Properties

Label 1.28.a.a.1.1
Level $1$
Weight $28$
Character 1.1
Self dual yes
Analytic conductor $4.619$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 28 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.61855574838\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{18209}) \)
Defining polynomial: \(x^{2} - x - 4552\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{3}\cdot 3^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(67.9704\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-18713.6 q^{2} -3.44127e6 q^{3} +2.15981e8 q^{4} +5.76560e8 q^{5} +6.43986e10 q^{6} -1.96873e11 q^{7} -1.53009e12 q^{8} +4.21675e12 q^{9} +O(q^{10})\) \(q-18713.6 q^{2} -3.44127e6 q^{3} +2.15981e8 q^{4} +5.76560e8 q^{5} +6.43986e10 q^{6} -1.96873e11 q^{7} -1.53009e12 q^{8} +4.21675e12 q^{9} -1.07895e13 q^{10} +2.06714e14 q^{11} -7.43249e14 q^{12} -1.66656e14 q^{13} +3.68421e15 q^{14} -1.98410e15 q^{15} -3.55072e14 q^{16} -5.47219e15 q^{17} -7.89105e16 q^{18} +1.61471e17 q^{19} +1.24526e17 q^{20} +6.77495e17 q^{21} -3.86837e18 q^{22} +2.80341e18 q^{23} +5.26544e18 q^{24} -7.11816e18 q^{25} +3.11874e18 q^{26} +1.17308e19 q^{27} -4.25209e19 q^{28} -2.99842e18 q^{29} +3.71297e19 q^{30} +9.09190e19 q^{31} +2.12009e20 q^{32} -7.11360e20 q^{33} +1.02404e20 q^{34} -1.13509e20 q^{35} +9.10738e20 q^{36} +1.50001e21 q^{37} -3.02171e21 q^{38} +5.73510e20 q^{39} -8.82187e20 q^{40} +5.47146e21 q^{41} -1.26784e22 q^{42} -6.81035e21 q^{43} +4.46463e22 q^{44} +2.43121e21 q^{45} -5.24619e22 q^{46} -9.41657e21 q^{47} +1.22190e21 q^{48} -2.69532e22 q^{49} +1.33206e23 q^{50} +1.88313e22 q^{51} -3.59946e22 q^{52} -5.35936e22 q^{53} -2.19525e23 q^{54} +1.19183e23 q^{55} +3.01233e23 q^{56} -5.55667e23 q^{57} +5.61113e22 q^{58} +9.16258e23 q^{59} -4.28528e23 q^{60} +1.47362e24 q^{61} -1.70142e24 q^{62} -8.30166e23 q^{63} -3.91980e24 q^{64} -9.60874e22 q^{65} +1.33121e25 q^{66} -3.21915e24 q^{67} -1.18189e24 q^{68} -9.64729e24 q^{69} +2.12417e24 q^{70} +3.38255e24 q^{71} -6.45199e24 q^{72} +1.32172e25 q^{73} -2.80705e25 q^{74} +2.44955e25 q^{75} +3.48748e25 q^{76} -4.06965e25 q^{77} -1.07324e25 q^{78} +4.66230e25 q^{79} -2.04720e23 q^{80} -7.25240e25 q^{81} -1.02391e26 q^{82} +7.14690e25 q^{83} +1.46326e26 q^{84} -3.15505e24 q^{85} +1.27446e26 q^{86} +1.03184e25 q^{87} -3.16290e26 q^{88} -1.40708e26 q^{89} -4.54967e25 q^{90} +3.28102e25 q^{91} +6.05484e26 q^{92} -3.12877e26 q^{93} +1.76218e26 q^{94} +9.30980e25 q^{95} -7.29582e26 q^{96} +3.77568e26 q^{97} +5.04391e26 q^{98} +8.71662e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 8280q^{2} - 1286280q^{3} + 190623296q^{4} + 5443587900q^{5} + 86882873184q^{6} - 175391963600q^{7} - 3195032348160q^{8} + 1235136554154q^{9} + O(q^{10}) \) \( 2q - 8280q^{2} - 1286280q^{3} + 190623296q^{4} + 5443587900q^{5} + 86882873184q^{6} - 175391963600q^{7} - 3195032348160q^{8} + 1235136554154q^{9} + 39991096148400q^{10} + 138167337691944q^{11} - 797895007176960q^{12} - 753433801271060q^{13} + 3908340052811712q^{14} + 8504300488438800q^{15} - 14322995785166848q^{16} - 29753620331011740q^{17} - 110019470226337080q^{18} + 404565810372684760q^{19} + 1109219331427200q^{20} + 723787313583184704q^{21} - 4583556785578779360q^{22} + 2929078923121218960q^{23} + 1677495533792532480q^{24} + 9119218786673228750q^{25} - 3003459254146640016q^{26} - 11127665129740313040q^{27} - 43065656535315868160q^{28} - 15546679995448558260q^{29} + \)\(14\!\cdots\!00\)\(q^{30} + 28544554594467385024q^{31} + \)\(28\!\cdots\!20\)\(q^{32} - \)\(85\!\cdots\!60\)\(q^{33} - \)\(15\!\cdots\!68\)\(q^{34} - 8958395384765013600q^{35} + \)\(98\!\cdots\!92\)\(q^{36} + \)\(18\!\cdots\!80\)\(q^{37} - \)\(48\!\cdots\!40\)\(q^{38} - \)\(69\!\cdots\!72\)\(q^{39} - \)\(89\!\cdots\!00\)\(q^{40} + \)\(90\!\cdots\!64\)\(q^{41} - \)\(12\!\cdots\!40\)\(q^{42} + \)\(51\!\cdots\!00\)\(q^{43} + \)\(46\!\cdots\!12\)\(q^{44} - \)\(12\!\cdots\!00\)\(q^{45} - \)\(51\!\cdots\!16\)\(q^{46} - \)\(11\!\cdots\!60\)\(q^{47} - \)\(28\!\cdots\!40\)\(q^{48} - \)\(92\!\cdots\!14\)\(q^{49} + \)\(30\!\cdots\!00\)\(q^{50} - \)\(33\!\cdots\!56\)\(q^{51} - \)\(21\!\cdots\!00\)\(q^{52} + \)\(10\!\cdots\!20\)\(q^{53} - \)\(45\!\cdots\!40\)\(q^{54} - \)\(21\!\cdots\!00\)\(q^{55} + \)\(26\!\cdots\!40\)\(q^{56} - \)\(31\!\cdots\!80\)\(q^{57} - \)\(74\!\cdots\!60\)\(q^{58} + \)\(20\!\cdots\!80\)\(q^{59} - \)\(69\!\cdots\!00\)\(q^{60} + \)\(14\!\cdots\!44\)\(q^{61} - \)\(23\!\cdots\!60\)\(q^{62} - \)\(89\!\cdots\!20\)\(q^{63} - \)\(12\!\cdots\!24\)\(q^{64} - \)\(29\!\cdots\!00\)\(q^{65} + \)\(11\!\cdots\!48\)\(q^{66} + \)\(30\!\cdots\!60\)\(q^{67} - \)\(56\!\cdots\!80\)\(q^{68} - \)\(93\!\cdots\!72\)\(q^{69} + \)\(32\!\cdots\!00\)\(q^{70} - \)\(13\!\cdots\!16\)\(q^{71} - \)\(14\!\cdots\!20\)\(q^{72} + \)\(52\!\cdots\!60\)\(q^{73} - \)\(24\!\cdots\!28\)\(q^{74} + \)\(59\!\cdots\!00\)\(q^{75} + \)\(28\!\cdots\!80\)\(q^{76} - \)\(42\!\cdots\!00\)\(q^{77} - \)\(23\!\cdots\!00\)\(q^{78} + \)\(62\!\cdots\!40\)\(q^{79} - \)\(68\!\cdots\!00\)\(q^{80} - \)\(99\!\cdots\!78\)\(q^{81} - \)\(64\!\cdots\!60\)\(q^{82} + \)\(17\!\cdots\!80\)\(q^{83} + \)\(14\!\cdots\!92\)\(q^{84} - \)\(12\!\cdots\!00\)\(q^{85} + \)\(25\!\cdots\!84\)\(q^{86} - \)\(16\!\cdots\!20\)\(q^{87} - \)\(20\!\cdots\!20\)\(q^{88} - \)\(31\!\cdots\!80\)\(q^{89} - \)\(19\!\cdots\!00\)\(q^{90} + \)\(20\!\cdots\!04\)\(q^{91} + \)\(60\!\cdots\!60\)\(q^{92} - \)\(44\!\cdots\!60\)\(q^{93} + \)\(26\!\cdots\!92\)\(q^{94} + \)\(12\!\cdots\!00\)\(q^{95} - \)\(56\!\cdots\!56\)\(q^{96} - \)\(65\!\cdots\!60\)\(q^{97} - \)\(17\!\cdots\!40\)\(q^{98} + \)\(10\!\cdots\!88\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −18713.6 −1.61530 −0.807648 0.589664i \(-0.799260\pi\)
−0.807648 + 0.589664i \(0.799260\pi\)
\(3\) −3.44127e6 −1.24618 −0.623092 0.782149i \(-0.714124\pi\)
−0.623092 + 0.782149i \(0.714124\pi\)
\(4\) 2.15981e8 1.60918
\(5\) 5.76560e8 0.211227 0.105614 0.994407i \(-0.466319\pi\)
