Properties

Label 4598.2.a.bn.1.1
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.76156\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.76156 q^{3} +1.00000 q^{4} +1.76156 q^{5} -2.76156 q^{6} -3.62620 q^{7} +1.00000 q^{8} +4.62620 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.76156 q^{3} +1.00000 q^{4} +1.76156 q^{5} -2.76156 q^{6} -3.62620 q^{7} +1.00000 q^{8} +4.62620 q^{9} +1.76156 q^{10} -2.76156 q^{12} +2.62620 q^{13} -3.62620 q^{14} -4.86464 q^{15} +1.00000 q^{16} -4.62620 q^{17} +4.62620 q^{18} -1.00000 q^{19} +1.76156 q^{20} +10.0140 q^{21} +3.62620 q^{23} -2.76156 q^{24} -1.89692 q^{25} +2.62620 q^{26} -4.49084 q^{27} -3.62620 q^{28} +5.38776 q^{29} -4.86464 q^{30} -1.72928 q^{31} +1.00000 q^{32} -4.62620 q^{34} -6.38776 q^{35} +4.62620 q^{36} -2.61224 q^{37} -1.00000 q^{38} -7.25240 q^{39} +1.76156 q^{40} +5.01395 q^{41} +10.0140 q^{42} +7.25240 q^{43} +8.14931 q^{45} +3.62620 q^{46} -7.42003 q^{47} -2.76156 q^{48} +6.14931 q^{49} -1.89692 q^{50} +12.7755 q^{51} +2.62620 q^{52} -5.11704 q^{53} -4.49084 q^{54} -3.62620 q^{56} +2.76156 q^{57} +5.38776 q^{58} -14.0140 q^{59} -4.86464 q^{60} +4.59392 q^{61} -1.72928 q^{62} -16.7755 q^{63} +1.00000 q^{64} +4.62620 q^{65} -14.5048 q^{67} -4.62620 q^{68} -10.0140 q^{69} -6.38776 q^{70} -0.864641 q^{71} +4.62620 q^{72} +5.79383 q^{73} -2.61224 q^{74} +5.23844 q^{75} -1.00000 q^{76} -7.25240 q^{78} -6.38776 q^{79} +1.76156 q^{80} -1.47689 q^{81} +5.01395 q^{82} +6.38776 q^{83} +10.0140 q^{84} -8.14931 q^{85} +7.25240 q^{86} -14.8786 q^{87} +16.2663 q^{89} +8.14931 q^{90} -9.52311 q^{91} +3.62620 q^{92} +4.77551 q^{93} -7.42003 q^{94} -1.76156 q^{95} -2.76156 q^{96} +1.10308 q^{97} +6.14931 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} - 2 q^{12} - q^{13} - 2 q^{14} - 12 q^{15} + 3 q^{16} - 5 q^{17} + 5 q^{18} - 3 q^{19} - q^{20} + 6 q^{21} + 2 q^{23} - 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + q^{29} - 12 q^{30} + 3 q^{32} - 5 q^{34} - 4 q^{35} + 5 q^{36} - 23 q^{37} - 3 q^{38} - 4 q^{39} - q^{40} - 9 q^{41} + 6 q^{42} + 4 q^{43} + 3 q^{45} + 2 q^{46} - 6 q^{47} - 2 q^{48} - 3 q^{49} - 2 q^{50} + 8 q^{51} - q^{52} + 5 q^{53} - 2 q^{54} - 2 q^{56} + 2 q^{57} + q^{58} - 18 q^{59} - 12 q^{60} + 6 q^{61} - 20 q^{63} + 3 q^{64} + 5 q^{65} - 8 q^{67} - 5 q^{68} - 6 q^{69} - 4 q^{70} + 5 q^{72} + 10 q^{73} - 23 q^{74} + 22 q^{75} - 3 q^{76} - 4 q^{78} - 4 q^{79} - q^{80} - 17 q^{81} - 9 q^{82} + 4 q^{83} + 6 q^{84} - 3 q^{85} + 4 q^{86} - 18 q^{87} + 7 q^{89} + 3 q^{90} - 16 q^{91} + 2 q^{92} - 16 q^{93} - 6 q^{94} + q^{95} - 2 q^{96} + 7 q^{97} - 3 q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.76156 −1.59439 −0.797193 0.603725i \(-0.793683\pi\)
−0.797193 + 0.603725i \(0.793683\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.76156 0.787792 0.393896 0.919155i \(-0.371127\pi\)
0.393896 + 0.919155i \(0.371127\pi\)
\(6\) −2.76156 −1.12740
\(7\) −3.62620 −1.37057 −0.685287 0.728273i \(-0.740323\pi\)
−0.685287 + 0.728273i \(0.740323\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.62620 1.54207
\(10\) 1.76156 0.557053
\(11\) 0 0
\(12\) −2.76156 −0.797193
\(13\) 2.62620 0.728376 0.364188 0.931325i \(-0.381347\pi\)
0.364188 + 0.931325i \(0.381347\pi\)
\(14\) −3.62620 −0.969142
\(15\) −4.86464 −1.25604
\(16\) 1.00000 0.250000
\(17\) −4.62620 −1.12202 −0.561009 0.827810i \(-0.689587\pi\)
−0.561009 + 0.827810i \(0.689587\pi\)
\(18\) 4.62620 1.09041
\(19\) −1.00000 −0.229416
\(20\) 1.76156 0.393896
\(21\) 10.0140 2.18522
\(22\) 0 0
\(23\) 3.62620 0.756115 0.378057 0.925782i \(-0.376592\pi\)
0.378057 + 0.925782i \(0.376592\pi\)
\(24\) −2.76156 −0.563700
\(25\) −1.89692 −0.379383
\(26\) 2.62620 0.515040
\(27\) −4.49084 −0.864262
\(28\) −3.62620 −0.685287
\(29\) 5.38776 1.00048 0.500241 0.865886i \(-0.333245\pi\)
0.500241 + 0.865886i \(0.333245\pi\)
\(30\) −4.86464 −0.888158
\(31\) −1.72928 −0.310588 −0.155294 0.987868i \(-0.549633\pi\)
−0.155294 + 0.987868i \(0.549633\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −4.62620 −0.793386
\(35\) −6.38776 −1.07973
\(36\) 4.62620 0.771033
\(37\) −2.61224 −0.429450 −0.214725 0.976675i \(-0.568886\pi\)
−0.214725 + 0.976675i \(0.568886\pi\)
\(38\) −1.00000 −0.162221
\(39\) −7.25240 −1.16131
\(40\) 1.76156 0.278527
\(41\) 5.01395 0.783048 0.391524 0.920168i \(-0.371948\pi\)
0.391524 + 0.920168i \(0.371948\pi\)
\(42\) 10.0140 1.54519
\(43\) 7.25240 1.10598 0.552990 0.833188i \(-0.313487\pi\)
0.552990 + 0.833188i \(0.313487\pi\)
\(44\) 0 0
\(45\) 8.14931 1.21483
\(46\) 3.62620 0.534654
\(47\) −7.42003 −1.08232 −0.541161 0.840919i \(-0.682015\pi\)
−0.541161 + 0.840919i \(0.682015\pi\)
\(48\) −2.76156 −0.398596
\(49\) 6.14931 0.878473
\(50\) −1.89692 −0.268264
\(51\) 12.7755 1.78893
\(52\) 2.62620 0.364188
\(53\) −5.11704 −0.702879 −0.351440 0.936211i \(-0.614308\pi\)
−0.351440 + 0.936211i \(0.614308\pi\)
\(54\) −4.49084 −0.611126
\(55\) 0 0
\(56\) −3.62620 −0.484571
\(57\) 2.76156 0.365777
\(58\) 5.38776 0.707447
