Properties

Label 4730.2.a.z.1.9
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-1.68568\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.68568 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.68568 q^{6} +4.03613 q^{7} -1.00000 q^{8} +4.21287 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.68568 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.68568 q^{6} +4.03613 q^{7} -1.00000 q^{8} +4.21287 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.68568 q^{12} +4.50732 q^{13} -4.03613 q^{14} +2.68568 q^{15} +1.00000 q^{16} -5.71882 q^{17} -4.21287 q^{18} +0.726777 q^{19} +1.00000 q^{20} +10.8397 q^{21} -1.00000 q^{22} -3.76465 q^{23} -2.68568 q^{24} +1.00000 q^{25} -4.50732 q^{26} +3.25739 q^{27} +4.03613 q^{28} +0.439002 q^{29} -2.68568 q^{30} -0.158220 q^{31} -1.00000 q^{32} +2.68568 q^{33} +5.71882 q^{34} +4.03613 q^{35} +4.21287 q^{36} +2.90049 q^{37} -0.726777 q^{38} +12.1052 q^{39} -1.00000 q^{40} -9.05460 q^{41} -10.8397 q^{42} +1.00000 q^{43} +1.00000 q^{44} +4.21287 q^{45} +3.76465 q^{46} +12.3291 q^{47} +2.68568 q^{48} +9.29031 q^{49} -1.00000 q^{50} -15.3589 q^{51} +4.50732 q^{52} +5.86744 q^{53} -3.25739 q^{54} +1.00000 q^{55} -4.03613 q^{56} +1.95189 q^{57} -0.439002 q^{58} -4.85755 q^{59} +2.68568 q^{60} +8.76979 q^{61} +0.158220 q^{62} +17.0037 q^{63} +1.00000 q^{64} +4.50732 q^{65} -2.68568 q^{66} -5.33538 q^{67} -5.71882 q^{68} -10.1106 q^{69} -4.03613 q^{70} +13.1410 q^{71} -4.21287 q^{72} +5.57033 q^{73} -2.90049 q^{74} +2.68568 q^{75} +0.726777 q^{76} +4.03613 q^{77} -12.1052 q^{78} -0.750555 q^{79} +1.00000 q^{80} -3.89033 q^{81} +9.05460 q^{82} -1.03270 q^{83} +10.8397 q^{84} -5.71882 q^{85} -1.00000 q^{86} +1.17902 q^{87} -1.00000 q^{88} -1.17265 q^{89} -4.21287 q^{90} +18.1921 q^{91} -3.76465 q^{92} -0.424928 q^{93} -12.3291 q^{94} +0.726777 q^{95} -2.68568 q^{96} -5.36406 q^{97} -9.29031 q^{98} +4.21287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} - 10q^{10} + 10q^{11} + 8q^{12} + 7q^{13} - 3q^{14} + 8q^{15} + 10q^{16} + 2q^{17} - 14q^{18} - 7q^{19} + 10q^{20} - 2q^{21} - 10q^{22} + 12q^{23} - 8q^{24} + 10q^{25} - 7q^{26} + 23q^{27} + 3q^{28} - 12q^{29} - 8q^{30} + 16q^{31} - 10q^{32} + 8q^{33} - 2q^{34} + 3q^{35} + 14q^{36} + 19q^{37} + 7q^{38} + 6q^{39} - 10q^{40} + 9q^{41} + 2q^{42} + 10q^{43} + 10q^{44} + 14q^{45} - 12q^{46} + 29q^{47} + 8q^{48} + 23q^{49} - 10q^{50} - 7q^{51} + 7q^{52} + 6q^{53} - 23q^{54} + 10q^{55} - 3q^{56} + 23q^{57} + 12q^{58} + 29q^{59} + 8q^{60} - 4q^{61} - 16q^{62} + 10q^{64} + 7q^{65} - 8q^{66} + 45q^{67} + 2q^{68} + 24q^{69} - 3q^{70} - 18q^{71} - 14q^{72} + 3q^{73} - 19q^{74} + 8q^{75} - 7q^{76} + 3q^{77} - 6q^{78} - 14q^{79} + 10q^{80} + 6q^{81} - 9q^{82} + 23q^{83} - 2q^{84} + 2q^{85} - 10q^{86} + 25q^{87} - 10q^{88} + q^{89} - 14q^{90} + q^{91} + 12q^{92} + 35q^{93} - 29q^{94} - 7q^{95} - 8q^{96} + 30q^{97} - 23q^{98} + 14q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.68568 1.55058 0.775289 0.631607i \(-0.217604\pi\)
0.775289 + 0.631607i \(0.217604\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.68568 −1.09642
\(7\) 4.03613 1.52551 0.762756 0.646686i \(-0.223846\pi\)
0.762756 + 0.646686i \(0.223846\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.21287 1.40429
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 2.68568 0.775289
\(13\) 4.50732 1.25011 0.625053 0.780582i \(-0.285077\pi\)
0.625053 + 0.780582i \(0.285077\pi\)
\(14\) −4.03613 −1.07870
\(15\) 2.68568 0.693439
\(16\) 1.00000 0.250000
\(17\) −5.71882 −1.38702 −0.693509 0.720448i \(-0.743936\pi\)
−0.693509 + 0.720448i \(0.743936\pi\)
\(18\) −4.21287 −0.992983
\(19\) 0.726777 0.166734 0.0833671 0.996519i \(-0.473433\pi\)
0.0833671 + 0.996519i \(0.473433\pi\)
\(20\) 1.00000 0.223607
\(21\) 10.8397 2.36542
\(22\) −1.00000 −0.213201
\(23\) −3.76465 −0.784984 −0.392492 0.919755i \(-0.628387\pi\)
−0.392492 + 0.919755i \(0.628387\pi\)
\(24\) −2.68568 −0.548212
\(25\) 1.00000 0.200000
\(26\) −4.50732 −0.883958
\(27\) 3.25739 0.626884
\(28\) 4.03613 0.762756
\(29\) 0.439002 0.0815206 0.0407603 0.999169i \(-0.487022\pi\)
0.0407603 + 0.999169i \(0.487022\pi\)
\(30\) −2.68568 −0.490336
\(31\) −0.158220 −0.0284171 −0.0142086 0.999899i \(-0.504523\pi\)
−0.0142086 + 0.999899i \(0.504523\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.68568 0.467517
\(34\) 5.71882 0.980770
\(35\) 4.03613 0.682230
\(36\) 4.21287 0.702145
\(37\) 2.90049 0.476837 0.238419 0.971162i \(-0.423371\pi\)
0.238419 + 0.971162i \(0.423371\pi\)
\(38\) −0.726777 −0.117899
\(39\) 12.1052 1.93839
\(40\) −1.00000 −0.158114
\(41\) −9.05460 −1.41409 −0.707045 0.707168i \(-0.749972\pi\)
−0.707045 + 0.707168i \(0.749972\pi\)
\(42\) −10.8397 −1.67261
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 4.21287 0.628018
\(46\) 3.76465 0.555068
\(47\) 12.3291 1.79839 0.899195 0.437548i \(-0.144153\pi\)
0.899195 + 0.437548i \(0.144153\pi\)
\(48\) 2.68568 0.387644
\(49\) 9.29031 1.32719
\(50\) −1.00000 −0.141421
\(51\) −15.3589 −2.15068
\(52\) 4.50732 0.625053
\(53\) 5.86744 0.805955 0.402978 0.915210i \(-0.367975\pi\)
0.402978 + 0.915210i \(0.367975\pi\)
\(54\) −3.25739 −0.443274
\(55\) 1.00000 0.134840
\(56\) −4.03613 −0.539350
