Properties

Label 4033.2.a.f.1.9
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.27621 q^{2} -2.60153 q^{3} +3.18111 q^{4} +2.30412 q^{5} +5.92161 q^{6} +1.78008 q^{7} -2.68845 q^{8} +3.76795 q^{9} +O(q^{10})\) \(q-2.27621 q^{2} -2.60153 q^{3} +3.18111 q^{4} +2.30412 q^{5} +5.92161 q^{6} +1.78008 q^{7} -2.68845 q^{8} +3.76795 q^{9} -5.24464 q^{10} +3.06113 q^{11} -8.27574 q^{12} +2.16510 q^{13} -4.05183 q^{14} -5.99422 q^{15} -0.242762 q^{16} -2.52261 q^{17} -8.57662 q^{18} -3.18685 q^{19} +7.32965 q^{20} -4.63093 q^{21} -6.96777 q^{22} -4.94642 q^{23} +6.99407 q^{24} +0.308954 q^{25} -4.92822 q^{26} -1.99784 q^{27} +5.66263 q^{28} +4.73582 q^{29} +13.6441 q^{30} -4.47090 q^{31} +5.92947 q^{32} -7.96362 q^{33} +5.74198 q^{34} +4.10152 q^{35} +11.9863 q^{36} +1.00000 q^{37} +7.25393 q^{38} -5.63258 q^{39} -6.19450 q^{40} -7.23262 q^{41} +10.5409 q^{42} +11.0794 q^{43} +9.73780 q^{44} +8.68179 q^{45} +11.2591 q^{46} +7.47598 q^{47} +0.631553 q^{48} -3.83131 q^{49} -0.703243 q^{50} +6.56264 q^{51} +6.88743 q^{52} -4.10255 q^{53} +4.54749 q^{54} +7.05321 q^{55} -4.78565 q^{56} +8.29068 q^{57} -10.7797 q^{58} -2.91589 q^{59} -19.0683 q^{60} +5.95510 q^{61} +10.1767 q^{62} +6.70725 q^{63} -13.0112 q^{64} +4.98865 q^{65} +18.1268 q^{66} +14.6837 q^{67} -8.02470 q^{68} +12.8683 q^{69} -9.33589 q^{70} -2.66884 q^{71} -10.1299 q^{72} -6.69619 q^{73} -2.27621 q^{74} -0.803752 q^{75} -10.1377 q^{76} +5.44907 q^{77} +12.8209 q^{78} +5.77436 q^{79} -0.559353 q^{80} -6.10641 q^{81} +16.4629 q^{82} +10.0472 q^{83} -14.7315 q^{84} -5.81239 q^{85} -25.2189 q^{86} -12.3204 q^{87} -8.22969 q^{88} +11.7392 q^{89} -19.7615 q^{90} +3.85406 q^{91} -15.7351 q^{92} +11.6312 q^{93} -17.0169 q^{94} -7.34288 q^{95} -15.4257 q^{96} +0.218286 q^{97} +8.72085 q^{98} +11.5342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27621 −1.60952 −0.804760 0.593600i \(-0.797706\pi\)
−0.804760 + 0.593600i \(0.797706\pi\)
\(3\) −2.60153 −1.50199 −0.750996 0.660306i \(-0.770426\pi\)
−0.750996 + 0.660306i \(0.770426\pi\)
\(4\) 3.18111 1.59055
\(5\) 2.30412 1.03043 0.515216 0.857060i \(-0.327712\pi\)
0.515216 + 0.857060i \(0.327712\pi\)
\(6\) 5.92161 2.41749
\(7\) 1.78008 0.672808 0.336404 0.941718i \(-0.390789\pi\)
0.336404 + 0.941718i \(0.390789\pi\)
\(8\) −2.68845 −0.950510
\(9\) 3.76795 1.25598
\(10\) −5.24464 −1.65850
\(11\) 3.06113 0.922966 0.461483 0.887149i \(-0.347317\pi\)
0.461483 + 0.887149i \(0.347317\pi\)
\(12\) −8.27574 −2.38900
\(13\) 2.16510 0.600492 0.300246 0.953862i \(-0.402931\pi\)
0.300246 + 0.953862i \(0.402931\pi\)
\(14\) −4.05183 −1.08290
\(15\) −5.99422 −1.54770
\(16\) −0.242762 −0.0606906
\(17\) −2.52261 −0.611823 −0.305912 0.952060i \(-0.598961\pi\)
−0.305912 + 0.952060i \(0.598961\pi\)
\(18\) −8.57662 −2.02153
\(19\) −3.18685 −0.731114 −0.365557 0.930789i \(-0.619121\pi\)
−0.365557 + 0.930789i \(0.619121\pi\)
\(20\) 7.32965 1.63896
\(21\) −4.63093 −1.01055
\(22\) −6.96777 −1.48553
\(23\) −4.94642 −1.03140 −0.515700 0.856769i \(-0.672468\pi\)
−0.515700 + 0.856769i \(0.672468\pi\)
\(24\) 6.99407 1.42766
\(25\) 0.308954 0.0617908
\(26\) −4.92822 −0.966503
\(27\) −1.99784 −0.384484
\(28\) 5.66263 1.07014
\(29\) 4.73582 0.879419 0.439710 0.898140i \(-0.355081\pi\)
0.439710 + 0.898140i \(0.355081\pi\)
\(30\) 13.6441 2.49106
\(31\) −4.47090 −0.802998 −0.401499 0.915860i \(-0.631511\pi\)
−0.401499 + 0.915860i \(0.631511\pi\)
\(32\) 5.92947 1.04819
\(33\) −7.96362 −1.38629
\(34\) 5.74198 0.984742
\(35\) 4.10152 0.693283
\(36\) 11.9863 1.99771
\(37\) 1.00000 0.164399
\(38\) 7.25393 1.17674
\(39\) −5.63258 −0.901934
\(40\) −6.19450 −0.979436
\(41\) −7.23262 −1.12955 −0.564773 0.825246i \(-0.691036\pi\)
−0.564773 + 0.825246i \(0.691036\pi\)
\(42\) 10.5409 1.62650
\(43\) 11.0794 1.68959 0.844793 0.535093i \(-0.179723\pi\)
0.844793 + 0.535093i \(0.179723\pi\)
\(44\) 9.73780 1.46803
\(45\) 8.68179 1.29421
\(46\) 11.2591 1.66006
\(47\) 7.47598 1.09048 0.545242 0.838279i \(-0.316438\pi\)
0.545242 + 0.838279i \(0.316438\pi\)
\(48\) 0.631553 0.0911568
\(49\) −3.83131 −0.547330
\(50\) −0.703243 −0.0994535
\(51\) 6.56264 0.918954
\(52\) 6.88743 0.955115
\(53\) −4.10255 −0.563528 −0.281764 0.959484i \(-0.590920\pi\)
−0.281764 + 0.959484i \(0.590920\pi\)
\(54\) 4.54749 0.618835
\(55\) 7.05321 0.951054
\(56\) −4.78565 −0.639510
\(57\) 8.29068 1.09813
\(58\) −10.7797 −1.41544
\(59\) −2.91589 −0.379616 −0.189808 0.981821i \(-0.560787\pi\)
−0.189808 + 0.981821i \(0.560787\pi\)
\(60\) −19.0683 −2.46170
\(61\) 5.95510 0.762473 0.381236 0.924478i \(-0.375498\pi\)
0.381236 + 0.924478i \(0.375498\pi\)
\(62\) 10.1767 1.29244
\(63\) 6.70725 0.845035
\(64\) −13.0112 −1.62640
\(65\) 4.98865 0.618766
\(66\) 18.1268 2.23126
\(67\) 14.6837 1.79390 0.896952 0.442127i \(-0.145776\pi\)
0.896952 + 0.442127i \(0.145776\pi\)
