Properties

Label 1225.4.a.q.1.2
Level $1225$
Weight $4$
Character 1225.1
Self dual yes
Analytic conductor $72.277$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.2773397570\)
Analytic rank: \(1\)
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: no (minimal twist has level 245)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.31662\) of defining polynomial
Character \(\chi\) \(=\) 1225.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.31662 q^{2} +5.00000 q^{3} -2.63325 q^{4} +11.5831 q^{6} -24.6332 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+2.31662 q^{2} +5.00000 q^{3} -2.63325 q^{4} +11.5831 q^{6} -24.6332 q^{8} -2.00000 q^{9} +46.2665 q^{11} -13.1662 q^{12} -61.3325 q^{13} -36.0000 q^{16} +101.332 q^{17} -4.63325 q^{18} -3.66750 q^{19} +107.182 q^{22} -84.8655 q^{23} -123.166 q^{24} -142.084 q^{26} -145.000 q^{27} +30.1980 q^{29} -188.997 q^{31} +113.668 q^{32} +231.332 q^{33} +234.749 q^{34} +5.26650 q^{36} -18.0685 q^{37} -8.49623 q^{38} -306.662 q^{39} -481.662 q^{41} +97.7995 q^{43} -121.831 q^{44} -196.602 q^{46} +117.665 q^{47} -180.000 q^{48} +506.662 q^{51} +161.504 q^{52} -667.995 q^{53} -335.911 q^{54} -18.3375 q^{57} +69.9574 q^{58} -57.3350 q^{59} -738.997 q^{61} -437.836 q^{62} +551.325 q^{64} +535.911 q^{66} -552.396 q^{67} -266.834 q^{68} -424.327 q^{69} -740.264 q^{71} +49.2665 q^{72} +233.325 q^{73} -41.8580 q^{74} +9.65745 q^{76} -710.422 q^{78} -1075.19 q^{79} -671.000 q^{81} -1115.83 q^{82} +683.325 q^{83} +226.565 q^{86} +150.990 q^{87} -1139.69 q^{88} +1380.32 q^{89} +223.472 q^{92} -944.987 q^{93} +272.586 q^{94} +568.338 q^{96} +218.008 q^{97} -92.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 10 q^{3} + 8 q^{4} - 10 q^{6} - 36 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 10 q^{3} + 8 q^{4} - 10 q^{6} - 36 q^{8} - 4 q^{9} + 66 q^{11} + 40 q^{12} + 10 q^{13} - 72 q^{16} + 70 q^{17} + 4 q^{18} - 140 q^{19} + 22 q^{22} + 16 q^{23} - 180 q^{24} - 450 q^{26} - 290 q^{27} - 258 q^{29} + 20 q^{31} + 360 q^{32} + 330 q^{33} + 370 q^{34} - 16 q^{36} - 328 q^{37} + 580 q^{38} + 50 q^{39} - 300 q^{41} + 116 q^{43} + 88 q^{44} - 632 q^{46} - 30 q^{47} - 360 q^{48} + 350 q^{51} + 920 q^{52} - 540 q^{53} + 290 q^{54} - 700 q^{57} + 1314 q^{58} - 380 q^{59} - 1080 q^{61} - 1340 q^{62} - 224 q^{64} + 110 q^{66} - 468 q^{67} - 600 q^{68} + 80 q^{69} - 1056 q^{71} + 72 q^{72} - 860 q^{73} + 1296 q^{74} - 1440 q^{76} - 2250 q^{78} + 158 q^{79} - 1342 q^{81} - 1900 q^{82} + 40 q^{83} + 148 q^{86} - 1290 q^{87} - 1364 q^{88} + 240 q^{89} + 1296 q^{92} + 100 q^{93} + 910 q^{94} + 1800 q^{96} + 1630 q^{97} - 132 q^{99}+O(q^{100}) \) 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 \(-0.365694\pi\)
0.409525 + 0.912299i \(0.365694\pi\)
\(3\) 5.00000 0.962250 0.481125 0.876652i \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(4\) −2.63325 −0.329156
\(5\) 0 0
\(6\) 11.5831 0.788132
\(7\) 0 0
\(8\) −24.6332 −1.08865
\(9\) −2.00000 −0.0740741
\(10\) 0 0
\(11\) 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
\(15\) 0 0
\(16\) −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 \(-0.507048\pi\)
−0.0221417 + 0.999755i \(0.507048\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 107.182 1.03870
\(23\) −84.8655 −0.769377 −0.384689 0.923046i \(-0.625691\pi\)
−0.384689 + 0.923046i \(0.625691\pi\)
