Properties

Label 6017.2.a.f.1.5
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.5
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68922 q^{2} +1.49908 q^{3} +5.23192 q^{4} -2.86648 q^{5} -4.03136 q^{6} +3.78429 q^{7} -8.69136 q^{8} -0.752759 q^{9} +O(q^{10})\) \(q-2.68922 q^{2} +1.49908 q^{3} +5.23192 q^{4} -2.86648 q^{5} -4.03136 q^{6} +3.78429 q^{7} -8.69136 q^{8} -0.752759 q^{9} +7.70861 q^{10} -1.00000 q^{11} +7.84307 q^{12} +1.85578 q^{13} -10.1768 q^{14} -4.29709 q^{15} +12.9092 q^{16} +3.20703 q^{17} +2.02434 q^{18} -4.08784 q^{19} -14.9972 q^{20} +5.67295 q^{21} +2.68922 q^{22} -2.33132 q^{23} -13.0290 q^{24} +3.21672 q^{25} -4.99060 q^{26} -5.62569 q^{27} +19.7991 q^{28} +0.511276 q^{29} +11.5558 q^{30} -4.10058 q^{31} -17.3329 q^{32} -1.49908 q^{33} -8.62441 q^{34} -10.8476 q^{35} -3.93837 q^{36} +6.63750 q^{37} +10.9931 q^{38} +2.78196 q^{39} +24.9136 q^{40} +3.51367 q^{41} -15.2558 q^{42} +0.148781 q^{43} -5.23192 q^{44} +2.15777 q^{45} +6.26944 q^{46} -10.7846 q^{47} +19.3519 q^{48} +7.32084 q^{49} -8.65047 q^{50} +4.80759 q^{51} +9.70928 q^{52} +3.16790 q^{53} +15.1287 q^{54} +2.86648 q^{55} -32.8906 q^{56} -6.12800 q^{57} -1.37494 q^{58} +10.0087 q^{59} -22.4820 q^{60} -2.13383 q^{61} +11.0274 q^{62} -2.84866 q^{63} +20.7937 q^{64} -5.31955 q^{65} +4.03136 q^{66} +0.293049 q^{67} +16.7789 q^{68} -3.49483 q^{69} +29.1716 q^{70} +14.0686 q^{71} +6.54250 q^{72} +0.0439670 q^{73} -17.8497 q^{74} +4.82212 q^{75} -21.3873 q^{76} -3.78429 q^{77} -7.48131 q^{78} +15.4089 q^{79} -37.0039 q^{80} -6.17508 q^{81} -9.44905 q^{82} -10.2564 q^{83} +29.6804 q^{84} -9.19288 q^{85} -0.400106 q^{86} +0.766444 q^{87} +8.69136 q^{88} -4.14310 q^{89} -5.80272 q^{90} +7.02280 q^{91} -12.1973 q^{92} -6.14710 q^{93} +29.0023 q^{94} +11.7177 q^{95} -25.9834 q^{96} +19.2019 q^{97} -19.6874 q^{98} +0.752759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68922 −1.90157 −0.950784 0.309854i \(-0.899720\pi\)
−0.950784 + 0.309854i \(0.899720\pi\)
\(3\) 1.49908 0.865494 0.432747 0.901515i \(-0.357544\pi\)
0.432747 + 0.901515i \(0.357544\pi\)
\(4\) 5.23192 2.61596
\(5\) −2.86648 −1.28193 −0.640965 0.767570i \(-0.721466\pi\)
−0.640965 + 0.767570i \(0.721466\pi\)
\(6\) −4.03136 −1.64580
\(7\) 3.78429 1.43033 0.715163 0.698957i \(-0.246352\pi\)
0.715163 + 0.698957i \(0.246352\pi\)
\(8\) −8.69136 −3.07286
\(9\) −0.752759 −0.250920
\(10\) 7.70861 2.43768
\(11\) −1.00000 −0.301511
\(12\) 7.84307 2.26410
\(13\) 1.85578 0.514700 0.257350 0.966318i \(-0.417151\pi\)
0.257350 + 0.966318i \(0.417151\pi\)
\(14\) −10.1768 −2.71986
\(15\) −4.29709 −1.10950
\(16\) 12.9092 3.22729
\(17\) 3.20703 0.777818 0.388909 0.921276i \(-0.372852\pi\)
0.388909 + 0.921276i \(0.372852\pi\)
\(18\) 2.02434 0.477141
\(19\) −4.08784 −0.937814 −0.468907 0.883247i \(-0.655352\pi\)
−0.468907 + 0.883247i \(0.655352\pi\)
\(20\) −14.9972 −3.35348
\(21\) 5.67295 1.23794
\(22\) 2.68922 0.573344
\(23\) −2.33132 −0.486114 −0.243057 0.970012i \(-0.578150\pi\)
−0.243057 + 0.970012i \(0.578150\pi\)
\(24\) −13.0290 −2.65954
\(25\) 3.21672 0.643343
\(26\) −4.99060 −0.978737
\(27\) −5.62569 −1.08266
\(28\) 19.7991 3.74168
\(29\) 0.511276 0.0949416 0.0474708 0.998873i \(-0.484884\pi\)
0.0474708 + 0.998873i \(0.484884\pi\)
\(30\) 11.5558 2.10979
\(31\) −4.10058 −0.736486 −0.368243 0.929730i \(-0.620040\pi\)
−0.368243 + 0.929730i \(0.620040\pi\)
\(32\) −17.3329 −3.06405
\(33\) −1.49908 −0.260956
\(34\) −8.62441 −1.47907
\(35\) −10.8476 −1.83358
\(36\) −3.93837 −0.656396
\(37\) 6.63750 1.09120 0.545599 0.838046i \(-0.316302\pi\)
0.545599 + 0.838046i \(0.316302\pi\)
\(38\) 10.9931 1.78332
\(39\) 2.78196 0.445470
\(40\) 24.9136 3.93919
\(41\) 3.51367 0.548744 0.274372 0.961624i \(-0.411530\pi\)
0.274372 + 0.961624i \(0.411530\pi\)
\(42\) −15.2558 −2.35403
\(43\) 0.148781 0.0226890 0.0113445 0.999936i \(-0.496389\pi\)
0.0113445 + 0.999936i \(0.496389\pi\)
\(44\) −5.23192 −0.788742
\(45\) 2.15777 0.321661
\(46\) 6.26944 0.924378
\(47\) −10.7846 −1.57310 −0.786550 0.617527i \(-0.788135\pi\)
−0.786550 + 0.617527i \(0.788135\pi\)
\(48\) 19.3519 2.79320
\(49\) 7.32084 1.04583
\(50\) −8.65047 −1.22336
\(51\) 4.80759 0.673197
\(52\) 9.70928 1.34644
\(53\) 3.16790 0.435144 0.217572 0.976044i \(-0.430186\pi\)
0.217572 + 0.976044i \(0.430186\pi\)
\(54\) 15.1287 2.05876
\(55\) 2.86648 0.386516
\(56\) −32.8906 −4.39519
\(57\) −6.12800 −0.811673
\(58\) −1.37494 −0.180538
\(59\) 10.0087 1.30302 0.651510 0.758640i \(-0.274136\pi\)
0.651510 + 0.758640i \(0.274136\pi\)
\(60\) −22.4820 −2.90242
\(61\) −2.13383 −0.273209 −0.136605 0.990626i \(-0.543619\pi\)
−0.136605 + 0.990626i \(0.543619\pi\)
\(62\) 11.0274 1.40048
\(63\) −2.84866 −0.358897
\(64\) 20.7937 2.59922
\(65\) −5.31955 −0.659809
\(66\) 4.03136 0.496226
\(67\) 0.293049 0.0358016 0.0179008 0.999840i \(-0.494302\pi\)
0.0179008 + 0.999840i \(0.494302\pi\)
\(68\) 16.7789 2.03474
\(69\) −3.49483 −0.420729
\(70\) 29.1716 3.48667
\(71\) 14.0686 1.66963 0.834816 0.550529i \(-0.185574\pi\)
0.834816 + 0.550529i \(0.185574\pi\)