\(59\) −14.0140 −1.82446 −0.912231 0.409677i \(-0.865641\pi\)
−0.912231 + 0.409677i \(0.865641\pi\)
\(60\) −4.86464 −0.628022
\(61\) 4.59392 0.588192 0.294096 0.955776i \(-0.404982\pi\)
0.294096 + 0.955776i \(0.404982\pi\)
\(62\) −1.72928 −0.219619
\(63\) −16.7755 −2.11352
\(64\) 1.00000 0.125000
\(65\) 4.62620 0.573809
\(66\) 0 0
\(67\) −14.5048 −1.77204 −0.886021 0.463645i \(-0.846541\pi\)
−0.886021 + 0.463645i \(0.846541\pi\)
\(68\) −4.62620 −0.561009
\(69\) −10.0140 −1.20554
\(70\) −6.38776 −0.763483
\(71\) −0.864641 −0.102614 −0.0513070 0.998683i \(-0.516339\pi\)
−0.0513070 + 0.998683i \(0.516339\pi\)
\(72\) 4.62620 0.545203
\(73\) 5.79383 0.678117 0.339058 0.940765i \(-0.389892\pi\)
0.339058 + 0.940765i \(0.389892\pi\)
\(74\) −2.61224 −0.303667
\(75\) 5.23844 0.604883
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −7.25240 −0.821172
\(79\) −6.38776 −0.718679 −0.359339 0.933207i \(-0.616998\pi\)
−0.359339 + 0.933207i \(0.616998\pi\)
\(80\) 1.76156 0.196948
\(81\) −1.47689 −0.164098
\(82\) 5.01395 0.553699
\(83\) 6.38776 0.701147 0.350574 0.936535i \(-0.385987\pi\)
0.350574 + 0.936535i \(0.385987\pi\)
\(84\) 10.0140 1.09261
\(85\) −8.14931 −0.883917
\(86\) 7.25240 0.782046
\(87\) −14.8786 −1.59515
\(88\) 0 0
\(89\) 16.2663 1.72423 0.862115 0.506713i \(-0.169140\pi\)
0.862115 + 0.506713i \(0.169140\pi\)
\(90\) 8.14931 0.859013
\(91\) −9.52311 −0.998294
\(92\) 3.62620 0.378057
\(93\) 4.77551 0.495197
\(94\) −7.42003 −0.765318
\(95\) −1.76156 −0.180732
\(96\) −2.76156 −0.281850
\(97\) 1.10308 0.112001 0.0560006 0.998431i \(-0.482165\pi\)
0.0560006 + 0.998431i \(0.482165\pi\)
\(98\) 6.14931 0.621174
\(99\) 0 0
\(100\) −1.89692 −0.189692
\(101\) 17.3694 1.72832 0.864162 0.503214i \(-0.167849\pi\)
0.864162 + 0.503214i \(0.167849\pi\)
\(102\) 12.7755 1.26496
\(103\) 12.8925 1.27034 0.635170 0.772372i \(-0.280930\pi\)
0.635170 + 0.772372i \(0.280930\pi\)
\(104\) 2.62620 0.257520
\(105\) 17.6402 1.72150
\(106\) −5.11704 −0.497011
\(107\) −3.50916 −0.339243 −0.169622 0.985509i \(-0.554255\pi\)
−0.169622 + 0.985509i \(0.554255\pi\)
\(108\) −4.49084 −0.432131
\(109\) −16.1633 −1.54816 −0.774080 0.633088i \(-0.781787\pi\)
−0.774080 + 0.633088i \(0.781787\pi\)
\(110\) 0 0
\(111\) 7.21386 0.684710
\(112\) −3.62620 −0.342644
\(113\) −15.7616 −1.48272 −0.741361 0.671106i \(-0.765819\pi\)
−0.741361 + 0.671106i \(0.765819\pi\)
\(114\) 2.76156 0.258644
\(115\) 6.38776 0.595661
\(116\) 5.38776 0.500241
\(117\) 12.1493 1.12320
\(118\) −14.0140 −1.29009
\(119\) 16.7755 1.53781
\(120\) −4.86464 −0.444079
\(121\) 0 0
\(122\) 4.59392 0.415914
\(123\) −13.8463 −1.24848
\(124\) −1.72928 −0.155294
\(125\) −12.1493 −1.08667
\(126\) −16.7755 −1.49448
\(127\) −16.7755 −1.48859 −0.744293 0.667853i \(-0.767213\pi\)
−0.744293 + 0.667853i \(0.767213\pi\)
\(128\) 1.00000 0.0883883
\(129\) −20.0279 −1.76336
\(130\) 4.62620 0.405744
\(131\) −20.9817 −1.83318 −0.916589 0.399831i \(-0.869069\pi\)
−0.916589 + 0.399831i \(0.869069\pi\)
\(132\) 0 0
\(133\) 3.62620 0.314431
\(134\) −14.5048 −1.25302
\(135\) −7.91087 −0.680859
\(136\) −4.62620 −0.396693
\(137\) −5.25240 −0.448742 −0.224371 0.974504i \(-0.572033\pi\)
−0.224371 + 0.974504i \(0.572033\pi\)
\(138\) −10.0140 −0.852444
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) −6.38776 −0.539864
\(141\) 20.4908 1.72564
\(142\) −0.864641 −0.0725591
\(143\) 0 0
\(144\) 4.62620 0.385517
\(145\) 9.49084 0.788171
\(146\) 5.79383 0.479501
\(147\) −16.9817 −1.40063
\(148\) −2.61224 −0.214725
\(149\) −12.0848 −0.990022 −0.495011 0.868887i \(-0.664836\pi\)
−0.495011 + 0.868887i \(0.664836\pi\)
\(150\) 5.23844 0.427717
\(151\) 19.5756 1.59304 0.796520 0.604612i \(-0.206672\pi\)
0.796520 + 0.604612i \(0.206672\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −21.4017 −1.73023
\(154\) 0 0
\(155\) −3.04623 −0.244679
\(156\) −7.25240 −0.580656
\(157\) −17.5756 −1.40269 −0.701343 0.712824i \(-0.747416\pi\)
−0.701343 + 0.712824i \(0.747416\pi\)
\(158\) −6.38776 −0.508183
\(159\) 14.1310 1.12066
\(160\) 1.76156 0.139263
\(161\) −13.1493 −1.03631
\(162\) −1.47689 −0.116035
\(163\) −15.2524 −1.19466 −0.597330 0.801996i \(-0.703772\pi\)
−0.597330 + 0.801996i \(0.703772\pi\)
\(164\) 5.01395 0.391524
\(165\) 0 0
\(166\) 6.38776 0.495786
\(167\) 2.47689 0.191667 0.0958336 0.995397i \(-0.469448\pi\)
0.0958336 + 0.995397i \(0.469448\pi\)
\(168\) 10.0140 0.772593
\(169\) −6.10308 −0.469468
\(170\) −8.14931 −0.625024
\(171\) −4.62620 −0.353774
\(172\) 7.25240 0.552990
\(173\) −7.06018 −0.536776 −0.268388 0.963311i \(-0.586491\pi\)
−0.268388 + 0.963311i \(0.586491\pi\)
\(174\) −14.8786 −1.12794
\(175\) 6.87859 0.519973
\(176\) 0 0
\(177\) 38.7003 2.90890
\(178\) 16.2663 1.21921
\(179\) −5.44461 −0.406949 −0.203475 0.979080i \(-0.565223\pi\)
−0.203475 + 0.979080i \(0.565223\pi\)
\(180\) 8.14931 0.607414
\(181\) 3.40171 0.252847 0.126424 0.991976i \(-0.459650\pi\)
0.126424 + 0.991976i \(0.459650\pi\)
\(182\) −9.52311 −0.705900
\(183\) −12.6864 −0.937804