0.105614 + 0.994407i \(0.466319\pi\)
\(6\) 6.43986e10 2.01296
\(7\) −1.96873e11 −0.768004 −0.384002 0.923332i \(-0.625454\pi\)
−0.384002 + 0.923332i \(0.625454\pi\)
\(8\) −1.53009e12 −0.984013
\(9\) 4.21675e12 0.552973
\(10\) −1.07895e13 −0.341194
\(11\) 2.06714e14 1.80538 0.902691 0.430290i \(-0.141589\pi\)
0.902691 + 0.430290i \(0.141589\pi\)
\(12\) −7.43249e14 −2.00534
\(13\) −1.66656e14 −0.152611 −0.0763057 0.997084i \(-0.524312\pi\)
−0.0763057 + 0.997084i \(0.524312\pi\)
\(14\) 3.68421e15 1.24055
\(15\) −1.98410e15 −0.263228
\(16\) −3.55072e14 −0.0197105
\(17\) −5.47219e15 −0.133999 −0.0669994 0.997753i \(-0.521343\pi\)
−0.0669994 + 0.997753i \(0.521343\pi\)
\(18\) −7.89105e16 −0.893215
\(19\) 1.61471e17 0.880891 0.440445 0.897779i \(-0.354821\pi\)
0.440445 + 0.897779i \(0.354821\pi\)
\(20\) 1.24526e17 0.339903
\(21\) 6.77495e17 0.957074
\(22\) −3.86837e18 −2.91623
\(23\) 2.80341e18 1.15974 0.579870 0.814709i \(-0.303103\pi\)
0.579870 + 0.814709i \(0.303103\pi\)
\(24\) 5.26544e18 1.22626
\(25\) −7.11816e18 −0.955383
\(26\) 3.11874e18 0.246513
\(27\) 1.17308e19 0.557078
\(28\) −4.25209e19 −1.23586
\(29\) −2.99842e18 −0.0542650 −0.0271325 0.999632i \(-0.508638\pi\)
−0.0271325 + 0.999632i \(0.508638\pi\)
\(30\) 3.71297e19 0.425191
\(31\) 9.09190e19 0.668763 0.334381 0.942438i \(-0.391473\pi\)
0.334381 + 0.942438i \(0.391473\pi\)
\(32\) 2.12009e20 1.01585
\(33\) −7.11360e20 −2.24984
\(34\) 1.02404e20 0.216448
\(35\) −1.13509e20 −0.162223
\(36\) 9.10738e20 0.889835
\(37\) 1.50001e21 1.01244 0.506220 0.862404i \(-0.331042\pi\)
0.506220 + 0.862404i \(0.331042\pi\)
\(38\) −3.02171e21 −1.42290
\(39\) 5.73510e20 0.190182
\(40\) −8.82187e20 −0.207850
\(41\) 5.47146e21 0.923679 0.461840 0.886963i \(-0.347190\pi\)
0.461840 + 0.886963i \(0.347190\pi\)
\(42\) −1.26784e22 −1.54596
\(43\) −6.81035e21 −0.604429 −0.302215 0.953240i \(-0.597726\pi\)
−0.302215 + 0.953240i \(0.597726\pi\)
\(44\) 4.46463e22 2.90519
\(45\) 2.43121e21 0.116803
\(46\) −5.24619e22 −1.87333
\(47\) −9.41657e21 −0.251520 −0.125760 0.992061i \(-0.540137\pi\)
−0.125760 + 0.992061i \(0.540137\pi\)
\(48\) 1.22190e21 0.0245628
\(49\) −2.69532e22 −0.410169
\(50\) 1.33206e23 1.54323
\(51\) 1.88313e22 0.166987
\(52\) −3.59946e22 −0.245580
\(53\) −5.35936e22 −0.282741 −0.141370 0.989957i \(-0.545151\pi\)
−0.141370 + 0.989957i \(0.545151\pi\)
\(54\) −2.19525e23 −0.899846
\(55\) 1.19183e23 0.381346
\(56\) 3.01233e23 0.755726
\(57\) −5.55667e23 −1.09775
\(58\) 5.61113e22 0.0876541
\(59\) 9.16258e23 1.13636 0.568180 0.822904i \(-0.307648\pi\)
0.568180 + 0.822904i \(0.307648\pi\)
\(60\) −4.28528e23 −0.423582
\(61\) 1.47362e24 1.16529 0.582643 0.812728i \(-0.302019\pi\)
0.582643 + 0.812728i \(0.302019\pi\)
\(62\) −1.70142e24 −1.08025
\(63\) −8.30166e23 −0.424685
\(64\) −3.91980e24 −1.62119
\(65\) −9.60874e22 −0.0322356
\(66\) 1.33121e25 3.63415
\(67\) −3.21915e24 −0.717349 −0.358675 0.933463i \(-0.616771\pi\)
−0.358675 + 0.933463i \(0.616771\pi\)
\(68\) −1.18189e24 −0.215629
\(69\) −9.64729e24 −1.44525
\(70\) 2.12417e24 0.262039
\(71\) 3.38255e24 0.344554 0.172277 0.985049i \(-0.444888\pi\)
0.172277 + 0.985049i \(0.444888\pi\)
\(72\) −6.45199e24 −0.544133
\(73\) 1.32172e25 0.925295 0.462648 0.886542i \(-0.346900\pi\)
0.462648 + 0.886542i \(0.346900\pi\)
\(74\) −2.80705e25 −1.63539
\(75\) 2.44955e25 1.19058
\(76\) 3.48748e25 1.41752
\(77\) −4.06965e25 −1.38654
\(78\) −1.07324e25 −0.307200
\(79\) 4.66230e25 1.12366 0.561830 0.827253i \(-0.310098\pi\)
0.561830 + 0.827253i \(0.310098\pi\)
\(80\) −2.04720e23 −0.00416338
\(81\) −7.25240e25 −1.24719
\(82\) −1.02391e26 −1.49202
\(83\) 7.14690e25 0.884226 0.442113 0.896959i \(-0.354229\pi\)
0.442113 + 0.896959i \(0.354229\pi\)
\(84\) 1.46326e26 1.54011
\(85\) −3.15505e24 −0.0283042
\(86\) 1.27446e26 0.976332
\(87\) 1.03184e25 0.0676242
\(88\) −3.16290e26 −1.77652
\(89\) −1.40708e26 −0.678504 −0.339252 0.940696i \(-0.610174\pi\)
−0.339252 + 0.940696i \(0.610174\pi\)
\(90\) −4.54967e25 −0.188671
\(91\) 3.28102e25 0.117206
\(92\) 6.05484e26 1.86624
\(93\) −3.12877e26 −0.833401
\(94\) 1.76218e26 0.406279
\(95\) 9.30980e25 0.186068
\(96\) −7.29582e26 −1.26594
\(97\) 3.77568e26 0.569609 0.284805 0.958586i \(-0.408071\pi\)
0.284805 + 0.958586i \(0.408071\pi\)
\(98\) 5.04391e26 0.662545
\(99\) 8.71662e26 0.998327
\(100\) −1.53739e27 −1.53739
\(101\) −1.82546e27 −1.59600 −0.798002 0.602654i \(-0.794110\pi\)
−0.798002 + 0.602654i \(0.794110\pi\)
\(102\) −3.52401e26 −0.269734
\(103\) 2.87048e27 1.92598 0.962991 0.269534i \(-0.0868695\pi\)
0.962991 + 0.269534i \(0.0868695\pi\)
\(104\) 2.54999e26 0.150172
\(105\) 3.90617e26 0.202160
\(106\) 1.00293e27 0.456710
\(107\) −1.31331e27 −0.526849 −0.263425 0.964680i \(-0.584852\pi\)
−0.263425 + 0.964680i \(0.584852\pi\)
\(108\) 2.53362e27 0.896441
\(109\) −3.16013e27 −0.987296 −0.493648 0.869662i \(-0.664337\pi\)
−0.493648 + 0.869662i \(0.664337\pi\)
\(110\) −2.23035e27 −0.615986
\(111\) −5.16192e27 −1.26169
\(112\) 6.99043e25 0.0151377
\(113\) 3.68033e27 0.706851 0.353425 0.935463i \(-0.385017\pi\)
0.353425 + 0.935463i \(0.385017\pi\)
\(114\) 1.03985e28 1.77319
\(115\) 1.61633e27 0.244969
\(116\) −6.47603e26 −0.0873224
\(117\) −7.02748e26 −0.0843899
\(118\) −1.71465e28 −1.83556
\(119\) 1.07733e27 0.102912
\(120\) 3.03584e27 0.259020
\(121\) 2.96208e28 2.25940
\(122\) −2.75767e28 −1.88228
\(123\) −1.88288e28 −1.15107
\(124\) 1.96368e28 1.07616
\(125\) −8.39976e27 −0.413030
\(126\) 1.55354e28 0.685993
\(127\) −2.69227e28 −1.06849 −0.534243 0.845331i \(-0.679403\pi\)
−0.534243 + 0.845331i \(0.679403\pi\)
\(128\) 4.48982e28 1.60285
\(129\) 2.34363e28 0.753229
\(130\) 1.79814e27 0.0520701
\(131\) 3.17810e28 0.829860 0.414930 0.909853i \(-0.363806\pi\)
0.414930 + 0.909853i \(0.363806\pi\)
\(132\) −1.53640e29 −3.62040
\(133\) −3.17894e28 −0.676528
\(134\) 6.02418e28 1.15873
\(135\) 6.76350e27 0.117670
\(136\) 8.37292e27 0.131857
\(137\) 2.13194e28 0.304122 0.152061 0.988371i \(-0.451409\pi\)
