Properties

Label 4027.2.a.c.1.16
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 1.16
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.37550 q^{2} -3.14920 q^{3} +3.64299 q^{4} +0.257515 q^{5} +7.48091 q^{6} +1.36222 q^{7} -3.90291 q^{8} +6.91744 q^{9} +O(q^{10})\) \(q-2.37550 q^{2} -3.14920 q^{3} +3.64299 q^{4} +0.257515 q^{5} +7.48091 q^{6} +1.36222 q^{7} -3.90291 q^{8} +6.91744 q^{9} -0.611727 q^{10} -3.32871 q^{11} -11.4725 q^{12} -0.510496 q^{13} -3.23596 q^{14} -0.810967 q^{15} +1.98538 q^{16} -5.42456 q^{17} -16.4324 q^{18} -5.24636 q^{19} +0.938125 q^{20} -4.28991 q^{21} +7.90733 q^{22} +1.00135 q^{23} +12.2910 q^{24} -4.93369 q^{25} +1.21268 q^{26} -12.3368 q^{27} +4.96257 q^{28} -1.81807 q^{29} +1.92645 q^{30} -10.5761 q^{31} +3.08956 q^{32} +10.4827 q^{33} +12.8860 q^{34} +0.350794 q^{35} +25.2001 q^{36} -1.60885 q^{37} +12.4627 q^{38} +1.60765 q^{39} -1.00506 q^{40} -7.60662 q^{41} +10.1907 q^{42} -5.13321 q^{43} -12.1264 q^{44} +1.78135 q^{45} -2.37871 q^{46} +6.92612 q^{47} -6.25234 q^{48} -5.14434 q^{49} +11.7200 q^{50} +17.0830 q^{51} -1.85973 q^{52} +9.39911 q^{53} +29.3060 q^{54} -0.857193 q^{55} -5.31664 q^{56} +16.5218 q^{57} +4.31881 q^{58} +10.6471 q^{59} -2.95434 q^{60} -8.61638 q^{61} +25.1235 q^{62} +9.42310 q^{63} -11.3100 q^{64} -0.131461 q^{65} -24.9017 q^{66} -5.63991 q^{67} -19.7616 q^{68} -3.15346 q^{69} -0.833310 q^{70} -3.79151 q^{71} -26.9981 q^{72} +2.36989 q^{73} +3.82182 q^{74} +15.5371 q^{75} -19.1124 q^{76} -4.53445 q^{77} -3.81898 q^{78} -5.01780 q^{79} +0.511265 q^{80} +18.0986 q^{81} +18.0695 q^{82} -2.46922 q^{83} -15.6281 q^{84} -1.39691 q^{85} +12.1939 q^{86} +5.72545 q^{87} +12.9916 q^{88} +11.3518 q^{89} -4.23158 q^{90} -0.695411 q^{91} +3.64791 q^{92} +33.3062 q^{93} -16.4530 q^{94} -1.35102 q^{95} -9.72964 q^{96} +4.70569 q^{97} +12.2204 q^{98} -23.0261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37550 −1.67973 −0.839865 0.542795i \(-0.817366\pi\)
−0.839865 + 0.542795i \(0.817366\pi\)
\(3\) −3.14920 −1.81819 −0.909095 0.416590i \(-0.863225\pi\)
−0.909095 + 0.416590i \(0.863225\pi\)
\(4\) 3.64299 1.82149
\(5\) 0.257515 0.115164 0.0575822 0.998341i \(-0.481661\pi\)
0.0575822 + 0.998341i \(0.481661\pi\)
\(6\) 7.48091 3.05407
\(7\) 1.36222 0.514872 0.257436 0.966295i \(-0.417122\pi\)
0.257436 + 0.966295i \(0.417122\pi\)
\(8\) −3.90291 −1.37989
\(9\) 6.91744 2.30581
\(10\) −0.611727 −0.193445
\(11\) −3.32871 −1.00364 −0.501821 0.864971i \(-0.667337\pi\)
−0.501821 + 0.864971i \(0.667337\pi\)
\(12\) −11.4725 −3.31182
\(13\) −0.510496 −0.141586 −0.0707931 0.997491i \(-0.522553\pi\)
−0.0707931 + 0.997491i \(0.522553\pi\)
\(14\) −3.23596 −0.864847
\(15\) −0.810967 −0.209391
\(16\) 1.98538 0.496344
\(17\) −5.42456 −1.31565 −0.657824 0.753171i \(-0.728523\pi\)
−0.657824 + 0.753171i \(0.728523\pi\)
\(18\) −16.4324 −3.87314
\(19\) −5.24636 −1.20360 −0.601799 0.798647i \(-0.705549\pi\)
−0.601799 + 0.798647i \(0.705549\pi\)
\(20\) 0.938125 0.209771
\(21\) −4.28991 −0.936136
\(22\) 7.90733 1.68585
\(23\) 1.00135 0.208796 0.104398 0.994536i \(-0.466708\pi\)
0.104398 + 0.994536i \(0.466708\pi\)
\(24\) 12.2910 2.50889
\(25\) −4.93369 −0.986737
\(26\) 1.21268 0.237827
\(27\) −12.3368 −2.37421
\(28\) 4.96257 0.937837
\(29\) −1.81807 −0.337606 −0.168803 0.985650i \(-0.553990\pi\)
−0.168803 + 0.985650i \(0.553990\pi\)
\(30\) 1.92645 0.351720
\(31\) −10.5761 −1.89952 −0.949761 0.312977i \(-0.898674\pi\)
−0.949761 + 0.312977i \(0.898674\pi\)
\(32\) 3.08956 0.546163
\(33\) 10.4827 1.82481
\(34\) 12.8860 2.20993
\(35\) 0.350794 0.0592950
\(36\) 25.2001 4.20002
\(37\) −1.60885 −0.264493 −0.132247 0.991217i \(-0.542219\pi\)
−0.132247 + 0.991217i \(0.542219\pi\)
\(38\) 12.4627 2.02172
\(39\) 1.60765 0.257431
\(40\) −1.00506 −0.158914
\(41\) −7.60662 −1.18795 −0.593977 0.804482i \(-0.702443\pi\)
−0.593977 + 0.804482i \(0.702443\pi\)
\(42\) 10.1907 1.57246
\(43\) −5.13321 −0.782807 −0.391403 0.920219i \(-0.628010\pi\)
−0.391403 + 0.920219i \(0.628010\pi\)
\(44\) −12.1264 −1.82813
\(45\) 1.78135 0.265548
\(46\) −2.37871 −0.350722
\(47\) 6.92612 1.01028 0.505139 0.863038i \(-0.331441\pi\)
0.505139 + 0.863038i \(0.331441\pi\)
\(48\) −6.25234 −0.902447
\(49\) −5.14434 −0.734906
\(50\) 11.7200 1.65745
\(51\) 17.0830 2.39210
\(52\) −1.85973 −0.257898
\(53\) 9.39911 1.29107 0.645534 0.763732i \(-0.276635\pi\)
0.645534 + 0.763732i \(0.276635\pi\)
\(54\) 29.3060 3.98804
\(55\) −0.857193 −0.115584
\(56\) −5.31664 −0.710466
\(57\) 16.5218 2.18837
\(58\) 4.31881 0.567088
\(59\) 10.6471 1.38613 0.693067 0.720873i \(-0.256259\pi\)
0.693067 + 0.720873i \(0.256259\pi\)
\(60\) −2.95434 −0.381404
\(61\) −8.61638 −1.10321 −0.551607 0.834104i \(-0.685985\pi\)
−0.551607 + 0.834104i \(0.685985\pi\)
\(62\) 25.1235 3.19068
\(63\) 9.42310 1.18720
\(64\) −11.3100 −1.41375
\(65\) −0.131461 −0.0163057
\(66\) −24.9017 −3.06519
\(67\) −5.63991 −0.689024 −0.344512 0.938782i \(-0.611956\pi\)
−0.344512 + 0.938782i \(0.611956\pi\)
\(68\) −19.7616 −2.39644
\(69\) −3.15346 −0.379631
\(70\) −0.833310 −0.0995996