\(184\) 3.62620 0.267327
\(185\) −4.60162 −0.338318
\(186\) 4.77551 0.350157
\(187\) 0 0
\(188\) −7.42003 −0.541161
\(189\) 16.2847 1.18454
\(190\) −1.76156 −0.127797
\(191\) 7.83237 0.566730 0.283365 0.959012i \(-0.408549\pi\)
0.283365 + 0.959012i \(0.408549\pi\)
\(192\) −2.76156 −0.199298
\(193\) 7.94315 0.571760 0.285880 0.958265i \(-0.407714\pi\)
0.285880 + 0.958265i \(0.407714\pi\)
\(194\) 1.10308 0.0791968
\(195\) −12.7755 −0.914873
\(196\) 6.14931 0.439237
\(197\) −8.21386 −0.585214 −0.292607 0.956233i \(-0.594523\pi\)
−0.292607 + 0.956233i \(0.594523\pi\)
\(198\) 0 0
\(199\) −20.0279 −1.41974 −0.709870 0.704332i \(-0.751246\pi\)
−0.709870 + 0.704332i \(0.751246\pi\)
\(200\) −1.89692 −0.134132
\(201\) 40.0558 2.82532
\(202\) 17.3694 1.22211
\(203\) −19.5371 −1.37123
\(204\) 12.7755 0.894465
\(205\) 8.83237 0.616879
\(206\) 12.8925 0.898266
\(207\) 16.7755 1.16598
\(208\) 2.62620 0.182094
\(209\) 0 0
\(210\) 17.6402 1.21729
\(211\) −20.3126 −1.39838 −0.699188 0.714938i \(-0.746455\pi\)
−0.699188 + 0.714938i \(0.746455\pi\)
\(212\) −5.11704 −0.351440
\(213\) 2.38776 0.163606
\(214\) −3.50916 −0.239881
\(215\) 12.7755 0.871283
\(216\) −4.49084 −0.305563
\(217\) 6.27072 0.425684
\(218\) −16.1633 −1.09471
\(219\) −16.0000 −1.08118
\(220\) 0 0
\(221\) −12.1493 −0.817251
\(222\) 7.21386 0.484163
\(223\) 14.4157 0.965344 0.482672 0.875801i \(-0.339666\pi\)
0.482672 + 0.875801i \(0.339666\pi\)
\(224\) −3.62620 −0.242286
\(225\) −8.77551 −0.585034
\(226\) −15.7616 −1.04844
\(227\) −20.3632 −1.35155 −0.675776 0.737107i \(-0.736191\pi\)
−0.675776 + 0.737107i \(0.736191\pi\)
\(228\) 2.76156 0.182889
\(229\) −19.6724 −1.29999 −0.649995 0.759938i \(-0.725229\pi\)
−0.649995 + 0.759938i \(0.725229\pi\)
\(230\) 6.38776 0.421196
\(231\) 0 0
\(232\) 5.38776 0.353723
\(233\) −4.25240 −0.278584 −0.139292 0.990251i \(-0.544483\pi\)
−0.139292 + 0.990251i \(0.544483\pi\)
\(234\) 12.1493 0.794225
\(235\) −13.0708 −0.852646
\(236\) −14.0140 −0.912231
\(237\) 17.6402 1.14585
\(238\) 16.7755 1.08739
\(239\) −20.8140 −1.34635 −0.673174 0.739484i \(-0.735070\pi\)
−0.673174 + 0.739484i \(0.735070\pi\)
\(240\) −4.86464 −0.314011
\(241\) 30.6864 1.97668 0.988342 0.152252i \(-0.0486524\pi\)
0.988342 + 0.152252i \(0.0486524\pi\)
\(242\) 0 0
\(243\) 17.5510 1.12590
\(244\) 4.59392 0.294096
\(245\) 10.8324 0.692054
\(246\) −13.8463 −0.882809
\(247\) −2.62620 −0.167101
\(248\) −1.72928 −0.109810
\(249\) −17.6402 −1.11790
\(250\) −12.1493 −0.768390
\(251\) 16.5693 1.04585 0.522924 0.852379i \(-0.324841\pi\)
0.522924 + 0.852379i \(0.324841\pi\)
\(252\) −16.7755 −1.05676
\(253\) 0 0
\(254\) −16.7755 −1.05259
\(255\) 22.5048 1.40930
\(256\) 1.00000 0.0625000
\(257\) −17.1676 −1.07089 −0.535444 0.844571i \(-0.679856\pi\)
−0.535444 + 0.844571i \(0.679856\pi\)
\(258\) −20.0279 −1.24688
\(259\) 9.47252 0.588594
\(260\) 4.62620 0.286905
\(261\) 24.9248 1.54281
\(262\) −20.9817 −1.29625
\(263\) −31.0741 −1.91611 −0.958057 0.286579i \(-0.907482\pi\)
−0.958057 + 0.286579i \(0.907482\pi\)
\(264\) 0 0
\(265\) −9.01395 −0.553723
\(266\) 3.62620 0.222336
\(267\) −44.9205 −2.74909
\(268\) −14.5048 −0.886021
\(269\) 0.406077 0.0247590 0.0123795 0.999923i \(-0.496059\pi\)
0.0123795 + 0.999923i \(0.496059\pi\)
\(270\) −7.91087 −0.481440
\(271\) −3.79383 −0.230459 −0.115229 0.993339i \(-0.536760\pi\)
−0.115229 + 0.993339i \(0.536760\pi\)
\(272\) −4.62620 −0.280504
\(273\) 26.2986 1.59167
\(274\) −5.25240 −0.317309
\(275\) 0 0
\(276\) −10.0140 −0.602769
\(277\) 23.3126 1.40072 0.700359 0.713791i \(-0.253023\pi\)
0.700359 + 0.713791i \(0.253023\pi\)
\(278\) 4.00000 0.239904
\(279\) −8.00000 −0.478947
\(280\) −6.38776 −0.381741
\(281\) 11.6402 0.694393 0.347197 0.937792i \(-0.387134\pi\)
0.347197 + 0.937792i \(0.387134\pi\)
\(282\) 20.4908 1.22021
\(283\) −5.31695 −0.316060 −0.158030 0.987434i \(-0.550514\pi\)
−0.158030 + 0.987434i \(0.550514\pi\)
\(284\) −0.864641 −0.0513070
\(285\) 4.86464 0.288156
\(286\) 0 0
\(287\) −18.1816 −1.07323
\(288\) 4.62620 0.272601
\(289\) 4.40171 0.258924
\(290\) 9.49084 0.557321
\(291\) −3.04623 −0.178573
\(292\) 5.79383 0.339058
\(293\) −2.84632 −0.166284 −0.0831419 0.996538i \(-0.526495\pi\)
−0.0831419 + 0.996538i \(0.526495\pi\)
\(294\) −16.9817 −0.990392
\(295\) −24.6864 −1.43730
\(296\) −2.61224 −0.151834
\(297\) 0 0
\(298\) −12.0848 −0.700051
\(299\) 9.52311 0.550736
\(300\) 5.23844 0.302442
\(301\) −26.2986 −1.51583
\(302\) 19.5756 1.12645
\(303\) −47.9667 −2.75561
\(304\) −1.00000 −0.0573539
\(305\) 8.09246 0.463373
\(306\) −21.4017 −1.22345
\(307\) −17.6016 −1.00458 −0.502289 0.864700i \(-0.667509\pi\)
−0.502289 + 0.864700i \(0.667509\pi\)
\(308\) 0 0
\(309\) −35.6035 −2.02541
\(310\) −3.04623 −0.173014
\(311\) 13.7572 0.780099 0.390049 0.920794i \(-0.372458\pi\)
0.390049 + 0.920794i \(0.372458\pi\)
\(312\) −7.25240 −0.410586
\(313\) −20.4586 −1.15639 −0.578193 0.815900i \(-0.696242\pi\)
−0.578193 + 0.815900i \(0.696242\pi\)
\(314\) −17.5756 −0.991849
