Properties

Label 4027.2.a.c.1.11
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 1.11
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.50865 q^{2} -1.26179 q^{3} +4.29331 q^{4} -1.32725 q^{5} +3.16538 q^{6} -1.28298 q^{7} -5.75310 q^{8} -1.40789 q^{9} +O(q^{10})\) \(q-2.50865 q^{2} -1.26179 q^{3} +4.29331 q^{4} -1.32725 q^{5} +3.16538 q^{6} -1.28298 q^{7} -5.75310 q^{8} -1.40789 q^{9} +3.32960 q^{10} +0.495698 q^{11} -5.41725 q^{12} -1.46946 q^{13} +3.21853 q^{14} +1.67471 q^{15} +5.84588 q^{16} -0.136396 q^{17} +3.53189 q^{18} -6.52844 q^{19} -5.69830 q^{20} +1.61885 q^{21} -1.24353 q^{22} -5.31274 q^{23} +7.25920 q^{24} -3.23840 q^{25} +3.68636 q^{26} +5.56183 q^{27} -5.50821 q^{28} -0.800090 q^{29} -4.20126 q^{30} -7.02532 q^{31} -3.15904 q^{32} -0.625467 q^{33} +0.342170 q^{34} +1.70283 q^{35} -6.04449 q^{36} +4.87496 q^{37} +16.3775 q^{38} +1.85415 q^{39} +7.63581 q^{40} -1.51408 q^{41} -4.06111 q^{42} -5.37060 q^{43} +2.12818 q^{44} +1.86862 q^{45} +13.3278 q^{46} +3.92264 q^{47} -7.37626 q^{48} -5.35397 q^{49} +8.12401 q^{50} +0.172104 q^{51} -6.30885 q^{52} -11.2735 q^{53} -13.9527 q^{54} -0.657916 q^{55} +7.38109 q^{56} +8.23751 q^{57} +2.00714 q^{58} -14.6776 q^{59} +7.19005 q^{60} -0.888705 q^{61} +17.6241 q^{62} +1.80629 q^{63} -3.76684 q^{64} +1.95034 q^{65} +1.56907 q^{66} -3.05723 q^{67} -0.585592 q^{68} +6.70356 q^{69} -4.27180 q^{70} +8.58849 q^{71} +8.09972 q^{72} +0.232212 q^{73} -12.2295 q^{74} +4.08618 q^{75} -28.0286 q^{76} -0.635968 q^{77} -4.65141 q^{78} -2.17991 q^{79} -7.75895 q^{80} -2.79419 q^{81} +3.79829 q^{82} +1.17038 q^{83} +6.95020 q^{84} +0.181032 q^{85} +13.4729 q^{86} +1.00954 q^{87} -2.85180 q^{88} -3.90114 q^{89} -4.68771 q^{90} +1.88528 q^{91} -22.8092 q^{92} +8.86448 q^{93} -9.84053 q^{94} +8.66487 q^{95} +3.98604 q^{96} -12.1943 q^{97} +13.4312 q^{98} -0.697887 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50865 −1.77388 −0.886941 0.461884i \(-0.847174\pi\)
−0.886941 + 0.461884i \(0.847174\pi\)
\(3\) −1.26179 −0.728494 −0.364247 0.931302i \(-0.618674\pi\)
−0.364247 + 0.931302i \(0.618674\pi\)
\(4\) 4.29331 2.14665
\(5\) −1.32725 −0.593565 −0.296782 0.954945i \(-0.595914\pi\)
−0.296782 + 0.954945i \(0.595914\pi\)
\(6\) 3.16538 1.29226
\(7\) −1.28298 −0.484919 −0.242460 0.970162i \(-0.577954\pi\)
−0.242460 + 0.970162i \(0.577954\pi\)
\(8\) −5.75310 −2.03403
\(9\) −1.40789 −0.469296
\(10\) 3.32960 1.05291
\(11\) 0.495698 0.149459 0.0747293 0.997204i \(-0.476191\pi\)
0.0747293 + 0.997204i \(0.476191\pi\)
\(12\) −5.41725 −1.56383
\(13\) −1.46946 −0.407555 −0.203778 0.979017i \(-0.565322\pi\)
−0.203778 + 0.979017i \(0.565322\pi\)
\(14\) 3.21853 0.860189
\(15\) 1.67471 0.432409
\(16\) 5.84588 1.46147
\(17\) −0.136396 −0.0330810 −0.0165405 0.999863i \(-0.505265\pi\)
−0.0165405 + 0.999863i \(0.505265\pi\)
\(18\) 3.53189 0.832475
\(19\) −6.52844 −1.49773 −0.748863 0.662725i \(-0.769400\pi\)
−0.748863 + 0.662725i \(0.769400\pi\)
\(20\) −5.69830 −1.27418
\(21\) 1.61885 0.353261
\(22\) −1.24353 −0.265122
\(23\) −5.31274 −1.10778 −0.553891 0.832589i \(-0.686858\pi\)
−0.553891 + 0.832589i \(0.686858\pi\)
\(24\) 7.25920 1.48178
\(25\) −3.23840 −0.647681
\(26\) 3.68636 0.722954
\(27\) 5.56183 1.07037
\(28\) −5.50821 −1.04095
\(29\) −0.800090 −0.148573 −0.0742865 0.997237i \(-0.523668\pi\)
−0.0742865 + 0.997237i \(0.523668\pi\)
\(30\) −4.20126 −0.767042
\(31\) −7.02532 −1.26179 −0.630893 0.775870i \(-0.717311\pi\)
−0.630893 + 0.775870i \(0.717311\pi\)
\(32\) −3.15904 −0.558445
\(33\) −0.625467 −0.108880
\(34\) 0.342170 0.0586817
\(35\) 1.70283 0.287831
\(36\) −6.04449 −1.00742
\(37\) 4.87496 0.801438 0.400719 0.916201i \(-0.368760\pi\)
0.400719 + 0.916201i \(0.368760\pi\)
\(38\) 16.3775 2.65679
\(39\) 1.85415 0.296902
\(40\) 7.63581 1.20733
\(41\) −1.51408 −0.236459 −0.118230 0.992986i \(-0.537722\pi\)
−0.118230 + 0.992986i \(0.537722\pi\)
\(42\) −4.06111 −0.626643
\(43\) −5.37060 −0.819010 −0.409505 0.912308i \(-0.634298\pi\)
−0.409505 + 0.912308i \(0.634298\pi\)
\(44\) 2.12818 0.320836
\(45\) 1.86862 0.278557
\(46\) 13.3278 1.96507
\(47\) 3.92264 0.572176 0.286088 0.958203i \(-0.407645\pi\)
0.286088 + 0.958203i \(0.407645\pi\)
\(48\) −7.37626 −1.06467
\(49\) −5.35397 −0.764853
\(50\) 8.12401 1.14891
\(51\) 0.172104 0.0240993
\(52\) −6.30885 −0.874880
\(53\) −11.2735 −1.54854 −0.774269 0.632856i \(-0.781882\pi\)
−0.774269 + 0.632856i \(0.781882\pi\)
\(54\) −13.9527 −1.89872
\(55\) −0.657916 −0.0887133
\(56\) 7.38109 0.986339
\(57\) 8.23751 1.09108
\(58\) 2.00714 0.263551
\(59\) −14.6776 −1.91086 −0.955432 0.295211i \(-0.904610\pi\)
−0.955432 + 0.295211i \(0.904610\pi\)
\(60\) 7.19005 0.928232
\(61\) −0.888705 −0.113787 −0.0568935 0.998380i \(-0.518120\pi\)
−0.0568935 + 0.998380i \(0.518120\pi\)
\(62\) 17.6241 2.23826
\(63\) 1.80629 0.227571
\(64\) −3.76684 −0.470855
\(65\) 1.95034 0.241910
\(66\) 1.56907 0.193140
\(67\) −3.05723 −0.373500 −0.186750 0.982408i \(-0.559795\pi\)
−0.186750 + 0.982408i \(0.559795\pi\)
\(68\) −0.585592 −0.0710134
\(69\) 6.70356 0.807014
\(70\) −4.27180 −0.510578
