Properties

Label 4598.2.a.bm.1.2
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.469.1
Defining polynomial: \(x^{3} - x^{2} - 5 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.772866\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.772866 q^{3} +1.00000 q^{4} +1.22713 q^{5} -0.772866 q^{6} -3.40268 q^{7} -1.00000 q^{8} -2.40268 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.772866 q^{3} +1.00000 q^{4} +1.22713 q^{5} -0.772866 q^{6} -3.40268 q^{7} -1.00000 q^{8} -2.40268 q^{9} -1.22713 q^{10} +0.772866 q^{12} +1.40268 q^{13} +3.40268 q^{14} +0.948410 q^{15} +1.00000 q^{16} +4.80536 q^{17} +2.40268 q^{18} +1.00000 q^{19} +1.22713 q^{20} -2.62981 q^{21} +6.80536 q^{23} -0.772866 q^{24} -3.49414 q^{25} -1.40268 q^{26} -4.17554 q^{27} -3.40268 q^{28} -8.03249 q^{29} -0.948410 q^{30} -4.94841 q^{31} -1.00000 q^{32} -4.80536 q^{34} -4.17554 q^{35} -2.40268 q^{36} +2.35109 q^{37} -1.00000 q^{38} +1.08408 q^{39} -1.22713 q^{40} -2.94841 q^{41} +2.62981 q^{42} +9.12395 q^{43} -2.94841 q^{45} -6.80536 q^{46} +5.25963 q^{47} +0.772866 q^{48} +4.57822 q^{49} +3.49414 q^{50} +3.71390 q^{51} +1.40268 q^{52} -4.45427 q^{53} +4.17554 q^{54} +3.40268 q^{56} +0.772866 q^{57} +8.03249 q^{58} -14.5193 q^{59} +0.948410 q^{60} -2.00000 q^{61} +4.94841 q^{62} +8.17554 q^{63} +1.00000 q^{64} +1.72128 q^{65} +3.40268 q^{67} +4.80536 q^{68} +5.25963 q^{69} +4.17554 q^{70} -7.57822 q^{71} +2.40268 q^{72} +10.0650 q^{73} -2.35109 q^{74} -2.70050 q^{75} +1.00000 q^{76} -1.08408 q^{78} +3.71390 q^{79} +1.22713 q^{80} +3.98090 q^{81} +2.94841 q^{82} -10.6697 q^{83} -2.62981 q^{84} +5.89682 q^{85} -9.12395 q^{86} -6.20804 q^{87} +14.9883 q^{89} +2.94841 q^{90} -4.77287 q^{91} +6.80536 q^{92} -3.82446 q^{93} -5.25963 q^{94} +1.22713 q^{95} -0.772866 q^{96} +2.35109 q^{97} -4.57822 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - q^{6} - q^{7} - 3 q^{8} + 2 q^{9} + O(q^{10}) \) \( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - q^{6} - q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} + q^{12} - 5 q^{13} + q^{14} - 9 q^{15} + 3 q^{16} - 4 q^{17} - 2 q^{18} + 3 q^{19} + 5 q^{20} + 2 q^{23} - q^{24} + 4 q^{25} + 5 q^{26} - 2 q^{27} - q^{28} - 7 q^{29} + 9 q^{30} - 3 q^{31} - 3 q^{32} + 4 q^{34} - 2 q^{35} + 2 q^{36} - 14 q^{37} - 3 q^{38} - 2 q^{39} - 5 q^{40} + 3 q^{41} + 5 q^{43} + 3 q^{45} - 2 q^{46} + q^{48} - 6 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} - 16 q^{53} + 2 q^{54} + q^{56} + q^{57} + 7 q^{58} - 12 q^{59} - 9 q^{60} - 6 q^{61} + 3 q^{62} + 14 q^{63} + 3 q^{64} - 8 q^{65} + q^{67} - 4 q^{68} + 2 q^{70} - 3 q^{71} - 2 q^{72} - 4 q^{73} + 14 q^{74} - 41 q^{75} + 3 q^{76} + 2 q^{78} - 2 q^{79} + 5 q^{80} - 17 q^{81} - 3 q^{82} - 7 q^{83} - 6 q^{85} - 5 q^{86} + 9 q^{87} + 16 q^{89} - 3 q^{90} - 13 q^{91} + 2 q^{92} - 22 q^{93} + 5 q^{95} - q^{96} - 14 q^{97} + 6 q^{98} + O(q^{100}) \)

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
\(3\) 0.772866 0.446214 0.223107 0.974794i \(-0.428380\pi\)
0.223107 + 0.974794i \(0.428380\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.22713 0.548791 0.274396 0.961617i \(-0.411522\pi\)
0.274396 + 0.961617i \(0.411522\pi\)
\(6\) −0.772866 −0.315521
\(7\) −3.40268 −1.28609 −0.643046 0.765828i \(-0.722330\pi\)
−0.643046 + 0.765828i \(0.722330\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.40268 −0.800893
\(10\) −1.22713 −0.388054
\(11\) 0 0
\(12\) 0.772866 0.223107
\(13\) 1.40268 0.389033 0.194517 0.980899i \(-0.437686\pi\)
0.194517 + 0.980899i \(0.437686\pi\)
\(14\) 3.40268 0.909404
\(15\) 0.948410 0.244878
\(16\) 1.00000 0.250000
\(17\) 4.80536 1.16547 0.582735 0.812662i \(-0.301982\pi\)
0.582735 + 0.812662i \(0.301982\pi\)
\(18\) 2.40268 0.566317
\(19\) 1.00000 0.229416
\(20\) 1.22713 0.274396
\(21\) −2.62981 −0.573872
\(22\) 0 0
\(23\) 6.80536 1.41902 0.709508 0.704698i \(-0.248917\pi\)
0.709508 + 0.704698i \(0.248917\pi\)
\(24\) −0.772866 −0.157761
\(25\) −3.49414 −0.698828
\(26\) −1.40268 −0.275088
\(27\) −4.17554 −0.803584
\(28\) −3.40268 −0.643046
\(29\) −8.03249 −1.49160 −0.745798 0.666172i \(-0.767932\pi\)
−0.745798 + 0.666172i \(0.767932\pi\)
\(30\) −0.948410 −0.173155
\(31\) −4.94841 −0.888761 −0.444380 0.895838i \(-0.646576\pi\)
−0.444380 + 0.895838i \(0.646576\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −4.80536 −0.824112
\(35\) −4.17554 −0.705796
\(36\) −2.40268 −0.400446
\(37\) 2.35109 0.386517 0.193258 0.981148i \(-0.438094\pi\)
0.193258 + 0.981148i \(0.438094\pi\)
\(38\) −1.00000 −0.162221
\(39\) 1.08408 0.173592
\(40\) −1.22713 −0.194027
\(41\) −2.94841 −0.460464 −0.230232 0.973136i \(-0.573949\pi\)
−0.230232 + 0.973136i \(0.573949\pi\)
\(42\) 2.62981 0.405789
\(43\) 9.12395 1.39139 0.695695 0.718337i \(-0.255097\pi\)
0.695695 + 0.718337i \(0.255097\pi\)
\(44\) 0 0
\(45\) −2.94841 −0.439523
\(46\) −6.80536 −1.00340
\(47\) 5.25963 0.767195 0.383598 0.923500i \(-0.374685\pi\)
0.383598 + 0.923500i \(0.374685\pi\)
\(48\) 0.772866 0.111554
\(49\) 4.57822 0.654032
\(50\) 3.49414 0.494146
\(51\) 3.71390 0.520049