\(68\) −8.02470 −0.973138
\(69\) 12.8683 1.54916
\(70\) −9.33589 −1.11585
\(71\) −2.66884 −0.316733 −0.158366 0.987380i \(-0.550623\pi\)
−0.158366 + 0.987380i \(0.550623\pi\)
\(72\) −10.1299 −1.19382
\(73\) −6.69619 −0.783729 −0.391865 0.920023i \(-0.628170\pi\)
−0.391865 + 0.920023i \(0.628170\pi\)
\(74\) −2.27621 −0.264603
\(75\) −0.803752 −0.0928093
\(76\) −10.1377 −1.16288
\(77\) 5.44907 0.620979
\(78\) 12.8209 1.45168
\(79\) 5.77436 0.649666 0.324833 0.945771i \(-0.394692\pi\)
0.324833 + 0.945771i \(0.394692\pi\)
\(80\) −0.559353 −0.0625375
\(81\) −6.10641 −0.678490
\(82\) 16.4629 1.81803
\(83\) 10.0472 1.10282 0.551411 0.834234i \(-0.314090\pi\)
0.551411 + 0.834234i \(0.314090\pi\)
\(84\) −14.7315 −1.60734
\(85\) −5.81239 −0.630442
\(86\) −25.2189 −2.71942
\(87\) −12.3204 −1.32088
\(88\) −8.22969 −0.877288
\(89\) 11.7392 1.24436 0.622178 0.782876i \(-0.286248\pi\)
0.622178 + 0.782876i \(0.286248\pi\)
\(90\) −19.7615 −2.08305
\(91\) 3.85406 0.404015
\(92\) −15.7351 −1.64050
\(93\) 11.6312 1.20610
\(94\) −17.0169 −1.75516
\(95\) −7.34288 −0.753363
\(96\) −15.4257 −1.57438
\(97\) 0.218286 0.0221635 0.0110818 0.999939i \(-0.496472\pi\)
0.0110818 + 0.999939i \(0.496472\pi\)
\(98\) 8.72085 0.880939
\(99\) 11.5342 1.15923
\(100\) 0.982816 0.0982816
\(101\) 1.67934 0.167100 0.0835502 0.996504i \(-0.473374\pi\)
0.0835502 + 0.996504i \(0.473374\pi\)
\(102\) −14.9379 −1.47907
\(103\) 0.793145 0.0781509 0.0390754 0.999236i \(-0.487559\pi\)
0.0390754 + 0.999236i \(0.487559\pi\)
\(104\) −5.82077 −0.570773
\(105\) −10.6702 −1.04131
\(106\) 9.33824 0.907010
\(107\) 12.3414 1.19309 0.596545 0.802579i \(-0.296540\pi\)
0.596545 + 0.802579i \(0.296540\pi\)
\(108\) −6.35534 −0.611543
\(109\) −1.00000 −0.0957826
\(110\) −16.0545 −1.53074
\(111\) −2.60153 −0.246926
\(112\) −0.432137 −0.0408331
\(113\) −7.35071 −0.691497 −0.345749 0.938327i \(-0.612375\pi\)
−0.345749 + 0.938327i \(0.612375\pi\)
\(114\) −18.8713 −1.76746
\(115\) −11.3971 −1.06279
\(116\) 15.0652 1.39876
\(117\) 8.15800 0.754207
\(118\) 6.63715 0.611000
\(119\) −4.49045 −0.411639
\(120\) 16.1152 1.47111
\(121\) −1.62947 −0.148133
\(122\) −13.5550 −1.22722
\(123\) 18.8159 1.69657
\(124\) −14.2224 −1.27721
\(125\) −10.8087 −0.966761
\(126\) −15.2671 −1.36010
\(127\) 9.40888 0.834904 0.417452 0.908699i \(-0.362923\pi\)
0.417452 + 0.908699i \(0.362923\pi\)
\(128\) 17.7571 1.56952
\(129\) −28.8233 −2.53775
\(130\) −11.3552 −0.995916
\(131\) 13.4113 1.17175 0.585874 0.810402i \(-0.300751\pi\)
0.585874 + 0.810402i \(0.300751\pi\)
\(132\) −25.3332 −2.20497
\(133\) −5.67285 −0.491899
\(134\) −33.4232 −2.88733
\(135\) −4.60325 −0.396185
\(136\) 6.78191 0.581544
\(137\) 0.961966 0.0821863 0.0410931 0.999155i \(-0.486916\pi\)
0.0410931 + 0.999155i \(0.486916\pi\)
\(138\) −29.2908 −2.49340
\(139\) −17.1814 −1.45731 −0.728653 0.684883i \(-0.759853\pi\)
−0.728653 + 0.684883i \(0.759853\pi\)
\(140\) 13.0474 1.10270
\(141\) −19.4490 −1.63790
\(142\) 6.07482 0.509787
\(143\) 6.62767 0.554233
\(144\) −0.914716 −0.0762263
\(145\) 10.9119 0.906182
\(146\) 15.2419 1.26143
\(147\) 9.96726 0.822086
\(148\) 3.18111 0.261486
\(149\) 6.61781 0.542152 0.271076 0.962558i \(-0.412621\pi\)
0.271076 + 0.962558i \(0.412621\pi\)
\(150\) 1.82951 0.149378
\(151\) −0.0342275 −0.00278540 −0.00139270 0.999999i \(-0.500443\pi\)
−0.00139270 + 0.999999i \(0.500443\pi\)
\(152\) 8.56768 0.694931
\(153\) −9.50507 −0.768439
\(154\) −12.4032 −0.999477
\(155\) −10.3015 −0.827435
\(156\) −17.9178 −1.43458
\(157\) 0.603937 0.0481994 0.0240997 0.999710i \(-0.492328\pi\)
0.0240997 + 0.999710i \(0.492328\pi\)
\(158\) −13.1436 −1.04565
\(159\) 10.6729 0.846416
\(160\) 13.6622 1.08009
\(161\) −8.80504 −0.693934
\(162\) 13.8994 1.09204
\(163\) −19.7366 −1.54589 −0.772943 0.634475i \(-0.781216\pi\)
−0.772943 + 0.634475i \(0.781216\pi\)
\(164\) −23.0078 −1.79660
\(165\) −18.3491 −1.42848
\(166\) −22.8695 −1.77501
\(167\) 9.92336 0.767893 0.383946 0.923355i \(-0.374565\pi\)
0.383946 + 0.923355i \(0.374565\pi\)
\(168\) 12.4500 0.960539
\(169\) −8.31233 −0.639410
\(170\) 13.2302 1.01471
\(171\) −12.0079 −0.918266
\(172\) 35.2447 2.68738
\(173\) 22.0909 1.67954 0.839769 0.542943i \(-0.182690\pi\)
0.839769 + 0.542943i \(0.182690\pi\)
\(174\) 28.0437 2.12599
\(175\) 0.549963 0.0415733
\(176\) −0.743128 −0.0560154
\(177\) 7.58576 0.570181
\(178\) −26.7209 −2.00282
\(179\) 24.1558 1.80549 0.902746 0.430175i \(-0.141548\pi\)
0.902746 + 0.430175i \(0.141548\pi\)
\(180\) 27.6177 2.05850
\(181\) 12.9350 0.961452 0.480726 0.876871i \(-0.340373\pi\)
0.480726 + 0.876871i \(0.340373\pi\)
\(182\) −8.77263 −0.650271
\(183\) −15.4924 −1.14523
\(184\) 13.2982 0.980356
\(185\) 2.30412 0.169402
\(186\) −26.4749 −1.94124
\(187\) −7.72205 −0.564692
\(188\) 23.7819 1.73447
\(189\) −3.55631 −0.258684
\(190\) 16.7139 1.21255
