Properties

Label 43.8.a.a.1.10
Level $43$
Weight $8$
Character 43.1
Self dual yes
Analytic conductor $13.433$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.4325560958\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + 209758592 x^{4} + 3410917248 x^{3} - 14180732672 x^{2} - 60918607872 x + 238240894976\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-17.2185\) of defining polynomial
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+15.2185 q^{2} -9.20709 q^{3} +103.603 q^{4} -537.911 q^{5} -140.118 q^{6} +1471.62 q^{7} -371.288 q^{8} -2102.23 q^{9} +O(q^{10})\) \(q+15.2185 q^{2} -9.20709 q^{3} +103.603 q^{4} -537.911 q^{5} -140.118 q^{6} +1471.62 q^{7} -371.288 q^{8} -2102.23 q^{9} -8186.21 q^{10} -3353.32 q^{11} -953.881 q^{12} -12401.8 q^{13} +22395.8 q^{14} +4952.60 q^{15} -18911.6 q^{16} +20775.2 q^{17} -31992.8 q^{18} -1067.31 q^{19} -55729.2 q^{20} -13549.3 q^{21} -51032.5 q^{22} -17801.1 q^{23} +3418.48 q^{24} +211224. q^{25} -188736. q^{26} +39491.3 q^{27} +152464. q^{28} +99935.2 q^{29} +75371.2 q^{30} -30140.3 q^{31} -240282. q^{32} +30874.3 q^{33} +316168. q^{34} -791601. q^{35} -217797. q^{36} -174672. q^{37} -16242.9 q^{38} +114184. q^{39} +199720. q^{40} -45042.7 q^{41} -206201. q^{42} +79507.0 q^{43} -347414. q^{44} +1.13081e6 q^{45} -270907. q^{46} -319582. q^{47} +174121. q^{48} +1.34212e6 q^{49} +3.21451e6 q^{50} -191279. q^{51} -1.28486e6 q^{52} +72727.4 q^{53} +600999. q^{54} +1.80379e6 q^{55} -546394. q^{56} +9826.85 q^{57} +1.52086e6 q^{58} -2.67444e6 q^{59} +513104. q^{60} -2.37204e6 q^{61} -458690. q^{62} -3.09368e6 q^{63} -1.23604e6 q^{64} +6.67106e6 q^{65} +469861. q^{66} +3.70267e6 q^{67} +2.15237e6 q^{68} +163897. q^{69} -1.20470e7 q^{70} -4.04493e6 q^{71} +780532. q^{72} +862213. q^{73} -2.65824e6 q^{74} -1.94476e6 q^{75} -110577. q^{76} -4.93481e6 q^{77} +1.73771e6 q^{78} -3.18079e6 q^{79} +1.01728e7 q^{80} +4.23398e6 q^{81} -685483. q^{82} -2.05380e6 q^{83} -1.40375e6 q^{84} -1.11752e7 q^{85} +1.20998e6 q^{86} -920113. q^{87} +1.24505e6 q^{88} -1.05466e7 q^{89} +1.72093e7 q^{90} -1.82507e7 q^{91} -1.84425e6 q^{92} +277505. q^{93} -4.86356e6 q^{94} +574120. q^{95} +2.21230e6 q^{96} +849791. q^{97} +2.04251e7 q^{98} +7.04945e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 24q^{2} - 68q^{3} + 602q^{4} - 752q^{5} - 681q^{6} - 12q^{7} - 3810q^{8} + 2721q^{9} + O(q^{10}) \) \( 11q - 24q^{2} - 68q^{3} + 602q^{4} - 752q^{5} - 681q^{6} - 12q^{7} - 3810q^{8} + 2721q^{9} - 1333q^{10} + 1333q^{11} + 5089q^{12} - 17967q^{13} - 22352q^{14} - 49504q^{15} - 34406q^{16} - 63095q^{17} - 165931q^{18} - 54524q^{19} - 280995q^{20} - 139788q^{21} - 289358q^{22} - 138139q^{23} - 429583q^{24} + 3455q^{25} - 132946q^{26} - 240356q^{27} - 12704q^{28} - 308658q^{29} + 421284q^{30} - 209523q^{31} - 644934q^{32} + 96814q^{33} + 762435q^{34} - 578892q^{35} + 426161q^{36} - 298472q^{37} - 369707q^{38} + 292298q^{39} + 2633173q^{40} - 1346735q^{41} + 1173266q^{42} + 874577q^{43} + 3134292q^{44} + 1893784q^{45} + 3588111q^{46} + 499284q^{47} + 5647533q^{48} + 2544563q^{49} + 3049745q^{50} + 1258424q^{51} + 983088q^{52} - 2210495q^{53} + 6789698q^{54} - 1855072q^{55} - 469976q^{56} - 1238444q^{57} + 4397067q^{58} - 5824216q^{59} - 2889372q^{60} - 4453034q^{61} + 1002789q^{62} - 6240564q^{63} + 4757538q^{64} - 2162872q^{65} - 258940q^{66} - 6859513q^{67} - 9397005q^{68} - 10040030q^{69} + 845078q^{70} - 10726554q^{71} + 1199517q^{72} - 4456898q^{73} + 1046637q^{74} - 3349114q^{75} + 5861267q^{76} - 17019816q^{77} + 1999122q^{78} - 15541320q^{79} - 15680911q^{80} - 12976697q^{81} + 20233655q^{82} - 11146767q^{83} + 12348278q^{84} - 12471976q^{85} - 1908168q^{86} - 18648900q^{87} - 24463544q^{88} - 13531356q^{89} + 20858990q^{90} - 19746448q^{91} - 26023161q^{92} - 21903110q^{93} + 20288857q^{94} - 12291624q^{95} - 13954503q^{96} - 10999901q^{97} + 29909168q^{98} + 29396057q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.2185 1.34514 0.672569 0.740034i \(-0.265191\pi\)
0.672569 + 0.740034i \(0.265191\pi\)
\(3\) −9.20709 −0.196878 −0.0984392 0.995143i \(-0.531385\pi\)
−0.0984392 + 0.995143i \(0.531385\pi\)
\(4\) 103.603 0.809397
\(5\) −537.911 −1.92449 −0.962245 0.272184i \(-0.912254\pi\)
−0.962245 + 0.272184i \(0.912254\pi\)
\(6\) −140.118 −0.264829
\(7\) 1471.62 1.62163 0.810816 0.585301i \(-0.199024\pi\)
0.810816 + 0.585301i \(0.199024\pi\)
\(8\) −371.288 −0.256387
\(9\) −2102.23 −0.961239
\(10\) −8186.21 −2.58871
\(11\) −3353.32 −0.759628 −0.379814 0.925063i \(-0.624012\pi\)
−0.379814 + 0.925063i \(0.624012\pi\)
\(12\) −953.881 −0.159353
\(13\) −12401.8 −1.56560 −0.782802 0.622270i \(-0.786210\pi\)
−0.782802 + 0.622270i \(0.786210\pi\)
\(14\) 22395.8 2.18132
\(15\) 4952.60 0.378891
\(16\) −18911.6 −1.15427
\(17\) 20775.2 1.02559 0.512796 0.858511i \(-0.328610\pi\)
0.512796 + 0.858511i \(0.328610\pi\)
\(18\) −31992.8 −1.29300
\(19\) −1067.31 −0.0356988 −0.0178494 0.999841i \(-0.505682\pi\)
−0.0178494 + 0.999841i \(0.505682\pi\)
\(20\) −55729.2 −1.55768
\(21\) −13549.3 −0.319264
\(22\) −51032.5 −1.02180
\(23\) −17801.1 −0.305071 −0.152535 0.988298i \(-0.548744\pi\)
−0.152535 + 0.988298i \(0.548744\pi\)
\(24\) 3418.48 0.0504771
\(25\) 211224. 2.70366
\(26\) −188736. −2.10596
\(27\) 39491.3 0.386126
\(28\) 152464. 1.31254
\(29\) 99935.2 0.760897 0.380448 0.924802i \(-0.375770\pi\)
0.380448 + 0.924802i \(0.375770\pi\)
\(30\) 75371.2 0.509660
\(31\) −30140.3 −0.181711 −0.0908556 0.995864i \(-0.528960\pi\)
−0.0908556 + 0.995864i \(0.528960\pi\)
\(32\) −240282. −1.29627
\(33\) 30874.3 0.149554
