Properties

Label 966.4.a.f.1.1
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.9958450655\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.12197.1
Defining polynomial: \( x^{3} - x^{2} - 15x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.51691\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -9.55073 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -9.55073 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -19.1015 q^{10} -35.9402 q^{11} -12.0000 q^{12} +6.86023 q^{13} +14.0000 q^{14} +28.6522 q^{15} +16.0000 q^{16} -16.4786 q^{17} +18.0000 q^{18} -27.6437 q^{19} -38.2029 q^{20} -21.0000 q^{21} -71.8804 q^{22} -23.0000 q^{23} -24.0000 q^{24} -33.7836 q^{25} +13.7205 q^{26} -27.0000 q^{27} +28.0000 q^{28} +307.579 q^{29} +57.3044 q^{30} +278.757 q^{31} +32.0000 q^{32} +107.821 q^{33} -32.9572 q^{34} -66.8551 q^{35} +36.0000 q^{36} -225.756 q^{37} -55.2874 q^{38} -20.5807 q^{39} -76.4058 q^{40} +151.015 q^{41} -42.0000 q^{42} -434.639 q^{43} -143.761 q^{44} -85.9566 q^{45} -46.0000 q^{46} +281.123 q^{47} -48.0000 q^{48} +49.0000 q^{49} -67.5672 q^{50} +49.4358 q^{51} +27.4409 q^{52} -337.199 q^{53} -54.0000 q^{54} +343.255 q^{55} +56.0000 q^{56} +82.9311 q^{57} +615.158 q^{58} +744.753 q^{59} +114.609 q^{60} -345.004 q^{61} +557.514 q^{62} +63.0000 q^{63} +64.0000 q^{64} -65.5202 q^{65} +215.641 q^{66} +465.795 q^{67} -65.9144 q^{68} +69.0000 q^{69} -133.710 q^{70} +956.929 q^{71} +72.0000 q^{72} +536.007 q^{73} -451.512 q^{74} +101.351 q^{75} -110.575 q^{76} -251.582 q^{77} -41.1614 q^{78} -541.100 q^{79} -152.812 q^{80} +81.0000 q^{81} +302.030 q^{82} +352.599 q^{83} -84.0000 q^{84} +157.383 q^{85} -869.278 q^{86} -922.736 q^{87} -287.522 q^{88} +1532.67 q^{89} -171.913 q^{90} +48.0216 q^{91} -92.0000 q^{92} -836.271 q^{93} +562.246 q^{94} +264.017 q^{95} -96.0000 q^{96} -226.807 q^{97} +98.0000 q^{98} -323.462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9} + 18 q^{10} + 53 q^{11} - 36 q^{12} + 61 q^{13} + 42 q^{14} - 27 q^{15} + 48 q^{16} - 2 q^{17} + 54 q^{18} + 63 q^{19} + 36 q^{20} - 63 q^{21} + 106 q^{22} - 69 q^{23} - 72 q^{24} - 72 q^{25} + 122 q^{26} - 81 q^{27} + 84 q^{28} + 312 q^{29} - 54 q^{30} + 220 q^{31} + 96 q^{32} - 159 q^{33} - 4 q^{34} + 63 q^{35} + 108 q^{36} - 44 q^{37} + 126 q^{38} - 183 q^{39} + 72 q^{40} + 171 q^{41} - 126 q^{42} - 627 q^{43} + 212 q^{44} + 81 q^{45} - 138 q^{46} + 353 q^{47} - 144 q^{48} + 147 q^{49} - 144 q^{50} + 6 q^{51} + 244 q^{52} - 504 q^{53} - 162 q^{54} + 1181 q^{55} + 168 q^{56} - 189 q^{57} + 624 q^{58} + 538 q^{59} - 108 q^{60} + 256 q^{61} + 440 q^{62} + 189 q^{63} + 192 q^{64} + 244 q^{65} - 318 q^{66} + 1113 q^{67} - 8 q^{68} + 207 q^{69} + 126 q^{70} + 53 q^{71} + 216 q^{72} + 360 q^{73} - 88 q^{74} + 216 q^{75} + 252 q^{76} + 371 q^{77} - 366 q^{78} + 134 q^{79} + 144 q^{80} + 243 q^{81} + 342 q^{82} + 1506 q^{83} - 252 q^{84} + 577 q^{85} - 1254 q^{86} - 936 q^{87} + 424 q^{88} + 2381 q^{89} + 162 q^{90} + 427 q^{91} - 276 q^{92} - 660 q^{93} + 706 q^{94} + 945 q^{95} - 288 q^{96} - 88 q^{97} + 294 q^{98} + 477 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) −9.55073 −0.854243 −0.427122 0.904194i \(-0.640472\pi\)
−0.427122 + 0.904194i \(0.640472\pi\)
\(6\) −6.00000 −0.408248
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −19.1015 −0.604041
\(11\) −35.9402 −0.985126 −0.492563 0.870277i \(-0.663940\pi\)
−0.492563 + 0.870277i \(0.663940\pi\)
\(12\) −12.0000 −0.288675
\(13\) 6.86023 0.146360 0.0731802 0.997319i \(-0.476685\pi\)
0.0731802 + 0.997319i \(0.476685\pi\)
\(14\) 14.0000 0.267261
\(15\) 28.6522 0.493197
\(16\) 16.0000 0.250000
\(17\) −16.4786 −0.235097 −0.117548 0.993067i \(-0.537504\pi\)
−0.117548 + 0.993067i \(0.537504\pi\)
\(18\) 18.0000 0.235702
\(19\) −27.6437 −0.333784 −0.166892 0.985975i \(-0.553373\pi\)
−0.166892 + 0.985975i \(0.553373\pi\)
\(20\) −38.2029 −0.427122
\(21\) −21.0000 −0.218218
\(22\) −71.8804 −0.696589
\(23\) −23.0000 −0.208514
\(24\) −24.0000 −0.204124
\(25\) −33.7836 −0.270269
\(26\) 13.7205 0.103492
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) 307.579 1.96952 0.984758 0.173932i \(-0.0556472\pi\)
0.984758 + 0.173932i \(0.0556472\pi\)
\(30\) 57.3044 0.348743
\(31\) 278.757 1.61504 0.807520 0.589841i \(-0.200809\pi\)
0.807520 + 0.589841i \(0.200809\pi\)
\(32\) 32.0000 0.176777
\(33\) 107.821 0.568763
\(34\) −32.9572 −0.166239
\(35\) −66.8551 −0.322874
\(36\) 36.0000 0.166667
\(37\) −225.756 −1.00308 −0.501541 0.865134i \(-0.667233\pi\)
−0.501541 + 0.865134i \(0.667233\pi\)
\(38\) −55.2874 −0.236021
\(39\) −20.5807 −0.0845012
\(40\) −76.4058 −0.302021
\(41\) 151.015 0.575233 0.287617 0.957746i \(-0.407137\pi\)
0.287617 + 0.957746i \(0.407137\pi\)
\(42\) −42.0000 −0.154303
\(43\) −434.639 −1.54144 −0.770719 0.637176i \(-0.780103\pi\)
−0.770719 + 0.637176i \(0.780103\pi\)
\(44\) −143.761 −0.492563
\(45\) −85.9566 −0.284748
\(46\) −46.0000 −0.147442
\(47\) 281.123 0.872468 0.436234 0.899833i \(-0.356312\pi\)
0.436234 + 0.899833i \(0.356312\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −67.5672 −0.191109
\(51\) 49.4358 0.135733
\(52\) 27.4409 0.0731802
\(53\) −337.199 −0.873922 −0.436961 0.899480i \(-0.643945\pi\)
