Properties

Label 245.4.a.i.1.1
Level $245$
Weight $4$
Character 245.1
Self dual yes
Analytic conductor $14.455$
Analytic rank $1$
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: \(1\)
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: 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 \(-0.659772\pi\)
−0.481125 + 0.876652i \(0.659772\pi\)
\(4\) −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 \(-0.272983\pi\)
0.654253 + 0.756276i \(0.272983\pi\)
\(14\) 0 0
\(15\) 25.0000 0.430331
\(16\) −36.0000 −0.562500
\(17\) −101.332 −1.44569 −0.722845 0.691010i \(-0.757166\pi\)
−0.722845 + 0.691010i \(0.757166\pi\)
\(18\) 4.63325 0.0606704
\(19\) −3.66750 −0.0442833 −0.0221417 0.999755i \(-0.507048\pi\)
−0.0221417 + 0.999755i \(0.507048\pi\)
\(20\) 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 \(-0.684420\pi\)
−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 \(-0.487219\pi\)
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 \(-0.869679\pi\)
−0.917354 + 0.398072i \(0.869679\pi\)
\(42\) 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 \(-0.558447\pi\)
−0.182587 + 0.983190i \(0.558447\pi\)
\(48\) 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 \(-0.520149\pi\)
−0.0632575 + 0.997997i \(0.520149\pi\)
\(60\) −65.8312 −0.141646
\(61\) −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
\(65\) −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 \(-0.559891\pi\)
−0.187045 + 0.982351i \(0.559891\pi\)
\(74\) −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 \(-0.649231\pi\)
−0.451835 + 0.892101i \(0.649231\pi\)
\(84\) 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 \(-0.192867\pi\)
0.821985 + 0.569509i \(0.192867\pi\)
\(90\) −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 \(-0.536398\pi\)
−0.114100 + 0.993469i \(0.536398\pi\)
\(98\) 0 0
\(99\) −92.5330 −0.0939385
\(100\) −65.8312 −0.0658312
\(101\) 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 \(-0.373198\pi\)
0.387909 + 0.921698i \(0.373198\pi\)
\(104\) 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 \(-0.347741\pi\)
0.460301 + 0.887763i \(0.347741\pi\)
\(132\) 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 \(-0.826008\pi\)
−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
\(145\) −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 \(-0.503290\pi\)
−0.0103345 + 0.999947i \(0.503290\pi\)
\(158\) 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 \(-0.786394\pi\)
−0.783161 + 0.621819i \(0.786394\pi\)
\(168\) 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 \(-0.748882\pi\)
−0.704619 + 0.709586i \(0.748882\pi\)
\(174\) 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 \(-0.440260\pi\)
0.186579 + 0.982440i \(0.440260\pi\)
\(182\) 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 \(-0.757681\pi\)
−0.723962 + 0.689840i \(0.757681\pi\)
\(200\) 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 \(-0.452849\pi\)
0.147589 + 0.989049i \(0.452849\pi\)
\(224\) 0 0
\(225\) −50.0000 −0.0148148
\(226\) −2229.68 −0.656266
\(227\) 1660.96 0.485648 0.242824 0.970070i \(-0.421926\pi\)
0.242824 + 0.970070i \(0.421926\pi\)
\(228\) −48.2873 −0.0140259
\(229\) 574.327 0.165732 0.0828660 0.996561i \(-0.473593\pi\)
0.0828660 + 0.996561i \(0.473593\pi\)
\(230\) 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 \(-0.606015\pi\)
−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
\(250\) 289.578 0.0732581
\(251\) 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
\(255\) −2533.31 −0.622126
\(256\) −3558.38 −0.868744
\(257\) −168.680 −0.0409415 −0.0204708 0.999790i \(-0.506517\pi\)
−0.0204708 + 0.999790i \(0.506517\pi\)
\(258\) −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 \(-0.395364\pi\)
