Properties

Label 4003.2.a.c.1.5
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 1.5
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.63071 q^{2} +2.57872 q^{3} +4.92061 q^{4} -1.88131 q^{5} -6.78385 q^{6} -5.19574 q^{7} -7.68328 q^{8} +3.64979 q^{9} +O(q^{10})\) \(q-2.63071 q^{2} +2.57872 q^{3} +4.92061 q^{4} -1.88131 q^{5} -6.78385 q^{6} -5.19574 q^{7} -7.68328 q^{8} +3.64979 q^{9} +4.94917 q^{10} -2.38632 q^{11} +12.6889 q^{12} -1.49198 q^{13} +13.6685 q^{14} -4.85136 q^{15} +10.3712 q^{16} -1.62869 q^{17} -9.60151 q^{18} -5.84283 q^{19} -9.25719 q^{20} -13.3983 q^{21} +6.27770 q^{22} -1.73420 q^{23} -19.8130 q^{24} -1.46068 q^{25} +3.92496 q^{26} +1.67561 q^{27} -25.5662 q^{28} +6.97607 q^{29} +12.7625 q^{30} -0.537433 q^{31} -11.9171 q^{32} -6.15364 q^{33} +4.28459 q^{34} +9.77478 q^{35} +17.9592 q^{36} +4.57588 q^{37} +15.3708 q^{38} -3.84740 q^{39} +14.4546 q^{40} -10.2985 q^{41} +35.2471 q^{42} -1.45623 q^{43} -11.7421 q^{44} -6.86637 q^{45} +4.56217 q^{46} +5.01724 q^{47} +26.7444 q^{48} +19.9957 q^{49} +3.84262 q^{50} -4.19992 q^{51} -7.34146 q^{52} +9.61811 q^{53} -4.40805 q^{54} +4.48940 q^{55} +39.9203 q^{56} -15.0670 q^{57} -18.3520 q^{58} -2.80946 q^{59} -23.8717 q^{60} -9.67030 q^{61} +1.41383 q^{62} -18.9633 q^{63} +10.6078 q^{64} +2.80688 q^{65} +16.1884 q^{66} -4.15099 q^{67} -8.01413 q^{68} -4.47202 q^{69} -25.7146 q^{70} -9.14923 q^{71} -28.0423 q^{72} -3.83807 q^{73} -12.0378 q^{74} -3.76668 q^{75} -28.7503 q^{76} +12.3987 q^{77} +10.1214 q^{78} +1.17242 q^{79} -19.5114 q^{80} -6.62842 q^{81} +27.0922 q^{82} +16.3741 q^{83} -65.9280 q^{84} +3.06406 q^{85} +3.83092 q^{86} +17.9893 q^{87} +18.3347 q^{88} +15.3462 q^{89} +18.0634 q^{90} +7.75194 q^{91} -8.53334 q^{92} -1.38589 q^{93} -13.1989 q^{94} +10.9922 q^{95} -30.7307 q^{96} +7.15550 q^{97} -52.6027 q^{98} -8.70955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63071 −1.86019 −0.930095 0.367319i \(-0.880276\pi\)
−0.930095 + 0.367319i \(0.880276\pi\)
\(3\) 2.57872 1.48882 0.744412 0.667721i \(-0.232730\pi\)
0.744412 + 0.667721i \(0.232730\pi\)
\(4\) 4.92061 2.46031
\(5\) −1.88131 −0.841347 −0.420673 0.907212i \(-0.638206\pi\)
−0.420673 + 0.907212i \(0.638206\pi\)
\(6\) −6.78385 −2.76949
\(7\) −5.19574 −1.96380 −0.981902 0.189392i \(-0.939348\pi\)
−0.981902 + 0.189392i \(0.939348\pi\)
\(8\) −7.68328 −2.71645
\(9\) 3.64979 1.21660
\(10\) 4.94917 1.56506
\(11\) −2.38632 −0.719502 −0.359751 0.933048i \(-0.617138\pi\)
−0.359751 + 0.933048i \(0.617138\pi\)
\(12\) 12.6889 3.66296
\(13\) −1.49198 −0.413801 −0.206901 0.978362i \(-0.566338\pi\)
−0.206901 + 0.978362i \(0.566338\pi\)
\(14\) 13.6685 3.65305
\(15\) −4.85136 −1.25262
\(16\) 10.3712 2.59280
\(17\) −1.62869 −0.395014 −0.197507 0.980301i \(-0.563285\pi\)
−0.197507 + 0.980301i \(0.563285\pi\)
\(18\) −9.60151 −2.26310
\(19\) −5.84283 −1.34044 −0.670218 0.742164i \(-0.733800\pi\)
−0.670218 + 0.742164i \(0.733800\pi\)
\(20\) −9.25719 −2.06997
\(21\) −13.3983 −2.92376
\(22\) 6.27770 1.33841
\(23\) −1.73420 −0.361606 −0.180803 0.983519i \(-0.557870\pi\)
−0.180803 + 0.983519i \(0.557870\pi\)
\(24\) −19.8130 −4.04431
\(25\) −1.46068 −0.292136
\(26\) 3.92496 0.769749
\(27\) 1.67561 0.322472
\(28\) −25.5662 −4.83156
\(29\) 6.97607 1.29542 0.647712 0.761886i \(-0.275726\pi\)
0.647712 + 0.761886i \(0.275726\pi\)
\(30\) 12.7625 2.33011
\(31\) −0.537433 −0.0965258 −0.0482629 0.998835i \(-0.515369\pi\)
−0.0482629 + 0.998835i \(0.515369\pi\)
\(32\) −11.9171 −2.10666
\(33\) −6.15364 −1.07121
\(34\) 4.28459 0.734802
\(35\) 9.77478 1.65224
\(36\) 17.9592 2.99320
\(37\) 4.57588 0.752270 0.376135 0.926565i \(-0.377253\pi\)
0.376135 + 0.926565i \(0.377253\pi\)
\(38\) 15.3708 2.49347
\(39\) −3.84740 −0.616077
\(40\) 14.4546 2.28547
\(41\) −10.2985 −1.60835 −0.804175 0.594392i \(-0.797393\pi\)
−0.804175 + 0.594392i \(0.797393\pi\)
\(42\) 35.2471 5.43874
\(43\) −1.45623 −0.222073 −0.111037 0.993816i \(-0.535417\pi\)
−0.111037 + 0.993816i \(0.535417\pi\)
\(44\) −11.7421 −1.77020
\(45\) −6.86637 −1.02358
\(46\) 4.56217 0.672656
\(47\) 5.01724 0.731840 0.365920 0.930646i \(-0.380754\pi\)
0.365920 + 0.930646i \(0.380754\pi\)
\(48\) 26.7444 3.86023
\(49\) 19.9957 2.85652
\(50\) 3.84262 0.543428
\(51\) −4.19992 −0.588107
\(52\) −7.34146 −1.01808
\(53\) 9.61811 1.32115 0.660575 0.750760i \(-0.270313\pi\)
0.660575 + 0.750760i \(0.270313\pi\)
\(54\) −4.40805 −0.599860
\(55\) 4.48940 0.605351
\(56\) 39.9203 5.33457
\(57\) −15.0670 −1.99567
\(58\) −18.3520 −2.40973
\(59\) −2.80946 −0.365761 −0.182881 0.983135i \(-0.558542\pi\)
−0.182881 + 0.983135i \(0.558542\pi\)
\(60\) −23.8717 −3.08182
\(61\) −9.67030 −1.23816 −0.619078 0.785330i \(-0.712493\pi\)
−0.619078 + 0.785330i \(0.712493\pi\)
\(62\) 1.41383 0.179556
\(63\) −18.9633 −2.38915
\(64\) 10.6078 1.32598
\(65\) 2.80688 0.348150
\(66\) 16.1884 1.99266
\(67\) −4.15099 −0.507124 −0.253562 0.967319i \(-0.581602\pi\)
−0.253562 + 0.967319i \(0.581602\pi\)
\(68\) −8.01413 −0.971856
\(69\) −4.47202 −0.538368
\(70\) −25.7146 −3.07348
