Properties

Label 5.34.a.b.1.1
Level 5
Weight 34
Character 5.1
Self dual yes
Analytic conductor 34.491
Analytic rank 0
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(34.4914144405\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-75479.4\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q-126401. q^{2} -8.63211e7 q^{3} +7.38725e9 q^{4} +1.52588e11 q^{5} +1.09111e13 q^{6} +7.78650e13 q^{7} +1.52021e14 q^{8} +1.89228e15 q^{9} +O(q^{10})\) \(q-126401. q^{2} -8.63211e7 q^{3} +7.38725e9 q^{4} +1.52588e11 q^{5} +1.09111e13 q^{6} +7.78650e13 q^{7} +1.52021e14 q^{8} +1.89228e15 q^{9} -1.92872e16 q^{10} +1.61939e17 q^{11} -6.37676e17 q^{12} -2.28706e18 q^{13} -9.84220e18 q^{14} -1.31716e19 q^{15} -8.26715e19 q^{16} +2.46494e20 q^{17} -2.39186e20 q^{18} -1.53881e21 q^{19} +1.12720e21 q^{20} -6.72140e21 q^{21} -2.04692e22 q^{22} -2.16284e22 q^{23} -1.31226e22 q^{24} +2.32831e22 q^{25} +2.89086e23 q^{26} +3.16521e23 q^{27} +5.75208e23 q^{28} -2.07535e23 q^{29} +1.66490e24 q^{30} +1.75532e24 q^{31} +9.14391e24 q^{32} -1.39788e25 q^{33} -3.11571e25 q^{34} +1.18813e25 q^{35} +1.39787e25 q^{36} +8.12289e25 q^{37} +1.94506e26 q^{38} +1.97422e26 q^{39} +2.31965e25 q^{40} -1.92486e26 q^{41} +8.49590e26 q^{42} +8.01003e26 q^{43} +1.19628e27 q^{44} +2.88739e26 q^{45} +2.73385e27 q^{46} -7.53703e27 q^{47} +7.13630e27 q^{48} -1.66804e27 q^{49} -2.94300e27 q^{50} -2.12777e28 q^{51} -1.68951e28 q^{52} +1.75257e28 q^{53} -4.00085e28 q^{54} +2.47099e28 q^{55} +1.18371e28 q^{56} +1.32832e29 q^{57} +2.62326e28 q^{58} -2.97225e29 q^{59} -9.73016e28 q^{60} -3.70944e29 q^{61} -2.21873e29 q^{62} +1.47342e29 q^{63} -4.45655e29 q^{64} -3.48978e29 q^{65} +1.76693e30 q^{66} +8.43824e29 q^{67} +1.82091e30 q^{68} +1.86699e30 q^{69} -1.50180e30 q^{70} +5.92473e30 q^{71} +2.87666e29 q^{72} +7.49289e30 q^{73} -1.02674e31 q^{74} -2.00982e30 q^{75} -1.13675e31 q^{76} +1.26094e31 q^{77} -2.49543e31 q^{78} +6.07295e30 q^{79} -1.26147e31 q^{80} -3.78417e31 q^{81} +2.43304e31 q^{82} +3.47153e31 q^{83} -4.96526e31 q^{84} +3.76120e31 q^{85} -1.01248e32 q^{86} +1.79147e31 q^{87} +2.46181e31 q^{88} +1.80671e32 q^{89} -3.64969e31 q^{90} -1.78082e32 q^{91} -1.59775e32 q^{92} -1.51521e32 q^{93} +9.52688e32 q^{94} -2.34803e32 q^{95} -7.89312e32 q^{96} +1.09143e33 q^{97} +2.10841e32 q^{98} +3.06434e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + O(q^{10}) \) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + 22483825683593750q^{10} + 150760896555890192q^{11} + 466351581756413200q^{12} - 1403095636752804700q^{13} - 7086110008989891456q^{14} + 4045700073242187500q^{15} + 64511520005858668816q^{16} + \)\(13\!\cdots\!00\)\(q^{17} + \)\(67\!\cdots\!50\)\(q^{18} + \)\(17\!\cdots\!00\)\(q^{19} + \)\(45\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(24\!\cdots\!00\)\(q^{22} + \)\(68\!\cdots\!00\)\(q^{23} + \)\(21\!\cdots\!00\)\(q^{24} + \)\(13\!\cdots\!50\)\(q^{25} - \)\(36\!\cdots\!88\)\(q^{26} - \)\(34\!\cdots\!00\)\(q^{27} - \)\(17\!\cdots\!00\)\(q^{28} + \)\(13\!\cdots\!00\)\(q^{29} + \)\(10\!\cdots\!00\)\(q^{30} + \)\(10\!\cdots\!52\)\(q^{31} + \)\(26\!\cdots\!00\)\(q^{32} + \)\(34\!\cdots\!00\)\(q^{33} + \)\(88\!\cdots\!24\)\(q^{34} + \)\(29\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!96\)\(q^{36} + \)\(27\!\cdots\!00\)\(q^{37} + \)\(83\!\cdots\!00\)\(q^{38} + \)\(57\!\cdots\!56\)\(q^{39} + \)\(46\!\cdots\!00\)\(q^{40} + \)\(44\!\cdots\!32\)\(q^{41} + \)\(14\!\cdots\!00\)\(q^{42} + \)\(22\!\cdots\!00\)\(q^{43} + \)\(71\!\cdots\!64\)\(q^{44} + \)\(20\!\cdots\!50\)\(q^{45} + \)\(34\!\cdots\!72\)\(q^{46} + \)\(38\!\cdots\!00\)\(q^{47} + \)\(24\!\cdots\!00\)\(q^{48} - \)\(71\!\cdots\!58\)\(q^{49} + \)\(34\!\cdots\!50\)\(q^{50} - \)\(54\!\cdots\!88\)\(q^{51} - \)\(90\!\cdots\!00\)\(q^{52} + \)\(47\!\cdots\!00\)\(q^{53} - \)\(18\!\cdots\!00\)\(q^{54} + \)\(23\!\cdots\!00\)\(q^{55} - \)\(39\!\cdots\!00\)\(q^{56} - \)\(24\!\cdots\!00\)\(q^{57} - \)\(44\!\cdots\!00\)\(q^{58} - \)\(17\!\cdots\!00\)\(q^{59} + \)\(71\!\cdots\!00\)\(q^{60} - \)\(28\!\cdots\!08\)\(q^{61} + \)\(34\!\cdots\!00\)\(q^{62} - \)\(55\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!72\)\(q^{64} - \)\(21\!\cdots\!00\)\(q^{65} + \)\(50\!\cdots\!64\)\(q^{66} + \)\(33\!\cdots\!00\)\(q^{67} + \)\(38\!\cdots\!00\)\(q^{68} + \)\(31\!\cdots\!36\)\(q^{69} - \)\(10\!\cdots\!00\)\(q^{70} + \)\(84\!\cdots\!72\)\(q^{71} + \)\(87\!\cdots\!00\)\(q^{72} - \)\(17\!\cdots\!00\)\(q^{73} + \)\(20\!\cdots\!84\)\(q^{74} + \)\(61\!\cdots\!00\)\(q^{75} + \)\(29\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!00\)\(q^{77} - \)\(57\!\cdots\!00\)\(q^{78} - \)\(22\!\cdots\!00\)\(q^{79} + \)\(98\!\cdots\!00\)\(q^{80} - \)\(13\!\cdots\!74\)\(q^{81} - \)\(15\!\cdots\!00\)\(q^{82} - \)\(47\!\cdots\!00\)\(q^{83} - \)\(23\!\cdots\!76\)\(q^{84} + \)\(20\!\cdots\!00\)\(q^{85} - \)\(12\!\cdots\!08\)\(q^{86} - \)\(17\!\cdots\!00\)\(q^{87} + \)\(49\!\cdots\!00\)\(q^{88} - \)\(33\!\cdots\!00\)\(q^{89} + \)\(10\!\cdots\!50\)\(q^{90} + \)\(19\!\cdots\!32\)\(q^{91} - \)\(41\!\cdots\!00\)\(q^{92} + \)\(21\!\cdots\!00\)\(q^{93} + \)\(14\!\cdots\!64\)\(q^{94} + \)\(26\!\cdots\!00\)\(q^{95} + \)\(31\!\cdots\!72\)\(q^{96} + \)\(25\!\cdots\!00\)\(q^{97} + \)\(69\!\cdots\!50\)\(q^{98} + \)\(16\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −126401. −1.36381 −0.681907 0.731439i \(-0.738849\pi\)
−0.681907 + 0.731439i \(0.738849\pi\)
\(3\) −8.63211e7 −1.15775 −0.578877 0.815415i \(-0.696509\pi\)
−0.578877 + 0.815415i \(0.696509\pi\)
\(4\) 7.38725e9 0.859989
\(5\) 1.52588e11 0.447214
\(6\) 1.09111e13 1.57896
\(7\) 7.78650e13 0.885573 0.442787 0.896627i \(-0.353990\pi\)
0.442787 + 0.896627i \(0.353990\pi\)
\(8\) 1.52021e14 0.190949
\(9\) 1.89228e15 0.340396
\(10\) −1.92872e16 −0.609916
\(11\) 1.61939e17 1.06260 0.531302 0.847182i \(-0.321703\pi\)
0.531302 + 0.847182i \(0.321703\pi\)
