Properties

Label 4029.2.a.l.1.16
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 1.16
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0772262 q^{2} -1.00000 q^{3} -1.99404 q^{4} +3.97384 q^{5} +0.0772262 q^{6} +0.969209 q^{7} +0.308444 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.0772262 q^{2} -1.00000 q^{3} -1.99404 q^{4} +3.97384 q^{5} +0.0772262 q^{6} +0.969209 q^{7} +0.308444 q^{8} +1.00000 q^{9} -0.306884 q^{10} +2.24354 q^{11} +1.99404 q^{12} +4.20360 q^{13} -0.0748483 q^{14} -3.97384 q^{15} +3.96425 q^{16} -1.00000 q^{17} -0.0772262 q^{18} +5.15523 q^{19} -7.92398 q^{20} -0.969209 q^{21} -0.173260 q^{22} +0.911156 q^{23} -0.308444 q^{24} +10.7914 q^{25} -0.324628 q^{26} -1.00000 q^{27} -1.93264 q^{28} +8.81167 q^{29} +0.306884 q^{30} -5.98124 q^{31} -0.923033 q^{32} -2.24354 q^{33} +0.0772262 q^{34} +3.85148 q^{35} -1.99404 q^{36} +4.64710 q^{37} -0.398119 q^{38} -4.20360 q^{39} +1.22571 q^{40} -10.0598 q^{41} +0.0748483 q^{42} +9.32461 q^{43} -4.47370 q^{44} +3.97384 q^{45} -0.0703651 q^{46} +6.28523 q^{47} -3.96425 q^{48} -6.06063 q^{49} -0.833378 q^{50} +1.00000 q^{51} -8.38212 q^{52} -4.67370 q^{53} +0.0772262 q^{54} +8.91546 q^{55} +0.298947 q^{56} -5.15523 q^{57} -0.680492 q^{58} -7.12284 q^{59} +7.92398 q^{60} -7.64526 q^{61} +0.461908 q^{62} +0.969209 q^{63} -7.85722 q^{64} +16.7044 q^{65} +0.173260 q^{66} +10.6038 q^{67} +1.99404 q^{68} -0.911156 q^{69} -0.297435 q^{70} +0.523273 q^{71} +0.308444 q^{72} -9.82633 q^{73} -0.358878 q^{74} -10.7914 q^{75} -10.2797 q^{76} +2.17446 q^{77} +0.324628 q^{78} +1.00000 q^{79} +15.7533 q^{80} +1.00000 q^{81} +0.776883 q^{82} +12.4060 q^{83} +1.93264 q^{84} -3.97384 q^{85} -0.720104 q^{86} -8.81167 q^{87} +0.692006 q^{88} +11.7149 q^{89} -0.306884 q^{90} +4.07416 q^{91} -1.81688 q^{92} +5.98124 q^{93} -0.485385 q^{94} +20.4861 q^{95} +0.923033 q^{96} -15.9767 q^{97} +0.468040 q^{98} +2.24354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0772262 −0.0546072 −0.0273036 0.999627i \(-0.508692\pi\)
−0.0273036 + 0.999627i \(0.508692\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99404 −0.997018
\(5\) 3.97384 1.77715 0.888577 0.458727i \(-0.151695\pi\)
0.888577 + 0.458727i \(0.151695\pi\)
\(6\) 0.0772262 0.0315275
\(7\) 0.969209 0.366327 0.183163 0.983083i \(-0.441366\pi\)
0.183163 + 0.983083i \(0.441366\pi\)
\(8\) 0.308444 0.109052
\(9\) 1.00000 0.333333
\(10\) −0.306884 −0.0970454
\(11\) 2.24354 0.676452 0.338226 0.941065i \(-0.390173\pi\)
0.338226 + 0.941065i \(0.390173\pi\)
\(12\) 1.99404 0.575629
\(13\) 4.20360 1.16587 0.582934 0.812520i \(-0.301905\pi\)
0.582934 + 0.812520i \(0.301905\pi\)
\(14\) −0.0748483 −0.0200041
\(15\) −3.97384 −1.02604
\(16\) 3.96425 0.991063
\(17\) −1.00000 −0.242536
\(18\) −0.0772262 −0.0182024
\(19\) 5.15523 1.18269 0.591346 0.806418i \(-0.298597\pi\)
0.591346 + 0.806418i \(0.298597\pi\)
\(20\) −7.92398 −1.77185
\(21\) −0.969209 −0.211499
\(22\) −0.173260 −0.0369391
\(23\) 0.911156 0.189989 0.0949946 0.995478i \(-0.469717\pi\)
0.0949946 + 0.995478i \(0.469717\pi\)
\(24\) −0.308444 −0.0629609
\(25\) 10.7914 2.15828
\(26\) −0.324628 −0.0636647
\(27\) −1.00000 −0.192450
\(28\) −1.93264 −0.365234
\(29\) 8.81167 1.63629 0.818143 0.575014i \(-0.195003\pi\)
0.818143 + 0.575014i \(0.195003\pi\)
\(30\) 0.306884 0.0560292
\(31\) −5.98124 −1.07426 −0.537131 0.843499i \(-0.680492\pi\)
−0.537131 + 0.843499i \(0.680492\pi\)
\(32\) −0.923033 −0.163171
\(33\) −2.24354 −0.390550
\(34\) 0.0772262 0.0132442
\(35\) 3.85148 0.651019
\(36\) −1.99404 −0.332339
\(37\) 4.64710 0.763979 0.381989 0.924167i \(-0.375239\pi\)
0.381989 + 0.924167i \(0.375239\pi\)
\(38\) −0.398119 −0.0645835
\(39\) −4.20360 −0.673114
\(40\) 1.22571 0.193801
\(41\) −10.0598 −1.57108 −0.785541 0.618810i \(-0.787615\pi\)
−0.785541 + 0.618810i \(0.787615\pi\)
\(42\) 0.0748483 0.0115493
\(43\) 9.32461 1.42199 0.710995 0.703198i \(-0.248245\pi\)
0.710995 + 0.703198i \(0.248245\pi\)
\(44\) −4.47370 −0.674435
\(45\) 3.97384 0.592385
\(46\) −0.0703651 −0.0103748
\(47\) 6.28523 0.916796 0.458398 0.888747i \(-0.348423\pi\)
0.458398 + 0.888747i \(0.348423\pi\)
\(48\) −3.96425 −0.572191
\(49\) −6.06063 −0.865805
\(50\) −0.833378 −0.117857
\(51\) 1.00000 0.140028
\(52\) −8.38212 −1.16239
\(53\) −4.67370 −0.641981 −0.320991 0.947082i \(-0.604016\pi\)
−0.320991 + 0.947082i \(0.604016\pi\)
\(54\) 0.0772262 0.0105092
\(55\) 8.91546 1.20216
\(56\) 0.298947 0.0399485
\(57\) −5.15523 −0.682827
\(58\) −0.680492 −0.0893530
\(59\) −7.12284 −0.927315 −0.463658 0.886014i \(-0.653463\pi\)
−0.463658 + 0.886014i \(0.653463\pi\)
\(60\) 7.92398 1.02298
\(61\) −7.64526 −0.978875 −0.489437 0.872038i \(-0.662798\pi\)
−0.489437 + 0.872038i \(0.662798\pi\)
\(62\) 0.461908 0.0586624
\(63\) 0.969209 0.122109
\(64\) −7.85722 −0.982153
\(65\) 16.7044 2.07193
\(66\) 0.173260 0.0213268
\(67\) 10.6038 1.29546 0.647728 0.761871i \(-0.275719\pi\)
0.647728 + 0.761871i \(0.275719\pi\)
\(68\) 1.99404 0.241812
\(69\) −0.911156 −0.109690
\(70\) −0.297435 −0.0355503
\(71\) 0.523273 0.0621010 0.0310505 0.999518i \(-0.490115\pi\)
0.0310505 + 0.999518i \(0.490115\pi\)
