Properties

Label 4029.2.a.k.1.16
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.16
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0509119 q^{2} +1.00000 q^{3} -1.99741 q^{4} +3.95784 q^{5} +0.0509119 q^{6} +1.89285 q^{7} -0.203515 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.0509119 q^{2} +1.00000 q^{3} -1.99741 q^{4} +3.95784 q^{5} +0.0509119 q^{6} +1.89285 q^{7} -0.203515 q^{8} +1.00000 q^{9} +0.201501 q^{10} +5.26878 q^{11} -1.99741 q^{12} -2.15571 q^{13} +0.0963686 q^{14} +3.95784 q^{15} +3.98445 q^{16} +1.00000 q^{17} +0.0509119 q^{18} +3.28525 q^{19} -7.90542 q^{20} +1.89285 q^{21} +0.268243 q^{22} -2.60175 q^{23} -0.203515 q^{24} +10.6645 q^{25} -0.109751 q^{26} +1.00000 q^{27} -3.78080 q^{28} +1.79464 q^{29} +0.201501 q^{30} +1.06539 q^{31} +0.609887 q^{32} +5.26878 q^{33} +0.0509119 q^{34} +7.49161 q^{35} -1.99741 q^{36} -6.27633 q^{37} +0.167258 q^{38} -2.15571 q^{39} -0.805482 q^{40} +8.76444 q^{41} +0.0963686 q^{42} -10.2465 q^{43} -10.5239 q^{44} +3.95784 q^{45} -0.132460 q^{46} +6.79563 q^{47} +3.98445 q^{48} -3.41711 q^{49} +0.542950 q^{50} +1.00000 q^{51} +4.30584 q^{52} -6.84440 q^{53} +0.0509119 q^{54} +20.8530 q^{55} -0.385225 q^{56} +3.28525 q^{57} +0.0913684 q^{58} -13.4533 q^{59} -7.90542 q^{60} +10.8439 q^{61} +0.0542410 q^{62} +1.89285 q^{63} -7.93786 q^{64} -8.53197 q^{65} +0.268243 q^{66} +10.6925 q^{67} -1.99741 q^{68} -2.60175 q^{69} +0.381412 q^{70} -0.635598 q^{71} -0.203515 q^{72} -3.45288 q^{73} -0.319540 q^{74} +10.6645 q^{75} -6.56198 q^{76} +9.97301 q^{77} -0.109751 q^{78} +1.00000 q^{79} +15.7698 q^{80} +1.00000 q^{81} +0.446214 q^{82} -12.9078 q^{83} -3.78080 q^{84} +3.95784 q^{85} -0.521670 q^{86} +1.79464 q^{87} -1.07228 q^{88} -6.91898 q^{89} +0.201501 q^{90} -4.08045 q^{91} +5.19675 q^{92} +1.06539 q^{93} +0.345978 q^{94} +13.0025 q^{95} +0.609887 q^{96} +2.23271 q^{97} -0.173972 q^{98} +5.26878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0509119 0.0360001 0.0180001 0.999838i \(-0.494270\pi\)
0.0180001 + 0.999838i \(0.494270\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.99741 −0.998704
\(5\) 3.95784 1.77000 0.885000 0.465590i \(-0.154158\pi\)
0.885000 + 0.465590i \(0.154158\pi\)
\(6\) 0.0509119 0.0207847
\(7\) 1.89285 0.715431 0.357715 0.933831i \(-0.383556\pi\)
0.357715 + 0.933831i \(0.383556\pi\)
\(8\) −0.203515 −0.0719536
\(9\) 1.00000 0.333333
\(10\) 0.201501 0.0637202
\(11\) 5.26878 1.58860 0.794298 0.607528i \(-0.207839\pi\)
0.794298 + 0.607528i \(0.207839\pi\)
\(12\) −1.99741 −0.576602
\(13\) −2.15571 −0.597887 −0.298944 0.954271i \(-0.596634\pi\)
−0.298944 + 0.954271i \(0.596634\pi\)
\(14\) 0.0963686 0.0257556
\(15\) 3.95784 1.02191
\(16\) 3.98445 0.996114
\(17\) 1.00000 0.242536
\(18\) 0.0509119 0.0120000
\(19\) 3.28525 0.753688 0.376844 0.926277i \(-0.377009\pi\)
0.376844 + 0.926277i \(0.377009\pi\)
\(20\) −7.90542 −1.76771
\(21\) 1.89285 0.413054
\(22\) 0.268243 0.0571897
\(23\) −2.60175 −0.542501 −0.271251 0.962509i \(-0.587437\pi\)
−0.271251 + 0.962509i \(0.587437\pi\)
\(24\) −0.203515 −0.0415424
\(25\) 10.6645 2.13290
\(26\) −0.109751 −0.0215240
\(27\) 1.00000 0.192450
\(28\) −3.78080 −0.714504
\(29\) 1.79464 0.333256 0.166628 0.986020i \(-0.446712\pi\)
0.166628 + 0.986020i \(0.446712\pi\)
\(30\) 0.201501 0.0367889
\(31\) 1.06539 0.191350 0.0956749 0.995413i \(-0.469499\pi\)
0.0956749 + 0.995413i \(0.469499\pi\)
\(32\) 0.609887 0.107814
\(33\) 5.26878 0.917176
\(34\) 0.0509119 0.00873131
\(35\) 7.49161 1.26631
\(36\) −1.99741 −0.332901
\(37\) −6.27633 −1.03182 −0.515911 0.856642i \(-0.672547\pi\)
−0.515911 + 0.856642i \(0.672547\pi\)
\(38\) 0.167258 0.0271328
\(39\) −2.15571 −0.345190
\(40\) −0.805482 −0.127358
\(41\) 8.76444 1.36878 0.684388 0.729118i \(-0.260070\pi\)
0.684388 + 0.729118i \(0.260070\pi\)
\(42\) 0.0963686 0.0148700
\(43\) −10.2465 −1.56258 −0.781291 0.624167i \(-0.785438\pi\)
−0.781291 + 0.624167i \(0.785438\pi\)
\(44\) −10.5239 −1.58654
\(45\) 3.95784 0.590000
\(46\) −0.132460 −0.0195301
\(47\) 6.79563 0.991244 0.495622 0.868538i \(-0.334940\pi\)
0.495622 + 0.868538i \(0.334940\pi\)
\(48\) 3.98445 0.575106
\(49\) −3.41711 −0.488159
\(50\) 0.542950 0.0767847
\(51\) 1.00000 0.140028
\(52\) 4.30584 0.597113
\(53\) −6.84440 −0.940150 −0.470075 0.882626i \(-0.655773\pi\)
−0.470075 + 0.882626i \(0.655773\pi\)
\(54\) 0.0509119 0.00692823
\(55\) 20.8530 2.81182
\(56\) −0.385225 −0.0514778
\(57\) 3.28525 0.435142
\(58\) 0.0913684 0.0119973
\(59\) −13.4533 −1.75147 −0.875736 0.482791i \(-0.839623\pi\)
−0.875736 + 0.482791i \(0.839623\pi\)
\(60\) −7.90542 −1.02059
\(61\) 10.8439 1.38842 0.694210 0.719773i \(-0.255754\pi\)
0.694210 + 0.719773i \(0.255754\pi\)
\(62\) 0.0542410 0.00688862
\(63\) 1.89285 0.238477
\(64\) −7.93786 −0.992232
\(65\) −8.53197 −1.05826
\(66\) 0.268243 0.0330185
\(67\) 10.6925 1.30630 0.653150 0.757228i \(-0.273447\pi\)
0.653150 + 0.757228i \(0.273447\pi\)
\(68\) −1.99741 −0.242221
\(69\) −2.60175 −0.313213
\(70\) 0.381412 0.0455874
\(71\) −0.635598 −0.0754316 −0.0377158 0.999289i \(-0.512008\pi\)
−0.0377158 + 0.999289i \(0.512008\pi\)
\(72\) −0.203515 −0.0239845