\(34\) 316168. 1.37956
\(35\) −791601. −3.12081
\(36\) −217797. −0.778024
\(37\) −174672. −0.566913 −0.283457 0.958985i \(-0.591481\pi\)
−0.283457 + 0.958985i \(0.591481\pi\)
\(38\) −16242.9 −0.0480199
\(39\) 114184. 0.308234
\(40\) 199720. 0.493414
\(41\) −45042.7 −0.102066 −0.0510330 0.998697i \(-0.516251\pi\)
−0.0510330 + 0.998697i \(0.516251\pi\)
\(42\) −206201. −0.429455
\(43\) 79507.0 0.152499
\(44\) −347414. −0.614841
\(45\) 1.13081e6 1.84989
\(46\) −270907. −0.410362
\(47\) −319582. −0.448993 −0.224497 0.974475i \(-0.572074\pi\)
−0.224497 + 0.974475i \(0.572074\pi\)
\(48\) 174121. 0.227252
\(49\) 1.34212e6 1.62969
\(50\) 3.21451e6 3.63680
\(51\) −191279. −0.201917
\(52\) −1.28486e6 −1.26720
\(53\) 72727.4 0.0671016 0.0335508 0.999437i \(-0.489318\pi\)
0.0335508 + 0.999437i \(0.489318\pi\)
\(54\) 600999. 0.519392
\(55\) 1.80379e6 1.46190
\(56\) −546394. −0.415765
\(57\) 9826.85 0.00702833
\(58\) 1.52086e6 1.02351
\(59\) −2.67444e6 −1.69531 −0.847657 0.530544i \(-0.821988\pi\)
−0.847657 + 0.530544i \(0.821988\pi\)
\(60\) 513104. 0.306673
\(61\) −2.37204e6 −1.33804 −0.669019 0.743246i \(-0.733285\pi\)
−0.669019 + 0.743246i \(0.733285\pi\)
\(62\) −458690. −0.244427
\(63\) −3.09368e6 −1.55878
\(64\) −1.23604e6 −0.589390
\(65\) 6.67106e6 3.01299
\(66\) 469861. 0.201171
\(67\) 3.70267e6 1.50402 0.752009 0.659153i \(-0.229085\pi\)
0.752009 + 0.659153i \(0.229085\pi\)
\(68\) 2.15237e6 0.830111
\(69\) 163897. 0.0600618
\(70\) −1.20470e7 −4.19793
\(71\) −4.04493e6 −1.34124 −0.670620 0.741801i \(-0.733972\pi\)
−0.670620 + 0.741801i \(0.733972\pi\)
\(72\) 780532. 0.246449
\(73\) 862213. 0.259409 0.129704 0.991553i \(-0.458597\pi\)
0.129704 + 0.991553i \(0.458597\pi\)
\(74\) −2.65824e6 −0.762577
\(75\) −1.94476e6 −0.532293
\(76\) −110577. −0.0288945
\(77\) −4.93481e6 −1.23184
\(78\) 1.73771e6 0.414617
\(79\) −3.18079e6 −0.725839 −0.362920 0.931820i \(-0.618220\pi\)
−0.362920 + 0.931820i \(0.618220\pi\)
\(80\) 1.01728e7 2.22139
\(81\) 4.23398e6 0.885219
\(82\) −685483. −0.137293
\(83\) −2.05380e6 −0.394262 −0.197131 0.980377i \(-0.563162\pi\)
−0.197131 + 0.980377i \(0.563162\pi\)
\(84\) −1.40375e6 −0.258412
\(85\) −1.11752e7 −1.97374
\(86\) 1.20998e6 0.205132
\(87\) −920113. −0.149804
\(88\) 1.24505e6 0.194759
\(89\) −1.05466e7 −1.58580 −0.792899 0.609353i \(-0.791429\pi\)
−0.792899 + 0.609353i \(0.791429\pi\)
\(90\) 1.72093e7 2.48836
\(91\) −1.82507e7 −2.53883
\(92\) −1.84425e6 −0.246923
\(93\) 277505. 0.0357750
\(94\) −4.86356e6 −0.603958
\(95\) 574120. 0.0687021
\(96\) 2.21230e6 0.255208
\(97\) 849791. 0.0945390 0.0472695 0.998882i \(-0.484948\pi\)
0.0472695 + 0.998882i \(0.484948\pi\)
\(98\) 2.04251e7 2.19216
\(99\) 7.04945e6 0.730184
\(100\) 2.18834e7 2.18834
\(101\) 106287. 0.0102649 0.00513244 0.999987i \(-0.498366\pi\)
0.00513244 + 0.999987i \(0.498366\pi\)
\(102\) −2.91099e6 −0.271606
\(103\) 9.84740e6 0.887956 0.443978 0.896038i \(-0.353567\pi\)
0.443978 + 0.896038i \(0.353567\pi\)
\(104\) 4.60463e6 0.401401
\(105\) 7.28834e6 0.614421
\(106\) 1.10680e6 0.0902609
\(107\) −7.20095e6 −0.568260 −0.284130 0.958786i \(-0.591705\pi\)
−0.284130 + 0.958786i \(0.591705\pi\)
\(108\) 4.09142e6 0.312529
\(109\) 5.59758e6 0.414007 0.207003 0.978340i \(-0.433629\pi\)
0.207003 + 0.978340i \(0.433629\pi\)
\(110\) 2.74510e7 1.96645
\(111\) 1.60822e6 0.111613
\(112\) −2.78307e7 −1.87181
\(113\) −2.45481e7 −1.60046 −0.800229 0.599695i \(-0.795289\pi\)
−0.800229 + 0.599695i \(0.795289\pi\)
\(114\) 149550. 0.00945408
\(115\) 9.57543e6 0.587105
\(116\) 1.03536e7 0.615868
\(117\) 2.60714e7 1.50492
\(118\) −4.07009e7 −2.28043
\(119\) 3.05732e7 1.66313
\(120\) −1.83884e6 −0.0971426
\(121\) −8.24241e6 −0.422966
\(122\) −3.60990e7 −1.79985
\(123\) 414713. 0.0200946
\(124\) −3.12262e6 −0.147077
\(125\) −7.15953e7 −3.27868
\(126\) −4.70812e7 −2.09677
\(127\) 3.30101e7 1.42999 0.714995 0.699129i \(-0.246429\pi\)
0.714995 + 0.699129i \(0.246429\pi\)
\(128\) 1.19454e7 0.503460
\(129\) −732028. −0.0300237
\(130\) 1.01524e8 4.05289
\(131\) −2.31631e7 −0.900216 −0.450108 0.892974i \(-0.648615\pi\)
−0.450108 + 0.892974i \(0.648615\pi\)
\(132\) 3.19867e6 0.121049
\(133\) −1.57068e6 −0.0578904
\(134\) 5.63490e7 2.02311
\(135\) −2.12428e7 −0.743095
\(136\) −7.71359e6 −0.262948
\(137\) 4.28026e7 1.42216 0.711079 0.703112i \(-0.248207\pi\)
0.711079 + 0.703112i \(0.248207\pi\)
\(138\) 2.49426e6 0.0807915
\(139\) 1.99694e6 0.0630688 0.0315344 0.999503i \(-0.489961\pi\)
0.0315344 + 0.999503i \(0.489961\pi\)
\(140\) −8.20121e7 −2.52598
\(141\) 2.94242e6 0.0883971
\(142\) −6.15577e7 −1.80415
\(143\) 4.15871e7 1.18928
\(144\) 3.97566e7 1.10953
\(145\) −5.37563e7 −1.46434
\(146\) 1.31216e7 0.348941
\(147\) −1.23570e7 −0.320851
\(148\) −1.80965e7 −0.458858
\(149\) 4.86799e7 1.20558 0.602792 0.797898i \(-0.294055\pi\)
0.602792 + 0.797898i \(0.294055\pi\)
\(150\) −2.95963e7 −0.716008
\(151\) 2.21291e7 0.523051 0.261525 0.965197i \(-0.415775\pi\)
0.261525 + 0.965197i \(0.415775\pi\)
\(152\) 396280. 0.00915272
\(153\) −4.36743e7 −0.985838
\(154\) −7.51004e7 −1.65699
\(155\) 1.62128e7 0.349702
\(156\) 1.18298e7 0.249484
\(157\) −1.06571e7 −0.219782 −0.109891 0.993944i \(-0.535050\pi\)
−0.109891 + 0.993944i \(0.535050\pi\)
\(158\) −4.84069e7 −0.976354
\(159\) −669608. −0.0132109
\(160\) 1.29250e8 2.49466
\(161\) −2.61965e7 −0.494712
\(162\) 6.44348e7 1.19074
\(163\) 1.16225e7 0.210205 0.105103 0.994461i \(-0.466483\pi\)
0.105103 + 0.994461i \(0.466483\pi\)
\(164\) −4.66656e6 −0.0826120
\(165\) −1.66077e7 −0.287816
\(166\) −3.12557e7 −0.530336
\(167\) −1.81744e7 −0.301962 −0.150981 0.988537i \(-0.548243\pi\)