\(24\) −123.166 −1.04755
\(25\) 0 0
\(26\) −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 \(0.469177\pi\)
\(30\) 0 0
\(31\) −188.997 −1.09500 −0.547499 0.836806i \(-0.684420\pi\)
−0.547499 + 0.836806i \(0.684420\pi\)
\(32\) 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 \(-0.512781\pi\)
−0.0401411 + 0.999194i \(0.512781\pi\)
\(38\) −8.49623 −0.0362703
\(39\) −306.662 −1.25911
\(40\) 0 0
\(41\) −481.662 −1.83471 −0.917354 0.398072i \(-0.869679\pi\)
−0.917354 + 0.398072i \(0.869679\pi\)
\(42\) 0 0
\(43\) 97.7995 0.346844 0.173422 0.984848i \(-0.444518\pi\)
0.173422 + 0.984848i \(0.444518\pi\)
\(44\) −121.831 −0.417426
\(45\) 0 0
\(46\) −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
\(50\) 0 0
\(51\) 506.662 1.39112
\(52\) 161.504 0.430703
\(53\) −667.995 −1.73125 −0.865624 0.500694i \(-0.833078\pi\)
−0.865624 + 0.500694i \(0.833078\pi\)
\(54\) −335.911 −0.846512
\(55\) 0 0
\(56\) 0 0
\(57\) −18.3375 −0.0426116
\(58\) 69.9574 0.158377
\(59\) −57.3350 −0.126515 −0.0632575 0.997997i \(-0.520149\pi\)
−0.0632575 + 0.997997i \(0.520149\pi\)
\(60\) 0 0
\(61\) −738.997 −1.55113 −0.775565 0.631268i \(-0.782535\pi\)
−0.775565 + 0.631268i \(0.782535\pi\)
\(62\) −437.836 −0.896859
\(63\) 0 0
\(64\) 551.325 1.07681
\(65\) 0 0
\(66\) 535.911 0.999485
\(67\) −552.396 −1.00725 −0.503626 0.863922i \(-0.668001\pi\)
−0.503626 + 0.863922i \(0.668001\pi\)
\(68\) −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
\(75\) 0 0
\(76\) 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 \(0.777567\pi\)
\(80\) 0 0
\(81\) −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
\(85\) 0 0
\(86\) 226.565 0.284083
\(87\) 150.990 0.186067
\(88\) −1139.69 −1.38059
\(89\) 1380.32 1.64397 0.821985 0.569509i \(-0.192867\pi\)
0.821985 + 0.569509i \(0.192867\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 223.472 0.253245
\(93\) −944.987 −1.05366
\(94\) 272.586 0.299096
\(95\) 0 0
\(96\) 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
\(100\) 0 0
\(101\) 1474.33 1.45249 0.726243 0.687438i \(-0.241265\pi\)
0.726243 + 0.687438i \(0.241265\pi\)
\(102\) 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 \(-0.563791\pi\)
−0.199066 + 0.979986i \(0.563791\pi\)
\(108\) 381.821 0.340192
\(109\) −1906.19 −1.67504 −0.837522 0.546404i \(-0.815996\pi\)
−0.837522 + 0.546404i \(0.815996\pi\)
\(110\) 0 0
\(111\) −90.3425 −0.0772517
\(112\) 0 0
\(113\) −962.470 −0.801252 −0.400626 0.916242i \(-0.631207\pi\)
−0.400626 + 0.916242i \(0.631207\pi\)
\(114\) −42.4812 −0.0349011
\(115\) 0 0
\(116\) −79.5188 −0.0636478
\(117\) 122.665 0.0969263
\(118\) −132.824 −0.103622
\(119\) 0 0
\(120\) 0 0
\(121\) 809.589 0.608256
\(122\) −1711.98 −1.27045
\(123\) −2408.31 −1.76545
\(124\) 497.678 0.360426
\(125\) 0 0
\(126\) 0 0
\(127\) 1621.74 1.13312 0.566558 0.824022i \(-0.308275\pi\)
0.566558 + 0.824022i \(0.308275\pi\)
\(128\) 367.873 0.254029
\(129\) 488.997 0.333751
\(130\) 0 0
\(131\) 1380.32 0.920602 0.460301 0.887763i \(-0.347741\pi\)
0.460301 + 0.887763i \(0.347741\pi\)
\(132\) −609.156 −0.401668
\(133\) 0 0
\(134\) −1279.69 −0.824991
\(135\) 0 0
\(136\) −2496.15 −1.57385
\(137\) 1949.66 1.21584 0.607921 0.793997i \(-0.292004\pi\)
0.607921 + 0.793997i \(0.292004\pi\)
\(138\) −983.008 −0.606371
\(139\) −2800.00 −1.70858 −0.854291 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(140\) 0 0
