Properties

Label 2205.4.a.be.1.1
Level 2205
Weight 4
Character 2205.1
Self dual yes
Analytic conductor 130.099
Analytic rank 0
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(130.099211563\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 105)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 2205.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.236068 q^{2} -7.94427 q^{4} -5.00000 q^{5} +3.76393 q^{8} +O(q^{10})\) \(q-0.236068 q^{2} -7.94427 q^{4} -5.00000 q^{5} +3.76393 q^{8} +1.18034 q^{10} +50.4721 q^{11} +80.9706 q^{13} +62.6656 q^{16} +76.3870 q^{17} -4.13777 q^{19} +39.7214 q^{20} -11.9149 q^{22} +204.721 q^{23} +25.0000 q^{25} -19.1146 q^{26} +91.1672 q^{29} -198.079 q^{31} -44.9048 q^{32} -18.0325 q^{34} +155.666 q^{37} +0.976794 q^{38} -18.8197 q^{40} -156.885 q^{41} +354.217 q^{43} -400.964 q^{44} -48.3282 q^{46} -175.659 q^{47} -5.90170 q^{50} -643.252 q^{52} -200.302 q^{53} -252.361 q^{55} -21.5217 q^{58} -312.498 q^{59} +154.170 q^{61} +46.7601 q^{62} -490.724 q^{64} -404.853 q^{65} +734.715 q^{67} -606.839 q^{68} +678.577 q^{71} +60.8003 q^{73} -36.7477 q^{74} +32.8715 q^{76} -1286.26 q^{79} -313.328 q^{80} +37.0356 q^{82} +116.170 q^{83} -381.935 q^{85} -83.6192 q^{86} +189.974 q^{88} -916.440 q^{89} -1626.36 q^{92} +41.4676 q^{94} +20.6888 q^{95} +1416.30 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{2} + 2q^{4} - 10q^{5} + 12q^{8} + O(q^{10}) \) \( 2q + 4q^{2} + 2q^{4} - 10q^{5} + 12q^{8} - 20q^{10} + 92q^{11} - 8q^{13} + 18q^{16} - 44q^{17} + 108q^{19} - 10q^{20} + 164q^{22} + 320q^{23} + 50q^{25} - 396q^{26} + 236q^{29} + 60q^{31} - 300q^{32} - 528q^{34} + 204q^{37} + 476q^{38} - 60q^{40} + 44q^{41} + 136q^{43} + 12q^{44} + 440q^{46} + 400q^{47} + 100q^{50} - 1528q^{52} - 16q^{53} - 460q^{55} + 592q^{58} - 464q^{59} + 684q^{61} + 1140q^{62} - 1214q^{64} + 40q^{65} + 736q^{67} - 1804q^{68} + 740q^{71} - 424q^{73} + 168q^{74} + 1148q^{76} - 408q^{79} - 90q^{80} + 888q^{82} + 608q^{83} + 220q^{85} - 1008q^{86} + 532q^{88} - 1332q^{89} - 480q^{92} + 2480q^{94} - 540q^{95} + 2448q^{97} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.236068 −0.0834626 −0.0417313 0.999129i \(-0.513287\pi\)
−0.0417313 + 0.999129i \(0.513287\pi\)
\(3\) 0 0
\(4\) −7.94427 −0.993034
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) 3.76393 0.166344
\(9\) 0 0
\(10\) 1.18034 0.0373256
\(11\) 50.4721 1.38345 0.691724 0.722162i \(-0.256852\pi\)
0.691724 + 0.722162i \(0.256852\pi\)
\(12\) 0 0
\(13\) 80.9706 1.72748 0.863738 0.503940i \(-0.168117\pi\)
0.863738 + 0.503940i \(0.168117\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 62.6656 0.979150
\(17\) 76.3870 1.08980 0.544899 0.838502i \(-0.316568\pi\)
0.544899 + 0.838502i \(0.316568\pi\)
\(18\) 0 0
\(19\) −4.13777 −0.0499615 −0.0249808 0.999688i \(-0.507952\pi\)
−0.0249808 + 0.999688i \(0.507952\pi\)
\(20\) 39.7214 0.444098
\(21\) 0 0
\(22\) −11.9149 −0.115466
\(23\) 204.721 1.85597 0.927986 0.372615i \(-0.121539\pi\)
0.927986 + 0.372615i \(0.121539\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −19.1146 −0.144180
\(27\) 0 0
\(28\) 0 0
\(29\) 91.1672 0.583770 0.291885 0.956453i \(-0.405718\pi\)
0.291885 + 0.956453i \(0.405718\pi\)
\(30\) 0 0
\(31\) −198.079 −1.14761 −0.573807 0.818991i \(-0.694534\pi\)
−0.573807 + 0.818991i \(0.694534\pi\)
\(32\) −44.9048 −0.248066
\(33\) 0 0
\(34\) −18.0325 −0.0909574
\(35\) 0 0
\(36\) 0 0
\(37\) 155.666 0.691656 0.345828 0.938298i \(-0.387598\pi\)
0.345828 + 0.938298i \(0.387598\pi\)
\(38\) 0.976794 0.00416992
\(39\) 0 0
\(40\) −18.8197 −0.0743912
\(41\) −156.885 −0.597595 −0.298797 0.954317i \(-0.596585\pi\)
−0.298797 + 0.954317i \(0.596585\pi\)
\(42\) 0 0
\(43\) 354.217 1.25622 0.628111 0.778124i \(-0.283828\pi\)
0.628111 + 0.778124i \(0.283828\pi\)
\(44\) −400.964 −1.37381
\(45\) 0 0
\(46\) −48.3282 −0.154904
\(47\) −175.659 −0.545161 −0.272580 0.962133i \(-0.587877\pi\)
−0.272580 + 0.962133i \(0.587877\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −5.90170 −0.0166925
\(51\) 0 0
\(52\) −643.252 −1.71544
\(53\) −200.302 −0.519124 −0.259562 0.965726i \(-0.583578\pi\)
−0.259562 + 0.965726i \(0.583578\pi\)
\(54\) 0 0
\(55\) −252.361 −0.618696
\(56\) 0 0
\(57\) 0 0
\(58\) −21.5217 −0.0487230
\(59\) −312.498 −0.689556 −0.344778 0.938684i \(-0.612046\pi\)
−0.344778 + 0.938684i \(0.612046\pi\)
\(60\) 0 0
\(61\) 154.170 0.323598 0.161799 0.986824i \(-0.448270\pi\)
0.161799 + 0.986824i \(0.448270\pi\)
\(62\) 46.7601 0.0957829
