Properties

Label 245.4.a.j.1.1
Level $245$
Weight $4$
Character 245.1
Self dual yes
Analytic conductor $14.455$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{11}) \)
Defining polynomial: \( x^{2} - 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.31662\) of defining polynomial
Character \(\chi\) \(=\) 245.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.31662 q^{2} +5.00000 q^{3} -2.63325 q^{4} +5.00000 q^{5} -11.5831 q^{6} +24.6332 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-2.31662 q^{2} +5.00000 q^{3} -2.63325 q^{4} +5.00000 q^{5} -11.5831 q^{6} +24.6332 q^{8} -2.00000 q^{9} -11.5831 q^{10} +46.2665 q^{11} -13.1662 q^{12} -61.3325 q^{13} +25.0000 q^{15} -36.0000 q^{16} +101.332 q^{17} +4.63325 q^{18} +3.66750 q^{19} -13.1662 q^{20} -107.182 q^{22} +84.8655 q^{23} +123.166 q^{24} +25.0000 q^{25} +142.084 q^{26} -145.000 q^{27} +30.1980 q^{29} -57.9156 q^{30} +188.997 q^{31} -113.668 q^{32} +231.332 q^{33} -234.749 q^{34} +5.26650 q^{36} +18.0685 q^{37} -8.49623 q^{38} -306.662 q^{39} +123.166 q^{40} +481.662 q^{41} -97.7995 q^{43} -121.831 q^{44} -10.0000 q^{45} -196.602 q^{46} +117.665 q^{47} -180.000 q^{48} -57.9156 q^{50} +506.662 q^{51} +161.504 q^{52} +667.995 q^{53} +335.911 q^{54} +231.332 q^{55} +18.3375 q^{57} -69.9574 q^{58} +57.3350 q^{59} -65.8312 q^{60} +738.997 q^{61} -437.836 q^{62} +551.325 q^{64} -306.662 q^{65} -535.911 q^{66} +552.396 q^{67} -266.834 q^{68} +424.327 q^{69} -740.264 q^{71} -49.2665 q^{72} +233.325 q^{73} -41.8580 q^{74} +125.000 q^{75} -9.65745 q^{76} +710.422 q^{78} -1075.19 q^{79} -180.000 q^{80} -671.000 q^{81} -1115.83 q^{82} +683.325 q^{83} +506.662 q^{85} +226.565 q^{86} +150.990 q^{87} +1139.69 q^{88} -1380.32 q^{89} +23.1662 q^{90} -223.472 q^{92} +944.987 q^{93} -272.586 q^{94} +18.3375 q^{95} -568.338 q^{96} +218.008 q^{97} -92.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 10 q^{3} + 8 q^{4} + 10 q^{5} + 10 q^{6} + 36 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 10 q^{3} + 8 q^{4} + 10 q^{5} + 10 q^{6} + 36 q^{8} - 4 q^{9} + 10 q^{10} + 66 q^{11} + 40 q^{12} + 10 q^{13} + 50 q^{15} - 72 q^{16} + 70 q^{17} - 4 q^{18} + 140 q^{19} + 40 q^{20} - 22 q^{22} - 16 q^{23} + 180 q^{24} + 50 q^{25} + 450 q^{26} - 290 q^{27} - 258 q^{29} + 50 q^{30} - 20 q^{31} - 360 q^{32} + 330 q^{33} - 370 q^{34} - 16 q^{36} + 328 q^{37} + 580 q^{38} + 50 q^{39} + 180 q^{40} + 300 q^{41} - 116 q^{43} + 88 q^{44} - 20 q^{45} - 632 q^{46} - 30 q^{47} - 360 q^{48} + 50 q^{50} + 350 q^{51} + 920 q^{52} + 540 q^{53} - 290 q^{54} + 330 q^{55} + 700 q^{57} - 1314 q^{58} + 380 q^{59} + 200 q^{60} + 1080 q^{61} - 1340 q^{62} - 224 q^{64} + 50 q^{65} - 110 q^{66} + 468 q^{67} - 600 q^{68} - 80 q^{69} - 1056 q^{71} - 72 q^{72} - 860 q^{73} + 1296 q^{74} + 250 q^{75} + 1440 q^{76} + 2250 q^{78} + 158 q^{79} - 360 q^{80} - 1342 q^{81} - 1900 q^{82} + 40 q^{83} + 350 q^{85} + 148 q^{86} - 1290 q^{87} + 1364 q^{88} - 240 q^{89} - 20 q^{90} - 1296 q^{92} - 100 q^{93} - 910 q^{94} + 700 q^{95} - 1800 q^{96} + 1630 q^{97} - 132 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31662 −0.819051 −0.409525 0.912299i \(-0.634306\pi\)
−0.409525 + 0.912299i \(0.634306\pi\)
\(3\) 5.00000 0.962250 0.481125 0.876652i \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(4\) −2.63325 −0.329156
\(5\) 5.00000 0.447214
\(6\) −11.5831 −0.788132
\(7\) 0 0
\(8\) 24.6332 1.08865
\(9\) −2.00000 −0.0740741
\(10\) −11.5831 −0.366291
\(11\) 46.2665 1.26817 0.634085 0.773263i \(-0.281377\pi\)
0.634085 + 0.773263i \(0.281377\pi\)
\(12\) −13.1662 −0.316731
\(13\) −61.3325 −1.30851 −0.654253 0.756276i \(-0.727017\pi\)
−0.654253 + 0.756276i \(0.727017\pi\)
\(14\) 0 0
\(15\) 25.0000 0.430331
\(16\) −36.0000 −0.562500
\(17\) 101.332 1.44569 0.722845 0.691010i \(-0.242834\pi\)
0.722845 + 0.691010i \(0.242834\pi\)
\(18\) 4.63325 0.0606704
\(19\) 3.66750 0.0442833 0.0221417 0.999755i \(-0.492952\pi\)
0.0221417 + 0.999755i \(0.492952\pi\)
\(20\) −13.1662 −0.147203
\(21\) 0 0
\(22\) −107.182 −1.03870
\(23\) 84.8655 0.769377 0.384689 0.923046i \(-0.374309\pi\)
0.384689 + 0.923046i \(0.374309\pi\)
\(24\) 123.166 1.04755
\(25\) 25.0000 0.200000
\(26\) 142.084 1.07173
\(27\) −145.000 −1.03353
\(28\) 0 0
\(29\) 30.1980 0.193366 0.0966832 0.995315i \(-0.469177\pi\)
0.0966832 + 0.995315i \(0.469177\pi\)
\(30\) −57.9156 −0.352463
\(31\) 188.997 1.09500 0.547499 0.836806i \(-0.315580\pi\)
0.547499 + 0.836806i \(0.315580\pi\)
\(32\) −113.668 −0.627930
\(33\) 231.332 1.22030
\(34\) −234.749 −1.18409
\(35\) 0 0
\(36\) 5.26650 0.0243819
\(37\) 18.0685 0.0802823 0.0401411 0.999194i \(-0.487219\pi\)
0.0401411 + 0.999194i \(0.487219\pi\)
\(38\) −8.49623 −0.0362703
\(39\) −306.662 −1.25911
\(40\) 123.166 0.486857
\(41\) 481.662 1.83471 0.917354 0.398072i \(-0.130321\pi\)
0.917354 + 0.398072i \(0.130321\pi\)
\(42\) 0 0
\(43\) −97.7995 −0.346844 −0.173422 0.984848i \(-0.555482\pi\)
−0.173422 + 0.984848i \(0.555482\pi\)
\(44\) −121.831 −0.417426
\(45\) −10.0000 −0.0331269
\(46\) −196.602 −0.630159