\(72\) 0.308444 0.0363505
\(73\) −9.82633 −1.15008 −0.575042 0.818124i \(-0.695014\pi\)
−0.575042 + 0.818124i \(0.695014\pi\)
\(74\) −0.358878 −0.0417187
\(75\) −10.7914 −1.24608
\(76\) −10.2797 −1.17917
\(77\) 2.17446 0.247802
\(78\) 0.324628 0.0367569
\(79\) 1.00000 0.112509
\(80\) 15.7533 1.76127
\(81\) 1.00000 0.111111
\(82\) 0.776883 0.0857923
\(83\) 12.4060 1.36173 0.680865 0.732409i \(-0.261604\pi\)
0.680865 + 0.732409i \(0.261604\pi\)
\(84\) 1.93264 0.210868
\(85\) −3.97384 −0.431023
\(86\) −0.720104 −0.0776508
\(87\) −8.81167 −0.944711
\(88\) 0.692006 0.0737681
\(89\) 11.7149 1.24178 0.620889 0.783898i \(-0.286772\pi\)
0.620889 + 0.783898i \(0.286772\pi\)
\(90\) −0.306884 −0.0323485
\(91\) 4.07416 0.427088
\(92\) −1.81688 −0.189423
\(93\) 5.98124 0.620225
\(94\) −0.485385 −0.0500636
\(95\) 20.4861 2.10183
\(96\) 0.923033 0.0942066
\(97\) −15.9767 −1.62219 −0.811093 0.584917i \(-0.801127\pi\)
−0.811093 + 0.584917i \(0.801127\pi\)
\(98\) 0.468040 0.0472792
\(99\) 2.24354 0.225484
\(100\) −21.5184 −2.15184
\(101\) −3.75524 −0.373660 −0.186830 0.982392i \(-0.559821\pi\)
−0.186830 + 0.982392i \(0.559821\pi\)
\(102\) −0.0772262 −0.00764653
\(103\) 9.38168 0.924404 0.462202 0.886775i \(-0.347059\pi\)
0.462202 + 0.886775i \(0.347059\pi\)
\(104\) 1.29657 0.127140
\(105\) −3.85148 −0.375866
\(106\) 0.360932 0.0350568
\(107\) −17.8136 −1.72211 −0.861055 0.508513i \(-0.830195\pi\)
−0.861055 + 0.508513i \(0.830195\pi\)
\(108\) 1.99404 0.191876
\(109\) −17.9566 −1.71993 −0.859964 0.510355i \(-0.829514\pi\)
−0.859964 + 0.510355i \(0.829514\pi\)
\(110\) −0.688507 −0.0656466
\(111\) −4.64710 −0.441083
\(112\) 3.84219 0.363053
\(113\) −15.5944 −1.46700 −0.733499 0.679691i \(-0.762114\pi\)
−0.733499 + 0.679691i \(0.762114\pi\)
\(114\) 0.398119 0.0372873
\(115\) 3.62079 0.337640
\(116\) −17.5708 −1.63141
\(117\) 4.20360 0.388623
\(118\) 0.550070 0.0506381
\(119\) −0.969209 −0.0888472
\(120\) −1.22571 −0.111891
\(121\) −5.96654 −0.542412
\(122\) 0.590414 0.0534536
\(123\) 10.0598 0.907064
\(124\) 11.9268 1.07106
\(125\) 23.0140 2.05844
\(126\) −0.0748483 −0.00666802
\(127\) 6.24289 0.553967 0.276984 0.960875i \(-0.410665\pi\)
0.276984 + 0.960875i \(0.410665\pi\)
\(128\) 2.45285 0.216803
\(129\) −9.32461 −0.820986
\(130\) −1.29002 −0.113142
\(131\) 2.03547 0.177840 0.0889198 0.996039i \(-0.471659\pi\)
0.0889198 + 0.996039i \(0.471659\pi\)
\(132\) 4.47370 0.389385
\(133\) 4.99650 0.433251
\(134\) −0.818889 −0.0707412
\(135\) −3.97384 −0.342013
\(136\) −0.308444 −0.0264489
\(137\) 9.67979 0.827000 0.413500 0.910504i \(-0.364306\pi\)
0.413500 + 0.910504i \(0.364306\pi\)
\(138\) 0.0703651 0.00598987
\(139\) −11.1227 −0.943416 −0.471708 0.881755i \(-0.656362\pi\)
−0.471708 + 0.881755i \(0.656362\pi\)
\(140\) −7.67999 −0.649077
\(141\) −6.28523 −0.529312
\(142\) −0.0404104 −0.00339116
\(143\) 9.43093 0.788654
\(144\) 3.96425 0.330354
\(145\) 35.0162 2.90793
\(146\) 0.758850 0.0628029
\(147\) 6.06063 0.499873
\(148\) −9.26649 −0.761700
\(149\) −14.8967 −1.22038 −0.610192 0.792254i \(-0.708908\pi\)
−0.610192 + 0.792254i \(0.708908\pi\)
\(150\) 0.833378 0.0680450
\(151\) 11.1404 0.906593 0.453297 0.891360i \(-0.350248\pi\)
0.453297 + 0.891360i \(0.350248\pi\)
\(152\) 1.59010 0.128974
\(153\) −1.00000 −0.0808452
\(154\) −0.167925 −0.0135318
\(155\) −23.7685 −1.90913
\(156\) 8.38212 0.671107
\(157\) −5.48902 −0.438072 −0.219036 0.975717i \(-0.570291\pi\)
−0.219036 + 0.975717i \(0.570291\pi\)
\(158\) −0.0772262 −0.00614379
\(159\) 4.67370 0.370648
\(160\) −3.66798 −0.289979
\(161\) 0.883100 0.0695981
\(162\) −0.0772262 −0.00606746
\(163\) −7.76532 −0.608227 −0.304113 0.952636i \(-0.598360\pi\)
−0.304113 + 0.952636i \(0.598360\pi\)
\(164\) 20.0597 1.56640
\(165\) −8.91546 −0.694067
\(166\) −0.958065 −0.0743603
\(167\) 11.4568 0.886550 0.443275 0.896386i \(-0.353817\pi\)
0.443275 + 0.896386i \(0.353817\pi\)
\(168\) −0.298947 −0.0230643
\(169\) 4.67022 0.359247
\(170\) 0.306884 0.0235370
\(171\) 5.15523 0.394231
\(172\) −18.5936 −1.41775
\(173\) 6.32459 0.480850 0.240425 0.970668i \(-0.422713\pi\)
0.240425 + 0.970668i \(0.422713\pi\)
\(174\) 0.680492 0.0515880
\(175\) 10.4591 0.790634
\(176\) 8.89395 0.670407
\(177\) 7.12284 0.535386
\(178\) −0.904699 −0.0678100
\(179\) −0.513577 −0.0383865 −0.0191933 0.999816i \(-0.506110\pi\)
−0.0191933 + 0.999816i \(0.506110\pi\)
\(180\) −7.92398 −0.590618
\(181\) 5.46475 0.406192 0.203096 0.979159i \(-0.434900\pi\)
0.203096 + 0.979159i \(0.434900\pi\)
\(182\) −0.314632 −0.0233221
\(183\) 7.64526 0.565154
\(184\) 0.281041 0.0207186
\(185\) 18.4668 1.35771
\(186\) −0.461908 −0.0338687
\(187\) −2.24354 −0.164064
\(188\) −12.5330 −0.914062
\(189\) −0.969209 −0.0704996
\(190\) −1.58206 −0.114775
\(191\) 11.9704 0.866147 0.433073 0.901359i \(-0.357429\pi\)
0.433073 + 0.901359i \(0.357429\pi\)
\(192\) 7.85722 0.567046
\(193\) −19.2282 −1.38408 −0.692038 0.721861i \(-0.743287\pi\)
−0.692038 + 0.721861i \(0.743287\pi\)
\(194\) 1.23382 0.0885830
\(195\) −16.7044 −1.19623
\(196\) 12.0851 0.863223
\(197\) −2.72447 −0.194111 −0.0970553 0.995279i \(-0.530942\pi\)
−0.0970553 + 0.995279i \(0.530942\pi\)
