Properties

Label 4730.2.a.bb.1.3
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 11
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.17792\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.17792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.17792 q^{6} +4.63803 q^{7} -1.00000 q^{8} +1.74332 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.17792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.17792 q^{6} +4.63803 q^{7} -1.00000 q^{8} +1.74332 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.17792 q^{12} -5.80630 q^{13} -4.63803 q^{14} +2.17792 q^{15} +1.00000 q^{16} -7.18366 q^{17} -1.74332 q^{18} -6.16042 q^{19} -1.00000 q^{20} -10.1012 q^{21} +1.00000 q^{22} -7.80630 q^{23} +2.17792 q^{24} +1.00000 q^{25} +5.80630 q^{26} +2.73694 q^{27} +4.63803 q^{28} +1.51070 q^{29} -2.17792 q^{30} -3.25777 q^{31} -1.00000 q^{32} +2.17792 q^{33} +7.18366 q^{34} -4.63803 q^{35} +1.74332 q^{36} +3.52240 q^{37} +6.16042 q^{38} +12.6456 q^{39} +1.00000 q^{40} -8.02297 q^{41} +10.1012 q^{42} +1.00000 q^{43} -1.00000 q^{44} -1.74332 q^{45} +7.80630 q^{46} -7.28953 q^{47} -2.17792 q^{48} +14.5113 q^{49} -1.00000 q^{50} +15.6454 q^{51} -5.80630 q^{52} -0.333481 q^{53} -2.73694 q^{54} +1.00000 q^{55} -4.63803 q^{56} +13.4169 q^{57} -1.51070 q^{58} -1.57764 q^{59} +2.17792 q^{60} +14.7118 q^{61} +3.25777 q^{62} +8.08559 q^{63} +1.00000 q^{64} +5.80630 q^{65} -2.17792 q^{66} +3.48438 q^{67} -7.18366 q^{68} +17.0015 q^{69} +4.63803 q^{70} -9.42285 q^{71} -1.74332 q^{72} -3.01257 q^{73} -3.52240 q^{74} -2.17792 q^{75} -6.16042 q^{76} -4.63803 q^{77} -12.6456 q^{78} +5.06019 q^{79} -1.00000 q^{80} -11.1908 q^{81} +8.02297 q^{82} +13.5518 q^{83} -10.1012 q^{84} +7.18366 q^{85} -1.00000 q^{86} -3.29018 q^{87} +1.00000 q^{88} +13.5086 q^{89} +1.74332 q^{90} -26.9298 q^{91} -7.80630 q^{92} +7.09514 q^{93} +7.28953 q^{94} +6.16042 q^{95} +2.17792 q^{96} -15.3042 q^{97} -14.5113 q^{98} -1.74332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.17792 −1.25742 −0.628711 0.777639i \(-0.716417\pi\)
−0.628711 + 0.777639i \(0.716417\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.17792 0.889131
\(7\) 4.63803 1.75301 0.876505 0.481392i \(-0.159869\pi\)
0.876505 + 0.481392i \(0.159869\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.74332 0.581108
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −2.17792 −0.628711
\(13\) −5.80630 −1.61038 −0.805189 0.593018i \(-0.797936\pi\)
−0.805189 + 0.593018i \(0.797936\pi\)
\(14\) −4.63803 −1.23957
\(15\) 2.17792 0.562336
\(16\) 1.00000 0.250000
\(17\) −7.18366 −1.74229 −0.871146 0.491024i \(-0.836623\pi\)
−0.871146 + 0.491024i \(0.836623\pi\)
\(18\) −1.74332 −0.410905
\(19\) −6.16042 −1.41330 −0.706649 0.707565i \(-0.749794\pi\)
−0.706649 + 0.707565i \(0.749794\pi\)
\(20\) −1.00000 −0.223607
\(21\) −10.1012 −2.20427
\(22\) 1.00000 0.213201
\(23\) −7.80630 −1.62773 −0.813863 0.581057i \(-0.802639\pi\)
−0.813863 + 0.581057i \(0.802639\pi\)
\(24\) 2.17792 0.444565
\(25\) 1.00000 0.200000
\(26\) 5.80630 1.13871
\(27\) 2.73694 0.526724
\(28\) 4.63803 0.876505
\(29\) 1.51070 0.280530 0.140265 0.990114i \(-0.455205\pi\)
0.140265 + 0.990114i \(0.455205\pi\)
\(30\) −2.17792 −0.397631
\(31\) −3.25777 −0.585112 −0.292556 0.956248i \(-0.594506\pi\)
−0.292556 + 0.956248i \(0.594506\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.17792 0.379127
\(34\) 7.18366 1.23199
\(35\) −4.63803 −0.783970
\(36\) 1.74332 0.290554
\(37\) 3.52240 0.579079 0.289540 0.957166i \(-0.406498\pi\)
0.289540 + 0.957166i \(0.406498\pi\)
\(38\) 6.16042 0.999352
\(39\) 12.6456 2.02492
\(40\) 1.00000 0.158114
\(41\) −8.02297 −1.25298 −0.626489 0.779431i \(-0.715509\pi\)
−0.626489 + 0.779431i \(0.715509\pi\)
\(42\) 10.1012 1.55866
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) −1.74332 −0.259879
\(46\) 7.80630 1.15098
\(47\) −7.28953 −1.06329 −0.531644 0.846968i \(-0.678425\pi\)
−0.531644 + 0.846968i \(0.678425\pi\)
\(48\) −2.17792 −0.314355
\(49\) 14.5113 2.07305
\(50\) −1.00000 −0.141421
\(51\) 15.6454 2.19080
\(52\) −5.80630 −0.805189
\(53\) −0.333481 −0.0458072 −0.0229036 0.999738i \(-0.507291\pi\)
−0.0229036 + 0.999738i \(0.507291\pi\)
\(54\) −2.73694 −0.372450
\(55\) 1.00000 0.134840
\(56\) −4.63803 −0.619783
\(57\) 13.4169 1.77711
\(58\) −1.51070 −0.198365
\(59\) −1.57764 −0.205391 −0.102696 0.994713i \(-0.532747\pi\)
−0.102696 + 0.994713i \(0.532747\pi\)
\(60\) 2.17792 0.281168
\(61\) 14.7118 1.88366 0.941829 0.336092i \(-0.109105\pi\)
0.941829 + 0.336092i \(0.109105\pi\)
\(62\) 3.25777 0.413737
\(63\) 8.08559 1.01869
\(64\) 1.00000 0.125000
\(65\) 5.80630 0.720183
\(66\) −2.17792 −0.268083
\(67\) 3.48438 0.425685 0.212842 0.977087i \(-0.431728\pi\)
0.212842 + 0.977087i \(0.431728\pi\)
\(68\) −7.18366 −0.871146
\(69\) 17.0015 2.04674
\(70\) 4.63803 0.554351
\(71\) −9.42285 −1.11829 −0.559144 0.829071i \(-0.688870\pi\)
−0.559144 + 0.829071i \(0.688870\pi\)
\(72\) −1.74332 −0.205453
\(73\) −3.01257 −0.352595 −0.176297 0.984337i \(-0.556412\pi\)
−0.176297 + 0.984337i \(0.556412\pi\)
