Properties

Label 4003.2.a.c.1.11
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 1.11
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53975 q^{2} -3.24477 q^{3} +4.45032 q^{4} +3.59171 q^{5} +8.24090 q^{6} +4.74281 q^{7} -6.22319 q^{8} +7.52854 q^{9} +O(q^{10})\) \(q-2.53975 q^{2} -3.24477 q^{3} +4.45032 q^{4} +3.59171 q^{5} +8.24090 q^{6} +4.74281 q^{7} -6.22319 q^{8} +7.52854 q^{9} -9.12202 q^{10} +4.76337 q^{11} -14.4403 q^{12} +3.36742 q^{13} -12.0455 q^{14} -11.6543 q^{15} +6.90469 q^{16} +5.35637 q^{17} -19.1206 q^{18} -2.01798 q^{19} +15.9842 q^{20} -15.3893 q^{21} -12.0978 q^{22} -2.21388 q^{23} +20.1928 q^{24} +7.90035 q^{25} -8.55240 q^{26} -14.6941 q^{27} +21.1070 q^{28} -3.92084 q^{29} +29.5989 q^{30} -6.33401 q^{31} -5.08979 q^{32} -15.4560 q^{33} -13.6038 q^{34} +17.0348 q^{35} +33.5044 q^{36} +9.40711 q^{37} +5.12516 q^{38} -10.9265 q^{39} -22.3519 q^{40} +0.410884 q^{41} +39.0850 q^{42} -10.6813 q^{43} +21.1985 q^{44} +27.0403 q^{45} +5.62270 q^{46} -2.33990 q^{47} -22.4041 q^{48} +15.4942 q^{49} -20.0649 q^{50} -17.3802 q^{51} +14.9861 q^{52} +12.5748 q^{53} +37.3192 q^{54} +17.1086 q^{55} -29.5154 q^{56} +6.54789 q^{57} +9.95796 q^{58} -6.43629 q^{59} -51.8652 q^{60} -9.91875 q^{61} +16.0868 q^{62} +35.7064 q^{63} -0.882591 q^{64} +12.0948 q^{65} +39.2544 q^{66} +13.7899 q^{67} +23.8376 q^{68} +7.18354 q^{69} -43.2640 q^{70} +10.7550 q^{71} -46.8515 q^{72} -3.56896 q^{73} -23.8917 q^{74} -25.6348 q^{75} -8.98065 q^{76} +22.5917 q^{77} +27.7506 q^{78} -1.58288 q^{79} +24.7996 q^{80} +25.0933 q^{81} -1.04354 q^{82} +1.22307 q^{83} -68.4874 q^{84} +19.2385 q^{85} +27.1278 q^{86} +12.7222 q^{87} -29.6433 q^{88} -3.37179 q^{89} -68.6755 q^{90} +15.9710 q^{91} -9.85248 q^{92} +20.5524 q^{93} +5.94275 q^{94} -7.24799 q^{95} +16.5152 q^{96} +2.68050 q^{97} -39.3514 q^{98} +35.8612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53975 −1.79587 −0.897936 0.440125i \(-0.854934\pi\)
−0.897936 + 0.440125i \(0.854934\pi\)
\(3\) −3.24477 −1.87337 −0.936685 0.350174i \(-0.886123\pi\)
−0.936685 + 0.350174i \(0.886123\pi\)
\(4\) 4.45032 2.22516
\(5\) 3.59171 1.60626 0.803130 0.595804i \(-0.203167\pi\)
0.803130 + 0.595804i \(0.203167\pi\)
\(6\) 8.24090 3.36433
\(7\) 4.74281 1.79261 0.896306 0.443436i \(-0.146241\pi\)
0.896306 + 0.443436i \(0.146241\pi\)
\(8\) −6.22319 −2.20023
\(9\) 7.52854 2.50951
\(10\) −9.12202 −2.88464
\(11\) 4.76337 1.43621 0.718105 0.695935i \(-0.245010\pi\)
0.718105 + 0.695935i \(0.245010\pi\)
\(12\) −14.4403 −4.16854
\(13\) 3.36742 0.933954 0.466977 0.884269i \(-0.345343\pi\)
0.466977 + 0.884269i \(0.345343\pi\)
\(14\) −12.0455 −3.21930
\(15\) −11.6543 −3.00912
\(16\) 6.90469 1.72617
\(17\) 5.35637 1.29911 0.649555 0.760314i \(-0.274955\pi\)
0.649555 + 0.760314i \(0.274955\pi\)
\(18\) −19.1206 −4.50677
\(19\) −2.01798 −0.462957 −0.231478 0.972840i \(-0.574356\pi\)
−0.231478 + 0.972840i \(0.574356\pi\)
\(20\) 15.9842 3.57418
\(21\) −15.3893 −3.35823
\(22\) −12.0978 −2.57925
\(23\) −2.21388 −0.461627 −0.230813 0.972998i \(-0.574139\pi\)
−0.230813 + 0.972998i \(0.574139\pi\)
\(24\) 20.1928 4.12184
\(25\) 7.90035 1.58007
\(26\) −8.55240 −1.67726
\(27\) −14.6941 −2.82788
\(28\) 21.1070 3.98885
\(29\) −3.92084 −0.728083 −0.364041 0.931383i \(-0.618603\pi\)
−0.364041 + 0.931383i \(0.618603\pi\)
\(30\) 29.5989 5.40399
\(31\) −6.33401 −1.13762 −0.568811 0.822468i \(-0.692596\pi\)
−0.568811 + 0.822468i \(0.692596\pi\)
\(32\) −5.08979 −0.899757
\(33\) −15.4560 −2.69055
\(34\) −13.6038 −2.33304
\(35\) 17.0348 2.87940
\(36\) 33.5044 5.58407
\(37\) 9.40711 1.54652 0.773260 0.634089i \(-0.218625\pi\)
0.773260 + 0.634089i \(0.218625\pi\)
\(38\) 5.12516 0.831411
\(39\) −10.9265 −1.74964
\(40\) −22.3519 −3.53414
\(41\) 0.410884 0.0641693 0.0320847 0.999485i \(-0.489785\pi\)
0.0320847 + 0.999485i \(0.489785\pi\)
\(42\) 39.0850 6.03095
\(43\) −10.6813 −1.62888 −0.814441 0.580246i \(-0.802956\pi\)
−0.814441 + 0.580246i \(0.802956\pi\)
\(44\) 21.1985 3.19579
\(45\) 27.0403 4.03093
\(46\) 5.62270 0.829023
\(47\) −2.33990 −0.341309 −0.170655 0.985331i \(-0.554588\pi\)
−0.170655 + 0.985331i \(0.554588\pi\)
\(48\) −22.4041 −3.23376
\(49\) 15.4942 2.21346
\(50\) −20.0649 −2.83760
\(51\) −17.3802 −2.43371
\(52\) 14.9861 2.07820
\(53\) 12.5748 1.72728 0.863642 0.504105i \(-0.168177\pi\)
0.863642 + 0.504105i \(0.168177\pi\)
\(54\) 37.3192 5.07851
\(55\) 17.1086 2.30693
\(56\) −29.5154 −3.94416
\(57\) 6.54789 0.867289
\(58\) 9.95796 1.30754
\(59\) −6.43629 −0.837934 −0.418967 0.908001i \(-0.637608\pi\)
−0.418967 + 0.908001i \(0.637608\pi\)
\(60\) −51.8652 −6.69576
\(61\) −9.91875 −1.26997 −0.634983 0.772526i \(-0.718993\pi\)
−0.634983 + 0.772526i \(0.718993\pi\)
\(62\) 16.0868 2.04302
\(63\) 35.7064 4.49858
\(64\) −0.882591 −0.110324
\(65\) 12.0948 1.50017
\(66\) 39.2544 4.83189
\(67\) 13.7899 1.68470 0.842350 0.538931i \(-0.181172\pi\)
0.842350 + 0.538931i \(0.181172\pi\)
\(68\) 23.8376 2.89073
\(69\) 7.18354 0.864797
\(70\) −43.2640 −5.17104
