Properties

Label 22.10.a.d.1.1
Level $22$
Weight $10$
Character 22.1
Self dual yes
Analytic conductor $11.331$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 22.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.3307883956\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{889}) \)
Defining polynomial: \( x^{2} - x - 222 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(15.4081\) of defining polynomial
Character \(\chi\) \(=\) 22.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} +2314.76 q^{6} -8664.66 q^{7} -4096.00 q^{8} +1247.12 q^{9} +O(q^{10})\) \(q-16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} +2314.76 q^{6} -8664.66 q^{7} -4096.00 q^{8} +1247.12 q^{9} +27305.3 q^{10} +14641.0 q^{11} -37036.2 q^{12} +67852.1 q^{13} +138635. q^{14} +246895. q^{15} +65536.0 q^{16} +249646. q^{17} -19953.9 q^{18} -293189. q^{19} -436885. q^{20} +1.25354e6 q^{21} -234256. q^{22} +1.10315e6 q^{23} +592578. q^{24} +959294. q^{25} -1.08563e6 q^{26} +2.66716e6 q^{27} -2.21815e6 q^{28} -5.23603e6 q^{29} -3.95032e6 q^{30} -8.38378e6 q^{31} -1.04858e6 q^{32} -2.11815e6 q^{33} -3.99433e6 q^{34} +1.47869e7 q^{35} +319263. q^{36} +7.34600e6 q^{37} +4.69103e6 q^{38} -9.81632e6 q^{39} +6.99016e6 q^{40} +1.01256e7 q^{41} -2.00566e7 q^{42} -2.56347e7 q^{43} +3.74810e6 q^{44} -2.12831e6 q^{45} -1.76505e7 q^{46} +5.88993e7 q^{47} -9.48125e6 q^{48} +3.47227e7 q^{49} -1.53487e7 q^{50} -3.61168e7 q^{51} +1.73701e7 q^{52} +8.68723e7 q^{53} -4.26746e7 q^{54} -2.49861e7 q^{55} +3.54904e7 q^{56} +4.24164e7 q^{57} +8.37764e7 q^{58} -1.82302e8 q^{59} +6.32052e7 q^{60} +1.22104e8 q^{61} +1.34141e8 q^{62} -1.08059e7 q^{63} +1.67772e7 q^{64} -1.15795e8 q^{65} +3.38904e7 q^{66} -6.80532e7 q^{67} +6.39093e7 q^{68} -1.59596e8 q^{69} -2.36591e8 q^{70} -1.67349e8 q^{71} -5.10821e6 q^{72} -1.51799e8 q^{73} -1.17536e8 q^{74} -1.38783e8 q^{75} -7.50564e7 q^{76} -1.26859e8 q^{77} +1.57061e8 q^{78} +2.95735e8 q^{79} -1.11842e8 q^{80} -4.10412e8 q^{81} -1.62010e8 q^{82} +4.61094e8 q^{83} +3.20906e8 q^{84} -4.26040e8 q^{85} +4.10156e8 q^{86} +7.57509e8 q^{87} -5.99695e7 q^{88} +4.63623e8 q^{89} +3.40530e7 q^{90} -5.87915e8 q^{91} +2.82407e8 q^{92} +1.21290e9 q^{93} -9.42388e8 q^{94} +5.00351e8 q^{95} +1.51700e8 q^{96} +1.06866e8 q^{97} -5.55563e8 q^{98} +1.82591e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9} + 8336 q^{10} + 29282 q^{11} - 5376 q^{12} + 150314 q^{13} + 119840 q^{14} + 393519 q^{15} + 131072 q^{16} + 690472 q^{17} + 50256 q^{18} + 511212 q^{19} - 133376 q^{20} + 1398810 q^{21} - 468512 q^{22} + 874751 q^{23} + 86016 q^{24} + 411771 q^{25} - 2405024 q^{26} - 309771 q^{27} - 1917440 q^{28} - 2951058 q^{29} - 6296304 q^{30} - 5818705 q^{31} - 2097152 q^{32} - 307461 q^{33} - 11047552 q^{34} + 16179590 q^{35} - 804096 q^{36} + 2658905 q^{37} - 8179392 q^{38} + 381948 q^{39} + 2134016 q^{40} + 13427994 q^{41} - 22380960 q^{42} - 17820762 q^{43} + 7496192 q^{44} - 7330788 q^{45} - 13996016 q^{46} + 56044104 q^{47} - 1376256 q^{48} - 4251114 q^{49} - 6588336 q^{50} + 18401250 q^{51} + 38480384 q^{52} + 96842752 q^{53} + 4956336 q^{54} - 7627961 q^{55} + 30679040 q^{56} + 141898680 q^{57} + 47216928 q^{58} - 119136183 q^{59} + 100740864 q^{60} - 90424326 q^{61} + 93099280 q^{62} - 15960420 q^{63} + 33554432 q^{64} - 18029712 q^{65} + 4919376 q^{66} - 295944891 q^{67} + 176760832 q^{68} - 187843215 q^{69} - 258873440 q^{70} - 322953267 q^{71} + 12865536 q^{72} - 255975514 q^{73} - 42542480 q^{74} - 206496864 q^{75} + 130870272 q^{76} - 109661090 q^{77} - 6111168 q^{78} - 889658 q^{79} - 34144256 q^{80} - 692205750 q^{81} - 214847904 q^{82} - 277699042 q^{83} + 358095360 q^{84} + 96595042 q^{85} + 285132192 q^{86} + 1040096232 q^{87} - 119939072 q^{88} + 1363672217 q^{89} + 117292608 q^{90} - 491050280 q^{91} + 223936256 q^{92} + 1530132009 q^{93} - 896705664 q^{94} + 1454033872 q^{95} + 22020096 q^{96} + 1398434043 q^{97} + 68017824 q^{98} - 45987381 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.0000 −0.707107
\(3\) −144.672 −1.03119 −0.515597 0.856831i \(-0.672430\pi\)
−0.515597 + 0.856831i \(0.672430\pi\)
\(4\) 256.000 0.500000
\(5\) −1706.58 −1.22113 −0.610565 0.791966i \(-0.709058\pi\)
−0.610565 + 0.791966i \(0.709058\pi\)
\(6\) 2314.76 0.729164
\(7\) −8664.66 −1.36399 −0.681993 0.731358i \(-0.738887\pi\)
−0.681993 + 0.731358i \(0.738887\pi\)
\(8\) −4096.00 −0.353553
\(9\) 1247.12 0.0633603
\(10\) 27305.3 0.863469
\(11\) 14641.0 0.301511
\(12\) −37036.2 −0.515597
\(13\) 67852.1 0.658898 0.329449 0.944173i \(-0.393137\pi\)
0.329449 + 0.944173i \(0.393137\pi\)
\(14\) 138635. 0.964484
\(15\) 246895. 1.25922
\(16\) 65536.0 0.250000
\(17\) 249646. 0.724943 0.362471 0.931995i \(-0.381933\pi\)
0.362471 + 0.931995i \(0.381933\pi\)
\(18\) −19953.9 −0.0448025
\(19\) −293189. −0.516127 −0.258064 0.966128i \(-0.583084\pi\)
−0.258064 + 0.966128i \(0.583084\pi\)
\(20\) −436885. −0.610565
\(21\) 1.25354e6 1.40653
\(22\) −234256. −0.213201
\(23\) 1.10315e6 0.821979 0.410990 0.911640i \(-0.365183\pi\)
0.410990 + 0.911640i \(0.365183\pi\)
\(24\) 592578. 0.364582
\(25\) 959294. 0.491158
\(26\) −1.08563e6 −0.465911
\(27\) 2.66716e6 0.965857
\(28\) −2.21815e6 −0.681993
\(29\) −5.23603e6 −1.37471 −0.687354 0.726322i \(-0.741228\pi\)
−0.687354 + 0.726322i \(0.741228\pi\)
\(30\) −3.95032e6 −0.890404
\(31\) −8.38378e6 −1.63047 −0.815234 0.579131i \(-0.803392\pi\)
−0.815234 + 0.579131i \(0.803392\pi\)
\(32\) −1.04858e6 −0.176777
\(33\) −2.11815e6 −0.310917
\(34\) −3.99433e6 −0.512612
\(35\) 1.47869e7 1.66561
\(36\) 319263. 0.0316802
\(37\) 7.34600e6 0.644382 0.322191 0.946675i \(-0.395581\pi\)
0.322191 + 0.946675i \(0.395581\pi\)
\(38\) 4.69103e6 0.364957