\(141\) 588.325 0.351389
\(142\) −1714.91 −1.01347
\(143\) −2837.64 −1.65941
\(144\) 72.0000 0.0416667
\(145\) 0 0
\(146\) 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 \(0.628997\pi\)
\(150\) 0 0
\(151\) −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
\(155\) 0 0
\(156\) 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
\(160\) 0 0
\(161\) 0 0
\(162\) −1554.46 −0.753886
\(163\) 3953.98 1.90000 0.950000 0.312250i \(-0.101083\pi\)
0.950000 + 0.312250i \(0.101083\pi\)
\(164\) 1268.34 0.603906
\(165\) 0 0
\(166\) 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
\(170\) 0 0
\(171\) 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 \(0.402614\pi\)
\(180\) 0 0
\(181\) 908.680 0.373158 0.186579 0.982440i \(-0.440260\pi\)
0.186579 + 0.982440i \(0.440260\pi\)
\(182\) 0 0
\(183\) −3694.99 −1.49258
\(184\) 2090.51 0.837580
\(185\) 0 0
\(186\) −2189.18 −0.863003
\(187\) 4688.30 1.83338
\(188\) −309.841 −0.120199
\(189\) 0 0
\(190\) 0 0
\(191\) 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 \(-0.728992\pi\)
−0.658934 + 0.752201i \(0.728992\pi\)
\(194\) 505.042 0.186907
\(195\) 0 0
\(196\) 0 0
\(197\) 1952.57 0.706165 0.353083 0.935592i \(-0.385133\pi\)
0.353083 + 0.935592i \(0.385133\pi\)
\(198\) −214.364 −0.0769404
\(199\) −4064.67 −1.44792 −0.723962 0.689840i \(-0.757681\pi\)
−0.723962 + 0.689840i \(0.757681\pi\)
\(200\) 0 0
\(201\) −2761.98 −0.969229
\(202\) 3415.46 1.18966
\(203\) 0 0
\(204\) −1334.17 −0.457895
\(205\) 0 0
\(206\) −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
\(215\) 0 0
\(216\) 3571.82 1.12515
\(217\) 0 0
\(218\) −4415.92 −1.37194
\(219\) 1166.62 0.359969
\(220\) 0 0
\(221\) −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
\(225\) 0 0
\(226\) −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 \(-0.473593\pi\)
0.0828660 + 0.996561i \(0.473593\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −743.875 −0.210508
\(233\) 2316.48 0.651320 0.325660 0.945487i \(-0.394414\pi\)
0.325660 + 0.945487i \(0.394414\pi\)
\(234\) 284.169 0.0793876
\(235\) 0 0
\(236\) 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 \(0.664902\pi\)
\(240\) 0 0
\(241\) −2446.33 −0.653868 −0.326934 0.945047i \(-0.606015\pi\)
−0.326934 + 0.945047i \(0.606015\pi\)
\(242\) 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
\(250\) 0 0
\(251\) 2909.29 0.731605 0.365802 0.930693i \(-0.380795\pi\)
0.365802 + 0.930693i \(0.380795\pi\)
\(252\) 0 0
\(253\) −3926.43 −0.975702
\(254\) 3756.95 0.928080
\(255\) 0 0
\(256\) −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
\(260\) 0 0
\(261\) −60.3960 −0.0143234
\(262\) 3197.68 0.754020
\(263\) 3244.47 0.760695 0.380347 0.924844i \(-0.375804\pi\)
0.380347 + 0.924844i \(0.375804\pi\)
\(264\) −5698.47 −1.32847
\(265\) 0 0
\(266\) 0 0
\(267\) 6901.59 1.58191
\(268\) 1454.60 0.331543
\(269\) 2848.65 0.645671 0.322836 0.946455i \(-0.395364\pi\)
0.322836 + 0.946455i \(0.395364\pi\)
\(270\) 0 0
\(271\) 2850.98 0.639057 0.319529 0.947577i \(-0.396475\pi\)
0.319529 + 0.947577i \(0.396475\pi\)
\(272\) −3647.97 −0.813201
\(273\) 0 0
\(274\) 4516.62 0.995837
\(275\) 0 0
\(276\) 1117.36 0.243685
\(277\) −2298.63 −0.498597 −0.249298 0.968427i \(-0.580200\pi\)
−0.249298 + 0.968427i \(0.580200\pi\)
\(278\) −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
\(285\) 0 0
\(286\) −6573.75 −1.35914
\(287\) 0 0
