Properties

Label 4003.2.a.c.1.17
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.34837 q^{2} -3.35198 q^{3} +3.51485 q^{4} -2.33127 q^{5} +7.87170 q^{6} -2.55818 q^{7} -3.55742 q^{8} +8.23579 q^{9} +O(q^{10})\) \(q-2.34837 q^{2} -3.35198 q^{3} +3.51485 q^{4} -2.33127 q^{5} +7.87170 q^{6} -2.55818 q^{7} -3.55742 q^{8} +8.23579 q^{9} +5.47468 q^{10} -5.01759 q^{11} -11.7817 q^{12} +2.16479 q^{13} +6.00757 q^{14} +7.81437 q^{15} +1.32445 q^{16} +6.46936 q^{17} -19.3407 q^{18} +2.40547 q^{19} -8.19405 q^{20} +8.57499 q^{21} +11.7832 q^{22} +8.42083 q^{23} +11.9244 q^{24} +0.434808 q^{25} -5.08373 q^{26} -17.5503 q^{27} -8.99162 q^{28} +9.20678 q^{29} -18.3510 q^{30} -8.50137 q^{31} +4.00454 q^{32} +16.8189 q^{33} -15.1925 q^{34} +5.96381 q^{35} +28.9475 q^{36} +9.55203 q^{37} -5.64895 q^{38} -7.25633 q^{39} +8.29330 q^{40} +1.38908 q^{41} -20.1373 q^{42} +11.1994 q^{43} -17.6360 q^{44} -19.1998 q^{45} -19.7752 q^{46} -2.04731 q^{47} -4.43953 q^{48} -0.455691 q^{49} -1.02109 q^{50} -21.6852 q^{51} +7.60890 q^{52} +12.9487 q^{53} +41.2146 q^{54} +11.6973 q^{55} +9.10054 q^{56} -8.06311 q^{57} -21.6209 q^{58} +0.380262 q^{59} +27.4663 q^{60} +7.31995 q^{61} +19.9644 q^{62} -21.0687 q^{63} -12.0530 q^{64} -5.04670 q^{65} -39.4969 q^{66} +3.63536 q^{67} +22.7388 q^{68} -28.2265 q^{69} -14.0052 q^{70} +4.61567 q^{71} -29.2982 q^{72} -0.625275 q^{73} -22.4317 q^{74} -1.45747 q^{75} +8.45487 q^{76} +12.8359 q^{77} +17.0406 q^{78} +0.553808 q^{79} -3.08765 q^{80} +34.1209 q^{81} -3.26209 q^{82} +9.65313 q^{83} +30.1398 q^{84} -15.0818 q^{85} -26.3004 q^{86} -30.8610 q^{87} +17.8497 q^{88} +1.30307 q^{89} +45.0883 q^{90} -5.53793 q^{91} +29.5979 q^{92} +28.4965 q^{93} +4.80784 q^{94} -5.60780 q^{95} -13.4232 q^{96} -4.63431 q^{97} +1.07013 q^{98} -41.3238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34837 −1.66055 −0.830274 0.557355i \(-0.811816\pi\)
−0.830274 + 0.557355i \(0.811816\pi\)
\(3\) −3.35198 −1.93527 −0.967634 0.252357i \(-0.918794\pi\)
−0.967634 + 0.252357i \(0.918794\pi\)
\(4\) 3.51485 1.75742
\(5\) −2.33127 −1.04257 −0.521287 0.853381i \(-0.674548\pi\)
−0.521287 + 0.853381i \(0.674548\pi\)
\(6\) 7.87170 3.21361
\(7\) −2.55818 −0.966903 −0.483451 0.875371i \(-0.660617\pi\)
−0.483451 + 0.875371i \(0.660617\pi\)
\(8\) −3.55742 −1.25774
\(9\) 8.23579 2.74526
\(10\) 5.47468 1.73125
\(11\) −5.01759 −1.51286 −0.756430 0.654075i \(-0.773058\pi\)
−0.756430 + 0.654075i \(0.773058\pi\)
\(12\) −11.7817 −3.40109
\(13\) 2.16479 0.600404 0.300202 0.953876i \(-0.402946\pi\)
0.300202 + 0.953876i \(0.402946\pi\)
\(14\) 6.00757 1.60559
\(15\) 7.81437 2.01766
\(16\) 1.32445 0.331112
\(17\) 6.46936 1.56905 0.784525 0.620097i \(-0.212907\pi\)
0.784525 + 0.620097i \(0.212907\pi\)
\(18\) −19.3407 −4.55865
\(19\) 2.40547 0.551854 0.275927 0.961179i \(-0.411015\pi\)
0.275927 + 0.961179i \(0.411015\pi\)
\(20\) −8.19405 −1.83224
\(21\) 8.57499 1.87122
\(22\) 11.7832 2.51218
\(23\) 8.42083 1.75586 0.877932 0.478785i \(-0.158923\pi\)
0.877932 + 0.478785i \(0.158923\pi\)
\(24\) 11.9244 2.43406
\(25\) 0.434808 0.0869616
\(26\) −5.08373 −0.997001
\(27\) −17.5503 −3.37755
\(28\) −8.99162 −1.69926
\(29\) 9.20678 1.70966 0.854828 0.518911i \(-0.173663\pi\)
0.854828 + 0.518911i \(0.173663\pi\)
\(30\) −18.3510 −3.35043
\(31\) −8.50137 −1.52689 −0.763446 0.645872i \(-0.776494\pi\)
−0.763446 + 0.645872i \(0.776494\pi\)
\(32\) 4.00454 0.707910
\(33\) 16.8189 2.92779
\(34\) −15.1925 −2.60549
\(35\) 5.96381 1.00807
\(36\) 28.9475 4.82459
\(37\) 9.55203 1.57034 0.785172 0.619278i \(-0.212575\pi\)
0.785172 + 0.619278i \(0.212575\pi\)
\(38\) −5.64895 −0.916380
\(39\) −7.25633 −1.16194
\(40\) 8.29330 1.31129
\(41\) 1.38908 0.216939 0.108469 0.994100i \(-0.465405\pi\)
0.108469 + 0.994100i \(0.465405\pi\)
\(42\) −20.1373 −3.10725
\(43\) 11.1994 1.70789 0.853947 0.520360i \(-0.174202\pi\)
0.853947 + 0.520360i \(0.174202\pi\)
\(44\) −17.6360 −2.65873
\(45\) −19.1998 −2.86214
\(46\) −19.7752 −2.91570
\(47\) −2.04731 −0.298631 −0.149315 0.988790i \(-0.547707\pi\)
−0.149315 + 0.988790i \(0.547707\pi\)
\(48\) −4.43953 −0.640791
\(49\) −0.455691 −0.0650987
\(50\) −1.02109 −0.144404
\(51\) −21.6852 −3.03653
\(52\) 7.60890 1.05516
\(53\) 12.9487 1.77864 0.889322 0.457282i \(-0.151177\pi\)
0.889322 + 0.457282i \(0.151177\pi\)
\(54\) 41.2146 5.60859
\(55\) 11.6973 1.57727
\(56\) 9.10054 1.21611
\(57\) −8.06311 −1.06799
\(58\) −21.6209 −2.83897
\(59\) 0.380262 0.0495058 0.0247529 0.999694i \(-0.492120\pi\)
0.0247529 + 0.999694i \(0.492120\pi\)
\(60\) 27.4663 3.54588
\(61\) 7.31995 0.937223 0.468612 0.883404i \(-0.344754\pi\)
0.468612 + 0.883404i \(0.344754\pi\)
\(62\) 19.9644 2.53548
\(63\) −21.0687 −2.65440
\(64\) −12.0530 −1.50663
\(65\) −5.04670 −0.625966
\(66\) −39.4969 −4.86174
\(67\) 3.63536 0.444129 0.222065 0.975032i \(-0.428720\pi\)
0.222065 + 0.975032i \(0.428720\pi\)
\(68\) 22.7388 2.75749
\(69\) −28.2265 −3.39807
\(70\) −14.0052 −1.67395
\(71\) 4.61567 0.547779 0.273890 0.961761i \(-0.411690\pi\)
0.273890 + 0.961761i \(0.411690\pi\)