\(198\) −0.173260 −0.0123130
\(199\) 7.25954 0.514615 0.257308 0.966330i \(-0.417165\pi\)
0.257308 + 0.966330i \(0.417165\pi\)
\(200\) 3.32854 0.235363
\(201\) −10.6038 −0.747932
\(202\) 0.290003 0.0204045
\(203\) 8.54035 0.599415
\(204\) −1.99404 −0.139610
\(205\) −39.9761 −2.79205
\(206\) −0.724511 −0.0504791
\(207\) 0.911156 0.0633297
\(208\) 16.6641 1.15545
\(209\) 11.5660 0.800035
\(210\) 0.297435 0.0205250
\(211\) 12.2282 0.841827 0.420913 0.907101i \(-0.361710\pi\)
0.420913 + 0.907101i \(0.361710\pi\)
\(212\) 9.31952 0.640067
\(213\) −0.523273 −0.0358540
\(214\) 1.37568 0.0940395
\(215\) 37.0545 2.52709
\(216\) −0.308444 −0.0209870
\(217\) −5.79707 −0.393531
\(218\) 1.38672 0.0939204
\(219\) 9.82633 0.664002
\(220\) −17.7777 −1.19858
\(221\) −4.20360 −0.282764
\(222\) 0.358878 0.0240863
\(223\) −5.02084 −0.336221 −0.168110 0.985768i \(-0.553766\pi\)
−0.168110 + 0.985768i \(0.553766\pi\)
\(224\) −0.894611 −0.0597737
\(225\) 10.7914 0.719426
\(226\) 1.20430 0.0801086
\(227\) 26.4815 1.75764 0.878821 0.477152i \(-0.158331\pi\)
0.878821 + 0.477152i \(0.158331\pi\)
\(228\) 10.2797 0.680791
\(229\) 17.7040 1.16991 0.584956 0.811065i \(-0.301112\pi\)
0.584956 + 0.811065i \(0.301112\pi\)
\(230\) −0.279619 −0.0184376
\(231\) −2.17446 −0.143069
\(232\) 2.71791 0.178440
\(233\) −10.5370 −0.690303 −0.345152 0.938547i \(-0.612173\pi\)
−0.345152 + 0.938547i \(0.612173\pi\)
\(234\) −0.324628 −0.0212216
\(235\) 24.9765 1.62929
\(236\) 14.2032 0.924550
\(237\) −1.00000 −0.0649570
\(238\) 0.0748483 0.00485170
\(239\) 2.98042 0.192788 0.0963938 0.995343i \(-0.469269\pi\)
0.0963938 + 0.995343i \(0.469269\pi\)
\(240\) −15.7533 −1.01687
\(241\) 30.6112 1.97184 0.985922 0.167207i \(-0.0534750\pi\)
0.985922 + 0.167207i \(0.0534750\pi\)
\(242\) 0.460773 0.0296196
\(243\) −1.00000 −0.0641500
\(244\) 15.2449 0.975956
\(245\) −24.0840 −1.53867
\(246\) −0.776883 −0.0495322
\(247\) 21.6705 1.37886
\(248\) −1.84488 −0.117150
\(249\) −12.4060 −0.786196
\(250\) −1.77729 −0.112405
\(251\) 7.16445 0.452216 0.226108 0.974102i \(-0.427400\pi\)
0.226108 + 0.974102i \(0.427400\pi\)
\(252\) −1.93264 −0.121745
\(253\) 2.04421 0.128519
\(254\) −0.482115 −0.0302506
\(255\) 3.97384 0.248851
\(256\) 15.5250 0.970314
\(257\) −21.1190 −1.31737 −0.658684 0.752419i \(-0.728887\pi\)
−0.658684 + 0.752419i \(0.728887\pi\)
\(258\) 0.720104 0.0448317
\(259\) 4.50401 0.279866
\(260\) −33.3092 −2.06575
\(261\) 8.81167 0.545429
\(262\) −0.157191 −0.00971132
\(263\) 7.71210 0.475548 0.237774 0.971320i \(-0.423582\pi\)
0.237774 + 0.971320i \(0.423582\pi\)
\(264\) −0.692006 −0.0425901
\(265\) −18.5725 −1.14090
\(266\) −0.385861 −0.0236586
\(267\) −11.7149 −0.716941
\(268\) −21.1443 −1.29159
\(269\) −14.4083 −0.878488 −0.439244 0.898368i \(-0.644754\pi\)
−0.439244 + 0.898368i \(0.644754\pi\)
\(270\) 0.306884 0.0186764
\(271\) 17.8076 1.08174 0.540868 0.841107i \(-0.318096\pi\)
0.540868 + 0.841107i \(0.318096\pi\)
\(272\) −3.96425 −0.240368
\(273\) −4.07416 −0.246580
\(274\) −0.747533 −0.0451601
\(275\) 24.2109 1.45997
\(276\) 1.81688 0.109363
\(277\) −8.79316 −0.528330 −0.264165 0.964478i \(-0.585096\pi\)
−0.264165 + 0.964478i \(0.585096\pi\)
\(278\) 0.858965 0.0515173
\(279\) −5.98124 −0.358087
\(280\) 1.18797 0.0709946
\(281\) 13.1633 0.785256 0.392628 0.919697i \(-0.371566\pi\)
0.392628 + 0.919697i \(0.371566\pi\)
\(282\) 0.485385 0.0289042
\(283\) −6.40170 −0.380542 −0.190271 0.981732i \(-0.560937\pi\)
−0.190271 + 0.981732i \(0.560937\pi\)
\(284\) −1.04342 −0.0619158
\(285\) −20.4861 −1.21349
\(286\) −0.728315 −0.0430662
\(287\) −9.75008 −0.575529
\(288\) −0.923033 −0.0543902
\(289\) 1.00000 0.0588235
\(290\) −2.70417 −0.158794
\(291\) 15.9767 0.936570
\(292\) 19.5941 1.14666
\(293\) 13.6630 0.798200 0.399100 0.916907i \(-0.369323\pi\)
0.399100 + 0.916907i \(0.369323\pi\)
\(294\) −0.468040 −0.0272966
\(295\) −28.3050 −1.64798
\(296\) 1.43337 0.0833130
\(297\) −2.24354 −0.130183
\(298\) 1.15041 0.0666417
\(299\) 3.83013 0.221502
\(300\) 21.5184 1.24237
\(301\) 9.03749 0.520912
\(302\) −0.860331 −0.0495065
\(303\) 3.75524 0.215733
\(304\) 20.4366 1.17212
\(305\) −30.3810 −1.73961
\(306\) 0.0772262 0.00441473
\(307\) −10.0727 −0.574877 −0.287438 0.957799i \(-0.592804\pi\)
−0.287438 + 0.957799i \(0.592804\pi\)
\(308\) −4.33595 −0.247063
\(309\) −9.38168 −0.533705
\(310\) 1.83555 0.104252
\(311\) −12.2887 −0.696830 −0.348415 0.937340i \(-0.613280\pi\)
−0.348415 + 0.937340i \(0.613280\pi\)
\(312\) −1.29657 −0.0734041
\(313\) 23.9963 1.35635 0.678176 0.734900i \(-0.262771\pi\)
0.678176 + 0.734900i \(0.262771\pi\)
\(314\) 0.423896 0.0239219
\(315\) 3.85148 0.217006
\(316\) −1.99404 −0.112173
\(317\) 11.6608 0.654933 0.327467 0.944863i \(-0.393805\pi\)
0.327467 + 0.944863i \(0.393805\pi\)
\(318\) −0.360932 −0.0202400
\(319\) 19.7693 1.10687
\(320\) −31.2233 −1.74544
\(321\) 17.8136 0.994260
\(322\) −0.0681985 −0.00380055
\(323\) −5.15523 −0.286845
\(324\) −1.99404 −0.110780
\(325\) 45.3626 2.51627
\(326\) 0.599686 0.0332135
\(327\) 17.9566 0.993001
\(328\) −3.10290 −0.171329
\(329\) 6.09171 0.335847
\(330\) 0.688507 0.0379011