\(71\) 8.58849 1.01927 0.509633 0.860392i \(-0.329781\pi\)
0.509633 + 0.860392i \(0.329781\pi\)
\(72\) 8.09972 0.954561
\(73\) 0.232212 0.0271784 0.0135892 0.999908i \(-0.495674\pi\)
0.0135892 + 0.999908i \(0.495674\pi\)
\(74\) −12.2295 −1.42166
\(75\) 4.08618 0.471832
\(76\) −28.0286 −3.21510
\(77\) −0.635968 −0.0724753
\(78\) −4.65141 −0.526668
\(79\) −2.17991 −0.245259 −0.122629 0.992453i \(-0.539133\pi\)
−0.122629 + 0.992453i \(0.539133\pi\)
\(80\) −7.75895 −0.867477
\(81\) −2.79419 −0.310466
\(82\) 3.79829 0.419451
\(83\) 1.17038 0.128466 0.0642328 0.997935i \(-0.479540\pi\)
0.0642328 + 0.997935i \(0.479540\pi\)
\(84\) 6.95020 0.758329
\(85\) 0.181032 0.0196357
\(86\) 13.4729 1.45283
\(87\) 1.00954 0.108235
\(88\) −2.85180 −0.304003
\(89\) −3.90114 −0.413520 −0.206760 0.978392i \(-0.566292\pi\)
−0.206760 + 0.978392i \(0.566292\pi\)
\(90\) −4.68771 −0.494128
\(91\) 1.88528 0.197631
\(92\) −22.8092 −2.37803
\(93\) 8.86448 0.919204
\(94\) −9.84053 −1.01497
\(95\) 8.66487 0.888997
\(96\) 3.98604 0.406824
\(97\) −12.1943 −1.23814 −0.619072 0.785334i \(-0.712491\pi\)
−0.619072 + 0.785334i \(0.712491\pi\)
\(98\) 13.4312 1.35676
\(99\) −0.697887 −0.0701403
\(100\) −13.9035 −1.39035
\(101\) −8.74945 −0.870603 −0.435301 0.900285i \(-0.643358\pi\)
−0.435301 + 0.900285i \(0.643358\pi\)
\(102\) −0.431747 −0.0427493
\(103\) 9.18930 0.905448 0.452724 0.891651i \(-0.350452\pi\)
0.452724 + 0.891651i \(0.350452\pi\)
\(104\) 8.45395 0.828978
\(105\) −2.14861 −0.209683
\(106\) 28.2813 2.74692
\(107\) −5.18893 −0.501633 −0.250817 0.968035i \(-0.580699\pi\)
−0.250817 + 0.968035i \(0.580699\pi\)
\(108\) 23.8786 2.29772
\(109\) 2.50207 0.239655 0.119827 0.992795i \(-0.461766\pi\)
0.119827 + 0.992795i \(0.461766\pi\)
\(110\) 1.65048 0.157367
\(111\) −6.15117 −0.583843
\(112\) −7.50012 −0.708694
\(113\) 13.8422 1.30217 0.651084 0.759005i \(-0.274314\pi\)
0.651084 + 0.759005i \(0.274314\pi\)
\(114\) −20.6650 −1.93545
\(115\) 7.05134 0.657541
\(116\) −3.43503 −0.318935
\(117\) 2.06884 0.191264
\(118\) 36.8210 3.38965
\(119\) 0.174993 0.0160416
\(120\) −9.63478 −0.879531
\(121\) −10.7543 −0.977662
\(122\) 2.22945 0.201845
\(123\) 1.91045 0.172259
\(124\) −30.1619 −2.70862
\(125\) 10.9344 0.978005
\(126\) −4.53133 −0.403683
\(127\) −20.5289 −1.82164 −0.910821 0.412801i \(-0.864550\pi\)
−0.910821 + 0.412801i \(0.864550\pi\)
\(128\) 15.7677 1.39368
\(129\) 6.77657 0.596644
\(130\) −4.89272 −0.429120
\(131\) 6.92706 0.605220 0.302610 0.953114i \(-0.402142\pi\)
0.302610 + 0.953114i \(0.402142\pi\)
\(132\) −2.68532 −0.233727
\(133\) 8.37582 0.726276
\(134\) 7.66950 0.662544
\(135\) −7.38194 −0.635336
\(136\) 0.784702 0.0672876
\(137\) 13.9823 1.19459 0.597295 0.802022i \(-0.296242\pi\)
0.597295 + 0.802022i \(0.296242\pi\)
\(138\) −16.8169 −1.43155
\(139\) −8.38431 −0.711148 −0.355574 0.934648i \(-0.615715\pi\)
−0.355574 + 0.934648i \(0.615715\pi\)
\(140\) 7.31078 0.617873
\(141\) −4.94955 −0.416827
\(142\) −21.5455 −1.80806
\(143\) −0.728409 −0.0609126
\(144\) −8.23034 −0.685861
\(145\) 1.06192 0.0881877
\(146\) −0.582539 −0.0482112
\(147\) 6.75559 0.557191
\(148\) 20.9297 1.72041
\(149\) −11.0540 −0.905583 −0.452792 0.891616i \(-0.649572\pi\)
−0.452792 + 0.891616i \(0.649572\pi\)
\(150\) −10.2508 −0.836974
\(151\) −10.7265 −0.872913 −0.436457 0.899725i \(-0.643767\pi\)
−0.436457 + 0.899725i \(0.643767\pi\)
\(152\) 37.5587 3.04642
\(153\) 0.192031 0.0155248
\(154\) 1.59542 0.128563
\(155\) 9.32437 0.748951
\(156\) 7.96044 0.637345
\(157\) −2.88338 −0.230118 −0.115059 0.993359i \(-0.536706\pi\)
−0.115059 + 0.993359i \(0.536706\pi\)
\(158\) 5.46862 0.435060
\(159\) 14.2248 1.12810
\(160\) 4.19284 0.331473
\(161\) 6.81612 0.537185
\(162\) 7.00964 0.550729
\(163\) −14.1435 −1.10781 −0.553903 0.832581i \(-0.686862\pi\)
−0.553903 + 0.832581i \(0.686862\pi\)
\(164\) −6.50041 −0.507597
\(165\) 0.830151 0.0646272
\(166\) −2.93606 −0.227883
\(167\) −16.9374 −1.31065 −0.655326 0.755346i \(-0.727469\pi\)
−0.655326 + 0.755346i \(0.727469\pi\)
\(168\) −9.31338 −0.718542
\(169\) −10.8407 −0.833899
\(170\) −0.454146 −0.0348314
\(171\) 9.19130 0.702876
\(172\) −23.0577 −1.75813
\(173\) −11.8132 −0.898141 −0.449070 0.893496i \(-0.648245\pi\)
−0.449070 + 0.893496i \(0.648245\pi\)
\(174\) −2.53259 −0.191995
\(175\) 4.15479 0.314073
\(176\) 2.89779 0.218429
\(177\) 18.5201 1.39205
\(178\) 9.78658 0.733535
\(179\) 6.23628 0.466121 0.233061 0.972462i \(-0.425126\pi\)
0.233061 + 0.972462i \(0.425126\pi\)
\(180\) 8.02256 0.597966
\(181\) 2.52235 0.187485 0.0937423 0.995596i \(-0.470117\pi\)
0.0937423 + 0.995596i \(0.470117\pi\)
\(182\) −4.72951 −0.350574
\(183\) 1.12136 0.0828932
\(184\) 30.5647 2.25326
\(185\) −6.47029 −0.475705
\(186\) −22.2378 −1.63056
\(187\) −0.0676114 −0.00494424
\(188\) 16.8411 1.22826
\(189\) −7.13569 −0.519045
\(190\) −21.7371 −1.57698
\(191\) −14.5806 −1.05501 −0.527506 0.849551i \(-0.676873\pi\)
−0.527506 + 0.849551i \(0.676873\pi\)
\(192\) 4.75296 0.343015
\(193\) −8.19903 −0.590179 −0.295090 0.955470i \(-0.595350\pi\)
−0.295090 + 0.955470i \(0.595350\pi\)
\(194\) 30.5912 2.19632
