Properties

Label 6003.2.a.m.1.8
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-1.05971\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.05971 q^{2} -0.877023 q^{4} +1.30384 q^{5} +0.720797 q^{7} -3.04880 q^{8} +O(q^{10})\) \(q+1.05971 q^{2} -0.877023 q^{4} +1.30384 q^{5} +0.720797 q^{7} -3.04880 q^{8} +1.38169 q^{10} -4.26781 q^{11} +6.49237 q^{13} +0.763833 q^{14} -1.47678 q^{16} -1.60761 q^{17} +0.0676063 q^{19} -1.14350 q^{20} -4.52262 q^{22} -1.00000 q^{23} -3.30000 q^{25} +6.88000 q^{26} -0.632156 q^{28} +1.00000 q^{29} -3.80124 q^{31} +4.53264 q^{32} -1.70359 q^{34} +0.939804 q^{35} -3.80081 q^{37} +0.0716428 q^{38} -3.97515 q^{40} +0.467762 q^{41} +0.971410 q^{43} +3.74296 q^{44} -1.05971 q^{46} -7.97915 q^{47} -6.48045 q^{49} -3.49703 q^{50} -5.69396 q^{52} -13.3791 q^{53} -5.56454 q^{55} -2.19756 q^{56} +1.05971 q^{58} +4.90374 q^{59} +7.29114 q^{61} -4.02820 q^{62} +7.75683 q^{64} +8.46502 q^{65} +13.6988 q^{67} +1.40991 q^{68} +0.995916 q^{70} +0.843676 q^{71} -3.56146 q^{73} -4.02774 q^{74} -0.0592923 q^{76} -3.07622 q^{77} +3.50616 q^{79} -1.92549 q^{80} +0.495690 q^{82} +8.90808 q^{83} -2.09606 q^{85} +1.02941 q^{86} +13.0117 q^{88} -15.1294 q^{89} +4.67968 q^{91} +0.877023 q^{92} -8.45555 q^{94} +0.0881479 q^{95} +0.847630 q^{97} -6.86737 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05971 0.749325 0.374663 0.927161i \(-0.377759\pi\)
0.374663 + 0.927161i \(0.377759\pi\)
\(3\) 0 0
\(4\) −0.877023 −0.438512
\(5\) 1.30384 0.583095 0.291548 0.956556i \(-0.405830\pi\)
0.291548 + 0.956556i \(0.405830\pi\)
\(6\) 0 0
\(7\) 0.720797 0.272436 0.136218 0.990679i \(-0.456505\pi\)
0.136218 + 0.990679i \(0.456505\pi\)
\(8\) −3.04880 −1.07791
\(9\) 0 0
\(10\) 1.38169 0.436928
\(11\) −4.26781 −1.28679 −0.643396 0.765534i \(-0.722475\pi\)
−0.643396 + 0.765534i \(0.722475\pi\)
\(12\) 0 0
\(13\) 6.49237 1.80066 0.900330 0.435208i \(-0.143325\pi\)
0.900330 + 0.435208i \(0.143325\pi\)
\(14\) 0.763833 0.204143
\(15\) 0 0
\(16\) −1.47678 −0.369196
\(17\) −1.60761 −0.389902 −0.194951 0.980813i \(-0.562455\pi\)
−0.194951 + 0.980813i \(0.562455\pi\)
\(18\) 0 0
\(19\) 0.0676063 0.0155100 0.00775498 0.999970i \(-0.497531\pi\)
0.00775498 + 0.999970i \(0.497531\pi\)
\(20\) −1.14350 −0.255694
\(21\) 0 0
\(22\) −4.52262 −0.964226
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −3.30000 −0.660000
\(26\) 6.88000 1.34928
\(27\) 0 0
\(28\) −0.632156 −0.119466
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −3.80124 −0.682723 −0.341362 0.939932i \(-0.610888\pi\)
−0.341362 + 0.939932i \(0.610888\pi\)
\(32\) 4.53264 0.801265
\(33\) 0 0
\(34\) −1.70359 −0.292163
\(35\) 0.939804 0.158856
\(36\) 0 0
\(37\) −3.80081 −0.624849 −0.312425 0.949943i \(-0.601141\pi\)
−0.312425 + 0.949943i \(0.601141\pi\)
\(38\) 0.0716428 0.0116220
\(39\) 0 0
\(40\) −3.97515 −0.628526
\(41\) 0.467762 0.0730521 0.0365261 0.999333i \(-0.488371\pi\)
0.0365261 + 0.999333i \(0.488371\pi\)
\(42\) 0 0
\(43\) 0.971410 0.148139 0.0740693 0.997253i \(-0.476401\pi\)
0.0740693 + 0.997253i \(0.476401\pi\)
\(44\) 3.74296 0.564273
\(45\) 0 0
\(46\) −1.05971 −0.156245
\(47\) −7.97915 −1.16388 −0.581939 0.813232i \(-0.697706\pi\)
−0.581939 + 0.813232i \(0.697706\pi\)
\(48\) 0 0
\(49\) −6.48045 −0.925779
\(50\) −3.49703 −0.494555
\(51\) 0 0
\(52\) −5.69396 −0.789610
\(53\) −13.3791 −1.83776 −0.918881 0.394535i \(-0.870906\pi\)
−0.918881 + 0.394535i \(0.870906\pi\)
\(54\) 0 0
\(55\) −5.56454 −0.750322
\(56\) −2.19756 −0.293662
\(57\) 0 0
\(58\) 1.05971 0.139146
\(59\) 4.90374 0.638413 0.319206 0.947685i \(-0.396584\pi\)
0.319206 + 0.947685i \(0.396584\pi\)
\(60\) 0 0
\(61\) 7.29114 0.933534 0.466767 0.884380i \(-0.345419\pi\)
0.466767 + 0.884380i \(0.345419\pi\)
\(62\) −4.02820 −0.511582
\(63\) 0 0
\(64\) 7.75683 0.969604
\(65\) 8.46502 1.04996
\(66\) 0 0
\(67\) 13.6988 1.67358 0.836788 0.547526i \(-0.184430\pi\)
0.836788 + 0.547526i \(0.184430\pi\)
\(68\) 1.40991 0.170977
\(69\) 0 0
\(70\) 0.995916 0.119035
\(71\) 0.843676 0.100126 0.0500630 0.998746i \(-0.484058\pi\)
0.0500630 + 0.998746i \(0.484058\pi\)
\(72\) 0 0
\(73\) −3.56146 −0.416837 −0.208419 0.978040i \(-0.566832\pi\)
−0.208419 + 0.978040i \(0.566832\pi\)
\(74\) −4.02774 −0.468215
\(75\) 0 0
\(76\) −0.0592923 −0.00680130
\(77\) −3.07622 −0.350568
\(78\) 0 0
\(79\) 3.50616 0.394474 0.197237 0.980356i \(-0.436803\pi\)
0.197237 + 0.980356i \(0.436803\pi\)
\(80\) −1.92549 −0.215276
\(81\) 0 0