\(71\) 10.7550 1.27639 0.638193 0.769877i \(-0.279682\pi\)
0.638193 + 0.769877i \(0.279682\pi\)
\(72\) −46.8515 −5.52150
\(73\) −3.56896 −0.417715 −0.208858 0.977946i \(-0.566975\pi\)
−0.208858 + 0.977946i \(0.566975\pi\)
\(74\) −23.8917 −2.77735
\(75\) −25.6348 −2.96005
\(76\) −8.98065 −1.03015
\(77\) 22.5917 2.57457
\(78\) 27.7506 3.14213
\(79\) −1.58288 −0.178088 −0.0890442 0.996028i \(-0.528381\pi\)
−0.0890442 + 0.996028i \(0.528381\pi\)
\(80\) 24.7996 2.77268
\(81\) 25.0933 2.78814
\(82\) −1.04354 −0.115240
\(83\) 1.22307 0.134249 0.0671244 0.997745i \(-0.478618\pi\)
0.0671244 + 0.997745i \(0.478618\pi\)
\(84\) −68.4874 −7.47258
\(85\) 19.2385 2.08671
\(86\) 27.1278 2.92526
\(87\) 12.7222 1.36397
\(88\) −29.6433 −3.15999
\(89\) −3.37179 −0.357409 −0.178705 0.983903i \(-0.557191\pi\)
−0.178705 + 0.983903i \(0.557191\pi\)
\(90\) −68.6755 −7.23904
\(91\) 15.9710 1.67422
\(92\) −9.85248 −1.02719
\(93\) 20.5524 2.13119
\(94\) 5.94275 0.612948
\(95\) −7.24799 −0.743628
\(96\) 16.5152 1.68558
\(97\) 2.68050 0.272164 0.136082 0.990698i \(-0.456549\pi\)
0.136082 + 0.990698i \(0.456549\pi\)
\(98\) −39.3514 −3.97509
\(99\) 35.8612 3.60419
\(100\) 35.1591 3.51591
\(101\) −9.82006 −0.977133 −0.488566 0.872527i \(-0.662480\pi\)
−0.488566 + 0.872527i \(0.662480\pi\)
\(102\) 44.1413 4.37064
\(103\) −7.58336 −0.747211 −0.373605 0.927588i \(-0.621879\pi\)
−0.373605 + 0.927588i \(0.621879\pi\)
\(104\) −20.9561 −2.05491
\(105\) −55.2739 −5.39418
\(106\) −31.9369 −3.10198
\(107\) 15.0921 1.45901 0.729506 0.683975i \(-0.239750\pi\)
0.729506 + 0.683975i \(0.239750\pi\)
\(108\) −65.3933 −6.29247
\(109\) −12.7695 −1.22310 −0.611549 0.791206i \(-0.709453\pi\)
−0.611549 + 0.791206i \(0.709453\pi\)
\(110\) −43.4516 −4.14294
\(111\) −30.5239 −2.89720
\(112\) 32.7476 3.09436
\(113\) −8.09113 −0.761149 −0.380575 0.924750i \(-0.624274\pi\)
−0.380575 + 0.924750i \(0.624274\pi\)
\(114\) −16.6300 −1.55754
\(115\) −7.95162 −0.741492
\(116\) −17.4490 −1.62010
\(117\) 25.3518 2.34377
\(118\) 16.3466 1.50482
\(119\) 25.4042 2.32880
\(120\) 72.5267 6.62075
\(121\) 11.6897 1.06270
\(122\) 25.1911 2.28070
\(123\) −1.33323 −0.120213
\(124\) −28.1884 −2.53139
\(125\) 10.4172 0.931742
\(126\) −90.6853 −8.07889
\(127\) −15.6124 −1.38538 −0.692689 0.721236i \(-0.743574\pi\)
−0.692689 + 0.721236i \(0.743574\pi\)
\(128\) 12.4211 1.09788
\(129\) 34.6584 3.05150
\(130\) −30.7177 −2.69412
\(131\) 11.1016 0.969950 0.484975 0.874528i \(-0.338829\pi\)
0.484975 + 0.874528i \(0.338829\pi\)
\(132\) −68.7843 −5.98690
\(133\) −9.57089 −0.829902
\(134\) −35.0228 −3.02551
\(135\) −52.7768 −4.54230
\(136\) −33.3337 −2.85834
\(137\) 12.8982 1.10197 0.550984 0.834516i \(-0.314252\pi\)
0.550984 + 0.834516i \(0.314252\pi\)
\(138\) −18.2444 −1.55307
\(139\) −7.25627 −0.615469 −0.307735 0.951472i \(-0.599571\pi\)
−0.307735 + 0.951472i \(0.599571\pi\)
\(140\) 75.8101 6.40712
\(141\) 7.59243 0.639398
\(142\) −27.3150 −2.29223
\(143\) 16.0403 1.34135
\(144\) 51.9822 4.33185
\(145\) −14.0825 −1.16949
\(146\) 9.06426 0.750163
\(147\) −50.2752 −4.14663
\(148\) 41.8646 3.44125
\(149\) −9.21475 −0.754902 −0.377451 0.926030i \(-0.623199\pi\)
−0.377451 + 0.926030i \(0.623199\pi\)
\(150\) 65.1060 5.31588
\(151\) 3.45983 0.281557 0.140778 0.990041i \(-0.455040\pi\)
0.140778 + 0.990041i \(0.455040\pi\)
\(152\) 12.5583 1.01861
\(153\) 40.3257 3.26014
\(154\) −57.3773 −4.62360
\(155\) −22.7499 −1.82732
\(156\) −48.6264 −3.89323
\(157\) 22.7776 1.81785 0.908926 0.416957i \(-0.136903\pi\)
0.908926 + 0.416957i \(0.136903\pi\)
\(158\) 4.02013 0.319824
\(159\) −40.8024 −3.23584
\(160\) −18.2810 −1.44524
\(161\) −10.5000 −0.827518
\(162\) −63.7306 −5.00715
\(163\) 9.31838 0.729872 0.364936 0.931033i \(-0.381091\pi\)
0.364936 + 0.931033i \(0.381091\pi\)
\(164\) 1.82856 0.142787
\(165\) −55.5136 −4.32172
\(166\) −3.10628 −0.241094
\(167\) −6.63149 −0.513160 −0.256580 0.966523i \(-0.582596\pi\)
−0.256580 + 0.966523i \(0.582596\pi\)
\(168\) 95.7706 7.38886
\(169\) −1.66048 −0.127729
\(170\) −48.8610 −3.74746
\(171\) −15.1924 −1.16180
\(172\) −47.5351 −3.62452
\(173\) −16.0378 −1.21933 −0.609667 0.792658i \(-0.708697\pi\)
−0.609667 + 0.792658i \(0.708697\pi\)
\(174\) −32.3113 −2.44951
\(175\) 37.4698 2.83245
\(176\) 32.8896 2.47915
\(177\) 20.8843 1.56976
\(178\) 8.56350 0.641862
\(179\) 20.3352 1.51992 0.759960 0.649969i \(-0.225218\pi\)
0.759960 + 0.649969i \(0.225218\pi\)
\(180\) 120.338 8.96946
\(181\) −9.42876 −0.700835 −0.350417 0.936594i \(-0.613960\pi\)
−0.350417 + 0.936594i \(0.613960\pi\)
\(182\) −40.5624 −3.00668
\(183\) 32.1841 2.37912
\(184\) 13.7774 1.01568
\(185\) 33.7876 2.48411
\(186\) −52.1980 −3.82734
\(187\) 25.5144 1.86580
\(188\) −10.4133 −0.759467
\(189\) −69.6912 −5.06929
\(190\) 18.4081 1.33546
\(191\) −3.26886 −0.236527 −0.118263 0.992982i \(-0.537733\pi\)
−0.118263 + 0.992982i \(0.537733\pi\)
\(192\) 2.86380 0.206677
\(193\) −9.31156 −0.670261 −0.335130 0.942172i \(-0.608780\pi\)
−0.335130 + 0.942172i \(0.608780\pi\)
\(194\) −6.80780 −0.488771
