Properties

Label 4034.2.a.d.1.18
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.905567 q^{3} +1.00000 q^{4} -1.11072 q^{5} -0.905567 q^{6} -1.83235 q^{7} +1.00000 q^{8} -2.17995 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.905567 q^{3} +1.00000 q^{4} -1.11072 q^{5} -0.905567 q^{6} -1.83235 q^{7} +1.00000 q^{8} -2.17995 q^{9} -1.11072 q^{10} +3.15031 q^{11} -0.905567 q^{12} -6.12471 q^{13} -1.83235 q^{14} +1.00583 q^{15} +1.00000 q^{16} +1.33116 q^{17} -2.17995 q^{18} +1.55764 q^{19} -1.11072 q^{20} +1.65932 q^{21} +3.15031 q^{22} +5.24174 q^{23} -0.905567 q^{24} -3.76629 q^{25} -6.12471 q^{26} +4.69079 q^{27} -1.83235 q^{28} -1.90586 q^{29} +1.00583 q^{30} +5.13820 q^{31} +1.00000 q^{32} -2.85282 q^{33} +1.33116 q^{34} +2.03524 q^{35} -2.17995 q^{36} -8.79434 q^{37} +1.55764 q^{38} +5.54633 q^{39} -1.11072 q^{40} -1.96990 q^{41} +1.65932 q^{42} -2.51896 q^{43} +3.15031 q^{44} +2.42132 q^{45} +5.24174 q^{46} +7.53212 q^{47} -0.905567 q^{48} -3.64248 q^{49} -3.76629 q^{50} -1.20546 q^{51} -6.12471 q^{52} +2.37305 q^{53} +4.69079 q^{54} -3.49912 q^{55} -1.83235 q^{56} -1.41054 q^{57} -1.90586 q^{58} +13.3052 q^{59} +1.00583 q^{60} -2.35511 q^{61} +5.13820 q^{62} +3.99444 q^{63} +1.00000 q^{64} +6.80285 q^{65} -2.85282 q^{66} +5.23120 q^{67} +1.33116 q^{68} -4.74675 q^{69} +2.03524 q^{70} +2.21953 q^{71} -2.17995 q^{72} +7.62746 q^{73} -8.79434 q^{74} +3.41063 q^{75} +1.55764 q^{76} -5.77249 q^{77} +5.54633 q^{78} +5.41653 q^{79} -1.11072 q^{80} +2.29202 q^{81} -1.96990 q^{82} +13.7768 q^{83} +1.65932 q^{84} -1.47856 q^{85} -2.51896 q^{86} +1.72588 q^{87} +3.15031 q^{88} -3.22130 q^{89} +2.42132 q^{90} +11.2226 q^{91} +5.24174 q^{92} -4.65298 q^{93} +7.53212 q^{94} -1.73010 q^{95} -0.905567 q^{96} -0.906230 q^{97} -3.64248 q^{98} -6.86752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.905567 −0.522829 −0.261415 0.965227i \(-0.584189\pi\)
−0.261415 + 0.965227i \(0.584189\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.11072 −0.496731 −0.248365 0.968666i \(-0.579893\pi\)
−0.248365 + 0.968666i \(0.579893\pi\)
\(6\) −0.905567 −0.369696
\(7\) −1.83235 −0.692565 −0.346282 0.938130i \(-0.612556\pi\)
−0.346282 + 0.938130i \(0.612556\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.17995 −0.726650
\(10\) −1.11072 −0.351242
\(11\) 3.15031 0.949855 0.474927 0.880025i \(-0.342474\pi\)
0.474927 + 0.880025i \(0.342474\pi\)
\(12\) −0.905567 −0.261415
\(13\) −6.12471 −1.69869 −0.849344 0.527840i \(-0.823002\pi\)
−0.849344 + 0.527840i \(0.823002\pi\)
\(14\) −1.83235 −0.489717
\(15\) 1.00583 0.259705
\(16\) 1.00000 0.250000
\(17\) 1.33116 0.322855 0.161427 0.986885i \(-0.448390\pi\)
0.161427 + 0.986885i \(0.448390\pi\)
\(18\) −2.17995 −0.513819
\(19\) 1.55764 0.357346 0.178673 0.983909i \(-0.442820\pi\)
0.178673 + 0.983909i \(0.442820\pi\)
\(20\) −1.11072 −0.248365
\(21\) 1.65932 0.362093
\(22\) 3.15031 0.671649
\(23\) 5.24174 1.09298 0.546489 0.837466i \(-0.315964\pi\)
0.546489 + 0.837466i \(0.315964\pi\)
\(24\) −0.905567 −0.184848
\(25\) −3.76629 −0.753259
\(26\) −6.12471 −1.20115
\(27\) 4.69079 0.902743
\(28\) −1.83235 −0.346282
\(29\) −1.90586 −0.353909 −0.176955 0.984219i \(-0.556625\pi\)
−0.176955 + 0.984219i \(0.556625\pi\)
\(30\) 1.00583 0.183639
\(31\) 5.13820 0.922848 0.461424 0.887180i \(-0.347339\pi\)
0.461424 + 0.887180i \(0.347339\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.85282 −0.496612
\(34\) 1.33116 0.228293
\(35\) 2.03524 0.344018
\(36\) −2.17995 −0.363325
\(37\) −8.79434 −1.44578 −0.722890 0.690963i \(-0.757187\pi\)
−0.722890 + 0.690963i \(0.757187\pi\)
\(38\) 1.55764 0.252682
\(39\) 5.54633 0.888124
\(40\) −1.11072 −0.175621
\(41\) −1.96990 −0.307647 −0.153824 0.988098i \(-0.549159\pi\)
−0.153824 + 0.988098i \(0.549159\pi\)
\(42\) 1.65932 0.256039
\(43\) −2.51896 −0.384138 −0.192069 0.981381i \(-0.561520\pi\)
−0.192069 + 0.981381i \(0.561520\pi\)
\(44\) 3.15031 0.474927
\(45\) 2.42132 0.360949
\(46\) 5.24174 0.772853
\(47\) 7.53212 1.09867 0.549336 0.835602i \(-0.314881\pi\)
0.549336 + 0.835602i \(0.314881\pi\)
\(48\) −0.905567 −0.130707
\(49\) −3.64248 −0.520354
\(50\) −3.76629 −0.532634
\(51\) −1.20546 −0.168798
\(52\) −6.12471 −0.849344
\(53\) 2.37305 0.325963 0.162982 0.986629i \(-0.447889\pi\)
0.162982 + 0.986629i \(0.447889\pi\)
\(54\) 4.69079 0.638336
\(55\) −3.49912 −0.471822
\(56\) −1.83235 −0.244859
\(57\) −1.41054 −0.186831
\(58\) −1.90586 −0.250252
\(59\) 13.3052 1.73218 0.866092 0.499885i \(-0.166624\pi\)
0.866092 + 0.499885i \(0.166624\pi\)
\(60\) 1.00583 0.129853
\(61\) −2.35511 −0.301541 −0.150770 0.988569i \(-0.548175\pi\)
−0.150770 + 0.988569i \(0.548175\pi\)
\(62\) 5.13820 0.652552
\(63\) 3.99444 0.503252
\(64\) 1.00000 0.125000
\(65\) 6.80285 0.843790
\(66\) −2.85282 −0.351158
\(67\) 5.23120 0.639092 0.319546 0.947571i \(-0.396470\pi\)
0.319546 + 0.947571i \(0.396470\pi\)
\(68\) 1.33116 0.161427
\(69\) −4.74675 −0.571441
\(70\) 2.03524 0.243258
\(71\) 2.21953 0.263410 0.131705 0.991289i \(-0.457955\pi\)
0.131705 + 0.991289i \(0.457955\pi\)
\(72\) −2.17995 −0.256909
