Properties

Label 4029.2.a.l.1.12
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.17408 q^{2} -1.00000 q^{3} -0.621542 q^{4} +3.86856 q^{5} +1.17408 q^{6} +3.06255 q^{7} +3.07789 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.17408 q^{2} -1.00000 q^{3} -0.621542 q^{4} +3.86856 q^{5} +1.17408 q^{6} +3.06255 q^{7} +3.07789 q^{8} +1.00000 q^{9} -4.54199 q^{10} +1.94563 q^{11} +0.621542 q^{12} -4.31087 q^{13} -3.59567 q^{14} -3.86856 q^{15} -2.37060 q^{16} -1.00000 q^{17} -1.17408 q^{18} -5.08811 q^{19} -2.40447 q^{20} -3.06255 q^{21} -2.28432 q^{22} -2.65257 q^{23} -3.07789 q^{24} +9.96577 q^{25} +5.06129 q^{26} -1.00000 q^{27} -1.90350 q^{28} +5.36141 q^{29} +4.54199 q^{30} +0.729477 q^{31} -3.37252 q^{32} -1.94563 q^{33} +1.17408 q^{34} +11.8477 q^{35} -0.621542 q^{36} -6.55851 q^{37} +5.97384 q^{38} +4.31087 q^{39} +11.9070 q^{40} +8.81303 q^{41} +3.59567 q^{42} +5.21086 q^{43} -1.20929 q^{44} +3.86856 q^{45} +3.11433 q^{46} +5.95297 q^{47} +2.37060 q^{48} +2.37920 q^{49} -11.7006 q^{50} +1.00000 q^{51} +2.67938 q^{52} -1.03559 q^{53} +1.17408 q^{54} +7.52677 q^{55} +9.42620 q^{56} +5.08811 q^{57} -6.29472 q^{58} +12.5431 q^{59} +2.40447 q^{60} +5.20694 q^{61} -0.856463 q^{62} +3.06255 q^{63} +8.70080 q^{64} -16.6768 q^{65} +2.28432 q^{66} -7.84025 q^{67} +0.621542 q^{68} +2.65257 q^{69} -13.9101 q^{70} +12.0605 q^{71} +3.07789 q^{72} -14.0089 q^{73} +7.70020 q^{74} -9.96577 q^{75} +3.16247 q^{76} +5.95857 q^{77} -5.06129 q^{78} +1.00000 q^{79} -9.17082 q^{80} +1.00000 q^{81} -10.3472 q^{82} +1.61708 q^{83} +1.90350 q^{84} -3.86856 q^{85} -6.11795 q^{86} -5.36141 q^{87} +5.98843 q^{88} -2.37602 q^{89} -4.54199 q^{90} -13.2022 q^{91} +1.64869 q^{92} -0.729477 q^{93} -6.98925 q^{94} -19.6837 q^{95} +3.37252 q^{96} +15.2428 q^{97} -2.79337 q^{98} +1.94563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17408 −0.830198 −0.415099 0.909776i \(-0.636253\pi\)
−0.415099 + 0.909776i \(0.636253\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.621542 −0.310771
\(5\) 3.86856 1.73007 0.865037 0.501709i \(-0.167295\pi\)
0.865037 + 0.501709i \(0.167295\pi\)
\(6\) 1.17408 0.479315
\(7\) 3.06255 1.15753 0.578767 0.815493i \(-0.303534\pi\)
0.578767 + 0.815493i \(0.303534\pi\)
\(8\) 3.07789 1.08820
\(9\) 1.00000 0.333333
\(10\) −4.54199 −1.43630
\(11\) 1.94563 0.586628 0.293314 0.956016i \(-0.405242\pi\)
0.293314 + 0.956016i \(0.405242\pi\)
\(12\) 0.621542 0.179424
\(13\) −4.31087 −1.19562 −0.597809 0.801638i \(-0.703962\pi\)
−0.597809 + 0.801638i \(0.703962\pi\)
\(14\) −3.59567 −0.960983
\(15\) −3.86856 −0.998858
\(16\) −2.37060 −0.592651
\(17\) −1.00000 −0.242536
\(18\) −1.17408 −0.276733
\(19\) −5.08811 −1.16729 −0.583647 0.812008i \(-0.698375\pi\)
−0.583647 + 0.812008i \(0.698375\pi\)
\(20\) −2.40447 −0.537656
\(21\) −3.06255 −0.668303
\(22\) −2.28432 −0.487018
\(23\) −2.65257 −0.553100 −0.276550 0.961000i \(-0.589191\pi\)
−0.276550 + 0.961000i \(0.589191\pi\)
\(24\) −3.07789 −0.628272
\(25\) 9.96577 1.99315
\(26\) 5.06129 0.992601
\(27\) −1.00000 −0.192450
\(28\) −1.90350 −0.359728
\(29\) 5.36141 0.995590 0.497795 0.867295i \(-0.334143\pi\)
0.497795 + 0.867295i \(0.334143\pi\)
\(30\) 4.54199 0.829251
\(31\) 0.729477 0.131018 0.0655090 0.997852i \(-0.479133\pi\)
0.0655090 + 0.997852i \(0.479133\pi\)
\(32\) −3.37252 −0.596182
\(33\) −1.94563 −0.338690
\(34\) 1.17408 0.201353
\(35\) 11.8477 2.00262
\(36\) −0.621542 −0.103590
\(37\) −6.55851 −1.07821 −0.539106 0.842238i \(-0.681238\pi\)
−0.539106 + 0.842238i \(0.681238\pi\)
\(38\) 5.97384 0.969085
\(39\) 4.31087 0.690291
\(40\) 11.9070 1.88267
\(41\) 8.81303 1.37636 0.688182 0.725538i \(-0.258409\pi\)
0.688182 + 0.725538i \(0.258409\pi\)
\(42\) 3.59567 0.554824
\(43\) 5.21086 0.794649 0.397324 0.917678i \(-0.369939\pi\)
0.397324 + 0.917678i \(0.369939\pi\)
\(44\) −1.20929 −0.182307
\(45\) 3.86856 0.576691
\(46\) 3.11433 0.459183
\(47\) 5.95297 0.868330 0.434165 0.900833i \(-0.357043\pi\)
0.434165 + 0.900833i \(0.357043\pi\)
\(48\) 2.37060 0.342167
\(49\) 2.37920 0.339886
\(50\) −11.7006 −1.65471
\(51\) 1.00000 0.140028
\(52\) 2.67938 0.371563
\(53\) −1.03559 −0.142249 −0.0711243 0.997467i \(-0.522659\pi\)
−0.0711243 + 0.997467i \(0.522659\pi\)
\(54\) 1.17408 0.159772
\(55\) 7.52677 1.01491
\(56\) 9.42620 1.25963
\(57\) 5.08811 0.673937
\(58\) −6.29472 −0.826537
\(59\) 12.5431 1.63297 0.816484 0.577368i \(-0.195920\pi\)
0.816484 + 0.577368i \(0.195920\pi\)
\(60\) 2.40447 0.310416
\(61\) 5.20694 0.666681 0.333340 0.942807i \(-0.391824\pi\)
0.333340 + 0.942807i \(0.391824\pi\)
\(62\) −0.856463 −0.108771
\(63\) 3.06255 0.385845
\(64\) 8.70080 1.08760
\(65\) −16.6768 −2.06851
\(66\) 2.28432 0.281180
\(67\) −7.84025 −0.957839 −0.478920 0.877859i \(-0.658972\pi\)
−0.478920 + 0.877859i \(0.658972\pi\)
\(68\) 0.621542 0.0753730
\(69\) 2.65257 0.319332
\(70\) −13.9101 −1.66257
\(71\) 12.0605 1.43132 0.715658 0.698451i \(-0.246127\pi\)
0.715658 + 0.698451i \(0.246127\pi\)
\(72\) 3.07789 0.362733
\(73\) −14.0089 −1.63962 −0.819810 0.572636i \(-0.805921\pi\)