\(71\) −3.79151 −0.449969 −0.224985 0.974362i \(-0.572233\pi\)
−0.224985 + 0.974362i \(0.572233\pi\)
\(72\) −26.9981 −3.18176
\(73\) 2.36989 0.277375 0.138688 0.990336i \(-0.455712\pi\)
0.138688 + 0.990336i \(0.455712\pi\)
\(74\) 3.82182 0.444278
\(75\) 15.5371 1.79407
\(76\) −19.1124 −2.19235
\(77\) −4.53445 −0.516748
\(78\) −3.81898 −0.432414
\(79\) −5.01780 −0.564547 −0.282273 0.959334i \(-0.591088\pi\)
−0.282273 + 0.959334i \(0.591088\pi\)
\(80\) 0.511265 0.0571611
\(81\) 18.0986 2.01096
\(82\) 18.0695 1.99544
\(83\) −2.46922 −0.271032 −0.135516 0.990775i \(-0.543269\pi\)
−0.135516 + 0.990775i \(0.543269\pi\)
\(84\) −15.6281 −1.70516
\(85\) −1.39691 −0.151516
\(86\) 12.1939 1.31490
\(87\) 5.72545 0.613832
\(88\) 12.9916 1.38491
\(89\) 11.3518 1.20329 0.601646 0.798763i \(-0.294512\pi\)
0.601646 + 0.798763i \(0.294512\pi\)
\(90\) −4.23158 −0.446048
\(91\) −0.695411 −0.0728988
\(92\) 3.64791 0.380321
\(93\) 33.3062 3.45369
\(94\) −16.4530 −1.69699
\(95\) −1.35102 −0.138612
\(96\) −9.72964 −0.993028
\(97\) 4.70569 0.477791 0.238895 0.971045i \(-0.423215\pi\)
0.238895 + 0.971045i \(0.423215\pi\)
\(98\) 12.2204 1.23444
\(99\) −23.0261 −2.31421
\(100\) −17.9733 −1.79733
\(101\) 3.05575 0.304058 0.152029 0.988376i \(-0.451419\pi\)
0.152029 + 0.988376i \(0.451419\pi\)
\(102\) −40.5806 −4.01808
\(103\) −13.3310 −1.31354 −0.656771 0.754090i \(-0.728078\pi\)
−0.656771 + 0.754090i \(0.728078\pi\)
\(104\) 1.99242 0.195373
\(105\) −1.10472 −0.107810
\(106\) −22.3276 −2.16864
\(107\) −5.23489 −0.506076 −0.253038 0.967456i \(-0.581430\pi\)
−0.253038 + 0.967456i \(0.581430\pi\)
\(108\) −44.9427 −4.32461
\(109\) 6.12469 0.586639 0.293320 0.956014i \(-0.405240\pi\)
0.293320 + 0.956014i \(0.405240\pi\)
\(110\) 2.03626 0.194150
\(111\) 5.06659 0.480899
\(112\) 2.70453 0.255554
\(113\) −15.5134 −1.45938 −0.729689 0.683779i \(-0.760335\pi\)
−0.729689 + 0.683779i \(0.760335\pi\)
\(114\) −39.2476 −3.67587
\(115\) 0.257864 0.0240459
\(116\) −6.62319 −0.614948
\(117\) −3.53133 −0.326471
\(118\) −25.2922 −2.32833
\(119\) −7.38947 −0.677391
\(120\) 3.16513 0.288935
\(121\) 0.0802846 0.00729860
\(122\) 20.4682 1.85310
\(123\) 23.9547 2.15993
\(124\) −38.5285 −3.45997
\(125\) −2.55808 −0.228801
\(126\) −22.3846 −1.99417
\(127\) −2.68495 −0.238251 −0.119125 0.992879i \(-0.538009\pi\)
−0.119125 + 0.992879i \(0.538009\pi\)
\(128\) 20.6877 1.82856
\(129\) 16.1655 1.42329
\(130\) 0.312285 0.0273892
\(131\) −6.43565 −0.562285 −0.281143 0.959666i \(-0.590713\pi\)
−0.281143 + 0.959666i \(0.590713\pi\)
\(132\) 38.1885 3.32388
\(133\) −7.14673 −0.619700
\(134\) 13.3976 1.15738
\(135\) −3.17691 −0.273425
\(136\) 21.1716 1.81545
\(137\) −10.7590 −0.919204 −0.459602 0.888125i \(-0.652008\pi\)
−0.459602 + 0.888125i \(0.652008\pi\)
\(138\) 7.49103 0.637678
\(139\) 1.67615 0.142169 0.0710846 0.997470i \(-0.477354\pi\)
0.0710846 + 0.997470i \(0.477354\pi\)
\(140\) 1.27794 0.108005
\(141\) −21.8117 −1.83688
\(142\) 9.00672 0.755827
\(143\) 1.69929 0.142102
\(144\) 13.7337 1.14448
\(145\) −0.468180 −0.0388802
\(146\) −5.62968 −0.465915
\(147\) 16.2005 1.33620
\(148\) −5.86102 −0.481773
\(149\) 20.8704 1.70977 0.854886 0.518816i \(-0.173627\pi\)
0.854886 + 0.518816i \(0.173627\pi\)
\(150\) −36.9084 −3.01356
\(151\) −20.9891 −1.70807 −0.854035 0.520216i \(-0.825852\pi\)
−0.854035 + 0.520216i \(0.825852\pi\)
\(152\) 20.4761 1.66083
\(153\) −37.5240 −3.03364
\(154\) 10.7716 0.867997
\(155\) −2.72351 −0.218757
\(156\) 5.85666 0.468908
\(157\) 17.4466 1.39239 0.696196 0.717852i \(-0.254874\pi\)
0.696196 + 0.717852i \(0.254874\pi\)
\(158\) 11.9198 0.948286
\(159\) −29.5997 −2.34740
\(160\) 0.795610 0.0628985
\(161\) 1.36407 0.107504
\(162\) −42.9932 −3.37787
\(163\) 6.66717 0.522213 0.261107 0.965310i \(-0.415913\pi\)
0.261107 + 0.965310i \(0.415913\pi\)
\(164\) −27.7108 −2.16385
\(165\) 2.69947 0.210153
\(166\) 5.86563 0.455261
\(167\) −2.01771 −0.156135 −0.0780674 0.996948i \(-0.524875\pi\)
−0.0780674 + 0.996948i \(0.524875\pi\)
\(168\) 16.7431 1.29176
\(169\) −12.7394 −0.979953
\(170\) 3.31835 0.254506
\(171\) −36.2914 −2.77527
\(172\) −18.7002 −1.42588
\(173\) 19.9014 1.51308 0.756539 0.653949i \(-0.226889\pi\)
0.756539 + 0.653949i \(0.226889\pi\)
\(174\) −13.6008 −1.03107
\(175\) −6.72079 −0.508044
\(176\) −6.60873 −0.498152
\(177\) −33.5298 −2.52026
\(178\) −26.9662 −2.02120
\(179\) −23.1915 −1.73341 −0.866706 0.498819i \(-0.833767\pi\)
−0.866706 + 0.498819i \(0.833767\pi\)
\(180\) 6.48942 0.483693
\(181\) −21.4387 −1.59353 −0.796763 0.604292i \(-0.793456\pi\)
−0.796763 + 0.604292i \(0.793456\pi\)
\(182\) 1.65195 0.122450
\(183\) 27.1347 2.00585
\(184\) −3.90819 −0.288115
\(185\) −0.414304 −0.0304602
\(186\) −79.1187 −5.80127
\(187\) 18.0568 1.32044
\(188\) 25.2318 1.84022
\(189\) −16.8055 −1.22242
\(190\) 3.20934 0.232830
\(191\) −25.2067 −1.82389 −0.911946 0.410309i \(-0.865421\pi\)
−0.911946 + 0.410309i \(0.865421\pi\)
\(192\) 35.6174 2.57047
\(193\) 16.3858 1.17947 0.589737 0.807596i \(-0.299232\pi\)
0.589737 + 0.807596i \(0.299232\pi\)
\(194\) −11.1784 −0.802559
