Properties

Label 4010.2.a.i.1.2
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 1.2
Root \(1.47143\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.70072 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70072 q^{6} -1.21166 q^{7} -1.00000 q^{8} +4.29386 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.70072 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70072 q^{6} -1.21166 q^{7} -1.00000 q^{8} +4.29386 q^{9} -1.00000 q^{10} -5.34303 q^{11} -2.70072 q^{12} +4.99519 q^{13} +1.21166 q^{14} -2.70072 q^{15} +1.00000 q^{16} +1.52346 q^{17} -4.29386 q^{18} -5.54062 q^{19} +1.00000 q^{20} +3.27234 q^{21} +5.34303 q^{22} -2.17276 q^{23} +2.70072 q^{24} +1.00000 q^{25} -4.99519 q^{26} -3.49436 q^{27} -1.21166 q^{28} +5.67740 q^{29} +2.70072 q^{30} +7.09841 q^{31} -1.00000 q^{32} +14.4300 q^{33} -1.52346 q^{34} -1.21166 q^{35} +4.29386 q^{36} +1.20281 q^{37} +5.54062 q^{38} -13.4906 q^{39} -1.00000 q^{40} -10.3503 q^{41} -3.27234 q^{42} -12.2971 q^{43} -5.34303 q^{44} +4.29386 q^{45} +2.17276 q^{46} +12.4866 q^{47} -2.70072 q^{48} -5.53188 q^{49} -1.00000 q^{50} -4.11443 q^{51} +4.99519 q^{52} +10.8717 q^{53} +3.49436 q^{54} -5.34303 q^{55} +1.21166 q^{56} +14.9636 q^{57} -5.67740 q^{58} +3.79149 q^{59} -2.70072 q^{60} -6.62515 q^{61} -7.09841 q^{62} -5.20270 q^{63} +1.00000 q^{64} +4.99519 q^{65} -14.4300 q^{66} -7.49485 q^{67} +1.52346 q^{68} +5.86800 q^{69} +1.21166 q^{70} -0.842329 q^{71} -4.29386 q^{72} +8.60525 q^{73} -1.20281 q^{74} -2.70072 q^{75} -5.54062 q^{76} +6.47392 q^{77} +13.4906 q^{78} +4.99850 q^{79} +1.00000 q^{80} -3.44432 q^{81} +10.3503 q^{82} -1.39402 q^{83} +3.27234 q^{84} +1.52346 q^{85} +12.2971 q^{86} -15.3330 q^{87} +5.34303 q^{88} +1.31290 q^{89} -4.29386 q^{90} -6.05247 q^{91} -2.17276 q^{92} -19.1708 q^{93} -12.4866 q^{94} -5.54062 q^{95} +2.70072 q^{96} -9.84430 q^{97} +5.53188 q^{98} -22.9422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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
\(3\) −2.70072 −1.55926 −0.779629 0.626241i \(-0.784593\pi\)
−0.779629 + 0.626241i \(0.784593\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 2.70072 1.10256
\(7\) −1.21166 −0.457964 −0.228982 0.973431i \(-0.573540\pi\)
−0.228982 + 0.973431i \(0.573540\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.29386 1.43129
\(10\) −1.00000 −0.316228
\(11\) −5.34303 −1.61098 −0.805492 0.592607i \(-0.798099\pi\)
−0.805492 + 0.592607i \(0.798099\pi\)
\(12\) −2.70072 −0.779629
\(13\) 4.99519 1.38542 0.692709 0.721218i \(-0.256417\pi\)
0.692709 + 0.721218i \(0.256417\pi\)
\(14\) 1.21166 0.323829
\(15\) −2.70072 −0.697322
\(16\) 1.00000 0.250000
\(17\) 1.52346 0.369493 0.184746 0.982786i \(-0.440854\pi\)
0.184746 + 0.982786i \(0.440854\pi\)
\(18\) −4.29386 −1.01207
\(19\) −5.54062 −1.27111 −0.635553 0.772057i \(-0.719228\pi\)
−0.635553 + 0.772057i \(0.719228\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.27234 0.714084
\(22\) 5.34303 1.13914
\(23\) −2.17276 −0.453051 −0.226526 0.974005i \(-0.572737\pi\)
−0.226526 + 0.974005i \(0.572737\pi\)
\(24\) 2.70072 0.551281
\(25\) 1.00000 0.200000
\(26\) −4.99519 −0.979638
\(27\) −3.49436 −0.672490
\(28\) −1.21166 −0.228982
\(29\) 5.67740 1.05427 0.527133 0.849783i \(-0.323267\pi\)
0.527133 + 0.849783i \(0.323267\pi\)
\(30\) 2.70072 0.493081
\(31\) 7.09841 1.27491 0.637456 0.770487i \(-0.279987\pi\)
0.637456 + 0.770487i \(0.279987\pi\)
\(32\) −1.00000 −0.176777
\(33\) 14.4300 2.51194
\(34\) −1.52346 −0.261271
\(35\) −1.21166 −0.204808
\(36\) 4.29386 0.715644
\(37\) 1.20281 0.197740 0.0988701 0.995100i \(-0.468477\pi\)
0.0988701 + 0.995100i \(0.468477\pi\)
\(38\) 5.54062 0.898807
\(39\) −13.4906 −2.16022
\(40\) −1.00000 −0.158114
\(41\) −10.3503 −1.61644 −0.808220 0.588880i \(-0.799569\pi\)
−0.808220 + 0.588880i \(0.799569\pi\)
\(42\) −3.27234 −0.504934
\(43\) −12.2971 −1.87530 −0.937649 0.347585i \(-0.887002\pi\)
−0.937649 + 0.347585i \(0.887002\pi\)
\(44\) −5.34303 −0.805492
\(45\) 4.29386 0.640091
\(46\) 2.17276 0.320356
\(47\) 12.4866 1.82136 0.910682 0.413108i \(-0.135557\pi\)
0.910682 + 0.413108i \(0.135557\pi\)
\(48\) −2.70072 −0.389815
\(49\) −5.53188 −0.790269
\(50\) −1.00000 −0.141421
\(51\) −4.11443 −0.576135
\(52\) 4.99519 0.692709
\(53\) 10.8717 1.49334 0.746668 0.665197i \(-0.231652\pi\)
0.746668 + 0.665197i \(0.231652\pi\)
\(54\) 3.49436 0.475522
\(55\) −5.34303 −0.720454
\(56\) 1.21166 0.161915
\(57\) 14.9636 1.98198
\(58\) −5.67740 −0.745479
\(59\) 3.79149 0.493611 0.246805 0.969065i \(-0.420619\pi\)
0.246805 + 0.969065i \(0.420619\pi\)
\(60\) −2.70072 −0.348661
\(61\) −6.62515 −0.848263 −0.424132 0.905601i \(-0.639421\pi\)
−0.424132 + 0.905601i \(0.639421\pi\)
\(62\) −7.09841 −0.901499
\(63\) −5.20270 −0.655478
\(64\) 1.00000 0.125000
\(65\) 4.99519 0.619577
\(66\) −14.4300 −1.77621
\(67\) −7.49485 −0.915641 −0.457821 0.889045i \(-0.651370\pi\)
−0.457821 + 0.889045i \(0.651370\pi\)
\(68\) 1.52346 0.184746
\(69\) 5.86800 0.706424
\(70\) 1.21166 0.144821
\(71\) −0.842329 −0.0999661 −0.0499830 0.998750i \(-0.515917\pi\)
