Properties

Label 4029.2.a.l.1.10
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 1.10
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.60231 q^{2} -1.00000 q^{3} +0.567397 q^{4} -0.489899 q^{5} +1.60231 q^{6} -0.574101 q^{7} +2.29547 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.60231 q^{2} -1.00000 q^{3} +0.567397 q^{4} -0.489899 q^{5} +1.60231 q^{6} -0.574101 q^{7} +2.29547 q^{8} +1.00000 q^{9} +0.784971 q^{10} -0.698667 q^{11} -0.567397 q^{12} +2.26250 q^{13} +0.919888 q^{14} +0.489899 q^{15} -4.81285 q^{16} -1.00000 q^{17} -1.60231 q^{18} +1.07352 q^{19} -0.277968 q^{20} +0.574101 q^{21} +1.11948 q^{22} -7.79211 q^{23} -2.29547 q^{24} -4.76000 q^{25} -3.62522 q^{26} -1.00000 q^{27} -0.325743 q^{28} +5.05791 q^{29} -0.784971 q^{30} +9.16611 q^{31} +3.12074 q^{32} +0.698667 q^{33} +1.60231 q^{34} +0.281252 q^{35} +0.567397 q^{36} -0.352965 q^{37} -1.72011 q^{38} -2.26250 q^{39} -1.12455 q^{40} +9.93207 q^{41} -0.919888 q^{42} +7.78761 q^{43} -0.396422 q^{44} -0.489899 q^{45} +12.4854 q^{46} +2.72064 q^{47} +4.81285 q^{48} -6.67041 q^{49} +7.62699 q^{50} +1.00000 q^{51} +1.28373 q^{52} -3.40047 q^{53} +1.60231 q^{54} +0.342277 q^{55} -1.31783 q^{56} -1.07352 q^{57} -8.10435 q^{58} -6.49490 q^{59} +0.277968 q^{60} -3.39102 q^{61} -14.6869 q^{62} -0.574101 q^{63} +4.62532 q^{64} -1.10840 q^{65} -1.11948 q^{66} +3.05135 q^{67} -0.567397 q^{68} +7.79211 q^{69} -0.450653 q^{70} +3.33996 q^{71} +2.29547 q^{72} -6.93796 q^{73} +0.565559 q^{74} +4.76000 q^{75} +0.609112 q^{76} +0.401106 q^{77} +3.62522 q^{78} +1.00000 q^{79} +2.35782 q^{80} +1.00000 q^{81} -15.9142 q^{82} -11.1415 q^{83} +0.325743 q^{84} +0.489899 q^{85} -12.4782 q^{86} -5.05791 q^{87} -1.60377 q^{88} -6.31600 q^{89} +0.784971 q^{90} -1.29890 q^{91} -4.42122 q^{92} -9.16611 q^{93} -4.35931 q^{94} -0.525917 q^{95} -3.12074 q^{96} -1.51033 q^{97} +10.6881 q^{98} -0.698667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.60231 −1.13300 −0.566502 0.824060i \(-0.691704\pi\)
−0.566502 + 0.824060i \(0.691704\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.567397 0.283699
\(5\) −0.489899 −0.219090 −0.109545 0.993982i \(-0.534939\pi\)
−0.109545 + 0.993982i \(0.534939\pi\)
\(6\) 1.60231 0.654140
\(7\) −0.574101 −0.216990 −0.108495 0.994097i \(-0.534603\pi\)
−0.108495 + 0.994097i \(0.534603\pi\)
\(8\) 2.29547 0.811573
\(9\) 1.00000 0.333333
\(10\) 0.784971 0.248230
\(11\) −0.698667 −0.210656 −0.105328 0.994438i \(-0.533589\pi\)
−0.105328 + 0.994438i \(0.533589\pi\)
\(12\) −0.567397 −0.163793
\(13\) 2.26250 0.627504 0.313752 0.949505i \(-0.398414\pi\)
0.313752 + 0.949505i \(0.398414\pi\)
\(14\) 0.919888 0.245850
\(15\) 0.489899 0.126492
\(16\) −4.81285 −1.20321
\(17\) −1.00000 −0.242536
\(18\) −1.60231 −0.377668
\(19\) 1.07352 0.246282 0.123141 0.992389i \(-0.460703\pi\)
0.123141 + 0.992389i \(0.460703\pi\)
\(20\) −0.277968 −0.0621554
\(21\) 0.574101 0.125279
\(22\) 1.11948 0.238674
\(23\) −7.79211 −1.62477 −0.812384 0.583123i \(-0.801831\pi\)
−0.812384 + 0.583123i \(0.801831\pi\)
\(24\) −2.29547 −0.468562
\(25\) −4.76000 −0.952000
\(26\) −3.62522 −0.710965
\(27\) −1.00000 −0.192450
\(28\) −0.325743 −0.0615597
\(29\) 5.05791 0.939231 0.469616 0.882871i \(-0.344393\pi\)
0.469616 + 0.882871i \(0.344393\pi\)
\(30\) −0.784971 −0.143315
\(31\) 9.16611 1.64628 0.823141 0.567838i \(-0.192220\pi\)
0.823141 + 0.567838i \(0.192220\pi\)
\(32\) 3.12074 0.551674
\(33\) 0.698667 0.121622
\(34\) 1.60231 0.274794
\(35\) 0.281252 0.0475402
\(36\) 0.567397 0.0945662
\(37\) −0.352965 −0.0580270 −0.0290135 0.999579i \(-0.509237\pi\)
−0.0290135 + 0.999579i \(0.509237\pi\)
\(38\) −1.72011 −0.279039
\(39\) −2.26250 −0.362290
\(40\) −1.12455 −0.177807
\(41\) 9.93207 1.55113 0.775564 0.631269i \(-0.217466\pi\)
0.775564 + 0.631269i \(0.217466\pi\)
\(42\) −0.919888 −0.141942
\(43\) 7.78761 1.18760 0.593800 0.804613i \(-0.297627\pi\)
0.593800 + 0.804613i \(0.297627\pi\)
\(44\) −0.396422 −0.0597628
\(45\) −0.489899 −0.0730299
\(46\) 12.4854 1.84087
\(47\) 2.72064 0.396847 0.198423 0.980116i \(-0.436418\pi\)
0.198423 + 0.980116i \(0.436418\pi\)
\(48\) 4.81285 0.694676
\(49\) −6.67041 −0.952915
\(50\) 7.62699 1.07862
\(51\) 1.00000 0.140028
\(52\) 1.28373 0.178022
\(53\) −3.40047 −0.467091 −0.233546 0.972346i \(-0.575033\pi\)
−0.233546 + 0.972346i \(0.575033\pi\)
\(54\) 1.60231 0.218047
\(55\) 0.342277 0.0461526
\(56\) −1.31783 −0.176103
\(57\) −1.07352 −0.142191
\(58\) −8.10435 −1.06415
\(59\) −6.49490 −0.845564 −0.422782 0.906231i \(-0.638946\pi\)
−0.422782 + 0.906231i \(0.638946\pi\)
\(60\) 0.277968 0.0358855
\(61\) −3.39102 −0.434176 −0.217088 0.976152i \(-0.569656\pi\)
−0.217088 + 0.976152i \(0.569656\pi\)
\(62\) −14.6869 −1.86524
\(63\) −0.574101 −0.0723299
\(64\) 4.62532 0.578165
\(65\) −1.10840 −0.137480
\(66\) −1.11948 −0.137799
\(67\) 3.05135 0.372781 0.186391 0.982476i \(-0.440321\pi\)
0.186391 + 0.982476i \(0.440321\pi\)
\(68\) −0.567397 −0.0688070
\(69\) 7.79211 0.938060
\(70\) −0.450653 −0.0538633
\(71\) 3.33996 0.396381 0.198190 0.980164i \(-0.436494\pi\)
0.198190 + 0.980164i \(0.436494\pi\)