\(73\) −3.45288 −0.404129 −0.202064 0.979372i \(-0.564765\pi\)
−0.202064 + 0.979372i \(0.564765\pi\)
\(74\) −0.319540 −0.0371457
\(75\) 10.6645 1.23143
\(76\) −6.56198 −0.752711
\(77\) 9.97301 1.13653
\(78\) −0.109751 −0.0124269
\(79\) 1.00000 0.112509
\(80\) 15.7698 1.76312
\(81\) 1.00000 0.111111
\(82\) 0.446214 0.0492761
\(83\) −12.9078 −1.41682 −0.708410 0.705801i \(-0.750587\pi\)
−0.708410 + 0.705801i \(0.750587\pi\)
\(84\) −3.78080 −0.412519
\(85\) 3.95784 0.429288
\(86\) −0.521670 −0.0562531
\(87\) 1.79464 0.192405
\(88\) −1.07228 −0.114305
\(89\) −6.91898 −0.733411 −0.366705 0.930337i \(-0.619514\pi\)
−0.366705 + 0.930337i \(0.619514\pi\)
\(90\) 0.201501 0.0212401
\(91\) −4.08045 −0.427747
\(92\) 5.19675 0.541798
\(93\) 1.06539 0.110476
\(94\) 0.345978 0.0356849
\(95\) 13.0025 1.33403
\(96\) 0.609887 0.0622463
\(97\) 2.23271 0.226697 0.113349 0.993555i \(-0.463842\pi\)
0.113349 + 0.993555i \(0.463842\pi\)
\(98\) −0.173972 −0.0175738
\(99\) 5.26878 0.529532
\(100\) −21.3014 −2.13014
\(101\) −7.71317 −0.767490 −0.383745 0.923439i \(-0.625366\pi\)
−0.383745 + 0.923439i \(0.625366\pi\)
\(102\) 0.0509119 0.00504103
\(103\) 6.30662 0.621410 0.310705 0.950506i \(-0.399435\pi\)
0.310705 + 0.950506i \(0.399435\pi\)
\(104\) 0.438721 0.0430201
\(105\) 7.49161 0.731106
\(106\) −0.348461 −0.0338455
\(107\) −18.0287 −1.74290 −0.871450 0.490484i \(-0.836820\pi\)
−0.871450 + 0.490484i \(0.836820\pi\)
\(108\) −1.99741 −0.192201
\(109\) 15.0394 1.44051 0.720256 0.693709i \(-0.244024\pi\)
0.720256 + 0.693709i \(0.244024\pi\)
\(110\) 1.06166 0.101226
\(111\) −6.27633 −0.595723
\(112\) 7.54198 0.712650
\(113\) −1.47464 −0.138722 −0.0693610 0.997592i \(-0.522096\pi\)
−0.0693610 + 0.997592i \(0.522096\pi\)
\(114\) 0.167258 0.0156652
\(115\) −10.2973 −0.960228
\(116\) −3.58462 −0.332824
\(117\) −2.15571 −0.199296
\(118\) −0.684933 −0.0630532
\(119\) 1.89285 0.173517
\(120\) −0.805482 −0.0735301
\(121\) 16.7600 1.52364
\(122\) 0.552083 0.0499833
\(123\) 8.76444 0.790263
\(124\) −2.12802 −0.191102
\(125\) 22.4192 2.00524
\(126\) 0.0963686 0.00858520
\(127\) −3.07151 −0.272553 −0.136276 0.990671i \(-0.543514\pi\)
−0.136276 + 0.990671i \(0.543514\pi\)
\(128\) −1.62391 −0.143534
\(129\) −10.2465 −0.902157
\(130\) −0.434379 −0.0380975
\(131\) 7.42141 0.648412 0.324206 0.945987i \(-0.394903\pi\)
0.324206 + 0.945987i \(0.394903\pi\)
\(132\) −10.5239 −0.915988
\(133\) 6.21849 0.539211
\(134\) 0.544377 0.0470270
\(135\) 3.95784 0.340637
\(136\) −0.203515 −0.0174513
\(137\) −20.7596 −1.77361 −0.886805 0.462144i \(-0.847080\pi\)
−0.886805 + 0.462144i \(0.847080\pi\)
\(138\) −0.132460 −0.0112757
\(139\) −6.99991 −0.593725 −0.296862 0.954920i \(-0.595940\pi\)
−0.296862 + 0.954920i \(0.595940\pi\)
\(140\) −14.9638 −1.26467
\(141\) 6.79563 0.572295
\(142\) −0.0323595 −0.00271555
\(143\) −11.3580 −0.949802
\(144\) 3.98445 0.332038
\(145\) 7.10289 0.589863
\(146\) −0.175792 −0.0145487
\(147\) −3.41711 −0.281839
\(148\) 12.5364 1.03049
\(149\) −2.52004 −0.206449 −0.103225 0.994658i \(-0.532916\pi\)
−0.103225 + 0.994658i \(0.532916\pi\)
\(150\) 0.542950 0.0443317
\(151\) 2.39953 0.195271 0.0976357 0.995222i \(-0.468872\pi\)
0.0976357 + 0.995222i \(0.468872\pi\)
\(152\) −0.668599 −0.0542305
\(153\) 1.00000 0.0808452
\(154\) 0.507745 0.0409152
\(155\) 4.21665 0.338689
\(156\) 4.30584 0.344743
\(157\) −7.13021 −0.569053 −0.284526 0.958668i \(-0.591836\pi\)
−0.284526 + 0.958668i \(0.591836\pi\)
\(158\) 0.0509119 0.00405033
\(159\) −6.84440 −0.542796
\(160\) 2.41384 0.190830
\(161\) −4.92472 −0.388122
\(162\) 0.0509119 0.00400001
\(163\) 9.18135 0.719139 0.359570 0.933118i \(-0.382924\pi\)
0.359570 + 0.933118i \(0.382924\pi\)
\(164\) −17.5062 −1.36700
\(165\) 20.8530 1.62340
\(166\) −0.657162 −0.0510057
\(167\) 11.7414 0.908574 0.454287 0.890855i \(-0.349894\pi\)
0.454287 + 0.890855i \(0.349894\pi\)
\(168\) −0.385225 −0.0297207
\(169\) −8.35290 −0.642531
\(170\) 0.201501 0.0154544
\(171\) 3.28525 0.251229
\(172\) 20.4665 1.56056
\(173\) −17.3164 −1.31654 −0.658270 0.752782i \(-0.728711\pi\)
−0.658270 + 0.752782i \(0.728711\pi\)
\(174\) 0.0913684 0.00692662
\(175\) 20.1863 1.52594
\(176\) 20.9932 1.58242
\(177\) −13.4533 −1.01121
\(178\) −0.352258 −0.0264029
\(179\) 23.2880 1.74063 0.870314 0.492497i \(-0.163916\pi\)
0.870314 + 0.492497i \(0.163916\pi\)
\(180\) −7.90542 −0.589236
\(181\) 1.61698 0.120189 0.0600946 0.998193i \(-0.480860\pi\)
0.0600946 + 0.998193i \(0.480860\pi\)
\(182\) −0.207743 −0.0153989
\(183\) 10.8439 0.801604
\(184\) 0.529496 0.0390349
\(185\) −24.8407 −1.82633
\(186\) 0.0542410 0.00397714
\(187\) 5.26878 0.385291
\(188\) −13.5736 −0.989960
\(189\) 1.89285 0.137685
\(190\) 0.661981 0.0480252
\(191\) −8.53278 −0.617410 −0.308705 0.951158i \(-0.599896\pi\)
−0.308705 + 0.951158i \(0.599896\pi\)
\(192\) −7.93786 −0.572866
\(193\) −21.0273 −1.51358 −0.756790 0.653658i \(-0.773233\pi\)
−0.756790 + 0.653658i \(0.773233\pi\)
\(194\) 0.113671 0.00816113
\(195\) −8.53197 −0.610987
\(196\) 6.82537 0.487526
\(197\) 18.1465 1.29288 0.646441 0.762964i \(-0.276256\pi\)
0.646441 + 0.762964i \(0.276256\pi\)
\(198\) 0.268243 0.0190632