\(191\) −12.0463 −0.871642 −0.435821 0.900033i \(-0.643542\pi\)
−0.435821 + 0.900033i \(0.643542\pi\)
\(192\) 33.8489 2.44283
\(193\) −6.94115 −0.499635 −0.249817 0.968293i \(-0.580371\pi\)
−0.249817 + 0.968293i \(0.580371\pi\)
\(194\) −0.496863 −0.0356727
\(195\) −12.9781 −0.929382
\(196\) −12.1878 −0.870558
\(197\) −9.13803 −0.651058 −0.325529 0.945532i \(-0.605542\pi\)
−0.325529 + 0.945532i \(0.605542\pi\)
\(198\) −26.2542 −1.86580
\(199\) 1.17005 0.0829430 0.0414715 0.999140i \(-0.486795\pi\)
0.0414715 + 0.999140i \(0.486795\pi\)
\(200\) −0.830606 −0.0587327
\(201\) −38.2002 −2.69443
\(202\) −3.82252 −0.268952
\(203\) 8.43014 0.591680
\(204\) 20.8765 1.46165
\(205\) −16.6648 −1.16392
\(206\) −1.80536 −0.125785
\(207\) −18.6379 −1.29542
\(208\) −0.525606 −0.0364442
\(209\) −9.75538 −0.674793
\(210\) 24.2876 1.67600
\(211\) −9.49782 −0.653857 −0.326928 0.945049i \(-0.606014\pi\)
−0.326928 + 0.945049i \(0.606014\pi\)
\(212\) −13.0507 −0.896323
\(213\) 6.94305 0.475730
\(214\) −28.0916 −1.92030
\(215\) 25.5281 1.74100
\(216\) 5.37108 0.365456
\(217\) −7.95857 −0.540263
\(218\) 2.27621 0.154164
\(219\) 17.4203 1.17716
\(220\) 22.4370 1.51270
\(221\) −5.46171 −0.367395
\(222\) 5.92161 0.397433
\(223\) 6.74230 0.451498 0.225749 0.974186i \(-0.427517\pi\)
0.225749 + 0.974186i \(0.427517\pi\)
\(224\) 10.5549 0.705232
\(225\) 1.16412 0.0776082
\(226\) 16.7317 1.11298
\(227\) 6.33521 0.420483 0.210241 0.977650i \(-0.432575\pi\)
0.210241 + 0.977650i \(0.432575\pi\)
\(228\) 26.3736 1.74663
\(229\) −11.9262 −0.788103 −0.394051 0.919088i \(-0.628927\pi\)
−0.394051 + 0.919088i \(0.628927\pi\)
\(230\) 25.9422 1.71058
\(231\) −14.1759 −0.932705
\(232\) −12.7320 −0.835896
\(233\) 22.3073 1.46140 0.730700 0.682698i \(-0.239194\pi\)
0.730700 + 0.682698i \(0.239194\pi\)
\(234\) −18.5693 −1.21391
\(235\) 17.2255 1.12367
\(236\) −9.27575 −0.603800
\(237\) −15.0222 −0.975794
\(238\) 10.2212 0.662541
\(239\) −26.4152 −1.70866 −0.854329 0.519732i \(-0.826032\pi\)
−0.854329 + 0.519732i \(0.826032\pi\)
\(240\) 1.45517 0.0939309
\(241\) 5.64714 0.363764 0.181882 0.983320i \(-0.441781\pi\)
0.181882 + 0.983320i \(0.441781\pi\)
\(242\) 3.70900 0.238424
\(243\) 21.8795 1.40357
\(244\) 18.9438 1.21275
\(245\) −8.82779 −0.563987
\(246\) −42.8288 −2.73066
\(247\) −6.89986 −0.439028
\(248\) 12.0198 0.763257
\(249\) −26.1380 −1.65643
\(250\) 24.6029 1.55602
\(251\) 13.8354 0.873285 0.436642 0.899635i \(-0.356168\pi\)
0.436642 + 0.899635i \(0.356168\pi\)
\(252\) 21.3365 1.34407
\(253\) −15.1417 −0.951948
\(254\) −21.4166 −1.34379
\(255\) 15.1211 0.946920
\(256\) −14.3966 −0.899785
\(257\) 23.9869 1.49626 0.748132 0.663550i \(-0.230951\pi\)
0.748132 + 0.663550i \(0.230951\pi\)
\(258\) 65.6077 4.08455
\(259\) 1.78008 0.110609
\(260\) 15.8694 0.984181
\(261\) 17.8443 1.10454
\(262\) −30.5268 −1.88595
\(263\) 7.12389 0.439278 0.219639 0.975581i \(-0.429512\pi\)
0.219639 + 0.975581i \(0.429512\pi\)
\(264\) 21.4098 1.31768
\(265\) −9.45275 −0.580678
\(266\) 12.9126 0.791721
\(267\) −30.5399 −1.86901
\(268\) 46.7106 2.85330
\(269\) −3.57039 −0.217691 −0.108845 0.994059i \(-0.534715\pi\)
−0.108845 + 0.994059i \(0.534715\pi\)
\(270\) 10.4779 0.637668
\(271\) 14.5470 0.883669 0.441835 0.897097i \(-0.354328\pi\)
0.441835 + 0.897097i \(0.354328\pi\)
\(272\) 0.612395 0.0371319
\(273\) −10.0264 −0.606828
\(274\) −2.18963 −0.132280
\(275\) 0.945749 0.0570308
\(276\) 40.9353 2.46402
\(277\) −6.75810 −0.406055 −0.203027 0.979173i \(-0.565078\pi\)
−0.203027 + 0.979173i \(0.565078\pi\)
\(278\) 39.1083 2.34556
\(279\) −16.8461 −1.00855
\(280\) −11.0267 −0.658972
\(281\) 15.7938 0.942180 0.471090 0.882085i \(-0.343861\pi\)
0.471090 + 0.882085i \(0.343861\pi\)
\(282\) 44.2699 2.63623
\(283\) 3.42122 0.203371 0.101685 0.994817i \(-0.467577\pi\)
0.101685 + 0.994817i \(0.467577\pi\)
\(284\) −8.48986 −0.503780
\(285\) 19.1027 1.13155
\(286\) −15.0859 −0.892050
\(287\) −12.8747 −0.759967
\(288\) 22.3419 1.31651
\(289\) −10.6364 −0.625672
\(290\) −24.8377 −1.45852
\(291\) −0.567876 −0.0332895
\(292\) −21.3013 −1.24656
\(293\) 21.3139 1.24517 0.622587 0.782551i \(-0.286082\pi\)
0.622587 + 0.782551i \(0.286082\pi\)
\(294\) −22.6875 −1.32316
\(295\) −6.71854 −0.391169
\(296\) −2.68845 −0.156263
\(297\) −6.11565 −0.354866
\(298\) −15.0635 −0.872604
\(299\) −10.7095 −0.619347
\(300\) −2.55682 −0.147618
\(301\) 19.7222 1.13677
\(302\) 0.0779089 0.00448315
\(303\) −4.36885 −0.250984
\(304\) 0.773647 0.0443717
\(305\) 13.7213 0.785677
\(306\) 21.6355 1.23682
\(307\) 13.2408 0.755691 0.377845 0.925869i \(-0.376665\pi\)
0.377845 + 0.925869i \(0.376665\pi\)
\(308\) 17.3341 0.987700
\(309\) −2.06339 −0.117382
\(310\) 23.4483 1.33177
\(311\) −14.1311 −0.801299 −0.400649 0.916232i \(-0.631215\pi\)
−0.400649 + 0.916232i \(0.631215\pi\)
\(312\) 15.1429 0.857297