\(72\) 2.29547 0.270524
\(73\) −6.93796 −0.812027 −0.406013 0.913867i \(-0.633081\pi\)
−0.406013 + 0.913867i \(0.633081\pi\)
\(74\) 0.565559 0.0657449
\(75\) 4.76000 0.549637
\(76\) 0.609112 0.0698700
\(77\) 0.401106 0.0457102
\(78\) 3.62522 0.410476
\(79\) 1.00000 0.112509
\(80\) 2.35782 0.263612
\(81\) 1.00000 0.111111
\(82\) −15.9142 −1.75743
\(83\) −11.1415 −1.22294 −0.611471 0.791267i \(-0.709422\pi\)
−0.611471 + 0.791267i \(0.709422\pi\)
\(84\) 0.325743 0.0355415
\(85\) 0.489899 0.0531371
\(86\) −12.4782 −1.34555
\(87\) −5.05791 −0.542265
\(88\) −1.60377 −0.170963
\(89\) −6.31600 −0.669494 −0.334747 0.942308i \(-0.608651\pi\)
−0.334747 + 0.942308i \(0.608651\pi\)
\(90\) 0.784971 0.0827432
\(91\) −1.29890 −0.136162
\(92\) −4.42122 −0.460944
\(93\) −9.16611 −0.950481
\(94\) −4.35931 −0.449629
\(95\) −0.525917 −0.0539579
\(96\) −3.12074 −0.318509
\(97\) −1.51033 −0.153351 −0.0766754 0.997056i \(-0.524431\pi\)
−0.0766754 + 0.997056i \(0.524431\pi\)
\(98\) 10.6881 1.07966
\(99\) −0.698667 −0.0702187
\(100\) −2.70081 −0.270081
\(101\) −11.9380 −1.18787 −0.593936 0.804512i \(-0.702427\pi\)
−0.593936 + 0.804512i \(0.702427\pi\)
\(102\) −1.60231 −0.158652
\(103\) −7.29866 −0.719158 −0.359579 0.933115i \(-0.617080\pi\)
−0.359579 + 0.933115i \(0.617080\pi\)
\(104\) 5.19351 0.509265
\(105\) −0.281252 −0.0274474
\(106\) 5.44861 0.529216
\(107\) −10.5574 −1.02062 −0.510309 0.859991i \(-0.670469\pi\)
−0.510309 + 0.859991i \(0.670469\pi\)
\(108\) −0.567397 −0.0545978
\(109\) 2.02361 0.193827 0.0969136 0.995293i \(-0.469103\pi\)
0.0969136 + 0.995293i \(0.469103\pi\)
\(110\) −0.548433 −0.0522911
\(111\) 0.352965 0.0335019
\(112\) 2.76306 0.261085
\(113\) 0.257584 0.0242315 0.0121157 0.999927i \(-0.496143\pi\)
0.0121157 + 0.999927i \(0.496143\pi\)
\(114\) 1.72011 0.161103
\(115\) 3.81735 0.355970
\(116\) 2.86985 0.266458
\(117\) 2.26250 0.209168
\(118\) 10.4068 0.958028
\(119\) 0.574101 0.0526278
\(120\) 1.12455 0.102657
\(121\) −10.5119 −0.955624
\(122\) 5.43347 0.491923
\(123\) −9.93207 −0.895544
\(124\) 5.20082 0.467048
\(125\) 4.78142 0.427663
\(126\) 0.919888 0.0819501
\(127\) 11.9765 1.06275 0.531373 0.847138i \(-0.321676\pi\)
0.531373 + 0.847138i \(0.321676\pi\)
\(128\) −13.6527 −1.20674
\(129\) −7.78761 −0.685661
\(130\) 1.77600 0.155765
\(131\) −12.0690 −1.05448 −0.527238 0.849717i \(-0.676773\pi\)
−0.527238 + 0.849717i \(0.676773\pi\)
\(132\) 0.396422 0.0345041
\(133\) −0.616309 −0.0534408
\(134\) −4.88920 −0.422363
\(135\) 0.489899 0.0421638
\(136\) −2.29547 −0.196835
\(137\) 15.3158 1.30852 0.654260 0.756270i \(-0.272980\pi\)
0.654260 + 0.756270i \(0.272980\pi\)
\(138\) −12.4854 −1.06283
\(139\) 17.0014 1.44204 0.721020 0.692914i \(-0.243674\pi\)
0.721020 + 0.692914i \(0.243674\pi\)
\(140\) 0.159581 0.0134871
\(141\) −2.72064 −0.229119
\(142\) −5.35166 −0.449101
\(143\) −1.58073 −0.132188
\(144\) −4.81285 −0.401071
\(145\) −2.47787 −0.205776
\(146\) 11.1168 0.920029
\(147\) 6.67041 0.550166
\(148\) −0.200271 −0.0164622
\(149\) 5.12625 0.419958 0.209979 0.977706i \(-0.432660\pi\)
0.209979 + 0.977706i \(0.432660\pi\)
\(150\) −7.62699 −0.622741
\(151\) 17.1238 1.39352 0.696759 0.717306i \(-0.254625\pi\)
0.696759 + 0.717306i \(0.254625\pi\)
\(152\) 2.46424 0.199876
\(153\) −1.00000 −0.0808452
\(154\) −0.642696 −0.0517899
\(155\) −4.49047 −0.360683
\(156\) −1.28373 −0.102781
\(157\) 6.71405 0.535840 0.267920 0.963441i \(-0.413664\pi\)
0.267920 + 0.963441i \(0.413664\pi\)
\(158\) −1.60231 −0.127473
\(159\) 3.40047 0.269675
\(160\) −1.52885 −0.120866
\(161\) 4.47346 0.352558
\(162\) −1.60231 −0.125889
\(163\) 16.8836 1.32243 0.661213 0.750198i \(-0.270042\pi\)
0.661213 + 0.750198i \(0.270042\pi\)
\(164\) 5.63543 0.440053
\(165\) −0.342277 −0.0266462
\(166\) 17.8522 1.38560
\(167\) 16.1012 1.24595 0.622974 0.782242i \(-0.285924\pi\)
0.622974 + 0.782242i \(0.285924\pi\)
\(168\) 1.31783 0.101673
\(169\) −7.88110 −0.606239
\(170\) −0.784971 −0.0602045
\(171\) 1.07352 0.0820941
\(172\) 4.41867 0.336920
\(173\) −4.66812 −0.354911 −0.177455 0.984129i \(-0.556787\pi\)
−0.177455 + 0.984129i \(0.556787\pi\)
\(174\) 8.10435 0.614389
\(175\) 2.73272 0.206574
\(176\) 3.36258 0.253464
\(177\) 6.49490 0.488187
\(178\) 10.1202 0.758540
\(179\) 11.8916 0.888817 0.444409 0.895824i \(-0.353414\pi\)
0.444409 + 0.895824i \(0.353414\pi\)
\(180\) −0.277968 −0.0207185
\(181\) 10.8727 0.808161 0.404080 0.914723i \(-0.367592\pi\)
0.404080 + 0.914723i \(0.367592\pi\)
\(182\) 2.08124 0.154272
\(183\) 3.39102 0.250672
\(184\) −17.8866 −1.31862
\(185\) 0.172917 0.0127131
\(186\) 14.6869 1.07690
\(187\) 0.698667 0.0510916
\(188\) 1.54368 0.112585
\(189\) 0.574101 0.0417597
\(190\) 0.842682 0.0611346
\(191\) −22.7980 −1.64960 −0.824802 0.565422i \(-0.808713\pi\)
−0.824802 + 0.565422i \(0.808713\pi\)
\(192\) −4.62532 −0.333804
\(193\) −0.849871 −0.0611751 −0.0305875 0.999532i \(-0.509738\pi\)
−0.0305875 + 0.999532i \(0.509738\pi\)
\(194\) 2.42002 0.173747
\(195\) 1.10840 0.0793739
\(196\) −3.78477 −0.270341
\(197\) −25.4230 −1.81131 −0.905657 0.424012i \(-0.860622\pi\)
−0.905657 + 0.424012i \(0.860622\pi\)