\(74\) −3.52240 −0.409471
\(75\) −2.17792 −0.251484
\(76\) −6.16042 −0.706649
\(77\) −4.63803 −0.528553
\(78\) −12.6456 −1.43184
\(79\) 5.06019 0.569316 0.284658 0.958629i \(-0.408120\pi\)
0.284658 + 0.958629i \(0.408120\pi\)
\(80\) −1.00000 −0.111803
\(81\) −11.1908 −1.24342
\(82\) 8.02297 0.885989
\(83\) 13.5518 1.48750 0.743749 0.668459i \(-0.233046\pi\)
0.743749 + 0.668459i \(0.233046\pi\)
\(84\) −10.1012 −1.10214
\(85\) 7.18366 0.779177
\(86\) −1.00000 −0.107833
\(87\) −3.29018 −0.352745
\(88\) 1.00000 0.106600
\(89\) 13.5086 1.43191 0.715955 0.698146i \(-0.245991\pi\)
0.715955 + 0.698146i \(0.245991\pi\)
\(90\) 1.74332 0.183762
\(91\) −26.9298 −2.82301
\(92\) −7.80630 −0.813863
\(93\) 7.09514 0.735732
\(94\) 7.28953 0.751858
\(95\) 6.16042 0.632046
\(96\) 2.17792 0.222283
\(97\) −15.3042 −1.55391 −0.776954 0.629557i \(-0.783236\pi\)
−0.776954 + 0.629557i \(0.783236\pi\)
\(98\) −14.5113 −1.46586
\(99\) −1.74332 −0.175211
\(100\) 1.00000 0.100000
\(101\) 4.61357 0.459068 0.229534 0.973301i \(-0.426280\pi\)
0.229534 + 0.973301i \(0.426280\pi\)
\(102\) −15.6454 −1.54913
\(103\) −4.67551 −0.460692 −0.230346 0.973109i \(-0.573986\pi\)
−0.230346 + 0.973109i \(0.573986\pi\)
\(104\) 5.80630 0.569355
\(105\) 10.1012 0.985781
\(106\) 0.333481 0.0323906
\(107\) −13.4710 −1.30229 −0.651146 0.758952i \(-0.725712\pi\)
−0.651146 + 0.758952i \(0.725712\pi\)
\(108\) 2.73694 0.263362
\(109\) 10.6732 1.02231 0.511155 0.859488i \(-0.329218\pi\)
0.511155 + 0.859488i \(0.329218\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −7.67150 −0.728146
\(112\) 4.63803 0.438253
\(113\) 9.96108 0.937060 0.468530 0.883448i \(-0.344784\pi\)
0.468530 + 0.883448i \(0.344784\pi\)
\(114\) −13.4169 −1.25661
\(115\) 7.80630 0.727941
\(116\) 1.51070 0.140265
\(117\) −10.1223 −0.935803
\(118\) 1.57764 0.145233
\(119\) −33.3180 −3.05426
\(120\) −2.17792 −0.198816
\(121\) 1.00000 0.0909091
\(122\) −14.7118 −1.33195
\(123\) 17.4734 1.57552
\(124\) −3.25777 −0.292556
\(125\) −1.00000 −0.0894427
\(126\) −8.08559 −0.720321
\(127\) 7.03779 0.624503 0.312251 0.950000i \(-0.398917\pi\)
0.312251 + 0.950000i \(0.398917\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.17792 −0.191755
\(130\) −5.80630 −0.509246
\(131\) 13.0432 1.13959 0.569793 0.821788i \(-0.307023\pi\)
0.569793 + 0.821788i \(0.307023\pi\)
\(132\) 2.17792 0.189563
\(133\) −28.5722 −2.47753
\(134\) −3.48438 −0.301004
\(135\) −2.73694 −0.235558
\(136\) 7.18366 0.615993
\(137\) −10.7505 −0.918478 −0.459239 0.888313i \(-0.651878\pi\)
−0.459239 + 0.888313i \(0.651878\pi\)
\(138\) −17.0015 −1.44726
\(139\) −16.6220 −1.40986 −0.704930 0.709277i \(-0.749022\pi\)
−0.704930 + 0.709277i \(0.749022\pi\)
\(140\) −4.63803 −0.391985
\(141\) 15.8760 1.33700
\(142\) 9.42285 0.790748
\(143\) 5.80630 0.485547
\(144\) 1.74332 0.145277
\(145\) −1.51070 −0.125457
\(146\) 3.01257 0.249322
\(147\) −31.6045 −2.60669
\(148\) 3.52240 0.289540
\(149\) 8.69614 0.712415 0.356208 0.934407i \(-0.384070\pi\)
0.356208 + 0.934407i \(0.384070\pi\)
\(150\) 2.17792 0.177826
\(151\) −8.11885 −0.660703 −0.330351 0.943858i \(-0.607167\pi\)
−0.330351 + 0.943858i \(0.607167\pi\)
\(152\) 6.16042 0.499676
\(153\) −12.5234 −1.01246
\(154\) 4.63803 0.373743
\(155\) 3.25777 0.261670
\(156\) 12.6456 1.01246
\(157\) 6.54941 0.522700 0.261350 0.965244i \(-0.415832\pi\)
0.261350 + 0.965244i \(0.415832\pi\)
\(158\) −5.06019 −0.402567
\(159\) 0.726295 0.0575989
\(160\) 1.00000 0.0790569
\(161\) −36.2059 −2.85342
\(162\) 11.1908 0.879232
\(163\) 4.34472 0.340305 0.170152 0.985418i \(-0.445574\pi\)
0.170152 + 0.985418i \(0.445574\pi\)
\(164\) −8.02297 −0.626489
\(165\) −2.17792 −0.169551
\(166\) −13.5518 −1.05182
\(167\) −10.6765 −0.826176 −0.413088 0.910691i \(-0.635550\pi\)
−0.413088 + 0.910691i \(0.635550\pi\)
\(168\) 10.1012 0.779328
\(169\) 20.7131 1.59332
\(170\) −7.18366 −0.550961
\(171\) −10.7396 −0.821278
\(172\) 1.00000 0.0762493
\(173\) −15.2008 −1.15569 −0.577847 0.816145i \(-0.696107\pi\)
−0.577847 + 0.816145i \(0.696107\pi\)
\(174\) 3.29018 0.249428
\(175\) 4.63803 0.350602
\(176\) −1.00000 −0.0753778
\(177\) 3.43597 0.258263
\(178\) −13.5086 −1.01251
\(179\) 17.0492 1.27431 0.637157 0.770734i \(-0.280110\pi\)
0.637157 + 0.770734i \(0.280110\pi\)
\(180\) −1.74332 −0.129940
\(181\) −22.8842 −1.70097 −0.850484 0.526001i \(-0.823691\pi\)
−0.850484 + 0.526001i \(0.823691\pi\)
\(182\) 26.9298 1.99617
\(183\) −32.0412 −2.36855
\(184\) 7.80630 0.575488
\(185\) −3.52240 −0.258972
\(186\) −7.09514 −0.520241
\(187\) 7.18366 0.525321
\(188\) −7.28953 −0.531644
\(189\) 12.6940 0.923352
\(190\) −6.16042 −0.446924
\(191\) 9.36038 0.677293 0.338647 0.940914i \(-0.390031\pi\)
0.338647 + 0.940914i \(0.390031\pi\)
\(192\) −2.17792 −0.157178
\(193\) −5.84595 −0.420801 −0.210400 0.977615i \(-0.567477\pi\)
−0.210400 + 0.977615i \(0.567477\pi\)
\(194\) 15.3042 1.09878
\(195\) −12.6456 −0.905573
\(196\) 14.5113 1.03652
\(197\) 5.86569 0.417913 0.208956 0.977925i \(-0.432993\pi\)
0.208956 + 0.977925i \(0.432993\pi\)
\(198\) 1.74332 0.123893
