Properties

Label 6001.2.a.d.1.5
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.63308 q^{2} +2.70578 q^{3} +4.93313 q^{4} +2.79051 q^{5} -7.12456 q^{6} -5.09743 q^{7} -7.72317 q^{8} +4.32127 q^{9} +O(q^{10})\) \(q-2.63308 q^{2} +2.70578 q^{3} +4.93313 q^{4} +2.79051 q^{5} -7.12456 q^{6} -5.09743 q^{7} -7.72317 q^{8} +4.32127 q^{9} -7.34766 q^{10} -0.629200 q^{11} +13.3480 q^{12} -1.20129 q^{13} +13.4220 q^{14} +7.55053 q^{15} +10.4695 q^{16} +1.00000 q^{17} -11.3783 q^{18} -4.74739 q^{19} +13.7660 q^{20} -13.7925 q^{21} +1.65674 q^{22} -1.58864 q^{23} -20.8972 q^{24} +2.78697 q^{25} +3.16309 q^{26} +3.57506 q^{27} -25.1463 q^{28} -6.31747 q^{29} -19.8812 q^{30} +9.25295 q^{31} -12.1207 q^{32} -1.70248 q^{33} -2.63308 q^{34} -14.2245 q^{35} +21.3174 q^{36} +3.59230 q^{37} +12.5003 q^{38} -3.25043 q^{39} -21.5516 q^{40} +5.58238 q^{41} +36.3169 q^{42} +8.15637 q^{43} -3.10393 q^{44} +12.0586 q^{45} +4.18303 q^{46} +2.64958 q^{47} +28.3282 q^{48} +18.9838 q^{49} -7.33832 q^{50} +2.70578 q^{51} -5.92611 q^{52} -10.7493 q^{53} -9.41344 q^{54} -1.75579 q^{55} +39.3683 q^{56} -12.8454 q^{57} +16.6344 q^{58} +5.28430 q^{59} +37.2477 q^{60} +9.37335 q^{61} -24.3638 q^{62} -22.0274 q^{63} +10.9759 q^{64} -3.35221 q^{65} +4.48277 q^{66} -0.944014 q^{67} +4.93313 q^{68} -4.29852 q^{69} +37.4542 q^{70} +13.8769 q^{71} -33.3739 q^{72} -5.11346 q^{73} -9.45884 q^{74} +7.54094 q^{75} -23.4195 q^{76} +3.20730 q^{77} +8.55865 q^{78} +12.7727 q^{79} +29.2153 q^{80} -3.29045 q^{81} -14.6989 q^{82} +14.5151 q^{83} -68.0404 q^{84} +2.79051 q^{85} -21.4764 q^{86} -17.0937 q^{87} +4.85942 q^{88} +10.3474 q^{89} -31.7512 q^{90} +6.12349 q^{91} -7.83698 q^{92} +25.0365 q^{93} -6.97657 q^{94} -13.2477 q^{95} -32.7961 q^{96} -6.69361 q^{97} -49.9859 q^{98} -2.71894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63308 −1.86187 −0.930936 0.365183i \(-0.881006\pi\)
−0.930936 + 0.365183i \(0.881006\pi\)
\(3\) 2.70578 1.56219 0.781093 0.624415i \(-0.214663\pi\)
0.781093 + 0.624415i \(0.214663\pi\)
\(4\) 4.93313 2.46656
\(5\) 2.79051 1.24796 0.623978 0.781442i \(-0.285516\pi\)
0.623978 + 0.781442i \(0.285516\pi\)
\(6\) −7.12456 −2.90859
\(7\) −5.09743 −1.92665 −0.963324 0.268342i \(-0.913524\pi\)
−0.963324 + 0.268342i \(0.913524\pi\)
\(8\) −7.72317 −2.73055
\(9\) 4.32127 1.44042
\(10\) −7.34766 −2.32353
\(11\) −0.629200 −0.189711 −0.0948555 0.995491i \(-0.530239\pi\)
−0.0948555 + 0.995491i \(0.530239\pi\)
\(12\) 13.3480 3.85323
\(13\) −1.20129 −0.333178 −0.166589 0.986026i \(-0.553275\pi\)
−0.166589 + 0.986026i \(0.553275\pi\)
\(14\) 13.4220 3.58717
\(15\) 7.55053 1.94954
\(16\) 10.4695 2.61738
\(17\) 1.00000 0.242536
\(18\) −11.3783 −2.68188
\(19\) −4.74739 −1.08913 −0.544563 0.838720i \(-0.683305\pi\)
−0.544563 + 0.838720i \(0.683305\pi\)
\(20\) 13.7660 3.07816
\(21\) −13.7925 −3.00978
\(22\) 1.65674 0.353217
\(23\) −1.58864 −0.331255 −0.165627 0.986188i \(-0.552965\pi\)
−0.165627 + 0.986188i \(0.552965\pi\)
\(24\) −20.8972 −4.26563
\(25\) 2.78697 0.557394
\(26\) 3.16309 0.620334
\(27\) 3.57506 0.688022
\(28\) −25.1463 −4.75220
\(29\) −6.31747 −1.17312 −0.586562 0.809904i \(-0.699519\pi\)
−0.586562 + 0.809904i \(0.699519\pi\)
\(30\) −19.8812 −3.62979
\(31\) 9.25295 1.66188 0.830939 0.556363i \(-0.187804\pi\)
0.830939 + 0.556363i \(0.187804\pi\)
\(32\) −12.1207 −2.14266
\(33\) −1.70248 −0.296364
\(34\) −2.63308 −0.451570
\(35\) −14.2245 −2.40437
\(36\) 21.3174 3.55290
\(37\) 3.59230 0.590571 0.295286 0.955409i \(-0.404585\pi\)
0.295286 + 0.955409i \(0.404585\pi\)
\(38\) 12.5003 2.02781
\(39\) −3.25043 −0.520485
\(40\) −21.5516 −3.40761
\(41\) 5.58238 0.871822 0.435911 0.899990i \(-0.356426\pi\)
0.435911 + 0.899990i \(0.356426\pi\)
\(42\) 36.3169 5.60382
\(43\) 8.15637 1.24384 0.621918 0.783083i \(-0.286354\pi\)
0.621918 + 0.783083i \(0.286354\pi\)
\(44\) −3.10393 −0.467934
\(45\) 12.0586 1.79758
\(46\) 4.18303 0.616754
\(47\) 2.64958 0.386481 0.193241 0.981151i \(-0.438100\pi\)
0.193241 + 0.981151i \(0.438100\pi\)
\(48\) 28.3282 4.08883
\(49\) 18.9838 2.71197
\(50\) −7.33832 −1.03780
\(51\) 2.70578 0.378886
\(52\) −5.92611 −0.821804
\(53\) −10.7493 −1.47653 −0.738267 0.674508i \(-0.764356\pi\)
−0.738267 + 0.674508i \(0.764356\pi\)
\(54\) −9.41344 −1.28101
\(55\) −1.75579 −0.236751
\(56\) 39.3683 5.26082
\(57\) −12.8454 −1.70142
\(58\) 16.6344 2.18421
\(59\) 5.28430 0.687958 0.343979 0.938977i \(-0.388225\pi\)
0.343979 + 0.938977i \(0.388225\pi\)
\(60\) 37.2477 4.80866
\(61\) 9.37335 1.20013 0.600067 0.799950i \(-0.295141\pi\)
0.600067 + 0.799950i \(0.295141\pi\)
\(62\) −24.3638 −3.09420
\(63\) −22.0274 −2.77519
\(64\) 10.9759 1.37199
\(65\) −3.35221 −0.415791
\(66\) 4.48277 0.551791
\(67\) −0.944014 −0.115330 −0.0576648 0.998336i \(-0.518365\pi\)
−0.0576648 + 0.998336i \(0.518365\pi\)
\(68\) 4.93313 0.598230
\(69\) −4.29852 −0.517481
\(70\) 37.4542 4.47663
\(71\) 13.8769 1.64688 0.823440 0.567403i \(-0.192052\pi\)
0.823440 + 0.567403i \(0.192052\pi\)
\(72\) −33.3739 −3.93315
