Properties

Label 6017.2.a.f.1.6
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
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 1.6
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66480 q^{2} -1.17356 q^{3} +5.10118 q^{4} +4.42559 q^{5} +3.12731 q^{6} +1.20677 q^{7} -8.26404 q^{8} -1.62275 q^{9} +O(q^{10})\) \(q-2.66480 q^{2} -1.17356 q^{3} +5.10118 q^{4} +4.42559 q^{5} +3.12731 q^{6} +1.20677 q^{7} -8.26404 q^{8} -1.62275 q^{9} -11.7933 q^{10} -1.00000 q^{11} -5.98655 q^{12} +3.53290 q^{13} -3.21580 q^{14} -5.19370 q^{15} +11.8197 q^{16} -4.17739 q^{17} +4.32432 q^{18} +5.96661 q^{19} +22.5758 q^{20} -1.41622 q^{21} +2.66480 q^{22} -1.37608 q^{23} +9.69835 q^{24} +14.5859 q^{25} -9.41449 q^{26} +5.42508 q^{27} +6.15594 q^{28} -4.09416 q^{29} +13.8402 q^{30} +4.26025 q^{31} -14.9691 q^{32} +1.17356 q^{33} +11.1319 q^{34} +5.34067 q^{35} -8.27797 q^{36} +11.1171 q^{37} -15.8998 q^{38} -4.14607 q^{39} -36.5733 q^{40} +6.73017 q^{41} +3.77394 q^{42} +5.32446 q^{43} -5.10118 q^{44} -7.18165 q^{45} +3.66699 q^{46} -1.86392 q^{47} -13.8711 q^{48} -5.54371 q^{49} -38.8685 q^{50} +4.90242 q^{51} +18.0220 q^{52} -14.0322 q^{53} -14.4568 q^{54} -4.42559 q^{55} -9.97278 q^{56} -7.00218 q^{57} +10.9101 q^{58} -8.53852 q^{59} -26.4940 q^{60} -8.66438 q^{61} -11.3527 q^{62} -1.95829 q^{63} +16.2503 q^{64} +15.6352 q^{65} -3.12731 q^{66} +12.7341 q^{67} -21.3096 q^{68} +1.61492 q^{69} -14.2318 q^{70} +16.6868 q^{71} +13.4105 q^{72} +6.24979 q^{73} -29.6249 q^{74} -17.1174 q^{75} +30.4368 q^{76} -1.20677 q^{77} +11.0485 q^{78} -12.5123 q^{79} +52.3091 q^{80} -1.49840 q^{81} -17.9346 q^{82} -1.67501 q^{83} -7.22437 q^{84} -18.4874 q^{85} -14.1886 q^{86} +4.80474 q^{87} +8.26404 q^{88} -0.148598 q^{89} +19.1377 q^{90} +4.26339 q^{91} -7.01964 q^{92} -4.99967 q^{93} +4.96697 q^{94} +26.4058 q^{95} +17.5671 q^{96} +2.40260 q^{97} +14.7729 q^{98} +1.62275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66480 −1.88430 −0.942151 0.335190i \(-0.891199\pi\)
−0.942151 + 0.335190i \(0.891199\pi\)
\(3\) −1.17356 −0.677556 −0.338778 0.940866i \(-0.610014\pi\)
−0.338778 + 0.940866i \(0.610014\pi\)
\(4\) 5.10118 2.55059
\(5\) 4.42559 1.97919 0.989593 0.143896i \(-0.0459631\pi\)
0.989593 + 0.143896i \(0.0459631\pi\)
\(6\) 3.12731 1.27672
\(7\) 1.20677 0.456115 0.228058 0.973648i \(-0.426763\pi\)
0.228058 + 0.973648i \(0.426763\pi\)
\(8\) −8.26404 −2.92178
\(9\) −1.62275 −0.540918
\(10\) −11.7933 −3.72938
\(11\) −1.00000 −0.301511
\(12\) −5.98655 −1.72817
\(13\) 3.53290 0.979850 0.489925 0.871765i \(-0.337024\pi\)
0.489925 + 0.871765i \(0.337024\pi\)
\(14\) −3.21580 −0.859459
\(15\) −5.19370 −1.34101
\(16\) 11.8197 2.95492
\(17\) −4.17739 −1.01317 −0.506583 0.862191i \(-0.669092\pi\)
−0.506583 + 0.862191i \(0.669092\pi\)
\(18\) 4.32432 1.01925
\(19\) 5.96661 1.36883 0.684417 0.729091i \(-0.260057\pi\)
0.684417 + 0.729091i \(0.260057\pi\)
\(20\) 22.5758 5.04809
\(21\) −1.41622 −0.309044
\(22\) 2.66480 0.568138
\(23\) −1.37608 −0.286933 −0.143466 0.989655i \(-0.545825\pi\)
−0.143466 + 0.989655i \(0.545825\pi\)
\(24\) 9.69835 1.97967
\(25\) 14.5859 2.91718
\(26\) −9.41449 −1.84633
\(27\) 5.42508 1.04406
\(28\) 6.15594 1.16336
\(29\) −4.09416 −0.760266 −0.380133 0.924932i \(-0.624122\pi\)
−0.380133 + 0.924932i \(0.624122\pi\)
\(30\) 13.8402 2.52686
\(31\) 4.26025 0.765164 0.382582 0.923922i \(-0.375035\pi\)
0.382582 + 0.923922i \(0.375035\pi\)
\(32\) −14.9691 −2.64618
\(33\) 1.17356 0.204291
\(34\) 11.1319 1.90911
\(35\) 5.34067 0.902737
\(36\) −8.27797 −1.37966
\(37\) 11.1171 1.82764 0.913820 0.406118i \(-0.133118\pi\)
0.913820 + 0.406118i \(0.133118\pi\)
\(38\) −15.8998 −2.57930
\(39\) −4.14607 −0.663903
\(40\) −36.5733 −5.78274
\(41\) 6.73017 1.05108 0.525538 0.850770i \(-0.323864\pi\)
0.525538 + 0.850770i \(0.323864\pi\)
\(42\) 3.77394 0.582331
\(43\) 5.32446 0.811972 0.405986 0.913879i \(-0.366928\pi\)
0.405986 + 0.913879i \(0.366928\pi\)
\(44\) −5.10118 −0.769032
\(45\) −7.18165 −1.07058
\(46\) 3.66699 0.540668
\(47\) −1.86392 −0.271880 −0.135940 0.990717i \(-0.543405\pi\)
−0.135940 + 0.990717i \(0.543405\pi\)
\(48\) −13.8711 −2.00212
\(49\) −5.54371 −0.791959
\(50\) −38.8685 −5.49684
\(51\) 4.90242 0.686477
\(52\) 18.0220 2.49920
\(53\) −14.0322 −1.92747 −0.963735 0.266861i \(-0.914014\pi\)
−0.963735 + 0.266861i \(0.914014\pi\)
\(54\) −14.4568 −1.96732
\(55\) −4.42559 −0.596747
\(56\) −9.97278 −1.33267
\(57\) −7.00218 −0.927461
\(58\) 10.9101 1.43257
\(59\) −8.53852 −1.11162 −0.555810 0.831309i \(-0.687592\pi\)
−0.555810 + 0.831309i \(0.687592\pi\)
\(60\) −26.4940 −3.42036
\(61\) −8.66438 −1.10936 −0.554680 0.832064i \(-0.687159\pi\)
−0.554680 + 0.832064i \(0.687159\pi\)
\(62\) −11.3527 −1.44180
\(63\) −1.95829 −0.246721
\(64\) 16.2503 2.03128
\(65\) 15.6352 1.93931
\(66\) −3.12731 −0.384945
\(67\) 12.7341 1.55571 0.777857 0.628441i \(-0.216307\pi\)
0.777857 + 0.628441i \(0.216307\pi\)
\(68\) −21.3096 −2.58417
\(69\) 1.61492 0.194413
\(70\) −14.2318 −1.70103
\(71\) 16.6868 1.98036 0.990182 0.139784i \(-0.0446408\pi\)