−0.436961 + 0.899480i \(0.643945\pi\)
\(54\) −54.0000 −0.136083
\(55\) 343.255 0.841537
\(56\) 56.0000 0.133631
\(57\) 82.9311 0.192710
\(58\) 615.158 1.39266
\(59\) 744.753 1.64337 0.821683 0.569945i \(-0.193036\pi\)
0.821683 + 0.569945i \(0.193036\pi\)
\(60\) 114.609 0.246599
\(61\) −345.004 −0.724151 −0.362076 0.932149i \(-0.617932\pi\)
−0.362076 + 0.932149i \(0.617932\pi\)
\(62\) 557.514 1.14201
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) −65.5202 −0.125027
\(66\) 215.641 0.402176
\(67\) 465.795 0.849341 0.424671 0.905348i \(-0.360390\pi\)
0.424671 + 0.905348i \(0.360390\pi\)
\(68\) −65.9144 −0.117548
\(69\) 69.0000 0.120386
\(70\) −133.710 −0.228306
\(71\) 956.929 1.59953 0.799765 0.600313i \(-0.204957\pi\)
0.799765 + 0.600313i \(0.204957\pi\)
\(72\) 72.0000 0.117851
\(73\) 536.007 0.859383 0.429691 0.902976i \(-0.358622\pi\)
0.429691 + 0.902976i \(0.358622\pi\)
\(74\) −451.512 −0.709286
\(75\) 101.351 0.156040
\(76\) −110.575 −0.166892
\(77\) −251.582 −0.372343
\(78\) −41.1614 −0.0597514
\(79\) −541.100 −0.770614 −0.385307 0.922789i \(-0.625904\pi\)
−0.385307 + 0.922789i \(0.625904\pi\)
\(80\) −152.812 −0.213561
\(81\) 81.0000 0.111111
\(82\) 302.030 0.406751
\(83\) 352.599 0.466299 0.233149 0.972441i \(-0.425097\pi\)
0.233149 + 0.972441i \(0.425097\pi\)
\(84\) −84.0000 −0.109109
\(85\) 157.383 0.200830
\(86\) −869.278 −1.08996
\(87\) −922.736 −1.13710
\(88\) −287.522 −0.348295
\(89\) 1532.67 1.82542 0.912709 0.408609i \(-0.133986\pi\)
0.912709 + 0.408609i \(0.133986\pi\)
\(90\) −171.913 −0.201347
\(91\) 48.0216 0.0553190
\(92\) −92.0000 −0.104257
\(93\) −836.271 −0.932443
\(94\) 562.246 0.616928
\(95\) 264.017 0.285133
\(96\) −96.0000 −0.102062
\(97\) −226.807 −0.237410 −0.118705 0.992930i \(-0.537874\pi\)
−0.118705 + 0.992930i \(0.537874\pi\)
\(98\) 98.0000 0.101015
\(99\) −323.462 −0.328375
\(100\) −135.134 −0.135134
\(101\) 1469.57 1.44780 0.723898 0.689907i \(-0.242348\pi\)
0.723898 + 0.689907i \(0.242348\pi\)
\(102\) 98.8715 0.0959779
\(103\) 385.377 0.368664 0.184332 0.982864i \(-0.440988\pi\)
0.184332 + 0.982864i \(0.440988\pi\)
\(104\) 54.8818 0.0517462
\(105\) 200.565 0.186411
\(106\) −674.398 −0.617956
\(107\) −800.857 −0.723568 −0.361784 0.932262i \(-0.617832\pi\)
−0.361784 + 0.932262i \(0.617832\pi\)
\(108\) −108.000 −0.0962250
\(109\) 1223.90 1.07549 0.537746 0.843107i \(-0.319276\pi\)
0.537746 + 0.843107i \(0.319276\pi\)
\(110\) 686.510 0.595056
\(111\) 677.268 0.579130
\(112\) 112.000 0.0944911
\(113\) 1282.72 1.06786 0.533929 0.845529i \(-0.320715\pi\)
0.533929 + 0.845529i \(0.320715\pi\)
\(114\) 165.862 0.136267
\(115\) 219.667 0.178122
\(116\) 1230.32 0.984758
\(117\) 61.7420 0.0487868
\(118\) 1489.51 1.16204
\(119\) −115.350 −0.0888582
\(120\) 229.217 0.174372
\(121\) −39.3008 −0.0295273
\(122\) −690.008 −0.512052
\(123\) −453.045 −0.332111
\(124\) 1115.03 0.807520
\(125\) 1516.50 1.08512
\(126\) 126.000 0.0890871
\(127\) 2271.45 1.58708 0.793538 0.608521i \(-0.208237\pi\)
0.793538 + 0.608521i \(0.208237\pi\)
\(128\) 128.000 0.0883883
\(129\) 1303.92 0.889949
\(130\) −131.040 −0.0884077
\(131\) 564.729 0.376646 0.188323 0.982107i \(-0.439695\pi\)
0.188323 + 0.982107i \(0.439695\pi\)
\(132\) 431.283 0.284381
\(133\) −193.506 −0.126159
\(134\) 931.589 0.600575
\(135\) 257.870 0.164399
\(136\) −131.829 −0.0831193
\(137\) 328.883 0.205097 0.102549 0.994728i \(-0.467300\pi\)
0.102549 + 0.994728i \(0.467300\pi\)
\(138\) 138.000 0.0851257
\(139\) −2044.79 −1.24775 −0.623874 0.781525i \(-0.714442\pi\)
−0.623874 + 0.781525i \(0.714442\pi\)
\(140\) −267.420 −0.161437
\(141\) −843.369 −0.503720
\(142\) 1913.86 1.13104
\(143\) −246.558 −0.144183
\(144\) 144.000 0.0833333
\(145\) −2937.60 −1.68244
\(146\) 1072.01 0.607675
\(147\) −147.000 −0.0824786
\(148\) −903.024 −0.501541
\(149\) 579.529 0.318637 0.159318 0.987227i \(-0.449070\pi\)
0.159318 + 0.987227i \(0.449070\pi\)
\(150\) 202.702 0.110337
\(151\) 3304.67 1.78100 0.890498 0.454988i \(-0.150357\pi\)
0.890498 + 0.454988i \(0.150357\pi\)
\(152\) −221.150 −0.118011
\(153\) −148.307 −0.0783656
\(154\) −503.163 −0.263286
\(155\) −2662.33 −1.37964
\(156\) −82.3227 −0.0422506
\(157\) −1808.40 −0.919272 −0.459636 0.888107i \(-0.652020\pi\)
−0.459636 + 0.888107i \(0.652020\pi\)
\(158\) −1082.20 −0.544906
\(159\) 1011.60 0.504559
\(160\) −305.623 −0.151010
\(161\) −161.000 −0.0788110
\(162\) 162.000 0.0785674
\(163\) −66.5723 −0.0319898 −0.0159949 0.999872i \(-0.505092\pi\)
−0.0159949 + 0.999872i \(0.505092\pi\)
\(164\) 604.060 0.287617
\(165\) −1029.77 −0.485862
\(166\) 705.198 0.329723
\(167\) −336.954 −0.156133 −0.0780667 0.996948i \(-0.524875\pi\)
−0.0780667 + 0.996948i \(0.524875\pi\)
\(168\) −168.000 −0.0771517
\(169\) −2149.94 −0.978579
\(170\) 314.765 0.142008
\(171\) −248.793 −0.111261
\(172\) −1738.56 −0.770719
\(173\) −318.130 −0.139809 −0.0699045 0.997554i \(-0.522269\pi\)
−0.0699045 + 0.997554i \(0.522269\pi\)
\(174\) −1845.47 −0.804051
\(175\) −236.485 −0.102152
\(176\) −575.043 −0.246281
\(177\) −2234.26 −0.948798
\(178\) 3065.33 1.29077
\(179\) −1968.94 −0.822152 −0.411076 0.911601i \(-0.634847\pi\)
−0.411076 + 0.911601i \(0.634847\pi\)
\(180\) −343.826 −0.142374