\(82\) 0.495690 0.0547398
\(83\) 8.90808 0.977789 0.488894 0.872343i \(-0.337400\pi\)
0.488894 + 0.872343i \(0.337400\pi\)
\(84\) 0 0
\(85\) −2.09606 −0.227350
\(86\) 1.02941 0.111004
\(87\) 0 0
\(88\) 13.0117 1.38705
\(89\) −15.1294 −1.60371 −0.801856 0.597517i \(-0.796154\pi\)
−0.801856 + 0.597517i \(0.796154\pi\)
\(90\) 0 0
\(91\) 4.67968 0.490564
\(92\) 0.877023 0.0914360
\(93\) 0 0
\(94\) −8.45555 −0.872124
\(95\) 0.0881479 0.00904378
\(96\) 0 0
\(97\) 0.847630 0.0860637 0.0430319 0.999074i \(-0.486298\pi\)
0.0430319 + 0.999074i \(0.486298\pi\)
\(98\) −6.86737 −0.693709
\(99\) 0 0
\(100\) 2.89418 0.289418
\(101\) 4.21499 0.419407 0.209704 0.977765i \(-0.432750\pi\)
0.209704 + 0.977765i \(0.432750\pi\)
\(102\) 0 0
\(103\) −3.25548 −0.320772 −0.160386 0.987054i \(-0.551274\pi\)
−0.160386 + 0.987054i \(0.551274\pi\)
\(104\) −19.7939 −1.94095
\(105\) 0 0
\(106\) −14.1779 −1.37708
\(107\) −9.91828 −0.958836 −0.479418 0.877587i \(-0.659152\pi\)
−0.479418 + 0.877587i \(0.659152\pi\)
\(108\) 0 0
\(109\) −14.9445 −1.43142 −0.715711 0.698396i \(-0.753897\pi\)
−0.715711 + 0.698396i \(0.753897\pi\)
\(110\) −5.89677 −0.562235
\(111\) 0 0
\(112\) −1.06446 −0.100582
\(113\) −9.05430 −0.851757 −0.425879 0.904780i \(-0.640035\pi\)
−0.425879 + 0.904780i \(0.640035\pi\)
\(114\) 0 0
\(115\) −1.30384 −0.121584
\(116\) −0.877023 −0.0814296
\(117\) 0 0
\(118\) 5.19653 0.478379
\(119\) −1.15876 −0.106223
\(120\) 0 0
\(121\) 7.21416 0.655833
\(122\) 7.72646 0.699521
\(123\) 0 0
\(124\) 3.33378 0.299382
\(125\) −10.8219 −0.967938
\(126\) 0 0
\(127\) −16.8234 −1.49284 −0.746420 0.665476i \(-0.768229\pi\)
−0.746420 + 0.665476i \(0.768229\pi\)
\(128\) −0.845320 −0.0747164
\(129\) 0 0
\(130\) 8.97043 0.786759
\(131\) −20.0112 −1.74838 −0.874192 0.485581i \(-0.838608\pi\)
−0.874192 + 0.485581i \(0.838608\pi\)
\(132\) 0 0
\(133\) 0.0487304 0.00422547
\(134\) 14.5167 1.25405
\(135\) 0 0
\(136\) 4.90127 0.420280
\(137\) 17.5827 1.50219 0.751097 0.660192i \(-0.229525\pi\)
0.751097 + 0.660192i \(0.229525\pi\)
\(138\) 0 0
\(139\) −11.2785 −0.956634 −0.478317 0.878187i \(-0.658753\pi\)
−0.478317 + 0.878187i \(0.658753\pi\)
\(140\) −0.824230 −0.0696602
\(141\) 0 0
\(142\) 0.894049 0.0750269
\(143\) −27.7082 −2.31707
\(144\) 0 0
\(145\) 1.30384 0.108278
\(146\) −3.77410 −0.312347
\(147\) 0 0
\(148\) 3.33340 0.274004
\(149\) −8.68520 −0.711519 −0.355760 0.934578i \(-0.615778\pi\)
−0.355760 + 0.934578i \(0.615778\pi\)
\(150\) 0 0
\(151\) −3.77830 −0.307474 −0.153737 0.988112i \(-0.549131\pi\)
−0.153737 + 0.988112i \(0.549131\pi\)
\(152\) −0.206118 −0.0167184
\(153\) 0 0
\(154\) −3.25989 −0.262689
\(155\) −4.95621 −0.398093
\(156\) 0 0
\(157\) −22.4357 −1.79056 −0.895280 0.445503i \(-0.853025\pi\)
−0.895280 + 0.445503i \(0.853025\pi\)
\(158\) 3.71550 0.295589
\(159\) 0 0
\(160\) 5.90984 0.467214
\(161\) −0.720797 −0.0568068
\(162\) 0 0
\(163\) 9.58430 0.750701 0.375350 0.926883i \(-0.377522\pi\)
0.375350 + 0.926883i \(0.377522\pi\)
\(164\) −0.410238 −0.0320342
\(165\) 0 0
\(166\) 9.43994 0.732682
\(167\) 22.7911 1.76363 0.881816 0.471594i \(-0.156321\pi\)
0.881816 + 0.471594i \(0.156321\pi\)
\(168\) 0 0
\(169\) 29.1509 2.24238
\(170\) −2.22121 −0.170359
\(171\) 0 0
\(172\) −0.851949 −0.0649605
\(173\) −3.11958 −0.237177 −0.118589 0.992943i \(-0.537837\pi\)
−0.118589 + 0.992943i \(0.537837\pi\)
\(174\) 0 0
\(175\) −2.37863 −0.179808
\(176\) 6.30262 0.475078
\(177\) 0 0
\(178\) −16.0327 −1.20170
\(179\) 4.43515 0.331499 0.165749 0.986168i \(-0.446996\pi\)
0.165749 + 0.986168i \(0.446996\pi\)
\(180\) 0 0
\(181\) 7.57878 0.563326 0.281663 0.959513i \(-0.409114\pi\)
0.281663 + 0.959513i \(0.409114\pi\)
\(182\) 4.95909 0.367592
\(183\) 0 0
\(184\) 3.04880 0.224760
\(185\) −4.95565 −0.364347
\(186\) 0 0
\(187\) 6.86095 0.501722
\(188\) 6.99790 0.510374
\(189\) 0 0
\(190\) 0.0934108 0.00677673
\(191\) −23.8728 −1.72738 −0.863688 0.504026i \(-0.831851\pi\)
−0.863688 + 0.504026i \(0.831851\pi\)
\(192\) 0 0
\(193\) −23.7901 −1.71245 −0.856224 0.516605i \(-0.827196\pi\)
−0.856224 + 0.516605i \(0.827196\pi\)
\(194\) 0.898238 0.0644897
\(195\) 0 0
\(196\) 5.68351 0.405965
\(197\) −10.2899 −0.733125 −0.366562 0.930393i \(-0.619465\pi\)
−0.366562 + 0.930393i \(0.619465\pi\)
\(198\) 0 0
\(199\) 6.69895 0.474876 0.237438 0.971403i \(-0.423692\pi\)
0.237438 + 0.971403i \(0.423692\pi\)
\(200\) 10.0610 0.711423
\(201\) 0 0
\(202\) 4.46665 0.314273
