Properties

Label 4029.2.a.k.1.9
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.27443 q^{2} +1.00000 q^{3} -0.375837 q^{4} -3.50336 q^{5} -1.27443 q^{6} -0.192219 q^{7} +3.02783 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.27443 q^{2} +1.00000 q^{3} -0.375837 q^{4} -3.50336 q^{5} -1.27443 q^{6} -0.192219 q^{7} +3.02783 q^{8} +1.00000 q^{9} +4.46478 q^{10} +3.68610 q^{11} -0.375837 q^{12} -3.36950 q^{13} +0.244970 q^{14} -3.50336 q^{15} -3.10707 q^{16} +1.00000 q^{17} -1.27443 q^{18} +6.71698 q^{19} +1.31669 q^{20} -0.192219 q^{21} -4.69767 q^{22} +6.93165 q^{23} +3.02783 q^{24} +7.27356 q^{25} +4.29417 q^{26} +1.00000 q^{27} +0.0722432 q^{28} -7.85494 q^{29} +4.46478 q^{30} +6.58645 q^{31} -2.09592 q^{32} +3.68610 q^{33} -1.27443 q^{34} +0.673415 q^{35} -0.375837 q^{36} -4.80266 q^{37} -8.56029 q^{38} -3.36950 q^{39} -10.6076 q^{40} -10.0592 q^{41} +0.244970 q^{42} -12.2298 q^{43} -1.38537 q^{44} -3.50336 q^{45} -8.83388 q^{46} +6.12284 q^{47} -3.10707 q^{48} -6.96305 q^{49} -9.26962 q^{50} +1.00000 q^{51} +1.26638 q^{52} +5.67828 q^{53} -1.27443 q^{54} -12.9138 q^{55} -0.582008 q^{56} +6.71698 q^{57} +10.0105 q^{58} -4.78465 q^{59} +1.31669 q^{60} -8.22716 q^{61} -8.39395 q^{62} -0.192219 q^{63} +8.88525 q^{64} +11.8046 q^{65} -4.69767 q^{66} +9.89341 q^{67} -0.375837 q^{68} +6.93165 q^{69} -0.858218 q^{70} -9.09158 q^{71} +3.02783 q^{72} +14.6430 q^{73} +6.12064 q^{74} +7.27356 q^{75} -2.52449 q^{76} -0.708541 q^{77} +4.29417 q^{78} +1.00000 q^{79} +10.8852 q^{80} +1.00000 q^{81} +12.8197 q^{82} -4.79363 q^{83} +0.0722432 q^{84} -3.50336 q^{85} +15.5860 q^{86} -7.85494 q^{87} +11.1609 q^{88} +18.0558 q^{89} +4.46478 q^{90} +0.647682 q^{91} -2.60517 q^{92} +6.58645 q^{93} -7.80311 q^{94} -23.5320 q^{95} -2.09592 q^{96} -9.13412 q^{97} +8.87390 q^{98} +3.68610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27443 −0.901156 −0.450578 0.892737i \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.375837 −0.187919
\(5\) −3.50336 −1.56675 −0.783376 0.621548i \(-0.786504\pi\)
−0.783376 + 0.621548i \(0.786504\pi\)
\(6\) −1.27443 −0.520282
\(7\) −0.192219 −0.0726521 −0.0363261 0.999340i \(-0.511565\pi\)
−0.0363261 + 0.999340i \(0.511565\pi\)
\(8\) 3.02783 1.07050
\(9\) 1.00000 0.333333
\(10\) 4.46478 1.41189
\(11\) 3.68610 1.11140 0.555701 0.831382i \(-0.312450\pi\)
0.555701 + 0.831382i \(0.312450\pi\)
\(12\) −0.375837 −0.108495
\(13\) −3.36950 −0.934530 −0.467265 0.884117i \(-0.654761\pi\)
−0.467265 + 0.884117i \(0.654761\pi\)
\(14\) 0.244970 0.0654709
\(15\) −3.50336 −0.904565
\(16\) −3.10707 −0.776768
\(17\) 1.00000 0.242536
\(18\) −1.27443 −0.300385
\(19\) 6.71698 1.54098 0.770490 0.637452i \(-0.220012\pi\)
0.770490 + 0.637452i \(0.220012\pi\)
\(20\) 1.31669 0.294422
\(21\) −0.192219 −0.0419457
\(22\) −4.69767 −1.00155
\(23\) 6.93165 1.44535 0.722674 0.691189i \(-0.242913\pi\)
0.722674 + 0.691189i \(0.242913\pi\)
\(24\) 3.02783 0.618053
\(25\) 7.27356 1.45471
\(26\) 4.29417 0.842157
\(27\) 1.00000 0.192450
\(28\) 0.0722432 0.0136527
\(29\) −7.85494 −1.45863 −0.729313 0.684180i \(-0.760160\pi\)
−0.729313 + 0.684180i \(0.760160\pi\)
\(30\) 4.46478 0.815154
\(31\) 6.58645 1.18296 0.591481 0.806319i \(-0.298544\pi\)
0.591481 + 0.806319i \(0.298544\pi\)
\(32\) −2.09592 −0.370511
\(33\) 3.68610 0.641668
\(34\) −1.27443 −0.218562
\(35\) 0.673415 0.113828
\(36\) −0.375837 −0.0626395
\(37\) −4.80266 −0.789553 −0.394776 0.918777i \(-0.629178\pi\)
−0.394776 + 0.918777i \(0.629178\pi\)
\(38\) −8.56029 −1.38866
\(39\) −3.36950 −0.539551
\(40\) −10.6076 −1.67721
\(41\) −10.0592 −1.57098 −0.785492 0.618871i \(-0.787590\pi\)
−0.785492 + 0.618871i \(0.787590\pi\)
\(42\) 0.244970 0.0377996
\(43\) −12.2298 −1.86503 −0.932513 0.361135i \(-0.882389\pi\)
−0.932513 + 0.361135i \(0.882389\pi\)
\(44\) −1.38537 −0.208853
\(45\) −3.50336 −0.522251
\(46\) −8.83388 −1.30248
\(47\) 6.12284 0.893108 0.446554 0.894757i \(-0.352651\pi\)
0.446554 + 0.894757i \(0.352651\pi\)
\(48\) −3.10707 −0.448467
\(49\) −6.96305 −0.994722
\(50\) −9.26962 −1.31092
\(51\) 1.00000 0.140028
\(52\) 1.26638 0.175615
\(53\) 5.67828 0.779972 0.389986 0.920821i \(-0.372480\pi\)
0.389986 + 0.920821i \(0.372480\pi\)
\(54\) −1.27443 −0.173427
\(55\) −12.9138 −1.74129
\(56\) −0.582008 −0.0777741
\(57\) 6.71698 0.889685
\(58\) 10.0105 1.31445
\(59\) −4.78465 −0.622908 −0.311454 0.950261i \(-0.600816\pi\)
−0.311454 + 0.950261i \(0.600816\pi\)
\(60\) 1.31669 0.169984
\(61\) −8.22716 −1.05338 −0.526690 0.850058i \(-0.676567\pi\)
−0.526690 + 0.850058i \(0.676567\pi\)
\(62\) −8.39395 −1.06603
\(63\) −0.192219 −0.0242174
\(64\) 8.88525 1.11066
\(65\) 11.8046 1.46418
\(66\) −4.69767 −0.578243
\(67\) 9.89341 1.20867 0.604336 0.796729i \(-0.293438\pi\)
0.604336 + 0.796729i \(0.293438\pi\)
\(68\) −0.375837 −0.0455769
\(69\) 6.93165 0.834472
\(70\) −0.858218 −0.102577
\(71\) −9.09158 −1.07897 −0.539486 0.841995i \(-0.681381\pi\)
−0.539486 + 0.841995i \(0.681381\pi\)
\(72\) 3.02783 0.356833
\(73\) 14.6430 1.71383 0.856916 0.515456i \(-0.172377\pi\)