0.152061 + 0.988371i \(0.451409\pi\)
\(138\) 1.80536e29 2.33451
\(139\) −1.15969e29 −1.36032 −0.680161 0.733062i \(-0.738090\pi\)
−0.680161 + 0.733062i \(0.738090\pi\)
\(140\) −2.45159e28 −0.261047
\(141\) 3.24050e28 0.313439
\(142\) −6.32998e28 −0.556557
\(143\) −3.44502e28 −0.275522
\(144\) −1.49725e27 −0.0108993
\(145\) −1.72877e27 −0.0114622
\(146\) −2.47341e29 −1.49463
\(147\) 9.27533e28 0.511146
\(148\) 3.23973e29 1.62920
\(149\) 2.70481e29 1.24200 0.621000 0.783810i \(-0.286727\pi\)
0.621000 + 0.783810i \(0.286727\pi\)
\(150\) −4.58399e29 −1.92314
\(151\) 6.43669e28 0.246873 0.123437 0.992352i \(-0.460608\pi\)
0.123437 + 0.992352i \(0.460608\pi\)
\(152\) −2.47065e29 −0.866808
\(153\) −2.30748e28 −0.0740977
\(154\) 7.61579e29 2.23968
\(155\) 5.24203e28 0.141261
\(156\) 1.23867e29 0.306037
\(157\) −7.36476e29 −1.66922 −0.834609 0.550842i \(-0.814307\pi\)
−0.834609 + 0.550842i \(0.814307\pi\)
\(158\) −8.72484e29 −1.81504
\(159\) 1.84430e29 0.352347
\(160\) 1.22236e29 0.214575
\(161\) −5.51917e29 −0.890686
\(162\) 1.35718e30 2.01459
\(163\) 4.91659e29 0.671632 0.335816 0.941928i \(-0.390988\pi\)
0.335816 + 0.941928i \(0.390988\pi\)
\(164\) 1.18173e30 1.48637
\(165\) −4.10142e29 −0.475226
\(166\) −1.33744e30 −1.42829
\(167\) 6.37427e29 0.627709 0.313854 0.949471i \(-0.398380\pi\)
0.313854 + 0.949471i \(0.398380\pi\)
\(168\) −1.03663e30 −0.941774
\(169\) −1.16476e30 −0.976710
\(170\) 5.90423e28 0.0457196
\(171\) 6.80884e29 0.487109
\(172\) −1.47091e30 −0.972638
\(173\) 2.71145e30 1.65798 0.828989 0.559265i \(-0.188917\pi\)
0.828989 + 0.559265i \(0.188917\pi\)
\(174\) −1.93094e29 −0.109233
\(175\) 1.40138e30 0.733738
\(176\) −7.33984e28 −0.0355849
\(177\) −3.15309e30 −1.41611
\(178\) 2.63315e30 1.09599
\(179\) −1.65055e30 −0.636961 −0.318481 0.947929i \(-0.603173\pi\)
−0.318481 + 0.947929i \(0.603173\pi\)
\(180\) 5.25095e29 0.187957
\(181\) 4.30260e30 1.42913 0.714563 0.699571i \(-0.246626\pi\)
0.714563 + 0.699571i \(0.246626\pi\)
\(182\) −6.13997e29 −0.189323
\(183\) −5.07112e30 −1.45216
\(184\) −4.28946e30 −1.14120
\(185\) 8.64843e29 0.213855
\(186\) 5.85506e30 1.34619
\(187\) −1.13118e30 −0.241919
\(188\) −2.03380e30 −0.404741
\(189\) −2.30948e30 −0.427838
\(190\) −1.74220e30 −0.300555
\(191\) 5.35850e30 0.861177 0.430589 0.902548i \(-0.358306\pi\)
0.430589 + 0.902548i \(0.358306\pi\)
\(192\) 1.34891e31 2.02030
\(193\) 2.47114e30 0.345044 0.172522 0.985006i \(-0.444808\pi\)
0.172522 + 0.985006i \(0.444808\pi\)
\(194\) −7.06566e30 −0.920088
\(195\) 3.30663e29 0.0401715
\(196\) −5.82138e30 −0.660038
\(197\) −4.41349e30 −0.467185 −0.233592 0.972335i \(-0.575048\pi\)
−0.233592 + 0.972335i \(0.575048\pi\)
\(198\) −1.63119e31 −1.61259
\(199\) −1.58034e31 −1.45960 −0.729802 0.683658i \(-0.760388\pi\)
−0.729802 + 0.683658i \(0.760388\pi\)
\(200\) 1.08914e31 0.940110
\(201\) 1.10780e31 0.893949
\(202\) 3.41610e31 2.57802
\(203\) 5.90310e29 0.0416758
\(204\) 4.06720e30 0.268713
\(205\) 3.15463e30 0.195106
\(206\) −5.37170e31 −3.11103
\(207\) 1.18213e31 0.641305
\(208\) 5.91750e28 0.00300804
\(209\) 3.33784e31 1.59034
\(210\) −7.30984e30 −0.326548
\(211\) −1.50086e31 −0.628820 −0.314410 0.949287i \(-0.601807\pi\)
−0.314410 + 0.949287i \(0.601807\pi\)
\(212\) −1.15752e31 −0.454982
\(213\) −1.16403e31 −0.429377
\(214\) 2.45768e31 0.851018
\(215\) −3.92658e30 −0.127672
\(216\) −1.79491e31 −0.548172
\(217\) −1.78995e31 −0.513613
\(218\) 5.91374e31 1.59478
\(219\) −4.54839e31 −1.15309
\(220\) 2.57413e31 0.613655
\(221\) 9.11975e29 0.0204497
\(222\) 9.65982e31 2.03800
\(223\) −1.04534e31 −0.207559 −0.103779 0.994600i \(-0.533094\pi\)
−0.103779 + 0.994600i \(0.533094\pi\)
\(224\) −4.17390e31 −0.780178
\(225\) −3.00155e31 −0.528301
\(226\) −6.88722e31 −1.14177
\(227\) 9.45028e31 1.47603 0.738016 0.674783i \(-0.235763\pi\)
0.738016 + 0.674783i \(0.235763\pi\)
\(228\) −1.20013e32 −1.76648
\(229\) −6.26689e31 −0.869508 −0.434754 0.900549i \(-0.643165\pi\)
−0.434754 + 0.900549i \(0.643165\pi\)
\(230\) −3.02474e31 −0.395697
\(231\) 1.40048e32 1.72788
\(232\) 4.58785e30 0.0533975
\(233\) 7.87335e31 0.864678 0.432339 0.901711i \(-0.357688\pi\)
0.432339 + 0.901711i \(0.357688\pi\)
\(234\) 1.31509e31 0.136315
\(235\) −5.42922e30 −0.0531277
\(236\) 1.97894e32 1.82861
\(237\) −1.60442e32 −1.40029
\(238\) −2.01607e31 −0.166233
\(239\) −5.65108e30 −0.0440311 −0.0220156 0.999758i \(-0.507008\pi\)
−0.0220156 + 0.999758i \(0.507008\pi\)
\(240\) 7.04498e29 0.00518834
\(241\) −4.42939e31 −0.308400 −0.154200 0.988040i \(-0.549280\pi\)
−0.154200 + 0.988040i \(0.549280\pi\)
\(242\) −5.54311e32 −3.64961
\(243\) 1.60121e32 0.997154
\(244\) 3.18274e32 1.87516
\(245\) −1.55401e31 −0.0866389
\(246\) 3.52354e32 1.85933
\(247\) −2.69102e31 −0.134434
\(248\) −1.39114e32 −0.658071
\(249\) −2.45944e32 −1.10191
\(250\) 1.57190e32 0.667166
\(251\) −3.28116e32 −1.31957 −0.659785 0.751454i \(-0.729353\pi\)
−0.659785 + 0.751454i \(0.729353\pi\)
\(252\) −1.79300e32 −0.683397
\(253\) 5.79505e32 2.09377
\(254\) 5.03822e32 1.72592
\(255\) 1.08574e31 0.0352722
\(256\) −3.14099e32 −0.967894
\(257\) 3.48288e31 0.101822 0.0509109 0.998703i \(-0.483788\pi\)
0.0509109 + 0.998703i \(0.483788\pi\)
\(258\) −4.38577e32 −1.21669
\(259\) −2.95311e32 −0.777559
\(260\) −2.07531e31 −0.0518731
\(261\) −1.26436e31 −0.0300071
\(262\) −5.94736e32 −1.34047
\(263\) 3.82694e31 0.0819311 0.0409656 0.999161i \(-0.486957\pi\)
0.0409656 + 0.999161i \(0.486957\pi\)
\(264\) 1.08844e33 2.21387
\(265\) −3.08999e31 −0.0597225
\(266\) 5.94895e32 1.09279
\(267\) 4.84213e32 0.845541
\(268\) −6.95274e32 −1.15435
\(269\) −4.44965e31 −0.0702539 −0.0351269 0.999383i \(-0.511184\pi\)
−0.0351269 + 0.999383i \(0.511184\pi\)
\(270\) −1.26569e32 −0.190072
\(271\) 3.62870e32 0.518401 0.259200 0.965824i \(-0.416541\pi\)
0.259200 + 0.965824i \(0.416541\pi\)
\(272\) 1.94302e30 0.00264118
\(273\) −1.12909e32 −0.146060
\(274\) −3.98963e32 −0.491247
\(275\) −1.47142e33 −1.72483