−0.819810 + 0.572636i \(0.805921\pi\)
\(74\) 7.70020 0.895130
\(75\) −9.96577 −1.15075
\(76\) 3.16247 0.362761
\(77\) 5.95857 0.679042
\(78\) −5.06129 −0.573078
\(79\) 1.00000 0.112509
\(80\) −9.17082 −1.02533
\(81\) 1.00000 0.111111
\(82\) −10.3472 −1.14265
\(83\) 1.61708 0.177497 0.0887487 0.996054i \(-0.471713\pi\)
0.0887487 + 0.996054i \(0.471713\pi\)
\(84\) 1.90350 0.207689
\(85\) −3.86856 −0.419604
\(86\) −6.11795 −0.659716
\(87\) −5.36141 −0.574804
\(88\) 5.98843 0.638369
\(89\) −2.37602 −0.251858 −0.125929 0.992039i \(-0.540191\pi\)
−0.125929 + 0.992039i \(0.540191\pi\)
\(90\) −4.54199 −0.478768
\(91\) −13.2022 −1.38397
\(92\) 1.64869 0.171887
\(93\) −0.729477 −0.0756433
\(94\) −6.98925 −0.720886
\(95\) −19.6837 −2.01950
\(96\) 3.37252 0.344206
\(97\) 15.2428 1.54767 0.773834 0.633389i \(-0.218337\pi\)
0.773834 + 0.633389i \(0.218337\pi\)
\(98\) −2.79337 −0.282173
\(99\) 1.94563 0.195543
\(100\) −6.19414 −0.619414
\(101\) 3.95894 0.393930 0.196965 0.980411i \(-0.436892\pi\)
0.196965 + 0.980411i \(0.436892\pi\)
\(102\) −1.17408 −0.116251
\(103\) 6.36157 0.626824 0.313412 0.949617i \(-0.398528\pi\)
0.313412 + 0.949617i \(0.398528\pi\)
\(104\) −13.2684 −1.30107
\(105\) −11.8477 −1.15621
\(106\) 1.21586 0.118095
\(107\) 8.16730 0.789563 0.394781 0.918775i \(-0.370820\pi\)
0.394781 + 0.918775i \(0.370820\pi\)
\(108\) 0.621542 0.0598079
\(109\) 17.9770 1.72189 0.860944 0.508700i \(-0.169874\pi\)
0.860944 + 0.508700i \(0.169874\pi\)
\(110\) −8.83702 −0.842577
\(111\) 6.55851 0.622506
\(112\) −7.26008 −0.686014
\(113\) −1.08216 −0.101801 −0.0509005 0.998704i \(-0.516209\pi\)
−0.0509005 + 0.998704i \(0.516209\pi\)
\(114\) −5.97384 −0.559501
\(115\) −10.2616 −0.956904
\(116\) −3.33234 −0.309400
\(117\) −4.31087 −0.398540
\(118\) −14.7265 −1.35569
\(119\) −3.06255 −0.280743
\(120\) −11.9070 −1.08696
\(121\) −7.21454 −0.655867
\(122\) −6.11336 −0.553477
\(123\) −8.81303 −0.794644
\(124\) −0.453401 −0.0407166
\(125\) 19.2104 1.71823
\(126\) −3.59567 −0.320328
\(127\) 2.99327 0.265610 0.132805 0.991142i \(-0.457602\pi\)
0.132805 + 0.991142i \(0.457602\pi\)
\(128\) −3.47038 −0.306742
\(129\) −5.21086 −0.458791
\(130\) 19.5799 1.71727
\(131\) −11.3887 −0.995031 −0.497516 0.867455i \(-0.665754\pi\)
−0.497516 + 0.867455i \(0.665754\pi\)
\(132\) 1.20929 0.105255
\(133\) −15.5826 −1.35118
\(134\) 9.20507 0.795197
\(135\) −3.86856 −0.332953
\(136\) −3.07789 −0.263927
\(137\) −6.43962 −0.550174 −0.275087 0.961419i \(-0.588707\pi\)
−0.275087 + 0.961419i \(0.588707\pi\)
\(138\) −3.11433 −0.265109
\(139\) −7.72668 −0.655369 −0.327684 0.944787i \(-0.606268\pi\)
−0.327684 + 0.944787i \(0.606268\pi\)
\(140\) −7.36381 −0.622356
\(141\) −5.95297 −0.501331
\(142\) −14.1599 −1.18828
\(143\) −8.38733 −0.701384
\(144\) −2.37060 −0.197550
\(145\) 20.7410 1.72244
\(146\) 16.4476 1.36121
\(147\) −2.37920 −0.196233
\(148\) 4.07639 0.335077
\(149\) −5.37588 −0.440410 −0.220205 0.975454i \(-0.570673\pi\)
−0.220205 + 0.975454i \(0.570673\pi\)
\(150\) 11.7006 0.955349
\(151\) 14.5639 1.18519 0.592597 0.805499i \(-0.298103\pi\)
0.592597 + 0.805499i \(0.298103\pi\)
\(152\) −15.6607 −1.27025
\(153\) −1.00000 −0.0808452
\(154\) −6.99583 −0.563740
\(155\) 2.82203 0.226671
\(156\) −2.67938 −0.214522
\(157\) 17.2692 1.37823 0.689115 0.724652i \(-0.258000\pi\)
0.689115 + 0.724652i \(0.258000\pi\)
\(158\) −1.17408 −0.0934046
\(159\) 1.03559 0.0821273
\(160\) −13.0468 −1.03144
\(161\) −8.12364 −0.640232
\(162\) −1.17408 −0.0922443
\(163\) 1.10148 0.0862742 0.0431371 0.999069i \(-0.486265\pi\)
0.0431371 + 0.999069i \(0.486265\pi\)
\(164\) −5.47766 −0.427734
\(165\) −7.52677 −0.585959
\(166\) −1.89858 −0.147358
\(167\) −13.5588 −1.04922 −0.524608 0.851344i \(-0.675788\pi\)
−0.524608 + 0.851344i \(0.675788\pi\)
\(168\) −9.42620 −0.727247
\(169\) 5.58356 0.429505
\(170\) 4.54199 0.348355
\(171\) −5.08811 −0.389098
\(172\) −3.23877 −0.246954
\(173\) 23.7333 1.80441 0.902204 0.431310i \(-0.141948\pi\)
0.902204 + 0.431310i \(0.141948\pi\)
\(174\) 6.29472 0.477201
\(175\) 30.5207 2.30714
\(176\) −4.61231 −0.347666
\(177\) −12.5431 −0.942795
\(178\) 2.78963 0.209092
\(179\) −1.96158 −0.146616 −0.0733078 0.997309i \(-0.523356\pi\)
−0.0733078 + 0.997309i \(0.523356\pi\)
\(180\) −2.40447 −0.179219
\(181\) −25.4621 −1.89258 −0.946291 0.323318i \(-0.895202\pi\)
−0.946291 + 0.323318i \(0.895202\pi\)
\(182\) 15.5004 1.14897
\(183\) −5.20694 −0.384908
\(184\) −8.16434 −0.601883
\(185\) −25.3720 −1.86539
\(186\) 0.856463 0.0627989
\(187\) −1.94563 −0.142278
\(188\) −3.70002 −0.269852
\(189\) −3.06255 −0.222768
\(190\) 23.1102 1.67659
\(191\) 16.0338 1.16016 0.580082 0.814558i \(-0.303021\pi\)
0.580082 + 0.814558i \(0.303021\pi\)
\(192\) −8.70080 −0.627926
\(193\) 19.9539 1.43632 0.718158 0.695881i \(-0.244986\pi\)
0.718158 + 0.695881i \(0.244986\pi\)
\(194\) −17.8962 −1.28487
\(195\) 16.6768 1.19425
\(196\) −1.47877 −0.105627
\(197\) 10.1361 0.722169 0.361085 0.932533i \(-0.382407\pi\)
0.361085 + 0.932533i \(0.382407\pi\)
\(198\) −2.28432 −0.162339