−0.150981 + 0.988537i \(0.548243\pi\)
\(168\) 5.03071e6 0.0818552
\(169\) 9.10556e7 1.45112
\(170\) −1.70070e8 −2.65495
\(171\) 2.24374e6 0.0343151
\(172\) 8.23715e6 0.123432
\(173\) −8.49183e7 −1.24692 −0.623462 0.781854i \(-0.714274\pi\)
−0.623462 + 0.781854i \(0.714274\pi\)
\(174\) −1.40027e7 −0.201507
\(175\) 3.10841e8 4.38435
\(176\) 6.34167e7 0.876818
\(177\) 2.46238e7 0.333771
\(178\) −1.60504e8 −2.13312
\(179\) −1.24796e8 −1.62636 −0.813179 0.582014i \(-0.802265\pi\)
−0.813179 + 0.582014i \(0.802265\pi\)
\(180\) 1.17155e8 1.49730
\(181\) 1.02160e7 0.128058 0.0640289 0.997948i \(-0.479605\pi\)
0.0640289 + 0.997948i \(0.479605\pi\)
\(182\) −2.77748e8 −3.41508
\(183\) 2.18396e7 0.263431
\(184\) 6.60935e6 0.0782161
\(185\) 9.39579e7 1.09102
\(186\) 4.22321e6 0.0481224
\(187\) −6.96660e7 −0.779067
\(188\) −3.31096e7 −0.363414
\(189\) 5.81162e7 0.626154
\(190\) 8.73724e6 0.0924138
\(191\) −1.39911e8 −1.45290 −0.726449 0.687221i \(-0.758831\pi\)
−0.726449 + 0.687221i \(0.758831\pi\)
\(192\) 1.13803e7 0.116038
\(193\) 7.00658e7 0.701545 0.350773 0.936461i \(-0.385919\pi\)
0.350773 + 0.936461i \(0.385919\pi\)
\(194\) 1.29325e7 0.127168
\(195\) −6.14211e7 −0.593193
\(196\) 1.39047e8 1.31907
\(197\) 1.41757e8 1.32103 0.660513 0.750814i \(-0.270339\pi\)
0.660513 + 0.750814i \(0.270339\pi\)
\(198\) 1.07282e8 0.982198
\(199\) −1.58549e8 −1.42620 −0.713098 0.701065i \(-0.752708\pi\)
−0.713098 + 0.701065i \(0.752708\pi\)
\(200\) −7.84248e7 −0.693184
\(201\) −3.40908e7 −0.296109
\(202\) 1.61752e6 0.0138077
\(203\) 1.47067e8 1.23389
\(204\) −1.98171e7 −0.163431
\(205\) 2.42290e7 0.196425
\(206\) 1.49863e8 1.19442
\(207\) 3.74221e7 0.293246
\(208\) 2.34538e8 1.80714
\(209\) 3.57904e6 0.0271178
\(210\) 1.10918e8 0.826482
\(211\) 2.65269e8 1.94400 0.972002 0.234972i \(-0.0755000\pi\)
0.972002 + 0.234972i \(0.0755000\pi\)
\(212\) 7.53477e6 0.0543118
\(213\) 3.72420e7 0.264061
\(214\) −1.09588e8 −0.764388
\(215\) −4.27677e7 −0.293482
\(216\) −1.46627e7 −0.0989976
\(217\) −4.43551e7 −0.294669
\(218\) 8.51868e7 0.556897
\(219\) −7.93848e6 −0.0510720
\(220\) 1.86878e8 1.18325
\(221\) −2.57650e8 −1.60567
\(222\) 2.44747e7 0.150135
\(223\) 1.05872e8 0.639315 0.319658 0.947533i \(-0.396432\pi\)
0.319658 + 0.947533i \(0.396432\pi\)
\(224\) −3.53603e8 −2.10207
\(225\) −4.44041e8 −2.59887
\(226\) −3.73586e8 −2.15284
\(227\) 1.29359e8 0.734014 0.367007 0.930218i \(-0.380382\pi\)
0.367007 + 0.930218i \(0.380382\pi\)
\(228\) 1.01809e6 0.00568871
\(229\) −9.87515e7 −0.543400 −0.271700 0.962382i \(-0.587586\pi\)
−0.271700 + 0.962382i \(0.587586\pi\)
\(230\) 1.45724e8 0.789738
\(231\) 4.54353e7 0.242522
\(232\) −3.71047e7 −0.195084
\(233\) 3.20820e8 1.66156 0.830779 0.556602i \(-0.187895\pi\)
0.830779 + 0.556602i \(0.187895\pi\)
\(234\) 3.96767e8 2.02433
\(235\) 1.71907e8 0.864083
\(236\) −2.77079e8 −1.37218
\(237\) 2.92858e7 0.142902
\(238\) 4.65278e8 2.23714
\(239\) 1.03848e8 0.492045 0.246023 0.969264i \(-0.420876\pi\)
0.246023 + 0.969264i \(0.420876\pi\)
\(240\) −9.36617e7 −0.437343
\(241\) 7.62277e7 0.350795 0.175397 0.984498i \(-0.443879\pi\)
0.175397 + 0.984498i \(0.443879\pi\)
\(242\) −1.25437e8 −0.568948
\(243\) −1.25350e8 −0.560406
\(244\) −2.45751e8 −1.08300
\(245\) −7.21942e8 −3.13632
\(246\) 6.31131e6 0.0270300
\(247\) 1.32366e7 0.0558903
\(248\) 1.11907e7 0.0465884
\(249\) 1.89095e7 0.0776216
\(250\) −1.08957e9 −4.41028
\(251\) −4.49350e8 −1.79360 −0.896802 0.442432i \(-0.854116\pi\)
−0.896802 + 0.442432i \(0.854116\pi\)
\(252\) −3.20514e8 −1.26167
\(253\) 5.96929e7 0.231740
\(254\) 5.02364e8 1.92354
\(255\) 1.02891e8 0.388587
\(256\) 3.40004e8 1.26661
\(257\) 8.54500e7 0.314012 0.157006 0.987598i \(-0.449816\pi\)
0.157006 + 0.987598i \(0.449816\pi\)
\(258\) −1.11404e7 −0.0403860
\(259\) −2.57050e8 −0.919325
\(260\) 6.91141e8 2.43871
\(261\) −2.10087e8 −0.731403
\(262\) −3.52507e8 −1.21092
\(263\) −1.42757e8 −0.483896 −0.241948 0.970289i \(-0.577786\pi\)
−0.241948 + 0.970289i \(0.577786\pi\)
\(264\) −1.14633e7 −0.0383438
\(265\) −3.91209e7 −0.129136
\(266\) −2.39034e7 −0.0778706
\(267\) 9.71036e7 0.312209
\(268\) 3.83607e8 1.21735
\(269\) 1.00980e8 0.316302 0.158151 0.987415i \(-0.449447\pi\)
0.158151 + 0.987415i \(0.449447\pi\)
\(270\) −3.23284e8 −0.999566
\(271\) 9.22392e7 0.281529 0.140765 0.990043i \(-0.455044\pi\)
0.140765 + 0.990043i \(0.455044\pi\)
\(272\) −3.92893e8 −1.18381
\(273\) 1.68036e8 0.499842
\(274\) 6.51391e8 1.91300
\(275\) −7.08301e8 −2.05378
\(276\) 1.69802e7 0.0486139
\(277\) 1.50780e8 0.426249 0.213125 0.977025i \(-0.431636\pi\)
0.213125 + 0.977025i \(0.431636\pi\)
\(278\) 3.03905e7 0.0848362
\(279\) 6.33618e7 0.174668
\(280\) 2.93912e8 0.800136
\(281\) 2.04352e8 0.549424 0.274712 0.961527i \(-0.411418\pi\)
0.274712 + 0.961527i \(0.411418\pi\)
\(282\) 4.47793e7 0.118906
\(283\) −1.63381e8 −0.428499 −0.214250 0.976779i \(-0.568731\pi\)
−0.214250 + 0.976779i \(0.568731\pi\)
\(284\) −4.19066e8 −1.08560
\(285\) −5.28597e6 −0.0135260
\(286\) 6.32894e8 1.59974
\(287\) −6.62858e7 −0.165514
\(288\) 5.05127e8 1.24603
\(289\) 2.12708e7 0.0518372
\(290\) −8.18090e8 −1.96974
\(291\) −7.82410e6 −0.0186127
\(292\) 8.93278e7 0.209965
\(293\) 4.41998e8 1.02656 0.513279 0.858222i \(-0.328431\pi\)
0.513279 + 0.858222i \(0.328431\pi\)
\(294\) −1.88055e8 −0.431589
\(295\) 1.43861e9 3.26262
\(296\) 6.48535e7 0.145349
\(297\) −1.32427e8 −0.293312
\(298\) 7.40835e8 1.62168
\(299\) 2.20766e8 0.477620
\(300\) −2.01482e8 −0.430837
\(301\) 1.17004e8 0.247297
\(302\) 3.36771e8 0.703576
\(303\) −978590. −0.00202093