\(73\) −5.11346 −0.598485 −0.299242 0.954177i \(-0.596734\pi\)
−0.299242 + 0.954177i \(0.596734\pi\)
\(74\) −9.45884 −1.09957
\(75\) 7.54094 0.870752
\(76\) −23.4195 −2.68640
\(77\) 3.20730 0.365506
\(78\) 8.55865 0.969076
\(79\) 12.7727 1.43704 0.718518 0.695508i \(-0.244821\pi\)
0.718518 + 0.695508i \(0.244821\pi\)
\(80\) 29.2153 3.26637
\(81\) −3.29045 −0.365605
\(82\) −14.6989 −1.62322
\(83\) 14.5151 1.59324 0.796620 0.604480i \(-0.206619\pi\)
0.796620 + 0.604480i \(0.206619\pi\)
\(84\) −68.0404 −7.42382
\(85\) 2.79051 0.302674
\(86\) −21.4764 −2.31586
\(87\) −17.0937 −1.83264
\(88\) 4.85942 0.518016
\(89\) 10.3474 1.09682 0.548411 0.836209i \(-0.315233\pi\)
0.548411 + 0.836209i \(0.315233\pi\)
\(90\) −31.7512 −3.34687
\(91\) 6.12349 0.641916
\(92\) −7.83698 −0.817062
\(93\) 25.0365 2.59616
\(94\) −6.97657 −0.719578
\(95\) −13.2477 −1.35918
\(96\) −32.7961 −3.34724
\(97\) −6.69361 −0.679633 −0.339816 0.940492i \(-0.610365\pi\)
−0.339816 + 0.940492i \(0.610365\pi\)
\(98\) −49.9859 −5.04934
\(99\) −2.71894 −0.273264
\(100\) 13.7485 1.37485
\(101\) 2.61584 0.260286 0.130143 0.991495i \(-0.458456\pi\)
0.130143 + 0.991495i \(0.458456\pi\)
\(102\) −7.12456 −0.705436
\(103\) −12.3409 −1.21598 −0.607992 0.793943i \(-0.708025\pi\)
−0.607992 + 0.793943i \(0.708025\pi\)
\(104\) 9.27776 0.909759
\(105\) −38.4883 −3.75607
\(106\) 28.3039 2.74912
\(107\) 1.23460 0.119354 0.0596768 0.998218i \(-0.480993\pi\)
0.0596768 + 0.998218i \(0.480993\pi\)
\(108\) 17.6363 1.69705
\(109\) 16.5492 1.58513 0.792563 0.609791i \(-0.208746\pi\)
0.792563 + 0.609791i \(0.208746\pi\)
\(110\) 4.62315 0.440800
\(111\) 9.72000 0.922581
\(112\) −53.3676 −5.04276
\(113\) −14.9594 −1.40726 −0.703632 0.710565i \(-0.748440\pi\)
−0.703632 + 0.710565i \(0.748440\pi\)
\(114\) 33.8231 3.16782
\(115\) −4.43313 −0.413391
\(116\) −31.1649 −2.89359
\(117\) −5.19109 −0.479916
\(118\) −13.9140 −1.28089
\(119\) −5.09743 −0.467281
\(120\) −58.3140 −5.32332
\(121\) −10.6041 −0.964010
\(122\) −24.6808 −2.23450
\(123\) 15.1047 1.36195
\(124\) 45.6460 4.09913
\(125\) −6.17549 −0.552353
\(126\) 57.9999 5.16704
\(127\) −7.77864 −0.690242 −0.345121 0.938558i \(-0.612162\pi\)
−0.345121 + 0.938558i \(0.612162\pi\)
\(128\) −4.65898 −0.411799
\(129\) 22.0694 1.94310
\(130\) 8.82666 0.774149
\(131\) −7.38141 −0.644917 −0.322458 0.946584i \(-0.604509\pi\)
−0.322458 + 0.946584i \(0.604509\pi\)
\(132\) −8.39855 −0.731000
\(133\) 24.1995 2.09836
\(134\) 2.48567 0.214729
\(135\) 9.97627 0.858621
\(136\) −7.72317 −0.662257
\(137\) 7.11938 0.608250 0.304125 0.952632i \(-0.401636\pi\)
0.304125 + 0.952632i \(0.401636\pi\)
\(138\) 11.3184 0.963484
\(139\) 4.08365 0.346370 0.173185 0.984889i \(-0.444594\pi\)
0.173185 + 0.984889i \(0.444594\pi\)
\(140\) −70.1711 −5.93054
\(141\) 7.16919 0.603755
\(142\) −36.5389 −3.06628
\(143\) 0.755851 0.0632074
\(144\) 45.2415 3.77013
\(145\) −17.6290 −1.46401
\(146\) 13.4642 1.11430
\(147\) 51.3661 4.23660
\(148\) 17.7213 1.45668
\(149\) 15.6416 1.28141 0.640706 0.767786i \(-0.278642\pi\)
0.640706 + 0.767786i \(0.278642\pi\)
\(150\) −19.8559 −1.62123
\(151\) 13.5726 1.10452 0.552261 0.833671i \(-0.313765\pi\)
0.552261 + 0.833671i \(0.313765\pi\)
\(152\) 36.6650 2.97392
\(153\) 4.32127 0.349354
\(154\) −8.44510 −0.680525
\(155\) 25.8205 2.07395
\(156\) −16.0348 −1.28381
\(157\) 17.4093 1.38941 0.694706 0.719293i \(-0.255534\pi\)
0.694706 + 0.719293i \(0.255534\pi\)
\(158\) −33.6315 −2.67558
\(159\) −29.0854 −2.30662
\(160\) −33.8231 −2.67395
\(161\) 8.09800 0.638211
\(162\) 8.66403 0.680710
\(163\) 20.6814 1.61989 0.809944 0.586507i \(-0.199497\pi\)
0.809944 + 0.586507i \(0.199497\pi\)
\(164\) 27.5386 2.15040
\(165\) −4.75079 −0.369849
\(166\) −38.2195 −2.96641
\(167\) 18.1352 1.40335 0.701673 0.712500i \(-0.252437\pi\)
0.701673 + 0.712500i \(0.252437\pi\)
\(168\) 106.522 8.21837
\(169\) −11.5569 −0.888993
\(170\) −7.34766 −0.563540
\(171\) −20.5148 −1.56880
\(172\) 40.2364 3.06800
\(173\) 17.3581 1.31971 0.659855 0.751393i \(-0.270618\pi\)
0.659855 + 0.751393i \(0.270618\pi\)
\(174\) 45.0092 3.41214
\(175\) −14.2064 −1.07390
\(176\) −6.58741 −0.496545
\(177\) 14.2982 1.07472
\(178\) −27.2455 −2.04214
\(179\) 4.46749 0.333916 0.166958 0.985964i \(-0.446606\pi\)
0.166958 + 0.985964i \(0.446606\pi\)
\(180\) 59.4864 4.43386
\(181\) −12.2531 −0.910766 −0.455383 0.890296i \(-0.650498\pi\)
−0.455383 + 0.890296i \(0.650498\pi\)
\(182\) −16.1236 −1.19516
\(183\) 25.3623 1.87483
\(184\) 12.2694 0.904510
\(185\) 10.0244 0.737007
\(186\) −65.9231 −4.83372
\(187\) −0.629200 −0.0460117
\(188\) 13.0707 0.953280
\(189\) −18.2236 −1.32558
\(190\) 34.8822 2.53062
\(191\) −7.99654 −0.578609 −0.289305 0.957237i \(-0.593424\pi\)
−0.289305 + 0.957237i \(0.593424\pi\)
\(192\) 29.6984 2.14330
\(193\) 14.7125 1.05903 0.529516 0.848300i \(-0.322374\pi\)
0.529516 + 0.848300i \(0.322374\pi\)
\(194\) 17.6248 1.26539
\(195\) −9.07036 −0.649542
\(196\) 93.6495 6.68925
\(197\) −18.2213 −1.29822 −0.649108 0.760696i \(-0.724858\pi\)