\(313\) −15.4827 −0.875132 −0.437566 0.899186i \(-0.644159\pi\)
−0.437566 + 0.899186i \(0.644159\pi\)
\(314\) −1.37468 −0.0775779
\(315\) 15.4543 0.870751
\(316\) 18.3689 1.03333
\(317\) −21.1989 −1.19065 −0.595325 0.803485i \(-0.702977\pi\)
−0.595325 + 0.803485i \(0.702977\pi\)
\(318\) −24.2937 −1.36232
\(319\) 14.4970 0.811674
\(320\) −29.9792 −1.67589
\(321\) −32.1066 −1.79201
\(322\) 20.0421 1.11690
\(323\) 8.03919 0.447312
\(324\) −19.4252 −1.07918
\(325\) 0.668917 0.0371049
\(326\) 44.9245 2.48814
\(327\) 2.60153 0.143865
\(328\) 19.4445 1.07364
\(329\) 13.3079 0.733686
\(330\) 41.7663 2.29916
\(331\) 8.52828 0.468757 0.234378 0.972145i \(-0.424695\pi\)
0.234378 + 0.972145i \(0.424695\pi\)
\(332\) 31.9612 1.75410
\(333\) 3.76795 0.206482
\(334\) −22.5876 −1.23594
\(335\) 33.8331 1.84850
\(336\) 1.12422 0.0613310
\(337\) −26.3753 −1.43675 −0.718377 0.695654i \(-0.755115\pi\)
−0.718377 + 0.695654i \(0.755115\pi\)
\(338\) 18.9206 1.02914
\(339\) 19.1231 1.03862
\(340\) −18.4899 −1.00275
\(341\) −13.6860 −0.741140
\(342\) 27.3324 1.47797
\(343\) −19.2806 −1.04106
\(344\) −29.7863 −1.60597
\(345\) 29.6500 1.59630
\(346\) −50.2834 −2.70325
\(347\) −1.09619 −0.0588468 −0.0294234 0.999567i \(-0.509367\pi\)
−0.0294234 + 0.999567i \(0.509367\pi\)
\(348\) −39.1924 −2.10093
\(349\) 33.8074 1.80967 0.904835 0.425761i \(-0.139994\pi\)
0.904835 + 0.425761i \(0.139994\pi\)
\(350\) −1.25183 −0.0669131
\(351\) −4.32553 −0.230880
\(352\) 18.1509 0.967446
\(353\) −8.07857 −0.429979 −0.214990 0.976616i \(-0.568972\pi\)
−0.214990 + 0.976616i \(0.568972\pi\)
\(354\) −17.2667 −0.917717
\(355\) −6.14931 −0.326371
\(356\) 37.3438 1.97922
\(357\) 11.6820 0.618279
\(358\) −54.9836 −2.90597
\(359\) 21.8228 1.15177 0.575883 0.817532i \(-0.304659\pi\)
0.575883 + 0.817532i \(0.304659\pi\)
\(360\) −23.3405 −1.23015
\(361\) −8.84398 −0.465473
\(362\) −29.4427 −1.54748
\(363\) 4.23910 0.222495
\(364\) 12.2602 0.642608
\(365\) −15.4288 −0.807580
\(366\) 35.2638 1.84327
\(367\) 27.7672 1.44944 0.724719 0.689044i \(-0.241969\pi\)
0.724719 + 0.689044i \(0.241969\pi\)
\(368\) 1.20081 0.0625963
\(369\) −27.2521 −1.41869
\(370\) −5.24464 −0.272656
\(371\) −7.30287 −0.379146
\(372\) 37.0000 1.91836
\(373\) 16.1304 0.835200 0.417600 0.908631i \(-0.362871\pi\)
0.417600 + 0.908631i \(0.362871\pi\)
\(374\) 17.5770 0.908883
\(375\) 28.1192 1.45207
\(376\) −20.0988 −1.03652
\(377\) 10.2535 0.528084
\(378\) 8.09490 0.416357
\(379\) 27.0434 1.38913 0.694563 0.719432i \(-0.255598\pi\)
0.694563 + 0.719432i \(0.255598\pi\)
\(380\) −23.3585 −1.19827
\(381\) −24.4775 −1.25402
\(382\) 27.4199 1.40293
\(383\) 28.9379 1.47866 0.739328 0.673345i \(-0.235143\pi\)
0.739328 + 0.673345i \(0.235143\pi\)
\(384\) −46.1957 −2.35741
\(385\) 12.5553 0.639876
\(386\) 15.7995 0.804172
\(387\) 41.7464 2.12209
\(388\) 0.694390 0.0352523
\(389\) 26.0718 1.32189 0.660946 0.750433i \(-0.270155\pi\)
0.660946 + 0.750433i \(0.270155\pi\)
\(390\) 29.5409 1.49586
\(391\) 12.4779 0.631035
\(392\) 10.3003 0.520242
\(393\) −34.8898 −1.75996
\(394\) 20.8000 1.04789
\(395\) 13.3048 0.669437
\(396\) 36.6915 1.84382
\(397\) −5.57264 −0.279683 −0.139841 0.990174i \(-0.544659\pi\)
−0.139841 + 0.990174i \(0.544659\pi\)
\(398\) −2.66328 −0.133498
\(399\) 14.7581 0.738829
\(400\) −0.0750024 −0.00375012
\(401\) −7.45875 −0.372472 −0.186236 0.982505i \(-0.559629\pi\)
−0.186236 + 0.982505i \(0.559629\pi\)
\(402\) 86.9514 4.33674
\(403\) −9.67997 −0.482193
\(404\) 5.34216 0.265782
\(405\) −14.0699 −0.699138
\(406\) −19.1887 −0.952321
\(407\) 3.06113 0.151735
\(408\) −17.6433 −0.873474
\(409\) −26.7456 −1.32248 −0.661242 0.750173i \(-0.729970\pi\)
−0.661242 + 0.750173i \(0.729970\pi\)
\(410\) 37.9325 1.87335
\(411\) −2.50258 −0.123443
\(412\) 2.52308 0.124303
\(413\) −5.19051 −0.255408
\(414\) 42.4236 2.08501
\(415\) 23.1499 1.13638
\(416\) 12.8379 0.629431
\(417\) 44.6978 2.18886
\(418\) 22.2052 1.08609
\(419\) −20.2407 −0.988824 −0.494412 0.869228i \(-0.664617\pi\)
−0.494412 + 0.869228i \(0.664617\pi\)
\(420\) −33.9431 −1.65625
\(421\) 12.8898 0.628210 0.314105 0.949388i \(-0.398296\pi\)
0.314105 + 0.949388i \(0.398296\pi\)
\(422\) 21.6190 1.05240
\(423\) 28.1691 1.36963
\(424\) 11.0295 0.535639
\(425\) −0.779371 −0.0378050
\(426\) −15.8038 −0.765697
\(427\) 10.6006 0.512997
\(428\) 39.2594 1.89768
\(429\) −17.2421 −0.832455
\(430\) −58.1073 −2.80218
\(431\) −19.9228 −0.959647 −0.479824 0.877365i \(-0.659299\pi\)
−0.479824 + 0.877365i \(0.659299\pi\)
\(432\) 0.485000 0.0233346
\(433\) 32.8998 1.58106 0.790532 0.612420i \(-0.209804\pi\)
0.790532 + 0.612420i \(0.209804\pi\)
\(434\) 18.1153 0.869564
\(435\) −28.3876 −1.36108
\(436\) −3.18111 −0.152348
\(437\) 15.7635 0.754071
\(438\) −39.6522 −1.89466
\(439\) −0.709157 −0.0338462 −0.0169231 0.999857i \(-0.505387\pi\)