\(195\) −39.2448 −2.81038
\(196\) 68.9542 4.92530
\(197\) 14.2685 1.01659 0.508296 0.861183i \(-0.330276\pi\)
0.508296 + 0.861183i \(0.330276\pi\)
\(198\) −91.0784 −6.47266
\(199\) −5.91968 −0.419635 −0.209817 0.977741i \(-0.567287\pi\)
−0.209817 + 0.977741i \(0.567287\pi\)
\(200\) −49.1653 −3.47651
\(201\) −44.7449 −3.15607
\(202\) 24.9405 1.75481
\(203\) −18.5958 −1.30517
\(204\) −77.3474 −5.41540
\(205\) 1.47577 0.103073
\(206\) 19.2598 1.34190
\(207\) −16.6673 −1.15846
\(208\) 23.2510 1.61217
\(209\) −9.61239 −0.664903
\(210\) 140.382 9.68726
\(211\) 5.48689 0.377733 0.188866 0.982003i \(-0.439519\pi\)
0.188866 + 0.982003i \(0.439519\pi\)
\(212\) 55.9620 3.84348
\(213\) −34.8976 −2.39114
\(214\) −38.3302 −2.62020
\(215\) −38.3641 −2.61641
\(216\) 91.4440 6.22198
\(217\) −30.0410 −2.03932
\(218\) 32.4314 2.19653
\(219\) 11.5805 0.782535
\(220\) 76.1388 5.13328
\(221\) 18.0372 1.21331
\(222\) 77.5231 5.20301
\(223\) −14.9949 −1.00414 −0.502068 0.864828i \(-0.667427\pi\)
−0.502068 + 0.864828i \(0.667427\pi\)
\(224\) −24.1399 −1.61292
\(225\) 59.4781 3.96521
\(226\) 20.5494 1.36693
\(227\) −10.9200 −0.724783 −0.362391 0.932026i \(-0.618040\pi\)
−0.362391 + 0.932026i \(0.618040\pi\)
\(228\) 29.1402 1.92985
\(229\) −6.08968 −0.402418 −0.201209 0.979548i \(-0.564487\pi\)
−0.201209 + 0.979548i \(0.564487\pi\)
\(230\) 20.1951 1.33163
\(231\) −73.3050 −4.82312
\(232\) 24.4002 1.60195
\(233\) 2.71107 0.177608 0.0888041 0.996049i \(-0.471696\pi\)
0.0888041 + 0.996049i \(0.471696\pi\)
\(234\) −64.3871 −4.20911
\(235\) −8.40422 −0.548231
\(236\) −28.6436 −1.86454
\(237\) 5.13610 0.333625
\(238\) −64.5203 −4.18223
\(239\) 5.81499 0.376140 0.188070 0.982156i \(-0.439777\pi\)
0.188070 + 0.982156i \(0.439777\pi\)
\(240\) −80.4691 −5.19426
\(241\) 10.9275 0.703904 0.351952 0.936018i \(-0.385518\pi\)
0.351952 + 0.936018i \(0.385518\pi\)
\(242\) −29.6889 −1.90847
\(243\) −37.3398 −2.39535
\(244\) −44.1416 −2.82588
\(245\) 55.6507 3.55539
\(246\) 3.38605 0.215887
\(247\) −6.79539 −0.432380
\(248\) 39.4177 2.50303
\(249\) −3.96857 −0.251498
\(250\) −26.4570 −1.67329
\(251\) 25.8279 1.63024 0.815121 0.579291i \(-0.196671\pi\)
0.815121 + 0.579291i \(0.196671\pi\)
\(252\) 158.905 10.0101
\(253\) −10.5455 −0.662993
\(254\) 39.6516 2.48796
\(255\) −62.4246 −3.90918
\(256\) −29.7814 −1.86134
\(257\) −8.60565 −0.536805 −0.268403 0.963307i \(-0.586496\pi\)
−0.268403 + 0.963307i \(0.586496\pi\)
\(258\) −88.0235 −5.48010
\(259\) 44.6161 2.77231
\(260\) 53.8256 3.33812
\(261\) −29.5182 −1.82713
\(262\) −28.1952 −1.74191
\(263\) 10.2459 0.631789 0.315895 0.948794i \(-0.397695\pi\)
0.315895 + 0.948794i \(0.397695\pi\)
\(264\) 96.1858 5.91983
\(265\) 45.1651 2.77447
\(266\) 24.3076 1.49040
\(267\) 10.9407 0.669560
\(268\) 61.3693 3.74872
\(269\) 16.7723 1.02262 0.511311 0.859396i \(-0.329160\pi\)
0.511311 + 0.859396i \(0.329160\pi\)
\(270\) 134.040 8.15740
\(271\) 18.1711 1.10382 0.551908 0.833905i \(-0.313900\pi\)
0.551908 + 0.833905i \(0.313900\pi\)
\(272\) 36.9841 2.24249
\(273\) −51.8223 −3.13643
\(274\) −32.7582 −1.97900
\(275\) 37.6323 2.26931
\(276\) 31.9691 1.92431
\(277\) 21.1181 1.26886 0.634432 0.772979i \(-0.281234\pi\)
0.634432 + 0.772979i \(0.281234\pi\)
\(278\) 18.4291 1.10530
\(279\) −47.6859 −2.85488
\(280\) −106.011 −6.33534
\(281\) 25.3073 1.50971 0.754855 0.655892i \(-0.227707\pi\)
0.754855 + 0.655892i \(0.227707\pi\)
\(282\) −19.2829 −1.14828
\(283\) −3.63388 −0.216012 −0.108006 0.994150i \(-0.534447\pi\)
−0.108006 + 0.994150i \(0.534447\pi\)
\(284\) 47.8632 2.84016
\(285\) 23.5181 1.39309
\(286\) −40.7382 −2.40890
\(287\) 1.94874 0.115031
\(288\) −38.3187 −2.25795
\(289\) 11.6907 0.687689
\(290\) 35.7660 2.10025
\(291\) −8.69762 −0.509863
\(292\) −15.8830 −0.929483
\(293\) 13.2491 0.774020 0.387010 0.922075i \(-0.373508\pi\)
0.387010 + 0.922075i \(0.373508\pi\)
\(294\) 127.686 7.44682
\(295\) −23.1173 −1.34594
\(296\) −58.5422 −3.40270
\(297\) −69.9933 −4.06142
\(298\) 23.4031 1.35571
\(299\) −7.45508 −0.431138
\(300\) −114.083 −6.58659
\(301\) −50.6593 −2.91995
\(302\) −8.78708 −0.505640
\(303\) 31.8639 1.83053
\(304\) −13.9335 −0.799143
\(305\) −35.6252 −2.03990
\(306\) −102.417 −5.85479
\(307\) −3.26910 −0.186578 −0.0932888 0.995639i \(-0.529738\pi\)
−0.0932888 + 0.995639i \(0.529738\pi\)
\(308\) 100.540 5.72882
\(309\) 24.6063 1.39980
\(310\) 57.7790 3.28163
\(311\) −11.3857 −0.645626 −0.322813 0.946463i \(-0.604628\pi\)
−0.322813 + 0.946463i \(0.604628\pi\)
\(312\) 67.9977 3.84961
\(313\) −3.94201 −0.222815 −0.111408 0.993775i \(-0.535536\pi\)
−0.111408 + 0.993775i \(0.535536\pi\)
\(314\) −57.8494 −3.26463
\(315\) 128.247 7.22589
\(316\) −7.04434 −0.396275
\(317\) 12.6385 0.709847 0.354924 0.934895i \(-0.384507\pi\)
0.354924 + 0.934895i \(0.384507\pi\)
\(318\) 103.628 5.81116
\(319\) −18.6764 −1.04568
\(320\) −3.17001 −0.177209
\(321\) −48.9705 −2.73327
\(322\) 26.6674 1.48612
\(323\) −10.8091 −0.601432
\(324\) 111.673 6.20406
\(325\) 26.6038 1.47571
\(326\) −23.6663 −1.31076
