Properties

Label 4034.2.a.d.1.8
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.49412 q^{3} +1.00000 q^{4} +2.01405 q^{5} -2.49412 q^{6} +2.26153 q^{7} +1.00000 q^{8} +3.22062 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.49412 q^{3} +1.00000 q^{4} +2.01405 q^{5} -2.49412 q^{6} +2.26153 q^{7} +1.00000 q^{8} +3.22062 q^{9} +2.01405 q^{10} -3.70387 q^{11} -2.49412 q^{12} -3.55865 q^{13} +2.26153 q^{14} -5.02328 q^{15} +1.00000 q^{16} +6.88697 q^{17} +3.22062 q^{18} +2.37414 q^{19} +2.01405 q^{20} -5.64052 q^{21} -3.70387 q^{22} -2.90483 q^{23} -2.49412 q^{24} -0.943592 q^{25} -3.55865 q^{26} -0.550262 q^{27} +2.26153 q^{28} +5.51423 q^{29} -5.02328 q^{30} -6.05211 q^{31} +1.00000 q^{32} +9.23790 q^{33} +6.88697 q^{34} +4.55484 q^{35} +3.22062 q^{36} +4.05981 q^{37} +2.37414 q^{38} +8.87569 q^{39} +2.01405 q^{40} +5.33998 q^{41} -5.64052 q^{42} -1.25313 q^{43} -3.70387 q^{44} +6.48651 q^{45} -2.90483 q^{46} +6.32993 q^{47} -2.49412 q^{48} -1.88548 q^{49} -0.943592 q^{50} -17.1769 q^{51} -3.55865 q^{52} +12.2322 q^{53} -0.550262 q^{54} -7.45980 q^{55} +2.26153 q^{56} -5.92139 q^{57} +5.51423 q^{58} -4.09159 q^{59} -5.02328 q^{60} +2.55932 q^{61} -6.05211 q^{62} +7.28354 q^{63} +1.00000 q^{64} -7.16730 q^{65} +9.23790 q^{66} +15.7411 q^{67} +6.88697 q^{68} +7.24498 q^{69} +4.55484 q^{70} +0.641025 q^{71} +3.22062 q^{72} -8.54143 q^{73} +4.05981 q^{74} +2.35343 q^{75} +2.37414 q^{76} -8.37642 q^{77} +8.87569 q^{78} +2.47415 q^{79} +2.01405 q^{80} -8.28945 q^{81} +5.33998 q^{82} +5.59401 q^{83} -5.64052 q^{84} +13.8707 q^{85} -1.25313 q^{86} -13.7531 q^{87} -3.70387 q^{88} +8.40142 q^{89} +6.48651 q^{90} -8.04799 q^{91} -2.90483 q^{92} +15.0947 q^{93} +6.32993 q^{94} +4.78164 q^{95} -2.49412 q^{96} -7.21256 q^{97} -1.88548 q^{98} -11.9288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.49412 −1.43998 −0.719990 0.693985i \(-0.755854\pi\)
−0.719990 + 0.693985i \(0.755854\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.01405 0.900712 0.450356 0.892849i \(-0.351297\pi\)
0.450356 + 0.892849i \(0.351297\pi\)
\(6\) −2.49412 −1.01822
\(7\) 2.26153 0.854778 0.427389 0.904068i \(-0.359433\pi\)
0.427389 + 0.904068i \(0.359433\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.22062 1.07354
\(10\) 2.01405 0.636899
\(11\) −3.70387 −1.11676 −0.558380 0.829585i \(-0.688577\pi\)
−0.558380 + 0.829585i \(0.688577\pi\)
\(12\) −2.49412 −0.719990
\(13\) −3.55865 −0.986991 −0.493496 0.869748i \(-0.664281\pi\)
−0.493496 + 0.869748i \(0.664281\pi\)
\(14\) 2.26153 0.604419
\(15\) −5.02328 −1.29701
\(16\) 1.00000 0.250000
\(17\) 6.88697 1.67034 0.835168 0.549995i \(-0.185370\pi\)
0.835168 + 0.549995i \(0.185370\pi\)
\(18\) 3.22062 0.759108
\(19\) 2.37414 0.544665 0.272333 0.962203i \(-0.412205\pi\)
0.272333 + 0.962203i \(0.412205\pi\)
\(20\) 2.01405 0.450356
\(21\) −5.64052 −1.23086
\(22\) −3.70387 −0.789669
\(23\) −2.90483 −0.605698 −0.302849 0.953038i \(-0.597938\pi\)
−0.302849 + 0.953038i \(0.597938\pi\)
\(24\) −2.49412 −0.509110
\(25\) −0.943592 −0.188718
\(26\) −3.55865 −0.697908
\(27\) −0.550262 −0.105898
\(28\) 2.26153 0.427389
\(29\) 5.51423 1.02397 0.511983 0.858995i \(-0.328911\pi\)
0.511983 + 0.858995i \(0.328911\pi\)
\(30\) −5.02328 −0.917122
\(31\) −6.05211 −1.08699 −0.543495 0.839412i \(-0.682899\pi\)
−0.543495 + 0.839412i \(0.682899\pi\)
\(32\) 1.00000 0.176777
\(33\) 9.23790 1.60811
\(34\) 6.88697 1.18111
\(35\) 4.55484 0.769909
\(36\) 3.22062 0.536771
\(37\) 4.05981 0.667428 0.333714 0.942674i \(-0.391698\pi\)
0.333714 + 0.942674i \(0.391698\pi\)
\(38\) 2.37414 0.385136
\(39\) 8.87569 1.42125
\(40\) 2.01405 0.318450
\(41\) 5.33998 0.833964 0.416982 0.908915i \(-0.363088\pi\)
0.416982 + 0.908915i \(0.363088\pi\)
\(42\) −5.64052 −0.870351
\(43\) −1.25313 −0.191101 −0.0955505 0.995425i \(-0.530461\pi\)
−0.0955505 + 0.995425i \(0.530461\pi\)
\(44\) −3.70387 −0.558380
\(45\) 6.48651 0.966951
\(46\) −2.90483 −0.428293
\(47\) 6.32993 0.923315 0.461658 0.887058i \(-0.347255\pi\)
0.461658 + 0.887058i \(0.347255\pi\)
\(48\) −2.49412 −0.359995
\(49\) −1.88548 −0.269355
\(50\) −0.943592 −0.133444
\(51\) −17.1769 −2.40525
\(52\) −3.55865 −0.493496
\(53\) 12.2322 1.68023 0.840114 0.542410i \(-0.182488\pi\)
0.840114 + 0.542410i \(0.182488\pi\)
\(54\) −0.550262 −0.0748811
\(55\) −7.45980 −1.00588
\(56\) 2.26153 0.302210
\(57\) −5.92139 −0.784307
\(58\) 5.51423 0.724054
\(59\) −4.09159 −0.532679 −0.266340 0.963879i \(-0.585814\pi\)
−0.266340 + 0.963879i \(0.585814\pi\)
\(60\) −5.02328 −0.648503
\(61\) 2.55932 0.327687 0.163843 0.986486i \(-0.447611\pi\)
0.163843 + 0.986486i \(0.447611\pi\)
\(62\) −6.05211 −0.768618
\(63\) 7.28354 0.917639
\(64\) 1.00000 0.125000
\(65\) −7.16730 −0.888994
\(66\) 9.23790 1.13711
\(67\) 15.7411 1.92308 0.961540 0.274665i \(-0.0885668\pi\)
0.961540 + 0.274665i \(0.0885668\pi\)
\(68\) 6.88697 0.835168
\(69\) 7.24498 0.872193
\(70\) 4.55484 0.544408
\(71\) 0.641025 0.0760757 0.0380379 0.999276i \(-0.487889\pi\)
0.0380379 + 0.999276i \(0.487889\pi\)
\(72\) 3.22062 0.379554
\(73\) −8.54143 −0.999699 −0.499849 0.866112i \(-0.666611\pi\)