\(203\) 0.720797 0.0505900
\(204\) 0 0
\(205\) 0.609887 0.0425964
\(206\) −3.44986 −0.240363
\(207\) 0 0
\(208\) −9.58783 −0.664796
\(209\) −0.288531 −0.0199581
\(210\) 0 0
\(211\) 19.4730 1.34058 0.670288 0.742101i \(-0.266170\pi\)
0.670288 + 0.742101i \(0.266170\pi\)
\(212\) 11.7338 0.805880
\(213\) 0 0
\(214\) −10.5105 −0.718480
\(215\) 1.26656 0.0863789
\(216\) 0 0
\(217\) −2.73992 −0.185998
\(218\) −15.8368 −1.07260
\(219\) 0 0
\(220\) 4.88023 0.329025
\(221\) −10.4372 −0.702081
\(222\) 0 0
\(223\) 5.45268 0.365138 0.182569 0.983193i \(-0.441559\pi\)
0.182569 + 0.983193i \(0.441559\pi\)
\(224\) 3.26711 0.218293
\(225\) 0 0
\(226\) −9.59490 −0.638243
\(227\) −12.7976 −0.849407 −0.424704 0.905332i \(-0.639622\pi\)
−0.424704 + 0.905332i \(0.639622\pi\)
\(228\) 0 0
\(229\) −17.9481 −1.18604 −0.593021 0.805187i \(-0.702065\pi\)
−0.593021 + 0.805187i \(0.702065\pi\)
\(230\) −1.38169 −0.0911058
\(231\) 0 0
\(232\) −3.04880 −0.200163
\(233\) −24.8070 −1.62516 −0.812579 0.582851i \(-0.801937\pi\)
−0.812579 + 0.582851i \(0.801937\pi\)
\(234\) 0 0
\(235\) −10.4035 −0.678652
\(236\) −4.30070 −0.279952
\(237\) 0 0
\(238\) −1.22794 −0.0795957
\(239\) −6.47432 −0.418789 −0.209394 0.977831i \(-0.567149\pi\)
−0.209394 + 0.977831i \(0.567149\pi\)
\(240\) 0 0
\(241\) −1.06870 −0.0688413 −0.0344207 0.999407i \(-0.510959\pi\)
−0.0344207 + 0.999407i \(0.510959\pi\)
\(242\) 7.64489 0.491432
\(243\) 0 0
\(244\) −6.39450 −0.409366
\(245\) −8.44948 −0.539817
\(246\) 0 0
\(247\) 0.438925 0.0279282
\(248\) 11.5892 0.735916
\(249\) 0 0
\(250\) −11.4680 −0.725300
\(251\) 10.6611 0.672920 0.336460 0.941698i \(-0.390770\pi\)
0.336460 + 0.941698i \(0.390770\pi\)
\(252\) 0 0
\(253\) 4.26781 0.268315
\(254\) −17.8279 −1.11862
\(255\) 0 0
\(256\) −16.4095 −1.02559
\(257\) −26.4765 −1.65156 −0.825781 0.563991i \(-0.809265\pi\)
−0.825781 + 0.563991i \(0.809265\pi\)
\(258\) 0 0
\(259\) −2.73961 −0.170231
\(260\) −7.42402 −0.460418
\(261\) 0 0
\(262\) −21.2059 −1.31011
\(263\) −3.04107 −0.187520 −0.0937602 0.995595i \(-0.529889\pi\)
−0.0937602 + 0.995595i \(0.529889\pi\)
\(264\) 0 0
\(265\) −17.4442 −1.07159
\(266\) 0.0516399 0.00316625
\(267\) 0 0
\(268\) −12.0142 −0.733883
\(269\) 30.1319 1.83718 0.918589 0.395215i \(-0.129330\pi\)
0.918589 + 0.395215i \(0.129330\pi\)
\(270\) 0 0
\(271\) 18.0654 1.09740 0.548699 0.836020i \(-0.315123\pi\)
0.548699 + 0.836020i \(0.315123\pi\)
\(272\) 2.37409 0.143950
\(273\) 0 0
\(274\) 18.6325 1.12563
\(275\) 14.0838 0.849283
\(276\) 0 0
\(277\) 15.0741 0.905712 0.452856 0.891584i \(-0.350405\pi\)
0.452856 + 0.891584i \(0.350405\pi\)
\(278\) −11.9519 −0.716830
\(279\) 0 0
\(280\) −2.86527 −0.171233
\(281\) −17.4085 −1.03850 −0.519252 0.854621i \(-0.673789\pi\)
−0.519252 + 0.854621i \(0.673789\pi\)
\(282\) 0 0
\(283\) 27.6295 1.64240 0.821202 0.570638i \(-0.193304\pi\)
0.821202 + 0.570638i \(0.193304\pi\)
\(284\) −0.739924 −0.0439064
\(285\) 0 0
\(286\) −29.3625 −1.73624
\(287\) 0.337161 0.0199020
\(288\) 0 0
\(289\) −14.4156 −0.847977
\(290\) 1.38169 0.0811355
\(291\) 0 0
\(292\) 3.12348 0.182788
\(293\) −9.65321 −0.563946 −0.281973 0.959422i \(-0.590989\pi\)
−0.281973 + 0.959422i \(0.590989\pi\)
\(294\) 0 0
\(295\) 6.39370 0.372256
\(296\) 11.5879 0.673533
\(297\) 0 0
\(298\) −9.20376 −0.533159
\(299\) −6.49237 −0.375464
\(300\) 0 0
\(301\) 0.700189 0.0403582
\(302\) −4.00389 −0.230398
\(303\) 0 0
\(304\) −0.0998399 −0.00572621
\(305\) 9.50648 0.544339
\(306\) 0 0
\(307\) 23.4872 1.34048 0.670242 0.742143i \(-0.266190\pi\)
0.670242 + 0.742143i \(0.266190\pi\)
\(308\) 2.69792 0.153728
\(309\) 0 0
\(310\) −5.25213 −0.298301
\(311\) −10.2227 −0.579679 −0.289839 0.957075i \(-0.593602\pi\)
−0.289839 + 0.957075i \(0.593602\pi\)
\(312\) 0 0
\(313\) 4.95500 0.280073 0.140036 0.990146i \(-0.455278\pi\)
0.140036 + 0.990146i \(0.455278\pi\)
\(314\) −23.7752 −1.34171
\(315\) 0 0
\(316\) −3.07498 −0.172981
\(317\) −6.20695 −0.348617 −0.174309 0.984691i \(-0.555769\pi\)
−0.174309 + 0.984691i \(0.555769\pi\)
\(318\) 0 0
\(319\) −4.26781 −0.238951
\(320\) 10.1137 0.565372
\(321\) 0 0
\(322\) −0.763833 −0.0425667
\(323\) −0.108684 −0.00604736
\(324\) 0 0
\(325\) −21.4248 −1.18844
\(326\) 10.1565 0.562519
\(327\) 0 0
\(328\) −1.42611 −0.0787439
\(329\) −5.75135 −0.317082
\(330\) 0 0
\(331\) 4.70041 0.258358 0.129179 0.991621i \(-0.458766\pi\)
0.129179 + 0.991621i \(0.458766\pi\)
\(332\) −7.81259 −0.428772
\(333\) 0 0
\(334\) 24.1519 1.32153
