Properties

Label 4010.2.a.i.1.4
Level 4010
Weight 2
Character 4010.1
Self dual yes
Analytic conductor 32.020
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.0585304\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.47624 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.47624 q^{6} -2.32277 q^{7} -1.00000 q^{8} -0.820714 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.47624 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.47624 q^{6} -2.32277 q^{7} -1.00000 q^{8} -0.820714 q^{9} -1.00000 q^{10} +1.34500 q^{11} -1.47624 q^{12} +3.18375 q^{13} +2.32277 q^{14} -1.47624 q^{15} +1.00000 q^{16} +3.91915 q^{17} +0.820714 q^{18} -4.40549 q^{19} +1.00000 q^{20} +3.42897 q^{21} -1.34500 q^{22} -4.06300 q^{23} +1.47624 q^{24} +1.00000 q^{25} -3.18375 q^{26} +5.64029 q^{27} -2.32277 q^{28} -8.96640 q^{29} +1.47624 q^{30} +1.15541 q^{31} -1.00000 q^{32} -1.98554 q^{33} -3.91915 q^{34} -2.32277 q^{35} -0.820714 q^{36} +0.657687 q^{37} +4.40549 q^{38} -4.69998 q^{39} -1.00000 q^{40} +7.76836 q^{41} -3.42897 q^{42} +5.75543 q^{43} +1.34500 q^{44} -0.820714 q^{45} +4.06300 q^{46} -7.10781 q^{47} -1.47624 q^{48} -1.60474 q^{49} -1.00000 q^{50} -5.78561 q^{51} +3.18375 q^{52} +14.3417 q^{53} -5.64029 q^{54} +1.34500 q^{55} +2.32277 q^{56} +6.50357 q^{57} +8.96640 q^{58} -2.03120 q^{59} -1.47624 q^{60} +1.33841 q^{61} -1.15541 q^{62} +1.90633 q^{63} +1.00000 q^{64} +3.18375 q^{65} +1.98554 q^{66} -1.04497 q^{67} +3.91915 q^{68} +5.99796 q^{69} +2.32277 q^{70} +3.41086 q^{71} +0.820714 q^{72} -7.58356 q^{73} -0.657687 q^{74} -1.47624 q^{75} -4.40549 q^{76} -3.12412 q^{77} +4.69998 q^{78} -8.46523 q^{79} +1.00000 q^{80} -5.86429 q^{81} -7.76836 q^{82} -3.04080 q^{83} +3.42897 q^{84} +3.91915 q^{85} -5.75543 q^{86} +13.2366 q^{87} -1.34500 q^{88} -1.14409 q^{89} +0.820714 q^{90} -7.39512 q^{91} -4.06300 q^{92} -1.70567 q^{93} +7.10781 q^{94} -4.40549 q^{95} +1.47624 q^{96} +13.4841 q^{97} +1.60474 q^{98} -1.10386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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
\(3\) −1.47624 −0.852308 −0.426154 0.904651i \(-0.640132\pi\)
−0.426154 + 0.904651i \(0.640132\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.47624 0.602673
\(7\) −2.32277 −0.877924 −0.438962 0.898506i \(-0.644654\pi\)
−0.438962 + 0.898506i \(0.644654\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.820714 −0.273571
\(10\) −1.00000 −0.316228
\(11\) 1.34500 0.405532 0.202766 0.979227i \(-0.435007\pi\)
0.202766 + 0.979227i \(0.435007\pi\)
\(12\) −1.47624 −0.426154
\(13\) 3.18375 0.883014 0.441507 0.897258i \(-0.354444\pi\)
0.441507 + 0.897258i \(0.354444\pi\)
\(14\) 2.32277 0.620786
\(15\) −1.47624 −0.381164
\(16\) 1.00000 0.250000
\(17\) 3.91915 0.950534 0.475267 0.879842i \(-0.342351\pi\)
0.475267 + 0.879842i \(0.342351\pi\)
\(18\) 0.820714 0.193444
\(19\) −4.40549 −1.01069 −0.505345 0.862917i \(-0.668635\pi\)
−0.505345 + 0.862917i \(0.668635\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.42897 0.748262
\(22\) −1.34500 −0.286755
\(23\) −4.06300 −0.847193 −0.423597 0.905851i \(-0.639233\pi\)
−0.423597 + 0.905851i \(0.639233\pi\)
\(24\) 1.47624 0.301336
\(25\) 1.00000 0.200000
\(26\) −3.18375 −0.624385
\(27\) 5.64029 1.08547
\(28\) −2.32277 −0.438962
\(29\) −8.96640 −1.66502 −0.832509 0.554011i \(-0.813097\pi\)
−0.832509 + 0.554011i \(0.813097\pi\)
\(30\) 1.47624 0.269523
\(31\) 1.15541 0.207518 0.103759 0.994602i \(-0.466913\pi\)
0.103759 + 0.994602i \(0.466913\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.98554 −0.345638
\(34\) −3.91915 −0.672129
\(35\) −2.32277 −0.392620
\(36\) −0.820714 −0.136786
\(37\) 0.657687 0.108123 0.0540615 0.998538i \(-0.482783\pi\)
0.0540615 + 0.998538i \(0.482783\pi\)
\(38\) 4.40549 0.714666
\(39\) −4.69998 −0.752599
\(40\) −1.00000 −0.158114
\(41\) 7.76836 1.21321 0.606607 0.795002i \(-0.292530\pi\)
0.606607 + 0.795002i \(0.292530\pi\)
\(42\) −3.42897 −0.529101
\(43\) 5.75543 0.877694 0.438847 0.898562i \(-0.355387\pi\)
0.438847 + 0.898562i \(0.355387\pi\)
\(44\) 1.34500 0.202766
\(45\) −0.820714 −0.122345
\(46\) 4.06300 0.599056
\(47\) −7.10781 −1.03678 −0.518391 0.855144i \(-0.673469\pi\)
−0.518391 + 0.855144i \(0.673469\pi\)
\(48\) −1.47624 −0.213077
\(49\) −1.60474 −0.229249
\(50\) −1.00000 −0.141421
\(51\) −5.78561 −0.810148
\(52\) 3.18375 0.441507
\(53\) 14.3417 1.96998 0.984991 0.172608i \(-0.0552193\pi\)
0.984991 + 0.172608i \(0.0552193\pi\)
\(54\) −5.64029 −0.767547
\(55\) 1.34500 0.181360
\(56\) 2.32277 0.310393
\(57\) 6.50357 0.861419
\(58\) 8.96640 1.17735
\(59\) −2.03120 −0.264440 −0.132220 0.991220i \(-0.542211\pi\)
−0.132220 + 0.991220i \(0.542211\pi\)
\(60\) −1.47624 −0.190582
\(61\) 1.33841 0.171366 0.0856829 0.996322i \(-0.472693\pi\)
0.0856829 + 0.996322i \(0.472693\pi\)
\(62\) −1.15541 −0.146738
\(63\) 1.90633 0.240175
\(64\) 1.00000 0.125000
\(65\) 3.18375 0.394896
\(66\) 1.98554 0.244403
\(67\) −1.04497 −0.127663 −0.0638315 0.997961i \(-0.520332\pi\)
−0.0638315 + 0.997961i \(0.520332\pi\)
\(68\) 3.91915 0.475267
\(69\) 5.99796 0.722069
\(70\) 2.32277 0.277624
