Properties

Label 8003.2.a.b.1.2
Level 8003
Weight 2
Character 8003.1
Self dual yes
Analytic conductor 63.904
Analytic rank 1
Dimension 153
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.76122 q^{2} -1.93941 q^{3} +5.62432 q^{4} -0.205414 q^{5} +5.35515 q^{6} -1.99038 q^{7} -10.0076 q^{8} +0.761331 q^{9} +O(q^{10})\) \(q-2.76122 q^{2} -1.93941 q^{3} +5.62432 q^{4} -0.205414 q^{5} +5.35515 q^{6} -1.99038 q^{7} -10.0076 q^{8} +0.761331 q^{9} +0.567192 q^{10} -3.85911 q^{11} -10.9079 q^{12} +2.35317 q^{13} +5.49587 q^{14} +0.398382 q^{15} +16.3844 q^{16} +6.01787 q^{17} -2.10220 q^{18} -0.129844 q^{19} -1.15531 q^{20} +3.86017 q^{21} +10.6558 q^{22} +3.90927 q^{23} +19.4088 q^{24} -4.95781 q^{25} -6.49761 q^{26} +4.34171 q^{27} -11.1945 q^{28} +0.957838 q^{29} -1.10002 q^{30} -1.15433 q^{31} -25.2257 q^{32} +7.48442 q^{33} -16.6167 q^{34} +0.408851 q^{35} +4.28197 q^{36} -7.73361 q^{37} +0.358529 q^{38} -4.56377 q^{39} +2.05569 q^{40} -4.49823 q^{41} -10.6588 q^{42} -0.734170 q^{43} -21.7049 q^{44} -0.156388 q^{45} -10.7944 q^{46} +0.262826 q^{47} -31.7761 q^{48} -3.03840 q^{49} +13.6896 q^{50} -11.6712 q^{51} +13.2350 q^{52} -1.00000 q^{53} -11.9884 q^{54} +0.792714 q^{55} +19.9188 q^{56} +0.251822 q^{57} -2.64480 q^{58} +11.0473 q^{59} +2.24063 q^{60} -3.50583 q^{61} +3.18737 q^{62} -1.51534 q^{63} +36.8850 q^{64} -0.483373 q^{65} -20.6661 q^{66} -14.4410 q^{67} +33.8465 q^{68} -7.58170 q^{69} -1.12893 q^{70} +14.4755 q^{71} -7.61905 q^{72} -11.8770 q^{73} +21.3542 q^{74} +9.61524 q^{75} -0.730288 q^{76} +7.68109 q^{77} +12.6016 q^{78} +8.94065 q^{79} -3.36558 q^{80} -10.7044 q^{81} +12.4206 q^{82} -9.37659 q^{83} +21.7108 q^{84} -1.23615 q^{85} +2.02720 q^{86} -1.85764 q^{87} +38.6202 q^{88} +5.83301 q^{89} +0.431820 q^{90} -4.68370 q^{91} +21.9870 q^{92} +2.23873 q^{93} -0.725720 q^{94} +0.0266718 q^{95} +48.9232 q^{96} -8.77372 q^{97} +8.38967 q^{98} -2.93806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76122 −1.95248 −0.976238 0.216701i \(-0.930470\pi\)
−0.976238 + 0.216701i \(0.930470\pi\)
\(3\) −1.93941 −1.11972 −0.559861 0.828587i \(-0.689145\pi\)
−0.559861 + 0.828587i \(0.689145\pi\)
\(4\) 5.62432 2.81216
\(5\) −0.205414 −0.0918638 −0.0459319 0.998945i \(-0.514626\pi\)
−0.0459319 + 0.998945i \(0.514626\pi\)
\(6\) 5.35515 2.18623
\(7\) −1.99038 −0.752292 −0.376146 0.926560i \(-0.622751\pi\)
−0.376146 + 0.926560i \(0.622751\pi\)
\(8\) −10.0076 −3.53820
\(9\) 0.761331 0.253777
\(10\) 0.567192 0.179362
\(11\) −3.85911 −1.16357 −0.581783 0.813344i \(-0.697645\pi\)
−0.581783 + 0.813344i \(0.697645\pi\)
\(12\) −10.9079 −3.14884
\(13\) 2.35317 0.652652 0.326326 0.945257i \(-0.394189\pi\)
0.326326 + 0.945257i \(0.394189\pi\)
\(14\) 5.49587 1.46883
\(15\) 0.398382 0.102862
\(16\) 16.3844 4.09610
\(17\) 6.01787 1.45955 0.729774 0.683688i \(-0.239625\pi\)
0.729774 + 0.683688i \(0.239625\pi\)
\(18\) −2.10220 −0.495493
\(19\) −0.129844 −0.0297884 −0.0148942 0.999889i \(-0.504741\pi\)
−0.0148942 + 0.999889i \(0.504741\pi\)
\(20\) −1.15531 −0.258336
\(21\) 3.86017 0.842358
\(22\) 10.6558 2.27183
\(23\) 3.90927 0.815140 0.407570 0.913174i \(-0.366376\pi\)
0.407570 + 0.913174i \(0.366376\pi\)
\(24\) 19.4088 3.96180
\(25\) −4.95781 −0.991561
\(26\) −6.49761 −1.27429
\(27\) 4.34171 0.835562
\(28\) −11.1945 −2.11557
\(29\) 0.957838 0.177866 0.0889330 0.996038i \(-0.471654\pi\)
0.0889330 + 0.996038i \(0.471654\pi\)
\(30\) −1.10002 −0.200835
\(31\) −1.15433 −0.207324 −0.103662 0.994613i \(-0.533056\pi\)
−0.103662 + 0.994613i \(0.533056\pi\)
\(32\) −25.2257 −4.45932
\(33\) 7.48442 1.30287
\(34\) −16.6167 −2.84973
\(35\) 0.408851 0.0691084
\(36\) 4.28197 0.713662
\(37\) −7.73361 −1.27140 −0.635699 0.771937i \(-0.719288\pi\)
−0.635699 + 0.771937i \(0.719288\pi\)
\(38\) 0.358529 0.0581611
\(39\) −4.56377 −0.730788
\(40\) 2.05569 0.325033
\(41\) −4.49823 −0.702506 −0.351253 0.936281i \(-0.614244\pi\)
−0.351253 + 0.936281i \(0.614244\pi\)
\(42\) −10.6588 −1.64468
\(43\) −0.734170 −0.111960 −0.0559800 0.998432i \(-0.517828\pi\)
−0.0559800 + 0.998432i \(0.517828\pi\)
\(44\) −21.7049 −3.27214
\(45\) −0.156388 −0.0233129
\(46\) −10.7944 −1.59154
\(47\) 0.262826 0.0383371 0.0191686 0.999816i \(-0.493898\pi\)
0.0191686 + 0.999816i \(0.493898\pi\)
\(48\) −31.7761 −4.58649
\(49\) −3.03840 −0.434057
\(50\) 13.6896 1.93600
\(51\) −11.6712 −1.63429
\(52\) 13.2350 1.83536
\(53\) −1.00000 −0.137361
\(54\) −11.9884 −1.63142
\(55\) 0.792714 0.106890
\(56\) 19.9188 2.66176
\(57\) 0.251822 0.0333547
\(58\) −2.64480 −0.347279
\(59\) 11.0473 1.43824 0.719121 0.694885i \(-0.244545\pi\)
0.719121 + 0.694885i \(0.244545\pi\)
\(60\) 2.24063 0.289264
\(61\) −3.50583 −0.448876 −0.224438 0.974488i \(-0.572055\pi\)
−0.224438 + 0.974488i \(0.572055\pi\)
\(62\) 3.18737 0.404796
\(63\) −1.51534 −0.190914
\(64\) 36.8850 4.61063
\(65\) −0.483373 −0.0599551
\(66\) −20.6661 −2.54382
\(67\) −14.4410 −1.76425 −0.882126 0.471013i \(-0.843889\pi\)
−0.882126 + 0.471013i \(0.843889\pi\)
\(68\) 33.8465 4.10449
\(69\) −7.58170 −0.912730
\(70\) −1.12893 −0.134932