\(199\) 13.5383 0.959705 0.479853 0.877349i \(-0.340690\pi\)
0.479853 + 0.877349i \(0.340690\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −7.58869 −0.535265
\(202\) −4.61357 −0.324610
\(203\) 7.00668 0.491773
\(204\) 15.6454 1.09540
\(205\) 8.02297 0.560348
\(206\) 4.67551 0.325758
\(207\) −13.6089 −0.945884
\(208\) −5.80630 −0.402594
\(209\) 6.16042 0.426125
\(210\) −10.1012 −0.697052
\(211\) 10.7018 0.736740 0.368370 0.929679i \(-0.379916\pi\)
0.368370 + 0.929679i \(0.379916\pi\)
\(212\) −0.333481 −0.0229036
\(213\) 20.5222 1.40616
\(214\) 13.4710 0.920860
\(215\) −1.00000 −0.0681994
\(216\) −2.73694 −0.186225
\(217\) −15.1096 −1.02571
\(218\) −10.6732 −0.722883
\(219\) 6.56113 0.443360
\(220\) 1.00000 0.0674200
\(221\) 41.7105 2.80575
\(222\) 7.67150 0.514877
\(223\) 0.474339 0.0317641 0.0158820 0.999874i \(-0.494944\pi\)
0.0158820 + 0.999874i \(0.494944\pi\)
\(224\) −4.63803 −0.309891
\(225\) 1.74332 0.116222
\(226\) −9.96108 −0.662601
\(227\) 22.9170 1.52105 0.760526 0.649308i \(-0.224941\pi\)
0.760526 + 0.649308i \(0.224941\pi\)
\(228\) 13.4169 0.888555
\(229\) −1.74361 −0.115221 −0.0576107 0.998339i \(-0.518348\pi\)
−0.0576107 + 0.998339i \(0.518348\pi\)
\(230\) −7.80630 −0.514732
\(231\) 10.1012 0.664613
\(232\) −1.51070 −0.0991824
\(233\) −14.1046 −0.924023 −0.462011 0.886874i \(-0.652872\pi\)
−0.462011 + 0.886874i \(0.652872\pi\)
\(234\) 10.1223 0.661713
\(235\) 7.28953 0.475517
\(236\) −1.57764 −0.102696
\(237\) −11.0207 −0.715870
\(238\) 33.3180 2.15969
\(239\) 22.2167 1.43708 0.718538 0.695488i \(-0.244812\pi\)
0.718538 + 0.695488i \(0.244812\pi\)
\(240\) 2.17792 0.140584
\(241\) 15.9469 1.02723 0.513615 0.858021i \(-0.328306\pi\)
0.513615 + 0.858021i \(0.328306\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 16.1618 1.03678
\(244\) 14.7118 0.941829
\(245\) −14.5113 −0.927094
\(246\) −17.4734 −1.11406
\(247\) 35.7692 2.27594
\(248\) 3.25777 0.206868
\(249\) −29.5146 −1.87041
\(250\) 1.00000 0.0632456
\(251\) −2.78403 −0.175726 −0.0878632 0.996133i \(-0.528004\pi\)
−0.0878632 + 0.996133i \(0.528004\pi\)
\(252\) 8.08559 0.509344
\(253\) 7.80630 0.490778
\(254\) −7.03779 −0.441590
\(255\) −15.6454 −0.979753
\(256\) 1.00000 0.0625000
\(257\) 15.5851 0.972173 0.486086 0.873911i \(-0.338424\pi\)
0.486086 + 0.873911i \(0.338424\pi\)
\(258\) 2.17792 0.135591
\(259\) 16.3370 1.01513
\(260\) 5.80630 0.360091
\(261\) 2.63364 0.163018
\(262\) −13.0432 −0.805810
\(263\) −11.5563 −0.712590 −0.356295 0.934373i \(-0.615960\pi\)
−0.356295 + 0.934373i \(0.615960\pi\)
\(264\) −2.17792 −0.134042
\(265\) 0.333481 0.0204856
\(266\) 28.5722 1.75187
\(267\) −29.4206 −1.80051
\(268\) 3.48438 0.212842
\(269\) 7.46417 0.455098 0.227549 0.973767i \(-0.426929\pi\)
0.227549 + 0.973767i \(0.426929\pi\)
\(270\) 2.73694 0.166565
\(271\) −5.60803 −0.340663 −0.170332 0.985387i \(-0.554484\pi\)
−0.170332 + 0.985387i \(0.554484\pi\)
\(272\) −7.18366 −0.435573
\(273\) 58.6509 3.54971
\(274\) 10.7505 0.649462
\(275\) −1.00000 −0.0603023
\(276\) 17.0015 1.02337
\(277\) −13.3255 −0.800654 −0.400327 0.916372i \(-0.631103\pi\)
−0.400327 + 0.916372i \(0.631103\pi\)
\(278\) 16.6220 0.996922
\(279\) −5.67934 −0.340013
\(280\) 4.63803 0.277175
\(281\) −24.1984 −1.44356 −0.721779 0.692124i \(-0.756675\pi\)
−0.721779 + 0.692124i \(0.756675\pi\)
\(282\) −15.8760 −0.945402
\(283\) −3.49895 −0.207991 −0.103996 0.994578i \(-0.533163\pi\)
−0.103996 + 0.994578i \(0.533163\pi\)
\(284\) −9.42285 −0.559144
\(285\) −13.4169 −0.794748
\(286\) −5.80630 −0.343334
\(287\) −37.2108 −2.19648
\(288\) −1.74332 −0.102726
\(289\) 34.6049 2.03558
\(290\) 1.51070 0.0887115
\(291\) 33.3313 1.95392
\(292\) −3.01257 −0.176297
\(293\) −11.9897 −0.700444 −0.350222 0.936667i \(-0.613894\pi\)
−0.350222 + 0.936667i \(0.613894\pi\)
\(294\) 31.6045 1.84321
\(295\) 1.57764 0.0918537
\(296\) −3.52240 −0.204735
\(297\) −2.73694 −0.158813
\(298\) −8.69614 −0.503754
\(299\) 45.3257 2.62125
\(300\) −2.17792 −0.125742
\(301\) 4.63803 0.267332
\(302\) 8.11885 0.467187
\(303\) −10.0480 −0.577242
\(304\) −6.16042 −0.353324
\(305\) −14.7118 −0.842397
\(306\) 12.5234 0.715917
\(307\) 6.33882 0.361775 0.180888 0.983504i \(-0.442103\pi\)
0.180888 + 0.983504i \(0.442103\pi\)
\(308\) −4.63803 −0.264276
\(309\) 10.1829 0.579283
\(310\) −3.25777 −0.185029
\(311\) 20.2786 1.14989 0.574946 0.818191i \(-0.305023\pi\)
0.574946 + 0.818191i \(0.305023\pi\)
\(312\) −12.6456 −0.715918
\(313\) −17.7146 −1.00129 −0.500644 0.865653i \(-0.666903\pi\)
−0.500644 + 0.865653i \(0.666903\pi\)
\(314\) −6.54941 −0.369605
\(315\) −8.08559 −0.455571
\(316\) 5.06019 0.284658
\(317\) 9.14582 0.513681 0.256840 0.966454i \(-0.417319\pi\)
0.256840 + 0.966454i \(0.417319\pi\)
\(318\) −0.726295 −0.0407286
\(319\) −1.51070 −0.0845831
\(320\) −1.00000 −0.0559017
\(321\) 29.3388 1.63753
\(322\) 36.2059 2.01767
\(323\) 44.2543 2.46238
\(324\) −11.1908 −0.621711
\(325\) −5.80630 −0.322076
\(326\) −4.34472 −0.240632
\(327\) −23.2454 −1.28547
\(328\) 8.02297 0.442994
\(329\) −33.8091 −1.86395
\(330\) 2.17792 0.119890
