Properties

Label 1.22.a.a.1.1
Level $1$
Weight $22$
Character 1.1
Self dual yes
Analytic conductor $2.795$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.79477344287\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-288.000 q^{2} -128844. q^{3} -2.01421e6 q^{4} +2.16410e7 q^{5} +3.71071e7 q^{6} -7.68079e8 q^{7} +1.18407e9 q^{8} +6.14042e9 q^{9} +O(q^{10})\) \(q-288.000 q^{2} -128844. q^{3} -2.01421e6 q^{4} +2.16410e7 q^{5} +3.71071e7 q^{6} -7.68079e8 q^{7} +1.18407e9 q^{8} +6.14042e9 q^{9} -6.23259e9 q^{10} -9.47249e10 q^{11} +2.59519e11 q^{12} -8.06218e10 q^{13} +2.21207e11 q^{14} -2.78831e12 q^{15} +3.88309e12 q^{16} +3.05228e12 q^{17} -1.76844e12 q^{18} -7.92079e12 q^{19} -4.35894e13 q^{20} +9.89623e13 q^{21} +2.72808e13 q^{22} -7.38454e13 q^{23} -1.52561e14 q^{24} -8.50644e12 q^{25} +2.32191e13 q^{26} +5.56597e14 q^{27} +1.54707e15 q^{28} -4.25303e15 q^{29} +8.03032e14 q^{30} +1.90054e15 q^{31} -3.60151e15 q^{32} +1.22047e16 q^{33} -8.79057e14 q^{34} -1.66220e16 q^{35} -1.23681e16 q^{36} +2.21914e16 q^{37} +2.28119e15 q^{38} +1.03876e16 q^{39} +2.56244e16 q^{40} -2.06228e16 q^{41} -2.85012e16 q^{42} -1.93606e17 q^{43} +1.90796e17 q^{44} +1.32885e17 q^{45} +2.12675e16 q^{46} +1.46961e17 q^{47} -5.00313e17 q^{48} +3.13992e16 q^{49} +2.44986e15 q^{50} -3.93268e17 q^{51} +1.62389e17 q^{52} +2.03827e18 q^{53} -1.60300e17 q^{54} -2.04994e18 q^{55} -9.09460e17 q^{56} +1.02055e18 q^{57} +1.22487e18 q^{58} -5.97588e18 q^{59} +5.61623e18 q^{60} +6.19062e18 q^{61} -5.47356e17 q^{62} -4.71633e18 q^{63} -7.10619e18 q^{64} -1.74473e18 q^{65} -3.51496e18 q^{66} +1.69613e19 q^{67} -6.14793e18 q^{68} +9.51454e18 q^{69} +4.78712e18 q^{70} -5.63276e18 q^{71} +7.27070e18 q^{72} -4.32848e19 q^{73} -6.39113e18 q^{74} +1.09600e18 q^{75} +1.59541e19 q^{76} +7.27562e19 q^{77} -2.99164e18 q^{78} -5.12649e19 q^{79} +8.40337e19 q^{80} -1.35945e20 q^{81} +5.93937e18 q^{82} +4.89119e19 q^{83} -1.99331e20 q^{84} +6.60543e19 q^{85} +5.57585e19 q^{86} +5.47978e20 q^{87} -1.12161e20 q^{88} -5.04303e20 q^{89} -3.82708e19 q^{90} +6.19239e19 q^{91} +1.48740e20 q^{92} -2.44873e20 q^{93} -4.23246e19 q^{94} -1.71413e20 q^{95} +4.64033e20 q^{96} +8.08275e20 q^{97} -9.04297e18 q^{98} -5.81651e20 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −288.000 −0.198874 −0.0994369 0.995044i \(-0.531704\pi\)
−0.0994369 + 0.995044i \(0.531704\pi\)
\(3\) −128844. −1.25977 −0.629885 0.776689i \(-0.716898\pi\)
−0.629885 + 0.776689i \(0.716898\pi\)
\(4\) −2.01421e6 −0.960449
\(5\) 2.16410e7 0.991040 0.495520 0.868596i \(-0.334977\pi\)
0.495520 + 0.868596i \(0.334977\pi\)
\(6\) 3.71071e7 0.250535
\(7\) −7.68079e8 −1.02772 −0.513862 0.857873i \(-0.671786\pi\)
−0.513862 + 0.857873i \(0.671786\pi\)
\(8\) 1.18407e9 0.389882
\(9\) 6.14042e9 0.587019
\(10\) −6.23259e9 −0.197092
\(11\) −9.47249e10 −1.10114 −0.550568 0.834790i \(-0.685589\pi\)
−0.550568 + 0.834790i \(0.685589\pi\)
\(12\) 2.59519e11 1.20994
\(13\) −8.06218e10 −0.162199 −0.0810993 0.996706i \(-0.525843\pi\)
−0.0810993 + 0.996706i \(0.525843\pi\)
\(14\) 2.21207e11 0.204387
\(15\) −2.78831e12 −1.24848
\(16\) 3.88309e12 0.882912
\(17\) 3.05228e12 0.367207 0.183604 0.983000i \(-0.441224\pi\)
0.183604 + 0.983000i \(0.441224\pi\)
\(18\) −1.76844e12 −0.116743
\(19\) −7.92079e12 −0.296385 −0.148192 0.988959i \(-0.547345\pi\)
−0.148192 + 0.988959i \(0.547345\pi\)
\(20\) −4.35894e13 −0.951844
\(21\) 9.89623e13 1.29469
\(22\) 2.72808e13 0.218987
\(23\) −7.38454e13 −0.371690 −0.185845 0.982579i \(-0.559502\pi\)
−0.185845 + 0.982579i \(0.559502\pi\)
\(24\) −1.52561e14 −0.491161
\(25\) −8.50644e12 −0.0178393
\(26\) 2.32191e13 0.0322571
\(27\) 5.56597e14 0.520261
\(28\) 1.54707e15 0.987076
\(29\) −4.25303e15 −1.87724 −0.938620 0.344954i \(-0.887895\pi\)
−0.938620 + 0.344954i \(0.887895\pi\)
\(30\) 8.03032e14 0.248290
\(31\) 1.90054e15 0.416466 0.208233 0.978079i \(-0.433229\pi\)
0.208233 + 0.978079i \(0.433229\pi\)
\(32\) −3.60151e15 −0.565470
\(33\) 1.22047e16 1.38718
\(34\) −8.79057e14 −0.0730279
\(35\) −1.66220e16 −1.01852
\(36\) −1.23681e16 −0.563802
\(37\) 2.21914e16 0.758695 0.379347 0.925254i \(-0.376149\pi\)
0.379347 + 0.925254i \(0.376149\pi\)
\(38\) 2.28119e15 0.0589431
\(39\) 1.03876e16 0.204333
\(40\) 2.56244e16 0.386389
\(41\) −2.06228e16 −0.239948 −0.119974 0.992777i \(-0.538281\pi\)
−0.119974 + 0.992777i \(0.538281\pi\)
\(42\) −2.85012e16 −0.257481
\(43\) −1.93606e17 −1.36615 −0.683077 0.730346i \(-0.739359\pi\)
−0.683077 + 0.730346i \(0.739359\pi\)
\(44\) 1.90796e17 1.05759
\(45\) 1.32885e17 0.581759
\(46\) 2.12675e16 0.0739195
\(47\) 1.46961e17 0.407543 0.203771 0.979019i \(-0.434680\pi\)
0.203771 + 0.979019i \(0.434680\pi\)
\(48\) −5.00313e17 −1.11227
\(49\) 3.13992e16 0.0562160
\(50\) 2.44986e15 0.00354777
\(51\) −3.93268e17 −0.462596
\(52\) 1.62389e17 0.155784
\(53\) 2.03827e18 1.60090 0.800450 0.599399i \(-0.204594\pi\)
0.800450 + 0.599399i \(0.204594\pi\)
\(54\) −1.60300e17 −0.103466
\(55\) −2.04994e18 −1.09127
\(56\) −9.09460e17 −0.400691
\(57\) 1.02055e18 0.373376
\(58\) 1.22487e18 0.373334
\(59\) −5.97588e18 −1.52214 −0.761072 0.648667i \(-0.775327\pi\)
−0.761072 + 0.648667i \(0.775327\pi\)
\(60\) 5.61623e18 1.19910
\(61\) 6.19062e18 1.11114 0.555572 0.831468i \(-0.312499\pi\)
0.555572 + 0.831468i \(0.312499\pi\)
\(62\) −5.47356e17 −0.0828242
\(63\) −4.71633e18 −0.603293
\(64\) −7.10619e18 −0.770455
\(65\) −1.74473e18 −0.160745
\(66\) −3.51496e18 −0.275873
\(67\) 1.69613e19 1.13677 0.568387 0.822761i \(-0.307568\pi\)
0.568387 + 0.822761i \(0.307568\pi\)
\(68\) −6.14793e18 −0.352684
