Properties

Label 1875.4.a.g.1.9
Level $1875$
Weight $4$
Character 1875.1
Self dual yes
Analytic conductor $110.629$
Analytic rank $1$
Dimension $14$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1875.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(110.628581261\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \( x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + 125779 x^{5} - 718713 x^{4} - 371750 x^{3} + 579848 x^{2} + \cdots + 42064 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 5^{3} \)
Twist minimal: no (minimal twist has level 75)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(1.33976\) of defining polynomial
Character \(\chi\) \(=\) 1875.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.33976 q^{2} +3.00000 q^{3} -6.20504 q^{4} +4.01928 q^{6} -12.2101 q^{7} -19.0313 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+1.33976 q^{2} +3.00000 q^{3} -6.20504 q^{4} +4.01928 q^{6} -12.2101 q^{7} -19.0313 q^{8} +9.00000 q^{9} -2.48229 q^{11} -18.6151 q^{12} +85.6202 q^{13} -16.3586 q^{14} +24.1429 q^{16} -5.54850 q^{17} +12.0578 q^{18} -24.1374 q^{19} -36.6303 q^{21} -3.32567 q^{22} -103.353 q^{23} -57.0940 q^{24} +114.710 q^{26} +27.0000 q^{27} +75.7642 q^{28} -114.245 q^{29} +153.871 q^{31} +184.596 q^{32} -7.44687 q^{33} -7.43365 q^{34} -55.8454 q^{36} -342.674 q^{37} -32.3383 q^{38} +256.861 q^{39} +34.6755 q^{41} -49.0758 q^{42} -154.740 q^{43} +15.4027 q^{44} -138.468 q^{46} +338.534 q^{47} +72.4288 q^{48} -193.913 q^{49} -16.6455 q^{51} -531.277 q^{52} +645.636 q^{53} +36.1735 q^{54} +232.375 q^{56} -72.4123 q^{57} -153.060 q^{58} +662.854 q^{59} -357.681 q^{61} +206.150 q^{62} -109.891 q^{63} +54.1714 q^{64} -9.97701 q^{66} -531.377 q^{67} +34.4287 q^{68} -310.059 q^{69} -634.801 q^{71} -171.282 q^{72} +962.898 q^{73} -459.101 q^{74} +149.774 q^{76} +30.3090 q^{77} +344.131 q^{78} +568.744 q^{79} +81.0000 q^{81} +46.4568 q^{82} -319.838 q^{83} +227.293 q^{84} -207.315 q^{86} -342.734 q^{87} +47.2413 q^{88} -1334.71 q^{89} -1045.43 q^{91} +641.309 q^{92} +461.613 q^{93} +453.554 q^{94} +553.789 q^{96} +399.297 q^{97} -259.797 q^{98} -22.3406 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9} - 33 q^{11} + 150 q^{12} - 188 q^{13} - 287 q^{14} + 82 q^{16} - 146 q^{17} - 184 q^{19} - 81 q^{21} - 277 q^{22} - 164 q^{23} + 63 q^{24} + 103 q^{26} + 378 q^{27} + 224 q^{28} + 252 q^{29} - 889 q^{31} - 422 q^{32} - 99 q^{33} - 230 q^{34} + 450 q^{36} - 642 q^{37} - 1833 q^{38} - 564 q^{39} - 164 q^{41} - 861 q^{42} - 696 q^{43} - 6 q^{44} - 419 q^{46} + 92 q^{47} + 246 q^{48} + 81 q^{49} - 438 q^{51} - 1956 q^{52} - 949 q^{53} - 2380 q^{56} - 552 q^{57} - 1041 q^{58} - 81 q^{59} - 496 q^{61} - 1454 q^{62} - 243 q^{63} - 3903 q^{64} - 831 q^{66} - 1926 q^{67} - 685 q^{68} - 492 q^{69} + 2498 q^{71} + 189 q^{72} + 1026 q^{73} - 707 q^{74} - 5704 q^{76} - 5434 q^{77} + 309 q^{78} - 695 q^{79} + 1134 q^{81} + 886 q^{82} - 5315 q^{83} + 672 q^{84} + 3997 q^{86} + 756 q^{87} - 2969 q^{88} - 1424 q^{89} - 1194 q^{91} - 1607 q^{92} - 2667 q^{93} - 629 q^{94} - 1266 q^{96} - 291 q^{97} + 1018 q^{98} - 297 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33976 0.473676 0.236838 0.971549i \(-0.423889\pi\)
0.236838 + 0.971549i \(0.423889\pi\)
\(3\) 3.00000 0.577350
\(4\) −6.20504 −0.775631
\(5\) 0 0
\(6\) 4.01928 0.273477
\(7\) −12.2101 −0.659284 −0.329642 0.944106i \(-0.606928\pi\)
−0.329642 + 0.944106i \(0.606928\pi\)
\(8\) −19.0313 −0.841074
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −2.48229 −0.0680398 −0.0340199 0.999421i \(-0.510831\pi\)
−0.0340199 + 0.999421i \(0.510831\pi\)
\(12\) −18.6151 −0.447811
\(13\) 85.6202 1.82667 0.913337 0.407204i \(-0.133496\pi\)
0.913337 + 0.407204i \(0.133496\pi\)
\(14\) −16.3586 −0.312287
\(15\) 0 0
\(16\) 24.1429 0.377233
\(17\) −5.54850 −0.0791593 −0.0395797 0.999216i \(-0.512602\pi\)
−0.0395797 + 0.999216i \(0.512602\pi\)
\(18\) 12.0578 0.157892
\(19\) −24.1374 −0.291448 −0.145724 0.989325i \(-0.546551\pi\)
−0.145724 + 0.989325i \(0.546551\pi\)
\(20\) 0 0
\(21\) −36.6303 −0.380638
\(22\) −3.32567 −0.0322289
\(23\) −103.353 −0.936981 −0.468491 0.883468i \(-0.655202\pi\)
−0.468491 + 0.883468i \(0.655202\pi\)
\(24\) −57.0940 −0.485595
\(25\) 0 0
\(26\) 114.710 0.865253
\(27\) 27.0000 0.192450
\(28\) 75.7642 0.511361
\(29\) −114.245 −0.731541 −0.365770 0.930705i \(-0.619194\pi\)
−0.365770 + 0.930705i \(0.619194\pi\)
\(30\) 0 0
\(31\) 153.871 0.891485 0.445742 0.895161i \(-0.352940\pi\)
0.445742 + 0.895161i \(0.352940\pi\)
\(32\) 184.596 1.01976
\(33\) −7.44687 −0.0392828
\(34\) −7.43365 −0.0374959
\(35\) 0 0
\(36\) −55.8454 −0.258544
\(37\) −342.674 −1.52258 −0.761288 0.648414i \(-0.775433\pi\)
−0.761288 + 0.648414i \(0.775433\pi\)
\(38\) −32.3383 −0.138052
\(39\) 256.861 1.05463
\(40\) 0 0
\(41\) 34.6755 0.132083 0.0660414 0.997817i \(-0.478963\pi\)
0.0660414 + 0.997817i \(0.478963\pi\)
\(42\) −49.0758 −0.180299
