Properties

Label 4029.2.a.k.1.11
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
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: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.719826 q^{2} +1.00000 q^{3} -1.48185 q^{4} +1.82945 q^{5} -0.719826 q^{6} +0.414755 q^{7} +2.50633 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.719826 q^{2} +1.00000 q^{3} -1.48185 q^{4} +1.82945 q^{5} -0.719826 q^{6} +0.414755 q^{7} +2.50633 q^{8} +1.00000 q^{9} -1.31688 q^{10} -2.75956 q^{11} -1.48185 q^{12} +0.245564 q^{13} -0.298551 q^{14} +1.82945 q^{15} +1.15958 q^{16} +1.00000 q^{17} -0.719826 q^{18} +0.386626 q^{19} -2.71096 q^{20} +0.414755 q^{21} +1.98641 q^{22} +6.58248 q^{23} +2.50633 q^{24} -1.65313 q^{25} -0.176764 q^{26} +1.00000 q^{27} -0.614604 q^{28} -0.775585 q^{29} -1.31688 q^{30} +2.70422 q^{31} -5.84735 q^{32} -2.75956 q^{33} -0.719826 q^{34} +0.758771 q^{35} -1.48185 q^{36} +7.95789 q^{37} -0.278304 q^{38} +0.245564 q^{39} +4.58519 q^{40} -4.65488 q^{41} -0.298551 q^{42} -1.77108 q^{43} +4.08926 q^{44} +1.82945 q^{45} -4.73824 q^{46} +1.23213 q^{47} +1.15958 q^{48} -6.82798 q^{49} +1.18997 q^{50} +1.00000 q^{51} -0.363890 q^{52} +3.82181 q^{53} -0.719826 q^{54} -5.04847 q^{55} +1.03951 q^{56} +0.386626 q^{57} +0.558286 q^{58} +2.36846 q^{59} -2.71096 q^{60} +5.98058 q^{61} -1.94657 q^{62} +0.414755 q^{63} +1.88991 q^{64} +0.449247 q^{65} +1.98641 q^{66} +9.15259 q^{67} -1.48185 q^{68} +6.58248 q^{69} -0.546183 q^{70} -3.23725 q^{71} +2.50633 q^{72} -3.86850 q^{73} -5.72829 q^{74} -1.65313 q^{75} -0.572922 q^{76} -1.14454 q^{77} -0.176764 q^{78} +1.00000 q^{79} +2.12139 q^{80} +1.00000 q^{81} +3.35070 q^{82} +15.9173 q^{83} -0.614604 q^{84} +1.82945 q^{85} +1.27487 q^{86} -0.775585 q^{87} -6.91637 q^{88} -0.214602 q^{89} -1.31688 q^{90} +0.101849 q^{91} -9.75425 q^{92} +2.70422 q^{93} -0.886922 q^{94} +0.707311 q^{95} -5.84735 q^{96} +18.6375 q^{97} +4.91496 q^{98} -2.75956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.719826 −0.508994 −0.254497 0.967074i \(-0.581910\pi\)
−0.254497 + 0.967074i \(0.581910\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.48185 −0.740925
\(5\) 1.82945 0.818153 0.409076 0.912500i \(-0.365851\pi\)
0.409076 + 0.912500i \(0.365851\pi\)
\(6\) −0.719826 −0.293868
\(7\) 0.414755 0.156762 0.0783812 0.996923i \(-0.475025\pi\)
0.0783812 + 0.996923i \(0.475025\pi\)
\(8\) 2.50633 0.886120
\(9\) 1.00000 0.333333
\(10\) −1.31688 −0.416435
\(11\) −2.75956 −0.832040 −0.416020 0.909356i \(-0.636575\pi\)
−0.416020 + 0.909356i \(0.636575\pi\)
\(12\) −1.48185 −0.427773
\(13\) 0.245564 0.0681073 0.0340536 0.999420i \(-0.489158\pi\)
0.0340536 + 0.999420i \(0.489158\pi\)
\(14\) −0.298551 −0.0797911
\(15\) 1.82945 0.472361
\(16\) 1.15958 0.289895
\(17\) 1.00000 0.242536
\(18\) −0.719826 −0.169665
\(19\) 0.386626 0.0886981 0.0443491 0.999016i \(-0.485879\pi\)
0.0443491 + 0.999016i \(0.485879\pi\)
\(20\) −2.71096 −0.606190
\(21\) 0.414755 0.0905069
\(22\) 1.98641 0.423503
\(23\) 6.58248 1.37254 0.686271 0.727346i \(-0.259246\pi\)
0.686271 + 0.727346i \(0.259246\pi\)
\(24\) 2.50633 0.511602
\(25\) −1.65313 −0.330626
\(26\) −0.176764 −0.0346662
\(27\) 1.00000 0.192450
\(28\) −0.614604 −0.116149
\(29\) −0.775585 −0.144022 −0.0720112 0.997404i \(-0.522942\pi\)
−0.0720112 + 0.997404i \(0.522942\pi\)
\(30\) −1.31688 −0.240429
\(31\) 2.70422 0.485693 0.242846 0.970065i \(-0.421919\pi\)
0.242846 + 0.970065i \(0.421919\pi\)
\(32\) −5.84735 −1.03368
\(33\) −2.75956 −0.480378
\(34\) −0.719826 −0.123449
\(35\) 0.758771 0.128256
\(36\) −1.48185 −0.246975
\(37\) 7.95789 1.30827 0.654134 0.756379i \(-0.273033\pi\)
0.654134 + 0.756379i \(0.273033\pi\)
\(38\) −0.278304 −0.0451468
\(39\) 0.245564 0.0393218
\(40\) 4.58519 0.724982
\(41\) −4.65488 −0.726970 −0.363485 0.931600i \(-0.618413\pi\)
−0.363485 + 0.931600i \(0.618413\pi\)
\(42\) −0.298551 −0.0460674
\(43\) −1.77108 −0.270088 −0.135044 0.990840i \(-0.543118\pi\)
−0.135044 + 0.990840i \(0.543118\pi\)
\(44\) 4.08926 0.616479
\(45\) 1.82945 0.272718
\(46\) −4.73824 −0.698615
\(47\) 1.23213 0.179725 0.0898626 0.995954i \(-0.471357\pi\)
0.0898626 + 0.995954i \(0.471357\pi\)
\(48\) 1.15958 0.167371
\(49\) −6.82798 −0.975426
\(50\) 1.18997 0.168287
\(51\) 1.00000 0.140028
\(52\) −0.363890 −0.0504624
\(53\) 3.82181 0.524966 0.262483 0.964937i \(-0.415459\pi\)
0.262483 + 0.964937i \(0.415459\pi\)
\(54\) −0.719826 −0.0979559
\(55\) −5.04847 −0.680736
\(56\) 1.03951 0.138910
\(57\) 0.386626 0.0512099
\(58\) 0.558286 0.0733066
\(59\) 2.36846 0.308348 0.154174 0.988044i \(-0.450728\pi\)
0.154174 + 0.988044i \(0.450728\pi\)
\(60\) −2.71096 −0.349984
\(61\) 5.98058 0.765735 0.382867 0.923803i \(-0.374937\pi\)
0.382867 + 0.923803i \(0.374937\pi\)
\(62\) −1.94657 −0.247215
\(63\) 0.414755 0.0522542
\(64\) 1.88991 0.236239
\(65\) 0.449247 0.0557222
\(66\) 1.98641 0.244510
\(67\) 9.15259 1.11817 0.559083 0.829111i \(-0.311153\pi\)
0.559083 + 0.829111i \(0.311153\pi\)
\(68\) −1.48185 −0.179701
\(69\) 6.58248 0.792437
\(70\) −0.546183 −0.0652813
\(71\) −3.23725 −0.384191 −0.192095 0.981376i \(-0.561528\pi\)
−0.192095 + 0.981376i \(0.561528\pi\)