\(57\) 1.95189 0.258534
\(58\) −0.439002 −0.0576438
\(59\) −4.85755 −0.632399 −0.316199 0.948693i \(-0.602407\pi\)
−0.316199 + 0.948693i \(0.602407\pi\)
\(60\) 2.68568 0.346720
\(61\) 8.76979 1.12286 0.561429 0.827525i \(-0.310252\pi\)
0.561429 + 0.827525i \(0.310252\pi\)
\(62\) 0.158220 0.0200939
\(63\) 17.0037 2.14226
\(64\) 1.00000 0.125000
\(65\) 4.50732 0.559064
\(66\) −2.68568 −0.330584
\(67\) −5.33538 −0.651821 −0.325910 0.945401i \(-0.605671\pi\)
−0.325910 + 0.945401i \(0.605671\pi\)
\(68\) −5.71882 −0.693509
\(69\) −10.1106 −1.21718
\(70\) −4.03613 −0.482409
\(71\) 13.1410 1.55955 0.779773 0.626062i \(-0.215334\pi\)
0.779773 + 0.626062i \(0.215334\pi\)
\(72\) −4.21287 −0.496492
\(73\) 5.57033 0.651958 0.325979 0.945377i \(-0.394306\pi\)
0.325979 + 0.945377i \(0.394306\pi\)
\(74\) −2.90049 −0.337175
\(75\) 2.68568 0.310116
\(76\) 0.726777 0.0833671
\(77\) 4.03613 0.459959
\(78\) −12.1052 −1.37065
\(79\) −0.750555 −0.0844441 −0.0422220 0.999108i \(-0.513444\pi\)
−0.0422220 + 0.999108i \(0.513444\pi\)
\(80\) 1.00000 0.111803
\(81\) −3.89033 −0.432258
\(82\) 9.05460 0.999913
\(83\) −1.03270 −0.113354 −0.0566770 0.998393i \(-0.518051\pi\)
−0.0566770 + 0.998393i \(0.518051\pi\)
\(84\) 10.8397 1.18271
\(85\) −5.71882 −0.620293
\(86\) −1.00000 −0.107833
\(87\) 1.17902 0.126404
\(88\) −1.00000 −0.106600
\(89\) −1.17265 −0.124300 −0.0621502 0.998067i \(-0.519796\pi\)
−0.0621502 + 0.998067i \(0.519796\pi\)
\(90\) −4.21287 −0.444076
\(91\) 18.1921 1.90705
\(92\) −3.76465 −0.392492
\(93\) −0.424928 −0.0440629
\(94\) −12.3291 −1.27165
\(95\) 0.726777 0.0745658
\(96\) −2.68568 −0.274106
\(97\) −5.36406 −0.544637 −0.272319 0.962207i \(-0.587790\pi\)
−0.272319 + 0.962207i \(0.587790\pi\)
\(98\) −9.29031 −0.938463
\(99\) 4.21287 0.423410
\(100\) 1.00000 0.100000
\(101\) −10.0398 −0.998998 −0.499499 0.866314i \(-0.666483\pi\)
−0.499499 + 0.866314i \(0.666483\pi\)
\(102\) 15.3589 1.52076
\(103\) 3.78461 0.372909 0.186454 0.982464i \(-0.440300\pi\)
0.186454 + 0.982464i \(0.440300\pi\)
\(104\) −4.50732 −0.441979
\(105\) 10.8397 1.05785
\(106\) −5.86744 −0.569896
\(107\) −9.75462 −0.943015 −0.471507 0.881862i \(-0.656290\pi\)
−0.471507 + 0.881862i \(0.656290\pi\)
\(108\) 3.25739 0.313442
\(109\) 8.38098 0.802753 0.401376 0.915913i \(-0.368532\pi\)
0.401376 + 0.915913i \(0.368532\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 7.78978 0.739373
\(112\) 4.03613 0.381378
\(113\) −0.886368 −0.0833825 −0.0416912 0.999131i \(-0.513275\pi\)
−0.0416912 + 0.999131i \(0.513275\pi\)
\(114\) −1.95189 −0.182811
\(115\) −3.76465 −0.351056
\(116\) 0.439002 0.0407603
\(117\) 18.9888 1.75551
\(118\) 4.85755 0.447173
\(119\) −23.0819 −2.11591
\(120\) −2.68568 −0.245168
\(121\) 1.00000 0.0909091
\(122\) −8.76979 −0.793980
\(123\) −24.3178 −2.19266
\(124\) −0.158220 −0.0142086
\(125\) 1.00000 0.0894427
\(126\) −17.0037 −1.51481
\(127\) −12.4763 −1.10709 −0.553545 0.832819i \(-0.686725\pi\)
−0.553545 + 0.832819i \(0.686725\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.68568 0.236461
\(130\) −4.50732 −0.395318
\(131\) −2.00453 −0.175136 −0.0875681 0.996159i \(-0.527910\pi\)
−0.0875681 + 0.996159i \(0.527910\pi\)
\(132\) 2.68568 0.233758
\(133\) 2.93336 0.254355
\(134\) 5.33538 0.460907
\(135\) 3.25739 0.280351
\(136\) 5.71882 0.490385
\(137\) −18.3974 −1.57180 −0.785900 0.618354i \(-0.787800\pi\)
−0.785900 + 0.618354i \(0.787800\pi\)
\(138\) 10.1106 0.860676
\(139\) 11.5109 0.976343 0.488172 0.872748i \(-0.337664\pi\)
0.488172 + 0.872748i \(0.337664\pi\)
\(140\) 4.03613 0.341115
\(141\) 33.1121 2.78854
\(142\) −13.1410 −1.10277
\(143\) 4.50732 0.376921
\(144\) 4.21287 0.351073
\(145\) 0.439002 0.0364571
\(146\) −5.57033 −0.461004
\(147\) 24.9508 2.05791
\(148\) 2.90049 0.238419
\(149\) −2.50497 −0.205215 −0.102608 0.994722i \(-0.532719\pi\)
−0.102608 + 0.994722i \(0.532719\pi\)
\(150\) −2.68568 −0.219285
\(151\) −4.31360 −0.351036 −0.175518 0.984476i \(-0.556160\pi\)
−0.175518 + 0.984476i \(0.556160\pi\)
\(152\) −0.726777 −0.0589494
\(153\) −24.0927 −1.94778
\(154\) −4.03613 −0.325240
\(155\) −0.158220 −0.0127085
\(156\) 12.1052 0.969193
\(157\) 22.8158 1.82090 0.910451 0.413616i \(-0.135735\pi\)
0.910451 + 0.413616i \(0.135735\pi\)
\(158\) 0.750555 0.0597110
\(159\) 15.7581 1.24970
\(160\) −1.00000 −0.0790569
\(161\) −15.1946 −1.19750
\(162\) 3.89033 0.305653
\(163\) −9.31122 −0.729311 −0.364655 0.931143i \(-0.618813\pi\)
−0.364655 + 0.931143i \(0.618813\pi\)
\(164\) −9.05460 −0.707045
\(165\) 2.68568 0.209080
\(166\) 1.03270 0.0801534
\(167\) −17.8990 −1.38507 −0.692534 0.721385i \(-0.743506\pi\)
−0.692534 + 0.721385i \(0.743506\pi\)
\(168\) −10.8397 −0.836304
\(169\) 7.31595 0.562765
\(170\) 5.71882 0.438614
\(171\) 3.06182 0.234143
\(172\) 1.00000 0.0762493
\(173\) −19.3800 −1.47343 −0.736715 0.676203i \(-0.763624\pi\)
−0.736715 + 0.676203i \(0.763624\pi\)
\(174\) −1.17902 −0.0893812
\(175\) 4.03613 0.305102
\(176\) 1.00000 0.0753778
\(177\) −13.0458 −0.980583
\(178\) 1.17265 0.0878937
\(179\) 10.4063 0.777806 0.388903 0.921279i \(-0.372854\pi\)
0.388903 + 0.921279i \(0.372854\pi\)
\(180\) 4.21287 0.314009
\(181\) −14.6822 −1.09132 −0.545661 0.838006i \(-0.683721\pi\)