\(195\) 0.413996 0.0296468
\(196\) −18.7408 −1.33863
\(197\) 22.5909 1.60953 0.804766 0.593592i \(-0.202291\pi\)
0.804766 + 0.593592i \(0.202291\pi\)
\(198\) 54.6985 3.88725
\(199\) 14.7323 1.04434 0.522171 0.852841i \(-0.325122\pi\)
0.522171 + 0.852841i \(0.325122\pi\)
\(200\) 19.2557 1.36159
\(201\) 17.7612 1.25278
\(202\) −7.25892 −0.510736
\(203\) −2.47661 −0.173824
\(204\) 62.2331 4.35719
\(205\) −1.95882 −0.136810
\(206\) 31.6678 2.20640
\(207\) 6.92679 0.481445
\(208\) −1.01353 −0.0702754
\(209\) 17.4636 1.20798
\(210\) 2.62426 0.181091
\(211\) −8.70414 −0.599218 −0.299609 0.954062i \(-0.596856\pi\)
−0.299609 + 0.954062i \(0.596856\pi\)
\(212\) 34.2408 2.35167
\(213\) 11.9402 0.818130
\(214\) 12.4355 0.850070
\(215\) −1.32188 −0.0901515
\(216\) 48.1493 3.27615
\(217\) −14.4070 −0.978011
\(218\) −14.5492 −0.985396
\(219\) −7.46326 −0.504321
\(220\) −3.12274 −0.210535
\(221\) 2.76922 0.186278
\(222\) −12.0357 −0.807781
\(223\) −4.33002 −0.289960 −0.144980 0.989435i \(-0.546312\pi\)
−0.144980 + 0.989435i \(0.546312\pi\)
\(224\) 4.20868 0.281204
\(225\) −34.1285 −2.27523
\(226\) 36.8520 2.45136
\(227\) 13.8183 0.917153 0.458576 0.888655i \(-0.348360\pi\)
0.458576 + 0.888655i \(0.348360\pi\)
\(228\) 60.1888 3.98610
\(229\) 9.51506 0.628773 0.314387 0.949295i \(-0.398201\pi\)
0.314387 + 0.949295i \(0.398201\pi\)
\(230\) −0.612555 −0.0403907
\(231\) 14.2799 0.939546
\(232\) 7.09574 0.465858
\(233\) −22.3604 −1.46488 −0.732439 0.680832i \(-0.761618\pi\)
−0.732439 + 0.680832i \(0.761618\pi\)
\(234\) 8.38866 0.548384
\(235\) 1.78358 0.116348
\(236\) 38.7872 2.52483
\(237\) 15.8020 1.02645
\(238\) 17.5537 1.13783
\(239\) −9.79186 −0.633383 −0.316691 0.948529i \(-0.602572\pi\)
−0.316691 + 0.948529i \(0.602572\pi\)
\(240\) −1.61007 −0.103930
\(241\) 17.9058 1.15341 0.576707 0.816951i \(-0.304337\pi\)
0.576707 + 0.816951i \(0.304337\pi\)
\(242\) −0.190716 −0.0122597
\(243\) −19.9858 −1.28209
\(244\) −31.3894 −2.00950
\(245\) −1.32475 −0.0846351
\(246\) −56.9044 −3.62809
\(247\) 2.67825 0.170413
\(248\) 41.2775 2.62112
\(249\) 7.77607 0.492788
\(250\) 6.07671 0.384325
\(251\) −2.56292 −0.161770 −0.0808852 0.996723i \(-0.525775\pi\)
−0.0808852 + 0.996723i \(0.525775\pi\)
\(252\) 34.3282 2.16248
\(253\) −3.33321 −0.209557
\(254\) 6.37809 0.400197
\(255\) 4.39914 0.275485
\(256\) −26.5237 −1.65773
\(257\) 13.3002 0.829646 0.414823 0.909902i \(-0.363844\pi\)
0.414823 + 0.909902i \(0.363844\pi\)
\(258\) −38.4010 −2.39074
\(259\) −2.19162 −0.136180
\(260\) −0.478910 −0.0297007
\(261\) −12.5764 −0.778457
\(262\) 15.2879 0.944487
\(263\) 10.7524 0.663024 0.331512 0.943451i \(-0.392441\pi\)
0.331512 + 0.943451i \(0.392441\pi\)
\(264\) −40.9132 −2.51803
\(265\) 2.42042 0.148685
\(266\) 16.9770 1.04093
\(267\) −35.7491 −2.18781
\(268\) −20.5461 −1.25505
\(269\) 3.03387 0.184979 0.0924893 0.995714i \(-0.470518\pi\)
0.0924893 + 0.995714i \(0.470518\pi\)
\(270\) 7.54674 0.459280
\(271\) 19.7373 1.19895 0.599477 0.800392i \(-0.295375\pi\)
0.599477 + 0.800392i \(0.295375\pi\)
\(272\) −10.7698 −0.653014
\(273\) 2.18998 0.132544
\(274\) 25.5580 1.54401
\(275\) 16.4228 0.990332
\(276\) −11.4880 −0.691496
\(277\) 5.66693 0.340493 0.170246 0.985402i \(-0.445544\pi\)
0.170246 + 0.985402i \(0.445544\pi\)
\(278\) −3.98169 −0.238806
\(279\) −73.1594 −4.37994
\(280\) −1.36912 −0.0818204
\(281\) −16.5821 −0.989207 −0.494604 0.869119i \(-0.664687\pi\)
−0.494604 + 0.869119i \(0.664687\pi\)
\(282\) 51.8137 3.08546
\(283\) −11.7045 −0.695759 −0.347880 0.937539i \(-0.613098\pi\)
−0.347880 + 0.937539i \(0.613098\pi\)
\(284\) −13.8124 −0.819616
\(285\) 4.25463 0.252022
\(286\) −4.03666 −0.238693
\(287\) −10.3619 −0.611645
\(288\) 21.3719 1.25935
\(289\) 12.4258 0.730931
\(290\) 1.11216 0.0653083
\(291\) −14.8191 −0.868714
\(292\) 8.63349 0.505237
\(293\) −23.9233 −1.39761 −0.698807 0.715311i \(-0.746285\pi\)
−0.698807 + 0.715311i \(0.746285\pi\)
\(294\) −38.4844 −2.24445
\(295\) 2.74179 0.159633
\(296\) 6.27920 0.364971
\(297\) 41.0655 2.38286
\(298\) −49.5776 −2.87195
\(299\) −0.511187 −0.0295627
\(300\) 56.6016 3.26790
\(301\) −6.99258 −0.403046
\(302\) 49.8596 2.86910
\(303\) −9.62316 −0.552836
\(304\) −10.4160 −0.597399
\(305\) −2.21885 −0.127051
\(306\) 89.1382 5.09569
\(307\) −17.2159 −0.982564 −0.491282 0.871000i \(-0.663472\pi\)
−0.491282 + 0.871000i \(0.663472\pi\)
\(308\) −16.5189 −0.941253
\(309\) 41.9820 2.38827
\(310\) 6.46968 0.367453
\(311\) −11.3081 −0.641223 −0.320611 0.947211i \(-0.603888\pi\)
−0.320611 + 0.947211i \(0.603888\pi\)
\(312\) −6.27452 −0.355225
\(313\) 18.9565 1.07149 0.535743 0.844381i \(-0.320031\pi\)
0.535743 + 0.844381i \(0.320031\pi\)
\(314\) −41.4444 −2.33884
\(315\) 2.42659 0.136723
\(316\) −18.2798 −1.02832
\(317\) 11.1468 0.626064 0.313032 0.949743i \(-0.398655\pi\)
0.313032 + 0.949743i \(0.398655\pi\)
\(318\) 70.3139 3.94301
\(319\) 6.05181 0.338836
\(320\) −2.91250 −0.162814
\(321\) 16.4857 0.920141
\(322\) −3.24034 −0.180577
\(323\) 28.4592 1.58351
\(324\) 65.9330 3.66295
\(325\) 2.51863 0.139708
\(326\) −15.8378 −0.877177