\(73\) 7.62746 0.892727 0.446363 0.894852i \(-0.352719\pi\)
0.446363 + 0.894852i \(0.352719\pi\)
\(74\) −8.79434 −1.02232
\(75\) 3.41063 0.393826
\(76\) 1.55764 0.178673
\(77\) −5.77249 −0.657836
\(78\) 5.54633 0.627998
\(79\) 5.41653 0.609407 0.304703 0.952447i \(-0.401443\pi\)
0.304703 + 0.952447i \(0.401443\pi\)
\(80\) −1.11072 −0.124183
\(81\) 2.29202 0.254669
\(82\) −1.96990 −0.217540
\(83\) 13.7768 1.51220 0.756098 0.654459i \(-0.227103\pi\)
0.756098 + 0.654459i \(0.227103\pi\)
\(84\) 1.65932 0.181047
\(85\) −1.47856 −0.160372
\(86\) −2.51896 −0.271626
\(87\) 1.72588 0.185034
\(88\) 3.15031 0.335824
\(89\) −3.22130 −0.341457 −0.170728 0.985318i \(-0.554612\pi\)
−0.170728 + 0.985318i \(0.554612\pi\)
\(90\) 2.42132 0.255230
\(91\) 11.2226 1.17645
\(92\) 5.24174 0.546489
\(93\) −4.65298 −0.482492
\(94\) 7.53212 0.776878
\(95\) −1.73010 −0.177505
\(96\) −0.905567 −0.0924240
\(97\) −0.906230 −0.0920137 −0.0460069 0.998941i \(-0.514650\pi\)
−0.0460069 + 0.998941i \(0.514650\pi\)
\(98\) −3.64248 −0.367946
\(99\) −6.86752 −0.690211
\(100\) −3.76629 −0.376629
\(101\) 15.5762 1.54989 0.774947 0.632026i \(-0.217776\pi\)
0.774947 + 0.632026i \(0.217776\pi\)
\(102\) −1.20546 −0.119358
\(103\) −4.69566 −0.462677 −0.231338 0.972873i \(-0.574310\pi\)
−0.231338 + 0.972873i \(0.574310\pi\)
\(104\) −6.12471 −0.600577
\(105\) −1.84305 −0.179863
\(106\) 2.37305 0.230491
\(107\) 5.27981 0.510418 0.255209 0.966886i \(-0.417856\pi\)
0.255209 + 0.966886i \(0.417856\pi\)
\(108\) 4.69079 0.451371
\(109\) 15.1914 1.45507 0.727536 0.686069i \(-0.240665\pi\)
0.727536 + 0.686069i \(0.240665\pi\)
\(110\) −3.49912 −0.333628
\(111\) 7.96386 0.755897
\(112\) −1.83235 −0.173141
\(113\) 15.7089 1.47777 0.738884 0.673833i \(-0.235353\pi\)
0.738884 + 0.673833i \(0.235353\pi\)
\(114\) −1.41054 −0.132109
\(115\) −5.82213 −0.542916
\(116\) −1.90586 −0.176955
\(117\) 13.3515 1.23435
\(118\) 13.3052 1.22484
\(119\) −2.43917 −0.223598
\(120\) 1.00583 0.0918197
\(121\) −1.07554 −0.0977763
\(122\) −2.35511 −0.213222
\(123\) 1.78388 0.160847
\(124\) 5.13820 0.461424
\(125\) 9.73693 0.870897
\(126\) 3.99444 0.355853
\(127\) −16.9589 −1.50486 −0.752431 0.658671i \(-0.771119\pi\)
−0.752431 + 0.658671i \(0.771119\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.28109 0.200838
\(130\) 6.80285 0.596650
\(131\) 1.09649 0.0958012 0.0479006 0.998852i \(-0.484747\pi\)
0.0479006 + 0.998852i \(0.484747\pi\)
\(132\) −2.85282 −0.248306
\(133\) −2.85414 −0.247485
\(134\) 5.23120 0.451907
\(135\) −5.21017 −0.448420
\(136\) 1.33116 0.114146
\(137\) 3.71597 0.317477 0.158739 0.987321i \(-0.449257\pi\)
0.158739 + 0.987321i \(0.449257\pi\)
\(138\) −4.74675 −0.404070
\(139\) −17.8798 −1.51654 −0.758271 0.651940i \(-0.773956\pi\)
−0.758271 + 0.651940i \(0.773956\pi\)
\(140\) 2.03524 0.172009
\(141\) −6.82083 −0.574418
\(142\) 2.21953 0.186259
\(143\) −19.2947 −1.61351
\(144\) −2.17995 −0.181662
\(145\) 2.11688 0.175798
\(146\) 7.62746 0.631253
\(147\) 3.29851 0.272056
\(148\) −8.79434 −0.722890
\(149\) 3.61186 0.295895 0.147948 0.988995i \(-0.452733\pi\)
0.147948 + 0.988995i \(0.452733\pi\)
\(150\) 3.41063 0.278477
\(151\) 11.5629 0.940974 0.470487 0.882407i \(-0.344078\pi\)
0.470487 + 0.882407i \(0.344078\pi\)
\(152\) 1.55764 0.126341
\(153\) −2.90187 −0.234602
\(154\) −5.77249 −0.465160
\(155\) −5.70712 −0.458407
\(156\) 5.54633 0.444062
\(157\) −0.651038 −0.0519585 −0.0259793 0.999662i \(-0.508270\pi\)
−0.0259793 + 0.999662i \(0.508270\pi\)
\(158\) 5.41653 0.430916
\(159\) −2.14895 −0.170423
\(160\) −1.11072 −0.0878104
\(161\) −9.60473 −0.756959
\(162\) 2.29202 0.180078
\(163\) 13.4358 1.05237 0.526186 0.850370i \(-0.323622\pi\)
0.526186 + 0.850370i \(0.323622\pi\)
\(164\) −1.96990 −0.153824
\(165\) 3.16869 0.246682
\(166\) 13.7768 1.06928
\(167\) 5.77053 0.446537 0.223268 0.974757i \(-0.428327\pi\)
0.223268 + 0.974757i \(0.428327\pi\)
\(168\) 1.65932 0.128019
\(169\) 24.5120 1.88554
\(170\) −1.47856 −0.113400
\(171\) −3.39556 −0.259665
\(172\) −2.51896 −0.192069
\(173\) −7.86912 −0.598278 −0.299139 0.954210i \(-0.596699\pi\)
−0.299139 + 0.954210i \(0.596699\pi\)
\(174\) 1.72588 0.130839
\(175\) 6.90118 0.521680
\(176\) 3.15031 0.237464
\(177\) −12.0487 −0.905637
\(178\) −3.22130 −0.241446
\(179\) 9.51175 0.710942 0.355471 0.934687i \(-0.384321\pi\)
0.355471 + 0.934687i \(0.384321\pi\)
\(180\) 2.42132 0.180475
\(181\) 3.98713 0.296361 0.148181 0.988960i \(-0.452658\pi\)
0.148181 + 0.988960i \(0.452658\pi\)
\(182\) 11.2226 0.831877
\(183\) 2.13271 0.157654
\(184\) 5.24174 0.386426
\(185\) 9.76808 0.718164
\(186\) −4.65298 −0.341173
\(187\) 4.19358 0.306665
\(188\) 7.53212 0.549336
\(189\) −8.59519 −0.625208
\(190\) −1.73010 −0.125515
\(191\) −20.1158 −1.45553 −0.727763 0.685829i \(-0.759440\pi\)
−0.727763 + 0.685829i \(0.759440\pi\)
\(192\) −0.905567 −0.0653537
\(193\) −9.29027 −0.668729 −0.334364 0.942444i \(-0.608522\pi\)
−0.334364 + 0.942444i \(0.608522\pi\)
\(194\) −0.906230 −0.0650635
\(195\) −6.16044 −0.441158
\(196\) −3.64248 −0.260177
\(197\) 8.76077 0.624179 0.312089 0.950053i \(-0.398971\pi\)
