Properties

Label 1560.4.a.n.1.4
Level $1560$
Weight $4$
Character 1560.1
Self dual yes
Analytic conductor $92.043$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1560.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(92.0429796090\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \( x^{4} - x^{3} - 41x^{2} - 30x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.574597\) of defining polynomial
Character \(\chi\) \(=\) 1560.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{3} +5.00000 q^{5} +11.0618 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +5.00000 q^{5} +11.0618 q^{7} +9.00000 q^{9} -35.6586 q^{11} +13.0000 q^{13} +15.0000 q^{15} +9.34984 q^{17} -77.5269 q^{19} +33.1855 q^{21} -204.486 q^{23} +25.0000 q^{25} +27.0000 q^{27} +176.219 q^{29} -216.206 q^{31} -106.976 q^{33} +55.3092 q^{35} -190.820 q^{37} +39.0000 q^{39} -315.241 q^{41} +33.6302 q^{43} +45.0000 q^{45} -203.252 q^{47} -220.636 q^{49} +28.0495 q^{51} +487.637 q^{53} -178.293 q^{55} -232.581 q^{57} +176.742 q^{59} -234.540 q^{61} +99.5565 q^{63} +65.0000 q^{65} -608.529 q^{67} -613.459 q^{69} -454.705 q^{71} -427.982 q^{73} +75.0000 q^{75} -394.450 q^{77} +1177.90 q^{79} +81.0000 q^{81} +821.981 q^{83} +46.7492 q^{85} +528.658 q^{87} -549.649 q^{89} +143.804 q^{91} -648.619 q^{93} -387.635 q^{95} +213.703 q^{97} -320.928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{3} + 20 q^{5} - 34 q^{7} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{3} + 20 q^{5} - 34 q^{7} + 36 q^{9} - 38 q^{11} + 52 q^{13} + 60 q^{15} - 50 q^{17} - 180 q^{19} - 102 q^{21} - 170 q^{23} + 100 q^{25} + 108 q^{27} - 84 q^{29} - 408 q^{31} - 114 q^{33} - 170 q^{35} - 38 q^{37} + 156 q^{39} - 90 q^{41} - 732 q^{43} + 180 q^{45} - 520 q^{47} + 230 q^{49} - 150 q^{51} - 338 q^{53} - 190 q^{55} - 540 q^{57} - 232 q^{59} + 326 q^{61} - 306 q^{63} + 260 q^{65} - 1040 q^{67} - 510 q^{69} - 702 q^{71} - 368 q^{73} + 300 q^{75} + 14 q^{77} - 678 q^{79} + 324 q^{81} - 1888 q^{83} - 250 q^{85} - 252 q^{87} - 2070 q^{89} - 442 q^{91} - 1224 q^{93} - 900 q^{95} + 1126 q^{97} - 342 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 11.0618 0.597283 0.298642 0.954365i \(-0.403467\pi\)
0.298642 + 0.954365i \(0.403467\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −35.6586 −0.977407 −0.488703 0.872450i \(-0.662530\pi\)
−0.488703 + 0.872450i \(0.662530\pi\)
\(12\) 0 0
\(13\) 13.0000 0.277350
\(14\) 0 0
\(15\) 15.0000 0.258199
\(16\) 0 0
\(17\) 9.34984 0.133392 0.0666962 0.997773i \(-0.478754\pi\)
0.0666962 + 0.997773i \(0.478754\pi\)
\(18\) 0 0
\(19\) −77.5269 −0.936100 −0.468050 0.883702i \(-0.655043\pi\)
−0.468050 + 0.883702i \(0.655043\pi\)
\(20\) 0 0
\(21\) 33.1855 0.344842
\(22\) 0 0
\(23\) −204.486 −1.85384 −0.926920 0.375259i \(-0.877554\pi\)
−0.926920 + 0.375259i \(0.877554\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 176.219 1.12838 0.564192 0.825644i \(-0.309188\pi\)
0.564192 + 0.825644i \(0.309188\pi\)
\(30\) 0 0
\(31\) −216.206 −1.25264 −0.626319 0.779567i \(-0.715439\pi\)
−0.626319 + 0.779567i \(0.715439\pi\)
\(32\) 0 0
\(33\) −106.976 −0.564306
\(34\) 0 0
\(35\) 55.3092 0.267113
\(36\) 0 0
\(37\) −190.820 −0.847853 −0.423926 0.905697i \(-0.639348\pi\)
−0.423926 + 0.905697i \(0.639348\pi\)
\(38\) 0 0
\(39\) 39.0000 0.160128
\(40\) 0 0
\(41\) −315.241 −1.20079 −0.600394 0.799704i \(-0.704990\pi\)
−0.600394 + 0.799704i \(0.704990\pi\)
\(42\) 0 0
\(43\) 33.6302 0.119269 0.0596344 0.998220i \(-0.481007\pi\)
0.0596344 + 0.998220i \(0.481007\pi\)
\(44\) 0 0
\(45\) 45.0000 0.149071
\(46\) 0 0
\(47\) −203.252 −0.630793 −0.315397 0.948960i \(-0.602138\pi\)
−0.315397 + 0.948960i \(0.602138\pi\)
\(48\) 0 0
\(49\) −220.636 −0.643253
\(50\) 0 0
\(51\) 28.0495 0.0770141
\(52\) 0 0
\(53\) 487.637 1.26381 0.631906 0.775045i \(-0.282273\pi\)
0.631906 + 0.775045i \(0.282273\pi\)
\(54\) 0 0
\(55\) −178.293 −0.437110
\(56\) 0 0
\(57\) −232.581 −0.540457
\(58\) 0 0
\(59\) 176.742 0.389998 0.194999 0.980803i \(-0.437530\pi\)
0.194999 + 0.980803i \(0.437530\pi\)
\(60\) 0 0
\(61\) −234.540 −0.492292 −0.246146 0.969233i \(-0.579164\pi\)
−0.246146 + 0.969233i \(0.579164\pi\)
\(62\) 0 0
\(63\) 99.5565 0.199094