\(39\) −9.81632e6 −0.679451
\(40\) 6.99016e6 0.431735
\(41\) 1.01256e7 0.559623 0.279811 0.960055i \(-0.409728\pi\)
0.279811 + 0.960055i \(0.409728\pi\)
\(42\) −2.00566e7 −0.994570
\(43\) −2.56347e7 −1.14346 −0.571730 0.820442i \(-0.693727\pi\)
−0.571730 + 0.820442i \(0.693727\pi\)
\(44\) 3.74810e6 0.150756
\(45\) −2.12831e6 −0.0773712
\(46\) −1.76505e7 −0.581227
\(47\) 5.88993e7 1.76064 0.880318 0.474385i \(-0.157329\pi\)
0.880318 + 0.474385i \(0.157329\pi\)
\(48\) −9.48125e6 −0.257798
\(49\) 3.47227e7 0.860460
\(50\) −1.53487e7 −0.347301
\(51\) −3.61168e7 −0.747556
\(52\) 1.73701e7 0.329449
\(53\) 8.68723e7 1.51231 0.756153 0.654395i \(-0.227076\pi\)
0.756153 + 0.654395i \(0.227076\pi\)
\(54\) −4.26746e7 −0.682964
\(55\) −2.49861e7 −0.368185
\(56\) 3.54904e7 0.482242
\(57\) 4.24164e7 0.532227
\(58\) 8.37764e7 0.972066
\(59\) −1.82302e8 −1.95865 −0.979326 0.202289i \(-0.935162\pi\)
−0.979326 + 0.202289i \(0.935162\pi\)
\(60\) 6.32052e7 0.629611
\(61\) 1.22104e8 1.12914 0.564569 0.825386i \(-0.309042\pi\)
0.564569 + 0.825386i \(0.309042\pi\)
\(62\) 1.34141e8 1.15292
\(63\) −1.08059e7 −0.0864227
\(64\) 1.67772e7 0.125000
\(65\) −1.15795e8 −0.804600
\(66\) 3.38904e7 0.219851
\(67\) −6.80532e7 −0.412584 −0.206292 0.978491i \(-0.566140\pi\)
−0.206292 + 0.978491i \(0.566140\pi\)
\(68\) 6.39093e7 0.362471
\(69\) −1.59596e8 −0.847620
\(70\) −2.36591e8 −1.17776
\(71\) −1.67349e8 −0.781555 −0.390777 0.920485i \(-0.627794\pi\)
−0.390777 + 0.920485i \(0.627794\pi\)
\(72\) −5.10821e6 −0.0224013
\(73\) −1.51799e8 −0.625626 −0.312813 0.949815i \(-0.601271\pi\)
−0.312813 + 0.949815i \(0.601271\pi\)
\(74\) −1.17536e8 −0.455647
\(75\) −1.38783e8 −0.506479
\(76\) −7.50564e7 −0.258064
\(77\) −1.26859e8 −0.411258
\(78\) 1.57061e8 0.480444
\(79\) 2.95735e8 0.854241 0.427120 0.904195i \(-0.359528\pi\)
0.427120 + 0.904195i \(0.359528\pi\)
\(80\) −1.11842e8 −0.305282
\(81\) −4.10412e8 −1.05935
\(82\) −1.62010e8 −0.395713
\(83\) 4.61094e8 1.06644 0.533222 0.845975i \(-0.320981\pi\)
0.533222 + 0.845975i \(0.320981\pi\)
\(84\) 3.20906e8 0.703267
\(85\) −4.26040e8 −0.885249
\(86\) 4.10156e8 0.808548
\(87\) 7.57509e8 1.41759
\(88\) −5.99695e7 −0.106600
\(89\) 4.63623e8 0.783267 0.391634 0.920121i \(-0.371910\pi\)
0.391634 + 0.920121i \(0.371910\pi\)
\(90\) 3.40530e7 0.0547097
\(91\) −5.87915e8 −0.898728
\(92\) 2.82407e8 0.410990
\(93\) 1.21290e9 1.68133
\(94\) −9.42388e8 −1.24496
\(95\) 5.00351e8 0.630258
\(96\) 1.51700e8 0.182291
\(97\) 1.06866e8 0.122565 0.0612825 0.998120i \(-0.480481\pi\)
0.0612825 + 0.998120i \(0.480481\pi\)
\(98\) −5.55563e8 −0.608437
\(99\) 1.82591e7 0.0191039
\(100\) 2.45579e8 0.245579
\(101\) 1.38561e9 1.32494 0.662470 0.749088i \(-0.269508\pi\)
0.662470 + 0.749088i \(0.269508\pi\)
\(102\) 5.77869e8 0.528602
\(103\) −1.45242e9 −1.27152 −0.635760 0.771886i \(-0.719313\pi\)
−0.635760 + 0.771886i \(0.719313\pi\)
\(104\) −2.77922e8 −0.232955
\(105\) −2.13926e9 −1.71756
\(106\) −1.38996e9 −1.06936
\(107\) 1.44377e9 1.06481 0.532405 0.846490i \(-0.321288\pi\)
0.532405 + 0.846490i \(0.321288\pi\)
\(108\) 6.82794e8 0.482928
\(109\) 2.58675e9 1.75524 0.877618 0.479361i \(-0.159132\pi\)
0.877618 + 0.479361i \(0.159132\pi\)
\(110\) 3.99777e8 0.260346
\(111\) −1.06276e9 −0.664482
\(112\) −5.67847e8 −0.340997
\(113\) 1.13601e9 0.655433 0.327717 0.944776i \(-0.393721\pi\)
0.327717 + 0.944776i \(0.393721\pi\)
\(114\) −6.78662e8 −0.376341
\(115\) −1.88262e9 −1.00374
\(116\) −1.34042e9 −0.687354
\(117\) 8.46198e7 0.0417480
\(118\) 2.91683e9 1.38498
\(119\) −2.16309e9 −0.988812
\(120\) −1.01128e9 −0.445202
\(121\) 2.14359e8 0.0909091
\(122\) −1.95367e9 −0.798422
\(123\) −1.46490e9 −0.577079
\(124\) −2.14625e9 −0.815234
\(125\) 1.69605e9 0.621362
\(126\) 1.72894e8 0.0611101
\(127\) −3.27848e9 −1.11829 −0.559147 0.829068i \(-0.688871\pi\)
−0.559147 + 0.829068i \(0.688871\pi\)
\(128\) −2.68435e8 −0.0883883
\(129\) 3.70864e9 1.17913
\(130\) 1.85272e9 0.568938
\(131\) 1.81056e9 0.537146 0.268573 0.963259i \(-0.413448\pi\)
0.268573 + 0.963259i \(0.413448\pi\)
\(132\) −5.42246e8 −0.155458
\(133\) 2.54038e9 0.703991
\(134\) 1.08885e9 0.291741
\(135\) −4.55173e9 −1.17944
\(136\) −1.02255e9 −0.256306
\(137\) −3.19317e9 −0.774425 −0.387213 0.921990i \(-0.626562\pi\)
−0.387213 + 0.921990i \(0.626562\pi\)
\(138\) 2.55354e9 0.599358
\(139\) −8.30571e8 −0.188717 −0.0943583 0.995538i \(-0.530080\pi\)
−0.0943583 + 0.995538i \(0.530080\pi\)
\(140\) 3.78546e9 0.832803
\(141\) −8.52110e9 −1.81556
\(142\) 2.67758e9 0.552643
\(143\) 9.93422e8 0.198665
\(144\) 8.17314e7 0.0158401
\(145\) 8.93570e9 1.67870
\(146\) 2.42878e9 0.442384
\(147\) −5.02341e9 −0.887301
\(148\) 1.88058e9 0.322191
\(149\) 8.83876e9 1.46911 0.734553 0.678551i \(-0.237392\pi\)
0.734553 + 0.678551i \(0.237392\pi\)
\(150\) 2.22053e9 0.358135
\(151\) −6.05461e9 −0.947742 −0.473871 0.880594i \(-0.657144\pi\)
−0.473871 + 0.880594i \(0.657144\pi\)
\(152\) 1.20090e9 0.182479
\(153\) 3.11338e8 0.0459326
\(154\) 2.02975e9 0.290803
\(155\) 1.43076e10 1.99101
\(156\) −2.51298e9 −0.339726
\(157\) −3.21421e9 −0.422208 −0.211104 0.977464i \(-0.567706\pi\)
−0.211104 + 0.977464i \(0.567706\pi\)
\(158\) −4.73176e9 −0.604040
\(159\) −1.25680e10 −1.55948
\(160\) 1.78948e9 0.215867
\(161\) −9.55845e9 −1.12117
\(162\) 6.56660e9 0.749071
\(163\) 3.35516e9 0.372279 0.186140 0.982523i \(-0.440402\pi\)
0.186140 + 0.982523i \(0.440402\pi\)
\(164\) 2.59217e9 0.279811
\(165\) 3.61479e9 0.379670
\(166\) −7.37750e9 −0.754090
\(167\) 1.13205e10 1.12627 0.563136 0.826364i \(-0.309595\pi\)
0.563136 + 0.826364i \(0.309595\pi\)
\(168\) −5.13449e9 −0.497285
\(169\) −6.00060e9 −0.565854
\(170\) 6.81665e9 0.625966
\(171\) −3.65643e8 −0.0327020