−0.499849 + 0.866112i \(0.666611\pi\)
\(74\) 4.05981 0.471943
\(75\) 2.35343 0.271751
\(76\) 2.37414 0.272333
\(77\) −8.37642 −0.954582
\(78\) 8.87569 1.00497
\(79\) 2.47415 0.278363 0.139182 0.990267i \(-0.455553\pi\)
0.139182 + 0.990267i \(0.455553\pi\)
\(80\) 2.01405 0.225178
\(81\) −8.28945 −0.921050
\(82\) 5.33998 0.589702
\(83\) 5.59401 0.614022 0.307011 0.951706i \(-0.400671\pi\)
0.307011 + 0.951706i \(0.400671\pi\)
\(84\) −5.64052 −0.615431
\(85\) 13.8707 1.50449
\(86\) −1.25313 −0.135129
\(87\) −13.7531 −1.47449
\(88\) −3.70387 −0.394834
\(89\) 8.40142 0.890549 0.445275 0.895394i \(-0.353106\pi\)
0.445275 + 0.895394i \(0.353106\pi\)
\(90\) 6.48651 0.683738
\(91\) −8.04799 −0.843658
\(92\) −2.90483 −0.302849
\(93\) 15.0947 1.56524
\(94\) 6.32993 0.652882
\(95\) 4.78164 0.490586
\(96\) −2.49412 −0.254555
\(97\) −7.21256 −0.732324 −0.366162 0.930551i \(-0.619328\pi\)
−0.366162 + 0.930551i \(0.619328\pi\)
\(98\) −1.88548 −0.190462
\(99\) −11.9288 −1.19889
\(100\) −0.943592 −0.0943592
\(101\) −6.35568 −0.632414 −0.316207 0.948690i \(-0.602409\pi\)
−0.316207 + 0.948690i \(0.602409\pi\)
\(102\) −17.1769 −1.70077
\(103\) −11.2162 −1.10516 −0.552582 0.833459i \(-0.686357\pi\)
−0.552582 + 0.833459i \(0.686357\pi\)
\(104\) −3.55865 −0.348954
\(105\) −11.3603 −1.10865
\(106\) 12.2322 1.18810
\(107\) −13.6183 −1.31653 −0.658267 0.752785i \(-0.728710\pi\)
−0.658267 + 0.752785i \(0.728710\pi\)
\(108\) −0.550262 −0.0529490
\(109\) 0.0239725 0.00229615 0.00114807 0.999999i \(-0.499635\pi\)
0.00114807 + 0.999999i \(0.499635\pi\)
\(110\) −7.45980 −0.711264
\(111\) −10.1256 −0.961083
\(112\) 2.26153 0.213694
\(113\) 20.2362 1.90366 0.951831 0.306624i \(-0.0991994\pi\)
0.951831 + 0.306624i \(0.0991994\pi\)
\(114\) −5.92139 −0.554589
\(115\) −5.85048 −0.545560
\(116\) 5.51423 0.511983
\(117\) −11.4611 −1.05958
\(118\) −4.09159 −0.376661
\(119\) 15.5751 1.42777
\(120\) −5.02328 −0.458561
\(121\) 2.71868 0.247153
\(122\) 2.55932 0.231710
\(123\) −13.3185 −1.20089
\(124\) −6.05211 −0.543495
\(125\) −11.9707 −1.07069
\(126\) 7.28354 0.648869
\(127\) −15.7777 −1.40004 −0.700022 0.714121i \(-0.746826\pi\)
−0.700022 + 0.714121i \(0.746826\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.12546 0.275182
\(130\) −7.16730 −0.628614
\(131\) −5.27108 −0.460536 −0.230268 0.973127i \(-0.573960\pi\)
−0.230268 + 0.973127i \(0.573960\pi\)
\(132\) 9.23790 0.804056
\(133\) 5.36919 0.465568
\(134\) 15.7411 1.35982
\(135\) −1.10826 −0.0953835
\(136\) 6.88697 0.590553
\(137\) 14.6575 1.25228 0.626138 0.779712i \(-0.284635\pi\)
0.626138 + 0.779712i \(0.284635\pi\)
\(138\) 7.24498 0.616734
\(139\) 21.7180 1.84210 0.921048 0.389448i \(-0.127334\pi\)
0.921048 + 0.389448i \(0.127334\pi\)
\(140\) 4.55484 0.384954
\(141\) −15.7876 −1.32956
\(142\) 0.641025 0.0537937
\(143\) 13.1808 1.10223
\(144\) 3.22062 0.268385
\(145\) 11.1059 0.922299
\(146\) −8.54143 −0.706894
\(147\) 4.70261 0.387865
\(148\) 4.05981 0.333714
\(149\) 19.8344 1.62490 0.812449 0.583032i \(-0.198134\pi\)
0.812449 + 0.583032i \(0.198134\pi\)
\(150\) 2.35343 0.192157
\(151\) −4.66734 −0.379823 −0.189911 0.981801i \(-0.560820\pi\)
−0.189911 + 0.981801i \(0.560820\pi\)
\(152\) 2.37414 0.192568
\(153\) 22.1803 1.79317
\(154\) −8.37642 −0.674991
\(155\) −12.1893 −0.979065
\(156\) 8.87569 0.710624
\(157\) 21.6430 1.72730 0.863652 0.504089i \(-0.168172\pi\)
0.863652 + 0.504089i \(0.168172\pi\)
\(158\) 2.47415 0.196833
\(159\) −30.5087 −2.41949
\(160\) 2.01405 0.159225
\(161\) −6.56935 −0.517738
\(162\) −8.28945 −0.651281
\(163\) 10.8339 0.848576 0.424288 0.905527i \(-0.360524\pi\)
0.424288 + 0.905527i \(0.360524\pi\)
\(164\) 5.33998 0.416982
\(165\) 18.6056 1.44845
\(166\) 5.59401 0.434179
\(167\) 13.3377 1.03211 0.516053 0.856557i \(-0.327401\pi\)
0.516053 + 0.856557i \(0.327401\pi\)
\(168\) −5.64052 −0.435176
\(169\) −0.336031 −0.0258485
\(170\) 13.8707 1.06384
\(171\) 7.64621 0.584721
\(172\) −1.25313 −0.0955505
\(173\) −22.9937 −1.74818 −0.874088 0.485767i \(-0.838540\pi\)
−0.874088 + 0.485767i \(0.838540\pi\)
\(174\) −13.7531 −1.04262
\(175\) −2.13396 −0.161312
\(176\) −3.70387 −0.279190
\(177\) 10.2049 0.767047
\(178\) 8.40142 0.629713
\(179\) 0.526188 0.0393292 0.0196646 0.999807i \(-0.493740\pi\)
0.0196646 + 0.999807i \(0.493740\pi\)
\(180\) 6.48651 0.483476
\(181\) 22.4799 1.67092 0.835460 0.549551i \(-0.185201\pi\)
0.835460 + 0.549551i \(0.185201\pi\)
\(182\) −8.04799 −0.596556
\(183\) −6.38323 −0.471862
\(184\) −2.90483 −0.214147
\(185\) 8.17666 0.601160
\(186\) 15.0947 1.10679
\(187\) −25.5085 −1.86536
\(188\) 6.32993 0.461658
\(189\) −1.24443 −0.0905192
\(190\) 4.78164 0.346897
\(191\) 11.3651 0.822349 0.411175 0.911557i \(-0.365119\pi\)
0.411175 + 0.911557i \(0.365119\pi\)
\(192\) −2.49412 −0.179997
\(193\) −6.87508 −0.494879 −0.247440 0.968903i \(-0.579589\pi\)
−0.247440 + 0.968903i \(0.579589\pi\)
\(194\) −7.21256 −0.517832
\(195\) 17.8761 1.28013
\(196\) −1.88548 −0.134677
\(197\) 19.5956 1.39613 0.698064 0.716035i \(-0.254045\pi\)
0.698064 + 0.716035i \(0.254045\pi\)