\(304\) 2.01846e7 0.0412062
\(305\) 1.27595e9 2.57504
\(306\) −6.64657e8 −1.32609
\(307\) −4.00924e8 −0.790820 −0.395410 0.918505i \(-0.629397\pi\)
−0.395410 + 0.918505i \(0.629397\pi\)
\(308\) −5.11261e8 −0.997045
\(309\) −9.06660e7 −0.174819
\(310\) 2.46735e8 0.470397
\(311\) 3.36264e8 0.633897 0.316948 0.948443i \(-0.397342\pi\)
0.316948 + 0.948443i \(0.397342\pi\)
\(312\) −4.23953e7 −0.0790271
\(313\) −1.24177e7 −0.0228895 −0.0114448 0.999935i \(-0.503643\pi\)
−0.0114448 + 0.999935i \(0.503643\pi\)
\(314\) −1.62186e8 −0.295637
\(315\) 1.66413e9 2.99985
\(316\) −3.29539e8 −0.587492
\(317\) −8.50201e8 −1.49904 −0.749521 0.661980i \(-0.769716\pi\)
−0.749521 + 0.661980i \(0.769716\pi\)
\(318\) −1.01904e7 −0.0177704
\(319\) −3.35115e8 −0.577998
\(320\) 6.64880e8 1.13427
\(321\) 6.62999e7 0.111878
\(322\) −3.98671e8 −0.665456
\(323\) −2.21736e7 −0.0366124
\(324\) 4.38652e8 0.716494
\(325\) −2.61955e9 −4.23287
\(326\) 1.76877e8 0.282755
\(327\) −5.15375e7 −0.0815090
\(328\) 1.67238e7 0.0261684
\(329\) −4.70303e8 −0.728102
\(330\) −2.52744e8 −0.387152
\(331\) −4.63676e8 −0.702775 −0.351388 0.936230i \(-0.614290\pi\)
−0.351388 + 0.936230i \(0.614290\pi\)
\(332\) −2.12779e8 −0.319114
\(333\) 3.67200e8 0.544939
\(334\) −2.76587e8 −0.406180
\(335\) −1.99171e9 −2.89447
\(336\) 2.56240e8 0.368518
\(337\) −8.51629e8 −1.21212 −0.606060 0.795419i \(-0.707251\pi\)
−0.606060 + 0.795419i \(0.707251\pi\)
\(338\) 1.38573e9 1.95196
\(339\) 2.26017e8 0.315096
\(340\) −1.15779e9 −1.59754
\(341\) 1.01070e8 0.138033
\(342\) 3.41463e7 0.0461586
\(343\) 7.63148e8 1.02113
\(344\) −2.95200e7 −0.0390986
\(345\) −8.81619e7 −0.115588
\(346\) −1.29233e9 −1.67729
\(347\) 9.08191e8 1.16687 0.583437 0.812159i \(-0.301708\pi\)
0.583437 + 0.812159i \(0.301708\pi\)
\(348\) −9.53263e7 −0.121251
\(349\) −1.24649e9 −1.56963 −0.784817 0.619728i \(-0.787243\pi\)
−0.784817 + 0.619728i \(0.787243\pi\)
\(350\) 4.73053e9 5.89755
\(351\) −4.89763e8 −0.604520
\(352\) 8.05741e8 0.984683
\(353\) 7.48315e8 0.905467 0.452734 0.891646i \(-0.350449\pi\)
0.452734 + 0.891646i \(0.350449\pi\)
\(354\) 3.74737e8 0.448968
\(355\) 2.17581e9 2.58120
\(356\) −1.09266e9 −1.28354
\(357\) −2.81490e8 −0.327435
\(358\) −1.89921e9 −2.18768
\(359\) −5.31954e8 −0.606798 −0.303399 0.952864i \(-0.598121\pi\)
−0.303399 + 0.952864i \(0.598121\pi\)
\(360\) −4.19857e8 −0.474289
\(361\) −8.92733e8 −0.998726
\(362\) 1.55472e8 0.172256
\(363\) 7.58887e7 0.0832729
\(364\) −1.89082e9 −2.05493
\(365\) −4.63794e8 −0.499230
\(366\) 3.32367e8 0.354351
\(367\) 1.07856e9 1.13897 0.569485 0.822001i \(-0.307142\pi\)
0.569485 + 0.822001i \(0.307142\pi\)
\(368\) 3.36648e8 0.352135
\(369\) 9.46902e7 0.0981098
\(370\) 1.42990e9 1.46757
\(371\) 1.07027e8 0.108814
\(372\) 2.87503e7 0.0289562
\(373\) −1.07870e9 −1.07626 −0.538132 0.842860i \(-0.680870\pi\)
−0.538132 + 0.842860i \(0.680870\pi\)
\(374\) −1.06021e9 −1.04795
\(375\) 6.59184e8 0.645502
\(376\) 1.18657e8 0.115116
\(377\) −1.23937e9 −1.19126
\(378\) 8.84442e8 0.842263
\(379\) −7.68170e8 −0.724803 −0.362401 0.932022i \(-0.618043\pi\)
−0.362401 + 0.932022i \(0.618043\pi\)
\(380\) 5.94804e7 0.0556073
\(381\) −3.03927e8 −0.281534
\(382\) −2.12924e9 −1.95435
\(383\) 2.81285e8 0.255829 0.127915 0.991785i \(-0.459172\pi\)
0.127915 + 0.991785i \(0.459172\pi\)
\(384\) −1.09982e8 −0.0991203
\(385\) 2.65449e9 2.37066
\(386\) 1.06630e9 0.943675
\(387\) −1.67142e8 −0.146588
\(388\) 8.80407e7 0.0765196
\(389\) −1.52136e9 −1.31041 −0.655206 0.755450i \(-0.727418\pi\)
−0.655206 + 0.755450i \(0.727418\pi\)
\(390\) −9.34736e8 −0.797927
\(391\) −3.69822e8 −0.312878
\(392\) −4.98313e8 −0.417831
\(393\) 2.13265e8 0.177233
\(394\) 2.15732e9 1.77696
\(395\) 1.71098e9 1.39687
\(396\) 7.30343e8 0.591009
\(397\) 9.64243e8 0.773428 0.386714 0.922200i \(-0.373610\pi\)
0.386714 + 0.922200i \(0.373610\pi\)
\(398\) −2.41289e9 −1.91843
\(399\) 1.44614e7 0.0113974
\(400\) −3.99458e9 −3.12077
\(401\) 1.46162e9 1.13195 0.565977 0.824421i \(-0.308499\pi\)
0.565977 + 0.824421i \(0.308499\pi\)
\(402\) −5.18811e8 −0.398307
\(403\) 3.73793e8 0.284488
\(404\) 1.10116e7 0.00830836
\(405\) −2.27750e9 −1.70360
\(406\) 2.23813e9 1.65976
\(407\) 5.85730e8 0.430643
\(408\) 7.10197e7 0.0517688
\(409\) −1.40198e9 −1.01324 −0.506619 0.862170i \(-0.669105\pi\)
−0.506619 + 0.862170i \(0.669105\pi\)
\(410\) 3.68729e8 0.264219
\(411\) −3.94087e8 −0.279992
\(412\) 1.02022e9 0.718709
\(413\) −3.93575e9 −2.74918
\(414\) 5.69508e8 0.394456
\(415\) 1.10476e9 0.758753
\(416\) 2.97992e9 2.02945
\(417\) −1.83861e7 −0.0124169
\(418\) 5.44677e7 0.0364772
\(419\) 2.20128e9 1.46193 0.730964 0.682416i \(-0.239071\pi\)
0.730964 + 0.682416i \(0.239071\pi\)
\(420\) 7.55093e8 0.497311
\(421\) 1.37650e9 0.899061 0.449530 0.893265i \(-0.351591\pi\)
0.449530 + 0.893265i \(0.351591\pi\)
\(422\) 4.03699e9 2.61495
\(423\) 6.71835e8 0.431590
\(424\) −2.70028e7 −0.0172040
\(425\) 4.38822e9 2.77285
\(426\) 5.66768e8 0.355199
\(427\) −3.49075e9 −2.16980
\(428\) −7.46039e8 −0.459948
\(429\) −3.82897e8 −0.234143
\(430\) −6.50861e8 −0.394774
\(431\) −1.13829e9 −0.684832 −0.342416 0.939548i \(-0.611245\pi\)
−0.342416 + 0.939548i \(0.611245\pi\)
\(432\) −7.46845e8 −0.445695
\(433\) −3.25059e8 −0.192422 −0.0962111 0.995361i \(-0.530672\pi\)
−0.0962111 + 0.995361i \(0.530672\pi\)
\(434\) −6.75018e8 −0.396370
\(435\) 4.94939e8 0.288297
\(436\) 5.79925e8 0.335096
\(437\) 1.89994e7 0.0108907
\(438\) −1.20812e8 −0.0686989
\(439\) −2.09252e9 −1.18044 −0.590219 0.807243i \(-0.700959\pi\)
−0.590219 + 0.807243i \(0.700959\pi\)
\(440\) −6.69725e8 −0.374811
