Properties

Label 4010.2.a.i.1.1
Level 4010
Weight 2
Character 4010.1
Self dual yes
Analytic conductor 32.020
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.08731\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.13000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.13000 q^{6} +2.49851 q^{7} -1.00000 q^{8} +6.79692 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.13000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.13000 q^{6} +2.49851 q^{7} -1.00000 q^{8} +6.79692 q^{9} -1.00000 q^{10} -1.60279 q^{11} -3.13000 q^{12} -0.554325 q^{13} -2.49851 q^{14} -3.13000 q^{15} +1.00000 q^{16} +5.26951 q^{17} -6.79692 q^{18} -2.32369 q^{19} +1.00000 q^{20} -7.82035 q^{21} +1.60279 q^{22} +4.26393 q^{23} +3.13000 q^{24} +1.00000 q^{25} +0.554325 q^{26} -11.8844 q^{27} +2.49851 q^{28} -2.40114 q^{29} +3.13000 q^{30} -10.2745 q^{31} -1.00000 q^{32} +5.01675 q^{33} -5.26951 q^{34} +2.49851 q^{35} +6.79692 q^{36} -0.359181 q^{37} +2.32369 q^{38} +1.73504 q^{39} -1.00000 q^{40} -2.50682 q^{41} +7.82035 q^{42} +1.01036 q^{43} -1.60279 q^{44} +6.79692 q^{45} -4.26393 q^{46} -6.02260 q^{47} -3.13000 q^{48} -0.757432 q^{49} -1.00000 q^{50} -16.4936 q^{51} -0.554325 q^{52} -11.4646 q^{53} +11.8844 q^{54} -1.60279 q^{55} -2.49851 q^{56} +7.27317 q^{57} +2.40114 q^{58} -5.94415 q^{59} -3.13000 q^{60} +0.692162 q^{61} +10.2745 q^{62} +16.9822 q^{63} +1.00000 q^{64} -0.554325 q^{65} -5.01675 q^{66} -3.85892 q^{67} +5.26951 q^{68} -13.3461 q^{69} -2.49851 q^{70} -6.49192 q^{71} -6.79692 q^{72} +5.75377 q^{73} +0.359181 q^{74} -3.13000 q^{75} -2.32369 q^{76} -4.00460 q^{77} -1.73504 q^{78} +1.29382 q^{79} +1.00000 q^{80} +16.8073 q^{81} +2.50682 q^{82} +2.60037 q^{83} -7.82035 q^{84} +5.26951 q^{85} -1.01036 q^{86} +7.51558 q^{87} +1.60279 q^{88} +9.62868 q^{89} -6.79692 q^{90} -1.38499 q^{91} +4.26393 q^{92} +32.1593 q^{93} +6.02260 q^{94} -2.32369 q^{95} +3.13000 q^{96} +7.34064 q^{97} +0.757432 q^{98} -10.8941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.13000 −1.80711 −0.903554 0.428474i \(-0.859051\pi\)
−0.903554 + 0.428474i \(0.859051\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 3.13000 1.27782
\(7\) 2.49851 0.944349 0.472175 0.881505i \(-0.343469\pi\)
0.472175 + 0.881505i \(0.343469\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.79692 2.26564
\(10\) −1.00000 −0.316228
\(11\) −1.60279 −0.483260 −0.241630 0.970368i \(-0.577682\pi\)
−0.241630 + 0.970368i \(0.577682\pi\)
\(12\) −3.13000 −0.903554
\(13\) −0.554325 −0.153742 −0.0768711 0.997041i \(-0.524493\pi\)
−0.0768711 + 0.997041i \(0.524493\pi\)
\(14\) −2.49851 −0.667756
\(15\) −3.13000 −0.808163
\(16\) 1.00000 0.250000
\(17\) 5.26951 1.27804 0.639022 0.769188i \(-0.279339\pi\)
0.639022 + 0.769188i \(0.279339\pi\)
\(18\) −6.79692 −1.60205
\(19\) −2.32369 −0.533092 −0.266546 0.963822i \(-0.585882\pi\)
−0.266546 + 0.963822i \(0.585882\pi\)
\(20\) 1.00000 0.223607
\(21\) −7.82035 −1.70654
\(22\) 1.60279 0.341717
\(23\) 4.26393 0.889092 0.444546 0.895756i \(-0.353365\pi\)
0.444546 + 0.895756i \(0.353365\pi\)
\(24\) 3.13000 0.638909
\(25\) 1.00000 0.200000
\(26\) 0.554325 0.108712
\(27\) −11.8844 −2.28715
\(28\) 2.49851 0.472175
\(29\) −2.40114 −0.445881 −0.222940 0.974832i \(-0.571566\pi\)
−0.222940 + 0.974832i \(0.571566\pi\)
\(30\) 3.13000 0.571458
\(31\) −10.2745 −1.84536 −0.922680 0.385567i \(-0.874006\pi\)
−0.922680 + 0.385567i \(0.874006\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.01675 0.873304
\(34\) −5.26951 −0.903714
\(35\) 2.49851 0.422326
\(36\) 6.79692 1.13282
\(37\) −0.359181 −0.0590490 −0.0295245 0.999564i \(-0.509399\pi\)
−0.0295245 + 0.999564i \(0.509399\pi\)
\(38\) 2.32369 0.376953
\(39\) 1.73504 0.277829
\(40\) −1.00000 −0.158114
\(41\) −2.50682 −0.391500 −0.195750 0.980654i \(-0.562714\pi\)
−0.195750 + 0.980654i \(0.562714\pi\)
\(42\) 7.82035 1.20671
\(43\) 1.01036 0.154078 0.0770391 0.997028i \(-0.475453\pi\)
0.0770391 + 0.997028i \(0.475453\pi\)
\(44\) −1.60279 −0.241630
\(45\) 6.79692 1.01322
\(46\) −4.26393 −0.628683
\(47\) −6.02260 −0.878486 −0.439243 0.898368i \(-0.644753\pi\)
−0.439243 + 0.898368i \(0.644753\pi\)
\(48\) −3.13000 −0.451777
\(49\) −0.757432 −0.108205
\(50\) −1.00000 −0.141421
\(51\) −16.4936 −2.30956
\(52\) −0.554325 −0.0768711
\(53\) −11.4646 −1.57478 −0.787390 0.616455i \(-0.788568\pi\)
−0.787390 + 0.616455i \(0.788568\pi\)
\(54\) 11.8844 1.61726
\(55\) −1.60279 −0.216121
\(56\) −2.49851 −0.333878
\(57\) 7.27317 0.963354
\(58\) 2.40114 0.315285
\(59\) −5.94415 −0.773862 −0.386931 0.922109i \(-0.626465\pi\)
−0.386931 + 0.922109i \(0.626465\pi\)
\(60\) −3.13000 −0.404082
\(61\) 0.692162 0.0886223 0.0443111 0.999018i \(-0.485891\pi\)
0.0443111 + 0.999018i \(0.485891\pi\)
\(62\) 10.2745 1.30487
\(63\) 16.9822 2.13955
\(64\) 1.00000 0.125000
\(65\) −0.554325 −0.0687556
\(66\) −5.01675 −0.617519
\(67\) −3.85892 −0.471442 −0.235721 0.971821i \(-0.575745\pi\)
−0.235721 + 0.971821i \(0.575745\pi\)
\(68\) 5.26951 0.639022
\(69\) −13.3461 −1.60669
\(70\) −2.49851 −0.298629
\(71\) −6.49192 −0.770449 −0.385224 0.922823i \(-0.625876\pi\)