\(198\) 1.11948 0.0795581
\(199\) 20.6740 1.46554 0.732771 0.680476i \(-0.238227\pi\)
0.732771 + 0.680476i \(0.238227\pi\)
\(200\) −10.9265 −0.772617
\(201\) −3.05135 −0.215225
\(202\) 19.1283 1.34586
\(203\) −2.90375 −0.203804
\(204\) 0.567397 0.0397257
\(205\) −4.86571 −0.339836
\(206\) 11.6947 0.814809
\(207\) −7.79211 −0.541589
\(208\) −10.8891 −0.755022
\(209\) −0.750033 −0.0518809
\(210\) 0.450653 0.0310980
\(211\) −11.5984 −0.798467 −0.399233 0.916849i \(-0.630724\pi\)
−0.399233 + 0.916849i \(0.630724\pi\)
\(212\) −1.92942 −0.132513
\(213\) −3.33996 −0.228850
\(214\) 16.9162 1.15637
\(215\) −3.81515 −0.260191
\(216\) −2.29547 −0.156187
\(217\) −5.26227 −0.357226
\(218\) −3.24246 −0.219607
\(219\) 6.93796 0.468824
\(220\) 0.194207 0.0130934
\(221\) −2.26250 −0.152192
\(222\) −0.565559 −0.0379578
\(223\) −9.20846 −0.616644 −0.308322 0.951282i \(-0.599767\pi\)
−0.308322 + 0.951282i \(0.599767\pi\)
\(224\) −1.79162 −0.119708
\(225\) −4.76000 −0.317333
\(226\) −0.412730 −0.0274544
\(227\) −13.9762 −0.927632 −0.463816 0.885931i \(-0.653520\pi\)
−0.463816 + 0.885931i \(0.653520\pi\)
\(228\) −0.609112 −0.0403394
\(229\) 23.3438 1.54260 0.771301 0.636471i \(-0.219607\pi\)
0.771301 + 0.636471i \(0.219607\pi\)
\(230\) −6.11658 −0.403315
\(231\) −0.401106 −0.0263908
\(232\) 11.6103 0.762254
\(233\) 3.44550 0.225722 0.112861 0.993611i \(-0.463999\pi\)
0.112861 + 0.993611i \(0.463999\pi\)
\(234\) −3.62522 −0.236988
\(235\) −1.33284 −0.0869450
\(236\) −3.68519 −0.239885
\(237\) −1.00000 −0.0649570
\(238\) −0.919888 −0.0596275
\(239\) 19.8842 1.28620 0.643100 0.765782i \(-0.277648\pi\)
0.643100 + 0.765782i \(0.277648\pi\)
\(240\) −2.35782 −0.152196
\(241\) −7.29299 −0.469783 −0.234891 0.972022i \(-0.575473\pi\)
−0.234891 + 0.972022i \(0.575473\pi\)
\(242\) 16.8433 1.08273
\(243\) −1.00000 −0.0641500
\(244\) −1.92406 −0.123175
\(245\) 3.26783 0.208774
\(246\) 15.9142 1.01466
\(247\) 2.42884 0.154543
\(248\) 21.0406 1.33608
\(249\) 11.1415 0.706066
\(250\) −7.66131 −0.484544
\(251\) −10.1340 −0.639655 −0.319828 0.947476i \(-0.603625\pi\)
−0.319828 + 0.947476i \(0.603625\pi\)
\(252\) −0.325743 −0.0205199
\(253\) 5.44409 0.342267
\(254\) −19.1901 −1.20410
\(255\) −0.489899 −0.0306787
\(256\) 12.6252 0.789073
\(257\) 11.2550 0.702068 0.351034 0.936363i \(-0.385830\pi\)
0.351034 + 0.936363i \(0.385830\pi\)
\(258\) 12.4782 0.776856
\(259\) 0.202637 0.0125913
\(260\) −0.628901 −0.0390028
\(261\) 5.05791 0.313077
\(262\) 19.3383 1.19473
\(263\) 3.88146 0.239341 0.119670 0.992814i \(-0.461816\pi\)
0.119670 + 0.992814i \(0.461816\pi\)
\(264\) 1.60377 0.0987054
\(265\) 1.66589 0.102335
\(266\) 0.987518 0.0605486
\(267\) 6.31600 0.386533
\(268\) 1.73132 0.105757
\(269\) −15.9238 −0.970893 −0.485446 0.874266i \(-0.661343\pi\)
−0.485446 + 0.874266i \(0.661343\pi\)
\(270\) −0.784971 −0.0477718
\(271\) 21.9553 1.33369 0.666845 0.745197i \(-0.267644\pi\)
0.666845 + 0.745197i \(0.267644\pi\)
\(272\) 4.81285 0.291822
\(273\) 1.29890 0.0786132
\(274\) −24.5407 −1.48256
\(275\) 3.32566 0.200545
\(276\) 4.42122 0.266126
\(277\) 30.3549 1.82385 0.911925 0.410357i \(-0.134596\pi\)
0.911925 + 0.410357i \(0.134596\pi\)
\(278\) −27.2415 −1.63384
\(279\) 9.16611 0.548760
\(280\) 0.645606 0.0385823
\(281\) 8.60041 0.513057 0.256529 0.966537i \(-0.417421\pi\)
0.256529 + 0.966537i \(0.417421\pi\)
\(282\) 4.35931 0.259593
\(283\) 28.4638 1.69199 0.845997 0.533187i \(-0.179006\pi\)
0.845997 + 0.533187i \(0.179006\pi\)
\(284\) 1.89509 0.112453
\(285\) 0.525917 0.0311526
\(286\) 2.53283 0.149769
\(287\) −5.70201 −0.336579
\(288\) 3.12074 0.183891
\(289\) 1.00000 0.0588235
\(290\) 3.97031 0.233145
\(291\) 1.51033 0.0885371
\(292\) −3.93658 −0.230371
\(293\) 4.49834 0.262796 0.131398 0.991330i \(-0.458053\pi\)
0.131398 + 0.991330i \(0.458053\pi\)
\(294\) −10.6881 −0.623340
\(295\) 3.18185 0.185254
\(296\) −0.810221 −0.0470932
\(297\) 0.698667 0.0405408
\(298\) −8.21383 −0.475815
\(299\) −17.6296 −1.01955
\(300\) 2.70081 0.155931
\(301\) −4.47087 −0.257697
\(302\) −27.4377 −1.57886
\(303\) 11.9380 0.685819
\(304\) −5.16670 −0.296330
\(305\) 1.66126 0.0951235
\(306\) 1.60231 0.0915980
\(307\) 4.25804 0.243019 0.121510 0.992590i \(-0.461227\pi\)
0.121510 + 0.992590i \(0.461227\pi\)
\(308\) 0.227586 0.0129679
\(309\) 7.29866 0.415206
\(310\) 7.19513 0.408656
\(311\) 17.9692 1.01894 0.509469 0.860489i \(-0.329842\pi\)
0.509469 + 0.860489i \(0.329842\pi\)
\(312\) −5.19351 −0.294024
\(313\) 21.7435 1.22902 0.614508 0.788910i \(-0.289354\pi\)
0.614508 + 0.788910i \(0.289354\pi\)
\(314\) −10.7580 −0.607109
\(315\) 0.281252 0.0158467
\(316\) 0.567397 0.0319186
\(317\) −31.0138 −1.74191 −0.870955 0.491363i \(-0.836499\pi\)
−0.870955 + 0.491363i \(0.836499\pi\)
\(318\) −5.44861 −0.305543
\(319\) −3.53380 −0.197855
\(320\) −2.26594 −0.126670
\(321\) 10.5574 0.589254
\(322\) −7.16787 −0.399450
\(323\) −1.07352 −0.0597323
\(324\) 0.567397 0.0315221
\(325\) −10.7695 −0.597384
\(326\) −27.0528 −1.49832
\(327\) −2.02361 −0.111906
\(328\) 22.7988 1.25885
\(329\) −1.56192 −0.0861116
\(330\) 0.548433 0.0301903