\(441\) −2.82144e9 −1.56652
\(442\) −3.92104e9 −2.15985
\(443\) −1.93713e9 −1.05863 −0.529316 0.848425i \(-0.677551\pi\)
−0.529316 + 0.848425i \(0.677551\pi\)
\(444\) 1.66616e8 0.0903393
\(445\) 5.67314e9 3.05185
\(446\) 1.61122e9 0.859968
\(447\) −4.48200e8 −0.237354
\(448\) −1.81898e9 −0.955773
\(449\) −1.43342e9 −0.747329 −0.373665 0.927564i \(-0.621899\pi\)
−0.373665 + 0.927564i \(0.621899\pi\)
\(450\) −6.75763e9 −3.49583
\(451\) 1.51043e8 0.0775322
\(452\) −2.54326e9 −1.29541
\(453\) −2.03744e8 −0.102977
\(454\) 1.96864e9 0.987351
\(455\) 9.81725e9 4.88596
\(456\) −3.64859e6 −0.00180197
\(457\) 3.05243e8 0.149602 0.0748012 0.997198i \(-0.476168\pi\)
0.0748012 + 0.997198i \(0.476168\pi\)
\(458\) −1.50285e9 −0.730948
\(459\) 8.20441e8 0.396007
\(460\) 9.92042e8 0.475202
\(461\) −3.07533e9 −1.46197 −0.730986 0.682392i \(-0.760940\pi\)
−0.730986 + 0.682392i \(0.760940\pi\)
\(462\) 6.91457e8 0.326226
\(463\) −6.71289e8 −0.314323 −0.157162 0.987573i \(-0.550234\pi\)
−0.157162 + 0.987573i \(0.550234\pi\)
\(464\) −1.88994e9 −0.878283
\(465\) −1.49273e8 −0.0688487
\(466\) 4.88240e9 2.23503
\(467\) 1.81833e9 0.826160 0.413080 0.910695i \(-0.364453\pi\)
0.413080 + 0.910695i \(0.364453\pi\)
\(468\) 2.70107e9 1.21808
\(469\) 5.44891e9 2.43896
\(470\) 2.61616e9 1.16231
\(471\) 9.81213e7 0.0432703
\(472\) 9.92986e8 0.434657
\(473\) −2.66612e8 −0.115842
\(474\) 4.45687e8 0.192223
\(475\) −2.25442e8 −0.0965176
\(476\) 3.16747e9 1.34613
\(477\) −1.52890e8 −0.0645006
\(478\) 1.58041e9 0.661869
\(479\) −2.05954e9 −0.856240 −0.428120 0.903722i \(-0.640824\pi\)
−0.428120 + 0.903722i \(0.640824\pi\)
\(480\) −1.19002e9 −0.491145
\(481\) 2.16624e9 0.887562
\(482\) 1.16007e9 0.471867
\(483\) 2.41194e8 0.0973982
\(484\) −8.53937e8 −0.342348
\(485\) −4.57112e8 −0.181939
\(486\) −1.90764e9 −0.753824
\(487\) −2.54877e9 −0.999954 −0.499977 0.866039i \(-0.666658\pi\)
−0.499977 + 0.866039i \(0.666658\pi\)
\(488\) 8.80711e8 0.343055
\(489\) −1.07010e8 −0.0413849
\(490\) −1.09869e10 −4.21879
\(491\) 2.32288e9 0.885607 0.442804 0.896619i \(-0.353984\pi\)
0.442804 + 0.896619i \(0.353984\pi\)
\(492\) 4.29654e7 0.0162645
\(493\) 2.07618e9 0.780369
\(494\) 2.01441e8 0.0751802
\(495\) −3.79198e9 −1.40523
\(496\) 5.70002e8 0.209744
\(497\) −5.95259e9 −2.17500
\(498\) 2.87775e8 0.104412
\(499\) 5.35418e9 1.92904 0.964520 0.264009i \(-0.0850450\pi\)
0.964520 + 0.264009i \(0.0850450\pi\)
\(500\) −7.41748e9 −2.65376
\(501\) 1.67333e8 0.0594497
\(502\) −6.83843e9 −2.41265
\(503\) −4.36661e9 −1.52988 −0.764938 0.644104i \(-0.777230\pi\)
−0.764938 + 0.644104i \(0.777230\pi\)
\(504\) 1.14865e9 0.399650
\(505\) −5.71727e7 −0.0197546
\(506\) 9.08437e8 0.311722
\(507\) −8.38357e8 −0.285694
\(508\) 3.41994e9 1.15743
\(509\) 3.03093e9 1.01874 0.509371 0.860547i \(-0.329878\pi\)
0.509371 + 0.860547i \(0.329878\pi\)
\(510\) 1.56585e9 0.522703
\(511\) 1.26885e9 0.420666
\(512\) 3.64534e9 1.20031
\(513\) −4.21496e7 −0.0137842
\(514\) 1.30042e9 0.422389
\(515\) −5.29703e9 −1.70886
\(516\) −7.58402e7 −0.0243011
\(517\) 1.07166e9 0.341068
\(518\) −3.91192e9 −1.23662
\(519\) 7.81851e8 0.245493
\(520\) −2.47688e9 −0.772492
\(521\) 7.54943e8 0.233874 0.116937 0.993139i \(-0.462692\pi\)
0.116937 + 0.993139i \(0.462692\pi\)
\(522\) −3.19721e9 −0.983839
\(523\) 1.20927e9 0.369630 0.184815 0.982773i \(-0.440831\pi\)
0.184815 + 0.982773i \(0.440831\pi\)
\(524\) −2.39976e9 −0.728632
\(525\) −2.86194e9 −0.863183
\(526\) −2.17255e9 −0.650908
\(527\) −6.26171e8 −0.186361
\(528\) −5.83884e8 −0.172627
\(529\) −3.08794e9 −0.906932
\(530\) −5.95362e8 −0.173706
\(531\) 5.62228e9 1.62960
\(532\) −1.62727e8 −0.0468563
\(533\) 5.58610e8 0.159795
\(534\) 1.47777e9 0.419965
\(535\) 3.87347e9 1.09361
\(536\) −1.37476e9 −0.385610
\(537\) 1.14901e9 0.320195
\(538\) 1.53676e9 0.425470
\(539\) −4.50056e9 −1.23796
\(540\) −2.20082e9 −0.601459
\(541\) 3.74130e9 1.01586 0.507928 0.861400i \(-0.330412\pi\)
0.507928 + 0.861400i \(0.330412\pi\)
\(542\) 1.40374e9 0.378696
\(543\) −9.40597e7 −0.0252118
\(544\) −4.99190e9 −1.32944
\(545\) −3.01100e9 −0.796752
\(546\) 2.55725e9 0.672357
\(547\) 1.07121e8 0.0279845 0.0139923 0.999902i \(-0.495546\pi\)
0.0139923 + 0.999902i \(0.495546\pi\)
\(548\) 4.43447e9 1.15109
\(549\) 4.98658e9 1.28617
\(550\) −1.07793e10 −2.76261
\(551\) −1.06662e8 −0.0271631
\(552\) −6.08529e7 −0.0153991
\(553\) −4.68091e9 −1.17704
\(554\) 2.29464e9 0.573364
\(555\) −8.65080e8 −0.214798
\(556\) 2.06889e8 0.0510477
\(557\) −1.84003e9 −0.451160 −0.225580 0.974225i \(-0.572428\pi\)
−0.225580 + 0.974225i \(0.572428\pi\)
\(558\) 9.64273e8 0.234953
\(559\) −9.86028e8 −0.238753
\(560\) 1.49704e10 3.60227
\(561\) 6.41421e8 0.153382
\(562\) 3.10994e9 0.739051
\(563\) −2.91696e8 −0.0688892 −0.0344446 0.999407i \(-0.510966\pi\)
−0.0344446 + 0.999407i \(0.510966\pi\)
\(564\) 3.04843e8 0.0715484
\(565\) 1.32047e10 3.08006
\(566\) −2.48642e9 −0.576391
\(567\) 6.23080e9 1.43550
\(568\) 1.50183e9 0.343876
\(569\) 1.23531e9 0.281114 0.140557 0.990073i \(-0.455111\pi\)
0.140557 + 0.990073i \(0.455111\pi\)
\(570\) −8.04446e7 −0.0181943
\(571\) 6.32334e9 1.42141 0.710706 0.703489i \(-0.248375\pi\)
0.710706 + 0.703489i \(0.248375\pi\)
\(572\) 4.30855e9 0.962597
\(573\) 1.28817e9 0.286044
\(574\) −1.00877e9 −0.222639
\(575\) −3.76002e9 −0.824808
\(576\) 2.59844e9 0.566544
\(577\) −2.79809e9 −0.606381 −0.303191 0.952930i \(-0.598052\pi\)
−0.303191 + 0.952930i \(0.598052\pi\)
\(578\) 3.23710e8 0.0697282
\(579\) −6.45103e8 −0.138119
\(580\) −5.56931e9 −1.18523
\(581\) −3.02241e9 −0.639347
\(582\) −1.19071e8 −0.0250366