0.990182 + 0.139784i \(0.0446408\pi\)
\(72\) 13.4105 1.58044
\(73\) 6.24979 0.731482 0.365741 0.930717i \(-0.380816\pi\)
0.365741 + 0.930717i \(0.380816\pi\)
\(74\) −29.6249 −3.44383
\(75\) −17.1174 −1.97655
\(76\) 30.4368 3.49134
\(77\) −1.20677 −0.137524
\(78\) 11.0485 1.25099
\(79\) −12.5123 −1.40775 −0.703873 0.710326i \(-0.748547\pi\)
−0.703873 + 0.710326i \(0.748547\pi\)
\(80\) 52.3091 5.84834
\(81\) −1.49840 −0.166489
\(82\) −17.9346 −1.98054
\(83\) −1.67501 −0.183856 −0.0919279 0.995766i \(-0.529303\pi\)
−0.0919279 + 0.995766i \(0.529303\pi\)
\(84\) −7.22437 −0.788244
\(85\) −18.4874 −2.00524
\(86\) −14.1886 −1.53000
\(87\) 4.80474 0.515123
\(88\) 8.26404 0.880950
\(89\) −0.148598 −0.0157513 −0.00787565 0.999969i \(-0.502507\pi\)
−0.00787565 + 0.999969i \(0.502507\pi\)
\(90\) 19.1377 2.01729
\(91\) 4.26339 0.446925
\(92\) −7.01964 −0.731848
\(93\) −4.99967 −0.518441
\(94\) 4.96697 0.512304
\(95\) 26.4058 2.70918
\(96\) 17.5671 1.79294
\(97\) 2.40260 0.243947 0.121974 0.992533i \(-0.461078\pi\)
0.121974 + 0.992533i \(0.461078\pi\)
\(98\) 14.7729 1.49229
\(99\) 1.62275 0.163093
\(100\) 74.4052 7.44052
\(101\) 9.33560 0.928927 0.464464 0.885592i \(-0.346247\pi\)
0.464464 + 0.885592i \(0.346247\pi\)
\(102\) −13.0640 −1.29353
\(103\) −5.34343 −0.526504 −0.263252 0.964727i \(-0.584795\pi\)
−0.263252 + 0.964727i \(0.584795\pi\)
\(104\) −29.1960 −2.86291
\(105\) −6.26760 −0.611655
\(106\) 37.3930 3.63193
\(107\) 15.8395 1.53126 0.765630 0.643281i \(-0.222427\pi\)
0.765630 + 0.643281i \(0.222427\pi\)
\(108\) 27.6743 2.66296
\(109\) −13.8658 −1.32810 −0.664052 0.747687i \(-0.731165\pi\)
−0.664052 + 0.747687i \(0.731165\pi\)
\(110\) 11.7933 1.12445
\(111\) −13.0466 −1.23833
\(112\) 14.2636 1.34779
\(113\) 13.4483 1.26511 0.632555 0.774515i \(-0.282006\pi\)
0.632555 + 0.774515i \(0.282006\pi\)
\(114\) 18.6594 1.74762
\(115\) −6.08998 −0.567893
\(116\) −20.8850 −1.93913
\(117\) −5.73303 −0.530019
\(118\) 22.7535 2.09463
\(119\) −5.04114 −0.462121
\(120\) 42.9210 3.91813
\(121\) 1.00000 0.0909091
\(122\) 23.0889 2.09037
\(123\) −7.89827 −0.712163
\(124\) 21.7323 1.95162
\(125\) 42.4232 3.79445
\(126\) 5.21846 0.464897
\(127\) −14.4303 −1.28048 −0.640241 0.768174i \(-0.721165\pi\)
−0.640241 + 0.768174i \(0.721165\pi\)
\(128\) −13.3656 −1.18137
\(129\) −6.24858 −0.550156
\(130\) −41.6647 −3.65424
\(131\) −8.74743 −0.764267 −0.382133 0.924107i \(-0.624810\pi\)
−0.382133 + 0.924107i \(0.624810\pi\)
\(132\) 5.98655 0.521062
\(133\) 7.20031 0.624346
\(134\) −33.9338 −2.93143
\(135\) 24.0092 2.06638
\(136\) 34.5221 2.96025
\(137\) 5.49126 0.469150 0.234575 0.972098i \(-0.424630\pi\)
0.234575 + 0.972098i \(0.424630\pi\)
\(138\) −4.30343 −0.366332
\(139\) 4.37455 0.371044 0.185522 0.982640i \(-0.440602\pi\)
0.185522 + 0.982640i \(0.440602\pi\)
\(140\) 27.2437 2.30251
\(141\) 2.18742 0.184214
\(142\) −44.4672 −3.73160
\(143\) −3.53290 −0.295436
\(144\) −19.1805 −1.59837
\(145\) −18.1191 −1.50471
\(146\) −16.6545 −1.37833
\(147\) 6.50588 0.536596
\(148\) 56.7104 4.66156
\(149\) −6.21984 −0.509549 −0.254775 0.967000i \(-0.582001\pi\)
−0.254775 + 0.967000i \(0.582001\pi\)
\(150\) 45.6146 3.72441
\(151\) −11.4140 −0.928860 −0.464430 0.885610i \(-0.653741\pi\)
−0.464430 + 0.885610i \(0.653741\pi\)
\(152\) −49.3083 −3.99943
\(153\) 6.77888 0.548040
\(154\) 3.21580 0.259137
\(155\) 18.8542 1.51440
\(156\) −21.1499 −1.69334
\(157\) 20.7566 1.65656 0.828279 0.560316i \(-0.189320\pi\)
0.828279 + 0.560316i \(0.189320\pi\)
\(158\) 33.3429 2.65262
\(159\) 16.4676 1.30597
\(160\) −66.2470 −5.23729
\(161\) −1.66061 −0.130874
\(162\) 3.99295 0.313715
\(163\) −1.58768 −0.124356 −0.0621782 0.998065i \(-0.519805\pi\)
−0.0621782 + 0.998065i \(0.519805\pi\)
\(164\) 34.3318 2.68087
\(165\) 5.19370 0.404329
\(166\) 4.46357 0.346440
\(167\) −4.64398 −0.359362 −0.179681 0.983725i \(-0.557507\pi\)
−0.179681 + 0.983725i \(0.557507\pi\)
\(168\) 11.7037 0.902957
\(169\) −0.518618 −0.0398937
\(170\) 49.2654 3.77848
\(171\) −9.68234 −0.740427
\(172\) 27.1610 2.07101
\(173\) −14.7938 −1.12475 −0.562377 0.826881i \(-0.690113\pi\)
−0.562377 + 0.826881i \(0.690113\pi\)
\(174\) −12.8037 −0.970646
\(175\) 17.6018 1.33057
\(176\) −11.8197 −0.890943
\(177\) 10.0205 0.753184
\(178\) 0.395983 0.0296802
\(179\) −8.85649 −0.661965 −0.330983 0.943637i \(-0.607380\pi\)
−0.330983 + 0.943637i \(0.607380\pi\)
\(180\) −36.6349 −2.73061
\(181\) 21.6872 1.61200 0.805998 0.591918i \(-0.201629\pi\)
0.805998 + 0.591918i \(0.201629\pi\)
\(182\) −11.3611 −0.842141
\(183\) 10.1682 0.751654
\(184\) 11.3720 0.838354
\(185\) 49.1998 3.61724
\(186\) 13.3231 0.976900
\(187\) 4.17739 0.305481
\(188\) −9.50817 −0.693455
\(189\) 6.54682 0.476211
\(190\) −70.3662 −5.10490
\(191\) −1.27549 −0.0922915 −0.0461458 0.998935i \(-0.514694\pi\)
−0.0461458 + 0.998935i \(0.514694\pi\)
\(192\) −19.0707 −1.37631
\(193\) −8.57805 −0.617461 −0.308731 0.951150i \(-0.599904\pi\)
−0.308731 + 0.951150i \(0.599904\pi\)
\(194\) −6.40246 −0.459670
\(195\) −18.3488 −1.31399