\(331\) −7.20057 −0.395779 −0.197890 0.980224i \(-0.563409\pi\)
−0.197890 + 0.980224i \(0.563409\pi\)
\(332\) 13.5518 0.743749
\(333\) 6.14068 0.336507
\(334\) 10.6765 0.584195
\(335\) −3.48438 −0.190372
\(336\) −10.1012 −0.551068
\(337\) 3.67433 0.200154 0.100077 0.994980i \(-0.468091\pi\)
0.100077 + 0.994980i \(0.468091\pi\)
\(338\) −20.7131 −1.12665
\(339\) −21.6944 −1.17828
\(340\) 7.18366 0.389588
\(341\) 3.25777 0.176418
\(342\) 10.7396 0.580731
\(343\) 34.8377 1.88106
\(344\) −1.00000 −0.0539164
\(345\) −17.0015 −0.915329
\(346\) 15.2008 0.817199
\(347\) 1.54550 0.0829668 0.0414834 0.999139i \(-0.486792\pi\)
0.0414834 + 0.999139i \(0.486792\pi\)
\(348\) −3.29018 −0.176372
\(349\) −15.3442 −0.821354 −0.410677 0.911781i \(-0.634708\pi\)
−0.410677 + 0.911781i \(0.634708\pi\)
\(350\) −4.63803 −0.247913
\(351\) −15.8915 −0.848224
\(352\) 1.00000 0.0533002
\(353\) 20.4471 1.08829 0.544146 0.838991i \(-0.316854\pi\)
0.544146 + 0.838991i \(0.316854\pi\)
\(354\) −3.43597 −0.182620
\(355\) 9.42285 0.500113
\(356\) 13.5086 0.715955
\(357\) 72.5639 3.84049
\(358\) −17.0492 −0.901076
\(359\) 35.1254 1.85385 0.926923 0.375252i \(-0.122444\pi\)
0.926923 + 0.375252i \(0.122444\pi\)
\(360\) 1.74332 0.0918812
\(361\) 18.9508 0.997409
\(362\) 22.8842 1.20277
\(363\) −2.17792 −0.114311
\(364\) −26.9298 −1.41150
\(365\) 3.01257 0.157685
\(366\) 32.0412 1.67482
\(367\) −23.0698 −1.20424 −0.602118 0.798407i \(-0.705676\pi\)
−0.602118 + 0.798407i \(0.705676\pi\)
\(368\) −7.80630 −0.406932
\(369\) −13.9866 −0.728115
\(370\) 3.52240 0.183121
\(371\) −1.54670 −0.0803005
\(372\) 7.09514 0.367866
\(373\) 11.3400 0.587160 0.293580 0.955934i \(-0.405153\pi\)
0.293580 + 0.955934i \(0.405153\pi\)
\(374\) −7.18366 −0.371458
\(375\) 2.17792 0.112467
\(376\) 7.28953 0.375929
\(377\) −8.77159 −0.451760
\(378\) −12.6940 −0.652909
\(379\) 20.2144 1.03834 0.519171 0.854670i \(-0.326241\pi\)
0.519171 + 0.854670i \(0.326241\pi\)
\(380\) 6.16042 0.316023
\(381\) −15.3277 −0.785263
\(382\) −9.36038 −0.478919
\(383\) −35.3883 −1.80826 −0.904129 0.427260i \(-0.859479\pi\)
−0.904129 + 0.427260i \(0.859479\pi\)
\(384\) 2.17792 0.111141
\(385\) 4.63803 0.236376
\(386\) 5.84595 0.297551
\(387\) 1.74332 0.0886181
\(388\) −15.3042 −0.776954
\(389\) −36.6686 −1.85917 −0.929586 0.368606i \(-0.879835\pi\)
−0.929586 + 0.368606i \(0.879835\pi\)
\(390\) 12.6456 0.640337
\(391\) 56.0778 2.83597
\(392\) −14.5113 −0.732932
\(393\) −28.4069 −1.43294
\(394\) −5.86569 −0.295509
\(395\) −5.06019 −0.254606
\(396\) −1.74332 −0.0876053
\(397\) 9.61333 0.482479 0.241240 0.970466i \(-0.422446\pi\)
0.241240 + 0.970466i \(0.422446\pi\)
\(398\) −13.5383 −0.678614
\(399\) 62.2279 3.11529
\(400\) 1.00000 0.0500000
\(401\) −29.2222 −1.45929 −0.729643 0.683828i \(-0.760314\pi\)
−0.729643 + 0.683828i \(0.760314\pi\)
\(402\) 7.58869 0.378489
\(403\) 18.9156 0.942251
\(404\) 4.61357 0.229534
\(405\) 11.1908 0.556075
\(406\) −7.00668 −0.347736
\(407\) −3.52240 −0.174599
\(408\) −15.6454 −0.774563
\(409\) 38.3348 1.89553 0.947767 0.318963i \(-0.103335\pi\)
0.947767 + 0.318963i \(0.103335\pi\)
\(410\) −8.02297 −0.396226
\(411\) 23.4137 1.15491
\(412\) −4.67551 −0.230346
\(413\) −7.31714 −0.360053
\(414\) 13.6089 0.668841
\(415\) −13.5518 −0.665230
\(416\) 5.80630 0.284677
\(417\) 36.2014 1.77279
\(418\) −6.16042 −0.301316
\(419\) −20.7961 −1.01596 −0.507978 0.861370i \(-0.669607\pi\)
−0.507978 + 0.861370i \(0.669607\pi\)
\(420\) 10.1012 0.492890
\(421\) 12.0941 0.589432 0.294716 0.955585i \(-0.404775\pi\)
0.294716 + 0.955585i \(0.404775\pi\)
\(422\) −10.7018 −0.520954
\(423\) −12.7080 −0.617885
\(424\) 0.333481 0.0161953
\(425\) −7.18366 −0.348458
\(426\) −20.5222 −0.994304
\(427\) 68.2340 3.30207
\(428\) −13.4710 −0.651146
\(429\) −12.6456 −0.610537
\(430\) 1.00000 0.0482243
\(431\) 3.40970 0.164240 0.0821198 0.996622i \(-0.473831\pi\)
0.0821198 + 0.996622i \(0.473831\pi\)
\(432\) 2.73694 0.131681
\(433\) −29.8176 −1.43294 −0.716471 0.697617i \(-0.754244\pi\)
−0.716471 + 0.697617i \(0.754244\pi\)
\(434\) 15.1096 0.725285
\(435\) 3.29018 0.157752
\(436\) 10.6732 0.511155
\(437\) 48.0901 2.30046
\(438\) −6.56113 −0.313503
\(439\) −18.5112 −0.883492 −0.441746 0.897140i \(-0.645641\pi\)
−0.441746 + 0.897140i \(0.645641\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 25.2979 1.20466
\(442\) −41.7105 −1.98396
\(443\) −4.84563 −0.230223 −0.115111 0.993353i \(-0.536722\pi\)
−0.115111 + 0.993353i \(0.536722\pi\)
\(444\) −7.67150 −0.364073
\(445\) −13.5086 −0.640370
\(446\) −0.474339 −0.0224606
\(447\) −18.9395 −0.895806
\(448\) 4.63803 0.219126
\(449\) 1.78702 0.0843349 0.0421674 0.999111i \(-0.486574\pi\)
0.0421674 + 0.999111i \(0.486574\pi\)
\(450\) −1.74332 −0.0821811
\(451\) 8.02297 0.377787
\(452\) 9.96108 0.468530
\(453\) 17.6822 0.830781
\(454\) −22.9170 −1.07555
\(455\) 26.9298 1.26249
\(456\) −13.4169 −0.628303
\(457\) 15.6591 0.732503 0.366252 0.930516i \(-0.380641\pi\)
0.366252 + 0.930516i \(0.380641\pi\)
\(458\) 1.74361 0.0814738
\(459\) −19.6612 −0.917707
\(460\) 7.80630 0.363971