\(43\) −154.740 −0.548783 −0.274391 0.961618i \(-0.588476\pi\)
−0.274391 + 0.961618i \(0.588476\pi\)
\(44\) 15.4027 0.0527738
\(45\) 0 0
\(46\) −138.468 −0.443826
\(47\) 338.534 1.05064 0.525321 0.850904i \(-0.323945\pi\)
0.525321 + 0.850904i \(0.323945\pi\)
\(48\) 72.4288 0.217796
\(49\) −193.913 −0.565345
\(50\) 0 0
\(51\) −16.6455 −0.0457027
\(52\) −531.277 −1.41682
\(53\) 645.636 1.67330 0.836650 0.547738i \(-0.184511\pi\)
0.836650 + 0.547738i \(0.184511\pi\)
\(54\) 36.1735 0.0911591
\(55\) 0 0
\(56\) 232.375 0.554507
\(57\) −72.4123 −0.168267
\(58\) −153.060 −0.346514
\(59\) 662.854 1.46265 0.731325 0.682030i \(-0.238903\pi\)
0.731325 + 0.682030i \(0.238903\pi\)
\(60\) 0 0
\(61\) −357.681 −0.750759 −0.375379 0.926871i \(-0.622488\pi\)
−0.375379 + 0.926871i \(0.622488\pi\)
\(62\) 206.150 0.422275
\(63\) −109.891 −0.219761
\(64\) 54.1714 0.105803
\(65\) 0 0
\(66\) −9.97701 −0.0186073
\(67\) −531.377 −0.968926 −0.484463 0.874812i \(-0.660985\pi\)
−0.484463 + 0.874812i \(0.660985\pi\)
\(68\) 34.4287 0.0613984
\(69\) −310.059 −0.540966
\(70\) 0 0
\(71\) −634.801 −1.06109 −0.530543 0.847658i \(-0.678012\pi\)
−0.530543 + 0.847658i \(0.678012\pi\)
\(72\) −171.282 −0.280358
\(73\) 962.898 1.54382 0.771909 0.635734i \(-0.219302\pi\)
0.771909 + 0.635734i \(0.219302\pi\)
\(74\) −459.101 −0.721208
\(75\) 0 0
\(76\) 149.774 0.226056
\(77\) 30.3090 0.0448576
\(78\) 344.131 0.499554
\(79\) 568.744 0.809984 0.404992 0.914320i \(-0.367274\pi\)
0.404992 + 0.914320i \(0.367274\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 46.4568 0.0625645
\(83\) −319.838 −0.422973 −0.211486 0.977381i \(-0.567830\pi\)
−0.211486 + 0.977381i \(0.567830\pi\)
\(84\) 227.293 0.295234
\(85\) 0 0
\(86\) −207.315 −0.259945
\(87\) −342.734 −0.422355
\(88\) 47.2413 0.0572266
\(89\) −1334.71 −1.58966 −0.794828 0.606835i \(-0.792439\pi\)
−0.794828 + 0.606835i \(0.792439\pi\)
\(90\) 0 0
\(91\) −1045.43 −1.20430
\(92\) 641.309 0.726751
\(93\) 461.613 0.514699
\(94\) 453.554 0.497665
\(95\) 0 0
\(96\) 553.789 0.588759
\(97\) 399.297 0.417964 0.208982 0.977920i \(-0.432985\pi\)
0.208982 + 0.977920i \(0.432985\pi\)
\(98\) −259.797 −0.267791
\(99\) −22.3406 −0.0226799
\(100\) 0 0
\(101\) −131.408 −0.129461 −0.0647307 0.997903i \(-0.520619\pi\)
−0.0647307 + 0.997903i \(0.520619\pi\)
\(102\) −22.3010 −0.0216483
\(103\) 18.8410 0.0180238 0.00901192 0.999959i \(-0.497131\pi\)
0.00901192 + 0.999959i \(0.497131\pi\)
\(104\) −1629.47 −1.53637
\(105\) 0 0
\(106\) 864.997 0.792603
\(107\) −1832.09 −1.65528 −0.827640 0.561259i \(-0.810317\pi\)
−0.827640 + 0.561259i \(0.810317\pi\)
\(108\) −167.536 −0.149270
\(109\) −1337.65 −1.17544 −0.587722 0.809063i \(-0.699975\pi\)
−0.587722 + 0.809063i \(0.699975\pi\)
\(110\) 0 0
\(111\) −1028.02 −0.879059
\(112\) −294.788 −0.248704
\(113\) 36.2244 0.0301566 0.0150783 0.999886i \(-0.495200\pi\)
0.0150783 + 0.999886i \(0.495200\pi\)
\(114\) −97.0150 −0.0797043
\(115\) 0 0
\(116\) 708.893 0.567405
\(117\) 770.582 0.608891
\(118\) 888.065 0.692822
\(119\) 67.7477 0.0521884
\(120\) 0 0
\(121\) −1324.84 −0.995371
\(122\) −479.206 −0.355617
\(123\) 104.026 0.0762581
\(124\) −954.776 −0.691463
\(125\) 0 0
\(126\) −147.227 −0.104096
\(127\) −1397.61 −0.976520 −0.488260 0.872698i \(-0.662368\pi\)
−0.488260 + 0.872698i \(0.662368\pi\)
\(128\) −1404.20 −0.969644
\(129\) −464.220 −0.316840
\(130\) 0 0
\(131\) −2838.05 −1.89284 −0.946418 0.322945i \(-0.895327\pi\)
−0.946418 + 0.322945i \(0.895327\pi\)
\(132\) 46.2081 0.0304690
\(133\) 294.720 0.192147
\(134\) −711.918 −0.458958
\(135\) 0 0
\(136\) 105.595 0.0665789
\(137\) −810.294 −0.505314 −0.252657 0.967556i \(-0.581304\pi\)
−0.252657 + 0.967556i \(0.581304\pi\)
\(138\) −415.404 −0.256243
\(139\) −3140.44 −1.91632 −0.958161 0.286230i \(-0.907598\pi\)
−0.958161 + 0.286230i \(0.907598\pi\)
\(140\) 0 0
\(141\) 1015.60 0.606589
\(142\) −850.481 −0.502611
\(143\) −212.534 −0.124287
\(144\) 217.286 0.125744
\(145\) 0 0
\(146\) 1290.05 0.731270
\(147\) −581.740 −0.326402
\(148\) 2126.31 1.18096
\(149\) −1008.26 −0.554362 −0.277181 0.960818i \(-0.589400\pi\)
−0.277181 + 0.960818i \(0.589400\pi\)
\(150\) 0 0
\(151\) −2162.97 −1.16570 −0.582848 0.812581i \(-0.698062\pi\)
−0.582848 + 0.812581i \(0.698062\pi\)
\(152\) 459.368 0.245129
\(153\) −49.9365 −0.0263864
\(154\) 40.6068 0.0212480
\(155\) 0 0
\(156\) −1593.83 −0.818004
\(157\) −2618.64 −1.33115 −0.665575 0.746331i \(-0.731814\pi\)
−0.665575 + 0.746331i \(0.731814\pi\)
\(158\) 761.980 0.383670
\(159\) 1936.91 0.966080
\(160\) 0 0
\(161\) 1261.95 0.617737
\(162\) 108.521 0.0526307
\(163\) −323.254 −0.155333 −0.0776663 0.996979i \(-0.524747\pi\)
−0.0776663 + 0.996979i \(0.524747\pi\)
\(164\) −215.163 −0.102447
\(165\) 0 0
\(166\) −428.505 −0.200352
\(167\) 158.987 0.0736692 0.0368346 0.999321i \(-0.488273\pi\)
0.0368346 + 0.999321i \(0.488273\pi\)
\(168\) 697.124 0.320145
\(169\) 5133.82 2.33674
\(170\) 0 0
\(171\) −217.237 −0.0971492