\(47\) 117.665 0.365175 0.182587 0.983190i \(-0.441553\pi\)
0.182587 + 0.983190i \(0.441553\pi\)
\(48\) −180.000 −0.541266
\(49\) 0 0
\(50\) −57.9156 −0.163810
\(51\) 506.662 1.39112
\(52\) 161.504 0.430703
\(53\) 667.995 1.73125 0.865624 0.500694i \(-0.166922\pi\)
0.865624 + 0.500694i \(0.166922\pi\)
\(54\) 335.911 0.846512
\(55\) 231.332 0.567143
\(56\) 0 0
\(57\) 18.3375 0.0426116
\(58\) −69.9574 −0.158377
\(59\) 57.3350 0.126515 0.0632575 0.997997i \(-0.479851\pi\)
0.0632575 + 0.997997i \(0.479851\pi\)
\(60\) −65.8312 −0.141646
\(61\) 738.997 1.55113 0.775565 0.631268i \(-0.217465\pi\)
0.775565 + 0.631268i \(0.217465\pi\)
\(62\) −437.836 −0.896859
\(63\) 0 0
\(64\) 551.325 1.07681
\(65\) −306.662 −0.585182
\(66\) −535.911 −0.999485
\(67\) 552.396 1.00725 0.503626 0.863922i \(-0.331999\pi\)
0.503626 + 0.863922i \(0.331999\pi\)
\(68\) −266.834 −0.475858
\(69\) 424.327 0.740334
\(70\) 0 0
\(71\) −740.264 −1.23737 −0.618684 0.785640i \(-0.712334\pi\)
−0.618684 + 0.785640i \(0.712334\pi\)
\(72\) −49.2665 −0.0806405
\(73\) 233.325 0.374091 0.187045 0.982351i \(-0.440109\pi\)
0.187045 + 0.982351i \(0.440109\pi\)
\(74\) −41.8580 −0.0657553
\(75\) 125.000 0.192450
\(76\) −9.65745 −0.0145761
\(77\) 0 0
\(78\) 710.422 1.03127
\(79\) −1075.19 −1.53124 −0.765619 0.643294i \(-0.777567\pi\)
−0.765619 + 0.643294i \(0.777567\pi\)
\(80\) −180.000 −0.251558
\(81\) −671.000 −0.920439
\(82\) −1115.83 −1.50272
\(83\) 683.325 0.903671 0.451835 0.892101i \(-0.350769\pi\)
0.451835 + 0.892101i \(0.350769\pi\)
\(84\) 0 0
\(85\) 506.662 0.646532
\(86\) 226.565 0.284083
\(87\) 150.990 0.186067
\(88\) 1139.69 1.38059
\(89\) −1380.32 −1.64397 −0.821985 0.569509i \(-0.807133\pi\)
−0.821985 + 0.569509i \(0.807133\pi\)
\(90\) 23.1662 0.0271326
\(91\) 0 0
\(92\) −223.472 −0.253245
\(93\) 944.987 1.05366
\(94\) −272.586 −0.299096
\(95\) 18.3375 0.0198041
\(96\) −568.338 −0.604226
\(97\) 218.008 0.228199 0.114100 0.993469i \(-0.463602\pi\)
0.114100 + 0.993469i \(0.463602\pi\)
\(98\) 0 0
\(99\) −92.5330 −0.0939385
\(100\) −65.8312 −0.0658312
\(101\) −1474.33 −1.45249 −0.726243 0.687438i \(-0.758735\pi\)
−0.726243 + 0.687438i \(0.758735\pi\)
\(102\) −1173.75 −1.13939
\(103\) −810.990 −0.775818 −0.387909 0.921698i \(-0.626802\pi\)
−0.387909 + 0.921698i \(0.626802\pi\)
\(104\) −1510.82 −1.42450
\(105\) 0 0
\(106\) −1547.49 −1.41798
\(107\) 440.660 0.398133 0.199066 0.979986i \(-0.436209\pi\)
0.199066 + 0.979986i \(0.436209\pi\)
\(108\) 381.821 0.340192
\(109\) −1906.19 −1.67504 −0.837522 0.546404i \(-0.815996\pi\)
−0.837522 + 0.546404i \(0.815996\pi\)
\(110\) −535.911 −0.464519
\(111\) 90.3425 0.0772517
\(112\) 0 0
\(113\) 962.470 0.801252 0.400626 0.916242i \(-0.368793\pi\)
0.400626 + 0.916242i \(0.368793\pi\)
\(114\) −42.4812 −0.0349011
\(115\) 424.327 0.344076
\(116\) −79.5188 −0.0636478
\(117\) 122.665 0.0969263
\(118\) −132.824 −0.103622
\(119\) 0 0
\(120\) 615.831 0.468479
\(121\) 809.589 0.608256
\(122\) −1711.98 −1.27045
\(123\) 2408.31 1.76545
\(124\) −497.678 −0.360426
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1621.74 −1.13312 −0.566558 0.824022i \(-0.691725\pi\)
−0.566558 + 0.824022i \(0.691725\pi\)
\(128\) −367.873 −0.254029
\(129\) −488.997 −0.333751
\(130\) 710.422 0.479293
\(131\) −1380.32 −0.920602 −0.460301 0.887763i \(-0.652259\pi\)
−0.460301 + 0.887763i \(0.652259\pi\)
\(132\) −609.156 −0.401668
\(133\) 0 0
\(134\) −1279.69 −0.824991
\(135\) −725.000 −0.462208
\(136\) 2496.15 1.57385
\(137\) −1949.66 −1.21584 −0.607921 0.793997i \(-0.707996\pi\)
−0.607921 + 0.793997i \(0.707996\pi\)
\(138\) −983.008 −0.606371
\(139\) 2800.00 1.70858 0.854291 0.519795i \(-0.173992\pi\)
0.854291 + 0.519795i \(0.173992\pi\)
\(140\) 0 0
\(141\) 588.325 0.351389
\(142\) 1714.91 1.01347
\(143\) −2837.64 −1.65941
\(144\) 72.0000 0.0416667
\(145\) 150.990 0.0864761
\(146\) −540.526 −0.306399
\(147\) 0 0
\(148\) −47.5789 −0.0264254
\(149\) −1434.12 −0.788506 −0.394253 0.919002i \(-0.628997\pi\)
−0.394253 + 0.919002i \(0.628997\pi\)
\(150\) −289.578 −0.157626
\(151\) −1985.58 −1.07009 −0.535047 0.844822i \(-0.679706\pi\)
−0.535047 + 0.844822i \(0.679706\pi\)
\(152\) 90.3425 0.0482089
\(153\) −202.665 −0.107088
\(154\) 0 0
\(155\) 944.987 0.489698
\(156\) 807.519 0.414444
\(157\) 40.6600 0.0206689 0.0103345 0.999947i \(-0.496710\pi\)
0.0103345 + 0.999947i \(0.496710\pi\)
\(158\) 2490.80 1.25416
\(159\) 3339.97 1.66589
\(160\) −568.338 −0.280819
\(161\) 0 0
\(162\) 1554.46 0.753886
\(163\) −3953.98 −1.90000 −0.950000 0.312250i \(-0.898917\pi\)
−0.950000 + 0.312250i \(0.898917\pi\)
\(164\) −1268.34 −0.603906
\(165\) 1156.66 0.545734
\(166\) −1583.01 −0.740152
\(167\) 3380.30 1.56632 0.783161 0.621819i \(-0.213606\pi\)
0.783161 + 0.621819i \(0.213606\pi\)
\(168\) 0 0
\(169\) 1564.68 0.712187
\(170\) −1173.75 −0.529543
\(171\) −7.33501 −0.00328025
\(172\) 257.530 0.114166
\(173\) 3206.66 1.40924 0.704619 0.709586i \(-0.251118\pi\)
0.704619 + 0.709586i \(0.251118\pi\)
\(174\) −349.787 −0.152398
\(175\) 0 0
\(176\) −1665.59 −0.713346