\(276\) −2.08363e33 −2.32567
\(277\) 1.40758e33 1.49622 0.748111 0.663574i \(-0.230961\pi\)
0.748111 + 0.663574i \(0.230961\pi\)
\(278\) 2.17020e33 2.19733
\(279\) 3.83383e32 0.369808
\(280\) 1.73679e32 0.159630
\(281\) 3.59534e32 0.314924 0.157462 0.987525i \(-0.449669\pi\)
0.157462 + 0.987525i \(0.449669\pi\)
\(282\) −6.06414e32 −0.506298
\(283\) −3.59177e32 −0.285885 −0.142943 0.989731i \(-0.545656\pi\)
−0.142943 + 0.989731i \(0.545656\pi\)
\(284\) 7.30568e32 0.554451
\(285\) −3.20375e32 −0.231875
\(286\) 6.44688e32 0.445049
\(287\) −1.07719e33 −0.709390
\(288\) 8.93990e32 0.561738
\(289\) −1.63777e33 −0.982044
\(290\) 3.23515e31 0.0185149
\(291\) −1.29931e33 −0.709838
\(292\) 2.85466e33 1.48897
\(293\) 3.51312e32 0.174976 0.0874882 0.996166i \(-0.472116\pi\)
0.0874882 + 0.996166i \(0.472116\pi\)
\(294\) −1.73575e33 −0.825653
\(295\) 5.28278e32 0.240030
\(296\) −2.29514e33 −0.996255
\(297\) 2.42492e33 1.00574
\(298\) −5.06167e33 −2.00620
\(299\) −4.67206e32 −0.176990
\(300\) 5.29057e33 1.91587
\(301\) 1.34078e33 0.464204
\(302\) −1.20454e33 −0.398773
\(303\) 6.28191e33 1.98891
\(304\) −5.73340e31 −0.0173628
\(305\) 8.49630e32 0.246140
\(306\) 4.31813e32 0.119690
\(307\) −6.75654e32 −0.179208 −0.0896038 0.995977i \(-0.528560\pi\)
−0.0896038 + 0.995977i \(0.528560\pi\)
\(308\) −8.78968e33 −2.23120
\(309\) −9.87810e33 −2.40013
\(310\) −9.80972e32 −0.228178
\(311\) 5.16690e33 1.15071 0.575354 0.817905i \(-0.304864\pi\)
0.575354 + 0.817905i \(0.304864\pi\)
\(312\) −8.77519e32 −0.187141
\(313\) −1.10679e33 −0.226056 −0.113028 0.993592i \(-0.536055\pi\)
−0.113028 + 0.993592i \(0.536055\pi\)
\(314\) 1.37821e34 2.69628
\(315\) −4.78641e32 −0.0897051
\(316\) 1.00697e34 1.80817
\(317\) −9.49991e33 −1.63463 −0.817315 0.576191i \(-0.804539\pi\)
−0.817315 + 0.576191i \(0.804539\pi\)
\(318\) −3.45135e33 −0.569145
\(319\) −6.19817e32 −0.0979691
\(320\) −2.26000e33 −0.342440
\(321\) 4.51946e33 0.656551
\(322\) 1.03284e34 1.43872
\(323\) −8.83602e32 −0.118038
\(324\) −1.56638e34 −2.00696
\(325\) 1.18629e33 0.145802
\(326\) −9.20072e33 −1.08489
\(327\) 1.08749e34 1.23035
\(328\) −8.37180e33 −0.908913
\(329\) 1.85387e33 0.193168
\(330\) 7.67523e33 0.767632
\(331\) −1.25351e34 −1.20351 −0.601757 0.798679i \(-0.705533\pi\)
−0.601757 + 0.798679i \(0.705533\pi\)
\(332\) 1.54359e34 1.42288
\(333\) 6.32514e33 0.559852
\(334\) −1.19286e34 −1.01394
\(335\) −1.85603e33 −0.151524
\(336\) −2.40560e32 −0.0188644
\(337\) −3.36740e33 −0.253683 −0.126842 0.991923i \(-0.540484\pi\)
−0.126842 + 0.991923i \(0.540484\pi\)
\(338\) 2.17968e34 1.57768
\(339\) −1.26650e34 −0.880865
\(340\) −6.81430e32 −0.0455466
\(341\) 1.87943e34 1.20737
\(342\) −1.27418e34 −0.786825
\(343\) 1.82434e34 1.08302
\(344\) 1.04204e34 0.594766
\(345\) −5.56225e33 −0.305276
\(346\) −5.07409e34 −2.67813
\(347\) −1.91545e34 −0.972353 −0.486177 0.873861i \(-0.661609\pi\)
−0.486177 + 0.873861i \(0.661609\pi\)
\(348\) 2.22858e33 0.108820
\(349\) 1.45433e34 0.683158 0.341579 0.939853i \(-0.389038\pi\)
0.341579 + 0.939853i \(0.389038\pi\)
\(350\) −2.62248e34 −1.18521
\(351\) −1.95501e33 −0.0850164
\(352\) 4.38253e34 1.83400
\(353\) −4.39359e33 −0.176954 −0.0884772 0.996078i \(-0.528200\pi\)
−0.0884772 + 0.996078i \(0.528200\pi\)
\(354\) 5.90057e34 2.28744
\(355\) 1.95025e33 0.0727791
\(356\) −3.03902e34 −1.09184
\(357\) −3.70738e33 −0.128247
\(358\) 3.08877e34 1.02888
\(359\) 2.60550e34 0.835828 0.417914 0.908487i \(-0.362761\pi\)
0.417914 + 0.908487i \(0.362761\pi\)
\(360\) −3.71996e33 −0.114936
\(361\) −7.52760e33 −0.224032
\(362\) −8.05172e34 −2.30846
\(363\) −1.01933e35 −2.81563
\(364\) 7.08639e33 0.188606
\(365\) 7.62050e33 0.195447
\(366\) 9.48990e34 2.34567
\(367\) 3.50053e34 0.833953 0.416977 0.908917i \(-0.363090\pi\)
0.416977 + 0.908917i \(0.363090\pi\)
\(368\) −9.95413e32 −0.0228590
\(369\) 2.30718e34 0.510770
\(370\) −1.61843e34 −0.345439
\(371\) 1.05512e34 0.217146
\(372\) −6.75755e34 −1.34110
\(373\) −2.06100e34 −0.394464 −0.197232 0.980357i \(-0.563195\pi\)
−0.197232 + 0.980357i \(0.563195\pi\)
\(374\) 2.11684e34 0.390771
\(375\) 2.89058e34 0.514711
\(376\) 1.44082e34 0.247499
\(377\) 4.99707e32 0.00828146
\(378\) 4.32186e34 0.691086
\(379\) −3.69120e34 −0.569559 −0.284779 0.958593i \(-0.591920\pi\)
−0.284779 + 0.958593i \(0.591920\pi\)
\(380\) 2.01074e34 0.299418
\(381\) 9.26485e34 1.33153
\(382\) −1.00277e35 −1.39106
\(383\) 6.12833e34 0.820652 0.410326 0.911939i \(-0.365415\pi\)
0.410326 + 0.911939i \(0.365415\pi\)
\(384\) −1.54507e35 −1.99745
\(385\) −2.34640e34 −0.292875
\(386\) −4.62439e34 −0.557348
\(387\) −2.87175e34 −0.334233
\(388\) 8.15476e34 0.916606
\(389\) 5.65060e34 0.613444 0.306722 0.951799i \(-0.400768\pi\)
0.306722 + 0.951799i \(0.400768\pi\)
\(390\) −6.18789e33 −0.0648889
\(391\) −1.53408e34 −0.155404
\(392\) 4.12407e34 0.403612
\(393\) −1.09367e35 −1.03416
\(394\) 8.25924e34 0.754642
\(395\) 2.68810e34 0.237347
\(396\) 1.88262e35 1.60649
\(397\) −2.20649e35 −1.81983 −0.909915 0.414794i \(-0.863854\pi\)
−0.909915 + 0.414794i \(0.863854\pi\)
\(398\) 2.95739e35 2.35769
\(399\) 1.09396e35 0.843078
\(400\) 2.52746e33 0.0188310
\(401\) −1.87612e35 −1.35148 −0.675741 0.737139i \(-0.736176\pi\)
−0.675741 + 0.737139i \(0.736176\pi\)
\(402\) −2.07308e35 −1.44399
\(403\) −1.51522e34 −0.102061
\(404\) −3.94265e35 −2.56827
\(405\) −4.18145e34 −0.263441
\(406\) −1.10468e34 −0.0673188
\(407\) 3.10072e35 1.82784
\(408\) −2.88135e34 −0.164317
\(409\) 2.22853e35 1.22957 0.614786 0.788694i \(-0.289242\pi\)
0.614786 + 0.788694i \(0.289242\pi\)
\(410\) −5.90344e34 −0.315154
\(411\) −7.33658e34 −0.378991
\(412\) 6.19970e35 3.09926
\(413\) −1.80387e35 −0.872729
\(414\) −2.21219e35 −1.03590
\(415\) 4.12062e34 0.186773
\(416\) −3.53327e34 −0.155030
\(417\) 3.99081e35 1.69521
\(418\) −6.24631e35 −2.56888
\(419\) −5.47879e34 −0.218170 −0.109085 0.994032i \(-0.534792\pi\)
−0.109085 + 0.994032i \(0.534792\pi\)
\(420\) 8.43658e34 0.325313