\(72\) −29.2982 −3.45282
\(73\) −0.625275 −0.0731829 −0.0365914 0.999330i \(-0.511650\pi\)
−0.0365914 + 0.999330i \(0.511650\pi\)
\(74\) −22.4317 −2.60763
\(75\) −1.45747 −0.168294
\(76\) 8.45487 0.969840
\(77\) 12.8359 1.46279
\(78\) 17.0406 1.92946
\(79\) 0.553808 0.0623083 0.0311541 0.999515i \(-0.490082\pi\)
0.0311541 + 0.999515i \(0.490082\pi\)
\(80\) −3.08765 −0.345209
\(81\) 34.1209 3.79121
\(82\) −3.26209 −0.360237
\(83\) 9.65313 1.05957 0.529784 0.848132i \(-0.322273\pi\)
0.529784 + 0.848132i \(0.322273\pi\)
\(84\) 30.1398 3.28852
\(85\) −15.0818 −1.63585
\(86\) −26.3004 −2.83604
\(87\) −30.8610 −3.30864
\(88\) 17.8497 1.90278
\(89\) 1.30307 0.138125 0.0690627 0.997612i \(-0.477999\pi\)
0.0690627 + 0.997612i \(0.477999\pi\)
\(90\) 45.0883 4.75273
\(91\) −5.53793 −0.580533
\(92\) 29.5979 3.08580
\(93\) 28.4965 2.95495
\(94\) 4.80784 0.495891
\(95\) −5.60780 −0.575349
\(96\) −13.4232 −1.36999
\(97\) −4.63431 −0.470542 −0.235271 0.971930i \(-0.575598\pi\)
−0.235271 + 0.971930i \(0.575598\pi\)
\(98\) 1.07013 0.108100
\(99\) −41.3238 −4.15320
\(100\) 1.52828 0.152828
\(101\) 8.72026 0.867699 0.433849 0.900985i \(-0.357155\pi\)
0.433849 + 0.900985i \(0.357155\pi\)
\(102\) 50.9249 5.04231
\(103\) −14.4897 −1.42771 −0.713854 0.700294i \(-0.753052\pi\)
−0.713854 + 0.700294i \(0.753052\pi\)
\(104\) −7.70106 −0.755151
\(105\) −19.9906 −1.95088
\(106\) −30.4084 −2.95352
\(107\) 1.13406 0.109634 0.0548170 0.998496i \(-0.482542\pi\)
0.0548170 + 0.998496i \(0.482542\pi\)
\(108\) −61.6866 −5.93579
\(109\) −8.29776 −0.794781 −0.397391 0.917650i \(-0.630084\pi\)
−0.397391 + 0.917650i \(0.630084\pi\)
\(110\) −27.4697 −2.61913
\(111\) −32.0182 −3.03904
\(112\) −3.38819 −0.320154
\(113\) 0.873059 0.0821305 0.0410652 0.999156i \(-0.486925\pi\)
0.0410652 + 0.999156i \(0.486925\pi\)
\(114\) 18.9352 1.77344
\(115\) −19.6312 −1.83062
\(116\) 32.3604 3.00459
\(117\) 17.8287 1.64827
\(118\) −0.892995 −0.0822069
\(119\) −16.5498 −1.51712
\(120\) −27.7990 −2.53769
\(121\) 14.1762 1.28874
\(122\) −17.1899 −1.55630
\(123\) −4.65619 −0.419834
\(124\) −29.8810 −2.68339
\(125\) 10.6427 0.951911
\(126\) 49.4771 4.40777
\(127\) 4.17780 0.370720 0.185360 0.982671i \(-0.440655\pi\)
0.185360 + 0.982671i \(0.440655\pi\)
\(128\) 20.2959 1.79392
\(129\) −37.5402 −3.30523
\(130\) 11.8515 1.03945
\(131\) 5.85221 0.511310 0.255655 0.966768i \(-0.417709\pi\)
0.255655 + 0.966768i \(0.417709\pi\)
\(132\) 59.1157 5.14536
\(133\) −6.15365 −0.533589
\(134\) −8.53716 −0.737499
\(135\) 40.9144 3.52135
\(136\) −23.0142 −1.97345
\(137\) −9.20645 −0.786561 −0.393280 0.919419i \(-0.628660\pi\)
−0.393280 + 0.919419i \(0.628660\pi\)
\(138\) 66.2862 5.64266
\(139\) −3.53429 −0.299775 −0.149887 0.988703i \(-0.547891\pi\)
−0.149887 + 0.988703i \(0.547891\pi\)
\(140\) 20.9619 1.77160
\(141\) 6.86254 0.577931
\(142\) −10.8393 −0.909614
\(143\) −10.8620 −0.908327
\(144\) 10.9079 0.908991
\(145\) −21.4635 −1.78244
\(146\) 1.46838 0.121524
\(147\) 1.52747 0.125983
\(148\) 33.5739 2.75976
\(149\) −4.19058 −0.343306 −0.171653 0.985157i \(-0.554911\pi\)
−0.171653 + 0.985157i \(0.554911\pi\)
\(150\) 3.42268 0.279461
\(151\) 5.95922 0.484954 0.242477 0.970157i \(-0.422040\pi\)
0.242477 + 0.970157i \(0.422040\pi\)
\(152\) −8.55728 −0.694087
\(153\) 53.2803 4.30746
\(154\) −30.1435 −2.42903
\(155\) 19.8190 1.59190
\(156\) −25.5049 −2.04203
\(157\) −13.8794 −1.10770 −0.553850 0.832616i \(-0.686842\pi\)
−0.553850 + 0.832616i \(0.686842\pi\)
\(158\) −1.30055 −0.103466
\(159\) −43.4039 −3.44215
\(160\) −9.33566 −0.738048
\(161\) −21.5420 −1.69775
\(162\) −80.1285 −6.29549
\(163\) 10.4746 0.820437 0.410218 0.911987i \(-0.365453\pi\)
0.410218 + 0.911987i \(0.365453\pi\)
\(164\) 4.88242 0.381253
\(165\) −39.2093 −3.05244
\(166\) −22.6691 −1.75947
\(167\) −6.90718 −0.534493 −0.267247 0.963628i \(-0.586114\pi\)
−0.267247 + 0.963628i \(0.586114\pi\)
\(168\) −30.5048 −2.35350
\(169\) −8.31369 −0.639515
\(170\) 35.4177 2.71641
\(171\) 19.8110 1.51498
\(172\) 39.3642 3.00149
\(173\) −21.9224 −1.66673 −0.833365 0.552723i \(-0.813589\pi\)
−0.833365 + 0.552723i \(0.813589\pi\)
\(174\) 72.4730 5.49416
\(175\) −1.11232 −0.0840834
\(176\) −6.64554 −0.500926
\(177\) −1.27463 −0.0958071
\(178\) −3.06010 −0.229364
\(179\) 2.24464 0.167772 0.0838862 0.996475i \(-0.473267\pi\)
0.0838862 + 0.996475i \(0.473267\pi\)
\(180\) −67.4845 −5.02999
\(181\) 11.7608 0.874170 0.437085 0.899420i \(-0.356011\pi\)
0.437085 + 0.899420i \(0.356011\pi\)
\(182\) 13.0051 0.964003
\(183\) −24.5363 −1.81378
\(184\) −29.9564 −2.20842
\(185\) −22.2683 −1.63720
\(186\) −66.9203 −4.90683
\(187\) −32.4606 −2.37375
\(188\) −7.19597 −0.524820
\(189\) 44.8969 3.26577
\(190\) 13.1692 0.955395
\(191\) 12.5971 0.911497 0.455749 0.890108i \(-0.349372\pi\)
0.455749 + 0.890108i \(0.349372\pi\)
\(192\) 40.4016 2.91574
\(193\) −5.00262 −0.360096 −0.180048 0.983658i \(-0.557625\pi\)
−0.180048 + 0.983658i \(0.557625\pi\)
\(194\) 10.8831 0.781359
\(195\) 16.9165 1.21141
\(196\) −1.60168 −0.114406