\(71\) 14.4755 1.71792 0.858961 0.512041i \(-0.171110\pi\)
0.858961 + 0.512041i \(0.171110\pi\)
\(72\) −7.61905 −0.897914
\(73\) −11.8770 −1.39010 −0.695051 0.718960i \(-0.744618\pi\)
−0.695051 + 0.718960i \(0.744618\pi\)
\(74\) 21.3542 2.48237
\(75\) 9.61524 1.11027
\(76\) −0.730288 −0.0837697
\(77\) 7.68109 0.875341
\(78\) 12.6016 1.42685
\(79\) 8.94065 1.00590 0.502951 0.864315i \(-0.332248\pi\)
0.502951 + 0.864315i \(0.332248\pi\)
\(80\) −3.36558 −0.376283
\(81\) −10.7044 −1.18937
\(82\) 12.4206 1.37163
\(83\) −9.37659 −1.02921 −0.514607 0.857426i \(-0.672062\pi\)
−0.514607 + 0.857426i \(0.672062\pi\)
\(84\) 21.7108 2.36885
\(85\) −1.23615 −0.134080
\(86\) 2.02720 0.218599
\(87\) −1.85764 −0.199160
\(88\) 38.6202 4.11693
\(89\) 5.83301 0.618298 0.309149 0.951014i \(-0.399956\pi\)
0.309149 + 0.951014i \(0.399956\pi\)
\(90\) 0.431820 0.0455179
\(91\) −4.68370 −0.490985
\(92\) 21.9870 2.29231
\(93\) 2.23873 0.232146
\(94\) −0.725720 −0.0748523
\(95\) 0.0266718 0.00273647
\(96\) 48.9232 4.99320
\(97\) −8.77372 −0.890836 −0.445418 0.895323i \(-0.646945\pi\)
−0.445418 + 0.895323i \(0.646945\pi\)
\(98\) 8.38967 0.847485
\(99\) −2.93806 −0.295286
\(100\) −27.8843 −2.78843
\(101\) 2.64614 0.263301 0.131651 0.991296i \(-0.457972\pi\)
0.131651 + 0.991296i \(0.457972\pi\)
\(102\) 32.2266 3.19091
\(103\) −2.24563 −0.221269 −0.110634 0.993861i \(-0.535288\pi\)
−0.110634 + 0.993861i \(0.535288\pi\)
\(104\) −23.5495 −2.30921
\(105\) −0.792931 −0.0773822
\(106\) 2.76122 0.268193
\(107\) 1.50317 0.145317 0.0726587 0.997357i \(-0.476852\pi\)
0.0726587 + 0.997357i \(0.476852\pi\)
\(108\) 24.4192 2.34974
\(109\) 15.4062 1.47565 0.737823 0.674995i \(-0.235854\pi\)
0.737823 + 0.674995i \(0.235854\pi\)
\(110\) −2.18886 −0.208699
\(111\) 14.9987 1.42361
\(112\) −32.6111 −3.08146
\(113\) 19.0646 1.79344 0.896721 0.442595i \(-0.145942\pi\)
0.896721 + 0.442595i \(0.145942\pi\)
\(114\) −0.695336 −0.0651242
\(115\) −0.803018 −0.0748818
\(116\) 5.38719 0.500188
\(117\) 1.79154 0.165628
\(118\) −30.5041 −2.80813
\(119\) −11.9778 −1.09801
\(120\) −3.98683 −0.363946
\(121\) 3.89273 0.353885
\(122\) 9.68036 0.876419
\(123\) 8.72394 0.786611
\(124\) −6.49235 −0.583030
\(125\) 2.04547 0.182952
\(126\) 4.18417 0.372756
\(127\) 11.8907 1.05513 0.527565 0.849515i \(-0.323105\pi\)
0.527565 + 0.849515i \(0.323105\pi\)
\(128\) −51.3961 −4.54282
\(129\) 1.42386 0.125364
\(130\) 1.33470 0.117061
\(131\) 11.5171 1.00626 0.503129 0.864211i \(-0.332182\pi\)
0.503129 + 0.864211i \(0.332182\pi\)
\(132\) 42.0948 3.66388
\(133\) 0.258440 0.0224096
\(134\) 39.8748 3.44466
\(135\) −0.891846 −0.0767579
\(136\) −60.2242 −5.16418
\(137\) −10.8520 −0.927149 −0.463575 0.886058i \(-0.653433\pi\)
−0.463575 + 0.886058i \(0.653433\pi\)
\(138\) 20.9347 1.78208
\(139\) 6.10227 0.517588 0.258794 0.965933i \(-0.416675\pi\)
0.258794 + 0.965933i \(0.416675\pi\)
\(140\) 2.29951 0.194344
\(141\) −0.509729 −0.0429269
\(142\) −39.9699 −3.35420
\(143\) −9.08114 −0.759403
\(144\) 12.4739 1.03949
\(145\) −0.196753 −0.0163394
\(146\) 32.7951 2.71414
\(147\) 5.89271 0.486023
\(148\) −43.4964 −3.57538
\(149\) 9.37744 0.768230 0.384115 0.923285i \(-0.374507\pi\)
0.384115 + 0.923285i \(0.374507\pi\)
\(150\) −26.5498 −2.16778
\(151\) −1.00000 −0.0813788
\(152\) 1.29943 0.105397
\(153\) 4.58159 0.370400
\(154\) −21.2092 −1.70908
\(155\) 0.237116 0.0190456
\(156\) −25.6681 −2.05510
\(157\) 6.80516 0.543111 0.271555 0.962423i \(-0.412462\pi\)
0.271555 + 0.962423i \(0.412462\pi\)
\(158\) −24.6871 −1.96400
\(159\) 1.93941 0.153806
\(160\) 5.18171 0.409650
\(161\) −7.78093 −0.613223
\(162\) 29.5571 2.32222
\(163\) 6.50108 0.509204 0.254602 0.967046i \(-0.418056\pi\)
0.254602 + 0.967046i \(0.418056\pi\)
\(164\) −25.2995 −1.97556
\(165\) −1.53740 −0.119687
\(166\) 25.8908 2.00952
\(167\) −19.4983 −1.50882 −0.754410 0.656403i \(-0.772077\pi\)
−0.754410 + 0.656403i \(0.772077\pi\)
\(168\) −38.6308 −2.98043
\(169\) −7.46259 −0.574046
\(170\) 3.41329 0.261787
\(171\) −0.0988546 −0.00755960
\(172\) −4.12921 −0.314849
\(173\) −2.38549 −0.181365 −0.0906827 0.995880i \(-0.528905\pi\)
−0.0906827 + 0.995880i \(0.528905\pi\)
\(174\) 5.12936 0.388856
\(175\) 9.86791 0.745944
\(176\) −63.2291 −4.76607
\(177\) −21.4254 −1.61043
\(178\) −16.1062 −1.20721
\(179\) −8.75832 −0.654628 −0.327314 0.944916i \(-0.606143\pi\)
−0.327314 + 0.944916i \(0.606143\pi\)
\(180\) −0.879575 −0.0655596
\(181\) −12.2071 −0.907344 −0.453672 0.891169i \(-0.649886\pi\)
−0.453672 + 0.891169i \(0.649886\pi\)
\(182\) 12.9327 0.958636
\(183\) 6.79926 0.502616
\(184\) −39.1223 −2.88413
\(185\) 1.58859 0.116795
\(186\) −6.18163 −0.453259
\(187\) −23.2236 −1.69828
\(188\) 1.47822 0.107810
\(189\) −8.64164 −0.628587
\(190\) −0.0736467 −0.00534290
\(191\) 21.0990 1.52667 0.763336 0.646002i \(-0.223560\pi\)
0.763336 + 0.646002i \(0.223560\pi\)
\(192\) −71.5354 −5.16262
\(193\) −9.37943 −0.675146 −0.337573 0.941299i \(-0.609606\pi\)
−0.337573 + 0.941299i \(0.609606\pi\)
\(194\) 24.2261 1.73934
\(195\) 0.937461 0.0671330
\(196\) −17.0889 −1.22064
\(197\) 8.20728 0.584744 0.292372 0.956305i \(-0.405555\pi\)