−0.0499830 + 0.998750i \(0.515917\pi\)
\(72\) −4.29386 −0.506037
\(73\) 8.60525 1.00717 0.503584 0.863946i \(-0.332014\pi\)
0.503584 + 0.863946i \(0.332014\pi\)
\(74\) −1.20281 −0.139823
\(75\) −2.70072 −0.311852
\(76\) −5.54062 −0.635553
\(77\) 6.47392 0.737772
\(78\) 13.4906 1.52751
\(79\) 4.99850 0.562376 0.281188 0.959653i \(-0.409272\pi\)
0.281188 + 0.959653i \(0.409272\pi\)
\(80\) 1.00000 0.111803
\(81\) −3.44432 −0.382703
\(82\) 10.3503 1.14300
\(83\) −1.39402 −0.153013 −0.0765066 0.997069i \(-0.524377\pi\)
−0.0765066 + 0.997069i \(0.524377\pi\)
\(84\) 3.27234 0.357042
\(85\) 1.52346 0.165242
\(86\) 12.2971 1.32604
\(87\) −15.3330 −1.64387
\(88\) 5.34303 0.569569
\(89\) 1.31290 0.139168 0.0695838 0.997576i \(-0.477833\pi\)
0.0695838 + 0.997576i \(0.477833\pi\)
\(90\) −4.29386 −0.452613
\(91\) −6.05247 −0.634471
\(92\) −2.17276 −0.226526
\(93\) −19.1708 −1.98792
\(94\) −12.4866 −1.28790
\(95\) −5.54062 −0.568456
\(96\) 2.70072 0.275641
\(97\) −9.84430 −0.999537 −0.499769 0.866159i \(-0.666582\pi\)
−0.499769 + 0.866159i \(0.666582\pi\)
\(98\) 5.53188 0.558805
\(99\) −22.9422 −2.30578
\(100\) 1.00000 0.100000
\(101\) −0.695446 −0.0691994 −0.0345997 0.999401i \(-0.511016\pi\)
−0.0345997 + 0.999401i \(0.511016\pi\)
\(102\) 4.11443 0.407389
\(103\) 5.37457 0.529572 0.264786 0.964307i \(-0.414699\pi\)
0.264786 + 0.964307i \(0.414699\pi\)
\(104\) −4.99519 −0.489819
\(105\) 3.27234 0.319348
\(106\) −10.8717 −1.05595
\(107\) 16.0568 1.55227 0.776135 0.630567i \(-0.217178\pi\)
0.776135 + 0.630567i \(0.217178\pi\)
\(108\) −3.49436 −0.336245
\(109\) 3.85240 0.368993 0.184496 0.982833i \(-0.440935\pi\)
0.184496 + 0.982833i \(0.440935\pi\)
\(110\) 5.34303 0.509438
\(111\) −3.24844 −0.308328
\(112\) −1.21166 −0.114491
\(113\) 15.5965 1.46719 0.733597 0.679585i \(-0.237840\pi\)
0.733597 + 0.679585i \(0.237840\pi\)
\(114\) −14.9636 −1.40147
\(115\) −2.17276 −0.202611
\(116\) 5.67740 0.527133
\(117\) 21.4487 1.98293
\(118\) −3.79149 −0.349035
\(119\) −1.84591 −0.169214
\(120\) 2.70072 0.246540
\(121\) 17.5479 1.59527
\(122\) 6.62515 0.599813
\(123\) 27.9531 2.52045
\(124\) 7.09841 0.637456
\(125\) 1.00000 0.0894427
\(126\) 5.20270 0.463493
\(127\) 9.13270 0.810396 0.405198 0.914229i \(-0.367203\pi\)
0.405198 + 0.914229i \(0.367203\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 33.2111 2.92407
\(130\) −4.99519 −0.438107
\(131\) 4.16835 0.364190 0.182095 0.983281i \(-0.441712\pi\)
0.182095 + 0.983281i \(0.441712\pi\)
\(132\) 14.4300 1.25597
\(133\) 6.71334 0.582120
\(134\) 7.49485 0.647456
\(135\) −3.49436 −0.300746
\(136\) −1.52346 −0.130635
\(137\) 7.64930 0.653524 0.326762 0.945107i \(-0.394042\pi\)
0.326762 + 0.945107i \(0.394042\pi\)
\(138\) −5.86800 −0.499517
\(139\) −19.2278 −1.63088 −0.815441 0.578840i \(-0.803506\pi\)
−0.815441 + 0.578840i \(0.803506\pi\)
\(140\) −1.21166 −0.102404
\(141\) −33.7229 −2.83998
\(142\) 0.842329 0.0706867
\(143\) −26.6895 −2.23188
\(144\) 4.29386 0.357822
\(145\) 5.67740 0.471482
\(146\) −8.60525 −0.712175
\(147\) 14.9400 1.23223
\(148\) 1.20281 0.0988701
\(149\) −0.566681 −0.0464243 −0.0232122 0.999731i \(-0.507389\pi\)
−0.0232122 + 0.999731i \(0.507389\pi\)
\(150\) 2.70072 0.220512
\(151\) −8.98225 −0.730965 −0.365483 0.930818i \(-0.619096\pi\)
−0.365483 + 0.930818i \(0.619096\pi\)
\(152\) 5.54062 0.449404
\(153\) 6.54152 0.528851
\(154\) −6.47392 −0.521684
\(155\) 7.09841 0.570158
\(156\) −13.4906 −1.08011
\(157\) −21.7627 −1.73685 −0.868426 0.495819i \(-0.834868\pi\)
−0.868426 + 0.495819i \(0.834868\pi\)
\(158\) −4.99850 −0.397660
\(159\) −29.3612 −2.32850
\(160\) −1.00000 −0.0790569
\(161\) 2.63264 0.207481
\(162\) 3.44432 0.270612
\(163\) 12.0025 0.940110 0.470055 0.882637i \(-0.344234\pi\)
0.470055 + 0.882637i \(0.344234\pi\)
\(164\) −10.3503 −0.808220
\(165\) 14.4300 1.12337
\(166\) 1.39402 0.108197
\(167\) 17.3770 1.34467 0.672337 0.740245i \(-0.265290\pi\)
0.672337 + 0.740245i \(0.265290\pi\)
\(168\) −3.27234 −0.252467
\(169\) 11.9520 0.919381
\(170\) −1.52346 −0.116844
\(171\) −23.7907 −1.81932
\(172\) −12.2971 −0.937649
\(173\) −5.25782 −0.399745 −0.199872 0.979822i \(-0.564053\pi\)
−0.199872 + 0.979822i \(0.564053\pi\)
\(174\) 15.3330 1.16239
\(175\) −1.21166 −0.0915928
\(176\) −5.34303 −0.402746
\(177\) −10.2397 −0.769667
\(178\) −1.31290 −0.0984063
\(179\) 7.13480 0.533280 0.266640 0.963796i \(-0.414087\pi\)
0.266640 + 0.963796i \(0.414087\pi\)
\(180\) 4.29386 0.320046
\(181\) −14.3555 −1.06704 −0.533520 0.845788i \(-0.679131\pi\)
−0.533520 + 0.845788i \(0.679131\pi\)
\(182\) 6.05247 0.448639
\(183\) 17.8926 1.32266
\(184\) 2.17276 0.160178
\(185\) 1.20281 0.0884321
\(186\) 19.1708 1.40567
\(187\) −8.13988 −0.595247
\(188\) 12.4866 0.910682
\(189\) 4.23397 0.307976
\(190\) 5.54062 0.401959
\(191\) −21.8421 −1.58044 −0.790220 0.612823i \(-0.790034\pi\)
−0.790220 + 0.612823i \(0.790034\pi\)
\(192\) −2.70072 −0.194907
\(193\) −23.8668 −1.71797 −0.858986 0.511999i \(-0.828905\pi\)
−0.858986 + 0.511999i \(0.828905\pi\)
\(194\) 9.84430 0.706780
\(195\) −13.4906 −0.966082