\(71\) 3.41086 0.404794 0.202397 0.979304i \(-0.435127\pi\)
0.202397 + 0.979304i \(0.435127\pi\)
\(72\) 0.820714 0.0967221
\(73\) −7.58356 −0.887589 −0.443794 0.896129i \(-0.646368\pi\)
−0.443794 + 0.896129i \(0.646368\pi\)
\(74\) −0.657687 −0.0764545
\(75\) −1.47624 −0.170462
\(76\) −4.40549 −0.505345
\(77\) −3.12412 −0.356027
\(78\) 4.69998 0.532168
\(79\) −8.46523 −0.952412 −0.476206 0.879334i \(-0.657988\pi\)
−0.476206 + 0.879334i \(0.657988\pi\)
\(80\) 1.00000 0.111803
\(81\) −5.86429 −0.651587
\(82\) −7.76836 −0.857872
\(83\) −3.04080 −0.333772 −0.166886 0.985976i \(-0.553371\pi\)
−0.166886 + 0.985976i \(0.553371\pi\)
\(84\) 3.42897 0.374131
\(85\) 3.91915 0.425092
\(86\) −5.75543 −0.620624
\(87\) 13.2366 1.41911
\(88\) −1.34500 −0.143377
\(89\) −1.14409 −0.121273 −0.0606366 0.998160i \(-0.519313\pi\)
−0.0606366 + 0.998160i \(0.519313\pi\)
\(90\) 0.820714 0.0865109
\(91\) −7.39512 −0.775219
\(92\) −4.06300 −0.423597
\(93\) −1.70567 −0.176870
\(94\) 7.10781 0.733115
\(95\) −4.40549 −0.451994
\(96\) 1.47624 0.150668
\(97\) 13.4841 1.36910 0.684549 0.728966i \(-0.259999\pi\)
0.684549 + 0.728966i \(0.259999\pi\)
\(98\) 1.60474 0.162103
\(99\) −1.10386 −0.110942
\(100\) 1.00000 0.100000
\(101\) −14.2856 −1.42147 −0.710733 0.703462i \(-0.751637\pi\)
−0.710733 + 0.703462i \(0.751637\pi\)
\(102\) 5.78561 0.572861
\(103\) −0.775780 −0.0764399 −0.0382200 0.999269i \(-0.512169\pi\)
−0.0382200 + 0.999269i \(0.512169\pi\)
\(104\) −3.18375 −0.312192
\(105\) 3.42897 0.334633
\(106\) −14.3417 −1.39299
\(107\) 8.33906 0.806168 0.403084 0.915163i \(-0.367938\pi\)
0.403084 + 0.915163i \(0.367938\pi\)
\(108\) 5.64029 0.542737
\(109\) 9.07998 0.869704 0.434852 0.900502i \(-0.356801\pi\)
0.434852 + 0.900502i \(0.356801\pi\)
\(110\) −1.34500 −0.128241
\(111\) −0.970904 −0.0921541
\(112\) −2.32277 −0.219481
\(113\) −6.70185 −0.630457 −0.315229 0.949016i \(-0.602081\pi\)
−0.315229 + 0.949016i \(0.602081\pi\)
\(114\) −6.50357 −0.609115
\(115\) −4.06300 −0.378876
\(116\) −8.96640 −0.832509
\(117\) −2.61295 −0.241567
\(118\) 2.03120 0.186987
\(119\) −9.10329 −0.834497
\(120\) 1.47624 0.134762
\(121\) −9.19098 −0.835543
\(122\) −1.33841 −0.121174
\(123\) −11.4680 −1.03403
\(124\) 1.15541 0.103759
\(125\) 1.00000 0.0894427
\(126\) −1.90633 −0.169829
\(127\) −8.13046 −0.721462 −0.360731 0.932670i \(-0.617473\pi\)
−0.360731 + 0.932670i \(0.617473\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.49639 −0.748066
\(130\) −3.18375 −0.279233
\(131\) −13.4752 −1.17733 −0.588667 0.808375i \(-0.700347\pi\)
−0.588667 + 0.808375i \(0.700347\pi\)
\(132\) −1.98554 −0.172819
\(133\) 10.2330 0.887309
\(134\) 1.04497 0.0902713
\(135\) 5.64029 0.485439
\(136\) −3.91915 −0.336065
\(137\) 9.92905 0.848296 0.424148 0.905593i \(-0.360574\pi\)
0.424148 + 0.905593i \(0.360574\pi\)
\(138\) −5.99796 −0.510580
\(139\) 1.27837 0.108430 0.0542148 0.998529i \(-0.482734\pi\)
0.0542148 + 0.998529i \(0.482734\pi\)
\(140\) −2.32277 −0.196310
\(141\) 10.4928 0.883657
\(142\) −3.41086 −0.286233
\(143\) 4.28214 0.358091
\(144\) −0.820714 −0.0683928
\(145\) −8.96640 −0.744619
\(146\) 7.58356 0.627620
\(147\) 2.36898 0.195390
\(148\) 0.657687 0.0540615
\(149\) −0.681369 −0.0558199 −0.0279100 0.999610i \(-0.508885\pi\)
−0.0279100 + 0.999610i \(0.508885\pi\)
\(150\) 1.47624 0.120535
\(151\) 19.5237 1.58882 0.794408 0.607385i \(-0.207781\pi\)
0.794408 + 0.607385i \(0.207781\pi\)
\(152\) 4.40549 0.357333
\(153\) −3.21650 −0.260039
\(154\) 3.12412 0.251749
\(155\) 1.15541 0.0928051
\(156\) −4.69998 −0.376300
\(157\) 2.19525 0.175200 0.0875999 0.996156i \(-0.472080\pi\)
0.0875999 + 0.996156i \(0.472080\pi\)
\(158\) 8.46523 0.673457
\(159\) −21.1718 −1.67903
\(160\) −1.00000 −0.0790569
\(161\) 9.43740 0.743772
\(162\) 5.86429 0.460742
\(163\) −11.2919 −0.884448 −0.442224 0.896905i \(-0.645810\pi\)
−0.442224 + 0.896905i \(0.645810\pi\)
\(164\) 7.76836 0.606607
\(165\) −1.98554 −0.154574
\(166\) 3.04080 0.236012
\(167\) 4.27804 0.331045 0.165522 0.986206i \(-0.447069\pi\)
0.165522 + 0.986206i \(0.447069\pi\)
\(168\) −3.42897 −0.264551
\(169\) −2.86373 −0.220287
\(170\) −3.91915 −0.300585
\(171\) 3.61565 0.276496
\(172\) 5.75543 0.438847
\(173\) 11.8805 0.903256 0.451628 0.892206i \(-0.350843\pi\)
0.451628 + 0.892206i \(0.350843\pi\)
\(174\) −13.2366 −1.00346
\(175\) −2.32277 −0.175585
\(176\) 1.34500 0.101383
\(177\) 2.99854 0.225384
\(178\) 1.14409 0.0857531
\(179\) −7.09205 −0.530085 −0.265042 0.964237i \(-0.585386\pi\)
−0.265042 + 0.964237i \(0.585386\pi\)
\(180\) −0.820714 −0.0611724
\(181\) 0.861521 0.0640364 0.0320182 0.999487i \(-0.489807\pi\)
0.0320182 + 0.999487i \(0.489807\pi\)
\(182\) 7.39512 0.548163
\(183\) −1.97581 −0.146056
\(184\) 4.06300 0.299528
\(185\) 0.657687 0.0483541
\(186\) 1.70567 0.125066
\(187\) 5.27126 0.385472
\(188\) −7.10781 −0.518391
\(189\) −13.1011 −0.952965
\(190\) 4.40549 0.319608
\(191\) −16.2924 −1.17888 −0.589438 0.807814i \(-0.700651\pi\)
−0.589438 + 0.807814i \(0.700651\pi\)
\(192\) −1.47624 −0.106538
\(193\) −8.15952 −0.587335 −0.293668 0.955908i \(-0.594876\pi\)
−0.293668 + 0.955908i \(0.594876\pi\)