\(72\) 6.54250 0.771041
\(73\) 0.0439670 0.00514595 0.00257298 0.999997i \(-0.499181\pi\)
0.00257298 + 0.999997i \(0.499181\pi\)
\(74\) −17.8497 −2.07499
\(75\) 4.82212 0.556810
\(76\) −21.3873 −2.45329
\(77\) −3.78429 −0.431260
\(78\) −7.48131 −0.847091
\(79\) 15.4089 1.73363 0.866817 0.498626i \(-0.166162\pi\)
0.866817 + 0.498626i \(0.166162\pi\)
\(80\) −37.0039 −4.13716
\(81\) −6.17508 −0.686120
\(82\) −9.44905 −1.04347
\(83\) −10.2564 −1.12579 −0.562895 0.826528i \(-0.690312\pi\)
−0.562895 + 0.826528i \(0.690312\pi\)
\(84\) 29.6804 3.23840
\(85\) −9.19288 −0.997108
\(86\) −0.400106 −0.0431446
\(87\) 0.766444 0.0821714
\(88\) 8.69136 0.926502
\(89\) −4.14310 −0.439167 −0.219584 0.975594i \(-0.570470\pi\)
−0.219584 + 0.975594i \(0.570470\pi\)
\(90\) −5.80272 −0.611661
\(91\) 7.02280 0.736189
\(92\) −12.1973 −1.27165
\(93\) −6.14710 −0.637424
\(94\) 29.0023 2.99136
\(95\) 11.7177 1.20221
\(96\) −25.9834 −2.65192
\(97\) 19.2019 1.94966 0.974831 0.222944i \(-0.0715668\pi\)
0.974831 + 0.222944i \(0.0715668\pi\)
\(98\) −19.6874 −1.98873
\(99\) 0.752759 0.0756551
\(100\) 16.8296 1.68296
\(101\) −8.62601 −0.858320 −0.429160 0.903228i \(-0.641190\pi\)
−0.429160 + 0.903228i \(0.641190\pi\)
\(102\) −12.9287 −1.28013
\(103\) −8.48439 −0.835992 −0.417996 0.908449i \(-0.637267\pi\)
−0.417996 + 0.908449i \(0.637267\pi\)
\(104\) −16.1292 −1.58160
\(105\) −16.2614 −1.58695
\(106\) −8.51919 −0.827457
\(107\) 3.00743 0.290739 0.145370 0.989377i \(-0.453563\pi\)
0.145370 + 0.989377i \(0.453563\pi\)
\(108\) −29.4332 −2.83221
\(109\) 4.70299 0.450464 0.225232 0.974305i \(-0.427686\pi\)
0.225232 + 0.974305i \(0.427686\pi\)
\(110\) −7.70861 −0.734987
\(111\) 9.95015 0.944427
\(112\) 48.8520 4.61608
\(113\) −13.1078 −1.23308 −0.616538 0.787325i \(-0.711465\pi\)
−0.616538 + 0.787325i \(0.711465\pi\)
\(114\) 16.4796 1.54345
\(115\) 6.68268 0.623164
\(116\) 2.67496 0.248363
\(117\) −1.39695 −0.129148
\(118\) −26.9156 −2.47778
\(119\) 12.1363 1.11253
\(120\) 37.3475 3.40935
\(121\) 1.00000 0.0909091
\(122\) 5.73836 0.519526
\(123\) 5.26728 0.474935
\(124\) −21.4539 −1.92662
\(125\) 5.11175 0.457209
\(126\) 7.66067 0.682467
\(127\) −9.02513 −0.800851 −0.400425 0.916329i \(-0.631138\pi\)
−0.400425 + 0.916329i \(0.631138\pi\)
\(128\) −21.2532 −1.87853
\(129\) 0.223035 0.0196372
\(130\) 14.3055 1.25467
\(131\) 11.9248 1.04187 0.520936 0.853595i \(-0.325583\pi\)
0.520936 + 0.853595i \(0.325583\pi\)
\(132\) −7.84307 −0.682652
\(133\) −15.4696 −1.34138
\(134\) −0.788074 −0.0680792
\(135\) 16.1259 1.38790
\(136\) −27.8734 −2.39013
\(137\) 22.8099 1.94878 0.974392 0.224854i \(-0.0721906\pi\)
0.974392 + 0.224854i \(0.0721906\pi\)
\(138\) 9.39839 0.800044
\(139\) −10.5106 −0.891499 −0.445750 0.895158i \(-0.647063\pi\)
−0.445750 + 0.895158i \(0.647063\pi\)
\(140\) −56.7538 −4.79657
\(141\) −16.1670 −1.36151
\(142\) −37.8335 −3.17492
\(143\) −1.85578 −0.155188
\(144\) −9.71749 −0.809790
\(145\) −1.46556 −0.121708
\(146\) −0.118237 −0.00978538
\(147\) 10.9745 0.905164
\(148\) 34.7269 2.85453
\(149\) −7.14234 −0.585123 −0.292562 0.956247i \(-0.594508\pi\)
−0.292562 + 0.956247i \(0.594508\pi\)
\(150\) −12.9677 −1.05881
\(151\) 22.4610 1.82785 0.913924 0.405886i \(-0.133037\pi\)
0.913924 + 0.405886i \(0.133037\pi\)
\(152\) 35.5289 2.88177
\(153\) −2.41412 −0.195170
\(154\) 10.1768 0.820070
\(155\) 11.7542 0.944123
\(156\) 14.5550 1.16533
\(157\) −2.95748 −0.236033 −0.118016 0.993012i \(-0.537654\pi\)
−0.118016 + 0.993012i \(0.537654\pi\)
\(158\) −41.4379 −3.29662
\(159\) 4.74894 0.376615
\(160\) 49.6845 3.92790
\(161\) −8.82239 −0.695301
\(162\) 16.6062 1.30470
\(163\) 14.1849 1.11105 0.555523 0.831501i \(-0.312518\pi\)
0.555523 + 0.831501i \(0.312518\pi\)
\(164\) 18.3833 1.43549
\(165\) 4.29709 0.334528
\(166\) 27.5818 2.14077
\(167\) 1.38595 0.107248 0.0536239 0.998561i \(-0.482923\pi\)
0.0536239 + 0.998561i \(0.482923\pi\)
\(168\) −49.3057 −3.80401
\(169\) −9.55609 −0.735084
\(170\) 24.7217 1.89607
\(171\) 3.07716 0.235316
\(172\) 0.778413 0.0593534
\(173\) −2.10820 −0.160284 −0.0801418 0.996783i \(-0.525537\pi\)
−0.0801418 + 0.996783i \(0.525537\pi\)
\(174\) −2.06114 −0.156254
\(175\) 12.1730 0.920191
\(176\) −12.9092 −0.973065
\(177\) 15.0038 1.12776
\(178\) 11.1417 0.835107
\(179\) 0.0684199 0.00511394 0.00255697 0.999997i \(-0.499186\pi\)
0.00255697 + 0.999997i \(0.499186\pi\)
\(180\) 11.2893 0.841453
\(181\) 1.09426 0.0813361 0.0406680 0.999173i \(-0.487051\pi\)
0.0406680 + 0.999173i \(0.487051\pi\)
\(182\) −18.8859 −1.39991
\(183\) −3.19879 −0.236461
\(184\) 20.2623 1.49376
\(185\) −19.0263 −1.39884
\(186\) 16.5309 1.21211
\(187\) −3.20703 −0.234521
\(188\) −56.4243 −4.11517
\(189\) −21.2892 −1.54856
\(190\) −31.5115 −2.28609
\(191\) −6.55699 −0.474447 −0.237224 0.971455i \(-0.576237\pi\)
−0.237224 + 0.971455i \(0.576237\pi\)
\(192\) 31.1715 2.24961
\(193\) 11.1730 0.804247 0.402124 0.915585i \(-0.368272\pi\)
0.402124 + 0.915585i \(0.368272\pi\)
\(194\) −51.6383 −3.70742
\(195\) −7.97443 −0.571061
\(196\) 38.3021 2.73586