\(71\) −9.14923 −1.08581 −0.542907 0.839793i \(-0.682676\pi\)
−0.542907 + 0.839793i \(0.682676\pi\)
\(72\) −28.0423 −3.30482
\(73\) −3.83807 −0.449212 −0.224606 0.974450i \(-0.572110\pi\)
−0.224606 + 0.974450i \(0.572110\pi\)
\(74\) −12.0378 −1.39937
\(75\) −3.76668 −0.434939
\(76\) −28.7503 −3.29789
\(77\) 12.3987 1.41296
\(78\) 10.1214 1.14602
\(79\) 1.17242 0.131908 0.0659539 0.997823i \(-0.478991\pi\)
0.0659539 + 0.997823i \(0.478991\pi\)
\(80\) −19.5114 −2.18145
\(81\) −6.62842 −0.736491
\(82\) 27.0922 2.99184
\(83\) 16.3741 1.79729 0.898647 0.438674i \(-0.144552\pi\)
0.898647 + 0.438674i \(0.144552\pi\)
\(84\) −65.9280 −7.19334
\(85\) 3.06406 0.332344
\(86\) 3.83092 0.413099
\(87\) 17.9893 1.92866
\(88\) 18.3347 1.95449
\(89\) 15.3462 1.62669 0.813345 0.581782i \(-0.197644\pi\)
0.813345 + 0.581782i \(0.197644\pi\)
\(90\) 18.0634 1.90405
\(91\) 7.75194 0.812624
\(92\) −8.53334 −0.889662
\(93\) −1.38589 −0.143710
\(94\) −13.1989 −1.36136
\(95\) 10.9922 1.12777
\(96\) −30.7307 −3.13644
\(97\) 7.15550 0.726531 0.363266 0.931686i \(-0.381662\pi\)
0.363266 + 0.931686i \(0.381662\pi\)
\(98\) −52.6027 −5.31368
\(99\) −8.70955 −0.875343
\(100\) −7.18743 −0.718743
\(101\) −15.0255 −1.49509 −0.747545 0.664211i \(-0.768768\pi\)
−0.747545 + 0.664211i \(0.768768\pi\)
\(102\) 11.0488 1.09399
\(103\) −16.9391 −1.66906 −0.834531 0.550961i \(-0.814261\pi\)
−0.834531 + 0.550961i \(0.814261\pi\)
\(104\) 11.4633 1.12407
\(105\) 25.2064 2.45989
\(106\) −25.3024 −2.45759
\(107\) 5.15097 0.497963 0.248981 0.968508i \(-0.419904\pi\)
0.248981 + 0.968508i \(0.419904\pi\)
\(108\) 8.24505 0.793381
\(109\) −7.31183 −0.700346 −0.350173 0.936685i \(-0.613877\pi\)
−0.350173 + 0.936685i \(0.613877\pi\)
\(110\) −11.8103 −1.12607
\(111\) 11.7999 1.12000
\(112\) −53.8861 −5.09175
\(113\) 20.8908 1.96525 0.982623 0.185614i \(-0.0594274\pi\)
0.982623 + 0.185614i \(0.0594274\pi\)
\(114\) 39.6369 3.71233
\(115\) 3.26257 0.304236
\(116\) 34.3265 3.18714
\(117\) −5.44541 −0.503428
\(118\) 7.39088 0.680385
\(119\) 8.46222 0.775730
\(120\) 37.2744 3.40267
\(121\) −5.30549 −0.482317
\(122\) 25.4397 2.30320
\(123\) −26.5568 −2.39455
\(124\) −2.64450 −0.237483
\(125\) 12.1545 1.08713
\(126\) 49.8869 4.44428
\(127\) 5.18532 0.460122 0.230061 0.973176i \(-0.426107\pi\)
0.230061 + 0.973176i \(0.426107\pi\)
\(128\) −4.07201 −0.359918
\(129\) −3.75521 −0.330628
\(130\) −7.38407 −0.647625
\(131\) −4.26329 −0.372485 −0.186243 0.982504i \(-0.559631\pi\)
−0.186243 + 0.982504i \(0.559631\pi\)
\(132\) −30.2797 −2.63551
\(133\) 30.3578 2.63235
\(134\) 10.9200 0.943347
\(135\) −3.15235 −0.271311
\(136\) 12.5136 1.07304
\(137\) −0.905625 −0.0773727 −0.0386864 0.999251i \(-0.512317\pi\)
−0.0386864 + 0.999251i \(0.512317\pi\)
\(138\) 11.7646 1.00147
\(139\) 11.4149 0.968198 0.484099 0.875013i \(-0.339147\pi\)
0.484099 + 0.875013i \(0.339147\pi\)
\(140\) 48.0979 4.06502
\(141\) 12.9380 1.08958
\(142\) 24.0689 2.01982
\(143\) 3.56034 0.297731
\(144\) 37.8527 3.15439
\(145\) −13.1241 −1.08990
\(146\) 10.0968 0.835620
\(147\) 51.5632 4.25286
\(148\) 22.5161 1.85082
\(149\) 0.763666 0.0625619 0.0312810 0.999511i \(-0.490041\pi\)
0.0312810 + 0.999511i \(0.490041\pi\)
\(150\) 9.90902 0.809068
\(151\) 11.4798 0.934211 0.467105 0.884202i \(-0.345297\pi\)
0.467105 + 0.884202i \(0.345297\pi\)
\(152\) 44.8921 3.64123
\(153\) −5.94435 −0.480573
\(154\) −32.6173 −2.62837
\(155\) 1.01108 0.0812117
\(156\) −18.9316 −1.51574
\(157\) 6.40914 0.511505 0.255752 0.966742i \(-0.417677\pi\)
0.255752 + 0.966742i \(0.417677\pi\)
\(158\) −3.08430 −0.245374
\(159\) 24.8024 1.96696
\(160\) 22.4197 1.77243
\(161\) 9.01045 0.710123
\(162\) 17.4374 1.37001
\(163\) 10.0008 0.783320 0.391660 0.920110i \(-0.371901\pi\)
0.391660 + 0.920110i \(0.371901\pi\)
\(164\) −50.6748 −3.95704
\(165\) 11.5769 0.901260
\(166\) −43.0755 −3.34331
\(167\) 19.5792 1.51509 0.757544 0.652785i \(-0.226399\pi\)
0.757544 + 0.652785i \(0.226399\pi\)
\(168\) 102.943 7.94223
\(169\) −10.7740 −0.828769
\(170\) −8.06064 −0.618223
\(171\) −21.3251 −1.63077
\(172\) −7.16556 −0.546369
\(173\) 13.3702 1.01652 0.508259 0.861204i \(-0.330289\pi\)
0.508259 + 0.861204i \(0.330289\pi\)
\(174\) −47.3246 −3.58767
\(175\) 7.58930 0.573697
\(176\) −24.7490 −1.86553
\(177\) −7.24482 −0.544554
\(178\) −40.3712 −3.02595
\(179\) −24.8686 −1.85877 −0.929385 0.369113i \(-0.879662\pi\)
−0.929385 + 0.369113i \(0.879662\pi\)
\(180\) −33.7868 −2.51832
\(181\) 13.0404 0.969285 0.484643 0.874712i \(-0.338950\pi\)
0.484643 + 0.874712i \(0.338950\pi\)
\(182\) −20.3931 −1.51163
\(183\) −24.9370 −1.84339
\(184\) 13.3243 0.982284
\(185\) −8.60864 −0.632920
\(186\) 3.64586 0.267328
\(187\) 3.88656 0.284214
\(188\) 24.6879 1.80055
\(189\) −8.70605 −0.633272
\(190\) −28.9171 −2.09787
\(191\) 0.713105 0.0515985 0.0257992 0.999667i \(-0.491787\pi\)
0.0257992 + 0.999667i \(0.491787\pi\)
\(192\) 27.3546 1.97415
\(193\) −14.0872 −1.01402 −0.507009 0.861941i \(-0.669249\pi\)
−0.507009 + 0.861941i \(0.669249\pi\)
\(194\) −18.8240 −1.35149