\(195\) −2.46092 −0.176230
\(196\) −22.9863 −1.64188
\(197\) 13.1145 0.934370 0.467185 0.884160i \(-0.345268\pi\)
0.467185 + 0.884160i \(0.345268\pi\)
\(198\) 1.75075 0.124421
\(199\) −14.8296 −1.05124 −0.525620 0.850719i \(-0.676167\pi\)
−0.525620 + 0.850719i \(0.676167\pi\)
\(200\) 18.6309 1.31740
\(201\) 3.85758 0.272092
\(202\) 21.9493 1.54435
\(203\) 1.02650 0.0720459
\(204\) 0.738894 0.0517329
\(205\) 2.00956 0.140354
\(206\) −23.0527 −1.60616
\(207\) 7.47974 0.519878
\(208\) −8.59029 −0.595629
\(209\) −3.23613 −0.223848
\(210\) 5.39011 0.371953
\(211\) 0.665975 0.0458476 0.0229238 0.999737i \(-0.492702\pi\)
0.0229238 + 0.999737i \(0.492702\pi\)
\(212\) −48.4007 −3.32418
\(213\) −10.8369 −0.742530
\(214\) 13.0172 0.889838
\(215\) 7.12814 0.486135
\(216\) −31.9977 −2.17717
\(217\) 9.01332 0.611864
\(218\) −6.27681 −0.425119
\(219\) −0.293003 −0.0197993
\(220\) −2.82463 −0.190437
\(221\) 0.200429 0.0134823
\(222\) 15.4311 1.03567
\(223\) −18.9018 −1.26576 −0.632878 0.774252i \(-0.718126\pi\)
−0.632878 + 0.774252i \(0.718126\pi\)
\(224\) 4.05297 0.270801
\(225\) 4.55931 0.303954
\(226\) −34.7253 −2.30989
\(227\) 8.09957 0.537587 0.268794 0.963198i \(-0.413375\pi\)
0.268794 + 0.963198i \(0.413375\pi\)
\(228\) 35.3662 2.34218
\(229\) −23.3047 −1.54002 −0.770009 0.638033i \(-0.779748\pi\)
−0.770009 + 0.638033i \(0.779748\pi\)
\(230\) −17.6893 −1.16640
\(231\) 0.802458 0.0527979
\(232\) 4.60299 0.302201
\(233\) −3.87260 −0.253703 −0.126851 0.991922i \(-0.540487\pi\)
−0.126851 + 0.991922i \(0.540487\pi\)
\(234\) −5.18998 −0.339279
\(235\) −5.20633 −0.339624
\(236\) −63.0156 −4.10196
\(237\) 2.75059 0.178670
\(238\) −0.438996 −0.0284559
\(239\) −16.8934 −1.09274 −0.546372 0.837543i \(-0.683991\pi\)
−0.546372 + 0.837543i \(0.683991\pi\)
\(240\) 9.79016 0.631952
\(241\) −11.1519 −0.718360 −0.359180 0.933268i \(-0.616944\pi\)
−0.359180 + 0.933268i \(0.616944\pi\)
\(242\) 26.9787 1.73426
\(243\) −13.1598 −0.844201
\(244\) −3.81549 −0.244261
\(245\) 7.10607 0.453990
\(246\) −4.79264 −0.305568
\(247\) 9.59328 0.610406
\(248\) 40.4174 2.56651
\(249\) −1.47677 −0.0935864
\(250\) −27.4306 −1.73487
\(251\) −21.0799 −1.33055 −0.665277 0.746597i \(-0.731686\pi\)
−0.665277 + 0.746597i \(0.731686\pi\)
\(252\) 7.75494 0.488515
\(253\) −2.63351 −0.165568
\(254\) 51.4997 3.23138
\(255\) −0.228425 −0.0143045
\(256\) −32.0220 −2.00138
\(257\) 23.6370 1.47444 0.737218 0.675655i \(-0.236139\pi\)
0.737218 + 0.675655i \(0.236139\pi\)
\(258\) −17.0000 −1.05838
\(259\) −6.25445 −0.388633
\(260\) 8.37343 0.519298
\(261\) 1.12644 0.0697246
\(262\) −17.3775 −1.07359
\(263\) 5.64893 0.348328 0.174164 0.984717i \(-0.444278\pi\)
0.174164 + 0.984717i \(0.444278\pi\)
\(264\) 3.59837 0.221464
\(265\) 14.9628 0.919158
\(266\) −21.0120 −1.28833
\(267\) 4.92241 0.301247
\(268\) −13.1256 −0.801774
\(269\) 26.8710 1.63836 0.819178 0.573539i \(-0.194430\pi\)
0.819178 + 0.573539i \(0.194430\pi\)
\(270\) 18.5187 1.12701
\(271\) 0.0464063 0.00281898 0.00140949 0.999999i \(-0.499551\pi\)
0.00140949 + 0.999999i \(0.499551\pi\)
\(272\) −0.797357 −0.0483468
\(273\) −2.37883 −0.143973
\(274\) −35.0767 −2.11906
\(275\) −1.60527 −0.0968015
\(276\) 28.7804 1.73238
\(277\) −18.6901 −1.12298 −0.561491 0.827483i \(-0.689772\pi\)
−0.561491 + 0.827483i \(0.689772\pi\)
\(278\) 21.0333 1.26149
\(279\) 9.89086 0.592151
\(280\) −9.79655 −0.585456
\(281\) 26.9714 1.60898 0.804488 0.593969i \(-0.202440\pi\)
0.804488 + 0.593969i \(0.202440\pi\)
\(282\) 12.4167 0.739402
\(283\) 20.2359 1.20290 0.601450 0.798910i \(-0.294590\pi\)
0.601450 + 0.798910i \(0.294590\pi\)
\(284\) 36.8730 2.18801
\(285\) −10.9332 −0.647630
\(286\) 1.82732 0.108052
\(287\) 1.94253 0.114664
\(288\) 4.44757 0.262076
\(289\) −16.9814 −0.998906
\(290\) −2.66398 −0.156434
\(291\) 15.3866 0.901981
\(292\) 0.996959 0.0583426
\(293\) 23.6195 1.37986 0.689932 0.723874i \(-0.257640\pi\)
0.689932 + 0.723874i \(0.257640\pi\)
\(294\) −16.9474 −0.988391
\(295\) 19.4809 1.13422
\(296\) −28.0461 −1.63015
\(297\) 2.75699 0.159977
\(298\) 27.7307 1.60640
\(299\) 7.80686 0.451483
\(300\) 17.5432 1.01286
\(301\) 6.89035 0.397153
\(302\) 26.9091 1.54844
\(303\) 11.0400 0.634229
\(304\) −38.1644 −2.18888
\(305\) 1.17954 0.0675400
\(306\) −0.481737 −0.0275391
\(307\) 26.3774 1.50544 0.752719 0.658342i \(-0.228742\pi\)
0.752719 + 0.658342i \(0.228742\pi\)
\(308\) −2.73041 −0.155579
\(309\) −11.5950 −0.659614
\(310\) −23.3915 −1.32855
\(311\) 20.7081 1.17425 0.587124 0.809497i \(-0.300260\pi\)
0.587124 + 0.809497i \(0.300260\pi\)
\(312\) −10.6671 −0.603906
\(313\) 21.1800 1.19716 0.598581 0.801062i \(-0.295732\pi\)
0.598581 + 0.801062i \(0.295732\pi\)
\(314\) 7.23337 0.408203
\(315\) −2.39739 −0.135078
\(316\) −9.35902 −0.526486
\(317\) −23.9156 −1.34324 −0.671618 0.740898i \(-0.734400\pi\)
−0.671618 + 0.740898i \(0.734400\pi\)
\(318\) −35.6851 −2.00112
\(319\) −0.396603 −0.0222055
\(320\) 4.99954 0.279483
\(321\) 6.54734 0.365437
\(322\) −17.0992 −0.952902
\(323\) 0.890455 0.0495463
\(324\) −11.9963 −0.666462
\(325\) 4.75871 0.263966
\(326\) 35.4811 1.96512
