Properties

Label 8007.2.a.f.1.29
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.29
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.522212 q^{2} -1.00000 q^{3} -1.72729 q^{4} -2.49100 q^{5} -0.522212 q^{6} +5.20591 q^{7} -1.94644 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.522212 q^{2} -1.00000 q^{3} -1.72729 q^{4} -2.49100 q^{5} -0.522212 q^{6} +5.20591 q^{7} -1.94644 q^{8} +1.00000 q^{9} -1.30083 q^{10} +3.79213 q^{11} +1.72729 q^{12} +1.98902 q^{13} +2.71859 q^{14} +2.49100 q^{15} +2.43813 q^{16} -1.00000 q^{17} +0.522212 q^{18} -4.44935 q^{19} +4.30269 q^{20} -5.20591 q^{21} +1.98030 q^{22} +1.01413 q^{23} +1.94644 q^{24} +1.20509 q^{25} +1.03869 q^{26} -1.00000 q^{27} -8.99213 q^{28} -8.84805 q^{29} +1.30083 q^{30} -7.21004 q^{31} +5.16610 q^{32} -3.79213 q^{33} -0.522212 q^{34} -12.9679 q^{35} -1.72729 q^{36} -11.2380 q^{37} -2.32350 q^{38} -1.98902 q^{39} +4.84859 q^{40} +3.60771 q^{41} -2.71859 q^{42} +3.48456 q^{43} -6.55012 q^{44} -2.49100 q^{45} +0.529593 q^{46} -0.328790 q^{47} -2.43813 q^{48} +20.1015 q^{49} +0.629315 q^{50} +1.00000 q^{51} -3.43562 q^{52} +7.74323 q^{53} -0.522212 q^{54} -9.44620 q^{55} -10.1330 q^{56} +4.44935 q^{57} -4.62056 q^{58} +9.57031 q^{59} -4.30269 q^{60} -4.50698 q^{61} -3.76517 q^{62} +5.20591 q^{63} -2.17846 q^{64} -4.95466 q^{65} -1.98030 q^{66} +1.51522 q^{67} +1.72729 q^{68} -1.01413 q^{69} -6.77201 q^{70} +0.798424 q^{71} -1.94644 q^{72} -2.42446 q^{73} -5.86862 q^{74} -1.20509 q^{75} +7.68533 q^{76} +19.7415 q^{77} -1.03869 q^{78} -0.0708311 q^{79} -6.07340 q^{80} +1.00000 q^{81} +1.88399 q^{82} -6.45036 q^{83} +8.99213 q^{84} +2.49100 q^{85} +1.81968 q^{86} +8.84805 q^{87} -7.38114 q^{88} -9.71172 q^{89} -1.30083 q^{90} +10.3547 q^{91} -1.75171 q^{92} +7.21004 q^{93} -0.171698 q^{94} +11.0833 q^{95} -5.16610 q^{96} +6.02464 q^{97} +10.4972 q^{98} +3.79213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.522212 0.369260 0.184630 0.982808i \(-0.440891\pi\)
0.184630 + 0.982808i \(0.440891\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.72729 −0.863647
\(5\) −2.49100 −1.11401 −0.557005 0.830509i \(-0.688050\pi\)
−0.557005 + 0.830509i \(0.688050\pi\)
\(6\) −0.522212 −0.213192
\(7\) 5.20591 1.96765 0.983824 0.179138i \(-0.0573309\pi\)
0.983824 + 0.179138i \(0.0573309\pi\)
\(8\) −1.94644 −0.688170
\(9\) 1.00000 0.333333
\(10\) −1.30083 −0.411359
\(11\) 3.79213 1.14337 0.571684 0.820474i \(-0.306290\pi\)
0.571684 + 0.820474i \(0.306290\pi\)
\(12\) 1.72729 0.498627
\(13\) 1.98902 0.551655 0.275828 0.961207i \(-0.411048\pi\)
0.275828 + 0.961207i \(0.411048\pi\)
\(14\) 2.71859 0.726574
\(15\) 2.49100 0.643174
\(16\) 2.43813 0.609533
\(17\) −1.00000 −0.242536
\(18\) 0.522212 0.123087
\(19\) −4.44935 −1.02075 −0.510375 0.859952i \(-0.670493\pi\)
−0.510375 + 0.859952i \(0.670493\pi\)
\(20\) 4.30269 0.962112
\(21\) −5.20591 −1.13602
\(22\) 1.98030 0.422200
\(23\) 1.01413 0.211461 0.105731 0.994395i \(-0.466282\pi\)
0.105731 + 0.994395i \(0.466282\pi\)
\(24\) 1.94644 0.397315
\(25\) 1.20509 0.241019
\(26\) 1.03869 0.203704
\(27\) −1.00000 −0.192450
\(28\) −8.99213 −1.69935
\(29\) −8.84805 −1.64304 −0.821521 0.570179i \(-0.806874\pi\)
−0.821521 + 0.570179i \(0.806874\pi\)
\(30\) 1.30083 0.237498
\(31\) −7.21004 −1.29496 −0.647481 0.762082i \(-0.724177\pi\)
−0.647481 + 0.762082i \(0.724177\pi\)
\(32\) 5.16610 0.913246
\(33\) −3.79213 −0.660124
\(34\) −0.522212 −0.0895587
\(35\) −12.9679 −2.19198
\(36\) −1.72729 −0.287882
\(37\) −11.2380 −1.84751 −0.923757 0.382979i \(-0.874898\pi\)
−0.923757 + 0.382979i \(0.874898\pi\)
\(38\) −2.32350 −0.376922
\(39\) −1.98902 −0.318498
\(40\) 4.84859 0.766629
\(41\) 3.60771 0.563429 0.281715 0.959498i \(-0.409097\pi\)
0.281715 + 0.959498i \(0.409097\pi\)
\(42\) −2.71859 −0.419487
\(43\) 3.48456 0.531390 0.265695 0.964057i \(-0.414399\pi\)
0.265695 + 0.964057i \(0.414399\pi\)
\(44\) −6.55012 −0.987467
\(45\) −2.49100 −0.371337
\(46\) 0.529593 0.0780842
\(47\) −0.328790 −0.0479590 −0.0239795 0.999712i \(-0.507634\pi\)
−0.0239795 + 0.999712i \(0.507634\pi\)
\(48\) −2.43813 −0.351914
\(49\) 20.1015 2.87164
\(50\) 0.629315 0.0889986
\(51\) 1.00000 0.140028
\(52\) −3.43562 −0.476435
\(53\) 7.74323 1.06361 0.531807 0.846865i \(-0.321513\pi\)
0.531807 + 0.846865i \(0.321513\pi\)
\(54\) −0.522212 −0.0710641
\(55\) −9.44620 −1.27372
\(56\) −10.1330 −1.35408
\(57\) 4.44935 0.589330
\(58\) −4.62056 −0.606709
\(59\) 9.57031 1.24595 0.622974 0.782242i \(-0.285924\pi\)
0.622974 + 0.782242i \(0.285924\pi\)
\(60\) −4.30269 −0.555475
\(61\) −4.50698 −0.577060 −0.288530 0.957471i \(-0.593166\pi\)
−0.288530 + 0.957471i \(0.593166\pi\)
\(62\) −3.76517 −0.478178
\(63\) 5.20591 0.655883
\(64\) −2.17846 −0.272308
\(65\) −4.95466 −0.614549
\(66\) −1.98030 −0.243757
\(67\) 1.51522 0.185114 0.0925568 0.995707i \(-0.470496\pi\)
0.0925568 + 0.995707i \(0.470496\pi\)
\(68\) 1.72729 0.209465
\(69\) −1.01413 −0.122087
\(70\) −6.77201 −0.809410
\(71\) 0.798424 0.0947556 0.0473778 0.998877i \(-0.484914\pi\)
0.0473778 + 0.998877i \(0.484914\pi\)
\(72\) −1.94644 −0.229390