\(194\) −13.4841 −0.968099
\(195\) −4.69998 −0.336573
\(196\) −1.60474 −0.114624
\(197\) 0.519778 0.0370326 0.0185163 0.999829i \(-0.494106\pi\)
0.0185163 + 0.999829i \(0.494106\pi\)
\(198\) 1.10386 0.0784479
\(199\) −26.9093 −1.90755 −0.953775 0.300522i \(-0.902839\pi\)
−0.953775 + 0.300522i \(0.902839\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 1.54262 0.108808
\(202\) 14.2856 1.00513
\(203\) 20.8269 1.46176
\(204\) −5.78561 −0.405074
\(205\) 7.76836 0.542566
\(206\) 0.775780 0.0540512
\(207\) 3.33456 0.231768
\(208\) 3.18375 0.220753
\(209\) −5.92539 −0.409868
\(210\) −3.42897 −0.236621
\(211\) −18.0183 −1.24043 −0.620217 0.784430i \(-0.712955\pi\)
−0.620217 + 0.784430i \(0.712955\pi\)
\(212\) 14.3417 0.984991
\(213\) −5.03525 −0.345009
\(214\) −8.33906 −0.570047
\(215\) 5.75543 0.392517
\(216\) −5.64029 −0.383773
\(217\) −2.68376 −0.182186
\(218\) −9.07998 −0.614974
\(219\) 11.1952 0.756499
\(220\) 1.34500 0.0906798
\(221\) 12.4776 0.839335
\(222\) 0.970904 0.0651628
\(223\) 21.7185 1.45438 0.727188 0.686438i \(-0.240827\pi\)
0.727188 + 0.686438i \(0.240827\pi\)
\(224\) 2.32277 0.155197
\(225\) −0.820714 −0.0547143
\(226\) 6.70185 0.445801
\(227\) −9.53252 −0.632695 −0.316348 0.948643i \(-0.602457\pi\)
−0.316348 + 0.948643i \(0.602457\pi\)
\(228\) 6.50357 0.430709
\(229\) −10.7735 −0.711935 −0.355967 0.934498i \(-0.615849\pi\)
−0.355967 + 0.934498i \(0.615849\pi\)
\(230\) 4.06300 0.267906
\(231\) 4.61196 0.303444
\(232\) 8.96640 0.588673
\(233\) −9.78815 −0.641243 −0.320622 0.947207i \(-0.603892\pi\)
−0.320622 + 0.947207i \(0.603892\pi\)
\(234\) 2.61295 0.170814
\(235\) −7.10781 −0.463663
\(236\) −2.03120 −0.132220
\(237\) 12.4967 0.811748
\(238\) 9.10329 0.590079
\(239\) 11.1373 0.720412 0.360206 0.932873i \(-0.382706\pi\)
0.360206 + 0.932873i \(0.382706\pi\)
\(240\) −1.47624 −0.0952909
\(241\) 8.44784 0.544173 0.272087 0.962273i \(-0.412286\pi\)
0.272087 + 0.962273i \(0.412286\pi\)
\(242\) 9.19098 0.590818
\(243\) −8.26378 −0.530122
\(244\) 1.33841 0.0856829
\(245\) −1.60474 −0.102523
\(246\) 11.4680 0.731171
\(247\) −14.0260 −0.892453
\(248\) −1.15541 −0.0733688
\(249\) 4.48896 0.284476
\(250\) −1.00000 −0.0632456
\(251\) −4.85336 −0.306342 −0.153171 0.988200i \(-0.548948\pi\)
−0.153171 + 0.988200i \(0.548948\pi\)
\(252\) 1.90633 0.120088
\(253\) −5.46472 −0.343564
\(254\) 8.13046 0.510151
\(255\) −5.78561 −0.362309
\(256\) 1.00000 0.0625000
\(257\) −14.3234 −0.893471 −0.446736 0.894666i \(-0.647414\pi\)
−0.446736 + 0.894666i \(0.647414\pi\)
\(258\) 8.49639 0.528962
\(259\) −1.52765 −0.0949238
\(260\) 3.18375 0.197448
\(261\) 7.35885 0.455501
\(262\) 13.4752 0.832501
\(263\) −22.5762 −1.39211 −0.696055 0.717988i \(-0.745063\pi\)
−0.696055 + 0.717988i \(0.745063\pi\)
\(264\) 1.98554 0.122202
\(265\) 14.3417 0.881002
\(266\) −10.2330 −0.627422
\(267\) 1.68895 0.103362
\(268\) −1.04497 −0.0638315
\(269\) −8.32706 −0.507710 −0.253855 0.967242i \(-0.581699\pi\)
−0.253855 + 0.967242i \(0.581699\pi\)
\(270\) −5.64029 −0.343257
\(271\) −7.35226 −0.446618 −0.223309 0.974748i \(-0.571686\pi\)
−0.223309 + 0.974748i \(0.571686\pi\)
\(272\) 3.91915 0.237633
\(273\) 10.9170 0.660726
\(274\) −9.92905 −0.599836
\(275\) 1.34500 0.0811065
\(276\) 5.99796 0.361035
\(277\) 10.8848 0.654007 0.327003 0.945023i \(-0.393961\pi\)
0.327003 + 0.945023i \(0.393961\pi\)
\(278\) −1.27837 −0.0766713
\(279\) −0.948264 −0.0567711
\(280\) 2.32277 0.138812
\(281\) −14.5030 −0.865177 −0.432589 0.901591i \(-0.642400\pi\)
−0.432589 + 0.901591i \(0.642400\pi\)
\(282\) −10.4928 −0.624840
\(283\) −6.97140 −0.414406 −0.207203 0.978298i \(-0.566436\pi\)
−0.207203 + 0.978298i \(0.566436\pi\)
\(284\) 3.41086 0.202397
\(285\) 6.50357 0.385238
\(286\) −4.28214 −0.253208
\(287\) −18.0441 −1.06511
\(288\) 0.820714 0.0483610
\(289\) −1.64025 −0.0964851
\(290\) 8.96640 0.526525
\(291\) −19.9057 −1.16689
\(292\) −7.58356 −0.443794
\(293\) 20.4970 1.19745 0.598725 0.800955i \(-0.295674\pi\)
0.598725 + 0.800955i \(0.295674\pi\)
\(294\) −2.36898 −0.138162
\(295\) −2.03120 −0.118261
\(296\) −0.657687 −0.0382273
\(297\) 7.58619 0.440195
\(298\) 0.681369 0.0394706
\(299\) −12.9356 −0.748083
\(300\) −1.47624 −0.0852308
\(301\) −13.3685 −0.770549
\(302\) −19.5237 −1.12346
\(303\) 21.0889 1.21153
\(304\) −4.40549 −0.252672
\(305\) 1.33841 0.0766371
\(306\) 3.21650 0.183875
\(307\) −16.0697 −0.917149 −0.458574 0.888656i \(-0.651640\pi\)
−0.458574 + 0.888656i \(0.651640\pi\)
\(308\) −3.12412 −0.178013
\(309\) 1.14524 0.0651503
\(310\) −1.15541 −0.0656231
\(311\) 1.53839 0.0872342 0.0436171 0.999048i \(-0.486112\pi\)
0.0436171 + 0.999048i \(0.486112\pi\)
\(312\) 4.69998 0.266084
\(313\) −22.2204 −1.25597 −0.627986 0.778224i \(-0.716121\pi\)
−0.627986 + 0.778224i \(0.716121\pi\)
\(314\) −2.19525 −0.123885
\(315\) 1.90633 0.107410
\(316\) −8.46523 −0.476206
\(317\) −27.5374 −1.54665 −0.773327 0.634007i \(-0.781409\pi\)
−0.773327 + 0.634007i \(0.781409\pi\)
\(318\) 21.1718 1.18725
\(319\) −12.0598 −0.675219
\(320\) 1.00000 0.0559017
\(321\) −12.3105 −0.687103
\(322\) −9.43740 −0.525926
\(323\) −17.2658 −0.960695
