Properties

Label 4034.2.a.d.1.9
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.36933 q^{3} +1.00000 q^{4} -2.34107 q^{5} -2.36933 q^{6} +4.14004 q^{7} +1.00000 q^{8} +2.61374 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.36933 q^{3} +1.00000 q^{4} -2.34107 q^{5} -2.36933 q^{6} +4.14004 q^{7} +1.00000 q^{8} +2.61374 q^{9} -2.34107 q^{10} +0.755051 q^{11} -2.36933 q^{12} +5.20636 q^{13} +4.14004 q^{14} +5.54677 q^{15} +1.00000 q^{16} -0.343613 q^{17} +2.61374 q^{18} +3.14510 q^{19} -2.34107 q^{20} -9.80914 q^{21} +0.755051 q^{22} +3.00025 q^{23} -2.36933 q^{24} +0.480595 q^{25} +5.20636 q^{26} +0.915175 q^{27} +4.14004 q^{28} +0.0845158 q^{29} +5.54677 q^{30} -1.30032 q^{31} +1.00000 q^{32} -1.78897 q^{33} -0.343613 q^{34} -9.69212 q^{35} +2.61374 q^{36} -3.42817 q^{37} +3.14510 q^{38} -12.3356 q^{39} -2.34107 q^{40} -10.4772 q^{41} -9.80914 q^{42} +1.80280 q^{43} +0.755051 q^{44} -6.11894 q^{45} +3.00025 q^{46} +7.76816 q^{47} -2.36933 q^{48} +10.1399 q^{49} +0.480595 q^{50} +0.814133 q^{51} +5.20636 q^{52} -3.31248 q^{53} +0.915175 q^{54} -1.76762 q^{55} +4.14004 q^{56} -7.45180 q^{57} +0.0845158 q^{58} -6.69383 q^{59} +5.54677 q^{60} +6.64404 q^{61} -1.30032 q^{62} +10.8210 q^{63} +1.00000 q^{64} -12.1884 q^{65} -1.78897 q^{66} +8.31293 q^{67} -0.343613 q^{68} -7.10859 q^{69} -9.69212 q^{70} -6.11170 q^{71} +2.61374 q^{72} -0.836250 q^{73} -3.42817 q^{74} -1.13869 q^{75} +3.14510 q^{76} +3.12594 q^{77} -12.3356 q^{78} -5.99442 q^{79} -2.34107 q^{80} -10.0096 q^{81} -10.4772 q^{82} +4.33584 q^{83} -9.80914 q^{84} +0.804420 q^{85} +1.80280 q^{86} -0.200246 q^{87} +0.755051 q^{88} +8.23783 q^{89} -6.11894 q^{90} +21.5545 q^{91} +3.00025 q^{92} +3.08090 q^{93} +7.76816 q^{94} -7.36290 q^{95} -2.36933 q^{96} +16.4266 q^{97} +10.1399 q^{98} +1.97351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.36933 −1.36794 −0.683968 0.729512i \(-0.739747\pi\)
−0.683968 + 0.729512i \(0.739747\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.34107 −1.04696 −0.523479 0.852039i \(-0.675366\pi\)
−0.523479 + 0.852039i \(0.675366\pi\)
\(6\) −2.36933 −0.967276
\(7\) 4.14004 1.56479 0.782394 0.622783i \(-0.213998\pi\)
0.782394 + 0.622783i \(0.213998\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.61374 0.871247
\(10\) −2.34107 −0.740310
\(11\) 0.755051 0.227656 0.113828 0.993500i \(-0.463689\pi\)
0.113828 + 0.993500i \(0.463689\pi\)
\(12\) −2.36933 −0.683968
\(13\) 5.20636 1.44398 0.721992 0.691902i \(-0.243227\pi\)
0.721992 + 0.691902i \(0.243227\pi\)
\(14\) 4.14004 1.10647
\(15\) 5.54677 1.43217
\(16\) 1.00000 0.250000
\(17\) −0.343613 −0.0833383 −0.0416691 0.999131i \(-0.513268\pi\)
−0.0416691 + 0.999131i \(0.513268\pi\)
\(18\) 2.61374 0.616065
\(19\) 3.14510 0.721536 0.360768 0.932656i \(-0.382515\pi\)
0.360768 + 0.932656i \(0.382515\pi\)
\(20\) −2.34107 −0.523479
\(21\) −9.80914 −2.14053
\(22\) 0.755051 0.160977
\(23\) 3.00025 0.625595 0.312798 0.949820i \(-0.398734\pi\)
0.312798 + 0.949820i \(0.398734\pi\)
\(24\) −2.36933 −0.483638
\(25\) 0.480595 0.0961190
\(26\) 5.20636 1.02105
\(27\) 0.915175 0.176125
\(28\) 4.14004 0.782394
\(29\) 0.0845158 0.0156942 0.00784709 0.999969i \(-0.497502\pi\)
0.00784709 + 0.999969i \(0.497502\pi\)
\(30\) 5.54677 1.01270
\(31\) −1.30032 −0.233545 −0.116773 0.993159i \(-0.537255\pi\)
−0.116773 + 0.993159i \(0.537255\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.78897 −0.311419
\(34\) −0.343613 −0.0589291
\(35\) −9.69212 −1.63827
\(36\) 2.61374 0.435624
\(37\) −3.42817 −0.563588 −0.281794 0.959475i \(-0.590929\pi\)
−0.281794 + 0.959475i \(0.590929\pi\)
\(38\) 3.14510 0.510203
\(39\) −12.3356 −1.97528
\(40\) −2.34107 −0.370155
\(41\) −10.4772 −1.63626 −0.818132 0.575030i \(-0.804990\pi\)
−0.818132 + 0.575030i \(0.804990\pi\)
\(42\) −9.80914 −1.51358
\(43\) 1.80280 0.274924 0.137462 0.990507i \(-0.456106\pi\)
0.137462 + 0.990507i \(0.456106\pi\)
\(44\) 0.755051 0.113828
\(45\) −6.11894 −0.912158
\(46\) 3.00025 0.442363
\(47\) 7.76816 1.13310 0.566552 0.824026i \(-0.308277\pi\)
0.566552 + 0.824026i \(0.308277\pi\)
\(48\) −2.36933 −0.341984
\(49\) 10.1399 1.44856
\(50\) 0.480595 0.0679664
\(51\) 0.814133 0.114001
\(52\) 5.20636 0.721992
\(53\) −3.31248 −0.455004 −0.227502 0.973778i \(-0.573056\pi\)
−0.227502 + 0.973778i \(0.573056\pi\)
\(54\) 0.915175 0.124540
\(55\) −1.76762 −0.238346
\(56\) 4.14004 0.553236
\(57\) −7.45180 −0.987015
\(58\) 0.0845158 0.0110975
\(59\) −6.69383 −0.871463 −0.435731 0.900077i \(-0.643510\pi\)
−0.435731 + 0.900077i \(0.643510\pi\)
\(60\) 5.54677 0.716085
\(61\) 6.64404 0.850682 0.425341 0.905033i \(-0.360154\pi\)
0.425341 + 0.905033i \(0.360154\pi\)
\(62\) −1.30032 −0.165141
\(63\) 10.8210 1.36332
\(64\) 1.00000 0.125000
\(65\) −12.1884 −1.51179
\(66\) −1.78897 −0.220207
\(67\) 8.31293 1.01559 0.507793 0.861479i \(-0.330461\pi\)
0.507793 + 0.861479i \(0.330461\pi\)
\(68\) −0.343613 −0.0416691
\(69\) −7.10859 −0.855774
\(70\) −9.69212 −1.15843
\(71\) −6.11170 −0.725325 −0.362662 0.931921i \(-0.618132\pi\)
−0.362662 + 0.931921i \(0.618132\pi\)
\(72\) 2.61374 0.308032