0.292372 + 0.956305i \(0.405555\pi\)
\(198\) 8.11262 0.576539
\(199\) 23.4110 1.65956 0.829780 0.558091i \(-0.188466\pi\)
0.829780 + 0.558091i \(0.188466\pi\)
\(200\) 49.6155 3.50834
\(201\) 28.0072 1.97547
\(202\) −7.30658 −0.514089
\(203\) −1.90646 −0.133807
\(204\) −65.6424 −4.59589
\(205\) 0.923998 0.0645349
\(206\) 6.20069 0.432022
\(207\) 2.97625 0.206864
\(208\) 38.5552 2.67332
\(209\) 0.501084 0.0346607
\(210\) 2.18946 0.151087
\(211\) −13.6393 −0.938969 −0.469485 0.882941i \(-0.655560\pi\)
−0.469485 + 0.882941i \(0.655560\pi\)
\(212\) −5.62432 −0.386280
\(213\) −28.0739 −1.92359
\(214\) −4.15059 −0.283729
\(215\) 0.150809 0.0102851
\(216\) −43.4499 −2.95639
\(217\) 2.29756 0.155969
\(218\) −42.5398 −2.88116
\(219\) 23.0345 1.55653
\(220\) 4.45848 0.300591
\(221\) 14.1611 0.952577
\(222\) −41.4146 −2.77957
\(223\) 7.66713 0.513429 0.256715 0.966487i \(-0.417360\pi\)
0.256715 + 0.966487i \(0.417360\pi\)
\(224\) 50.2088 3.35471
\(225\) −3.77453 −0.251635
\(226\) −52.6414 −3.50165
\(227\) −3.45779 −0.229501 −0.114751 0.993394i \(-0.536607\pi\)
−0.114751 + 0.993394i \(0.536607\pi\)
\(228\) 1.41633 0.0937988
\(229\) 12.9231 0.853984 0.426992 0.904255i \(-0.359573\pi\)
0.426992 + 0.904255i \(0.359573\pi\)
\(230\) 2.21731 0.146205
\(231\) −14.8968 −0.980139
\(232\) −9.58561 −0.629326
\(233\) −27.0050 −1.76916 −0.884578 0.466393i \(-0.845553\pi\)
−0.884578 + 0.466393i \(0.845553\pi\)
\(234\) −4.94683 −0.323385
\(235\) −0.0539880 −0.00352179
\(236\) 62.1339 4.04457
\(237\) −17.3396 −1.12633
\(238\) 33.0734 2.14383
\(239\) 23.1943 1.50031 0.750157 0.661260i \(-0.229978\pi\)
0.750157 + 0.661260i \(0.229978\pi\)
\(240\) 6.52725 0.421332
\(241\) 15.4009 0.992058 0.496029 0.868306i \(-0.334791\pi\)
0.496029 + 0.868306i \(0.334791\pi\)
\(242\) −10.7487 −0.690951
\(243\) 7.73508 0.496206
\(244\) −19.7179 −1.26231
\(245\) 0.624128 0.0398741
\(246\) −24.0887 −1.53584
\(247\) −0.305546 −0.0194414
\(248\) 11.5521 0.733556
\(249\) 18.1851 1.15243
\(250\) −5.64799 −0.357210
\(251\) 10.2340 0.645966 0.322983 0.946405i \(-0.395314\pi\)
0.322983 + 0.946405i \(0.395314\pi\)
\(252\) −8.52274 −0.536882
\(253\) −15.0863 −0.948469
\(254\) −32.8328 −2.06012
\(255\) 2.39741 0.150132
\(256\) 68.1458 4.25911
\(257\) 10.4985 0.654878 0.327439 0.944872i \(-0.393814\pi\)
0.327439 + 0.944872i \(0.393814\pi\)
\(258\) −3.93159 −0.244770
\(259\) 15.3928 0.956463
\(260\) −2.71865 −0.168603
\(261\) 0.729231 0.0451383
\(262\) −31.8014 −1.96469
\(263\) 15.4749 0.954224 0.477112 0.878842i \(-0.341684\pi\)
0.477112 + 0.878842i \(0.341684\pi\)
\(264\) −74.9007 −4.60982
\(265\) 0.205414 0.0126185
\(266\) −0.713608 −0.0437541
\(267\) −11.3126 −0.692321
\(268\) −81.2211 −4.96137
\(269\) 7.60631 0.463765 0.231882 0.972744i \(-0.425512\pi\)
0.231882 + 0.972744i \(0.425512\pi\)
\(270\) 2.46258 0.149868
\(271\) 9.13029 0.554626 0.277313 0.960780i \(-0.410556\pi\)
0.277313 + 0.960780i \(0.410556\pi\)
\(272\) 98.5991 5.97845
\(273\) 9.08363 0.549766
\(274\) 29.9647 1.81024
\(275\) 19.1327 1.15375
\(276\) −42.6420 −2.56674
\(277\) −22.8088 −1.37045 −0.685224 0.728332i \(-0.740296\pi\)
−0.685224 + 0.728332i \(0.740296\pi\)
\(278\) −16.8497 −1.01058
\(279\) −0.878829 −0.0526141
\(280\) −4.09159 −0.244520
\(281\) −4.99900 −0.298215 −0.149108 0.988821i \(-0.547640\pi\)
−0.149108 + 0.988821i \(0.547640\pi\)
\(282\) 1.40747 0.0838137
\(283\) −19.5383 −1.16143 −0.580717 0.814106i \(-0.697228\pi\)
−0.580717 + 0.814106i \(0.697228\pi\)
\(284\) 81.4147 4.83108
\(285\) −0.0517277 −0.00306409
\(286\) 25.0750 1.48272
\(287\) 8.95318 0.528490
\(288\) −19.2051 −1.13167
\(289\) 19.2148 1.13028
\(290\) 0.543278 0.0319024
\(291\) 17.0159 0.997488
\(292\) −66.8003 −3.90919
\(293\) 16.1349 0.942609 0.471304 0.881971i \(-0.343783\pi\)
0.471304 + 0.881971i \(0.343783\pi\)
\(294\) −16.2711 −0.948947
\(295\) −2.26928 −0.132122
\(296\) 77.3945 4.49847
\(297\) −16.7551 −0.972231
\(298\) −25.8932 −1.49995
\(299\) 9.19918 0.532002
\(300\) 54.0792 3.12227
\(301\) 1.46128 0.0842266
\(302\) 2.76122 0.158890
\(303\) −5.13197 −0.294824
\(304\) −2.12742 −0.122016
\(305\) 0.720145 0.0412354
\(306\) −12.6508 −0.723197
\(307\) 21.1283 1.20586 0.602928 0.797796i \(-0.294001\pi\)
0.602928 + 0.797796i \(0.294001\pi\)
\(308\) 43.2009 2.46160
\(309\) 4.35522 0.247760
\(310\) −0.654729 −0.0371861
\(311\) 17.0463 0.966609 0.483305 0.875452i \(-0.339436\pi\)
0.483305 + 0.875452i \(0.339436\pi\)
\(312\) 45.6722 2.58568
\(313\) 13.2234 0.747432 0.373716 0.927543i \(-0.378083\pi\)
0.373716 + 0.927543i \(0.378083\pi\)
\(314\) −18.7905 −1.06041
\(315\) 0.311271 0.0175381
\(316\) 50.2851 2.82876
\(317\) −15.3395 −0.861553 −0.430776 0.902459i \(-0.641760\pi\)
−0.430776 + 0.902459i \(0.641760\pi\)
\(318\) −5.35515 −0.300302
\(319\) −3.69640 −0.206959
\(320\) −7.57669 −0.423550
\(321\) −2.91528 −0.162715
\(322\) 21.4848 1.19730
\(323\) −0.781388 −0.0434776
\(324\) −60.2048 −3.34471
\(325\) −11.6666 −0.647144
\(326\) −17.9509 −0.994208
\(327\) −29.8790 −1.65231
\(328\) 45.0163 2.48561
\(329\) −0.523123 −0.0288407