\(177\) 286.675 0.121739
\(178\) 3197.68 1.34649
\(179\) 1442.65 0.602395 0.301198 0.953562i \(-0.402614\pi\)
0.301198 + 0.953562i \(0.402614\pi\)
\(180\) 26.3325 0.0109039
\(181\) −908.680 −0.373158 −0.186579 0.982440i \(-0.559740\pi\)
−0.186579 + 0.982440i \(0.559740\pi\)
\(182\) 0 0
\(183\) 3694.99 1.49258
\(184\) 2090.51 0.837580
\(185\) 90.3425 0.0359033
\(186\) −2189.18 −0.863003
\(187\) 4688.30 1.83338
\(188\) −309.841 −0.120199
\(189\) 0 0
\(190\) −42.4812 −0.0162206
\(191\) 2474.64 0.937479 0.468739 0.883336i \(-0.344708\pi\)
0.468739 + 0.883336i \(0.344708\pi\)
\(192\) 2756.62 1.03616
\(193\) 3533.52 1.31787 0.658934 0.752201i \(-0.271008\pi\)
0.658934 + 0.752201i \(0.271008\pi\)
\(194\) −505.042 −0.186907
\(195\) −1533.31 −0.563091
\(196\) 0 0
\(197\) −1952.57 −0.706165 −0.353083 0.935592i \(-0.614867\pi\)
−0.353083 + 0.935592i \(0.614867\pi\)
\(198\) 214.364 0.0769404
\(199\) 4064.67 1.44792 0.723962 0.689840i \(-0.242319\pi\)
0.723962 + 0.689840i \(0.242319\pi\)
\(200\) 615.831 0.217729
\(201\) 2761.98 0.969229
\(202\) 3415.46 1.18966
\(203\) 0 0
\(204\) −1334.17 −0.457895
\(205\) 2408.31 0.820507
\(206\) 1878.76 0.635434
\(207\) −169.731 −0.0569909
\(208\) 2207.97 0.736034
\(209\) 169.683 0.0561588
\(210\) 0 0
\(211\) −4325.34 −1.41123 −0.705613 0.708598i \(-0.749328\pi\)
−0.705613 + 0.708598i \(0.749328\pi\)
\(212\) −1759.00 −0.569851
\(213\) −3701.32 −1.19066
\(214\) −1020.84 −0.326091
\(215\) −488.997 −0.155113
\(216\) −3571.82 −1.12515
\(217\) 0 0
\(218\) 4415.92 1.37194
\(219\) 1166.62 0.359969
\(220\) −609.156 −0.186679
\(221\) −6214.97 −1.89169
\(222\) −209.290 −0.0632730
\(223\) −982.970 −0.295177 −0.147589 0.989049i \(-0.547151\pi\)
−0.147589 + 0.989049i \(0.547151\pi\)
\(224\) 0 0
\(225\) −50.0000 −0.0148148
\(226\) −2229.68 −0.656266
\(227\) −1660.96 −0.485648 −0.242824 0.970070i \(-0.578074\pi\)
−0.242824 + 0.970070i \(0.578074\pi\)
\(228\) −48.2873 −0.0140259
\(229\) −574.327 −0.165732 −0.0828660 0.996561i \(-0.526407\pi\)
−0.0828660 + 0.996561i \(0.526407\pi\)
\(230\) −983.008 −0.281816
\(231\) 0 0
\(232\) 743.875 0.210508
\(233\) −2316.48 −0.651320 −0.325660 0.945487i \(-0.605586\pi\)
−0.325660 + 0.945487i \(0.605586\pi\)
\(234\) −284.169 −0.0793876
\(235\) 588.325 0.163311
\(236\) −150.977 −0.0416432
\(237\) −5375.93 −1.47343
\(238\) 0 0
\(239\) −3659.31 −0.990382 −0.495191 0.868784i \(-0.664902\pi\)
−0.495191 + 0.868784i \(0.664902\pi\)
\(240\) −900.000 −0.242061
\(241\) 2446.33 0.653868 0.326934 0.945047i \(-0.393985\pi\)
0.326934 + 0.945047i \(0.393985\pi\)
\(242\) −1875.51 −0.498193
\(243\) 560.000 0.147835
\(244\) −1945.96 −0.510564
\(245\) 0 0
\(246\) −5579.16 −1.44599
\(247\) −224.937 −0.0579450
\(248\) 4655.62 1.19207
\(249\) 3416.62 0.869557
\(250\) −289.578 −0.0732581
\(251\) −2909.29 −0.731605 −0.365802 0.930693i \(-0.619205\pi\)
−0.365802 + 0.930693i \(0.619205\pi\)
\(252\) 0 0
\(253\) 3926.43 0.975702
\(254\) 3756.95 0.928080
\(255\) 2533.31 0.622126
\(256\) −3558.38 −0.868744
\(257\) 168.680 0.0409415 0.0204708 0.999790i \(-0.493483\pi\)
0.0204708 + 0.999790i \(0.493483\pi\)
\(258\) 1132.82 0.273359
\(259\) 0 0
\(260\) 807.519 0.192616
\(261\) −60.3960 −0.0143234
\(262\) 3197.68 0.754020
\(263\) −3244.47 −0.760695 −0.380347 0.924844i \(-0.624196\pi\)
−0.380347 + 0.924844i \(0.624196\pi\)
\(264\) 5698.47 1.32847
\(265\) 3339.97 0.774238
\(266\) 0 0
\(267\) −6901.59 −1.58191
\(268\) −1454.60 −0.331543
\(269\) −2848.65 −0.645671 −0.322836 0.946455i \(-0.604636\pi\)
−0.322836 + 0.946455i \(0.604636\pi\)
\(270\) 1679.55 0.378572
\(271\) −2850.98 −0.639057 −0.319529 0.947577i \(-0.603525\pi\)
−0.319529 + 0.947577i \(0.603525\pi\)
\(272\) −3647.97 −0.813201
\(273\) 0 0
\(274\) 4516.62 0.995837
\(275\) 1156.66 0.253634
\(276\) −1117.36 −0.243685
\(277\) 2298.63 0.498597 0.249298 0.968427i \(-0.419800\pi\)
0.249298 + 0.968427i \(0.419800\pi\)
\(278\) −6486.55 −1.39942
\(279\) −377.995 −0.0811110
\(280\) 0 0
\(281\) 6109.20 1.29695 0.648477 0.761234i \(-0.275406\pi\)
0.648477 + 0.761234i \(0.275406\pi\)
\(282\) −1362.93 −0.287806
\(283\) 5854.95 1.22983 0.614913 0.788595i \(-0.289191\pi\)
0.614913 + 0.788595i \(0.289191\pi\)
\(284\) 1949.30 0.407288
\(285\) 91.6876 0.0190565
\(286\) 6573.75 1.35914
\(287\) 0 0
\(288\) 227.335 0.0465133
\(289\) 5355.27 1.09002
\(290\) −349.787 −0.0708283
\(291\) 1090.04 0.219585
\(292\) −614.403 −0.123134
\(293\) −5135.34 −1.02392 −0.511962 0.859008i \(-0.671081\pi\)
−0.511962 + 0.859008i \(0.671081\pi\)
\(294\) 0 0
\(295\) 286.675 0.0565792
\(296\) 445.086 0.0873990
\(297\) −6708.64 −1.31069
\(298\) 3322.31 0.645827
\(299\) −5205.01 −1.00673
\(300\) −329.156 −0.0633461
\(301\) 0 0
\(302\) 4599.85 0.876462
\(303\) −7371.64 −1.39766
\(304\) −132.030 −0.0249094
\(305\) 3694.99 0.693686
\(306\) 469.499 0.0877106
\(307\) 2102.97 0.390954 0.195477 0.980708i \(-0.437375\pi\)
0.195477 + 0.980708i \(0.437375\pi\)
\(308\) 0 0
\(309\) −4054.95 −0.746531
\(310\) −2189.18 −0.401088
\(311\) −5764.30 −1.05101 −0.525504 0.850791i \(-0.676123\pi\)
