Properties

Label 7942.2.a.bc.1.1
Level $7942$
Weight $2$
Character 7942.1
Self dual yes
Analytic conductor $63.417$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7942.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.4171892853\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.469.1
Defining polynomial: \( x^{3} - x^{2} - 5x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.39138\) of defining polynomial
Character \(\chi\) \(=\) 7942.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.39138 q^{3} +1.00000 q^{4} -0.391382 q^{5} +2.39138 q^{6} -1.71871 q^{7} -1.00000 q^{8} +2.71871 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.39138 q^{3} +1.00000 q^{4} -0.391382 q^{5} +2.39138 q^{6} -1.71871 q^{7} -1.00000 q^{8} +2.71871 q^{9} +0.391382 q^{10} -1.00000 q^{11} -2.39138 q^{12} -3.71871 q^{13} +1.71871 q^{14} +0.935945 q^{15} +1.00000 q^{16} +5.43742 q^{17} -2.71871 q^{18} -0.391382 q^{20} +4.11009 q^{21} +1.00000 q^{22} -3.43742 q^{23} +2.39138 q^{24} -4.84682 q^{25} +3.71871 q^{26} +0.672673 q^{27} -1.71871 q^{28} +3.82880 q^{29} -0.935945 q^{30} +3.06406 q^{31} -1.00000 q^{32} +2.39138 q^{33} -5.43742 q^{34} +0.672673 q^{35} +2.71871 q^{36} +4.65465 q^{37} +8.89286 q^{39} +0.391382 q^{40} -1.06406 q^{41} -4.11009 q^{42} -3.73673 q^{43} -1.00000 q^{44} -1.06406 q^{45} +3.43742 q^{46} -8.22018 q^{47} -2.39138 q^{48} -4.04604 q^{49} +4.84682 q^{50} -13.0029 q^{51} -3.71871 q^{52} +1.21724 q^{53} -0.672673 q^{54} +0.391382 q^{55} +1.71871 q^{56} -3.82880 q^{58} -12.4404 q^{59} +0.935945 q^{60} +2.00000 q^{61} -3.06406 q^{62} -4.67267 q^{63} +1.00000 q^{64} +1.45544 q^{65} -2.39138 q^{66} +1.71871 q^{67} +5.43742 q^{68} +8.22018 q^{69} -0.672673 q^{70} -1.04604 q^{71} -2.71871 q^{72} +13.6576 q^{73} -4.65465 q^{74} +11.5906 q^{75} +1.71871 q^{77} -8.89286 q^{78} -13.0029 q^{79} -0.391382 q^{80} -9.76475 q^{81} +1.06406 q^{82} +8.51949 q^{83} +4.11009 q^{84} -2.12811 q^{85} +3.73673 q^{86} -9.15613 q^{87} +1.00000 q^{88} -17.6936 q^{89} +1.06406 q^{90} +6.39138 q^{91} -3.43742 q^{92} -7.32733 q^{93} +8.22018 q^{94} +2.39138 q^{96} +4.65465 q^{97} +4.04604 q^{98} -2.71871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{5} + q^{6} + q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{5} + q^{6} + q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} - 3 q^{11} - q^{12} - 5 q^{13} - q^{14} + 9 q^{15} + 3 q^{16} + 4 q^{17} - 2 q^{18} + 5 q^{20} + 3 q^{22} + 2 q^{23} + q^{24} + 4 q^{25} + 5 q^{26} + 2 q^{27} + q^{28} - 7 q^{29} - 9 q^{30} + 3 q^{31} - 3 q^{32} + q^{33} - 4 q^{34} + 2 q^{35} + 2 q^{36} + 14 q^{37} + 2 q^{39} - 5 q^{40} + 3 q^{41} - 5 q^{43} - 3 q^{44} + 3 q^{45} - 2 q^{46} - q^{48} - 6 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} + 16 q^{53} - 2 q^{54} - 5 q^{55} - q^{56} + 7 q^{58} + 12 q^{59} + 9 q^{60} + 6 q^{61} - 3 q^{62} - 14 q^{63} + 3 q^{64} - 8 q^{65} - q^{66} - q^{67} + 4 q^{68} - 2 q^{70} + 3 q^{71} - 2 q^{72} + 4 q^{73} - 14 q^{74} + 41 q^{75} - q^{77} - 2 q^{78} - 2 q^{79} + 5 q^{80} - 17 q^{81} - 3 q^{82} + 7 q^{83} + 6 q^{85} + 5 q^{86} - 9 q^{87} + 3 q^{88} - 16 q^{89} - 3 q^{90} + 13 q^{91} + 2 q^{92} - 22 q^{93} + q^{96} + 14 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −2.39138 −1.38067 −0.690333 0.723492i \(-0.742536\pi\)
−0.690333 + 0.723492i \(0.742536\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.391382 −0.175032 −0.0875158 0.996163i \(-0.527893\pi\)
−0.0875158 + 0.996163i \(0.527893\pi\)
\(6\) 2.39138 0.976278
\(7\) −1.71871 −0.649611 −0.324806 0.945781i \(-0.605299\pi\)
−0.324806 + 0.945781i \(0.605299\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.71871 0.906237
\(10\) 0.391382 0.123766
\(11\) −1.00000 −0.301511
\(12\) −2.39138 −0.690333
\(13\) −3.71871 −1.03138 −0.515692 0.856774i \(-0.672465\pi\)
−0.515692 + 0.856774i \(0.672465\pi\)
\(14\) 1.71871 0.459344
\(15\) 0.935945 0.241660
\(16\) 1.00000 0.250000
\(17\) 5.43742 1.31877 0.659384 0.751806i \(-0.270817\pi\)
0.659384 + 0.751806i \(0.270817\pi\)
\(18\) −2.71871 −0.640806
\(19\) 0 0
\(20\) −0.391382 −0.0875158
\(21\) 4.11009 0.896896
\(22\) 1.00000 0.213201
\(23\) −3.43742 −0.716751 −0.358376 0.933577i \(-0.616669\pi\)
−0.358376 + 0.933577i \(0.616669\pi\)
\(24\) 2.39138 0.488139
\(25\) −4.84682 −0.969364
\(26\) 3.71871 0.729299
\(27\) 0.672673 0.129456
\(28\) −1.71871 −0.324806
\(29\) 3.82880 0.710991 0.355495 0.934678i \(-0.384312\pi\)
0.355495 + 0.934678i \(0.384312\pi\)
\(30\) −0.935945 −0.170879
\(31\) 3.06406 0.550321 0.275160 0.961398i \(-0.411269\pi\)
0.275160 + 0.961398i \(0.411269\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.39138 0.416286
\(34\) −5.43742 −0.932510
\(35\) 0.672673 0.113702
\(36\) 2.71871 0.453118
\(37\) 4.65465 0.765221 0.382610 0.923910i \(-0.375025\pi\)
0.382610 + 0.923910i \(0.375025\pi\)
\(38\) 0 0
\(39\) 8.89286 1.42400
\(40\) 0.391382 0.0618830
\(41\) −1.06406 −0.166177 −0.0830887 0.996542i \(-0.526478\pi\)
−0.0830887 + 0.996542i \(0.526478\pi\)
\(42\) −4.11009 −0.634201
\(43\) −3.73673 −0.569846 −0.284923 0.958550i \(-0.591968\pi\)
−0.284923 + 0.958550i \(0.591968\pi\)
\(44\) −1.00000 −0.150756
\(45\) −1.06406 −0.158620