\(181\) 3805.14 1.56262 0.781308 0.624146i \(-0.214553\pi\)
0.781308 + 0.624146i \(0.214553\pi\)
\(182\) 96.0432 0.0391164
\(183\) 1035.01 0.418089
\(184\) −184.000 −0.0737210
\(185\) 2156.13 0.856876
\(186\) −1672.54 −0.659337
\(187\) 592.244 0.231600
\(188\) 1124.49 0.436234
\(189\) −189.000 −0.0727393
\(190\) 528.035 0.201619
\(191\) 1563.67 0.592374 0.296187 0.955130i \(-0.404285\pi\)
0.296187 + 0.955130i \(0.404285\pi\)
\(192\) −192.000 −0.0721688
\(193\) −4114.00 −1.53436 −0.767182 0.641430i \(-0.778342\pi\)
−0.767182 + 0.641430i \(0.778342\pi\)
\(194\) −453.614 −0.167874
\(195\) 196.560 0.0721845
\(196\) 196.000 0.0714286
\(197\) 1143.47 0.413548 0.206774 0.978389i \(-0.433703\pi\)
0.206774 + 0.978389i \(0.433703\pi\)
\(198\) −646.924 −0.232196
\(199\) −4.64969 −0.00165632 −0.000828161 1.00000i \(-0.500264\pi\)
−0.000828161 1.00000i \(0.500264\pi\)
\(200\) −270.269 −0.0955544
\(201\) −1397.38 −0.490367
\(202\) 2939.14 1.02375
\(203\) 2153.05 0.744407
\(204\) 197.743 0.0678666
\(205\) −1442.30 −0.491389
\(206\) 770.754 0.260685
\(207\) −207.000 −0.0695048
\(208\) 109.764 0.0365901
\(209\) 993.521 0.328819
\(210\) 401.131 0.131813
\(211\) −164.636 −0.0537157 −0.0268579 0.999639i \(-0.508550\pi\)
−0.0268579 + 0.999639i \(0.508550\pi\)
\(212\) −1348.80 −0.436961
\(213\) −2870.79 −0.923489
\(214\) −1601.71 −0.511640
\(215\) 4151.12 1.31676
\(216\) −216.000 −0.0680414
\(217\) 1951.30 0.610427
\(218\) 2447.81 0.760488
\(219\) −1608.02 −0.496165
\(220\) 1373.02 0.420768
\(221\) −113.047 −0.0344088
\(222\) 1354.54 0.409507
\(223\) −4061.56 −1.21965 −0.609826 0.792536i \(-0.708761\pi\)
−0.609826 + 0.792536i \(0.708761\pi\)
\(224\) 224.000 0.0668153
\(225\) −304.052 −0.0900896
\(226\) 2565.44 0.755090
\(227\) −3183.98 −0.930961 −0.465481 0.885058i \(-0.654118\pi\)
−0.465481 + 0.885058i \(0.654118\pi\)
\(228\) 331.724 0.0963552
\(229\) 1190.00 0.343395 0.171697 0.985150i \(-0.445075\pi\)
0.171697 + 0.985150i \(0.445075\pi\)
\(230\) 439.333 0.125951
\(231\) 754.745 0.214972
\(232\) 2460.63 0.696329
\(233\) −6794.69 −1.91045 −0.955225 0.295880i \(-0.904387\pi\)
−0.955225 + 0.295880i \(0.904387\pi\)
\(234\) 123.484 0.0344975
\(235\) −2684.93 −0.745300
\(236\) 2979.01 0.821683
\(237\) 1623.30 0.444914
\(238\) −230.700 −0.0628323
\(239\) −4026.00 −1.08962 −0.544812 0.838558i \(-0.683399\pi\)
−0.544812 + 0.838558i \(0.683399\pi\)
\(240\) 458.435 0.123299
\(241\) 4787.52 1.27963 0.639816 0.768528i \(-0.279011\pi\)
0.639816 + 0.768528i \(0.279011\pi\)
\(242\) −78.6016 −0.0208789
\(243\) −243.000 −0.0641500
\(244\) −1380.02 −0.362076
\(245\) −467.986 −0.122035
\(246\) −906.089 −0.234838
\(247\) −189.642 −0.0488528
\(248\) 2230.06 0.571003
\(249\) −1057.80 −0.269218
\(250\) 3033.00 0.767295
\(251\) −5233.59 −1.31610 −0.658050 0.752974i \(-0.728618\pi\)
−0.658050 + 0.752974i \(0.728618\pi\)
\(252\) 252.000 0.0629941
\(253\) 826.625 0.205413
\(254\) 4542.90 1.12223
\(255\) −472.148 −0.115949
\(256\) 256.000 0.0625000
\(257\) 3160.14 0.767020 0.383510 0.923537i \(-0.374715\pi\)
0.383510 + 0.923537i \(0.374715\pi\)
\(258\) 2607.83 0.629289
\(259\) −1580.29 −0.379130
\(260\) −262.081 −0.0625137
\(261\) 2768.21 0.656505
\(262\) 1129.46 0.266329
\(263\) 5199.28 1.21902 0.609509 0.792779i \(-0.291367\pi\)
0.609509 + 0.792779i \(0.291367\pi\)
\(264\) 862.565 0.201088
\(265\) 3220.50 0.746542
\(266\) −387.012 −0.0892076
\(267\) −4598.00 −1.05391
\(268\) 1863.18 0.424671
\(269\) −4909.49 −1.11278 −0.556389 0.830922i \(-0.687813\pi\)
−0.556389 + 0.830922i \(0.687813\pi\)
\(270\) 515.739 0.116248
\(271\) 4007.30 0.898252 0.449126 0.893468i \(-0.351735\pi\)
0.449126 + 0.893468i \(0.351735\pi\)
\(272\) −263.657 −0.0587742
\(273\) −144.065 −0.0319384
\(274\) 657.766 0.145026
\(275\) 1214.19 0.266249
\(276\) 276.000 0.0601929
\(277\) 2529.96 0.548775 0.274388 0.961619i \(-0.411525\pi\)
0.274388 + 0.961619i \(0.411525\pi\)
\(278\) −4089.59 −0.882292
\(279\) 2508.81 0.538346
\(280\) −534.841 −0.114153
\(281\) −8234.37 −1.74812 −0.874059 0.485820i \(-0.838521\pi\)
−0.874059 + 0.485820i \(0.838521\pi\)
\(282\) −1686.74 −0.356184
\(283\) 6374.51 1.33896 0.669479 0.742831i \(-0.266517\pi\)
0.669479 + 0.742831i \(0.266517\pi\)
\(284\) 3827.72 0.799765
\(285\) −792.052 −0.164622
\(286\) −493.116 −0.101953
\(287\) 1057.10 0.217418
\(288\) 288.000 0.0589256
\(289\) −4641.46 −0.944729
\(290\) −5875.20 −1.18967
\(291\) 680.420 0.137069
\(292\) 2144.03 0.429691
\(293\) 3946.21 0.786825 0.393413 0.919362i \(-0.371294\pi\)
0.393413 + 0.919362i \(0.371294\pi\)
\(294\) −294.000 −0.0583212
\(295\) −7112.93 −1.40383
\(296\) −1806.05 −0.354643
\(297\) 970.386 0.189588
\(298\) 1159.06 0.225310
\(299\) −157.785 −0.0305182
\(300\) 405.403 0.0780199
\(301\) −3042.47 −0.582609
\(302\) 6609.34 1.25935
\(303\) −4408.70 −0.835886
\(304\) −442.299 −0.0834461
\(305\) 3295.04 0.618601
\(306\) −296.615 −0.0554128
\(307\) −251.364 −0.0467300 −0.0233650 0.999727i \(-0.507438\pi\)
−0.0233650 + 0.999727i \(0.507438\pi\)
\(308\) −1006.33 −0.186171
\(309\) −1156.13 −0.212848
\(310\) −5324.66 −0.975550
\(311\) −2787.66 −0.508276 −0.254138 0.967168i \(-0.581792\pi\)
−0.254138 + 0.967168i \(0.581792\pi\)
\(312\) −164.645 −0.0298757