\(69\) 9.51454e18 0.468244
\(70\) 4.78712e18 0.202556
\(71\) −5.63276e18 −0.205357 −0.102678 0.994715i \(-0.532741\pi\)
−0.102678 + 0.994715i \(0.532741\pi\)
\(72\) 7.27070e18 0.228868
\(73\) −4.32848e19 −1.17881 −0.589407 0.807837i \(-0.700638\pi\)
−0.589407 + 0.807837i \(0.700638\pi\)
\(74\) −6.39113e18 −0.150885
\(75\) 1.09600e18 0.0224734
\(76\) 1.59541e19 0.284662
\(77\) 7.27562e19 1.13166
\(78\) −2.99164e18 −0.0406365
\(79\) −5.12649e19 −0.609166 −0.304583 0.952486i \(-0.598517\pi\)
−0.304583 + 0.952486i \(0.598517\pi\)
\(80\) 8.40337e19 0.875001
\(81\) −1.35945e20 −1.24243
\(82\) 5.93937e18 0.0477194
\(83\) 4.89119e19 0.346014 0.173007 0.984921i \(-0.444652\pi\)
0.173007 + 0.984921i \(0.444652\pi\)
\(84\) −1.99331e20 −1.24349
\(85\) 6.60543e19 0.363917
\(86\) 5.57585e19 0.271692
\(87\) 5.47978e20 2.36489
\(88\) −1.12161e20 −0.429313
\(89\) −5.04303e20 −1.71434 −0.857170 0.515034i \(-0.827779\pi\)
−0.857170 + 0.515034i \(0.827779\pi\)
\(90\) −3.82708e19 −0.115697
\(91\) 6.19239e19 0.166695
\(92\) 1.48740e20 0.356990
\(93\) −2.44873e20 −0.524651
\(94\) −4.23246e19 −0.0810496
\(95\) −1.71413e20 −0.293729
\(96\) 4.64033e20 0.712362
\(97\) 8.08275e20 1.11290 0.556450 0.830881i \(-0.312163\pi\)
0.556450 + 0.830881i \(0.312163\pi\)
\(98\) −9.04297e18 −0.0111799
\(99\) −5.81651e20 −0.646388
\(100\) 1.71337e19 0.0171337
\(101\) −1.00202e21 −0.902612 −0.451306 0.892369i \(-0.649042\pi\)
−0.451306 + 0.892369i \(0.649042\pi\)
\(102\) 1.13261e20 0.0919983
\(103\) −5.89747e20 −0.432389 −0.216195 0.976350i \(-0.569365\pi\)
−0.216195 + 0.976350i \(0.569365\pi\)
\(104\) −9.54620e19 −0.0632383
\(105\) 2.14164e21 1.28309
\(106\) −5.87021e20 −0.318377
\(107\) 1.12210e21 0.551445 0.275723 0.961237i \(-0.411083\pi\)
0.275723 + 0.961237i \(0.411083\pi\)
\(108\) −1.12110e21 −0.499684
\(109\) 1.72394e21 0.697499 0.348750 0.937216i \(-0.386606\pi\)
0.348750 + 0.937216i \(0.386606\pi\)
\(110\) 5.90382e20 0.217025
\(111\) −2.85923e21 −0.955781
\(112\) −2.98252e21 −0.907389
\(113\) 4.95810e20 0.137402 0.0687008 0.997637i \(-0.478115\pi\)
0.0687008 + 0.997637i \(0.478115\pi\)
\(114\) −2.93917e20 −0.0742547
\(115\) −1.59809e21 −0.368360
\(116\) 8.56649e21 1.80299
\(117\) −4.95052e20 −0.0952136
\(118\) 1.72105e21 0.302715
\(119\) −2.34439e21 −0.377387
\(120\) −3.30155e21 −0.486761
\(121\) 1.57256e21 0.212501
\(122\) −1.78290e21 −0.220978
\(123\) 2.65712e21 0.302279
\(124\) −3.82809e21 −0.399994
\(125\) −1.05033e22 −1.00872
\(126\) 1.35830e21 0.119979
\(127\) 1.63609e21 0.133005 0.0665027 0.997786i \(-0.478816\pi\)
0.0665027 + 0.997786i \(0.478816\pi\)
\(128\) 9.59949e21 0.718693
\(129\) 2.49450e22 1.72104
\(130\) 5.02483e20 0.0319680
\(131\) −1.38650e22 −0.813898 −0.406949 0.913451i \(-0.633407\pi\)
−0.406949 + 0.913451i \(0.633407\pi\)
\(132\) −2.45829e22 −1.33231
\(133\) 6.08379e21 0.304601
\(134\) −4.88486e21 −0.226075
\(135\) 1.20453e22 0.515600
\(136\) 3.61412e21 0.143167
\(137\) −4.00789e22 −1.47011 −0.735055 0.678007i \(-0.762844\pi\)
−0.735055 + 0.678007i \(0.762844\pi\)
\(138\) −2.74019e21 −0.0931215
\(139\) 4.47585e22 1.41000 0.705001 0.709206i \(-0.250946\pi\)
0.705001 + 0.709206i \(0.250946\pi\)
\(140\) 3.34801e22 0.978232
\(141\) −1.89350e22 −0.513410
\(142\) 1.62223e21 0.0408400
\(143\) 7.63689e21 0.178603
\(144\) 2.38438e22 0.518286
\(145\) −9.20396e22 −1.86042
\(146\) 1.24660e22 0.234435
\(147\) −4.04560e21 −0.0708191
\(148\) −4.46982e22 −0.728688
\(149\) 4.93289e22 0.749283 0.374641 0.927170i \(-0.377766\pi\)
0.374641 + 0.927170i \(0.377766\pi\)
\(150\) −3.15649e20 −0.00446937
\(151\) 5.70415e22 0.753239 0.376620 0.926368i \(-0.377086\pi\)
0.376620 + 0.926368i \(0.377086\pi\)
\(152\) −9.37878e21 −0.115555
\(153\) 1.87423e22 0.215557
\(154\) −2.09538e22 −0.225058
\(155\) 4.11295e22 0.412735
\(156\) −2.09229e22 −0.196251
\(157\) 6.35623e22 0.557511 0.278756 0.960362i \(-0.410078\pi\)
0.278756 + 0.960362i \(0.410078\pi\)
\(158\) 1.47643e22 0.121147
\(159\) −2.62618e23 −2.01677
\(160\) −7.79400e22 −0.560403
\(161\) 5.67191e22 0.381995
\(162\) 3.91522e22 0.247086
\(163\) 8.68484e22 0.513797 0.256899 0.966438i \(-0.417299\pi\)
0.256899 + 0.966438i \(0.417299\pi\)
\(164\) 4.15386e22 0.230458
\(165\) 2.64122e23 1.37475
\(166\) −1.40866e22 −0.0688132
\(167\) −1.89411e23 −0.868726 −0.434363 0.900738i \(-0.643026\pi\)
−0.434363 + 0.900738i \(0.643026\pi\)
\(168\) 1.17179e23 0.504778
\(169\) −2.40565e23 −0.973692
\(170\) −1.90236e22 −0.0723736
\(171\) −4.86370e22 −0.173983
\(172\) 3.89962e23 1.31212
\(173\) −4.18508e23 −1.32501 −0.662506 0.749057i \(-0.730507\pi\)
−0.662506 + 0.749057i \(0.730507\pi\)
\(174\) −1.57818e23 −0.470314
\(175\) 6.53362e21 0.0183339
\(176\) −3.67825e23 −0.972206
\(177\) 7.69957e23 1.91755
\(178\) 1.45239e23 0.340937
\(179\) 4.76752e23 1.05520 0.527601 0.849493i \(-0.323092\pi\)
0.527601 + 0.849493i \(0.323092\pi\)
\(180\) −2.67657e23 −0.558750
\(181\) −2.88627e22 −0.0568476 −0.0284238 0.999596i \(-0.509049\pi\)
−0.0284238 + 0.999596i \(0.509049\pi\)
\(182\) −1.78341e22 −0.0331513
\(183\) −7.97624e23 −1.39979
\(184\) −8.74383e22 −0.144915
\(185\) 4.80244e23 0.751897
\(186\) 7.05235e22 0.104339
\(187\) −2.89127e23 −0.404345
\(188\) −2.96009e23 −0.391424
\(189\) −4.27510e23 −0.534685
\(190\) 4.93671e22 0.0584150
\(191\) 8.86378e23 0.992587 0.496293 0.868155i \(-0.334694\pi\)
0.496293 + 0.868155i \(0.334694\pi\)
\(192\) 9.15590e23 0.970595
\(193\) 8.63509e22 0.0866792 0.0433396 0.999060i \(-0.486200\pi\)
0.0433396 + 0.999060i \(0.486200\pi\)
\(194\) −2.32783e23 −0.221327
\(195\) 2.24798e23 0.202502