\(52\) 1.40268 0.194517
\(53\) −4.45427 −0.611841 −0.305920 0.952057i \(-0.598964\pi\)
−0.305920 + 0.952057i \(0.598964\pi\)
\(54\) 4.17554 0.568220
\(55\) 0 0
\(56\) 3.40268 0.454702
\(57\) 0.772866 0.102369
\(58\) 8.03249 1.05472
\(59\) −14.5193 −1.89025 −0.945123 0.326715i \(-0.894058\pi\)
−0.945123 + 0.326715i \(0.894058\pi\)
\(60\) 0.948410 0.122439
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 4.94841 0.628449
\(63\) 8.17554 1.03002
\(64\) 1.00000 0.125000
\(65\) 1.72128 0.213498
\(66\) 0 0
\(67\) 3.40268 0.415703 0.207852 0.978160i \(-0.433353\pi\)
0.207852 + 0.978160i \(0.433353\pi\)
\(68\) 4.80536 0.582735
\(69\) 5.25963 0.633185
\(70\) 4.17554 0.499073
\(71\) −7.57822 −0.899370 −0.449685 0.893187i \(-0.648464\pi\)
−0.449685 + 0.893187i \(0.648464\pi\)
\(72\) 2.40268 0.283158
\(73\) 10.0650 1.17802 0.589009 0.808127i \(-0.299518\pi\)
0.589009 + 0.808127i \(0.299518\pi\)
\(74\) −2.35109 −0.273309
\(75\) −2.70050 −0.311827
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −1.08408 −0.122748
\(79\) 3.71390 0.417846 0.208923 0.977932i \(-0.433004\pi\)
0.208923 + 0.977932i \(0.433004\pi\)
\(80\) 1.22713 0.137198
\(81\) 3.98090 0.442322
\(82\) 2.94841 0.325597
\(83\) −10.6697 −1.17115 −0.585575 0.810618i \(-0.699131\pi\)
−0.585575 + 0.810618i \(0.699131\pi\)
\(84\) −2.62981 −0.286936
\(85\) 5.89682 0.639600
\(86\) −9.12395 −0.983861
\(87\) −6.20804 −0.665571
\(88\) 0 0
\(89\) 14.9883 1.58875 0.794377 0.607425i \(-0.207797\pi\)
0.794377 + 0.607425i \(0.207797\pi\)
\(90\) 2.94841 0.310790
\(91\) −4.77287 −0.500332
\(92\) 6.80536 0.709508
\(93\) −3.82446 −0.396578
\(94\) −5.25963 −0.542489
\(95\) 1.22713 0.125901
\(96\) −0.772866 −0.0788803
\(97\) 2.35109 0.238717 0.119358 0.992851i \(-0.461916\pi\)
0.119358 + 0.992851i \(0.461916\pi\)
\(98\) −4.57822 −0.462470
\(99\) 0 0
\(100\) −3.49414 −0.349414
\(101\) −14.0650 −1.39952 −0.699759 0.714379i \(-0.746709\pi\)
−0.699759 + 0.714379i \(0.746709\pi\)
\(102\) −3.71390 −0.367730
\(103\) −15.5782 −1.53497 −0.767484 0.641068i \(-0.778492\pi\)
−0.767484 + 0.641068i \(0.778492\pi\)
\(104\) −1.40268 −0.137544
\(105\) −3.22713 −0.314936
\(106\) 4.45427 0.432637
\(107\) 4.35109 0.420636 0.210318 0.977633i \(-0.432550\pi\)
0.210318 + 0.977633i \(0.432550\pi\)
\(108\) −4.17554 −0.401792
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) 1.81708 0.172469
\(112\) −3.40268 −0.321523
\(113\) −19.9618 −1.87785 −0.938924 0.344124i \(-0.888176\pi\)
−0.938924 + 0.344124i \(0.888176\pi\)
\(114\) −0.772866 −0.0723855
\(115\) 8.35109 0.778743
\(116\) −8.03249 −0.745798
\(117\) −3.37019 −0.311574
\(118\) 14.5193 1.33661
\(119\) −16.3511 −1.49890
\(120\) −0.948410 −0.0865776
\(121\) 0 0
\(122\) 2.00000 0.181071
\(123\) −2.27872 −0.205466
\(124\) −4.94841 −0.444380
\(125\) −10.4235 −0.932302
\(126\) −8.17554 −0.728335
\(127\) −11.7139 −1.03944 −0.519720 0.854337i \(-0.673964\pi\)
−0.519720 + 0.854337i \(0.673964\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.05159 0.620858
\(130\) −1.72128 −0.150966
\(131\) −1.85695 −0.162242 −0.0811211 0.996704i \(-0.525850\pi\)
−0.0811211 + 0.996704i \(0.525850\pi\)
\(132\) 0 0
\(133\) −3.40268 −0.295050
\(134\) −3.40268 −0.293947
\(135\) −5.12395 −0.441000
\(136\) −4.80536 −0.412056
\(137\) 10.5973 0.905390 0.452695 0.891665i \(-0.350463\pi\)
0.452695 + 0.891665i \(0.350463\pi\)
\(138\) −5.25963 −0.447729
\(139\) −14.7347 −1.24978 −0.624889 0.780713i \(-0.714856\pi\)
−0.624889 + 0.780713i \(0.714856\pi\)
\(140\) −4.17554 −0.352898
\(141\) 4.06498 0.342333
\(142\) 7.57822 0.635950
\(143\) 0 0
\(144\) −2.40268 −0.200223
\(145\) −9.85695 −0.818575
\(146\) −10.0650 −0.832984
\(147\) 3.53835 0.291838
\(148\) 2.35109 0.193258
\(149\) −18.3511 −1.50338 −0.751690 0.659517i \(-0.770761\pi\)
−0.751690 + 0.659517i \(0.770761\pi\)
\(150\) 2.70050 0.220495
\(151\) 7.64891 0.622460 0.311230 0.950335i \(-0.399259\pi\)
0.311230 + 0.950335i \(0.399259\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −11.5457 −0.933417
\(154\) 0 0
\(155\) −6.07236 −0.487744
\(156\) 1.08408 0.0867960
\(157\) 8.38358 0.669083 0.334541 0.942381i \(-0.391419\pi\)
0.334541 + 0.942381i \(0.391419\pi\)
\(158\) −3.71390 −0.295462
\(159\) −3.44255 −0.273012
\(160\) −1.22713 −0.0970135
\(161\) −23.1564 −1.82498
\(162\) −3.98090 −0.312769
\(163\) −14.2479 −1.11598 −0.557991 0.829847i \(-0.688428\pi\)
−0.557991 + 0.829847i \(0.688428\pi\)
\(164\) −2.94841 −0.230232
\(165\) 0 0
\(166\) 10.6697 0.828128
\(167\) 10.8703 0.841172 0.420586 0.907253i \(-0.361824\pi\)
0.420586 + 0.907253i \(0.361824\pi\)
\(168\) 2.62981 0.202894
\(169\) −11.0325 −0.848653
\(170\) −5.89682 −0.452265
\(171\) −2.40268 −0.183737
\(172\) 9.12395 0.695695
\(173\) −3.39530 −0.258140 −0.129070 0.991635i \(-0.541199\pi\)
−0.129070 + 0.991635i \(0.541199\pi\)
\(174\) 6.20804 0.470630
\(175\) 11.8894 0.898757
\(176\) 0 0
\(177\) −11.2214 −0.843454
\(178\) −14.9883 −1.12342
\(179\) −0.311217 −0.0232614 −0.0116307 0.999932i \(-0.503702\pi\)
−0.0116307 + 0.999932i \(0.503702\pi\)
\(180\) −2.94841 −0.219762