\(73\) −0.836250 −0.0978756 −0.0489378 0.998802i \(-0.515584\pi\)
−0.0489378 + 0.998802i \(0.515584\pi\)
\(74\) −3.42817 −0.398517
\(75\) −1.13869 −0.131485
\(76\) 3.14510 0.360768
\(77\) 3.12594 0.356234
\(78\) −12.3356 −1.39673
\(79\) −5.99442 −0.674424 −0.337212 0.941429i \(-0.609484\pi\)
−0.337212 + 0.941429i \(0.609484\pi\)
\(80\) −2.34107 −0.261739
\(81\) −10.0096 −1.11218
\(82\) −10.4772 −1.15701
\(83\) 4.33584 0.475921 0.237960 0.971275i \(-0.423521\pi\)
0.237960 + 0.971275i \(0.423521\pi\)
\(84\) −9.80914 −1.07026
\(85\) 0.804420 0.0872516
\(86\) 1.80280 0.194401
\(87\) −0.200246 −0.0214686
\(88\) 0.755051 0.0804887
\(89\) 8.23783 0.873208 0.436604 0.899654i \(-0.356181\pi\)
0.436604 + 0.899654i \(0.356181\pi\)
\(90\) −6.11894 −0.644993
\(91\) 21.5545 2.25953
\(92\) 3.00025 0.312798
\(93\) 3.08090 0.319474
\(94\) 7.76816 0.801225
\(95\) −7.36290 −0.755417
\(96\) −2.36933 −0.241819
\(97\) 16.4266 1.66787 0.833936 0.551862i \(-0.186082\pi\)
0.833936 + 0.551862i \(0.186082\pi\)
\(98\) 10.1399 1.02429
\(99\) 1.97351 0.198345
\(100\) 0.480595 0.0480595
\(101\) −0.616998 −0.0613936 −0.0306968 0.999529i \(-0.509773\pi\)
−0.0306968 + 0.999529i \(0.509773\pi\)
\(102\) 0.814133 0.0806112
\(103\) −7.49611 −0.738614 −0.369307 0.929307i \(-0.620405\pi\)
−0.369307 + 0.929307i \(0.620405\pi\)
\(104\) 5.20636 0.510525
\(105\) 22.9639 2.24104
\(106\) −3.31248 −0.321736
\(107\) 13.6226 1.31695 0.658473 0.752605i \(-0.271203\pi\)
0.658473 + 0.752605i \(0.271203\pi\)
\(108\) 0.915175 0.0880627
\(109\) 8.30128 0.795119 0.397559 0.917576i \(-0.369857\pi\)
0.397559 + 0.917576i \(0.369857\pi\)
\(110\) −1.76762 −0.168536
\(111\) 8.12248 0.770952
\(112\) 4.14004 0.391197
\(113\) −1.84052 −0.173141 −0.0865706 0.996246i \(-0.527591\pi\)
−0.0865706 + 0.996246i \(0.527591\pi\)
\(114\) −7.45180 −0.697925
\(115\) −7.02379 −0.654971
\(116\) 0.0845158 0.00784709
\(117\) 13.6081 1.25807
\(118\) −6.69383 −0.616217
\(119\) −1.42257 −0.130407
\(120\) 5.54677 0.506348
\(121\) −10.4299 −0.948173
\(122\) 6.64404 0.601523
\(123\) 24.8240 2.23830
\(124\) −1.30032 −0.116773
\(125\) 10.5802 0.946325
\(126\) 10.8210 0.964011
\(127\) 1.17295 0.104082 0.0520411 0.998645i \(-0.483427\pi\)
0.0520411 + 0.998645i \(0.483427\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.27143 −0.376078
\(130\) −12.1884 −1.06900
\(131\) −6.58080 −0.574968 −0.287484 0.957786i \(-0.592819\pi\)
−0.287484 + 0.957786i \(0.592819\pi\)
\(132\) −1.78897 −0.155710
\(133\) 13.0209 1.12905
\(134\) 8.31293 0.718128
\(135\) −2.14249 −0.184396
\(136\) −0.343613 −0.0294645
\(137\) −4.72294 −0.403508 −0.201754 0.979436i \(-0.564664\pi\)
−0.201754 + 0.979436i \(0.564664\pi\)
\(138\) −7.10859 −0.605124
\(139\) 16.7008 1.41655 0.708273 0.705939i \(-0.249475\pi\)
0.708273 + 0.705939i \(0.249475\pi\)
\(140\) −9.69212 −0.819133
\(141\) −18.4054 −1.55001
\(142\) −6.11170 −0.512882
\(143\) 3.93106 0.328732
\(144\) 2.61374 0.217812
\(145\) −0.197857 −0.0164311
\(146\) −0.836250 −0.0692085
\(147\) −24.0249 −1.98154
\(148\) −3.42817 −0.281794
\(149\) 11.5419 0.945546 0.472773 0.881184i \(-0.343253\pi\)
0.472773 + 0.881184i \(0.343253\pi\)
\(150\) −1.13869 −0.0929736
\(151\) −0.545605 −0.0444007 −0.0222004 0.999754i \(-0.507067\pi\)
−0.0222004 + 0.999754i \(0.507067\pi\)
\(152\) 3.14510 0.255102
\(153\) −0.898114 −0.0726083
\(154\) 3.12594 0.251896
\(155\) 3.04414 0.244512
\(156\) −12.3356 −0.987638
\(157\) −4.50559 −0.359585 −0.179792 0.983705i \(-0.557543\pi\)
−0.179792 + 0.983705i \(0.557543\pi\)
\(158\) −5.99442 −0.476890
\(159\) 7.84837 0.622416
\(160\) −2.34107 −0.185078
\(161\) 12.4212 0.978925
\(162\) −10.0096 −0.786427
\(163\) 2.14088 0.167686 0.0838432 0.996479i \(-0.473281\pi\)
0.0838432 + 0.996479i \(0.473281\pi\)
\(164\) −10.4772 −0.818132
\(165\) 4.18809 0.326043
\(166\) 4.33584 0.336527
\(167\) 15.0791 1.16685 0.583427 0.812166i \(-0.301712\pi\)
0.583427 + 0.812166i \(0.301712\pi\)
\(168\) −9.80914 −0.756792
\(169\) 14.1062 1.08509
\(170\) 0.804420 0.0616962
\(171\) 8.22049 0.628636
\(172\) 1.80280 0.137462
\(173\) 14.1736 1.07760 0.538800 0.842433i \(-0.318878\pi\)
0.538800 + 0.842433i \(0.318878\pi\)
\(174\) −0.200246 −0.0151806
\(175\) 1.98968 0.150406
\(176\) 0.755051 0.0569141
\(177\) 15.8599 1.19210
\(178\) 8.23783 0.617451
\(179\) −12.3698 −0.924563 −0.462282 0.886733i \(-0.652969\pi\)
−0.462282 + 0.886733i \(0.652969\pi\)
\(180\) −6.11894 −0.456079
\(181\) −10.2887 −0.764756 −0.382378 0.924006i \(-0.624895\pi\)
−0.382378 + 0.924006i \(0.624895\pi\)
\(182\) 21.5545 1.59773
\(183\) −15.7419 −1.16368
\(184\) 3.00025 0.221181
\(185\) 8.02558 0.590053
\(186\) 3.08090 0.225903
\(187\) −0.259445 −0.0189725
\(188\) 7.76816 0.566552
\(189\) 3.78886 0.275599
\(190\) −7.36290 −0.534161
\(191\) −8.22711 −0.595293 −0.297647 0.954676i \(-0.596202\pi\)
−0.297647 + 0.954676i \(0.596202\pi\)
\(192\) −2.36933 −0.170992
\(193\) −2.60862 −0.187773 −0.0938864 0.995583i \(-0.529929\pi\)
−0.0938864 + 0.995583i \(0.529929\pi\)
\(194\) 16.4266 1.17936
\(195\) 28.8785 2.06803
\(196\) 10.1399 0.724282
\(197\) 2.73344 0.194750 0.0973749 0.995248i \(-0.468955\pi\)