\(73\) −2.42446 −0.283761 −0.141881 0.989884i \(-0.545315\pi\)
−0.141881 + 0.989884i \(0.545315\pi\)
\(74\) −5.86862 −0.682213
\(75\) −1.20509 −0.139152
\(76\) 7.68533 0.881568
\(77\) 19.7415 2.24975
\(78\) −1.03869 −0.117609
\(79\) −0.0708311 −0.00796912 −0.00398456 0.999992i \(-0.501268\pi\)
−0.00398456 + 0.999992i \(0.501268\pi\)
\(80\) −6.07340 −0.679026
\(81\) 1.00000 0.111111
\(82\) 1.88399 0.208052
\(83\) −6.45036 −0.708019 −0.354010 0.935242i \(-0.615182\pi\)
−0.354010 + 0.935242i \(0.615182\pi\)
\(84\) 8.99213 0.981122
\(85\) 2.49100 0.270187
\(86\) 1.81968 0.196221
\(87\) 8.84805 0.948610
\(88\) −7.38114 −0.786832
\(89\) −9.71172 −1.02944 −0.514720 0.857358i \(-0.672104\pi\)
−0.514720 + 0.857358i \(0.672104\pi\)
\(90\) −1.30083 −0.137120
\(91\) 10.3547 1.08546
\(92\) −1.75171 −0.182628
\(93\) 7.21004 0.747647
\(94\) −0.171698 −0.0177093
\(95\) 11.0833 1.13713
\(96\) −5.16610 −0.527263
\(97\) 6.02464 0.611710 0.305855 0.952078i \(-0.401058\pi\)
0.305855 + 0.952078i \(0.401058\pi\)
\(98\) 10.4972 1.06038
\(99\) 3.79213 0.381123
\(100\) −2.08155 −0.208155
\(101\) 16.1285 1.60485 0.802424 0.596754i \(-0.203543\pi\)
0.802424 + 0.596754i \(0.203543\pi\)
\(102\) 0.522212 0.0517067
\(103\) −11.4708 −1.13025 −0.565125 0.825005i \(-0.691172\pi\)
−0.565125 + 0.825005i \(0.691172\pi\)
\(104\) −3.87151 −0.379633
\(105\) 12.9679 1.26554
\(106\) 4.04361 0.392750
\(107\) 18.1871 1.75821 0.879107 0.476625i \(-0.158140\pi\)
0.879107 + 0.476625i \(0.158140\pi\)
\(108\) 1.72729 0.166209
\(109\) −16.0166 −1.53411 −0.767054 0.641583i \(-0.778278\pi\)
−0.767054 + 0.641583i \(0.778278\pi\)
\(110\) −4.93292 −0.470336
\(111\) 11.2380 1.06666
\(112\) 12.6927 1.19935
\(113\) −16.9067 −1.59044 −0.795222 0.606318i \(-0.792646\pi\)
−0.795222 + 0.606318i \(0.792646\pi\)
\(114\) 2.32350 0.217616
\(115\) −2.52621 −0.235570
\(116\) 15.2832 1.41901
\(117\) 1.98902 0.183885
\(118\) 4.99773 0.460079
\(119\) −5.20591 −0.477225
\(120\) −4.84859 −0.442613
\(121\) 3.38022 0.307292
\(122\) −2.35360 −0.213085
\(123\) −3.60771 −0.325296
\(124\) 12.4539 1.11839
\(125\) 9.45312 0.845513
\(126\) 2.71859 0.242191
\(127\) 6.58334 0.584177 0.292089 0.956391i \(-0.405650\pi\)
0.292089 + 0.956391i \(0.405650\pi\)
\(128\) −11.4698 −1.01380
\(129\) −3.48456 −0.306798
\(130\) −2.58738 −0.226928
\(131\) −9.63710 −0.841997 −0.420999 0.907061i \(-0.638320\pi\)
−0.420999 + 0.907061i \(0.638320\pi\)
\(132\) 6.55012 0.570114
\(133\) −23.1629 −2.00848
\(134\) 0.791266 0.0683550
\(135\) 2.49100 0.214391
\(136\) 1.94644 0.166906
\(137\) −14.6891 −1.25498 −0.627489 0.778625i \(-0.715917\pi\)
−0.627489 + 0.778625i \(0.715917\pi\)
\(138\) −0.529593 −0.0450819
\(139\) −0.760234 −0.0644822 −0.0322411 0.999480i \(-0.510264\pi\)
−0.0322411 + 0.999480i \(0.510264\pi\)
\(140\) 22.3994 1.89310
\(141\) 0.328790 0.0276891
\(142\) 0.416947 0.0349894
\(143\) 7.54262 0.630745
\(144\) 2.43813 0.203178
\(145\) 22.0405 1.83036
\(146\) −1.26608 −0.104782
\(147\) −20.1015 −1.65794
\(148\) 19.4113 1.59560
\(149\) −2.99363 −0.245248 −0.122624 0.992453i \(-0.539131\pi\)
−0.122624 + 0.992453i \(0.539131\pi\)
\(150\) −0.629315 −0.0513834
\(151\) −2.14812 −0.174812 −0.0874058 0.996173i \(-0.527858\pi\)
−0.0874058 + 0.996173i \(0.527858\pi\)
\(152\) 8.66038 0.702450
\(153\) −1.00000 −0.0808452
\(154\) 10.3092 0.830742
\(155\) 17.9602 1.44260
\(156\) 3.43562 0.275070
\(157\) −1.00000 −0.0798087
\(158\) −0.0369889 −0.00294268
\(159\) −7.74323 −0.614078
\(160\) −12.8688 −1.01737
\(161\) 5.27948 0.416081
\(162\) 0.522212 0.0410289
\(163\) −6.26047 −0.490358 −0.245179 0.969478i \(-0.578847\pi\)
−0.245179 + 0.969478i \(0.578847\pi\)
\(164\) −6.23157 −0.486604
\(165\) 9.44620 0.735385
\(166\) −3.36846 −0.261443
\(167\) −11.7678 −0.910621 −0.455311 0.890333i \(-0.650472\pi\)
−0.455311 + 0.890333i \(0.650472\pi\)
\(168\) 10.1330 0.781777
\(169\) −9.04380 −0.695677
\(170\) 1.30083 0.0997693
\(171\) −4.44935 −0.340250
\(172\) −6.01886 −0.458934
\(173\) 19.4467 1.47850 0.739252 0.673429i \(-0.235179\pi\)
0.739252 + 0.673429i \(0.235179\pi\)
\(174\) 4.62056 0.350284
\(175\) 6.27361 0.474240
\(176\) 9.24571 0.696922
\(177\) −9.57031 −0.719349
\(178\) −5.07158 −0.380131
\(179\) 21.8141 1.63047 0.815233 0.579133i \(-0.196609\pi\)
0.815233 + 0.579133i \(0.196609\pi\)
\(180\) 4.30269 0.320704
\(181\) 11.0565 0.821823 0.410912 0.911675i \(-0.365210\pi\)
0.410912 + 0.911675i \(0.365210\pi\)
\(182\) 5.40733 0.400818
\(183\) 4.50698 0.333165
\(184\) −1.97395 −0.145521
\(185\) 27.9939 2.05815
\(186\) 3.76517 0.276076
\(187\) −3.79213 −0.277308
\(188\) 0.567917 0.0414196
\(189\) −5.20591 −0.378674
\(190\) 5.78785 0.419895
\(191\) −8.95026 −0.647618 −0.323809 0.946122i \(-0.604964\pi\)
−0.323809 + 0.946122i \(0.604964\pi\)
\(192\) 2.17846 0.157217
\(193\) 6.05971 0.436187 0.218094 0.975928i \(-0.430016\pi\)
0.218094 + 0.975928i \(0.430016\pi\)
\(194\) 3.14614 0.225880
\(195\) 4.95466 0.354810
\(196\) −34.7211 −2.48008
\(197\) 8.51967 0.607001 0.303501 0.952831i \(-0.401845\pi\)
0.303501 + 0.952831i \(0.401845\pi\)
\(198\) 1.98030 0.140733