\(327\) 41.4342 2.29132
\(328\) −2.55701 −0.141187
\(329\) −11.0977 −0.611835
\(330\) 140.990 7.76127
\(331\) −34.4138 −1.89155 −0.945776 0.324821i \(-0.894696\pi\)
−0.945776 + 0.324821i \(0.894696\pi\)
\(332\) 5.44303 0.298725
\(333\) 70.8218 3.88101
\(334\) 16.8423 0.921571
\(335\) 49.5291 2.70607
\(336\) −106.258 −5.79688
\(337\) −11.9311 −0.649927 −0.324963 0.945727i \(-0.605352\pi\)
−0.324963 + 0.945727i \(0.605352\pi\)
\(338\) 4.21720 0.229385
\(339\) 26.2539 1.42591
\(340\) 85.6175 4.64326
\(341\) −30.1712 −1.63386
\(342\) 38.5850 2.08644
\(343\) 40.2864 2.17526
\(344\) 66.4717 3.58391
\(345\) 25.8012 1.38909
\(346\) 40.7320 2.18977
\(347\) −16.3853 −0.879611 −0.439805 0.898093i \(-0.644953\pi\)
−0.439805 + 0.898093i \(0.644953\pi\)
\(348\) 56.6180 3.03504
\(349\) −14.7671 −0.790465 −0.395233 0.918581i \(-0.629336\pi\)
−0.395233 + 0.918581i \(0.629336\pi\)
\(350\) −95.1639 −5.08672
\(351\) −49.4811 −2.64111
\(352\) −24.2446 −1.29224
\(353\) −10.5677 −0.562462 −0.281231 0.959640i \(-0.590743\pi\)
−0.281231 + 0.959640i \(0.590743\pi\)
\(354\) −53.0409 −2.81909
\(355\) 38.6288 2.05021
\(356\) −15.0055 −0.795292
\(357\) −82.4309 −4.36271
\(358\) −51.6462 −2.72958
\(359\) 0.0478943 0.00252776 0.00126388 0.999999i \(-0.499598\pi\)
0.00126388 + 0.999999i \(0.499598\pi\)
\(360\) −168.277 −8.86897
\(361\) −14.9278 −0.785671
\(362\) 23.9467 1.25861
\(363\) −37.9304 −1.99083
\(364\) 71.0761 3.72540
\(365\) −12.8187 −0.670959
\(366\) −81.7395 −4.27259
\(367\) −17.3593 −0.906146 −0.453073 0.891473i \(-0.649672\pi\)
−0.453073 + 0.891473i \(0.649672\pi\)
\(368\) −15.2862 −0.796847
\(369\) 3.09336 0.161034
\(370\) −85.8119 −4.46115
\(371\) 59.6400 3.09635
\(372\) 91.4648 4.74223
\(373\) −14.3286 −0.741907 −0.370954 0.928651i \(-0.620969\pi\)
−0.370954 + 0.928651i \(0.620969\pi\)
\(374\) −64.8001 −3.35073
\(375\) −33.8014 −1.74550
\(376\) 14.5616 0.750958
\(377\) −13.2031 −0.679996
\(378\) 176.998 9.10379
\(379\) 11.1668 0.573599 0.286800 0.957991i \(-0.407409\pi\)
0.286800 + 0.957991i \(0.407409\pi\)
\(380\) −32.2559 −1.65469
\(381\) 50.6587 2.59533
\(382\) 8.30208 0.424772
\(383\) 0.758264 0.0387455 0.0193727 0.999812i \(-0.493833\pi\)
0.0193727 + 0.999812i \(0.493833\pi\)
\(384\) −40.3038 −2.05674
\(385\) 81.1429 4.13542
\(386\) 23.6490 1.20370
\(387\) −80.4145 −4.08770
\(388\) 11.9291 0.605607
\(389\) 8.42979 0.427407 0.213704 0.976899i \(-0.431447\pi\)
0.213704 + 0.976899i \(0.431447\pi\)
\(390\) 99.6719 5.04708
\(391\) −11.8584 −0.599704
\(392\) −96.4234 −4.87012
\(393\) −36.0221 −1.81707
\(394\) −36.2385 −1.82567
\(395\) −5.68525 −0.286056
\(396\) 159.594 8.01989
\(397\) −10.2386 −0.513858 −0.256929 0.966430i \(-0.582711\pi\)
−0.256929 + 0.966430i \(0.582711\pi\)
\(398\) 15.0345 0.753611
\(399\) 31.0554 1.55471
\(400\) 54.5494 2.72747
\(401\) −17.7390 −0.885846 −0.442923 0.896560i \(-0.646058\pi\)
−0.442923 + 0.896560i \(0.646058\pi\)
\(402\) 113.641 5.66789
\(403\) −21.3293 −1.06249
\(404\) −43.7024 −2.17428
\(405\) 90.1277 4.47848
\(406\) 47.2287 2.34392
\(407\) 44.8096 2.22113
\(408\) 108.160 5.35473
\(409\) 25.5946 1.26557 0.632786 0.774326i \(-0.281911\pi\)
0.632786 + 0.774326i \(0.281911\pi\)
\(410\) −3.74810 −0.185105
\(411\) −41.8517 −2.06439
\(412\) −33.7484 −1.66266
\(413\) −30.5261 −1.50209
\(414\) 42.3308 2.08044
\(415\) 4.39289 0.215639
\(416\) −17.1395 −0.840332
\(417\) 23.5449 1.15300
\(418\) 24.4130 1.19408
\(419\) −22.1386 −1.08154 −0.540772 0.841169i \(-0.681868\pi\)
−0.540772 + 0.841169i \(0.681868\pi\)
\(420\) −245.986 −12.0029
\(421\) 0.347309 0.0169268 0.00846340 0.999964i \(-0.497306\pi\)
0.00846340 + 0.999964i \(0.497306\pi\)
\(422\) −13.9353 −0.678360
\(423\) −17.6160 −0.856520
\(424\) −78.2555 −3.80042
\(425\) 42.3172 2.05269
\(426\) 88.6310 4.29419
\(427\) −47.0427 −2.27656
\(428\) 67.1648 3.24653
\(429\) −52.0470 −2.51285
\(430\) 97.4350 4.69873
\(431\) 21.3345 1.02765 0.513824 0.857896i \(-0.328228\pi\)
0.513824 + 0.857896i \(0.328228\pi\)
\(432\) −101.458 −4.88140
\(433\) 8.85380 0.425487 0.212743 0.977108i \(-0.431760\pi\)
0.212743 + 0.977108i \(0.431760\pi\)
\(434\) 76.2966 3.66235
\(435\) 45.6946 2.19089
\(436\) −56.8284 −2.72159
\(437\) 4.46757 0.213713
\(438\) −29.4114 −1.40533
\(439\) −9.72648 −0.464219 −0.232110 0.972690i \(-0.574563\pi\)
−0.232110 + 0.972690i \(0.574563\pi\)
\(440\) −106.470 −5.07576
\(441\) 116.649 5.55471
\(442\) −45.8098 −2.17895
\(443\) −18.6532 −0.886239 −0.443119 0.896463i \(-0.646128\pi\)
−0.443119 + 0.896463i \(0.646128\pi\)
\(444\) −135.841 −6.44674
\(445\) −12.1105 −0.574092
\(446\) 38.0834 1.80330
\(447\) 29.8998 1.41421
\(448\) −4.18596 −0.197768
\(449\) 20.6696 0.975461 0.487730 0.872994i \(-0.337825\pi\)
0.487730 + 0.872994i \(0.337825\pi\)
\(450\) −151.059 −7.12100
\(451\) 1.95719 0.0921606
\(452\) −36.0081 −1.69368
\(453\) −11.2263 −0.527460
\(454\) 27.7339 1.30162
\(455\) 57.3632 2.68923
\(456\) −40.7487 −1.90823
\(457\) 4.34037 0.203034 0.101517 0.994834i \(-0.467630\pi\)