\(196\) −6.32445e22 −0.0539926
\(197\) −6.99008e23 −0.565701 −0.282850 0.959164i \(-0.591280\pi\)
−0.282850 + 0.959164i \(0.591280\pi\)
\(198\) 1.67516e23 0.128550
\(199\) −1.24542e24 −0.906483 −0.453242 0.891388i \(-0.649732\pi\)
−0.453242 + 0.891388i \(0.649732\pi\)
\(200\) −1.00722e22 −0.00695522
\(201\) −2.18536e24 −1.43207
\(202\) 2.88581e23 0.179506
\(203\) 3.26666e24 1.92928
\(204\) 7.92124e23 0.444300
\(205\) −4.46297e23 −0.237798
\(206\) 1.69847e23 0.0859909
\(207\) −4.53442e23 −0.218189
\(208\) −3.13061e23 −0.143207
\(209\) 7.50296e23 0.326360
\(210\) −6.16792e23 −0.255174
\(211\) 3.50841e24 1.38085 0.690423 0.723406i \(-0.257425\pi\)
0.690423 + 0.723406i \(0.257425\pi\)
\(212\) −4.10549e24 −1.53758
\(213\) 7.25747e23 0.258702
\(214\) −3.23165e23 −0.109668
\(215\) −4.18981e24 −1.35391
\(216\) 6.59051e23 0.202840
\(217\) −1.45977e24 −0.428012
\(218\) −4.96495e23 −0.138714
\(219\) 5.57698e24 1.48503
\(220\) 4.12900e24 1.04811
\(221\) −2.46081e23 −0.0595605
\(222\) 8.23459e23 0.190080
\(223\) −4.72350e24 −1.04007 −0.520035 0.854145i \(-0.674081\pi\)
−0.520035 + 0.854145i \(0.674081\pi\)
\(224\) 2.76624e24 0.581147
\(225\) −5.22331e22 −0.0104720
\(226\) −1.42793e23 −0.0273256
\(227\) −5.44317e24 −0.994444 −0.497222 0.867623i \(-0.665647\pi\)
−0.497222 + 0.867623i \(0.665647\pi\)
\(228\) −2.05559e24 −0.358609
\(229\) 6.90677e24 1.15081 0.575403 0.817870i \(-0.304845\pi\)
0.575403 + 0.817870i \(0.304845\pi\)
\(230\) 4.60249e23 0.0732572
\(231\) −9.37420e24 −1.42564
\(232\) −5.03589e24 −0.731902
\(233\) 4.53650e24 0.630208 0.315104 0.949057i \(-0.397961\pi\)
0.315104 + 0.949057i \(0.397961\pi\)
\(234\) 1.42575e23 0.0189355
\(235\) 3.18036e24 0.403891
\(236\) 1.20367e25 1.46194
\(237\) 6.60518e24 0.767409
\(238\) 6.75185e23 0.0750525
\(239\) −2.73493e24 −0.290916 −0.145458 0.989364i \(-0.546466\pi\)
−0.145458 + 0.989364i \(0.546466\pi\)
\(240\) −1.08272e25 −1.10230
\(241\) −8.08907e24 −0.788351 −0.394175 0.919035i \(-0.628970\pi\)
−0.394175 + 0.919035i \(0.628970\pi\)
\(242\) −4.52898e23 −0.0422609
\(243\) 1.16935e25 1.04491
\(244\) −1.24692e25 −1.06720
\(245\) 6.79508e23 0.0557123
\(246\) −7.65252e23 −0.0601154
\(247\) 6.38588e23 0.0480732
\(248\) 2.25038e24 0.162373
\(249\) −6.30200e24 −0.435898
\(250\) 3.02495e24 0.200608
\(251\) 6.63927e24 0.422227 0.211113 0.977462i \(-0.432291\pi\)
0.211113 + 0.977462i \(0.432291\pi\)
\(252\) 9.49967e24 0.579432
\(253\) 6.99500e24 0.409282
\(254\) −4.71195e23 −0.0264513
\(255\) −8.51070e24 −0.458452
\(256\) 1.21381e25 0.627526
\(257\) 1.57278e24 0.0780497 0.0390249 0.999238i \(-0.487575\pi\)
0.0390249 + 0.999238i \(0.487575\pi\)
\(258\) −7.18415e24 −0.342270
\(259\) −1.70448e25 −0.779729
\(260\) 3.51425e24 0.154388
\(261\) −2.61154e25 −1.10197
\(262\) 3.99311e24 0.161863
\(263\) −3.40077e25 −1.32447 −0.662235 0.749296i \(-0.730392\pi\)
−0.662235 + 0.749296i \(0.730392\pi\)
\(264\) 1.44513e25 0.540836
\(265\) 4.41100e25 1.58656
\(266\) −1.75213e24 −0.0605772
\(267\) 6.49765e25 2.15967
\(268\) −3.41636e25 −1.09181
\(269\) −3.57975e25 −1.10015 −0.550077 0.835114i \(-0.685402\pi\)
−0.550077 + 0.835114i \(0.685402\pi\)
\(270\) −3.46904e24 −0.102539
\(271\) 2.46104e25 0.699746 0.349873 0.936797i \(-0.386225\pi\)
0.349873 + 0.936797i \(0.386225\pi\)
\(272\) 1.18523e25 0.324212
\(273\) −7.97852e24 −0.209998
\(274\) 1.15427e25 0.292366
\(275\) 8.05772e23 0.0196435
\(276\) −1.91643e25 −0.449725
\(277\) −6.11679e25 −1.38193 −0.690965 0.722888i \(-0.742814\pi\)
−0.690965 + 0.722888i \(0.742814\pi\)
\(278\) −1.28904e25 −0.280413
\(279\) 1.16701e25 0.244473
\(280\) −1.96816e25 −0.397101
\(281\) 1.73710e25 0.337605 0.168802 0.985650i \(-0.446010\pi\)
0.168802 + 0.985650i \(0.446010\pi\)
\(282\) 5.45327e24 0.102104
\(283\) 7.57237e25 1.36607 0.683037 0.730383i \(-0.260659\pi\)
0.683037 + 0.730383i \(0.260659\pi\)
\(284\) 1.13455e25 0.197235
\(285\) 2.20856e25 0.370031
\(286\) −2.19943e24 −0.0355194
\(287\) 1.58399e25 0.246600
\(288\) −2.21148e25 −0.331941
\(289\) −5.97755e25 −0.865159
\(290\) 2.65074e25 0.369989
\(291\) −1.04141e26 −1.40200
\(292\) 8.71845e25 1.13219
\(293\) 4.88684e25 0.612235 0.306118 0.951994i \(-0.400970\pi\)
0.306118 + 0.951994i \(0.400970\pi\)
\(294\) 1.16513e24 0.0140841
\(295\) −1.29324e26 −1.50851
\(296\) 2.62762e25 0.295801
\(297\) −5.27236e25 −0.572878
\(298\) −1.42067e25 −0.149013
\(299\) 5.95355e24 0.0602877
\(300\) −2.20758e24 −0.0215846
\(301\) 1.48705e26 1.40403
\(302\) −1.64279e25 −0.149800
\(303\) 1.29104e26 1.13708
\(304\) −3.07571e25 −0.261681
\(305\) 1.33971e26 1.10119
\(306\) −5.39778e24 −0.0428687
\(307\) −2.17987e26 −1.67293 −0.836466 0.548019i \(-0.815382\pi\)
−0.836466 + 0.548019i \(0.815382\pi\)
\(308\) −1.46546e26 −1.08691
\(309\) 7.59854e25 0.544711
\(310\) −1.18453e25 −0.0820821
\(311\) −4.04644e25 −0.271075 −0.135538 0.990772i \(-0.543276\pi\)
−0.135538 + 0.990772i \(0.543276\pi\)
\(312\) 1.22997e25 0.0796657
\(313\) −8.74174e24 −0.0547498 −0.0273749 0.999625i \(-0.508715\pi\)
−0.0273749 + 0.999625i \(0.508715\pi\)
\(314\) −1.83060e25 −0.110874
\(315\) −1.02066e26 −0.597888
\(316\) 1.03258e26 0.585073
\(317\) −3.19758e25 −0.175267 −0.0876334 0.996153i \(-0.527930\pi\)
−0.0876334 + 0.996153i \(0.527930\pi\)
\(318\) 7.56341e25 0.401082
\(319\) 4.02868e26 2.06710
\(320\) −1.53785e26 −0.763552
\(321\) −1.44576e26 −0.694694
\(322\) −1.63351e25 −0.0759688
\(323\) −2.41765e25 −0.108835
\(324\) 2.73822e26 1.19329
\(325\) 6.85805e23 0.00289351
\(326\) −2.50123e25 −0.102181
\(327\) −2.22119e26 −0.878688
\(328\) −2.44189e25 −0.0935514
\(329\) −1.12877e26 −0.418841