\(313\) −585.191 −0.105677 −0.0528386 0.998603i \(-0.516827\pi\)
−0.0528386 + 0.998603i \(0.516827\pi\)
\(314\) −3616.79 −0.650024
\(315\) −601.696 −0.107625
\(316\) −2164.40 −0.385307
\(317\) 2421.83 0.429096 0.214548 0.976713i \(-0.431172\pi\)
0.214548 + 0.976713i \(0.431172\pi\)
\(318\) 2023.19 0.356777
\(319\) −11054.4 −1.94022
\(320\) −611.247 −0.106780
\(321\) 2402.57 0.417752
\(322\) −322.000 −0.0557278
\(323\) 455.529 0.0784716
\(324\) 324.000 0.0555556
\(325\) −231.763 −0.0395566
\(326\) −133.145 −0.0226202
\(327\) −3671.71 −0.620936
\(328\) 1208.12 0.203376
\(329\) 1967.86 0.329762
\(330\) −2059.53 −0.343556
\(331\) 1910.61 0.317270 0.158635 0.987337i \(-0.449291\pi\)
0.158635 + 0.987337i \(0.449291\pi\)
\(332\) 1410.40 0.233149
\(333\) −2031.80 −0.334361
\(334\) −673.908 −0.110403
\(335\) −4448.68 −0.725544
\(336\) −336.000 −0.0545545
\(337\) −1119.18 −0.180907 −0.0904533 0.995901i \(-0.528832\pi\)
−0.0904533 + 0.995901i \(0.528832\pi\)
\(338\) −4299.87 −0.691960
\(339\) −3848.15 −0.616528
\(340\) 629.530 0.100415
\(341\) −10018.6 −1.59102
\(342\) −497.587 −0.0786737
\(343\) 343.000 0.0539949
\(344\) −3477.11 −0.544980
\(345\) −659.000 −0.102839
\(346\) −636.260 −0.0988599
\(347\) 11398.3 1.76338 0.881688 0.471833i \(-0.156407\pi\)
0.881688 + 0.471833i \(0.156407\pi\)
\(348\) −3690.95 −0.568550
\(349\) 1577.30 0.241922 0.120961 0.992657i \(-0.461402\pi\)
0.120961 + 0.992657i \(0.461402\pi\)
\(350\) −472.970 −0.0722324
\(351\) −185.226 −0.0281671
\(352\) −1150.09 −0.174147
\(353\) −4929.64 −0.743282 −0.371641 0.928377i \(-0.621205\pi\)
−0.371641 + 0.928377i \(0.621205\pi\)
\(354\) −4468.52 −0.670901
\(355\) −9139.37 −1.36639
\(356\) 6130.66 0.912709
\(357\) 346.050 0.0513023
\(358\) −3937.87 −0.581349
\(359\) 5323.22 0.782588 0.391294 0.920266i \(-0.372028\pi\)
0.391294 + 0.920266i \(0.372028\pi\)
\(360\) −687.652 −0.100674
\(361\) −6094.83 −0.888588
\(362\) 7610.27 1.10494
\(363\) 117.902 0.0170476
\(364\) 192.086 0.0276595
\(365\) −5119.26 −0.734122
\(366\) 2070.02 0.295633
\(367\) −3760.29 −0.534839 −0.267419 0.963580i \(-0.586171\pi\)
−0.267419 + 0.963580i \(0.586171\pi\)
\(368\) −368.000 −0.0521286
\(369\) 1359.13 0.191744
\(370\) 4312.27 0.605903
\(371\) −2360.39 −0.330311
\(372\) −3345.08 −0.466222
\(373\) −9210.62 −1.27857 −0.639287 0.768969i \(-0.720770\pi\)
−0.639287 + 0.768969i \(0.720770\pi\)
\(374\) 1184.49 0.163766
\(375\) −4549.50 −0.626493
\(376\) 2248.98 0.308464
\(377\) 2110.06 0.288259
\(378\) −378.000 −0.0514344
\(379\) 6305.61 0.854611 0.427305 0.904107i \(-0.359463\pi\)
0.427305 + 0.904107i \(0.359463\pi\)
\(380\) 1056.07 0.142566
\(381\) −6814.35 −0.916299
\(382\) 3127.35 0.418872
\(383\) 13571.9 1.81069 0.905344 0.424679i \(-0.139613\pi\)
0.905344 + 0.424679i \(0.139613\pi\)
\(384\) −384.000 −0.0510310
\(385\) 2402.79 0.318071
\(386\) −8228.00 −1.08496
\(387\) −3911.75 −0.513812
\(388\) −907.227 −0.118705
\(389\) −7448.01 −0.970769 −0.485384 0.874301i \(-0.661320\pi\)
−0.485384 + 0.874301i \(0.661320\pi\)
\(390\) 393.121 0.0510422
\(391\) 379.008 0.0490211
\(392\) 392.000 0.0505076
\(393\) −1694.19 −0.217456
\(394\) 2286.94 0.292423
\(395\) 5167.90 0.658291
\(396\) −1293.85 −0.164188
\(397\) 9795.19 1.23830 0.619152 0.785271i \(-0.287477\pi\)
0.619152 + 0.785271i \(0.287477\pi\)
\(398\) −9.29939 −0.00117120
\(399\) 580.518 0.0728377
\(400\) −540.537 −0.0675672
\(401\) −7996.68 −0.995848 −0.497924 0.867221i \(-0.665904\pi\)
−0.497924 + 0.867221i \(0.665904\pi\)
\(402\) −2794.77 −0.346742
\(403\) 1912.34 0.236378
\(404\) 5878.27 0.723898
\(405\) −773.609 −0.0949159
\(406\) 4306.10 0.526375
\(407\) 8113.72 0.988162
\(408\) 395.486 0.0479889
\(409\) 5516.67 0.666948 0.333474 0.942759i \(-0.391779\pi\)
0.333474 + 0.942759i \(0.391779\pi\)
\(410\) −2884.60 −0.347465
\(411\) −986.648 −0.118413
\(412\) 1541.51 0.184332
\(413\) 5213.27 0.621134
\(414\) −414.000 −0.0491473
\(415\) −3367.58 −0.398332
\(416\) 219.527 0.0258731
\(417\) 6134.38 0.720388
\(418\) 1987.04 0.232510
\(419\) 4037.28 0.470726 0.235363 0.971908i \(-0.424372\pi\)
0.235363 + 0.971908i \(0.424372\pi\)
\(420\) 802.261 0.0932056
\(421\) 6466.80 0.748629 0.374314 0.927302i \(-0.377878\pi\)
0.374314 + 0.927302i \(0.377878\pi\)
\(422\) −329.272 −0.0379828
\(423\) 2530.11 0.290823
\(424\) −2697.59 −0.308978
\(425\) 556.706 0.0635393
\(426\) −5741.58 −0.653005
\(427\) −2415.03 −0.273703
\(428\) −3203.43 −0.361784
\(429\) 739.674 0.0832443
\(430\) 8302.24 0.931091
\(431\) −7418.83 −0.829124 −0.414562 0.910021i \(-0.636065\pi\)
−0.414562 + 0.910021i \(0.636065\pi\)
\(432\) −432.000 −0.0481125
\(433\) −16487.7 −1.82990 −0.914952 0.403563i \(-0.867772\pi\)
−0.914952 + 0.403563i \(0.867772\pi\)
\(434\) 3902.60 0.431637
\(435\) 8812.80 0.971360
\(436\) 4895.61 0.537746
\(437\) 635.805 0.0695988
\(438\) −3216.04 −0.350841
\(439\) −15767.2 −1.71418 −0.857091 0.515165i \(-0.827731\pi\)
−0.857091 + 0.515165i \(0.827731\pi\)
\(440\) 2746.04 0.297528
\(441\) 441.000 0.0476190
\(442\) −226.094 −0.0243307
\(443\) −17663.7 −1.89442 −0.947208 0.320619i \(-0.896109\pi\)
−0.947208 + 0.320619i \(0.896109\pi\)
\(444\) 2709.07 0.289565
\(445\) −14638.1 −1.55935
\(446\) −8123.12 −0.862424
\(447\) −1738.59 −0.183965