\(327\) −19.2879 −1.06662
\(328\) 29.6879 1.63924
\(329\) 9.43493 0.520165
\(330\) −6.41258 −0.353001
\(331\) 19.9074 1.09421 0.547105 0.837064i \(-0.315730\pi\)
0.547105 + 0.837064i \(0.315730\pi\)
\(332\) −8.99534 −0.493684
\(333\) −11.1291 −0.609872
\(334\) 4.79306 0.262264
\(335\) −1.45236 −0.0793511
\(336\) −8.51709 −0.464645
\(337\) −13.7659 −0.749876 −0.374938 0.927050i \(-0.622336\pi\)
−0.374938 + 0.927050i \(0.622336\pi\)
\(338\) 30.2624 1.64606
\(339\) 48.8548 2.65343
\(340\) −5.08891 −0.275985
\(341\) 35.2047 1.90644
\(342\) 86.2101 4.66171
\(343\) −16.5433 −0.893256
\(344\) 20.0344 1.08018
\(345\) −0.812064 −0.0437200
\(346\) −47.2758 −2.54156
\(347\) −21.3444 −1.14583 −0.572915 0.819615i \(-0.694188\pi\)
−0.572915 + 0.819615i \(0.694188\pi\)
\(348\) 20.8577 1.11809
\(349\) 13.4918 0.722200 0.361100 0.932527i \(-0.382401\pi\)
0.361100 + 0.932527i \(0.382401\pi\)
\(350\) 15.9652 0.853376
\(351\) 6.29788 0.336156
\(352\) −10.2843 −0.548152
\(353\) 30.9464 1.64711 0.823555 0.567237i \(-0.191988\pi\)
0.823555 + 0.567237i \(0.191988\pi\)
\(354\) 79.6500 4.23335
\(355\) −0.976372 −0.0518205
\(356\) 41.3545 2.19179
\(357\) 23.2709 1.23163
\(358\) 55.0913 2.91166
\(359\) −20.7124 −1.09316 −0.546579 0.837407i \(-0.684070\pi\)
−0.546579 + 0.837407i \(0.684070\pi\)
\(360\) −6.95243 −0.366425
\(361\) 8.52434 0.448650
\(362\) 50.9275 2.67669
\(363\) −0.252832 −0.0132702
\(364\) −2.53337 −0.132785
\(365\) 0.610284 0.0319437
\(366\) −64.4584 −3.36929
\(367\) 7.03868 0.367416 0.183708 0.982981i \(-0.441190\pi\)
0.183708 + 0.982981i \(0.441190\pi\)
\(368\) 1.98806 0.103635
\(369\) −52.6183 −2.73920
\(370\) 0.984178 0.0511650
\(371\) 12.8037 0.664735
\(372\) 121.334 6.29087
\(373\) 17.9134 0.927522 0.463761 0.885960i \(-0.346500\pi\)
0.463761 + 0.885960i \(0.346500\pi\)
\(374\) −42.8938 −2.21798
\(375\) 8.05589 0.416004
\(376\) −27.0320 −1.39407
\(377\) 0.928116 0.0478004
\(378\) 39.9213 2.05333
\(379\) −17.7910 −0.913864 −0.456932 0.889502i \(-0.651052\pi\)
−0.456932 + 0.889502i \(0.651052\pi\)
\(380\) −4.92175 −0.252480
\(381\) 8.45543 0.433185
\(382\) 59.8784 3.06365
\(383\) −24.8579 −1.27018 −0.635090 0.772438i \(-0.719037\pi\)
−0.635090 + 0.772438i \(0.719037\pi\)
\(384\) −65.1498 −3.32466
\(385\) −1.16769 −0.0595110
\(386\) −38.9243 −1.98120
\(387\) −35.5086 −1.80501
\(388\) 17.1428 0.870292
\(389\) 16.0088 0.811676 0.405838 0.913945i \(-0.366980\pi\)
0.405838 + 0.913945i \(0.366980\pi\)
\(390\) −0.983445 −0.0497987
\(391\) −5.43190 −0.274703
\(392\) 20.0779 1.01409
\(393\) 20.2671 1.02234
\(394\) −53.6645 −2.70358
\(395\) −1.29216 −0.0650157
\(396\) −83.8838 −4.21532
\(397\) −19.5753 −0.982458 −0.491229 0.871030i \(-0.663452\pi\)
−0.491229 + 0.871030i \(0.663452\pi\)
\(398\) −34.9964 −1.75421
\(399\) 22.5064 1.12673
\(400\) −9.79522 −0.489761
\(401\) −32.3746 −1.61671 −0.808354 0.588696i \(-0.799641\pi\)
−0.808354 + 0.588696i \(0.799641\pi\)
\(402\) −42.1916 −2.10433
\(403\) 5.39905 0.268946
\(404\) 11.1321 0.553840
\(405\) 4.66068 0.231591
\(406\) 5.88319 0.291978
\(407\) 5.35539 0.265457
\(408\) −66.6734 −3.30082
\(409\) 38.6399 1.91062 0.955309 0.295609i \(-0.0955227\pi\)
0.955309 + 0.295609i \(0.0955227\pi\)
\(410\) 4.65318 0.229804
\(411\) 33.8822 1.67129
\(412\) −48.5647 −2.39261
\(413\) 14.5037 0.713683
\(414\) −16.4546 −0.808698
\(415\) −0.635863 −0.0312133
\(416\) −1.57721 −0.0773291
\(417\) −5.27853 −0.258491
\(418\) −41.4847 −2.02909
\(419\) 22.2236 1.08570 0.542848 0.839831i \(-0.317346\pi\)
0.542848 + 0.839831i \(0.317346\pi\)
\(420\) −4.02448 −0.196374
\(421\) −9.89661 −0.482331 −0.241166 0.970484i \(-0.577530\pi\)
−0.241166 + 0.970484i \(0.577530\pi\)
\(422\) 20.6767 1.00652
\(423\) 47.9110 2.32951
\(424\) −36.6839 −1.78153
\(425\) 26.7631 1.29820
\(426\) −28.3639 −1.37424
\(427\) −11.7374 −0.568015
\(428\) −19.0706 −0.921813
\(429\) −5.35141 −0.258368
\(430\) 3.14012 0.151430
\(431\) 7.03386 0.338809 0.169405 0.985547i \(-0.445816\pi\)
0.169405 + 0.985547i \(0.445816\pi\)
\(432\) −24.4931 −1.17843
\(433\) 0.439539 0.0211229 0.0105614 0.999944i \(-0.496638\pi\)
0.0105614 + 0.999944i \(0.496638\pi\)
\(434\) 34.2238 1.64279
\(435\) 1.47439 0.0706916
\(436\) 22.3122 1.06856
\(437\) −5.25346 −0.251307
\(438\) 17.7290 0.847122
\(439\) 20.6962 0.987775 0.493888 0.869526i \(-0.335575\pi\)
0.493888 + 0.869526i \(0.335575\pi\)
\(440\) 3.34555 0.159493
\(441\) −35.5857 −1.69456
\(442\) −6.57827 −0.312896
\(443\) −13.0884 −0.621847 −0.310923 0.950435i \(-0.600638\pi\)
−0.310923 + 0.950435i \(0.600638\pi\)
\(444\) 18.4575 0.875954
\(445\) 2.92327 0.138576
\(446\) 10.2860 0.487054
\(447\) −65.7251 −3.10869
\(448\) −15.4068 −0.727901
\(449\) −38.7491 −1.82868 −0.914341 0.404946i \(-0.867290\pi\)
−0.914341 + 0.404946i \(0.867290\pi\)
\(450\) 81.0721 3.82177
\(451\) 25.3202 1.19228
\(452\) −56.5151 −2.65825
\(453\) 66.0988 3.10559
\(454\) −32.8253 −1.54057
\(455\) −0.179079 −0.00839535
\(456\) −64.4832 −3.01970
\(457\) 13.5536 0.634011 0.317006 0.948424i \(-0.397323\pi\)
0.317006 + 0.948424i \(0.397323\pi\)