\(72\) 2.50633 0.295373
\(73\) −3.86850 −0.452774 −0.226387 0.974037i \(-0.572691\pi\)
−0.226387 + 0.974037i \(0.572691\pi\)
\(74\) −5.72829 −0.665901
\(75\) −1.65313 −0.190887
\(76\) −0.572922 −0.0657187
\(77\) −1.14454 −0.130433
\(78\) −0.176764 −0.0200145
\(79\) 1.00000 0.112509
\(80\) 2.12139 0.237179
\(81\) 1.00000 0.111111
\(82\) 3.35070 0.370023
\(83\) 15.9173 1.74715 0.873574 0.486692i \(-0.161796\pi\)
0.873574 + 0.486692i \(0.161796\pi\)
\(84\) −0.614604 −0.0670588
\(85\) 1.82945 0.198431
\(86\) 1.27487 0.137473
\(87\) −0.775585 −0.0831514
\(88\) −6.91637 −0.737287
\(89\) −0.214602 −0.0227478 −0.0113739 0.999935i \(-0.503621\pi\)
−0.0113739 + 0.999935i \(0.503621\pi\)
\(90\) −1.31688 −0.138812
\(91\) 0.101849 0.0106767
\(92\) −9.75425 −1.01695
\(93\) 2.70422 0.280415
\(94\) −0.886922 −0.0914790
\(95\) 0.707311 0.0725686
\(96\) −5.84735 −0.596793
\(97\) 18.6375 1.89235 0.946174 0.323660i \(-0.104913\pi\)
0.946174 + 0.323660i \(0.104913\pi\)
\(98\) 4.91496 0.496486
\(99\) −2.75956 −0.277347
\(100\) 2.44969 0.244969
\(101\) 4.52955 0.450707 0.225353 0.974277i \(-0.427646\pi\)
0.225353 + 0.974277i \(0.427646\pi\)
\(102\) −0.719826 −0.0712734
\(103\) −4.82523 −0.475444 −0.237722 0.971333i \(-0.576401\pi\)
−0.237722 + 0.971333i \(0.576401\pi\)
\(104\) 0.615464 0.0603513
\(105\) 0.758771 0.0740484
\(106\) −2.75104 −0.267204
\(107\) −17.0658 −1.64981 −0.824907 0.565269i \(-0.808772\pi\)
−0.824907 + 0.565269i \(0.808772\pi\)
\(108\) −1.48185 −0.142591
\(109\) 16.0479 1.53711 0.768556 0.639782i \(-0.220976\pi\)
0.768556 + 0.639782i \(0.220976\pi\)
\(110\) 3.63402 0.346490
\(111\) 7.95789 0.755329
\(112\) 0.480942 0.0454447
\(113\) 2.71994 0.255870 0.127935 0.991783i \(-0.459165\pi\)
0.127935 + 0.991783i \(0.459165\pi\)
\(114\) −0.278304 −0.0260655
\(115\) 12.0423 1.12295
\(116\) 1.14930 0.106710
\(117\) 0.245564 0.0227024
\(118\) −1.70488 −0.156947
\(119\) 0.414755 0.0380205
\(120\) 4.58519 0.418568
\(121\) −3.38481 −0.307710
\(122\) −4.30498 −0.389754
\(123\) −4.65488 −0.419717
\(124\) −4.00725 −0.359862
\(125\) −12.1715 −1.08866
\(126\) −0.298551 −0.0265970
\(127\) 9.03607 0.801821 0.400911 0.916117i \(-0.368694\pi\)
0.400911 + 0.916117i \(0.368694\pi\)
\(128\) 10.3343 0.913431
\(129\) −1.77108 −0.155935
\(130\) −0.323379 −0.0283622
\(131\) −10.2707 −0.897360 −0.448680 0.893693i \(-0.648106\pi\)
−0.448680 + 0.893693i \(0.648106\pi\)
\(132\) 4.08926 0.355924
\(133\) 0.160355 0.0139045
\(134\) −6.58827 −0.569140
\(135\) 1.82945 0.157454
\(136\) 2.50633 0.214916
\(137\) 4.90565 0.419118 0.209559 0.977796i \(-0.432797\pi\)
0.209559 + 0.977796i \(0.432797\pi\)
\(138\) −4.73824 −0.403346
\(139\) −14.1097 −1.19677 −0.598386 0.801208i \(-0.704191\pi\)
−0.598386 + 0.801208i \(0.704191\pi\)
\(140\) −1.12438 −0.0950279
\(141\) 1.23213 0.103764
\(142\) 2.33026 0.195551
\(143\) −0.677651 −0.0566680
\(144\) 1.15958 0.0966318
\(145\) −1.41889 −0.117832
\(146\) 2.78465 0.230459
\(147\) −6.82798 −0.563162
\(148\) −11.7924 −0.969329
\(149\) 11.9807 0.981499 0.490750 0.871301i \(-0.336723\pi\)
0.490750 + 0.871301i \(0.336723\pi\)
\(150\) 1.18997 0.0971603
\(151\) 7.94967 0.646935 0.323467 0.946239i \(-0.395151\pi\)
0.323467 + 0.946239i \(0.395151\pi\)
\(152\) 0.969011 0.0785972
\(153\) 1.00000 0.0808452
\(154\) 0.823871 0.0663894
\(155\) 4.94723 0.397371
\(156\) −0.363890 −0.0291345
\(157\) −8.53506 −0.681172 −0.340586 0.940213i \(-0.610625\pi\)
−0.340586 + 0.940213i \(0.610625\pi\)
\(158\) −0.719826 −0.0572663
\(159\) 3.82181 0.303089
\(160\) −10.6974 −0.845704
\(161\) 2.73011 0.215163
\(162\) −0.719826 −0.0565549
\(163\) 8.76964 0.686891 0.343446 0.939173i \(-0.388406\pi\)
0.343446 + 0.939173i \(0.388406\pi\)
\(164\) 6.89784 0.538631
\(165\) −5.04847 −0.393023
\(166\) −11.4577 −0.889287
\(167\) 6.48978 0.502194 0.251097 0.967962i \(-0.419209\pi\)
0.251097 + 0.967962i \(0.419209\pi\)
\(168\) 1.03951 0.0802000
\(169\) −12.9397 −0.995361
\(170\) −1.31688 −0.101000
\(171\) 0.386626 0.0295660
\(172\) 2.62448 0.200115
\(173\) 7.89825 0.600493 0.300246 0.953862i \(-0.402931\pi\)
0.300246 + 0.953862i \(0.402931\pi\)
\(174\) 0.558286 0.0423236
\(175\) −0.685643 −0.0518298
\(176\) −3.19994 −0.241205
\(177\) 2.36846 0.178025
\(178\) 0.154476 0.0115785
\(179\) 4.81548 0.359926 0.179963 0.983673i \(-0.442402\pi\)
0.179963 + 0.983673i \(0.442402\pi\)
\(180\) −2.71096 −0.202063
\(181\) −13.9833 −1.03937 −0.519686 0.854357i \(-0.673951\pi\)
−0.519686 + 0.854357i \(0.673951\pi\)
\(182\) −0.0733135 −0.00543436
\(183\) 5.98058 0.442097
\(184\) 16.4978 1.21624
\(185\) 14.5585 1.07036
\(186\) −1.94657 −0.142729
\(187\) −2.75956 −0.201799
\(188\) −1.82584 −0.133163
\(189\) 0.414755 0.0301690
\(190\) −0.509141 −0.0369370
\(191\) −12.1242 −0.877280 −0.438640 0.898663i \(-0.644540\pi\)
−0.438640 + 0.898663i \(0.644540\pi\)
\(192\) 1.88991 0.136393
\(193\) −2.70545 −0.194743 −0.0973713 0.995248i \(-0.531043\pi\)
−0.0973713 + 0.995248i \(0.531043\pi\)
\(194\) −13.4157 −0.963193
\(195\) 0.449247 0.0321712
\(196\) 10.1180 0.722717
\(197\) 8.78690 0.626041 0.313020 0.949746i \(-0.398659\pi\)
0.313020 + 0.949746i \(0.398659\pi\)