\(330\) 4.24510 0.233685
\(331\) 0.301712 0.0165836 0.00829180 0.999966i \(-0.497361\pi\)
0.00829180 + 0.999966i \(0.497361\pi\)
\(332\) −52.7370 −2.89432
\(333\) −5.88784 −0.322651
\(334\) 53.8389 2.94594
\(335\) 2.96638 0.162071
\(336\) 63.2465 3.45038
\(337\) 3.99156 0.217434 0.108717 0.994073i \(-0.465326\pi\)
0.108717 + 0.994073i \(0.465326\pi\)
\(338\) 20.6058 1.12081
\(339\) −36.9741 −2.00816
\(340\) −6.95253 −0.377054
\(341\) 4.45470 0.241236
\(342\) 0.272959 0.0147599
\(343\) 19.9802 1.07883
\(344\) 7.34725 0.396137
\(345\) 1.55739 0.0838468
\(346\) 6.58685 0.354111
\(347\) −0.796848 −0.0427771 −0.0213885 0.999771i \(-0.506809\pi\)
−0.0213885 + 0.999771i \(0.506809\pi\)
\(348\) −10.4480 −0.560071
\(349\) 14.7230 0.788105 0.394052 0.919088i \(-0.371073\pi\)
0.394052 + 0.919088i \(0.371073\pi\)
\(350\) −27.2474 −1.45644
\(351\) 10.2168 0.545331
\(352\) 97.3489 5.18872
\(353\) −1.24726 −0.0663852 −0.0331926 0.999449i \(-0.510567\pi\)
−0.0331926 + 0.999449i \(0.510567\pi\)
\(354\) 59.1602 3.14433
\(355\) −2.97346 −0.157815
\(356\) 32.8067 1.73875
\(357\) 23.2300 1.22946
\(358\) 24.1836 1.27814
\(359\) −15.1924 −0.801827 −0.400913 0.916116i \(-0.631307\pi\)
−0.400913 + 0.916116i \(0.631307\pi\)
\(360\) 1.56506 0.0824858
\(361\) −18.9831 −0.999113
\(362\) 33.7064 1.77157
\(363\) −7.54962 −0.396252
\(364\) −26.3426 −1.38073
\(365\) 2.43971 0.127700
\(366\) −18.7742 −0.981345
\(367\) −3.74708 −0.195596 −0.0977981 0.995206i \(-0.531180\pi\)
−0.0977981 + 0.995206i \(0.531180\pi\)
\(368\) 64.0510 3.33889
\(369\) −3.42464 −0.178280
\(370\) −4.38644 −0.228040
\(371\) 1.99038 0.103335
\(372\) 12.5914 0.652831
\(373\) 19.3559 1.00221 0.501104 0.865387i \(-0.332927\pi\)
0.501104 + 0.865387i \(0.332927\pi\)
\(374\) 64.1255 3.31585
\(375\) −3.96701 −0.204856
\(376\) −2.63024 −0.135645
\(377\) 2.25395 0.116085
\(378\) 23.8615 1.22730
\(379\) −35.5976 −1.82853 −0.914264 0.405119i \(-0.867230\pi\)
−0.914264 + 0.405119i \(0.867230\pi\)
\(380\) 0.150011 0.00769540
\(381\) −23.0610 −1.18145
\(382\) −58.2590 −2.98079
\(383\) 6.94785 0.355019 0.177509 0.984119i \(-0.443196\pi\)
0.177509 + 0.984119i \(0.443196\pi\)
\(384\) 99.6783 5.08669
\(385\) −1.57780 −0.0804121
\(386\) 25.8986 1.31821
\(387\) −0.558946 −0.0284128
\(388\) −49.3462 −2.50518
\(389\) −38.7304 −1.96371 −0.981855 0.189632i \(-0.939270\pi\)
−0.981855 + 0.189632i \(0.939270\pi\)
\(390\) −2.58853 −0.131076
\(391\) 23.5255 1.18974
\(392\) 30.4069 1.53578
\(393\) −22.3365 −1.12673
\(394\) −22.6621 −1.14170
\(395\) −1.83653 −0.0924059
\(396\) −16.5246 −0.830392
\(397\) −3.78207 −0.189817 −0.0949083 0.995486i \(-0.530256\pi\)
−0.0949083 + 0.995486i \(0.530256\pi\)
\(398\) −64.6428 −3.24025
\(399\) −0.501222 −0.0250925
\(400\) −81.2306 −4.06153
\(401\) 7.15639 0.357373 0.178687 0.983906i \(-0.442815\pi\)
0.178687 + 0.983906i \(0.442815\pi\)
\(402\) −77.3339 −3.85706
\(403\) −2.71634 −0.135311
\(404\) 14.8828 0.740446
\(405\) 2.19882 0.109260
\(406\) 5.26415 0.261255
\(407\) 29.8449 1.47936
\(408\) 116.800 5.78245
\(409\) 22.5027 1.11269 0.556344 0.830952i \(-0.312204\pi\)
0.556344 + 0.830952i \(0.312204\pi\)
\(410\) −2.55136 −0.126003
\(411\) 21.0465 1.03815
\(412\) −12.6302 −0.622244
\(413\) −21.9884 −1.08198
\(414\) −8.21807 −0.403896
\(415\) 1.92608 0.0945475
\(416\) −59.3605 −2.91039
\(417\) −11.8348 −0.579555
\(418\) −1.38360 −0.0676742
\(419\) −23.9718 −1.17110 −0.585550 0.810636i \(-0.699121\pi\)
−0.585550 + 0.810636i \(0.699121\pi\)
\(420\) −4.45970 −0.217611
\(421\) 16.1850 0.788809 0.394404 0.918937i \(-0.370951\pi\)
0.394404 + 0.918937i \(0.370951\pi\)
\(422\) 37.6611 1.83331
\(423\) 0.200097 0.00972907
\(424\) 10.0076 0.486010
\(425\) −29.8354 −1.44723
\(426\) 77.5183 3.75577
\(427\) 6.97793 0.337686
\(428\) 8.45434 0.408656
\(429\) 17.6121 0.850320
\(430\) −0.416415 −0.0200813
\(431\) −29.3626 −1.41435 −0.707173 0.707040i \(-0.750030\pi\)
−0.707173 + 0.707040i \(0.750030\pi\)
\(432\) 71.1362 3.42254
\(433\) 8.93518 0.429398 0.214699 0.976680i \(-0.431123\pi\)
0.214699 + 0.976680i \(0.431123\pi\)
\(434\) −6.34406 −0.304525
\(435\) 0.381586 0.0182956
\(436\) 86.6494 4.14975
\(437\) −0.507598 −0.0242817
\(438\) −63.6033 −3.03908
\(439\) 19.0134 0.907461 0.453731 0.891139i \(-0.350093\pi\)
0.453731 + 0.891139i \(0.350093\pi\)
\(440\) −7.93312 −0.378197
\(441\) −2.31322 −0.110154
\(442\) −39.1018 −1.85988
\(443\) 6.10126 0.289879 0.144940 0.989440i \(-0.453701\pi\)
0.144940 + 0.989440i \(0.453701\pi\)
\(444\) 84.3575 4.00343
\(445\) −1.19818 −0.0567991
\(446\) −21.1706 −1.00246
\(447\) −18.1867 −0.860204
\(448\) −73.4151 −3.46854
\(449\) −32.0433 −1.51222 −0.756109 0.654446i \(-0.772902\pi\)
−0.756109 + 0.654446i \(0.772902\pi\)
\(450\) 10.4223 0.491312
\(451\) 17.3592 0.817412
\(452\) 107.225 5.04345
\(453\) 1.93941 0.0911217
\(454\) 9.54771 0.448096
\(455\) 0.962095 0.0451037
\(456\) −2.52013 −0.118016
\(457\) −34.2680 −1.60299 −0.801495 0.598002i \(-0.795961\pi\)
−0.801495 + 0.598002i \(0.795961\pi\)
\(458\) −35.6836 −1.66738
\(459\) 26.1279 1.21954
\(460\) −4.51643 −0.210580