0.856916 + 0.515456i \(0.172377\pi\)
\(74\) 6.12064 0.711510
\(75\) 7.27356 0.839879
\(76\) −2.52449 −0.289579
\(77\) −0.708541 −0.0807457
\(78\) 4.29417 0.486219
\(79\) 1.00000 0.112509
\(80\) 10.8852 1.21700
\(81\) 1.00000 0.111111
\(82\) 12.8197 1.41570
\(83\) −4.79363 −0.526169 −0.263084 0.964773i \(-0.584740\pi\)
−0.263084 + 0.964773i \(0.584740\pi\)
\(84\) 0.0722432 0.00788238
\(85\) −3.50336 −0.379993
\(86\) 15.5860 1.68068
\(87\) −7.85494 −0.842138
\(88\) 11.1609 1.18976
\(89\) 18.0558 1.91391 0.956955 0.290236i \(-0.0937339\pi\)
0.956955 + 0.290236i \(0.0937339\pi\)
\(90\) 4.46478 0.470629
\(91\) 0.647682 0.0678956
\(92\) −2.60517 −0.271608
\(93\) 6.58645 0.682983
\(94\) −7.80311 −0.804829
\(95\) −23.5320 −2.41433
\(96\) −2.09592 −0.213914
\(97\) −9.13412 −0.927430 −0.463715 0.885984i \(-0.653484\pi\)
−0.463715 + 0.885984i \(0.653484\pi\)
\(98\) 8.87390 0.896399
\(99\) 3.68610 0.370467
\(100\) −2.73367 −0.273367
\(101\) 10.5019 1.04497 0.522487 0.852647i \(-0.325004\pi\)
0.522487 + 0.852647i \(0.325004\pi\)
\(102\) −1.27443 −0.126187
\(103\) −10.3810 −1.02287 −0.511437 0.859321i \(-0.670887\pi\)
−0.511437 + 0.859321i \(0.670887\pi\)
\(104\) −10.2023 −1.00041
\(105\) 0.673415 0.0657186
\(106\) −7.23656 −0.702876
\(107\) 17.8893 1.72943 0.864714 0.502264i \(-0.167500\pi\)
0.864714 + 0.502264i \(0.167500\pi\)
\(108\) −0.375837 −0.0361649
\(109\) −3.37660 −0.323420 −0.161710 0.986838i \(-0.551701\pi\)
−0.161710 + 0.986838i \(0.551701\pi\)
\(110\) 16.4576 1.56917
\(111\) −4.80266 −0.455848
\(112\) 0.597240 0.0564338
\(113\) 17.3123 1.62861 0.814303 0.580440i \(-0.197120\pi\)
0.814303 + 0.580440i \(0.197120\pi\)
\(114\) −8.56029 −0.801745
\(115\) −24.2841 −2.26450
\(116\) 2.95218 0.274103
\(117\) −3.36950 −0.311510
\(118\) 6.09768 0.561337
\(119\) −0.192219 −0.0176207
\(120\) −10.6076 −0.968336
\(121\) 2.58736 0.235215
\(122\) 10.4849 0.949259
\(123\) −10.0592 −0.907008
\(124\) −2.47543 −0.222300
\(125\) −7.96512 −0.712422
\(126\) 0.244970 0.0218236
\(127\) −17.2313 −1.52903 −0.764515 0.644606i \(-0.777021\pi\)
−0.764515 + 0.644606i \(0.777021\pi\)
\(128\) −7.13175 −0.630363
\(129\) −12.2298 −1.07677
\(130\) −15.0441 −1.31945
\(131\) 8.59473 0.750925 0.375463 0.926838i \(-0.377484\pi\)
0.375463 + 0.926838i \(0.377484\pi\)
\(132\) −1.38537 −0.120581
\(133\) −1.29113 −0.111955
\(134\) −12.6084 −1.08920
\(135\) −3.50336 −0.301522
\(136\) 3.02783 0.259634
\(137\) 2.88609 0.246575 0.123288 0.992371i \(-0.460656\pi\)
0.123288 + 0.992371i \(0.460656\pi\)
\(138\) −8.83388 −0.751990
\(139\) 19.2120 1.62954 0.814772 0.579781i \(-0.196862\pi\)
0.814772 + 0.579781i \(0.196862\pi\)
\(140\) −0.253094 −0.0213904
\(141\) 6.12284 0.515636
\(142\) 11.5866 0.972322
\(143\) −12.4203 −1.03864
\(144\) −3.10707 −0.258923
\(145\) 27.5187 2.28531
\(146\) −18.6614 −1.54443
\(147\) −6.96305 −0.574303
\(148\) 1.80502 0.148372
\(149\) 21.1504 1.73271 0.866354 0.499431i \(-0.166457\pi\)
0.866354 + 0.499431i \(0.166457\pi\)
\(150\) −9.26962 −0.756862
\(151\) −4.95582 −0.403299 −0.201649 0.979458i \(-0.564630\pi\)
−0.201649 + 0.979458i \(0.564630\pi\)
\(152\) 20.3379 1.64962
\(153\) 1.00000 0.0808452
\(154\) 0.902983 0.0727645
\(155\) −23.0747 −1.85341
\(156\) 1.26638 0.101392
\(157\) 0.301101 0.0240305 0.0120152 0.999928i \(-0.496175\pi\)
0.0120152 + 0.999928i \(0.496175\pi\)
\(158\) −1.27443 −0.101388
\(159\) 5.67828 0.450317
\(160\) 7.34279 0.580498
\(161\) −1.33240 −0.105008
\(162\) −1.27443 −0.100128
\(163\) −7.53850 −0.590461 −0.295231 0.955426i \(-0.595396\pi\)
−0.295231 + 0.955426i \(0.595396\pi\)
\(164\) 3.78062 0.295217
\(165\) −12.9138 −1.00534
\(166\) 6.10913 0.474160
\(167\) 6.09009 0.471265 0.235633 0.971842i \(-0.424284\pi\)
0.235633 + 0.971842i \(0.424284\pi\)
\(168\) −0.582008 −0.0449029
\(169\) −1.64650 −0.126654
\(170\) 4.46478 0.342433
\(171\) 6.71698 0.513660
\(172\) 4.59641 0.350473
\(173\) 4.41379 0.335574 0.167787 0.985823i \(-0.446338\pi\)
0.167787 + 0.985823i \(0.446338\pi\)
\(174\) 10.0105 0.758898
\(175\) −1.39812 −0.105688
\(176\) −11.4530 −0.863302
\(177\) −4.78465 −0.359636
\(178\) −23.0108 −1.72473
\(179\) 19.7257 1.47437 0.737183 0.675694i \(-0.236156\pi\)
0.737183 + 0.675694i \(0.236156\pi\)
\(180\) 1.31669 0.0981406
\(181\) 9.79219 0.727848 0.363924 0.931429i \(-0.381437\pi\)
0.363924 + 0.931429i \(0.381437\pi\)
\(182\) −0.825424 −0.0611845
\(183\) −8.22716 −0.608169
\(184\) 20.9879 1.54724
\(185\) 16.8255 1.23703
\(186\) −8.39395 −0.615474
\(187\) 3.68610 0.269555
\(188\) −2.30119 −0.167832
\(189\) −0.192219 −0.0139819
\(190\) 29.9898 2.17569
\(191\) −10.1503 −0.734447 −0.367223 0.930133i \(-0.619692\pi\)
−0.367223 + 0.930133i \(0.619692\pi\)
\(192\) 8.88525 0.641237
\(193\) −13.3311 −0.959592 −0.479796 0.877380i \(-0.659289\pi\)
−0.479796 + 0.877380i \(0.659289\pi\)
\(194\) 11.6408 0.835759
\(195\) 11.8046 0.845343
\(196\) 2.61697 0.186927
\(197\) 17.6002 1.25396 0.626982 0.779034i \(-0.284290\pi\)
0.626982 + 0.779034i \(0.284290\pi\)
\(198\) −4.69767 −0.333849
\(199\) −17.3624 −1.23079 −0.615393 0.788220i \(-0.711003\pi\)