\(198\) 1.98641 0.141168
\(199\) 7.23231 0.512685 0.256343 0.966586i \(-0.417482\pi\)
0.256343 + 0.966586i \(0.417482\pi\)
\(200\) −4.14328 −0.292974
\(201\) 9.15259 0.645574
\(202\) −3.26048 −0.229407
\(203\) −0.321677 −0.0225773
\(204\) −1.48185 −0.103750
\(205\) −8.51585 −0.594773
\(206\) 3.47332 0.241998
\(207\) 6.58248 0.457514
\(208\) 0.284752 0.0197440
\(209\) −1.06692 −0.0738004
\(210\) −0.546183 −0.0376902
\(211\) −25.5292 −1.75750 −0.878750 0.477283i \(-0.841622\pi\)
−0.878750 + 0.477283i \(0.841622\pi\)
\(212\) −5.66335 −0.388961
\(213\) −3.23725 −0.221813
\(214\) 12.2844 0.839745
\(215\) −3.24010 −0.220973
\(216\) 2.50633 0.170534
\(217\) 1.12159 0.0761384
\(218\) −11.5517 −0.782381
\(219\) −3.86850 −0.261409
\(220\) 7.48108 0.504374
\(221\) 0.245564 0.0165184
\(222\) −5.72829 −0.384458
\(223\) 17.2162 1.15288 0.576441 0.817139i \(-0.304441\pi\)
0.576441 + 0.817139i \(0.304441\pi\)
\(224\) −2.42522 −0.162041
\(225\) −1.65313 −0.110209
\(226\) −1.95788 −0.130236
\(227\) 18.3239 1.21620 0.608099 0.793862i \(-0.291933\pi\)
0.608099 + 0.793862i \(0.291933\pi\)
\(228\) −0.572922 −0.0379427
\(229\) −24.4035 −1.61263 −0.806315 0.591486i \(-0.798542\pi\)
−0.806315 + 0.591486i \(0.798542\pi\)
\(230\) −8.66835 −0.571574
\(231\) −1.14454 −0.0753053
\(232\) −1.94387 −0.127621
\(233\) 24.0462 1.57532 0.787659 0.616112i \(-0.211293\pi\)
0.787659 + 0.616112i \(0.211293\pi\)
\(234\) −0.176764 −0.0115554
\(235\) 2.25412 0.147043
\(236\) −3.50971 −0.228462
\(237\) 1.00000 0.0649570
\(238\) −0.298551 −0.0193522
\(239\) 22.5991 1.46181 0.730906 0.682478i \(-0.239098\pi\)
0.730906 + 0.682478i \(0.239098\pi\)
\(240\) 2.12139 0.136935
\(241\) 25.1640 1.62095 0.810477 0.585770i \(-0.199208\pi\)
0.810477 + 0.585770i \(0.199208\pi\)
\(242\) 2.43647 0.156622
\(243\) 1.00000 0.0641500
\(244\) −8.86233 −0.567352
\(245\) −12.4914 −0.798047
\(246\) 3.35070 0.213633
\(247\) 0.0949416 0.00604099
\(248\) 6.77767 0.430382
\(249\) 15.9173 1.00872
\(250\) 8.76139 0.554119
\(251\) −19.9536 −1.25946 −0.629729 0.776815i \(-0.716834\pi\)
−0.629729 + 0.776815i \(0.716834\pi\)
\(252\) −0.614604 −0.0387164
\(253\) −18.1648 −1.14201
\(254\) −6.50439 −0.408122
\(255\) 1.82945 0.114564
\(256\) −11.2187 −0.701170
\(257\) 6.37818 0.397860 0.198930 0.980014i \(-0.436253\pi\)
0.198930 + 0.980014i \(0.436253\pi\)
\(258\) 1.27487 0.0793701
\(259\) 3.30057 0.205087
\(260\) −0.665716 −0.0412860
\(261\) −0.775585 −0.0480075
\(262\) 7.39315 0.456751
\(263\) 28.4679 1.75541 0.877704 0.479203i \(-0.159074\pi\)
0.877704 + 0.479203i \(0.159074\pi\)
\(264\) −6.91637 −0.425673
\(265\) 6.99179 0.429502
\(266\) −0.115428 −0.00707732
\(267\) −0.214602 −0.0131334
\(268\) −13.5628 −0.828478
\(269\) 16.5425 1.00861 0.504307 0.863524i \(-0.331748\pi\)
0.504307 + 0.863524i \(0.331748\pi\)
\(270\) −1.31688 −0.0801429
\(271\) 24.4858 1.48741 0.743705 0.668508i \(-0.233067\pi\)
0.743705 + 0.668508i \(0.233067\pi\)
\(272\) 1.15958 0.0703100
\(273\) 0.101849 0.00616418
\(274\) −3.53121 −0.213328
\(275\) 4.56192 0.275094
\(276\) −9.75425 −0.587137
\(277\) 2.17957 0.130958 0.0654789 0.997854i \(-0.479143\pi\)
0.0654789 + 0.997854i \(0.479143\pi\)
\(278\) 10.1566 0.609149
\(279\) 2.70422 0.161898
\(280\) 1.90173 0.113650
\(281\) −2.91692 −0.174009 −0.0870043 0.996208i \(-0.527729\pi\)
−0.0870043 + 0.996208i \(0.527729\pi\)
\(282\) −0.886922 −0.0528154
\(283\) −9.99042 −0.593869 −0.296934 0.954898i \(-0.595964\pi\)
−0.296934 + 0.954898i \(0.595964\pi\)
\(284\) 4.79712 0.284657
\(285\) 0.707311 0.0418975
\(286\) 0.487790 0.0288437
\(287\) −1.93063 −0.113962
\(288\) −5.84735 −0.344558
\(289\) 1.00000 0.0588235
\(290\) 1.02135 0.0599760
\(291\) 18.6375 1.09255
\(292\) 5.73254 0.335471
\(293\) 5.35560 0.312877 0.156439 0.987688i \(-0.449999\pi\)
0.156439 + 0.987688i \(0.449999\pi\)
\(294\) 4.91496 0.286646
\(295\) 4.33297 0.252275
\(296\) 19.9451 1.15928
\(297\) −2.75956 −0.160126
\(298\) −8.62404 −0.499577
\(299\) 1.61642 0.0934801
\(300\) 2.44969 0.141433
\(301\) −0.734565 −0.0423396
\(302\) −5.72238 −0.329286
\(303\) 4.52955 0.260216
\(304\) 0.448325 0.0257132
\(305\) 10.9411 0.626488
\(306\) −0.719826 −0.0411497
\(307\) 20.0480 1.14420 0.572099 0.820185i \(-0.306129\pi\)
0.572099 + 0.820185i \(0.306129\pi\)
\(308\) 1.69604 0.0966408
\(309\) −4.82523 −0.274498
\(310\) −3.56114 −0.202259
\(311\) 14.8123 0.839931 0.419965 0.907540i \(-0.362042\pi\)
0.419965 + 0.907540i \(0.362042\pi\)
\(312\) 0.615464 0.0348438
\(313\) 2.76838 0.156478 0.0782390 0.996935i \(-0.475070\pi\)
0.0782390 + 0.996935i \(0.475070\pi\)
\(314\) 6.14376 0.346712
\(315\) 0.758771 0.0427519
\(316\) −1.48185 −0.0833606
\(317\) 18.8127 1.05662 0.528312 0.849050i \(-0.322825\pi\)
0.528312 + 0.849050i \(0.322825\pi\)
\(318\) −2.75104 −0.154271
\(319\) 2.14028 0.119832
\(320\) 3.45749 0.193280
\(321\) −17.0658 −0.952520
\(322\) −1.96521 −0.109517
\(323\) 0.386626 0.0215125
\(324\) −1.48185 −0.0823250
\(325\) −0.405950 −0.0225180
\(326\) −6.31262 −0.349623
\(327\) 16.0479 0.887452
\(328\) −11.6667 −0.644183
\(329\) 0.511033 0.0281742
\(330\) 3.63402 0.200046