−0.385224 + 0.922823i \(0.625876\pi\)
\(72\) −6.79692 −0.801025
\(73\) 5.75377 0.673428 0.336714 0.941607i \(-0.390685\pi\)
0.336714 + 0.941607i \(0.390685\pi\)
\(74\) 0.359181 0.0417540
\(75\) −3.13000 −0.361422
\(76\) −2.32369 −0.266546
\(77\) −4.00460 −0.456367
\(78\) −1.73504 −0.196455
\(79\) 1.29382 0.145566 0.0727829 0.997348i \(-0.476812\pi\)
0.0727829 + 0.997348i \(0.476812\pi\)
\(80\) 1.00000 0.111803
\(81\) 16.8073 1.86748
\(82\) 2.50682 0.276832
\(83\) 2.60037 0.285428 0.142714 0.989764i \(-0.454417\pi\)
0.142714 + 0.989764i \(0.454417\pi\)
\(84\) −7.82035 −0.853271
\(85\) 5.26951 0.571559
\(86\) −1.01036 −0.108950
\(87\) 7.51558 0.805755
\(88\) 1.60279 0.170858
\(89\) 9.62868 1.02064 0.510319 0.859985i \(-0.329527\pi\)
0.510319 + 0.859985i \(0.329527\pi\)
\(90\) −6.79692 −0.716458
\(91\) −1.38499 −0.145186
\(92\) 4.26393 0.444546
\(93\) 32.1593 3.33476
\(94\) 6.02260 0.621183
\(95\) −2.32369 −0.238406
\(96\) 3.13000 0.319455
\(97\) 7.34064 0.745329 0.372664 0.927966i \(-0.378444\pi\)
0.372664 + 0.927966i \(0.378444\pi\)
\(98\) 0.757432 0.0765122
\(99\) −10.8941 −1.09489
\(100\) 1.00000 0.100000
\(101\) −0.841840 −0.0837662 −0.0418831 0.999123i \(-0.513336\pi\)
−0.0418831 + 0.999123i \(0.513336\pi\)
\(102\) 16.4936 1.63311
\(103\) 13.3474 1.31516 0.657580 0.753385i \(-0.271580\pi\)
0.657580 + 0.753385i \(0.271580\pi\)
\(104\) 0.554325 0.0543561
\(105\) −7.82035 −0.763188
\(106\) 11.4646 1.11354
\(107\) 2.35230 0.227405 0.113703 0.993515i \(-0.463729\pi\)
0.113703 + 0.993515i \(0.463729\pi\)
\(108\) −11.8844 −1.14357
\(109\) −1.08799 −0.104210 −0.0521052 0.998642i \(-0.516593\pi\)
−0.0521052 + 0.998642i \(0.516593\pi\)
\(110\) 1.60279 0.152820
\(111\) 1.12424 0.106708
\(112\) 2.49851 0.236087
\(113\) 16.3637 1.53937 0.769684 0.638426i \(-0.220414\pi\)
0.769684 + 0.638426i \(0.220414\pi\)
\(114\) −7.27317 −0.681194
\(115\) 4.26393 0.397614
\(116\) −2.40114 −0.222940
\(117\) −3.76770 −0.348324
\(118\) 5.94415 0.547203
\(119\) 13.1659 1.20692
\(120\) 3.13000 0.285729
\(121\) −8.43105 −0.766459
\(122\) −0.692162 −0.0626654
\(123\) 7.84637 0.707483
\(124\) −10.2745 −0.922680
\(125\) 1.00000 0.0894427
\(126\) −16.9822 −1.51289
\(127\) −15.2216 −1.35070 −0.675351 0.737497i \(-0.736008\pi\)
−0.675351 + 0.737497i \(0.736008\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.16243 −0.278436
\(130\) 0.554325 0.0486176
\(131\) −1.48407 −0.129664 −0.0648319 0.997896i \(-0.520651\pi\)
−0.0648319 + 0.997896i \(0.520651\pi\)
\(132\) 5.01675 0.436652
\(133\) −5.80578 −0.503425
\(134\) 3.85892 0.333360
\(135\) −11.8844 −1.02284
\(136\) −5.26951 −0.451857
\(137\) −14.8058 −1.26495 −0.632475 0.774581i \(-0.717961\pi\)
−0.632475 + 0.774581i \(0.717961\pi\)
\(138\) 13.3461 1.13610
\(139\) −8.84411 −0.750148 −0.375074 0.926995i \(-0.622383\pi\)
−0.375074 + 0.926995i \(0.622383\pi\)
\(140\) 2.49851 0.211163
\(141\) 18.8507 1.58752
\(142\) 6.49192 0.544790
\(143\) 0.888469 0.0742975
\(144\) 6.79692 0.566410
\(145\) −2.40114 −0.199404
\(146\) −5.75377 −0.476185
\(147\) 2.37077 0.195537
\(148\) −0.359181 −0.0295245
\(149\) 2.76125 0.226210 0.113105 0.993583i \(-0.463920\pi\)
0.113105 + 0.993583i \(0.463920\pi\)
\(150\) 3.13000 0.255564
\(151\) 10.9291 0.889395 0.444698 0.895681i \(-0.353311\pi\)
0.444698 + 0.895681i \(0.353311\pi\)
\(152\) 2.32369 0.188476
\(153\) 35.8164 2.89559
\(154\) 4.00460 0.322700
\(155\) −10.2745 −0.825270
\(156\) 1.73504 0.138914
\(157\) 8.69993 0.694330 0.347165 0.937804i \(-0.387144\pi\)
0.347165 + 0.937804i \(0.387144\pi\)
\(158\) −1.29382 −0.102931
\(159\) 35.8841 2.84580
\(160\) −1.00000 −0.0790569
\(161\) 10.6535 0.839613
\(162\) −16.8073 −1.32051
\(163\) −13.4903 −1.05664 −0.528321 0.849045i \(-0.677178\pi\)
−0.528321 + 0.849045i \(0.677178\pi\)
\(164\) −2.50682 −0.195750
\(165\) 5.01675 0.390553
\(166\) −2.60037 −0.201828
\(167\) −5.17486 −0.400443 −0.200221 0.979751i \(-0.564166\pi\)
−0.200221 + 0.979751i \(0.564166\pi\)
\(168\) 7.82035 0.603353
\(169\) −12.6927 −0.976363
\(170\) −5.26951 −0.404153
\(171\) −15.7940 −1.20779
\(172\) 1.01036 0.0770391
\(173\) 16.3903 1.24613 0.623064 0.782171i \(-0.285888\pi\)
0.623064 + 0.782171i \(0.285888\pi\)
\(174\) −7.51558 −0.569755
\(175\) 2.49851 0.188870
\(176\) −1.60279 −0.120815
\(177\) 18.6052 1.39845
\(178\) −9.62868 −0.721700
\(179\) 7.00317 0.523442 0.261721 0.965144i \(-0.415710\pi\)
0.261721 + 0.965144i \(0.415710\pi\)
\(180\) 6.79692 0.506612
\(181\) −15.4015 −1.14479 −0.572393 0.819980i \(-0.693985\pi\)
−0.572393 + 0.819980i \(0.693985\pi\)
\(182\) 1.38499 0.102662
\(183\) −2.16647 −0.160150
\(184\) −4.26393 −0.314341
\(185\) −0.359181 −0.0264075
\(186\) −32.1593 −2.35803
\(187\) −8.44594 −0.617628
\(188\) −6.02260 −0.439243
\(189\) −29.6932 −2.15987
\(190\) 2.32369 0.168578
\(191\) −15.8806 −1.14908 −0.574541 0.818476i \(-0.694819\pi\)
−0.574541 + 0.818476i \(0.694819\pi\)
\(192\) −3.13000 −0.225889
\(193\) −2.11003 −0.151883 −0.0759416 0.997112i \(-0.524196\pi\)
−0.0759416 + 0.997112i \(0.524196\pi\)
\(194\) −7.34064 −0.527027
\(195\) 1.73504 0.124249