\(12\) −6.37676e17 −0.995656
\(13\) −2.28706e18 −0.953262 −0.476631 0.879104i \(-0.658142\pi\)
−0.476631 + 0.879104i \(0.658142\pi\)
\(14\) −9.84220e18 −1.20776
\(15\) −1.31716e19 −0.517764
\(16\) −8.26715e19 −1.12041
\(17\) 2.46494e20 1.22857 0.614284 0.789085i \(-0.289445\pi\)
0.614284 + 0.789085i \(0.289445\pi\)
\(18\) −2.39186e20 −0.464236
\(19\) −1.53881e21 −1.22391 −0.611955 0.790893i \(-0.709617\pi\)
−0.611955 + 0.790893i \(0.709617\pi\)
\(20\) 1.12720e21 0.384599
\(21\) −6.72140e21 −1.02528
\(22\) −2.04692e22 −1.44920
\(23\) −2.16284e22 −0.735387 −0.367693 0.929947i \(-0.619852\pi\)
−0.367693 + 0.929947i \(0.619852\pi\)
\(24\) −1.31226e22 −0.221072
\(25\) 2.32831e22 0.200000
\(26\) 2.89086e23 1.30007
\(27\) 3.16521e23 0.763660
\(28\) 5.75208e23 0.761583
\(29\) −2.07535e23 −0.154001 −0.0770007 0.997031i \(-0.524534\pi\)
−0.0770007 + 0.997031i \(0.524534\pi\)
\(30\) 1.66490e24 0.706133
\(31\) 1.75532e24 0.433398 0.216699 0.976238i \(-0.430471\pi\)
0.216699 + 0.976238i \(0.430471\pi\)
\(32\) 9.14391e24 1.33708
\(33\) −1.39788e25 −1.23024
\(34\) −3.11571e25 −1.67554
\(35\) 1.18813e25 0.396040
\(36\) 1.39787e25 0.292736
\(37\) 8.12289e25 1.08239 0.541193 0.840898i \(-0.317973\pi\)
0.541193 + 0.840898i \(0.317973\pi\)
\(38\) 1.94506e26 1.66919
\(39\) 1.97422e26 1.10364
\(40\) 2.31965e25 0.0853951
\(41\) −1.92486e26 −0.471483 −0.235741 0.971816i \(-0.575752\pi\)
−0.235741 + 0.971816i \(0.575752\pi\)
\(42\) 8.49590e26 1.39829
\(43\) 8.01003e26 0.894139 0.447069 0.894499i \(-0.352468\pi\)
0.447069 + 0.894499i \(0.352468\pi\)
\(44\) 1.19628e27 0.913828
\(45\) 2.88739e26 0.152230
\(46\) 2.73385e27 1.00293
\(47\) −7.53703e27 −1.93904 −0.969518 0.245021i \(-0.921205\pi\)
−0.969518 + 0.245021i \(0.921205\pi\)
\(48\) 7.13630e27 1.29716
\(49\) −1.66804e27 −0.215760
\(50\) −2.94300e27 −0.272763
\(51\) −2.12777e28 −1.42238
\(52\) −1.68951e28 −0.819795
\(53\) 1.75257e28 0.621047 0.310523 0.950566i \(-0.399496\pi\)
0.310523 + 0.950566i \(0.399496\pi\)
\(54\) −4.00085e28 −1.04149
\(55\) 2.47099e28 0.475211
\(56\) 1.18371e28 0.169100
\(57\) 1.32832e29 1.41699
\(58\) 2.62326e28 0.210029
\(59\) −2.97225e29 −1.79484 −0.897422 0.441172i \(-0.854563\pi\)
−0.897422 + 0.441172i \(0.854563\pi\)
\(60\) −9.73016e28 −0.445271
\(61\) −3.70944e29 −1.29231 −0.646154 0.763207i \(-0.723624\pi\)
−0.646154 + 0.763207i \(0.723624\pi\)
\(62\) −2.21873e29 −0.591075
\(63\) 1.47342e29 0.301445
\(64\) −4.45655e29 −0.703119
\(65\) −3.48978e29 −0.426312
\(66\) 1.76693e30 1.67781
\(67\) 8.43824e29 0.625198 0.312599 0.949885i \(-0.398800\pi\)
0.312599 + 0.949885i \(0.398800\pi\)
\(68\) 1.82091e30 1.05656
\(69\) 1.86699e30 0.851397
\(70\) −1.50180e30 −0.540126
\(71\) 5.92473e30 1.68619 0.843094 0.537767i \(-0.180732\pi\)
0.843094 + 0.537767i \(0.180732\pi\)
\(72\) 2.87666e29 0.0649982
\(73\) 7.49289e30 1.34841 0.674205 0.738544i \(-0.264486\pi\)
0.674205 + 0.738544i \(0.264486\pi\)
\(74\) −1.02674e31 −1.47617
\(75\) −2.00982e30 −0.231551
\(76\) −1.13675e31 −1.05255
\(77\) 1.26094e31 0.941015
\(78\) −2.49543e31 −1.50516
\(79\) 6.07295e30 0.296861 0.148430 0.988923i \(-0.452578\pi\)
0.148430 + 0.988923i \(0.452578\pi\)
\(80\) −1.26147e31 −0.501062
\(81\) −3.78417e31 −1.22453
\(82\) 2.43304e31 0.643015
\(83\) 3.47153e31 0.751160 0.375580 0.926790i \(-0.377444\pi\)
0.375580 + 0.926790i \(0.377444\pi\)
\(84\) −4.96526e31 −0.881727
\(85\) 3.76120e31 0.549433
\(86\) −1.01248e32 −1.21944
\(87\) 1.79147e31 0.178296
\(88\) 2.46181e31 0.202904
\(89\) 1.80671e32 1.23582 0.617909 0.786250i \(-0.287980\pi\)
0.617909 + 0.786250i \(0.287980\pi\)
\(90\) −3.64969e31 −0.207613
\(91\) −1.78082e32 −0.844183
\(92\) −1.59775e32 −0.632424
\(93\) −1.51521e32 −0.501769
\(94\) 9.52688e32 2.64448
\(95\) −2.34803e32 −0.547349
\(96\) −7.89312e32 −1.54801
\(97\) 1.09143e33 1.80411 0.902055 0.431622i \(-0.142058\pi\)
0.902055 + 0.431622i \(0.142058\pi\)
\(98\) 2.10841e32 0.294256
\(99\) 3.06434e32 0.361706
\(100\) 1.71998e32 0.171998
\(101\) −7.13542e32 −0.605504 −0.302752 0.953069i \(-0.597905\pi\)
−0.302752 + 0.953069i \(0.597905\pi\)
\(102\) 2.68952e33 1.93986
\(103\) −1.80265e33 −1.10687 −0.553437 0.832891i \(-0.686684\pi\)
−0.553437 + 0.832891i \(0.686684\pi\)
\(104\) −3.47680e32 −0.182025
\(105\) −1.02560e33 −0.458518
\(106\) −2.21527e33 −0.846992
\(107\) 4.02336e33 1.31752 0.658759 0.752354i \(-0.271082\pi\)
0.658759 + 0.752354i \(0.271082\pi\)
\(108\) 2.33822e33 0.656739
\(109\) 2.00598e33 0.483937 0.241968 0.970284i \(-0.422207\pi\)
0.241968 + 0.970284i \(0.422207\pi\)
\(110\) −3.12335e33 −0.648100
\(111\) −7.01177e33 −1.25314
\(112\) −6.43722e33 −0.992204
\(113\) −6.69356e33 −0.890970 −0.445485 0.895289i \(-0.646969\pi\)
−0.445485 + 0.895289i \(0.646969\pi\)
\(114\) −1.67900e34 −1.93251
\(115\) −3.30024e33 −0.328875
\(116\) −1.53311e33 −0.132440
\(117\) −4.32776e33 −0.324486
\(118\) 3.75695e34 2.44783
\(119\) 1.91933e34 1.08799
\(120\) −2.00235e33 −0.0988665
\(121\) 2.99905e33 0.129129
\(122\) 4.68877e34 1.76247
\(123\) 1.66156e34 0.545861
\(124\) 1.29670e34 0.372718
\(125\) 3.55271e33 0.0894427
\(126\) −1.86242e34 −0.411115
\(127\) −1.27300e34 −0.246643 −0.123321 0.992367i \(-0.539355\pi\)
−0.123321 + 0.992367i \(0.539355\pi\)
\(128\) −2.22144e34 −0.378155
\(129\) −6.91435e34 −1.03519
\(130\) 4.41111e34 0.581410
\(131\) 1.12002e35 1.30092 0.650461 0.759540i \(-0.274576\pi\)
0.650461 + 0.759540i \(0.274576\pi\)
\(132\) −1.03264e35 −1.05799
\(133\) −1.19819e35 −1.08386
\(134\) −1.06660e35 −0.852653
\(135\) 4.82972e34 0.341519
\(136\) 3.74722e34 0.234594
\(137\) 7.78279e34 0.431763 0.215882 0.976420i \(-0.430737\pi\)
0.215882 + 0.976420i \(0.430737\pi\)
\(138\) −2.35989e35 −1.16115
\(139\) 3.58047e35 1.56385 0.781925 0.623372i \(-0.214238\pi\)
0.781925 + 0.623372i \(0.214238\pi\)
\(140\) 8.77698e34 0.340590
\(141\) 6.50605e35 2.24493
\(142\) −7.48891e35 −2.29965
