Properties

Label 8007.2.a.f.1.33
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.33
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.04801 q^{2} -1.00000 q^{3} -0.901675 q^{4} +2.25717 q^{5} -1.04801 q^{6} -3.56643 q^{7} -3.04098 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.04801 q^{2} -1.00000 q^{3} -0.901675 q^{4} +2.25717 q^{5} -1.04801 q^{6} -3.56643 q^{7} -3.04098 q^{8} +1.00000 q^{9} +2.36554 q^{10} -0.421505 q^{11} +0.901675 q^{12} +1.27099 q^{13} -3.73765 q^{14} -2.25717 q^{15} -1.38363 q^{16} -1.00000 q^{17} +1.04801 q^{18} +7.63021 q^{19} -2.03524 q^{20} +3.56643 q^{21} -0.441741 q^{22} -3.06983 q^{23} +3.04098 q^{24} +0.0948310 q^{25} +1.33201 q^{26} -1.00000 q^{27} +3.21576 q^{28} +6.05741 q^{29} -2.36554 q^{30} +0.390628 q^{31} +4.63191 q^{32} +0.421505 q^{33} -1.04801 q^{34} -8.05005 q^{35} -0.901675 q^{36} -8.69864 q^{37} +7.99653 q^{38} -1.27099 q^{39} -6.86403 q^{40} -5.09143 q^{41} +3.73765 q^{42} +4.23838 q^{43} +0.380060 q^{44} +2.25717 q^{45} -3.21721 q^{46} -4.45646 q^{47} +1.38363 q^{48} +5.71941 q^{49} +0.0993838 q^{50} +1.00000 q^{51} -1.14602 q^{52} +5.96794 q^{53} -1.04801 q^{54} -0.951409 q^{55} +10.8455 q^{56} -7.63021 q^{57} +6.34823 q^{58} +13.2068 q^{59} +2.03524 q^{60} +3.31573 q^{61} +0.409382 q^{62} -3.56643 q^{63} +7.62155 q^{64} +2.86884 q^{65} +0.441741 q^{66} -9.42494 q^{67} +0.901675 q^{68} +3.06983 q^{69} -8.43653 q^{70} -3.49949 q^{71} -3.04098 q^{72} -2.53428 q^{73} -9.11626 q^{74} -0.0948310 q^{75} -6.87997 q^{76} +1.50327 q^{77} -1.33201 q^{78} +3.30310 q^{79} -3.12310 q^{80} +1.00000 q^{81} -5.33587 q^{82} +7.63814 q^{83} -3.21576 q^{84} -2.25717 q^{85} +4.44186 q^{86} -6.05741 q^{87} +1.28179 q^{88} -6.18787 q^{89} +2.36554 q^{90} -4.53290 q^{91} +2.76799 q^{92} -0.390628 q^{93} -4.67041 q^{94} +17.2227 q^{95} -4.63191 q^{96} -15.5958 q^{97} +5.99400 q^{98} -0.421505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.04801 0.741055 0.370527 0.928822i \(-0.379177\pi\)
0.370527 + 0.928822i \(0.379177\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.901675 −0.450838
\(5\) 2.25717 1.00944 0.504719 0.863284i \(-0.331596\pi\)
0.504719 + 0.863284i \(0.331596\pi\)
\(6\) −1.04801 −0.427848
\(7\) −3.56643 −1.34798 −0.673992 0.738739i \(-0.735422\pi\)
−0.673992 + 0.738739i \(0.735422\pi\)
\(8\) −3.04098 −1.07515
\(9\) 1.00000 0.333333
\(10\) 2.36554 0.748049
\(11\) −0.421505 −0.127088 −0.0635442 0.997979i \(-0.520240\pi\)
−0.0635442 + 0.997979i \(0.520240\pi\)
\(12\) 0.901675 0.260291
\(13\) 1.27099 0.352509 0.176255 0.984345i \(-0.443602\pi\)
0.176255 + 0.984345i \(0.443602\pi\)
\(14\) −3.73765 −0.998930
\(15\) −2.25717 −0.582800
\(16\) −1.38363 −0.345908
\(17\) −1.00000 −0.242536
\(18\) 1.04801 0.247018
\(19\) 7.63021 1.75049 0.875245 0.483680i \(-0.160700\pi\)
0.875245 + 0.483680i \(0.160700\pi\)
\(20\) −2.03524 −0.455093
\(21\) 3.56643 0.778259
\(22\) −0.441741 −0.0941795
\(23\) −3.06983 −0.640103 −0.320052 0.947400i \(-0.603700\pi\)
−0.320052 + 0.947400i \(0.603700\pi\)
\(24\) 3.04098 0.620738
\(25\) 0.0948310 0.0189662
\(26\) 1.33201 0.261229
\(27\) −1.00000 −0.192450
\(28\) 3.21576 0.607722
\(29\) 6.05741 1.12483 0.562417 0.826854i \(-0.309872\pi\)
0.562417 + 0.826854i \(0.309872\pi\)
\(30\) −2.36554 −0.431887
\(31\) 0.390628 0.0701589 0.0350794 0.999385i \(-0.488832\pi\)
0.0350794 + 0.999385i \(0.488832\pi\)
\(32\) 4.63191 0.818814
\(33\) 0.421505 0.0733745
\(34\) −1.04801 −0.179732
\(35\) −8.05005 −1.36071
\(36\) −0.901675 −0.150279
\(37\) −8.69864 −1.43005 −0.715024 0.699100i \(-0.753584\pi\)
−0.715024 + 0.699100i \(0.753584\pi\)
\(38\) 7.99653 1.29721
\(39\) −1.27099 −0.203521
\(40\) −6.86403 −1.08530
\(41\) −5.09143 −0.795148 −0.397574 0.917570i \(-0.630148\pi\)
−0.397574 + 0.917570i \(0.630148\pi\)
\(42\) 3.73765 0.576732
\(43\) 4.23838 0.646346 0.323173 0.946340i \(-0.395250\pi\)
0.323173 + 0.946340i \(0.395250\pi\)
\(44\) 0.380060 0.0572962
\(45\) 2.25717 0.336480
\(46\) −3.21721 −0.474352
\(47\) −4.45646 −0.650041 −0.325020 0.945707i \(-0.605371\pi\)
−0.325020 + 0.945707i \(0.605371\pi\)
\(48\) 1.38363 0.199710
\(49\) 5.71941 0.817059
\(50\) 0.0993838 0.0140550
\(51\) 1.00000 0.140028
\(52\) −1.14602 −0.158924
\(53\) 5.96794 0.819760 0.409880 0.912139i \(-0.365571\pi\)
0.409880 + 0.912139i \(0.365571\pi\)
\(54\) −1.04801 −0.142616
\(55\) −0.951409 −0.128288
\(56\) 10.8455 1.44928
\(57\) −7.63021 −1.01065
\(58\) 6.34823 0.833563
\(59\) 13.2068 1.71938 0.859688 0.510819i \(-0.170658\pi\)
0.859688 + 0.510819i \(0.170658\pi\)
\(60\) 2.03524 0.262748
\(61\) 3.31573 0.424536 0.212268 0.977211i \(-0.431915\pi\)
0.212268 + 0.977211i \(0.431915\pi\)
\(62\) 0.409382 0.0519916
\(63\) −3.56643 −0.449328
\(64\) 7.62155 0.952694
\(65\) 2.86884 0.355836
\(66\) 0.441741 0.0543746
\(67\) −9.42494 −1.15144 −0.575720 0.817647i \(-0.695278\pi\)
−0.575720 + 0.817647i \(0.695278\pi\)
\(68\) 0.901675 0.109344
\(69\) 3.06983 0.369564
\(70\) −8.43653 −1.00836
\(71\) −3.49949 −0.415313 −0.207656 0.978202i \(-0.566584\pi\)
−0.207656 + 0.978202i \(0.566584\pi\)
\(72\) −3.04098 −0.358383