\(197\) −13.4058 −0.955123 −0.477562 0.878598i \(-0.658479\pi\)
−0.477562 + 0.878598i \(0.658479\pi\)
\(198\) 97.0436 6.89659
\(199\) −21.5031 −1.52431 −0.762156 0.647394i \(-0.775859\pi\)
−0.762156 + 0.647394i \(0.775859\pi\)
\(200\) −1.54679 −0.109375
\(201\) −12.1857 −0.859510
\(202\) −20.4784 −1.44086
\(203\) −23.5526 −1.65307
\(204\) −76.2201 −5.33648
\(205\) −3.23833 −0.226175
\(206\) 34.0271 2.37078
\(207\) 69.3522 4.82031
\(208\) 2.86715 0.198801
\(209\) −12.0697 −0.834877
\(210\) 46.9453 3.23954
\(211\) −5.54882 −0.381996 −0.190998 0.981590i \(-0.561172\pi\)
−0.190998 + 0.981590i \(0.561172\pi\)
\(212\) 45.5127 3.12583
\(213\) −15.4717 −1.06010
\(214\) −2.66320 −0.182052
\(215\) −26.1088 −1.78061
\(216\) 62.4337 4.24808
\(217\) 21.7481 1.47636
\(218\) 19.4862 1.31977
\(219\) 2.09591 0.141629
\(220\) 41.1143 2.77193
\(221\) 14.0048 0.942065
\(222\) 75.1907 5.04647
\(223\) 23.9664 1.60491 0.802453 0.596715i \(-0.203528\pi\)
0.802453 + 0.596715i \(0.203528\pi\)
\(224\) −10.2444 −0.684480
\(225\) 3.58099 0.238733
\(226\) −2.05027 −0.136382
\(227\) 19.7136 1.30844 0.654220 0.756304i \(-0.272997\pi\)
0.654220 + 0.756304i \(0.272997\pi\)
\(228\) −28.3406 −1.87690
\(229\) 5.67747 0.375178 0.187589 0.982248i \(-0.439933\pi\)
0.187589 + 0.982248i \(0.439933\pi\)
\(230\) 46.1013 3.03983
\(231\) −43.0258 −2.83089
\(232\) −32.7524 −2.15030
\(233\) 13.1975 0.864597 0.432298 0.901731i \(-0.357703\pi\)
0.432298 + 0.901731i \(0.357703\pi\)
\(234\) −41.8685 −2.73703
\(235\) 4.77282 0.311345
\(236\) 1.33656 0.0870027
\(237\) −1.85636 −0.120583
\(238\) 38.8651 2.51925
\(239\) 19.7106 1.27497 0.637487 0.770461i \(-0.279974\pi\)
0.637487 + 0.770461i \(0.279974\pi\)
\(240\) 10.3497 0.668073
\(241\) 2.11242 0.136073 0.0680365 0.997683i \(-0.478327\pi\)
0.0680365 + 0.997683i \(0.478327\pi\)
\(242\) −33.2909 −2.14002
\(243\) −61.7218 −3.95946
\(244\) 25.7285 1.64710
\(245\) 1.06234 0.0678702
\(246\) 10.9345 0.697156
\(247\) 5.20734 0.331335
\(248\) 30.2430 1.92043
\(249\) −32.3571 −2.05055
\(250\) −24.9930 −1.58069
\(251\) −9.75347 −0.615633 −0.307817 0.951446i \(-0.599598\pi\)
−0.307817 + 0.951446i \(0.599598\pi\)
\(252\) −74.0532 −4.66491
\(253\) −42.2522 −2.65638
\(254\) −9.81103 −0.615599
\(255\) 50.5540 3.16581
\(256\) −23.5563 −1.47227
\(257\) 20.2417 1.26265 0.631323 0.775520i \(-0.282512\pi\)
0.631323 + 0.775520i \(0.282512\pi\)
\(258\) 88.1584 5.48850
\(259\) −24.4359 −1.51837
\(260\) −17.7384 −1.10009
\(261\) 75.8251 4.69346
\(262\) −13.7432 −0.849055
\(263\) 12.7769 0.787855 0.393928 0.919142i \(-0.371116\pi\)
0.393928 + 0.919142i \(0.371116\pi\)
\(264\) −59.8318 −3.68239
\(265\) −30.1869 −1.85437
\(266\) 14.4510 0.886051
\(267\) −4.36787 −0.267310
\(268\) 12.7777 0.780523
\(269\) −6.64960 −0.405433 −0.202717 0.979237i \(-0.564977\pi\)
−0.202717 + 0.979237i \(0.564977\pi\)
\(270\) −96.0822 −5.84738
\(271\) 14.0441 0.853120 0.426560 0.904459i \(-0.359725\pi\)
0.426560 + 0.904459i \(0.359725\pi\)
\(272\) 8.56834 0.519532
\(273\) 18.5630 1.12349
\(274\) 21.6202 1.30612
\(275\) −2.18169 −0.131561
\(276\) −99.2117 −5.97184
\(277\) 9.62697 0.578429 0.289214 0.957264i \(-0.406606\pi\)
0.289214 + 0.957264i \(0.406606\pi\)
\(278\) 8.29983 0.497791
\(279\) −70.0155 −4.19172
\(280\) −21.2158 −1.26789
\(281\) −0.293482 −0.0175077 −0.00875383 0.999962i \(-0.502786\pi\)
−0.00875383 + 0.999962i \(0.502786\pi\)
\(282\) −16.1158 −0.959682
\(283\) −16.0668 −0.955073 −0.477536 0.878612i \(-0.658470\pi\)
−0.477536 + 0.878612i \(0.658470\pi\)
\(284\) 16.2234 0.962680
\(285\) 18.7973 1.11345
\(286\) 25.5080 1.50832
\(287\) −3.55353 −0.209759
\(288\) 32.9806 1.94340
\(289\) 24.8527 1.46192
\(290\) 50.4042 2.95984
\(291\) 15.5341 0.910626
\(292\) −2.19774 −0.128613
\(293\) 14.3964 0.841048 0.420524 0.907281i \(-0.361846\pi\)
0.420524 + 0.907281i \(0.361846\pi\)
\(294\) −3.58706 −0.209202
\(295\) −0.886492 −0.0516135
\(296\) −33.9806 −1.97508
\(297\) 88.0601 5.10976
\(298\) 9.84104 0.570076
\(299\) 18.2293 1.05423
\(300\) −5.12278 −0.295764
\(301\) −28.6502 −1.65137
\(302\) −13.9945 −0.805290
\(303\) −29.2302 −1.67923
\(304\) 3.18593 0.182726
\(305\) −17.0648 −0.977125
\(306\) −125.122 −7.15275
\(307\) 34.0961 1.94597 0.972984 0.230871i \(-0.0741576\pi\)
0.972984 + 0.230871i \(0.0741576\pi\)
\(308\) 45.1163 2.57074
\(309\) 48.5691 2.76300
\(310\) −46.5423 −2.64342
\(311\) −5.73215 −0.325041 −0.162520 0.986705i \(-0.551962\pi\)
−0.162520 + 0.986705i \(0.551962\pi\)
\(312\) 25.8138 1.46142
\(313\) 31.3084 1.76966 0.884828 0.465917i \(-0.154276\pi\)
0.884828 + 0.465917i \(0.154276\pi\)
\(314\) 32.5941 1.83939
\(315\) 49.1167 2.76741
\(316\) 1.94655 0.109502
\(317\) −4.73628 −0.266016 −0.133008 0.991115i \(-0.542464\pi\)
−0.133008 + 0.991115i \(0.542464\pi\)
\(318\) 101.928 5.71586
\(319\) −46.1958 −2.58647
\(320\) 28.0989 1.57077
\(321\) −3.80136 −0.212171
\(322\) 50.5887 2.81920
\(323\) 15.5619 0.865887
\(324\) 119.930 6.66276
\(325\) 0.941267 0.0522121
\(326\) −24.5983 −1.36238
\(327\) 27.8140 1.53812
\(328\) −4.94156 −0.272852