\(143\) −3.70364e35 −1.01294
\(144\) −1.56438e35 −0.381382
\(145\) −3.16674e34 −0.0688716
\(146\) −9.47108e35 −1.83898
\(147\) 1.43987e35 0.249797
\(148\) 6.00058e35 0.930840
\(149\) −1.72179e35 −0.239005 −0.119502 0.992834i \(-0.538130\pi\)
−0.119502 + 0.992834i \(0.538130\pi\)
\(150\) 2.54043e35 0.315792
\(151\) 1.08017e36 1.20330 0.601651 0.798759i \(-0.294510\pi\)
0.601651 + 0.798759i \(0.294510\pi\)
\(152\) −2.33930e35 −0.233705
\(153\) 4.66436e35 0.418199
\(154\) −1.59384e36 −1.28337
\(155\) 2.67840e35 0.193822
\(156\) 1.45840e36 0.949121
\(157\) 2.63407e36 1.54271 0.771353 0.636407i \(-0.219580\pi\)
0.771353 + 0.636407i \(0.219580\pi\)
\(158\) −7.67626e35 −0.404863
\(159\) −1.51284e36 −0.719019
\(160\) 1.39525e36 0.597960
\(161\) −1.68410e36 −0.651239
\(162\) 4.78323e36 1.67003
\(163\) 5.17457e36 1.63222 0.816111 0.577896i \(-0.196126\pi\)
0.816111 + 0.577896i \(0.196126\pi\)
\(164\) −1.42194e36 −0.405470
\(165\) −2.13299e36 −0.550178
\(166\) −4.38804e36 −1.02444
\(167\) −4.37605e36 −0.925252 −0.462626 0.886553i \(-0.653093\pi\)
−0.462626 + 0.886553i \(0.653093\pi\)
\(168\) −1.02179e36 −0.195776
\(169\) −5.25488e35 −0.0912919
\(170\) −4.75419e36 −0.749324
\(171\) −2.91185e36 −0.416614
\(172\) 5.91721e36 0.768949
\(173\) −1.16497e37 −1.37580 −0.687900 0.725805i \(-0.741467\pi\)
−0.687900 + 0.725805i \(0.741467\pi\)
\(174\) −2.26443e36 −0.243162
\(175\) 1.81294e36 0.177115
\(176\) −1.33877e37 −1.19055
\(177\) 2.56568e37 2.07799
\(178\) −2.28370e37 −1.68543
\(179\) 3.52955e36 0.237490 0.118745 0.992925i \(-0.462113\pi\)
0.118745 + 0.992925i \(0.462113\pi\)
\(180\) 2.13299e36 0.130916
\(181\) −1.74051e37 −0.974947 −0.487473 0.873138i \(-0.662081\pi\)
−0.487473 + 0.873138i \(0.662081\pi\)
\(182\) 2.25097e37 1.15131
\(183\) 3.20203e37 1.49618
\(184\) −3.28797e36 −0.140421
\(185\) 1.23945e37 0.484058
\(186\) 1.91524e37 0.684320
\(187\) 3.99170e37 1.30548
\(188\) −5.56779e37 −1.66755
\(189\) 2.46459e37 0.676277
\(190\) 2.96793e37 0.746483
\(191\) −2.24606e36 −0.0518048 −0.0259024 0.999664i \(-0.508246\pi\)
−0.0259024 + 0.999664i \(0.508246\pi\)
\(192\) 3.84694e37 0.814040
\(193\) 2.96630e37 0.576129 0.288064 0.957611i \(-0.406988\pi\)
0.288064 + 0.957611i \(0.406988\pi\)
\(194\) −1.37958e38 −2.46047
\(195\) 3.01241e37 0.493564
\(196\) −1.23222e37 −0.185551
\(197\) −5.56817e37 −0.770939 −0.385470 0.922721i \(-0.625961\pi\)
−0.385470 + 0.922721i \(0.625961\pi\)
\(198\) −3.87335e37 −0.493300
\(199\) −6.53016e36 −0.0765328 −0.0382664 0.999268i \(-0.512184\pi\)
−0.0382664 + 0.999268i \(0.512184\pi\)
\(200\) 3.53951e36 0.0381898
\(201\) −7.28398e37 −0.723826
\(202\) 9.01924e37 0.825795
\(203\) −1.61597e37 −0.136380
\(204\) −1.57183e38 −1.22323
\(205\) −2.93711e37 −0.210853
\(206\) 2.27857e38 1.50957
\(207\) −4.09270e37 −0.250322
\(208\) 1.89075e38 1.06804
\(209\) −2.49193e38 −1.30053
\(210\) 1.29637e38 0.625333
\(211\) 4.18954e38 1.86856 0.934278 0.356545i \(-0.116045\pi\)
0.934278 + 0.356545i \(0.116045\pi\)
\(212\) 1.29467e38 0.534093
\(213\) −5.11429e38 −1.95219
\(214\) −5.08556e38 −1.79685
\(215\) 1.22223e38 0.399871
\(216\) 4.81177e37 0.145820
\(217\) 1.36678e38 0.383806
\(218\) −2.53557e38 −0.660000
\(219\) −6.46795e38 −1.56113
\(220\) 1.82538e38 0.408677
\(221\) −5.63747e38 −1.17115
\(222\) 8.86294e38 1.70905
\(223\) −1.62044e38 −0.290136 −0.145068 0.989422i \(-0.546340\pi\)
−0.145068 + 0.989422i \(0.546340\pi\)
\(224\) 7.11990e38 1.18408
\(225\) 4.40581e37 0.0680791
\(226\) 8.46072e38 1.21512
\(227\) 9.68892e38 1.29375 0.646873 0.762598i \(-0.276076\pi\)
0.646873 + 0.762598i \(0.276076\pi\)
\(228\) 9.81259e38 1.21859
\(229\) 4.72860e38 0.546320 0.273160 0.961969i \(-0.411931\pi\)
0.273160 + 0.961969i \(0.411931\pi\)
\(230\) 4.17153e38 0.448524
\(231\) −1.08846e39 −1.08946
\(232\) −3.15496e37 −0.0294065
\(233\) −2.32086e38 −0.201501 −0.100750 0.994912i \(-0.532124\pi\)
−0.100750 + 0.994912i \(0.532124\pi\)
\(234\) 5.47032e38 0.442539
\(235\) −1.15006e39 −0.867163
\(236\) −2.19567e39 −1.54355
\(237\) −5.24224e38 −0.343692
\(238\) −2.42605e39 −1.48381
\(239\) 1.78755e39 1.02022 0.510109 0.860110i \(-0.329605\pi\)
0.510109 + 0.860110i \(0.329605\pi\)
\(240\) 1.08891e39 0.580106
\(241\) −2.68792e39 −1.33701 −0.668506 0.743707i \(-0.733066\pi\)
−0.668506 + 0.743707i \(0.733066\pi\)
\(242\) −3.79082e38 −0.176108
\(243\) 1.50698e39 0.654041
\(244\) −2.74026e39 −1.11137
\(245\) −2.54522e38 −0.0964906
\(246\) −2.10023e39 −0.744453
\(247\) 3.51934e39 1.16671
\(248\) 2.66844e38 0.0827571
\(249\) −2.99666e39 −0.869659
\(250\) −4.49066e38 −0.121983
\(251\) 2.18494e39 0.555677 0.277838 0.960628i \(-0.410382\pi\)
0.277838 + 0.960628i \(0.410382\pi\)
\(252\) 1.08845e39 0.259240
\(253\) −3.50248e39 −0.781426
\(254\) 1.60909e39 0.336375
\(255\) −3.24671e39 −0.636108
\(256\) 6.63606e39 1.21885
\(257\) 8.25568e39 1.42186 0.710929 0.703264i \(-0.248275\pi\)
0.710929 + 0.703264i \(0.248275\pi\)
\(258\) 8.73980e39 1.41181
\(259\) 6.32489e39 0.958532
\(260\) −2.57798e39 −0.366623
\(261\) −3.92715e38 −0.0524214
\(262\) −1.41572e40 −1.77422
\(263\) 2.69949e39 0.317697 0.158848 0.987303i \(-0.449222\pi\)
0.158848 + 0.987303i \(0.449222\pi\)
\(264\) −2.12506e39 −0.234912
\(265\) 2.67421e39 0.277740
\(266\) 1.51452e40 1.47819
\(267\) −1.55958e40 −1.43077
\(268\) 6.23353e39 0.537663
\(269\) 1.21756e40 0.987592 0.493796 0.869578i \(-0.335609\pi\)
0.493796 + 0.869578i \(0.335609\pi\)
\(270\) −6.10481e39 −0.465769
\(271\) −9.05453e39 −0.649939 −0.324969 0.945725i \(-0.605354\pi\)
−0.324969 + 0.945725i \(0.605354\pi\)
\(272\) −2.03781e40 −1.37650
\(273\) 1.53722e40 0.977357
\(274\) −9.83751e39 −0.588845
\(275\) 3.77043e39 0.212521
\(276\) 1.37919e40 0.732192
\(277\) −6.18766e39 −0.309464 −0.154732 0.987956i \(-0.549451\pi\)
−0.154732 + 0.987956i \(0.549451\pi\)
\(278\) −4.52574e40 −2.13280
\(279\) 3.32155e39 0.147527
\(280\) 1.80620e39 0.0756236