\(448\) 448.000 0.0472456
\(449\) 11973.0 1.25844 0.629222 0.777226i \(-0.283374\pi\)
0.629222 + 0.777226i \(0.283374\pi\)
\(450\) −608.105 −0.0637029
\(451\) −5427.51 −0.566677
\(452\) 5130.87 0.533929
\(453\) −9914.01 −1.02826
\(454\) −6367.96 −0.658289
\(455\) −458.641 −0.0472559
\(456\) 663.449 0.0681334
\(457\) −1742.13 −0.178323 −0.0891614 0.996017i \(-0.528419\pi\)
−0.0891614 + 0.996017i \(0.528419\pi\)
\(458\) 2380.00 0.242817
\(459\) 444.922 0.0452444
\(460\) 878.667 0.0890610
\(461\) 12085.2 1.22097 0.610483 0.792030i \(-0.290975\pi\)
0.610483 + 0.792030i \(0.290975\pi\)
\(462\) 1509.49 0.152008
\(463\) 13460.5 1.35110 0.675551 0.737313i \(-0.263906\pi\)
0.675551 + 0.737313i \(0.263906\pi\)
\(464\) 4921.26 0.492379
\(465\) 7986.99 0.796533
\(466\) −13589.4 −1.35089
\(467\) −3956.79 −0.392074 −0.196037 0.980597i \(-0.562807\pi\)
−0.196037 + 0.980597i \(0.562807\pi\)
\(468\) 246.968 0.0243934
\(469\) 3260.56 0.321021
\(470\) −5369.86 −0.527007
\(471\) 5425.19 0.530742
\(472\) 5958.02 0.581018
\(473\) 15621.0 1.51851
\(474\) 3246.60 0.314602
\(475\) 933.903 0.0902114
\(476\) −461.401 −0.0444291
\(477\) −3034.79 −0.291307
\(478\) −8052.00 −0.770481
\(479\) 16387.3 1.56316 0.781579 0.623806i \(-0.214414\pi\)
0.781579 + 0.623806i \(0.214414\pi\)
\(480\) 916.870 0.0871858
\(481\) −1548.74 −0.146811
\(482\) 9575.04 0.904836
\(483\) 483.000 0.0455016
\(484\) −157.203 −0.0147636
\(485\) 2166.17 0.202806
\(486\) −486.000 −0.0453609
\(487\) 8974.92 0.835097 0.417549 0.908655i \(-0.362889\pi\)
0.417549 + 0.908655i \(0.362889\pi\)
\(488\) −2760.03 −0.256026
\(489\) 199.717 0.0184693
\(490\) −935.971 −0.0862916
\(491\) 14046.8 1.29109 0.645544 0.763723i \(-0.276631\pi\)
0.645544 + 0.763723i \(0.276631\pi\)
\(492\) −1812.18 −0.166056
\(493\) −5068.47 −0.463027
\(494\) −379.284 −0.0345441
\(495\) 3089.30 0.280512
\(496\) 4460.11 0.403760
\(497\) 6698.51 0.604565
\(498\) −2115.60 −0.190366
\(499\) −15952.7 −1.43114 −0.715570 0.698541i \(-0.753833\pi\)
−0.715570 + 0.698541i \(0.753833\pi\)
\(500\) 6066.00 0.542559
\(501\) 1010.86 0.0901436
\(502\) −10467.2 −0.930623
\(503\) 16375.1 1.45155 0.725776 0.687931i \(-0.241481\pi\)
0.725776 + 0.687931i \(0.241481\pi\)
\(504\) 504.000 0.0445435
\(505\) −14035.4 −1.23677
\(506\) 1653.25 0.145249
\(507\) 6449.81 0.564983
\(508\) 9085.80 0.793538
\(509\) −22768.3 −1.98269 −0.991345 0.131283i \(-0.958090\pi\)
−0.991345 + 0.131283i \(0.958090\pi\)
\(510\) −944.295 −0.0819884
\(511\) 3752.05 0.324816
\(512\) 512.000 0.0441942
\(513\) 746.380 0.0642368
\(514\) 6320.28 0.542365
\(515\) −3680.63 −0.314928
\(516\) 5215.67 0.444975
\(517\) −10103.6 −0.859491
\(518\) −3160.58 −0.268085
\(519\) 954.389 0.0807188
\(520\) −524.161 −0.0442038
\(521\) 528.725 0.0444604 0.0222302 0.999753i \(-0.492923\pi\)
0.0222302 + 0.999753i \(0.492923\pi\)
\(522\) 5536.42 0.464219
\(523\) −13524.7 −1.13078 −0.565388 0.824825i \(-0.691273\pi\)
−0.565388 + 0.824825i \(0.691273\pi\)
\(524\) 2258.91 0.188323
\(525\) 709.455 0.0589775
\(526\) 10398.6 0.861975
\(527\) −4593.52 −0.379691
\(528\) 1725.13 0.142191
\(529\) 529.000 0.0434783
\(530\) 6440.99 0.527885
\(531\) 6702.78 0.547789
\(532\) −774.024 −0.0630793
\(533\) 1036.00 0.0841913
\(534\) −9196.00 −0.745224
\(535\) 7648.77 0.618103
\(536\) 3726.36 0.300287
\(537\) 5906.81 0.474670
\(538\) −9818.99 −0.786852
\(539\) −1761.07 −0.140732
\(540\) 1031.48 0.0821996
\(541\) −10436.3 −0.829371 −0.414686 0.909965i \(-0.636108\pi\)
−0.414686 + 0.909965i \(0.636108\pi\)
\(542\) 8014.60 0.635160
\(543\) −11415.4 −0.902177
\(544\) −527.315 −0.0415596
\(545\) −11689.2 −0.918732
\(546\) −288.129 −0.0225839
\(547\) −17369.1 −1.35768 −0.678838 0.734288i \(-0.737516\pi\)
−0.678838 + 0.734288i \(0.737516\pi\)
\(548\) 1315.53 0.102549
\(549\) −3105.04 −0.241384
\(550\) 2428.38 0.188266
\(551\) −8502.62 −0.657393
\(552\) 552.000 0.0425628
\(553\) −3787.70 −0.291265
\(554\) 5059.92 0.388043
\(555\) −6468.40 −0.494718
\(556\) −8179.17 −0.623874
\(557\) −13555.3 −1.03116 −0.515579 0.856842i \(-0.672423\pi\)
−0.515579 + 0.856842i \(0.672423\pi\)
\(558\) 5017.62 0.380668
\(559\) −2981.72 −0.225605
\(560\) −1069.68 −0.0807184
\(561\) −1776.73 −0.133714
\(562\) −16468.7 −1.23611
\(563\) −5311.89 −0.397636 −0.198818 0.980036i \(-0.563710\pi\)
−0.198818 + 0.980036i \(0.563710\pi\)
\(564\) −3373.48 −0.251860
\(565\) −12250.9 −0.912210
\(566\) 12749.0 0.946786
\(567\) 567.000 0.0419961
\(568\) 7655.43 0.565519
\(569\) 17501.8 1.28948 0.644738 0.764403i \(-0.276966\pi\)
0.644738 + 0.764403i \(0.276966\pi\)
\(570\) −1584.10 −0.116405
\(571\) 16321.0 1.19617 0.598083 0.801434i \(-0.295929\pi\)
0.598083 + 0.801434i \(0.295929\pi\)
\(572\) −986.232 −0.0720917
\(573\) −4691.02 −0.342007
\(574\) 2114.21 0.153738
\(575\) 777.023 0.0563549
\(576\) 576.000 0.0416667
\(577\) 5414.53 0.390659 0.195329 0.980738i \(-0.437422\pi\)
0.195329 + 0.980738i \(0.437422\pi\)
\(578\) −9282.91 −0.668025
\(579\) 12342.0 0.885865
\(580\) −11750.4 −0.841222
\(581\) 2468.19 0.176244
\(582\) 1360.84 0.0969221
\(583\) 12119.0 0.860923
\(584\) 4288.06 0.303838
\(585\) −589.681 −0.0416758
\(586\) 7892.41 0.556369
\(587\) 20409.5 1.43507 0.717537 0.696520i \(-0.245269\pi\)