\(64\) 0 0
\(65\) 65.0000 0.124035
\(66\) 0 0
\(67\) −608.529 −1.10961 −0.554803 0.831982i \(-0.687206\pi\)
−0.554803 + 0.831982i \(0.687206\pi\)
\(68\) 0 0
\(69\) −613.459 −1.07032
\(70\) 0 0
\(71\) −454.705 −0.760050 −0.380025 0.924976i \(-0.624085\pi\)
−0.380025 + 0.924976i \(0.624085\pi\)
\(72\) 0 0
\(73\) −427.982 −0.686184 −0.343092 0.939302i \(-0.611474\pi\)
−0.343092 + 0.939302i \(0.611474\pi\)
\(74\) 0 0
\(75\) 75.0000 0.115470
\(76\) 0 0
\(77\) −394.450 −0.583789
\(78\) 0 0
\(79\) 1177.90 1.67753 0.838763 0.544497i \(-0.183279\pi\)
0.838763 + 0.544497i \(0.183279\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 821.981 1.08704 0.543519 0.839397i \(-0.317092\pi\)
0.543519 + 0.839397i \(0.317092\pi\)
\(84\) 0 0
\(85\) 46.7492 0.0596549
\(86\) 0 0
\(87\) 528.658 0.651472
\(88\) 0 0
\(89\) −549.649 −0.654637 −0.327318 0.944914i \(-0.606145\pi\)
−0.327318 + 0.944914i \(0.606145\pi\)
\(90\) 0 0
\(91\) 143.804 0.165657
\(92\) 0 0
\(93\) −648.619 −0.723211
\(94\) 0 0
\(95\) −387.635 −0.418636
\(96\) 0 0
\(97\) 213.703 0.223693 0.111847 0.993725i \(-0.464323\pi\)
0.111847 + 0.993725i \(0.464323\pi\)
\(98\) 0 0
\(99\) −320.928 −0.325802
\(100\) 0 0
\(101\) 1368.56 1.34829 0.674144 0.738600i \(-0.264513\pi\)
0.674144 + 0.738600i \(0.264513\pi\)
\(102\) 0 0
\(103\) −2084.25 −1.99385 −0.996926 0.0783455i \(-0.975036\pi\)
−0.996926 + 0.0783455i \(0.975036\pi\)
\(104\) 0 0
\(105\) 165.928 0.154218
\(106\) 0 0
\(107\) −1837.09 −1.65980 −0.829899 0.557913i \(-0.811602\pi\)
−0.829899 + 0.557913i \(0.811602\pi\)
\(108\) 0 0
\(109\) −173.527 −0.152485 −0.0762425 0.997089i \(-0.524292\pi\)
−0.0762425 + 0.997089i \(0.524292\pi\)
\(110\) 0 0
\(111\) −572.459 −0.489508
\(112\) 0 0
\(113\) 377.475 0.314247 0.157123 0.987579i \(-0.449778\pi\)
0.157123 + 0.987579i \(0.449778\pi\)
\(114\) 0 0
\(115\) −1022.43 −0.829063
\(116\) 0 0
\(117\) 117.000 0.0924500
\(118\) 0 0
\(119\) 103.426 0.0796730
\(120\) 0 0
\(121\) −59.4634 −0.0446757
\(122\) 0 0
\(123\) −945.722 −0.693275
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1453.58 1.01562 0.507812 0.861468i \(-0.330455\pi\)
0.507812 + 0.861468i \(0.330455\pi\)
\(128\) 0 0
\(129\) 100.891 0.0688599
\(130\) 0 0
\(131\) 1106.58 0.738034 0.369017 0.929423i \(-0.379694\pi\)
0.369017 + 0.929423i \(0.379694\pi\)
\(132\) 0 0
\(133\) −857.590 −0.559116
\(134\) 0 0
\(135\) 135.000 0.0860663
\(136\) 0 0
\(137\) 677.130 0.422271 0.211135 0.977457i \(-0.432284\pi\)
0.211135 + 0.977457i \(0.432284\pi\)
\(138\) 0 0
\(139\) 1536.91 0.937834 0.468917 0.883242i \(-0.344644\pi\)
0.468917 + 0.883242i \(0.344644\pi\)
\(140\) 0 0
\(141\) −609.755 −0.364189
\(142\) 0 0
\(143\) −463.562 −0.271084
\(144\) 0 0
\(145\) 881.097 0.504628
\(146\) 0 0
\(147\) −661.907 −0.371382
\(148\) 0 0
\(149\) −948.631 −0.521576 −0.260788 0.965396i \(-0.583982\pi\)
−0.260788 + 0.965396i \(0.583982\pi\)
\(150\) 0 0
\(151\) 3315.66 1.78692 0.893460 0.449143i \(-0.148271\pi\)
0.893460 + 0.449143i \(0.148271\pi\)
\(152\) 0 0
\(153\) 84.1486 0.0444641
\(154\) 0 0
\(155\) −1081.03 −0.560197
\(156\) 0 0
\(157\) −1419.72 −0.721697 −0.360848 0.932625i \(-0.617513\pi\)
−0.360848 + 0.932625i \(0.617513\pi\)
\(158\) 0 0
\(159\) 1462.91 0.729662
\(160\) 0 0
\(161\) −2261.99 −1.10727
\(162\) 0 0
\(163\) −3144.63 −1.51108 −0.755541 0.655101i \(-0.772626\pi\)
−0.755541 + 0.655101i \(0.772626\pi\)
\(164\) 0 0
\(165\) −534.879 −0.252365
\(166\) 0 0
\(167\) 1290.24 0.597854 0.298927 0.954276i \(-0.403371\pi\)
0.298927 + 0.954276i \(0.403371\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) −697.742 −0.312033
\(172\) 0 0
\(173\) 671.469 0.295092 0.147546 0.989055i \(-0.452863\pi\)
0.147546 + 0.989055i \(0.452863\pi\)
\(174\) 0 0
\(175\) 276.546 0.119457
\(176\) 0 0
\(177\) 530.226 0.225165
\(178\) 0 0
\(179\) −3002.08 −1.25355 −0.626777 0.779199i \(-0.715626\pi\)
−0.626777 + 0.779199i \(0.715626\pi\)
\(180\) 0 0
\(181\) −232.735 −0.0955750 −0.0477875 0.998858i \(-0.515217\pi\)
−0.0477875 + 0.998858i \(0.515217\pi\)
\(182\) 0 0
\(183\) −703.621 −0.284225
\(184\) 0 0
\(185\) −954.098 −0.379171
\(186\) 0 0
\(187\) −333.402 −0.130379
\(188\) 0 0
\(189\) 298.670 0.114947
\(190\) 0 0