\(197\) −22.0077 −1.56798 −0.783992 0.620771i \(-0.786820\pi\)
−0.783992 + 0.620771i \(0.786820\pi\)
\(198\) −2.02434 −0.143863
\(199\) 25.8829 1.83479 0.917396 0.397975i \(-0.130287\pi\)
0.917396 + 0.397975i \(0.130287\pi\)
\(200\) −27.9576 −1.97690
\(201\) 0.439304 0.0309861
\(202\) 23.1973 1.63215
\(203\) 1.93482 0.135797
\(204\) 25.1529 1.76106
\(205\) −10.0719 −0.703451
\(206\) 22.8164 1.58970
\(207\) 1.75492 0.121975
\(208\) 23.9565 1.66109
\(209\) 4.08784 0.282762
\(210\) 43.7306 3.01770
\(211\) −19.7742 −1.36131 −0.680656 0.732603i \(-0.738305\pi\)
−0.680656 + 0.732603i \(0.738305\pi\)
\(212\) 16.5742 1.13832
\(213\) 21.0899 1.44506
\(214\) −8.08766 −0.552861
\(215\) −0.426479 −0.0290856
\(216\) 48.8949 3.32687
\(217\) −15.5178 −1.05342
\(218\) −12.6474 −0.856589
\(219\) 0.0659101 0.00445379
\(220\) 14.9972 1.01111
\(221\) 5.95153 0.400343
\(222\) −26.7582 −1.79589
\(223\) 16.8864 1.13080 0.565398 0.824818i \(-0.308722\pi\)
0.565398 + 0.824818i \(0.308722\pi\)
\(224\) −65.5927 −4.38260
\(225\) −2.42141 −0.161427
\(226\) 35.2498 2.34478
\(227\) 1.78535 0.118498 0.0592490 0.998243i \(-0.481129\pi\)
0.0592490 + 0.998243i \(0.481129\pi\)
\(228\) −32.0612 −2.12331
\(229\) 18.5017 1.22263 0.611313 0.791389i \(-0.290642\pi\)
0.611313 + 0.791389i \(0.290642\pi\)
\(230\) −17.9712 −1.18499
\(231\) −5.67295 −0.373253
\(232\) −4.44368 −0.291742
\(233\) 11.8720 0.777762 0.388881 0.921288i \(-0.372862\pi\)
0.388881 + 0.921288i \(0.372862\pi\)
\(234\) 3.75672 0.245584
\(235\) 30.9139 2.01660
\(236\) 52.3647 3.40865
\(237\) 23.0991 1.50045
\(238\) −32.6372 −2.11556
\(239\) −3.08304 −0.199425 −0.0997125 0.995016i \(-0.531792\pi\)
−0.0997125 + 0.995016i \(0.531792\pi\)
\(240\) −55.4718 −3.58069
\(241\) 21.5953 1.39108 0.695538 0.718489i \(-0.255166\pi\)
0.695538 + 0.718489i \(0.255166\pi\)
\(242\) −2.68922 −0.172870
\(243\) 7.62012 0.488831
\(244\) −11.1641 −0.714705
\(245\) −20.9851 −1.34069
\(246\) −14.1649 −0.903120
\(247\) −7.58612 −0.482693
\(248\) 35.6396 2.26312
\(249\) −15.3752 −0.974365
\(250\) −13.7466 −0.869413
\(251\) 7.85921 0.496069 0.248034 0.968751i \(-0.420215\pi\)
0.248034 + 0.968751i \(0.420215\pi\)
\(252\) −14.9039 −0.938860
\(253\) 2.33132 0.146569
\(254\) 24.2706 1.52287
\(255\) −13.7809 −0.862991
\(256\) 15.5670 0.972939
\(257\) 9.44886 0.589404 0.294702 0.955589i \(-0.404780\pi\)
0.294702 + 0.955589i \(0.404780\pi\)
\(258\) −0.599792 −0.0373414
\(259\) 25.1182 1.56077
\(260\) −27.8315 −1.72604
\(261\) −0.384867 −0.0238227
\(262\) −32.0684 −1.98119
\(263\) 18.0588 1.11355 0.556777 0.830662i \(-0.312038\pi\)
0.556777 + 0.830662i \(0.312038\pi\)
\(264\) 13.0290 0.801882
\(265\) −9.08073 −0.557825
\(266\) 41.6011 2.55073
\(267\) −6.21083 −0.380097
\(268\) 1.53321 0.0936556
\(269\) 2.47730 0.151044 0.0755219 0.997144i \(-0.475938\pi\)
0.0755219 + 0.997144i \(0.475938\pi\)
\(270\) −43.3662 −2.63918
\(271\) −6.83552 −0.415228 −0.207614 0.978211i \(-0.566570\pi\)
−0.207614 + 0.978211i \(0.566570\pi\)
\(272\) 41.4000 2.51024
\(273\) 10.5277 0.637168
\(274\) −61.3410 −3.70575
\(275\) −3.21672 −0.193975
\(276\) −18.2847 −1.10061
\(277\) −20.9540 −1.25900 −0.629501 0.777000i \(-0.716741\pi\)
−0.629501 + 0.777000i \(0.716741\pi\)
\(278\) 28.2654 1.69525
\(279\) 3.08675 0.184799
\(280\) 94.2803 5.63433
\(281\) 20.2014 1.20511 0.602557 0.798076i \(-0.294149\pi\)
0.602557 + 0.798076i \(0.294149\pi\)
\(282\) 43.4767 2.58900
\(283\) −0.866820 −0.0515271 −0.0257635 0.999668i \(-0.508202\pi\)
−0.0257635 + 0.999668i \(0.508202\pi\)
\(284\) 73.6057 4.36769
\(285\) 17.5658 1.04051
\(286\) 4.99060 0.295100
\(287\) 13.2968 0.784883
\(288\) 13.0475 0.768831
\(289\) −6.71499 −0.394999
\(290\) 3.94123 0.231437
\(291\) 28.7853 1.68742
\(292\) 0.230032 0.0134616
\(293\) −8.47648 −0.495201 −0.247601 0.968862i \(-0.579642\pi\)
−0.247601 + 0.968862i \(0.579642\pi\)
\(294\) −29.5130 −1.72123
\(295\) −28.6897 −1.67038
\(296\) −57.6889 −3.35310
\(297\) 5.62569 0.326435
\(298\) 19.2073 1.11265
\(299\) −4.32641 −0.250203
\(300\) 25.2289 1.45659
\(301\) 0.563032 0.0324526
\(302\) −60.4025 −3.47578
\(303\) −12.9311 −0.742871
\(304\) −52.7706 −3.02660
\(305\) 6.11660 0.350235
\(306\) 6.49210 0.371129
\(307\) 16.4243 0.937384 0.468692 0.883362i \(-0.344725\pi\)
0.468692 + 0.883362i \(0.344725\pi\)
\(308\) −19.7991 −1.12816
\(309\) −12.7188 −0.723546
\(310\) −31.6098 −1.79531
\(311\) 25.4844 1.44509 0.722543 0.691326i \(-0.242973\pi\)
0.722543 + 0.691326i \(0.242973\pi\)
\(312\) −24.1790 −1.36887
\(313\) −29.3229 −1.65743 −0.828715 0.559671i \(-0.810927\pi\)
−0.828715 + 0.559671i \(0.810927\pi\)
\(314\) 7.95332 0.448832
\(315\) 8.16562 0.460081
\(316\) 80.6181 4.53512
\(317\) 11.8245 0.664129 0.332064 0.943257i \(-0.392255\pi\)
0.332064 + 0.943257i \(0.392255\pi\)
\(318\) −12.7709 −0.716159
\(319\) −0.511276 −0.0286260
\(320\) −59.6048 −3.33201
\(321\) 4.50838 0.251633
\(322\) 23.7254 1.32216
\(323\) −13.1098 −0.729449
\(324\) −32.3075 −1.79486
\(325\) 5.96951 0.331129
\(326\) −38.1463 −2.11273
\(327\) 7.05015 0.389874