\(329\) 5.23739 0.288747
\(330\) 92.0779 5.06872
\(331\) 0.731781 0.0402223 0.0201112 0.999798i \(-0.493598\pi\)
0.0201112 + 0.999798i \(0.493598\pi\)
\(332\) 33.9293 1.86211
\(333\) 78.6685 4.31101
\(334\) 16.2206 0.887552
\(335\) −8.47499 −0.463038
\(336\) 11.3571 0.619583
\(337\) 15.4726 0.842847 0.421424 0.906864i \(-0.361531\pi\)
0.421424 + 0.906864i \(0.361531\pi\)
\(338\) 19.5236 1.06195
\(339\) −2.92648 −0.158945
\(340\) −53.0103 −2.87488
\(341\) 42.6564 2.30997
\(342\) −46.5235 −2.51571
\(343\) 19.0730 1.02985
\(344\) −39.8410 −2.14808
\(345\) 65.8035 3.54274
\(346\) 51.4820 2.76769
\(347\) 28.4847 1.52914 0.764570 0.644541i \(-0.222951\pi\)
0.764570 + 0.644541i \(0.222951\pi\)
\(348\) −108.472 −5.81469
\(349\) 0.509260 0.0272601 0.0136300 0.999907i \(-0.495661\pi\)
0.0136300 + 0.999907i \(0.495661\pi\)
\(350\) 2.61214 0.139625
\(351\) −37.9927 −2.02790
\(352\) −20.0931 −1.07097
\(353\) −28.6602 −1.52543 −0.762713 0.646737i \(-0.776133\pi\)
−0.762713 + 0.646737i \(0.776133\pi\)
\(354\) 2.99331 0.159092
\(355\) −10.7604 −0.571101
\(356\) 4.58010 0.242745
\(357\) 55.4747 2.93603
\(358\) −5.27125 −0.278594
\(359\) −2.02732 −0.106998 −0.0534988 0.998568i \(-0.517037\pi\)
−0.0534988 + 0.998568i \(0.517037\pi\)
\(360\) 68.3019 3.59982
\(361\) −13.2137 −0.695458
\(362\) −27.6186 −1.45160
\(363\) −47.5183 −2.49406
\(364\) −19.4650 −1.02024
\(365\) 1.45768 0.0762986
\(366\) 57.6204 3.01187
\(367\) −16.9759 −0.886137 −0.443068 0.896488i \(-0.646110\pi\)
−0.443068 + 0.896488i \(0.646110\pi\)
\(368\) 11.1530 0.581388
\(369\) 11.4402 0.595554
\(370\) 52.2943 2.71865
\(371\) −33.1252 −1.71978
\(372\) 100.161 5.19309
\(373\) −7.40719 −0.383530 −0.191765 0.981441i \(-0.561421\pi\)
−0.191765 + 0.981441i \(0.561421\pi\)
\(374\) 76.2295 3.94173
\(375\) −35.6741 −1.84220
\(376\) 7.28314 0.375599
\(377\) 19.9307 1.02648
\(378\) −105.435 −5.42297
\(379\) −12.0836 −0.620691 −0.310345 0.950624i \(-0.600445\pi\)
−0.310345 + 0.950624i \(0.600445\pi\)
\(380\) −19.7106 −1.01113
\(381\) −14.0039 −0.717443
\(382\) −29.5828 −1.51359
\(383\) −11.0936 −0.566856 −0.283428 0.958994i \(-0.591472\pi\)
−0.283428 + 0.958994i \(0.591472\pi\)
\(384\) −68.0317 −3.47173
\(385\) −29.9239 −1.52507
\(386\) 11.7480 0.597957
\(387\) 92.2360 4.68862
\(388\) −16.2889 −0.826942
\(389\) −24.3086 −1.23250 −0.616248 0.787552i \(-0.711348\pi\)
−0.616248 + 0.787552i \(0.711348\pi\)
\(390\) −39.7261 −2.01161
\(391\) 54.4774 2.75504
\(392\) 1.62108 0.0818771
\(393\) −19.6165 −0.989522
\(394\) 31.4818 1.58603
\(395\) −1.29107 −0.0649610
\(396\) −145.247 −7.29893
\(397\) −0.411585 −0.0206569 −0.0103284 0.999947i \(-0.503288\pi\)
−0.0103284 + 0.999947i \(0.503288\pi\)
\(398\) 50.4971 2.53119
\(399\) 20.6269 1.03264
\(400\) 0.575881 0.0287941
\(401\) −14.3825 −0.718229 −0.359115 0.933293i \(-0.616921\pi\)
−0.359115 + 0.933293i \(0.616921\pi\)
\(402\) 28.6164 1.42726
\(403\) −18.4037 −0.916752
\(404\) 30.6504 1.52491
\(405\) −79.5449 −3.95262
\(406\) 55.3103 2.74501
\(407\) −47.9281 −2.37571
\(408\) 77.1433 3.81916
\(409\) 22.9567 1.13514 0.567568 0.823327i \(-0.307885\pi\)
0.567568 + 0.823327i \(0.307885\pi\)
\(410\) 7.60479 0.375574
\(411\) 30.8599 1.52221
\(412\) −50.9289 −2.50909
\(413\) −0.972779 −0.0478673
\(414\) −162.865 −8.00436
\(415\) −22.5040 −1.10468
\(416\) 8.66898 0.425032
\(417\) 11.8469 0.580145
\(418\) 28.3441 1.38635
\(419\) 25.9209 1.26632 0.633160 0.774021i \(-0.281757\pi\)
0.633160 + 0.774021i \(0.281757\pi\)
\(420\) −70.2639 −3.42853
\(421\) −33.2524 −1.62062 −0.810311 0.585999i \(-0.800702\pi\)
−0.810311 + 0.585999i \(0.800702\pi\)
\(422\) 13.0307 0.634324
\(423\) −16.8612 −0.819820
\(424\) −46.0640 −2.23707
\(425\) 2.81293 0.136447
\(426\) 36.3332 1.76035
\(427\) −18.7258 −0.906204
\(428\) 3.98605 0.192673
\(429\) 36.4093 1.75786
\(430\) 61.3132 2.95678
\(431\) 28.5586 1.37562 0.687809 0.725892i \(-0.258573\pi\)
0.687809 + 0.725892i \(0.258573\pi\)
\(432\) −23.2445 −1.11835
\(433\) 28.4687 1.36812 0.684060 0.729426i \(-0.260213\pi\)
0.684060 + 0.729426i \(0.260213\pi\)
\(434\) −51.0726 −2.45156
\(435\) 71.9452 3.44951
\(436\) −29.1654 −1.39677
\(437\) 20.2561 0.968980
\(438\) −4.92198 −0.235181
\(439\) −15.0407 −0.717851 −0.358926 0.933366i \(-0.616857\pi\)
−0.358926 + 0.933366i \(0.616857\pi\)
\(440\) −41.6123 −1.98379
\(441\) −3.75298 −0.178713
\(442\) −32.8885 −1.56434
\(443\) 1.04456 0.0496285 0.0248142 0.999692i \(-0.492101\pi\)
0.0248142 + 0.999692i \(0.492101\pi\)
\(444\) −112.539 −5.34087
\(445\) −3.03781 −0.144006
\(446\) −56.2819 −2.66503
\(447\) 14.0468 0.664389
\(448\) 30.8339 1.45677
\(449\) −9.12813 −0.430783 −0.215391 0.976528i \(-0.569103\pi\)
−0.215391 + 0.976528i \(0.569103\pi\)
\(450\) −8.40949 −0.396427
\(451\) −6.96985 −0.328198
\(452\) 3.06867 0.144338
\(453\) −19.9752 −0.938517
\(454\) −46.2949 −2.17273
\(455\) 12.9104 0.605248
\(456\) 28.6839 1.34325
\(457\) −20.2093 −0.945349 −0.472675 0.881237i \(-0.656711\pi\)
−0.472675 + 0.881237i \(0.656711\pi\)
\(458\) −13.3328 −0.623001