\(330\) −7.60672e25 −0.273402
\(331\) −2.52215e26 −0.878166 −0.439083 0.898446i \(-0.644697\pi\)
−0.439083 + 0.898446i \(0.644697\pi\)
\(332\) −9.85186e25 −0.332329
\(333\) 1.36265e26 0.445368
\(334\) 5.45504e25 0.172767
\(335\) 3.67059e26 1.12659
\(336\) 3.84279e26 1.14310
\(337\) −1.53127e26 −0.441507 −0.220753 0.975330i \(-0.570852\pi\)
−0.220753 + 0.975330i \(0.570852\pi\)
\(338\) 6.92826e25 0.193642
\(339\) −6.38821e25 −0.173094
\(340\) −1.33047e26 −0.349524
\(341\) −1.80029e26 −0.458586
\(342\) 1.40075e25 0.0346007
\(343\) 4.04890e26 0.969949
\(344\) −2.29243e26 −0.532639
\(345\) 2.05904e26 0.464049
\(346\) 1.20530e26 0.263510
\(347\) 3.23436e26 0.686008 0.343004 0.939334i \(-0.388556\pi\)
0.343004 + 0.939334i \(0.388556\pi\)
\(348\) −1.10374e27 −2.27136
\(349\) −6.77854e26 −1.35353 −0.676767 0.736197i \(-0.736620\pi\)
−0.676767 + 0.736197i \(0.736620\pi\)
\(350\) −1.88168e24 −0.00364613
\(351\) −4.48739e25 −0.0843857
\(352\) 3.41153e26 0.622660
\(353\) 6.84291e26 1.21229 0.606145 0.795354i \(-0.292715\pi\)
0.606145 + 0.795354i \(0.292715\pi\)
\(354\) −2.21748e26 −0.381351
\(355\) −1.21898e26 −0.203517
\(356\) 1.01577e27 1.64654
\(357\) 3.02061e26 0.475421
\(358\) −1.37304e26 −0.209852
\(359\) −6.85500e25 −0.101746 −0.0508728 0.998705i \(-0.516200\pi\)
−0.0508728 + 0.998705i \(0.516200\pi\)
\(360\) 1.57345e26 0.226817
\(361\) −6.51471e26 −0.912156
\(362\) 8.31247e24 0.0113055
\(363\) −2.02615e26 −0.267703
\(364\) −1.24728e26 −0.160102
\(365\) −9.36723e26 −1.16825
\(366\) 2.29716e26 0.278381
\(367\) 1.13575e27 1.33749 0.668745 0.743492i \(-0.266832\pi\)
0.668745 + 0.743492i \(0.266832\pi\)
\(368\) −2.86748e26 −0.328170
\(369\) −1.26633e26 −0.140854
\(370\) −1.38310e26 −0.149533
\(371\) −1.56555e27 −1.64528
\(372\) 4.93226e26 0.503901
\(373\) 3.82975e26 0.380389 0.190195 0.981746i \(-0.439088\pi\)
0.190195 + 0.981746i \(0.439088\pi\)
\(374\) 8.32687e25 0.0804136
\(375\) 1.35329e27 1.27075
\(376\) 1.74012e26 0.158894
\(377\) 3.42887e26 0.304486
\(378\) 1.23123e26 0.106335
\(379\) 7.14767e25 0.0600417 0.0300208 0.999549i \(-0.490443\pi\)
0.0300208 + 0.999549i \(0.490443\pi\)
\(380\) 3.45262e26 0.282112
\(381\) −2.10801e26 −0.167556
\(382\) −2.55277e26 −0.197400
\(383\) −1.38425e27 −1.04142 −0.520712 0.853732i \(-0.674334\pi\)
−0.520712 + 0.853732i \(0.674334\pi\)
\(384\) −1.23684e27 −0.905388
\(385\) 1.57451e27 1.12152
\(386\) −2.48690e25 −0.0172382
\(387\) −1.18882e27 −0.801958
\(388\) −1.62803e27 −1.06888
\(389\) 1.63213e27 1.04300 0.521500 0.853251i \(-0.325373\pi\)
0.521500 + 0.853251i \(0.325373\pi\)
\(390\) −6.47419e25 −0.0402724
\(391\) −2.25397e26 −0.136487
\(392\) 3.71789e25 0.0219176
\(393\) 1.78642e27 1.02532
\(394\) 2.01314e26 0.112503
\(395\) −1.10942e27 −0.603708
\(396\) 1.17157e27 0.620823
\(397\) 1.21029e27 0.624581 0.312291 0.949987i \(-0.398904\pi\)
0.312291 + 0.949987i \(0.398904\pi\)
\(398\) 3.58682e26 0.180276
\(399\) −7.83860e26 −0.383728
\(400\) −3.30313e25 −0.0157505
\(401\) −6.51358e26 −0.302555 −0.151277 0.988491i \(-0.548339\pi\)
−0.151277 + 0.988491i \(0.548339\pi\)
\(402\) 6.29385e26 0.284802
\(403\) −1.53225e26 −0.0675502
\(404\) 2.01827e27 0.866913
\(405\) −2.94198e27 −1.23130
\(406\) −9.40799e26 −0.383684
\(407\) −2.10208e27 −0.835427
\(408\) −4.65658e26 −0.180358
\(409\) −4.45251e27 −1.68078 −0.840389 0.541984i \(-0.817673\pi\)
−0.840389 + 0.541984i \(0.817673\pi\)
\(410\) 1.28534e26 0.0472918
\(411\) 5.16393e27 1.85200
\(412\) 1.18787e27 0.415288
\(413\) 4.58995e27 1.56434
\(414\) 1.30591e26 0.0433921
\(415\) 1.05850e27 0.342914
\(416\) 2.90360e26 0.0917185
\(417\) −5.76686e27 −1.77628
\(418\) −2.16085e26 −0.0649044
\(419\) 4.92912e27 1.44385 0.721925 0.691972i \(-0.243258\pi\)
0.721925 + 0.691972i \(0.243258\pi\)
\(420\) −4.31371e27 −1.23235
\(421\) 1.50145e27 0.418359 0.209180 0.977877i \(-0.432921\pi\)
0.209180 + 0.977877i \(0.432921\pi\)
\(422\) −1.01042e27 −0.274614
\(423\) 9.02400e26 0.239235
\(424\) 2.41345e27 0.624162
\(425\) −2.59641e25 −0.00655072
\(426\) −2.09015e26 −0.0514490
\(427\) −4.75488e27 −1.14195
\(428\) −2.26014e27 −0.529635
\(429\) −9.83968e26 −0.224998
\(430\) 1.20667e27 0.269258
\(431\) −7.19221e27 −1.56621 −0.783107 0.621887i \(-0.786366\pi\)
−0.783107 + 0.621887i \(0.786366\pi\)
\(432\) 2.16132e27 0.459345
\(433\) 4.23104e27 0.877656 0.438828 0.898571i \(-0.355394\pi\)
0.438828 + 0.898571i \(0.355394\pi\)
\(434\) 4.20412e26 0.0851203
\(435\) 1.18588e28 2.34370
\(436\) −3.47237e27 −0.669913
\(437\) 5.84914e26 0.110163
\(438\) −1.60617e27 −0.295334
\(439\) 4.53235e27 0.813665 0.406832 0.913503i \(-0.366633\pi\)
0.406832 + 0.913503i \(0.366633\pi\)
\(440\) −2.42727e27 −0.425467
\(441\) 1.92804e26 0.0329998
\(442\) 7.08712e25 0.0118450
\(443\) −4.61186e27 −0.752726 −0.376363 0.926472i \(-0.622826\pi\)
−0.376363 + 0.926472i \(0.622826\pi\)
\(444\) 5.75909e27 0.917979
\(445\) −1.09136e28 −1.69898
\(446\) 1.36037e27 0.206843
\(447\) −6.35573e27 −0.943923
\(448\) 5.45811e27 0.791815
\(449\) −1.25692e26 −0.0178123 −0.00890615 0.999960i \(-0.502835\pi\)
−0.00890615 + 0.999960i \(0.502835\pi\)
\(450\) 1.50431e25 0.00208261
\(451\) 1.95349e27 0.264216
\(452\) −9.98664e26 −0.131967
\(453\) −7.34945e27 −0.948907
\(454\) 1.56763e27 0.197769
\(455\) 1.34009e27 0.165202
\(456\) 1.20840e27 0.145573
\(457\) 1.15924e28 1.36475 0.682374 0.731003i \(-0.260948\pi\)
0.682374 + 0.731003i \(0.260948\pi\)
\(458\) −1.98915e27 −0.228865
\(459\) 1.69889e27 0.191044
\(460\) 3.21888e27 0.353791
\(461\) 1.02514e28 1.10134 0.550671 0.834723i \(-0.314372\pi\)
0.550671 + 0.834723i \(0.314372\pi\)