−0.525504 + 0.850791i \(0.676123\pi\)
\(312\) −7554.09 −1.37073
\(313\) −1360.01 −0.245599 −0.122799 0.992432i \(-0.539187\pi\)
−0.122799 + 0.992432i \(0.539187\pi\)
\(314\) −94.1939 −0.0169289
\(315\) 0 0
\(316\) 2831.23 0.504017
\(317\) 5138.95 0.910511 0.455256 0.890361i \(-0.349548\pi\)
0.455256 + 0.890361i \(0.349548\pi\)
\(318\) −7737.47 −1.36445
\(319\) 1397.16 0.245222
\(320\) 2756.62 0.481563
\(321\) 2203.30 0.383103
\(322\) 0 0
\(323\) 371.637 0.0640200
\(324\) 1766.91 0.302968
\(325\) −1533.31 −0.261701
\(326\) 9159.90 1.55620
\(327\) −9530.94 −1.61181
\(328\) 11864.9 1.99735
\(329\) 0 0
\(330\) −2679.55 −0.446983
\(331\) 1825.70 0.303171 0.151585 0.988444i \(-0.451562\pi\)
0.151585 + 0.988444i \(0.451562\pi\)
\(332\) −1799.37 −0.297449
\(333\) −36.1370 −0.00594684
\(334\) −7830.90 −1.28290
\(335\) 2761.98 0.450457
\(336\) 0 0
\(337\) 153.985 0.0248905 0.0124452 0.999923i \(-0.496038\pi\)
0.0124452 + 0.999923i \(0.496038\pi\)
\(338\) −3624.76 −0.583317
\(339\) 4812.35 0.771005
\(340\) −1334.17 −0.212810
\(341\) 8744.25 1.38864
\(342\) 16.9925 0.00268669
\(343\) 0 0
\(344\) −2409.12 −0.377590
\(345\) 2121.64 0.331087
\(346\) −7428.63 −1.15424
\(347\) 4359.39 0.674421 0.337211 0.941429i \(-0.390517\pi\)
0.337211 + 0.941429i \(0.390517\pi\)
\(348\) −397.594 −0.0612451
\(349\) 1689.00 0.259054 0.129527 0.991576i \(-0.458654\pi\)
0.129527 + 0.991576i \(0.458654\pi\)
\(350\) 0 0
\(351\) 8893.21 1.35238
\(352\) −5259.00 −0.796322
\(353\) −3921.36 −0.591254 −0.295627 0.955303i \(-0.595529\pi\)
−0.295627 + 0.955303i \(0.595529\pi\)
\(354\) −664.119 −0.0997105
\(355\) −3701.32 −0.553368
\(356\) 3634.72 0.541123
\(357\) 0 0
\(358\) −3342.08 −0.493392
\(359\) −2867.86 −0.421616 −0.210808 0.977528i \(-0.567609\pi\)
−0.210808 + 0.977528i \(0.567609\pi\)
\(360\) −246.332 −0.0360635
\(361\) −6845.55 −0.998039
\(362\) 2105.07 0.305636
\(363\) 4047.94 0.585295
\(364\) 0 0
\(365\) 1166.62 0.167298
\(366\) −8559.90 −1.22249
\(367\) 11503.0 1.63611 0.818054 0.575142i \(-0.195053\pi\)
0.818054 + 0.575142i \(0.195053\pi\)
\(368\) −3055.16 −0.432775
\(369\) −963.325 −0.135904
\(370\) −209.290 −0.0294066
\(371\) 0 0
\(372\) −2488.39 −0.346820
\(373\) 5086.43 0.706073 0.353037 0.935610i \(-0.385149\pi\)
0.353037 + 0.935610i \(0.385149\pi\)
\(374\) −10861.0 −1.50163
\(375\) 625.000 0.0860663
\(376\) 2898.47 0.397546
\(377\) −1852.12 −0.253021
\(378\) 0 0
\(379\) 954.827 0.129409 0.0647047 0.997904i \(-0.479389\pi\)
0.0647047 + 0.997904i \(0.479389\pi\)
\(380\) −48.2873 −0.00651864
\(381\) −8108.68 −1.09034
\(382\) −5732.81 −0.767843
\(383\) 3083.91 0.411437 0.205719 0.978611i \(-0.434047\pi\)
0.205719 + 0.978611i \(0.434047\pi\)
\(384\) −1839.37 −0.244439
\(385\) 0 0
\(386\) −8185.84 −1.07940
\(387\) 195.599 0.0256921
\(388\) −574.068 −0.0751131
\(389\) −6331.15 −0.825198 −0.412599 0.910913i \(-0.635379\pi\)
−0.412599 + 0.910913i \(0.635379\pi\)
\(390\) 3552.11 0.461200
\(391\) 8599.63 1.11228
\(392\) 0 0
\(393\) −6901.59 −0.885850
\(394\) 4523.36 0.578385
\(395\) −5375.93 −0.684791
\(396\) 243.662 0.0309205
\(397\) −12133.2 −1.53388 −0.766939 0.641720i \(-0.778221\pi\)
−0.766939 + 0.641720i \(0.778221\pi\)
\(398\) −9416.32 −1.18592
\(399\) 0 0
\(400\) −900.000 −0.112500
\(401\) −270.669 −0.0337072 −0.0168536 0.999858i \(-0.505365\pi\)
−0.0168536 + 0.999858i \(0.505365\pi\)
\(402\) −6398.47 −0.793848
\(403\) −11591.7 −1.43281
\(404\) 3882.27 0.478095
\(405\) −3355.00 −0.411633
\(406\) 0 0
\(407\) 835.967 0.101812
\(408\) 12480.7 1.51443
\(409\) 4019.92 0.485996 0.242998 0.970027i \(-0.421869\pi\)
0.242998 + 0.970027i \(0.421869\pi\)
\(410\) −5579.16 −0.672036
\(411\) −9748.29 −1.16995
\(412\) 2135.54 0.255365
\(413\) 0 0
\(414\) 393.203 0.0466784
\(415\) 3416.62 0.404134
\(416\) 6971.51 0.821650
\(417\) 14000.0 1.64408
\(418\) −393.091 −0.0459969
\(419\) 2437.28 0.284175 0.142087 0.989854i \(-0.454619\pi\)
0.142087 + 0.989854i \(0.454619\pi\)
\(420\) 0 0
\(421\) −4751.36 −0.550041 −0.275020 0.961438i \(-0.588685\pi\)
−0.275020 + 0.961438i \(0.588685\pi\)
\(422\) 10020.2 1.15586
\(423\) −235.330 −0.0270500
\(424\) 16454.9 1.88472
\(425\) 2533.31 0.289138
\(426\) 8574.57 0.975210
\(427\) 0 0
\(428\) −1160.37 −0.131048
\(429\) −14188.2 −1.59677
\(430\) 1132.82 0.127046
\(431\) 7925.19 0.885714 0.442857 0.896592i \(-0.353965\pi\)
0.442857 + 0.896592i \(0.353965\pi\)
\(432\) 5220.00 0.581360
\(433\) −11487.3 −1.27492 −0.637462 0.770481i \(-0.720016\pi\)
−0.637462 + 0.770481i \(0.720016\pi\)
\(434\) 0 0
\(435\) 754.950 0.0832117
\(436\) 5019.47 0.551351
\(437\) 311.245 0.0340706
\(438\) −2702.63 −0.294833
\(439\) −9147.92 −0.994548 −0.497274 0.867594i \(-0.665666\pi\)
−0.497274 + 0.867594i \(0.665666\pi\)
\(440\) 5698.47 0.617418
\(441\) 0 0
\(442\) 14397.8 1.54939
\(443\) 1864.35 0.199950 0.0999752 0.994990i \(-0.468124\pi\)
0.0999752 + 0.994990i \(0.468124\pi\)
\(444\) −237.894 −0.0254279
\(445\) −6901.59 −0.735206
\(446\) 2277.17 0.241765
\(447\) −7170.58 −0.758741
\(448\) 0 0
\(449\) 4490.88 0.472022 0.236011 0.971750i \(-0.424160\pi\)