\(196\) −28.2795 −2.01996
\(197\) −0.521401 −0.0371483 −0.0185742 0.999827i \(-0.505913\pi\)
−0.0185742 + 0.999827i \(0.505913\pi\)
\(198\) −4.32432 −0.307316
\(199\) 6.38405 0.452553 0.226277 0.974063i \(-0.427345\pi\)
0.226277 + 0.974063i \(0.427345\pi\)
\(200\) −120.538 −8.52334
\(201\) −14.9442 −1.05408
\(202\) −24.8776 −1.75038
\(203\) −4.94070 −0.346769
\(204\) 25.0082 1.75092
\(205\) 29.7850 2.08028
\(206\) 14.2392 0.992092
\(207\) 2.23304 0.155207
\(208\) 41.7578 2.89538
\(209\) −5.96661 −0.412719
\(210\) 16.7019 1.15254
\(211\) −0.918310 −0.0632191 −0.0316095 0.999500i \(-0.510063\pi\)
−0.0316095 + 0.999500i \(0.510063\pi\)
\(212\) −71.5808 −4.91619
\(213\) −19.5830 −1.34181
\(214\) −42.2091 −2.88536
\(215\) 23.5639 1.60704
\(216\) −44.8331 −3.05051
\(217\) 5.14114 0.349003
\(218\) 36.9497 2.50255
\(219\) −7.33451 −0.495620
\(220\) −22.5758 −1.52206
\(221\) −14.7583 −0.992751
\(222\) 34.7666 2.33338
\(223\) 15.1138 1.01210 0.506048 0.862505i \(-0.331106\pi\)
0.506048 + 0.862505i \(0.331106\pi\)
\(224\) −18.0642 −1.20697
\(225\) −23.6693 −1.57795
\(226\) −35.8371 −2.38385
\(227\) −13.3852 −0.888410 −0.444205 0.895925i \(-0.646514\pi\)
−0.444205 + 0.895925i \(0.646514\pi\)
\(228\) −35.7194 −2.36557
\(229\) 24.0496 1.58924 0.794620 0.607108i \(-0.207670\pi\)
0.794620 + 0.607108i \(0.207670\pi\)
\(230\) 16.2286 1.07008
\(231\) 1.41622 0.0931802
\(232\) 33.8343 2.22133
\(233\) 10.2563 0.671915 0.335958 0.941877i \(-0.390940\pi\)
0.335958 + 0.941877i \(0.390940\pi\)
\(234\) 15.2774 0.998715
\(235\) −8.24893 −0.538101
\(236\) −43.5565 −2.83529
\(237\) 14.6840 0.953826
\(238\) 13.4337 0.870775
\(239\) 8.74016 0.565354 0.282677 0.959215i \(-0.408778\pi\)
0.282677 + 0.959215i \(0.408778\pi\)
\(240\) −61.3880 −3.96258
\(241\) −29.7991 −1.91953 −0.959765 0.280805i \(-0.909398\pi\)
−0.959765 + 0.280805i \(0.909398\pi\)
\(242\) −2.66480 −0.171300
\(243\) −14.5168 −0.931252
\(244\) −44.1986 −2.82952
\(245\) −24.5342 −1.56743
\(246\) 21.0473 1.34193
\(247\) 21.0794 1.34125
\(248\) −35.2069 −2.23564
\(249\) 1.96572 0.124573
\(250\) −113.050 −7.14988
\(251\) 18.3075 1.15556 0.577780 0.816192i \(-0.303919\pi\)
0.577780 + 0.816192i \(0.303919\pi\)
\(252\) −9.98959 −0.629285
\(253\) 1.37608 0.0865135
\(254\) 38.4539 2.41281
\(255\) 21.6961 1.35866
\(256\) 3.11628 0.194768
\(257\) 23.1631 1.44487 0.722436 0.691438i \(-0.243023\pi\)
0.722436 + 0.691438i \(0.243023\pi\)
\(258\) 16.6512 1.03666
\(259\) 13.4158 0.833615
\(260\) 79.7579 4.94637
\(261\) 6.64382 0.411242
\(262\) 23.3102 1.44011
\(263\) 29.7571 1.83490 0.917451 0.397848i \(-0.130243\pi\)
0.917451 + 0.397848i \(0.130243\pi\)
\(264\) −9.69835 −0.596892
\(265\) −62.1008 −3.81482
\(266\) −19.1874 −1.17646
\(267\) 0.174388 0.0106724
\(268\) 64.9588 3.96799
\(269\) −12.0675 −0.735769 −0.367885 0.929871i \(-0.619918\pi\)
−0.367885 + 0.929871i \(0.619918\pi\)
\(270\) −63.9799 −3.89369
\(271\) 4.76998 0.289756 0.144878 0.989450i \(-0.453721\pi\)
0.144878 + 0.989450i \(0.453721\pi\)
\(272\) −49.3755 −2.99383
\(273\) −5.00335 −0.302816
\(274\) −14.6331 −0.884020
\(275\) −14.5859 −0.879562
\(276\) 8.23797 0.495868
\(277\) −4.24061 −0.254794 −0.127397 0.991852i \(-0.540662\pi\)
−0.127397 + 0.991852i \(0.540662\pi\)
\(278\) −11.6573 −0.699160
\(279\) −6.91335 −0.413891
\(280\) −44.1355 −2.63760
\(281\) −13.3372 −0.795629 −0.397814 0.917466i \(-0.630231\pi\)
−0.397814 + 0.917466i \(0.630231\pi\)
\(282\) −5.82904 −0.347114
\(283\) −0.407839 −0.0242435 −0.0121217 0.999927i \(-0.503859\pi\)
−0.0121217 + 0.999927i \(0.503859\pi\)
\(284\) 85.1226 5.05110
\(285\) −30.9888 −1.83562
\(286\) 9.41449 0.556690
\(287\) 8.12176 0.479412
\(288\) 24.2911 1.43137
\(289\) 0.450605 0.0265062
\(290\) 48.2838 2.83532
\(291\) −2.81960 −0.165288
\(292\) 31.8813 1.86571
\(293\) −8.75333 −0.511375 −0.255687 0.966760i \(-0.582302\pi\)
−0.255687 + 0.966760i \(0.582302\pi\)
\(294\) −17.3369 −1.01111
\(295\) −37.7880 −2.20010
\(296\) −91.8722 −5.33996
\(297\) −5.42508 −0.314795
\(298\) 16.5747 0.960144
\(299\) −4.86156 −0.281151
\(300\) −87.3190 −5.04137
\(301\) 6.42539 0.370353
\(302\) 30.4161 1.75025
\(303\) −10.9559 −0.629400
\(304\) 70.5235 4.04480
\(305\) −38.3450 −2.19563
\(306\) −18.0644 −1.03267
\(307\) 26.1385 1.49180 0.745902 0.666055i \(-0.232018\pi\)
0.745902 + 0.666055i \(0.232018\pi\)
\(308\) −6.15594 −0.350767
\(309\) 6.27084 0.356736
\(310\) −50.2426 −2.85359
\(311\) 20.4254 1.15822 0.579108 0.815251i \(-0.303401\pi\)
0.579108 + 0.815251i \(0.303401\pi\)
\(312\) 34.2633 1.93978
\(313\) −29.9494 −1.69284 −0.846421 0.532514i \(-0.821247\pi\)
−0.846421 + 0.532514i \(0.821247\pi\)
\(314\) −55.3123 −3.12145
\(315\) −8.66659 −0.488307
\(316\) −63.8276 −3.59058
\(317\) −28.6448 −1.60885 −0.804425 0.594054i \(-0.797526\pi\)
−0.804425 + 0.594054i \(0.797526\pi\)
\(318\) −43.8830 −2.46084
\(319\) 4.09416 0.229229
\(320\) 71.9171 4.02029
\(321\) −18.5886 −1.03751
\(322\) 4.42520 0.246607
\(323\) −24.9249 −1.38686
\(324\) −7.64362 −0.424645
\(325\) 51.5305 2.85840
