Properties

Label 245.4.a.o.1.5
Level $245$
Weight $4$
Character 245.1
Self dual yes
Analytic conductor $14.455$
Analytic rank $1$
Dimension $6$
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: \(6\)
Coefficient field: 6.6.1163891200.1
Defining polynomial: \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 7 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.241849\) of defining polynomial
Character \(\chi\) \(=\) 245.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.65606 q^{2} +0.332888 q^{3} -5.25746 q^{4} +5.00000 q^{5} +0.551283 q^{6} -21.9552 q^{8} -26.8892 q^{9} +O(q^{10})\) \(q+1.65606 q^{2} +0.332888 q^{3} -5.25746 q^{4} +5.00000 q^{5} +0.551283 q^{6} -21.9552 q^{8} -26.8892 q^{9} +8.28031 q^{10} +69.5726 q^{11} -1.75014 q^{12} -68.4326 q^{13} +1.66444 q^{15} +5.70053 q^{16} -104.332 q^{17} -44.5302 q^{18} -71.8929 q^{19} -26.2873 q^{20} +115.217 q^{22} -101.031 q^{23} -7.30861 q^{24} +25.0000 q^{25} -113.329 q^{26} -17.9390 q^{27} -114.661 q^{29} +2.75641 q^{30} +73.6505 q^{31} +185.082 q^{32} +23.1599 q^{33} -172.780 q^{34} +141.369 q^{36} -200.933 q^{37} -119.059 q^{38} -22.7803 q^{39} -109.776 q^{40} -417.308 q^{41} +311.175 q^{43} -365.775 q^{44} -134.446 q^{45} -167.313 q^{46} -149.697 q^{47} +1.89763 q^{48} +41.4016 q^{50} -34.7307 q^{51} +359.781 q^{52} +271.474 q^{53} -29.7082 q^{54} +347.863 q^{55} -23.9323 q^{57} -189.885 q^{58} +518.028 q^{59} -8.75071 q^{60} +219.926 q^{61} +121.970 q^{62} +260.903 q^{64} -342.163 q^{65} +38.3542 q^{66} +80.6950 q^{67} +548.520 q^{68} -33.6319 q^{69} -91.0463 q^{71} +590.357 q^{72} -882.282 q^{73} -332.758 q^{74} +8.32219 q^{75} +377.974 q^{76} -37.7257 q^{78} +599.877 q^{79} +28.5026 q^{80} +720.036 q^{81} -691.087 q^{82} -70.8820 q^{83} -521.659 q^{85} +515.325 q^{86} -38.1691 q^{87} -1527.48 q^{88} -802.592 q^{89} -222.651 q^{90} +531.165 q^{92} +24.5173 q^{93} -247.908 q^{94} -359.465 q^{95} +61.6114 q^{96} -145.648 q^{97} -1870.75 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} - 16 q^{3} + 14 q^{4} + 30 q^{5} - 24 q^{6} - 66 q^{8} + 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} - 16 q^{3} + 14 q^{4} + 30 q^{5} - 24 q^{6} - 66 q^{8} + 70 q^{9} - 10 q^{10} - 16 q^{11} - 160 q^{12} - 168 q^{13} - 80 q^{15} + 298 q^{16} + 4 q^{17} + 354 q^{18} - 308 q^{19} + 70 q^{20} - 236 q^{22} - 336 q^{23} + 92 q^{24} + 150 q^{25} - 56 q^{26} - 964 q^{27} + 176 q^{29} - 120 q^{30} - 392 q^{31} - 770 q^{32} - 188 q^{33} - 812 q^{34} + 230 q^{36} - 140 q^{37} - 20 q^{38} + 140 q^{39} - 330 q^{40} - 656 q^{41} - 388 q^{43} - 160 q^{44} + 350 q^{45} - 388 q^{46} - 628 q^{47} - 1396 q^{48} - 50 q^{50} + 744 q^{51} - 1520 q^{52} - 676 q^{53} - 2284 q^{54} - 80 q^{55} + 1468 q^{57} - 2012 q^{58} - 996 q^{59} - 800 q^{60} - 740 q^{61} + 364 q^{62} + 1426 q^{64} - 840 q^{65} + 3620 q^{66} + 1768 q^{67} + 2940 q^{68} + 1048 q^{69} - 224 q^{71} + 2858 q^{72} - 2640 q^{73} + 928 q^{74} - 400 q^{75} + 1340 q^{76} + 8 q^{78} + 1636 q^{79} + 1490 q^{80} + 4442 q^{81} + 1756 q^{82} - 140 q^{83} + 20 q^{85} + 1180 q^{86} - 1940 q^{87} - 5652 q^{88} + 1904 q^{89} + 1770 q^{90} - 1952 q^{92} - 1592 q^{93} + 3332 q^{94} - 1540 q^{95} + 6460 q^{96} - 516 q^{97} - 2804 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.65606 0.585506 0.292753 0.956188i \(-0.405429\pi\)
0.292753 + 0.956188i \(0.405429\pi\)
\(3\) 0.332888 0.0640643 0.0320321 0.999487i \(-0.489802\pi\)
0.0320321 + 0.999487i \(0.489802\pi\)
\(4\) −5.25746 −0.657182
\(5\) 5.00000 0.447214
\(6\) 0.551283 0.0375100
\(7\) 0 0
\(8\) −21.9552 −0.970291
\(9\) −26.8892 −0.995896
\(10\) 8.28031 0.261846
\(11\) 69.5726 1.90699 0.953497 0.301402i \(-0.0974546\pi\)
0.953497 + 0.301402i \(0.0974546\pi\)
\(12\) −1.75014 −0.0421019
\(13\) −68.4326 −1.45998 −0.729991 0.683456i \(-0.760476\pi\)
−0.729991 + 0.683456i \(0.760476\pi\)
\(14\) 0 0
\(15\) 1.66444 0.0286504
\(16\) 5.70053 0.0890707
\(17\) −104.332 −1.48848 −0.744240 0.667912i \(-0.767188\pi\)
−0.744240 + 0.667912i \(0.767188\pi\)
\(18\) −44.5302 −0.583103
\(19\) −71.8929 −0.868072 −0.434036 0.900896i \(-0.642911\pi\)
−0.434036 + 0.900896i \(0.642911\pi\)
\(20\) −26.2873 −0.293901
\(21\) 0 0
\(22\) 115.217 1.11656
\(23\) −101.031 −0.915929 −0.457964 0.888970i \(-0.651421\pi\)
−0.457964 + 0.888970i \(0.651421\pi\)
\(24\) −7.30861 −0.0621610
\(25\) 25.0000 0.200000
\(26\) −113.329 −0.854829
\(27\) −17.9390 −0.127866
\(28\) 0 0
\(29\) −114.661 −0.734205 −0.367102 0.930181i \(-0.619650\pi\)
−0.367102 + 0.930181i \(0.619650\pi\)
\(30\) 2.75641 0.0167750
\(31\) 73.6505 0.426710 0.213355 0.976975i \(-0.431561\pi\)
0.213355 + 0.976975i \(0.431561\pi\)
\(32\) 185.082 1.02244
\(33\) 23.1599 0.122170
\(34\) −172.780 −0.871514
\(35\) 0 0
\(36\) 141.369 0.654485
\(37\) −200.933 −0.892790 −0.446395 0.894836i \(-0.647292\pi\)
−0.446395 + 0.894836i \(0.647292\pi\)
\(38\) −119.059 −0.508262
\(39\) −22.7803 −0.0935327
\(40\) −109.776 −0.433927
\(41\) −417.308 −1.58957 −0.794786 0.606889i \(-0.792417\pi\)
−0.794786 + 0.606889i \(0.792417\pi\)
\(42\) 0 0
\(43\) 311.175 1.10357 0.551787 0.833985i \(-0.313946\pi\)