\(335\) 17.8611 0.975855
\(336\) 0 0
\(337\) −9.18682 −0.500438 −0.250219 0.968189i \(-0.580503\pi\)
−0.250219 + 0.968189i \(0.580503\pi\)
\(338\) 30.8914 1.68027
\(339\) 0 0
\(340\) 1.83830 0.0996956
\(341\) 16.2230 0.878523
\(342\) 0 0
\(343\) −9.71667 −0.524651
\(344\) −2.96163 −0.159681
\(345\) 0 0
\(346\) −3.30584 −0.177723
\(347\) 19.5451 1.04923 0.524617 0.851339i \(-0.324209\pi\)
0.524617 + 0.851339i \(0.324209\pi\)
\(348\) 0 0
\(349\) 35.7643 1.91442 0.957209 0.289398i \(-0.0934551\pi\)
0.957209 + 0.289398i \(0.0934551\pi\)
\(350\) −2.52065 −0.134734
\(351\) 0 0
\(352\) −19.3444 −1.03106
\(353\) −17.5958 −0.936532 −0.468266 0.883588i \(-0.655121\pi\)
−0.468266 + 0.883588i \(0.655121\pi\)
\(354\) 0 0
\(355\) 1.10002 0.0583830
\(356\) 13.2688 0.703246
\(357\) 0 0
\(358\) 4.69995 0.248400
\(359\) −5.45515 −0.287912 −0.143956 0.989584i \(-0.545982\pi\)
−0.143956 + 0.989584i \(0.545982\pi\)
\(360\) 0 0
\(361\) −18.9954 −0.999759
\(362\) 8.03128 0.422115
\(363\) 0 0
\(364\) −4.10419 −0.215118
\(365\) −4.64358 −0.243056
\(366\) 0 0
\(367\) 7.87986 0.411326 0.205663 0.978623i \(-0.434065\pi\)
0.205663 + 0.978623i \(0.434065\pi\)
\(368\) 1.47678 0.0769827
\(369\) 0 0
\(370\) −5.25153 −0.273014
\(371\) −9.64362 −0.500672
\(372\) 0 0
\(373\) −12.3211 −0.637961 −0.318980 0.947761i \(-0.603340\pi\)
−0.318980 + 0.947761i \(0.603340\pi\)
\(374\) 7.27059 0.375953
\(375\) 0 0
\(376\) 24.3268 1.25456
\(377\) 6.49237 0.334374
\(378\) 0 0
\(379\) 21.0221 1.07983 0.539916 0.841719i \(-0.318456\pi\)
0.539916 + 0.841719i \(0.318456\pi\)
\(380\) −0.0773078 −0.00396580
\(381\) 0 0
\(382\) −25.2982 −1.29437
\(383\) 26.7325 1.36597 0.682983 0.730434i \(-0.260682\pi\)
0.682983 + 0.730434i \(0.260682\pi\)
\(384\) 0 0
\(385\) −4.01090 −0.204414
\(386\) −25.2105 −1.28318
\(387\) 0 0
\(388\) −0.743391 −0.0377400
\(389\) −18.2034 −0.922949 −0.461474 0.887154i \(-0.652679\pi\)
−0.461474 + 0.887154i \(0.652679\pi\)
\(390\) 0 0
\(391\) 1.60761 0.0813002
\(392\) 19.7576 0.997909
\(393\) 0 0
\(394\) −10.9043 −0.549349
\(395\) 4.57147 0.230016
\(396\) 0 0
\(397\) −14.9475 −0.750193 −0.375096 0.926986i \(-0.622390\pi\)
−0.375096 + 0.926986i \(0.622390\pi\)
\(398\) 7.09892 0.355837
\(399\) 0 0
\(400\) 4.87339 0.243669
\(401\) −5.93728 −0.296494 −0.148247 0.988950i \(-0.547363\pi\)
−0.148247 + 0.988950i \(0.547363\pi\)
\(402\) 0 0
\(403\) −24.6791 −1.22935
\(404\) −3.69665 −0.183915
\(405\) 0 0
\(406\) 0.763833 0.0379084
\(407\) 16.2211 0.804051
\(408\) 0 0
\(409\) 28.1625 1.39255 0.696274 0.717776i \(-0.254840\pi\)
0.696274 + 0.717776i \(0.254840\pi\)
\(410\) 0.646301 0.0319185
\(411\) 0 0
\(412\) 2.85514 0.140662
\(413\) 3.53460 0.173926
\(414\) 0 0
\(415\) 11.6147 0.570144
\(416\) 29.4276 1.44281
\(417\) 0 0
\(418\) −0.305758 −0.0149551
\(419\) 15.7587 0.769862 0.384931 0.922945i \(-0.374225\pi\)
0.384931 + 0.922945i \(0.374225\pi\)
\(420\) 0 0
\(421\) −37.5081 −1.82803 −0.914017 0.405676i \(-0.867036\pi\)
−0.914017 + 0.405676i \(0.867036\pi\)
\(422\) 20.6357 1.00453
\(423\) 0 0
\(424\) 40.7902 1.98095
\(425\) 5.30510 0.257335
\(426\) 0 0
\(427\) 5.25543 0.254328
\(428\) 8.69856 0.420461
\(429\) 0 0
\(430\) 1.34218 0.0647259
\(431\) −10.7335 −0.517013 −0.258507 0.966009i \(-0.583230\pi\)
−0.258507 + 0.966009i \(0.583230\pi\)
\(432\) 0 0
\(433\) 29.9000 1.43690 0.718452 0.695576i \(-0.244851\pi\)
0.718452 + 0.695576i \(0.244851\pi\)
\(434\) −2.90351 −0.139373
\(435\) 0 0
\(436\) 13.1067 0.627696
\(437\) −0.0676063 −0.00323405
\(438\) 0 0
\(439\) 27.6423 1.31930 0.659648 0.751575i \(-0.270705\pi\)
0.659648 + 0.751575i \(0.270705\pi\)
\(440\) 16.9652 0.808782
\(441\) 0 0
\(442\) −11.0603 −0.526087
\(443\) −16.5336 −0.785534 −0.392767 0.919638i \(-0.628482\pi\)
−0.392767 + 0.919638i \(0.628482\pi\)
\(444\) 0 0
\(445\) −19.7263 −0.935117
\(446\) 5.77823 0.273607
\(447\) 0 0
\(448\) 5.59110 0.264155
\(449\) −15.6126 −0.736805 −0.368403 0.929666i \(-0.620095\pi\)
−0.368403 + 0.929666i \(0.620095\pi\)
\(450\) 0 0
\(451\) −1.99632 −0.0940029
\(452\) 7.94084 0.373506
\(453\) 0 0
\(454\) −13.5617 −0.636482
\(455\) 6.10156 0.286045
\(456\) 0 0
\(457\) −39.1168 −1.82981 −0.914903 0.403674i \(-0.867733\pi\)
−0.914903 + 0.403674i \(0.867733\pi\)
\(458\) −19.0197 −0.888731
\(459\) 0 0
\(460\) 1.14350 0.0533159
\(461\) −27.3047 −1.27171 −0.635854 0.771810i \(-0.719352\pi\)
−0.635854 + 0.771810i \(0.719352\pi\)
\(462\) 0 0