\(328\) −30.5386 −1.68621
\(329\) −40.8121 −2.25005
\(330\) −11.5558 −0.636127
\(331\) −2.23342 −0.122760 −0.0613800 0.998114i \(-0.519550\pi\)
−0.0613800 + 0.998114i \(0.519550\pi\)
\(332\) −53.6609 −2.94502
\(333\) −4.99644 −0.273803
\(334\) −3.72712 −0.203939
\(335\) −0.840019 −0.0458951
\(336\) 73.2331 3.99519
\(337\) −12.1560 −0.662181 −0.331090 0.943599i \(-0.607416\pi\)
−0.331090 + 0.943599i \(0.607416\pi\)
\(338\) 25.6985 1.39781
\(339\) −19.6496 −1.06722
\(340\) −48.0964 −2.60840
\(341\) 4.10058 0.222059
\(342\) −8.27516 −0.447469
\(343\) 1.21416 0.0655584
\(344\) −1.29311 −0.0697200
\(345\) 10.0179 0.539345
\(346\) 5.66943 0.304790
\(347\) −0.487087 −0.0261482 −0.0130741 0.999915i \(-0.504162\pi\)
−0.0130741 + 0.999915i \(0.504162\pi\)
\(348\) 4.00997 0.214957
\(349\) −20.8734 −1.11733 −0.558663 0.829394i \(-0.688686\pi\)
−0.558663 + 0.829394i \(0.688686\pi\)
\(350\) −32.7359 −1.74981
\(351\) −10.4400 −0.557247
\(352\) 17.3329 0.923847
\(353\) 24.8871 1.32461 0.662304 0.749235i \(-0.269579\pi\)
0.662304 + 0.749235i \(0.269579\pi\)
\(354\) −40.3486 −2.14451
\(355\) −40.3273 −2.14035
\(356\) −21.6764 −1.14884
\(357\) 18.1933 0.962892
\(358\) −0.183996 −0.00972450
\(359\) 0.678665 0.0358186 0.0179093 0.999840i \(-0.494299\pi\)
0.0179093 + 0.999840i \(0.494299\pi\)
\(360\) −18.7539 −0.988420
\(361\) −2.28958 −0.120504
\(362\) −2.94272 −0.154666
\(363\) 1.49908 0.0786813
\(364\) 36.7427 1.92584
\(365\) −0.126031 −0.00659675
\(366\) 8.60226 0.449647
\(367\) 8.86766 0.462888 0.231444 0.972848i \(-0.425655\pi\)
0.231444 + 0.972848i \(0.425655\pi\)
\(368\) −30.0954 −1.56883
\(369\) −2.64495 −0.137691
\(370\) 51.1659 2.65999
\(371\) 11.9882 0.622399
\(372\) −32.1611 −1.66748
\(373\) −22.4992 −1.16496 −0.582481 0.812844i \(-0.697918\pi\)
−0.582481 + 0.812844i \(0.697918\pi\)
\(374\) 8.62441 0.445957
\(375\) 7.66292 0.395711
\(376\) 93.7331 4.83391
\(377\) 0.948814 0.0488664
\(378\) 57.2515 2.94470
\(379\) 18.3335 0.941730 0.470865 0.882205i \(-0.343942\pi\)
0.470865 + 0.882205i \(0.343942\pi\)
\(380\) 61.3062 3.14494
\(381\) −13.5294 −0.693132
\(382\) 17.6332 0.902193
\(383\) −12.4785 −0.637621 −0.318811 0.947818i \(-0.603283\pi\)
−0.318811 + 0.947818i \(0.603283\pi\)
\(384\) −31.8602 −1.62586
\(385\) 10.8476 0.552845
\(386\) −30.0466 −1.52933
\(387\) −0.111996 −0.00569310
\(388\) 100.463 5.10024
\(389\) 7.16831 0.363448 0.181724 0.983350i \(-0.441832\pi\)
0.181724 + 0.983350i \(0.441832\pi\)
\(390\) 21.4450 1.08591
\(391\) −7.47660 −0.378108
\(392\) −63.6281 −3.21370
\(393\) 17.8762 0.901735
\(394\) 59.1836 2.98163
\(395\) −44.1693 −2.22240
\(396\) 3.93837 0.197911
\(397\) 36.0707 1.81034 0.905169 0.425052i \(-0.139744\pi\)
0.905169 + 0.425052i \(0.139744\pi\)
\(398\) −69.6050 −3.48898
\(399\) −23.1901 −1.16096
\(400\) 41.5251 2.07626
\(401\) 17.7890 0.888339 0.444170 0.895943i \(-0.353499\pi\)
0.444170 + 0.895943i \(0.353499\pi\)
\(402\) −1.18139 −0.0589222
\(403\) −7.60976 −0.379069
\(404\) −45.1306 −2.24533
\(405\) 17.7007 0.879557
\(406\) −5.20315 −0.258228
\(407\) −6.63750 −0.329009
\(408\) −41.7845 −2.06864
\(409\) −3.65192 −0.180576 −0.0902878 0.995916i \(-0.528779\pi\)
−0.0902878 + 0.995916i \(0.528779\pi\)
\(410\) 27.0855 1.33766
\(411\) 34.1939 1.68666
\(412\) −44.3897 −2.18692
\(413\) 37.8758 1.86374
\(414\) −4.71937 −0.231945
\(415\) 29.3999 1.44318
\(416\) −32.1660 −1.57707
\(417\) −15.7563 −0.771587
\(418\) −10.9931 −0.537691
\(419\) −22.7534 −1.11158 −0.555789 0.831324i \(-0.687584\pi\)
−0.555789 + 0.831324i \(0.687584\pi\)
\(420\) −85.0784 −4.15140
\(421\) −22.9314 −1.11761 −0.558803 0.829300i \(-0.688739\pi\)
−0.558803 + 0.829300i \(0.688739\pi\)
\(422\) 53.1772 2.58863
\(423\) 8.11822 0.394721
\(424\) −27.5334 −1.33714
\(425\) 10.3161 0.500404
\(426\) −56.7155 −2.74788
\(427\) −8.07504 −0.390779
\(428\) 15.7346 0.760563
\(429\) −2.78196 −0.134314
\(430\) 1.14690 0.0553083
\(431\) 2.84079 0.136836 0.0684181 0.997657i \(-0.478205\pi\)
0.0684181 + 0.997657i \(0.478205\pi\)
\(432\) −72.6229 −3.49407
\(433\) 28.8377 1.38585 0.692926 0.721009i \(-0.256321\pi\)
0.692926 + 0.721009i \(0.256321\pi\)
\(434\) 41.7308 2.00314
\(435\) −2.19700 −0.105338
\(436\) 24.6057 1.17840
\(437\) 9.53006 0.455884
\(438\) −0.177247 −0.00846919
\(439\) −8.03415 −0.383449 −0.191725 0.981449i \(-0.561408\pi\)
−0.191725 + 0.981449i \(0.561408\pi\)
\(440\) −24.9136 −1.18771
\(441\) −5.51083 −0.262420
\(442\) −16.0050 −0.761279
\(443\) −34.4702 −1.63773 −0.818864 0.573987i \(-0.805396\pi\)
−0.818864 + 0.573987i \(0.805396\pi\)
\(444\) 52.0584 2.47058
\(445\) 11.8761 0.562982
\(446\) −45.4113 −2.15029
\(447\) −10.7069 −0.506421
\(448\) 78.6894 3.71773
\(449\) −30.3079 −1.43032 −0.715160 0.698961i \(-0.753646\pi\)
−0.715160 + 0.698961i \(0.753646\pi\)
\(450\) 6.51172 0.306965
\(451\) −3.51367 −0.165452
\(452\) −68.5789 −3.22568
\(453\) 33.6708 1.58199
\(454\) −4.80121 −0.225332
\(455\) −20.1307 −0.943743
\(456\) 53.2606 2.49416
\(457\) −15.2224 −0.712072 −0.356036 0.934472i \(-0.615872\pi\)