−0.649108 + 0.760696i \(0.724858\pi\)
\(198\) 7.15920 0.508782
\(199\) 18.2708 1.29518 0.647590 0.761989i \(-0.275777\pi\)
0.647590 + 0.761989i \(0.275777\pi\)
\(200\) −21.5242 −1.52199
\(201\) −2.55430 −0.180166
\(202\) −6.88773 −0.484619
\(203\) 32.2029 2.26020
\(204\) 13.3480 0.934546
\(205\) 15.5777 1.08800
\(206\) 32.4946 2.26400
\(207\) −6.86495 −0.477147
\(208\) −12.5769 −0.872051
\(209\) 2.98706 0.206619
\(210\) 101.343 6.99332
\(211\) −17.2474 −1.18736 −0.593681 0.804700i \(-0.702326\pi\)
−0.593681 + 0.804700i \(0.702326\pi\)
\(212\) −53.0279 −3.64197
\(213\) 37.5478 2.57273
\(214\) −3.25081 −0.222221
\(215\) 22.7605 1.55225
\(216\) −27.6108 −1.87868
\(217\) −47.1662 −3.20185
\(218\) −43.5754 −2.95130
\(219\) −13.8359 −0.934944
\(220\) −8.66155 −0.583961
\(221\) −1.20129 −0.0808074
\(222\) −25.5936 −1.71773
\(223\) 1.93787 0.129769 0.0648847 0.997893i \(-0.479332\pi\)
0.0648847 + 0.997893i \(0.479332\pi\)
\(224\) 61.7846 4.12816
\(225\) 12.0432 0.802883
\(226\) 39.3894 2.62014
\(227\) 21.0477 1.39698 0.698492 0.715618i \(-0.253855\pi\)
0.698492 + 0.715618i \(0.253855\pi\)
\(228\) −63.3681 −4.19666
\(229\) −1.28845 −0.0851431 −0.0425715 0.999093i \(-0.513555\pi\)
−0.0425715 + 0.999093i \(0.513555\pi\)
\(230\) 11.6728 0.769682
\(231\) 8.67827 0.570988
\(232\) 48.7909 3.20328
\(233\) −7.00149 −0.458683 −0.229341 0.973346i \(-0.573657\pi\)
−0.229341 + 0.973346i \(0.573657\pi\)
\(234\) 13.6686 0.893543
\(235\) 7.39369 0.482311
\(236\) 26.0681 1.69689
\(237\) 34.5601 2.24492
\(238\) 13.4220 0.870016
\(239\) −10.0232 −0.648344 −0.324172 0.945998i \(-0.605086\pi\)
−0.324172 + 0.945998i \(0.605086\pi\)
\(240\) 79.0503 5.10267
\(241\) −23.6446 −1.52308 −0.761541 0.648117i \(-0.775557\pi\)
−0.761541 + 0.648117i \(0.775557\pi\)
\(242\) 27.9215 1.79486
\(243\) −19.6284 −1.25916
\(244\) 46.2399 2.96021
\(245\) 52.9746 3.38442
\(246\) −39.7720 −2.53577
\(247\) 5.70299 0.362873
\(248\) −71.4621 −4.53785
\(249\) 39.2748 2.48894
\(250\) 16.2606 1.02841
\(251\) 11.9889 0.756733 0.378366 0.925656i \(-0.376486\pi\)
0.378366 + 0.925656i \(0.376486\pi\)
\(252\) −108.664 −6.84518
\(253\) 0.999574 0.0628427
\(254\) 20.4818 1.28514
\(255\) 7.55053 0.472832
\(256\) −9.68431 −0.605269
\(257\) 28.2659 1.76318 0.881589 0.472017i \(-0.156474\pi\)
0.881589 + 0.472017i \(0.156474\pi\)
\(258\) −58.1105 −3.61780
\(259\) −18.3115 −1.13782
\(260\) −16.5369 −1.02557
\(261\) −27.2995 −1.68980
\(262\) 19.4359 1.20075
\(263\) −7.93940 −0.489565 −0.244782 0.969578i \(-0.578716\pi\)
−0.244782 + 0.969578i \(0.578716\pi\)
\(264\) 13.1485 0.809237
\(265\) −29.9962 −1.84265
\(266\) −63.7193 −3.90688
\(267\) 27.9978 1.71344
\(268\) −4.65694 −0.284468
\(269\) 23.2796 1.41938 0.709690 0.704514i \(-0.248835\pi\)
0.709690 + 0.704514i \(0.248835\pi\)
\(270\) −26.2684 −1.59864
\(271\) −6.93319 −0.421162 −0.210581 0.977576i \(-0.567536\pi\)
−0.210581 + 0.977576i \(0.567536\pi\)
\(272\) 10.4695 0.634807
\(273\) 16.5688 1.00279
\(274\) −18.7459 −1.13248
\(275\) −1.75356 −0.105744
\(276\) −21.2052 −1.27640
\(277\) 4.55603 0.273745 0.136873 0.990589i \(-0.456295\pi\)
0.136873 + 0.990589i \(0.456295\pi\)
\(278\) −10.7526 −0.644897
\(279\) 39.9845 2.39381
\(280\) 109.858 6.56527
\(281\) −12.9068 −0.769956 −0.384978 0.922926i \(-0.625791\pi\)
−0.384978 + 0.922926i \(0.625791\pi\)
\(282\) −18.8771 −1.12411
\(283\) 12.4555 0.740404 0.370202 0.928951i \(-0.379288\pi\)
0.370202 + 0.928951i \(0.379288\pi\)
\(284\) 68.4564 4.06214
\(285\) −35.8453 −2.12329
\(286\) −1.99022 −0.117684
\(287\) −28.4558 −1.67969
\(288\) −52.3769 −3.08634
\(289\) 1.00000 0.0588235
\(290\) 46.4186 2.72579
\(291\) −18.1115 −1.06171
\(292\) −25.2253 −1.47620
\(293\) −14.0921 −0.823267 −0.411633 0.911350i \(-0.635042\pi\)
−0.411633 + 0.911350i \(0.635042\pi\)
\(294\) −135.251 −7.88801
\(295\) 14.7459 0.858541
\(296\) −27.7440 −1.61259
\(297\) −2.24943 −0.130525
\(298\) −41.1857 −2.38582
\(299\) 1.90842 0.110367
\(300\) 37.2004 2.14777
\(301\) −41.5765 −2.39643
\(302\) −35.7378 −2.05648
\(303\) 7.07791 0.406615
\(304\) −49.7029 −2.85065
\(305\) 26.1565 1.49771
\(306\) −11.3783 −0.650452
\(307\) −8.67457 −0.495084 −0.247542 0.968877i \(-0.579623\pi\)
−0.247542 + 0.968877i \(0.579623\pi\)
\(308\) 15.8220 0.901545
\(309\) −33.3918 −1.89959
\(310\) −67.9875 −3.86143
\(311\) −6.16714 −0.349707 −0.174853 0.984594i \(-0.555945\pi\)
−0.174853 + 0.984594i \(0.555945\pi\)
\(312\) 25.1036 1.42121
\(313\) 3.33188 0.188329 0.0941645 0.995557i \(-0.469982\pi\)
0.0941645 + 0.995557i \(0.469982\pi\)
\(314\) −45.8401 −2.58691
\(315\) −61.4677 −3.46331
\(316\) 63.0092 3.54454
\(317\) 19.2978 1.08387 0.541936 0.840420i \(-0.317692\pi\)
0.541936 + 0.840420i \(0.317692\pi\)
\(318\) 76.5842 4.29463
\(319\) 3.97495 0.222555
\(320\) 30.6284 1.71218
\(321\) 3.34057 0.186452
\(322\) −21.3227 −1.18827
\(323\) −4.74739 −0.264152
\(324\) −16.2322 −0.901789
\(325\) −3.34795 −0.185711
\(326\) −54.4557 −3.01602
\(327\) 44.7785 2.47626
\(328\) −43.1137 −2.38056