\(288\) −227.335 −0.0465133
\(289\) 5355.27 1.09002
\(290\) 0 0
\(291\) 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
\(295\) 0 0
\(296\) 445.086 0.0873990
\(297\) −6708.64 −1.31069
\(298\) −3322.31 −0.645827
\(299\) 5205.01 1.00673
\(300\) 0 0
\(301\) 0 0
\(302\) −4599.85 −0.876462
\(303\) 7371.64 1.39766
\(304\) 132.030 0.0249094
\(305\) 0 0
\(306\) −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
\(310\) 0 0
\(311\) 5764.30 1.05101 0.525504 0.850791i \(-0.323877\pi\)
0.525504 + 0.850791i \(0.323877\pi\)
\(312\) 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 \(-0.650452\pi\)
−0.455256 + 0.890361i \(0.650452\pi\)
\(318\) −7737.47 −1.36445
\(319\) 1397.16 0.245222
\(320\) 0 0
\(321\) −2203.30 −0.383103
\(322\) 0 0
\(323\) −371.637 −0.0640200
\(324\) 1766.91 0.302968
\(325\) 0 0
\(326\) 9159.90 1.55620
\(327\) −9530.94 −1.61181
\(328\) 11864.9 1.99735
\(329\) 0 0
\(330\) 0 0
\(331\) 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
\(335\) 0 0
\(336\) 0 0
\(337\) −153.985 −0.0248905 −0.0124452 0.999923i \(-0.503962\pi\)
−0.0124452 + 0.999923i \(0.503962\pi\)
\(338\) 3624.76 0.583317
\(339\) −4812.35 −0.771005
\(340\) 0 0
\(341\) −8744.25 −1.38864
\(342\) 16.9925 0.00268669
\(343\) 0 0
\(344\) −2409.12 −0.377590
\(345\) 0 0
\(346\) 7428.63 1.15424
\(347\) −4359.39 −0.674421 −0.337211 0.941429i \(-0.609483\pi\)
−0.337211 + 0.941429i \(0.609483\pi\)
\(348\) −397.594 −0.0612451
\(349\) −1689.00 −0.259054 −0.129527 0.991576i \(-0.541346\pi\)
−0.129527 + 0.991576i \(0.541346\pi\)
\(350\) 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
\(355\) 0 0
\(356\) −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 \(0.567609\pi\)
\(360\) 0 0
\(361\) −6845.55 −0.998039
\(362\) 2105.07 0.305636
\(363\) 4047.94 0.585295
\(364\) 0 0
\(365\) 0 0
\(366\) −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
\(370\) 0 0
\(371\) 0 0
\(372\) 2488.39 0.346820
\(373\) −5086.43 −0.706073 −0.353037 0.935610i \(-0.614851\pi\)
−0.353037 + 0.935610i \(0.614851\pi\)
\(374\) 10861.0 1.50163
\(375\) 0 0
\(376\) −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 \(0.479389\pi\)
\(380\) 0 0
\(381\) 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 \(0.635379\pi\)
\(390\) 0 0
\(391\) −8599.63 −1.11228
\(392\) 0 0
\(393\) 6901.59 0.885850
\(394\) 4523.36 0.578385
\(395\) 0 0
\(396\) 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
\(400\) 0 0
\(401\) −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
\(405\) 0 0
\(406\) 0 0
\(407\) −835.967 −0.101812
\(408\) −12480.7 −1.51443
\(409\) −4019.92 −0.485996 −0.242998 0.970027i \(-0.578131\pi\)
−0.242998 + 0.970027i \(0.578131\pi\)
\(410\) 0 0
\(411\) 9748.29 1.16995
\(412\) 2135.54 0.255365
\(413\) 0 0
\(414\) 393.203 0.0466784
\(415\) 0 0
\(416\) −6971.51 −0.821650
\(417\) −14000.0 −1.64408
\(418\) −393.091 −0.0459969
\(419\) −2437.28 −0.284175 −0.142087 0.989854i \(-0.545381\pi\)
−0.142087 + 0.989854i \(0.545381\pi\)
\(420\) 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
\(425\) 0 0
\(426\) −8574.57 −0.975210
\(427\) 0 0
\(428\) 1160.37 0.131048
\(429\) −14188.2 −1.59677
\(430\) 0 0
\(431\) 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
\(435\) 0 0
\(436\) 5019.47 0.551351
\(437\) 311.245 0.0340706
\(438\) 2702.63 0.294833
\(439\) 9147.92 0.994548 0.497274 0.867594i \(-0.334334\pi\)
