Properties

Label 4027.2.a.c.1.13
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45988 q^{2} +0.0412137 q^{3} +4.05100 q^{4} -0.833121 q^{5} -0.101381 q^{6} -2.59297 q^{7} -5.04521 q^{8} -2.99830 q^{9} +O(q^{10})\) \(q-2.45988 q^{2} +0.0412137 q^{3} +4.05100 q^{4} -0.833121 q^{5} -0.101381 q^{6} -2.59297 q^{7} -5.04521 q^{8} -2.99830 q^{9} +2.04937 q^{10} -3.29667 q^{11} +0.166956 q^{12} +1.64955 q^{13} +6.37839 q^{14} -0.0343359 q^{15} +4.30860 q^{16} -3.95016 q^{17} +7.37546 q^{18} -4.26985 q^{19} -3.37497 q^{20} -0.106866 q^{21} +8.10941 q^{22} +6.26903 q^{23} -0.207931 q^{24} -4.30591 q^{25} -4.05768 q^{26} -0.247212 q^{27} -10.5041 q^{28} +3.42826 q^{29} +0.0844622 q^{30} -0.471240 q^{31} -0.508207 q^{32} -0.135868 q^{33} +9.71691 q^{34} +2.16026 q^{35} -12.1461 q^{36} -10.1343 q^{37} +10.5033 q^{38} +0.0679838 q^{39} +4.20327 q^{40} -6.82459 q^{41} +0.262877 q^{42} -0.688204 q^{43} -13.3548 q^{44} +2.49795 q^{45} -15.4210 q^{46} -13.3807 q^{47} +0.177573 q^{48} -0.276502 q^{49} +10.5920 q^{50} -0.162801 q^{51} +6.68231 q^{52} -2.16101 q^{53} +0.608111 q^{54} +2.74652 q^{55} +13.0821 q^{56} -0.175976 q^{57} -8.43309 q^{58} +13.3220 q^{59} -0.139095 q^{60} -5.10292 q^{61} +1.15919 q^{62} +7.77451 q^{63} -7.36707 q^{64} -1.37427 q^{65} +0.334218 q^{66} -12.6006 q^{67} -16.0021 q^{68} +0.258369 q^{69} -5.31397 q^{70} -7.73875 q^{71} +15.1271 q^{72} -7.25260 q^{73} +24.9292 q^{74} -0.177462 q^{75} -17.2971 q^{76} +8.54817 q^{77} -0.167232 q^{78} +7.17556 q^{79} -3.58958 q^{80} +8.98472 q^{81} +16.7877 q^{82} -2.75476 q^{83} -0.432913 q^{84} +3.29096 q^{85} +1.69290 q^{86} +0.141291 q^{87} +16.6324 q^{88} -6.67981 q^{89} -6.14464 q^{90} -4.27723 q^{91} +25.3958 q^{92} -0.0194215 q^{93} +32.9148 q^{94} +3.55730 q^{95} -0.0209451 q^{96} -2.66279 q^{97} +0.680162 q^{98} +9.88441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45988 −1.73940 −0.869698 0.493584i \(-0.835687\pi\)
−0.869698 + 0.493584i \(0.835687\pi\)
\(3\) 0.0412137 0.0237947 0.0118974 0.999929i \(-0.496213\pi\)
0.0118974 + 0.999929i \(0.496213\pi\)
\(4\) 4.05100 2.02550
\(5\) −0.833121 −0.372583 −0.186291 0.982495i \(-0.559647\pi\)
−0.186291 + 0.982495i \(0.559647\pi\)
\(6\) −0.101381 −0.0413884
\(7\) −2.59297 −0.980051 −0.490025 0.871708i \(-0.663013\pi\)
−0.490025 + 0.871708i \(0.663013\pi\)
\(8\) −5.04521 −1.78375
\(9\) −2.99830 −0.999434
\(10\) 2.04937 0.648069
\(11\) −3.29667 −0.993983 −0.496992 0.867755i \(-0.665562\pi\)
−0.496992 + 0.867755i \(0.665562\pi\)
\(12\) 0.166956 0.0481962
\(13\) 1.64955 0.457502 0.228751 0.973485i \(-0.426536\pi\)
0.228751 + 0.973485i \(0.426536\pi\)
\(14\) 6.37839 1.70470
\(15\) −0.0343359 −0.00886550
\(16\) 4.30860 1.07715
\(17\) −3.95016 −0.958054 −0.479027 0.877800i \(-0.659010\pi\)
−0.479027 + 0.877800i \(0.659010\pi\)
\(18\) 7.37546 1.73841
\(19\) −4.26985 −0.979570 −0.489785 0.871843i \(-0.662925\pi\)
−0.489785 + 0.871843i \(0.662925\pi\)
\(20\) −3.37497 −0.754666
\(21\) −0.106866 −0.0233200
\(22\) 8.10941 1.72893
\(23\) 6.26903 1.30718 0.653591 0.756848i \(-0.273262\pi\)
0.653591 + 0.756848i \(0.273262\pi\)
\(24\) −0.207931 −0.0424438
\(25\) −4.30591 −0.861182
\(26\) −4.05768 −0.795777
\(27\) −0.247212 −0.0475760
\(28\) −10.5041 −1.98509
\(29\) 3.42826 0.636611 0.318306 0.947988i \(-0.396886\pi\)
0.318306 + 0.947988i \(0.396886\pi\)
\(30\) 0.0844622 0.0154206
\(31\) −0.471240 −0.0846373 −0.0423186 0.999104i \(-0.513474\pi\)
−0.0423186 + 0.999104i \(0.513474\pi\)
\(32\) −0.508207 −0.0898392
\(33\) −0.135868 −0.0236516
\(34\) 9.71691 1.66644
\(35\) 2.16026 0.365150
\(36\) −12.1461 −2.02435
\(37\) −10.1343 −1.66607 −0.833037 0.553217i \(-0.813400\pi\)
−0.833037 + 0.553217i \(0.813400\pi\)
\(38\) 10.5033 1.70386
\(39\) 0.0679838 0.0108861
\(40\) 4.20327 0.664595
\(41\) −6.82459 −1.06582 −0.532911 0.846171i \(-0.678902\pi\)
−0.532911 + 0.846171i \(0.678902\pi\)
\(42\) 0.262877 0.0405628
\(43\) −0.688204 −0.104950 −0.0524751 0.998622i \(-0.516711\pi\)
−0.0524751 + 0.998622i \(0.516711\pi\)
\(44\) −13.3548 −2.01331
\(45\) 2.49795 0.372372
\(46\) −15.4210 −2.27371
\(47\) −13.3807 −1.95177 −0.975884 0.218288i \(-0.929953\pi\)
−0.975884 + 0.218288i \(0.929953\pi\)
\(48\) 0.177573 0.0256305
\(49\) −0.276502 −0.0395004
\(50\) 10.5920 1.49794
\(51\) −0.162801 −0.0227966
\(52\) 6.68231 0.926670
\(53\) −2.16101 −0.296837 −0.148419 0.988925i \(-0.547418\pi\)
−0.148419 + 0.988925i \(0.547418\pi\)
\(54\) 0.608111 0.0827534
\(55\) 2.74652 0.370341
\(56\) 13.0821 1.74817
\(57\) −0.175976 −0.0233086
\(58\) −8.43309 −1.10732
\(59\) 13.3220 1.73438 0.867190 0.497977i \(-0.165924\pi\)
0.867190 + 0.497977i \(0.165924\pi\)
\(60\) −0.139095 −0.0179571
\(61\) −5.10292 −0.653362 −0.326681 0.945135i \(-0.605930\pi\)
−0.326681 + 0.945135i \(0.605930\pi\)
\(62\) 1.15919 0.147218
\(63\) 7.77451 0.979496
\(64\) −7.36707 −0.920883
\(65\) −1.37427 −0.170457
\(66\) 0.334218 0.0411394
\(67\) −12.6006 −1.53941 −0.769707 0.638397i \(-0.779598\pi\)
−0.769707 + 0.638397i \(0.779598\pi\)
\(68\) −16.0021 −1.94054
\(69\) 0.258369 0.0311040
\(70\) −5.31397 −0.635141
\(71\) −7.73875 −0.918421 −0.459211 0.888327i \(-0.651868\pi\)