\(324\) −5.86429 −0.325794
\(325\) 3.18375 0.176603
\(326\) 11.2919 0.625399
\(327\) −13.4042 −0.741256
\(328\) −7.76836 −0.428936
\(329\) 16.5098 0.910216
\(330\) 1.98554 0.109300
\(331\) −21.3607 −1.17409 −0.587045 0.809555i \(-0.699709\pi\)
−0.587045 + 0.809555i \(0.699709\pi\)
\(332\) −3.04080 −0.166886
\(333\) −0.539773 −0.0295794
\(334\) −4.27804 −0.234084
\(335\) −1.04497 −0.0570926
\(336\) 3.42897 0.187065
\(337\) 17.1788 0.935791 0.467895 0.883784i \(-0.345012\pi\)
0.467895 + 0.883784i \(0.345012\pi\)
\(338\) 2.86373 0.155766
\(339\) 9.89355 0.537344
\(340\) 3.91915 0.212546
\(341\) 1.55403 0.0841555
\(342\) −3.61565 −0.195512
\(343\) 19.9868 1.07919
\(344\) −5.75543 −0.310312
\(345\) 5.99796 0.322919
\(346\) −11.8805 −0.638698
\(347\) 4.60290 0.247097 0.123548 0.992339i \(-0.460573\pi\)
0.123548 + 0.992339i \(0.460573\pi\)
\(348\) 13.2366 0.709554
\(349\) 3.88184 0.207790 0.103895 0.994588i \(-0.466869\pi\)
0.103895 + 0.994588i \(0.466869\pi\)
\(350\) 2.32277 0.124157
\(351\) 17.9573 0.958489
\(352\) −1.34500 −0.0716887
\(353\) −25.3254 −1.34794 −0.673968 0.738761i \(-0.735411\pi\)
−0.673968 + 0.738761i \(0.735411\pi\)
\(354\) −2.99854 −0.159371
\(355\) 3.41086 0.181030
\(356\) −1.14409 −0.0606366
\(357\) 13.4386 0.711248
\(358\) 7.09205 0.374826
\(359\) 7.07677 0.373497 0.186749 0.982408i \(-0.440205\pi\)
0.186749 + 0.982408i \(0.440205\pi\)
\(360\) 0.820714 0.0432554
\(361\) 0.408385 0.0214940
\(362\) −0.861521 −0.0452805
\(363\) 13.5681 0.712140
\(364\) −7.39512 −0.387610
\(365\) −7.58356 −0.396942
\(366\) 1.97581 0.103277
\(367\) −26.2743 −1.37151 −0.685754 0.727833i \(-0.740527\pi\)
−0.685754 + 0.727833i \(0.740527\pi\)
\(368\) −4.06300 −0.211798
\(369\) −6.37561 −0.331901
\(370\) −0.657687 −0.0341915
\(371\) −33.3124 −1.72949
\(372\) −1.70567 −0.0884348
\(373\) 5.63212 0.291620 0.145810 0.989313i \(-0.453421\pi\)
0.145810 + 0.989313i \(0.453421\pi\)
\(374\) −5.27126 −0.272570
\(375\) −1.47624 −0.0762327
\(376\) 7.10781 0.366558
\(377\) −28.5468 −1.47023
\(378\) 13.1011 0.673848
\(379\) −26.3918 −1.35566 −0.677829 0.735220i \(-0.737079\pi\)
−0.677829 + 0.735220i \(0.737079\pi\)
\(380\) −4.40549 −0.225997
\(381\) 12.0025 0.614908
\(382\) 16.2924 0.833591
\(383\) −14.4963 −0.740729 −0.370364 0.928887i \(-0.620767\pi\)
−0.370364 + 0.928887i \(0.620767\pi\)
\(384\) 1.47624 0.0753341
\(385\) −3.12412 −0.159220
\(386\) 8.15952 0.415309
\(387\) −4.72356 −0.240112
\(388\) 13.4841 0.684549
\(389\) 10.9095 0.553133 0.276566 0.960995i \(-0.410803\pi\)
0.276566 + 0.960995i \(0.410803\pi\)
\(390\) 4.69998 0.237993
\(391\) −15.9235 −0.805286
\(392\) 1.60474 0.0810516
\(393\) 19.8926 1.00345
\(394\) −0.519778 −0.0261860
\(395\) −8.46523 −0.425932
\(396\) −1.10386 −0.0554710
\(397\) −10.1383 −0.508826 −0.254413 0.967096i \(-0.581882\pi\)
−0.254413 + 0.967096i \(0.581882\pi\)
\(398\) 26.9093 1.34884
\(399\) −15.1063 −0.756261
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −1.54262 −0.0769390
\(403\) 3.67855 0.183242
\(404\) −14.2856 −0.710733
\(405\) −5.86429 −0.291399
\(406\) −20.8269 −1.03362
\(407\) 0.884588 0.0438474
\(408\) 5.78561 0.286430
\(409\) −35.2694 −1.74396 −0.871980 0.489541i \(-0.837164\pi\)
−0.871980 + 0.489541i \(0.837164\pi\)
\(410\) −7.76836 −0.383652
\(411\) −14.6577 −0.723009
\(412\) −0.775780 −0.0382200
\(413\) 4.71801 0.232158
\(414\) −3.33456 −0.163885
\(415\) −3.04080 −0.149267
\(416\) −3.18375 −0.156096
\(417\) −1.88717 −0.0924153
\(418\) 5.92539 0.289820
\(419\) 14.0642 0.687081 0.343540 0.939138i \(-0.388374\pi\)
0.343540 + 0.939138i \(0.388374\pi\)
\(420\) 3.42897 0.167316
\(421\) −5.76802 −0.281116 −0.140558 0.990072i \(-0.544890\pi\)
−0.140558 + 0.990072i \(0.544890\pi\)
\(422\) 18.0183 0.877119
\(423\) 5.83348 0.283634
\(424\) −14.3417 −0.696494
\(425\) 3.91915 0.190107
\(426\) 5.03525 0.243958
\(427\) −3.10882 −0.150446
\(428\) 8.33906 0.403084
\(429\) −6.32147 −0.305203
\(430\) −5.75543 −0.277551
\(431\) −23.5594 −1.13482 −0.567408 0.823437i \(-0.692054\pi\)
−0.567408 + 0.823437i \(0.692054\pi\)
\(432\) 5.64029 0.271369
\(433\) −22.2265 −1.06814 −0.534069 0.845441i \(-0.679338\pi\)
−0.534069 + 0.845441i \(0.679338\pi\)
\(434\) 2.68376 0.128825
\(435\) 13.2366 0.634645
\(436\) 9.07998 0.434852
\(437\) 17.8995 0.856250
\(438\) −11.1952 −0.534926
\(439\) −26.5932 −1.26922 −0.634611 0.772832i \(-0.718840\pi\)
−0.634611 + 0.772832i \(0.718840\pi\)
\(440\) −1.34500 −0.0641203
\(441\) 1.31703 0.0627159
\(442\) −12.4776 −0.593499
\(443\) 38.3551 1.82231 0.911153 0.412069i \(-0.135194\pi\)
0.911153 + 0.412069i \(0.135194\pi\)
\(444\) −0.970904 −0.0460770
\(445\) −1.14409 −0.0542350
\(446\) −21.7185 −1.02840
\(447\) 1.00586 0.0475757
\(448\) −2.32277 −0.109741
\(449\) 3.33232 0.157262 0.0786309 0.996904i \(-0.474945\pi\)
0.0786309 + 0.996904i \(0.474945\pi\)
\(450\) 0.820714 0.0386888
\(451\) 10.4484 0.491998
\(452\) −6.70185 −0.315229
\(453\) −28.8217 −1.35416
\(454\) 9.53252 0.447383
\(455\) −7.39512 −0.346689
\(456\) −6.50357 −0.304558
\(457\) −24.6255 −1.15193 −0.575965 0.817474i \(-0.695374\pi\)
−0.575965 + 0.817474i \(0.695374\pi\)