\(172\) −6.56249e9 −0.571730
\(173\) 1.24081e10 1.05317 0.526586 0.850122i \(-0.323472\pi\)
0.526586 + 0.850122i \(0.323472\pi\)
\(174\) −1.21201e10 −1.00239
\(175\) −8.31195e9 −0.669934
\(176\) 9.59513e8 0.0753778
\(177\) 2.63741e10 2.01975
\(178\) −7.41797e9 −0.553854
\(179\) −1.78548e10 −1.29992 −0.649960 0.759968i \(-0.725215\pi\)
−0.649960 + 0.759968i \(0.725215\pi\)
\(180\) −5.44848e8 −0.0386856
\(181\) 2.69794e10 1.86844 0.934220 0.356698i \(-0.116098\pi\)
0.934220 + 0.356698i \(0.116098\pi\)
\(182\) 9.40664e9 0.635496
\(183\) −1.76652e10 −1.16436
\(184\) −4.51852e9 −0.290614
\(185\) −1.25365e10 −0.786874
\(186\) −1.94064e10 −1.18888
\(187\) 3.65506e9 0.218578
\(188\) 1.50782e10 0.880318
\(189\) −2.31101e10 −1.31742
\(190\) −8.00562e9 −0.445660
\(191\) −1.88704e10 −1.02596 −0.512980 0.858400i \(-0.671459\pi\)
−0.512980 + 0.858400i \(0.671459\pi\)
\(192\) −2.42720e9 −0.128899
\(193\) −1.63769e10 −0.849618 −0.424809 0.905283i \(-0.639659\pi\)
−0.424809 + 0.905283i \(0.639659\pi\)
\(194\) −1.70985e9 −0.0866665
\(195\) 1.67524e10 0.829698
\(196\) 8.88900e9 0.430230
\(197\) −2.41377e10 −1.14182 −0.570909 0.821013i \(-0.693409\pi\)
−0.570909 + 0.821013i \(0.693409\pi\)
\(198\) −2.92146e8 −0.0135085
\(199\) −6.98474e7 −0.00315727 −0.00157863 0.999999i \(-0.500502\pi\)
−0.00157863 + 0.999999i \(0.500502\pi\)
\(200\) −3.92927e9 −0.173651
\(201\) 9.84543e9 0.425454
\(202\) −2.21698e10 −0.936874
\(203\) 4.53684e10 1.87508
\(204\) −9.24591e9 −0.373778
\(205\) −1.72802e10 −0.683372
\(206\) 2.32387e10 0.899101
\(207\) 1.37577e9 0.0520809
\(208\) 4.44675e9 0.164724
\(209\) −4.29258e9 −0.155618
\(210\) 3.42282e10 1.21450
\(211\) 3.34436e10 1.16156 0.580780 0.814061i \(-0.302748\pi\)
0.580780 + 0.814061i \(0.302748\pi\)
\(212\) 2.22393e10 0.756153
\(213\) 2.42107e10 0.805935
\(214\) −2.31004e10 −0.752935
\(215\) 4.37478e10 1.39631
\(216\) −1.09247e10 −0.341482
\(217\) 7.26426e10 2.22394
\(218\) −4.13880e10 −1.24114
\(219\) 2.19611e10 0.645141
\(220\) −6.39643e9 −0.184092
\(221\) 1.69390e10 0.477663
\(222\) 1.70042e10 0.469860
\(223\) −1.74786e10 −0.473299 −0.236650 0.971595i \(-0.576049\pi\)
−0.236650 + 0.971595i \(0.576049\pi\)
\(224\) 9.08555e9 0.241121
\(225\) 1.19636e9 0.0311200
\(226\) −1.81761e10 −0.463461
\(227\) −1.99552e10 −0.498816 −0.249408 0.968398i \(-0.580236\pi\)
−0.249408 + 0.968398i \(0.580236\pi\)
\(228\) 1.08586e10 0.266114
\(229\) −7.45741e10 −1.79196 −0.895980 0.444095i \(-0.853525\pi\)
−0.895980 + 0.444095i \(0.853525\pi\)
\(230\) 3.01220e10 0.709754
\(231\) 1.83530e10 0.424086
\(232\) 2.14468e10 0.486033
\(233\) −4.84331e10 −1.07657 −0.538283 0.842764i \(-0.680927\pi\)
−0.538283 + 0.842764i \(0.680927\pi\)
\(234\) −1.35392e9 −0.0295203
\(235\) −1.00516e11 −2.14996
\(236\) −4.66693e10 −0.979326
\(237\) −4.27847e10 −0.880888
\(238\) 3.46095e10 0.699196
\(239\) −2.76719e10 −0.548591 −0.274295 0.961645i \(-0.588445\pi\)
−0.274295 + 0.961645i \(0.588445\pi\)
\(240\) 1.61805e10 0.314805
\(241\) 5.23953e10 1.00050 0.500248 0.865882i \(-0.333242\pi\)
0.500248 + 0.865882i \(0.333242\pi\)
\(242\) −3.42974e9 −0.0642824
\(243\) 6.87757e9 0.126534
\(244\) 3.12587e10 0.564569
\(245\) −5.92571e10 −1.05073
\(246\) 2.34384e10 0.408057
\(247\) −1.98935e10 −0.340075
\(248\) 3.43400e10 0.576458
\(249\) −6.67076e10 −1.09971
\(250\) −2.71369e10 −0.439369
\(251\) 5.45608e10 0.867659 0.433829 0.900995i \(-0.357162\pi\)
0.433829 + 0.900995i \(0.357162\pi\)
\(252\) −2.76631e9 −0.0432113
\(253\) 1.61513e10 0.247836
\(254\) 5.24557e10 0.790754
\(255\) 6.16363e10 0.912863
\(256\) 4.29497e9 0.0625000
\(257\) 1.72020e10 0.245969 0.122985 0.992409i \(-0.460753\pi\)
0.122985 + 0.992409i \(0.460753\pi\)
\(258\) −5.93383e10 −0.833770
\(259\) −6.36506e10 −0.878928
\(260\) −2.96435e10 −0.402300
\(261\) −6.52996e9 −0.0871020
\(262\) −2.89690e10 −0.379819
\(263\) −2.32552e10 −0.299722 −0.149861 0.988707i \(-0.547883\pi\)
−0.149861 + 0.988707i \(0.547883\pi\)
\(264\) 8.67594e9 0.109926
\(265\) −1.48255e11 −1.84672
\(266\) −4.06461e10 −0.497797
\(267\) −6.70735e10 −0.807700
\(268\) −1.74216e10 −0.206292
\(269\) 2.82157e10 0.328554 0.164277 0.986414i \(-0.447471\pi\)
0.164277 + 0.986414i \(0.447471\pi\)
\(270\) 7.28277e10 0.833988
\(271\) 1.37207e11 1.54530 0.772651 0.634831i \(-0.218930\pi\)
0.772651 + 0.634831i \(0.218930\pi\)
\(272\) 1.63608e10 0.181236
\(273\) 8.50551e10 0.926762
\(274\) 5.10907e10 0.547601
\(275\) 1.40450e10 0.148090
\(276\) −4.08566e10 −0.423810
\(277\) 1.85402e11 1.89215 0.946074 0.323949i \(-0.105011\pi\)
0.946074 + 0.323949i \(0.105011\pi\)
\(278\) 1.32891e10 0.133443
\(279\) −1.04556e10 −0.103307
\(280\) −6.05673e10 −0.588880
\(281\) −5.20765e10 −0.498268 −0.249134 0.968469i \(-0.580146\pi\)
−0.249134 + 0.968469i \(0.580146\pi\)
\(282\) 1.36338e11 1.28379
\(283\) 1.03796e11 0.961925 0.480963 0.876741i \(-0.340287\pi\)
0.480963 + 0.876741i \(0.340287\pi\)
\(284\) −4.28412e10 −0.390777
\(285\) −7.23870e10 −0.649918
\(286\) −1.58948e10 −0.140477
\(287\) −8.77352e10 −0.763318
\(288\) −1.30770e9 −0.0112006
\(289\) −5.62650e10 −0.474458
\(290\) −1.42971e11 −1.18702
\(291\) −1.54606e10 −0.126388
\(292\) −3.88604e10 −0.312813
\(293\) −8.51536e10 −0.674992 −0.337496 0.941327i \(-0.609580\pi\)
−0.337496 + 0.941327i \(0.609580\pi\)
\(294\) 8.03746e10 0.627417
\(295\) 3.11113e11 2.39177
\(296\) −3.00892e10 −0.227823
\(297\) 3.90499e10 0.291217
\(298\) −1.41420e11 −1.03881
\(299\) 7.48513e10 0.541600
\(300\) −3.55285e10 −0.253240
\(301\) 2.22116e11 1.55966
\(302\) 9.68738e10 0.670155
\(303\) −2.00460e11 −1.36627
\(304\) −1.92144e10 −0.129032
\(305\) −2.08381e11 −1.37882
\(306\) −4.98141e9 −0.0324793