−0.459211 + 0.888327i \(0.651868\pi\)
\(72\) 15.1271 1.78274
\(73\) −7.25260 −0.848852 −0.424426 0.905463i \(-0.639524\pi\)
−0.424426 + 0.905463i \(0.639524\pi\)
\(74\) 24.9292 2.89796
\(75\) −0.177462 −0.0204916
\(76\) −17.2971 −1.98412
\(77\) 8.54817 0.974154
\(78\) −0.167232 −0.0189353
\(79\) 7.17556 0.807313 0.403657 0.914911i \(-0.367739\pi\)
0.403657 + 0.914911i \(0.367739\pi\)
\(80\) −3.58958 −0.401327
\(81\) 8.98472 0.998302
\(82\) 16.7877 1.85389
\(83\) −2.75476 −0.302374 −0.151187 0.988505i \(-0.548310\pi\)
−0.151187 + 0.988505i \(0.548310\pi\)
\(84\) −0.432913 −0.0472347
\(85\) 3.29096 0.356955
\(86\) 1.69290 0.182550
\(87\) 0.141291 0.0151480
\(88\) 16.6324 1.77302
\(89\) −6.67981 −0.708058 −0.354029 0.935234i \(-0.615189\pi\)
−0.354029 + 0.935234i \(0.615189\pi\)
\(90\) −6.14464 −0.647702
\(91\) −4.27723 −0.448375
\(92\) 25.3958 2.64770
\(93\) −0.0194215 −0.00201392
\(94\) 32.9148 3.39490
\(95\) 3.55730 0.364971
\(96\) −0.0209451 −0.00213770
\(97\) −2.66279 −0.270365 −0.135183 0.990821i \(-0.543162\pi\)
−0.135183 + 0.990821i \(0.543162\pi\)
\(98\) 0.680162 0.0687068
\(99\) 9.88441 0.993421
\(100\) −17.4432 −1.74432
\(101\) 1.53041 0.152281 0.0761405 0.997097i \(-0.475740\pi\)
0.0761405 + 0.997097i \(0.475740\pi\)
\(102\) 0.400469 0.0396524
\(103\) −8.99885 −0.886683 −0.443341 0.896353i \(-0.646207\pi\)
−0.443341 + 0.896353i \(0.646207\pi\)
\(104\) −8.32231 −0.816069
\(105\) 0.0890321 0.00868864
\(106\) 5.31582 0.516318
\(107\) −0.491948 −0.0475584 −0.0237792 0.999717i \(-0.507570\pi\)
−0.0237792 + 0.999717i \(0.507570\pi\)
\(108\) −1.00146 −0.0963651
\(109\) −12.9048 −1.23605 −0.618027 0.786157i \(-0.712068\pi\)
−0.618027 + 0.786157i \(0.712068\pi\)
\(110\) −6.75611 −0.644170
\(111\) −0.417673 −0.0396438
\(112\) −11.1721 −1.05566
\(113\) 18.7939 1.76798 0.883990 0.467506i \(-0.154847\pi\)
0.883990 + 0.467506i \(0.154847\pi\)
\(114\) 0.432879 0.0405429
\(115\) −5.22285 −0.487034
\(116\) 13.8879 1.28946
\(117\) −4.94584 −0.457243
\(118\) −32.7706 −3.01678
\(119\) 10.2426 0.938942
\(120\) 0.173232 0.0158138
\(121\) −0.131967 −0.0119970
\(122\) 12.5526 1.13645
\(123\) −0.281266 −0.0253609
\(124\) −1.90899 −0.171433
\(125\) 7.75295 0.693444
\(126\) −19.1243 −1.70373
\(127\) 10.9387 0.970655 0.485327 0.874333i \(-0.338700\pi\)
0.485327 + 0.874333i \(0.338700\pi\)
\(128\) 19.1385 1.69162
\(129\) −0.0283634 −0.00249726
\(130\) 3.38054 0.296493
\(131\) −2.74635 −0.239950 −0.119975 0.992777i \(-0.538281\pi\)
−0.119975 + 0.992777i \(0.538281\pi\)
\(132\) −0.550400 −0.0479062
\(133\) 11.0716 0.960028
\(134\) 30.9961 2.67765
\(135\) 0.205957 0.0177260
\(136\) 19.9294 1.70893
\(137\) 22.1436 1.89185 0.945927 0.324379i \(-0.105155\pi\)
0.945927 + 0.324379i \(0.105155\pi\)
\(138\) −0.635557 −0.0541022
\(139\) 7.59085 0.643847 0.321924 0.946766i \(-0.395671\pi\)
0.321924 + 0.946766i \(0.395671\pi\)
\(140\) 8.75120 0.739611
\(141\) −0.551466 −0.0464418
\(142\) 19.0364 1.59750
\(143\) −5.43801 −0.454749
\(144\) −12.9185 −1.07654
\(145\) −2.85615 −0.237190
\(146\) 17.8405 1.47649
\(147\) −0.0113957 −0.000939900 0
\(148\) −41.0542 −3.37463
\(149\) −11.8227 −0.968555 −0.484278 0.874914i \(-0.660918\pi\)
−0.484278 + 0.874914i \(0.660918\pi\)
\(150\) 0.436536 0.0356430
\(151\) −7.87209 −0.640621 −0.320311 0.947313i \(-0.603787\pi\)
−0.320311 + 0.947313i \(0.603787\pi\)
\(152\) 21.5423 1.74731
\(153\) 11.8438 0.957512
\(154\) −21.0275 −1.69444
\(155\) 0.392600 0.0315344
\(156\) 0.275403 0.0220498
\(157\) 13.2824 1.06005 0.530025 0.847982i \(-0.322183\pi\)
0.530025 + 0.847982i \(0.322183\pi\)
\(158\) −17.6510 −1.40424
\(159\) −0.0890631 −0.00706316
\(160\) 0.423398 0.0334726
\(161\) −16.2554 −1.28111
\(162\) −22.1013 −1.73644
\(163\) −1.55257 −0.121607 −0.0608035 0.998150i \(-0.519366\pi\)
−0.0608035 + 0.998150i \(0.519366\pi\)
\(164\) −27.6464 −2.15882
\(165\) 0.113194 0.00881216
\(166\) 6.77638 0.525949
\(167\) 22.5595 1.74571 0.872855 0.487980i \(-0.162266\pi\)
0.872855 + 0.487980i \(0.162266\pi\)
\(168\) 0.539160 0.0415971
\(169\) −10.2790 −0.790692
\(170\) −8.09536 −0.620886
\(171\) 12.8023 0.979015
\(172\) −2.78792 −0.212577
\(173\) −15.2211 −1.15724 −0.578620 0.815597i \(-0.696409\pi\)
−0.578620 + 0.815597i \(0.696409\pi\)
\(174\) −0.347559 −0.0263483
\(175\) 11.1651 0.844002
\(176\) −14.2040 −1.07067
\(177\) 0.549050 0.0412691
\(178\) 16.4315 1.23159
\(179\) 7.58726 0.567099 0.283549 0.958958i \(-0.408488\pi\)
0.283549 + 0.958958i \(0.408488\pi\)
\(180\) 10.1192 0.754239
\(181\) −2.81087 −0.208930 −0.104465 0.994529i \(-0.533313\pi\)
−0.104465 + 0.994529i \(0.533313\pi\)
\(182\) 10.5215 0.779902
\(183\) −0.210310 −0.0155466
\(184\) −31.6285 −2.33169
\(185\) 8.44312 0.620751
\(186\) 0.0477746 0.00350301
\(187\) 13.0224 0.952290
\(188\) −54.2050 −3.95331
\(189\) 0.641013 0.0466269
\(190\) −8.75052 −0.634829
\(191\) −8.49846 −0.614927 −0.307463 0.951560i \(-0.599480\pi\)
−0.307463 + 0.951560i \(0.599480\pi\)
\(192\) −0.303624 −0.0219122
\(193\) 7.07402 0.509199 0.254600 0.967047i \(-0.418056\pi\)
0.254600 + 0.967047i \(0.418056\pi\)
\(194\) 6.55014 0.470272
\(195\) −0.0566387 −0.00405598