0.236011 + 0.971750i \(0.424160\pi\)
\(450\) 115.831 0.0121341
\(451\) 22284.8 2.32672
\(452\) −2534.42 −0.263737
\(453\) −9927.91 −1.02970
\(454\) 3847.83 0.397770
\(455\) 0 0
\(456\) 451.713 0.0463890
\(457\) −14343.8 −1.46822 −0.734109 0.679032i \(-0.762400\pi\)
−0.734109 + 0.679032i \(0.762400\pi\)
\(458\) 1330.50 0.135743
\(459\) −14693.2 −1.49416
\(460\) −1117.36 −0.113255
\(461\) −14558.7 −1.47086 −0.735429 0.677602i \(-0.763019\pi\)
−0.735429 + 0.677602i \(0.763019\pi\)
\(462\) 0 0
\(463\) −1809.56 −0.181636 −0.0908178 0.995868i \(-0.528948\pi\)
−0.0908178 + 0.995868i \(0.528948\pi\)
\(464\) −1087.13 −0.108769
\(465\) 4724.94 0.471212
\(466\) 5366.41 0.533464
\(467\) 5981.65 0.592715 0.296357 0.955077i \(-0.404228\pi\)
0.296357 + 0.955077i \(0.404228\pi\)
\(468\) −323.008 −0.0319039
\(469\) 0 0
\(470\) −1362.93 −0.133760
\(471\) 203.300 0.0198887
\(472\) 1412.35 0.137730
\(473\) −4524.84 −0.439857
\(474\) 12454.0 1.20682
\(475\) 91.6876 0.00885666
\(476\) 0 0
\(477\) −1335.99 −0.128241
\(478\) 8477.25 0.811173
\(479\) 11527.5 1.09959 0.549796 0.835299i \(-0.314705\pi\)
0.549796 + 0.835299i \(0.314705\pi\)
\(480\) −2841.69 −0.270218
\(481\) −1108.19 −0.105050
\(482\) −5667.23 −0.535551
\(483\) 0 0
\(484\) −2131.85 −0.200211
\(485\) 1090.04 0.102054
\(486\) −1297.31 −0.121085
\(487\) 15791.5 1.46936 0.734682 0.678411i \(-0.237331\pi\)
0.734682 + 0.678411i \(0.237331\pi\)
\(488\) 18203.9 1.68863
\(489\) −19769.9 −1.82828
\(490\) 0 0
\(491\) 13064.9 1.20083 0.600417 0.799687i \(-0.295001\pi\)
0.600417 + 0.799687i \(0.295001\pi\)
\(492\) −6341.69 −0.581108
\(493\) 3060.04 0.279548
\(494\) 521.095 0.0474599
\(495\) −462.665 −0.0420106
\(496\) −6803.91 −0.615937
\(497\) 0 0
\(498\) −7915.04 −0.712211
\(499\) −20135.8 −1.80642 −0.903209 0.429201i \(-0.858795\pi\)
−0.903209 + 0.429201i \(0.858795\pi\)
\(500\) −329.156 −0.0294406
\(501\) 16901.5 1.50719
\(502\) 6739.73 0.599221
\(503\) 751.675 0.0666313 0.0333156 0.999445i \(-0.489393\pi\)
0.0333156 + 0.999445i \(0.489393\pi\)
\(504\) 0 0
\(505\) −7371.64 −0.649571
\(506\) −9096.06 −0.799149
\(507\) 7823.38 0.685302
\(508\) 4270.44 0.372972
\(509\) 12334.5 1.07410 0.537049 0.843551i \(-0.319539\pi\)
0.537049 + 0.843551i \(0.319539\pi\)
\(510\) −5868.73 −0.509553
\(511\) 0 0
\(512\) 11186.4 0.965574
\(513\) −531.788 −0.0457681
\(514\) −390.768 −0.0335332
\(515\) −4054.95 −0.346956
\(516\) 1287.65 0.109856
\(517\) 5443.95 0.463104
\(518\) 0 0
\(519\) 16033.3 1.35604
\(520\) −7554.09 −0.637056
\(521\) 1736.43 0.146016 0.0730082 0.997331i \(-0.476740\pi\)
0.0730082 + 0.997331i \(0.476740\pi\)
\(522\) 139.915 0.0117316
\(523\) 1421.42 0.118842 0.0594210 0.998233i \(-0.481075\pi\)
0.0594210 + 0.998233i \(0.481075\pi\)
\(524\) 3634.72 0.303022
\(525\) 0 0
\(526\) 7516.23 0.623048
\(527\) 19151.6 1.58303
\(528\) −8327.97 −0.686417
\(529\) −4964.85 −0.408059
\(530\) −7737.47 −0.634140
\(531\) −114.670 −0.00937148
\(532\) 0 0
\(533\) −29541.6 −2.40073
\(534\) 15988.4 1.29567
\(535\) 2203.30 0.178050
\(536\) 13607.3 1.09654
\(537\) 7213.25 0.579655
\(538\) 6599.26 0.528837
\(539\) 0 0
\(540\) 1909.11 0.152139
\(541\) 5773.27 0.458802 0.229401 0.973332i \(-0.426323\pi\)
0.229401 + 0.973332i \(0.426323\pi\)
\(542\) 6604.64 0.523420
\(543\) −4543.40 −0.359072
\(544\) −11518.2 −0.907793
\(545\) −9530.94 −0.749102
\(546\) 0 0
\(547\) −3941.30 −0.308076 −0.154038 0.988065i \(-0.549228\pi\)
−0.154038 + 0.988065i \(0.549228\pi\)
\(548\) 5133.93 0.400202
\(549\) −1477.99 −0.114899
\(550\) −2679.55 −0.207739
\(551\) 110.751 0.00856291
\(552\) 10452.6 0.805961
\(553\) 0 0
\(554\) −5325.06 −0.408376
\(555\) 451.713 0.0345480
\(556\) −7373.10 −0.562390
\(557\) −6951.74 −0.528823 −0.264412 0.964410i \(-0.585178\pi\)
−0.264412 + 0.964410i \(0.585178\pi\)
\(558\) 875.673 0.0664340
\(559\) 5998.29 0.453847
\(560\) 0 0
\(561\) 23441.5 1.76417
\(562\) −14152.7 −1.06227
\(563\) 24284.6 1.81789 0.908946 0.416913i \(-0.136888\pi\)
0.908946 + 0.416913i \(0.136888\pi\)
\(564\) −1549.21 −0.115662
\(565\) 4812.35 0.358331
\(566\) −13563.7 −1.00729
\(567\) 0 0
\(568\) −18235.1 −1.34706
\(569\) −21563.4 −1.58873 −0.794363 0.607443i \(-0.792195\pi\)
−0.794363 + 0.607443i \(0.792195\pi\)
\(570\) −212.406 −0.0156082
\(571\) −3689.56 −0.270409 −0.135204 0.990818i \(-0.543169\pi\)
−0.135204 + 0.990818i \(0.543169\pi\)
\(572\) 7472.21 0.546204
\(573\) 12373.2 0.902090
\(574\) 0 0
\(575\) 2121.64 0.153875
\(576\) −1102.65 −0.0797634
\(577\) −22183.9 −1.60057 −0.800285 0.599620i \(-0.795318\pi\)
−0.800285 + 0.599620i \(0.795318\pi\)
\(578\) −12406.2 −0.892783
\(579\) 17667.6 1.26812
\(580\) −397.594 −0.0284641
\(581\) 0 0
\(582\) −2525.21 −0.179851
\(583\) 30905.8 2.19552
\(584\) 5747.55 0.407252
\(585\) 613.325 0.0433468
\(586\) 11896.7 0.838646
\(587\) 10605.3 0.745705 0.372852 0.927891i \(-0.378380\pi\)
0.372852 + 0.927891i \(0.378380\pi\)
\(588\) 0 0
\(589\) 693.149 0.0484902
\(590\) −664.119 −0.0463412
\(591\) −9762.83 −0.679508
\(592\) −650.466 −0.0451588