\(421\) −1.97758e35 −0.738458 −0.369229 0.929338i \(-0.620378\pi\)
−0.369229 + 0.929338i \(0.620378\pi\)
\(422\) 2.80864e35 1.01573
\(423\) −3.97073e34 −0.139083
\(424\) 8.20028e34 0.278221
\(425\) 3.89519e34 0.128020
\(426\) 2.17832e35 0.693572
\(427\) −2.90116e35 −0.894945
\(428\) −2.83650e35 −0.847798
\(429\) 1.18553e35 0.343350
\(430\) 7.34804e34 0.206228
\(431\) −4.94928e35 −1.34617 −0.673083 0.739567i \(-0.735030\pi\)
−0.673083 + 0.739567i \(0.735030\pi\)
\(432\) −4.16527e33 −0.0109803
\(433\) 3.12882e35 0.799454 0.399727 0.916634i \(-0.369105\pi\)
0.399727 + 0.916634i \(0.369105\pi\)
\(434\) 3.34965e35 0.829637
\(435\) 5.94917e33 0.0142841
\(436\) −6.82528e35 −1.58874
\(437\) 4.52671e35 1.02160
\(438\) 8.51168e35 1.86258
\(439\) 7.22790e35 1.53370 0.766852 0.641824i \(-0.221822\pi\)
0.766852 + 0.641824i \(0.221822\pi\)
\(440\) −1.82361e35 −0.375249
\(441\) −1.13655e35 −0.226813
\(442\) −1.70663e34 −0.0330324
\(443\) −7.68142e35 −1.44209 −0.721043 0.692891i \(-0.756337\pi\)
−0.721043 + 0.692891i \(0.756337\pi\)
\(444\) −1.11488e36 −2.03029
\(445\) −8.11264e34 −0.143318
\(446\) 1.95620e35 0.335269
\(447\) −9.30798e35 −1.54776
\(448\) 7.71705e35 1.24508
\(449\) −6.52536e35 −1.02160 −0.510798 0.859701i \(-0.670650\pi\)
−0.510798 + 0.859701i \(0.670650\pi\)
\(450\) 5.61698e35 0.853363
\(451\) 1.13103e36 1.66759
\(452\) 7.94881e35 1.13745
\(453\) −2.21504e35 −0.307649
\(454\) −1.76849e36 −2.38423
\(455\) 1.89171e34 0.0247571
\(456\) 8.50218e35 1.08020
\(457\) 6.21081e35 0.766090 0.383045 0.923730i \(-0.374875\pi\)
0.383045 + 0.923730i \(0.374875\pi\)
\(458\) 1.17276e36 1.40451
\(459\) −6.41930e34 −0.0746477
\(460\) 3.49098e35 0.394200
\(461\) 1.02161e36 1.12027 0.560133 0.828402i \(-0.310750\pi\)
0.560133 + 0.828402i \(0.310750\pi\)
\(462\) −2.62080e36 −2.79105
\(463\) −1.10341e36 −1.14129 −0.570643 0.821199i \(-0.693306\pi\)
−0.570643 + 0.821199i \(0.693306\pi\)
\(464\) 1.06466e33 0.00106959
\(465\) −1.80392e35 −0.176037
\(466\) −1.47339e36 −1.39671
\(467\) 8.66440e35 0.797922 0.398961 0.916968i \(-0.369371\pi\)
0.398961 + 0.916968i \(0.369371\pi\)
\(468\) −1.51780e35 −0.135799
\(469\) 6.33764e35 0.550927
\(470\) 1.01600e35 0.0858171
\(471\) 2.53441e36 2.08015
\(472\) −1.40195e36 −1.11819
\(473\) −1.40780e36 −1.09123
\(474\) 3.00246e36 2.26188
\(475\) −1.14938e36 −0.841588
\(476\) 2.32683e35 0.165604
\(477\) −2.25991e35 −0.156348
\(478\) 1.05752e35 0.0711234
\(479\) −2.57345e36 −1.68262 −0.841311 0.540552i \(-0.818215\pi\)
−0.841311 + 0.540552i \(0.818215\pi\)
\(480\) −4.20648e35 −0.267400
\(481\) −2.49985e35 −0.154510
\(482\) 8.28899e35 0.498157
\(483\) 1.89930e36 1.10996
\(484\) 6.39752e36 3.63580
\(485\) 2.17691e35 0.120317
\(486\) −2.99643e36 −1.61070
\(487\) −2.28927e36 −1.19690 −0.598448 0.801162i \(-0.704216\pi\)
−0.598448 + 0.801162i \(0.704216\pi\)
\(488\) −2.25476e36 −1.14666
\(489\) −1.69193e36 −0.836977
\(490\) 2.90812e35 0.139948
\(491\) 1.74114e36 0.815142 0.407571 0.913174i \(-0.366376\pi\)
0.407571 + 0.913174i \(0.366376\pi\)
\(492\) −4.06666e36 −1.85229
\(493\) 1.64079e34 0.00727145
\(494\) 5.03587e35 0.217151
\(495\) 5.02565e35 0.210874
\(496\) −3.22828e34 −0.0131816
\(497\) −6.65935e35 −0.264619
\(498\) 4.60250e36 1.77991
\(499\) 2.80174e36 1.05456 0.527278 0.849693i \(-0.323213\pi\)
0.527278 + 0.849693i \(0.323213\pi\)
\(500\) −1.81419e36 −0.664641
\(501\) −2.19356e36 −0.782240
\(502\) 6.14024e36 2.13150
\(503\) 3.44032e36 1.16260 0.581301 0.813688i \(-0.302544\pi\)
0.581301 + 0.813688i \(0.302544\pi\)
\(504\) 1.27022e36 0.417896
\(505\) −1.05249e36 −0.337119
\(506\) −1.08446e37 −3.38207
\(507\) 4.00825e36 1.21716
\(508\) −5.81480e36 −1.71939
\(509\) 1.50719e35 0.0433989 0.0216995 0.999765i \(-0.493092\pi\)
0.0216995 + 0.999765i \(0.493092\pi\)
\(510\) −2.03180e35 −0.0569750
\(511\) −2.60211e36 −0.710631
\(512\) −1.48198e35 −0.0394183
\(513\) 1.89418e36 0.490725
\(514\) −6.51772e35 −0.164473
\(515\) 1.65501e36 0.406820
\(516\) 5.06179e36 1.21208
\(517\) −1.94654e36 −0.454089
\(518\) 5.52634e36 1.25599
\(519\) −9.33082e36 −2.06614
\(520\) 1.47022e35 0.0317203
\(521\) 8.14778e36 1.71289 0.856446 0.516236i \(-0.172667\pi\)
0.856446 + 0.516236i \(0.172667\pi\)
\(522\) 2.36607e35 0.0484704
\(523\) −4.14380e36 −0.827229 −0.413615 0.910452i \(-0.635734\pi\)
−0.413615 + 0.910452i \(0.635734\pi\)
\(524\) 6.86409e36 1.33540
\(525\) −4.82252e36 −0.914372
\(526\) −7.16158e35 −0.132343
\(527\) −4.97526e35 −0.0896133
\(528\) 2.52584e35 0.0443453
\(529\) 2.01590e36 0.344999
\(530\) 5.78249e35 0.0964696
\(531\) 3.86363e36 0.628376
\(532\) −6.86591e36 −1.08866
\(533\) −9.11854e35 −0.140964
\(534\) −9.06137e36 −1.36580
\(535\) −7.57203e35 −0.111285
\(536\) 4.92557e36 0.705881
\(537\) 5.67999e36 0.793770
\(538\) 8.32690e35 0.113481
\(539\) −5.57161e36 −0.740512
\(540\) 1.46079e36 0.189353
\(541\) 1.06017e37 1.34033 0.670163 0.742214i \(-0.266224\pi\)
0.670163 + 0.742214i \(0.266224\pi\)
\(542\) −6.79060e36 −0.837371
\(543\) −1.48064e37 −1.78095
\(544\) −1.16016e36 −0.136123
\(545\) −1.82201e36 −0.208544
\(546\) 2.11293e36 0.235931
\(547\) 8.42305e36 0.917573 0.458786 0.888547i \(-0.348284\pi\)
0.458786 + 0.888547i \(0.348284\pi\)
\(548\) 4.60459e36 0.489388
\(549\) 6.21388e36 0.644371
\(550\) 2.75356e37 2.78611
\(551\) −4.84160e35 −0.0478016
\(552\) 1.47612e37 1.42214
\(553\) −9.17883e36 −0.862975
\(554\) −2.63409e37 −2.41684
\(555\) −2.97616e36 −0.266502
\(556\) −2.50471e37 −2.18901
\(557\) −5.59363e36 −0.477143 −0.238571 0.971125i \(-0.576679\pi\)
−0.238571 + 0.971125i \(0.576679\pi\)
\(558\) −7.17447e36 −0.597349
\(559\) 1.13499e36 0.0922427
\(560\) 4.03040e34 0.00319750
\(561\) 3.89269e36 0.301475
\(562\) −6.72818e36 −0.508695
\(563\) 2.06136e37 1.52157 0.760783 0.649006i \(-0.224815\pi\)
0.760783 + 0.649006i \(0.224815\pi\)
\(564\) 6.99886e36 0.504382
\(565\) 2.12193e36 0.149306
\(566\) 6.72150e36 0.461790
\(567\) 1.42780e37 0.957850
\(568\) −5.17560e36 −0.339046