0.717537 + 0.696520i \(0.245269\pi\)
\(588\) −588.000 −0.0412393
\(589\) −7705.87 −0.539075
\(590\) −14225.9 −0.992660
\(591\) −3430.42 −0.238762
\(592\) −3612.10 −0.250771
\(593\) 3585.23 0.248276 0.124138 0.992265i \(-0.460383\pi\)
0.124138 + 0.992265i \(0.460383\pi\)
\(594\) 1940.77 0.134059
\(595\) 1101.68 0.0759065
\(596\) 2318.12 0.159318
\(597\) 13.9491 0.000956278 0
\(598\) −315.570 −0.0215797
\(599\) 19228.3 1.31159 0.655797 0.754937i \(-0.272333\pi\)
0.655797 + 0.754937i \(0.272333\pi\)
\(600\) 810.806 0.0551684
\(601\) −27989.7 −1.89971 −0.949853 0.312698i \(-0.898767\pi\)
−0.949853 + 0.312698i \(0.898767\pi\)
\(602\) −6084.94 −0.411966
\(603\) 4192.15 0.283114
\(604\) 13218.7 0.890498
\(605\) 375.351 0.0252235
\(606\) −8817.41 −0.591061
\(607\) −13757.2 −0.919915 −0.459958 0.887941i \(-0.652135\pi\)
−0.459958 + 0.887941i \(0.652135\pi\)
\(608\) −884.598 −0.0590053
\(609\) −6459.15 −0.429784
\(610\) 6590.08 0.437417
\(611\) 1928.57 0.127695
\(612\) −593.229 −0.0391828
\(613\) 10360.3 0.682626 0.341313 0.939950i \(-0.389128\pi\)
0.341313 + 0.939950i \(0.389128\pi\)
\(614\) −502.729 −0.0330431
\(615\) 4326.91 0.283704
\(616\) −2012.65 −0.131643
\(617\) −2143.45 −0.139858 −0.0699288 0.997552i \(-0.522277\pi\)
−0.0699288 + 0.997552i \(0.522277\pi\)
\(618\) −2312.26 −0.150506
\(619\) 23282.7 1.51181 0.755906 0.654680i \(-0.227197\pi\)
0.755906 + 0.654680i \(0.227197\pi\)
\(620\) −10649.3 −0.689818
\(621\) 621.000 0.0401286
\(622\) −5575.33 −0.359406
\(623\) 10728.7 0.689944
\(624\) −329.291 −0.0211253
\(625\) −10260.7 −0.656686
\(626\) −1170.38 −0.0747250
\(627\) −2980.56 −0.189844
\(628\) −7233.59 −0.459636
\(629\) 3720.14 0.235821
\(630\) −1203.39 −0.0761020
\(631\) 10965.6 0.691813 0.345906 0.938269i \(-0.387571\pi\)
0.345906 + 0.938269i \(0.387571\pi\)
\(632\) −4328.80 −0.272453
\(633\) 493.909 0.0310128
\(634\) 4843.65 0.303416
\(635\) −21694.0 −1.35575
\(636\) 4046.39 0.252280
\(637\) 336.151 0.0209086
\(638\) −22108.9 −1.37194
\(639\) 8612.36 0.533177
\(640\) −1222.49 −0.0755051
\(641\) 13655.3 0.841425 0.420712 0.907194i \(-0.361780\pi\)
0.420712 + 0.907194i \(0.361780\pi\)
\(642\) 4805.14 0.295395
\(643\) 4110.59 0.252109 0.126054 0.992023i \(-0.459769\pi\)
0.126054 + 0.992023i \(0.459769\pi\)
\(644\) −644.000 −0.0394055
\(645\) −12453.4 −0.760233
\(646\) 911.059 0.0554878
\(647\) 18237.5 1.10818 0.554088 0.832458i \(-0.313067\pi\)
0.554088 + 0.832458i \(0.313067\pi\)
\(648\) 648.000 0.0392837
\(649\) −26766.6 −1.61892
\(650\) −463.526 −0.0279708
\(651\) −5853.89 −0.352430
\(652\) −266.289 −0.0159949
\(653\) −28056.9 −1.68140 −0.840699 0.541503i \(-0.817855\pi\)
−0.840699 + 0.541503i \(0.817855\pi\)
\(654\) −7343.42 −0.439068
\(655\) −5393.57 −0.321747
\(656\) 2416.24 0.143808
\(657\) 4824.07 0.286461
\(658\) 3935.72 0.233177
\(659\) 10838.1 0.640655 0.320328 0.947307i \(-0.396207\pi\)
0.320328 + 0.947307i \(0.396207\pi\)
\(660\) −4119.06 −0.242931
\(661\) −21151.8 −1.24464 −0.622321 0.782762i \(-0.713810\pi\)
−0.622321 + 0.782762i \(0.713810\pi\)
\(662\) 3821.22 0.224344
\(663\) 339.141 0.0198660
\(664\) 2820.79 0.164861
\(665\) 1848.12 0.107770
\(666\) −4063.61 −0.236429
\(667\) −7074.31 −0.410672
\(668\) −1347.82 −0.0780667
\(669\) 12184.7 0.704166
\(670\) −8897.35 −0.513037
\(671\) 12399.5 0.713380
\(672\) −672.000 −0.0385758
\(673\) 5933.06 0.339826 0.169913 0.985459i \(-0.445651\pi\)
0.169913 + 0.985459i \(0.445651\pi\)
\(674\) −2238.36 −0.127920
\(675\) 912.157 0.0520132
\(676\) −8599.75 −0.489289
\(677\) 22207.5 1.26071 0.630357 0.776305i \(-0.282908\pi\)
0.630357 + 0.776305i \(0.282908\pi\)
\(678\) −7696.31 −0.435951
\(679\) −1587.65 −0.0897324
\(680\) 1259.06 0.0710041
\(681\) 9551.94 0.537491
\(682\) −20037.2 −1.12502
\(683\) 7323.69 0.410298 0.205149 0.978731i \(-0.434232\pi\)
0.205149 + 0.978731i \(0.434232\pi\)
\(684\) −995.173 −0.0556307
\(685\) −3141.07 −0.175203
\(686\) 686.000 0.0381802
\(687\) −3570.00 −0.198259
\(688\) −6954.22 −0.385359
\(689\) −2313.26 −0.127907
\(690\) −1318.00 −0.0727180
\(691\) −9596.05 −0.528294 −0.264147 0.964482i \(-0.585090\pi\)
−0.264147 + 0.964482i \(0.585090\pi\)
\(692\) −1272.52 −0.0699045
\(693\) −2264.23 −0.124114
\(694\) 22796.5 1.24690
\(695\) 19529.3 1.06588
\(696\) −7381.89 −0.402026
\(697\) −2488.51 −0.135236
\(698\) 3154.60 0.171065
\(699\) 20384.1 1.10300
\(700\) −945.941 −0.0510760
\(701\) −28684.1 −1.54548 −0.772740 0.634722i \(-0.781115\pi\)
−0.772740 + 0.634722i \(0.781115\pi\)
\(702\) −370.452 −0.0199171
\(703\) 6240.73 0.334813
\(704\) −2300.17 −0.123141
\(705\) 8054.79 0.430299
\(706\) −9859.29 −0.525580
\(707\) 10287.0 0.547216
\(708\) −8937.04 −0.474399
\(709\) −10857.3 −0.575111 −0.287555 0.957764i \(-0.592843\pi\)
−0.287555 + 0.957764i \(0.592843\pi\)
\(710\) −18278.7 −0.966182
\(711\) −4869.90 −0.256871
\(712\) 12261.3 0.645383
\(713\) −6411.41 −0.336759
\(714\) 692.101 0.0362762
\(715\) 2354.81 0.123168
\(716\) −7875.74 −0.411076
\(717\) 12078.0 0.629095
\(718\) 10646.4 0.553373
\(719\) −19066.6 −0.988962 −0.494481 0.869188i \(-0.664642\pi\)
−0.494481 + 0.869188i \(0.664642\pi\)
\(720\) −1375.30 −0.0711869
\(721\) 2697.64 0.139342
\(722\) −12189.7 −0.628327