\(329\) −13.5061 −0.744613
\(330\) 12.5092 0.688611
\(331\) −17.0096 −0.934930 −0.467465 0.884012i \(-0.654833\pi\)
−0.467465 + 0.884012i \(0.654833\pi\)
\(332\) 71.6049 3.92983
\(333\) 15.5233 0.850672
\(334\) −47.7515 −2.61285
\(335\) −2.63428 −0.143926
\(336\) −144.401 −7.87773
\(337\) −11.5670 −0.630093 −0.315046 0.949076i \(-0.602020\pi\)
−0.315046 + 0.949076i \(0.602020\pi\)
\(338\) 30.4303 1.65519
\(339\) −40.4770 −2.19841
\(340\) 13.7660 0.746564
\(341\) −5.82195 −0.315277
\(342\) 54.0171 2.92091
\(343\) −61.0866 −3.29836
\(344\) −62.9931 −3.39636
\(345\) −11.9951 −0.645794
\(346\) −45.7053 −2.45713
\(347\) −6.69435 −0.359372 −0.179686 0.983724i \(-0.557508\pi\)
−0.179686 + 0.983724i \(0.557508\pi\)
\(348\) −84.3255 −4.52032
\(349\) 29.5670 1.58268 0.791341 0.611374i \(-0.209383\pi\)
0.791341 + 0.611374i \(0.209383\pi\)
\(350\) 37.4066 1.99947
\(351\) −4.29469 −0.229233
\(352\) 7.62637 0.406487
\(353\) −1.00000 −0.0532246
\(354\) −37.6483 −2.00098
\(355\) 38.7236 2.05523
\(356\) 51.0450 2.70538
\(357\) −13.7925 −0.729979
\(358\) −11.7633 −0.621709
\(359\) 20.6343 1.08904 0.544518 0.838749i \(-0.316713\pi\)
0.544518 + 0.838749i \(0.316713\pi\)
\(360\) −93.1303 −4.90840
\(361\) 3.53775 0.186197
\(362\) 32.2635 1.69573
\(363\) −28.6924 −1.50596
\(364\) 30.2079 1.58333
\(365\) −14.2692 −0.746883
\(366\) −66.7809 −3.49070
\(367\) −21.1046 −1.10165 −0.550825 0.834621i \(-0.685687\pi\)
−0.550825 + 0.834621i \(0.685687\pi\)
\(368\) −16.6323 −0.867019
\(369\) 24.1230 1.25579
\(370\) −26.3950 −1.37221
\(371\) 54.7940 2.84476
\(372\) 123.508 6.40360
\(373\) 3.49642 0.181038 0.0905189 0.995895i \(-0.471147\pi\)
0.0905189 + 0.995895i \(0.471147\pi\)
\(374\) 1.65674 0.0856678
\(375\) −16.7096 −0.862878
\(376\) −20.4632 −1.05531
\(377\) 7.58911 0.390859
\(378\) 47.9844 2.46805
\(379\) −19.8239 −1.01828 −0.509142 0.860683i \(-0.670037\pi\)
−0.509142 + 0.860683i \(0.670037\pi\)
\(380\) −65.3525 −3.35251
\(381\) −21.0473 −1.07829
\(382\) 21.0556 1.07730
\(383\) −2.69266 −0.137589 −0.0687943 0.997631i \(-0.521915\pi\)
−0.0687943 + 0.997631i \(0.521915\pi\)
\(384\) −12.6062 −0.643307
\(385\) 8.95003 0.456136
\(386\) −38.7394 −1.97178
\(387\) 35.2459 1.79165
\(388\) −33.0204 −1.67636
\(389\) 14.2518 0.722594 0.361297 0.932451i \(-0.382334\pi\)
0.361297 + 0.932451i \(0.382334\pi\)
\(390\) 23.8830 1.20936
\(391\) −1.58864 −0.0803411
\(392\) −146.615 −7.40518
\(393\) −19.9725 −1.00748
\(394\) 47.9783 2.41711
\(395\) 35.6423 1.79336
\(396\) −13.4129 −0.674023
\(397\) −15.7945 −0.792703 −0.396351 0.918099i \(-0.629724\pi\)
−0.396351 + 0.918099i \(0.629724\pi\)
\(398\) −48.1085 −2.41146
\(399\) 65.4787 3.27803
\(400\) 29.1782 1.45891
\(401\) −0.423162 −0.0211317 −0.0105658 0.999944i \(-0.503363\pi\)
−0.0105658 + 0.999944i \(0.503363\pi\)
\(402\) 6.72568 0.335446
\(403\) −11.1155 −0.553700
\(404\) 12.9043 0.642012
\(405\) −9.18204 −0.456259
\(406\) −84.7928 −4.20820
\(407\) −2.26028 −0.112038
\(408\) −20.8972 −1.03457
\(409\) −18.8010 −0.929648 −0.464824 0.885403i \(-0.653882\pi\)
−0.464824 + 0.885403i \(0.653882\pi\)
\(410\) −41.0174 −2.02571
\(411\) 19.2635 0.950199
\(412\) −60.8792 −2.99930
\(413\) −26.9364 −1.32545
\(414\) 18.0760 0.888386
\(415\) 40.5046 1.98829
\(416\) 14.5605 0.713887
\(417\) 11.0495 0.541095
\(418\) −7.86518 −0.384699
\(419\) −3.04013 −0.148520 −0.0742599 0.997239i \(-0.523659\pi\)
−0.0742599 + 0.997239i \(0.523659\pi\)
\(420\) −189.868 −9.26460
\(421\) 19.1728 0.934423 0.467211 0.884146i \(-0.345259\pi\)
0.467211 + 0.884146i \(0.345259\pi\)
\(422\) 45.4139 2.21072
\(423\) 11.4495 0.556696
\(424\) 83.0190 4.03176
\(425\) 2.78697 0.135188
\(426\) −98.8665 −4.79010
\(427\) −47.7800 −2.31224
\(428\) 6.09046 0.294393
\(429\) 2.04517 0.0987417
\(430\) −59.9302 −2.89009
\(431\) 11.9769 0.576906 0.288453 0.957494i \(-0.406859\pi\)
0.288453 + 0.957494i \(0.406859\pi\)
\(432\) 37.4292 1.80081
\(433\) 14.5934 0.701313 0.350657 0.936504i \(-0.385958\pi\)
0.350657 + 0.936504i \(0.385958\pi\)
\(434\) 124.193 5.96144
\(435\) −47.7002 −2.28705
\(436\) 81.6393 3.90981
\(437\) 7.54191 0.360779
\(438\) 36.4311 1.74075
\(439\) 7.81298 0.372893 0.186447 0.982465i \(-0.440303\pi\)
0.186447 + 0.982465i \(0.440303\pi\)
\(440\) 13.5603 0.646461
\(441\) 82.0341 3.90638
\(442\) 3.16309 0.150453
\(443\) 21.1567 1.00518 0.502591 0.864524i \(-0.332380\pi\)
0.502591 + 0.864524i \(0.332380\pi\)
\(444\) 47.9500 2.27561
\(445\) 28.8745 1.36878
\(446\) −5.10257 −0.241614
\(447\) 42.3229 2.00180
\(448\) −55.9489 −2.64333
\(449\) −17.9303 −0.846185 −0.423093 0.906086i \(-0.639055\pi\)
−0.423093 + 0.906086i \(0.639055\pi\)
\(450\) −31.7109 −1.49486
\(451\) −3.51244 −0.165394
\(452\) −73.7967 −3.47111
\(453\) 36.7245 1.72547
\(454\) −55.4203 −2.60100
\(455\) 17.0877 0.801082
\(456\) 99.2074 4.64581
\(457\) 7.42332 0.347248 0.173624 0.984812i \(-0.444452\pi\)
0.173624 + 0.984812i \(0.444452\pi\)
\(458\) 3.39259 0.158525
\(459\) 3.57506 0.166870
\(460\) −21.8692 −1.01966