\(461\) 1.93745 0.0902358 0.0451179 0.998982i \(-0.485634\pi\)
0.0451179 + 0.998982i \(0.485634\pi\)
\(462\) −10.1012 −0.469952
\(463\) 31.1924 1.44963 0.724816 0.688942i \(-0.241925\pi\)
0.724816 + 0.688942i \(0.241925\pi\)
\(464\) 1.51070 0.0701326
\(465\) −7.09514 −0.329029
\(466\) 14.1046 0.653383
\(467\) −33.1793 −1.53536 −0.767678 0.640836i \(-0.778588\pi\)
−0.767678 + 0.640836i \(0.778588\pi\)
\(468\) −10.1223 −0.467902
\(469\) 16.1607 0.746230
\(470\) −7.28953 −0.336241
\(471\) −14.2641 −0.657254
\(472\) 1.57764 0.0726167
\(473\) −1.00000 −0.0459800
\(474\) 11.0207 0.506197
\(475\) −6.16042 −0.282659
\(476\) −33.3180 −1.52713
\(477\) −0.581366 −0.0266189
\(478\) −22.2167 −1.01617
\(479\) −24.9337 −1.13925 −0.569625 0.821905i \(-0.692911\pi\)
−0.569625 + 0.821905i \(0.692911\pi\)
\(480\) −2.17792 −0.0994079
\(481\) −20.4521 −0.932536
\(482\) −15.9469 −0.726361
\(483\) 78.8534 3.58795
\(484\) 1.00000 0.0454545
\(485\) 15.3042 0.694929
\(486\) −16.1618 −0.733115
\(487\) 27.1636 1.23090 0.615451 0.788175i \(-0.288974\pi\)
0.615451 + 0.788175i \(0.288974\pi\)
\(488\) −14.7118 −0.665974
\(489\) −9.46244 −0.427906
\(490\) 14.5113 0.655555
\(491\) −31.2621 −1.41084 −0.705420 0.708789i \(-0.749242\pi\)
−0.705420 + 0.708789i \(0.749242\pi\)
\(492\) 17.4734 0.787760
\(493\) −10.8524 −0.488766
\(494\) −35.7692 −1.60933
\(495\) 1.74332 0.0783566
\(496\) −3.25777 −0.146278
\(497\) −43.7035 −1.96037
\(498\) 29.5146 1.32258
\(499\) 22.5838 1.01099 0.505496 0.862829i \(-0.331310\pi\)
0.505496 + 0.862829i \(0.331310\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 23.2526 1.03885
\(502\) 2.78403 0.124257
\(503\) 37.9353 1.69145 0.845726 0.533618i \(-0.179168\pi\)
0.845726 + 0.533618i \(0.179168\pi\)
\(504\) −8.08559 −0.360161
\(505\) −4.61357 −0.205301
\(506\) −7.80630 −0.347032
\(507\) −45.1115 −2.00347
\(508\) 7.03779 0.312251
\(509\) 4.31530 0.191272 0.0956361 0.995416i \(-0.469511\pi\)
0.0956361 + 0.995416i \(0.469511\pi\)
\(510\) 15.6454 0.692790
\(511\) −13.9724 −0.618102
\(512\) −1.00000 −0.0441942
\(513\) −16.8607 −0.744417
\(514\) −15.5851 −0.687430
\(515\) 4.67551 0.206028
\(516\) −2.17792 −0.0958775
\(517\) 7.28953 0.320593
\(518\) −16.3370 −0.717807
\(519\) 33.1060 1.45319
\(520\) −5.80630 −0.254623
\(521\) −5.38821 −0.236062 −0.118031 0.993010i \(-0.537658\pi\)
−0.118031 + 0.993010i \(0.537658\pi\)
\(522\) −2.63364 −0.115271
\(523\) 34.3705 1.50292 0.751459 0.659779i \(-0.229350\pi\)
0.751459 + 0.659779i \(0.229350\pi\)
\(524\) 13.0432 0.569793
\(525\) −10.1012 −0.440855
\(526\) 11.5563 0.503877
\(527\) 23.4027 1.01944
\(528\) 2.17792 0.0947817
\(529\) 37.9383 1.64949
\(530\) −0.333481 −0.0144855
\(531\) −2.75034 −0.119354
\(532\) −28.5722 −1.23876
\(533\) 46.5838 2.01777
\(534\) 29.4206 1.27316
\(535\) 13.4710 0.582403
\(536\) −3.48438 −0.150502
\(537\) −37.1317 −1.60235
\(538\) −7.46417 −0.321803
\(539\) −14.5113 −0.625047
\(540\) −2.73694 −0.117779
\(541\) 21.7848 0.936603 0.468301 0.883569i \(-0.344866\pi\)
0.468301 + 0.883569i \(0.344866\pi\)
\(542\) 5.60803 0.240885
\(543\) 49.8399 2.13883
\(544\) 7.18366 0.307997
\(545\) −10.6732 −0.457191
\(546\) −58.6509 −2.51003
\(547\) −40.0504 −1.71243 −0.856216 0.516618i \(-0.827191\pi\)
−0.856216 + 0.516618i \(0.827191\pi\)
\(548\) −10.7505 −0.459239
\(549\) 25.6475 1.09461
\(550\) 1.00000 0.0426401
\(551\) −9.30656 −0.396473
\(552\) −17.0015 −0.723631
\(553\) 23.4693 0.998017
\(554\) 13.3255 0.566148
\(555\) 7.67150 0.325637
\(556\) −16.6220 −0.704930
\(557\) −16.6440 −0.705230 −0.352615 0.935769i \(-0.614707\pi\)
−0.352615 + 0.935769i \(0.614707\pi\)
\(558\) 5.67934 0.240426
\(559\) −5.80630 −0.245580
\(560\) −4.63803 −0.195993
\(561\) −15.6454 −0.660550
\(562\) 24.1984 1.02075
\(563\) 19.3161 0.814075 0.407038 0.913411i \(-0.366562\pi\)
0.407038 + 0.913411i \(0.366562\pi\)
\(564\) 15.8760 0.668500
\(565\) −9.96108 −0.419066
\(566\) 3.49895 0.147072
\(567\) −51.9032 −2.17973
\(568\) 9.42285 0.395374
\(569\) −19.1536 −0.802963 −0.401481 0.915867i \(-0.631505\pi\)
−0.401481 + 0.915867i \(0.631505\pi\)
\(570\) 13.4169 0.561971
\(571\) 41.8316 1.75060 0.875299 0.483583i \(-0.160665\pi\)
0.875299 + 0.483583i \(0.160665\pi\)
\(572\) 5.80630 0.242774
\(573\) −20.3861 −0.851643
\(574\) 37.2108 1.55315
\(575\) −7.80630 −0.325545
\(576\) 1.74332 0.0726385
\(577\) −2.64311 −0.110034 −0.0550171 0.998485i \(-0.517521\pi\)
−0.0550171 + 0.998485i \(0.517521\pi\)
\(578\) −34.6049 −1.43937
\(579\) 12.7320 0.529124
\(580\) −1.51070 −0.0627285
\(581\) 62.8535 2.60760
\(582\) −33.3313 −1.38163
\(583\) 0.333481 0.0138114
\(584\) 3.01257 0.124661
\(585\) 10.1223 0.418504
\(586\) 11.9897 0.495288
\(587\) 37.1898 1.53499 0.767494 0.641056i \(-0.221503\pi\)
0.767494 + 0.641056i \(0.221503\pi\)
\(588\) −31.6045 −1.30335
\(589\) 20.0692 0.826937
\(590\) −1.57764 −0.0649504
\(591\) −12.7750 −0.525492
\(592\) 3.52240 0.144770
\(593\) −47.9818 −1.97038 −0.985188 0.171478i \(-0.945146\pi\)
−0.985188 + 0.171478i \(0.945146\pi\)
\(594\) 2.73694 0.112298
\(595\) 33.3180 1.36591
\(596\) 8.69614 0.356208
\(597\) −29.4853 −1.20675