\(198\) −11.9288 −0.847742
\(199\) 21.9514 1.55609 0.778045 0.628208i \(-0.216211\pi\)
0.778045 + 0.628208i \(0.216211\pi\)
\(200\) −0.943592 −0.0667220
\(201\) −39.2601 −2.76920
\(202\) −6.35568 −0.447184
\(203\) 12.4706 0.875264
\(204\) −17.1769 −1.20262
\(205\) 10.7550 0.751162
\(206\) −11.2162 −0.781469
\(207\) −9.35536 −0.650242
\(208\) −3.55865 −0.246748
\(209\) −8.79352 −0.608260
\(210\) −11.3603 −0.783936
\(211\) 2.41930 0.166551 0.0832757 0.996527i \(-0.473462\pi\)
0.0832757 + 0.996527i \(0.473462\pi\)
\(212\) 12.2322 0.840114
\(213\) −1.59879 −0.109547
\(214\) −13.6183 −0.930930
\(215\) −2.52388 −0.172127
\(216\) −0.550262 −0.0374406
\(217\) −13.6870 −0.929135
\(218\) 0.0239725 0.00162362
\(219\) 21.3033 1.43955
\(220\) −7.45980 −0.502939
\(221\) −24.5083 −1.64861
\(222\) −10.1256 −0.679588
\(223\) 23.7336 1.58932 0.794660 0.607055i \(-0.207649\pi\)
0.794660 + 0.607055i \(0.207649\pi\)
\(224\) 2.26153 0.151105
\(225\) −3.03895 −0.202597
\(226\) 20.2362 1.34609
\(227\) 3.74598 0.248629 0.124315 0.992243i \(-0.460327\pi\)
0.124315 + 0.992243i \(0.460327\pi\)
\(228\) −5.92139 −0.392153
\(229\) −6.05569 −0.400171 −0.200085 0.979778i \(-0.564122\pi\)
−0.200085 + 0.979778i \(0.564122\pi\)
\(230\) −5.85048 −0.385769
\(231\) 20.8918 1.37458
\(232\) 5.51423 0.362027
\(233\) −4.78829 −0.313691 −0.156846 0.987623i \(-0.550133\pi\)
−0.156846 + 0.987623i \(0.550133\pi\)
\(234\) −11.4611 −0.749233
\(235\) 12.7488 0.831641
\(236\) −4.09159 −0.266340
\(237\) −6.17081 −0.400837
\(238\) 15.5751 1.00958
\(239\) −23.7507 −1.53630 −0.768151 0.640268i \(-0.778823\pi\)
−0.768151 + 0.640268i \(0.778823\pi\)
\(240\) −5.02328 −0.324252
\(241\) 14.2155 0.915700 0.457850 0.889029i \(-0.348620\pi\)
0.457850 + 0.889029i \(0.348620\pi\)
\(242\) 2.71868 0.174764
\(243\) 22.3257 1.43219
\(244\) 2.55932 0.163843
\(245\) −3.79746 −0.242611
\(246\) −13.3185 −0.849159
\(247\) −8.44873 −0.537580
\(248\) −6.05211 −0.384309
\(249\) −13.9521 −0.884179
\(250\) −11.9707 −0.757094
\(251\) −0.0817027 −0.00515703 −0.00257852 0.999997i \(-0.500821\pi\)
−0.00257852 + 0.999997i \(0.500821\pi\)
\(252\) 7.28354 0.458820
\(253\) 10.7591 0.676420
\(254\) −15.7777 −0.989980
\(255\) −34.5952 −2.16644
\(256\) 1.00000 0.0625000
\(257\) −8.34170 −0.520341 −0.260171 0.965563i \(-0.583779\pi\)
−0.260171 + 0.965563i \(0.583779\pi\)
\(258\) 3.12546 0.194583
\(259\) 9.18137 0.570503
\(260\) −7.16730 −0.444497
\(261\) 17.7593 1.09927
\(262\) −5.27108 −0.325648
\(263\) −5.21436 −0.321531 −0.160766 0.986993i \(-0.551396\pi\)
−0.160766 + 0.986993i \(0.551396\pi\)
\(264\) 9.23790 0.568553
\(265\) 24.6364 1.51340
\(266\) 5.36919 0.329206
\(267\) −20.9541 −1.28237
\(268\) 15.7411 0.961540
\(269\) −8.22161 −0.501280 −0.250640 0.968080i \(-0.580641\pi\)
−0.250640 + 0.968080i \(0.580641\pi\)
\(270\) −1.10826 −0.0674463
\(271\) −15.5448 −0.944279 −0.472140 0.881524i \(-0.656518\pi\)
−0.472140 + 0.881524i \(0.656518\pi\)
\(272\) 6.88697 0.417584
\(273\) 20.0726 1.21485
\(274\) 14.6575 0.885493
\(275\) 3.49494 0.210753
\(276\) 7.24498 0.436097
\(277\) −12.3455 −0.741768 −0.370884 0.928679i \(-0.620945\pi\)
−0.370884 + 0.928679i \(0.620945\pi\)
\(278\) 21.7180 1.30256
\(279\) −19.4916 −1.16693
\(280\) 4.55484 0.272204
\(281\) 10.2175 0.609523 0.304761 0.952429i \(-0.401423\pi\)
0.304761 + 0.952429i \(0.401423\pi\)
\(282\) −15.7876 −0.940137
\(283\) 17.1257 1.01802 0.509010 0.860761i \(-0.330012\pi\)
0.509010 + 0.860761i \(0.330012\pi\)
\(284\) 0.641025 0.0380379
\(285\) −11.9260 −0.706434
\(286\) 13.1808 0.779396
\(287\) 12.0765 0.712854
\(288\) 3.22062 0.189777
\(289\) 30.4304 1.79002
\(290\) 11.1059 0.652164
\(291\) 17.9890 1.05453
\(292\) −8.54143 −0.499849
\(293\) −1.28713 −0.0751952 −0.0375976 0.999293i \(-0.511971\pi\)
−0.0375976 + 0.999293i \(0.511971\pi\)
\(294\) 4.70261 0.274262
\(295\) −8.24067 −0.479790
\(296\) 4.05981 0.235971
\(297\) 2.03810 0.118263
\(298\) 19.8344 1.14898
\(299\) 10.3373 0.597819
\(300\) 2.35343 0.135875
\(301\) −2.83400 −0.163349
\(302\) −4.66734 −0.268575
\(303\) 15.8518 0.910663
\(304\) 2.37414 0.136166
\(305\) 5.15460 0.295151
\(306\) 22.1803 1.26797
\(307\) −2.79331 −0.159423 −0.0797113 0.996818i \(-0.525400\pi\)
−0.0797113 + 0.996818i \(0.525400\pi\)
\(308\) −8.37642 −0.477291
\(309\) 27.9745 1.59141
\(310\) −12.1893 −0.692304
\(311\) −23.6621 −1.34175 −0.670877 0.741569i \(-0.734082\pi\)
−0.670877 + 0.741569i \(0.734082\pi\)
\(312\) 8.87569 0.502487
\(313\) 18.7782 1.06140 0.530702 0.847558i \(-0.321928\pi\)
0.530702 + 0.847558i \(0.321928\pi\)
\(314\) 21.6430 1.22139
\(315\) 14.6694 0.826529
\(316\) 2.47415 0.139182
\(317\) 22.9427 1.28859 0.644295 0.764777i \(-0.277151\pi\)
0.644295 + 0.764777i \(0.277151\pi\)
\(318\) −30.5087 −1.71084
\(319\) −20.4240 −1.14353
\(320\) 2.01405 0.112589
\(321\) 33.9657 1.89578
\(322\) −6.56935 −0.366096
\(323\) 16.3506 0.909774
\(324\) −8.28945 −0.460525
\(325\) 3.35791 0.186263
\(326\) 10.8339 0.600034
\(327\) −0.0597902 −0.00330641
\(328\) 5.33998 0.294851
\(329\) 14.3153 0.789230
\(330\) 18.6056 1.02421