\(195\) 7.23814 0.518334
\(196\) 98.3909 7.02792
\(197\) 8.52399 0.607309 0.303655 0.952782i \(-0.401793\pi\)
0.303655 + 0.952782i \(0.401793\pi\)
\(198\) 22.9123 1.62830
\(199\) 6.81923 0.483402 0.241701 0.970351i \(-0.422295\pi\)
0.241701 + 0.970351i \(0.422295\pi\)
\(200\) 11.2228 0.793572
\(201\) −10.7042 −0.755018
\(202\) 39.5276 2.78115
\(203\) −36.2458 −2.54396
\(204\) −20.6662 −1.44692
\(205\) 19.3746 1.35318
\(206\) 44.5619 3.10477
\(207\) −6.32946 −0.439928
\(208\) −15.4736 −1.07290
\(209\) 13.9428 0.964447
\(210\) −66.3106 −4.57587
\(211\) −4.43404 −0.305252 −0.152626 0.988284i \(-0.548773\pi\)
−0.152626 + 0.988284i \(0.548773\pi\)
\(212\) 47.3270 3.25043
\(213\) −23.5933 −1.61658
\(214\) −13.5507 −0.926305
\(215\) 2.73962 0.186841
\(216\) −12.8742 −0.875979
\(217\) 2.79236 0.189558
\(218\) 19.2353 1.30278
\(219\) −9.89730 −0.668797
\(220\) 22.0906 1.48935
\(221\) 2.42997 0.163457
\(222\) −31.0421 −2.08341
\(223\) −12.0251 −0.805259 −0.402629 0.915363i \(-0.631904\pi\)
−0.402629 + 0.915363i \(0.631904\pi\)
\(224\) 61.9179 4.13706
\(225\) −5.33116 −0.355411
\(226\) −54.9577 −3.65573
\(227\) 0.292622 0.0194220 0.00971101 0.999953i \(-0.496909\pi\)
0.00971101 + 0.999953i \(0.496909\pi\)
\(228\) −74.1389 −4.90997
\(229\) 16.8685 1.11470 0.557350 0.830277i \(-0.311818\pi\)
0.557350 + 0.830277i \(0.311818\pi\)
\(230\) −8.58286 −0.565937
\(231\) 31.9727 2.10365
\(232\) −53.5991 −3.51895
\(233\) 4.70627 0.308318 0.154159 0.988046i \(-0.450733\pi\)
0.154159 + 0.988046i \(0.450733\pi\)
\(234\) 14.3253 0.936473
\(235\) −9.43897 −0.615731
\(236\) −13.8243 −0.899885
\(237\) 3.02335 0.196388
\(238\) −22.2616 −1.44301
\(239\) −23.0029 −1.48793 −0.743966 0.668218i \(-0.767058\pi\)
−0.743966 + 0.668218i \(0.767058\pi\)
\(240\) −50.3145 −3.24779
\(241\) 3.72857 0.240179 0.120089 0.992763i \(-0.461682\pi\)
0.120089 + 0.992763i \(0.461682\pi\)
\(242\) 13.9572 0.897201
\(243\) −22.1197 −1.41898
\(244\) −47.5838 −3.04624
\(245\) −37.6180 −2.40333
\(246\) 69.8633 4.45432
\(247\) 8.71739 0.554674
\(248\) 4.12925 0.262207
\(249\) 42.2242 2.67585
\(250\) −31.9750 −2.02228
\(251\) −10.8855 −0.687086 −0.343543 0.939137i \(-0.611627\pi\)
−0.343543 + 0.939137i \(0.611627\pi\)
\(252\) −93.3112 −5.87805
\(253\) 4.13836 0.260176
\(254\) −13.6410 −0.855915
\(255\) 7.90135 0.494801
\(256\) −10.5034 −0.656464
\(257\) 9.52337 0.594052 0.297026 0.954869i \(-0.404005\pi\)
0.297026 + 0.954869i \(0.404005\pi\)
\(258\) 9.87886 0.615031
\(259\) −23.7751 −1.47731
\(260\) 13.8116 0.856556
\(261\) 25.4612 1.57601
\(262\) 11.2155 0.692893
\(263\) 26.4678 1.63207 0.816037 0.578000i \(-0.196167\pi\)
0.816037 + 0.578000i \(0.196167\pi\)
\(264\) 47.2801 2.90989
\(265\) −18.0946 −1.11154
\(266\) −79.8624 −4.89668
\(267\) 39.5734 2.42185
\(268\) −20.4254 −1.24768
\(269\) 8.53934 0.520653 0.260327 0.965521i \(-0.416170\pi\)
0.260327 + 0.965521i \(0.416170\pi\)
\(270\) 8.29290 0.504690
\(271\) 18.2190 1.10673 0.553364 0.832940i \(-0.313344\pi\)
0.553364 + 0.832940i \(0.313344\pi\)
\(272\) −16.8914 −1.02419
\(273\) 19.9901 1.20985
\(274\) 2.38243 0.143928
\(275\) 3.48564 0.210192
\(276\) −22.0051 −1.32455
\(277\) −4.46205 −0.268099 −0.134049 0.990975i \(-0.542798\pi\)
−0.134049 + 0.990975i \(0.542798\pi\)
\(278\) −30.0292 −1.80103
\(279\) −1.96152 −0.117433
\(280\) −75.1023 −4.48822
\(281\) −8.84325 −0.527544 −0.263772 0.964585i \(-0.584967\pi\)
−0.263772 + 0.964585i \(0.584967\pi\)
\(282\) −34.0362 −2.02683
\(283\) −3.26057 −0.193821 −0.0969104 0.995293i \(-0.530896\pi\)
−0.0969104 + 0.995293i \(0.530896\pi\)
\(284\) −45.0198 −2.67143
\(285\) 28.3457 1.67905
\(286\) −9.36621 −0.553836
\(287\) 53.5081 3.15848
\(288\) −43.4947 −2.56295
\(289\) −14.3474 −0.843964
\(290\) 34.5257 2.02742
\(291\) 18.4520 1.08168
\(292\) −18.8857 −1.10520
\(293\) −2.42903 −0.141906 −0.0709528 0.997480i \(-0.522604\pi\)
−0.0709528 + 0.997480i \(0.522604\pi\)
\(294\) −135.648 −7.91113
\(295\) 5.28547 0.307732
\(296\) −35.1578 −2.04350
\(297\) −3.99855 −0.232019
\(298\) −2.00898 −0.116377
\(299\) 2.58740 0.149633
\(300\) −18.5344 −1.07008
\(301\) 7.56620 0.436109
\(302\) −30.1999 −1.73781
\(303\) −38.7464 −2.22592
\(304\) −60.5972 −3.47549
\(305\) 18.1928 1.04172
\(306\) 15.6378 0.893956
\(307\) 2.78603 0.159007 0.0795036 0.996835i \(-0.474666\pi\)
0.0795036 + 0.996835i \(0.474666\pi\)
\(308\) 61.0091 3.47632
\(309\) −43.6812 −2.48494
\(310\) −2.65985 −0.151069
\(311\) 14.3571 0.814117 0.407058 0.913402i \(-0.366555\pi\)
0.407058 + 0.913402i \(0.366555\pi\)
\(312\) 29.5606 1.67354
\(313\) −17.6347 −0.996770 −0.498385 0.866956i \(-0.666073\pi\)
−0.498385 + 0.866956i \(0.666073\pi\)
\(314\) −16.8606 −0.951496
\(315\) 35.6759 2.01011
\(316\) 5.76904 0.324534
\(317\) 29.2835 1.64473 0.822363 0.568963i \(-0.192655\pi\)
0.822363 + 0.568963i \(0.192655\pi\)
\(318\) −65.2478 −3.65892
\(319\) −16.6471 −0.932060
\(320\) −19.9566 −1.11561
\(321\) 13.2829 0.741379
\(322\) −23.7038 −1.32096
\(323\) 9.51613 0.529492
\(324\) −32.6159 −1.81199
\(325\) 2.17930 0.120886