0.551787 + 0.833985i \(0.313946\pi\)
\(44\) −365.775 −1.25324
\(45\) −134.446 −0.445378
\(46\) −167.313 −0.536282
\(47\) −149.697 −0.464586 −0.232293 0.972646i \(-0.574623\pi\)
−0.232293 + 0.972646i \(0.574623\pi\)
\(48\) 1.89763 0.00570625
\(49\) 0 0
\(50\) 41.4016 0.117101
\(51\) −34.7307 −0.0953583
\(52\) 359.781 0.959475
\(53\) 271.474 0.703582 0.351791 0.936078i \(-0.385573\pi\)
0.351791 + 0.936078i \(0.385573\pi\)
\(54\) −29.7082 −0.0748661
\(55\) 347.863 0.852834
\(56\) 0 0
\(57\) −23.9323 −0.0556124
\(58\) −189.885 −0.429882
\(59\) 518.028 1.14308 0.571538 0.820575i \(-0.306347\pi\)
0.571538 + 0.820575i \(0.306347\pi\)
\(60\) −8.75071 −0.0188285
\(61\) 219.926 0.461616 0.230808 0.972999i \(-0.425863\pi\)
0.230808 + 0.972999i \(0.425863\pi\)
\(62\) 121.970 0.249842
\(63\) 0 0
\(64\) 260.903 0.509576
\(65\) −342.163 −0.652924
\(66\) 38.3542 0.0715314
\(67\) 80.6950 0.147141 0.0735706 0.997290i \(-0.476561\pi\)
0.0735706 + 0.997290i \(0.476561\pi\)
\(68\) 548.520 0.978202
\(69\) −33.6319 −0.0586783
\(70\) 0 0
\(71\) −91.0463 −0.152186 −0.0760930 0.997101i \(-0.524245\pi\)
−0.0760930 + 0.997101i \(0.524245\pi\)
\(72\) 590.357 0.966309
\(73\) −882.282 −1.41457 −0.707283 0.706931i \(-0.750079\pi\)
−0.707283 + 0.706931i \(0.750079\pi\)
\(74\) −332.758 −0.522734
\(75\) 8.32219 0.0128129
\(76\) 377.974 0.570481
\(77\) 0 0
\(78\) −37.7257 −0.0547640
\(79\) 599.877 0.854322 0.427161 0.904175i \(-0.359514\pi\)
0.427161 + 0.904175i \(0.359514\pi\)
\(80\) 28.5026 0.0398336
\(81\) 720.036 0.987704
\(82\) −691.087 −0.930705
\(83\) −70.8820 −0.0937387 −0.0468694 0.998901i \(-0.514924\pi\)
−0.0468694 + 0.998901i \(0.514924\pi\)
\(84\) 0 0
\(85\) −521.659 −0.665668
\(86\) 515.325 0.646150
\(87\) −38.1691 −0.0470363
\(88\) −1527.48 −1.85034
\(89\) −802.592 −0.955894 −0.477947 0.878389i \(-0.658619\pi\)
−0.477947 + 0.878389i \(0.658619\pi\)
\(90\) −222.651 −0.260772
\(91\) 0 0
\(92\) 531.165 0.601932
\(93\) 24.5173 0.0273369
\(94\) −247.908 −0.272018
\(95\) −359.465 −0.388214
\(96\) 61.6114 0.0655020
\(97\) −145.648 −0.152457 −0.0762283 0.997090i \(-0.524288\pi\)
−0.0762283 + 0.997090i \(0.524288\pi\)
\(98\) 0 0
\(99\) −1870.75 −1.89917
\(100\) −131.436 −0.131436
\(101\) 619.435 0.610259 0.305129 0.952311i \(-0.401300\pi\)
0.305129 + 0.952311i \(0.401300\pi\)
\(102\) −57.5163 −0.0558329
\(103\) 1822.08 1.74306 0.871528 0.490345i \(-0.163129\pi\)
0.871528 + 0.490345i \(0.163129\pi\)
\(104\) 1502.45 1.41661
\(105\) 0 0
\(106\) 449.578 0.411952
\(107\) 1089.70 0.984536 0.492268 0.870444i \(-0.336168\pi\)
0.492268 + 0.870444i \(0.336168\pi\)
\(108\) 94.3138 0.0840310
\(109\) 589.667 0.518164 0.259082 0.965855i \(-0.416580\pi\)
0.259082 + 0.965855i \(0.416580\pi\)
\(110\) 576.083 0.499340
\(111\) −66.8882 −0.0571959
\(112\) 0 0
\(113\) −900.358 −0.749544 −0.374772 0.927117i \(-0.622279\pi\)
−0.374772 + 0.927117i \(0.622279\pi\)
\(114\) −39.6333 −0.0325614
\(115\) −505.154 −0.409616
\(116\) 602.823 0.482506
\(117\) 1840.10 1.45399
\(118\) 857.887 0.669279
\(119\) 0 0
\(120\) −36.5430 −0.0277992
\(121\) 3509.35 2.63663
\(122\) 364.210 0.270279
\(123\) −138.917 −0.101835
\(124\) −387.214 −0.280426
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1755.75 −1.22676 −0.613378 0.789790i \(-0.710190\pi\)
−0.613378 + 0.789790i \(0.710190\pi\)
\(128\) −1048.58 −0.724082
\(129\) 103.586 0.0706996
\(130\) −566.643 −0.382291
\(131\) −1809.10 −1.20658 −0.603289 0.797523i \(-0.706143\pi\)
−0.603289 + 0.797523i \(0.706143\pi\)
\(132\) −121.762 −0.0802881
\(133\) 0 0
\(134\) 133.636 0.0861521
\(135\) −89.6952 −0.0571832
\(136\) 2290.62 1.44426
\(137\) −18.5134 −0.0115453 −0.00577265 0.999983i \(-0.501838\pi\)
−0.00577265 + 0.999983i \(0.501838\pi\)
\(138\) −55.6965 −0.0343565
\(139\) 625.608 0.381751 0.190875 0.981614i \(-0.438867\pi\)
0.190875 + 0.981614i \(0.438867\pi\)
\(140\) 0 0
\(141\) −49.8323 −0.0297634
\(142\) −150.778 −0.0891059
\(143\) −4761.03 −2.78418
\(144\) −153.283 −0.0887052
\(145\) −573.303 −0.328346
\(146\) −1461.11 −0.828237
\(147\) 0 0
\(148\) 1056.40 0.586725
\(149\) −1028.63 −0.565563 −0.282782 0.959184i \(-0.591257\pi\)
−0.282782 + 0.959184i \(0.591257\pi\)
\(150\) 13.7821 0.00750201
\(151\) 71.0073 0.0382682 0.0191341 0.999817i \(-0.493909\pi\)
0.0191341 + 0.999817i \(0.493909\pi\)
\(152\) 1578.42 0.842282
\(153\) 2805.39 1.48237
\(154\) 0 0
\(155\) 368.252 0.190831
\(156\) 119.767 0.0614680
\(157\) 2061.32 1.04784 0.523922 0.851767i \(-0.324468\pi\)
0.523922 + 0.851767i \(0.324468\pi\)
\(158\) 993.434 0.500211
\(159\) 90.3704 0.0450745
\(160\) 925.409 0.457250
\(161\) 0 0
\(162\) 1192.42 0.578307
\(163\) −1963.80 −0.943660 −0.471830 0.881690i \(-0.656406\pi\)
−0.471830 + 0.881690i \(0.656406\pi\)
\(164\) 2193.98 1.04464
\(165\) 115.799 0.0546362
\(166\) −117.385 −0.0548846
\(167\) −2855.04 −1.32293 −0.661467 0.749974i \(-0.730066\pi\)
−0.661467 + 0.749974i \(0.730066\pi\)
\(168\) 0 0
\(169\) 2486.01 1.13155
\(170\) −863.899 −0.389753
\(171\) 1933.14 0.864509
\(172\) −1635.99 −0.725249
\(173\) 1553.21 0.682590 0.341295 0.939956i \(-0.389134\pi\)