\(196\) −0.757432 −0.0541023
\(197\) 9.59731 0.683780 0.341890 0.939740i \(-0.388933\pi\)
0.341890 + 0.939740i \(0.388933\pi\)
\(198\) 10.8941 0.774207
\(199\) −8.29416 −0.587957 −0.293979 0.955812i \(-0.594979\pi\)
−0.293979 + 0.955812i \(0.594979\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 12.0784 0.851946
\(202\) 0.841840 0.0592316
\(203\) −5.99928 −0.421067
\(204\) −16.4936 −1.15478
\(205\) −2.50682 −0.175084
\(206\) −13.3474 −0.929958
\(207\) 28.9816 2.01436
\(208\) −0.554325 −0.0384356
\(209\) 3.72440 0.257622
\(210\) 7.82035 0.539656
\(211\) −24.5118 −1.68746 −0.843729 0.536769i \(-0.819645\pi\)
−0.843729 + 0.536769i \(0.819645\pi\)
\(212\) −11.4646 −0.787390
\(213\) 20.3197 1.39228
\(214\) −2.35230 −0.160800
\(215\) 1.01036 0.0689059
\(216\) 11.8844 0.808629
\(217\) −25.6710 −1.74266
\(218\) 1.08799 0.0736878
\(219\) −18.0093 −1.21696
\(220\) −1.60279 −0.108060
\(221\) −2.92102 −0.196489
\(222\) −1.12424 −0.0754539
\(223\) 12.8558 0.860890 0.430445 0.902617i \(-0.358357\pi\)
0.430445 + 0.902617i \(0.358357\pi\)
\(224\) −2.49851 −0.166939
\(225\) 6.79692 0.453128
\(226\) −16.3637 −1.08850
\(227\) 4.85991 0.322564 0.161282 0.986908i \(-0.448437\pi\)
0.161282 + 0.986908i \(0.448437\pi\)
\(228\) 7.27317 0.481677
\(229\) 1.31204 0.0867017 0.0433509 0.999060i \(-0.486197\pi\)
0.0433509 + 0.999060i \(0.486197\pi\)
\(230\) −4.26393 −0.281156
\(231\) 12.5344 0.824704
\(232\) 2.40114 0.157643
\(233\) 11.2852 0.739317 0.369658 0.929168i \(-0.379475\pi\)
0.369658 + 0.929168i \(0.379475\pi\)
\(234\) 3.76770 0.246303
\(235\) −6.02260 −0.392871
\(236\) −5.94415 −0.386931
\(237\) −4.04965 −0.263053
\(238\) −13.1659 −0.853422
\(239\) 3.82979 0.247729 0.123864 0.992299i \(-0.460471\pi\)
0.123864 + 0.992299i \(0.460471\pi\)
\(240\) −3.13000 −0.202041
\(241\) −14.3377 −0.923570 −0.461785 0.886992i \(-0.652791\pi\)
−0.461785 + 0.886992i \(0.652791\pi\)
\(242\) 8.43105 0.541969
\(243\) −16.9539 −1.08760
\(244\) 0.692162 0.0443111
\(245\) −0.757432 −0.0483906
\(246\) −7.84637 −0.500266
\(247\) 1.28808 0.0819587
\(248\) 10.2745 0.652433
\(249\) −8.13917 −0.515799
\(250\) −1.00000 −0.0632456
\(251\) 16.0603 1.01372 0.506858 0.862029i \(-0.330807\pi\)
0.506858 + 0.862029i \(0.330807\pi\)
\(252\) 16.9822 1.06978
\(253\) −6.83421 −0.429663
\(254\) 15.2216 0.955090
\(255\) −16.4936 −1.03287
\(256\) 1.00000 0.0625000
\(257\) −5.18645 −0.323522 −0.161761 0.986830i \(-0.551717\pi\)
−0.161761 + 0.986830i \(0.551717\pi\)
\(258\) 3.16243 0.196884
\(259\) −0.897419 −0.0557629
\(260\) −0.554325 −0.0343778
\(261\) −16.3204 −1.01021
\(262\) 1.48407 0.0916861
\(263\) −16.6803 −1.02855 −0.514276 0.857625i \(-0.671939\pi\)
−0.514276 + 0.857625i \(0.671939\pi\)
\(264\) −5.01675 −0.308760
\(265\) −11.4646 −0.704263
\(266\) 5.80578 0.355975
\(267\) −30.1378 −1.84440
\(268\) −3.85892 −0.235721
\(269\) −27.5502 −1.67977 −0.839883 0.542768i \(-0.817376\pi\)
−0.839883 + 0.542768i \(0.817376\pi\)
\(270\) 11.8844 0.723260
\(271\) 0.902248 0.0548077 0.0274038 0.999624i \(-0.491276\pi\)
0.0274038 + 0.999624i \(0.491276\pi\)
\(272\) 5.26951 0.319511
\(273\) 4.33502 0.262367
\(274\) 14.8058 0.894454
\(275\) −1.60279 −0.0966521
\(276\) −13.3461 −0.803343
\(277\) −26.1112 −1.56887 −0.784434 0.620213i \(-0.787046\pi\)
−0.784434 + 0.620213i \(0.787046\pi\)
\(278\) 8.84411 0.530435
\(279\) −69.8351 −4.18092
\(280\) −2.49851 −0.149315
\(281\) 25.6505 1.53018 0.765092 0.643921i \(-0.222694\pi\)
0.765092 + 0.643921i \(0.222694\pi\)
\(282\) −18.8507 −1.12255
\(283\) −22.6307 −1.34525 −0.672627 0.739982i \(-0.734834\pi\)
−0.672627 + 0.739982i \(0.734834\pi\)
\(284\) −6.49192 −0.385224
\(285\) 7.27317 0.430825
\(286\) −0.888469 −0.0525363
\(287\) −6.26333 −0.369713
\(288\) −6.79692 −0.400512
\(289\) 10.7678 0.633398
\(290\) 2.40114 0.141000
\(291\) −22.9762 −1.34689
\(292\) 5.75377 0.336714
\(293\) −2.90031 −0.169438 −0.0847190 0.996405i \(-0.526999\pi\)
−0.0847190 + 0.996405i \(0.526999\pi\)
\(294\) −2.37077 −0.138266
\(295\) −5.94415 −0.346082
\(296\) 0.359181 0.0208770
\(297\) 19.0482 1.10529
\(298\) −2.76125 −0.159955
\(299\) −2.36361 −0.136691
\(300\) −3.13000 −0.180711
\(301\) 2.52439 0.145504
\(302\) −10.9291 −0.628897
\(303\) 2.63496 0.151375
\(304\) −2.32369 −0.133273
\(305\) 0.692162 0.0396331
\(306\) −35.8164 −2.04749
\(307\) −19.0094 −1.08492 −0.542462 0.840080i \(-0.682508\pi\)
−0.542462 + 0.840080i \(0.682508\pi\)
\(308\) −4.00460 −0.228183
\(309\) −41.7775 −2.37664
\(310\) 10.2745 0.583554
\(311\) 23.9786 1.35970 0.679850 0.733351i \(-0.262045\pi\)
0.679850 + 0.733351i \(0.262045\pi\)
\(312\) −1.73504 −0.0982273
\(313\) −1.02820 −0.0581172 −0.0290586 0.999578i \(-0.509251\pi\)
−0.0290586 + 0.999578i \(0.509251\pi\)
\(314\) −8.69993 −0.490965
\(315\) 16.9822 0.956838
\(316\) 1.29382 0.0727829
\(317\) −4.13918 −0.232479 −0.116240 0.993221i \(-0.537084\pi\)
−0.116240 + 0.993221i \(0.537084\pi\)
\(318\) −35.8841 −2.01228
\(319\) 3.84853 0.215477
\(320\) 1.00000 0.0559017
\(321\) −7.36270 −0.410946
\(322\) −10.6535 −0.593696
\(323\) −12.2447 −0.681315
\(324\) 16.8073 0.933742