\(46\) 3.43742 0.506820
\(47\) −8.22018 −1.19904 −0.599519 0.800361i \(-0.704641\pi\)
−0.599519 + 0.800361i \(0.704641\pi\)
\(48\) −2.39138 −0.345166
\(49\) −4.04604 −0.578005
\(50\) 4.84682 0.685444
\(51\) −13.0029 −1.82078
\(52\) −3.71871 −0.515692
\(53\) 1.21724 0.167200 0.0836001 0.996499i \(-0.473358\pi\)
0.0836001 + 0.996499i \(0.473358\pi\)
\(54\) −0.672673 −0.0915392
\(55\) 0.391382 0.0527740
\(56\) 1.71871 0.229672
\(57\) 0 0
\(58\) −3.82880 −0.502746
\(59\) −12.4404 −1.61960 −0.809799 0.586707i \(-0.800424\pi\)
−0.809799 + 0.586707i \(0.800424\pi\)
\(60\) 0.935945 0.120830
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −3.06406 −0.389135
\(63\) −4.67267 −0.588701
\(64\) 1.00000 0.125000
\(65\) 1.45544 0.180525
\(66\) −2.39138 −0.294359
\(67\) 1.71871 0.209974 0.104987 0.994474i \(-0.466520\pi\)
0.104987 + 0.994474i \(0.466520\pi\)
\(68\) 5.43742 0.659384
\(69\) 8.22018 0.989594
\(70\) −0.672673 −0.0803998
\(71\) −1.04604 −0.124142 −0.0620709 0.998072i \(-0.519770\pi\)
−0.0620709 + 0.998072i \(0.519770\pi\)
\(72\) −2.71871 −0.320403
\(73\) 13.6576 1.59850 0.799251 0.600998i \(-0.205230\pi\)
0.799251 + 0.600998i \(0.205230\pi\)
\(74\) −4.65465 −0.541093
\(75\) 11.5906 1.33837
\(76\) 0 0
\(77\) 1.71871 0.195865
\(78\) −8.89286 −1.00692
\(79\) −13.0029 −1.46295 −0.731473 0.681870i \(-0.761167\pi\)
−0.731473 + 0.681870i \(0.761167\pi\)
\(80\) −0.391382 −0.0437579
\(81\) −9.76475 −1.08497
\(82\) 1.06406 0.117505
\(83\) 8.51949 0.935136 0.467568 0.883957i \(-0.345130\pi\)
0.467568 + 0.883957i \(0.345130\pi\)
\(84\) 4.11009 0.448448
\(85\) −2.12811 −0.230826
\(86\) 3.73673 0.402942
\(87\) −9.15613 −0.981640
\(88\) 1.00000 0.106600
\(89\) −17.6936 −1.87552 −0.937761 0.347281i \(-0.887105\pi\)
−0.937761 + 0.347281i \(0.887105\pi\)
\(90\) 1.06406 0.112161
\(91\) 6.39138 0.669999
\(92\) −3.43742 −0.358376
\(93\) −7.32733 −0.759808
\(94\) 8.22018 0.847847
\(95\) 0 0
\(96\) 2.39138 0.244069
\(97\) 4.65465 0.472609 0.236304 0.971679i \(-0.424064\pi\)
0.236304 + 0.971679i \(0.424064\pi\)
\(98\) 4.04604 0.408711
\(99\) −2.71871 −0.273241
\(100\) −4.84682 −0.484682
\(101\) −9.65760 −0.960967 −0.480484 0.877004i \(-0.659539\pi\)
−0.480484 + 0.877004i \(0.659539\pi\)
\(102\) 13.0029 1.28748
\(103\) 6.95396 0.685194 0.342597 0.939482i \(-0.388693\pi\)
0.342597 + 0.939482i \(0.388693\pi\)
\(104\) 3.71871 0.364649
\(105\) −1.60862 −0.156985
\(106\) −1.21724 −0.118228
\(107\) −2.65465 −0.256635 −0.128318 0.991733i \(-0.540958\pi\)
−0.128318 + 0.991733i \(0.540958\pi\)
\(108\) 0.672673 0.0647280
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) −0.391382 −0.0373168
\(111\) −11.1311 −1.05651
\(112\) −1.71871 −0.162403
\(113\) −7.52949 −0.708315 −0.354158 0.935186i \(-0.615232\pi\)
−0.354158 + 0.935186i \(0.615232\pi\)
\(114\) 0 0
\(115\) 1.34535 0.125454
\(116\) 3.82880 0.355495
\(117\) −10.1101 −0.934678
\(118\) 12.4404 1.14523
\(119\) −9.34535 −0.856686
\(120\) −0.935945 −0.0854397
\(121\) 1.00000 0.0909091
\(122\) −2.00000 −0.181071
\(123\) 2.54456 0.229435
\(124\) 3.06406 0.275160
\(125\) 3.85387 0.344701
\(126\) 4.67267 0.416275
\(127\) 5.00295 0.443940 0.221970 0.975054i \(-0.428751\pi\)
0.221970 + 0.975054i \(0.428751\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.93594 0.786766
\(130\) −1.45544 −0.127650
\(131\) −6.50147 −0.568036 −0.284018 0.958819i \(-0.591668\pi\)
−0.284018 + 0.958819i \(0.591668\pi\)
\(132\) 2.39138 0.208143
\(133\) 0 0
\(134\) −1.71871 −0.148474
\(135\) −0.263272 −0.0226589
\(136\) −5.43742 −0.466255
\(137\) 15.7187 1.34294 0.671470 0.741032i \(-0.265663\pi\)
0.671470 + 0.741032i \(0.265663\pi\)
\(138\) −8.22018 −0.699749
\(139\) −11.1381 −0.944722 −0.472361 0.881405i \(-0.656598\pi\)
−0.472361 + 0.881405i \(0.656598\pi\)
\(140\) 0.672673 0.0568512
\(141\) 19.6576 1.65547
\(142\) 1.04604 0.0877815
\(143\) 3.71871 0.310974
\(144\) 2.71871 0.226559
\(145\) −1.49853 −0.124446
\(146\) −13.6576 −1.13031
\(147\) 9.67562 0.798032
\(148\) 4.65465 0.382610
\(149\) 11.3453 0.929447 0.464723 0.885456i \(-0.346154\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(150\) −11.5906 −0.946368
\(151\) 14.6547 1.19258 0.596289 0.802770i \(-0.296641\pi\)
0.596289 + 0.802770i \(0.296641\pi\)
\(152\) 0 0
\(153\) 14.7828 1.19512
\(154\) −1.71871 −0.138498
\(155\) −1.19922 −0.0963234
\(156\) 8.89286 0.711998
\(157\) −10.4835 −0.836671 −0.418335 0.908293i \(-0.637386\pi\)
−0.418335 + 0.908293i \(0.637386\pi\)
\(158\) 13.0029 1.03446
\(159\) −2.91087 −0.230847
\(160\) 0.391382 0.0309415
\(161\) 5.90793 0.465610
\(162\) 9.76475 0.767191
\(163\) −3.47346 −0.272062 −0.136031 0.990705i \(-0.543435\pi\)
−0.136031 + 0.990705i \(0.543435\pi\)
\(164\) −1.06406 −0.0830887
\(165\) −0.935945 −0.0728632
\(166\) −8.51949 −0.661241
\(167\) −23.0950 −1.78715 −0.893573 0.448917i \(-0.851810\pi\)
−0.893573 + 0.448917i \(0.851810\pi\)
\(168\) −4.11009 −0.317100
\(169\) 0.828802 0.0637540
\(170\) 2.12811 0.163219
\(171\) 0 0
\(172\) −3.73673 −0.284923
\(173\) 18.1771 1.38198 0.690990 0.722865i \(-0.257175\pi\)
0.690990 + 0.722865i \(0.257175\pi\)
\(174\) 9.15613 0.694124
\(175\) 8.33028 0.629710
\(176\) −1.00000 −0.0753778