\(461\) −13.3395 −0.621281 −0.310640 0.950527i \(-0.600544\pi\)
−0.310640 + 0.950527i \(0.600544\pi\)
\(462\) 41.1334 1.91370
\(463\) −19.7956 −0.919981 −0.459991 0.887924i \(-0.652147\pi\)
−0.459991 + 0.887924i \(0.652147\pi\)
\(464\) 15.6936 0.728556
\(465\) −0.459866 −0.0213258
\(466\) 74.5666 3.45423
\(467\) 41.1409 1.90377 0.951886 0.306451i \(-0.0991415\pi\)
0.951886 + 0.306451i \(0.0991415\pi\)
\(468\) 10.0762 0.465773
\(469\) 28.7431 1.32723
\(470\) 0.149073 0.00687621
\(471\) −13.1980 −0.608133
\(472\) −110.557 −5.08879
\(473\) 2.83324 0.130273
\(474\) 47.8785 2.19913
\(475\) 0.643744 0.0295370
\(476\) −67.3673 −3.08777
\(477\) −0.761331 −0.0348589
\(478\) −64.0445 −2.92933
\(479\) 11.1634 0.510070 0.255035 0.966932i \(-0.417913\pi\)
0.255035 + 0.966932i \(0.417913\pi\)
\(480\) −10.0495 −0.458694
\(481\) −18.1985 −0.829780
\(482\) −42.5252 −1.93697
\(483\) 15.0905 0.686639
\(484\) 21.8940 0.995181
\(485\) 1.80224 0.0818355
\(486\) −21.3583 −0.968830
\(487\) 25.1289 1.13870 0.569350 0.822096i \(-0.307195\pi\)
0.569350 + 0.822096i \(0.307195\pi\)
\(488\) 35.0848 1.58821
\(489\) −12.6083 −0.570167
\(490\) −1.72335 −0.0778532
\(491\) 3.18771 0.143859 0.0719297 0.997410i \(-0.477084\pi\)
0.0719297 + 0.997410i \(0.477084\pi\)
\(492\) 49.0663 2.21208
\(493\) 5.76415 0.259604
\(494\) 0.843679 0.0379589
\(495\) 0.603517 0.0271261
\(496\) −18.9130 −0.849221
\(497\) −28.8116 −1.29238
\(498\) −50.2130 −2.25010
\(499\) 29.8587 1.33666 0.668330 0.743865i \(-0.267009\pi\)
0.668330 + 0.743865i \(0.267009\pi\)
\(500\) 11.5044 0.514492
\(501\) 37.8152 1.68946
\(502\) −28.2584 −1.26123
\(503\) 26.1012 1.16379 0.581897 0.813262i \(-0.302311\pi\)
0.581897 + 0.813262i \(0.302311\pi\)
\(504\) 15.1648 0.675494
\(505\) −0.543554 −0.0241878
\(506\) 41.6566 1.85186
\(507\) 14.4731 0.642771
\(508\) 66.8772 2.96720
\(509\) −20.4312 −0.905599 −0.452799 0.891612i \(-0.649575\pi\)
−0.452799 + 0.891612i \(0.649575\pi\)
\(510\) −6.61978 −0.293129
\(511\) 23.6398 1.04576
\(512\) −85.3731 −3.77300
\(513\) −0.563747 −0.0248900
\(514\) −28.9886 −1.27863
\(515\) 0.461284 0.0203266
\(516\) 8.00826 0.352544
\(517\) −1.01427 −0.0446077
\(518\) −42.5029 −1.86747
\(519\) 4.62645 0.203079
\(520\) 4.83738 0.212133
\(521\) −14.7118 −0.644535 −0.322268 0.946649i \(-0.604445\pi\)
−0.322268 + 0.946649i \(0.604445\pi\)
\(522\) −2.01357 −0.0881314
\(523\) −17.9535 −0.785051 −0.392525 0.919741i \(-0.628398\pi\)
−0.392525 + 0.919741i \(0.628398\pi\)
\(524\) 64.7762 2.82976
\(525\) −19.1380 −0.835249
\(526\) −42.7296 −1.86310
\(527\) −6.94663 −0.302600
\(528\) 122.628 5.33668
\(529\) −7.71758 −0.335547
\(530\) −0.567192 −0.0246372
\(531\) 8.41068 0.364992
\(532\) 1.45355 0.0630193
\(533\) −10.5851 −0.458492
\(534\) 31.2366 1.35174
\(535\) −0.308772 −0.0133494
\(536\) 144.519 6.24229
\(537\) 16.9860 0.733001
\(538\) −21.0027 −0.905490
\(539\) 11.7255 0.505053
\(540\) −5.01603 −0.215856
\(541\) 36.0689 1.55072 0.775361 0.631519i \(-0.217568\pi\)
0.775361 + 0.631519i \(0.217568\pi\)
\(542\) −25.2107 −1.08289
\(543\) 23.6746 1.01597
\(544\) −151.805 −6.50860
\(545\) −3.16464 −0.135558
\(546\) −25.0819 −1.07341
\(547\) −33.7246 −1.44196 −0.720979 0.692957i \(-0.756308\pi\)
−0.720979 + 0.692957i \(0.756308\pi\)
\(548\) −61.0352 −2.60729
\(549\) −2.66910 −0.113914
\(550\) −52.8296 −2.25266
\(551\) −0.124370 −0.00529834
\(552\) 75.8743 3.22942
\(553\) −17.7953 −0.756732
\(554\) 62.9801 2.67577
\(555\) −3.08094 −0.130778
\(556\) 34.3212 1.45554
\(557\) −19.1321 −0.810654 −0.405327 0.914172i \(-0.632842\pi\)
−0.405327 + 0.914172i \(0.632842\pi\)
\(558\) 2.42664 0.102728
\(559\) −1.72763 −0.0730708
\(560\) 6.69877 0.283075
\(561\) 45.0403 1.90160
\(562\) 13.8033 0.582258
\(563\) 23.0855 0.972940 0.486470 0.873697i \(-0.338284\pi\)
0.486470 + 0.873697i \(0.338284\pi\)
\(564\) −2.86688 −0.120717
\(565\) −3.91612 −0.164752
\(566\) 53.9496 2.26767
\(567\) 21.3057 0.894757
\(568\) −144.864 −6.07836
\(569\) −31.9175 −1.33805 −0.669027 0.743238i \(-0.733289\pi\)
−0.669027 + 0.743238i \(0.733289\pi\)
\(570\) 0.142832 0.00598256
\(571\) 34.0889 1.42658 0.713289 0.700870i \(-0.247205\pi\)
0.713289 + 0.700870i \(0.247205\pi\)
\(572\) −51.0753 −2.13556
\(573\) −40.9198 −1.70945
\(574\) −24.7217 −1.03186
\(575\) −19.3814 −0.808261
\(576\) 28.0817 1.17007
\(577\) 1.59831 0.0665384 0.0332692 0.999446i \(-0.489408\pi\)
0.0332692 + 0.999446i \(0.489408\pi\)
\(578\) −53.0563 −2.20685
\(579\) 18.1906 0.755976
\(580\) −1.10660 −0.0459492
\(581\) 18.6630 0.774270
\(582\) −46.9845 −1.94757
\(583\) 3.85911 0.159828
\(584\) 118.860 4.91847
\(585\) −0.368007 −0.0152152
\(586\) −44.5519 −1.84042
\(587\) −26.2172 −1.08210 −0.541050 0.840990i \(-0.681973\pi\)
−0.541050 + 0.840990i \(0.681973\pi\)
\(588\) 33.1425 1.36677
\(589\) 0.149884 0.00617586
\(590\) 6.26596 0.257966
\(591\) −15.9173 −0.654751
\(592\) −126.710 −5.20777
\(593\) −32.6121 −1.33922 −0.669610 0.742713i \(-0.733539\pi\)
−0.669610 + 0.742713i \(0.733539\pi\)
\(594\) 46.2646 1.89826
\(595\) 2.46041 0.100867
\(596\) 52.7418 2.16039
\(597\) −45.4036 −1.85825