\(458\) −22.6030 −1.05617
\(459\) 66.9216 3.12363
\(460\) 0.939394 0.0437995
\(461\) 26.4032 1.22972 0.614859 0.788637i \(-0.289213\pi\)
0.614859 + 0.788637i \(0.289213\pi\)
\(462\) −33.9218 −1.57818
\(463\) 19.2860 0.896296 0.448148 0.893959i \(-0.352084\pi\)
0.448148 + 0.893959i \(0.352084\pi\)
\(464\) −3.60954 −0.167569
\(465\) 8.57686 0.397742
\(466\) 53.1171 2.46060
\(467\) −31.9229 −1.47722 −0.738608 0.674135i \(-0.764517\pi\)
−0.738608 + 0.674135i \(0.764517\pi\)
\(468\) −12.8646 −0.594665
\(469\) −7.68282 −0.354760
\(470\) −4.23690 −0.195433
\(471\) −54.9429 −2.53163
\(472\) −41.5547 −1.91271
\(473\) 17.0869 0.785658
\(474\) −37.5377 −1.72416
\(475\) 25.8839 1.18764
\(476\) −26.9197 −1.23386
\(477\) 65.0178 2.97696
\(478\) 23.2605 1.06391
\(479\) 15.0799 0.689017 0.344508 0.938783i \(-0.388046\pi\)
0.344508 + 0.938783i \(0.388046\pi\)
\(480\) −2.50553 −0.114361
\(481\) 0.821312 0.0374486
\(482\) −42.5352 −1.93742
\(483\) −4.29572 −0.195462
\(484\) 0.292476 0.0132944
\(485\) 1.21179 0.0550245
\(486\) 47.4762 2.15356
\(487\) −27.0282 −1.22477 −0.612383 0.790561i \(-0.709789\pi\)
−0.612383 + 0.790561i \(0.709789\pi\)
\(488\) 33.6290 1.52231
\(489\) −20.9962 −0.949482
\(490\) 3.14694 0.142164
\(491\) 13.4967 0.609095 0.304548 0.952497i \(-0.401495\pi\)
0.304548 + 0.952497i \(0.401495\pi\)
\(492\) 87.2668 3.93429
\(493\) 9.86220 0.444171
\(494\) −6.36218 −0.286248
\(495\) −5.92958 −0.266515
\(496\) −20.9975 −0.942816
\(497\) −5.16489 −0.231677
\(498\) −18.4720 −0.827751
\(499\) −6.48723 −0.290408 −0.145204 0.989402i \(-0.546384\pi\)
−0.145204 + 0.989402i \(0.546384\pi\)
\(500\) −9.31904 −0.416760
\(501\) 6.35416 0.283883
\(502\) 6.08822 0.271731
\(503\) −3.72853 −0.166247 −0.0831236 0.996539i \(-0.526490\pi\)
−0.0831236 + 0.996539i \(0.526490\pi\)
\(504\) −36.7775 −1.63820
\(505\) 0.786903 0.0350167
\(506\) 7.91803 0.351999
\(507\) 40.1189 1.78174
\(508\) −9.78123 −0.433972
\(509\) 11.0316 0.488965 0.244483 0.969654i \(-0.421382\pi\)
0.244483 + 0.969654i \(0.421382\pi\)
\(510\) −10.4501 −0.462740
\(511\) 3.22833 0.142813
\(512\) 21.6314 0.955983
\(513\) 64.7232 2.85760
\(514\) −31.5947 −1.39358
\(515\) −3.43294 −0.151273
\(516\) 58.8906 2.59251
\(517\) −23.0550 −1.01396
\(518\) 5.20618 0.228746
\(519\) −62.6735 −2.75106
\(520\) 0.513079 0.0225000
\(521\) −22.2941 −0.976724 −0.488362 0.872641i \(-0.662405\pi\)
−0.488362 + 0.872641i \(0.662405\pi\)
\(522\) 29.8751 1.30760
\(523\) 18.8397 0.823801 0.411900 0.911229i \(-0.364865\pi\)
0.411900 + 0.911229i \(0.364865\pi\)
\(524\) −23.4450 −1.02420
\(525\) 21.1651 0.923720
\(526\) −25.5424 −1.11370
\(527\) 57.3706 2.49910
\(528\) 20.8122 0.905734
\(529\) −21.9973 −0.956404
\(530\) −5.74969 −0.249751
\(531\) 73.6507 3.19617
\(532\) −26.0354 −1.12878
\(533\) 3.88315 0.168198
\(534\) 84.9219 3.67493
\(535\) −1.34806 −0.0582819
\(536\) 22.0120 0.950776
\(537\) 73.0345 3.15167
\(538\) −7.20696 −0.310714
\(539\) 17.1240 0.737583
\(540\) −11.5734 −0.498042
\(541\) −36.4191 −1.56578 −0.782890 0.622160i \(-0.786255\pi\)
−0.782890 + 0.622160i \(0.786255\pi\)
\(542\) −46.8859 −2.01392
\(543\) 67.5146 2.89733
\(544\) −16.7595 −0.718558
\(545\) 1.57720 0.0675600
\(546\) −5.20230 −0.222638
\(547\) 30.7460 1.31460 0.657302 0.753627i \(-0.271698\pi\)
0.657302 + 0.753627i \(0.271698\pi\)
\(548\) −39.1949 −1.67432
\(549\) −59.6033 −2.54381
\(550\) −39.0123 −1.66349
\(551\) 9.53824 0.406343
\(552\) 12.3076 0.523848
\(553\) −6.83537 −0.290669
\(554\) −13.4618 −0.571936
\(555\) 1.30472 0.0553825
\(556\) 6.10619 0.258960
\(557\) 9.17074 0.388577 0.194288 0.980944i \(-0.437760\pi\)
0.194288 + 0.980944i \(0.437760\pi\)
\(558\) 173.790 7.35712
\(559\) 2.62048 0.110835
\(560\) 0.696457 0.0294307
\(561\) −56.8643 −2.40081
\(562\) 39.3908 1.66160
\(563\) 3.86804 0.163018 0.0815092 0.996673i \(-0.474026\pi\)
0.0815092 + 0.996673i \(0.474026\pi\)
\(564\) −79.4598 −3.34586
\(565\) −3.99494 −0.168068
\(566\) 27.8040 1.16869
\(567\) 24.6544 1.03539
\(568\) 14.7979 0.620907
\(569\) −11.7985 −0.494620 −0.247310 0.968936i \(-0.579547\pi\)
−0.247310 + 0.968936i \(0.579547\pi\)
\(570\) −10.1069 −0.423330
\(571\) 22.4402 0.939093 0.469547 0.882908i \(-0.344417\pi\)
0.469547 + 0.882908i \(0.344417\pi\)
\(572\) 6.19050 0.258838
\(573\) 79.3808 3.31618
\(574\) 24.6147 1.02740
\(575\) −4.94036 −0.206027
\(576\) −78.2362 −3.25984
\(577\) −21.5746 −0.898164 −0.449082 0.893490i \(-0.648249\pi\)
−0.449082 + 0.893490i \(0.648249\pi\)
\(578\) −29.5175 −1.22777
\(579\) −51.6020 −2.14451
\(580\) −1.70557 −0.0708201
\(581\) −3.36364 −0.139547
\(582\) 35.2028 1.45920
\(583\) −31.2869 −1.29577
\(584\) −9.24948 −0.382746
\(585\) −0.909371 −0.0375979
\(586\) 56.8297 2.34761
\(587\) −0.809854 −0.0334263 −0.0167131 0.999860i \(-0.505320\pi\)
−0.0167131 + 0.999860i \(0.505320\pi\)
\(588\) 59.0184 2.43388
\(589\) 55.4860 2.28626
\(590\) −6.51312 −0.268141
\(591\) −71.1430 −2.92643
\(592\) −3.19417 −0.131280
\(593\) 46.5243 1.91053 0.955263 0.295759i \(-0.0955726\pi\)
0.955263 + 0.295759i \(0.0955726\pi\)
\(594\) −97.5510 −4.00257