\(196\) −1.12011 −0.0800080
\(197\) −18.6397 −1.32802 −0.664012 0.747722i \(-0.731148\pi\)
−0.664012 + 0.747722i \(0.731148\pi\)
\(198\) −24.3144 −1.72795
\(199\) −12.9504 −0.918028 −0.459014 0.888429i \(-0.651797\pi\)
−0.459014 + 0.888429i \(0.651797\pi\)
\(200\) 21.7242 1.53613
\(201\) −0.519319 −0.0366299
\(202\) −3.76461 −0.264877
\(203\) −8.88937 −0.623911
\(204\) −0.659505 −0.0461746
\(205\) 5.68571 0.397107
\(206\) 22.1361 1.54229
\(207\) −18.7964 −1.30644
\(208\) 7.10723 0.492798
\(209\) 14.0763 0.973676
\(210\) −0.219008 −0.0151130
\(211\) 4.12813 0.284192 0.142096 0.989853i \(-0.454616\pi\)
0.142096 + 0.989853i \(0.454616\pi\)
\(212\) −8.75424 −0.601244
\(213\) −0.318942 −0.0218536
\(214\) 1.21013 0.0827228
\(215\) 0.573357 0.0391026
\(216\) 1.24724 0.0848636
\(217\) 1.22191 0.0829488
\(218\) 31.7442 2.14999
\(219\) −0.298906 −0.0201982
\(220\) 11.1262 0.750126
\(221\) −6.51597 −0.438312
\(222\) 1.02742 0.0689562
\(223\) 15.6401 1.04734 0.523669 0.851922i \(-0.324563\pi\)
0.523669 + 0.851922i \(0.324563\pi\)
\(224\) 1.31777 0.0880470
\(225\) 12.9104 0.860694
\(226\) −46.2307 −3.07522
\(227\) −9.94944 −0.660368 −0.330184 0.943917i \(-0.607111\pi\)
−0.330184 + 0.943917i \(0.607111\pi\)
\(228\) −0.712879 −0.0472115
\(229\) 23.1286 1.52838 0.764189 0.644992i \(-0.223139\pi\)
0.764189 + 0.644992i \(0.223139\pi\)
\(230\) 12.8476 0.847145
\(231\) 0.352301 0.0231797
\(232\) −17.2963 −1.13556
\(233\) 2.89898 0.189919 0.0949593 0.995481i \(-0.469728\pi\)
0.0949593 + 0.995481i \(0.469728\pi\)
\(234\) 12.1662 0.795327
\(235\) 11.1477 0.727196
\(236\) 53.9675 3.51299
\(237\) 0.295731 0.0192098
\(238\) −25.1957 −1.63319
\(239\) −15.6702 −1.01362 −0.506811 0.862057i \(-0.669176\pi\)
−0.506811 + 0.862057i \(0.669176\pi\)
\(240\) −0.147940 −0.00954947
\(241\) −5.83796 −0.376056 −0.188028 0.982164i \(-0.560210\pi\)
−0.188028 + 0.982164i \(0.560210\pi\)
\(242\) 0.324623 0.0208676
\(243\) 1.11193 0.0713303
\(244\) −20.6719 −1.32338
\(245\) 0.230360 0.0147172
\(246\) 0.691881 0.0441127
\(247\) −7.04331 −0.448155
\(248\) 2.37751 0.150972
\(249\) −0.113534 −0.00719491
\(250\) −19.0713 −1.20617
\(251\) 3.72421 0.235070 0.117535 0.993069i \(-0.462501\pi\)
0.117535 + 0.993069i \(0.462501\pi\)
\(252\) 31.4945 1.98397
\(253\) −20.6669 −1.29932
\(254\) −26.9079 −1.68835
\(255\) 0.135632 0.00849363
\(256\) −32.3442 −2.02151
\(257\) −2.25990 −0.140968 −0.0704842 0.997513i \(-0.522454\pi\)
−0.0704842 + 0.997513i \(0.522454\pi\)
\(258\) 0.0697706 0.00434372
\(259\) 26.2780 1.63284
\(260\) −5.56717 −0.345261
\(261\) −10.2789 −0.636251
\(262\) 6.75569 0.417368
\(263\) −19.7880 −1.22018 −0.610091 0.792332i \(-0.708867\pi\)
−0.610091 + 0.792332i \(0.708867\pi\)
\(264\) 0.685481 0.0421885
\(265\) 1.80038 0.110596
\(266\) −27.2347 −1.66987
\(267\) −0.275299 −0.0168480
\(268\) −51.0452 −3.11808
\(269\) 11.3361 0.691172 0.345586 0.938387i \(-0.387680\pi\)
0.345586 + 0.938387i \(0.387680\pi\)
\(270\) −0.506630 −0.0308325
\(271\) −22.0747 −1.34094 −0.670472 0.741935i \(-0.733908\pi\)
−0.670472 + 0.741935i \(0.733908\pi\)
\(272\) −17.0196 −1.03197
\(273\) −0.176280 −0.0106690
\(274\) −54.4705 −3.29068
\(275\) 14.1952 0.856001
\(276\) 1.04665 0.0630012
\(277\) −27.6007 −1.65837 −0.829184 0.558976i \(-0.811194\pi\)
−0.829184 + 0.558976i \(0.811194\pi\)
\(278\) −18.6726 −1.11991
\(279\) 1.41292 0.0845894
\(280\) −10.8989 −0.651337
\(281\) 6.66511 0.397607 0.198804 0.980039i \(-0.436294\pi\)
0.198804 + 0.980039i \(0.436294\pi\)
\(282\) 1.35654 0.0807807
\(283\) −13.9409 −0.828702 −0.414351 0.910117i \(-0.635991\pi\)
−0.414351 + 0.910117i \(0.635991\pi\)
\(284\) −31.3497 −1.86026
\(285\) 0.146609 0.00868438
\(286\) 13.3768 0.790989
\(287\) 17.6960 1.04456
\(288\) 1.52376 0.0897884
\(289\) −1.39624 −0.0821318
\(290\) 7.02578 0.412568
\(291\) −0.109743 −0.00643326
\(292\) −29.3803 −1.71935
\(293\) 32.0970 1.87513 0.937563 0.347816i \(-0.113076\pi\)
0.937563 + 0.347816i \(0.113076\pi\)
\(294\) 0.0280320 0.00163486
\(295\) −11.0989 −0.646200
\(296\) 51.1298 2.97186
\(297\) 0.814976 0.0472897
\(298\) 29.0825 1.68470
\(299\) 10.3411 0.598038
\(300\) −0.718900 −0.0415057
\(301\) 1.78449 0.102857
\(302\) 19.3644 1.11429
\(303\) 0.0630736 0.00362348
\(304\) −18.3970 −1.05514
\(305\) 4.25135 0.243431
\(306\) −29.1342 −1.66549
\(307\) −8.23901 −0.470225 −0.235113 0.971968i \(-0.575546\pi\)
−0.235113 + 0.971968i \(0.575546\pi\)
\(308\) 34.6286 1.97315
\(309\) −0.370875 −0.0210984
\(310\) −0.965748 −0.0548508
\(311\) −20.5617 −1.16594 −0.582972 0.812492i \(-0.698110\pi\)
−0.582972 + 0.812492i \(0.698110\pi\)
\(312\) −0.342993 −0.0194181
\(313\) 29.8138 1.68517 0.842587 0.538560i \(-0.181032\pi\)
0.842587 + 0.538560i \(0.181032\pi\)
\(314\) −32.6731 −1.84385
\(315\) −6.47710 −0.364943
\(316\) 29.0682 1.63521
\(317\) 11.5247 0.647292 0.323646 0.946178i \(-0.395091\pi\)
0.323646 + 0.946178i \(0.395091\pi\)
\(318\) 0.219084 0.0122856
\(319\) −11.3018 −0.632781
\(320\) 6.13765 0.343105
\(321\) −0.0202750 −0.00113164
\(322\) 39.9863 2.22835
\(323\) 16.8666 0.938481
\(324\) 36.3971 2.02206
\(325\) −7.10280 −0.393992
\(326\) 3.81914 0.211523