−0.0169231 + 0.999857i \(0.505387\pi\)
\(440\) −18.9622 −0.903986
\(441\) −14.4362 −0.687437
\(442\) 12.4320 0.591329
\(443\) 13.9415 0.662379 0.331189 0.943564i \(-0.392550\pi\)
0.331189 + 0.943564i \(0.392550\pi\)
\(444\) −8.27574 −0.392749
\(445\) 27.0485 1.28222
\(446\) −15.3469 −0.726695
\(447\) −17.2164 −0.814308
\(448\) −23.1609 −1.09425
\(449\) 7.39625 0.349051 0.174525 0.984653i \(-0.444161\pi\)
0.174525 + 0.984653i \(0.444161\pi\)
\(450\) −2.64978 −0.124912
\(451\) −22.1400 −1.04253
\(452\) −23.3834 −1.09986
\(453\) 0.0890439 0.00418365
\(454\) −14.4202 −0.676776
\(455\) 8.88020 0.416310
\(456\) −22.2891 −1.04378
\(457\) −21.2702 −0.994976 −0.497488 0.867471i \(-0.665744\pi\)
−0.497488 + 0.867471i \(0.665744\pi\)
\(458\) 27.1464 1.26847
\(459\) 5.03977 0.235236
\(460\) −36.2555 −1.69042
\(461\) −4.36175 −0.203147 −0.101573 0.994828i \(-0.532388\pi\)
−0.101573 + 0.994828i \(0.532388\pi\)
\(462\) 32.2672 1.50121
\(463\) −23.2399 −1.08005 −0.540026 0.841649i \(-0.681585\pi\)
−0.540026 + 0.841649i \(0.681585\pi\)
\(464\) −1.14968 −0.0533725
\(465\) 26.7996 1.24280
\(466\) −50.7760 −2.35215
\(467\) 37.6605 1.74272 0.871360 0.490645i \(-0.163239\pi\)
0.871360 + 0.490645i \(0.163239\pi\)
\(468\) 25.9515 1.19961
\(469\) 26.1383 1.20695
\(470\) −39.2089 −1.80857
\(471\) −1.57116 −0.0723951
\(472\) 7.83920 0.360829
\(473\) 33.9154 1.55943
\(474\) 34.1935 1.57056
\(475\) −0.984590 −0.0451761
\(476\) −14.2846 −0.654735
\(477\) −15.4582 −0.707782
\(478\) 60.1265 2.75012
\(479\) 18.8384 0.860749 0.430374 0.902651i \(-0.358382\pi\)
0.430374 + 0.902651i \(0.358382\pi\)
\(480\) −35.5426 −1.62229
\(481\) 2.16510 0.0987202
\(482\) −12.8540 −0.585485
\(483\) 22.9065 1.04228
\(484\) −5.18351 −0.235614
\(485\) 0.502956 0.0228380
\(486\) −49.8023 −2.25908
\(487\) −10.3555 −0.469251 −0.234625 0.972086i \(-0.575386\pi\)
−0.234625 + 0.972086i \(0.575386\pi\)
\(488\) −16.0100 −0.724738
\(489\) 51.3452 2.32191
\(490\) 20.0939 0.907748
\(491\) 41.7718 1.88514 0.942568 0.334013i \(-0.108403\pi\)
0.942568 + 0.334013i \(0.108403\pi\)
\(492\) 59.8553 2.69849
\(493\) −11.9466 −0.538049
\(494\) 15.7055 0.706624
\(495\) 26.5761 1.19451
\(496\) 1.08537 0.0487344
\(497\) −4.75074 −0.213100
\(498\) 59.4955 2.66606
\(499\) 11.4619 0.513106 0.256553 0.966530i \(-0.417413\pi\)
0.256553 + 0.966530i \(0.417413\pi\)
\(500\) −34.3837 −1.53769
\(501\) −25.8159 −1.15337
\(502\) −31.4923 −1.40557
\(503\) 0.661678 0.0295028 0.0147514 0.999891i \(-0.495304\pi\)
0.0147514 + 0.999891i \(0.495304\pi\)
\(504\) −18.0321 −0.803213
\(505\) 3.86939 0.172186
\(506\) 34.4655 1.53218
\(507\) 21.6248 0.960389
\(508\) 29.9307 1.32796
\(509\) 4.60859 0.204272 0.102136 0.994770i \(-0.467432\pi\)
0.102136 + 0.994770i \(0.467432\pi\)
\(510\) −34.4187 −1.52409
\(511\) −11.9198 −0.527299
\(512\) −2.74476 −0.121302
\(513\) 6.36681 0.281102
\(514\) −54.5992 −2.40827
\(515\) 1.82750 0.0805292
\(516\) −91.6899 −4.03642
\(517\) 22.8850 1.00648
\(518\) −4.05183 −0.178027
\(519\) −57.4701 −2.52266
\(520\) −13.4117 −0.588143
\(521\) −27.7391 −1.21527 −0.607636 0.794216i \(-0.707882\pi\)
−0.607636 + 0.794216i \(0.707882\pi\)
\(522\) −40.6173 −1.77777
\(523\) 19.4634 0.851074 0.425537 0.904941i \(-0.360085\pi\)
0.425537 + 0.904941i \(0.360085\pi\)
\(524\) 42.6627 1.86373
\(525\) −1.43074 −0.0624428
\(526\) −16.2154 −0.707027
\(527\) 11.2783 0.491293
\(528\) 1.93327 0.0841347
\(529\) 1.46710 0.0637870
\(530\) 21.5164 0.934613
\(531\) −10.9869 −0.476791
\(532\) −18.0460 −0.782392
\(533\) −15.6594 −0.678283
\(534\) 69.5151 3.00821
\(535\) 28.4361 1.22940
\(536\) −39.4765 −1.70512
\(537\) −62.8421 −2.71184
\(538\) 8.12695 0.350378
\(539\) −11.7281 −0.505167
\(540\) −14.6434 −0.630154
\(541\) −42.4407 −1.82467 −0.912333 0.409448i \(-0.865721\pi\)
−0.912333 + 0.409448i \(0.865721\pi\)
\(542\) −33.1120 −1.42228
\(543\) −33.6508 −1.44409
\(544\) −14.9577 −0.641308
\(545\) −2.30412 −0.0986975
\(546\) 22.8222 0.976702
\(547\) −2.03806 −0.0871410 −0.0435705 0.999050i \(-0.513873\pi\)
−0.0435705 + 0.999050i \(0.513873\pi\)
\(548\) 3.06012 0.130722
\(549\) 22.4385 0.957653
\(550\) −2.15272 −0.0917922
\(551\) −15.0923 −0.642956
\(552\) −34.5956 −1.47249
\(553\) 10.2788 0.437100
\(554\) 15.3828 0.653553
\(555\) −5.99422 −0.254441
\(556\) −54.6559 −2.31792
\(557\) −28.6139 −1.21241 −0.606204 0.795309i \(-0.707309\pi\)
−0.606204 + 0.795309i \(0.707309\pi\)
\(558\) 38.3452 1.62328
\(559\) 23.9880 1.01458
\(560\) −0.995693 −0.0420757
\(561\) 20.0891 0.848163
\(562\) −35.9500 −1.51646
\(563\) −9.54571 −0.402304 −0.201152 0.979560i \(-0.564468\pi\)
−0.201152 + 0.979560i \(0.564468\pi\)
\(564\) −61.8693 −2.60517
\(565\) −16.9369 −0.712541
\(566\) −7.78741 −0.327329
\(567\) −10.8699 −0.456493
\(568\) 7.17502 0.301057
\(569\) 39.3428 1.64933 0.824667 0.565618i \(-0.191362\pi\)