\(325\) −0.554325 −0.0307484
\(326\) 13.4903 0.747158
\(327\) 3.40540 0.188319
\(328\) 2.50682 0.138416
\(329\) −15.0475 −0.829597
\(330\) −5.01675 −0.276163
\(331\) −13.6861 −0.752254 −0.376127 0.926568i \(-0.622744\pi\)
−0.376127 + 0.926568i \(0.622744\pi\)
\(332\) 2.60037 0.142714
\(333\) −2.44133 −0.133784
\(334\) 5.17486 0.283156
\(335\) −3.85892 −0.210835
\(336\) −7.82035 −0.426635
\(337\) −25.3412 −1.38042 −0.690211 0.723608i \(-0.742482\pi\)
−0.690211 + 0.723608i \(0.742482\pi\)
\(338\) 12.6927 0.690393
\(339\) −51.2184 −2.78180
\(340\) 5.26951 0.285779
\(341\) 16.4679 0.891789
\(342\) 15.7940 0.854039
\(343\) −19.3820 −1.04653
\(344\) −1.01036 −0.0544749
\(345\) −13.3461 −0.718531
\(346\) −16.3903 −0.881145
\(347\) −1.18759 −0.0637530 −0.0318765 0.999492i \(-0.510148\pi\)
−0.0318765 + 0.999492i \(0.510148\pi\)
\(348\) 7.51558 0.402877
\(349\) 12.1807 0.652016 0.326008 0.945367i \(-0.394296\pi\)
0.326008 + 0.945367i \(0.394296\pi\)
\(350\) −2.49851 −0.133551
\(351\) 6.58781 0.351631
\(352\) 1.60279 0.0854292
\(353\) 13.1057 0.697543 0.348772 0.937208i \(-0.386599\pi\)
0.348772 + 0.937208i \(0.386599\pi\)
\(354\) −18.6052 −0.988855
\(355\) −6.49192 −0.344555
\(356\) 9.62868 0.510319
\(357\) −41.2095 −2.18104
\(358\) −7.00317 −0.370129
\(359\) −17.1135 −0.903218 −0.451609 0.892216i \(-0.649150\pi\)
−0.451609 + 0.892216i \(0.649150\pi\)
\(360\) −6.79692 −0.358229
\(361\) −13.6005 −0.715813
\(362\) 15.4015 0.809485
\(363\) 26.3892 1.38507
\(364\) −1.38499 −0.0725932
\(365\) 5.75377 0.301166
\(366\) 2.16647 0.113243
\(367\) 2.81757 0.147076 0.0735380 0.997292i \(-0.476571\pi\)
0.0735380 + 0.997292i \(0.476571\pi\)
\(368\) 4.26393 0.222273
\(369\) −17.0387 −0.886998
\(370\) 0.359181 0.0186729
\(371\) −28.6444 −1.48714
\(372\) 32.1593 1.66738
\(373\) −35.9524 −1.86155 −0.930773 0.365597i \(-0.880865\pi\)
−0.930773 + 0.365597i \(0.880865\pi\)
\(374\) 8.44594 0.436729
\(375\) −3.13000 −0.161633
\(376\) 6.02260 0.310592
\(377\) 1.33101 0.0685507
\(378\) 29.6932 1.52726
\(379\) −22.1707 −1.13883 −0.569415 0.822050i \(-0.692830\pi\)
−0.569415 + 0.822050i \(0.692830\pi\)
\(380\) −2.32369 −0.119203
\(381\) 47.6438 2.44086
\(382\) 15.8806 0.812523
\(383\) 2.99160 0.152864 0.0764319 0.997075i \(-0.475647\pi\)
0.0764319 + 0.997075i \(0.475647\pi\)
\(384\) 3.13000 0.159727
\(385\) −4.00460 −0.204093
\(386\) 2.11003 0.107398
\(387\) 6.86733 0.349086
\(388\) 7.34064 0.372664
\(389\) 17.2293 0.873562 0.436781 0.899568i \(-0.356118\pi\)
0.436781 + 0.899568i \(0.356118\pi\)
\(390\) −1.73504 −0.0878572
\(391\) 22.4689 1.13630
\(392\) 0.757432 0.0382561
\(393\) 4.64514 0.234316
\(394\) −9.59731 −0.483505
\(395\) 1.29382 0.0650990
\(396\) −10.8941 −0.547447
\(397\) 38.4232 1.92841 0.964203 0.265163i \(-0.0854259\pi\)
0.964203 + 0.265163i \(0.0854259\pi\)
\(398\) 8.29416 0.415749
\(399\) 18.1721 0.909743
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −12.0784 −0.602417
\(403\) 5.69543 0.283710
\(404\) −0.841840 −0.0418831
\(405\) 16.8073 0.835164
\(406\) 5.99928 0.297739
\(407\) 0.575693 0.0285361
\(408\) 16.4936 0.816554
\(409\) −15.4432 −0.763618 −0.381809 0.924241i \(-0.624699\pi\)
−0.381809 + 0.924241i \(0.624699\pi\)
\(410\) 2.50682 0.123803
\(411\) 46.3424 2.28590
\(412\) 13.3474 0.657580
\(413\) −14.8515 −0.730796
\(414\) −28.9816 −1.42437
\(415\) 2.60037 0.127647
\(416\) 0.554325 0.0271780
\(417\) 27.6821 1.35560
\(418\) −3.72440 −0.182166
\(419\) −14.4186 −0.704396 −0.352198 0.935925i \(-0.614566\pi\)
−0.352198 + 0.935925i \(0.614566\pi\)
\(420\) −7.82035 −0.381594
\(421\) 0.880335 0.0429049 0.0214524 0.999770i \(-0.493171\pi\)
0.0214524 + 0.999770i \(0.493171\pi\)
\(422\) 24.5118 1.19321
\(423\) −40.9351 −1.99033
\(424\) 11.4646 0.556769
\(425\) 5.26951 0.255609
\(426\) −20.3197 −0.984494
\(427\) 1.72938 0.0836904
\(428\) 2.35230 0.113703
\(429\) −2.78091 −0.134264
\(430\) −1.01036 −0.0487238
\(431\) 23.8006 1.14643 0.573217 0.819404i \(-0.305695\pi\)
0.573217 + 0.819404i \(0.305695\pi\)
\(432\) −11.8844 −0.571787
\(433\) 1.78662 0.0858597 0.0429299 0.999078i \(-0.486331\pi\)
0.0429299 + 0.999078i \(0.486331\pi\)
\(434\) 25.6710 1.23225
\(435\) 7.51558 0.360345
\(436\) −1.08799 −0.0521052
\(437\) −9.90807 −0.473967
\(438\) 18.0093 0.860518
\(439\) 10.5565 0.503833 0.251917 0.967749i \(-0.418939\pi\)
0.251917 + 0.967749i \(0.418939\pi\)
\(440\) 1.60279 0.0764102
\(441\) −5.14821 −0.245153
\(442\) 2.92102 0.138939
\(443\) 23.5700 1.11984 0.559922 0.828545i \(-0.310831\pi\)
0.559922 + 0.828545i \(0.310831\pi\)
\(444\) 1.12424 0.0533540
\(445\) 9.62868 0.456443
\(446\) −12.8558 −0.608741
\(447\) −8.64271 −0.408786
\(448\) 2.49851 0.118044
\(449\) 15.9106 0.750868 0.375434 0.926849i \(-0.377494\pi\)
0.375434 + 0.926849i \(0.377494\pi\)
\(450\) −6.79692 −0.320410
\(451\) 4.01792 0.189197
\(452\) 16.3637 0.769684
\(453\) −34.2080 −1.60723
\(454\) −4.85991 −0.228087
\(455\) −1.38499 −0.0649293
\(456\) −7.27317 −0.340597
\(457\) 11.1245 0.520382 0.260191 0.965557i \(-0.416214\pi\)
0.260191 + 0.965557i \(0.416214\pi\)
\(458\) −1.31204 −0.0613074
\(459\) −62.6248 −2.92308
