Properties

Label 8007.2.a.f.1.34
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 1.34
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.18815 q^{2} -1.00000 q^{3} -0.588311 q^{4} -3.84337 q^{5} -1.18815 q^{6} -5.02013 q^{7} -3.07529 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.18815 q^{2} -1.00000 q^{3} -0.588311 q^{4} -3.84337 q^{5} -1.18815 q^{6} -5.02013 q^{7} -3.07529 q^{8} +1.00000 q^{9} -4.56649 q^{10} +1.17485 q^{11} +0.588311 q^{12} +4.56005 q^{13} -5.96465 q^{14} +3.84337 q^{15} -2.47727 q^{16} -1.00000 q^{17} +1.18815 q^{18} -5.09079 q^{19} +2.26110 q^{20} +5.02013 q^{21} +1.39589 q^{22} +0.118540 q^{23} +3.07529 q^{24} +9.77153 q^{25} +5.41801 q^{26} -1.00000 q^{27} +2.95340 q^{28} +0.483859 q^{29} +4.56649 q^{30} +2.83970 q^{31} +3.20722 q^{32} -1.17485 q^{33} -1.18815 q^{34} +19.2942 q^{35} -0.588311 q^{36} -0.774252 q^{37} -6.04860 q^{38} -4.56005 q^{39} +11.8195 q^{40} +1.91141 q^{41} +5.96465 q^{42} +0.0806862 q^{43} -0.691175 q^{44} -3.84337 q^{45} +0.140843 q^{46} +0.641314 q^{47} +2.47727 q^{48} +18.2017 q^{49} +11.6100 q^{50} +1.00000 q^{51} -2.68273 q^{52} +1.13291 q^{53} -1.18815 q^{54} -4.51538 q^{55} +15.4384 q^{56} +5.09079 q^{57} +0.574895 q^{58} +14.7903 q^{59} -2.26110 q^{60} +4.40403 q^{61} +3.37397 q^{62} -5.02013 q^{63} +8.76519 q^{64} -17.5260 q^{65} -1.39589 q^{66} +3.88247 q^{67} +0.588311 q^{68} -0.118540 q^{69} +22.9244 q^{70} -2.48521 q^{71} -3.07529 q^{72} -9.15915 q^{73} -0.919924 q^{74} -9.77153 q^{75} +2.99496 q^{76} -5.89789 q^{77} -5.41801 q^{78} +0.193340 q^{79} +9.52107 q^{80} +1.00000 q^{81} +2.27104 q^{82} -6.84589 q^{83} -2.95340 q^{84} +3.84337 q^{85} +0.0958669 q^{86} -0.483859 q^{87} -3.61299 q^{88} -4.55261 q^{89} -4.56649 q^{90} -22.8921 q^{91} -0.0697385 q^{92} -2.83970 q^{93} +0.761974 q^{94} +19.5658 q^{95} -3.20722 q^{96} -1.32321 q^{97} +21.6263 q^{98} +1.17485 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18815 0.840146 0.420073 0.907490i \(-0.362005\pi\)
0.420073 + 0.907490i \(0.362005\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.588311 −0.294155
\(5\) −3.84337 −1.71881 −0.859405 0.511296i \(-0.829166\pi\)
−0.859405 + 0.511296i \(0.829166\pi\)
\(6\) −1.18815 −0.485058
\(7\) −5.02013 −1.89743 −0.948716 0.316130i \(-0.897616\pi\)
−0.948716 + 0.316130i \(0.897616\pi\)
\(8\) −3.07529 −1.08728
\(9\) 1.00000 0.333333
\(10\) −4.56649 −1.44405
\(11\) 1.17485 0.354230 0.177115 0.984190i \(-0.443324\pi\)
0.177115 + 0.984190i \(0.443324\pi\)
\(12\) 0.588311 0.169831
\(13\) 4.56005 1.26473 0.632366 0.774670i \(-0.282084\pi\)
0.632366 + 0.774670i \(0.282084\pi\)
\(14\) −5.96465 −1.59412
\(15\) 3.84337 0.992355
\(16\) −2.47727 −0.619317
\(17\) −1.00000 −0.242536
\(18\) 1.18815 0.280049
\(19\) −5.09079 −1.16791 −0.583953 0.811787i \(-0.698495\pi\)
−0.583953 + 0.811787i \(0.698495\pi\)
\(20\) 2.26110 0.505597
\(21\) 5.02013 1.09548
\(22\) 1.39589 0.297604
\(23\) 0.118540 0.0247174 0.0123587 0.999924i \(-0.496066\pi\)
0.0123587 + 0.999924i \(0.496066\pi\)
\(24\) 3.07529 0.627741
\(25\) 9.77153 1.95431
\(26\) 5.41801 1.06256
\(27\) −1.00000 −0.192450
\(28\) 2.95340 0.558140
\(29\) 0.483859 0.0898504 0.0449252 0.998990i \(-0.485695\pi\)
0.0449252 + 0.998990i \(0.485695\pi\)
\(30\) 4.56649 0.833723
\(31\) 2.83970 0.510025 0.255012 0.966938i \(-0.417920\pi\)
0.255012 + 0.966938i \(0.417920\pi\)
\(32\) 3.20722 0.566962
\(33\) −1.17485 −0.204515
\(34\) −1.18815 −0.203765
\(35\) 19.2942 3.26132
\(36\) −0.588311 −0.0980518
\(37\) −0.774252 −0.127286 −0.0636432 0.997973i \(-0.520272\pi\)
−0.0636432 + 0.997973i \(0.520272\pi\)
\(38\) −6.04860 −0.981212
\(39\) −4.56005 −0.730193
\(40\) 11.8195 1.86883
\(41\) 1.91141 0.298513 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(42\) 5.96465 0.920365
\(43\) 0.0806862 0.0123045 0.00615226 0.999981i \(-0.498042\pi\)
0.00615226 + 0.999981i \(0.498042\pi\)
\(44\) −0.691175 −0.104199
\(45\) −3.84337 −0.572936
\(46\) 0.140843 0.0207662
\(47\) 0.641314 0.0935453 0.0467726 0.998906i \(-0.485106\pi\)
0.0467726 + 0.998906i \(0.485106\pi\)
\(48\) 2.47727 0.357563
\(49\) 18.2017 2.60025
\(50\) 11.6100 1.64190
\(51\) 1.00000 0.140028
\(52\) −2.68273 −0.372028
\(53\) 1.13291 0.155617 0.0778084 0.996968i \(-0.475208\pi\)
0.0778084 + 0.996968i \(0.475208\pi\)
\(54\) −1.18815 −0.161686
\(55\) −4.51538 −0.608853
\(56\) 15.4384 2.06304
\(57\) 5.09079 0.674291
\(58\) 0.574895 0.0754875
\(59\) 14.7903 1.92553 0.962767 0.270333i \(-0.0871339\pi\)
0.962767 + 0.270333i \(0.0871339\pi\)
\(60\) −2.26110 −0.291907
\(61\) 4.40403 0.563879 0.281939 0.959432i \(-0.409022\pi\)
0.281939 + 0.959432i \(0.409022\pi\)
\(62\) 3.37397 0.428495
\(63\) −5.02013 −0.632477
\(64\) 8.76519 1.09565
\(65\) −17.5260 −2.17383
\(66\) −1.39589 −0.171822
\(67\) 3.88247 0.474320 0.237160 0.971471i \(-0.423784\pi\)
0.237160 + 0.971471i \(0.423784\pi\)
\(68\) 0.588311 0.0713431
\(69\) −0.118540 −0.0142706
\(70\) 22.9244 2.73999
\(71\) −2.48521 −0.294940 −0.147470 0.989067i \(-0.547113\pi\)
−0.147470 + 0.989067i \(0.547113\pi\)
\(72\) −3.07529 −0.362426
\(73\) −9.15915 −1.07200 −0.535999 0.844219i \(-0.680065\pi\)