\(315\) −29.5510 −1.66501
\(316\) −6.38776 −0.359339
\(317\) −14.3632 −0.806716 −0.403358 0.915042i \(-0.632157\pi\)
−0.403358 + 0.915042i \(0.632157\pi\)
\(318\) 14.1310 0.792427
\(319\) 0 0
\(320\) 1.76156 0.0984740
\(321\) 9.69075 0.540885
\(322\) −13.1493 −0.732783
\(323\) 4.62620 0.257409
\(324\) −1.47689 −0.0820492
\(325\) −4.98168 −0.276334
\(326\) −15.2524 −0.844752
\(327\) 44.6358 2.46836
\(328\) 5.01395 0.276849
\(329\) 26.9065 1.48340
\(330\) 0 0
\(331\) −24.1064 −1.32501 −0.662504 0.749058i \(-0.730506\pi\)
−0.662504 + 0.749058i \(0.730506\pi\)
\(332\) 6.38776 0.350574
\(333\) −12.0848 −0.662241
\(334\) 2.47689 0.135529
\(335\) −25.5510 −1.39600
\(336\) 10.0140 0.546306
\(337\) 6.09683 0.332115 0.166058 0.986116i \(-0.446896\pi\)
0.166058 + 0.986116i \(0.446896\pi\)
\(338\) −6.10308 −0.331964
\(339\) 43.5264 2.36403
\(340\) −8.14931 −0.441959
\(341\) 0 0
\(342\) −4.62620 −0.250156
\(343\) 3.08476 0.166561
\(344\) 7.25240 0.391023
\(345\) −17.6402 −0.949714
\(346\) −7.06018 −0.379558
\(347\) 27.1633 1.45820 0.729100 0.684407i \(-0.239939\pi\)
0.729100 + 0.684407i \(0.239939\pi\)
\(348\) −14.8786 −0.797576
\(349\) 18.2139 0.974966 0.487483 0.873133i \(-0.337915\pi\)
0.487483 + 0.873133i \(0.337915\pi\)
\(350\) 6.87859 0.367676
\(351\) −11.7938 −0.629508
\(352\) 0 0
\(353\) −26.5510 −1.41317 −0.706584 0.707629i \(-0.749765\pi\)
−0.706584 + 0.707629i \(0.749765\pi\)
\(354\) 38.7003 2.05690
\(355\) −1.52311 −0.0808385
\(356\) 16.2663 0.862115
\(357\) −46.3265 −2.45186
\(358\) −5.44461 −0.287757
\(359\) −22.4277 −1.18369 −0.591845 0.806052i \(-0.701600\pi\)
−0.591845 + 0.806052i \(0.701600\pi\)
\(360\) 8.14931 0.429506
\(361\) 1.00000 0.0526316
\(362\) 3.40171 0.178790
\(363\) 0 0
\(364\) −9.52311 −0.499147
\(365\) 10.2062 0.534215
\(366\) −12.6864 −0.663128
\(367\) −21.4846 −1.12149 −0.560743 0.827990i \(-0.689484\pi\)
−0.560743 + 0.827990i \(0.689484\pi\)
\(368\) 3.62620 0.189029
\(369\) 23.1955 1.20751
\(370\) −4.60162 −0.239227
\(371\) 18.5554 0.963348
\(372\) 4.77551 0.247599
\(373\) −0.632456 −0.0327473 −0.0163737 0.999866i \(-0.505212\pi\)
−0.0163737 + 0.999866i \(0.505212\pi\)
\(374\) 0 0
\(375\) 33.5510 1.73257
\(376\) −7.42003 −0.382659
\(377\) 14.1493 0.728727
\(378\) 16.2847 0.837593
\(379\) 33.4725 1.71937 0.859684 0.510826i \(-0.170661\pi\)
0.859684 + 0.510826i \(0.170661\pi\)
\(380\) −1.76156 −0.0903660
\(381\) 46.3265 2.37338
\(382\) 7.83237 0.400739
\(383\) −13.0096 −0.664759 −0.332379 0.943146i \(-0.607851\pi\)
−0.332379 + 0.943146i \(0.607851\pi\)
\(384\) −2.76156 −0.140925
\(385\) 0 0
\(386\) 7.94315 0.404295
\(387\) 33.5510 1.70549
\(388\) 1.10308 0.0560006
\(389\) −10.8078 −0.547976 −0.273988 0.961733i \(-0.588343\pi\)
−0.273988 + 0.961733i \(0.588343\pi\)
\(390\) −12.7755 −0.646913
\(391\) −16.7755 −0.848374
\(392\) 6.14931 0.310587
\(393\) 57.9421 2.92279
\(394\) −8.21386 −0.413808
\(395\) −11.2524 −0.566169
\(396\) 0 0
\(397\) −21.7370 −1.09095 −0.545474 0.838128i \(-0.683650\pi\)
−0.545474 + 0.838128i \(0.683650\pi\)
\(398\) −20.0279 −1.00391
\(399\) −10.0140 −0.501325
\(400\) −1.89692 −0.0948458
\(401\) 15.9311 0.795560 0.397780 0.917481i \(-0.369781\pi\)
0.397780 + 0.917481i \(0.369781\pi\)
\(402\) 40.0558 1.99780
\(403\) −4.54144 −0.226225
\(404\) 17.3694 0.864162
\(405\) −2.60162 −0.129275
\(406\) −19.5371 −0.969608
\(407\) 0 0
\(408\) 12.7755 0.632482
\(409\) −38.4113 −1.89932 −0.949658 0.313288i \(-0.898569\pi\)
−0.949658 + 0.313288i \(0.898569\pi\)
\(410\) 8.83237 0.436199
\(411\) 14.5048 0.715469
\(412\) 12.8925 0.635170
\(413\) 50.8174 2.50056
\(414\) 16.7755 0.824471
\(415\) 11.2524 0.552358
\(416\) 2.62620 0.128760
\(417\) −11.0462 −0.540936
\(418\) 0 0
\(419\) 5.07081 0.247725 0.123863 0.992299i \(-0.460472\pi\)
0.123863 + 0.992299i \(0.460472\pi\)
\(420\) 17.6402 0.860751
\(421\) 6.16327 0.300379 0.150190 0.988657i \(-0.452012\pi\)
0.150190 + 0.988657i \(0.452012\pi\)
\(422\) −20.3126 −0.988801
\(423\) −34.3265 −1.66901
\(424\) −5.11704 −0.248505
\(425\) 8.77551 0.425675
\(426\) 2.38776 0.115687
\(427\) −16.6585 −0.806160
\(428\) −3.50916 −0.169622
\(429\) 0 0
\(430\) 12.7755 0.616090
\(431\) −25.6681 −1.23639 −0.618193 0.786026i \(-0.712135\pi\)
−0.618193 + 0.786026i \(0.712135\pi\)
\(432\) −4.49084 −0.216066
\(433\) 29.5433 1.41976 0.709881 0.704322i \(-0.248749\pi\)
0.709881 + 0.704322i \(0.248749\pi\)
\(434\) 6.27072 0.301004
\(435\) −26.2095 −1.25665
\(436\) −16.1633 −0.774080
\(437\) −3.62620 −0.173465
\(438\) −16.0000 −0.764510
\(439\) 11.5877 0.553049 0.276525 0.961007i \(-0.410817\pi\)
0.276525 + 0.961007i \(0.410817\pi\)
\(440\) 0 0
\(441\) 28.4479 1.35466
\(442\) −12.1493 −0.577884
\(443\) −3.97209 −0.188720 −0.0943599 0.995538i \(-0.530080\pi\)
−0.0943599 + 0.995538i \(0.530080\pi\)
\(444\) 7.21386 0.342355
\(445\) 28.6541 1.35833
\(446\) 14.4157 0.682601
\(447\) 33.3728 1.57848
\(448\) −3.62620 −0.171322
\(449\) 7.03853 0.332169 0.166084 0.986112i \(-0.446888\pi\)
0.166084 + 0.986112i \(0.446888\pi\)