\(462\) 2.69977e27 0.283522
\(463\) −5.72801e27 −0.588035 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(464\) −1.65149e28 −1.65744
\(465\) −5.29929e27 −0.519950
\(466\) −1.30651e27 −0.125332
\(467\) 1.12658e28 1.05666 0.528329 0.849040i \(-0.322819\pi\)
0.528329 + 0.849040i \(0.322819\pi\)
\(468\) 9.97138e26 0.0914479
\(469\) −1.30276e28 −1.16829
\(470\) −9.15945e26 −0.0803234
\(471\) −8.18963e27 −0.702335
\(472\) −7.07587e27 −0.593457
\(473\) 1.83393e28 1.50432
\(474\) −1.90229e27 −0.152618
\(475\) 6.73777e25 0.00528729
\(476\) 4.72210e27 0.362462
\(477\) 1.25158e28 0.939759
\(478\) 7.87660e26 0.0578557
\(479\) −1.17373e28 −0.843422 −0.421711 0.906730i \(-0.638570\pi\)
−0.421711 + 0.906730i \(0.638570\pi\)
\(480\) 1.00421e28 0.705979
\(481\) −1.78911e27 −0.123059
\(482\) 2.32965e27 0.156782
\(483\) −7.30792e27 −0.481226
\(484\) −3.16747e27 −0.204097
\(485\) 1.74918e28 1.10293
\(486\) −3.36773e27 −0.207805
\(487\) 4.75272e27 0.287004 0.143502 0.989650i \(-0.454164\pi\)
0.143502 + 0.989650i \(0.454164\pi\)
\(488\) 7.33013e27 0.433215
\(489\) −1.11899e28 −0.647266
\(490\) −1.95698e26 −0.0110797
\(491\) −2.59837e28 −1.43994 −0.719971 0.694004i \(-0.755845\pi\)
−0.719971 + 0.694004i \(0.755845\pi\)
\(492\) −5.35200e27 −0.290324
\(493\) −1.29815e28 −0.689336
\(494\) −1.83913e26 −0.00956049
\(495\) −1.25875e28 −0.640596
\(496\) 7.37997e27 0.367703
\(497\) 4.32640e27 0.211050
\(498\) 1.81498e27 0.0866887
\(499\) 3.84508e28 1.79825 0.899124 0.437695i \(-0.144205\pi\)
0.899124 + 0.437695i \(0.144205\pi\)
\(500\) 2.11558e28 0.968824
\(501\) 2.44045e28 1.09439
\(502\) −1.91211e27 −0.0839699
\(503\) −3.27446e28 −1.40824 −0.704118 0.710083i \(-0.748657\pi\)
−0.704118 + 0.710083i \(0.748657\pi\)
\(504\) −5.58447e27 −0.235213
\(505\) −2.16846e28 −0.894525
\(506\) −2.01456e27 −0.0813954
\(507\) 3.09953e28 1.22663
\(508\) −3.29543e27 −0.127745
\(509\) −2.02472e28 −0.768826 −0.384413 0.923161i \(-0.625596\pi\)
−0.384413 + 0.923161i \(0.625596\pi\)
\(510\) 2.45108e27 0.0911740
\(511\) 3.32461e28 1.21149
\(512\) −2.36274e28 −0.843492
\(513\) −4.40869e27 −0.154197
\(514\) −4.52962e26 −0.0155220
\(515\) −1.27627e28 −0.428515
\(516\) −5.02443e28 −1.65297
\(517\) −1.39208e28 −0.448760
\(518\) 4.90889e27 0.155068
\(519\) 5.39222e28 1.66921
\(520\) −2.06589e27 −0.0626717
\(521\) 4.75207e27 0.141282 0.0706411 0.997502i \(-0.477496\pi\)
0.0706411 + 0.997502i \(0.477496\pi\)
\(522\) 7.52124e27 0.219154
\(523\) −1.28180e26 −0.00366061 −0.00183030 0.999998i \(-0.500583\pi\)
−0.00183030 + 0.999998i \(0.500583\pi\)
\(524\) 2.79269e28 0.781708
\(525\) −8.41817e26 −0.0230964
\(526\) 9.79422e27 0.263402
\(527\) 5.80099e27 0.152929
\(528\) 4.73921e28 1.22476
\(529\) −3.40184e28 −0.861846
\(530\) −1.27037e28 −0.315525
\(531\) −3.66944e28 −0.893527
\(532\) −1.22540e28 −0.292554
\(533\) 1.66265e27 0.0389192
\(534\) −1.87132e28 −0.429502
\(535\) 2.42833e28 0.546504
\(536\) 2.00834e28 0.443208
\(537\) −6.14266e28 −1.32931
\(538\) 1.03097e28 0.218792
\(539\) −2.97429e27 −0.0619014
\(540\) −2.42617e28 −0.495207
\(541\) 3.42747e28 0.686123 0.343061 0.939313i \(-0.388536\pi\)
0.343061 + 0.939313i \(0.388536\pi\)
\(542\) −7.08778e27 −0.139161
\(543\) 3.71879e27 0.0716149
\(544\) −1.09928e28 −0.207645
\(545\) 3.73077e28 0.691250
\(546\) 2.29781e27 0.0417630
\(547\) −7.30329e28 −1.30212 −0.651061 0.759026i \(-0.725676\pi\)
−0.651061 + 0.759026i \(0.725676\pi\)
\(548\) 8.07273e28 1.41197
\(549\) 3.80130e28 0.652263
\(550\) −2.32062e26 −0.00390658
\(551\) 3.36874e28 0.556385
\(552\) 1.12659e28 0.182560
\(553\) 3.93755e28 0.626055
\(554\) 1.76164e28 0.274830
\(555\) −6.18765e28 −0.947217
\(556\) −9.01529e28 −1.35424
\(557\) −3.32597e28 −0.490274 −0.245137 0.969488i \(-0.578833\pi\)
−0.245137 + 0.969488i \(0.578833\pi\)
\(558\) −3.36100e27 −0.0486193
\(559\) 1.56089e28 0.221588
\(560\) −6.45445e28 −0.899259
\(561\) 3.72523e28 0.509382
\(562\) −5.00285e27 −0.0671407
\(563\) −8.28332e28 −1.09110 −0.545552 0.838077i \(-0.683680\pi\)
−0.545552 + 0.838077i \(0.683680\pi\)
\(564\) 3.81390e28 0.493104
\(565\) 1.07298e28 0.136170
\(566\) −2.18084e28 −0.271676
\(567\) 1.04417e29 1.27687
\(568\) −6.66959e27 −0.0800648
\(569\) 7.35414e28 0.866669 0.433335 0.901233i \(-0.357337\pi\)
0.433335 + 0.901233i \(0.357337\pi\)
\(570\) −6.36065e27 −0.0735894
\(571\) 1.09131e29 1.23956 0.619780 0.784776i \(-0.287222\pi\)
0.619780 + 0.784776i \(0.287222\pi\)
\(572\) −1.53823e28 −0.171539
\(573\) −1.14204e29 −1.25043
\(574\) −4.56190e27 −0.0490423
\(575\) 6.28162e26 0.00663070
\(576\) −4.36350e28 −0.452271
\(577\) 1.30727e28 0.133051 0.0665257 0.997785i \(-0.478809\pi\)
0.0665257 + 0.997785i \(0.478809\pi\)
\(578\) 1.72153e28 0.172057
\(579\) −1.11258e28 −0.109196
\(580\) 1.85387e29 1.78684
\(581\) −3.75682e28 −0.355607
\(582\) 2.99927e28 0.278820
\(583\) −1.93075e29 −1.76281
\(584\) −5.12523e28 −0.459598
\(585\) −1.07134e28 −0.0943605
\(586\) −1.40741e28 −0.121758
\(587\) −1.71459e29 −1.45701 −0.728503 0.685043i \(-0.759784\pi\)
−0.728503 + 0.685043i \(0.759784\pi\)
\(588\) 8.14867e27 0.0680182
\(589\) −1.50538e28 −0.123434
\(590\) 3.72452e28 0.300002
\(591\) 9.00630e28 0.712652
\(592\) 8.61713e28 0.669861
\(593\) 2.35277e29 1.79682 0.898412 0.439153i \(-0.144721\pi\)
0.898412 + 0.439153i \(0.144721\pi\)
\(594\) 1.51844e28 0.113931
\(595\) −5.07349e28 −0.374006
\(596\) −9.93587e28 −0.719648
\(597\) 1.60465e29 1.14196
\(598\) −1.71462e27 −0.0119896
\(599\) −1.33384e29 −0.916481 −0.458240 0.888828i \(-0.651520\pi\)
−0.458240 + 0.888828i \(0.651520\pi\)
\(600\) 1.29775e27 0.00876197