0.312089 + 0.950053i \(0.398971\pi\)
\(198\) −6.86752 −0.488053
\(199\) −18.5188 −1.31276 −0.656382 0.754429i \(-0.727914\pi\)
−0.656382 + 0.754429i \(0.727914\pi\)
\(200\) −3.76629 −0.266317
\(201\) −4.73720 −0.334136
\(202\) 15.5762 1.09594
\(203\) 3.49221 0.245105
\(204\) −1.20546 −0.0843990
\(205\) 2.18802 0.152818
\(206\) −4.69566 −0.327162
\(207\) −11.4267 −0.794212
\(208\) −6.12471 −0.424672
\(209\) 4.90704 0.339427
\(210\) −1.84305 −0.127182
\(211\) −4.14174 −0.285129 −0.142564 0.989786i \(-0.545535\pi\)
−0.142564 + 0.989786i \(0.545535\pi\)
\(212\) 2.37305 0.162982
\(213\) −2.00993 −0.137718
\(214\) 5.27981 0.360920
\(215\) 2.79787 0.190813
\(216\) 4.69079 0.319168
\(217\) −9.41500 −0.639132
\(218\) 15.1914 1.02889
\(219\) −6.90718 −0.466744
\(220\) −3.49912 −0.235911
\(221\) −8.15299 −0.548430
\(222\) 7.96386 0.534500
\(223\) 16.4997 1.10490 0.552452 0.833545i \(-0.313692\pi\)
0.552452 + 0.833545i \(0.313692\pi\)
\(224\) −1.83235 −0.122429
\(225\) 8.21033 0.547355
\(226\) 15.7089 1.04494
\(227\) −14.8796 −0.987593 −0.493796 0.869577i \(-0.664391\pi\)
−0.493796 + 0.869577i \(0.664391\pi\)
\(228\) −1.41054 −0.0934155
\(229\) −21.2658 −1.40529 −0.702643 0.711542i \(-0.747997\pi\)
−0.702643 + 0.711542i \(0.747997\pi\)
\(230\) −5.82213 −0.383900
\(231\) 5.22737 0.343936
\(232\) −1.90586 −0.125126
\(233\) −16.2103 −1.06197 −0.530985 0.847381i \(-0.678178\pi\)
−0.530985 + 0.847381i \(0.678178\pi\)
\(234\) 13.3515 0.872818
\(235\) −8.36610 −0.545744
\(236\) 13.3052 0.866092
\(237\) −4.90503 −0.318616
\(238\) −2.43917 −0.158108
\(239\) 21.1470 1.36788 0.683942 0.729536i \(-0.260264\pi\)
0.683942 + 0.729536i \(0.260264\pi\)
\(240\) 1.00583 0.0649263
\(241\) 22.3968 1.44271 0.721353 0.692568i \(-0.243521\pi\)
0.721353 + 0.692568i \(0.243521\pi\)
\(242\) −1.07554 −0.0691383
\(243\) −16.1479 −1.03589
\(244\) −2.35511 −0.150770
\(245\) 4.04579 0.258476
\(246\) 1.78388 0.113736
\(247\) −9.54006 −0.607019
\(248\) 5.13820 0.326276
\(249\) −12.4758 −0.790620
\(250\) 9.73693 0.615817
\(251\) 29.5345 1.86420 0.932102 0.362196i \(-0.117973\pi\)
0.932102 + 0.362196i \(0.117973\pi\)
\(252\) 3.99444 0.251626
\(253\) 16.5131 1.03817
\(254\) −16.9589 −1.06410
\(255\) 1.33893 0.0838472
\(256\) 1.00000 0.0625000
\(257\) −8.15983 −0.508996 −0.254498 0.967073i \(-0.581910\pi\)
−0.254498 + 0.967073i \(0.581910\pi\)
\(258\) 2.28109 0.142014
\(259\) 16.1144 1.00130
\(260\) 6.80285 0.421895
\(261\) 4.15468 0.257168
\(262\) 1.09649 0.0677417
\(263\) −6.98993 −0.431018 −0.215509 0.976502i \(-0.569141\pi\)
−0.215509 + 0.976502i \(0.569141\pi\)
\(264\) −2.85282 −0.175579
\(265\) −2.63580 −0.161916
\(266\) −2.85414 −0.174999
\(267\) 2.91710 0.178524
\(268\) 5.23120 0.319546
\(269\) 18.8231 1.14767 0.573833 0.818972i \(-0.305456\pi\)
0.573833 + 0.818972i \(0.305456\pi\)
\(270\) −5.21017 −0.317081
\(271\) 27.9400 1.69724 0.848618 0.529006i \(-0.177435\pi\)
0.848618 + 0.529006i \(0.177435\pi\)
\(272\) 1.33116 0.0807137
\(273\) −10.1628 −0.615083
\(274\) 3.71597 0.224490
\(275\) −11.8650 −0.715486
\(276\) −4.74675 −0.285721
\(277\) −5.83152 −0.350382 −0.175191 0.984534i \(-0.556054\pi\)
−0.175191 + 0.984534i \(0.556054\pi\)
\(278\) −17.8798 −1.07236
\(279\) −11.2010 −0.670587
\(280\) 2.03524 0.121629
\(281\) 18.3223 1.09302 0.546509 0.837453i \(-0.315956\pi\)
0.546509 + 0.837453i \(0.315956\pi\)
\(282\) −6.82083 −0.406175
\(283\) 13.6532 0.811601 0.405801 0.913962i \(-0.366993\pi\)
0.405801 + 0.913962i \(0.366993\pi\)
\(284\) 2.21953 0.131705
\(285\) 1.56672 0.0928047
\(286\) −19.2947 −1.14092
\(287\) 3.60956 0.213066
\(288\) −2.17995 −0.128455
\(289\) −15.2280 −0.895765
\(290\) 2.11688 0.124308
\(291\) 0.820652 0.0481075
\(292\) 7.62746 0.446363
\(293\) 17.3412 1.01309 0.506543 0.862215i \(-0.330923\pi\)
0.506543 + 0.862215i \(0.330923\pi\)
\(294\) 3.29851 0.192373
\(295\) −14.7784 −0.860429
\(296\) −8.79434 −0.511161
\(297\) 14.7774 0.857475
\(298\) 3.61186 0.209230
\(299\) −32.1041 −1.85663
\(300\) 3.41063 0.196913
\(301\) 4.61563 0.266040
\(302\) 11.5629 0.665369
\(303\) −14.1053 −0.810330
\(304\) 1.55764 0.0893365
\(305\) 2.61588 0.149785
\(306\) −2.90187 −0.165889
\(307\) −14.9562 −0.853598 −0.426799 0.904347i \(-0.640359\pi\)
−0.426799 + 0.904347i \(0.640359\pi\)
\(308\) −5.77249 −0.328918
\(309\) 4.25223 0.241901
\(310\) −5.70712 −0.324143
\(311\) 14.5546 0.825313 0.412657 0.910887i \(-0.364601\pi\)
0.412657 + 0.910887i \(0.364601\pi\)
\(312\) 5.54633 0.313999
\(313\) 1.34600 0.0760804 0.0380402 0.999276i \(-0.487889\pi\)
0.0380402 + 0.999276i \(0.487889\pi\)
\(314\) −0.651038 −0.0367402
\(315\) −4.43672 −0.249981
\(316\) 5.41653 0.304703
\(317\) 9.02892 0.507115 0.253557 0.967320i \(-0.418399\pi\)
0.253557 + 0.967320i \(0.418399\pi\)
\(318\) −2.14895 −0.120507
\(319\) −6.00405 −0.336163
\(320\) −1.11072 −0.0620913
\(321\) −4.78122 −0.266862
\(322\) −9.60473 −0.535251
\(323\) 2.07347 0.115371
\(324\) 2.29202 0.127335
\(325\) 23.0674 1.27955
\(326\) 13.4358 0.744139
\(327\) −13.7568 −0.760755
\(328\) −1.96990 −0.108770
\(329\) −13.8015 −0.760902
\(330\) 3.16869 0.174431