\(177\) 29.7497 2.23612
\(178\) 17.6936 1.32619
\(179\) −11.2842 −0.843424 −0.421712 0.906730i \(-0.638571\pi\)
−0.421712 + 0.906730i \(0.638571\pi\)
\(180\) −1.06406 −0.0793100
\(181\) −21.8778 −1.62616 −0.813082 0.582150i \(-0.802212\pi\)
−0.813082 + 0.582150i \(0.802212\pi\)
\(182\) −6.39138 −0.473761
\(183\) −4.78276 −0.353552
\(184\) 3.43742 0.253410
\(185\) −1.82175 −0.133938
\(186\) 7.32733 0.537266
\(187\) −5.43742 −0.397623
\(188\) −8.22018 −0.599519
\(189\) −1.15613 −0.0840960
\(190\) 0 0
\(191\) −7.09502 −0.513378 −0.256689 0.966494i \(-0.582632\pi\)
−0.256689 + 0.966494i \(0.582632\pi\)
\(192\) −2.39138 −0.172583
\(193\) −12.6476 −0.910394 −0.455197 0.890391i \(-0.650431\pi\)
−0.455197 + 0.890391i \(0.650431\pi\)
\(194\) −4.65465 −0.334185
\(195\) −3.48051 −0.249244
\(196\) −4.04604 −0.289003
\(197\) 8.43447 0.600931 0.300466 0.953793i \(-0.402858\pi\)
0.300466 + 0.953793i \(0.402858\pi\)
\(198\) 2.71871 0.193210
\(199\) −2.09207 −0.148303 −0.0741516 0.997247i \(-0.523625\pi\)
−0.0741516 + 0.997247i \(0.523625\pi\)
\(200\) 4.84682 0.342722
\(201\) −4.11009 −0.289904
\(202\) 9.65760 0.679507
\(203\) −6.58060 −0.461867
\(204\) −13.0029 −0.910389
\(205\) 0.416452 0.0290863
\(206\) −6.95396 −0.484506
\(207\) −9.34535 −0.649546
\(208\) −3.71871 −0.257846
\(209\) 0 0
\(210\) 1.60862 0.111005
\(211\) 6.09207 0.419396 0.209698 0.977766i \(-0.432752\pi\)
0.209698 + 0.977766i \(0.432752\pi\)
\(212\) 1.21724 0.0836001
\(213\) 2.50147 0.171398
\(214\) 2.65465 0.181468
\(215\) 1.46249 0.0997409
\(216\) −0.672673 −0.0457696
\(217\) −5.26622 −0.357494
\(218\) 6.00000 0.406371
\(219\) −32.6606 −2.20700
\(220\) 0.391382 0.0263870
\(221\) −20.2202 −1.36016
\(222\) 11.1311 0.747068
\(223\) 18.8748 1.26395 0.631976 0.774988i \(-0.282244\pi\)
0.631976 + 0.774988i \(0.282244\pi\)
\(224\) 1.71871 0.114836
\(225\) −13.1771 −0.878473
\(226\) 7.52949 0.500854
\(227\) −20.9669 −1.39162 −0.695811 0.718225i \(-0.744955\pi\)
−0.695811 + 0.718225i \(0.744955\pi\)
\(228\) 0 0
\(229\) 13.8108 0.912642 0.456321 0.889815i \(-0.349167\pi\)
0.456321 + 0.889815i \(0.349167\pi\)
\(230\) −1.34535 −0.0887094
\(231\) −4.11009 −0.270424
\(232\) −3.82880 −0.251373
\(233\) 4.91087 0.321722 0.160861 0.986977i \(-0.448573\pi\)
0.160861 + 0.986977i \(0.448573\pi\)
\(234\) 10.1101 0.660917
\(235\) 3.21724 0.209869
\(236\) −12.4404 −0.809799
\(237\) 31.0950 2.01984
\(238\) 9.34535 0.605769
\(239\) −14.0490 −0.908753 −0.454377 0.890810i \(-0.650138\pi\)
−0.454377 + 0.890810i \(0.650138\pi\)
\(240\) 0.935945 0.0604150
\(241\) −22.7397 −1.46479 −0.732396 0.680879i \(-0.761598\pi\)
−0.732396 + 0.680879i \(0.761598\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 21.3332 1.36853
\(244\) 2.00000 0.128037
\(245\) 1.58355 0.101169
\(246\) −2.54456 −0.162235
\(247\) 0 0
\(248\) −3.06406 −0.194568
\(249\) −20.3734 −1.29111
\(250\) −3.85387 −0.243740
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −4.67267 −0.294351
\(253\) 3.43742 0.216109
\(254\) −5.00295 −0.313913
\(255\) 5.08913 0.318693
\(256\) 1.00000 0.0625000
\(257\) 19.4433 1.21284 0.606420 0.795144i \(-0.292605\pi\)
0.606420 + 0.795144i \(0.292605\pi\)
\(258\) −8.93594 −0.556328
\(259\) −8.00000 −0.497096
\(260\) 1.45544 0.0902624
\(261\) 10.4094 0.644326
\(262\) 6.50147 0.401662
\(263\) 14.6476 0.903210 0.451605 0.892218i \(-0.350852\pi\)
0.451605 + 0.892218i \(0.350852\pi\)
\(264\) −2.39138 −0.147179
\(265\) −0.476404 −0.0292653
\(266\) 0 0
\(267\) 42.3123 2.58947
\(268\) 1.71871 0.104987
\(269\) −8.34829 −0.509004 −0.254502 0.967072i \(-0.581912\pi\)
−0.254502 + 0.967072i \(0.581912\pi\)
\(270\) 0.263272 0.0160222
\(271\) −10.5375 −0.640108 −0.320054 0.947399i \(-0.603701\pi\)
−0.320054 + 0.947399i \(0.603701\pi\)
\(272\) 5.43742 0.329692
\(273\) −15.2842 −0.925044
\(274\) −15.7187 −0.949602
\(275\) 4.84682 0.292274
\(276\) 8.22018 0.494797
\(277\) −22.8807 −1.37477 −0.687385 0.726293i \(-0.741242\pi\)
−0.687385 + 0.726293i \(0.741242\pi\)
\(278\) 11.1381 0.668020
\(279\) 8.33028 0.498721
\(280\) −0.672673 −0.0401999
\(281\) 4.39138 0.261968 0.130984 0.991384i \(-0.458186\pi\)
0.130984 + 0.991384i \(0.458186\pi\)
\(282\) −19.6576 −1.17059
\(283\) −24.0670 −1.43063 −0.715317 0.698800i \(-0.753718\pi\)
−0.715317 + 0.698800i \(0.753718\pi\)
\(284\) −1.04604 −0.0620709
\(285\) 0 0
\(286\) −3.71871 −0.219892
\(287\) 1.82880 0.107951
\(288\) −2.71871 −0.160202
\(289\) 12.5655 0.739149
\(290\) 1.49853 0.0879965
\(291\) −11.1311 −0.652514
\(292\) 13.6576 0.799251
\(293\) 27.2901 1.59431 0.797153 0.603777i \(-0.206338\pi\)
0.797153 + 0.603777i \(0.206338\pi\)
\(294\) −9.67562 −0.564294
\(295\) 4.86894 0.283481
\(296\) −4.65465 −0.270546
\(297\) −0.672673 −0.0390324
\(298\) −11.3453 −0.657218
\(299\) 12.7828 0.739246
\(300\) 11.5906 0.669184
\(301\) 6.42235 0.370178
\(302\) −14.6547 −0.843281
\(303\) 23.0950 1.32677
\(304\) 0 0
\(305\) −0.782765 −0.0448210
\(306\) −14.7828 −0.845074
\(307\) 9.22313 0.526392 0.263196 0.964742i \(-0.415223\pi\)
0.263196 + 0.964742i \(0.415223\pi\)
\(308\) 1.71871 0.0979326
\(309\) −16.6296 −0.946024
\(310\) 1.19922 0.0681110
\(311\) 6.34829 0.359979 0.179989 0.983669i \(-0.442394\pi\)