\(307\) 2.79447e11 1.79547 0.897734 0.440539i \(-0.145213\pi\)
0.897734 + 0.440539i \(0.145213\pi\)
\(308\) −3.24760e10 −0.205629
\(309\) 2.10125e11 1.31118
\(310\) −2.28922e11 −1.40786
\(311\) 2.40111e11 1.45543 0.727714 0.685881i \(-0.240583\pi\)
0.727714 + 0.685881i \(0.240583\pi\)
\(312\) 4.02077e10 0.240222
\(313\) 9.68635e10 0.570441 0.285220 0.958462i \(-0.407933\pi\)
0.285220 + 0.958462i \(0.407933\pi\)
\(314\) 5.14274e10 0.298546
\(315\) 1.84411e10 0.105533
\(316\) 7.57081e10 0.427120
\(317\) −1.70124e11 −0.946237 −0.473118 0.880999i \(-0.656872\pi\)
−0.473118 + 0.880999i \(0.656872\pi\)
\(318\) 2.01088e11 1.10272
\(319\) −7.66606e10 −0.414490
\(320\) −2.86317e10 −0.152641
\(321\) −2.08874e11 −1.09803
\(322\) 1.52935e11 0.792786
\(323\) −7.31934e10 −0.374163
\(324\) −1.05066e11 −0.529673
\(325\) 6.50900e10 0.323623
\(326\) −5.36825e10 −0.263241
\(327\) −3.74232e11 −1.80999
\(328\) −4.14746e10 −0.197857
\(329\) −5.10342e11 −2.40148
\(330\) −5.78367e10 −0.268467
\(331\) 2.45318e10 0.112332 0.0561661 0.998421i \(-0.482112\pi\)
0.0561661 + 0.998421i \(0.482112\pi\)
\(332\) 1.18040e11 0.533222
\(333\) 9.16136e9 0.0408282
\(334\) −1.81129e11 −0.796394
\(335\) 1.16138e11 0.503818
\(336\) 8.21518e10 0.351634
\(337\) 9.64453e10 0.407330 0.203665 0.979041i \(-0.434715\pi\)
0.203665 + 0.979041i \(0.434715\pi\)
\(338\) 9.60096e10 0.400119
\(339\) −1.64349e11 −0.675879
\(340\) −1.09066e11 −0.442625
\(341\) −1.22747e11 −0.491605
\(342\) 5.85028e9 0.0231238
\(343\) 4.87901e10 0.190330
\(344\) 1.05000e11 0.404274
\(345\) 2.72364e11 1.03505
\(346\) −1.98530e11 −0.744704
\(347\) −1.02569e11 −0.379783 −0.189891 0.981805i \(-0.560814\pi\)
−0.189891 + 0.981805i \(0.560814\pi\)
\(348\) 1.93922e11 0.708796
\(349\) −3.59960e11 −1.29879 −0.649397 0.760450i \(-0.724979\pi\)
−0.649397 + 0.760450i \(0.724979\pi\)
\(350\) 1.32991e11 0.473715
\(351\) 1.80973e11 0.636401
\(352\) −1.53522e10 −0.0533002
\(353\) −6.23410e10 −0.213692 −0.106846 0.994276i \(-0.534075\pi\)
−0.106846 + 0.994276i \(0.534075\pi\)
\(354\) −4.21985e11 −1.42818
\(355\) 2.85594e11 0.954380
\(356\) 1.18687e11 0.391634
\(357\) 3.12940e11 1.01966
\(358\) 2.85677e11 0.919183
\(359\) −1.12478e11 −0.357391 −0.178696 0.983904i \(-0.557188\pi\)
−0.178696 + 0.983904i \(0.557188\pi\)
\(360\) 8.71758e9 0.0273549
\(361\) −2.36728e11 −0.733613
\(362\) −4.31671e11 −1.32119
\(363\) −3.10118e10 −0.0937449
\(364\) −1.50506e11 −0.449364
\(365\) 2.59056e11 0.763970
\(366\) 2.82642e11 0.823327
\(367\) 1.51938e11 0.437189 0.218594 0.975816i \(-0.429853\pi\)
0.218594 + 0.975816i \(0.429853\pi\)
\(368\) 7.22963e10 0.205495
\(369\) 1.26279e10 0.0354579
\(370\) 2.00585e11 0.556404
\(371\) −7.52719e11 −2.06277
\(372\) 3.10503e11 0.840664
\(373\) 1.79048e11 0.478938 0.239469 0.970904i \(-0.423027\pi\)
0.239469 + 0.970904i \(0.423027\pi\)
\(374\) −5.84810e10 −0.154558
\(375\) −2.45372e11 −0.640744
\(376\) −2.41251e11 −0.622479
\(377\) −3.55275e11 −0.905792
\(378\) 3.69761e11 0.931554
\(379\) 2.31277e11 0.575780 0.287890 0.957663i \(-0.407046\pi\)
0.287890 + 0.957663i \(0.407046\pi\)
\(380\) 1.28090e11 0.315129
\(381\) 4.74306e11 1.15318
\(382\) 3.01926e11 0.725463
\(383\) 3.53920e11 0.840448 0.420224 0.907420i \(-0.361951\pi\)
0.420224 + 0.907420i \(0.361951\pi\)
\(384\) 3.88352e10 0.0911455
\(385\) 2.16496e11 0.502199
\(386\) 2.62030e11 0.600771
\(387\) −3.19696e10 −0.0724500
\(388\) 2.73577e10 0.0612825
\(389\) 4.20470e11 0.931027 0.465513 0.885041i \(-0.345870\pi\)
0.465513 + 0.885041i \(0.345870\pi\)
\(390\) −2.68038e11 −0.586685
\(391\) 2.75398e11 0.595888
\(392\) −1.42224e11 −0.304219
\(393\) −2.61938e11 −0.553901
\(394\) 3.86203e11 0.807388
\(395\) −5.04695e11 −1.04314
\(396\) 4.67433e9 0.00955193
\(397\) −3.43330e11 −0.693672 −0.346836 0.937926i \(-0.612744\pi\)
−0.346836 + 0.937926i \(0.612744\pi\)
\(398\) 1.11756e9 0.00223253
\(399\) −3.67524e11 −0.725951
\(400\) 6.28683e10 0.122790
\(401\) 5.15897e11 0.996354 0.498177 0.867075i \(-0.334003\pi\)
0.498177 + 0.867075i \(0.334003\pi\)
\(402\) −1.57527e11 −0.300841
\(403\) −5.68857e11 −1.07431
\(404\) 3.54717e11 0.662470
\(405\) 7.00402e11 1.29360
\(406\) −7.25894e11 −1.32589
\(407\) 1.07553e11 0.194288
\(408\) 1.47935e11 0.264301
\(409\) −4.68357e11 −0.827604 −0.413802 0.910367i \(-0.635799\pi\)
−0.413802 + 0.910367i \(0.635799\pi\)
\(410\) 2.76484e11 0.483217
\(411\) 4.61964e11 0.798582
\(412\) −3.71819e11 −0.635760
\(413\) 1.57958e12 2.67158
\(414\) −2.20123e10 −0.0368268
\(415\) −7.86894e11 −1.30227
\(416\) −7.11480e10 −0.116478
\(417\) 1.20161e11 0.194603
\(418\) 6.86813e10 0.110039
\(419\) −1.15054e12 −1.82364 −0.911820 0.410590i \(-0.865323\pi\)
−0.911820 + 0.410590i \(0.865323\pi\)
\(420\) −5.47651e11 −0.858781
\(421\) −2.49749e11 −0.387467 −0.193734 0.981054i \(-0.562060\pi\)
−0.193734 + 0.981054i \(0.562060\pi\)
\(422\) −5.35097e11 −0.821347
\(423\) 7.34545e10 0.111554
\(424\) −3.55829e11 −0.534681
\(425\) 2.39483e11 0.356062
\(426\) −3.87372e11 −0.569882
\(427\) −1.05799e12 −1.54013
\(428\) 3.69606e11 0.532405
\(429\) −1.43721e11 −0.204862
\(430\) −6.99964e11 −0.987342
\(431\) 2.80621e11 0.391717 0.195858 0.980632i \(-0.437251\pi\)
0.195858 + 0.980632i \(0.437251\pi\)
\(432\) 1.74795e11 0.241464
\(433\) 1.07421e12 1.46857 0.734285 0.678841i \(-0.237518\pi\)
0.734285 + 0.678841i \(0.237518\pi\)
\(434\) −1.16228e12 −1.57256
\(435\) −1.29275e12 −1.73106
\(436\) 6.62208e11 0.877618
\(437\) −3.23433e11 −0.424246
\(438\) −3.51377e11 −0.456184
\(439\) 9.45531e11 1.21503 0.607513 0.794310i \(-0.292167\pi\)
0.607513 + 0.794310i \(0.292167\pi\)
\(440\) 1.02343e11 0.130173
\(441\) 4.33034e10 0.0545191
\(442\) −2.71023e11 −0.337759
\(443\) 1.41348e12 1.74370 0.871852 0.489769i \(-0.162919\pi\)