\(199\) −8.58119 −0.608305 −0.304152 0.952623i \(-0.598373\pi\)
−0.304152 + 0.952623i \(0.598373\pi\)
\(200\) −2.17039 −0.153470
\(201\) 10.6925 0.754193
\(202\) −0.392692 −0.0276297
\(203\) 3.39698 0.238422
\(204\) −1.99741 −0.139847
\(205\) 34.6883 2.42273
\(206\) 0.321082 0.0223708
\(207\) −2.60175 −0.180834
\(208\) −8.58934 −0.595564
\(209\) 17.3092 1.19731
\(210\) 0.381412 0.0263199
\(211\) 24.2509 1.66950 0.834749 0.550631i \(-0.185613\pi\)
0.834749 + 0.550631i \(0.185613\pi\)
\(212\) 13.6711 0.938932
\(213\) −0.635598 −0.0435505
\(214\) −0.917875 −0.0627446
\(215\) −40.5542 −2.76577
\(216\) −0.203515 −0.0138475
\(217\) 2.01663 0.136898
\(218\) 0.765683 0.0518586
\(219\) −3.45288 −0.233324
\(220\) −41.6519 −2.80817
\(221\) −2.15571 −0.145009
\(222\) −0.319540 −0.0214461
\(223\) −9.47539 −0.634519 −0.317260 0.948339i \(-0.602763\pi\)
−0.317260 + 0.948339i \(0.602763\pi\)
\(224\) 1.15443 0.0771333
\(225\) 10.6645 0.710967
\(226\) −0.0750764 −0.00499401
\(227\) −15.6787 −1.04063 −0.520317 0.853973i \(-0.674186\pi\)
−0.520317 + 0.853973i \(0.674186\pi\)
\(228\) −6.56198 −0.434578
\(229\) 18.9379 1.25145 0.625727 0.780042i \(-0.284802\pi\)
0.625727 + 0.780042i \(0.284802\pi\)
\(230\) −0.524255 −0.0345683
\(231\) 9.97301 0.656176
\(232\) −0.365237 −0.0239790
\(233\) 28.1117 1.84166 0.920829 0.389967i \(-0.127514\pi\)
0.920829 + 0.389967i \(0.127514\pi\)
\(234\) −0.109751 −0.00717467
\(235\) 26.8960 1.75450
\(236\) 26.8717 1.74920
\(237\) 1.00000 0.0649570
\(238\) 0.0963686 0.00624665
\(239\) 24.0586 1.55622 0.778110 0.628128i \(-0.216179\pi\)
0.778110 + 0.628128i \(0.216179\pi\)
\(240\) 15.7698 1.01794
\(241\) 11.1814 0.720258 0.360129 0.932902i \(-0.382733\pi\)
0.360129 + 0.932902i \(0.382733\pi\)
\(242\) 0.853284 0.0548511
\(243\) 1.00000 0.0641500
\(244\) −21.6597 −1.38662
\(245\) −13.5244 −0.864042
\(246\) 0.446214 0.0284496
\(247\) −7.08205 −0.450620
\(248\) −0.216823 −0.0137683
\(249\) −12.9078 −0.818001
\(250\) 1.14140 0.0721888
\(251\) 13.3467 0.842437 0.421218 0.906959i \(-0.361603\pi\)
0.421218 + 0.906959i \(0.361603\pi\)
\(252\) −3.78080 −0.238168
\(253\) −13.7080 −0.861816
\(254\) −0.156377 −0.00981194
\(255\) 3.95784 0.247850
\(256\) 15.7930 0.987065
\(257\) 16.1906 1.00994 0.504971 0.863137i \(-0.331503\pi\)
0.504971 + 0.863137i \(0.331503\pi\)
\(258\) −0.521670 −0.0324778
\(259\) −11.8802 −0.738197
\(260\) 17.0418 1.05689
\(261\) 1.79464 0.111085
\(262\) 0.377838 0.0233429
\(263\) −17.8736 −1.10214 −0.551068 0.834460i \(-0.685779\pi\)
−0.551068 + 0.834460i \(0.685779\pi\)
\(264\) −1.07228 −0.0659941
\(265\) −27.0890 −1.66407
\(266\) 0.316595 0.0194117
\(267\) −6.91898 −0.423435
\(268\) −21.3573 −1.30461
\(269\) 15.7614 0.960992 0.480496 0.876997i \(-0.340457\pi\)
0.480496 + 0.876997i \(0.340457\pi\)
\(270\) 0.201501 0.0122630
\(271\) −17.7427 −1.07779 −0.538897 0.842372i \(-0.681159\pi\)
−0.538897 + 0.842372i \(0.681159\pi\)
\(272\) 3.98445 0.241593
\(273\) −4.08045 −0.246960
\(274\) −1.05691 −0.0638502
\(275\) 56.1889 3.38832
\(276\) 5.19675 0.312807
\(277\) −14.7538 −0.886471 −0.443235 0.896405i \(-0.646169\pi\)
−0.443235 + 0.896405i \(0.646169\pi\)
\(278\) −0.356378 −0.0213742
\(279\) 1.06539 0.0637833
\(280\) −1.52466 −0.0911158
\(281\) −32.3269 −1.92846 −0.964230 0.265066i \(-0.914606\pi\)
−0.964230 + 0.265066i \(0.914606\pi\)
\(282\) 0.345978 0.0206027
\(283\) −15.7050 −0.933565 −0.466782 0.884372i \(-0.654587\pi\)
−0.466782 + 0.884372i \(0.654587\pi\)
\(284\) 1.26955 0.0753339
\(285\) 13.0025 0.770201
\(286\) −0.578256 −0.0341930
\(287\) 16.5898 0.979264
\(288\) 0.609887 0.0359379
\(289\) 1.00000 0.0588235
\(290\) 0.361622 0.0212352
\(291\) 2.23271 0.130884
\(292\) 6.89681 0.403605
\(293\) −10.2116 −0.596570 −0.298285 0.954477i \(-0.596415\pi\)
−0.298285 + 0.954477i \(0.596415\pi\)
\(294\) −0.173972 −0.0101462
\(295\) −53.2461 −3.10011
\(296\) 1.27733 0.0742433
\(297\) 5.26878 0.305725
\(298\) −0.128300 −0.00743221
\(299\) 5.60862 0.324355
\(300\) −21.3014 −1.22984
\(301\) −19.3952 −1.11792
\(302\) 0.122165 0.00702979
\(303\) −7.71317 −0.443110
\(304\) 13.0899 0.750758
\(305\) 42.9185 2.45750
\(306\) 0.0509119 0.00291044
\(307\) −10.2616 −0.585660 −0.292830 0.956165i \(-0.594597\pi\)
−0.292830 + 0.956165i \(0.594597\pi\)
\(308\) −19.9202 −1.13506
\(309\) 6.30662 0.358771
\(310\) 0.214677 0.0121929
\(311\) −3.07625 −0.174438 −0.0872191 0.996189i \(-0.527798\pi\)
−0.0872191 + 0.996189i \(0.527798\pi\)
\(312\) 0.438721 0.0248377
\(313\) −6.77918 −0.383182 −0.191591 0.981475i \(-0.561365\pi\)
−0.191591 + 0.981475i \(0.561365\pi\)
\(314\) −0.363012 −0.0204860
\(315\) 7.49161 0.422104
\(316\) −1.99741 −0.112363
\(317\) 27.8869 1.56628 0.783142 0.621842i \(-0.213616\pi\)
0.783142 + 0.621842i \(0.213616\pi\)
\(318\) −0.348461 −0.0195407
\(319\) 9.45555 0.529409
\(320\) −31.4168 −1.75625
\(321\) −18.0287 −1.00626
\(322\) −0.250727 −0.0139724
\(323\) 3.28525 0.182796
\(324\) −1.99741 −0.110967
\(325\) −22.9896 −1.27524
\(326\) 0.467440 0.0258891
\(327\) 15.0394 0.831680
\(328\) −1.78370 −0.0984883
\(329\) 12.8631 0.709167
\(330\) 1.06166 0.0584427