\(172\) 960.170 0.425653
\(173\) −3292.67 −1.44703 −0.723516 0.690307i \(-0.757475\pi\)
−0.723516 + 0.690307i \(0.757475\pi\)
\(174\) −459.181 −0.200060
\(175\) 0 0
\(176\) −59.9297 −0.0256669
\(177\) 1988.56 0.844461
\(178\) −1788.20 −0.752983
\(179\) 2818.95 1.17708 0.588542 0.808467i \(-0.299702\pi\)
0.588542 + 0.808467i \(0.299702\pi\)
\(180\) 0 0
\(181\) 417.600 0.171492 0.0857458 0.996317i \(-0.472673\pi\)
0.0857458 + 0.996317i \(0.472673\pi\)
\(182\) −1400.63 −0.570447
\(183\) −1073.04 −0.433451
\(184\) 1966.94 0.788071
\(185\) 0 0
\(186\) 618.450 0.243801
\(187\) 13.7730 0.00538599
\(188\) −2100.62 −0.814911
\(189\) −329.673 −0.126879
\(190\) 0 0
\(191\) 521.598 0.197599 0.0987997 0.995107i \(-0.468500\pi\)
0.0987997 + 0.995107i \(0.468500\pi\)
\(192\) 162.514 0.0610857
\(193\) −4528.65 −1.68901 −0.844506 0.535547i \(-0.820106\pi\)
−0.844506 + 0.535547i \(0.820106\pi\)
\(194\) 534.962 0.197980
\(195\) 0 0
\(196\) 1203.24 0.438499
\(197\) −2780.69 −1.00566 −0.502832 0.864384i \(-0.667709\pi\)
−0.502832 + 0.864384i \(0.667709\pi\)
\(198\) −29.9310 −0.0107430
\(199\) 4988.03 1.77685 0.888423 0.459026i \(-0.151801\pi\)
0.888423 + 0.459026i \(0.151801\pi\)
\(200\) 0 0
\(201\) −1594.13 −0.559410
\(202\) −176.055 −0.0613228
\(203\) 1394.94 0.482293
\(204\) 103.286 0.0354484
\(205\) 0 0
\(206\) 25.2424 0.00853747
\(207\) −930.176 −0.312327
\(208\) 2067.12 0.689083
\(209\) 59.9161 0.0198300
\(210\) 0 0
\(211\) 3752.11 1.22420 0.612100 0.790781i \(-0.290325\pi\)
0.612100 + 0.790781i \(0.290325\pi\)
\(212\) −4006.20 −1.29786
\(213\) −1904.40 −0.612618
\(214\) −2454.56 −0.784068
\(215\) 0 0
\(216\) −513.846 −0.161865
\(217\) −1878.78 −0.587741
\(218\) −1792.13 −0.556780
\(219\) 2888.69 0.891323
\(220\) 0 0
\(221\) −475.063 −0.144598
\(222\) −1377.30 −0.416390
\(223\) 1637.57 0.491748 0.245874 0.969302i \(-0.420925\pi\)
0.245874 + 0.969302i \(0.420925\pi\)
\(224\) −2253.94 −0.672312
\(225\) 0 0
\(226\) 48.5319 0.0142845
\(227\) −3793.11 −1.10906 −0.554532 0.832162i \(-0.687103\pi\)
−0.554532 + 0.832162i \(0.687103\pi\)
\(228\) 449.321 0.130513
\(229\) 90.2198 0.0260345 0.0130172 0.999915i \(-0.495856\pi\)
0.0130172 + 0.999915i \(0.495856\pi\)
\(230\) 0 0
\(231\) 90.9270 0.0258985
\(232\) 2174.23 0.615280
\(233\) 3618.41 1.01738 0.508691 0.860949i \(-0.330130\pi\)
0.508691 + 0.860949i \(0.330130\pi\)
\(234\) 1032.39 0.288418
\(235\) 0 0
\(236\) −4113.04 −1.13448
\(237\) 1706.23 0.467644
\(238\) 90.7657 0.0247204
\(239\) −1470.76 −0.398056 −0.199028 0.979994i \(-0.563778\pi\)
−0.199028 + 0.979994i \(0.563778\pi\)
\(240\) 0 0
\(241\) −3946.47 −1.05483 −0.527416 0.849607i \(-0.676839\pi\)
−0.527416 + 0.849607i \(0.676839\pi\)
\(242\) −1774.96 −0.471484
\(243\) 243.000 0.0641500
\(244\) 2219.42 0.582312
\(245\) 0 0
\(246\) 139.370 0.0361217
\(247\) −2066.65 −0.532380
\(248\) −2928.37 −0.749805
\(249\) −959.513 −0.244203
\(250\) 0 0
\(251\) 3410.52 0.857649 0.428825 0.903388i \(-0.358928\pi\)
0.428825 + 0.903388i \(0.358928\pi\)
\(252\) 681.878 0.170454
\(253\) 256.552 0.0637521
\(254\) −1872.46 −0.462554
\(255\) 0 0
\(256\) −2314.65 −0.565101
\(257\) −6919.87 −1.67957 −0.839785 0.542918i \(-0.817319\pi\)
−0.839785 + 0.542918i \(0.817319\pi\)
\(258\) −621.944 −0.150080
\(259\) 4184.09 1.00381
\(260\) 0 0
\(261\) −1028.20 −0.243847
\(262\) −3802.30 −0.896592
\(263\) 3808.56 0.892951 0.446475 0.894796i \(-0.352679\pi\)
0.446475 + 0.894796i \(0.352679\pi\)
\(264\) 141.724 0.0330398
\(265\) 0 0
\(266\) 394.855 0.0910154
\(267\) −4004.14 −0.917788
\(268\) 3297.22 0.751529
\(269\) 2586.34 0.586214 0.293107 0.956080i \(-0.405311\pi\)
0.293107 + 0.956080i \(0.405311\pi\)
\(270\) 0 0
\(271\) 1065.41 0.238816 0.119408 0.992845i \(-0.461900\pi\)
0.119408 + 0.992845i \(0.461900\pi\)
\(272\) −133.957 −0.0298615
\(273\) −3136.29 −0.695301
\(274\) −1085.60 −0.239356
\(275\) 0 0
\(276\) 1923.93 0.419590
\(277\) −2468.28 −0.535396 −0.267698 0.963503i \(-0.586263\pi\)
−0.267698 + 0.963503i \(0.586263\pi\)
\(278\) −4207.44 −0.907717
\(279\) 1384.84 0.297162
\(280\) 0 0
\(281\) 3108.83 0.659991 0.329996 0.943982i \(-0.392953\pi\)
0.329996 + 0.943982i \(0.392953\pi\)
\(282\) 1360.66 0.287327
\(283\) −6454.03 −1.35566 −0.677831 0.735217i \(-0.737080\pi\)
−0.677831 + 0.735217i \(0.737080\pi\)
\(284\) 3938.97 0.823010
\(285\) 0 0
\(286\) −284.744 −0.0588717
\(287\) −423.391 −0.0870801
\(288\) 1661.37 0.339920
\(289\) −4882.21 −0.993734
\(290\) 0 0
\(291\) 1197.89 0.241312
\(292\) −5974.82 −1.19743
\(293\) 835.063 0.166501 0.0832507 0.996529i \(-0.473470\pi\)
0.0832507 + 0.996529i \(0.473470\pi\)
\(294\) −779.392 −0.154609
\(295\) 0 0
\(296\) 6521.55 1.28060
\(297\) −67.0218 −0.0130943
\(298\) −1350.83 −0.262588
\(299\) −8849.10 −1.71156
\(300\) 0 0
\(301\) 1889.39 0.361803
\(302\) −2897.86 −0.552163
\(303\) −394.224 −0.0747445
\(304\) −582.748 −0.109944
\(305\) 0 0
\(306\) −66.9029 −0.0124986