0.0973749 + 0.995248i \(0.468955\pi\)
\(198\) 1.97351 0.140251
\(199\) 23.9101 1.69494 0.847472 0.530839i \(-0.178123\pi\)
0.847472 + 0.530839i \(0.178123\pi\)
\(200\) 0.480595 0.0339832
\(201\) −19.6961 −1.38926
\(202\) −0.616998 −0.0434118
\(203\) 0.349899 0.0245581
\(204\) 0.814133 0.0570007
\(205\) 24.5278 1.71310
\(206\) −7.49611 −0.522279
\(207\) 7.84188 0.545048
\(208\) 5.20636 0.360996
\(209\) 2.37471 0.164262
\(210\) 22.9639 1.58466
\(211\) 11.5749 0.796846 0.398423 0.917202i \(-0.369558\pi\)
0.398423 + 0.917202i \(0.369558\pi\)
\(212\) −3.31248 −0.227502
\(213\) 14.4806 0.992198
\(214\) 13.6226 0.931221
\(215\) −4.22047 −0.287834
\(216\) 0.915175 0.0622698
\(217\) −5.38339 −0.365449
\(218\) 8.30128 0.562234
\(219\) 1.98135 0.133888
\(220\) −1.76762 −0.119173
\(221\) −1.78897 −0.120339
\(222\) 8.12248 0.545145
\(223\) 16.4678 1.10276 0.551382 0.834253i \(-0.314101\pi\)
0.551382 + 0.834253i \(0.314101\pi\)
\(224\) 4.14004 0.276618
\(225\) 1.25615 0.0837434
\(226\) −1.84052 −0.122429
\(227\) −2.29445 −0.152288 −0.0761438 0.997097i \(-0.524261\pi\)
−0.0761438 + 0.997097i \(0.524261\pi\)
\(228\) −7.45180 −0.493507
\(229\) 2.55902 0.169105 0.0845525 0.996419i \(-0.473054\pi\)
0.0845525 + 0.996419i \(0.473054\pi\)
\(230\) −7.02379 −0.463135
\(231\) −7.40640 −0.487305
\(232\) 0.0845158 0.00554873
\(233\) 9.25024 0.606003 0.303002 0.952990i \(-0.402011\pi\)
0.303002 + 0.952990i \(0.402011\pi\)
\(234\) 13.6081 0.889588
\(235\) −18.1858 −1.18631
\(236\) −6.69383 −0.435731
\(237\) 14.2028 0.922569
\(238\) −1.42257 −0.0922115
\(239\) −25.7318 −1.66445 −0.832226 0.554437i \(-0.812934\pi\)
−0.832226 + 0.554437i \(0.812934\pi\)
\(240\) 5.54677 0.358042
\(241\) 1.06429 0.0685572 0.0342786 0.999412i \(-0.489087\pi\)
0.0342786 + 0.999412i \(0.489087\pi\)
\(242\) −10.4299 −0.670459
\(243\) 20.9705 1.34526
\(244\) 6.64404 0.425341
\(245\) −23.7383 −1.51658
\(246\) 24.8240 1.58272
\(247\) 16.3745 1.04189
\(248\) −1.30032 −0.0825706
\(249\) −10.2731 −0.651029
\(250\) 10.5802 0.669153
\(251\) 0.401328 0.0253316 0.0126658 0.999920i \(-0.495968\pi\)
0.0126658 + 0.999920i \(0.495968\pi\)
\(252\) 10.8210 0.681659
\(253\) 2.26534 0.142421
\(254\) 1.17295 0.0735973
\(255\) −1.90594 −0.119355
\(256\) 1.00000 0.0625000
\(257\) −21.6886 −1.35290 −0.676448 0.736490i \(-0.736482\pi\)
−0.676448 + 0.736490i \(0.736482\pi\)
\(258\) −4.27143 −0.265927
\(259\) −14.1928 −0.881896
\(260\) −12.1884 −0.755894
\(261\) 0.220902 0.0136735
\(262\) −6.58080 −0.406563
\(263\) −8.24604 −0.508473 −0.254236 0.967142i \(-0.581824\pi\)
−0.254236 + 0.967142i \(0.581824\pi\)
\(264\) −1.78897 −0.110103
\(265\) 7.75474 0.476370
\(266\) 13.0209 0.798360
\(267\) −19.5182 −1.19449
\(268\) 8.31293 0.507793
\(269\) 18.2646 1.11361 0.556807 0.830642i \(-0.312026\pi\)
0.556807 + 0.830642i \(0.312026\pi\)
\(270\) −2.14249 −0.130388
\(271\) 22.8042 1.38526 0.692629 0.721294i \(-0.256453\pi\)
0.692629 + 0.721294i \(0.256453\pi\)
\(272\) −0.343613 −0.0208346
\(273\) −51.0699 −3.09089
\(274\) −4.72294 −0.285323
\(275\) 0.362873 0.0218821
\(276\) −7.10859 −0.427887
\(277\) −4.27071 −0.256602 −0.128301 0.991735i \(-0.540952\pi\)
−0.128301 + 0.991735i \(0.540952\pi\)
\(278\) 16.7008 1.00165
\(279\) −3.39871 −0.203475
\(280\) −9.69212 −0.579215
\(281\) −5.93422 −0.354006 −0.177003 0.984210i \(-0.556640\pi\)
−0.177003 + 0.984210i \(0.556640\pi\)
\(282\) −18.4054 −1.09602
\(283\) 16.9149 1.00549 0.502743 0.864436i \(-0.332324\pi\)
0.502743 + 0.864436i \(0.332324\pi\)
\(284\) −6.11170 −0.362662
\(285\) 17.4452 1.03336
\(286\) 3.93106 0.232449
\(287\) −43.3761 −2.56041
\(288\) 2.61374 0.154016
\(289\) −16.8819 −0.993055
\(290\) −0.197857 −0.0116186
\(291\) −38.9202 −2.28154
\(292\) −0.836250 −0.0489378
\(293\) 23.5952 1.37845 0.689223 0.724550i \(-0.257952\pi\)
0.689223 + 0.724550i \(0.257952\pi\)
\(294\) −24.0249 −1.40116
\(295\) 15.6707 0.912384
\(296\) −3.42817 −0.199258
\(297\) 0.691004 0.0400961
\(298\) 11.5419 0.668602
\(299\) 15.6204 0.903350
\(300\) −1.13869 −0.0657423
\(301\) 7.46365 0.430198
\(302\) −0.545605 −0.0313961
\(303\) 1.46187 0.0839825
\(304\) 3.14510 0.180384
\(305\) −15.5541 −0.890628
\(306\) −0.898114 −0.0513418
\(307\) −17.3589 −0.990727 −0.495364 0.868686i \(-0.664965\pi\)
−0.495364 + 0.868686i \(0.664965\pi\)
\(308\) 3.12594 0.178117
\(309\) 17.7608 1.01038
\(310\) 3.04414 0.172896
\(311\) 10.4240 0.591089 0.295545 0.955329i \(-0.404499\pi\)
0.295545 + 0.955329i \(0.404499\pi\)
\(312\) −12.3356 −0.698366
\(313\) 3.48391 0.196922 0.0984612 0.995141i \(-0.468608\pi\)
0.0984612 + 0.995141i \(0.468608\pi\)
\(314\) −4.50559 −0.254265
\(315\) −25.3327 −1.42734
\(316\) −5.99442 −0.337212
\(317\) 26.2911 1.47666 0.738329 0.674441i \(-0.235615\pi\)
0.738329 + 0.674441i \(0.235615\pi\)
\(318\) 7.84837 0.440115
\(319\) 0.0638137 0.00357288
\(320\) −2.34107 −0.130870
\(321\) −32.2765 −1.80150
\(322\) 12.4212 0.692204
\(323\) −1.08070 −0.0601316
\(324\) −10.0096 −0.556088
\(325\) 2.50215 0.138794
\(326\) 2.14088 0.118572
\(327\) −19.6685 −1.08767
\(328\) −10.4772 −0.578507
\(329\) 32.1605 1.77307