\(331\) 35.6022 1.95687 0.978436 0.206548i \(-0.0662231\pi\)
0.978436 + 0.206548i \(0.0662231\pi\)
\(332\) −6.32167 −0.346947
\(333\) −0.352965 −0.0193423
\(334\) −25.7991 −1.41166
\(335\) −1.49485 −0.0816725
\(336\) −2.76306 −0.150738
\(337\) −10.8761 −0.592461 −0.296230 0.955117i \(-0.595730\pi\)
−0.296230 + 0.955117i \(0.595730\pi\)
\(338\) 12.6280 0.686871
\(339\) −0.257584 −0.0139901
\(340\) 0.277968 0.0150749
\(341\) −6.40406 −0.346799
\(342\) −1.72011 −0.0930130
\(343\) 7.84820 0.423763
\(344\) 17.8763 0.963823
\(345\) −3.81735 −0.205519
\(346\) 7.47978 0.402115
\(347\) 10.2697 0.551304 0.275652 0.961257i \(-0.411106\pi\)
0.275652 + 0.961257i \(0.411106\pi\)
\(348\) −2.86985 −0.153840
\(349\) 18.4409 0.987120 0.493560 0.869712i \(-0.335695\pi\)
0.493560 + 0.869712i \(0.335695\pi\)
\(350\) −4.37866 −0.234049
\(351\) −2.26250 −0.120763
\(352\) −2.18036 −0.116213
\(353\) 5.30021 0.282101 0.141051 0.990002i \(-0.454952\pi\)
0.141051 + 0.990002i \(0.454952\pi\)
\(354\) −10.4068 −0.553118
\(355\) −1.63625 −0.0868429
\(356\) −3.58368 −0.189935
\(357\) −0.574101 −0.0303846
\(358\) −19.0540 −1.00703
\(359\) 32.2104 1.70000 0.849999 0.526784i \(-0.176602\pi\)
0.849999 + 0.526784i \(0.176602\pi\)
\(360\) −1.12455 −0.0592691
\(361\) −17.8476 −0.939345
\(362\) −17.4214 −0.915650
\(363\) 10.5119 0.551730
\(364\) −0.736994 −0.0386290
\(365\) 3.39890 0.177907
\(366\) −5.43347 −0.284012
\(367\) −27.3496 −1.42764 −0.713818 0.700331i \(-0.753036\pi\)
−0.713818 + 0.700331i \(0.753036\pi\)
\(368\) 37.5023 1.95494
\(369\) 9.93207 0.517043
\(370\) −0.277067 −0.0144040
\(371\) 1.95222 0.101354
\(372\) −5.20082 −0.269650
\(373\) −20.7592 −1.07487 −0.537435 0.843305i \(-0.680607\pi\)
−0.537435 + 0.843305i \(0.680607\pi\)
\(374\) −1.11948 −0.0578870
\(375\) −4.78142 −0.246911
\(376\) 6.24516 0.322070
\(377\) 11.4435 0.589371
\(378\) −0.919888 −0.0473139
\(379\) 25.8674 1.32872 0.664359 0.747414i \(-0.268705\pi\)
0.664359 + 0.747414i \(0.268705\pi\)
\(380\) −0.298404 −0.0153078
\(381\) −11.9765 −0.613576
\(382\) 36.5294 1.86901
\(383\) 32.3795 1.65451 0.827257 0.561824i \(-0.189900\pi\)
0.827257 + 0.561824i \(0.189900\pi\)
\(384\) 13.6527 0.696710
\(385\) −0.196501 −0.0100146
\(386\) 1.36176 0.0693116
\(387\) 7.78761 0.395866
\(388\) −0.856957 −0.0435054
\(389\) −0.907985 −0.0460367 −0.0230183 0.999735i \(-0.507328\pi\)
−0.0230183 + 0.999735i \(0.507328\pi\)
\(390\) −1.77600 −0.0899310
\(391\) 7.79211 0.394064
\(392\) −15.3117 −0.773360
\(393\) 12.0690 0.608803
\(394\) 40.7355 2.05223
\(395\) −0.489899 −0.0246495
\(396\) −0.396422 −0.0199209
\(397\) −18.5764 −0.932323 −0.466161 0.884700i \(-0.654363\pi\)
−0.466161 + 0.884700i \(0.654363\pi\)
\(398\) −33.1262 −1.66046
\(399\) 0.616309 0.0308540
\(400\) 22.9092 1.14546
\(401\) 0.0418962 0.00209219 0.00104610 0.999999i \(-0.499667\pi\)
0.00104610 + 0.999999i \(0.499667\pi\)
\(402\) 4.88920 0.243851
\(403\) 20.7383 1.03305
\(404\) −6.77357 −0.336998
\(405\) −0.489899 −0.0243433
\(406\) 4.65271 0.230910
\(407\) 0.246605 0.0122238
\(408\) 2.29547 0.113643
\(409\) 27.7478 1.37204 0.686019 0.727583i \(-0.259356\pi\)
0.686019 + 0.727583i \(0.259356\pi\)
\(410\) 7.79638 0.385036
\(411\) −15.3158 −0.755474
\(412\) −4.14124 −0.204024
\(413\) 3.72873 0.183479
\(414\) 12.4854 0.613623
\(415\) 5.45823 0.267934
\(416\) 7.06066 0.346177
\(417\) −17.0014 −0.832562
\(418\) 1.20179 0.0587813
\(419\) 16.1724 0.790074 0.395037 0.918665i \(-0.370732\pi\)
0.395037 + 0.918665i \(0.370732\pi\)
\(420\) −0.159581 −0.00778678
\(421\) 16.4390 0.801190 0.400595 0.916255i \(-0.368803\pi\)
0.400595 + 0.916255i \(0.368803\pi\)
\(422\) 18.5842 0.904666
\(423\) 2.72064 0.132282
\(424\) −7.80570 −0.379078
\(425\) 4.76000 0.230894
\(426\) 5.35166 0.259289
\(427\) 1.94679 0.0942117
\(428\) −5.99022 −0.289548
\(429\) 1.58073 0.0763185
\(430\) 6.11305 0.294797
\(431\) −16.5452 −0.796956 −0.398478 0.917178i \(-0.630462\pi\)
−0.398478 + 0.917178i \(0.630462\pi\)
\(432\) 4.81285 0.231559
\(433\) 2.68854 0.129203 0.0646016 0.997911i \(-0.479422\pi\)
0.0646016 + 0.997911i \(0.479422\pi\)
\(434\) 8.43179 0.404739
\(435\) 2.47787 0.118805
\(436\) 1.14819 0.0549885
\(437\) −8.36499 −0.400152
\(438\) −11.1168 −0.531179
\(439\) −39.4729 −1.88394 −0.941970 0.335696i \(-0.891028\pi\)
−0.941970 + 0.335696i \(0.891028\pi\)
\(440\) 0.785687 0.0374562
\(441\) −6.67041 −0.317638
\(442\) 3.62522 0.172434
\(443\) 8.90882 0.423271 0.211635 0.977349i \(-0.432121\pi\)
0.211635 + 0.977349i \(0.432121\pi\)
\(444\) 0.200271 0.00950445
\(445\) 3.09420 0.146679
\(446\) 14.7548 0.698660
\(447\) −5.12625 −0.242463
\(448\) −2.65540 −0.125456
\(449\) 6.53782 0.308539 0.154269 0.988029i \(-0.450698\pi\)
0.154269 + 0.988029i \(0.450698\pi\)
\(450\) 7.62699 0.359540
\(451\) −6.93921 −0.326755
\(452\) 0.146153 0.00687444
\(453\) −17.1238 −0.804547
\(454\) 22.3942 1.05101
\(455\) 0.636332 0.0298317
\(456\) −2.46424 −0.115398
\(457\) −3.87714 −0.181365 −0.0906824 0.995880i \(-0.528905\pi\)
−0.0906824 + 0.995880i \(0.528905\pi\)
\(458\) −37.4040 −1.74777
\(459\) 1.00000 0.0466760
\(460\) 2.16595 0.100988
\(461\) 4.35167 0.202678 0.101339 0.994852i \(-0.467687\pi\)