−0.535999 + 0.844219i \(0.680065\pi\)
\(74\) −0.919924 −0.106939
\(75\) −9.77153 −1.12832
\(76\) 2.99496 0.343546
\(77\) −5.89789 −0.672127
\(78\) −5.41801 −0.613469
\(79\) 0.193340 0.0217525 0.0108762 0.999941i \(-0.496538\pi\)
0.0108762 + 0.999941i \(0.496538\pi\)
\(80\) 9.52107 1.06449
\(81\) 1.00000 0.111111
\(82\) 2.27104 0.250794
\(83\) −6.84589 −0.751434 −0.375717 0.926735i \(-0.622603\pi\)
−0.375717 + 0.926735i \(0.622603\pi\)
\(84\) −2.95340 −0.322242
\(85\) 3.84337 0.416873
\(86\) 0.0958669 0.0103376
\(87\) −0.483859 −0.0518752
\(88\) −3.61299 −0.385146
\(89\) −4.55261 −0.482576 −0.241288 0.970454i \(-0.577570\pi\)
−0.241288 + 0.970454i \(0.577570\pi\)
\(90\) −4.56649 −0.481350
\(91\) −22.8921 −2.39974
\(92\) −0.0697385 −0.00727074
\(93\) −2.83970 −0.294463
\(94\) 0.761974 0.0785917
\(95\) 19.5658 2.00741
\(96\) −3.20722 −0.327336
\(97\) −1.32321 −0.134351 −0.0671756 0.997741i \(-0.521399\pi\)
−0.0671756 + 0.997741i \(0.521399\pi\)
\(98\) 21.6263 2.18459
\(99\) 1.17485 0.118077
\(100\) −5.74870 −0.574870
\(101\) 0.241677 0.0240478 0.0120239 0.999928i \(-0.496173\pi\)
0.0120239 + 0.999928i \(0.496173\pi\)
\(102\) 1.18815 0.117644
\(103\) −7.68238 −0.756967 −0.378484 0.925608i \(-0.623554\pi\)
−0.378484 + 0.925608i \(0.623554\pi\)
\(104\) −14.0235 −1.37512
\(105\) −19.2942 −1.88293
\(106\) 1.34606 0.130741
\(107\) −7.24061 −0.699976 −0.349988 0.936754i \(-0.613814\pi\)
−0.349988 + 0.936754i \(0.613814\pi\)
\(108\) 0.588311 0.0566102
\(109\) −2.12835 −0.203859 −0.101929 0.994792i \(-0.532502\pi\)
−0.101929 + 0.994792i \(0.532502\pi\)
\(110\) −5.36492 −0.511525
\(111\) 0.774252 0.0734888
\(112\) 12.4362 1.17511
\(113\) −4.12701 −0.388237 −0.194118 0.980978i \(-0.562185\pi\)
−0.194118 + 0.980978i \(0.562185\pi\)
\(114\) 6.04860 0.566503
\(115\) −0.455595 −0.0424844
\(116\) −0.284660 −0.0264300
\(117\) 4.56005 0.421577
\(118\) 17.5730 1.61773
\(119\) 5.02013 0.460195
\(120\) −11.8195 −1.07897
\(121\) −9.61973 −0.874521
\(122\) 5.23263 0.473740
\(123\) −1.91141 −0.172346
\(124\) −1.67062 −0.150026
\(125\) −18.3388 −1.64027
\(126\) −5.96465 −0.531373
\(127\) 0.0280070 0.00248522 0.00124261 0.999999i \(-0.499604\pi\)
0.00124261 + 0.999999i \(0.499604\pi\)
\(128\) 3.99987 0.353542
\(129\) −0.0806862 −0.00710402
\(130\) −20.8234 −1.82634
\(131\) 15.4637 1.35107 0.675533 0.737329i \(-0.263913\pi\)
0.675533 + 0.737329i \(0.263913\pi\)
\(132\) 0.691175 0.0601591
\(133\) 25.5564 2.21602
\(134\) 4.61294 0.398498
\(135\) 3.84337 0.330785
\(136\) 3.07529 0.263704
\(137\) 5.63978 0.481839 0.240920 0.970545i \(-0.422551\pi\)
0.240920 + 0.970545i \(0.422551\pi\)
\(138\) −0.140843 −0.0119894
\(139\) 1.70309 0.144454 0.0722270 0.997388i \(-0.476989\pi\)
0.0722270 + 0.997388i \(0.476989\pi\)
\(140\) −11.3510 −0.959336
\(141\) −0.641314 −0.0540084
\(142\) −2.95279 −0.247792
\(143\) 5.35737 0.448005
\(144\) −2.47727 −0.206439
\(145\) −1.85965 −0.154436
\(146\) −10.8824 −0.900634
\(147\) −18.2017 −1.50125
\(148\) 0.455501 0.0374419
\(149\) −18.3377 −1.50229 −0.751143 0.660139i \(-0.770497\pi\)
−0.751143 + 0.660139i \(0.770497\pi\)
\(150\) −11.6100 −0.947952
\(151\) 22.6194 1.84074 0.920371 0.391046i \(-0.127887\pi\)
0.920371 + 0.391046i \(0.127887\pi\)
\(152\) 15.6556 1.26984
\(153\) −1.00000 −0.0808452
\(154\) −7.00755 −0.564684
\(155\) −10.9140 −0.876635
\(156\) 2.68273 0.214790
\(157\) −1.00000 −0.0798087
\(158\) 0.229716 0.0182753
\(159\) −1.13291 −0.0898454
\(160\) −12.3266 −0.974500
\(161\) −0.595088 −0.0468995
\(162\) 1.18815 0.0933495
\(163\) −2.05607 −0.161044 −0.0805218 0.996753i \(-0.525659\pi\)
−0.0805218 + 0.996753i \(0.525659\pi\)
\(164\) −1.12451 −0.0878092
\(165\) 4.51538 0.351522
\(166\) −8.13391 −0.631314
\(167\) 15.6503 1.21105 0.605527 0.795825i \(-0.292962\pi\)
0.605527 + 0.795825i \(0.292962\pi\)
\(168\) −15.4384 −1.19110
\(169\) 7.79410 0.599546
\(170\) 4.56649 0.350234
\(171\) −5.09079 −0.389302
\(172\) −0.0474685 −0.00361944
\(173\) −20.3537 −1.54746 −0.773731 0.633514i \(-0.781612\pi\)
−0.773731 + 0.633514i \(0.781612\pi\)
\(174\) −0.574895 −0.0435827
\(175\) −49.0544 −3.70816
\(176\) −2.91041 −0.219381
\(177\) −14.7903 −1.11171
\(178\) −5.40916 −0.405434
\(179\) 12.9224 0.965869 0.482934 0.875657i \(-0.339571\pi\)
0.482934 + 0.875657i \(0.339571\pi\)
\(180\) 2.26110 0.168532
\(181\) −17.7219 −1.31726 −0.658630 0.752467i \(-0.728864\pi\)
−0.658630 + 0.752467i \(0.728864\pi\)
\(182\) −27.1991 −2.01613
\(183\) −4.40403 −0.325555
\(184\) −0.364546 −0.0268747
\(185\) 2.97574 0.218781
\(186\) −3.37397 −0.247392
\(187\) −1.17485 −0.0859133
\(188\) −0.377292 −0.0275168
\(189\) 5.02013 0.365161
\(190\) 23.2470 1.68652
\(191\) 20.7123 1.49869 0.749344 0.662181i \(-0.230369\pi\)
0.749344 + 0.662181i \(0.230369\pi\)
\(192\) −8.76519 −0.632573
\(193\) −22.7026 −1.63417 −0.817083 0.576520i \(-0.804410\pi\)
−0.817083 + 0.576520i \(0.804410\pi\)
\(194\) −1.57216 −0.112875
\(195\) 17.5260 1.25506
\(196\) −10.7083 −0.764876
\(197\) 7.53823 0.537077 0.268538 0.963269i \(-0.413459\pi\)
0.268538 + 0.963269i \(0.413459\pi\)