\(326\) 4.23084 0.234325
\(327\) 16.2724 0.899864
\(328\) −55.6184 −3.07101
\(329\) −2.24931 −0.124009
\(330\) −13.8402 −0.761878
\(331\) −9.64005 −0.529865 −0.264932 0.964267i \(-0.585350\pi\)
−0.264932 + 0.964267i \(0.585350\pi\)
\(332\) −8.54451 −0.468941
\(333\) −18.0403 −0.988605
\(334\) 12.3753 0.677147
\(335\) 56.3558 3.07905
\(336\) −16.7392 −0.913200
\(337\) −2.66031 −0.144916 −0.0724581 0.997371i \(-0.523084\pi\)
−0.0724581 + 0.997371i \(0.523084\pi\)
\(338\) 1.38201 0.0751717
\(339\) −15.7824 −0.857183
\(340\) −94.3078 −5.11456
\(341\) −4.26025 −0.230706
\(342\) 25.8016 1.39519
\(343\) −15.1374 −0.817340
\(344\) −44.0015 −2.37240
\(345\) 7.14696 0.384779
\(346\) 39.4227 2.11937
\(347\) 31.6867 1.70103 0.850514 0.525952i \(-0.176291\pi\)
0.850514 + 0.525952i \(0.176291\pi\)
\(348\) 24.5099 1.31387
\(349\) −19.4782 −1.04264 −0.521321 0.853361i \(-0.674561\pi\)
−0.521321 + 0.853361i \(0.674561\pi\)
\(350\) −46.9053 −2.50719
\(351\) 19.1663 1.02302
\(352\) 14.9691 0.797854
\(353\) 2.78124 0.148031 0.0740153 0.997257i \(-0.476419\pi\)
0.0740153 + 0.997257i \(0.476419\pi\)
\(354\) −26.7026 −1.41923
\(355\) 73.8492 3.91951
\(356\) −0.758023 −0.0401751
\(357\) 5.91609 0.313113
\(358\) 23.6008 1.24734
\(359\) −4.11703 −0.217289 −0.108644 0.994081i \(-0.534651\pi\)
−0.108644 + 0.994081i \(0.534651\pi\)
\(360\) 59.3495 3.12799
\(361\) 16.6004 0.873706
\(362\) −57.7921 −3.03749
\(363\) −1.17356 −0.0615960
\(364\) 21.7483 1.13992
\(365\) 27.6590 1.44774
\(366\) −27.0962 −1.41634
\(367\) 28.3119 1.47787 0.738934 0.673778i \(-0.235330\pi\)
0.738934 + 0.673778i \(0.235330\pi\)
\(368\) −16.2649 −0.847864
\(369\) −10.9214 −0.568546
\(370\) −131.108 −6.81597
\(371\) −16.9336 −0.879149
\(372\) −25.5042 −1.32233
\(373\) −3.30806 −0.171285 −0.0856423 0.996326i \(-0.527294\pi\)
−0.0856423 + 0.996326i \(0.527294\pi\)
\(374\) −11.1319 −0.575619
\(375\) −49.7862 −2.57095
\(376\) 15.4035 0.794373
\(377\) −14.4643 −0.744947
\(378\) −17.4460 −0.897325
\(379\) −14.6808 −0.754102 −0.377051 0.926192i \(-0.623062\pi\)
−0.377051 + 0.926192i \(0.623062\pi\)
\(380\) 134.701 6.91000
\(381\) 16.9348 0.867598
\(382\) 3.39894 0.173905
\(383\) 0.0119913 0.000612725 0 0.000306363 1.00000i \(-0.499902\pi\)
0.000306363 1.00000i \(0.499902\pi\)
\(384\) 15.6854 0.800442
\(385\) −5.34067 −0.272186
\(386\) 22.8588 1.16348
\(387\) −8.64029 −0.439211
\(388\) 12.2561 0.622210
\(389\) 27.4932 1.39396 0.696980 0.717090i \(-0.254527\pi\)
0.696980 + 0.717090i \(0.254527\pi\)
\(390\) 48.8961 2.47595
\(391\) 5.74843 0.290711
\(392\) 45.8135 2.31393
\(393\) 10.2656 0.517833
\(394\) 1.38943 0.0699986
\(395\) −55.3744 −2.78619
\(396\) 8.27797 0.415984
\(397\) −10.9738 −0.550759 −0.275380 0.961336i \(-0.588804\pi\)
−0.275380 + 0.961336i \(0.588804\pi\)
\(398\) −17.0122 −0.852746
\(399\) −8.45001 −0.423029
\(400\) 172.401 8.62003
\(401\) −22.2630 −1.11176 −0.555880 0.831263i \(-0.687619\pi\)
−0.555880 + 0.831263i \(0.687619\pi\)
\(402\) 39.8234 1.98621
\(403\) 15.0511 0.749746
\(404\) 47.6226 2.36931
\(405\) −6.63131 −0.329513
\(406\) 13.1660 0.653417
\(407\) −11.1171 −0.551054
\(408\) −40.5138 −2.00573
\(409\) 19.5897 0.968647 0.484324 0.874889i \(-0.339066\pi\)
0.484324 + 0.874889i \(0.339066\pi\)
\(410\) −79.3712 −3.91987
\(411\) −6.44433 −0.317875
\(412\) −27.2578 −1.34290
\(413\) −10.3040 −0.507027
\(414\) −5.95062 −0.292457
\(415\) −7.41290 −0.363885
\(416\) −52.8842 −2.59286
\(417\) −5.13380 −0.251403
\(418\) 15.8998 0.777687
\(419\) 11.0588 0.540259 0.270129 0.962824i \(-0.412933\pi\)
0.270129 + 0.962824i \(0.412933\pi\)
\(420\) −31.9721 −1.56008
\(421\) 6.43504 0.313625 0.156812 0.987628i \(-0.449878\pi\)
0.156812 + 0.987628i \(0.449878\pi\)
\(422\) 2.44712 0.119124
\(423\) 3.02468 0.147065
\(424\) 115.963 5.63164
\(425\) −60.9309 −2.95558
\(426\) 52.1849 2.52837
\(427\) −10.4559 −0.505997
\(428\) 80.8001 3.90562
\(429\) 4.14607 0.200174
\(430\) −62.7931 −3.02815
\(431\) 21.6944 1.04498 0.522491 0.852645i \(-0.325003\pi\)
0.522491 + 0.852645i \(0.325003\pi\)
\(432\) 64.1228 3.08511
\(433\) −10.1195 −0.486312 −0.243156 0.969987i \(-0.578183\pi\)
−0.243156 + 0.969987i \(0.578183\pi\)
\(434\) −13.7001 −0.657627
\(435\) 21.2638 1.01952
\(436\) −70.7320 −3.38745
\(437\) −8.21054 −0.392763
\(438\) 19.5450 0.933897
\(439\) 14.5697 0.695374 0.347687 0.937611i \(-0.386967\pi\)
0.347687 + 0.937611i \(0.386967\pi\)
\(440\) 36.5733 1.74356
\(441\) 8.99608 0.428385
\(442\) 39.3280 1.87064
\(443\) 1.75637 0.0834476 0.0417238 0.999129i \(-0.486715\pi\)
0.0417238 + 0.999129i \(0.486715\pi\)
\(444\) −66.5531 −3.15847
\(445\) −0.657632 −0.0311748
\(446\) −40.2754 −1.90709
\(447\) 7.29936 0.345248
\(448\) 19.6103 0.926500
\(449\) −28.2700 −1.33414 −0.667072 0.744994i \(-0.732453\pi\)
−0.667072 + 0.744994i \(0.732453\pi\)
\(450\) 63.0741 2.97334
\(451\) −6.73017 −0.316911
\(452\) 68.6022 3.22678
\(453\) 13.3951 0.629355
\(454\) 35.6690 1.67403
\(455\) 18.8680 0.884547
\(456\) 57.8663 2.70984
\(457\) −20.3435 −0.951629 −0.475815 0.879546i \(-0.657847\pi\)