\(569\) 4.96854e36 0.317844 0.158922 0.987291i \(-0.449198\pi\)
0.158922 + 0.987291i \(0.449198\pi\)
\(570\) 5.99538e36 0.374547
\(571\) 1.02940e36 0.0628055 0.0314028 0.999507i \(-0.490003\pi\)
0.0314028 + 0.999507i \(0.490003\pi\)
\(572\) −7.44060e36 −0.443365
\(573\) −1.84400e37 −1.07318
\(574\) 2.01580e37 1.14587
\(575\) −1.99551e37 −1.10800
\(576\) −1.65288e37 −0.896475
\(577\) −4.63258e36 −0.245442 −0.122721 0.992441i \(-0.539162\pi\)
−0.122721 + 0.992441i \(0.539162\pi\)
\(578\) 3.06485e37 1.58629
\(579\) −8.50387e36 −0.429987
\(580\) −3.73382e35 −0.0184449
\(581\) −1.40703e37 −0.679090
\(582\) 2.43149e37 1.14660
\(583\) −1.10786e37 −0.510455
\(584\) −2.02234e37 −0.910503
\(585\) −4.05177e35 −0.0178254
\(586\) −6.57430e36 −0.282639
\(587\) 2.64137e36 0.110972 0.0554862 0.998459i \(-0.482329\pi\)
0.0554862 + 0.998459i \(0.482329\pi\)
\(588\) 2.00330e37 0.822529
\(589\) 1.46808e37 0.589107
\(590\) −9.88599e36 −0.387720
\(591\) 1.51880e37 0.582198
\(592\) −5.32610e35 −0.0199557
\(593\) −3.52090e37 −1.28948 −0.644741 0.764401i \(-0.723035\pi\)
−0.644741 + 0.764401i \(0.723035\pi\)
\(594\) −4.53789e37 −1.62457
\(595\) 6.21145e35 0.0217377
\(596\) 5.84187e37 1.99861
\(597\) 5.43839e37 1.81893
\(598\) 8.74311e36 0.285891
\(599\) 4.76915e37 1.52468 0.762341 0.647176i \(-0.224050\pi\)
0.762341 + 0.647176i \(0.224050\pi\)
\(600\) −3.74802e37 −1.17155
\(601\) −2.39124e37 −0.730831 −0.365416 0.930844i \(-0.619073\pi\)
−0.365416 + 0.930844i \(0.619073\pi\)
\(602\) −2.50908e37 −0.749827
\(603\) −1.35743e37 −0.396675
\(604\) 1.39020e37 0.397264
\(605\) 1.70782e37 0.477247
\(606\) −1.17557e38 −3.21269
\(607\) 3.35424e37 0.896493 0.448246 0.893910i \(-0.352049\pi\)
0.448246 + 0.893910i \(0.352049\pi\)
\(608\) 3.42334e37 0.894854
\(609\) −2.03142e36 −0.0519357
\(610\) −1.58996e37 −0.397589
\(611\) 1.56933e36 0.0383847
\(612\) −4.98373e36 −0.119237
\(613\) −6.25036e37 −1.46281 −0.731407 0.681942i \(-0.761136\pi\)
−0.731407 + 0.681942i \(0.761136\pi\)
\(614\) 1.26439e37 0.289474
\(615\) −1.08559e37 −0.243138
\(616\) 6.22692e37 1.36437
\(617\) −6.57455e37 −1.40934 −0.704671 0.709534i \(-0.748906\pi\)
−0.704671 + 0.709534i \(0.748906\pi\)
\(618\) 1.84855e38 3.87692
\(619\) 2.39694e37 0.491851 0.245926 0.969289i \(-0.420908\pi\)
0.245926 + 0.969289i \(0.420908\pi\)
\(620\) 1.13218e37 0.227315
\(621\) 3.28862e37 0.646066
\(622\) −9.66913e37 −1.85873
\(623\) 2.77016e37 0.521094
\(624\) −2.03637e35 −0.00374857
\(625\) 4.81915e37 0.868140
\(626\) 2.07120e37 0.365148
\(627\) −1.14864e38 −1.98186
\(628\) −1.59065e38 −2.68608
\(629\) −8.20831e36 −0.135666
\(630\) 8.95709e36 0.144900
\(631\) −2.72032e37 −0.430748 −0.215374 0.976532i \(-0.569097\pi\)
−0.215374 + 0.976532i \(0.569097\pi\)
\(632\) −7.13372e37 −1.10570
\(633\) 5.16486e37 0.783625
\(634\) 1.77778e38 2.64041
\(635\) −1.55226e37 −0.225693
\(636\) 3.98334e37 0.566991
\(637\) 4.49192e36 0.0625965
\(638\) 1.15990e37 0.158249
\(639\) 1.42634e37 0.190529
\(640\) 2.58865e37 0.338566
\(641\) 6.03099e37 0.772334 0.386167 0.922429i \(-0.373799\pi\)
0.386167 + 0.922429i \(0.373799\pi\)
\(642\) −8.45753e37 −1.06052
\(643\) −1.01937e38 −1.25165 −0.625823 0.779965i \(-0.715237\pi\)
−0.625823 + 0.779965i \(0.715237\pi\)
\(644\) −1.19204e38 −1.43328
\(645\) 1.35124e37 0.159102
\(646\) 1.65354e37 0.190667
\(647\) 1.38190e36 0.0156052 0.00780260 0.999970i \(-0.497516\pi\)
0.00780260 + 0.999970i \(0.497516\pi\)
\(648\) 1.10968e38 1.22726
\(649\) 1.89404e38 2.05156
\(650\) −2.21997e37 −0.235514
\(651\) 6.15972e37 0.640055
\(652\) 1.06189e38 1.08078
\(653\) −1.67383e38 −1.66872 −0.834358 0.551224i \(-0.814161\pi\)
−0.834358 + 0.551224i \(0.814161\pi\)
\(654\) −2.03508e38 −1.98738
\(655\) 1.83236e37 0.175289
\(656\) −1.94276e36 −0.0182061
\(657\) 5.57335e37 0.511663
\(658\) −3.46926e37 −0.312024
\(659\) −1.83021e38 −1.61268 −0.806339 0.591454i \(-0.798554\pi\)
−0.806339 + 0.591454i \(0.798554\pi\)
\(660\) −8.85828e37 −0.764727
\(661\) 6.09366e37 0.515417 0.257708 0.966223i \(-0.417033\pi\)
0.257708 + 0.966223i \(0.417033\pi\)
\(662\) 2.34578e38 1.94403
\(663\) −3.13835e36 −0.0254841
\(664\) −1.09354e38 −0.870090
\(665\) −1.83285e37 −0.142901
\(666\) −1.18366e38 −0.904327
\(667\) −8.40581e36 −0.0629334
\(668\) 1.37672e38 1.01010
\(669\) 3.59729e37 0.258656
\(670\) 3.47330e37 0.244756
\(671\) 3.04618e38 2.10379
\(672\) 1.43635e38 0.972245
\(673\) −6.36340e37 −0.422168 −0.211084 0.977468i \(-0.567699\pi\)
−0.211084 + 0.977468i \(0.567699\pi\)
\(674\) 6.30163e37 0.409774
\(675\) −8.35015e37 −0.532223
\(676\) −2.51566e38 −1.57171
\(677\) −5.37104e37 −0.328936 −0.164468 0.986382i \(-0.552591\pi\)
−0.164468 + 0.986382i \(0.552591\pi\)
\(678\) 2.37008e38 1.42286
\(679\) −7.43332e37 −0.437462
\(680\) 4.82749e36 0.0278517
\(681\) −3.25210e38 −1.83941
\(682\) −3.51708e38 −1.95026
\(683\) 1.59190e38 0.865437 0.432718 0.901529i \(-0.357554\pi\)
0.432718 + 0.901529i \(0.357554\pi\)
\(684\) 1.47058e38 0.783847
\(685\) 1.22919e37 0.0642387
\(686\) −3.41399e38 −1.74939
\(687\) 2.15661e38 1.08357
\(688\) 2.41817e36 0.0119136
\(689\) 8.93171e36 0.0431495
\(690\) 1.04090e38 0.493111
\(691\) −1.11503e38 −0.518006 −0.259003 0.965877i \(-0.583394\pi\)
−0.259003 + 0.965877i \(0.583394\pi\)
\(692\) 5.85621e38 2.66799
\(693\) −1.71607e38 −0.766719
\(694\) 3.58451e38 1.57064
\(695\) −6.68631e37 −0.287337
\(696\) −1.57880e37 −0.0665431
\(697\) −2.99409e37 −0.123772
\(698\) −2.72158e38 −1.10350
\(699\) −2.70943e38 −1.07755
\(700\) 3.02671e38 1.18072
\(701\) 9.04824e37 0.346235 0.173117 0.984901i \(-0.444616\pi\)
0.173117 + 0.984901i \(0.444616\pi\)
\(702\) 3.65852e37 0.137327
\(703\) 2.42208e38 0.891849
\(704\) −8.10278e38 −2.92687
\(705\) 1.86834e37 0.0662069
\(706\) 8.22199e37 0.285834
\(707\) 3.59385e38 1.22574
\(708\) −6.81008e38 −2.27879
\(709\) 2.52263e38 0.828190 0.414095 0.910234i \(-0.364098\pi\)
0.414095 + 0.910234i \(0.364098\pi\)
\(710\) −3.64961e37 −0.117560
\(711\) 1.96598e38 0.621353
\(712\) 2.15295e38 0.667657