\(198\) 1.39589 0.0992015
\(199\) 12.3704 0.876915 0.438458 0.898752i \(-0.355525\pi\)
0.438458 + 0.898752i \(0.355525\pi\)
\(200\) −30.0503 −2.12488
\(201\) −3.88247 −0.273849
\(202\) 0.287147 0.0202036
\(203\) −2.42904 −0.170485
\(204\) −0.588311 −0.0411900
\(205\) −7.34628 −0.513087
\(206\) −9.12778 −0.635963
\(207\) 0.118540 0.00823912
\(208\) −11.2965 −0.783270
\(209\) −5.98090 −0.413707
\(210\) −22.9244 −1.58193
\(211\) −22.7571 −1.56667 −0.783333 0.621602i \(-0.786482\pi\)
−0.783333 + 0.621602i \(0.786482\pi\)
\(212\) −0.666501 −0.0457755
\(213\) 2.48521 0.170284
\(214\) −8.60290 −0.588082
\(215\) −0.310107 −0.0211491
\(216\) 3.07529 0.209247
\(217\) −14.2557 −0.967737
\(218\) −2.52878 −0.171271
\(219\) 9.15915 0.618918
\(220\) 2.65644 0.179097
\(221\) −4.56005 −0.306742
\(222\) 0.919924 0.0617413
\(223\) 14.7887 0.990326 0.495163 0.868800i \(-0.335108\pi\)
0.495163 + 0.868800i \(0.335108\pi\)
\(224\) −16.1007 −1.07577
\(225\) 9.77153 0.651435
\(226\) −4.90349 −0.326175
\(227\) 19.3291 1.28292 0.641459 0.767157i \(-0.278330\pi\)
0.641459 + 0.767157i \(0.278330\pi\)
\(228\) −2.99496 −0.198346
\(229\) 23.1244 1.52810 0.764052 0.645154i \(-0.223207\pi\)
0.764052 + 0.645154i \(0.223207\pi\)
\(230\) −0.541313 −0.0356931
\(231\) 5.89789 0.388052
\(232\) −1.48801 −0.0976925
\(233\) −23.2370 −1.52231 −0.761155 0.648570i \(-0.775367\pi\)
−0.761155 + 0.648570i \(0.775367\pi\)
\(234\) 5.41801 0.354186
\(235\) −2.46481 −0.160787
\(236\) −8.70129 −0.566406
\(237\) −0.193340 −0.0125588
\(238\) 5.96465 0.386631
\(239\) 19.2054 1.24230 0.621148 0.783693i \(-0.286667\pi\)
0.621148 + 0.783693i \(0.286667\pi\)
\(240\) −9.52107 −0.614583
\(241\) 24.0043 1.54625 0.773126 0.634253i \(-0.218692\pi\)
0.773126 + 0.634253i \(0.218692\pi\)
\(242\) −11.4296 −0.734725
\(243\) −1.00000 −0.0641500
\(244\) −2.59094 −0.165868
\(245\) −69.9561 −4.46933
\(246\) −2.27104 −0.144796
\(247\) −23.2143 −1.47709
\(248\) −8.73289 −0.554539
\(249\) 6.84589 0.433840
\(250\) −21.7891 −1.37807
\(251\) −20.2627 −1.27897 −0.639485 0.768804i \(-0.720852\pi\)
−0.639485 + 0.768804i \(0.720852\pi\)
\(252\) 2.95340 0.186047
\(253\) 0.139267 0.00875562
\(254\) 0.0332764 0.00208794
\(255\) −3.84337 −0.240681
\(256\) −12.7779 −0.798622
\(257\) 22.3132 1.39186 0.695928 0.718111i \(-0.254993\pi\)
0.695928 + 0.718111i \(0.254993\pi\)
\(258\) −0.0958669 −0.00596841
\(259\) 3.88685 0.241517
\(260\) 10.3107 0.639445
\(261\) 0.483859 0.0299501
\(262\) 18.3731 1.13509
\(263\) −19.1595 −1.18143 −0.590714 0.806881i \(-0.701154\pi\)
−0.590714 + 0.806881i \(0.701154\pi\)
\(264\) 3.61299 0.222364
\(265\) −4.35419 −0.267476
\(266\) 30.3648 1.86178
\(267\) 4.55261 0.278615
\(268\) −2.28410 −0.139524
\(269\) 16.5414 1.00854 0.504272 0.863545i \(-0.331761\pi\)
0.504272 + 0.863545i \(0.331761\pi\)
\(270\) 4.56649 0.277908
\(271\) 23.9458 1.45461 0.727303 0.686317i \(-0.240774\pi\)
0.727303 + 0.686317i \(0.240774\pi\)
\(272\) 2.47727 0.150207
\(273\) 22.8921 1.38549
\(274\) 6.70088 0.404815
\(275\) 11.4801 0.692273
\(276\) 0.0697385 0.00419777
\(277\) −30.0068 −1.80293 −0.901466 0.432850i \(-0.857508\pi\)
−0.901466 + 0.432850i \(0.857508\pi\)
\(278\) 2.02351 0.121362
\(279\) 2.83970 0.170008
\(280\) −59.3354 −3.54597
\(281\) −25.4712 −1.51949 −0.759743 0.650224i \(-0.774675\pi\)
−0.759743 + 0.650224i \(0.774675\pi\)
\(282\) −0.761974 −0.0453749
\(283\) 21.9793 1.30653 0.653267 0.757127i \(-0.273398\pi\)
0.653267 + 0.757127i \(0.273398\pi\)
\(284\) 1.46207 0.0867581
\(285\) −19.5658 −1.15898
\(286\) 6.36533 0.376390
\(287\) −9.59556 −0.566408
\(288\) 3.20722 0.188987
\(289\) 1.00000 0.0588235
\(290\) −2.20954 −0.129749
\(291\) 1.32321 0.0775677
\(292\) 5.38843 0.315334
\(293\) 2.20695 0.128931 0.0644657 0.997920i \(-0.479466\pi\)
0.0644657 + 0.997920i \(0.479466\pi\)
\(294\) −21.6263 −1.26127
\(295\) −56.8447 −3.30963
\(296\) 2.38105 0.138396
\(297\) −1.17485 −0.0681715
\(298\) −21.7879 −1.26214
\(299\) 0.540550 0.0312608
\(300\) 5.74870 0.331901
\(301\) −0.405055 −0.0233470
\(302\) 26.8752 1.54649
\(303\) −0.241677 −0.0138840
\(304\) 12.6113 0.723305
\(305\) −16.9263 −0.969200
\(306\) −1.18815 −0.0679217
\(307\) 0.998472 0.0569858 0.0284929 0.999594i \(-0.490929\pi\)
0.0284929 + 0.999594i \(0.490929\pi\)
\(308\) 3.46979 0.197710
\(309\) 7.68238 0.437035
\(310\) −12.9674 −0.736501
\(311\) 9.90215 0.561500 0.280750 0.959781i \(-0.409417\pi\)
0.280750 + 0.959781i \(0.409417\pi\)
\(312\) 14.0235 0.793924
\(313\) −8.86140 −0.500876 −0.250438 0.968133i \(-0.580575\pi\)
−0.250438 + 0.968133i \(0.580575\pi\)
\(314\) −1.18815 −0.0670509
\(315\) 19.2942 1.08711
\(316\) −0.113744 −0.00639861
\(317\) 6.77340 0.380432 0.190216 0.981742i \(-0.439081\pi\)
0.190216 + 0.981742i \(0.439081\pi\)
\(318\) −1.34606 −0.0754832
\(319\) 0.568461 0.0318277
\(320\) −33.6879 −1.88321
\(321\) 7.24061 0.404132
\(322\) −0.707051 −0.0394024
\(323\) 5.09079 0.283259
\(324\) −0.588311 −0.0326839
\(325\) 44.5587 2.47167
\(326\) −2.44291 −0.135300
\(327\) 2.12835 0.117698
\(328\) −5.87815 −0.324567
\(329\) −3.21948 −0.177496
\(330\) 5.36492 0.295329