0.101339 + 0.994852i \(0.467687\pi\)
\(462\) 0.642696 0.0299009
\(463\) 30.2355 1.40516 0.702582 0.711603i \(-0.252030\pi\)
0.702582 + 0.711603i \(0.252030\pi\)
\(464\) −24.3430 −1.13010
\(465\) 4.49047 0.208241
\(466\) −5.52075 −0.255744
\(467\) 34.5291 1.59781 0.798907 0.601454i \(-0.205412\pi\)
0.798907 + 0.601454i \(0.205412\pi\)
\(468\) 1.28373 0.0593407
\(469\) −1.75178 −0.0808897
\(470\) 2.13563 0.0985090
\(471\) −6.71405 −0.309367
\(472\) −14.9089 −0.686237
\(473\) −5.44095 −0.250175
\(474\) 1.60231 0.0735965
\(475\) −5.10995 −0.234461
\(476\) 0.325743 0.0149304
\(477\) −3.40047 −0.155697
\(478\) −31.8606 −1.45727
\(479\) −19.6477 −0.897728 −0.448864 0.893600i \(-0.648171\pi\)
−0.448864 + 0.893600i \(0.648171\pi\)
\(480\) 1.52885 0.0697820
\(481\) −0.798582 −0.0364122
\(482\) 11.6856 0.532266
\(483\) −4.47346 −0.203549
\(484\) −5.96440 −0.271109
\(485\) 0.739910 0.0335976
\(486\) 1.60231 0.0726823
\(487\) 21.2907 0.964775 0.482387 0.875958i \(-0.339770\pi\)
0.482387 + 0.875958i \(0.339770\pi\)
\(488\) −7.78400 −0.352365
\(489\) −16.8836 −0.763504
\(490\) −5.23608 −0.236542
\(491\) −32.7613 −1.47850 −0.739248 0.673433i \(-0.764819\pi\)
−0.739248 + 0.673433i \(0.764819\pi\)
\(492\) −5.63543 −0.254065
\(493\) −5.05791 −0.227797
\(494\) −3.89175 −0.175098
\(495\) 0.342277 0.0153842
\(496\) −44.1151 −1.98083
\(497\) −1.91748 −0.0860106
\(498\) −17.8522 −0.799976
\(499\) −3.55771 −0.159265 −0.0796326 0.996824i \(-0.525375\pi\)
−0.0796326 + 0.996824i \(0.525375\pi\)
\(500\) 2.71296 0.121327
\(501\) −16.1012 −0.719349
\(502\) 16.2379 0.724732
\(503\) −36.8868 −1.64470 −0.822350 0.568981i \(-0.807338\pi\)
−0.822350 + 0.568981i \(0.807338\pi\)
\(504\) −1.31783 −0.0587010
\(505\) 5.84841 0.260251
\(506\) −8.72313 −0.387790
\(507\) 7.88110 0.350012
\(508\) 6.79545 0.301499
\(509\) 34.0191 1.50787 0.753936 0.656948i \(-0.228153\pi\)
0.753936 + 0.656948i \(0.228153\pi\)
\(510\) 0.784971 0.0347591
\(511\) 3.98309 0.176201
\(512\) 7.07591 0.312714
\(513\) −1.07352 −0.0473971
\(514\) −18.0340 −0.795447
\(515\) 3.57561 0.157560
\(516\) −4.41867 −0.194521
\(517\) −1.90082 −0.0835982
\(518\) −0.324688 −0.0142660
\(519\) 4.66812 0.204908
\(520\) −2.54430 −0.111575
\(521\) −12.6791 −0.555482 −0.277741 0.960656i \(-0.589586\pi\)
−0.277741 + 0.960656i \(0.589586\pi\)
\(522\) −8.10435 −0.354718
\(523\) −14.3810 −0.628839 −0.314420 0.949284i \(-0.601810\pi\)
−0.314420 + 0.949284i \(0.601810\pi\)
\(524\) −6.84794 −0.299154
\(525\) −2.73272 −0.119266
\(526\) −6.21929 −0.271174
\(527\) −9.16611 −0.399282
\(528\) −3.36258 −0.146338
\(529\) 37.7170 1.63987
\(530\) −2.66927 −0.115946
\(531\) −6.49490 −0.281855
\(532\) −0.349692 −0.0151611
\(533\) 22.4713 0.973339
\(534\) −10.1202 −0.437943
\(535\) 5.17205 0.223607
\(536\) 7.00428 0.302539
\(537\) −11.8916 −0.513159
\(538\) 25.5149 1.10003
\(539\) 4.66040 0.200737
\(540\) 0.277968 0.0119618
\(541\) −2.38103 −0.102368 −0.0511842 0.998689i \(-0.516300\pi\)
−0.0511842 + 0.998689i \(0.516300\pi\)
\(542\) −35.1792 −1.51108
\(543\) −10.8727 −0.466592
\(544\) −3.12074 −0.133800
\(545\) −0.991368 −0.0424655
\(546\) −2.08124 −0.0890690
\(547\) −18.1173 −0.774640 −0.387320 0.921945i \(-0.626599\pi\)
−0.387320 + 0.921945i \(0.626599\pi\)
\(548\) 8.69016 0.371225
\(549\) −3.39102 −0.144725
\(550\) −5.32873 −0.227218
\(551\) 5.42977 0.231316
\(552\) 17.8866 0.761304
\(553\) −0.574101 −0.0244133
\(554\) −48.6380 −2.06643
\(555\) −0.172917 −0.00733993
\(556\) 9.64654 0.409105
\(557\) 31.9345 1.35311 0.676555 0.736392i \(-0.263472\pi\)
0.676555 + 0.736392i \(0.263472\pi\)
\(558\) −14.6869 −0.621748
\(559\) 17.6195 0.745223
\(560\) −1.35362 −0.0572011
\(561\) −0.698667 −0.0294978
\(562\) −13.7805 −0.581296
\(563\) 12.1716 0.512970 0.256485 0.966548i \(-0.417436\pi\)
0.256485 + 0.966548i \(0.417436\pi\)
\(564\) −1.54368 −0.0650008
\(565\) −0.126190 −0.00530887
\(566\) −45.6078 −1.91704
\(567\) −0.574101 −0.0241100
\(568\) 7.66680 0.321692
\(569\) −1.16814 −0.0489710 −0.0244855 0.999700i \(-0.507795\pi\)
−0.0244855 + 0.999700i \(0.507795\pi\)
\(570\) −0.842682 −0.0352961
\(571\) −4.92214 −0.205985 −0.102993 0.994682i \(-0.532842\pi\)
−0.102993 + 0.994682i \(0.532842\pi\)
\(572\) −0.896904 −0.0375014
\(573\) 22.7980 0.952399
\(574\) 9.13639 0.381345
\(575\) 37.0904 1.54678
\(576\) 4.62532 0.192722
\(577\) −2.56160 −0.106641 −0.0533205 0.998577i \(-0.516980\pi\)
−0.0533205 + 0.998577i \(0.516980\pi\)
\(578\) −1.60231 −0.0666473
\(579\) 0.849871 0.0353194
\(580\) −1.40594 −0.0583783
\(581\) 6.39637 0.265366
\(582\) −2.42002 −0.100313
\(583\) 2.37580 0.0983956
\(584\) −15.9259 −0.659018
\(585\) −1.10840 −0.0458266
\(586\) −7.20773 −0.297749
\(587\) 29.4450 1.21533 0.607663 0.794195i \(-0.292107\pi\)
0.607663 + 0.794195i \(0.292107\pi\)
\(588\) 3.78477 0.156081
\(589\) 9.84000 0.405450
\(590\) −5.09831 −0.209894
\(591\) 25.4230 1.04576
\(592\) 1.69877 0.0698189
\(593\) −2.63492 −0.108203 −0.0541015 0.998535i \(-0.517229\pi\)
−0.0541015 + 0.998535i \(0.517229\pi\)
\(594\) −1.11948 −0.0459329
\(595\) −0.281252 −0.0115302
\(596\) 2.90862 0.119142