\(450\) −8.77551 −0.413682
\(451\) 0 0
\(452\) −15.7616 −0.741361
\(453\) −54.0591 −2.53992
\(454\) −20.3632 −0.955691
\(455\) −16.7755 −0.786448
\(456\) 2.76156 0.129322
\(457\) 9.29862 0.434971 0.217486 0.976064i \(-0.430214\pi\)
0.217486 + 0.976064i \(0.430214\pi\)
\(458\) −19.6724 −0.919232
\(459\) 20.7755 0.969718
\(460\) 6.38776 0.297831
\(461\) −12.3309 −0.574307 −0.287154 0.957885i \(-0.592709\pi\)
−0.287154 + 0.957885i \(0.592709\pi\)
\(462\) 0 0
\(463\) −28.1570 −1.30857 −0.654284 0.756249i \(-0.727030\pi\)
−0.654284 + 0.756249i \(0.727030\pi\)
\(464\) 5.38776 0.250120
\(465\) 8.41233 0.390113
\(466\) −4.25240 −0.196988
\(467\) 35.4865 1.64212 0.821059 0.570843i \(-0.193384\pi\)
0.821059 + 0.570843i \(0.193384\pi\)
\(468\) 12.1493 0.561602
\(469\) 52.5972 2.42872
\(470\) −13.0708 −0.602911
\(471\) 48.5360 2.23642
\(472\) −14.0140 −0.645044
\(473\) 0 0
\(474\) 17.6402 0.810239
\(475\) 1.89692 0.0870365
\(476\) 16.7755 0.768904
\(477\) −23.6724 −1.08389
\(478\) −20.8140 −0.952012
\(479\) −0.195541 −0.00893450 −0.00446725 0.999990i \(-0.501422\pi\)
−0.00446725 + 0.999990i \(0.501422\pi\)
\(480\) −4.86464 −0.222039
\(481\) −6.86027 −0.312801
\(482\) 30.6864 1.39773
\(483\) 36.3126 1.65228
\(484\) 0 0
\(485\) 1.94315 0.0882337
\(486\) 17.5510 0.796130
\(487\) −24.0279 −1.08881 −0.544404 0.838823i \(-0.683244\pi\)
−0.544404 + 0.838823i \(0.683244\pi\)
\(488\) 4.59392 0.207957
\(489\) 42.1204 1.90475
\(490\) 10.8324 0.489356
\(491\) −4.23407 −0.191081 −0.0955405 0.995426i \(-0.530458\pi\)
−0.0955405 + 0.995426i \(0.530458\pi\)
\(492\) −13.8463 −0.624240
\(493\) −24.9248 −1.12256
\(494\) −2.62620 −0.118158
\(495\) 0 0
\(496\) −1.72928 −0.0776470
\(497\) 3.13536 0.140640
\(498\) −17.6402 −0.790474
\(499\) 33.2278 1.48748 0.743741 0.668468i \(-0.233050\pi\)
0.743741 + 0.668468i \(0.233050\pi\)
\(500\) −12.1493 −0.543334
\(501\) −6.84006 −0.305591
\(502\) 16.5693 0.739526
\(503\) 21.1493 0.943001 0.471501 0.881866i \(-0.343713\pi\)
0.471501 + 0.881866i \(0.343713\pi\)
\(504\) −16.7755 −0.747241
\(505\) 30.5972 1.36156
\(506\) 0 0
\(507\) 16.8540 0.748513
\(508\) −16.7755 −0.744293
\(509\) 35.8078 1.58715 0.793576 0.608471i \(-0.208217\pi\)
0.793576 + 0.608471i \(0.208217\pi\)
\(510\) 22.5048 0.996529
\(511\) −21.0096 −0.929409
\(512\) 1.00000 0.0441942
\(513\) 4.49084 0.198275
\(514\) −17.1676 −0.757232
\(515\) 22.7110 1.00076
\(516\) −20.0279 −0.881679
\(517\) 0 0
\(518\) 9.47252 0.416198
\(519\) 19.4971 0.855828
\(520\) 4.62620 0.202872
\(521\) −7.96336 −0.348881 −0.174440 0.984668i \(-0.555812\pi\)
−0.174440 + 0.984668i \(0.555812\pi\)
\(522\) 24.9248 1.09093
\(523\) 27.3030 1.19388 0.596938 0.802287i \(-0.296384\pi\)
0.596938 + 0.802287i \(0.296384\pi\)
\(524\) −20.9817 −0.916589
\(525\) −18.9956 −0.829037
\(526\) −31.0741 −1.35490
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −9.85069 −0.428291
\(530\) −9.01395 −0.391541
\(531\) −64.8313 −2.81344
\(532\) 3.62620 0.157216
\(533\) 13.1676 0.570354
\(534\) −44.9205 −1.94390
\(535\) −6.18159 −0.267253
\(536\) −14.5048 −0.626512
\(537\) 15.0356 0.648834
\(538\) 0.406077 0.0175072
\(539\) 0 0
\(540\) −7.91087 −0.340430
\(541\) 31.7851 1.36655 0.683274 0.730162i \(-0.260555\pi\)
0.683274 + 0.730162i \(0.260555\pi\)
\(542\) −3.79383 −0.162959
\(543\) −9.39401 −0.403136
\(544\) −4.62620 −0.198347
\(545\) −28.4725 −1.21963
\(546\) 26.2986 1.12548
\(547\) 1.44461 0.0617671 0.0308835 0.999523i \(-0.490168\pi\)
0.0308835 + 0.999523i \(0.490168\pi\)
\(548\) −5.25240 −0.224371
\(549\) 21.2524 0.907030
\(550\) 0 0
\(551\) −5.38776 −0.229526
\(552\) −10.0140 −0.426222
\(553\) 23.1633 0.985002
\(554\) 23.3126 0.990457
\(555\) 12.7076 0.539409
\(556\) 4.00000 0.169638
\(557\) 26.3632 1.11704 0.558522 0.829490i \(-0.311369\pi\)
0.558522 + 0.829490i \(0.311369\pi\)
\(558\) −8.00000 −0.338667
\(559\) 19.0462 0.805570
\(560\) −6.38776 −0.269932
\(561\) 0 0
\(562\) 11.6402 0.491010
\(563\) −11.7711 −0.496094 −0.248047 0.968748i \(-0.579789\pi\)
−0.248047 + 0.968748i \(0.579789\pi\)
\(564\) 20.4908 0.862820
\(565\) −27.7649 −1.16808
\(566\) −5.31695 −0.223488
\(567\) 5.35548 0.224909
\(568\) −0.864641 −0.0362795
\(569\) −21.2524 −0.890947 −0.445473 0.895295i \(-0.646965\pi\)
−0.445473 + 0.895295i \(0.646965\pi\)
\(570\) 4.86464 0.203757
\(571\) 4.14494 0.173460 0.0867302 0.996232i \(-0.472358\pi\)
0.0867302 + 0.996232i \(0.472358\pi\)
\(572\) 0 0
\(573\) −21.6295 −0.903586
\(574\) −18.1816 −0.758885
\(575\) −6.87859 −0.286857
\(576\) 4.62620 0.192758
\(577\) 0.690749 0.0287563 0.0143781 0.999897i \(-0.495423\pi\)
0.0143781 + 0.999897i \(0.495423\pi\)
\(578\) 4.40171 0.183087
\(579\) −21.9354 −0.911606
\(580\) 9.49084 0.394086
\(581\) −23.1633 −0.960974
\(582\) −3.04623 −0.126270
\(583\) 0 0
\(584\) 5.79383 0.239750
\(585\) 21.4017 0.884852
\(586\) −2.84632 −0.117580
\(587\) −1.30488 −0.0538583 −0.0269291 0.999637i \(-0.508573\pi\)
−0.0269291 + 0.999637i \(0.508573\pi\)
\(588\) −16.9817 −0.700313