\(307\) 2681.88 0.498577 0.249289 0.968429i \(-0.419803\pi\)
0.249289 + 0.968429i \(0.419803\pi\)
\(308\) −188.069 −0.0347929
\(309\) 56.5229 0.0104061
\(310\) 0 0
\(311\) 8133.63 1.48301 0.741504 0.670948i \(-0.234113\pi\)
0.741504 + 0.670948i \(0.234113\pi\)
\(312\) −4888.40 −0.887023
\(313\) 7723.68 1.39479 0.697394 0.716688i \(-0.254343\pi\)
0.697394 + 0.716688i \(0.254343\pi\)
\(314\) −3508.35 −0.630534
\(315\) 0 0
\(316\) −3529.08 −0.628248
\(317\) 3220.49 0.570602 0.285301 0.958438i \(-0.407907\pi\)
0.285301 + 0.958438i \(0.407907\pi\)
\(318\) 2594.99 0.457610
\(319\) 283.588 0.0497739
\(320\) 0 0
\(321\) −5496.28 −0.955677
\(322\) 1690.71 0.292607
\(323\) 133.926 0.0230708
\(324\) −502.609 −0.0861812
\(325\) 0 0
\(326\) −433.083 −0.0735774
\(327\) −4012.94 −0.678643
\(328\) −659.920 −0.111092
\(329\) −4133.53 −0.692672
\(330\) 0 0
\(331\) 4197.98 0.697105 0.348553 0.937289i \(-0.386673\pi\)
0.348553 + 0.937289i \(0.386673\pi\)
\(332\) 1984.61 0.328071
\(333\) −3084.07 −0.507525
\(334\) 213.004 0.0348954
\(335\) 0 0
\(336\) −884.363 −0.143589
\(337\) 1285.13 0.207731 0.103865 0.994591i \(-0.466879\pi\)
0.103865 + 0.994591i \(0.466879\pi\)
\(338\) 6878.08 1.10686
\(339\) 108.673 0.0174109
\(340\) 0 0
\(341\) −381.952 −0.0606565
\(342\) −291.045 −0.0460173
\(343\) 6555.77 1.03201
\(344\) 2944.91 0.461567
\(345\) 0 0
\(346\) −4411.38 −0.685425
\(347\) −311.212 −0.0481461 −0.0240731 0.999710i \(-0.507663\pi\)
−0.0240731 + 0.999710i \(0.507663\pi\)
\(348\) 2126.68 0.327592
\(349\) −3853.76 −0.591081 −0.295540 0.955330i \(-0.595500\pi\)
−0.295540 + 0.955330i \(0.595500\pi\)
\(350\) 0 0
\(351\) 2311.75 0.351544
\(352\) −458.222 −0.0693844
\(353\) 1202.75 0.181349 0.0906743 0.995881i \(-0.471098\pi\)
0.0906743 + 0.995881i \(0.471098\pi\)
\(354\) 2664.20 0.400001
\(355\) 0 0
\(356\) 8281.96 1.23299
\(357\) 203.243 0.0301310
\(358\) 3776.71 0.557557
\(359\) 10915.2 1.60469 0.802345 0.596860i \(-0.203585\pi\)
0.802345 + 0.596860i \(0.203585\pi\)
\(360\) 0 0
\(361\) −6276.38 −0.915058
\(362\) 559.484 0.0812315
\(363\) −3974.51 −0.574677
\(364\) 6486.95 0.934089
\(365\) 0 0
\(366\) −1437.62 −0.205316
\(367\) −145.288 −0.0206647 −0.0103324 0.999947i \(-0.503289\pi\)
−0.0103324 + 0.999947i \(0.503289\pi\)
\(368\) −2495.24 −0.353461
\(369\) 312.079 0.0440276
\(370\) 0 0
\(371\) −7883.28 −1.10318
\(372\) −2864.33 −0.399216
\(373\) −3519.41 −0.488547 −0.244274 0.969706i \(-0.578549\pi\)
−0.244274 + 0.969706i \(0.578549\pi\)
\(374\) 18.4525 0.00255122
\(375\) 0 0
\(376\) −6442.75 −0.883669
\(377\) −9781.64 −1.33629
\(378\) −441.682 −0.0600997
\(379\) −404.362 −0.0548040 −0.0274020 0.999624i \(-0.508723\pi\)
−0.0274020 + 0.999624i \(0.508723\pi\)
\(380\) 0 0
\(381\) −4192.84 −0.563794
\(382\) 698.816 0.0935982
\(383\) −4183.62 −0.558154 −0.279077 0.960269i \(-0.590029\pi\)
−0.279077 + 0.960269i \(0.590029\pi\)
\(384\) −4212.59 −0.559824
\(385\) 0 0
\(386\) −6067.30 −0.800045
\(387\) −1392.66 −0.182928
\(388\) −2477.66 −0.324185
\(389\) −10258.6 −1.33710 −0.668551 0.743666i \(-0.733085\pi\)
−0.668551 + 0.743666i \(0.733085\pi\)
\(390\) 0 0
\(391\) 573.453 0.0741708
\(392\) 3690.43 0.475497
\(393\) −8514.15 −1.09283
\(394\) −3725.45 −0.476360
\(395\) 0 0
\(396\) 138.624 0.0175913
\(397\) −10191.6 −1.28841 −0.644207 0.764852i \(-0.722812\pi\)
−0.644207 + 0.764852i \(0.722812\pi\)
\(398\) 6682.77 0.841650
\(399\) 884.161 0.110936
\(400\) 0 0
\(401\) 5912.32 0.736277 0.368139 0.929771i \(-0.379995\pi\)
0.368139 + 0.929771i \(0.379995\pi\)
\(402\) −2135.75 −0.264979
\(403\) 13174.5 1.62845
\(404\) 815.393 0.100414
\(405\) 0 0
\(406\) 1868.88 0.228451
\(407\) 850.616 0.103596
\(408\) 316.786 0.0384393
\(409\) 5656.62 0.683867 0.341934 0.939724i \(-0.388918\pi\)
0.341934 + 0.939724i \(0.388918\pi\)
\(410\) 0 0
\(411\) −2430.88 −0.291743
\(412\) −116.909 −0.0139798
\(413\) −8093.52 −0.964301
\(414\) −1246.21 −0.147942
\(415\) 0 0
\(416\) 15805.2 1.86277
\(417\) −9421.32 −1.10639
\(418\) 80.2731 0.00939303
\(419\) 13703.9 1.59781 0.798903 0.601460i \(-0.205414\pi\)
0.798903 + 0.601460i \(0.205414\pi\)
\(420\) 0 0
\(421\) 9214.65 1.06673 0.533367 0.845884i \(-0.320927\pi\)
0.533367 + 0.845884i \(0.320927\pi\)
\(422\) 5026.93 0.579874
\(423\) 3046.80 0.350214
\(424\) −12287.3 −1.40737
\(425\) 0 0
\(426\) −2551.44 −0.290183
\(427\) 4367.32 0.494963
\(428\) 11368.2 1.28389
\(429\) −637.602 −0.0717569
\(430\) 0 0
\(431\) 7565.73 0.845542 0.422771 0.906237i \(-0.361058\pi\)
0.422771 + 0.906237i \(0.361058\pi\)
\(432\) 651.859 0.0725986
\(433\) 4046.69 0.449126 0.224563 0.974460i \(-0.427905\pi\)
0.224563 + 0.974460i \(0.427905\pi\)
\(434\) −2517.11 −0.278399
\(435\) 0 0
\(436\) 8300.17 0.911711
\(437\) 2494.67 0.273081
\(438\) 3870.15 0.422199
\(439\) 3903.40 0.424372 0.212186 0.977229i \(-0.431942\pi\)
0.212186 + 0.977229i \(0.431942\pi\)
\(440\) 0 0
\(441\) −1745.22 −0.188448
\(442\) −636.471 −0.0684928
\(443\) 2288.91 0.245484 0.122742 0.992439i \(-0.460831\pi\)