\(327\) −0.531854 −0.0294116
\(328\) 34.4315 1.90116
\(329\) 34.6956 1.91283
\(330\) −0.278444 −0.0153278
\(331\) −32.0902 −1.76384 −0.881918 0.471403i \(-0.843748\pi\)
−0.881918 + 0.471403i \(0.843748\pi\)
\(332\) −11.1595 −0.612459
\(333\) 30.3858 1.66513
\(334\) −55.4937 −3.03648
\(335\) 10.4979 0.573559
\(336\) −0.460442 −0.0251192
\(337\) 33.0250 1.79899 0.899494 0.436934i \(-0.143936\pi\)
0.899494 + 0.436934i \(0.143936\pi\)
\(338\) 25.2851 1.37533
\(339\) 0.774564 0.0420686
\(340\) 13.3317 0.723012
\(341\) 1.55352 0.0841281
\(342\) −31.4921 −1.70290
\(343\) 18.8678 1.01876
\(344\) 3.47213 0.187205
\(345\) −0.215253 −0.0115888
\(346\) 37.4421 2.01290
\(347\) 29.5577 1.58674 0.793371 0.608738i \(-0.208324\pi\)
0.793371 + 0.608738i \(0.208324\pi\)
\(348\) 0.572370 0.0306822
\(349\) 24.3241 1.30204 0.651020 0.759060i \(-0.274341\pi\)
0.651020 + 0.759060i \(0.274341\pi\)
\(350\) −27.4648 −1.46805
\(351\) −0.407788 −0.0217661
\(352\) 1.67539 0.0892987
\(353\) −11.2754 −0.600130 −0.300065 0.953919i \(-0.597008\pi\)
−0.300065 + 0.953919i \(0.597008\pi\)
\(354\) −1.35059 −0.0717833
\(355\) 6.44732 0.342188
\(356\) −27.0599 −1.43417
\(357\) 0.422137 0.0223419
\(358\) −18.6637 −0.986409
\(359\) 29.5456 1.55936 0.779678 0.626181i \(-0.215383\pi\)
0.779678 + 0.626181i \(0.215383\pi\)
\(360\) −12.6027 −0.664219
\(361\) −0.768415 −0.0404429
\(362\) 6.91440 0.363413
\(363\) −0.00543885 −0.000285465 0
\(364\) −17.3270 −0.908184
\(365\) 6.04229 0.316268
\(366\) 0.517337 0.0270416
\(367\) −9.51852 −0.496863 −0.248431 0.968650i \(-0.579915\pi\)
−0.248431 + 0.968650i \(0.579915\pi\)
\(368\) 27.0107 1.40803
\(369\) 20.4622 1.06522
\(370\) −20.7691 −1.07973
\(371\) 5.60343 0.290916
\(372\) −0.0786767 −0.00407919
\(373\) 23.1384 1.19806 0.599032 0.800725i \(-0.295552\pi\)
0.599032 + 0.800725i \(0.295552\pi\)
\(374\) −32.0334 −1.65641
\(375\) 0.319527 0.0165003
\(376\) 67.5082 3.48147
\(377\) 5.65507 0.291251
\(378\) −1.57681 −0.0811026
\(379\) −14.6046 −0.750190 −0.375095 0.926986i \(-0.622390\pi\)
−0.375095 + 0.926986i \(0.622390\pi\)
\(380\) 14.4106 0.739248
\(381\) 0.450825 0.0230964
\(382\) 20.9052 1.06960
\(383\) 3.36817 0.172105 0.0860527 0.996291i \(-0.472575\pi\)
0.0860527 + 0.996291i \(0.472575\pi\)
\(384\) 0.788768 0.0402516
\(385\) −7.12166 −0.362953
\(386\) −17.4012 −0.885699
\(387\) 2.06344 0.104891
\(388\) −10.7870 −0.547625
\(389\) −8.98901 −0.455761 −0.227881 0.973689i \(-0.573180\pi\)
−0.227881 + 0.973689i \(0.573180\pi\)
\(390\) 0.139324 0.00705496
\(391\) −24.7637 −1.25235
\(392\) 1.39501 0.0704588
\(393\) −0.113187 −0.00570954
\(394\) 45.8514 2.30996
\(395\) −5.97811 −0.300791
\(396\) 40.0417 2.01217
\(397\) −2.71515 −0.136270 −0.0681348 0.997676i \(-0.521705\pi\)
−0.0681348 + 0.997676i \(0.521705\pi\)
\(398\) 31.8564 1.59682
\(399\) 0.456301 0.0228436
\(400\) −18.5524 −0.927622
\(401\) 26.4247 1.31958 0.659792 0.751448i \(-0.270644\pi\)
0.659792 + 0.751448i \(0.270644\pi\)
\(402\) 1.27746 0.0637140
\(403\) −0.777333 −0.0387217
\(404\) 6.19967 0.308445
\(405\) −7.48535 −0.371950
\(406\) 21.8668 1.08523
\(407\) 33.4096 1.65605
\(408\) 0.821362 0.0406635
\(409\) 6.76150 0.334334 0.167167 0.985929i \(-0.446538\pi\)
0.167167 + 0.985929i \(0.446538\pi\)
\(410\) −13.9861 −0.690727
\(411\) 0.912618 0.0450161
\(412\) −36.4543 −1.79598
\(413\) −34.5436 −1.69978
\(414\) 46.2369 2.27242
\(415\) 2.29505 0.112660
\(416\) −0.838312 −0.0411016
\(417\) 0.312847 0.0153202
\(418\) −34.6259 −1.69361
\(419\) −25.0679 −1.22465 −0.612323 0.790608i \(-0.709765\pi\)
−0.612323 + 0.790608i \(0.709765\pi\)
\(420\) 0.360669 0.0175988
\(421\) 26.5711 1.29500 0.647498 0.762068i \(-0.275816\pi\)
0.647498 + 0.762068i \(0.275816\pi\)
\(422\) −10.1547 −0.494323
\(423\) 40.1192 1.95066
\(424\) 10.9027 0.529484
\(425\) 17.0090 0.825059
\(426\) 0.784559 0.0380120
\(427\) 13.2317 0.640328
\(428\) −1.99288 −0.0963295
\(429\) −0.224120 −0.0108206
\(430\) −1.41039 −0.0680150
\(431\) 12.9413 0.623359 0.311680 0.950187i \(-0.399108\pi\)
0.311680 + 0.950187i \(0.399108\pi\)
\(432\) −1.06514 −0.0512464
\(433\) 8.20557 0.394334 0.197167 0.980370i \(-0.436826\pi\)
0.197167 + 0.980370i \(0.436826\pi\)
\(434\) −3.00576 −0.144281
\(435\) −0.117712 −0.00564388
\(436\) −52.2773 −2.50363
\(437\) −26.7678 −1.28048
\(438\) 0.735272 0.0351327
\(439\) 14.7891 0.705843 0.352922 0.935653i \(-0.385188\pi\)
0.352922 + 0.935653i \(0.385188\pi\)
\(440\) −13.8568 −0.660596
\(441\) 0.829038 0.0394780
\(442\) 16.0285 0.762398
\(443\) 36.7452 1.74582 0.872909 0.487883i \(-0.162231\pi\)
0.872909 + 0.487883i \(0.162231\pi\)
\(444\) −1.69199 −0.0802984
\(445\) 5.56508 0.263810
\(446\) −38.4727 −1.82174
\(447\) −0.487258 −0.0230465
\(448\) 19.1026 0.902513
\(449\) −2.71926 −0.128330 −0.0641649 0.997939i \(-0.520438\pi\)
−0.0641649 + 0.997939i \(0.520438\pi\)
\(450\) −31.7580 −1.49709
\(451\) 22.4984 1.05941
\(452\) 76.1340 3.58104
\(453\) −0.324437 −0.0152434
\(454\) 24.4744 1.14864
\(455\) 3.56345 0.167057
\(456\) 0.887835 0.0415767
\(457\) 12.8150 0.599460 0.299730 0.954024i \(-0.403103\pi\)
0.299730 + 0.954024i \(0.403103\pi\)
\(458\) −56.8935 −2.65846