\(598\) −45.3257 −1.85351
\(599\) 14.1921 0.579872 0.289936 0.957046i \(-0.406366\pi\)
0.289936 + 0.957046i \(0.406366\pi\)
\(600\) 2.17792 0.0889131
\(601\) −6.37582 −0.260075 −0.130038 0.991509i \(-0.541510\pi\)
−0.130038 + 0.991509i \(0.541510\pi\)
\(602\) −4.63803 −0.189032
\(603\) 6.07440 0.247369
\(604\) −8.11885 −0.330351
\(605\) −1.00000 −0.0406558
\(606\) 10.0480 0.408171
\(607\) 28.5905 1.16045 0.580227 0.814455i \(-0.302964\pi\)
0.580227 + 0.814455i \(0.302964\pi\)
\(608\) 6.16042 0.249838
\(609\) −15.2600 −0.618365
\(610\) 14.7118 0.595665
\(611\) 42.3252 1.71229
\(612\) −12.5234 −0.506230
\(613\) −28.2920 −1.14270 −0.571351 0.820706i \(-0.693581\pi\)
−0.571351 + 0.820706i \(0.693581\pi\)
\(614\) −6.33882 −0.255814
\(615\) −17.4734 −0.704594
\(616\) 4.63803 0.186872
\(617\) −40.6714 −1.63737 −0.818685 0.574243i \(-0.805296\pi\)
−0.818685 + 0.574243i \(0.805296\pi\)
\(618\) −10.1829 −0.409615
\(619\) −12.0151 −0.482927 −0.241463 0.970410i \(-0.577627\pi\)
−0.241463 + 0.970410i \(0.577627\pi\)
\(620\) 3.25777 0.130835
\(621\) −21.3654 −0.857362
\(622\) −20.2786 −0.813096
\(623\) 62.6534 2.51015
\(624\) 12.6456 0.506231
\(625\) 1.00000 0.0400000
\(626\) 17.7146 0.708017
\(627\) −13.4169 −0.535819
\(628\) 6.54941 0.261350
\(629\) −25.3037 −1.00893
\(630\) 8.08559 0.322138
\(631\) −30.7436 −1.22388 −0.611942 0.790903i \(-0.709611\pi\)
−0.611942 + 0.790903i \(0.709611\pi\)
\(632\) −5.06019 −0.201284
\(633\) −23.3075 −0.926392
\(634\) −9.14582 −0.363227
\(635\) −7.03779 −0.279286
\(636\) 0.726295 0.0287995
\(637\) −84.2571 −3.33839
\(638\) 1.51070 0.0598093
\(639\) −16.4271 −0.649845
\(640\) 1.00000 0.0395285
\(641\) −11.4765 −0.453295 −0.226648 0.973977i \(-0.572777\pi\)
−0.226648 + 0.973977i \(0.572777\pi\)
\(642\) −29.3388 −1.15791
\(643\) −18.8176 −0.742095 −0.371048 0.928614i \(-0.621001\pi\)
−0.371048 + 0.928614i \(0.621001\pi\)
\(644\) −36.2059 −1.42671
\(645\) 2.17792 0.0857554
\(646\) −44.2543 −1.74116
\(647\) −13.6044 −0.534844 −0.267422 0.963579i \(-0.586172\pi\)
−0.267422 + 0.963579i \(0.586172\pi\)
\(648\) 11.1908 0.439616
\(649\) 1.57764 0.0619277
\(650\) 5.80630 0.227742
\(651\) 32.9075 1.28975
\(652\) 4.34472 0.170152
\(653\) 40.9051 1.60074 0.800371 0.599505i \(-0.204636\pi\)
0.800371 + 0.599505i \(0.204636\pi\)
\(654\) 23.2454 0.908968
\(655\) −13.0432 −0.509639
\(656\) −8.02297 −0.313244
\(657\) −5.25189 −0.204896
\(658\) 33.8091 1.31801
\(659\) −6.14372 −0.239325 −0.119663 0.992815i \(-0.538181\pi\)
−0.119663 + 0.992815i \(0.538181\pi\)
\(660\) −2.17792 −0.0847753
\(661\) 11.6935 0.454824 0.227412 0.973799i \(-0.426974\pi\)
0.227412 + 0.973799i \(0.426974\pi\)
\(662\) 7.20057 0.279858
\(663\) −90.8419 −3.52801
\(664\) −13.5518 −0.525910
\(665\) 28.5722 1.10798
\(666\) −6.14068 −0.237947
\(667\) −11.7930 −0.456626
\(668\) −10.6765 −0.413088
\(669\) −1.03307 −0.0399408
\(670\) 3.48438 0.134613
\(671\) −14.7118 −0.567944
\(672\) 10.1012 0.389664
\(673\) −0.279963 −0.0107918 −0.00539589 0.999985i \(-0.501718\pi\)
−0.00539589 + 0.999985i \(0.501718\pi\)
\(674\) −3.67433 −0.141530
\(675\) 2.73694 0.105345
\(676\) 20.7131 0.796658
\(677\) −43.8456 −1.68512 −0.842561 0.538601i \(-0.818953\pi\)
−0.842561 + 0.538601i \(0.818953\pi\)
\(678\) 21.6944 0.833169
\(679\) −70.9814 −2.72402
\(680\) −7.18366 −0.275481
\(681\) −49.9112 −1.91260
\(682\) −3.25777 −0.124746
\(683\) −20.5824 −0.787562 −0.393781 0.919204i \(-0.628833\pi\)
−0.393781 + 0.919204i \(0.628833\pi\)
\(684\) −10.7396 −0.410639
\(685\) 10.7505 0.410756
\(686\) −34.8377 −1.33011
\(687\) 3.79745 0.144882
\(688\) 1.00000 0.0381246
\(689\) 1.93629 0.0737669
\(690\) 17.0015 0.647235
\(691\) 39.6324 1.50769 0.753844 0.657053i \(-0.228197\pi\)
0.753844 + 0.657053i \(0.228197\pi\)
\(692\) −15.2008 −0.577847
\(693\) −8.08559 −0.307146
\(694\) −1.54550 −0.0586664
\(695\) 16.6220 0.630509
\(696\) 3.29018 0.124714
\(697\) 57.6342 2.18305
\(698\) 15.3442 0.580785
\(699\) 30.7186 1.16189
\(700\) 4.63803 0.175301
\(701\) 19.7081 0.744365 0.372182 0.928160i \(-0.378610\pi\)
0.372182 + 0.928160i \(0.378610\pi\)
\(702\) 15.8915 0.599785
\(703\) −21.6995 −0.818411
\(704\) −1.00000 −0.0376889
\(705\) −15.8760 −0.597925
\(706\) −20.4471 −0.769539
\(707\) 21.3979 0.804751
\(708\) 3.43597 0.129132
\(709\) 7.36825 0.276720 0.138360 0.990382i \(-0.455817\pi\)
0.138360 + 0.990382i \(0.455817\pi\)
\(710\) −9.42285 −0.353633
\(711\) 8.82155 0.330834
\(712\) −13.5086 −0.506257
\(713\) 25.4311 0.952402
\(714\) −72.5639 −2.71563
\(715\) −5.80630 −0.217143
\(716\) 17.0492 0.637157
\(717\) −48.3860 −1.80701
\(718\) −35.1254 −1.31087
\(719\) −10.3342 −0.385399 −0.192700 0.981258i \(-0.561724\pi\)
−0.192700 + 0.981258i \(0.561724\pi\)
\(720\) −1.74332 −0.0649698
\(721\) −21.6852 −0.807597
\(722\) −18.9508 −0.705275
\(723\) −34.7310 −1.29166
\(724\) −22.8842 −0.850484
\(725\) 1.51070 0.0561061
\(726\) 2.17792 0.0808301
\(727\) −31.5464 −1.16999 −0.584996 0.811036i \(-0.698904\pi\)
−0.584996 + 0.811036i \(0.698904\pi\)
\(728\) 26.9298 0.998085
\(729\) −1.62671 −0.0602484