\(595\) −1.90290 −0.0780114
\(596\) 76.0307 3.11434
\(597\) −46.3948 −1.89881
\(598\) 1.21432 0.0496574
\(599\) −19.9992 −0.817144 −0.408572 0.912726i \(-0.633973\pi\)
−0.408572 + 0.912726i \(0.633973\pi\)
\(600\) −60.6401 −2.47562
\(601\) −37.0818 −1.51260 −0.756300 0.654225i \(-0.772995\pi\)
−0.756300 + 0.654225i \(0.772995\pi\)
\(602\) 16.6108 0.677008
\(603\) −39.0137 −1.58876
\(604\) −76.4630 −3.11124
\(605\) 0.0206745 0.000840539 0
\(606\) 22.8598 0.928615
\(607\) −9.56025 −0.388039 −0.194019 0.980998i \(-0.562152\pi\)
−0.194019 + 0.980998i \(0.562152\pi\)
\(608\) −16.2090 −0.657361
\(609\) 7.79934 0.316045
\(610\) 5.27088 0.213412
\(611\) −3.53576 −0.143041
\(612\) −136.700 −5.52575
\(613\) −25.4099 −1.02630 −0.513148 0.858300i \(-0.671521\pi\)
−0.513148 + 0.858300i \(0.671521\pi\)
\(614\) 40.8964 1.65044
\(615\) 6.16872 0.248747
\(616\) 17.6975 0.713054
\(617\) 9.91528 0.399174 0.199587 0.979880i \(-0.436040\pi\)
0.199587 + 0.979880i \(0.436040\pi\)
\(618\) −99.7280 −4.01165
\(619\) −13.6350 −0.548036 −0.274018 0.961725i \(-0.588353\pi\)
−0.274018 + 0.961725i \(0.588353\pi\)
\(620\) −9.92169 −0.398465
\(621\) −12.3535 −0.495728
\(622\) 26.8623 1.07708
\(623\) 15.4637 0.619541
\(624\) 3.19180 0.127774
\(625\) 24.0097 0.960387
\(626\) −45.0312 −1.79981
\(627\) −54.9963 −2.19634
\(628\) 63.5578 2.53623
\(629\) 8.72730 0.347980
\(630\) −5.76437 −0.229658
\(631\) −2.40724 −0.0958307 −0.0479154 0.998851i \(-0.515258\pi\)
−0.0479154 + 0.998851i \(0.515258\pi\)
\(632\) 19.5840 0.779010
\(633\) 27.4110 1.08949
\(634\) −26.4791 −1.05162
\(635\) −0.691416 −0.0274380
\(636\) −107.831 −4.27578
\(637\) 2.62617 0.104053
\(638\) −14.3760 −0.569153
\(639\) −26.2275 −1.03755
\(640\) 5.32741 0.210585
\(641\) 38.2740 1.51173 0.755866 0.654726i \(-0.227216\pi\)
0.755866 + 0.654726i \(0.227216\pi\)
\(642\) −39.1617 −1.54559
\(643\) 8.77021 0.345863 0.172932 0.984934i \(-0.444676\pi\)
0.172932 + 0.984934i \(0.444676\pi\)
\(644\) 4.96928 0.195817
\(645\) 4.16286 0.163912
\(646\) −67.6048 −2.65987
\(647\) 16.0783 0.632105 0.316052 0.948742i \(-0.397642\pi\)
0.316052 + 0.948742i \(0.397642\pi\)
\(648\) −70.6373 −2.77489
\(649\) −35.4411 −1.39118
\(650\) −5.98299 −0.234672
\(651\) 45.3705 1.77821
\(652\) 24.2884 0.951208
\(653\) 27.1359 1.06191 0.530954 0.847400i \(-0.321834\pi\)
0.530954 + 0.847400i \(0.321834\pi\)
\(654\) 45.8183 1.79164
\(655\) −1.65728 −0.0647552
\(656\) −15.1020 −0.589634
\(657\) 16.3936 0.639575
\(658\) −22.4126 −0.873736
\(659\) 17.3085 0.674244 0.337122 0.941461i \(-0.390546\pi\)
0.337122 + 0.941461i \(0.390546\pi\)
\(660\) 9.83413 0.382793
\(661\) −34.5305 −1.34308 −0.671541 0.740967i \(-0.734367\pi\)
−0.671541 + 0.740967i \(0.734367\pi\)
\(662\) −47.2900 −1.83798
\(663\) −8.72081 −0.338688
\(664\) 9.63715 0.373994
\(665\) −1.84039 −0.0713674
\(666\) 26.4372 1.02442
\(667\) −1.82052 −0.0704910
\(668\) −7.35048 −0.284399
\(669\) 13.6361 0.527202
\(670\) 3.45009 0.133288
\(671\) 28.6814 1.10723
\(672\) −13.2540 −0.511283
\(673\) −34.7086 −1.33792 −0.668958 0.743300i \(-0.733260\pi\)
−0.668958 + 0.743300i \(0.733260\pi\)
\(674\) 32.7008 1.25959
\(675\) 60.8658 2.34273
\(676\) −46.4094 −1.78498
\(677\) −3.02595 −0.116297 −0.0581483 0.998308i \(-0.518520\pi\)
−0.0581483 + 0.998308i \(0.518520\pi\)
\(678\) −116.054 −4.45704
\(679\) 6.41021 0.246001
\(680\) 5.45200 0.209075
\(681\) −43.5165 −1.66756
\(682\) −83.6286 −3.20231
\(683\) −8.49337 −0.324990 −0.162495 0.986709i \(-0.551954\pi\)
−0.162495 + 0.986709i \(0.551954\pi\)
\(684\) −132.209 −5.05514
\(685\) −2.77061 −0.105860
\(686\) 39.2986 1.50043
\(687\) −29.9648 −1.14323
\(688\) −10.1913 −0.388541
\(689\) −4.79821 −0.182797
\(690\) 1.92905 0.0734379
\(691\) 46.5144 1.76949 0.884745 0.466075i \(-0.154332\pi\)
0.884745 + 0.466075i \(0.154332\pi\)
\(692\) 72.5006 2.75606
\(693\) −31.3667 −1.19152
\(694\) 50.7037 1.92469
\(695\) 0.431635 0.0163728
\(696\) −22.3459 −0.847019
\(697\) 41.2626 1.56293
\(698\) −32.0498 −1.21310
\(699\) 70.4173 2.66343
\(700\) −24.4837 −0.925398
\(701\) −6.76295 −0.255433 −0.127716 0.991811i \(-0.540765\pi\)
−0.127716 + 0.991811i \(0.540765\pi\)
\(702\) −14.9606 −0.564651
\(703\) 8.44062 0.318344
\(704\) 37.6477 1.41890
\(705\) −5.61685 −0.211543
\(706\) −73.5130 −2.76670
\(707\) 4.16262 0.156551
\(708\) −122.149 −4.59063
\(709\) −6.48783 −0.243655 −0.121828 0.992551i \(-0.538876\pi\)
−0.121828 + 0.992551i \(0.538876\pi\)
\(710\) 2.31937 0.0870444
\(711\) −34.7103 −1.30174
\(712\) −44.3051 −1.66041
\(713\) −10.5904 −0.396613
\(714\) −55.2799 −2.06880
\(715\) 0.437594 0.0163651
\(716\) −84.4862 −3.15740
\(717\) 30.8365 1.15161
\(718\) 49.2022 1.83621
\(719\) −11.7708 −0.438978 −0.219489 0.975615i \(-0.570439\pi\)
−0.219489 + 0.975615i \(0.570439\pi\)
\(720\) 3.53664 0.131803
\(721\) −18.1598 −0.676307
\(722\) −20.2495 −0.753610
\(723\) −56.3889 −2.09712
\(724\) −78.1008 −2.90260
\(725\) 8.96977 0.333129
\(726\) 0.600602 0.0222904
\(727\) 30.5804 1.13416 0.567082 0.823661i \(-0.308072\pi\)
0.567082 + 0.823661i \(0.308072\pi\)