0.497274 + 0.867594i \(0.334334\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −14397.8 −1.54939
\(443\) −1864.35 −0.199950 −0.0999752 0.994990i \(-0.531876\pi\)
−0.0999752 + 0.994990i \(0.531876\pi\)
\(444\) 237.894 0.0254279
\(445\) 0 0
\(446\) −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 \(0.424160\pi\)
\(450\) 0 0
\(451\) −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 \(-0.237600\pi\)
0.734109 + 0.679032i \(0.237600\pi\)
\(458\) 1330.50 0.135743
\(459\) −14693.2 −1.49416
\(460\) 0 0
\(461\) 14558.7 1.47086 0.735429 0.677602i \(-0.236981\pi\)
0.735429 + 0.677602i \(0.236981\pi\)
\(462\) 0 0
\(463\) 1809.56 0.181636 0.0908178 0.995868i \(-0.471052\pi\)
0.0908178 + 0.995868i \(0.471052\pi\)
\(464\) −1087.13 −0.108769
\(465\) 0 0
\(466\) 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
\(470\) 0 0
\(471\) 203.300 0.0198887
\(472\) 1412.35 0.137730
\(473\) 4524.84 0.439857
\(474\) −12454.0 −1.20682
\(475\) 0 0
\(476\) 0 0
\(477\) 1335.99 0.128241
\(478\) −8477.25 −0.811173
\(479\) −11527.5 −1.09959 −0.549796 0.835299i \(-0.685295\pi\)
−0.549796 + 0.835299i \(0.685295\pi\)
\(480\) 0 0
\(481\) 1108.19 0.105050
\(482\) −5667.23 −0.535551
\(483\) 0 0
\(484\) −2131.85 −0.200211
\(485\) 0 0
\(486\) 1297.31 0.121085
\(487\) −15791.5 −1.46936 −0.734682 0.678411i \(-0.762669\pi\)
−0.734682 + 0.678411i \(0.762669\pi\)
\(488\) 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
\(495\) 0 0
\(496\) 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 \(0.858795\pi\)
\(500\) 0 0
\(501\) 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
\(505\) 0 0
\(506\) −9096.06 −0.799149
\(507\) 7823.38 0.685302
\(508\) −4270.44 −0.372972
\(509\) −12334.5 −1.07410 −0.537049 0.843551i \(-0.680461\pi\)
−0.537049 + 0.843551i \(0.680461\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −11186.4 −0.965574
\(513\) 531.788 0.0457681
\(514\) 390.768 0.0335332
\(515\) 0 0
\(516\) −1287.65 −0.109856
\(517\) 5443.95 0.463104
\(518\) 0 0
\(519\) 16033.3 1.35604
\(520\) 0 0
\(521\) −1736.43 −0.146016 −0.0730082 0.997331i \(-0.523260\pi\)
−0.0730082 + 0.997331i \(0.523260\pi\)
\(522\) −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
\(530\) 0 0
\(531\) 114.670 0.00937148
\(532\) 0 0
\(533\) 29541.6 2.40073
\(534\) 15988.4 1.29567
\(535\) 0 0
\(536\) 13607.3 1.09654
\(537\) 7213.25 0.579655
\(538\) 6599.26 0.528837
\(539\) 0 0
\(540\) 0 0
\(541\) 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
\(545\) 0 0
\(546\) 0 0
\(547\) 3941.30 0.308076 0.154038 0.988065i \(-0.450772\pi\)
0.154038 + 0.988065i \(0.450772\pi\)
\(548\) −5133.93 −0.400202
\(549\) 1477.99 0.114899
\(550\) 0 0
\(551\) −110.751 −0.00856291
\(552\) 10452.6 0.805961
\(553\) 0 0
\(554\) −5325.06 −0.408376
\(555\) 0 0
\(556\) 7373.10 0.562390
\(557\) 6951.74 0.528823 0.264412 0.964410i \(-0.414822\pi\)
0.264412 + 0.964410i \(0.414822\pi\)
\(558\) 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
\(565\) 0 0
\(566\) 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 \(0.792195\pi\)
\(570\) 0 0
\(571\) −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
\(575\) 0 0
\(576\) −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
\(580\) 0 0
\(581\) 0 0
\(582\) 2525.21 0.179851
\(583\) −30905.8 −2.19552
\(584\) −5747.55 −0.407252
\(585\) 0 0
\(586\) −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
\(590\) 0 0