\(331\) 8.21275 0.451413 0.225707 0.974195i \(-0.427531\pi\)
0.225707 + 0.974195i \(0.427531\pi\)
\(332\) −24.7379 −1.35767
\(333\) 4.64710 0.254660
\(334\) −0.884761 −0.0484120
\(335\) 42.1377 2.30223
\(336\) −3.84219 −0.209609
\(337\) 28.2986 1.54152 0.770761 0.637124i \(-0.219876\pi\)
0.770761 + 0.637124i \(0.219876\pi\)
\(338\) −0.360663 −0.0196175
\(339\) 15.5944 0.846971
\(340\) 7.92398 0.429738
\(341\) −13.4191 −0.726687
\(342\) −0.398119 −0.0215278
\(343\) −12.6585 −0.683494
\(344\) 2.87612 0.155070
\(345\) −3.62079 −0.194937
\(346\) −0.488424 −0.0262578
\(347\) −36.4996 −1.95940 −0.979702 0.200462i \(-0.935756\pi\)
−0.979702 + 0.200462i \(0.935756\pi\)
\(348\) 17.5708 0.941894
\(349\) −19.4833 −1.04291 −0.521457 0.853277i \(-0.674611\pi\)
−0.521457 + 0.853277i \(0.674611\pi\)
\(350\) −0.807717 −0.0431743
\(351\) −4.20360 −0.224371
\(352\) −2.07086 −0.110377
\(353\) −7.15305 −0.380719 −0.190359 0.981714i \(-0.560965\pi\)
−0.190359 + 0.981714i \(0.560965\pi\)
\(354\) −0.550070 −0.0292359
\(355\) 2.07940 0.110363
\(356\) −23.3600 −1.23808
\(357\) 0.969209 0.0512960
\(358\) 0.0396616 0.00209618
\(359\) −21.6440 −1.14233 −0.571164 0.820836i \(-0.693508\pi\)
−0.571164 + 0.820836i \(0.693508\pi\)
\(360\) 1.22571 0.0646004
\(361\) 7.57644 0.398760
\(362\) −0.422022 −0.0221810
\(363\) 5.96654 0.313162
\(364\) −8.12403 −0.425815
\(365\) −39.0482 −2.04388
\(366\) −0.590414 −0.0308614
\(367\) 8.73558 0.455994 0.227997 0.973662i \(-0.426782\pi\)
0.227997 + 0.973662i \(0.426782\pi\)
\(368\) 3.61205 0.188291
\(369\) −10.0598 −0.523694
\(370\) −1.42612 −0.0741406
\(371\) −4.52979 −0.235175
\(372\) −11.9268 −0.618376
\(373\) 17.9776 0.930847 0.465423 0.885088i \(-0.345902\pi\)
0.465423 + 0.885088i \(0.345902\pi\)
\(374\) 0.173260 0.00895906
\(375\) −23.0140 −1.18844
\(376\) 1.93864 0.0999779
\(377\) 37.0407 1.90769
\(378\) 0.0748483 0.00384978
\(379\) 9.12246 0.468589 0.234295 0.972166i \(-0.424722\pi\)
0.234295 + 0.972166i \(0.424722\pi\)
\(380\) −40.8500 −2.09556
\(381\) −6.24289 −0.319833
\(382\) −0.924427 −0.0472978
\(383\) −7.15889 −0.365802 −0.182901 0.983131i \(-0.558549\pi\)
−0.182901 + 0.983131i \(0.558549\pi\)
\(384\) −2.45285 −0.125171
\(385\) 8.64094 0.440383
\(386\) 1.48492 0.0755805
\(387\) 9.32461 0.473996
\(388\) 31.8581 1.61735
\(389\) −6.40124 −0.324556 −0.162278 0.986745i \(-0.551884\pi\)
−0.162278 + 0.986745i \(0.551884\pi\)
\(390\) 1.29002 0.0653226
\(391\) −0.911156 −0.0460791
\(392\) −1.86937 −0.0944173
\(393\) −2.03547 −0.102676
\(394\) 0.210401 0.0105998
\(395\) 3.97384 0.199945
\(396\) −4.47370 −0.224812
\(397\) −12.8193 −0.643382 −0.321691 0.946845i \(-0.604251\pi\)
−0.321691 + 0.946845i \(0.604251\pi\)
\(398\) −0.560627 −0.0281017
\(399\) −4.99650 −0.250138
\(400\) 42.7798 2.13899
\(401\) −13.7344 −0.685865 −0.342932 0.939360i \(-0.611420\pi\)
−0.342932 + 0.939360i \(0.611420\pi\)
\(402\) 0.818889 0.0408425
\(403\) −25.1427 −1.25245
\(404\) 7.48808 0.372546
\(405\) 3.97384 0.197462
\(406\) −0.659539 −0.0327324
\(407\) 10.4259 0.516795
\(408\) 0.308444 0.0152703
\(409\) 35.9545 1.77783 0.888917 0.458068i \(-0.151458\pi\)
0.888917 + 0.458068i \(0.151458\pi\)
\(410\) 3.08720 0.152466
\(411\) −9.67979 −0.477469
\(412\) −18.7074 −0.921648
\(413\) −6.90352 −0.339700
\(414\) −0.0703651 −0.00345826
\(415\) 49.2993 2.42001
\(416\) −3.88006 −0.190235
\(417\) 11.1227 0.544682
\(418\) −0.893196 −0.0436876
\(419\) −19.5474 −0.954954 −0.477477 0.878644i \(-0.658449\pi\)
−0.477477 + 0.878644i \(0.658449\pi\)
\(420\) 7.67999 0.374745
\(421\) −33.1930 −1.61773 −0.808865 0.587994i \(-0.799918\pi\)
−0.808865 + 0.587994i \(0.799918\pi\)
\(422\) −0.944340 −0.0459698
\(423\) 6.28523 0.305599
\(424\) −1.44157 −0.0700090
\(425\) −10.7914 −0.523459
\(426\) 0.0404104 0.00195789
\(427\) −7.40985 −0.358588
\(428\) 35.5210 1.71697
\(429\) −9.43093 −0.455329
\(430\) −2.86158 −0.137997
\(431\) 28.5281 1.37415 0.687075 0.726587i \(-0.258894\pi\)
0.687075 + 0.726587i \(0.258894\pi\)
\(432\) −3.96425 −0.190730
\(433\) −1.31607 −0.0632463 −0.0316232 0.999500i \(-0.510068\pi\)
−0.0316232 + 0.999500i \(0.510068\pi\)
\(434\) 0.447685 0.0214896
\(435\) −35.0162 −1.67890
\(436\) 35.8060 1.71480
\(437\) 4.69722 0.224699
\(438\) −0.758850 −0.0362593
\(439\) −14.3459 −0.684691 −0.342345 0.939574i \(-0.611221\pi\)
−0.342345 + 0.939574i \(0.611221\pi\)
\(440\) 2.74992 0.131097
\(441\) −6.06063 −0.288602
\(442\) 0.324628 0.0154410
\(443\) −33.3972 −1.58675 −0.793373 0.608735i \(-0.791677\pi\)
−0.793373 + 0.608735i \(0.791677\pi\)
\(444\) 9.26649 0.439768
\(445\) 46.5532 2.20683
\(446\) 0.387741 0.0183601
\(447\) 14.8967 0.704589
\(448\) −7.61529 −0.359789
\(449\) 17.5037 0.826049 0.413025 0.910720i \(-0.364472\pi\)
0.413025 + 0.910720i \(0.364472\pi\)
\(450\) −0.833378 −0.0392858
\(451\) −22.5696 −1.06276
\(452\) 31.0958 1.46262
\(453\) −11.1404 −0.523422
\(454\) −2.04507 −0.0959798
\(455\) 16.1901 0.759002
\(456\) −1.59010 −0.0744634
\(457\) 37.9848 1.77686 0.888428 0.459017i \(-0.151798\pi\)
0.888428 + 0.459017i \(0.151798\pi\)
\(458\) −1.36721 −0.0638856
\(459\) 1.00000 0.0466760
\(460\) −7.21998 −0.336633