0.179989 + 0.983669i \(0.442394\pi\)
\(312\) −8.89286 −0.503459
\(313\) 13.3943 0.757092 0.378546 0.925582i \(-0.376424\pi\)
0.378546 + 0.925582i \(0.376424\pi\)
\(314\) 10.4835 0.591616
\(315\) 1.82880 0.103041
\(316\) −13.0029 −0.731473
\(317\) −31.0029 −1.74130 −0.870650 0.491904i \(-0.836301\pi\)
−0.870650 + 0.491904i \(0.836301\pi\)
\(318\) 2.91087 0.163234
\(319\) −3.82880 −0.214372
\(320\) −0.391382 −0.0218789
\(321\) 6.34829 0.354327
\(322\) −5.90793 −0.329236
\(323\) 0 0
\(324\) −9.76475 −0.542486
\(325\) 18.0239 0.999787
\(326\) 3.47346 0.192377
\(327\) 14.3483 0.793462
\(328\) 1.06406 0.0587526
\(329\) 14.1281 0.778908
\(330\) 0.935945 0.0515221
\(331\) 16.2993 0.895891 0.447946 0.894061i \(-0.352156\pi\)
0.447946 + 0.894061i \(0.352156\pi\)
\(332\) 8.51949 0.467568
\(333\) 12.6547 0.693471
\(334\) 23.0950 1.26370
\(335\) −0.672673 −0.0367520
\(336\) 4.11009 0.224224
\(337\) 3.19217 0.173888 0.0869442 0.996213i \(-0.472290\pi\)
0.0869442 + 0.996213i \(0.472290\pi\)
\(338\) −0.828802 −0.0450809
\(339\) 18.0059 0.977946
\(340\) −2.12811 −0.115413
\(341\) −3.06406 −0.165928
\(342\) 0 0
\(343\) 18.9849 1.02509
\(344\) 3.73673 0.201471
\(345\) −3.21724 −0.173210
\(346\) −18.1771 −0.977207
\(347\) 24.6966 1.32578 0.662891 0.748716i \(-0.269329\pi\)
0.662891 + 0.748716i \(0.269329\pi\)
\(348\) −9.15613 −0.490820
\(349\) −4.43447 −0.237372 −0.118686 0.992932i \(-0.537868\pi\)
−0.118686 + 0.992932i \(0.537868\pi\)
\(350\) −8.33028 −0.445272
\(351\) −2.50147 −0.133519
\(352\) 1.00000 0.0533002
\(353\) 25.3152 1.34739 0.673696 0.739008i \(-0.264706\pi\)
0.673696 + 0.739008i \(0.264706\pi\)
\(354\) −29.7497 −1.58118
\(355\) 0.409400 0.0217287
\(356\) −17.6936 −0.937761
\(357\) 22.3483 1.18280
\(358\) 11.2842 0.596391
\(359\) −13.9749 −0.737569 −0.368784 0.929515i \(-0.620226\pi\)
−0.368784 + 0.929515i \(0.620226\pi\)
\(360\) 1.06406 0.0560806
\(361\) 0 0
\(362\) 21.8778 1.14987
\(363\) −2.39138 −0.125515
\(364\) 6.39138 0.334999
\(365\) −5.34535 −0.279788
\(366\) 4.78276 0.249999
\(367\) −25.3453 −1.32302 −0.661508 0.749938i \(-0.730083\pi\)
−0.661508 + 0.749938i \(0.730083\pi\)
\(368\) −3.43742 −0.179188
\(369\) −2.89286 −0.150596
\(370\) 1.82175 0.0947083
\(371\) −2.09207 −0.108615
\(372\) −7.32733 −0.379904
\(373\) −8.95396 −0.463619 −0.231809 0.972761i \(-0.574465\pi\)
−0.231809 + 0.972761i \(0.574465\pi\)
\(374\) 5.43742 0.281162
\(375\) −9.21608 −0.475916
\(376\) 8.22018 0.423924
\(377\) −14.2382 −0.733305
\(378\) 1.15613 0.0594649
\(379\) 25.8527 1.32796 0.663982 0.747748i \(-0.268865\pi\)
0.663982 + 0.747748i \(0.268865\pi\)
\(380\) 0 0
\(381\) −11.9640 −0.612932
\(382\) 7.09502 0.363013
\(383\) 20.6296 1.05412 0.527061 0.849827i \(-0.323294\pi\)
0.527061 + 0.849827i \(0.323294\pi\)
\(384\) 2.39138 0.122035
\(385\) −0.672673 −0.0342826
\(386\) 12.6476 0.643746
\(387\) −10.1591 −0.516415
\(388\) 4.65465 0.236304
\(389\) 15.6086 0.791388 0.395694 0.918382i \(-0.370504\pi\)
0.395694 + 0.918382i \(0.370504\pi\)
\(390\) 3.48051 0.176242
\(391\) −18.6907 −0.945229
\(392\) 4.04604 0.204356
\(393\) 15.5475 0.784268
\(394\) −8.43447 −0.424922
\(395\) 5.08913 0.256062
\(396\) −2.71871 −0.136620
\(397\) −34.2512 −1.71902 −0.859508 0.511122i \(-0.829230\pi\)
−0.859508 + 0.511122i \(0.829230\pi\)
\(398\) 2.09207 0.104866
\(399\) 0 0
\(400\) −4.84682 −0.242341
\(401\) −4.09207 −0.204348 −0.102174 0.994767i \(-0.532580\pi\)
−0.102174 + 0.994767i \(0.532580\pi\)
\(402\) 4.11009 0.204993
\(403\) −11.3943 −0.567592
\(404\) −9.65760 −0.480484
\(405\) 3.82175 0.189904
\(406\) 6.58060 0.326590
\(407\) −4.65465 −0.230723
\(408\) 13.0029 0.643742
\(409\) −2.48346 −0.122799 −0.0613995 0.998113i \(-0.519556\pi\)
−0.0613995 + 0.998113i \(0.519556\pi\)
\(410\) −0.416452 −0.0205671
\(411\) −37.5894 −1.85415
\(412\) 6.95396 0.342597
\(413\) 21.3814 1.05211
\(414\) 9.34535 0.459299
\(415\) −3.33438 −0.163678
\(416\) 3.71871 0.182325
\(417\) 26.6355 1.30435
\(418\) 0 0
\(419\) 35.0950 1.71450 0.857252 0.514897i \(-0.172170\pi\)
0.857252 + 0.514897i \(0.172170\pi\)
\(420\) −1.60862 −0.0784925
\(421\) 12.3483 0.601819 0.300910 0.953653i \(-0.402710\pi\)
0.300910 + 0.953653i \(0.402710\pi\)
\(422\) −6.09207 −0.296558
\(423\) −22.3483 −1.08661
\(424\) −1.21724 −0.0591142
\(425\) −26.3542 −1.27837
\(426\) −2.50147 −0.121197
\(427\) −3.43742 −0.166348
\(428\) −2.65465 −0.128318
\(429\) −8.89286 −0.429351
\(430\) −1.46249 −0.0705275
\(431\) 6.94691 0.334621 0.167310 0.985904i \(-0.446492\pi\)
0.167310 + 0.985904i \(0.446492\pi\)
\(432\) 0.672673 0.0323640
\(433\) 13.2533 0.636912 0.318456 0.947938i \(-0.396836\pi\)
0.318456 + 0.947938i \(0.396836\pi\)
\(434\) 5.26622 0.252787
\(435\) 3.58355 0.171818
\(436\) −6.00000 −0.287348
\(437\) 0 0
\(438\) 32.6606 1.56058
\(439\) −15.3152 −0.730955 −0.365477 0.930820i \(-0.619094\pi\)
−0.365477 + 0.930820i \(0.619094\pi\)
\(440\) −0.391382 −0.0186584
\(441\) −11.0000 −0.523810
\(442\) 20.2202 0.961776
\(443\) −20.8807 −0.992074 −0.496037 0.868301i \(-0.665212\pi\)
−0.496037 + 0.868301i \(0.665212\pi\)
\(444\) −11.1311 −0.528257
\(445\) 6.92498 0.328275
\(446\) −18.8748 −0.893750
\(447\) −27.1311 −1.28326
