Properties

Label 177.6.a.a.1.11
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3879361069\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + 13849341 x^{3} - 23890558 x^{2} - 74443300 x - 14846072\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(9.42442\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.42442 q^{2} +9.00000 q^{3} +38.9709 q^{4} -30.3784 q^{5} +75.8198 q^{6} -197.653 q^{7} +58.7254 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+8.42442 q^{2} +9.00000 q^{3} +38.9709 q^{4} -30.3784 q^{5} +75.8198 q^{6} -197.653 q^{7} +58.7254 q^{8} +81.0000 q^{9} -255.921 q^{10} -604.600 q^{11} +350.738 q^{12} -893.648 q^{13} -1665.11 q^{14} -273.406 q^{15} -752.340 q^{16} +1088.04 q^{17} +682.378 q^{18} +2022.78 q^{19} -1183.87 q^{20} -1778.88 q^{21} -5093.40 q^{22} +1324.04 q^{23} +528.528 q^{24} -2202.15 q^{25} -7528.47 q^{26} +729.000 q^{27} -7702.70 q^{28} +2519.29 q^{29} -2303.29 q^{30} +8782.14 q^{31} -8217.24 q^{32} -5441.40 q^{33} +9166.09 q^{34} +6004.38 q^{35} +3156.64 q^{36} -13007.9 q^{37} +17040.7 q^{38} -8042.83 q^{39} -1783.98 q^{40} +10648.4 q^{41} -14986.0 q^{42} +7396.68 q^{43} -23561.8 q^{44} -2460.65 q^{45} +11154.3 q^{46} -23429.3 q^{47} -6771.06 q^{48} +22259.6 q^{49} -18551.9 q^{50} +9792.34 q^{51} -34826.2 q^{52} -17464.3 q^{53} +6141.40 q^{54} +18366.8 q^{55} -11607.2 q^{56} +18205.0 q^{57} +21223.6 q^{58} +3481.00 q^{59} -10654.9 q^{60} -11795.1 q^{61} +73984.4 q^{62} -16009.9 q^{63} -45150.6 q^{64} +27147.6 q^{65} -45840.6 q^{66} -46995.6 q^{67} +42401.8 q^{68} +11916.4 q^{69} +50583.4 q^{70} -34625.3 q^{71} +4756.76 q^{72} -31175.2 q^{73} -109584. q^{74} -19819.4 q^{75} +78829.3 q^{76} +119501. q^{77} -67756.2 q^{78} -72100.3 q^{79} +22854.9 q^{80} +6561.00 q^{81} +89706.8 q^{82} +31482.3 q^{83} -69324.3 q^{84} -33052.9 q^{85} +62312.7 q^{86} +22673.7 q^{87} -35505.4 q^{88} +101434. q^{89} -20729.6 q^{90} +176632. q^{91} +51599.0 q^{92} +79039.2 q^{93} -197378. q^{94} -61448.7 q^{95} -73955.2 q^{96} -182378. q^{97} +187525. q^{98} -48972.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.42442 1.48924 0.744621 0.667488i \(-0.232630\pi\)
0.744621 + 0.667488i \(0.232630\pi\)
\(3\) 9.00000 0.577350
\(4\) 38.9709 1.21784
\(5\) −30.3784 −0.543426 −0.271713 0.962378i \(-0.587590\pi\)
−0.271713 + 0.962378i \(0.587590\pi\)
\(6\) 75.8198 0.859814
\(7\) −197.653 −1.52461 −0.762304 0.647220i \(-0.775932\pi\)
−0.762304 + 0.647220i \(0.775932\pi\)
\(8\) 58.7254 0.324415
\(9\) 81.0000 0.333333
\(10\) −255.921 −0.809292
\(11\) −604.600 −1.50656 −0.753280 0.657700i \(-0.771529\pi\)
−0.753280 + 0.657700i \(0.771529\pi\)
\(12\) 350.738 0.703120
\(13\) −893.648 −1.46659 −0.733294 0.679912i \(-0.762018\pi\)
−0.733294 + 0.679912i \(0.762018\pi\)
\(14\) −1665.11 −2.27051
\(15\) −273.406 −0.313747
\(16\) −752.340 −0.734707
\(17\) 1088.04 0.913107 0.456553 0.889696i \(-0.349084\pi\)
0.456553 + 0.889696i \(0.349084\pi\)
\(18\) 682.378 0.496414
\(19\) 2022.78 1.28548 0.642738 0.766086i \(-0.277799\pi\)
0.642738 + 0.766086i \(0.277799\pi\)
\(20\) −1183.87 −0.661805
\(21\) −1778.88 −0.880232
\(22\) −5093.40 −2.24363
\(23\) 1324.04 0.521894 0.260947 0.965353i \(-0.415965\pi\)
0.260947 + 0.965353i \(0.415965\pi\)
\(24\) 528.528 0.187301
\(25\) −2202.15 −0.704689
\(26\) −7528.47 −2.18410
\(27\) 729.000 0.192450
\(28\) −7702.70 −1.85673
\(29\) 2519.29 0.556268 0.278134 0.960542i \(-0.410284\pi\)
0.278134 + 0.960542i \(0.410284\pi\)
\(30\) −2303.29 −0.467245
\(31\) 8782.14 1.64133 0.820665 0.571409i \(-0.193603\pi\)
0.820665 + 0.571409i \(0.193603\pi\)
\(32\) −8217.24 −1.41857
\(33\) −5441.40 −0.869813
\(34\) 9166.09 1.35984
\(35\) 6004.38 0.828511
\(36\) 3156.64 0.405946
\(37\) −13007.9 −1.56208 −0.781038 0.624484i \(-0.785309\pi\)
−0.781038 + 0.624484i \(0.785309\pi\)
\(38\) 17040.7 1.91438
\(39\) −8042.83 −0.846735
\(40\) −1783.98 −0.176295
\(41\) 10648.4 0.989295 0.494648 0.869094i \(-0.335297\pi\)
0.494648 + 0.869094i \(0.335297\pi\)
\(42\) −14986.0 −1.31088
\(43\) 7396.68 0.610050 0.305025 0.952344i \(-0.401335\pi\)
0.305025 + 0.952344i \(0.401335\pi\)
\(44\) −23561.8 −1.83475
\(45\) −2460.65 −0.181142
\(46\) 11154.3 0.777226
\(47\) −23429.3 −1.54709 −0.773543 0.633744i \(-0.781517\pi\)
−0.773543 + 0.633744i \(0.781517\pi\)
\(48\) −6771.06 −0.424183
\(49\) 22259.6 1.32443
\(50\) −18551.9 −1.04945
\(51\) 9792.34 0.527183
\(52\) −34826.2 −1.78607
\(53\) −17464.3 −0.854006 −0.427003 0.904250i \(-0.640431\pi\)
−0.427003 + 0.904250i \(0.640431\pi\)
\(54\) 6141.40 0.286605
\(55\) 18366.8 0.818703
\(56\) −11607.2 −0.494605
\(57\) 18205.0 0.742169
\(58\) 21223.6 0.828417
\(59\) 3481.00 0.130189
\(60\) −10654.9 −0.382093
\(61\) −11795.1 −0.405861 −0.202930 0.979193i \(-0.565047\pi\)
−0.202930 + 0.979193i \(0.565047\pi\)
\(62\) 73984.4 2.44434
\(63\) −16009.9 −0.508202
\(64\) −45150.6 −1.37789
\(65\) 27147.6 0.796981
\(66\) −45840.6 −1.29536
\(67\) −46995.6 −1.27900 −0.639499 0.768792i \(-0.720858\pi\)
−0.639499 + 0.768792i \(0.720858\pi\)
\(68\) 42401.8 1.11202
\(69\) 11916.4 0.301316
\(70\) 50583.4 1.23385
\(71\) −34625.3 −0.815170 −0.407585 0.913167i \(-0.633629\pi\)
−0.407585 + 0.913167i \(0.633629\pi\)
\(72\) 4756.76 0.108138
\(73\) −31175.2 −0.684703 −0.342351 0.939572i \(-0.611223\pi\)