\(181\) −15.3246 −1.13907 −0.569535 0.821967i \(-0.692877\pi\)
−0.569535 + 0.821967i \(0.692877\pi\)
\(182\) 4.77287 0.353788
\(183\) −1.54573 −0.114264
\(184\) −6.80536 −0.501698
\(185\) 2.88510 0.212117
\(186\) 3.82446 0.280423
\(187\) 0 0
\(188\) 5.25963 0.383598
\(189\) 14.2080 1.03348
\(190\) −1.22713 −0.0890257
\(191\) 26.8703 1.94427 0.972135 0.234422i \(-0.0753199\pi\)
0.972135 + 0.234422i \(0.0753199\pi\)
\(192\) 0.772866 0.0557768
\(193\) −18.5665 −1.33645 −0.668223 0.743961i \(-0.732945\pi\)
−0.668223 + 0.743961i \(0.732945\pi\)
\(194\) −2.35109 −0.168798
\(195\) 1.33031 0.0952658
\(196\) 4.57822 0.327016
\(197\) −14.9085 −1.06219 −0.531095 0.847312i \(-0.678219\pi\)
−0.531095 + 0.847312i \(0.678219\pi\)
\(198\) 0 0
\(199\) 15.1564 1.07441 0.537206 0.843451i \(-0.319480\pi\)
0.537206 + 0.843451i \(0.319480\pi\)
\(200\) 3.49414 0.247073
\(201\) 2.62981 0.185493
\(202\) 14.0650 0.989609
\(203\) 27.3320 1.91833
\(204\) 3.71390 0.260025
\(205\) −3.61810 −0.252699
\(206\) 15.5782 1.08539
\(207\) −16.3511 −1.13648
\(208\) 1.40268 0.0972583
\(209\) 0 0
\(210\) 3.22713 0.222693
\(211\) −11.1564 −0.768041 −0.384021 0.923324i \(-0.625461\pi\)
−0.384021 + 0.923324i \(0.625461\pi\)
\(212\) −4.45427 −0.305920
\(213\) −5.85695 −0.401311
\(214\) −4.35109 −0.297434
\(215\) 11.1963 0.763583
\(216\) 4.17554 0.284110
\(217\) 16.8378 1.14303
\(218\) 6.00000 0.406371
\(219\) 7.77888 0.525648
\(220\) 0 0
\(221\) 6.74037 0.453407
\(222\) −1.81708 −0.121954
\(223\) 1.61072 0.107861 0.0539307 0.998545i \(-0.482825\pi\)
0.0539307 + 0.998545i \(0.482825\pi\)
\(224\) 3.40268 0.227351
\(225\) 8.39530 0.559687
\(226\) 19.9618 1.32784
\(227\) 16.7672 1.11288 0.556438 0.830889i \(-0.312168\pi\)
0.556438 + 0.830889i \(0.312168\pi\)
\(228\) 0.772866 0.0511843
\(229\) −8.55913 −0.565603 −0.282801 0.959178i \(-0.591264\pi\)
−0.282801 + 0.959178i \(0.591264\pi\)
\(230\) −8.35109 −0.550654
\(231\) 0 0
\(232\) 8.03249 0.527359
\(233\) −5.44255 −0.356553 −0.178277 0.983980i \(-0.557052\pi\)
−0.178277 + 0.983980i \(0.557052\pi\)
\(234\) 3.37019 0.220316
\(235\) 6.45427 0.421030
\(236\) −14.5193 −0.945123
\(237\) 2.87034 0.186449
\(238\) 16.3511 1.05988
\(239\) −11.2921 −0.730426 −0.365213 0.930924i \(-0.619004\pi\)
−0.365213 + 0.930924i \(0.619004\pi\)
\(240\) 0.948410 0.0612196
\(241\) −11.4101 −0.734987 −0.367493 0.930026i \(-0.619784\pi\)
−0.367493 + 0.930026i \(0.619784\pi\)
\(242\) 0 0
\(243\) 15.6033 1.00095
\(244\) −2.00000 −0.128037
\(245\) 5.61810 0.358927
\(246\) 2.27872 0.145286
\(247\) 1.40268 0.0892503
\(248\) 4.94841 0.314224
\(249\) −8.24623 −0.522584
\(250\) 10.4235 0.659237
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 8.17554 0.515011
\(253\) 0 0
\(254\) 11.7139 0.734995
\(255\) 4.55745 0.285399
\(256\) 1.00000 0.0625000
\(257\) 24.2331 1.51162 0.755811 0.654790i \(-0.227243\pi\)
0.755811 + 0.654790i \(0.227243\pi\)
\(258\) −7.05159 −0.439013
\(259\) −8.00000 −0.497096
\(260\) 1.72128 0.106749
\(261\) 19.2995 1.19461
\(262\) 1.85695 0.114723
\(263\) −20.5665 −1.26819 −0.634093 0.773257i \(-0.718626\pi\)
−0.634093 + 0.773257i \(0.718626\pi\)
\(264\) 0 0
\(265\) −5.46599 −0.335773
\(266\) 3.40268 0.208632
\(267\) 11.5839 0.708925
\(268\) 3.40268 0.207852
\(269\) −1.36281 −0.0830918 −0.0415459 0.999137i \(-0.513228\pi\)
−0.0415459 + 0.999137i \(0.513228\pi\)
\(270\) 5.12395 0.311834
\(271\) 23.1963 1.40908 0.704538 0.709666i \(-0.251154\pi\)
0.704538 + 0.709666i \(0.251154\pi\)
\(272\) 4.80536 0.291368
\(273\) −3.68878 −0.223255
\(274\) −10.5973 −0.640208
\(275\) 0 0
\(276\) 5.25963 0.316592
\(277\) −31.0385 −1.86492 −0.932462 0.361269i \(-0.882344\pi\)
−0.932462 + 0.361269i \(0.882344\pi\)
\(278\) 14.7347 0.883727
\(279\) 11.8894 0.711802
\(280\) 4.17554 0.249537
\(281\) 2.77287 0.165415 0.0827076 0.996574i \(-0.473643\pi\)
0.0827076 + 0.996574i \(0.473643\pi\)
\(282\) −4.06498 −0.242066
\(283\) 9.23451 0.548935 0.274467 0.961596i \(-0.411498\pi\)
0.274467 + 0.961596i \(0.411498\pi\)
\(284\) −7.57822 −0.449685
\(285\) 0.948410 0.0561790
\(286\) 0 0
\(287\) 10.0325 0.592199
\(288\) 2.40268 0.141579
\(289\) 6.09146 0.358321
\(290\) 9.85695 0.578820
\(291\) 1.81708 0.106519
\(292\) 10.0650 0.589009
\(293\) −17.7390 −1.03632 −0.518162 0.855283i \(-0.673384\pi\)
−0.518162 + 0.855283i \(0.673384\pi\)
\(294\) −3.53835 −0.206361
\(295\) −17.8171 −1.03735
\(296\) −2.35109 −0.136654
\(297\) 0 0
\(298\) 18.3511 1.06305
\(299\) 9.54573 0.552044
\(300\) −2.70050 −0.155914
\(301\) −31.0459 −1.78946
\(302\) −7.64891 −0.440145
\(303\) −10.8703 −0.624485
\(304\) 1.00000 0.0573539
\(305\) −2.45427 −0.140531
\(306\) 11.5457 0.660026
\(307\) −20.9735 −1.19702 −0.598511 0.801115i \(-0.704241\pi\)
−0.598511 + 0.801115i \(0.704241\pi\)
\(308\) 0 0
\(309\) −12.0399 −0.684924
\(310\) 6.07236 0.344887
\(311\) −3.36281 −0.190687 −0.0953436 0.995444i \(-0.530395\pi\)
−0.0953436 + 0.995444i \(0.530395\pi\)
\(312\) −1.08408 −0.0613741
\(313\) −4.94103 −0.279284 −0.139642 0.990202i \(-0.544595\pi\)
−0.139642 + 0.990202i \(0.544595\pi\)