\(591\) 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 \(0.610448\pi\)
\(600\) 0 0
\(601\) 24619.2 1.67094 0.835472 0.549533i \(-0.185194\pi\)
0.835472 + 0.549533i \(0.185194\pi\)
\(602\) 0 0
\(603\) 1104.79 0.0746113
\(604\) 5228.53 0.352228
\(605\) 0 0
\(606\) 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
\(610\) 0 0
\(611\) −7216.69 −0.477833
\(612\) 533.668 0.0352487
\(613\) 15293.2 1.00765 0.503824 0.863807i \(-0.331926\pi\)
0.503824 + 0.863807i \(0.331926\pi\)
\(614\) 4871.79 0.320211
\(615\) 0 0
\(616\) 0 0
\(617\) 17589.4 1.14769 0.573843 0.818966i \(-0.305452\pi\)
0.573843 + 0.818966i \(0.305452\pi\)
\(618\) −9393.80 −0.611446
\(619\) 23467.4 1.52380 0.761900 0.647694i \(-0.224267\pi\)
0.761900 + 0.647694i \(0.224267\pi\)
\(620\) 0 0
\(621\) 12305.5 0.795173
\(622\) 13353.7 0.860829
\(623\) 0 0
\(624\) 11039.8 0.708249
\(625\) 0 0
\(626\) −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
\(635\) 0 0
\(636\) 8794.99 0.548340
\(637\) 0 0
\(638\) 3236.68 0.200849
\(639\) 1480.53 0.0916569
\(640\) 0 0
\(641\) 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
\(645\) 0 0
\(646\) −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
\(650\) 0 0
\(651\) 0 0
\(652\) −10411.8 −0.625397
\(653\) 14438.4 0.865265 0.432632 0.901570i \(-0.357585\pi\)
0.432632 + 0.901570i \(0.357585\pi\)
\(654\) −22079.6 −1.32015
\(655\) 0 0
\(656\) 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 \(0.527322\pi\)
\(660\) 0 0
\(661\) −9976.52 −0.587053 −0.293526 0.955951i \(-0.594829\pi\)
−0.293526 + 0.955951i \(0.594829\pi\)
\(662\) 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
\(670\) 0 0
\(671\) −34190.8 −1.96710
\(672\) 0 0
\(673\) −20760.8 −1.18911 −0.594554 0.804055i \(-0.702671\pi\)
−0.594554 + 0.804055i \(0.702671\pi\)
\(674\) −356.725 −0.0203866
\(675\) 0 0
\(676\) −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
\(680\) 0 0
\(681\) −8304.82 −0.467315
\(682\) −20257.2 −1.13737
\(683\) −4333.57 −0.242781 −0.121391 0.992605i \(-0.538735\pi\)
−0.121391 + 0.992605i \(0.538735\pi\)
\(684\) −19.3149 −0.00107971
\(685\) 0 0
\(686\) 0 0
\(687\) 2871.64 0.159476
\(688\) −3520.78 −0.195100
\(689\) 40969.8 2.26535
\(690\) 0 0
\(691\) 14446.0 0.795297 0.397649 0.917538i \(-0.369826\pi\)
0.397649 + 0.917538i \(0.369826\pi\)
\(692\) −8443.94 −0.463859
\(693\) 0 0
\(694\) −10099.1 −0.552385
\(695\) 0 0
\(696\) −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
\(705\) 0 0
\(706\) −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 \(0.567779\pi\)
\(710\) 0 0
\(711\) 2150.37 0.113425
\(712\) −34001.7 −1.78970
\(713\) 16039.4 0.842467
\(714\) 0 0
\(715\) 0 0
\(716\) −3798.86 −0.198282
\(717\) −18296.6 −0.952995
\(718\) −6643.76 −0.345325
\(719\) 33703.3 1.74815 0.874076 0.485790i \(-0.161468\pi\)
0.874076 + 0.485790i \(0.161468\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15858.6 −0.817444
\(723\) −12231.7 −0.629185
\(724\) −2392.78 −0.122827
\(725\) 0 0
\(726\) 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
\(730\) 0 0
\(731\) 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 \(0.286713\pi\)
\(740\) 0 0
\(741\) 1124.69 0.0557576
\(742\) 0 0
\(743\) 8154.54 0.402640 0.201320 0.979526i \(-0.435477\pi\)
0.201320 + 0.979526i \(0.435477\pi\)
\(744\) 23278.1 1.14707
\(745\) 0 0
\(746\) −11783.3 −0.578310
\(747\) −1366.65 −0.0669386