0.341295 + 0.939956i \(0.389134\pi\)
\(174\) −63.2104 −0.0275400
\(175\) 0 0
\(176\) 396.601 0.169857
\(177\) 172.445 0.0732303
\(178\) −1329.14 −0.559682
\(179\) 269.841 0.112675 0.0563376 0.998412i \(-0.482058\pi\)
0.0563376 + 0.998412i \(0.482058\pi\)
\(180\) 706.844 0.292695
\(181\) −2229.61 −0.915613 −0.457806 0.889052i \(-0.651365\pi\)
−0.457806 + 0.889052i \(0.651365\pi\)
\(182\) 0 0
\(183\) 73.2105 0.0295731
\(184\) 2218.15 0.888717
\(185\) −1004.67 −0.399268
\(186\) 40.6022 0.0160059
\(187\) −7258.63 −2.83852
\(188\) 787.026 0.305318
\(189\) 0 0
\(190\) −595.296 −0.227302
\(191\) −465.920 −0.176507 −0.0882533 0.996098i \(-0.528129\pi\)
−0.0882533 + 0.996098i \(0.528129\pi\)
\(192\) 86.8513 0.0326456
\(193\) −4414.46 −1.64642 −0.823212 0.567734i \(-0.807820\pi\)
−0.823212 + 0.567734i \(0.807820\pi\)
\(194\) −241.202 −0.0892643
\(195\) −113.902 −0.0418291
\(196\) 0 0
\(197\) −289.812 −0.104814 −0.0524068 0.998626i \(-0.516689\pi\)
−0.0524068 + 0.998626i \(0.516689\pi\)
\(198\) −3098.08 −1.11197
\(199\) −4817.73 −1.71618 −0.858091 0.513498i \(-0.828349\pi\)
−0.858091 + 0.513498i \(0.828349\pi\)
\(200\) −548.879 −0.194058
\(201\) 26.8624 0.00942649
\(202\) 1025.82 0.357310
\(203\) 0 0
\(204\) 182.595 0.0626678
\(205\) −2086.54 −0.710879
\(206\) 3017.48 1.02057
\(207\) 2716.63 0.912170
\(208\) −390.102 −0.130042
\(209\) −5001.78 −1.65541
\(210\) 0 0
\(211\) 2022.01 0.659719 0.329859 0.944030i \(-0.392999\pi\)
0.329859 + 0.944030i \(0.392999\pi\)
\(212\) −1427.26 −0.462382
\(213\) −30.3082 −0.00974968
\(214\) 1804.61 0.576452
\(215\) 1555.87 0.493533
\(216\) 393.855 0.124067
\(217\) 0 0
\(218\) 976.525 0.303388
\(219\) −293.701 −0.0906231
\(220\) −1828.88 −0.560467
\(221\) 7139.69 2.17315
\(222\) −110.771 −0.0334886
\(223\) −4343.86 −1.30442 −0.652211 0.758037i \(-0.726158\pi\)
−0.652211 + 0.758037i \(0.726158\pi\)
\(224\) 0 0
\(225\) −672.230 −0.199179
\(226\) −1491.05 −0.438863
\(227\) 2647.59 0.774127 0.387064 0.922053i \(-0.373489\pi\)
0.387064 + 0.922053i \(0.373489\pi\)
\(228\) 125.823 0.0365475
\(229\) 1445.09 0.417006 0.208503 0.978022i \(-0.433141\pi\)
0.208503 + 0.978022i \(0.433141\pi\)
\(230\) −836.566 −0.239833
\(231\) 0 0
\(232\) 2517.39 0.712392
\(233\) −6245.91 −1.75615 −0.878076 0.478522i \(-0.841173\pi\)
−0.878076 + 0.478522i \(0.841173\pi\)
\(234\) 3047.31 0.851321
\(235\) −748.485 −0.207769
\(236\) −2723.51 −0.751209
\(237\) 199.692 0.0547315
\(238\) 0 0
\(239\) 1340.24 0.362731 0.181366 0.983416i \(-0.441948\pi\)
0.181366 + 0.983416i \(0.441948\pi\)
\(240\) 9.48817 0.00255191
\(241\) −3369.92 −0.900729 −0.450364 0.892845i \(-0.648706\pi\)
−0.450364 + 0.892845i \(0.648706\pi\)
\(242\) 5811.70 1.54376
\(243\) 724.045 0.191142
\(244\) −1156.25 −0.303366
\(245\) 0 0
\(246\) −230.054 −0.0596249
\(247\) 4919.82 1.26737
\(248\) −1617.01 −0.414033
\(249\) −23.5958 −0.00600530
\(250\) 207.008 0.0523693
\(251\) 3592.64 0.903449 0.451724 0.892158i \(-0.350809\pi\)
0.451724 + 0.892158i \(0.350809\pi\)
\(252\) 0 0
\(253\) −7028.97 −1.74667
\(254\) −2907.64 −0.718273
\(255\) −173.654 −0.0426455
\(256\) −3823.74 −0.933531
\(257\) 2.84763 0.000691167 0 0.000345584 1.00000i \(-0.499890\pi\)
0.000345584 1.00000i \(0.499890\pi\)
\(258\) 171.545 0.0413951
\(259\) 0 0
\(260\) 1798.91 0.429090
\(261\) 3083.13 0.731191
\(262\) −2995.98 −0.706459
\(263\) −2817.07 −0.660488 −0.330244 0.943896i \(-0.607131\pi\)
−0.330244 + 0.943896i \(0.607131\pi\)
\(264\) −508.479 −0.118541
\(265\) 1357.37 0.314652
\(266\) 0 0
\(267\) −267.173 −0.0612386
\(268\) −424.250 −0.0966986
\(269\) 1447.43 0.328072 0.164036 0.986454i \(-0.447549\pi\)
0.164036 + 0.986454i \(0.447549\pi\)
\(270\) −148.541 −0.0334811
\(271\) −8054.50 −1.80545 −0.902724 0.430221i \(-0.858436\pi\)
−0.902724 + 0.430221i \(0.858436\pi\)
\(272\) −594.746 −0.132580
\(273\) 0 0
\(274\) −30.6593 −0.00675985
\(275\) 1739.32 0.381399
\(276\) 176.818 0.0385623
\(277\) −571.300 −0.123921 −0.0619604 0.998079i \(-0.519735\pi\)
−0.0619604 + 0.998079i \(0.519735\pi\)
\(278\) 1036.05 0.223518
\(279\) −1980.40 −0.424959
\(280\) 0 0
\(281\) −1784.48 −0.378837 −0.189418 0.981896i \(-0.560660\pi\)
−0.189418 + 0.981896i \(0.560660\pi\)
\(282\) −82.5254 −0.0174267
\(283\) −3321.05 −0.697582 −0.348791 0.937201i \(-0.613408\pi\)
−0.348791 + 0.937201i \(0.613408\pi\)
\(284\) 478.672 0.100014
\(285\) −119.661 −0.0248706
\(286\) −7884.57 −1.63015
\(287\) 0 0
\(288\) −4976.70 −1.01825
\(289\) 5972.11 1.21557
\(290\) −949.425 −0.192249
\(291\) −48.4843 −0.00976701
\(292\) 4638.56 0.929627
\(293\) 5049.54 1.00682 0.503408 0.864049i \(-0.332079\pi\)
0.503408 + 0.864049i \(0.332079\pi\)
\(294\) 0 0
\(295\) 2590.14 0.511199
\(296\) 4411.52 0.866266
\(297\) −1248.07 −0.243839
\(298\) −1703.48 −0.331141
\(299\) 6913.79 1.33724
\(300\) −43.7536 −0.00842038
\(301\) 0 0
\(302\) 117.593 0.0224063
\(303\) 206.202 0.0390958
\(304\) −409.828 −0.0773198
\(305\) 1099.63 0.206441
\(306\) 4645.91 0.867938
\(307\) 1535.73 0.285500 0.142750 0.989759i \(-0.454405\pi\)
0.142750 + 0.989759i \(0.454405\pi\)