\(327\) −3.15709 −0.174587
\(328\) 8.71065 0.480965
\(329\) −5.03266 −0.277459
\(330\) −2.08256 −0.114641
\(331\) 9.33571 0.513137 0.256568 0.966526i \(-0.417408\pi\)
0.256568 + 0.966526i \(0.417408\pi\)
\(332\) 5.02479 0.275771
\(333\) −6.86339 −0.376111
\(334\) 42.4899 2.32494
\(335\) 4.05771 0.221696
\(336\) 9.46357 0.516280
\(337\) 10.0513 0.547527 0.273763 0.961797i \(-0.411732\pi\)
0.273763 + 0.961797i \(0.411732\pi\)
\(338\) 27.1954 1.47924
\(339\) −17.4660 −0.948623
\(340\) 0.777227 0.0421511
\(341\) −3.48244 −0.188585
\(342\) −23.0577 −1.24682
\(343\) 15.8498 0.855811
\(344\) 30.8976 1.66589
\(345\) −8.89731 −0.479015
\(346\) 29.6351 1.59320
\(347\) 7.22103 0.387645 0.193823 0.981037i \(-0.437911\pi\)
0.193823 + 0.981037i \(0.437911\pi\)
\(348\) 4.33429 0.232342
\(349\) 1.08094 0.0578614 0.0289307 0.999581i \(-0.490790\pi\)
0.0289307 + 0.999581i \(0.490790\pi\)
\(350\) −10.4229 −0.557128
\(351\) −8.17289 −0.436236
\(352\) −1.56593 −0.0834643
\(353\) 23.3346 1.24197 0.620987 0.783821i \(-0.286732\pi\)
0.620987 + 0.783821i \(0.286732\pi\)
\(354\) −46.4603 −2.46934
\(355\) −11.3991 −0.605001
\(356\) −16.7488 −0.887684
\(357\) −0.220805 −0.0116862
\(358\) −15.6446 −0.826844
\(359\) −36.5990 −1.93162 −0.965811 0.259249i \(-0.916525\pi\)
−0.965811 + 0.259249i \(0.916525\pi\)
\(360\) −10.7504 −0.566594
\(361\) 23.6205 1.24318
\(362\) −6.32768 −0.332575
\(363\) 13.5696 0.712221
\(364\) 8.09410 0.424246
\(365\) −0.308204 −0.0161321
\(366\) −2.81309 −0.147043
\(367\) 37.7460 1.97032 0.985161 0.171631i \(-0.0549036\pi\)
0.985161 + 0.171631i \(0.0549036\pi\)
\(368\) −31.0576 −1.61899
\(369\) 2.13165 0.110969
\(370\) 16.2317 0.843845
\(371\) 14.4637 0.750916
\(372\) 38.0579 1.97321
\(373\) −9.80494 −0.507680 −0.253840 0.967246i \(-0.581694\pi\)
−0.253840 + 0.967246i \(0.581694\pi\)
\(374\) 0.169613 0.00877049
\(375\) −13.7970 −0.712471
\(376\) −22.5674 −1.16382
\(377\) 1.17570 0.0605517
\(378\) 17.9009 0.920724
\(379\) 27.5306 1.41415 0.707077 0.707137i \(-0.250013\pi\)
0.707077 + 0.707137i \(0.250013\pi\)
\(380\) 37.2010 1.90837
\(381\) 25.9031 1.32706
\(382\) 36.5775 1.87147
\(383\) 10.5698 0.540091 0.270045 0.962848i \(-0.412961\pi\)
0.270045 + 0.962848i \(0.412961\pi\)
\(384\) −19.8956 −1.01529
\(385\) 0.844090 0.0430188
\(386\) 20.5685 1.04691
\(387\) 7.56121 0.384358
\(388\) −52.3539 −2.65787
\(389\) 10.7892 0.547034 0.273517 0.961867i \(-0.411813\pi\)
0.273517 + 0.961867i \(0.411813\pi\)
\(390\) 6.17359 0.312612
\(391\) 0.724639 0.0366466
\(392\) 30.8019 1.55573
\(393\) −8.74049 −0.440899
\(394\) −32.8997 −1.65746
\(395\) 2.89329 0.145577
\(396\) −2.99624 −0.150567
\(397\) −13.4501 −0.675040 −0.337520 0.941318i \(-0.609588\pi\)
−0.337520 + 0.941318i \(0.609588\pi\)
\(398\) 37.2022 1.86478
\(399\) −10.5685 −0.529088
\(400\) −18.9313 −0.946566
\(401\) −34.2202 −1.70887 −0.854437 0.519555i \(-0.826098\pi\)
−0.854437 + 0.519555i \(0.826098\pi\)
\(402\) −9.67729 −0.482660
\(403\) 10.3234 0.514247
\(404\) −37.5641 −1.86888
\(405\) 3.70859 0.184281
\(406\) −2.57511 −0.127801
\(407\) 2.41651 0.119782
\(408\) −0.990129 −0.0490187
\(409\) 0.282386 0.0139631 0.00698155 0.999976i \(-0.497778\pi\)
0.00698155 + 0.999976i \(0.497778\pi\)
\(410\) −5.04128 −0.248971
\(411\) −17.6427 −0.870252
\(412\) 39.4525 1.94368
\(413\) 18.8310 0.926615
\(414\) −18.7640 −0.922201
\(415\) −1.55338 −0.0762526
\(416\) 4.64209 0.227597
\(417\) 10.5792 0.518067
\(418\) 8.11831 0.397080
\(419\) 14.0753 0.687622 0.343811 0.939039i \(-0.388282\pi\)
0.343811 + 0.939039i \(0.388282\pi\)
\(420\) −9.22466 −0.450117
\(421\) 4.88820 0.238236 0.119118 0.992880i \(-0.461993\pi\)
0.119118 + 0.992880i \(0.461993\pi\)
\(422\) −1.67070 −0.0813282
\(423\) −5.52264 −0.268520
\(424\) 64.8577 3.14977
\(425\) 0.441707 0.0214259
\(426\) 27.1859 1.31716
\(427\) 1.14019 0.0551775
\(428\) −22.2777 −1.07683
\(429\) 0.919099 0.0443745
\(430\) −17.8820 −0.862346
\(431\) −7.94861 −0.382871 −0.191436 0.981505i \(-0.561314\pi\)
−0.191436 + 0.981505i \(0.561314\pi\)
\(432\) 32.5137 1.56432
\(433\) −1.44879 −0.0696245 −0.0348122 0.999394i \(-0.511083\pi\)
−0.0348122 + 0.999394i \(0.511083\pi\)
\(434\) −22.6112 −1.08537
\(435\) −1.33992 −0.0642442
\(436\) 10.7422 0.514456
\(437\) 34.6839 1.65915
\(438\) 0.735041 0.0351216
\(439\) −24.7621 −1.18183 −0.590915 0.806734i \(-0.701233\pi\)
−0.590915 + 0.806734i \(0.701233\pi\)
\(440\) 3.78505 0.180445
\(441\) 7.53779 0.358942
\(442\) −0.502806 −0.0239160
\(443\) 12.1476 0.577148 0.288574 0.957458i \(-0.406819\pi\)
0.288574 + 0.957458i \(0.406819\pi\)
\(444\) −26.4089 −1.25331
\(445\) 5.17779 0.245451
\(446\) 47.4178 2.24530
\(447\) 13.9479 0.659712
\(448\) 4.83276 0.228326
\(449\) 4.83356 0.228110 0.114055 0.993474i \(-0.463616\pi\)
0.114055 + 0.993474i \(0.463616\pi\)
\(450\) −11.4377 −0.539178
\(451\) −0.750526 −0.0353409
\(452\) 59.4290 2.79531
\(453\) 13.5346 0.635912
\(454\) −20.3190 −0.953616
\(455\) −2.50224 −0.117307
\(456\) −47.3912 −2.21930
\(457\) −10.6289 −0.497197 −0.248599 0.968607i \(-0.579970\pi\)
−0.248599 + 0.968607i \(0.579970\pi\)