\(331\) 1.57418 0.0865249 0.0432625 0.999064i \(-0.486225\pi\)
0.0432625 + 0.999064i \(0.486225\pi\)
\(332\) 5.59401 0.307011
\(333\) 13.0751 0.716511
\(334\) 13.3377 0.729809
\(335\) 31.7034 1.73214
\(336\) −5.64052 −0.307716
\(337\) −0.477872 −0.0260313 −0.0130157 0.999915i \(-0.504143\pi\)
−0.0130157 + 0.999915i \(0.504143\pi\)
\(338\) −0.336031 −0.0182777
\(339\) −50.4715 −2.74123
\(340\) 13.8707 0.752246
\(341\) 22.4162 1.21391
\(342\) 7.64621 0.413460
\(343\) −20.0948 −1.08502
\(344\) −1.25313 −0.0675644
\(345\) 14.5918 0.785595
\(346\) −22.9937 −1.23615
\(347\) −20.1302 −1.08064 −0.540322 0.841458i \(-0.681698\pi\)
−0.540322 + 0.841458i \(0.681698\pi\)
\(348\) −13.7531 −0.737246
\(349\) 15.7844 0.844920 0.422460 0.906382i \(-0.361167\pi\)
0.422460 + 0.906382i \(0.361167\pi\)
\(350\) −2.13396 −0.114065
\(351\) 1.95819 0.104520
\(352\) −3.70387 −0.197417
\(353\) 16.6971 0.888696 0.444348 0.895854i \(-0.353435\pi\)
0.444348 + 0.895854i \(0.353435\pi\)
\(354\) 10.2049 0.542384
\(355\) 1.29106 0.0685223
\(356\) 8.40142 0.445275
\(357\) −38.8461 −2.05595
\(358\) 0.526188 0.0278099
\(359\) −28.5977 −1.50933 −0.754663 0.656112i \(-0.772200\pi\)
−0.754663 + 0.656112i \(0.772200\pi\)
\(360\) 6.48651 0.341869
\(361\) −13.3635 −0.703340
\(362\) 22.4799 1.18152
\(363\) −6.78071 −0.355895
\(364\) −8.04799 −0.421829
\(365\) −17.2029 −0.900441
\(366\) −6.38323 −0.333657
\(367\) 1.18623 0.0619208 0.0309604 0.999521i \(-0.490143\pi\)
0.0309604 + 0.999521i \(0.490143\pi\)
\(368\) −2.90483 −0.151425
\(369\) 17.1981 0.895295
\(370\) 8.17666 0.425084
\(371\) 27.6636 1.43622
\(372\) 15.0947 0.782622
\(373\) −2.98533 −0.154574 −0.0772872 0.997009i \(-0.524626\pi\)
−0.0772872 + 0.997009i \(0.524626\pi\)
\(374\) −25.5085 −1.31901
\(375\) 29.8564 1.54178
\(376\) 6.32993 0.326441
\(377\) −19.6232 −1.01065
\(378\) −1.24443 −0.0640067
\(379\) 3.12466 0.160503 0.0802516 0.996775i \(-0.474428\pi\)
0.0802516 + 0.996775i \(0.474428\pi\)
\(380\) 4.78164 0.245293
\(381\) 39.3514 2.01603
\(382\) 11.3651 0.581489
\(383\) −9.08236 −0.464087 −0.232044 0.972705i \(-0.574541\pi\)
−0.232044 + 0.972705i \(0.574541\pi\)
\(384\) −2.49412 −0.127277
\(385\) −16.8706 −0.859803
\(386\) −6.87508 −0.349932
\(387\) −4.03587 −0.205155
\(388\) −7.21256 −0.366162
\(389\) −28.3345 −1.43661 −0.718307 0.695726i \(-0.755083\pi\)
−0.718307 + 0.695726i \(0.755083\pi\)
\(390\) 17.8761 0.905191
\(391\) −20.0055 −1.01172
\(392\) −1.88548 −0.0952312
\(393\) 13.1467 0.663163
\(394\) 19.5956 0.987212
\(395\) 4.98306 0.250725
\(396\) −11.9288 −0.599444
\(397\) 18.5496 0.930976 0.465488 0.885054i \(-0.345879\pi\)
0.465488 + 0.885054i \(0.345879\pi\)
\(398\) 21.9514 1.10032
\(399\) −13.3914 −0.670408
\(400\) −0.943592 −0.0471796
\(401\) −0.135001 −0.00674164 −0.00337082 0.999994i \(-0.501073\pi\)
−0.00337082 + 0.999994i \(0.501073\pi\)
\(402\) −39.2601 −1.95812
\(403\) 21.5373 1.07285
\(404\) −6.35568 −0.316207
\(405\) −16.6954 −0.829601
\(406\) 12.4706 0.618905
\(407\) −15.0370 −0.745357
\(408\) −17.1769 −0.850384
\(409\) 25.1046 1.24134 0.620672 0.784070i \(-0.286860\pi\)
0.620672 + 0.784070i \(0.286860\pi\)
\(410\) 10.7550 0.531151
\(411\) −36.5576 −1.80325
\(412\) −11.2162 −0.552582
\(413\) −9.25325 −0.455322
\(414\) −9.35536 −0.459791
\(415\) 11.2666 0.553057
\(416\) −3.55865 −0.174477
\(417\) −54.1672 −2.65258
\(418\) −8.79352 −0.430105
\(419\) 27.8624 1.36117 0.680585 0.732669i \(-0.261726\pi\)
0.680585 + 0.732669i \(0.261726\pi\)
\(420\) −11.3603 −0.554326
\(421\) 20.2765 0.988215 0.494107 0.869401i \(-0.335495\pi\)
0.494107 + 0.869401i \(0.335495\pi\)
\(422\) 2.41930 0.117770
\(423\) 20.3863 0.991217
\(424\) 12.2322 0.594050
\(425\) −6.49849 −0.315223
\(426\) −1.59879 −0.0774618
\(427\) 5.78797 0.280099
\(428\) −13.6183 −0.658267
\(429\) −32.8744 −1.58719
\(430\) −2.52388 −0.121712
\(431\) 17.8164 0.858183 0.429092 0.903261i \(-0.358834\pi\)
0.429092 + 0.903261i \(0.358834\pi\)
\(432\) −0.550262 −0.0264745
\(433\) −36.7403 −1.76563 −0.882814 0.469722i \(-0.844354\pi\)
−0.882814 + 0.469722i \(0.844354\pi\)
\(434\) −13.6870 −0.656998
\(435\) −27.6995 −1.32809
\(436\) 0.0239725 0.00114807
\(437\) −6.89647 −0.329903
\(438\) 21.3033 1.01791
\(439\) −27.3337 −1.30456 −0.652282 0.757976i \(-0.726188\pi\)
−0.652282 + 0.757976i \(0.726188\pi\)
\(440\) −7.45980 −0.355632
\(441\) −6.07243 −0.289163
\(442\) −24.5083 −1.16574
\(443\) 11.9975 0.570020 0.285010 0.958524i \(-0.408003\pi\)
0.285010 + 0.958524i \(0.408003\pi\)
\(444\) −10.1256 −0.480541
\(445\) 16.9209 0.802128
\(446\) 23.7336 1.12382
\(447\) −49.4694 −2.33982
\(448\) 2.26153 0.106847
\(449\) −31.4885 −1.48603 −0.743017 0.669272i \(-0.766606\pi\)
−0.743017 + 0.669272i \(0.766606\pi\)
\(450\) −3.03895 −0.143258
\(451\) −19.7786 −0.931338
\(452\) 20.2362 0.951831
\(453\) 11.6409 0.546937
\(454\) 3.74598 0.175808
\(455\) −16.2091 −0.759893
\(456\) −5.92139 −0.277294
\(457\) −5.43642 −0.254305 −0.127153 0.991883i \(-0.540584\pi\)
−0.127153 + 0.991883i \(0.540584\pi\)
\(458\) −6.05569 −0.282964
\(459\) −3.78964 −0.176885
\(460\) −5.85048 −0.272780