\(314\) −8.38358 −0.473113
\(315\) 10.0325 0.565267
\(316\) 3.71390 0.208923
\(317\) 14.2861 0.802388 0.401194 0.915993i \(-0.368595\pi\)
0.401194 + 0.915993i \(0.368595\pi\)
\(318\) 3.44255 0.193049
\(319\) 0 0
\(320\) 1.22713 0.0685989
\(321\) 3.36281 0.187694
\(322\) 23.1564 1.29046
\(323\) 4.80536 0.267377
\(324\) 3.98090 0.221161
\(325\) −4.90116 −0.271867
\(326\) 14.2479 0.789119
\(327\) −4.63719 −0.256437
\(328\) 2.94841 0.162799
\(329\) −17.8968 −0.986684
\(330\) 0 0
\(331\) −31.9293 −1.75499 −0.877497 0.479582i \(-0.840788\pi\)
−0.877497 + 0.479582i \(0.840788\pi\)
\(332\) −10.6697 −0.585575
\(333\) −5.64891 −0.309558
\(334\) −10.8703 −0.594799
\(335\) 4.17554 0.228134
\(336\) −2.62981 −0.143468
\(337\) 8.84523 0.481830 0.240915 0.970546i \(-0.422552\pi\)
0.240915 + 0.970546i \(0.422552\pi\)
\(338\) 11.0325 0.600088
\(339\) −15.4278 −0.837923
\(340\) 5.89682 0.319800
\(341\) 0 0
\(342\) 2.40268 0.129922
\(343\) 8.24053 0.444947
\(344\) −9.12395 −0.491931
\(345\) 6.45427 0.347486
\(346\) 3.39530 0.182532
\(347\) −5.27439 −0.283144 −0.141572 0.989928i \(-0.545216\pi\)
−0.141572 + 0.989928i \(0.545216\pi\)
\(348\) −6.20804 −0.332786
\(349\) 10.9085 0.583921 0.291960 0.956430i \(-0.405692\pi\)
0.291960 + 0.956430i \(0.405692\pi\)
\(350\) −11.8894 −0.635517
\(351\) −5.85695 −0.312621
\(352\) 0 0
\(353\) −22.1300 −1.17786 −0.588930 0.808184i \(-0.700451\pi\)
−0.588930 + 0.808184i \(0.700451\pi\)
\(354\) 11.2214 0.596412
\(355\) −9.29950 −0.493566
\(356\) 14.9883 0.794377
\(357\) −12.6372 −0.668831
\(358\) 0.311217 0.0164483
\(359\) 16.3910 0.865082 0.432541 0.901614i \(-0.357617\pi\)
0.432541 + 0.901614i \(0.357617\pi\)
\(360\) 2.94841 0.155395
\(361\) 1.00000 0.0526316
\(362\) 15.3246 0.805444
\(363\) 0 0
\(364\) −4.77287 −0.250166
\(365\) 12.3511 0.646486
\(366\) 1.54573 0.0807967
\(367\) −32.3511 −1.68871 −0.844357 0.535782i \(-0.820017\pi\)
−0.844357 + 0.535782i \(0.820017\pi\)
\(368\) 6.80536 0.354754
\(369\) 7.08408 0.368783
\(370\) −2.88510 −0.149989
\(371\) 15.1564 0.786883
\(372\) −3.82446 −0.198289
\(373\) −17.5782 −0.910166 −0.455083 0.890449i \(-0.650390\pi\)
−0.455083 + 0.890449i \(0.650390\pi\)
\(374\) 0 0
\(375\) −8.05593 −0.416006
\(376\) −5.25963 −0.271245
\(377\) −11.2670 −0.580280
\(378\) −14.2080 −0.730783
\(379\) 8.93365 0.458891 0.229445 0.973322i \(-0.426309\pi\)
0.229445 + 0.973322i \(0.426309\pi\)
\(380\) 1.22713 0.0629507
\(381\) −9.05327 −0.463813
\(382\) −26.8703 −1.37481
\(383\) −16.0399 −0.819599 −0.409800 0.912176i \(-0.634401\pi\)
−0.409800 + 0.912176i \(0.634401\pi\)
\(384\) −0.772866 −0.0394401
\(385\) 0 0
\(386\) 18.5665 0.945010
\(387\) −21.9219 −1.11435
\(388\) 2.35109 0.119358
\(389\) 17.2271 0.873450 0.436725 0.899595i \(-0.356138\pi\)
0.436725 + 0.899595i \(0.356138\pi\)
\(390\) −1.33031 −0.0673631
\(391\) 32.7022 1.65382
\(392\) −4.57822 −0.231235
\(393\) −1.43517 −0.0723948
\(394\) 14.9085 0.751081
\(395\) 4.55745 0.229310
\(396\) 0 0
\(397\) 15.0784 0.756762 0.378381 0.925650i \(-0.376481\pi\)
0.378381 + 0.925650i \(0.376481\pi\)
\(398\) −15.1564 −0.759724
\(399\) −2.62981 −0.131655
\(400\) −3.49414 −0.174707
\(401\) −13.1564 −0.657002 −0.328501 0.944504i \(-0.606543\pi\)
−0.328501 + 0.944504i \(0.606543\pi\)
\(402\) −2.62981 −0.131163
\(403\) −6.94103 −0.345757
\(404\) −14.0650 −0.699759
\(405\) 4.88510 0.242743
\(406\) −27.3320 −1.35646
\(407\) 0 0
\(408\) −3.71390 −0.183865
\(409\) 16.3836 0.810116 0.405058 0.914291i \(-0.367251\pi\)
0.405058 + 0.914291i \(0.367251\pi\)
\(410\) 3.61810 0.178685
\(411\) 8.19030 0.403998
\(412\) −15.5782 −0.767484
\(413\) 49.4044 2.43103
\(414\) 16.3511 0.803612
\(415\) −13.0931 −0.642717
\(416\) −1.40268 −0.0687720
\(417\) −11.3879 −0.557669
\(418\) 0 0
\(419\) 1.12966 0.0551874 0.0275937 0.999619i \(-0.491216\pi\)
0.0275937 + 0.999619i \(0.491216\pi\)
\(420\) −3.22713 −0.157468
\(421\) −2.63719 −0.128529 −0.0642645 0.997933i \(-0.520470\pi\)
−0.0642645 + 0.997933i \(0.520470\pi\)
\(422\) 11.1564 0.543087
\(423\) −12.6372 −0.614441
\(424\) 4.45427 0.216318
\(425\) −16.7906 −0.814464
\(426\) 5.85695 0.283770
\(427\) 6.80536 0.329334
\(428\) 4.35109 0.210318
\(429\) 0 0
\(430\) −11.1963 −0.539934
\(431\) 28.4958 1.37260 0.686298 0.727321i \(-0.259235\pi\)
0.686298 + 0.727321i \(0.259235\pi\)
\(432\) −4.17554 −0.200896
\(433\) −37.5075 −1.80250 −0.901249 0.433302i \(-0.857348\pi\)
−0.901249 + 0.433302i \(0.857348\pi\)
\(434\) −16.8378 −0.808243
\(435\) −7.61810 −0.365260
\(436\) −6.00000 −0.287348
\(437\) 6.80536 0.325544
\(438\) −7.77888 −0.371689
\(439\) 32.1300 1.53348 0.766740 0.641958i \(-0.221878\pi\)
0.766740 + 0.641958i \(0.221878\pi\)
\(440\) 0 0
\(441\) −11.0000 −0.523810
\(442\) −6.74037 −0.320607
\(443\) 33.0385 1.56971 0.784853 0.619681i \(-0.212738\pi\)
0.784853 + 0.619681i \(0.212738\pi\)
\(444\) 1.81708 0.0862346
\(445\) 18.3926 0.871895
\(446\) −1.61072 −0.0762696
\(447\) −14.1829 −0.670829
\(448\) −3.40268 −0.160761
\(449\) 7.88206 0.371977 0.185989 0.982552i \(-0.440451\pi\)
0.185989 + 0.982552i \(0.440451\pi\)