\(448\) −1.71871 −0.0812014
\(449\) 28.7887 1.35862 0.679310 0.733851i \(-0.262279\pi\)
0.679310 + 0.733851i \(0.262279\pi\)
\(450\) 13.1771 0.621174
\(451\) 1.06406 0.0501044
\(452\) −7.52949 −0.354158
\(453\) −35.0449 −1.64655
\(454\) 20.9669 0.984026
\(455\) −2.50147 −0.117271
\(456\) 0 0
\(457\) −32.7526 −1.53210 −0.766052 0.642779i \(-0.777781\pi\)
−0.766052 + 0.642779i \(0.777781\pi\)
\(458\) −13.8108 −0.645336
\(459\) 3.65760 0.170722
\(460\) 1.34535 0.0627271
\(461\) 20.2261 0.942023 0.471011 0.882127i \(-0.343889\pi\)
0.471011 + 0.882127i \(0.343889\pi\)
\(462\) 4.11009 0.191219
\(463\) −18.6907 −0.868630 −0.434315 0.900761i \(-0.643010\pi\)
−0.434315 + 0.900761i \(0.643010\pi\)
\(464\) 3.82880 0.177748
\(465\) 2.86779 0.132990
\(466\) −4.91087 −0.227492
\(467\) 34.5685 1.59964 0.799819 0.600241i \(-0.204929\pi\)
0.799819 + 0.600241i \(0.204929\pi\)
\(468\) −10.1101 −0.467339
\(469\) −2.95396 −0.136401
\(470\) −3.21724 −0.148400
\(471\) 25.0700 1.15516
\(472\) 12.4404 0.572614
\(473\) 3.73673 0.171815
\(474\) −31.0950 −1.42824
\(475\) 0 0
\(476\) −9.34535 −0.428343
\(477\) 3.30931 0.151523
\(478\) 14.0490 0.642586
\(479\) −17.7187 −0.809589 −0.404794 0.914408i \(-0.632657\pi\)
−0.404794 + 0.914408i \(0.632657\pi\)
\(480\) −0.935945 −0.0427198
\(481\) −17.3093 −0.789237
\(482\) 22.7397 1.03576
\(483\) −14.1281 −0.642851
\(484\) 1.00000 0.0454545
\(485\) −1.82175 −0.0827214
\(486\) −21.3332 −0.967695
\(487\) −37.7426 −1.71028 −0.855141 0.518396i \(-0.826529\pi\)
−0.855141 + 0.518396i \(0.826529\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 8.30636 0.375627
\(490\) −1.58355 −0.0715374
\(491\) 0.373364 0.0168497 0.00842485 0.999965i \(-0.497318\pi\)
0.00842485 + 0.999965i \(0.497318\pi\)
\(492\) 2.54456 0.114718
\(493\) 20.8188 0.937632
\(494\) 0 0
\(495\) 1.06406 0.0478257
\(496\) 3.06406 0.137580
\(497\) 1.79783 0.0806439
\(498\) 20.3734 0.912952
\(499\) −14.8388 −0.664276 −0.332138 0.943231i \(-0.607770\pi\)
−0.332138 + 0.943231i \(0.607770\pi\)
\(500\) 3.85387 0.172350
\(501\) 55.2290 2.46745
\(502\) 12.0000 0.535586
\(503\) 33.2662 1.48327 0.741634 0.670805i \(-0.234051\pi\)
0.741634 + 0.670805i \(0.234051\pi\)
\(504\) 4.67267 0.208137
\(505\) 3.77982 0.168200
\(506\) −3.43742 −0.152812
\(507\) −1.98198 −0.0880229
\(508\) 5.00295 0.221970
\(509\) 8.47051 0.375449 0.187724 0.982222i \(-0.439889\pi\)
0.187724 + 0.982222i \(0.439889\pi\)
\(510\) −5.08913 −0.225350
\(511\) −23.4735 −1.03840
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −19.4433 −0.857608
\(515\) −2.72166 −0.119931
\(516\) 8.93594 0.393383
\(517\) 8.22018 0.361523
\(518\) 8.00000 0.351500
\(519\) −43.4684 −1.90805
\(520\) −1.45544 −0.0638252
\(521\) 37.3152 1.63481 0.817404 0.576064i \(-0.195412\pi\)
0.817404 + 0.576064i \(0.195412\pi\)
\(522\) −10.4094 −0.455607
\(523\) 31.6576 1.38429 0.692145 0.721758i \(-0.256666\pi\)
0.692145 + 0.721758i \(0.256666\pi\)
\(524\) −6.50147 −0.284018
\(525\) −19.9209 −0.869418
\(526\) −14.6476 −0.638666
\(527\) 16.6606 0.725745
\(528\) 2.39138 0.104072
\(529\) −11.1841 −0.486267
\(530\) 0.476404 0.0206937
\(531\) −33.8217 −1.46774
\(532\) 0 0
\(533\) 3.95691 0.171393
\(534\) −42.3123 −1.83103
\(535\) 1.03899 0.0449192
\(536\) −1.71871 −0.0742370
\(537\) 26.9849 1.16449
\(538\) 8.34829 0.359921
\(539\) 4.04604 0.174275
\(540\) −0.263272 −0.0113294
\(541\) 28.0921 1.20777 0.603886 0.797070i \(-0.293618\pi\)
0.603886 + 0.797070i \(0.293618\pi\)
\(542\) 10.5375 0.452625
\(543\) 52.3182 2.24519
\(544\) −5.43742 −0.233127
\(545\) 2.34829 0.100590
\(546\) 15.2842 0.654105
\(547\) −24.1841 −1.03404 −0.517020 0.855973i \(-0.672959\pi\)
−0.517020 + 0.855973i \(0.672959\pi\)
\(548\) 15.7187 0.671470
\(549\) 5.43742 0.232063
\(550\) −4.84682 −0.206669
\(551\) 0 0
\(552\) −8.22018 −0.349874
\(553\) 22.3483 0.950346
\(554\) 22.8807 0.972109
\(555\) 4.35650 0.184923
\(556\) −11.1381 −0.472361
\(557\) 39.9699 1.69358 0.846789 0.531929i \(-0.178533\pi\)
0.846789 + 0.531929i \(0.178533\pi\)
\(558\) −8.33028 −0.352649
\(559\) 13.8958 0.587730
\(560\) 0.672673 0.0284256
\(561\) 13.0029 0.548985
\(562\) −4.39138 −0.185239
\(563\) −16.4764 −0.694398 −0.347199 0.937792i \(-0.612867\pi\)
−0.347199 + 0.937792i \(0.612867\pi\)
\(564\) 19.6576 0.827734
\(565\) 2.94691 0.123977
\(566\) 24.0670 1.01161
\(567\) 16.7828 0.704810
\(568\) 1.04604 0.0438907
\(569\) 24.9418 1.04562 0.522808 0.852450i \(-0.324884\pi\)
0.522808 + 0.852450i \(0.324884\pi\)
\(570\) 0 0
\(571\) −8.50737 −0.356022 −0.178011 0.984028i \(-0.556966\pi\)
−0.178011 + 0.984028i \(0.556966\pi\)
\(572\) 3.71871 0.155487
\(573\) 16.9669 0.708803
\(574\) −1.82880 −0.0763327
\(575\) 16.6606 0.694793
\(576\) 2.71871 0.113280
\(577\) 31.8527 1.32605 0.663023 0.748599i \(-0.269273\pi\)
0.663023 + 0.748599i \(0.269273\pi\)
\(578\) −12.5655 −0.522657
\(579\) 30.2453 1.25695
\(580\) −1.49853 −0.0622229
\(581\) −14.6425 −0.607475
\(582\) 11.1311 0.461397
\(583\) −1.21724 −0.0504127
\(584\) −13.6576 −0.565156
\(585\) 3.95691 0.163598
\(586\) −27.2901 −1.12735
\(587\) 2.43447 0.100481 0.0502407 0.998737i \(-0.484001\pi\)
0.0502407 + 0.998737i \(0.484001\pi\)