0.101517 + 0.994834i \(0.467630\pi\)
\(458\) 15.4663 0.722691
\(459\) −78.7069 −3.67373
\(460\) −35.3872 −1.64994
\(461\) 20.1046 0.936366 0.468183 0.883632i \(-0.344909\pi\)
0.468183 + 0.883632i \(0.344909\pi\)
\(462\) 186.176 8.66170
\(463\) 4.90993 0.228184 0.114092 0.993470i \(-0.463604\pi\)
0.114092 + 0.993470i \(0.463604\pi\)
\(464\) −27.0722 −1.25680
\(465\) 73.8183 3.42324
\(466\) −6.88543 −0.318962
\(467\) 30.9924 1.43416 0.717078 0.696992i \(-0.245479\pi\)
0.717078 + 0.696992i \(0.245479\pi\)
\(468\) 112.823 5.21526
\(469\) 65.4027 3.02001
\(470\) 21.3446 0.984553
\(471\) −73.9082 −3.40551
\(472\) 40.0543 1.84365
\(473\) −50.8789 −2.33942
\(474\) −13.0444 −0.599149
\(475\) −15.9427 −0.731504
\(476\) 113.057 5.18195
\(477\) 94.6701 4.33464
\(478\) −14.7686 −0.675500
\(479\) −39.0254 −1.78312 −0.891559 0.452905i \(-0.850388\pi\)
−0.891559 + 0.452905i \(0.850388\pi\)
\(480\) 59.3178 2.70747
\(481\) 31.6777 1.44438
\(482\) −27.7532 −1.26412
\(483\) 34.0702 1.55025
\(484\) 52.0228 2.36467
\(485\) 9.62757 0.437166
\(486\) 94.8336 4.30174
\(487\) −0.560130 −0.0253819 −0.0126909 0.999919i \(-0.504040\pi\)
−0.0126909 + 0.999919i \(0.504040\pi\)
\(488\) 61.7263 2.79422
\(489\) −30.2360 −1.36732
\(490\) −141.339 −6.38503
\(491\) 6.53601 0.294966 0.147483 0.989065i \(-0.452883\pi\)
0.147483 + 0.989065i \(0.452883\pi\)
\(492\) −5.93327 −0.267493
\(493\) −21.0015 −0.945860
\(494\) 17.2586 0.776500
\(495\) 128.803 5.78926
\(496\) −43.7344 −1.96373
\(497\) 51.0090 2.28806
\(498\) 10.0792 0.451658
\(499\) −9.20441 −0.412046 −0.206023 0.978547i \(-0.566052\pi\)
−0.206023 + 0.978547i \(0.566052\pi\)
\(500\) 46.3598 2.07327
\(501\) 21.5177 0.961339
\(502\) −65.5963 −2.92771
\(503\) −0.0865584 −0.00385945 −0.00192972 0.999998i \(-0.500614\pi\)
−0.00192972 + 0.999998i \(0.500614\pi\)
\(504\) −222.208 −9.89792
\(505\) −35.2708 −1.56953
\(506\) 26.7830 1.19065
\(507\) 5.38787 0.239284
\(508\) −69.4802 −3.08269
\(509\) 14.9959 0.664680 0.332340 0.943160i \(-0.392162\pi\)
0.332340 + 0.943160i \(0.392162\pi\)
\(510\) 158.543 7.02039
\(511\) −16.9269 −0.748801
\(512\) 50.7949 2.24484
\(513\) 29.6524 1.30918
\(514\) 21.8562 0.964034
\(515\) −27.2372 −1.20021
\(516\) 154.241 6.79007
\(517\) −11.1458 −0.490192
\(518\) −113.314 −4.97872
\(519\) 52.0391 2.28426
\(520\) −75.2681 −3.30072
\(521\) −27.1293 −1.18856 −0.594278 0.804260i \(-0.702562\pi\)
−0.594278 + 0.804260i \(0.702562\pi\)
\(522\) 74.9689 3.28130
\(523\) 13.1053 0.573056 0.286528 0.958072i \(-0.407499\pi\)
0.286528 + 0.958072i \(0.407499\pi\)
\(524\) 49.4056 2.15829
\(525\) −121.581 −5.30623
\(526\) −26.0220 −1.13461
\(527\) −33.9273 −1.47790
\(528\) −106.719 −4.64436
\(529\) −18.0987 −0.786901
\(530\) −114.708 −4.98259
\(531\) −48.4559 −2.10281
\(532\) −42.5935 −1.84666
\(533\) 1.38362 0.0599312
\(534\) −27.7866 −1.20244
\(535\) 54.2065 2.34355
\(536\) −85.8169 −3.70673
\(537\) −65.9829 −2.84737
\(538\) −42.5973 −1.83650
\(539\) 73.8047 3.17899
\(540\) −234.873 −10.1073
\(541\) −27.4875 −1.18178 −0.590890 0.806752i \(-0.701223\pi\)
−0.590890 + 0.806752i \(0.701223\pi\)
\(542\) −46.1500 −1.98231
\(543\) 30.5942 1.31292
\(544\) −27.2628 −1.16888
\(545\) −45.8644 −1.96461
\(546\) 131.616 5.63263
\(547\) 17.2159 0.736100 0.368050 0.929806i \(-0.380026\pi\)
0.368050 + 0.929806i \(0.380026\pi\)
\(548\) 57.4011 2.45205
\(549\) −74.6737 −3.18700
\(550\) −95.5765 −4.07539
\(551\) 7.91219 0.337071
\(552\) −44.7045 −1.90275
\(553\) −7.50731 −0.319243
\(554\) −53.6347 −2.27872
\(555\) −109.633 −4.65366
\(556\) −32.2927 −1.36952
\(557\) 44.6026 1.88987 0.944937 0.327251i \(-0.106122\pi\)
0.944937 + 0.327251i \(0.106122\pi\)
\(558\) 121.110 5.12700
\(559\) −35.9684 −1.52130
\(560\) 117.620 4.97034
\(561\) −82.7883 −3.49533
\(562\) −64.2743 −2.71125
\(563\) −23.0818 −0.972780 −0.486390 0.873742i \(-0.661687\pi\)
−0.486390 + 0.873742i \(0.661687\pi\)
\(564\) 33.7887 1.42276
\(565\) −29.0610 −1.22260
\(566\) 9.22914 0.387930
\(567\) 119.013 4.99806
\(568\) −66.9305 −2.80834
\(569\) 14.6720 0.615082 0.307541 0.951535i \(-0.400494\pi\)
0.307541 + 0.951535i \(0.400494\pi\)
\(570\) −59.7300 −2.50181
\(571\) −24.3728 −1.01997 −0.509984 0.860184i \(-0.670349\pi\)
−0.509984 + 0.860184i \(0.670349\pi\)
\(572\) 71.3843 2.98473
\(573\) 10.6067 0.443102
\(574\) −4.94932 −0.206581
\(575\) −17.4904 −0.729402
\(576\) −6.64462 −0.276859
\(577\) 19.4507 0.809744 0.404872 0.914373i \(-0.367316\pi\)
0.404872 + 0.914373i \(0.367316\pi\)
\(578\) −29.6915 −1.23500
\(579\) 30.2139 1.25565
\(580\) −62.6717 −2.60230
\(581\) 5.80076 0.240656
\(582\) 22.0897 0.915649
\(583\) 59.8985 2.48074
\(584\) 22.2103 0.919069
\(585\) 91.0561 3.76470
\(586\) −33.6493 −1.39004
\(587\) −17.0384 −0.703250 −0.351625 0.936141i \(-0.614371\pi\)
−0.351625 + 0.936141i \(0.614371\pi\)
\(588\) −223.741 −9.22690
\(589\) 12.7819 0.526670
\(590\) 58.7120 2.41714
\(591\) −46.2981 −1.90445
\(592\) 64.9532 2.66956
\(593\) −13.0652 −0.536522 −0.268261 0.963346i \(-0.586449\pi\)
−0.268261 + 0.963346i \(0.586449\pi\)