\(63\) 0 0
\(64\) −490.724 −0.958446
\(65\) −404.853 −0.772551
\(66\) 0 0
\(67\) 734.715 1.33970 0.669849 0.742498i \(-0.266359\pi\)
0.669849 + 0.742498i \(0.266359\pi\)
\(68\) −606.839 −1.08221
\(69\) 0 0
\(70\) 0 0
\(71\) 678.577 1.13426 0.567129 0.823629i \(-0.308054\pi\)
0.567129 + 0.823629i \(0.308054\pi\)
\(72\) 0 0
\(73\) 60.8003 0.0974813 0.0487407 0.998811i \(-0.484479\pi\)
0.0487407 + 0.998811i \(0.484479\pi\)
\(74\) −36.7477 −0.0577274
\(75\) 0 0
\(76\) 32.8715 0.0496135
\(77\) 0 0
\(78\) 0 0
\(79\) −1286.26 −1.83184 −0.915919 0.401363i \(-0.868537\pi\)
−0.915919 + 0.401363i \(0.868537\pi\)
\(80\) −313.328 −0.437889
\(81\) 0 0
\(82\) 37.0356 0.0498768
\(83\) 116.170 0.153631 0.0768153 0.997045i \(-0.475525\pi\)
0.0768153 + 0.997045i \(0.475525\pi\)
\(84\) 0 0
\(85\) −381.935 −0.487372
\(86\) −83.6192 −0.104848
\(87\) 0 0
\(88\) 189.974 0.230128
\(89\) −916.440 −1.09149 −0.545744 0.837952i \(-0.683753\pi\)
−0.545744 + 0.837952i \(0.683753\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1626.36 −1.84304
\(93\) 0 0
\(94\) 41.4676 0.0455006
\(95\) 20.6888 0.0223435
\(96\) 0 0
\(97\) 1416.30 1.48251 0.741256 0.671222i \(-0.234230\pi\)
0.741256 + 0.671222i \(0.234230\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −198.607 −0.198607
\(101\) −1379.19 −1.35876 −0.679381 0.733785i \(-0.737752\pi\)
−0.679381 + 0.733785i \(0.737752\pi\)
\(102\) 0 0
\(103\) 1308.43 1.25169 0.625844 0.779949i \(-0.284755\pi\)
0.625844 + 0.779949i \(0.284755\pi\)
\(104\) 304.768 0.287355
\(105\) 0 0
\(106\) 47.2849 0.0433275
\(107\) −1265.65 −1.14351 −0.571754 0.820425i \(-0.693737\pi\)
−0.571754 + 0.820425i \(0.693737\pi\)
\(108\) 0 0
\(109\) 2069.32 1.81839 0.909196 0.416368i \(-0.136697\pi\)
0.909196 + 0.416368i \(0.136697\pi\)
\(110\) 59.5743 0.0516380
\(111\) 0 0
\(112\) 0 0
\(113\) 1953.89 1.62661 0.813303 0.581840i \(-0.197667\pi\)
0.813303 + 0.581840i \(0.197667\pi\)
\(114\) 0 0
\(115\) −1023.61 −0.830016
\(116\) −724.257 −0.579703
\(117\) 0 0
\(118\) 73.7709 0.0575522
\(119\) 0 0
\(120\) 0 0
\(121\) 1216.44 0.913927
\(122\) −36.3947 −0.0270083
\(123\) 0 0
\(124\) 1573.59 1.13962
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 224.251 0.156685 0.0783426 0.996926i \(-0.475037\pi\)
0.0783426 + 0.996926i \(0.475037\pi\)
\(128\) 475.083 0.328061
\(129\) 0 0
\(130\) 95.5728 0.0644792
\(131\) −490.898 −0.327404 −0.163702 0.986510i \(-0.552344\pi\)
−0.163702 + 0.986510i \(0.552344\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −173.443 −0.111815
\(135\) 0 0
\(136\) 287.515 0.181281
\(137\) −1831.12 −1.14192 −0.570961 0.820977i \(-0.693429\pi\)
−0.570961 + 0.820977i \(0.693429\pi\)
\(138\) 0 0
\(139\) 3050.84 1.86165 0.930823 0.365469i \(-0.119091\pi\)
0.930823 + 0.365469i \(0.119091\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −160.190 −0.0946682
\(143\) 4086.76 2.38987
\(144\) 0 0
\(145\) −455.836 −0.261070
\(146\) −14.3530 −0.00813605
\(147\) 0 0
\(148\) −1236.65 −0.686838
\(149\) −2246.55 −1.23520 −0.617599 0.786493i \(-0.711895\pi\)
−0.617599 + 0.786493i \(0.711895\pi\)
\(150\) 0 0
\(151\) −1311.53 −0.706826 −0.353413 0.935467i \(-0.614979\pi\)
−0.353413 + 0.935467i \(0.614979\pi\)
\(152\) −15.5743 −0.00831079
\(153\) 0 0
\(154\) 0 0
\(155\) 990.395 0.513228
\(156\) 0 0
\(157\) −1790.94 −0.910398 −0.455199 0.890390i \(-0.650432\pi\)
−0.455199 + 0.890390i \(0.650432\pi\)
\(158\) 303.644 0.152890
\(159\) 0 0
\(160\) 224.524 0.110939
\(161\) 0 0
\(162\) 0 0
\(163\) −491.108 −0.235991 −0.117996 0.993014i \(-0.537647\pi\)
−0.117996 + 0.993014i \(0.537647\pi\)
\(164\) 1246.34 0.593432
\(165\) 0 0
\(166\) −27.4241 −0.0128224
\(167\) −826.059 −0.382769 −0.191384 0.981515i \(-0.561298\pi\)
−0.191384 + 0.981515i \(0.561298\pi\)
\(168\) 0 0
\(169\) 4359.24 1.98418
\(170\) 90.1626 0.0406774
\(171\) 0 0
\(172\) −2813.99 −1.24747
\(173\) 2918.00 1.28238 0.641190 0.767382i \(-0.278441\pi\)
0.641190 + 0.767382i \(0.278441\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3162.87 1.35460
\(177\) 0 0
\(178\) 216.342 0.0910984
\(179\) −955.745 −0.399082 −0.199541 0.979889i \(-0.563945\pi\)
−0.199541 + 0.979889i \(0.563945\pi\)
\(180\) 0 0
\(181\) −206.080 −0.0846289 −0.0423145 0.999104i \(-0.513473\pi\)
−0.0423145 + 0.999104i \(0.513473\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 770.557 0.308730
\(185\) −778.328 −0.309318
\(186\) 0 0
\(187\) 3855.41 1.50768
\(188\) 1395.49 0.541363
\(189\) 0 0
\(190\) −4.88397 −0.00186485