\(461\) −0.418075 −0.0194717 −0.00973585 0.999953i \(-0.503099\pi\)
−0.00973585 + 0.999953i \(0.503099\pi\)
\(462\) 20.8918 0.971974
\(463\) 2.04479 0.0950296 0.0475148 0.998871i \(-0.484870\pi\)
0.0475148 + 0.998871i \(0.484870\pi\)
\(464\) 5.51423 0.255992
\(465\) 30.4015 1.40983
\(466\) −4.78829 −0.221813
\(467\) −35.7920 −1.65626 −0.828129 0.560538i \(-0.810594\pi\)
−0.828129 + 0.560538i \(0.810594\pi\)
\(468\) −11.4611 −0.529788
\(469\) 35.5989 1.64381
\(470\) 12.7488 0.588059
\(471\) −53.9803 −2.48728
\(472\) −4.09159 −0.188331
\(473\) 4.64145 0.213414
\(474\) −6.17081 −0.283435
\(475\) −2.24022 −0.102788
\(476\) 15.5751 0.713883
\(477\) 39.3955 1.80379
\(478\) −23.7507 −1.08633
\(479\) 4.99316 0.228143 0.114072 0.993473i \(-0.463611\pi\)
0.114072 + 0.993473i \(0.463611\pi\)
\(480\) −5.02328 −0.229281
\(481\) −14.4474 −0.658745
\(482\) 14.2155 0.647498
\(483\) 16.3847 0.745532
\(484\) 2.71868 0.123576
\(485\) −14.5265 −0.659613
\(486\) 22.3257 1.01271
\(487\) −9.48550 −0.429829 −0.214915 0.976633i \(-0.568947\pi\)
−0.214915 + 0.976633i \(0.568947\pi\)
\(488\) 2.55932 0.115855
\(489\) −27.0210 −1.22193
\(490\) −3.79746 −0.171552
\(491\) 33.4510 1.50962 0.754811 0.655942i \(-0.227729\pi\)
0.754811 + 0.655942i \(0.227729\pi\)
\(492\) −13.3185 −0.600446
\(493\) 37.9763 1.71037
\(494\) −8.44873 −0.380126
\(495\) −24.0252 −1.07985
\(496\) −6.05211 −0.271748
\(497\) 1.44970 0.0650278
\(498\) −13.9521 −0.625209
\(499\) 26.4188 1.18267 0.591334 0.806426i \(-0.298601\pi\)
0.591334 + 0.806426i \(0.298601\pi\)
\(500\) −11.9707 −0.535346
\(501\) −33.2659 −1.48621
\(502\) −0.0817027 −0.00364657
\(503\) −34.0270 −1.51719 −0.758594 0.651564i \(-0.774113\pi\)
−0.758594 + 0.651564i \(0.774113\pi\)
\(504\) 7.28354 0.324435
\(505\) −12.8007 −0.569623
\(506\) 10.7591 0.478301
\(507\) 0.838101 0.0372214
\(508\) −15.7777 −0.700022
\(509\) 26.3595 1.16836 0.584182 0.811623i \(-0.301415\pi\)
0.584182 + 0.811623i \(0.301415\pi\)
\(510\) −34.5952 −1.53190
\(511\) −19.3167 −0.854521
\(512\) 1.00000 0.0441942
\(513\) −1.30640 −0.0576789
\(514\) −8.34170 −0.367937
\(515\) −22.5900 −0.995434
\(516\) 3.12546 0.137591
\(517\) −23.4453 −1.03112
\(518\) 9.18137 0.403406
\(519\) 57.3489 2.51734
\(520\) −7.16730 −0.314307
\(521\) −43.5700 −1.90883 −0.954417 0.298476i \(-0.903522\pi\)
−0.954417 + 0.298476i \(0.903522\pi\)
\(522\) 17.7593 0.777302
\(523\) −26.7780 −1.17092 −0.585461 0.810701i \(-0.699086\pi\)
−0.585461 + 0.810701i \(0.699086\pi\)
\(524\) −5.27108 −0.230268
\(525\) 5.32235 0.232286
\(526\) −5.21436 −0.227357
\(527\) −41.6807 −1.81564
\(528\) 9.23790 0.402028
\(529\) −14.5620 −0.633129
\(530\) 24.6364 1.07014
\(531\) −13.1775 −0.571853
\(532\) 5.36919 0.232784
\(533\) −19.0031 −0.823116
\(534\) −20.9541 −0.906774
\(535\) −27.4280 −1.18582
\(536\) 15.7411 0.679912
\(537\) −1.31238 −0.0566332
\(538\) −8.22161 −0.354459
\(539\) 6.98359 0.300804
\(540\) −1.10826 −0.0476917
\(541\) −27.6992 −1.19088 −0.595441 0.803399i \(-0.703023\pi\)
−0.595441 + 0.803399i \(0.703023\pi\)
\(542\) −15.5448 −0.667706
\(543\) −56.0676 −2.40609
\(544\) 6.88697 0.295276
\(545\) 0.0482819 0.00206817
\(546\) 20.0726 0.859029
\(547\) −2.36790 −0.101244 −0.0506222 0.998718i \(-0.516120\pi\)
−0.0506222 + 0.998718i \(0.516120\pi\)
\(548\) 14.6575 0.626138
\(549\) 8.24259 0.351785
\(550\) 3.49494 0.149025
\(551\) 13.0916 0.557719
\(552\) 7.24498 0.308367
\(553\) 5.59536 0.237939
\(554\) −12.3455 −0.524509
\(555\) −20.3936 −0.865658
\(556\) 21.7180 0.921048
\(557\) −23.7533 −1.00646 −0.503231 0.864152i \(-0.667855\pi\)
−0.503231 + 0.864152i \(0.667855\pi\)
\(558\) −19.4916 −0.825143
\(559\) 4.45946 0.188615
\(560\) 4.55484 0.192477
\(561\) 63.6211 2.68609
\(562\) 10.2175 0.430998
\(563\) −15.8021 −0.665980 −0.332990 0.942930i \(-0.608058\pi\)
−0.332990 + 0.942930i \(0.608058\pi\)
\(564\) −15.7876 −0.664778
\(565\) 40.7568 1.71465
\(566\) 17.1257 0.719848
\(567\) −18.7468 −0.787294
\(568\) 0.641025 0.0268968
\(569\) −9.81604 −0.411510 −0.205755 0.978604i \(-0.565965\pi\)
−0.205755 + 0.978604i \(0.565965\pi\)
\(570\) −11.9260 −0.499525
\(571\) −23.6515 −0.989785 −0.494892 0.868954i \(-0.664792\pi\)
−0.494892 + 0.868954i \(0.664792\pi\)
\(572\) 13.1808 0.551116
\(573\) −28.3459 −1.18417
\(574\) 12.0765 0.504064
\(575\) 2.74097 0.114306
\(576\) 3.22062 0.134193
\(577\) −12.9868 −0.540646 −0.270323 0.962770i \(-0.587130\pi\)
−0.270323 + 0.962770i \(0.587130\pi\)
\(578\) 30.4304 1.26574
\(579\) 17.1473 0.712616
\(580\) 11.1059 0.461149
\(581\) 12.6510 0.524852
\(582\) 17.9890 0.745667
\(583\) −45.3067 −1.87641
\(584\) −8.54143 −0.353447
\(585\) −23.0832 −0.954372
\(586\) −1.28713 −0.0531710
\(587\) 35.9740 1.48480 0.742402 0.669955i \(-0.233686\pi\)
0.742402 + 0.669955i \(0.233686\pi\)
\(588\) 4.70261 0.193933
\(589\) −14.3686 −0.592046
\(590\) −8.24067 −0.339263
\(591\) −48.8737 −2.01040
\(592\) 4.05981 0.166857
\(593\) −6.08419 −0.249848 −0.124924 0.992166i \(-0.539869\pi\)
−0.124924 + 0.992166i \(0.539869\pi\)
\(594\) 2.03810 0.0836243
\(595\) 31.3691 1.28601
\(596\) 19.8344 0.812449
\(597\) −54.7493 −2.24074