\(308\) 0 0
\(309\) 606.548 0.111668
\(310\) 609.849 0.111733
\(311\) 9283.05 1.69258 0.846291 0.532720i \(-0.178830\pi\)
0.846291 + 0.532720i \(0.178830\pi\)
\(312\) 500.147 0.0907539
\(313\) −6025.43 −1.08811 −0.544054 0.839050i \(-0.683111\pi\)
−0.544054 + 0.839050i \(0.683111\pi\)
\(314\) 3413.68 0.613519
\(315\) 0 0
\(316\) −3153.83 −0.561445
\(317\) −6977.58 −1.23628 −0.618139 0.786069i \(-0.712113\pi\)
−0.618139 + 0.786069i \(0.712113\pi\)
\(318\) 149.659 0.0263914
\(319\) −7977.24 −1.40012
\(320\) 1304.51 0.227889
\(321\) 362.748 0.0630736
\(322\) 0 0
\(323\) 7500.71 1.29211
\(324\) −3785.56 −0.649102
\(325\) −1710.81 −0.291997
\(326\) −3252.17 −0.552519
\(327\) 196.293 0.0331958
\(328\) 9162.06 1.54235
\(329\) 0 0
\(330\) 191.771 0.0319898
\(331\) 984.878 0.163546 0.0817731 0.996651i \(-0.473942\pi\)
0.0817731 + 0.996651i \(0.473942\pi\)
\(332\) 372.659 0.0616034
\(333\) 5402.93 0.889125
\(334\) −4728.13 −0.774586
\(335\) 403.475 0.0658035
\(336\) 0 0
\(337\) 51.9653 0.00839979 0.00419990 0.999991i \(-0.498663\pi\)
0.00419990 + 0.999991i \(0.498663\pi\)
\(338\) 4116.99 0.662529
\(339\) −299.718 −0.0480190
\(340\) 2742.60 0.437465
\(341\) 5124.06 0.813734
\(342\) 3201.40 0.506176
\(343\) 0 0
\(344\) −6831.89 −1.07079
\(345\) −168.159 −0.0262417
\(346\) 2572.21 0.399661
\(347\) −11300.5 −1.74825 −0.874123 0.485704i \(-0.838563\pi\)
−0.874123 + 0.485704i \(0.838563\pi\)
\(348\) 200.672 0.0309114
\(349\) 2016.91 0.309349 0.154674 0.987966i \(-0.450567\pi\)
0.154674 + 0.987966i \(0.450567\pi\)
\(350\) 0 0
\(351\) 1227.61 0.186682
\(352\) 12876.6 1.94979
\(353\) 7589.41 1.14432 0.572158 0.820143i \(-0.306106\pi\)
0.572158 + 0.820143i \(0.306106\pi\)
\(354\) 285.580 0.0428768
\(355\) −455.232 −0.0680597
\(356\) 4219.59 0.628196
\(357\) 0 0
\(358\) 446.873 0.0659720
\(359\) 8734.24 1.28405 0.642027 0.766682i \(-0.278094\pi\)
0.642027 + 0.766682i \(0.278094\pi\)
\(360\) 2951.78 0.432146
\(361\) −1690.41 −0.246451
\(362\) −3692.38 −0.536097
\(363\) 1168.22 0.168914
\(364\) 0 0
\(365\) −4411.41 −0.632613
\(366\) 121.241 0.0173152
\(367\) 1890.54 0.268898 0.134449 0.990921i \(-0.457074\pi\)
0.134449 + 0.990921i \(0.457074\pi\)
\(368\) −575.928 −0.0815825
\(369\) 11221.1 1.58305
\(370\) −1663.79 −0.233774
\(371\) 0 0
\(372\) −128.899 −0.0179653
\(373\) 2713.88 0.376728 0.188364 0.982099i \(-0.439682\pi\)
0.188364 + 0.982099i \(0.439682\pi\)
\(374\) −12020.7 −1.66197
\(375\) 41.6110 0.00573008
\(376\) 3286.63 0.450784
\(377\) 7846.52 1.07193
\(378\) 0 0
\(379\) 8941.19 1.21182 0.605908 0.795535i \(-0.292810\pi\)
0.605908 + 0.795535i \(0.292810\pi\)
\(380\) 1889.87 0.255127
\(381\) −584.469 −0.0785912
\(382\) −771.592 −0.103346
\(383\) 9293.88 1.23994 0.619968 0.784627i \(-0.287146\pi\)
0.619968 + 0.784627i \(0.287146\pi\)
\(384\) −349.060 −0.0463878
\(385\) 0 0
\(386\) −7310.62 −0.963992
\(387\) −8367.23 −1.09904
\(388\) 765.737 0.100192
\(389\) 10454.8 1.36267 0.681333 0.731974i \(-0.261401\pi\)
0.681333 + 0.731974i \(0.261401\pi\)
\(390\) −188.628 −0.0244912
\(391\) 10540.7 1.36334
\(392\) 0 0
\(393\) −602.226 −0.0772985
\(394\) −479.947 −0.0613690
\(395\) 2999.39 0.382065
\(396\) 9835.40 1.24810
\(397\) 3626.03 0.458401 0.229200 0.973379i \(-0.426389\pi\)
0.229200 + 0.973379i \(0.426389\pi\)
\(398\) −7978.47 −1.00484
\(399\) 0 0
\(400\) 142.513 0.0178141
\(401\) −8422.52 −1.04888 −0.524440 0.851448i \(-0.675725\pi\)
−0.524440 + 0.851448i \(0.675725\pi\)
\(402\) 44.4857 0.00551927
\(403\) −5040.09 −0.622989
\(404\) −3256.65 −0.401051
\(405\) 3600.18 0.441715
\(406\) 0 0
\(407\) −13979.5 −1.70254
\(408\) 762.519 0.0925253
\(409\) 14580.7 1.76276 0.881379 0.472409i \(-0.156616\pi\)
0.881379 + 0.472409i \(0.156616\pi\)
\(410\) −3455.44 −0.416224
\(411\) −6.16288 −0.000739641 0
\(412\) −9579.51 −1.14551
\(413\) 0 0
\(414\) 4498.92 0.534081
\(415\) −354.410 −0.0419212
\(416\) −12665.6 −1.49275
\(417\) 208.257 0.0244566
\(418\) −8283.26 −0.969252
\(419\) 2537.53 0.295863 0.147931 0.988998i \(-0.452739\pi\)
0.147931 + 0.988998i \(0.452739\pi\)
\(420\) 0 0
\(421\) 9649.52 1.11708 0.558538 0.829479i \(-0.311363\pi\)
0.558538 + 0.829479i \(0.311363\pi\)
\(422\) 3348.57 0.386269
\(423\) 4025.23 0.462680
\(424\) −5960.27 −0.682680
\(425\) −2608.29 −0.297696
\(426\) −50.1922 −0.00570850
\(427\) 0 0
\(428\) −5729.06 −0.647020
\(429\) −1584.89 −0.178366
\(430\) 2576.62 0.288967
\(431\) −7262.56 −0.811660 −0.405830 0.913949i \(-0.633017\pi\)
−0.405830 + 0.913949i \(0.633017\pi\)
\(432\) −102.262 −0.0113891
\(433\) −11345.0 −1.25914 −0.629570 0.776944i \(-0.716769\pi\)
−0.629570 + 0.776944i \(0.716769\pi\)
\(434\) 0 0
\(435\) −190.845 −0.0210353
\(436\) −3100.15 −0.340528
\(437\) 7263.40 0.795092
\(438\) −486.387 −0.0530604
\(439\) −11705.9 −1.27265 −0.636323 0.771423i \(-0.719545\pi\)
−0.636323 + 0.771423i \(0.719545\pi\)
\(440\) −7637.40 −0.827497
\(441\) 0 0
\(442\) 11823.8 1.27240
\(443\) 15078.0 1.61710 0.808551 0.588426i \(-0.200252\pi\)
0.808551 + 0.588426i \(0.200252\pi\)
\(444\) 351.662 0.0375881
\(445\) −4012.96 −0.427489
\(446\) −7193.70 −0.763747