\(463\) 25.1953 1.17093 0.585463 0.810699i \(-0.300913\pi\)
0.585463 + 0.810699i \(0.300913\pi\)
\(464\) −1.47678 −0.0685580
\(465\) 0 0
\(466\) −26.2881 −1.21777
\(467\) −10.5362 −0.487556 −0.243778 0.969831i \(-0.578387\pi\)
−0.243778 + 0.969831i \(0.578387\pi\)
\(468\) 0 0
\(469\) 9.87407 0.455942
\(470\) −11.0247 −0.508531
\(471\) 0 0
\(472\) −14.9505 −0.688154
\(473\) −4.14579 −0.190624
\(474\) 0 0
\(475\) −0.223101 −0.0102366
\(476\) 1.01626 0.0465801
\(477\) 0 0
\(478\) −6.86087 −0.313809
\(479\) −22.6259 −1.03380 −0.516902 0.856045i \(-0.672915\pi\)
−0.516902 + 0.856045i \(0.672915\pi\)
\(480\) 0 0
\(481\) −24.6763 −1.12514
\(482\) −1.13251 −0.0515845
\(483\) 0 0
\(484\) −6.32699 −0.287590
\(485\) 1.10517 0.0501834
\(486\) 0 0
\(487\) −1.33179 −0.0603490 −0.0301745 0.999545i \(-0.509606\pi\)
−0.0301745 + 0.999545i \(0.509606\pi\)
\(488\) −22.2292 −1.00627
\(489\) 0 0
\(490\) −8.95396 −0.404499
\(491\) 37.5483 1.69453 0.847265 0.531170i \(-0.178247\pi\)
0.847265 + 0.531170i \(0.178247\pi\)
\(492\) 0 0
\(493\) −1.60761 −0.0724030
\(494\) 0.465132 0.0209273
\(495\) 0 0
\(496\) 5.61361 0.252059
\(497\) 0.608119 0.0272779
\(498\) 0 0
\(499\) −34.2219 −1.53198 −0.765992 0.642850i \(-0.777752\pi\)
−0.765992 + 0.642850i \(0.777752\pi\)
\(500\) 9.49104 0.424452
\(501\) 0 0
\(502\) 11.2976 0.504236
\(503\) −28.4032 −1.26643 −0.633217 0.773974i \(-0.718266\pi\)
−0.633217 + 0.773974i \(0.718266\pi\)
\(504\) 0 0
\(505\) 5.49568 0.244554
\(506\) 4.52262 0.201055
\(507\) 0 0
\(508\) 14.7546 0.654627
\(509\) 6.08138 0.269553 0.134776 0.990876i \(-0.456968\pi\)
0.134776 + 0.990876i \(0.456968\pi\)
\(510\) 0 0
\(511\) −2.56709 −0.113561
\(512\) −15.6986 −0.693785
\(513\) 0 0
\(514\) −28.0573 −1.23756
\(515\) −4.24463 −0.187041
\(516\) 0 0
\(517\) 34.0535 1.49767
\(518\) −2.90318 −0.127559
\(519\) 0 0
\(520\) −25.8081 −1.13176
\(521\) 38.6489 1.69324 0.846619 0.532200i \(-0.178634\pi\)
0.846619 + 0.532200i \(0.178634\pi\)
\(522\) 0 0
\(523\) 2.97908 0.130266 0.0651331 0.997877i \(-0.479253\pi\)
0.0651331 + 0.997877i \(0.479253\pi\)
\(524\) 17.5503 0.766686
\(525\) 0 0
\(526\) −3.22264 −0.140514
\(527\) 6.11090 0.266195
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −18.4857 −0.802970
\(531\) 0 0
\(532\) −0.0427377 −0.00185292
\(533\) 3.03688 0.131542
\(534\) 0 0
\(535\) −12.9319 −0.559093
\(536\) −41.7649 −1.80397
\(537\) 0 0
\(538\) 31.9310 1.37664
\(539\) 27.6573 1.19128
\(540\) 0 0
\(541\) 26.1703 1.12515 0.562574 0.826747i \(-0.309811\pi\)
0.562574 + 0.826747i \(0.309811\pi\)
\(542\) 19.1441 0.822308
\(543\) 0 0
\(544\) −7.28670 −0.312415
\(545\) −19.4852 −0.834656
\(546\) 0 0
\(547\) 11.0205 0.471204 0.235602 0.971850i \(-0.424294\pi\)
0.235602 + 0.971850i \(0.424294\pi\)
\(548\) −15.4205 −0.658729
\(549\) 0 0
\(550\) 14.9246 0.636389
\(551\) 0.0676063 0.00288013
\(552\) 0 0
\(553\) 2.52723 0.107469
\(554\) 15.9741 0.678673
\(555\) 0 0
\(556\) 9.89155 0.419495
\(557\) 26.2157 1.11080 0.555398 0.831585i \(-0.312566\pi\)
0.555398 + 0.831585i \(0.312566\pi\)
\(558\) 0 0
\(559\) 6.30675 0.266747
\(560\) −1.38789 −0.0586489
\(561\) 0 0
\(562\) −18.4479 −0.778177
\(563\) 39.8761 1.68058 0.840288 0.542140i \(-0.182386\pi\)
0.840288 + 0.542140i \(0.182386\pi\)
\(564\) 0 0
\(565\) −11.8054 −0.496656
\(566\) 29.2791 1.23069
\(567\) 0 0
\(568\) −2.57220 −0.107927
\(569\) 15.2160 0.637886 0.318943 0.947774i \(-0.396672\pi\)
0.318943 + 0.947774i \(0.396672\pi\)
\(570\) 0 0
\(571\) −11.9807 −0.501377 −0.250688 0.968068i \(-0.580657\pi\)
−0.250688 + 0.968068i \(0.580657\pi\)
\(572\) 24.3007 1.01606
\(573\) 0 0
\(574\) 0.357292 0.0149131
\(575\) 3.30000 0.137620
\(576\) 0 0
\(577\) −21.5518 −0.897212 −0.448606 0.893730i \(-0.648079\pi\)
−0.448606 + 0.893730i \(0.648079\pi\)
\(578\) −15.2763 −0.635410
\(579\) 0 0
\(580\) −1.14350 −0.0474812
\(581\) 6.42092 0.266384
\(582\) 0 0
\(583\) 57.0994 2.36482
\(584\) 10.8582 0.449314
\(585\) 0 0
\(586\) −10.2296 −0.422579
\(587\) 21.9895 0.907604 0.453802 0.891102i \(-0.350067\pi\)
0.453802 + 0.891102i \(0.350067\pi\)
\(588\) 0 0
\(589\) −0.256988 −0.0105890
\(590\) 6.77544 0.278940
\(591\) 0 0
\(592\) 5.61297 0.230692
\(593\) 18.0058 0.739411 0.369706 0.929149i \(-0.379459\pi\)
0.369706 + 0.929149i \(0.379459\pi\)
\(594\) 0 0
\(595\) −1.51084 −0.0619382
\(596\) 7.61712 0.312009
\(597\) 0 0
\(598\) −6.88000 −0.281344
\(599\) −42.1452 −1.72201 −0.861004 0.508599i \(-0.830164\pi\)
−0.861004 + 0.508599i \(0.830164\pi\)