−0.545661 + 0.838006i \(0.683721\pi\)
\(182\) −18.1921 −1.34849
\(183\) 23.5529 1.74108
\(184\) 3.76465 0.277534
\(185\) 2.90049 0.213248
\(186\) 0.424928 0.0311572
\(187\) −5.71882 −0.418202
\(188\) 12.3291 0.899195
\(189\) 13.1472 0.956319
\(190\) −0.726777 −0.0527260
\(191\) 20.8338 1.50748 0.753740 0.657173i \(-0.228248\pi\)
0.753740 + 0.657173i \(0.228248\pi\)
\(192\) 2.68568 0.193822
\(193\) 2.97751 0.214326 0.107163 0.994241i \(-0.465823\pi\)
0.107163 + 0.994241i \(0.465823\pi\)
\(194\) 5.36406 0.385117
\(195\) 12.1052 0.866873
\(196\) 9.29031 0.663593
\(197\) −4.35502 −0.310282 −0.155141 0.987892i \(-0.549583\pi\)
−0.155141 + 0.987892i \(0.549583\pi\)
\(198\) −4.21287 −0.299396
\(199\) 12.0519 0.854335 0.427168 0.904172i \(-0.359511\pi\)
0.427168 + 0.904172i \(0.359511\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −14.3291 −1.01070
\(202\) 10.0398 0.706399
\(203\) 1.77187 0.124361
\(204\) −15.3589 −1.07534
\(205\) −9.05460 −0.632401
\(206\) −3.78461 −0.263686
\(207\) −15.8600 −1.10235
\(208\) 4.50732 0.312527
\(209\) 0.726777 0.0502722
\(210\) −10.8397 −0.748013
\(211\) −11.7432 −0.808432 −0.404216 0.914664i \(-0.632456\pi\)
−0.404216 + 0.914664i \(0.632456\pi\)
\(212\) 5.86744 0.402978
\(213\) 35.2924 2.41820
\(214\) 9.75462 0.666812
\(215\) 1.00000 0.0681994
\(216\) −3.25739 −0.221637
\(217\) −0.638595 −0.0433506
\(218\) −8.38098 −0.567632
\(219\) 14.9601 1.01091
\(220\) 1.00000 0.0674200
\(221\) −25.7766 −1.73392
\(222\) −7.78978 −0.522816
\(223\) −25.6670 −1.71879 −0.859395 0.511313i \(-0.829159\pi\)
−0.859395 + 0.511313i \(0.829159\pi\)
\(224\) −4.03613 −0.269675
\(225\) 4.21287 0.280858
\(226\) 0.886368 0.0589603
\(227\) 4.46614 0.296428 0.148214 0.988955i \(-0.452648\pi\)
0.148214 + 0.988955i \(0.452648\pi\)
\(228\) 1.95189 0.129267
\(229\) 13.9524 0.921998 0.460999 0.887401i \(-0.347491\pi\)
0.460999 + 0.887401i \(0.347491\pi\)
\(230\) 3.76465 0.248234
\(231\) 10.8397 0.713202
\(232\) −0.439002 −0.0288219
\(233\) 8.04351 0.526948 0.263474 0.964667i \(-0.415132\pi\)
0.263474 + 0.964667i \(0.415132\pi\)
\(234\) −18.9888 −1.24133
\(235\) 12.3291 0.804264
\(236\) −4.85755 −0.316199
\(237\) −2.01575 −0.130937
\(238\) 23.0819 1.49618
\(239\) 13.1546 0.850903 0.425451 0.904981i \(-0.360115\pi\)
0.425451 + 0.904981i \(0.360115\pi\)
\(240\) 2.68568 0.173360
\(241\) −3.94270 −0.253971 −0.126986 0.991905i \(-0.540530\pi\)
−0.126986 + 0.991905i \(0.540530\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −20.2203 −1.29713
\(244\) 8.76979 0.561429
\(245\) 9.29031 0.593536
\(246\) 24.3178 1.55044
\(247\) 3.27582 0.208435
\(248\) 0.158220 0.0100470
\(249\) −2.77351 −0.175764
\(250\) −1.00000 −0.0632456
\(251\) 5.58605 0.352588 0.176294 0.984338i \(-0.443589\pi\)
0.176294 + 0.984338i \(0.443589\pi\)
\(252\) 17.0037 1.07113
\(253\) −3.76465 −0.236682
\(254\) 12.4763 0.782831
\(255\) −15.3589 −0.961813
\(256\) 1.00000 0.0625000
\(257\) 1.66810 0.104053 0.0520266 0.998646i \(-0.483432\pi\)
0.0520266 + 0.998646i \(0.483432\pi\)
\(258\) −2.68568 −0.167203
\(259\) 11.7067 0.727421
\(260\) 4.50732 0.279532
\(261\) 1.84946 0.114479
\(262\) 2.00453 0.123840
\(263\) 0.235369 0.0145135 0.00725674 0.999974i \(-0.497690\pi\)
0.00725674 + 0.999974i \(0.497690\pi\)
\(264\) −2.68568 −0.165292
\(265\) 5.86744 0.360434
\(266\) −2.93336 −0.179856
\(267\) −3.14936 −0.192738
\(268\) −5.33538 −0.325910
\(269\) 7.77021 0.473758 0.236879 0.971539i \(-0.423875\pi\)
0.236879 + 0.971539i \(0.423875\pi\)
\(270\) −3.25739 −0.198238
\(271\) −8.68735 −0.527719 −0.263859 0.964561i \(-0.584995\pi\)
−0.263859 + 0.964561i \(0.584995\pi\)
\(272\) −5.71882 −0.346755
\(273\) 48.8582 2.95703
\(274\) 18.3974 1.11143
\(275\) 1.00000 0.0603023
\(276\) −10.1106 −0.608590
\(277\) −23.3828 −1.40493 −0.702467 0.711717i \(-0.747918\pi\)
−0.702467 + 0.711717i \(0.747918\pi\)
\(278\) −11.5109 −0.690379
\(279\) −0.666560 −0.0399059
\(280\) −4.03613 −0.241205
\(281\) −22.9108 −1.36674 −0.683372 0.730070i \(-0.739487\pi\)
−0.683372 + 0.730070i \(0.739487\pi\)
\(282\) −33.1121 −1.97180
\(283\) −25.9531 −1.54275 −0.771375 0.636381i \(-0.780431\pi\)
−0.771375 + 0.636381i \(0.780431\pi\)
\(284\) 13.1410 0.779773
\(285\) 1.95189 0.115620
\(286\) −4.50732 −0.266524
\(287\) −36.5455 −2.15721
\(288\) −4.21287 −0.248246
\(289\) 15.7049 0.923820
\(290\) −0.439002 −0.0257791
\(291\) −14.4061 −0.844502
\(292\) 5.57033 0.325979
\(293\) 30.7157 1.79443 0.897214 0.441596i \(-0.145588\pi\)
0.897214 + 0.441596i \(0.145588\pi\)
\(294\) −24.9508 −1.45516
\(295\) −4.85755 −0.282817
\(296\) −2.90049 −0.168587
\(297\) 3.25739 0.189013
\(298\) 2.50497 0.145109
\(299\) −16.9685 −0.981314
\(300\) 2.68568 0.155058
\(301\) 4.03613 0.232638
\(302\) 4.31360 0.248220
\(303\) −26.9637 −1.54902
\(304\) 0.726777 0.0416835
\(305\) 8.76979 0.502157
\(306\) 24.0927 1.37729
\(307\) −31.3822 −1.79108 −0.895539 0.444984i \(-0.853209\pi\)
−0.895539 + 0.444984i \(0.853209\pi\)
\(308\) 4.03613 0.229980
\(309\) 10.1642 0.578224
\(310\) 0.158220 0.00898628
\(311\) 0.0582887 0.00330525 0.00165262 0.999999i \(-0.499474\pi\)
0.00165262 + 0.999999i \(0.499474\pi\)
\(312\) −12.1052 −0.685323
\(313\) 34.8463 1.96963 0.984814 0.173613i \(-0.0555443\pi\)