\(728\) 2.71412 0.100592
\(729\) 8.64330 0.320122
\(730\) −1.44973 −0.0536569
\(731\) 27.8454 1.02990
\(732\) 98.8513 3.65365
\(733\) −5.36073 −0.198003 −0.0990015 0.995087i \(-0.531565\pi\)
−0.0990015 + 0.995087i \(0.531565\pi\)
\(734\) −16.7204 −0.617160
\(735\) 4.17189 0.153883
\(736\) 3.09374 0.114037
\(737\) 18.7736 0.691534
\(738\) 124.995 4.60112
\(739\) 15.7047 0.577708 0.288854 0.957373i \(-0.406726\pi\)
0.288854 + 0.957373i \(0.406726\pi\)
\(740\) −1.50930 −0.0554831
\(741\) −8.43434 −0.309843
\(742\) −30.4152 −1.11658
\(743\) −10.8041 −0.396365 −0.198183 0.980165i \(-0.563504\pi\)
−0.198183 + 0.980165i \(0.563504\pi\)
\(744\) −129.991 −4.76570
\(745\) 5.37446 0.196905
\(746\) −42.5533 −1.55799
\(747\) −17.0807 −0.624950
\(748\) 65.7805 2.40517
\(749\) −7.13109 −0.260564
\(750\) −19.1367 −0.698775
\(751\) −37.4901 −1.36803 −0.684017 0.729466i \(-0.739769\pi\)
−0.684017 + 0.729466i \(0.739769\pi\)
\(752\) 13.7509 0.501445
\(753\) 8.07115 0.294129
\(754\) −2.20474 −0.0802918
\(755\) −5.40502 −0.196709
\(756\) −61.2221 −2.22663
\(757\) 6.88177 0.250122 0.125061 0.992149i \(-0.460087\pi\)
0.125061 + 0.992149i \(0.460087\pi\)
\(758\) 42.2625 1.53504
\(759\) 10.4969 0.381014
\(760\) 5.27291 0.191268
\(761\) 13.5102 0.489743 0.244872 0.969555i \(-0.421254\pi\)
0.244872 + 0.969555i \(0.421254\pi\)
\(762\) −20.0859 −0.727634
\(763\) 8.34321 0.302044
\(764\) −91.8277 −3.32221
\(765\) −9.66302 −0.349367
\(766\) 59.0499 2.13356
\(767\) −5.43531 −0.196258
\(768\) 83.5283 3.01407
\(769\) 8.40472 0.303082 0.151541 0.988451i \(-0.451576\pi\)
0.151541 + 0.988451i \(0.451576\pi\)
\(770\) 2.77384 0.0999624
\(771\) −41.8850 −1.50845
\(772\) 59.6931 2.14840
\(773\) 3.08327 0.110898 0.0554488 0.998462i \(-0.482341\pi\)
0.0554488 + 0.998462i \(0.482341\pi\)
\(774\) 84.3506 3.03192
\(775\) 52.1791 1.87433
\(776\) −18.3659 −0.659297
\(777\) 6.90183 0.247602
\(778\) −38.0287 −1.36340
\(779\) 39.9071 1.42982
\(780\) 1.50818 0.0540015
\(781\) 12.6208 0.451608
\(782\) 12.9035 0.461426
\(783\) 22.4291 0.801550
\(784\) −10.2135 −0.364766
\(785\) 4.49278 0.160354
\(786\) −48.1445 −1.71726
\(787\) −32.5837 −1.16149 −0.580743 0.814087i \(-0.697238\pi\)
−0.580743 + 0.814087i \(0.697238\pi\)
\(788\) 82.2982 2.93175
\(789\) −33.8615 −1.20550
\(790\) 3.06952 0.109209
\(791\) −21.1327 −0.751394
\(792\) 89.8688 3.19335
\(793\) 4.39863 0.156200
\(794\) 46.5012 1.65026
\(795\) −7.62237 −0.270338
\(796\) 53.6694 1.90226
\(797\) −26.3308 −0.932684 −0.466342 0.884604i \(-0.654428\pi\)
−0.466342 + 0.884604i \(0.654428\pi\)
\(798\) −53.4640 −1.89260
\(799\) −37.5711 −1.32917
\(800\) −15.2429 −0.538919
\(801\) 78.5255 2.77456
\(802\) 76.9057 2.71563
\(803\) −7.88868 −0.278386
\(804\) 64.7037 2.28192
\(805\) 0.351268 0.0123806
\(806\) −12.8254 −0.451757
\(807\) −9.55426 −0.336326
\(808\) −11.9263 −0.419566
\(809\) 44.8063 1.57531 0.787654 0.616118i \(-0.211296\pi\)
0.787654 + 0.616118i \(0.211296\pi\)
\(810\) −11.0714 −0.389010
\(811\) 22.9713 0.806631 0.403316 0.915061i \(-0.367858\pi\)
0.403316 + 0.915061i \(0.367858\pi\)
\(812\) −9.02227 −0.316620
\(813\) −62.1566 −2.17993
\(814\) −12.7217 −0.445896
\(815\) 1.71690 0.0601404
\(816\) 33.9162 1.18730
\(817\) 26.9307 0.942185
\(818\) −91.7889 −3.20932
\(819\) −4.81046 −0.168091
\(820\) −7.13596 −0.249199
\(821\) 36.3150 1.26740 0.633702 0.773578i \(-0.281535\pi\)
0.633702 + 0.773578i \(0.281535\pi\)
\(822\) −80.4871 −2.80731
\(823\) −0.892369 −0.0311060 −0.0155530 0.999879i \(-0.504951\pi\)
−0.0155530 + 0.999879i \(0.504951\pi\)
\(824\) 52.0297 1.81254
\(825\) −51.7186 −1.80061
\(826\) −34.4536 −1.19879
\(827\) 8.96114 0.311609 0.155805 0.987788i \(-0.450203\pi\)
0.155805 + 0.987788i \(0.450203\pi\)
\(828\) 25.2342 0.876950
\(829\) −47.4898 −1.64939 −0.824695 0.565578i \(-0.808653\pi\)
−0.824695 + 0.565578i \(0.808653\pi\)
\(830\) 1.51049 0.0524299
\(831\) −17.8463 −0.619081
\(832\) 5.77371 0.200168
\(833\) 27.9058 0.966878
\(834\) 12.5391 0.434194
\(835\) −0.519591 −0.0179812
\(836\) 63.6197 2.20033
\(837\) 130.475 4.50987
\(838\) −52.7922 −1.82367
\(839\) −28.1043 −0.970267 −0.485134 0.874440i \(-0.661229\pi\)
−0.485134 + 0.874440i \(0.661229\pi\)
\(840\) 4.31162 0.148765
\(841\) −25.6946 −0.886022
\(842\) 23.5094 0.810186
\(843\) 52.2204 1.79857
\(844\) −31.7091 −1.09147
\(845\) −3.28059 −0.112856
\(846\) −113.812 −3.91295
\(847\) 0.109366 0.00375785
\(848\) 18.6608 0.640813
\(849\) 36.8597 1.26502
\(850\) −63.5756 −2.18062
\(851\) −1.61103 −0.0552253
\(852\) 43.4980 1.49022
\(853\) −20.6354 −0.706542 −0.353271 0.935521i \(-0.614931\pi\)
−0.353271 + 0.935521i \(0.614931\pi\)
\(854\) 27.8823 0.954112
\(855\) −9.34560 −0.319613
\(856\) 20.4313 0.698327
\(857\) −32.7456 −1.11857 −0.559283 0.828976i \(-0.688924\pi\)
−0.559283 + 0.828976i \(0.688924\pi\)
\(858\) 12.7122 0.433989
\(859\) 42.0035 1.43314 0.716571 0.697514i \(-0.245710\pi\)
0.716571 + 0.697514i \(0.245710\pi\)
\(860\) −4.81559 −0.164210
\(861\) 32.6317 1.11209
\(862\) −16.7089 −0.569108
\(863\) −54.9388 −1.87014 −0.935070 0.354463i \(-0.884664\pi\)