\(461\) −8.34655 −0.388737 −0.194369 0.980929i \(-0.562266\pi\)
−0.194369 + 0.980929i \(0.562266\pi\)
\(462\) 0.167925 0.00781258
\(463\) −18.2607 −0.848646 −0.424323 0.905511i \(-0.639488\pi\)
−0.424323 + 0.905511i \(0.639488\pi\)
\(464\) 34.9317 1.62166
\(465\) 23.7685 1.10224
\(466\) 0.813734 0.0376955
\(467\) 32.1981 1.48995 0.744974 0.667093i \(-0.232462\pi\)
0.744974 + 0.667093i \(0.232462\pi\)
\(468\) −8.38212 −0.387464
\(469\) 10.2773 0.474560
\(470\) −1.92884 −0.0889708
\(471\) 5.48902 0.252921
\(472\) −2.19700 −0.101125
\(473\) 20.9201 0.961908
\(474\) 0.0772262 0.00354712
\(475\) 55.6321 2.55258
\(476\) 1.93264 0.0885823
\(477\) −4.67370 −0.213994
\(478\) −0.230167 −0.0105276
\(479\) −21.3171 −0.974005 −0.487002 0.873401i \(-0.661910\pi\)
−0.487002 + 0.873401i \(0.661910\pi\)
\(480\) 3.66798 0.167420
\(481\) 19.5345 0.890698
\(482\) −2.36399 −0.107677
\(483\) −0.883100 −0.0401825
\(484\) 11.8975 0.540795
\(485\) −63.4887 −2.88288
\(486\) 0.0772262 0.00350305
\(487\) 16.2627 0.736933 0.368467 0.929641i \(-0.379883\pi\)
0.368467 + 0.929641i \(0.379883\pi\)
\(488\) −2.35814 −0.106748
\(489\) 7.76532 0.351160
\(490\) 1.85991 0.0840223
\(491\) −30.6258 −1.38212 −0.691061 0.722796i \(-0.742857\pi\)
−0.691061 + 0.722796i \(0.742857\pi\)
\(492\) −20.0597 −0.904360
\(493\) −8.81167 −0.396858
\(494\) −1.67353 −0.0752958
\(495\) 8.91546 0.400720
\(496\) −23.7111 −1.06466
\(497\) 0.507160 0.0227493
\(498\) 0.958065 0.0429319
\(499\) 22.8563 1.02319 0.511593 0.859228i \(-0.329055\pi\)
0.511593 + 0.859228i \(0.329055\pi\)
\(500\) −45.8908 −2.05230
\(501\) −11.4568 −0.511850
\(502\) −0.553283 −0.0246942
\(503\) −18.8295 −0.839567 −0.419784 0.907624i \(-0.637894\pi\)
−0.419784 + 0.907624i \(0.637894\pi\)
\(504\) 0.298947 0.0133162
\(505\) −14.9227 −0.664052
\(506\) −0.157867 −0.00701803
\(507\) −4.67022 −0.207412
\(508\) −12.4486 −0.552315
\(509\) 40.6522 1.80188 0.900939 0.433946i \(-0.142879\pi\)
0.900939 + 0.433946i \(0.142879\pi\)
\(510\) −0.306884 −0.0135891
\(511\) −9.52377 −0.421307
\(512\) −6.10464 −0.269789
\(513\) −5.15523 −0.227609
\(514\) 1.63094 0.0719378
\(515\) 37.2813 1.64281
\(516\) 18.5936 0.818538
\(517\) 14.1012 0.620169
\(518\) −0.347828 −0.0152827
\(519\) −6.32459 −0.277619
\(520\) 5.15238 0.225947
\(521\) 0.364352 0.0159625 0.00798127 0.999968i \(-0.497459\pi\)
0.00798127 + 0.999968i \(0.497459\pi\)
\(522\) −0.680492 −0.0297843
\(523\) 26.3168 1.15075 0.575376 0.817889i \(-0.304856\pi\)
0.575376 + 0.817889i \(0.304856\pi\)
\(524\) −4.05880 −0.177309
\(525\) −10.4591 −0.456473
\(526\) −0.595576 −0.0259684
\(527\) 5.98124 0.260547
\(528\) −8.89395 −0.387060
\(529\) −22.1698 −0.963904
\(530\) 1.43428 0.0623013
\(531\) −7.12284 −0.309105
\(532\) −9.96320 −0.431959
\(533\) −42.2875 −1.83167
\(534\) 0.904699 0.0391501
\(535\) −70.7885 −3.06045
\(536\) 3.27067 0.141271
\(537\) 0.513577 0.0221625
\(538\) 1.11270 0.0479717
\(539\) −13.5973 −0.585676
\(540\) 7.92398 0.340994
\(541\) 43.4504 1.86808 0.934038 0.357173i \(-0.116259\pi\)
0.934038 + 0.357173i \(0.116259\pi\)
\(542\) −1.37522 −0.0590706
\(543\) −5.46475 −0.234515
\(544\) 0.923033 0.0395747
\(545\) −71.3565 −3.05658
\(546\) 0.314632 0.0134650
\(547\) −26.3597 −1.12706 −0.563530 0.826095i \(-0.690557\pi\)
−0.563530 + 0.826095i \(0.690557\pi\)
\(548\) −19.3019 −0.824534
\(549\) −7.64526 −0.326292
\(550\) −1.86971 −0.0797249
\(551\) 45.4262 1.93522
\(552\) −0.281041 −0.0119619
\(553\) 0.969209 0.0412150
\(554\) 0.679062 0.0288506
\(555\) −18.4668 −0.783873
\(556\) 22.1791 0.940603
\(557\) 16.2713 0.689435 0.344718 0.938706i \(-0.387975\pi\)
0.344718 + 0.938706i \(0.387975\pi\)
\(558\) 0.461908 0.0195541
\(559\) 39.1969 1.65785
\(560\) 15.2682 0.645201
\(561\) 2.24354 0.0947223
\(562\) −1.01655 −0.0428806
\(563\) −30.6509 −1.29178 −0.645891 0.763429i \(-0.723514\pi\)
−0.645891 + 0.763429i \(0.723514\pi\)
\(564\) 12.5330 0.527734
\(565\) −61.9696 −2.60708
\(566\) 0.494379 0.0207803
\(567\) 0.969209 0.0407029
\(568\) 0.161400 0.00677221
\(569\) −25.2340 −1.05786 −0.528932 0.848664i \(-0.677407\pi\)
−0.528932 + 0.848664i \(0.677407\pi\)
\(570\) 1.58206 0.0662652
\(571\) −10.5534 −0.441647 −0.220824 0.975314i \(-0.570874\pi\)
−0.220824 + 0.975314i \(0.570874\pi\)
\(572\) −18.8056 −0.786302
\(573\) −11.9704 −0.500070
\(574\) 0.752961 0.0314280
\(575\) 9.83263 0.410049
\(576\) −7.85722 −0.327384
\(577\) 36.2607 1.50955 0.754777 0.655981i \(-0.227745\pi\)
0.754777 + 0.655981i \(0.227745\pi\)
\(578\) −0.0772262 −0.00321219
\(579\) 19.2282 0.799097
\(580\) −69.8235 −2.89926
\(581\) 12.0240 0.498838
\(582\) −1.23382 −0.0511434
\(583\) −10.4856 −0.434270
\(584\) −3.03087 −0.125418
\(585\) 16.7044 0.690642
\(586\) −1.05514 −0.0435874
\(587\) −36.3668 −1.50102 −0.750509 0.660860i \(-0.770192\pi\)
−0.750509 + 0.660860i \(0.770192\pi\)
\(588\) −12.0851 −0.498382
\(589\) −30.8347 −1.27052
\(590\) 2.18589 0.0899916
\(591\) 2.72447 0.112070
\(592\) 18.4223 0.757151
\(593\) −1.21333 −0.0498256 −0.0249128 0.999690i \(-0.507931\pi\)
−0.0249128 + 0.999690i \(0.507931\pi\)
\(594\) 0.173260 0.00710894
\(595\) −3.85148 −0.157895
\(596\) 29.7045 1.21674