\(191\) 2018.63 0.764727 0.382364 0.924012i \(-0.375110\pi\)
0.382364 + 0.924012i \(0.375110\pi\)
\(192\) 0 0
\(193\) 1031.69 0.384781 0.192390 0.981318i \(-0.438376\pi\)
0.192390 + 0.981318i \(0.438376\pi\)
\(194\) −334.344 −0.123734
\(195\) 0 0
\(196\) 0 0
\(197\) 205.955 0.0744857 0.0372429 0.999306i \(-0.488142\pi\)
0.0372429 + 0.999306i \(0.488142\pi\)
\(198\) 0 0
\(199\) 1831.38 0.652376 0.326188 0.945305i \(-0.394236\pi\)
0.326188 + 0.945305i \(0.394236\pi\)
\(200\) 94.0983 0.0332688
\(201\) 0 0
\(202\) 325.584 0.113406
\(203\) 0 0
\(204\) 0 0
\(205\) 784.427 0.267253
\(206\) −308.879 −0.104469
\(207\) 0 0
\(208\) 5074.07 1.69146
\(209\) −208.842 −0.0691191
\(210\) 0 0
\(211\) 1030.19 0.336119 0.168060 0.985777i \(-0.446250\pi\)
0.168060 + 0.985777i \(0.446250\pi\)
\(212\) 1591.25 0.515508
\(213\) 0 0
\(214\) 298.780 0.0954402
\(215\) −1771.08 −0.561800
\(216\) 0 0
\(217\) 0 0
\(218\) −488.500 −0.151768
\(219\) 0 0
\(220\) 2004.82 0.614387
\(221\) 6185.10 1.88260
\(222\) 0 0
\(223\) −5368.67 −1.61217 −0.806083 0.591803i \(-0.798416\pi\)
−0.806083 + 0.591803i \(0.798416\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −461.251 −0.135761
\(227\) −932.121 −0.272542 −0.136271 0.990672i \(-0.543512\pi\)
−0.136271 + 0.990672i \(0.543512\pi\)
\(228\) 0 0
\(229\) −3163.05 −0.912752 −0.456376 0.889787i \(-0.650853\pi\)
−0.456376 + 0.889787i \(0.650853\pi\)
\(230\) 241.641 0.0692753
\(231\) 0 0
\(232\) 343.147 0.0971065
\(233\) −436.562 −0.122747 −0.0613737 0.998115i \(-0.519548\pi\)
−0.0613737 + 0.998115i \(0.519548\pi\)
\(234\) 0 0
\(235\) 878.297 0.243803
\(236\) 2482.57 0.684753
\(237\) 0 0
\(238\) 0 0
\(239\) 1980.82 0.536103 0.268051 0.963405i \(-0.413620\pi\)
0.268051 + 0.963405i \(0.413620\pi\)
\(240\) 0 0
\(241\) −5303.55 −1.41756 −0.708780 0.705430i \(-0.750754\pi\)
−0.708780 + 0.705430i \(0.750754\pi\)
\(242\) −287.162 −0.0762787
\(243\) 0 0
\(244\) −1224.77 −0.321344
\(245\) 0 0
\(246\) 0 0
\(247\) −335.037 −0.0863074
\(248\) −745.556 −0.190899
\(249\) 0 0
\(250\) 29.5085 0.00746512
\(251\) −2996.04 −0.753420 −0.376710 0.926331i \(-0.622945\pi\)
−0.376710 + 0.926331i \(0.622945\pi\)
\(252\) 0 0
\(253\) 10332.7 2.56764
\(254\) −52.9384 −0.0130774
\(255\) 0 0
\(256\) 3813.64 0.931065
\(257\) 968.861 0.235159 0.117580 0.993063i \(-0.462487\pi\)
0.117580 + 0.993063i \(0.462487\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3216.26 0.767170
\(261\) 0 0
\(262\) 115.885 0.0273260
\(263\) 4830.18 1.13248 0.566239 0.824241i \(-0.308398\pi\)
0.566239 + 0.824241i \(0.308398\pi\)
\(264\) 0 0
\(265\) 1001.51 0.232159
\(266\) 0 0
\(267\) 0 0
\(268\) −5836.78 −1.33037
\(269\) −4774.97 −1.08229 −0.541143 0.840930i \(-0.682008\pi\)
−0.541143 + 0.840930i \(0.682008\pi\)
\(270\) 0 0
\(271\) −141.909 −0.0318094 −0.0159047 0.999874i \(-0.505063\pi\)
−0.0159047 + 0.999874i \(0.505063\pi\)
\(272\) 4786.84 1.06708
\(273\) 0 0
\(274\) 432.269 0.0953078
\(275\) 1261.80 0.276689
\(276\) 0 0
\(277\) −3621.13 −0.785460 −0.392730 0.919654i \(-0.628469\pi\)
−0.392730 + 0.919654i \(0.628469\pi\)
\(278\) −720.206 −0.155378
\(279\) 0 0
\(280\) 0 0
\(281\) −5790.87 −1.22937 −0.614687 0.788771i \(-0.710718\pi\)
−0.614687 + 0.788771i \(0.710718\pi\)
\(282\) 0 0
\(283\) −526.043 −0.110495 −0.0552474 0.998473i \(-0.517595\pi\)
−0.0552474 + 0.998473i \(0.517595\pi\)
\(284\) −5390.80 −1.12636
\(285\) 0 0
\(286\) −964.753 −0.199465
\(287\) 0 0
\(288\) 0 0
\(289\) 921.972 0.187660
\(290\) 107.608 0.0217896
\(291\) 0 0
\(292\) −483.014 −0.0968023
\(293\) 1914.88 0.381803 0.190901 0.981609i \(-0.438859\pi\)
0.190901 + 0.981609i \(0.438859\pi\)
\(294\) 0 0
\(295\) 1562.49 0.308379
\(296\) 585.915 0.115053
\(297\) 0 0
\(298\) 530.339 0.103093
\(299\) 16576.4 3.20615
\(300\) 0 0
\(301\) 0 0
\(302\) 309.610 0.0589936
\(303\) 0 0
\(304\) −259.296 −0.0489199
\(305\) −770.851 −0.144717
\(306\) 0 0
\(307\) 6244.17 1.16083 0.580413 0.814322i \(-0.302891\pi\)
0.580413 + 0.814322i \(0.302891\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −233.800 −0.0428354
\(311\) −9658.78 −1.76109 −0.880545 0.473962i \(-0.842823\pi\)
−0.880545 + 0.473962i \(0.842823\pi\)
\(312\) 0 0
\(313\) −2198.34 −0.396988 −0.198494 0.980102i \(-0.563605\pi\)
−0.198494 + 0.980102i \(0.563605\pi\)
\(314\) 422.783 0.0759842
\(315\) 0 0
\(316\) 10218.4 1.81908
\(317\) −3030.78 −0.536990 −0.268495 0.963281i \(-0.586526\pi\)
−0.268495 + 0.963281i \(0.586526\pi\)
\(318\) 0 0
\(319\) 4601.40 0.807615
\(320\) 2453.62 0.428630