0.871852 + 0.489769i \(0.162919\pi\)
\(444\) −2.72068e11 −0.332241
\(445\) −7.91210e11 −0.956471
\(446\) 2.79658e11 0.334673
\(447\) −1.27873e12 −1.51493
\(448\) −1.45369e11 −0.170498
\(449\) 3.24374e11 0.376650 0.188325 0.982107i \(-0.439694\pi\)
0.188325 + 0.982107i \(0.439694\pi\)
\(450\) −1.91417e10 −0.0220051
\(451\) 1.48250e11 0.168733
\(452\) 2.90818e11 0.327717
\(453\) 8.75936e11 0.977305
\(454\) 3.19284e11 0.352716
\(455\) 1.00332e12 1.09746
\(456\) −1.73738e11 −0.188171
\(457\) −1.44780e11 −0.155269 −0.0776344 0.996982i \(-0.524737\pi\)
−0.0776344 + 0.996982i \(0.524737\pi\)
\(458\) 1.19319e12 1.26711
\(459\) 6.65846e11 0.700191
\(460\) −4.81951e11 −0.501872
\(461\) 2.94094e11 0.303271 0.151636 0.988436i \(-0.451546\pi\)
0.151636 + 0.988436i \(0.451546\pi\)
\(462\) −2.93649e11 −0.299874
\(463\) 8.78478e11 0.888416 0.444208 0.895924i \(-0.353485\pi\)
0.444208 + 0.895924i \(0.353485\pi\)
\(464\) −3.43148e11 −0.343677
\(465\) −2.06992e12 −2.05312
\(466\) 7.74930e11 0.761247
\(467\) 6.31625e11 0.614516 0.307258 0.951626i \(-0.400589\pi\)
0.307258 + 0.951626i \(0.400589\pi\)
\(468\) 2.16627e10 0.0208740
\(469\) 5.89658e11 0.562759
\(470\) 1.60826e12 1.52025
\(471\) 4.65008e11 0.435378
\(472\) 7.46709e11 0.692488
\(473\) −3.75318e11 −0.344766
\(474\) 6.84555e11 0.622882
\(475\) −2.81255e11 −0.253500
\(476\) −5.53752e11 −0.494406
\(477\) 1.08340e11 0.0958203
\(478\) 4.42750e11 0.387912
\(479\) −1.70132e12 −1.47664 −0.738321 0.674449i \(-0.764381\pi\)
−0.738321 + 0.674449i \(0.764381\pi\)
\(480\) −2.58888e11 −0.222601
\(481\) 4.98441e11 0.424581
\(482\) −8.38324e11 −0.707458
\(483\) 1.38284e12 1.15614
\(484\) 5.48759e10 0.0454545
\(485\) −1.82375e11 −0.149668
\(486\) −1.10041e11 −0.0894729
\(487\) 2.17815e11 0.175472 0.0877358 0.996144i \(-0.472037\pi\)
0.0877358 + 0.996144i \(0.472037\pi\)
\(488\) −5.00140e11 −0.399211
\(489\) −4.85399e11 −0.383892
\(490\) 9.48113e11 0.742981
\(491\) 2.45219e11 0.190409 0.0952045 0.995458i \(-0.469649\pi\)
0.0952045 + 0.995458i \(0.469649\pi\)
\(492\) −3.75015e11 −0.288540
\(493\) −1.30715e12 −0.996585
\(494\) 3.18296e11 0.240469
\(495\) −3.11606e10 −0.0233283
\(496\) −5.49440e11 −0.407617
\(497\) 1.45002e12 1.06603
\(498\) 1.06732e12 0.777612
\(499\) −2.14365e12 −1.54775 −0.773876 0.633337i \(-0.781685\pi\)
−0.773876 + 0.633337i \(0.781685\pi\)
\(500\) 4.34190e11 0.310681
\(501\) −1.63777e12 −1.16140
\(502\) −8.72973e11 −0.613528
\(503\) 7.47725e11 0.520818 0.260409 0.965498i \(-0.416143\pi\)
0.260409 + 0.965498i \(0.416143\pi\)
\(504\) 4.42609e10 0.0305550
\(505\) −2.36466e12 −1.61792
\(506\) −2.58420e11 −0.175247
\(507\) 8.68121e11 0.583505
\(508\) −8.39292e11 −0.559147
\(509\) 3.60539e11 0.238079 0.119040 0.992889i \(-0.462018\pi\)
0.119040 + 0.992889i \(0.462018\pi\)
\(510\) −9.86181e11 −0.645492
\(511\) 1.31528e12 0.853345
\(512\) −6.87195e10 −0.0441942
\(513\) −7.81984e11 −0.498505
\(514\) −2.75232e11 −0.173926
\(515\) 2.47867e12 1.55269
\(516\) 9.49412e11 0.589564
\(517\) 8.62344e11 0.530852
\(518\) 1.01841e12 0.621496
\(519\) −1.79511e12 −1.08602
\(520\) 4.74296e11 0.284469
\(521\) −1.98989e12 −1.18320 −0.591602 0.806230i \(-0.701504\pi\)
−0.591602 + 0.806230i \(0.701504\pi\)
\(522\) 1.04479e11 0.0615904
\(523\) 1.26127e12 0.737140 0.368570 0.929600i \(-0.379847\pi\)
0.368570 + 0.929600i \(0.379847\pi\)
\(524\) 4.63503e11 0.268573
\(525\) 1.20251e12 0.690831
\(526\) 3.72083e11 0.211936
\(527\) −2.09297e12 −1.18200
\(528\) −1.38815e11 −0.0777291
\(529\) −5.84204e11 −0.324350
\(530\) 2.37207e12 1.30583
\(531\) −2.27353e11 −0.124101
\(532\) 6.50338e11 0.351995
\(533\) 6.87046e11 0.368734
\(534\) 1.07318e12 0.571130
\(535\) −2.46392e12 −1.30027
\(536\) 2.78746e11 0.145870
\(537\) 2.58310e12 1.34047
\(538\) −4.51452e11 −0.232322
\(539\) 5.08375e11 0.259439
\(540\) −1.16524e12 −0.589718
\(541\) 3.48950e12 1.75136 0.875679 0.482893i \(-0.160414\pi\)
0.875679 + 0.482893i \(0.160414\pi\)
\(542\) −2.19531e12 −1.09269
\(543\) −3.90318e12 −1.92672
\(544\) −2.61772e11 −0.128153
\(545\) −4.41450e12 −2.14337
\(546\) −1.36088e12 −0.655320
\(547\) −2.03037e12 −0.969687 −0.484844 0.874601i \(-0.661123\pi\)
−0.484844 + 0.874601i \(0.661123\pi\)
\(548\) −8.17452e11 −0.387213
\(549\) 1.52279e11 0.0715426
\(550\) −2.24720e11 −0.104715
\(551\) 1.53515e12 0.709525
\(552\) 6.53705e11 0.299679
\(553\) −2.56244e12 −1.16517
\(554\) −2.96643e12 −1.33795
\(555\) 1.81369e12 0.811419
\(556\) −2.12626e11 −0.0943583
\(557\) 2.94692e12 1.29724 0.648620 0.761112i \(-0.275346\pi\)
0.648620 + 0.761112i \(0.275346\pi\)
\(558\) 1.67290e11 0.0730491
\(559\) −1.73937e12 −0.753423
\(560\) 9.69077e11 0.416401
\(561\) −5.28787e11 −0.225397
\(562\) 8.33224e11 0.352329
\(563\) −7.94805e11 −0.333405 −0.166703 0.986007i \(-0.553312\pi\)
−0.166703 + 0.986007i \(0.553312\pi\)
\(564\) −2.18140e12 −0.907778
\(565\) −1.93869e12 −0.800369
\(566\) −1.66073e12 −0.680184
\(567\) 3.55608e12 1.44493
\(568\) 6.85460e11 0.276321
\(569\) 1.51857e12 0.607338 0.303669 0.952778i \(-0.401788\pi\)
0.303669 + 0.952778i \(0.401788\pi\)
\(570\) 1.15819e12 0.459562
\(571\) −2.97779e11 −0.117228 −0.0586140 0.998281i \(-0.518668\pi\)
−0.0586140 + 0.998281i \(0.518668\pi\)
\(572\) 2.54316e11 0.0993325
\(573\) 2.73002e12 1.05796
\(574\) 1.40376e12 0.539747
\(575\) 1.05825e12 0.403722
\(576\) 2.09232e10 0.00792004
\(577\) 1.81913e12 0.683241 0.341620 0.939838i \(-0.389024\pi\)
0.341620 + 0.939838i \(0.389024\pi\)
\(578\) 9.00239e11 0.335492
\(579\) 2.36929e12 0.876121
\(580\) 2.28754e12 0.839349
\(581\) −3.99522e12 −1.45462
\(582\) 2.47369e11 0.0893700
\(583\) 1.27190e12 0.455978
\(584\) 6.21767e11 0.221192
\(585\) −1.44410e11 −0.0509797