−0.475815 + 0.879546i \(0.657847\pi\)
\(458\) −64.0873 −2.99461
\(459\) −22.6627 −1.05780
\(460\) −31.0661 −1.44846
\(461\) 20.8216 0.969761 0.484880 0.874581i \(-0.338863\pi\)
0.484880 + 0.874581i \(0.338863\pi\)
\(462\) −3.77394 −0.175579
\(463\) −0.171608 −0.00797530 −0.00398765 0.999992i \(-0.501269\pi\)
−0.00398765 + 0.999992i \(0.501269\pi\)
\(464\) −48.3917 −2.24653
\(465\) −22.1265 −1.02609
\(466\) −27.3311 −1.26609
\(467\) −15.3572 −0.710645 −0.355323 0.934744i \(-0.615629\pi\)
−0.355323 + 0.934744i \(0.615629\pi\)
\(468\) −29.2452 −1.35186
\(469\) 15.3671 0.709585
\(470\) 21.9818 1.01394
\(471\) −24.3592 −1.12241
\(472\) 70.5626 3.24791
\(473\) −5.32446 −0.244819
\(474\) −39.1299 −1.79730
\(475\) 87.0282 3.99313
\(476\) −25.7158 −1.17868
\(477\) 22.7708 1.04260
\(478\) −23.2908 −1.06530
\(479\) −2.83173 −0.129385 −0.0646926 0.997905i \(-0.520607\pi\)
−0.0646926 + 0.997905i \(0.520607\pi\)
\(480\) 77.7449 3.54855
\(481\) 39.2756 1.79081
\(482\) 79.4088 3.61697
\(483\) 1.94883 0.0886747
\(484\) 5.10118 0.231872
\(485\) 10.6329 0.482817
\(486\) 38.6844 1.75476
\(487\) 10.9060 0.494198 0.247099 0.968990i \(-0.420523\pi\)
0.247099 + 0.968990i \(0.420523\pi\)
\(488\) 71.6028 3.24131
\(489\) 1.86323 0.0842583
\(490\) 65.3789 2.95352
\(491\) 22.7853 1.02829 0.514144 0.857704i \(-0.328110\pi\)
0.514144 + 0.857704i \(0.328110\pi\)
\(492\) −40.2905 −1.81644
\(493\) 17.1029 0.770276
\(494\) −56.1726 −2.52732
\(495\) 7.18165 0.322791
\(496\) 50.3549 2.26100
\(497\) 20.1372 0.903275
\(498\) −5.23827 −0.234732
\(499\) 14.2476 0.637810 0.318905 0.947787i \(-0.396685\pi\)
0.318905 + 0.947787i \(0.396685\pi\)
\(500\) 216.408 9.67808
\(501\) 5.45000 0.243488
\(502\) −48.7859 −2.17742
\(503\) −15.4032 −0.686794 −0.343397 0.939190i \(-0.611578\pi\)
−0.343397 + 0.939190i \(0.611578\pi\)
\(504\) 16.1834 0.720865
\(505\) 41.3156 1.83852
\(506\) −3.66699 −0.163017
\(507\) 0.608630 0.0270302
\(508\) −73.6116 −3.26599
\(509\) −4.36561 −0.193502 −0.0967510 0.995309i \(-0.530845\pi\)
−0.0967510 + 0.995309i \(0.530845\pi\)
\(510\) −57.8160 −2.56013
\(511\) 7.54205 0.333640
\(512\) 18.4270 0.814366
\(513\) 32.3694 1.42914
\(514\) −61.7250 −2.72257
\(515\) −23.6478 −1.04205
\(516\) −31.8751 −1.40322
\(517\) 1.86392 0.0819749
\(518\) −35.7504 −1.57078
\(519\) 17.3615 0.762083
\(520\) −129.210 −5.66622
\(521\) −16.9197 −0.741267 −0.370634 0.928779i \(-0.620859\pi\)
−0.370634 + 0.928779i \(0.620859\pi\)
\(522\) −17.7045 −0.774904
\(523\) 37.2713 1.62976 0.814879 0.579631i \(-0.196803\pi\)
0.814879 + 0.579631i \(0.196803\pi\)
\(524\) −44.6222 −1.94933
\(525\) −20.6568 −0.901535
\(526\) −79.2969 −3.45751
\(527\) −17.7968 −0.775239
\(528\) 13.8711 0.603663
\(529\) −21.1064 −0.917670
\(530\) 165.486 7.18827
\(531\) 13.8559 0.601296
\(532\) 36.7301 1.59245
\(533\) 23.7770 1.02990
\(534\) −0.464710 −0.0201100
\(535\) 70.0991 3.03065
\(536\) −105.235 −4.54545
\(537\) 10.3936 0.448518
\(538\) 32.1576 1.38641
\(539\) 5.54371 0.238785
\(540\) 122.475 5.27050
\(541\) −31.7940 −1.36693 −0.683465 0.729983i \(-0.739528\pi\)
−0.683465 + 0.729983i \(0.739528\pi\)
\(542\) −12.7111 −0.545987
\(543\) −25.4512 −1.09222
\(544\) 62.5317 2.68102
\(545\) −61.3644 −2.62856
\(546\) 13.3329 0.570597
\(547\) 1.00000 0.0427569
\(548\) 28.0119 1.19661
\(549\) 14.0602 0.600073
\(550\) 38.8685 1.65736
\(551\) −24.4282 −1.04068
\(552\) −13.3457 −0.568032
\(553\) −15.0995 −0.642094
\(554\) 11.3004 0.480108
\(555\) −57.7390 −2.45088
\(556\) 22.3154 0.946383
\(557\) 18.7401 0.794045 0.397022 0.917809i \(-0.370043\pi\)
0.397022 + 0.917809i \(0.370043\pi\)
\(558\) 18.4227 0.779896
\(559\) 18.8108 0.795611
\(560\) 63.1250 2.66752
\(561\) −4.90242 −0.206980
\(562\) 35.5409 1.49920
\(563\) −9.17942 −0.386866 −0.193433 0.981113i \(-0.561962\pi\)
−0.193433 + 0.981113i \(0.561962\pi\)
\(564\) 11.1584 0.469854
\(565\) 59.5167 2.50389
\(566\) 1.08681 0.0456821
\(567\) −1.80822 −0.0759382
\(568\) −137.901 −5.78619
\(569\) 32.1296 1.34694 0.673472 0.739213i \(-0.264802\pi\)
0.673472 + 0.739213i \(0.264802\pi\)
\(570\) 82.5791 3.45886
\(571\) 31.0483 1.29933 0.649665 0.760221i \(-0.274909\pi\)
0.649665 + 0.760221i \(0.274909\pi\)
\(572\) −18.0220 −0.753536
\(573\) 1.49687 0.0625327
\(574\) −21.6429 −0.903357
\(575\) −20.0714 −0.837033
\(576\) −26.3702 −1.09876
\(577\) −13.6337 −0.567579 −0.283790 0.958887i \(-0.591592\pi\)
−0.283790 + 0.958887i \(0.591592\pi\)
\(578\) −1.20077 −0.0499457
\(579\) 10.0669 0.418364
\(580\) −92.4287 −3.83789
\(581\) −2.02134 −0.0838595
\(582\) 7.51368 0.311452
\(583\) 14.0322 0.581154
\(584\) −51.6485 −2.13723
\(585\) −25.3721 −1.04901
\(586\) 23.3259 0.963584
\(587\) 31.2328 1.28911 0.644557 0.764556i \(-0.277042\pi\)
0.644557 + 0.764556i \(0.277042\pi\)
\(588\) 33.1877 1.36864
\(589\) 25.4193 1.04738
\(590\) 100.698 4.14566
\(591\) 0.611896 0.0251700
\(592\) 131.401 5.40054
\(593\) 5.49897 0.225815 0.112908 0.993605i \(-0.463984\pi\)
0.112908 + 0.993605i \(0.463984\pi\)
\(594\) 14.4568 0.593169
\(595\) −22.3101 −0.914623