\(331\) 17.5993 0.967347 0.483674 0.875248i \(-0.339302\pi\)
0.483674 + 0.875248i \(0.339302\pi\)
\(332\) 13.7768 0.756098
\(333\) 19.1712 1.05058
\(334\) 5.77053 0.315749
\(335\) −5.81041 −0.317457
\(336\) 1.65932 0.0905233
\(337\) −27.8689 −1.51811 −0.759057 0.651025i \(-0.774339\pi\)
−0.759057 + 0.651025i \(0.774339\pi\)
\(338\) 24.5120 1.33328
\(339\) −14.2255 −0.772620
\(340\) −1.47856 −0.0801860
\(341\) 16.1869 0.876571
\(342\) −3.39556 −0.183611
\(343\) 19.5008 1.05294
\(344\) −2.51896 −0.135813
\(345\) 5.27232 0.283852
\(346\) −7.86912 −0.423047
\(347\) 9.61696 0.516265 0.258133 0.966109i \(-0.416893\pi\)
0.258133 + 0.966109i \(0.416893\pi\)
\(348\) 1.72588 0.0925171
\(349\) −22.0680 −1.18127 −0.590637 0.806937i \(-0.701123\pi\)
−0.590637 + 0.806937i \(0.701123\pi\)
\(350\) 6.90118 0.368884
\(351\) −28.7297 −1.53348
\(352\) 3.15031 0.167912
\(353\) 21.9797 1.16986 0.584930 0.811084i \(-0.301122\pi\)
0.584930 + 0.811084i \(0.301122\pi\)
\(354\) −12.0487 −0.640382
\(355\) −2.46528 −0.130844
\(356\) −3.22130 −0.170728
\(357\) 2.20883 0.116904
\(358\) 9.51175 0.502712
\(359\) −14.5307 −0.766904 −0.383452 0.923561i \(-0.625265\pi\)
−0.383452 + 0.923561i \(0.625265\pi\)
\(360\) 2.42132 0.127615
\(361\) −16.5738 −0.872304
\(362\) 3.98713 0.209559
\(363\) 0.973973 0.0511203
\(364\) 11.2226 0.588226
\(365\) −8.47200 −0.443445
\(366\) 2.13271 0.111479
\(367\) −16.9474 −0.884648 −0.442324 0.896855i \(-0.645846\pi\)
−0.442324 + 0.896855i \(0.645846\pi\)
\(368\) 5.24174 0.273245
\(369\) 4.29429 0.223552
\(370\) 9.76808 0.507818
\(371\) −4.34827 −0.225751
\(372\) −4.65298 −0.241246
\(373\) −26.1033 −1.35158 −0.675789 0.737095i \(-0.736197\pi\)
−0.675789 + 0.737095i \(0.736197\pi\)
\(374\) 4.19358 0.216845
\(375\) −8.81744 −0.455331
\(376\) 7.53212 0.388439
\(377\) 11.6728 0.601182
\(378\) −8.59519 −0.442089
\(379\) 3.91896 0.201303 0.100652 0.994922i \(-0.467907\pi\)
0.100652 + 0.994922i \(0.467907\pi\)
\(380\) −1.73010 −0.0887524
\(381\) 15.3575 0.786786
\(382\) −20.1158 −1.02921
\(383\) −15.8472 −0.809756 −0.404878 0.914371i \(-0.632686\pi\)
−0.404878 + 0.914371i \(0.632686\pi\)
\(384\) −0.905567 −0.0462120
\(385\) 6.41164 0.326767
\(386\) −9.29027 −0.472862
\(387\) 5.49120 0.279133
\(388\) −0.906230 −0.0460069
\(389\) −7.21865 −0.366000 −0.183000 0.983113i \(-0.558581\pi\)
−0.183000 + 0.983113i \(0.558581\pi\)
\(390\) −6.16044 −0.311946
\(391\) 6.97762 0.352873
\(392\) −3.64248 −0.183973
\(393\) −0.992950 −0.0500877
\(394\) 8.76077 0.441361
\(395\) −6.01626 −0.302711
\(396\) −6.86752 −0.345106
\(397\) −15.8773 −0.796859 −0.398430 0.917199i \(-0.630445\pi\)
−0.398430 + 0.917199i \(0.630445\pi\)
\(398\) −18.5188 −0.928264
\(399\) 2.58461 0.129393
\(400\) −3.76629 −0.188315
\(401\) 1.27789 0.0638149 0.0319075 0.999491i \(-0.489842\pi\)
0.0319075 + 0.999491i \(0.489842\pi\)
\(402\) −4.73720 −0.236270
\(403\) −31.4700 −1.56763
\(404\) 15.5762 0.774947
\(405\) −2.54580 −0.126502
\(406\) 3.49221 0.173316
\(407\) −27.7049 −1.37328
\(408\) −1.20546 −0.0596791
\(409\) 34.1182 1.68704 0.843519 0.537100i \(-0.180480\pi\)
0.843519 + 0.537100i \(0.180480\pi\)
\(410\) 2.18802 0.108059
\(411\) −3.36506 −0.165986
\(412\) −4.69566 −0.231338
\(413\) −24.3798 −1.19965
\(414\) −11.4267 −0.561593
\(415\) −15.3022 −0.751154
\(416\) −6.12471 −0.300288
\(417\) 16.1913 0.792893
\(418\) 4.90704 0.240011
\(419\) 17.3757 0.848856 0.424428 0.905462i \(-0.360475\pi\)
0.424428 + 0.905462i \(0.360475\pi\)
\(420\) −1.84305 −0.0899314
\(421\) 20.8473 1.01603 0.508017 0.861347i \(-0.330379\pi\)
0.508017 + 0.861347i \(0.330379\pi\)
\(422\) −4.14174 −0.201617
\(423\) −16.4196 −0.798350
\(424\) 2.37305 0.115245
\(425\) −5.01356 −0.243193
\(426\) −2.00993 −0.0973816
\(427\) 4.31540 0.208837
\(428\) 5.27981 0.255209
\(429\) 17.4727 0.843588
\(430\) 2.79787 0.134925
\(431\) 10.5659 0.508940 0.254470 0.967081i \(-0.418099\pi\)
0.254470 + 0.967081i \(0.418099\pi\)
\(432\) 4.69079 0.225686
\(433\) −26.6808 −1.28220 −0.641099 0.767458i \(-0.721521\pi\)
−0.641099 + 0.767458i \(0.721521\pi\)
\(434\) −9.41500 −0.451935
\(435\) −1.91698 −0.0919122
\(436\) 15.1914 0.727536
\(437\) 8.16472 0.390572
\(438\) −6.90718 −0.330038
\(439\) −11.2927 −0.538973 −0.269487 0.963004i \(-0.586854\pi\)
−0.269487 + 0.963004i \(0.586854\pi\)
\(440\) −3.49912 −0.166814
\(441\) 7.94041 0.378115
\(442\) −8.15299 −0.387798
\(443\) −24.0916 −1.14463 −0.572314 0.820034i \(-0.693954\pi\)
−0.572314 + 0.820034i \(0.693954\pi\)
\(444\) 7.96386 0.377948
\(445\) 3.57797 0.169612
\(446\) 16.4997 0.781285
\(447\) −3.27078 −0.154703
\(448\) −1.83235 −0.0865706
\(449\) −6.74186 −0.318168 −0.159084 0.987265i \(-0.550854\pi\)
−0.159084 + 0.987265i \(0.550854\pi\)
\(450\) 8.21033 0.387038
\(451\) −6.20581 −0.292220
\(452\) 15.7089 0.738884
\(453\) −10.4710 −0.491969
\(454\) −14.8796 −0.698334
\(455\) −12.4652 −0.584380
\(456\) −1.41054 −0.0660547
\(457\) 26.9300 1.25973 0.629865 0.776704i \(-0.283110\pi\)
0.629865 + 0.776704i \(0.283110\pi\)
\(458\) −21.2658 −0.993687
\(459\) 6.24421 0.291455
\(460\) −5.82213 −0.271458