\(461\) 9.33948 0.434983 0.217492 0.976062i \(-0.430213\pi\)
0.217492 + 0.976062i \(0.430213\pi\)
\(462\) −22.8506 −1.06311
\(463\) 16.4791 0.765850 0.382925 0.923779i \(-0.374917\pi\)
0.382925 + 0.923779i \(0.374917\pi\)
\(464\) −66.1408 −3.07051
\(465\) 69.8646 3.23989
\(466\) 18.4355 0.854008
\(467\) −7.02063 −0.324876 −0.162438 0.986719i \(-0.551936\pi\)
−0.162438 + 0.986719i \(0.551936\pi\)
\(468\) −25.6083 −1.18374
\(469\) 4.81204 0.222200
\(470\) −19.4682 −0.898001
\(471\) 47.1058 2.17052
\(472\) −40.8116 −1.87851
\(473\) −5.13199 −0.235969
\(474\) −90.9995 −4.17975
\(475\) −13.2308 −0.607073
\(476\) −25.1463 −1.15258
\(477\) −46.4508 −2.12683
\(478\) 26.3918 1.20713
\(479\) 11.3866 0.520268 0.260134 0.965572i \(-0.416233\pi\)
0.260134 + 0.965572i \(0.416233\pi\)
\(480\) −91.5179 −4.17720
\(481\) −4.31539 −0.196765
\(482\) 62.2582 2.83578
\(483\) 21.9114 0.997004
\(484\) −52.3114 −2.37779
\(485\) −18.6786 −0.848152
\(486\) 51.6833 2.34440
\(487\) −31.7884 −1.44047 −0.720235 0.693730i \(-0.755966\pi\)
−0.720235 + 0.693730i \(0.755966\pi\)
\(488\) −72.3920 −3.27703
\(489\) 55.9593 2.53057
\(490\) −139.486 −6.30135
\(491\) 14.9969 0.676799 0.338400 0.941002i \(-0.390114\pi\)
0.338400 + 0.941002i \(0.390114\pi\)
\(492\) 74.5136 3.35933
\(493\) −6.31747 −0.284525
\(494\) −15.0165 −0.675622
\(495\) −7.58725 −0.341021
\(496\) 96.8738 4.34976
\(497\) −70.7363 −3.17296
\(498\) −103.414 −4.63408
\(499\) −17.2507 −0.772248 −0.386124 0.922447i \(-0.626186\pi\)
−0.386124 + 0.922447i \(0.626186\pi\)
\(500\) −30.4645 −1.36241
\(501\) 49.0700 2.19228
\(502\) −31.5678 −1.40894
\(503\) −34.6405 −1.54454 −0.772271 0.635293i \(-0.780879\pi\)
−0.772271 + 0.635293i \(0.780879\pi\)
\(504\) 170.121 7.57780
\(505\) 7.29955 0.324826
\(506\) −2.63196 −0.117005
\(507\) −31.2705 −1.38877
\(508\) −38.3730 −1.70253
\(509\) 4.86172 0.215492 0.107746 0.994178i \(-0.465637\pi\)
0.107746 + 0.994178i \(0.465637\pi\)
\(510\) −19.8812 −0.880353
\(511\) 26.0655 1.15307
\(512\) 34.8175 1.53873
\(513\) −16.9722 −0.749343
\(514\) −74.4265 −3.28281
\(515\) −34.4374 −1.51749
\(516\) 108.871 4.79278
\(517\) −1.66712 −0.0733197
\(518\) 48.2158 2.11848
\(519\) 46.9672 2.06163
\(520\) 25.8897 1.13534
\(521\) −32.1808 −1.40987 −0.704934 0.709273i \(-0.749023\pi\)
−0.704934 + 0.709273i \(0.749023\pi\)
\(522\) 71.8818 3.14618
\(523\) 7.36268 0.321948 0.160974 0.986959i \(-0.448537\pi\)
0.160974 + 0.986959i \(0.448537\pi\)
\(524\) −36.4135 −1.59073
\(525\) −38.4394 −1.67763
\(526\) 20.9051 0.911506
\(527\) 9.25295 0.403065
\(528\) −17.8241 −0.775695
\(529\) −20.4762 −0.890270
\(530\) 78.9824 3.43078
\(531\) 22.8349 0.990950
\(532\) 119.379 5.17575
\(533\) −6.70605 −0.290471
\(534\) −73.7206 −3.19020
\(535\) 3.44518 0.148948
\(536\) 7.29078 0.314914
\(537\) 12.0881 0.521639
\(538\) −61.2970 −2.64270
\(539\) −11.9446 −0.514491
\(540\) 49.2142 2.11784
\(541\) −21.2582 −0.913962 −0.456981 0.889477i \(-0.651069\pi\)
−0.456981 + 0.889477i \(0.651069\pi\)
\(542\) 18.2557 0.784149
\(543\) −33.1543 −1.42279
\(544\) −12.1207 −0.519672
\(545\) 46.1808 1.97817
\(546\) −43.6271 −1.86707
\(547\) −32.8677 −1.40532 −0.702661 0.711525i \(-0.748005\pi\)
−0.702661 + 0.711525i \(0.748005\pi\)
\(548\) 35.1208 1.50029
\(549\) 40.5047 1.72870
\(550\) 4.61727 0.196881
\(551\) 29.9915 1.27768
\(552\) 33.1983 1.41301
\(553\) −65.1077 −2.76866
\(554\) −11.9964 −0.509678
\(555\) 27.1238 1.15134
\(556\) 20.1452 0.854345
\(557\) 39.3424 1.66699 0.833496 0.552525i \(-0.186336\pi\)
0.833496 + 0.552525i \(0.186336\pi\)
\(558\) −105.282 −4.45696
\(559\) −9.79816 −0.414418
\(560\) −148.923 −6.29314
\(561\) −1.70248 −0.0718787
\(562\) 33.9847 1.43356
\(563\) −27.6562 −1.16557 −0.582785 0.812626i \(-0.698037\pi\)
−0.582785 + 0.812626i \(0.698037\pi\)
\(564\) 35.3666 1.48920
\(565\) −41.7445 −1.75620
\(566\) −32.7964 −1.37854
\(567\) 16.7728 0.704393
\(568\) −107.173 −4.49690
\(569\) −32.2565 −1.35226 −0.676132 0.736780i \(-0.736345\pi\)
−0.676132 + 0.736780i \(0.736345\pi\)
\(570\) 94.3838 3.95330
\(571\) 20.0863 0.840585 0.420292 0.907389i \(-0.361927\pi\)
0.420292 + 0.907389i \(0.361927\pi\)
\(572\) 3.72871 0.155905
\(573\) −21.6369 −0.903895
\(574\) 74.9265 3.12737
\(575\) −4.42750 −0.184639
\(576\) 47.4298 1.97624
\(577\) 12.7216 0.529609 0.264804 0.964302i \(-0.414693\pi\)
0.264804 + 0.964302i \(0.414693\pi\)
\(578\) −2.63308 −0.109522
\(579\) 39.8090 1.65440
\(580\) −86.9661 −3.61107
\(581\) −73.9898 −3.06961
\(582\) 47.6890 1.97677
\(583\) 6.76348 0.280115
\(584\) 39.4921 1.63420
\(585\) −14.4858 −0.598915
\(586\) 37.1056 1.53282
\(587\) 30.8908 1.27500 0.637499 0.770451i \(-0.279969\pi\)
0.637499 + 0.770451i \(0.279969\pi\)
\(588\) 253.395 10.4498
\(589\) −43.9274 −1.81000
\(590\) −38.8272 −1.59849
\(591\) −49.3030 −2.02805
\(592\) 37.6096 1.54575
\(593\) 18.4540 0.757815 0.378908 0.925435i \(-0.376300\pi\)
0.378908 + 0.925435i \(0.376300\pi\)
\(594\) 5.92294 0.243021
\(595\) −14.2245 −0.583146
\(596\) 77.1622 3.16069
\(597\) 49.4368 2.02331
\(598\) −5.02503 −0.205489