\(191\) −1741.88 −0.659886 −0.329943 0.944001i \(-0.607029\pi\)
−0.329943 + 0.944001i \(0.607029\pi\)
\(192\) 0 0
\(193\) −659.276 −0.245885 −0.122942 0.992414i \(-0.539233\pi\)
−0.122942 + 0.992414i \(0.539233\pi\)
\(194\) 0 0
\(195\) 195.000 0.0716115
\(196\) 0 0
\(197\) −775.667 −0.280528 −0.140264 0.990114i \(-0.544795\pi\)
−0.140264 + 0.990114i \(0.544795\pi\)
\(198\) 0 0
\(199\) 2030.26 0.723222 0.361611 0.932329i \(-0.382227\pi\)
0.361611 + 0.932329i \(0.382227\pi\)
\(200\) 0 0
\(201\) −1825.59 −0.640631
\(202\) 0 0
\(203\) 1949.31 0.673964
\(204\) 0 0
\(205\) −1576.20 −0.537009
\(206\) 0 0
\(207\) −1840.38 −0.617947
\(208\) 0 0
\(209\) 2764.50 0.914950
\(210\) 0 0
\(211\) −4994.83 −1.62966 −0.814830 0.579701i \(-0.803170\pi\)
−0.814830 + 0.579701i \(0.803170\pi\)
\(212\) 0 0
\(213\) −1364.11 −0.438815
\(214\) 0 0
\(215\) 168.151 0.0533386
\(216\) 0 0
\(217\) −2391.64 −0.748180
\(218\) 0 0
\(219\) −1283.94 −0.396169
\(220\) 0 0
\(221\) 121.548 0.0369964
\(222\) 0 0
\(223\) −3662.17 −1.09972 −0.549859 0.835258i \(-0.685318\pi\)
−0.549859 + 0.835258i \(0.685318\pi\)
\(224\) 0 0
\(225\) 225.000 0.0666667
\(226\) 0 0
\(227\) 959.714 0.280610 0.140305 0.990108i \(-0.455192\pi\)
0.140305 + 0.990108i \(0.455192\pi\)
\(228\) 0 0
\(229\) −2816.91 −0.812867 −0.406433 0.913680i \(-0.633228\pi\)
−0.406433 + 0.913680i \(0.633228\pi\)
\(230\) 0 0
\(231\) −1183.35 −0.337051
\(232\) 0 0
\(233\) −2411.40 −0.678009 −0.339004 0.940785i \(-0.610090\pi\)
−0.339004 + 0.940785i \(0.610090\pi\)
\(234\) 0 0
\(235\) −1016.26 −0.282099
\(236\) 0 0
\(237\) 3533.71 0.968520
\(238\) 0 0
\(239\) −2702.81 −0.731509 −0.365754 0.930711i \(-0.619189\pi\)
−0.365754 + 0.930711i \(0.619189\pi\)
\(240\) 0 0
\(241\) −1591.74 −0.425448 −0.212724 0.977112i \(-0.568234\pi\)
−0.212724 + 0.977112i \(0.568234\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) −1103.18 −0.287671
\(246\) 0 0
\(247\) −1007.85 −0.259627
\(248\) 0 0
\(249\) 2465.94 0.627602
\(250\) 0 0
\(251\) −3515.20 −0.883974 −0.441987 0.897022i \(-0.645726\pi\)
−0.441987 + 0.897022i \(0.645726\pi\)
\(252\) 0 0
\(253\) 7291.69 1.81196
\(254\) 0 0
\(255\) 140.248 0.0344417
\(256\) 0 0
\(257\) −685.648 −0.166418 −0.0832092 0.996532i \(-0.526517\pi\)
−0.0832092 + 0.996532i \(0.526517\pi\)
\(258\) 0 0
\(259\) −2110.82 −0.506408
\(260\) 0 0
\(261\) 1585.97 0.376128
\(262\) 0 0
\(263\) −317.057 −0.0743368 −0.0371684 0.999309i \(-0.511834\pi\)
−0.0371684 + 0.999309i \(0.511834\pi\)
\(264\) 0 0
\(265\) 2438.18 0.565194
\(266\) 0 0
\(267\) −1648.95 −0.377955
\(268\) 0 0
\(269\) 3176.23 0.719920 0.359960 0.932968i \(-0.382790\pi\)
0.359960 + 0.932968i \(0.382790\pi\)
\(270\) 0 0
\(271\) 3891.72 0.872344 0.436172 0.899863i \(-0.356334\pi\)
0.436172 + 0.899863i \(0.356334\pi\)
\(272\) 0 0
\(273\) 431.412 0.0956418
\(274\) 0 0
\(275\) −891.465 −0.195481
\(276\) 0 0
\(277\) 2397.76 0.520100 0.260050 0.965595i \(-0.416261\pi\)
0.260050 + 0.965595i \(0.416261\pi\)
\(278\) 0 0
\(279\) −1945.86 −0.417546
\(280\) 0 0
\(281\) 5736.10 1.21775 0.608874 0.793267i \(-0.291622\pi\)
0.608874 + 0.793267i \(0.291622\pi\)
\(282\) 0 0
\(283\) 2296.93 0.482467 0.241233 0.970467i \(-0.422448\pi\)
0.241233 + 0.970467i \(0.422448\pi\)
\(284\) 0 0
\(285\) −1162.90 −0.241700
\(286\) 0 0
\(287\) −3487.14 −0.717210
\(288\) 0 0
\(289\) −4825.58 −0.982206
\(290\) 0 0
\(291\) 641.108 0.129149
\(292\) 0 0
\(293\) 3464.41 0.690762 0.345381 0.938463i \(-0.387750\pi\)
0.345381 + 0.938463i \(0.387750\pi\)
\(294\) 0 0
\(295\) 883.710 0.174412
\(296\) 0 0
\(297\) −962.783 −0.188102
\(298\) 0 0
\(299\) −2658.32 −0.514163
\(300\) 0 0
\(301\) 372.012 0.0712372
\(302\) 0 0
\(303\) 4105.69 0.778434
\(304\) 0 0
\(305\) −1172.70 −0.220160
\(306\) 0 0
\(307\) 1025.10 0.190571 0.0952855 0.995450i \(-0.469624\pi\)
0.0952855 + 0.995450i \(0.469624\pi\)
\(308\) 0 0
\(309\) −6252.74 −1.15115
\(310\) 0 0
\(311\) 3394.75 0.618967 0.309484 0.950905i \(-0.399844\pi\)
0.309484 + 0.950905i \(0.399844\pi\)
\(312\) 0 0
\(313\) 3430.63 0.619522 0.309761 0.950814i \(-0.399751\pi\)
0.309761 + 0.950814i \(0.399751\pi\)
\(314\) 0 0
\(315\) 497.783 0.0890377
\(316\) 0 0
\(317\) −7137.48 −1.26461 −0.632304 0.774720i \(-0.717891\pi\)