\(461\) −34.2071 −1.59318 −0.796591 0.604519i \(-0.793365\pi\)
−0.796591 + 0.604519i \(0.793365\pi\)
\(462\) 5.22737 0.243199
\(463\) −25.3289 −1.17713 −0.588567 0.808449i \(-0.700308\pi\)
−0.588567 + 0.808449i \(0.700308\pi\)
\(464\) −1.90586 −0.0884774
\(465\) 5.16818 0.239669
\(466\) −16.2103 −0.750926
\(467\) 41.3175 1.91194 0.955972 0.293456i \(-0.0948055\pi\)
0.955972 + 0.293456i \(0.0948055\pi\)
\(468\) 13.3515 0.617175
\(469\) −9.58541 −0.442613
\(470\) −8.36610 −0.385899
\(471\) 0.589559 0.0271654
\(472\) 13.3052 0.612420
\(473\) −7.93551 −0.364875
\(474\) −4.90503 −0.225295
\(475\) −5.86651 −0.269174
\(476\) −2.43917 −0.111799
\(477\) −5.17312 −0.236861
\(478\) 21.1470 0.967240
\(479\) 14.2931 0.653067 0.326533 0.945186i \(-0.394119\pi\)
0.326533 + 0.945186i \(0.394119\pi\)
\(480\) 1.00583 0.0459099
\(481\) 53.8628 2.45593
\(482\) 22.3968 1.02015
\(483\) 8.69772 0.395760
\(484\) −1.07554 −0.0488882
\(485\) 1.00657 0.0457060
\(486\) −16.1479 −0.732486
\(487\) −2.49634 −0.113120 −0.0565600 0.998399i \(-0.518013\pi\)
−0.0565600 + 0.998399i \(0.518013\pi\)
\(488\) −2.35511 −0.106611
\(489\) −12.1670 −0.550211
\(490\) 4.04579 0.182770
\(491\) 0.912369 0.0411747 0.0205873 0.999788i \(-0.493446\pi\)
0.0205873 + 0.999788i \(0.493446\pi\)
\(492\) 1.78388 0.0804236
\(493\) −2.53702 −0.114261
\(494\) −9.54006 −0.429227
\(495\) 7.62791 0.342849
\(496\) 5.13820 0.230712
\(497\) −4.06697 −0.182428
\(498\) −12.4758 −0.559053
\(499\) −19.7594 −0.884552 −0.442276 0.896879i \(-0.645829\pi\)
−0.442276 + 0.896879i \(0.645829\pi\)
\(500\) 9.73693 0.435449
\(501\) −5.22560 −0.233463
\(502\) 29.5345 1.31819
\(503\) 2.37585 0.105934 0.0529669 0.998596i \(-0.483132\pi\)
0.0529669 + 0.998596i \(0.483132\pi\)
\(504\) 3.99444 0.177926
\(505\) −17.3009 −0.769880
\(506\) 16.5131 0.734098
\(507\) −22.1973 −0.985815
\(508\) −16.9589 −0.752431
\(509\) −31.5294 −1.39751 −0.698757 0.715359i \(-0.746263\pi\)
−0.698757 + 0.715359i \(0.746263\pi\)
\(510\) 1.33893 0.0592889
\(511\) −13.9762 −0.618271
\(512\) 1.00000 0.0441942
\(513\) 7.30654 0.322592
\(514\) −8.15983 −0.359915
\(515\) 5.21558 0.229826
\(516\) 2.28109 0.100419
\(517\) 23.7285 1.04358
\(518\) 16.1144 0.708024
\(519\) 7.12602 0.312797
\(520\) 6.80285 0.298325
\(521\) 5.02777 0.220271 0.110135 0.993917i \(-0.464872\pi\)
0.110135 + 0.993917i \(0.464872\pi\)
\(522\) 4.15468 0.181845
\(523\) −10.1924 −0.445684 −0.222842 0.974855i \(-0.571533\pi\)
−0.222842 + 0.974855i \(0.571533\pi\)
\(524\) 1.09649 0.0479006
\(525\) −6.24948 −0.272750
\(526\) −6.98993 −0.304775
\(527\) 6.83979 0.297946
\(528\) −2.85282 −0.124153
\(529\) 4.47585 0.194602
\(530\) −2.63580 −0.114492
\(531\) −29.0046 −1.25869
\(532\) −2.85414 −0.123743
\(533\) 12.0651 0.522597
\(534\) 2.91710 0.126235
\(535\) −5.86441 −0.253540
\(536\) 5.23120 0.225953
\(537\) −8.61353 −0.371701
\(538\) 18.8231 0.811523
\(539\) −11.4749 −0.494260
\(540\) −5.21017 −0.224210
\(541\) −30.4397 −1.30871 −0.654353 0.756190i \(-0.727059\pi\)
−0.654353 + 0.756190i \(0.727059\pi\)
\(542\) 27.9400 1.20013
\(543\) −3.61061 −0.154946
\(544\) 1.33116 0.0570732
\(545\) −16.8735 −0.722779
\(546\) −10.1628 −0.434930
\(547\) −17.8855 −0.764730 −0.382365 0.924011i \(-0.624890\pi\)
−0.382365 + 0.924011i \(0.624890\pi\)
\(548\) 3.71597 0.158739
\(549\) 5.13402 0.219115
\(550\) −11.8650 −0.505925
\(551\) −2.96864 −0.126468
\(552\) −4.74675 −0.202035
\(553\) −9.92500 −0.422054
\(554\) −5.83152 −0.247758
\(555\) −8.84565 −0.375477
\(556\) −17.8798 −0.758271
\(557\) −22.0185 −0.932955 −0.466478 0.884533i \(-0.654477\pi\)
−0.466478 + 0.884533i \(0.654477\pi\)
\(558\) −11.2010 −0.474177
\(559\) 15.4279 0.652530
\(560\) 2.03524 0.0860046
\(561\) −3.79757 −0.160334
\(562\) 18.3223 0.772881
\(563\) 24.2447 1.02179 0.510896 0.859642i \(-0.329314\pi\)
0.510896 + 0.859642i \(0.329314\pi\)
\(564\) −6.82083 −0.287209
\(565\) −17.4482 −0.734053
\(566\) 13.6532 0.573889
\(567\) −4.19980 −0.176375
\(568\) 2.21953 0.0931294
\(569\) −20.0874 −0.842109 −0.421054 0.907035i \(-0.638340\pi\)
−0.421054 + 0.907035i \(0.638340\pi\)
\(570\) 1.56672 0.0656228
\(571\) 34.0325 1.42422 0.712109 0.702069i \(-0.247740\pi\)
0.712109 + 0.702069i \(0.247740\pi\)
\(572\) −19.2947 −0.806753
\(573\) 18.2162 0.760992
\(574\) 3.60956 0.150660
\(575\) −19.7419 −0.823296
\(576\) −2.17995 −0.0908312
\(577\) 26.9081 1.12020 0.560100 0.828425i \(-0.310763\pi\)
0.560100 + 0.828425i \(0.310763\pi\)
\(578\) −15.2280 −0.633401
\(579\) 8.41296 0.349631
\(580\) 2.11688 0.0878989
\(581\) −25.2439 −1.04729
\(582\) 0.820652 0.0340171
\(583\) 7.47584 0.309618
\(584\) 7.62746 0.315627
\(585\) −14.8299 −0.613140
\(586\) 17.3412 0.716360
\(587\) −18.8926 −0.779782 −0.389891 0.920861i \(-0.627487\pi\)
−0.389891 + 0.920861i \(0.627487\pi\)
\(588\) 3.29851 0.136028
\(589\) 8.00344 0.329776
\(590\) −14.7784 −0.608415
\(591\) −7.93346 −0.326339
\(592\) −8.79434 −0.361445
\(593\) −8.89094 −0.365107 −0.182554 0.983196i \(-0.558436\pi\)
−0.182554 + 0.983196i \(0.558436\pi\)
\(594\) 14.7774 0.606326
\(595\) 2.70924 0.111068
\(596\) 3.61186 0.147948
\(597\) 16.7700 0.686351