\(594\) 177.765 7.29380
\(595\) 91.2445 3.74066
\(596\) −41.0086 −1.67978
\(597\) 19.2080 0.786131
\(598\) 18.9340 0.774269
\(599\) −47.9088 −1.95750 −0.978750 0.205056i \(-0.934262\pi\)
−0.978750 + 0.205056i \(0.934262\pi\)
\(600\) 159.530 6.51280
\(601\) 23.6529 0.964824 0.482412 0.875945i \(-0.339761\pi\)
0.482412 + 0.875945i \(0.339761\pi\)
\(602\) 128.662 5.24387
\(603\) 103.818 4.22778
\(604\) 15.3973 0.626508
\(605\) 41.9859 1.70697
\(606\) −80.9261 −3.28740
\(607\) 2.59796 0.105448 0.0527240 0.998609i \(-0.483210\pi\)
0.0527240 + 0.998609i \(0.483210\pi\)
\(608\) 10.2711 0.416548
\(609\) 60.3391 2.44507
\(610\) 90.4791 3.66339
\(611\) −7.87942 −0.318767
\(612\) 179.462 7.25432
\(613\) −35.6594 −1.44027 −0.720135 0.693834i \(-0.755920\pi\)
−0.720135 + 0.693834i \(0.755920\pi\)
\(614\) 8.30270 0.335070
\(615\) −4.78855 −0.193093
\(616\) −140.593 −5.66464
\(617\) −41.2502 −1.66067 −0.830335 0.557264i \(-0.811851\pi\)
−0.830335 + 0.557264i \(0.811851\pi\)
\(618\) −62.4937 −2.51387
\(619\) −33.0594 −1.32877 −0.664385 0.747391i \(-0.731306\pi\)
−0.664385 + 0.747391i \(0.731306\pi\)
\(620\) −101.244 −4.06607
\(621\) 32.5310 1.30542
\(622\) 28.9169 1.15946
\(623\) −15.9918 −0.640696
\(624\) −75.4441 −3.02018
\(625\) −2.08624 −0.0834496
\(626\) 10.0117 0.400148
\(627\) 31.1900 1.24561
\(628\) 101.368 4.04501
\(629\) 50.3880 2.00910
\(630\) −325.715 −12.9768
\(631\) −44.0046 −1.75179 −0.875897 0.482497i \(-0.839730\pi\)
−0.875897 + 0.482497i \(0.839730\pi\)
\(632\) 9.85058 0.391835
\(633\) −17.8037 −0.707633
\(634\) −32.0985 −1.27480
\(635\) −56.0752 −2.22528
\(636\) −181.584 −7.20026
\(637\) 52.1755 2.06727
\(638\) 47.4334 1.87791
\(639\) 80.9696 3.20311
\(640\) 44.6131 1.76349
\(641\) −12.0311 −0.475200 −0.237600 0.971363i \(-0.576361\pi\)
−0.237600 + 0.971363i \(0.576361\pi\)
\(642\) 124.373 4.90860
\(643\) 15.6142 0.615764 0.307882 0.951425i \(-0.400380\pi\)
0.307882 + 0.951425i \(0.400380\pi\)
\(644\) −46.7284 −1.84136
\(645\) 124.483 4.90150
\(646\) 27.4523 1.08010
\(647\) −23.3538 −0.918134 −0.459067 0.888402i \(-0.651816\pi\)
−0.459067 + 0.888402i \(0.651816\pi\)
\(648\) −156.160 −6.13455
\(649\) −30.6584 −1.20345
\(650\) −67.5669 −2.65019
\(651\) 97.4762 3.82039
\(652\) 41.4697 1.62408
\(653\) 23.6841 0.926829 0.463415 0.886142i \(-0.346624\pi\)
0.463415 + 0.886142i \(0.346624\pi\)
\(654\) −105.232 −4.11491
\(655\) 39.8736 1.55799
\(656\) 2.83703 0.110767
\(657\) −26.8691 −1.04826
\(658\) 28.1853 1.09878
\(659\) −41.8663 −1.63088 −0.815439 0.578843i \(-0.803505\pi\)
−0.815439 + 0.578843i \(0.803505\pi\)
\(660\) −247.053 −9.61652
\(661\) −15.5783 −0.605927 −0.302964 0.953002i \(-0.597976\pi\)
−0.302964 + 0.953002i \(0.597976\pi\)
\(662\) 87.4023 3.39699
\(663\) −58.5264 −2.27298
\(664\) −7.61137 −0.295378
\(665\) −34.3758 −1.33304
\(666\) −179.870 −6.96980
\(667\) 8.68029 0.336102
\(668\) −29.5122 −1.14186
\(669\) 48.6552 1.88112
\(670\) −125.791 −4.85975
\(671\) −47.2467 −1.82394
\(672\) 78.3285 3.02159
\(673\) −28.3857 −1.09419 −0.547095 0.837071i \(-0.684266\pi\)
−0.547095 + 0.837071i \(0.684266\pi\)
\(674\) 30.3019 1.16719
\(675\) −116.088 −4.46824
\(676\) −7.38966 −0.284218
\(677\) 29.2089 1.12259 0.561294 0.827616i \(-0.310304\pi\)
0.561294 + 0.827616i \(0.310304\pi\)
\(678\) −66.6782 −2.56076
\(679\) 12.7131 0.487884
\(680\) −119.725 −4.59124
\(681\) 35.4327 1.35779
\(682\) 76.6273 2.93421
\(683\) −28.0978 −1.07513 −0.537567 0.843221i \(-0.680656\pi\)
−0.537567 + 0.843221i \(0.680656\pi\)
\(684\) −67.6112 −2.58518
\(685\) 46.3266 1.77005
\(686\) −102.317 −3.90649
\(687\) 19.7596 0.753877
\(688\) −73.7510 −2.81173
\(689\) 42.3447 1.61321
\(690\) −65.5285 −2.49463
\(691\) 15.5707 0.592337 0.296169 0.955136i \(-0.404291\pi\)
0.296169 + 0.955136i \(0.404291\pi\)
\(692\) −71.3734 −2.71321
\(693\) 170.083 6.46091
\(694\) 41.6146 1.57967
\(695\) −26.0624 −0.988603
\(696\) −79.1729 −3.00104
\(697\) 2.20085 0.0833631
\(698\) 37.5047 1.41957
\(699\) −8.79680 −0.332726
\(700\) 166.753 6.30266
\(701\) −7.53946 −0.284761 −0.142381 0.989812i \(-0.545476\pi\)
−0.142381 + 0.989812i \(0.545476\pi\)
\(702\) 125.670 4.74309
\(703\) −18.9834 −0.715971
\(704\) −4.20410 −0.158448
\(705\) 27.2698 1.02704
\(706\) 26.8393 1.01011
\(707\) −46.5747 −1.75162
\(708\) 92.9418 3.49297
\(709\) 46.8627 1.75996 0.879982 0.475006i \(-0.157554\pi\)
0.879982 + 0.475006i \(0.157554\pi\)
\(710\) −98.1075 −3.68191
\(711\) −11.9168 −0.446915
\(712\) 20.9833 0.786382
\(713\) 14.0228 0.525157
\(714\) 209.354 7.83487
\(715\) 57.6119 2.15456
\(716\) 90.4979 3.38206
\(717\) −18.8683 −0.704650
\(718\) −0.121639 −0.00453954
\(719\) 2.55536 0.0952987 0.0476494 0.998864i \(-0.484827\pi\)
0.0476494 + 0.998864i \(0.484827\pi\)
\(720\) 186.705 6.95808
\(721\) −35.9664 −1.33946
\(722\) 37.9127 1.41097
\(723\) −35.4573 −1.31867
\(724\) −41.9610 −1.55947
\(725\) −30.9760 −1.15042
\(726\) 96.3335 3.57527
\(727\) 10.4017 0.385777 0.192889 0.981221i \(-0.438214\pi\)
0.192889 + 0.981221i \(0.438214\pi\)