\(723\) −14362.6 −0.738796
\(724\) 15220.5 0.781308
\(725\) −10391.1 −0.532298
\(726\) 235.805 0.0120545
\(727\) 23234.8 1.18533 0.592663 0.805451i \(-0.298077\pi\)
0.592663 + 0.805451i \(0.298077\pi\)
\(728\) 384.173 0.0195582
\(729\) 729.000 0.0370370
\(730\) −10238.5 −0.519102
\(731\) 7162.24 0.362387
\(732\) 4140.05 0.209044
\(733\) −10581.8 −0.533218 −0.266609 0.963805i \(-0.585903\pi\)
−0.266609 + 0.963805i \(0.585903\pi\)
\(734\) −7520.59 −0.378188
\(735\) 1403.96 0.0704568
\(736\) −736.000 −0.0368605
\(737\) −16740.8 −0.836708
\(738\) 2718.27 0.135584
\(739\) −33930.6 −1.68898 −0.844491 0.535570i \(-0.820097\pi\)
−0.844491 + 0.535570i \(0.820097\pi\)
\(740\) 8624.54 0.428438
\(741\) 568.926 0.0282052
\(742\) −4720.79 −0.233565
\(743\) 35816.7 1.76849 0.884245 0.467023i \(-0.154673\pi\)
0.884245 + 0.467023i \(0.154673\pi\)
\(744\) −6690.17 −0.329668
\(745\) −5534.92 −0.272193
\(746\) −18421.2 −0.904088
\(747\) 3173.39 0.155433
\(748\) 2368.98 0.115800
\(749\) −5606.00 −0.273483
\(750\) −9098.99 −0.442998
\(751\) 36266.5 1.76216 0.881081 0.472966i \(-0.156817\pi\)
0.881081 + 0.472966i \(0.156817\pi\)
\(752\) 4497.97 0.218117
\(753\) 15700.8 0.759851
\(754\) 4220.12 0.203830
\(755\) −31562.0 −1.52140
\(756\) −756.000 −0.0363696
\(757\) 10970.6 0.526727 0.263363 0.964697i \(-0.415168\pi\)
0.263363 + 0.964697i \(0.415168\pi\)
\(758\) 12611.2 0.604301
\(759\) −2479.87 −0.118595
\(760\) 2112.14 0.100810
\(761\) 12254.8 0.583752 0.291876 0.956456i \(-0.405721\pi\)
0.291876 + 0.956456i \(0.405721\pi\)
\(762\) −13628.7 −0.647921
\(763\) 8567.32 0.406498
\(764\) 6254.69 0.296187
\(765\) 1416.44 0.0669433
\(766\) 27143.9 1.28035
\(767\) 5109.17 0.240524
\(768\) −768.000 −0.0360844
\(769\) 9003.57 0.422207 0.211103 0.977464i \(-0.432294\pi\)
0.211103 + 0.977464i \(0.432294\pi\)
\(770\) 4805.57 0.224910
\(771\) −9480.42 −0.442839
\(772\) −16456.0 −0.767182
\(773\) 8783.80 0.408708 0.204354 0.978897i \(-0.434491\pi\)
0.204354 + 0.978897i \(0.434491\pi\)
\(774\) −7823.50 −0.363320
\(775\) −9417.41 −0.436495
\(776\) −1814.45 −0.0839370
\(777\) 4740.88 0.218891
\(778\) −14896.0 −0.686437
\(779\) −4174.61 −0.192004
\(780\) 786.242 0.0360923
\(781\) −34392.2 −1.57574
\(782\) 758.015 0.0346631
\(783\) −8304.63 −0.379033
\(784\) 784.000 0.0357143
\(785\) 17271.5 0.785282
\(786\) −3388.37 −0.153765
\(787\) 28920.9 1.30994 0.654968 0.755656i \(-0.272682\pi\)
0.654968 + 0.755656i \(0.272682\pi\)
\(788\) 4573.89 0.206774
\(789\) −15597.9 −0.703800
\(790\) 10335.8 0.465482
\(791\) 8979.02 0.403612
\(792\) −2587.70 −0.116098
\(793\) −2366.80 −0.105987
\(794\) 19590.4 0.875613
\(795\) −9661.49 −0.431016
\(796\) −18.5988 −0.000828161 0
\(797\) −18091.1 −0.804039 −0.402019 0.915631i \(-0.631692\pi\)
−0.402019 + 0.915631i \(0.631692\pi\)
\(798\) 1161.04 0.0515040
\(799\) −4632.51 −0.205114
\(800\) −1081.07 −0.0477772
\(801\) 13794.0 0.608473
\(802\) −15993.4 −0.704171
\(803\) −19264.2 −0.846600
\(804\) −5589.53 −0.245184
\(805\) 1537.67 0.0673238
\(806\) 3824.67 0.167144
\(807\) 14728.5 0.642462
\(808\) 11756.5 0.511873
\(809\) −31525.0 −1.37004 −0.685018 0.728526i \(-0.740206\pi\)
−0.685018 + 0.728526i \(0.740206\pi\)
\(810\) −1547.22 −0.0671157
\(811\) 1459.50 0.0631936 0.0315968 0.999501i \(-0.489941\pi\)
0.0315968 + 0.999501i \(0.489941\pi\)
\(812\) 8612.21 0.372203
\(813\) −12021.9 −0.518606
\(814\) 16227.4 0.698736
\(815\) 635.814 0.0273271
\(816\) 790.972 0.0339333
\(817\) 12015.0 0.514507
\(818\) 11033.3 0.471604
\(819\) 432.194 0.0184397
\(820\) −5769.21 −0.245695
\(821\) 34470.9 1.46534 0.732669 0.680585i \(-0.238274\pi\)
0.732669 + 0.680585i \(0.238274\pi\)
\(822\) −1973.30 −0.0837307
\(823\) −12245.1 −0.518635 −0.259317 0.965792i \(-0.583498\pi\)
−0.259317 + 0.965792i \(0.583498\pi\)
\(824\) 3083.02 0.130342
\(825\) −3642.57 −0.153719
\(826\) 10426.5 0.439208
\(827\) 21699.6 0.912418 0.456209 0.889873i \(-0.349207\pi\)
0.456209 + 0.889873i \(0.349207\pi\)
\(828\) −828.000 −0.0347524
\(829\) 9666.34 0.404977 0.202489 0.979285i \(-0.435097\pi\)
0.202489 + 0.979285i \(0.435097\pi\)
\(830\) −6735.16 −0.281664
\(831\) −7589.89 −0.316835
\(832\) 439.054 0.0182950
\(833\) −807.451 −0.0335853
\(834\) 12268.8 0.509391
\(835\) 3218.15 0.133376
\(836\) 3974.08 0.164410
\(837\) −7526.44 −0.310814
\(838\) 8074.56 0.332853
\(839\) 6492.29 0.267150 0.133575 0.991039i \(-0.457354\pi\)
0.133575 + 0.991039i \(0.457354\pi\)
\(840\) 1604.52 0.0659063
\(841\) 70215.7 2.87899
\(842\) 12933.6 0.529360
\(843\) 24703.1 1.00928
\(844\) −658.545 −0.0268579
\(845\) 20533.5 0.835944
\(846\) 5060.21 0.205643
\(847\) −275.106 −0.0111603
\(848\) −5395.19 −0.218480
\(849\) −19123.5 −0.773048
\(850\) 1113.41 0.0449291
\(851\) 5192.39 0.209157
\(852\) −11483.2 −0.461744
\(853\) −273.587 −0.0109818 −0.00549088 0.999985i \(-0.501748\pi\)
−0.00549088 + 0.999985i \(0.501748\pi\)
\(854\) −4830.05 −0.193538
\(855\) 2376.16 0.0950443
\(856\) −6406.85 −0.255820
\(857\) 20910.7 0.833483 0.416741 0.909025i \(-0.363172\pi\)
0.416741 + 0.909025i \(0.363172\pi\)
\(858\) 1479.35 0.0588626
\(859\) 43191.5 1.71557 0.857785 0.514009i \(-0.171840\pi\)
0.857785 + 0.514009i \(0.171840\pi\)
\(860\) 16604.5 0.658381
\(861\) −3171.31 −0.125526