\(447\) −342.419 −0.0362324
\(448\) 0 0
\(449\) 1075.45 0.113037 0.0565185 0.998402i \(-0.482000\pi\)
0.0565185 + 0.998402i \(0.482000\pi\)
\(450\) −1113.25 −0.116621
\(451\) −29033.2 −3.03131
\(452\) 4733.59 0.492587
\(453\) 23.6375 0.00245162
\(454\) 4384.58 0.453257
\(455\) 0 0
\(456\) 525.437 0.0539602
\(457\) −10736.9 −1.09902 −0.549511 0.835487i \(-0.685186\pi\)
−0.549511 + 0.835487i \(0.685186\pi\)
\(458\) 2393.16 0.244159
\(459\) 1871.61 0.190325
\(460\) 2655.82 0.269192
\(461\) −452.568 −0.0457228 −0.0228614 0.999739i \(-0.507278\pi\)
−0.0228614 + 0.999739i \(0.507278\pi\)
\(462\) 0 0
\(463\) 7118.15 0.714489 0.357244 0.934011i \(-0.383716\pi\)
0.357244 + 0.934011i \(0.383716\pi\)
\(464\) −653.626 −0.0653962
\(465\) 122.587 0.0122254
\(466\) −10343.6 −1.02824
\(467\) −973.800 −0.0964927 −0.0482463 0.998835i \(-0.515363\pi\)
−0.0482463 + 0.998835i \(0.515363\pi\)
\(468\) −9674.23 −0.955537
\(469\) 0 0
\(470\) −1239.54 −0.121650
\(471\) 686.188 0.0671293
\(472\) −11373.4 −1.10912
\(473\) 21649.2 2.10451
\(474\) 330.702 0.0320457
\(475\) −1797.32 −0.173614
\(476\) 0 0
\(477\) −7299.72 −0.700695
\(478\) 2219.52 0.212381
\(479\) −9714.00 −0.926606 −0.463303 0.886200i \(-0.653336\pi\)
−0.463303 + 0.886200i \(0.653336\pi\)
\(480\) 308.057 0.0292934
\(481\) 13750.4 1.30346
\(482\) −5580.80 −0.527383
\(483\) 0 0
\(484\) −18450.3 −1.73274
\(485\) −728.239 −0.0681806
\(486\) 1199.06 0.111915
\(487\) 923.389 0.0859194 0.0429597 0.999077i \(-0.486321\pi\)
0.0429597 + 0.999077i \(0.486321\pi\)
\(488\) −4828.50 −0.447902
\(489\) −653.724 −0.0604549
\(490\) 0 0
\(491\) 1289.11 0.118486 0.0592430 0.998244i \(-0.481131\pi\)
0.0592430 + 0.998244i \(0.481131\pi\)
\(492\) 730.348 0.0669240
\(493\) 11962.7 1.09285
\(494\) 8147.52 0.742053
\(495\) −9353.76 −0.849334
\(496\) 419.846 0.0380074
\(497\) 0 0
\(498\) −39.0760 −0.00351614
\(499\) −19338.3 −1.73487 −0.867436 0.497549i \(-0.834234\pi\)
−0.867436 + 0.497549i \(0.834234\pi\)
\(500\) −657.182 −0.0587802
\(501\) −950.409 −0.0847528
\(502\) 5949.64 0.528975
\(503\) 1772.84 0.157151 0.0785757 0.996908i \(-0.474963\pi\)
0.0785757 + 0.996908i \(0.474963\pi\)
\(504\) 0 0
\(505\) 3097.18 0.272916
\(506\) −11640.4 −1.02269
\(507\) 827.563 0.0724919
\(508\) 9230.80 0.806202
\(509\) −3151.75 −0.274458 −0.137229 0.990539i \(-0.543820\pi\)
−0.137229 + 0.990539i \(0.543820\pi\)
\(510\) −287.581 −0.0249692
\(511\) 0 0
\(512\) 2056.31 0.177494
\(513\) 1289.69 0.110997
\(514\) 4.71585 0.000404683 0
\(515\) 9110.40 0.779519
\(516\) −544.600 −0.0464626
\(517\) −10414.8 −0.885964
\(518\) 0 0
\(519\) 517.043 0.0437296
\(520\) 7512.24 0.633526
\(521\) 11029.4 0.927458 0.463729 0.885977i \(-0.346511\pi\)
0.463729 + 0.885977i \(0.346511\pi\)
\(522\) 5105.85 0.428117
\(523\) −14448.4 −1.20800 −0.604002 0.796983i \(-0.706428\pi\)
−0.604002 + 0.796983i \(0.706428\pi\)
\(524\) 9511.26 0.792941
\(525\) 0 0
\(526\) −4665.25 −0.386720
\(527\) −7684.08 −0.635149
\(528\) 132.023 0.0108818
\(529\) −1959.79 −0.161074
\(530\) 2247.89 0.184231
\(531\) −13929.4 −1.13838
\(532\) 0 0
\(533\) 28557.4 2.32075
\(534\) −442.455 −0.0358556
\(535\) 5448.51 0.440298
\(536\) −1771.67 −0.142770
\(537\) 89.8266 0.00721845
\(538\) 2397.04 0.192089
\(539\) 0 0
\(540\) 471.569 0.0375798
\(541\) −22274.8 −1.77018 −0.885091 0.465418i \(-0.845904\pi\)
−0.885091 + 0.465418i \(0.845904\pi\)
\(542\) −13338.8 −1.05710
\(543\) −742.211 −0.0586580
\(544\) −19309.9 −1.52188
\(545\) 2948.33 0.231730
\(546\) 0 0
\(547\) 18642.6 1.45722 0.728609 0.684930i \(-0.240167\pi\)
0.728609 + 0.684930i \(0.240167\pi\)
\(548\) 97.3334 0.00758737
\(549\) −5913.62 −0.459721
\(550\) 2880.42 0.223311
\(551\) 8243.28 0.637343
\(552\) 738.394 0.0569350
\(553\) 0 0
\(554\) −946.108 −0.0725565
\(555\) −334.441 −0.0255788
\(556\) −3289.11 −0.250880
\(557\) −21431.8 −1.63033 −0.815165 0.579229i \(-0.803354\pi\)
−0.815165 + 0.579229i \(0.803354\pi\)
\(558\) −3279.67 −0.248816
\(559\) −21294.5 −1.61120
\(560\) 0 0
\(561\) −2416.31 −0.181848
\(562\) −2955.21 −0.221811
\(563\) 6154.85 0.460739 0.230370 0.973103i \(-0.426007\pi\)
0.230370 + 0.973103i \(0.426007\pi\)
\(564\) 261.991 0.0195600
\(565\) −4501.79 −0.335206
\(566\) −5499.86 −0.408439
\(567\) 0 0
\(568\) 1998.94 0.147665
\(569\) −8389.99 −0.618149 −0.309074 0.951038i \(-0.600019\pi\)
−0.309074 + 0.951038i \(0.600019\pi\)
\(570\) −198.167 −0.0145619
\(571\) −600.502 −0.0440109 −0.0220055 0.999758i \(-0.507005\pi\)
−0.0220055 + 0.999758i \(0.507005\pi\)
\(572\) 25030.9 1.82971
\(573\) −155.099 −0.0113078
\(574\) 0 0
\(575\) −2525.77 −0.183186
\(576\) −7015.46 −0.507484
\(577\) −4062.35 −0.293098 −0.146549 0.989203i \(-0.546817\pi\)
−0.146549 + 0.989203i \(0.546817\pi\)
\(578\) 9890.18 0.711725
\(579\) −1469.52 −0.105477
\(580\) 3014.12 0.215783
\(581\) 0 0
\(582\) −80.2931 −0.00571865
\(583\) 18887.2 1.34173
\(584\) 19370.6 1.37254
\(585\) 9200.48 0.650244
\(586\) 8362.35 0.589498
\(587\) 8387.50 0.589760 0.294880 0.955534i \(-0.404720\pi\)
0.294880 + 0.955534i \(0.404720\pi\)
\(588\) 0 0
\(589\) −5294.95 −0.370415