\(459\) 0.976527 0.0455804
\(460\) −21.1578 −0.986487
\(461\) −14.5339 −0.676911 −0.338455 0.940982i \(-0.609904\pi\)
−0.338455 + 0.940982i \(0.609904\pi\)
\(462\) −0.866618 −0.0403187
\(463\) −25.5856 −1.18906 −0.594531 0.804072i \(-0.702662\pi\)
−0.594531 + 0.804072i \(0.702662\pi\)
\(464\) 14.7710 0.685725
\(465\) 0.0161805 0.000750352 0
\(466\) −7.13114 −0.330344
\(467\) −5.87108 −0.271681 −0.135841 0.990731i \(-0.543374\pi\)
−0.135841 + 0.990731i \(0.543374\pi\)
\(468\) −20.0356 −0.926145
\(469\) 32.6731 1.50870
\(470\) −27.4220 −1.26488
\(471\) 0.547416 0.0252236
\(472\) −67.2124 −3.09370
\(473\) 2.26878 0.104319
\(474\) −0.727462 −0.0334134
\(475\) 18.3856 0.843588
\(476\) 41.4930 1.90183
\(477\) 6.47935 0.296669
\(478\) 38.5469 1.76309
\(479\) −14.3953 −0.657736 −0.328868 0.944376i \(-0.606667\pi\)
−0.328868 + 0.944376i \(0.606667\pi\)
\(480\) 0.0174498 0.000796470 0
\(481\) −16.7171 −0.762232
\(482\) 14.3607 0.654111
\(483\) −0.669945 −0.0304835
\(484\) −0.534599 −0.0242999
\(485\) 2.21842 0.100733
\(486\) −2.73521 −0.124072
\(487\) 31.0074 1.40508 0.702540 0.711644i \(-0.252049\pi\)
0.702540 + 0.711644i \(0.252049\pi\)
\(488\) 25.7453 1.16543
\(489\) −0.0639872 −0.00289360
\(490\) −0.566657 −0.0255990
\(491\) −13.4606 −0.607467 −0.303733 0.952757i \(-0.598233\pi\)
−0.303733 + 0.952757i \(0.598233\pi\)
\(492\) −1.13941 −0.0513686
\(493\) −13.5422 −0.609908
\(494\) 17.3257 0.779519
\(495\) −8.23491 −0.370131
\(496\) −2.03039 −0.0911670
\(497\) 20.0664 0.900099
\(498\) 0.279279 0.0125148
\(499\) −30.0192 −1.34385 −0.671923 0.740621i \(-0.734531\pi\)
−0.671923 + 0.740621i \(0.734531\pi\)
\(500\) 31.4072 1.40457
\(501\) 0.929761 0.0415387
\(502\) −9.16111 −0.408880
\(503\) 28.1894 1.25690 0.628451 0.777849i \(-0.283689\pi\)
0.628451 + 0.777849i \(0.283689\pi\)
\(504\) −39.2240 −1.74718
\(505\) −1.27501 −0.0567373
\(506\) 50.8381 2.26003
\(507\) −0.423635 −0.0188143
\(508\) 44.3128 1.96606
\(509\) 5.87060 0.260210 0.130105 0.991500i \(-0.458469\pi\)
0.130105 + 0.991500i \(0.458469\pi\)
\(510\) −0.333639 −0.0147738
\(511\) 18.8058 0.831918
\(512\) 41.2859 1.82460
\(513\) 1.05556 0.0466040
\(514\) 5.55907 0.245200
\(515\) 7.49712 0.330363
\(516\) −0.114900 −0.00505820
\(517\) 44.1116 1.94003
\(518\) −64.6408 −2.84015
\(519\) −0.627318 −0.0275362
\(520\) 6.93348 0.304053
\(521\) 25.9356 1.13626 0.568129 0.822940i \(-0.307668\pi\)
0.568129 + 0.822940i \(0.307668\pi\)
\(522\) 25.2850 1.10669
\(523\) 24.7906 1.08402 0.542008 0.840373i \(-0.317664\pi\)
0.542008 + 0.840373i \(0.317664\pi\)
\(524\) −11.1255 −0.486018
\(525\) 0.460155 0.0200828
\(526\) 48.6761 2.12238
\(527\) 1.86147 0.0810871
\(528\) −0.585400 −0.0254763
\(529\) 16.3007 0.708726
\(530\) −4.42872 −0.192371
\(531\) −39.9435 −1.73340
\(532\) 44.8510 1.94454
\(533\) −11.2575 −0.487616
\(534\) 0.677203 0.0293054
\(535\) 0.409852 0.0177194
\(536\) 63.5729 2.74593
\(537\) 0.312699 0.0134939
\(538\) −27.8853 −1.20222
\(539\) 0.911537 0.0392627
\(540\) 0.834333 0.0359040
\(541\) −26.0672 −1.12072 −0.560359 0.828250i \(-0.689337\pi\)
−0.560359 + 0.828250i \(0.689337\pi\)
\(542\) 54.3011 2.33243
\(543\) −0.115846 −0.00497144
\(544\) 2.00750 0.0860709
\(545\) 10.7512 0.460533
\(546\) 0.433628 0.0185575
\(547\) −21.2955 −0.910531 −0.455265 0.890356i \(-0.650456\pi\)
−0.455265 + 0.890356i \(0.650456\pi\)
\(548\) 89.7037 3.83195
\(549\) 15.3001 0.652992
\(550\) −34.9184 −1.48892
\(551\) −14.6381 −0.623605
\(552\) −1.30353 −0.0554818
\(553\) −18.6060 −0.791208
\(554\) 67.8944 2.88456
\(555\) 0.347972 0.0147706
\(556\) 30.7505 1.30411
\(557\) 12.2279 0.518114 0.259057 0.965862i \(-0.416588\pi\)
0.259057 + 0.965862i \(0.416588\pi\)
\(558\) −3.47561 −0.147134
\(559\) −1.13523 −0.0480149
\(560\) 9.30768 0.393321
\(561\) 0.536700 0.0226595
\(562\) −16.3954 −0.691597
\(563\) −22.6059 −0.952726 −0.476363 0.879249i \(-0.658045\pi\)
−0.476363 + 0.879249i \(0.658045\pi\)
\(564\) −2.23399 −0.0940678
\(565\) −15.6576 −0.658719
\(566\) 34.2930 1.44144
\(567\) −23.2971 −0.978386
\(568\) 39.0436 1.63823
\(569\) −26.1129 −1.09471 −0.547356 0.836900i \(-0.684365\pi\)
−0.547356 + 0.836900i \(0.684365\pi\)
\(570\) −0.360641 −0.0151056
\(571\) −11.8682 −0.496670 −0.248335 0.968674i \(-0.579883\pi\)
−0.248335 + 0.968674i \(0.579883\pi\)
\(572\) −22.0294 −0.921095
\(573\) −0.350252 −0.0146320
\(574\) −43.5299 −1.81690
\(575\) −26.9939 −1.12572
\(576\) 22.0887 0.920362
\(577\) −39.0291 −1.62480 −0.812402 0.583097i \(-0.801841\pi\)
−0.812402 + 0.583097i \(0.801841\pi\)
\(578\) 3.43458 0.142860
\(579\) 0.291546 0.0121162
\(580\) −11.5703 −0.480429
\(581\) 7.14302 0.296342
\(582\) 0.269955 0.0111900
\(583\) 7.12413 0.295051
\(584\) 36.5909 1.51414
\(585\) 4.12048 0.170361
\(586\) −78.9547 −3.26159
\(587\) 16.2379 0.670210 0.335105 0.942181i \(-0.391228\pi\)
0.335105 + 0.942181i \(0.391228\pi\)
\(588\) −0.0461639 −0.00190377
\(589\) 2.01212 0.0829081
\(590\) 27.3018 1.12400
\(591\) −0.768211 −0.0316000
\(592\) −43.6648 −1.79461
\(593\) 36.7567 1.50942 0.754709 0.656059i \(-0.227778\pi\)
0.754709 + 0.656059i \(0.227778\pi\)
\(594\) −2.00474 −0.0822556
\(595\) −8.53336 −0.349834