\(450\) −8.39530 −0.395758
\(451\) 0 0
\(452\) −19.9618 −0.938924
\(453\) 5.91158 0.277750
\(454\) −16.7672 −0.786922
\(455\) −5.85695 −0.274578
\(456\) −0.772866 −0.0361927
\(457\) −24.9353 −1.16643 −0.583213 0.812320i \(-0.698205\pi\)
−0.583213 + 0.812320i \(0.698205\pi\)
\(458\) 8.55913 0.399942
\(459\) −20.0650 −0.936553
\(460\) 8.35109 0.389372
\(461\) 26.6874 1.24296 0.621478 0.783431i \(-0.286532\pi\)
0.621478 + 0.783431i \(0.286532\pi\)
\(462\) 0 0
\(463\) −32.7022 −1.51980 −0.759900 0.650041i \(-0.774752\pi\)
−0.759900 + 0.650041i \(0.774752\pi\)
\(464\) −8.03249 −0.372899
\(465\) −4.69312 −0.217638
\(466\) 5.44255 0.252121
\(467\) 11.3776 0.526491 0.263246 0.964729i \(-0.415207\pi\)
0.263246 + 0.964729i \(0.415207\pi\)
\(468\) −3.37019 −0.155787
\(469\) −11.5782 −0.534633
\(470\) −6.45427 −0.297713
\(471\) 6.47938 0.298554
\(472\) 14.5193 0.668303
\(473\) 0 0
\(474\) −2.87034 −0.131839
\(475\) −3.49414 −0.160322
\(476\) −16.3511 −0.749451
\(477\) 10.7022 0.490019
\(478\) 11.2921 0.516489
\(479\) 12.5973 0.575586 0.287793 0.957693i \(-0.407078\pi\)
0.287793 + 0.957693i \(0.407078\pi\)
\(480\) −0.948410 −0.0432888
\(481\) 3.29782 0.150368
\(482\) 11.4101 0.519714
\(483\) −17.8968 −0.814334
\(484\) 0 0
\(485\) 2.88510 0.131006
\(486\) −15.6033 −0.707782
\(487\) 9.69616 0.439375 0.219688 0.975570i \(-0.429496\pi\)
0.219688 + 0.975570i \(0.429496\pi\)
\(488\) 2.00000 0.0905357
\(489\) −11.0117 −0.497967
\(490\) −5.61810 −0.253800
\(491\) 11.7538 0.530440 0.265220 0.964188i \(-0.414555\pi\)
0.265220 + 0.964188i \(0.414555\pi\)
\(492\) −2.27872 −0.102733
\(493\) −38.5990 −1.73841
\(494\) −1.40268 −0.0631095
\(495\) 0 0
\(496\) −4.94841 −0.222190
\(497\) 25.7863 1.15667
\(498\) 8.24623 0.369523
\(499\) 26.6640 1.19364 0.596822 0.802374i \(-0.296430\pi\)
0.596822 + 0.802374i \(0.296430\pi\)
\(500\) −10.4235 −0.466151
\(501\) 8.40131 0.375343
\(502\) 12.0000 0.535586
\(503\) −11.1622 −0.497696 −0.248848 0.968543i \(-0.580052\pi\)
−0.248848 + 0.968543i \(0.580052\pi\)
\(504\) −8.17554 −0.364168
\(505\) −17.2596 −0.768043
\(506\) 0 0
\(507\) −8.52663 −0.378681
\(508\) −11.7139 −0.519720
\(509\) −35.9618 −1.59398 −0.796989 0.603993i \(-0.793575\pi\)
−0.796989 + 0.603993i \(0.793575\pi\)
\(510\) −4.55745 −0.201807
\(511\) −34.2479 −1.51504
\(512\) −1.00000 −0.0441942
\(513\) −4.17554 −0.184355
\(514\) −24.2331 −1.06888
\(515\) −19.1166 −0.842377
\(516\) 7.05159 0.310429
\(517\) 0 0
\(518\) 8.00000 0.351500
\(519\) −2.62411 −0.115186
\(520\) −1.72128 −0.0754829
\(521\) 10.1300 0.443802 0.221901 0.975069i \(-0.428774\pi\)
0.221901 + 0.975069i \(0.428774\pi\)
\(522\) −19.2995 −0.844716
\(523\) 7.93502 0.346974 0.173487 0.984836i \(-0.444497\pi\)
0.173487 + 0.984836i \(0.444497\pi\)
\(524\) −1.85695 −0.0811211
\(525\) 9.18894 0.401038
\(526\) 20.5665 0.896742
\(527\) −23.7789 −1.03582
\(528\) 0 0
\(529\) 23.3129 1.01360
\(530\) 5.46599 0.237427
\(531\) 34.8851 1.51388
\(532\) −3.40268 −0.147525
\(533\) −4.13567 −0.179136
\(534\) −11.5839 −0.501286
\(535\) 5.33937 0.230841
\(536\) −3.40268 −0.146973
\(537\) −0.240529 −0.0103796
\(538\) 1.36281 0.0587548
\(539\) 0 0
\(540\) −5.12395 −0.220500
\(541\) −10.8436 −0.466201 −0.233100 0.972453i \(-0.574887\pi\)
−0.233100 + 0.972453i \(0.574887\pi\)
\(542\) −23.1963 −0.996367
\(543\) −11.8439 −0.508269
\(544\) −4.80536 −0.206028
\(545\) −7.36281 −0.315388
\(546\) 3.68878 0.157865
\(547\) 10.3129 0.440947 0.220474 0.975393i \(-0.429240\pi\)
0.220474 + 0.975393i \(0.429240\pi\)
\(548\) 10.5973 0.452695
\(549\) 4.80536 0.205088
\(550\) 0 0
\(551\) −8.03249 −0.342196
\(552\) −5.25963 −0.223865
\(553\) −12.6372 −0.537388
\(554\) 31.0385 1.31870
\(555\) 2.22980 0.0946496
\(556\) −14.7347 −0.624889
\(557\) 14.4811 0.613582 0.306791 0.951777i \(-0.400745\pi\)
0.306791 + 0.951777i \(0.400745\pi\)
\(558\) −11.8894 −0.503320
\(559\) 12.7980 0.541297
\(560\) −4.17554 −0.176449
\(561\) 0 0
\(562\) −2.77287 −0.116966
\(563\) −10.5340 −0.443956 −0.221978 0.975052i \(-0.571251\pi\)
−0.221978 + 0.975052i \(0.571251\pi\)
\(564\) 4.06498 0.171167
\(565\) −24.4958 −1.03055
\(566\) −9.23451 −0.388156
\(567\) −13.5457 −0.568867
\(568\) 7.57822 0.317975
\(569\) −10.3762 −0.434993 −0.217496 0.976061i \(-0.569789\pi\)
−0.217496 + 0.976061i \(0.569789\pi\)
\(570\) −0.948410 −0.0397245
\(571\) −33.2847 −1.39292 −0.696461 0.717594i \(-0.745243\pi\)
−0.696461 + 0.717594i \(0.745243\pi\)
\(572\) 0 0
\(573\) 20.7672 0.867561
\(574\) −10.0325 −0.418748
\(575\) −23.7789 −0.991648
\(576\) −2.40268 −0.100112
\(577\) −2.93365 −0.122129 −0.0610647 0.998134i \(-0.519450\pi\)
−0.0610647 + 0.998134i \(0.519450\pi\)
\(578\) −6.09146 −0.253371
\(579\) −14.3494 −0.596341
\(580\) −9.85695 −0.409287
\(581\) 36.3055 1.50621
\(582\) −1.81708 −0.0753202
\(583\) 0 0
\(584\) −10.0650 −0.416492
\(585\) −4.13567 −0.170989
\(586\) 17.7390 0.732792
\(587\) 8.90854 0.367695 0.183847 0.982955i \(-0.441145\pi\)
0.183847 + 0.982955i \(0.441145\pi\)
\(588\) 3.53835 0.145919
\(589\) −4.94841 −0.203896
\(590\) 17.8171 0.733517
\(591\) −11.5223 −0.473964