−0.342351 + 0.939572i \(0.611223\pi\)
\(74\) −109584. −2.32631
\(75\) −19819.4 −0.406852
\(76\) 78829.3 1.56550
\(77\) 119501. 2.29691
\(78\) −67756.2 −1.26099
\(79\) −72100.3 −1.29978 −0.649889 0.760029i \(-0.725185\pi\)
−0.649889 + 0.760029i \(0.725185\pi\)
\(80\) 22854.9 0.399259
\(81\) 6561.00 0.111111
\(82\) 89706.8 1.47330
\(83\) 31482.3 0.501616 0.250808 0.968037i \(-0.419304\pi\)
0.250808 + 0.968037i \(0.419304\pi\)
\(84\) −69324.3 −1.07198
\(85\) −33052.9 −0.496206
\(86\) 62312.7 0.908512
\(87\) 22673.7 0.321161
\(88\) −35505.4 −0.488751
\(89\) 101434. 1.35740 0.678702 0.734414i \(-0.262543\pi\)
0.678702 + 0.734414i \(0.262543\pi\)
\(90\) −20729.6 −0.269764
\(91\) 176632. 2.23597
\(92\) 51599.0 0.635583
\(93\) 79039.2 0.947622
\(94\) −197378. −2.30398
\(95\) −61448.7 −0.698560
\(96\) −73955.2 −0.819012
\(97\) −182378. −1.96808 −0.984042 0.177938i \(-0.943057\pi\)
−0.984042 + 0.177938i \(0.943057\pi\)
\(98\) 187525. 1.97239
\(99\) −48972.6 −0.502187
\(100\) −85819.7 −0.858197
\(101\) −103804. −1.01253 −0.506267 0.862377i \(-0.668975\pi\)
−0.506267 + 0.862377i \(0.668975\pi\)
\(102\) 82494.8 0.785102
\(103\) −106395. −0.988166 −0.494083 0.869415i \(-0.664496\pi\)
−0.494083 + 0.869415i \(0.664496\pi\)
\(104\) −52479.8 −0.475783
\(105\) 54039.4 0.478341
\(106\) −147126. −1.27182
\(107\) −53771.6 −0.454039 −0.227020 0.973890i \(-0.572898\pi\)
−0.227020 + 0.973890i \(0.572898\pi\)
\(108\) 28409.8 0.234373
\(109\) 114408. 0.922336 0.461168 0.887313i \(-0.347431\pi\)
0.461168 + 0.887313i \(0.347431\pi\)
\(110\) 154730. 1.21925
\(111\) −117071. −0.901864
\(112\) 148702. 1.12014
\(113\) 53614.8 0.394992 0.197496 0.980304i \(-0.436719\pi\)
0.197496 + 0.980304i \(0.436719\pi\)
\(114\) 153366. 1.10527
\(115\) −40222.3 −0.283610
\(116\) 98179.1 0.677445
\(117\) −72385.5 −0.488863
\(118\) 29325.4 0.193883
\(119\) −215054. −1.39213
\(120\) −16055.9 −0.101784
\(121\) 204490. 1.26972
\(122\) −99366.9 −0.604425
\(123\) 95835.8 0.571170
\(124\) 342247. 1.99888
\(125\) 161830. 0.926372
\(126\) −134874. −0.756836
\(127\) 109149. 0.600496 0.300248 0.953861i \(-0.402931\pi\)
0.300248 + 0.953861i \(0.402931\pi\)
\(128\) −117416. −0.633435
\(129\) 66570.1 0.352213
\(130\) 228703. 1.18690
\(131\) −236500. −1.20407 −0.602037 0.798468i \(-0.705644\pi\)
−0.602037 + 0.798468i \(0.705644\pi\)
\(132\) −212056. −1.05929
\(133\) −399807. −1.95984
\(134\) −395910. −1.90474
\(135\) −22145.9 −0.104582
\(136\) 63895.4 0.296226
\(137\) −106227. −0.483542 −0.241771 0.970333i \(-0.577728\pi\)
−0.241771 + 0.970333i \(0.577728\pi\)
\(138\) 100389. 0.448731
\(139\) 422871. 1.85640 0.928199 0.372084i \(-0.121357\pi\)
0.928199 + 0.372084i \(0.121357\pi\)
\(140\) 233996. 1.00899
\(141\) −210864. −0.893210
\(142\) −291698. −1.21398
\(143\) 540300. 2.20950
\(144\) −60939.5 −0.244902
\(145\) −76532.2 −0.302290
\(146\) −262633. −1.01969
\(147\) 200337. 0.764658
\(148\) −506928. −1.90236
\(149\) 15495.1 0.0571781 0.0285891 0.999591i \(-0.490899\pi\)
0.0285891 + 0.999591i \(0.490899\pi\)
\(150\) −166967. −0.605901
\(151\) 309025. 1.10294 0.551469 0.834195i \(-0.314067\pi\)
0.551469 + 0.834195i \(0.314067\pi\)
\(152\) 118788. 0.417027
\(153\) 88131.1 0.304369
\(154\) 1.00673e6 3.42066
\(155\) −266787. −0.891941
\(156\) −313436. −1.03119
\(157\) 505383. 1.63633 0.818166 0.574982i \(-0.194991\pi\)
0.818166 + 0.574982i \(0.194991\pi\)
\(158\) −607403. −1.93568
\(159\) −157178. −0.493061
\(160\) 249627. 0.770888
\(161\) −261701. −0.795683
\(162\) 55272.6 0.165471
\(163\) 48063.9 0.141694 0.0708468 0.997487i \(-0.477430\pi\)
0.0708468 + 0.997487i \(0.477430\pi\)
\(164\) 414978. 1.20480
\(165\) 165301. 0.472679
\(166\) 265220. 0.747028
\(167\) −609677. −1.69164 −0.845821 0.533467i \(-0.820889\pi\)
−0.845821 + 0.533467i \(0.820889\pi\)
\(168\) −104465. −0.285561
\(169\) 427314. 1.15088
\(170\) −278451. −0.738970
\(171\) 163845. 0.428492
\(172\) 288255. 0.742943
\(173\) 679574. 1.72632 0.863160 0.504930i \(-0.168482\pi\)
0.863160 + 0.504930i \(0.168482\pi\)
\(174\) 191012. 0.478287
\(175\) 435262. 1.07437
\(176\) 454865. 1.10688
\(177\) 31329.0 0.0751646
\(178\) 854524. 2.02150
\(179\) −47499.1 −0.110803 −0.0554017 0.998464i \(-0.517644\pi\)
−0.0554017 + 0.998464i \(0.517644\pi\)
\(180\) −95893.7 −0.220602
\(181\) −520.636 −0.00118124 −0.000590619 1.00000i \(-0.500188\pi\)
−0.000590619 1.00000i \(0.500188\pi\)
\(182\) 1.48802e6 3.32990
\(183\) −106156. −0.234324
\(184\) 77754.9 0.169310
\(185\) 395159. 0.848872
\(186\) 665860. 1.41124
\(187\) −657828. −1.37565
\(188\) −913059. −1.88410
\(189\) −144089. −0.293411
\(190\) −517670. −1.04032
\(191\) 630499. 1.25055 0.625275 0.780405i \(-0.284987\pi\)
0.625275 + 0.780405i \(0.284987\pi\)
\(192\) −406355. −0.795523
\(193\) 338210. 0.653572 0.326786 0.945098i \(-0.394034\pi\)
0.326786 + 0.945098i \(0.394034\pi\)
\(194\) −1.53643e6 −2.93095
\(195\) 244328. 0.460137
\(196\) 867477. 1.61294
\(197\) −968902. −1.77875 −0.889373 0.457181i \(-0.848859\pi\)
−0.889373 + 0.457181i \(0.848859\pi\)
\(198\) −412566. −0.747877
\(199\) −287993. −0.515525 −0.257763 0.966208i \(-0.582985\pi\)
−0.257763 + 0.966208i \(0.582985\pi\)
\(200\) −129322. −0.228611
\(201\) −422960. −0.738430
\(202\) −874486. −1.50791