\(331\) 28.0154 1.53986 0.769932 0.638126i \(-0.220290\pi\)
0.769932 + 0.638126i \(0.220290\pi\)
\(332\) 25.7822 1.41498
\(333\) −6.27633 −0.343941
\(334\) 0.597775 0.0327088
\(335\) 42.3193 2.31215
\(336\) 7.54198 0.411449
\(337\) −26.2695 −1.43099 −0.715495 0.698618i \(-0.753799\pi\)
−0.715495 + 0.698618i \(0.753799\pi\)
\(338\) −0.425262 −0.0231312
\(339\) −1.47464 −0.0800912
\(340\) −7.90542 −0.428732
\(341\) 5.61330 0.303978
\(342\) 0.167258 0.00904428
\(343\) −19.7180 −1.06467
\(344\) 2.08533 0.112433
\(345\) −10.2973 −0.554388
\(346\) −0.881609 −0.0473956
\(347\) −1.44253 −0.0774390 −0.0387195 0.999250i \(-0.512328\pi\)
−0.0387195 + 0.999250i \(0.512328\pi\)
\(348\) −3.58462 −0.192156
\(349\) 17.5904 0.941595 0.470797 0.882241i \(-0.343966\pi\)
0.470797 + 0.882241i \(0.343966\pi\)
\(350\) 1.02772 0.0549342
\(351\) −2.15571 −0.115063
\(352\) 3.21336 0.171273
\(353\) 35.2617 1.87679 0.938394 0.345566i \(-0.112313\pi\)
0.938394 + 0.345566i \(0.112313\pi\)
\(354\) −0.684933 −0.0364038
\(355\) −2.51560 −0.133514
\(356\) 13.8200 0.732460
\(357\) 1.89285 0.100180
\(358\) 1.18564 0.0626628
\(359\) 27.6109 1.45725 0.728623 0.684915i \(-0.240161\pi\)
0.728623 + 0.684915i \(0.240161\pi\)
\(360\) −0.805482 −0.0424526
\(361\) −8.20715 −0.431955
\(362\) 0.0823235 0.00432683
\(363\) 16.7600 0.879673
\(364\) 8.15032 0.427193
\(365\) −13.6659 −0.715308
\(366\) 0.552083 0.0288579
\(367\) −12.7400 −0.665022 −0.332511 0.943099i \(-0.607896\pi\)
−0.332511 + 0.943099i \(0.607896\pi\)
\(368\) −10.3665 −0.540393
\(369\) 8.76444 0.456258
\(370\) −1.26469 −0.0657480
\(371\) −12.9554 −0.672612
\(372\) −2.12802 −0.110333
\(373\) 14.7130 0.761808 0.380904 0.924615i \(-0.375613\pi\)
0.380904 + 0.924615i \(0.375613\pi\)
\(374\) 0.268243 0.0138705
\(375\) 22.4192 1.15772
\(376\) −1.38302 −0.0713236
\(377\) −3.86873 −0.199250
\(378\) 0.0963686 0.00495667
\(379\) 4.68446 0.240625 0.120312 0.992736i \(-0.461610\pi\)
0.120312 + 0.992736i \(0.461610\pi\)
\(380\) −25.9713 −1.33230
\(381\) −3.07151 −0.157358
\(382\) −0.434420 −0.0222269
\(383\) 27.1546 1.38753 0.693767 0.720199i \(-0.255950\pi\)
0.693767 + 0.720199i \(0.255950\pi\)
\(384\) −1.62391 −0.0828696
\(385\) 39.4716 2.01166
\(386\) −1.07054 −0.0544891
\(387\) −10.2465 −0.520861
\(388\) −4.45963 −0.226404
\(389\) −7.35108 −0.372715 −0.186357 0.982482i \(-0.559668\pi\)
−0.186357 + 0.982482i \(0.559668\pi\)
\(390\) −0.434379 −0.0219956
\(391\) −2.60175 −0.131576
\(392\) 0.695435 0.0351248
\(393\) 7.42141 0.374361
\(394\) 0.923871 0.0465439
\(395\) 3.95784 0.199141
\(396\) −10.5239 −0.528846
\(397\) 1.86641 0.0936722 0.0468361 0.998903i \(-0.485086\pi\)
0.0468361 + 0.998903i \(0.485086\pi\)
\(398\) −0.436884 −0.0218990
\(399\) 6.21849 0.311314
\(400\) 42.4923 2.12461
\(401\) 15.5893 0.778491 0.389246 0.921134i \(-0.372736\pi\)
0.389246 + 0.921134i \(0.372736\pi\)
\(402\) 0.544377 0.0271510
\(403\) −2.29668 −0.114406
\(404\) 15.4064 0.766495
\(405\) 3.95784 0.196667
\(406\) 0.172947 0.00858321
\(407\) −33.0686 −1.63915
\(408\) −0.203515 −0.0100755
\(409\) 19.8656 0.982291 0.491145 0.871078i \(-0.336578\pi\)
0.491145 + 0.871078i \(0.336578\pi\)
\(410\) 1.76604 0.0872187
\(411\) −20.7596 −1.02399
\(412\) −12.5969 −0.620605
\(413\) −25.4651 −1.25306
\(414\) −0.132460 −0.00651004
\(415\) −51.0872 −2.50777
\(416\) −1.31474 −0.0644605
\(417\) −6.99991 −0.342787
\(418\) 0.881246 0.0431031
\(419\) 24.8173 1.21241 0.606203 0.795310i \(-0.292692\pi\)
0.606203 + 0.795310i \(0.292692\pi\)
\(420\) −14.9638 −0.730158
\(421\) 0.949942 0.0462974 0.0231487 0.999732i \(-0.492631\pi\)
0.0231487 + 0.999732i \(0.492631\pi\)
\(422\) 1.23466 0.0601021
\(423\) 6.79563 0.330415
\(424\) 1.39294 0.0676472
\(425\) 10.6645 0.517305
\(426\) −0.0323595 −0.00156782
\(427\) 20.5259 0.993318
\(428\) 36.0107 1.74064
\(429\) −11.3580 −0.548368
\(430\) −2.06469 −0.0995681
\(431\) −37.6436 −1.81323 −0.906613 0.421962i \(-0.861341\pi\)
−0.906613 + 0.421962i \(0.861341\pi\)
\(432\) 3.98445 0.191702
\(433\) 26.7637 1.28618 0.643090 0.765791i \(-0.277652\pi\)
0.643090 + 0.765791i \(0.277652\pi\)
\(434\) 0.102670 0.00492833
\(435\) 7.10289 0.340558
\(436\) −30.0398 −1.43864
\(437\) −8.54738 −0.408877
\(438\) −0.175792 −0.00839969
\(439\) 36.4366 1.73902 0.869512 0.493912i \(-0.164433\pi\)
0.869512 + 0.493912i \(0.164433\pi\)
\(440\) −4.24391 −0.202320
\(441\) −3.41711 −0.162720
\(442\) −0.109751 −0.00522034
\(443\) 11.0897 0.526889 0.263444 0.964675i \(-0.415141\pi\)
0.263444 + 0.964675i \(0.415141\pi\)
\(444\) 12.5364 0.594951
\(445\) −27.3842 −1.29814
\(446\) −0.482410 −0.0228428
\(447\) −2.52004 −0.119194
\(448\) −15.0252 −0.709873
\(449\) −14.4035 −0.679745 −0.339872 0.940472i \(-0.610384\pi\)
−0.339872 + 0.940472i \(0.610384\pi\)
\(450\) 0.542950 0.0255949
\(451\) 46.1779 2.17443
\(452\) 2.94545 0.138542
\(453\) 2.39953 0.112740
\(454\) −0.798234 −0.0374630
\(455\) −16.1498 −0.757112
\(456\) −0.668599 −0.0313100
\(457\) 2.53031 0.118363 0.0591815 0.998247i \(-0.481151\pi\)
0.0591815 + 0.998247i \(0.481151\pi\)
\(458\) 0.964166 0.0450525
\(459\) 1.00000 0.0466760
\(460\) 20.5679 0.958983
\(461\) −26.2235 −1.22135 −0.610675 0.791881i \(-0.709102\pi\)