−0.356036 + 0.934472i \(0.615872\pi\)
\(458\) −49.7551 −2.32490
\(459\) −18.0417 −0.842115
\(460\) 34.9633 1.63017
\(461\) 3.56188 0.165893 0.0829466 0.996554i \(-0.473567\pi\)
0.0829466 + 0.996554i \(0.473567\pi\)
\(462\) 15.2558 0.709766
\(463\) 11.5986 0.539033 0.269516 0.962996i \(-0.413136\pi\)
0.269516 + 0.962996i \(0.413136\pi\)
\(464\) 6.60015 0.306404
\(465\) 17.6205 0.817133
\(466\) −31.9265 −1.47897
\(467\) 7.98447 0.369477 0.184739 0.982788i \(-0.440856\pi\)
0.184739 + 0.982788i \(0.440856\pi\)
\(468\) −7.30875 −0.337847
\(469\) 1.10898 0.0512080
\(470\) −83.1345 −3.83471
\(471\) −4.43350 −0.204285
\(472\) −86.9891 −4.00400
\(473\) −0.148781 −0.00684098
\(474\) −62.1188 −2.85321
\(475\) −13.1494 −0.603337
\(476\) 63.4962 2.91034
\(477\) −2.38466 −0.109186
\(478\) 8.29097 0.379220
\(479\) −36.8952 −1.68579 −0.842893 0.538081i \(-0.819149\pi\)
−0.842893 + 0.538081i \(0.819149\pi\)
\(480\) 74.4810 3.39958
\(481\) 12.3177 0.561640
\(482\) −58.0746 −2.64523
\(483\) −13.2255 −0.601779
\(484\) 5.23192 0.237815
\(485\) −55.0420 −2.49933
\(486\) −20.4922 −0.929545
\(487\) 0.241817 0.0109578 0.00547888 0.999985i \(-0.498256\pi\)
0.00547888 + 0.999985i \(0.498256\pi\)
\(488\) 18.5459 0.839534
\(489\) 21.2643 0.961603
\(490\) 56.4335 2.54941
\(491\) 35.4717 1.60082 0.800409 0.599455i \(-0.204616\pi\)
0.800409 + 0.599455i \(0.204616\pi\)
\(492\) 27.5580 1.24241
\(493\) 1.63967 0.0738472
\(494\) 20.4008 0.917874
\(495\) −2.15777 −0.0969845
\(496\) −52.9350 −2.37685
\(497\) 53.2395 2.38812
\(498\) 41.3474 1.85282
\(499\) 2.98552 0.133650 0.0668251 0.997765i \(-0.478713\pi\)
0.0668251 + 0.997765i \(0.478713\pi\)
\(500\) 26.7443 1.19604
\(501\) 2.07765 0.0928224
\(502\) −21.1352 −0.943309
\(503\) −19.4881 −0.868932 −0.434466 0.900688i \(-0.643063\pi\)
−0.434466 + 0.900688i \(0.643063\pi\)
\(504\) 24.7587 1.10284
\(505\) 24.7263 1.10031
\(506\) −6.26944 −0.278711
\(507\) −14.3253 −0.636211
\(508\) −47.2188 −2.09499
\(509\) 28.1571 1.24804 0.624022 0.781407i \(-0.285498\pi\)
0.624022 + 0.781407i \(0.285498\pi\)
\(510\) 37.0598 1.64104
\(511\) 0.166384 0.00736039
\(512\) 0.643083 0.0284205
\(513\) 22.9969 1.01534
\(514\) −25.4101 −1.12079
\(515\) 24.3204 1.07168
\(516\) 1.16690 0.0513700
\(517\) 10.7846 0.474307
\(518\) −67.5485 −2.96791
\(519\) −3.16036 −0.138725
\(520\) 46.2341 2.02750
\(521\) −1.91922 −0.0840826 −0.0420413 0.999116i \(-0.513386\pi\)
−0.0420413 + 0.999116i \(0.513386\pi\)
\(522\) 1.03499 0.0453005
\(523\) 34.1008 1.49112 0.745562 0.666436i \(-0.232181\pi\)
0.745562 + 0.666436i \(0.232181\pi\)
\(524\) 62.3895 2.72550
\(525\) 18.2483 0.796420
\(526\) −48.5642 −2.11750
\(527\) −13.1507 −0.572852
\(528\) −19.3519 −0.842182
\(529\) −17.5649 −0.763693
\(530\) 24.4201 1.06074
\(531\) −7.53413 −0.326953
\(532\) −80.9355 −3.50900
\(533\) 6.52060 0.282438
\(534\) 16.7023 0.722780
\(535\) −8.62075 −0.372707
\(536\) −2.54699 −0.110013
\(537\) 0.102567 0.00442609
\(538\) −6.66202 −0.287220
\(539\) −7.32084 −0.315331
\(540\) 84.3696 3.63069
\(541\) −30.3588 −1.30523 −0.652614 0.757691i \(-0.726328\pi\)
−0.652614 + 0.757691i \(0.726328\pi\)
\(542\) 18.3822 0.789584
\(543\) 1.64039 0.0703959
\(544\) −55.5871 −2.38328
\(545\) −13.4810 −0.577464
\(546\) −28.3114 −1.21162
\(547\) 1.00000 0.0427569
\(548\) 119.340 5.09795
\(549\) 1.60626 0.0685536
\(550\) 8.65047 0.368857
\(551\) −2.09001 −0.0890376
\(552\) 30.3749 1.29284
\(553\) 58.3117 2.47966
\(554\) 56.3499 2.39408
\(555\) −28.5219 −1.21069
\(556\) −54.9907 −2.33213
\(557\) −6.90150 −0.292426 −0.146213 0.989253i \(-0.546708\pi\)
−0.146213 + 0.989253i \(0.546708\pi\)
\(558\) −8.30095 −0.351407
\(559\) 0.276105 0.0116780
\(560\) −140.033 −5.91749
\(561\) −4.80759 −0.202977
\(562\) −54.3261 −2.29161
\(563\) 23.4173 0.986923 0.493461 0.869768i \(-0.335731\pi\)
0.493461 + 0.869768i \(0.335731\pi\)
\(564\) −84.5846 −3.56165
\(565\) 37.5732 1.58072
\(566\) 2.33107 0.0979823
\(567\) −23.3683 −0.981375
\(568\) −122.275 −5.13055
\(569\) 1.70409 0.0714390 0.0357195 0.999362i \(-0.488628\pi\)
0.0357195 + 0.999362i \(0.488628\pi\)
\(570\) −47.2383 −1.97860
\(571\) 8.94488 0.374332 0.187166 0.982328i \(-0.440070\pi\)
0.187166 + 0.982328i \(0.440070\pi\)
\(572\) −9.70928 −0.405965
\(573\) −9.82945 −0.410631
\(574\) −35.7580 −1.49251
\(575\) −7.49920 −0.312738
\(576\) −15.6527 −0.652194
\(577\) 9.66451 0.402339 0.201169 0.979556i \(-0.435526\pi\)
0.201169 + 0.979556i \(0.435526\pi\)
\(578\) 18.0581 0.751118
\(579\) 16.7492 0.696072
\(580\) −7.66771 −0.318384
\(581\) −38.8133 −1.61025
\(582\) −77.4100 −3.20875
\(583\) −3.16790 −0.131201
\(584\) −0.382133 −0.0158128
\(585\) 4.00434 0.165559
\(586\) 22.7951 0.941659
\(587\) 35.6758 1.47250 0.736248 0.676712i \(-0.236596\pi\)
0.736248 + 0.676712i \(0.236596\pi\)
\(588\) 57.4179 2.36787
\(589\) 16.7625 0.690687
\(590\) 77.1531 3.17634
\(591\) −32.9913 −1.35708
\(592\) 85.6846 3.52162
\(593\) −10.6862 −0.438829 −0.219415 0.975632i \(-0.570415\pi\)
−0.219415 + 0.975632i \(0.570415\pi\)
\(594\) −15.1287 −0.620739