\(730\) −3.01257 −0.111500
\(731\) −7.18366 −0.265697
\(732\) −32.0412 −1.18428
\(733\) −9.14996 −0.337961 −0.168981 0.985619i \(-0.554048\pi\)
−0.168981 + 0.985619i \(0.554048\pi\)
\(734\) 23.0698 0.851524
\(735\) 31.6045 1.16575
\(736\) 7.80630 0.287744
\(737\) −3.48438 −0.128349
\(738\) 13.9866 0.514855
\(739\) 16.8841 0.621090 0.310545 0.950559i \(-0.399488\pi\)
0.310545 + 0.950559i \(0.399488\pi\)
\(740\) −3.52240 −0.129486
\(741\) −77.9025 −2.86182
\(742\) 1.54670 0.0567810
\(743\) 38.1690 1.40028 0.700142 0.714004i \(-0.253120\pi\)
0.700142 + 0.714004i \(0.253120\pi\)
\(744\) −7.09514 −0.260121
\(745\) −8.69614 −0.318602
\(746\) −11.3400 −0.415185
\(747\) 23.6251 0.864397
\(748\) 7.18366 0.262660
\(749\) −62.4790 −2.28293
\(750\) −2.17792 −0.0795263
\(751\) 2.04969 0.0747944 0.0373972 0.999300i \(-0.488093\pi\)
0.0373972 + 0.999300i \(0.488093\pi\)
\(752\) −7.28953 −0.265822
\(753\) 6.06339 0.220962
\(754\) 8.77159 0.319442
\(755\) 8.11885 0.295475
\(756\) 12.6940 0.461676
\(757\) 14.8304 0.539019 0.269510 0.962998i \(-0.413138\pi\)
0.269510 + 0.962998i \(0.413138\pi\)
\(758\) −20.2144 −0.734219
\(759\) −17.0015 −0.617114
\(760\) −6.16042 −0.223462
\(761\) 12.1243 0.439506 0.219753 0.975556i \(-0.429475\pi\)
0.219753 + 0.975556i \(0.429475\pi\)
\(762\) 15.3277 0.555265
\(763\) 49.5028 1.79212
\(764\) 9.36038 0.338647
\(765\) 12.5234 0.452786
\(766\) 35.3883 1.27863
\(767\) 9.16024 0.330757
\(768\) −2.17792 −0.0785888
\(769\) 42.9199 1.54773 0.773866 0.633349i \(-0.218320\pi\)
0.773866 + 0.633349i \(0.218320\pi\)
\(770\) −4.63803 −0.167143
\(771\) −33.9431 −1.22243
\(772\) −5.84595 −0.210400
\(773\) 10.9632 0.394320 0.197160 0.980371i \(-0.436828\pi\)
0.197160 + 0.980371i \(0.436828\pi\)
\(774\) −1.74332 −0.0626625
\(775\) −3.25777 −0.117022
\(776\) 15.3042 0.549389
\(777\) −35.5806 −1.27645
\(778\) 36.6686 1.31463
\(779\) 49.4249 1.77083
\(780\) −12.6456 −0.452787
\(781\) 9.42285 0.337176
\(782\) −56.0778 −2.00534
\(783\) 4.13470 0.147762
\(784\) 14.5113 0.518262
\(785\) −6.54941 −0.233758
\(786\) 28.4069 1.01324
\(787\) −49.9397 −1.78016 −0.890079 0.455807i \(-0.849351\pi\)
−0.890079 + 0.455807i \(0.849351\pi\)
\(788\) 5.86569 0.208956
\(789\) 25.1686 0.896026
\(790\) 5.06019 0.180034
\(791\) 46.1998 1.64268
\(792\) 1.74332 0.0619463
\(793\) −85.4214 −3.03340
\(794\) −9.61333 −0.341164
\(795\) −0.726295 −0.0257590
\(796\) 13.5383 0.479853
\(797\) 41.1063 1.45606 0.728030 0.685545i \(-0.240436\pi\)
0.728030 + 0.685545i \(0.240436\pi\)
\(798\) −62.2279 −2.20284
\(799\) 52.3655 1.85256
\(800\) −1.00000 −0.0353553
\(801\) 23.5499 0.832094
\(802\) 29.2222 1.03187
\(803\) 3.01257 0.106311
\(804\) −7.58869 −0.267632
\(805\) 36.2059 1.27609
\(806\) −18.9156 −0.666272
\(807\) −16.2563 −0.572250
\(808\) −4.61357 −0.162305
\(809\) 21.5610 0.758045 0.379023 0.925387i \(-0.376260\pi\)
0.379023 + 0.925387i \(0.376260\pi\)
\(810\) −11.1908 −0.393204
\(811\) −5.47442 −0.192233 −0.0961164 0.995370i \(-0.530642\pi\)
−0.0961164 + 0.995370i \(0.530642\pi\)
\(812\) 7.00668 0.245886
\(813\) 12.2138 0.428357
\(814\) 3.52240 0.123460
\(815\) −4.34472 −0.152189
\(816\) 15.6454 0.547699
\(817\) −6.16042 −0.215526
\(818\) −38.3348 −1.34035
\(819\) −46.9473 −1.64047
\(820\) 8.02297 0.280174
\(821\) 46.1977 1.61231 0.806155 0.591705i \(-0.201545\pi\)
0.806155 + 0.591705i \(0.201545\pi\)
\(822\) −23.4137 −0.816647
\(823\) 16.7693 0.584540 0.292270 0.956336i \(-0.405589\pi\)
0.292270 + 0.956336i \(0.405589\pi\)
\(824\) 4.67551 0.162879
\(825\) 2.17792 0.0758253
\(826\) 7.31714 0.254596
\(827\) −16.5294 −0.574784 −0.287392 0.957813i \(-0.592788\pi\)
−0.287392 + 0.957813i \(0.592788\pi\)
\(828\) −13.6089 −0.472942
\(829\) 0.371395 0.0128991 0.00644954 0.999979i \(-0.497947\pi\)
0.00644954 + 0.999979i \(0.497947\pi\)
\(830\) 13.5518 0.470388
\(831\) 29.0219 1.00676
\(832\) −5.80630 −0.201297
\(833\) −104.244 −3.61185
\(834\) −36.2014 −1.25355
\(835\) 10.6765 0.369477
\(836\) 6.16042 0.213063
\(837\) −8.91630 −0.308192
\(838\) 20.7961 0.718389
\(839\) −40.4614 −1.39688 −0.698442 0.715667i \(-0.746123\pi\)
−0.698442 + 0.715667i \(0.746123\pi\)
\(840\) −10.1012 −0.348526
\(841\) −26.7178 −0.921303
\(842\) −12.0941 −0.416791
\(843\) 52.7022 1.81516
\(844\) 10.7018 0.368370
\(845\) −20.7131 −0.712553
\(846\) 12.7080 0.436910
\(847\) 4.63803 0.159365
\(848\) −0.333481 −0.0114518
\(849\) 7.62042 0.261532
\(850\) 7.18366 0.246397
\(851\) −27.4969 −0.942582
\(852\) 20.5222 0.703079
\(853\) −21.1766 −0.725071 −0.362536 0.931970i \(-0.618089\pi\)
−0.362536 + 0.931970i \(0.618089\pi\)
\(854\) −68.2340 −2.33492
\(855\) 10.7396 0.367287
\(856\) 13.4710 0.460430
\(857\) 43.4091 1.48283 0.741413 0.671049i \(-0.234156\pi\)
0.741413 + 0.671049i \(0.234156\pi\)
\(858\) 12.6456 0.431715
\(859\) 23.0665 0.787020 0.393510 0.919320i \(-0.371261\pi\)
0.393510 + 0.919320i \(0.371261\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 81.0420 2.76190
\(862\) −3.40970 −0.116135
\(863\) 23.7305 0.807797 0.403898 0.914804i \(-0.367655\pi\)
0.403898 + 0.914804i \(0.367655\pi\)