−0.610675 + 0.791881i \(0.709102\pi\)
\(462\) 0.507745 0.0236224
\(463\) −33.4646 −1.55523 −0.777617 0.628739i \(-0.783572\pi\)
−0.777617 + 0.628739i \(0.783572\pi\)
\(464\) 7.15066 0.331961
\(465\) 4.21665 0.195542
\(466\) 1.43122 0.0662999
\(467\) −8.60118 −0.398015 −0.199008 0.979998i \(-0.563772\pi\)
−0.199008 + 0.979998i \(0.563772\pi\)
\(468\) 4.30584 0.199038
\(469\) 20.2394 0.934567
\(470\) 1.36933 0.0631623
\(471\) −7.13021 −0.328543
\(472\) 2.73796 0.126025
\(473\) −53.9867 −2.48231
\(474\) 0.0509119 0.00233846
\(475\) 35.0356 1.60754
\(476\) −3.78080 −0.173293
\(477\) −6.84440 −0.313383
\(478\) 1.22487 0.0560241
\(479\) −22.0804 −1.00888 −0.504439 0.863447i \(-0.668301\pi\)
−0.504439 + 0.863447i \(0.668301\pi\)
\(480\) 2.41384 0.110176
\(481\) 13.5300 0.616914
\(482\) 0.569267 0.0259294
\(483\) −4.92472 −0.224082
\(484\) −33.4766 −1.52166
\(485\) 8.83671 0.401255
\(486\) 0.0509119 0.00230941
\(487\) −3.82625 −0.173384 −0.0866920 0.996235i \(-0.527630\pi\)
−0.0866920 + 0.996235i \(0.527630\pi\)
\(488\) −2.20690 −0.0999018
\(489\) 9.18135 0.415195
\(490\) −0.688552 −0.0311056
\(491\) −17.9562 −0.810353 −0.405177 0.914238i \(-0.632790\pi\)
−0.405177 + 0.914238i \(0.632790\pi\)
\(492\) −17.5062 −0.789239
\(493\) 1.79464 0.0808264
\(494\) −0.360561 −0.0162224
\(495\) 20.8530 0.937272
\(496\) 4.24500 0.190606
\(497\) −1.20309 −0.0539661
\(498\) −0.657162 −0.0294481
\(499\) −20.8933 −0.935311 −0.467656 0.883911i \(-0.654901\pi\)
−0.467656 + 0.883911i \(0.654901\pi\)
\(500\) −44.7804 −2.00264
\(501\) 11.7414 0.524566
\(502\) 0.679506 0.0303278
\(503\) −36.3950 −1.62277 −0.811386 0.584511i \(-0.801286\pi\)
−0.811386 + 0.584511i \(0.801286\pi\)
\(504\) −0.385225 −0.0171593
\(505\) −30.5275 −1.35846
\(506\) −0.697901 −0.0310255
\(507\) −8.35290 −0.370965
\(508\) 6.13507 0.272200
\(509\) −27.7110 −1.22827 −0.614133 0.789202i \(-0.710494\pi\)
−0.614133 + 0.789202i \(0.710494\pi\)
\(510\) 0.201501 0.00892262
\(511\) −6.53579 −0.289126
\(512\) 4.05186 0.179069
\(513\) 3.28525 0.145047
\(514\) 0.824293 0.0363580
\(515\) 24.9606 1.09990
\(516\) 20.4665 0.900988
\(517\) 35.8047 1.57469
\(518\) −0.604841 −0.0265752
\(519\) −17.3164 −0.760104
\(520\) 1.73639 0.0761457
\(521\) 15.1921 0.665580 0.332790 0.943001i \(-0.392010\pi\)
0.332790 + 0.943001i \(0.392010\pi\)
\(522\) 0.0913684 0.00399909
\(523\) −13.9690 −0.610822 −0.305411 0.952221i \(-0.598794\pi\)
−0.305411 + 0.952221i \(0.598794\pi\)
\(524\) −14.8236 −0.647571
\(525\) 20.1863 0.881004
\(526\) −0.909980 −0.0396770
\(527\) 1.06539 0.0464091
\(528\) 20.9932 0.913612
\(529\) −16.2309 −0.705692
\(530\) −1.37915 −0.0599066
\(531\) −13.4533 −0.583824
\(532\) −12.4209 −0.538512
\(533\) −18.8936 −0.818374
\(534\) −0.352258 −0.0152437
\(535\) −71.3547 −3.08493
\(536\) −2.17610 −0.0939930
\(537\) 23.2880 1.00495
\(538\) 0.802444 0.0345958
\(539\) −18.0040 −0.775487
\(540\) −7.90542 −0.340195
\(541\) −2.79015 −0.119958 −0.0599790 0.998200i \(-0.519103\pi\)
−0.0599790 + 0.998200i \(0.519103\pi\)
\(542\) −0.903316 −0.0388007
\(543\) 1.61698 0.0693913
\(544\) 0.609887 0.0261487
\(545\) 59.5235 2.54971
\(546\) −0.207743 −0.00889059
\(547\) 13.7464 0.587755 0.293877 0.955843i \(-0.405054\pi\)
0.293877 + 0.955843i \(0.405054\pi\)
\(548\) 41.4653 1.77131
\(549\) 10.8439 0.462807
\(550\) 2.86068 0.121980
\(551\) 5.89583 0.251171
\(552\) 0.529496 0.0225368
\(553\) 1.89285 0.0804922
\(554\) −0.751144 −0.0319131
\(555\) −24.8407 −1.05443
\(556\) 13.9817 0.592955
\(557\) 20.9519 0.887762 0.443881 0.896086i \(-0.353601\pi\)
0.443881 + 0.896086i \(0.353601\pi\)
\(558\) 0.0542410 0.00229621
\(559\) 22.0886 0.934248
\(560\) 29.8500 1.26139
\(561\) 5.26878 0.222448
\(562\) −1.64582 −0.0694248
\(563\) 42.8573 1.80622 0.903109 0.429411i \(-0.141279\pi\)
0.903109 + 0.429411i \(0.141279\pi\)
\(564\) −13.5736 −0.571553
\(565\) −5.83637 −0.245538
\(566\) −0.799570 −0.0336084
\(567\) 1.89285 0.0794923
\(568\) 0.129354 0.00542758
\(569\) 4.96177 0.208008 0.104004 0.994577i \(-0.466834\pi\)
0.104004 + 0.994577i \(0.466834\pi\)
\(570\) 0.661981 0.0277273
\(571\) 4.32863 0.181147 0.0905737 0.995890i \(-0.471130\pi\)
0.0905737 + 0.995890i \(0.471130\pi\)
\(572\) 22.6865 0.948571
\(573\) −8.53278 −0.356462
\(574\) 0.844617 0.0352536
\(575\) −27.7463 −1.15710
\(576\) −7.93786 −0.330744
\(577\) −40.8018 −1.69860 −0.849301 0.527909i \(-0.822976\pi\)
−0.849301 + 0.527909i \(0.822976\pi\)
\(578\) 0.0509119 0.00211765
\(579\) −21.0273 −0.873866
\(580\) −14.1874 −0.589099
\(581\) −24.4326 −1.01364
\(582\) 0.113671 0.00471183
\(583\) −36.0616 −1.49352
\(584\) 0.702714 0.0290785
\(585\) −8.53197 −0.352754
\(586\) −0.519893 −0.0214766
\(587\) −36.6535 −1.51285 −0.756427 0.654079i \(-0.773057\pi\)
−0.756427 + 0.654079i \(0.773057\pi\)
\(588\) 6.82537 0.281473
\(589\) 3.50007 0.144218
\(590\) −2.71086 −0.111604
\(591\) 18.1465 0.746446
\(592\) −25.0078 −1.02781
\(593\) 1.21468 0.0498807 0.0249404 0.999689i \(-0.492060\pi\)
0.0249404 + 0.999689i \(0.492060\pi\)
\(594\) 0.268243 0.0110062
\(595\) 7.49161 0.307126
\(596\) 5.03354 0.206182
\(597\) −8.58119 −0.351205