0.984814 + 0.173613i \(0.0555443\pi\)
\(314\) −22.8158 −1.28757
\(315\) 17.0037 0.958049
\(316\) −0.750555 −0.0422220
\(317\) 4.32945 0.243166 0.121583 0.992581i \(-0.461203\pi\)
0.121583 + 0.992581i \(0.461203\pi\)
\(318\) −15.7581 −0.883669
\(319\) 0.439002 0.0245794
\(320\) 1.00000 0.0559017
\(321\) −26.1978 −1.46222
\(322\) 15.1946 0.846762
\(323\) −4.15631 −0.231263
\(324\) −3.89033 −0.216129
\(325\) 4.50732 0.250021
\(326\) 9.31122 0.515701
\(327\) 22.5086 1.24473
\(328\) 9.05460 0.499957
\(329\) 49.7620 2.74347
\(330\) −2.68568 −0.147842
\(331\) −34.2982 −1.88520 −0.942599 0.333928i \(-0.891626\pi\)
−0.942599 + 0.333928i \(0.891626\pi\)
\(332\) −1.03270 −0.0566770
\(333\) 12.2194 0.669618
\(334\) 17.8990 0.979391
\(335\) −5.33538 −0.291503
\(336\) 10.8397 0.591356
\(337\) 2.85858 0.155717 0.0778583 0.996964i \(-0.475192\pi\)
0.0778583 + 0.996964i \(0.475192\pi\)
\(338\) −7.31595 −0.397935
\(339\) −2.38050 −0.129291
\(340\) −5.71882 −0.310147
\(341\) −0.158220 −0.00856808
\(342\) −3.06182 −0.165564
\(343\) 9.24396 0.499127
\(344\) −1.00000 −0.0539164
\(345\) −10.1106 −0.544339
\(346\) 19.3800 1.04187
\(347\) 35.0563 1.88192 0.940959 0.338520i \(-0.109926\pi\)
0.940959 + 0.338520i \(0.109926\pi\)
\(348\) 1.17902 0.0632020
\(349\) −6.80924 −0.364490 −0.182245 0.983253i \(-0.558336\pi\)
−0.182245 + 0.983253i \(0.558336\pi\)
\(350\) −4.03613 −0.215740
\(351\) 14.6821 0.783672
\(352\) −1.00000 −0.0533002
\(353\) 3.46593 0.184473 0.0922363 0.995737i \(-0.470598\pi\)
0.0922363 + 0.995737i \(0.470598\pi\)
\(354\) 13.0458 0.693377
\(355\) 13.1410 0.697451
\(356\) −1.17265 −0.0621502
\(357\) −61.9905 −3.28089
\(358\) −10.4063 −0.549992
\(359\) −1.81960 −0.0960348 −0.0480174 0.998846i \(-0.515290\pi\)
−0.0480174 + 0.998846i \(0.515290\pi\)
\(360\) −4.21287 −0.222038
\(361\) −18.4718 −0.972200
\(362\) 14.6822 0.771681
\(363\) 2.68568 0.140962
\(364\) 18.1921 0.953526
\(365\) 5.57033 0.291564
\(366\) −23.5529 −1.23113
\(367\) 29.3384 1.53145 0.765726 0.643167i \(-0.222380\pi\)
0.765726 + 0.643167i \(0.222380\pi\)
\(368\) −3.76465 −0.196246
\(369\) −38.1459 −1.98579
\(370\) −2.90049 −0.150789
\(371\) 23.6817 1.22949
\(372\) −0.424928 −0.0220315
\(373\) −12.0503 −0.623942 −0.311971 0.950092i \(-0.600989\pi\)
−0.311971 + 0.950092i \(0.600989\pi\)
\(374\) 5.71882 0.295713
\(375\) 2.68568 0.138688
\(376\) −12.3291 −0.635827
\(377\) 1.97872 0.101909
\(378\) −13.1472 −0.676220
\(379\) −28.7165 −1.47507 −0.737534 0.675310i \(-0.764010\pi\)
−0.737534 + 0.675310i \(0.764010\pi\)
\(380\) 0.726777 0.0372829
\(381\) −33.5073 −1.71663
\(382\) −20.8338 −1.06595
\(383\) 8.14499 0.416189 0.208095 0.978109i \(-0.433274\pi\)
0.208095 + 0.978109i \(0.433274\pi\)
\(384\) −2.68568 −0.137053
\(385\) 4.03613 0.205700
\(386\) −2.97751 −0.151552
\(387\) 4.21287 0.214152
\(388\) −5.36406 −0.272319
\(389\) 14.1842 0.719166 0.359583 0.933113i \(-0.382919\pi\)
0.359583 + 0.933113i \(0.382919\pi\)
\(390\) −12.1052 −0.612972
\(391\) 21.5294 1.08879
\(392\) −9.29031 −0.469231
\(393\) −5.38351 −0.271562
\(394\) 4.35502 0.219403
\(395\) −0.750555 −0.0377645
\(396\) 4.21287 0.211705
\(397\) 1.83752 0.0922223 0.0461111 0.998936i \(-0.485317\pi\)
0.0461111 + 0.998936i \(0.485317\pi\)
\(398\) −12.0519 −0.604106
\(399\) 7.87807 0.394397
\(400\) 1.00000 0.0500000
\(401\) −20.3011 −1.01379 −0.506893 0.862009i \(-0.669206\pi\)
−0.506893 + 0.862009i \(0.669206\pi\)
\(402\) 14.3291 0.714672
\(403\) −0.713147 −0.0355244
\(404\) −10.0398 −0.499499
\(405\) −3.89033 −0.193312
\(406\) −1.77187 −0.0879363
\(407\) 2.90049 0.143772
\(408\) 15.3589 0.760380
\(409\) −17.9381 −0.886984 −0.443492 0.896278i \(-0.646261\pi\)
−0.443492 + 0.896278i \(0.646261\pi\)
\(410\) 9.05460 0.447175
\(411\) −49.4096 −2.43720
\(412\) 3.78461 0.186454
\(413\) −19.6057 −0.964731
\(414\) 15.8600 0.779476
\(415\) −1.03270 −0.0506935
\(416\) −4.50732 −0.220990
\(417\) 30.9146 1.51390
\(418\) −0.726777 −0.0355478
\(419\) −36.3304 −1.77486 −0.887428 0.460947i \(-0.847510\pi\)
−0.887428 + 0.460947i \(0.847510\pi\)
\(420\) 10.8397 0.528925
\(421\) 3.41690 0.166529 0.0832647 0.996527i \(-0.473465\pi\)
0.0832647 + 0.996527i \(0.473465\pi\)
\(422\) 11.7432 0.571648
\(423\) 51.9411 2.52546
\(424\) −5.86744 −0.284948
\(425\) −5.71882 −0.277404
\(426\) −35.2924 −1.70992
\(427\) 35.3960 1.71293
\(428\) −9.75462 −0.471507
\(429\) 12.1052 0.584445
\(430\) −1.00000 −0.0482243
\(431\) −2.97747 −0.143420 −0.0717099 0.997426i \(-0.522846\pi\)
−0.0717099 + 0.997426i \(0.522846\pi\)
\(432\) 3.25739 0.156721
\(433\) 12.5958 0.605316 0.302658 0.953099i \(-0.402126\pi\)
0.302658 + 0.953099i \(0.402126\pi\)
\(434\) 0.638595 0.0306535
\(435\) 1.17902 0.0565296
\(436\) 8.38098 0.401376
\(437\) −2.73606 −0.130884
\(438\) −14.9601 −0.714822
\(439\) −12.4899 −0.596109 −0.298055 0.954549i \(-0.596338\pi\)
−0.298055 + 0.954549i \(0.596338\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 39.1389 1.86376
\(442\) 25.7766 1.22607
\(443\) −5.84964 −0.277925 −0.138962 0.990298i \(-0.544377\pi\)
−0.138962 + 0.990298i \(0.544377\pi\)
\(444\) 7.78978 0.369687
\(445\) −1.17265 −0.0555889
\(446\) 25.6670 1.21537
\(447\) −6.72755 −0.318202
\(448\) 4.03613 0.190689