\(598\) −32.1041 −1.31284
\(599\) −5.17748 −0.211546 −0.105773 0.994390i \(-0.533732\pi\)
−0.105773 + 0.994390i \(0.533732\pi\)
\(600\) 3.41063 0.139238
\(601\) 47.0867 1.92071 0.960354 0.278784i \(-0.0899315\pi\)
0.960354 + 0.278784i \(0.0899315\pi\)
\(602\) 4.61563 0.188119
\(603\) −11.4037 −0.464396
\(604\) 11.5629 0.470487
\(605\) 1.19463 0.0485685
\(606\) −14.1053 −0.572990
\(607\) 42.8514 1.73928 0.869642 0.493683i \(-0.164350\pi\)
0.869642 + 0.493683i \(0.164350\pi\)
\(608\) 1.55764 0.0631705
\(609\) −3.16243 −0.128148
\(610\) 2.61588 0.105914
\(611\) −46.1320 −1.86630
\(612\) −2.90187 −0.117301
\(613\) −3.39865 −0.137270 −0.0686351 0.997642i \(-0.521864\pi\)
−0.0686351 + 0.997642i \(0.521864\pi\)
\(614\) −14.9562 −0.603585
\(615\) −1.98140 −0.0798977
\(616\) −5.77249 −0.232580
\(617\) −12.9012 −0.519382 −0.259691 0.965692i \(-0.583621\pi\)
−0.259691 + 0.965692i \(0.583621\pi\)
\(618\) 4.25223 0.171050
\(619\) 40.9295 1.64510 0.822548 0.568695i \(-0.192552\pi\)
0.822548 + 0.568695i \(0.192552\pi\)
\(620\) −5.70712 −0.229203
\(621\) 24.5879 0.986679
\(622\) 14.5546 0.583584
\(623\) 5.90256 0.236481
\(624\) 5.54633 0.222031
\(625\) 8.01643 0.320657
\(626\) 1.34600 0.0537969
\(627\) −4.44365 −0.177462
\(628\) −0.651038 −0.0259793
\(629\) −11.7067 −0.466777
\(630\) −4.43672 −0.176763
\(631\) 35.8511 1.42721 0.713606 0.700548i \(-0.247061\pi\)
0.713606 + 0.700548i \(0.247061\pi\)
\(632\) 5.41653 0.215458
\(633\) 3.75062 0.149074
\(634\) 9.02892 0.358584
\(635\) 18.8367 0.747511
\(636\) −2.14895 −0.0852116
\(637\) 22.3091 0.883919
\(638\) −6.00405 −0.237703
\(639\) −4.83846 −0.191407
\(640\) −1.11072 −0.0439052
\(641\) −9.10277 −0.359538 −0.179769 0.983709i \(-0.557535\pi\)
−0.179769 + 0.983709i \(0.557535\pi\)
\(642\) −4.78122 −0.188700
\(643\) 14.3229 0.564842 0.282421 0.959291i \(-0.408863\pi\)
0.282421 + 0.959291i \(0.408863\pi\)
\(644\) −9.60473 −0.378479
\(645\) −2.53366 −0.0997626
\(646\) 2.07347 0.0815796
\(647\) −1.94348 −0.0764062 −0.0382031 0.999270i \(-0.512163\pi\)
−0.0382031 + 0.999270i \(0.512163\pi\)
\(648\) 2.29202 0.0900391
\(649\) 41.9154 1.64532
\(650\) 23.0674 0.904779
\(651\) 8.52592 0.334157
\(652\) 13.4358 0.526186
\(653\) −1.16538 −0.0456047 −0.0228023 0.999740i \(-0.507259\pi\)
−0.0228023 + 0.999740i \(0.507259\pi\)
\(654\) −13.7568 −0.537935
\(655\) −1.21790 −0.0475874
\(656\) −1.96990 −0.0769119
\(657\) −16.6275 −0.648700
\(658\) −13.8015 −0.538039
\(659\) 1.29591 0.0504816 0.0252408 0.999681i \(-0.491965\pi\)
0.0252408 + 0.999681i \(0.491965\pi\)
\(660\) 3.16869 0.123341
\(661\) −6.48999 −0.252431 −0.126216 0.992003i \(-0.540283\pi\)
−0.126216 + 0.992003i \(0.540283\pi\)
\(662\) 17.5993 0.684018
\(663\) 7.38308 0.286735
\(664\) 13.7768 0.534642
\(665\) 3.17016 0.122934
\(666\) 19.1712 0.742869
\(667\) −9.99003 −0.386815
\(668\) 5.77053 0.223268
\(669\) −14.9416 −0.577676
\(670\) −5.81041 −0.224476
\(671\) −7.41933 −0.286420
\(672\) 1.65932 0.0640096
\(673\) −49.1916 −1.89620 −0.948099 0.317976i \(-0.896997\pi\)
−0.948099 + 0.317976i \(0.896997\pi\)
\(674\) −27.8689 −1.07347
\(675\) −17.6669 −0.679999
\(676\) 24.5120 0.942770
\(677\) −26.9734 −1.03667 −0.518337 0.855177i \(-0.673449\pi\)
−0.518337 + 0.855177i \(0.673449\pi\)
\(678\) −14.2255 −0.546325
\(679\) 1.66053 0.0637255
\(680\) −1.47856 −0.0567000
\(681\) 13.4745 0.516343
\(682\) 16.1869 0.619830
\(683\) −5.23521 −0.200320 −0.100160 0.994971i \(-0.531935\pi\)
−0.100160 + 0.994971i \(0.531935\pi\)
\(684\) −3.39556 −0.129833
\(685\) −4.12742 −0.157701
\(686\) 19.5008 0.744544
\(687\) 19.2576 0.734725
\(688\) −2.51896 −0.0960344
\(689\) −14.5342 −0.553710
\(690\) 5.27232 0.200714
\(691\) −1.23484 −0.0469755 −0.0234878 0.999724i \(-0.507477\pi\)
−0.0234878 + 0.999724i \(0.507477\pi\)
\(692\) −7.86912 −0.299139
\(693\) 12.5837 0.478016
\(694\) 9.61696 0.365055
\(695\) 19.8595 0.753313
\(696\) 1.72588 0.0654195
\(697\) −2.62227 −0.0993255
\(698\) −22.0680 −0.835287
\(699\) 14.6795 0.555229
\(700\) 6.90118 0.260840
\(701\) −10.9735 −0.414463 −0.207232 0.978292i \(-0.566445\pi\)
−0.207232 + 0.978292i \(0.566445\pi\)
\(702\) −28.7297 −1.08433
\(703\) −13.6984 −0.516644
\(704\) 3.15031 0.118732
\(705\) 7.57606 0.285331
\(706\) 21.9797 0.827216
\(707\) −28.5412 −1.07340
\(708\) −12.0487 −0.452818
\(709\) 13.1590 0.494195 0.247098 0.968991i \(-0.420523\pi\)
0.247098 + 0.968991i \(0.420523\pi\)
\(710\) −2.46528 −0.0925205
\(711\) −11.8078 −0.442825
\(712\) −3.22130 −0.120723
\(713\) 26.9331 1.00865
\(714\) 2.20883 0.0826633
\(715\) 21.4311 0.801478
\(716\) 9.51175 0.355471
\(717\) −19.1500 −0.715170
\(718\) −14.5307 −0.542283
\(719\) −16.5511 −0.617252 −0.308626 0.951183i \(-0.599869\pi\)
−0.308626 + 0.951183i \(0.599869\pi\)
\(720\) 2.42132 0.0902373
\(721\) 8.60411 0.320434
\(722\) −16.5738 −0.616812
\(723\) −20.2818 −0.754289
\(724\) 3.98713 0.148181
\(725\) 7.17803 0.266585
\(726\) 0.973973 0.0361475
\(727\) 28.7031 1.06454 0.532269 0.846575i \(-0.321339\pi\)
0.532269 + 0.846575i \(0.321339\pi\)
\(728\) 11.2226 0.415938
\(729\) 7.74698 0.286925
\(730\) −8.47200 −0.313563