\(586\) 1.36246e12 0.477292
\(587\) 2.78354e12 0.967666 0.483833 0.875160i \(-0.339244\pi\)
0.483833 + 0.875160i \(0.339244\pi\)
\(588\) −1.28599e12 −0.443651
\(589\) 2.45803e12 0.841529
\(590\) −4.97781e12 −1.69124
\(591\) 3.49205e12 1.17744
\(592\) 4.81427e11 0.161095
\(593\) −5.56438e11 −0.184787 −0.0923933 0.995723i \(-0.529452\pi\)
−0.0923933 + 0.995723i \(0.529452\pi\)
\(594\) −6.24799e11 −0.205921
\(595\) 3.69149e12 1.20747
\(596\) 2.26272e12 0.734553
\(597\) 1.01050e10 0.00325576
\(598\) −1.19762e12 −0.382969
\(599\) −5.73449e12 −1.82001 −0.910006 0.414595i \(-0.863923\pi\)
−0.910006 + 0.414595i \(0.863923\pi\)
\(600\) 5.68457e11 0.179068
\(601\) 5.50049e11 0.171975 0.0859877 0.996296i \(-0.472595\pi\)
0.0859877 + 0.996296i \(0.472595\pi\)
\(602\) −3.55386e12 −1.10285
\(603\) −8.48707e10 −0.0261415
\(604\) −1.54998e12 −0.473871
\(605\) −3.65821e11 −0.111012
\(606\) 3.20736e12 0.966099
\(607\) 3.73380e12 1.11635 0.558177 0.829722i \(-0.311501\pi\)
0.558177 + 0.829722i \(0.311501\pi\)
\(608\) 3.07431e11 0.0912393
\(609\) −6.56355e12 −1.93358
\(610\) 3.33410e12 0.974976
\(611\) 3.99644e12 1.16008
\(612\) 7.97026e10 0.0229663
\(613\) 3.83812e12 1.09786 0.548929 0.835869i \(-0.315036\pi\)
0.548929 + 0.835869i \(0.315036\pi\)
\(614\) −4.47116e12 −1.26959
\(615\) 2.49997e12 0.704689
\(616\) 5.19615e11 0.145401
\(617\) −2.53329e12 −0.703723 −0.351861 0.936052i \(-0.614451\pi\)
−0.351861 + 0.936052i \(0.614451\pi\)
\(618\) −3.36199e12 −0.927147
\(619\) 3.23255e12 0.884988 0.442494 0.896772i \(-0.354094\pi\)
0.442494 + 0.896772i \(0.354094\pi\)
\(620\) 3.66275e12 0.995507
\(621\) 2.94229e12 0.793914
\(622\) −3.84178e12 −1.02914
\(623\) −4.01713e12 −1.06837
\(624\) −6.43323e11 −0.169863
\(625\) −4.76807e12 −1.24992
\(626\) −1.54982e12 −0.403363
\(627\) 6.21019e11 0.160473
\(628\) −8.22838e11 −0.211104
\(629\) 1.83390e12 0.467140
\(630\) −2.95058e11 −0.0746233
\(631\) 3.95011e11 0.0991921 0.0495961 0.998769i \(-0.484207\pi\)
0.0495961 + 0.998769i \(0.484207\pi\)
\(632\) −1.21133e12 −0.302020
\(633\) −4.83836e12 −1.19779
\(634\) 2.72199e12 0.669090
\(635\) 5.59500e12 1.36558
\(636\) −3.21741e12 −0.779740
\(637\) 2.35600e12 0.566955
\(638\) 1.22657e12 0.293089
\(639\) −2.08704e11 −0.0495196
\(640\) 4.58107e11 0.107934
\(641\) −3.96414e12 −0.927444 −0.463722 0.885981i \(-0.653486\pi\)
−0.463722 + 0.885981i \(0.653486\pi\)
\(642\) 3.34199e12 0.776422
\(643\) −7.33426e12 −1.69203 −0.846013 0.533163i \(-0.821003\pi\)
−0.846013 + 0.533163i \(0.821003\pi\)
\(644\) −2.44696e12 −0.560585
\(645\) −6.32910e12 −1.43987
\(646\) 1.17109e12 0.264573
\(647\) −1.01763e12 −0.228308 −0.114154 0.993463i \(-0.536416\pi\)
−0.114154 + 0.993463i \(0.536416\pi\)
\(648\) 1.68105e12 0.374535
\(649\) −2.66908e12 −0.590556
\(650\) −1.04144e12 −0.228836
\(651\) −1.05094e13 −2.29331
\(652\) 8.58921e11 0.186140
\(653\) 6.78338e12 1.45995 0.729973 0.683476i \(-0.239533\pi\)
0.729973 + 0.683476i \(0.239533\pi\)
\(654\) 5.98771e12 1.27985
\(655\) −3.08987e12 −0.655925
\(656\) 6.63594e11 0.139906
\(657\) −1.89311e11 −0.0396399
\(658\) 8.16547e12 1.69811
\(659\) 1.83983e12 0.380008 0.190004 0.981783i \(-0.439150\pi\)
0.190004 + 0.981783i \(0.439150\pi\)
\(660\) 9.25387e11 0.189835
\(661\) −3.08220e12 −0.627992 −0.313996 0.949424i \(-0.601668\pi\)
−0.313996 + 0.949424i \(0.601668\pi\)
\(662\) −3.92509e11 −0.0794308
\(663\) −2.45060e12 −0.492563
\(664\) −1.88864e12 −0.377045
\(665\) −4.33537e12 −0.859664
\(666\) −1.46582e11 −0.0288699
\(667\) −5.77614e12 −1.12998
\(668\) 2.89806e12 0.563136
\(669\) 2.52868e12 0.488063
\(670\) −1.85821e12 −0.356253
\(671\) 1.78773e12 0.340448
\(672\) −1.31443e12 −0.248643
\(673\) −7.07648e12 −1.32969 −0.664844 0.746983i \(-0.731502\pi\)
−0.664844 + 0.746983i \(0.731502\pi\)
\(674\) −1.54313e12 −0.288026
\(675\) 2.55859e12 0.474389
\(676\) −1.53615e12 −0.282927
\(677\) 1.18522e11 0.0216846 0.0108423 0.999941i \(-0.496549\pi\)
0.0108423 + 0.999941i \(0.496549\pi\)
\(678\) 2.62959e12 0.477918
\(679\) −9.25956e11 −0.167177
\(680\) 1.74506e12 0.312983
\(681\) 2.88697e12 0.514376
\(682\) 1.96395e12 0.347617
\(683\) −4.08882e12 −0.718961 −0.359480 0.933153i \(-0.617046\pi\)
−0.359480 + 0.933153i \(0.617046\pi\)
\(684\) −9.36045e10 −0.0163510
\(685\) 5.44940e12 0.945674
\(686\) −7.80642e11 −0.134584
\(687\) 1.07888e13 1.84786
\(688\) −1.68000e12 −0.285865
\(689\) 5.89446e12 0.996455
\(690\) −4.35782e12 −0.731894
\(691\) 2.48976e12 0.415438 0.207719 0.978189i \(-0.433396\pi\)
0.207719 + 0.978189i \(0.433396\pi\)
\(692\) 3.17648e12 0.526586
\(693\) −1.58209e11 −0.0260574
\(694\) 1.64111e12 0.268547
\(695\) 1.41744e12 0.230447
\(696\) −3.10276e12 −0.501194
\(697\) 2.52782e12 0.405694
\(698\) 5.75936e12 0.918386
\(699\) 7.00694e12 1.11015
\(700\) −2.12786e12 −0.334967
\(701\) 6.94398e12 1.08612 0.543059 0.839694i \(-0.317266\pi\)
0.543059 + 0.839694i \(0.317266\pi\)
\(702\) −2.89556e12 −0.450003
\(703\) −2.15377e12 −0.332583
\(704\) 2.45635e11 0.0376889
\(705\) 1.45419e13 2.21703
\(706\) 9.97457e11 0.151103
\(707\) −1.20059e13 −1.80720
\(708\) 6.75176e12 1.00987
\(709\) −1.00274e13 −1.49032 −0.745159 0.666887i \(-0.767626\pi\)
−0.745159 + 0.666887i \(0.767626\pi\)
\(710\) −4.56950e12 −0.674849
\(711\) 3.68817e11 0.0541250
\(712\) −1.89900e12 −0.276927
\(713\) −9.24861e12 −1.34021
\(714\) −5.00704e12 −0.721006
\(715\) −1.69535e12 −0.242596
\(716\) −4.57083e12 −0.649960
\(717\) 4.00336e12 0.565703
\(718\) 1.79965e12 0.252714
\(719\) 8.41668e12 1.17452 0.587261 0.809398i \(-0.300206\pi\)
0.587261 + 0.809398i \(0.300206\pi\)
\(720\) −1.39481e11 −0.0193428
\(721\) 1.25847e13 1.73434
\(722\) 3.78764e12 0.518743
\(723\) −7.58015e12 −1.03171
\(724\) 6.90673e12 0.934220