\(598\) 10.3373 0.422722
\(599\) 4.09711 0.167403 0.0837016 0.996491i \(-0.473326\pi\)
0.0837016 + 0.996491i \(0.473326\pi\)
\(600\) 2.35343 0.0960783
\(601\) 40.1134 1.63626 0.818130 0.575033i \(-0.195011\pi\)
0.818130 + 0.575033i \(0.195011\pi\)
\(602\) −2.83400 −0.115505
\(603\) 50.6961 2.06451
\(604\) −4.66734 −0.189911
\(605\) 5.47557 0.222614
\(606\) 15.8518 0.643936
\(607\) −43.2460 −1.75530 −0.877652 0.479299i \(-0.840891\pi\)
−0.877652 + 0.479299i \(0.840891\pi\)
\(608\) 2.37414 0.0962841
\(609\) −31.1031 −1.26036
\(610\) 5.15460 0.208704
\(611\) −22.5260 −0.911304
\(612\) 22.1803 0.896587
\(613\) 20.9795 0.847356 0.423678 0.905813i \(-0.360739\pi\)
0.423678 + 0.905813i \(0.360739\pi\)
\(614\) −2.79331 −0.112729
\(615\) −26.8242 −1.08166
\(616\) −8.37642 −0.337496
\(617\) 41.0688 1.65337 0.826684 0.562666i \(-0.190224\pi\)
0.826684 + 0.562666i \(0.190224\pi\)
\(618\) 27.9745 1.12530
\(619\) 35.2143 1.41538 0.707691 0.706522i \(-0.249737\pi\)
0.707691 + 0.706522i \(0.249737\pi\)
\(620\) −12.1893 −0.489533
\(621\) 1.59842 0.0641422
\(622\) −23.6621 −0.948763
\(623\) 19.0001 0.761222
\(624\) 8.87569 0.355312
\(625\) −19.3917 −0.775667
\(626\) 18.7782 0.750526
\(627\) 21.9321 0.875882
\(628\) 21.6430 0.863652
\(629\) 27.9598 1.11483
\(630\) 14.6694 0.584444
\(631\) −19.4169 −0.772975 −0.386488 0.922295i \(-0.626312\pi\)
−0.386488 + 0.922295i \(0.626312\pi\)
\(632\) 2.47415 0.0984163
\(633\) −6.03401 −0.239830
\(634\) 22.9427 0.911171
\(635\) −31.7771 −1.26104
\(636\) −30.5087 −1.20975
\(637\) 6.70977 0.265851
\(638\) −20.4240 −0.808594
\(639\) 2.06450 0.0816704
\(640\) 2.01405 0.0796124
\(641\) 2.74610 0.108464 0.0542322 0.998528i \(-0.482729\pi\)
0.0542322 + 0.998528i \(0.482729\pi\)
\(642\) 33.9657 1.34052
\(643\) 20.4085 0.804833 0.402417 0.915457i \(-0.368170\pi\)
0.402417 + 0.915457i \(0.368170\pi\)
\(644\) −6.56935 −0.258869
\(645\) 6.29485 0.247859
\(646\) 16.3506 0.643307
\(647\) −15.2695 −0.600305 −0.300152 0.953891i \(-0.597038\pi\)
−0.300152 + 0.953891i \(0.597038\pi\)
\(648\) −8.28945 −0.325641
\(649\) 15.1547 0.594875
\(650\) 3.35791 0.131708
\(651\) 34.1370 1.33794
\(652\) 10.8339 0.424288
\(653\) −45.6646 −1.78699 −0.893497 0.449070i \(-0.851755\pi\)
−0.893497 + 0.449070i \(0.851755\pi\)
\(654\) −0.0597902 −0.00233798
\(655\) −10.6162 −0.414810
\(656\) 5.33998 0.208491
\(657\) −27.5087 −1.07322
\(658\) 14.3153 0.558070
\(659\) 13.9482 0.543344 0.271672 0.962390i \(-0.412423\pi\)
0.271672 + 0.962390i \(0.412423\pi\)
\(660\) 18.6056 0.724223
\(661\) 30.9262 1.20289 0.601445 0.798914i \(-0.294592\pi\)
0.601445 + 0.798914i \(0.294592\pi\)
\(662\) 1.57418 0.0611824
\(663\) 61.1266 2.37396
\(664\) 5.59401 0.217090
\(665\) 10.8138 0.419342
\(666\) 13.0751 0.506650
\(667\) −16.0179 −0.620215
\(668\) 13.3377 0.516053
\(669\) −59.1944 −2.28859
\(670\) 31.7034 1.22481
\(671\) −9.47938 −0.365947
\(672\) −5.64052 −0.217588
\(673\) −9.57022 −0.368905 −0.184452 0.982841i \(-0.559051\pi\)
−0.184452 + 0.982841i \(0.559051\pi\)
\(674\) −0.477872 −0.0184069
\(675\) 0.519222 0.0199849
\(676\) −0.336031 −0.0129243
\(677\) −25.9543 −0.997506 −0.498753 0.866744i \(-0.666209\pi\)
−0.498753 + 0.866744i \(0.666209\pi\)
\(678\) −50.4715 −1.93834
\(679\) −16.3114 −0.625975
\(680\) 13.8707 0.531918
\(681\) −9.34291 −0.358021
\(682\) 22.4162 0.858362
\(683\) −13.8477 −0.529869 −0.264935 0.964266i \(-0.585350\pi\)
−0.264935 + 0.964266i \(0.585350\pi\)
\(684\) 7.64621 0.292360
\(685\) 29.5210 1.12794
\(686\) −20.0948 −0.767222
\(687\) 15.1036 0.576238
\(688\) −1.25313 −0.0477753
\(689\) −43.5302 −1.65837
\(690\) 14.5918 0.555499
\(691\) −31.2996 −1.19069 −0.595347 0.803469i \(-0.702985\pi\)
−0.595347 + 0.803469i \(0.702985\pi\)
\(692\) −22.9937 −0.874088
\(693\) −26.9773 −1.02478
\(694\) −20.1302 −0.764131
\(695\) 43.7412 1.65920
\(696\) −13.7531 −0.521311
\(697\) 36.7763 1.39300
\(698\) 15.7844 0.597449
\(699\) 11.9426 0.451709
\(700\) −2.13396 −0.0806561
\(701\) −32.9107 −1.24302 −0.621510 0.783407i \(-0.713480\pi\)
−0.621510 + 0.783407i \(0.713480\pi\)
\(702\) 1.95819 0.0739070
\(703\) 9.63855 0.363525
\(704\) −3.70387 −0.139595
\(705\) −31.7970 −1.19755
\(706\) 16.6971 0.628403
\(707\) −14.3736 −0.540574
\(708\) 10.2049 0.383524
\(709\) −16.5984 −0.623366 −0.311683 0.950186i \(-0.600893\pi\)
−0.311683 + 0.950186i \(0.600893\pi\)
\(710\) 1.29106 0.0484526
\(711\) 7.96830 0.298834
\(712\) 8.40142 0.314857
\(713\) 17.5803 0.658388
\(714\) −38.8461 −1.45378
\(715\) 26.5468 0.992794
\(716\) 0.526188 0.0196646
\(717\) 59.2369 2.21224
\(718\) −28.5977 −1.06726
\(719\) −46.7763 −1.74446 −0.872231 0.489094i \(-0.837328\pi\)
−0.872231 + 0.489094i \(0.837328\pi\)
\(720\) 6.48651 0.241738
\(721\) −25.3657 −0.944669
\(722\) −13.3635 −0.497336
\(723\) −35.4551 −1.31859
\(724\) 22.4799 0.835460
\(725\) −5.20318 −0.193241
\(726\) −6.78071 −0.251656
\(727\) 9.39673 0.348505 0.174253 0.984701i \(-0.444249\pi\)
0.174253 + 0.984701i \(0.444249\pi\)
\(728\) −8.04799 −0.298278
\(729\) −30.8145 −1.14128
\(730\) −17.2029 −0.636708
\(731\) −8.63029 −0.319203