0.122742 + 0.992439i \(0.460831\pi\)
\(444\) 6378.93 0.681825
\(445\) 0 0
\(446\) 2193.95 0.232930
\(447\) −3024.78 −0.320061
\(448\) −661.438 −0.0697545
\(449\) 10025.3 1.05373 0.526863 0.849950i \(-0.323368\pi\)
0.526863 + 0.849950i \(0.323368\pi\)
\(450\) 0 0
\(451\) −86.0745 −0.00898690
\(452\) −224.774 −0.0233904
\(453\) −6488.92 −0.673015
\(454\) −5081.86 −0.525338
\(455\) 0 0
\(456\) 1378.10 0.141525
\(457\) −3293.06 −0.337075 −0.168537 0.985695i \(-0.553904\pi\)
−0.168537 + 0.985695i \(0.553904\pi\)
\(458\) 120.873 0.0123319
\(459\) −149.809 −0.0152342
\(460\) 0 0
\(461\) −831.332 −0.0839891 −0.0419945 0.999118i \(-0.513371\pi\)
−0.0419945 + 0.999118i \(0.513371\pi\)
\(462\) 121.820 0.0122675
\(463\) −9026.62 −0.906053 −0.453027 0.891497i \(-0.649656\pi\)
−0.453027 + 0.891497i \(0.649656\pi\)
\(464\) −2758.20 −0.275962
\(465\) 0 0
\(466\) 4847.80 0.481910
\(467\) 1315.72 0.130373 0.0651867 0.997873i \(-0.479236\pi\)
0.0651867 + 0.997873i \(0.479236\pi\)
\(468\) −4781.49 −0.472275
\(469\) 6488.17 0.638797
\(470\) 0 0
\(471\) −7855.93 −0.768540
\(472\) −12615.0 −1.23020
\(473\) 384.110 0.0373391
\(474\) 2285.94 0.221512
\(475\) 0 0
\(476\) −420.378 −0.0404790
\(477\) 5810.72 0.557767
\(478\) −1970.46 −0.188550
\(479\) 9331.15 0.890086 0.445043 0.895509i \(-0.353188\pi\)
0.445043 + 0.895509i \(0.353188\pi\)
\(480\) 0 0
\(481\) −29339.8 −2.78125
\(482\) −5287.32 −0.499649
\(483\) 3785.85 0.356650
\(484\) 8220.68 0.772040
\(485\) 0 0
\(486\) 325.562 0.0303864
\(487\) −2055.48 −0.191258 −0.0956288 0.995417i \(-0.530486\pi\)
−0.0956288 + 0.995417i \(0.530486\pi\)
\(488\) 6807.14 0.631444
\(489\) −969.763 −0.0896814
\(490\) 0 0
\(491\) 3570.13 0.328142 0.164071 0.986449i \(-0.447537\pi\)
0.164071 + 0.986449i \(0.447537\pi\)
\(492\) −645.488 −0.0591481
\(493\) 633.886 0.0579083
\(494\) −2768.81 −0.252176
\(495\) 0 0
\(496\) 3714.89 0.336298
\(497\) 7750.99 0.699556
\(498\) −1285.52 −0.115673
\(499\) −316.957 −0.0284347 −0.0142174 0.999899i \(-0.504526\pi\)
−0.0142174 + 0.999899i \(0.504526\pi\)
\(500\) 0 0
\(501\) 476.960 0.0425329
\(502\) 4569.27 0.406248
\(503\) −10584.0 −0.938204 −0.469102 0.883144i \(-0.655422\pi\)
−0.469102 + 0.883144i \(0.655422\pi\)
\(504\) 2091.37 0.184836
\(505\) 0 0
\(506\) 343.718 0.0301979
\(507\) 15401.4 1.34912
\(508\) 8672.24 0.757418
\(509\) −14819.6 −1.29051 −0.645253 0.763969i \(-0.723248\pi\)
−0.645253 + 0.763969i \(0.723248\pi\)
\(510\) 0 0
\(511\) −11757.1 −1.01781
\(512\) 8132.48 0.701969
\(513\) −651.710 −0.0560891
\(514\) −9270.96 −0.795573
\(515\) 0 0
\(516\) 2880.51 0.245751
\(517\) −840.338 −0.0714856
\(518\) 5605.67 0.475481
\(519\) −9878.00 −0.835445
\(520\) 0 0
\(521\) 4097.71 0.344576 0.172288 0.985047i \(-0.444884\pi\)
0.172288 + 0.985047i \(0.444884\pi\)
\(522\) −1377.54 −0.115505
\(523\) 6037.27 0.504764 0.252382 0.967628i \(-0.418786\pi\)
0.252382 + 0.967628i \(0.418786\pi\)
\(524\) 17610.2 1.46814
\(525\) 0 0
\(526\) 5102.56 0.422970
\(527\) −853.752 −0.0705693
\(528\) −179.789 −0.0148188
\(529\) −1485.18 −0.122066
\(530\) 0 0
\(531\) 5965.69 0.487550
\(532\) −1828.75 −0.149035
\(533\) 2968.92 0.241272
\(534\) −5364.59 −0.434735
\(535\) 0 0
\(536\) 10112.8 0.814939
\(537\) 8456.84 0.679589
\(538\) 3465.07 0.277676
\(539\) 481.349 0.0384660
\(540\) 0 0
\(541\) 4908.65 0.390091 0.195046 0.980794i \(-0.437515\pi\)
0.195046 + 0.980794i \(0.437515\pi\)
\(542\) 1427.39 0.113121
\(543\) 1252.80 0.0990107
\(544\) −1024.23 −0.0807236
\(545\) 0 0
\(546\) −4201.88 −0.329348
\(547\) −17573.7 −1.37367 −0.686836 0.726812i \(-0.741001\pi\)
−0.686836 + 0.726812i \(0.741001\pi\)
\(548\) 5027.91 0.391937
\(549\) −3219.12 −0.250253
\(550\) 0 0
\(551\) 2757.57 0.213206
\(552\) 5900.83 0.454993
\(553\) −6944.43 −0.534009
\(554\) −3306.90 −0.253604
\(555\) 0 0
\(556\) 19486.6 1.48636
\(557\) −23625.5 −1.79721 −0.898603 0.438764i \(-0.855417\pi\)
−0.898603 + 0.438764i \(0.855417\pi\)
\(558\) 1855.35 0.140758
\(559\) −13248.9 −1.00245
\(560\) 0 0
\(561\) 41.3189 0.00310960
\(562\) 4165.09 0.312622
\(563\) −23159.1 −1.73364 −0.866819 0.498623i \(-0.833839\pi\)
−0.866819 + 0.498623i \(0.833839\pi\)
\(564\) −6301.85 −0.470489
\(565\) 0 0
\(566\) −8646.85 −0.642146
\(567\) −989.018 −0.0732537
\(568\) 12081.1 0.892452
\(569\) −8494.69 −0.625862 −0.312931 0.949776i \(-0.601311\pi\)
−0.312931 + 0.949776i \(0.601311\pi\)
\(570\) 0 0
\(571\) 15461.7 1.13319 0.566594 0.823997i \(-0.308261\pi\)
0.566594 + 0.823997i \(0.308261\pi\)
\(572\) 1318.78 0.0964005
\(573\) 1564.79 0.114084
\(574\) −567.242 −0.0412478
\(575\) 0 0
\(576\) 487.542 0.0352678
\(577\) 26438.3 1.90752 0.953760 0.300570i \(-0.0971768\pi\)
0.953760 + 0.300570i \(0.0971768\pi\)
\(578\) −6540.99 −0.470708
\(579\) −13585.9 −0.975151
\(580\) 0 0
\(581\) 3905.25 0.278859
\(582\) 1604.89 0.114304
\(583\) −1602.65 −0.113851
\(584\) −18325.2 −1.29847
\(585\) 0 0
\(586\) 1118.78 0.0788678