−0.632304 + 0.774720i \(0.717891\pi\)
\(318\) 0 0
\(319\) −6283.74 −1.10289
\(320\) 0 0
\(321\) −5511.28 −0.958285
\(322\) 0 0
\(323\) −724.864 −0.124868
\(324\) 0 0
\(325\) 325.000 0.0554700
\(326\) 0 0
\(327\) −520.581 −0.0880372
\(328\) 0 0
\(329\) −2248.34 −0.376762
\(330\) 0 0
\(331\) 5543.07 0.920468 0.460234 0.887798i \(-0.347766\pi\)
0.460234 + 0.887798i \(0.347766\pi\)
\(332\) 0 0
\(333\) −1717.38 −0.282618
\(334\) 0 0
\(335\) −3042.64 −0.496231
\(336\) 0 0
\(337\) 9773.05 1.57974 0.789869 0.613275i \(-0.210148\pi\)
0.789869 + 0.613275i \(0.210148\pi\)
\(338\) 0 0
\(339\) 1132.43 0.181430
\(340\) 0 0
\(341\) 7709.61 1.22434
\(342\) 0 0
\(343\) −6234.85 −0.981487
\(344\) 0 0
\(345\) −3067.29 −0.478659
\(346\) 0 0
\(347\) −3741.52 −0.578834 −0.289417 0.957203i \(-0.593461\pi\)
−0.289417 + 0.957203i \(0.593461\pi\)
\(348\) 0 0
\(349\) −4116.43 −0.631368 −0.315684 0.948864i \(-0.602234\pi\)
−0.315684 + 0.948864i \(0.602234\pi\)
\(350\) 0 0
\(351\) 351.000 0.0533761
\(352\) 0 0
\(353\) 10581.9 1.59552 0.797762 0.602973i \(-0.206017\pi\)
0.797762 + 0.602973i \(0.206017\pi\)
\(354\) 0 0
\(355\) −2273.52 −0.339904
\(356\) 0 0
\(357\) 310.279 0.0459992
\(358\) 0 0
\(359\) 1887.32 0.277462 0.138731 0.990330i \(-0.455698\pi\)
0.138731 + 0.990330i \(0.455698\pi\)
\(360\) 0 0
\(361\) −848.580 −0.123718
\(362\) 0 0
\(363\) −178.390 −0.0257935
\(364\) 0 0
\(365\) −2139.91 −0.306871
\(366\) 0 0
\(367\) −13302.3 −1.89203 −0.946015 0.324121i \(-0.894931\pi\)
−0.946015 + 0.324121i \(0.894931\pi\)
\(368\) 0 0
\(369\) −2837.16 −0.400263
\(370\) 0 0
\(371\) 5394.16 0.754853
\(372\) 0 0
\(373\) −9798.85 −1.36023 −0.680114 0.733106i \(-0.738070\pi\)
−0.680114 + 0.733106i \(0.738070\pi\)
\(374\) 0 0
\(375\) 375.000 0.0516398
\(376\) 0 0
\(377\) 2290.85 0.312957
\(378\) 0 0
\(379\) −10426.1 −1.41307 −0.706534 0.707679i \(-0.749742\pi\)
−0.706534 + 0.707679i \(0.749742\pi\)
\(380\) 0 0
\(381\) 4360.73 0.586371
\(382\) 0 0
\(383\) −9010.04 −1.20207 −0.601033 0.799224i \(-0.705244\pi\)
−0.601033 + 0.799224i \(0.705244\pi\)
\(384\) 0 0
\(385\) −1972.25 −0.261078
\(386\) 0 0
\(387\) 302.672 0.0397563
\(388\) 0 0
\(389\) 8329.22 1.08563 0.542813 0.839854i \(-0.317359\pi\)
0.542813 + 0.839854i \(0.317359\pi\)
\(390\) 0 0
\(391\) −1911.91 −0.247288
\(392\) 0 0
\(393\) 3319.74 0.426104
\(394\) 0 0
\(395\) 5889.52 0.750212
\(396\) 0 0
\(397\) −9157.34 −1.15767 −0.578833 0.815446i \(-0.696492\pi\)
−0.578833 + 0.815446i \(0.696492\pi\)
\(398\) 0 0
\(399\) −2572.77 −0.322806
\(400\) 0 0
\(401\) −1373.73 −0.171075 −0.0855374 0.996335i \(-0.527261\pi\)
−0.0855374 + 0.996335i \(0.527261\pi\)
\(402\) 0 0
\(403\) −2810.68 −0.347419
\(404\) 0 0
\(405\) 405.000 0.0496904
\(406\) 0 0
\(407\) 6804.36 0.828697
\(408\) 0 0
\(409\) −5743.14 −0.694328 −0.347164 0.937804i \(-0.612855\pi\)
−0.347164 + 0.937804i \(0.612855\pi\)
\(410\) 0 0
\(411\) 2031.39 0.243798
\(412\) 0 0
\(413\) 1955.09 0.232939
\(414\) 0 0
\(415\) 4109.91 0.486138
\(416\) 0 0
\(417\) 4610.73 0.541459
\(418\) 0 0
\(419\) 1765.62 0.205862 0.102931 0.994689i \(-0.467178\pi\)
0.102931 + 0.994689i \(0.467178\pi\)
\(420\) 0 0
\(421\) 3626.15 0.419781 0.209890 0.977725i \(-0.432689\pi\)
0.209890 + 0.977725i \(0.432689\pi\)
\(422\) 0 0
\(423\) −1829.26 −0.210264
\(424\) 0 0
\(425\) 233.746 0.0266785
\(426\) 0 0
\(427\) −2594.45 −0.294038
\(428\) 0 0
\(429\) −1390.69 −0.156510
\(430\) 0 0
\(431\) 3219.85 0.359848 0.179924 0.983680i \(-0.442415\pi\)
0.179924 + 0.983680i \(0.442415\pi\)
\(432\) 0 0
\(433\) −3020.19 −0.335199 −0.167599 0.985855i \(-0.553601\pi\)
−0.167599 + 0.985855i \(0.553601\pi\)
\(434\) 0 0
\(435\) 2643.29 0.291347
\(436\) 0 0
\(437\) 15853.2 1.73538
\(438\) 0 0
\(439\) −16314.0 −1.77363 −0.886815 0.462124i \(-0.847088\pi\)
−0.886815 + 0.462124i \(0.847088\pi\)
\(440\) 0 0
\(441\) −1985.72 −0.214418
\(442\) 0 0
\(443\) −948.348 −0.101710 −0.0508548 0.998706i \(-0.516195\pi\)
−0.0508548 + 0.998706i \(0.516195\pi\)
\(444\) 0 0
\(445\) −2748.25 −0.292762
\(446\) 0 0
\(447\) −2845.89 −0.301132
\(448\) 0 0
\(449\) −3371.66 −0.354384 −0.177192 0.984176i \(-0.556701\pi\)
−0.177192 + 0.984176i \(0.556701\pi\)