\(590\) 4289.43 0.299310
\(591\) −96.4749 −0.00671480
\(592\) −1145.43 −0.0795214
\(593\) 15342.6 1.06247 0.531236 0.847224i \(-0.321728\pi\)
0.531236 + 0.847224i \(0.321728\pi\)
\(594\) −2066.88 −0.142769
\(595\) 0 0
\(596\) 5408.00 0.371678
\(597\) −1603.76 −0.109946
\(598\) 11449.7 0.782963
\(599\) −19708.5 −1.34435 −0.672175 0.740392i \(-0.734640\pi\)
−0.672175 + 0.740392i \(0.734640\pi\)
\(600\) −182.715 −0.0124322
\(601\) 19002.5 1.28973 0.644866 0.764295i \(-0.276913\pi\)
0.644866 + 0.764295i \(0.276913\pi\)
\(602\) 0 0
\(603\) −2169.82 −0.146537
\(604\) −373.318 −0.0251492
\(605\) 17546.8 1.17914
\(606\) 341.484 0.0228908
\(607\) −29453.1 −1.96946 −0.984732 0.174076i \(-0.944306\pi\)
−0.984732 + 0.174076i \(0.944306\pi\)
\(608\) −13306.1 −0.887553
\(609\) 0 0
\(610\) 1821.05 0.120873
\(611\) 10244.2 0.678288
\(612\) −14749.2 −0.974188
\(613\) 9987.27 0.658045 0.329023 0.944322i \(-0.393281\pi\)
0.329023 + 0.944322i \(0.393281\pi\)
\(614\) 2543.26 0.167162
\(615\) −694.583 −0.0455419
\(616\) 0 0
\(617\) −21076.1 −1.37519 −0.687593 0.726096i \(-0.741333\pi\)
−0.687593 + 0.726096i \(0.741333\pi\)
\(618\) 1004.48 0.0653821
\(619\) 314.668 0.0204323 0.0102161 0.999948i \(-0.496748\pi\)
0.0102161 + 0.999948i \(0.496748\pi\)
\(620\) −1936.07 −0.125410
\(621\) 1812.39 0.117116
\(622\) 15373.3 0.991018
\(623\) 0 0
\(624\) −129.860 −0.00833103
\(625\) 625.000 0.0400000
\(626\) −9978.49 −0.637094
\(627\) −1665.03 −0.106052
\(628\) −10837.3 −0.688624
\(629\) 20963.7 1.32890
\(630\) 0 0
\(631\) 3314.96 0.209138 0.104569 0.994518i \(-0.466654\pi\)
0.104569 + 0.994518i \(0.466654\pi\)
\(632\) −13170.4 −0.828941
\(633\) 673.101 0.0422644
\(634\) −11555.3 −0.723849
\(635\) −8778.77 −0.548622
\(636\) −475.119 −0.0296221
\(637\) 0 0
\(638\) −13210.8 −0.819782
\(639\) 2448.16 0.151561
\(640\) −5242.92 −0.323820
\(641\) 3005.12 0.185172 0.0925858 0.995705i \(-0.470487\pi\)
0.0925858 + 0.995705i \(0.470487\pi\)
\(642\) 600.733 0.0369300
\(643\) −21225.7 −1.30180 −0.650902 0.759162i \(-0.725609\pi\)
−0.650902 + 0.759162i \(0.725609\pi\)
\(644\) 0 0
\(645\) 517.931 0.0316178
\(646\) 12421.6 0.756537
\(647\) 2740.35 0.166514 0.0832568 0.996528i \(-0.473468\pi\)
0.0832568 + 0.996528i \(0.473468\pi\)
\(648\) −15808.5 −0.958360
\(649\) 36040.6 2.17984
\(650\) −2833.21 −0.170966
\(651\) 0 0
\(652\) 10324.6 0.620157
\(653\) 22790.7 1.36580 0.682900 0.730511i \(-0.260718\pi\)
0.682900 + 0.730511i \(0.260718\pi\)
\(654\) 325.073 0.0194363
\(655\) −9045.49 −0.539598
\(656\) −2378.87 −0.141584
\(657\) 23723.8 1.40876
\(658\) 0 0
\(659\) 19405.1 1.14706 0.573532 0.819183i \(-0.305573\pi\)
0.573532 + 0.819183i \(0.305573\pi\)
\(660\) −608.810 −0.0359059
\(661\) −15637.3 −0.920150 −0.460075 0.887880i \(-0.652177\pi\)
−0.460075 + 0.887880i \(0.652177\pi\)
\(662\) 1631.02 0.0957574
\(663\) 2376.71 0.139222
\(664\) 1556.23 0.0909538
\(665\) 0 0
\(666\) 8947.59 0.520589
\(667\) 11584.2 0.672479
\(668\) 15010.3 0.869409
\(669\) −1446.02 −0.0835668
\(670\) 668.179 0.0385284
\(671\) 15300.8 0.880299
\(672\) 0 0
\(673\) −2579.54 −0.147747 −0.0738735 0.997268i \(-0.523536\pi\)
−0.0738735 + 0.997268i \(0.523536\pi\)
\(674\) 86.0578 0.00491813
\(675\) −448.476 −0.0255731
\(676\) −13070.1 −0.743634
\(677\) −8159.56 −0.463216 −0.231608 0.972809i \(-0.574399\pi\)
−0.231608 + 0.972809i \(0.574399\pi\)
\(678\) −496.351 −0.0281154
\(679\) 0 0
\(680\) 11453.1 0.645892
\(681\) 881.351 0.0495939
\(682\) 8485.76 0.476446
\(683\) −20529.3 −1.15012 −0.575059 0.818112i \(-0.695021\pi\)
−0.575059 + 0.818112i \(0.695021\pi\)
\(684\) −10163.4 −0.568140
\(685\) −92.5670 −0.00516321
\(686\) 0 0
\(687\) 481.053 0.0267151
\(688\) 1773.86 0.0982961
\(689\) −18577.7 −1.02722
\(690\) −278.482 −0.0153647
\(691\) 917.295 0.0505001 0.0252500 0.999681i \(-0.491962\pi\)
0.0252500 + 0.999681i \(0.491962\pi\)
\(692\) −8165.92 −0.448586
\(693\) 0 0
\(694\) −18714.3 −1.02361
\(695\) 3128.04 0.170724
\(696\) 838.009 0.0456389
\(697\) 43538.4 2.36605
\(698\) 3340.13 0.181126
\(699\) −2079.19 −0.112507
\(700\) 0 0
\(701\) −10491.3 −0.565266 −0.282633 0.959228i \(-0.591208\pi\)
−0.282633 + 0.959228i \(0.591208\pi\)
\(702\) 2033.01 0.109303
\(703\) 14445.7 0.775006
\(704\) 18151.7 0.971758
\(705\) −249.162 −0.0133106
\(706\) 12568.5 0.670005
\(707\) 0 0
\(708\) −906.623 −0.0481257
\(709\) 23837.6 1.26268 0.631339 0.775507i \(-0.282506\pi\)
0.631339 + 0.775507i \(0.282506\pi\)
\(710\) −753.892 −0.0398494
\(711\) −16130.2 −0.850816
\(712\) 17621.0 0.927495
\(713\) −7440.96 −0.390836
\(714\) 0 0
\(715\) −23805.2 −1.24512
\(716\) −1418.68 −0.0740481
\(717\) 446.148 0.0232381
\(718\) 14464.4 0.751822
\(719\) 3926.19 0.203647 0.101824 0.994802i \(-0.467532\pi\)
0.101824 + 0.994802i \(0.467532\pi\)
\(720\) −766.413 −0.0396702
\(721\) 0 0
\(722\) −2799.42 −0.144299
\(723\) −1121.80 −0.0577045
\(724\) 11722.1 0.601724
\(725\) −2866.51 −0.146841
\(726\) 1934.64 0.0989000
\(727\) 21071.2 1.07495 0.537474 0.843281i \(-0.319379\pi\)
0.537474 + 0.843281i \(0.319379\pi\)
\(728\) 0 0
\(729\) −19200.0 −0.975459
\(730\) −7305.57 −0.370399