\(196\) −5.53188 −0.395135
\(197\) −15.7907 −1.12504 −0.562519 0.826784i \(-0.690168\pi\)
−0.562519 + 0.826784i \(0.690168\pi\)
\(198\) 22.9422 1.63043
\(199\) −5.88423 −0.417122 −0.208561 0.978009i \(-0.566878\pi\)
−0.208561 + 0.978009i \(0.566878\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 20.2414 1.42772
\(202\) 0.695446 0.0489314
\(203\) −6.87907 −0.482816
\(204\) −4.11443 −0.288068
\(205\) −10.3503 −0.722894
\(206\) −5.37457 −0.374464
\(207\) −9.32953 −0.648447
\(208\) 4.99519 0.346354
\(209\) 29.6037 2.04773
\(210\) −3.27234 −0.225813
\(211\) 21.9315 1.50983 0.754914 0.655823i \(-0.227678\pi\)
0.754914 + 0.655823i \(0.227678\pi\)
\(212\) 10.8717 0.746668
\(213\) 2.27489 0.155873
\(214\) −16.0568 −1.09762
\(215\) −12.2971 −0.838658
\(216\) 3.49436 0.237761
\(217\) −8.60085 −0.583864
\(218\) −3.85240 −0.260917
\(219\) −23.2403 −1.57044
\(220\) −5.34303 −0.360227
\(221\) 7.60997 0.511902
\(222\) 3.24844 0.218021
\(223\) −5.44147 −0.364388 −0.182194 0.983263i \(-0.558320\pi\)
−0.182194 + 0.983263i \(0.558320\pi\)
\(224\) 1.21166 0.0809573
\(225\) 4.29386 0.286258
\(226\) −15.5965 −1.03746
\(227\) 1.13806 0.0755356 0.0377678 0.999287i \(-0.487975\pi\)
0.0377678 + 0.999287i \(0.487975\pi\)
\(228\) 14.9636 0.990991
\(229\) −3.68354 −0.243415 −0.121708 0.992566i \(-0.538837\pi\)
−0.121708 + 0.992566i \(0.538837\pi\)
\(230\) 2.17276 0.143267
\(231\) −17.4842 −1.15038
\(232\) −5.67740 −0.372739
\(233\) −6.60386 −0.432633 −0.216317 0.976323i \(-0.569404\pi\)
−0.216317 + 0.976323i \(0.569404\pi\)
\(234\) −21.4487 −1.40214
\(235\) 12.4866 0.814539
\(236\) 3.79149 0.246805
\(237\) −13.4995 −0.876889
\(238\) 1.84591 0.119653
\(239\) −20.7947 −1.34510 −0.672550 0.740052i \(-0.734801\pi\)
−0.672550 + 0.740052i \(0.734801\pi\)
\(240\) −2.70072 −0.174330
\(241\) −1.42726 −0.0919379 −0.0459689 0.998943i \(-0.514638\pi\)
−0.0459689 + 0.998943i \(0.514638\pi\)
\(242\) −17.5479 −1.12802
\(243\) 19.7852 1.26922
\(244\) −6.62515 −0.424132
\(245\) −5.53188 −0.353419
\(246\) −27.9531 −1.78223
\(247\) −27.6765 −1.76101
\(248\) −7.09841 −0.450749
\(249\) 3.76484 0.238587
\(250\) −1.00000 −0.0632456
\(251\) −18.9136 −1.19382 −0.596909 0.802309i \(-0.703605\pi\)
−0.596909 + 0.802309i \(0.703605\pi\)
\(252\) −5.20270 −0.327739
\(253\) 11.6091 0.729858
\(254\) −9.13270 −0.573036
\(255\) −4.11443 −0.257655
\(256\) 1.00000 0.0625000
\(257\) −14.9072 −0.929887 −0.464944 0.885340i \(-0.653925\pi\)
−0.464944 + 0.885340i \(0.653925\pi\)
\(258\) −33.2111 −2.06763
\(259\) −1.45739 −0.0905578
\(260\) 4.99519 0.309789
\(261\) 24.3780 1.50896
\(262\) −4.16835 −0.257521
\(263\) 12.2108 0.752948 0.376474 0.926427i \(-0.377136\pi\)
0.376474 + 0.926427i \(0.377136\pi\)
\(264\) −14.4300 −0.888105
\(265\) 10.8717 0.667840
\(266\) −6.71334 −0.411621
\(267\) −3.54578 −0.216998
\(268\) −7.49485 −0.457821
\(269\) −27.5270 −1.67835 −0.839177 0.543859i \(-0.816963\pi\)
−0.839177 + 0.543859i \(0.816963\pi\)
\(270\) 3.49436 0.212660
\(271\) 13.4256 0.815548 0.407774 0.913083i \(-0.366305\pi\)
0.407774 + 0.913083i \(0.366305\pi\)
\(272\) 1.52346 0.0923732
\(273\) 16.3460 0.989304
\(274\) −7.64930 −0.462111
\(275\) −5.34303 −0.322197
\(276\) 5.86800 0.353212
\(277\) 10.3268 0.620477 0.310238 0.950659i \(-0.399591\pi\)
0.310238 + 0.950659i \(0.399591\pi\)
\(278\) 19.2278 1.15321
\(279\) 30.4796 1.82477
\(280\) 1.21166 0.0724104
\(281\) 21.9607 1.31006 0.655032 0.755601i \(-0.272655\pi\)
0.655032 + 0.755601i \(0.272655\pi\)
\(282\) 33.7229 2.00817
\(283\) 17.6226 1.04755 0.523777 0.851856i \(-0.324523\pi\)
0.523777 + 0.851856i \(0.324523\pi\)
\(284\) −0.842329 −0.0499830
\(285\) 14.9636 0.886369
\(286\) 26.6895 1.57818
\(287\) 12.5410 0.740271
\(288\) −4.29386 −0.253018
\(289\) −14.6791 −0.863475
\(290\) −5.67740 −0.333388
\(291\) 26.5867 1.55854
\(292\) 8.60525 0.503584
\(293\) 0.289555 0.0169160 0.00845800 0.999964i \(-0.497308\pi\)
0.00845800 + 0.999964i \(0.497308\pi\)
\(294\) −14.9400 −0.871321
\(295\) 3.79149 0.220749
\(296\) −1.20281 −0.0699117
\(297\) 18.6705 1.08337
\(298\) 0.566681 0.0328270
\(299\) −10.8533 −0.627665
\(300\) −2.70072 −0.155926
\(301\) 14.8999 0.858818
\(302\) 8.98225 0.516870
\(303\) 1.87820 0.107900
\(304\) −5.54062 −0.317776
\(305\) −6.62515 −0.379355
\(306\) −6.54152 −0.373954
\(307\) −27.4609 −1.56728 −0.783639 0.621216i \(-0.786639\pi\)
−0.783639 + 0.621216i \(0.786639\pi\)
\(308\) 6.47392 0.368886
\(309\) −14.5152 −0.825740
\(310\) −7.09841 −0.403163
\(311\) 0.821358 0.0465749 0.0232875 0.999729i \(-0.492587\pi\)
0.0232875 + 0.999729i \(0.492587\pi\)
\(312\) 13.4906 0.763755
\(313\) −7.59705 −0.429411 −0.214705 0.976679i \(-0.568879\pi\)
−0.214705 + 0.976679i \(0.568879\pi\)
\(314\) 21.7627 1.22814
\(315\) −5.20270 −0.293139
\(316\) 4.99850 0.281188
\(317\) −21.7001 −1.21880 −0.609400 0.792863i \(-0.708590\pi\)
−0.609400 + 0.792863i \(0.708590\pi\)
\(318\) 29.3612 1.64650
\(319\) −30.3345 −1.69841
\(320\) 1.00000 0.0559017
\(321\) −43.3649 −2.42039
\(322\) −2.63264 −0.146711
\(323\) −8.44090 −0.469664
\(324\) −3.44432 −0.191351