\(587\) −5948.84 −0.418288 −0.209144 0.977885i \(-0.567068\pi\)
−0.209144 + 0.977885i \(0.567068\pi\)
\(588\) 3609.72 0.253167
\(589\) −3714.05 −0.259821
\(590\) 0 0
\(591\) −8342.07 −0.580621
\(592\) −8273.16 −0.574366
\(593\) −11755.3 −0.814054 −0.407027 0.913416i \(-0.633434\pi\)
−0.407027 + 0.913416i \(0.633434\pi\)
\(594\) −89.7931 −0.00620245
\(595\) 0 0
\(596\) 6256.31 0.429980
\(597\) 14964.1 1.02586
\(598\) −11855.7 −0.810726
\(599\) −10184.4 −0.694698 −0.347349 0.937736i \(-0.612918\pi\)
−0.347349 + 0.937736i \(0.612918\pi\)
\(600\) 0 0
\(601\) −16384.2 −1.11202 −0.556012 0.831174i \(-0.687669\pi\)
−0.556012 + 0.831174i \(0.687669\pi\)
\(602\) 2531.33 0.171378
\(603\) −4782.39 −0.322975
\(604\) 13421.3 0.904150
\(605\) 0 0
\(606\) −528.166 −0.0354047
\(607\) 20161.1 1.34813 0.674066 0.738672i \(-0.264547\pi\)
0.674066 + 0.738672i \(0.264547\pi\)
\(608\) −4455.68 −0.297207
\(609\) 4184.81 0.278452
\(610\) 0 0
\(611\) 28985.3 1.91918
\(612\) 309.858 0.0204661
\(613\) −3158.17 −0.208087 −0.104043 0.994573i \(-0.533178\pi\)
−0.104043 + 0.994573i \(0.533178\pi\)
\(614\) 3593.08 0.236164
\(615\) 0 0
\(616\) −576.821 −0.0377285
\(617\) 6576.62 0.429116 0.214558 0.976711i \(-0.431169\pi\)
0.214558 + 0.976711i \(0.431169\pi\)
\(618\) 75.7271 0.00492911
\(619\) −21106.1 −1.37048 −0.685240 0.728318i \(-0.740303\pi\)
−0.685240 + 0.728318i \(0.740303\pi\)
\(620\) 0 0
\(621\) −2790.53 −0.180322
\(622\) 10897.1 0.702466
\(623\) 16297.0 1.04803
\(624\) 6201.37 0.397842
\(625\) 0 0
\(626\) 10347.9 0.660678
\(627\) 179.748 0.0114489
\(628\) 16248.8 1.03248
\(629\) 1901.33 0.120526
\(630\) 0 0
\(631\) −26852.1 −1.69408 −0.847039 0.531530i \(-0.821617\pi\)
−0.847039 + 0.531530i \(0.821617\pi\)
\(632\) −10824.0 −0.681257
\(633\) 11256.3 0.706792
\(634\) 4314.68 0.270281
\(635\) 0 0
\(636\) −12018.6 −0.749322
\(637\) −16602.9 −1.03270
\(638\) 379.940 0.0235767
\(639\) −5713.21 −0.353695
\(640\) 0 0
\(641\) 25421.5 1.56644 0.783221 0.621743i \(-0.213575\pi\)
0.783221 + 0.621743i \(0.213575\pi\)
\(642\) −7363.69 −0.452682
\(643\) −10481.7 −0.642856 −0.321428 0.946934i \(-0.604163\pi\)
−0.321428 + 0.946934i \(0.604163\pi\)
\(644\) −7830.46 −0.479135
\(645\) 0 0
\(646\) 179.429 0.0109281
\(647\) 18921.8 1.14975 0.574877 0.818240i \(-0.305050\pi\)
0.574877 + 0.818240i \(0.305050\pi\)
\(648\) −1541.54 −0.0934527
\(649\) −1645.40 −0.0995184
\(650\) 0 0
\(651\) −5636.34 −0.339333
\(652\) 2005.81 0.120481
\(653\) −12657.4 −0.758536 −0.379268 0.925287i \(-0.623824\pi\)
−0.379268 + 0.925287i \(0.623824\pi\)
\(654\) −5376.38 −0.321457
\(655\) 0 0
\(656\) 837.167 0.0498261
\(657\) 8666.08 0.514606
\(658\) −5537.94 −0.328102
\(659\) 12138.5 0.717526 0.358763 0.933429i \(-0.383199\pi\)
0.358763 + 0.933429i \(0.383199\pi\)
\(660\) 0 0
\(661\) 4177.69 0.245830 0.122915 0.992417i \(-0.460776\pi\)
0.122915 + 0.992417i \(0.460776\pi\)
\(662\) 5624.28 0.330202
\(663\) −1425.19 −0.0834839
\(664\) 6086.94 0.355752
\(665\) 0 0
\(666\) −4131.91 −0.240403
\(667\) 11807.5 0.685440
\(668\) −986.519 −0.0571401
\(669\) 4912.71 0.283911
\(670\) 0 0
\(671\) 887.866 0.0510815
\(672\) −6761.83 −0.388159
\(673\) 7570.21 0.433596 0.216798 0.976216i \(-0.430439\pi\)
0.216798 + 0.976216i \(0.430439\pi\)
\(674\) 1721.76 0.0983972
\(675\) 0 0
\(676\) −31855.6 −1.81245
\(677\) −33332.1 −1.89226 −0.946128 0.323791i \(-0.895042\pi\)
−0.946128 + 0.323791i \(0.895042\pi\)
\(678\) 145.596 0.00824716
\(679\) −4875.46 −0.275557
\(680\) 0 0
\(681\) −11379.3 −0.640319
\(682\) −511.724 −0.0287315
\(683\) −34915.5 −1.95608 −0.978042 0.208408i \(-0.933172\pi\)
−0.978042 + 0.208408i \(0.933172\pi\)
\(684\) 1347.96 0.0753519
\(685\) 0 0
\(686\) 8783.15 0.488837
\(687\) 270.659 0.0150310
\(688\) −3735.88 −0.207019
\(689\) 55279.5 3.05658
\(690\) 0 0
\(691\) −33698.0 −1.85519 −0.927593 0.373593i \(-0.878126\pi\)
−0.927593 + 0.373593i \(0.878126\pi\)
\(692\) 20431.1 1.12236
\(693\) 272.781 0.0149525
\(694\) −416.949 −0.0228057
\(695\) 0 0
\(696\) 6522.68 0.355232
\(697\) −192.397 −0.0104556
\(698\) −5163.12 −0.279981
\(699\) 10855.2 0.587385
\(700\) 0 0
\(701\) 23077.6 1.24341 0.621704 0.783252i \(-0.286441\pi\)
0.621704 + 0.783252i \(0.286441\pi\)
\(702\) 3097.18 0.166518
\(703\) 8271.27 0.443751
\(704\) −134.469 −0.00719885
\(705\) 0 0
\(706\) 1611.40 0.0859006
\(707\) 1604.51 0.0853518
\(708\) −12339.1 −0.654990
\(709\) −18761.4 −0.993795 −0.496898 0.867809i \(-0.665528\pi\)
−0.496898 + 0.867809i \(0.665528\pi\)
\(710\) 0 0
\(711\) 5118.70 0.269995
\(712\) 25401.4 1.33702
\(713\) −15903.0 −0.835305
\(714\) 272.297 0.0142724
\(715\) 0 0
\(716\) −17491.7 −0.912982
\(717\) −4412.27 −0.229818
\(718\) 14623.8 0.760104
\(719\) −13386.3 −0.694334 −0.347167 0.937803i \(-0.612856\pi\)
−0.347167 + 0.937803i \(0.612856\pi\)
\(720\) 0 0
\(721\) −230.050 −0.0118828
\(722\) −8408.85 −0.433442
\(723\) −11839.4 −0.609007
\(724\) −2591.23 −0.133014
\(725\) 0 0
\(726\) −5324.89 −0.272211