\(600\) 0 0
\(601\) −1.18690 −0.0484145 −0.0242073 0.999707i \(-0.507706\pi\)
−0.0242073 + 0.999707i \(0.507706\pi\)
\(602\) 0.741995 0.0302414
\(603\) 0 0
\(604\) 3.31366 0.134831
\(605\) 9.40612 0.382413
\(606\) 0 0
\(607\) −21.2693 −0.863296 −0.431648 0.902042i \(-0.642068\pi\)
−0.431648 + 0.902042i \(0.642068\pi\)
\(608\) 0.306435 0.0124276
\(609\) 0 0
\(610\) 10.0741 0.407887
\(611\) −51.8036 −2.09575
\(612\) 0 0
\(613\) 3.41464 0.137916 0.0689580 0.997620i \(-0.478033\pi\)
0.0689580 + 0.997620i \(0.478033\pi\)
\(614\) 24.8895 1.00446
\(615\) 0 0
\(616\) 9.37878 0.377882
\(617\) 3.56041 0.143337 0.0716684 0.997429i \(-0.477168\pi\)
0.0716684 + 0.997429i \(0.477168\pi\)
\(618\) 0 0
\(619\) −19.6807 −0.791033 −0.395516 0.918459i \(-0.629434\pi\)
−0.395516 + 0.918459i \(0.629434\pi\)
\(620\) 4.34671 0.174568
\(621\) 0 0
\(622\) −10.8331 −0.434368
\(623\) −10.9052 −0.436908
\(624\) 0 0
\(625\) 2.39000 0.0956000
\(626\) 5.25084 0.209866
\(627\) 0 0
\(628\) 19.6766 0.785182
\(629\) 6.11021 0.243630
\(630\) 0 0
\(631\) −39.8399 −1.58600 −0.793000 0.609221i \(-0.791482\pi\)
−0.793000 + 0.609221i \(0.791482\pi\)
\(632\) −10.6896 −0.425208
\(633\) 0 0
\(634\) −6.57755 −0.261228
\(635\) −21.9351 −0.870467
\(636\) 0 0
\(637\) −42.0735 −1.66701
\(638\) −4.52262 −0.179052
\(639\) 0 0
\(640\) −1.10216 −0.0435668
\(641\) −5.19938 −0.205363 −0.102682 0.994714i \(-0.532742\pi\)
−0.102682 + 0.994714i \(0.532742\pi\)
\(642\) 0 0
\(643\) −9.54077 −0.376251 −0.188126 0.982145i \(-0.560241\pi\)
−0.188126 + 0.982145i \(0.560241\pi\)
\(644\) 0.632156 0.0249104
\(645\) 0 0
\(646\) −0.115173 −0.00453144
\(647\) 38.0573 1.49619 0.748093 0.663594i \(-0.230970\pi\)
0.748093 + 0.663594i \(0.230970\pi\)
\(648\) 0 0
\(649\) −20.9282 −0.821505
\(650\) −22.7040 −0.890525
\(651\) 0 0
\(652\) −8.40566 −0.329191
\(653\) 7.10248 0.277942 0.138971 0.990296i \(-0.455621\pi\)
0.138971 + 0.990296i \(0.455621\pi\)
\(654\) 0 0
\(655\) −26.0914 −1.01947
\(656\) −0.690783 −0.0269706
\(657\) 0 0
\(658\) −6.09474 −0.237598
\(659\) −17.2293 −0.671157 −0.335579 0.942012i \(-0.608932\pi\)
−0.335579 + 0.942012i \(0.608932\pi\)
\(660\) 0 0
\(661\) 6.28912 0.244618 0.122309 0.992492i \(-0.460970\pi\)
0.122309 + 0.992492i \(0.460970\pi\)
\(662\) 4.98105 0.193594
\(663\) 0 0
\(664\) −27.1589 −1.05397
\(665\) 0.0635367 0.00246385
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) −19.9884 −0.773373
\(669\) 0 0
\(670\) 18.9275 0.731233
\(671\) −31.1172 −1.20126
\(672\) 0 0
\(673\) −33.1852 −1.27920 −0.639598 0.768709i \(-0.720899\pi\)
−0.639598 + 0.768709i \(0.720899\pi\)
\(674\) −9.73533 −0.374991
\(675\) 0 0
\(676\) −25.5660 −0.983308
\(677\) 27.3019 1.04930 0.524649 0.851318i \(-0.324196\pi\)
0.524649 + 0.851318i \(0.324196\pi\)
\(678\) 0 0
\(679\) 0.610969 0.0234468
\(680\) 6.39047 0.245063
\(681\) 0 0
\(682\) 17.1916 0.658299
\(683\) 5.32782 0.203863 0.101932 0.994791i \(-0.467498\pi\)
0.101932 + 0.994791i \(0.467498\pi\)
\(684\) 0 0
\(685\) 22.9251 0.875922
\(686\) −10.2968 −0.393134
\(687\) 0 0
\(688\) −1.43456 −0.0546922
\(689\) −86.8621 −3.30918
\(690\) 0 0
\(691\) −2.75150 −0.104672 −0.0523360 0.998630i \(-0.516667\pi\)
−0.0523360 + 0.998630i \(0.516667\pi\)
\(692\) 2.73594 0.104005
\(693\) 0 0
\(694\) 20.7120 0.786217
\(695\) −14.7054 −0.557808
\(696\) 0 0
\(697\) −0.751977 −0.0284832
\(698\) 37.8996 1.43452
\(699\) 0 0
\(700\) 2.08611 0.0788477
\(701\) 37.4534 1.41460 0.707298 0.706916i \(-0.249914\pi\)
0.707298 + 0.706916i \(0.249914\pi\)
\(702\) 0 0
\(703\) −0.256959 −0.00969139
\(704\) −33.1047 −1.24768
\(705\) 0 0
\(706\) −18.6464 −0.701767
\(707\) 3.03815 0.114262
\(708\) 0 0
\(709\) 29.7909 1.11882 0.559411 0.828891i \(-0.311028\pi\)
0.559411 + 0.828891i \(0.311028\pi\)
\(710\) 1.16570 0.0437478
\(711\) 0 0
\(712\) 46.1265 1.72866
\(713\) 3.80124 0.142358
\(714\) 0 0
\(715\) −36.1270 −1.35107
\(716\) −3.88973 −0.145366
\(717\) 0 0
\(718\) −5.78086 −0.215740
\(719\) 2.28034 0.0850422 0.0425211 0.999096i \(-0.486461\pi\)
0.0425211 + 0.999096i \(0.486461\pi\)
\(720\) 0 0
\(721\) −2.34654 −0.0873898
\(722\) −20.1296 −0.749145
\(723\) 0 0
\(724\) −6.64677 −0.247025
\(725\) −3.30000 −0.122559
\(726\) 0 0
\(727\) 17.1529 0.636164 0.318082 0.948063i \(-0.396961\pi\)
0.318082 + 0.948063i \(0.396961\pi\)
\(728\) −14.2674 −0.528785
\(729\) 0 0
\(730\) −4.92082 −0.182128
\(731\) −1.56164 −0.0577595
\(732\) 0 0