0.322836 + 0.946455i \(0.395364\pi\)
\(270\) 1679.55 0.378572
\(271\) 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
\(275\) 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 \(-0.710809\pi\)
−0.614913 + 0.788595i \(0.710809\pi\)
\(284\) 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 \(-0.328919\pi\)
0.511962 + 0.859008i \(0.328919\pi\)
\(294\) 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 \(-0.562625\pi\)
−0.195477 + 0.980708i \(0.562625\pi\)
\(308\) 0 0
\(309\) −4054.95 −0.746531
\(310\) −2189.18 −0.401088
\(311\) 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 \(-0.460813\pi\)
0.122799 + 0.992432i \(0.460813\pi\)
\(314\) 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 \(-0.541346\pi\)
−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 \(-0.404471\pi\)
0.295627 + 0.955303i \(0.404471\pi\)
\(354\) −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 \(-0.804947\pi\)
−0.818054 + 0.575142i \(0.804947\pi\)
\(368\) −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 \(-0.565953\pi\)
−0.205719 + 0.978611i \(0.565953\pi\)
\(384\) 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 \(-0.221779\pi\)
0.766939 + 0.641720i \(0.221779\pi\)
\(398\) 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 \(-0.578131\pi\)
−0.242998 + 0.970027i \(0.578131\pi\)
\(410\) −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 \(-0.545381\pi\)
−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
\(425\) −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 \(-0.279984\pi\)
0.637462 + 0.770481i \(0.279984\pi\)
\(434\) 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 \(-0.334334\pi\)
0.497274 + 0.867594i \(0.334334\pi\)
\(440\) −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 \(-0.236981\pi\)
0.735429 + 0.677602i \(0.236981\pi\)
\(462\) 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 \(-0.595772\pi\)
−0.296357 + 0.955077i \(0.595772\pi\)
\(468\) 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 \(-0.685295\pi\)
−0.549796 + 0.835299i \(0.685295\pi\)
\(480\) −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 \(-0.510607\pi\)
−0.0333156 + 0.999445i \(0.510607\pi\)
\(504\) 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 \(-0.680461\pi\)
−0.537049 + 0.843551i \(0.680461\pi\)
\(510\) 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 \(-0.523260\pi\)
−0.0730082 + 0.997331i \(0.523260\pi\)
\(522\) 139.915 0.0117316
\(523\) −1421.42 −0.118842 −0.0594210 0.998233i \(-0.518925\pi\)
−0.0594210 + 0.998233i \(0.518925\pi\)
\(524\) −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 \(-0.863112\pi\)
−0.908946 + 0.416913i \(0.863112\pi\)
\(564\) −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 \(-0.204682\pi\)
0.800285 + 0.599620i \(0.204682\pi\)
\(578\) −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 \(-0.621620\pi\)
−0.372852 + 0.927891i \(0.621620\pi\)
\(588\) 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 \(-0.569741\pi\)
−0.217349 + 0.976094i \(0.569741\pi\)
\(594\) −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 \(-0.185194\pi\)
0.835472 + 0.549533i \(0.185194\pi\)
\(602\) 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 \(-0.622780\pi\)
−0.376230 + 0.926526i \(0.622780\pi\)
\(608\) 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 \(-0.224267\pi\)
0.761900 + 0.647694i \(0.224267\pi\)
\(620\) −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 \(-0.530257\pi\)
−0.0949113 + 0.995486i \(0.530257\pi\)
\(644\) 0 0
\(645\) −2444.99 −0.149258
\(646\) −860.944 −0.0524356
\(647\) −9178.63 −0.557727 −0.278863 0.960331i \(-0.589958\pi\)
−0.278863 + 0.960331i \(0.589958\pi\)