\(73\) −2.53428 −0.296615 −0.148307 0.988941i \(-0.547382\pi\)
−0.148307 + 0.988941i \(0.547382\pi\)
\(74\) −9.11626 −1.05974
\(75\) −0.0948310 −0.0109501
\(76\) −6.87997 −0.789186
\(77\) 1.50327 0.171313
\(78\) −1.33201 −0.150820
\(79\) 3.30310 0.371627 0.185814 0.982585i \(-0.440508\pi\)
0.185814 + 0.982585i \(0.440508\pi\)
\(80\) −3.12310 −0.349173
\(81\) 1.00000 0.111111
\(82\) −5.33587 −0.589248
\(83\) 7.63814 0.838394 0.419197 0.907895i \(-0.362312\pi\)
0.419197 + 0.907895i \(0.362312\pi\)
\(84\) −3.21576 −0.350868
\(85\) −2.25717 −0.244825
\(86\) 4.44186 0.478978
\(87\) −6.05741 −0.649423
\(88\) 1.28179 0.136639
\(89\) −6.18787 −0.655913 −0.327957 0.944693i \(-0.606360\pi\)
−0.327957 + 0.944693i \(0.606360\pi\)
\(90\) 2.36554 0.249350
\(91\) −4.53290 −0.475177
\(92\) 2.76799 0.288583
\(93\) −0.390628 −0.0405062
\(94\) −4.67041 −0.481716
\(95\) 17.2227 1.76701
\(96\) −4.63191 −0.472742
\(97\) −15.5958 −1.58352 −0.791759 0.610834i \(-0.790834\pi\)
−0.791759 + 0.610834i \(0.790834\pi\)
\(98\) 5.99400 0.605486
\(99\) −0.421505 −0.0423628
\(100\) −0.0855067 −0.00855067
\(101\) −6.17997 −0.614930 −0.307465 0.951559i \(-0.599481\pi\)
−0.307465 + 0.951559i \(0.599481\pi\)
\(102\) 1.04801 0.103768
\(103\) 8.29378 0.817210 0.408605 0.912711i \(-0.366015\pi\)
0.408605 + 0.912711i \(0.366015\pi\)
\(104\) −3.86506 −0.379000
\(105\) 8.05005 0.785604
\(106\) 6.25446 0.607487
\(107\) −8.12096 −0.785083 −0.392542 0.919734i \(-0.628404\pi\)
−0.392542 + 0.919734i \(0.628404\pi\)
\(108\) 0.901675 0.0867637
\(109\) −4.46239 −0.427420 −0.213710 0.976897i \(-0.568555\pi\)
−0.213710 + 0.976897i \(0.568555\pi\)
\(110\) −0.997086 −0.0950684
\(111\) 8.69864 0.825639
\(112\) 4.93462 0.466278
\(113\) 4.59014 0.431804 0.215902 0.976415i \(-0.430731\pi\)
0.215902 + 0.976415i \(0.430731\pi\)
\(114\) −7.99653 −0.748944
\(115\) −6.92913 −0.646145
\(116\) −5.46182 −0.507117
\(117\) 1.27099 0.117503
\(118\) 13.8408 1.27415
\(119\) 3.56643 0.326934
\(120\) 6.86403 0.626597
\(121\) −10.8223 −0.983849
\(122\) 3.47492 0.314605
\(123\) 5.09143 0.459079
\(124\) −0.352220 −0.0316303
\(125\) −11.0718 −0.990293
\(126\) −3.73765 −0.332977
\(127\) 20.1734 1.79010 0.895049 0.445967i \(-0.147140\pi\)
0.895049 + 0.445967i \(0.147140\pi\)
\(128\) −1.27636 −0.112815
\(129\) −4.23838 −0.373168
\(130\) 3.00658 0.263694
\(131\) −3.99782 −0.349291 −0.174645 0.984631i \(-0.555878\pi\)
−0.174645 + 0.984631i \(0.555878\pi\)
\(132\) −0.380060 −0.0330800
\(133\) −27.2126 −2.35963
\(134\) −9.87744 −0.853280
\(135\) −2.25717 −0.194267
\(136\) 3.04098 0.260762
\(137\) −5.00848 −0.427903 −0.213952 0.976844i \(-0.568633\pi\)
−0.213952 + 0.976844i \(0.568633\pi\)
\(138\) 3.21721 0.273867
\(139\) 3.93158 0.333473 0.166736 0.986002i \(-0.446677\pi\)
0.166736 + 0.986002i \(0.446677\pi\)
\(140\) 7.25853 0.613458
\(141\) 4.45646 0.375301
\(142\) −3.66750 −0.307769
\(143\) −0.535728 −0.0447998
\(144\) −1.38363 −0.115303
\(145\) 13.6726 1.13545
\(146\) −2.65595 −0.219808
\(147\) −5.71941 −0.471729
\(148\) 7.84335 0.644719
\(149\) −7.57201 −0.620323 −0.310162 0.950684i \(-0.600383\pi\)
−0.310162 + 0.950684i \(0.600383\pi\)
\(150\) −0.0993838 −0.00811465
\(151\) −11.5120 −0.936834 −0.468417 0.883508i \(-0.655175\pi\)
−0.468417 + 0.883508i \(0.655175\pi\)
\(152\) −23.2033 −1.88204
\(153\) −1.00000 −0.0808452
\(154\) 1.57544 0.126952
\(155\) 0.881715 0.0708211
\(156\) 1.14602 0.0917550
\(157\) −1.00000 −0.0798087
\(158\) 3.46168 0.275396
\(159\) −5.96794 −0.473289
\(160\) 10.4550 0.826542
\(161\) 10.9483 0.862849
\(162\) 1.04801 0.0823394
\(163\) −1.21962 −0.0955283 −0.0477642 0.998859i \(-0.515210\pi\)
−0.0477642 + 0.998859i \(0.515210\pi\)
\(164\) 4.59081 0.358482
\(165\) 0.951409 0.0740671
\(166\) 8.00484 0.621296
\(167\) −0.879959 −0.0680933 −0.0340466 0.999420i \(-0.510839\pi\)
−0.0340466 + 0.999420i \(0.510839\pi\)
\(168\) −10.8455 −0.836745
\(169\) −11.3846 −0.875737
\(170\) −2.36554 −0.181429
\(171\) 7.63021 0.583496
\(172\) −3.82164 −0.291397
\(173\) 2.61409 0.198746 0.0993728 0.995050i \(-0.468316\pi\)
0.0993728 + 0.995050i \(0.468316\pi\)
\(174\) −6.34823 −0.481258
\(175\) −0.338208 −0.0255661
\(176\) 0.583207 0.0439609
\(177\) −13.2068 −0.992682
\(178\) −6.48495 −0.486068
\(179\) 19.6040 1.46527 0.732637 0.680620i \(-0.238289\pi\)
0.732637 + 0.680620i \(0.238289\pi\)
\(180\) −2.03524 −0.151698
\(181\) −12.1854 −0.905733 −0.452866 0.891578i \(-0.649599\pi\)
−0.452866 + 0.891578i \(0.649599\pi\)
\(182\) −4.75052 −0.352132
\(183\) −3.31573 −0.245106
\(184\) 9.33530 0.688207
\(185\) −19.6343 −1.44355
\(186\) −0.409382 −0.0300174
\(187\) 0.421505 0.0308235
\(188\) 4.01828 0.293063
\(189\) 3.56643 0.259420
\(190\) 18.0496 1.30945
\(191\) −23.0490 −1.66777 −0.833884 0.551939i \(-0.813888\pi\)
−0.833884 + 0.551939i \(0.813888\pi\)
\(192\) −7.62155 −0.550038
\(193\) −7.07541 −0.509299 −0.254650 0.967033i \(-0.581960\pi\)
−0.254650 + 0.967033i \(0.581960\pi\)
\(194\) −16.3446 −1.17347
\(195\) −2.86884 −0.205442
\(196\) −5.15705 −0.368361
\(197\) −23.2658 −1.65762 −0.828809 0.559532i \(-0.810981\pi\)
−0.828809 + 0.559532i \(0.810981\pi\)
