Properties

Label 4029.2.a.l.1.5
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 1.5
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.27866 q^{2} -1.00000 q^{3} +3.19228 q^{4} -3.13196 q^{5} +2.27866 q^{6} -0.0802156 q^{7} -2.71679 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.27866 q^{2} -1.00000 q^{3} +3.19228 q^{4} -3.13196 q^{5} +2.27866 q^{6} -0.0802156 q^{7} -2.71679 q^{8} +1.00000 q^{9} +7.13667 q^{10} -5.00047 q^{11} -3.19228 q^{12} +3.99267 q^{13} +0.182784 q^{14} +3.13196 q^{15} -0.193918 q^{16} -1.00000 q^{17} -2.27866 q^{18} +2.46147 q^{19} -9.99809 q^{20} +0.0802156 q^{21} +11.3944 q^{22} +2.52357 q^{23} +2.71679 q^{24} +4.80919 q^{25} -9.09792 q^{26} -1.00000 q^{27} -0.256070 q^{28} -8.32033 q^{29} -7.13667 q^{30} -0.805575 q^{31} +5.87546 q^{32} +5.00047 q^{33} +2.27866 q^{34} +0.251232 q^{35} +3.19228 q^{36} +10.3580 q^{37} -5.60884 q^{38} -3.99267 q^{39} +8.50889 q^{40} -0.183280 q^{41} -0.182784 q^{42} -7.55934 q^{43} -15.9629 q^{44} -3.13196 q^{45} -5.75036 q^{46} -4.65435 q^{47} +0.193918 q^{48} -6.99357 q^{49} -10.9585 q^{50} +1.00000 q^{51} +12.7457 q^{52} +5.82371 q^{53} +2.27866 q^{54} +15.6613 q^{55} +0.217929 q^{56} -2.46147 q^{57} +18.9592 q^{58} +4.80944 q^{59} +9.99809 q^{60} -10.0824 q^{61} +1.83563 q^{62} -0.0802156 q^{63} -13.0003 q^{64} -12.5049 q^{65} -11.3944 q^{66} -8.96523 q^{67} -3.19228 q^{68} -2.52357 q^{69} -0.572472 q^{70} +7.92651 q^{71} -2.71679 q^{72} -4.57642 q^{73} -23.6024 q^{74} -4.80919 q^{75} +7.85768 q^{76} +0.401116 q^{77} +9.09792 q^{78} +1.00000 q^{79} +0.607343 q^{80} +1.00000 q^{81} +0.417632 q^{82} +9.12814 q^{83} +0.256070 q^{84} +3.13196 q^{85} +17.2251 q^{86} +8.32033 q^{87} +13.5852 q^{88} -0.860630 q^{89} +7.13667 q^{90} -0.320274 q^{91} +8.05594 q^{92} +0.805575 q^{93} +10.6057 q^{94} -7.70922 q^{95} -5.87546 q^{96} -15.2883 q^{97} +15.9359 q^{98} -5.00047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27866 −1.61125 −0.805627 0.592423i \(-0.798171\pi\)
−0.805627 + 0.592423i \(0.798171\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.19228 1.59614
\(5\) −3.13196 −1.40066 −0.700328 0.713821i \(-0.746963\pi\)
−0.700328 + 0.713821i \(0.746963\pi\)
\(6\) 2.27866 0.930258
\(7\) −0.0802156 −0.0303186 −0.0151593 0.999885i \(-0.504826\pi\)
−0.0151593 + 0.999885i \(0.504826\pi\)
\(8\) −2.71679 −0.960531
\(9\) 1.00000 0.333333
\(10\) 7.13667 2.25681
\(11\) −5.00047 −1.50770 −0.753849 0.657047i \(-0.771805\pi\)
−0.753849 + 0.657047i \(0.771805\pi\)
\(12\) −3.19228 −0.921531
\(13\) 3.99267 1.10737 0.553683 0.832727i \(-0.313222\pi\)
0.553683 + 0.832727i \(0.313222\pi\)
\(14\) 0.182784 0.0488510
\(15\) 3.13196 0.808669
\(16\) −0.193918 −0.0484794
\(17\) −1.00000 −0.242536
\(18\) −2.27866 −0.537085
\(19\) 2.46147 0.564699 0.282350 0.959312i \(-0.408886\pi\)
0.282350 + 0.959312i \(0.408886\pi\)
\(20\) −9.99809 −2.23564
\(21\) 0.0802156 0.0175045
\(22\) 11.3944 2.42929
\(23\) 2.52357 0.526201 0.263101 0.964768i \(-0.415255\pi\)
0.263101 + 0.964768i \(0.415255\pi\)
\(24\) 2.71679 0.554563
\(25\) 4.80919 0.961838
\(26\) −9.09792 −1.78425
\(27\) −1.00000 −0.192450
\(28\) −0.256070 −0.0483927
\(29\) −8.32033 −1.54505 −0.772523 0.634987i \(-0.781006\pi\)
−0.772523 + 0.634987i \(0.781006\pi\)
\(30\) −7.13667 −1.30297
\(31\) −0.805575 −0.144686 −0.0723428 0.997380i \(-0.523048\pi\)
−0.0723428 + 0.997380i \(0.523048\pi\)
\(32\) 5.87546 1.03864
\(33\) 5.00047 0.870470
\(34\) 2.27866 0.390786
\(35\) 0.251232 0.0424660
\(36\) 3.19228 0.532046
\(37\) 10.3580 1.70285 0.851426 0.524475i \(-0.175738\pi\)
0.851426 + 0.524475i \(0.175738\pi\)
\(38\) −5.60884 −0.909874
\(39\) −3.99267 −0.639338
\(40\) 8.50889 1.34537
\(41\) −0.183280 −0.0286235 −0.0143118 0.999898i \(-0.504556\pi\)
−0.0143118 + 0.999898i \(0.504556\pi\)
\(42\) −0.182784 −0.0282041
\(43\) −7.55934 −1.15279 −0.576394 0.817172i \(-0.695541\pi\)
−0.576394 + 0.817172i \(0.695541\pi\)
\(44\) −15.9629 −2.40650
\(45\) −3.13196 −0.466885
\(46\) −5.75036 −0.847844
\(47\) −4.65435 −0.678907 −0.339453 0.940623i \(-0.610242\pi\)
−0.339453 + 0.940623i \(0.610242\pi\)
\(48\) 0.193918 0.0279896
\(49\) −6.99357 −0.999081
\(50\) −10.9585 −1.54976
\(51\) 1.00000 0.140028
\(52\) 12.7457 1.76751
\(53\) 5.82371 0.799948 0.399974 0.916527i \(-0.369019\pi\)
0.399974 + 0.916527i \(0.369019\pi\)
\(54\) 2.27866 0.310086
\(55\) 15.6613 2.11177
\(56\) 0.217929 0.0291220
\(57\) −2.46147 −0.326029
\(58\) 18.9592 2.48946
\(59\) 4.80944 0.626135 0.313068 0.949731i \(-0.398643\pi\)
0.313068 + 0.949731i \(0.398643\pi\)
\(60\) 9.99809 1.29075
\(61\) −10.0824 −1.29092 −0.645461 0.763793i \(-0.723335\pi\)
−0.645461 + 0.763793i \(0.723335\pi\)
\(62\) 1.83563 0.233125
\(63\) −0.0802156 −0.0101062
\(64\) −13.0003 −1.62504
\(65\) −12.5049 −1.55104
\(66\) −11.3944 −1.40255
\(67\) −8.96523 −1.09528 −0.547639 0.836715i \(-0.684473\pi\)
−0.547639 + 0.836715i \(0.684473\pi\)
\(68\) −3.19228 −0.387121
\(69\) −2.52357 −0.303802
\(70\) −0.572472 −0.0684235
\(71\) 7.92651 0.940704 0.470352 0.882479i \(-0.344127\pi\)
0.470352 + 0.882479i \(0.344127\pi\)
\(72\) −2.71679 −0.320177