\(450\) 0 0
\(451\) 11241.0 1.17366
\(452\) 0 0
\(453\) 9946.99 1.03168
\(454\) 0 0
\(455\) 719.019 0.0740838
\(456\) 0 0
\(457\) 5898.46 0.603760 0.301880 0.953346i \(-0.402386\pi\)
0.301880 + 0.953346i \(0.402386\pi\)
\(458\) 0 0
\(459\) 252.446 0.0256714
\(460\) 0 0
\(461\) −16370.6 −1.65391 −0.826955 0.562268i \(-0.809929\pi\)
−0.826955 + 0.562268i \(0.809929\pi\)
\(462\) 0 0
\(463\) −13334.3 −1.33844 −0.669221 0.743063i \(-0.733372\pi\)
−0.669221 + 0.743063i \(0.733372\pi\)
\(464\) 0 0
\(465\) −3243.09 −0.323430
\(466\) 0 0
\(467\) 6584.38 0.652439 0.326219 0.945294i \(-0.394225\pi\)
0.326219 + 0.945294i \(0.394225\pi\)
\(468\) 0 0
\(469\) −6731.44 −0.662749
\(470\) 0 0
\(471\) −4259.17 −0.416672
\(472\) 0 0
\(473\) −1199.21 −0.116574
\(474\) 0 0
\(475\) −1938.17 −0.187220
\(476\) 0 0
\(477\) 4388.73 0.421271
\(478\) 0 0
\(479\) 18224.3 1.73839 0.869196 0.494467i \(-0.164637\pi\)
0.869196 + 0.494467i \(0.164637\pi\)
\(480\) 0 0
\(481\) −2480.65 −0.235152
\(482\) 0 0
\(483\) −6785.98 −0.639281
\(484\) 0 0
\(485\) 1068.51 0.100039
\(486\) 0 0
\(487\) −6708.02 −0.624167 −0.312084 0.950055i \(-0.601027\pi\)
−0.312084 + 0.950055i \(0.601027\pi\)
\(488\) 0 0
\(489\) −9433.89 −0.872424
\(490\) 0 0
\(491\) 12035.2 1.10620 0.553099 0.833116i \(-0.313445\pi\)
0.553099 + 0.833116i \(0.313445\pi\)
\(492\) 0 0
\(493\) 1647.62 0.150518
\(494\) 0 0
\(495\) −1604.64 −0.145703
\(496\) 0 0
\(497\) −5029.87 −0.453965
\(498\) 0 0
\(499\) −16094.3 −1.44384 −0.721922 0.691974i \(-0.756741\pi\)
−0.721922 + 0.691974i \(0.756741\pi\)
\(500\) 0 0
\(501\) 3870.71 0.345171
\(502\) 0 0
\(503\) −11793.3 −1.04541 −0.522703 0.852515i \(-0.675076\pi\)
−0.522703 + 0.852515i \(0.675076\pi\)
\(504\) 0 0
\(505\) 6842.81 0.602973
\(506\) 0 0
\(507\) 507.000 0.0444116
\(508\) 0 0
\(509\) 8249.74 0.718396 0.359198 0.933261i \(-0.383050\pi\)
0.359198 + 0.933261i \(0.383050\pi\)
\(510\) 0 0
\(511\) −4734.26 −0.409846
\(512\) 0 0
\(513\) −2093.23 −0.180152
\(514\) 0 0
\(515\) −10421.2 −0.891678
\(516\) 0 0
\(517\) 7247.67 0.616542
\(518\) 0 0
\(519\) 2014.41 0.170371
\(520\) 0 0
\(521\) 21345.2 1.79491 0.897455 0.441105i \(-0.145413\pi\)
0.897455 + 0.441105i \(0.145413\pi\)
\(522\) 0 0
\(523\) 16607.7 1.38853 0.694266 0.719718i \(-0.255729\pi\)
0.694266 + 0.719718i \(0.255729\pi\)
\(524\) 0 0
\(525\) 829.638 0.0689683
\(526\) 0 0
\(527\) −2021.49 −0.167092
\(528\) 0 0
\(529\) 29647.6 2.43672
\(530\) 0 0
\(531\) 1590.68 0.129999
\(532\) 0 0
\(533\) −4098.13 −0.333039
\(534\) 0 0
\(535\) −9185.46 −0.742285
\(536\) 0 0
\(537\) −9006.25 −0.723740
\(538\) 0 0
\(539\) 7867.56 0.628720
\(540\) 0 0
\(541\) 16180.6 1.28588 0.642939 0.765917i \(-0.277715\pi\)
0.642939 + 0.765917i \(0.277715\pi\)
\(542\) 0 0
\(543\) −698.206 −0.0551803
\(544\) 0 0
\(545\) −867.634 −0.0681934
\(546\) 0 0
\(547\) 12935.7 1.01114 0.505568 0.862786i \(-0.331283\pi\)
0.505568 + 0.862786i \(0.331283\pi\)
\(548\) 0 0
\(549\) −2110.86 −0.164097
\(550\) 0 0
\(551\) −13661.7 −1.05628
\(552\) 0 0
\(553\) 13029.8 1.00196
\(554\) 0 0
\(555\) −2862.29 −0.218915
\(556\) 0 0
\(557\) 11049.1 0.840510 0.420255 0.907406i \(-0.361941\pi\)
0.420255 + 0.907406i \(0.361941\pi\)
\(558\) 0 0
\(559\) 437.193 0.0330792
\(560\) 0 0
\(561\) −1000.21 −0.0752741
\(562\) 0 0
\(563\) 6681.42 0.500157 0.250078 0.968226i \(-0.419544\pi\)
0.250078 + 0.968226i \(0.419544\pi\)
\(564\) 0 0
\(565\) 1887.38 0.140535
\(566\) 0 0
\(567\) 896.009 0.0663648
\(568\) 0 0
\(569\) −11299.5 −0.832510 −0.416255 0.909248i \(-0.636658\pi\)
−0.416255 + 0.909248i \(0.636658\pi\)
\(570\) 0 0
\(571\) −11280.1 −0.826724 −0.413362 0.910567i \(-0.635646\pi\)
−0.413362 + 0.910567i \(0.635646\pi\)
\(572\) 0 0
\(573\) −5225.65 −0.380985
\(574\) 0 0
\(575\) −5112.16 −0.370768
\(576\) 0 0
\(577\) 21169.9 1.52741 0.763703 0.645567i \(-0.223379\pi\)
0.763703 + 0.645567i \(0.223379\pi\)
\(578\) 0 0
\(579\) −1977.83 −0.141962
\(580\) 0 0
\(581\) 9092.62 0.649269
\(582\) 0 0
\(583\) −17388.4 −1.23526
\(584\) 0 0
\(585\) 585.000 0.0413449
\(586\) 0 0
\(587\) −4014.61 −0.282284 −0.141142 0.989989i \(-0.545077\pi\)
−0.141142 + 0.989989i \(0.545077\pi\)
\(588\) 0 0
\(589\) 16761.8 1.17259
\(590\) 0 0