\(198\) −0.441741 −0.0313932
\(199\) −11.4408 −0.811015 −0.405507 0.914092i \(-0.632905\pi\)
−0.405507 + 0.914092i \(0.632905\pi\)
\(200\) −0.288380 −0.0203915
\(201\) 9.42494 0.664784
\(202\) −6.47667 −0.455697
\(203\) −21.6033 −1.51626
\(204\) −0.901675 −0.0631299
\(205\) −11.4922 −0.802653
\(206\) 8.69196 0.605598
\(207\) −3.06983 −0.213368
\(208\) −1.75858 −0.121936
\(209\) −3.21617 −0.222467
\(210\) 8.43653 0.582176
\(211\) 0.124091 0.00854280 0.00427140 0.999991i \(-0.498640\pi\)
0.00427140 + 0.999991i \(0.498640\pi\)
\(212\) −5.38115 −0.369579
\(213\) 3.49949 0.239781
\(214\) −8.51085 −0.581790
\(215\) 9.56675 0.652447
\(216\) 3.04098 0.206913
\(217\) −1.39315 −0.0945730
\(218\) −4.67663 −0.316741
\(219\) 2.53428 0.171251
\(220\) 0.857862 0.0578370
\(221\) −1.27099 −0.0854960
\(222\) 9.11626 0.611843
\(223\) −2.00533 −0.134287 −0.0671435 0.997743i \(-0.521389\pi\)
−0.0671435 + 0.997743i \(0.521389\pi\)
\(224\) −16.5194 −1.10375
\(225\) 0.0948310 0.00632207
\(226\) 4.81051 0.319990
\(227\) −12.3595 −0.820327 −0.410163 0.912012i \(-0.634528\pi\)
−0.410163 + 0.912012i \(0.634528\pi\)
\(228\) 6.87997 0.455637
\(229\) 8.69393 0.574511 0.287256 0.957854i \(-0.407257\pi\)
0.287256 + 0.957854i \(0.407257\pi\)
\(230\) −7.26180 −0.478829
\(231\) −1.50327 −0.0989076
\(232\) −18.4205 −1.20937
\(233\) −28.2536 −1.85095 −0.925477 0.378804i \(-0.876336\pi\)
−0.925477 + 0.378804i \(0.876336\pi\)
\(234\) 1.33201 0.0870762
\(235\) −10.0590 −0.656176
\(236\) −11.9082 −0.775159
\(237\) −3.30310 −0.214559
\(238\) 3.73765 0.242276
\(239\) −6.43478 −0.416232 −0.208116 0.978104i \(-0.566733\pi\)
−0.208116 + 0.978104i \(0.566733\pi\)
\(240\) 3.12310 0.201595
\(241\) −5.43886 −0.350347 −0.175174 0.984538i \(-0.556049\pi\)
−0.175174 + 0.984538i \(0.556049\pi\)
\(242\) −11.3419 −0.729086
\(243\) −1.00000 −0.0641500
\(244\) −2.98971 −0.191397
\(245\) 12.9097 0.824771
\(246\) 5.33587 0.340202
\(247\) 9.69792 0.617064
\(248\) −1.18789 −0.0754313
\(249\) −7.63814 −0.484047
\(250\) −11.6034 −0.733862
\(251\) −9.26943 −0.585081 −0.292541 0.956253i \(-0.594501\pi\)
−0.292541 + 0.956253i \(0.594501\pi\)
\(252\) 3.21576 0.202574
\(253\) 1.29395 0.0813497
\(254\) 21.1419 1.32656
\(255\) 2.25717 0.141350
\(256\) −16.5807 −1.03630
\(257\) −22.9228 −1.42989 −0.714943 0.699182i \(-0.753548\pi\)
−0.714943 + 0.699182i \(0.753548\pi\)
\(258\) −4.44186 −0.276538
\(259\) 31.0231 1.92768
\(260\) −2.58677 −0.160424
\(261\) 6.05741 0.374944
\(262\) −4.18975 −0.258844
\(263\) 16.7423 1.03237 0.516186 0.856477i \(-0.327351\pi\)
0.516186 + 0.856477i \(0.327351\pi\)
\(264\) −1.28179 −0.0788887
\(265\) 13.4707 0.827497
\(266\) −28.5191 −1.74862
\(267\) 6.18787 0.378692
\(268\) 8.49824 0.519113
\(269\) 5.40082 0.329294 0.164647 0.986353i \(-0.447352\pi\)
0.164647 + 0.986353i \(0.447352\pi\)
\(270\) −2.36554 −0.143962
\(271\) 4.80776 0.292050 0.146025 0.989281i \(-0.453352\pi\)
0.146025 + 0.989281i \(0.453352\pi\)
\(272\) 1.38363 0.0838950
\(273\) 4.53290 0.274343
\(274\) −5.24894 −0.317100
\(275\) −0.0399717 −0.00241038
\(276\) −2.76799 −0.166613
\(277\) −13.2220 −0.794431 −0.397215 0.917725i \(-0.630023\pi\)
−0.397215 + 0.917725i \(0.630023\pi\)
\(278\) 4.12034 0.247121
\(279\) 0.390628 0.0233863
\(280\) 24.4801 1.46296
\(281\) 10.7484 0.641195 0.320597 0.947216i \(-0.396116\pi\)
0.320597 + 0.947216i \(0.396116\pi\)
\(282\) 4.67041 0.278119
\(283\) −11.3334 −0.673700 −0.336850 0.941558i \(-0.609362\pi\)
−0.336850 + 0.941558i \(0.609362\pi\)
\(284\) 3.15540 0.187238
\(285\) −17.2227 −1.02018
\(286\) −0.561448 −0.0331991
\(287\) 18.1582 1.07185
\(288\) 4.63191 0.272938
\(289\) 1.00000 0.0588235
\(290\) 14.3291 0.841431
\(291\) 15.5958 0.914245
\(292\) 2.28509 0.133725
\(293\) −31.4410 −1.83680 −0.918402 0.395648i \(-0.870520\pi\)
−0.918402 + 0.395648i \(0.870520\pi\)
\(294\) −5.99400 −0.349577
\(295\) 29.8100 1.73560
\(296\) 26.4524 1.53752
\(297\) 0.421505 0.0244582
\(298\) −7.93554 −0.459694
\(299\) −3.90172 −0.225642
\(300\) 0.0855067 0.00493673
\(301\) −15.1159 −0.871264
\(302\) −12.0647 −0.694245
\(303\) 6.17997 0.355030
\(304\) −10.5574 −0.605508
\(305\) 7.48418 0.428543
\(306\) −1.04801 −0.0599107
\(307\) 2.77979 0.158651 0.0793255 0.996849i \(-0.474723\pi\)
0.0793255 + 0.996849i \(0.474723\pi\)
\(308\) −1.35546 −0.0772344
\(309\) −8.29378 −0.471817
\(310\) 0.924046 0.0524823
\(311\) 18.3551 1.04082 0.520410 0.853917i \(-0.325779\pi\)
0.520410 + 0.853917i \(0.325779\pi\)
\(312\) 3.86506 0.218816
\(313\) 23.4219 1.32388 0.661941 0.749556i \(-0.269733\pi\)
0.661941 + 0.749556i \(0.269733\pi\)
\(314\) −1.04801 −0.0591426
\(315\) −8.05005 −0.453569
\(316\) −2.97832 −0.167544
\(317\) 4.76548 0.267656 0.133828 0.991005i \(-0.457273\pi\)
0.133828 + 0.991005i \(0.457273\pi\)
\(318\) −6.25446 −0.350733
\(319\) −2.55323 −0.142953
\(320\) 17.2032 0.961686
\(321\) 8.12096 0.453268
\(322\) 11.4739 0.639418
\(323\) −7.63021 −0.424556
\(324\) −0.901675 −0.0500931
\(325\) 0.120529 0.00668576
\(326\) −1.27818 −0.0707917
\(327\) 4.46239 0.246771
\(328\) 15.4830 0.854903
\(329\) 15.8936 0.876244