\(73\) −4.57642 −0.535630 −0.267815 0.963470i \(-0.586302\pi\)
−0.267815 + 0.963470i \(0.586302\pi\)
\(74\) −23.6024 −2.74373
\(75\) −4.80919 −0.555317
\(76\) 7.85768 0.901338
\(77\) 0.401116 0.0457114
\(78\) 9.09792 1.03014
\(79\) 1.00000 0.112509
\(80\) 0.607343 0.0679030
\(81\) 1.00000 0.111111
\(82\) 0.417632 0.0461198
\(83\) 9.12814 1.00194 0.500972 0.865464i \(-0.332976\pi\)
0.500972 + 0.865464i \(0.332976\pi\)
\(84\) 0.256070 0.0279396
\(85\) 3.13196 0.339709
\(86\) 17.2251 1.85743
\(87\) 8.32033 0.892033
\(88\) 13.5852 1.44819
\(89\) −0.860630 −0.0912265 −0.0456133 0.998959i \(-0.514524\pi\)
−0.0456133 + 0.998959i \(0.514524\pi\)
\(90\) 7.13667 0.752271
\(91\) −0.320274 −0.0335738
\(92\) 8.05594 0.839890
\(93\) 0.805575 0.0835342
\(94\) 10.6057 1.09389
\(95\) −7.70922 −0.790949
\(96\) −5.87546 −0.599661
\(97\) −15.2883 −1.55229 −0.776144 0.630556i \(-0.782827\pi\)
−0.776144 + 0.630556i \(0.782827\pi\)
\(98\) 15.9359 1.60977
\(99\) −5.00047 −0.502566
\(100\) 15.3523 1.53523
\(101\) 5.41552 0.538864 0.269432 0.963019i \(-0.413164\pi\)
0.269432 + 0.963019i \(0.413164\pi\)
\(102\) −2.27866 −0.225621
\(103\) −18.1777 −1.79110 −0.895551 0.444959i \(-0.853218\pi\)
−0.895551 + 0.444959i \(0.853218\pi\)
\(104\) −10.8472 −1.06366
\(105\) −0.251232 −0.0245177
\(106\) −13.2702 −1.28892
\(107\) −6.64674 −0.642565 −0.321283 0.946983i \(-0.604114\pi\)
−0.321283 + 0.946983i \(0.604114\pi\)
\(108\) −3.19228 −0.307177
\(109\) −0.892414 −0.0854778 −0.0427389 0.999086i \(-0.513608\pi\)
−0.0427389 + 0.999086i \(0.513608\pi\)
\(110\) −35.6867 −3.40259
\(111\) −10.3580 −0.983142
\(112\) 0.0155552 0.00146983
\(113\) −17.6218 −1.65772 −0.828860 0.559457i \(-0.811010\pi\)
−0.828860 + 0.559457i \(0.811010\pi\)
\(114\) 5.60884 0.525316
\(115\) −7.90373 −0.737027
\(116\) −26.5608 −2.46611
\(117\) 3.99267 0.369122
\(118\) −10.9591 −1.00886
\(119\) 0.0802156 0.00735335
\(120\) −8.50889 −0.776752
\(121\) 14.0047 1.27316
\(122\) 22.9744 2.08000
\(123\) 0.183280 0.0165258
\(124\) −2.57162 −0.230938
\(125\) 0.597617 0.0534525
\(126\) 0.182784 0.0162837
\(127\) 16.4533 1.45999 0.729996 0.683451i \(-0.239522\pi\)
0.729996 + 0.683451i \(0.239522\pi\)
\(128\) 17.8723 1.57971
\(129\) 7.55934 0.665562
\(130\) 28.4943 2.49912
\(131\) −9.58929 −0.837820 −0.418910 0.908028i \(-0.637588\pi\)
−0.418910 + 0.908028i \(0.637588\pi\)
\(132\) 15.9629 1.38939
\(133\) −0.197448 −0.0171209
\(134\) 20.4287 1.76477
\(135\) 3.13196 0.269556
\(136\) 2.71679 0.232963
\(137\) −14.7192 −1.25754 −0.628771 0.777590i \(-0.716442\pi\)
−0.628771 + 0.777590i \(0.716442\pi\)
\(138\) 5.75036 0.489503
\(139\) 21.6385 1.83535 0.917675 0.397332i \(-0.130064\pi\)
0.917675 + 0.397332i \(0.130064\pi\)
\(140\) 0.802003 0.0677816
\(141\) 4.65435 0.391967
\(142\) −18.0618 −1.51571
\(143\) −19.9652 −1.66957
\(144\) −0.193918 −0.0161598
\(145\) 26.0589 2.16408
\(146\) 10.4281 0.863036
\(147\) 6.99357 0.576820
\(148\) 33.0658 2.71799
\(149\) −10.8910 −0.892228 −0.446114 0.894976i \(-0.647192\pi\)
−0.446114 + 0.894976i \(0.647192\pi\)
\(150\) 10.9585 0.894757
\(151\) −4.99158 −0.406209 −0.203104 0.979157i \(-0.565103\pi\)
−0.203104 + 0.979157i \(0.565103\pi\)
\(152\) −6.68729 −0.542411
\(153\) −1.00000 −0.0808452
\(154\) −0.914005 −0.0736526
\(155\) 2.52303 0.202655
\(156\) −12.7457 −1.02047
\(157\) −6.57973 −0.525119 −0.262560 0.964916i \(-0.584567\pi\)
−0.262560 + 0.964916i \(0.584567\pi\)
\(158\) −2.27866 −0.181280
\(159\) −5.82371 −0.461850
\(160\) −18.4017 −1.45478
\(161\) −0.202430 −0.0159537
\(162\) −2.27866 −0.179028
\(163\) −0.857319 −0.0671504 −0.0335752 0.999436i \(-0.510689\pi\)
−0.0335752 + 0.999436i \(0.510689\pi\)
\(164\) −0.585081 −0.0456871
\(165\) −15.6613 −1.21923
\(166\) −20.7999 −1.61438
\(167\) −9.20838 −0.712566 −0.356283 0.934378i \(-0.615956\pi\)
−0.356283 + 0.934378i \(0.615956\pi\)
\(168\) −0.217929 −0.0168136
\(169\) 2.94138 0.226260
\(170\) −7.13667 −0.547357
\(171\) 2.46147 0.188233
\(172\) −24.1315 −1.84001
\(173\) 11.7701 0.894867 0.447433 0.894317i \(-0.352338\pi\)
0.447433 + 0.894317i \(0.352338\pi\)
\(174\) −18.9592 −1.43729
\(175\) −0.385772 −0.0291616
\(176\) 0.969680 0.0730923
\(177\) −4.80944 −0.361499
\(178\) 1.96108 0.146989
\(179\) 1.68419 0.125882 0.0629412 0.998017i \(-0.479952\pi\)
0.0629412 + 0.998017i \(0.479952\pi\)
\(180\) −9.99809 −0.745214
\(181\) 24.5296 1.82327 0.911636 0.410998i \(-0.134820\pi\)
0.911636 + 0.410998i \(0.134820\pi\)
\(182\) 0.729794 0.0540960
\(183\) 10.0824 0.745315
\(184\) −6.85602 −0.505433
\(185\) −32.4410 −2.38511
\(186\) −1.83563 −0.134595
\(187\) 5.00047 0.365671
\(188\) −14.8580 −1.08363
\(189\) 0.0802156 0.00583482
\(190\) 17.5667 1.27442
\(191\) 13.2575 0.959276 0.479638 0.877466i \(-0.340768\pi\)
0.479638 + 0.877466i \(0.340768\pi\)
\(192\) 13.0003 0.938217
\(193\) −5.21102 −0.375097 −0.187549 0.982255i \(-0.560054\pi\)
−0.187549 + 0.982255i \(0.560054\pi\)
\(194\) 34.8367 2.50113
\(195\) 12.5049 0.895493
\(196\) −22.3254 −1.59467
\(197\) −19.6192 −1.39781 −0.698905 0.715214i \(-0.746329\pi\)
−0.698905 + 0.715214i \(0.746329\pi\)