\(321\) 0 0
\(322\) 0 0
\(323\) −316.072 −0.0544480
\(324\) 0 0
\(325\) 2024.26 0.345495
\(326\) 115.935 0.0196965
\(327\) 0 0
\(328\) −590.506 −0.0994062
\(329\) 0 0
\(330\) 0 0
\(331\) 4753.74 0.789393 0.394696 0.918812i \(-0.370850\pi\)
0.394696 + 0.918812i \(0.370850\pi\)
\(332\) −922.888 −0.152560
\(333\) 0 0
\(334\) 195.006 0.0319469
\(335\) −3673.58 −0.599131
\(336\) 0 0
\(337\) 8824.40 1.42640 0.713199 0.700962i \(-0.247246\pi\)
0.713199 + 0.700962i \(0.247246\pi\)
\(338\) −1029.08 −0.165605
\(339\) 0 0
\(340\) 3034.20 0.483977
\(341\) −9997.47 −1.58766
\(342\) 0 0
\(343\) 0 0
\(344\) 1333.25 0.208965
\(345\) 0 0
\(346\) −688.847 −0.107031
\(347\) 3413.97 0.528160 0.264080 0.964501i \(-0.414932\pi\)
0.264080 + 0.964501i \(0.414932\pi\)
\(348\) 0 0
\(349\) 5676.32 0.870621 0.435310 0.900280i \(-0.356639\pi\)
0.435310 + 0.900280i \(0.356639\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2266.44 −0.343187
\(353\) 6225.80 0.938713 0.469357 0.883009i \(-0.344486\pi\)
0.469357 + 0.883009i \(0.344486\pi\)
\(354\) 0 0
\(355\) −3392.89 −0.507256
\(356\) 7280.45 1.08388
\(357\) 0 0
\(358\) 225.621 0.0333084
\(359\) 4907.73 0.721505 0.360752 0.932662i \(-0.382520\pi\)
0.360752 + 0.932662i \(0.382520\pi\)
\(360\) 0 0
\(361\) −6841.88 −0.997504
\(362\) 48.6490 0.00706335
\(363\) 0 0
\(364\) 0 0
\(365\) −304.001 −0.0435950
\(366\) 0 0
\(367\) 3906.48 0.555631 0.277816 0.960634i \(-0.410390\pi\)
0.277816 + 0.960634i \(0.410390\pi\)
\(368\) 12829.0 1.81728
\(369\) 0 0
\(370\) 183.738 0.0258165
\(371\) 0 0
\(372\) 0 0
\(373\) −2102.52 −0.291862 −0.145931 0.989295i \(-0.546618\pi\)
−0.145931 + 0.989295i \(0.546618\pi\)
\(374\) −910.140 −0.125835
\(375\) 0 0
\(376\) −661.170 −0.0906842
\(377\) 7381.86 1.00845
\(378\) 0 0
\(379\) −6612.76 −0.896239 −0.448120 0.893974i \(-0.647906\pi\)
−0.448120 + 0.893974i \(0.647906\pi\)
\(380\) −164.358 −0.0221878
\(381\) 0 0
\(382\) −476.534 −0.0638262
\(383\) 2.37457 0.000316801 0 0.000158401 1.00000i \(-0.499950\pi\)
0.000158401 1.00000i \(0.499950\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −243.549 −0.0321148
\(387\) 0 0
\(388\) −11251.5 −1.47218
\(389\) −7716.98 −1.00583 −0.502913 0.864337i \(-0.667739\pi\)
−0.502913 + 0.864337i \(0.667739\pi\)
\(390\) 0 0
\(391\) 15638.0 2.02263
\(392\) 0 0
\(393\) 0 0
\(394\) −48.6194 −0.00621678
\(395\) 6431.28 0.819223
\(396\) 0 0
\(397\) −6403.95 −0.809584 −0.404792 0.914409i \(-0.632656\pi\)
−0.404792 + 0.914409i \(0.632656\pi\)
\(398\) −432.329 −0.0544490
\(399\) 0 0
\(400\) 1566.64 0.195830
\(401\) 10969.9 1.36611 0.683054 0.730368i \(-0.260651\pi\)
0.683054 + 0.730368i \(0.260651\pi\)
\(402\) 0 0
\(403\) −16038.6 −1.98248
\(404\) 10956.7 1.34930
\(405\) 0 0
\(406\) 0 0
\(407\) 7856.78 0.956870
\(408\) 0 0
\(409\) 400.353 0.0484015 0.0242007 0.999707i \(-0.492296\pi\)
0.0242007 + 0.999707i \(0.492296\pi\)
\(410\) −185.178 −0.0223056
\(411\) 0 0
\(412\) −10394.6 −1.24297
\(413\) 0 0
\(414\) 0 0
\(415\) −580.851 −0.0687057
\(416\) −3635.97 −0.428529
\(417\) 0 0
\(418\) 49.3009 0.00576887
\(419\) −15815.4 −1.84399 −0.921995 0.387201i \(-0.873442\pi\)
−0.921995 + 0.387201i \(0.873442\pi\)
\(420\) 0 0
\(421\) 1936.53 0.224182 0.112091 0.993698i \(-0.464245\pi\)
0.112091 + 0.993698i \(0.464245\pi\)
\(422\) −243.195 −0.0280534
\(423\) 0 0
\(424\) −753.923 −0.0863531
\(425\) 1909.67 0.217960
\(426\) 0 0
\(427\) 0 0
\(428\) 10054.7 1.13554
\(429\) 0 0
\(430\) 418.096 0.0468893
\(431\) −2030.91 −0.226973 −0.113487 0.993540i \(-0.536202\pi\)
−0.113487 + 0.993540i \(0.536202\pi\)
\(432\) 0 0
\(433\) 10784.1 1.19689 0.598443 0.801165i \(-0.295786\pi\)
0.598443 + 0.801165i \(0.295786\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16439.2 −1.80573
\(437\) −847.089 −0.0927272
\(438\) 0 0
\(439\) 6304.19 0.685382 0.342691 0.939448i \(-0.388662\pi\)
0.342691 + 0.939448i \(0.388662\pi\)
\(440\) −949.868 −0.102916
\(441\) 0 0
\(442\) −1460.10 −0.157127
\(443\) −15494.8 −1.66181 −0.830905 0.556414i \(-0.812177\pi\)
−0.830905 + 0.556414i \(0.812177\pi\)
\(444\) 0 0
\(445\) 4582.20 0.488128
\(446\) 1267.37 0.134556
\(447\) 0 0
\(448\) 0 0
\(449\) 242.018 0.0254377 0.0127189 0.999919i \(-0.495951\pi\)
0.0127189 + 0.999919i \(0.495951\pi\)
\(450\) 0 0
\(451\) −7918.34 −0.826741
\(452\) −15522.2 −1.61528
\(453\) 0 0
\(454\) 220.044 0.0227471
\(455\) 0 0
\(456\) 0 0
\(457\) −11670.4 −1.19457 −0.597283 0.802030i \(-0.703753\pi\)
−0.597283 + 0.802030i \(0.703753\pi\)