0.824667 + 0.565618i \(0.191362\pi\)
\(570\) −43.4817 −1.82125
\(571\) −4.95288 −0.207272 −0.103636 0.994615i \(-0.533048\pi\)
−0.103636 + 0.994615i \(0.533048\pi\)
\(572\) 21.0833 0.881539
\(573\) 31.3389 1.30920
\(574\) 29.3054 1.22318
\(575\) −1.52822 −0.0637311
\(576\) −49.0254 −2.04272
\(577\) −7.41897 −0.308856 −0.154428 0.988004i \(-0.549353\pi\)
−0.154428 + 0.988004i \(0.549353\pi\)
\(578\) 24.2107 1.00703
\(579\) 18.0576 0.750448
\(580\) 34.7119 1.44133
\(581\) 17.8848 0.741987
\(582\) 1.29260 0.0535801
\(583\) −12.5584 −0.520118
\(584\) 18.0023 0.744942
\(585\) 18.7970 0.777159
\(586\) −48.5149 −2.00413
\(587\) −25.6191 −1.05741 −0.528707 0.848805i \(-0.677323\pi\)
−0.528707 + 0.848805i \(0.677323\pi\)
\(588\) 31.7069 1.30757
\(589\) 14.2481 0.587083
\(590\) 15.2928 0.629594
\(591\) 23.7728 0.977884
\(592\) −0.242762 −0.00997747
\(593\) 7.74015 0.317850 0.158925 0.987291i \(-0.449197\pi\)
0.158925 + 0.987291i \(0.449197\pi\)
\(594\) 13.9205 0.571164
\(595\) −10.3465 −0.424166
\(596\) 21.0520 0.862322
\(597\) −3.04393 −0.124580
\(598\) 24.3771 0.996852
\(599\) −19.4907 −0.796367 −0.398184 0.917306i \(-0.630359\pi\)
−0.398184 + 0.917306i \(0.630359\pi\)
\(600\) 2.16085 0.0882162
\(601\) 21.3851 0.872318 0.436159 0.899870i \(-0.356339\pi\)
0.436159 + 0.899870i \(0.356339\pi\)
\(602\) −44.8917 −1.82965
\(603\) 55.3276 2.25311
\(604\) −0.108882 −0.00443033
\(605\) −3.75448 −0.152641
\(606\) 9.94439 0.403963
\(607\) −31.6412 −1.28428 −0.642138 0.766589i \(-0.721953\pi\)
−0.642138 + 0.766589i \(0.721953\pi\)
\(608\) −18.8963 −0.766348
\(609\) −21.9312 −0.888699
\(610\) −31.2324 −1.26456
\(611\) 16.1863 0.654827
\(612\) −30.2367 −1.22224
\(613\) 12.4421 0.502531 0.251265 0.967918i \(-0.419153\pi\)
0.251265 + 0.967918i \(0.419153\pi\)
\(614\) −30.1387 −1.21630
\(615\) 43.3540 1.74820
\(616\) −14.6495 −0.590246
\(617\) −1.84147 −0.0741346 −0.0370673 0.999313i \(-0.511802\pi\)
−0.0370673 + 0.999313i \(0.511802\pi\)
\(618\) 4.69669 0.188929
\(619\) −33.5204 −1.34730 −0.673650 0.739051i \(-0.735274\pi\)
−0.673650 + 0.739051i \(0.735274\pi\)
\(620\) −32.7701 −1.31608
\(621\) 9.88215 0.396557
\(622\) 32.1652 1.28971
\(623\) 20.8968 0.837212
\(624\) 1.36738 0.0547389
\(625\) −26.4493 −1.05797
\(626\) 35.2417 1.40854
\(627\) 25.3789 1.01353
\(628\) 1.92119 0.0766637
\(629\) −2.52261 −0.100583
\(630\) −35.1771 −1.40149
\(631\) 31.6029 1.25809 0.629045 0.777369i \(-0.283446\pi\)
0.629045 + 0.777369i \(0.283446\pi\)
\(632\) −15.5241 −0.617514
\(633\) 24.7088 0.982088
\(634\) 48.2531 1.91638
\(635\) 21.6792 0.860312
\(636\) 33.9516 1.34627
\(637\) −8.29518 −0.328667
\(638\) −32.9981 −1.30641
\(639\) −10.0560 −0.397811
\(640\) 40.9145 1.61729
\(641\) −43.4450 −1.71597 −0.857987 0.513672i \(-0.828285\pi\)
−0.857987 + 0.513672i \(0.828285\pi\)
\(642\) 73.0811 2.88428
\(643\) −29.3200 −1.15627 −0.578134 0.815942i \(-0.696219\pi\)
−0.578134 + 0.815942i \(0.696219\pi\)
\(644\) −28.0098 −1.10374
\(645\) −66.4122 −2.61498
\(646\) −18.2988 −0.719958
\(647\) 32.3450 1.27161 0.635807 0.771848i \(-0.280668\pi\)
0.635807 + 0.771848i \(0.280668\pi\)
\(648\) 16.4168 0.644911
\(649\) −8.92591 −0.350373
\(650\) −1.52259 −0.0597210
\(651\) 20.7044 0.811471
\(652\) −62.7842 −2.45882
\(653\) 13.4291 0.525523 0.262761 0.964861i \(-0.415367\pi\)
0.262761 + 0.964861i \(0.415367\pi\)
\(654\) −5.92161 −0.231553
\(655\) 30.9012 1.20741
\(656\) 1.75581 0.0685528
\(657\) −25.2309 −0.984350
\(658\) −30.2914 −1.18088
\(659\) −25.3452 −0.987310 −0.493655 0.869658i \(-0.664339\pi\)
−0.493655 + 0.869658i \(0.664339\pi\)
\(660\) −58.3705 −2.27207
\(661\) −11.0144 −0.428411 −0.214205 0.976789i \(-0.568716\pi\)
−0.214205 + 0.976789i \(0.568716\pi\)
\(662\) −19.4121 −0.754473
\(663\) 14.2088 0.551824
\(664\) −27.0113 −1.04824
\(665\) −13.0709 −0.506869
\(666\) −8.57662 −0.332337
\(667\) −23.4254 −0.907033
\(668\) 31.5673 1.22138
\(669\) −17.5403 −0.678147
\(670\) −77.0110 −2.97519
\(671\) 18.2294 0.703737
\(672\) −27.4590 −1.05925
\(673\) 29.2102 1.12597 0.562985 0.826467i \(-0.309653\pi\)
0.562985 + 0.826467i \(0.309653\pi\)
\(674\) 60.0356 2.31248
\(675\) −0.617240 −0.0237576
\(676\) −26.4424 −1.01702
\(677\) 19.6309 0.754478 0.377239 0.926116i \(-0.376874\pi\)
0.377239 + 0.926116i \(0.376874\pi\)
\(678\) −43.5281 −1.67169
\(679\) 0.388566 0.0149118
\(680\) 15.6263 0.599241
\(681\) −16.4812 −0.631562
\(682\) 31.1522 1.19288
\(683\) −41.0700 −1.57150 −0.785749 0.618545i \(-0.787722\pi\)
−0.785749 + 0.618545i \(0.787722\pi\)
\(684\) −38.1984 −1.46055
\(685\) 2.21648 0.0846874
\(686\) 43.8866 1.67560
\(687\) 31.0262 1.18372
\(688\) −2.68965 −0.102542
\(689\) −8.88244 −0.338394
\(690\) −67.4894 −2.56928
\(691\) −3.77631 −0.143658 −0.0718288 0.997417i \(-0.522884\pi\)
−0.0718288 + 0.997417i \(0.522884\pi\)
\(692\) 70.2735 2.67140