\(198\) 11.3944 0.809762
\(199\) −20.5492 −1.45669 −0.728347 0.685209i \(-0.759711\pi\)
−0.728347 + 0.685209i \(0.759711\pi\)
\(200\) −13.0656 −0.923875
\(201\) 8.96523 0.632359
\(202\) −12.3401 −0.868247
\(203\) 0.667420 0.0468437
\(204\) 3.19228 0.223504
\(205\) 0.574026 0.0400917
\(206\) 41.4207 2.88592
\(207\) 2.52357 0.175400
\(208\) −0.774248 −0.0536845
\(209\) −12.3085 −0.851396
\(210\) 0.572472 0.0395043
\(211\) 3.60397 0.248108 0.124054 0.992275i \(-0.460410\pi\)
0.124054 + 0.992275i \(0.460410\pi\)
\(212\) 18.5909 1.27683
\(213\) −7.92651 −0.543116
\(214\) 15.1457 1.03534
\(215\) 23.6756 1.61466
\(216\) 2.71679 0.184854
\(217\) 0.0646196 0.00438667
\(218\) 2.03351 0.137726
\(219\) 4.57642 0.309246
\(220\) 49.9952 3.37067
\(221\) −3.99267 −0.268576
\(222\) 23.6024 1.58409
\(223\) 11.5968 0.776578 0.388289 0.921538i \(-0.373066\pi\)
0.388289 + 0.921538i \(0.373066\pi\)
\(224\) −0.471303 −0.0314903
\(225\) 4.80919 0.320613
\(226\) 40.1540 2.67101
\(227\) −17.2034 −1.14183 −0.570914 0.821010i \(-0.693411\pi\)
−0.570914 + 0.821010i \(0.693411\pi\)
\(228\) −7.85768 −0.520388
\(229\) 4.97398 0.328690 0.164345 0.986403i \(-0.447449\pi\)
0.164345 + 0.986403i \(0.447449\pi\)
\(230\) 18.0099 1.18754
\(231\) −0.401116 −0.0263915
\(232\) 22.6046 1.48406
\(233\) 21.9040 1.43498 0.717488 0.696571i \(-0.245292\pi\)
0.717488 + 0.696571i \(0.245292\pi\)
\(234\) −9.09792 −0.594749
\(235\) 14.5772 0.950915
\(236\) 15.3531 0.999399
\(237\) −1.00000 −0.0649570
\(238\) −0.182784 −0.0118481
\(239\) −0.639024 −0.0413350 −0.0206675 0.999786i \(-0.506579\pi\)
−0.0206675 + 0.999786i \(0.506579\pi\)
\(240\) −0.607343 −0.0392038
\(241\) −12.4379 −0.801197 −0.400599 0.916254i \(-0.631198\pi\)
−0.400599 + 0.916254i \(0.631198\pi\)
\(242\) −31.9119 −2.05138
\(243\) −1.00000 −0.0641500
\(244\) −32.1859 −2.06049
\(245\) 21.9036 1.39937
\(246\) −0.417632 −0.0266273
\(247\) 9.82781 0.625329
\(248\) 2.18858 0.138975
\(249\) −9.12814 −0.578472
\(250\) −1.36176 −0.0861255
\(251\) 16.4360 1.03743 0.518715 0.854947i \(-0.326411\pi\)
0.518715 + 0.854947i \(0.326411\pi\)
\(252\) −0.256070 −0.0161309
\(253\) −12.6191 −0.793353
\(254\) −37.4914 −2.35242
\(255\) −3.13196 −0.196131
\(256\) −14.7243 −0.920270
\(257\) −21.6122 −1.34813 −0.674067 0.738670i \(-0.735454\pi\)
−0.674067 + 0.738670i \(0.735454\pi\)
\(258\) −17.2251 −1.07239
\(259\) −0.830876 −0.0516281
\(260\) −39.9190 −2.47567
\(261\) −8.32033 −0.515015
\(262\) 21.8507 1.34994
\(263\) 29.9488 1.84672 0.923361 0.383932i \(-0.125430\pi\)
0.923361 + 0.383932i \(0.125430\pi\)
\(264\) −13.5852 −0.836114
\(265\) −18.2396 −1.12045
\(266\) 0.449916 0.0275861
\(267\) 0.860630 0.0526697
\(268\) −28.6195 −1.74822
\(269\) 14.5218 0.885408 0.442704 0.896668i \(-0.354019\pi\)
0.442704 + 0.896668i \(0.354019\pi\)
\(270\) −7.13667 −0.434324
\(271\) −8.49164 −0.515831 −0.257915 0.966168i \(-0.583036\pi\)
−0.257915 + 0.966168i \(0.583036\pi\)
\(272\) 0.193918 0.0117580
\(273\) 0.320274 0.0193839
\(274\) 33.5399 2.02622
\(275\) −24.0482 −1.45016
\(276\) −8.05594 −0.484911
\(277\) −29.6576 −1.78195 −0.890976 0.454051i \(-0.849978\pi\)
−0.890976 + 0.454051i \(0.849978\pi\)
\(278\) −49.3066 −2.95722
\(279\) −0.805575 −0.0482285
\(280\) −0.682545 −0.0407899
\(281\) −6.07216 −0.362234 −0.181117 0.983462i \(-0.557971\pi\)
−0.181117 + 0.983462i \(0.557971\pi\)
\(282\) −10.6057 −0.631558
\(283\) −7.51003 −0.446425 −0.223213 0.974770i \(-0.571654\pi\)
−0.223213 + 0.974770i \(0.571654\pi\)
\(284\) 25.3036 1.50149
\(285\) 7.70922 0.456655
\(286\) 45.4939 2.69011
\(287\) 0.0147019 0.000867826 0
\(288\) 5.87546 0.346215
\(289\) 1.00000 0.0588235
\(290\) −59.3794 −3.48688
\(291\) 15.2883 0.896214
\(292\) −14.6092 −0.854940
\(293\) 5.79465 0.338527 0.169264 0.985571i \(-0.445861\pi\)
0.169264 + 0.985571i \(0.445861\pi\)
\(294\) −15.9359 −0.929403
\(295\) −15.0630 −0.877000
\(296\) −28.1407 −1.63564
\(297\) 5.00047 0.290157
\(298\) 24.8169 1.43761
\(299\) 10.0758 0.582698
\(300\) −15.3523 −0.886363
\(301\) 0.606376 0.0349509
\(302\) 11.3741 0.654506
\(303\) −5.41552 −0.311113
\(304\) −0.477322 −0.0273763
\(305\) 31.5778 1.80814
\(306\) 2.27866 0.130262
\(307\) 5.18300 0.295810 0.147905 0.989002i \(-0.452747\pi\)
0.147905 + 0.989002i \(0.452747\pi\)
\(308\) 1.28047 0.0729617
\(309\) 18.1777 1.03409
\(310\) −5.74912 −0.326528
\(311\) 2.73651 0.155173 0.0775866 0.996986i \(-0.475279\pi\)
0.0775866 + 0.996986i \(0.475279\pi\)
\(312\) 10.8472 0.614104
\(313\) 25.8591 1.46165 0.730823 0.682568i \(-0.239137\pi\)
0.730823 + 0.682568i \(0.239137\pi\)
\(314\) 14.9929 0.846101
\(315\) 0.251232 0.0141553
\(316\) 3.19228 0.179580
\(317\) −8.90858 −0.500356 −0.250178 0.968200i \(-0.580489\pi\)
−0.250178 + 0.968200i \(0.580489\pi\)
\(318\) 13.2702 0.744158
\(319\) 41.6056 2.32946
\(320\) 40.7165 2.27612
\(321\) 6.64674 0.370985
\(322\) 0.461268 0.0257055
\(323\) −2.46147 −0.136960
\(324\) 3.19228 0.177349
\(325\) 19.2015 1.06511
\(326\) 1.95354 0.108196
\(327\) 0.892414 0.0493506
\(328\) 0.497934 0.0274938
\(329\) 0.373351 0.0205835
\(330\) 35.6867 1.96449