\(331\) −23.3912 −1.28569 −0.642847 0.765994i \(-0.722247\pi\)
−0.642847 + 0.765994i \(0.722247\pi\)
\(332\) −23.5870 −1.29451
\(333\) 7.95789 0.436089
\(334\) −4.67151 −0.255614
\(335\) 16.7442 0.914831
\(336\) 0.480942 0.0262375
\(337\) −11.9605 −0.651529 −0.325765 0.945451i \(-0.605622\pi\)
−0.325765 + 0.945451i \(0.605622\pi\)
\(338\) 9.31433 0.506633
\(339\) 2.71994 0.147727
\(340\) −2.71096 −0.147023
\(341\) −7.46248 −0.404116
\(342\) −0.278304 −0.0150489
\(343\) −5.73522 −0.309673
\(344\) −4.43892 −0.239330
\(345\) 12.0423 0.648335
\(346\) −5.68537 −0.305647
\(347\) −11.1748 −0.599892 −0.299946 0.953956i \(-0.596969\pi\)
−0.299946 + 0.953956i \(0.596969\pi\)
\(348\) 1.14930 0.0616090
\(349\) 34.0195 1.82102 0.910511 0.413485i \(-0.135689\pi\)
0.910511 + 0.413485i \(0.135689\pi\)
\(350\) 0.493544 0.0263810
\(351\) 0.245564 0.0131073
\(352\) 16.1361 0.860059
\(353\) −26.9914 −1.43661 −0.718303 0.695731i \(-0.755081\pi\)
−0.718303 + 0.695731i \(0.755081\pi\)
\(354\) −1.70488 −0.0906134
\(355\) −5.92237 −0.314327
\(356\) 0.318009 0.0168544
\(357\) 0.414755 0.0219511
\(358\) −3.46631 −0.183200
\(359\) 28.5330 1.50591 0.752957 0.658069i \(-0.228627\pi\)
0.752957 + 0.658069i \(0.228627\pi\)
\(360\) 4.58519 0.241661
\(361\) −18.8505 −0.992133
\(362\) 10.0656 0.529034
\(363\) −3.38481 −0.177656
\(364\) −0.150925 −0.00791061
\(365\) −7.07721 −0.370438
\(366\) −4.30498 −0.225025
\(367\) 34.1865 1.78452 0.892261 0.451521i \(-0.149118\pi\)
0.892261 + 0.451521i \(0.149118\pi\)
\(368\) 7.63292 0.397894
\(369\) −4.65488 −0.242323
\(370\) −10.4796 −0.544808
\(371\) 1.58511 0.0822950
\(372\) −4.00725 −0.207766
\(373\) 32.4578 1.68060 0.840300 0.542121i \(-0.182379\pi\)
0.840300 + 0.542121i \(0.182379\pi\)
\(374\) 1.98641 0.102715
\(375\) −12.1715 −0.628535
\(376\) 3.08813 0.159258
\(377\) −0.190456 −0.00980898
\(378\) −0.298551 −0.0153558
\(379\) −7.52217 −0.386388 −0.193194 0.981161i \(-0.561885\pi\)
−0.193194 + 0.981161i \(0.561885\pi\)
\(380\) −1.04813 −0.0537679
\(381\) 9.03607 0.462932
\(382\) 8.72735 0.446530
\(383\) −3.83802 −0.196113 −0.0980567 0.995181i \(-0.531263\pi\)
−0.0980567 + 0.995181i \(0.531263\pi\)
\(384\) 10.3343 0.527370
\(385\) −2.09388 −0.106714
\(386\) 1.94745 0.0991228
\(387\) −1.77108 −0.0900293
\(388\) −27.6179 −1.40209
\(389\) 4.16830 0.211341 0.105671 0.994401i \(-0.466301\pi\)
0.105671 + 0.994401i \(0.466301\pi\)
\(390\) −0.323379 −0.0163749
\(391\) 6.58248 0.332890
\(392\) −17.1131 −0.864344
\(393\) −10.2707 −0.518091
\(394\) −6.32504 −0.318651
\(395\) 1.82945 0.0920494
\(396\) 4.08926 0.205493
\(397\) −19.5347 −0.980417 −0.490209 0.871605i \(-0.663079\pi\)
−0.490209 + 0.871605i \(0.663079\pi\)
\(398\) −5.20601 −0.260954
\(399\) 0.160355 0.00802779
\(400\) −1.91694 −0.0958470
\(401\) −24.1661 −1.20680 −0.603399 0.797440i \(-0.706187\pi\)
−0.603399 + 0.797440i \(0.706187\pi\)
\(402\) −6.58827 −0.328593
\(403\) 0.664061 0.0330792
\(404\) −6.71211 −0.333940
\(405\) 1.82945 0.0909059
\(406\) 0.231552 0.0114917
\(407\) −21.9603 −1.08853
\(408\) 2.50633 0.124082
\(409\) −20.9646 −1.03663 −0.518316 0.855189i \(-0.673441\pi\)
−0.518316 + 0.855189i \(0.673441\pi\)
\(410\) 6.12993 0.302736
\(411\) 4.90565 0.241978
\(412\) 7.15026 0.352268
\(413\) 0.982330 0.0483373
\(414\) −4.73824 −0.232872
\(415\) 29.1198 1.42943
\(416\) −1.43590 −0.0704008
\(417\) −14.1097 −0.690956
\(418\) 0.767997 0.0375639
\(419\) 10.3584 0.506041 0.253021 0.967461i \(-0.418576\pi\)
0.253021 + 0.967461i \(0.418576\pi\)
\(420\) −1.12438 −0.0548644
\(421\) −38.6490 −1.88364 −0.941819 0.336121i \(-0.890885\pi\)
−0.941819 + 0.336121i \(0.890885\pi\)
\(422\) 18.3766 0.894557
\(423\) 1.23213 0.0599084
\(424\) 9.57870 0.465183
\(425\) −1.65313 −0.0801886
\(426\) 2.33026 0.112901
\(427\) 2.48047 0.120039
\(428\) 25.2890 1.22239
\(429\) −0.677651 −0.0327173
\(430\) 2.33231 0.112474
\(431\) 33.6185 1.61934 0.809672 0.586882i \(-0.199645\pi\)
0.809672 + 0.586882i \(0.199645\pi\)
\(432\) 1.15958 0.0557904
\(433\) −3.19007 −0.153305 −0.0766525 0.997058i \(-0.524423\pi\)
−0.0766525 + 0.997058i \(0.524423\pi\)
\(434\) −0.807349 −0.0387540
\(435\) −1.41889 −0.0680306
\(436\) −23.7806 −1.13889
\(437\) 2.54496 0.121742
\(438\) 2.78465 0.133056
\(439\) −38.7166 −1.84784 −0.923921 0.382582i \(-0.875035\pi\)
−0.923921 + 0.382582i \(0.875035\pi\)
\(440\) −12.6531 −0.603214
\(441\) −6.82798 −0.325142
\(442\) −0.176764 −0.00840779
\(443\) 0.0361883 0.00171936 0.000859680 1.00000i \(-0.499726\pi\)
0.000859680 1.00000i \(0.499726\pi\)
\(444\) −11.7924 −0.559642
\(445\) −0.392603 −0.0186112
\(446\) −12.3927 −0.586810
\(447\) 11.9807 0.566669
\(448\) 0.783849 0.0370334
\(449\) 3.50805 0.165555 0.0827776 0.996568i \(-0.473621\pi\)
0.0827776 + 0.996568i \(0.473621\pi\)
\(450\) 1.18997 0.0560955
\(451\) 12.8454 0.604868
\(452\) −4.03054 −0.189581
\(453\) 7.94967 0.373508
\(454\) −13.1900 −0.619037
\(455\) 0.186327 0.00873515
\(456\) 0.969011 0.0453781
\(457\) 7.99570 0.374023 0.187011 0.982358i \(-0.440120\pi\)
0.187011 + 0.982358i \(0.440120\pi\)
\(458\) 17.5663 0.820819
\(459\) 1.00000 0.0466760
\(460\) −17.8449 −0.832021