\(713\) 2.54883e38 0.775591
\(714\) 6.93784e37 0.207157
\(715\) −1.98626e37 −0.0581976
\(716\) −3.56488e38 −1.02499
\(717\) 1.94469e37 0.0548709
\(718\) −4.87584e38 −1.35011
\(719\) −2.15368e38 −0.585249 −0.292624 0.956227i \(-0.594529\pi\)
−0.292624 + 0.956227i \(0.594529\pi\)
\(720\) −8.63254e35 −0.00230224
\(721\) −5.65122e38 −1.47916
\(722\) 1.40869e38 0.361878
\(723\) 1.52427e38 0.384323
\(724\) 9.29280e38 2.29973
\(725\) 2.13433e37 0.0518439
\(726\) 1.90753e39 4.54808
\(727\) −6.18554e38 −1.44765 −0.723824 0.689985i \(-0.757617\pi\)
−0.723824 + 0.689985i \(0.757617\pi\)
\(728\) −5.02025e37 −0.115332
\(729\) 2.02058e36 0.00455675
\(730\) −1.42607e38 −0.315706
\(731\) 3.72675e37 0.0809927
\(732\) −1.09527e39 −2.33679
\(733\) −5.13013e36 −0.0107455 −0.00537273 0.999986i \(-0.501710\pi\)
−0.00537273 + 0.999986i \(0.501710\pi\)
\(734\) −6.55075e38 −1.34708
\(735\) 5.34779e37 0.107968
\(736\) 5.94349e38 1.17812
\(737\) −6.65443e38 −1.29509
\(738\) −4.31756e38 −0.825044
\(739\) −5.22466e38 −0.980298 −0.490149 0.871639i \(-0.663058\pi\)
−0.490149 + 0.871639i \(0.663058\pi\)
\(740\) 1.86790e38 0.344132
\(741\) 9.26054e37 0.167529
\(742\) −1.97450e38 −0.350756
\(743\) 1.00984e39 1.76158 0.880789 0.473509i \(-0.157013\pi\)
0.880789 + 0.473509i \(0.157013\pi\)
\(744\) 4.78729e38 0.820077
\(745\) 1.55948e38 0.262344
\(746\) 3.85686e38 0.637177
\(747\) 3.01367e38 0.488953
\(748\) −2.44313e38 −0.389292
\(749\) 2.58556e38 0.404622
\(750\) −5.40932e38 −0.831411
\(751\) −4.44629e38 −0.671210 −0.335605 0.942003i \(-0.608941\pi\)
−0.335605 + 0.942003i \(0.608941\pi\)
\(752\) 3.34356e36 0.00495757
\(753\) 1.12914e39 1.64443
\(754\) −9.35131e36 −0.0133770
\(755\) 3.71114e37 0.0521463
\(756\) −4.98803e38 −0.688470
\(757\) 8.24934e38 1.11847 0.559235 0.829009i \(-0.311095\pi\)
0.559235 + 0.829009i \(0.311095\pi\)
\(758\) 6.90757e38 0.920007
\(759\) −1.99423e39 −2.60923
\(760\) −1.42448e38 −0.183093
\(761\) −5.69669e38 −0.719333 −0.359666 0.933081i \(-0.617109\pi\)
−0.359666 + 0.933081i \(0.617109\pi\)
\(762\) −1.73379e39 −2.15082
\(763\) 6.22146e38 0.758248
\(764\) 1.15733e39 1.38579
\(765\) −1.33040e37 −0.0156514
\(766\) −1.14683e39 −1.32560
\(767\) −1.52700e38 −0.173421
\(768\) 1.08090e39 1.20617
\(769\) 1.47938e39 1.62209 0.811043 0.584986i \(-0.198900\pi\)
0.811043 + 0.584986i \(0.198900\pi\)
\(770\) 4.39096e38 0.473080
\(771\) −1.19855e38 −0.126889
\(772\) 5.33720e38 0.555239
\(773\) −1.83758e39 −1.87855 −0.939277 0.343160i \(-0.888503\pi\)
−0.939277 + 0.343160i \(0.888503\pi\)
\(774\) 5.37408e38 0.539885
\(775\) −6.47176e38 −0.638924
\(776\) −5.77712e38 −0.560503
\(777\) 1.01625e39 0.968981
\(778\) −1.05743e39 −0.990894
\(779\) 8.83484e38 0.813660
\(780\) 7.14169e37 0.0646434
\(781\) 6.99222e38 0.622051
\(782\) 2.87081e38 0.251023
\(783\) −3.51738e37 −0.0302298
\(784\) 9.57033e36 0.00808463
\(785\) −4.24623e38 −0.352584
\(786\) 2.04665e39 1.67047
\(787\) −3.93218e38 −0.315482 −0.157741 0.987481i \(-0.550421\pi\)
−0.157741 + 0.987481i \(0.550421\pi\)
\(788\) −9.53231e38 −0.751786
\(789\) −1.31695e38 −0.102101
\(790\) −5.03040e38 −0.383386
\(791\) −7.24559e38 −0.542864
\(792\) −1.33372e39 −0.982367
\(793\) −2.45588e38 −0.177836
\(794\) 4.12914e39 2.93957
\(795\) 1.06335e38 0.0744252
\(796\) −3.41324e39 −2.34877
\(797\) −1.32458e39 −0.896168 −0.448084 0.893991i \(-0.647893\pi\)
−0.448084 + 0.893991i \(0.647893\pi\)
\(798\) −2.04719e39 −1.36182
\(799\) 5.15293e37 0.0337033
\(800\) −1.50912e39 −0.970527
\(801\) −5.93329e38 −0.375194
\(802\) 3.51089e39 2.18305
\(803\) 2.73218e39 1.67051
\(804\) 2.39263e39 1.43853
\(805\) −3.18213e38 −0.188137
\(806\) 2.83553e38 0.164858
\(807\) 1.53125e38 0.0875492
\(808\) 2.79311e39 1.57049
\(809\) −2.19258e39 −1.21241 −0.606206 0.795308i \(-0.707309\pi\)
−0.606206 + 0.795308i \(0.707309\pi\)
\(810\) 7.82499e38 0.425536
\(811\) 2.76373e39 1.47813 0.739066 0.673633i \(-0.235267\pi\)
0.739066 + 0.673633i \(0.235267\pi\)
\(812\) 1.27496e38 0.0670640
\(813\) −1.24873e39 −0.646022
\(814\) −5.80257e39 −2.95251
\(815\) 2.83471e38 0.141867
\(816\) −6.68646e36 −0.00329139
\(817\) −1.09968e39 −0.532436
\(818\) −4.17038e39 −1.98612
\(819\) 1.38352e38 0.0648118
\(820\) 6.81340e38 0.313962
\(821\) −9.42212e38 −0.427087 −0.213543 0.976934i \(-0.568500\pi\)
−0.213543 + 0.976934i \(0.568500\pi\)
\(822\) 1.37294e39 0.612183
\(823\) 2.17900e39 0.955782 0.477891 0.878419i \(-0.341401\pi\)
0.477891 + 0.878419i \(0.341401\pi\)
\(824\) −4.39208e39 −1.89519
\(825\) 5.06357e39 2.14946
\(826\) 3.37569e39 1.40972
\(827\) −8.15484e38 −0.335036 −0.167518 0.985869i \(-0.553575\pi\)
−0.167518 + 0.985869i \(0.553575\pi\)
\(828\) 2.55317e39 1.03198
\(829\) 1.51577e39 0.602763 0.301382 0.953504i \(-0.402552\pi\)
0.301382 + 0.953504i \(0.402552\pi\)
\(830\) −7.71116e38 −0.301693
\(831\) −4.84386e39 −1.86457
\(832\) 6.53260e38 0.247412
\(833\) 1.47493e38 0.0549622
\(834\) −7.46823e39 −2.73827
\(835\) 3.67515e38 0.132589
\(836\) 7.20911e39 2.55916
\(837\) 1.06655e39 0.372553
\(838\) 1.02528e39 0.352409
\(839\) 3.04177e39 1.02882 0.514410 0.857544i \(-0.328011\pi\)
0.514410 + 0.857544i \(0.328011\pi\)
\(840\) −5.97677e38 −0.198928
\(841\) −3.04414e39 −0.997055
\(842\) 3.70077e39 1.19283
\(843\) −1.23726e39 −0.392453
\(844\) −3.24157e39 −1.01189
\(845\) −6.71554e38 −0.206308
\(846\) 7.43067e38 0.224661
\(847\) −5.83154e39 −1.73523
\(848\) 1.90296e37 0.00557295
\(849\) 1.23603e39 0.356266
\(850\) −7.28931e38 −0.206791
\(851\) 4.20513e39 1.17417
\(852\) −2.51408e39 −0.690947
\(853\) −9.78044e38 −0.264574 −0.132287 0.991211i \(-0.542232\pi\)
−0.132287 + 0.991211i \(0.542232\pi\)
\(854\) 5.42912e39 1.44560
\(855\) 3.92571e38 0.102891
\(856\) 2.00948e39 0.518427
\(857\) −6.93851e39 −1.76208 −0.881039 0.473044i \(-0.843155\pi\)
−0.881039 + 0.473044i \(0.843155\pi\)
\(858\) −2.21855e39 −0.554613
\(859\) −6.79141e39 −1.67129 −0.835646 0.549268i \(-0.814907\pi\)
−0.835646 + 0.549268i \(0.814907\pi\)