\(331\) −8.31021 −0.456771 −0.228385 0.973571i \(-0.573345\pi\)
−0.228385 + 0.973571i \(0.573345\pi\)
\(332\) 4.02751 0.221038
\(333\) −0.774252 −0.0424288
\(334\) 18.5948 1.01746
\(335\) −14.9218 −0.815265
\(336\) −12.4362 −0.678451
\(337\) 7.68995 0.418898 0.209449 0.977820i \(-0.432833\pi\)
0.209449 + 0.977820i \(0.432833\pi\)
\(338\) 9.26053 0.503706
\(339\) 4.12701 0.224149
\(340\) −2.26110 −0.122625
\(341\) 3.33621 0.180666
\(342\) −6.04860 −0.327071
\(343\) −56.2342 −3.03636
\(344\) −0.248133 −0.0133784
\(345\) 0.455595 0.0245284
\(346\) −24.1831 −1.30009
\(347\) 16.5830 0.890224 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(348\) 0.284660 0.0152594
\(349\) 0.549394 0.0294084 0.0147042 0.999892i \(-0.495319\pi\)
0.0147042 + 0.999892i \(0.495319\pi\)
\(350\) −58.2837 −3.11540
\(351\) −4.56005 −0.243398
\(352\) 3.76800 0.200835
\(353\) −11.7068 −0.623091 −0.311545 0.950231i \(-0.600847\pi\)
−0.311545 + 0.950231i \(0.600847\pi\)
\(354\) −17.5730 −0.933996
\(355\) 9.55158 0.506945
\(356\) 2.67835 0.141952
\(357\) −5.02013 −0.265694
\(358\) 15.3537 0.811470
\(359\) 0.235266 0.0124169 0.00620843 0.999981i \(-0.498024\pi\)
0.00620843 + 0.999981i \(0.498024\pi\)
\(360\) 11.8195 0.622942
\(361\) 6.91612 0.364006
\(362\) −21.0562 −1.10669
\(363\) 9.61973 0.504905
\(364\) 13.4677 0.705897
\(365\) 35.2021 1.84256
\(366\) −5.23263 −0.273514
\(367\) −14.7870 −0.771875 −0.385937 0.922525i \(-0.626122\pi\)
−0.385937 + 0.922525i \(0.626122\pi\)
\(368\) −0.293656 −0.0153079
\(369\) 1.91141 0.0995043
\(370\) 3.53561 0.183808
\(371\) −5.68734 −0.295272
\(372\) 1.67062 0.0866178
\(373\) 12.1448 0.628833 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(374\) −1.39589 −0.0721797
\(375\) 18.3388 0.947010
\(376\) −1.97223 −0.101710
\(377\) 2.20643 0.113637
\(378\) 5.96465 0.306788
\(379\) −3.26264 −0.167591 −0.0837953 0.996483i \(-0.526704\pi\)
−0.0837953 + 0.996483i \(0.526704\pi\)
\(380\) −11.5108 −0.590490
\(381\) −0.0280070 −0.00143484
\(382\) 24.6092 1.25912
\(383\) −9.91788 −0.506780 −0.253390 0.967364i \(-0.581546\pi\)
−0.253390 + 0.967364i \(0.581546\pi\)
\(384\) −3.99987 −0.204117
\(385\) 22.6678 1.15526
\(386\) −26.9740 −1.37294
\(387\) 0.0806862 0.00410151
\(388\) 0.778456 0.0395201
\(389\) −9.22013 −0.467479 −0.233740 0.972299i \(-0.575096\pi\)
−0.233740 + 0.972299i \(0.575096\pi\)
\(390\) 20.8234 1.05444
\(391\) −0.118540 −0.00599484
\(392\) −55.9756 −2.82719
\(393\) −15.4637 −0.780039
\(394\) 8.95652 0.451223
\(395\) −0.743079 −0.0373884
\(396\) −0.691175 −0.0347328
\(397\) −7.06405 −0.354535 −0.177267 0.984163i \(-0.556726\pi\)
−0.177267 + 0.984163i \(0.556726\pi\)
\(398\) 14.6978 0.736737
\(399\) −25.5564 −1.27942
\(400\) −24.2067 −1.21034
\(401\) 5.98441 0.298847 0.149424 0.988773i \(-0.452258\pi\)
0.149424 + 0.988773i \(0.452258\pi\)
\(402\) −4.61294 −0.230073
\(403\) 12.9492 0.645044
\(404\) −0.142181 −0.00707378
\(405\) −3.84337 −0.190979
\(406\) −2.88605 −0.143232
\(407\) −0.909628 −0.0450886
\(408\) −3.07529 −0.152250
\(409\) −36.0175 −1.78095 −0.890477 0.455029i \(-0.849629\pi\)
−0.890477 + 0.455029i \(0.849629\pi\)
\(410\) −8.72845 −0.431068
\(411\) −5.63978 −0.278190
\(412\) 4.51963 0.222666
\(413\) −74.2493 −3.65357
\(414\) 0.140843 0.00692206
\(415\) 26.3113 1.29157
\(416\) 14.6251 0.717055
\(417\) −1.70309 −0.0834005
\(418\) −7.10617 −0.347574
\(419\) −32.3489 −1.58035 −0.790175 0.612882i \(-0.790010\pi\)
−0.790175 + 0.612882i \(0.790010\pi\)
\(420\) 11.3510 0.553873
\(421\) −7.80652 −0.380467 −0.190233 0.981739i \(-0.560924\pi\)
−0.190233 + 0.981739i \(0.560924\pi\)
\(422\) −27.0388 −1.31623
\(423\) 0.641314 0.0311818
\(424\) −3.48402 −0.169199
\(425\) −9.77153 −0.473989
\(426\) 2.95279 0.143063
\(427\) −22.1088 −1.06992
\(428\) 4.25973 0.205902
\(429\) −5.35737 −0.258656
\(430\) −0.368452 −0.0177683
\(431\) 7.23554 0.348524 0.174262 0.984699i \(-0.444246\pi\)
0.174262 + 0.984699i \(0.444246\pi\)
\(432\) 2.47727 0.119188
\(433\) −18.1709 −0.873236 −0.436618 0.899647i \(-0.643824\pi\)
−0.436618 + 0.899647i \(0.643824\pi\)
\(434\) −16.9378 −0.813040
\(435\) 1.85965 0.0891635
\(436\) 1.25213 0.0599661
\(437\) −0.603463 −0.0288676
\(438\) 10.8824 0.519981
\(439\) 9.03632 0.431280 0.215640 0.976473i \(-0.430816\pi\)
0.215640 + 0.976473i \(0.430816\pi\)
\(440\) 13.8861 0.661993
\(441\) 18.2017 0.866749
\(442\) −5.41801 −0.257708
\(443\) −8.46783 −0.402319 −0.201159 0.979559i \(-0.564471\pi\)
−0.201159 + 0.979559i \(0.564471\pi\)
\(444\) −0.455501 −0.0216171
\(445\) 17.4974 0.829456
\(446\) 17.5711 0.832018
\(447\) 18.3377 0.867345
\(448\) −44.0024 −2.07892
\(449\) 14.4508 0.681974 0.340987 0.940068i \(-0.389239\pi\)
0.340987 + 0.940068i \(0.389239\pi\)
\(450\) 11.6100 0.547301
\(451\) 2.24562 0.105742
\(452\) 2.42797 0.114202
\(453\) −22.6194 −1.06275
\(454\) 22.9658 1.07784
\(455\) 87.9828 4.12470
\(456\) −15.6556 −0.733143
\(457\) 21.2804 0.995457 0.497729 0.867333i \(-0.334168\pi\)
0.497729 + 0.867333i \(0.334168\pi\)
\(458\) 27.4752 1.28383
\(459\) 1.00000 0.0466760
\(460\) 0.268031 0.0124970
\(461\) −15.7070 −0.731546 −0.365773 0.930704i \(-0.619195\pi\)