\(598\) 0.285545 0.0116768
\(599\) 10.0949 0.412466 0.206233 0.978503i \(-0.433879\pi\)
0.206233 + 0.978503i \(0.433879\pi\)
\(600\) −2.17039 −0.0886059
\(601\) −17.6006 −0.717943 −0.358972 0.933348i \(-0.616873\pi\)
−0.358972 + 0.933348i \(0.616873\pi\)
\(602\) −0.987444 −0.0402452
\(603\) 10.6925 0.435433
\(604\) −4.79285 −0.195018
\(605\) 66.3335 2.69684
\(606\) −0.392692 −0.0159520
\(607\) −7.07116 −0.287010 −0.143505 0.989650i \(-0.545837\pi\)
−0.143505 + 0.989650i \(0.545837\pi\)
\(608\) 2.00363 0.0812579
\(609\) 3.39698 0.137653
\(610\) 2.18506 0.0884704
\(611\) −14.6494 −0.592652
\(612\) −1.99741 −0.0807404
\(613\) −24.6259 −0.994631 −0.497315 0.867570i \(-0.665681\pi\)
−0.497315 + 0.867570i \(0.665681\pi\)
\(614\) −0.522436 −0.0210838
\(615\) 34.6883 1.39877
\(616\) −2.02966 −0.0817774
\(617\) −44.2311 −1.78068 −0.890338 0.455300i \(-0.849532\pi\)
−0.890338 + 0.455300i \(0.849532\pi\)
\(618\) 0.321082 0.0129158
\(619\) −21.7895 −0.875794 −0.437897 0.899025i \(-0.644277\pi\)
−0.437897 + 0.899025i \(0.644277\pi\)
\(620\) −8.42236 −0.338250
\(621\) −2.60175 −0.104404
\(622\) −0.156618 −0.00627979
\(623\) −13.0966 −0.524705
\(624\) −8.58934 −0.343849
\(625\) 35.4092 1.41637
\(626\) −0.345141 −0.0137946
\(627\) 17.3092 0.691264
\(628\) 14.2419 0.568315
\(629\) −6.27633 −0.250254
\(630\) 0.381412 0.0151958
\(631\) −16.6559 −0.663062 −0.331531 0.943444i \(-0.607565\pi\)
−0.331531 + 0.943444i \(0.607565\pi\)
\(632\) −0.203515 −0.00809541
\(633\) 24.2509 0.963885
\(634\) 1.41977 0.0563865
\(635\) −12.1566 −0.482419
\(636\) 13.6711 0.542093
\(637\) 7.36632 0.291864
\(638\) 0.481400 0.0190588
\(639\) −0.635598 −0.0251439
\(640\) −6.42716 −0.254056
\(641\) 39.3415 1.55390 0.776949 0.629564i \(-0.216766\pi\)
0.776949 + 0.629564i \(0.216766\pi\)
\(642\) −0.917875 −0.0362256
\(643\) −29.6872 −1.17075 −0.585374 0.810763i \(-0.699052\pi\)
−0.585374 + 0.810763i \(0.699052\pi\)
\(644\) 9.83667 0.387619
\(645\) −40.5542 −1.59682
\(646\) 0.167258 0.00658068
\(647\) 10.7626 0.423123 0.211562 0.977365i \(-0.432145\pi\)
0.211562 + 0.977365i \(0.432145\pi\)
\(648\) −0.203515 −0.00799484
\(649\) −70.8825 −2.78238
\(650\) −1.17044 −0.0459086
\(651\) 2.01663 0.0790378
\(652\) −18.3389 −0.718207
\(653\) −41.0151 −1.60505 −0.802523 0.596621i \(-0.796510\pi\)
−0.802523 + 0.596621i \(0.796510\pi\)
\(654\) 0.765683 0.0299406
\(655\) 29.3728 1.14769
\(656\) 34.9215 1.36346
\(657\) −3.45288 −0.134710
\(658\) 0.654885 0.0255301
\(659\) −41.0426 −1.59879 −0.799397 0.600804i \(-0.794847\pi\)
−0.799397 + 0.600804i \(0.794847\pi\)
\(660\) −41.6519 −1.62130
\(661\) −14.7998 −0.575645 −0.287822 0.957684i \(-0.592931\pi\)
−0.287822 + 0.957684i \(0.592931\pi\)
\(662\) 1.42632 0.0554353
\(663\) −2.15571 −0.0837210
\(664\) 2.62695 0.101945
\(665\) 24.6118 0.954404
\(666\) −0.319540 −0.0123819
\(667\) −4.66919 −0.180792
\(668\) −23.4523 −0.907397
\(669\) −9.47539 −0.366340
\(670\) 2.15456 0.0832378
\(671\) 57.1341 2.20564
\(672\) 1.15443 0.0445329
\(673\) 50.4582 1.94502 0.972510 0.232862i \(-0.0748092\pi\)
0.972510 + 0.232862i \(0.0748092\pi\)
\(674\) −1.33743 −0.0515158
\(675\) 10.6645 0.410477
\(676\) 16.6841 0.641698
\(677\) −16.6894 −0.641425 −0.320713 0.947177i \(-0.603922\pi\)
−0.320713 + 0.947177i \(0.603922\pi\)
\(678\) −0.0750764 −0.00288329
\(679\) 4.22619 0.162186
\(680\) −0.805482 −0.0308888
\(681\) −15.6787 −0.600811
\(682\) 0.285784 0.0109432
\(683\) 17.3496 0.663865 0.331932 0.943303i \(-0.392299\pi\)
0.331932 + 0.943303i \(0.392299\pi\)
\(684\) −6.56198 −0.250904
\(685\) −82.1631 −3.13929
\(686\) −1.00388 −0.0383284
\(687\) 18.9379 0.722528
\(688\) −40.8269 −1.55651
\(689\) 14.7546 0.562104
\(690\) −0.524255 −0.0199580
\(691\) −31.5049 −1.19850 −0.599251 0.800562i \(-0.704535\pi\)
−0.599251 + 0.800562i \(0.704535\pi\)
\(692\) 34.5879 1.31483
\(693\) 9.97301 0.378843
\(694\) −0.0734418 −0.00278781
\(695\) −27.7045 −1.05089
\(696\) −0.365237 −0.0138443
\(697\) 8.76444 0.331977
\(698\) 0.895562 0.0338975
\(699\) 28.1117 1.06328
\(700\) −40.3203 −1.52397
\(701\) −16.8050 −0.634715 −0.317357 0.948306i \(-0.602795\pi\)
−0.317357 + 0.948306i \(0.602795\pi\)
\(702\) −0.109751 −0.00414230
\(703\) −20.6193 −0.777672
\(704\) −41.8228 −1.57626
\(705\) 26.8960 1.01296
\(706\) 1.79524 0.0675646
\(707\) −14.5999 −0.549086
\(708\) 26.8717 1.00990
\(709\) −34.7618 −1.30551 −0.652753 0.757571i \(-0.726386\pi\)
−0.652753 + 0.757571i \(0.726386\pi\)
\(710\) −0.128074 −0.00480652
\(711\) 1.00000 0.0375029
\(712\) 1.40812 0.0527715
\(713\) −2.77188 −0.103808
\(714\) 0.0963686 0.00360650
\(715\) −44.9531 −1.68115
\(716\) −46.5157 −1.73837
\(717\) 24.0586 0.898484
\(718\) 1.40572 0.0524610
\(719\) 2.59739 0.0968663 0.0484332 0.998826i \(-0.484577\pi\)
0.0484332 + 0.998826i \(0.484577\pi\)
\(720\) 15.7698 0.587707
\(721\) 11.9375 0.444576
\(722\) −0.417841 −0.0155504
\(723\) 11.1814 0.415841
\(724\) −3.22977 −0.120034
\(725\) 19.1389 0.710802
\(726\) 0.853284 0.0316683
\(727\) 27.1767 1.00793 0.503964 0.863724i \(-0.331874\pi\)
0.503964 + 0.863724i \(0.331874\pi\)
\(728\) 0.830434 0.0307779
\(729\) 1.00000 0.0370370