\(199\) 16.8867 1.19707 0.598535 0.801097i \(-0.295750\pi\)
0.598535 + 0.801097i \(0.295750\pi\)
\(200\) 30.6736 2.16895
\(201\) 7.84025 0.553009
\(202\) −4.64811 −0.327040
\(203\) 16.4196 1.15243
\(204\) −0.621542 −0.0435166
\(205\) 34.0937 2.38121
\(206\) −7.46898 −0.520389
\(207\) −2.65257 −0.184367
\(208\) 10.2193 0.708584
\(209\) −9.89956 −0.684767
\(210\) 13.9101 0.959886
\(211\) 26.1952 1.80335 0.901677 0.432410i \(-0.142337\pi\)
0.901677 + 0.432410i \(0.142337\pi\)
\(212\) 0.643660 0.0442067
\(213\) −12.0605 −0.826371
\(214\) −9.58905 −0.655494
\(215\) 20.1585 1.37480
\(216\) −3.07789 −0.209424
\(217\) 2.23406 0.151658
\(218\) −21.1064 −1.42951
\(219\) 14.0089 0.946635
\(220\) −4.67820 −0.315404
\(221\) 4.31087 0.289980
\(222\) −7.70020 −0.516804
\(223\) −14.8016 −0.991185 −0.495593 0.868555i \(-0.665049\pi\)
−0.495593 + 0.868555i \(0.665049\pi\)
\(224\) −10.3285 −0.690101
\(225\) 9.96577 0.664385
\(226\) 1.27054 0.0845150
\(227\) 12.5129 0.830509 0.415255 0.909705i \(-0.363692\pi\)
0.415255 + 0.909705i \(0.363692\pi\)
\(228\) −3.16247 −0.209440
\(229\) −26.3090 −1.73855 −0.869275 0.494328i \(-0.835414\pi\)
−0.869275 + 0.494328i \(0.835414\pi\)
\(230\) 12.0480 0.794420
\(231\) −5.95857 −0.392045
\(232\) 16.5019 1.08340
\(233\) −24.8250 −1.62634 −0.813170 0.582026i \(-0.802260\pi\)
−0.813170 + 0.582026i \(0.802260\pi\)
\(234\) 5.06129 0.330867
\(235\) 23.0294 1.50227
\(236\) −7.79604 −0.507479
\(237\) −1.00000 −0.0649570
\(238\) 3.59567 0.233073
\(239\) −18.5884 −1.20239 −0.601193 0.799104i \(-0.705308\pi\)
−0.601193 + 0.799104i \(0.705308\pi\)
\(240\) 9.17082 0.591974
\(241\) 5.15833 0.332277 0.166139 0.986102i \(-0.446870\pi\)
0.166139 + 0.986102i \(0.446870\pi\)
\(242\) 8.47043 0.544500
\(243\) −1.00000 −0.0641500
\(244\) −3.23633 −0.207185
\(245\) 9.20409 0.588028
\(246\) 10.3472 0.659712
\(247\) 21.9342 1.39564
\(248\) 2.24525 0.142574
\(249\) −1.61708 −0.102478
\(250\) −22.5545 −1.42647
\(251\) 27.7239 1.74992 0.874958 0.484199i \(-0.160889\pi\)
0.874958 + 0.484199i \(0.160889\pi\)
\(252\) −1.90350 −0.119909
\(253\) −5.16092 −0.324464
\(254\) −3.51433 −0.220509
\(255\) 3.86856 0.242259
\(256\) −13.3271 −0.832944
\(257\) 22.5261 1.40514 0.702569 0.711616i \(-0.252036\pi\)
0.702569 + 0.711616i \(0.252036\pi\)
\(258\) 6.11795 0.380887
\(259\) −20.0858 −1.24807
\(260\) 10.3654 0.642832
\(261\) 5.36141 0.331863
\(262\) 13.3712 0.826073
\(263\) −8.77673 −0.541196 −0.270598 0.962692i \(-0.587221\pi\)
−0.270598 + 0.962692i \(0.587221\pi\)
\(264\) −5.98843 −0.368562
\(265\) −4.00623 −0.246101
\(266\) 18.2952 1.12175
\(267\) 2.37602 0.145410
\(268\) 4.87304 0.297669
\(269\) −5.93332 −0.361761 −0.180880 0.983505i \(-0.557895\pi\)
−0.180880 + 0.983505i \(0.557895\pi\)
\(270\) 4.54199 0.276417
\(271\) −5.77322 −0.350698 −0.175349 0.984506i \(-0.556105\pi\)
−0.175349 + 0.984506i \(0.556105\pi\)
\(272\) 2.37060 0.143739
\(273\) 13.2022 0.799035
\(274\) 7.56061 0.456753
\(275\) 19.3897 1.16924
\(276\) −1.64869 −0.0992392
\(277\) 21.3232 1.28119 0.640593 0.767881i \(-0.278689\pi\)
0.640593 + 0.767881i \(0.278689\pi\)
\(278\) 9.07173 0.544086
\(279\) 0.729477 0.0436727
\(280\) 36.4658 2.17925
\(281\) −26.4249 −1.57638 −0.788190 0.615432i \(-0.788982\pi\)
−0.788190 + 0.615432i \(0.788982\pi\)
\(282\) 6.98925 0.416204
\(283\) 12.9095 0.767389 0.383695 0.923460i \(-0.374652\pi\)
0.383695 + 0.923460i \(0.374652\pi\)
\(284\) −7.49609 −0.444811
\(285\) 19.6837 1.16596
\(286\) 9.84738 0.582288
\(287\) 26.9903 1.59319
\(288\) −3.37252 −0.198727
\(289\) 1.00000 0.0588235
\(290\) −24.3515 −1.42997
\(291\) −15.2428 −0.893546
\(292\) 8.70713 0.509546
\(293\) −28.7843 −1.68159 −0.840797 0.541350i \(-0.817913\pi\)
−0.840797 + 0.541350i \(0.817913\pi\)
\(294\) 2.79337 0.162912
\(295\) 48.5236 2.82516
\(296\) −20.1864 −1.17331
\(297\) −1.94563 −0.112897
\(298\) 6.31171 0.365627
\(299\) 11.4349 0.661297
\(300\) 6.19414 0.357619
\(301\) 15.9585 0.919833
\(302\) −17.0992 −0.983946
\(303\) −3.95894 −0.227435
\(304\) 12.0619 0.691797
\(305\) 20.1434 1.15341
\(306\) 1.17408 0.0671176
\(307\) −5.62415 −0.320987 −0.160494 0.987037i \(-0.551309\pi\)
−0.160494 + 0.987037i \(0.551309\pi\)
\(308\) −3.70350 −0.211027
\(309\) −6.36157 −0.361897
\(310\) −3.31328 −0.188182
\(311\) −12.4134 −0.703902 −0.351951 0.936018i \(-0.614482\pi\)
−0.351951 + 0.936018i \(0.614482\pi\)
\(312\) 13.2684 0.751174
\(313\) 0.954605 0.0539575 0.0269787 0.999636i \(-0.491411\pi\)
0.0269787 + 0.999636i \(0.491411\pi\)
\(314\) −20.2753 −1.14420
\(315\) 11.8477 0.667540
\(316\) −0.621542 −0.0349645
\(317\) −4.18916 −0.235286 −0.117643 0.993056i \(-0.537534\pi\)
−0.117643 + 0.993056i \(0.537534\pi\)
\(318\) −1.21586 −0.0681819
\(319\) 10.4313 0.584041
\(320\) 33.6596 1.88163
\(321\) −8.16730 −0.455854
\(322\) 9.53778 0.531520
\(323\) 5.08811 0.283110
\(324\) −0.621542 −0.0345301
\(325\) −42.9611 −2.38305
\(326\) −1.29322 −0.0716247
\(327\) −17.9770 −0.994132
\(328\) 27.1256 1.49776
\(329\) 18.2313 1.00512
\(330\) 8.83702 0.486462
\(331\) 6.26454 0.344330 0.172165 0.985068i \(-0.444924\pi\)