\(731\) −32465.4 −1.64265
\(732\) −384.901 −0.0194349
\(733\) 22840.7 1.15094 0.575470 0.817823i \(-0.304819\pi\)
0.575470 + 0.817823i \(0.304819\pi\)
\(734\) 3130.86 0.157441
\(735\) 0 0
\(736\) −18699.0 −0.936485
\(737\) 5614.16 0.280597
\(738\) 18582.8 0.926885
\(739\) 10837.3 0.539456 0.269728 0.962937i \(-0.413066\pi\)
0.269728 + 0.962937i \(0.413066\pi\)
\(740\) 5281.99 0.262392
\(741\) 1637.75 0.0811931
\(742\) 0 0
\(743\) −21631.9 −1.06810 −0.534050 0.845453i \(-0.679331\pi\)
−0.534050 + 0.845453i \(0.679331\pi\)
\(744\) −538.282 −0.0265247
\(745\) −5143.17 −0.252928
\(746\) 4494.36 0.220577
\(747\) 1905.96 0.0933540
\(748\) 38161.9 1.86543
\(749\) 0 0
\(750\) 68.9103 0.00335500
\(751\) −16179.2 −0.786133 −0.393067 0.919510i \(-0.628586\pi\)
−0.393067 + 0.919510i \(0.628586\pi\)
\(752\) −853.352 −0.0413811
\(753\) 1195.95 0.0578788
\(754\) 12994.3 0.627620
\(755\) 355.037 0.0171140
\(756\) 0 0
\(757\) −40930.9 −1.96520 −0.982601 0.185727i \(-0.940536\pi\)
−0.982601 + 0.185727i \(0.940536\pi\)
\(758\) 14807.2 0.709526
\(759\) −2339.86 −0.111899
\(760\) 7892.11 0.376680
\(761\) −3183.97 −0.151667 −0.0758337 0.997120i \(-0.524162\pi\)
−0.0758337 + 0.997120i \(0.524162\pi\)
\(762\) −967.917 −0.0460157
\(763\) 0 0
\(764\) 2449.55 0.115997
\(765\) 14027.0 0.662936
\(766\) 15391.2 0.725990
\(767\) −35450.0 −1.66887
\(768\) −1272.88 −0.0598059
\(769\) −33595.8 −1.57542 −0.787708 0.616048i \(-0.788733\pi\)
−0.787708 + 0.616048i \(0.788733\pi\)
\(770\) 0 0
\(771\) 0.947940 4.42791e−5 0
\(772\) 23208.8 1.08200
\(773\) −34386.0 −1.59997 −0.799986 0.600019i \(-0.795160\pi\)
−0.799986 + 0.600019i \(0.795160\pi\)
\(774\) −13856.7 −0.643498
\(775\) 1841.26 0.0853420
\(776\) 3197.72 0.147927
\(777\) 0 0
\(778\) 17313.7 0.797849
\(779\) 30001.5 1.37986
\(780\) 598.834 0.0274893
\(781\) −6334.33 −0.290218
\(782\) 17456.1 0.798245
\(783\) 2056.90 0.0938795
\(784\) 0 0
\(785\) 10306.6 0.468610
\(786\) −997.324 −0.0452588
\(787\) 8212.43 0.371972 0.185986 0.982552i \(-0.440452\pi\)
0.185986 + 0.982552i \(0.440452\pi\)
\(788\) 1523.68 0.0688816
\(789\) −937.769 −0.0423136
\(790\) 4967.17 0.223701
\(791\) 0 0
\(792\) 41072.7 1.84274
\(793\) −15050.1 −0.673951
\(794\) 6004.92 0.268396
\(795\) 451.852 0.0201579
\(796\) 25329.0 1.12784
\(797\) −36798.3 −1.63546 −0.817732 0.575600i \(-0.804769\pi\)
−0.817732 + 0.575600i \(0.804769\pi\)
\(798\) 0 0
\(799\) 15618.2 0.691528
\(800\) 4627.05 0.204488
\(801\) 21581.0 0.951971
\(802\) −13948.2 −0.614125
\(803\) −61382.7 −2.69757
\(804\) −141.228 −0.00619492
\(805\) 0 0
\(806\) −8346.70 −0.364764
\(807\) 481.832 0.0210177
\(808\) −13599.8 −0.592128
\(809\) 10186.2 0.442678 0.221339 0.975197i \(-0.428957\pi\)
0.221339 + 0.975197i \(0.428957\pi\)
\(810\) 5962.12 0.258627
\(811\) −21196.9 −0.917786 −0.458893 0.888492i \(-0.651754\pi\)
−0.458893 + 0.888492i \(0.651754\pi\)
\(812\) 0 0
\(813\) −2681.24 −0.115665
\(814\) −23150.8 −0.996851
\(815\) −9818.99 −0.422018
\(816\) −197.983 −0.00849364
\(817\) −22371.3 −0.957982
\(818\) 24146.5 1.03211
\(819\) 0 0
\(820\) 10969.9 0.467177
\(821\) 7563.94 0.321539 0.160769 0.986992i \(-0.448602\pi\)
0.160769 + 0.986992i \(0.448602\pi\)
\(822\) −10.2061 −0.000433065 0
\(823\) 8399.80 0.355770 0.177885 0.984051i \(-0.443075\pi\)
0.177885 + 0.984051i \(0.443075\pi\)
\(824\) −40004.1 −1.69127
\(825\) 578.997 0.0244340
\(826\) 0 0
\(827\) 5479.54 0.230402 0.115201 0.993342i \(-0.463249\pi\)
0.115201 + 0.993342i \(0.463249\pi\)
\(828\) −14282.6 −0.599462
\(829\) −9252.56 −0.387641 −0.193821 0.981037i \(-0.562088\pi\)
−0.193821 + 0.981037i \(0.562088\pi\)
\(830\) −586.925 −0.0245452
\(831\) −190.179 −0.00793890
\(832\) −17854.2 −0.743972
\(833\) 0 0
\(834\) 344.887 0.0143195
\(835\) −14275.2 −0.591634
\(836\) 26296.6 1.08790
\(837\) −1321.22 −0.0545615
\(838\) 4202.31 0.173230
\(839\) 34517.6 1.42036 0.710178 0.704022i \(-0.248614\pi\)
0.710178 + 0.704022i \(0.248614\pi\)
\(840\) 0 0
\(841\) −11241.9 −0.460943
\(842\) 15980.2 0.654055
\(843\) −594.031 −0.0242699
\(844\) −10630.6 −0.433555
\(845\) 12430.1 0.506044
\(846\) 6666.04 0.270902
\(847\) 0 0
\(848\) 1547.55 0.0626686
\(849\) −1105.54 −0.0446901
\(850\) −4319.50 −0.174303
\(851\) 20300.4 0.817732
\(852\) 159.344 0.00640732
\(853\) 1498.57 0.0601525 0.0300763 0.999548i \(-0.490425\pi\)
0.0300763 + 0.999548i \(0.490425\pi\)
\(854\) 0 0
\(855\) 9665.71 0.386620
\(856\) −23924.6 −0.955287
\(857\) 9357.02 0.372963 0.186482 0.982458i \(-0.440291\pi\)
0.186482 + 0.982458i \(0.440291\pi\)
\(858\) −2624.67 −0.104435
\(859\) 29960.9 1.19005 0.595025 0.803707i \(-0.297142\pi\)
0.595025 + 0.803707i \(0.297142\pi\)
\(860\) −8179.94 −0.324341
\(861\) 0 0
\(862\) −12027.3 −0.475232
\(863\) −33941.0 −1.33878 −0.669389 0.742912i \(-0.733444\pi\)
−0.669389 + 0.742912i \(0.733444\pi\)
\(864\) −3320.19 −0.130735
\(865\) 7766.03 0.305264
\(866\) −18788.1 −0.737235
\(867\) 1988.04 0.0778747
\(868\) 0 0
\(869\) 41735.0 1.62919
\(870\) −316.052 −0.0123163
\(871\) −5522.16 −0.214824
\(872\) −12946.2 −0.502769
\(873\) 3916.35 0.151831