\(325\) 4.99519 0.277083
\(326\) −12.0025 −0.664758
\(327\) −10.4042 −0.575355
\(328\) 10.3503 0.571498
\(329\) −15.1295 −0.834119
\(330\) −14.4300 −0.794345
\(331\) 16.9939 0.934070 0.467035 0.884239i \(-0.345322\pi\)
0.467035 + 0.884239i \(0.345322\pi\)
\(332\) −1.39402 −0.0765066
\(333\) 5.16469 0.283023
\(334\) −17.3770 −0.950828
\(335\) −7.49485 −0.409487
\(336\) 3.27234 0.178521
\(337\) −23.2625 −1.26719 −0.633595 0.773665i \(-0.718422\pi\)
−0.633595 + 0.773665i \(0.718422\pi\)
\(338\) −11.9520 −0.650101
\(339\) −42.1217 −2.28774
\(340\) 1.52346 0.0826211
\(341\) −37.9270 −2.05386
\(342\) 23.7907 1.28645
\(343\) 15.1844 0.819878
\(344\) 12.2971 0.663018
\(345\) 5.86800 0.315922
\(346\) 5.25782 0.282662
\(347\) 8.73692 0.469022 0.234511 0.972113i \(-0.424651\pi\)
0.234511 + 0.972113i \(0.424651\pi\)
\(348\) −15.3330 −0.821937
\(349\) −24.1059 −1.29036 −0.645180 0.764031i \(-0.723217\pi\)
−0.645180 + 0.764031i \(0.723217\pi\)
\(350\) 1.21166 0.0647659
\(351\) −17.4550 −0.931679
\(352\) 5.34303 0.284784
\(353\) −14.6510 −0.779793 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(354\) 10.2397 0.544236
\(355\) −0.842329 −0.0447062
\(356\) 1.31290 0.0695838
\(357\) 4.98528 0.263849
\(358\) −7.13480 −0.377086
\(359\) −3.20140 −0.168963 −0.0844816 0.996425i \(-0.526923\pi\)
−0.0844816 + 0.996425i \(0.526923\pi\)
\(360\) −4.29386 −0.226307
\(361\) 11.6985 0.615709
\(362\) 14.3555 0.754511
\(363\) −47.3920 −2.48743
\(364\) −6.05247 −0.317235
\(365\) 8.60525 0.450419
\(366\) −17.8926 −0.935263
\(367\) −34.4463 −1.79808 −0.899042 0.437862i \(-0.855736\pi\)
−0.899042 + 0.437862i \(0.855736\pi\)
\(368\) −2.17276 −0.113263
\(369\) −44.4427 −2.31359
\(370\) −1.20281 −0.0625309
\(371\) −13.1727 −0.683894
\(372\) −19.1708 −0.993959
\(373\) 9.02476 0.467284 0.233642 0.972323i \(-0.424936\pi\)
0.233642 + 0.972323i \(0.424936\pi\)
\(374\) 8.13988 0.420903
\(375\) −2.70072 −0.139464
\(376\) −12.4866 −0.643950
\(377\) 28.3597 1.46060
\(378\) −4.23397 −0.217772
\(379\) −36.0474 −1.85163 −0.925815 0.377977i \(-0.876620\pi\)
−0.925815 + 0.377977i \(0.876620\pi\)
\(380\) −5.54062 −0.284228
\(381\) −24.6648 −1.26362
\(382\) 21.8421 1.11754
\(383\) −9.20022 −0.470109 −0.235055 0.971982i \(-0.575527\pi\)
−0.235055 + 0.971982i \(0.575527\pi\)
\(384\) 2.70072 0.137820
\(385\) 6.47392 0.329942
\(386\) 23.8668 1.21479
\(387\) −52.8023 −2.68409
\(388\) −9.84430 −0.499769
\(389\) −18.2536 −0.925494 −0.462747 0.886490i \(-0.653136\pi\)
−0.462747 + 0.886490i \(0.653136\pi\)
\(390\) 13.4906 0.683123
\(391\) −3.31011 −0.167399
\(392\) 5.53188 0.279402
\(393\) −11.2575 −0.567867
\(394\) 15.7907 0.795522
\(395\) 4.99850 0.251502
\(396\) −22.9422 −1.15289
\(397\) −10.5197 −0.527970 −0.263985 0.964527i \(-0.585037\pi\)
−0.263985 + 0.964527i \(0.585037\pi\)
\(398\) 5.88423 0.294950
\(399\) −18.1308 −0.907676
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −20.2414 −1.00955
\(403\) 35.4579 1.76629
\(404\) −0.695446 −0.0345997
\(405\) −3.44432 −0.171150
\(406\) 6.87907 0.341402
\(407\) −6.42663 −0.318556
\(408\) 4.11443 0.203694
\(409\) −2.94928 −0.145833 −0.0729163 0.997338i \(-0.523231\pi\)
−0.0729163 + 0.997338i \(0.523231\pi\)
\(410\) 10.3503 0.511163
\(411\) −20.6586 −1.01901
\(412\) 5.37457 0.264786
\(413\) −4.59400 −0.226056
\(414\) 9.32953 0.458521
\(415\) −1.39402 −0.0684296
\(416\) −4.99519 −0.244909
\(417\) 51.9289 2.54297
\(418\) −29.6037 −1.44796
\(419\) −0.557921 −0.0272562 −0.0136281 0.999907i \(-0.504338\pi\)
−0.0136281 + 0.999907i \(0.504338\pi\)
\(420\) 3.27234 0.159674
\(421\) −37.7997 −1.84225 −0.921123 0.389271i \(-0.872727\pi\)
−0.921123 + 0.389271i \(0.872727\pi\)
\(422\) −21.9315 −1.06761
\(423\) 53.6160 2.60690
\(424\) −10.8717 −0.527974
\(425\) 1.52346 0.0738986
\(426\) −2.27489 −0.110219
\(427\) 8.02742 0.388474
\(428\) 16.0568 0.776135
\(429\) 72.0806 3.48008
\(430\) 12.2971 0.593021
\(431\) 4.48691 0.216127 0.108063 0.994144i \(-0.465535\pi\)
0.108063 + 0.994144i \(0.465535\pi\)
\(432\) −3.49436 −0.168122
\(433\) −5.08697 −0.244464 −0.122232 0.992502i \(-0.539005\pi\)
−0.122232 + 0.992502i \(0.539005\pi\)
\(434\) 8.60085 0.412854
\(435\) −15.3330 −0.735163
\(436\) 3.85240 0.184496
\(437\) 12.0384 0.575876
\(438\) 23.2403 1.11047
\(439\) 14.0287 0.669555 0.334777 0.942297i \(-0.391339\pi\)
0.334777 + 0.942297i \(0.391339\pi\)
\(440\) 5.34303 0.254719
\(441\) −23.7532 −1.13110
\(442\) −7.60997 −0.361969
\(443\) −38.4453 −1.82659 −0.913296 0.407297i \(-0.866471\pi\)
−0.913296 + 0.407297i \(0.866471\pi\)
\(444\) −3.24844 −0.154164
\(445\) 1.31290 0.0622376
\(446\) 5.44147 0.257661
\(447\) 1.53044 0.0723875
\(448\) −1.21166 −0.0572455
\(449\) −26.4681 −1.24911 −0.624554 0.780981i \(-0.714719\pi\)
−0.624554 + 0.780981i \(0.714719\pi\)
\(450\) −4.29386 −0.202415
\(451\) 55.3018 2.60406
\(452\) 15.5965 0.733597
\(453\) 24.2585 1.13976
\(454\) −1.13806 −0.0534117
\(455\) −6.05247 −0.283744
\(456\) −14.9636 −0.700737
\(457\) −37.0750 −1.73429 −0.867147 0.498052i \(-0.834049\pi\)
−0.867147 + 0.498052i \(0.834049\pi\)
\(458\) 3.68354 0.172121