\(601\) −3.64474e28 −0.241816 −0.120908 0.992664i \(-0.538581\pi\)
−0.120908 + 0.992664i \(0.538581\pi\)
\(602\) −4.28269e28 −0.279225
\(603\) 1.04150e29 0.667308
\(604\) −1.14893e29 −0.723448
\(605\) 3.40317e28 0.210597
\(606\) −3.71820e28 −0.226136
\(607\) 2.71228e29 1.62126 0.810630 0.585559i \(-0.199125\pi\)
0.810630 + 0.585559i \(0.199125\pi\)
\(608\) 2.85268e28 0.167597
\(609\) −4.20890e29 −2.43045
\(610\) −3.85836e28 −0.218998
\(611\) −1.18482e28 −0.0661029
\(612\) −3.77509e28 −0.207032
\(613\) −2.02699e29 −1.09274 −0.546370 0.837544i \(-0.683991\pi\)
−0.546370 + 0.837544i \(0.683991\pi\)
\(614\) 6.27803e28 0.332702
\(615\) 5.75027e28 0.299571
\(616\) 8.61486e28 0.441215
\(617\) 3.04169e29 1.53151 0.765757 0.643130i \(-0.222364\pi\)
0.765757 + 0.643130i \(0.222364\pi\)
\(618\) −2.18838e28 −0.108329
\(619\) 1.21487e29 0.591262 0.295631 0.955302i \(-0.404470\pi\)
0.295631 + 0.955302i \(0.404470\pi\)
\(620\) −8.28434e28 −0.396411
\(621\) −4.11022e28 −0.193376
\(622\) 1.16538e28 0.0539097
\(623\) 3.87345e29 1.76187
\(624\) 4.03361e28 0.180408
\(625\) −2.23245e29 −0.981842
\(626\) 2.51762e27 0.0108883
\(627\) −9.66712e28 −0.411138
\(628\) −1.28028e29 −0.535461
\(629\) 6.77345e28 0.278598
\(630\) 2.93950e28 0.118904
\(631\) −1.79118e29 −0.712577 −0.356288 0.934376i \(-0.615958\pi\)
−0.356288 + 0.934376i \(0.615958\pi\)
\(632\) −6.07014e28 −0.237503
\(633\) −4.52038e29 −1.73955
\(634\) 9.20904e27 0.0348560
\(635\) 3.54066e28 0.131814
\(636\) 5.28968e29 1.93700
\(637\) −2.53146e27 −0.00911815
\(638\) −1.16026e29 −0.411091
\(639\) −3.45875e28 −0.120548
\(640\) 2.07742e29 0.712254
\(641\) −3.41742e29 −1.15263 −0.576315 0.817228i \(-0.695510\pi\)
−0.576315 + 0.817228i \(0.695510\pi\)
\(642\) 4.16379e28 0.138156
\(643\) 7.57582e28 0.247294 0.123647 0.992326i \(-0.460541\pi\)
0.123647 + 0.992326i \(0.460541\pi\)
\(644\) −1.14244e29 −0.366887
\(645\) 5.39832e29 1.70562
\(646\) 6.96283e27 0.0216443
\(647\) −2.99088e29 −0.914755 −0.457377 0.889273i \(-0.651211\pi\)
−0.457377 + 0.889273i \(0.651211\pi\)
\(648\) −1.60969e29 −0.484400
\(649\) 5.66065e29 1.67609
\(650\) −1.97512e26 −0.000575443 0
\(651\) 1.88082e29 0.539196
\(652\) −1.74931e29 −0.493476
\(653\) 5.40507e28 0.150042 0.0750210 0.997182i \(-0.476098\pi\)
0.0750210 + 0.997182i \(0.476098\pi\)
\(654\) 6.39703e28 0.174748
\(655\) −3.00051e29 −0.806606
\(656\) −8.00802e28 −0.211853
\(657\) −2.65787e29 −0.691985
\(658\) 3.25086e28 0.0832966
\(659\) 2.26606e28 0.0571446 0.0285723 0.999592i \(-0.490904\pi\)
0.0285723 + 0.999592i \(0.490904\pi\)
\(660\) −5.31997e29 −1.32038
\(661\) −1.87483e29 −0.457980 −0.228990 0.973429i \(-0.573542\pi\)
−0.228990 + 0.973429i \(0.573542\pi\)
\(662\) 7.26379e28 0.174644
\(663\) 3.17060e28 0.0750325
\(664\) 5.79151e28 0.134905
\(665\) 1.31659e29 0.301872
\(666\) −3.92443e28 −0.0885720
\(667\) 3.14067e29 0.697752
\(668\) 3.81513e29 0.834367
\(669\) 6.08595e29 1.31025
\(670\) −1.05713e29 −0.224049
\(671\) −5.86406e29 −1.22352
\(672\) −3.56414e29 −0.732111
\(673\) 7.53001e29 1.52278 0.761390 0.648294i \(-0.224517\pi\)
0.761390 + 0.648294i \(0.224517\pi\)
\(674\) 4.41005e28 0.0878041
\(675\) −4.73466e27 −0.00928109
\(676\) 4.84547e29 0.935181
\(677\) −8.12052e29 −1.54313 −0.771565 0.636150i \(-0.780526\pi\)
−0.771565 + 0.636150i \(0.780526\pi\)
\(678\) 1.83981e28 0.0344239
\(679\) −6.20819e29 −1.14375
\(680\) 7.82130e28 0.141885
\(681\) 7.01320e29 1.25277
\(682\) 5.18482e28 0.0912007
\(683\) 4.69973e29 0.814058 0.407029 0.913415i \(-0.366565\pi\)
0.407029 + 0.913415i \(0.366565\pi\)
\(684\) 9.79650e28 0.167102
\(685\) −8.67346e29 −1.45694
\(686\) −1.16608e29 −0.192897
\(687\) −8.89896e29 −1.44975
\(688\) −7.51789e29 −1.20619
\(689\) −1.64329e29 −0.259664
\(690\) −5.93003e28 −0.0922871
\(691\) 3.58806e29 0.549971 0.274985 0.961448i \(-0.411327\pi\)
0.274985 + 0.961448i \(0.411327\pi\)
\(692\) 8.42962e29 1.27261
\(693\) 4.46754e29 0.664308
\(694\) −9.31496e28 −0.136429
\(695\) 9.68616e29 1.39737
\(696\) 6.48845e29 0.922027
\(697\) −6.29466e28 −0.0881106
\(698\) 1.95222e29 0.269183
\(699\) −5.84501e29 −0.793917
\(700\) −1.31601e28 −0.0176088
\(701\) −7.33110e29 −0.966339 −0.483170 0.875527i \(-0.660515\pi\)
−0.483170 + 0.875527i \(0.660515\pi\)
\(702\) 1.29237e28 0.0167821
\(703\) −1.75774e29 −0.224865
\(704\) 6.73133e29 0.848376
\(705\) −4.09771e29 −0.508810
\(706\) −1.97076e29 −0.241093
\(707\) 7.69629e29 0.927636
\(708\) −1.55085e30 −1.84171
\(709\) 1.20909e30 1.41473 0.707365 0.706848i \(-0.249884\pi\)
0.707365 + 0.706848i \(0.249884\pi\)
\(710\) 3.51067e28 0.0404741
\(711\) −3.14788e29 −0.357592
\(712\) −5.97131e29 −0.668390
\(713\) −1.40346e29 −0.154796
\(714\) −8.69936e28 −0.0945488
\(715\) 1.65270e29 0.177003
\(716\) −9.60277e29 −1.01347
\(717\) 3.52379e29 0.366488
\(718\) 1.97424e28 0.0202345
\(719\) −5.25189e29 −0.530472 −0.265236 0.964183i \(-0.585450\pi\)
−0.265236 + 0.964183i \(0.585450\pi\)
\(720\) 5.16003e29 0.513642
\(721\) 4.52972e29 0.444377
\(722\) 1.87624e29 0.181404
\(723\) 1.04223e30 0.993140
\(724\) 5.81356e28 0.0545993
\(725\) 3.61782e28 0.0334886
\(726\) 5.83532e28 0.0532390
\(727\) 7.23318e29 0.650456 0.325228 0.945636i \(-0.394559\pi\)
0.325228 + 0.945636i \(0.394559\pi\)
\(728\) 7.33223e28 0.0649915
\(729\) −8.46052e28 −0.0739193
\(730\) 2.69776e29 0.232335
\(731\) −5.90940e29 −0.501662
\(732\) 1.60658e30 1.34442
\(733\) −2.11409e30 −1.74394 −0.871969 0.489560i \(-0.837157\pi\)
−0.871969 + 0.489560i \(0.837157\pi\)
\(734\) −3.27097e29 −0.265992
\(735\) −8.75506e28 −0.0701846
\(736\) 2.65955e29 0.210180