\(583\) −2.43878e8 −0.0509722
\(584\) −3.20129e8 −0.0665090
\(585\) −1.40241e10 −2.89620
\(586\) 6.72654e9 1.38086
\(587\) 2.66505e9 0.543841 0.271921 0.962320i \(-0.412341\pi\)
0.271921 + 0.962320i \(0.412341\pi\)
\(588\) −1.28022e9 −0.259696
\(589\) 3.21691e7 0.00648688
\(590\) 2.18935e10 4.38867
\(591\) −1.30517e9 −0.260082
\(592\) 3.30332e9 0.654373
\(593\) −2.31869e9 −0.456616 −0.228308 0.973589i \(-0.573319\pi\)
−0.228308 + 0.973589i \(0.573319\pi\)
\(594\) −2.01534e9 −0.394545
\(595\) −1.64457e10 −3.20068
\(596\) 5.04337e9 0.975797
\(597\) 1.45978e9 0.280787
\(598\) 3.35972e9 0.642465
\(599\) −2.38951e9 −0.454271 −0.227135 0.973863i \(-0.572936\pi\)
−0.227135 + 0.973863i \(0.572936\pi\)
\(600\) 7.22065e8 0.136473
\(601\) −5.85741e9 −1.10064 −0.550320 0.834954i \(-0.685494\pi\)
−0.550320 + 0.834954i \(0.685494\pi\)
\(602\) 1.78063e9 0.332648
\(603\) −7.78385e9 −1.44572
\(604\) 2.29263e9 0.423356
\(605\) 4.43369e9 0.813994
\(606\) −1.48927e7 −0.00271843
\(607\) 1.64112e8 0.0297838 0.0148919 0.999889i \(-0.495260\pi\)
0.0148919 + 0.999889i \(0.495260\pi\)
\(608\) 2.56456e8 0.0462753
\(609\) −1.35406e9 −0.242927
\(610\) 1.94180e10 3.46379
\(611\) 3.96339e9 0.702946
\(612\) −4.52478e9 −0.797935
\(613\) −6.13717e9 −1.07611 −0.538055 0.842910i \(-0.680841\pi\)
−0.538055 + 0.842910i \(0.680841\pi\)
\(614\) −6.10146e9 −1.06376
\(615\) −2.23079e8 −0.0386719
\(616\) 1.83224e9 0.315827
\(617\) −1.73030e9 −0.296567 −0.148284 0.988945i \(-0.547375\pi\)
−0.148284 + 0.988945i \(0.547375\pi\)
\(618\) −1.37980e9 −0.235156
\(619\) 3.65743e9 0.619811 0.309906 0.950767i \(-0.399703\pi\)
0.309906 + 0.950767i \(0.399703\pi\)
\(620\) 1.67969e9 0.283047
\(621\) −7.02991e8 −0.117796
\(622\) 5.11743e9 0.852679
\(623\) −1.55206e10 −2.57158
\(624\) −2.15941e9 −0.355786
\(625\) 2.20101e10 3.60613
\(626\) −1.88979e8 −0.0307896
\(627\) −3.29526e7 −0.00533891
\(628\) −1.10411e9 −0.177891
\(629\) −3.62884e9 −0.581421
\(630\) 2.53255e10 4.03521
\(631\) −8.67078e9 −1.37390 −0.686951 0.726704i \(-0.741051\pi\)
−0.686951 + 0.726704i \(0.741051\pi\)
\(632\) 1.18099e9 0.186096
\(633\) −2.44235e9 −0.382733
\(634\) −1.29388e10 −2.01642
\(635\) −1.77565e10 −2.75200
\(636\) −6.93733e7 −0.0106928
\(637\) −1.66447e10 −2.55145
\(638\) −5.09995e9 −0.777487
\(639\) 8.50336e9 1.28925
\(640\) −6.42555e9 −0.968903
\(641\) 5.26409e9 0.789442 0.394721 0.918801i \(-0.370841\pi\)
0.394721 + 0.918801i \(0.370841\pi\)
\(642\) 1.00898e9 0.150491
\(643\) −3.46768e9 −0.514399 −0.257200 0.966358i \(-0.582800\pi\)
−0.257200 + 0.966358i \(0.582800\pi\)
\(644\) −2.71403e9 −0.400419
\(645\) 3.93766e8 0.0577803
\(646\) −3.37450e8 −0.0492488
\(647\) 3.80535e9 0.552369 0.276185 0.961105i \(-0.410930\pi\)
0.276185 + 0.961105i \(0.410930\pi\)
\(648\) −1.57202e9 −0.226959
\(649\) 8.96824e9 1.28781
\(650\) −3.98656e10 −5.69379
\(651\) 4.08381e8 0.0580139
\(652\) 1.20413e9 0.170140
\(653\) 2.84050e9 0.399207 0.199603 0.979877i \(-0.436035\pi\)
0.199603 + 0.979877i \(0.436035\pi\)
\(654\) −7.84323e8 −0.109641
\(655\) 1.24597e10 1.73246
\(656\) 8.51831e8 0.117812
\(657\) −1.81257e9 −0.249354
\(658\) −7.15731e9 −0.979398
\(659\) 3.52181e9 0.479365 0.239683 0.970851i \(-0.422957\pi\)
0.239683 + 0.970851i \(0.422957\pi\)
\(660\) −1.72060e9 −0.232957
\(661\) 7.62689e9 1.02717 0.513585 0.858039i \(-0.328317\pi\)
0.513585 + 0.858039i \(0.328317\pi\)
\(662\) −7.05645e9 −0.945330
\(663\) 2.37220e9 0.316122
\(664\) 7.62551e8 0.101084
\(665\) 8.44885e8 0.111409
\(666\) 5.58824e9 0.733019
\(667\) −1.77896e9 −0.232127
\(668\) −1.88292e9 −0.244407
\(669\) −9.74776e8 −0.125867
\(670\) −3.03108e10 −3.89346
\(671\) 7.95422e9 1.01641
\(672\) 3.25566e9 0.413853
\(673\) 1.76513e9 0.223216 0.111608 0.993752i \(-0.464400\pi\)
0.111608 + 0.993752i \(0.464400\pi\)
\(674\) −1.29605e10 −1.63047
\(675\) 8.34150e9 1.04395
\(676\) 9.43362e9 1.17453
\(677\) −1.21822e10 −1.50892 −0.754461 0.656345i \(-0.772102\pi\)
−0.754461 + 0.656345i \(0.772102\pi\)
\(678\) 3.43964e9 0.423847
\(679\) 1.25057e9 0.153307
\(680\) 4.14923e9 0.506041
\(681\) −1.19102e9 −0.144512
\(682\) 1.53814e9 0.185673
\(683\) 9.06722e9 1.08893 0.544467 0.838782i \(-0.316732\pi\)
0.544467 + 0.838782i \(0.316732\pi\)
\(684\) 2.32457e8 0.0277746
\(685\) −2.30240e10 −2.73693
\(686\) 1.16140e10 1.37356
\(687\) 9.09214e8 0.106984
\(688\) −1.50361e9 −0.176025
\(689\) −9.01949e8 −0.105055
\(690\) −1.34169e9 −0.155482
\(691\) 1.27877e10 1.47441 0.737206 0.675668i \(-0.236145\pi\)
0.737206 + 0.675668i \(0.236145\pi\)
\(692\) −8.79778e9 −1.00926
\(693\) 1.03741e10 1.18409
\(694\) 1.38213e10 1.56961
\(695\) −1.07418e9 −0.121375
\(696\) 3.41627e8 0.0384078
\(697\) −9.35772e8 −0.104678
\(698\) −1.89696e10 −2.11137
\(699\) −2.95382e9 −0.327125
\(700\) 3.22040e10 3.54868
\(701\) 1.61492e10 1.77068 0.885338 0.464948i \(-0.153927\pi\)
0.885338 + 0.464948i \(0.153927\pi\)
\(702\) −7.45346e9 −0.813163
\(703\) 1.86429e8 0.0202381
\(704\) 4.14484e9 0.447717
\(705\) −1.58276e9 −0.170119
\(706\) 1.13882e10 1.21798
\(707\) 1.56413e8 0.0166458
\(708\) 2.55110e9 0.270153
\(709\) −4.31415e9 −0.454604 −0.227302 0.973824i \(-0.572991\pi\)
−0.227302 + 0.973824i \(0.572991\pi\)
\(710\) 3.31126e10 3.47207
\(711\) 6.68675e9 0.697705
\(712\) 3.91583e9 0.406578
\(713\) 5.36532e8 0.0554348
\(714\) −4.28386e9 −0.440445
\(715\) −2.23702e10 −2.28875
\(716\) −1.29293e10 −1.31637
\(717\) −9.56138e8 −0.0968731
\(718\) −8.09555e9 −0.816227
\(719\) 8.62138e9 0.865019 0.432509 0.901629i \(-0.357628\pi\)
0.432509 + 0.901629i \(0.357628\pi\)
\(720\) −2.13855e10 −2.13528
\(721\) 1.44916e10 1.43994
\(722\) −1.35861e10 −1.34342