\(459\) −113.539 −5.29956
\(460\) −69.0006 −3.21717
\(461\) −5.58958 −0.260333 −0.130166 0.991492i \(-0.541551\pi\)
−0.130166 + 0.991492i \(0.541551\pi\)
\(462\) 101.040 4.70083
\(463\) −22.2166 −1.03249 −0.516246 0.856440i \(-0.672671\pi\)
−0.516246 + 0.856440i \(0.672671\pi\)
\(464\) 12.1939 0.566088
\(465\) −66.4329 −3.08075
\(466\) −30.9926 −1.43571
\(467\) 4.99723 0.231244 0.115622 0.993293i \(-0.463114\pi\)
0.115622 + 0.993293i \(0.463114\pi\)
\(468\) 62.6653 2.89670
\(469\) −9.29991 −0.429430
\(470\) −11.2084 −0.517003
\(471\) 46.5237 2.14370
\(472\) −1.35275 −0.0622654
\(473\) −56.1940 −2.58380
\(474\) 4.35941 0.200234
\(475\) 1.04592 0.0479901
\(476\) −58.1701 −2.66622
\(477\) 106.643 4.88285
\(478\) −46.2879 −2.11716
\(479\) −13.9884 −0.639146 −0.319573 0.947562i \(-0.603539\pi\)
−0.319573 + 0.947562i \(0.603539\pi\)
\(480\) 31.2930 1.42832
\(481\) 20.6781 0.942841
\(482\) −4.96075 −0.225956
\(483\) 72.2085 3.28560
\(484\) 49.8271 2.26487
\(485\) 10.8038 0.490576
\(486\) 144.946 6.57487
\(487\) 6.57673 0.298020 0.149010 0.988836i \(-0.452391\pi\)
0.149010 + 0.988836i \(0.452391\pi\)
\(488\) −26.0401 −1.17878
\(489\) −35.1108 −1.58777
\(490\) −2.49476 −0.112702
\(491\) 38.1736 1.72275 0.861375 0.507970i \(-0.169604\pi\)
0.861375 + 0.507970i \(0.169604\pi\)
\(492\) −16.3658 −0.737827
\(493\) 59.5620 2.68254
\(494\) −12.2288 −0.550198
\(495\) 96.3368 4.33002
\(496\) −11.2596 −0.505573
\(497\) −11.8077 −0.529649
\(498\) 75.9865 3.40504
\(499\) −6.36117 −0.284765 −0.142383 0.989812i \(-0.545476\pi\)
−0.142383 + 0.989812i \(0.545476\pi\)
\(500\) 37.4074 1.67291
\(501\) 23.1527 1.03439
\(502\) 22.9048 1.02229
\(503\) 4.05126 0.180637 0.0903184 0.995913i \(-0.471212\pi\)
0.0903184 + 0.995913i \(0.471212\pi\)
\(504\) 74.9501 3.33854
\(505\) −20.3293 −0.904640
\(506\) 99.2239 4.41104
\(507\) 27.8674 1.23763
\(508\) 14.6843 0.651512
\(509\) 25.8712 1.14672 0.573361 0.819303i \(-0.305639\pi\)
0.573361 + 0.819303i \(0.305639\pi\)
\(510\) −118.720 −5.25699
\(511\) 1.59957 0.0707607
\(512\) 14.7271 0.650850
\(513\) −42.2168 −1.86392
\(514\) −47.5351 −2.09668
\(515\) 33.7793 1.48849
\(516\) −131.948 −5.80869
\(517\) 10.2725 0.451786
\(518\) 57.3844 2.52133
\(519\) 73.4836 3.22557
\(520\) 17.9532 0.787301
\(521\) −1.07627 −0.0471522 −0.0235761 0.999722i \(-0.507505\pi\)
−0.0235761 + 0.999722i \(0.507505\pi\)
\(522\) −178.066 −7.79372
\(523\) 37.7227 1.64950 0.824748 0.565500i \(-0.191317\pi\)
0.824748 + 0.565500i \(0.191317\pi\)
\(524\) 20.5696 0.898588
\(525\) 3.72848 0.162724
\(526\) −30.0048 −1.30827
\(527\) −54.9985 −2.39577
\(528\) 22.2757 0.969427
\(529\) 47.9103 2.08306
\(530\) 70.8901 3.07927
\(531\) 3.13176 0.135907
\(532\) −21.6291 −0.937741
\(533\) 3.00707 0.130251
\(534\) 10.2574 0.443881
\(535\) −2.64380 −0.114302
\(536\) −12.9325 −0.558598
\(537\) −7.52400 −0.324685
\(538\) 15.6157 0.673242
\(539\) 2.28647 0.0984852
\(540\) 143.808 6.18851
\(541\) 37.0227 1.59173 0.795866 0.605473i \(-0.207016\pi\)
0.795866 + 0.605473i \(0.207016\pi\)
\(542\) −32.9808 −1.41665
\(543\) −39.4219 −1.69175
\(544\) 25.9068 1.11075
\(545\) 19.3443 0.828619
\(546\) −43.5929 −1.86560
\(547\) −30.6705 −1.31137 −0.655687 0.755033i \(-0.727621\pi\)
−0.655687 + 0.755033i \(0.727621\pi\)
\(548\) −32.3593 −1.38232
\(549\) 60.2856 2.57292
\(550\) 5.12341 0.218463
\(551\) 22.1467 0.943480
\(552\) 100.413 4.27388
\(553\) −1.41674 −0.0602460
\(554\) −22.6077 −0.960509
\(555\) 74.6431 3.16842
\(556\) −12.4225 −0.526831
\(557\) 27.5702 1.16819 0.584094 0.811686i \(-0.301450\pi\)
0.584094 + 0.811686i \(0.301450\pi\)
\(558\) 164.422 6.96056
\(559\) 24.2443 1.02543
\(560\) 7.89877 0.333784
\(561\) 108.807 4.59385
\(562\) 0.689205 0.0290723
\(563\) 19.8423 0.836254 0.418127 0.908388i \(-0.362687\pi\)
0.418127 + 0.908388i \(0.362687\pi\)
\(564\) 24.1208 1.01567
\(565\) −2.03533 −0.0856271
\(566\) 37.7308 1.58594
\(567\) −87.2876 −3.66573
\(568\) −16.4199 −0.688963
\(569\) −23.9841 −1.00547 −0.502733 0.864442i \(-0.667672\pi\)
−0.502733 + 0.864442i \(0.667672\pi\)
\(570\) −44.1430 −1.84894
\(571\) 26.8357 1.12304 0.561520 0.827463i \(-0.310217\pi\)
0.561520 + 0.827463i \(0.310217\pi\)
\(572\) −38.1783 −1.59631
\(573\) −42.2254 −1.76399
\(574\) 8.34502 0.348314
\(575\) 3.66144 0.152693
\(576\) −99.2664 −4.13610
\(577\) −41.7175 −1.73672 −0.868360 0.495934i \(-0.834826\pi\)
−0.868360 + 0.495934i \(0.834826\pi\)
\(578\) −58.3633 −2.42759
\(579\) 16.7687 0.696883
\(580\) −75.4408 −3.13251
\(581\) −24.6945 −1.02450
\(582\) −36.4799 −1.51214
\(583\) −64.9713 −2.69084
\(584\) 2.22437 0.0920449
\(585\) −41.5636 −1.71844
\(586\) −33.8082 −1.39660
\(587\) −43.9966 −1.81593 −0.907967 0.419041i \(-0.862366\pi\)
−0.907967 + 0.419041i \(0.862366\pi\)
\(588\) 5.36882 0.221406
\(589\) −20.4498 −0.842621
\(590\) 2.08181 0.0857068
\(591\) 44.9360 1.84842
\(592\) 12.6512 0.519960
\(593\) 24.1414 0.991367 0.495683 0.868503i \(-0.334918\pi\)
0.495683 + 0.868503i \(0.334918\pi\)
\(594\) −206.798 −8.48501
\(595\) 38.5821 1.58171
\(596\) −14.7292 −0.603334