\(593\) 6277.25 0.434698 0.217349 0.976094i \(-0.430259\pi\)
0.217349 + 0.976094i \(0.430259\pi\)
\(594\) 15541.4 1.07352
\(595\) 0 0
\(596\) 3776.39 0.259542
\(597\) 20323.4 1.39327
\(598\) 12058.1 0.824567
\(599\) −9970.73 −0.680122 −0.340061 0.940403i \(-0.610448\pi\)
−0.340061 + 0.940403i \(0.610448\pi\)
\(600\) 3079.16 0.209510
\(601\) −24619.2 −1.67094 −0.835472 0.549533i \(-0.814806\pi\)
−0.835472 + 0.549533i \(0.814806\pi\)
\(602\) 0 0
\(603\) −1104.79 −0.0746113
\(604\) 5228.53 0.352228
\(605\) 4047.94 0.272020
\(606\) 17077.3 1.14475
\(607\) 11252.9 0.752460 0.376230 0.926526i \(-0.377220\pi\)
0.376230 + 0.926526i \(0.377220\pi\)
\(608\) −416.876 −0.0278068
\(609\) 0 0
\(610\) −8559.90 −0.568164
\(611\) −7216.69 −0.477833
\(612\) 533.668 0.0352487
\(613\) −15293.2 −1.00765 −0.503824 0.863807i \(-0.668074\pi\)
−0.503824 + 0.863807i \(0.668074\pi\)
\(614\) −4871.79 −0.320211
\(615\) 12041.6 0.789533
\(616\) 0 0
\(617\) −17589.4 −1.14769 −0.573843 0.818966i \(-0.694548\pi\)
−0.573843 + 0.818966i \(0.694548\pi\)
\(618\) 9393.80 0.611446
\(619\) −23467.4 −1.52380 −0.761900 0.647694i \(-0.775733\pi\)
−0.761900 + 0.647694i \(0.775733\pi\)
\(620\) −2488.39 −0.161187
\(621\) −12305.5 −0.795173
\(622\) 13353.7 0.860829
\(623\) 0 0
\(624\) 11039.8 0.708249
\(625\) 625.000 0.0400000
\(626\) 3150.64 0.201158
\(627\) 848.413 0.0540388
\(628\) −107.068 −0.00680330
\(629\) 1830.93 0.116063
\(630\) 0 0
\(631\) −6040.86 −0.381114 −0.190557 0.981676i \(-0.561029\pi\)
−0.190557 + 0.981676i \(0.561029\pi\)
\(632\) −26485.3 −1.66698
\(633\) −21626.7 −1.35795
\(634\) −11905.0 −0.745755
\(635\) −8108.68 −0.506745
\(636\) −8794.99 −0.548340
\(637\) 0 0
\(638\) −3236.68 −0.200849
\(639\) 1480.53 0.0916569
\(640\) −1839.37 −0.113605
\(641\) 25111.6 1.54735 0.773673 0.633586i \(-0.218418\pi\)
0.773673 + 0.633586i \(0.218418\pi\)
\(642\) −5104.22 −0.313781
\(643\) 3095.03 0.189823 0.0949113 0.995486i \(-0.469743\pi\)
0.0949113 + 0.995486i \(0.469743\pi\)
\(644\) 0 0
\(645\) −2444.99 −0.149258
\(646\) −860.944 −0.0524356
\(647\) 9178.63 0.557727 0.278863 0.960331i \(-0.410042\pi\)
0.278863 + 0.960331i \(0.410042\pi\)
\(648\) −16528.9 −1.00203
\(649\) 2652.69 0.160443
\(650\) 3552.11 0.214346
\(651\) 0 0
\(652\) 10411.8 0.625397
\(653\) −14438.4 −0.865265 −0.432632 0.901570i \(-0.642415\pi\)
−0.432632 + 0.901570i \(0.642415\pi\)
\(654\) 22079.6 1.32015
\(655\) −6901.59 −0.411706
\(656\) −17339.8 −1.03202
\(657\) −466.650 −0.0277104
\(658\) 0 0
\(659\) −2900.64 −0.171461 −0.0857305 0.996318i \(-0.527322\pi\)
−0.0857305 + 0.996318i \(0.527322\pi\)
\(660\) −3045.78 −0.179632
\(661\) 9976.52 0.587053 0.293526 0.955951i \(-0.405171\pi\)
0.293526 + 0.955951i \(0.405171\pi\)
\(662\) −4229.46 −0.248312
\(663\) −31074.9 −1.82028
\(664\) 16832.5 0.983777
\(665\) 0 0
\(666\) 83.7159 0.00487076
\(667\) 2562.77 0.148772
\(668\) −8901.19 −0.515565
\(669\) −4914.85 −0.284034
\(670\) −6398.47 −0.368947
\(671\) 34190.8 1.96710
\(672\) 0 0
\(673\) 20760.8 1.18911 0.594554 0.804055i \(-0.297329\pi\)
0.594554 + 0.804055i \(0.297329\pi\)
\(674\) −356.725 −0.0203866
\(675\) −3625.00 −0.206706
\(676\) −4120.18 −0.234421
\(677\) 3209.13 0.182181 0.0910907 0.995843i \(-0.470965\pi\)
0.0910907 + 0.995843i \(0.470965\pi\)
\(678\) −11148.4 −0.631492
\(679\) 0 0
\(680\) 12480.7 0.703845
\(681\) −8304.82 −0.467315
\(682\) −20257.2 −1.13737
\(683\) 4333.57 0.242781 0.121391 0.992605i \(-0.461265\pi\)
0.121391 + 0.992605i \(0.461265\pi\)
\(684\) 19.3149 0.00107971
\(685\) −9748.29 −0.543741
\(686\) 0 0
\(687\) −2871.64 −0.159476
\(688\) 3520.78 0.195100
\(689\) −40969.8 −2.26535
\(690\) −4915.04 −0.271177
\(691\) −14446.0 −0.795297 −0.397649 0.917538i \(-0.630174\pi\)
−0.397649 + 0.917538i \(0.630174\pi\)
\(692\) −8443.94 −0.463859
\(693\) 0 0
\(694\) −10099.1 −0.552385
\(695\) 14000.0 0.764101
\(696\) 3719.37 0.202561
\(697\) 48808.1 2.65242
\(698\) −3912.77 −0.212179
\(699\) −11582.4 −0.626733
\(700\) 0 0
\(701\) −859.801 −0.0463256 −0.0231628 0.999732i \(-0.507374\pi\)
−0.0231628 + 0.999732i \(0.507374\pi\)
\(702\) −20602.2 −1.10767
\(703\) 66.2663 0.00355517
\(704\) 25507.9 1.36557
\(705\) 2941.62 0.157146
\(706\) 9084.31 0.484267
\(707\) 0 0
\(708\) −754.887 −0.0400712
\(709\) −7979.13 −0.422655 −0.211327 0.977415i \(-0.567779\pi\)
−0.211327 + 0.977415i \(0.567779\pi\)
\(710\) 8574.57 0.453236
\(711\) 2150.37 0.113425
\(712\) −34001.7 −1.78970
\(713\) 16039.4 0.842467
\(714\) 0 0
\(715\) −14188.2 −0.742110
\(716\) −3798.86 −0.198282
\(717\) −18296.6 −0.952995
\(718\) 6643.76 0.345325
\(719\) −33703.3 −1.74815 −0.874076 0.485790i \(-0.838532\pi\)
−0.874076 + 0.485790i \(0.838532\pi\)
\(720\) 360.000 0.0186339
\(721\) 0 0
\(722\) 15858.6 0.817444
\(723\) 12231.7 0.629185
\(724\) 2392.78 0.122827
\(725\) 754.950 0.0386733
\(726\) −9377.57 −0.479386
\(727\) −30277.0 −1.54458 −0.772290 0.635270i \(-0.780889\pi\)
−0.772290 + 0.635270i \(0.780889\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) −2702.63 −0.137026
\(731\) −9910.27 −0.501429