\(588\) 9.67562 0.399016
\(589\) 0 0
\(590\) −4.86894 −0.200451
\(591\) −20.1700 −0.829685
\(592\) 4.65465 0.191305
\(593\) −18.1841 −0.746733 −0.373367 0.927684i \(-0.621797\pi\)
−0.373367 + 0.927684i \(0.621797\pi\)
\(594\) 0.672673 0.0276001
\(595\) 3.65760 0.149947
\(596\) 11.3453 0.464723
\(597\) 5.00295 0.204757
\(598\) −12.7828 −0.522726
\(599\) −4.33534 −0.177137 −0.0885687 0.996070i \(-0.528229\pi\)
−0.0885687 + 0.996070i \(0.528229\pi\)
\(600\) −11.5906 −0.473184
\(601\) −16.2453 −0.662658 −0.331329 0.943515i \(-0.607497\pi\)
−0.331329 + 0.943515i \(0.607497\pi\)
\(602\) −6.42235 −0.261755
\(603\) 4.67267 0.190286
\(604\) 14.6547 0.596289
\(605\) −0.391382 −0.0159120
\(606\) −23.0950 −0.938171
\(607\) −41.6995 −1.69253 −0.846266 0.532761i \(-0.821155\pi\)
−0.846266 + 0.532761i \(0.821155\pi\)
\(608\) 0 0
\(609\) 15.7367 0.637684
\(610\) 0.782765 0.0316932
\(611\) 30.5685 1.23667
\(612\) 14.7828 0.597558
\(613\) 48.1900 1.94638 0.973189 0.230008i \(-0.0738751\pi\)
0.973189 + 0.230008i \(0.0738751\pi\)
\(614\) −9.22313 −0.372215
\(615\) −0.995897 −0.0401584
\(616\) −1.71871 −0.0692488
\(617\) 15.7187 0.632811 0.316406 0.948624i \(-0.397524\pi\)
0.316406 + 0.948624i \(0.397524\pi\)
\(618\) 16.6296 0.668940
\(619\) 44.6606 1.79506 0.897530 0.440954i \(-0.145360\pi\)
0.897530 + 0.440954i \(0.145360\pi\)
\(620\) −1.19922 −0.0481617
\(621\) −2.31226 −0.0927877
\(622\) −6.34829 −0.254543
\(623\) 30.4102 1.21836
\(624\) 8.89286 0.355999
\(625\) 22.7258 0.909030
\(626\) −13.3943 −0.535345
\(627\) 0 0
\(628\) −10.4835 −0.418335
\(629\) 25.3093 1.00915
\(630\) −1.82880 −0.0728612
\(631\) 2.38433 0.0949187 0.0474593 0.998873i \(-0.484888\pi\)
0.0474593 + 0.998873i \(0.484888\pi\)
\(632\) 13.0029 0.517230
\(633\) −14.5685 −0.579045
\(634\) 31.0029 1.23128
\(635\) −1.95807 −0.0777035
\(636\) −2.91087 −0.115424
\(637\) 15.0460 0.596146
\(638\) 3.82880 0.151584
\(639\) −2.84387 −0.112502
\(640\) 0.391382 0.0154707
\(641\) 45.6936 1.80479 0.902395 0.430910i \(-0.141807\pi\)
0.902395 + 0.430910i \(0.141807\pi\)
\(642\) −6.34829 −0.250547
\(643\) 42.2621 1.66666 0.833328 0.552779i \(-0.186433\pi\)
0.833328 + 0.552779i \(0.186433\pi\)
\(644\) 5.90793 0.232805
\(645\) −3.49737 −0.137709
\(646\) 0 0
\(647\) −38.7166 −1.52211 −0.761053 0.648690i \(-0.775317\pi\)
−0.761053 + 0.648690i \(0.775317\pi\)
\(648\) 9.76475 0.383595
\(649\) 12.4404 0.488327
\(650\) −18.0239 −0.706956
\(651\) 12.5935 0.493580
\(652\) −3.47346 −0.136031
\(653\) 38.6915 1.51412 0.757058 0.653348i \(-0.226636\pi\)
0.757058 + 0.653348i \(0.226636\pi\)
\(654\) −14.3483 −0.561063
\(655\) 2.54456 0.0994243
\(656\) −1.06406 −0.0415444
\(657\) 37.1311 1.44862
\(658\) −14.1281 −0.550771
\(659\) −12.7467 −0.496542 −0.248271 0.968691i \(-0.579862\pi\)
−0.248271 + 0.968691i \(0.579862\pi\)
\(660\) −0.935945 −0.0364316
\(661\) 21.1671 0.823305 0.411652 0.911341i \(-0.364952\pi\)
0.411652 + 0.911341i \(0.364952\pi\)
\(662\) −16.2993 −0.633491
\(663\) 48.3542 1.87792
\(664\) −8.51949 −0.330620
\(665\) 0 0
\(666\) −12.6547 −0.490358
\(667\) −13.1612 −0.509604
\(668\) −23.0950 −0.893573
\(669\) −45.1370 −1.74510
\(670\) 0.672673 0.0259876
\(671\) −2.00000 −0.0772091
\(672\) −4.11009 −0.158550
\(673\) −2.25115 −0.0867755 −0.0433878 0.999058i \(-0.513815\pi\)
−0.0433878 + 0.999058i \(0.513815\pi\)
\(674\) −3.19217 −0.122958
\(675\) −3.26032 −0.125490
\(676\) 0.828802 0.0318770
\(677\) 9.57848 0.368131 0.184065 0.982914i \(-0.441074\pi\)
0.184065 + 0.982914i \(0.441074\pi\)
\(678\) −18.0059 −0.691512
\(679\) −8.00000 −0.307012
\(680\) 2.12811 0.0816093
\(681\) 50.1399 1.92137
\(682\) 3.06406 0.117329
\(683\) 32.0118 1.22490 0.612449 0.790510i \(-0.290185\pi\)
0.612449 + 0.790510i \(0.290185\pi\)
\(684\) 0 0
\(685\) −6.15203 −0.235057
\(686\) −18.9849 −0.724848
\(687\) −33.0269 −1.26005
\(688\) −3.73673 −0.142461
\(689\) −4.52654 −0.172448
\(690\) 3.21724 0.122478
\(691\) −25.9699 −0.987940 −0.493970 0.869479i \(-0.664455\pi\)
−0.493970 + 0.869479i \(0.664455\pi\)
\(692\) 18.1771 0.690990
\(693\) 4.67267 0.177500
\(694\) −24.6966 −0.937470
\(695\) 4.35926 0.165356
\(696\) 9.15613 0.347062
\(697\) −5.78571 −0.219150
\(698\) 4.43447 0.167847
\(699\) −11.7438 −0.444191
\(700\) 8.33028 0.314855
\(701\) −21.0950 −0.796748 −0.398374 0.917223i \(-0.630425\pi\)
−0.398374 + 0.917223i \(0.630425\pi\)
\(702\) 2.50147 0.0944121
\(703\) 0 0
\(704\) −1.00000 −0.0376889
\(705\) −7.69364 −0.289759
\(706\) −25.3152 −0.952750
\(707\) 16.5986 0.624255
\(708\) 29.7497 1.11806
\(709\) 29.1981 1.09656 0.548278 0.836296i \(-0.315284\pi\)
0.548278 + 0.836296i \(0.315284\pi\)
\(710\) −0.409400 −0.0153645
\(711\) −35.3512 −1.32578
\(712\) 17.6936 0.663097
\(713\) −10.5324 −0.394443
\(714\) −22.3483 −0.836364
\(715\) −1.45544 −0.0544303
\(716\) −11.2842 −0.421712
\(717\) 33.5965 1.25468
\(718\) 13.9749 0.521540
\(719\) −13.9079 −0.518678 −0.259339 0.965786i \(-0.583505\pi\)
−0.259339 + 0.965786i \(0.583505\pi\)
\(720\) −1.06406 −0.0396550
\(721\) −11.9518 −0.445110
\(722\) 0 0
\(723\) 54.3793 2.02239
\(724\) −21.8778 −0.813082
\(725\) −18.5575 −0.689209
\(726\) 2.39138 0.0887525
\(727\) −42.0059 −1.55791 −0.778956 0.627078i \(-0.784251\pi\)