\(737\) −1.60666e30 −1.25174
\(738\) 3.64702e28 0.0280122
\(739\) −7.42069e29 −0.561924 −0.280962 0.959719i \(-0.590653\pi\)
−0.280962 + 0.959719i \(0.590653\pi\)
\(740\) −9.67311e29 −0.722159
\(741\) −8.22782e28 −0.0605611
\(742\) 4.50878e29 0.327204
\(743\) 1.69968e30 1.21614 0.608071 0.793882i \(-0.291943\pi\)
0.608071 + 0.793882i \(0.291943\pi\)
\(744\) −2.89948e29 −0.204552
\(745\) 1.06752e30 0.742569
\(746\) −1.10297e29 −0.0756494
\(747\) 3.00339e29 0.203117
\(748\) 5.82362e29 0.388353
\(749\) −8.61862e29 −0.566733
\(750\) −3.89747e29 −0.252720
\(751\) 5.90225e29 0.377397 0.188698 0.982035i \(-0.439573\pi\)
0.188698 + 0.982035i \(0.439573\pi\)
\(752\) 5.70661e29 0.359824
\(753\) −8.55430e29 −0.531909
\(754\) −9.87515e28 −0.0605542
\(755\) 1.23443e30 0.746490
\(756\) 8.61095e29 0.513537
\(757\) 1.33308e30 0.784058 0.392029 0.919953i \(-0.371773\pi\)
0.392029 + 0.919953i \(0.371773\pi\)
\(758\) −2.05853e28 −0.0119407
\(759\) −9.01264e29 −0.515601
\(760\) −2.02966e29 −0.114520
\(761\) −7.86217e29 −0.437526 −0.218763 0.975778i \(-0.570202\pi\)
−0.218763 + 0.975778i \(0.570202\pi\)
\(762\) 6.07106e28 0.0333225
\(763\) −1.32412e30 −0.716837
\(764\) −1.78535e30 −0.953329
\(765\) 4.05601e29 0.213626
\(766\) 3.98665e29 0.207112
\(767\) 4.81786e29 0.246890
\(768\) −1.56392e30 −0.790537
\(769\) −1.65083e30 −0.823142 −0.411571 0.911378i \(-0.635020\pi\)
−0.411571 + 0.911378i \(0.635020\pi\)
\(770\) −4.53460e29 −0.223042
\(771\) −2.02644e29 −0.0983247
\(772\) −1.73929e29 −0.0832510
\(773\) 3.77930e30 1.78454 0.892271 0.451499i \(-0.149111\pi\)
0.892271 + 0.451499i \(0.149111\pi\)
\(774\) 3.42381e29 0.159488
\(775\) −1.61668e28 −0.00742946
\(776\) 9.57056e29 0.433899
\(777\) 2.19612e30 0.982278
\(778\) −4.70054e29 −0.207425
\(779\) 1.63349e29 0.0711169
\(780\) −4.52790e29 −0.194493
\(781\) 5.33563e29 0.226126
\(782\) 6.49144e28 0.0271438
\(783\) −2.36723e30 −0.976655
\(784\) 1.21926e29 0.0496337
\(785\) 1.37555e30 0.552516
\(786\) −5.14488e29 −0.203910
\(787\) −3.58219e30 −1.40092 −0.700461 0.713691i \(-0.747022\pi\)
−0.700461 + 0.713691i \(0.747022\pi\)
\(788\) 1.40795e30 0.543327
\(789\) 4.38169e30 1.66853
\(790\) 3.19514e29 0.120062
\(791\) −3.80821e29 −0.141211
\(792\) −6.88717e29 −0.252015
\(793\) −4.99099e29 −0.180226
\(794\) −3.48564e29 −0.124213
\(795\) −5.68331e30 −1.99870
\(796\) 2.50854e30 0.870631
\(797\) −4.45901e30 −1.52731 −0.763654 0.645626i \(-0.776596\pi\)
−0.763654 + 0.645626i \(0.776596\pi\)
\(798\) 2.25752e29 0.0763134
\(799\) 4.48565e29 0.149653
\(800\) 3.06360e28 0.0100876
\(801\) −3.09664e30 −1.00635
\(802\) 1.87591e29 0.0601702
\(803\) 4.10015e30 1.29803
\(804\) 4.40178e30 1.37543
\(805\) 1.22746e30 0.378572
\(806\) 4.41288e28 0.0134340
\(807\) 4.61229e30 1.38594
\(808\) −1.18646e30 −0.351912
\(809\) 3.09156e30 0.905144 0.452572 0.891728i \(-0.350507\pi\)
0.452572 + 0.891728i \(0.350507\pi\)
\(810\) 8.47291e29 0.244872
\(811\) −9.85711e29 −0.281210 −0.140605 0.990066i \(-0.544905\pi\)
−0.140605 + 0.990066i \(0.544905\pi\)
\(812\) −6.57974e30 −1.85298
\(813\) −3.17090e30 −0.881518
\(814\) 6.05400e29 0.166144
\(815\) 1.87948e30 0.509194
\(816\) −1.52710e30 −0.408432
\(817\) 1.53351e30 0.404907
\(818\) 1.28232e30 0.334262
\(819\) 3.80239e29 0.0978533
\(820\) 8.98935e29 0.228393
\(821\) −5.81930e30 −1.45971 −0.729856 0.683601i \(-0.760413\pi\)
−0.729856 + 0.683601i \(0.760413\pi\)
\(822\) −1.48721e30 −0.368314
\(823\) 1.82848e30 0.447086 0.223543 0.974694i \(-0.428238\pi\)
0.223543 + 0.974694i \(0.428238\pi\)
\(824\) −6.98303e29 −0.168581
\(825\) −1.03819e29 −0.0247463
\(826\) −1.32191e30 −0.311107
\(827\) −3.80997e30 −0.885347 −0.442673 0.896683i \(-0.645970\pi\)
−0.442673 + 0.896683i \(0.645970\pi\)
\(828\) 9.13327e29 0.209560
\(829\) 9.24247e29 0.209395 0.104697 0.994504i \(-0.466613\pi\)
0.104697 + 0.994504i \(0.466613\pi\)
\(830\) −3.04848e29 −0.0681966
\(831\) 7.88112e30 1.74091
\(832\) 5.72914e29 0.124967
\(833\) 9.58392e28 0.0206429
\(834\) 1.66086e30 0.353255
\(835\) −4.09904e30 −0.860942
\(836\) −1.51125e30 −0.313452
\(837\) 1.05784e30 0.216671
\(838\) −1.41959e30 −0.287144
\(839\) 2.18057e30 0.435582 0.217791 0.975995i \(-0.430115\pi\)
0.217791 + 0.975995i \(0.430115\pi\)
\(840\) 2.53585e30 0.500255
\(841\) 1.29554e31 2.52403
\(842\) −4.32418e29 −0.0832007
\(843\) −2.23815e30 −0.425304
\(844\) −7.06668e30 −1.32623
\(845\) −5.20605e30 −0.964968
\(846\) −2.59891e29 −0.0475776
\(847\) −1.20785e30 −0.218393
\(848\) 7.91477e30 1.41345
\(849\) −9.75655e30 −1.72094
\(850\) 7.47765e27 0.00130277
\(851\) −1.63874e30 −0.282000
\(852\) −1.46181e30 −0.248470
\(853\) −4.27754e30 −0.718173 −0.359087 0.933304i \(-0.616912\pi\)
−0.359087 + 0.933304i \(0.616912\pi\)
\(854\) 1.36941e30 0.227104
\(855\) −1.05255e30 −0.172424
\(856\) 1.32865e30 0.214998
\(857\) −1.76322e29 −0.0281843 −0.0140922 0.999901i \(-0.504486\pi\)
−0.0140922 + 0.999901i \(0.504486\pi\)
\(858\) 2.83383e29 0.0447463
\(859\) 4.74009e30 0.739365 0.369682 0.929158i \(-0.379467\pi\)
0.369682 + 0.929158i \(0.379467\pi\)
\(860\) 8.43916e30 1.30037
\(861\) −2.04088e30 −0.310659
\(862\) 2.07136e30 0.311479
\(863\) 8.10824e29 0.120452 0.0602259 0.998185i \(-0.480818\pi\)
0.0602259 + 0.998185i \(0.480818\pi\)
\(864\) −2.00459e30 −0.294192
\(865\) −9.05691e30 −1.31314
\(866\) −1.21854e30 −0.174543
\(867\) 7.70171e30 1.08990
\(868\) 2.94027e30 0.411084
\(869\) 4.85607e30 0.670775
\(870\) −3.41532e30 −0.466100
\(871\) −1.36745e30 −0.184383
\(872\) 2.04127e30 0.271942
\(873\) 4.96315e30 0.653293
\(874\) −1.68455e29 −0.0219086
\(875\) 8.06736e30 1.03669
