.98233e120 −0.779100
\(957\) 2.14386e118 0.00402035
\(958\) −5.87755e119 −0.105656
\(959\) 4.82080e120 0.830740
\(960\) 8.53452e118 0.0140992
\(961\) 1.12158e121 1.77638
\(962\) −6.52128e120 −0.990245
\(963\) −1.83973e118 −0.00267849
\(964\) 4.53031e120 0.632424
\(965\) 5.26231e119 0.0704401
\(966\) −5.66732e119 −0.0727452
\(967\) 1.02043e121 1.25607 0.628033 0.778186i \(-0.283860\pi\)
0.628033 + 0.778186i \(0.283860\pi\)
\(968\) 2.99482e120 0.353524
\(969\) 1.87666e120 0.212457
\(970\) −9.87422e119 −0.107213
\(971\) 6.21115e120 0.646835 0.323418 0.946256i \(-0.395168\pi\)
0.323418 + 0.946256i \(0.395168\pi\)
\(972\) −3.07615e118 −0.00307272
\(973\) 2.36340e121 2.26447
\(974\) −4.00064e120 −0.367698
\(975\) −1.22260e121 −1.07794
\(976\) 3.50754e120 0.296678
\(977\) −5.68540e120 −0.461351 −0.230675 0.973031i \(-0.574094\pi\)
−0.230675 + 0.973031i \(0.574094\pi\)
\(978\) −1.35911e121 −1.05811
\(979\) 1.97095e119 0.0147223
\(980\) −3.43487e119 −0.0246181
\(981\) 6.92529e118 0.00476259
\(982\) −9.36009e120 −0.617682
\(983\) −1.36633e121 −0.865244 −0.432622 0.901575i \(-0.642411\pi\)
−0.432622 + 0.901575i \(0.642411\pi\)
\(984\) 6.89067e120 0.418755
\(985\) 2.44735e120 0.142735
\(986\) 2.05043e120 0.114771
\(987\) −2.41548e121 −1.29765
\(988\) −6.16787e120 −0.318038
\(989\) −5.28896e119 −0.0261770
\(990\) 4.68864e115 2.22752e−6 0
\(991\) −1.22989e121 −0.560899 −0.280450 0.959869i \(-0.590484\pi\)
−0.280450 + 0.959869i \(0.590484\pi\)
\(992\) −6.72801e120 −0.294553
\(993\) 1.11285e120 0.0467728
\(994\) 2.82050e121 1.13809
\(995\) 3.99097e120 0.154612
\(996\) 8.74769e120 0.325380
\(997\) 4.61180e121 1.64709 0.823543 0.567254i \(-0.191994\pi\)
0.823543 + 0.567254i \(0.191994\pi\)
\(998\) −1.34038e121 −0.459666
\(999\) −3.89477e121 −1.28257
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 2.82.a.a.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2.82.a.a.1.1 3 1.1 even 1 trivial