\(748\) −12345.5 −0.603469
\(749\) 0 0
\(750\) 0 0
\(751\) −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
\(755\) 0 0
\(756\) 0 0
\(757\) −3624.79 −0.174036 −0.0870179 0.996207i \(-0.527734\pi\)
−0.0870179 + 0.996207i \(0.527734\pi\)
\(758\) 2211.98 0.105993
\(759\) −19632.1 −0.938869
\(760\) 0 0
\(761\) −20576.4 −0.980150 −0.490075 0.871680i \(-0.663031\pi\)
−0.490075 + 0.871680i \(0.663031\pi\)
\(762\) 18784.8 0.893045
\(763\) 0 0
\(764\) −6516.34 −0.308577
\(765\) 0 0
\(766\) 7144.26 0.336988
\(767\) 3516.50 0.165546
\(768\) −17791.9 −0.835949
\(769\) 3066.14 0.143781 0.0718907 0.997413i \(-0.477097\pi\)
0.0718907 + 0.997413i \(0.477097\pi\)
\(770\) 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
\(775\) 0 0
\(776\) −5370.23 −0.248428
\(777\) 0 0
\(778\) −14666.9 −0.675879
\(779\) 1766.50 0.0812470
\(780\) 0 0
\(781\) −34249.4 −1.56919
\(782\) −19922.1 −0.911015
\(783\) −4378.71 −0.199850
\(784\) 0 0
\(785\) 0 0
\(786\) 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
\(790\) 0 0
\(791\) 0 0
\(792\) 2279.39 0.102266
\(793\) 45324.6 2.02966
\(794\) −28108.2 −1.25632
\(795\) 0 0
\(796\) 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
\(800\) 0 0
\(801\) −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 \(0.507474\pi\)
\(810\) 0 0
\(811\) −19593.9 −0.848378 −0.424189 0.905574i \(-0.639441\pi\)
−0.424189 + 0.905574i \(0.639441\pi\)
\(812\) 0 0
\(813\) 14254.9 0.614933
\(814\) −1936.62 −0.0833889
\(815\) 0 0
\(816\) −18239.8 −0.782503
\(817\) −358.680 −0.0153594
\(818\) −9312.66 −0.398056
\(819\) 0 0
\(820\) 0 0
\(821\) 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 \(-0.409930\pi\)
0.279202 + 0.960232i \(0.409930\pi\)
\(824\) 19977.3 0.844591
\(825\) 0 0
\(826\) 0 0
\(827\) −24658.7 −1.03684 −0.518421 0.855126i \(-0.673480\pi\)
−0.518421 + 0.855126i \(0.673480\pi\)
\(828\) −446.944 −0.0187589
\(829\) 28562.3 1.19664 0.598318 0.801259i \(-0.295836\pi\)
0.598318 + 0.801259i \(0.295836\pi\)
\(830\) 0 0
\(831\) −11493.1 −0.479775
\(832\) −33814.1 −1.40901
\(833\) 0 0
\(834\) −32432.7 −1.34659
\(835\) 0 0
\(836\) 446.817 0.0184850
\(837\) 27404.6 1.13171
\(838\) −5646.27 −0.232753
\(839\) −31106.0 −1.27997 −0.639987 0.768386i \(-0.721060\pi\)
−0.639987 + 0.768386i \(0.721060\pi\)
\(840\) 0 0
\(841\) −23477.1 −0.962609
\(842\) −11007.1 −0.450511
\(843\) 30546.0 1.24800
\(844\) 11389.7 0.464514
\(845\) 0 0
\(846\) −545.171 −0.0221553
\(847\) 0 0
\(848\) 24047.8 0.973827
\(849\) 29274.7 1.18340
\(850\) 0 0
\(851\) 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
\(855\) 0 0
\(856\) 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 \(-0.906910\pi\)
−0.957541 + 0.288298i \(0.906910\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 18359.7 0.725445
\(863\) 31709.5 1.25076 0.625378 0.780322i \(-0.284945\pi\)
0.625378 + 0.780322i \(0.284945\pi\)
\(864\) −16481.8 −0.648984
\(865\) 0 0
\(866\) −26611.7 −1.04423
\(867\) 26776.4 1.04887
\(868\) 0 0
\(869\) −49745.1 −1.94187
\(870\) 0 0
\(871\) 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 \(-0.664429\pi\)
−0.493900 + 0.869519i \(0.664429\pi\)
\(878\) 21192.3 0.814585
\(879\) −25676.7 −0.985272
\(880\) 0 0
\(881\) −11470.4 −0.438647 −0.219323 0.975652i \(-0.570385\pi\)
−0.219323 + 0.975652i \(0.570385\pi\)
\(882\) 0 0
\(883\) −39124.0 −1.49108 −0.745542 0.666459i \(-0.767809\pi\)