\(598\) −25.4009 −1.03872
\(599\) 17.7319 0.724506 0.362253 0.932080i \(-0.382008\pi\)
0.362253 + 0.932080i \(0.382008\pi\)
\(600\) −96.2250 −3.92837
\(601\) −26.0475 −1.06250 −0.531250 0.847215i \(-0.678278\pi\)
−0.531250 + 0.847215i \(0.678278\pi\)
\(602\) −4.03490 −0.164450
\(603\) −10.9944 −0.447726
\(604\) −5.62432 −0.228851
\(605\) −0.799620 −0.0325092
\(606\) 14.1705 0.575637
\(607\) −29.9550 −1.21584 −0.607918 0.794000i \(-0.707995\pi\)
−0.607918 + 0.794000i \(0.707995\pi\)
\(608\) 3.27542 0.132836
\(609\) 3.69741 0.149827
\(610\) −1.98848 −0.0805111
\(611\) 0.618474 0.0250208
\(612\) 25.7684 1.04162
\(613\) −22.3007 −0.900715 −0.450358 0.892848i \(-0.648704\pi\)
−0.450358 + 0.892848i \(0.648704\pi\)
\(614\) −58.3399 −2.35440
\(615\) −1.79202 −0.0722611
\(616\) −76.8689 −3.09714
\(617\) −10.5056 −0.422939 −0.211470 0.977385i \(-0.567825\pi\)
−0.211470 + 0.977385i \(0.567825\pi\)
\(618\) −12.0257 −0.483745
\(619\) 36.1598 1.45339 0.726693 0.686963i \(-0.241056\pi\)
0.726693 + 0.686963i \(0.241056\pi\)
\(620\) 1.33362 0.0535593
\(621\) 16.9729 0.681100
\(622\) −47.0687 −1.88728
\(623\) −11.6099 −0.465140
\(624\) −74.7746 −2.99338
\(625\) 24.3689 0.974754
\(626\) −36.5128 −1.45934
\(627\) −0.971810 −0.0388104
\(628\) 38.2744 1.52732
\(629\) −46.5399 −1.85567
\(630\) −0.859486 −0.0342427
\(631\) 0.817036 0.0325257 0.0162628 0.999868i \(-0.494823\pi\)
0.0162628 + 0.999868i \(0.494823\pi\)
\(632\) −89.4740 −3.55909
\(633\) 26.4523 1.05138
\(634\) 42.3557 1.68216
\(635\) −2.44251 −0.0969282
\(636\) 10.9079 0.432526
\(637\) −7.14986 −0.283288
\(638\) 10.2066 0.404082
\(639\) 11.0206 0.435969
\(640\) 10.5575 0.417320
\(641\) −30.2915 −1.19644 −0.598221 0.801331i \(-0.704125\pi\)
−0.598221 + 0.801331i \(0.704125\pi\)
\(642\) 8.04972 0.317697
\(643\) −32.3198 −1.27457 −0.637285 0.770628i \(-0.719943\pi\)
−0.637285 + 0.770628i \(0.719943\pi\)
\(644\) −43.7625 −1.72448
\(645\) −0.292480 −0.0115164
\(646\) 2.15758 0.0848889
\(647\) 13.9782 0.549540 0.274770 0.961510i \(-0.411398\pi\)
0.274770 + 0.961510i \(0.411398\pi\)
\(648\) 107.125 4.20825
\(649\) −42.6329 −1.67349
\(650\) 32.2139 1.26353
\(651\) −4.45592 −0.174641
\(652\) 36.5642 1.43196
\(653\) 0.497245 0.0194587 0.00972935 0.999953i \(-0.496903\pi\)
0.00972935 + 0.999953i \(0.496903\pi\)
\(654\) 82.5024 3.22610
\(655\) −2.36578 −0.0924387
\(656\) −73.7008 −2.87753
\(657\) −9.04235 −0.352776
\(658\) 1.44446 0.0563108
\(659\) −2.10716 −0.0820832 −0.0410416 0.999157i \(-0.513068\pi\)
−0.0410416 + 0.999157i \(0.513068\pi\)
\(660\) −8.64684 −0.336578
\(661\) −32.4626 −1.26265 −0.631325 0.775518i \(-0.717489\pi\)
−0.631325 + 0.775518i \(0.717489\pi\)
\(662\) −0.833093 −0.0323791
\(663\) −27.4642 −1.06662
\(664\) 93.8367 3.64157
\(665\) −0.0530870 −0.00205863
\(666\) 16.2576 0.629969
\(667\) 3.74445 0.144986
\(668\) −109.665 −4.24305
\(669\) −14.8697 −0.574898
\(670\) −8.19083 −0.316440
\(671\) 13.5294 0.522296
\(672\) −97.3756 −3.75635
\(673\) 42.6044 1.64228 0.821140 0.570726i \(-0.193338\pi\)
0.821140 + 0.570726i \(0.193338\pi\)
\(674\) −11.0216 −0.424535
\(675\) −21.5253 −0.828511
\(676\) −41.9720 −1.61431
\(677\) 20.8069 0.799675 0.399838 0.916586i \(-0.369066\pi\)
0.399838 + 0.916586i \(0.369066\pi\)
\(678\) 102.094 3.92088
\(679\) 17.4630 0.670169
\(680\) 12.3709 0.474401
\(681\) 6.70609 0.256978
\(682\) −12.3004 −0.471007
\(683\) 20.2171 0.773585 0.386792 0.922167i \(-0.373583\pi\)
0.386792 + 0.922167i \(0.373583\pi\)
\(684\) −0.555990 −0.0212588
\(685\) 2.22915 0.0851714
\(686\) −55.1697 −2.10639
\(687\) −25.0633 −0.956224
\(688\) −12.0289 −0.458598
\(689\) −2.35317 −0.0896486
\(690\) −4.30028 −0.163709
\(691\) −45.4363 −1.72848 −0.864239 0.503081i \(-0.832200\pi\)
−0.864239 + 0.503081i \(0.832200\pi\)
\(692\) −13.4168 −0.510029
\(693\) 5.84785 0.222141
\(694\) 2.20027 0.0835212
\(695\) −1.25349 −0.0475476
\(696\) 18.5905 0.704670
\(697\) −27.0698 −1.02534
\(698\) −40.6535 −1.53876
\(699\) 52.3739 1.98096
\(700\) 55.5003 2.09771
\(701\) −19.2151 −0.725744 −0.362872 0.931839i \(-0.618204\pi\)
−0.362872 + 0.931839i \(0.618204\pi\)
\(702\) −28.2108 −1.06475
\(703\) 1.00417 0.0378729
\(704\) −142.343 −5.36477
\(705\) 0.104705 0.00394343
\(706\) 3.44397 0.129616
\(707\) −5.26683 −0.198079
\(708\) −120.503 −4.52879
\(709\) 2.98664 0.112166 0.0560828 0.998426i \(-0.482139\pi\)
0.0560828 + 0.998426i \(0.482139\pi\)
\(710\) 8.21037 0.308130
\(711\) 6.80679 0.255275
\(712\) −58.3741 −2.18766
\(713\) −4.51261 −0.168998
\(714\) −64.1431 −2.40050
\(715\) 1.86539 0.0697616
\(716\) −49.2597 −1.84092
\(717\) −44.9833 −1.67993
\(718\) 41.9497 1.56555
\(719\) −18.5296 −0.691038 −0.345519 0.938412i \(-0.612297\pi\)
−0.345519 + 0.938412i \(0.612297\pi\)
\(720\) −2.56231 −0.0954918
\(721\) 4.46966 0.166459
\(722\) 52.4166 1.95074
\(723\) −29.8687 −1.11083
\(724\) −68.6565 −2.55160
\(725\) −4.74877 −0.176365
\(726\) 20.8462 0.773673
\(727\) −8.40272 −0.311640 −0.155820 0.987786i \(-0.549802\pi\)
−0.155820 + 0.987786i \(0.549802\pi\)
\(728\) 46.8723 1.73720
\(729\) 17.1116 0.633762
\(730\) −6.73656 −0.249331