\(460\) 4.26393 0.198807
\(461\) −19.0227 −0.885978 −0.442989 0.896527i \(-0.646082\pi\)
−0.442989 + 0.896527i \(0.646082\pi\)
\(462\) −12.5344 −0.583154
\(463\) 16.3268 0.758769 0.379385 0.925239i \(-0.376136\pi\)
0.379385 + 0.925239i \(0.376136\pi\)
\(464\) −2.40114 −0.111470
\(465\) 32.1593 1.49135
\(466\) −11.2852 −0.522776
\(467\) −10.6304 −0.491918 −0.245959 0.969280i \(-0.579103\pi\)
−0.245959 + 0.969280i \(0.579103\pi\)
\(468\) −3.76770 −0.174162
\(469\) −9.64155 −0.445206
\(470\) 6.02260 0.277802
\(471\) −27.2308 −1.25473
\(472\) 5.94415 0.273602
\(473\) −1.61940 −0.0744599
\(474\) 4.04965 0.186007
\(475\) −2.32369 −0.106618
\(476\) 13.1659 0.603460
\(477\) −77.9237 −3.56788
\(478\) −3.82979 −0.175171
\(479\) 2.81613 0.128672 0.0643360 0.997928i \(-0.479507\pi\)
0.0643360 + 0.997928i \(0.479507\pi\)
\(480\) 3.13000 0.142864
\(481\) 0.199103 0.00907833
\(482\) 14.3377 0.653063
\(483\) −33.3455 −1.51727
\(484\) −8.43105 −0.383230
\(485\) 7.34064 0.333321
\(486\) 16.9539 0.769047
\(487\) −31.0010 −1.40479 −0.702395 0.711788i \(-0.747886\pi\)
−0.702395 + 0.711788i \(0.747886\pi\)
\(488\) −0.692162 −0.0313327
\(489\) 42.2247 1.90946
\(490\) 0.757432 0.0342173
\(491\) −4.69437 −0.211854 −0.105927 0.994374i \(-0.533781\pi\)
−0.105927 + 0.994374i \(0.533781\pi\)
\(492\) 7.84637 0.353742
\(493\) −12.6528 −0.569856
\(494\) −1.28808 −0.0579536
\(495\) −10.8941 −0.489651
\(496\) −10.2745 −0.461340
\(497\) −16.2201 −0.727573
\(498\) 8.13917 0.364725
\(499\) 32.5480 1.45705 0.728524 0.685021i \(-0.240207\pi\)
0.728524 + 0.685021i \(0.240207\pi\)
\(500\) 1.00000 0.0447214
\(501\) 16.1973 0.723643
\(502\) −16.0603 −0.716806
\(503\) −25.0655 −1.11761 −0.558807 0.829298i \(-0.688741\pi\)
−0.558807 + 0.829298i \(0.688741\pi\)
\(504\) −16.9822 −0.756447
\(505\) −0.841840 −0.0374614
\(506\) 6.83421 0.303818
\(507\) 39.7283 1.76439
\(508\) −15.2216 −0.675351
\(509\) 16.8920 0.748726 0.374363 0.927282i \(-0.377861\pi\)
0.374363 + 0.927282i \(0.377861\pi\)
\(510\) 16.4936 0.730348
\(511\) 14.3759 0.635951
\(512\) −1.00000 −0.0441942
\(513\) 27.6156 1.21926
\(514\) 5.18645 0.228765
\(515\) 13.3474 0.588157
\(516\) −3.16243 −0.139218
\(517\) 9.65298 0.424537
\(518\) 0.897419 0.0394303
\(519\) −51.3015 −2.25189
\(520\) 0.554325 0.0243088
\(521\) −11.4351 −0.500979 −0.250490 0.968119i \(-0.580592\pi\)
−0.250490 + 0.968119i \(0.580592\pi\)
\(522\) 16.3204 0.714323
\(523\) −2.75185 −0.120330 −0.0601650 0.998188i \(-0.519163\pi\)
−0.0601650 + 0.998188i \(0.519163\pi\)
\(524\) −1.48407 −0.0648319
\(525\) −7.82035 −0.341308
\(526\) 16.6803 0.727296
\(527\) −54.1418 −2.35845
\(528\) 5.01675 0.218326
\(529\) −4.81886 −0.209516
\(530\) 11.4646 0.497989
\(531\) −40.4019 −1.75329
\(532\) −5.80578 −0.251712
\(533\) 1.38960 0.0601901
\(534\) 30.1378 1.30419
\(535\) 2.35230 0.101699
\(536\) 3.85892 0.166680
\(537\) −21.9199 −0.945916
\(538\) 27.5502 1.18777
\(539\) 1.21401 0.0522910
\(540\) −11.8844 −0.511422
\(541\) 33.4085 1.43635 0.718173 0.695865i \(-0.244979\pi\)
0.718173 + 0.695865i \(0.244979\pi\)
\(542\) −0.902248 −0.0387549
\(543\) 48.2068 2.06875
\(544\) −5.26951 −0.225928
\(545\) −1.08799 −0.0466043
\(546\) −4.33502 −0.185522
\(547\) −46.1416 −1.97287 −0.986436 0.164149i \(-0.947512\pi\)
−0.986436 + 0.164149i \(0.947512\pi\)
\(548\) −14.8058 −0.632475
\(549\) 4.70457 0.200786
\(550\) 1.60279 0.0683433
\(551\) 5.57952 0.237695
\(552\) 13.3461 0.568049
\(553\) 3.23262 0.137465
\(554\) 26.1112 1.10936
\(555\) 1.12424 0.0477213
\(556\) −8.84411 −0.375074
\(557\) 22.8300 0.967340 0.483670 0.875251i \(-0.339304\pi\)
0.483670 + 0.875251i \(0.339304\pi\)
\(558\) 69.8351 2.95636
\(559\) −0.560068 −0.0236883
\(560\) 2.49851 0.105581
\(561\) 26.4358 1.11612
\(562\) −25.6505 −1.08200
\(563\) −27.4350 −1.15625 −0.578124 0.815949i \(-0.696215\pi\)
−0.578124 + 0.815949i \(0.696215\pi\)
\(564\) 18.8507 0.793759
\(565\) 16.3637 0.688426
\(566\) 22.6307 0.951238
\(567\) 41.9934 1.76356
\(568\) 6.49192 0.272395
\(569\) 15.3967 0.645464 0.322732 0.946490i \(-0.395399\pi\)
0.322732 + 0.946490i \(0.395399\pi\)
\(570\) −7.27317 −0.304639
\(571\) −6.82895 −0.285783 −0.142891 0.989738i \(-0.545640\pi\)
−0.142891 + 0.989738i \(0.545640\pi\)
\(572\) 0.888469 0.0371488
\(573\) 49.7064 2.07651
\(574\) 6.26333 0.261427
\(575\) 4.26393 0.177818
\(576\) 6.79692 0.283205
\(577\) −16.1557 −0.672570 −0.336285 0.941760i \(-0.609171\pi\)
−0.336285 + 0.941760i \(0.609171\pi\)
\(578\) −10.7678 −0.447880
\(579\) 6.60440 0.274469
\(580\) −2.40114 −0.0997020
\(581\) 6.49706 0.269543
\(582\) 22.9762 0.952395
\(583\) 18.3753 0.761029
\(584\) −5.75377 −0.238093
\(585\) −3.76770 −0.155775
\(586\) 2.90031 0.119811
\(587\) 26.0086 1.07349 0.536744 0.843745i \(-0.319654\pi\)
0.536744 + 0.843745i \(0.319654\pi\)
\(588\) 2.37077 0.0977687
\(589\) 23.8749 0.983746
\(590\) 5.94415 0.244717
\(591\) −30.0396 −1.23566
\(592\) −0.359181 −0.0147623
\(593\) −25.0795 −1.02989 −0.514946 0.857223i \(-0.672188\pi\)
−0.514946 + 0.857223i \(0.672188\pi\)
\(594\) −19.0482 −0.781557
\(595\) 13.1659 0.539751
\(596\) 2.76125 0.113105