\(461\) 18.4814 0.860766 0.430383 0.902646i \(-0.358378\pi\)
0.430383 + 0.902646i \(0.358378\pi\)
\(462\) 0.823871 0.0383299
\(463\) −26.8168 −1.24628 −0.623142 0.782109i \(-0.714144\pi\)
−0.623142 + 0.782109i \(0.714144\pi\)
\(464\) −0.899354 −0.0417515
\(465\) 4.94723 0.229422
\(466\) −17.3091 −0.801827
\(467\) 33.0861 1.53104 0.765522 0.643410i \(-0.222481\pi\)
0.765522 + 0.643410i \(0.222481\pi\)
\(468\) −0.363890 −0.0168208
\(469\) 3.79608 0.175287
\(470\) −1.62258 −0.0748438
\(471\) −8.53506 −0.393275
\(472\) 5.93614 0.273233
\(473\) 4.88742 0.224724
\(474\) −0.719826 −0.0330627
\(475\) −0.639143 −0.0293259
\(476\) −0.614604 −0.0281703
\(477\) 3.82181 0.174989
\(478\) −16.2674 −0.744053
\(479\) 13.6621 0.624239 0.312120 0.950043i \(-0.398961\pi\)
0.312120 + 0.950043i \(0.398961\pi\)
\(480\) −10.6974 −0.488268
\(481\) 1.95417 0.0891026
\(482\) −18.1137 −0.825056
\(483\) 2.73011 0.124224
\(484\) 5.01578 0.227990
\(485\) 34.0962 1.54823
\(486\) −0.719826 −0.0326520
\(487\) −25.0693 −1.13600 −0.568000 0.823029i \(-0.692283\pi\)
−0.568000 + 0.823029i \(0.692283\pi\)
\(488\) 14.9893 0.678533
\(489\) 8.76964 0.396577
\(490\) 8.99164 0.406201
\(491\) 29.1872 1.31720 0.658600 0.752493i \(-0.271149\pi\)
0.658600 + 0.752493i \(0.271149\pi\)
\(492\) 6.89784 0.310979
\(493\) −0.775585 −0.0349306
\(494\) −0.0683414 −0.00307483
\(495\) −5.04847 −0.226912
\(496\) 3.13577 0.140800
\(497\) −1.34266 −0.0602267
\(498\) −11.4577 −0.513430
\(499\) 17.8077 0.797184 0.398592 0.917128i \(-0.369499\pi\)
0.398592 + 0.917128i \(0.369499\pi\)
\(500\) 18.0364 0.806612
\(501\) 6.48978 0.289942
\(502\) 14.3631 0.641056
\(503\) 3.69088 0.164568 0.0822841 0.996609i \(-0.473779\pi\)
0.0822841 + 0.996609i \(0.473779\pi\)
\(504\) 1.03951 0.0463035
\(505\) 8.28656 0.368747
\(506\) 13.0755 0.581276
\(507\) −12.9397 −0.574672
\(508\) −13.3901 −0.594090
\(509\) −11.4789 −0.508792 −0.254396 0.967100i \(-0.581877\pi\)
−0.254396 + 0.967100i \(0.581877\pi\)
\(510\) −1.31688 −0.0583125
\(511\) −1.60448 −0.0709779
\(512\) −12.5931 −0.556540
\(513\) 0.386626 0.0170700
\(514\) −4.59118 −0.202508
\(515\) −8.82749 −0.388986
\(516\) 2.62448 0.115536
\(517\) −3.40015 −0.149539
\(518\) −2.37584 −0.104388
\(519\) 7.89825 0.346695
\(520\) 1.12596 0.0493765
\(521\) −25.6691 −1.12458 −0.562291 0.826939i \(-0.690080\pi\)
−0.562291 + 0.826939i \(0.690080\pi\)
\(522\) 0.558286 0.0244355
\(523\) −40.2412 −1.75962 −0.879812 0.475322i \(-0.842332\pi\)
−0.879812 + 0.475322i \(0.842332\pi\)
\(524\) 15.2197 0.664876
\(525\) −0.685643 −0.0299239
\(526\) −20.4920 −0.893492
\(527\) 2.70422 0.117798
\(528\) −3.19994 −0.139260
\(529\) 20.3290 0.883871
\(530\) −5.03287 −0.218614
\(531\) 2.36846 0.102783
\(532\) −0.237622 −0.0103022
\(533\) −1.14307 −0.0495120
\(534\) 0.154476 0.00668485
\(535\) −31.2210 −1.34980
\(536\) 22.9394 0.990830
\(537\) 4.81548 0.207803
\(538\) −11.9077 −0.513379
\(539\) 18.8422 0.811593
\(540\) −2.71096 −0.116661
\(541\) −44.1060 −1.89626 −0.948132 0.317876i \(-0.897030\pi\)
−0.948132 + 0.317876i \(0.897030\pi\)
\(542\) −17.6255 −0.757082
\(543\) −13.9833 −0.600082
\(544\) −5.84735 −0.250703
\(545\) 29.3588 1.25759
\(546\) −0.0733135 −0.00313753
\(547\) −35.4235 −1.51460 −0.757299 0.653068i \(-0.773481\pi\)
−0.757299 + 0.653068i \(0.773481\pi\)
\(548\) −7.26943 −0.310535
\(549\) 5.98058 0.255245
\(550\) −3.28379 −0.140021
\(551\) −0.299861 −0.0127745
\(552\) 16.4978 0.702195
\(553\) 0.414755 0.0176372
\(554\) −1.56891 −0.0666567
\(555\) 14.5585 0.617975
\(556\) 20.9085 0.886718
\(557\) 21.1443 0.895912 0.447956 0.894056i \(-0.352152\pi\)
0.447956 + 0.894056i \(0.352152\pi\)
\(558\) −1.94657 −0.0824049
\(559\) −0.434915 −0.0183950
\(560\) 0.879857 0.0371807
\(561\) −2.75956 −0.116509
\(562\) 2.09967 0.0885693
\(563\) 8.02512 0.338218 0.169109 0.985597i \(-0.445911\pi\)
0.169109 + 0.985597i \(0.445911\pi\)
\(564\) −1.82584 −0.0768817
\(565\) 4.97598 0.209341
\(566\) 7.19136 0.302275
\(567\) 0.414755 0.0174181
\(568\) −8.11361 −0.340439
\(569\) −36.4770 −1.52919 −0.764597 0.644509i \(-0.777062\pi\)
−0.764597 + 0.644509i \(0.777062\pi\)
\(570\) −0.509141 −0.0213256
\(571\) −1.68511 −0.0705195 −0.0352597 0.999378i \(-0.511226\pi\)
−0.0352597 + 0.999378i \(0.511226\pi\)
\(572\) 1.00418 0.0419867
\(573\) −12.1242 −0.506498
\(574\) 1.38972 0.0580058
\(575\) −10.8817 −0.453798
\(576\) 1.88991 0.0787463
\(577\) −27.6311 −1.15030 −0.575149 0.818048i \(-0.695056\pi\)
−0.575149 + 0.818048i \(0.695056\pi\)
\(578\) −0.719826 −0.0299408
\(579\) −2.70545 −0.112435
\(580\) 2.10258 0.0873050
\(581\) 6.60176 0.273887
\(582\) −13.4157 −0.556100
\(583\) −10.5465 −0.436793
\(584\) −9.69572 −0.401212
\(585\) 0.449247 0.0185741
\(586\) −3.85510 −0.159253
\(587\) 36.6930 1.51448 0.757241 0.653136i \(-0.226547\pi\)
0.757241 + 0.653136i \(0.226547\pi\)
\(588\) 10.1180 0.417261
\(589\) 1.04552 0.0430800
\(590\) −3.11899 −0.128407
\(591\) 8.78690 0.361445
\(592\) 9.22782 0.379261
\(593\) −28.8174 −1.18339 −0.591695 0.806162i \(-0.701541\pi\)
−0.591695 + 0.806162i \(0.701541\pi\)
\(594\) 1.98641 0.0815032
\(595\) 0.758771 0.0311066
\(596\) −17.7536 −0.727217
\(597\) 7.23231 0.295999