\(597\) −7.25954 −0.297113
\(598\) −0.295786 −0.0120956
\(599\) 1.45725 0.0595416 0.0297708 0.999557i \(-0.490522\pi\)
0.0297708 + 0.999557i \(0.490522\pi\)
\(600\) −3.32854 −0.135887
\(601\) −11.7909 −0.480962 −0.240481 0.970654i \(-0.577305\pi\)
−0.240481 + 0.970654i \(0.577305\pi\)
\(602\) −0.697931 −0.0284455
\(603\) 10.6038 0.431819
\(604\) −22.2144 −0.903890
\(605\) −23.7100 −0.963950
\(606\) −0.290003 −0.0117806
\(607\) −4.32566 −0.175573 −0.0877865 0.996139i \(-0.527979\pi\)
−0.0877865 + 0.996139i \(0.527979\pi\)
\(608\) −4.75845 −0.192981
\(609\) −8.54035 −0.346073
\(610\) 2.34621 0.0949953
\(611\) 26.4206 1.06886
\(612\) 1.99404 0.0806041
\(613\) −41.7279 −1.68537 −0.842687 0.538404i \(-0.819028\pi\)
−0.842687 + 0.538404i \(0.819028\pi\)
\(614\) 0.777873 0.0313924
\(615\) 39.9761 1.61199
\(616\) 0.670699 0.0270232
\(617\) −8.35316 −0.336285 −0.168143 0.985763i \(-0.553777\pi\)
−0.168143 + 0.985763i \(0.553777\pi\)
\(618\) 0.724511 0.0291441
\(619\) −26.2401 −1.05468 −0.527339 0.849655i \(-0.676810\pi\)
−0.527339 + 0.849655i \(0.676810\pi\)
\(620\) 47.3952 1.90344
\(621\) −0.911156 −0.0365634
\(622\) 0.949012 0.0380519
\(623\) 11.3542 0.454897
\(624\) −16.6641 −0.667098
\(625\) 37.4971 1.49988
\(626\) −1.85314 −0.0740665
\(627\) −11.5660 −0.461900
\(628\) 10.9453 0.436765
\(629\) −4.64710 −0.185292
\(630\) −0.297435 −0.0118501
\(631\) −20.9242 −0.832977 −0.416489 0.909141i \(-0.636739\pi\)
−0.416489 + 0.909141i \(0.636739\pi\)
\(632\) 0.308444 0.0122693
\(633\) −12.2282 −0.486029
\(634\) −0.900516 −0.0357641
\(635\) 24.8082 0.984485
\(636\) −9.31952 −0.369543
\(637\) −25.4765 −1.00941
\(638\) −1.52671 −0.0604430
\(639\) 0.523273 0.0207003
\(640\) 9.74722 0.385293
\(641\) −9.44361 −0.373000 −0.186500 0.982455i \(-0.559714\pi\)
−0.186500 + 0.982455i \(0.559714\pi\)
\(642\) −1.37568 −0.0542937
\(643\) −16.6916 −0.658254 −0.329127 0.944286i \(-0.606754\pi\)
−0.329127 + 0.944286i \(0.606754\pi\)
\(644\) −1.76093 −0.0693905
\(645\) −37.0545 −1.45902
\(646\) 0.398119 0.0156638
\(647\) −18.6044 −0.731414 −0.365707 0.930730i \(-0.619173\pi\)
−0.365707 + 0.930730i \(0.619173\pi\)
\(648\) 0.308444 0.0121168
\(649\) −15.9804 −0.627284
\(650\) −3.50318 −0.137406
\(651\) 5.79707 0.227205
\(652\) 15.4843 0.606413
\(653\) 19.3276 0.756349 0.378174 0.925734i \(-0.376552\pi\)
0.378174 + 0.925734i \(0.376552\pi\)
\(654\) −1.38672 −0.0542249
\(655\) 8.08862 0.316049
\(656\) −39.8797 −1.55704
\(657\) −9.82633 −0.383362
\(658\) −0.470439 −0.0183396
\(659\) −1.21646 −0.0473866 −0.0236933 0.999719i \(-0.507543\pi\)
−0.0236933 + 0.999719i \(0.507543\pi\)
\(660\) 17.7777 0.691998
\(661\) 25.0595 0.974702 0.487351 0.873206i \(-0.337963\pi\)
0.487351 + 0.873206i \(0.337963\pi\)
\(662\) −0.634239 −0.0246504
\(663\) 4.20360 0.163254
\(664\) 3.82655 0.148499
\(665\) 19.8553 0.769955
\(666\) −0.358878 −0.0139062
\(667\) 8.02881 0.310877
\(668\) −22.8452 −0.883906
\(669\) 5.02084 0.194117
\(670\) −3.25413 −0.125718
\(671\) −17.1524 −0.662162
\(672\) 0.894611 0.0345104
\(673\) −24.9616 −0.962200 −0.481100 0.876666i \(-0.659763\pi\)
−0.481100 + 0.876666i \(0.659763\pi\)
\(674\) −2.18539 −0.0841782
\(675\) −10.7914 −0.415361
\(676\) −9.31258 −0.358176
\(677\) −1.69418 −0.0651126 −0.0325563 0.999470i \(-0.510365\pi\)
−0.0325563 + 0.999470i \(0.510365\pi\)
\(678\) −1.20430 −0.0462507
\(679\) −15.4847 −0.594250
\(680\) −1.22571 −0.0470037
\(681\) −26.4815 −1.01477
\(682\) 1.03631 0.0396823
\(683\) −35.5865 −1.36168 −0.680839 0.732433i \(-0.738385\pi\)
−0.680839 + 0.732433i \(0.738385\pi\)
\(684\) −10.2797 −0.393055
\(685\) 38.4659 1.46971
\(686\) 0.977567 0.0373237
\(687\) −17.7040 −0.675449
\(688\) 36.9651 1.40928
\(689\) −19.6463 −0.748465
\(690\) 0.279619 0.0106449
\(691\) −20.8279 −0.792329 −0.396165 0.918180i \(-0.629659\pi\)
−0.396165 + 0.918180i \(0.629659\pi\)
\(692\) −12.6115 −0.479416
\(693\) 2.17446 0.0826008
\(694\) 2.81873 0.106997
\(695\) −44.1999 −1.67660
\(696\) −2.71791 −0.103022
\(697\) 10.0598 0.381043
\(698\) 1.50462 0.0569506
\(699\) 10.5370 0.398547
\(700\) −20.8558 −0.788277
\(701\) −6.18028 −0.233426 −0.116713 0.993166i \(-0.537236\pi\)
−0.116713 + 0.993166i \(0.537236\pi\)
\(702\) 0.324628 0.0122523
\(703\) 23.9569 0.903551
\(704\) −17.6280 −0.664379
\(705\) −24.9765 −0.940669
\(706\) 0.552403 0.0207900
\(707\) −3.63961 −0.136882
\(708\) −14.2032 −0.533789
\(709\) −30.4078 −1.14199 −0.570994 0.820954i \(-0.693442\pi\)
−0.570994 + 0.820954i \(0.693442\pi\)
\(710\) −0.160584 −0.00602662
\(711\) 1.00000 0.0375029
\(712\) 3.61340 0.135418
\(713\) −5.44984 −0.204098
\(714\) −0.0748483 −0.00280113
\(715\) 37.4770 1.40156
\(716\) 1.02409 0.0382721
\(717\) −2.98042 −0.111306
\(718\) 1.67148 0.0623793
\(719\) 12.5377 0.467578 0.233789 0.972287i \(-0.424887\pi\)
0.233789 + 0.972287i \(0.424887\pi\)
\(720\) 15.7533 0.587091
\(721\) 9.09280 0.338634
\(722\) −0.585100 −0.0217752
\(723\) −30.6112 −1.13844
\(724\) −10.8969 −0.404981
\(725\) 95.0902 3.53156
\(726\) −0.460773 −0.0171009
\(727\) −38.4249 −1.42510 −0.712550 0.701621i \(-0.752460\pi\)
−0.712550 + 0.701621i \(0.752460\pi\)
\(728\) 1.25665 0.0465746