−0.935070 + 0.354463i \(0.884664\pi\)
\(864\) −38.1153 −1.29671
\(865\) 5.12492 0.174253
\(866\) −1.04412 −0.0354808
\(867\) −39.1314 −1.32897
\(868\) −52.4845 −1.78144
\(869\) 16.7028 0.566603
\(870\) −3.50241 −0.118743
\(871\) 2.87915 0.0975564
\(872\) −23.9041 −0.809496
\(873\) 32.5513 1.10170
\(874\) 12.4796 0.422128
\(875\) −3.48468 −0.117804
\(876\) −27.1886 −0.918616
\(877\) −39.9192 −1.34798 −0.673988 0.738742i \(-0.735420\pi\)
−0.673988 + 0.738742i \(0.735420\pi\)
\(878\) −49.1637 −1.65920
\(879\) 75.3391 2.54113
\(880\) −1.70185 −0.0573694
\(881\) 58.6066 1.97451 0.987253 0.159157i \(-0.0508775\pi\)
0.987253 + 0.159157i \(0.0508775\pi\)
\(882\) 84.5337 2.84640
\(883\) 16.1178 0.542408 0.271204 0.962522i \(-0.412578\pi\)
0.271204 + 0.962522i \(0.412578\pi\)
\(884\) 10.0882 0.339304
\(885\) −8.63445 −0.290244
\(886\) 31.0914 1.04453
\(887\) 14.0681 0.472361 0.236181 0.971709i \(-0.424104\pi\)
0.236181 + 0.971709i \(0.424104\pi\)
\(888\) −19.7744 −0.663586
\(889\) −3.65750 −0.122669
\(890\) −6.94422 −0.232771
\(891\) −60.2450 −2.01828
\(892\) −15.7742 −0.528160
\(893\) −36.3369 −1.21597
\(894\) 156.130 5.22176
\(895\) −5.97216 −0.199627
\(896\) 28.1814 0.941473
\(897\) 1.60983 0.0537506
\(898\) 92.0483 3.07169
\(899\) 19.2280 0.641290
\(900\) −124.330 −4.14432
\(901\) −50.9860 −1.69859
\(902\) −60.1481 −2.00271
\(903\) 22.0210 0.732813
\(904\) 60.5474 2.01378
\(905\) −5.52079 −0.183517
\(906\) −157.018 −5.21656
\(907\) −9.66339 −0.320868 −0.160434 0.987047i \(-0.551289\pi\)
−0.160434 + 0.987047i \(0.551289\pi\)
\(908\) 50.3399 1.67059
\(909\) 21.1380 0.701102
\(910\) 0.425402 0.0141019
\(911\) 48.6316 1.61124 0.805618 0.592435i \(-0.201833\pi\)
0.805618 + 0.592435i \(0.201833\pi\)
\(912\) 32.8020 1.08618
\(913\) 8.21932 0.272020
\(914\) −32.1966 −1.06497
\(915\) 6.98760 0.231003
\(916\) 34.6632 1.14531
\(917\) −8.76680 −0.289505
\(918\) −158.972 −5.24686
\(919\) 23.5429 0.776607 0.388304 0.921532i \(-0.373061\pi\)
0.388304 + 0.921532i \(0.373061\pi\)
\(920\) −1.00642 −0.0331806
\(921\) 54.2163 1.78649
\(922\) −62.7206 −2.06559
\(923\) 1.93555 0.0637095
\(924\) 52.0213 1.71138
\(925\) 7.93756 0.260985
\(926\) −45.8138 −1.50553
\(927\) −92.2164 −3.02878
\(928\) −5.61703 −0.184388
\(929\) −41.6091 −1.36515 −0.682575 0.730816i \(-0.739140\pi\)
−0.682575 + 0.730816i \(0.739140\pi\)
\(930\) −20.3743 −0.668099
\(931\) 26.9891 0.884532
\(932\) −81.4586 −2.66827
\(933\) 35.6114 1.16586
\(934\) 75.8328 2.48132
\(935\) 4.64989 0.152068
\(936\) 13.7824 0.450493
\(937\) −5.84007 −0.190787 −0.0953934 0.995440i \(-0.530411\pi\)
−0.0953934 + 0.995440i \(0.530411\pi\)
\(938\) 18.2505 0.595901
\(939\) −59.6979 −1.94817
\(940\) 6.49757 0.211927
\(941\) 1.30421 0.0425161 0.0212580 0.999774i \(-0.493233\pi\)
0.0212580 + 0.999774i \(0.493233\pi\)
\(942\) 130.517 4.25246
\(943\) −7.61691 −0.248041
\(944\) 21.1385 0.687999
\(945\) −4.32767 −0.140779
\(946\) −40.5900 −1.31969
\(947\) −31.0763 −1.00985 −0.504923 0.863165i \(-0.668479\pi\)
−0.504923 + 0.863165i \(0.668479\pi\)
\(948\) 57.5666 1.86968
\(949\) −1.20982 −0.0392725
\(950\) −61.4872 −1.99491
\(951\) −35.1033 −1.13830
\(952\) 28.8404 0.934723
\(953\) 6.12360 0.198363 0.0991814 0.995069i \(-0.468378\pi\)
0.0991814 + 0.995069i \(0.468378\pi\)
\(954\) −154.450 −5.00049
\(955\) −6.49111 −0.210048
\(956\) −35.6716 −1.15370
\(957\) −19.0583 −0.616068
\(958\) −35.8222 −1.15736
\(959\) −14.6562 −0.473273
\(960\) 9.17203 0.296026
\(961\) 80.8536 2.60818
\(962\) −1.95103 −0.0629036
\(963\) −36.2120 −1.16692
\(964\) 65.2306 2.10094
\(965\) 4.21959 0.135833
\(966\) 10.2045 0.328323
\(967\) 15.5385 0.499685 0.249842 0.968287i \(-0.419621\pi\)
0.249842 + 0.968287i \(0.419621\pi\)
\(968\) −0.313344 −0.0100712
\(969\) −89.6236 −2.87913
\(970\) −2.87860 −0.0924263
\(971\) 36.0405 1.15660 0.578298 0.815826i \(-0.303717\pi\)
0.578298 + 0.815826i \(0.303717\pi\)
\(972\) −72.8080 −2.33532
\(973\) 2.28329 0.0731990
\(974\) 64.2055 2.05728
\(975\) −7.93166 −0.254016
\(976\) −17.1068 −0.547574
\(977\) −28.2358 −0.903342 −0.451671 0.892185i \(-0.649172\pi\)
−0.451671 + 0.892185i \(0.649172\pi\)
\(978\) 49.8765 1.59487
\(979\) −37.7869 −1.20767
\(980\) −4.82604 −0.154162
\(981\) 42.3672 1.35268
\(982\) −32.0613 −1.02312
\(983\) 0.807825 0.0257656 0.0128828 0.999917i \(-0.495899\pi\)
0.0128828 + 0.999917i \(0.495899\pi\)
\(984\) −93.4932 −2.98045
\(985\) 5.81749 0.185361
\(986\) −23.4276 −0.746088
\(987\) −29.7124 −0.945758
\(988\) 9.75683 0.310406
\(989\) −5.14015 −0.163447
\(990\) 14.0857 0.447673
\(991\) −34.8995 −1.10862 −0.554309 0.832311i \(-0.687017\pi\)
−0.554309 + 0.832311i \(0.687017\pi\)
\(992\) −32.6755 −1.03745
\(993\) −62.6923 −1.98948
\(994\) 12.2692 0.389155
\(995\) 3.79378 0.120271
\(996\) 28.3281 0.897610
\(997\) 36.3725 1.15193 0.575965 0.817474i \(-0.304626\pi\)
0.575965 + 0.817474i \(0.304626\pi\)
\(998\) 15.4104 0.487808
\(999\) 19.8480 0.627964
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.1.16 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.16 174 1.1 even 1 trivial