−0.365773 + 0.930704i \(0.619195\pi\)
\(462\) 7.00755 0.326021
\(463\) −22.5481 −1.04790 −0.523949 0.851749i \(-0.675542\pi\)
−0.523949 + 0.851749i \(0.675542\pi\)
\(464\) −1.19865 −0.0556459
\(465\) 10.9140 0.506126
\(466\) −27.6090 −1.27896
\(467\) −15.8490 −0.733406 −0.366703 0.930338i \(-0.619513\pi\)
−0.366703 + 0.930338i \(0.619513\pi\)
\(468\) −2.68273 −0.124009
\(469\) −19.4905 −0.899989
\(470\) −2.92855 −0.135084
\(471\) 1.00000 0.0460776
\(472\) −45.4845 −2.09359
\(473\) 0.0947939 0.00435863
\(474\) −0.229716 −0.0105512
\(475\) −49.7448 −2.28245
\(476\) −2.95340 −0.135369
\(477\) 1.13291 0.0518723
\(478\) 22.8188 1.04371
\(479\) 17.6303 0.805551 0.402775 0.915299i \(-0.368046\pi\)
0.402775 + 0.915299i \(0.368046\pi\)
\(480\) 12.3266 0.562628
\(481\) −3.53063 −0.160983
\(482\) 28.5206 1.29908
\(483\) 0.595088 0.0270774
\(484\) 5.65939 0.257245
\(485\) 5.08557 0.230924
\(486\) −1.18815 −0.0538954
\(487\) −29.8625 −1.35320 −0.676600 0.736350i \(-0.736548\pi\)
−0.676600 + 0.736350i \(0.736548\pi\)
\(488\) −13.5437 −0.613093
\(489\) 2.05607 0.0929786
\(490\) −83.1180 −3.75489
\(491\) −24.4846 −1.10497 −0.552487 0.833522i \(-0.686321\pi\)
−0.552487 + 0.833522i \(0.686321\pi\)
\(492\) 1.12451 0.0506966
\(493\) −0.483859 −0.0217919
\(494\) −27.5819 −1.24097
\(495\) −4.51538 −0.202951
\(496\) −7.03469 −0.315867
\(497\) 12.4761 0.559628
\(498\) 8.13391 0.364489
\(499\) 21.4869 0.961886 0.480943 0.876752i \(-0.340294\pi\)
0.480943 + 0.876752i \(0.340294\pi\)
\(500\) 10.7889 0.482494
\(501\) −15.6503 −0.699203
\(502\) −24.0750 −1.07452
\(503\) 37.4588 1.67021 0.835103 0.550094i \(-0.185408\pi\)
0.835103 + 0.550094i \(0.185408\pi\)
\(504\) 15.4384 0.687679
\(505\) −0.928855 −0.0413335
\(506\) 0.165469 0.00735600
\(507\) −7.79410 −0.346148
\(508\) −0.0164768 −0.000731040 0
\(509\) 22.6036 1.00189 0.500944 0.865479i \(-0.332986\pi\)
0.500944 + 0.865479i \(0.332986\pi\)
\(510\) −4.56649 −0.202207
\(511\) 45.9802 2.03404
\(512\) −23.1818 −1.02450
\(513\) 5.09079 0.224764
\(514\) 26.5113 1.16936
\(515\) 29.5263 1.30108
\(516\) 0.0474685 0.00208969
\(517\) 0.753446 0.0331365
\(518\) 4.61814 0.202910
\(519\) 20.3537 0.893428
\(520\) 53.8975 2.36356
\(521\) −13.2533 −0.580638 −0.290319 0.956930i \(-0.593761\pi\)
−0.290319 + 0.956930i \(0.593761\pi\)
\(522\) 0.574895 0.0251625
\(523\) −5.14882 −0.225142 −0.112571 0.993644i \(-0.535909\pi\)
−0.112571 + 0.993644i \(0.535909\pi\)
\(524\) −9.09744 −0.397424
\(525\) 49.0544 2.14091
\(526\) −22.7643 −0.992572
\(527\) −2.83970 −0.123699
\(528\) 2.91041 0.126659
\(529\) −22.9859 −0.999389
\(530\) −5.17341 −0.224718
\(531\) 14.7903 0.641845
\(532\) −15.0351 −0.651855
\(533\) 8.71616 0.377539
\(534\) 5.40916 0.234077
\(535\) 27.8284 1.20313
\(536\) −11.9397 −0.515718
\(537\) −12.9224 −0.557645
\(538\) 19.6535 0.847324
\(539\) 21.3842 0.921085
\(540\) −2.26110 −0.0973022
\(541\) −27.3251 −1.17480 −0.587400 0.809297i \(-0.699848\pi\)
−0.587400 + 0.809297i \(0.699848\pi\)
\(542\) 28.4511 1.22208
\(543\) 17.7219 0.760521
\(544\) −3.20722 −0.137509
\(545\) 8.18003 0.350394
\(546\) 27.1991 1.16401
\(547\) 28.8887 1.23519 0.617597 0.786495i \(-0.288106\pi\)
0.617597 + 0.786495i \(0.288106\pi\)
\(548\) −3.31794 −0.141736
\(549\) 4.40403 0.187960
\(550\) 13.6400 0.581610
\(551\) −2.46323 −0.104937
\(552\) 0.364546 0.0155161
\(553\) −0.970594 −0.0412738
\(554\) −35.6524 −1.51473
\(555\) −2.97574 −0.126313
\(556\) −1.00194 −0.0424919
\(557\) 32.6810 1.38474 0.692369 0.721544i \(-0.256567\pi\)
0.692369 + 0.721544i \(0.256567\pi\)
\(558\) 3.37397 0.142832
\(559\) 0.367933 0.0155619
\(560\) −47.7971 −2.01979
\(561\) 1.17485 0.0496021
\(562\) −30.2635 −1.27659
\(563\) −6.79956 −0.286567 −0.143284 0.989682i \(-0.545766\pi\)
−0.143284 + 0.989682i \(0.545766\pi\)
\(564\) 0.377292 0.0158869
\(565\) 15.8617 0.667305
\(566\) 26.1146 1.09768
\(567\) −5.02013 −0.210826
\(568\) 7.64273 0.320682
\(569\) −3.86595 −0.162069 −0.0810344 0.996711i \(-0.525822\pi\)
−0.0810344 + 0.996711i \(0.525822\pi\)
\(570\) −23.2470 −0.973711
\(571\) −25.7320 −1.07685 −0.538424 0.842674i \(-0.680980\pi\)
−0.538424 + 0.842674i \(0.680980\pi\)
\(572\) −3.15180 −0.131783
\(573\) −20.7123 −0.865268
\(574\) −11.4009 −0.475865
\(575\) 1.15832 0.0483053
\(576\) 8.76519 0.365216
\(577\) 14.6372 0.609355 0.304678 0.952456i \(-0.401451\pi\)
0.304678 + 0.952456i \(0.401451\pi\)
\(578\) 1.18815 0.0494203
\(579\) 22.7026 0.943487
\(580\) 1.09405 0.0454281
\(581\) 34.3673 1.42579
\(582\) 1.57216 0.0651681
\(583\) 1.33099 0.0551241
\(584\) 28.1670 1.16556
\(585\) −17.5260 −0.724611
\(586\) 2.62218 0.108321
\(587\) 30.4250 1.25577 0.627887 0.778305i \(-0.283920\pi\)
0.627887 + 0.778305i \(0.283920\pi\)
\(588\) 10.7083 0.441602
\(589\) −14.4563 −0.595661
\(590\) −67.5397 −2.78057
\(591\) −7.53823 −0.310081
\(592\) 1.91803 0.0788306
\(593\) 9.22355 0.378766 0.189383 0.981903i \(-0.439351\pi\)
0.189383 + 0.981903i \(0.439351\pi\)
\(594\) −1.39589 −0.0572740
\(595\) −19.2942 −0.790987
\(596\) 10.7883 0.441906
\(597\) −12.3704 −0.506287
\(598\) 0.642252 0.0262636