\(281\) 4.51611e39 0.178283 0.0891415 0.996019i \(-0.471588\pi\)
0.0891415 + 0.996019i \(0.471588\pi\)
\(282\) −8.22371e40 −3.06166
\(283\) 3.25719e40 1.14384 0.571921 0.820308i \(-0.306198\pi\)
0.571921 + 0.820308i \(0.306198\pi\)
\(284\) 4.37674e40 1.45010
\(285\) 2.02685e40 0.633696
\(286\) 4.68143e40 1.38146
\(287\) −1.49879e40 −0.417533
\(288\) 1.73028e40 0.455136
\(289\) 2.05049e40 0.509382
\(290\) 4.00278e39 0.0939280
\(291\) −9.42136e40 −2.08872
\(292\) 5.53518e40 1.15962
\(293\) −6.99032e40 −1.38414 −0.692072 0.721829i \(-0.743302\pi\)
−0.692072 + 0.721829i \(0.743302\pi\)
\(294\) −1.82001e40 −0.340676
\(295\) −4.53529e40 −0.802679
\(296\) 1.23485e40 0.206681
\(297\) 5.12570e40 0.811469
\(298\) 2.17636e40 0.325958
\(299\) 4.94655e40 0.701016
\(300\) −1.48470e40 −0.199131
\(301\) 6.23701e40 0.791825
\(302\) −1.36535e41 −1.64108
\(303\) 6.15938e40 0.701025
\(304\) 1.27215e41 1.37128
\(305\) −5.66016e40 −0.577938
\(306\) −5.89579e40 −0.570346
\(307\) 1.35007e40 0.123758 0.0618788 0.998084i \(-0.480291\pi\)
0.0618788 + 0.998084i \(0.480291\pi\)
\(308\) 9.31485e40 0.809262
\(309\) 1.55607e41 1.28149
\(310\) −3.38552e40 −0.264337
\(311\) 5.12682e40 0.379579 0.189789 0.981825i \(-0.439220\pi\)
0.189789 + 0.981825i \(0.439220\pi\)
\(312\) 3.00122e40 0.210740
\(313\) 1.36507e39 0.00909232 0.00454616 0.999990i \(-0.498553\pi\)
0.00454616 + 0.999990i \(0.498553\pi\)
\(314\) −3.32949e41 −2.10397
\(315\) 2.24827e40 0.134810
\(316\) 4.48624e40 0.255297
\(317\) 2.88324e41 1.55741 0.778705 0.627390i \(-0.215877\pi\)
0.778705 + 0.627390i \(0.215877\pi\)
\(318\) 1.91224e41 0.980609
\(319\) −3.36080e40 −0.163643
\(320\) −6.80015e40 −0.314444
\(321\) −3.47301e41 −1.52536
\(322\) 2.12871e41 0.888169
\(323\) −3.79307e41 −1.50366
\(324\) −2.79546e41 −1.05308
\(325\) −5.32498e40 −0.190652
\(326\) −6.54070e41 −2.22605
\(327\) −1.73158e41 −0.560280
\(328\) −2.92619e40 −0.0900292
\(329\) −5.86871e41 −1.71716
\(330\) 2.69612e41 0.750341
\(331\) 1.22306e41 0.323808 0.161904 0.986807i \(-0.448237\pi\)
0.161904 + 0.986807i \(0.448237\pi\)
\(332\) 2.56450e41 0.645989
\(333\) 1.53708e41 0.368439
\(334\) 5.53136e41 1.26187
\(335\) 1.28757e41 0.279597
\(336\) 5.55668e41 1.14873
\(337\) 1.95036e40 0.0383902 0.0191951 0.999816i \(-0.493890\pi\)
0.0191951 + 0.999816i \(0.493890\pi\)
\(338\) 6.64222e40 0.124505
\(339\) 5.77796e41 1.03152
\(340\) 2.77849e41 0.472506
\(341\) 2.84254e41 0.460531
\(342\) 3.68061e41 0.568183
\(343\) −7.31855e41 −1.07664
\(344\) 1.21769e41 0.170735
\(345\) 2.84880e41 0.380756
\(346\) 1.47254e42 1.87634
\(347\) −8.38690e41 −1.01898 −0.509490 0.860477i \(-0.670166\pi\)
−0.509490 + 0.860477i \(0.670166\pi\)
\(348\) 1.32340e41 0.153333
\(349\) −2.92359e40 −0.0323070 −0.0161535 0.999870i \(-0.505142\pi\)
−0.0161535 + 0.999870i \(0.505142\pi\)
\(350\) −2.29157e41 −0.241552
\(351\) −7.23902e41 −0.727968
\(352\) 1.48075e42 1.42079
\(353\) −1.88083e42 −1.72213 −0.861067 0.508492i \(-0.830203\pi\)
−0.861067 + 0.508492i \(0.830203\pi\)
\(354\) −3.24304e42 −2.83399
\(355\) 9.04042e41 0.754086
\(356\) 1.33466e42 1.06279
\(357\) −1.65679e42 −1.25962
\(358\) −4.46139e41 −0.323892
\(359\) 1.60953e41 0.111594 0.0557968 0.998442i \(-0.482230\pi\)
0.0557968 + 0.998442i \(0.482230\pi\)
\(360\) 4.38943e40 0.0290681
\(361\) 7.87154e41 0.497956
\(362\) 2.20002e42 1.32965
\(363\) −2.58881e41 −0.149500
\(364\) −1.31554e42 −0.725988
\(365\) 1.14332e42 0.603028
\(366\) −4.04740e42 −2.04051
\(367\) 2.15460e42 1.03843 0.519213 0.854645i \(-0.326225\pi\)
0.519213 + 0.854645i \(0.326225\pi\)
\(368\) 1.78806e42 0.823933
\(369\) −3.64238e41 −0.160491
\(370\) −1.56668e42 −0.660165
\(371\) 1.36464e42 0.549982
\(372\) −1.11932e42 −0.431516
\(373\) 2.59028e42 0.955325 0.477663 0.878543i \(-0.341484\pi\)
0.477663 + 0.878543i \(0.341484\pi\)
\(374\) −5.04554e42 −1.78044
\(375\) −3.06674e41 −0.103553
\(376\) −1.14578e42 −0.370257
\(377\) 4.74646e41 0.146804
\(378\) −3.11526e42 −0.922316
\(379\) 4.01905e42 1.13914 0.569568 0.821944i \(-0.307110\pi\)
0.569568 + 0.821944i \(0.307110\pi\)
\(380\) −1.73455e42 −0.470714
\(381\) 1.09887e42 0.285551
\(382\) 2.83904e41 0.0706522
\(383\) 5.03299e42 1.19963 0.599813 0.800140i \(-0.295242\pi\)
0.599813 + 0.800140i \(0.295242\pi\)
\(384\) 1.91757e42 0.437811
\(385\) 1.92404e42 0.420835
\(386\) −3.74943e42 −0.785732
\(387\) 1.51572e42 0.304361
\(388\) 8.06268e42 1.55151
\(389\) 4.14807e42 0.765029 0.382515 0.923949i \(-0.375058\pi\)
0.382515 + 0.923949i \(0.375058\pi\)
\(390\) −3.80772e42 −0.673130
\(391\) −5.33128e42 −0.903473
\(392\) −2.53576e41 −0.0411991
\(393\) −9.66818e42 −1.50615
\(394\) 7.03822e42 1.05142
\(395\) 9.26658e41 0.132760
\(396\) 2.26370e42 0.311063
\(397\) −8.89168e42 −1.17203 −0.586017 0.810299i \(-0.699305\pi\)
−0.586017 + 0.810299i \(0.699305\pi\)
\(398\) 8.25418e41 0.104377
\(399\) 1.03429e43 1.25485
\(400\) −1.92485e42 −0.224082
\(401\) 1.71192e41 0.0191250 0.00956251 0.999954i \(-0.496956\pi\)
0.00956251 + 0.999954i \(0.496956\pi\)
\(402\) 9.20702e42 0.987163
\(403\) −4.01451e42 −0.413142
\(404\) −5.27111e42 −0.520727
\(405\) −5.77419e42 −0.547625
\(406\) 2.04260e42 0.185996
\(407\) 1.31541e43 1.15015
\(408\) −3.23464e42 −0.271603
\(409\) 1.40883e43 1.13612 0.568061 0.822986i \(-0.307694\pi\)
0.568061 + 0.822986i \(0.307694\pi\)
\(410\) 3.71253e42 0.287565
\(411\) −6.71819e42 −0.499876
\(412\) −1.33166e43 −0.951899
\(413\) −2.31434e43 −1.58947
\(414\) 5.17321e42 0.341393
\(415\) 5.29713e42 0.335929
\(416\) −2.09127e43 −1.27459
\(417\) −3.09070e43 −1.81056
\(418\) 3.14982e43 1.77369
\(419\) −2.03304e43 −1.10056 −0.550280 0.834980i \(-0.685479\pi\)
−0.550280 + 0.834980i \(0.685479\pi\)
\(420\) −7.57639e42 −0.394320
\(421\) 2.81610e43 1.40927 0.704633 0.709572i \(-0.251111\pi\)
0.704633 + 0.709572i \(0.251111\pi\)
\(422\) −5.29562e43 −2.54836
\(423\) −1.42622e43 −0.660039