\(876\) −1.12332e31 −1.42630
\(877\) 1.55255e30 0.194782 0.0973912 0.995246i \(-0.468950\pi\)
0.0973912 + 0.995246i \(0.468950\pi\)
\(878\) −1.30532e30 −0.161817
\(879\) −6.29641e30 −0.771275
\(880\) −7.96009e30 −0.963496
\(881\) −5.75722e30 −0.688598 −0.344299 0.938860i \(-0.611883\pi\)
−0.344299 + 0.938860i \(0.611883\pi\)
\(882\) −5.55276e28 −0.00656280
\(883\) −1.29134e31 −1.50818 −0.754088 0.656774i \(-0.771921\pi\)
−0.754088 + 0.656774i \(0.771921\pi\)
\(884\) 4.95657e29 0.0572048
\(885\) 1.66626e31 1.90037
\(886\) 1.32822e30 0.149698
\(887\) −4.22752e30 −0.470856 −0.235428 0.971892i \(-0.575649\pi\)
−0.235428 + 0.971892i \(0.575649\pi\)
\(888\) −3.38554e30 −0.372642
\(889\) −1.25665e30 −0.136693
\(890\) 3.14312e30 0.337883
\(891\) 1.28774e31 1.36808
\(892\) 9.51411e30 0.998935
\(893\) −1.16404e30 −0.120789
\(894\) 1.83045e30 0.187722
\(895\) 1.03174e31 1.04575
\(896\) −7.37317e30 −0.738618
\(897\) −7.67079e29 −0.0759486
\(898\) 3.61992e28 0.00354240
\(899\) −8.08306e30 −0.781806
\(900\) 1.05208e29 0.0100578
\(901\) 6.22137e30 0.587862
\(902\) −5.62606e29 −0.0525455
\(903\) −1.91597e31 −1.76875
\(904\) 5.87074e29 0.0535704
\(905\) −6.24617e29 −0.0563383
\(906\) 2.11664e30 0.188713
\(907\) 1.34786e31 1.18787 0.593935 0.804513i \(-0.297574\pi\)
0.593935 + 0.804513i \(0.297574\pi\)
\(908\) 1.09637e31 0.955113
\(909\) −6.15281e30 −0.529850
\(910\) −3.85946e29 −0.0328543
\(911\) −1.28886e31 −1.08458 −0.542292 0.840190i \(-0.682443\pi\)
−0.542292 + 0.840190i \(0.682443\pi\)
\(912\) 3.96287e30 0.329658
\(913\) −4.63317e30 −0.381009
\(914\) −3.33860e30 −0.271413
\(915\) −1.72613e31 −1.38724
\(916\) −1.39117e31 −1.10529
\(917\) 1.06494e31 0.836463
\(918\) −4.89281e29 −0.0379936
\(919\) 1.25018e30 0.0959753 0.0479876 0.998848i \(-0.484719\pi\)
0.0479876 + 0.998848i \(0.484719\pi\)
\(920\) −1.89225e30 −0.143617
\(921\) 2.80864e31 2.10751
\(922\) −2.95239e30 −0.219028
\(923\) 4.54123e29 0.0333086
\(924\) 1.88816e31 1.36925
\(925\) −1.88770e29 −0.0135346
\(926\) 1.64967e30 0.116945
\(927\) −3.62130e30 −0.253821
\(928\) 1.53173e31 1.06152
\(929\) −1.41245e31 −0.967850 −0.483925 0.875109i \(-0.660789\pi\)
−0.483925 + 0.875109i \(0.660789\pi\)
\(930\) 1.52620e30 0.103404
\(931\) −2.48706e29 −0.0166615
\(932\) −9.13746e30 −0.605283
\(933\) 5.21360e30 0.341492
\(934\) −3.24455e30 −0.210142
\(935\) −6.25699e30 −0.400722
\(936\) −5.86177e29 −0.0371221
\(937\) −7.12851e30 −0.446409 −0.223204 0.974772i \(-0.571652\pi\)
−0.223204 + 0.974772i \(0.571652\pi\)
\(938\) 3.75196e30 0.232342
\(939\) 1.12632e30 0.0689721
\(940\) −6.40592e30 −0.387917
\(941\) −1.07254e29 −0.00642275 −0.00321138 0.999995i \(-0.501022\pi\)
−0.00321138 + 0.999995i \(0.501022\pi\)
\(942\) 2.35861e30 0.139676
\(943\) 1.52290e30 0.0891864
\(944\) −2.32049e31 −1.34392
\(945\) −9.25173e30 −0.529894
\(946\) −5.28172e30 −0.299170
\(947\) 2.92935e31 1.64095 0.820477 0.571680i \(-0.193708\pi\)
0.820477 + 0.571680i \(0.193708\pi\)
\(948\) −1.33042e31 −0.737058
\(949\) 3.48969e30 0.191202
\(950\) −1.94048e28 −0.00105150
\(951\) 4.11989e30 0.220796
\(952\) −2.77593e30 −0.147137
\(953\) 3.04320e31 1.59535 0.797675 0.603088i \(-0.206063\pi\)
0.797675 + 0.603088i \(0.206063\pi\)
\(954\) −3.60456e30 −0.186893
\(955\) 1.91821e31 0.983694
\(956\) 5.50872e30 0.279410
\(957\) −5.19071e31 −2.60406
\(958\) 3.38034e30 0.167735
\(959\) 3.07838e31 1.51087
\(960\) 1.98142e31 0.961899
\(961\) −1.72134e31 −0.826556
\(962\) 5.15264e29 0.0244733
\(963\) 6.89017e30 0.323709
\(964\) 1.62931e31 0.757171
\(965\) 1.86871e30 0.0859026
\(966\) 2.10468e30 0.0957032
\(967\) −3.78485e31 −1.70244 −0.851218 0.524813i \(-0.824135\pi\)
−0.851218 + 0.524813i \(0.824135\pi\)
\(968\) 1.86203e30 0.0828504
\(969\) 3.11500e30 0.137106
\(970\) −5.03765e30 −0.219344
\(971\) −1.62334e31 −0.699212 −0.349606 0.936897i \(-0.613684\pi\)
−0.349606 + 0.936897i \(0.613684\pi\)
\(972\) −2.35532e31 −1.00358
\(973\) −3.43780e31 −1.44909
\(974\) −1.36878e30 −0.0570776
\(975\) −8.83618e28 −0.00364516
\(976\) 2.40387e31 0.981043
\(977\) 2.98858e30 0.120662 0.0603312 0.998178i \(-0.480784\pi\)
0.0603312 + 0.998178i \(0.480784\pi\)
\(978\) 3.22269e30 0.128724
\(979\) 4.77701e31 1.88772
\(980\) −1.36867e30 −0.0535088
\(981\) 1.05857e31 0.409445
\(982\) 7.48330e30 0.286367
\(983\) −2.41371e31 −0.913846 −0.456923 0.889506i \(-0.651049\pi\)
−0.456923 + 0.889506i \(0.651049\pi\)
\(984\) 3.14623e30 0.117853
\(985\) −1.51272e31 −0.560632
\(986\) 3.73866e30 0.137091
\(987\) 1.45436e31 0.527643
\(988\) −1.28625e30 −0.0461718
\(989\) 1.42969e31 0.507786
\(990\) 3.62520e30 0.127398
\(991\) −2.29436e31 −0.797790 −0.398895 0.916997i \(-0.630606\pi\)
−0.398895 + 0.916997i \(0.630606\pi\)
\(992\) −6.84481e30 −0.235499
\(993\) 3.24964e31 1.10629
\(994\) −1.24600e30 −0.0419723
\(995\) −2.69521e31 −0.898361
\(996\) 1.26935e31 0.418658
\(997\) 3.55036e31 1.15871 0.579354 0.815076i \(-0.303305\pi\)
0.579354 + 0.815076i \(0.303305\pi\)
\(998\) −1.10738e31 −0.357624
\(999\) 1.23517e31 0.394719
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 1.22.a.a.1.1 1
3.2 odd 2 9.22.a.c.1.1 1
4.3 odd 2 16.22.a.c.1.1 1
5.2 odd 4 25.22.b.a.24.1 2
5.3 odd 4 25.22.b.a.24.2 2
5.4 even 2 25.22.a.a.1.1 1
7.6 odd 2 49.22.a.a.1.1 1
8.3 odd 2 64.22.a.a.1.1 1
8.5 even 2 64.22.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.22.a.a.1.1 1 1.1 even 1 trivial
9.22.a.c.1.1 1 3.2 odd 2
16.22.a.c.1.1 1 4.3 odd 2
25.22.a.a.1.1 1 5.4 even 2
25.22.b.a.24.1 2 5.2 odd 4
25.22.b.a.24.2 2 5.3 odd 4
49.22.a.a.1.1 1 7.6 odd 2
64.22.a.a.1.1 1 8.3 odd 2
64.22.a.g.1.1 1 8.5 even 2