\(729\) 1.00000 0.0370370
\(730\) 3.01555 0.111610
\(731\) −9.32461 −0.344883
\(732\) −15.2449 −0.563468
\(733\) −17.5766 −0.649205 −0.324602 0.945851i \(-0.605231\pi\)
−0.324602 + 0.945851i \(0.605231\pi\)
\(734\) −0.674616 −0.0249005
\(735\) 24.0840 0.888351
\(736\) −0.841026 −0.0310006
\(737\) 23.7900 0.876315
\(738\) 0.776883 0.0285974
\(739\) 28.7956 1.05926 0.529631 0.848228i \(-0.322330\pi\)
0.529631 + 0.848228i \(0.322330\pi\)
\(740\) −36.8235 −1.35366
\(741\) −21.6705 −0.796086
\(742\) 0.349818 0.0128422
\(743\) 51.0891 1.87428 0.937139 0.348958i \(-0.113464\pi\)
0.937139 + 0.348958i \(0.113464\pi\)
\(744\) 1.84488 0.0676365
\(745\) −59.1970 −2.16881
\(746\) −1.38834 −0.0508309
\(747\) 12.4060 0.453910
\(748\) 4.47370 0.163575
\(749\) −17.2651 −0.630854
\(750\) 1.77729 0.0648973
\(751\) 6.85072 0.249986 0.124993 0.992158i \(-0.460109\pi\)
0.124993 + 0.992158i \(0.460109\pi\)
\(752\) 24.9163 0.908602
\(753\) −7.16445 −0.261087
\(754\) −2.86051 −0.104174
\(755\) 44.2702 1.61116
\(756\) 1.93264 0.0702893
\(757\) 12.8676 0.467681 0.233841 0.972275i \(-0.424871\pi\)
0.233841 + 0.972275i \(0.424871\pi\)
\(758\) −0.704493 −0.0255883
\(759\) −2.04421 −0.0742002
\(760\) 6.31881 0.229207
\(761\) −34.4489 −1.24877 −0.624385 0.781116i \(-0.714651\pi\)
−0.624385 + 0.781116i \(0.714651\pi\)
\(762\) 0.482115 0.0174652
\(763\) −17.4037 −0.630055
\(764\) −23.8694 −0.863564
\(765\) −3.97384 −0.143674
\(766\) 0.552854 0.0199754
\(767\) −29.9416 −1.08113
\(768\) −15.5250 −0.560211
\(769\) 13.7035 0.494160 0.247080 0.968995i \(-0.420529\pi\)
0.247080 + 0.968995i \(0.420529\pi\)
\(770\) −0.667307 −0.0240481
\(771\) 21.1190 0.760583
\(772\) 38.3417 1.37995
\(773\) −33.9039 −1.21944 −0.609719 0.792618i \(-0.708718\pi\)
−0.609719 + 0.792618i \(0.708718\pi\)
\(774\) −0.720104 −0.0258836
\(775\) −64.5458 −2.31855
\(776\) −4.92792 −0.176902
\(777\) −4.50401 −0.161581
\(778\) 0.494344 0.0177231
\(779\) −51.8608 −1.85811
\(780\) 33.3092 1.19266
\(781\) 1.17398 0.0420084
\(782\) 0.0703651 0.00251625
\(783\) −8.81167 −0.314904
\(784\) −24.0259 −0.858067
\(785\) −21.8125 −0.778521
\(786\) 0.157191 0.00560683
\(787\) −26.2076 −0.934199 −0.467099 0.884205i \(-0.654701\pi\)
−0.467099 + 0.884205i \(0.654701\pi\)
\(788\) 5.43269 0.193532
\(789\) −7.71210 −0.274558
\(790\) −0.306884 −0.0109185
\(791\) −15.1142 −0.537400
\(792\) 0.692006 0.0245894
\(793\) −32.1376 −1.14124
\(794\) 0.989985 0.0351332
\(795\) 18.5725 0.658699
\(796\) −14.4758 −0.513081
\(797\) 21.2731 0.753533 0.376766 0.926308i \(-0.377036\pi\)
0.376766 + 0.926308i \(0.377036\pi\)
\(798\) 0.385861 0.0136593
\(799\) −6.28523 −0.222356
\(800\) −9.96080 −0.352167
\(801\) 11.7149 0.413926
\(802\) 1.06066 0.0374531
\(803\) −22.0457 −0.777978
\(804\) 21.1443 0.745702
\(805\) 3.50930 0.123686
\(806\) 1.94168 0.0683926
\(807\) 14.4083 0.507195
\(808\) −1.15828 −0.0407482
\(809\) −24.8521 −0.873754 −0.436877 0.899521i \(-0.643915\pi\)
−0.436877 + 0.899521i \(0.643915\pi\)
\(810\) −0.306884 −0.0107828
\(811\) 22.7050 0.797280 0.398640 0.917108i \(-0.369482\pi\)
0.398640 + 0.917108i \(0.369482\pi\)
\(812\) −17.0298 −0.597628
\(813\) −17.8076 −0.624541
\(814\) −0.805156 −0.0282207
\(815\) −30.8581 −1.08091
\(816\) 3.96425 0.138777
\(817\) 48.0705 1.68177
\(818\) −2.77663 −0.0970825
\(819\) 4.07416 0.142363
\(820\) 79.7139 2.78373
\(821\) −9.70595 −0.338740 −0.169370 0.985553i \(-0.554173\pi\)
−0.169370 + 0.985553i \(0.554173\pi\)
\(822\) 0.747533 0.0260732
\(823\) 40.9355 1.42692 0.713461 0.700695i \(-0.247127\pi\)
0.713461 + 0.700695i \(0.247127\pi\)
\(824\) 2.89372 0.100808
\(825\) −24.2109 −0.842915
\(826\) 0.533133 0.0185501
\(827\) −1.97906 −0.0688186 −0.0344093 0.999408i \(-0.510955\pi\)
−0.0344093 + 0.999408i \(0.510955\pi\)
\(828\) −1.81688 −0.0631409
\(829\) 22.1285 0.768554 0.384277 0.923218i \(-0.374451\pi\)
0.384277 + 0.923218i \(0.374451\pi\)
\(830\) −3.80719 −0.132150
\(831\) 8.79316 0.305031
\(832\) −33.0286 −1.14506
\(833\) 6.06063 0.209989
\(834\) −0.858965 −0.0297435
\(835\) 45.5273 1.57554
\(836\) −23.0630 −0.797649
\(837\) 5.98124 0.206742
\(838\) 1.50957 0.0521473
\(839\) −54.0788 −1.86701 −0.933504 0.358567i \(-0.883265\pi\)
−0.933504 + 0.358567i \(0.883265\pi\)
\(840\) −1.18797 −0.0409887
\(841\) 48.6456 1.67743
\(842\) 2.56337 0.0883397
\(843\) −13.1633 −0.453368
\(844\) −24.3835 −0.839316
\(845\) 18.5587 0.638438
\(846\) −0.485385 −0.0166879
\(847\) −5.78282 −0.198700
\(848\) −18.5277 −0.636244
\(849\) 6.40170 0.219706
\(850\) 0.833378 0.0285846
\(851\) 4.23423 0.145148
\(852\) 1.04342 0.0357471
\(853\) −11.0610 −0.378722 −0.189361 0.981908i \(-0.560642\pi\)
−0.189361 + 0.981908i \(0.560642\pi\)
\(854\) 0.572235 0.0195815
\(855\) 20.4861 0.700609
\(856\) −5.49451 −0.187799
\(857\) −3.19086 −0.108998 −0.0544989 0.998514i \(-0.517356\pi\)
−0.0544989 + 0.998514i \(0.517356\pi\)
\(858\) 0.728315 0.0248643
\(859\) −23.6911 −0.808331 −0.404166 0.914686i \(-0.632438\pi\)
−0.404166 + 0.914686i \(0.632438\pi\)
\(860\) −73.8880 −2.51956
\(861\) 9.75008 0.332282
\(862\) −2.20312 −0.0750384
\(863\) −17.0542 −0.580532 −0.290266 0.956946i \(-0.593744\pi\)