\(458\) 746.695 0.0761807
\(459\) 0 0
\(460\) 8131.81 0.824234
\(461\) 12128.1 1.22530 0.612649 0.790355i \(-0.290104\pi\)
0.612649 + 0.790355i \(0.290104\pi\)
\(462\) 0 0
\(463\) 5161.64 0.518103 0.259051 0.965864i \(-0.416590\pi\)
0.259051 + 0.965864i \(0.416590\pi\)
\(464\) 5713.05 0.571598
\(465\) 0 0
\(466\) 103.058 0.0102448
\(467\) 11680.2 1.15738 0.578691 0.815547i \(-0.303564\pi\)
0.578691 + 0.815547i \(0.303564\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −207.338 −0.0203485
\(471\) 0 0
\(472\) −1176.22 −0.114703
\(473\) 17878.1 1.73792
\(474\) 0 0
\(475\) −103.444 −0.00999230
\(476\) 0 0
\(477\) 0 0
\(478\) −467.608 −0.0447445
\(479\) −18458.7 −1.76075 −0.880373 0.474282i \(-0.842708\pi\)
−0.880373 + 0.474282i \(0.842708\pi\)
\(480\) 0 0
\(481\) 12604.3 1.19482
\(482\) 1252.00 0.118313
\(483\) 0 0
\(484\) −9663.70 −0.907560
\(485\) −7081.51 −0.663000
\(486\) 0 0
\(487\) 8630.11 0.803014 0.401507 0.915856i \(-0.368487\pi\)
0.401507 + 0.915856i \(0.368487\pi\)
\(488\) 580.286 0.0538286
\(489\) 0 0
\(490\) 0 0
\(491\) −17801.6 −1.63621 −0.818103 0.575072i \(-0.804974\pi\)
−0.818103 + 0.575072i \(0.804974\pi\)
\(492\) 0 0
\(493\) 6963.99 0.636191
\(494\) 79.0916 0.00720344
\(495\) 0 0
\(496\) −12412.7 −1.12369
\(497\) 0 0
\(498\) 0 0
\(499\) 200.167 0.0179574 0.00897868 0.999960i \(-0.497142\pi\)
0.00897868 + 0.999960i \(0.497142\pi\)
\(500\) 993.034 0.0888197
\(501\) 0 0
\(502\) 707.269 0.0628824
\(503\) 16400.4 1.45379 0.726896 0.686747i \(-0.240962\pi\)
0.726896 + 0.686747i \(0.240962\pi\)
\(504\) 0 0
\(505\) 6895.97 0.607657
\(506\) −2439.23 −0.214302
\(507\) 0 0
\(508\) −1781.51 −0.155594
\(509\) −15006.6 −1.30679 −0.653394 0.757018i \(-0.726656\pi\)
−0.653394 + 0.757018i \(0.726656\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −4700.94 −0.405770
\(513\) 0 0
\(514\) −228.717 −0.0196270
\(515\) −6542.17 −0.559772
\(516\) 0 0
\(517\) −8865.91 −0.754201
\(518\) 0 0
\(519\) 0 0
\(520\) −1523.84 −0.128509
\(521\) 7113.18 0.598146 0.299073 0.954230i \(-0.403323\pi\)
0.299073 + 0.954230i \(0.403323\pi\)
\(522\) 0 0
\(523\) 8888.46 0.743146 0.371573 0.928404i \(-0.378819\pi\)
0.371573 + 0.928404i \(0.378819\pi\)
\(524\) 3899.83 0.325123
\(525\) 0 0
\(526\) −1140.25 −0.0945196
\(527\) −15130.7 −1.25067
\(528\) 0 0
\(529\) 29743.8 2.44463
\(530\) −236.424 −0.0193766
\(531\) 0 0
\(532\) 0 0
\(533\) −12703.1 −1.03233
\(534\) 0 0
\(535\) 6328.27 0.511392
\(536\) 2765.42 0.222850
\(537\) 0 0
\(538\) 1127.22 0.0903305
\(539\) 0 0
\(540\) 0 0
\(541\) −653.827 −0.0519597 −0.0259799 0.999662i \(-0.508271\pi\)
−0.0259799 + 0.999662i \(0.508271\pi\)
\(542\) 33.5001 0.00265489
\(543\) 0 0
\(544\) −3430.14 −0.270342
\(545\) −10346.6 −0.813210
\(546\) 0 0
\(547\) 1138.52 0.0889940 0.0444970 0.999010i \(-0.485831\pi\)
0.0444970 + 0.999010i \(0.485831\pi\)
\(548\) 14546.9 1.13397
\(549\) 0 0
\(550\) −297.871 −0.0230932
\(551\) −377.229 −0.0291660
\(552\) 0 0
\(553\) 0 0
\(554\) 854.832 0.0655566
\(555\) 0 0
\(556\) −24236.7 −1.84868
\(557\) 19804.8 1.50657 0.753283 0.657696i \(-0.228469\pi\)
0.753283 + 0.657696i \(0.228469\pi\)
\(558\) 0 0
\(559\) 28681.1 2.17009
\(560\) 0 0
\(561\) 0 0
\(562\) 1367.04 0.102607
\(563\) 10276.3 0.769265 0.384632 0.923070i \(-0.374328\pi\)
0.384632 + 0.923070i \(0.374328\pi\)
\(564\) 0 0
\(565\) −9769.45 −0.727440
\(566\) 124.182 0.00922219
\(567\) 0 0
\(568\) 2554.12 0.188677
\(569\) −4139.03 −0.304951 −0.152475 0.988307i \(-0.548724\pi\)
−0.152475 + 0.988307i \(0.548724\pi\)
\(570\) 0 0
\(571\) −4486.81 −0.328839 −0.164420 0.986390i \(-0.552575\pi\)
−0.164420 + 0.986390i \(0.552575\pi\)
\(572\) −32466.3 −2.37323
\(573\) 0 0
\(574\) 0 0
\(575\) 5118.03 0.371194
\(576\) 0 0
\(577\) 1104.77 0.0797093 0.0398547 0.999205i \(-0.487311\pi\)
0.0398547 + 0.999205i \(0.487311\pi\)
\(578\) −217.648 −0.0156626
\(579\) 0 0
\(580\) 3621.28 0.259251
\(581\) 0 0
\(582\) 0 0
\(583\) −10109.7 −0.718181
\(584\) 228.848 0.0162154
\(585\) 0 0
\(586\) −452.041 −0.0318663
\(587\) −10413.2 −0.732199 −0.366100 0.930576i \(-0.619307\pi\)
−0.366100 + 0.930576i \(0.619307\pi\)
\(588\) 0 0
\(589\) 819.605 0.0573365
\(590\) −368.854 −0.0257381
\(591\) 0 0
\(592\) 9754.89 0.677235
\(593\) −3235.16 −0.224034 −0.112017 0.993706i \(-0.535731\pi\)
−0.112017 + 0.993706i \(0.535731\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 17847.2 1.22659
\(597\) 0 0
\(598\) −3913.16 −0.267594
\(599\) −569.048 −0.0388158 −0.0194079 0.999812i \(-0.506178\pi\)