\(331\) −3.14995 −0.173137 −0.0865684 0.996246i \(-0.527590\pi\)
−0.0865684 + 0.996246i \(0.527590\pi\)
\(332\) 29.1395 1.59924
\(333\) 10.3580 0.567617
\(334\) 20.9827 1.14812
\(335\) 28.0788 1.53411
\(336\) −0.0155552 −0.000848606 0
\(337\) 4.15782 0.226491 0.113245 0.993567i \(-0.463875\pi\)
0.113245 + 0.993567i \(0.463875\pi\)
\(338\) −6.70240 −0.364562
\(339\) 17.6218 0.957085
\(340\) 9.99809 0.542223
\(341\) 4.02825 0.218142
\(342\) −5.60884 −0.303291
\(343\) 1.12250 0.0606094
\(344\) 20.5371 1.10729
\(345\) 7.90373 0.425523
\(346\) −26.8201 −1.44186
\(347\) 29.4796 1.58255 0.791274 0.611462i \(-0.209418\pi\)
0.791274 + 0.611462i \(0.209418\pi\)
\(348\) 26.5608 1.42381
\(349\) 16.6926 0.893536 0.446768 0.894650i \(-0.352575\pi\)
0.446768 + 0.894650i \(0.352575\pi\)
\(350\) 0.879041 0.0469867
\(351\) −3.99267 −0.213113
\(352\) −29.3801 −1.56596
\(353\) −30.1349 −1.60392 −0.801961 0.597377i \(-0.796210\pi\)
−0.801961 + 0.597377i \(0.796210\pi\)
\(354\) 10.9591 0.582467
\(355\) −24.8255 −1.31760
\(356\) −2.74737 −0.145610
\(357\) −0.0802156 −0.00424546
\(358\) −3.83769 −0.202828
\(359\) 23.1741 1.22308 0.611541 0.791213i \(-0.290550\pi\)
0.611541 + 0.791213i \(0.290550\pi\)
\(360\) 8.50889 0.448458
\(361\) −12.9412 −0.681115
\(362\) −55.8946 −2.93775
\(363\) −14.0047 −0.735057
\(364\) −1.02240 −0.0535885
\(365\) 14.3332 0.750233
\(366\) −22.9744 −1.20089
\(367\) 20.9380 1.09295 0.546476 0.837474i \(-0.315969\pi\)
0.546476 + 0.837474i \(0.315969\pi\)
\(368\) −0.489365 −0.0255099
\(369\) −0.183280 −0.00954118
\(370\) 73.9219 3.84302
\(371\) −0.467152 −0.0242533
\(372\) 2.57162 0.133332
\(373\) 36.5130 1.89057 0.945285 0.326246i \(-0.105784\pi\)
0.945285 + 0.326246i \(0.105784\pi\)
\(374\) −11.3944 −0.589188
\(375\) −0.597617 −0.0308608
\(376\) 12.6449 0.652111
\(377\) −33.2203 −1.71093
\(378\) −0.182784 −0.00940138
\(379\) 35.5181 1.82444 0.912221 0.409699i \(-0.134366\pi\)
0.912221 + 0.409699i \(0.134366\pi\)
\(380\) −24.6100 −1.26246
\(381\) −16.4533 −0.842927
\(382\) −30.2092 −1.54564
\(383\) 6.70074 0.342392 0.171196 0.985237i \(-0.445237\pi\)
0.171196 + 0.985237i \(0.445237\pi\)
\(384\) −17.8723 −0.912044
\(385\) −1.25628 −0.0640259
\(386\) 11.8741 0.604377
\(387\) −7.55934 −0.384263
\(388\) −48.8044 −2.47767
\(389\) 20.8753 1.05842 0.529211 0.848491i \(-0.322488\pi\)
0.529211 + 0.848491i \(0.322488\pi\)
\(390\) −28.4943 −1.44287
\(391\) −2.52357 −0.127623
\(392\) 19.0001 0.959648
\(393\) 9.58929 0.483715
\(394\) 44.7054 2.25223
\(395\) −3.13196 −0.157586
\(396\) −15.9629 −0.802166
\(397\) −17.4239 −0.874482 −0.437241 0.899344i \(-0.644044\pi\)
−0.437241 + 0.899344i \(0.644044\pi\)
\(398\) 46.8245 2.34710
\(399\) 0.197448 0.00988476
\(400\) −0.932586 −0.0466293
\(401\) 20.2799 1.01273 0.506366 0.862319i \(-0.330988\pi\)
0.506366 + 0.862319i \(0.330988\pi\)
\(402\) −20.4287 −1.01889
\(403\) −3.21639 −0.160220
\(404\) 17.2878 0.860102
\(405\) −3.13196 −0.155628
\(406\) −1.52082 −0.0754770
\(407\) −51.7951 −2.56739
\(408\) −2.71679 −0.134501
\(409\) −6.31609 −0.312310 −0.156155 0.987733i \(-0.549910\pi\)
−0.156155 + 0.987733i \(0.549910\pi\)
\(410\) −1.30801 −0.0645980
\(411\) 14.7192 0.726043
\(412\) −58.0283 −2.85885
\(413\) −0.385792 −0.0189836
\(414\) −5.75036 −0.282615
\(415\) −28.5890 −1.40338
\(416\) 23.4587 1.15016
\(417\) −21.6385 −1.05964
\(418\) 28.0468 1.37182
\(419\) −6.94256 −0.339166 −0.169583 0.985516i \(-0.554242\pi\)
−0.169583 + 0.985516i \(0.554242\pi\)
\(420\) −0.802003 −0.0391337
\(421\) 32.6805 1.59275 0.796375 0.604803i \(-0.206748\pi\)
0.796375 + 0.604803i \(0.206748\pi\)
\(422\) −8.21222 −0.399765
\(423\) −4.65435 −0.226302
\(424\) −15.8218 −0.768375
\(425\) −4.80919 −0.233280
\(426\) 18.0618 0.875097
\(427\) 0.808768 0.0391390
\(428\) −21.2183 −1.02562
\(429\) 19.9652 0.963930
\(430\) −53.9485 −2.60163
\(431\) −5.96004 −0.287085 −0.143543 0.989644i \(-0.545849\pi\)
−0.143543 + 0.989644i \(0.545849\pi\)
\(432\) 0.193918 0.00932987
\(433\) 19.3247 0.928686 0.464343 0.885655i \(-0.346290\pi\)
0.464343 + 0.885655i \(0.346290\pi\)
\(434\) −0.147246 −0.00706803
\(435\) −26.0589 −1.24943
\(436\) −2.84883 −0.136434
\(437\) 6.21169 0.297145
\(438\) −10.4281 −0.498274
\(439\) 17.7190 0.845681 0.422841 0.906204i \(-0.361033\pi\)
0.422841 + 0.906204i \(0.361033\pi\)
\(440\) −42.5485 −2.02842
\(441\) −6.99357 −0.333027
\(442\) 9.09792 0.432744
\(443\) −9.58390 −0.455345 −0.227672 0.973738i \(-0.573112\pi\)
−0.227672 + 0.973738i \(0.573112\pi\)
\(444\) −33.0658 −1.56923
\(445\) 2.69546 0.127777
\(446\) −26.4251 −1.25126
\(447\) 10.8910 0.515128
\(448\) 1.04283 0.0492690
\(449\) 5.77131 0.272365 0.136182 0.990684i \(-0.456517\pi\)
0.136182 + 0.990684i \(0.456517\pi\)
\(450\) −10.9585 −0.516588
\(451\) 0.916487 0.0431557
\(452\) −56.2537 −2.64595
\(453\) 4.99158 0.234525
\(454\) 39.2006 1.83977
\(455\) 1.00309 0.0470254
\(456\) 6.68729 0.313161
\(457\) 11.4674 0.536422 0.268211 0.963360i \(-0.413568\pi\)
0.268211 + 0.963360i \(0.413568\pi\)
\(458\) −11.3340 −0.529602
\(459\) 1.00000 0.0466760
\(460\) −25.2309 −1.17640