\(597\) −20.6740 −0.846131
\(598\) 28.2481 1.15515
\(599\) 11.2767 0.460754 0.230377 0.973101i \(-0.426004\pi\)
0.230377 + 0.973101i \(0.426004\pi\)
\(600\) 10.9265 0.446071
\(601\) −17.2047 −0.701793 −0.350896 0.936414i \(-0.614123\pi\)
−0.350896 + 0.936414i \(0.614123\pi\)
\(602\) 7.16373 0.291972
\(603\) 3.05135 0.124260
\(604\) 9.71601 0.395339
\(605\) 5.14976 0.209367
\(606\) −19.1283 −0.777035
\(607\) −4.81057 −0.195255 −0.0976275 0.995223i \(-0.531125\pi\)
−0.0976275 + 0.995223i \(0.531125\pi\)
\(608\) 3.35017 0.135867
\(609\) 2.90375 0.117666
\(610\) −2.66185 −0.107775
\(611\) 6.15545 0.249023
\(612\) −0.567397 −0.0229357
\(613\) 35.0556 1.41588 0.707941 0.706272i \(-0.249624\pi\)
0.707941 + 0.706272i \(0.249624\pi\)
\(614\) −6.82270 −0.275342
\(615\) 4.86571 0.196205
\(616\) 0.920728 0.0370972
\(617\) 37.0697 1.49237 0.746184 0.665739i \(-0.231884\pi\)
0.746184 + 0.665739i \(0.231884\pi\)
\(618\) −11.6947 −0.470430
\(619\) −34.6064 −1.39095 −0.695474 0.718551i \(-0.744805\pi\)
−0.695474 + 0.718551i \(0.744805\pi\)
\(620\) −2.54788 −0.102325
\(621\) 7.79211 0.312687
\(622\) −28.7922 −1.15446
\(623\) 3.62602 0.145273
\(624\) 10.8891 0.435912
\(625\) 21.4576 0.858303
\(626\) −34.8399 −1.39248
\(627\) 0.750033 0.0299534
\(628\) 3.80953 0.152017
\(629\) 0.352965 0.0140736
\(630\) −0.450653 −0.0179544
\(631\) 45.6281 1.81643 0.908214 0.418506i \(-0.137446\pi\)
0.908214 + 0.418506i \(0.137446\pi\)
\(632\) 2.29547 0.0913090
\(633\) 11.5984 0.460995
\(634\) 49.6938 1.97359
\(635\) −5.86730 −0.232837
\(636\) 1.92942 0.0765064
\(637\) −15.0918 −0.597958
\(638\) 5.66224 0.224170
\(639\) 3.33996 0.132127
\(640\) 6.68844 0.264384
\(641\) 14.8843 0.587895 0.293948 0.955822i \(-0.405031\pi\)
0.293948 + 0.955822i \(0.405031\pi\)
\(642\) −16.9162 −0.667628
\(643\) −10.4041 −0.410298 −0.205149 0.978731i \(-0.565768\pi\)
−0.205149 + 0.978731i \(0.565768\pi\)
\(644\) 2.53823 0.100020
\(645\) 3.81515 0.150221
\(646\) 1.72011 0.0676769
\(647\) −24.1055 −0.947686 −0.473843 0.880609i \(-0.657133\pi\)
−0.473843 + 0.880609i \(0.657133\pi\)
\(648\) 2.29547 0.0901747
\(649\) 4.53778 0.178123
\(650\) 17.2561 0.676838
\(651\) 5.26227 0.206245
\(652\) 9.57971 0.375171
\(653\) 21.4039 0.837599 0.418799 0.908079i \(-0.362451\pi\)
0.418799 + 0.908079i \(0.362451\pi\)
\(654\) 3.24246 0.126790
\(655\) 5.91262 0.231025
\(656\) −47.8016 −1.86634
\(657\) −6.93796 −0.270676
\(658\) 2.50269 0.0975648
\(659\) 18.7219 0.729300 0.364650 0.931145i \(-0.381189\pi\)
0.364650 + 0.931145i \(0.381189\pi\)
\(660\) −0.194207 −0.00755949
\(661\) 33.8495 1.31659 0.658297 0.752758i \(-0.271277\pi\)
0.658297 + 0.752758i \(0.271277\pi\)
\(662\) −57.0457 −2.21715
\(663\) 2.26250 0.0878682
\(664\) −25.5751 −0.992506
\(665\) 0.301929 0.0117083
\(666\) 0.565559 0.0219150
\(667\) −39.4118 −1.52603
\(668\) 9.13578 0.353474
\(669\) 9.20846 0.356019
\(670\) 2.39522 0.0925353
\(671\) 2.36920 0.0914618
\(672\) 1.79162 0.0691132
\(673\) −27.9586 −1.07773 −0.538863 0.842393i \(-0.681146\pi\)
−0.538863 + 0.842393i \(0.681146\pi\)
\(674\) 17.4269 0.671260
\(675\) 4.76000 0.183212
\(676\) −4.47171 −0.171989
\(677\) −23.1635 −0.890246 −0.445123 0.895469i \(-0.646840\pi\)
−0.445123 + 0.895469i \(0.646840\pi\)
\(678\) 0.412730 0.0158508
\(679\) 0.867082 0.0332755
\(680\) 1.12455 0.0431246
\(681\) 13.9762 0.535569
\(682\) 10.2613 0.392925
\(683\) −5.61775 −0.214957 −0.107479 0.994207i \(-0.534278\pi\)
−0.107479 + 0.994207i \(0.534278\pi\)
\(684\) 0.609112 0.0232900
\(685\) −7.50322 −0.286683
\(686\) −12.5752 −0.480125
\(687\) −23.3438 −0.890621
\(688\) −37.4806 −1.42894
\(689\) −7.69357 −0.293102
\(690\) 6.11658 0.232854
\(691\) 18.5513 0.705725 0.352862 0.935675i \(-0.385208\pi\)
0.352862 + 0.935675i \(0.385208\pi\)
\(692\) −2.64868 −0.100688
\(693\) 0.401106 0.0152367
\(694\) −16.4552 −0.624630
\(695\) −8.32898 −0.315936
\(696\) −11.6103 −0.440088
\(697\) −9.93207 −0.376204
\(698\) −29.5481 −1.11841
\(699\) −3.44550 −0.130321
\(700\) 1.55054 0.0586048
\(701\) 11.7218 0.442728 0.221364 0.975191i \(-0.428949\pi\)
0.221364 + 0.975191i \(0.428949\pi\)
\(702\) 3.62522 0.136825
\(703\) −0.378915 −0.0142910
\(704\) −3.23156 −0.121794
\(705\) 1.33284 0.0501977
\(706\) −8.49257 −0.319622
\(707\) 6.85360 0.257756
\(708\) 3.68519 0.138498
\(709\) 18.9333 0.711054 0.355527 0.934666i \(-0.384301\pi\)
0.355527 + 0.934666i \(0.384301\pi\)
\(710\) 2.62177 0.0983934
\(711\) 1.00000 0.0375029
\(712\) −14.4982 −0.543343
\(713\) −71.4233 −2.67482
\(714\) 0.919888 0.0344259
\(715\) 0.774401 0.0289609
\(716\) 6.74724 0.252156
\(717\) −19.8842 −0.742588
\(718\) −51.6110 −1.92611
\(719\) 11.4781 0.428061 0.214030 0.976827i \(-0.431341\pi\)
0.214030 + 0.976827i \(0.431341\pi\)
\(720\) 2.35782 0.0878706
\(721\) 4.19017 0.156050
\(722\) 28.5973 1.06428
\(723\) 7.29299 0.271229
\(724\) 6.16913 0.229274
\(725\) −24.0757 −0.894148
\(726\) −16.8433 −0.625112
\(727\) 38.8740 1.44176 0.720879 0.693061i \(-0.243738\pi\)
0.720879 + 0.693061i \(0.243738\pi\)
\(728\) −2.98160 −0.110505
\(729\) 1.00000 0.0370370
\(730\) −5.44609 −0.201569
\(731\) −7.78761 −0.288035