0.172165 + 0.985068i \(0.444924\pi\)
\(332\) −1.00508 −0.0551610
\(333\) −6.55851 −0.359404
\(334\) 15.9191 0.871057
\(335\) −30.3305 −1.65713
\(336\) 7.26008 0.396070
\(337\) −9.69837 −0.528304 −0.264152 0.964481i \(-0.585092\pi\)
−0.264152 + 0.964481i \(0.585092\pi\)
\(338\) −6.55553 −0.356574
\(339\) 1.08216 0.0587748
\(340\) 2.40447 0.130401
\(341\) 1.41929 0.0768589
\(342\) 5.97384 0.323028
\(343\) −14.1514 −0.764105
\(344\) 16.0385 0.864736
\(345\) 10.2616 0.552469
\(346\) −27.8647 −1.49802
\(347\) 17.1481 0.920558 0.460279 0.887774i \(-0.347749\pi\)
0.460279 + 0.887774i \(0.347749\pi\)
\(348\) 3.33234 0.178632
\(349\) 18.1728 0.972765 0.486383 0.873746i \(-0.338316\pi\)
0.486383 + 0.873746i \(0.338316\pi\)
\(350\) −35.8336 −1.91539
\(351\) 4.31087 0.230097
\(352\) −6.56165 −0.349737
\(353\) −25.1078 −1.33636 −0.668178 0.744001i \(-0.732926\pi\)
−0.668178 + 0.744001i \(0.732926\pi\)
\(354\) 14.7265 0.782707
\(355\) 46.6567 2.47628
\(356\) 1.47680 0.0782700
\(357\) 3.06255 0.162087
\(358\) 2.30305 0.121720
\(359\) −22.9349 −1.21046 −0.605230 0.796051i \(-0.706919\pi\)
−0.605230 + 0.796051i \(0.706919\pi\)
\(360\) 11.9070 0.627555
\(361\) 6.88890 0.362574
\(362\) 29.8945 1.57122
\(363\) 7.21454 0.378665
\(364\) 8.20574 0.430097
\(365\) −54.1944 −2.83666
\(366\) 6.11336 0.319550
\(367\) 29.2301 1.52580 0.762900 0.646517i \(-0.223775\pi\)
0.762900 + 0.646517i \(0.223775\pi\)
\(368\) 6.28820 0.327795
\(369\) 8.81303 0.458788
\(370\) 29.7887 1.54864
\(371\) −3.17153 −0.164658
\(372\) 0.453401 0.0235077
\(373\) −10.7822 −0.558284 −0.279142 0.960250i \(-0.590050\pi\)
−0.279142 + 0.960250i \(0.590050\pi\)
\(374\) 2.28432 0.118119
\(375\) −19.2104 −0.992020
\(376\) 18.3226 0.944916
\(377\) −23.1123 −1.19035
\(378\) 3.59567 0.184941
\(379\) 6.51981 0.334900 0.167450 0.985881i \(-0.446447\pi\)
0.167450 + 0.985881i \(0.446447\pi\)
\(380\) 12.2342 0.627603
\(381\) −2.99327 −0.153350
\(382\) −18.8249 −0.963166
\(383\) −6.34519 −0.324224 −0.162112 0.986772i \(-0.551831\pi\)
−0.162112 + 0.986772i \(0.551831\pi\)
\(384\) 3.47038 0.177097
\(385\) 23.0511 1.17479
\(386\) −23.4275 −1.19243
\(387\) 5.21086 0.264883
\(388\) −9.47401 −0.480970
\(389\) 23.3425 1.18351 0.591755 0.806118i \(-0.298435\pi\)
0.591755 + 0.806118i \(0.298435\pi\)
\(390\) −19.5799 −0.991468
\(391\) 2.65257 0.134146
\(392\) 7.32293 0.369864
\(393\) 11.3887 0.574482
\(394\) −11.9006 −0.599544
\(395\) 3.86856 0.194648
\(396\) −1.20929 −0.0607690
\(397\) −12.8069 −0.642760 −0.321380 0.946950i \(-0.604147\pi\)
−0.321380 + 0.946950i \(0.604147\pi\)
\(398\) −19.8263 −0.993805
\(399\) 15.5826 0.780105
\(400\) −23.6249 −1.18124
\(401\) −9.01114 −0.449995 −0.224997 0.974359i \(-0.572237\pi\)
−0.224997 + 0.974359i \(0.572237\pi\)
\(402\) −9.20507 −0.459107
\(403\) −3.14468 −0.156648
\(404\) −2.46065 −0.122422
\(405\) 3.86856 0.192230
\(406\) −19.2779 −0.956745
\(407\) −12.7604 −0.632510
\(408\) 3.07789 0.152378
\(409\) 17.9837 0.889238 0.444619 0.895720i \(-0.353339\pi\)
0.444619 + 0.895720i \(0.353339\pi\)
\(410\) −40.0287 −1.97688
\(411\) 6.43962 0.317643
\(412\) −3.95398 −0.194799
\(413\) 38.4138 1.89022
\(414\) 3.11433 0.153061
\(415\) 6.25577 0.307083
\(416\) 14.5385 0.712807
\(417\) 7.72668 0.378377
\(418\) 11.6229 0.568493
\(419\) −7.33658 −0.358415 −0.179208 0.983811i \(-0.557353\pi\)
−0.179208 + 0.983811i \(0.557353\pi\)
\(420\) 7.36381 0.359317
\(421\) −1.71174 −0.0834251 −0.0417125 0.999130i \(-0.513281\pi\)
−0.0417125 + 0.999130i \(0.513281\pi\)
\(422\) −30.7552 −1.49714
\(423\) 5.95297 0.289443
\(424\) −3.18742 −0.154795
\(425\) −9.96577 −0.483411
\(426\) 14.1599 0.686052
\(427\) 15.9465 0.771706
\(428\) −5.07632 −0.245373
\(429\) 8.38733 0.404944
\(430\) −23.6677 −1.14136
\(431\) 32.8465 1.58216 0.791081 0.611711i \(-0.209519\pi\)
0.791081 + 0.611711i \(0.209519\pi\)
\(432\) 2.37060 0.114056
\(433\) 31.9411 1.53499 0.767495 0.641055i \(-0.221503\pi\)
0.767495 + 0.641055i \(0.221503\pi\)
\(434\) −2.62296 −0.125906
\(435\) −20.7410 −0.994453
\(436\) −11.1735 −0.535112
\(437\) 13.4966 0.645630
\(438\) −16.4476 −0.785895
\(439\) 31.0882 1.48376 0.741879 0.670534i \(-0.233935\pi\)
0.741879 + 0.670534i \(0.233935\pi\)
\(440\) 23.1666 1.10442
\(441\) 2.37920 0.113295
\(442\) −5.06129 −0.240741
\(443\) 30.2297 1.43626 0.718129 0.695910i \(-0.244999\pi\)
0.718129 + 0.695910i \(0.244999\pi\)
\(444\) −4.07639 −0.193457
\(445\) −9.19178 −0.435732
\(446\) 17.3782 0.822880
\(447\) 5.37588 0.254271
\(448\) 26.6466 1.25893
\(449\) −24.1267 −1.13861 −0.569305 0.822126i \(-0.692788\pi\)
−0.569305 + 0.822126i \(0.692788\pi\)
\(450\) −11.7006 −0.551571
\(451\) 17.1469 0.807414
\(452\) 0.672607 0.0316368
\(453\) −14.5639 −0.684272
\(454\) −14.6911 −0.689487
\(455\) −51.0737 −2.39437
\(456\) 15.6607 0.733378
\(457\) −35.1710 −1.64523 −0.822616 0.568598i \(-0.807486\pi\)
−0.822616 + 0.568598i \(0.807486\pi\)
\(458\) 30.8889 1.44334
\(459\) 1.00000 0.0466760
\(460\) 6.37804 0.297378
\(461\) 6.98243 0.325204 0.162602 0.986692i \(-0.448011\pi\)
0.162602 + 0.986692i \(0.448011\pi\)