\(596\) −47.8938 −1.96181
\(597\) −0.533733 −0.0218442
\(598\) −25.4377 −1.04023
\(599\) −19.9701 −0.815958 −0.407979 0.912991i \(-0.633766\pi\)
−0.407979 + 0.912991i \(0.633766\pi\)
\(600\) 0.895334 0.0365519
\(601\) 9.30689 0.379636 0.189818 0.981819i \(-0.439210\pi\)
0.189818 + 0.981819i \(0.439210\pi\)
\(602\) −4.38964 −0.178908
\(603\) 37.7805 1.53854
\(604\) −31.8898 −1.29758
\(605\) 0.109945 0.00446988
\(606\) −0.155153 −0.00630268
\(607\) 40.3221 1.63662 0.818312 0.574775i \(-0.194910\pi\)
0.818312 + 0.574775i \(0.194910\pi\)
\(608\) 2.16997 0.0880038
\(609\) −0.366363 −0.0148458
\(610\) −10.4578 −0.423424
\(611\) −22.0720 −0.892938
\(612\) 47.9791 1.93944
\(613\) 25.1006 1.01380 0.506902 0.862004i \(-0.330791\pi\)
0.506902 + 0.862004i \(0.330791\pi\)
\(614\) 20.2670 0.817908
\(615\) 0.234329 0.00944905
\(616\) −43.1273 −1.73765
\(617\) −36.0159 −1.44995 −0.724973 0.688777i \(-0.758148\pi\)
−0.724973 + 0.688777i \(0.758148\pi\)
\(618\) 0.912308 0.0366984
\(619\) 13.6473 0.548530 0.274265 0.961654i \(-0.411566\pi\)
0.274265 + 0.961654i \(0.411566\pi\)
\(620\) 1.59042 0.0638729
\(621\) −1.54978 −0.0621905
\(622\) 50.5792 2.02804
\(623\) 17.3205 0.693933
\(624\) 0.292915 0.0117260
\(625\) 15.0704 0.602816
\(626\) −73.3382 −2.93119
\(627\) 0.580135 0.0231683
\(628\) 53.8069 2.14713
\(629\) 40.0322 1.59619
\(630\) 15.9329 0.634781
\(631\) −38.8056 −1.54483 −0.772413 0.635121i \(-0.780950\pi\)
−0.772413 + 0.635121i \(0.780950\pi\)
\(632\) −36.2022 −1.44005
\(633\) 0.170135 0.00676227
\(634\) −28.3494 −1.12590
\(635\) −9.11327 −0.361649
\(636\) −0.360794 −0.0143064
\(637\) −0.456104 −0.0180715
\(638\) 27.8011 1.10066
\(639\) 23.2031 0.917901
\(640\) −15.9447 −0.630269
\(641\) −5.74792 −0.227029 −0.113515 0.993536i \(-0.536211\pi\)
−0.113515 + 0.993536i \(0.536211\pi\)
\(642\) 0.0498739 0.00196837
\(643\) 10.4255 0.411141 0.205571 0.978642i \(-0.434095\pi\)
0.205571 + 0.978642i \(0.434095\pi\)
\(644\) −65.8506 −2.59488
\(645\) 0.0236301 0.000930436 0
\(646\) −41.4897 −1.63239
\(647\) −9.96556 −0.391787 −0.195893 0.980625i \(-0.562761\pi\)
−0.195893 + 0.980625i \(0.562761\pi\)
\(648\) −45.3298 −1.78072
\(649\) −43.9183 −1.72395
\(650\) 17.4720 0.685309
\(651\) 0.0503595 0.00197374
\(652\) −6.28947 −0.246315
\(653\) −15.3501 −0.600695 −0.300347 0.953830i \(-0.597103\pi\)
−0.300347 + 0.953830i \(0.597103\pi\)
\(654\) 1.30829 0.0511584
\(655\) 2.28804 0.0894012
\(656\) −29.4044 −1.14805
\(657\) 21.7455 0.848372
\(658\) −85.3470 −3.32717
\(659\) −29.7244 −1.15790 −0.578950 0.815363i \(-0.696537\pi\)
−0.578950 + 0.815363i \(0.696537\pi\)
\(660\) 0.458550 0.0178490
\(661\) −43.4794 −1.69115 −0.845576 0.533855i \(-0.820743\pi\)
−0.845576 + 0.533855i \(0.820743\pi\)
\(662\) 78.9379 3.06801
\(663\) −0.268547 −0.0104295
\(664\) 13.8983 0.539361
\(665\) −9.22397 −0.357690
\(666\) −74.7453 −2.89632
\(667\) 21.4918 0.832167
\(668\) 91.3887 3.53593
\(669\) 0.644585 0.0249211
\(670\) −25.8235 −0.997647
\(671\) 16.8226 0.649431
\(672\) 0.0543100 0.00209505
\(673\) 33.6795 1.29825 0.649124 0.760683i \(-0.275136\pi\)
0.649124 + 0.760683i \(0.275136\pi\)
\(674\) −81.2375 −3.12915
\(675\) 1.06447 0.0409716
\(676\) −41.6402 −1.60155
\(677\) 3.58906 0.137939 0.0689694 0.997619i \(-0.478029\pi\)
0.0689694 + 0.997619i \(0.478029\pi\)
\(678\) −1.90533 −0.0731739
\(679\) 6.90453 0.264972
\(680\) −16.6036 −0.636718
\(681\) −0.410053 −0.0157133
\(682\) −3.82148 −0.146332
\(683\) −12.8870 −0.493108 −0.246554 0.969129i \(-0.579298\pi\)
−0.246554 + 0.969129i \(0.579298\pi\)
\(684\) 51.8621 1.98300
\(685\) −18.4483 −0.704873
\(686\) −46.4124 −1.77203
\(687\) 0.953213 0.0363673
\(688\) −2.96520 −0.113047
\(689\) −3.56468 −0.135804
\(690\) 0.529496 0.0201576
\(691\) −21.7475 −0.827314 −0.413657 0.910433i \(-0.635749\pi\)
−0.413657 + 0.910433i \(0.635749\pi\)
\(692\) −61.6608 −2.34399
\(693\) −25.6300 −0.973603
\(694\) −72.7084 −2.75997
\(695\) −6.32409 −0.239886
\(696\) −0.712842 −0.0270202
\(697\) 26.9582 1.02112
\(698\) −59.8344 −2.26476
\(699\) 0.119478 0.00451906
\(700\) 45.2298 1.70953
\(701\) 43.8653 1.65677 0.828385 0.560159i \(-0.189260\pi\)
0.828385 + 0.560159i \(0.189260\pi\)
\(702\) 1.00311 0.0378599
\(703\) 43.2720 1.63204
\(704\) 24.2868 0.915343
\(705\) 0.459437 0.0173034
\(706\) 27.7362 1.04386
\(707\) −3.96830 −0.149243
\(708\) 2.22420 0.0835905
\(709\) −28.3456 −1.06454 −0.532271 0.846574i \(-0.678661\pi\)
−0.532271 + 0.846574i \(0.678661\pi\)
\(710\) −15.8596 −0.595200
\(711\) −21.5145 −0.806856
\(712\) 33.7010 1.26300
\(713\) −2.95422 −0.110636
\(714\) −1.03841 −0.0388613
\(715\) 4.53052 0.169432
\(716\) 30.7360 1.14866
\(717\) −0.645827 −0.0241189
\(718\) −72.6785 −2.71234
\(719\) −51.5280 −1.92167 −0.960834 0.277124i \(-0.910619\pi\)
−0.960834 + 0.277124i \(0.910619\pi\)
\(720\) 10.7626 0.401100
\(721\) 23.3337 0.868994
\(722\) 1.89021 0.0703463
\(723\) −0.240604 −0.00894815
\(724\) −11.3868 −0.423189
\(725\) −14.7618 −0.548238
\(726\) 0.0133789 0.000496538 0
\(727\) 12.6348 0.468600 0.234300 0.972164i \(-0.424720\pi\)
0.234300 + 0.972164i \(0.424720\pi\)
\(728\) 21.5795 0.799789
\(729\) −26.9083 −0.996604