\(326\) −26.3090 −1.45712
\(327\) −18.8552 −1.04269
\(328\) 79.1260 4.36900
\(329\) −26.0682 −1.43719
\(330\) −30.4554 −1.67652
\(331\) −13.9913 −0.769032 −0.384516 0.923118i \(-0.625632\pi\)
−0.384516 + 0.923118i \(0.625632\pi\)
\(332\) 80.5707 4.42189
\(333\) 16.7010 0.915209
\(334\) −51.5072 −2.81835
\(335\) 7.80929 0.426667
\(336\) −138.957 −7.58072
\(337\) −15.6645 −0.853299 −0.426650 0.904417i \(-0.640306\pi\)
−0.426650 + 0.904417i \(0.640306\pi\)
\(338\) 28.3432 1.54167
\(339\) 53.8716 2.92590
\(340\) 15.0771 0.817668
\(341\) 1.28249 0.0694505
\(342\) 56.1000 3.03354
\(343\) −67.5220 −3.64585
\(344\) 11.1886 0.603251
\(345\) 8.41324 0.452954
\(346\) −35.1731 −1.89092
\(347\) −14.9588 −0.803031 −0.401515 0.915852i \(-0.631516\pi\)
−0.401515 + 0.915852i \(0.631516\pi\)
\(348\) 88.5185 4.74509
\(349\) 23.1858 1.24111 0.620555 0.784163i \(-0.286907\pi\)
0.620555 + 0.784163i \(0.286907\pi\)
\(350\) −19.9652 −1.06719
\(351\) −2.49999 −0.133439
\(352\) 28.4379 1.51574
\(353\) 28.8079 1.53329 0.766645 0.642072i \(-0.221925\pi\)
0.766645 + 0.642072i \(0.221925\pi\)
\(354\) 19.0590 1.01297
\(355\) 17.2125 0.913546
\(356\) 75.5125 4.00216
\(357\) 21.8217 1.15493
\(358\) 65.4221 3.45766
\(359\) 16.1183 0.850693 0.425346 0.905031i \(-0.360152\pi\)
0.425346 + 0.905031i \(0.360152\pi\)
\(360\) 52.7562 2.78050
\(361\) 15.1386 0.796770
\(362\) −34.3055 −1.80305
\(363\) −13.6814 −0.718085
\(364\) 38.1443 1.99930
\(365\) 7.22059 0.377943
\(366\) 65.6019 3.42906
\(367\) −4.14453 −0.216343 −0.108171 0.994132i \(-0.534500\pi\)
−0.108171 + 0.994132i \(0.534500\pi\)
\(368\) −17.9858 −0.937573
\(369\) −37.5872 −1.95671
\(370\) 22.6468 1.17735
\(371\) −49.9732 −2.59448
\(372\) −6.81942 −0.353570
\(373\) 0.618856 0.0320432 0.0160216 0.999872i \(-0.494900\pi\)
0.0160216 + 0.999872i \(0.494900\pi\)
\(374\) −10.2244 −0.528691
\(375\) 31.3431 1.61855
\(376\) −38.5488 −1.98800
\(377\) −10.4082 −0.536048
\(378\) 22.9031 1.17801
\(379\) −34.5814 −1.77633 −0.888163 0.459528i \(-0.848018\pi\)
−0.888163 + 0.459528i \(0.848018\pi\)
\(380\) 54.0882 2.77466
\(381\) 13.3715 0.685041
\(382\) −1.87597 −0.0959830
\(383\) −26.5601 −1.35716 −0.678579 0.734527i \(-0.737404\pi\)
−0.678579 + 0.734527i \(0.737404\pi\)
\(384\) −10.5006 −0.535855
\(385\) −23.3257 −1.18879
\(386\) 37.0593 1.88627
\(387\) −5.31494 −0.270173
\(388\) 35.2095 1.78749
\(389\) 10.2333 0.518848 0.259424 0.965763i \(-0.416467\pi\)
0.259424 + 0.965763i \(0.416467\pi\)
\(390\) −19.0414 −0.964200
\(391\) 2.82447 0.142840
\(392\) −153.632 −7.75960
\(393\) −10.9938 −0.554565
\(394\) −22.4241 −1.12971
\(395\) −2.20569 −0.110980
\(396\) −42.8563 −2.15361
\(397\) −25.1226 −1.26087 −0.630435 0.776242i \(-0.717123\pi\)
−0.630435 + 0.776242i \(0.717123\pi\)
\(398\) −17.9394 −0.899220
\(399\) 78.2842 3.91911
\(400\) −15.1490 −0.757450
\(401\) 6.98287 0.348708 0.174354 0.984683i \(-0.444216\pi\)
0.174354 + 0.984683i \(0.444216\pi\)
\(402\) 28.1597 1.40448
\(403\) 0.801840 0.0399425
\(404\) −73.9345 −3.67838
\(405\) 12.4701 0.619644
\(406\) 95.3521 4.73224
\(407\) −10.9195 −0.541260
\(408\) 32.2691 1.59756
\(409\) 19.5955 0.968934 0.484467 0.874809i \(-0.339014\pi\)
0.484467 + 0.874809i \(0.339014\pi\)
\(410\) −50.9689 −2.51717
\(411\) −2.33535 −0.115194
\(412\) −83.3509 −4.10640
\(413\) 14.5972 0.718283
\(414\) 16.6510 0.818350
\(415\) −30.8048 −1.51215
\(416\) 17.7800 0.871737
\(417\) 29.4358 1.44148
\(418\) −36.6795 −1.79405
\(419\) −25.5195 −1.24671 −0.623355 0.781939i \(-0.714231\pi\)
−0.623355 + 0.781939i \(0.714231\pi\)
\(420\) 124.031 6.05209
\(421\) 18.9026 0.921256 0.460628 0.887593i \(-0.347624\pi\)
0.460628 + 0.887593i \(0.347624\pi\)
\(422\) 11.6646 0.567826
\(423\) 18.3118 0.890353
\(424\) −73.8986 −3.58883
\(425\) 2.37899 0.115398
\(426\) 62.0670 3.00715
\(427\) 50.2443 2.43149
\(428\) 25.3459 1.22514
\(429\) 9.18111 0.443268
\(430\) −7.20714 −0.347559
\(431\) −2.12608 −0.102410 −0.0512049 0.998688i \(-0.516306\pi\)
−0.0512049 + 0.998688i \(0.516306\pi\)
\(432\) 17.3782 0.836107
\(433\) 14.4247 0.693205 0.346603 0.938012i \(-0.387335\pi\)
0.346603 + 0.938012i \(0.387335\pi\)
\(434\) −7.34588 −0.352613
\(435\) −33.8434 −1.62267
\(436\) −35.9787 −1.72307
\(437\) 10.1326 0.484710
\(438\) 26.0369 1.24409
\(439\) −5.30809 −0.253341 −0.126671 0.991945i \(-0.540429\pi\)
−0.126671 + 0.991945i \(0.540429\pi\)
\(440\) −34.4933 −1.64440
\(441\) 72.9799 3.47523
\(442\) −6.39253 −0.304062
\(443\) −16.2659 −0.772819 −0.386409 0.922327i \(-0.626285\pi\)
−0.386409 + 0.922327i \(0.626285\pi\)
\(444\) 58.0628 2.75554
\(445\) −28.8709 −1.36861
\(446\) 31.6344 1.49793
\(447\) 1.96928 0.0931437
\(448\) −55.1156 −2.60397
\(449\) 32.6158 1.53924 0.769618 0.638504i \(-0.220447\pi\)
0.769618 + 0.638504i \(0.220447\pi\)
\(450\) 14.0247 0.661132
\(451\) 24.5754 1.15721
\(452\) 102.796 4.83511
\(453\) 29.6031 1.39088
\(454\) −0.769803 −0.0361286
\(455\) −14.5838 −0.683698
\(456\) 115.764 5.42114
\(457\) −37.0849 −1.73476 −0.867380 0.497646i \(-0.834198\pi\)
−0.867380 + 0.497646i \(0.834198\pi\)