\(461\) 20.0962 0.935976 0.467988 0.883735i \(-0.344979\pi\)
0.467988 + 0.883735i \(0.344979\pi\)
\(462\) 0.914005 0.0425234
\(463\) 19.8957 0.924631 0.462315 0.886716i \(-0.347019\pi\)
0.462315 + 0.886716i \(0.347019\pi\)
\(464\) 1.61346 0.0749029
\(465\) −2.52303 −0.117003
\(466\) −49.9116 −2.31211
\(467\) 38.1231 1.76413 0.882063 0.471132i \(-0.156154\pi\)
0.882063 + 0.471132i \(0.156154\pi\)
\(468\) 12.7457 0.589170
\(469\) 0.719151 0.0332073
\(470\) −33.2165 −1.53216
\(471\) 6.57973 0.303178
\(472\) −13.0662 −0.601422
\(473\) 37.8002 1.73806
\(474\) 2.27866 0.104662
\(475\) 11.8377 0.543149
\(476\) 0.256070 0.0117370
\(477\) 5.82371 0.266649
\(478\) 1.45612 0.0666012
\(479\) −5.17431 −0.236420 −0.118210 0.992989i \(-0.537716\pi\)
−0.118210 + 0.992989i \(0.537716\pi\)
\(480\) 18.4017 0.839919
\(481\) 41.3562 1.88568
\(482\) 28.3418 1.29093
\(483\) 0.202430 0.00921087
\(484\) 44.7069 2.03213
\(485\) 47.8823 2.17422
\(486\) 2.27866 0.103362
\(487\) −31.1587 −1.41193 −0.705967 0.708244i \(-0.749487\pi\)
−0.705967 + 0.708244i \(0.749487\pi\)
\(488\) 27.3919 1.23997
\(489\) 0.857319 0.0387693
\(490\) −49.9108 −2.25474
\(491\) 33.7654 1.52381 0.761906 0.647688i \(-0.224264\pi\)
0.761906 + 0.647688i \(0.224264\pi\)
\(492\) 0.585081 0.0263775
\(493\) 8.32033 0.374729
\(494\) −22.3942 −1.00756
\(495\) 15.6613 0.703923
\(496\) 0.156215 0.00701427
\(497\) −0.635830 −0.0285209
\(498\) 20.7999 0.932065
\(499\) 5.17688 0.231749 0.115874 0.993264i \(-0.463033\pi\)
0.115874 + 0.993264i \(0.463033\pi\)
\(500\) 1.90776 0.0853176
\(501\) 9.20838 0.411400
\(502\) −37.4519 −1.67156
\(503\) −30.2454 −1.34858 −0.674289 0.738468i \(-0.735550\pi\)
−0.674289 + 0.738468i \(0.735550\pi\)
\(504\) 0.217929 0.00970733
\(505\) −16.9612 −0.754764
\(506\) 28.7545 1.27829
\(507\) −2.94138 −0.130631
\(508\) 52.5235 2.33035
\(509\) 1.03524 0.0458861 0.0229431 0.999737i \(-0.492696\pi\)
0.0229431 + 0.999737i \(0.492696\pi\)
\(510\) 7.13667 0.316017
\(511\) 0.367100 0.0162396
\(512\) −2.19302 −0.0969188
\(513\) −2.46147 −0.108676
\(514\) 49.2469 2.17219
\(515\) 56.9319 2.50872
\(516\) 24.1315 1.06233
\(517\) 23.2739 1.02359
\(518\) 1.89328 0.0831860
\(519\) −11.7701 −0.516652
\(520\) 33.9732 1.48982
\(521\) −35.6551 −1.56208 −0.781039 0.624482i \(-0.785310\pi\)
−0.781039 + 0.624482i \(0.785310\pi\)
\(522\) 18.9592 0.829820
\(523\) −26.2397 −1.14738 −0.573691 0.819072i \(-0.694489\pi\)
−0.573691 + 0.819072i \(0.694489\pi\)
\(524\) −30.6117 −1.33728
\(525\) 0.385772 0.0168365
\(526\) −68.2431 −2.97554
\(527\) 0.805575 0.0350914
\(528\) −0.969680 −0.0421999
\(529\) −16.6316 −0.723112
\(530\) 41.5619 1.80533
\(531\) 4.80944 0.208712
\(532\) −0.630309 −0.0273273
\(533\) −0.731776 −0.0316967
\(534\) −1.96108 −0.0848642
\(535\) 20.8174 0.900013
\(536\) 24.3567 1.05205
\(537\) −1.68419 −0.0726782
\(538\) −33.0901 −1.42662
\(539\) 34.9711 1.50631
\(540\) 9.99809 0.430249
\(541\) 38.4426 1.65277 0.826387 0.563102i \(-0.190392\pi\)
0.826387 + 0.563102i \(0.190392\pi\)
\(542\) 19.3495 0.831134
\(543\) −24.5296 −1.05267
\(544\) −5.87546 −0.251908
\(545\) 2.79501 0.119725
\(546\) −0.729794 −0.0312323
\(547\) 2.92026 0.124861 0.0624307 0.998049i \(-0.480115\pi\)
0.0624307 + 0.998049i \(0.480115\pi\)
\(548\) −46.9877 −2.00721
\(549\) −10.0824 −0.430308
\(550\) 54.7976 2.33658
\(551\) −20.4802 −0.872486
\(552\) 6.85602 0.291812
\(553\) −0.0802156 −0.00341111
\(554\) 67.5795 2.87118
\(555\) 32.4410 1.37704
\(556\) 69.0760 2.92947
\(557\) 5.31643 0.225264 0.112632 0.993637i \(-0.464072\pi\)
0.112632 + 0.993637i \(0.464072\pi\)
\(558\) 1.83563 0.0777084
\(559\) −30.1819 −1.27656
\(560\) −0.0487183 −0.00205873
\(561\) −5.00047 −0.211120
\(562\) 13.8364 0.583652
\(563\) 28.2136 1.18906 0.594530 0.804073i \(-0.297338\pi\)
0.594530 + 0.804073i \(0.297338\pi\)
\(564\) 14.8580 0.625634
\(565\) 55.1908 2.32189
\(566\) 17.1128 0.719304
\(567\) −0.0802156 −0.00336874
\(568\) −21.5347 −0.903576
\(569\) 31.7669 1.33174 0.665868 0.746070i \(-0.268061\pi\)
0.665868 + 0.746070i \(0.268061\pi\)
\(570\) −17.5667 −0.735787
\(571\) −24.7303 −1.03493 −0.517465 0.855705i \(-0.673124\pi\)
−0.517465 + 0.855705i \(0.673124\pi\)
\(572\) −63.7345 −2.66487
\(573\) −13.2575 −0.553838
\(574\) −0.0335006 −0.00139829
\(575\) 12.1363 0.506120
\(576\) −13.0003 −0.541680
\(577\) 24.8099 1.03285 0.516424 0.856333i \(-0.327263\pi\)
0.516424 + 0.856333i \(0.327263\pi\)
\(578\) −2.27866 −0.0947796
\(579\) 5.21102 0.216563
\(580\) 83.1874 3.45417
\(581\) −0.732218 −0.0303775
\(582\) −34.8367 −1.44403
\(583\) −29.1213 −1.20608
\(584\) 12.4332 0.514489
\(585\) −12.5049 −0.517013
\(586\) −13.2040 −0.545453
\(587\) 18.5163 0.764248 0.382124 0.924111i \(-0.375193\pi\)
0.382124 + 0.924111i \(0.375193\pi\)
\(588\) 22.3254 0.920684
\(589\) −1.98290 −0.0817038
\(590\) 34.3234 1.41307
\(591\) 19.6192 0.807026
\(592\) −2.00861 −0.0825533
\(593\) 1.94295 0.0797872 0.0398936 0.999204i \(-0.487298\pi\)
0.0398936 + 0.999204i \(0.487298\pi\)
\(594\) −11.3944 −0.467516
\(595\) −0.251232 −0.0102995
\(596\) −34.7672 −1.42412
\(597\) 20.5492 0.841022