\(458\) 10.7735 0.503414
\(459\) 22.1052 1.03178
\(460\) −4.06300 −0.189438
\(461\) −10.4502 −0.486713 −0.243356 0.969937i \(-0.578248\pi\)
−0.243356 + 0.969937i \(0.578248\pi\)
\(462\) −4.61196 −0.214568
\(463\) −13.0520 −0.606577 −0.303288 0.952899i \(-0.598085\pi\)
−0.303288 + 0.952899i \(0.598085\pi\)
\(464\) −8.96640 −0.416255
\(465\) −1.70567 −0.0790985
\(466\) 9.78815 0.453427
\(467\) 11.2065 0.518574 0.259287 0.965800i \(-0.416512\pi\)
0.259287 + 0.965800i \(0.416512\pi\)
\(468\) −2.61295 −0.120784
\(469\) 2.42722 0.112078
\(470\) 7.10781 0.327859
\(471\) −3.24071 −0.149324
\(472\) 2.03120 0.0934936
\(473\) 7.74104 0.355933
\(474\) −12.4967 −0.573993
\(475\) −4.40549 −0.202138
\(476\) −9.10329 −0.417249
\(477\) −11.7704 −0.538931
\(478\) −11.1373 −0.509408
\(479\) −3.08020 −0.140738 −0.0703691 0.997521i \(-0.522418\pi\)
−0.0703691 + 0.997521i \(0.522418\pi\)
\(480\) 1.47624 0.0673808
\(481\) 2.09391 0.0954741
\(482\) −8.44784 −0.384789
\(483\) −13.9319 −0.633922
\(484\) −9.19098 −0.417772
\(485\) 13.4841 0.612280
\(486\) 8.26378 0.374853
\(487\) −6.57151 −0.297784 −0.148892 0.988853i \(-0.547571\pi\)
−0.148892 + 0.988853i \(0.547571\pi\)
\(488\) −1.33841 −0.0605869
\(489\) 16.6695 0.753822
\(490\) 1.60474 0.0724948
\(491\) 21.6738 0.978126 0.489063 0.872248i \(-0.337339\pi\)
0.489063 + 0.872248i \(0.337339\pi\)
\(492\) −11.4680 −0.517016
\(493\) −35.1407 −1.58266
\(494\) 14.0260 0.631060
\(495\) −1.10386 −0.0496148
\(496\) 1.15541 0.0518796
\(497\) −7.92264 −0.355379
\(498\) −4.48896 −0.201155
\(499\) 6.40991 0.286947 0.143473 0.989654i \(-0.454173\pi\)
0.143473 + 0.989654i \(0.454173\pi\)
\(500\) 1.00000 0.0447214
\(501\) −6.31541 −0.282152
\(502\) 4.85336 0.216616
\(503\) 8.99634 0.401127 0.200564 0.979681i \(-0.435723\pi\)
0.200564 + 0.979681i \(0.435723\pi\)
\(504\) −1.90633 −0.0849147
\(505\) −14.2856 −0.635699
\(506\) 5.46472 0.242937
\(507\) 4.22755 0.187752
\(508\) −8.13046 −0.360731
\(509\) 14.3619 0.636582 0.318291 0.947993i \(-0.396891\pi\)
0.318291 + 0.947993i \(0.396891\pi\)
\(510\) 5.78561 0.256191
\(511\) 17.6149 0.779236
\(512\) −1.00000 −0.0441942
\(513\) −24.8483 −1.09708
\(514\) 14.3234 0.631780
\(515\) −0.775780 −0.0341850
\(516\) −8.49639 −0.374033
\(517\) −9.56000 −0.420448
\(518\) 1.52765 0.0671213
\(519\) −17.5384 −0.769852
\(520\) −3.18375 −0.139617
\(521\) 1.51348 0.0663069 0.0331534 0.999450i \(-0.489445\pi\)
0.0331534 + 0.999450i \(0.489445\pi\)
\(522\) −7.35885 −0.322088
\(523\) −39.3370 −1.72009 −0.860043 0.510222i \(-0.829563\pi\)
−0.860043 + 0.510222i \(0.829563\pi\)
\(524\) −13.4752 −0.588667
\(525\) 3.42897 0.149652
\(526\) 22.5762 0.984370
\(527\) 4.52824 0.197253
\(528\) −1.98554 −0.0864096
\(529\) −6.49207 −0.282264
\(530\) −14.3417 −0.622963
\(531\) 1.66704 0.0723432
\(532\) 10.2330 0.443655
\(533\) 24.7325 1.07129
\(534\) −1.68895 −0.0730881
\(535\) 8.33906 0.360529
\(536\) 1.04497 0.0451357
\(537\) 10.4696 0.451795
\(538\) 8.32706 0.359005
\(539\) −2.15837 −0.0929677
\(540\) 5.64029 0.242720
\(541\) −11.7550 −0.505386 −0.252693 0.967547i \(-0.581316\pi\)
−0.252693 + 0.967547i \(0.581316\pi\)
\(542\) 7.35226 0.315807
\(543\) −1.27181 −0.0545787
\(544\) −3.91915 −0.168032
\(545\) 9.07998 0.388944
\(546\) −10.9170 −0.467203
\(547\) −30.7898 −1.31648 −0.658239 0.752809i \(-0.728698\pi\)
−0.658239 + 0.752809i \(0.728698\pi\)
\(548\) 9.92905 0.424148
\(549\) −1.09845 −0.0468808
\(550\) −1.34500 −0.0573509
\(551\) 39.5014 1.68282
\(552\) −5.99796 −0.255290
\(553\) 19.6628 0.836146
\(554\) −10.8848 −0.462453
\(555\) −0.970904 −0.0412126
\(556\) 1.27837 0.0542148
\(557\) −8.73904 −0.370285 −0.185143 0.982712i \(-0.559275\pi\)
−0.185143 + 0.982712i \(0.559275\pi\)
\(558\) 0.948264 0.0401432
\(559\) 18.3238 0.775016
\(560\) −2.32277 −0.0981549
\(561\) −7.78164 −0.328541
\(562\) 14.5030 0.611773
\(563\) 25.5868 1.07836 0.539178 0.842192i \(-0.318735\pi\)
0.539178 + 0.842192i \(0.318735\pi\)
\(564\) 10.4928 0.441828
\(565\) −6.70185 −0.281949
\(566\) 6.97140 0.293030
\(567\) 13.6214 0.572044
\(568\) −3.41086 −0.143116
\(569\) 31.8055 1.33335 0.666677 0.745346i \(-0.267716\pi\)
0.666677 + 0.745346i \(0.267716\pi\)
\(570\) −6.50357 −0.272405
\(571\) 5.58253 0.233622 0.116811 0.993154i \(-0.462733\pi\)
0.116811 + 0.993154i \(0.462733\pi\)
\(572\) 4.28214 0.179045
\(573\) 24.0515 1.00476
\(574\) 18.0441 0.753147
\(575\) −4.06300 −0.169439
\(576\) −0.820714 −0.0341964
\(577\) −8.62270 −0.358968 −0.179484 0.983761i \(-0.557443\pi\)
−0.179484 + 0.983761i \(0.557443\pi\)
\(578\) 1.64025 0.0682253
\(579\) 12.0454 0.500590
\(580\) −8.96640 −0.372309
\(581\) 7.06309 0.293026
\(582\) 19.9057 0.825118
\(583\) 19.2895 0.798891
\(584\) 7.58356 0.313810
\(585\) −2.61295 −0.108032
\(586\) −20.4970 −0.846725
\(587\) −9.41965 −0.388790 −0.194395 0.980923i \(-0.562274\pi\)
−0.194395 + 0.980923i \(0.562274\pi\)
\(588\) 2.36898 0.0976952
\(589\) −5.09017 −0.209737
\(590\) 2.03120 0.0836232
\(591\) −0.767317 −0.0315632
\(592\) 0.657687 0.0270308
\(593\) 6.14848 0.252488 0.126244 0.991999i \(-0.459708\pi\)
0.126244 + 0.991999i \(0.459708\pi\)