\(599\) 47.3061 1.93287 0.966437 0.256902i \(-0.0827019\pi\)
0.966437 + 0.256902i \(0.0827019\pi\)
\(600\) −58.2400 −2.37764
\(601\) −39.6256 −1.61636 −0.808181 0.588934i \(-0.799548\pi\)
−0.808181 + 0.588934i \(0.799548\pi\)
\(602\) 109.475 4.46185
\(603\) −4.07933 −0.166123
\(604\) 66.9554 2.72438
\(605\) −29.5909 −1.20304
\(606\) −18.6367 −0.757065
\(607\) 38.9455 1.58075 0.790374 0.612625i \(-0.209886\pi\)
0.790374 + 0.612625i \(0.209886\pi\)
\(608\) 57.5419 2.33363
\(609\) 87.1340 3.53085
\(610\) −68.8721 −2.78855
\(611\) −3.18291 −0.128767
\(612\) 21.3174 0.861704
\(613\) −23.7534 −0.959391 −0.479695 0.877435i \(-0.659253\pi\)
−0.479695 + 0.877435i \(0.659253\pi\)
\(614\) 22.8409 0.921782
\(615\) 42.1499 1.69965
\(616\) −24.7706 −0.998034
\(617\) −1.45981 −0.0587697 −0.0293848 0.999568i \(-0.509355\pi\)
−0.0293848 + 0.999568i \(0.509355\pi\)
\(618\) 87.9233 3.53679
\(619\) −33.9880 −1.36609 −0.683046 0.730376i \(-0.739345\pi\)
−0.683046 + 0.730376i \(0.739345\pi\)
\(620\) 127.376 5.11553
\(621\) −5.67950 −0.227911
\(622\) 16.2386 0.651109
\(623\) −52.7451 −2.11319
\(624\) −34.0304 −1.36231
\(625\) −31.1676 −1.24671
\(626\) −8.77312 −0.350644
\(627\) 8.08234 0.322778
\(628\) 85.8823 3.42708
\(629\) 3.59230 0.143235
\(630\) 161.849 6.44824
\(631\) −8.84464 −0.352100 −0.176050 0.984381i \(-0.556332\pi\)
−0.176050 + 0.984381i \(0.556332\pi\)
\(632\) −98.6455 −3.92391
\(633\) −46.6678 −1.85488
\(634\) −50.8127 −2.01803
\(635\) −21.7064 −0.861392
\(636\) −143.482 −5.68943
\(637\) −22.8050 −0.903568
\(638\) −10.4664 −0.414368
\(639\) 59.9656 2.37220
\(640\) −13.0009 −0.513908
\(641\) 3.82470 0.151067 0.0755334 0.997143i \(-0.475934\pi\)
0.0755334 + 0.997143i \(0.475934\pi\)
\(642\) −8.79600 −0.347150
\(643\) −11.4785 −0.452669 −0.226335 0.974050i \(-0.572674\pi\)
−0.226335 + 0.974050i \(0.572674\pi\)
\(644\) 39.9485 1.57419
\(645\) 61.5849 2.42490
\(646\) 12.5003 0.491817
\(647\) −18.4076 −0.723678 −0.361839 0.932241i \(-0.617851\pi\)
−0.361839 + 0.932241i \(0.617851\pi\)
\(648\) 25.4127 0.998306
\(649\) −3.32488 −0.130513
\(650\) 8.81544 0.345770
\(651\) −127.622 −5.00189
\(652\) 102.024 3.99556
\(653\) −14.4054 −0.563726 −0.281863 0.959455i \(-0.590952\pi\)
−0.281863 + 0.959455i \(0.590952\pi\)
\(654\) −117.906 −4.61048
\(655\) −20.5979 −0.804828
\(656\) 58.4448 2.28189
\(657\) −22.0966 −0.862071
\(658\) 35.5626 1.38637
\(659\) 24.5298 0.955546 0.477773 0.878483i \(-0.341444\pi\)
0.477773 + 0.878483i \(0.341444\pi\)
\(660\) −23.4363 −0.912256
\(661\) −31.9769 −1.24376 −0.621878 0.783114i \(-0.713630\pi\)
−0.621878 + 0.783114i \(0.713630\pi\)
\(662\) 44.7876 1.74072
\(663\) −3.25043 −0.126236
\(664\) −112.103 −4.35043
\(665\) 67.5291 2.61867
\(666\) −40.8742 −1.58384
\(667\) 10.0362 0.388603
\(668\) 89.4634 3.46144
\(669\) 5.24346 0.202724
\(670\) 6.93629 0.267972
\(671\) −5.89771 −0.227679
\(672\) 167.176 6.44895
\(673\) 3.84789 0.148325 0.0741626 0.997246i \(-0.476372\pi\)
0.0741626 + 0.997246i \(0.476372\pi\)
\(674\) 30.4568 1.17315
\(675\) 9.96359 0.383499
\(676\) −57.0117 −2.19276
\(677\) −27.5568 −1.05910 −0.529548 0.848280i \(-0.677638\pi\)
−0.529548 + 0.848280i \(0.677638\pi\)
\(678\) 106.579 4.09315
\(679\) 34.1202 1.30941
\(680\) −21.5516 −0.826467
\(681\) 56.9505 2.18235
\(682\) 15.3297 0.587004
\(683\) 34.6126 1.32441 0.662207 0.749321i \(-0.269620\pi\)
0.662207 + 0.749321i \(0.269620\pi\)
\(684\) −101.202 −3.86955
\(685\) 19.8667 0.759069
\(686\) 160.846 6.14113
\(687\) −3.48626 −0.133009
\(688\) 85.3932 3.25559
\(689\) 12.9131 0.491948
\(690\) 31.5841 1.20239
\(691\) −8.73729 −0.332382 −0.166191 0.986094i \(-0.553147\pi\)
−0.166191 + 0.986094i \(0.553147\pi\)
\(692\) 85.6297 3.25515
\(693\) 13.8596 0.526483
\(694\) 17.6268 0.669104
\(695\) 11.3955 0.432255
\(696\) 132.018 5.00412
\(697\) 5.58238 0.211448
\(698\) −77.8523 −2.94675
\(699\) −18.9445 −0.716547
\(700\) −70.0819 −2.64885
\(701\) 16.9615 0.640629 0.320314 0.947311i \(-0.396211\pi\)
0.320314 + 0.947311i \(0.396211\pi\)
\(702\) 11.3083 0.426803
\(703\) −17.0541 −0.643207
\(704\) −6.90603 −0.260281
\(705\) 20.0057 0.753460
\(706\) 2.63308 0.0990974
\(707\) −13.3341 −0.501480
\(708\) 70.5348 2.65086
\(709\) −7.22766 −0.271441 −0.135720 0.990747i \(-0.543335\pi\)
−0.135720 + 0.990747i \(0.543335\pi\)
\(710\) −101.962 −3.82658
\(711\) 55.1941 2.06994
\(712\) −79.9147 −2.99493
\(713\) −14.6996 −0.550505
\(714\) 36.3169 1.35913
\(715\) 2.10921 0.0788801
\(716\) 22.0387 0.823625
\(717\) −27.1205 −1.01283
\(718\) −54.3318 −2.02764
\(719\) 32.2279 1.20190 0.600948 0.799288i \(-0.294790\pi\)
0.600948 + 0.799288i \(0.294790\pi\)
\(720\) 126.247 4.70495
\(721\) 62.9068 2.34277
\(722\) −9.31519 −0.346676
\(723\) −63.9771 −2.37934
\(724\) −60.4462 −2.24646
\(725\) −17.6066 −0.653892
\(726\) 75.5496 2.80391
\(727\) −22.4636 −0.833130 −0.416565 0.909106i \(-0.636766\pi\)
−0.416565 + 0.909106i \(0.636766\pi\)
\(728\) −47.2927 −1.75279
\(729\) −43.2390 −1.60144
\(730\) 37.5719 1.39060