\(458\) 58.4633 2.73181
\(459\) −0.758613 −0.0354090
\(460\) 30.2736 1.41151
\(461\) 19.6158 0.913597 0.456799 0.889570i \(-0.348996\pi\)
0.456799 + 0.889570i \(0.348996\pi\)
\(462\) −2.01308 −0.0936572
\(463\) 2.58632 0.120196 0.0600981 0.998192i \(-0.480859\pi\)
0.0600981 + 0.998192i \(0.480859\pi\)
\(464\) −4.67723 −0.217135
\(465\) −11.7654 −0.545607
\(466\) 9.71499 0.450038
\(467\) −24.9586 −1.15495 −0.577473 0.816410i \(-0.695961\pi\)
−0.577473 + 0.816410i \(0.695961\pi\)
\(468\) 8.88215 0.410577
\(469\) 3.92235 0.181117
\(470\) 13.0608 0.602452
\(471\) 3.63821 0.167640
\(472\) 84.4418 3.88675
\(473\) −2.66220 −0.122408
\(474\) −6.90025 −0.316939
\(475\) 21.1417 0.970048
\(476\) 0.751300 0.0344358
\(477\) 15.8719 0.726723
\(478\) 42.3796 1.93840
\(479\) 13.0764 0.597475 0.298738 0.954335i \(-0.403434\pi\)
0.298738 + 0.954335i \(0.403434\pi\)
\(480\) −5.29048 −0.241476
\(481\) −7.16356 −0.326630
\(482\) 27.9763 1.27428
\(483\) −8.60050 −0.391336
\(484\) −46.1714 −2.09870
\(485\) 16.1849 0.734918
\(486\) 33.0133 1.49751
\(487\) 36.6145 1.65916 0.829581 0.558386i \(-0.188579\pi\)
0.829581 + 0.558386i \(0.188579\pi\)
\(488\) 5.11281 0.231446
\(489\) 17.8461 0.807031
\(490\) −17.8266 −0.805324
\(491\) 32.0216 1.44511 0.722557 0.691312i \(-0.242967\pi\)
0.722557 + 0.691312i \(0.242967\pi\)
\(492\) 8.20215 0.369781
\(493\) 0.109129 0.00491494
\(494\) −24.0662 −1.08279
\(495\) 0.926271 0.0416328
\(496\) −41.0692 −1.84406
\(497\) −11.0188 −0.494262
\(498\) 3.70469 0.166011
\(499\) −36.6685 −1.64151 −0.820754 0.571282i \(-0.806446\pi\)
−0.820754 + 0.571282i \(0.806446\pi\)
\(500\) 46.9449 2.09944
\(501\) 21.3714 0.954803
\(502\) 52.8821 2.36024
\(503\) 1.70453 0.0760013 0.0380007 0.999278i \(-0.487901\pi\)
0.0380007 + 0.999278i \(0.487901\pi\)
\(504\) −10.3917 −0.462885
\(505\) 11.6127 0.516759
\(506\) 6.60656 0.293697
\(507\) 13.6787 0.607491
\(508\) −88.1367 −3.91044
\(509\) −32.1356 −1.42439 −0.712193 0.701984i \(-0.752298\pi\)
−0.712193 + 0.701984i \(0.752298\pi\)
\(510\) 0.573037 0.0253745
\(511\) −0.297923 −0.0131793
\(512\) 48.7965 2.15652
\(513\) −36.3100 −1.60313
\(514\) −59.2969 −2.61547
\(515\) −12.1965 −0.537442
\(516\) 29.0939 1.28079
\(517\) 1.94445 0.0855167
\(518\) 15.6902 0.689388
\(519\) 14.9058 0.654291
\(520\) −11.2205 −0.492052
\(521\) 19.6829 0.862322 0.431161 0.902275i \(-0.358104\pi\)
0.431161 + 0.902275i \(0.358104\pi\)
\(522\) −2.82583 −0.123683
\(523\) −2.22306 −0.0972077 −0.0486039 0.998818i \(-0.515477\pi\)
−0.0486039 + 0.998818i \(0.515477\pi\)
\(524\) 29.7400 1.29920
\(525\) −5.24247 −0.228800
\(526\) −14.1712 −0.617893
\(527\) 0.958229 0.0417411
\(528\) −3.65640 −0.159124
\(529\) 5.22520 0.227183
\(530\) −37.5364 −1.63048
\(531\) 20.6644 0.896760
\(532\) 35.9600 1.55906
\(533\) 2.22488 0.0963703
\(534\) −12.3486 −0.534376
\(535\) 6.88702 0.297752
\(536\) 17.5885 0.759709
\(537\) −7.86887 −0.339567
\(538\) −67.4099 −2.90625
\(539\) −2.65395 −0.114314
\(540\) −31.6929 −1.36385
\(541\) 32.6995 1.40586 0.702931 0.711258i \(-0.251874\pi\)
0.702931 + 0.711258i \(0.251874\pi\)
\(542\) −0.116417 −0.00500054
\(543\) −3.18267 −0.136581
\(544\) 0.430882 0.0184739
\(545\) −3.32088 −0.142251
\(546\) 5.96764 0.255392
\(547\) 24.4758 1.04651 0.523254 0.852177i \(-0.324718\pi\)
0.523254 + 0.852177i \(0.324718\pi\)
\(548\) 60.0303 2.56437
\(549\) 1.25120 0.0533998
\(550\) 4.02706 0.171714
\(551\) 5.22333 0.222521
\(552\) −38.5662 −1.64149
\(553\) 2.79677 0.118931
\(554\) 46.8870 1.99204
\(555\) 8.16415 0.346549
\(556\) −35.9964 −1.52659
\(557\) −28.3326 −1.20049 −0.600246 0.799815i \(-0.704931\pi\)
−0.600246 + 0.799815i \(0.704931\pi\)
\(558\) −24.8127 −1.05040
\(559\) 7.89189 0.333792
\(560\) 9.95454 0.420656
\(561\) 0.0853114 0.00360185
\(562\) −67.6616 −2.85413
\(563\) −27.5614 −1.16157 −0.580787 0.814055i \(-0.697255\pi\)
−0.580787 + 0.814055i \(0.697255\pi\)
\(564\) −21.2499 −0.894784
\(565\) −18.3721 −0.772922
\(566\) −50.7648 −2.13380
\(567\) 3.58488 0.150551
\(568\) −49.4104 −2.07322
\(569\) −0.370577 −0.0155354 −0.00776770 0.999970i \(-0.502473\pi\)
−0.00776770 + 0.999970i \(0.502473\pi\)
\(570\) 27.4276 1.14882
\(571\) 21.6690 0.906820 0.453410 0.891302i \(-0.350207\pi\)
0.453410 + 0.891302i \(0.350207\pi\)
\(572\) −3.12728 −0.130758
\(573\) 18.3976 0.768570
\(574\) −4.87311 −0.203400
\(575\) 17.2048 0.717490
\(576\) 5.30328 0.220970
\(577\) −17.6870 −0.736318 −0.368159 0.929763i \(-0.620012\pi\)
−0.368159 + 0.929763i \(0.620012\pi\)
\(578\) 42.6003 1.77194
\(579\) 10.3455 0.429942
\(580\) 4.55915 0.189308
\(581\) −1.50156 −0.0622954
\(582\) −38.5996 −1.60001
\(583\) −5.58827 −0.231442
\(584\) −1.33594 −0.0552816
\(585\) −2.74586 −0.113528
\(586\) −59.2529 −2.44772
\(587\) −37.6819 −1.55530 −0.777649 0.628699i \(-0.783588\pi\)
−0.777649 + 0.628699i \(0.783588\pi\)
\(588\) 29.0038 1.19610
\(589\) 45.8644 1.88981
\(590\) −48.8707 −2.01197
\(591\) −16.5477 −0.680683
\(592\) 28.4984 1.17128
\(593\) 15.5305 0.637760 0.318880 0.947795i \(-0.396693\pi\)
0.318880 + 0.947795i \(0.396693\pi\)
\(594\) −6.91630 −0.283779
\(595\) −0.232260 −0.00952173