\(330\) 4.18809 0.230547
\(331\) 2.86964 0.157730 0.0788648 0.996885i \(-0.474870\pi\)
0.0788648 + 0.996885i \(0.474870\pi\)
\(332\) 4.33584 0.237960
\(333\) −8.96036 −0.491025
\(334\) 15.0791 0.825090
\(335\) −19.4611 −1.06328
\(336\) −9.80914 −0.535132
\(337\) −9.68411 −0.527527 −0.263763 0.964587i \(-0.584964\pi\)
−0.263763 + 0.964587i \(0.584964\pi\)
\(338\) 14.1062 0.767274
\(339\) 4.36080 0.236846
\(340\) 0.804420 0.0436258
\(341\) −0.981810 −0.0531680
\(342\) 8.22049 0.444513
\(343\) 12.9995 0.701908
\(344\) 1.80280 0.0972003
\(345\) 16.6417 0.895959
\(346\) 14.1736 0.761979
\(347\) 5.83173 0.313064 0.156532 0.987673i \(-0.449969\pi\)
0.156532 + 0.987673i \(0.449969\pi\)
\(348\) −0.200246 −0.0107343
\(349\) −8.77677 −0.469810 −0.234905 0.972018i \(-0.575478\pi\)
−0.234905 + 0.972018i \(0.575478\pi\)
\(350\) 1.98968 0.106353
\(351\) 4.76473 0.254322
\(352\) 0.755051 0.0402443
\(353\) −0.0838628 −0.00446357 −0.00223178 0.999998i \(-0.500710\pi\)
−0.00223178 + 0.999998i \(0.500710\pi\)
\(354\) 15.8599 0.842945
\(355\) 14.3079 0.759384
\(356\) 8.23783 0.436604
\(357\) 3.37054 0.178388
\(358\) −12.3698 −0.653765
\(359\) −4.99511 −0.263632 −0.131816 0.991274i \(-0.542081\pi\)
−0.131816 + 0.991274i \(0.542081\pi\)
\(360\) −6.11894 −0.322497
\(361\) −9.10832 −0.479386
\(362\) −10.2887 −0.540764
\(363\) 24.7119 1.29704
\(364\) 21.5545 1.12976
\(365\) 1.95772 0.102472
\(366\) −15.7419 −0.822845
\(367\) −35.6347 −1.86012 −0.930059 0.367409i \(-0.880245\pi\)
−0.930059 + 0.367409i \(0.880245\pi\)
\(368\) 3.00025 0.156399
\(369\) −27.3847 −1.42559
\(370\) 8.02558 0.417230
\(371\) −13.7138 −0.711985
\(372\) 3.08090 0.159737
\(373\) 9.03274 0.467697 0.233849 0.972273i \(-0.424868\pi\)
0.233849 + 0.972273i \(0.424868\pi\)
\(374\) −0.259445 −0.0134156
\(375\) −25.0681 −1.29451
\(376\) 7.76816 0.400612
\(377\) 0.440019 0.0226621
\(378\) 3.78886 0.194878
\(379\) 27.2329 1.39886 0.699429 0.714702i \(-0.253438\pi\)
0.699429 + 0.714702i \(0.253438\pi\)
\(380\) −7.36290 −0.377709
\(381\) −2.77910 −0.142378
\(382\) −8.22711 −0.420936
\(383\) −21.1512 −1.08078 −0.540389 0.841415i \(-0.681723\pi\)
−0.540389 + 0.841415i \(0.681723\pi\)
\(384\) −2.36933 −0.120910
\(385\) −7.31804 −0.372962
\(386\) −2.60862 −0.132775
\(387\) 4.71204 0.239527
\(388\) 16.4266 0.833936
\(389\) 2.69212 0.136496 0.0682478 0.997668i \(-0.478259\pi\)
0.0682478 + 0.997668i \(0.478259\pi\)
\(390\) 28.8785 1.46232
\(391\) −1.03092 −0.0521360
\(392\) 10.1399 0.512145
\(393\) 15.5921 0.786519
\(394\) 2.73344 0.137709
\(395\) 14.0333 0.706093
\(396\) 1.97351 0.0991725
\(397\) 32.2819 1.62018 0.810092 0.586303i \(-0.199417\pi\)
0.810092 + 0.586303i \(0.199417\pi\)
\(398\) 23.9101 1.19851
\(399\) −30.8508 −1.54447
\(400\) 0.480595 0.0240297
\(401\) −6.63858 −0.331515 −0.165757 0.986167i \(-0.553007\pi\)
−0.165757 + 0.986167i \(0.553007\pi\)
\(402\) −19.6961 −0.982353
\(403\) −6.76995 −0.337235
\(404\) −0.616998 −0.0306968
\(405\) 23.4331 1.16440
\(406\) 0.349899 0.0173652
\(407\) −2.58844 −0.128304
\(408\) 0.814133 0.0403056
\(409\) 2.28005 0.112741 0.0563705 0.998410i \(-0.482047\pi\)
0.0563705 + 0.998410i \(0.482047\pi\)
\(410\) 24.5278 1.21134
\(411\) 11.1902 0.551973
\(412\) −7.49611 −0.369307
\(413\) −27.7127 −1.36365
\(414\) 7.84188 0.385407
\(415\) −10.1505 −0.498268
\(416\) 5.20636 0.255263
\(417\) −39.5698 −1.93774
\(418\) 2.37471 0.116151
\(419\) −35.3845 −1.72864 −0.864322 0.502939i \(-0.832252\pi\)
−0.864322 + 0.502939i \(0.832252\pi\)
\(420\) 22.9639 1.12052
\(421\) 25.3165 1.23385 0.616924 0.787022i \(-0.288378\pi\)
0.616924 + 0.787022i \(0.288378\pi\)
\(422\) 11.5749 0.563455
\(423\) 20.3040 0.987213
\(424\) −3.31248 −0.160868
\(425\) −0.165138 −0.00801039
\(426\) 14.4806 0.701590
\(427\) 27.5066 1.33114
\(428\) 13.6226 0.658473
\(429\) −9.31400 −0.449684
\(430\) −4.22047 −0.203529
\(431\) −2.94430 −0.141822 −0.0709111 0.997483i \(-0.522591\pi\)
−0.0709111 + 0.997483i \(0.522591\pi\)
\(432\) 0.915175 0.0440314
\(433\) 41.1769 1.97883 0.989417 0.145101i \(-0.0463508\pi\)
0.989417 + 0.145101i \(0.0463508\pi\)
\(434\) −5.38339 −0.258411
\(435\) 0.468789 0.0224767
\(436\) 8.30128 0.397559
\(437\) 9.43610 0.451390
\(438\) 1.98135 0.0946728
\(439\) 20.0910 0.958889 0.479444 0.877572i \(-0.340838\pi\)
0.479444 + 0.877572i \(0.340838\pi\)
\(440\) −1.76762 −0.0842682
\(441\) 26.5032 1.26206
\(442\) −1.78897 −0.0850926
\(443\) 25.9539 1.23311 0.616554 0.787313i \(-0.288528\pi\)
0.616554 + 0.787313i \(0.288528\pi\)
\(444\) 8.12248 0.385476
\(445\) −19.2853 −0.914211
\(446\) 16.4678 0.779772
\(447\) −27.3465 −1.29345
\(448\) 4.14004 0.195599
\(449\) 29.0725 1.37202 0.686008 0.727594i \(-0.259362\pi\)
0.686008 + 0.727594i \(0.259362\pi\)
\(450\) 1.25615 0.0592155
\(451\) −7.91082 −0.372506
\(452\) −1.84052 −0.0865706
\(453\) 1.29272 0.0607373
\(454\) −2.29445 −0.107684
\(455\) −50.4606 −2.36563
\(456\) −7.45180 −0.348962
\(457\) −0.918963 −0.0429873 −0.0214936 0.999769i \(-0.506842\pi\)
−0.0214936 + 0.999769i \(0.506842\pi\)
\(458\) 2.55902 0.119575
\(459\) −0.314466 −0.0146780
\(460\) −7.02379 −0.327486