\(693\) 20.5318 0.779938
\(694\) 2.49516 0.0947151
\(695\) −39.5879 −1.50165
\(696\) 33.1226 1.25551
\(697\) 18.2451 0.691082
\(698\) −76.9527 −2.91270
\(699\) −58.0331 −2.19501
\(700\) 1.74949 0.0661246
\(701\) −36.7183 −1.38683 −0.693416 0.720538i \(-0.743895\pi\)
−0.693416 + 0.720538i \(0.743895\pi\)
\(702\) 9.84578 0.371605
\(703\) −3.18685 −0.120194
\(704\) −39.8289 −1.50111
\(705\) −44.8127 −1.68774
\(706\) 18.3885 0.692060
\(707\) 2.98936 0.112426
\(708\) 24.1311 0.906903
\(709\) 24.8667 0.933889 0.466945 0.884287i \(-0.345355\pi\)
0.466945 + 0.884287i \(0.345355\pi\)
\(710\) 13.9971 0.525301
\(711\) 21.7575 0.815969
\(712\) −31.5603 −1.18277
\(713\) 22.1150 0.828212
\(714\) −26.5907 −0.995133
\(715\) 15.2709 0.571100
\(716\) 76.8423 2.87173
\(717\) 68.7199 2.56639
\(718\) −49.6732 −1.85379
\(719\) 23.2438 0.866846 0.433423 0.901191i \(-0.357306\pi\)
0.433423 + 0.901191i \(0.357306\pi\)
\(720\) −2.10761 −0.0785461
\(721\) 1.41186 0.0525805
\(722\) 20.1307 0.749187
\(723\) −14.6912 −0.546371
\(724\) 41.1477 1.52924
\(725\) 1.46315 0.0543400
\(726\) −9.64907 −0.358111
\(727\) −2.05092 −0.0760643 −0.0380321 0.999277i \(-0.512109\pi\)
−0.0380321 + 0.999277i \(0.512109\pi\)
\(728\) −10.3614 −0.384020
\(729\) −38.6009 −1.42966
\(730\) 35.1191 1.29982
\(731\) −27.9489 −1.03373
\(732\) −49.2829 −1.82155
\(733\) −13.0524 −0.482102 −0.241051 0.970512i \(-0.577492\pi\)
−0.241051 + 0.970512i \(0.577492\pi\)
\(734\) −63.2039 −2.33290
\(735\) 22.9657 0.847104
\(736\) −29.3297 −1.08111
\(737\) 44.9489 1.65571
\(738\) 62.0315 2.28341
\(739\) −7.45642 −0.274289 −0.137144 0.990551i \(-0.543792\pi\)
−0.137144 + 0.990551i \(0.543792\pi\)
\(740\) 7.32965 0.269443
\(741\) 17.9502 0.659417
\(742\) 16.6228 0.610243
\(743\) −23.4636 −0.860796 −0.430398 0.902639i \(-0.641627\pi\)
−0.430398 + 0.902639i \(0.641627\pi\)
\(744\) −31.2698 −1.14641
\(745\) 15.2482 0.558651
\(746\) −36.7161 −1.34427
\(747\) 37.8573 1.38513
\(748\) −24.5647 −0.898174
\(749\) 21.9687 0.802720
\(750\) −64.0050 −2.33713
\(751\) −32.2120 −1.17543 −0.587716 0.809067i \(-0.699973\pi\)
−0.587716 + 0.809067i \(0.699973\pi\)
\(752\) −1.81489 −0.0661821
\(753\) −35.9933 −1.31167
\(754\) −23.3391 −0.849962
\(755\) −0.0788643 −0.00287016
\(756\) −11.3130 −0.411451
\(757\) 48.7545 1.77201 0.886006 0.463673i \(-0.153469\pi\)
0.886006 + 0.463673i \(0.153469\pi\)
\(758\) −61.5563 −2.23583
\(759\) 39.3914 1.42982
\(760\) 19.7409 0.716079
\(761\) 22.9274 0.831119 0.415560 0.909566i \(-0.363586\pi\)
0.415560 + 0.909566i \(0.363586\pi\)
\(762\) 55.7158 2.01837
\(763\) −1.78008 −0.0644433
\(764\) −38.3207 −1.38639
\(765\) −21.9008 −0.791825
\(766\) −65.8686 −2.37993
\(767\) −6.31319 −0.227956
\(768\) 37.4531 1.35147
\(769\) 13.6321 0.491588 0.245794 0.969322i \(-0.420951\pi\)
0.245794 + 0.969322i \(0.420951\pi\)
\(770\) −28.5784 −1.02989
\(771\) −62.4027 −2.24738
\(772\) −22.0806 −0.794697
\(773\) −1.06631 −0.0383525 −0.0191763 0.999816i \(-0.506104\pi\)
−0.0191763 + 0.999816i \(0.506104\pi\)
\(774\) −95.0235 −3.41555
\(775\) −1.38130 −0.0496179
\(776\) −0.586849 −0.0210667
\(777\) −4.63093 −0.166134
\(778\) −59.3447 −2.12761
\(779\) 23.0493 0.825827
\(780\) −41.2848 −1.47823
\(781\) −8.16966 −0.292333
\(782\) −28.4023 −1.01566
\(783\) −9.46140 −0.338123
\(784\) 0.930098 0.0332178
\(785\) 1.39154 0.0496662
\(786\) 79.4164 2.83269
\(787\) 40.9392 1.45932 0.729662 0.683808i \(-0.239678\pi\)
0.729662 + 0.683808i \(0.239678\pi\)
\(788\) −29.0691 −1.03554
\(789\) −18.5330 −0.659793
\(790\) −30.2844 −1.07747
\(791\) −13.0849 −0.465244
\(792\) −31.0091 −1.10186
\(793\) 12.8934 0.457859
\(794\) 12.6845 0.450155
\(795\) 24.5916 0.872174
\(796\) 3.72207 0.131925
\(797\) −20.2227 −0.716323 −0.358162 0.933660i \(-0.616596\pi\)
−0.358162 + 0.933660i \(0.616596\pi\)
\(798\) −33.5924 −1.18916
\(799\) −18.8590 −0.667184
\(800\) 1.83193 0.0647686
\(801\) 44.2328 1.56289
\(802\) 16.9776 0.599502
\(803\) −20.4979 −0.723356
\(804\) −121.519 −4.28564
\(805\) −20.2878 −0.715052
\(806\) 22.0336 0.776100
\(807\) 9.28848 0.326970
\(808\) −4.51481 −0.158831
\(809\) 39.8473 1.40096 0.700479 0.713673i \(-0.252970\pi\)
0.700479 + 0.713673i \(0.252970\pi\)
\(810\) 32.0259 1.12528
\(811\) −40.2351 −1.41284 −0.706422 0.707791i \(-0.749692\pi\)
−0.706422 + 0.707791i \(0.749692\pi\)
\(812\) 26.8172 0.941099
\(813\) −37.8445 −1.32726
\(814\) −6.96777 −0.244220
\(815\) −45.4753 −1.59293
\(816\) −1.59316 −0.0557719
\(817\) −35.3083 −1.23528
\(818\) 60.8784 2.12856
\(819\) 14.5219 0.507436
\(820\) −53.0126 −1.85128
\(821\) 10.2981 0.359406 0.179703 0.983721i \(-0.442486\pi\)
0.179703 + 0.983721i \(0.442486\pi\)
\(822\) 5.69639 0.198684
\(823\) −0.385341 −0.0134322 −0.00671608 0.999977i \(-0.502138\pi\)
−0.00671608 + 0.999977i \(0.502138\pi\)
\(824\) −2.13233 −0.0742831