−0.0194079 + 0.999812i \(0.506178\pi\)
\(600\) 0 0
\(601\) −3760.89 −0.255258 −0.127629 0.991822i \(-0.540737\pi\)
−0.127629 + 0.991822i \(0.540737\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 10419.1 0.701902
\(605\) −6082.18 −0.408720
\(606\) 0 0
\(607\) 2224.05 0.148717 0.0743585 0.997232i \(-0.476309\pi\)
0.0743585 + 0.997232i \(0.476309\pi\)
\(608\) 185.806 0.0123938
\(609\) 0 0
\(610\) 181.973 0.0120785
\(611\) −14223.2 −0.941753
\(612\) 0 0
\(613\) 5914.50 0.389697 0.194849 0.980833i \(-0.437578\pi\)
0.194849 + 0.980833i \(0.437578\pi\)
\(614\) −1474.05 −0.0968856
\(615\) 0 0
\(616\) 0 0
\(617\) 18591.2 1.21306 0.606528 0.795062i \(-0.292562\pi\)
0.606528 + 0.795062i \(0.292562\pi\)
\(618\) 0 0
\(619\) −5125.97 −0.332844 −0.166422 0.986055i \(-0.553221\pi\)
−0.166422 + 0.986055i \(0.553221\pi\)
\(620\) −7867.96 −0.509653
\(621\) 0 0
\(622\) 2280.13 0.146985
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 518.957 0.0331337
\(627\) 0 0
\(628\) 14227.7 0.904056
\(629\) 11890.8 0.753765
\(630\) 0 0
\(631\) −10649.0 −0.671839 −0.335919 0.941891i \(-0.609047\pi\)
−0.335919 + 0.941891i \(0.609047\pi\)
\(632\) −4841.38 −0.304715
\(633\) 0 0
\(634\) 715.471 0.0448186
\(635\) −1121.25 −0.0700718
\(636\) 0 0
\(637\) 0 0
\(638\) −1086.24 −0.0674056
\(639\) 0 0
\(640\) −2375.41 −0.146713
\(641\) −24025.7 −1.48044 −0.740218 0.672367i \(-0.765278\pi\)
−0.740218 + 0.672367i \(0.765278\pi\)
\(642\) 0 0
\(643\) −14929.3 −0.915638 −0.457819 0.889045i \(-0.651369\pi\)
−0.457819 + 0.889045i \(0.651369\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 74.6144 0.00454437
\(647\) 14479.1 0.879801 0.439901 0.898046i \(-0.355014\pi\)
0.439901 + 0.898046i \(0.355014\pi\)
\(648\) 0 0
\(649\) −15772.5 −0.953965
\(650\) −477.864 −0.0288360
\(651\) 0 0
\(652\) 3901.50 0.234347
\(653\) −898.168 −0.0538255 −0.0269127 0.999638i \(-0.508568\pi\)
−0.0269127 + 0.999638i \(0.508568\pi\)
\(654\) 0 0
\(655\) 2454.49 0.146420
\(656\) −9831.33 −0.585135
\(657\) 0 0
\(658\) 0 0
\(659\) 30198.0 1.78505 0.892526 0.450997i \(-0.148931\pi\)
0.892526 + 0.450997i \(0.148931\pi\)
\(660\) 0 0
\(661\) 19337.8 1.13790 0.568952 0.822371i \(-0.307349\pi\)
0.568952 + 0.822371i \(0.307349\pi\)
\(662\) −1122.20 −0.0658848
\(663\) 0 0
\(664\) 437.257 0.0255555
\(665\) 0 0
\(666\) 0 0
\(667\) 18663.9 1.08346
\(668\) 6562.44 0.380102
\(669\) 0 0
\(670\) 867.214 0.0500051
\(671\) 7781.30 0.447681
\(672\) 0 0
\(673\) 10132.2 0.580336 0.290168 0.956976i \(-0.406289\pi\)
0.290168 + 0.956976i \(0.406289\pi\)
\(674\) −2083.16 −0.119051
\(675\) 0 0
\(676\) −34631.0 −1.97035
\(677\) −33177.3 −1.88347 −0.941733 0.336361i \(-0.890804\pi\)
−0.941733 + 0.336361i \(0.890804\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1437.58 −0.0810714
\(681\) 0 0
\(682\) 2360.08 0.132511
\(683\) 11423.6 0.639987 0.319994 0.947420i \(-0.396319\pi\)
0.319994 + 0.947420i \(0.396319\pi\)
\(684\) 0 0
\(685\) 9155.61 0.510683
\(686\) 0 0
\(687\) 0 0
\(688\) 22197.2 1.23003
\(689\) −16218.6 −0.896775
\(690\) 0 0
\(691\) 19737.4 1.08661 0.543304 0.839536i \(-0.317173\pi\)
0.543304 + 0.839536i \(0.317173\pi\)
\(692\) −23181.4 −1.27345
\(693\) 0 0
\(694\) −805.929 −0.0440816
\(695\) −15254.2 −0.832554
\(696\) 0 0
\(697\) −11984.0 −0.651258
\(698\) −1340.00 −0.0726643
\(699\) 0 0
\(700\) 0 0
\(701\) −11307.8 −0.609258 −0.304629 0.952471i \(-0.598532\pi\)
−0.304629 + 0.952471i \(0.598532\pi\)
\(702\) 0 0
\(703\) −644.108 −0.0345562
\(704\) −24767.9 −1.32596
\(705\) 0 0
\(706\) −1469.71 −0.0783475
\(707\) 0 0
\(708\) 0 0
\(709\) 30859.2 1.63461 0.817307 0.576202i \(-0.195466\pi\)
0.817307 + 0.576202i \(0.195466\pi\)
\(710\) 800.952 0.0423369
\(711\) 0 0
\(712\) −3449.42 −0.181562
\(713\) −40551.0 −2.12994
\(714\) 0 0
\(715\) −20433.8 −1.06878
\(716\) 7592.69 0.396302
\(717\) 0 0
\(718\) −1158.56 −0.0602187
\(719\) 33152.4 1.71958 0.859789 0.510650i \(-0.170595\pi\)
0.859789 + 0.510650i \(0.170595\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1615.15 0.0832543
\(723\) 0 0
\(724\) 1637.16 0.0840394
\(725\) 2279.18 0.116754
\(726\) 0 0
\(727\) 16743.0 0.854146 0.427073 0.904217i \(-0.359545\pi\)
0.427073 + 0.904217i \(0.359545\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 71.7650 0.00363855
\(731\) 27057.5 1.36903
\(732\) 0 0
\(733\) 8827.55 0.444820 0.222410 0.974953i \(-0.428608\pi\)
0.222410 + 0.974953i \(0.428608\pi\)
\(734\) −922.195 −0.0463744
\(735\) 0 0
\(736\) −9192.97 −0.460404
\(737\) 37082.6 1.85340