\(597\) 25.9607 1.06250
\(598\) 2.36361 0.0966551
\(599\) 38.0130 1.55317 0.776584 0.630014i \(-0.216951\pi\)
0.776584 + 0.630014i \(0.216951\pi\)
\(600\) 3.13000 0.127782
\(601\) −30.5002 −1.24413 −0.622065 0.782966i \(-0.713706\pi\)
−0.622065 + 0.782966i \(0.713706\pi\)
\(602\) −2.52439 −0.102887
\(603\) −26.2287 −1.06812
\(604\) 10.9291 0.444698
\(605\) −8.43105 −0.342771
\(606\) −2.63496 −0.107038
\(607\) −27.5176 −1.11690 −0.558452 0.829537i \(-0.688604\pi\)
−0.558452 + 0.829537i \(0.688604\pi\)
\(608\) 2.32369 0.0942382
\(609\) 18.7778 0.760914
\(610\) −0.692162 −0.0280248
\(611\) 3.33848 0.135060
\(612\) 35.8164 1.44779
\(613\) −9.51619 −0.384355 −0.192178 0.981360i \(-0.561555\pi\)
−0.192178 + 0.981360i \(0.561555\pi\)
\(614\) 19.0094 0.767157
\(615\) 7.84637 0.316396
\(616\) 4.00460 0.161350
\(617\) −10.3721 −0.417565 −0.208783 0.977962i \(-0.566950\pi\)
−0.208783 + 0.977962i \(0.566950\pi\)
\(618\) 41.7775 1.68054
\(619\) −1.99419 −0.0801532 −0.0400766 0.999197i \(-0.512760\pi\)
−0.0400766 + 0.999197i \(0.512760\pi\)
\(620\) −10.2745 −0.412635
\(621\) −50.6742 −2.03348
\(622\) −23.9786 −0.961453
\(623\) 24.0574 0.963839
\(624\) 1.73504 0.0694572
\(625\) 1.00000 0.0400000
\(626\) 1.02820 0.0410951
\(627\) −11.6574 −0.465551
\(628\) 8.69993 0.347165
\(629\) −1.89271 −0.0754673
\(630\) −16.9822 −0.676587
\(631\) −5.45354 −0.217102 −0.108551 0.994091i \(-0.534621\pi\)
−0.108551 + 0.994091i \(0.534621\pi\)
\(632\) −1.29382 −0.0514653
\(633\) 76.7219 3.04942
\(634\) 4.13918 0.164388
\(635\) −15.2216 −0.604052
\(636\) 35.8841 1.42290
\(637\) 0.419864 0.0166356
\(638\) −3.84853 −0.152365
\(639\) −44.1250 −1.74556
\(640\) −1.00000 −0.0395285
\(641\) −33.0227 −1.30432 −0.652160 0.758081i \(-0.726137\pi\)
−0.652160 + 0.758081i \(0.726137\pi\)
\(642\) 7.36270 0.290583
\(643\) −15.8321 −0.624359 −0.312179 0.950023i \(-0.601059\pi\)
−0.312179 + 0.950023i \(0.601059\pi\)
\(644\) 10.6535 0.419807
\(645\) −3.16243 −0.124520
\(646\) 12.2447 0.481762
\(647\) 26.6391 1.04729 0.523645 0.851937i \(-0.324572\pi\)
0.523645 + 0.851937i \(0.324572\pi\)
\(648\) −16.8073 −0.660255
\(649\) 9.52724 0.373977
\(650\) 0.554325 0.0217424
\(651\) 80.3505 3.14918
\(652\) −13.4903 −0.528321
\(653\) 11.2504 0.440264 0.220132 0.975470i \(-0.429351\pi\)
0.220132 + 0.975470i \(0.429351\pi\)
\(654\) −3.40540 −0.133162
\(655\) −1.48407 −0.0579874
\(656\) −2.50682 −0.0978751
\(657\) 39.1079 1.52574
\(658\) 15.0475 0.586614
\(659\) −27.4914 −1.07091 −0.535456 0.844563i \(-0.679860\pi\)
−0.535456 + 0.844563i \(0.679860\pi\)
\(660\) 5.01675 0.195277
\(661\) 9.44399 0.367329 0.183664 0.982989i \(-0.441204\pi\)
0.183664 + 0.982989i \(0.441204\pi\)
\(662\) 13.6861 0.531924
\(663\) 9.14282 0.355078
\(664\) −2.60037 −0.100914
\(665\) −5.80578 −0.225138
\(666\) 2.44133 0.0945994
\(667\) −10.2383 −0.396429
\(668\) −5.17486 −0.200221
\(669\) −40.2388 −1.55572
\(670\) 3.85892 0.149083
\(671\) −1.10939 −0.0428276
\(672\) 7.82035 0.301677
\(673\) 50.7619 1.95673 0.978364 0.206890i \(-0.0663343\pi\)
0.978364 + 0.206890i \(0.0663343\pi\)
\(674\) 25.3412 0.976106
\(675\) −11.8844 −0.457429
\(676\) −12.6927 −0.488182
\(677\) −9.90968 −0.380860 −0.190430 0.981701i \(-0.560988\pi\)
−0.190430 + 0.981701i \(0.560988\pi\)
\(678\) 51.2184 1.96703
\(679\) 18.3407 0.703850
\(680\) −5.26951 −0.202077
\(681\) −15.2115 −0.582908
\(682\) −16.4679 −0.630590
\(683\) −24.6540 −0.943358 −0.471679 0.881770i \(-0.656352\pi\)
−0.471679 + 0.881770i \(0.656352\pi\)
\(684\) −15.7940 −0.603897
\(685\) −14.8058 −0.565702
\(686\) 19.3820 0.740010
\(687\) −4.10667 −0.156679
\(688\) 1.01036 0.0385196
\(689\) 6.35510 0.242110
\(690\) 13.3461 0.508078
\(691\) 27.1337 1.03221 0.516107 0.856524i \(-0.327381\pi\)
0.516107 + 0.856524i \(0.327381\pi\)
\(692\) 16.3903 0.623064
\(693\) −27.2189 −1.03396
\(694\) 1.18759 0.0450801
\(695\) −8.84411 −0.335476
\(696\) −7.51558 −0.284877
\(697\) −13.2097 −0.500355
\(698\) −12.1807 −0.461045
\(699\) −35.3226 −1.33602
\(700\) 2.49851 0.0944349
\(701\) 10.8978 0.411604 0.205802 0.978594i \(-0.434020\pi\)
0.205802 + 0.978594i \(0.434020\pi\)
\(702\) −6.58781 −0.248641
\(703\) 0.834627 0.0314785
\(704\) −1.60279 −0.0604076
\(705\) 18.8507 0.709960
\(706\) −13.1057 −0.493238
\(707\) −2.10335 −0.0791045
\(708\) 18.6052 0.699226
\(709\) −33.8638 −1.27178 −0.635890 0.771780i \(-0.719367\pi\)
−0.635890 + 0.771780i \(0.719367\pi\)
\(710\) 6.49192 0.243637
\(711\) 8.79397 0.329800
\(712\) −9.62868 −0.360850
\(713\) −43.8099 −1.64069
\(714\) 41.2095 1.54222
\(715\) 0.888469 0.0332269
\(716\) 7.00317 0.261721
\(717\) −11.9873 −0.447672
\(718\) 17.1135 0.638671
\(719\) −17.2931 −0.644925 −0.322463 0.946582i \(-0.604511\pi\)
−0.322463 + 0.946582i \(0.604511\pi\)
\(720\) 6.79692 0.253306
\(721\) 33.3487 1.24197
\(722\) 13.6005 0.506156
\(723\) 44.8769 1.66899
\(724\) −15.4015 −0.572393
\(725\) −2.40114 −0.0891762
\(726\) −26.3892 −0.979396
\(727\) 31.6920 1.17539 0.587696 0.809082i \(-0.300035\pi\)
0.587696 + 0.809082i \(0.300035\pi\)
\(728\) 1.38499 0.0513311
\(729\) 2.64387 0.0979210