\(594\) −7.58619 −0.311265
\(595\) −9.10329 −0.373198
\(596\) −0.681369 −0.0279100
\(597\) 39.7246 1.62582
\(598\) 12.9356 0.528975
\(599\) −13.8997 −0.567928 −0.283964 0.958835i \(-0.591650\pi\)
−0.283964 + 0.958835i \(0.591650\pi\)
\(600\) 1.47624 0.0602673
\(601\) 29.2093 1.19147 0.595735 0.803181i \(-0.296861\pi\)
0.595735 + 0.803181i \(0.296861\pi\)
\(602\) 13.3685 0.544861
\(603\) 0.857619 0.0349249
\(604\) 19.5237 0.794408
\(605\) −9.19098 −0.373666
\(606\) −21.0889 −0.856679
\(607\) 7.88674 0.320113 0.160056 0.987108i \(-0.448832\pi\)
0.160056 + 0.987108i \(0.448832\pi\)
\(608\) 4.40549 0.178666
\(609\) −30.7455 −1.24587
\(610\) −1.33841 −0.0541906
\(611\) −22.6295 −0.915492
\(612\) −3.21650 −0.130019
\(613\) −21.1977 −0.856167 −0.428084 0.903739i \(-0.640811\pi\)
−0.428084 + 0.903739i \(0.640811\pi\)
\(614\) 16.0697 0.648522
\(615\) −11.4680 −0.462433
\(616\) 3.12412 0.125874
\(617\) 7.45682 0.300200 0.150100 0.988671i \(-0.452040\pi\)
0.150100 + 0.988671i \(0.452040\pi\)
\(618\) −1.14524 −0.0460682
\(619\) −26.1113 −1.04950 −0.524751 0.851256i \(-0.675842\pi\)
−0.524751 + 0.851256i \(0.675842\pi\)
\(620\) 1.15541 0.0464025
\(621\) −22.9165 −0.919607
\(622\) −1.53839 −0.0616839
\(623\) 2.65746 0.106469
\(624\) −4.69998 −0.188150
\(625\) 1.00000 0.0400000
\(626\) 22.2204 0.888107
\(627\) 8.74729 0.349333
\(628\) 2.19525 0.0875999
\(629\) 2.57757 0.102775
\(630\) −1.90633 −0.0759500
\(631\) 48.9494 1.94865 0.974323 0.225156i \(-0.0722891\pi\)
0.974323 + 0.225156i \(0.0722891\pi\)
\(632\) 8.46523 0.336729
\(633\) 26.5994 1.05723
\(634\) 27.5374 1.09365
\(635\) −8.13046 −0.322648
\(636\) −21.1718 −0.839515
\(637\) −5.10909 −0.202430
\(638\) 12.0598 0.477452
\(639\) −2.79934 −0.110740
\(640\) −1.00000 −0.0395285
\(641\) 40.1041 1.58402 0.792009 0.610509i \(-0.209035\pi\)
0.792009 + 0.610509i \(0.209035\pi\)
\(642\) 12.3105 0.485855
\(643\) 5.29357 0.208758 0.104379 0.994538i \(-0.466715\pi\)
0.104379 + 0.994538i \(0.466715\pi\)
\(644\) 9.43740 0.371886
\(645\) −8.49639 −0.334545
\(646\) 17.2658 0.679314
\(647\) 7.86240 0.309103 0.154551 0.987985i \(-0.450607\pi\)
0.154551 + 0.987985i \(0.450607\pi\)
\(648\) 5.86429 0.230371
\(649\) −2.73196 −0.107239
\(650\) −3.18375 −0.124877
\(651\) 3.96188 0.155278
\(652\) −11.2919 −0.442224
\(653\) −0.370814 −0.0145111 −0.00725554 0.999974i \(-0.502310\pi\)
−0.00725554 + 0.999974i \(0.502310\pi\)
\(654\) 13.4042 0.524147
\(655\) −13.4752 −0.526520
\(656\) 7.76836 0.303304
\(657\) 6.22394 0.242819
\(658\) −16.5098 −0.643620
\(659\) 10.7571 0.419038 0.209519 0.977805i \(-0.432810\pi\)
0.209519 + 0.977805i \(0.432810\pi\)
\(660\) −1.98554 −0.0772871
\(661\) 17.7361 0.689855 0.344927 0.938629i \(-0.387904\pi\)
0.344927 + 0.938629i \(0.387904\pi\)
\(662\) 21.3607 0.830206
\(663\) −18.4199 −0.715371
\(664\) 3.04080 0.118006
\(665\) 10.2330 0.396817
\(666\) 0.539773 0.0209158
\(667\) 36.4304 1.41059
\(668\) 4.27804 0.165522
\(669\) −32.0617 −1.23958
\(670\) 1.04497 0.0403706
\(671\) 1.80016 0.0694944
\(672\) −3.42897 −0.132275
\(673\) −11.0896 −0.427472 −0.213736 0.976891i \(-0.568563\pi\)
−0.213736 + 0.976891i \(0.568563\pi\)
\(674\) −17.1788 −0.661704
\(675\) 5.64029 0.217095
\(676\) −2.86373 −0.110143
\(677\) −11.1620 −0.428990 −0.214495 0.976725i \(-0.568811\pi\)
−0.214495 + 0.976725i \(0.568811\pi\)
\(678\) −9.89355 −0.379959
\(679\) −31.3204 −1.20197
\(680\) −3.91915 −0.150293
\(681\) 14.0723 0.539251
\(682\) −1.55403 −0.0595069
\(683\) 42.1623 1.61330 0.806648 0.591032i \(-0.201279\pi\)
0.806648 + 0.591032i \(0.201279\pi\)
\(684\) 3.61565 0.138248
\(685\) 9.92905 0.379369
\(686\) −19.9868 −0.763101
\(687\) 15.9043 0.606787
\(688\) 5.75543 0.219424
\(689\) 45.6603 1.73952
\(690\) −5.99796 −0.228338
\(691\) 21.7076 0.825796 0.412898 0.910777i \(-0.364517\pi\)
0.412898 + 0.910777i \(0.364517\pi\)
\(692\) 11.8805 0.451628
\(693\) 2.56401 0.0973988
\(694\) −4.60290 −0.174724
\(695\) 1.27837 0.0484912
\(696\) −13.2366 −0.501731
\(697\) 30.4454 1.15320
\(698\) −3.88184 −0.146930
\(699\) 14.4497 0.546537
\(700\) −2.32277 −0.0877924
\(701\) 20.7094 0.782184 0.391092 0.920352i \(-0.372097\pi\)
0.391092 + 0.920352i \(0.372097\pi\)
\(702\) −17.9573 −0.677754
\(703\) −2.89743 −0.109279
\(704\) 1.34500 0.0506916
\(705\) 10.4928 0.395183
\(706\) 25.3254 0.953135
\(707\) 33.1821 1.24794
\(708\) 2.99854 0.112692
\(709\) −36.9626 −1.38816 −0.694081 0.719897i \(-0.744189\pi\)
−0.694081 + 0.719897i \(0.744189\pi\)
\(710\) −3.41086 −0.128007
\(711\) 6.94753 0.260553
\(712\) 1.14409 0.0428766
\(713\) −4.69444 −0.175808
\(714\) −13.4386 −0.502929
\(715\) 4.28214 0.160143
\(716\) −7.09205 −0.265042
\(717\) −16.4413 −0.614013
\(718\) −7.07677 −0.264103
\(719\) −9.63101 −0.359176 −0.179588 0.983742i \(-0.557476\pi\)
−0.179588 + 0.983742i \(0.557476\pi\)
\(720\) −0.820714 −0.0305862
\(721\) 1.80196 0.0671085
\(722\) −0.408385 −0.0151985
\(723\) −12.4710 −0.463803
\(724\) 0.861521 0.0320182
\(725\) −8.96640 −0.333004
\(726\) −13.5681 −0.503559
\(727\) −5.92699 −0.219820 −0.109910 0.993942i \(-0.535056\pi\)
−0.109910 + 0.993942i \(0.535056\pi\)