\(730\) −0.695759 −0.0257512
\(731\) −10.2465 −0.378982
\(732\) −21.6597 −0.800565
\(733\) 11.0733 0.409001 0.204501 0.978866i \(-0.434443\pi\)
0.204501 + 0.978866i \(0.434443\pi\)
\(734\) −0.648617 −0.0239409
\(735\) −13.5244 −0.498855
\(736\) −1.58677 −0.0584891
\(737\) 56.3366 2.07518
\(738\) 0.446214 0.0164254
\(739\) 39.7289 1.46145 0.730725 0.682672i \(-0.239182\pi\)
0.730725 + 0.682672i \(0.239182\pi\)
\(740\) 49.6171 1.82396
\(741\) −7.08205 −0.260166
\(742\) −0.659585 −0.0242141
\(743\) 10.0844 0.369959 0.184980 0.982742i \(-0.440778\pi\)
0.184980 + 0.982742i \(0.440778\pi\)
\(744\) −0.216823 −0.00794913
\(745\) −9.97391 −0.365416
\(746\) 0.749064 0.0274252
\(747\) −12.9078 −0.472273
\(748\) −10.5239 −0.384792
\(749\) −34.1257 −1.24692
\(750\) 1.14140 0.0416782
\(751\) 13.6380 0.497659 0.248830 0.968547i \(-0.419954\pi\)
0.248830 + 0.968547i \(0.419954\pi\)
\(752\) 27.0769 0.987392
\(753\) 13.3467 0.486381
\(754\) −0.196964 −0.00717301
\(755\) 9.49698 0.345630
\(756\) −3.78080 −0.137506
\(757\) 4.64496 0.168824 0.0844119 0.996431i \(-0.473099\pi\)
0.0844119 + 0.996431i \(0.473099\pi\)
\(758\) 0.238495 0.00866251
\(759\) −13.7080 −0.497570
\(760\) −2.64621 −0.0959881
\(761\) 25.3506 0.918958 0.459479 0.888189i \(-0.348036\pi\)
0.459479 + 0.888189i \(0.348036\pi\)
\(762\) −0.156377 −0.00566492
\(763\) 28.4673 1.03059
\(764\) 17.0434 0.616610
\(765\) 3.95784 0.143096
\(766\) 1.38249 0.0499514
\(767\) 29.0015 1.04718
\(768\) 15.7930 0.569882
\(769\) 26.6305 0.960322 0.480161 0.877180i \(-0.340578\pi\)
0.480161 + 0.877180i \(0.340578\pi\)
\(770\) 2.00957 0.0724200
\(771\) 16.1906 0.583090
\(772\) 42.0001 1.51162
\(773\) −0.763296 −0.0274538 −0.0137269 0.999906i \(-0.504370\pi\)
−0.0137269 + 0.999906i \(0.504370\pi\)
\(774\) −0.521670 −0.0187510
\(775\) 11.3619 0.408130
\(776\) −0.454391 −0.0163117
\(777\) −11.8802 −0.426198
\(778\) −0.374257 −0.0134178
\(779\) 28.7934 1.03163
\(780\) 17.0418 0.610195
\(781\) −3.34883 −0.119830
\(782\) −0.132460 −0.00473675
\(783\) 1.79464 0.0641351
\(784\) −13.6153 −0.486262
\(785\) −28.2202 −1.00722
\(786\) 0.377838 0.0134770
\(787\) 11.1190 0.396351 0.198175 0.980167i \(-0.436498\pi\)
0.198175 + 0.980167i \(0.436498\pi\)
\(788\) −36.2459 −1.29121
\(789\) −17.8736 −0.636318
\(790\) 0.201501 0.00716909
\(791\) −2.79127 −0.0992460
\(792\) −1.07228 −0.0381017
\(793\) −23.3763 −0.830119
\(794\) 0.0950222 0.00337221
\(795\) −27.0890 −0.960749
\(796\) 17.1401 0.607516
\(797\) −46.4224 −1.64436 −0.822182 0.569224i \(-0.807244\pi\)
−0.822182 + 0.569224i \(0.807244\pi\)
\(798\) 0.316595 0.0112073
\(799\) 6.79563 0.240412
\(800\) 6.50415 0.229956
\(801\) −6.91898 −0.244470
\(802\) 0.793679 0.0280258
\(803\) −18.1924 −0.641998
\(804\) −21.3573 −0.753215
\(805\) −19.4913 −0.686977
\(806\) −0.116928 −0.00411862
\(807\) 15.7614 0.554829
\(808\) 1.56975 0.0552236
\(809\) −42.7065 −1.50148 −0.750741 0.660597i \(-0.770303\pi\)
−0.750741 + 0.660597i \(0.770303\pi\)
\(810\) 0.201501 0.00708003
\(811\) −28.4024 −0.997343 −0.498672 0.866791i \(-0.666179\pi\)
−0.498672 + 0.866791i \(0.666179\pi\)
\(812\) −6.78516 −0.238113
\(813\) −17.7427 −0.622265
\(814\) −1.68358 −0.0590096
\(815\) 36.3383 1.27288
\(816\) 3.98445 0.139484
\(817\) −33.6624 −1.17770
\(818\) 1.01139 0.0353626
\(819\) −4.08045 −0.142582
\(820\) −69.2866 −2.41959
\(821\) 17.2823 0.603156 0.301578 0.953441i \(-0.402487\pi\)
0.301578 + 0.953441i \(0.402487\pi\)
\(822\) −1.05691 −0.0368639
\(823\) −28.3635 −0.988688 −0.494344 0.869266i \(-0.664592\pi\)
−0.494344 + 0.869266i \(0.664592\pi\)
\(824\) −1.28350 −0.0447127
\(825\) 56.1889 1.95625
\(826\) −1.29648 −0.0451102
\(827\) 42.4452 1.47597 0.737983 0.674820i \(-0.235779\pi\)
0.737983 + 0.674820i \(0.235779\pi\)
\(828\) 5.19675 0.180599
\(829\) −32.3382 −1.12315 −0.561576 0.827425i \(-0.689805\pi\)
−0.561576 + 0.827425i \(0.689805\pi\)
\(830\) −2.60094 −0.0902801
\(831\) −14.7538 −0.511804
\(832\) 17.1118 0.593243
\(833\) −3.41711 −0.118396
\(834\) −0.356378 −0.0123404
\(835\) 46.4705 1.60818
\(836\) −34.5736 −1.19575
\(837\) 1.06539 0.0368253
\(838\) 1.26350 0.0436468
\(839\) 13.1367 0.453530 0.226765 0.973950i \(-0.427185\pi\)
0.226765 + 0.973950i \(0.427185\pi\)
\(840\) −1.52466 −0.0526057
\(841\) −25.7793 −0.888940
\(842\) 0.0483633 0.00166671
\(843\) −32.3269 −1.11340
\(844\) −48.4389 −1.66733
\(845\) −33.0595 −1.13728
\(846\) 0.345978 0.0118950
\(847\) 31.7242 1.09006
\(848\) −27.2712 −0.936496
\(849\) −15.7050 −0.538994
\(850\) 0.542950 0.0186230
\(851\) 16.3294 0.559765
\(852\) 1.26955 0.0434940
\(853\) −23.1614 −0.793030 −0.396515 0.918028i \(-0.629781\pi\)
−0.396515 + 0.918028i \(0.629781\pi\)
\(854\) 1.04501 0.0357596
\(855\) 13.0025 0.444676
\(856\) 3.66912 0.125408
\(857\) −20.1442 −0.688113 −0.344056 0.938949i \(-0.611801\pi\)
−0.344056 + 0.938949i \(0.611801\pi\)
\(858\) −0.578256 −0.0197413
\(859\) 9.63077 0.328598 0.164299 0.986411i \(-0.447464\pi\)
0.164299 + 0.986411i \(0.447464\pi\)
\(860\) 81.0032 2.76219
\(861\) 16.5898 0.565378
\(862\) −1.91650 −0.0652764
\(863\) 25.8298 0.879257 0.439629 0.898180i \(-0.355110\pi\)
0.439629 + 0.898180i \(0.355110\pi\)