\(725\) −5.02289e12 −0.675200
\(726\) 4.96189e11 0.0662876
\(727\) −4.69707e10 −0.00623622 −0.00311811 0.999995i \(-0.500993\pi\)
−0.00311811 + 0.999995i \(0.500993\pi\)
\(728\) 2.40810e12 0.317748
\(729\) 7.08315e12 0.928865
\(730\) −4.14490e12 −0.540209
\(731\) −6.39960e12 −0.828943
\(732\) −4.52228e12 −0.582180
\(733\) 6.70015e12 0.857269 0.428634 0.903478i \(-0.358995\pi\)
0.428634 + 0.903478i \(0.358995\pi\)
\(734\) −2.43101e12 −0.309139
\(735\) 8.57286e12 1.08351
\(736\) −1.15674e12 −0.145307
\(737\) −9.96367e11 −0.124399
\(738\) −2.02047e11 −0.0250725
\(739\) −1.71079e11 −0.0211007 −0.0105503 0.999944i \(-0.503358\pi\)
−0.0105503 + 0.999944i \(0.503358\pi\)
\(740\) −3.20935e12 −0.393437
\(741\) 2.87804e12 0.350683
\(742\) 1.20435e13 1.45860
\(743\) 6.82102e12 0.821106 0.410553 0.911837i \(-0.365336\pi\)
0.410553 + 0.911837i \(0.365336\pi\)
\(744\) −4.96805e12 −0.594439
\(745\) −1.50841e13 −1.79397
\(746\) −2.86477e12 −0.338661
\(747\) 5.75040e11 0.0675702
\(748\) 9.35696e11 0.109289
\(749\) −1.25098e13 −1.45239
\(750\) 3.92596e12 0.453075
\(751\) 5.72654e12 0.656920 0.328460 0.944518i \(-0.393470\pi\)
0.328460 + 0.944518i \(0.393470\pi\)
\(752\) 3.86002e12 0.440159
\(753\) −7.89345e12 −0.894724
\(754\) 5.68440e12 0.640492
\(755\) 1.03327e13 1.15732
\(756\) −5.91618e12 −0.658708
\(757\) 2.98205e12 0.330052 0.165026 0.986289i \(-0.447229\pi\)
0.165026 + 0.986289i \(0.447229\pi\)
\(758\) −3.70044e12 −0.407138
\(759\) −2.33665e12 −0.255567
\(760\) −2.04944e12 −0.222830
\(761\) −8.46525e12 −0.914974 −0.457487 0.889216i \(-0.651250\pi\)
−0.457487 + 0.889216i \(0.651250\pi\)
\(762\) −7.58890e12 −0.815420
\(763\) −2.24133e13 −2.39412
\(764\) −4.83082e12 −0.512980
\(765\) −5.31324e11 −0.0560897
\(766\) −5.66273e12 −0.594287
\(767\) −1.23696e13 −1.29055
\(768\) −6.21363e11 −0.0644496
\(769\) 1.77112e13 1.82633 0.913164 0.407592i \(-0.133631\pi\)
0.913164 + 0.407592i \(0.133631\pi\)
\(770\) −3.46393e12 −0.355108
\(771\) −2.48866e12 −0.253642
\(772\) −4.19249e12 −0.424809
\(773\) 9.83204e12 0.990458 0.495229 0.868763i \(-0.335084\pi\)
0.495229 + 0.868763i \(0.335084\pi\)
\(774\) 5.11514e11 0.0512299
\(775\) −8.04251e12 −0.800818
\(776\) −4.37723e11 −0.0433333
\(777\) 9.20848e12 0.906345
\(778\) −6.72753e12 −0.658335
\(779\) −2.96873e12 −0.288837
\(780\) 4.28860e12 0.414849
\(781\) −2.45015e12 −0.235648
\(782\) −4.40636e12 −0.421356
\(783\) −1.39653e13 −1.32777
\(784\) 2.27559e12 0.215115
\(785\) 5.48531e12 0.515570
\(786\) 4.19101e12 0.391667
\(787\) −1.78869e12 −0.166207 −0.0831036 0.996541i \(-0.526483\pi\)
−0.0831036 + 0.996541i \(0.526483\pi\)
\(788\) −6.17924e12 −0.570909
\(789\) 3.36439e12 0.309072
\(790\) 8.07512e12 0.737611
\(791\) −9.84312e12 −0.894002
\(792\) −7.47893e10 −0.00675424
\(793\) 8.28504e12 0.743987
\(794\) 5.49328e12 0.490500
\(795\) 2.14484e13 1.90433
\(796\) −1.78809e10 −0.00157863
\(797\) 1.04170e13 0.914496 0.457248 0.889339i \(-0.348835\pi\)
0.457248 + 0.889339i \(0.348835\pi\)
\(798\) 5.88038e12 0.513325
\(799\) 1.47039e13 1.27636
\(800\) −1.00589e12 −0.0868254
\(801\) 5.78194e11 0.0496281
\(802\) −8.25436e12 −0.704529
\(803\) −2.22248e12 −0.188633
\(804\) 2.52043e12 0.212727
\(805\) 1.63123e13 1.36909
\(806\) 9.10171e12 0.759653
\(807\) −4.08204e12 −0.338802
\(808\) −5.67548e12 −0.468437
\(809\) −7.91008e10 −0.00649251 −0.00324625 0.999995i \(-0.501033\pi\)
−0.00324625 + 0.999995i \(0.501033\pi\)
\(810\) −1.12064e13 −0.914713
\(811\) 7.52015e12 0.610425 0.305213 0.952284i \(-0.401272\pi\)
0.305213 + 0.952284i \(0.401272\pi\)
\(812\) 1.16143e13 0.937542
\(813\) −1.98500e13 −1.59351
\(814\) −1.72084e12 −0.137383
\(815\) −5.72585e12 −0.454601
\(816\) −2.36695e12 −0.186889
\(817\) 7.51583e12 0.590171
\(818\) 7.49372e12 0.585204
\(819\) −7.33201e11 −0.0569437
\(820\) −4.42374e12 −0.341686
\(821\) 4.67347e12 0.359000 0.179500 0.983758i \(-0.442552\pi\)
0.179500 + 0.983758i \(0.442552\pi\)
\(822\) −7.39142e12 −0.564683
\(823\) −4.06045e12 −0.308514 −0.154257 0.988031i \(-0.549298\pi\)
−0.154257 + 0.988031i \(0.549298\pi\)
\(824\) 5.94910e12 0.449551
\(825\) −2.03193e12 −0.152709
\(826\) −2.52733e13 −1.88909
\(827\) −2.53074e12 −0.188136 −0.0940682 0.995566i \(-0.529987\pi\)
−0.0940682 + 0.995566i \(0.529987\pi\)
\(828\) 3.52196e11 0.0260405
\(829\) −2.26450e12 −0.166524 −0.0832620 0.996528i \(-0.526534\pi\)
−0.0832620 + 0.996528i \(0.526534\pi\)
\(830\) 1.25903e13 0.920841
\(831\) −2.68226e13 −1.95117
\(832\) 1.13837e12 0.0823622
\(833\) 8.66836e12 0.623784
\(834\) −1.92257e12 −0.137605
\(835\) −1.93194e13 −1.37532
\(836\) −1.09890e12 −0.0778091
\(837\) −2.23609e13 −1.57480
\(838\) 1.84087e13 1.28951
\(839\) 7.42242e12 0.517150 0.258575 0.965991i \(-0.416747\pi\)
0.258575 + 0.965991i \(0.416747\pi\)
\(840\) 8.76242e12 0.607250
\(841\) 1.29088e13 0.889825
\(842\) 3.99599e12 0.273981
\(843\) 7.53404e12 0.513811
\(844\) 8.56156e12 0.580780
\(845\) 1.02405e13 0.690981
\(846\) −1.17527e12 −0.0788809
\(847\) −1.85735e12 −0.123999
\(848\) 5.69326e12 0.378077
\(849\) −1.50164e13 −0.991931
\(850\) −3.83173e12 −0.251774
\(851\) 8.10377e12 0.529668
\(852\) 6.19795e12 0.402967
\(853\) 1.60812e13 1.04004 0.520019 0.854155i \(-0.325925\pi\)
0.520019 + 0.854155i \(0.325925\pi\)
\(854\) 1.69279e13 1.08904
\(855\) 6.23999e11 0.0399334
\(856\) −5.91370e12 −0.376467
\(857\) 8.68029e11 0.0549693 0.0274847 0.999622i \(-0.491250\pi\)
0.0274847 + 0.999622i \(0.491250\pi\)
\(858\) 2.29953e12 0.144859
\(859\) −1.16610e13 −0.730748 −0.365374 0.930861i \(-0.619059\pi\)
−0.365374 + 0.930861i \(0.619059\pi\)
\(860\) 1.11994e13 0.698156
\(861\) 1.26929e13 0.787129
\(862\) −4.48993e12 −0.276986
\(863\) 2.04030e13 1.25212 0.626060 0.779775i \(-0.284666\pi\)