\(589\) 1.72928 0.0712538
\(590\) −24.6864 −1.01632
\(591\) 22.6831 0.933056
\(592\) −2.61224 −0.107363
\(593\) −21.6743 −0.890057 −0.445029 0.895516i \(-0.646807\pi\)
−0.445029 + 0.895516i \(0.646807\pi\)
\(594\) 0 0
\(595\) 29.5510 1.21147
\(596\) −12.0848 −0.495011
\(597\) 55.3082 2.26361
\(598\) 9.52311 0.389429
\(599\) 18.6339 0.761360 0.380680 0.924707i \(-0.375690\pi\)
0.380680 + 0.924707i \(0.375690\pi\)
\(600\) 5.23844 0.213859
\(601\) 37.1310 1.51460 0.757302 0.653064i \(-0.226517\pi\)
0.757302 + 0.653064i \(0.226517\pi\)
\(602\) −26.2986 −1.07185
\(603\) −67.1020 −2.73261
\(604\) 19.5756 0.796520
\(605\) 0 0
\(606\) −47.9667 −1.94851
\(607\) 14.7509 0.598722 0.299361 0.954140i \(-0.403227\pi\)
0.299361 + 0.954140i \(0.403227\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 53.9527 2.18627
\(610\) 8.09246 0.327654
\(611\) −19.4865 −0.788338
\(612\) −21.4017 −0.865113
\(613\) 0.238443 0.00963061 0.00481531 0.999988i \(-0.498467\pi\)
0.00481531 + 0.999988i \(0.498467\pi\)
\(614\) −17.6016 −0.710344
\(615\) −24.3911 −0.983543
\(616\) 0 0
\(617\) −36.8217 −1.48239 −0.741194 0.671291i \(-0.765740\pi\)
−0.741194 + 0.671291i \(0.765740\pi\)
\(618\) −35.6035 −1.43218
\(619\) 5.75719 0.231401 0.115700 0.993284i \(-0.463089\pi\)
0.115700 + 0.993284i \(0.463089\pi\)
\(620\) −3.04623 −0.122339
\(621\) −16.2847 −0.653481
\(622\) 13.7572 0.551613
\(623\) −58.9850 −2.36318
\(624\) −7.25240 −0.290328
\(625\) −11.9171 −0.476685
\(626\) −20.4586 −0.817689
\(627\) 0 0
\(628\) −17.5756 −0.701343
\(629\) 12.0848 0.481851
\(630\) −29.5510 −1.17734
\(631\) 23.4479 0.933448 0.466724 0.884403i \(-0.345434\pi\)
0.466724 + 0.884403i \(0.345434\pi\)
\(632\) −6.38776 −0.254091
\(633\) 56.0943 2.22955
\(634\) −14.3632 −0.570435
\(635\) −29.5510 −1.17270
\(636\) 14.1310 0.560330
\(637\) 16.1493 0.639859
\(638\) 0 0
\(639\) −4.00000 −0.158238
\(640\) 1.76156 0.0696317
\(641\) −7.45419 −0.294423 −0.147211 0.989105i \(-0.547030\pi\)
−0.147211 + 0.989105i \(0.547030\pi\)
\(642\) 9.69075 0.382463
\(643\) 38.7110 1.52661 0.763306 0.646038i \(-0.223575\pi\)
0.763306 + 0.646038i \(0.223575\pi\)
\(644\) −13.1493 −0.518155
\(645\) −35.2803 −1.38916
\(646\) 4.62620 0.182015
\(647\) 3.42003 0.134455 0.0672276 0.997738i \(-0.478585\pi\)
0.0672276 + 0.997738i \(0.478585\pi\)
\(648\) −1.47689 −0.0580175
\(649\) 0 0
\(650\) −4.98168 −0.195397
\(651\) −17.3169 −0.678705
\(652\) −15.2524 −0.597330
\(653\) 32.4556 1.27009 0.635044 0.772476i \(-0.280982\pi\)
0.635044 + 0.772476i \(0.280982\pi\)
\(654\) 44.6358 1.74540
\(655\) −36.9604 −1.44416
\(656\) 5.01395 0.195762
\(657\) 26.8034 1.04570
\(658\) 26.9065 1.04892
\(659\) 34.4277 1.34111 0.670557 0.741858i \(-0.266055\pi\)
0.670557 + 0.741858i \(0.266055\pi\)
\(660\) 0 0
\(661\) 33.4436 1.30080 0.650402 0.759590i \(-0.274600\pi\)
0.650402 + 0.759590i \(0.274600\pi\)
\(662\) −24.1064 −0.936922
\(663\) 33.5510 1.30301
\(664\) 6.38776 0.247893
\(665\) 6.38776 0.247707
\(666\) −12.0848 −0.468275
\(667\) 19.5371 0.756478
\(668\) 2.47689 0.0958336
\(669\) −39.8097 −1.53913
\(670\) −25.5510 −0.987122
\(671\) 0 0
\(672\) 10.0140 0.386297
\(673\) −9.54769 −0.368037 −0.184018 0.982923i \(-0.558911\pi\)
−0.184018 + 0.982923i \(0.558911\pi\)
\(674\) 6.09683 0.234841
\(675\) 8.51875 0.327887
\(676\) −6.10308 −0.234734
\(677\) −32.1912 −1.23721 −0.618604 0.785703i \(-0.712301\pi\)
−0.618604 + 0.785703i \(0.712301\pi\)
\(678\) 43.5264 1.67162
\(679\) −4.00000 −0.153506
\(680\) −8.14931 −0.312512
\(681\) 56.2341 2.15489
\(682\) 0 0
\(683\) −43.1020 −1.64925 −0.824627 0.565677i \(-0.808615\pi\)
−0.824627 + 0.565677i \(0.808615\pi\)
\(684\) −4.62620 −0.176887
\(685\) −9.25240 −0.353516
\(686\) 3.08476 0.117777
\(687\) 54.3265 2.07269
\(688\) 7.25240 0.276495
\(689\) −13.4384 −0.511960
\(690\) −17.6402 −0.671549
\(691\) 22.7509 0.865486 0.432743 0.901517i \(-0.357546\pi\)
0.432743 + 0.901517i \(0.357546\pi\)
\(692\) −7.06018 −0.268388
\(693\) 0 0
\(694\) 27.1633 1.03110
\(695\) 7.04623 0.267279
\(696\) −14.8786 −0.563972
\(697\) −23.1955 −0.878594
\(698\) 18.2139 0.689405
\(699\) 11.7432 0.444170
\(700\) 6.87859 0.259986
\(701\) −30.3063 −1.14465 −0.572327 0.820026i \(-0.693959\pi\)
−0.572327 + 0.820026i \(0.693959\pi\)
\(702\) −11.7938 −0.445130
\(703\) 2.61224 0.0985227
\(704\) 0 0
\(705\) 36.0958 1.35945
\(706\) −26.5510 −0.999261
\(707\) −62.9850 −2.36879
\(708\) 38.7003 1.45445
\(709\) 0.655146 0.0246045 0.0123023 0.999924i \(-0.496084\pi\)
0.0123023 + 0.999924i \(0.496084\pi\)
\(710\) −1.52311 −0.0571615
\(711\) −29.5510 −1.10825
\(712\) 16.2663 0.609607
\(713\) −6.27072 −0.234840
\(714\) −46.3265 −1.73373
\(715\) 0 0
\(716\) −5.44461 −0.203475
\(717\) 57.4792 2.14660
\(718\) −22.4277 −0.836995
\(719\) −20.0558 −0.747956 −0.373978 0.927438i \(-0.622006\pi\)
−0.373978 + 0.927438i \(0.622006\pi\)
\(720\) 8.14931 0.303707
\(721\) −46.7509 −1.74110
\(722\) 1.00000 0.0372161
\(723\) −84.7422 −3.15160
\(724\) 3.40171 0.126424
\(725\) −10.2201 −0.379566
\(726\) 0 0