\(458\) −44.3760 −2.07355
\(459\) −2.72905 −0.127381
\(460\) 16.0538 0.748514
\(461\) −42.0065 −1.95644 −0.978219 0.207575i \(-0.933443\pi\)
−0.978219 + 0.207575i \(0.933443\pi\)
\(462\) −84.1107 −3.91319
\(463\) −2.02304 −0.0940187 −0.0470093 0.998894i \(-0.514969\pi\)
−0.0470093 + 0.998894i \(0.514969\pi\)
\(464\) 72.3503 3.35878
\(465\) 2.60728 0.120910
\(466\) −12.3808 −0.573530
\(467\) −15.7542 −0.729016 −0.364508 0.931200i \(-0.618763\pi\)
−0.364508 + 0.931200i \(0.618763\pi\)
\(468\) −26.7948 −1.23859
\(469\) 21.5674 0.995892
\(470\) 24.8312 1.14538
\(471\) 16.5274 0.761541
\(472\) 21.5859 0.993571
\(473\) 3.47503 0.159782
\(474\) −7.95354 −0.365318
\(475\) 8.53449 0.391589
\(476\) 41.6393 1.90853
\(477\) 35.1040 1.60730
\(478\) 60.5138 2.76784
\(479\) 25.7390 1.17605 0.588023 0.808844i \(-0.299906\pi\)
0.588023 + 0.808844i \(0.299906\pi\)
\(480\) 57.8140 2.63883
\(481\) −6.82713 −0.311290
\(482\) −9.80878 −0.446778
\(483\) 23.2354 1.05725
\(484\) −26.1063 −1.18665
\(485\) −13.4617 −0.611265
\(486\) 58.1903 2.63957
\(487\) 37.7771 1.71184 0.855921 0.517107i \(-0.172991\pi\)
0.855921 + 0.517107i \(0.172991\pi\)
\(488\) 74.2996 3.36338
\(489\) 25.7891 1.16622
\(490\) 98.9619 4.47064
\(491\) −30.2872 −1.36684 −0.683422 0.730024i \(-0.739509\pi\)
−0.683422 + 0.730024i \(0.739509\pi\)
\(492\) −130.676 −5.89133
\(493\) −11.3618 −0.511711
\(494\) −22.9329 −1.03180
\(495\) 16.3853 0.736467
\(496\) −5.57383 −0.250272
\(497\) 47.5370 2.13232
\(498\) −111.080 −4.97759
\(499\) −39.0529 −1.74825 −0.874125 0.485701i \(-0.838564\pi\)
−0.874125 + 0.485701i \(0.838564\pi\)
\(500\) 59.8077 2.67468
\(501\) 50.4893 2.25570
\(502\) 28.6365 1.27811
\(503\) 33.1690 1.47893 0.739465 0.673195i \(-0.235078\pi\)
0.739465 + 0.673195i \(0.235078\pi\)
\(504\) 145.700 6.49001
\(505\) 28.2675 1.25789
\(506\) −10.8868 −0.483977
\(507\) −27.7831 −1.23389
\(508\) 25.5149 1.13204
\(509\) 2.44491 0.108369 0.0541843 0.998531i \(-0.482744\pi\)
0.0541843 + 0.998531i \(0.482744\pi\)
\(510\) −20.7861 −0.920425
\(511\) 19.9416 0.882164
\(512\) 35.7754 1.58107
\(513\) −9.79033 −0.432254
\(514\) −25.0532 −1.10505
\(515\) 31.8677 1.40426
\(516\) −18.4780 −0.813447
\(517\) −11.9727 −0.526560
\(518\) 62.5452 2.74808
\(519\) 34.4780 1.51342
\(520\) −21.5660 −0.945732
\(521\) −10.0990 −0.442447 −0.221223 0.975223i \(-0.571005\pi\)
−0.221223 + 0.975223i \(0.571005\pi\)
\(522\) −66.9808 −2.93167
\(523\) 12.5025 0.546697 0.273349 0.961915i \(-0.411869\pi\)
0.273349 + 0.961915i \(0.411869\pi\)
\(524\) −20.9780 −0.916428
\(525\) 19.5707 0.854134
\(526\) −69.6290 −3.03597
\(527\) 0.875309 0.0381291
\(528\) −63.8207 −2.77744
\(529\) −19.9925 −0.869241
\(530\) 47.6017 2.06768
\(531\) −10.2539 −0.444983
\(532\) 149.379 6.47640
\(533\) 15.3651 0.665537
\(534\) −104.106 −4.50511
\(535\) −9.69056 −0.418959
\(536\) 31.8932 1.37758
\(537\) −64.1292 −2.76738
\(538\) −22.4645 −0.968514
\(539\) −47.7160 −2.05527
\(540\) −15.5115 −0.667508
\(541\) 19.8871 0.855012 0.427506 0.904012i \(-0.359392\pi\)
0.427506 + 0.904012i \(0.359392\pi\)
\(542\) −47.9289 −2.05872
\(543\) 33.6275 1.44309
\(544\) 19.4091 0.832160
\(545\) 13.7558 0.589234
\(546\) −52.5880 −2.25056
\(547\) 12.4081 0.530532 0.265266 0.964175i \(-0.414540\pi\)
0.265266 + 0.964175i \(0.414540\pi\)
\(548\) −4.45623 −0.190361
\(549\) −35.2945 −1.50633
\(550\) −9.16970 −0.390997
\(551\) −40.7600 −1.73643
\(552\) 34.3597 1.46245
\(553\) −6.09160 −0.259041
\(554\) 11.7384 0.498715
\(555\) −22.1993 −0.942306
\(556\) 56.1682 2.38206
\(557\) 35.1163 1.48792 0.743962 0.668222i \(-0.232944\pi\)
0.743962 + 0.668222i \(0.232944\pi\)
\(558\) 5.16017 0.218447
\(559\) 2.17267 0.0918942
\(560\) 101.376 4.28393
\(561\) 10.0223 0.423144
\(562\) 23.2640 0.981332
\(563\) −22.6183 −0.953247 −0.476624 0.879108i \(-0.658140\pi\)
−0.476624 + 0.879108i \(0.658140\pi\)
\(564\) 63.6631 2.68070
\(565\) −39.3021 −1.65345
\(566\) 8.57760 0.360543
\(567\) 34.4395 1.44632
\(568\) 70.2960 2.94956
\(569\) 22.8212 0.956714 0.478357 0.878165i \(-0.341232\pi\)
0.478357 + 0.878165i \(0.341232\pi\)
\(570\) −74.5691 −3.12336
\(571\) 31.3680 1.31271 0.656356 0.754451i \(-0.272097\pi\)
0.656356 + 0.754451i \(0.272097\pi\)
\(572\) 17.5191 0.732509
\(573\) 1.83890 0.0768210
\(574\) −140.764 −5.87538
\(575\) 2.53311 0.105638
\(576\) 38.7164 1.61318
\(577\) −1.13044 −0.0470607 −0.0235303 0.999723i \(-0.507491\pi\)
−0.0235303 + 0.999723i \(0.507491\pi\)
\(578\) 37.7437 1.56993
\(579\) −36.3269 −1.50969
\(580\) −64.5788 −2.68149
\(581\) −85.0756 −3.52953
\(582\) −48.5418 −2.01212
\(583\) −22.9519 −0.950569
\(584\) 29.4889 1.22026
\(585\) 10.2445 0.423558
\(586\) 6.39007 0.263971
\(587\) 13.3150 0.549569 0.274785 0.961506i \(-0.411393\pi\)
0.274785 + 0.961506i \(0.411393\pi\)
\(588\) 253.722 10.4633
\(589\) 3.14013 0.129387
\(590\) −13.9045 −0.572440
\(591\) 21.9810 0.904176
\(592\) 47.4574 1.95049
\(593\) −23.2620 −0.955254 −0.477627 0.878563i \(-0.658503\pi\)
−0.477627 + 0.878563i \(0.658503\pi\)
\(594\) 10.5190 0.431600