\(727\) −10059.3 −0.513177 −0.256589 0.966521i \(-0.582599\pi\)
−0.256589 + 0.966521i \(0.582599\pi\)
\(728\) 19896.0 1.01290
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 858.576 0.0434413
\(732\) 6658.27 0.336198
\(733\) −2861.45 −0.144189 −0.0720943 0.997398i \(-0.522968\pi\)
−0.0720943 + 0.997398i \(0.522968\pi\)
\(734\) −194.650 −0.00978839
\(735\) 0 0
\(736\) −19078.6 −0.955497
\(737\) 1319.03 0.0659256
\(738\) 418.111 0.0208548
\(739\) 30134.2 1.50000 0.750002 0.661436i \(-0.230053\pi\)
0.750002 + 0.661436i \(0.230053\pi\)
\(740\) 0 0
\(741\) −6199.95 −0.307370
\(742\) −10561.7 −0.522550
\(743\) 1183.79 0.0584508 0.0292254 0.999573i \(-0.490696\pi\)
0.0292254 + 0.999573i \(0.490696\pi\)
\(744\) −8785.11 −0.432900
\(745\) 0 0
\(746\) −4715.16 −0.231413
\(747\) −2878.54 −0.140991
\(748\) −85.4619 −0.00417754
\(749\) 22370.0 1.09130
\(750\) 0 0
\(751\) 33092.2 1.60793 0.803964 0.594679i \(-0.202721\pi\)
0.803964 + 0.594679i \(0.202721\pi\)
\(752\) 8173.20 0.396338
\(753\) 10231.6 0.495164
\(754\) −13105.0 −0.632968
\(755\) 0 0
\(756\) 2045.63 0.0984114
\(757\) 14001.4 0.672246 0.336123 0.941818i \(-0.390884\pi\)
0.336123 + 0.941818i \(0.390884\pi\)
\(758\) −541.748 −0.0259593
\(759\) 769.655 0.0368073
\(760\) 0 0
\(761\) −16873.5 −0.803765 −0.401883 0.915691i \(-0.631644\pi\)
−0.401883 + 0.915691i \(0.631644\pi\)
\(762\) −5617.39 −0.267056
\(763\) 16332.8 0.774951
\(764\) −3236.54 −0.153264
\(765\) 0 0
\(766\) −5605.05 −0.264385
\(767\) 56753.7 2.67178
\(768\) −6943.96 −0.326261
\(769\) 6946.78 0.325757 0.162879 0.986646i \(-0.447922\pi\)
0.162879 + 0.986646i \(0.447922\pi\)
\(770\) 0 0
\(771\) −20759.6 −0.969701
\(772\) 28100.5 1.31005
\(773\) −8416.36 −0.391611 −0.195806 0.980643i \(-0.562732\pi\)
−0.195806 + 0.980643i \(0.562732\pi\)
\(774\) −1865.83 −0.0866485
\(775\) 0 0
\(776\) −7599.16 −0.351539
\(777\) 12552.3 0.579550
\(778\) −13744.1 −0.633354
\(779\) −836.976 −0.0384952
\(780\) 0 0
\(781\) 1575.76 0.0721961
\(782\) 768.290 0.0351330
\(783\) −3084.60 −0.140785
\(784\) −4681.64 −0.213267
\(785\) 0 0
\(786\) −11406.9 −0.517647
\(787\) −12401.9 −0.561729 −0.280864 0.959747i \(-0.590621\pi\)
−0.280864 + 0.959747i \(0.590621\pi\)
\(788\) 17254.3 0.780024
\(789\) 11425.7 0.515545
\(790\) 0 0
\(791\) −442.303 −0.0198818
\(792\) 425.172 0.0190755
\(793\) −30624.7 −1.37139
\(794\) −13654.2 −0.610291
\(795\) 0 0
\(796\) −30951.0 −1.37818
\(797\) 33365.5 1.48290 0.741448 0.671010i \(-0.234139\pi\)
0.741448 + 0.671010i \(0.234139\pi\)
\(798\) 1184.56 0.0525477
\(799\) −1878.35 −0.0831682
\(800\) 0 0
\(801\) −12012.4 −0.529885
\(802\) 7921.09 0.348757
\(803\) −2390.19 −0.105041
\(804\) 9891.66 0.433895
\(805\) 0 0
\(806\) 17650.6 0.771360
\(807\) 7759.01 0.338451
\(808\) 2500.87 0.108887
\(809\) 14601.5 0.634561 0.317281 0.948332i \(-0.397230\pi\)
0.317281 + 0.948332i \(0.397230\pi\)
\(810\) 0 0
\(811\) 5860.35 0.253742 0.126871 0.991919i \(-0.459507\pi\)
0.126871 + 0.991919i \(0.459507\pi\)
\(812\) −8655.65 −0.374081
\(813\) 3196.23 0.137880
\(814\) 1139.62 0.0490709
\(815\) 0 0
\(816\) −401.871 −0.0172406
\(817\) 3735.03 0.159941
\(818\) 7578.50 0.323932
\(819\) −9408.88 −0.401432
\(820\) 0 0
\(821\) 15407.4 0.654961 0.327480 0.944858i \(-0.393800\pi\)
0.327480 + 0.944858i \(0.393800\pi\)
\(822\) −3256.80 −0.138192
\(823\) −41672.3 −1.76501 −0.882505 0.470303i \(-0.844145\pi\)
−0.882505 + 0.470303i \(0.844145\pi\)
\(824\) −358.569 −0.0151594
\(825\) 0 0
\(826\) −10843.4 −0.456767
\(827\) −15362.1 −0.645939 −0.322969 0.946409i \(-0.604681\pi\)
−0.322969 + 0.946409i \(0.604681\pi\)
\(828\) 5771.78 0.242250
\(829\) 14841.3 0.621783 0.310892 0.950445i \(-0.399372\pi\)
0.310892 + 0.950445i \(0.399372\pi\)
\(830\) 0 0
\(831\) −7404.84 −0.309111
\(832\) 4638.16 0.193268
\(833\) 1075.93 0.0447523
\(834\) −12622.3 −0.524070
\(835\) 0 0
\(836\) −371.782 −0.0153808
\(837\) 4154.51 0.171566
\(838\) 18360.0 0.756843
\(839\) 4413.86 0.181625 0.0908126 0.995868i \(-0.471054\pi\)
0.0908126 + 0.995868i \(0.471054\pi\)
\(840\) 0 0
\(841\) −11337.2 −0.464848
\(842\) 12345.4 0.505287
\(843\) 9326.50 0.381046
\(844\) −23282.0 −0.949526
\(845\) 0 0
\(846\) 4081.98 0.165888
\(847\) 16176.4 0.656232
\(848\) 15587.5 0.631225
\(849\) −19362.1 −0.782692
\(850\) 0 0
\(851\) 35416.4 1.42663
\(852\) 11816.9 0.475165
\(853\) −5775.19 −0.231816 −0.115908 0.993260i \(-0.536978\pi\)
−0.115908 + 0.993260i \(0.536978\pi\)
\(854\) 5851.15 0.234452
\(855\) 0 0
\(856\) 34867.2 1.39221
\(857\) −4100.45 −0.163441 −0.0817203 0.996655i \(-0.526041\pi\)
−0.0817203 + 0.996655i \(0.526041\pi\)
\(858\) −854.233 −0.0339896
\(859\) −9834.24 −0.390617 −0.195308 0.980742i \(-0.562571\pi\)
−0.195308 + 0.980742i \(0.562571\pi\)
\(860\) 0 0
\(861\) −1270.17 −0.0502757
\(862\) 10136.3 0.400513
\(863\) 17159.3 0.676835 0.338418 0.940996i \(-0.390108\pi\)
0.338418 + 0.940996i \(0.390108\pi\)
\(864\) 4984.10 0.196253
\(865\) 0 0
\(866\) 5421.59 0.212740