\(199\) −4.14330 −0.293710 −0.146855 0.989158i \(-0.546915\pi\)
−0.146855 + 0.989158i \(0.546915\pi\)
\(200\) −2.34564 −0.165862
\(201\) −1.51522 −0.106875
\(202\) 8.42252 0.592606
\(203\) −46.0621 −3.23293
\(204\) −1.72729 −0.120935
\(205\) −8.98681 −0.627666
\(206\) −5.99019 −0.417356
\(207\) 1.01413 0.0704871
\(208\) 4.84950 0.336252
\(209\) −16.8725 −1.16709
\(210\) 6.77201 0.467313
\(211\) −21.8940 −1.50725 −0.753623 0.657307i \(-0.771695\pi\)
−0.753623 + 0.657307i \(0.771695\pi\)
\(212\) −13.3748 −0.918588
\(213\) −0.798424 −0.0547071
\(214\) 9.49753 0.649238
\(215\) −8.68005 −0.591974
\(216\) 1.94644 0.132438
\(217\) −37.5348 −2.54803
\(218\) −8.36404 −0.566485
\(219\) 2.42446 0.163830
\(220\) 16.3164 1.10005
\(221\) −1.98902 −0.133796
\(222\) 5.86862 0.393876
\(223\) −18.6656 −1.24994 −0.624971 0.780648i \(-0.714889\pi\)
−0.624971 + 0.780648i \(0.714889\pi\)
\(224\) 26.8942 1.79695
\(225\) 1.20509 0.0803396
\(226\) −8.82887 −0.587287
\(227\) 6.96732 0.462437 0.231219 0.972902i \(-0.425729\pi\)
0.231219 + 0.972902i \(0.425729\pi\)
\(228\) −7.68533 −0.508973
\(229\) −10.7510 −0.710444 −0.355222 0.934782i \(-0.615595\pi\)
−0.355222 + 0.934782i \(0.615595\pi\)
\(230\) −1.31922 −0.0869866
\(231\) −19.7415 −1.29889
\(232\) 17.2222 1.13069
\(233\) −21.1681 −1.38677 −0.693385 0.720568i \(-0.743881\pi\)
−0.693385 + 0.720568i \(0.743881\pi\)
\(234\) 1.03869 0.0679014
\(235\) 0.819017 0.0534268
\(236\) −16.5307 −1.07606
\(237\) 0.0708311 0.00460097
\(238\) −2.71859 −0.176220
\(239\) −19.0843 −1.23446 −0.617229 0.786784i \(-0.711745\pi\)
−0.617229 + 0.786784i \(0.711745\pi\)
\(240\) 6.07340 0.392036
\(241\) −20.0543 −1.29181 −0.645907 0.763416i \(-0.723521\pi\)
−0.645907 + 0.763416i \(0.723521\pi\)
\(242\) 1.76519 0.113471
\(243\) −1.00000 −0.0641500
\(244\) 7.78488 0.498376
\(245\) −50.0728 −3.19903
\(246\) −1.88399 −0.120119
\(247\) −8.84984 −0.563102
\(248\) 14.0339 0.891154
\(249\) 6.45036 0.408775
\(250\) 4.93654 0.312214
\(251\) 16.9195 1.06795 0.533975 0.845501i \(-0.320698\pi\)
0.533975 + 0.845501i \(0.320698\pi\)
\(252\) −8.99213 −0.566451
\(253\) 3.84572 0.241778
\(254\) 3.43790 0.215713
\(255\) −2.49100 −0.155993
\(256\) −1.63276 −0.102047
\(257\) 4.62699 0.288623 0.144312 0.989532i \(-0.453903\pi\)
0.144312 + 0.989532i \(0.453903\pi\)
\(258\) −1.81968 −0.113288
\(259\) −58.5039 −3.63526
\(260\) 8.55815 0.530754
\(261\) −8.84805 −0.547680
\(262\) −5.03261 −0.310916
\(263\) −11.4847 −0.708178 −0.354089 0.935212i \(-0.615209\pi\)
−0.354089 + 0.935212i \(0.615209\pi\)
\(264\) 7.38114 0.454278
\(265\) −19.2884 −1.18488
\(266\) −12.0959 −0.741650
\(267\) 9.71172 0.594348
\(268\) −2.61723 −0.159873
\(269\) 26.0351 1.58739 0.793695 0.608316i \(-0.208155\pi\)
0.793695 + 0.608316i \(0.208155\pi\)
\(270\) 1.30083 0.0791661
\(271\) −21.6310 −1.31399 −0.656996 0.753894i \(-0.728173\pi\)
−0.656996 + 0.753894i \(0.728173\pi\)
\(272\) −2.43813 −0.147834
\(273\) −10.3547 −0.626692
\(274\) −7.67085 −0.463413
\(275\) 4.56987 0.275573
\(276\) 1.75171 0.105440
\(277\) −13.8130 −0.829942 −0.414971 0.909835i \(-0.636208\pi\)
−0.414971 + 0.909835i \(0.636208\pi\)
\(278\) −0.397004 −0.0238107
\(279\) −7.21004 −0.431654
\(280\) 25.2413 1.50846
\(281\) −10.6326 −0.634286 −0.317143 0.948378i \(-0.602724\pi\)
−0.317143 + 0.948378i \(0.602724\pi\)
\(282\) 0.171698 0.0102245
\(283\) 18.4505 1.09677 0.548385 0.836226i \(-0.315243\pi\)
0.548385 + 0.836226i \(0.315243\pi\)
\(284\) −1.37911 −0.0818354
\(285\) −11.0833 −0.656520
\(286\) 3.93885 0.232909
\(287\) 18.7814 1.10863
\(288\) 5.16610 0.304415
\(289\) 1.00000 0.0588235
\(290\) 11.5098 0.675880
\(291\) −6.02464 −0.353171
\(292\) 4.18775 0.245069
\(293\) 18.0697 1.05564 0.527820 0.849356i \(-0.323010\pi\)
0.527820 + 0.849356i \(0.323010\pi\)
\(294\) −10.4972 −0.612211
\(295\) −23.8397 −1.38800
\(296\) 21.8741 1.27140
\(297\) −3.79213 −0.220041
\(298\) −1.56331 −0.0905601
\(299\) 2.01713 0.116654
\(300\) 2.08155 0.120178
\(301\) 18.1403 1.04559
\(302\) −1.12178 −0.0645510
\(303\) −16.1285 −0.926559
\(304\) −10.8481 −0.622181
\(305\) 11.2269 0.642850
\(306\) −0.522212 −0.0298529
\(307\) −25.7624 −1.47034 −0.735170 0.677883i \(-0.762898\pi\)
−0.735170 + 0.677883i \(0.762898\pi\)
\(308\) −34.0993 −1.94299
\(309\) 11.4708 0.652550
\(310\) 9.37906 0.532695
\(311\) −1.44216 −0.0817771 −0.0408886 0.999164i \(-0.513019\pi\)
−0.0408886 + 0.999164i \(0.513019\pi\)
\(312\) 3.87151 0.219181
\(313\) −19.1869 −1.08451 −0.542253 0.840215i \(-0.682429\pi\)
−0.542253 + 0.840215i \(0.682429\pi\)
\(314\) −0.522212 −0.0294702
\(315\) −12.9679 −0.730660
\(316\) 0.122346 0.00688251
\(317\) 16.6819 0.936950 0.468475 0.883477i \(-0.344804\pi\)
0.468475 + 0.883477i \(0.344804\pi\)
\(318\) −4.04361 −0.226755
\(319\) −33.5529 −1.87860
\(320\) 5.42656 0.303354
\(321\) −18.1871 −1.01510
\(322\) 2.75701 0.153642
\(323\) 4.44935 0.247568
\(324\) −1.72729 −0.0959608
\(325\) 2.39696 0.132959
\(326\) −3.26929 −0.181069
\(327\) 16.0166 0.885717
\(328\) −7.02218 −0.387735
\(329\) −1.71165 −0.0943664
\(330\) 4.93292 0.271548