\(732\) −6.38323 −0.235931
\(733\) 15.7585 0.582052 0.291026 0.956715i \(-0.406003\pi\)
0.291026 + 0.956715i \(0.406003\pi\)
\(734\) 1.18623 0.0437846
\(735\) 9.47131 0.349355
\(736\) −2.90483 −0.107073
\(737\) −58.3030 −2.14762
\(738\) 17.1981 0.633069
\(739\) 26.5556 0.976862 0.488431 0.872603i \(-0.337569\pi\)
0.488431 + 0.872603i \(0.337569\pi\)
\(740\) 8.17666 0.300580
\(741\) 21.0721 0.774104
\(742\) 27.6636 1.01556
\(743\) −26.2022 −0.961267 −0.480633 0.876922i \(-0.659593\pi\)
−0.480633 + 0.876922i \(0.659593\pi\)
\(744\) 15.0947 0.553397
\(745\) 39.9476 1.46357
\(746\) −2.98533 −0.109301
\(747\) 18.0162 0.659178
\(748\) −25.5085 −0.932682
\(749\) −30.7983 −1.12534
\(750\) 29.8564 1.09020
\(751\) −28.1226 −1.02621 −0.513104 0.858326i \(-0.671505\pi\)
−0.513104 + 0.858326i \(0.671505\pi\)
\(752\) 6.32993 0.230829
\(753\) 0.203776 0.00742602
\(754\) −19.6232 −0.714635
\(755\) −9.40027 −0.342111
\(756\) −1.24443 −0.0452596
\(757\) −31.8928 −1.15916 −0.579582 0.814914i \(-0.696784\pi\)
−0.579582 + 0.814914i \(0.696784\pi\)
\(758\) 3.12466 0.113493
\(759\) −26.8345 −0.974031
\(760\) 4.78164 0.173448
\(761\) 8.87040 0.321552 0.160776 0.986991i \(-0.448600\pi\)
0.160776 + 0.986991i \(0.448600\pi\)
\(762\) 39.3514 1.42555
\(763\) 0.0542145 0.00196270
\(764\) 11.3651 0.411175
\(765\) 44.6724 1.61513
\(766\) −9.08236 −0.328159
\(767\) 14.5605 0.525750
\(768\) −2.49412 −0.0899987
\(769\) 0.145034 0.00523005 0.00261503 0.999997i \(-0.499168\pi\)
0.00261503 + 0.999997i \(0.499168\pi\)
\(770\) −16.8706 −0.607973
\(771\) 20.8052 0.749280
\(772\) −6.87508 −0.247440
\(773\) −28.1788 −1.01352 −0.506761 0.862086i \(-0.669157\pi\)
−0.506761 + 0.862086i \(0.669157\pi\)
\(774\) −4.03587 −0.145066
\(775\) 5.71072 0.205135
\(776\) −7.21256 −0.258916
\(777\) −22.8994 −0.821512
\(778\) −28.3345 −1.01584
\(779\) 12.6779 0.454231
\(780\) 17.8761 0.640067
\(781\) −2.37428 −0.0849583
\(782\) −20.0055 −0.715394
\(783\) −3.03427 −0.108436
\(784\) −1.88548 −0.0673386
\(785\) 43.5902 1.55580
\(786\) 13.1467 0.468927
\(787\) −4.62878 −0.164998 −0.0824990 0.996591i \(-0.526290\pi\)
−0.0824990 + 0.996591i \(0.526290\pi\)
\(788\) 19.5956 0.698064
\(789\) 13.0052 0.462998
\(790\) 4.98306 0.177289
\(791\) 45.7648 1.62721
\(792\) −11.9288 −0.423871
\(793\) −9.10770 −0.323424
\(794\) 18.5496 0.658299
\(795\) −61.4460 −2.17927
\(796\) 21.9514 0.778045
\(797\) 23.3111 0.825721 0.412861 0.910794i \(-0.364530\pi\)
0.412861 + 0.910794i \(0.364530\pi\)
\(798\) −13.3914 −0.474050
\(799\) 43.5941 1.54225
\(800\) −0.943592 −0.0333610
\(801\) 27.0578 0.956041
\(802\) −0.135001 −0.00476706
\(803\) 31.6364 1.11642
\(804\) −39.2601 −1.38460
\(805\) −13.2310 −0.466332
\(806\) 21.5373 0.758619
\(807\) 20.5057 0.721833
\(808\) −6.35568 −0.223592
\(809\) 3.93721 0.138425 0.0692125 0.997602i \(-0.477951\pi\)
0.0692125 + 0.997602i \(0.477951\pi\)
\(810\) −16.6954 −0.586616
\(811\) −8.77345 −0.308077 −0.154039 0.988065i \(-0.549228\pi\)
−0.154039 + 0.988065i \(0.549228\pi\)
\(812\) 12.4706 0.437632
\(813\) 38.7706 1.35974
\(814\) −15.0370 −0.527047
\(815\) 21.8200 0.764322
\(816\) −17.1769 −0.601312
\(817\) −2.97511 −0.104086
\(818\) 25.1046 0.877763
\(819\) −25.9195 −0.905702
\(820\) 10.7550 0.375581
\(821\) 0.517055 0.0180453 0.00902267 0.999959i \(-0.497128\pi\)
0.00902267 + 0.999959i \(0.497128\pi\)
\(822\) −36.5576 −1.27509
\(823\) 16.0261 0.558636 0.279318 0.960199i \(-0.409892\pi\)
0.279318 + 0.960199i \(0.409892\pi\)
\(824\) −11.2162 −0.390734
\(825\) −8.71680 −0.303480
\(826\) −9.25325 −0.321962
\(827\) −49.1062 −1.70759 −0.853795 0.520609i \(-0.825705\pi\)
−0.853795 + 0.520609i \(0.825705\pi\)
\(828\) −9.35536 −0.325121
\(829\) −33.7931 −1.17368 −0.586841 0.809702i \(-0.699629\pi\)
−0.586841 + 0.809702i \(0.699629\pi\)
\(830\) 11.2666 0.391070
\(831\) 30.7911 1.06813
\(832\) −3.55865 −0.123374
\(833\) −12.9853 −0.449913
\(834\) −54.1672 −1.87566
\(835\) 26.8629 0.929630
\(836\) −8.79352 −0.304130
\(837\) 3.33024 0.115110
\(838\) 27.8624 0.962492
\(839\) 47.4779 1.63912 0.819559 0.572994i \(-0.194218\pi\)
0.819559 + 0.572994i \(0.194218\pi\)
\(840\) −11.3603 −0.391968
\(841\) 1.40673 0.0485078
\(842\) 20.2765 0.698773
\(843\) −25.4836 −0.877700
\(844\) 2.41930 0.0832757
\(845\) −0.676784 −0.0232821
\(846\) 20.3863 0.700896
\(847\) 6.14838 0.211261
\(848\) 12.2322 0.420057
\(849\) −42.7136 −1.46593
\(850\) −6.49849 −0.222896
\(851\) −11.7930 −0.404260
\(852\) −1.59879 −0.0547737
\(853\) −32.2823 −1.10533 −0.552663 0.833405i \(-0.686388\pi\)
−0.552663 + 0.833405i \(0.686388\pi\)
\(854\) 5.78797 0.198060
\(855\) 15.3999 0.526665
\(856\) −13.6183 −0.465465
\(857\) −8.60550 −0.293958 −0.146979 0.989140i \(-0.546955\pi\)
−0.146979 + 0.989140i \(0.546955\pi\)
\(858\) −32.8744 −1.12231
\(859\) −34.7924 −1.18710 −0.593551 0.804797i \(-0.702274\pi\)
−0.593551 + 0.804797i \(0.702274\pi\)
\(860\) −2.52388 −0.0860635
\(861\) −30.1203 −1.02650
\(862\) 17.8164 0.606827
\(863\) 1.13842 0.0387522 0.0193761 0.999812i \(-0.493832\pi\)
0.0193761 + 0.999812i \(0.493832\pi\)
\(864\) −0.550262 −0.0187203