−0.615393 + 0.788220i \(0.711003\pi\)
\(200\) 22.0231 1.55727
\(201\) 9.89341 0.697827
\(202\) −13.3838 −0.941684
\(203\) 1.50987 0.105972
\(204\) −0.375837 −0.0263139
\(205\) 35.2411 2.46134
\(206\) 13.2299 0.921768
\(207\) 6.93165 0.481783
\(208\) 10.4693 0.725913
\(209\) 24.7595 1.71265
\(210\) −0.858218 −0.0592226
\(211\) 7.55215 0.519912 0.259956 0.965621i \(-0.416292\pi\)
0.259956 + 0.965621i \(0.416292\pi\)
\(212\) −2.13411 −0.146571
\(213\) −9.09158 −0.622945
\(214\) −22.7987 −1.55848
\(215\) 42.8454 2.92204
\(216\) 3.02783 0.206018
\(217\) −1.26604 −0.0859446
\(218\) 4.30323 0.291452
\(219\) 14.6430 0.989481
\(220\) 4.85347 0.327221
\(221\) −3.36950 −0.226657
\(222\) 6.12064 0.410790
\(223\) 1.30002 0.0870556 0.0435278 0.999052i \(-0.486140\pi\)
0.0435278 + 0.999052i \(0.486140\pi\)
\(224\) 0.402877 0.0269184
\(225\) 7.27356 0.484904
\(226\) −22.0633 −1.46763
\(227\) 8.80920 0.584687 0.292344 0.956313i \(-0.405565\pi\)
0.292344 + 0.956313i \(0.405565\pi\)
\(228\) −2.52449 −0.167188
\(229\) −19.5184 −1.28981 −0.644905 0.764263i \(-0.723103\pi\)
−0.644905 + 0.764263i \(0.723103\pi\)
\(230\) 30.9483 2.04067
\(231\) −0.708541 −0.0466186
\(232\) −23.7834 −1.56146
\(233\) 6.28816 0.411951 0.205975 0.978557i \(-0.433963\pi\)
0.205975 + 0.978557i \(0.433963\pi\)
\(234\) 4.29417 0.280719
\(235\) −21.4505 −1.39928
\(236\) 1.79825 0.117056
\(237\) 1.00000 0.0649570
\(238\) 0.244970 0.0158790
\(239\) 5.25186 0.339714 0.169857 0.985469i \(-0.445669\pi\)
0.169857 + 0.985469i \(0.445669\pi\)
\(240\) 10.8852 0.702637
\(241\) 9.96133 0.641666 0.320833 0.947136i \(-0.396037\pi\)
0.320833 + 0.947136i \(0.396037\pi\)
\(242\) −3.29740 −0.211965
\(243\) 1.00000 0.0641500
\(244\) 3.09207 0.197950
\(245\) 24.3941 1.55848
\(246\) 12.8197 0.817356
\(247\) −22.6328 −1.44009
\(248\) 19.9426 1.26636
\(249\) −4.79363 −0.303784
\(250\) 10.1510 0.642003
\(251\) 0.268213 0.0169295 0.00846473 0.999964i \(-0.497306\pi\)
0.00846473 + 0.999964i \(0.497306\pi\)
\(252\) 0.0722432 0.00455089
\(253\) 25.5508 1.60636
\(254\) 21.9600 1.37789
\(255\) −3.50336 −0.219389
\(256\) −8.68161 −0.542600
\(257\) −30.2087 −1.88437 −0.942184 0.335096i \(-0.891231\pi\)
−0.942184 + 0.335096i \(0.891231\pi\)
\(258\) 15.5860 0.970341
\(259\) 0.923165 0.0573627
\(260\) −4.43659 −0.275146
\(261\) −7.85494 −0.486209
\(262\) −10.9534 −0.676700
\(263\) −9.04646 −0.557828 −0.278914 0.960316i \(-0.589975\pi\)
−0.278914 + 0.960316i \(0.589975\pi\)
\(264\) 11.1609 0.686906
\(265\) −19.8931 −1.22202
\(266\) 1.64545 0.100889
\(267\) 18.0558 1.10500
\(268\) −3.71831 −0.227132
\(269\) 23.9856 1.46243 0.731215 0.682148i \(-0.238954\pi\)
0.731215 + 0.682148i \(0.238954\pi\)
\(270\) 4.46478 0.271718
\(271\) 16.3823 0.995155 0.497577 0.867420i \(-0.334223\pi\)
0.497577 + 0.867420i \(0.334223\pi\)
\(272\) −3.10707 −0.188394
\(273\) 0.647682 0.0391995
\(274\) −3.67811 −0.222203
\(275\) 26.8111 1.61677
\(276\) −2.60517 −0.156813
\(277\) −1.97824 −0.118861 −0.0594306 0.998232i \(-0.518928\pi\)
−0.0594306 + 0.998232i \(0.518928\pi\)
\(278\) −24.4843 −1.46847
\(279\) 6.58645 0.394320
\(280\) 2.03899 0.121853
\(281\) 18.7517 1.11863 0.559315 0.828955i \(-0.311064\pi\)
0.559315 + 0.828955i \(0.311064\pi\)
\(282\) −7.80311 −0.464668
\(283\) 14.8609 0.883389 0.441694 0.897166i \(-0.354378\pi\)
0.441694 + 0.897166i \(0.354378\pi\)
\(284\) 3.41695 0.202759
\(285\) −23.5320 −1.39392
\(286\) 15.8288 0.935975
\(287\) 1.93358 0.114135
\(288\) −2.09592 −0.123504
\(289\) 1.00000 0.0588235
\(290\) −35.0706 −2.05942
\(291\) −9.13412 −0.535452
\(292\) −5.50338 −0.322061
\(293\) 4.11538 0.240423 0.120212 0.992748i \(-0.461643\pi\)
0.120212 + 0.992748i \(0.461643\pi\)
\(294\) 8.87390 0.517536
\(295\) 16.7624 0.975943
\(296\) −14.5416 −0.845216
\(297\) 3.68610 0.213889
\(298\) −26.9546 −1.56144
\(299\) −23.3562 −1.35072
\(300\) −2.73367 −0.157829
\(301\) 2.35080 0.135498
\(302\) 6.31583 0.363435
\(303\) 10.5019 0.603316
\(304\) −20.8701 −1.19698
\(305\) 28.8227 1.65038
\(306\) −1.27443 −0.0728541
\(307\) −0.0476785 −0.00272116 −0.00136058 0.999999i \(-0.500433\pi\)
−0.00136058 + 0.999999i \(0.500433\pi\)
\(308\) 0.266296 0.0151736
\(309\) −10.3810 −0.590556
\(310\) 29.4071 1.67021
\(311\) −29.3859 −1.66632 −0.833162 0.553029i \(-0.813472\pi\)
−0.833162 + 0.553029i \(0.813472\pi\)
\(312\) −10.2023 −0.577589
\(313\) −5.04218 −0.285001 −0.142501 0.989795i \(-0.545514\pi\)
−0.142501 + 0.989795i \(0.545514\pi\)
\(314\) −0.383731 −0.0216552
\(315\) 0.673415 0.0379426
\(316\) −0.375837 −0.0211425
\(317\) −26.3090 −1.47766 −0.738829 0.673893i \(-0.764621\pi\)
−0.738829 + 0.673893i \(0.764621\pi\)
\(318\) −7.23656 −0.405806
\(319\) −28.9541 −1.62112
\(320\) −31.1283 −1.74012
\(321\) 17.8893 0.998486
\(322\) 1.69804 0.0946282
\(323\) 6.71698 0.373743
\(324\) −0.375837 −0.0208798
\(325\) −24.5082 −1.35947
\(326\) 9.60727 0.532097
\(327\) −3.37660 −0.186727
\(328\) −30.4576 −1.68174
\(329\) −1.17693 −0.0648862
\(330\) 16.4576 0.905964
\(331\) 18.3348 1.00777 0.503885 0.863771i \(-0.331903\pi\)