0.626060 + 0.779775i \(0.284666\pi\)
\(864\) −2.79672e12 −0.170741
\(865\) −2.11755e13 −1.28606
\(866\) −1.71874e13 −1.03844
\(867\) 8.13999e12 0.489258
\(868\) 1.85965e13 1.11197
\(869\) 4.32985e12 0.257563
\(870\) 2.06840e13 1.22405
\(871\) −4.61755e12 −0.271850
\(872\) −1.05953e13 −0.620570
\(873\) 1.33275e11 0.00776576
\(874\) 5.17493e12 0.299987
\(875\) −1.46957e13 −0.847529
\(876\) 5.62203e12 0.322571
\(877\) −3.26576e13 −1.86417 −0.932085 0.362239i \(-0.882012\pi\)
−0.932085 + 0.362239i \(0.882012\pi\)
\(878\) −1.51285e13 −0.859153
\(879\) 1.23194e13 0.696048
\(880\) −1.63749e12 −0.0920461
\(881\) 1.89169e13 1.05793 0.528966 0.848643i \(-0.322580\pi\)
0.528966 + 0.848643i \(0.322580\pi\)
\(882\) −6.92854e11 −0.0385508
\(883\) −4.52036e12 −0.250236 −0.125118 0.992142i \(-0.539931\pi\)
−0.125118 + 0.992142i \(0.539931\pi\)
\(884\) 4.33638e12 0.238832
\(885\) −4.50095e13 −2.46638
\(886\) −2.26157e13 −1.23299
\(887\) 1.67209e13 0.906994 0.453497 0.891258i \(-0.350176\pi\)
0.453497 + 0.891258i \(0.350176\pi\)
\(888\) 4.35308e12 0.234930
\(889\) 2.84069e13 1.52534
\(890\) 1.26594e13 0.676327
\(891\) −6.00885e12 −0.319405
\(892\) −4.47453e12 −0.236650
\(893\) −1.72686e13 −0.908712
\(894\) 2.04596e13 1.07122
\(895\) 3.04707e13 1.58737
\(896\) 2.32590e12 0.120561
\(897\) −1.08289e13 −0.558495
\(898\) −5.18999e12 −0.266332
\(899\) 4.38977e13 2.24142
\(900\) 3.06267e11 0.0155600
\(901\) 2.16873e13 1.09634
\(902\) −2.37199e12 −0.119312
\(903\) −3.21341e13 −1.60832
\(904\) −4.65309e12 −0.231731
\(905\) −4.60426e13 −2.28161
\(906\) −1.40150e13 −0.691059
\(907\) −2.68525e13 −1.31751 −0.658753 0.752359i \(-0.728916\pi\)
−0.658753 + 0.752359i \(0.728916\pi\)
\(908\) −5.10854e12 −0.249408
\(909\) 1.72803e12 0.0839487
\(910\) −1.60532e13 −0.776024
\(911\) 8.77113e12 0.421913 0.210957 0.977495i \(-0.432342\pi\)
0.210957 + 0.977495i \(0.432342\pi\)
\(912\) 2.77980e12 0.133057
\(913\) 6.75088e12 0.321545
\(914\) 2.31647e12 0.109792
\(915\) 3.01470e13 1.42184
\(916\) −1.90910e13 −0.895980
\(917\) −1.56879e13 −0.732660
\(918\) −1.06535e13 −0.495110
\(919\) −8.62159e11 −0.0398720 −0.0199360 0.999801i \(-0.506346\pi\)
−0.0199360 + 0.999801i \(0.506346\pi\)
\(920\) 7.71122e12 0.354877
\(921\) −4.04284e13 −1.85147
\(922\) −4.70550e12 −0.214445
\(923\) −1.13549e13 −0.514965
\(924\) 4.69838e12 0.212043
\(925\) 7.04697e12 0.316493
\(926\) −1.40557e13 −0.628205
\(927\) −1.81134e12 −0.0805640
\(928\) 5.49037e12 0.243017
\(929\) 1.65304e12 0.0728138 0.0364069 0.999337i \(-0.488409\pi\)
0.0364069 + 0.999337i \(0.488409\pi\)
\(930\) 3.31187e13 1.45178
\(931\) −1.01803e13 −0.444107
\(932\) −1.23989e13 −0.538283
\(933\) −3.47375e13 −1.50083
\(934\) −1.01060e13 −0.434529
\(935\) −6.23766e12 −0.266913
\(936\) −3.46603e11 −0.0147601
\(937\) −2.41842e13 −1.02495 −0.512476 0.858702i \(-0.671272\pi\)
−0.512476 + 0.858702i \(0.671272\pi\)
\(938\) −9.43453e12 −0.397931
\(939\) −1.40135e13 −0.588235
\(940\) −2.57322e13 −1.07498
\(941\) 3.40036e13 1.41375 0.706874 0.707340i \(-0.250105\pi\)
0.706874 + 0.707340i \(0.250105\pi\)
\(942\) −7.44013e12 −0.307859
\(943\) 1.11701e13 0.459998
\(944\) −1.19473e13 −0.489663
\(945\) 3.94392e13 1.60874
\(946\) 6.00509e12 0.243786
\(947\) 1.65859e13 0.670138 0.335069 0.942194i \(-0.391240\pi\)
0.335069 + 0.942194i \(0.391240\pi\)
\(948\) −1.09529e13 −0.440444
\(949\) −1.02998e13 −0.412223
\(950\) 4.50007e12 0.179252
\(951\) 2.46123e13 0.975753
\(952\) 8.86003e12 0.349598
\(953\) −2.57430e13 −1.01098 −0.505489 0.862833i \(-0.668688\pi\)
−0.505489 + 0.862833i \(0.668688\pi\)
\(954\) −1.73344e12 −0.0677552
\(955\) 3.22038e13 1.25283
\(956\) −7.08401e12 −0.274295
\(957\) 1.10907e13 0.427420
\(958\) 2.72211e13 1.04414
\(959\) 2.76677e13 1.05631
\(960\) 4.14222e12 0.157403
\(961\) 4.38482e13 1.65843
\(962\) −7.97506e12 −0.300224
\(963\) 1.80056e12 0.0674668
\(964\) 1.34132e13 0.500248
\(965\) 2.79485e13 1.03749
\(966\) −2.21255e13 −0.817516
\(967\) 4.94862e12 0.181997 0.0909986 0.995851i \(-0.470994\pi\)
0.0909986 + 0.995851i \(0.470994\pi\)
\(968\) −8.78014e11 −0.0321412
\(969\) 1.05891e13 0.385834
\(970\) 2.91801e12 0.105831
\(971\) 1.45094e13 0.523799 0.261899 0.965095i \(-0.415651\pi\)
0.261899 + 0.965095i \(0.415651\pi\)
\(972\) 1.76066e12 0.0632669
\(973\) 7.19661e12 0.257407
\(974\) −3.48504e12 −0.124077
\(975\) −9.41674e12 −0.333718
\(976\) 8.00224e12 0.282285
\(977\) −8.00736e12 −0.281167 −0.140583 0.990069i \(-0.544898\pi\)
−0.140583 + 0.990069i \(0.544898\pi\)
\(978\) 7.76638e12 0.271453
\(979\) 6.78790e12 0.236164
\(980\) −1.51698e13 −0.525367
\(981\) 3.22599e12 0.111212
\(982\) −3.92351e12 −0.134640
\(983\) −3.29697e13 −1.12622 −0.563111 0.826381i \(-0.690396\pi\)
−0.563111 + 0.826381i \(0.690396\pi\)
\(984\) 6.00024e12 0.204028
\(985\) 4.11929e13 1.39431
\(986\) 2.09144e13 0.704692
\(987\) 7.38324e13 2.47639
\(988\) −5.09273e12 −0.170037
\(989\) −2.82791e13 −0.939900
\(990\) 4.98570e11 0.0164956
\(991\) 1.22142e12 0.0402286 0.0201143 0.999798i \(-0.493597\pi\)
0.0201143 + 0.999798i \(0.493597\pi\)
\(992\) 8.79103e12 0.288229
\(993\) −3.54908e12 −0.115836
\(994\) −2.32003e13 −0.753798
\(995\) 1.19200e11 0.00385544
\(996\) −1.70771e13 −0.549855
\(997\) −3.27455e13 −1.04960 −0.524800 0.851226i \(-0.675860\pi\)
−0.524800 + 0.851226i \(0.675860\pi\)
\(998\) 3.42984e13 1.09443
\(999\) 1.95930e13 0.622380
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 22.10.a.d.1.1 2
3.2 odd 2 198.10.a.n.1.2 2
4.3 odd 2 176.10.a.e.1.2 2
11.10 odd 2 242.10.a.e.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.10.a.d.1.1 2 1.1 even 1 trivial
176.10.a.e.1.2 2 4.3 odd 2
198.10.a.n.1.2 2 3.2 odd 2
242.10.a.e.1.1 2 11.10 odd 2