\(648\) −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 \(-0.594829\pi\)
−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
\(670\) 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 \(-0.529035\pi\)
−0.0910907 + 0.995843i \(0.529035\pi\)
\(678\) 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 \(-0.369826\pi\)
0.397649 + 0.917538i \(0.369826\pi\)
\(692\) 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 \(-0.161468\pi\)
0.874076 + 0.485790i \(0.161468\pi\)
\(720\) −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 \(-0.219111\pi\)
0.772290 + 0.635270i \(0.219111\pi\)
\(728\) 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 \(-0.662228\pi\)
−0.487874 + 0.872914i \(0.662228\pi\)
\(734\) 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 \(-0.663031\pi\)
−0.490075 + 0.871680i \(0.663031\pi\)
\(762\) −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 \(-0.477097\pi\)
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 \(-0.351054\pi\)
0.451037 + 0.892505i \(0.351054\pi\)
\(774\) −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 \(-0.939588\pi\)
−0.982044 + 0.188651i \(0.939588\pi\)
\(788\) 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 \(-0.624324\pi\)
−0.380720 + 0.924691i \(0.624324\pi\)
\(798\) 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 \(-0.639441\pi\)
−0.424189 + 0.905574i \(0.639441\pi\)
\(812\) 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 \(-0.295836\pi\)
0.598318 + 0.801259i \(0.295836\pi\)
\(830\) −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 \(-0.721060\pi\)
−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
\(845\) −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 \(-0.364552\pi\)
0.412798 + 0.910823i \(0.364552\pi\)
\(854\) 0 0
\(855\) −36.6750 −0.00146697
\(856\) 10854.9 0.433426
\(857\) 6459.44 0.257468 0.128734 0.991679i \(-0.458909\pi\)
0.128734 + 0.991679i \(0.458909\pi\)
\(858\) 32868.7 1.30783
\(859\) −48214.4 −1.91508 −0.957541 0.288298i \(-0.906910\pi\)
−0.957541 + 0.288298i \(0.906910\pi\)
\(860\) −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 \(-0.570385\pi\)
−0.219323 + 0.975652i \(0.570385\pi\)
\(882\) 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 \(-0.404682\pi\)
0.294994 + 0.955499i \(0.404682\pi\)
\(888\) −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 \(-0.536615\pi\)
−0.114776 + 0.993391i \(0.536615\pi\)
\(930\) 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 \(-0.442705\pi\)
0.179028 + 0.983844i \(0.442705\pi\)
\(938\) 0 0
\(939\) −6800.06 −0.236328
\(940\) −1549.21 −0.0537548
\(941\) −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 \(-0.345501\pi\)
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 \(-0.286472\pi\)
0.621626 + 0.783314i \(0.286472\pi\)
\(972\) 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 \(-0.379649\pi\)
0.369149 + 0.929370i \(0.379649\pi\)
\(984\) 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 \(-0.422481\pi\)
0.241132 + 0.970492i \(0.422481\pi\)
\(998\) 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.i.1.1 2
3.2 odd 2 2205.4.a.x.1.2 2
5.4 even 2 1225.4.a.q.1.2 2
7.2 even 3 245.4.e.k.116.2 4
7.3 odd 6 245.4.e.j.226.2 4
7.4 even 3 245.4.e.k.226.2 4
7.5 odd 6 245.4.e.j.116.2 4
7.6 odd 2 245.4.a.j.1.1 yes 2
21.20 even 2 2205.4.a.w.1.2 2
35.34 odd 2 1225.4.a.p.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.i.1.1 2 1.1 even 1 trivial
245.4.a.j.1.1 yes 2 7.6 odd 2
245.4.e.j.116.2 4 7.5 odd 6
245.4.e.j.226.2 4 7.3 odd 6
245.4.e.k.116.2 4 7.2 even 3
245.4.e.k.226.2 4 7.4 even 3
1225.4.a.p.1.2 2 35.34 odd 2
1225.4.a.q.1.2 2 5.4 even 2
2205.4.a.w.1.2 2 21.20 even 2
2205.4.a.x.1.2 2 3.2 odd 2