\(591\) −2327.00 −0.161963
\(592\) 0 0
\(593\) 6045.14 0.418624 0.209312 0.977849i \(-0.432878\pi\)
0.209312 + 0.977849i \(0.432878\pi\)
\(594\) 0 0
\(595\) 517.132 0.0356308
\(596\) 0 0
\(597\) 6090.78 0.417553
\(598\) 0 0
\(599\) 26952.7 1.83849 0.919246 0.393684i \(-0.128800\pi\)
0.919246 + 0.393684i \(0.128800\pi\)
\(600\) 0 0
\(601\) 4064.24 0.275846 0.137923 0.990443i \(-0.455957\pi\)
0.137923 + 0.990443i \(0.455957\pi\)
\(602\) 0 0
\(603\) −5476.76 −0.369869
\(604\) 0 0
\(605\) −297.317 −0.0199796
\(606\) 0 0
\(607\) 17221.0 1.15153 0.575765 0.817615i \(-0.304704\pi\)
0.575765 + 0.817615i \(0.304704\pi\)
\(608\) 0 0
\(609\) 5847.93 0.389113
\(610\) 0 0
\(611\) −2642.27 −0.174951
\(612\) 0 0
\(613\) 14810.5 0.975838 0.487919 0.872889i \(-0.337756\pi\)
0.487919 + 0.872889i \(0.337756\pi\)
\(614\) 0 0
\(615\) −4728.61 −0.310042
\(616\) 0 0
\(617\) 21995.4 1.43517 0.717585 0.696470i \(-0.245247\pi\)
0.717585 + 0.696470i \(0.245247\pi\)
\(618\) 0 0
\(619\) −28215.2 −1.83209 −0.916045 0.401077i \(-0.868636\pi\)
−0.916045 + 0.401077i \(0.868636\pi\)
\(620\) 0 0
\(621\) −5521.13 −0.356772
\(622\) 0 0
\(623\) −6080.13 −0.391004
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 8293.50 0.528247
\(628\) 0 0
\(629\) −1784.13 −0.113097
\(630\) 0 0
\(631\) −9709.56 −0.612569 −0.306285 0.951940i \(-0.599086\pi\)
−0.306285 + 0.951940i \(0.599086\pi\)
\(632\) 0 0
\(633\) −14984.5 −0.940884
\(634\) 0 0
\(635\) 7267.89 0.454201
\(636\) 0 0
\(637\) −2868.26 −0.178406
\(638\) 0 0
\(639\) −4092.34 −0.253350
\(640\) 0 0
\(641\) 27122.9 1.67128 0.835641 0.549276i \(-0.185097\pi\)
0.835641 + 0.549276i \(0.185097\pi\)
\(642\) 0 0
\(643\) 23741.6 1.45611 0.728055 0.685519i \(-0.240425\pi\)
0.728055 + 0.685519i \(0.240425\pi\)
\(644\) 0 0
\(645\) 504.453 0.0307951
\(646\) 0 0
\(647\) 13313.5 0.808974 0.404487 0.914544i \(-0.367450\pi\)
0.404487 + 0.914544i \(0.367450\pi\)
\(648\) 0 0
\(649\) −6302.38 −0.381186
\(650\) 0 0
\(651\) −7174.92 −0.431962
\(652\) 0 0
\(653\) 12314.4 0.737976 0.368988 0.929434i \(-0.379704\pi\)
0.368988 + 0.929434i \(0.379704\pi\)
\(654\) 0 0
\(655\) 5532.91 0.330059
\(656\) 0 0
\(657\) −3851.83 −0.228728
\(658\) 0 0
\(659\) −22580.7 −1.33478 −0.667389 0.744709i \(-0.732588\pi\)
−0.667389 + 0.744709i \(0.732588\pi\)
\(660\) 0 0
\(661\) −5125.08 −0.301577 −0.150789 0.988566i \(-0.548181\pi\)
−0.150789 + 0.988566i \(0.548181\pi\)
\(662\) 0 0
\(663\) 364.644 0.0213599
\(664\) 0 0
\(665\) −4287.95 −0.250044
\(666\) 0 0
\(667\) −36034.4 −2.09184
\(668\) 0 0
\(669\) −10986.5 −0.634922
\(670\) 0 0
\(671\) 8363.38 0.481170
\(672\) 0 0
\(673\) 6059.06 0.347043 0.173521 0.984830i \(-0.444485\pi\)
0.173521 + 0.984830i \(0.444485\pi\)
\(674\) 0 0
\(675\) 675.000 0.0384900
\(676\) 0 0
\(677\) −16337.2 −0.927461 −0.463731 0.885976i \(-0.653489\pi\)
−0.463731 + 0.885976i \(0.653489\pi\)
\(678\) 0 0
\(679\) 2363.95 0.133608
\(680\) 0 0
\(681\) 2879.14 0.162010
\(682\) 0 0
\(683\) 28871.6 1.61749 0.808743 0.588162i \(-0.200148\pi\)
0.808743 + 0.588162i \(0.200148\pi\)
\(684\) 0 0
\(685\) 3385.65 0.188845
\(686\) 0 0
\(687\) −8450.72 −0.469309
\(688\) 0 0
\(689\) 6339.27 0.350518
\(690\) 0 0
\(691\) −3611.03 −0.198799 −0.0993993 0.995048i \(-0.531692\pi\)
−0.0993993 + 0.995048i \(0.531692\pi\)
\(692\) 0 0
\(693\) −3550.05 −0.194596
\(694\) 0 0
\(695\) 7684.55 0.419412
\(696\) 0 0
\(697\) −2947.45 −0.160176
\(698\) 0 0
\(699\) −7234.20 −0.391449
\(700\) 0 0
\(701\) −19383.1 −1.04435 −0.522176 0.852837i \(-0.674880\pi\)
−0.522176 + 0.852837i \(0.674880\pi\)
\(702\) 0 0
\(703\) 14793.7 0.793674
\(704\) 0 0
\(705\) −3048.77 −0.162870
\(706\) 0 0
\(707\) 15138.8 0.805310
\(708\) 0 0
\(709\) 15298.3 0.810355 0.405177 0.914238i \(-0.367210\pi\)
0.405177 + 0.914238i \(0.367210\pi\)
\(710\) 0 0
\(711\) 10601.1 0.559175
\(712\) 0 0
\(713\) 44211.2 2.32219
\(714\) 0 0
\(715\) −2317.81 −0.121232
\(716\) 0 0
\(717\) −8108.44 −0.422337
\(718\) 0 0
\(719\) −19824.5 −1.02827 −0.514137 0.857708i \(-0.671888\pi\)
−0.514137 + 0.857708i \(0.671888\pi\)
\(720\) 0 0
\(721\) −23055.6 −1.19089
\(722\) 0 0
\(723\) −4775.22 −0.245633
\(724\) 0 0
\(725\) 4405.48 0.225677
\(726\) 0 0