\(449\) 19.1094 0.901830 0.450915 0.892567i \(-0.351098\pi\)
0.450915 + 0.892567i \(0.351098\pi\)
\(450\) −4.21287 −0.198597
\(451\) −9.05460 −0.426364
\(452\) −0.886368 −0.0416912
\(453\) −11.5849 −0.544308
\(454\) −4.46614 −0.209606
\(455\) 18.1921 0.852859
\(456\) −1.95189 −0.0914056
\(457\) 11.4338 0.534853 0.267426 0.963578i \(-0.413827\pi\)
0.267426 + 0.963578i \(0.413827\pi\)
\(458\) −13.9524 −0.651951
\(459\) −18.6284 −0.869500
\(460\) −3.76465 −0.175528
\(461\) −22.6868 −1.05663 −0.528315 0.849049i \(-0.677176\pi\)
−0.528315 + 0.849049i \(0.677176\pi\)
\(462\) −10.8397 −0.504310
\(463\) 6.36213 0.295673 0.147837 0.989012i \(-0.452769\pi\)
0.147837 + 0.989012i \(0.452769\pi\)
\(464\) 0.439002 0.0203802
\(465\) −0.424928 −0.0197055
\(466\) −8.04351 −0.372608
\(467\) 26.9634 1.24772 0.623859 0.781537i \(-0.285564\pi\)
0.623859 + 0.781537i \(0.285564\pi\)
\(468\) 18.9888 0.877756
\(469\) −21.5343 −0.994360
\(470\) −12.3291 −0.568701
\(471\) 61.2760 2.82345
\(472\) 4.85755 0.223587
\(473\) 1.00000 0.0459800
\(474\) 2.01575 0.0925865
\(475\) 0.726777 0.0333468
\(476\) −23.0819 −1.05796
\(477\) 24.7188 1.13180
\(478\) −13.1546 −0.601679
\(479\) −21.1574 −0.966706 −0.483353 0.875426i \(-0.660581\pi\)
−0.483353 + 0.875426i \(0.660581\pi\)
\(480\) −2.68568 −0.122584
\(481\) 13.0734 0.596097
\(482\) 3.94270 0.179585
\(483\) −40.8078 −1.85682
\(484\) 1.00000 0.0454545
\(485\) −5.36406 −0.243569
\(486\) 20.2203 0.917212
\(487\) −4.38219 −0.198576 −0.0992880 0.995059i \(-0.531657\pi\)
−0.0992880 + 0.995059i \(0.531657\pi\)
\(488\) −8.76979 −0.396990
\(489\) −25.0069 −1.13085
\(490\) −9.29031 −0.419693
\(491\) −36.4434 −1.64467 −0.822334 0.569005i \(-0.807329\pi\)
−0.822334 + 0.569005i \(0.807329\pi\)
\(492\) −24.3178 −1.09633
\(493\) −2.51057 −0.113071
\(494\) −3.27582 −0.147386
\(495\) 4.21287 0.189355
\(496\) −0.158220 −0.00710428
\(497\) 53.0386 2.37911
\(498\) 2.77351 0.124284
\(499\) 24.1642 1.08174 0.540869 0.841107i \(-0.318095\pi\)
0.540869 + 0.841107i \(0.318095\pi\)
\(500\) 1.00000 0.0447214
\(501\) −48.0711 −2.14766
\(502\) −5.58605 −0.249318
\(503\) −1.04078 −0.0464060 −0.0232030 0.999731i \(-0.507386\pi\)
−0.0232030 + 0.999731i \(0.507386\pi\)
\(504\) −17.0037 −0.757404
\(505\) −10.0398 −0.446766
\(506\) 3.76465 0.167359
\(507\) 19.6483 0.872611
\(508\) −12.4763 −0.553545
\(509\) −17.6057 −0.780358 −0.390179 0.920739i \(-0.627587\pi\)
−0.390179 + 0.920739i \(0.627587\pi\)
\(510\) 15.3589 0.680105
\(511\) 22.4825 0.994569
\(512\) −1.00000 −0.0441942
\(513\) 2.36739 0.104523
\(514\) −1.66810 −0.0735767
\(515\) 3.78461 0.166770
\(516\) 2.68568 0.118230
\(517\) 12.3291 0.542235
\(518\) −11.7067 −0.514364
\(519\) −52.0483 −2.28467
\(520\) −4.50732 −0.197659
\(521\) 15.5035 0.679219 0.339609 0.940567i \(-0.389705\pi\)
0.339609 + 0.940567i \(0.389705\pi\)
\(522\) −1.84946 −0.0809486
\(523\) −23.2595 −1.01707 −0.508533 0.861042i \(-0.669812\pi\)
−0.508533 + 0.861042i \(0.669812\pi\)
\(524\) −2.00453 −0.0875681
\(525\) 10.8397 0.473085
\(526\) −0.235369 −0.0102626
\(527\) 0.904831 0.0394151
\(528\) 2.68568 0.116879
\(529\) −8.82739 −0.383800
\(530\) −5.86744 −0.254865
\(531\) −20.4642 −0.888071
\(532\) 2.93336 0.127177
\(533\) −40.8120 −1.76776
\(534\) 3.14936 0.136286
\(535\) −9.75462 −0.421729
\(536\) 5.33538 0.230453
\(537\) 27.9481 1.20605
\(538\) −7.77021 −0.334998
\(539\) 9.29031 0.400162
\(540\) 3.25739 0.140176
\(541\) 17.4581 0.750582 0.375291 0.926907i \(-0.377543\pi\)
0.375291 + 0.926907i \(0.377543\pi\)
\(542\) 8.68735 0.373154
\(543\) −39.4318 −1.69218
\(544\) 5.71882 0.245193
\(545\) 8.38098 0.359002
\(546\) −48.8582 −2.09094
\(547\) 34.1394 1.45970 0.729848 0.683609i \(-0.239591\pi\)
0.729848 + 0.683609i \(0.239591\pi\)
\(548\) −18.3974 −0.785900
\(549\) 36.9460 1.57682
\(550\) −1.00000 −0.0426401
\(551\) 0.319057 0.0135923
\(552\) 10.1106 0.430338
\(553\) −3.02934 −0.128820
\(554\) 23.3828 0.993438
\(555\) 7.78978 0.330658
\(556\) 11.5109 0.488172
\(557\) 15.2381 0.645661 0.322830 0.946457i \(-0.395366\pi\)
0.322830 + 0.946457i \(0.395366\pi\)
\(558\) 0.666560 0.0282177
\(559\) 4.50732 0.190639
\(560\) 4.03613 0.170557
\(561\) −15.3589 −0.648454
\(562\) 22.9108 0.966434
\(563\) −28.4428 −1.19872 −0.599360 0.800480i \(-0.704578\pi\)
−0.599360 + 0.800480i \(0.704578\pi\)
\(564\) 33.1121 1.39427
\(565\) −0.886368 −0.0372898
\(566\) 25.9531 1.09089
\(567\) −15.7018 −0.659415
\(568\) −13.1410 −0.551383
\(569\) −0.174420 −0.00731208 −0.00365604 0.999993i \(-0.501164\pi\)
−0.00365604 + 0.999993i \(0.501164\pi\)
\(570\) −1.95189 −0.0817557
\(571\) −9.83697 −0.411664 −0.205832 0.978587i \(-0.565990\pi\)
−0.205832 + 0.978587i \(0.565990\pi\)
\(572\) 4.50732 0.188461
\(573\) 55.9528 2.33746
\(574\) 36.5455 1.52538
\(575\) −3.76465 −0.156997
\(576\) 4.21287 0.175536
\(577\) 11.5851 0.482294 0.241147 0.970489i \(-0.422476\pi\)
0.241147 + 0.970489i \(0.422476\pi\)
\(578\) −15.7049 −0.653239
\(579\) 7.99665 0.332329
\(580\) 0.439002 0.0182286
\(581\) −4.16812 −0.172923
\(582\) 14.4061 0.597153
\(583\) 5.86744 0.243005
\(584\) −5.57033 −0.230502
\(585\) 18.9888 0.785089
\(586\) −30.7157 −1.26885
\(587\) 9.48513 0.391493 0.195747 0.980655i \(-0.437287\pi\)