\(597\) 72.0779 2.94995
\(598\) −42.8092 −1.75060
\(599\) −14.2352 −0.581633 −0.290817 0.956779i \(-0.593927\pi\)
−0.290817 + 0.956779i \(0.593927\pi\)
\(600\) 5.18483 0.211670
\(601\) −27.9009 −1.13810 −0.569052 0.822302i \(-0.692690\pi\)
−0.569052 + 0.822302i \(0.692690\pi\)
\(602\) 67.2812 2.74218
\(603\) 29.9400 1.21925
\(604\) 20.9457 0.852270
\(605\) −33.0485 −1.34361
\(606\) 68.6433 2.78844
\(607\) 26.7049 1.08392 0.541959 0.840405i \(-0.317683\pi\)
0.541959 + 0.840405i \(0.317683\pi\)
\(608\) 9.63282 0.390662
\(609\) 78.9481 3.19914
\(610\) 40.0744 1.62256
\(611\) −4.43199 −0.179299
\(612\) 187.272 7.57003
\(613\) 7.82828 0.316181 0.158091 0.987425i \(-0.449466\pi\)
0.158091 + 0.987425i \(0.449466\pi\)
\(614\) −80.0703 −3.23138
\(615\) 10.8548 0.437709
\(616\) −45.6627 −1.83980
\(617\) −20.0774 −0.808286 −0.404143 0.914696i \(-0.632430\pi\)
−0.404143 + 0.914696i \(0.632430\pi\)
\(618\) −114.058 −4.58810
\(619\) −9.94420 −0.399691 −0.199846 0.979827i \(-0.564044\pi\)
−0.199846 + 0.979827i \(0.564044\pi\)
\(620\) 69.6606 2.79764
\(621\) −147.788 −5.93053
\(622\) 13.4612 0.539746
\(623\) −3.33350 −0.133554
\(624\) −9.61065 −0.384734
\(625\) −26.9850 −1.07940
\(626\) −73.5238 −2.93860
\(627\) 40.4574 1.61571
\(628\) −48.7841 −1.94670
\(629\) 61.7955 2.46395
\(630\) −115.344 −4.59543
\(631\) 33.1269 1.31876 0.659381 0.751809i \(-0.270819\pi\)
0.659381 + 0.751809i \(0.270819\pi\)
\(632\) −1.97013 −0.0783675
\(633\) 18.5995 0.739266
\(634\) 11.1225 0.441733
\(635\) −9.73958 −0.386503
\(636\) −152.558 −6.04932
\(637\) −0.986474 −0.0390855
\(638\) 108.485 4.29496
\(639\) 38.0137 1.50380
\(640\) −47.3153 −1.87030
\(641\) −41.4471 −1.63706 −0.818532 0.574461i \(-0.805212\pi\)
−0.818532 + 0.574461i \(0.805212\pi\)
\(642\) 8.92700 0.352320
\(643\) 10.7638 0.424485 0.212242 0.977217i \(-0.431923\pi\)
0.212242 + 0.977217i \(0.431923\pi\)
\(644\) −75.7169 −2.98366
\(645\) 87.5163 3.44595
\(646\) −36.5451 −1.43785
\(647\) −34.8785 −1.37122 −0.685608 0.727971i \(-0.740464\pi\)
−0.685608 + 0.727971i \(0.740464\pi\)
\(648\) −121.382 −4.76835
\(649\) −1.90800 −0.0748954
\(650\) −2.21044 −0.0867008
\(651\) −72.8992 −2.85715
\(652\) 36.8167 1.44185
\(653\) 12.1977 0.477331 0.238666 0.971102i \(-0.423290\pi\)
0.238666 + 0.971102i \(0.423290\pi\)
\(654\) −65.3175 −2.55412
\(655\) −13.6431 −0.533079
\(656\) 1.83977 0.0718310
\(657\) −5.14963 −0.200906
\(658\) −12.2993 −0.479478
\(659\) 30.2241 1.17736 0.588681 0.808365i \(-0.299647\pi\)
0.588681 + 0.808365i \(0.299647\pi\)
\(660\) −137.815 −5.36442
\(661\) −16.1415 −0.627830 −0.313915 0.949451i \(-0.601641\pi\)
−0.313915 + 0.949451i \(0.601641\pi\)
\(662\) −1.71849 −0.0667912
\(663\) −46.9439 −1.82315
\(664\) −34.3402 −1.33266
\(665\) 14.3458 0.556306
\(666\) −184.743 −7.15864
\(667\) 77.5287 3.00192
\(668\) −24.2777 −0.939331
\(669\) −80.3348 −3.10592
\(670\) 19.9024 0.768897
\(671\) −36.7285 −1.41789
\(672\) 34.3389 1.32465
\(673\) −11.6709 −0.449878 −0.224939 0.974373i \(-0.572218\pi\)
−0.224939 + 0.974373i \(0.572218\pi\)
\(674\) −36.3355 −1.39959
\(675\) −7.63101 −0.293718
\(676\) −29.2213 −1.12390
\(677\) −37.4911 −1.44090 −0.720450 0.693507i \(-0.756065\pi\)
−0.720450 + 0.693507i \(0.756065\pi\)
\(678\) 6.87246 0.263935
\(679\) 11.8554 0.454969
\(680\) 53.6523 2.05747
\(681\) −66.0798 −2.53218
\(682\) −100.173 −3.83582
\(683\) 45.8571 1.75467 0.877337 0.479874i \(-0.159318\pi\)
0.877337 + 0.479874i \(0.159318\pi\)
\(684\) 69.6326 2.66247
\(685\) 21.4627 0.820048
\(686\) −44.7906 −1.71011
\(687\) −19.0308 −0.726070
\(688\) 14.8331 0.565505
\(689\) 28.0312 1.06790
\(690\) −154.531 −5.88289
\(691\) 18.9082 0.719304 0.359652 0.933087i \(-0.382895\pi\)
0.359652 + 0.933087i \(0.382895\pi\)
\(692\) −77.0539 −2.92915
\(693\) 105.714 4.01574
\(694\) −66.8927 −2.53921
\(695\) 8.23939 0.312538
\(696\) 109.785 4.16141
\(697\) 8.98649 0.340388
\(698\) −1.19593 −0.0452667
\(699\) −44.2378 −1.67323
\(700\) −3.90963 −0.147770
\(701\) 23.9743 0.905497 0.452749 0.891638i \(-0.350443\pi\)
0.452749 + 0.891638i \(0.350443\pi\)
\(702\) 89.2208 3.36742
\(703\) 22.9772 0.866600
\(704\) 60.4772 2.27932
\(705\) −15.9984 −0.602536
\(706\) 67.3047 2.53304
\(707\) −22.3080 −0.838980
\(708\) −4.48013 −0.168374
\(709\) −9.18817 −0.345069 −0.172534 0.985003i \(-0.555196\pi\)
−0.172534 + 0.985003i \(0.555196\pi\)
\(710\) 25.2693 0.948341
\(711\) 4.56105 0.171053
\(712\) −4.63557 −0.173725
\(713\) −71.5886 −2.68101
\(714\) −130.275 −4.87543
\(715\) 25.3223 0.946999
\(716\) 7.88957 0.294847
\(717\) −66.0697 −2.46742
\(718\) 4.76089 0.177675
\(719\) −31.2302 −1.16469 −0.582345 0.812942i \(-0.697865\pi\)
−0.582345 + 0.812942i \(0.697865\pi\)
\(720\) −25.4292 −0.947691
\(721\) 37.0672 1.38046
\(722\) 31.0307 1.15484
\(723\) −7.08080 −0.263338
\(724\) 41.3372 1.53629
\(725\) 4.00318 0.148674
\(726\) 111.591 4.14152
\(727\) −50.7900 −1.88370 −0.941849 0.336037i \(-0.890913\pi\)
−0.941849 + 0.336037i \(0.890913\pi\)
\(728\) 19.7007 0.730158
\(729\) 104.528 3.87140