\(728\) −99.3907 −3.68366
\(729\) 45.8791 1.69923
\(730\) 32.5561 1.20496
\(731\) −57.2130 −2.11610
\(732\) 143.229 5.29391
\(733\) −49.7404 −1.83720 −0.918602 0.395184i \(-0.870681\pi\)
−0.918602 + 0.395184i \(0.870681\pi\)
\(734\) 44.0881 1.62732
\(735\) −180.574 −6.66056
\(736\) 11.2682 0.415352
\(737\) 65.6862 2.41958
\(738\) −7.85635 −0.289196
\(739\) −22.2977 −0.820234 −0.410117 0.912033i \(-0.634512\pi\)
−0.410117 + 0.912033i \(0.634512\pi\)
\(740\) 150.365 5.52754
\(741\) 22.0495 0.810008
\(742\) −151.470 −5.56066
\(743\) −1.05428 −0.0386777 −0.0193388 0.999813i \(-0.506156\pi\)
−0.0193388 + 0.999813i \(0.506156\pi\)
\(744\) −127.902 −4.68910
\(745\) −33.0967 −1.21257
\(746\) 36.3910 1.33237
\(747\) 9.20790 0.336899
\(748\) 113.547 4.15169
\(749\) 71.5790 2.61544
\(750\) 85.8471 3.13469
\(751\) 26.3770 0.962512 0.481256 0.876580i \(-0.340181\pi\)
0.481256 + 0.876580i \(0.340181\pi\)
\(752\) −16.1563 −0.589158
\(753\) −83.8056 −3.05404
\(754\) 33.5326 1.22119
\(755\) 12.4267 0.452253
\(756\) −310.148 −11.2800
\(757\) 13.0679 0.474963 0.237481 0.971392i \(-0.423678\pi\)
0.237481 + 0.971392i \(0.423678\pi\)
\(758\) −28.3608 −1.03011
\(759\) 34.2179 1.24203
\(760\) 45.1056 1.63615
\(761\) −4.60361 −0.166881 −0.0834403 0.996513i \(-0.526591\pi\)
−0.0834403 + 0.996513i \(0.526591\pi\)
\(762\) −128.660 −4.66087
\(763\) −60.5634 −2.19254
\(764\) −14.5475 −0.526309
\(765\) 144.838 5.23662
\(766\) −1.92580 −0.0695819
\(767\) −21.6737 −0.782592
\(768\) 96.6338 3.48697
\(769\) 33.8700 1.22138 0.610692 0.791868i \(-0.290891\pi\)
0.610692 + 0.791868i \(0.290891\pi\)
\(770\) −206.082 −7.42669
\(771\) 27.9234 1.00563
\(772\) −41.4394 −1.49144
\(773\) −25.0964 −0.902653 −0.451327 0.892359i \(-0.649049\pi\)
−0.451327 + 0.892359i \(0.649049\pi\)
\(774\) 204.233 7.34099
\(775\) −50.0409 −1.79752
\(776\) −16.6813 −0.598822
\(777\) −144.769 −5.19356
\(778\) −21.4095 −0.767569
\(779\) −0.829156 −0.0297076
\(780\) −174.652 −6.25354
\(781\) 51.2301 1.83316
\(782\) 30.1173 1.07699
\(783\) 57.6132 2.05893
\(784\) 106.983 3.82081
\(785\) 81.8105 2.91994
\(786\) 91.4870 3.26323
\(787\) −14.3551 −0.511705 −0.255852 0.966716i \(-0.582356\pi\)
−0.255852 + 0.966716i \(0.582356\pi\)
\(788\) 63.4995 2.26208
\(789\) −33.2456 −1.18358
\(790\) 14.4391 0.513720
\(791\) −38.3747 −1.36445
\(792\) −223.171 −7.93004
\(793\) −33.4006 −1.18609
\(794\) 26.0033 0.922824
\(795\) −146.550 −5.19760
\(796\) −26.3444 −0.933754
\(797\) 47.1912 1.67160 0.835799 0.549035i \(-0.185005\pi\)
0.835799 + 0.549035i \(0.185005\pi\)
\(798\) −78.8728 −2.79207
\(799\) −12.5334 −0.443398
\(800\) −40.2111 −1.42168
\(801\) −25.3847 −0.896923
\(802\) 45.0527 1.59087
\(803\) −17.0003 −0.599927
\(804\) −199.129 −7.02275
\(805\) −37.7130 −1.32921
\(806\) 54.1710 1.90809
\(807\) −54.4221 −1.91575
\(808\) 61.1121 2.14992
\(809\) −27.0460 −0.950888 −0.475444 0.879746i \(-0.657713\pi\)
−0.475444 + 0.879746i \(0.657713\pi\)
\(810\) −228.902 −8.04278
\(811\) 20.4598 0.718442 0.359221 0.933253i \(-0.383042\pi\)
0.359221 + 0.933253i \(0.383042\pi\)
\(812\) −82.7573 −2.90421
\(813\) −58.9610 −2.06785
\(814\) −113.805 −3.98886
\(815\) 33.4689 1.17236
\(816\) −120.005 −4.20101
\(817\) 21.5546 0.754102
\(818\) −65.0039 −2.27281
\(819\) 120.239 4.20147
\(820\) 6.56767 0.229353
\(821\) 13.1333 0.458355 0.229178 0.973385i \(-0.426396\pi\)
0.229178 + 0.973385i \(0.426396\pi\)
\(822\) 106.293 3.70739
\(823\) 45.1745 1.57468 0.787341 0.616517i \(-0.211457\pi\)
0.787341 + 0.616517i \(0.211457\pi\)
\(824\) 47.1927 1.64403
\(825\) −122.108 −4.25126
\(826\) 77.5286 2.69756
\(827\) −9.17208 −0.318944 −0.159472 0.987202i \(-0.550979\pi\)
−0.159472 + 0.987202i \(0.550979\pi\)
\(828\) −74.1748 −2.57775
\(829\) 42.0193 1.45939 0.729695 0.683773i \(-0.239662\pi\)
0.729695 + 0.683773i \(0.239662\pi\)
\(830\) −11.1568 −0.387259
\(831\) −68.5234 −2.37705
\(832\) −2.97205 −0.103037
\(833\) 82.9928 2.87553
\(834\) −59.7982 −2.07064
\(835\) −23.8184 −0.824269
\(836\) −42.7782 −1.47951
\(837\) 93.0725 3.21706
\(838\) 56.2265 1.94231
\(839\) −14.9279 −0.515367 −0.257683 0.966229i \(-0.582959\pi\)
−0.257683 + 0.966229i \(0.582959\pi\)
\(840\) 343.980 11.8684
\(841\) −13.6270 −0.469896
\(842\) −0.882077 −0.0303984
\(843\) −82.1165 −2.82824
\(844\) 24.4184 0.840515
\(845\) −5.96395 −0.205166
\(846\) 44.7402 1.53820
\(847\) 55.4419 1.90501
\(848\) 86.8253 2.98159
\(849\) 11.7911 0.404670
\(850\) −107.475 −3.68636
\(851\) −20.8263 −0.713915
\(852\) −155.305 −5.32067
\(853\) −35.6711 −1.22136 −0.610678 0.791879i \(-0.709103\pi\)
−0.610678 + 0.791879i \(0.709103\pi\)
\(854\) 119.477 4.08841
\(855\) −54.5668 −1.86615
\(856\) −93.9211 −3.21016
\(857\) −50.2470 −1.71640 −0.858202 0.513312i \(-0.828419\pi\)
−0.858202 + 0.513312i \(0.828419\pi\)
\(858\) 132.186 4.51276
\(859\) 32.3848 1.10496 0.552478 0.833528i \(-0.313682\pi\)
0.552478 + 0.833528i \(0.313682\pi\)
\(860\) −170.732 −5.82192
\(861\) −6.32323 −0.215495
\(862\) −54.1843 −1.84552
\(863\) 57.2987 1.95047 0.975235 0.221172i \(-0.0709881\pi\)