\(331\) −4.91999 −0.270427 −0.135213 0.990816i \(-0.543172\pi\)
−0.135213 + 0.990816i \(0.543172\pi\)
\(332\) 11.1417 0.611479
\(333\) −11.2380 −0.615838
\(334\) −6.14530 −0.336256
\(335\) −3.77442 −0.206218
\(336\) −12.6927 −0.692443
\(337\) −14.7265 −0.802205 −0.401102 0.916033i \(-0.631373\pi\)
−0.401102 + 0.916033i \(0.631373\pi\)
\(338\) −4.72278 −0.256886
\(339\) 16.9067 0.918243
\(340\) −4.30269 −0.233346
\(341\) −27.3414 −1.48062
\(342\) −2.32350 −0.125641
\(343\) 68.2050 3.68272
\(344\) −6.78248 −0.365687
\(345\) 2.52621 0.136006
\(346\) 10.1553 0.545952
\(347\) −1.32420 −0.0710867 −0.0355434 0.999368i \(-0.511316\pi\)
−0.0355434 + 0.999368i \(0.511316\pi\)
\(348\) −15.2832 −0.819264
\(349\) 1.58381 0.0847795 0.0423897 0.999101i \(-0.486503\pi\)
0.0423897 + 0.999101i \(0.486503\pi\)
\(350\) 3.27616 0.175118
\(351\) −1.98902 −0.106166
\(352\) 19.5905 1.04418
\(353\) 0.214568 0.0114203 0.00571016 0.999984i \(-0.498182\pi\)
0.00571016 + 0.999984i \(0.498182\pi\)
\(354\) −4.99773 −0.265627
\(355\) −1.98888 −0.105559
\(356\) 16.7750 0.889073
\(357\) 5.20591 0.275526
\(358\) 11.3916 0.602066
\(359\) −0.503239 −0.0265599 −0.0132800 0.999912i \(-0.504227\pi\)
−0.0132800 + 0.999912i \(0.504227\pi\)
\(360\) 4.84859 0.255543
\(361\) 0.796677 0.0419304
\(362\) 5.77384 0.303466
\(363\) −3.38022 −0.177415
\(364\) −17.8855 −0.937457
\(365\) 6.03933 0.316113
\(366\) 2.35360 0.123025
\(367\) 17.4872 0.912826 0.456413 0.889768i \(-0.349134\pi\)
0.456413 + 0.889768i \(0.349134\pi\)
\(368\) 2.47259 0.128893
\(369\) 3.60771 0.187810
\(370\) 14.6187 0.759992
\(371\) 40.3106 2.09282
\(372\) −12.4539 −0.645703
\(373\) 21.3453 1.10522 0.552610 0.833440i \(-0.313632\pi\)
0.552610 + 0.833440i \(0.313632\pi\)
\(374\) −1.98030 −0.102399
\(375\) −9.45312 −0.488157
\(376\) 0.639970 0.0330039
\(377\) −17.5989 −0.906392
\(378\) −2.71859 −0.139829
\(379\) −37.6086 −1.93182 −0.965912 0.258870i \(-0.916650\pi\)
−0.965912 + 0.258870i \(0.916650\pi\)
\(380\) −19.1442 −0.982075
\(381\) −6.58334 −0.337275
\(382\) −4.67394 −0.239139
\(383\) 7.85675 0.401461 0.200731 0.979646i \(-0.435668\pi\)
0.200731 + 0.979646i \(0.435668\pi\)
\(384\) 11.4698 0.585317
\(385\) −49.1760 −2.50624
\(386\) 3.16445 0.161066
\(387\) 3.48456 0.177130
\(388\) −10.4063 −0.528302
\(389\) −31.0418 −1.57388 −0.786940 0.617029i \(-0.788336\pi\)
−0.786940 + 0.617029i \(0.788336\pi\)
\(390\) 2.58738 0.131017
\(391\) −1.01413 −0.0512869
\(392\) −39.1263 −1.97618
\(393\) 9.63710 0.486127
\(394\) 4.44908 0.224141
\(395\) 0.176440 0.00887768
\(396\) −6.55012 −0.329156
\(397\) 4.96984 0.249429 0.124714 0.992193i \(-0.460199\pi\)
0.124714 + 0.992193i \(0.460199\pi\)
\(398\) −2.16368 −0.108455
\(399\) 23.1629 1.15959
\(400\) 2.93818 0.146909
\(401\) 15.5267 0.775367 0.387684 0.921793i \(-0.373275\pi\)
0.387684 + 0.921793i \(0.373275\pi\)
\(402\) −0.791266 −0.0394648
\(403\) −14.3409 −0.714372
\(404\) −27.8587 −1.38602
\(405\) −2.49100 −0.123779
\(406\) −24.0542 −1.19379
\(407\) −42.6159 −2.11239
\(408\) −1.94644 −0.0963631
\(409\) 21.7623 1.07607 0.538037 0.842921i \(-0.319166\pi\)
0.538037 + 0.842921i \(0.319166\pi\)
\(410\) −4.69302 −0.231772
\(411\) 14.6891 0.724562
\(412\) 19.8134 0.976138
\(413\) 49.8221 2.45159
\(414\) 0.529593 0.0260281
\(415\) 16.0679 0.788741
\(416\) 10.2755 0.503797
\(417\) 0.760234 0.0372288
\(418\) −8.81102 −0.430961
\(419\) 29.1199 1.42260 0.711299 0.702889i \(-0.248107\pi\)
0.711299 + 0.702889i \(0.248107\pi\)
\(420\) −22.3994 −1.09298
\(421\) 29.3418 1.43003 0.715017 0.699107i \(-0.246419\pi\)
0.715017 + 0.699107i \(0.246419\pi\)
\(422\) −11.4333 −0.556565
\(423\) −0.328790 −0.0159863
\(424\) −15.0717 −0.731948
\(425\) −1.20509 −0.0584556
\(426\) −0.416947 −0.0202012
\(427\) −23.4629 −1.13545
\(428\) −31.4145 −1.51848
\(429\) −7.54262 −0.364161
\(430\) −4.53283 −0.218592
\(431\) −2.24604 −0.108188 −0.0540940 0.998536i \(-0.517227\pi\)
−0.0540940 + 0.998536i \(0.517227\pi\)
\(432\) −2.43813 −0.117305
\(433\) 2.63146 0.126460 0.0632298 0.997999i \(-0.479860\pi\)
0.0632298 + 0.997999i \(0.479860\pi\)
\(434\) −19.6011 −0.940885
\(435\) −22.0405 −1.05676
\(436\) 27.6653 1.32493
\(437\) −4.51223 −0.215849
\(438\) 1.26608 0.0604957
\(439\) −33.1159 −1.58053 −0.790267 0.612762i \(-0.790058\pi\)
−0.790267 + 0.612762i \(0.790058\pi\)
\(440\) 18.3864 0.876539
\(441\) 20.1015 0.957213
\(442\) −1.03869 −0.0494055
\(443\) −20.3229 −0.965572 −0.482786 0.875738i \(-0.660375\pi\)
−0.482786 + 0.875738i \(0.660375\pi\)
\(444\) −19.4113 −0.921220
\(445\) 24.1919 1.14681
\(446\) −9.74742 −0.461554
\(447\) 2.99363 0.141594
\(448\) −11.3409 −0.535806
\(449\) −19.2412 −0.908047 −0.454023 0.890990i \(-0.650012\pi\)
−0.454023 + 0.890990i \(0.650012\pi\)
\(450\) 0.629315 0.0296662
\(451\) 13.6809 0.644208
\(452\) 29.2028 1.37358
\(453\) 2.14812 0.100928
\(454\) 3.63842 0.170760
\(455\) −25.7935 −1.20922
\(456\) −8.66038 −0.405560
\(457\) 33.2178 1.55387 0.776933 0.629584i \(-0.216775\pi\)
0.776933 + 0.629584i \(0.216775\pi\)
\(458\) −5.61429 −0.262338
\(459\) 1.00000 0.0466760
\(460\) 4.36350 0.203449