0.195747 + 0.980655i \(0.437287\pi\)
\(588\) 24.9508 1.02895
\(589\) −0.114991 −0.00473810
\(590\) 4.85755 0.199982
\(591\) −11.6962 −0.481117
\(592\) 2.90049 0.119209
\(593\) −34.0358 −1.39768 −0.698841 0.715277i \(-0.746301\pi\)
−0.698841 + 0.715277i \(0.746301\pi\)
\(594\) −3.25739 −0.133652
\(595\) −23.0819 −0.946265
\(596\) −2.50497 −0.102608
\(597\) 32.3675 1.32471
\(598\) 16.9685 0.693894
\(599\) 42.3037 1.72848 0.864240 0.503079i \(-0.167800\pi\)
0.864240 + 0.503079i \(0.167800\pi\)
\(600\) −2.68568 −0.109642
\(601\) −11.6708 −0.476063 −0.238031 0.971257i \(-0.576502\pi\)
−0.238031 + 0.971257i \(0.576502\pi\)
\(602\) −4.03613 −0.164500
\(603\) −22.4773 −0.915346
\(604\) −4.31360 −0.175518
\(605\) 1.00000 0.0406558
\(606\) 26.9637 1.09533
\(607\) 16.6101 0.674183 0.337091 0.941472i \(-0.390557\pi\)
0.337091 + 0.941472i \(0.390557\pi\)
\(608\) −0.726777 −0.0294747
\(609\) 4.75867 0.192831
\(610\) −8.76979 −0.355079
\(611\) 55.5714 2.24818
\(612\) −24.0927 −0.973888
\(613\) 18.1911 0.734730 0.367365 0.930077i \(-0.380260\pi\)
0.367365 + 0.930077i \(0.380260\pi\)
\(614\) 31.3822 1.26648
\(615\) −24.3178 −0.980586
\(616\) −4.03613 −0.162620
\(617\) 18.5577 0.747104 0.373552 0.927609i \(-0.378140\pi\)
0.373552 + 0.927609i \(0.378140\pi\)
\(618\) −10.1642 −0.408866
\(619\) −22.1186 −0.889021 −0.444511 0.895774i \(-0.646622\pi\)
−0.444511 + 0.895774i \(0.646622\pi\)
\(620\) −0.158220 −0.00635426
\(621\) −12.2629 −0.492094
\(622\) −0.0582887 −0.00233716
\(623\) −4.73296 −0.189622
\(624\) 12.1052 0.484597
\(625\) 1.00000 0.0400000
\(626\) −34.8463 −1.39274
\(627\) 1.95189 0.0779510
\(628\) 22.8158 0.910451
\(629\) −16.5874 −0.661382
\(630\) −17.0037 −0.677443
\(631\) 24.7453 0.985097 0.492548 0.870285i \(-0.336065\pi\)
0.492548 + 0.870285i \(0.336065\pi\)
\(632\) 0.750555 0.0298555
\(633\) −31.5383 −1.25354
\(634\) −4.32945 −0.171944
\(635\) −12.4763 −0.495106
\(636\) 15.7581 0.624848
\(637\) 41.8744 1.65912
\(638\) −0.439002 −0.0173803
\(639\) 55.3612 2.19006
\(640\) −1.00000 −0.0395285
\(641\) 6.11770 0.241635 0.120817 0.992675i \(-0.461448\pi\)
0.120817 + 0.992675i \(0.461448\pi\)
\(642\) 26.1978 1.03394
\(643\) 33.7504 1.33098 0.665492 0.746405i \(-0.268222\pi\)
0.665492 + 0.746405i \(0.268222\pi\)
\(644\) −15.1946 −0.598751
\(645\) 2.68568 0.105749
\(646\) 4.15631 0.163528
\(647\) −15.7248 −0.618204 −0.309102 0.951029i \(-0.600029\pi\)
−0.309102 + 0.951029i \(0.600029\pi\)
\(648\) 3.89033 0.152826
\(649\) −4.85755 −0.190675
\(650\) −4.50732 −0.176792
\(651\) −1.71506 −0.0672185
\(652\) −9.31122 −0.364655
\(653\) 15.3568 0.600959 0.300479 0.953788i \(-0.402853\pi\)
0.300479 + 0.953788i \(0.402853\pi\)
\(654\) −22.5086 −0.880157
\(655\) −2.00453 −0.0783233
\(656\) −9.05460 −0.353523
\(657\) 23.4671 0.915538
\(658\) −49.7620 −1.93992
\(659\) 17.9440 0.698999 0.349499 0.936937i \(-0.386352\pi\)
0.349499 + 0.936937i \(0.386352\pi\)
\(660\) 2.68568 0.104540
\(661\) 12.1764 0.473606 0.236803 0.971558i \(-0.423900\pi\)
0.236803 + 0.971558i \(0.423900\pi\)
\(662\) 34.2982 1.33304
\(663\) −69.2276 −2.68858
\(664\) 1.03270 0.0400767
\(665\) 2.93336 0.113751
\(666\) −12.2194 −0.473492
\(667\) −1.65269 −0.0639924
\(668\) −17.8990 −0.692534
\(669\) −68.9333 −2.66512
\(670\) 5.33538 0.206124
\(671\) 8.76979 0.338554
\(672\) −10.8397 −0.418152
\(673\) 40.8234 1.57363 0.786813 0.617192i \(-0.211730\pi\)
0.786813 + 0.617192i \(0.211730\pi\)
\(674\) −2.85858 −0.110108
\(675\) 3.25739 0.125377
\(676\) 7.31595 0.281383
\(677\) 10.8623 0.417473 0.208737 0.977972i \(-0.433065\pi\)
0.208737 + 0.977972i \(0.433065\pi\)
\(678\) 2.38050 0.0914225
\(679\) −21.6500 −0.830851
\(680\) 5.71882 0.219307
\(681\) 11.9946 0.459635
\(682\) 0.158220 0.00605855
\(683\) 16.2402 0.621413 0.310706 0.950506i \(-0.399434\pi\)
0.310706 + 0.950506i \(0.399434\pi\)
\(684\) 3.06182 0.117072
\(685\) −18.3974 −0.702930
\(686\) −9.24396 −0.352936
\(687\) 37.4715 1.42963
\(688\) 1.00000 0.0381246
\(689\) 26.4464 1.00753
\(690\) 10.1106 0.384906
\(691\) −24.0637 −0.915426 −0.457713 0.889100i \(-0.651331\pi\)
−0.457713 + 0.889100i \(0.651331\pi\)
\(692\) −19.3800 −0.736715
\(693\) 17.0037 0.645916
\(694\) −35.0563 −1.33072
\(695\) 11.5109 0.436634
\(696\) −1.17902 −0.0446906
\(697\) 51.7817 1.96137
\(698\) 6.80924 0.257734
\(699\) 21.6023 0.817073
\(700\) 4.03613 0.152551
\(701\) −38.7175 −1.46234 −0.731170 0.682195i \(-0.761025\pi\)
−0.731170 + 0.682195i \(0.761025\pi\)
\(702\) −14.6821 −0.554139
\(703\) 2.10801 0.0795051
\(704\) 1.00000 0.0376889
\(705\) 33.1121 1.24707
\(706\) −3.46593 −0.130442
\(707\) −40.5219 −1.52398
\(708\) −13.0458 −0.490291
\(709\) 32.5123 1.22103 0.610513 0.792006i \(-0.290963\pi\)
0.610513 + 0.792006i \(0.290963\pi\)
\(710\) −13.1410 −0.493172
\(711\) −3.16199 −0.118584
\(712\) 1.17265 0.0439469
\(713\) 0.595643 0.0223070
\(714\) 61.9905 2.31994
\(715\) 4.50732 0.168564
\(716\) 10.4063 0.388903
\(717\) 35.3291 1.31939
\(718\) 1.81960 0.0679069
\(719\) 1.84506 0.0688093 0.0344046 0.999408i \(-0.489046\pi\)
0.0344046 + 0.999408i \(0.489046\pi\)
\(720\) 4.21287 0.157004
\(721\) 15.2752 0.568877
\(722\) 18.4718 0.687449
\(723\) −10.5888 −0.393802
\(724\) −14.6822 −0.545661