0.503885 + 0.863771i \(0.331903\pi\)
\(332\) 1.80162 0.0988769
\(333\) −4.80266 −0.263184
\(334\) −7.76137 −0.424683
\(335\) −34.6602 −1.89369
\(336\) 0.597240 0.0325821
\(337\) −4.01853 −0.218903 −0.109452 0.993992i \(-0.534909\pi\)
−0.109452 + 0.993992i \(0.534909\pi\)
\(338\) 2.09834 0.114135
\(339\) 17.3123 0.940276
\(340\) 1.31669 0.0714078
\(341\) 24.2783 1.31475
\(342\) −8.56029 −0.462888
\(343\) 2.68397 0.144921
\(344\) −37.0297 −1.99651
\(345\) −24.2841 −1.30741
\(346\) −5.62505 −0.302404
\(347\) 17.8880 0.960277 0.480138 0.877193i \(-0.340586\pi\)
0.480138 + 0.877193i \(0.340586\pi\)
\(348\) 2.95218 0.158253
\(349\) 28.6959 1.53606 0.768029 0.640415i \(-0.221238\pi\)
0.768029 + 0.640415i \(0.221238\pi\)
\(350\) 1.78180 0.0952413
\(351\) −3.36950 −0.179850
\(352\) −7.72579 −0.411786
\(353\) 8.25538 0.439389 0.219695 0.975569i \(-0.429494\pi\)
0.219695 + 0.975569i \(0.429494\pi\)
\(354\) 6.09768 0.324088
\(355\) 31.8511 1.69048
\(356\) −6.78604 −0.359659
\(357\) −0.192219 −0.0101733
\(358\) −25.1389 −1.32863
\(359\) 18.9600 1.00067 0.500334 0.865832i \(-0.333211\pi\)
0.500334 + 0.865832i \(0.333211\pi\)
\(360\) −10.6076 −0.559069
\(361\) 26.1178 1.37462
\(362\) −12.4794 −0.655904
\(363\) 2.58736 0.135801
\(364\) −0.243423 −0.0127588
\(365\) −51.2997 −2.68515
\(366\) 10.4849 0.548055
\(367\) 21.7468 1.13517 0.567586 0.823314i \(-0.307877\pi\)
0.567586 + 0.823314i \(0.307877\pi\)
\(368\) −21.5371 −1.12270
\(369\) −10.0592 −0.523662
\(370\) −21.4428 −1.11476
\(371\) −1.09148 −0.0566666
\(372\) −2.47543 −0.128345
\(373\) 13.3769 0.692630 0.346315 0.938118i \(-0.387433\pi\)
0.346315 + 0.938118i \(0.387433\pi\)
\(374\) −4.69767 −0.242911
\(375\) −7.96512 −0.411317
\(376\) 18.5389 0.956072
\(377\) 26.4672 1.36313
\(378\) 0.244970 0.0125999
\(379\) 24.5327 1.26016 0.630079 0.776531i \(-0.283023\pi\)
0.630079 + 0.776531i \(0.283023\pi\)
\(380\) 8.84420 0.453698
\(381\) −17.2313 −0.882786
\(382\) 12.9358 0.661851
\(383\) −0.818733 −0.0418353 −0.0209176 0.999781i \(-0.506659\pi\)
−0.0209176 + 0.999781i \(0.506659\pi\)
\(384\) −7.13175 −0.363940
\(385\) 2.48228 0.126509
\(386\) 16.9895 0.864742
\(387\) −12.2298 −0.621676
\(388\) 3.43294 0.174281
\(389\) 17.8825 0.906679 0.453340 0.891338i \(-0.350233\pi\)
0.453340 + 0.891338i \(0.350233\pi\)
\(390\) −15.0441 −0.761785
\(391\) 6.93165 0.350549
\(392\) −21.0829 −1.06485
\(393\) 8.59473 0.433547
\(394\) −22.4302 −1.13002
\(395\) −3.50336 −0.176273
\(396\) −1.38537 −0.0696177
\(397\) 12.0334 0.603937 0.301968 0.953318i \(-0.402356\pi\)
0.301968 + 0.953318i \(0.402356\pi\)
\(398\) 22.1271 1.10913
\(399\) −1.29113 −0.0646375
\(400\) −22.5995 −1.12997
\(401\) −25.7019 −1.28349 −0.641745 0.766918i \(-0.721789\pi\)
−0.641745 + 0.766918i \(0.721789\pi\)
\(402\) −12.6084 −0.628851
\(403\) −22.1930 −1.10551
\(404\) −3.94699 −0.196370
\(405\) −3.50336 −0.174084
\(406\) −1.92422 −0.0954975
\(407\) −17.7031 −0.877511
\(408\) 3.02783 0.149900
\(409\) 3.19789 0.158125 0.0790627 0.996870i \(-0.474807\pi\)
0.0790627 + 0.996870i \(0.474807\pi\)
\(410\) −44.9122 −2.21805
\(411\) 2.88609 0.142360
\(412\) 3.90158 0.192217
\(413\) 0.919702 0.0452556
\(414\) −8.83388 −0.434161
\(415\) 16.7938 0.824376
\(416\) 7.06221 0.346253
\(417\) 19.2120 0.940818
\(418\) −31.5541 −1.54336
\(419\) 25.9647 1.26846 0.634230 0.773145i \(-0.281317\pi\)
0.634230 + 0.773145i \(0.281317\pi\)
\(420\) −0.253094 −0.0123497
\(421\) 14.7904 0.720839 0.360420 0.932790i \(-0.382633\pi\)
0.360420 + 0.932790i \(0.382633\pi\)
\(422\) −9.62466 −0.468521
\(423\) 6.12284 0.297703
\(424\) 17.1929 0.834960
\(425\) 7.27356 0.352820
\(426\) 11.5866 0.561370
\(427\) 1.58142 0.0765302
\(428\) −6.72348 −0.324992
\(429\) −12.4203 −0.599658
\(430\) −54.6034 −2.63321
\(431\) −37.9041 −1.82578 −0.912889 0.408209i \(-0.866153\pi\)
−0.912889 + 0.408209i \(0.866153\pi\)
\(432\) −3.10707 −0.149489
\(433\) −27.5366 −1.32332 −0.661662 0.749802i \(-0.730149\pi\)
−0.661662 + 0.749802i \(0.730149\pi\)
\(434\) 1.61348 0.0774495
\(435\) 27.5187 1.31942
\(436\) 1.26905 0.0607766
\(437\) 46.5597 2.22725
\(438\) −18.6614 −0.891677
\(439\) −9.45115 −0.451079 −0.225539 0.974234i \(-0.572414\pi\)
−0.225539 + 0.974234i \(0.572414\pi\)
\(440\) −39.1007 −1.86405
\(441\) −6.96305 −0.331574
\(442\) 4.29417 0.204253
\(443\) −14.2238 −0.675795 −0.337898 0.941183i \(-0.609716\pi\)
−0.337898 + 0.941183i \(0.609716\pi\)
\(444\) 1.80502 0.0856624
\(445\) −63.2560 −2.99862
\(446\) −1.65678 −0.0784507
\(447\) 21.1504 1.00038
\(448\) −1.70792 −0.0806915
\(449\) 16.9095 0.798009 0.399004 0.916949i \(-0.369356\pi\)
0.399004 + 0.916949i \(0.369356\pi\)
\(450\) −9.26962 −0.436974
\(451\) −37.0793 −1.74600
\(452\) −6.50661 −0.306045
\(453\) −4.95582 −0.232845
\(454\) −11.2267 −0.526894
\(455\) −2.26907 −0.106376
\(456\) 20.3379 0.952408
\(457\) −18.0421 −0.843975 −0.421987 0.906602i \(-0.638667\pi\)
−0.421987 + 0.906602i \(0.638667\pi\)
\(458\) 24.8747 1.16232
\(459\) 1.00000 0.0466760
\(460\) 9.12686 0.425542
\(461\) 26.3375 1.22666 0.613330 0.789827i \(-0.289830\pi\)