\(424\) 2.66427e42 0.118588
\(425\) 5.73914e42 0.245714
\(426\) 6.46451e43 2.66243
\(427\) −2.88836e43 −1.14443
\(428\) 2.97216e43 1.13305
\(429\) 3.19702e43 1.17274
\(430\) −1.54491e43 −0.545350
\(431\) −1.08445e43 −0.368412 −0.184206 0.982888i \(-0.558971\pi\)
−0.184206 + 0.982888i \(0.558971\pi\)
\(432\) −2.61673e43 −0.855611
\(433\) 3.95138e43 1.24365 0.621825 0.783156i \(-0.286392\pi\)
0.621825 + 0.783156i \(0.286392\pi\)
\(434\) −1.72762e43 −0.523440
\(435\) 2.73356e42 0.0797364
\(436\) 1.48186e43 0.416180
\(437\) 3.32820e43 0.900047
\(438\) 8.17554e43 2.12909
\(439\) 1.22543e43 0.307342 0.153671 0.988122i \(-0.450890\pi\)
0.153671 + 0.988122i \(0.450890\pi\)
\(440\) 3.75642e42 0.0907412
\(441\) −3.15639e42 −0.0734436
\(442\) 7.12581e43 1.59723
\(443\) −5.64830e43 −1.21971 −0.609855 0.792513i \(-0.708772\pi\)
−0.609855 + 0.792513i \(0.708772\pi\)
\(444\) −5.17977e43 −1.07768
\(445\) 2.75683e43 0.552674
\(446\) 2.04825e43 0.395692
\(447\) 1.48627e43 0.276709
\(448\) −3.47009e43 −0.622664
\(449\) 2.63282e43 0.455362 0.227681 0.973736i \(-0.426886\pi\)
0.227681 + 0.973736i \(0.426886\pi\)
\(450\) −5.56898e42 −0.0928473
\(451\) −3.11710e43 −0.501000
\(452\) −4.94470e43 −0.766224
\(453\) −9.32419e43 −1.39313
\(454\) −1.22469e44 −1.76443
\(455\) −2.71731e43 −0.377530
\(456\) 2.01931e43 0.270573
\(457\) −4.92089e43 −0.635955 −0.317977 0.948098i \(-0.603004\pi\)
−0.317977 + 0.948098i \(0.603004\pi\)
\(458\) −5.97700e43 −0.745079
\(459\) 7.80205e43 0.938209
\(460\) −2.43797e43 −0.282829
\(461\) −1.35047e44 −1.51154 −0.755771 0.654836i \(-0.772737\pi\)
−0.755771 + 0.654836i \(0.772737\pi\)
\(462\) 1.37582e44 1.48583
\(463\) 9.98444e42 0.104049 0.0520244 0.998646i \(-0.483433\pi\)
0.0520244 + 0.998646i \(0.483433\pi\)
\(464\) 1.71573e43 0.172544
\(465\) −2.31203e43 −0.224398
\(466\) 2.93359e43 0.274810
\(467\) 1.53367e44 1.38677 0.693384 0.720568i \(-0.256119\pi\)
0.693384 + 0.720568i \(0.256119\pi\)
\(468\) −3.19702e43 −0.279054
\(469\) 6.57043e43 0.553659
\(470\) 1.45369e44 1.18265
\(471\) −2.27376e44 −1.78608
\(472\) −4.51843e43 −0.342724
\(473\) 1.29714e44 0.950116
\(474\) 6.62624e43 0.468732
\(475\) −3.58281e43 −0.244782
\(476\) 1.41785e44 0.935658
\(477\) 3.31636e43 0.211401
\(478\) −2.25948e44 −1.39139
\(479\) 5.80916e43 0.345603 0.172802 0.984957i \(-0.444718\pi\)
0.172802 + 0.984957i \(0.444718\pi\)
\(480\) −1.20440e44 −0.692291
\(481\) −1.85775e44 −1.03180
\(482\) 3.39755e44 1.82344
\(483\) 1.45373e44 0.753975
\(484\) 2.21547e43 0.111050
\(485\) 1.66539e44 0.806822
\(486\) −1.90484e44 −0.891990
\(487\) 6.21415e43 0.281290 0.140645 0.990060i \(-0.455082\pi\)
0.140645 + 0.990060i \(0.455082\pi\)
\(488\) −5.63912e43 −0.246765
\(489\) −4.46675e44 −1.88971
\(490\) 3.21718e43 0.131595
\(491\) 1.52856e44 0.604557 0.302278 0.953220i \(-0.402253\pi\)
0.302278 + 0.953220i \(0.402253\pi\)
\(492\) 1.22744e44 0.469435
\(493\) −5.11562e43 −0.189201
\(494\) −4.44848e44 −1.59117
\(495\) 4.67581e43 0.161760
\(496\) −1.45115e44 −0.485583
\(497\) 4.61329e44 1.49324
\(498\) 3.78781e44 1.18605
\(499\) 9.99203e43 0.302688 0.151344 0.988481i \(-0.451640\pi\)
0.151344 + 0.988481i \(0.451640\pi\)
\(500\) 2.62448e43 0.0769197
\(501\) 3.77745e44 1.07122
\(502\) −2.76178e44 −0.757840
\(503\) 9.03153e43 0.239822 0.119911 0.992785i \(-0.461739\pi\)
0.119911 + 0.992785i \(0.461739\pi\)
\(504\) 2.23991e43 0.0575607
\(505\) −1.08878e44 −0.270790
\(506\) 4.42717e44 1.06572
\(507\) 4.53607e43 0.105694
\(508\) −9.40399e43 −0.212110
\(509\) −5.47217e44 −1.19486 −0.597429 0.801922i \(-0.703811\pi\)
−0.597429 + 0.801922i \(0.703811\pi\)
\(510\) 4.10387e44 0.867533
\(511\) 5.83434e44 1.19412
\(512\) −6.47984e44 −1.28413
\(513\) −4.87064e44 −0.934651
\(514\) −1.04353e45 −1.93915
\(515\) −2.75063e44 −0.495009
\(516\) −5.10780e44 −0.890254
\(517\) −1.22054e45 −2.06043
\(518\) −7.99471e44 −1.30726
\(519\) 1.00562e45 1.59284
\(520\) −5.30518e43 −0.0814038
\(521\) 1.19671e45 1.77897 0.889484 0.456966i \(-0.151064\pi\)
0.889484 + 0.456966i \(0.151064\pi\)
\(522\) 4.96395e43 0.0714931
\(523\) −6.44705e43 −0.0899670 −0.0449835 0.998988i \(-0.514324\pi\)
−0.0449835 + 0.998988i \(0.514324\pi\)
\(524\) 8.27390e44 1.11878
\(525\) −1.56495e44 −0.205055
\(526\) −3.41218e44 −0.433279
\(527\) 4.32675e44 0.532460
\(528\) 1.15564e45 1.37837
\(529\) −3.97216e44 −0.459206
\(530\) −3.38023e44 −0.378786
\(531\) −5.62432e44 −0.610957
\(532\) −8.85134e44 −0.932110
\(533\) 4.40227e44 0.449446
\(534\) 1.97132e45 1.95131
\(535\) 6.13916e44 0.589212
\(536\) 1.28279e44 0.119381
\(537\) −3.04675e44 −0.274955
\(538\) −1.53901e45 −1.34689
\(539\) −2.70120e44 −0.229267
\(540\) 3.56784e44 0.293703
\(541\) −3.00892e44 −0.240246 −0.120123 0.992759i \(-0.538329\pi\)
−0.120123 + 0.992759i \(0.538329\pi\)
\(542\) 1.14450e45 0.886396
\(543\) 1.50243e45 1.12875
\(544\) 2.25392e45 1.64269
\(545\) 3.06088e44 0.216423
\(546\) −1.94306e45 −1.33293
\(547\) 9.15780e44 0.609537 0.304769 0.952426i \(-0.401421\pi\)
0.304769 + 0.952426i \(0.401421\pi\)
\(548\) 5.74934e44 0.371312
\(549\) −7.01930e44 −0.439896
\(550\) −4.76586e44 −0.289839
\(551\) 3.19357e44 0.188484
\(552\) 2.83821e44 0.162574
\(553\) 4.72870e44 0.262892
\(554\) 7.82126e44 0.422052
\(555\) −1.06991e45 −0.560420
\(556\) 2.64498e45 1.34489
\(557\) −3.51921e45 −1.73714 −0.868569 0.495568i \(-0.834960\pi\)
−0.868569 + 0.495568i \(0.834960\pi\)
\(558\) −4.19847e44 −0.201199
\(559\) −1.83194e45 −0.852348
\(560\) −9.82241e44 −0.443727
\(561\) −3.44568e45 −1.51143
\(562\) −5.70840e44 −0.243145
\(563\) 1.25910e45 0.520802 0.260401 0.965501i \(-0.416145\pi\)
0.260401 + 0.965501i \(0.416145\pi\)
\(564\) 4.80618e45 1.93061
\(565\) −1.02136e45 −0.398454
\(566\) −4.11711e45 −1.55999
\(567\) −2.94655e45 −1.08441
\(568\) 9.00681e44 0.321976
\(569\) −1.60105e45 −0.555972 −0.277986 0.960585i \(-0.589667\pi\)
−0.277986 + 0.960585i \(0.589667\pi\)