\(461\) 11.3985 0.530883 0.265441 0.964127i \(-0.414482\pi\)
0.265441 + 0.964127i \(0.414482\pi\)
\(462\) −10.3092 −0.479629
\(463\) 24.7190 1.14879 0.574395 0.818578i \(-0.305237\pi\)
0.574395 + 0.818578i \(0.305237\pi\)
\(464\) −21.5727 −1.00149
\(465\) −17.9602 −0.832886
\(466\) −11.0543 −0.512078
\(467\) −12.7157 −0.588413 −0.294207 0.955742i \(-0.595055\pi\)
−0.294207 + 0.955742i \(0.595055\pi\)
\(468\) −3.43562 −0.158812
\(469\) 7.88809 0.364238
\(470\) 0.427701 0.0197284
\(471\) 1.00000 0.0460776
\(472\) −18.6280 −0.857424
\(473\) 13.2139 0.607575
\(474\) 0.0369889 0.00169896
\(475\) −5.36188 −0.246020
\(476\) 8.99213 0.412154
\(477\) 7.74323 0.354538
\(478\) −9.96604 −0.455836
\(479\) −29.0324 −1.32652 −0.663262 0.748387i \(-0.730829\pi\)
−0.663262 + 0.748387i \(0.730829\pi\)
\(480\) 12.8688 0.587377
\(481\) −22.3526 −1.01919
\(482\) −10.4726 −0.477015
\(483\) −5.27948 −0.240225
\(484\) −5.83863 −0.265392
\(485\) −15.0074 −0.681451
\(486\) −0.522212 −0.0236880
\(487\) −16.4916 −0.747306 −0.373653 0.927568i \(-0.621895\pi\)
−0.373653 + 0.927568i \(0.621895\pi\)
\(488\) 8.77256 0.397115
\(489\) 6.26047 0.283108
\(490\) −26.1486 −1.18128
\(491\) −21.8575 −0.986416 −0.493208 0.869912i \(-0.664176\pi\)
−0.493208 + 0.869912i \(0.664176\pi\)
\(492\) 6.23157 0.280941
\(493\) 8.84805 0.398496
\(494\) −4.62150 −0.207931
\(495\) −9.44620 −0.424575
\(496\) −17.5790 −0.789323
\(497\) 4.15652 0.186446
\(498\) 3.36846 0.150944
\(499\) 7.19177 0.321948 0.160974 0.986959i \(-0.448537\pi\)
0.160974 + 0.986959i \(0.448537\pi\)
\(500\) −16.3283 −0.730225
\(501\) 11.7678 0.525747
\(502\) 8.83557 0.394351
\(503\) −43.3914 −1.93473 −0.967364 0.253390i \(-0.918454\pi\)
−0.967364 + 0.253390i \(0.918454\pi\)
\(504\) −10.1330 −0.451359
\(505\) −40.1762 −1.78782
\(506\) 2.00828 0.0892790
\(507\) 9.04380 0.401649
\(508\) −11.3714 −0.504523
\(509\) 0.935730 0.0414755 0.0207378 0.999785i \(-0.493398\pi\)
0.0207378 + 0.999785i \(0.493398\pi\)
\(510\) −1.30083 −0.0576018
\(511\) −12.6215 −0.558342
\(512\) 22.0870 0.976117
\(513\) 4.44935 0.196443
\(514\) 2.41627 0.106577
\(515\) 28.5738 1.25911
\(516\) 6.01886 0.264966
\(517\) −1.24681 −0.0548348
\(518\) −30.5515 −1.34235
\(519\) −19.4467 −0.853615
\(520\) 9.64394 0.422915
\(521\) −17.3502 −0.760125 −0.380062 0.924961i \(-0.624097\pi\)
−0.380062 + 0.924961i \(0.624097\pi\)
\(522\) −4.62056 −0.202236
\(523\) 17.7575 0.776480 0.388240 0.921558i \(-0.373083\pi\)
0.388240 + 0.921558i \(0.373083\pi\)
\(524\) 16.6461 0.727189
\(525\) −6.27361 −0.273803
\(526\) −5.99746 −0.261502
\(527\) 7.21004 0.314074
\(528\) −9.24571 −0.402368
\(529\) −21.9715 −0.955284
\(530\) −10.0727 −0.437528
\(531\) 9.57031 0.415316
\(532\) 40.0091 1.73461
\(533\) 7.17580 0.310819
\(534\) 5.07158 0.219469
\(535\) −45.3041 −1.95867
\(536\) −2.94928 −0.127390
\(537\) −21.8141 −0.941350
\(538\) 13.5959 0.586160
\(539\) 76.2273 3.28334
\(540\) −4.30269 −0.185158
\(541\) 0.123900 0.00532689 0.00266345 0.999996i \(-0.499152\pi\)
0.00266345 + 0.999996i \(0.499152\pi\)
\(542\) −11.2960 −0.485205
\(543\) −11.0565 −0.474480
\(544\) −5.16610 −0.221495
\(545\) 39.8973 1.70901
\(546\) −5.40733 −0.231412
\(547\) −38.8959 −1.66307 −0.831533 0.555475i \(-0.812537\pi\)
−0.831533 + 0.555475i \(0.812537\pi\)
\(548\) 25.3725 1.08386
\(549\) −4.50698 −0.192353
\(550\) 2.38644 0.101758
\(551\) 39.3680 1.67713
\(552\) 1.97395 0.0840168
\(553\) −0.368740 −0.0156804
\(554\) −7.21331 −0.306464
\(555\) −27.9939 −1.18827
\(556\) 1.31315 0.0556899
\(557\) 20.3271 0.861289 0.430644 0.902522i \(-0.358286\pi\)
0.430644 + 0.902522i \(0.358286\pi\)
\(558\) −3.76517 −0.159393
\(559\) 6.93086 0.293144
\(560\) −31.6175 −1.33608
\(561\) 3.79213 0.160104
\(562\) −5.55246 −0.234217
\(563\) 0.687516 0.0289753 0.0144877 0.999895i \(-0.495388\pi\)
0.0144877 + 0.999895i \(0.495388\pi\)
\(564\) −0.567917 −0.0239136
\(565\) 42.1145 1.77177
\(566\) 9.63509 0.404993
\(567\) 5.20591 0.218628
\(568\) −1.55408 −0.0652079
\(569\) −13.4798 −0.565104 −0.282552 0.959252i \(-0.591181\pi\)
−0.282552 + 0.959252i \(0.591181\pi\)
\(570\) −5.78785 −0.242427
\(571\) −33.1731 −1.38825 −0.694125 0.719854i \(-0.744209\pi\)
−0.694125 + 0.719854i \(0.744209\pi\)
\(572\) −13.0283 −0.544741
\(573\) 8.95026 0.373903
\(574\) 9.80788 0.409373
\(575\) 1.22212 0.0509661
\(576\) −2.17846 −0.0907693
\(577\) 18.5904 0.773928 0.386964 0.922095i \(-0.373524\pi\)
0.386964 + 0.922095i \(0.373524\pi\)
\(578\) 0.522212 0.0217212
\(579\) −6.05971 −0.251833
\(580\) −38.0704 −1.58079
\(581\) −33.5800 −1.39313
\(582\) −3.14614 −0.130412
\(583\) 29.3633 1.21610
\(584\) 4.71906 0.195276
\(585\) −4.95466 −0.204850
\(586\) 9.43620 0.389806
\(587\) −48.0234 −1.98214 −0.991068 0.133355i \(-0.957425\pi\)
−0.991068 + 0.133355i \(0.957425\pi\)
\(588\) 34.7211 1.43188
\(589\) 32.0800 1.32183
\(590\) −12.4494 −0.512532
\(591\) −8.51967 −0.350452
\(592\) −27.3997 −1.12612
\(593\) −39.2854 −1.61326 −0.806628 0.591059i \(-0.798710\pi\)
−0.806628 + 0.591059i \(0.798710\pi\)
\(594\) −1.98030 −0.0812525
\(595\) 12.9679 0.531633