0.613330 + 0.789827i \(0.289830\pi\)
\(462\) 0.902983 0.0420106
\(463\) 10.7625 0.500177 0.250088 0.968223i \(-0.419540\pi\)
0.250088 + 0.968223i \(0.419540\pi\)
\(464\) 24.4059 1.13301
\(465\) −23.0747 −1.07007
\(466\) −8.01380 −0.371232
\(467\) −3.25445 −0.150598 −0.0752990 0.997161i \(-0.523991\pi\)
−0.0752990 + 0.997161i \(0.523991\pi\)
\(468\) 1.26638 0.0585385
\(469\) −1.90171 −0.0878126
\(470\) 27.3371 1.26097
\(471\) 0.301101 0.0138740
\(472\) −14.4871 −0.666823
\(473\) −45.0803 −2.07279
\(474\) −1.27443 −0.0585363
\(475\) 48.8564 2.24168
\(476\) 0.0722432 0.00331126
\(477\) 5.67828 0.259991
\(478\) −6.69310 −0.306135
\(479\) −29.8212 −1.36256 −0.681282 0.732021i \(-0.738577\pi\)
−0.681282 + 0.732021i \(0.738577\pi\)
\(480\) 7.34279 0.335151
\(481\) 16.1825 0.737861
\(482\) −12.6950 −0.578241
\(483\) −1.33240 −0.0606262
\(484\) −0.972426 −0.0442012
\(485\) 32.0002 1.45305
\(486\) −1.27443 −0.0578092
\(487\) 34.8281 1.57821 0.789107 0.614256i \(-0.210544\pi\)
0.789107 + 0.614256i \(0.210544\pi\)
\(488\) −24.9104 −1.12764
\(489\) −7.53850 −0.340903
\(490\) −31.0885 −1.40444
\(491\) −42.7565 −1.92957 −0.964787 0.263032i \(-0.915278\pi\)
−0.964787 + 0.263032i \(0.915278\pi\)
\(492\) 3.78062 0.170444
\(493\) −7.85494 −0.353769
\(494\) 28.8439 1.29775
\(495\) −12.9138 −0.580431
\(496\) −20.4646 −0.918886
\(497\) 1.74758 0.0783896
\(498\) 6.10913 0.273756
\(499\) 35.7840 1.60191 0.800957 0.598722i \(-0.204325\pi\)
0.800957 + 0.598722i \(0.204325\pi\)
\(500\) 2.99359 0.133877
\(501\) 6.09009 0.272085
\(502\) −0.341818 −0.0152561
\(503\) 4.57535 0.204005 0.102002 0.994784i \(-0.467475\pi\)
0.102002 + 0.994784i \(0.467475\pi\)
\(504\) −0.582008 −0.0259247
\(505\) −36.7918 −1.63722
\(506\) −32.5626 −1.44758
\(507\) −1.64650 −0.0731237
\(508\) 6.47616 0.287333
\(509\) −10.3504 −0.458773 −0.229387 0.973335i \(-0.573672\pi\)
−0.229387 + 0.973335i \(0.573672\pi\)
\(510\) 4.46478 0.197704
\(511\) −2.81467 −0.124514
\(512\) 25.3276 1.11933
\(513\) 6.71698 0.296562
\(514\) 38.4988 1.69811
\(515\) 36.3685 1.60259
\(516\) 4.59641 0.202346
\(517\) 22.5694 0.992602
\(518\) −1.17651 −0.0516927
\(519\) 4.41379 0.193744
\(520\) 35.7422 1.56740
\(521\) −8.66459 −0.379602 −0.189801 0.981823i \(-0.560784\pi\)
−0.189801 + 0.981823i \(0.560784\pi\)
\(522\) 10.0105 0.438150
\(523\) 30.5072 1.33399 0.666993 0.745064i \(-0.267581\pi\)
0.666993 + 0.745064i \(0.267581\pi\)
\(524\) −3.23022 −0.141113
\(525\) −1.39812 −0.0610190
\(526\) 11.5290 0.502690
\(527\) 6.58645 0.286910
\(528\) −11.4530 −0.498427
\(529\) 25.0477 1.08903
\(530\) 25.3523 1.10123
\(531\) −4.78465 −0.207636
\(532\) 0.485256 0.0210385
\(533\) 33.8945 1.46813
\(534\) −23.0108 −0.995774
\(535\) −62.6729 −2.70959
\(536\) 29.9556 1.29388
\(537\) 19.7257 0.851225
\(538\) −30.5679 −1.31788
\(539\) −25.6665 −1.10554
\(540\) 1.31669 0.0566615
\(541\) 9.90014 0.425640 0.212820 0.977091i \(-0.431735\pi\)
0.212820 + 0.977091i \(0.431735\pi\)
\(542\) −20.8781 −0.896789
\(543\) 9.79219 0.420223
\(544\) −2.09592 −0.0898620
\(545\) 11.8295 0.506719
\(546\) −0.825424 −0.0353249
\(547\) 20.0729 0.858255 0.429128 0.903244i \(-0.358821\pi\)
0.429128 + 0.903244i \(0.358821\pi\)
\(548\) −1.08470 −0.0463360
\(549\) −8.22716 −0.351126
\(550\) −34.1688 −1.45696
\(551\) −52.7615 −2.24771
\(552\) 20.9879 0.893302
\(553\) −0.192219 −0.00817400
\(554\) 2.52113 0.107112
\(555\) 16.8255 0.714202
\(556\) −7.22060 −0.306222
\(557\) 15.6393 0.662660 0.331330 0.943515i \(-0.392503\pi\)
0.331330 + 0.943515i \(0.392503\pi\)
\(558\) −8.39395 −0.355344
\(559\) 41.2082 1.74292
\(560\) −2.09235 −0.0884179
\(561\) 3.68610 0.155627
\(562\) −23.8976 −1.00806
\(563\) 12.0160 0.506416 0.253208 0.967412i \(-0.418514\pi\)
0.253208 + 0.967412i \(0.418514\pi\)
\(564\) −2.30119 −0.0968976
\(565\) −60.6513 −2.55162
\(566\) −18.9391 −0.796071
\(567\) −0.192219 −0.00807246
\(568\) −27.5278 −1.15504
\(569\) 21.2291 0.889971 0.444985 0.895538i \(-0.353209\pi\)
0.444985 + 0.895538i \(0.353209\pi\)
\(570\) 29.9898 1.25614
\(571\) 1.25416 0.0524850 0.0262425 0.999656i \(-0.491646\pi\)
0.0262425 + 0.999656i \(0.491646\pi\)
\(572\) 4.66801 0.195179
\(573\) −10.1503 −0.424033
\(574\) −2.46420 −0.102854
\(575\) 50.4178 2.10257
\(576\) 8.88525 0.370219
\(577\) −2.40212 −0.100002 −0.0500008 0.998749i \(-0.515922\pi\)
−0.0500008 + 0.998749i \(0.515922\pi\)
\(578\) −1.27443 −0.0530092
\(579\) −13.3311 −0.554021
\(580\) −10.3426 −0.429451
\(581\) 0.921428 0.0382273
\(582\) 11.6408 0.482525
\(583\) 20.9307 0.866863
\(584\) 44.3365 1.83466
\(585\) 11.8046 0.488059
\(586\) −5.24475 −0.216659
\(587\) −4.88794 −0.201747 −0.100873 0.994899i \(-0.532164\pi\)
−0.100873 + 0.994899i \(0.532164\pi\)
\(588\) 2.61697 0.107922
\(589\) 44.2410 1.82292
\(590\) −21.3624 −0.879476
\(591\) 17.6002 0.723977
\(592\) 14.9222 0.613299
\(593\) −12.4675 −0.511979 −0.255989 0.966680i \(-0.582401\pi\)
−0.255989 + 0.966680i \(0.582401\pi\)
\(594\) −4.69767 −0.192748
\(595\) 0.673415 0.0276073
\(596\) −7.94910 −0.325608
\(597\) −17.3624 −0.710595
\(598\) 29.7657 1.21721