\(462\) 6.99583 0.325475
\(463\) −29.5160 −1.37172 −0.685862 0.727732i \(-0.740574\pi\)
−0.685862 + 0.727732i \(0.740574\pi\)
\(464\) −12.7098 −0.590037
\(465\) −2.82203 −0.130868
\(466\) 29.1465 1.35018
\(467\) −25.4834 −1.17923 −0.589615 0.807684i \(-0.700721\pi\)
−0.589615 + 0.807684i \(0.700721\pi\)
\(468\) 2.67938 0.123854
\(469\) −24.0112 −1.10873
\(470\) −27.0383 −1.24719
\(471\) −17.2692 −0.795721
\(472\) 38.6062 1.77700
\(473\) 10.1384 0.466163
\(474\) 1.17408 0.0539272
\(475\) −50.7070 −2.32660
\(476\) 1.90350 0.0872468
\(477\) −1.03559 −0.0474162
\(478\) 21.8243 0.998219
\(479\) 34.7839 1.58932 0.794658 0.607057i \(-0.207650\pi\)
0.794658 + 0.607057i \(0.207650\pi\)
\(480\) 13.0468 0.595502
\(481\) 28.2729 1.28913
\(482\) −6.05628 −0.275856
\(483\) 8.12364 0.369638
\(484\) 4.48414 0.203824
\(485\) 58.9675 2.67758
\(486\) 1.17408 0.0532572
\(487\) −34.6682 −1.57097 −0.785483 0.618883i \(-0.787585\pi\)
−0.785483 + 0.618883i \(0.787585\pi\)
\(488\) 16.0264 0.725482
\(489\) −1.10148 −0.0498104
\(490\) −10.8063 −0.488179
\(491\) −0.471690 −0.0212871 −0.0106435 0.999943i \(-0.503388\pi\)
−0.0106435 + 0.999943i \(0.503388\pi\)
\(492\) 5.47766 0.246952
\(493\) −5.36141 −0.241466
\(494\) −25.7524 −1.15866
\(495\) 7.52677 0.338303
\(496\) −1.72930 −0.0776479
\(497\) 36.9358 1.65680
\(498\) 1.89858 0.0850772
\(499\) −12.6542 −0.566480 −0.283240 0.959049i \(-0.591409\pi\)
−0.283240 + 0.959049i \(0.591409\pi\)
\(500\) −11.9401 −0.533976
\(501\) 13.5588 0.605765
\(502\) −32.5500 −1.45278
\(503\) 4.17905 0.186335 0.0931673 0.995650i \(-0.470301\pi\)
0.0931673 + 0.995650i \(0.470301\pi\)
\(504\) 9.42620 0.419876
\(505\) 15.3154 0.681527
\(506\) 6.05932 0.269370
\(507\) −5.58356 −0.247975
\(508\) −1.86044 −0.0825438
\(509\) −9.49524 −0.420869 −0.210435 0.977608i \(-0.567488\pi\)
−0.210435 + 0.977608i \(0.567488\pi\)
\(510\) −4.54199 −0.201123
\(511\) −42.9030 −1.89792
\(512\) 22.5878 0.998250
\(513\) 5.08811 0.224646
\(514\) −26.4474 −1.16654
\(515\) 24.6101 1.08445
\(516\) 3.23877 0.142579
\(517\) 11.5823 0.509387
\(518\) 23.5822 1.03614
\(519\) −23.7333 −1.04178
\(520\) −51.3296 −2.25095
\(521\) 15.3199 0.671178 0.335589 0.942008i \(-0.391065\pi\)
0.335589 + 0.942008i \(0.391065\pi\)
\(522\) −6.29472 −0.275512
\(523\) −11.8995 −0.520327 −0.260164 0.965565i \(-0.583777\pi\)
−0.260164 + 0.965565i \(0.583777\pi\)
\(524\) 7.07852 0.309227
\(525\) −30.5207 −1.33203
\(526\) 10.3046 0.449300
\(527\) −0.729477 −0.0317765
\(528\) 4.61231 0.200725
\(529\) −15.9638 −0.694080
\(530\) 4.70362 0.204312
\(531\) 12.5431 0.544323
\(532\) 9.68523 0.419908
\(533\) −37.9918 −1.64561
\(534\) −2.78963 −0.120719
\(535\) 31.5957 1.36600
\(536\) −24.1315 −1.04232
\(537\) 1.96158 0.0846485
\(538\) 6.96618 0.300333
\(539\) 4.62904 0.199387
\(540\) 2.40447 0.103472
\(541\) 12.7572 0.548474 0.274237 0.961662i \(-0.411575\pi\)
0.274237 + 0.961662i \(0.411575\pi\)
\(542\) 6.77821 0.291149
\(543\) 25.4621 1.09268
\(544\) 3.37252 0.144595
\(545\) 69.5453 2.97899
\(546\) −15.5004 −0.663358
\(547\) 19.9692 0.853822 0.426911 0.904294i \(-0.359602\pi\)
0.426911 + 0.904294i \(0.359602\pi\)
\(548\) 4.00249 0.170978
\(549\) 5.20694 0.222227
\(550\) −22.7650 −0.970702
\(551\) −27.2795 −1.16215
\(552\) 8.16434 0.347497
\(553\) 3.06255 0.130233
\(554\) −25.0351 −1.06364
\(555\) 25.3720 1.07698
\(556\) 4.80246 0.203669
\(557\) −23.7516 −1.00639 −0.503194 0.864173i \(-0.667842\pi\)
−0.503194 + 0.864173i \(0.667842\pi\)
\(558\) −0.856463 −0.0362570
\(559\) −22.4633 −0.950097
\(560\) −28.0861 −1.18685
\(561\) 1.94563 0.0821444
\(562\) 31.0249 1.30871
\(563\) −25.9984 −1.09570 −0.547850 0.836577i \(-0.684554\pi\)
−0.547850 + 0.836577i \(0.684554\pi\)
\(564\) 3.70002 0.155799
\(565\) −4.18640 −0.176123
\(566\) −15.1567 −0.637085
\(567\) 3.06255 0.128615
\(568\) 37.1209 1.55756
\(569\) −15.8543 −0.664649 −0.332324 0.943165i \(-0.607833\pi\)
−0.332324 + 0.943165i \(0.607833\pi\)
\(570\) −23.1102 −0.967979
\(571\) 9.65382 0.404000 0.202000 0.979386i \(-0.435256\pi\)
0.202000 + 0.979386i \(0.435256\pi\)
\(572\) 5.21308 0.217970
\(573\) −16.0338 −0.669821
\(574\) −31.6887 −1.32266
\(575\) −26.4350 −1.10241
\(576\) 8.70080 0.362533
\(577\) 9.77777 0.407054 0.203527 0.979069i \(-0.434760\pi\)
0.203527 + 0.979069i \(0.434760\pi\)
\(578\) −1.17408 −0.0488352
\(579\) −19.9539 −0.829257
\(580\) −12.8914 −0.535285
\(581\) 4.95238 0.205459
\(582\) 17.8962 0.741820
\(583\) −2.01486 −0.0834471
\(584\) −43.1180 −1.78423
\(585\) −16.6768 −0.689503
\(586\) 33.7950 1.39606
\(587\) −18.0640 −0.745582 −0.372791 0.927915i \(-0.621599\pi\)
−0.372791 + 0.927915i \(0.621599\pi\)
\(588\) 1.47877 0.0609836
\(589\) −3.71166 −0.152936
\(590\) −56.9705 −2.34544
\(591\) −10.1361 −0.416945
\(592\) 15.5476 0.639003
\(593\) −20.5894 −0.845505 −0.422753 0.906245i \(-0.638936\pi\)
−0.422753 + 0.906245i \(0.638936\pi\)
\(594\) 2.28432 0.0937266
\(595\) −11.8477 −0.485707
\(596\) 3.34134 0.136866
\(597\) −16.8867 −0.691128
\(598\) −13.4255 −0.549007
\(599\) −45.5410 −1.86076 −0.930378 0.366603i \(-0.880521\pi\)