\(874\) 12028.6 0.465532
\(875\) 0 0
\(876\) 1544.12 0.0595559
\(877\) −39436.6 −1.51845 −0.759224 0.650830i \(-0.774421\pi\)
−0.759224 + 0.650830i \(0.774421\pi\)
\(878\) −19385.7 −0.745142
\(879\) 1680.93 0.0645010
\(880\) 1983.00 0.0759625
\(881\) −32411.4 −1.23946 −0.619732 0.784813i \(-0.712759\pi\)
−0.619732 + 0.784813i \(0.712759\pi\)
\(882\) 0 0
\(883\) −17121.4 −0.652526 −0.326263 0.945279i \(-0.605790\pi\)
−0.326263 + 0.945279i \(0.605790\pi\)
\(884\) −37536.6 −1.42816
\(885\) 862.226 0.0327496
\(886\) 24970.1 0.946824
\(887\) 687.797 0.0260360 0.0130180 0.999915i \(-0.495856\pi\)
0.0130180 + 0.999915i \(0.495856\pi\)
\(888\) 1468.54 0.0554967
\(889\) 0 0
\(890\) −6645.71 −0.250297
\(891\) 50094.8 1.88355
\(892\) 22837.6 0.857243
\(893\) 10762.2 0.403294
\(894\) −567.068 −0.0212143
\(895\) 1349.20 0.0503898
\(896\) 0 0
\(897\) 2301.52 0.0856693
\(898\) 1781.01 0.0661839
\(899\) −8444.81 −0.313293
\(900\) 3534.22 0.130897
\(901\) −28323.4 −1.04727
\(902\) −48080.8 −1.77485
\(903\) 0 0
\(904\) 19767.5 0.727276
\(905\) −11148.1 −0.409474
\(906\) 39.1451 0.00143544
\(907\) 19104.2 0.699388 0.349694 0.936864i \(-0.386286\pi\)
0.349694 + 0.936864i \(0.386286\pi\)
\(908\) −13919.6 −0.508743
\(909\) −16656.1 −0.607754
\(910\) 0 0
\(911\) 23135.3 0.841390 0.420695 0.907202i \(-0.361786\pi\)
0.420695 + 0.907202i \(0.361786\pi\)
\(912\) −136.427 −0.00495344
\(913\) −4931.45 −0.178759
\(914\) −17781.0 −0.643484
\(915\) 366.052 0.0132255
\(916\) −7597.50 −0.274049
\(917\) 0 0
\(918\) 3099.50 0.111437
\(919\) 47373.9 1.70046 0.850230 0.526412i \(-0.176463\pi\)
0.850230 + 0.526412i \(0.176463\pi\)
\(920\) 11090.7 0.397447
\(921\) 511.224 0.0182903
\(922\) −749.481 −0.0267710
\(923\) 6230.53 0.222189
\(924\) 0 0
\(925\) −5023.33 −0.178558
\(926\) 11788.1 0.418338
\(927\) −48994.2 −1.73590
\(928\) −21221.6 −0.750682
\(929\) 7617.72 0.269031 0.134515 0.990912i \(-0.457052\pi\)
0.134515 + 0.990912i \(0.457052\pi\)
\(930\) 203.011 0.00715806
\(931\) 0 0
\(932\) 32837.6 1.15411
\(933\) 3090.21 0.108434
\(934\) −1612.67 −0.0564971
\(935\) −36293.2 −1.26943
\(936\) −40399.6 −1.41079
\(937\) 52091.2 1.81616 0.908082 0.418792i \(-0.137546\pi\)
0.908082 + 0.418792i \(0.137546\pi\)
\(938\) 0 0
\(939\) −2005.79 −0.0697088
\(940\) 3935.13 0.136542
\(941\) 56765.1 1.96651 0.983257 0.182225i \(-0.0583299\pi\)
0.983257 + 0.182225i \(0.0583299\pi\)
\(942\) 1136.37 0.0393046
\(943\) 42160.9 1.45594
\(944\) 2953.03 0.101815
\(945\) 0 0
\(946\) 35852.5 1.23220
\(947\) −47629.2 −1.63436 −0.817181 0.576381i \(-0.804465\pi\)
−0.817181 + 0.576381i \(0.804465\pi\)
\(948\) −1049.87 −0.0359686
\(949\) 60376.8 2.06524
\(950\) −2976.48 −0.101652
\(951\) −2322.75 −0.0792012
\(952\) 0 0
\(953\) 12893.5 0.438259 0.219129 0.975696i \(-0.429678\pi\)
0.219129 + 0.975696i \(0.429678\pi\)
\(954\) −12088.8 −0.410261
\(955\) −2329.60 −0.0789362
\(956\) −7046.24 −0.238380
\(957\) −2655.52 −0.0896979
\(958\) −16087.0 −0.542534
\(959\) 0 0
\(960\) 434.257 0.0145996
\(961\) −24366.6 −0.817918
\(962\) 22771.5 0.763183
\(963\) −29301.2 −0.980496
\(964\) 17717.2 0.591943
\(965\) −22072.3 −0.736303
\(966\) 0 0
\(967\) −28420.0 −0.945114 −0.472557 0.881300i \(-0.656669\pi\)
−0.472557 + 0.881300i \(0.656669\pi\)
\(968\) −77048.4 −2.55830
\(969\) 2496.89 0.0827779
\(970\) −1206.01 −0.0399202
\(971\) −29273.8 −0.967497 −0.483749 0.875207i \(-0.660725\pi\)
−0.483749 + 0.875207i \(0.660725\pi\)
\(972\) −3806.64 −0.125615
\(973\) 0 0
\(974\) 1529.19 0.0503063
\(975\) −569.509 −0.0187065
\(976\) 1253.69 0.0411165
\(977\) 12055.0 0.394753 0.197377 0.980328i \(-0.436758\pi\)
0.197377 + 0.980328i \(0.436758\pi\)
\(978\) −1082.61 −0.0353967
\(979\) −55838.4 −1.82288
\(980\) 0 0
\(981\) −15855.7 −0.516037
\(982\) 2134.84 0.0693743
\(983\) −10605.1 −0.344099 −0.172049 0.985088i \(-0.555039\pi\)
−0.172049 + 0.985088i \(0.555039\pi\)
\(984\) 3049.94 0.0988094
\(985\) −1449.06 −0.0468740
\(986\) 19811.0 0.639870
\(987\) 0 0
\(988\) −25865.7 −0.832893
\(989\) −31438.2 −1.01080
\(990\) −15490.4 −0.497290
\(991\) 45229.1 1.44980 0.724898 0.688856i \(-0.241887\pi\)
0.724898 + 0.688856i \(0.241887\pi\)
\(992\) 13631.4 0.436287
\(993\) 327.854 0.0104775
\(994\) 0 0
\(995\) −24088.7 −0.767500
\(996\) 124.054 0.00394658
\(997\) 49676.8 1.57802 0.789008 0.614383i \(-0.210595\pi\)
0.789008 + 0.614383i \(0.210595\pi\)
\(998\) −32025.4 −1.01578
\(999\) 3604.55 0.114157
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.o.1.5 6
3.2 odd 2 2205.4.a.bz.1.2 6
5.4 even 2 1225.4.a.bj.1.2 6
7.2 even 3 245.4.e.q.116.2 12
7.3 odd 6 245.4.e.p.226.2 12
7.4 even 3 245.4.e.q.226.2 12
7.5 odd 6 245.4.e.p.116.2 12
7.6 odd 2 245.4.a.p.1.5 yes 6
21.20 even 2 2205.4.a.ca.1.2 6
35.34 odd 2 1225.4.a.bi.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.5 6 1.1 even 1 trivial
245.4.a.p.1.5 yes 6 7.6 odd 2
245.4.e.p.116.2 12 7.5 odd 6
245.4.e.p.226.2 12 7.3 odd 6
245.4.e.q.116.2 12 7.2 even 3
245.4.e.q.226.2 12 7.4 even 3
1225.4.a.bi.1.2 6 35.34 odd 2
1225.4.a.bj.1.2 6 5.4 even 2
2205.4.a.bz.1.2 6 3.2 odd 2
2205.4.a.ca.1.2 6 21.20 even 2