\(330\) 0.997086 0.0548878
\(331\) 6.21994 0.341879 0.170939 0.985282i \(-0.445320\pi\)
0.170939 + 0.985282i \(0.445320\pi\)
\(332\) −6.88712 −0.377980
\(333\) −8.69864 −0.476683
\(334\) −0.922206 −0.0504609
\(335\) −21.2737 −1.16231
\(336\) −4.93462 −0.269206
\(337\) −16.6725 −0.908208 −0.454104 0.890949i \(-0.650041\pi\)
−0.454104 + 0.890949i \(0.650041\pi\)
\(338\) −11.9312 −0.648969
\(339\) −4.59014 −0.249302
\(340\) 2.03524 0.110376
\(341\) −0.164652 −0.00891638
\(342\) 7.99653 0.432403
\(343\) 4.56712 0.246601
\(344\) −12.8888 −0.694919
\(345\) 6.92913 0.373052
\(346\) 2.73959 0.147281
\(347\) 21.8226 1.17150 0.585750 0.810492i \(-0.300800\pi\)
0.585750 + 0.810492i \(0.300800\pi\)
\(348\) 5.46182 0.292784
\(349\) −10.4391 −0.558794 −0.279397 0.960176i \(-0.590135\pi\)
−0.279397 + 0.960176i \(0.590135\pi\)
\(350\) −0.354445 −0.0189459
\(351\) −1.27099 −0.0678404
\(352\) −1.95237 −0.104062
\(353\) −20.4592 −1.08893 −0.544467 0.838783i \(-0.683268\pi\)
−0.544467 + 0.838783i \(0.683268\pi\)
\(354\) −13.8408 −0.735632
\(355\) −7.89895 −0.419232
\(356\) 5.57945 0.295710
\(357\) −3.56643 −0.188755
\(358\) 20.5452 1.08585
\(359\) −30.0263 −1.58473 −0.792364 0.610049i \(-0.791150\pi\)
−0.792364 + 0.610049i \(0.791150\pi\)
\(360\) −6.86403 −0.361766
\(361\) 39.2200 2.06421
\(362\) −12.7704 −0.671198
\(363\) 10.8223 0.568025
\(364\) 4.08720 0.214227
\(365\) −5.72030 −0.299414
\(366\) −3.47492 −0.181637
\(367\) 26.8682 1.40251 0.701255 0.712910i \(-0.252623\pi\)
0.701255 + 0.712910i \(0.252623\pi\)
\(368\) 4.24751 0.221417
\(369\) −5.09143 −0.265049
\(370\) −20.5770 −1.06975
\(371\) −21.2842 −1.10502
\(372\) 0.352220 0.0182617
\(373\) −35.9335 −1.86057 −0.930283 0.366842i \(-0.880439\pi\)
−0.930283 + 0.366842i \(0.880439\pi\)
\(374\) 0.441741 0.0228419
\(375\) 11.0718 0.571746
\(376\) 13.5520 0.698892
\(377\) 7.69891 0.396514
\(378\) 3.73765 0.192244
\(379\) 7.61080 0.390940 0.195470 0.980710i \(-0.437377\pi\)
0.195470 + 0.980710i \(0.437377\pi\)
\(380\) −15.5293 −0.796635
\(381\) −20.1734 −1.03351
\(382\) −24.1556 −1.23591
\(383\) −20.2083 −1.03260 −0.516299 0.856408i \(-0.672691\pi\)
−0.516299 + 0.856408i \(0.672691\pi\)
\(384\) 1.27636 0.0651339
\(385\) 3.39313 0.172930
\(386\) −7.41510 −0.377419
\(387\) 4.23838 0.215449
\(388\) 14.0624 0.713909
\(389\) 5.63426 0.285668 0.142834 0.989747i \(-0.454378\pi\)
0.142834 + 0.989747i \(0.454378\pi\)
\(390\) −3.00658 −0.152244
\(391\) 3.06983 0.155248
\(392\) −17.3926 −0.878461
\(393\) 3.99782 0.201663
\(394\) −24.3828 −1.22839
\(395\) 7.45566 0.375135
\(396\) 0.380060 0.0190987
\(397\) −22.6177 −1.13515 −0.567574 0.823322i \(-0.692118\pi\)
−0.567574 + 0.823322i \(0.692118\pi\)
\(398\) −11.9900 −0.601006
\(399\) 27.2126 1.36233
\(400\) −0.131211 −0.00656056
\(401\) −9.68940 −0.483866 −0.241933 0.970293i \(-0.577781\pi\)
−0.241933 + 0.970293i \(0.577781\pi\)
\(402\) 9.87744 0.492642
\(403\) 0.496484 0.0247316
\(404\) 5.57233 0.277234
\(405\) 2.25717 0.112160
\(406\) −22.6405 −1.12363
\(407\) 3.66652 0.181743
\(408\) −3.04098 −0.150551
\(409\) 11.0779 0.547768 0.273884 0.961763i \(-0.411692\pi\)
0.273884 + 0.961763i \(0.411692\pi\)
\(410\) −12.0440 −0.594810
\(411\) 5.00848 0.247050
\(412\) −7.47829 −0.368429
\(413\) −47.1010 −2.31769
\(414\) −3.21721 −0.158117
\(415\) 17.2406 0.846308
\(416\) 5.88711 0.288639
\(417\) −3.93158 −0.192530
\(418\) −3.37057 −0.164860
\(419\) −17.7910 −0.869147 −0.434574 0.900636i \(-0.643101\pi\)
−0.434574 + 0.900636i \(0.643101\pi\)
\(420\) −7.25853 −0.354180
\(421\) 9.33643 0.455030 0.227515 0.973775i \(-0.426940\pi\)
0.227515 + 0.973775i \(0.426940\pi\)
\(422\) 0.130049 0.00633068
\(423\) −4.45646 −0.216680
\(424\) −18.1484 −0.881365
\(425\) −0.0948310 −0.00459998
\(426\) 3.66750 0.177691
\(427\) −11.8253 −0.572267
\(428\) 7.32247 0.353945
\(429\) 0.535728 0.0258652
\(430\) 10.0260 0.483499
\(431\) −8.79932 −0.423848 −0.211924 0.977286i \(-0.567973\pi\)
−0.211924 + 0.977286i \(0.567973\pi\)
\(432\) 1.38363 0.0665700
\(433\) 18.3743 0.883010 0.441505 0.897259i \(-0.354445\pi\)
0.441505 + 0.897259i \(0.354445\pi\)
\(434\) −1.46003 −0.0700838
\(435\) −13.6726 −0.655553
\(436\) 4.02363 0.192697
\(437\) −23.4234 −1.12049
\(438\) 2.65595 0.126906
\(439\) 17.6191 0.840911 0.420456 0.907313i \(-0.361870\pi\)
0.420456 + 0.907313i \(0.361870\pi\)
\(440\) 2.89322 0.137929
\(441\) 5.71941 0.272353
\(442\) −1.33201 −0.0633573
\(443\) 7.11162 0.337883 0.168942 0.985626i \(-0.445965\pi\)
0.168942 + 0.985626i \(0.445965\pi\)
\(444\) −7.84335 −0.372229
\(445\) −13.9671 −0.662104
\(446\) −2.10161 −0.0995141
\(447\) 7.57201 0.358144
\(448\) −27.1817 −1.28422
\(449\) 16.1775 0.763461 0.381731 0.924274i \(-0.375328\pi\)
0.381731 + 0.924274i \(0.375328\pi\)
\(450\) 0.0993838 0.00468500
\(451\) 2.14606 0.101054
\(452\) −4.13881 −0.194673
\(453\) 11.5120 0.540881
\(454\) −12.9528 −0.607907
\(455\) −10.2315 −0.479661
\(456\) 23.2033 1.08660
\(457\) −0.714642 −0.0334295 −0.0167148 0.999860i \(-0.505321\pi\)
−0.0167148 + 0.999860i \(0.505321\pi\)
\(458\) 9.11133 0.425744
\(459\) 1.00000 0.0466760
\(460\) 6.24783 0.291306