\(595\) −15.9200 −0.652658
\(596\) 3.75770 0.153922
\(597\) 17.5849 0.719701
\(598\) −6.80668 −0.278346
\(599\) −34.6224 −1.41463 −0.707317 0.706896i \(-0.750095\pi\)
−0.707317 + 0.706896i \(0.750095\pi\)
\(600\) 28.9404 1.18149
\(601\) −5.35627 −0.218487 −0.109243 0.994015i \(-0.534843\pi\)
−0.109243 + 0.994015i \(0.534843\pi\)
\(602\) −19.9044 −0.811245
\(603\) −15.1502 −0.616965
\(604\) 56.4875 2.29845
\(605\) 9.98126 0.405796
\(606\) 101.930 4.14064
\(607\) −27.1448 −1.10178 −0.550888 0.834579i \(-0.685711\pi\)
−0.550888 + 0.834579i \(0.685711\pi\)
\(608\) 69.6293 2.82384
\(609\) −93.4677 −3.78750
\(610\) −47.8600 −1.93779
\(611\) −7.48563 −0.302836
\(612\) −29.2499 −1.18236
\(613\) 12.2180 0.493480 0.246740 0.969082i \(-0.420641\pi\)
0.246740 + 0.969082i \(0.420641\pi\)
\(614\) −7.32923 −0.295783
\(615\) 49.9616 2.01465
\(616\) −95.2624 −3.83823
\(617\) 12.2204 0.491975 0.245987 0.969273i \(-0.420888\pi\)
0.245987 + 0.969273i \(0.420888\pi\)
\(618\) 114.912 4.62246
\(619\) 7.24260 0.291105 0.145552 0.989351i \(-0.453504\pi\)
0.145552 + 0.989351i \(0.453504\pi\)
\(620\) 4.97512 0.199806
\(621\) −2.90585 −0.116608
\(622\) −37.7693 −1.51441
\(623\) −79.7346 −3.19450
\(624\) −39.9022 −1.59737
\(625\) −15.5630 −0.622521
\(626\) 46.3916 1.85418
\(627\) 35.9547 1.43589
\(628\) 31.5369 1.25846
\(629\) −7.45267 −0.297158
\(630\) −93.8527 −3.73918
\(631\) −22.0512 −0.877844 −0.438922 0.898525i \(-0.644640\pi\)
−0.438922 + 0.898525i \(0.644640\pi\)
\(632\) −9.00805 −0.358321
\(633\) −11.4341 −0.454466
\(634\) −77.0363 −3.05950
\(635\) −9.75518 −0.387123
\(636\) 122.043 4.83932
\(637\) −29.8331 −1.18203
\(638\) 43.7937 1.73381
\(639\) −33.3927 −1.32100
\(640\) 7.66071 0.302816
\(641\) 20.8398 0.823123 0.411561 0.911382i \(-0.364984\pi\)
0.411561 + 0.911382i \(0.364984\pi\)
\(642\) −34.9434 −1.37911
\(643\) 23.4145 0.923379 0.461689 0.887042i \(-0.347243\pi\)
0.461689 + 0.887042i \(0.347243\pi\)
\(644\) 44.3370 1.74712
\(645\) 7.06471 0.278173
\(646\) −25.0341 −0.984955
\(647\) 37.6497 1.48016 0.740081 0.672518i \(-0.234787\pi\)
0.740081 + 0.672518i \(0.234787\pi\)
\(648\) 50.9280 2.00064
\(649\) 6.70428 0.263166
\(650\) −5.73311 −0.224871
\(651\) 7.20071 0.282218
\(652\) 49.2099 1.92721
\(653\) −15.4474 −0.604504 −0.302252 0.953228i \(-0.597738\pi\)
−0.302252 + 0.953228i \(0.597738\pi\)
\(654\) 49.6024 1.93961
\(655\) 8.02056 0.313389
\(656\) −106.808 −4.17014
\(657\) −14.0081 −0.546509
\(658\) 68.5779 2.67344
\(659\) 2.30952 0.0899661 0.0449831 0.998988i \(-0.485677\pi\)
0.0449831 + 0.998988i \(0.485677\pi\)
\(660\) 56.9654 2.21738
\(661\) −4.41238 −0.171622 −0.0858108 0.996311i \(-0.527348\pi\)
−0.0858108 + 0.996311i \(0.527348\pi\)
\(662\) 36.8070 1.43055
\(663\) 6.26620 0.243359
\(664\) −125.807 −4.88225
\(665\) −57.1124 −2.21472
\(666\) −43.9354 −1.70246
\(667\) −12.0979 −0.468433
\(668\) 96.3419 3.72758
\(669\) −31.0093 −1.19889
\(670\) −20.5439 −0.793682
\(671\) 23.0764 0.890855
\(672\) 159.669 6.15935
\(673\) 20.7020 0.798005 0.399003 0.916950i \(-0.369356\pi\)
0.399003 + 0.916950i \(0.369356\pi\)
\(674\) 41.2087 1.58730
\(675\) −2.44753 −0.0942057
\(676\) −53.0147 −2.03903
\(677\) −40.3643 −1.55133 −0.775663 0.631148i \(-0.782584\pi\)
−0.775663 + 0.631148i \(0.782584\pi\)
\(678\) −141.720 −5.44274
\(679\) −37.1781 −1.42676
\(680\) −23.5420 −0.902795
\(681\) 0.754590 0.0289160
\(682\) −3.37384 −0.129191
\(683\) −30.9344 −1.18367 −0.591837 0.806058i \(-0.701597\pi\)
−0.591837 + 0.806058i \(0.701597\pi\)
\(684\) −104.932 −4.01219
\(685\) 1.70376 0.0650973
\(686\) 177.631 6.78197
\(687\) 43.4991 1.65959
\(688\) −15.1029 −0.575793
\(689\) −14.3500 −0.546693
\(690\) −22.1328 −0.842580
\(691\) −19.3918 −0.737700 −0.368850 0.929489i \(-0.620248\pi\)
−0.368850 + 0.929489i \(0.620248\pi\)
\(692\) 65.7896 2.50095
\(693\) 45.2525 1.71900
\(694\) 39.3522 1.49379
\(695\) −21.4749 −0.814590
\(696\) −138.217 −5.23910
\(697\) 16.7730 0.635321
\(698\) −60.9951 −2.30870
\(699\) 12.1361 0.459031
\(700\) 37.3440 1.41147
\(701\) 26.5665 1.00340 0.501701 0.865041i \(-0.332708\pi\)
0.501701 + 0.865041i \(0.332708\pi\)
\(702\) 6.57673 0.248223
\(703\) −26.7361 −1.00837
\(704\) −25.3137 −0.954046
\(705\) −24.3405 −0.916714
\(706\) −75.7851 −2.85221
\(707\) 78.0683 2.93606
\(708\) −35.6489 −1.33977
\(709\) −12.3303 −0.463075 −0.231538 0.972826i \(-0.574376\pi\)
−0.231538 + 0.972826i \(0.574376\pi\)
\(710\) −45.2811 −1.69937
\(711\) 4.27909 0.160479
\(712\) −117.909 −4.41882
\(713\) 0.932017 0.0349043
\(714\) −57.4064 −2.14838
\(715\) −6.69810 −0.250495
\(716\) −122.369 −4.57314
\(717\) −59.3179 −2.21527
\(718\) −42.4026 −1.58245
\(719\) −3.67714 −0.137134 −0.0685671 0.997647i \(-0.521843\pi\)
−0.0685671 + 0.997647i \(0.521843\pi\)
\(720\) −71.2126 −2.65394
\(721\) 88.0112 3.27771
\(722\) −39.8253 −1.48214
\(723\) 9.61494 0.357583
\(724\) 64.1668 2.38474
\(725\) −10.1898 −0.378439
\(726\) 35.9916 1.33577
\(727\) −24.6617 −0.914651 −0.457326 0.889299i \(-0.651193\pi\)
−0.457326 + 0.889299i \(0.651193\pi\)
\(728\) −59.5603 −2.20745