\(867\) −14646.6 −0.573732
\(868\) 11657.9 0.455870
\(869\) −1411.79 −0.0551112
\(870\) 0 0
\(871\) −45496.6 −1.76991
\(872\) 25457.2 0.988636
\(873\) 3593.67 0.139321
\(874\) 3342.26 0.129352
\(875\) 0 0
\(876\) −17924.5 −0.691338
\(877\) −8821.46 −0.339657 −0.169829 0.985474i \(-0.554321\pi\)
−0.169829 + 0.985474i \(0.554321\pi\)
\(878\) 5229.62 0.201015
\(879\) 2505.19 0.0961296
\(880\) 0 0
\(881\) −29862.0 −1.14197 −0.570986 0.820960i \(-0.693439\pi\)
−0.570986 + 0.820960i \(0.693439\pi\)
\(882\) −2338.18 −0.0892635
\(883\) 6987.51 0.266306 0.133153 0.991095i \(-0.457490\pi\)
0.133153 + 0.991095i \(0.457490\pi\)
\(884\) 2947.79 0.112155
\(885\) 0 0
\(886\) 3066.58 0.116280
\(887\) 43884.1 1.66120 0.830599 0.556871i \(-0.187998\pi\)
0.830599 + 0.556871i \(0.187998\pi\)
\(888\) 19564.7 0.739354
\(889\) 17065.0 0.643803
\(890\) 0 0
\(891\) −201.065 −0.00755998
\(892\) −10161.2 −0.381415
\(893\) −8171.33 −0.306207
\(894\) −4052.48 −0.151605
\(895\) 0 0
\(896\) 17145.4 0.639271
\(897\) −26547.3 −0.988170
\(898\) 13431.5 0.499125
\(899\) −17578.9 −0.652157
\(900\) 0 0
\(901\) −3582.31 −0.132457
\(902\) −115.319 −0.00425688
\(903\) 5668.18 0.208887
\(904\) −689.398 −0.0253640
\(905\) 0 0
\(906\) −8693.59 −0.318791
\(907\) 20572.4 0.753138 0.376569 0.926389i \(-0.377104\pi\)
0.376569 + 0.926389i \(0.377104\pi\)
\(908\) 23536.4 0.860225
\(909\) −1182.67 −0.0431538
\(910\) 0 0
\(911\) −7334.49 −0.266743 −0.133371 0.991066i \(-0.542580\pi\)
−0.133371 + 0.991066i \(0.542580\pi\)
\(912\) −1748.24 −0.0634761
\(913\) 793.929 0.0287790
\(914\) −4411.91 −0.159664
\(915\) 0 0
\(916\) −559.818 −0.0201931
\(917\) 34652.9 1.24792
\(918\) −200.709 −0.00721609
\(919\) −39912.4 −1.43263 −0.716316 0.697776i \(-0.754173\pi\)
−0.716316 + 0.697776i \(0.754173\pi\)
\(920\) 0 0
\(921\) 8045.65 0.287854
\(922\) −1113.78 −0.0397837
\(923\) −54351.8 −1.93826
\(924\) −564.206 −0.0200877
\(925\) 0 0
\(926\) −12093.5 −0.429176
\(927\) 169.569 0.00600794
\(928\) −21089.1 −0.745997
\(929\) 20640.3 0.728939 0.364470 0.931215i \(-0.381250\pi\)
0.364470 + 0.931215i \(0.381250\pi\)
\(930\) 0 0
\(931\) 4680.57 0.164768
\(932\) −22452.4 −0.789112
\(933\) 24400.9 0.856216
\(934\) 1762.75 0.0617548
\(935\) 0 0
\(936\) −14665.2 −0.512123
\(937\) 26571.7 0.926426 0.463213 0.886247i \(-0.346697\pi\)
0.463213 + 0.886247i \(0.346697\pi\)
\(938\) 8692.59 0.302583
\(939\) 23171.1 0.805281
\(940\) 0 0
\(941\) 12981.8 0.449729 0.224864 0.974390i \(-0.427806\pi\)
0.224864 + 0.974390i \(0.427806\pi\)
\(942\) −10525.1 −0.364039
\(943\) −3583.81 −0.123759
\(944\) 16003.3 0.551760
\(945\) 0 0
\(946\) 514.615 0.0176866
\(947\) 46541.8 1.59705 0.798525 0.601962i \(-0.205614\pi\)
0.798525 + 0.601962i \(0.205614\pi\)
\(948\) −10587.2 −0.362719
\(949\) 82443.5 2.82005
\(950\) 0 0
\(951\) 9661.47 0.329437
\(952\) −1289.33 −0.0438944
\(953\) −37254.2 −1.26630 −0.633149 0.774030i \(-0.718238\pi\)
−0.633149 + 0.774030i \(0.718238\pi\)
\(954\) 7784.97 0.264201
\(955\) 0 0
\(956\) 9126.11 0.308744
\(957\) 850.764 0.0287370
\(958\) 12501.5 0.421613
\(959\) 9893.77 0.333146
\(960\) 0 0
\(961\) −6114.75 −0.205255
\(962\) −39308.3 −1.31741
\(963\) −16488.8 −0.551760
\(964\) 24488.0 0.818160
\(965\) 0 0
\(966\) 5072.13 0.168937
\(967\) −31683.5 −1.05364 −0.526822 0.849976i \(-0.676616\pi\)
−0.526822 + 0.849976i \(0.676616\pi\)
\(968\) 25213.5 0.837181
\(969\) 401.779 0.0133199
\(970\) 0 0
\(971\) 27098.4 0.895600 0.447800 0.894134i \(-0.352208\pi\)
0.447800 + 0.894134i \(0.352208\pi\)
\(972\) −1507.83 −0.0497567
\(973\) 38345.1 1.26340
\(974\) −2753.84 −0.0905943
\(975\) 0 0
\(976\) −8635.46 −0.283211
\(977\) 49633.9 1.62531 0.812655 0.582745i \(-0.198021\pi\)
0.812655 + 0.582745i \(0.198021\pi\)
\(978\) −1299.25 −0.0424799
\(979\) 3313.15 0.108160
\(980\) 0 0
\(981\) −12038.8 −0.391815
\(982\) 4783.11 0.155433
\(983\) 34761.1 1.12788 0.563940 0.825816i \(-0.309285\pi\)
0.563940 + 0.825816i \(0.309285\pi\)
\(984\) −1979.76 −0.0641387
\(985\) 0 0
\(986\) 849.254 0.0274298
\(987\) −12400.6 −0.399914
\(988\) 12823.7 0.412930
\(989\) 15992.8 0.514199
\(990\) 0 0
\(991\) 19537.0 0.626249 0.313125 0.949712i \(-0.398624\pi\)
0.313125 + 0.949712i \(0.398624\pi\)
\(992\) 28404.0 0.909101
\(993\) 12593.9 0.402474
\(994\) 10384.5 0.331363
\(995\) 0 0
\(996\) 5953.82 0.189412
\(997\) 33389.3 1.06063 0.530315 0.847801i \(-0.322074\pi\)
0.530315 + 0.847801i \(0.322074\pi\)
\(998\) −424.646 −0.0134689
\(999\) −9252.20 −0.293020
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 1875.4.a.g.1.9 14
5.4 even 2 1875.4.a.f.1.6 14
25.6 even 5 75.4.g.b.61.3 yes 28
25.21 even 5 75.4.g.b.16.3 28
75.56 odd 10 225.4.h.a.136.5 28
75.71 odd 10 225.4.h.a.91.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.4.g.b.16.3 28 25.21 even 5
75.4.g.b.61.3 yes 28 25.6 even 5
225.4.h.a.91.5 28 75.71 odd 10
225.4.h.a.136.5 28 75.56 odd 10
1875.4.a.f.1.6 14 5.4 even 2
1875.4.a.g.1.9 14 1.1 even 1 trivial