\(728\) 7.39512 0.274081
\(729\) 29.7922 1.10341
\(730\) 7.58356 0.280680
\(731\) 22.5564 0.834278
\(732\) −1.97581 −0.0730282
\(733\) 0.775978 0.0286614 0.0143307 0.999897i \(-0.495438\pi\)
0.0143307 + 0.999897i \(0.495438\pi\)
\(734\) 26.2743 0.969803
\(735\) 2.36898 0.0873812
\(736\) 4.06300 0.149764
\(737\) −1.40548 −0.0517715
\(738\) 6.37561 0.234689
\(739\) −48.5768 −1.78693 −0.893463 0.449137i \(-0.851732\pi\)
−0.893463 + 0.449137i \(0.851732\pi\)
\(740\) 0.657687 0.0241770
\(741\) 20.7057 0.760645
\(742\) 33.3124 1.22294
\(743\) 6.88535 0.252599 0.126299 0.991992i \(-0.459690\pi\)
0.126299 + 0.991992i \(0.459690\pi\)
\(744\) 1.70567 0.0625328
\(745\) −0.681369 −0.0249634
\(746\) −5.63212 −0.206207
\(747\) 2.49563 0.0913104
\(748\) 5.27126 0.192736
\(749\) −19.3697 −0.707754
\(750\) 1.47624 0.0539047
\(751\) 7.52640 0.274642 0.137321 0.990527i \(-0.456151\pi\)
0.137321 + 0.990527i \(0.456151\pi\)
\(752\) −7.10781 −0.259195
\(753\) 7.16473 0.261097
\(754\) 28.5468 1.03961
\(755\) 19.5237 0.710540
\(756\) −13.1011 −0.476482
\(757\) 32.9357 1.19707 0.598535 0.801097i \(-0.295750\pi\)
0.598535 + 0.801097i \(0.295750\pi\)
\(758\) 26.3918 0.958594
\(759\) 8.06725 0.292823
\(760\) 4.40549 0.159804
\(761\) 16.1450 0.585258 0.292629 0.956226i \(-0.405470\pi\)
0.292629 + 0.956226i \(0.405470\pi\)
\(762\) −12.0025 −0.434805
\(763\) −21.0907 −0.763535
\(764\) −16.2924 −0.589438
\(765\) −3.21650 −0.116293
\(766\) 14.4963 0.523774
\(767\) −6.46684 −0.233504
\(768\) −1.47624 −0.0532692
\(769\) −32.9580 −1.18850 −0.594249 0.804281i \(-0.702551\pi\)
−0.594249 + 0.804281i \(0.702551\pi\)
\(770\) 3.12412 0.112586
\(771\) 21.1448 0.761513
\(772\) −8.15952 −0.293668
\(773\) −2.86137 −0.102916 −0.0514582 0.998675i \(-0.516387\pi\)
−0.0514582 + 0.998675i \(0.516387\pi\)
\(774\) 4.72356 0.169785
\(775\) 1.15541 0.0415037
\(776\) −13.4841 −0.484050
\(777\) 2.25519 0.0809043
\(778\) −10.9095 −0.391124
\(779\) −34.2235 −1.22618
\(780\) −4.69998 −0.168286
\(781\) 4.58760 0.164157
\(782\) 15.9235 0.569423
\(783\) −50.5731 −1.80734
\(784\) −1.60474 −0.0573121
\(785\) 2.19525 0.0783518
\(786\) −19.8926 −0.709547
\(787\) 9.82801 0.350331 0.175165 0.984539i \(-0.443954\pi\)
0.175165 + 0.984539i \(0.443954\pi\)
\(788\) 0.519778 0.0185163
\(789\) 33.3279 1.18651
\(790\) 8.46523 0.301179
\(791\) 15.5669 0.553494
\(792\) 1.10386 0.0392239
\(793\) 4.26116 0.151318
\(794\) 10.1383 0.359794
\(795\) −21.1718 −0.750885
\(796\) −26.9093 −0.953775
\(797\) −7.07485 −0.250604 −0.125302 0.992119i \(-0.539990\pi\)
−0.125302 + 0.992119i \(0.539990\pi\)
\(798\) 15.1063 0.534757
\(799\) −27.8566 −0.985496
\(800\) −1.00000 −0.0353553
\(801\) 0.938970 0.0331769
\(802\) −1.00000 −0.0353112
\(803\) −10.1999 −0.359946
\(804\) 1.54262 0.0544041
\(805\) 9.43740 0.332625
\(806\) −3.67855 −0.129571
\(807\) 12.2927 0.432725
\(808\) 14.2856 0.502564
\(809\) 38.0755 1.33866 0.669331 0.742965i \(-0.266581\pi\)
0.669331 + 0.742965i \(0.266581\pi\)
\(810\) 5.86429 0.206050
\(811\) −8.49597 −0.298334 −0.149167 0.988812i \(-0.547659\pi\)
−0.149167 + 0.988812i \(0.547659\pi\)
\(812\) 20.8269 0.730880
\(813\) 10.8537 0.380656
\(814\) −0.884588 −0.0310048
\(815\) −11.2919 −0.395537
\(816\) −5.78561 −0.202537
\(817\) −25.3555 −0.887077
\(818\) 35.2694 1.23317
\(819\) 6.06928 0.212078
\(820\) 7.76836 0.271283
\(821\) 38.7707 1.35311 0.676553 0.736394i \(-0.263473\pi\)
0.676553 + 0.736394i \(0.263473\pi\)
\(822\) 14.6577 0.511245
\(823\) 36.3890 1.26844 0.634220 0.773153i \(-0.281321\pi\)
0.634220 + 0.773153i \(0.281321\pi\)
\(824\) 0.775780 0.0270256
\(825\) −1.98554 −0.0691277
\(826\) −4.71801 −0.164161
\(827\) 10.3868 0.361184 0.180592 0.983558i \(-0.442199\pi\)
0.180592 + 0.983558i \(0.442199\pi\)
\(828\) 3.33456 0.115884
\(829\) 55.8712 1.94049 0.970244 0.242129i \(-0.0778458\pi\)
0.970244 + 0.242129i \(0.0778458\pi\)
\(830\) 3.04080 0.105548
\(831\) −16.0686 −0.557415
\(832\) 3.18375 0.110377
\(833\) −6.28922 −0.217909
\(834\) 1.88717 0.0653475
\(835\) 4.27804 0.148048
\(836\) −5.92539 −0.204934
\(837\) 6.51687 0.225256
\(838\) −14.0642 −0.485840
\(839\) −31.2402 −1.07853 −0.539266 0.842136i \(-0.681298\pi\)
−0.539266 + 0.842136i \(0.681298\pi\)
\(840\) −3.42897 −0.118311
\(841\) 51.3963 1.77229
\(842\) 5.76802 0.198779
\(843\) 21.4099 0.737397
\(844\) −18.0183 −0.620217
\(845\) −2.86373 −0.0985152
\(846\) −5.83348 −0.200559
\(847\) 21.3485 0.733544
\(848\) 14.3417 0.492495
\(849\) 10.2915 0.353202
\(850\) −3.91915 −0.134426
\(851\) −2.67218 −0.0916011
\(852\) −5.03525 −0.172505
\(853\) 23.4882 0.804222 0.402111 0.915591i \(-0.368277\pi\)
0.402111 + 0.915591i \(0.368277\pi\)
\(854\) 3.10882 0.106381
\(855\) 3.61565 0.123653
\(856\) −8.33906 −0.285023
\(857\) −48.2529 −1.64829 −0.824143 0.566382i \(-0.808343\pi\)
−0.824143 + 0.566382i \(0.808343\pi\)
\(858\) 6.32147 0.215811
\(859\) −39.4759 −1.34690 −0.673450 0.739232i \(-0.735188\pi\)
−0.673450 + 0.739232i \(0.735188\pi\)
\(860\) 5.75543 0.196258
\(861\) 26.6375 0.907802
\(862\) 23.5594 0.802436
\(863\) 9.61873 0.327425 0.163713 0.986508i \(-0.447653\pi\)