\(461\) 33.0737 1.54039 0.770197 0.637806i \(-0.220158\pi\)
0.770197 + 0.637806i \(0.220158\pi\)
\(462\) −1.57544 −0.0732960
\(463\) 40.4768 1.88112 0.940559 0.339630i \(-0.110302\pi\)
0.940559 + 0.339630i \(0.110302\pi\)
\(464\) −8.38123 −0.389089
\(465\) −0.881715 −0.0408886
\(466\) −29.6100 −1.37166
\(467\) −8.17607 −0.378343 −0.189172 0.981944i \(-0.560580\pi\)
−0.189172 + 0.981944i \(0.560580\pi\)
\(468\) −1.14602 −0.0529748
\(469\) 33.6134 1.55212
\(470\) −10.5419 −0.486263
\(471\) 1.00000 0.0460776
\(472\) −40.1616 −1.84859
\(473\) −1.78649 −0.0821431
\(474\) −3.46168 −0.159000
\(475\) 0.723580 0.0332001
\(476\) −3.21576 −0.147394
\(477\) 5.96794 0.273253
\(478\) −6.74372 −0.308450
\(479\) −36.3104 −1.65907 −0.829533 0.558458i \(-0.811393\pi\)
−0.829533 + 0.558458i \(0.811393\pi\)
\(480\) −10.4550 −0.477204
\(481\) −11.0559 −0.504105
\(482\) −5.69997 −0.259627
\(483\) −10.9483 −0.498166
\(484\) 9.75823 0.443556
\(485\) −35.2025 −1.59846
\(486\) −1.04801 −0.0475387
\(487\) 14.7074 0.666458 0.333229 0.942846i \(-0.391862\pi\)
0.333229 + 0.942846i \(0.391862\pi\)
\(488\) −10.0831 −0.456440
\(489\) 1.21962 0.0551533
\(490\) 13.5295 0.611201
\(491\) 36.6252 1.65287 0.826437 0.563029i \(-0.190364\pi\)
0.826437 + 0.563029i \(0.190364\pi\)
\(492\) −4.59081 −0.206970
\(493\) −6.05741 −0.272812
\(494\) 10.1635 0.457278
\(495\) −0.951409 −0.0427626
\(496\) −0.540485 −0.0242685
\(497\) 12.4807 0.559834
\(498\) −8.00484 −0.358706
\(499\) −23.3665 −1.04603 −0.523014 0.852324i \(-0.675192\pi\)
−0.523014 + 0.852324i \(0.675192\pi\)
\(500\) 9.98318 0.446461
\(501\) 0.879959 0.0393137
\(502\) −9.71446 −0.433577
\(503\) −36.0217 −1.60613 −0.803065 0.595892i \(-0.796799\pi\)
−0.803065 + 0.595892i \(0.796799\pi\)
\(504\) 10.8455 0.483095
\(505\) −13.9493 −0.620734
\(506\) 1.35607 0.0602846
\(507\) 11.3846 0.505607
\(508\) −18.1898 −0.807044
\(509\) 20.0525 0.888811 0.444405 0.895826i \(-0.353415\pi\)
0.444405 + 0.895826i \(0.353415\pi\)
\(510\) 2.36554 0.104748
\(511\) 9.03832 0.399832
\(512\) −14.8241 −0.655137
\(513\) −7.63021 −0.336882
\(514\) −24.0234 −1.05962
\(515\) 18.7205 0.824923
\(516\) 3.82164 0.168238
\(517\) 1.87842 0.0826127
\(518\) 32.5125 1.42852
\(519\) −2.61409 −0.114746
\(520\) −8.72411 −0.382578
\(521\) 6.21976 0.272493 0.136246 0.990675i \(-0.456496\pi\)
0.136246 + 0.990675i \(0.456496\pi\)
\(522\) 6.34823 0.277854
\(523\) −40.9217 −1.78938 −0.894690 0.446687i \(-0.852604\pi\)
−0.894690 + 0.446687i \(0.852604\pi\)
\(524\) 3.60473 0.157473
\(525\) 0.338208 0.0147606
\(526\) 17.5460 0.765044
\(527\) −0.390628 −0.0170160
\(528\) −0.583207 −0.0253808
\(529\) −13.5762 −0.590268
\(530\) 14.1174 0.613221
\(531\) 13.2068 0.573125
\(532\) 24.5369 1.06381
\(533\) −6.47115 −0.280297
\(534\) 6.48495 0.280631
\(535\) −18.3304 −0.792493
\(536\) 28.6611 1.23797
\(537\) −19.6040 −0.845976
\(538\) 5.66012 0.244025
\(539\) −2.41076 −0.103839
\(540\) 2.03524 0.0875827
\(541\) 18.2912 0.786398 0.393199 0.919453i \(-0.371368\pi\)
0.393199 + 0.919453i \(0.371368\pi\)
\(542\) 5.03858 0.216425
\(543\) 12.1854 0.522925
\(544\) −4.63191 −0.198591
\(545\) −10.0724 −0.431454
\(546\) 4.75052 0.203303
\(547\) −8.62032 −0.368578 −0.184289 0.982872i \(-0.558998\pi\)
−0.184289 + 0.982872i \(0.558998\pi\)
\(548\) 4.51602 0.192915
\(549\) 3.31573 0.141512
\(550\) −0.0418907 −0.00178623
\(551\) 46.2193 1.96901
\(552\) −9.33530 −0.397337
\(553\) −11.7803 −0.500948
\(554\) −13.8568 −0.588717
\(555\) 19.6343 0.833431
\(556\) −3.54501 −0.150342
\(557\) 6.27485 0.265874 0.132937 0.991124i \(-0.457559\pi\)
0.132937 + 0.991124i \(0.457559\pi\)
\(558\) 0.409382 0.0173305
\(559\) 5.38693 0.227843
\(560\) 11.1383 0.470679
\(561\) −0.421505 −0.0177959
\(562\) 11.2644 0.475161
\(563\) −35.2018 −1.48358 −0.741789 0.670633i \(-0.766023\pi\)
−0.741789 + 0.670633i \(0.766023\pi\)
\(564\) −4.01828 −0.169200
\(565\) 10.3607 0.435879
\(566\) −11.8775 −0.499249
\(567\) −3.56643 −0.149776
\(568\) 10.6419 0.446523
\(569\) 38.1849 1.60079 0.800397 0.599471i \(-0.204622\pi\)
0.800397 + 0.599471i \(0.204622\pi\)
\(570\) −18.0496 −0.756013
\(571\) −11.7239 −0.490632 −0.245316 0.969443i \(-0.578892\pi\)
−0.245316 + 0.969443i \(0.578892\pi\)
\(572\) 0.483053 0.0201974
\(573\) 23.0490 0.962887
\(574\) 19.0300 0.794296
\(575\) −0.291115 −0.0121403
\(576\) 7.62155 0.317565
\(577\) 10.5620 0.439703 0.219852 0.975533i \(-0.429443\pi\)
0.219852 + 0.975533i \(0.429443\pi\)
\(578\) 1.04801 0.0435915
\(579\) 7.07541 0.294044
\(580\) −12.3283 −0.511904
\(581\) −27.2409 −1.13014
\(582\) 16.3446 0.677505
\(583\) −2.51552 −0.104182
\(584\) 7.70670 0.318905
\(585\) 2.86884 0.118612
\(586\) −32.9505 −1.36117
\(587\) 1.48901 0.0614579 0.0307290 0.999528i \(-0.490217\pi\)
0.0307290 + 0.999528i \(0.490217\pi\)
\(588\) 5.15705 0.212673
\(589\) 2.98057 0.122812
\(590\) 31.2412 1.28618
\(591\) 23.2658 0.957026
\(592\) 12.0357 0.494665
\(593\) −30.5617 −1.25502 −0.627509 0.778609i \(-0.715926\pi\)
−0.627509 + 0.778609i \(0.715926\pi\)
\(594\) 0.441741 0.0181249
\(595\) 8.05005 0.330020
\(596\) 6.82750 0.279665