\(738\) 0 0
\(739\) 36154.0 1.79966 0.899829 0.436243i \(-0.143691\pi\)
0.899829 + 0.436243i \(0.143691\pi\)
\(740\) 6183.25 0.307163
\(741\) 0 0
\(742\) 0 0
\(743\) 1820.69 0.0898987 0.0449494 0.998989i \(-0.485687\pi\)
0.0449494 + 0.998989i \(0.485687\pi\)
\(744\) 0 0
\(745\) 11232.8 0.552398
\(746\) 496.338 0.0243596
\(747\) 0 0
\(748\) −30628.5 −1.49718
\(749\) 0 0
\(750\) 0 0
\(751\) 27764.4 1.34905 0.674526 0.738251i \(-0.264348\pi\)
0.674526 + 0.738251i \(0.264348\pi\)
\(752\) −11007.8 −0.533795
\(753\) 0 0
\(754\) −1742.62 −0.0841678
\(755\) 6557.65 0.316102
\(756\) 0 0
\(757\) −13518.3 −0.649050 −0.324525 0.945877i \(-0.605205\pi\)
−0.324525 + 0.945877i \(0.605205\pi\)
\(758\) 1561.06 0.0748025
\(759\) 0 0
\(760\) 77.8714 0.00371670
\(761\) 30695.2 1.46216 0.731078 0.682294i \(-0.239017\pi\)
0.731078 + 0.682294i \(0.239017\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −16036.5 −0.759400
\(765\) 0 0
\(766\) −0.560560 −2.64410e−5 0
\(767\) −25303.2 −1.19119
\(768\) 0 0
\(769\) −4536.39 −0.212726 −0.106363 0.994327i \(-0.533921\pi\)
−0.106363 + 0.994327i \(0.533921\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8196.03 −0.382100
\(773\) 31238.9 1.45354 0.726768 0.686883i \(-0.241022\pi\)
0.726768 + 0.686883i \(0.241022\pi\)
\(774\) 0 0
\(775\) −4951.97 −0.229523
\(776\) 5330.86 0.246607
\(777\) 0 0
\(778\) 1821.73 0.0839490
\(779\) 649.155 0.0298567
\(780\) 0 0
\(781\) 34249.2 1.56919
\(782\) −3691.64 −0.168814
\(783\) 0 0
\(784\) 0 0
\(785\) 8954.70 0.407143
\(786\) 0 0
\(787\) −39597.2 −1.79350 −0.896752 0.442534i \(-0.854079\pi\)
−0.896752 + 0.442534i \(0.854079\pi\)
\(788\) −1636.16 −0.0739669
\(789\) 0 0
\(790\) −1518.22 −0.0683745
\(791\) 0 0
\(792\) 0 0
\(793\) 12483.3 0.559008
\(794\) 1511.77 0.0675700
\(795\) 0 0
\(796\) −14549.0 −0.647832
\(797\) −16567.0 −0.736302 −0.368151 0.929766i \(-0.620009\pi\)
−0.368151 + 0.929766i \(0.620009\pi\)
\(798\) 0 0
\(799\) −13418.1 −0.594115
\(800\) −1122.62 −0.0496133
\(801\) 0 0
\(802\) −2589.63 −0.114019
\(803\) 3068.72 0.134860
\(804\) 0 0
\(805\) 0 0
\(806\) 3786.19 0.165463
\(807\) 0 0
\(808\) −5191.20 −0.226022
\(809\) 12141.6 0.527657 0.263828 0.964570i \(-0.415015\pi\)
0.263828 + 0.964570i \(0.415015\pi\)
\(810\) 0 0
\(811\) −30295.6 −1.31174 −0.655870 0.754873i \(-0.727698\pi\)
−0.655870 + 0.754873i \(0.727698\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1854.73 −0.0798629
\(815\) 2455.54 0.105538
\(816\) 0 0
\(817\) −1465.67 −0.0627628
\(818\) −94.5106 −0.00403971
\(819\) 0 0
\(820\) −6231.70 −0.265391
\(821\) 14914.8 0.634018 0.317009 0.948423i \(-0.397322\pi\)
0.317009 + 0.948423i \(0.397322\pi\)
\(822\) 0 0
\(823\) −31077.6 −1.31628 −0.658138 0.752897i \(-0.728656\pi\)
−0.658138 + 0.752897i \(0.728656\pi\)
\(824\) 4924.85 0.208210
\(825\) 0 0
\(826\) 0 0
\(827\) −15527.8 −0.652908 −0.326454 0.945213i \(-0.605854\pi\)
−0.326454 + 0.945213i \(0.605854\pi\)
\(828\) 0 0
\(829\) 40221.5 1.68510 0.842551 0.538617i \(-0.181053\pi\)
0.842551 + 0.538617i \(0.181053\pi\)
\(830\) 137.120 0.00573436
\(831\) 0 0
\(832\) −39734.2 −1.65569
\(833\) 0 0
\(834\) 0 0
\(835\) 4130.29 0.171179
\(836\) 1659.10 0.0686377
\(837\) 0 0
\(838\) 3733.51 0.153904
\(839\) −21153.7 −0.870448 −0.435224 0.900322i \(-0.643331\pi\)
−0.435224 + 0.900322i \(0.643331\pi\)
\(840\) 0 0
\(841\) −16077.5 −0.659213
\(842\) −457.152 −0.0187108
\(843\) 0 0
\(844\) −8184.10 −0.333778
\(845\) −21796.2 −0.887351
\(846\) 0 0
\(847\) 0 0
\(848\) −12552.0 −0.508301
\(849\) 0 0
\(850\) −450.813 −0.0181915
\(851\) 31868.1 1.28369
\(852\) 0 0
\(853\) −636.075 −0.0255320 −0.0127660 0.999919i \(-0.504064\pi\)
−0.0127660 + 0.999919i \(0.504064\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −4763.83 −0.190215
\(857\) −3941.46 −0.157104 −0.0785518 0.996910i \(-0.525030\pi\)
−0.0785518 + 0.996910i \(0.525030\pi\)
\(858\) 0 0
\(859\) 21781.6 0.865165 0.432583 0.901594i \(-0.357602\pi\)
0.432583 + 0.901594i \(0.357602\pi\)
\(860\) 14070.0 0.557886
\(861\) 0 0
\(862\) 479.432 0.0189438
\(863\) 44697.9 1.76308 0.881538 0.472112i \(-0.156508\pi\)
0.881538 + 0.472112i \(0.156508\pi\)
\(864\) 0 0
\(865\) −14590.0 −0.573498
\(866\) −2545.79 −0.0998953
\(867\) 0 0
\(868\) 0 0
\(869\) −64920.1 −2.53425
\(870\) 0 0
\(871\) 59490.3 2.31430
\(872\) 7788.78 0.302478
\(873\) 0 0
\(874\) 199.971 0.00773926
\(875\) 0 0
\(876\) 0 0
\(877\) −20171.7 −0.776682 −0.388341 0.921516i \(-0.626952\pi\)
−0.388341 + 0.921516i \(0.626952\pi\)