\(570\) −2.56195e45 −0.864244
\(571\) 5.75140e44 0.188485 0.0942427 0.995549i \(-0.469957\pi\)
0.0942427 + 0.995549i \(0.469957\pi\)
\(572\) −2.73597e45 −0.871118
\(573\) 1.93882e44 0.0599773
\(574\) 1.89449e45 0.569437
\(575\) −5.03576e44 −0.147077
\(576\) −8.43303e44 −0.239339
\(577\) 3.64572e45 1.00550 0.502750 0.864432i \(-0.332321\pi\)
0.502750 + 0.864432i \(0.332321\pi\)
\(578\) −2.59184e45 −0.694702
\(579\) −2.56054e45 −0.667016
\(580\) −2.33935e44 −0.0592288
\(581\) 2.70311e45 0.665207
\(582\) 1.19087e46 2.84862
\(583\) 2.83810e45 0.659927
\(584\) 1.13907e45 0.257478
\(585\) −6.60363e44 −0.145115
\(586\) 8.83582e45 1.88771
\(587\) −2.48055e45 −0.515251 −0.257626 0.966245i \(-0.582940\pi\)
−0.257626 + 0.966245i \(0.582940\pi\)
\(588\) 1.06367e45 0.214822
\(589\) −2.70109e45 −0.530441
\(590\) 5.73265e45 1.09470
\(591\) 4.80651e45 0.892558
\(592\) −6.71532e45 −1.21271
\(593\) 2.97630e45 0.522726 0.261363 0.965241i \(-0.415828\pi\)
0.261363 + 0.965241i \(0.415828\pi\)
\(594\) −6.47893e45 −1.10669
\(595\) 2.92866e45 0.486563
\(596\) −1.27193e45 −0.205541
\(597\) 5.63691e44 0.0886062
\(598\) −6.25249e45 −0.956056
\(599\) −3.09884e45 −0.460953 −0.230476 0.973078i \(-0.574028\pi\)
−0.230476 + 0.973078i \(0.574028\pi\)
\(600\) −3.05534e44 −0.0442145
\(601\) −5.90335e45 −0.831132 −0.415566 0.909563i \(-0.636417\pi\)
−0.415566 + 0.909563i \(0.636417\pi\)
\(602\) −7.88364e45 −1.07990
\(603\) 1.59675e45 0.212815
\(604\) 7.97952e45 1.03483
\(605\) 4.57619e44 0.0577484
\(606\) −7.78551e45 −0.956068
\(607\) 6.02204e45 0.719664 0.359832 0.933017i \(-0.382834\pi\)
0.359832 + 0.933017i \(0.382834\pi\)
\(608\) −1.40707e46 −1.63646
\(609\) 1.39493e45 0.157894
\(610\) 7.15449e45 0.788200
\(611\) 1.72376e46 1.84841
\(612\) 3.44568e45 0.359647
\(613\) 7.92968e45 0.805671 0.402836 0.915272i \(-0.368025\pi\)
0.402836 + 0.915272i \(0.368025\pi\)
\(614\) −1.70650e45 −0.168782
\(615\) 2.53534e45 0.244117
\(616\) 1.91688e45 0.179686
\(617\) −7.56919e45 −0.690787 −0.345394 0.938458i \(-0.612255\pi\)
−0.345394 + 0.938458i \(0.612255\pi\)
\(618\) −1.96689e46 −1.74771
\(619\) −4.72940e45 −0.409176 −0.204588 0.978848i \(-0.565585\pi\)
−0.204588 + 0.978848i \(0.565585\pi\)
\(620\) 1.97860e45 0.166684
\(621\) −6.84585e45 −0.561585
\(622\) −6.48035e45 −0.517675
\(623\) 1.40680e46 1.09441
\(624\) −1.63211e46 −1.23653
\(625\) 5.42101e44 0.0400000
\(626\) −1.72547e44 −0.0124002
\(627\) 2.15106e46 1.50570
\(628\) 1.94585e46 1.32671
\(629\) 2.00225e46 1.32979
\(630\) −2.84183e45 −0.183856
\(631\) −9.12534e45 −0.575128 −0.287564 0.957761i \(-0.592845\pi\)
−0.287564 + 0.957761i \(0.592845\pi\)
\(632\) 9.23213e44 0.0566853
\(633\) −3.61646e46 −2.16333
\(634\) −3.64444e46 −2.12402
\(635\) −1.94245e45 −0.110302
\(636\) −1.11757e46 −0.618349
\(637\) 3.81490e45 0.205675
\(638\) 4.24808e45 0.223178
\(639\) 1.12112e46 0.573971
\(640\) −3.38965e45 −0.169116
\(641\) −1.89987e46 −0.923774 −0.461887 0.886939i \(-0.652827\pi\)
−0.461887 + 0.886939i \(0.652827\pi\)
\(642\) 4.38992e46 2.08031
\(643\) −1.26235e46 −0.583040 −0.291520 0.956565i \(-0.594161\pi\)
−0.291520 + 0.956565i \(0.594161\pi\)
\(644\) −1.24408e46 −0.560058
\(645\) −1.05505e46 −0.462952
\(646\) 4.79447e46 2.05071
\(647\) 1.12690e46 0.469855 0.234927 0.972013i \(-0.424515\pi\)
0.234927 + 0.972013i \(0.424515\pi\)
\(648\) −5.75272e45 −0.233822
\(649\) −4.81323e46 −1.90721
\(650\) 6.73082e45 0.260014
\(651\) −1.17982e46 −0.444353
\(652\) 3.82258e46 1.40369
\(653\) −3.57189e45 −0.127888 −0.0639440 0.997953i \(-0.520368\pi\)
−0.0639440 + 0.997953i \(0.520368\pi\)
\(654\) 2.18873e46 0.764118
\(655\) 1.70902e46 0.581790
\(656\) 1.59131e46 0.528253
\(657\) 1.41786e46 0.458993
\(658\) 7.41810e46 2.34189
\(659\) 4.26159e46 1.31209 0.656043 0.754723i \(-0.272229\pi\)
0.656043 + 0.754723i \(0.272229\pi\)
\(660\) −1.57569e46 −0.473147
\(661\) −2.93053e46 −0.858268 −0.429134 0.903241i \(-0.641181\pi\)
−0.429134 + 0.903241i \(0.641181\pi\)
\(662\) −1.54596e46 −0.441613
\(663\) 4.86633e46 1.35590
\(664\) 5.27744e45 0.143433
\(665\) −1.82830e46 −0.484718
\(666\) −1.94288e46 −0.502483
\(667\) 4.48866e45 0.113251
\(668\) −3.23269e46 −0.795707
\(669\) 1.39878e46 0.335907
\(670\) −1.62750e46 −0.381318
\(671\) −6.00703e46 −1.37321
\(672\) −6.14598e46 −1.37088
\(673\) −7.94628e44 −0.0172948 −0.00864740 0.999963i \(-0.502753\pi\)
−0.00864740 + 0.999963i \(0.502753\pi\)
\(674\) −2.46527e45 −0.0523571
\(675\) 7.36957e45 0.152732
\(676\) −3.88191e45 −0.0785100
\(677\) −5.41689e46 −1.06915 −0.534573 0.845122i \(-0.679527\pi\)
−0.534573 + 0.845122i \(0.679527\pi\)
\(678\) −7.30339e46 −1.40681
\(679\) 8.49843e46 1.59767
\(680\) 5.71780e45 0.104914
\(681\) −8.36359e46 −1.49784
\(682\) −3.59299e46 −0.628079
\(683\) 4.80553e46 0.819973 0.409986 0.912092i \(-0.365533\pi\)
0.409986 + 0.912092i \(0.365533\pi\)
\(684\) −2.15106e46 −0.358283
\(685\) 1.18756e46 0.193090
\(686\) 9.25072e46 1.46834
\(687\) −4.08178e46 −0.632505
\(688\) −6.62202e46 −1.00180
\(689\) −4.00824e46 −0.592020
\(690\) −3.60091e46 −0.519281
\(691\) 9.58471e46 1.34956 0.674779 0.738020i \(-0.264239\pi\)
0.674779 + 0.738020i \(0.264239\pi\)
\(692\) −8.60595e46 −1.18317
\(693\) 2.38605e46 0.320317
\(694\) 1.06011e47 1.38970
\(695\) 5.46336e46 0.699375
\(696\) 2.72340e45 0.0340455
\(697\) −4.74467e46 −0.579249
\(698\) 3.69544e45 0.0440607
\(699\) 2.00340e46 0.233288
\(700\) 1.33926e46 0.152317
\(701\) 3.14053e46 0.348863 0.174432 0.984669i \(-0.444191\pi\)
0.174432 + 0.984669i \(0.444191\pi\)
\(702\) 9.15018e46 0.992813
\(703\) −1.24996e47 −1.32474
\(704\) −7.21688e46 −0.747138
\(705\) 9.92745e46 1.00396
\(706\) 2.37738e47 2.34867
\(707\) −5.55600e46 −0.536218
\(708\) 1.89533e47 1.78705
\(709\) −1.07691e47 −0.992009 −0.496005 0.868320i \(-0.665200\pi\)
−0.496005 + 0.868320i \(0.665200\pi\)
\(710\) −1.14272e47 −1.02843
\(711\) 1.14917e46 0.101050