\(595\) −34.7885 −1.42619
\(596\) −37.3682 −1.53066
\(597\) 38.8006 1.58800
\(598\) 11.6347 0.475778
\(599\) 30.3999 1.24210 0.621052 0.783769i \(-0.286706\pi\)
0.621052 + 0.783769i \(0.286706\pi\)
\(600\) −41.9108 −1.71100
\(601\) −1.23305 −0.0502971 −0.0251486 0.999684i \(-0.508006\pi\)
−0.0251486 + 0.999684i \(0.508006\pi\)
\(602\) −1.51412 −0.0617109
\(603\) −0.220595 −0.00898333
\(604\) 117.514 4.78158
\(605\) −2.86648 −0.116539
\(606\) 34.7746 1.41262
\(607\) 9.34057 0.379122 0.189561 0.981869i \(-0.439294\pi\)
0.189561 + 0.981869i \(0.439294\pi\)
\(608\) 70.8541 2.87351
\(609\) 2.90044 0.117532
\(610\) −16.4489 −0.665996
\(611\) −20.0139 −0.809674
\(612\) −12.6305 −0.510556
\(613\) 11.5064 0.464739 0.232370 0.972628i \(-0.425352\pi\)
0.232370 + 0.972628i \(0.425352\pi\)
\(614\) −44.1686 −1.78250
\(615\) −15.0986 −0.608833
\(616\) 32.8906 1.32520
\(617\) 24.4136 0.982853 0.491426 0.870919i \(-0.336476\pi\)
0.491426 + 0.870919i \(0.336476\pi\)
\(618\) 34.2037 1.37587
\(619\) −12.9428 −0.520213 −0.260107 0.965580i \(-0.583758\pi\)
−0.260107 + 0.965580i \(0.583758\pi\)
\(620\) 61.4972 2.46979
\(621\) 13.1153 0.526298
\(622\) −68.5331 −2.74793
\(623\) −15.6787 −0.628153
\(624\) 35.9128 1.43766
\(625\) −30.7363 −1.22945
\(626\) 78.8559 3.15171
\(627\) 6.12800 0.244729
\(628\) −15.4733 −0.617452
\(629\) 21.2866 0.848754
\(630\) −21.9592 −0.874875
\(631\) −7.48790 −0.298089 −0.149044 0.988831i \(-0.547620\pi\)
−0.149044 + 0.988831i \(0.547620\pi\)
\(632\) −133.924 −5.32722
\(633\) −29.6431 −1.17821
\(634\) −31.7987 −1.26289
\(635\) 25.8704 1.02663
\(636\) 24.8461 0.985210
\(637\) 13.5859 0.538291
\(638\) 1.37494 0.0544342
\(639\) −10.5902 −0.418943
\(640\) 60.9218 2.40814
\(641\) 17.1326 0.676696 0.338348 0.941021i \(-0.390132\pi\)
0.338348 + 0.941021i \(0.390132\pi\)
\(642\) −12.1240 −0.478498
\(643\) 44.7953 1.76655 0.883276 0.468853i \(-0.155333\pi\)
0.883276 + 0.468853i \(0.155333\pi\)
\(644\) −46.1580 −1.81888
\(645\) −0.639326 −0.0251735
\(646\) 35.2552 1.38710
\(647\) 9.55465 0.375632 0.187816 0.982204i \(-0.439859\pi\)
0.187816 + 0.982204i \(0.439859\pi\)
\(648\) 53.6698 2.10835
\(649\) −10.0087 −0.392875
\(650\) −16.0533 −0.629664
\(651\) −23.2624 −0.911725
\(652\) 74.2142 2.90645
\(653\) 41.8770 1.63877 0.819387 0.573241i \(-0.194314\pi\)
0.819387 + 0.573241i \(0.194314\pi\)
\(654\) −18.9594 −0.741373
\(655\) −34.1822 −1.33561
\(656\) 45.3586 1.77096
\(657\) −0.0330966 −0.00129122
\(658\) 109.753 4.27862
\(659\) 22.6216 0.881213 0.440607 0.897700i \(-0.354763\pi\)
0.440607 + 0.897700i \(0.354763\pi\)
\(660\) 22.4820 0.875111
\(661\) 27.5445 1.07136 0.535679 0.844422i \(-0.320056\pi\)
0.535679 + 0.844422i \(0.320056\pi\)
\(662\) 6.00617 0.233436
\(663\) 8.92181 0.346495
\(664\) 89.1424 3.45939
\(665\) 44.3432 1.71956
\(666\) 13.4365 0.520655
\(667\) −1.19195 −0.0461524
\(668\) 7.25117 0.280556
\(669\) 25.3141 0.978698
\(670\) 2.25900 0.0872727
\(671\) 2.13383 0.0823757
\(672\) −98.3287 −3.79311
\(673\) 18.9592 0.730822 0.365411 0.930846i \(-0.380928\pi\)
0.365411 + 0.930846i \(0.380928\pi\)
\(674\) 32.6903 1.25918
\(675\) −18.0962 −0.696525
\(676\) −49.9967 −1.92295
\(677\) 10.8045 0.415252 0.207626 0.978208i \(-0.433426\pi\)
0.207626 + 0.978208i \(0.433426\pi\)
\(678\) 52.8422 2.02939
\(679\) 72.6657 2.78865
\(680\) 79.8986 3.06397
\(681\) 2.67639 0.102559
\(682\) −11.0274 −0.422260
\(683\) −7.69990 −0.294629 −0.147314 0.989090i \(-0.547063\pi\)
−0.147314 + 0.989090i \(0.547063\pi\)
\(684\) 16.0994 0.615577
\(685\) −65.3843 −2.49820
\(686\) −3.26514 −0.124664
\(687\) 27.7355 1.05818
\(688\) 1.92064 0.0732238
\(689\) 5.87892 0.223969
\(690\) −26.9403 −1.02560
\(691\) 1.63084 0.0620400 0.0310200 0.999519i \(-0.490124\pi\)
0.0310200 + 0.999519i \(0.490124\pi\)
\(692\) −11.0299 −0.419296
\(693\) 2.84866 0.108212
\(694\) 1.30989 0.0497226
\(695\) 30.1285 1.14284
\(696\) −6.66144 −0.252501
\(697\) 11.2684 0.426823
\(698\) 56.1332 2.12467
\(699\) 17.7971 0.673149
\(700\) 63.6881 2.40718
\(701\) 42.0925 1.58981 0.794906 0.606733i \(-0.207520\pi\)
0.794906 + 0.606733i \(0.207520\pi\)
\(702\) 28.0755 1.05964
\(703\) −27.1330 −1.02334
\(704\) −20.7937 −0.783693
\(705\) 46.3425 1.74536
\(706\) −66.9270 −2.51883
\(707\) −32.6433 −1.22768
\(708\) 78.4988 2.95017
\(709\) 38.8295 1.45827 0.729136 0.684369i \(-0.239922\pi\)
0.729136 + 0.684369i \(0.239922\pi\)
\(710\) 108.449 4.07002
\(711\) −11.5992 −0.435003
\(712\) 36.0091 1.34950
\(713\) 9.55976 0.358016
\(714\) −48.9259 −1.83100
\(715\) 5.31955 0.198940
\(716\) 0.357967 0.0133779
\(717\) −4.62172 −0.172601
\(718\) −1.82508 −0.0681114
\(719\) 28.1310 1.04911 0.524554 0.851377i \(-0.324232\pi\)
0.524554 + 0.851377i \(0.324232\pi\)
\(720\) 27.8550 1.03809
\(721\) −32.1074 −1.19574
\(722\) 6.15719 0.229147
\(723\) 32.3731 1.20397
\(724\) 5.72511 0.212772
\(725\) 1.64463 0.0610800
\(726\) −4.03136 −0.149618
\(727\) −13.2382 −0.490980 −0.245490 0.969399i \(-0.578949\pi\)
−0.245490 + 0.969399i \(0.578949\pi\)
\(728\) −61.0377 −2.26221
\(729\) 29.9484 1.10920