\(730\) −5.75377 −0.212957
\(731\) 5.32410 0.196919
\(732\) −2.16647 −0.0800750
\(733\) −24.9775 −0.922565 −0.461282 0.887253i \(-0.652611\pi\)
−0.461282 + 0.887253i \(0.652611\pi\)
\(734\) −2.81757 −0.103998
\(735\) 2.37077 0.0874470
\(736\) −4.26393 −0.157171
\(737\) 6.18505 0.227829
\(738\) 17.0387 0.627203
\(739\) −23.5856 −0.867609 −0.433805 0.901007i \(-0.642829\pi\)
−0.433805 + 0.901007i \(0.642829\pi\)
\(740\) −0.359181 −0.0132038
\(741\) −4.03170 −0.148108
\(742\) 28.6444 1.05157
\(743\) −15.1399 −0.555430 −0.277715 0.960664i \(-0.589577\pi\)
−0.277715 + 0.960664i \(0.589577\pi\)
\(744\) −32.1593 −1.17902
\(745\) 2.76125 0.101164
\(746\) 35.9524 1.31631
\(747\) 17.6745 0.646676
\(748\) −8.44594 −0.308814
\(749\) 5.87725 0.214750
\(750\) 3.13000 0.114292
\(751\) 32.7312 1.19438 0.597189 0.802100i \(-0.296284\pi\)
0.597189 + 0.802100i \(0.296284\pi\)
\(752\) −6.02260 −0.219621
\(753\) −50.2687 −1.83189
\(754\) −1.33101 −0.0484727
\(755\) 10.9291 0.397750
\(756\) −29.6932 −1.07993
\(757\) −50.5083 −1.83576 −0.917878 0.396862i \(-0.870099\pi\)
−0.917878 + 0.396862i \(0.870099\pi\)
\(758\) 22.1707 0.805275
\(759\) 21.3911 0.776447
\(760\) 2.32369 0.0842892
\(761\) −33.1475 −1.20160 −0.600799 0.799400i \(-0.705151\pi\)
−0.600799 + 0.799400i \(0.705151\pi\)
\(762\) −47.6438 −1.72595
\(763\) −2.71835 −0.0984109
\(764\) −15.8806 −0.574541
\(765\) 35.8164 1.29495
\(766\) −2.99160 −0.108091
\(767\) 3.29499 0.118975
\(768\) −3.13000 −0.112944
\(769\) 22.8414 0.823682 0.411841 0.911256i \(-0.364886\pi\)
0.411841 + 0.911256i \(0.364886\pi\)
\(770\) 4.00460 0.144316
\(771\) 16.2336 0.584639
\(772\) −2.11003 −0.0759416
\(773\) 10.5613 0.379864 0.189932 0.981797i \(-0.439173\pi\)
0.189932 + 0.981797i \(0.439173\pi\)
\(774\) −6.86733 −0.246841
\(775\) −10.2745 −0.369072
\(776\) −7.34064 −0.263513
\(777\) 2.80892 0.100770
\(778\) −17.2293 −0.617702
\(779\) 5.82509 0.208706
\(780\) 1.73504 0.0621244
\(781\) 10.4052 0.372327
\(782\) −22.4689 −0.803485
\(783\) 28.5361 1.01980
\(784\) −0.757432 −0.0270512
\(785\) 8.69993 0.310514
\(786\) −4.64514 −0.165687
\(787\) 44.5194 1.58694 0.793472 0.608607i \(-0.208271\pi\)
0.793472 + 0.608607i \(0.208271\pi\)
\(788\) 9.59731 0.341890
\(789\) 52.2094 1.85870
\(790\) −1.29382 −0.0460320
\(791\) 40.8849 1.45370
\(792\) 10.8941 0.387103
\(793\) −0.383683 −0.0136250
\(794\) −38.4232 −1.36359
\(795\) 35.8841 1.27268
\(796\) −8.29416 −0.293979
\(797\) 5.40818 0.191568 0.0957838 0.995402i \(-0.469464\pi\)
0.0957838 + 0.995402i \(0.469464\pi\)
\(798\) −18.1721 −0.643285
\(799\) −31.7361 −1.12274
\(800\) −1.00000 −0.0353553
\(801\) 65.4454 2.31240
\(802\) −1.00000 −0.0353112
\(803\) −9.22210 −0.325441
\(804\) 12.0784 0.425973
\(805\) 10.6535 0.375486
\(806\) −5.69543 −0.200613
\(807\) 86.2322 3.03552
\(808\) 0.841840 0.0296158
\(809\) −28.4191 −0.999161 −0.499580 0.866268i \(-0.666512\pi\)
−0.499580 + 0.866268i \(0.666512\pi\)
\(810\) −16.8073 −0.590550
\(811\) 30.9856 1.08805 0.544025 0.839069i \(-0.316900\pi\)
0.544025 + 0.839069i \(0.316900\pi\)
\(812\) −5.99928 −0.210534
\(813\) −2.82404 −0.0990434
\(814\) −0.575693 −0.0201780
\(815\) −13.4903 −0.472544
\(816\) −16.4936 −0.577391
\(817\) −2.34776 −0.0821378
\(818\) 15.4432 0.539960
\(819\) −9.41366 −0.328940
\(820\) −2.50682 −0.0875421
\(821\) −32.2652 −1.12606 −0.563032 0.826435i \(-0.690365\pi\)
−0.563032 + 0.826435i \(0.690365\pi\)
\(822\) −46.3424 −1.61638
\(823\) −6.94412 −0.242057 −0.121028 0.992649i \(-0.538619\pi\)
−0.121028 + 0.992649i \(0.538619\pi\)
\(824\) −13.3474 −0.464979
\(825\) 5.01675 0.174661
\(826\) 14.8515 0.516751
\(827\) −36.7619 −1.27834 −0.639169 0.769066i \(-0.720722\pi\)
−0.639169 + 0.769066i \(0.720722\pi\)
\(828\) 28.9816 1.00718
\(829\) 1.75980 0.0611205 0.0305603 0.999533i \(-0.490271\pi\)
0.0305603 + 0.999533i \(0.490271\pi\)
\(830\) −2.60037 −0.0902602
\(831\) 81.7280 2.83511
\(832\) −0.554325 −0.0192178
\(833\) −3.99130 −0.138290
\(834\) −27.6821 −0.958553
\(835\) −5.17486 −0.179083
\(836\) 3.72440 0.128811
\(837\) 122.106 4.22061
\(838\) 14.4186 0.498083
\(839\) −19.7231 −0.680917 −0.340459 0.940259i \(-0.610582\pi\)
−0.340459 + 0.940259i \(0.610582\pi\)
\(840\) 7.82035 0.269828
\(841\) −23.2345 −0.801190
\(842\) −0.880335 −0.0303383
\(843\) −80.2863 −2.76521
\(844\) −24.5118 −0.843729
\(845\) −12.6927 −0.436643
\(846\) 40.9351 1.40738
\(847\) −21.0651 −0.723805
\(848\) −11.4646 −0.393695
\(849\) 70.8341 2.43102
\(850\) −5.26951 −0.180743
\(851\) −1.53153 −0.0525000
\(852\) 20.3197 0.696142
\(853\) 25.4131 0.870128 0.435064 0.900399i \(-0.356726\pi\)
0.435064 + 0.900399i \(0.356726\pi\)
\(854\) −1.72938 −0.0591780
\(855\) −15.7940 −0.540142
\(856\) −2.35230 −0.0803999
\(857\) 35.0259 1.19646 0.598232 0.801323i \(-0.295870\pi\)
0.598232 + 0.801323i \(0.295870\pi\)
\(858\) 2.78091 0.0949387
\(859\) 36.0120 1.22871 0.614357 0.789028i \(-0.289416\pi\)
0.614357 + 0.789028i \(0.289416\pi\)
\(860\) 1.01036 0.0344529
\(861\) 19.6043 0.668111
\(862\) −23.8006 −0.810651
\(863\) 16.5093 0.561984 0.280992 0.959710i \(-0.409336\pi\)
0.280992 + 0.959710i \(0.409336\pi\)