\(597\) 11.4408 0.468240
\(598\) −4.08904 −0.167213
\(599\) −23.0670 −0.942493 −0.471246 0.882002i \(-0.656196\pi\)
−0.471246 + 0.882002i \(0.656196\pi\)
\(600\) 0.288380 0.0117730
\(601\) −39.8889 −1.62710 −0.813551 0.581493i \(-0.802469\pi\)
−0.813551 + 0.581493i \(0.802469\pi\)
\(602\) −15.8416 −0.645654
\(603\) −9.42494 −0.383813
\(604\) 10.3801 0.422360
\(605\) −24.4279 −0.993135
\(606\) 6.47667 0.263097
\(607\) 2.80259 0.113754 0.0568769 0.998381i \(-0.481886\pi\)
0.0568769 + 0.998381i \(0.481886\pi\)
\(608\) 35.3424 1.43332
\(609\) 21.6033 0.875411
\(610\) 7.84350 0.317574
\(611\) −5.66411 −0.229145
\(612\) 0.901675 0.0364481
\(613\) 13.3848 0.540607 0.270303 0.962775i \(-0.412876\pi\)
0.270303 + 0.962775i \(0.412876\pi\)
\(614\) 2.91325 0.117569
\(615\) 11.4922 0.463412
\(616\) −4.57141 −0.184187
\(617\) 44.7508 1.80160 0.900801 0.434233i \(-0.142981\pi\)
0.900801 + 0.434233i \(0.142981\pi\)
\(618\) −8.69196 −0.349642
\(619\) −9.06908 −0.364517 −0.182259 0.983251i \(-0.558341\pi\)
−0.182259 + 0.983251i \(0.558341\pi\)
\(620\) −0.795021 −0.0319288
\(621\) 3.06983 0.123188
\(622\) 19.2363 0.771304
\(623\) 22.0686 0.884160
\(624\) 1.75858 0.0703996
\(625\) −25.4652 −1.01861
\(626\) 24.5463 0.981069
\(627\) 3.21617 0.128441
\(628\) 0.901675 0.0359808
\(629\) 8.69864 0.346838
\(630\) −8.43653 −0.336119
\(631\) −16.1839 −0.644271 −0.322135 0.946694i \(-0.604401\pi\)
−0.322135 + 0.946694i \(0.604401\pi\)
\(632\) −10.0447 −0.399555
\(633\) −0.124091 −0.00493219
\(634\) 4.99427 0.198348
\(635\) 45.5348 1.80699
\(636\) 5.38115 0.213376
\(637\) 7.26932 0.288021
\(638\) −2.67581 −0.105936
\(639\) −3.49949 −0.138438
\(640\) −2.88096 −0.113880
\(641\) 26.2476 1.03672 0.518358 0.855164i \(-0.326543\pi\)
0.518358 + 0.855164i \(0.326543\pi\)
\(642\) 8.51085 0.335896
\(643\) 1.97964 0.0780695 0.0390347 0.999238i \(-0.487572\pi\)
0.0390347 + 0.999238i \(0.487572\pi\)
\(644\) −9.87183 −0.389005
\(645\) −9.56675 −0.376690
\(646\) −7.99653 −0.314619
\(647\) −33.1377 −1.30278 −0.651388 0.758744i \(-0.725813\pi\)
−0.651388 + 0.758744i \(0.725813\pi\)
\(648\) −3.04098 −0.119461
\(649\) −5.56672 −0.218513
\(650\) 0.126316 0.00495451
\(651\) 1.39315 0.0546017
\(652\) 1.09970 0.0430678
\(653\) 35.6631 1.39561 0.697803 0.716290i \(-0.254161\pi\)
0.697803 + 0.716290i \(0.254161\pi\)
\(654\) 4.67663 0.182871
\(655\) −9.02376 −0.352588
\(656\) 7.04466 0.275048
\(657\) −2.53428 −0.0988716
\(658\) 16.6567 0.649345
\(659\) −37.0274 −1.44238 −0.721191 0.692736i \(-0.756405\pi\)
−0.721191 + 0.692736i \(0.756405\pi\)
\(660\) −0.857862 −0.0333922
\(661\) −46.0223 −1.79006 −0.895029 0.446008i \(-0.852845\pi\)
−0.895029 + 0.446008i \(0.852845\pi\)
\(662\) 6.51856 0.253351
\(663\) 1.27099 0.0493612
\(664\) −23.2275 −0.901400
\(665\) −61.4235 −2.38190
\(666\) −9.11626 −0.353248
\(667\) −18.5952 −0.720010
\(668\) 0.793437 0.0306990
\(669\) 2.00533 0.0775307
\(670\) −22.2951 −0.861334
\(671\) −1.39760 −0.0539536
\(672\) 16.5194 0.637249
\(673\) −26.9682 −1.03955 −0.519774 0.854304i \(-0.673984\pi\)
−0.519774 + 0.854304i \(0.673984\pi\)
\(674\) −17.4729 −0.673032
\(675\) −0.0948310 −0.00365005
\(676\) 10.2652 0.394815
\(677\) −12.6308 −0.485440 −0.242720 0.970096i \(-0.578040\pi\)
−0.242720 + 0.970096i \(0.578040\pi\)
\(678\) −4.81051 −0.184747
\(679\) 55.6215 2.13456
\(680\) 6.86403 0.263223
\(681\) 12.3595 0.473616
\(682\) −0.172556 −0.00660753
\(683\) −24.6097 −0.941664 −0.470832 0.882223i \(-0.656046\pi\)
−0.470832 + 0.882223i \(0.656046\pi\)
\(684\) −6.87997 −0.263062
\(685\) −11.3050 −0.431942
\(686\) 4.78639 0.182745
\(687\) −8.69393 −0.331694
\(688\) −5.86435 −0.223576
\(689\) 7.58520 0.288973
\(690\) 7.26180 0.276452
\(691\) −10.6772 −0.406179 −0.203090 0.979160i \(-0.565098\pi\)
−0.203090 + 0.979160i \(0.565098\pi\)
\(692\) −2.35706 −0.0896020
\(693\) 1.50327 0.0571044
\(694\) 22.8703 0.868145
\(695\) 8.87426 0.336620
\(696\) 18.4205 0.698227
\(697\) 5.09143 0.192852
\(698\) −10.9403 −0.414097
\(699\) 28.2536 1.06865
\(700\) 0.304954 0.0115262
\(701\) −12.3930 −0.468076 −0.234038 0.972227i \(-0.575194\pi\)
−0.234038 + 0.972227i \(0.575194\pi\)
\(702\) −1.33201 −0.0502735
\(703\) −66.3724 −2.50328
\(704\) −3.21252 −0.121076
\(705\) 10.0590 0.378844
\(706\) −21.4414 −0.806959
\(707\) 22.0404 0.828916
\(708\) 11.9082 0.447538
\(709\) 38.0417 1.42868 0.714342 0.699796i \(-0.246726\pi\)
0.714342 + 0.699796i \(0.246726\pi\)
\(710\) −8.27817 −0.310674
\(711\) 3.30310 0.123876
\(712\) 18.8172 0.705205
\(713\) −1.19916 −0.0449089
\(714\) −3.73765 −0.139878
\(715\) −1.20923 −0.0452227
\(716\) −17.6765 −0.660600
\(717\) 6.43478 0.240311
\(718\) −31.4679 −1.17437
\(719\) 35.8137 1.33562 0.667812 0.744330i \(-0.267231\pi\)
0.667812 + 0.744330i \(0.267231\pi\)
\(720\) −3.12310 −0.116391
\(721\) −29.5792 −1.10159
\(722\) 41.1030 1.52970
\(723\) 5.43886 0.202273
\(724\) 10.9873 0.408338
\(725\) 0.574430 0.0213338
\(726\) 11.3419 0.420938
\(727\) 42.4575 1.57466 0.787330 0.616531i \(-0.211463\pi\)
0.787330 + 0.616531i \(0.211463\pi\)
\(728\) 13.7845 0.510886
\(729\) 1.00000 0.0370370
\(730\) −5.99493 −0.221882