\(596\) 5.17088 0.211807
\(597\) 4.14330 0.169574
\(598\) 1.05337 0.0430755
\(599\) −9.01560 −0.368367 −0.184184 0.982892i \(-0.558964\pi\)
−0.184184 + 0.982892i \(0.558964\pi\)
\(600\) 2.34564 0.0957604
\(601\) 43.2024 1.76226 0.881132 0.472871i \(-0.156782\pi\)
0.881132 + 0.472871i \(0.156782\pi\)
\(602\) 9.47309 0.386094
\(603\) 1.51522 0.0617045
\(604\) 3.71044 0.150976
\(605\) −8.42013 −0.342327
\(606\) −8.42252 −0.342141
\(607\) 14.1323 0.573610 0.286805 0.957989i \(-0.407407\pi\)
0.286805 + 0.957989i \(0.407407\pi\)
\(608\) −22.9858 −0.932196
\(609\) 46.0621 1.86653
\(610\) 5.86283 0.237379
\(611\) −0.653971 −0.0264568
\(612\) 1.72729 0.0698217
\(613\) 4.12819 0.166736 0.0833681 0.996519i \(-0.473432\pi\)
0.0833681 + 0.996519i \(0.473432\pi\)
\(614\) −13.4535 −0.542938
\(615\) 8.98681 0.362383
\(616\) −38.4255 −1.54821
\(617\) 20.8254 0.838399 0.419199 0.907894i \(-0.362311\pi\)
0.419199 + 0.907894i \(0.362311\pi\)
\(618\) 5.99019 0.240961
\(619\) −13.7296 −0.551840 −0.275920 0.961181i \(-0.588982\pi\)
−0.275920 + 0.961181i \(0.588982\pi\)
\(620\) −31.0226 −1.24590
\(621\) −1.01413 −0.0406957
\(622\) −0.753112 −0.0301970
\(623\) −50.5583 −2.02558
\(624\) −4.84950 −0.194135
\(625\) −29.5732 −1.18293
\(626\) −10.0196 −0.400465
\(627\) 16.8725 0.673822
\(628\) 1.72729 0.0689265
\(629\) 11.2380 0.448088
\(630\) −6.77201 −0.269803
\(631\) −11.2146 −0.446445 −0.223222 0.974768i \(-0.571658\pi\)
−0.223222 + 0.974768i \(0.571658\pi\)
\(632\) 0.137868 0.00548411
\(633\) 21.8940 0.870209
\(634\) 8.71150 0.345978
\(635\) −16.3991 −0.650779
\(636\) 13.3748 0.530347
\(637\) 39.9822 1.58415
\(638\) −17.5217 −0.693693
\(639\) 0.798424 0.0315852
\(640\) 28.5714 1.12938
\(641\) 12.7651 0.504189 0.252095 0.967703i \(-0.418881\pi\)
0.252095 + 0.967703i \(0.418881\pi\)
\(642\) −9.49753 −0.374838
\(643\) −35.8234 −1.41274 −0.706369 0.707843i \(-0.749668\pi\)
−0.706369 + 0.707843i \(0.749668\pi\)
\(644\) −9.11921 −0.359347
\(645\) 8.68005 0.341777
\(646\) 2.32350 0.0914170
\(647\) 40.8681 1.60669 0.803346 0.595512i \(-0.203051\pi\)
0.803346 + 0.595512i \(0.203051\pi\)
\(648\) −1.94644 −0.0764634
\(649\) 36.2918 1.42458
\(650\) 1.25172 0.0490965
\(651\) 37.5348 1.47111
\(652\) 10.8137 0.423496
\(653\) −4.36228 −0.170709 −0.0853547 0.996351i \(-0.527202\pi\)
−0.0853547 + 0.996351i \(0.527202\pi\)
\(654\) 8.36404 0.327060
\(655\) 24.0060 0.937994
\(656\) 8.79607 0.343429
\(657\) −2.42446 −0.0945870
\(658\) −0.893846 −0.0348457
\(659\) −18.8712 −0.735116 −0.367558 0.930001i \(-0.619806\pi\)
−0.367558 + 0.930001i \(0.619806\pi\)
\(660\) −16.3164 −0.635113
\(661\) 14.0194 0.545290 0.272645 0.962115i \(-0.412102\pi\)
0.272645 + 0.962115i \(0.412102\pi\)
\(662\) −2.56928 −0.0998578
\(663\) 1.98902 0.0772472
\(664\) 12.5552 0.487238
\(665\) 57.6988 2.23746
\(666\) −5.86862 −0.227404
\(667\) −8.97309 −0.347440
\(668\) 20.3265 0.786455
\(669\) 18.6656 0.721655
\(670\) −1.97105 −0.0761482
\(671\) −17.0910 −0.659792
\(672\) −26.8942 −1.03747
\(673\) 15.3836 0.592994 0.296497 0.955034i \(-0.404181\pi\)
0.296497 + 0.955034i \(0.404181\pi\)
\(674\) −7.69037 −0.296222
\(675\) −1.20509 −0.0463841
\(676\) 15.6213 0.600819
\(677\) −6.08494 −0.233863 −0.116932 0.993140i \(-0.537306\pi\)
−0.116932 + 0.993140i \(0.537306\pi\)
\(678\) 8.82887 0.339071
\(679\) 31.3637 1.20363
\(680\) −4.84859 −0.185935
\(681\) −6.96732 −0.266988
\(682\) −14.2780 −0.546733
\(683\) 15.3846 0.588674 0.294337 0.955702i \(-0.404901\pi\)
0.294337 + 0.955702i \(0.404901\pi\)
\(684\) 7.68533 0.293856
\(685\) 36.5907 1.39806
\(686\) 35.6175 1.35988
\(687\) 10.7510 0.410175
\(688\) 8.49582 0.323900
\(689\) 15.4015 0.586749
\(690\) 1.31922 0.0502217
\(691\) 24.9157 0.947839 0.473920 0.880568i \(-0.342839\pi\)
0.473920 + 0.880568i \(0.342839\pi\)
\(692\) −33.5901 −1.27691
\(693\) 19.7415 0.749916
\(694\) −0.691513 −0.0262495
\(695\) 1.89374 0.0718338
\(696\) −17.2222 −0.652805
\(697\) −3.60771 −0.136652
\(698\) 0.827086 0.0313057
\(699\) 21.1681 0.800652
\(700\) −10.8364 −0.409576
\(701\) −11.0105 −0.415861 −0.207930 0.978144i \(-0.566673\pi\)
−0.207930 + 0.978144i \(0.566673\pi\)
\(702\) −1.03869 −0.0392029
\(703\) 50.0017 1.88585
\(704\) −8.26101 −0.311349
\(705\) −0.819017 −0.0308460
\(706\) 0.112050 0.00421707
\(707\) 83.9636 3.15778
\(708\) 16.5307 0.621263
\(709\) 8.85382 0.332512 0.166256 0.986083i \(-0.446832\pi\)
0.166256 + 0.986083i \(0.446832\pi\)
\(710\) −1.03862 −0.0389786
\(711\) −0.0708311 −0.00265637
\(712\) 18.9033 0.708430
\(713\) −7.31194 −0.273834
\(714\) 2.71859 0.101741
\(715\) −18.7887 −0.702657
\(716\) −37.6795 −1.40815
\(717\) 19.0843 0.712715
\(718\) −0.262798 −0.00980752
\(719\) 1.50252 0.0560346 0.0280173 0.999607i \(-0.491081\pi\)
0.0280173 + 0.999607i \(0.491081\pi\)
\(720\) −6.07340 −0.226342
\(721\) −59.7159 −2.22394
\(722\) 0.416034 0.0154832
\(723\) 20.0543 0.745829
\(724\) −19.0978 −0.709765
\(725\) −10.6627 −0.396004
\(726\) −1.76519 −0.0655124
\(727\) −8.16987 −0.303004 −0.151502 0.988457i \(-0.548411\pi\)
−0.151502 + 0.988457i \(0.548411\pi\)
\(728\) −20.1547 −0.746983