\(459\) −5.32351 −0.248480
\(460\) −2.17276 −0.101305
\(461\) −20.4921 −0.954413 −0.477207 0.878791i \(-0.658351\pi\)
−0.477207 + 0.878791i \(0.658351\pi\)
\(462\) 17.4842 0.813440
\(463\) −8.88342 −0.412847 −0.206424 0.978463i \(-0.566183\pi\)
−0.206424 + 0.978463i \(0.566183\pi\)
\(464\) 5.67740 0.263567
\(465\) −19.1708 −0.889024
\(466\) 6.60386 0.305918
\(467\) −8.47376 −0.392119 −0.196059 0.980592i \(-0.562815\pi\)
−0.196059 + 0.980592i \(0.562815\pi\)
\(468\) 21.4487 0.991466
\(469\) 9.08119 0.419331
\(470\) −12.4866 −0.575966
\(471\) 58.7748 2.70820
\(472\) −3.79149 −0.174518
\(473\) 65.7040 3.02107
\(474\) 13.4995 0.620054
\(475\) −5.54062 −0.254221
\(476\) −1.84591 −0.0846072
\(477\) 46.6814 2.13739
\(478\) 20.7947 0.951130
\(479\) −0.931984 −0.0425834 −0.0212917 0.999773i \(-0.506778\pi\)
−0.0212917 + 0.999773i \(0.506778\pi\)
\(480\) 2.70072 0.123270
\(481\) 6.00825 0.273953
\(482\) 1.42726 0.0650099
\(483\) −7.11001 −0.323517
\(484\) 17.5479 0.797634
\(485\) −9.84430 −0.447007
\(486\) −19.7852 −0.897476
\(487\) 16.4234 0.744215 0.372108 0.928190i \(-0.378635\pi\)
0.372108 + 0.928190i \(0.378635\pi\)
\(488\) 6.62515 0.299906
\(489\) −32.4154 −1.46588
\(490\) 5.53188 0.249905
\(491\) 10.0951 0.455586 0.227793 0.973710i \(-0.426849\pi\)
0.227793 + 0.973710i \(0.426849\pi\)
\(492\) 27.9531 1.26022
\(493\) 8.64928 0.389544
\(494\) 27.6765 1.24522
\(495\) −22.9422 −1.03118
\(496\) 7.09841 0.318728
\(497\) 1.02062 0.0457809
\(498\) −3.76484 −0.168707
\(499\) −22.6531 −1.01409 −0.507045 0.861920i \(-0.669262\pi\)
−0.507045 + 0.861920i \(0.669262\pi\)
\(500\) 1.00000 0.0447214
\(501\) −46.9304 −2.09670
\(502\) 18.9136 0.844157
\(503\) −4.00867 −0.178738 −0.0893688 0.995999i \(-0.528485\pi\)
−0.0893688 + 0.995999i \(0.528485\pi\)
\(504\) 5.20270 0.231747
\(505\) −0.695446 −0.0309469
\(506\) −11.6091 −0.516088
\(507\) −32.2788 −1.43355
\(508\) 9.13270 0.405198
\(509\) 10.3818 0.460164 0.230082 0.973171i \(-0.426101\pi\)
0.230082 + 0.973171i \(0.426101\pi\)
\(510\) 4.11443 0.182190
\(511\) −10.4266 −0.461247
\(512\) −1.00000 −0.0441942
\(513\) 19.3609 0.854805
\(514\) 14.9072 0.657529
\(515\) 5.37457 0.236832
\(516\) 33.2111 1.46204
\(517\) −66.7165 −2.93419
\(518\) 1.45739 0.0640341
\(519\) 14.1999 0.623305
\(520\) −4.99519 −0.219054
\(521\) 14.6708 0.642740 0.321370 0.946954i \(-0.395857\pi\)
0.321370 + 0.946954i \(0.395857\pi\)
\(522\) −24.3780 −1.06699
\(523\) 4.56784 0.199738 0.0998688 0.995001i \(-0.468158\pi\)
0.0998688 + 0.995001i \(0.468158\pi\)
\(524\) 4.16835 0.182095
\(525\) 3.27234 0.142817
\(526\) −12.2108 −0.532415
\(527\) 10.8141 0.471071
\(528\) 14.4300 0.627985
\(529\) −18.2791 −0.794745
\(530\) −10.8717 −0.472234
\(531\) 16.2802 0.706499
\(532\) 6.71334 0.291060
\(533\) −51.7016 −2.23944
\(534\) 3.54578 0.153441
\(535\) 16.0568 0.694196
\(536\) 7.49485 0.323728
\(537\) −19.2691 −0.831521
\(538\) 27.5270 1.18677
\(539\) 29.5570 1.27311
\(540\) −3.49436 −0.150373
\(541\) 28.5670 1.22819 0.614096 0.789231i \(-0.289521\pi\)
0.614096 + 0.789231i \(0.289521\pi\)
\(542\) −13.4256 −0.576680
\(543\) 38.7702 1.66379
\(544\) −1.52346 −0.0653177
\(545\) 3.85240 0.165019
\(546\) −16.3460 −0.699544
\(547\) 31.6764 1.35439 0.677193 0.735805i \(-0.263196\pi\)
0.677193 + 0.735805i \(0.263196\pi\)
\(548\) 7.64930 0.326762
\(549\) −28.4475 −1.21411
\(550\) 5.34303 0.227827
\(551\) −31.4563 −1.34008
\(552\) −5.86800 −0.249759
\(553\) −6.05648 −0.257548
\(554\) −10.3268 −0.438743
\(555\) −3.24844 −0.137889
\(556\) −19.2278 −0.815441
\(557\) −42.9003 −1.81775 −0.908873 0.417073i \(-0.863056\pi\)
−0.908873 + 0.417073i \(0.863056\pi\)
\(558\) −30.4796 −1.29030
\(559\) −61.4266 −2.59807
\(560\) −1.21166 −0.0512019
\(561\) 21.9835 0.928144
\(562\) −21.9607 −0.926355
\(563\) −1.50822 −0.0635640 −0.0317820 0.999495i \(-0.510118\pi\)
−0.0317820 + 0.999495i \(0.510118\pi\)
\(564\) −33.7229 −1.41999
\(565\) 15.5965 0.656149
\(566\) −17.6226 −0.740732
\(567\) 4.17334 0.175264
\(568\) 0.842329 0.0353434
\(569\) 20.0853 0.842019 0.421009 0.907056i \(-0.361676\pi\)
0.421009 + 0.907056i \(0.361676\pi\)
\(570\) −14.9636 −0.626758
\(571\) −11.2142 −0.469298 −0.234649 0.972080i \(-0.575394\pi\)
−0.234649 + 0.972080i \(0.575394\pi\)
\(572\) −26.6895 −1.11594
\(573\) 58.9894 2.46432
\(574\) −12.5410 −0.523451
\(575\) −2.17276 −0.0906103
\(576\) 4.29386 0.178911
\(577\) 31.6646 1.31821 0.659107 0.752049i \(-0.270934\pi\)
0.659107 + 0.752049i \(0.270934\pi\)
\(578\) 14.6791 0.610569
\(579\) 64.4575 2.67876
\(580\) 5.67740 0.235741
\(581\) 1.68907 0.0700745
\(582\) −26.5867 −1.10205
\(583\) −58.0875 −2.40574
\(584\) −8.60525 −0.356088
\(585\) 21.4487 0.886794
\(586\) −0.289555 −0.0119614
\(587\) −18.3157 −0.755971 −0.377986 0.925811i \(-0.623383\pi\)
−0.377986 + 0.925811i \(0.623383\pi\)
\(588\) 14.9400 0.616117
\(589\) −39.3296 −1.62055
\(590\) −3.79149 −0.156093
\(591\) 42.6461 1.75423
\(592\) 1.20281 0.0494350
\(593\) 31.9549 1.31223 0.656115 0.754661i \(-0.272199\pi\)
0.656115 + 0.754661i \(0.272199\pi\)
\(594\) −18.6705 −0.766058