\(596\) −31.7285 −1.29965
\(597\) −7.49207 −0.306630
\(598\) 12.9551 0.529773
\(599\) −34.6193 −1.41451 −0.707253 0.706960i \(-0.750066\pi\)
−0.707253 + 0.706960i \(0.750066\pi\)
\(600\) 141.459 5.77504
\(601\) −7.94117 −0.323927 −0.161964 0.986797i \(-0.551783\pi\)
−0.161964 + 0.986797i \(0.551783\pi\)
\(602\) −17.1224 −0.697857
\(603\) −20.6643 −0.841514
\(604\) −58.2250 −2.36914
\(605\) 4.42559 0.179926
\(606\) 29.1953 1.18598
\(607\) −3.05546 −0.124017 −0.0620086 0.998076i \(-0.519751\pi\)
−0.0620086 + 0.998076i \(0.519751\pi\)
\(608\) −89.3146 −3.62219
\(609\) 5.79821 0.234955
\(610\) 102.182 4.13723
\(611\) −6.58503 −0.266402
\(612\) 34.5803 1.39783
\(613\) 45.1599 1.82399 0.911995 0.410200i \(-0.134541\pi\)
0.911995 + 0.410200i \(0.134541\pi\)
\(614\) −69.6541 −2.81101
\(615\) −34.9545 −1.40950
\(616\) 9.97278 0.401815
\(617\) 35.0194 1.40983 0.704915 0.709292i \(-0.250985\pi\)
0.704915 + 0.709292i \(0.250985\pi\)
\(618\) −16.7106 −0.672197
\(619\) 23.1479 0.930394 0.465197 0.885207i \(-0.345984\pi\)
0.465197 + 0.885207i \(0.345984\pi\)
\(620\) 96.1784 3.86262
\(621\) −7.46536 −0.299574
\(622\) −54.4296 −2.18243
\(623\) −0.179323 −0.00718441
\(624\) −49.0053 −1.96178
\(625\) 114.818 4.59274
\(626\) 79.8094 3.18982
\(627\) 7.00218 0.279640
\(628\) 105.883 4.22520
\(629\) −46.4405 −1.85170
\(630\) 23.0948 0.920118
\(631\) −30.3057 −1.20645 −0.603225 0.797571i \(-0.706118\pi\)
−0.603225 + 0.797571i \(0.706118\pi\)
\(632\) 103.402 4.11312
\(633\) 1.07769 0.0428344
\(634\) 76.3327 3.03156
\(635\) −63.8626 −2.53431
\(636\) 84.0044 3.33099
\(637\) −19.5854 −0.776001
\(638\) −10.9101 −0.431936
\(639\) −27.0787 −1.07122
\(640\) −59.1509 −2.33814
\(641\) −32.3153 −1.27638 −0.638188 0.769880i \(-0.720316\pi\)
−0.638188 + 0.769880i \(0.720316\pi\)
\(642\) 49.5350 1.95499
\(643\) 20.2927 0.800267 0.400134 0.916457i \(-0.368964\pi\)
0.400134 + 0.916457i \(0.368964\pi\)
\(644\) −8.47108 −0.333807
\(645\) −27.6537 −1.08886
\(646\) 66.4199 2.61326
\(647\) 22.7686 0.895125 0.447563 0.894253i \(-0.352292\pi\)
0.447563 + 0.894253i \(0.352292\pi\)
\(648\) 12.3828 0.486444
\(649\) 8.53852 0.335166
\(650\) −137.319 −5.38608
\(651\) −6.03344 −0.236469
\(652\) −8.09902 −0.317182
\(653\) −42.9788 −1.68189 −0.840946 0.541119i \(-0.818001\pi\)
−0.840946 + 0.541119i \(0.818001\pi\)
\(654\) −43.3627 −1.69562
\(655\) −38.7126 −1.51263
\(656\) 79.5485 3.10585
\(657\) −10.1419 −0.395672
\(658\) 5.99398 0.233670
\(659\) 12.5276 0.488006 0.244003 0.969775i \(-0.421539\pi\)
0.244003 + 0.969775i \(0.421539\pi\)
\(660\) 26.4940 1.03128
\(661\) 37.3192 1.45155 0.725775 0.687932i \(-0.241481\pi\)
0.725775 + 0.687932i \(0.241481\pi\)
\(662\) 25.6888 0.998425
\(663\) 17.3198 0.672644
\(664\) 13.8423 0.537186
\(665\) 31.8657 1.23570
\(666\) 48.0740 1.86283
\(667\) 5.63389 0.218145
\(668\) −23.6898 −0.916586
\(669\) −17.7370 −0.685751
\(670\) −150.177 −5.80185
\(671\) 8.66438 0.334485
\(672\) 21.1994 0.817786
\(673\) −16.2948 −0.628120 −0.314060 0.949403i \(-0.601689\pi\)
−0.314060 + 0.949403i \(0.601689\pi\)
\(674\) 7.08920 0.273066
\(675\) 79.1296 3.04570
\(676\) −2.64556 −0.101752
\(677\) −31.5661 −1.21318 −0.606591 0.795014i \(-0.707463\pi\)
−0.606591 + 0.795014i \(0.707463\pi\)
\(678\) 42.0570 1.61519
\(679\) 2.89938 0.111268
\(680\) 152.781 5.85888
\(681\) 15.7084 0.601947
\(682\) 11.3527 0.434719
\(683\) 33.4557 1.28015 0.640074 0.768314i \(-0.278904\pi\)
0.640074 + 0.768314i \(0.278904\pi\)
\(684\) −49.3914 −1.88853
\(685\) 24.3021 0.928536
\(686\) 40.3381 1.54011
\(687\) −28.2236 −1.07680
\(688\) 62.9334 2.39931
\(689\) −49.5743 −1.88863
\(690\) −19.0452 −0.725040
\(691\) −31.5598 −1.20059 −0.600295 0.799778i \(-0.704950\pi\)
−0.600295 + 0.799778i \(0.704950\pi\)
\(692\) −75.4660 −2.86879
\(693\) 1.95829 0.0743892
\(694\) −84.4387 −3.20525
\(695\) 19.3600 0.734366
\(696\) −39.7066 −1.50507
\(697\) −28.1146 −1.06492
\(698\) 51.9055 1.96465
\(699\) −12.0364 −0.455260
\(700\) 89.7898 3.39374
\(701\) −26.8933 −1.01575 −0.507874 0.861432i \(-0.669568\pi\)
−0.507874 + 0.861432i \(0.669568\pi\)
\(702\) −51.0744 −1.92768
\(703\) 66.3314 2.50174
\(704\) −16.2503 −0.612455
\(705\) 9.68062 0.364593
\(706\) −7.41147 −0.278934
\(707\) 11.2659 0.423698
\(708\) 51.1162 1.92107
\(709\) −31.9901 −1.20141 −0.600706 0.799470i \(-0.705114\pi\)
−0.600706 + 0.799470i \(0.705114\pi\)
\(710\) −196.794 −7.38553
\(711\) 20.3044 0.761475
\(712\) 1.22802 0.0460218
\(713\) −5.86246 −0.219551
\(714\) −15.7652 −0.589998
\(715\) −15.6352 −0.584723
\(716\) −45.1786 −1.68840
\(717\) −10.2571 −0.383059
\(718\) 10.9711 0.409437
\(719\) −21.4311 −0.799243 −0.399622 0.916680i \(-0.630859\pi\)
−0.399622 + 0.916680i \(0.630859\pi\)
\(720\) −84.8849 −3.16347
\(721\) −6.44828 −0.240147
\(722\) −44.2369 −1.64633
\(723\) 34.9711 1.30059
\(724\) 110.630 4.11154
\(725\) −59.7169 −2.21783
\(726\) 3.12731 0.116065
\(727\) 16.8462 0.624789 0.312395 0.949952i \(-0.398869\pi\)
0.312395 + 0.949952i \(0.398869\pi\)
\(728\) −35.2328 −1.30582
\(729\) 21.5315 0.797464