\(203\) −497946. −0.848090
\(204\) 381616. 0.642024
\(205\) −323482. −0.537608
\(206\) −896320. −1.47162
\(207\) 107247. 0.173965
\(208\) 672327. 1.07751
\(209\) −1.22297e6 −1.93665
\(210\) 455251. 0.712365
\(211\) 881159. 1.36254 0.681268 0.732034i \(-0.261429\pi\)
0.681268 + 0.732034i \(0.261429\pi\)
\(212\) −680598. −1.04004
\(213\) −311628. −0.470638
\(214\) −452994. −0.676174
\(215\) −224699. −0.331517
\(216\) 42810.8 0.0624337
\(217\) −1.73581e6 −2.50238
\(218\) 963819. 1.37358
\(219\) −280577. −0.395313
\(220\) 715770. 0.997049
\(221\) −972323. −1.33915
\(222\) −986254. −1.34309
\(223\) −1.14135e6 −1.53694 −0.768468 0.639889i \(-0.778980\pi\)
−0.768468 + 0.639889i \(0.778980\pi\)
\(224\) 1.62416e6 2.16276
\(225\) −178374. −0.234896
\(226\) 451673. 0.588238
\(227\) −640098. −0.824483 −0.412242 0.911075i \(-0.635254\pi\)
−0.412242 + 0.911075i \(0.635254\pi\)
\(228\) 709464. 0.903843
\(229\) 711235. 0.896241 0.448120 0.893973i \(-0.352094\pi\)
0.448120 + 0.893973i \(0.352094\pi\)
\(230\) −338850. −0.422364
\(231\) 1.07551e6 1.32612
\(232\) 147947. 0.180462
\(233\) −309299. −0.373240 −0.186620 0.982432i \(-0.559753\pi\)
−0.186620 + 0.982432i \(0.559753\pi\)
\(234\) −609806. −0.728034
\(235\) 711744. 0.840726
\(236\) 135658. 0.158549
\(237\) −648903. −0.750428
\(238\) −1.81170e6 −2.07322
\(239\) −826348. −0.935768 −0.467884 0.883790i \(-0.654983\pi\)
−0.467884 + 0.883790i \(0.654983\pi\)
\(240\) 205694. 0.230512
\(241\) −1.26956e6 −1.40802 −0.704011 0.710189i \(-0.748609\pi\)
−0.704011 + 0.710189i \(0.748609\pi\)
\(242\) 1.72271e6 1.89092
\(243\) 59049.0 0.0641500
\(244\) −459665. −0.494273
\(245\) −676213. −0.719728
\(246\) 807361. 0.850609
\(247\) −1.80765e6 −1.88526
\(248\) 515734. 0.532472
\(249\) 283341. 0.289608
\(250\) 1.36333e6 1.37959
\(251\) 147810. 0.148088 0.0740441 0.997255i \(-0.476409\pi\)
0.0740441 + 0.997255i \(0.476409\pi\)
\(252\) −623919. −0.618909
\(253\) −800516. −0.786264
\(254\) 919516. 0.894283
\(255\) −297476. −0.286485
\(256\) 455658. 0.434549
\(257\) −855931. −0.808362 −0.404181 0.914679i \(-0.632443\pi\)
−0.404181 + 0.914679i \(0.632443\pi\)
\(258\) 560815. 0.524530
\(259\) 2.57104e6 2.38155
\(260\) 1.05797e6 0.970595
\(261\) 204063. 0.185423
\(262\) −1.99238e6 −1.79316
\(263\) −1.75000e6 −1.56009 −0.780044 0.625725i \(-0.784803\pi\)
−0.780044 + 0.625725i \(0.784803\pi\)
\(264\) −319548. −0.282180
\(265\) 530537. 0.464089
\(266\) −3.36814e6 −2.91868
\(267\) 912907. 0.783698
\(268\) −1.83146e6 −1.55761
\(269\) 193488. 0.163032 0.0815161 0.996672i \(-0.474024\pi\)
0.0815161 + 0.996672i \(0.474024\pi\)
\(270\) −186566. −0.155748
\(271\) −106308. −0.0879308 −0.0439654 0.999033i \(-0.513999\pi\)
−0.0439654 + 0.999033i \(0.513999\pi\)
\(272\) −818574. −0.670866
\(273\) 1.58969e6 1.29094
\(274\) −894903. −0.720111
\(275\) 1.33142e6 1.06166
\(276\) 464391. 0.366954
\(277\) 1.54305e6 1.20832 0.604159 0.796864i \(-0.293509\pi\)
0.604159 + 0.796864i \(0.293509\pi\)
\(278\) 3.56244e6 2.76462
\(279\) 711353. 0.547110
\(280\) 352610. 0.268781
\(281\) −527848. −0.398789 −0.199394 0.979919i \(-0.563897\pi\)
−0.199394 + 0.979919i \(0.563897\pi\)
\(282\) −1.77640e6 −1.33021
\(283\) 1.29156e6 0.958628 0.479314 0.877644i \(-0.340886\pi\)
0.479314 + 0.877644i \(0.340886\pi\)
\(284\) −1.34938e6 −0.992745
\(285\) −553039. −0.403314
\(286\) 4.55171e6 3.29048
\(287\) −2.10469e6 −1.50829
\(288\) −665596. −0.472857
\(289\) −236031. −0.166236
\(290\) −644739. −0.450183
\(291\) −1.64140e6 −1.13627
\(292\) −1.21492e6 −0.833858
\(293\) −1.09687e6 −0.746422 −0.373211 0.927746i \(-0.621743\pi\)
−0.373211 + 0.927746i \(0.621743\pi\)
\(294\) 1.68772e6 1.13876
\(295\) −105747. −0.0707480
\(296\) −763892. −0.506760
\(297\) −440753. −0.289938
\(298\) 130538. 0.0851520
\(299\) −1.18323e6 −0.765403
\(300\) −772378. −0.495480
\(301\) −1.46197e6 −0.930087
\(302\) 2.60336e6 1.64254
\(303\) −934233. −0.584586
\(304\) −1.52182e6 −0.944448
\(305\) 358317. 0.220555
\(306\) 742453. 0.453279
\(307\) 813798. 0.492800 0.246400 0.969168i \(-0.420752\pi\)
0.246400 + 0.969168i \(0.420752\pi\)
\(308\) 4.65705e6 2.79727
\(309\) −957559. −0.570518
\(310\) −2.24753e6 −1.32832
\(311\) −1.55418e6 −0.911169 −0.455585 0.890192i \(-0.650570\pi\)
−0.455585 + 0.890192i \(0.650570\pi\)
\(312\) −472318. −0.274693
\(313\) 1.15183e6 0.664548 0.332274 0.943183i \(-0.392184\pi\)
0.332274 + 0.943183i \(0.392184\pi\)
\(314\) 4.25756e6 2.43689
\(315\) 486355. 0.276170
\(316\) −2.80981e6 −1.58292
\(317\) −159930. −0.0893888 −0.0446944 0.999001i \(-0.514231\pi\)
−0.0446944 + 0.999001i \(0.514231\pi\)
\(318\) −1.32414e6 −0.734286
\(319\) −1.52317e6 −0.838051
\(320\) 1.37160e6 0.748779
\(321\) −483944. −0.262140
\(322\) −2.20468e6 −1.18496
\(323\) 2.20086e6 1.17378
\(324\) 255688. 0.135315
\(325\) 1.96795e6 1.03349
\(326\) 404911. 0.211016
\(327\) 1.02967e6 0.532511
\(328\) 625333. 0.320942
\(329\) 4.63086e6 2.35870
\(330\) 1.39257e6 0.703932
\(331\) −547660. −0.274752 −0.137376 0.990519i \(-0.543867\pi\)
−0.137376 + 0.990519i \(0.543867\pi\)
\(332\) 1.22689e6 0.610888
\(333\) −1.05364e6 −0.520692
\(334\) −5.13617e6 −2.51926
\(335\) 1.42765e6 0.695041
\(336\) 1.33832e6 0.646713
\(337\) 1.00634e6 0.482693 0.241347 0.970439i \(-0.422411\pi\)