0.975235 + 0.221172i \(0.0709881\pi\)
\(864\) 74.7898 2.54440
\(865\) −57.6032 −1.95857
\(866\) −22.4864 −0.764120
\(867\) −37.9337 −1.28830
\(868\) −133.692 −4.53780
\(869\) −7.53986 −0.255772
\(870\) −116.053 −3.93455
\(871\) 46.4363 1.57343
\(872\) 79.4672 2.69110
\(873\) 20.1803 0.682998
\(874\) −11.3465 −0.383801
\(875\) 49.4068 1.67025
\(876\) 51.5367 1.74126
\(877\) 1.71786 0.0580079 0.0290039 0.999579i \(-0.490766\pi\)
0.0290039 + 0.999579i \(0.490766\pi\)
\(878\) 24.7028 0.833679
\(879\) −42.9903 −1.45003
\(880\) 118.130 3.98215
\(881\) 39.4879 1.33038 0.665190 0.746674i \(-0.268350\pi\)
0.665190 + 0.746674i \(0.268350\pi\)
\(882\) −296.259 −9.97555
\(883\) 5.17124 0.174026 0.0870131 0.996207i \(-0.472268\pi\)
0.0870131 + 0.996207i \(0.472268\pi\)
\(884\) 80.2711 2.69981
\(885\) 75.0103 2.52144
\(886\) 47.3743 1.59157
\(887\) 0.218500 0.00733652 0.00366826 0.999993i \(-0.498832\pi\)
0.00366826 + 0.999993i \(0.498832\pi\)
\(888\) 189.956 6.37451
\(889\) −74.0467 −2.48345
\(890\) 30.7576 1.03100
\(891\) 119.529 4.00436
\(892\) −66.7322 −2.23436
\(893\) 4.72187 0.158011
\(894\) −75.9378 −2.53974
\(895\) 73.0379 2.44139
\(896\) 58.9111 1.96808
\(897\) 24.1900 0.807681
\(898\) −52.4957 −1.75180
\(899\) 24.8347 0.828283
\(900\) 264.696 8.82321
\(901\) 67.3554 2.24393
\(902\) −4.97078 −0.165509
\(903\) 164.378 5.47015
\(904\) 50.3526 1.67470
\(905\) −33.8653 −1.12572
\(906\) 28.5121 0.947250
\(907\) 11.6504 0.386846 0.193423 0.981115i \(-0.438041\pi\)
0.193423 + 0.981115i \(0.438041\pi\)
\(908\) −48.5973 −1.61276
\(909\) −73.9307 −2.45213
\(910\) −145.688 −4.82951
\(911\) 6.79986 0.225289 0.112645 0.993635i \(-0.464068\pi\)
0.112645 + 0.993635i \(0.464068\pi\)
\(912\) 45.2111 1.49709
\(913\) 5.82591 0.192810
\(914\) −11.0234 −0.364623
\(915\) 115.596 3.82148
\(916\) −27.1010 −0.895443
\(917\) 52.6527 1.73874
\(918\) 199.896 6.59754
\(919\) 31.4247 1.03661 0.518303 0.855197i \(-0.326564\pi\)
0.518303 + 0.855197i \(0.326564\pi\)
\(920\) 49.4844 1.63145
\(921\) 10.6075 0.349529
\(922\) −51.0607 −1.68159
\(923\) 36.2167 1.19209
\(924\) −326.231 −10.7322
\(925\) 74.3195 2.44361
\(926\) −12.4700 −0.409789
\(927\) −57.0916 −1.87514
\(928\) 19.9563 0.655097
\(929\) −13.9089 −0.456336 −0.228168 0.973622i \(-0.573273\pi\)
−0.228168 + 0.973622i \(0.573273\pi\)
\(930\) −187.480 −6.14770
\(931\) −31.2670 −1.02474
\(932\) 12.0651 0.395206
\(933\) 36.9441 1.20950
\(934\) −78.7129 −2.57556
\(935\) 91.6401 2.99695
\(936\) −157.769 −5.15683
\(937\) −48.5608 −1.58641 −0.793205 0.608954i \(-0.791589\pi\)
−0.793205 + 0.608954i \(0.791589\pi\)
\(938\) −166.106 −5.42356
\(939\) 12.7909 0.417416
\(940\) −37.4015 −1.21990
\(941\) 25.5561 0.833105 0.416552 0.909112i \(-0.363238\pi\)
0.416552 + 0.909112i \(0.363238\pi\)
\(942\) 187.708 6.11586
\(943\) −0.909650 −0.0296223
\(944\) −44.4406 −1.44642
\(945\) −250.310 −8.14259
\(946\) 129.220 4.20129
\(947\) 51.3532 1.66875 0.834377 0.551194i \(-0.185828\pi\)
0.834377 + 0.551194i \(0.185828\pi\)
\(948\) 22.8573 0.742369
\(949\) −12.0182 −0.390127
\(950\) 40.4906 1.31369
\(951\) −41.0089 −1.32981
\(952\) −158.095 −5.12390
\(953\) 51.9020 1.68127 0.840635 0.541602i \(-0.182182\pi\)
0.840635 + 0.541602i \(0.182182\pi\)
\(954\) −240.438 −7.78447
\(955\) −11.7408 −0.379923
\(956\) 25.8785 0.836972
\(957\) 60.6007 1.95894
\(958\) 99.1148 3.20225
\(959\) 61.1737 1.97540
\(960\) 10.2859 0.331977
\(961\) 9.11972 0.294185
\(962\) −80.4534 −2.59392
\(963\) 113.622 3.66141
\(964\) 48.6310 1.56630
\(965\) −33.4444 −1.07661
\(966\) −86.5296 −2.78404
\(967\) 1.40827 0.0452869 0.0226434 0.999744i \(-0.492792\pi\)
0.0226434 + 0.999744i \(0.492792\pi\)
\(968\) −72.7471 −2.33818
\(969\) 35.0729 1.12670
\(970\) −24.4516 −0.785094
\(971\) −33.5172 −1.07562 −0.537810 0.843066i \(-0.680748\pi\)
−0.537810 + 0.843066i \(0.680748\pi\)
\(972\) −166.174 −5.33003
\(973\) −34.4151 −1.10330
\(974\) 1.42259 0.0455826
\(975\) −86.3232 −2.76456
\(976\) −68.4859 −2.19218
\(977\) 8.04807 0.257481 0.128740 0.991678i \(-0.458907\pi\)
0.128740 + 0.991678i \(0.458907\pi\)
\(978\) 76.7918 2.45553
\(979\) −16.0611 −0.513315
\(980\) 247.663 7.91131
\(981\) −96.1359 −3.06938
\(982\) −16.5998 −0.529722
\(983\) −34.2212 −1.09149 −0.545743 0.837953i \(-0.683752\pi\)
−0.545743 + 0.837953i \(0.683752\pi\)
\(984\) 8.29691 0.264496
\(985\) 51.2484 1.63291
\(986\) 53.3385 1.69864
\(987\) 36.0094 1.14619
\(988\) −30.2416 −0.962115
\(989\) 23.6471 0.751935
\(990\) −327.127 −10.3968
\(991\) −39.9411 −1.26877 −0.634386 0.773017i \(-0.718747\pi\)
−0.634386 + 0.773017i \(0.718747\pi\)
\(992\) 32.2388 1.02358
\(993\) 111.665 3.54357
\(994\) −129.550 −4.10907
\(995\) −21.2617 −0.674042
\(996\) −17.6614 −0.559622
\(997\) −28.6697 −0.907980 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(998\) 23.3769 0.739982
\(999\) −138.229 −4.37337
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.1.11 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.11 179 1.1 even 1 trivial