\(730\) 0.338925 0.0125442
\(731\) 0.477146 0.0176479
\(732\) −16.7358 −0.618573
\(733\) −3.14201 −0.116053 −0.0580264 0.998315i \(-0.518481\pi\)
−0.0580264 + 0.998315i \(0.518481\pi\)
\(734\) −23.8471 −0.880213
\(735\) −31.4583 −1.16036
\(736\) 40.4085 1.48948
\(737\) −0.293049 −0.0107946
\(738\) 7.11286 0.261828
\(739\) −22.5947 −0.831159 −0.415580 0.909557i \(-0.636421\pi\)
−0.415580 + 0.909557i \(0.636421\pi\)
\(740\) −99.5440 −3.65931
\(741\) −11.3722 −0.417768
\(742\) −32.2391 −1.18353
\(743\) 35.6512 1.30792 0.653959 0.756530i \(-0.273107\pi\)
0.653959 + 0.756530i \(0.273107\pi\)
\(744\) 53.4266 1.95872
\(745\) 20.4734 0.750087
\(746\) 60.5053 2.21526
\(747\) 7.72062 0.282483
\(748\) −16.7789 −0.613498
\(749\) 11.3810 0.415852
\(750\) −20.6073 −0.752472
\(751\) 27.8324 1.01562 0.507809 0.861470i \(-0.330456\pi\)
0.507809 + 0.861470i \(0.330456\pi\)
\(752\) −139.221 −5.07685
\(753\) 11.7816 0.429345
\(754\) −2.55157 −0.0929228
\(755\) −64.3839 −2.34317
\(756\) −111.384 −4.05098
\(757\) −6.43273 −0.233801 −0.116901 0.993144i \(-0.537296\pi\)
−0.116901 + 0.993144i \(0.537296\pi\)
\(758\) −49.3030 −1.79076
\(759\) 3.49483 0.126854
\(760\) −101.843 −3.69423
\(761\) 2.29774 0.0832931 0.0416466 0.999132i \(-0.486740\pi\)
0.0416466 + 0.999132i \(0.486740\pi\)
\(762\) 36.3836 1.31804
\(763\) 17.7975 0.644311
\(764\) −34.3057 −1.24113
\(765\) 6.92002 0.250194
\(766\) 33.5575 1.21248
\(767\) 18.5739 0.670664
\(768\) 23.3362 0.842074
\(769\) 23.7714 0.857218 0.428609 0.903490i \(-0.359004\pi\)
0.428609 + 0.903490i \(0.359004\pi\)
\(770\) −29.1716 −1.05127
\(771\) 14.1646 0.510126
\(772\) 58.4561 2.10388
\(773\) 5.20099 0.187066 0.0935332 0.995616i \(-0.470184\pi\)
0.0935332 + 0.995616i \(0.470184\pi\)
\(774\) 0.301184 0.0108258
\(775\) −13.1904 −0.473813
\(776\) −166.891 −5.99104
\(777\) 37.6542 1.35084
\(778\) −19.2772 −0.691120
\(779\) −14.3633 −0.514620
\(780\) −41.7216 −1.49387
\(781\) −14.0686 −0.503413
\(782\) 20.1063 0.718998
\(783\) −2.87628 −0.102790
\(784\) 94.5059 3.37521
\(785\) 8.47756 0.302577
\(786\) −48.0731 −1.71471
\(787\) 18.7886 0.669740 0.334870 0.942264i \(-0.391308\pi\)
0.334870 + 0.942264i \(0.391308\pi\)
\(788\) −115.143 −4.10178
\(789\) 27.0716 0.963775
\(790\) 118.781 4.22604
\(791\) −49.6036 −1.76370
\(792\) −6.54250 −0.232477
\(793\) −3.95992 −0.140621
\(794\) −97.0022 −3.44248
\(795\) −13.6127 −0.482794
\(796\) 135.417 4.79974
\(797\) 38.0448 1.34761 0.673807 0.738907i \(-0.264658\pi\)
0.673807 + 0.738907i \(0.264658\pi\)
\(798\) 62.3634 2.20764
\(799\) −34.5866 −1.22359
\(800\) −55.7550 −1.97124
\(801\) 3.11875 0.110196
\(802\) −47.8385 −1.68924
\(803\) −0.0439670 −0.00155156
\(804\) 2.29840 0.0810584
\(805\) 25.2892 0.891328
\(806\) 20.4643 0.720826
\(807\) 3.71368 0.130728
\(808\) 74.9718 2.63750
\(809\) 41.1574 1.44702 0.723509 0.690315i \(-0.242528\pi\)
0.723509 + 0.690315i \(0.242528\pi\)
\(810\) −47.6013 −1.67254
\(811\) −21.2599 −0.746536 −0.373268 0.927724i \(-0.621763\pi\)
−0.373268 + 0.927724i \(0.621763\pi\)
\(812\) 10.1228 0.355241
\(813\) −10.2470 −0.359377
\(814\) 17.8497 0.625633
\(815\) −40.6607 −1.42428
\(816\) 62.0619 2.17260
\(817\) −0.608194 −0.0212780
\(818\) 9.82082 0.343377
\(819\) −5.28647 −0.184724
\(820\) −52.6953 −1.84020
\(821\) −35.8402 −1.25083 −0.625416 0.780291i \(-0.715071\pi\)
−0.625416 + 0.780291i \(0.715071\pi\)
\(822\) −91.9551 −3.20730
\(823\) −30.9063 −1.07733 −0.538663 0.842522i \(-0.681070\pi\)
−0.538663 + 0.842522i \(0.681070\pi\)
\(824\) 73.7409 2.56889
\(825\) −4.82212 −0.167885
\(826\) −101.856 −3.54404
\(827\) 24.9100 0.866204 0.433102 0.901345i \(-0.357419\pi\)
0.433102 + 0.901345i \(0.357419\pi\)
\(828\) 9.18161 0.319083
\(829\) 18.2687 0.634497 0.317248 0.948342i \(-0.397241\pi\)
0.317248 + 0.948342i \(0.397241\pi\)
\(830\) −79.0628 −2.74431
\(831\) −31.4117 −1.08966
\(832\) 38.5885 1.33782
\(833\) 23.4781 0.813469
\(834\) 42.3721 1.46723
\(835\) −3.97279 −0.137484
\(836\) 21.3873 0.739694
\(837\) 23.0686 0.797366
\(838\) 61.1890 2.11374
\(839\) 39.7366 1.37186 0.685929 0.727668i \(-0.259396\pi\)
0.685929 + 0.727668i \(0.259396\pi\)
\(840\) 141.334 4.87648
\(841\) −28.7386 −0.990986
\(842\) 61.6676 2.12520
\(843\) 30.2835 1.04302
\(844\) −103.457 −3.56114
\(845\) 27.3924 0.942326
\(846\) −21.8317 −0.750590
\(847\) 3.78429 0.130030
\(848\) 40.8949 1.40434
\(849\) −1.29943 −0.0445964
\(850\) −27.7423 −0.951552
\(851\) −15.4741 −0.530447
\(852\) 110.341 3.78021
\(853\) −1.08257 −0.0370664 −0.0185332 0.999828i \(-0.505900\pi\)
−0.0185332 + 0.999828i \(0.505900\pi\)
\(854\) 21.7156 0.743092
\(855\) −8.82061 −0.301659
\(856\) −26.1387 −0.893401
\(857\) 24.6835 0.843173 0.421586 0.906788i \(-0.361473\pi\)
0.421586 + 0.906788i \(0.361473\pi\)
\(858\) 7.48131 0.255408
\(859\) −28.9608 −0.988129 −0.494065 0.869425i \(-0.664489\pi\)
−0.494065 + 0.869425i \(0.664489\pi\)
\(860\) −2.23131 −0.0760869
\(861\) 19.9329 0.679312
\(862\) −7.63953 −0.260203
\(863\) 1.29445 0.0440638 0.0220319 0.999757i \(-0.492986\pi\)