\(731\) −4.41814 −0.163411
\(732\) 38.2413 1.41344
\(733\) 31.7577 1.17300 0.586499 0.809950i \(-0.300506\pi\)
0.586499 + 0.809950i \(0.300506\pi\)
\(734\) 10.3465 0.381897
\(735\) −1.21044 −0.0446479
\(736\) −98.6143 −3.63497
\(737\) 55.7295 2.05282
\(738\) 9.45618 0.348087
\(739\) −18.9067 −0.695495 −0.347747 0.937588i \(-0.613053\pi\)
−0.347747 + 0.937588i \(0.613053\pi\)
\(740\) 8.93475 0.328448
\(741\) 0.592581 0.0217690
\(742\) −5.49587 −0.201760
\(743\) −37.1631 −1.36338 −0.681691 0.731640i \(-0.738755\pi\)
−0.681691 + 0.731640i \(0.738755\pi\)
\(744\) −22.4042 −0.821379
\(745\) −1.92625 −0.0705725
\(746\) −53.4458 −1.95679
\(747\) −7.13868 −0.261191
\(748\) −130.617 −4.77584
\(749\) −2.99188 −0.109321
\(750\) 10.9538 0.399976
\(751\) 4.75509 0.173516 0.0867578 0.996229i \(-0.472349\pi\)
0.0867578 + 0.996229i \(0.472349\pi\)
\(752\) 4.30624 0.157032
\(753\) −19.8480 −0.723302
\(754\) −6.22366 −0.226652
\(755\) 0.205414 0.00747577
\(756\) −48.6034 −1.76769
\(757\) 15.1677 0.551278 0.275639 0.961261i \(-0.411111\pi\)
0.275639 + 0.961261i \(0.411111\pi\)
\(758\) 98.2929 3.57016
\(759\) 29.2586 1.06202
\(760\) −0.266920 −0.00968219
\(761\) 0.618791 0.0224312 0.0112156 0.999937i \(-0.496430\pi\)
0.0112156 + 0.999937i \(0.496430\pi\)
\(762\) 63.6765 2.30676
\(763\) −30.6641 −1.11012
\(764\) 118.668 4.29325
\(765\) −0.941121 −0.0340263
\(766\) −19.1845 −0.693166
\(767\) 25.9963 0.938671
\(768\) −132.163 −4.76902
\(769\) 40.8060 1.47150 0.735751 0.677253i \(-0.236830\pi\)
0.735751 + 0.677253i \(0.236830\pi\)
\(770\) 4.35665 0.157003
\(771\) −20.3609 −0.733281
\(772\) −52.7529 −1.89862
\(773\) 6.92057 0.248916 0.124458 0.992225i \(-0.460281\pi\)
0.124458 + 0.992225i \(0.460281\pi\)
\(774\) 1.54337 0.0554754
\(775\) 5.72296 0.205575
\(776\) 87.8034 3.15196
\(777\) −29.8531 −1.07097
\(778\) 106.943 3.83410
\(779\) 0.584071 0.0209265
\(780\) 5.27259 0.188789
\(781\) −55.8624 −1.99891
\(782\) −64.9591 −2.32293
\(783\) 4.15865 0.148618
\(784\) −49.7822 −1.77794
\(785\) −1.39787 −0.0498922
\(786\) 61.6760 2.19991
\(787\) 3.63883 0.129710 0.0648551 0.997895i \(-0.479341\pi\)
0.0648551 + 0.997895i \(0.479341\pi\)
\(788\) 46.1604 1.64440
\(789\) −30.0123 −1.06847
\(790\) 5.07106 0.180420
\(791\) −37.9457 −1.34919
\(792\) 29.4028 1.04478
\(793\) −8.24981 −0.292960
\(794\) 10.4431 0.370612
\(795\) −0.398382 −0.0141292
\(796\) 131.671 4.66695
\(797\) 4.06092 0.143845 0.0719226 0.997410i \(-0.477087\pi\)
0.0719226 + 0.997410i \(0.477087\pi\)
\(798\) 1.38398 0.0489924
\(799\) 1.58165 0.0559549
\(800\) 125.064 4.42169
\(801\) 4.44085 0.156910
\(802\) −19.7604 −0.697763
\(803\) 45.8348 1.61748
\(804\) 157.521 5.55535
\(805\) 1.59831 0.0563330
\(806\) 7.50041 0.264191
\(807\) −14.7518 −0.519287
\(808\) −26.4814 −0.931613
\(809\) −3.51399 −0.123545 −0.0617727 0.998090i \(-0.519675\pi\)
−0.0617727 + 0.998090i \(0.519675\pi\)
\(810\) −6.07143 −0.213328
\(811\) −49.0909 −1.72381 −0.861907 0.507067i \(-0.830730\pi\)
−0.861907 + 0.507067i \(0.830730\pi\)
\(812\) −10.7225 −0.376288
\(813\) −17.7074 −0.621027
\(814\) −82.4082 −2.88841
\(815\) −1.33541 −0.0467774
\(816\) −191.225 −6.69420
\(817\) 0.0953280 0.00333510
\(818\) −62.1349 −2.17250
\(819\) −3.56584 −0.124601
\(820\) 5.19687 0.181482
\(821\) 4.25551 0.148518 0.0742592 0.997239i \(-0.476341\pi\)
0.0742592 + 0.997239i \(0.476341\pi\)
\(822\) −58.1141 −2.02696
\(823\) 37.5323 1.30829 0.654147 0.756367i \(-0.273028\pi\)
0.654147 + 0.756367i \(0.273028\pi\)
\(824\) 22.4733 0.782895
\(825\) −37.1063 −1.29187
\(826\) 60.7147 2.11254
\(827\) −36.5650 −1.27149 −0.635744 0.771900i \(-0.719307\pi\)
−0.635744 + 0.771900i \(0.719307\pi\)
\(828\) 16.7394 0.581734
\(829\) −0.910563 −0.0316252 −0.0158126 0.999875i \(-0.505034\pi\)
−0.0158126 + 0.999875i \(0.505034\pi\)
\(830\) −5.31833 −0.184602
\(831\) 44.2357 1.53452
\(832\) 86.7967 3.00913
\(833\) −18.2847 −0.633527
\(834\) 32.6786 1.13157
\(835\) 4.00521 0.138606
\(836\) 2.81826 0.0974716
\(837\) −5.01178 −0.173232
\(838\) 66.1914 2.28655
\(839\) 42.7814 1.47698 0.738489 0.674265i \(-0.235539\pi\)
0.738489 + 0.674265i \(0.235539\pi\)
\(840\) 7.93530 0.273794
\(841\) −28.0825 −0.968364
\(842\) −44.6903 −1.54013
\(843\) 9.69514 0.333918
\(844\) −76.7119 −2.64053
\(845\) 1.53292 0.0527340
\(846\) −0.552513 −0.0189958
\(847\) −7.74801 −0.266225
\(848\) −16.3844 −0.562642
\(849\) 37.8929 1.30048
\(850\) 82.3822 2.82569
\(851\) −30.2328 −1.03637
\(852\) −157.897 −5.40946
\(853\) −4.97060 −0.170190 −0.0850951 0.996373i \(-0.527119\pi\)
−0.0850951 + 0.996373i \(0.527119\pi\)
\(854\) −19.2676 −0.659323
\(855\) 0.0203061 0.000694453 0
\(856\) −15.0431 −0.514162
\(857\) 15.1043 0.515953 0.257976 0.966151i \(-0.416944\pi\)
0.257976 + 0.966151i \(0.416944\pi\)
\(858\) −48.6308 −1.66023
\(859\) 0.172905 0.00589943 0.00294971 0.999996i \(-0.499061\pi\)
0.00294971 + 0.999996i \(0.499061\pi\)
\(860\) 0.848196 0.0289233
\(861\) −17.3639 −0.591762
\(862\) 81.0765 2.76148
\(863\) −10.6838 −0.363680 −0.181840 0.983328i \(-0.558205\pi\)
−0.181840 + 0.983328i \(0.558205\pi\)