−0.930378 + 0.366603i \(0.880521\pi\)
\(600\) −30.6736 −1.25224
\(601\) −32.4613 −1.32412 −0.662062 0.749449i \(-0.730319\pi\)
−0.662062 + 0.749449i \(0.730319\pi\)
\(602\) −18.7365 −0.763644
\(603\) −7.84025 −0.319280
\(604\) −9.05208 −0.368324
\(605\) −27.9099 −1.13470
\(606\) 4.64811 0.188816
\(607\) 15.4134 0.625609 0.312804 0.949818i \(-0.398732\pi\)
0.312804 + 0.949818i \(0.398732\pi\)
\(608\) 17.1597 0.695919
\(609\) −16.4196 −0.665355
\(610\) −23.6499 −0.957556
\(611\) −25.6625 −1.03819
\(612\) 0.621542 0.0251243
\(613\) −38.6256 −1.56007 −0.780037 0.625734i \(-0.784800\pi\)
−0.780037 + 0.625734i \(0.784800\pi\)
\(614\) 6.60319 0.266483
\(615\) −34.0937 −1.37479
\(616\) 18.3399 0.738934
\(617\) 16.0846 0.647540 0.323770 0.946136i \(-0.395050\pi\)
0.323770 + 0.946136i \(0.395050\pi\)
\(618\) 7.46898 0.300446
\(619\) −7.16318 −0.287913 −0.143956 0.989584i \(-0.545982\pi\)
−0.143956 + 0.989584i \(0.545982\pi\)
\(620\) −1.75401 −0.0704427
\(621\) 2.65257 0.106444
\(622\) 14.5744 0.584378
\(623\) −7.27668 −0.291534
\(624\) −10.2193 −0.409101
\(625\) 24.4877 0.979509
\(626\) −1.12078 −0.0447954
\(627\) 9.89956 0.395351
\(628\) −10.7335 −0.428313
\(629\) 6.55851 0.261505
\(630\) −13.9101 −0.554190
\(631\) 6.77064 0.269535 0.134767 0.990877i \(-0.456971\pi\)
0.134767 + 0.990877i \(0.456971\pi\)
\(632\) 3.07789 0.122432
\(633\) −26.1952 −1.04117
\(634\) 4.91839 0.195334
\(635\) 11.5797 0.459525
\(636\) −0.643660 −0.0255228
\(637\) −10.2564 −0.406374
\(638\) −12.2472 −0.484870
\(639\) 12.0605 0.477105
\(640\) −13.4254 −0.530685
\(641\) 23.3188 0.921038 0.460519 0.887650i \(-0.347663\pi\)
0.460519 + 0.887650i \(0.347663\pi\)
\(642\) 9.58905 0.378449
\(643\) 0.529220 0.0208704 0.0104352 0.999946i \(-0.496678\pi\)
0.0104352 + 0.999946i \(0.496678\pi\)
\(644\) 5.04918 0.198966
\(645\) −20.1585 −0.793741
\(646\) −5.97384 −0.235038
\(647\) 11.0009 0.432488 0.216244 0.976339i \(-0.430619\pi\)
0.216244 + 0.976339i \(0.430619\pi\)
\(648\) 3.07789 0.120911
\(649\) 24.4041 0.957946
\(650\) 50.4397 1.97841
\(651\) −2.23406 −0.0875597
\(652\) −0.684613 −0.0268115
\(653\) −5.25251 −0.205547 −0.102773 0.994705i \(-0.532772\pi\)
−0.102773 + 0.994705i \(0.532772\pi\)
\(654\) 21.1064 0.825327
\(655\) −44.0577 −1.72148
\(656\) −20.8922 −0.815703
\(657\) −14.0089 −0.546540
\(658\) −21.4049 −0.834450
\(659\) −19.4695 −0.758423 −0.379212 0.925310i \(-0.623805\pi\)
−0.379212 + 0.925310i \(0.623805\pi\)
\(660\) 4.67820 0.182099
\(661\) −3.62286 −0.140913 −0.0704565 0.997515i \(-0.522446\pi\)
−0.0704565 + 0.997515i \(0.522446\pi\)
\(662\) −7.35506 −0.285862
\(663\) −4.31087 −0.167420
\(664\) 4.97719 0.193153
\(665\) −60.2822 −2.33764
\(666\) 7.70020 0.298377
\(667\) −14.2216 −0.550661
\(668\) 8.42739 0.326066
\(669\) 14.8016 0.572261
\(670\) 35.6104 1.37575
\(671\) 10.1308 0.391094
\(672\) 10.3285 0.398430
\(673\) −25.9398 −0.999907 −0.499953 0.866052i \(-0.666650\pi\)
−0.499953 + 0.866052i \(0.666650\pi\)
\(674\) 11.3866 0.438597
\(675\) −9.96577 −0.383583
\(676\) −3.47041 −0.133477
\(677\) 29.0251 1.11553 0.557763 0.830000i \(-0.311660\pi\)
0.557763 + 0.830000i \(0.311660\pi\)
\(678\) −1.27054 −0.0487948
\(679\) 46.6817 1.79148
\(680\) −11.9070 −0.456613
\(681\) −12.5129 −0.479495
\(682\) −1.66636 −0.0638081
\(683\) 40.5109 1.55011 0.775053 0.631896i \(-0.217723\pi\)
0.775053 + 0.631896i \(0.217723\pi\)
\(684\) 3.16247 0.120920
\(685\) −24.9121 −0.951841
\(686\) 16.6149 0.634358
\(687\) 26.3090 1.00375
\(688\) −12.3529 −0.470949
\(689\) 4.46427 0.170075
\(690\) −12.0480 −0.458658
\(691\) 32.0842 1.22054 0.610271 0.792193i \(-0.291061\pi\)
0.610271 + 0.792193i \(0.291061\pi\)
\(692\) −14.7512 −0.560757
\(693\) 5.95857 0.226347
\(694\) −20.1332 −0.764246
\(695\) −29.8912 −1.13384
\(696\) −16.5019 −0.625502
\(697\) −8.81303 −0.333817
\(698\) −21.3362 −0.807588
\(699\) 24.8250 0.938968
\(700\) −18.9699 −0.716993
\(701\) 11.6041 0.438281 0.219141 0.975693i \(-0.429675\pi\)
0.219141 + 0.975693i \(0.429675\pi\)
\(702\) −5.06129 −0.191026
\(703\) 33.3704 1.25859
\(704\) 16.9285 0.638017
\(705\) −23.0294 −0.867339
\(706\) 29.4786 1.10944
\(707\) 12.1245 0.455987
\(708\) 7.79604 0.292993
\(709\) 37.5902 1.41173 0.705865 0.708346i \(-0.250559\pi\)
0.705865 + 0.708346i \(0.250559\pi\)
\(710\) −54.7786 −2.05581
\(711\) 1.00000 0.0375029
\(712\) −7.31314 −0.274071
\(713\) −1.93499 −0.0724661
\(714\) −3.59567 −0.134565
\(715\) −32.4469 −1.21345
\(716\) 1.21920 0.0455638
\(717\) 18.5884 0.694198
\(718\) 26.9274 1.00492
\(719\) 11.3046 0.421590 0.210795 0.977530i \(-0.432395\pi\)
0.210795 + 0.977530i \(0.432395\pi\)
\(720\) −9.17082 −0.341776
\(721\) 19.4826 0.725571
\(722\) −8.08810 −0.301008
\(723\) −5.15833 −0.191840
\(724\) 15.8257 0.588159
\(725\) 53.4306 1.98436
\(726\) −8.47043 −0.314367
\(727\) −39.3354 −1.45887 −0.729434 0.684051i \(-0.760217\pi\)
−0.729434 + 0.684051i \(0.760217\pi\)
\(728\) −40.6351 −1.50604
\(729\) 1.00000 0.0370370
\(730\) 63.6284 2.35499
\(731\) −5.21086 −0.192731
\(732\) 3.23633 0.119618