0.241347 + 0.970439i \(0.422411\pi\)
\(338\) 3.59987e6 1.71394
\(339\) 482533. 0.228049
\(340\) −1.28810e6 −0.604299
\(341\) −5.30968e6 −2.47276
\(342\) 1.38030e6 0.638128
\(343\) −1.07773e6 −0.494624
\(344\) 434373. 0.197909
\(345\) −362001. −0.163743
\(346\) 5.72502e6 2.57091
\(347\) −306742. −0.136757 −0.0683786 0.997659i \(-0.521783\pi\)
−0.0683786 + 0.997659i \(0.521783\pi\)
\(348\) 883612. 0.391123
\(349\) 570494. 0.250719 0.125360 0.992111i \(-0.459992\pi\)
0.125360 + 0.992111i \(0.459992\pi\)
\(350\) 3.66683e6 1.60000
\(351\) −651469. −0.282245
\(352\) 4.96814e6 2.13716
\(353\) −906528. −0.387208 −0.193604 0.981080i \(-0.562018\pi\)
−0.193604 + 0.981080i \(0.562018\pi\)
\(354\) 263929. 0.111938
\(355\) 1.05186e6 0.442984
\(356\) 3.95298e6 1.65310
\(357\) −1.93548e6 −0.803746
\(358\) −400153. −0.165013
\(359\) 3.49718e6 1.43213 0.716065 0.698034i \(-0.245942\pi\)
0.716065 + 0.698034i \(0.245942\pi\)
\(360\) −144503. −0.0587651
\(361\) 1.61552e6 0.652447
\(362\) −4386.05 −0.00175915
\(363\) 1.84041e6 0.733075
\(364\) 6.88350e6 2.72305
\(365\) 947053. 0.372085
\(366\) −894302. −0.348965
\(367\) 848113. 0.328692 0.164346 0.986403i \(-0.447449\pi\)
0.164346 + 0.986403i \(0.447449\pi\)
\(368\) −996130. −0.383439
\(369\) 862523. 0.329765
\(370\) 3.32898e6 1.26417
\(371\) 3.45186e6 1.30202
\(372\) 3.08023e6 1.15405
\(373\) 269484. 0.100291 0.0501455 0.998742i \(-0.484032\pi\)
0.0501455 + 0.998742i \(0.484032\pi\)
\(374\) −5.54182e6 −2.04868
\(375\) 1.45647e6 0.534841
\(376\) −1.37589e6 −0.501898
\(377\) −2.25136e6 −0.815816
\(378\) −1.21387e6 −0.436959
\(379\) −4.75548e6 −1.70058 −0.850289 0.526316i \(-0.823573\pi\)
−0.850289 + 0.526316i \(0.823573\pi\)
\(380\) −2.39471e6 −0.850734
\(381\) 982340. 0.346696
\(382\) 5.31159e6 1.86237
\(383\) −5.52910e6 −1.92600 −0.963002 0.269493i \(-0.913144\pi\)
−0.963002 + 0.269493i \(0.913144\pi\)
\(384\) −1.05674e6 −0.365714
\(385\) −3.63025e6 −1.24820
\(386\) 2.84922e6 0.973326
\(387\) 599131. 0.203350
\(388\) −7.10743e6 −2.39681
\(389\) 1.57117e6 0.526440 0.263220 0.964736i \(-0.415215\pi\)
0.263220 + 0.964736i \(0.415215\pi\)
\(390\) 2.05833e6 0.685256
\(391\) 1.44061e6 0.476545
\(392\) 1.30721e6 0.429664
\(393\) −2.12850e6 −0.695172
\(394\) −8.16243e6 −2.64898
\(395\) 2.19029e6 0.706333
\(396\) −1.90850e6 −0.611583
\(397\) 1.51249e6 0.481632 0.240816 0.970571i \(-0.422585\pi\)
0.240816 + 0.970571i \(0.422585\pi\)
\(398\) −2.42618e6 −0.767741
\(399\) −3.59827e6 −1.13152
\(400\) 1.65677e6 0.517740
\(401\) 533958. 0.165824 0.0829118 0.996557i \(-0.473578\pi\)
0.0829118 + 0.996557i \(0.473578\pi\)
\(402\) −3.56319e6 −1.09970
\(403\) −7.84814e6 −2.40715
\(404\) −4.04532e6 −1.23310
\(405\) −199313. −0.0603806
\(406\) −4.19490e6 −1.26301
\(407\) 7.86456e6 2.35336
\(408\) 575059. 0.171026
\(409\) 5.73488e6 1.69518 0.847591 0.530650i \(-0.178052\pi\)
0.847591 + 0.530650i \(0.178052\pi\)
\(410\) −2.72515e6 −0.800628
\(411\) −956045. −0.279173
\(412\) −4.14632e6 −1.20343
\(413\) −688030. −0.198487
\(414\) 903497. 0.259075
\(415\) −956384. −0.272591
\(416\) 7.34332e6 2.08046
\(417\) 3.80584e6 1.07179
\(418\) −1.03028e7 −2.88413
\(419\) 3.45104e6 0.960318 0.480159 0.877182i \(-0.340579\pi\)
0.480159 + 0.877182i \(0.340579\pi\)
\(420\) 2.10596e6 0.582542
\(421\) −1.93686e6 −0.532590 −0.266295 0.963892i \(-0.585800\pi\)
−0.266295 + 0.963892i \(0.585800\pi\)
\(422\) 7.42325e6 2.02914
\(423\) −1.89777e6 −0.515695
\(424\) −1.02560e6 −0.277052
\(425\) −2.39602e6 −0.643456
\(426\) −2.62528e6 −0.700894
\(427\) 2.33134e6 0.618778
\(428\) −2.09552e6 −0.552947
\(429\) 4.86270e6 1.27566
\(430\) −1.89296e6 −0.493709
\(431\) −727579. −0.188663 −0.0943315 0.995541i \(-0.530071\pi\)
−0.0943315 + 0.995541i \(0.530071\pi\)
\(432\) −548456. −0.141394
\(433\) 108435. 0.0277938 0.0138969 0.999903i \(-0.495576\pi\)
0.0138969 + 0.999903i \(0.495576\pi\)
\(434\) −1.46232e7 −3.72665
\(435\) −688790. −0.174527
\(436\) 4.45857e6 1.12326
\(437\) 2.67824e6 0.670882
\(438\) −2.36370e6 −0.588717
\(439\) −1.97340e6 −0.488712 −0.244356 0.969686i \(-0.578577\pi\)
−0.244356 + 0.969686i \(0.578577\pi\)
\(440\) 1.07860e6 0.265600
\(441\) 1.80303e6 0.441476
\(442\) −8.19125e6 −1.99432
\(443\) 6.75043e6 1.63426 0.817131 0.576452i \(-0.195563\pi\)
0.817131 + 0.576452i \(0.195563\pi\)
\(444\) −4.56235e6 −1.09833
\(445\) −3.08141e6 −0.737648
\(446\) −9.61519e6 −2.28887
\(447\) 139456. 0.0330118
\(448\) 8.92414e6 2.10074
\(449\) −2.44220e6 −0.571697 −0.285849 0.958275i \(-0.592275\pi\)
−0.285849 + 0.958275i \(0.592275\pi\)
\(450\) −1.50270e6 −0.349817
\(451\) −6.43804e6 −1.49043
\(452\) 2.08941e6 0.481037
\(453\) 2.78122e6 0.636782
\(454\) −5.39245e6 −1.22785
\(455\) −5.36580e6 −1.21508
\(456\) 1.06909e6 0.240771
\(457\) 7.55416e6 1.69198 0.845991 0.533197i \(-0.179010\pi\)
0.845991 + 0.533197i \(0.179010\pi\)
\(458\) 5.99175e6 1.33472
\(459\) 793180. 0.175728
\(460\) −1.56750e6 −0.345392
\(461\) 4.16445e6 0.912652 0.456326 0.889813i \(-0.349165\pi\)
0.456326 + 0.889813i \(0.349165\pi\)
\(462\) 9.06053e6 1.97492
\(463\) 1.76553e6 0.382757 0.191378 0.981516i \(-0.438704\pi\)
0.191378 + 0.981516i \(0.438704\pi\)
\(464\) −1.89537e6 −0.408694
\(465\) −2.40109e6 −0.514962
\(466\) −2.60566e6 −0.555845