\(599\) 27.2671 1.11410 0.557052 0.830477i \(-0.311932\pi\)
0.557052 + 0.830477i \(0.311932\pi\)
\(600\) 30.0503 1.22680
\(601\) −17.8387 −0.727658 −0.363829 0.931466i \(-0.618531\pi\)
−0.363829 + 0.931466i \(0.618531\pi\)
\(602\) −0.481264 −0.0196149
\(603\) 3.88247 0.158107
\(604\) −13.3072 −0.541464
\(605\) 36.9722 1.50314
\(606\) −0.287147 −0.0116646
\(607\) 0.574338 0.0233117 0.0116558 0.999932i \(-0.496290\pi\)
0.0116558 + 0.999932i \(0.496290\pi\)
\(608\) −16.3273 −0.662159
\(609\) 2.42904 0.0984296
\(610\) −20.1110 −0.814269
\(611\) 2.92443 0.118310
\(612\) 0.588311 0.0237810
\(613\) 42.2247 1.70544 0.852720 0.522368i \(-0.174951\pi\)
0.852720 + 0.522368i \(0.174951\pi\)
\(614\) 1.18633 0.0478764
\(615\) 7.34628 0.296231
\(616\) 18.1377 0.730789
\(617\) −8.90341 −0.358438 −0.179219 0.983809i \(-0.557357\pi\)
−0.179219 + 0.983809i \(0.557357\pi\)
\(618\) 9.12778 0.367173
\(619\) 19.5496 0.785763 0.392882 0.919589i \(-0.371478\pi\)
0.392882 + 0.919589i \(0.371478\pi\)
\(620\) 6.42083 0.257867
\(621\) −0.118540 −0.00475686
\(622\) 11.7652 0.471741
\(623\) 22.8547 0.915655
\(624\) 11.2965 0.452221
\(625\) 21.6251 0.865006
\(626\) −10.5286 −0.420809
\(627\) 5.98090 0.238854
\(628\) 0.588311 0.0234762
\(629\) 0.774252 0.0308715
\(630\) 22.9244 0.913329
\(631\) −0.935282 −0.0372330 −0.0186165 0.999827i \(-0.505926\pi\)
−0.0186165 + 0.999827i \(0.505926\pi\)
\(632\) −0.594577 −0.0236510
\(633\) 22.7571 0.904515
\(634\) 8.04778 0.319618
\(635\) −0.107641 −0.00427161
\(636\) 0.666501 0.0264285
\(637\) 83.0009 3.28861
\(638\) 0.675414 0.0267399
\(639\) −2.48521 −0.0983133
\(640\) −15.3730 −0.607671
\(641\) −29.2071 −1.15361 −0.576805 0.816882i \(-0.695701\pi\)
−0.576805 + 0.816882i \(0.695701\pi\)
\(642\) 8.60290 0.339529
\(643\) 24.1361 0.951837 0.475918 0.879490i \(-0.342116\pi\)
0.475918 + 0.879490i \(0.342116\pi\)
\(644\) 0.350097 0.0137957
\(645\) 0.310107 0.0122105
\(646\) 6.04860 0.237979
\(647\) 22.5190 0.885312 0.442656 0.896691i \(-0.354036\pi\)
0.442656 + 0.896691i \(0.354036\pi\)
\(648\) −3.07529 −0.120809
\(649\) 17.3763 0.682081
\(650\) 52.9422 2.07656
\(651\) 14.2557 0.558723
\(652\) 1.20961 0.0473719
\(653\) 10.2446 0.400901 0.200451 0.979704i \(-0.435759\pi\)
0.200451 + 0.979704i \(0.435759\pi\)
\(654\) 2.52878 0.0988833
\(655\) −59.4327 −2.32223
\(656\) −4.73509 −0.184874
\(657\) −9.15915 −0.357333
\(658\) −3.82521 −0.149122
\(659\) 39.1301 1.52429 0.762145 0.647406i \(-0.224146\pi\)
0.762145 + 0.647406i \(0.224146\pi\)
\(660\) −2.65644 −0.103402
\(661\) −43.7425 −1.70139 −0.850694 0.525661i \(-0.823818\pi\)
−0.850694 + 0.525661i \(0.823818\pi\)
\(662\) −9.87374 −0.383754
\(663\) 4.56005 0.177098
\(664\) 21.0531 0.817018
\(665\) −98.2229 −3.80892
\(666\) −0.919924 −0.0356463
\(667\) 0.0573568 0.00222087
\(668\) −9.20722 −0.356238
\(669\) −14.7887 −0.571765
\(670\) −17.7293 −0.684941
\(671\) 5.17406 0.199742
\(672\) 16.1007 0.621097
\(673\) 13.0045 0.501285 0.250642 0.968080i \(-0.419358\pi\)
0.250642 + 0.968080i \(0.419358\pi\)
\(674\) 9.13677 0.351935
\(675\) −9.77153 −0.376106
\(676\) −4.58535 −0.176360
\(677\) 12.4576 0.478785 0.239393 0.970923i \(-0.423052\pi\)
0.239393 + 0.970923i \(0.423052\pi\)
\(678\) 4.90349 0.188317
\(679\) 6.64267 0.254922
\(680\) −11.8195 −0.453257
\(681\) −19.3291 −0.740693
\(682\) 3.96390 0.151786
\(683\) 3.41846 0.130804 0.0654018 0.997859i \(-0.479167\pi\)
0.0654018 + 0.997859i \(0.479167\pi\)
\(684\) 2.99496 0.114515
\(685\) −21.6758 −0.828190
\(686\) −66.8143 −2.55098
\(687\) −23.1244 −0.882252
\(688\) −0.199881 −0.00762040
\(689\) 5.16612 0.196813
\(690\) 0.541313 0.0206074
\(691\) 33.9308 1.29079 0.645394 0.763850i \(-0.276693\pi\)
0.645394 + 0.763850i \(0.276693\pi\)
\(692\) 11.9743 0.455194
\(693\) −5.89789 −0.224042
\(694\) 19.7031 0.747918
\(695\) −6.54560 −0.248289
\(696\) 1.48801 0.0564028
\(697\) −1.91141 −0.0724000
\(698\) 0.652760 0.0247073
\(699\) 23.2370 0.878906
\(700\) 28.8592 1.09078
\(701\) −41.2533 −1.55812 −0.779059 0.626951i \(-0.784303\pi\)
−0.779059 + 0.626951i \(0.784303\pi\)
\(702\) −5.41801 −0.204490
\(703\) 3.94155 0.148659
\(704\) 10.2977 0.388111
\(705\) 2.46481 0.0928301
\(706\) −13.9094 −0.523487
\(707\) −1.21325 −0.0456290
\(708\) 8.70129 0.327015
\(709\) −6.13360 −0.230352 −0.115176 0.993345i \(-0.536743\pi\)
−0.115176 + 0.993345i \(0.536743\pi\)
\(710\) 11.3487 0.425908
\(711\) 0.193340 0.00725083
\(712\) 14.0006 0.524695
\(713\) 0.336619 0.0126065
\(714\) −5.96465 −0.223221
\(715\) −20.5904 −0.770036
\(716\) −7.60241 −0.284115
\(717\) −19.2054 −0.717240
\(718\) 0.279530 0.0104320
\(719\) 15.8157 0.589825 0.294912 0.955524i \(-0.404710\pi\)
0.294912 + 0.955524i \(0.404710\pi\)
\(720\) 9.52107 0.354829
\(721\) 38.5666 1.43629
\(722\) 8.21736 0.305818
\(723\) −24.0043 −0.892728
\(724\) 10.4260 0.387479
\(725\) 4.72805 0.175595
\(726\) 11.4296 0.424194
\(727\) −33.5663 −1.24491 −0.622453 0.782657i \(-0.713864\pi\)
−0.622453 + 0.782657i \(0.713864\pi\)
\(728\) 70.3998 2.60919
\(729\) 1.00000 0.0370370
\(730\) 41.8252 1.54802
\(731\) −0.0806862 −0.00298429