\(595\) −1.84591 −0.0756750
\(596\) −0.566681 −0.0232122
\(597\) 15.8916 0.650401
\(598\) 10.8533 0.443826
\(599\) 27.3376 1.11698 0.558491 0.829510i \(-0.311380\pi\)
0.558491 + 0.829510i \(0.311380\pi\)
\(600\) 2.70072 0.110256
\(601\) 19.3201 0.788083 0.394041 0.919093i \(-0.371077\pi\)
0.394041 + 0.919093i \(0.371077\pi\)
\(602\) −14.8999 −0.607276
\(603\) −32.1819 −1.31055
\(604\) −8.98225 −0.365483
\(605\) 17.5479 0.713425
\(606\) −1.87820 −0.0762967
\(607\) 0.428965 0.0174112 0.00870558 0.999962i \(-0.497229\pi\)
0.00870558 + 0.999962i \(0.497229\pi\)
\(608\) 5.54062 0.224702
\(609\) 18.5784 0.752835
\(610\) 6.62515 0.268244
\(611\) 62.3732 2.52335
\(612\) 6.54152 0.264425
\(613\) 16.8503 0.680579 0.340289 0.940321i \(-0.389475\pi\)
0.340289 + 0.940321i \(0.389475\pi\)
\(614\) 27.4609 1.10823
\(615\) 27.9531 1.12718
\(616\) −6.47392 −0.260842
\(617\) −12.1060 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(618\) 14.5152 0.583886
\(619\) 15.9974 0.642991 0.321495 0.946911i \(-0.395815\pi\)
0.321495 + 0.946911i \(0.395815\pi\)
\(620\) 7.09841 0.285079
\(621\) 7.59239 0.304672
\(622\) −0.821358 −0.0329335
\(623\) −1.59079 −0.0637337
\(624\) −13.4906 −0.540056
\(625\) 1.00000 0.0400000
\(626\) 7.59705 0.303639
\(627\) −79.9511 −3.19294
\(628\) −21.7627 −0.868426
\(629\) 1.83243 0.0730636
\(630\) 5.20270 0.207280
\(631\) 23.0677 0.918312 0.459156 0.888356i \(-0.348152\pi\)
0.459156 + 0.888356i \(0.348152\pi\)
\(632\) −4.99850 −0.198830
\(633\) −59.2308 −2.35421
\(634\) 21.7001 0.861822
\(635\) 9.13270 0.362420
\(636\) −29.3612 −1.16425
\(637\) −27.6328 −1.09485
\(638\) 30.3345 1.20095
\(639\) −3.61685 −0.143080
\(640\) −1.00000 −0.0395285
\(641\) 15.9870 0.631449 0.315725 0.948851i \(-0.397752\pi\)
0.315725 + 0.948851i \(0.397752\pi\)
\(642\) 43.3649 1.71147
\(643\) −13.2518 −0.522598 −0.261299 0.965258i \(-0.584151\pi\)
−0.261299 + 0.965258i \(0.584151\pi\)
\(644\) 2.63264 0.103741
\(645\) 33.2111 1.30769
\(646\) 8.44090 0.332103
\(647\) 18.5071 0.727589 0.363794 0.931479i \(-0.381481\pi\)
0.363794 + 0.931479i \(0.381481\pi\)
\(648\) 3.44432 0.135306
\(649\) −20.2581 −0.795198
\(650\) −4.99519 −0.195928
\(651\) 23.2284 0.910394
\(652\) 12.0025 0.470055
\(653\) 28.5627 1.11775 0.558873 0.829253i \(-0.311234\pi\)
0.558873 + 0.829253i \(0.311234\pi\)
\(654\) 10.4042 0.406838
\(655\) 4.16835 0.162871
\(656\) −10.3503 −0.404110
\(657\) 36.9498 1.44155
\(658\) 15.1295 0.589811
\(659\) −33.8891 −1.32013 −0.660066 0.751208i \(-0.729472\pi\)
−0.660066 + 0.751208i \(0.729472\pi\)
\(660\) 14.4300 0.561687
\(661\) 40.1703 1.56244 0.781222 0.624253i \(-0.214596\pi\)
0.781222 + 0.624253i \(0.214596\pi\)
\(662\) −16.9939 −0.660487
\(663\) −20.5524 −0.798187
\(664\) 1.39402 0.0540983
\(665\) 6.71334 0.260332
\(666\) −5.16469 −0.200128
\(667\) −12.3356 −0.477637
\(668\) 17.3770 0.672337
\(669\) 14.6959 0.568175
\(670\) 7.49485 0.289551
\(671\) 35.3984 1.36654
\(672\) −3.27234 −0.126233
\(673\) −31.7673 −1.22454 −0.612271 0.790648i \(-0.709744\pi\)
−0.612271 + 0.790648i \(0.709744\pi\)
\(674\) 23.2625 0.896039
\(675\) −3.49436 −0.134498
\(676\) 11.9520 0.459691
\(677\) −30.9474 −1.18941 −0.594703 0.803945i \(-0.702731\pi\)
−0.594703 + 0.803945i \(0.702731\pi\)
\(678\) 42.1217 1.61767
\(679\) 11.9279 0.457752
\(680\) −1.52346 −0.0584220
\(681\) −3.07357 −0.117780
\(682\) 37.9270 1.45230
\(683\) 28.9294 1.10695 0.553477 0.832865i \(-0.313301\pi\)
0.553477 + 0.832865i \(0.313301\pi\)
\(684\) −23.7907 −0.909659
\(685\) 7.64930 0.292265
\(686\) −15.1844 −0.579742
\(687\) 9.94820 0.379548
\(688\) −12.2971 −0.468824
\(689\) 54.3060 2.06889
\(690\) −5.86800 −0.223391
\(691\) −35.4006 −1.34670 −0.673352 0.739322i \(-0.735146\pi\)
−0.673352 + 0.739322i \(0.735146\pi\)
\(692\) −5.25782 −0.199872
\(693\) 27.7981 1.05596
\(694\) −8.73692 −0.331649
\(695\) −19.2278 −0.729353
\(696\) 15.3330 0.581197
\(697\) −15.7682 −0.597263
\(698\) 24.1059 0.912422
\(699\) 17.8352 0.674588
\(700\) −1.21166 −0.0457964
\(701\) 6.80979 0.257202 0.128601 0.991696i \(-0.458951\pi\)
0.128601 + 0.991696i \(0.458951\pi\)
\(702\) 17.4550 0.658796
\(703\) −6.66429 −0.251349
\(704\) −5.34303 −0.201373
\(705\) −33.7229 −1.27008
\(706\) 14.6510 0.551397
\(707\) 0.842642 0.0316908
\(708\) −10.2397 −0.384833
\(709\) 1.45240 0.0545460 0.0272730 0.999628i \(-0.491318\pi\)
0.0272730 + 0.999628i \(0.491318\pi\)
\(710\) 0.842329 0.0316121
\(711\) 21.4629 0.804922
\(712\) −1.31290 −0.0492031
\(713\) −15.4231 −0.577601
\(714\) −4.98528 −0.186569
\(715\) −26.6895 −0.998129
\(716\) 7.13480 0.266640
\(717\) 56.1607 2.09736
\(718\) 3.20140 0.119475
\(719\) −21.0938 −0.786667 −0.393334 0.919396i \(-0.628678\pi\)
−0.393334 + 0.919396i \(0.628678\pi\)
\(720\) 4.29386 0.160023
\(721\) −6.51214 −0.242525
\(722\) −11.6985 −0.435372
\(723\) 3.85462 0.143355
\(724\) −14.3555 −0.533520
\(725\) 5.67740 0.210853
\(726\) 47.3920 1.75888
\(727\) −24.9938 −0.926970 −0.463485 0.886105i \(-0.653401\pi\)
−0.463485 + 0.886105i \(0.653401\pi\)
\(728\) 6.05247 0.224319
\(729\) −43.1013 −1.59634