\(592\) 2.35109 0.0966292
\(593\) −16.3129 −0.669890 −0.334945 0.942238i \(-0.608718\pi\)
−0.334945 + 0.942238i \(0.608718\pi\)
\(594\) 0 0
\(595\) −20.0650 −0.822584
\(596\) −18.3511 −0.751690
\(597\) 11.7139 0.479418
\(598\) −9.54573 −0.390354
\(599\) 40.9826 1.67450 0.837251 0.546818i \(-0.184161\pi\)
0.837251 + 0.546818i \(0.184161\pi\)
\(600\) 2.70050 0.110248
\(601\) −0.349413 −0.0142528 −0.00712642 0.999975i \(-0.502268\pi\)
−0.00712642 + 0.999975i \(0.502268\pi\)
\(602\) 31.0459 1.26534
\(603\) −8.17554 −0.332934
\(604\) 7.64891 0.311230
\(605\) 0 0
\(606\) 10.8703 0.441577
\(607\) −5.56049 −0.225693 −0.112847 0.993612i \(-0.535997\pi\)
−0.112847 + 0.993612i \(0.535997\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 21.1240 0.855986
\(610\) 2.45427 0.0993704
\(611\) 7.37757 0.298464
\(612\) −11.5457 −0.466709
\(613\) 19.7407 0.797319 0.398659 0.917099i \(-0.369476\pi\)
0.398659 + 0.917099i \(0.369476\pi\)
\(614\) 20.9735 0.846422
\(615\) −2.79630 −0.112758
\(616\) 0 0
\(617\) 10.5973 0.426632 0.213316 0.976983i \(-0.431574\pi\)
0.213316 + 0.976983i \(0.431574\pi\)
\(618\) 12.0399 0.484315
\(619\) 4.22112 0.169661 0.0848306 0.996395i \(-0.472965\pi\)
0.0848306 + 0.996395i \(0.472965\pi\)
\(620\) −6.07236 −0.243872
\(621\) −28.4161 −1.14030
\(622\) 3.36281 0.134836
\(623\) −51.0003 −2.04328
\(624\) 1.08408 0.0433980
\(625\) 4.67973 0.187189
\(626\) 4.94103 0.197483
\(627\) 0 0
\(628\) 8.38358 0.334541
\(629\) 11.2978 0.450474
\(630\) −10.0325 −0.399704
\(631\) 13.6905 0.545009 0.272504 0.962155i \(-0.412148\pi\)
0.272504 + 0.962155i \(0.412148\pi\)
\(632\) −3.71390 −0.147731
\(633\) −8.62243 −0.342711
\(634\) −14.2861 −0.567374
\(635\) −14.3745 −0.570436
\(636\) −3.44255 −0.136506
\(637\) 6.42178 0.254440
\(638\) 0 0
\(639\) 18.2080 0.720299
\(640\) −1.22713 −0.0485067
\(641\) −42.9883 −1.69794 −0.848968 0.528445i \(-0.822775\pi\)
−0.848968 + 0.528445i \(0.822775\pi\)
\(642\) −3.36281 −0.132719
\(643\) 16.3658 0.645406 0.322703 0.946500i \(-0.395408\pi\)
0.322703 + 0.946500i \(0.395408\pi\)
\(644\) −23.1564 −0.912492
\(645\) 8.65325 0.340721
\(646\) −4.80536 −0.189064
\(647\) 39.9886 1.57211 0.786057 0.618154i \(-0.212119\pi\)
0.786057 + 0.618154i \(0.212119\pi\)
\(648\) −3.98090 −0.156385
\(649\) 0 0
\(650\) 4.90116 0.192239
\(651\) 13.0134 0.510035
\(652\) −14.2479 −0.557991
\(653\) −37.5976 −1.47131 −0.735655 0.677357i \(-0.763125\pi\)
−0.735655 + 0.677357i \(0.763125\pi\)
\(654\) 4.63719 0.181329
\(655\) −2.27872 −0.0890371
\(656\) −2.94841 −0.115116
\(657\) −24.1829 −0.943466
\(658\) 17.8968 0.697691
\(659\) 11.5075 0.448270 0.224135 0.974558i \(-0.428044\pi\)
0.224135 + 0.974558i \(0.428044\pi\)
\(660\) 0 0
\(661\) −29.2362 −1.13716 −0.568578 0.822629i \(-0.692506\pi\)
−0.568578 + 0.822629i \(0.692506\pi\)
\(662\) 31.9293 1.24097
\(663\) 5.20940 0.202316
\(664\) 10.6697 0.414064
\(665\) −4.17554 −0.161921
\(666\) 5.64891 0.218891
\(667\) −54.6640 −2.11660
\(668\) 10.8703 0.420586
\(669\) 1.24487 0.0481293
\(670\) −4.17554 −0.161315
\(671\) 0 0
\(672\) 2.62981 0.101447
\(673\) 47.0784 1.81474 0.907369 0.420335i \(-0.138087\pi\)
0.907369 + 0.420335i \(0.138087\pi\)
\(674\) −8.84523 −0.340706
\(675\) 14.5899 0.561567
\(676\) −11.0325 −0.424327
\(677\) −43.2539 −1.66238 −0.831192 0.555986i \(-0.812341\pi\)
−0.831192 + 0.555986i \(0.812341\pi\)
\(678\) 15.4278 0.592501
\(679\) −8.00000 −0.307012
\(680\) −5.89682 −0.226133
\(681\) 12.9588 0.496581
\(682\) 0 0
\(683\) 34.8556 1.33371 0.666856 0.745187i \(-0.267640\pi\)
0.666856 + 0.745187i \(0.267640\pi\)
\(684\) −2.40268 −0.0918687
\(685\) 13.0043 0.496870
\(686\) −8.24053 −0.314625
\(687\) −6.61505 −0.252380
\(688\) 9.12395 0.347847
\(689\) −6.24791 −0.238026
\(690\) −6.45427 −0.245710
\(691\) 28.4811 1.08347 0.541735 0.840549i \(-0.317768\pi\)
0.541735 + 0.840549i \(0.317768\pi\)
\(692\) −3.39530 −0.129070
\(693\) 0 0
\(694\) 5.27439 0.200213
\(695\) −18.0814 −0.685867
\(696\) 6.20804 0.235315
\(697\) −14.1682 −0.536657
\(698\) −10.9085 −0.412894
\(699\) −4.20636 −0.159099
\(700\) 11.8894 0.449379
\(701\) −12.8703 −0.486106 −0.243053 0.970013i \(-0.578149\pi\)
−0.243053 + 0.970013i \(0.578149\pi\)
\(702\) 5.85695 0.221056
\(703\) 2.35109 0.0886730
\(704\) 0 0
\(705\) 4.98828 0.187870
\(706\) 22.1300 0.832872
\(707\) 47.8586 1.79991
\(708\) −11.2214 −0.421727
\(709\) 1.41744 0.0532330 0.0266165 0.999646i \(-0.491527\pi\)
0.0266165 + 0.999646i \(0.491527\pi\)
\(710\) 9.29950 0.349004
\(711\) −8.92330 −0.334650
\(712\) −14.9883 −0.561710
\(713\) −33.6757 −1.26116
\(714\) 12.6372 0.472935
\(715\) 0 0
\(716\) −0.311217 −0.0116307
\(717\) −8.72729 −0.325927
\(718\) −16.3910 −0.611705
\(719\) −31.1564 −1.16194 −0.580970 0.813925i \(-0.697327\pi\)
−0.580970 + 0.813925i \(0.697327\pi\)
\(720\) −2.94841 −0.109881
\(721\) 53.0077 1.97411
\(722\) −1.00000 −0.0372161
\(723\) −8.81844 −0.327961
\(724\) −15.3246 −0.569535
\(725\) 28.0667 1.04237
\(726\) 0 0
\(727\) −8.57221 −0.317926 −0.158963 0.987285i \(-0.550815\pi\)
−0.158963 + 0.987285i \(0.550815\pi\)