0.163713 + 0.986508i \(0.447653\pi\)
\(864\) −5.64029 −0.191887
\(865\) 11.8805 0.403948
\(866\) 22.2265 0.755287
\(867\) 2.42140 0.0822350
\(868\) −2.68376 −0.0910928
\(869\) −11.3857 −0.386234
\(870\) −13.2366 −0.448761
\(871\) −3.32691 −0.112728
\(872\) −9.07998 −0.307487
\(873\) −11.0666 −0.374546
\(874\) −17.8995 −0.605460
\(875\) −2.32277 −0.0785240
\(876\) 11.1952 0.378249
\(877\) 41.0508 1.38619 0.693093 0.720848i \(-0.256247\pi\)
0.693093 + 0.720848i \(0.256247\pi\)
\(878\) 26.5932 0.897476
\(879\) −30.2586 −1.02060
\(880\) 1.34500 0.0453399
\(881\) 21.6318 0.728792 0.364396 0.931244i \(-0.381275\pi\)
0.364396 + 0.931244i \(0.381275\pi\)
\(882\) −1.31703 −0.0443468
\(883\) −35.7699 −1.20375 −0.601876 0.798589i \(-0.705580\pi\)
−0.601876 + 0.798589i \(0.705580\pi\)
\(884\) 12.4776 0.419667
\(885\) 2.99854 0.100795
\(886\) −38.3551 −1.28856
\(887\) −13.2697 −0.445554 −0.222777 0.974869i \(-0.571512\pi\)
−0.222777 + 0.974869i \(0.571512\pi\)
\(888\) 0.970904 0.0325814
\(889\) 18.8852 0.633389
\(890\) 1.14409 0.0383500
\(891\) −7.88746 −0.264240
\(892\) 21.7185 0.727188
\(893\) 31.3134 1.04786
\(894\) −1.00586 −0.0336411
\(895\) −7.09205 −0.237061
\(896\) 2.32277 0.0775983
\(897\) 19.0960 0.637597
\(898\) −3.33232 −0.111201
\(899\) −10.3599 −0.345522
\(900\) −0.820714 −0.0273571
\(901\) 56.2072 1.87253
\(902\) −10.4484 −0.347895
\(903\) 19.7352 0.656745
\(904\) 6.70185 0.222900
\(905\) 0.861521 0.0286379
\(906\) 28.8217 0.957535
\(907\) −16.5813 −0.550574 −0.275287 0.961362i \(-0.588773\pi\)
−0.275287 + 0.961362i \(0.588773\pi\)
\(908\) −9.53252 −0.316348
\(909\) 11.7244 0.388873
\(910\) 7.39512 0.245146
\(911\) −19.4322 −0.643819 −0.321909 0.946770i \(-0.604325\pi\)
−0.321909 + 0.946770i \(0.604325\pi\)
\(912\) 6.50357 0.215355
\(913\) −4.08988 −0.135355
\(914\) 24.6255 0.814538
\(915\) −1.97581 −0.0653184
\(916\) −10.7735 −0.355967
\(917\) 31.2998 1.03361
\(918\) −22.1052 −0.729579
\(919\) 24.2476 0.799853 0.399927 0.916547i \(-0.369036\pi\)
0.399927 + 0.916547i \(0.369036\pi\)
\(920\) 4.06300 0.133953
\(921\) 23.7228 0.781693
\(922\) 10.4502 0.344158
\(923\) 10.8593 0.357439
\(924\) 4.61196 0.151722
\(925\) 0.657687 0.0216246
\(926\) 13.0520 0.428914
\(927\) 0.636694 0.0209118
\(928\) 8.96640 0.294336
\(929\) 1.52858 0.0501511 0.0250756 0.999686i \(-0.492017\pi\)
0.0250756 + 0.999686i \(0.492017\pi\)
\(930\) 1.70567 0.0559311
\(931\) 7.06967 0.231699
\(932\) −9.78815 −0.320622
\(933\) −2.27104 −0.0743504
\(934\) −11.2065 −0.366687
\(935\) 5.27126 0.172388
\(936\) 2.61295 0.0854069
\(937\) −30.9500 −1.01109 −0.505546 0.862800i \(-0.668709\pi\)
−0.505546 + 0.862800i \(0.668709\pi\)
\(938\) −2.42722 −0.0792514
\(939\) 32.8027 1.07048
\(940\) −7.10781 −0.231831
\(941\) −14.9037 −0.485848 −0.242924 0.970045i \(-0.578107\pi\)
−0.242924 + 0.970045i \(0.578107\pi\)
\(942\) 3.24071 0.105588
\(943\) −31.5628 −1.02783
\(944\) −2.03120 −0.0661100
\(945\) −13.1011 −0.426179
\(946\) −7.74104 −0.251683
\(947\) 28.5094 0.926431 0.463215 0.886246i \(-0.346696\pi\)
0.463215 + 0.886246i \(0.346696\pi\)
\(948\) 12.4967 0.405874
\(949\) −24.1442 −0.783753
\(950\) 4.40549 0.142933
\(951\) 40.6518 1.31823
\(952\) 9.10329 0.295039
\(953\) 23.1394 0.749559 0.374780 0.927114i \(-0.377718\pi\)
0.374780 + 0.927114i \(0.377718\pi\)
\(954\) 11.7704 0.381081
\(955\) −16.2924 −0.527209
\(956\) 11.1373 0.360206
\(957\) 17.8032 0.575494
\(958\) 3.08020 0.0995169
\(959\) −23.0629 −0.744740
\(960\) −1.47624 −0.0476455
\(961\) −29.6650 −0.956936
\(962\) −2.09391 −0.0675104
\(963\) −6.84399 −0.220544
\(964\) 8.44784 0.272087
\(965\) −8.15952 −0.262664
\(966\) 13.9319 0.448251
\(967\) −2.69699 −0.0867294 −0.0433647 0.999059i \(-0.513808\pi\)
−0.0433647 + 0.999059i \(0.513808\pi\)
\(968\) 9.19098 0.295409
\(969\) 25.4885 0.818808
\(970\) −13.4841 −0.432947
\(971\) 16.8068 0.539356 0.269678 0.962951i \(-0.413083\pi\)
0.269678 + 0.962951i \(0.413083\pi\)
\(972\) −8.26378 −0.265061
\(973\) −2.96935 −0.0951929
\(974\) 6.57151 0.210565
\(975\) −4.69998 −0.150520
\(976\) 1.33841 0.0428414
\(977\) 33.4094 1.06886 0.534431 0.845212i \(-0.320526\pi\)
0.534431 + 0.845212i \(0.320526\pi\)
\(978\) −16.6695 −0.533032
\(979\) −1.53880 −0.0491802
\(980\) −1.60474 −0.0512615
\(981\) −7.45207 −0.237926
\(982\) −21.6738 −0.691640
\(983\) −46.7735 −1.49184 −0.745921 0.666034i \(-0.767990\pi\)
−0.745921 + 0.666034i \(0.767990\pi\)
\(984\) 11.4680 0.365586
\(985\) 0.519778 0.0165615
\(986\) 35.1407 1.11911
\(987\) −24.3725 −0.775784
\(988\) −14.0260 −0.446226
\(989\) −23.3843 −0.743577
\(990\) 1.10386 0.0350830
\(991\) −10.3315 −0.328191 −0.164095 0.986444i \(-0.552470\pi\)
−0.164095 + 0.986444i \(0.552470\pi\)
\(992\) −1.15541 −0.0366844
\(993\) 31.5335 1.00069
\(994\) 7.92264 0.251291
\(995\) −26.9093 −0.853082
\(996\) 4.48896 0.142238
\(997\) −28.6650 −0.907829 −0.453915 0.891045i \(-0.649973\pi\)
−0.453915 + 0.891045i \(0.649973\pi\)
\(998\) −6.40991 −0.202902
\(999\) 3.70954 0.117365
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 4010.2.a.i.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.4 10 1.1 even 1 trivial