−0.778956 + 0.627078i \(0.784251\pi\)
\(728\) −6.39138 −0.236880
\(729\) −21.7217 −0.804506
\(730\) 5.34535 0.197840
\(731\) −20.3182 −0.751494
\(732\) −4.78276 −0.176776
\(733\) 36.0780 1.33257 0.666285 0.745697i \(-0.267883\pi\)
0.666285 + 0.745697i \(0.267883\pi\)
\(734\) 25.3453 0.935514
\(735\) −3.78687 −0.139681
\(736\) 3.43742 0.126705
\(737\) −1.71871 −0.0633095
\(738\) 2.89286 0.106488
\(739\) 49.9988 1.83924 0.919619 0.392812i \(-0.128498\pi\)
0.919619 + 0.392812i \(0.128498\pi\)
\(740\) −1.82175 −0.0669689
\(741\) 0 0
\(742\) 2.09207 0.0768025
\(743\) −0.220184 −0.00807777 −0.00403889 0.999992i \(-0.501286\pi\)
−0.00403889 + 0.999992i \(0.501286\pi\)
\(744\) 7.32733 0.268633
\(745\) −4.44037 −0.162683
\(746\) 8.95396 0.327828
\(747\) 23.1620 0.847454
\(748\) −5.43742 −0.198812
\(749\) 4.56258 0.166713
\(750\) 9.21608 0.336524
\(751\) 23.1311 0.844064 0.422032 0.906581i \(-0.361317\pi\)
0.422032 + 0.906581i \(0.361317\pi\)
\(752\) −8.22018 −0.299759
\(753\) 28.6966 1.04576
\(754\) 14.2382 0.518525
\(755\) −5.73557 −0.208739
\(756\) −1.15613 −0.0420480
\(757\) 37.4304 1.36043 0.680215 0.733013i \(-0.261886\pi\)
0.680215 + 0.733013i \(0.261886\pi\)
\(758\) −25.8527 −0.939013
\(759\) −8.22018 −0.298374
\(760\) 0 0
\(761\) −33.9499 −1.23068 −0.615341 0.788261i \(-0.710982\pi\)
−0.615341 + 0.788261i \(0.710982\pi\)
\(762\) 11.9640 0.433409
\(763\) 10.3123 0.373329
\(764\) −7.09502 −0.256689
\(765\) −5.78571 −0.209183
\(766\) −20.6296 −0.745377
\(767\) 46.2621 1.67043
\(768\) −2.39138 −0.0862916
\(769\) −44.7025 −1.61201 −0.806006 0.591907i \(-0.798375\pi\)
−0.806006 + 0.591907i \(0.798375\pi\)
\(770\) 0.672673 0.0242414
\(771\) −46.4964 −1.67453
\(772\) −12.6476 −0.455197
\(773\) 44.8748 1.61404 0.807018 0.590527i \(-0.201080\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) 10.1591 0.365161
\(775\) −14.8509 −0.533461
\(776\) −4.65465 −0.167092
\(777\) 19.1311 0.686323
\(778\) −15.6086 −0.559596
\(779\) 0 0
\(780\) −3.48051 −0.124622
\(781\) 1.04604 0.0374301
\(782\) 18.6907 0.668378
\(783\) 2.57553 0.0920419
\(784\) −4.04604 −0.144501
\(785\) 4.10304 0.146444
\(786\) −15.5475 −0.554561
\(787\) −11.8418 −0.422113 −0.211056 0.977474i \(-0.567690\pi\)
−0.211056 + 0.977474i \(0.567690\pi\)
\(788\) 8.43447 0.300466
\(789\) −35.0280 −1.24703
\(790\) −5.08913 −0.181063
\(791\) 12.9410 0.460129
\(792\) 2.71871 0.0966051
\(793\) −7.43742 −0.264111
\(794\) 34.2512 1.21553
\(795\) 1.13927 0.0404056
\(796\) −2.09207 −0.0741516
\(797\) −0.128110 −0.00453789 −0.00226895 0.999997i \(-0.500722\pi\)
−0.00226895 + 0.999997i \(0.500722\pi\)
\(798\) 0 0
\(799\) −44.6966 −1.58125
\(800\) 4.84682 0.171361
\(801\) −48.1039 −1.69967
\(802\) 4.09207 0.144496
\(803\) −13.6576 −0.481966
\(804\) −4.11009 −0.144952
\(805\) −2.31226 −0.0814964
\(806\) 11.3943 0.401348
\(807\) 19.9640 0.702765
\(808\) 9.65760 0.339753
\(809\) 17.5354 0.616512 0.308256 0.951304i \(-0.400255\pi\)
0.308256 + 0.951304i \(0.400255\pi\)
\(810\) −3.82175 −0.134283
\(811\) 39.3512 1.38181 0.690905 0.722946i \(-0.257212\pi\)
0.690905 + 0.722946i \(0.257212\pi\)
\(812\) −6.58060 −0.230934
\(813\) 25.1992 0.883775
\(814\) 4.65465 0.163146
\(815\) 1.35945 0.0476194
\(816\) −13.0029 −0.455194
\(817\) 0 0
\(818\) 2.48346 0.0868320
\(819\) 17.3763 0.607178
\(820\) 0.416452 0.0145431
\(821\) 14.0980 0.492023 0.246011 0.969267i \(-0.420880\pi\)
0.246011 + 0.969267i \(0.420880\pi\)
\(822\) 37.5894 1.31108
\(823\) −1.12516 −0.0392207 −0.0196103 0.999808i \(-0.506243\pi\)
−0.0196103 + 0.999808i \(0.506243\pi\)
\(824\) −6.95396 −0.242253
\(825\) −11.5906 −0.403533
\(826\) −21.3814 −0.743953
\(827\) 33.8217 1.17610 0.588049 0.808825i \(-0.299896\pi\)
0.588049 + 0.808825i \(0.299896\pi\)
\(828\) −9.34535 −0.324773
\(829\) 36.1900 1.25693 0.628466 0.777837i \(-0.283683\pi\)
0.628466 + 0.777837i \(0.283683\pi\)
\(830\) 3.33438 0.115738
\(831\) 54.7166 1.89810
\(832\) −3.71871 −0.128923
\(833\) −22.0000 −0.762255
\(834\) −26.6355 −0.922311
\(835\) 9.03899 0.312807
\(836\) 0 0
\(837\) 2.06111 0.0712423
\(838\) −35.0950 −1.21234
\(839\) 31.8347 1.09906 0.549528 0.835475i \(-0.314808\pi\)
0.549528 + 0.835475i \(0.314808\pi\)
\(840\) 1.60862 0.0555026
\(841\) −14.3403 −0.494492
\(842\) −12.3483 −0.425550
\(843\) −10.5015 −0.361690
\(844\) 6.09207 0.209698
\(845\) −0.324378 −0.0111590
\(846\) 22.3483 0.768350
\(847\) −1.71871 −0.0590556
\(848\) 1.21724 0.0418000
\(849\) 57.5534 1.97523
\(850\) 26.3542 0.903941
\(851\) −16.0000 −0.548473
\(852\) 2.50147 0.0856991
\(853\) −31.1009 −1.06488 −0.532438 0.846469i \(-0.678724\pi\)
−0.532438 + 0.846469i \(0.678724\pi\)
\(854\) 3.43742 0.117626
\(855\) 0 0
\(856\) 2.65465 0.0907342
\(857\) 35.4985 1.21261 0.606303 0.795234i \(-0.292652\pi\)
0.606303 + 0.795234i \(0.292652\pi\)
\(858\) 8.89286 0.303597
\(859\) −5.63760 −0.192352 −0.0961762 0.995364i \(-0.530661\pi\)
−0.0961762 + 0.995364i \(0.530661\pi\)
\(860\) 1.46249 0.0498705
\(861\) −4.37336 −0.149044
\(862\) −6.94691 −0.236613
\(863\) −31.9949 −1.08912 −0.544560 0.838722i \(-0.683303\pi\)
−0.544560 + 0.838722i \(0.683303\pi\)
\(864\) −0.672673 −0.0228848