\(730\) −8.60525 −0.318495
\(731\) −18.7342 −0.692909
\(732\) 17.8926 0.661331
\(733\) −40.5866 −1.49910 −0.749550 0.661947i \(-0.769730\pi\)
−0.749550 + 0.661947i \(0.769730\pi\)
\(734\) 34.4463 1.27144
\(735\) 14.9400 0.551072
\(736\) 2.17276 0.0800889
\(737\) 40.0452 1.47508
\(738\) 44.4427 1.63596
\(739\) 16.9594 0.623862 0.311931 0.950105i \(-0.399024\pi\)
0.311931 + 0.950105i \(0.399024\pi\)
\(740\) 1.20281 0.0442160
\(741\) 74.7463 2.74587
\(742\) 13.1727 0.483586
\(743\) 37.3868 1.37159 0.685794 0.727795i \(-0.259455\pi\)
0.685794 + 0.727795i \(0.259455\pi\)
\(744\) 19.1708 0.702835
\(745\) −0.566681 −0.0207616
\(746\) −9.02476 −0.330420
\(747\) −5.98572 −0.219006
\(748\) −8.13988 −0.297623
\(749\) −19.4554 −0.710883
\(750\) 2.70072 0.0986162
\(751\) −34.9924 −1.27689 −0.638445 0.769667i \(-0.720422\pi\)
−0.638445 + 0.769667i \(0.720422\pi\)
\(752\) 12.4866 0.455341
\(753\) 51.0804 1.86147
\(754\) −28.3597 −1.03280
\(755\) −8.98225 −0.326898
\(756\) 4.23397 0.153988
\(757\) −4.30523 −0.156476 −0.0782381 0.996935i \(-0.524929\pi\)
−0.0782381 + 0.996935i \(0.524929\pi\)
\(758\) 36.0474 1.30930
\(759\) −31.3529 −1.13804
\(760\) 5.54062 0.200979
\(761\) 14.2365 0.516072 0.258036 0.966135i \(-0.416925\pi\)
0.258036 + 0.966135i \(0.416925\pi\)
\(762\) 24.6648 0.893512
\(763\) −4.66779 −0.168985
\(764\) −21.8421 −0.790220
\(765\) 6.54152 0.236509
\(766\) 9.20022 0.332418
\(767\) 18.9392 0.683857
\(768\) −2.70072 −0.0974537
\(769\) 50.5184 1.82174 0.910871 0.412692i \(-0.135411\pi\)
0.910871 + 0.412692i \(0.135411\pi\)
\(770\) −6.47392 −0.233304
\(771\) 40.2602 1.44993
\(772\) −23.8668 −0.858986
\(773\) −33.9247 −1.22019 −0.610093 0.792330i \(-0.708868\pi\)
−0.610093 + 0.792330i \(0.708868\pi\)
\(774\) 52.8023 1.89794
\(775\) 7.09841 0.254982
\(776\) 9.84430 0.353390
\(777\) 3.93600 0.141203
\(778\) 18.2536 0.654423
\(779\) 57.3469 2.05467
\(780\) −13.4906 −0.483041
\(781\) 4.50059 0.161044
\(782\) 3.31011 0.118369
\(783\) −19.8389 −0.708983
\(784\) −5.53188 −0.197567
\(785\) −21.7627 −0.776744
\(786\) 11.2575 0.401542
\(787\) 27.1358 0.967287 0.483643 0.875265i \(-0.339313\pi\)
0.483643 + 0.875265i \(0.339313\pi\)
\(788\) −15.7907 −0.562519
\(789\) −32.9778 −1.17404
\(790\) −4.99850 −0.177839
\(791\) −18.8976 −0.671922
\(792\) 22.9422 0.815217
\(793\) −33.0939 −1.17520
\(794\) 10.5197 0.373331
\(795\) −29.3612 −1.04134
\(796\) −5.88423 −0.208561
\(797\) 2.13348 0.0755717 0.0377859 0.999286i \(-0.487970\pi\)
0.0377859 + 0.999286i \(0.487970\pi\)
\(798\) 18.1308 0.641824
\(799\) 19.0229 0.672981
\(800\) −1.00000 −0.0353553
\(801\) 5.63743 0.199189
\(802\) −1.00000 −0.0353112
\(803\) −45.9781 −1.62253
\(804\) 20.2414 0.713861
\(805\) 2.63264 0.0927884
\(806\) −35.4579 −1.24895
\(807\) 74.3427 2.61699
\(808\) 0.695446 0.0244657
\(809\) 18.6538 0.655833 0.327917 0.944707i \(-0.393653\pi\)
0.327917 + 0.944707i \(0.393653\pi\)
\(810\) 3.44432 0.121021
\(811\) 39.7943 1.39737 0.698684 0.715430i \(-0.253769\pi\)
0.698684 + 0.715430i \(0.253769\pi\)
\(812\) −6.87907 −0.241408
\(813\) −36.2588 −1.27165
\(814\) 6.42663 0.225253
\(815\) 12.0025 0.420430
\(816\) −4.11443 −0.144034
\(817\) 68.1338 2.38370
\(818\) 2.94928 0.103119
\(819\) −25.9885 −0.908111
\(820\) −10.3503 −0.361447
\(821\) 41.7529 1.45719 0.728593 0.684946i \(-0.240174\pi\)
0.728593 + 0.684946i \(0.240174\pi\)
\(822\) 20.6586 0.720551
\(823\) −33.6256 −1.17211 −0.586057 0.810270i \(-0.699320\pi\)
−0.586057 + 0.810270i \(0.699320\pi\)
\(824\) −5.37457 −0.187232
\(825\) 14.4300 0.502388
\(826\) 4.59400 0.159846
\(827\) −26.1355 −0.908822 −0.454411 0.890792i \(-0.650150\pi\)
−0.454411 + 0.890792i \(0.650150\pi\)
\(828\) −9.32953 −0.324223
\(829\) −14.0631 −0.488433 −0.244217 0.969721i \(-0.578531\pi\)
−0.244217 + 0.969721i \(0.578531\pi\)
\(830\) 1.39402 0.0483870
\(831\) −27.8897 −0.967484
\(832\) 4.99519 0.173177
\(833\) −8.42759 −0.291999
\(834\) −51.9289 −1.79815
\(835\) 17.3770 0.601357
\(836\) 29.6037 1.02386
\(837\) −24.8044 −0.857365
\(838\) 0.557921 0.0192730
\(839\) 41.9824 1.44939 0.724697 0.689067i \(-0.241980\pi\)
0.724697 + 0.689067i \(0.241980\pi\)
\(840\) −3.27234 −0.112907
\(841\) 3.23284 0.111477
\(842\) 37.7997 1.30266
\(843\) −59.3095 −2.04273
\(844\) 21.9315 0.754914
\(845\) 11.9520 0.411160
\(846\) −53.6160 −1.84335
\(847\) −21.2621 −0.730575
\(848\) 10.8717 0.373334
\(849\) −47.5936 −1.63341
\(850\) −1.52346 −0.0522542
\(851\) −2.61341 −0.0895864
\(852\) 2.27489 0.0779365
\(853\) −16.1430 −0.552726 −0.276363 0.961053i \(-0.589129\pi\)
−0.276363 + 0.961053i \(0.589129\pi\)
\(854\) −8.02742 −0.274693
\(855\) −23.7907 −0.813624
\(856\) −16.0568 −0.548810
\(857\) 47.3125 1.61616 0.808082 0.589069i \(-0.200506\pi\)
0.808082 + 0.589069i \(0.200506\pi\)
\(858\) −72.0806 −2.46079
\(859\) −12.6657 −0.432150 −0.216075 0.976377i \(-0.569325\pi\)
−0.216075 + 0.976377i \(0.569325\pi\)
\(860\) −12.2971 −0.419329
\(861\) −33.8696 −1.15427
\(862\) −4.48691 −0.152825
\(863\) −38.7489 −1.31903 −0.659514 0.751692i \(-0.729238\pi\)
−0.659514 + 0.751692i \(0.729238\pi\)