\(864\) 11.8844 0.404314
\(865\) 16.3903 0.557285
\(866\) −1.78662 −0.0607120
\(867\) −33.7031 −1.14462
\(868\) −25.6710 −0.871332
\(869\) −2.07372 −0.0703462
\(870\) −7.51558 −0.254802
\(871\) 2.13910 0.0724805
\(872\) 1.08799 0.0368439
\(873\) 49.8937 1.68865
\(874\) 9.90807 0.335146
\(875\) 2.49851 0.0844652
\(876\) −18.0093 −0.608478
\(877\) −9.65863 −0.326149 −0.163074 0.986614i \(-0.552141\pi\)
−0.163074 + 0.986614i \(0.552141\pi\)
\(878\) −10.5565 −0.356264
\(879\) 9.07798 0.306193
\(880\) −1.60279 −0.0540302
\(881\) −20.9669 −0.706392 −0.353196 0.935549i \(-0.614905\pi\)
−0.353196 + 0.935549i \(0.614905\pi\)
\(882\) 5.14821 0.173349
\(883\) −43.3765 −1.45973 −0.729867 0.683589i \(-0.760418\pi\)
−0.729867 + 0.683589i \(0.760418\pi\)
\(884\) −2.92102 −0.0982447
\(885\) 18.6052 0.625407
\(886\) −23.5700 −0.791849
\(887\) 3.45192 0.115904 0.0579520 0.998319i \(-0.481543\pi\)
0.0579520 + 0.998319i \(0.481543\pi\)
\(888\) −1.12424 −0.0377270
\(889\) −38.0315 −1.27553
\(890\) −9.62868 −0.322754
\(891\) −26.9387 −0.902481
\(892\) 12.8558 0.430445
\(893\) 13.9947 0.468313
\(894\) 8.64271 0.289055
\(895\) 7.00317 0.234090
\(896\) −2.49851 −0.0834695
\(897\) 7.39810 0.247015
\(898\) −15.9106 −0.530944
\(899\) 24.6706 0.822811
\(900\) 6.79692 0.226564
\(901\) −60.4127 −2.01264
\(902\) −4.01792 −0.133782
\(903\) −7.90136 −0.262941
\(904\) −16.3637 −0.544248
\(905\) −15.4015 −0.511963
\(906\) 34.2080 1.13649
\(907\) −5.38262 −0.178727 −0.0893634 0.995999i \(-0.528483\pi\)
−0.0893634 + 0.995999i \(0.528483\pi\)
\(908\) 4.85991 0.161282
\(909\) −5.72192 −0.189784
\(910\) 1.38499 0.0459119
\(911\) 47.2301 1.56480 0.782402 0.622774i \(-0.213995\pi\)
0.782402 + 0.622774i \(0.213995\pi\)
\(912\) 7.27317 0.240839
\(913\) −4.16786 −0.137936
\(914\) −11.1245 −0.367966
\(915\) −2.16647 −0.0716213
\(916\) 1.31204 0.0433509
\(917\) −3.70797 −0.122448
\(918\) 62.6248 2.06693
\(919\) −44.4070 −1.46485 −0.732426 0.680847i \(-0.761612\pi\)
−0.732426 + 0.680847i \(0.761612\pi\)
\(920\) −4.26393 −0.140578
\(921\) 59.4995 1.96057
\(922\) 19.0227 0.626481
\(923\) 3.59863 0.118451
\(924\) 12.5344 0.412352
\(925\) −0.359181 −0.0118098
\(926\) −16.3268 −0.536531
\(927\) 90.7213 2.97968
\(928\) 2.40114 0.0788213
\(929\) −51.5159 −1.69018 −0.845091 0.534623i \(-0.820454\pi\)
−0.845091 + 0.534623i \(0.820454\pi\)
\(930\) −32.1593 −1.05455
\(931\) 1.76004 0.0576830
\(932\) 11.2852 0.369658
\(933\) −75.0530 −2.45712
\(934\) 10.6304 0.347839
\(935\) −8.44594 −0.276212
\(936\) 3.76770 0.123151
\(937\) 23.2861 0.760722 0.380361 0.924838i \(-0.375800\pi\)
0.380361 + 0.924838i \(0.375800\pi\)
\(938\) 9.64155 0.314808
\(939\) 3.21827 0.105024
\(940\) −6.02260 −0.196435
\(941\) −19.9403 −0.650034 −0.325017 0.945708i \(-0.605370\pi\)
−0.325017 + 0.945708i \(0.605370\pi\)
\(942\) 27.2308 0.887227
\(943\) −10.6889 −0.348080
\(944\) −5.94415 −0.193465
\(945\) −29.6932 −0.965921
\(946\) 1.61940 0.0526511
\(947\) −3.03046 −0.0984769 −0.0492384 0.998787i \(-0.515679\pi\)
−0.0492384 + 0.998787i \(0.515679\pi\)
\(948\) −4.04965 −0.131527
\(949\) −3.18946 −0.103534
\(950\) 2.32369 0.0753906
\(951\) 12.9556 0.420115
\(952\) −13.1659 −0.426711
\(953\) 9.72369 0.314981 0.157491 0.987520i \(-0.449660\pi\)
0.157491 + 0.987520i \(0.449660\pi\)
\(954\) 77.9237 2.52287
\(955\) −15.8806 −0.513885
\(956\) 3.82979 0.123864
\(957\) −12.0459 −0.389389
\(958\) −2.81613 −0.0909849
\(959\) −36.9926 −1.19455
\(960\) −3.13000 −0.101020
\(961\) 74.5660 2.40535
\(962\) −0.199103 −0.00641935
\(963\) 15.9884 0.515218
\(964\) −14.3377 −0.461785
\(965\) −2.11003 −0.0679243
\(966\) 33.3455 1.07287
\(967\) −15.0536 −0.484090 −0.242045 0.970265i \(-0.577818\pi\)
−0.242045 + 0.970265i \(0.577818\pi\)
\(968\) 8.43105 0.270984
\(969\) 38.3260 1.23121
\(970\) −7.34064 −0.235694
\(971\) 54.2681 1.74155 0.870773 0.491684i \(-0.163619\pi\)
0.870773 + 0.491684i \(0.163619\pi\)
\(972\) −16.9539 −0.543798
\(973\) −22.0971 −0.708402
\(974\) 31.0010 0.993336
\(975\) 1.73504 0.0555658
\(976\) 0.692162 0.0221556
\(977\) 36.6108 1.17128 0.585641 0.810570i \(-0.300843\pi\)
0.585641 + 0.810570i \(0.300843\pi\)
\(978\) −42.2247 −1.35020
\(979\) −15.4328 −0.493234
\(980\) −0.757432 −0.0241953
\(981\) −7.39496 −0.236103
\(982\) 4.69437 0.149804
\(983\) 3.69731 0.117926 0.0589630 0.998260i \(-0.481221\pi\)
0.0589630 + 0.998260i \(0.481221\pi\)
\(984\) −7.84637 −0.250133
\(985\) 9.59731 0.305796
\(986\) 12.6528 0.402949
\(987\) 47.0988 1.49917
\(988\) 1.28808 0.0409793
\(989\) 4.30810 0.136990
\(990\) 10.8941 0.346236
\(991\) 12.9246 0.410565 0.205282 0.978703i \(-0.434189\pi\)
0.205282 + 0.978703i \(0.434189\pi\)
\(992\) 10.2745 0.326217
\(993\) 42.8374 1.35940
\(994\) 16.2201 0.514472
\(995\) −8.29416 −0.262943
\(996\) −8.13917 −0.257899
\(997\) 14.8534 0.470412 0.235206 0.971946i \(-0.424423\pi\)
0.235206 + 0.971946i \(0.424423\pi\)
\(998\) −32.5480 −1.03029
\(999\) 4.26864 0.135054
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 4010.2.a.i.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.1 10 1.1 even 1 trivial