\(731\) 8.15637 0.301674
\(732\) 125.115 4.62439
\(733\) −39.6452 −1.46433 −0.732165 0.681128i \(-0.761490\pi\)
−0.732165 + 0.681128i \(0.761490\pi\)
\(734\) 55.5701 2.05113
\(735\) 143.338 5.28709
\(736\) 19.2555 0.709768
\(737\) 0.593973 0.0218793
\(738\) −63.5178 −2.33812
\(739\) 31.3222 1.15221 0.576103 0.817377i \(-0.304573\pi\)
0.576103 + 0.817377i \(0.304573\pi\)
\(740\) 49.4515 1.81787
\(741\) 15.4311 0.566874
\(742\) −144.277 −5.29658
\(743\) 33.5752 1.23176 0.615878 0.787842i \(-0.288802\pi\)
0.615878 + 0.787842i \(0.288802\pi\)
\(744\) −193.361 −7.08896
\(745\) 43.6482 1.59915
\(746\) −9.20637 −0.337069
\(747\) 62.7237 2.29494
\(748\) −3.10393 −0.113491
\(749\) −6.29330 −0.229952
\(750\) 43.9977 1.60657
\(751\) −20.7154 −0.755915 −0.377957 0.925823i \(-0.623373\pi\)
−0.377957 + 0.925823i \(0.623373\pi\)
\(752\) 27.7398 1.01157
\(753\) 32.4394 1.18216
\(754\) −19.9828 −0.727729
\(755\) 37.8745 1.37840
\(756\) −89.8996 −3.26962
\(757\) −24.4176 −0.887474 −0.443737 0.896157i \(-0.646348\pi\)
−0.443737 + 0.896157i \(0.646348\pi\)
\(758\) 52.1979 1.89591
\(759\) 2.70463 0.0981719
\(760\) 102.314 3.71132
\(761\) −8.06229 −0.292258 −0.146129 0.989266i \(-0.546681\pi\)
−0.146129 + 0.989266i \(0.546681\pi\)
\(762\) 55.4193 2.00763
\(763\) −84.3584 −3.05398
\(764\) −39.4480 −1.42718
\(765\) 12.0586 0.435978
\(766\) 7.09001 0.256172
\(767\) −6.34797 −0.229212
\(768\) −26.2036 −0.945542
\(769\) 10.4938 0.378417 0.189208 0.981937i \(-0.439408\pi\)
0.189208 + 0.981937i \(0.439408\pi\)
\(770\) −23.5662 −0.849266
\(771\) 76.4814 2.75441
\(772\) 72.5789 2.61217
\(773\) −10.4408 −0.375529 −0.187765 0.982214i \(-0.560124\pi\)
−0.187765 + 0.982214i \(0.560124\pi\)
\(774\) −92.8053 −3.33582
\(775\) 25.7877 0.926321
\(776\) 51.6959 1.85577
\(777\) −49.5470 −1.77749
\(778\) −37.5261 −1.34538
\(779\) −26.5018 −0.949525
\(780\) −44.7453 −1.60214
\(781\) −8.73132 −0.312431
\(782\) 4.18303 0.149585
\(783\) −22.5854 −0.807135
\(784\) 198.751 7.09825
\(785\) 48.5809 1.73393
\(786\) 52.5893 1.87580
\(787\) −11.9673 −0.426588 −0.213294 0.976988i \(-0.568419\pi\)
−0.213294 + 0.976988i \(0.568419\pi\)
\(788\) −89.8882 −3.20213
\(789\) −21.4823 −0.764790
\(790\) −93.8491 −3.33900
\(791\) 76.2546 2.71130
\(792\) 20.9989 0.746162
\(793\) −11.2601 −0.399858
\(794\) 41.5882 1.47591
\(795\) −81.1632 −2.87856
\(796\) 90.1321 3.19465
\(797\) −21.4467 −0.759683 −0.379841 0.925052i \(-0.624021\pi\)
−0.379841 + 0.925052i \(0.624021\pi\)
\(798\) −172.411 −6.10327
\(799\) 2.64958 0.0937354
\(800\) −33.7801 −1.19431
\(801\) 44.7138 1.57989
\(802\) 1.11422 0.0393445
\(803\) 3.21739 0.113539
\(804\) −12.6007 −0.444392
\(805\) 22.5976 0.796460
\(806\) 29.2679 1.03092
\(807\) 62.9895 2.21733
\(808\) −20.2026 −0.710725
\(809\) 24.9347 0.876657 0.438328 0.898815i \(-0.355571\pi\)
0.438328 + 0.898815i \(0.355571\pi\)
\(810\) 24.1771 0.849496
\(811\) 13.6818 0.480435 0.240217 0.970719i \(-0.422781\pi\)
0.240217 + 0.970719i \(0.422781\pi\)
\(812\) 158.861 5.57493
\(813\) −18.7597 −0.657932
\(814\) 5.95150 0.208600
\(815\) 57.7116 2.02155
\(816\) 28.3282 0.991686
\(817\) −38.7215 −1.35469
\(818\) 49.5045 1.73088
\(819\) 26.4612 0.924630
\(820\) 76.8469 2.68361
\(821\) 13.1310 0.458274 0.229137 0.973394i \(-0.426410\pi\)
0.229137 + 0.973394i \(0.426410\pi\)
\(822\) −50.7224 −1.76915
\(823\) 13.9871 0.487559 0.243779 0.969831i \(-0.421613\pi\)
0.243779 + 0.969831i \(0.421613\pi\)
\(824\) 95.3108 3.32031
\(825\) −4.74476 −0.165191
\(826\) 70.9257 2.46782
\(827\) 2.39687 0.0833472 0.0416736 0.999131i \(-0.486731\pi\)
0.0416736 + 0.999131i \(0.486731\pi\)
\(828\) −33.8657 −1.17691
\(829\) 23.3984 0.812660 0.406330 0.913727i \(-0.366808\pi\)
0.406330 + 0.913727i \(0.366808\pi\)
\(830\) −106.652 −3.70195
\(831\) 12.3276 0.427641
\(832\) −13.1852 −0.457115
\(833\) 18.9838 0.657750
\(834\) −29.0942 −1.00745
\(835\) 50.6066 1.75131
\(836\) 14.7356 0.509640
\(837\) 33.0799 1.14341
\(838\) 8.00491 0.276525
\(839\) −18.7964 −0.648924 −0.324462 0.945899i \(-0.605183\pi\)
−0.324462 + 0.945899i \(0.605183\pi\)
\(840\) 297.252 10.2562
\(841\) 10.9104 0.376222
\(842\) −50.4835 −1.73977
\(843\) −34.9231 −1.20281
\(844\) −85.0838 −2.92871
\(845\) −32.2497 −1.10942
\(846\) −30.1476 −1.03650
\(847\) 54.0537 1.85731
\(848\) −112.540 −3.86465
\(849\) 33.7020 1.15665
\(850\) −7.33832 −0.251702
\(851\) −5.70689 −0.195630
\(852\) 185.228 6.34581
\(853\) 40.8049 1.39713 0.698566 0.715545i \(-0.253822\pi\)
0.698566 + 0.715545i \(0.253822\pi\)
\(854\) 125.809 4.30509
\(855\) −57.2467 −1.95780
\(856\) −9.53505 −0.325901
\(857\) −52.1108 −1.78007 −0.890035 0.455893i \(-0.849320\pi\)
−0.890035 + 0.455893i \(0.849320\pi\)
\(858\) −5.38510 −0.183844
\(859\) 37.2242 1.27007 0.635037 0.772482i \(-0.280985\pi\)
0.635037 + 0.772482i \(0.280985\pi\)
\(860\) 112.280 3.82873
\(861\) −76.9953 −2.62399
\(862\) −31.5361 −1.07412
\(863\) 23.5426 0.801400 0.400700 0.916209i \(-0.368767\pi\)
0.400700 + 0.916209i \(0.368767\pi\)
\(864\) −43.3324 −1.47420