\(728\) 4.77287 0.176894
\(729\) 0.116574 0.00431757
\(730\) −12.3511 −0.457134
\(731\) 43.8439 1.62162
\(732\) −1.54573 −0.0571319
\(733\) −44.6787 −1.65025 −0.825123 0.564952i \(-0.808895\pi\)
−0.825123 + 0.564952i \(0.808895\pi\)
\(734\) 32.3511 1.19410
\(735\) 4.34203 0.160158
\(736\) −6.80536 −0.250849
\(737\) 0 0
\(738\) −7.08408 −0.260769
\(739\) −29.4898 −1.08480 −0.542400 0.840120i \(-0.682484\pi\)
−0.542400 + 0.840120i \(0.682484\pi\)
\(740\) 2.88510 0.106058
\(741\) 1.08408 0.0398248
\(742\) −15.1564 −0.556411
\(743\) 13.2596 0.486449 0.243224 0.969970i \(-0.421795\pi\)
0.243224 + 0.969970i \(0.421795\pi\)
\(744\) 3.82446 0.140211
\(745\) −22.5193 −0.825042
\(746\) 17.5782 0.643584
\(747\) 25.6358 0.937966
\(748\) 0 0
\(749\) −14.8054 −0.540976
\(750\) 8.05593 0.294161
\(751\) −10.1829 −0.371580 −0.185790 0.982589i \(-0.559484\pi\)
−0.185790 + 0.982589i \(0.559484\pi\)
\(752\) 5.25963 0.191799
\(753\) −9.27439 −0.337977
\(754\) 11.2670 0.410320
\(755\) 9.38624 0.341600
\(756\) 14.2080 0.516741
\(757\) 40.1122 1.45790 0.728952 0.684565i \(-0.240008\pi\)
0.728952 + 0.684565i \(0.240008\pi\)
\(758\) −8.93365 −0.324485
\(759\) 0 0
\(760\) −1.22713 −0.0445128
\(761\) 38.7819 1.40584 0.702922 0.711267i \(-0.251878\pi\)
0.702922 + 0.711267i \(0.251878\pi\)
\(762\) 9.05327 0.327965
\(763\) 20.4161 0.739111
\(764\) 26.8703 0.972135
\(765\) −14.1682 −0.512251
\(766\) 16.0399 0.579544
\(767\) −20.3658 −0.735368
\(768\) 0.772866 0.0278884
\(769\) −8.15340 −0.294019 −0.147010 0.989135i \(-0.546965\pi\)
−0.147010 + 0.989135i \(0.546965\pi\)
\(770\) 0 0
\(771\) 18.7290 0.674507
\(772\) −18.5665 −0.668223
\(773\) −24.3893 −0.877222 −0.438611 0.898677i \(-0.644529\pi\)
−0.438611 + 0.898677i \(0.644529\pi\)
\(774\) 21.9219 0.787968
\(775\) 17.2904 0.621091
\(776\) −2.35109 −0.0843992
\(777\) −6.18292 −0.221811
\(778\) −17.2271 −0.617623
\(779\) −2.94841 −0.105638
\(780\) 1.33031 0.0476329
\(781\) 0 0
\(782\) −32.7022 −1.16943
\(783\) 33.5400 1.19862
\(784\) 4.57822 0.163508
\(785\) 10.2878 0.367187
\(786\) 1.43517 0.0511909
\(787\) 46.3779 1.65319 0.826596 0.562795i \(-0.190274\pi\)
0.826596 + 0.562795i \(0.190274\pi\)
\(788\) −14.9085 −0.531095
\(789\) −15.8951 −0.565882
\(790\) −4.55745 −0.162147
\(791\) 67.9236 2.41509
\(792\) 0 0
\(793\) −2.80536 −0.0996212
\(794\) −15.0784 −0.535112
\(795\) −4.22447 −0.149827
\(796\) 15.1564 0.537206
\(797\) 3.89682 0.138032 0.0690162 0.997616i \(-0.478014\pi\)
0.0690162 + 0.997616i \(0.478014\pi\)
\(798\) 2.62981 0.0930944
\(799\) 25.2744 0.894144
\(800\) 3.49414 0.123537
\(801\) −36.0120 −1.27242
\(802\) 13.1564 0.464570
\(803\) 0 0
\(804\) 2.62981 0.0927464
\(805\) −28.4161 −1.00153
\(806\) 6.94103 0.244487
\(807\) −1.05327 −0.0370767
\(808\) 14.0650 0.494804
\(809\) 43.3896 1.52550 0.762748 0.646695i \(-0.223849\pi\)
0.762748 + 0.646695i \(0.223849\pi\)
\(810\) −4.88510 −0.171645
\(811\) 12.9233 0.453798 0.226899 0.973918i \(-0.427141\pi\)
0.226899 + 0.973918i \(0.427141\pi\)
\(812\) 27.3320 0.959165
\(813\) 17.9276 0.628750
\(814\) 0 0
\(815\) −17.4841 −0.612441
\(816\) 3.71390 0.130012
\(817\) 9.12395 0.319207
\(818\) −16.3836 −0.572838
\(819\) 11.4677 0.400713
\(820\) −3.61810 −0.126349
\(821\) 36.5842 1.27680 0.638399 0.769705i \(-0.279597\pi\)
0.638399 + 0.769705i \(0.279597\pi\)
\(822\) −8.19030 −0.285670
\(823\) −21.6107 −0.753302 −0.376651 0.926355i \(-0.622924\pi\)
−0.376651 + 0.926355i \(0.622924\pi\)
\(824\) 15.5782 0.542693
\(825\) 0 0
\(826\) −49.4044 −1.71900
\(827\) 34.8851 1.21307 0.606537 0.795055i \(-0.292558\pi\)
0.606537 + 0.795055i \(0.292558\pi\)
\(828\) −16.3511 −0.568240
\(829\) 31.7407 1.10240 0.551200 0.834373i \(-0.314170\pi\)
0.551200 + 0.834373i \(0.314170\pi\)
\(830\) 13.0931 0.454469
\(831\) −23.9886 −0.832155
\(832\) 1.40268 0.0486291
\(833\) 22.0000 0.762255
\(834\) 11.3879 0.394331
\(835\) 13.3394 0.461628
\(836\) 0 0
\(837\) 20.6623 0.714194
\(838\) −1.12966 −0.0390234
\(839\) 13.4603 0.464701 0.232350 0.972632i \(-0.425358\pi\)
0.232350 + 0.972632i \(0.425358\pi\)
\(840\) 3.22713 0.111347
\(841\) 35.5209 1.22486
\(842\) 2.63719 0.0908837
\(843\) 2.14305 0.0738106
\(844\) −11.1564 −0.384021
\(845\) −13.5384 −0.465733
\(846\) 12.6372 0.434476
\(847\) 0 0
\(848\) −4.45427 −0.152960
\(849\) 7.13704 0.244943
\(850\) 16.7906 0.575913
\(851\) 16.0000 0.548473
\(852\) −5.85695 −0.200656
\(853\) −36.2981 −1.24282 −0.621412 0.783484i \(-0.713441\pi\)
−0.621412 + 0.783484i \(0.713441\pi\)
\(854\) −6.80536 −0.232875
\(855\) −2.94841 −0.100833
\(856\) −4.35109 −0.148717
\(857\) 43.8569 1.49812 0.749062 0.662499i \(-0.230504\pi\)
0.749062 + 0.662499i \(0.230504\pi\)
\(858\) 0 0
\(859\) −41.1980 −1.40566 −0.702829 0.711359i \(-0.748080\pi\)
−0.702829 + 0.711359i \(0.748080\pi\)
\(860\) 11.1963 0.381791
\(861\) 7.75377 0.264248
\(862\) −28.4958 −0.970571
\(863\) −24.8720 −0.846653 −0.423327 0.905977i \(-0.639138\pi\)
−0.423327 + 0.905977i \(0.639138\pi\)
\(864\) 4.17554 0.142055
\(865\) −4.16649 −0.141665
\(866\) 37.5075 1.27456
\(867\) 4.70788 0.159888