\(723\) −7.01835e8 −0.0690639
\(724\) 1.05841e9 0.103650
\(725\) 2.11087e10 2.05721
\(726\) 1.15491e9 0.112014
\(727\) −1.50745e10 −1.45503 −0.727517 0.686089i \(-0.759326\pi\)
−0.727517 + 0.686089i \(0.759326\pi\)
\(728\) 6.77626e9 0.650924
\(729\) −8.10559e9 −0.774887
\(730\) −7.05826e9 −0.671533
\(731\) 1.65177e9 0.156401
\(732\) 2.26265e9 0.213220
\(733\) 1.41082e10 1.32315 0.661574 0.749880i \(-0.269889\pi\)
0.661574 + 0.749880i \(0.269889\pi\)
\(734\) 1.64141e10 1.53207
\(735\) 6.64698e9 0.617474
\(736\) 4.27729e9 0.395454
\(737\) −1.24162e10 −1.14249
\(738\) 1.44104e9 0.131971
\(739\) −2.01127e10 −1.83322 −0.916611 0.399781i \(-0.869086\pi\)
−0.916611 + 0.399781i \(0.869086\pi\)
\(740\) 9.73431e9 0.883068
\(741\) −1.21870e8 −0.0110036
\(742\) 1.62879e9 0.146370
\(743\) 7.77437e9 0.695352 0.347676 0.937615i \(-0.386971\pi\)
0.347676 + 0.937615i \(0.386971\pi\)
\(744\) −1.03034e8 −0.00917225
\(745\) −2.61855e10 −2.32014
\(746\) −1.64162e10 −1.44772
\(747\) 4.31756e9 0.378980
\(748\) −7.21759e9 −0.630575
\(749\) −1.05971e10 −0.921508
\(750\) 1.00318e10 0.868289
\(751\) −1.36165e10 −1.17307 −0.586536 0.809923i \(-0.699509\pi\)
−0.586536 + 0.809923i \(0.699509\pi\)
\(752\) 6.04381e9 0.518261
\(753\) 4.13721e9 0.353122
\(754\) −1.88614e10 −1.60241
\(755\) −1.19035e10 −1.00661
\(756\) 6.02101e9 0.506807
\(757\) 1.37437e10 1.15151 0.575756 0.817622i \(-0.304708\pi\)
0.575756 + 0.817622i \(0.304708\pi\)
\(758\) −1.16904e10 −0.974960
\(759\) −5.49598e8 −0.0456246
\(760\) −2.13164e8 −0.0176143
\(761\) 9.87644e9 0.812370 0.406185 0.913791i \(-0.366859\pi\)
0.406185 + 0.913791i \(0.366859\pi\)
\(762\) −4.62531e9 −0.378703
\(763\) 8.23751e9 0.671367
\(764\) −1.44952e10 −1.17597
\(765\) 2.34929e10 1.89724
\(766\) 4.28073e9 0.344126
\(767\) 3.31678e10 2.65419
\(768\) −3.13045e9 −0.249369
\(769\) 1.45345e10 1.15254 0.576272 0.817258i \(-0.304507\pi\)
0.576272 + 0.817258i \(0.304507\pi\)
\(770\) 4.03974e10 3.18886
\(771\) −7.86746e8 −0.0618221
\(772\) 7.25902e9 0.567829
\(773\) −1.27560e10 −0.993312 −0.496656 0.867947i \(-0.665439\pi\)
−0.496656 + 0.867947i \(0.665439\pi\)
\(774\) −2.54365e9 −0.197181
\(775\) −6.36635e9 −0.491286
\(776\) −3.15517e8 −0.0242386
\(777\) 2.36669e9 0.180995
\(778\) −2.31528e10 −1.76269
\(779\) 4.80747e7 0.00364364
\(780\) −6.36340e9 −0.480129
\(781\) 1.35639e10 1.01884
\(782\) −5.62814e9 −0.420864
\(783\) 3.94658e9 0.293802
\(784\) −2.53817e10 −1.88111
\(785\) 5.73260e9 0.422968
\(786\) 3.24557e9 0.238403
\(787\) −8.63446e9 −0.631428 −0.315714 0.948854i \(-0.602244\pi\)
−0.315714 + 0.948854i \(0.602244\pi\)
\(788\) 1.46864e10 1.06924
\(789\) 1.31438e9 0.0952688
\(790\) 2.60386e10 1.87898
\(791\) −3.61255e10 −2.59535
\(792\) −2.61738e9 −0.187210
\(793\) 2.94176e10 2.09484
\(794\) 1.46743e10 1.04037
\(795\) 3.60190e8 0.0254242
\(796\) −1.64262e10 −1.15436
\(797\) −2.05828e10 −1.44012 −0.720061 0.693911i \(-0.755886\pi\)
−0.720061 + 0.693911i \(0.755886\pi\)
\(798\) 2.20081e8 0.0153310
\(799\) −6.63939e9 −0.460484
\(800\) −5.07532e10 −3.50468
\(801\) 2.21714e10 1.52433
\(802\) 2.22436e10 1.52263
\(803\) −2.89128e9 −0.197054
\(804\) −3.53190e9 −0.239670
\(805\) 1.40914e10 0.952069
\(806\) 5.68858e9 0.382676
\(807\) −9.29731e8 −0.0622730
\(808\) −3.94629e7 −0.00263178
\(809\) 1.96518e9 0.130492 0.0652459 0.997869i \(-0.479217\pi\)
0.0652459 + 0.997869i \(0.479217\pi\)
\(810\) −3.46602e10 −2.29157
\(811\) −9.82285e9 −0.646643 −0.323321 0.946289i \(-0.604799\pi\)
−0.323321 + 0.946289i \(0.604799\pi\)
\(812\) 1.52365e10 0.998711
\(813\) −8.49255e8 −0.0554270
\(814\) 8.91394e9 0.579274
\(815\) −6.25189e9 −0.404538
\(816\) 3.61740e9 0.233067
\(817\) −8.48588e7 −0.00544402
\(818\) −2.13361e10 −1.36295
\(819\) 3.83671e10 2.44043
\(820\) 2.51019e9 0.158986
\(821\) 1.17346e10 0.740060 0.370030 0.929020i \(-0.379347\pi\)
0.370030 + 0.929020i \(0.379347\pi\)
\(822\) −5.99742e9 −0.376628
\(823\) −1.25381e10 −0.784029 −0.392015 0.919959i \(-0.628222\pi\)
−0.392015 + 0.919959i \(0.628222\pi\)
\(824\) −3.65622e9 −0.227660
\(825\) 6.52139e9 0.404344
\(826\) −5.98963e10 −3.69802
\(827\) −7.60873e9 −0.467782 −0.233891 0.972263i \(-0.575146\pi\)
−0.233891 + 0.972263i \(0.575146\pi\)
\(828\) 3.87703e9 0.237352
\(829\) −1.26864e10 −0.773388 −0.386694 0.922208i \(-0.626383\pi\)
−0.386694 + 0.922208i \(0.626383\pi\)
\(830\) 1.68128e10 1.02063
\(831\) −1.38824e9 −0.0839193
\(832\) 1.53291e10 0.922752
\(833\) 2.78828e10 1.67140
\(834\) −2.79808e8 −0.0167024
\(835\) 9.77620e9 0.581122
\(836\) 3.70799e8 0.0219491
\(837\) −1.19028e9 −0.0701634
\(838\) 3.35002e10 1.96650
\(839\) −1.25954e10 −0.736282 −0.368141 0.929770i \(-0.620006\pi\)
−0.368141 + 0.929770i \(0.620006\pi\)
\(840\) −2.70607e9 −0.157530
\(841\) −7.26283e9 −0.421036
\(842\) 2.09483e10 1.20936
\(843\) −1.88149e9 −0.108170
\(844\) 2.74826e10 1.57347
\(845\) −4.89798e10 −2.79266
\(846\) 1.02243e10 0.580548
\(847\) −1.21297e10 −0.685895
\(848\) −1.37539e9 −0.0774535
\(849\) 1.50427e9 0.0843623
\(850\) 6.67821e10 3.72987
\(851\) 3.10936e9 0.172949
\(852\) 3.85838e9 0.213730
\(853\) −1.68559e10 −0.929890 −0.464945 0.885340i \(-0.653926\pi\)
−0.464945 + 0.885340i \(0.653926\pi\)
\(854\) −5.31239e10 −2.91869
\(855\) −1.20693e9 −0.0660391
\(856\) 2.67363e9 0.145694
\(857\) 3.15667e9 0.171315 0.0856577 0.996325i \(-0.472701\pi\)
0.0856577 + 0.996325i \(0.472701\pi\)
\(858\) −5.82711e9 −0.314955
\(859\) 1.47310e10 0.792969 0.396484 0.918041i \(-0.370230\pi\)
0.396484 + 0.918041i \(0.370230\pi\)
\(860\) −4.43086e9 −0.237544
\(861\) 6.10299e8 0.0325861
\(862\) −1.73231e10 −0.921194