\(865\) 48.4380 1.64694
\(866\) −38.4256 −1.30575
\(867\) 2.70578 0.0918932
\(868\) −232.677 −7.89758
\(869\) −8.03656 −0.272622
\(870\) 125.599 4.25820
\(871\) 1.13403 0.0384252
\(872\) −127.812 −4.32827
\(873\) −28.9249 −0.978959
\(874\) −19.8585 −0.671723
\(875\) 31.4792 1.06419
\(876\) −68.2543 −2.30610
\(877\) −2.93054 −0.0989573 −0.0494786 0.998775i \(-0.515756\pi\)
−0.0494786 + 0.998775i \(0.515756\pi\)
\(878\) −20.5722 −0.694279
\(879\) −38.1301 −1.28609
\(880\) −18.3823 −0.619666
\(881\) −17.9111 −0.603440 −0.301720 0.953397i \(-0.597561\pi\)
−0.301720 + 0.953397i \(0.597561\pi\)
\(882\) −216.003 −7.27318
\(883\) −53.4075 −1.79731 −0.898653 0.438661i \(-0.855453\pi\)
−0.898653 + 0.438661i \(0.855453\pi\)
\(884\) −5.92611 −0.199317
\(885\) 39.8993 1.34120
\(886\) −55.7072 −1.87152
\(887\) −3.12584 −0.104955 −0.0524777 0.998622i \(-0.516712\pi\)
−0.0524777 + 0.998622i \(0.516712\pi\)
\(888\) −75.0692 −2.51916
\(889\) 39.6511 1.32985
\(890\) −76.0291 −2.54850
\(891\) 2.07035 0.0693594
\(892\) 9.55976 0.320084
\(893\) −12.5786 −0.420927
\(894\) −111.440 −3.72710
\(895\) 12.4666 0.416712
\(896\) 23.7488 0.793392
\(897\) 5.16377 0.172413
\(898\) 47.2121 1.57549
\(899\) −58.4552 −1.94959
\(900\) 59.4108 1.98036
\(901\) −10.7493 −0.358112
\(902\) 9.24854 0.307943
\(903\) −112.497 −3.74367
\(904\) 115.534 3.84261
\(905\) −34.1925 −1.13660
\(906\) −96.6988 −3.21260
\(907\) 9.83541 0.326579 0.163290 0.986578i \(-0.447789\pi\)
0.163290 + 0.986578i \(0.447789\pi\)
\(908\) 103.831 3.44575
\(909\) 11.3038 0.374922
\(910\) −44.9933 −1.49151
\(911\) 27.9397 0.925683 0.462842 0.886441i \(-0.346830\pi\)
0.462842 + 0.886441i \(0.346830\pi\)
\(912\) −134.485 −4.45325
\(913\) −9.13291 −0.302255
\(914\) −19.5462 −0.646532
\(915\) 70.7737 2.33971
\(916\) −6.35608 −0.210011
\(917\) 37.6262 1.24253
\(918\) −9.41344 −0.310690
\(919\) −23.2793 −0.767913 −0.383957 0.923351i \(-0.625439\pi\)
−0.383957 + 0.923351i \(0.625439\pi\)
\(920\) 34.2378 1.12879
\(921\) −23.4715 −0.773412
\(922\) −24.5916 −0.809883
\(923\) −16.6701 −0.548704
\(924\) 42.8110 1.40838
\(925\) 10.0116 0.329181
\(926\) −43.3909 −1.42591
\(927\) −53.3283 −1.75153
\(928\) 76.5724 2.51361
\(929\) −11.1442 −0.365629 −0.182815 0.983147i \(-0.558521\pi\)
−0.182815 + 0.983147i \(0.558521\pi\)
\(930\) −183.959 −6.03227
\(931\) −90.1236 −2.95368
\(932\) −34.5392 −1.13137
\(933\) −16.6870 −0.546306
\(934\) 18.4859 0.604877
\(935\) −1.75579 −0.0574205
\(936\) 40.0917 1.31044
\(937\) 12.2398 0.399855 0.199928 0.979811i \(-0.435929\pi\)
0.199928 + 0.979811i \(0.435929\pi\)
\(938\) −12.6705 −0.413707
\(939\) 9.01535 0.294205
\(940\) 36.4740 1.18965
\(941\) −30.0195 −0.978608 −0.489304 0.872113i \(-0.662749\pi\)
−0.489304 + 0.872113i \(0.662749\pi\)
\(942\) −124.033 −4.04123
\(943\) −8.86841 −0.288795
\(944\) 55.3240 1.80064
\(945\) −50.8533 −1.65426
\(946\) 13.5130 0.439344
\(947\) 11.4160 0.370971 0.185486 0.982647i \(-0.440614\pi\)
0.185486 + 0.982647i \(0.440614\pi\)
\(948\) 170.489 5.53723
\(949\) 6.14274 0.199402
\(950\) 34.8379 1.13029
\(951\) 52.2156 1.69321
\(952\) 39.3683 1.27594
\(953\) −24.3550 −0.788935 −0.394468 0.918910i \(-0.629071\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(954\) 122.309 3.95989
\(955\) −22.3145 −0.722079
\(956\) −49.4455 −1.59918
\(957\) 10.7554 0.347672
\(958\) −29.9819 −0.968672
\(959\) −36.2905 −1.17188
\(960\) 82.8738 2.67474
\(961\) 54.6170 1.76184
\(962\) 11.3628 0.366351
\(963\) 5.33505 0.171920
\(964\) −116.642 −3.75678
\(965\) 41.0556 1.32163
\(966\) −57.6946 −1.85629
\(967\) −28.0613 −0.902392 −0.451196 0.892425i \(-0.649002\pi\)
−0.451196 + 0.892425i \(0.649002\pi\)
\(968\) 81.8974 2.63228
\(969\) −12.8454 −0.412654
\(970\) 49.1823 1.57915
\(971\) 44.1080 1.41549 0.707746 0.706467i \(-0.249712\pi\)
0.707746 + 0.706467i \(0.249712\pi\)
\(972\) −96.8296 −3.10581
\(973\) −20.8161 −0.667334
\(974\) 83.7015 2.68197
\(975\) −9.05884 −0.290115
\(976\) 98.1343 3.14120
\(977\) −2.74982 −0.0879747 −0.0439873 0.999032i \(-0.514006\pi\)
−0.0439873 + 0.999032i \(0.514006\pi\)
\(978\) −147.345 −4.71159
\(979\) −6.51058 −0.208079
\(980\) 261.330 8.34789
\(981\) 71.5135 2.28325
\(982\) −39.4880 −1.26011
\(983\) −27.7878 −0.886294 −0.443147 0.896449i \(-0.646138\pi\)
−0.443147 + 0.896449i \(0.646138\pi\)
\(984\) −116.656 −3.71887
\(985\) −50.8469 −1.62012
\(986\) 16.6344 0.529748
\(987\) −36.5445 −1.16322
\(988\) 28.1336 0.895049
\(989\) −12.9576 −0.412027
\(990\) 19.9779 0.634938
\(991\) 53.8238 1.70977 0.854885 0.518818i \(-0.173628\pi\)
0.854885 + 0.518818i \(0.173628\pi\)
\(992\) −112.152 −3.56085
\(993\) −46.0242 −1.46053
\(994\) 186.255 5.90764
\(995\) 50.9848 1.61633
\(996\) 193.747 6.13912
\(997\) −40.7736 −1.29131 −0.645656 0.763628i \(-0.723416\pi\)
−0.645656 + 0.763628i \(0.723416\pi\)
\(998\) 45.4226 1.43783
\(999\) 12.8427 0.406326
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 6001.2.a.d.1.5 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.5 121 1.1 even 1 trivial