\(864\) −2.73694 −0.0931125
\(865\) 15.2008 0.516842
\(866\) 29.8176 1.01324
\(867\) −75.3666 −2.55959
\(868\) −15.1096 −0.512854
\(869\) −5.06019 −0.171655
\(870\) −3.29018 −0.111548
\(871\) −20.2313 −0.685513
\(872\) −10.6732 −0.361441
\(873\) −26.6802 −0.902988
\(874\) −48.0901 −1.62667
\(875\) −4.63803 −0.156794
\(876\) 6.56113 0.221680
\(877\) −38.5945 −1.30324 −0.651622 0.758544i \(-0.725911\pi\)
−0.651622 + 0.758544i \(0.725911\pi\)
\(878\) 18.5112 0.624723
\(879\) 26.1125 0.880753
\(880\) 1.00000 0.0337100
\(881\) −7.88757 −0.265739 −0.132870 0.991134i \(-0.542419\pi\)
−0.132870 + 0.991134i \(0.542419\pi\)
\(882\) −25.2979 −0.851826
\(883\) 11.1519 0.375290 0.187645 0.982237i \(-0.439915\pi\)
0.187645 + 0.982237i \(0.439915\pi\)
\(884\) 41.7105 1.40287
\(885\) −3.43597 −0.115499
\(886\) 4.84563 0.162792
\(887\) 30.6592 1.02944 0.514718 0.857359i \(-0.327897\pi\)
0.514718 + 0.857359i \(0.327897\pi\)
\(888\) 7.67150 0.257439
\(889\) 32.6415 1.09476
\(890\) 13.5086 0.452810
\(891\) 11.1908 0.374906
\(892\) 0.474339 0.0158820
\(893\) 44.9066 1.50274
\(894\) 18.9395 0.633430
\(895\) −17.0492 −0.569891
\(896\) −4.63803 −0.154946
\(897\) −98.7157 −3.29602
\(898\) −1.78702 −0.0596338
\(899\) −4.92151 −0.164142
\(900\) 1.74332 0.0581108
\(901\) 2.39562 0.0798095
\(902\) −8.02297 −0.267136
\(903\) −10.1012 −0.336148
\(904\) −9.96108 −0.331301
\(905\) 22.8842 0.760696
\(906\) −17.6822 −0.587451
\(907\) 39.7812 1.32091 0.660456 0.750865i \(-0.270363\pi\)
0.660456 + 0.750865i \(0.270363\pi\)
\(908\) 22.9170 0.760526
\(909\) 8.04295 0.266768
\(910\) −26.9298 −0.892714
\(911\) −31.7767 −1.05281 −0.526405 0.850234i \(-0.676461\pi\)
−0.526405 + 0.850234i \(0.676461\pi\)
\(912\) 13.4169 0.444277
\(913\) −13.5518 −0.448498
\(914\) −15.6591 −0.517958
\(915\) 32.0412 1.05925
\(916\) −1.74361 −0.0576107
\(917\) 60.4946 1.99771
\(918\) 19.6612 0.648917
\(919\) 32.8697 1.08427 0.542136 0.840291i \(-0.317616\pi\)
0.542136 + 0.840291i \(0.317616\pi\)
\(920\) −7.80630 −0.257366
\(921\) −13.8054 −0.454904
\(922\) −1.93745 −0.0638064
\(923\) 54.7119 1.80086
\(924\) 10.1012 0.332307
\(925\) 3.52240 0.115816
\(926\) −31.1924 −1.02504
\(927\) −8.15093 −0.267712
\(928\) −1.51070 −0.0495912
\(929\) −52.8939 −1.73539 −0.867697 0.497094i \(-0.834400\pi\)
−0.867697 + 0.497094i \(0.834400\pi\)
\(930\) 7.09514 0.232659
\(931\) −89.3958 −2.92983
\(932\) −14.1046 −0.462011
\(933\) −44.1650 −1.44590
\(934\) 33.1793 1.08566
\(935\) −7.18366 −0.234931
\(936\) 10.1223 0.330856
\(937\) 2.67168 0.0872799 0.0436399 0.999047i \(-0.486105\pi\)
0.0436399 + 0.999047i \(0.486105\pi\)
\(938\) −16.1607 −0.527664
\(939\) 38.5809 1.25904
\(940\) 7.28953 0.237758
\(941\) 40.5921 1.32326 0.661632 0.749829i \(-0.269864\pi\)
0.661632 + 0.749829i \(0.269864\pi\)
\(942\) 14.2641 0.464749
\(943\) 62.6297 2.03950
\(944\) −1.57764 −0.0513478
\(945\) −12.6940 −0.412936
\(946\) 1.00000 0.0325128
\(947\) 4.30856 0.140009 0.0700047 0.997547i \(-0.477699\pi\)
0.0700047 + 0.997547i \(0.477699\pi\)
\(948\) −11.0207 −0.357935
\(949\) 17.4919 0.567811
\(950\) 6.16042 0.199870
\(951\) −19.9188 −0.645913
\(952\) 33.3180 1.07984
\(953\) 29.9630 0.970596 0.485298 0.874349i \(-0.338711\pi\)
0.485298 + 0.874349i \(0.338711\pi\)
\(954\) 0.581366 0.0188224
\(955\) −9.36038 −0.302895
\(956\) 22.2167 0.718538
\(957\) 3.29018 0.106357
\(958\) 24.9337 0.805571
\(959\) −49.8612 −1.61010
\(960\) 2.17792 0.0702920
\(961\) −20.3870 −0.657644
\(962\) 20.4521 0.659403
\(963\) −23.4843 −0.756772
\(964\) 15.9469 0.513615
\(965\) 5.84595 0.188188
\(966\) −78.8534 −2.53707
\(967\) 32.5276 1.04602 0.523008 0.852328i \(-0.324810\pi\)
0.523008 + 0.852328i \(0.324810\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −96.3823 −3.09625
\(970\) −15.3042 −0.491389
\(971\) 26.9186 0.863860 0.431930 0.901907i \(-0.357833\pi\)
0.431930 + 0.901907i \(0.357833\pi\)
\(972\) 16.1618 0.518390
\(973\) −77.0934 −2.47150
\(974\) −27.1636 −0.870379
\(975\) 12.6456 0.404985
\(976\) 14.7118 0.470915
\(977\) 1.86491 0.0596638 0.0298319 0.999555i \(-0.490503\pi\)
0.0298319 + 0.999555i \(0.490503\pi\)
\(978\) 9.46244 0.302575
\(979\) −13.5086 −0.431737
\(980\) −14.5113 −0.463547
\(981\) 18.6069 0.594073
\(982\) 31.2621 0.997615
\(983\) 46.1847 1.47306 0.736531 0.676404i \(-0.236463\pi\)
0.736531 + 0.676404i \(0.236463\pi\)
\(984\) −17.4734 −0.557030
\(985\) −5.86569 −0.186896
\(986\) 10.8524 0.345610
\(987\) 73.6333 2.34377
\(988\) 35.7692 1.13797
\(989\) −7.80630 −0.248226
\(990\) −1.74332 −0.0554065
\(991\) −0.401128 −0.0127422 −0.00637112 0.999980i \(-0.502028\pi\)
−0.00637112 + 0.999980i \(0.502028\pi\)
\(992\) 3.25777 0.103434
\(993\) 15.6823 0.497661
\(994\) 43.7035 1.38619
\(995\) −13.5383 −0.429193
\(996\) −29.5146 −0.935206
\(997\) 21.6030 0.684175 0.342087 0.939668i \(-0.388866\pi\)
0.342087 + 0.939668i \(0.388866\pi\)
\(998\) −22.5838 −0.714879
\(999\) 9.64059 0.305015
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 4730.2.a.bb.1.3 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.3 11 1.1 even 1 trivial