−0.745542 + 0.666459i \(0.767809\pi\)
\(884\) 16365.6 0.622663
\(885\) 0 0
\(886\) −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
\(890\) 0 0
\(891\) −31044.8 −1.16727
\(892\) 2588.40 0.0971594
\(893\) −431.537 −0.0161711
\(894\) −16611.6 −0.621447
\(895\) 0 0
\(896\) 0 0
\(897\) 26025.1 0.968731
\(898\) 10403.7 0.386610
\(899\) −5707.34 −0.211736
\(900\) 0 0
\(901\) −67689.6 −2.50285
\(902\) −51625.6 −1.90570
\(903\) 0 0
\(904\) 23708.8 0.872280
\(905\) 0 0
\(906\) −22999.2 −0.843376
\(907\) −27596.1 −1.01027 −0.505134 0.863041i \(-0.668557\pi\)
−0.505134 + 0.863041i \(0.668557\pi\)
\(908\) 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
\(915\) 0 0
\(916\) −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 \(0.440937\pi\)
\(920\) 0 0
\(921\) 10514.8 0.376196
\(922\) 33727.0 1.20471
\(923\) 45402.2 1.61910
\(924\) 0 0
\(925\) 0 0
\(926\) 4192.06 0.148769
\(927\) 1621.98 0.0574680
\(928\) 3432.53 0.121421
\(929\) −6499.87 −0.229552 −0.114776 0.993391i \(-0.536615\pi\)
−0.114776 + 0.993391i \(0.536615\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −6099.86 −0.214386
\(933\) 28821.5 1.01133
\(934\) 13857.2 0.485463
\(935\) 0 0
\(936\) −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
\(940\) 0 0
\(941\) −34396.2 −1.19159 −0.595794 0.803137i \(-0.703163\pi\)
−0.595794 + 0.803137i \(0.703163\pi\)
\(942\) 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 \(-0.654499\pi\)
−0.466539 + 0.884501i \(0.654499\pi\)
\(948\) 14156.2 0.484990
\(949\) −14310.4 −0.489500
\(950\) 0 0
\(951\) −25694.7 −0.876140
\(952\) 0 0
\(953\) −49965.2 −1.69836 −0.849178 0.528107i \(-0.822902\pi\)
−0.849178 + 0.528107i \(0.822902\pi\)
\(954\) 3094.99 0.105036
\(955\) 0 0
\(956\) 9635.88 0.325990
\(957\) 6985.78 0.235965
\(958\) −26704.9 −0.900622
\(959\) 0 0
\(960\) 0 0
\(961\) 5929.05 0.199022
\(962\) 2567.25 0.0860411
\(963\) 881.320 0.0294913
\(964\) 6441.80 0.215225
\(965\) 0 0
\(966\) 0 0
\(967\) 16755.5 0.557208 0.278604 0.960406i \(-0.410128\pi\)
0.278604 + 0.960406i \(0.410128\pi\)
\(968\) −19942.8 −0.662176
\(969\) −1858.19 −0.0616033
\(970\) 0 0
\(971\) 37617.4 1.24325 0.621626 0.783314i \(-0.286472\pi\)
0.621626 + 0.783314i \(0.286472\pi\)
\(972\) −1474.62 −0.0486610
\(973\) 0 0
\(974\) −36583.0 −1.20348
\(975\) 0 0
\(976\) 26603.9 0.872511
\(977\) 27690.9 0.906767 0.453384 0.891315i \(-0.350217\pi\)
0.453384 + 0.891315i \(0.350217\pi\)
\(978\) 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
\(985\) 0 0
\(986\) 7088.96 0.228964
\(987\) 0 0
\(988\) −592.316 −0.0190729
\(989\) −8299.80 −0.266854
\(990\) 0 0
\(991\) −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
\(995\) 0 0
\(996\) −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 1225.4.a.q.1.2 2
5.4 even 2 245.4.a.i.1.1 2
7.6 odd 2 1225.4.a.p.1.2 2
15.14 odd 2 2205.4.a.x.1.2 2
35.4 even 6 245.4.e.k.226.2 4
35.9 even 6 245.4.e.k.116.2 4
35.19 odd 6 245.4.e.j.116.2 4
35.24 odd 6 245.4.e.j.226.2 4
35.34 odd 2 245.4.a.j.1.1 yes 2
105.104 even 2 2205.4.a.w.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.i.1.1 2 5.4 even 2
245.4.a.j.1.1 yes 2 35.34 odd 2
245.4.e.j.116.2 4 35.19 odd 6
245.4.e.j.226.2 4 35.24 odd 6
245.4.e.k.116.2 4 35.9 even 6
245.4.e.k.226.2 4 35.4 even 6
1225.4.a.p.1.2 2 7.6 odd 2
1225.4.a.q.1.2 2 1.1 even 1 trivial
2205.4.a.w.1.2 2 105.104 even 2
2205.4.a.x.1.2 2 15.14 odd 2