\(596\) −47.4584 −1.94397
\(597\) 18.7118 0.765823
\(598\) −19.5847 −0.800876
\(599\) −14.6700 −0.599401 −0.299701 0.954033i \(-0.596887\pi\)
−0.299701 + 0.954033i \(0.596887\pi\)
\(600\) −23.5082 −0.959719
\(601\) −17.4163 −0.710428 −0.355214 0.934785i \(-0.615592\pi\)
−0.355214 + 0.934785i \(0.615592\pi\)
\(602\) −17.2855 −0.704503
\(603\) 4.30423 0.175282
\(604\) −46.0523 −1.87384
\(605\) 14.2736 0.580306
\(606\) −27.6954 −1.12505
\(607\) 33.8151 1.37251 0.686257 0.727359i \(-0.259253\pi\)
0.686257 + 0.727359i \(0.259253\pi\)
\(608\) 20.6236 0.836397
\(609\) −1.29522 −0.0524850
\(610\) −2.95904 −0.119808
\(611\) −5.76417 −0.233193
\(612\) 0.824447 0.0333263
\(613\) −2.85533 −0.115326 −0.0576628 0.998336i \(-0.518365\pi\)
−0.0576628 + 0.998336i \(0.518365\pi\)
\(614\) −66.1716 −2.67047
\(615\) −2.53565 −0.102247
\(616\) 3.65879 0.147417
\(617\) 20.5677 0.828023 0.414011 0.910272i \(-0.364127\pi\)
0.414011 + 0.910272i \(0.364127\pi\)
\(618\) 29.0876 1.17008
\(619\) 6.60051 0.265297 0.132649 0.991163i \(-0.457652\pi\)
0.132649 + 0.991163i \(0.457652\pi\)
\(620\) 40.0324 1.60774
\(621\) −29.5485 −1.18574
\(622\) −51.9492 −2.08297
\(623\) 5.00506 0.200524
\(624\) 10.8391 0.433913
\(625\) 1.67928 0.0671714
\(626\) −53.1330 −2.12362
\(627\) 4.08332 0.163072
\(628\) −12.3792 −0.493985
\(629\) −0.664927 −0.0265124
\(630\) 6.01421 0.239612
\(631\) 8.62745 0.343453 0.171727 0.985145i \(-0.445065\pi\)
0.171727 + 0.985145i \(0.445065\pi\)
\(632\) 12.5412 0.498863
\(633\) −0.840320 −0.0333997
\(634\) 59.9959 2.38274
\(635\) 27.2470 1.08126
\(636\) 61.0715 2.42164
\(637\) 7.86746 0.311720
\(638\) 0.994936 0.0393899
\(639\) −12.0916 −0.478337
\(640\) −20.9278 −0.827242
\(641\) 25.6025 1.01124 0.505619 0.862757i \(-0.331264\pi\)
0.505619 + 0.862757i \(0.331264\pi\)
\(642\) −16.4250 −0.648242
\(643\) 28.0412 1.10584 0.552919 0.833235i \(-0.313514\pi\)
0.552919 + 0.833235i \(0.313514\pi\)
\(644\) 29.2637 1.15315
\(645\) −8.99421 −0.354147
\(646\) −2.23384 −0.0878892
\(647\) −5.17910 −0.203611 −0.101806 0.994804i \(-0.532462\pi\)
−0.101806 + 0.994804i \(0.532462\pi\)
\(648\) 16.0753 0.631496
\(649\) −7.27567 −0.285595
\(650\) −11.9379 −0.468244
\(651\) −11.3729 −0.445739
\(652\) −60.7225 −2.37808
\(653\) −23.3641 −0.914309 −0.457154 0.889387i \(-0.651131\pi\)
−0.457154 + 0.889387i \(0.651131\pi\)
\(654\) 7.92001 0.309697
\(655\) −9.19395 −0.359237
\(656\) −8.85112 −0.345578
\(657\) −0.326929 −0.0127547
\(658\) 12.6252 0.492180
\(659\) −21.7663 −0.847894 −0.423947 0.905687i \(-0.639356\pi\)
−0.423947 + 0.905687i \(0.639356\pi\)
\(660\) 3.56409 0.138732
\(661\) 21.9263 0.852836 0.426418 0.904526i \(-0.359775\pi\)
0.426418 + 0.904526i \(0.359775\pi\)
\(662\) −23.4200 −0.910244
\(663\) −0.252899 −0.00982180
\(664\) −6.73329 −0.261302
\(665\) −11.1168 −0.431092
\(666\) 17.2178 0.667177
\(667\) 4.25067 0.164587
\(668\) −72.7173 −2.81352
\(669\) 23.8500 0.922096
\(670\) −10.1794 −0.393263
\(671\) −0.440529 −0.0170065
\(672\) −5.11400 −0.197277
\(673\) 23.0667 0.889156 0.444578 0.895740i \(-0.353354\pi\)
0.444578 + 0.895740i \(0.353354\pi\)
\(674\) −25.2150 −0.971247
\(675\) −18.0114 −0.693261
\(676\) −46.5424 −1.79009
\(677\) 21.7698 0.836680 0.418340 0.908291i \(-0.362612\pi\)
0.418340 + 0.908291i \(0.362612\pi\)
\(678\) 43.8160 1.68274
\(679\) 15.6450 0.600400
\(680\) −1.04150 −0.0399396
\(681\) −10.2199 −0.391629
\(682\) 8.73621 0.334527
\(683\) −50.6180 −1.93684 −0.968422 0.249319i \(-0.919793\pi\)
−0.968422 + 0.249319i \(0.919793\pi\)
\(684\) 39.4611 1.50883
\(685\) −18.5580 −0.709066
\(686\) −39.7617 −1.51811
\(687\) 29.4056 1.12189
\(688\) −31.3959 −1.19696
\(689\) 16.5660 0.631115
\(690\) 22.3202 0.849715
\(691\) −19.3061 −0.734440 −0.367220 0.930134i \(-0.619690\pi\)
−0.367220 + 0.930134i \(0.619690\pi\)
\(692\) −50.7177 −1.92800
\(693\) 0.895372 0.0340124
\(694\) −18.1150 −0.687637
\(695\) 11.1281 0.422112
\(696\) −5.80801 −0.220152
\(697\) 0.206515 0.00782231
\(698\) −2.71170 −0.102639
\(699\) 4.88641 0.184821
\(700\) 17.8378 0.674206
\(701\) −12.6756 −0.478750 −0.239375 0.970927i \(-0.576943\pi\)
−0.239375 + 0.970927i \(0.576943\pi\)
\(702\) 20.5029 0.773831
\(703\) −31.8258 −1.20033
\(704\) −1.86721 −0.0703733
\(705\) 6.56930 0.247414
\(706\) −58.5382 −2.20311
\(707\) 11.2253 0.422172
\(708\) 79.5124 2.98826
\(709\) 42.0191 1.57806 0.789030 0.614355i \(-0.210584\pi\)
0.789030 + 0.614355i \(0.210584\pi\)
\(710\) 28.5963 1.07320
\(711\) 3.06907 0.115099
\(712\) 22.4436 0.841111
\(713\) 37.3237 1.39778
\(714\) 0.553921 0.0207300
\(715\) 0.966782 0.0361556
\(716\) 26.7743 1.00060
\(717\) 21.3159 0.796058
\(718\) 91.8140 3.42647
\(719\) 22.8713 0.852957 0.426479 0.904498i \(-0.359754\pi\)
0.426479 + 0.904498i \(0.359754\pi\)
\(720\) 10.9237 0.407103
\(721\) −11.7896 −0.439069
\(722\) −59.2554 −2.20526
\(723\) 14.0714 0.523321
\(724\) 10.8292 0.402464
\(725\) 2.59101 0.0962278
\(726\) −34.0414 −1.26340
\(727\) −13.3120 −0.493714 −0.246857 0.969052i \(-0.579398\pi\)
−0.246857 + 0.969052i \(0.579398\pi\)
\(728\) −10.8462 −0.401988
\(729\) 24.9875 0.925462