\(732\) −9729.82 −0.491291
\(733\) 19363.9 0.975749 0.487874 0.872914i \(-0.337772\pi\)
0.487874 + 0.872914i \(0.337772\pi\)
\(734\) −26648.1 −1.34005
\(735\) 0 0
\(736\) −9646.45 −0.483115
\(737\) 25557.4 1.27737
\(738\) 2231.66 0.111313
\(739\) 24952.4 1.24207 0.621035 0.783783i \(-0.286713\pi\)
0.621035 + 0.783783i \(0.286713\pi\)
\(740\) −237.894 −0.0118178
\(741\) −1124.69 −0.0557576
\(742\) 0 0
\(743\) −8154.54 −0.402640 −0.201320 0.979526i \(-0.564523\pi\)
−0.201320 + 0.979526i \(0.564523\pi\)
\(744\) 23278.1 1.14707
\(745\) −7170.58 −0.352631
\(746\) −11783.3 −0.578310
\(747\) −1366.65 −0.0669386
\(748\) −12345.5 −0.603469
\(749\) 0 0
\(750\) −1447.89 −0.0704926
\(751\) −4311.26 −0.209481 −0.104740 0.994500i \(-0.533401\pi\)
−0.104740 + 0.994500i \(0.533401\pi\)
\(752\) −4235.94 −0.205411
\(753\) −14546.4 −0.703987
\(754\) 4290.66 0.207237
\(755\) −9927.91 −0.478561
\(756\) 0 0
\(757\) 3624.79 0.174036 0.0870179 0.996207i \(-0.472266\pi\)
0.0870179 + 0.996207i \(0.472266\pi\)
\(758\) −2211.98 −0.105993
\(759\) 19632.1 0.938869
\(760\) 451.713 0.0215597
\(761\) 20576.4 0.980150 0.490075 0.871680i \(-0.336969\pi\)
0.490075 + 0.871680i \(0.336969\pi\)
\(762\) 18784.8 0.893045
\(763\) 0 0
\(764\) −6516.34 −0.308577
\(765\) −1013.32 −0.0478913
\(766\) −7144.26 −0.336988
\(767\) −3516.50 −0.165546
\(768\) −17791.9 −0.835949
\(769\) −3066.14 −0.143781 −0.0718907 0.997413i \(-0.522903\pi\)
−0.0718907 + 0.997413i \(0.522903\pi\)
\(770\) 0 0
\(771\) 843.400 0.0393960
\(772\) −9304.64 −0.433784
\(773\) −19387.0 −0.902074 −0.451037 0.892505i \(-0.648946\pi\)
−0.451037 + 0.892505i \(0.648946\pi\)
\(774\) −453.129 −0.0210432
\(775\) 4724.94 0.219000
\(776\) 5370.23 0.248428
\(777\) 0 0
\(778\) 14666.9 0.675879
\(779\) 1766.50 0.0812470
\(780\) 4037.59 0.185345
\(781\) −34249.4 −1.56919
\(782\) −19922.1 −0.911015
\(783\) −4378.71 −0.199850
\(784\) 0 0
\(785\) 203.300 0.00924342
\(786\) 15988.4 0.725556
\(787\) 43363.4 1.96409 0.982044 0.188651i \(-0.0604115\pi\)
0.982044 + 0.188651i \(0.0604115\pi\)
\(788\) 5141.59 0.232439
\(789\) −16222.4 −0.731979
\(790\) 12454.0 0.560878
\(791\) 0 0
\(792\) −2279.39 −0.102266
\(793\) −45324.6 −2.02966
\(794\) 28108.2 1.25632
\(795\) 16699.9 0.745011
\(796\) −10703.3 −0.476593
\(797\) 17132.6 0.761439 0.380720 0.924691i \(-0.375676\pi\)
0.380720 + 0.924691i \(0.375676\pi\)
\(798\) 0 0
\(799\) 11923.3 0.527929
\(800\) −2841.69 −0.125586
\(801\) 2760.63 0.121776
\(802\) 627.039 0.0276079
\(803\) 10795.1 0.474411
\(804\) −7272.98 −0.319028
\(805\) 0 0
\(806\) 26853.6 1.17355
\(807\) −14243.3 −0.621297
\(808\) −36317.5 −1.58124
\(809\) −1080.49 −0.0469566 −0.0234783 0.999724i \(-0.507474\pi\)
−0.0234783 + 0.999724i \(0.507474\pi\)
\(810\) 7772.28 0.337148
\(811\) 19593.9 0.848378 0.424189 0.905574i \(-0.360559\pi\)
0.424189 + 0.905574i \(0.360559\pi\)
\(812\) 0 0
\(813\) −14254.9 −0.614933
\(814\) −1936.62 −0.0833889
\(815\) −19769.9 −0.849706
\(816\) −18239.8 −0.782503
\(817\) −358.680 −0.0153594
\(818\) −9312.66 −0.398056
\(819\) 0 0
\(820\) −6341.69 −0.270075
\(821\) 5123.80 0.217810 0.108905 0.994052i \(-0.465266\pi\)
0.108905 + 0.994052i \(0.465266\pi\)
\(822\) 22583.1 0.958244
\(823\) −13184.1 −0.558405 −0.279202 0.960232i \(-0.590070\pi\)
−0.279202 + 0.960232i \(0.590070\pi\)
\(824\) −19977.3 −0.844591
\(825\) 5783.31 0.244060
\(826\) 0 0
\(827\) 24658.7 1.03684 0.518421 0.855126i \(-0.326520\pi\)
0.518421 + 0.855126i \(0.326520\pi\)
\(828\) 446.944 0.0187589
\(829\) −28562.3 −1.19664 −0.598318 0.801259i \(-0.704164\pi\)
−0.598318 + 0.801259i \(0.704164\pi\)
\(830\) −7915.04 −0.331006
\(831\) 11493.1 0.479775
\(832\) −33814.1 −1.40901
\(833\) 0 0
\(834\) −32432.7 −1.34659
\(835\) 16901.5 0.700481
\(836\) −446.817 −0.0184850
\(837\) −27404.6 −1.13171
\(838\) −5646.27 −0.232753
\(839\) 31106.0 1.27997 0.639987 0.768386i \(-0.278940\pi\)
0.639987 + 0.768386i \(0.278940\pi\)
\(840\) 0 0
\(841\) −23477.1 −0.962609
\(842\) 11007.1 0.450511
\(843\) 30546.0 1.24800
\(844\) 11389.7 0.464514
\(845\) 7823.38 0.318500
\(846\) 545.171 0.0221553
\(847\) 0 0
\(848\) −24047.8 −0.973827
\(849\) 29274.7 1.18340
\(850\) −5868.73 −0.236819
\(851\) 1533.39 0.0617674
\(852\) 9746.50 0.391913
\(853\) −20567.9 −0.825596 −0.412798 0.910823i \(-0.635448\pi\)
−0.412798 + 0.910823i \(0.635448\pi\)
\(854\) 0 0
\(855\) −36.6750 −0.00146697
\(856\) 10854.9 0.433426
\(857\) −6459.44 −0.257468 −0.128734 0.991679i \(-0.541091\pi\)
−0.128734 + 0.991679i \(0.541091\pi\)
\(858\) 32868.7 1.30783
\(859\) 48214.4 1.91508 0.957541 0.288298i \(-0.0930895\pi\)
0.957541 + 0.288298i \(0.0930895\pi\)
\(860\) 1287.65 0.0510565
\(861\) 0 0
\(862\) −18359.7 −0.725445
\(863\) −31709.5 −1.25076 −0.625378 0.780322i \(-0.715055\pi\)
−0.625378 + 0.780322i \(0.715055\pi\)
\(864\) 16481.8 0.648984
\(865\) 16033.3 0.630230
\(866\) 26611.7 1.04423
\(867\) 26776.4 1.04887
\(868\) 0 0
\(869\) −49745.1 −1.94187
\(870\) −1748.94 −0.0681546
\(871\) −33879.8 −1.31800
\(872\) −46955.6 −1.82353
\(873\) −436.015 −0.0169036
\(874\) −721.037 −0.0279055