\(864\) 3.49436 0.118880
\(865\) −5.25782 −0.178771
\(866\) 5.08697 0.172862
\(867\) 39.6440 1.34638
\(868\) −8.60085 −0.291932
\(869\) −26.7071 −0.905978
\(870\) 15.3330 0.519839
\(871\) −37.4382 −1.26855
\(872\) −3.85240 −0.130459
\(873\) −42.2701 −1.43063
\(874\) −12.0384 −0.407206
\(875\) −1.21166 −0.0409615
\(876\) −23.2403 −0.785218
\(877\) −2.43898 −0.0823585 −0.0411792 0.999152i \(-0.513111\pi\)
−0.0411792 + 0.999152i \(0.513111\pi\)
\(878\) −14.0287 −0.473447
\(879\) −0.782006 −0.0263764
\(880\) −5.34303 −0.180113
\(881\) 9.18259 0.309369 0.154685 0.987964i \(-0.450564\pi\)
0.154685 + 0.987964i \(0.450564\pi\)
\(882\) 23.7532 0.799810
\(883\) 5.39833 0.181668 0.0908342 0.995866i \(-0.471047\pi\)
0.0908342 + 0.995866i \(0.471047\pi\)
\(884\) 7.60997 0.255951
\(885\) −10.2397 −0.344205
\(886\) 38.4453 1.29160
\(887\) 6.61687 0.222173 0.111086 0.993811i \(-0.464567\pi\)
0.111086 + 0.993811i \(0.464567\pi\)
\(888\) 3.24844 0.109010
\(889\) −11.0657 −0.371132
\(890\) −1.31290 −0.0440086
\(891\) 18.4031 0.616528
\(892\) −5.44147 −0.182194
\(893\) −69.1838 −2.31515
\(894\) −1.53044 −0.0511857
\(895\) 7.13480 0.238490
\(896\) 1.21166 0.0404787
\(897\) 29.3118 0.978692
\(898\) 26.4681 0.883253
\(899\) 40.3005 1.34410
\(900\) 4.29386 0.143129
\(901\) 16.5625 0.551777
\(902\) −55.3018 −1.84135
\(903\) −40.2405 −1.33912
\(904\) −15.5965 −0.518732
\(905\) −14.3555 −0.477194
\(906\) −24.2585 −0.805935
\(907\) −13.8899 −0.461207 −0.230604 0.973048i \(-0.574070\pi\)
−0.230604 + 0.973048i \(0.574070\pi\)
\(908\) 1.13806 0.0377678
\(909\) −2.98615 −0.0990443
\(910\) 6.05247 0.200637
\(911\) 58.3015 1.93162 0.965808 0.259258i \(-0.0834780\pi\)
0.965808 + 0.259258i \(0.0834780\pi\)
\(912\) 14.9636 0.495496
\(913\) 7.44827 0.246502
\(914\) 37.0750 1.22633
\(915\) 17.8926 0.591513
\(916\) −3.68354 −0.121708
\(917\) −5.05061 −0.166786
\(918\) 5.32351 0.175702
\(919\) 10.0652 0.332020 0.166010 0.986124i \(-0.446912\pi\)
0.166010 + 0.986124i \(0.446912\pi\)
\(920\) 2.17276 0.0716337
\(921\) 74.1642 2.44379
\(922\) 20.4921 0.674872
\(923\) −4.20760 −0.138495
\(924\) −17.4842 −0.575189
\(925\) 1.20281 0.0395480
\(926\) 8.88342 0.291927
\(927\) 23.0777 0.757970
\(928\) −5.67740 −0.186370
\(929\) −12.3800 −0.406174 −0.203087 0.979161i \(-0.565098\pi\)
−0.203087 + 0.979161i \(0.565098\pi\)
\(930\) 19.1708 0.628635
\(931\) 30.6501 1.00452
\(932\) −6.60386 −0.216317
\(933\) −2.21825 −0.0726224
\(934\) 8.47376 0.277270
\(935\) −8.13988 −0.266202
\(936\) −21.4487 −0.701072
\(937\) 48.3051 1.57806 0.789030 0.614355i \(-0.210584\pi\)
0.789030 + 0.614355i \(0.210584\pi\)
\(938\) −9.08119 −0.296512
\(939\) 20.5175 0.669562
\(940\) 12.4866 0.407269
\(941\) 47.5709 1.55077 0.775384 0.631490i \(-0.217556\pi\)
0.775384 + 0.631490i \(0.217556\pi\)
\(942\) −58.7748 −1.91499
\(943\) 22.4886 0.732330
\(944\) 3.79149 0.123403
\(945\) 4.23397 0.137731
\(946\) −65.7040 −2.13622
\(947\) −49.4700 −1.60756 −0.803780 0.594926i \(-0.797181\pi\)
−0.803780 + 0.594926i \(0.797181\pi\)
\(948\) −13.4995 −0.438445
\(949\) 42.9849 1.39535
\(950\) 5.54062 0.179761
\(951\) 58.6059 1.90043
\(952\) 1.84591 0.0598263
\(953\) −22.5320 −0.729884 −0.364942 0.931030i \(-0.618911\pi\)
−0.364942 + 0.931030i \(0.618911\pi\)
\(954\) −46.6814 −1.51137
\(955\) −21.8421 −0.706794
\(956\) −20.7947 −0.672550
\(957\) 81.9248 2.64825
\(958\) 0.931984 0.0301110
\(959\) −9.26834 −0.299290
\(960\) −2.70072 −0.0871652
\(961\) 19.3874 0.625401
\(962\) −6.00825 −0.193714
\(963\) 68.9457 2.22175
\(964\) −1.42726 −0.0459689
\(965\) −23.8668 −0.768301
\(966\) 7.11001 0.228761
\(967\) −23.2547 −0.747820 −0.373910 0.927465i \(-0.621983\pi\)
−0.373910 + 0.927465i \(0.621983\pi\)
\(968\) −17.5479 −0.564012
\(969\) 22.7965 0.732328
\(970\) 9.84430 0.316081
\(971\) −35.7342 −1.14677 −0.573383 0.819287i \(-0.694369\pi\)
−0.573383 + 0.819287i \(0.694369\pi\)
\(972\) 19.7852 0.634611
\(973\) 23.2976 0.746885
\(974\) −16.4234 −0.526240
\(975\) −13.4906 −0.432045
\(976\) −6.62515 −0.212066
\(977\) −38.7290 −1.23905 −0.619525 0.784977i \(-0.712675\pi\)
−0.619525 + 0.784977i \(0.712675\pi\)
\(978\) 32.4154 1.03653
\(979\) −7.01488 −0.224197
\(980\) −5.53188 −0.176710
\(981\) 16.5417 0.528135
\(982\) −10.0951 −0.322148
\(983\) 53.3366 1.70117 0.850587 0.525835i \(-0.176247\pi\)
0.850587 + 0.525835i \(0.176247\pi\)
\(984\) −27.9531 −0.891113
\(985\) −15.7907 −0.503132
\(986\) −8.64928 −0.275449
\(987\) 40.8606 1.30061
\(988\) −27.6765 −0.880506
\(989\) 26.7187 0.849606
\(990\) 22.9422 0.729152
\(991\) −41.5338 −1.31936 −0.659682 0.751545i \(-0.729309\pi\)
−0.659682 + 0.751545i \(0.729309\pi\)
\(992\) −7.09841 −0.225375
\(993\) −45.8957 −1.45646
\(994\) −1.02062 −0.0323720
\(995\) −5.88423 −0.186543
\(996\) 3.76484 0.119294
\(997\) 6.15493 0.194928 0.0974642 0.995239i \(-0.468927\pi\)
0.0974642 + 0.995239i \(0.468927\pi\)
\(998\) 22.6531 0.717070
\(999\) −4.20304 −0.132978
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.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.2 10 1.1 even 1 trivial