\(712\) 2.74658e46 0.235978
\(713\) −3.79647e46 −0.318715
\(714\) 2.09419e47 1.71789
\(715\) −5.65130e46 −0.453001
\(716\) 2.60737e46 0.204239
\(717\) −1.54303e47 −1.18116
\(718\) −2.03445e46 −0.152193
\(719\) 2.02046e47 1.47715 0.738573 0.674174i \(-0.235500\pi\)
0.738573 + 0.674174i \(0.235500\pi\)
\(720\) −2.38705e46 −0.170559
\(721\) −1.40364e47 −0.980218
\(722\) −9.94970e46 −0.679120
\(723\) 2.32024e47 1.54793
\(724\) −1.28576e47 −0.838444
\(725\) −4.83206e45 −0.0308003
\(726\) 3.27228e46 0.203890
\(727\) −2.34830e47 −1.43033 −0.715164 0.698957i \(-0.753648\pi\)
−0.715164 + 0.698957i \(0.753648\pi\)
\(728\) −2.70721e46 −0.161196
\(729\) 8.02799e46 0.467308
\(730\) −1.44517e47 −0.822417
\(731\) 1.97443e47 1.09851
\(732\) 2.36542e47 1.28669
\(733\) 7.07756e46 0.376416 0.188208 0.982129i \(-0.439732\pi\)
0.188208 + 0.982129i \(0.439732\pi\)
\(734\) −2.72343e47 −1.41622
\(735\) 2.19706e46 0.111712
\(736\) −1.97768e47 −0.983270
\(737\) 1.36648e47 0.664338
\(738\) 4.60399e46 0.218879
\(739\) −3.25905e47 −1.51516 −0.757578 0.652744i \(-0.773618\pi\)
−0.757578 + 0.652744i \(0.773618\pi\)
\(740\) 9.15616e46 0.416284
\(741\) −3.03794e47 −1.35076
\(742\) −1.72492e47 −0.750074
\(743\) −1.42154e47 −0.604568 −0.302284 0.953218i \(-0.597749\pi\)
−0.302284 + 0.953218i \(0.597749\pi\)
\(744\) −2.30343e46 −0.0958124
\(745\) −2.62724e46 −0.106886
\(746\) −3.27414e47 −1.30289
\(747\) 6.56910e46 0.255691
\(748\) 2.94877e47 1.12270
\(749\) 3.13279e47 1.16676
\(750\) 3.87639e46 0.141227
\(751\) −8.07948e45 −0.0287955 −0.0143978 0.999896i \(-0.504583\pi\)
−0.0143978 + 0.999896i \(0.504583\pi\)
\(752\) 6.23098e47 2.17251
\(753\) −1.88606e47 −0.643338
\(754\) −5.99956e46 −0.200213
\(755\) 1.64822e47 0.538133
\(756\) 1.82065e47 0.581591
\(757\) 2.98356e47 0.932509 0.466255 0.884651i \(-0.345603\pi\)
0.466255 + 0.884651i \(0.345603\pi\)
\(758\) −5.08011e47 −1.55357
\(759\) 3.02338e47 0.904699
\(760\) −3.56949e46 −0.104516
\(761\) 8.91821e46 0.255524 0.127762 0.991805i \(-0.459221\pi\)
0.127762 + 0.991805i \(0.459221\pi\)
\(762\) −1.38898e47 −0.389439
\(763\) 1.56195e47 0.428562
\(764\) −1.65922e46 −0.0445516
\(765\) 7.11725e46 0.187024
\(766\) −6.36174e47 −1.63607
\(767\) 6.79771e47 1.71096
\(768\) −5.72833e47 −1.41113
\(769\) −3.11972e47 −0.752195 −0.376098 0.926580i \(-0.622734\pi\)
−0.376098 + 0.926580i \(0.622734\pi\)
\(770\) −2.43200e47 −0.573940
\(771\) −7.12640e47 −1.64616
\(772\) 2.19128e47 0.495464
\(773\) 5.84176e47 1.29295 0.646475 0.762935i \(-0.276242\pi\)
0.646475 + 0.762935i \(0.276242\pi\)
\(774\) −1.91589e47 −0.415092
\(775\) 4.08691e46 0.0866797
\(776\) 1.65920e47 0.344493
\(777\) −5.45972e47 −1.10974
\(778\) −5.24320e47 −1.04336
\(779\) 2.96199e47 0.577053
\(780\) 2.22535e47 0.424460
\(781\) 9.59444e47 1.79175
\(782\) 6.73879e47 1.23217
\(783\) −6.56892e46 −0.117605
\(784\) 1.37899e47 0.241739
\(785\) 4.01927e47 0.689919
\(786\) 1.22207e48 2.05411
\(787\) 3.46036e47 0.569559 0.284779 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(788\) −4.11335e47 −0.662999
\(789\) −2.33023e47 −0.367815
\(790\) −1.17130e47 −0.181060
\(791\) −5.21194e47 −0.789019
\(792\) 4.65842e46 0.0690675
\(793\) 8.48371e47 1.23191
\(794\) 1.12392e48 1.59844
\(795\) −2.30841e47 −0.321555
\(796\) −4.82399e46 −0.0658174
\(797\) −8.43355e47 −1.12706 −0.563532 0.826095i \(-0.690558\pi\)
−0.563532 + 0.826095i \(0.690558\pi\)
\(798\) −1.30735e48 −1.71138
\(799\) −1.85784e48 −2.38224
\(800\) 2.12898e47 0.267416
\(801\) 3.41881e47 0.420667
\(802\) −2.16388e46 −0.0260830
\(803\) 1.21339e48 1.43283
\(804\) −5.38086e47 −0.622482
\(805\) −2.56973e47 −0.291243
\(806\) 5.07438e47 0.563449
\(807\) −1.05101e48 −1.14339
\(808\) −1.08473e47 −0.115620
\(809\) −1.87301e48 −1.95609 −0.978045 0.208392i \(-0.933177\pi\)
−0.978045 + 0.208392i \(0.933177\pi\)
\(810\) 7.29863e47 0.746859
\(811\) −1.53865e48 −1.54275 −0.771376 0.636380i \(-0.780431\pi\)
−0.771376 + 0.636380i \(0.780431\pi\)
\(812\) −1.19376e47 −0.117285
\(813\) 7.81597e47 0.752470
\(814\) −1.66269e48 −1.56859
\(815\) 7.89577e47 0.729951
\(816\) 1.75906e48 1.59365
\(817\) −1.23259e48 −1.09435
\(818\) −1.78078e48 −1.54946
\(819\) −3.36981e47 −0.287356
\(820\) −2.16971e47 −0.181332
\(821\) −1.66705e48 −1.36548 −0.682742 0.730660i \(-0.739213\pi\)
−0.682742 + 0.730660i \(0.739213\pi\)
\(822\) 8.49185e47 0.681738
\(823\) 2.01297e48 1.58394 0.791972 0.610557i \(-0.209055\pi\)
0.791972 + 0.610557i \(0.209055\pi\)
\(824\) −2.74041e47 −0.211357
\(825\) −3.25468e47 −0.246047
\(826\) 2.92535e48 2.16774
\(827\) 1.15395e48 0.838195 0.419098 0.907941i \(-0.362347\pi\)
0.419098 + 0.907941i \(0.362347\pi\)
\(828\) −3.02338e47 −0.215274
\(829\) 1.78893e48 1.24866 0.624331 0.781160i \(-0.285372\pi\)
0.624331 + 0.781160i \(0.285372\pi\)
\(830\) −6.69562e47 −0.458144
\(831\) 5.34126e47 0.358284
\(832\) 1.01924e48 0.670257
\(833\) −4.11161e47 −0.265076
\(834\) 3.90667e48 2.46926
\(835\) −6.67732e47 −0.413785
\(836\) −1.84085e48 −1.11844
\(837\) 5.55594e47 0.330969
\(838\) 2.56978e48 1.50096
\(839\) 2.30591e48 1.32059 0.660297 0.751004i \(-0.270430\pi\)
0.660297 + 0.751004i \(0.270430\pi\)
\(840\) −1.55913e47 −0.0875536
\(841\) −1.77300e48 −0.976284
\(842\) −3.55957e48 −1.92198
\(843\) −3.89835e47 −0.206408
\(844\) 3.09492e48 1.60694
\(845\) −8.01831e46 −0.0408270
\(846\) 1.80275e48 0.900171
\(847\) 2.33521e47 0.114354
\(848\) −1.44888e48 −0.695826
\(849\) −2.81164e48 −1.32429
\(850\) −7.25432e47 −0.335108
\(851\) −1.75685e48 −0.795972
\(852\) −3.77806e48 −1.67886
\(853\) 3.23565e48 1.41027 0.705135 0.709073i \(-0.250886\pi\)
0.705135 + 0.709073i \(0.250886\pi\)
\(854\) 3.65091e48 1.56080
\(855\) −4.44313e47 −0.186315
\(856\) 6.11634e47 0.251579
\(857\) 1.13232e48 0.456864 0.228432 0.973560i \(-0.426640\pi\)
0.228432 + 0.973560i \(0.426640\pi\)
\(858\) −4.04107e48 −1.59939
\(859\) −1.69678e48 −0.658777 −0.329388 0.944195i \(-0.606843\pi\)