0.0220319 + 0.999757i \(0.492986\pi\)
\(864\) 97.5095 3.31734
\(865\) 6.04312 0.205472
\(866\) −77.5510 −2.63529
\(867\) −10.0663 −0.341870
\(868\) −81.1878 −2.75569
\(869\) −15.4089 −0.522710
\(870\) 5.90821 0.200307
\(871\) 0.543833 0.0184271
\(872\) −40.8753 −1.38421
\(873\) −14.4544 −0.489208
\(874\) −25.6285 −0.866895
\(875\) 19.3443 0.653958
\(876\) 0.344837 0.0116509
\(877\) 35.7906 1.20856 0.604282 0.796771i \(-0.293460\pi\)
0.604282 + 0.796771i \(0.293460\pi\)
\(878\) 21.6056 0.729155
\(879\) −12.7069 −0.428594
\(880\) 37.0039 1.24740
\(881\) 6.20842 0.209167 0.104583 0.994516i \(-0.466649\pi\)
0.104583 + 0.994516i \(0.466649\pi\)
\(882\) 14.8198 0.499010
\(883\) −39.4455 −1.32745 −0.663723 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(884\) 31.1379 1.04728
\(885\) −43.0082 −1.44570
\(886\) 92.6981 3.11425
\(887\) −36.3707 −1.22121 −0.610605 0.791936i \(-0.709073\pi\)
−0.610605 + 0.791936i \(0.709073\pi\)
\(888\) −86.4803 −2.90209
\(889\) −34.1537 −1.14548
\(890\) −31.9375 −1.07055
\(891\) 6.17508 0.206873
\(892\) 88.3483 2.95812
\(893\) 44.0858 1.47528
\(894\) 28.7934 0.962994
\(895\) −0.196124 −0.00655571
\(896\) −80.4281 −2.68691
\(897\) −6.48564 −0.216549
\(898\) 81.5048 2.71985
\(899\) −2.09653 −0.0699231
\(900\) −12.6686 −0.422288
\(901\) 10.1595 0.338463
\(902\) 9.44905 0.314619
\(903\) 0.844030 0.0280876
\(904\) 113.924 3.78907
\(905\) −3.13669 −0.104267
\(906\) −90.5482 −3.00826
\(907\) −5.14358 −0.170790 −0.0853949 0.996347i \(-0.527215\pi\)
−0.0853949 + 0.996347i \(0.527215\pi\)
\(908\) 9.34082 0.309986
\(909\) 6.49330 0.215369
\(910\) 54.1360 1.79459
\(911\) −24.7301 −0.819343 −0.409672 0.912233i \(-0.634357\pi\)
−0.409672 + 0.912233i \(0.634357\pi\)
\(912\) −79.1073 −2.61951
\(913\) 10.2564 0.339438
\(914\) 40.9363 1.35405
\(915\) 9.16927 0.303127
\(916\) 96.7993 3.19834
\(917\) 45.1268 1.49022
\(918\) 48.5182 1.60134
\(919\) 41.8859 1.38169 0.690844 0.723004i \(-0.257239\pi\)
0.690844 + 0.723004i \(0.257239\pi\)
\(920\) −58.0816 −1.91489
\(921\) 24.6213 0.811300
\(922\) −9.57868 −0.315457
\(923\) 26.1081 0.859360
\(924\) −29.6804 −0.976415
\(925\) 21.3510 0.702016
\(926\) −31.1912 −1.02501
\(927\) 6.38670 0.209767
\(928\) −8.86190 −0.290906
\(929\) −26.3340 −0.863991 −0.431996 0.901876i \(-0.642190\pi\)
−0.431996 + 0.901876i \(0.642190\pi\)
\(930\) −47.3856 −1.55383
\(931\) −29.9264 −0.980799
\(932\) 62.1135 2.03460
\(933\) 38.2031 1.25071
\(934\) −21.4720 −0.702586
\(935\) 9.19288 0.300639
\(936\) 12.1414 0.396855
\(937\) −18.3210 −0.598520 −0.299260 0.954172i \(-0.596740\pi\)
−0.299260 + 0.954172i \(0.596740\pi\)
\(938\) −2.98230 −0.0973755
\(939\) −43.9574 −1.43450
\(940\) 161.739 5.27535
\(941\) −7.16209 −0.233477 −0.116739 0.993163i \(-0.537244\pi\)
−0.116739 + 0.993163i \(0.537244\pi\)
\(942\) 11.9227 0.388462
\(943\) −8.19150 −0.266752
\(944\) 129.204 4.20522
\(945\) 61.0252 1.98515
\(946\) 0.400106 0.0130086
\(947\) 30.5611 0.993104 0.496552 0.868007i \(-0.334599\pi\)
0.496552 + 0.868007i \(0.334599\pi\)
\(948\) 120.853 3.92512
\(949\) 0.0815930 0.00264862
\(950\) 35.3617 1.14729
\(951\) 17.7258 0.574800
\(952\) −105.481 −3.41866
\(953\) −15.5159 −0.502610 −0.251305 0.967908i \(-0.580860\pi\)
−0.251305 + 0.967908i \(0.580860\pi\)
\(954\) 6.41289 0.207625
\(955\) 18.7955 0.608208
\(956\) −16.1302 −0.521688
\(957\) −0.766444 −0.0247756
\(958\) 99.2195 3.20564
\(959\) 86.3194 2.78740
\(960\) −89.3524 −2.88384
\(961\) −14.1853 −0.457589
\(962\) −33.1251 −1.06800
\(963\) −2.26387 −0.0729522
\(964\) 112.985 3.63900
\(965\) −32.0271 −1.03099
\(966\) 35.5662 1.14432
\(967\) 14.7243 0.473501 0.236751 0.971570i \(-0.423918\pi\)
0.236751 + 0.971570i \(0.423918\pi\)
\(968\) −8.69136 −0.279351
\(969\) −19.6526 −0.631334
\(970\) 148.020 4.75265
\(971\) 36.8357 1.18212 0.591058 0.806629i \(-0.298711\pi\)
0.591058 + 0.806629i \(0.298711\pi\)
\(972\) 39.8679 1.27876
\(973\) −39.7752 −1.27513
\(974\) −0.650299 −0.0208369
\(975\) 8.94877 0.286590
\(976\) −27.5460 −0.881726
\(977\) −36.9872 −1.18333 −0.591663 0.806185i \(-0.701529\pi\)
−0.591663 + 0.806185i \(0.701529\pi\)
\(978\) −57.1844 −1.82855
\(979\) 4.14310 0.132414
\(980\) −109.792 −3.50718
\(981\) −3.54021 −0.113030
\(982\) −95.3914 −3.04406
\(983\) 30.3225 0.967136 0.483568 0.875307i \(-0.339341\pi\)
0.483568 + 0.875307i \(0.339341\pi\)
\(984\) −45.7798 −1.45941
\(985\) 63.0847 2.01004
\(986\) −4.40945 −0.140426
\(987\) −61.1807 −1.94740
\(988\) −39.6900 −1.26271
\(989\) −0.346857 −0.0110294
\(990\) 5.80272 0.184423
\(991\) −54.6520 −1.73608 −0.868038 0.496497i \(-0.834619\pi\)
−0.868038 + 0.496497i \(0.834619\pi\)
\(992\) 71.0749 2.25663
\(993\) −3.34808 −0.106248
\(994\) −143.173 −4.54117
\(995\) −74.1929 −2.35207
\(996\) −80.4419 −2.54890
\(997\) 59.3719 1.88033 0.940163 0.340725i \(-0.110673\pi\)
0.940163 + 0.340725i \(0.110673\pi\)
\(998\) −8.02873 −0.254145
\(999\) −37.3405 −1.18140
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.1.5 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.5 121 1.1 even 1 trivial