\(598\) −1.16354 −0.0475808
\(599\) −12.3914 −0.506298 −0.253149 0.967427i \(-0.581466\pi\)
−0.253149 + 0.967427i \(0.581466\pi\)
\(600\) −4.14328 −0.169149
\(601\) −16.2368 −0.662313 −0.331157 0.943576i \(-0.607439\pi\)
−0.331157 + 0.943576i \(0.607439\pi\)
\(602\) 0.528759 0.0215506
\(603\) 9.15259 0.372722
\(604\) −11.7802 −0.479330
\(605\) −6.19232 −0.251754
\(606\) −3.26048 −0.132448
\(607\) −5.80246 −0.235514 −0.117757 0.993042i \(-0.537570\pi\)
−0.117757 + 0.993042i \(0.537570\pi\)
\(608\) −2.26074 −0.0916851
\(609\) −0.321677 −0.0130350
\(610\) −7.87572 −0.318879
\(611\) 0.302568 0.0122406
\(612\) −1.48185 −0.0599003
\(613\) −23.3330 −0.942411 −0.471205 0.882024i \(-0.656181\pi\)
−0.471205 + 0.882024i \(0.656181\pi\)
\(614\) −14.4310 −0.582390
\(615\) −8.51585 −0.343392
\(616\) −2.86860 −0.115579
\(617\) 10.9987 0.442793 0.221396 0.975184i \(-0.428939\pi\)
0.221396 + 0.975184i \(0.428939\pi\)
\(618\) 3.47332 0.139718
\(619\) 19.2753 0.774739 0.387369 0.921925i \(-0.373384\pi\)
0.387369 + 0.921925i \(0.373384\pi\)
\(620\) −7.33105 −0.294422
\(621\) 6.58248 0.264146
\(622\) −10.6623 −0.427520
\(623\) −0.0890073 −0.00356600
\(624\) 0.284752 0.0113992
\(625\) −14.0015 −0.560060
\(626\) −1.99275 −0.0796463
\(627\) −1.06692 −0.0426087
\(628\) 12.6477 0.504698
\(629\) 7.95789 0.317302
\(630\) −0.546183 −0.0217604
\(631\) 17.4524 0.694768 0.347384 0.937723i \(-0.387070\pi\)
0.347384 + 0.937723i \(0.387070\pi\)
\(632\) 2.50633 0.0996963
\(633\) −25.5292 −1.01469
\(634\) −13.5418 −0.537815
\(635\) 16.5310 0.656012
\(636\) −5.66335 −0.224566
\(637\) −1.67671 −0.0664336
\(638\) −1.54063 −0.0609940
\(639\) −3.23725 −0.128064
\(640\) 18.9060 0.747326
\(641\) −42.4645 −1.67725 −0.838624 0.544711i \(-0.816639\pi\)
−0.838624 + 0.544711i \(0.816639\pi\)
\(642\) 12.2844 0.484827
\(643\) 10.1855 0.401677 0.200838 0.979624i \(-0.435633\pi\)
0.200838 + 0.979624i \(0.435633\pi\)
\(644\) −4.04562 −0.159420
\(645\) −3.24010 −0.127579
\(646\) −0.278304 −0.0109497
\(647\) 47.0665 1.85037 0.925187 0.379511i \(-0.123908\pi\)
0.925187 + 0.379511i \(0.123908\pi\)
\(648\) 2.50633 0.0984578
\(649\) −6.53592 −0.256557
\(650\) 0.292213 0.0114615
\(651\) 1.12159 0.0439585
\(652\) −12.9953 −0.508935
\(653\) −2.16854 −0.0848616 −0.0424308 0.999099i \(-0.513510\pi\)
−0.0424308 + 0.999099i \(0.513510\pi\)
\(654\) −11.5517 −0.451708
\(655\) −18.7898 −0.734177
\(656\) −5.39772 −0.210745
\(657\) −3.86850 −0.150925
\(658\) −0.367855 −0.0143405
\(659\) −47.4420 −1.84808 −0.924038 0.382300i \(-0.875132\pi\)
−0.924038 + 0.382300i \(0.875132\pi\)
\(660\) 7.48108 0.291201
\(661\) −23.1248 −0.899451 −0.449726 0.893167i \(-0.648478\pi\)
−0.449726 + 0.893167i \(0.648478\pi\)
\(662\) 16.8376 0.654411
\(663\) 0.245564 0.00953693
\(664\) 39.8939 1.54818
\(665\) 0.293361 0.0113760
\(666\) −5.72829 −0.221967
\(667\) −5.10527 −0.197677
\(668\) −9.61688 −0.372088
\(669\) 17.2162 0.665617
\(670\) −12.0529 −0.465643
\(671\) −16.5038 −0.637122
\(672\) −2.42522 −0.0935547
\(673\) 36.0969 1.39143 0.695717 0.718316i \(-0.255087\pi\)
0.695717 + 0.718316i \(0.255087\pi\)
\(674\) 8.60947 0.331624
\(675\) −1.65313 −0.0636290
\(676\) 19.1747 0.737488
\(677\) 20.6626 0.794130 0.397065 0.917791i \(-0.370029\pi\)
0.397065 + 0.917791i \(0.370029\pi\)
\(678\) −1.95788 −0.0751920
\(679\) 7.72997 0.296649
\(680\) 4.58519 0.175834
\(681\) 18.3239 0.702172
\(682\) 5.37169 0.205692
\(683\) 35.9726 1.37645 0.688227 0.725495i \(-0.258389\pi\)
0.688227 + 0.725495i \(0.258389\pi\)
\(684\) −0.572922 −0.0219062
\(685\) 8.97461 0.342902
\(686\) 4.12836 0.157621
\(687\) −24.4035 −0.931053
\(688\) −2.05372 −0.0782972
\(689\) 0.938500 0.0357540
\(690\) −8.66835 −0.329998
\(691\) −30.6870 −1.16739 −0.583694 0.811973i \(-0.698393\pi\)
−0.583694 + 0.811973i \(0.698393\pi\)
\(692\) −11.7040 −0.444920
\(693\) −1.14454 −0.0434775
\(694\) 8.04388 0.305342
\(695\) −25.8130 −0.979142
\(696\) −1.94387 −0.0736822
\(697\) −4.65488 −0.176316
\(698\) −24.4881 −0.926889
\(699\) 24.0462 0.909510
\(700\) 1.01602 0.0384020
\(701\) −47.7345 −1.80291 −0.901454 0.432876i \(-0.857499\pi\)
−0.901454 + 0.432876i \(0.857499\pi\)
\(702\) −0.176764 −0.00667151
\(703\) 3.07673 0.116041
\(704\) −5.21533 −0.196560
\(705\) 2.25412 0.0848951
\(706\) 19.4291 0.731223
\(707\) 1.87865 0.0706539
\(708\) −3.50971 −0.131903
\(709\) −0.239120 −0.00898033 −0.00449017 0.999990i \(-0.501429\pi\)
−0.00449017 + 0.999990i \(0.501429\pi\)
\(710\) 4.26308 0.159990
\(711\) 1.00000 0.0375029
\(712\) −0.537864 −0.0201573
\(713\) 17.8005 0.666634
\(714\) −0.298551 −0.0111730
\(715\) −1.23972 −0.0463631
\(716\) −7.13582 −0.266678
\(717\) 22.5991 0.843977
\(718\) −20.5388 −0.766501
\(719\) −30.6832 −1.14429 −0.572145 0.820152i \(-0.693889\pi\)
−0.572145 + 0.820152i \(0.693889\pi\)
\(720\) 2.12139 0.0790596
\(721\) −2.00128 −0.0745317
\(722\) 13.5691 0.504989
\(723\) 25.1640 0.935859
\(724\) 20.7212 0.770097
\(725\) 1.28214 0.0476176
\(726\) 2.43647 0.0904260
\(727\) 26.1729 0.970701 0.485350 0.874320i \(-0.338692\pi\)
0.485350 + 0.874320i \(0.338692\pi\)
\(728\) 0.255267 0.00946081
\(729\) 1.00000 0.0370370