\(864\) 0.609887 0.0207488
\(865\) −68.5355 −2.33028
\(866\) 1.36259 0.0463026
\(867\) 1.00000 0.0339618
\(868\) −4.02803 −0.136720
\(869\) 5.26878 0.178731
\(870\) 0.361622 0.0122601
\(871\) −23.0500 −0.781021
\(872\) −3.06075 −0.103650
\(873\) 2.23271 0.0755658
\(874\) −0.435163 −0.0147196
\(875\) 42.4363 1.43461
\(876\) 6.89681 0.233022
\(877\) −0.660738 −0.0223116 −0.0111558 0.999938i \(-0.503551\pi\)
−0.0111558 + 0.999938i \(0.503551\pi\)
\(878\) 1.85506 0.0626051
\(879\) −10.2116 −0.344430
\(880\) 83.0878 2.80089
\(881\) 25.7400 0.867203 0.433601 0.901105i \(-0.357243\pi\)
0.433601 + 0.901105i \(0.357243\pi\)
\(882\) −0.173972 −0.00585793
\(883\) 42.7441 1.43846 0.719228 0.694775i \(-0.244496\pi\)
0.719228 + 0.694775i \(0.244496\pi\)
\(884\) 4.30584 0.144821
\(885\) −53.2461 −1.78985
\(886\) 0.564599 0.0189681
\(887\) −41.2625 −1.38546 −0.692729 0.721198i \(-0.743592\pi\)
−0.692729 + 0.721198i \(0.743592\pi\)
\(888\) 1.27733 0.0428644
\(889\) −5.81392 −0.194993
\(890\) −1.39418 −0.0467331
\(891\) 5.26878 0.176511
\(892\) 18.9262 0.633697
\(893\) 22.3253 0.747089
\(894\) −0.128300 −0.00429099
\(895\) 92.1703 3.08091
\(896\) −3.07381 −0.102689
\(897\) 5.60862 0.187266
\(898\) −0.733311 −0.0244709
\(899\) 1.91199 0.0637685
\(900\) −21.3014 −0.710046
\(901\) −6.84440 −0.228020
\(902\) 2.35100 0.0782798
\(903\) −19.3952 −0.645431
\(904\) 0.300111 0.00998155
\(905\) 6.39976 0.212735
\(906\) 0.122165 0.00405865
\(907\) 16.0894 0.534241 0.267120 0.963663i \(-0.413928\pi\)
0.267120 + 0.963663i \(0.413928\pi\)
\(908\) 31.3168 1.03929
\(909\) −7.71317 −0.255830
\(910\) −0.822214 −0.0272561
\(911\) 36.7375 1.21717 0.608584 0.793489i \(-0.291738\pi\)
0.608584 + 0.793489i \(0.291738\pi\)
\(912\) 13.0899 0.433451
\(913\) −68.0086 −2.25075
\(914\) 0.128823 0.00426109
\(915\) 42.9185 1.41884
\(916\) −37.8268 −1.24983
\(917\) 14.0476 0.463894
\(918\) 0.0509119 0.00168034
\(919\) −3.82043 −0.126024 −0.0630122 0.998013i \(-0.520071\pi\)
−0.0630122 + 0.998013i \(0.520071\pi\)
\(920\) 2.09566 0.0690918
\(921\) −10.2616 −0.338131
\(922\) −1.33509 −0.0439688
\(923\) 1.37017 0.0450996
\(924\) −19.9202 −0.655326
\(925\) −66.9340 −2.20078
\(926\) −1.70375 −0.0559886
\(927\) 6.30662 0.207137
\(928\) 1.09453 0.0359296
\(929\) −27.1946 −0.892227 −0.446113 0.894976i \(-0.647192\pi\)
−0.446113 + 0.894976i \(0.647192\pi\)
\(930\) 0.214677 0.00703955
\(931\) −11.2261 −0.367919
\(932\) −56.1505 −1.83927
\(933\) −3.07625 −0.100712
\(934\) −0.437902 −0.0143286
\(935\) 20.8530 0.681966
\(936\) 0.438721 0.0143400
\(937\) 34.9947 1.14323 0.571613 0.820523i \(-0.306318\pi\)
0.571613 + 0.820523i \(0.306318\pi\)
\(938\) 1.03042 0.0336445
\(939\) −6.77918 −0.221230
\(940\) −53.7223 −1.75223
\(941\) −12.8381 −0.418509 −0.209255 0.977861i \(-0.567104\pi\)
−0.209255 + 0.977861i \(0.567104\pi\)
\(942\) −0.363012 −0.0118276
\(943\) −22.8028 −0.742563
\(944\) −53.6041 −1.74466
\(945\) 7.49161 0.243702
\(946\) −2.74856 −0.0893635
\(947\) 14.2263 0.462292 0.231146 0.972919i \(-0.425752\pi\)
0.231146 + 0.972919i \(0.425752\pi\)
\(948\) −1.99741 −0.0648728
\(949\) 7.44342 0.241624
\(950\) 1.78373 0.0578717
\(951\) 27.8869 0.904295
\(952\) −0.385225 −0.0124852
\(953\) −5.76547 −0.186762 −0.0933810 0.995630i \(-0.529767\pi\)
−0.0933810 + 0.995630i \(0.529767\pi\)
\(954\) −0.348461 −0.0112818
\(955\) −33.7714 −1.09282
\(956\) −48.0548 −1.55420
\(957\) 9.45555 0.305655
\(958\) −1.12415 −0.0363197
\(959\) −39.2948 −1.26889
\(960\) −31.4168 −1.01397
\(961\) −29.8649 −0.963385
\(962\) 0.688836 0.0222090
\(963\) −18.0287 −0.580967
\(964\) −22.3338 −0.719325
\(965\) −83.2228 −2.67904
\(966\) −0.250727 −0.00806700
\(967\) 44.3428 1.42597 0.712984 0.701181i \(-0.247343\pi\)
0.712984 + 0.701181i \(0.247343\pi\)
\(968\) −3.41092 −0.109631
\(969\) 3.28525 0.105537
\(970\) 0.449894 0.0144452
\(971\) 46.5023 1.49233 0.746165 0.665761i \(-0.231893\pi\)
0.746165 + 0.665761i \(0.231893\pi\)
\(972\) −1.99741 −0.0640669
\(973\) −13.2498 −0.424769
\(974\) −0.194802 −0.00624185
\(975\) −22.9896 −0.736257
\(976\) 43.2070 1.38302
\(977\) 1.00688 0.0322129 0.0161064 0.999870i \(-0.494873\pi\)
0.0161064 + 0.999870i \(0.494873\pi\)
\(978\) 0.467440 0.0149471
\(979\) −36.4546 −1.16509
\(980\) 27.0137 0.862922
\(981\) 15.0394 0.480170
\(982\) −0.914185 −0.0291728
\(983\) −7.22420 −0.230416 −0.115208 0.993341i \(-0.536753\pi\)
−0.115208 + 0.993341i \(0.536753\pi\)
\(984\) −1.78370 −0.0568622
\(985\) 71.8209 2.28840
\(986\) 0.0913684 0.00290976
\(987\) 12.8631 0.409438
\(988\) 14.1458 0.450036
\(989\) 26.6589 0.847703
\(990\) 1.06166 0.0337419
\(991\) −27.3165 −0.867738 −0.433869 0.900976i \(-0.642852\pi\)
−0.433869 + 0.900976i \(0.642852\pi\)
\(992\) 0.649768 0.0206301
\(993\) 28.0154 0.889041
\(994\) −0.0612517 −0.00194279
\(995\) −33.9630 −1.07670
\(996\) 25.7822 0.816941
\(997\) −36.6981 −1.16224 −0.581120 0.813818i \(-0.697385\pi\)
−0.581120 + 0.813818i \(0.697385\pi\)
\(998\) −1.06372 −0.0336713
\(999\) −6.27633 −0.198574
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.1.16 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.16 31 1.1 even 1 trivial