\(461\) −25.9230 −1.20735 −0.603677 0.797229i \(-0.706298\pi\)
−0.603677 + 0.797229i \(0.706298\pi\)
\(462\) −7.40640 −0.344577
\(463\) −30.5937 −1.42181 −0.710905 0.703288i \(-0.751714\pi\)
−0.710905 + 0.703288i \(0.751714\pi\)
\(464\) 0.0845158 0.00392355
\(465\) −7.21259 −0.334476
\(466\) 9.25024 0.428509
\(467\) 1.42500 0.0659412 0.0329706 0.999456i \(-0.489503\pi\)
0.0329706 + 0.999456i \(0.489503\pi\)
\(468\) 13.6081 0.629033
\(469\) 34.4159 1.58918
\(470\) −18.1858 −0.838848
\(471\) 10.6752 0.491889
\(472\) −6.69383 −0.308109
\(473\) 1.36120 0.0625882
\(474\) 14.2028 0.652355
\(475\) 1.51152 0.0693533
\(476\) −1.42257 −0.0652034
\(477\) −8.65797 −0.396421
\(478\) −25.7318 −1.17695
\(479\) −34.1758 −1.56153 −0.780765 0.624824i \(-0.785171\pi\)
−0.780765 + 0.624824i \(0.785171\pi\)
\(480\) 5.54677 0.253174
\(481\) −17.8483 −0.813812
\(482\) 1.06429 0.0484773
\(483\) −29.4299 −1.33911
\(484\) −10.4299 −0.474086
\(485\) −38.4558 −1.74619
\(486\) 20.9705 0.951242
\(487\) −19.6962 −0.892519 −0.446260 0.894904i \(-0.647244\pi\)
−0.446260 + 0.894904i \(0.647244\pi\)
\(488\) 6.64404 0.300762
\(489\) −5.07245 −0.229384
\(490\) −23.7383 −1.07239
\(491\) −43.0249 −1.94169 −0.970844 0.239711i \(-0.922947\pi\)
−0.970844 + 0.239711i \(0.922947\pi\)
\(492\) 24.8240 1.11915
\(493\) −0.0290407 −0.00130793
\(494\) 16.3745 0.736725
\(495\) −4.62011 −0.207659
\(496\) −1.30032 −0.0583863
\(497\) −25.3027 −1.13498
\(498\) −10.2731 −0.460347
\(499\) −31.1367 −1.39387 −0.696936 0.717133i \(-0.745454\pi\)
−0.696936 + 0.717133i \(0.745454\pi\)
\(500\) 10.5802 0.473162
\(501\) −35.7273 −1.59618
\(502\) 0.401328 0.0179122
\(503\) −0.810356 −0.0361320 −0.0180660 0.999837i \(-0.505751\pi\)
−0.0180660 + 0.999837i \(0.505751\pi\)
\(504\) 10.8210 0.482006
\(505\) 1.44443 0.0642764
\(506\) 2.26534 0.100707
\(507\) −33.4222 −1.48433
\(508\) 1.17295 0.0520411
\(509\) 2.55006 0.113030 0.0565148 0.998402i \(-0.482001\pi\)
0.0565148 + 0.998402i \(0.482001\pi\)
\(510\) −1.90594 −0.0843964
\(511\) −3.46211 −0.153155
\(512\) 1.00000 0.0441942
\(513\) 2.87832 0.127081
\(514\) −21.6886 −0.956642
\(515\) 17.5489 0.773297
\(516\) −4.27143 −0.188039
\(517\) 5.86536 0.257958
\(518\) −14.1928 −0.623595
\(519\) −33.5820 −1.47409
\(520\) −12.1884 −0.534498
\(521\) 6.87970 0.301405 0.150703 0.988579i \(-0.451846\pi\)
0.150703 + 0.988579i \(0.451846\pi\)
\(522\) 0.220902 0.00966863
\(523\) −24.2282 −1.05943 −0.529713 0.848177i \(-0.677700\pi\)
−0.529713 + 0.848177i \(0.677700\pi\)
\(524\) −6.58080 −0.287484
\(525\) −4.71422 −0.205746
\(526\) −8.24604 −0.359544
\(527\) 0.446808 0.0194632
\(528\) −1.78897 −0.0778548
\(529\) −13.9985 −0.608630
\(530\) 7.75474 0.336844
\(531\) −17.4959 −0.759259
\(532\) 13.0209 0.564526
\(533\) −54.5481 −2.36274
\(534\) −19.5182 −0.844633
\(535\) −31.8914 −1.37879
\(536\) 8.31293 0.359064
\(537\) 29.3082 1.26474
\(538\) 18.2646 0.787444
\(539\) 7.65617 0.329775
\(540\) −2.14249 −0.0921979
\(541\) 23.3047 1.00195 0.500973 0.865463i \(-0.332976\pi\)
0.500973 + 0.865463i \(0.332976\pi\)
\(542\) 22.8042 0.979525
\(543\) 24.3775 1.04614
\(544\) −0.343613 −0.0147323
\(545\) −19.4339 −0.832455
\(546\) −51.0699 −2.18559
\(547\) 8.77239 0.375080 0.187540 0.982257i \(-0.439949\pi\)
0.187540 + 0.982257i \(0.439949\pi\)
\(548\) −4.72294 −0.201754
\(549\) 17.3658 0.741155
\(550\) 0.362873 0.0154730
\(551\) 0.265811 0.0113239
\(552\) −7.10859 −0.302562
\(553\) −24.8171 −1.05533
\(554\) −4.27071 −0.181445
\(555\) −19.0153 −0.807154
\(556\) 16.7008 0.708273
\(557\) 3.00754 0.127433 0.0637167 0.997968i \(-0.479705\pi\)
0.0637167 + 0.997968i \(0.479705\pi\)
\(558\) −3.39871 −0.143879
\(559\) 9.38600 0.396986
\(560\) −9.69212 −0.409567
\(561\) 0.614712 0.0259531
\(562\) −5.93422 −0.250320
\(563\) −35.8924 −1.51268 −0.756342 0.654176i \(-0.773016\pi\)
−0.756342 + 0.654176i \(0.773016\pi\)
\(564\) −18.4054 −0.775006
\(565\) 4.30877 0.181271
\(566\) 16.9149 0.710986
\(567\) −41.4401 −1.74032
\(568\) −6.11170 −0.256441
\(569\) −27.5584 −1.15531 −0.577654 0.816282i \(-0.696032\pi\)
−0.577654 + 0.816282i \(0.696032\pi\)
\(570\) 17.4452 0.730697
\(571\) −21.1901 −0.886780 −0.443390 0.896329i \(-0.646224\pi\)
−0.443390 + 0.896329i \(0.646224\pi\)
\(572\) 3.93106 0.164366
\(573\) 19.4928 0.814322
\(574\) −43.3761 −1.81048
\(575\) 1.44190 0.0601316
\(576\) 2.61374 0.108906
\(577\) 8.62459 0.359047 0.179523 0.983754i \(-0.442544\pi\)
0.179523 + 0.983754i \(0.442544\pi\)
\(578\) −16.8819 −0.702196
\(579\) 6.18070 0.256861
\(580\) −0.197857 −0.00821557
\(581\) 17.9506 0.744715
\(582\) −38.9202 −1.61329
\(583\) −2.50109 −0.103585
\(584\) −0.836250 −0.0346043
\(585\) −31.8574 −1.31714
\(586\) 23.5952 0.974708
\(587\) −5.63720 −0.232672 −0.116336 0.993210i \(-0.537115\pi\)
−0.116336 + 0.993210i \(0.537115\pi\)
\(588\) −24.0249 −0.990771
\(589\) −4.08965 −0.168511
\(590\) 15.6707 0.645153
\(591\) −6.47644 −0.266405
\(592\) −3.42817 −0.140897
\(593\) 35.2054 1.44571 0.722855 0.690999i \(-0.242829\pi\)
0.722855 + 0.690999i \(0.242829\pi\)
\(594\) 0.691004 0.0283522
\(595\) 3.33033 0.136530
\(596\) 11.5419 0.472773