\(730\) 5.09436 0.188551
\(731\) −1.77108 −0.0655059
\(732\) −8.86233 −0.327561
\(733\) 7.82983 0.289202 0.144601 0.989490i \(-0.453810\pi\)
0.144601 + 0.989490i \(0.453810\pi\)
\(734\) −24.6083 −0.908310
\(735\) −12.4914 −0.460753
\(736\) −38.4901 −1.41876
\(737\) −25.2572 −0.930359
\(738\) 3.35070 0.123341
\(739\) 31.2670 1.15018 0.575088 0.818092i \(-0.304968\pi\)
0.575088 + 0.818092i \(0.304968\pi\)
\(740\) −21.5735 −0.793059
\(741\) 0.0949416 0.00348777
\(742\) −1.14101 −0.0418876
\(743\) −17.3813 −0.637658 −0.318829 0.947812i \(-0.603290\pi\)
−0.318829 + 0.947812i \(0.603290\pi\)
\(744\) 6.77767 0.248481
\(745\) 21.9181 0.803016
\(746\) −23.3640 −0.855415
\(747\) 15.9173 0.582383
\(748\) 4.08926 0.149518
\(749\) −7.07812 −0.258629
\(750\) 8.76139 0.319921
\(751\) 15.6507 0.571103 0.285551 0.958363i \(-0.407823\pi\)
0.285551 + 0.958363i \(0.407823\pi\)
\(752\) 1.42876 0.0521015
\(753\) −19.9536 −0.727148
\(754\) 0.137095 0.00499271
\(755\) 14.5435 0.529292
\(756\) −0.614604 −0.0223529
\(757\) 45.2503 1.64465 0.822326 0.569017i \(-0.192676\pi\)
0.822326 + 0.569017i \(0.192676\pi\)
\(758\) 5.41466 0.196669
\(759\) −18.1648 −0.659339
\(760\) 1.77275 0.0643045
\(761\) 33.9249 1.22978 0.614888 0.788614i \(-0.289201\pi\)
0.614888 + 0.788614i \(0.289201\pi\)
\(762\) −6.50439 −0.235629
\(763\) 6.65595 0.240962
\(764\) 17.9663 0.649999
\(765\) 1.82945 0.0661437
\(766\) 2.76270 0.0998206
\(767\) 0.581610 0.0210007
\(768\) −11.2187 −0.404821
\(769\) −50.3111 −1.81427 −0.907133 0.420844i \(-0.861734\pi\)
−0.907133 + 0.420844i \(0.861734\pi\)
\(770\) 1.50723 0.0543167
\(771\) 6.37818 0.229705
\(772\) 4.00907 0.144290
\(773\) 11.3678 0.408871 0.204436 0.978880i \(-0.434464\pi\)
0.204436 + 0.978880i \(0.434464\pi\)
\(774\) 1.27487 0.0458244
\(775\) −4.47043 −0.160583
\(776\) 46.7116 1.67685
\(777\) 3.30057 0.118407
\(778\) −3.00045 −0.107571
\(779\) −1.79970 −0.0644809
\(780\) −0.665716 −0.0238365
\(781\) 8.93340 0.319662
\(782\) −4.73824 −0.169439
\(783\) −0.775585 −0.0277171
\(784\) −7.91760 −0.282771
\(785\) −15.6144 −0.557303
\(786\) 7.39315 0.263705
\(787\) −18.8362 −0.671436 −0.335718 0.941962i \(-0.608979\pi\)
−0.335718 + 0.941962i \(0.608979\pi\)
\(788\) −13.0209 −0.463850
\(789\) 28.4679 1.01349
\(790\) −1.31688 −0.0468526
\(791\) 1.12811 0.0401108
\(792\) −6.91637 −0.245762
\(793\) 1.46862 0.0521521
\(794\) 14.0616 0.499026
\(795\) 6.99179 0.247973
\(796\) −10.7172 −0.379861
\(797\) −31.2170 −1.10576 −0.552882 0.833259i \(-0.686472\pi\)
−0.552882 + 0.833259i \(0.686472\pi\)
\(798\) −0.115428 −0.00408610
\(799\) 1.23213 0.0435898
\(800\) 9.66643 0.341760
\(801\) −0.214602 −0.00758260
\(802\) 17.3954 0.614252
\(803\) 10.6754 0.376726
\(804\) −13.5628 −0.478322
\(805\) 4.99459 0.176036
\(806\) −0.478008 −0.0168371
\(807\) 16.5425 0.582324
\(808\) 11.3525 0.399380
\(809\) 7.91592 0.278309 0.139154 0.990271i \(-0.455562\pi\)
0.139154 + 0.990271i \(0.455562\pi\)
\(810\) −1.31688 −0.0462705
\(811\) −12.3154 −0.432453 −0.216227 0.976343i \(-0.569375\pi\)
−0.216227 + 0.976343i \(0.569375\pi\)
\(812\) 0.476678 0.0167281
\(813\) 24.4858 0.858756
\(814\) 15.8076 0.554056
\(815\) 16.0436 0.561982
\(816\) 1.15958 0.0405935
\(817\) −0.684748 −0.0239563
\(818\) 15.0909 0.527639
\(819\) 0.101849 0.00355889
\(820\) 12.6192 0.440682
\(821\) −28.6856 −1.00113 −0.500567 0.865698i \(-0.666875\pi\)
−0.500567 + 0.865698i \(0.666875\pi\)
\(822\) −3.53121 −0.123165
\(823\) −10.0482 −0.350259 −0.175130 0.984545i \(-0.556034\pi\)
−0.175130 + 0.984545i \(0.556034\pi\)
\(824\) −12.0936 −0.421300
\(825\) 4.56192 0.158826
\(826\) −0.707107 −0.0246034
\(827\) −13.8280 −0.480846 −0.240423 0.970668i \(-0.577286\pi\)
−0.240423 + 0.970668i \(0.577286\pi\)
\(828\) −9.75425 −0.338984
\(829\) 41.1327 1.42860 0.714300 0.699840i \(-0.246745\pi\)
0.714300 + 0.699840i \(0.246745\pi\)
\(830\) −20.9612 −0.727573
\(831\) 2.17957 0.0756085
\(832\) 0.464095 0.0160896
\(833\) −6.82798 −0.236575
\(834\) 10.1566 0.351693
\(835\) 11.8727 0.410871
\(836\) 1.58102 0.0546806
\(837\) 2.70422 0.0934716
\(838\) −7.45625 −0.257572
\(839\) −31.3760 −1.08322 −0.541609 0.840630i \(-0.682185\pi\)
−0.541609 + 0.840630i \(0.682185\pi\)
\(840\) 1.90173 0.0656158
\(841\) −28.3985 −0.979258
\(842\) 27.8206 0.958760
\(843\) −2.91692 −0.100464
\(844\) 37.8304 1.30218
\(845\) −23.6725 −0.814358
\(846\) −0.886922 −0.0304930
\(847\) −1.40386 −0.0482373
\(848\) 4.43170 0.152185
\(849\) −9.99042 −0.342870
\(850\) 1.18997 0.0408155
\(851\) 52.3826 1.79565
\(852\) 4.79712 0.164347
\(853\) −4.24630 −0.145390 −0.0726952 0.997354i \(-0.523160\pi\)
−0.0726952 + 0.997354i \(0.523160\pi\)
\(854\) −1.78551 −0.0610989
\(855\) 0.707311 0.0241895
\(856\) −42.7725 −1.46193
\(857\) 34.1449 1.16637 0.583184 0.812340i \(-0.301807\pi\)
0.583184 + 0.812340i \(0.301807\pi\)
\(858\) 0.487790 0.0166529
\(859\) −22.5724 −0.770160 −0.385080 0.922883i \(-0.625826\pi\)
−0.385080 + 0.922883i \(0.625826\pi\)
\(860\) 4.80135 0.163725
\(861\) −1.93063 −0.0657958
\(862\) −24.1994 −0.824237
\(863\) −17.3207 −0.589604 −0.294802 0.955558i \(-0.595254\pi\)
−0.294802 + 0.955558i \(0.595254\pi\)