\(727\) −26379.1 −1.34573 −0.672866 0.739764i \(-0.734937\pi\)
−0.672866 + 0.739764i \(0.734937\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 314.437 0.0159095
\(732\) 0 0
\(733\) −5790.62 −0.291789 −0.145895 0.989300i \(-0.546606\pi\)
−0.145895 + 0.989300i \(0.546606\pi\)
\(734\) 0 0
\(735\) −3309.54 −0.166087
\(736\) 0 0
\(737\) 21699.3 1.08454
\(738\) 0 0
\(739\) 695.082 0.0345995 0.0172997 0.999850i \(-0.494493\pi\)
0.0172997 + 0.999850i \(0.494493\pi\)
\(740\) 0 0
\(741\) −3023.55 −0.149896
\(742\) 0 0
\(743\) 20134.8 0.994179 0.497089 0.867699i \(-0.334402\pi\)
0.497089 + 0.867699i \(0.334402\pi\)
\(744\) 0 0
\(745\) −4743.16 −0.233256
\(746\) 0 0
\(747\) 7397.83 0.362346
\(748\) 0 0
\(749\) −20321.6 −0.991370
\(750\) 0 0
\(751\) 22248.7 1.08105 0.540523 0.841329i \(-0.318226\pi\)
0.540523 + 0.841329i \(0.318226\pi\)
\(752\) 0 0
\(753\) −10545.6 −0.510362
\(754\) 0 0
\(755\) 16578.3 0.799135
\(756\) 0 0
\(757\) −1351.98 −0.0649124 −0.0324562 0.999473i \(-0.510333\pi\)
−0.0324562 + 0.999473i \(0.510333\pi\)
\(758\) 0 0
\(759\) 21875.1 1.04613
\(760\) 0 0
\(761\) 35726.0 1.70179 0.850897 0.525332i \(-0.176059\pi\)
0.850897 + 0.525332i \(0.176059\pi\)
\(762\) 0 0
\(763\) −1919.53 −0.0910767
\(764\) 0 0
\(765\) 420.743 0.0198850
\(766\) 0 0
\(767\) 2297.65 0.108166
\(768\) 0 0
\(769\) −4867.72 −0.228263 −0.114132 0.993466i \(-0.536409\pi\)
−0.114132 + 0.993466i \(0.536409\pi\)
\(770\) 0 0
\(771\) −2056.94 −0.0960817
\(772\) 0 0
\(773\) 18247.3 0.849044 0.424522 0.905418i \(-0.360442\pi\)
0.424522 + 0.905418i \(0.360442\pi\)
\(774\) 0 0
\(775\) −5405.16 −0.250528
\(776\) 0 0
\(777\) −6332.45 −0.292375
\(778\) 0 0
\(779\) 24439.6 1.12406
\(780\) 0 0
\(781\) 16214.1 0.742878
\(782\) 0 0
\(783\) 4757.92 0.217157
\(784\) 0 0
\(785\) −7098.62 −0.322752
\(786\) 0 0
\(787\) 18326.4 0.830072 0.415036 0.909805i \(-0.363769\pi\)
0.415036 + 0.909805i \(0.363769\pi\)
\(788\) 0 0
\(789\) −951.171 −0.0429184
\(790\) 0 0
\(791\) 4175.57 0.187694
\(792\) 0 0
\(793\) −3049.02 −0.136537
\(794\) 0 0
\(795\) 7314.55 0.326315
\(796\) 0 0
\(797\) 27446.9 1.21985 0.609924 0.792460i \(-0.291200\pi\)
0.609924 + 0.792460i \(0.291200\pi\)
\(798\) 0 0
\(799\) −1900.37 −0.0841430
\(800\) 0 0
\(801\) −4946.84 −0.218212
\(802\) 0 0
\(803\) 15261.2 0.670681
\(804\) 0 0
\(805\) −11310.0 −0.495185
\(806\) 0 0
\(807\) 9528.70 0.415646
\(808\) 0 0
\(809\) 39886.6 1.73342 0.866711 0.498810i \(-0.166229\pi\)
0.866711 + 0.498810i \(0.166229\pi\)
\(810\) 0 0
\(811\) 35333.6 1.52988 0.764938 0.644104i \(-0.222769\pi\)
0.764938 + 0.644104i \(0.222769\pi\)
\(812\) 0 0
\(813\) 11675.2 0.503648
\(814\) 0 0
\(815\) −15723.1 −0.675777
\(816\) 0 0
\(817\) −2607.24 −0.111647
\(818\) 0 0
\(819\) 1294.23 0.0552188
\(820\) 0 0
\(821\) −18360.4 −0.780491 −0.390245 0.920711i \(-0.627610\pi\)
−0.390245 + 0.920711i \(0.627610\pi\)
\(822\) 0 0
\(823\) 20535.7 0.869779 0.434889 0.900484i \(-0.356787\pi\)
0.434889 + 0.900484i \(0.356787\pi\)
\(824\) 0 0
\(825\) −2674.40 −0.112861
\(826\) 0 0
\(827\) 26977.3 1.13433 0.567166 0.823603i \(-0.308040\pi\)
0.567166 + 0.823603i \(0.308040\pi\)
\(828\) 0 0
\(829\) −29482.0 −1.23517 −0.617583 0.786506i \(-0.711888\pi\)
−0.617583 + 0.786506i \(0.711888\pi\)
\(830\) 0 0
\(831\) 7193.29 0.300280
\(832\) 0 0
\(833\) −2062.91 −0.0858050
\(834\) 0 0
\(835\) 6451.19 0.267368
\(836\) 0 0
\(837\) −5837.57 −0.241070
\(838\) 0 0
\(839\) −48464.4 −1.99425 −0.997126 0.0757571i \(-0.975863\pi\)
−0.997126 + 0.0757571i \(0.975863\pi\)
\(840\) 0 0
\(841\) 6664.26 0.273249
\(842\) 0 0
\(843\) 17208.3 0.703067
\(844\) 0 0
\(845\) 845.000 0.0344010
\(846\) 0 0
\(847\) −657.775 −0.0266841
\(848\) 0 0
\(849\) 6890.78 0.278552
\(850\) 0 0
\(851\) 39020.0 1.57178
\(852\) 0 0
\(853\) 21104.6 0.847135 0.423568 0.905864i \(-0.360778\pi\)
0.423568 + 0.905864i \(0.360778\pi\)
\(854\) 0 0
\(855\) −3488.71 −0.139545
\(856\) 0 0
\(857\) −36507.4 −1.45515 −0.727577 0.686026i \(-0.759354\pi\)
−0.727577 + 0.686026i \(0.759354\pi\)
\(858\) 0 0
\(859\) −25174.6 −0.999938 −0.499969 0.866043i \(-0.666655\pi\)
−0.499969 + 0.866043i \(0.666655\pi\)
\(860\) 0 0
\(861\) −10461.4 −0.414082
\(862\) 0 0