\(733\) 19.6713 0.726576 0.363288 0.931677i \(-0.381654\pi\)
0.363288 + 0.931677i \(0.381654\pi\)
\(734\) −34.3184 −1.26672
\(735\) −9.20409 −0.339498
\(736\) 8.94585 0.329748
\(737\) −15.2542 −0.561896
\(738\) −10.3472 −0.380885
\(739\) 48.7842 1.79456 0.897278 0.441466i \(-0.145541\pi\)
0.897278 + 0.441466i \(0.145541\pi\)
\(740\) 15.7698 0.579708
\(741\) −21.9342 −0.805772
\(742\) 3.72362 0.136699
\(743\) 1.75663 0.0644447 0.0322223 0.999481i \(-0.489742\pi\)
0.0322223 + 0.999481i \(0.489742\pi\)
\(744\) −2.24525 −0.0823150
\(745\) −20.7969 −0.761941
\(746\) 12.6592 0.463486
\(747\) 1.61708 0.0591658
\(748\) 1.20929 0.0442159
\(749\) 25.0128 0.913946
\(750\) 22.5545 0.823574
\(751\) 36.6840 1.33862 0.669309 0.742984i \(-0.266590\pi\)
0.669309 + 0.742984i \(0.266590\pi\)
\(752\) −14.1121 −0.514616
\(753\) −27.7239 −1.01031
\(754\) 27.1357 0.988223
\(755\) 56.3414 2.05047
\(756\) 1.90350 0.0692297
\(757\) 7.30491 0.265501 0.132751 0.991149i \(-0.457619\pi\)
0.132751 + 0.991149i \(0.457619\pi\)
\(758\) −7.65477 −0.278034
\(759\) 5.16092 0.187329
\(760\) −60.5843 −2.19762
\(761\) 40.6772 1.47455 0.737274 0.675594i \(-0.236113\pi\)
0.737274 + 0.675594i \(0.236113\pi\)
\(762\) 3.51433 0.127311
\(763\) 55.0555 1.99314
\(764\) −9.96566 −0.360545
\(765\) −3.86856 −0.139868
\(766\) 7.44975 0.269170
\(767\) −54.0715 −1.95241
\(768\) 13.3271 0.480900
\(769\) −45.8801 −1.65448 −0.827239 0.561851i \(-0.810089\pi\)
−0.827239 + 0.561851i \(0.810089\pi\)
\(770\) −27.0638 −0.975311
\(771\) −22.5261 −0.811257
\(772\) −12.4022 −0.446365
\(773\) −31.0341 −1.11622 −0.558109 0.829768i \(-0.688473\pi\)
−0.558109 + 0.829768i \(0.688473\pi\)
\(774\) −6.11795 −0.219905
\(775\) 7.26981 0.261139
\(776\) 46.9156 1.68417
\(777\) 20.0858 0.720572
\(778\) −27.4059 −0.982548
\(779\) −44.8417 −1.60662
\(780\) −10.3654 −0.371139
\(781\) 23.4652 0.839651
\(782\) −3.11433 −0.111368
\(783\) −5.36141 −0.191601
\(784\) −5.64014 −0.201434
\(785\) 66.8068 2.38444
\(786\) −13.3712 −0.476934
\(787\) −17.3722 −0.619253 −0.309627 0.950858i \(-0.600204\pi\)
−0.309627 + 0.950858i \(0.600204\pi\)
\(788\) −6.30003 −0.224429
\(789\) 8.77673 0.312460
\(790\) −4.54199 −0.161597
\(791\) −3.31417 −0.117838
\(792\) 5.98843 0.212790
\(793\) −22.4464 −0.797096
\(794\) 15.0363 0.533618
\(795\) 4.00623 0.142086
\(796\) −10.4958 −0.372014
\(797\) 17.3491 0.614538 0.307269 0.951623i \(-0.400585\pi\)
0.307269 + 0.951623i \(0.400585\pi\)
\(798\) −18.2952 −0.647642
\(799\) −5.95297 −0.210601
\(800\) −33.6097 −1.18828
\(801\) −2.37602 −0.0839526
\(802\) 10.5798 0.373585
\(803\) −27.2561 −0.961847
\(804\) −4.87304 −0.171859
\(805\) −31.4268 −1.10765
\(806\) 3.69210 0.130049
\(807\) 5.93332 0.208863
\(808\) 12.1852 0.428674
\(809\) −12.7366 −0.447794 −0.223897 0.974613i \(-0.571878\pi\)
−0.223897 + 0.974613i \(0.571878\pi\)
\(810\) −4.54199 −0.159589
\(811\) −6.71379 −0.235753 −0.117876 0.993028i \(-0.537609\pi\)
−0.117876 + 0.993028i \(0.537609\pi\)
\(812\) −10.2055 −0.358141
\(813\) 5.77322 0.202476
\(814\) 14.9817 0.525109
\(815\) 4.26112 0.149261
\(816\) −2.37060 −0.0829877
\(817\) −26.5134 −0.927588
\(818\) −21.1143 −0.738244
\(819\) −13.2022 −0.461323
\(820\) −21.1907 −0.740011
\(821\) −56.4520 −1.97019 −0.985094 0.172018i \(-0.944971\pi\)
−0.985094 + 0.172018i \(0.944971\pi\)
\(822\) −7.56061 −0.263707
\(823\) 36.6848 1.27875 0.639375 0.768895i \(-0.279193\pi\)
0.639375 + 0.768895i \(0.279193\pi\)
\(824\) 19.5802 0.682110
\(825\) −19.3897 −0.675061
\(826\) −45.1007 −1.56926
\(827\) 3.03726 0.105616 0.0528080 0.998605i \(-0.483183\pi\)
0.0528080 + 0.998605i \(0.483183\pi\)
\(828\) 1.64869 0.0572958
\(829\) 22.7431 0.789900 0.394950 0.918703i \(-0.370762\pi\)
0.394950 + 0.918703i \(0.370762\pi\)
\(830\) −7.34475 −0.254940
\(831\) −21.3232 −0.739693
\(832\) −37.5080 −1.30036
\(833\) −2.37920 −0.0824344
\(834\) −9.07173 −0.314128
\(835\) −52.4532 −1.81522
\(836\) 6.15299 0.212806
\(837\) −0.729477 −0.0252144
\(838\) 8.61372 0.297556
\(839\) −15.5849 −0.538049 −0.269025 0.963133i \(-0.586701\pi\)
−0.269025 + 0.963133i \(0.586701\pi\)
\(840\) −36.4658 −1.25819
\(841\) −0.255231 −0.00880106
\(842\) 2.00972 0.0692594
\(843\) 26.4249 0.910124
\(844\) −16.2814 −0.560430
\(845\) 21.6003 0.743074
\(846\) −6.98925 −0.240295
\(847\) −22.0949 −0.759189
\(848\) 2.45496 0.0843038
\(849\) −12.9095 −0.443052
\(850\) 11.7006 0.401327
\(851\) 17.3969 0.596359
\(852\) 7.49609 0.256812
\(853\) 6.94574 0.237818 0.118909 0.992905i \(-0.462060\pi\)
0.118909 + 0.992905i \(0.462060\pi\)
\(854\) −18.7224 −0.640669
\(855\) −19.6837 −0.673168
\(856\) 25.1381 0.859202
\(857\) 30.2494 1.03330 0.516650 0.856196i \(-0.327179\pi\)
0.516650 + 0.856196i \(0.327179\pi\)
\(858\) −9.84738 −0.336184
\(859\) 25.6789 0.876152 0.438076 0.898938i \(-0.355660\pi\)
0.438076 + 0.898938i \(0.355660\pi\)
\(860\) −12.5294 −0.427248
\(861\) −26.9903 −0.919827
\(862\) −38.5644 −1.31351
\(863\) −2.72120 −0.0926308 −0.0463154 0.998927i \(-0.514748\pi\)
−0.0463154 + 0.998927i \(0.514748\pi\)
\(864\) 3.37252 0.114735