\(731\) −3.35315 −0.124021
\(732\) 2.13271 0.0788272
\(733\) 49.3927 1.82436 0.912181 0.409787i \(-0.134397\pi\)
0.912181 + 0.409787i \(0.134397\pi\)
\(734\) −16.9474 −0.625541
\(735\) −3.66373 −0.135139
\(736\) 5.24174 0.193213
\(737\) 16.4799 0.607045
\(738\) 4.29429 0.158075
\(739\) −3.79336 −0.139541 −0.0697705 0.997563i \(-0.522227\pi\)
−0.0697705 + 0.997563i \(0.522227\pi\)
\(740\) 9.76808 0.359082
\(741\) 8.63916 0.317367
\(742\) −4.34827 −0.159630
\(743\) −39.3661 −1.44420 −0.722100 0.691788i \(-0.756823\pi\)
−0.722100 + 0.691788i \(0.756823\pi\)
\(744\) −4.65298 −0.170587
\(745\) −4.01178 −0.146980
\(746\) −26.1033 −0.955710
\(747\) −30.0326 −1.09884
\(748\) 4.19358 0.153333
\(749\) −9.67448 −0.353498
\(750\) −8.81744 −0.321967
\(751\) −46.0971 −1.68211 −0.841053 0.540952i \(-0.818064\pi\)
−0.841053 + 0.540952i \(0.818064\pi\)
\(752\) 7.53212 0.274668
\(753\) −26.7455 −0.974660
\(754\) 11.6728 0.425100
\(755\) −12.8432 −0.467411
\(756\) −8.59519 −0.312604
\(757\) −38.2945 −1.39184 −0.695919 0.718121i \(-0.745003\pi\)
−0.695919 + 0.718121i \(0.745003\pi\)
\(758\) 3.91896 0.142343
\(759\) −14.9537 −0.542786
\(760\) −1.73010 −0.0627574
\(761\) 21.0060 0.761465 0.380733 0.924685i \(-0.375672\pi\)
0.380733 + 0.924685i \(0.375672\pi\)
\(762\) 15.3575 0.556342
\(763\) −27.8360 −1.00773
\(764\) −20.1158 −0.727763
\(765\) 3.22318 0.116534
\(766\) −15.8472 −0.572584
\(767\) −81.4902 −2.94244
\(768\) −0.905567 −0.0326768
\(769\) 32.4373 1.16972 0.584859 0.811135i \(-0.301150\pi\)
0.584859 + 0.811135i \(0.301150\pi\)
\(770\) 6.41164 0.231059
\(771\) 7.38927 0.266118
\(772\) −9.29027 −0.334364
\(773\) 37.2488 1.33974 0.669872 0.742476i \(-0.266349\pi\)
0.669872 + 0.742476i \(0.266349\pi\)
\(774\) 5.49120 0.197377
\(775\) −19.3520 −0.695143
\(776\) −0.906230 −0.0325318
\(777\) −14.5926 −0.523507
\(778\) −7.21865 −0.258801
\(779\) −3.06839 −0.109937
\(780\) −6.16044 −0.220579
\(781\) 6.99221 0.250201
\(782\) 6.97762 0.249519
\(783\) −8.93999 −0.319489
\(784\) −3.64248 −0.130088
\(785\) 0.723124 0.0258094
\(786\) −0.992950 −0.0354173
\(787\) −33.9548 −1.21036 −0.605180 0.796089i \(-0.706899\pi\)
−0.605180 + 0.796089i \(0.706899\pi\)
\(788\) 8.76077 0.312089
\(789\) 6.32985 0.225349
\(790\) −6.01626 −0.214049
\(791\) −28.7843 −1.02345
\(792\) −6.86752 −0.244027
\(793\) 14.4244 0.512224
\(794\) −15.8773 −0.563465
\(795\) 2.38689 0.0846544
\(796\) −18.5188 −0.656382
\(797\) −6.26895 −0.222058 −0.111029 0.993817i \(-0.535415\pi\)
−0.111029 + 0.993817i \(0.535415\pi\)
\(798\) 2.58461 0.0914944
\(799\) 10.0265 0.354712
\(800\) −3.76629 −0.133159
\(801\) 7.02226 0.248119
\(802\) 1.27789 0.0451240
\(803\) 24.0289 0.847961
\(804\) −4.73720 −0.167068
\(805\) 10.6682 0.376005
\(806\) −31.4700 −1.10848
\(807\) −17.0456 −0.600034
\(808\) 15.5762 0.547970
\(809\) 25.6536 0.901934 0.450967 0.892541i \(-0.351079\pi\)
0.450967 + 0.892541i \(0.351079\pi\)
\(810\) −2.54580 −0.0894504
\(811\) 27.2425 0.956615 0.478307 0.878193i \(-0.341251\pi\)
0.478307 + 0.878193i \(0.341251\pi\)
\(812\) 3.49221 0.122553
\(813\) −25.3016 −0.887365
\(814\) −27.7049 −0.971057
\(815\) −14.9234 −0.522745
\(816\) −1.20546 −0.0421995
\(817\) −3.92362 −0.137270
\(818\) 34.1182 1.19292
\(819\) −24.4648 −0.854868
\(820\) 2.18802 0.0764090
\(821\) 28.3270 0.988618 0.494309 0.869286i \(-0.335421\pi\)
0.494309 + 0.869286i \(0.335421\pi\)
\(822\) −3.36506 −0.117370
\(823\) −26.6203 −0.927925 −0.463962 0.885855i \(-0.653573\pi\)
−0.463962 + 0.885855i \(0.653573\pi\)
\(824\) −4.69566 −0.163581
\(825\) 10.7445 0.374077
\(826\) −24.3798 −0.848281
\(827\) 19.5589 0.680129 0.340065 0.940402i \(-0.389551\pi\)
0.340065 + 0.940402i \(0.389551\pi\)
\(828\) −11.4267 −0.397106
\(829\) 7.24640 0.251678 0.125839 0.992051i \(-0.459838\pi\)
0.125839 + 0.992051i \(0.459838\pi\)
\(830\) −15.3022 −0.531146
\(831\) 5.28084 0.183190
\(832\) −6.12471 −0.212336
\(833\) −4.84874 −0.167999
\(834\) 16.1913 0.560660
\(835\) −6.40946 −0.221809
\(836\) 4.90704 0.169713
\(837\) 24.1022 0.833094
\(838\) 17.3757 0.600232
\(839\) −27.6676 −0.955191 −0.477596 0.878580i \(-0.658492\pi\)
−0.477596 + 0.878580i \(0.658492\pi\)
\(840\) −1.84305 −0.0635911
\(841\) −25.3677 −0.874748
\(842\) 20.8473 0.718444
\(843\) −16.5921 −0.571462
\(844\) −4.14174 −0.142564
\(845\) −27.2261 −0.936606
\(846\) −16.4196 −0.564518
\(847\) 1.97077 0.0677164
\(848\) 2.37305 0.0814908
\(849\) −12.3639 −0.424329
\(850\) −5.01356 −0.171964
\(851\) −46.0977 −1.58021
\(852\) −2.00993 −0.0688592
\(853\) −18.0666 −0.618589 −0.309294 0.950966i \(-0.600093\pi\)
−0.309294 + 0.950966i \(0.600093\pi\)
\(854\) 4.31540 0.147670
\(855\) 3.77153 0.128984
\(856\) 5.27981 0.180460
\(857\) −1.24424 −0.0425024 −0.0212512 0.999774i \(-0.506765\pi\)
−0.0212512 + 0.999774i \(0.506765\pi\)
\(858\) 17.4727 0.596507
\(859\) 45.4253 1.54989 0.774945 0.632029i \(-0.217777\pi\)
0.774945 + 0.632029i \(0.217777\pi\)
\(860\) 2.79787 0.0954065
\(861\) −3.26870 −0.111397
\(862\) 10.5659 0.359875
\(863\) 56.2099 1.91341 0.956704 0.291062i \(-0.0940087\pi\)
0.956704 + 0.291062i \(0.0940087\pi\)