\(732\) 2.59094 0.0957639
\(733\) −24.4196 −0.901958 −0.450979 0.892535i \(-0.648925\pi\)
−0.450979 + 0.892535i \(0.648925\pi\)
\(734\) −17.5691 −0.648487
\(735\) 69.9561 2.58037
\(736\) 0.380185 0.0140138
\(737\) 4.56131 0.168018
\(738\) 2.27104 0.0835981
\(739\) 30.3577 1.11673 0.558363 0.829597i \(-0.311430\pi\)
0.558363 + 0.829597i \(0.311430\pi\)
\(740\) −1.75066 −0.0643556
\(741\) 23.2143 0.852798
\(742\) −6.75739 −0.248072
\(743\) −15.9453 −0.584977 −0.292489 0.956269i \(-0.594483\pi\)
−0.292489 + 0.956269i \(0.594483\pi\)
\(744\) 8.73289 0.320163
\(745\) 70.4788 2.58214
\(746\) 14.4298 0.528311
\(747\) −6.84589 −0.250478
\(748\) 0.691175 0.0252719
\(749\) 36.3488 1.32816
\(750\) 21.7891 0.795627
\(751\) 0.273758 0.00998958 0.00499479 0.999988i \(-0.498410\pi\)
0.00499479 + 0.999988i \(0.498410\pi\)
\(752\) −1.58871 −0.0579342
\(753\) 20.2627 0.738413
\(754\) 2.62155 0.0954714
\(755\) −86.9349 −3.16389
\(756\) −2.95340 −0.107414
\(757\) 19.1900 0.697472 0.348736 0.937221i \(-0.386611\pi\)
0.348736 + 0.937221i \(0.386611\pi\)
\(758\) −3.87649 −0.140801
\(759\) −0.139267 −0.00505506
\(760\) −60.1705 −2.18261
\(761\) −28.1802 −1.02153 −0.510766 0.859720i \(-0.670638\pi\)
−0.510766 + 0.859720i \(0.670638\pi\)
\(762\) −0.0332764 −0.00120548
\(763\) 10.6846 0.386808
\(764\) −12.1853 −0.440847
\(765\) 3.84337 0.138958
\(766\) −11.7839 −0.425769
\(767\) 67.4446 2.43528
\(768\) 12.7779 0.461084
\(769\) 2.44796 0.0882759 0.0441379 0.999025i \(-0.485946\pi\)
0.0441379 + 0.999025i \(0.485946\pi\)
\(770\) 26.9326 0.970584
\(771\) −22.3132 −0.803589
\(772\) 13.3562 0.480699
\(773\) 34.8672 1.25409 0.627043 0.778984i \(-0.284265\pi\)
0.627043 + 0.778984i \(0.284265\pi\)
\(774\) 0.0958669 0.00344586
\(775\) 27.7482 0.996744
\(776\) 4.06924 0.146077
\(777\) −3.88685 −0.139440
\(778\) −10.9549 −0.392751
\(779\) −9.73061 −0.348635
\(780\) −10.3107 −0.369183
\(781\) −2.91974 −0.104476
\(782\) −0.140843 −0.00503654
\(783\) −0.483859 −0.0172917
\(784\) −45.0906 −1.61038
\(785\) 3.84337 0.137176
\(786\) −18.3731 −0.655346
\(787\) −47.9465 −1.70911 −0.854554 0.519363i \(-0.826169\pi\)
−0.854554 + 0.519363i \(0.826169\pi\)
\(788\) −4.43482 −0.157984
\(789\) 19.1595 0.682098
\(790\) −0.882886 −0.0314117
\(791\) 20.7182 0.736653
\(792\) −3.61299 −0.128382
\(793\) 20.0826 0.713155
\(794\) −8.39312 −0.297861
\(795\) 4.35419 0.154427
\(796\) −7.27765 −0.257949
\(797\) −16.4717 −0.583456 −0.291728 0.956501i \(-0.594230\pi\)
−0.291728 + 0.956501i \(0.594230\pi\)
\(798\) −30.3648 −1.07490
\(799\) −0.641314 −0.0226881
\(800\) 31.3395 1.10802
\(801\) −4.55261 −0.160859
\(802\) 7.11035 0.251075
\(803\) −10.7606 −0.379733
\(804\) 2.28410 0.0805540
\(805\) 2.28715 0.0806113
\(806\) 15.3855 0.541931
\(807\) −16.5414 −0.582283
\(808\) −0.743227 −0.0261466
\(809\) −35.8117 −1.25907 −0.629536 0.776971i \(-0.716755\pi\)
−0.629536 + 0.776971i \(0.716755\pi\)
\(810\) −4.56649 −0.160450
\(811\) −37.2845 −1.30924 −0.654618 0.755960i \(-0.727170\pi\)
−0.654618 + 0.755960i \(0.727170\pi\)
\(812\) 1.42903 0.0501491
\(813\) −23.9458 −0.839817
\(814\) −1.08077 −0.0378810
\(815\) 7.90224 0.276803
\(816\) −2.47727 −0.0867218
\(817\) −0.410756 −0.0143705
\(818\) −42.7941 −1.49626
\(819\) −22.8921 −0.799914
\(820\) 4.32190 0.150927
\(821\) 44.1705 1.54156 0.770780 0.637101i \(-0.219867\pi\)
0.770780 + 0.637101i \(0.219867\pi\)
\(822\) −6.70088 −0.233720
\(823\) 32.8716 1.14583 0.572917 0.819614i \(-0.305812\pi\)
0.572917 + 0.819614i \(0.305812\pi\)
\(824\) 23.6255 0.823035
\(825\) −11.4801 −0.399684
\(826\) −88.2189 −3.06953
\(827\) 27.9463 0.971789 0.485894 0.874017i \(-0.338494\pi\)
0.485894 + 0.874017i \(0.338494\pi\)
\(828\) −0.0697385 −0.00242358
\(829\) 16.7122 0.580438 0.290219 0.956960i \(-0.406272\pi\)
0.290219 + 0.956960i \(0.406272\pi\)
\(830\) 31.2617 1.08511
\(831\) 30.0068 1.04092
\(832\) 39.9697 1.38570
\(833\) −18.2017 −0.630652
\(834\) −2.02351 −0.0700686
\(835\) −60.1499 −2.08157
\(836\) 3.51862 0.121694
\(837\) −2.83970 −0.0981543
\(838\) −38.4352 −1.32772
\(839\) −33.7159 −1.16400 −0.582001 0.813188i \(-0.697730\pi\)
−0.582001 + 0.813188i \(0.697730\pi\)
\(840\) 59.3354 2.04727
\(841\) −28.7659 −0.991927
\(842\) −9.27528 −0.319647
\(843\) 25.4712 0.877275
\(844\) 13.3883 0.460843
\(845\) −29.9557 −1.03051
\(846\) 0.761974 0.0261972
\(847\) 48.2923 1.65934
\(848\) −2.80652 −0.0963762
\(849\) −21.9793 −0.754328
\(850\) −11.6100 −0.398220
\(851\) −0.0917801 −0.00314618
\(852\) −1.46207 −0.0500898
\(853\) 4.61320 0.157953 0.0789765 0.996876i \(-0.474835\pi\)
0.0789765 + 0.996876i \(0.474835\pi\)
\(854\) −26.2685 −0.898889
\(855\) 19.5658 0.669136
\(856\) 22.2670 0.761070
\(857\) −22.2479 −0.759972 −0.379986 0.924992i \(-0.624071\pi\)
−0.379986 + 0.924992i \(0.624071\pi\)
\(858\) −6.36533 −0.217309
\(859\) −47.4050 −1.61744 −0.808719 0.588196i \(-0.799839\pi\)
−0.808719 + 0.588196i \(0.799839\pi\)
\(860\) 0.182439 0.00622113
\(861\) 9.59556 0.327016
\(862\) 8.59687 0.292811
\(863\) 16.6358 0.566289 0.283144 0.959077i \(-0.408622\pi\)
0.283144 + 0.959077i \(0.408622\pi\)
\(864\) −3.20722 −0.109112