\(725\) 0.439002 0.0163041
\(726\) −2.68568 −0.0996749
\(727\) 32.0720 1.18948 0.594742 0.803917i \(-0.297254\pi\)
0.594742 + 0.803917i \(0.297254\pi\)
\(728\) −18.1921 −0.674245
\(729\) −42.6343 −1.57905
\(730\) −5.57033 −0.206167
\(731\) −5.71882 −0.211518
\(732\) 23.5529 0.870538
\(733\) 16.2652 0.600768 0.300384 0.953818i \(-0.402885\pi\)
0.300384 + 0.953818i \(0.402885\pi\)
\(734\) −29.3384 −1.08290
\(735\) 24.9508 0.920323
\(736\) 3.76465 0.138767
\(737\) −5.33538 −0.196531
\(738\) 38.1459 1.40417
\(739\) −29.6931 −1.09228 −0.546139 0.837695i \(-0.683903\pi\)
−0.546139 + 0.837695i \(0.683903\pi\)
\(740\) 2.90049 0.106624
\(741\) 8.79780 0.323195
\(742\) −23.6817 −0.869384
\(743\) −7.35234 −0.269731 −0.134866 0.990864i \(-0.543060\pi\)
−0.134866 + 0.990864i \(0.543060\pi\)
\(744\) 0.424928 0.0155786
\(745\) −2.50497 −0.0917751
\(746\) 12.0503 0.441194
\(747\) −4.35065 −0.159182
\(748\) −5.71882 −0.209101
\(749\) −39.3709 −1.43858
\(750\) −2.68568 −0.0980671
\(751\) 4.81681 0.175768 0.0878839 0.996131i \(-0.471990\pi\)
0.0878839 + 0.996131i \(0.471990\pi\)
\(752\) 12.3291 0.449597
\(753\) 15.0023 0.546715
\(754\) −1.97872 −0.0720608
\(755\) −4.31360 −0.156988
\(756\) 13.1472 0.478160
\(757\) −51.1734 −1.85993 −0.929965 0.367648i \(-0.880163\pi\)
−0.929965 + 0.367648i \(0.880163\pi\)
\(758\) 28.7165 1.04303
\(759\) −10.1106 −0.366993
\(760\) −0.726777 −0.0263630
\(761\) 42.4115 1.53742 0.768708 0.639599i \(-0.220900\pi\)
0.768708 + 0.639599i \(0.220900\pi\)
\(762\) 33.5073 1.21384
\(763\) 33.8267 1.22461
\(764\) 20.8338 0.753740
\(765\) −24.0927 −0.871072
\(766\) −8.14499 −0.294290
\(767\) −21.8945 −0.790565
\(768\) 2.68568 0.0969111
\(769\) 47.1086 1.69878 0.849390 0.527765i \(-0.176970\pi\)
0.849390 + 0.527765i \(0.176970\pi\)
\(770\) −4.03613 −0.145452
\(771\) 4.47998 0.161342
\(772\) 2.97751 0.107163
\(773\) −3.71435 −0.133596 −0.0667979 0.997767i \(-0.521278\pi\)
−0.0667979 + 0.997767i \(0.521278\pi\)
\(774\) −4.21287 −0.151429
\(775\) −0.158220 −0.00568342
\(776\) 5.36406 0.192558
\(777\) 31.4405 1.12792
\(778\) −14.1842 −0.508527
\(779\) −6.58068 −0.235777
\(780\) 12.1052 0.433436
\(781\) 13.1410 0.470221
\(782\) −21.5294 −0.769889
\(783\) 1.43000 0.0511040
\(784\) 9.29031 0.331797
\(785\) 22.8158 0.814332
\(786\) 5.38351 0.192024
\(787\) −40.9548 −1.45988 −0.729940 0.683511i \(-0.760452\pi\)
−0.729940 + 0.683511i \(0.760452\pi\)
\(788\) −4.35502 −0.155141
\(789\) 0.632126 0.0225043
\(790\) 0.750555 0.0267036
\(791\) −3.57749 −0.127201
\(792\) −4.21287 −0.149698
\(793\) 39.5283 1.40369
\(794\) −1.83752 −0.0652110
\(795\) 15.7581 0.558881
\(796\) 12.0519 0.427168
\(797\) −21.3456 −0.756101 −0.378050 0.925785i \(-0.623405\pi\)
−0.378050 + 0.925785i \(0.623405\pi\)
\(798\) −7.87807 −0.278881
\(799\) −70.5082 −2.49440
\(800\) −1.00000 −0.0353553
\(801\) −4.94022 −0.174554
\(802\) 20.3011 0.716855
\(803\) 5.57033 0.196573
\(804\) −14.3291 −0.505349
\(805\) −15.1946 −0.535540
\(806\) 0.713147 0.0251195
\(807\) 20.8683 0.734599
\(808\) 10.0398 0.353199
\(809\) −2.73636 −0.0962052 −0.0481026 0.998842i \(-0.515317\pi\)
−0.0481026 + 0.998842i \(0.515317\pi\)
\(810\) 3.89033 0.136692
\(811\) 6.38436 0.224185 0.112093 0.993698i \(-0.464245\pi\)
0.112093 + 0.993698i \(0.464245\pi\)
\(812\) 1.77187 0.0621803
\(813\) −23.3314 −0.818269
\(814\) −2.90049 −0.101662
\(815\) −9.31122 −0.326158
\(816\) −15.3589 −0.537670
\(817\) 0.726777 0.0254267
\(818\) 17.9381 0.627192
\(819\) 76.6410 2.67805
\(820\) −9.05460 −0.316200
\(821\) −41.9648 −1.46458 −0.732290 0.680993i \(-0.761549\pi\)
−0.732290 + 0.680993i \(0.761549\pi\)
\(822\) 49.4096 1.72336
\(823\) −37.0796 −1.29251 −0.646257 0.763120i \(-0.723667\pi\)
−0.646257 + 0.763120i \(0.723667\pi\)
\(824\) −3.78461 −0.131843
\(825\) 2.68568 0.0935033
\(826\) 19.6057 0.682168
\(827\) 18.9230 0.658016 0.329008 0.944327i \(-0.393286\pi\)
0.329008 + 0.944327i \(0.393286\pi\)
\(828\) −15.8600 −0.551173
\(829\) 17.0586 0.592471 0.296235 0.955115i \(-0.404269\pi\)
0.296235 + 0.955115i \(0.404269\pi\)
\(830\) 1.03270 0.0358457
\(831\) −62.7986 −2.17846
\(832\) 4.50732 0.156263
\(833\) −53.1296 −1.84083
\(834\) −30.9146 −1.07049
\(835\) −17.8990 −0.619422
\(836\) 0.726777 0.0251361
\(837\) −0.515383 −0.0178142
\(838\) 36.3304 1.25501
\(839\) 37.6563 1.30004 0.650021 0.759917i \(-0.274760\pi\)
0.650021 + 0.759917i \(0.274760\pi\)
\(840\) −10.8397 −0.374006
\(841\) −28.8073 −0.993354
\(842\) −3.41690 −0.117754
\(843\) −61.5311 −2.11924
\(844\) −11.7432 −0.404216
\(845\) 7.31595 0.251676
\(846\) −51.9411 −1.78577
\(847\) 4.03613 0.138683
\(848\) 5.86744 0.201489
\(849\) −69.7016 −2.39215
\(850\) 5.71882 0.196154
\(851\) −10.9193 −0.374310
\(852\) 35.2924 1.20910
\(853\) 1.72578 0.0590895 0.0295447 0.999563i \(-0.490594\pi\)
0.0295447 + 0.999563i \(0.490594\pi\)
\(854\) −35.3960 −1.21123
\(855\) 3.06182 0.104712
\(856\) 9.75462 0.333406
\(857\) 38.2570 1.30683 0.653417 0.756998i \(-0.273335\pi\)
0.653417 + 0.756998i \(0.273335\pi\)
\(858\) −12.1052 −0.413265
\(859\) 7.43934 0.253827 0.126913 0.991914i \(-0.459493\pi\)
0.126913 + 0.991914i \(0.459493\pi\)
\(860\) 1.00000 0.0340997
\(861\) −98.1495 −3.34493
\(862\) 2.97747 0.101413