\(597\) −56.6511 −2.31858
\(598\) 15.6204 0.638765
\(599\) 30.1767 1.23299 0.616493 0.787360i \(-0.288553\pi\)
0.616493 + 0.787360i \(0.288553\pi\)
\(600\) −1.13869 −0.0464868
\(601\) 17.1839 0.700946 0.350473 0.936573i \(-0.386021\pi\)
0.350473 + 0.936573i \(0.386021\pi\)
\(602\) 7.46365 0.304196
\(603\) 21.7279 0.884827
\(604\) −0.545605 −0.0222004
\(605\) 24.4171 0.992696
\(606\) 1.46187 0.0593846
\(607\) −12.7735 −0.518461 −0.259231 0.965815i \(-0.583469\pi\)
−0.259231 + 0.965815i \(0.583469\pi\)
\(608\) 3.14510 0.127551
\(609\) −0.829027 −0.0335939
\(610\) −15.5541 −0.629769
\(611\) 40.4438 1.63618
\(612\) −0.898114 −0.0363041
\(613\) 19.3065 0.779781 0.389891 0.920861i \(-0.372513\pi\)
0.389891 + 0.920861i \(0.372513\pi\)
\(614\) −17.3589 −0.700550
\(615\) −58.1146 −2.34341
\(616\) 3.12594 0.125948
\(617\) −4.37062 −0.175954 −0.0879772 0.996122i \(-0.528040\pi\)
−0.0879772 + 0.996122i \(0.528040\pi\)
\(618\) 17.7608 0.714444
\(619\) −17.9263 −0.720519 −0.360259 0.932852i \(-0.617312\pi\)
−0.360259 + 0.932852i \(0.617312\pi\)
\(620\) 3.04414 0.122256
\(621\) 2.74575 0.110183
\(622\) 10.4240 0.417963
\(623\) 34.1049 1.36639
\(624\) −12.3356 −0.493819
\(625\) −27.1720 −1.08688
\(626\) 3.48391 0.139245
\(627\) −5.62649 −0.224700
\(628\) −4.50559 −0.179792
\(629\) 1.17796 0.0469685
\(630\) −25.3327 −1.00928
\(631\) 33.0923 1.31738 0.658692 0.752413i \(-0.271110\pi\)
0.658692 + 0.752413i \(0.271110\pi\)
\(632\) −5.99442 −0.238445
\(633\) −27.4247 −1.09003
\(634\) 26.2911 1.04415
\(635\) −2.74595 −0.108970
\(636\) 7.84837 0.311208
\(637\) 52.7922 2.09170
\(638\) 0.0638137 0.00252641
\(639\) −15.9744 −0.631937
\(640\) −2.34107 −0.0925388
\(641\) 35.1585 1.38868 0.694339 0.719648i \(-0.255697\pi\)
0.694339 + 0.719648i \(0.255697\pi\)
\(642\) −32.2765 −1.27385
\(643\) −12.5694 −0.495689 −0.247845 0.968800i \(-0.579722\pi\)
−0.247845 + 0.968800i \(0.579722\pi\)
\(644\) 12.4212 0.489462
\(645\) 9.99970 0.393738
\(646\) −1.08070 −0.0425195
\(647\) 26.3334 1.03527 0.517637 0.855600i \(-0.326812\pi\)
0.517637 + 0.855600i \(0.326812\pi\)
\(648\) −10.0096 −0.393213
\(649\) −5.05418 −0.198394
\(650\) 2.50215 0.0981423
\(651\) 12.7551 0.499910
\(652\) 2.14088 0.0838432
\(653\) −8.19309 −0.320620 −0.160310 0.987067i \(-0.551249\pi\)
−0.160310 + 0.987067i \(0.551249\pi\)
\(654\) −19.6685 −0.769100
\(655\) 15.4061 0.601966
\(656\) −10.4772 −0.409066
\(657\) −2.18574 −0.0852739
\(658\) 32.1605 1.25375
\(659\) −40.0175 −1.55886 −0.779431 0.626489i \(-0.784491\pi\)
−0.779431 + 0.626489i \(0.784491\pi\)
\(660\) 4.18809 0.163021
\(661\) −31.2296 −1.21469 −0.607345 0.794438i \(-0.707765\pi\)
−0.607345 + 0.794438i \(0.707765\pi\)
\(662\) 2.86964 0.111532
\(663\) 4.23867 0.164616
\(664\) 4.33584 0.168263
\(665\) −30.4827 −1.18207
\(666\) −8.96036 −0.347207
\(667\) 0.253568 0.00981821
\(668\) 15.0791 0.583427
\(669\) −39.0177 −1.50851
\(670\) −19.4611 −0.751849
\(671\) 5.01659 0.193663
\(672\) −9.80914 −0.378396
\(673\) −32.5444 −1.25449 −0.627247 0.778820i \(-0.715818\pi\)
−0.627247 + 0.778820i \(0.715818\pi\)
\(674\) −9.68411 −0.373018
\(675\) 0.439828 0.0169290
\(676\) 14.1062 0.542545
\(677\) −17.5420 −0.674192 −0.337096 0.941470i \(-0.609445\pi\)
−0.337096 + 0.941470i \(0.609445\pi\)
\(678\) 4.36080 0.167475
\(679\) 68.0069 2.60987
\(680\) 0.804420 0.0308481
\(681\) 5.43631 0.208320
\(682\) −0.981810 −0.0375955
\(683\) 31.7755 1.21586 0.607928 0.793992i \(-0.292001\pi\)
0.607928 + 0.793992i \(0.292001\pi\)
\(684\) 8.22049 0.314318
\(685\) 11.0567 0.422455
\(686\) 12.9995 0.496324
\(687\) −6.06318 −0.231325
\(688\) 1.80280 0.0687310
\(689\) −17.2460 −0.657019
\(690\) 16.6417 0.633538
\(691\) 51.0411 1.94169 0.970847 0.239701i \(-0.0770495\pi\)
0.970847 + 0.239701i \(0.0770495\pi\)
\(692\) 14.1736 0.538800
\(693\) 8.17040 0.310368
\(694\) 5.83173 0.221370
\(695\) −39.0977 −1.48306
\(696\) −0.200246 −0.00759031
\(697\) 3.60010 0.136363
\(698\) −8.77677 −0.332206
\(699\) −21.9169 −0.828974
\(700\) 1.98968 0.0752029
\(701\) −20.0337 −0.756661 −0.378330 0.925671i \(-0.623502\pi\)
−0.378330 + 0.925671i \(0.623502\pi\)
\(702\) 4.76473 0.179833
\(703\) −10.7820 −0.406649
\(704\) 0.755051 0.0284570
\(705\) 43.0882 1.62280
\(706\) −0.0838628 −0.00315622
\(707\) −2.55440 −0.0960680
\(708\) 15.8599 0.596052
\(709\) −1.49693 −0.0562184 −0.0281092 0.999605i \(-0.508949\pi\)
−0.0281092 + 0.999605i \(0.508949\pi\)
\(710\) 14.3079 0.536966
\(711\) −15.6679 −0.587590
\(712\) 8.23783 0.308726
\(713\) −3.90130 −0.146105
\(714\) 3.37054 0.126139
\(715\) −9.20289 −0.344168
\(716\) −12.3698 −0.462282
\(717\) 60.9672 2.27686
\(718\) −4.99511 −0.186416
\(719\) 27.1554 1.01273 0.506363 0.862321i \(-0.330990\pi\)
0.506363 + 0.862321i \(0.330990\pi\)
\(720\) −6.11894 −0.228040
\(721\) −31.0342 −1.15577
\(722\) −9.10832 −0.338977
\(723\) −2.52167 −0.0937819
\(724\) −10.2887 −0.382378
\(725\) 0.0406178 0.00150851
\(726\) 24.7119 0.917145
\(727\) −35.1681 −1.30431 −0.652156 0.758084i \(-0.726135\pi\)
−0.652156 + 0.758084i \(0.726135\pi\)
\(728\) 21.5545 0.798864
\(729\) −19.6574 −0.728052