\(878\) −1488.22 −0.0572038
\(879\) 0 0
\(880\) −15814.3 −0.605797
\(881\) 11577.6 0.442744 0.221372 0.975189i \(-0.428946\pi\)
0.221372 + 0.975189i \(0.428946\pi\)
\(882\) 0 0
\(883\) −35388.3 −1.34871 −0.674355 0.738407i \(-0.735578\pi\)
−0.674355 + 0.738407i \(0.735578\pi\)
\(884\) −49136.1 −1.86949
\(885\) 0 0
\(886\) 3657.83 0.138699
\(887\) −41705.0 −1.57871 −0.789356 0.613936i \(-0.789585\pi\)
−0.789356 + 0.613936i \(0.789585\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −1081.71 −0.0407405
\(891\) 0 0
\(892\) 42650.2 1.60093
\(893\) 726.838 0.0272371
\(894\) 0 0
\(895\) 4778.72 0.178475
\(896\) 0 0
\(897\) 0 0
\(898\) −57.1328 −0.00212310
\(899\) −18058.3 −0.669942
\(900\) 0 0
\(901\) −15300.5 −0.565740
\(902\) 1869.27 0.0690020
\(903\) 0 0
\(904\) 7354.31 0.270576
\(905\) 1030.40 0.0378472
\(906\) 0 0
\(907\) −28645.1 −1.04867 −0.524336 0.851511i \(-0.675687\pi\)
−0.524336 + 0.851511i \(0.675687\pi\)
\(908\) 7405.02 0.270643
\(909\) 0 0
\(910\) 0 0
\(911\) −13337.8 −0.485074 −0.242537 0.970142i \(-0.577980\pi\)
−0.242537 + 0.970142i \(0.577980\pi\)
\(912\) 0 0
\(913\) 5863.36 0.212540
\(914\) 2755.00 0.0997016
\(915\) 0 0
\(916\) 25128.1 0.906394
\(917\) 0 0
\(918\) 0 0
\(919\) −28911.0 −1.03774 −0.518871 0.854853i \(-0.673647\pi\)
−0.518871 + 0.854853i \(0.673647\pi\)
\(920\) −3852.79 −0.138068
\(921\) 0 0
\(922\) −2863.06 −0.102267
\(923\) 54944.8 1.95940
\(924\) 0 0
\(925\) 3891.64 0.138331
\(926\) −1218.50 −0.0432422
\(927\) 0 0
\(928\) −4093.84 −0.144814
\(929\) 7093.88 0.250530 0.125265 0.992123i \(-0.460022\pi\)
0.125265 + 0.992123i \(0.460022\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 3468.17 0.121892
\(933\) 0 0
\(934\) −2757.33 −0.0965981
\(935\) −19277.1 −0.674254
\(936\) 0 0
\(937\) 19271.1 0.671888 0.335944 0.941882i \(-0.390945\pi\)
0.335944 + 0.941882i \(0.390945\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −6977.43 −0.242105
\(941\) −18115.2 −0.627563 −0.313782 0.949495i \(-0.601596\pi\)
−0.313782 + 0.949495i \(0.601596\pi\)
\(942\) 0 0
\(943\) −32117.8 −1.10912
\(944\) −19582.9 −0.675180
\(945\) 0 0
\(946\) −4220.44 −0.145051
\(947\) 2475.55 0.0849468 0.0424734 0.999098i \(-0.486476\pi\)
0.0424734 + 0.999098i \(0.486476\pi\)
\(948\) 0 0
\(949\) 4923.04 0.168397
\(950\) 24.4199 0.000833984 0
\(951\) 0 0
\(952\) 0 0
\(953\) −12866.6 −0.437344 −0.218672 0.975798i \(-0.570173\pi\)
−0.218672 + 0.975798i \(0.570173\pi\)
\(954\) 0 0
\(955\) −10093.2 −0.341997
\(956\) −15736.2 −0.532368
\(957\) 0 0
\(958\) 4357.50 0.146957
\(959\) 0 0
\(960\) 0 0
\(961\) 9444.26 0.317017
\(962\) −2975.48 −0.0997228
\(963\) 0 0
\(964\) 42132.9 1.40768
\(965\) −5158.45 −0.172079
\(966\) 0 0
\(967\) −2142.86 −0.0712614 −0.0356307 0.999365i \(-0.511344\pi\)
−0.0356307 + 0.999365i \(0.511344\pi\)
\(968\) 4578.58 0.152026
\(969\) 0 0
\(970\) 1671.72 0.0553357
\(971\) 2879.06 0.0951529 0.0475765 0.998868i \(-0.484850\pi\)
0.0475765 + 0.998868i \(0.484850\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −2037.29 −0.0670217
\(975\) 0 0
\(976\) 9661.18 0.316851
\(977\) −48741.1 −1.59607 −0.798037 0.602608i \(-0.794128\pi\)
−0.798037 + 0.602608i \(0.794128\pi\)
\(978\) 0 0
\(979\) −46254.7 −1.51002
\(980\) 0 0
\(981\) 0 0
\(982\) 4202.40 0.136562
\(983\) −45756.8 −1.48466 −0.742328 0.670037i \(-0.766278\pi\)
−0.742328 + 0.670037i \(0.766278\pi\)
\(984\) 0 0
\(985\) −1029.78 −0.0333110
\(986\) −1643.97 −0.0530982
\(987\) 0 0
\(988\) 2661.63 0.0857062
\(989\) 72515.7 2.33151
\(990\) 0 0
\(991\) −51552.1 −1.65248 −0.826240 0.563319i \(-0.809524\pi\)
−0.826240 + 0.563319i \(0.809524\pi\)
\(992\) 8894.70 0.284684
\(993\) 0 0
\(994\) 0 0
\(995\) −9156.88 −0.291751
\(996\) 0 0
\(997\) −25565.3 −0.812097 −0.406048 0.913852i \(-0.633094\pi\)
−0.406048 + 0.913852i \(0.633094\pi\)
\(998\) −47.2531 −0.00149877
\(999\) 0 0
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 2205.4.a.be.1.1 2
3.2 odd 2 735.4.a.m.1.2 2
7.6 odd 2 315.4.a.l.1.1 2
21.20 even 2 105.4.a.d.1.2 2
35.34 odd 2 1575.4.a.n.1.2 2
84.83 odd 2 1680.4.a.bd.1.2 2
105.62 odd 4 525.4.d.k.274.3 4
105.83 odd 4 525.4.d.k.274.2 4
105.104 even 2 525.4.a.o.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.d.1.2 2 21.20 even 2
315.4.a.l.1.1 2 7.6 odd 2
525.4.a.o.1.1 2 105.104 even 2
525.4.d.k.274.2 4 105.83 odd 4
525.4.d.k.274.3 4 105.62 odd 4
735.4.a.m.1.2 2 3.2 odd 2
1575.4.a.n.1.2 2 35.34 odd 2
1680.4.a.bd.1.2 2 84.83 odd 2
2205.4.a.be.1.1 2 1.1 even 1 trivial