\(863\) −29.9446 −1.01933 −0.509664 0.860374i \(-0.670230\pi\)
−0.509664 + 0.860374i \(0.670230\pi\)
\(864\) −3.25739 −0.110818
\(865\) −19.3800 −0.658938
\(866\) −12.5958 −0.428023
\(867\) 42.1784 1.43245
\(868\) −0.638595 −0.0216753
\(869\) −0.750555 −0.0254609
\(870\) −1.17902 −0.0399725
\(871\) −24.0483 −0.814845
\(872\) −8.38098 −0.283816
\(873\) −22.5981 −0.764829
\(874\) 2.73606 0.0925487
\(875\) 4.03613 0.136446
\(876\) 14.9601 0.505456
\(877\) −18.1849 −0.614059 −0.307030 0.951700i \(-0.599335\pi\)
−0.307030 + 0.951700i \(0.599335\pi\)
\(878\) 12.4899 0.421513
\(879\) 82.4924 2.78240
\(880\) 1.00000 0.0337100
\(881\) −32.8103 −1.10541 −0.552704 0.833378i \(-0.686404\pi\)
−0.552704 + 0.833378i \(0.686404\pi\)
\(882\) −39.1389 −1.31787
\(883\) −26.1867 −0.881253 −0.440626 0.897691i \(-0.645244\pi\)
−0.440626 + 0.897691i \(0.645244\pi\)
\(884\) −25.7766 −0.866960
\(885\) −13.0458 −0.438530
\(886\) 5.84964 0.196523
\(887\) 5.30684 0.178186 0.0890931 0.996023i \(-0.471603\pi\)
0.0890931 + 0.996023i \(0.471603\pi\)
\(888\) −7.78978 −0.261408
\(889\) −50.3558 −1.68888
\(890\) 1.17265 0.0393073
\(891\) −3.89033 −0.130331
\(892\) −25.6670 −0.859395
\(893\) 8.96054 0.299853
\(894\) 6.72755 0.225003
\(895\) 10.4063 0.347846
\(896\) −4.03613 −0.134837
\(897\) −45.5719 −1.52160
\(898\) −19.1094 −0.637690
\(899\) −0.0694588 −0.00231658
\(900\) 4.21287 0.140429
\(901\) −33.5549 −1.11787
\(902\) 9.05460 0.301485
\(903\) 10.8397 0.360724
\(904\) 0.886368 0.0294801
\(905\) −14.6822 −0.488054
\(906\) 11.5849 0.384884
\(907\) 50.5027 1.67692 0.838458 0.544967i \(-0.183458\pi\)
0.838458 + 0.544967i \(0.183458\pi\)
\(908\) 4.46614 0.148214
\(909\) −42.2964 −1.40288
\(910\) −18.1921 −0.603063
\(911\) 30.6067 1.01404 0.507022 0.861933i \(-0.330746\pi\)
0.507022 + 0.861933i \(0.330746\pi\)
\(912\) 1.95189 0.0646335
\(913\) −1.03270 −0.0341775
\(914\) −11.4338 −0.378198
\(915\) 23.5529 0.778633
\(916\) 13.9524 0.460999
\(917\) −8.09052 −0.267172
\(918\) 18.6284 0.614829
\(919\) −49.0686 −1.61862 −0.809312 0.587379i \(-0.800160\pi\)
−0.809312 + 0.587379i \(0.800160\pi\)
\(920\) 3.76465 0.124117
\(921\) −84.2825 −2.77720
\(922\) 22.6868 0.747150
\(923\) 59.2306 1.94960
\(924\) 10.8397 0.356601
\(925\) 2.90049 0.0953675
\(926\) −6.36213 −0.209072
\(927\) 15.9441 0.523672
\(928\) −0.439002 −0.0144109
\(929\) 41.1118 1.34884 0.674418 0.738350i \(-0.264395\pi\)
0.674418 + 0.738350i \(0.264395\pi\)
\(930\) 0.424928 0.0139339
\(931\) 6.75198 0.221287
\(932\) 8.04351 0.263474
\(933\) 0.156545 0.00512504
\(934\) −26.9634 −0.882270
\(935\) −5.71882 −0.187026
\(936\) −18.9888 −0.620667
\(937\) −4.27589 −0.139687 −0.0698436 0.997558i \(-0.522250\pi\)
−0.0698436 + 0.997558i \(0.522250\pi\)
\(938\) 21.5343 0.703119
\(939\) 93.5859 3.05406
\(940\) 12.3291 0.402132
\(941\) 15.9630 0.520378 0.260189 0.965558i \(-0.416215\pi\)
0.260189 + 0.965558i \(0.416215\pi\)
\(942\) −61.2760 −1.99648
\(943\) 34.0874 1.11004
\(944\) −4.85755 −0.158100
\(945\) 13.1472 0.427679
\(946\) −1.00000 −0.0325128
\(947\) 31.3512 1.01878 0.509388 0.860537i \(-0.329872\pi\)
0.509388 + 0.860537i \(0.329872\pi\)
\(948\) −2.01575 −0.0654686
\(949\) 25.1073 0.815016
\(950\) −0.726777 −0.0235798
\(951\) 11.6275 0.377048
\(952\) 23.0819 0.748088
\(953\) −23.5895 −0.764139 −0.382070 0.924134i \(-0.624789\pi\)
−0.382070 + 0.924134i \(0.624789\pi\)
\(954\) −24.7188 −0.800300
\(955\) 20.8338 0.674165
\(956\) 13.1546 0.425451
\(957\) 1.17902 0.0381123
\(958\) 21.1574 0.683564
\(959\) −74.2544 −2.39780
\(960\) 2.68568 0.0866799
\(961\) −30.9750 −0.999192
\(962\) −13.0734 −0.421504
\(963\) −41.0950 −1.32427
\(964\) −3.94270 −0.126986
\(965\) 2.97751 0.0958496
\(966\) 40.8078 1.31297
\(967\) −5.42913 −0.174589 −0.0872945 0.996183i \(-0.527822\pi\)
−0.0872945 + 0.996183i \(0.527822\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −11.1625 −0.358592
\(970\) 5.36406 0.172229
\(971\) −21.0286 −0.674841 −0.337421 0.941354i \(-0.609554\pi\)
−0.337421 + 0.941354i \(0.609554\pi\)
\(972\) −20.2203 −0.648567
\(973\) 46.4595 1.48942
\(974\) 4.38219 0.140414
\(975\) 12.1052 0.387677
\(976\) 8.76979 0.280714
\(977\) −34.1625 −1.09295 −0.546477 0.837474i \(-0.684031\pi\)
−0.546477 + 0.837474i \(0.684031\pi\)
\(978\) 25.0069 0.799634
\(979\) −1.17265 −0.0374780
\(980\) 9.29031 0.296768
\(981\) 35.3080 1.12730
\(982\) 36.4434 1.16296
\(983\) −59.3476 −1.89290 −0.946448 0.322857i \(-0.895357\pi\)
−0.946448 + 0.322857i \(0.895357\pi\)
\(984\) 24.3178 0.775222
\(985\) −4.35502 −0.138763
\(986\) 2.51057 0.0799530
\(987\) 133.645 4.25396
\(988\) 3.27582 0.104218
\(989\) −3.76465 −0.119709
\(990\) −4.21287 −0.133894
\(991\) −37.0321 −1.17636 −0.588181 0.808729i \(-0.700156\pi\)
−0.588181 + 0.808729i \(0.700156\pi\)
\(992\) 0.158220 0.00502348
\(993\) −92.1138 −2.92314
\(994\) −53.0386 −1.68228
\(995\) 12.0519 0.382070
\(996\) −2.77351 −0.0878821
\(997\) 31.7866 1.00669 0.503345 0.864085i \(-0.332102\pi\)
0.503345 + 0.864085i \(0.332102\pi\)
\(998\) −24.1642 −0.764905
\(999\) 9.44801 0.298922
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 4730.2.a.z.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.z.1.9 10 1.1 even 1 trivial