\(730\) −14.8633 −0.550115
\(731\) 2.71852 0.100548
\(732\) −0.851965 −0.0314895
\(733\) 1.13856 0.0420536 0.0210268 0.999779i \(-0.493306\pi\)
0.0210268 + 0.999779i \(0.493306\pi\)
\(734\) 23.4144 0.864241
\(735\) 0.00949397 0.000350190 0
\(736\) −3.18597 −0.117436
\(737\) 41.5402 1.53015
\(738\) −50.3345 −1.85284
\(739\) 35.5291 1.30696 0.653479 0.756945i \(-0.273309\pi\)
0.653479 + 0.756945i \(0.273309\pi\)
\(740\) 34.2031 1.25733
\(741\) −0.290281 −0.0106637
\(742\) −13.7838 −0.506018
\(743\) −11.8971 −0.436463 −0.218231 0.975897i \(-0.570029\pi\)
−0.218231 + 0.975897i \(0.570029\pi\)
\(744\) 0.0979857 0.00359233
\(745\) 9.84975 0.360867
\(746\) −56.9178 −2.08391
\(747\) 8.25961 0.302203
\(748\) 52.7536 1.92886
\(749\) 1.27561 0.0466096
\(750\) −0.785998 −0.0287006
\(751\) −41.4075 −1.51098 −0.755490 0.655160i \(-0.772601\pi\)
−0.755490 + 0.655160i \(0.772601\pi\)
\(752\) −57.6518 −2.10235
\(753\) 0.153488 0.00559343
\(754\) −13.9108 −0.506601
\(755\) 6.55840 0.238685
\(756\) 2.59674 0.0944427
\(757\) −33.1399 −1.20449 −0.602245 0.798311i \(-0.705727\pi\)
−0.602245 + 0.798311i \(0.705727\pi\)
\(758\) 35.9257 1.30488
\(759\) −0.851759 −0.0309169
\(760\) −17.9473 −0.651017
\(761\) 35.3423 1.28116 0.640578 0.767893i \(-0.278695\pi\)
0.640578 + 0.767893i \(0.278695\pi\)
\(762\) −1.10897 −0.0401739
\(763\) 33.4617 1.21140
\(764\) −34.4272 −1.24553
\(765\) −9.86729 −0.356753
\(766\) −8.28529 −0.299360
\(767\) 21.9753 0.793482
\(768\) −1.33302 −0.0481014
\(769\) −5.48456 −0.197778 −0.0988892 0.995098i \(-0.531529\pi\)
−0.0988892 + 0.995098i \(0.531529\pi\)
\(770\) 17.5184 0.631319
\(771\) −0.0931386 −0.00335430
\(772\) 28.6568 1.03138
\(773\) −41.6304 −1.49734 −0.748671 0.662942i \(-0.769308\pi\)
−0.748671 + 0.662942i \(0.769308\pi\)
\(774\) −5.07582 −0.182447
\(775\) 2.02912 0.0728881
\(776\) 13.4343 0.482264
\(777\) 1.08301 0.0388529
\(778\) 22.1119 0.792749
\(779\) 29.1400 1.04405
\(780\) −0.229444 −0.00821540
\(781\) 25.5121 0.912895
\(782\) 60.9156 2.17834
\(783\) −0.847506 −0.0302874
\(784\) −1.19134 −0.0425478
\(785\) −11.0658 −0.394956
\(786\) 0.278427 0.00993115
\(787\) −37.1210 −1.32322 −0.661610 0.749848i \(-0.730126\pi\)
−0.661610 + 0.749848i \(0.730126\pi\)
\(788\) −75.5095 −2.68991
\(789\) −0.815536 −0.0290339
\(790\) 14.7054 0.523195
\(791\) −48.7320 −1.73271
\(792\) −49.8689 −1.77201
\(793\) −8.41750 −0.298914
\(794\) 6.67894 0.237027
\(795\) 0.0742003 0.00263161
\(796\) −52.4620 −1.85947
\(797\) 10.8033 0.382672 0.191336 0.981525i \(-0.438718\pi\)
0.191336 + 0.981525i \(0.438718\pi\)
\(798\) −1.12244 −0.0397341
\(799\) 52.8557 1.86990
\(800\) 2.18830 0.0773679
\(801\) 20.0281 0.707657
\(802\) −65.0015 −2.29528
\(803\) 23.9094 0.843745
\(804\) −2.10376 −0.0741939
\(805\) 13.5427 0.477318
\(806\) 1.91214 0.0673524
\(807\) 0.467201 0.0164462
\(808\) −7.72122 −0.271631
\(809\) −23.2016 −0.815724 −0.407862 0.913043i \(-0.633726\pi\)
−0.407862 + 0.913043i \(0.633726\pi\)
\(810\) 18.4131 0.646969
\(811\) 43.8769 1.54073 0.770364 0.637605i \(-0.220075\pi\)
0.770364 + 0.637605i \(0.220075\pi\)
\(812\) −36.0108 −1.26373
\(813\) −0.909780 −0.0319074
\(814\) −82.1834 −2.88053
\(815\) 1.29348 0.0453087
\(816\) −0.701442 −0.0245554
\(817\) 2.93853 0.102806
\(818\) −16.6325 −0.581540
\(819\) 12.8244 0.448121
\(820\) 23.0328 0.804340
\(821\) −1.48524 −0.0518351 −0.0259176 0.999664i \(-0.508251\pi\)
−0.0259176 + 0.999664i \(0.508251\pi\)
\(822\) −2.24493 −0.0783009
\(823\) 21.7196 0.757098 0.378549 0.925581i \(-0.376423\pi\)
0.378549 + 0.925581i \(0.376423\pi\)
\(824\) 45.4011 1.58162
\(825\) 0.585035 0.0203683
\(826\) 84.9731 2.95659
\(827\) 23.7406 0.825541 0.412770 0.910835i \(-0.364561\pi\)
0.412770 + 0.910835i \(0.364561\pi\)
\(828\) −76.1443 −2.64620
\(829\) 37.4354 1.30019 0.650093 0.759855i \(-0.274730\pi\)
0.650093 + 0.759855i \(0.274730\pi\)
\(830\) −5.64554 −0.195960
\(831\) −1.13753 −0.0394604
\(832\) −12.1523 −0.421306
\(833\) 1.09223 0.0378435
\(834\) −0.769564 −0.0266478
\(835\) −18.7948 −0.650421
\(836\) 57.0230 1.97218
\(837\) 0.116496 0.00402670
\(838\) 61.6639 2.13014
\(839\) −31.2700 −1.07956 −0.539780 0.841806i \(-0.681493\pi\)
−0.539780 + 0.841806i \(0.681493\pi\)
\(840\) −0.449185 −0.0154984
\(841\) −17.2471 −0.594726
\(842\) −65.3616 −2.25251
\(843\) 0.274694 0.00946095
\(844\) 16.7231 0.575631
\(845\) 8.56364 0.294598
\(846\) −98.6884 −3.39298
\(847\) 0.342187 0.0117577
\(848\) −9.31092 −0.319738
\(849\) −0.574556 −0.0197187
\(850\) −41.8401 −1.43511
\(851\) −63.5324 −2.17786
\(852\) −1.29204 −0.0442644
\(853\) −12.0633 −0.413041 −0.206520 0.978442i \(-0.566214\pi\)
−0.206520 + 0.978442i \(0.566214\pi\)
\(854\) −32.5484 −1.11378
\(855\) −10.6658 −0.364764
\(856\) 2.48198 0.0848323
\(857\) 2.52431 0.0862289 0.0431144 0.999070i \(-0.486272\pi\)
0.0431144 + 0.999070i \(0.486272\pi\)
\(858\) 0.551309 0.0188214
\(859\) −12.6615 −0.432006 −0.216003 0.976393i \(-0.569302\pi\)
−0.216003 + 0.976393i \(0.569302\pi\)
\(860\) 2.32267 0.0792024
\(861\) 0.729315 0.0248550
\(862\) −31.8340 −1.08427
\(863\) 3.64629 0.124121 0.0620605 0.998072i \(-0.480233\pi\)
0.0620605 + 0.998072i \(0.480233\pi\)