\(733\) 7.35753 0.271757 0.135878 0.990726i \(-0.456614\pi\)
0.135878 + 0.990726i \(0.456614\pi\)
\(734\) 8.35034 0.308217
\(735\) 0 0
\(736\) −4.53264 −0.167075
\(737\) −58.4639 −2.15354
\(738\) 0 0
\(739\) 24.1145 0.887067 0.443534 0.896258i \(-0.353725\pi\)
0.443534 + 0.896258i \(0.353725\pi\)
\(740\) 4.34622 0.159770
\(741\) 0 0
\(742\) −10.2194 −0.375166
\(743\) −3.82636 −0.140376 −0.0701878 0.997534i \(-0.522360\pi\)
−0.0701878 + 0.997534i \(0.522360\pi\)
\(744\) 0 0
\(745\) −11.3241 −0.414883
\(746\) −13.0567 −0.478040
\(747\) 0 0
\(748\) −6.01721 −0.220011
\(749\) −7.14906 −0.261221
\(750\) 0 0
\(751\) 19.0615 0.695564 0.347782 0.937575i \(-0.386935\pi\)
0.347782 + 0.937575i \(0.386935\pi\)
\(752\) 11.7835 0.429699
\(753\) 0 0
\(754\) 6.88000 0.250555
\(755\) −4.92630 −0.179286
\(756\) 0 0
\(757\) 46.5969 1.69359 0.846797 0.531916i \(-0.178528\pi\)
0.846797 + 0.531916i \(0.178528\pi\)
\(758\) 22.2772 0.809146
\(759\) 0 0
\(760\) −0.268745 −0.00974841
\(761\) 13.6355 0.494288 0.247144 0.968979i \(-0.420508\pi\)
0.247144 + 0.968979i \(0.420508\pi\)
\(762\) 0 0
\(763\) −10.7719 −0.389971
\(764\) 20.9370 0.757475
\(765\) 0 0
\(766\) 28.3286 1.02355
\(767\) 31.8369 1.14956
\(768\) 0 0
\(769\) −7.50359 −0.270586 −0.135293 0.990806i \(-0.543198\pi\)
−0.135293 + 0.990806i \(0.543198\pi\)
\(770\) −4.25038 −0.153173
\(771\) 0 0
\(772\) 20.8645 0.750929
\(773\) 54.1536 1.94777 0.973885 0.227043i \(-0.0729058\pi\)
0.973885 + 0.227043i \(0.0729058\pi\)
\(774\) 0 0
\(775\) 12.5441 0.450597
\(776\) −2.58425 −0.0927692
\(777\) 0 0
\(778\) −19.2902 −0.691589
\(779\) 0.0316237 0.00113304
\(780\) 0 0
\(781\) −3.60065 −0.128841
\(782\) 1.70359 0.0609203
\(783\) 0 0
\(784\) 9.57022 0.341794
\(785\) −29.2525 −1.04407
\(786\) 0 0
\(787\) −29.3341 −1.04565 −0.522823 0.852441i \(-0.675121\pi\)
−0.522823 + 0.852441i \(0.675121\pi\)
\(788\) 9.02448 0.321484
\(789\) 0 0
\(790\) 4.84442 0.172357
\(791\) −6.52632 −0.232049
\(792\) 0 0
\(793\) 47.3368 1.68098
\(794\) −15.8399 −0.562139
\(795\) 0 0
\(796\) −5.87514 −0.208239
\(797\) 26.7775 0.948507 0.474253 0.880388i \(-0.342718\pi\)
0.474253 + 0.880388i \(0.342718\pi\)
\(798\) 0 0
\(799\) 12.8273 0.453798
\(800\) −14.9577 −0.528835
\(801\) 0 0
\(802\) −6.29177 −0.222170
\(803\) 15.1996 0.536383
\(804\) 0 0
\(805\) −0.939804 −0.0331237
\(806\) −26.1526 −0.921185
\(807\) 0 0
\(808\) −12.8507 −0.452085
\(809\) −44.6884 −1.57116 −0.785579 0.618761i \(-0.787635\pi\)
−0.785579 + 0.618761i \(0.787635\pi\)
\(810\) 0 0
\(811\) 44.3620 1.55776 0.778880 0.627174i \(-0.215788\pi\)
0.778880 + 0.627174i \(0.215788\pi\)
\(812\) −0.632156 −0.0221843
\(813\) 0 0
\(814\) 17.1896 0.602496
\(815\) 12.4964 0.437730
\(816\) 0 0
\(817\) 0.0656735 0.00229762
\(818\) 29.8440 1.04347
\(819\) 0 0
\(820\) −0.534885 −0.0186790
\(821\) 21.3612 0.745510 0.372755 0.927930i \(-0.378413\pi\)
0.372755 + 0.927930i \(0.378413\pi\)
\(822\) 0 0
\(823\) 16.2985 0.568131 0.284065 0.958805i \(-0.408317\pi\)
0.284065 + 0.958805i \(0.408317\pi\)
\(824\) 9.92532 0.345765
\(825\) 0 0
\(826\) 3.74564 0.130327
\(827\) −5.01177 −0.174276 −0.0871381 0.996196i \(-0.527772\pi\)
−0.0871381 + 0.996196i \(0.527772\pi\)
\(828\) 0 0
\(829\) −19.5777 −0.679962 −0.339981 0.940432i \(-0.610421\pi\)
−0.339981 + 0.940432i \(0.610421\pi\)
\(830\) 12.3082 0.427223
\(831\) 0 0
\(832\) 50.3602 1.74593
\(833\) 10.4180 0.360963
\(834\) 0 0
\(835\) 29.7160 1.02837
\(836\) 0.253048 0.00875185
\(837\) 0 0
\(838\) 16.6996 0.576877
\(839\) −43.9097 −1.51593 −0.757965 0.652295i \(-0.773806\pi\)
−0.757965 + 0.652295i \(0.773806\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −39.7476 −1.36979
\(843\) 0 0
\(844\) −17.0783 −0.587859
\(845\) 38.0081 1.30752
\(846\) 0 0
\(847\) 5.19995 0.178672
\(848\) 19.7580 0.678494
\(849\) 0 0
\(850\) 5.62185 0.192828
\(851\) 3.80081 0.130290
\(852\) 0 0
\(853\) 26.4519 0.905696 0.452848 0.891588i \(-0.350408\pi\)
0.452848 + 0.891588i \(0.350408\pi\)
\(854\) 5.56921 0.190574
\(855\) 0 0
\(856\) 30.2388 1.03354
\(857\) 26.0097 0.888475 0.444238 0.895909i \(-0.353475\pi\)
0.444238 + 0.895909i \(0.353475\pi\)
\(858\) 0 0
\(859\) 12.0451 0.410973 0.205486 0.978660i \(-0.434122\pi\)
0.205486 + 0.978660i \(0.434122\pi\)
\(860\) −1.11081 −0.0378782
\(861\) 0 0
\(862\) −11.3743 −0.387411
\(863\) 26.1020 0.888523 0.444262 0.895897i \(-0.353466\pi\)
0.444262 + 0.895897i \(0.353466\pi\)
\(864\) 0 0
\(865\) −4.06743 −0.138297
\(866\) 31.6853 1.07671