\(598\) −22.9593 −0.938874
\(599\) −18.1498 −0.741579 −0.370790 0.928717i \(-0.620913\pi\)
−0.370790 + 0.928717i \(0.620913\pi\)
\(600\) 13.0656 0.533399
\(601\) 14.5527 0.593615 0.296808 0.954937i \(-0.404078\pi\)
0.296808 + 0.954937i \(0.404078\pi\)
\(602\) −1.38172 −0.0563149
\(603\) −8.96523 −0.365093
\(604\) −15.9345 −0.648366
\(605\) −43.8622 −1.78325
\(606\) 12.3401 0.501283
\(607\) −10.9062 −0.442670 −0.221335 0.975198i \(-0.571041\pi\)
−0.221335 + 0.975198i \(0.571041\pi\)
\(608\) 14.4622 0.586521
\(609\) −0.667420 −0.0270452
\(610\) −71.9550 −2.91337
\(611\) −18.5833 −0.751798
\(612\) −3.19228 −0.129040
\(613\) 25.5889 1.03353 0.516763 0.856129i \(-0.327137\pi\)
0.516763 + 0.856129i \(0.327137\pi\)
\(614\) −11.8103 −0.476624
\(615\) −0.574026 −0.0231470
\(616\) −1.08975 −0.0439072
\(617\) 4.58156 0.184447 0.0922234 0.995738i \(-0.470603\pi\)
0.0922234 + 0.995738i \(0.470603\pi\)
\(618\) −41.4207 −1.66619
\(619\) 29.1831 1.17297 0.586483 0.809961i \(-0.300512\pi\)
0.586483 + 0.809961i \(0.300512\pi\)
\(620\) 8.05421 0.323465
\(621\) −2.52357 −0.101267
\(622\) −6.23557 −0.250023
\(623\) 0.0690359 0.00276586
\(624\) 0.774248 0.0309947
\(625\) −25.9177 −1.03671
\(626\) −58.9241 −2.35508
\(627\) 12.3085 0.491554
\(628\) −21.0043 −0.838163
\(629\) −10.3580 −0.413002
\(630\) −0.572472 −0.0228078
\(631\) −3.87039 −0.154078 −0.0770388 0.997028i \(-0.524547\pi\)
−0.0770388 + 0.997028i \(0.524547\pi\)
\(632\) −2.71679 −0.108068
\(633\) −3.60397 −0.143245
\(634\) 20.2996 0.806200
\(635\) −51.5311 −2.04495
\(636\) −18.5909 −0.737177
\(637\) −27.9230 −1.10635
\(638\) −94.8048 −3.75336
\(639\) 7.92651 0.313568
\(640\) −55.9755 −2.21263
\(641\) 37.1247 1.46634 0.733169 0.680047i \(-0.238040\pi\)
0.733169 + 0.680047i \(0.238040\pi\)
\(642\) −15.1457 −0.597751
\(643\) −5.02996 −0.198362 −0.0991811 0.995069i \(-0.531622\pi\)
−0.0991811 + 0.995069i \(0.531622\pi\)
\(644\) −0.646212 −0.0254643
\(645\) −23.6756 −0.932224
\(646\) 5.60884 0.220677
\(647\) 44.5467 1.75131 0.875656 0.482935i \(-0.160429\pi\)
0.875656 + 0.482935i \(0.160429\pi\)
\(648\) −2.71679 −0.106726
\(649\) −24.0494 −0.944023
\(650\) −43.7536 −1.71616
\(651\) −0.0646196 −0.00253264
\(652\) −2.73680 −0.107181
\(653\) −2.15396 −0.0842908 −0.0421454 0.999111i \(-0.513419\pi\)
−0.0421454 + 0.999111i \(0.513419\pi\)
\(654\) −2.03351 −0.0795164
\(655\) 30.0333 1.17350
\(656\) 0.0355412 0.00138765
\(657\) −4.57642 −0.178543
\(658\) −0.850739 −0.0331653
\(659\) 39.7479 1.54836 0.774178 0.632967i \(-0.218163\pi\)
0.774178 + 0.632967i \(0.218163\pi\)
\(660\) −49.9952 −1.94606
\(661\) −10.7167 −0.416832 −0.208416 0.978040i \(-0.566831\pi\)
−0.208416 + 0.978040i \(0.566831\pi\)
\(662\) 7.17765 0.278967
\(663\) 3.99267 0.155062
\(664\) −24.7993 −0.962398
\(665\) 0.618399 0.0239805
\(666\) −23.6024 −0.914576
\(667\) −20.9969 −0.813005
\(668\) −29.3957 −1.13735
\(669\) −11.5968 −0.448357
\(670\) −63.9819 −2.47184
\(671\) 50.4169 1.94632
\(672\) 0.471303 0.0181809
\(673\) −34.0914 −1.31413 −0.657063 0.753836i \(-0.728201\pi\)
−0.657063 + 0.753836i \(0.728201\pi\)
\(674\) −9.47424 −0.364934
\(675\) −4.80919 −0.185106
\(676\) 9.38970 0.361142
\(677\) −13.5518 −0.520839 −0.260419 0.965496i \(-0.583861\pi\)
−0.260419 + 0.965496i \(0.583861\pi\)
\(678\) −40.1540 −1.54211
\(679\) 1.22636 0.0470632
\(680\) −8.50889 −0.326301
\(681\) 17.2034 0.659234
\(682\) −9.17901 −0.351482
\(683\) −1.09317 −0.0418291 −0.0209146 0.999781i \(-0.506658\pi\)
−0.0209146 + 0.999781i \(0.506658\pi\)
\(684\) 7.85768 0.300446
\(685\) 46.0999 1.76139
\(686\) −2.55780 −0.0976571
\(687\) −4.97398 −0.189769
\(688\) 1.46589 0.0558865
\(689\) 23.2521 0.885835
\(690\) −18.0099 −0.685625
\(691\) 29.8337 1.13493 0.567463 0.823399i \(-0.307925\pi\)
0.567463 + 0.823399i \(0.307925\pi\)
\(692\) 37.5735 1.42833
\(693\) 0.401116 0.0152371
\(694\) −67.1739 −2.54989
\(695\) −67.7708 −2.57069
\(696\) −22.6046 −0.856825
\(697\) 0.183280 0.00694223
\(698\) −38.0368 −1.43971
\(699\) −21.9040 −0.828484
\(700\) −1.23149 −0.0465460
\(701\) −36.2508 −1.36917 −0.684587 0.728931i \(-0.740018\pi\)
−0.684587 + 0.728931i \(0.740018\pi\)
\(702\) 9.09792 0.343379
\(703\) 25.4960 0.961599
\(704\) 65.0077 2.45007
\(705\) −14.5772 −0.549011
\(706\) 68.6672 2.58432
\(707\) −0.434409 −0.0163376
\(708\) −15.3531 −0.577003
\(709\) 12.9505 0.486368 0.243184 0.969980i \(-0.421808\pi\)
0.243184 + 0.969980i \(0.421808\pi\)
\(710\) 56.5689 2.12299
\(711\) 1.00000 0.0375029
\(712\) 2.33815 0.0876259
\(713\) −2.03293 −0.0761337
\(714\) 0.182784 0.00684051
\(715\) 62.5303 2.33850
\(716\) 5.37640 0.200926
\(717\) 0.639024 0.0238648
\(718\) −52.8058 −1.97069
\(719\) −22.8899 −0.853648 −0.426824 0.904335i \(-0.640368\pi\)
−0.426824 + 0.904335i \(0.640368\pi\)
\(720\) 0.607343 0.0226343
\(721\) 1.45813 0.0543037
\(722\) 29.4885 1.09745
\(723\) 12.4379 0.462571
\(724\) 78.3054 2.91020
\(725\) −40.0140 −1.48608
\(726\) 31.9119 1.18436
\(727\) 41.8150 1.55083 0.775416 0.631451i \(-0.217540\pi\)
0.775416 + 0.631451i \(0.217540\pi\)
\(728\) 0.870118 0.0322487
\(729\) 1.00000 0.0370370