\(727\) −30.0539 −1.11464 −0.557319 0.830298i \(-0.688170\pi\)
−0.557319 + 0.830298i \(0.688170\pi\)
\(728\) −9.52311 −0.352950
\(729\) −44.0375 −1.63102
\(730\) 10.2062 0.377747
\(731\) −33.5510 −1.24093
\(732\) −12.6864 −0.468902
\(733\) −13.2726 −0.490235 −0.245117 0.969493i \(-0.578827\pi\)
−0.245117 + 0.969493i \(0.578827\pi\)
\(734\) −21.4846 −0.793010
\(735\) −29.9142 −1.10340
\(736\) 3.62620 0.133663
\(737\) 0 0
\(738\) 23.1955 0.853840
\(739\) 6.00333 0.220836 0.110418 0.993885i \(-0.464781\pi\)
0.110418 + 0.993885i \(0.464781\pi\)
\(740\) −4.60162 −0.169159
\(741\) 7.25240 0.266423
\(742\) 18.5554 0.681190
\(743\) 39.4865 1.44862 0.724309 0.689475i \(-0.242159\pi\)
0.724309 + 0.689475i \(0.242159\pi\)
\(744\) 4.77551 0.175079
\(745\) −21.2880 −0.779932
\(746\) −0.632456 −0.0231558
\(747\) 29.5510 1.08122
\(748\) 0 0
\(749\) 12.7249 0.464958
\(750\) 33.5510 1.22511
\(751\) 0.904612 0.0330098 0.0165049 0.999864i \(-0.494746\pi\)
0.0165049 + 0.999864i \(0.494746\pi\)
\(752\) −7.42003 −0.270581
\(753\) −45.7572 −1.66748
\(754\) 14.1493 0.515288
\(755\) 34.4835 1.25498
\(756\) 16.2847 0.592268
\(757\) −30.5004 −1.10856 −0.554278 0.832331i \(-0.687006\pi\)
−0.554278 + 0.832331i \(0.687006\pi\)
\(758\) 33.4725 1.21578
\(759\) 0 0
\(760\) −1.76156 −0.0638984
\(761\) 7.23407 0.262235 0.131117 0.991367i \(-0.458143\pi\)
0.131117 + 0.991367i \(0.458143\pi\)
\(762\) 46.3265 1.67823
\(763\) 58.6112 2.12187
\(764\) 7.83237 0.283365
\(765\) −37.7003 −1.36306
\(766\) −13.0096 −0.470055
\(767\) −36.8034 −1.32889
\(768\) −2.76156 −0.0996491
\(769\) 4.83048 0.174191 0.0870957 0.996200i \(-0.472241\pi\)
0.0870957 + 0.996200i \(0.472241\pi\)
\(770\) 0 0
\(771\) 47.4094 1.70741
\(772\) 7.94315 0.285880
\(773\) 24.9186 0.896259 0.448129 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(774\) 33.5510 1.20597
\(775\) 3.28030 0.117832
\(776\) 1.10308 0.0395984
\(777\) −26.1589 −0.938445
\(778\) −10.8078 −0.387478
\(779\) −5.01395 −0.179644
\(780\) −12.7755 −0.457437
\(781\) 0 0
\(782\) −16.7755 −0.599891
\(783\) −24.1955 −0.864678
\(784\) 6.14931 0.219618
\(785\) −30.9604 −1.10502
\(786\) 57.9421 2.06673
\(787\) 53.3222 1.90073 0.950365 0.311137i \(-0.100710\pi\)
0.950365 + 0.311137i \(0.100710\pi\)
\(788\) −8.21386 −0.292607
\(789\) 85.8130 3.05502
\(790\) −11.2524 −0.400342
\(791\) 57.1545 2.03218
\(792\) 0 0
\(793\) 12.0646 0.428425
\(794\) −21.7370 −0.771416
\(795\) 24.8925 0.882848
\(796\) −20.0279 −0.709870
\(797\) −10.0558 −0.356195 −0.178098 0.984013i \(-0.556994\pi\)
−0.178098 + 0.984013i \(0.556994\pi\)
\(798\) −10.0140 −0.354490
\(799\) 34.3265 1.21439
\(800\) −1.89692 −0.0670661
\(801\) 75.2514 2.65888
\(802\) 15.9311 0.562546
\(803\) 0 0
\(804\) 40.0558 1.41266
\(805\) −23.1633 −0.816398
\(806\) −4.54144 −0.159965
\(807\) −1.12141 −0.0394754
\(808\) 17.3694 0.611055
\(809\) −25.3188 −0.890163 −0.445081 0.895490i \(-0.646825\pi\)
−0.445081 + 0.895490i \(0.646825\pi\)
\(810\) −2.60162 −0.0914116
\(811\) 7.50916 0.263682 0.131841 0.991271i \(-0.457911\pi\)
0.131841 + 0.991271i \(0.457911\pi\)
\(812\) −19.5371 −0.685617
\(813\) 10.4769 0.367440
\(814\) 0 0
\(815\) −26.8680 −0.941144
\(816\) 12.7755 0.447232
\(817\) −7.25240 −0.253729
\(818\) −38.4113 −1.34302
\(819\) −44.0558 −1.53943
\(820\) 8.83237 0.308440
\(821\) −20.7230 −0.723239 −0.361619 0.932326i \(-0.617776\pi\)
−0.361619 + 0.932326i \(0.617776\pi\)
\(822\) 14.5048 0.505913
\(823\) 9.95273 0.346930 0.173465 0.984840i \(-0.444504\pi\)
0.173465 + 0.984840i \(0.444504\pi\)
\(824\) 12.8925 0.449133
\(825\) 0 0
\(826\) 50.8174 1.76816
\(827\) 45.4007 1.57874 0.789368 0.613920i \(-0.210408\pi\)
0.789368 + 0.613920i \(0.210408\pi\)
\(828\) 16.7755 0.582989
\(829\) −19.2081 −0.667123 −0.333562 0.942728i \(-0.608251\pi\)
−0.333562 + 0.942728i \(0.608251\pi\)
\(830\) 11.2524 0.390576
\(831\) −64.3790 −2.23328
\(832\) 2.62620 0.0910470
\(833\) −28.4479 −0.985663
\(834\) −11.0462 −0.382500
\(835\) 4.36318 0.150994
\(836\) 0 0
\(837\) 7.76593 0.268430
\(838\) 5.07081 0.175168
\(839\) −2.59392 −0.0895522 −0.0447761 0.998997i \(-0.514257\pi\)
−0.0447761 + 0.998997i \(0.514257\pi\)
\(840\) 17.6402 0.608643
\(841\) 0.0279066 0.000962298 0
\(842\) 6.16327 0.212400
\(843\) −32.1449 −1.10713
\(844\) −20.3126 −0.699188
\(845\) −10.7509 −0.369843
\(846\) −34.3265 −1.18017
\(847\) 0 0
\(848\) −5.11704 −0.175720
\(849\) 14.6831 0.503921
\(850\) 8.77551 0.300998
\(851\) −9.47252 −0.324714
\(852\) 2.38776 0.0818031
\(853\) −43.3372 −1.48384 −0.741918 0.670491i \(-0.766084\pi\)
−0.741918 + 0.670491i \(0.766084\pi\)
\(854\) −16.6585 −0.570041
\(855\) −8.14931 −0.278701
\(856\) −3.50916 −0.119941
\(857\) 5.22449 0.178465 0.0892326 0.996011i \(-0.471559\pi\)
0.0892326 + 0.996011i \(0.471559\pi\)
\(858\) 0 0
\(859\) 15.8830 0.541920 0.270960 0.962591i \(-0.412659\pi\)
0.270960 + 0.962591i \(0.412659\pi\)
\(860\) 12.7755 0.435641
\(861\) 50.2095 1.71113
\(862\) −25.6681 −0.874258
\(863\) 42.4556 1.44521 0.722603 0.691263i \(-0.242945\pi\)