\(867\) 0 0
\(868\) 2.40298 0.0815623
\(869\) −14.9636 −0.507606
\(870\) 0 0
\(871\) 88.9378 3.01354
\(872\) 45.5628 1.54295
\(873\) 0 0
\(874\) −0.0716428 −0.00242336
\(875\) −7.80038 −0.263701
\(876\) 0 0
\(877\) −7.72870 −0.260980 −0.130490 0.991450i \(-0.541655\pi\)
−0.130490 + 0.991450i \(0.541655\pi\)
\(878\) 29.2927 0.988582
\(879\) 0 0
\(880\) 8.21762 0.277016
\(881\) 14.2550 0.480262 0.240131 0.970741i \(-0.422810\pi\)
0.240131 + 0.970741i \(0.422810\pi\)
\(882\) 0 0
\(883\) 18.3998 0.619203 0.309601 0.950866i \(-0.399804\pi\)
0.309601 + 0.950866i \(0.399804\pi\)
\(884\) 9.15365 0.307871
\(885\) 0 0
\(886\) −17.5207 −0.588621
\(887\) −0.871823 −0.0292730 −0.0146365 0.999893i \(-0.504659\pi\)
−0.0146365 + 0.999893i \(0.504659\pi\)
\(888\) 0 0
\(889\) −12.1263 −0.406703
\(890\) −20.9041 −0.700707
\(891\) 0 0
\(892\) −4.78212 −0.160117
\(893\) −0.539441 −0.0180517
\(894\) 0 0
\(895\) 5.78273 0.193295
\(896\) −0.609304 −0.0203554
\(897\) 0 0
\(898\) −16.5448 −0.552107
\(899\) −3.80124 −0.126779
\(900\) 0 0
\(901\) 21.5083 0.716547
\(902\) −2.11551 −0.0704387
\(903\) 0 0
\(904\) 27.6048 0.918120
\(905\) 9.88152 0.328473
\(906\) 0 0
\(907\) 55.9890 1.85908 0.929542 0.368716i \(-0.120202\pi\)
0.929542 + 0.368716i \(0.120202\pi\)
\(908\) 11.2238 0.372475
\(909\) 0 0
\(910\) 6.46586 0.214341
\(911\) −53.4421 −1.77061 −0.885307 0.465007i \(-0.846052\pi\)
−0.885307 + 0.465007i \(0.846052\pi\)
\(912\) 0 0
\(913\) −38.0179 −1.25821
\(914\) −41.4523 −1.37112
\(915\) 0 0
\(916\) 15.7409 0.520093
\(917\) −14.4240 −0.476322
\(918\) 0 0
\(919\) 42.9636 1.41724 0.708619 0.705591i \(-0.249319\pi\)
0.708619 + 0.705591i \(0.249319\pi\)
\(920\) 3.97515 0.131057
\(921\) 0 0
\(922\) −28.9350 −0.952922
\(923\) 5.47746 0.180293
\(924\) 0 0
\(925\) 12.5427 0.412400
\(926\) 26.6996 0.877404
\(927\) 0 0
\(928\) 4.53264 0.148791
\(929\) −12.0253 −0.394537 −0.197269 0.980349i \(-0.563207\pi\)
−0.197269 + 0.980349i \(0.563207\pi\)
\(930\) 0 0
\(931\) −0.438120 −0.0143588
\(932\) 21.7563 0.712651
\(933\) 0 0
\(934\) −11.1652 −0.365338
\(935\) 8.94559 0.292552
\(936\) 0 0
\(937\) −30.0372 −0.981274 −0.490637 0.871364i \(-0.663236\pi\)
−0.490637 + 0.871364i \(0.663236\pi\)
\(938\) 10.4636 0.341649
\(939\) 0 0
\(940\) 9.12415 0.297597
\(941\) −19.6719 −0.641286 −0.320643 0.947200i \(-0.603899\pi\)
−0.320643 + 0.947200i \(0.603899\pi\)
\(942\) 0 0
\(943\) −0.467762 −0.0152324
\(944\) −7.24177 −0.235699
\(945\) 0 0
\(946\) −4.39332 −0.142839
\(947\) 18.8653 0.613041 0.306520 0.951864i \(-0.400835\pi\)
0.306520 + 0.951864i \(0.400835\pi\)
\(948\) 0 0
\(949\) −23.1223 −0.750582
\(950\) −0.236421 −0.00767052
\(951\) 0 0
\(952\) 3.53282 0.114499
\(953\) 33.1756 1.07466 0.537331 0.843371i \(-0.319432\pi\)
0.537331 + 0.843371i \(0.319432\pi\)
\(954\) 0 0
\(955\) −31.1263 −1.00722
\(956\) 5.67813 0.183644
\(957\) 0 0
\(958\) −23.9768 −0.774655
\(959\) 12.6736 0.409251
\(960\) 0 0
\(961\) −16.5506 −0.533889
\(962\) −26.1496 −0.843097
\(963\) 0 0
\(964\) 0.937279 0.0301877
\(965\) −31.0185 −0.998520
\(966\) 0 0
\(967\) −41.8683 −1.34640 −0.673198 0.739463i \(-0.735080\pi\)
−0.673198 + 0.739463i \(0.735080\pi\)
\(968\) −21.9945 −0.706931
\(969\) 0 0
\(970\) 1.17116 0.0376037
\(971\) −24.2057 −0.776799 −0.388400 0.921491i \(-0.626972\pi\)
−0.388400 + 0.921491i \(0.626972\pi\)
\(972\) 0 0
\(973\) −8.12954 −0.260621
\(974\) −1.41130 −0.0452210
\(975\) 0 0
\(976\) −10.7674 −0.344657
\(977\) −11.7282 −0.375218 −0.187609 0.982244i \(-0.560074\pi\)
−0.187609 + 0.982244i \(0.560074\pi\)
\(978\) 0 0
\(979\) 64.5693 2.06364
\(980\) 7.41039 0.236716
\(981\) 0 0
\(982\) 39.7902 1.26975
\(983\) 1.37537 0.0438675 0.0219338 0.999759i \(-0.493018\pi\)
0.0219338 + 0.999759i \(0.493018\pi\)
\(984\) 0 0
\(985\) −13.4164 −0.427482
\(986\) −1.70359 −0.0542534
\(987\) 0 0
\(988\) −0.384948 −0.0122468
\(989\) −0.971410 −0.0308890
\(990\) 0 0
\(991\) 60.9345 1.93565 0.967824 0.251629i \(-0.0809662\pi\)
0.967824 + 0.251629i \(0.0809662\pi\)
\(992\) −17.2297 −0.547042
\(993\) 0 0
\(994\) 0.644428 0.0204400
\(995\) 8.73436 0.276898
\(996\) 0 0
\(997\) −9.78792 −0.309986 −0.154993 0.987916i \(-0.549536\pi\)
−0.154993 + 0.987916i \(0.549536\pi\)
\(998\) −36.2652 −1.14795
\(999\) 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 6003.2.a.m.1.8 11
3.2 odd 2 2001.2.a.l.1.4 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.4 11 3.2 odd 2
6003.2.a.m.1.8 11 1.1 even 1 trivial