\(863\) 2.38879e10 1.26514 0.632571 0.774502i \(-0.282000\pi\)
0.632571 + 0.774502i \(0.282000\pi\)
\(864\) −9.48904e9 −0.500523
\(865\) 4.56785e10 2.39969
\(866\) −4.94692e9 −0.258834
\(867\) −1.95842e8 −0.0102056
\(868\) −4.59531e9 −0.238504
\(869\) 1.06662e10 0.551367
\(870\) 7.53224e9 0.387799
\(871\) −4.59196e10 −2.35470
\(872\) −2.07831e9 −0.106146
\(873\) −1.78645e9 −0.0908745
\(874\) 2.89142e8 0.0146495
\(875\) −1.05361e11 −5.31682
\(876\) −8.22449e8 −0.0413375
\(877\) 2.26234e10 1.13255 0.566277 0.824215i \(-0.308383\pi\)
0.566277 + 0.824215i \(0.308383\pi\)
\(878\) −3.18450e10 −1.58785
\(879\) −4.06951e9 −0.202107
\(880\) −3.41126e10 −1.68743
\(881\) −1.42978e8 −0.00704454 −0.00352227 0.999994i \(-0.501121\pi\)
−0.00352227 + 0.999994i \(0.501121\pi\)
\(882\) −4.29382e10 −2.10719
\(883\) −8.28063e9 −0.404763 −0.202381 0.979307i \(-0.564868\pi\)
−0.202381 + 0.979307i \(0.564868\pi\)
\(884\) −2.66932e10 −1.29963
\(885\) −1.32454e10 −0.642339
\(886\) −2.94802e10 −1.42401
\(887\) −3.14829e10 −1.51475 −0.757376 0.652979i \(-0.773519\pi\)
−0.757376 + 0.652979i \(0.773519\pi\)
\(888\) −5.97112e8 −0.0286161
\(889\) 4.85782e10 2.31892
\(890\) 8.63367e10 4.10516
\(891\) −1.41979e10 −0.672437
\(892\) 1.09687e10 0.517460
\(893\) 3.41094e8 0.0160285
\(894\) −6.82094e9 −0.319273
\(895\) 6.71294e10 3.12991
\(896\) 1.75790e10 0.816426
\(897\) −2.03261e9 −0.0940331
\(898\) −2.18145e10 −1.00526
\(899\) −3.01208e9 −0.138263
\(900\) −4.60039e10 −2.10352
\(901\) 1.51093e9 0.0688188
\(902\) 2.29864e9 0.104292
\(903\) −1.07727e9 −0.0486874
\(904\) 9.11443e9 0.410336
\(905\) −5.49531e9 −0.246446
\(906\) −3.10068e9 −0.138519
\(907\) −2.58557e10 −1.15062 −0.575308 0.817937i \(-0.695118\pi\)
−0.575308 + 0.817937i \(0.695118\pi\)
\(908\) 1.34019e10 0.594109
\(909\) −2.23439e8 −0.00986699
\(910\) 1.49404e11 6.57230
\(911\) 1.27853e10 0.560271 0.280136 0.959960i \(-0.409621\pi\)
0.280136 + 0.959960i \(0.409621\pi\)
\(912\) −1.85842e8 −0.00811262
\(913\) 6.88704e9 0.299492
\(914\) 4.64534e9 0.201236
\(915\) −1.17478e10 −0.506970
\(916\) −1.02309e10 −0.439826
\(917\) −3.40872e10 −1.45982
\(918\) 1.24859e10 0.532684
\(919\) −2.07808e10 −0.883197 −0.441599 0.897213i \(-0.645588\pi\)
−0.441599 + 0.897213i \(0.645588\pi\)
\(920\) −3.55524e9 −0.150526
\(921\) 3.69134e9 0.155695
\(922\) −4.68020e10 −1.96656
\(923\) 5.01643e10 2.09985
\(924\) 4.70722e9 0.196297
\(925\) −3.68948e10 −1.53274
\(926\) −1.02160e10 −0.422808
\(927\) −2.07015e10 −0.853538
\(928\) −2.40126e10 −0.986328
\(929\) 3.30915e10 1.35414 0.677068 0.735921i \(-0.263250\pi\)
0.677068 + 0.735921i \(0.263250\pi\)
\(930\) −2.27171e9 −0.0926110
\(931\) −1.43246e9 −0.0581780
\(932\) 3.32379e10 1.34486
\(933\) −3.09601e9 −0.124801
\(934\) 2.76723e10 1.11130
\(935\) 3.74741e10 1.49931
\(936\) −9.67999e9 −0.385842
\(937\) −2.83321e9 −0.112510 −0.0562548 0.998416i \(-0.517916\pi\)
−0.0562548 + 0.998416i \(0.517916\pi\)
\(938\) 8.29243e10 3.28074
\(939\) 1.14331e8 0.00450645
\(940\) 1.78100e10 0.699387
\(941\) −4.17032e10 −1.63157 −0.815786 0.578354i \(-0.803695\pi\)
−0.815786 + 0.578354i \(0.803695\pi\)
\(942\) 1.49326e9 0.0582046
\(943\) 8.01812e8 0.0311373
\(944\) 5.05779e10 1.95686
\(945\) −3.12614e10 −1.20503
\(946\) −4.05744e9 −0.155824
\(947\) 1.58387e10 0.606032 0.303016 0.952985i \(-0.402006\pi\)
0.303016 + 0.952985i \(0.402006\pi\)
\(948\) 3.03410e9 0.115665
\(949\) −1.06930e10 −0.406132
\(950\) −3.43089e9 −0.129830
\(951\) 7.82788e9 0.295129
\(952\) −1.13515e10 −0.426405
\(953\) −2.37238e10 −0.887889 −0.443944 0.896054i \(-0.646421\pi\)
−0.443944 + 0.896054i \(0.646421\pi\)
\(954\) −2.32675e9 −0.0867623
\(955\) 7.52597e10 2.79609
\(956\) 1.07589e10 0.398260
\(957\) 3.08543e9 0.113795
\(958\) −3.13431e10 −1.15176
\(959\) 6.29891e10 2.30622
\(960\) −6.12161e9 −0.223314
\(961\) −2.66042e10 −0.966981
\(962\) 3.29669e10 1.19389
\(963\) 1.51381e10 0.546233
\(964\) 7.89740e9 0.283932
\(965\) −3.76892e10 −1.35012
\(966\) 3.67061e9 0.131014
\(967\) 8.66320e9 0.308096 0.154048 0.988063i \(-0.450769\pi\)
0.154048 + 0.988063i \(0.450769\pi\)
\(968\) 3.06031e9 0.108443
\(969\) 2.04155e8 0.00720820
\(970\) −6.95656e9 −0.244734
\(971\) −2.16268e10 −0.758098 −0.379049 0.925377i \(-0.623749\pi\)
−0.379049 + 0.925377i \(0.623749\pi\)
\(972\) −1.29866e10 −0.453591
\(973\) 2.93874e9 0.102274
\(974\) −3.87885e10 −1.34508
\(975\) 2.41184e10 0.833360
\(976\) 4.48592e10 1.54446
\(977\) 3.39448e9 0.116451 0.0582255 0.998303i \(-0.481456\pi\)
0.0582255 + 0.998303i \(0.481456\pi\)
\(978\) −1.62853e9 −0.0556684
\(979\) 3.53662e10 1.20462
\(980\) −7.47952e10 −2.53853
\(981\) −1.17674e10 −0.397960
\(982\) 3.53507e10 1.19126
\(983\) 1.20191e10 0.403585 0.201792 0.979428i \(-0.435323\pi\)
0.201792 + 0.979428i \(0.435323\pi\)
\(984\) −1.53978e8 −0.00515199
\(985\) −7.62525e10 −2.54230
\(986\) 3.15963e10 1.04970
\(987\) 4.33013e9 0.143348
\(988\) 1.37135e9 0.0452374
\(989\) −1.41532e9 −0.0465228
\(990\) −5.77082e10 −1.89023
\(991\) −4.37960e10 −1.42948 −0.714738 0.699393i \(-0.753454\pi\)
−0.714738 + 0.699393i \(0.753454\pi\)
\(992\) 7.24216e9 0.235547
\(993\) 4.26911e9 0.138361
\(994\) −9.05895e10 −2.92567
\(995\) 8.52855e10 2.74470
\(996\) 1.95908e9 0.0628267
\(997\) −8.81226e9 −0.281614 −0.140807 0.990037i \(-0.544970\pi\)
−0.140807 + 0.990037i \(0.544970\pi\)
\(998\) 8.14827e10 2.59483
\(999\) −6.89802e9 −0.218900
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 43.8.a.a.1.10 11
3.2 odd 2 387.8.a.b.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.8.a.a.1.10 11 1.1 even 1 trivial
387.8.a.b.1.2 11 3.2 odd 2