\(864\) 0.125635 0.00427419
\(865\) 12.6810 0.431168
\(866\) −20.1847 −0.685904
\(867\) −0.0575441 −0.00195430
\(868\) 4.94997 0.168013
\(869\) −23.6555 −0.802456
\(870\) 0.289558 0.00981694
\(871\) −20.7854 −0.704285
\(872\) 65.1074 2.20481
\(873\) 7.98384 0.270212
\(874\) 65.8455 2.22726
\(875\) −20.1032 −0.679611
\(876\) −1.21087 −0.0409114
\(877\) −1.72340 −0.0581952 −0.0290976 0.999577i \(-0.509263\pi\)
−0.0290976 + 0.999577i \(0.509263\pi\)
\(878\) −36.3793 −1.22774
\(879\) 1.32283 0.0446181
\(880\) 11.8337 0.398913
\(881\) 0.531890 0.0179198 0.00895991 0.999960i \(-0.497148\pi\)
0.00895991 + 0.999960i \(0.497148\pi\)
\(882\) −2.03933 −0.0686679
\(883\) −19.9897 −0.672707 −0.336353 0.941736i \(-0.609194\pi\)
−0.336353 + 0.941736i \(0.609194\pi\)
\(884\) −26.3962 −0.887800
\(885\) −0.457424 −0.0153762
\(886\) −90.3888 −3.03667
\(887\) −8.32392 −0.279490 −0.139745 0.990188i \(-0.544628\pi\)
−0.139745 + 0.990188i \(0.544628\pi\)
\(888\) 2.10725 0.0707146
\(889\) −28.3638 −0.951291
\(890\) −13.6894 −0.458871
\(891\) −29.6196 −0.992295
\(892\) 63.3580 2.12138
\(893\) 57.1333 1.91189
\(894\) 1.19859 0.0400870
\(895\) −6.32110 −0.211291
\(896\) −49.6256 −1.65787
\(897\) 0.426193 0.0142302
\(898\) 6.68905 0.223216
\(899\) −1.61553 −0.0538811
\(900\) 52.3001 1.74334
\(901\) 8.53633 0.284386
\(902\) −55.3434 −1.84273
\(903\) 0.0735455 0.00244744
\(904\) −94.8190 −3.15363
\(905\) 2.34179 0.0778439
\(906\) 0.798077 0.0265143
\(907\) 12.5089 0.415352 0.207676 0.978198i \(-0.433410\pi\)
0.207676 + 0.978198i \(0.433410\pi\)
\(908\) −40.3052 −1.33757
\(909\) −4.58862 −0.152195
\(910\) −8.76564 −0.290578
\(911\) −5.87293 −0.194579 −0.0972895 0.995256i \(-0.531017\pi\)
−0.0972895 + 0.995256i \(0.531017\pi\)
\(912\) −0.758210 −0.0251068
\(913\) 9.08154 0.300555
\(914\) −31.5233 −1.04270
\(915\) 0.175213 0.00579238
\(916\) 93.6938 3.09573
\(917\) 7.12121 0.235163
\(918\) −2.40214 −0.0792823
\(919\) −27.9616 −0.922369 −0.461185 0.887304i \(-0.652575\pi\)
−0.461185 + 0.887304i \(0.652575\pi\)
\(920\) 26.3504 0.868747
\(921\) −0.339560 −0.0111889
\(922\) 35.7516 1.17742
\(923\) −12.7654 −0.420179
\(924\) 1.42717 0.0469505
\(925\) 43.6375 1.43479
\(926\) 62.9374 2.06825
\(927\) 26.9813 0.886181
\(928\) −1.74227 −0.0571927
\(929\) −20.2777 −0.665288 −0.332644 0.943052i \(-0.607941\pi\)
−0.332644 + 0.943052i \(0.607941\pi\)
\(930\) −0.0398020 −0.00130516
\(931\) 1.18062 0.0386934
\(932\) 11.7438 0.384680
\(933\) −0.847421 −0.0277433
\(934\) 14.4422 0.472562
\(935\) −10.8492 −0.354807
\(936\) 24.9528 0.815607
\(937\) −43.2752 −1.41374 −0.706869 0.707344i \(-0.749893\pi\)
−0.706869 + 0.707344i \(0.749893\pi\)
\(938\) −80.3719 −2.62423
\(939\) 1.22873 0.0400982
\(940\) 45.1593 1.47293
\(941\) 12.7329 0.415082 0.207541 0.978226i \(-0.433454\pi\)
0.207541 + 0.978226i \(0.433454\pi\)
\(942\) −1.34658 −0.0438738
\(943\) −42.7835 −1.39322
\(944\) 57.3993 1.86819
\(945\) −0.534041 −0.0173724
\(946\) −5.58093 −0.181452
\(947\) 30.0480 0.976428 0.488214 0.872724i \(-0.337649\pi\)
0.488214 + 0.872724i \(0.337649\pi\)
\(948\) 1.19801 0.0389094
\(949\) −11.9635 −0.388352
\(950\) −45.2263 −1.46733
\(951\) 0.474975 0.0154021
\(952\) −51.6763 −1.67484
\(953\) 45.9292 1.48779 0.743896 0.668295i \(-0.232976\pi\)
0.743896 + 0.668295i \(0.232976\pi\)
\(954\) −15.9384 −0.516025
\(955\) 7.08024 0.229111
\(956\) −63.4801 −2.05309
\(957\) −0.465790 −0.0150568
\(958\) 35.4106 1.14406
\(959\) −57.4177 −1.85411
\(960\) 0.252955 0.00816409
\(961\) −30.7779 −0.992837
\(962\) 41.1219 1.32582
\(963\) 1.47501 0.0475314
\(964\) −23.6496 −0.761701
\(965\) −5.89351 −0.189719
\(966\) 1.64798 0.0530229
\(967\) 7.63666 0.245579 0.122789 0.992433i \(-0.460816\pi\)
0.122789 + 0.992433i \(0.460816\pi\)
\(968\) 0.665802 0.0213997
\(969\) 0.695133 0.0223309
\(970\) −5.45705 −0.175215
\(971\) 47.4518 1.52280 0.761400 0.648283i \(-0.224513\pi\)
0.761400 + 0.648283i \(0.224513\pi\)
\(972\) 4.50442 0.144479
\(973\) −19.6828 −0.631003
\(974\) −76.2745 −2.44399
\(975\) −0.292732 −0.00937494
\(976\) −21.9864 −0.703768
\(977\) −2.99601 −0.0958509 −0.0479255 0.998851i \(-0.515261\pi\)
−0.0479255 + 0.998851i \(0.515261\pi\)
\(978\) 0.157401 0.00503312
\(979\) 22.0211 0.703798
\(980\) 0.933188 0.0298096
\(981\) 38.6925 1.23536
\(982\) 33.1114 1.05663
\(983\) 33.9488 1.08280 0.541399 0.840766i \(-0.317895\pi\)
0.541399 + 0.840766i \(0.317895\pi\)
\(984\) 1.41905 0.0452376
\(985\) 15.5291 0.494799
\(986\) 33.3121 1.06087
\(987\) 1.42993 0.0455153
\(988\) −28.5324 −0.907738
\(989\) −4.31437 −0.137189
\(990\) 20.2569 0.643805
\(991\) −22.3157 −0.708881 −0.354440 0.935079i \(-0.615329\pi\)
−0.354440 + 0.935079i \(0.615329\pi\)
\(992\) 0.239488 0.00760375
\(993\) −1.32255 −0.0419700
\(994\) −49.3608 −1.56563
\(995\) 10.7892 0.342042
\(996\) −0.459925 −0.0145733
\(997\) −47.6561 −1.50928 −0.754642 0.656137i \(-0.772190\pi\)
−0.754642 + 0.656137i \(0.772190\pi\)
\(998\) 73.8437 2.33748
\(999\) 2.50533 0.0792651
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 4027.2.a.c.1.13 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.13 174 1.1 even 1 trivial