\(599\) 35.9305 1.46808 0.734040 0.679107i \(-0.237633\pi\)
0.734040 + 0.679107i \(0.237633\pi\)
\(600\) 22.0231 0.899090
\(601\) −2.80054 −0.114236 −0.0571182 0.998367i \(-0.518191\pi\)
−0.0571182 + 0.998367i \(0.518191\pi\)
\(602\) −2.99593 −0.122105
\(603\) 9.89341 0.402891
\(604\) 1.86258 0.0757873
\(605\) −9.06447 −0.368523
\(606\) −13.3838 −0.543682
\(607\) −5.06541 −0.205599 −0.102799 0.994702i \(-0.532780\pi\)
−0.102799 + 0.994702i \(0.532780\pi\)
\(608\) −14.0783 −0.570949
\(609\) 1.50987 0.0611831
\(610\) −36.7325 −1.48725
\(611\) −20.6309 −0.834636
\(612\) −0.375837 −0.0151923
\(613\) 26.8378 1.08397 0.541985 0.840388i \(-0.317673\pi\)
0.541985 + 0.840388i \(0.317673\pi\)
\(614\) 0.0607627 0.00245218
\(615\) 35.2411 1.42106
\(616\) −2.14534 −0.0864382
\(617\) −3.70256 −0.149060 −0.0745298 0.997219i \(-0.523746\pi\)
−0.0745298 + 0.997219i \(0.523746\pi\)
\(618\) 13.2299 0.532183
\(619\) −14.2237 −0.571697 −0.285849 0.958275i \(-0.592275\pi\)
−0.285849 + 0.958275i \(0.592275\pi\)
\(620\) 8.67234 0.348290
\(621\) 6.93165 0.278157
\(622\) 37.4502 1.50162
\(623\) −3.47067 −0.139050
\(624\) 10.4693 0.419106
\(625\) −8.46309 −0.338523
\(626\) 6.42589 0.256830
\(627\) 24.7595 0.988798
\(628\) −0.113165 −0.00451577
\(629\) −4.80266 −0.191495
\(630\) −0.858218 −0.0341922
\(631\) −24.8511 −0.989308 −0.494654 0.869090i \(-0.664705\pi\)
−0.494654 + 0.869090i \(0.664705\pi\)
\(632\) 3.02783 0.120441
\(633\) 7.55215 0.300171
\(634\) 33.5288 1.33160
\(635\) 60.3675 2.39561
\(636\) −2.13411 −0.0846229
\(637\) 23.4620 0.929597
\(638\) 36.8999 1.46088
\(639\) −9.09158 −0.359657
\(640\) 24.9851 0.987623
\(641\) 7.66504 0.302751 0.151376 0.988476i \(-0.451630\pi\)
0.151376 + 0.988476i \(0.451630\pi\)
\(642\) −22.7987 −0.899791
\(643\) −46.7401 −1.84325 −0.921625 0.388083i \(-0.873138\pi\)
−0.921625 + 0.388083i \(0.873138\pi\)
\(644\) 0.500764 0.0197329
\(645\) 42.8454 1.68704
\(646\) −8.56029 −0.336800
\(647\) 45.5047 1.78897 0.894487 0.447094i \(-0.147541\pi\)
0.894487 + 0.447094i \(0.147541\pi\)
\(648\) 3.02783 0.118944
\(649\) −17.6367 −0.692301
\(650\) 31.2340 1.22510
\(651\) −1.26604 −0.0496202
\(652\) 2.83325 0.110959
\(653\) 21.2324 0.830886 0.415443 0.909619i \(-0.363627\pi\)
0.415443 + 0.909619i \(0.363627\pi\)
\(654\) 4.30323 0.168270
\(655\) −30.1105 −1.17651
\(656\) 31.2547 1.22029
\(657\) 14.6430 0.571277
\(658\) 1.49991 0.0584725
\(659\) 13.8010 0.537610 0.268805 0.963195i \(-0.413371\pi\)
0.268805 + 0.963195i \(0.413371\pi\)
\(660\) 4.85347 0.188921
\(661\) 10.5103 0.408801 0.204401 0.978887i \(-0.434475\pi\)
0.204401 + 0.978887i \(0.434475\pi\)
\(662\) −23.3663 −0.908158
\(663\) −3.36950 −0.130860
\(664\) −14.5143 −0.563264
\(665\) 4.52331 0.175406
\(666\) 6.12064 0.237170
\(667\) −54.4477 −2.10822
\(668\) −2.28888 −0.0885595
\(669\) 1.30002 0.0502616
\(670\) 44.1719 1.70651
\(671\) −30.3262 −1.17073
\(672\) 0.402877 0.0155413
\(673\) 3.06801 0.118263 0.0591316 0.998250i \(-0.481167\pi\)
0.0591316 + 0.998250i \(0.481167\pi\)
\(674\) 5.12132 0.197266
\(675\) 7.27356 0.279960
\(676\) 0.618816 0.0238006
\(677\) −23.9732 −0.921363 −0.460682 0.887565i \(-0.652395\pi\)
−0.460682 + 0.887565i \(0.652395\pi\)
\(678\) −22.0633 −0.847335
\(679\) 1.75576 0.0673797
\(680\) −10.6076 −0.406783
\(681\) 8.80920 0.337569
\(682\) −30.9410 −1.18479
\(683\) 23.1851 0.887154 0.443577 0.896236i \(-0.353709\pi\)
0.443577 + 0.896236i \(0.353709\pi\)
\(684\) −2.52449 −0.0965262
\(685\) −10.1110 −0.386322
\(686\) −3.42052 −0.130596
\(687\) −19.5184 −0.744672
\(688\) 37.9989 1.44869
\(689\) −19.1330 −0.728907
\(690\) 30.9483 1.17818
\(691\) 2.11309 0.0803858 0.0401929 0.999192i \(-0.487203\pi\)
0.0401929 + 0.999192i \(0.487203\pi\)
\(692\) −1.65886 −0.0630606
\(693\) −0.708541 −0.0269152
\(694\) −22.7969 −0.865359
\(695\) −67.3068 −2.55309
\(696\) −23.7834 −0.901509
\(697\) −10.0592 −0.381020
\(698\) −36.5709 −1.38423
\(699\) 6.28816 0.237840
\(700\) 0.525465 0.0198607
\(701\) −25.2892 −0.955160 −0.477580 0.878588i \(-0.658486\pi\)
−0.477580 + 0.878588i \(0.658486\pi\)
\(702\) 4.29417 0.162073
\(703\) −32.2594 −1.21669
\(704\) 32.7519 1.23439
\(705\) −21.4505 −0.807874
\(706\) −10.5209 −0.395958
\(707\) −2.01866 −0.0759196
\(708\) 1.79825 0.0675823
\(709\) 13.8230 0.519135 0.259567 0.965725i \(-0.416420\pi\)
0.259567 + 0.965725i \(0.416420\pi\)
\(710\) −40.5919 −1.52339
\(711\) 1.00000 0.0375029
\(712\) 54.6699 2.04884
\(713\) 45.6549 1.70979
\(714\) 0.244970 0.00916775
\(715\) 43.5129 1.62729
\(716\) −7.41363 −0.277061
\(717\) 5.25186 0.196134
\(718\) −24.1631 −0.901758
\(719\) −20.1596 −0.751827 −0.375913 0.926655i \(-0.622671\pi\)
−0.375913 + 0.926655i \(0.622671\pi\)
\(720\) 10.8852 0.405668
\(721\) 1.99544 0.0743139
\(722\) −33.2852 −1.23875
\(723\) 9.96133 0.370466
\(724\) −3.68027 −0.136776
\(725\) −57.1334 −2.12188
\(726\) −3.29740 −0.122378
\(727\) −36.7454 −1.36281 −0.681406 0.731906i \(-0.738631\pi\)
−0.681406 + 0.731906i \(0.738631\pi\)
\(728\) 1.96107 0.0726822
\(729\) 1.00000 0.0370370
\(730\) 65.3777 2.41974
\(731\) −12.2298 −0.452335