\(860\) −8.48066e38 −0.205447
\(861\) 3.70689e39 0.884030
\(862\) 9.26188e39 2.17446
\(863\) −5.27048e38 −0.121816 −0.0609080 0.998143i \(-0.519400\pi\)
−0.0609080 + 0.998143i \(0.519400\pi\)
\(864\) 2.48703e39 0.565908
\(865\) 1.56331e39 0.350210
\(866\) −5.85514e39 −1.29136
\(867\) 5.63600e39 1.22381
\(868\) −3.86596e39 −0.826497
\(869\) 9.63764e39 2.02863
\(870\) −1.11330e38 −0.0230730
\(871\) 5.36491e38 0.109476
\(872\) 4.83527e39 0.971512
\(873\) 1.59211e39 0.314978
\(874\) −8.47110e39 −1.65019
\(875\) 1.65369e39 0.317209
\(876\) −9.82366e39 −1.85553
\(877\) 3.42049e39 0.636200 0.318100 0.948057i \(-0.396955\pi\)
0.318100 + 0.948057i \(0.396955\pi\)
\(878\) −1.35260e40 −2.47739
\(879\) −1.20896e39 −0.218053
\(880\) −4.23186e37 −0.00751650
\(881\) −7.31752e39 −1.27994 −0.639969 0.768401i \(-0.721053\pi\)
−0.639969 + 0.768401i \(0.721053\pi\)
\(882\) 2.12689e39 0.366370
\(883\) −2.06213e39 −0.349821 −0.174910 0.984584i \(-0.555964\pi\)
−0.174910 + 0.984584i \(0.555964\pi\)
\(884\) 1.96969e38 0.0329074
\(885\) −1.81795e39 −0.299121
\(886\) 1.43747e40 2.32940
\(887\) 6.98969e39 1.11555 0.557775 0.829992i \(-0.311655\pi\)
0.557775 + 0.829992i \(0.311655\pi\)
\(888\) 7.89819e39 1.24152
\(889\) 5.30037e39 0.820602
\(890\) 1.51817e39 0.231502
\(891\) −1.49917e40 −2.25166
\(892\) −2.25773e39 −0.334000
\(893\) −1.52051e39 −0.221561
\(894\) 1.74186e40 2.50009
\(895\) −9.51642e38 −0.134543
\(896\) −8.83926e39 −1.23100
\(897\) 1.60778e39 0.220561
\(898\) 1.22113e40 1.65018
\(899\) −2.72614e38 −0.0362904
\(900\) −6.48278e39 −0.850133
\(901\) 2.93274e38 0.0378869
\(902\) −2.11656e40 −2.69366
\(903\) −4.61398e39 −0.578483
\(904\) −5.63122e39 −0.695550
\(905\) 2.48071e39 0.301870
\(906\) 4.14514e39 0.496945
\(907\) −2.28488e39 −0.269876 −0.134938 0.990854i \(-0.543084\pi\)
−0.134938 + 0.990854i \(0.543084\pi\)
\(908\) 2.04108e40 2.37521
\(909\) −7.69751e39 −0.882547
\(910\) −3.54006e38 −0.0399901
\(911\) 7.51662e39 0.836612 0.418306 0.908306i \(-0.362624\pi\)
0.418306 + 0.908306i \(0.362624\pi\)
\(912\) 1.97302e38 0.0216372
\(913\) 1.47737e40 1.59637
\(914\) −1.16227e40 −1.23746
\(915\) −2.92381e39 −0.306736
\(916\) −1.35353e40 −1.39920
\(917\) −6.25683e39 −0.637336
\(918\) 1.20128e39 0.120578
\(919\) 5.26405e39 0.520668 0.260334 0.965519i \(-0.416167\pi\)
0.260334 + 0.965519i \(0.416167\pi\)
\(920\) −2.47313e39 −0.241052
\(921\) 2.32511e39 0.223326
\(922\) −1.91179e40 −1.80956
\(923\) −5.63724e38 −0.0525828
\(924\) 3.02477e40 2.78048
\(925\) −1.06773e40 −0.967269
\(926\) 2.06488e40 1.84351
\(927\) 1.21041e40 1.06502
\(928\) −6.35694e38 −0.0551252
\(929\) −2.48177e39 −0.212104 −0.106052 0.994361i \(-0.533821\pi\)
−0.106052 + 0.994361i \(0.533821\pi\)
\(930\) 3.37579e39 0.284352
\(931\) −4.35217e39 −0.361314
\(932\) 1.70049e40 1.39143
\(933\) −1.77807e40 −1.43399
\(934\) −1.62142e40 −1.28888
\(935\) −6.52193e38 −0.0510998
\(936\) 1.07526e39 0.0830408
\(937\) −2.96211e39 −0.225485 −0.112742 0.993624i \(-0.535963\pi\)
−0.112742 + 0.993624i \(0.535963\pi\)
\(938\) −1.18600e40 −0.889911
\(939\) 3.80877e39 0.281708
\(940\) −1.17261e39 −0.0854923
\(941\) 1.23582e40 0.888168 0.444084 0.895985i \(-0.353529\pi\)
0.444084 + 0.895985i \(0.353529\pi\)
\(942\) −4.74280e40 −3.36006
\(943\) 1.53388e40 1.07123
\(944\) −3.25338e38 −0.0223982
\(945\) −1.33155e39 −0.0903710
\(946\) 2.63449e40 1.76265
\(947\) 3.62546e39 0.239132 0.119566 0.992826i \(-0.461850\pi\)
0.119566 + 0.992826i \(0.461850\pi\)
\(948\) −3.46525e40 −2.25332
\(949\) −2.20273e39 −0.141210
\(950\) 2.15090e40 1.35941
\(951\) 3.26918e40 2.03705
\(952\) −1.64841e39 −0.101266
\(953\) −2.05559e40 −1.24504 −0.622519 0.782605i \(-0.713891\pi\)
−0.622519 + 0.782605i \(0.713891\pi\)
\(954\) 4.22910e39 0.252548
\(955\) 3.08950e39 0.181904
\(956\) −1.22053e39 −0.0708542
\(957\) 2.13296e39 0.122087
\(958\) 4.81585e40 2.71793
\(959\) −4.19722e39 −0.233567
\(960\) 7.77728e39 0.426742
\(961\) −1.02164e40 −0.552757
\(962\) 4.67813e39 0.249579
\(963\) −5.53790e39 −0.291333
\(964\) −9.56665e39 −0.496272
\(965\) 1.42476e39 0.0728825
\(966\) −3.55427e40 −1.79291
\(967\) −2.81961e40 −1.40259 −0.701296 0.712871i \(-0.747395\pi\)
−0.701296 + 0.712871i \(0.747395\pi\)
\(968\) −4.53223e40 −2.22328
\(969\) 3.04071e39 0.147097
\(970\) −4.07378e39 −0.194348
\(971\) −1.81766e40 −0.855170 −0.427585 0.903975i \(-0.640636\pi\)
−0.427585 + 0.903975i \(0.640636\pi\)
\(972\) 3.45830e40 1.60461
\(973\) 2.28312e40 1.04473
\(974\) 4.28405e40 1.93334
\(975\) −4.08233e39 −0.181696
\(976\) −5.23241e38 −0.0229683
\(977\) 2.03258e40 0.879974 0.439987 0.898004i \(-0.354983\pi\)
0.439987 + 0.898004i \(0.354983\pi\)
\(978\) 3.16622e40 1.35197
\(979\) −2.90863e40 −1.22496
\(980\) −3.35638e39 −0.139418
\(981\) −1.33255e40 −0.545948
\(982\) −3.25830e40 −1.31670
\(983\) 7.72807e39 0.308034 0.154017 0.988068i \(-0.450779\pi\)
0.154017 + 0.988068i \(0.450779\pi\)
\(984\) 2.88096e40 1.13267
\(985\) −2.54465e39 −0.0986820
\(986\) −3.07052e38 −0.0117455
\(987\) −6.37968e39 −0.240723
\(988\) −5.81210e39 −0.216329
\(989\) −1.90922e40 −0.700981
\(990\) −9.40481e39 −0.340624
\(991\) 1.25885e40 0.449758 0.224879 0.974387i \(-0.427801\pi\)
0.224879 + 0.974387i \(0.427801\pi\)
\(992\) 1.92757e40 0.679364
\(993\) 4.31368e40 1.49980
\(994\) 1.24620e40 0.427438
\(995\) −9.11164e39 −0.308308
\(996\) −5.31193e40 −1.77317
\(997\) 4.50833e40 1.48467 0.742336 0.670028i \(-0.233718\pi\)
0.742336 + 0.670028i \(0.233718\pi\)
\(998\) −5.24306e40 −1.70342
\(999\) 1.75962e40 0.564008
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.28.a.a.1.1 2
3.2 odd 2 9.28.a.d.1.2 2
4.3 odd 2 16.28.a.d.1.2 2
5.2 odd 4 25.28.b.a.24.1 4
5.3 odd 4 25.28.b.a.24.4 4
5.4 even 2 25.28.a.a.1.2 2
7.6 odd 2 49.28.a.b.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.28.a.a.1.1 2 1.1 even 1 trivial
9.28.a.d.1.2 2 3.2 odd 2
16.28.a.d.1.2 2 4.3 odd 2
25.28.a.a.1.2 2 5.4 even 2
25.28.b.a.24.1 4 5.2 odd 4
25.28.b.a.24.4 4 5.3 odd 4
49.28.a.b.1.1 2 7.6 odd 2