\(864\) −109.523 −3.72604
\(865\) 0.490012 0.0166609
\(866\) −24.6720 −0.838388
\(867\) −37.2655 −1.26560
\(868\) 12.9222 0.438609
\(869\) −34.5030 −1.17043
\(870\) −1.05364 −0.0357218
\(871\) −33.9822 −1.15144
\(872\) −154.178 −5.22113
\(873\) −6.67970 −0.226074
\(874\) 1.40159 0.0474094
\(875\) −4.07126 −0.137634
\(876\) 129.554 4.37721
\(877\) 25.2885 0.853931 0.426966 0.904268i \(-0.359583\pi\)
0.426966 + 0.904268i \(0.359583\pi\)
\(878\) −52.5002 −1.77180
\(879\) −31.2922 −1.05546
\(880\) 12.9881 0.437830
\(881\) 1.33758 0.0450644 0.0225322 0.999746i \(-0.492827\pi\)
0.0225322 + 0.999746i \(0.492827\pi\)
\(882\) 6.38731 0.215072
\(883\) −23.2230 −0.781516 −0.390758 0.920494i \(-0.627787\pi\)
−0.390758 + 0.920494i \(0.627787\pi\)
\(884\) 79.6465 2.67880
\(885\) 4.40107 0.147940
\(886\) −16.8469 −0.565983
\(887\) 33.5458 1.12636 0.563178 0.826335i \(-0.309578\pi\)
0.563178 + 0.826335i \(0.309578\pi\)
\(888\) −150.100 −5.03703
\(889\) −23.6670 −0.793766
\(890\) 3.30843 0.110899
\(891\) 41.3093 1.38391
\(892\) 43.1224 1.44385
\(893\) −0.0341265 −0.00114200
\(894\) 50.2176 1.67953
\(895\) 1.79908 0.0601366
\(896\) 102.298 3.41752
\(897\) −17.8410 −0.595695
\(898\) 88.4786 2.95257
\(899\) −1.10566 −0.0368760
\(900\) −21.2292 −0.707639
\(901\) −6.01787 −0.200484
\(902\) −47.9325 −1.59598
\(903\) −2.83402 −0.0943103
\(904\) −190.790 −6.34557
\(905\) 2.50750 0.0833520
\(906\) −5.35515 −0.177913
\(907\) −0.884477 −0.0293686 −0.0146843 0.999892i \(-0.504674\pi\)
−0.0146843 + 0.999892i \(0.504674\pi\)
\(908\) −19.4477 −0.645395
\(909\) 2.01459 0.0668197
\(910\) −2.65655 −0.0880639
\(911\) −52.5849 −1.74221 −0.871107 0.491093i \(-0.836598\pi\)
−0.871107 + 0.491093i \(0.836598\pi\)
\(912\) 4.12595 0.136624
\(913\) 36.1853 1.19756
\(914\) 94.6214 3.12980
\(915\) −1.39666 −0.0461722
\(916\) 72.6838 2.40154
\(917\) −22.9235 −0.757000
\(918\) −72.1447 −2.38113
\(919\) −8.03210 −0.264954 −0.132477 0.991186i \(-0.542293\pi\)
−0.132477 + 0.991186i \(0.542293\pi\)
\(920\) 8.03624 0.264947
\(921\) −40.9765 −1.35022
\(922\) 36.8332 1.21304
\(923\) 34.0632 1.12120
\(924\) −83.7845 −2.75631
\(925\) 38.3418 1.26067
\(926\) 54.6601 1.79624
\(927\) −1.70967 −0.0561529
\(928\) −24.1622 −0.793162
\(929\) 17.0027 0.557839 0.278920 0.960314i \(-0.410024\pi\)
0.278920 + 0.960314i \(0.410024\pi\)
\(930\) 1.26979 0.0416381
\(931\) 0.394519 0.0129298
\(932\) −151.885 −4.97515
\(933\) −33.0599 −1.08233
\(934\) −113.599 −3.71707
\(935\) 4.77045 0.156010
\(936\) −17.9289 −0.586025
\(937\) −4.25305 −0.138941 −0.0694706 0.997584i \(-0.522131\pi\)
−0.0694706 + 0.997584i \(0.522131\pi\)
\(938\) −79.3660 −2.59139
\(939\) −25.6457 −0.836916
\(940\) −0.303646 −0.00990385
\(941\) −3.40934 −0.111141 −0.0555707 0.998455i \(-0.517698\pi\)
−0.0555707 + 0.998455i \(0.517698\pi\)
\(942\) 36.4426 1.18737
\(943\) −17.5848 −0.572641
\(944\) 181.004 5.89118
\(945\) 1.77511 0.0577444
\(946\) −7.82320 −0.254354
\(947\) −39.1120 −1.27097 −0.635485 0.772113i \(-0.719200\pi\)
−0.635485 + 0.772113i \(0.719200\pi\)
\(948\) −97.5237 −3.16742
\(949\) −27.9487 −0.907253
\(950\) −1.77752 −0.0576703
\(951\) 29.7497 0.964699
\(952\) 119.869 3.88497
\(953\) 8.90018 0.288305 0.144153 0.989555i \(-0.453954\pi\)
0.144153 + 0.989555i \(0.453954\pi\)
\(954\) 2.10220 0.0680612
\(955\) −4.33403 −0.140246
\(956\) 130.452 4.21912
\(957\) 7.16886 0.231736
\(958\) −30.8246 −0.995899
\(959\) 21.5996 0.697487
\(960\) 14.6943 0.474258
\(961\) −29.6675 −0.957017
\(962\) 50.2500 1.62013
\(963\) 1.14441 0.0368782
\(964\) 86.6195 2.78983
\(965\) 1.92666 0.0620214
\(966\) −41.6680 −1.34065
\(967\) −20.8010 −0.668915 −0.334457 0.942411i \(-0.608553\pi\)
−0.334457 + 0.942411i \(0.608553\pi\)
\(968\) −38.9567 −1.25212
\(969\) 1.51544 0.0486828
\(970\) −4.97638 −0.159782
\(971\) 8.61610 0.276504 0.138252 0.990397i \(-0.455852\pi\)
0.138252 + 0.990397i \(0.455852\pi\)
\(972\) 43.5046 1.39541
\(973\) −12.1458 −0.389377
\(974\) −69.3864 −2.22328
\(975\) 22.6263 0.724621
\(976\) −57.4409 −1.83864
\(977\) −5.01933 −0.160582 −0.0802912 0.996771i \(-0.525585\pi\)
−0.0802912 + 0.996771i \(0.525585\pi\)
\(978\) 34.8142 1.11324
\(979\) −22.5102 −0.719430
\(980\) 3.51030 0.112132
\(981\) 11.7292 0.374485
\(982\) −8.80197 −0.280882
\(983\) 33.6877 1.07447 0.537236 0.843432i \(-0.319468\pi\)
0.537236 + 0.843432i \(0.319468\pi\)
\(984\) −87.3053 −2.78319
\(985\) −1.68589 −0.0537168
\(986\) −15.9161 −0.506871
\(987\) 1.01455 0.0322936
\(988\) −1.71849 −0.0546725
\(989\) −2.87007 −0.0912630
\(990\) −1.66644 −0.0529630
\(991\) 15.4063 0.489397 0.244699 0.969599i \(-0.421311\pi\)
0.244699 + 0.969599i \(0.421311\pi\)
\(992\) 29.1189 0.924527
\(993\) −0.585145 −0.0185690
\(994\) 79.5552 2.52334
\(995\) −4.80893 −0.152453
\(996\) 102.279 3.24083
\(997\) −22.7283 −0.719813 −0.359907 0.932988i \(-0.617191\pi\)
−0.359907 + 0.932988i \(0.617191\pi\)
\(998\) −82.4464 −2.60980
\(999\) −33.5771 −1.06233
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 8003.2.a.b.1.2 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.2 153 1.1 even 1 trivial