\(729\) 1.00000 0.0370370
\(730\) 3.15381 0.116728
\(731\) −3.48456 −0.128881
\(732\) −7.78488 −0.287737
\(733\) −49.6438 −1.83363 −0.916817 0.399307i \(-0.869251\pi\)
−0.916817 + 0.399307i \(0.869251\pi\)
\(734\) 9.13205 0.337070
\(735\) 50.0728 1.84696
\(736\) 5.23911 0.193116
\(737\) 5.74590 0.211653
\(738\) 1.88399 0.0693506
\(739\) −14.2807 −0.525324 −0.262662 0.964888i \(-0.584600\pi\)
−0.262662 + 0.964888i \(0.584600\pi\)
\(740\) −48.3536 −1.77751
\(741\) 8.84984 0.325107
\(742\) 21.0507 0.772794
\(743\) −30.7706 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(744\) −14.0339 −0.514508
\(745\) 7.45713 0.273208
\(746\) 11.1468 0.408113
\(747\) −6.45036 −0.236006
\(748\) 6.55012 0.239496
\(749\) 94.6803 3.45954
\(750\) −4.93654 −0.180257
\(751\) −33.7472 −1.23145 −0.615727 0.787960i \(-0.711138\pi\)
−0.615727 + 0.787960i \(0.711138\pi\)
\(752\) −0.801635 −0.0292326
\(753\) −16.9195 −0.616581
\(754\) −9.19039 −0.334694
\(755\) 5.35098 0.194742
\(756\) 8.99213 0.327041
\(757\) −1.48260 −0.0538862 −0.0269431 0.999637i \(-0.508577\pi\)
−0.0269431 + 0.999637i \(0.508577\pi\)
\(758\) −19.6397 −0.713345
\(759\) −3.84572 −0.139591
\(760\) −21.5730 −0.782536
\(761\) −29.5931 −1.07275 −0.536374 0.843980i \(-0.680206\pi\)
−0.536374 + 0.843980i \(0.680206\pi\)
\(762\) −3.43790 −0.124542
\(763\) −83.3807 −3.01858
\(764\) 15.4597 0.559314
\(765\) 2.49100 0.0900624
\(766\) 4.10289 0.148244
\(767\) 19.0355 0.687334
\(768\) 1.63276 0.0589170
\(769\) −14.9783 −0.540131 −0.270065 0.962842i \(-0.587045\pi\)
−0.270065 + 0.962842i \(0.587045\pi\)
\(770\) −25.6803 −0.925455
\(771\) −4.62699 −0.166637
\(772\) −10.4669 −0.376712
\(773\) −20.1276 −0.723940 −0.361970 0.932190i \(-0.617896\pi\)
−0.361970 + 0.932190i \(0.617896\pi\)
\(774\) 1.81968 0.0654071
\(775\) −8.68878 −0.312110
\(776\) −11.7266 −0.420961
\(777\) 58.5039 2.09882
\(778\) −16.2104 −0.581171
\(779\) −16.0519 −0.575120
\(780\) −8.55815 −0.306431
\(781\) 3.02773 0.108341
\(782\) −0.529593 −0.0189382
\(783\) 8.84805 0.316203
\(784\) 49.0101 1.75036
\(785\) 2.49100 0.0889077
\(786\) 5.03261 0.179507
\(787\) −5.71390 −0.203679 −0.101839 0.994801i \(-0.532473\pi\)
−0.101839 + 0.994801i \(0.532473\pi\)
\(788\) −14.7160 −0.524235
\(789\) 11.4847 0.408867
\(790\) 0.0921394 0.00327817
\(791\) −88.0145 −3.12943
\(792\) −7.38114 −0.262277
\(793\) −8.96447 −0.318338
\(794\) 2.59531 0.0921041
\(795\) 19.2884 0.684090
\(796\) 7.15669 0.253662
\(797\) 14.2418 0.504470 0.252235 0.967666i \(-0.418834\pi\)
0.252235 + 0.967666i \(0.418834\pi\)
\(798\) 12.0959 0.428192
\(799\) 0.328790 0.0116318
\(800\) 6.22564 0.220110
\(801\) −9.71172 −0.343147
\(802\) 8.10824 0.286312
\(803\) −9.19384 −0.324444
\(804\) 2.61723 0.0923026
\(805\) −13.1512 −0.463519
\(806\) −7.48901 −0.263789
\(807\) −26.0351 −0.916480
\(808\) −31.3932 −1.10441
\(809\) −26.6439 −0.936751 −0.468375 0.883530i \(-0.655160\pi\)
−0.468375 + 0.883530i \(0.655160\pi\)
\(810\) −1.30083 −0.0457066
\(811\) 42.3718 1.48788 0.743938 0.668249i \(-0.232956\pi\)
0.743938 + 0.668249i \(0.232956\pi\)
\(812\) 79.5628 2.79211
\(813\) 21.6310 0.758634
\(814\) −22.2545 −0.780021
\(815\) 15.5948 0.546264
\(816\) 2.43813 0.0853517
\(817\) −15.5040 −0.542417
\(818\) 11.3645 0.397351
\(819\) 10.3547 0.361821
\(820\) 15.5229 0.542082
\(821\) −11.9910 −0.418488 −0.209244 0.977863i \(-0.567100\pi\)
−0.209244 + 0.977863i \(0.567100\pi\)
\(822\) 7.67085 0.267552
\(823\) −39.3510 −1.37169 −0.685845 0.727748i \(-0.740567\pi\)
−0.685845 + 0.727748i \(0.740567\pi\)
\(824\) 22.3272 0.777805
\(825\) −4.56987 −0.159102
\(826\) 26.0177 0.905273
\(827\) 27.0540 0.940759 0.470379 0.882464i \(-0.344117\pi\)
0.470379 + 0.882464i \(0.344117\pi\)
\(828\) −1.75171 −0.0608760
\(829\) −27.6852 −0.961546 −0.480773 0.876845i \(-0.659644\pi\)
−0.480773 + 0.876845i \(0.659644\pi\)
\(830\) 8.39084 0.291250
\(831\) 13.8130 0.479167
\(832\) −4.33301 −0.150220
\(833\) −20.1015 −0.696475
\(834\) 0.397004 0.0137471
\(835\) 29.3137 1.01444
\(836\) 29.1437 1.00796
\(837\) 7.21004 0.249216
\(838\) 15.2068 0.525309
\(839\) 3.36480 0.116166 0.0580829 0.998312i \(-0.481501\pi\)
0.0580829 + 0.998312i \(0.481501\pi\)
\(840\) −25.2413 −0.870907
\(841\) 49.2879 1.69958
\(842\) 15.3227 0.528054
\(843\) 10.6326 0.366205
\(844\) 37.8174 1.30173
\(845\) 22.5281 0.774991
\(846\) −0.171698 −0.00590311
\(847\) 17.5971 0.604643
\(848\) 18.8790 0.648309
\(849\) −18.4505 −0.633220
\(850\) −0.629315 −0.0215853
\(851\) −11.3968 −0.390678
\(852\) 1.37911 0.0472477
\(853\) −32.7232 −1.12042 −0.560210 0.828350i \(-0.689280\pi\)
−0.560210 + 0.828350i \(0.689280\pi\)
\(854\) −12.2526 −0.419276
\(855\) 11.0833 0.379042
\(856\) −35.4001 −1.20995
\(857\) −40.0228 −1.36715 −0.683576 0.729880i \(-0.739576\pi\)
−0.683576 + 0.729880i \(0.739576\pi\)
\(858\) −3.93885 −0.134470
\(859\) −45.8602 −1.56473 −0.782364 0.622821i \(-0.785986\pi\)
−0.782364 + 0.622821i \(0.785986\pi\)
\(860\) 14.9930 0.511257
\(861\) −18.7814 −0.640068
\(862\) −1.17291 −0.0399495
\(863\) 3.56646 0.121404 0.0607018 0.998156i \(-0.480666\pi\)