\(862\) −14837.7 −0.586279
\(863\) 15061.2 0.594077 0.297038 0.954866i \(-0.404001\pi\)
0.297038 + 0.954866i \(0.404001\pi\)
\(864\) −864.000 −0.0340207
\(865\) 3038.37 0.119431
\(866\) −32975.4 −1.29394
\(867\) 13924.4 0.545440
\(868\) 7805.19 0.305214
\(869\) 19447.2 0.759151
\(870\) 17625.6 0.686855
\(871\) 3195.46 0.124310
\(872\) 9791.22 0.380244
\(873\) −2041.26 −0.0791366
\(874\) 1271.61 0.0492138
\(875\) 10615.5 0.410136
\(876\) −6432.09 −0.248082
\(877\) −11979.5 −0.461252 −0.230626 0.973042i \(-0.574077\pi\)
−0.230626 + 0.973042i \(0.574077\pi\)
\(878\) −31534.3 −1.21211
\(879\) −11838.6 −0.454274
\(880\) 5492.08 0.210384
\(881\) 1497.59 0.0572703 0.0286352 0.999590i \(-0.490884\pi\)
0.0286352 + 0.999590i \(0.490884\pi\)
\(882\) 882.000 0.0336718
\(883\) −3415.01 −0.130152 −0.0650761 0.997880i \(-0.520729\pi\)
−0.0650761 + 0.997880i \(0.520729\pi\)
\(884\) −452.187 −0.0172044
\(885\) 21338.8 0.810504
\(886\) −35327.3 −1.33955
\(887\) −36693.1 −1.38899 −0.694495 0.719498i \(-0.744372\pi\)
−0.694495 + 0.719498i \(0.744372\pi\)
\(888\) 5418.14 0.204753
\(889\) 15900.2 0.599858
\(890\) −29276.2 −1.10263
\(891\) −2911.16 −0.109458
\(892\) −16246.2 −0.609826
\(893\) −7771.28 −0.291216
\(894\) −3477.17 −0.130083
\(895\) 18804.8 0.702318
\(896\) 896.000 0.0334077
\(897\) 473.356 0.0176197
\(898\) 23946.0 0.889854
\(899\) 85739.7 3.18084
\(900\) −1216.21 −0.0450448
\(901\) 5556.57 0.205456
\(902\) −10855.0 −0.400701
\(903\) 9127.42 0.336369
\(904\) 10261.7 0.377545
\(905\) −36341.8 −1.33485
\(906\) −19828.0 −0.727088
\(907\) −2621.57 −0.0959733 −0.0479866 0.998848i \(-0.515280\pi\)
−0.0479866 + 0.998848i \(0.515280\pi\)
\(908\) −12735.9 −0.465481
\(909\) 13226.1 0.482599
\(910\) −917.282 −0.0334150
\(911\) 18982.7 0.690368 0.345184 0.938535i \(-0.387817\pi\)
0.345184 + 0.938535i \(0.387817\pi\)
\(912\) 1326.90 0.0481776
\(913\) −12672.5 −0.459363
\(914\) −3484.26 −0.126093
\(915\) −9885.12 −0.357150
\(916\) 4760.00 0.171697
\(917\) 3953.10 0.142359
\(918\) 889.844 0.0319926
\(919\) −10192.2 −0.365845 −0.182922 0.983127i \(-0.558556\pi\)
−0.182922 + 0.983127i \(0.558556\pi\)
\(920\) 1757.33 0.0629756
\(921\) 754.093 0.0269796
\(922\) 24170.5 0.863353
\(923\) 6564.75 0.234108
\(924\) 3018.98 0.107486
\(925\) 7626.85 0.271102
\(926\) 26920.9 0.955373
\(927\) 3468.40 0.122888
\(928\) 9842.52 0.348164
\(929\) 53333.7 1.88355 0.941777 0.336238i \(-0.109155\pi\)
0.941777 + 0.336238i \(0.109155\pi\)
\(930\) 15974.0 0.563234
\(931\) −1354.54 −0.0476835
\(932\) −27178.8 −0.955225
\(933\) 8362.99 0.293453
\(934\) −7913.58 −0.277238
\(935\) −5656.36 −0.197843
\(936\) 493.936 0.0172487
\(937\) 40735.5 1.42025 0.710124 0.704077i \(-0.248639\pi\)
0.710124 + 0.704077i \(0.248639\pi\)
\(938\) 6521.12 0.226996
\(939\) 1755.57 0.0610127
\(940\) −10739.7 −0.372650
\(941\) −10130.8 −0.350963 −0.175481 0.984483i \(-0.556148\pi\)
−0.175481 + 0.984483i \(0.556148\pi\)
\(942\) 10850.4 0.375291
\(943\) −3473.34 −0.119944
\(944\) 11916.0 0.410841
\(945\) 1805.09 0.0621370
\(946\) 31242.0 1.07375
\(947\) −3536.91 −0.121367 −0.0606833 0.998157i \(-0.519328\pi\)
−0.0606833 + 0.998157i \(0.519328\pi\)
\(948\) 6493.20 0.222457
\(949\) 3677.13 0.125780
\(950\) 1867.81 0.0637891
\(951\) −7265.48 −0.247739
\(952\) −922.801 −0.0314161
\(953\) −30525.8 −1.03759 −0.518797 0.854897i \(-0.673620\pi\)
−0.518797 + 0.854897i \(0.673620\pi\)
\(954\) −6069.58 −0.205985
\(955\) −14934.2 −0.506031
\(956\) −16104.0 −0.544812
\(957\) 33163.3 1.12019
\(958\) 32774.5 1.10532
\(959\) 2302.18 0.0775196
\(960\) 1833.74 0.0616497
\(961\) 47914.4 1.60835
\(962\) −3097.47 −0.103811
\(963\) −7207.71 −0.241189
\(964\) 19150.1 0.639816
\(965\) 39291.7 1.31072
\(966\) 966.000 0.0321745
\(967\) 33897.9 1.12728 0.563642 0.826019i \(-0.309400\pi\)
0.563642 + 0.826019i \(0.309400\pi\)
\(968\) −314.407 −0.0104395
\(969\) −1366.59 −0.0453056
\(970\) 4332.34 0.143405
\(971\) −15613.9 −0.516040 −0.258020 0.966140i \(-0.583070\pi\)
−0.258020 + 0.966140i \(0.583070\pi\)
\(972\) −972.000 −0.0320750
\(973\) −14313.6 −0.471605
\(974\) 17949.8 0.590503
\(975\) 695.289 0.0228380
\(976\) −5520.06 −0.181038
\(977\) −30489.2 −0.998399 −0.499199 0.866487i \(-0.666372\pi\)
−0.499199 + 0.866487i \(0.666372\pi\)
\(978\) 399.434 0.0130598
\(979\) −55084.4 −1.79827
\(980\) −1871.94 −0.0610174
\(981\) 11015.1 0.358497
\(982\) 28093.7 0.912938
\(983\) 35753.1 1.16007 0.580034 0.814593i \(-0.303039\pi\)
0.580034 + 0.814593i \(0.303039\pi\)
\(984\) −3624.36 −0.117419
\(985\) −10921.0 −0.353271
\(986\) −10136.9 −0.327409
\(987\) −5903.58 −0.190388
\(988\) −758.568 −0.0244264
\(989\) 9996.69 0.321412
\(990\) 6178.59 0.198352
\(991\) 13696.3 0.439030 0.219515 0.975609i \(-0.429553\pi\)
0.219515 + 0.975609i \(0.429553\pi\)
\(992\) 8920.22 0.285501
\(993\) −5731.82 −0.183176
\(994\) 13397.0 0.427492
\(995\) 44.4080 0.00141490
\(996\) −4231.19 −0.134609
\(997\) 40838.4 1.29726 0.648628 0.761106i \(-0.275343\pi\)
0.648628 + 0.761106i \(0.275343\pi\)
\(998\) −31905.3 −1.01197
\(999\) 6095.41 0.193043
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 966.4.a.f.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.f.1.1 3 1.1 even 1 trivial