\(732\) 1.92406 0.0711151
\(733\) −15.8870 −0.586800 −0.293400 0.955990i \(-0.594787\pi\)
−0.293400 + 0.955990i \(0.594787\pi\)
\(734\) 43.8225 1.61752
\(735\) −3.26783 −0.120536
\(736\) −24.3171 −0.896341
\(737\) −2.13188 −0.0785286
\(738\) −15.9142 −0.585812
\(739\) 25.8495 0.950889 0.475445 0.879746i \(-0.342287\pi\)
0.475445 + 0.879746i \(0.342287\pi\)
\(740\) 0.0981127 0.00360670
\(741\) −2.42884 −0.0892256
\(742\) −3.12805 −0.114835
\(743\) 35.0359 1.28534 0.642671 0.766142i \(-0.277826\pi\)
0.642671 + 0.766142i \(0.277826\pi\)
\(744\) −21.0406 −0.771384
\(745\) −2.51134 −0.0920086
\(746\) 33.2626 1.21783
\(747\) −11.1415 −0.407647
\(748\) 0.396422 0.0144946
\(749\) 6.06099 0.221464
\(750\) 7.66131 0.279752
\(751\) 22.2508 0.811944 0.405972 0.913885i \(-0.366933\pi\)
0.405972 + 0.913885i \(0.366933\pi\)
\(752\) −13.0941 −0.477491
\(753\) 10.1340 0.369305
\(754\) −18.3361 −0.667760
\(755\) −8.38895 −0.305305
\(756\) 0.325743 0.0118472
\(757\) −54.7133 −1.98859 −0.994295 0.106669i \(-0.965981\pi\)
−0.994295 + 0.106669i \(0.965981\pi\)
\(758\) −41.4475 −1.50544
\(759\) −5.44409 −0.197608
\(760\) −1.20723 −0.0437908
\(761\) 22.0158 0.798073 0.399036 0.916935i \(-0.369345\pi\)
0.399036 + 0.916935i \(0.369345\pi\)
\(762\) 19.1901 0.695185
\(763\) −1.16176 −0.0420585
\(764\) −12.9355 −0.467990
\(765\) 0.489899 0.0177124
\(766\) −51.8819 −1.87457
\(767\) −14.6947 −0.530595
\(768\) −12.6252 −0.455572
\(769\) 18.0810 0.652017 0.326008 0.945367i \(-0.394296\pi\)
0.326008 + 0.945367i \(0.394296\pi\)
\(770\) 0.314856 0.0113466
\(771\) −11.2550 −0.405339
\(772\) −0.482214 −0.0173553
\(773\) 12.6102 0.453557 0.226779 0.973946i \(-0.427181\pi\)
0.226779 + 0.973946i \(0.427181\pi\)
\(774\) −12.4782 −0.448518
\(775\) −43.6306 −1.56726
\(776\) −3.46692 −0.124455
\(777\) −0.202637 −0.00726958
\(778\) 1.45487 0.0521597
\(779\) 10.6623 0.382016
\(780\) 0.628901 0.0225183
\(781\) −2.33352 −0.0835000
\(782\) −12.4854 −0.446476
\(783\) −5.05791 −0.180755
\(784\) 32.1037 1.14656
\(785\) −3.28921 −0.117397
\(786\) −19.3383 −0.689776
\(787\) 52.8292 1.88316 0.941578 0.336795i \(-0.109343\pi\)
0.941578 + 0.336795i \(0.109343\pi\)
\(788\) −14.4249 −0.513867
\(789\) −3.88146 −0.138183
\(790\) 0.784971 0.0279280
\(791\) −0.147879 −0.00525798
\(792\) −1.60377 −0.0569876
\(793\) −7.67218 −0.272447
\(794\) 29.7652 1.05633
\(795\) −1.66589 −0.0590831
\(796\) 11.7304 0.415772
\(797\) −25.2909 −0.895850 −0.447925 0.894071i \(-0.647837\pi\)
−0.447925 + 0.894071i \(0.647837\pi\)
\(798\) −0.987518 −0.0349578
\(799\) −2.72064 −0.0962494
\(800\) −14.8547 −0.525193
\(801\) −6.31600 −0.223165
\(802\) −0.0671306 −0.00237047
\(803\) 4.84732 0.171058
\(804\) −1.73132 −0.0610591
\(805\) −2.19155 −0.0772418
\(806\) −33.2292 −1.17045
\(807\) 15.9238 0.560545
\(808\) −27.4033 −0.964045
\(809\) 15.4002 0.541443 0.270722 0.962658i \(-0.412738\pi\)
0.270722 + 0.962658i \(0.412738\pi\)
\(810\) 0.784971 0.0275811
\(811\) −35.8840 −1.26006 −0.630029 0.776572i \(-0.716957\pi\)
−0.630029 + 0.776572i \(0.716957\pi\)
\(812\) −1.64758 −0.0578188
\(813\) −21.9553 −0.770006
\(814\) −0.395138 −0.0138496
\(815\) −8.27128 −0.289730
\(816\) −4.81285 −0.168484
\(817\) 8.36015 0.292485
\(818\) −44.4605 −1.55453
\(819\) −1.29890 −0.0453873
\(820\) −2.76079 −0.0964110
\(821\) −13.1523 −0.459020 −0.229510 0.973306i \(-0.573712\pi\)
−0.229510 + 0.973306i \(0.573712\pi\)
\(822\) 24.5407 0.855956
\(823\) −16.0495 −0.559449 −0.279724 0.960080i \(-0.590243\pi\)
−0.279724 + 0.960080i \(0.590243\pi\)
\(824\) −16.7539 −0.583649
\(825\) −3.32566 −0.115784
\(826\) −5.97458 −0.207882
\(827\) −21.4115 −0.744552 −0.372276 0.928122i \(-0.621423\pi\)
−0.372276 + 0.928122i \(0.621423\pi\)
\(828\) −4.42122 −0.153648
\(829\) 45.1129 1.56684 0.783418 0.621495i \(-0.213474\pi\)
0.783418 + 0.621495i \(0.213474\pi\)
\(830\) −8.74578 −0.303570
\(831\) −30.3549 −1.05300
\(832\) 10.4648 0.362801
\(833\) 6.67041 0.231116
\(834\) 27.2415 0.943296
\(835\) −7.88797 −0.272975
\(836\) −0.425567 −0.0147185
\(837\) −9.16611 −0.316827
\(838\) −25.9132 −0.895157
\(839\) 18.0718 0.623909 0.311954 0.950097i \(-0.399016\pi\)
0.311954 + 0.950097i \(0.399016\pi\)
\(840\) −0.645606 −0.0222755
\(841\) −3.41751 −0.117845
\(842\) −26.3404 −0.907752
\(843\) −8.60041 −0.296214
\(844\) −6.58090 −0.226524
\(845\) 3.86095 0.132821
\(846\) −4.35931 −0.149876
\(847\) 6.03487 0.207361
\(848\) 16.3660 0.562010
\(849\) −28.4638 −0.976874
\(850\) −7.62699 −0.261604
\(851\) 2.75034 0.0942805
\(852\) −1.89509 −0.0649245
\(853\) −47.8982 −1.64000 −0.820002 0.572361i \(-0.806028\pi\)
−0.820002 + 0.572361i \(0.806028\pi\)
\(854\) −3.11936 −0.106742
\(855\) −0.525917 −0.0179860
\(856\) −24.2341 −0.828306
\(857\) −22.5706 −0.770997 −0.385499 0.922708i \(-0.625971\pi\)
−0.385499 + 0.922708i \(0.625971\pi\)
\(858\) −2.53283 −0.0864692
\(859\) 4.34984 0.148415 0.0742073 0.997243i \(-0.476357\pi\)
0.0742073 + 0.997243i \(0.476357\pi\)
\(860\) −2.16470 −0.0738157
\(861\) 5.70201 0.194324
\(862\) 26.5106 0.902955
\(863\) −24.4102 −0.830932 −0.415466 0.909609i \(-0.636381\pi\)