\(731\) −4.23838 −0.156762
\(732\) 2.98971 0.110503
\(733\) −9.19777 −0.339728 −0.169864 0.985468i \(-0.554333\pi\)
−0.169864 + 0.985468i \(0.554333\pi\)
\(734\) 28.1582 1.03934
\(735\) −12.9097 −0.476182
\(736\) −14.2192 −0.524125
\(737\) 3.97266 0.146335
\(738\) −5.33587 −0.196416
\(739\) 1.19669 0.0440211 0.0220106 0.999758i \(-0.492993\pi\)
0.0220106 + 0.999758i \(0.492993\pi\)
\(740\) 17.7038 0.650805
\(741\) −9.69792 −0.356262
\(742\) −22.3061 −0.818883
\(743\) 10.8113 0.396629 0.198314 0.980138i \(-0.436453\pi\)
0.198314 + 0.980138i \(0.436453\pi\)
\(744\) 1.18789 0.0435503
\(745\) −17.0913 −0.626178
\(746\) −37.6587 −1.37878
\(747\) 7.63814 0.279465
\(748\) −0.380060 −0.0138964
\(749\) 28.9628 1.05828
\(750\) 11.6034 0.423695
\(751\) 17.4646 0.637291 0.318646 0.947874i \(-0.396772\pi\)
0.318646 + 0.947874i \(0.396772\pi\)
\(752\) 6.16609 0.224854
\(753\) 9.26943 0.337797
\(754\) 8.06854 0.293839
\(755\) −25.9846 −0.945676
\(756\) −3.21576 −0.116956
\(757\) −7.17784 −0.260883 −0.130441 0.991456i \(-0.541639\pi\)
−0.130441 + 0.991456i \(0.541639\pi\)
\(758\) 7.97619 0.289708
\(759\) −1.29395 −0.0469673
\(760\) −52.3740 −1.89980
\(761\) 25.1432 0.911441 0.455721 0.890123i \(-0.349382\pi\)
0.455721 + 0.890123i \(0.349382\pi\)
\(762\) −21.1419 −0.765891
\(763\) 15.9148 0.576154
\(764\) 20.7827 0.751893
\(765\) −2.25717 −0.0816083
\(766\) −21.1785 −0.765212
\(767\) 16.7857 0.606096
\(768\) 16.5807 0.598306
\(769\) 28.5661 1.03012 0.515061 0.857154i \(-0.327769\pi\)
0.515061 + 0.857154i \(0.327769\pi\)
\(770\) 3.55604 0.128151
\(771\) 22.9228 0.825546
\(772\) 6.37972 0.229611
\(773\) −16.5370 −0.594795 −0.297398 0.954754i \(-0.596119\pi\)
−0.297398 + 0.954754i \(0.596119\pi\)
\(774\) 4.44186 0.159659
\(775\) 0.0370436 0.00133065
\(776\) 47.4267 1.70252
\(777\) −31.0231 −1.11295
\(778\) 5.90476 0.211696
\(779\) −38.8486 −1.39190
\(780\) 2.58677 0.0926211
\(781\) 1.47505 0.0527814
\(782\) 3.21721 0.115047
\(783\) −6.05741 −0.216474
\(784\) −7.91356 −0.282627
\(785\) −2.25717 −0.0805620
\(786\) 4.18975 0.149443
\(787\) 26.6057 0.948389 0.474195 0.880420i \(-0.342739\pi\)
0.474195 + 0.880420i \(0.342739\pi\)
\(788\) 20.9782 0.747316
\(789\) −16.7423 −0.596040
\(790\) 7.81361 0.277996
\(791\) −16.3704 −0.582064
\(792\) 1.28179 0.0455464
\(793\) 4.21426 0.149653
\(794\) −23.7035 −0.841207
\(795\) −13.4707 −0.477756
\(796\) 10.3159 0.365636
\(797\) 1.21962 0.0432010 0.0216005 0.999767i \(-0.493124\pi\)
0.0216005 + 0.999767i \(0.493124\pi\)
\(798\) 28.5191 1.00956
\(799\) 4.45646 0.157658
\(800\) 0.439248 0.0155298
\(801\) −6.18787 −0.218638
\(802\) −10.1546 −0.358571
\(803\) 1.06821 0.0376963
\(804\) −8.49824 −0.299710
\(805\) 24.7123 0.870993
\(806\) 0.520321 0.0183275
\(807\) −5.40082 −0.190118
\(808\) 18.7932 0.661142
\(809\) −37.8086 −1.32928 −0.664640 0.747163i \(-0.731415\pi\)
−0.664640 + 0.747163i \(0.731415\pi\)
\(810\) 2.36554 0.0831166
\(811\) −17.3871 −0.610543 −0.305271 0.952265i \(-0.598747\pi\)
−0.305271 + 0.952265i \(0.598747\pi\)
\(812\) 19.4792 0.683586
\(813\) −4.80776 −0.168615
\(814\) 3.84255 0.134681
\(815\) −2.75290 −0.0964300
\(816\) −1.38363 −0.0484368
\(817\) 32.3397 1.13142
\(818\) 11.6098 0.405926
\(819\) −4.53290 −0.158392
\(820\) 10.3623 0.361866
\(821\) 44.8647 1.56579 0.782895 0.622154i \(-0.213742\pi\)
0.782895 + 0.622154i \(0.213742\pi\)
\(822\) 5.24894 0.183078
\(823\) −48.8419 −1.70252 −0.851261 0.524743i \(-0.824161\pi\)
−0.851261 + 0.524743i \(0.824161\pi\)
\(824\) −25.2212 −0.878624
\(825\) 0.0399717 0.00139164
\(826\) −49.3623 −1.71754
\(827\) 23.4411 0.815128 0.407564 0.913177i \(-0.366378\pi\)
0.407564 + 0.913177i \(0.366378\pi\)
\(828\) 2.76799 0.0961942
\(829\) −0.896816 −0.0311477 −0.0155739 0.999879i \(-0.504958\pi\)
−0.0155739 + 0.999879i \(0.504958\pi\)
\(830\) 18.0683 0.627160
\(831\) 13.2220 0.458665
\(832\) 9.68691 0.335833
\(833\) −5.71941 −0.198166
\(834\) −4.12034 −0.142676
\(835\) −1.98622 −0.0687360
\(836\) 2.89994 0.100296
\(837\) −0.390628 −0.0135021
\(838\) −18.6451 −0.644086
\(839\) −18.3829 −0.634648 −0.317324 0.948317i \(-0.602784\pi\)
−0.317324 + 0.948317i \(0.602784\pi\)
\(840\) −24.4801 −0.844643
\(841\) 7.69226 0.265250
\(842\) 9.78467 0.337202
\(843\) −10.7484 −0.370194
\(844\) −0.111890 −0.00385141
\(845\) −25.6970 −0.884003
\(846\) −4.67041 −0.160572
\(847\) 38.5971 1.32621
\(848\) −8.25744 −0.283561
\(849\) 11.3334 0.388961
\(850\) −0.0993838 −0.00340884
\(851\) 26.7033 0.915378
\(852\) −3.15540 −0.108102
\(853\) −41.8665 −1.43348 −0.716741 0.697339i \(-0.754367\pi\)
−0.716741 + 0.697339i \(0.754367\pi\)
\(854\) −12.3931 −0.424082
\(855\) 17.2227 0.589004
\(856\) 24.6957 0.844082
\(857\) 15.4003 0.526063 0.263031 0.964787i \(-0.415278\pi\)
0.263031 + 0.964787i \(0.415278\pi\)
\(858\) 0.561448 0.0191675
\(859\) 18.8746 0.643992 0.321996 0.946741i \(-0.395646\pi\)
0.321996 + 0.946741i \(0.395646\pi\)
\(860\) −8.62610 −0.294148
\(861\) −18.1582 −0.618830
\(862\) −9.22177 −0.314095
\(863\) 45.1180 1.53584 0.767918 0.640548i \(-0.221293\pi\)
0.767918 + 0.640548i \(0.221293\pi\)