\(730\) −73.7059 −2.72798
\(731\) −22.2424 −0.822663
\(732\) 51.8697 1.91716
\(733\) 10.1001 0.373057 0.186529 0.982450i \(-0.440276\pi\)
0.186529 + 0.982450i \(0.440276\pi\)
\(734\) −75.4456 −2.78475
\(735\) 28.7924 1.06202
\(736\) 20.5987 0.759277
\(737\) −12.7341 −0.469066
\(738\) 29.1034 1.07131
\(739\) 39.0134 1.43513 0.717566 0.696491i \(-0.245256\pi\)
0.717566 + 0.696491i \(0.245256\pi\)
\(740\) 250.977 9.22610
\(741\) −24.7380 −0.908773
\(742\) 45.1247 1.65658
\(743\) −4.19798 −0.154009 −0.0770044 0.997031i \(-0.524536\pi\)
−0.0770044 + 0.997031i \(0.524536\pi\)
\(744\) 41.3175 1.51477
\(745\) −27.5265 −1.00849
\(746\) 8.81532 0.322752
\(747\) 2.71813 0.0994510
\(748\) 21.3096 0.779157
\(749\) 19.1146 0.698432
\(750\) 132.671 4.84444
\(751\) −7.95253 −0.290192 −0.145096 0.989418i \(-0.546349\pi\)
−0.145096 + 0.989418i \(0.546349\pi\)
\(752\) −22.0309 −0.803384
\(753\) −21.4850 −0.782956
\(754\) 38.5444 1.40370
\(755\) −50.5138 −1.83839
\(756\) 33.3965 1.21462
\(757\) 0.550226 0.0199983 0.00999915 0.999950i \(-0.496817\pi\)
0.00999915 + 0.999950i \(0.496817\pi\)
\(758\) 39.1215 1.42096
\(759\) −1.61492 −0.0586177
\(760\) −218.218 −7.91562
\(761\) −23.7224 −0.859937 −0.429968 0.902844i \(-0.641475\pi\)
−0.429968 + 0.902844i \(0.641475\pi\)
\(762\) −45.1280 −1.63482
\(763\) −16.7328 −0.605769
\(764\) −6.50653 −0.235398
\(765\) 30.0006 1.08467
\(766\) −0.0319544 −0.00115456
\(767\) −30.1657 −1.08922
\(768\) −3.65715 −0.131966
\(769\) 34.7491 1.25309 0.626543 0.779387i \(-0.284469\pi\)
0.626543 + 0.779387i \(0.284469\pi\)
\(770\) 14.2318 0.512879
\(771\) −27.1833 −0.978981
\(772\) −43.7582 −1.57489
\(773\) 2.54252 0.0914480 0.0457240 0.998954i \(-0.485441\pi\)
0.0457240 + 0.998954i \(0.485441\pi\)
\(774\) 23.0247 0.827605
\(775\) 62.1395 2.23212
\(776\) −19.8552 −0.712760
\(777\) −15.7442 −0.564821
\(778\) −73.2640 −2.62664
\(779\) 40.1563 1.43875
\(780\) −93.6007 −3.35144
\(781\) −16.6868 −0.597102
\(782\) −15.3184 −0.547786
\(783\) −22.2112 −0.793762
\(784\) −65.5249 −2.34018
\(785\) 91.8603 3.27864
\(786\) −27.3559 −0.975754
\(787\) −40.1959 −1.43283 −0.716415 0.697674i \(-0.754218\pi\)
−0.716415 + 0.697674i \(0.754218\pi\)
\(788\) −2.65976 −0.0947501
\(789\) −34.9218 −1.24325
\(790\) 147.562 5.25002
\(791\) 16.2290 0.577036
\(792\) −13.4105 −0.476522
\(793\) −30.6104 −1.08701
\(794\) 29.2430 1.03780
\(795\) 72.8791 2.58475
\(796\) 32.5662 1.15428
\(797\) 19.4966 0.690605 0.345302 0.938491i \(-0.387776\pi\)
0.345302 + 0.938491i \(0.387776\pi\)
\(798\) 22.5176 0.797115
\(799\) 7.78631 0.275460
\(800\) −218.337 −7.71938
\(801\) 0.241137 0.00852017
\(802\) 59.3265 2.09489
\(803\) −6.24979 −0.220550
\(804\) −76.2331 −2.68853
\(805\) −7.34919 −0.259025
\(806\) −40.1081 −1.41275
\(807\) 14.1620 0.498525
\(808\) −77.1498 −2.71412
\(809\) −24.8823 −0.874815 −0.437408 0.899263i \(-0.644103\pi\)
−0.437408 + 0.899263i \(0.644103\pi\)
\(810\) 17.6712 0.620901
\(811\) −25.2285 −0.885891 −0.442945 0.896549i \(-0.646066\pi\)
−0.442945 + 0.896549i \(0.646066\pi\)
\(812\) −25.2034 −0.884466
\(813\) −5.59786 −0.196326
\(814\) 29.6249 1.03835
\(815\) −7.02641 −0.246124
\(816\) 57.9451 2.02848
\(817\) 31.7690 1.11146
\(818\) −52.2027 −1.82522
\(819\) −6.91844 −0.241750
\(820\) 151.939 5.30593
\(821\) −9.15930 −0.319662 −0.159831 0.987144i \(-0.551095\pi\)
−0.159831 + 0.987144i \(0.551095\pi\)
\(822\) 17.1729 0.598973
\(823\) −34.0908 −1.18833 −0.594166 0.804343i \(-0.702518\pi\)
−0.594166 + 0.804343i \(0.702518\pi\)
\(824\) 44.1583 1.53833
\(825\) 17.1174 0.595952
\(826\) 27.4582 0.955392
\(827\) 48.8108 1.69732 0.848659 0.528940i \(-0.177410\pi\)
0.848659 + 0.528940i \(0.177410\pi\)
\(828\) 11.3912 0.395870
\(829\) −46.7178 −1.62258 −0.811289 0.584645i \(-0.801234\pi\)
−0.811289 + 0.584645i \(0.801234\pi\)
\(830\) 19.7539 0.685669
\(831\) 4.97662 0.172637
\(832\) 57.4106 1.99035
\(833\) 23.1583 0.802386
\(834\) 13.6806 0.473720
\(835\) −20.5524 −0.711245
\(836\) −30.4368 −1.05268
\(837\) 23.1122 0.798876
\(838\) −29.4696 −1.01801
\(839\) 11.9581 0.412839 0.206420 0.978464i \(-0.433819\pi\)
0.206420 + 0.978464i \(0.433819\pi\)
\(840\) 51.7957 1.78712
\(841\) −12.2379 −0.421995
\(842\) −17.1481 −0.590964
\(843\) 15.6520 0.539083
\(844\) −4.68447 −0.161246
\(845\) −2.29519 −0.0789570
\(846\) −8.06017 −0.277115
\(847\) 1.20677 0.0414650
\(848\) −165.856 −5.69552
\(849\) 0.478624 0.0164263
\(850\) 162.369 5.56921
\(851\) −15.2980 −0.524410
\(852\) −99.8966 −3.42240
\(853\) 7.71211 0.264058 0.132029 0.991246i \(-0.457851\pi\)
0.132029 + 0.991246i \(0.457851\pi\)
\(854\) 27.8629 0.953450
\(855\) −42.8501 −1.46544
\(856\) −130.898 −4.47401
\(857\) −10.3856 −0.354764 −0.177382 0.984142i \(-0.556763\pi\)
−0.177382 + 0.984142i \(0.556763\pi\)
\(858\) −11.0485 −0.377189
\(859\) 7.95340 0.271367 0.135683 0.990752i \(-0.456677\pi\)
0.135683 + 0.990752i \(0.456677\pi\)
\(860\) 120.204 4.09891
\(861\) −9.53138 −0.324828
\(862\) −57.8113 −1.96906
\(863\) 41.6337 1.41723 0.708614 0.705596i \(-0.249321\pi\)