−0.415466 + 0.909609i \(0.636381\pi\)
\(864\) −3.12074 −0.106170
\(865\) 2.28691 0.0777573
\(866\) −4.30788 −0.146388
\(867\) −1.00000 −0.0339618
\(868\) −2.98580 −0.101345
\(869\) −0.698667 −0.0237007
\(870\) −3.97031 −0.134606
\(871\) 6.90366 0.233922
\(872\) 4.64515 0.157305
\(873\) −1.51033 −0.0511169
\(874\) 13.4033 0.453374
\(875\) −2.74502 −0.0927985
\(876\) 3.93658 0.133005
\(877\) −15.6442 −0.528267 −0.264134 0.964486i \(-0.585086\pi\)
−0.264134 + 0.964486i \(0.585086\pi\)
\(878\) 63.2479 2.13451
\(879\) −4.49834 −0.151725
\(880\) −1.64733 −0.0555314
\(881\) −22.8745 −0.770661 −0.385331 0.922779i \(-0.625913\pi\)
−0.385331 + 0.922779i \(0.625913\pi\)
\(882\) 10.6881 0.359886
\(883\) 8.88893 0.299136 0.149568 0.988751i \(-0.452212\pi\)
0.149568 + 0.988751i \(0.452212\pi\)
\(884\) −1.28373 −0.0431767
\(885\) −3.18185 −0.106957
\(886\) −14.2747 −0.479568
\(887\) 14.3487 0.481781 0.240890 0.970552i \(-0.422561\pi\)
0.240890 + 0.970552i \(0.422561\pi\)
\(888\) 0.810221 0.0271892
\(889\) −6.87574 −0.230605
\(890\) −4.95787 −0.166188
\(891\) −0.698667 −0.0234062
\(892\) −5.22485 −0.174941
\(893\) 2.92066 0.0977363
\(894\) 8.21383 0.274712
\(895\) −5.82567 −0.194731
\(896\) 7.83801 0.261850
\(897\) 17.6296 0.588637
\(898\) −10.4756 −0.349576
\(899\) 46.3614 1.54624
\(900\) −2.70081 −0.0900270
\(901\) 3.40047 0.113286
\(902\) 11.1188 0.370214
\(903\) 4.47087 0.148781
\(904\) 0.591278 0.0196656
\(905\) −5.32653 −0.177060
\(906\) 27.4377 0.911556
\(907\) −10.9434 −0.363369 −0.181685 0.983357i \(-0.558155\pi\)
−0.181685 + 0.983357i \(0.558155\pi\)
\(908\) −7.93005 −0.263168
\(909\) −11.9380 −0.395958
\(910\) −1.01960 −0.0337994
\(911\) 14.6004 0.483733 0.241867 0.970309i \(-0.422240\pi\)
0.241867 + 0.970309i \(0.422240\pi\)
\(912\) 5.16670 0.171086
\(913\) 7.78423 0.257620
\(914\) 6.21237 0.205487
\(915\) −1.66126 −0.0549196
\(916\) 13.2452 0.437634
\(917\) 6.92885 0.228811
\(918\) −1.60231 −0.0528841
\(919\) −7.97809 −0.263173 −0.131586 0.991305i \(-0.542007\pi\)
−0.131586 + 0.991305i \(0.542007\pi\)
\(920\) 8.76263 0.288895
\(921\) −4.25804 −0.140307
\(922\) −6.97273 −0.229635
\(923\) 7.55666 0.248731
\(924\) −0.227586 −0.00748703
\(925\) 1.68011 0.0552417
\(926\) −48.4467 −1.59206
\(927\) −7.29866 −0.239719
\(928\) 15.7844 0.518149
\(929\) 15.7669 0.517294 0.258647 0.965972i \(-0.416723\pi\)
0.258647 + 0.965972i \(0.416723\pi\)
\(930\) −7.19513 −0.235937
\(931\) −7.16082 −0.234686
\(932\) 1.95496 0.0640370
\(933\) −17.9692 −0.588284
\(934\) −55.3263 −1.81033
\(935\) −0.342277 −0.0111936
\(936\) 5.19351 0.169755
\(937\) 15.6047 0.509783 0.254891 0.966970i \(-0.417960\pi\)
0.254891 + 0.966970i \(0.417960\pi\)
\(938\) 2.80689 0.0916484
\(939\) −21.7435 −0.709573
\(940\) −0.756250 −0.0246662
\(941\) 3.36836 0.109806 0.0549028 0.998492i \(-0.482515\pi\)
0.0549028 + 0.998492i \(0.482515\pi\)
\(942\) 10.7580 0.350514
\(943\) −77.3918 −2.52022
\(944\) 31.2590 1.01739
\(945\) −0.281252 −0.00914912
\(946\) 8.71808 0.283449
\(947\) 44.4132 1.44323 0.721617 0.692293i \(-0.243399\pi\)
0.721617 + 0.692293i \(0.243399\pi\)
\(948\) −0.567397 −0.0184282
\(949\) −15.6971 −0.509550
\(950\) 8.18773 0.265645
\(951\) 31.0138 1.00569
\(952\) 1.31783 0.0427112
\(953\) −10.0975 −0.327091 −0.163545 0.986536i \(-0.552293\pi\)
−0.163545 + 0.986536i \(0.552293\pi\)
\(954\) 5.44861 0.176405
\(955\) 11.1687 0.361411
\(956\) 11.2822 0.364893
\(957\) 3.53380 0.114232
\(958\) 31.4818 1.01713
\(959\) −8.79284 −0.283935
\(960\) 2.26594 0.0731330
\(961\) 53.0175 1.71024
\(962\) 1.27958 0.0412552
\(963\) −10.5574 −0.340206
\(964\) −4.13802 −0.133277
\(965\) 0.416351 0.0134028
\(966\) 7.16787 0.230622
\(967\) 13.9841 0.449699 0.224849 0.974394i \(-0.427811\pi\)
0.224849 + 0.974394i \(0.427811\pi\)
\(968\) −24.1297 −0.775558
\(969\) 1.07352 0.0344864
\(970\) −1.18556 −0.0380662
\(971\) −36.0761 −1.15774 −0.578869 0.815421i \(-0.696506\pi\)
−0.578869 + 0.815421i \(0.696506\pi\)
\(972\) −0.567397 −0.0181993
\(973\) −9.76052 −0.312908
\(974\) −34.1143 −1.09309
\(975\) 10.7695 0.344900
\(976\) 16.3205 0.522406
\(977\) 25.5124 0.816215 0.408107 0.912934i \(-0.366189\pi\)
0.408107 + 0.912934i \(0.366189\pi\)
\(978\) 27.0528 0.865053
\(979\) 4.41278 0.141033
\(980\) 1.85416 0.0592289
\(981\) 2.02361 0.0646090
\(982\) 52.4937 1.67514
\(983\) 0.556483 0.0177490 0.00887452 0.999961i \(-0.497175\pi\)
0.00887452 + 0.999961i \(0.497175\pi\)
\(984\) −22.7988 −0.726799
\(985\) 12.4547 0.396840
\(986\) 8.10435 0.258095
\(987\) 1.56192 0.0497166
\(988\) 1.37812 0.0438437
\(989\) −60.6819 −1.92957
\(990\) −0.548433 −0.0174304
\(991\) −35.4825 −1.12714 −0.563569 0.826069i \(-0.690572\pi\)
−0.563569 + 0.826069i \(0.690572\pi\)
\(992\) 28.6050 0.908210
\(993\) −35.6022 −1.12980
\(994\) 3.07239 0.0974503
\(995\) −10.1282 −0.321085
\(996\) 6.32167 0.200310
\(997\) 17.0977 0.541489 0.270744 0.962651i \(-0.412730\pi\)
0.270744 + 0.962651i \(0.412730\pi\)
\(998\) 5.70056 0.180448
\(999\) 0.352965 0.0111673
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.1.10 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.10 32 1.1 even 1 trivial