\(865\) −46.3105 −1.57460
\(866\) −36.7403 −1.24849
\(867\) −75.8970 −2.57760
\(868\) −13.6870 −0.464568
\(869\) −9.16393 −0.310865
\(870\) −27.6995 −0.939103
\(871\) −56.0170 −1.89806
\(872\) 0.0239725 0.000811811 0
\(873\) −23.2289 −0.786180
\(874\) −6.89647 −0.233277
\(875\) −27.0721 −0.915204
\(876\) 21.3033 0.719773
\(877\) 31.2059 1.05375 0.526874 0.849943i \(-0.323364\pi\)
0.526874 + 0.849943i \(0.323364\pi\)
\(878\) −27.3337 −0.922466
\(879\) 3.21026 0.108280
\(880\) −7.45980 −0.251470
\(881\) 25.7583 0.867820 0.433910 0.900956i \(-0.357134\pi\)
0.433910 + 0.900956i \(0.357134\pi\)
\(882\) −6.07243 −0.204469
\(883\) −45.0254 −1.51523 −0.757613 0.652704i \(-0.773635\pi\)
−0.757613 + 0.652704i \(0.773635\pi\)
\(884\) −24.5083 −0.824303
\(885\) 20.5532 0.690888
\(886\) 11.9975 0.403065
\(887\) 0.401785 0.0134906 0.00674530 0.999977i \(-0.497853\pi\)
0.00674530 + 0.999977i \(0.497853\pi\)
\(888\) −10.1256 −0.339794
\(889\) −35.6817 −1.19673
\(890\) 16.9209 0.567190
\(891\) 30.7031 1.02859
\(892\) 23.7336 0.794660
\(893\) 15.0281 0.502898
\(894\) −49.4694 −1.65450
\(895\) 1.05977 0.0354242
\(896\) 2.26153 0.0755524
\(897\) −25.7823 −0.860847
\(898\) −31.4885 −1.05079
\(899\) −33.3727 −1.11304
\(900\) −3.03895 −0.101298
\(901\) 84.2431 2.80655
\(902\) −19.7786 −0.658556
\(903\) 7.06833 0.235219
\(904\) 20.2362 0.673046
\(905\) 45.2758 1.50502
\(906\) 11.6409 0.386743
\(907\) −46.5912 −1.54704 −0.773518 0.633775i \(-0.781505\pi\)
−0.773518 + 0.633775i \(0.781505\pi\)
\(908\) 3.74598 0.124315
\(909\) −20.4693 −0.678923
\(910\) −16.2091 −0.537325
\(911\) 21.6758 0.718152 0.359076 0.933308i \(-0.383092\pi\)
0.359076 + 0.933308i \(0.383092\pi\)
\(912\) −5.92139 −0.196077
\(913\) −20.7195 −0.685715
\(914\) −5.43642 −0.179821
\(915\) −12.8562 −0.425012
\(916\) −6.05569 −0.200085
\(917\) −11.9207 −0.393656
\(918\) −3.78964 −0.125077
\(919\) −28.2429 −0.931646 −0.465823 0.884878i \(-0.654242\pi\)
−0.465823 + 0.884878i \(0.654242\pi\)
\(920\) −5.85048 −0.192884
\(921\) 6.96684 0.229565
\(922\) −0.418075 −0.0137686
\(923\) −2.28118 −0.0750861
\(924\) 20.8918 0.687289
\(925\) −3.83080 −0.125956
\(926\) 2.04479 0.0671960
\(927\) −36.1231 −1.18644
\(928\) 5.51423 0.181013
\(929\) 42.2378 1.38578 0.692888 0.721045i \(-0.256338\pi\)
0.692888 + 0.721045i \(0.256338\pi\)
\(930\) 30.4015 0.996903
\(931\) −4.47640 −0.146708
\(932\) −4.78829 −0.156846
\(933\) 59.0160 1.93210
\(934\) −35.7920 −1.17115
\(935\) −51.3754 −1.68016
\(936\) −11.4611 −0.374617
\(937\) 13.3743 0.436918 0.218459 0.975846i \(-0.429897\pi\)
0.218459 + 0.975846i \(0.429897\pi\)
\(938\) 35.5989 1.16235
\(939\) −46.8349 −1.52840
\(940\) 12.7488 0.415820
\(941\) −5.34684 −0.174302 −0.0871510 0.996195i \(-0.527776\pi\)
−0.0871510 + 0.996195i \(0.527776\pi\)
\(942\) −53.9803 −1.75877
\(943\) −15.5117 −0.505131
\(944\) −4.09159 −0.133170
\(945\) −2.50635 −0.0815317
\(946\) 4.64145 0.150906
\(947\) −47.3436 −1.53846 −0.769231 0.638971i \(-0.779360\pi\)
−0.769231 + 0.638971i \(0.779360\pi\)
\(948\) −6.17081 −0.200419
\(949\) 30.3959 0.986694
\(950\) −2.24022 −0.0726823
\(951\) −57.2218 −1.85554
\(952\) 15.5751 0.504792
\(953\) −25.1830 −0.815757 −0.407879 0.913036i \(-0.633731\pi\)
−0.407879 + 0.913036i \(0.633731\pi\)
\(954\) 39.3955 1.27547
\(955\) 22.8899 0.740700
\(956\) −23.7507 −0.768151
\(957\) 50.9399 1.64665
\(958\) 4.99316 0.161322
\(959\) 33.1484 1.07042
\(960\) −5.02328 −0.162126
\(961\) 5.62799 0.181548
\(962\) −14.4474 −0.465803
\(963\) −43.8595 −1.41335
\(964\) 14.2155 0.457850
\(965\) −13.8468 −0.445743
\(966\) 16.3847 0.527171
\(967\) −18.1464 −0.583549 −0.291775 0.956487i \(-0.594246\pi\)
−0.291775 + 0.956487i \(0.594246\pi\)
\(968\) 2.71868 0.0873818
\(969\) −40.7804 −1.31006
\(970\) −14.5265 −0.466417
\(971\) −21.7629 −0.698406 −0.349203 0.937047i \(-0.613548\pi\)
−0.349203 + 0.937047i \(0.613548\pi\)
\(972\) 22.3257 0.716096
\(973\) 49.1159 1.57458
\(974\) −9.48550 −0.303935
\(975\) −8.37502 −0.268215
\(976\) 2.55932 0.0819217
\(977\) 2.63198 0.0842045 0.0421023 0.999113i \(-0.486594\pi\)
0.0421023 + 0.999113i \(0.486594\pi\)
\(978\) −27.0210 −0.864036
\(979\) −31.1178 −0.994530
\(980\) −3.79746 −0.121305
\(981\) 0.0772064 0.00246501
\(982\) 33.4510 1.06746
\(983\) 48.1572 1.53598 0.767988 0.640464i \(-0.221258\pi\)
0.767988 + 0.640464i \(0.221258\pi\)
\(984\) −13.3185 −0.424579
\(985\) 39.4666 1.25751
\(986\) 37.9763 1.20941
\(987\) −35.7041 −1.13647
\(988\) −8.44873 −0.268790
\(989\) 3.64014 0.115750
\(990\) −24.0252 −0.763571
\(991\) −0.147273 −0.00467829 −0.00233914 0.999997i \(-0.500745\pi\)
−0.00233914 + 0.999997i \(0.500745\pi\)
\(992\) −6.05211 −0.192155
\(993\) −3.92620 −0.124594
\(994\) 1.44970 0.0459816
\(995\) 44.2112 1.40159
\(996\) −13.9521 −0.442089
\(997\) −26.1014 −0.826639 −0.413319 0.910586i \(-0.635631\pi\)
−0.413319 + 0.910586i \(0.635631\pi\)
\(998\) 26.4188 0.836273
\(999\) −2.23396 −0.0706792
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4034.2.a.d.1.8 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.8 52 1.1 even 1 trivial