\(730\) 0.773175 0.0286165
\(731\) 0.732531 0.0270936
\(732\) 4.81434 0.177943
\(733\) −26.6587 −0.984663 −0.492331 0.870408i \(-0.663855\pi\)
−0.492331 + 0.870408i \(0.663855\pi\)
\(734\) −94.6913 −3.49512
\(735\) −8.96636 −0.330729
\(736\) 16.7832 0.618635
\(737\) −1.51546 −0.0558227
\(738\) −5.34756 −0.196847
\(739\) 8.51309 0.313159 0.156580 0.987665i \(-0.449953\pi\)
0.156580 + 0.987665i \(0.449953\pi\)
\(740\) −27.7790 −1.02117
\(741\) −12.1047 −0.444677
\(742\) −36.2842 −1.33204
\(743\) −32.0690 −1.17650 −0.588248 0.808681i \(-0.700182\pi\)
−0.588248 + 0.808681i \(0.700182\pi\)
\(744\) −50.9982 −1.86969
\(745\) 14.6715 0.537522
\(746\) 24.5971 0.900565
\(747\) −1.64776 −0.0602883
\(748\) −0.290277 −0.0106136
\(749\) 6.65728 0.243252
\(750\) 34.6117 1.26384
\(751\) −9.12856 −0.333106 −0.166553 0.986033i \(-0.553264\pi\)
−0.166553 + 0.986033i \(0.553264\pi\)
\(752\) 22.9313 0.836218
\(753\) 26.5984 0.969301
\(754\) −2.94942 −0.107411
\(755\) 14.2368 0.518131
\(756\) −30.6357 −1.11421
\(757\) 4.27777 0.155478 0.0777391 0.996974i \(-0.475230\pi\)
0.0777391 + 0.996974i \(0.475230\pi\)
\(758\) −69.0646 −2.50854
\(759\) 3.32294 0.120615
\(760\) −49.8499 −1.80824
\(761\) −38.6633 −1.40154 −0.700771 0.713386i \(-0.747161\pi\)
−0.700771 + 0.713386i \(0.747161\pi\)
\(762\) −64.9817 −2.35404
\(763\) −3.21010 −0.116213
\(764\) −62.5988 −2.26475
\(765\) −0.254873 −0.00921496
\(766\) −26.5159 −0.958057
\(767\) 21.5682 0.778782
\(768\) 40.4051 1.45799
\(769\) −6.73580 −0.242899 −0.121450 0.992598i \(-0.538754\pi\)
−0.121450 + 0.992598i \(0.538754\pi\)
\(770\) −2.11752 −0.0763102
\(771\) −29.8249 −1.07412
\(772\) −35.2010 −1.26691
\(773\) −21.5244 −0.774180 −0.387090 0.922042i \(-0.626520\pi\)
−0.387090 + 0.922042i \(0.626520\pi\)
\(774\) −18.9684 −0.681805
\(775\) 22.7508 0.817234
\(776\) 70.1550 2.51842
\(777\) 7.89180 0.283117
\(778\) −27.0663 −0.970373
\(779\) 9.88457 0.354151
\(780\) −10.5655 −0.378306
\(781\) 4.25730 0.152338
\(782\) −1.81786 −0.0650066
\(783\) −4.44996 −0.159029
\(784\) −31.2987 −1.11781
\(785\) 3.82696 0.136590
\(786\) 21.9268 0.782103
\(787\) −54.3757 −1.93829 −0.969143 0.246501i \(-0.920719\pi\)
−0.969143 + 0.246501i \(0.920719\pi\)
\(788\) 56.3046 2.00577
\(789\) −7.12776 −0.253755
\(790\) −7.25823 −0.258236
\(791\) −17.7593 −0.631447
\(792\) 4.01501 0.142667
\(793\) 1.30592 0.0463745
\(794\) 33.7415 1.19744
\(795\) −18.8799 −0.669602
\(796\) −63.6679 −2.25665
\(797\) 13.2704 0.470061 0.235031 0.971988i \(-0.424481\pi\)
0.235031 + 0.971988i \(0.424481\pi\)
\(798\) 26.5127 0.938539
\(799\) −0.535034 −0.0189282
\(800\) 10.2302 0.361694
\(801\) 5.49236 0.194063
\(802\) 85.8463 3.03134
\(803\) 0.115107 0.00406204
\(804\) 16.5618 0.584088
\(805\) −9.04670 −0.318854
\(806\) −25.8979 −0.912213
\(807\) −33.9056 −1.19353
\(808\) 50.3364 1.77083
\(809\) 49.4542 1.73872 0.869359 0.494182i \(-0.164532\pi\)
0.869359 + 0.494182i \(0.164532\pi\)
\(810\) −9.30355 −0.326893
\(811\) −23.8933 −0.839008 −0.419504 0.907753i \(-0.637796\pi\)
−0.419504 + 0.907753i \(0.637796\pi\)
\(812\) 4.40706 0.154658
\(813\) −0.0585550 −0.00205361
\(814\) −6.06216 −0.212479
\(815\) 18.7720 0.657555
\(816\) 1.00610 0.0352204
\(817\) 35.0616 1.22665
\(818\) −0.708407 −0.0247689
\(819\) −2.65427 −0.0927475
\(820\) 8.62767 0.301291
\(821\) 26.9302 0.939869 0.469935 0.882701i \(-0.344277\pi\)
0.469935 + 0.882701i \(0.344277\pi\)
\(822\) 44.2594 1.54372
\(823\) 30.1151 1.04975 0.524874 0.851180i \(-0.324113\pi\)
0.524874 + 0.851180i \(0.324113\pi\)
\(824\) −52.8669 −1.84171
\(825\) 2.02551 0.0705193
\(826\) −47.2404 −1.64370
\(827\) 18.5221 0.644075 0.322038 0.946727i \(-0.395632\pi\)
0.322038 + 0.946727i \(0.395632\pi\)
\(828\) 32.1128 1.11600
\(829\) 17.6217 0.612026 0.306013 0.952027i \(-0.401005\pi\)
0.306013 + 0.952027i \(0.401005\pi\)
\(830\) 3.89689 0.135263
\(831\) 23.5830 0.818086
\(832\) 5.53522 0.191899
\(833\) 0.730263 0.0253021
\(834\) −26.5396 −0.918990
\(835\) 22.4801 0.777957
\(836\) −13.8937 −0.480524
\(837\) −39.0736 −1.35058
\(838\) −35.3099 −1.21976
\(839\) 26.3821 0.910811 0.455406 0.890284i \(-0.349494\pi\)
0.455406 + 0.890284i \(0.349494\pi\)
\(840\) 12.3612 0.426502
\(841\) −28.3599 −0.977926
\(842\) −12.2628 −0.422603
\(843\) −34.0322 −1.17213
\(844\) 2.85924 0.0984190
\(845\) 14.3883 0.494973
\(846\) 13.8544 0.476322
\(847\) 13.7975 0.474087
\(848\) −65.9037 −2.26314
\(849\) −25.5335 −0.876306
\(850\) −1.10809 −0.0380070
\(851\) −25.8994 −0.887819
\(852\) −46.5260 −1.59395
\(853\) 29.4488 1.00831 0.504154 0.863614i \(-0.331805\pi\)
0.504154 + 0.863614i \(0.331805\pi\)
\(854\) −2.86033 −0.0978784
\(855\) −12.1992 −0.417203
\(856\) 29.8525 1.02034
\(857\) 24.6962 0.843607 0.421804 0.906687i \(-0.361397\pi\)
0.421804 + 0.906687i \(0.361397\pi\)
\(858\) −2.30569 −0.0787151
\(859\) −22.0870 −0.753598 −0.376799 0.926295i \(-0.622975\pi\)
−0.376799 + 0.926295i \(0.622975\pi\)
\(860\) 30.6033 1.04356
\(861\) −2.45106 −0.0835319
\(862\) 19.9403 0.679168
\(863\) 16.1082 0.548330 0.274165 0.961683i \(-0.411598\pi\)
0.274165 + 0.961683i \(0.411598\pi\)