0.722603 + 0.691263i \(0.242945\pi\)
\(864\) −4.49084 −0.152781
\(865\) −12.4369 −0.422868
\(866\) 29.5433 1.00392
\(867\) −12.1556 −0.412825
\(868\) 6.27072 0.212842
\(869\) 0 0
\(870\) −26.2095 −0.888585
\(871\) −38.0925 −1.29071
\(872\) −16.1633 −0.547357
\(873\) 5.10308 0.172713
\(874\) −3.62620 −0.122658
\(875\) 44.0558 1.48936
\(876\) −16.0000 −0.540590
\(877\) 40.7957 1.37757 0.688787 0.724964i \(-0.258144\pi\)
0.688787 + 0.724964i \(0.258144\pi\)
\(878\) 11.5877 0.391065
\(879\) 7.86027 0.265120
\(880\) 0 0
\(881\) 3.85258 0.129797 0.0648983 0.997892i \(-0.479328\pi\)
0.0648983 + 0.997892i \(0.479328\pi\)
\(882\) 28.4479 0.957892
\(883\) −32.4523 −1.09211 −0.546054 0.837750i \(-0.683870\pi\)
−0.546054 + 0.837750i \(0.683870\pi\)
\(884\) −12.1493 −0.408626
\(885\) 68.1729 2.29161
\(886\) −3.97209 −0.133445
\(887\) 32.8155 1.10184 0.550918 0.834559i \(-0.314278\pi\)
0.550918 + 0.834559i \(0.314278\pi\)
\(888\) 7.21386 0.242081
\(889\) 60.8313 2.04022
\(890\) 28.6541 0.960488
\(891\) 0 0
\(892\) 14.4157 0.482672
\(893\) 7.42003 0.248302
\(894\) 33.3728 1.11615
\(895\) −9.59099 −0.320592
\(896\) −3.62620 −0.121143
\(897\) −26.2986 −0.878086
\(898\) 7.03853 0.234879
\(899\) −9.31695 −0.310738
\(900\) −8.77551 −0.292517
\(901\) 23.6724 0.788643
\(902\) 0 0
\(903\) 72.6252 2.41681
\(904\) −15.7616 −0.524222
\(905\) 5.99230 0.199191
\(906\) −54.0591 −1.79599
\(907\) −12.9032 −0.428443 −0.214221 0.976785i \(-0.568721\pi\)
−0.214221 + 0.976785i \(0.568721\pi\)
\(908\) −20.3632 −0.675776
\(909\) 80.3544 2.66519
\(910\) −16.7755 −0.556103
\(911\) 39.3973 1.30529 0.652646 0.757663i \(-0.273659\pi\)
0.652646 + 0.757663i \(0.273659\pi\)
\(912\) 2.76156 0.0914443
\(913\) 0 0
\(914\) 9.29862 0.307571
\(915\) −22.3478 −0.738795
\(916\) −19.6724 −0.649995
\(917\) 76.0837 2.51251
\(918\) 20.7755 0.685694
\(919\) −6.44898 −0.212732 −0.106366 0.994327i \(-0.533922\pi\)
−0.106366 + 0.994327i \(0.533922\pi\)
\(920\) 6.38776 0.210598
\(921\) 48.6079 1.60168
\(922\) −12.3309 −0.406097
\(923\) −2.27072 −0.0747416
\(924\) 0 0
\(925\) 4.95521 0.162926
\(926\) −28.1570 −0.925297
\(927\) 59.6435 1.95895
\(928\) 5.38776 0.176862
\(929\) 40.1666 1.31782 0.658912 0.752220i \(-0.271017\pi\)
0.658912 + 0.752220i \(0.271017\pi\)
\(930\) 8.41233 0.275851
\(931\) −6.14931 −0.201536
\(932\) −4.25240 −0.139292
\(933\) −37.9913 −1.24378
\(934\) 35.4865 1.16115
\(935\) 0 0
\(936\) 12.1493 0.397113
\(937\) −46.9634 −1.53423 −0.767113 0.641512i \(-0.778307\pi\)
−0.767113 + 0.641512i \(0.778307\pi\)
\(938\) 52.5972 1.71736
\(939\) 56.4975 1.84373
\(940\) −13.0708 −0.426323
\(941\) 24.3063 0.792363 0.396182 0.918172i \(-0.370335\pi\)
0.396182 + 0.918172i \(0.370335\pi\)
\(942\) 48.5360 1.58139
\(943\) 18.1816 0.592074
\(944\) −14.0140 −0.456115
\(945\) 28.6864 0.933168
\(946\) 0 0
\(947\) −46.0192 −1.49542 −0.747711 0.664024i \(-0.768847\pi\)
−0.747711 + 0.664024i \(0.768847\pi\)
\(948\) 17.6402 0.572925
\(949\) 15.2158 0.493924
\(950\) 1.89692 0.0615441
\(951\) 39.6647 1.28622
\(952\) 16.7755 0.543697
\(953\) 52.5562 1.70246 0.851232 0.524790i \(-0.175856\pi\)
0.851232 + 0.524790i \(0.175856\pi\)
\(954\) −23.6724 −0.766423
\(955\) 13.7972 0.446466
\(956\) −20.8140 −0.673174
\(957\) 0 0
\(958\) −0.195541 −0.00631765
\(959\) 19.0462 0.615035
\(960\) −4.86464 −0.157006
\(961\) −28.0096 −0.903535
\(962\) −6.86027 −0.221184
\(963\) −16.2341 −0.523136
\(964\) 30.6864 0.988342
\(965\) 13.9923 0.450428
\(966\) 36.3126 1.16834
\(967\) 2.87859 0.0925693 0.0462847 0.998928i \(-0.485262\pi\)
0.0462847 + 0.998928i \(0.485262\pi\)
\(968\) 0 0
\(969\) −12.7755 −0.410409
\(970\) 1.94315 0.0623906
\(971\) −6.81737 −0.218780 −0.109390 0.993999i \(-0.534890\pi\)
−0.109390 + 0.993999i \(0.534890\pi\)
\(972\) 17.5510 0.562949
\(973\) −14.5048 −0.465002
\(974\) −24.0279 −0.769904
\(975\) 13.7572 0.440583
\(976\) 4.59392 0.147048
\(977\) 44.8969 1.43638 0.718190 0.695847i \(-0.244971\pi\)
0.718190 + 0.695847i \(0.244971\pi\)
\(978\) 42.1204 1.34686
\(979\) 0 0
\(980\) 10.8324 0.346027
\(981\) −74.7745 −2.38737
\(982\) −4.23407 −0.135115
\(983\) 35.7818 1.14126 0.570631 0.821207i \(-0.306699\pi\)
0.570631 + 0.821207i \(0.306699\pi\)
\(984\) −13.8463 −0.441405
\(985\) −14.4692 −0.461027
\(986\) −24.9248 −0.793768
\(987\) −74.3038 −2.36512
\(988\) −2.62620 −0.0835505
\(989\) 26.2986 0.836248
\(990\) 0 0
\(991\) −17.2278 −0.547260 −0.273630 0.961835i \(-0.588224\pi\)
−0.273630 + 0.961835i \(0.588224\pi\)
\(992\) −1.72928 −0.0549048
\(993\) 66.5712 2.11257
\(994\) 3.13536 0.0994476
\(995\) −35.2803 −1.11846
\(996\) −17.6402 −0.558950
\(997\) −3.19221 −0.101098 −0.0505492 0.998722i \(-0.516097\pi\)
−0.0505492 + 0.998722i \(0.516097\pi\)
\(998\) 33.2278 1.05181
\(999\) 11.7312 0.371158
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4598.2.a.bn.1.1 yes 3
11.10 odd 2 4598.2.a.bk.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bk.1.1 3 11.10 odd 2
4598.2.a.bn.1.1 yes 3 1.1 even 1 trivial