\(467\) −7.17957e6 −1.52337 −0.761686 0.647946i \(-0.775628\pi\)
−0.761686 + 0.647946i \(0.775628\pi\)
\(468\) −2.82092e6 −0.595356
\(469\) 9.28881e6 1.94997
\(470\) 5.99603e6 1.25204
\(471\) 4.54845e6 0.944737
\(472\) 204423. 0.0422352
\(473\) −4.47203e6 −0.919078
\(474\) −5.46663e6 −1.11757
\(475\) −4.45446e6 −0.905860
\(476\) −8.38083e6 −1.69539
\(477\) −1.41461e6 −0.284669
\(478\) −6.96150e6 −1.39358
\(479\) −3.33708e6 −0.664549 −0.332275 0.943183i \(-0.607816\pi\)
−0.332275 + 0.943183i \(0.607816\pi\)
\(480\) 2.24664e6 0.445072
\(481\) 1.16245e7 2.29092
\(482\) −1.06953e7 −2.09688
\(483\) −2.35531e6 −0.459388
\(484\) 7.96916e6 1.54632
\(485\) 5.54036e6 1.06951
\(486\) 497454. 0.0955349
\(487\) 5.15101e6 0.984170 0.492085 0.870547i \(-0.336235\pi\)
0.492085 + 0.870547i \(0.336235\pi\)
\(488\) −692672. −0.131667
\(489\) 432575. 0.0818068
\(490\) −5.69670e6 −1.07185
\(491\) −2.53964e6 −0.475410 −0.237705 0.971337i \(-0.576395\pi\)
−0.237705 + 0.971337i \(0.576395\pi\)
\(492\) 3.73480e6 0.695593
\(493\) 2.74109e6 0.507932
\(494\) −1.52284e7 −2.80761
\(495\) 1.48771e6 0.272901
\(496\) −6.60715e6 −1.20590
\(497\) 6.84379e6 1.24281
\(498\) 2.38698e6 0.431297
\(499\) −2.87671e6 −0.517184 −0.258592 0.965987i \(-0.583259\pi\)
−0.258592 + 0.965987i \(0.583259\pi\)
\(500\) 6.30667e6 1.12817
\(501\) −5.48709e6 −0.976670
\(502\) 1.24522e6 0.220539
\(503\) −7.87525e6 −1.38786 −0.693928 0.720044i \(-0.744122\pi\)
−0.693928 + 0.720044i \(0.744122\pi\)
\(504\) −940186. −0.164868
\(505\) 3.15339e6 0.550237
\(506\) −6.74388e6 −1.17094
\(507\) 3.84582e6 0.664461
\(508\) 4.25362e6 0.731307
\(509\) 5.21697e6 0.892532 0.446266 0.894900i \(-0.352753\pi\)
0.446266 + 0.894900i \(0.352753\pi\)
\(510\) −2.50606e6 −0.426645
\(511\) 6.16187e6 1.04390
\(512\) 7.59596e6 1.28058
\(513\) 1.47460e6 0.247390
\(514\) −7.21072e6 −1.20385
\(515\) 3.23213e6 0.536995
\(516\) 2.59429e6 0.428938
\(517\) 1.41653e7 2.33078
\(518\) 2.16595e7 3.54670
\(519\) 6.11617e6 0.996692
\(520\) 1.59425e6 0.258553
\(521\) −5.77782e6 −0.932544 −0.466272 0.884641i \(-0.654403\pi\)
−0.466272 + 0.884641i \(0.654403\pi\)
\(522\) 1.71911e6 0.276139
\(523\) −4.06016e6 −0.649067 −0.324533 0.945874i \(-0.605207\pi\)
−0.324533 + 0.945874i \(0.605207\pi\)
\(524\) −9.21661e6 −1.46637
\(525\) 3.91735e6 0.620290
\(526\) −1.47427e7 −2.32335
\(527\) 9.55530e6 1.49871
\(528\) 4.09378e6 0.639058
\(529\) −4.68326e6 −0.727627
\(530\) 4.46947e6 0.691140
\(531\) 281961. 0.0433963
\(532\) −1.55808e7 −2.38678
\(533\) −9.51594e6 −1.45089
\(534\) 7.69072e6 1.16711
\(535\) 1.63350e6 0.246737
\(536\) −2.75983e6 −0.414926
\(537\) −427492. −0.0639724
\(538\) 1.63002e6 0.242794
\(539\) −1.34582e7 −1.99533
\(540\) −863043. −0.127364
\(541\) 4.55205e6 0.668672 0.334336 0.942454i \(-0.391488\pi\)
0.334336 + 0.942454i \(0.391488\pi\)
\(542\) −895580. −0.130950
\(543\) −4685.72 −0.000681988 0
\(544\) −8.94067e6 −1.29531
\(545\) −3.47553e6 −0.501221
\(546\) 1.33922e7 1.92252
\(547\) 1.31265e6 0.187578 0.0937889 0.995592i \(-0.470102\pi\)
0.0937889 + 0.995592i \(0.470102\pi\)
\(548\) −4.13977e6 −0.588877
\(549\) −955404. −0.135287
\(550\) 1.12164e7 1.58106
\(551\) 5.09597e6 0.715069
\(552\) 699794. 0.0977513
\(553\) 1.42508e7 1.98165
\(554\) 1.29993e7 1.79948
\(555\) 3.55643e6 0.490096
\(556\) 1.64796e7 2.26079
\(557\) −8.08811e6 −1.10461 −0.552305 0.833642i \(-0.686252\pi\)
−0.552305 + 0.833642i \(0.686252\pi\)
\(558\) 5.99274e6 0.814779
\(559\) −6.61003e6 −0.894692
\(560\) −4.51734e6 −0.608713
\(561\) −5.92045e6 −0.794232
\(562\) −4.44681e6 −0.593893
\(563\) 606847. 0.0806878 0.0403439 0.999186i \(-0.487155\pi\)
0.0403439 + 0.999186i \(0.487155\pi\)
\(564\) −8.21753e6 −1.08779
\(565\) −1.62873e6 −0.214649
\(566\) 1.08807e7 1.42763
\(567\) −1.29680e6 −0.169401
\(568\) −2.03339e6 −0.264453
\(569\) −5.04180e6 −0.652837 −0.326418 0.945225i \(-0.605842\pi\)
−0.326418 + 0.945225i \(0.605842\pi\)
\(570\) −4.65903e6 −0.600632
\(571\) −9.40238e6 −1.20683 −0.603417 0.797426i \(-0.706194\pi\)
−0.603417 + 0.797426i \(0.706194\pi\)
\(572\) 2.10559e7 2.69082
\(573\) 5.67449e6 0.722005
\(574\) −1.77308e7 −2.24620
\(575\) −2.91574e6 −0.367773
\(576\) −3.65720e6 −0.459296
\(577\) −430213. −0.0537953 −0.0268977 0.999638i \(-0.508563\pi\)
−0.0268977 + 0.999638i \(0.508563\pi\)
\(578\) −1.98842e6 −0.247565
\(579\) 3.04389e6 0.377340
\(580\) −2.98252e6 −0.368141
\(581\) −6.22257e6 −0.764768
\(582\) −1.38279e7 −1.69219
\(583\) 1.05589e7 1.28661
\(584\) −1.83077e6 −0.222128
\(585\) 2.19896e6 0.265660
\(586\) −9.24046e6 −1.11160
\(587\) 6.88680e6 0.824940 0.412470 0.910971i \(-0.364666\pi\)
0.412470 + 0.910971i \(0.364666\pi\)
\(588\) 7.80730e6 0.931231
\(589\) 1.77643e7 2.10989
\(590\) −890859. −0.105361
\(591\) −8.72012e6 −1.02696
\(592\) 9.78634e6 1.14767
\(593\) 1.50380e7 1.75612 0.878059 0.478552i \(-0.158838\pi\)
0.878059 + 0.478552i \(0.158838\pi\)
\(594\) −3.71309e6 −0.431787
\(595\) 6.53299e6 0.756519
\(596\) 603859. 0.0696337
\(597\) −2.59194e6 −0.297639
\(598\) −9.96800e6 −1.13987
\(599\) −9.04381e6 −1.02987 −0.514937 0.857228i \(-0.672185\pi\)
−0.514937 + 0.857228i \(0.672185\pi\)
\(600\) −1.16390e6 −0.131989
\(601\) 4.79275e6 0.541250 0.270625 0.962685i \(-0.412770\pi\)