\(730\) −3.42318 −0.126698
\(731\) 72.4530 2.67977
\(732\) −86.2414 −3.18758
\(733\) 35.8726 1.32498 0.662492 0.749069i \(-0.269499\pi\)
0.662492 + 0.749069i \(0.269499\pi\)
\(734\) 39.8658 1.47147
\(735\) −3.56094 −0.131347
\(736\) 33.7215 1.24299
\(737\) −18.2407 −0.671905
\(738\) −26.8659 −0.988946
\(739\) 7.15515 0.263206 0.131603 0.991302i \(-0.457988\pi\)
0.131603 + 0.991302i \(0.457988\pi\)
\(740\) −78.2698 −2.87725
\(741\) −17.4549 −0.641223
\(742\) 77.7903 2.85577
\(743\) 31.1184 1.14163 0.570813 0.821080i \(-0.306628\pi\)
0.570813 + 0.821080i \(0.306628\pi\)
\(744\) −101.374 −3.71655
\(745\) 9.76937 0.357922
\(746\) 17.3948 0.636870
\(747\) 79.5012 2.90880
\(748\) −114.094 −4.17169
\(749\) −2.90114 −0.106005
\(750\) 83.7760 3.05907
\(751\) −1.45272 −0.0530107 −0.0265053 0.999649i \(-0.508438\pi\)
−0.0265053 + 0.999649i \(0.508438\pi\)
\(752\) −2.71156 −0.0988803
\(753\) 32.6935 1.19142
\(754\) −46.8047 −1.70453
\(755\) −13.8925 −0.505601
\(756\) 157.806 5.73933
\(757\) −9.78833 −0.355763 −0.177882 0.984052i \(-0.556924\pi\)
−0.177882 + 0.984052i \(0.556924\pi\)
\(758\) 28.3767 1.03069
\(759\) 141.629 5.14080
\(760\) 19.9493 0.723638
\(761\) −3.00244 −0.108838 −0.0544192 0.998518i \(-0.517331\pi\)
−0.0544192 + 0.998518i \(0.517331\pi\)
\(762\) 32.8864 1.19135
\(763\) 21.2272 0.768477
\(764\) 44.2770 1.60189
\(765\) −124.211 −4.49085
\(766\) 26.0519 0.941292
\(767\) 0.823186 0.0297235
\(768\) 78.9603 2.84924
\(769\) −9.23066 −0.332866 −0.166433 0.986053i \(-0.553225\pi\)
−0.166433 + 0.986053i \(0.553225\pi\)
\(770\) 70.2725 2.53245
\(771\) −67.8500 −2.44356
\(772\) −17.5834 −0.632841
\(773\) 9.33847 0.335881 0.167941 0.985797i \(-0.446288\pi\)
0.167941 + 0.985797i \(0.446288\pi\)
\(774\) −216.604 −7.78568
\(775\) −3.69647 −0.132781
\(776\) 16.4862 0.591819
\(777\) 81.9086 2.93845
\(778\) 57.0857 2.04662
\(779\) 3.34141 0.119718
\(780\) 59.4587 2.12896
\(781\) −23.1595 −0.828713
\(782\) −127.933 −4.57488
\(783\) −161.582 −5.77446
\(784\) −0.603540 −0.0215550
\(785\) 32.3567 1.15486
\(786\) 46.0669 1.64315
\(787\) 15.9068 0.567015 0.283507 0.958970i \(-0.408502\pi\)
0.283507 + 0.958970i \(0.408502\pi\)
\(788\) −47.1193 −1.67856
\(789\) −42.8278 −1.52471
\(790\) 3.03192 0.107871
\(791\) −2.23345 −0.0794122
\(792\) 147.006 5.22363
\(793\) 15.8461 0.562713
\(794\) 0.966554 0.0343017
\(795\) 101.186 3.58870
\(796\) −75.5799 −2.67886
\(797\) −50.1374 −1.77596 −0.887979 0.459884i \(-0.847891\pi\)
−0.887979 + 0.459884i \(0.847891\pi\)
\(798\) −48.4397 −1.71475
\(799\) −13.2448 −0.468567
\(800\) 1.74121 0.0615610
\(801\) 10.7318 0.379190
\(802\) 33.7755 1.19265
\(803\) 3.13737 0.110715
\(804\) −42.8307 −1.51052
\(805\) 50.2202 1.77003
\(806\) 43.2186 1.52231
\(807\) 22.2893 0.784622
\(808\) −31.0216 −1.09134
\(809\) −19.0548 −0.669933 −0.334966 0.942230i \(-0.608725\pi\)
−0.334966 + 0.942230i \(0.608725\pi\)
\(810\) 186.801 6.56352
\(811\) −37.9004 −1.33086 −0.665431 0.746460i \(-0.731752\pi\)
−0.665431 + 0.746460i \(0.731752\pi\)
\(812\) −82.7839 −2.90515
\(813\) −47.0757 −1.65102
\(814\) 112.553 3.94498
\(815\) −24.4192 −0.855366
\(816\) −28.7209 −1.00543
\(817\) 26.9399 0.942508
\(818\) −53.9108 −1.88495
\(819\) −45.6092 −1.59372
\(820\) −11.3822 −0.397484
\(821\) −28.7539 −1.00352 −0.501759 0.865007i \(-0.667314\pi\)
−0.501759 + 0.865007i \(0.667314\pi\)
\(822\) −72.4705 −2.52770
\(823\) −31.1456 −1.08567 −0.542834 0.839840i \(-0.682649\pi\)
−0.542834 + 0.839840i \(0.682649\pi\)
\(824\) 51.5458 1.79568
\(825\) 7.31298 0.254605
\(826\) 2.28445 0.0794861
\(827\) −36.7521 −1.27800 −0.638998 0.769209i \(-0.720651\pi\)
−0.638998 + 0.769209i \(0.720651\pi\)
\(828\) 243.762 8.47132
\(829\) −2.69920 −0.0937471 −0.0468736 0.998901i \(-0.514926\pi\)
−0.0468736 + 0.998901i \(0.514926\pi\)
\(830\) 52.8478 1.83437
\(831\) −32.2695 −1.11941
\(832\) −26.0923 −0.904587
\(833\) −2.94803 −0.102143
\(834\) −27.8209 −0.963359
\(835\) 16.1025 0.557249
\(836\) −42.4231 −1.46723
\(837\) 149.202 5.15716
\(838\) −60.8720 −2.10279
\(839\) −38.7361 −1.33732 −0.668659 0.743569i \(-0.733131\pi\)
−0.668659 + 0.743569i \(0.733131\pi\)
\(840\) 71.1150 2.45370
\(841\) 55.7648 1.92292
\(842\) 78.0890 2.69112
\(843\) 0.983747 0.0338820
\(844\) −19.5032 −0.671329
\(845\) 19.3814 0.666742
\(846\) 39.5964 1.36135
\(847\) −36.2653 −1.24609
\(848\) 17.1499 0.588931
\(849\) 53.8557 1.84832
\(850\) −6.60581 −0.226577
\(851\) 80.4360 2.75731
\(852\) −54.3805 −1.86304
\(853\) −9.27382 −0.317529 −0.158765 0.987316i \(-0.550751\pi\)
−0.158765 + 0.987316i \(0.550751\pi\)
\(854\) 43.9751 1.50480
\(855\) −46.1847 −1.57948
\(856\) −4.03433 −0.137891
\(857\) 54.4467 1.85986 0.929932 0.367731i \(-0.119865\pi\)
0.929932 + 0.367731i \(0.119865\pi\)
\(858\) −85.5025 −2.91901
\(859\) −35.5638 −1.21342 −0.606710 0.794923i \(-0.707511\pi\)
−0.606710 + 0.794923i \(0.707511\pi\)
\(860\) −91.7685 −3.12928
\(861\) 11.9114 0.405939
\(862\) −67.0661 −2.28428
\(863\) −17.4543 −0.594152 −0.297076 0.954854i \(-0.596011\pi\)
−0.297076 + 0.954854i \(0.596011\pi\)