\(875\) 0 0
\(876\) −3072.01 −0.118486
\(877\) 25654.8 0.987799 0.493900 0.869519i \(-0.335571\pi\)
0.493900 + 0.869519i \(0.335571\pi\)
\(878\) 21192.3 0.814585
\(879\) −25676.7 −0.985272
\(880\) −8327.97 −0.319018
\(881\) 11470.4 0.438647 0.219323 0.975652i \(-0.429615\pi\)
0.219323 + 0.975652i \(0.429615\pi\)
\(882\) 0 0
\(883\) 39124.0 1.49108 0.745542 0.666459i \(-0.232191\pi\)
0.745542 + 0.666459i \(0.232191\pi\)
\(884\) 16365.6 0.622663
\(885\) 1433.38 0.0544434
\(886\) −4319.01 −0.163770
\(887\) −15585.8 −0.589987 −0.294994 0.955499i \(-0.595318\pi\)
−0.294994 + 0.955499i \(0.595318\pi\)
\(888\) 2225.43 0.0840997
\(889\) 0 0
\(890\) 15988.4 0.602171
\(891\) −31044.8 −1.16727
\(892\) 2588.40 0.0971594
\(893\) 431.537 0.0161711
\(894\) 16611.6 0.621447
\(895\) 7213.25 0.269399
\(896\) 0 0
\(897\) −26025.1 −0.968731
\(898\) −10403.7 −0.386610
\(899\) 5707.34 0.211736
\(900\) 131.662 0.00487639
\(901\) 67689.6 2.50285
\(902\) −51625.6 −1.90570
\(903\) 0 0
\(904\) 23708.8 0.872280
\(905\) −4543.40 −0.166881
\(906\) 22999.2 0.843376
\(907\) 27596.1 1.01027 0.505134 0.863041i \(-0.331443\pi\)
0.505134 + 0.863041i \(0.331443\pi\)
\(908\) 4373.73 0.159854
\(909\) 2948.65 0.107592
\(910\) 0 0
\(911\) −14396.2 −0.523565 −0.261782 0.965127i \(-0.584310\pi\)
−0.261782 + 0.965127i \(0.584310\pi\)
\(912\) −660.151 −0.0239691
\(913\) 31615.1 1.14601
\(914\) 33229.2 1.20254
\(915\) 18474.9 0.667500
\(916\) 1512.35 0.0545517
\(917\) 0 0
\(918\) 34038.7 1.22379
\(919\) 10279.6 0.368978 0.184489 0.982835i \(-0.440937\pi\)
0.184489 + 0.982835i \(0.440937\pi\)
\(920\) 10452.6 0.374577
\(921\) 10514.8 0.376196
\(922\) 33727.0 1.20471
\(923\) 45402.2 1.61910
\(924\) 0 0
\(925\) 451.713 0.0160565
\(926\) 4192.06 0.148769
\(927\) 1621.98 0.0574680
\(928\) −3432.53 −0.121421
\(929\) 6499.87 0.229552 0.114776 0.993391i \(-0.463385\pi\)
0.114776 + 0.993391i \(0.463385\pi\)
\(930\) −10945.9 −0.385947
\(931\) 0 0
\(932\) 6099.86 0.214386
\(933\) −28821.5 −1.01133
\(934\) −13857.2 −0.485463
\(935\) 23441.5 0.819913
\(936\) 3021.64 0.105518
\(937\) −10269.8 −0.358056 −0.179028 0.983844i \(-0.557295\pi\)
−0.179028 + 0.983844i \(0.557295\pi\)
\(938\) 0 0
\(939\) −6800.06 −0.236328
\(940\) −1549.21 −0.0537548
\(941\) 34396.2 1.19159 0.595794 0.803137i \(-0.296837\pi\)
0.595794 + 0.803137i \(0.296837\pi\)
\(942\) −470.969 −0.0162898
\(943\) 40876.5 1.41158
\(944\) −2064.06 −0.0711647
\(945\) 0 0
\(946\) 10482.4 0.360265
\(947\) 27192.1 0.933078 0.466539 0.884501i \(-0.345501\pi\)
0.466539 + 0.884501i \(0.345501\pi\)
\(948\) 14156.2 0.484990
\(949\) −14310.4 −0.489500
\(950\) −212.406 −0.00725406
\(951\) 25694.7 0.876140
\(952\) 0 0
\(953\) 49965.2 1.69836 0.849178 0.528107i \(-0.177098\pi\)
0.849178 + 0.528107i \(0.177098\pi\)
\(954\) 3094.99 0.105036
\(955\) 12373.2 0.419253
\(956\) 9635.88 0.325990
\(957\) 6985.78 0.235965
\(958\) −26704.9 −0.900622
\(959\) 0 0
\(960\) 13783.1 0.463384
\(961\) 5929.05 0.199022
\(962\) 2567.25 0.0860411
\(963\) −881.320 −0.0294913
\(964\) −6441.80 −0.215225
\(965\) 17667.6 0.589368
\(966\) 0 0
\(967\) −16755.5 −0.557208 −0.278604 0.960406i \(-0.589872\pi\)
−0.278604 + 0.960406i \(0.589872\pi\)
\(968\) 19942.8 0.662176
\(969\) 1858.19 0.0616033
\(970\) −2525.21 −0.0835872
\(971\) −37617.4 −1.24325 −0.621626 0.783314i \(-0.713528\pi\)
−0.621626 + 0.783314i \(0.713528\pi\)
\(972\) −1474.62 −0.0486610
\(973\) 0 0
\(974\) −36583.0 −1.20348
\(975\) −7666.56 −0.251822
\(976\) −26603.9 −0.872511
\(977\) −27690.9 −0.906767 −0.453384 0.891315i \(-0.649783\pi\)
−0.453384 + 0.891315i \(0.649783\pi\)
\(978\) 45799.5 1.49745
\(979\) −63862.5 −2.08483
\(980\) 0 0
\(981\) 3812.38 0.124077
\(982\) −30266.4 −0.983544
\(983\) −22754.2 −0.738299 −0.369149 0.929370i \(-0.620351\pi\)
−0.369149 + 0.929370i \(0.620351\pi\)
\(984\) 59324.6 1.92195
\(985\) −9762.83 −0.315807
\(986\) −7088.96 −0.228964
\(987\) 0 0
\(988\) 592.316 0.0190729
\(989\) −8299.80 −0.266854
\(990\) 1071.82 0.0344088
\(991\) −55470.9 −1.77809 −0.889047 0.457816i \(-0.848632\pi\)
−0.889047 + 0.457816i \(0.848632\pi\)
\(992\) −21482.9 −0.687583
\(993\) 9128.50 0.291726
\(994\) 0 0
\(995\) 20323.4 0.647531
\(996\) −8996.83 −0.286220
\(997\) −15181.9 −0.482264 −0.241132 0.970492i \(-0.577519\pi\)
−0.241132 + 0.970492i \(0.577519\pi\)
\(998\) 46647.1 1.47955
\(999\) −2619.93 −0.0829740
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 245.4.a.j.1.1 yes 2
3.2 odd 2 2205.4.a.w.1.2 2
5.4 even 2 1225.4.a.p.1.2 2
7.2 even 3 245.4.e.j.116.2 4
7.3 odd 6 245.4.e.k.226.2 4
7.4 even 3 245.4.e.j.226.2 4
7.5 odd 6 245.4.e.k.116.2 4
7.6 odd 2 245.4.a.i.1.1 2
21.20 even 2 2205.4.a.x.1.2 2
35.34 odd 2 1225.4.a.q.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.i.1.1 2 7.6 odd 2
245.4.a.j.1.1 yes 2 1.1 even 1 trivial
245.4.e.j.116.2 4 7.2 even 3
245.4.e.j.226.2 4 7.4 even 3
245.4.e.k.116.2 4 7.5 odd 6
245.4.e.k.226.2 4 7.3 odd 6
1225.4.a.p.1.2 2 5.4 even 2
1225.4.a.q.1.2 2 35.34 odd 2
2205.4.a.w.1.2 2 3.2 odd 2
2205.4.a.x.1.2 2 21.20 even 2