\(729\) −37.1551 −1.37612
\(730\) −18.9953 −0.703046
\(731\) 2.37175 0.0877222
\(732\) −122.705 −4.53532
\(733\) 25.7280 0.950285 0.475142 0.879909i \(-0.342397\pi\)
0.475142 + 0.879909i \(0.342397\pi\)
\(734\) 10.9031 0.402439
\(735\) −97.0062 −3.57813
\(736\) 20.6666 0.761780
\(737\) 9.90558 0.364877
\(738\) 98.8809 3.63986
\(739\) 45.3275 1.66740 0.833700 0.552218i \(-0.186218\pi\)
0.833700 + 0.552218i \(0.186218\pi\)
\(740\) −42.3598 −1.55718
\(741\) 22.4797 0.825812
\(742\) 131.465 4.82622
\(743\) 10.1545 0.372533 0.186266 0.982499i \(-0.440361\pi\)
0.186266 + 0.982499i \(0.440361\pi\)
\(744\) 10.6482 0.390381
\(745\) −1.43669 −0.0526363
\(746\) −1.62803 −0.0596064
\(747\) 59.7620 2.18658
\(748\) 19.1243 0.699252
\(749\) −26.7631 −0.977901
\(750\) −82.4545 −3.01081
\(751\) 6.70177 0.244551 0.122275 0.992496i \(-0.460981\pi\)
0.122275 + 0.992496i \(0.460981\pi\)
\(752\) 52.0348 1.89752
\(753\) −28.0706 −1.02295
\(754\) 27.3808 0.997150
\(755\) −21.5970 −0.785995
\(756\) −42.8391 −1.55804
\(757\) −11.0870 −0.402963 −0.201482 0.979492i \(-0.564576\pi\)
−0.201482 + 0.979492i \(0.564576\pi\)
\(758\) 90.9734 3.30430
\(759\) 10.6717 0.387356
\(760\) −84.4558 −3.06353
\(761\) 14.2821 0.517725 0.258862 0.965914i \(-0.416652\pi\)
0.258862 + 0.965914i \(0.416652\pi\)
\(762\) −35.1764 −1.27431
\(763\) 37.9903 1.37534
\(764\) 3.50892 0.126948
\(765\) 11.1832 0.404328
\(766\) 69.8719 2.52457
\(767\) 4.19167 0.151352
\(768\) −27.0854 −0.977359
\(769\) 25.9443 0.935574 0.467787 0.883841i \(-0.345051\pi\)
0.467787 + 0.883841i \(0.345051\pi\)
\(770\) 61.3631 2.21137
\(771\) 24.5581 0.884438
\(772\) −69.3176 −2.49480
\(773\) 41.6109 1.49664 0.748320 0.663338i \(-0.230861\pi\)
0.748320 + 0.663338i \(0.230861\pi\)
\(774\) 13.9820 0.502574
\(775\) 0.785017 0.0281986
\(776\) −54.9777 −1.97358
\(777\) −61.3092 −2.19946
\(778\) −26.9208 −0.965157
\(779\) 60.1722 2.15589
\(780\) 35.6161 1.27526
\(781\) 21.8330 0.781245
\(782\) −7.43035 −0.265709
\(783\) 11.6892 0.417738
\(784\) 207.379 7.40640
\(785\) −12.0576 −0.430353
\(786\) 28.9215 1.03160
\(787\) −17.0112 −0.606384 −0.303192 0.952930i \(-0.598052\pi\)
−0.303192 + 0.952930i \(0.598052\pi\)
\(788\) 41.9433 1.49417
\(789\) 68.2530 2.42987
\(790\) 5.80252 0.206444
\(791\) −108.543 −3.85936
\(792\) 66.9179 2.37782
\(793\) 14.4279 0.512350
\(794\) 66.0903 2.34546
\(795\) −46.6610 −1.65489
\(796\) 33.5548 1.18932
\(797\) −39.9808 −1.41619 −0.708096 0.706117i \(-0.750445\pi\)
−0.708096 + 0.706117i \(0.750445\pi\)
\(798\) −205.943 −7.29029
\(799\) −8.17150 −0.289087
\(800\) 17.4070 0.615430
\(801\) 56.0102 1.97902
\(802\) −18.3699 −0.648663
\(803\) 9.15885 0.323209
\(804\) −52.6714 −1.85758
\(805\) −16.9514 −0.597460
\(806\) −2.10940 −0.0743006
\(807\) 22.0206 0.775160
\(808\) 115.445 4.06133
\(809\) 41.2774 1.45124 0.725618 0.688098i \(-0.241554\pi\)
0.725618 + 0.688098i \(0.241554\pi\)
\(810\) −32.8052 −1.15266
\(811\) 34.4106 1.20832 0.604159 0.796864i \(-0.293509\pi\)
0.604159 + 0.796864i \(0.293509\pi\)
\(812\) −178.352 −6.25891
\(813\) 46.9818 1.64772
\(814\) 28.7260 1.00685
\(815\) −18.8145 −0.659043
\(816\) −43.5583 −1.52484
\(817\) 8.50852 0.297675
\(818\) −51.5500 −1.80240
\(819\) 28.2929 0.988634
\(820\) 95.3349 3.32924
\(821\) −45.0807 −1.57333 −0.786663 0.617382i \(-0.788193\pi\)
−0.786663 + 0.617382i \(0.788193\pi\)
\(822\) 6.14362 0.214283
\(823\) 33.9845 1.18462 0.592312 0.805709i \(-0.298215\pi\)
0.592312 + 0.805709i \(0.298215\pi\)
\(824\) 130.148 4.53392
\(825\) 8.98849 0.312939
\(826\) −38.4010 −1.33614
\(827\) −39.7893 −1.38361 −0.691804 0.722085i \(-0.743184\pi\)
−0.691804 + 0.722085i \(0.743184\pi\)
\(828\) −31.1448 −1.08236
\(829\) −7.96733 −0.276717 −0.138358 0.990382i \(-0.544183\pi\)
−0.138358 + 0.990382i \(0.544183\pi\)
\(830\) 81.0383 2.81288
\(831\) −11.5064 −0.399152
\(832\) −15.8267 −0.548692
\(833\) −32.5666 −1.12837
\(834\) −77.4369 −2.68142
\(835\) −36.8346 −1.27471
\(836\) 68.6073 2.37283
\(837\) −0.900531 −0.0311269
\(838\) 67.1344 2.31912
\(839\) 20.5992 0.711163 0.355582 0.934645i \(-0.384283\pi\)
0.355582 + 0.934645i \(0.384283\pi\)
\(840\) −193.668 −6.68217
\(841\) 19.6655 0.678122
\(842\) −49.7271 −1.71371
\(843\) −22.8042 −0.785420
\(844\) −21.8182 −0.751013
\(845\) 20.2692 0.697282
\(846\) −48.1731 −1.65622
\(847\) 27.5659 0.947176
\(848\) 99.7515 3.42548
\(849\) −8.40809 −0.288565
\(850\) −6.25841 −0.214662
\(851\) −7.93550 −0.272025
\(852\) −116.093 −3.97729
\(853\) −20.6810 −0.708103 −0.354052 0.935226i \(-0.615196\pi\)
−0.354052 + 0.935226i \(0.615196\pi\)
\(854\) −132.178 −4.52304
\(855\) 40.1190 1.37204
\(856\) −39.5763 −1.35269
\(857\) −58.4352 −1.99611 −0.998054 0.0623527i \(-0.980140\pi\)
−0.998054 + 0.0623527i \(0.980140\pi\)
\(858\) −24.1528 −0.824563
\(859\) −4.63659 −0.158198 −0.0790992 0.996867i \(-0.525204\pi\)
−0.0790992 + 0.996867i \(0.525204\pi\)
\(860\) 13.4806 0.459686
\(861\) 137.982 4.70243
\(862\) 5.59310 0.190502
\(863\) −11.8668 −0.403951 −0.201976 0.979391i \(-0.564736\pi\)