0.270625 + 0.962685i \(0.412770\pi\)
\(602\) −1.23163e7 −1.38512
\(603\) −3.80664e6 −0.426333
\(604\) 1.20430e7 1.34320
\(605\) −6.21209e6 −0.690000
\(606\) −7.87037e6 −0.870590
\(607\) −8.02372e6 −0.883902 −0.441951 0.897039i \(-0.645713\pi\)
−0.441951 + 0.897039i \(0.645713\pi\)
\(608\) −1.66216e7 −1.82354
\(609\) −4.48151e6 −0.489645
\(610\) 3.01861e6 0.328460
\(611\) 2.09375e7 2.26894
\(612\) 3.43454e6 0.370672
\(613\) −1.08600e7 −1.16729 −0.583645 0.812009i \(-0.698374\pi\)
−0.583645 + 0.812009i \(0.698374\pi\)
\(614\) 6.85577e6 0.733898
\(615\) −2.91134e6 −0.310388
\(616\) 7.01774e6 0.745153
\(617\) 328233. 0.0347112 0.0173556 0.999849i \(-0.494475\pi\)
0.0173556 + 0.999849i \(0.494475\pi\)
\(618\) −8.06688e6 −0.849639
\(619\) 1.10733e7 1.16159 0.580793 0.814051i \(-0.302742\pi\)
0.580793 + 0.814051i \(0.302742\pi\)
\(620\) −1.03969e7 −1.08624
\(621\) 965227. 0.100439
\(622\) −1.30930e7 −1.35695
\(623\) −2.00487e7 −2.06951
\(624\) 6.05094e6 0.622102
\(625\) 1.96557e6 0.201274
\(626\) 9.70348e6 0.989673
\(627\) −1.10067e7 −1.11812
\(628\) 1.96952e7 1.99279
\(629\) −1.41531e7 −1.42634
\(630\) 4.09726e6 0.411284
\(631\) 8.11446e6 0.811309 0.405654 0.914027i \(-0.367044\pi\)
0.405654 + 0.914027i \(0.367044\pi\)
\(632\) −4.23412e6 −0.421668
\(633\) 7.93043e6 0.786661
\(634\) −1.34732e6 −0.133121
\(635\) −3.31577e6 −0.326325
\(636\) −6.12538e6 −0.600468
\(637\) −1.98923e7 −1.94239
\(638\) −1.28318e7 −1.24806
\(639\) −2.80465e6 −0.271723
\(640\) 3.56691e6 0.344225
\(641\) −3.81722e6 −0.366946 −0.183473 0.983025i \(-0.558734\pi\)
−0.183473 + 0.983025i \(0.558734\pi\)
\(642\) −4.07695e6 −0.390389
\(643\) −7.74644e6 −0.738881 −0.369441 0.929254i \(-0.620451\pi\)
−0.369441 + 0.929254i \(0.620451\pi\)
\(644\) −1.01987e7 −0.969014
\(645\) −2.02230e6 −0.191401
\(646\) 1.85409e7 1.74804
\(647\) 60872.6 0.00571691 0.00285845 0.999996i \(-0.499090\pi\)
0.00285845 + 0.999996i \(0.499090\pi\)
\(648\) 385297. 0.0360461
\(649\) −2.10461e6 −0.196137
\(650\) 1.65788e7 1.53911
\(651\) −1.56223e7 −1.44475
\(652\) 1.87309e6 0.172560
\(653\) 263078. 0.0241436 0.0120718 0.999927i \(-0.496157\pi\)
0.0120718 + 0.999927i \(0.496157\pi\)
\(654\) 8.67437e6 0.793037
\(655\) 7.18450e6 0.654324
\(656\) −8.01124e6 −0.726842
\(657\) −2.52519e6 −0.228234
\(658\) 3.90123e7 3.51267
\(659\) −6.13618e6 −0.550408 −0.275204 0.961386i \(-0.588745\pi\)
−0.275204 + 0.961386i \(0.588745\pi\)
\(660\) 6.44193e6 0.575647
\(661\) 5.91533e6 0.526593 0.263297 0.964715i \(-0.415190\pi\)
0.263297 + 0.964715i \(0.415190\pi\)
\(662\) −4.61372e6 −0.409172
\(663\) −8.75090e6 −0.773160
\(664\) 1.84881e6 0.162732
\(665\) 1.21455e7 1.06503
\(666\) −8.87628e6 −0.775435
\(667\) 3.33565e6 0.290313
\(668\) −2.37596e7 −2.06015
\(669\) −1.02721e7 −0.887350
\(670\) 1.20271e7 1.03508
\(671\) 7.13132e6 0.611454
\(672\) 1.46174e7 1.24867
\(673\) −351835. −0.0299434 −0.0149717 0.999888i \(-0.504766\pi\)
−0.0149717 + 0.999888i \(0.504766\pi\)
\(674\) 8.47785e6 0.718847
\(675\) −1.60537e6 −0.135617
\(676\) 1.66528e7 1.40159
\(677\) 7.74491e6 0.649449 0.324724 0.945809i \(-0.394728\pi\)
0.324724 + 0.945809i \(0.394728\pi\)
\(678\) 4.06506e6 0.339620
\(679\) 3.60476e7 3.00055
\(680\) −1.94104e6 −0.160977
\(681\) −5.76088e6 −0.476016
\(682\) −4.47310e7 −3.68254
\(683\) 33771.4 0.00277011 0.00138506 0.999999i \(-0.499559\pi\)
0.00138506 + 0.999999i \(0.499559\pi\)
\(684\) 6.38517e6 0.521834
\(685\) 3.22702e6 0.262769
\(686\) −9.07925e6 −0.736614
\(687\) 6.40112e6 0.517445
\(688\) −5.56482e6 −0.448208
\(689\) 1.56069e7 1.25247
\(690\) −3.04965e6 −0.243852
\(691\) 1.03899e6 0.0827782 0.0413891 0.999143i \(-0.486822\pi\)
0.0413891 + 0.999143i \(0.486822\pi\)
\(692\) 2.64836e7 2.10238
\(693\) 9.67957e6 0.765637
\(694\) −2.58413e6 −0.203664
\(695\) −1.28462e7 −1.00881
\(696\) 1.33152e6 0.104190
\(697\) 1.15859e7 0.903332
\(698\) 4.80608e6 0.373381
\(699\) −2.78369e6 −0.215490
\(700\) 1.69625e7 1.30841
\(701\) −1.05020e7 −0.807194 −0.403597 0.914937i \(-0.632240\pi\)
−0.403597 + 0.914937i \(0.632240\pi\)
\(702\) −5.48825e6 −0.420331
\(703\) −2.63120e7 −2.00801
\(704\) 2.72981e7 2.07587
\(705\) 6.40570e6 0.485393
\(706\) −7.63697e6 −0.576646
\(707\) 2.05171e7 1.54372
\(708\) 1.22092e6 0.0915384
\(709\) −2.35801e7 −1.76169 −0.880847 0.473402i \(-0.843026\pi\)
−0.880847 + 0.473402i \(0.843026\pi\)
\(710\) 8.86133e6 0.659710
\(711\) −5.84013e6 −0.433260
\(712\) 5.95676e6 0.440362
\(713\) 1.16279e7 0.856600
\(714\) −1.63053e7 −1.19697
\(715\) −1.64134e7 −1.20070
\(716\) −1.85108e6 −0.134941
\(717\) −7.43713e6 −0.540266
\(718\) 2.94617e7 2.13279
\(719\) −1.21771e7 −0.878459 −0.439230 0.898375i \(-0.644749\pi\)
−0.439230 + 0.898375i \(0.644749\pi\)
\(720\) 1.85125e6 0.133086
\(721\) 2.10294e7 1.50657
\(722\) 1.36098e7 0.971650
\(723\) −1.14260e7 −0.812922
\(724\) −20289.6 −0.00143856
\(725\) −5.54787e6 −0.391996
\(726\) 1.55044e7 1.09173
\(727\) 1.11269e7 0.780794 0.390397 0.920647i \(-0.372338\pi\)
0.390397 + 0.920647i \(0.372338\pi\)
\(728\) 1.03728e7 0.725382
\(729\) 531441. 0.0370370
\(730\) 7.97837e6 0.554124
\(731\) 8.04787e6 0.557041
\(732\) −4.13699e6 −0.285369
\(733\) −2.36514e7 −1.62591 −0.812955 0.582327i \(-0.802143\pi\)
−0.812955 + 0.582327i \(0.802143\pi\)
\(734\) 7.14486e6 0.489501