\(730\) 1.95772 0.0724583
\(731\) −0.619464 −0.0229117
\(732\) −15.7419 −0.581839
\(733\) 12.8903 0.476114 0.238057 0.971251i \(-0.423490\pi\)
0.238057 + 0.971251i \(0.423490\pi\)
\(734\) −35.6347 −1.31530
\(735\) 56.2439 2.07459
\(736\) 3.00025 0.110591
\(737\) 6.27669 0.231205
\(738\) −27.3847 −1.00805
\(739\) −36.9302 −1.35850 −0.679249 0.733908i \(-0.737694\pi\)
−0.679249 + 0.733908i \(0.737694\pi\)
\(740\) 8.02558 0.295026
\(741\) −38.7967 −1.42523
\(742\) −13.7138 −0.503450
\(743\) −18.5321 −0.679876 −0.339938 0.940448i \(-0.610406\pi\)
−0.339938 + 0.940448i \(0.610406\pi\)
\(744\) 3.08090 0.112951
\(745\) −27.0203 −0.989946
\(746\) 9.03274 0.330712
\(747\) 11.3328 0.414644
\(748\) −0.259445 −0.00948625
\(749\) 56.3981 2.06074
\(750\) −25.0681 −0.915357
\(751\) 25.3340 0.924451 0.462226 0.886762i \(-0.347051\pi\)
0.462226 + 0.886762i \(0.347051\pi\)
\(752\) 7.76816 0.283276
\(753\) −0.950881 −0.0346520
\(754\) 0.440019 0.0160246
\(755\) 1.27730 0.0464857
\(756\) 3.78886 0.137800
\(757\) 6.97120 0.253373 0.126686 0.991943i \(-0.459566\pi\)
0.126686 + 0.991943i \(0.459566\pi\)
\(758\) 27.2329 0.989142
\(759\) −5.36735 −0.194822
\(760\) −7.36290 −0.267080
\(761\) −13.3353 −0.483406 −0.241703 0.970350i \(-0.577706\pi\)
−0.241703 + 0.970350i \(0.577706\pi\)
\(762\) −2.77910 −0.100676
\(763\) 34.3677 1.24419
\(764\) −8.22711 −0.297647
\(765\) 2.10255 0.0760177
\(766\) −21.1512 −0.764226
\(767\) −34.8505 −1.25838
\(768\) −2.36933 −0.0854960
\(769\) 19.5668 0.705598 0.352799 0.935699i \(-0.385230\pi\)
0.352799 + 0.935699i \(0.385230\pi\)
\(770\) −7.31804 −0.263724
\(771\) 51.3875 1.85067
\(772\) −2.60862 −0.0938864
\(773\) −21.0374 −0.756664 −0.378332 0.925670i \(-0.623502\pi\)
−0.378332 + 0.925670i \(0.623502\pi\)
\(774\) 4.71204 0.169371
\(775\) −0.624929 −0.0224481
\(776\) 16.4266 0.589682
\(777\) 33.6274 1.20638
\(778\) 2.69212 0.0965170
\(779\) −32.9519 −1.18062
\(780\) 28.8785 1.03401
\(781\) −4.61464 −0.165125
\(782\) −1.03092 −0.0368658
\(783\) 0.0773467 0.00276415
\(784\) 10.1399 0.362141
\(785\) 10.5479 0.376470
\(786\) 15.5921 0.556153
\(787\) 36.6619 1.30686 0.653428 0.756989i \(-0.273330\pi\)
0.653428 + 0.756989i \(0.273330\pi\)
\(788\) 2.73344 0.0973749
\(789\) 19.5376 0.695558
\(790\) 14.0333 0.499283
\(791\) −7.61981 −0.270929
\(792\) 1.97351 0.0701255
\(793\) 34.5913 1.22837
\(794\) 32.2819 1.14564
\(795\) −18.3736 −0.651643
\(796\) 23.9101 0.847472
\(797\) 5.38270 0.190665 0.0953325 0.995445i \(-0.469609\pi\)
0.0953325 + 0.995445i \(0.469609\pi\)
\(798\) −30.8508 −1.09211
\(799\) −2.66924 −0.0944309
\(800\) 0.480595 0.0169916
\(801\) 21.5315 0.760780
\(802\) −6.63858 −0.234416
\(803\) −0.631411 −0.0222820
\(804\) −19.6961 −0.694628
\(805\) −29.0788 −1.02489
\(806\) −6.76995 −0.238461
\(807\) −43.2750 −1.52335
\(808\) −0.616998 −0.0217059
\(809\) −14.1124 −0.496164 −0.248082 0.968739i \(-0.579800\pi\)
−0.248082 + 0.968739i \(0.579800\pi\)
\(810\) 23.4331 0.823355
\(811\) −8.53214 −0.299604 −0.149802 0.988716i \(-0.547864\pi\)
−0.149802 + 0.988716i \(0.547864\pi\)
\(812\) 0.349899 0.0122790
\(813\) −54.0308 −1.89494
\(814\) −2.58844 −0.0907249
\(815\) −5.01194 −0.175561
\(816\) 0.814133 0.0285003
\(817\) 5.66998 0.198368
\(818\) 2.28005 0.0797200
\(819\) 56.3380 1.96861
\(820\) 24.5278 0.856549
\(821\) 16.3855 0.571858 0.285929 0.958251i \(-0.407698\pi\)
0.285929 + 0.958251i \(0.407698\pi\)
\(822\) 11.1902 0.390304
\(823\) 43.3833 1.51225 0.756123 0.654430i \(-0.227091\pi\)
0.756123 + 0.654430i \(0.227091\pi\)
\(824\) −7.49611 −0.261139
\(825\) −0.859768 −0.0299333
\(826\) −27.7127 −0.964250
\(827\) −26.6757 −0.927606 −0.463803 0.885938i \(-0.653515\pi\)
−0.463803 + 0.885938i \(0.653515\pi\)
\(828\) 7.84188 0.272524
\(829\) 14.9818 0.520338 0.260169 0.965563i \(-0.416222\pi\)
0.260169 + 0.965563i \(0.416222\pi\)
\(830\) −10.1505 −0.352329
\(831\) 10.1187 0.351015
\(832\) 5.20636 0.180498
\(833\) −3.48421 −0.120721
\(834\) −39.5698 −1.37019
\(835\) −35.3011 −1.22165
\(836\) 2.37471 0.0821312
\(837\) −1.19002 −0.0411332
\(838\) −35.3845 −1.22234
\(839\) 24.2894 0.838564 0.419282 0.907856i \(-0.362282\pi\)
0.419282 + 0.907856i \(0.362282\pi\)
\(840\) 22.9639 0.792328
\(841\) −28.9929 −0.999754
\(842\) 25.3165 0.872463
\(843\) 14.0601 0.484257
\(844\) 11.5749 0.398423
\(845\) −33.0235 −1.13604
\(846\) 20.3040 0.698065
\(847\) −43.1802 −1.48369
\(848\) −3.31248 −0.113751
\(849\) −40.0770 −1.37544
\(850\) −0.165138 −0.00566420
\(851\) −10.2854 −0.352578
\(852\) 14.4806 0.496099
\(853\) 28.4467 0.973996 0.486998 0.873403i \(-0.338092\pi\)
0.486998 + 0.873403i \(0.338092\pi\)
\(854\) 27.5066 0.941257
\(855\) −19.2447 −0.658155
\(856\) 13.6226 0.465610
\(857\) −20.8145 −0.711010 −0.355505 0.934674i \(-0.615691\pi\)
−0.355505 + 0.934674i \(0.615691\pi\)
\(858\) −9.31400 −0.317975
\(859\) 17.3985 0.593629 0.296815 0.954935i \(-0.404076\pi\)
0.296815 + 0.954935i \(0.404076\pi\)
\(860\) −4.22047 −0.143917
\(861\) 102.772 3.50247
\(862\) −2.94430 −0.100283
\(863\) 0.280666 0.00955397 0.00477699 0.999989i \(-0.498479\pi\)
0.00477699 + 0.999989i \(0.498479\pi\)