\(730\) −32.6604 −1.20882
\(731\) 7.55934 0.279592
\(732\) 32.1859 1.18963
\(733\) 20.3543 0.751805 0.375902 0.926659i \(-0.377333\pi\)
0.375902 + 0.926659i \(0.377333\pi\)
\(734\) −47.7104 −1.76102
\(735\) −21.9036 −0.807926
\(736\) 14.8271 0.546536
\(737\) 44.8304 1.65135
\(738\) 0.417632 0.0153733
\(739\) −41.4339 −1.52417 −0.762085 0.647478i \(-0.775824\pi\)
−0.762085 + 0.647478i \(0.775824\pi\)
\(740\) −103.561 −3.80697
\(741\) −9.82781 −0.361034
\(742\) 1.06448 0.0390783
\(743\) 9.15548 0.335882 0.167941 0.985797i \(-0.446288\pi\)
0.167941 + 0.985797i \(0.446288\pi\)
\(744\) −2.18858 −0.0802372
\(745\) 34.1103 1.24971
\(746\) −83.2005 −3.04619
\(747\) 9.12814 0.333981
\(748\) 15.9629 0.583661
\(749\) 0.533172 0.0194817
\(750\) 1.36176 0.0497246
\(751\) −11.8805 −0.433526 −0.216763 0.976224i \(-0.569550\pi\)
−0.216763 + 0.976224i \(0.569550\pi\)
\(752\) 0.902560 0.0329130
\(753\) −16.4360 −0.598960
\(754\) 75.6976 2.75675
\(755\) 15.6334 0.568959
\(756\) 0.256070 0.00931319
\(757\) 10.4120 0.378431 0.189216 0.981936i \(-0.439405\pi\)
0.189216 + 0.981936i \(0.439405\pi\)
\(758\) −80.9335 −2.93964
\(759\) 12.6191 0.458043
\(760\) 20.9444 0.759731
\(761\) −15.2424 −0.552538 −0.276269 0.961080i \(-0.589098\pi\)
−0.276269 + 0.961080i \(0.589098\pi\)
\(762\) 37.4914 1.35817
\(763\) 0.0715855 0.00259157
\(764\) 42.3215 1.53114
\(765\) 3.13196 0.113236
\(766\) −15.2687 −0.551680
\(767\) 19.2025 0.693361
\(768\) 14.7243 0.531318
\(769\) 9.11189 0.328583 0.164292 0.986412i \(-0.447466\pi\)
0.164292 + 0.986412i \(0.447466\pi\)
\(770\) 2.86263 0.103162
\(771\) 21.6122 0.778345
\(772\) −16.6350 −0.598708
\(773\) −30.8868 −1.11092 −0.555460 0.831543i \(-0.687458\pi\)
−0.555460 + 0.831543i \(0.687458\pi\)
\(774\) 17.2251 0.619145
\(775\) −3.87416 −0.139164
\(776\) 41.5350 1.49102
\(777\) 0.830876 0.0298075
\(778\) −47.5677 −1.70539
\(779\) −0.451138 −0.0161637
\(780\) 39.9190 1.42933
\(781\) −39.6363 −1.41830
\(782\) 5.75036 0.205632
\(783\) 8.32033 0.297344
\(784\) 1.35618 0.0484348
\(785\) 20.6075 0.735512
\(786\) −21.8507 −0.779388
\(787\) −38.2764 −1.36441 −0.682203 0.731163i \(-0.738978\pi\)
−0.682203 + 0.731163i \(0.738978\pi\)
\(788\) −62.6299 −2.23110
\(789\) −29.9488 −1.06621
\(790\) 7.13667 0.253911
\(791\) 1.41354 0.0502598
\(792\) 13.5852 0.482731
\(793\) −40.2558 −1.42952
\(794\) 39.7032 1.40901
\(795\) 18.2396 0.646893
\(796\) −65.5987 −2.32508
\(797\) 2.92436 0.103586 0.0517930 0.998658i \(-0.483506\pi\)
0.0517930 + 0.998658i \(0.483506\pi\)
\(798\) −0.449916 −0.0159269
\(799\) 4.65435 0.164659
\(800\) 28.2562 0.999007
\(801\) −0.860630 −0.0304088
\(802\) −46.2110 −1.63177
\(803\) 22.8843 0.807569
\(804\) 28.6195 1.00933
\(805\) 0.634002 0.0223456
\(806\) 7.32905 0.258155
\(807\) −14.5218 −0.511191
\(808\) −14.7128 −0.517596
\(809\) −38.8161 −1.36470 −0.682351 0.731024i \(-0.739043\pi\)
−0.682351 + 0.731024i \(0.739043\pi\)
\(810\) 7.13667 0.250757
\(811\) −21.2527 −0.746284 −0.373142 0.927774i \(-0.621719\pi\)
−0.373142 + 0.927774i \(0.621719\pi\)
\(812\) 2.13059 0.0747690
\(813\) 8.49164 0.297815
\(814\) 118.023 4.13671
\(815\) 2.68509 0.0940547
\(816\) −0.193918 −0.00678847
\(817\) −18.6071 −0.650978
\(818\) 14.3922 0.503211
\(819\) −0.320274 −0.0111913
\(820\) 1.83245 0.0639920
\(821\) −23.0227 −0.803498 −0.401749 0.915750i \(-0.631598\pi\)
−0.401749 + 0.915750i \(0.631598\pi\)
\(822\) −33.5399 −1.16984
\(823\) −18.9477 −0.660476 −0.330238 0.943898i \(-0.607129\pi\)
−0.330238 + 0.943898i \(0.607129\pi\)
\(824\) 49.3850 1.72041
\(825\) 24.0482 0.837251
\(826\) 0.879087 0.0305873
\(827\) −40.6847 −1.41475 −0.707373 0.706840i \(-0.750120\pi\)
−0.707373 + 0.706840i \(0.750120\pi\)
\(828\) 8.05594 0.279963
\(829\) −37.3942 −1.29875 −0.649377 0.760466i \(-0.724970\pi\)
−0.649377 + 0.760466i \(0.724970\pi\)
\(830\) 65.1445 2.26120
\(831\) 29.6576 1.02881
\(832\) −51.9059 −1.79951
\(833\) 6.99357 0.242313
\(834\) 49.3066 1.70735
\(835\) 28.8403 0.998060
\(836\) −39.2921 −1.35895
\(837\) 0.805575 0.0278447
\(838\) 15.8197 0.546483
\(839\) −55.9603 −1.93196 −0.965982 0.258610i \(-0.916736\pi\)
−0.965982 + 0.258610i \(0.916736\pi\)
\(840\) 0.682545 0.0235501
\(841\) 40.2278 1.38717
\(842\) −74.4677 −2.56632
\(843\) 6.07216 0.209136
\(844\) 11.5049 0.396014
\(845\) −9.21229 −0.316912
\(846\) 10.6057 0.364630
\(847\) −1.12340 −0.0386003
\(848\) −1.12932 −0.0387810
\(849\) 7.51003 0.257744
\(850\) 10.9585 0.375873
\(851\) 26.1393 0.896043
\(852\) −25.3036 −0.866888
\(853\) −14.5050 −0.496641 −0.248321 0.968678i \(-0.579879\pi\)
−0.248321 + 0.968678i \(0.579879\pi\)
\(854\) −1.84290 −0.0630629
\(855\) −7.70922 −0.263650
\(856\) 18.0578 0.617204
\(857\) 22.2635 0.760508 0.380254 0.924882i \(-0.375837\pi\)
0.380254 + 0.924882i \(0.375837\pi\)
\(858\) −45.4939 −1.55314
\(859\) −13.0018 −0.443614 −0.221807 0.975091i \(-0.571196\pi\)
−0.221807 + 0.975091i \(0.571196\pi\)
\(860\) 75.5789 2.57722
\(861\) −0.0147019 −0.000501040 0
\(862\) 13.5809 0.462567
\(863\) 15.7527 0.536228 0.268114 0.963387i \(-0.413600\pi\)
0.268114 + 0.963387i \(0.413600\pi\)