\(864\) −5.84735 −0.198931
\(865\) 14.4494 0.491295
\(866\) 2.29630 0.0780313
\(867\) 1.00000 0.0339618
\(868\) −1.66203 −0.0564129
\(869\) −2.75956 −0.0936118
\(870\) 1.02135 0.0346271
\(871\) 2.24755 0.0761553
\(872\) 40.2213 1.36207
\(873\) 18.6375 0.630782
\(874\) −1.83193 −0.0619659
\(875\) −5.04820 −0.170660
\(876\) 5.73254 0.193685
\(877\) −53.0590 −1.79167 −0.895837 0.444383i \(-0.853423\pi\)
−0.895837 + 0.444383i \(0.853423\pi\)
\(878\) 27.8692 0.940541
\(879\) 5.35560 0.180640
\(880\) −5.85412 −0.197342
\(881\) −46.9575 −1.58204 −0.791019 0.611791i \(-0.790449\pi\)
−0.791019 + 0.611791i \(0.790449\pi\)
\(882\) 4.91496 0.165495
\(883\) 27.4476 0.923684 0.461842 0.886962i \(-0.347189\pi\)
0.461842 + 0.886962i \(0.347189\pi\)
\(884\) −0.363890 −0.0122389
\(885\) 4.33297 0.145651
\(886\) −0.0260493 −0.000875143 0
\(887\) 38.7268 1.30032 0.650160 0.759797i \(-0.274702\pi\)
0.650160 + 0.759797i \(0.274702\pi\)
\(888\) 19.9451 0.669312
\(889\) 3.74775 0.125695
\(890\) 0.282606 0.00947297
\(891\) −2.75956 −0.0924489
\(892\) −25.5118 −0.854199
\(893\) 0.476375 0.0159413
\(894\) −8.62404 −0.288431
\(895\) 8.80965 0.294474
\(896\) 4.28620 0.143192
\(897\) 1.61642 0.0539708
\(898\) −2.52519 −0.0842666
\(899\) −2.09735 −0.0699507
\(900\) 2.44969 0.0816564
\(901\) 3.82181 0.127323
\(902\) −9.24648 −0.307874
\(903\) −0.734565 −0.0244448
\(904\) 6.81705 0.226732
\(905\) −25.5817 −0.850365
\(906\) −5.72238 −0.190113
\(907\) 6.62249 0.219896 0.109948 0.993937i \(-0.464932\pi\)
0.109948 + 0.993937i \(0.464932\pi\)
\(908\) −27.1532 −0.901111
\(909\) 4.52955 0.150236
\(910\) −0.134123 −0.00444614
\(911\) 36.4150 1.20648 0.603241 0.797559i \(-0.293876\pi\)
0.603241 + 0.797559i \(0.293876\pi\)
\(912\) 0.448325 0.0148455
\(913\) −43.9247 −1.45370
\(914\) −5.75551 −0.190375
\(915\) 10.9411 0.361703
\(916\) 36.1624 1.19484
\(917\) −4.25984 −0.140672
\(918\) −0.719826 −0.0237578
\(919\) −30.1480 −0.994490 −0.497245 0.867610i \(-0.665655\pi\)
−0.497245 + 0.867610i \(0.665655\pi\)
\(920\) 30.1819 0.995068
\(921\) 20.0480 0.660603
\(922\) −13.3034 −0.438125
\(923\) −0.794953 −0.0261662
\(924\) 1.69604 0.0557956
\(925\) −13.1554 −0.432548
\(926\) 19.3035 0.634351
\(927\) −4.82523 −0.158481
\(928\) 4.53512 0.148872
\(929\) −6.35944 −0.208646 −0.104323 0.994543i \(-0.533268\pi\)
−0.104323 + 0.994543i \(0.533268\pi\)
\(930\) −3.56114 −0.116775
\(931\) −2.63988 −0.0865184
\(932\) −35.6328 −1.16719
\(933\) 14.8123 0.484934
\(934\) −23.8163 −0.779292
\(935\) −5.04847 −0.165103
\(936\) 0.615464 0.0201171
\(937\) −43.7477 −1.42918 −0.714588 0.699545i \(-0.753386\pi\)
−0.714588 + 0.699545i \(0.753386\pi\)
\(938\) −2.73252 −0.0892198
\(939\) 2.76838 0.0903426
\(940\) −3.34027 −0.108948
\(941\) −39.9043 −1.30084 −0.650422 0.759573i \(-0.725408\pi\)
−0.650422 + 0.759573i \(0.725408\pi\)
\(942\) 6.14376 0.200175
\(943\) −30.6407 −0.997797
\(944\) 2.74643 0.0893886
\(945\) 0.758771 0.0246828
\(946\) −3.51809 −0.114383
\(947\) −44.7528 −1.45427 −0.727136 0.686494i \(-0.759149\pi\)
−0.727136 + 0.686494i \(0.759149\pi\)
\(948\) −1.48185 −0.0481283
\(949\) −0.949966 −0.0308372
\(950\) 0.460072 0.0149267
\(951\) 18.8127 0.610042
\(952\) 1.03951 0.0336907
\(953\) −16.6817 −0.540374 −0.270187 0.962808i \(-0.587085\pi\)
−0.270187 + 0.962808i \(0.587085\pi\)
\(954\) −2.75104 −0.0890681
\(955\) −22.1806 −0.717749
\(956\) −33.4884 −1.08309
\(957\) 2.14028 0.0691853
\(958\) −9.83436 −0.317734
\(959\) 2.03464 0.0657019
\(960\) 3.45749 0.111590
\(961\) −23.6872 −0.764102
\(962\) −1.40666 −0.0453527
\(963\) −17.0658 −0.549938
\(964\) −37.2893 −1.20101
\(965\) −4.94947 −0.159329
\(966\) −1.96521 −0.0632295
\(967\) 22.2995 0.717102 0.358551 0.933510i \(-0.383271\pi\)
0.358551 + 0.933510i \(0.383271\pi\)
\(968\) −8.48343 −0.272668
\(969\) 0.386626 0.0124202
\(970\) −24.5433 −0.788039
\(971\) −7.79177 −0.250050 −0.125025 0.992154i \(-0.539901\pi\)
−0.125025 + 0.992154i \(0.539901\pi\)
\(972\) −1.48185 −0.0475304
\(973\) −5.85207 −0.187609
\(974\) 18.0455 0.578217
\(975\) −0.405950 −0.0130008
\(976\) 6.93497 0.221983
\(977\) 13.9986 0.447856 0.223928 0.974606i \(-0.428112\pi\)
0.223928 + 0.974606i \(0.428112\pi\)
\(978\) −6.31262 −0.201855
\(979\) 0.592209 0.0189271
\(980\) 18.5104 0.591293
\(981\) 16.0479 0.512371
\(982\) −21.0097 −0.670447
\(983\) −22.6636 −0.722858 −0.361429 0.932400i \(-0.617711\pi\)
−0.361429 + 0.932400i \(0.617711\pi\)
\(984\) −11.6667 −0.371919
\(985\) 16.0752 0.512197
\(986\) 0.558286 0.0177795
\(987\) 0.511033 0.0162664
\(988\) −0.140689 −0.00447592
\(989\) −11.6581 −0.370707
\(990\) 3.63402 0.115497
\(991\) 16.9148 0.537318 0.268659 0.963235i \(-0.413420\pi\)
0.268659 + 0.963235i \(0.413420\pi\)
\(992\) −15.8125 −0.502049
\(993\) −23.3912 −0.742296
\(994\) 0.966485 0.0306550
\(995\) 13.2311 0.419455
\(996\) −23.5870 −0.747383
\(997\) −47.3564 −1.49979 −0.749896 0.661555i \(-0.769897\pi\)
−0.749896 + 0.661555i \(0.769897\pi\)
\(998\) −12.8185 −0.405762
\(999\) 7.95789 0.251776
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.k.1.11 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.11 31 1.1 even 1 trivial