\(864\) −17.5700 −0.597745
\(865\) 15.6791 0.533105
\(866\) 3.63451 0.123506
\(867\) 21.4269 0.727697
\(868\) 38.6969 1.31346
\(869\) −1.08058 −0.0366561
\(870\) 3.36138 0.113962
\(871\) 4.49247 0.152222
\(872\) −14.3947 −0.487465
\(873\) 17.1682 0.581056
\(874\) −87.0096 −2.94314
\(875\) −14.0286 −0.474254
\(876\) −1.25795 −0.0425023
\(877\) −11.5221 −0.389074 −0.194537 0.980895i \(-0.562321\pi\)
−0.194537 + 0.980895i \(0.562321\pi\)
\(878\) 62.1194 2.09643
\(879\) −29.8028 −1.00522
\(880\) −3.84609 −0.129652
\(881\) −21.9545 −0.739664 −0.369832 0.929099i \(-0.620585\pi\)
−0.369832 + 0.929099i \(0.620585\pi\)
\(882\) −18.9097 −0.636721
\(883\) −4.38186 −0.147461 −0.0737306 0.997278i \(-0.523490\pi\)
−0.0737306 + 0.997278i \(0.523490\pi\)
\(884\) 0.860504 0.0289419
\(885\) −24.5808 −0.826274
\(886\) −30.4739 −1.02379
\(887\) 32.1308 1.07885 0.539424 0.842035i \(-0.318642\pi\)
0.539424 + 0.842035i \(0.318642\pi\)
\(888\) 35.3883 1.18755
\(889\) 26.3380 0.883349
\(890\) −12.9892 −0.435400
\(891\) −1.38507 −0.0464018
\(892\) −81.1511 −2.71714
\(893\) −25.6087 −0.856963
\(894\) −34.9903 −1.17025
\(895\) −8.27711 −0.276673
\(896\) −20.2296 −0.675825
\(897\) −9.85062 −0.328903
\(898\) −12.1257 −0.404639
\(899\) 5.62089 0.187467
\(900\) 19.5745 0.652484
\(901\) 1.53767 0.0512272
\(902\) 1.88280 0.0626905
\(903\) −8.69418 −0.289324
\(904\) −79.6358 −2.64865
\(905\) −3.34779 −0.111284
\(906\) −33.9536 −1.12803
\(907\) −9.37012 −0.311130 −0.155565 0.987826i \(-0.549720\pi\)
−0.155565 + 0.987826i \(0.549720\pi\)
\(908\) 34.7739 1.15401
\(909\) 12.3182 0.408570
\(910\) 6.27724 0.208089
\(911\) −42.2698 −1.40046 −0.700230 0.713917i \(-0.746919\pi\)
−0.700230 + 0.713917i \(0.746919\pi\)
\(912\) 48.1555 1.59459
\(913\) 0.580154 0.0192003
\(914\) 26.6641 0.881969
\(915\) −1.48833 −0.0492025
\(916\) −100.054 −3.30589
\(917\) −8.88725 −0.293483
\(918\) 1.90309 0.0628114
\(919\) −12.2737 −0.404873 −0.202436 0.979295i \(-0.564886\pi\)
−0.202436 + 0.979295i \(0.564886\pi\)
\(920\) −40.5671 −1.33746
\(921\) −33.2827 −1.09670
\(922\) −49.2090 −1.62061
\(923\) −12.6205 −0.415407
\(924\) 3.44520 0.113339
\(925\) −15.7871 −0.519076
\(926\) −6.48815 −0.213214
\(927\) −12.9375 −0.424923
\(928\) 2.52752 0.0829697
\(929\) 2.66574 0.0874601 0.0437301 0.999043i \(-0.486076\pi\)
0.0437301 + 0.999043i \(0.486076\pi\)
\(930\) 29.5152 0.967842
\(931\) 34.9531 1.14554
\(932\) −16.6263 −0.544612
\(933\) −26.1292 −0.855433
\(934\) 62.6123 2.04874
\(935\) 0.0897374 0.00293473
\(936\) −11.9022 −0.389036
\(937\) −45.0249 −1.47090 −0.735449 0.677580i \(-0.763029\pi\)
−0.735449 + 0.677580i \(0.763029\pi\)
\(938\) −9.83978 −0.321280
\(939\) −26.7246 −0.872126
\(940\) −22.3524 −0.729055
\(941\) −56.3597 −1.83727 −0.918636 0.395104i \(-0.870708\pi\)
−0.918636 + 0.395104i \(0.870708\pi\)
\(942\) −9.12699 −0.297373
\(943\) 8.04391 0.261946
\(944\) −85.8036 −2.79267
\(945\) 9.47085 0.308087
\(946\) 6.67851 0.217137
\(947\) −27.2891 −0.886776 −0.443388 0.896330i \(-0.646224\pi\)
−0.443388 + 0.896330i \(0.646224\pi\)
\(948\) 11.8091 0.383542
\(949\) −0.341227 −0.0110767
\(950\) −53.0371 −1.72075
\(951\) 30.1765 0.978540
\(952\) −1.00675 −0.0326291
\(953\) −41.6875 −1.35039 −0.675195 0.737640i \(-0.735940\pi\)
−0.675195 + 0.737640i \(0.735940\pi\)
\(954\) −39.8169 −1.28912
\(955\) 19.3521 0.626218
\(956\) −72.5286 −2.34574
\(957\) 0.500429 0.0161766
\(958\) −32.8040 −1.05985
\(959\) −17.9390 −0.579279
\(960\) −6.30837 −0.203602
\(961\) 18.3552 0.592102
\(962\) 17.9708 0.579403
\(963\) 7.30544 0.235414
\(964\) −47.8787 −1.54207
\(965\) 10.8822 0.350310
\(966\) 21.5756 0.694184
\(967\) 6.57891 0.211564 0.105782 0.994389i \(-0.466266\pi\)
0.105782 + 0.994389i \(0.466266\pi\)
\(968\) 61.8705 1.98859
\(969\) −1.12357 −0.0360942
\(970\) −40.6022 −1.30366
\(971\) −20.9415 −0.672044 −0.336022 0.941854i \(-0.609082\pi\)
−0.336022 + 0.941854i \(0.609082\pi\)
\(972\) −56.4991 −1.81221
\(973\) 10.7569 0.344849
\(974\) −91.8529 −2.94316
\(975\) −6.00449 −0.192298
\(976\) −5.19526 −0.166296
\(977\) 12.3946 0.396540 0.198270 0.980147i \(-0.436468\pi\)
0.198270 + 0.980147i \(0.436468\pi\)
\(978\) −44.7697 −1.43158
\(979\) −1.93379 −0.0618041
\(980\) 30.5085 0.974559
\(981\) −3.52263 −0.112469
\(982\) −80.3308 −2.56346
\(983\) −27.8300 −0.887639 −0.443819 0.896116i \(-0.646377\pi\)
−0.443819 + 0.896116i \(0.646377\pi\)
\(984\) −10.9910 −0.350380
\(985\) −17.4062 −0.554609
\(986\) −0.273767 −0.00871852
\(987\) 6.35015 0.202128
\(988\) 41.1869 1.31033
\(989\) 28.5326 0.907285
\(990\) −2.32369 −0.0738516
\(991\) 36.1478 1.14827 0.574136 0.818760i \(-0.305338\pi\)
0.574136 + 0.818760i \(0.305338\pi\)
\(992\) 22.1933 0.704637
\(993\) −11.7797 −0.373817
\(994\) 27.6423 0.876762
\(995\) 19.6826 0.623979
\(996\) −6.34022 −0.200898
\(997\) 57.2963 1.81459 0.907296 0.420492i \(-0.138142\pi\)
0.907296 + 0.420492i \(0.138142\pi\)
\(998\) 91.9883 2.91184
\(999\) 27.1137 0.857838
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.1.11 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.11 174 1.1 even 1 trivial