\(864\) −4.63191 −0.157581
\(865\) 5.90045 0.200621
\(866\) 19.2564 0.654359
\(867\) −1.00000 −0.0339618
\(868\) 1.25617 0.0426371
\(869\) −1.39227 −0.0472295
\(870\) −14.3291 −0.485800
\(871\) −11.9790 −0.405893
\(872\) 13.5701 0.459540
\(873\) −15.5958 −0.527839
\(874\) −24.5480 −0.830348
\(875\) 39.4868 1.33490
\(876\) −2.28509 −0.0772062
\(877\) 27.5437 0.930084 0.465042 0.885289i \(-0.346039\pi\)
0.465042 + 0.885289i \(0.346039\pi\)
\(878\) 18.4649 0.623162
\(879\) 31.4410 1.06048
\(880\) 1.31640 0.0443758
\(881\) 7.79557 0.262639 0.131320 0.991340i \(-0.458079\pi\)
0.131320 + 0.991340i \(0.458079\pi\)
\(882\) 5.99400 0.201829
\(883\) 19.4591 0.654852 0.327426 0.944877i \(-0.393819\pi\)
0.327426 + 0.944877i \(0.393819\pi\)
\(884\) 1.14602 0.0385448
\(885\) −29.8100 −1.00205
\(886\) 7.45305 0.250390
\(887\) −31.2118 −1.04799 −0.523996 0.851721i \(-0.675559\pi\)
−0.523996 + 0.851721i \(0.675559\pi\)
\(888\) −26.4524 −0.887686
\(889\) −71.9469 −2.41302
\(890\) −14.6377 −0.490656
\(891\) −0.421505 −0.0141209
\(892\) 1.80816 0.0605417
\(893\) −34.0037 −1.13789
\(894\) 7.93554 0.265404
\(895\) 44.2497 1.47910
\(896\) 4.55204 0.152073
\(897\) 3.90172 0.130275
\(898\) 16.9541 0.565767
\(899\) 2.36620 0.0789170
\(900\) −0.0855067 −0.00285022
\(901\) −5.96794 −0.198821
\(902\) 2.24909 0.0748866
\(903\) 15.1159 0.503025
\(904\) −13.9585 −0.464254
\(905\) −27.5045 −0.914281
\(906\) 12.0647 0.400823
\(907\) −8.35956 −0.277575 −0.138787 0.990322i \(-0.544320\pi\)
−0.138787 + 0.990322i \(0.544320\pi\)
\(908\) 11.1442 0.369834
\(909\) −6.17997 −0.204977
\(910\) −10.7227 −0.355456
\(911\) 26.9822 0.893961 0.446981 0.894544i \(-0.352499\pi\)
0.446981 + 0.894544i \(0.352499\pi\)
\(912\) 10.5574 0.349590
\(913\) −3.21951 −0.106550
\(914\) −0.748952 −0.0247731
\(915\) −7.48418 −0.247419
\(916\) −7.83910 −0.259011
\(917\) 14.2579 0.470838
\(918\) 1.04801 0.0345895
\(919\) −47.6301 −1.57117 −0.785586 0.618753i \(-0.787638\pi\)
−0.785586 + 0.618753i \(0.787638\pi\)
\(920\) 21.0714 0.694703
\(921\) −2.77979 −0.0915972
\(922\) 34.6615 1.14152
\(923\) −4.44781 −0.146401
\(924\) 1.35546 0.0445913
\(925\) −0.824901 −0.0271226
\(926\) 42.4201 1.39401
\(927\) 8.29378 0.272403
\(928\) 28.0574 0.921029
\(929\) 36.8521 1.20908 0.604538 0.796576i \(-0.293358\pi\)
0.604538 + 0.796576i \(0.293358\pi\)
\(930\) −0.924046 −0.0303007
\(931\) 43.6403 1.43025
\(932\) 25.4756 0.834480
\(933\) −18.3551 −0.600917
\(934\) −8.56860 −0.280373
\(935\) 0.951409 0.0311144
\(936\) −3.86506 −0.126333
\(937\) −52.1678 −1.70425 −0.852124 0.523341i \(-0.824686\pi\)
−0.852124 + 0.523341i \(0.824686\pi\)
\(938\) 35.2272 1.15021
\(939\) −23.4219 −0.764344
\(940\) 9.06994 0.295829
\(941\) −22.8975 −0.746439 −0.373219 0.927743i \(-0.621746\pi\)
−0.373219 + 0.927743i \(0.621746\pi\)
\(942\) 1.04801 0.0341460
\(943\) 15.6298 0.508977
\(944\) −18.2733 −0.594746
\(945\) 8.05005 0.261868
\(946\) −1.87226 −0.0608726
\(947\) −10.2886 −0.334334 −0.167167 0.985929i \(-0.553462\pi\)
−0.167167 + 0.985929i \(0.553462\pi\)
\(948\) 2.97832 0.0967313
\(949\) −3.22104 −0.104559
\(950\) 0.758319 0.0246031
\(951\) −4.76548 −0.154531
\(952\) −10.8455 −0.351503
\(953\) 37.8773 1.22697 0.613483 0.789708i \(-0.289768\pi\)
0.613483 + 0.789708i \(0.289768\pi\)
\(954\) 6.25446 0.202496
\(955\) −52.0256 −1.68351
\(956\) 5.80208 0.187653
\(957\) 2.55323 0.0825341
\(958\) −38.0537 −1.22946
\(959\) 17.8624 0.576806
\(960\) −17.2032 −0.555230
\(961\) −30.8474 −0.995078
\(962\) −11.5867 −0.373569
\(963\) −8.12096 −0.261694
\(964\) 4.90408 0.157950
\(965\) −15.9704 −0.514106
\(966\) −11.4739 −0.369168
\(967\) 0.957426 0.0307888 0.0153944 0.999881i \(-0.495100\pi\)
0.0153944 + 0.999881i \(0.495100\pi\)
\(968\) 32.9105 1.05779
\(969\) 7.63021 0.245118
\(970\) −36.8926 −1.18455
\(971\) −22.4966 −0.721950 −0.360975 0.932576i \(-0.617556\pi\)
−0.360975 + 0.932576i \(0.617556\pi\)
\(972\) 0.901675 0.0289212
\(973\) −14.0217 −0.449515
\(974\) 15.4135 0.493882
\(975\) −0.120529 −0.00386002
\(976\) −4.58775 −0.146850
\(977\) −10.2955 −0.329384 −0.164692 0.986345i \(-0.552663\pi\)
−0.164692 + 0.986345i \(0.552663\pi\)
\(978\) 1.27818 0.0408716
\(979\) 2.60822 0.0833590
\(980\) −11.6404 −0.371838
\(981\) −4.46239 −0.142473
\(982\) 38.3836 1.22487
\(983\) −11.7517 −0.374822 −0.187411 0.982282i \(-0.560010\pi\)
−0.187411 + 0.982282i \(0.560010\pi\)
\(984\) −15.4830 −0.493579
\(985\) −52.5149 −1.67326
\(986\) −6.34823 −0.202169
\(987\) −15.8936 −0.505900
\(988\) −8.74437 −0.278195
\(989\) −13.0111 −0.413728
\(990\) −0.997086 −0.0316895
\(991\) 31.0682 0.986913 0.493457 0.869770i \(-0.335733\pi\)
0.493457 + 0.869770i \(0.335733\pi\)
\(992\) 1.80935 0.0574470
\(993\) −6.21994 −0.197384
\(994\) 13.0799 0.414868
\(995\) −25.8238 −0.818670
\(996\) 6.88712 0.218227
\(997\) 2.74773 0.0870215 0.0435108 0.999053i \(-0.486146\pi\)
0.0435108 + 0.999053i \(0.486146\pi\)
\(998\) −24.4883 −0.775164
\(999\) 8.69864 0.275213
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 8007.2.a.f.1.33 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.33 48 1.1 even 1 trivial