−0.201976 + 0.979391i \(0.564736\pi\)
\(864\) −19.9684 −0.679339
\(865\) −25.1535 −0.855244
\(866\) −37.9470 −1.28949
\(867\) −36.9979 −1.25651
\(868\) 13.7401 0.466370
\(869\) −2.79777 −0.0949080
\(870\) 89.0322 3.01847
\(871\) 6.19320 0.209848
\(872\) 56.1788 1.90245
\(873\) 26.1161 0.883894
\(874\) −26.6560 −0.901652
\(875\) −63.1517 −2.13492
\(876\) −48.7008 −1.64545
\(877\) 49.7547 1.68010 0.840048 0.542511i \(-0.182526\pi\)
0.840048 + 0.542511i \(0.182526\pi\)
\(878\) 13.9640 0.471263
\(879\) −6.26379 −0.211272
\(880\) 46.5605 1.56955
\(881\) −24.6769 −0.831385 −0.415693 0.909505i \(-0.636461\pi\)
−0.415693 + 0.909505i \(0.636461\pi\)
\(882\) −191.989 −6.46459
\(883\) 51.9930 1.74970 0.874851 0.484391i \(-0.160959\pi\)
0.874851 + 0.484391i \(0.160959\pi\)
\(884\) 11.9569 0.402155
\(885\) 13.6297 0.458159
\(886\) 42.7909 1.43759
\(887\) −52.4095 −1.75974 −0.879869 0.475216i \(-0.842370\pi\)
−0.879869 + 0.475216i \(0.842370\pi\)
\(888\) −90.6619 −3.04242
\(889\) −26.9415 −0.903590
\(890\) 75.9507 2.54587
\(891\) 15.8175 0.529907
\(892\) −59.1708 −1.98118
\(893\) −29.3149 −0.980984
\(894\) −5.18059 −0.173265
\(895\) 46.7856 1.56387
\(896\) 21.1571 0.706809
\(897\) 6.67216 0.222777
\(898\) −85.8027 −2.86327
\(899\) −3.74917 −0.125042
\(900\) −26.2326 −0.874420
\(901\) −15.6649 −0.521873
\(902\) −64.6507 −2.15263
\(903\) 19.5111 0.649289
\(904\) −160.510 −5.33849
\(905\) −24.5330 −0.815505
\(906\) −77.8771 −2.58729
\(907\) 55.7111 1.84986 0.924928 0.380142i \(-0.124125\pi\)
0.924928 + 0.380142i \(0.124125\pi\)
\(908\) 1.43988 0.0477841
\(909\) −54.8397 −1.81892
\(910\) 38.3657 1.27181
\(911\) 27.9443 0.925837 0.462918 0.886401i \(-0.346802\pi\)
0.462918 + 0.886401i \(0.346802\pi\)
\(912\) −156.263 −5.17439
\(913\) −39.0739 −1.29316
\(914\) 97.5596 3.22698
\(915\) 46.9142 1.55093
\(916\) 83.0033 2.74251
\(917\) 22.1509 0.731488
\(918\) 7.17933 0.236953
\(919\) 22.5498 0.743850 0.371925 0.928263i \(-0.378698\pi\)
0.371925 + 0.928263i \(0.378698\pi\)
\(920\) −25.0672 −0.826441
\(921\) 7.18439 0.236734
\(922\) 110.507 3.63935
\(923\) 13.6505 0.449311
\(924\) 157.325 5.17562
\(925\) −6.68389 −0.219765
\(926\) 5.32202 0.174893
\(927\) −61.8242 −2.03057
\(928\) −83.1342 −2.72901
\(929\) 4.20631 0.138005 0.0690023 0.997617i \(-0.478018\pi\)
0.0690023 + 0.997617i \(0.478018\pi\)
\(930\) −6.85900 −0.224915
\(931\) −116.831 −3.82899
\(932\) 23.1577 0.758556
\(933\) 37.0229 1.21208
\(934\) 41.4446 1.35611
\(935\) −7.31182 −0.239122
\(936\) 41.8386 1.36754
\(937\) −15.5299 −0.507340 −0.253670 0.967291i \(-0.581638\pi\)
−0.253670 + 0.967291i \(0.581638\pi\)
\(938\) −56.7376 −1.85255
\(939\) −45.4748 −1.48401
\(940\) −46.4455 −1.51489
\(941\) −27.9023 −0.909589 −0.454794 0.890596i \(-0.650287\pi\)
−0.454794 + 0.890596i \(0.650287\pi\)
\(942\) −43.4786 −1.41661
\(943\) 17.8596 0.581589
\(944\) −29.1375 −0.948346
\(945\) 16.3788 0.532801
\(946\) −9.14179 −0.297225
\(947\) −18.6431 −0.605819 −0.302909 0.953019i \(-0.597958\pi\)
−0.302909 + 0.953019i \(0.597958\pi\)
\(948\) 14.8767 0.483174
\(949\) 5.72633 0.185884
\(950\) −22.4517 −0.728431
\(951\) 75.5139 2.44871
\(952\) −65.0176 −2.10723
\(953\) 41.7706 1.35308 0.676542 0.736404i \(-0.263478\pi\)
0.676542 + 0.736404i \(0.263478\pi\)
\(954\) −92.3484 −2.98989
\(955\) −1.34157 −0.0434122
\(956\) −113.188 −3.66077
\(957\) −42.9282 −1.38767
\(958\) −67.7118 −2.18767
\(959\) 4.70539 0.151945
\(960\) −51.4625 −1.66095
\(961\) −30.7112 −0.990683
\(962\) 17.9602 0.579059
\(963\) 18.7999 0.605819
\(964\) 18.3469 0.590913
\(965\) 26.5023 0.853141
\(966\) −61.1255 −1.96668
\(967\) −14.4232 −0.463817 −0.231909 0.972738i \(-0.574497\pi\)
−0.231909 + 0.972738i \(0.574497\pi\)
\(968\) 40.7635 1.31019
\(969\) 24.5394 0.788319
\(970\) 35.4138 1.13707
\(971\) 50.8289 1.63118 0.815589 0.578632i \(-0.196413\pi\)
0.815589 + 0.578632i \(0.196413\pi\)
\(972\) −108.842 −3.49112
\(973\) −59.3087 −1.90135
\(974\) −99.3803 −3.18435
\(975\) 5.61981 0.179978
\(976\) −100.293 −3.21029
\(977\) 55.4883 1.77523 0.887614 0.460588i \(-0.152361\pi\)
0.887614 + 0.460588i \(0.152361\pi\)
\(978\) −67.8436 −2.16940
\(979\) −36.6208 −1.17041
\(980\) −185.104 −5.91292
\(981\) −26.6866 −0.852038
\(982\) 79.6768 2.54259
\(983\) −5.97313 −0.190513 −0.0952566 0.995453i \(-0.530367\pi\)
−0.0952566 + 0.995453i \(0.530367\pi\)
\(984\) 204.044 6.50467
\(985\) −16.0363 −0.510958
\(986\) 29.8896 0.951879
\(987\) −67.2227 −2.13972
\(988\) 42.8949 1.36467
\(989\) 2.52540 0.0803031
\(990\) −43.1050 −1.36997
\(991\) 58.7877 1.86745 0.933726 0.357988i \(-0.116537\pi\)
0.933726 + 0.357988i \(0.116537\pi\)
\(992\) 6.40462 0.203347
\(993\) −36.0797 −1.14495
\(994\) −125.056 −3.96653
\(995\) −12.8291 −0.406709
\(996\) 207.769 6.58342
\(997\) −20.4121 −0.646457 −0.323228 0.946321i \(-0.604768\pi\)
−0.323228 + 0.946321i \(0.604768\pi\)
\(998\) 102.737 3.25208
\(999\) 7.66742 0.242586
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.1.5 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.5 179 1.1 even 1 trivial