\(864\) −70.2808 −2.39100
\(865\) 51.1070 1.73769
\(866\) −66.8552 −2.27183
\(867\) −83.3057 −2.82921
\(868\) 76.4412 2.59458
\(869\) −2.77878 −0.0942636
\(870\) −168.954 −5.72808
\(871\) 7.86978 0.266657
\(872\) 29.5186 0.999627
\(873\) −38.1672 −1.29176
\(874\) −47.5688 −1.60904
\(875\) −27.2260 −0.920405
\(876\) 7.36680 0.248901
\(877\) −48.3978 −1.63428 −0.817139 0.576441i \(-0.804441\pi\)
−0.817139 + 0.576441i \(0.804441\pi\)
\(878\) 35.3210 1.19203
\(879\) −48.2566 −1.62765
\(880\) 15.4925 0.522253
\(881\) −5.75008 −0.193725 −0.0968626 0.995298i \(-0.530881\pi\)
−0.0968626 + 0.995298i \(0.530881\pi\)
\(882\) 8.81338 0.296762
\(883\) −6.01517 −0.202427 −0.101213 0.994865i \(-0.532272\pi\)
−0.101213 + 0.994865i \(0.532272\pi\)
\(884\) 49.2247 1.65561
\(885\) 2.97150 0.0998860
\(886\) −2.45301 −0.0824105
\(887\) 9.87434 0.331548 0.165774 0.986164i \(-0.446988\pi\)
0.165774 + 0.986164i \(0.446988\pi\)
\(888\) 113.902 3.82231
\(889\) −10.6876 −0.358450
\(890\) 7.13390 0.239129
\(891\) −171.205 −5.73557
\(892\) 84.2381 2.82050
\(893\) −4.92475 −0.164800
\(894\) −32.9870 −1.10325
\(895\) −5.23286 −0.174915
\(896\) −51.9208 −1.73455
\(897\) −61.1043 −2.04021
\(898\) 21.4362 0.715336
\(899\) −78.2703 −2.61046
\(900\) 12.5866 0.419554
\(901\) 83.7700 2.79078
\(902\) 16.3678 0.544988
\(903\) 96.0349 3.19584
\(904\) −3.10584 −0.103299
\(905\) −27.4175 −0.911387
\(906\) 46.9092 1.55845
\(907\) 31.5257 1.04679 0.523397 0.852089i \(-0.324664\pi\)
0.523397 + 0.852089i \(0.324664\pi\)
\(908\) 69.2904 2.29948
\(909\) 71.8183 2.38206
\(910\) −30.3184 −1.00504
\(911\) −52.7733 −1.74846 −0.874229 0.485513i \(-0.838633\pi\)
−0.874229 + 0.485513i \(0.838633\pi\)
\(912\) −10.6792 −0.353623
\(913\) −48.4354 −1.60298
\(914\) 47.4588 1.56980
\(915\) 57.2008 1.89100
\(916\) 19.9554 0.659346
\(917\) −14.9710 −0.494387
\(918\) 266.632 8.80017
\(919\) 47.8561 1.57863 0.789314 0.613990i \(-0.210437\pi\)
0.789314 + 0.613990i \(0.210437\pi\)
\(920\) 69.8364 2.30244
\(921\) −114.290 −3.76597
\(922\) 13.1264 0.432295
\(923\) 9.99195 0.328889
\(924\) −151.229 −4.97507
\(925\) 4.15330 0.136560
\(926\) 52.1728 1.71450
\(927\) −119.334 −3.91944
\(928\) 36.8689 1.21028
\(929\) 8.70839 0.285713 0.142857 0.989743i \(-0.454371\pi\)
0.142857 + 0.989743i \(0.454371\pi\)
\(930\) 156.009 5.11574
\(931\) −1.09615 −0.0359250
\(932\) 46.3872 1.51946
\(933\) 19.2141 0.629041
\(934\) −11.7354 −0.383993
\(935\) 75.6743 2.47481
\(936\) −63.4243 −2.07309
\(937\) −42.2895 −1.38154 −0.690768 0.723076i \(-0.742728\pi\)
−0.690768 + 0.723076i \(0.742728\pi\)
\(938\) 21.8396 0.713090
\(939\) −104.945 −3.42476
\(940\) 16.7757 0.547164
\(941\) −47.8757 −1.56070 −0.780351 0.625341i \(-0.784960\pi\)
−0.780351 + 0.625341i \(0.784960\pi\)
\(942\) −109.255 −3.55971
\(943\) 11.6972 0.380915
\(944\) 0.503637 0.0163920
\(945\) −104.667 −3.40481
\(946\) 131.964 4.29053
\(947\) −4.00507 −0.130147 −0.0650737 0.997880i \(-0.520728\pi\)
−0.0650737 + 0.997880i \(0.520728\pi\)
\(948\) −6.52480 −0.211916
\(949\) −1.35359 −0.0439393
\(950\) −2.45621 −0.0796899
\(951\) 15.8759 0.514813
\(952\) 58.8747 1.90814
\(953\) −1.22460 −0.0396686 −0.0198343 0.999803i \(-0.506314\pi\)
−0.0198343 + 0.999803i \(0.506314\pi\)
\(954\) −250.437 −8.10820
\(955\) −29.3673 −0.950304
\(956\) 69.2798 2.24067
\(957\) 154.848 5.00551
\(958\) 32.8499 1.06133
\(959\) 23.5518 0.760528
\(960\) −94.1870 −3.03987
\(961\) 41.2733 1.33140
\(962\) −48.5599 −1.56563
\(963\) 9.33990 0.300974
\(964\) 7.42483 0.239138
\(965\) 11.6624 0.375427
\(966\) −169.572 −5.45590
\(967\) −48.2682 −1.55220 −0.776101 0.630609i \(-0.782805\pi\)
−0.776101 + 0.630609i \(0.782805\pi\)
\(968\) −50.4306 −1.62090
\(969\) −52.1632 −1.67572
\(970\) −25.3713 −0.814625
\(971\) −16.8708 −0.541408 −0.270704 0.962663i \(-0.587257\pi\)
−0.270704 + 0.962663i \(0.587257\pi\)
\(972\) −216.943 −6.95844
\(973\) 9.04138 0.289853
\(974\) −15.4446 −0.494877
\(975\) −3.15511 −0.101044
\(976\) 9.69490 0.310326
\(977\) −15.5000 −0.495888 −0.247944 0.968774i \(-0.579755\pi\)
−0.247944 + 0.968774i \(0.579755\pi\)
\(978\) 82.4532 2.63656
\(979\) −6.53827 −0.208964
\(980\) 3.73395 0.119277
\(981\) −68.3386 −2.18189
\(982\) −89.6457 −2.86071
\(983\) −14.6282 −0.466567 −0.233284 0.972409i \(-0.574947\pi\)
−0.233284 + 0.972409i \(0.574947\pi\)
\(984\) 16.5640 0.528042
\(985\) 31.2525 0.995787
\(986\) −139.874 −4.45448
\(987\) −17.5557 −0.558803
\(988\) 18.3030 0.582296
\(989\) 94.3083 2.99883
\(990\) −226.235 −7.19021
\(991\) 50.5842 1.60686 0.803430 0.595399i \(-0.203006\pi\)
0.803430 + 0.595399i \(0.203006\pi\)
\(992\) −34.0441 −1.08090
\(993\) −2.45292 −0.0778410
\(994\) 27.7289 0.879509
\(995\) 50.1294 1.58921
\(996\) −113.730 −3.60368
\(997\) −7.54852 −0.239064 −0.119532 0.992830i \(-0.538139\pi\)
−0.119532 + 0.992830i \(0.538139\pi\)
\(998\) 14.9384 0.472866
\(999\) −167.641 −5.30392
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 4003.2.a.c.1.17 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.17 179 1.1 even 1 trivial