\(735\) −6.08592e6 −0.415535
\(736\) −1.08800e7 −0.740343
\(737\) 2.84135e7 1.92689
\(738\) 7.26625e6 0.491100
\(739\) −1.88274e7 −1.26817 −0.634087 0.773262i \(-0.718624\pi\)
−0.634087 + 0.773262i \(0.718624\pi\)
\(740\) 1.53997e7 1.03379
\(741\) −1.62688e7 −1.08846
\(742\) 2.90800e7 1.93903
\(743\) 4.04511e6 0.268818 0.134409 0.990926i \(-0.457086\pi\)
0.134409 + 0.990926i \(0.457086\pi\)
\(744\) 4.64161e6 0.307423
\(745\) −470718. −0.0310721
\(746\) 2.27025e6 0.149357
\(747\) 2.55007e6 0.167205
\(748\) −2.56361e7 −1.67532
\(749\) 1.06281e7 0.692232
\(750\) 1.22699e7 0.796507
\(751\) 8.38036e6 0.542204 0.271102 0.962551i \(-0.412612\pi\)
0.271102 + 0.962551i \(0.412612\pi\)
\(752\) 1.76268e7 1.13665
\(753\) 1.33029e6 0.0854987
\(754\) −1.89664e7 −1.21495
\(755\) −9.38769e6 −0.599365
\(756\) −5.61527e6 −0.357327
\(757\) 1.50776e7 0.956296 0.478148 0.878279i \(-0.341308\pi\)
0.478148 + 0.878279i \(0.341308\pi\)
\(758\) −4.00622e7 −2.53257
\(759\) −7.20464e6 −0.453950
\(760\) −3.60860e6 −0.226623
\(761\) 2.51452e6 0.157396 0.0786981 0.996898i \(-0.474924\pi\)
0.0786981 + 0.996898i \(0.474924\pi\)
\(762\) 8.27564e6 0.516315
\(763\) −2.26130e7 −1.40620
\(764\) 2.45711e7 1.52297
\(765\) −2.67728e6 −0.165402
\(766\) −4.65794e7 −2.86829
\(767\) −3.11079e6 −0.190933
\(768\) 4.10092e6 0.250887
\(769\) −2.14386e7 −1.30732 −0.653659 0.756790i \(-0.726767\pi\)
−0.653659 + 0.756790i \(0.726767\pi\)
\(770\) −3.05827e7 −1.85887
\(771\) −7.70338e6 −0.466708
\(772\) 1.31803e7 0.795945
\(773\) 8.22664e6 0.495192 0.247596 0.968863i \(-0.420359\pi\)
0.247596 + 0.968863i \(0.420359\pi\)
\(774\) 5.04733e6 0.302837
\(775\) −1.93396e7 −1.15663
\(776\) −1.07102e7 −0.638476
\(777\) 2.31394e7 1.37499
\(778\) 1.32362e7 0.783996
\(779\) 2.15394e7 1.27171
\(780\) 9.52169e6 0.560373
\(781\) 2.09345e7 1.22810
\(782\) 1.21363e7 0.709690
\(783\) 1.83657e6 0.107054
\(784\) −1.67468e7 −0.973066
\(785\) −1.53527e7 −0.889225
\(786\) −1.79314e7 −1.03528
\(787\) 8.31927e6 0.478793 0.239397 0.970922i \(-0.423050\pi\)
0.239397 + 0.970922i \(0.423050\pi\)
\(788\) −3.77589e7 −2.16623
\(789\) −1.57500e7 −0.900717
\(790\) 1.84520e7 1.05190
\(791\) −1.05971e7 −0.602208
\(792\) −2.87593e6 −0.162917
\(793\) 1.05407e7 0.595231
\(794\) 1.27418e7 0.717266
\(795\) 4.77483e6 0.267942
\(796\) −1.12234e7 −0.627827
\(797\) −648589. −0.0361679 −0.0180840 0.999836i \(-0.505757\pi\)
−0.0180840 + 0.999836i \(0.505757\pi\)
\(798\) −3.03133e7 −1.68510
\(799\) −2.54919e7 −1.41265
\(800\) 1.80956e7 0.999651
\(801\) 8.21617e6 0.452468
\(802\) 4.49829e6 0.246951
\(803\) 1.88485e7 1.03155
\(804\) −1.64831e7 −0.899289
\(805\) 7.95005e6 0.432395
\(806\) −6.61160e7 −3.58483
\(807\) 1.74139e6 0.0941267
\(808\) −6.09591e6 −0.328481
\(809\) 6.42299e6 0.345037 0.172519 0.985006i \(-0.444810\pi\)
0.172519 + 0.985006i \(0.444810\pi\)
\(810\) −1.67909e6 −0.0899213
\(811\) −3.00650e7 −1.60513 −0.802564 0.596566i \(-0.796531\pi\)
−0.802564 + 0.596566i \(0.796531\pi\)
\(812\) −1.94054e7 −1.03284
\(813\) −956768. −0.0507669
\(814\) 6.62543e7 3.50472
\(815\) −1.46011e6 −0.0769999
\(816\) −7.36717e6 −0.387325
\(817\) 1.49618e7 0.784205
\(818\) 4.83131e7 2.52453
\(819\) 1.43072e7 0.745323
\(820\) −1.26064e7 −0.654720
\(821\) 2.26374e7 1.17211 0.586056 0.810271i \(-0.300680\pi\)
0.586056 + 0.810271i \(0.300680\pi\)
\(822\) −8.05413e6 −0.415756
\(823\) −1.72791e7 −0.889245 −0.444622 0.895718i \(-0.646662\pi\)
−0.444622 + 0.895718i \(0.646662\pi\)
\(824\) −6.24811e6 −0.320576
\(825\) 1.19828e7 0.612947
\(826\) −5.79625e6 −0.295595
\(827\) 2.43809e6 0.123961 0.0619805 0.998077i \(-0.480258\pi\)
0.0619805 + 0.998077i \(0.480258\pi\)
\(828\) 4.17952e6 0.211861
\(829\) −2.40502e7 −1.21544 −0.607718 0.794153i \(-0.707915\pi\)
−0.607718 + 0.794153i \(0.707915\pi\)
\(830\) −8.05698e6 −0.405954
\(831\) 1.38875e7 0.697622
\(832\) 4.03487e7 2.02079
\(833\) 2.42193e7 1.20934
\(834\) 3.20620e7 1.59616
\(835\) 1.85210e7 0.919281
\(836\) −4.76602e7 −2.35852
\(837\) 6.40218e6 0.315874
\(838\) 2.90730e7 1.43014
\(839\) −2.36128e7 −1.15809 −0.579046 0.815295i \(-0.696575\pi\)
−0.579046 + 0.815295i \(0.696575\pi\)
\(840\) 3.17349e6 0.155181
\(841\) −1.41643e7 −0.690566
\(842\) −1.63169e7 −0.793155
\(843\) −4.75063e6 −0.230241
\(844\) 3.43395e7 1.65935
\(845\) −1.29811e7 −0.625418
\(846\) −1.59876e7 −0.767994
\(847\) −4.04181e7 −1.93583
\(848\) 1.31391e7 0.627444
\(849\) 1.16241e7 0.553464
\(850\) −2.01851e7 −0.958261
\(851\) −1.72230e7 −0.815237
\(852\) −1.21444e7 −0.573162
\(853\) −2.14660e7 −1.01013 −0.505067 0.863080i \(-0.668532\pi\)
−0.505067 + 0.863080i \(0.668532\pi\)
\(854\) 1.96402e7 0.921510
\(855\) −4.97735e6 −0.232853
\(856\) −3.15776e6 −0.147297
\(857\) 1.36770e7 0.636121 0.318060 0.948071i \(-0.396969\pi\)
0.318060 + 0.948071i \(0.396969\pi\)
\(858\) 4.09654e7 1.89976
\(859\) 6.29314e6 0.290994 0.145497 0.989359i \(-0.453522\pi\)
0.145497 + 0.989359i \(0.453522\pi\)
\(860\) −8.75673e6 −0.403734
\(861\) −1.89422e7 −0.870809
\(862\) −6.12943e6 −0.280965
\(863\) 5.79993e6 0.265092 0.132546 0.991177i \(-0.457685\pi\)
0.132546 + 0.991177i \(0.457685\pi\)
\(864\) −5.99037e6 −0.273004
\(865\) −2.06444e7 −0.938127
\(866\) 913499. 0.0413917
\(867\) −2.12428e6 −0.0959762