0.708614 + 0.705596i \(0.249321\pi\)
\(864\) −81.2085 −2.76277
\(865\) −65.4715 −2.22610
\(866\) 26.9665 0.916357
\(867\) −0.528813 −0.0179594
\(868\) 26.2259 0.890164
\(869\) 12.5123 0.424451
\(870\) −56.6640 −1.92109
\(871\) 44.9882 1.52437
\(872\) 114.588 3.88043
\(873\) −3.89884 −0.131956
\(874\) 21.8795 0.740084
\(875\) 51.1950 1.73071
\(876\) −37.4147 −1.26412
\(877\) −48.9084 −1.65152 −0.825759 0.564023i \(-0.809253\pi\)
−0.825759 + 0.564023i \(0.809253\pi\)
\(878\) −38.8254 −1.31029
\(879\) 10.2726 0.346485
\(880\) −52.3091 −1.76334
\(881\) −38.8566 −1.30911 −0.654556 0.756014i \(-0.727144\pi\)
−0.654556 + 0.756014i \(0.727144\pi\)
\(882\) −23.9728 −0.807206
\(883\) 25.6894 0.864519 0.432259 0.901749i \(-0.357716\pi\)
0.432259 + 0.901749i \(0.357716\pi\)
\(884\) −75.2848 −2.53210
\(885\) 44.3465 1.49069
\(886\) −4.68038 −0.157240
\(887\) 44.4514 1.49253 0.746266 0.665648i \(-0.231845\pi\)
0.746266 + 0.665648i \(0.231845\pi\)
\(888\) 107.818 3.61812
\(889\) −17.4140 −0.584048
\(890\) 1.75246 0.0587426
\(891\) 1.49840 0.0501983
\(892\) 77.0983 2.58144
\(893\) −11.1213 −0.372159
\(894\) −19.4514 −0.650551
\(895\) −39.1952 −1.31015
\(896\) −16.1292 −0.538840
\(897\) 5.70533 0.190496
\(898\) 75.3340 2.51393
\(899\) −17.4422 −0.581728
\(900\) −120.741 −4.02471
\(901\) 58.6180 1.95285
\(902\) 17.9346 0.597157
\(903\) −7.54058 −0.250935
\(904\) −111.137 −3.69637
\(905\) 95.9787 3.19044
\(906\) −35.6952 −1.18589
\(907\) 16.9032 0.561263 0.280631 0.959816i \(-0.409456\pi\)
0.280631 + 0.959816i \(0.409456\pi\)
\(908\) −68.2805 −2.26597
\(909\) −15.1494 −0.502474
\(910\) −50.2796 −1.66675
\(911\) 20.9836 0.695219 0.347610 0.937639i \(-0.386993\pi\)
0.347610 + 0.937639i \(0.386993\pi\)
\(912\) −82.7636 −2.74058
\(913\) 1.67501 0.0554346
\(914\) 54.2115 1.79316
\(915\) 45.0002 1.48766
\(916\) 122.681 4.05350
\(917\) −10.5561 −0.348594
\(918\) 60.3917 1.99322
\(919\) 40.3059 1.32957 0.664784 0.747035i \(-0.268523\pi\)
0.664784 + 0.747035i \(0.268523\pi\)
\(920\) 50.3278 1.65926
\(921\) −30.6752 −1.01078
\(922\) −55.4856 −1.82732
\(923\) 58.9530 1.94046
\(924\) 7.22437 0.237664
\(925\) 162.153 5.33155
\(926\) 0.457302 0.0150279
\(927\) 8.67108 0.284796
\(928\) 61.2858 2.01180
\(929\) −7.17121 −0.235280 −0.117640 0.993056i \(-0.537533\pi\)
−0.117640 + 0.993056i \(0.537533\pi\)
\(930\) 58.9628 1.93347
\(931\) −33.0772 −1.08406
\(932\) 52.3195 1.71378
\(933\) −23.9704 −0.784756
\(934\) 40.9239 1.33907
\(935\) 18.4874 0.604604
\(936\) 47.3780 1.54860
\(937\) −27.8906 −0.911145 −0.455573 0.890199i \(-0.650565\pi\)
−0.455573 + 0.890199i \(0.650565\pi\)
\(938\) −40.9502 −1.33707
\(939\) 35.1475 1.14699
\(940\) −42.0793 −1.37248
\(941\) 43.1463 1.40653 0.703264 0.710929i \(-0.251725\pi\)
0.703264 + 0.710929i \(0.251725\pi\)
\(942\) 64.9124 2.11496
\(943\) −9.26126 −0.301588
\(944\) −100.923 −3.28475
\(945\) 28.9736 0.942510
\(946\) 14.1886 0.461312
\(947\) −47.0670 −1.52947 −0.764736 0.644344i \(-0.777131\pi\)
−0.764736 + 0.644344i \(0.777131\pi\)
\(948\) 74.9056 2.43282
\(949\) 22.0799 0.716743
\(950\) −231.913 −7.52426
\(951\) 33.6164 1.09009
\(952\) 41.6602 1.35022
\(953\) 3.32097 0.107577 0.0537884 0.998552i \(-0.482870\pi\)
0.0537884 + 0.998552i \(0.482870\pi\)
\(954\) −60.6798 −1.96458
\(955\) −5.64482 −0.182662
\(956\) 44.5851 1.44199
\(957\) −4.80474 −0.155315
\(958\) 7.54601 0.243801
\(959\) 6.62668 0.213987
\(960\) −84.3991 −2.72397
\(961\) −12.8502 −0.414524
\(962\) −104.662 −3.37443
\(963\) −25.7036 −0.828287
\(964\) −152.011 −4.89593
\(965\) −37.9629 −1.22207
\(966\) −5.19324 −0.167090
\(967\) 10.3820 0.333864 0.166932 0.985968i \(-0.446614\pi\)
0.166932 + 0.985968i \(0.446614\pi\)
\(968\) −8.26404 −0.265616
\(969\) 29.2508 0.939673
\(970\) −28.3347 −0.909773
\(971\) −20.9803 −0.673289 −0.336645 0.941632i \(-0.609292\pi\)
−0.336645 + 0.941632i \(0.609292\pi\)
\(972\) −74.0528 −2.37524
\(973\) 5.27907 0.169239
\(974\) −29.0624 −0.931219
\(975\) −60.4741 −1.93672
\(976\) −102.410 −3.27807
\(977\) 44.5462 1.42516 0.712579 0.701592i \(-0.247527\pi\)
0.712579 + 0.701592i \(0.247527\pi\)
\(978\) −4.96515 −0.158768
\(979\) 0.148598 0.00474920
\(980\) −125.153 −3.99788
\(981\) 22.5008 0.718396
\(982\) −60.7185 −1.93760
\(983\) −22.1515 −0.706522 −0.353261 0.935525i \(-0.614927\pi\)
−0.353261 + 0.935525i \(0.614927\pi\)
\(984\) 65.2716 2.08078
\(985\) −2.30751 −0.0735234
\(986\) −45.5759 −1.45143
\(987\) 2.63971 0.0840228
\(988\) 107.530 3.42099
\(989\) −7.32689 −0.232981
\(990\) −19.1377 −0.608236
\(991\) −6.07060 −0.192839 −0.0964195 0.995341i \(-0.530739\pi\)
−0.0964195 + 0.995341i \(0.530739\pi\)
\(992\) −63.7720 −2.02476
\(993\) 11.3132 0.359013
\(994\) −53.6616 −1.70204
\(995\) 28.2532 0.895687
\(996\) 10.0275 0.317734
\(997\) 21.2719 0.673689 0.336844 0.941560i \(-0.390640\pi\)
0.336844 + 0.941560i \(0.390640\pi\)
\(998\) −37.9670 −1.20183
\(999\) 60.3112 1.90816
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 6017.2.a.f.1.6 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.6 121 1.1 even 1 trivial