\(864\) 4.69079 0.159584
\(865\) 8.74042 0.297183
\(866\) −26.6808 −0.906651
\(867\) 13.7900 0.468332
\(868\) −9.41500 −0.319566
\(869\) 17.0637 0.578848
\(870\) −1.91698 −0.0649917
\(871\) −32.0395 −1.08562
\(872\) 15.1914 0.514446
\(873\) 1.97554 0.0668617
\(874\) 8.16472 0.276176
\(875\) −17.8415 −0.603153
\(876\) −6.90718 −0.233372
\(877\) −51.0874 −1.72510 −0.862550 0.505973i \(-0.831134\pi\)
−0.862550 + 0.505973i \(0.831134\pi\)
\(878\) −11.2927 −0.381112
\(879\) −15.7037 −0.529671
\(880\) −3.49912 −0.117955
\(881\) 30.1872 1.01703 0.508516 0.861053i \(-0.330194\pi\)
0.508516 + 0.861053i \(0.330194\pi\)
\(882\) 7.94041 0.267368
\(883\) 34.8298 1.17212 0.586058 0.810269i \(-0.300679\pi\)
0.586058 + 0.810269i \(0.300679\pi\)
\(884\) −8.15299 −0.274215
\(885\) 13.3828 0.449857
\(886\) −24.0916 −0.809374
\(887\) −17.4849 −0.587086 −0.293543 0.955946i \(-0.594834\pi\)
−0.293543 + 0.955946i \(0.594834\pi\)
\(888\) 7.96386 0.267250
\(889\) 31.0748 1.04221
\(890\) 3.57797 0.119934
\(891\) 7.22058 0.241899
\(892\) 16.4997 0.552452
\(893\) 11.7323 0.392606
\(894\) −3.27078 −0.109391
\(895\) −10.5649 −0.353147
\(896\) −1.83235 −0.0612147
\(897\) 29.0724 0.970700
\(898\) −6.74186 −0.224979
\(899\) −9.79269 −0.326605
\(900\) 8.21033 0.273678
\(901\) 3.15892 0.105239
\(902\) −6.20581 −0.206631
\(903\) −4.17976 −0.139094
\(904\) 15.7089 0.522470
\(905\) −4.42860 −0.147212
\(906\) −10.4710 −0.347875
\(907\) 22.5762 0.749632 0.374816 0.927099i \(-0.377706\pi\)
0.374816 + 0.927099i \(0.377706\pi\)
\(908\) −14.8796 −0.493796
\(909\) −33.9554 −1.12623
\(910\) −12.4652 −0.413219
\(911\) −25.2613 −0.836946 −0.418473 0.908229i \(-0.637434\pi\)
−0.418473 + 0.908229i \(0.637434\pi\)
\(912\) −1.41054 −0.0467077
\(913\) 43.4011 1.43637
\(914\) 26.9300 0.890764
\(915\) −2.36885 −0.0783118
\(916\) −21.2658 −0.702643
\(917\) −2.00917 −0.0663486
\(918\) 6.24421 0.206090
\(919\) 12.5513 0.414028 0.207014 0.978338i \(-0.433625\pi\)
0.207014 + 0.978338i \(0.433625\pi\)
\(920\) −5.82213 −0.191950
\(921\) 13.5439 0.446286
\(922\) −34.2071 −1.12655
\(923\) −13.5940 −0.447451
\(924\) 5.22737 0.171968
\(925\) 33.1221 1.08905
\(926\) −25.3289 −0.832359
\(927\) 10.2363 0.336204
\(928\) −1.90586 −0.0625629
\(929\) −24.3258 −0.798103 −0.399051 0.916929i \(-0.630661\pi\)
−0.399051 + 0.916929i \(0.630661\pi\)
\(930\) 5.16818 0.169471
\(931\) −5.67365 −0.185946
\(932\) −16.2103 −0.530985
\(933\) −13.1801 −0.431498
\(934\) 41.3175 1.35195
\(935\) −4.65791 −0.152330
\(936\) 13.3515 0.436409
\(937\) −30.3504 −0.991505 −0.495752 0.868464i \(-0.665108\pi\)
−0.495752 + 0.868464i \(0.665108\pi\)
\(938\) −9.58541 −0.312975
\(939\) −1.21889 −0.0397770
\(940\) −8.36610 −0.272872
\(941\) 8.58976 0.280018 0.140009 0.990150i \(-0.455287\pi\)
0.140009 + 0.990150i \(0.455287\pi\)
\(942\) 0.589559 0.0192089
\(943\) −10.3257 −0.336252
\(944\) 13.3052 0.433046
\(945\) 9.54688 0.310560
\(946\) −7.93551 −0.258006
\(947\) 14.3460 0.466183 0.233091 0.972455i \(-0.425116\pi\)
0.233091 + 0.972455i \(0.425116\pi\)
\(948\) −4.90503 −0.159308
\(949\) −46.7160 −1.51646
\(950\) −5.86651 −0.190335
\(951\) −8.17630 −0.265135
\(952\) −2.43917 −0.0790538
\(953\) 16.7263 0.541817 0.270909 0.962605i \(-0.412676\pi\)
0.270909 + 0.962605i \(0.412676\pi\)
\(954\) −5.17312 −0.167486
\(955\) 22.3431 0.723004
\(956\) 21.1470 0.683942
\(957\) 5.43707 0.175756
\(958\) 14.2931 0.461788
\(959\) −6.80898 −0.219873
\(960\) 1.00583 0.0324632
\(961\) −4.59890 −0.148352
\(962\) 53.8628 1.73660
\(963\) −11.5097 −0.370895
\(964\) 22.3968 0.721353
\(965\) 10.3189 0.332178
\(966\) 8.69772 0.279845
\(967\) −13.0467 −0.419555 −0.209778 0.977749i \(-0.567274\pi\)
−0.209778 + 0.977749i \(0.567274\pi\)
\(968\) −1.07554 −0.0345691
\(969\) −1.87767 −0.0603193
\(970\) 1.00657 0.0323191
\(971\) 42.2755 1.35669 0.678343 0.734745i \(-0.262698\pi\)
0.678343 + 0.734745i \(0.262698\pi\)
\(972\) −16.1479 −0.517946
\(973\) 32.7621 1.05030
\(974\) −2.49634 −0.0799879
\(975\) −20.8891 −0.668987
\(976\) −2.35511 −0.0753852
\(977\) 27.9589 0.894484 0.447242 0.894413i \(-0.352406\pi\)
0.447242 + 0.894413i \(0.352406\pi\)
\(978\) −12.1670 −0.389058
\(979\) −10.1481 −0.324334
\(980\) 4.04579 0.129238
\(981\) −33.1165 −1.05733
\(982\) 0.912369 0.0291149
\(983\) 38.0913 1.21493 0.607463 0.794348i \(-0.292187\pi\)
0.607463 + 0.794348i \(0.292187\pi\)
\(984\) 1.78388 0.0568680
\(985\) −9.73079 −0.310049
\(986\) −2.53702 −0.0807950
\(987\) 12.4982 0.397822
\(988\) −9.54006 −0.303510
\(989\) −13.2037 −0.419854
\(990\) 7.62791 0.242431
\(991\) −28.9257 −0.918855 −0.459427 0.888215i \(-0.651945\pi\)
−0.459427 + 0.888215i \(0.651945\pi\)
\(992\) 5.13820 0.163138
\(993\) −15.9374 −0.505757
\(994\) −4.06697 −0.128996
\(995\) 20.5693 0.652090
\(996\) −12.4758 −0.395310
\(997\) 16.4437 0.520777 0.260388 0.965504i \(-0.416149\pi\)
0.260388 + 0.965504i \(0.416149\pi\)
\(998\) −19.7594 −0.625473
\(999\) −41.2524 −1.30517
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 4034.2.a.d.1.18 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.18 52 1.1 even 1 trivial