\(732\) 3.09207 0.114286
\(733\) 33.0162 1.21948 0.609740 0.792601i \(-0.291274\pi\)
0.609740 + 0.792601i \(0.291274\pi\)
\(734\) −27.7147 −1.02297
\(735\) 24.3941 0.899790
\(736\) −14.5282 −0.535517
\(737\) 36.4681 1.34332
\(738\) 12.8197 0.471901
\(739\) 30.9725 1.13934 0.569671 0.821873i \(-0.307070\pi\)
0.569671 + 0.821873i \(0.307070\pi\)
\(740\) −6.32364 −0.232462
\(741\) −22.6328 −0.831438
\(742\) 1.39101 0.0510655
\(743\) 0.433176 0.0158917 0.00794584 0.999968i \(-0.497471\pi\)
0.00794584 + 0.999968i \(0.497471\pi\)
\(744\) 19.9426 0.731133
\(745\) −74.0975 −2.71472
\(746\) −17.0479 −0.624168
\(747\) −4.79363 −0.175390
\(748\) −1.38537 −0.0506543
\(749\) −3.43868 −0.125647
\(750\) 10.1510 0.370661
\(751\) 44.6061 1.62770 0.813849 0.581076i \(-0.197368\pi\)
0.813849 + 0.581076i \(0.197368\pi\)
\(752\) −19.0241 −0.693738
\(753\) 0.268213 0.00977423
\(754\) −33.7305 −1.22839
\(755\) 17.3620 0.631869
\(756\) 0.0722432 0.00262746
\(757\) −22.7667 −0.827471 −0.413735 0.910397i \(-0.635776\pi\)
−0.413735 + 0.910397i \(0.635776\pi\)
\(758\) −31.2651 −1.13560
\(759\) 25.5508 0.927434
\(760\) −71.2509 −2.58454
\(761\) 30.9874 1.12329 0.561647 0.827377i \(-0.310168\pi\)
0.561647 + 0.827377i \(0.310168\pi\)
\(762\) 21.9600 0.795527
\(763\) 0.649049 0.0234972
\(764\) 3.81484 0.138016
\(765\) −3.50336 −0.126664
\(766\) 1.04341 0.0377001
\(767\) 16.1218 0.582126
\(768\) −8.68161 −0.313270
\(769\) 18.2462 0.657975 0.328987 0.944334i \(-0.393293\pi\)
0.328987 + 0.944334i \(0.393293\pi\)
\(770\) −3.16348 −0.114004
\(771\) −30.2087 −1.08794
\(772\) 5.01031 0.180325
\(773\) −3.93680 −0.141597 −0.0707985 0.997491i \(-0.522555\pi\)
−0.0707985 + 0.997491i \(0.522555\pi\)
\(774\) 15.5860 0.560226
\(775\) 47.9070 1.72087
\(776\) −27.6566 −0.992813
\(777\) 0.923165 0.0331184
\(778\) −22.7899 −0.817059
\(779\) −67.5675 −2.42086
\(780\) −4.43659 −0.158856
\(781\) −33.5125 −1.19917
\(782\) −8.83388 −0.315899
\(783\) −7.85494 −0.280713
\(784\) 21.6347 0.772668
\(785\) −1.05487 −0.0376498
\(786\) −10.9534 −0.390693
\(787\) 13.8283 0.492925 0.246462 0.969152i \(-0.420732\pi\)
0.246462 + 0.969152i \(0.420732\pi\)
\(788\) −6.61482 −0.235643
\(789\) −9.04646 −0.322062
\(790\) 4.46478 0.158850
\(791\) −3.32776 −0.118322
\(792\) 11.1609 0.396585
\(793\) 27.7214 0.984415
\(794\) −15.3356 −0.544241
\(795\) −19.8931 −0.705536
\(796\) 6.52543 0.231288
\(797\) −5.82441 −0.206311 −0.103156 0.994665i \(-0.532894\pi\)
−0.103156 + 0.994665i \(0.532894\pi\)
\(798\) 1.64545 0.0582485
\(799\) 6.12284 0.216610
\(800\) −15.2448 −0.538986
\(801\) 18.0558 0.637970
\(802\) 32.7552 1.15663
\(803\) 53.9756 1.90476
\(804\) −3.71831 −0.131135
\(805\) 4.66787 0.164521
\(806\) 28.2834 0.996239
\(807\) 23.9856 0.844334
\(808\) 31.7978 1.11864
\(809\) 17.6814 0.621644 0.310822 0.950468i \(-0.399396\pi\)
0.310822 + 0.950468i \(0.399396\pi\)
\(810\) 4.46478 0.156876
\(811\) −24.4341 −0.857998 −0.428999 0.903305i \(-0.641134\pi\)
−0.428999 + 0.903305i \(0.641134\pi\)
\(812\) −0.567466 −0.0199142
\(813\) 16.3823 0.574553
\(814\) 22.5613 0.790774
\(815\) 26.4101 0.925106
\(816\) −3.10707 −0.108769
\(817\) −82.1473 −2.87397
\(818\) −4.07547 −0.142496
\(819\) 0.647682 0.0226319
\(820\) −13.2449 −0.462532
\(821\) 27.7877 0.969796 0.484898 0.874571i \(-0.338857\pi\)
0.484898 + 0.874571i \(0.338857\pi\)
\(822\) −3.67811 −0.128289
\(823\) 16.9990 0.592548 0.296274 0.955103i \(-0.404256\pi\)
0.296274 + 0.955103i \(0.404256\pi\)
\(824\) −31.4320 −1.09499
\(825\) 26.8111 0.933443
\(826\) −1.17209 −0.0407823
\(827\) −54.9541 −1.91094 −0.955470 0.295089i \(-0.904651\pi\)
−0.955470 + 0.295089i \(0.904651\pi\)
\(828\) −2.60517 −0.0905359
\(829\) −14.9631 −0.519689 −0.259844 0.965651i \(-0.583671\pi\)
−0.259844 + 0.965651i \(0.583671\pi\)
\(830\) −21.4025 −0.742891
\(831\) −1.97824 −0.0686245
\(832\) −29.9388 −1.03794
\(833\) −6.96305 −0.241255
\(834\) −24.4843 −0.847824
\(835\) −21.3358 −0.738356
\(836\) −9.30553 −0.321838
\(837\) 6.58645 0.227661
\(838\) −33.0901 −1.14308
\(839\) 6.51771 0.225016 0.112508 0.993651i \(-0.464112\pi\)
0.112508 + 0.993651i \(0.464112\pi\)
\(840\) 2.03899 0.0703517
\(841\) 32.7001 1.12759
\(842\) −18.8493 −0.649589
\(843\) 18.7517 0.645841
\(844\) −2.83838 −0.0977010
\(845\) 5.76829 0.198435
\(846\) −7.80311 −0.268276
\(847\) −0.497341 −0.0170888
\(848\) −17.6428 −0.605858
\(849\) 14.8609 0.510025
\(850\) −9.26962 −0.317945
\(851\) −33.2904 −1.14118
\(852\) 3.41695 0.117063
\(853\) 17.5861 0.602138 0.301069 0.953602i \(-0.402657\pi\)
0.301069 + 0.953602i \(0.402657\pi\)
\(854\) −2.01540 −0.0689657
\(855\) −23.5320 −0.804778
\(856\) 54.1659 1.85135
\(857\) −26.9995 −0.922286 −0.461143 0.887326i \(-0.652560\pi\)
−0.461143 + 0.887326i \(0.652560\pi\)
\(858\) 15.8288 0.540385
\(859\) 5.78527 0.197391 0.0986954 0.995118i \(-0.468533\pi\)
0.0986954 + 0.995118i \(0.468533\pi\)
\(860\) −16.1029 −0.549105
\(861\) 1.93358 0.0658961
\(862\) 48.3060 1.64531
\(863\) −14.9079 −0.507469 −0.253735 0.967274i \(-0.581659\pi\)
−0.253735 + 0.967274i \(0.581659\pi\)