\(865\) 78.2269 2.65979
\(866\) −21.5896 −0.733646
\(867\) −1.00000 −0.0339618
\(868\) 8.38675 0.284665
\(869\) 0.227145 0.00770537
\(870\) 2.20954 0.0749104
\(871\) 17.7043 0.599887
\(872\) 6.54528 0.221651
\(873\) −1.32321 −0.0447837
\(874\) −0.717002 −0.0242530
\(875\) 92.0631 3.11230
\(876\) −5.38843 −0.182058
\(877\) 0.731181 0.0246902 0.0123451 0.999924i \(-0.496070\pi\)
0.0123451 + 0.999924i \(0.496070\pi\)
\(878\) 10.7365 0.362338
\(879\) −2.20695 −0.0744386
\(880\) 11.1858 0.377073
\(881\) 13.8625 0.467038 0.233519 0.972352i \(-0.424976\pi\)
0.233519 + 0.972352i \(0.424976\pi\)
\(882\) 21.6263 0.728195
\(883\) −17.8901 −0.602048 −0.301024 0.953617i \(-0.597328\pi\)
−0.301024 + 0.953617i \(0.597328\pi\)
\(884\) 2.68273 0.0902299
\(885\) 56.8447 1.91081
\(886\) −10.0610 −0.338006
\(887\) 17.5822 0.590353 0.295177 0.955443i \(-0.404621\pi\)
0.295177 + 0.955443i \(0.404621\pi\)
\(888\) −2.38105 −0.0799028
\(889\) −0.140599 −0.00471553
\(890\) 20.7894 0.696864
\(891\) 1.17485 0.0393588
\(892\) −8.70036 −0.291310
\(893\) −3.26479 −0.109252
\(894\) 21.7879 0.728697
\(895\) −49.6658 −1.66014
\(896\) −20.0799 −0.670821
\(897\) −0.540550 −0.0180484
\(898\) 17.1696 0.572957
\(899\) 1.37401 0.0458259
\(900\) −5.74870 −0.191623
\(901\) −1.13291 −0.0377426
\(902\) 2.66812 0.0888388
\(903\) 0.405055 0.0134794
\(904\) 12.6918 0.422122
\(905\) 68.1120 2.26412
\(906\) −26.8752 −0.892867
\(907\) 13.1856 0.437822 0.218911 0.975745i \(-0.429750\pi\)
0.218911 + 0.975745i \(0.429750\pi\)
\(908\) −11.3715 −0.377377
\(909\) 0.241677 0.00801592
\(910\) 104.536 3.46535
\(911\) −38.3718 −1.27131 −0.635657 0.771971i \(-0.719271\pi\)
−0.635657 + 0.771971i \(0.719271\pi\)
\(912\) −12.6113 −0.417600
\(913\) −8.04287 −0.266180
\(914\) 25.2843 0.836329
\(915\) 16.9263 0.559568
\(916\) −13.6043 −0.449500
\(917\) −77.6297 −2.56356
\(918\) 1.18815 0.0392146
\(919\) 52.9985 1.74826 0.874129 0.485693i \(-0.161433\pi\)
0.874129 + 0.485693i \(0.161433\pi\)
\(920\) 1.40109 0.0461924
\(921\) −0.998472 −0.0329008
\(922\) −18.6621 −0.614605
\(923\) −11.3327 −0.373020
\(924\) −3.46979 −0.114148
\(925\) −7.56563 −0.248756
\(926\) −26.7904 −0.880388
\(927\) −7.68238 −0.252322
\(928\) 1.55184 0.0509418
\(929\) −40.0709 −1.31468 −0.657342 0.753593i \(-0.728319\pi\)
−0.657342 + 0.753593i \(0.728319\pi\)
\(930\) 12.9674 0.425219
\(931\) −92.6611 −3.03685
\(932\) 13.6706 0.447795
\(933\) −9.90215 −0.324182
\(934\) −18.8310 −0.616168
\(935\) 4.51538 0.147669
\(936\) −14.0235 −0.458372
\(937\) −0.530328 −0.0173251 −0.00866254 0.999962i \(-0.502757\pi\)
−0.00866254 + 0.999962i \(0.502757\pi\)
\(938\) −23.1576 −0.756122
\(939\) 8.86140 0.289181
\(940\) 1.45007 0.0472962
\(941\) 1.09490 0.0356928 0.0178464 0.999841i \(-0.494319\pi\)
0.0178464 + 0.999841i \(0.494319\pi\)
\(942\) 1.18815 0.0387119
\(943\) 0.226580 0.00737845
\(944\) −36.6396 −1.19252
\(945\) −19.2942 −0.627642
\(946\) 0.112629 0.00366188
\(947\) −33.5395 −1.08989 −0.544944 0.838472i \(-0.683449\pi\)
−0.544944 + 0.838472i \(0.683449\pi\)
\(948\) 0.113744 0.00369424
\(949\) −41.7662 −1.35579
\(950\) −59.1040 −1.91759
\(951\) −6.77340 −0.219642
\(952\) −15.4384 −0.500360
\(953\) 36.0895 1.16905 0.584527 0.811374i \(-0.301280\pi\)
0.584527 + 0.811374i \(0.301280\pi\)
\(954\) 1.34606 0.0435803
\(955\) −79.6050 −2.57596
\(956\) −11.2988 −0.365428
\(957\) −0.568461 −0.0183757
\(958\) 20.9474 0.676780
\(959\) −28.3124 −0.914257
\(960\) 33.6879 1.08727
\(961\) −22.9361 −0.739875
\(962\) −4.19491 −0.135249
\(963\) −7.24061 −0.233325
\(964\) −14.1220 −0.454838
\(965\) 87.2545 2.80882
\(966\) 0.707051 0.0227490
\(967\) 35.1226 1.12947 0.564733 0.825274i \(-0.308979\pi\)
0.564733 + 0.825274i \(0.308979\pi\)
\(968\) 29.5835 0.950849
\(969\) −5.09079 −0.163540
\(970\) 6.04240 0.194010
\(971\) 47.7957 1.53384 0.766919 0.641744i \(-0.221789\pi\)
0.766919 + 0.641744i \(0.221789\pi\)
\(972\) 0.588311 0.0188701
\(973\) −8.54972 −0.274091
\(974\) −35.4810 −1.13689
\(975\) −44.5587 −1.42702
\(976\) −10.9100 −0.349220
\(977\) 32.8823 1.05200 0.525998 0.850486i \(-0.323692\pi\)
0.525998 + 0.850486i \(0.323692\pi\)
\(978\) 2.44291 0.0781156
\(979\) −5.34862 −0.170943
\(980\) 41.1559 1.31468
\(981\) −2.12835 −0.0679529
\(982\) −29.0912 −0.928338
\(983\) 5.08816 0.162287 0.0811436 0.996702i \(-0.474143\pi\)
0.0811436 + 0.996702i \(0.474143\pi\)
\(984\) 5.87815 0.187389
\(985\) −28.9723 −0.923133
\(986\) −0.574895 −0.0183084
\(987\) 3.21948 0.102477
\(988\) 13.6572 0.434494
\(989\) 0.00956456 0.000304135 0
\(990\) −5.36492 −0.170508
\(991\) −4.73117 −0.150291 −0.0751453 0.997173i \(-0.523942\pi\)
−0.0751453 + 0.997173i \(0.523942\pi\)
\(992\) 9.10754 0.289165
\(993\) 8.31021 0.263717
\(994\) 14.8234 0.470169
\(995\) −47.5441 −1.50725
\(996\) −4.02751 −0.127616
\(997\) −36.8310 −1.16645 −0.583224 0.812311i \(-0.698209\pi\)
−0.583224 + 0.812311i \(0.698209\pi\)
\(998\) 25.5296 0.808124
\(999\) 0.774252 0.0244963
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.1.34 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.34 48 1.1 even 1 trivial