\(865\) −7.11420 −0.241890
\(866\) −13.2533 −0.450364
\(867\) −30.0490 −1.02052
\(868\) −5.26622 −0.178747
\(869\) 13.0029 0.441095
\(870\) −3.58355 −0.121494
\(871\) −6.39138 −0.216564
\(872\) 6.00000 0.203186
\(873\) 12.6547 0.428295
\(874\) 0 0
\(875\) −6.62369 −0.223921
\(876\) −32.6606 −1.10350
\(877\) 3.23019 0.109076 0.0545378 0.998512i \(-0.482631\pi\)
0.0545378 + 0.998512i \(0.482631\pi\)
\(878\) 15.3152 0.516863
\(879\) −65.2612 −2.20120
\(880\) 0.391382 0.0131935
\(881\) −24.7217 −0.832894 −0.416447 0.909160i \(-0.636725\pi\)
−0.416447 + 0.909160i \(0.636725\pi\)
\(882\) 11.0000 0.370389
\(883\) 11.9138 0.400932 0.200466 0.979701i \(-0.435754\pi\)
0.200466 + 0.979701i \(0.435754\pi\)
\(884\) −20.2202 −0.680078
\(885\) −11.6435 −0.391392
\(886\) 20.8807 0.701502
\(887\) 12.1841 0.409104 0.204552 0.978856i \(-0.434426\pi\)
0.204552 + 0.978856i \(0.434426\pi\)
\(888\) 11.1311 0.373534
\(889\) −8.59862 −0.288388
\(890\) −6.92498 −0.232126
\(891\) 9.76475 0.327131
\(892\) 18.8748 0.631976
\(893\) 0 0
\(894\) 27.1311 0.907398
\(895\) 4.41645 0.147626
\(896\) 1.71871 0.0574181
\(897\) −30.5685 −1.02065
\(898\) −28.7887 −0.960690
\(899\) 11.7317 0.391273
\(900\) −13.1771 −0.439237
\(901\) 6.61862 0.220498
\(902\) −1.06406 −0.0354292
\(903\) −15.3583 −0.511092
\(904\) 7.52949 0.250427
\(905\) 8.56258 0.284630
\(906\) 35.0449 1.16429
\(907\) −45.3211 −1.50486 −0.752431 0.658671i \(-0.771119\pi\)
−0.752431 + 0.658671i \(0.771119\pi\)
\(908\) −20.9669 −0.695811
\(909\) −26.2562 −0.870864
\(910\) 2.50147 0.0829231
\(911\) 13.6376 0.451834 0.225917 0.974147i \(-0.427462\pi\)
0.225917 + 0.974147i \(0.427462\pi\)
\(912\) 0 0
\(913\) −8.51949 −0.281954
\(914\) 32.7526 1.08336
\(915\) 1.87189 0.0618828
\(916\) 13.8108 0.456321
\(917\) 11.1741 0.369003
\(918\) −3.65760 −0.120719
\(919\) 39.5283 1.30392 0.651960 0.758254i \(-0.273947\pi\)
0.651960 + 0.758254i \(0.273947\pi\)
\(920\) −1.34535 −0.0443547
\(921\) −22.0560 −0.726771
\(922\) −20.2261 −0.666111
\(923\) 3.88991 0.128038
\(924\) −4.11009 −0.135212
\(925\) −22.5603 −0.741777
\(926\) 18.6907 0.614214
\(927\) 18.9058 0.620948
\(928\) −3.82880 −0.125687
\(929\) 6.89991 0.226379 0.113189 0.993573i \(-0.463893\pi\)
0.113189 + 0.993573i \(0.463893\pi\)
\(930\) −2.86779 −0.0940384
\(931\) 0 0
\(932\) 4.91087 0.160861
\(933\) −15.1812 −0.497010
\(934\) −34.5685 −1.13112
\(935\) 2.12811 0.0695966
\(936\) 10.1101 0.330459
\(937\) −21.3873 −0.698692 −0.349346 0.936994i \(-0.613596\pi\)
−0.349346 + 0.936994i \(0.613596\pi\)
\(938\) 2.95396 0.0964503
\(939\) −32.0310 −1.04529
\(940\) 3.21724 0.104935
\(941\) 27.5655 0.898611 0.449305 0.893378i \(-0.351672\pi\)
0.449305 + 0.893378i \(0.351672\pi\)
\(942\) −25.0700 −0.816823
\(943\) 3.65760 0.119108
\(944\) −12.4404 −0.404899
\(945\) 0.452489 0.0147195
\(946\) −3.73673 −0.121491
\(947\) −9.22313 −0.299712 −0.149856 0.988708i \(-0.547881\pi\)
−0.149856 + 0.988708i \(0.547881\pi\)
\(948\) 31.0950 1.00992
\(949\) −50.7887 −1.64867
\(950\) 0 0
\(951\) 74.1399 2.40415
\(952\) 9.34535 0.302884
\(953\) −22.6966 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(954\) −3.30931 −0.107143
\(955\) 2.77687 0.0898573
\(956\) −14.0490 −0.454377
\(957\) 9.15613 0.295976
\(958\) 17.7187 0.572466
\(959\) −27.0159 −0.872389
\(960\) 0.935945 0.0302075
\(961\) −21.6116 −0.697147
\(962\) 17.3093 0.558075
\(963\) −7.21724 −0.232572
\(964\) −22.7397 −0.732396
\(965\) 4.95005 0.159348
\(966\) 14.1281 0.454564
\(967\) −48.6966 −1.56598 −0.782988 0.622036i \(-0.786306\pi\)
−0.782988 + 0.622036i \(0.786306\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 0 0
\(970\) 1.82175 0.0584929
\(971\) 19.5165 0.626316 0.313158 0.949701i \(-0.398613\pi\)
0.313158 + 0.949701i \(0.398613\pi\)
\(972\) 21.3332 0.684264
\(973\) 19.1432 0.613702
\(974\) 37.7426 1.20935
\(975\) −43.1021 −1.38037
\(976\) 2.00000 0.0640184
\(977\) −37.3512 −1.19497 −0.597486 0.801879i \(-0.703834\pi\)
−0.597486 + 0.801879i \(0.703834\pi\)
\(978\) −8.30636 −0.265608
\(979\) 17.6936 0.565491
\(980\) 1.58355 0.0505846
\(981\) −16.3123 −0.520810
\(982\) −0.373364 −0.0119145
\(983\) 45.8888 1.46362 0.731812 0.681507i \(-0.238675\pi\)
0.731812 + 0.681507i \(0.238675\pi\)
\(984\) −2.54456 −0.0811177
\(985\) −3.30110 −0.105182
\(986\) −20.8188 −0.663006
\(987\) −33.7857 −1.07541
\(988\) 0 0
\(989\) 12.8447 0.408438
\(990\) −1.06406 −0.0338179
\(991\) 30.9418 0.982900 0.491450 0.870906i \(-0.336467\pi\)
0.491450 + 0.870906i \(0.336467\pi\)
\(992\) −3.06406 −0.0972838
\(993\) −38.9779 −1.23693
\(994\) −1.79783 −0.0570238
\(995\) 0.818801 0.0259577
\(996\) −20.3734 −0.645555
\(997\) 49.8418 1.57850 0.789252 0.614069i \(-0.210469\pi\)
0.789252 + 0.614069i \(0.210469\pi\)
\(998\) 14.8388 0.469714
\(999\) 3.13106 0.0990623
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 7942.2.a.bc.1.1 3
19.18 odd 2 418.2.a.h.1.3 3
57.56 even 2 3762.2.a.bd.1.3 3
76.75 even 2 3344.2.a.p.1.1 3
209.208 even 2 4598.2.a.bm.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.a.h.1.3 3 19.18 odd 2
3344.2.a.p.1.1 3 76.75 even 2
3762.2.a.bd.1.3 3 57.56 even 2
4598.2.a.bm.1.3 3 209.208 even 2
7942.2.a.bc.1.1 3 1.1 even 1 trivial