\(868\) 16.8378 0.571514
\(869\) 0 0
\(870\) 7.61810 0.258278
\(871\) 4.77287 0.161722
\(872\) 6.00000 0.203186
\(873\) −5.64891 −0.191187
\(874\) −6.80536 −0.230195
\(875\) 35.4677 1.19903
\(876\) 7.77888 0.262824
\(877\) −39.8911 −1.34703 −0.673514 0.739175i \(-0.735216\pi\)
−0.673514 + 0.739175i \(0.735216\pi\)
\(878\) −32.1300 −1.08433
\(879\) −13.7099 −0.462422
\(880\) 0 0
\(881\) −2.88343 −0.0971451 −0.0485725 0.998820i \(-0.515467\pi\)
−0.0485725 + 0.998820i \(0.515467\pi\)
\(882\) 11.0000 0.370389
\(883\) −4.27134 −0.143742 −0.0718711 0.997414i \(-0.522897\pi\)
−0.0718711 + 0.997414i \(0.522897\pi\)
\(884\) 6.74037 0.226703
\(885\) −13.7702 −0.462880
\(886\) −33.0385 −1.10995
\(887\) −22.3129 −0.749194 −0.374597 0.927188i \(-0.622219\pi\)
−0.374597 + 0.927188i \(0.622219\pi\)
\(888\) −1.81708 −0.0609771
\(889\) 39.8586 1.33682
\(890\) −18.3926 −0.616523
\(891\) 0 0
\(892\) 1.61072 0.0539307
\(893\) 5.25963 0.176007
\(894\) 14.1829 0.474348
\(895\) −0.381905 −0.0127657
\(896\) 3.40268 0.113676
\(897\) 7.37757 0.246330
\(898\) −7.88206 −0.263028
\(899\) 39.7481 1.32567
\(900\) 8.39530 0.279843
\(901\) −21.4044 −0.713082
\(902\) 0 0
\(903\) −23.9943 −0.798480
\(904\) 19.9618 0.663920
\(905\) −18.8054 −0.625111
\(906\) −5.91158 −0.196399
\(907\) −35.5578 −1.18068 −0.590338 0.807156i \(-0.701006\pi\)
−0.590338 + 0.807156i \(0.701006\pi\)
\(908\) 16.7672 0.556438
\(909\) 33.7936 1.12086
\(910\) 5.85695 0.194156
\(911\) −49.1980 −1.63000 −0.815001 0.579459i \(-0.803264\pi\)
−0.815001 + 0.579459i \(0.803264\pi\)
\(912\) 0.772866 0.0255921
\(913\) 0 0
\(914\) 24.9353 0.824787
\(915\) −1.89682 −0.0627069
\(916\) −8.55913 −0.282801
\(917\) 6.31860 0.208658
\(918\) 20.0650 0.662243
\(919\) 8.47200 0.279466 0.139733 0.990189i \(-0.455376\pi\)
0.139733 + 0.990189i \(0.455376\pi\)
\(920\) −8.35109 −0.275327
\(921\) −16.2097 −0.534128
\(922\) −26.6874 −0.878903
\(923\) −10.6298 −0.349885
\(924\) 0 0
\(925\) −8.21504 −0.270109
\(926\) 32.7022 1.07466
\(927\) 37.4295 1.22934
\(928\) 8.03249 0.263679
\(929\) −16.0017 −0.524998 −0.262499 0.964932i \(-0.584547\pi\)
−0.262499 + 0.964932i \(0.584547\pi\)
\(930\) 4.69312 0.153894
\(931\) 4.57822 0.150045
\(932\) −5.44255 −0.178277
\(933\) −2.59900 −0.0850874
\(934\) −11.3776 −0.372285
\(935\) 0 0
\(936\) 3.37019 0.110158
\(937\) 15.9766 0.521932 0.260966 0.965348i \(-0.415959\pi\)
0.260966 + 0.965348i \(0.415959\pi\)
\(938\) 11.5782 0.378042
\(939\) −3.81875 −0.124620
\(940\) 6.45427 0.210515
\(941\) 21.0915 0.687562 0.343781 0.939050i \(-0.388292\pi\)
0.343781 + 0.939050i \(0.388292\pi\)
\(942\) −6.47938 −0.211110
\(943\) −20.0650 −0.653406
\(944\) −14.5193 −0.472561
\(945\) 17.4352 0.567166
\(946\) 0 0
\(947\) 20.9735 0.681548 0.340774 0.940145i \(-0.389311\pi\)
0.340774 + 0.940145i \(0.389311\pi\)
\(948\) 2.87034 0.0932244
\(949\) 14.1179 0.458288
\(950\) 3.49414 0.113365
\(951\) 11.0412 0.358037
\(952\) 16.3511 0.529942
\(953\) −3.27439 −0.106068 −0.0530339 0.998593i \(-0.516889\pi\)
−0.0530339 + 0.998593i \(0.516889\pi\)
\(954\) −10.7022 −0.346496
\(955\) 32.9735 1.06700
\(956\) −11.2921 −0.365213
\(957\) 0 0
\(958\) −12.5973 −0.407001
\(959\) −36.0593 −1.16441
\(960\) 0.948410 0.0306098
\(961\) −6.51324 −0.210104
\(962\) −3.29782 −0.106326
\(963\) −10.4543 −0.336884
\(964\) −11.4101 −0.367493
\(965\) −22.7836 −0.733430
\(966\) 17.8968 0.575821
\(967\) 29.2744 0.941401 0.470700 0.882293i \(-0.344001\pi\)
0.470700 + 0.882293i \(0.344001\pi\)
\(968\) 0 0
\(969\) 3.71390 0.119308
\(970\) −2.88510 −0.0926350
\(971\) −38.3836 −1.23179 −0.615894 0.787829i \(-0.711205\pi\)
−0.615894 + 0.787829i \(0.711205\pi\)
\(972\) 15.6033 0.500477
\(973\) 50.1373 1.60733
\(974\) −9.69616 −0.310685
\(975\) −3.78794 −0.121311
\(976\) −2.00000 −0.0640184
\(977\) 10.9233 0.349467 0.174734 0.984616i \(-0.444094\pi\)
0.174734 + 0.984616i \(0.444094\pi\)
\(978\) 11.0117 0.352116
\(979\) 0 0
\(980\) 5.61810 0.179463
\(981\) 14.4161 0.460270
\(982\) −11.7538 −0.375078
\(983\) −32.1196 −1.02446 −0.512228 0.858849i \(-0.671180\pi\)
−0.512228 + 0.858849i \(0.671180\pi\)
\(984\) 2.27872 0.0726431
\(985\) −18.2948 −0.582920
\(986\) 38.5990 1.22924
\(987\) −13.8318 −0.440272
\(988\) 1.40268 0.0446252
\(989\) 62.0918 1.97440
\(990\) 0 0
\(991\) 4.37620 0.139015 0.0695073 0.997581i \(-0.477857\pi\)
0.0695073 + 0.997581i \(0.477857\pi\)
\(992\) 4.94841 0.157112
\(993\) −24.6771 −0.783103
\(994\) −25.7863 −0.817890
\(995\) 18.5990 0.589628
\(996\) −8.24623 −0.261292
\(997\) 8.37788 0.265330 0.132665 0.991161i \(-0.457647\pi\)
0.132665 + 0.991161i \(0.457647\pi\)
\(998\) −26.6640 −0.844034
\(999\) −9.81708 −0.310599
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 4598.2.a.bm.1.2 3
11.10 odd 2 418.2.a.h.1.2 3
33.32 even 2 3762.2.a.bd.1.2 3
44.43 even 2 3344.2.a.p.1.2 3
209.208 even 2 7942.2.a.bc.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.a.h.1.2 3 11.10 odd 2
3344.2.a.p.1.2 3 44.43 even 2
3762.2.a.bd.1.2 3 33.32 even 2
4598.2.a.bm.1.2 3 1.1 even 1 trivial
7942.2.a.bc.1.2 3 209.208 even 2