−0.290266 + 0.956946i \(0.593744\pi\)
\(864\) 0.923033 0.0314022
\(865\) 25.1329 0.854544
\(866\) 0.101635 0.00345370
\(867\) −1.00000 −0.0339618
\(868\) 11.5596 0.392357
\(869\) 2.24354 0.0761068
\(870\) 2.70417 0.0916798
\(871\) 44.5740 1.51033
\(872\) −5.53860 −0.187561
\(873\) −15.9767 −0.540729
\(874\) −0.362749 −0.0122702
\(875\) 22.3054 0.754060
\(876\) −19.5941 −0.662022
\(877\) 18.9616 0.640286 0.320143 0.947369i \(-0.396269\pi\)
0.320143 + 0.947369i \(0.396269\pi\)
\(878\) 1.10788 0.0373890
\(879\) −13.6630 −0.460841
\(880\) 35.3431 1.19142
\(881\) 35.1250 1.18339 0.591696 0.806161i \(-0.298459\pi\)
0.591696 + 0.806161i \(0.298459\pi\)
\(882\) 0.468040 0.0157597
\(883\) −17.3198 −0.582859 −0.291430 0.956592i \(-0.594131\pi\)
−0.291430 + 0.956592i \(0.594131\pi\)
\(884\) 8.38212 0.281921
\(885\) 28.3050 0.951463
\(886\) 2.57914 0.0866477
\(887\) 11.3192 0.380061 0.190030 0.981778i \(-0.439141\pi\)
0.190030 + 0.981778i \(0.439141\pi\)
\(888\) −1.43337 −0.0481008
\(889\) 6.05067 0.202933
\(890\) −3.59513 −0.120509
\(891\) 2.24354 0.0751614
\(892\) 10.0117 0.335218
\(893\) 32.4019 1.08429
\(894\) −1.15041 −0.0384756
\(895\) −2.04087 −0.0682188
\(896\) 2.37732 0.0794208
\(897\) −3.83013 −0.127884
\(898\) −1.35174 −0.0451082
\(899\) −52.7047 −1.75780
\(900\) −21.5184 −0.717280
\(901\) 4.67370 0.155703
\(902\) 1.74297 0.0580344
\(903\) −9.03749 −0.300749
\(904\) −4.81000 −0.159978
\(905\) 21.7160 0.721865
\(906\) 0.860331 0.0285826
\(907\) 50.8849 1.68960 0.844802 0.535079i \(-0.179718\pi\)
0.844802 + 0.535079i \(0.179718\pi\)
\(908\) −52.8051 −1.75240
\(909\) −3.75524 −0.124553
\(910\) −1.25030 −0.0414469
\(911\) 14.5824 0.483137 0.241568 0.970384i \(-0.422338\pi\)
0.241568 + 0.970384i \(0.422338\pi\)
\(912\) −20.4366 −0.676725
\(913\) 27.8332 0.921146
\(914\) −2.93342 −0.0970290
\(915\) 30.3810 1.00437
\(916\) −35.3024 −1.16642
\(917\) 1.97279 0.0651474
\(918\) −0.0772262 −0.00254884
\(919\) −5.88730 −0.194204 −0.0971021 0.995274i \(-0.530957\pi\)
−0.0971021 + 0.995274i \(0.530957\pi\)
\(920\) 1.11681 0.0368201
\(921\) 10.0727 0.331905
\(922\) 0.644572 0.0212279
\(923\) 2.19963 0.0724016
\(924\) 4.33595 0.142642
\(925\) 50.1487 1.64888
\(926\) 1.41020 0.0463422
\(927\) 9.38168 0.308135
\(928\) −8.13346 −0.266994
\(929\) 50.7581 1.66532 0.832659 0.553786i \(-0.186818\pi\)
0.832659 + 0.553786i \(0.186818\pi\)
\(930\) −1.83555 −0.0601900
\(931\) −31.2440 −1.02398
\(932\) 21.0112 0.688245
\(933\) 12.2887 0.402315
\(934\) −2.48653 −0.0813619
\(935\) −8.91546 −0.291567
\(936\) 1.29657 0.0423799
\(937\) −52.1072 −1.70227 −0.851135 0.524947i \(-0.824085\pi\)
−0.851135 + 0.524947i \(0.824085\pi\)
\(938\) −0.793674 −0.0259144
\(939\) −23.9963 −0.783090
\(940\) −49.8040 −1.62443
\(941\) −25.2428 −0.822892 −0.411446 0.911434i \(-0.634976\pi\)
−0.411446 + 0.911434i \(0.634976\pi\)
\(942\) −0.423896 −0.0138113
\(943\) −9.16607 −0.298488
\(944\) −28.2367 −0.919028
\(945\) −3.85148 −0.125289
\(946\) −1.61558 −0.0525271
\(947\) 23.3555 0.758951 0.379475 0.925202i \(-0.376104\pi\)
0.379475 + 0.925202i \(0.376104\pi\)
\(948\) 1.99404 0.0647633
\(949\) −41.3059 −1.34085
\(950\) −4.29626 −0.139389
\(951\) −11.6608 −0.378126
\(952\) −0.298947 −0.00968892
\(953\) −46.3239 −1.50058 −0.750290 0.661109i \(-0.770086\pi\)
−0.750290 + 0.661109i \(0.770086\pi\)
\(954\) 0.360932 0.0116856
\(955\) 47.5684 1.53928
\(956\) −5.94307 −0.192213
\(957\) −19.7693 −0.639052
\(958\) 1.64624 0.0531877
\(959\) 9.38174 0.302952
\(960\) 31.2233 1.00773
\(961\) 4.77518 0.154038
\(962\) −1.50858 −0.0486385
\(963\) −17.8136 −0.574036
\(964\) −61.0399 −1.96596
\(965\) −76.4098 −2.45972
\(966\) 0.0681985 0.00219425
\(967\) 0.0804894 0.00258836 0.00129418 0.999999i \(-0.499588\pi\)
0.00129418 + 0.999999i \(0.499588\pi\)
\(968\) −1.84034 −0.0591509
\(969\) 5.15523 0.165610
\(970\) 4.90299 0.157426
\(971\) 49.7075 1.59519 0.797594 0.603194i \(-0.206106\pi\)
0.797594 + 0.603194i \(0.206106\pi\)
\(972\) 1.99404 0.0639587
\(973\) −10.7802 −0.345598
\(974\) −1.25591 −0.0402418
\(975\) −45.3626 −1.45277
\(976\) −30.3077 −0.970127
\(977\) 24.2420 0.775570 0.387785 0.921750i \(-0.373240\pi\)
0.387785 + 0.921750i \(0.373240\pi\)
\(978\) −0.599686 −0.0191758
\(979\) 26.2829 0.840004
\(980\) 48.0243 1.53408
\(981\) −17.9566 −0.573309
\(982\) 2.36511 0.0754738
\(983\) 37.3517 1.19133 0.595667 0.803232i \(-0.296888\pi\)
0.595667 + 0.803232i \(0.296888\pi\)
\(984\) 3.10290 0.0989167
\(985\) −10.8266 −0.344964
\(986\) 0.680492 0.0216713
\(987\) −6.09171 −0.193901
\(988\) −43.2118 −1.37475
\(989\) 8.49617 0.270162
\(990\) −0.688507 −0.0218822
\(991\) 40.4445 1.28476 0.642380 0.766386i \(-0.277947\pi\)
0.642380 + 0.766386i \(0.277947\pi\)
\(992\) 5.52088 0.175288
\(993\) −8.21275 −0.260624
\(994\) −0.0391661 −0.00124227
\(995\) 28.8482 0.914551
\(996\) 24.7379 0.783851
\(997\) 22.2361 0.704225 0.352113 0.935958i \(-0.385463\pi\)
0.352113 + 0.935958i \(0.385463\pi\)
\(998\) −1.76510 −0.0558733
\(999\) −4.64710 −0.147028
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.1.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.16 32 1.1 even 1 trivial