\(865\) 91.8137 3.12176
\(866\) −37.5013 −1.27435
\(867\) −1.00000 −0.0339618
\(868\) −1.38856 −0.0471308
\(869\) 1.94563 0.0660008
\(870\) 24.3515 0.825593
\(871\) 33.7983 1.14521
\(872\) 55.3314 1.87376
\(873\) 15.2428 0.515889
\(874\) −15.8461 −0.536001
\(875\) 58.8328 1.98891
\(876\) −8.70713 −0.294187
\(877\) −46.0784 −1.55596 −0.777979 0.628291i \(-0.783755\pi\)
−0.777979 + 0.628291i \(0.783755\pi\)
\(878\) −36.4999 −1.23181
\(879\) 28.7843 0.970869
\(880\) −17.8430 −0.601487
\(881\) −15.5276 −0.523139 −0.261570 0.965185i \(-0.584240\pi\)
−0.261570 + 0.965185i \(0.584240\pi\)
\(882\) −2.79337 −0.0940576
\(883\) 37.3026 1.25533 0.627666 0.778483i \(-0.284010\pi\)
0.627666 + 0.778483i \(0.284010\pi\)
\(884\) −2.67938 −0.0901174
\(885\) −48.5236 −1.63110
\(886\) −35.4921 −1.19238
\(887\) 51.0006 1.71243 0.856216 0.516618i \(-0.172809\pi\)
0.856216 + 0.516618i \(0.172809\pi\)
\(888\) 20.1864 0.677411
\(889\) 9.16704 0.307453
\(890\) 10.7919 0.361744
\(891\) 1.94563 0.0651809
\(892\) 9.19978 0.308031
\(893\) −30.2894 −1.01360
\(894\) −6.31171 −0.211095
\(895\) −7.58850 −0.253656
\(896\) −10.6282 −0.355064
\(897\) −11.4349 −0.381800
\(898\) 28.3266 0.945272
\(899\) 3.91103 0.130440
\(900\) −6.19414 −0.206471
\(901\) 1.03559 0.0345004
\(902\) −20.1317 −0.670313
\(903\) −15.9585 −0.531066
\(904\) −3.33077 −0.110780
\(905\) −98.5016 −3.27430
\(906\) 17.0992 0.568082
\(907\) 16.9256 0.562006 0.281003 0.959707i \(-0.409333\pi\)
0.281003 + 0.959707i \(0.409333\pi\)
\(908\) −7.77728 −0.258098
\(909\) 3.95894 0.131310
\(910\) 59.9644 1.98780
\(911\) −29.6254 −0.981532 −0.490766 0.871291i \(-0.663283\pi\)
−0.490766 + 0.871291i \(0.663283\pi\)
\(912\) −12.0619 −0.399409
\(913\) 3.14623 0.104125
\(914\) 41.2935 1.36587
\(915\) −20.1434 −0.665920
\(916\) 16.3522 0.540291
\(917\) −34.8783 −1.15178
\(918\) −1.17408 −0.0387503
\(919\) −10.8176 −0.356841 −0.178421 0.983954i \(-0.557099\pi\)
−0.178421 + 0.983954i \(0.557099\pi\)
\(920\) −31.5843 −1.04130
\(921\) 5.62415 0.185322
\(922\) −8.19791 −0.269984
\(923\) −51.9911 −1.71131
\(924\) 3.70350 0.121836
\(925\) −65.3606 −2.14904
\(926\) 34.6540 1.13880
\(927\) 6.36157 0.208941
\(928\) −18.0815 −0.593553
\(929\) −6.84401 −0.224545 −0.112272 0.993677i \(-0.535813\pi\)
−0.112272 + 0.993677i \(0.535813\pi\)
\(930\) 3.31328 0.108647
\(931\) −12.1056 −0.396746
\(932\) 15.4298 0.505419
\(933\) 12.4134 0.406398
\(934\) 29.9195 0.978995
\(935\) −7.52677 −0.246152
\(936\) −13.2684 −0.433691
\(937\) −16.8134 −0.549270 −0.274635 0.961549i \(-0.588557\pi\)
−0.274635 + 0.961549i \(0.588557\pi\)
\(938\) 28.1910 0.920467
\(939\) −0.954605 −0.0311524
\(940\) −14.3138 −0.466863
\(941\) 17.7542 0.578769 0.289385 0.957213i \(-0.406549\pi\)
0.289385 + 0.957213i \(0.406549\pi\)
\(942\) 20.2753 0.660606
\(943\) −23.3772 −0.761267
\(944\) −29.7346 −0.967780
\(945\) −11.8477 −0.385404
\(946\) −11.9032 −0.387008
\(947\) −35.6574 −1.15871 −0.579355 0.815075i \(-0.696696\pi\)
−0.579355 + 0.815075i \(0.696696\pi\)
\(948\) 0.621542 0.0201867
\(949\) 60.3906 1.96036
\(950\) 59.5339 1.93154
\(951\) 4.18916 0.135843
\(952\) −9.42620 −0.305505
\(953\) 15.8288 0.512746 0.256373 0.966578i \(-0.417472\pi\)
0.256373 + 0.966578i \(0.417472\pi\)
\(954\) 1.21586 0.0393649
\(955\) 62.0277 2.00717
\(956\) 11.5535 0.373667
\(957\) −10.4313 −0.337196
\(958\) −40.8390 −1.31945
\(959\) −19.7216 −0.636845
\(960\) −33.6596 −1.08636
\(961\) −30.4679 −0.982834
\(962\) −33.1945 −1.07023
\(963\) 8.16730 0.263188
\(964\) −3.20612 −0.103262
\(965\) 77.1930 2.48493
\(966\) −9.53778 −0.306873
\(967\) 15.8624 0.510102 0.255051 0.966928i \(-0.417908\pi\)
0.255051 + 0.966928i \(0.417908\pi\)
\(968\) −22.2056 −0.713715
\(969\) −5.08811 −0.163454
\(970\) −69.2325 −2.22292
\(971\) −1.91689 −0.0615161 −0.0307580 0.999527i \(-0.509792\pi\)
−0.0307580 + 0.999527i \(0.509792\pi\)
\(972\) 0.621542 0.0199360
\(973\) −23.6633 −0.758612
\(974\) 40.7032 1.30421
\(975\) 42.9611 1.37586
\(976\) −12.3436 −0.395109
\(977\) −20.1733 −0.645400 −0.322700 0.946501i \(-0.604590\pi\)
−0.322700 + 0.946501i \(0.604590\pi\)
\(978\) 1.29322 0.0413525
\(979\) −4.62285 −0.147747
\(980\) −5.72072 −0.182742
\(981\) 17.9770 0.573963
\(982\) 0.553801 0.0176725
\(983\) −42.6481 −1.36026 −0.680132 0.733090i \(-0.738078\pi\)
−0.680132 + 0.733090i \(0.738078\pi\)
\(984\) −27.1256 −0.864731
\(985\) 39.2122 1.24941
\(986\) 6.29472 0.200465
\(987\) −18.2313 −0.580307
\(988\) −13.6330 −0.433724
\(989\) −13.8222 −0.439520
\(990\) −8.83702 −0.280859
\(991\) −13.6091 −0.432309 −0.216154 0.976359i \(-0.569351\pi\)
−0.216154 + 0.976359i \(0.569351\pi\)
\(992\) −2.46017 −0.0781106
\(993\) −6.26454 −0.198799
\(994\) −43.3655 −1.37547
\(995\) 65.3274 2.07102
\(996\) 1.00508 0.0318472
\(997\) 11.7369 0.371712 0.185856 0.982577i \(-0.440494\pi\)
0.185856 + 0.982577i \(0.440494\pi\)
\(998\) 14.8570 0.470291
\(999\) 6.55851 0.207502
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 4029.2.a.l.1.12 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.12 32 1.1 even 1 trivial