\(864\) 0.915175 0.0311349
\(865\) −33.1814 −1.12820
\(866\) 41.1769 1.39925
\(867\) 39.9989 1.35843
\(868\) −5.38339 −0.182724
\(869\) −4.52609 −0.153537
\(870\) 0.468789 0.0158934
\(871\) 43.2801 1.46649
\(872\) 8.30128 0.281117
\(873\) 42.9350 1.45313
\(874\) 9.43610 0.319181
\(875\) 43.8026 1.48080
\(876\) 1.98135 0.0669438
\(877\) −13.9796 −0.472058 −0.236029 0.971746i \(-0.575846\pi\)
−0.236029 + 0.971746i \(0.575846\pi\)
\(878\) 20.0910 0.678037
\(879\) −55.9049 −1.88562
\(880\) −1.76762 −0.0595866
\(881\) −4.46270 −0.150352 −0.0751761 0.997170i \(-0.523952\pi\)
−0.0751761 + 0.997170i \(0.523952\pi\)
\(882\) 26.5032 0.892409
\(883\) −52.1843 −1.75614 −0.878070 0.478532i \(-0.841169\pi\)
−0.878070 + 0.478532i \(0.841169\pi\)
\(884\) −1.78897 −0.0601696
\(885\) −37.1291 −1.24808
\(886\) 25.9539 0.871938
\(887\) −14.9018 −0.500354 −0.250177 0.968200i \(-0.580489\pi\)
−0.250177 + 0.968200i \(0.580489\pi\)
\(888\) 8.12248 0.272573
\(889\) 4.85605 0.162867
\(890\) −19.2853 −0.646445
\(891\) −7.55774 −0.253194
\(892\) 16.4678 0.551382
\(893\) 24.4317 0.817575
\(894\) −27.3465 −0.914604
\(895\) 28.9586 0.967978
\(896\) 4.14004 0.138309
\(897\) −37.0099 −1.23572
\(898\) 29.0725 0.970161
\(899\) −0.109898 −0.00366530
\(900\) 1.25615 0.0418717
\(901\) 1.13821 0.0379193
\(902\) −7.91082 −0.263402
\(903\) −17.6839 −0.588483
\(904\) −1.84052 −0.0612146
\(905\) 24.0866 0.800667
\(906\) 1.29272 0.0429478
\(907\) −49.9055 −1.65709 −0.828543 0.559926i \(-0.810830\pi\)
−0.828543 + 0.559926i \(0.810830\pi\)
\(908\) −2.29445 −0.0761438
\(909\) −1.61267 −0.0534890
\(910\) −50.4606 −1.67275
\(911\) −1.87290 −0.0620518 −0.0310259 0.999519i \(-0.509877\pi\)
−0.0310259 + 0.999519i \(0.509877\pi\)
\(912\) −7.45180 −0.246754
\(913\) 3.27378 0.108346
\(914\) −0.918963 −0.0303966
\(915\) 36.8530 1.21832
\(916\) 2.55902 0.0845525
\(917\) −27.2448 −0.899703
\(918\) −0.314466 −0.0103789
\(919\) 10.3422 0.341156 0.170578 0.985344i \(-0.445436\pi\)
0.170578 + 0.985344i \(0.445436\pi\)
\(920\) −7.02379 −0.231567
\(921\) 41.1291 1.35525
\(922\) −25.9230 −0.853728
\(923\) −31.8197 −1.04736
\(924\) −7.40640 −0.243653
\(925\) −1.64756 −0.0541715
\(926\) −30.5937 −1.00537
\(927\) −19.5929 −0.643515
\(928\) 0.0845158 0.00277437
\(929\) 26.8316 0.880316 0.440158 0.897920i \(-0.354922\pi\)
0.440158 + 0.897920i \(0.354922\pi\)
\(930\) −7.21259 −0.236510
\(931\) 31.8912 1.04519
\(932\) 9.25024 0.303002
\(933\) −24.6979 −0.808572
\(934\) 1.42500 0.0466275
\(935\) 0.607378 0.0198634
\(936\) 13.6081 0.444794
\(937\) 9.70369 0.317006 0.158503 0.987359i \(-0.449333\pi\)
0.158503 + 0.987359i \(0.449333\pi\)
\(938\) 34.4159 1.12372
\(939\) −8.25455 −0.269377
\(940\) −18.1858 −0.593155
\(941\) −36.7138 −1.19684 −0.598419 0.801184i \(-0.704204\pi\)
−0.598419 + 0.801184i \(0.704204\pi\)
\(942\) 10.6752 0.347818
\(943\) −31.4342 −1.02364
\(944\) −6.69383 −0.217866
\(945\) −8.86998 −0.288540
\(946\) 1.36120 0.0442565
\(947\) −32.6468 −1.06088 −0.530440 0.847723i \(-0.677973\pi\)
−0.530440 + 0.847723i \(0.677973\pi\)
\(948\) 14.2028 0.461285
\(949\) −4.35381 −0.141331
\(950\) 1.51152 0.0490402
\(951\) −62.2925 −2.01997
\(952\) −1.42257 −0.0461058
\(953\) 18.0463 0.584577 0.292289 0.956330i \(-0.405583\pi\)
0.292289 + 0.956330i \(0.405583\pi\)
\(954\) −8.65797 −0.280312
\(955\) 19.2602 0.623246
\(956\) −25.7318 −0.832226
\(957\) −0.151196 −0.00488747
\(958\) −34.1758 −1.10417
\(959\) −19.5532 −0.631405
\(960\) 5.54677 0.179021
\(961\) −29.3092 −0.945457
\(962\) −17.8483 −0.575452
\(963\) 35.6059 1.14738
\(964\) 1.06429 0.0342786
\(965\) 6.10696 0.196590
\(966\) −29.4299 −0.946891
\(967\) 22.1558 0.712483 0.356241 0.934394i \(-0.384058\pi\)
0.356241 + 0.934394i \(0.384058\pi\)
\(968\) −10.4299 −0.335230
\(969\) 2.56053 0.0822561
\(970\) −38.4558 −1.23474
\(971\) 24.4008 0.783058 0.391529 0.920166i \(-0.371946\pi\)
0.391529 + 0.920166i \(0.371946\pi\)
\(972\) 20.9705 0.672629
\(973\) 69.1421 2.21659
\(974\) −19.6962 −0.631107
\(975\) −5.92842 −0.189862
\(976\) 6.64404 0.212671
\(977\) 41.3608 1.32325 0.661624 0.749836i \(-0.269867\pi\)
0.661624 + 0.749836i \(0.269867\pi\)
\(978\) −5.07245 −0.162199
\(979\) 6.21998 0.198791
\(980\) −23.7383 −0.758292
\(981\) 21.6974 0.692745
\(982\) −43.0249 −1.37298
\(983\) 8.38652 0.267489 0.133744 0.991016i \(-0.457300\pi\)
0.133744 + 0.991016i \(0.457300\pi\)
\(984\) 24.8240 0.791360
\(985\) −6.39917 −0.203895
\(986\) −0.0290407 −0.000924844 0
\(987\) −76.1990 −2.42544
\(988\) 16.3745 0.520943
\(989\) 5.40884 0.171991
\(990\) −4.62011 −0.146837
\(991\) 5.57407 0.177066 0.0885331 0.996073i \(-0.471782\pi\)
0.0885331 + 0.996073i \(0.471782\pi\)
\(992\) −1.30032 −0.0412853
\(993\) −6.79913 −0.215764
\(994\) −25.3027 −0.802552
\(995\) −55.9752 −1.77453
\(996\) −10.2731 −0.325514
\(997\) 37.0654 1.17387 0.586937 0.809633i \(-0.300334\pi\)
0.586937 + 0.809633i \(0.300334\pi\)
\(998\) −31.1367 −0.985616
\(999\) −3.13738 −0.0992622
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 4034.2.a.d.1.9 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.9 52 1.1 even 1 trivial