\(863\) 21109.2 0.832639 0.416319 0.909218i \(-0.363320\pi\)
0.416319 + 0.909218i \(0.363320\pi\)
\(864\) 0 0
\(865\) 3357.34 0.131969
\(866\) 0 0
\(867\) −14476.7 −0.567077
\(868\) 0 0
\(869\) −42002.4 −1.63963
\(870\) 0 0
\(871\) −7910.87 −0.307749
\(872\) 0 0
\(873\) 1923.33 0.0745644
\(874\) 0 0
\(875\) 1382.73 0.0534226
\(876\) 0 0
\(877\) 25911.4 0.997679 0.498839 0.866694i \(-0.333760\pi\)
0.498839 + 0.866694i \(0.333760\pi\)
\(878\) 0 0
\(879\) 10393.2 0.398812
\(880\) 0 0
\(881\) −28772.5 −1.10031 −0.550153 0.835064i \(-0.685431\pi\)
−0.550153 + 0.835064i \(0.685431\pi\)
\(882\) 0 0
\(883\) −35094.1 −1.33750 −0.668749 0.743488i \(-0.733170\pi\)
−0.668749 + 0.743488i \(0.733170\pi\)
\(884\) 0 0
\(885\) 2651.13 0.100697
\(886\) 0 0
\(887\) 10041.4 0.380109 0.190054 0.981774i \(-0.439134\pi\)
0.190054 + 0.981774i \(0.439134\pi\)
\(888\) 0 0
\(889\) 16079.2 0.606615
\(890\) 0 0
\(891\) −2888.35 −0.108601
\(892\) 0 0
\(893\) 15757.5 0.590485
\(894\) 0 0
\(895\) −15010.4 −0.560606
\(896\) 0 0
\(897\) −7974.96 −0.296852
\(898\) 0 0
\(899\) −38099.7 −1.41346
\(900\) 0 0
\(901\) 4559.32 0.168583
\(902\) 0 0
\(903\) 1116.04 0.0411288
\(904\) 0 0
\(905\) −1163.68 −0.0427425
\(906\) 0 0
\(907\) −22706.0 −0.831245 −0.415622 0.909537i \(-0.636436\pi\)
−0.415622 + 0.909537i \(0.636436\pi\)
\(908\) 0 0
\(909\) 12317.1 0.449429
\(910\) 0 0
\(911\) 24072.6 0.875479 0.437739 0.899102i \(-0.355779\pi\)
0.437739 + 0.899102i \(0.355779\pi\)
\(912\) 0 0
\(913\) −29310.7 −1.06248
\(914\) 0 0
\(915\) −3518.11 −0.127109
\(916\) 0 0
\(917\) 12240.8 0.440815
\(918\) 0 0
\(919\) −13036.6 −0.467941 −0.233970 0.972244i \(-0.575172\pi\)
−0.233970 + 0.972244i \(0.575172\pi\)
\(920\) 0 0
\(921\) 3075.29 0.110026
\(922\) 0 0
\(923\) −5911.16 −0.210800
\(924\) 0 0
\(925\) −4770.49 −0.169571
\(926\) 0 0
\(927\) −18758.2 −0.664618
\(928\) 0 0
\(929\) 2923.55 0.103249 0.0516246 0.998667i \(-0.483560\pi\)
0.0516246 + 0.998667i \(0.483560\pi\)
\(930\) 0 0
\(931\) 17105.2 0.602149
\(932\) 0 0
\(933\) 10184.3 0.357361
\(934\) 0 0
\(935\) −1667.01 −0.0583071
\(936\) 0 0
\(937\) 38569.5 1.34473 0.672365 0.740220i \(-0.265279\pi\)
0.672365 + 0.740220i \(0.265279\pi\)
\(938\) 0 0
\(939\) 10291.9 0.357681
\(940\) 0 0
\(941\) −39933.9 −1.38343 −0.691715 0.722170i \(-0.743145\pi\)
−0.691715 + 0.722170i \(0.743145\pi\)
\(942\) 0 0
\(943\) 64462.3 2.22607
\(944\) 0 0
\(945\) 1493.35 0.0514059
\(946\) 0 0
\(947\) 51099.1 1.75343 0.876715 0.481010i \(-0.159730\pi\)
0.876715 + 0.481010i \(0.159730\pi\)
\(948\) 0 0
\(949\) −5563.76 −0.190313
\(950\) 0 0
\(951\) −21412.5 −0.730122
\(952\) 0 0
\(953\) 38862.5 1.32097 0.660483 0.750841i \(-0.270351\pi\)
0.660483 + 0.750841i \(0.270351\pi\)
\(954\) 0 0
\(955\) −8709.41 −0.295110
\(956\) 0 0
\(957\) −18851.2 −0.636754
\(958\) 0 0
\(959\) 7490.30 0.252215
\(960\) 0 0
\(961\) 16954.1 0.569103
\(962\) 0 0
\(963\) −16533.8 −0.553266
\(964\) 0 0
\(965\) −3296.38 −0.109963
\(966\) 0 0
\(967\) −28744.4 −0.955903 −0.477952 0.878386i \(-0.658621\pi\)
−0.477952 + 0.878386i \(0.658621\pi\)
\(968\) 0 0
\(969\) −2174.59 −0.0720929
\(970\) 0 0
\(971\) 34207.9 1.13057 0.565285 0.824895i \(-0.308766\pi\)
0.565285 + 0.824895i \(0.308766\pi\)
\(972\) 0 0
\(973\) 17001.0 0.560152
\(974\) 0 0
\(975\) 975.000 0.0320256
\(976\) 0 0
\(977\) −54148.0 −1.77313 −0.886566 0.462603i \(-0.846916\pi\)
−0.886566 + 0.462603i \(0.846916\pi\)
\(978\) 0 0
\(979\) 19599.7 0.639847
\(980\) 0 0
\(981\) −1561.74 −0.0508283
\(982\) 0 0
\(983\) 20490.3 0.664841 0.332420 0.943131i \(-0.392135\pi\)
0.332420 + 0.943131i \(0.392135\pi\)
\(984\) 0 0
\(985\) −3878.34 −0.125456
\(986\) 0 0
\(987\) −6745.01 −0.217524
\(988\) 0 0
\(989\) −6876.91 −0.221105
\(990\) 0 0
\(991\) 44944.0 1.44066 0.720330 0.693631i \(-0.243990\pi\)
0.720330 + 0.693631i \(0.243990\pi\)
\(992\) 0 0
\(993\) 16629.2 0.531432
\(994\) 0 0
\(995\) 10151.3 0.323435
\(996\) 0 0
\(997\) −28863.0 −0.916852 −0.458426 0.888733i \(-0.651587\pi\)
−0.458426 + 0.888733i \(0.651587\pi\)
\(998\) 0 0
\(999\) −5152.13 −0.163169
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 1560.4.a.n.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.4.a.n.1.4 4 1.1 even 1 trivial