\(868\) −6.76462e7 −3.04750
\(869\) 4.35919e7 1.95819
\(870\) −5.80265e6 −0.259913
\(871\) 4.19975e7 1.87576
\(872\) 6.71864e6 0.299219
\(873\) −1.47726e7 −0.656028
\(874\) 2.25626e7 0.999104
\(875\) −3.19862e7 −1.41235
\(876\) −1.09343e7 −0.481428
\(877\) −1.16101e6 −0.0509728 −0.0254864 0.999675i \(-0.508113\pi\)
−0.0254864 + 0.999675i \(0.508113\pi\)
\(878\) −1.66247e7 −0.727810
\(879\) −9.87180e6 −0.430947
\(880\) −1.38181e7 −0.601507
\(881\) −2.13517e7 −0.926813 −0.463407 0.886146i \(-0.653373\pi\)
−0.463407 + 0.886146i \(0.653373\pi\)
\(882\) 1.51895e7 0.657464
\(883\) 2.62499e7 1.13299 0.566495 0.824065i \(-0.308299\pi\)
0.566495 + 0.824065i \(0.308299\pi\)
\(884\) −3.78922e7 −1.63087
\(885\) −951725. −0.0408464
\(886\) 5.68684e7 2.43381
\(887\) −4.59171e7 −1.95959 −0.979795 0.200006i \(-0.935904\pi\)
−0.979795 + 0.200006i \(0.935904\pi\)
\(888\) −6.87503e6 −0.292578
\(889\) −2.15736e7 −0.915520
\(890\) −2.59591e7 −1.09854
\(891\) −3.96678e6 −0.167396
\(892\) −4.44793e7 −1.87174
\(893\) −4.73922e7 −1.98874
\(894\) 1.17484e6 0.0491625
\(895\) 1.44295e6 0.0602134
\(896\) 2.32076e7 0.965740
\(897\) −1.06490e7 −0.441906
\(898\) −2.05742e7 −0.851395
\(899\) 2.21248e7 0.913019
\(900\) −6.95140e6 −0.286066
\(901\) −1.90018e7 −0.779799
\(902\) −5.42367e7 −2.21961
\(903\) −1.31578e7 −0.536986
\(904\) 3.14855e6 0.128141
\(905\) 15816.1 0.000641915 0
\(906\) 2.34302e7 0.948321
\(907\) 1.22694e7 0.495229 0.247614 0.968859i \(-0.420353\pi\)
0.247614 + 0.968859i \(0.420353\pi\)
\(908\) −2.49452e7 −1.00409
\(909\) −8.40810e6 −0.337511
\(910\) −4.52038e7 −1.80955
\(911\) −3.04688e7 −1.21635 −0.608175 0.793803i \(-0.708098\pi\)
−0.608175 + 0.793803i \(0.708098\pi\)
\(912\) −1.36963e7 −0.545277
\(913\) −1.90342e7 −0.755715
\(914\) 6.36394e7 2.51977
\(915\) 3.22485e6 0.127338
\(916\) 2.77174e7 1.09148
\(917\) 4.67449e7 1.83574
\(918\) 6.68208e6 0.261701
\(919\) 1.89310e7 0.739407 0.369704 0.929150i \(-0.379459\pi\)
0.369704 + 0.929150i \(0.379459\pi\)
\(920\) −2.36207e6 −0.0920075
\(921\) 7.32418e6 0.284518
\(922\) 3.50831e7 1.35916
\(923\) 3.09428e7 1.19552
\(924\) 4.19135e7 1.61500
\(925\) 2.86453e7 1.10078
\(926\) 1.48736e7 0.570017
\(927\) −8.61803e6 −0.329389
\(928\) −2.07016e7 −0.789105
\(929\) 7.49000e6 0.284736 0.142368 0.989814i \(-0.454528\pi\)
0.142368 + 0.989814i \(0.454528\pi\)
\(930\) −2.02278e7 −0.766903
\(931\) 4.50263e7 1.70252
\(932\) −1.20536e7 −0.454547
\(933\) −1.39876e7 −0.526064
\(934\) −6.04837e7 −2.26867
\(935\) 1.99838e7 0.747564
\(936\) −4.25086e6 −0.158594
\(937\) 2.44259e7 0.908871 0.454436 0.890780i \(-0.349841\pi\)
0.454436 + 0.890780i \(0.349841\pi\)
\(938\) 7.82528e7 2.90398
\(939\) 1.03664e7 0.383677
\(940\) 2.77373e7 1.02387
\(941\) −2.74938e7 −1.01219 −0.506094 0.862478i \(-0.668911\pi\)
−0.506094 + 0.862478i \(0.668911\pi\)
\(942\) 3.83180e7 1.40694
\(943\) 1.40990e7 0.516307
\(944\) −2.61890e6 −0.0956507
\(945\) 4.37719e6 0.159447
\(946\) −3.76743e7 −1.36873
\(947\) −2.86619e7 −1.03855 −0.519277 0.854606i \(-0.673799\pi\)
−0.519277 + 0.854606i \(0.673799\pi\)
\(948\) −2.52883e7 −0.913900
\(949\) 2.78596e7 1.00418
\(950\) −3.75262e7 −1.34904
\(951\) −1.43937e6 −0.0516086
\(952\) −1.26291e7 −0.451628
\(953\) 1.44834e7 0.516580 0.258290 0.966067i \(-0.416841\pi\)
0.258290 + 0.966067i \(0.416841\pi\)
\(954\) −1.19172e7 −0.423940
\(955\) −1.91536e7 −0.679581
\(956\) −3.22035e7 −1.13961
\(957\) −1.37085e7 −0.483849
\(958\) −2.81129e7 −0.989674
\(959\) 2.09961e7 0.737212
\(960\) 1.23444e7 0.432308
\(961\) 4.84968e7 1.69397
\(962\) 9.79293e7 3.41173
\(963\) −4.35550e6 −0.151346
\(964\) −4.94757e7 −1.71474
\(965\) −1.02743e7 −0.355168
\(966\) −1.98421e7 −0.684139
\(967\) 2.23539e7 0.768753 0.384376 0.923177i \(-0.374417\pi\)
0.384376 + 0.923177i \(0.374417\pi\)
\(968\) 1.20088e7 0.411917
\(969\) 1.98077e7 0.677680
\(970\) 4.66743e7 1.59275
\(971\) −5.00533e7 −1.70367 −0.851833 0.523814i \(-0.824509\pi\)
−0.851833 + 0.523814i \(0.824509\pi\)
\(972\) 2.30119e6 0.0781244
\(973\) −8.35817e7 −2.83028
\(974\) 4.33943e7 1.46567
\(975\) 1.77115e7 0.596684
\(976\) 8.87393e6 0.298189
\(977\) 4.82166e7 1.61607 0.808035 0.589134i \(-0.200531\pi\)
0.808035 + 0.589134i \(0.200531\pi\)
\(978\) 3.64419e6 0.121830
\(979\) −6.13271e7 −2.04501
\(980\) −2.63526e7 −0.876512
\(981\) 9.26702e6 0.307445
\(982\) −2.13950e7 −0.708000
\(983\) −3.21582e7 −1.06147 −0.530735 0.847538i \(-0.678084\pi\)
−0.530735 + 0.847538i \(0.678084\pi\)
\(984\) 5.62800e6 0.185296
\(985\) 2.94337e7 0.966617
\(986\) 2.30921e7 0.756433
\(987\) 4.16778e7 1.36179
\(988\) −7.04456e7 −2.29595
\(989\) 9.79351e6 0.318382
\(990\) 1.25331e7 0.406416
\(991\) −1.12835e7 −0.364972 −0.182486 0.983208i \(-0.558414\pi\)
−0.182486 + 0.983208i \(0.558414\pi\)
\(992\) −7.21649e7 −2.32834
\(993\) −4.92894e6 −0.158628
\(994\) 5.76550e7 1.85085
\(995\) 8.74879e6 0.280150
\(996\) 1.10420e7 0.352696
\(997\) 5.30973e7 1.69174 0.845872 0.533387i \(-0.179081\pi\)
0.845872 + 0.533387i \(0.179081\pi\)
\(998\) −2.42346e7 −0.770212
\(999\) −9.48274e6 −0.300621
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 177.6.a.a.1.11 11
3.2 odd 2 531.6.a.b.1.1 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.11 11 1.1 even 1 trivial
531.6.a.b.1.1 11 3.2 odd 2