\(864\) −2.09592 −0.0713048
\(865\) −15.4631 −0.525761
\(866\) 35.0934 1.19252
\(867\) 1.00000 0.0339618
\(868\) 0.475826 0.0161506
\(869\) 3.68610 0.125043
\(870\) −35.0706 −1.18900
\(871\) −33.3358 −1.12954
\(872\) −10.2238 −0.346221
\(873\) −9.13412 −0.309143
\(874\) −59.3369 −2.00710
\(875\) 1.53105 0.0517590
\(876\) −5.50338 −0.185942
\(877\) −22.3909 −0.756088 −0.378044 0.925788i \(-0.623403\pi\)
−0.378044 + 0.925788i \(0.623403\pi\)
\(878\) 12.0448 0.406492
\(879\) 4.11538 0.138808
\(880\) 40.1240 1.35258
\(881\) 35.8257 1.20700 0.603499 0.797364i \(-0.293773\pi\)
0.603499 + 0.797364i \(0.293773\pi\)
\(882\) 8.87390 0.298800
\(883\) −36.6604 −1.23372 −0.616860 0.787073i \(-0.711595\pi\)
−0.616860 + 0.787073i \(0.711595\pi\)
\(884\) 1.26638 0.0425930
\(885\) 16.7624 0.563461
\(886\) 18.1273 0.608997
\(887\) 43.6684 1.46624 0.733120 0.680099i \(-0.238063\pi\)
0.733120 + 0.680099i \(0.238063\pi\)
\(888\) −14.5416 −0.487986
\(889\) 3.31219 0.111087
\(890\) 80.6152 2.70223
\(891\) 3.68610 0.123489
\(892\) −0.488595 −0.0163594
\(893\) 41.1270 1.37626
\(894\) −26.9546 −0.901497
\(895\) −69.1062 −2.30997
\(896\) 1.37086 0.0457972
\(897\) −23.3562 −0.779839
\(898\) −21.5499 −0.719130
\(899\) −51.7362 −1.72550
\(900\) −2.73367 −0.0911225
\(901\) 5.67828 0.189171
\(902\) 47.2548 1.57341
\(903\) 2.35080 0.0782299
\(904\) 52.4187 1.74342
\(905\) −34.3056 −1.14036
\(906\) 6.31583 0.209829
\(907\) −35.9109 −1.19240 −0.596202 0.802835i \(-0.703324\pi\)
−0.596202 + 0.802835i \(0.703324\pi\)
\(908\) −3.31082 −0.109874
\(909\) 10.5019 0.348325
\(910\) 2.89176 0.0958609
\(911\) −48.1793 −1.59625 −0.798126 0.602491i \(-0.794175\pi\)
−0.798126 + 0.602491i \(0.794175\pi\)
\(912\) −20.8701 −0.691079
\(913\) −17.6698 −0.584785
\(914\) 22.9934 0.760553
\(915\) 28.8227 0.952850
\(916\) 7.33572 0.242379
\(917\) −1.65207 −0.0545563
\(918\) −1.27443 −0.0420623
\(919\) −29.3369 −0.967734 −0.483867 0.875142i \(-0.660768\pi\)
−0.483867 + 0.875142i \(0.660768\pi\)
\(920\) −73.5281 −2.42415
\(921\) −0.0476785 −0.00157106
\(922\) −33.5652 −1.10541
\(923\) 30.6340 1.00833
\(924\) 0.266296 0.00876049
\(925\) −34.9325 −1.14857
\(926\) −13.7160 −0.450737
\(927\) −10.3810 −0.340958
\(928\) 16.4634 0.540436
\(929\) −10.9329 −0.358696 −0.179348 0.983786i \(-0.557399\pi\)
−0.179348 + 0.983786i \(0.557399\pi\)
\(930\) 29.4071 0.964295
\(931\) −46.7707 −1.53285
\(932\) −2.36332 −0.0774132
\(933\) −29.3859 −0.962053
\(934\) 4.14756 0.135712
\(935\) −12.9138 −0.422325
\(936\) −10.2023 −0.333471
\(937\) −10.5590 −0.344947 −0.172473 0.985014i \(-0.555176\pi\)
−0.172473 + 0.985014i \(0.555176\pi\)
\(938\) 2.42358 0.0791328
\(939\) −5.04218 −0.164545
\(940\) 8.06191 0.262950
\(941\) −6.95161 −0.226616 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(942\) −0.383731 −0.0125026
\(943\) −69.7269 −2.27062
\(944\) 14.8662 0.483855
\(945\) 0.673415 0.0219062
\(946\) 57.4515 1.86791
\(947\) 35.0177 1.13792 0.568962 0.822364i \(-0.307345\pi\)
0.568962 + 0.822364i \(0.307345\pi\)
\(948\) −0.375837 −0.0122066
\(949\) −49.3395 −1.60163
\(950\) −62.2638 −2.02011
\(951\) −26.3090 −0.853126
\(952\) −0.582008 −0.0188630
\(953\) 22.4256 0.726436 0.363218 0.931704i \(-0.381678\pi\)
0.363218 + 0.931704i \(0.381678\pi\)
\(954\) −7.23656 −0.234292
\(955\) 35.5600 1.15070
\(956\) −1.97384 −0.0638386
\(957\) −28.9541 −0.935954
\(958\) 38.0049 1.22788
\(959\) −0.554762 −0.0179142
\(960\) −31.1283 −1.00466
\(961\) 12.3813 0.399397
\(962\) −20.6235 −0.664927
\(963\) 17.8893 0.576476
\(964\) −3.74384 −0.120581
\(965\) 46.7036 1.50344
\(966\) 1.69804 0.0546336
\(967\) −48.3180 −1.55380 −0.776900 0.629624i \(-0.783209\pi\)
−0.776900 + 0.629624i \(0.783209\pi\)
\(968\) 7.83409 0.251797
\(969\) 6.71698 0.215780
\(970\) −40.7819 −1.30943
\(971\) 9.95294 0.319405 0.159703 0.987165i \(-0.448947\pi\)
0.159703 + 0.987165i \(0.448947\pi\)
\(972\) −0.375837 −0.0120550
\(973\) −3.69293 −0.118390
\(974\) −44.3859 −1.42222
\(975\) −24.5082 −0.784892
\(976\) 25.5624 0.818232
\(977\) 8.22102 0.263014 0.131507 0.991315i \(-0.458018\pi\)
0.131507 + 0.991315i \(0.458018\pi\)
\(978\) 9.60727 0.307207
\(979\) 66.5555 2.12712
\(980\) −9.16821 −0.292868
\(981\) −3.37660 −0.107807
\(982\) 54.4900 1.73885
\(983\) 36.5641 1.16621 0.583106 0.812396i \(-0.301837\pi\)
0.583106 + 0.812396i \(0.301837\pi\)
\(984\) −30.4576 −0.970952
\(985\) −61.6600 −1.96465
\(986\) 10.0105 0.318801
\(987\) −1.17693 −0.0374621
\(988\) 8.50625 0.270620
\(989\) −84.7727 −2.69561
\(990\) 16.4576 0.523058
\(991\) 12.1880 0.387165 0.193583 0.981084i \(-0.437989\pi\)
0.193583 + 0.981084i \(0.437989\pi\)
\(992\) −13.8047 −0.438300
\(993\) 18.3348 0.581836
\(994\) −2.22716 −0.0706412
\(995\) 60.8268 1.92834
\(996\) 1.80162 0.0570866
\(997\) 44.3151 1.40347 0.701737 0.712436i \(-0.252408\pi\)
0.701737 + 0.712436i \(0.252408\pi\)
\(998\) −45.6041 −1.44357
\(999\) −4.80266 −0.151949
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 4029.2.a.k.1.9 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.9 31 1.1 even 1 trivial