\(864\) −5.87546 −0.199887
\(865\) −36.8636 −1.25340
\(866\) −44.0344 −1.49635
\(867\) −1.00000 −0.0339618
\(868\) 0.206284 0.00700173
\(869\) −5.00047 −0.169629
\(870\) 59.3794 2.01315
\(871\) −35.7952 −1.21287
\(872\) 2.42450 0.0821041
\(873\) −15.2883 −0.517429
\(874\) −14.1543 −0.478777
\(875\) −0.0479382 −0.00162061
\(876\) 14.6092 0.493600
\(877\) −47.5301 −1.60498 −0.802488 0.596668i \(-0.796491\pi\)
−0.802488 + 0.596668i \(0.796491\pi\)
\(878\) −40.3755 −1.36261
\(879\) −5.79465 −0.195449
\(880\) −3.03700 −0.102377
\(881\) 2.84828 0.0959611 0.0479805 0.998848i \(-0.484721\pi\)
0.0479805 + 0.998848i \(0.484721\pi\)
\(882\) 15.9359 0.536591
\(883\) 31.8623 1.07225 0.536126 0.844138i \(-0.319887\pi\)
0.536126 + 0.844138i \(0.319887\pi\)
\(884\) −12.7457 −0.428684
\(885\) 15.0630 0.506336
\(886\) 21.8384 0.733676
\(887\) −10.3429 −0.347280 −0.173640 0.984809i \(-0.555553\pi\)
−0.173640 + 0.984809i \(0.555553\pi\)
\(888\) 28.1407 0.944339
\(889\) −1.31981 −0.0442650
\(890\) −6.14203 −0.205881
\(891\) −5.00047 −0.167522
\(892\) 37.0201 1.23953
\(893\) −11.4565 −0.383378
\(894\) −24.8169 −0.830002
\(895\) −5.27482 −0.176318
\(896\) −1.43364 −0.0478946
\(897\) −10.0758 −0.336421
\(898\) −13.1508 −0.438849
\(899\) 6.70265 0.223546
\(900\) 15.3523 0.511742
\(901\) −5.82371 −0.194016
\(902\) −2.08836 −0.0695347
\(903\) −0.606376 −0.0201789
\(904\) 47.8748 1.59229
\(905\) −76.8259 −2.55378
\(906\) −11.3741 −0.377879
\(907\) 53.5268 1.77733 0.888664 0.458559i \(-0.151634\pi\)
0.888664 + 0.458559i \(0.151634\pi\)
\(908\) −54.9179 −1.82252
\(909\) 5.41552 0.179621
\(910\) −2.28569 −0.0757698
\(911\) −18.3563 −0.608170 −0.304085 0.952645i \(-0.598351\pi\)
−0.304085 + 0.952645i \(0.598351\pi\)
\(912\) 0.477322 0.0158057
\(913\) −45.6450 −1.51063
\(914\) −26.1302 −0.864311
\(915\) −31.5778 −1.04393
\(916\) 15.8783 0.524634
\(917\) 0.769210 0.0254015
\(918\) −2.27866 −0.0752069
\(919\) 17.8225 0.587909 0.293955 0.955819i \(-0.405029\pi\)
0.293955 + 0.955819i \(0.405029\pi\)
\(920\) 21.4728 0.707937
\(921\) −5.18300 −0.170786
\(922\) −45.7925 −1.50809
\(923\) 31.6479 1.04170
\(924\) −1.28047 −0.0421245
\(925\) 49.8138 1.63787
\(926\) −45.3354 −1.48981
\(927\) −18.1777 −0.597034
\(928\) −48.8857 −1.60475
\(929\) 50.1602 1.64570 0.822851 0.568257i \(-0.192382\pi\)
0.822851 + 0.568257i \(0.192382\pi\)
\(930\) 5.74912 0.188521
\(931\) −17.2144 −0.564180
\(932\) 69.9235 2.29042
\(933\) −2.73651 −0.0895893
\(934\) −86.8694 −2.84245
\(935\) −15.6613 −0.512179
\(936\) −10.8472 −0.354553
\(937\) 37.3705 1.22084 0.610421 0.792077i \(-0.291000\pi\)
0.610421 + 0.792077i \(0.291000\pi\)
\(938\) −1.63870 −0.0535054
\(939\) −25.8591 −0.843881
\(940\) 46.5346 1.51779
\(941\) 22.7989 0.743222 0.371611 0.928389i \(-0.378806\pi\)
0.371611 + 0.928389i \(0.378806\pi\)
\(942\) −14.9929 −0.488496
\(943\) −0.462521 −0.0150617
\(944\) −0.932634 −0.0303547
\(945\) −0.251232 −0.00817258
\(946\) −86.1338 −2.80045
\(947\) −4.19066 −0.136178 −0.0680890 0.997679i \(-0.521690\pi\)
−0.0680890 + 0.997679i \(0.521690\pi\)
\(948\) −3.19228 −0.103680
\(949\) −18.2721 −0.593138
\(950\) −26.9740 −0.875151
\(951\) 8.90858 0.288881
\(952\) −0.217929 −0.00706312
\(953\) 37.9263 1.22855 0.614277 0.789091i \(-0.289448\pi\)
0.614277 + 0.789091i \(0.289448\pi\)
\(954\) −13.2702 −0.429640
\(955\) −41.5219 −1.34362
\(956\) −2.03994 −0.0659764
\(957\) −41.6056 −1.34492
\(958\) 11.7905 0.380933
\(959\) 1.18071 0.0381270
\(960\) −40.7165 −1.31412
\(961\) −30.3510 −0.979066
\(962\) −94.2366 −3.03831
\(963\) −6.64674 −0.214188
\(964\) −39.7053 −1.27882
\(965\) 16.3207 0.525382
\(966\) −0.461268 −0.0148411
\(967\) −12.9773 −0.417322 −0.208661 0.977988i \(-0.566911\pi\)
−0.208661 + 0.977988i \(0.566911\pi\)
\(968\) −38.0479 −1.22291
\(969\) 2.46147 0.0790737
\(970\) −109.107 −3.50322
\(971\) 47.8786 1.53650 0.768248 0.640152i \(-0.221129\pi\)
0.768248 + 0.640152i \(0.221129\pi\)
\(972\) −3.19228 −0.102392
\(973\) −1.73574 −0.0556453
\(974\) 70.9999 2.27498
\(975\) −19.2015 −0.614939
\(976\) 1.95516 0.0625832
\(977\) −61.6649 −1.97283 −0.986417 0.164260i \(-0.947476\pi\)
−0.986417 + 0.164260i \(0.947476\pi\)
\(978\) −1.95354 −0.0624672
\(979\) 4.30355 0.137542
\(980\) 69.9223 2.23359
\(981\) −0.892414 −0.0284926
\(982\) −76.9398 −2.45525
\(983\) 43.1638 1.37671 0.688355 0.725374i \(-0.258333\pi\)
0.688355 + 0.725374i \(0.258333\pi\)
\(984\) −0.497934 −0.0158736
\(985\) 61.4466 1.95785
\(986\) −18.9592 −0.603783
\(987\) −0.373351 −0.0118839
\(988\) 31.3731 0.998112
\(989\) −19.0765 −0.606598
\(990\) −35.6867 −1.13420
\(991\) 39.2846 1.24792 0.623958 0.781458i \(-0.285524\pi\)
0.623958 + 0.781458i \(0.285524\pi\)
\(992\) −4.73312 −0.150277
\(993\) 3.14995 0.0999606
\(994\) 1.44884 0.0459543
\(995\) 64.3593 2.04033
\(996\) −29.1395 −0.923322
\(997\) 6.66094 0.210954 0.105477 0.994422i \(-0.466363\pi\)
0.105477 + 0.994422i \(0.466363\pi\)
\(998\) −11.7963 −0.373406
\(999\) −10.3580 −0.327714
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.1.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.5 32 1.1 even 1 trivial