−0.329388 + 0.944195i \(0.606843\pi\)
\(860\) 9.02895e47 0.343885
\(861\) 1.29378e48 0.483400
\(862\) 1.37075e48 0.502445
\(863\) −4.68742e48 −1.68561 −0.842803 0.538223i \(-0.819096\pi\)
−0.842803 + 0.538223i \(0.819096\pi\)
\(864\) 2.89424e48 1.02107
\(865\) −1.77761e48 −0.615277
\(866\) −4.99457e48 −1.69611
\(867\) −1.77001e48 −0.589739
\(868\) 1.00967e48 0.330069
\(869\) 9.83446e47 0.315446
\(870\) −3.45525e47 −0.108746
\(871\) −1.92987e48 −0.595977
\(872\) 3.04950e47 0.0924073
\(873\) 2.06529e48 0.614111
\(874\) −4.20687e48 −1.22750
\(875\) 2.76632e47 0.0792081
\(876\) −4.77803e48 −1.34255
\(877\) 6.18989e48 1.70683 0.853414 0.521234i \(-0.174528\pi\)
0.853414 + 0.521234i \(0.174528\pi\)
\(878\) −1.54895e48 −0.419158
\(879\) 6.03412e48 1.60250
\(880\) −2.04281e48 −0.532431
\(881\) 2.27101e48 0.580919 0.290460 0.956887i \(-0.406192\pi\)
0.290460 + 0.956887i \(0.406192\pi\)
\(882\) 3.98971e47 0.100163
\(883\) 6.78750e48 1.67247 0.836234 0.548372i \(-0.184752\pi\)
0.836234 + 0.548372i \(0.184752\pi\)
\(884\) −4.16454e48 −1.00717
\(885\) 3.91492e48 0.929305
\(886\) 7.13950e48 1.66346
\(887\) −6.24043e48 −1.42717 −0.713583 0.700570i \(-0.752929\pi\)
−0.713583 + 0.700570i \(0.752929\pi\)
\(888\) −1.06593e48 −0.239285
\(889\) −9.91224e47 −0.218420
\(890\) −3.48465e48 −0.753745
\(891\) −6.12805e48 −1.30119
\(892\) −1.19706e48 −0.249514
\(893\) 1.15980e49 2.37321
\(894\) −1.87866e48 −0.377379
\(895\) 5.38567e47 0.106209
\(896\) −1.72972e48 −0.334884
\(897\) −4.26992e48 −0.811605
\(898\) −3.32791e48 −0.621030
\(899\) −3.64290e47 −0.0667440
\(900\) 3.25468e47 0.0585473
\(901\) 4.31999e48 0.762998
\(902\) 3.94004e48 0.683271
\(903\) −5.38386e48 −0.916739
\(904\) −1.01756e48 −0.170130
\(905\) −2.65581e48 −0.436010
\(906\) 1.17859e49 1.89997
\(907\) −6.86902e48 −1.08736 −0.543681 0.839292i \(-0.682970\pi\)
−0.543681 + 0.839292i \(0.682970\pi\)
\(908\) 7.15745e48 1.11261
\(909\) −1.35022e48 −0.206111
\(910\) 3.43471e48 0.514881
\(911\) 7.47750e48 1.10079 0.550393 0.834906i \(-0.314478\pi\)
0.550393 + 0.834906i \(0.314478\pi\)
\(912\) −1.09814e49 −1.58760
\(913\) 5.62176e48 0.798186
\(914\) 6.22004e48 0.867324
\(915\) 4.88591e48 0.669110
\(916\) 3.49314e48 0.469829
\(917\) 8.72107e48 1.15206
\(918\) −9.86186e48 −1.27954
\(919\) −1.28656e49 −1.63955 −0.819777 0.572683i \(-0.805903\pi\)
−0.819777 + 0.572683i \(0.805903\pi\)
\(920\) −5.01704e47 −0.0627984
\(921\) −1.16539e48 −0.143281
\(922\) 1.70701e49 2.06146
\(923\) −1.35502e49 −1.60738
\(924\) −8.04069e48 −0.936927
\(925\) 1.89126e48 0.216477
\(926\) −1.26204e48 −0.141903
\(927\) −3.41112e48 −0.376775
\(928\) −1.89768e48 −0.205912
\(929\) 8.12716e48 0.866322 0.433161 0.901316i \(-0.357398\pi\)
0.433161 + 0.901316i \(0.357398\pi\)
\(930\) 2.92242e48 0.306037
\(931\) 2.56678e48 0.264070
\(932\) −1.71448e48 −0.173288
\(933\) −4.42553e48 −0.439459
\(934\) −1.93857e49 −1.89129
\(935\) 6.09085e48 0.583830
\(936\) −6.57908e47 −0.0619603
\(937\) 2.32824e48 0.215439 0.107720 0.994181i \(-0.465645\pi\)
0.107720 + 0.994181i \(0.465645\pi\)
\(938\) −8.30508e48 −0.755087
\(939\) −1.17835e47 −0.0105267
\(940\) −8.49578e48 −0.745751
\(941\) 3.65122e48 0.314926 0.157463 0.987525i \(-0.449668\pi\)
0.157463 + 0.987525i \(0.449668\pi\)
\(942\) 2.87405e49 2.43588
\(943\) 4.16317e48 0.346722
\(944\) 2.45720e49 2.01096
\(945\) 3.76066e48 0.302440
\(946\) −1.63959e49 −1.29578
\(947\) −1.76048e49 −1.36728 −0.683639 0.729821i \(-0.739604\pi\)
−0.683639 + 0.729821i \(0.739604\pi\)
\(948\) −3.87257e48 −0.295571
\(949\) −1.71367e49 −1.28539
\(950\) 4.52871e48 0.333837
\(951\) −2.48885e49 −1.80310
\(952\) 2.91777e48 0.207750
\(953\) −1.48539e49 −1.03946 −0.519731 0.854330i \(-0.673968\pi\)
−0.519731 + 0.854330i \(0.673968\pi\)
\(954\) −4.19190e48 −0.288312
\(955\) −3.42721e47 −0.0231678
\(956\) 1.32051e49 0.877377
\(957\) 2.90108e48 0.189458
\(958\) −7.34283e48 −0.471338
\(959\) 6.06007e48 0.382358
\(960\) 5.86997e48 0.364050
\(961\) −1.33223e49 −0.812166
\(962\) 2.34822e49 1.40718
\(963\) 7.61332e48 0.448477
\(964\) −1.98563e49 −1.14981
\(965\) 4.52621e48 0.257653
\(966\) −1.83753e49 −1.02828
\(967\) −7.36558e47 −0.0405200 −0.0202600 0.999795i \(-0.506449\pi\)
−0.0202600 + 0.999795i \(0.506449\pi\)
\(968\) 4.55917e47 0.0246571
\(969\) 3.27422e49 1.74087
\(970\) −2.10507e49 −1.10036
\(971\) −1.98790e49 −1.02159 −0.510797 0.859702i \(-0.670649\pi\)
−0.510797 + 0.859702i \(0.670649\pi\)
\(972\) 1.11325e49 0.562468
\(973\) 2.78793e49 1.38490
\(974\) −7.85474e48 −0.383627
\(975\) 4.59658e48 0.220729
\(976\) 3.06665e49 1.44791
\(977\) −1.42950e49 −0.663626 −0.331813 0.943345i \(-0.607660\pi\)
−0.331813 + 0.943345i \(0.607660\pi\)
\(978\) 5.64601e49 2.57721
\(979\) 2.92577e49 1.31319
\(980\) −1.88022e48 −0.0829809
\(981\) 3.79587e48 0.164730
\(982\) −1.93211e49 −0.824503
\(983\) −1.85942e49 −0.780271 −0.390136 0.920757i \(-0.627572\pi\)
−0.390136 + 0.920757i \(0.627572\pi\)
\(984\) 2.52592e48 0.104232
\(985\) −8.49636e48 −0.344774
\(986\) 6.46619e48 0.258036
\(987\) 5.06594e49 1.98805
\(988\) 2.59983e49 1.00335
\(989\) −1.73245e49 −0.657538
\(990\) −5.91026e48 −0.220610
\(991\) 3.51455e49 1.29019 0.645095 0.764102i \(-0.276818\pi\)
0.645095 + 0.764102i \(0.276818\pi\)
\(992\) 1.60504e49 0.579488
\(993\) −1.05576e49 −0.374890
\(994\) −5.83124e49 −2.03651
\(995\) −9.96423e47 −0.0342265
\(996\) −2.21371e49 −0.747897
\(997\) 2.49733e49 0.829862 0.414931 0.909853i \(-0.363806\pi\)
0.414931 + 0.909853i \(0.363806\pi\)
\(998\) −1.26300e49 −0.412810
\(999\) 2.57106e49 0.826575
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 5.34.a.b.1.1 6
5.2 odd 4 25.34.b.c.24.3 12
5.3 odd 4 25.34.b.c.24.10 12
5.4 even 2 25.34.a.c.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.34.a.b.1.1 6 1.1 even 1 trivial
25.34.a.c.1.6 6 5.4 even 2
25.34.b.c.24.3 12 5.2 odd 4
25.34.b.c.24.10 12 5.3 odd 4