0.0607018 + 0.998156i \(0.480666\pi\)
\(864\) −5.16610 −0.175754
\(865\) −48.4417 −1.64707
\(866\) 1.37418 0.0466965
\(867\) −1.00000 −0.0339618
\(868\) 64.8337 2.20060
\(869\) −0.268600 −0.00911165
\(870\) −11.5098 −0.390220
\(871\) 3.01380 0.102119
\(872\) 31.1753 1.05573
\(873\) 6.02464 0.203903
\(874\) −2.35634 −0.0797044
\(875\) 49.2121 1.66367
\(876\) −4.18775 −0.141491
\(877\) 27.2368 0.919722 0.459861 0.887991i \(-0.347899\pi\)
0.459861 + 0.887991i \(0.347899\pi\)
\(878\) −17.2935 −0.583628
\(879\) −18.0697 −0.609474
\(880\) −23.0311 −0.776378
\(881\) 6.92647 0.233359 0.116679 0.993170i \(-0.462775\pi\)
0.116679 + 0.993170i \(0.462775\pi\)
\(882\) 10.4972 0.353460
\(883\) −7.49222 −0.252133 −0.126067 0.992022i \(-0.540235\pi\)
−0.126067 + 0.992022i \(0.540235\pi\)
\(884\) 3.43562 0.115553
\(885\) 23.8397 0.801362
\(886\) −10.6129 −0.356547
\(887\) 16.3091 0.547605 0.273803 0.961786i \(-0.411719\pi\)
0.273803 + 0.961786i \(0.411719\pi\)
\(888\) −21.8741 −0.734046
\(889\) 34.2723 1.14945
\(890\) 12.6333 0.423470
\(891\) 3.79213 0.127041
\(892\) 32.2410 1.07951
\(893\) 1.46290 0.0489541
\(894\) 1.56331 0.0522849
\(895\) −54.3391 −1.81636
\(896\) −59.7108 −1.99480
\(897\) −2.01713 −0.0673500
\(898\) −10.0480 −0.335305
\(899\) 63.7948 2.12768
\(900\) −2.08155 −0.0693851
\(901\) −7.74323 −0.257965
\(902\) 7.14433 0.237880
\(903\) −18.1403 −0.603671
\(904\) 32.9078 1.09450
\(905\) −27.5418 −0.915520
\(906\) 1.12178 0.0372685
\(907\) −5.00073 −0.166047 −0.0830233 0.996548i \(-0.526458\pi\)
−0.0830233 + 0.996548i \(0.526458\pi\)
\(908\) −12.0346 −0.399383
\(909\) 16.1285 0.534949
\(910\) −13.4697 −0.446515
\(911\) −9.84715 −0.326251 −0.163125 0.986605i \(-0.552158\pi\)
−0.163125 + 0.986605i \(0.552158\pi\)
\(912\) 10.8481 0.359216
\(913\) −24.4606 −0.809527
\(914\) 17.3468 0.573780
\(915\) −11.2269 −0.371150
\(916\) 18.5701 0.613573
\(917\) −50.1698 −1.65675
\(918\) 0.522212 0.0172356
\(919\) 26.6248 0.878270 0.439135 0.898421i \(-0.355285\pi\)
0.439135 + 0.898421i \(0.355285\pi\)
\(920\) 4.91711 0.162112
\(921\) 25.7624 0.848901
\(922\) 5.95245 0.196034
\(923\) 1.58808 0.0522724
\(924\) 34.0993 1.12178
\(925\) −13.5428 −0.445286
\(926\) 12.9086 0.424202
\(927\) −11.4708 −0.376750
\(928\) −45.7099 −1.50050
\(929\) −23.4936 −0.770799 −0.385399 0.922750i \(-0.625936\pi\)
−0.385399 + 0.922750i \(0.625936\pi\)
\(930\) −9.37906 −0.307551
\(931\) −89.4384 −2.93122
\(932\) 36.5636 1.19768
\(933\) 1.44216 0.0472141
\(934\) −6.64031 −0.217277
\(935\) 9.44620 0.308924
\(936\) −3.87151 −0.126544
\(937\) 9.16463 0.299396 0.149698 0.988732i \(-0.452170\pi\)
0.149698 + 0.988732i \(0.452170\pi\)
\(938\) 4.11926 0.134499
\(939\) 19.1869 0.626140
\(940\) −1.41468 −0.0461419
\(941\) 33.1940 1.08209 0.541046 0.840993i \(-0.318028\pi\)
0.541046 + 0.840993i \(0.318028\pi\)
\(942\) 0.522212 0.0170146
\(943\) 3.65869 0.119143
\(944\) 23.3337 0.759447
\(945\) 12.9679 0.421847
\(946\) 6.90046 0.224353
\(947\) 39.4199 1.28097 0.640487 0.767969i \(-0.278733\pi\)
0.640487 + 0.767969i \(0.278733\pi\)
\(948\) −0.122346 −0.00397362
\(949\) −4.82229 −0.156538
\(950\) −2.80004 −0.0908453
\(951\) −16.6819 −0.540948
\(952\) 10.1330 0.328412
\(953\) −20.3173 −0.658141 −0.329070 0.944305i \(-0.606735\pi\)
−0.329070 + 0.944305i \(0.606735\pi\)
\(954\) 4.04361 0.130917
\(955\) 22.2951 0.721453
\(956\) 32.9641 1.06614
\(957\) 33.5529 1.08461
\(958\) −15.1611 −0.489832
\(959\) −76.4703 −2.46936
\(960\) −5.42656 −0.175141
\(961\) 20.9847 0.676927
\(962\) −11.6728 −0.376346
\(963\) 18.1871 0.586071
\(964\) 34.6398 1.11567
\(965\) −15.0947 −0.485917
\(966\) −2.75701 −0.0887053
\(967\) 50.5603 1.62591 0.812955 0.582327i \(-0.197858\pi\)
0.812955 + 0.582327i \(0.197858\pi\)
\(968\) −6.57939 −0.211470
\(969\) −4.44935 −0.142934
\(970\) −7.83705 −0.251633
\(971\) −36.0127 −1.15570 −0.577851 0.816142i \(-0.696109\pi\)
−0.577851 + 0.816142i \(0.696109\pi\)
\(972\) 1.72729 0.0554030
\(973\) −3.95771 −0.126878
\(974\) −8.61213 −0.275950
\(975\) −2.39696 −0.0767640
\(976\) −10.9886 −0.351737
\(977\) −16.9909 −0.543589 −0.271794 0.962355i \(-0.587617\pi\)
−0.271794 + 0.962355i \(0.587617\pi\)
\(978\) 3.26929 0.104541
\(979\) −36.8281 −1.17703
\(980\) 86.4905 2.76284
\(981\) −16.0166 −0.511369
\(982\) −11.4143 −0.364244
\(983\) 11.7320 0.374192 0.187096 0.982342i \(-0.440092\pi\)
0.187096 + 0.982342i \(0.440092\pi\)
\(984\) 7.02218 0.223859
\(985\) −21.2225 −0.676206
\(986\) 4.62056 0.147149
\(987\) 1.71165 0.0544825
\(988\) 15.2863 0.486321
\(989\) 3.53381 0.112368
\(990\) −4.93292 −0.156779
\(991\) −29.8970 −0.949709 −0.474855 0.880064i \(-0.657499\pi\)
−0.474855 + 0.880064i \(0.657499\pi\)
\(992\) −37.2478 −1.18262
\(993\) 4.91999 0.156131
\(994\) 2.17059 0.0688469
\(995\) 10.3210 0.327196
\(996\) −11.1417 −0.353037
\(997\) 47.7503 1.51227 0.756133 0.654417i \(-0.227086\pi\)
0.756133 + 0.654417i \(0.227086\pi\)
\(998\) 3.75563 0.118882
\(999\) 11.2380 0.355554
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.1.29 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.29 48 1.1 even 1 trivial