\(825\) −2.46039 −0.0856599
\(826\) 11.8147 0.411085
\(827\) 25.4124 0.883674 0.441837 0.897095i \(-0.354327\pi\)
0.441837 + 0.897095i \(0.354327\pi\)
\(828\) −59.2891 −2.06044
\(829\) −24.1983 −0.840441 −0.420220 0.907422i \(-0.638047\pi\)
−0.420220 + 0.907422i \(0.638047\pi\)
\(830\) −52.6939 −1.82903
\(831\) 17.5814 0.609891
\(832\) −28.1705 −0.976637
\(833\) 9.66491 0.334869
\(834\) −101.741 −3.52302
\(835\) 22.8646 0.791261
\(836\) −31.0329 −1.07330
\(837\) 8.93214 0.308740
\(838\) 46.0720 1.59153
\(839\) 21.5310 0.743334 0.371667 0.928366i \(-0.378786\pi\)
0.371667 + 0.928366i \(0.378786\pi\)
\(840\) 28.6863 0.989771
\(841\) −6.57203 −0.226622
\(842\) −29.3398 −1.01112
\(843\) −41.0881 −1.41515
\(844\) −30.2136 −1.03999
\(845\) −19.1526 −0.658869
\(846\) −64.1187 −2.20445
\(847\) −2.90058 −0.0996652
\(848\) 0.995944 0.0342009
\(849\) −8.90041 −0.305461
\(850\) 1.77401 0.0608480
\(851\) −4.94642 −0.169561
\(852\) 22.0866 0.756675
\(853\) 23.7664 0.813745 0.406872 0.913485i \(-0.366619\pi\)
0.406872 + 0.913485i \(0.366619\pi\)
\(854\) −24.1291 −0.825680
\(855\) −27.6676 −0.946211
\(856\) −33.1793 −1.13404
\(857\) 13.5643 0.463347 0.231673 0.972794i \(-0.425580\pi\)
0.231673 + 0.972794i \(0.425580\pi\)
\(858\) 39.2465 1.33985
\(859\) 2.32578 0.0793546 0.0396773 0.999213i \(-0.487367\pi\)
0.0396773 + 0.999213i \(0.487367\pi\)
\(860\) 81.2078 2.76916
\(861\) 33.4938 1.14146
\(862\) 45.3484 1.54457
\(863\) 45.2954 1.54187 0.770936 0.636912i \(-0.219789\pi\)
0.770936 + 0.636912i \(0.219789\pi\)
\(864\) −11.8461 −0.403013
\(865\) 50.9000 1.73065
\(866\) −74.8867 −2.54475
\(867\) 27.6710 0.939756
\(868\) −25.3171 −0.859318
\(869\) 17.6761 0.599620
\(870\) 64.6159 2.19068
\(871\) 31.7918 1.07722
\(872\) 2.68845 0.0910423
\(873\) 0.822489 0.0278370
\(874\) −35.8810 −1.21369
\(875\) −19.2404 −0.650444
\(876\) 55.4159 1.87233
\(877\) −10.3254 −0.348664 −0.174332 0.984687i \(-0.555777\pi\)
−0.174332 + 0.984687i \(0.555777\pi\)
\(878\) 1.61419 0.0544762
\(879\) −55.4488 −1.87024
\(880\) −1.71225 −0.0577200
\(881\) 39.2242 1.32150 0.660748 0.750608i \(-0.270239\pi\)
0.660748 + 0.750608i \(0.270239\pi\)
\(882\) 32.8597 1.10644
\(883\) 6.47276 0.217826 0.108913 0.994051i \(-0.465263\pi\)
0.108913 + 0.994051i \(0.465263\pi\)
\(884\) −17.3743 −0.584361
\(885\) 17.4785 0.587532
\(886\) −31.7336 −1.06611
\(887\) −15.6828 −0.526576 −0.263288 0.964717i \(-0.584807\pi\)
−0.263288 + 0.964717i \(0.584807\pi\)
\(888\) 6.99407 0.234706
\(889\) 16.7486 0.561729
\(890\) −61.5680 −2.06377
\(891\) −18.6925 −0.626224
\(892\) 21.4480 0.718132
\(893\) −23.8249 −0.797268
\(894\) 39.1881 1.31065
\(895\) 55.6579 1.86044
\(896\) 31.6092 1.05599
\(897\) 27.8611 0.930255
\(898\) −16.8354 −0.561804
\(899\) −21.1734 −0.706172
\(900\) 3.70320 0.123440
\(901\) 10.3491 0.344780
\(902\) 50.3952 1.67798
\(903\) −51.3078 −1.70742
\(904\) 19.7620 0.657275
\(905\) 29.8038 0.990711
\(906\) −0.202682 −0.00673367
\(907\) 39.0872 1.29787 0.648935 0.760844i \(-0.275215\pi\)
0.648935 + 0.760844i \(0.275215\pi\)
\(908\) 20.1530 0.668801
\(909\) 6.32766 0.209875
\(910\) −20.2132 −0.670060
\(911\) 28.8625 0.956256 0.478128 0.878290i \(-0.341315\pi\)
0.478128 + 0.878290i \(0.341315\pi\)
\(912\) −2.01267 −0.0666460
\(913\) 30.7558 1.01787
\(914\) 48.4152 1.60143
\(915\) −35.6962 −1.18008
\(916\) −37.9384 −1.25352
\(917\) 23.8732 0.788361
\(918\) −11.4715 −0.378617
\(919\) −9.09122 −0.299892 −0.149946 0.988694i \(-0.547910\pi\)
−0.149946 + 0.988694i \(0.547910\pi\)
\(920\) 30.6406 1.01019
\(921\) −34.4462 −1.13504
\(922\) 9.92824 0.326969
\(923\) −5.77830 −0.190195
\(924\) −45.0951 −1.48352
\(925\) 0.308954 0.0101583
\(926\) 52.8989 1.73836
\(927\) 2.98853 0.0981561
\(928\) 28.0809 0.921800
\(929\) 14.8996 0.488839 0.244420 0.969670i \(-0.421403\pi\)
0.244420 + 0.969670i \(0.421403\pi\)
\(930\) −61.0014 −2.00031
\(931\) 12.2098 0.400161
\(932\) 70.9620 2.32444
\(933\) 36.7623 1.20354
\(934\) −85.7230 −2.80494
\(935\) −17.7925 −0.581877
\(936\) −21.9323 −0.716881
\(937\) −21.3836 −0.698570 −0.349285 0.937016i \(-0.613576\pi\)
−0.349285 + 0.937016i \(0.613576\pi\)
\(938\) −59.4960 −1.94261
\(939\) 40.2786 1.31444
\(940\) 54.7963 1.78726
\(941\) 57.8756 1.88669 0.943346 0.331811i \(-0.107660\pi\)
0.943346 + 0.331811i \(0.107660\pi\)
\(942\) 3.57628 0.116521
\(943\) 35.7756 1.16501
\(944\) 0.707867 0.0230391
\(945\) −8.19416 −0.266556
\(946\) −77.1984 −2.50994
\(947\) −19.8508 −0.645064 −0.322532 0.946559i \(-0.604534\pi\)
−0.322532 + 0.946559i \(0.604534\pi\)
\(948\) −47.7871 −1.55205
\(949\) −14.4979 −0.470623
\(950\) 2.24113 0.0727118
\(951\) 55.1496 1.78835
\(952\) 12.0723 0.391267
\(953\) −48.2282 −1.56226 −0.781132 0.624366i \(-0.785357\pi\)
−0.781132 + 0.624366i \(0.785357\pi\)
\(954\) 35.1860 1.13919
\(955\) −27.7562 −0.898168
\(956\) −84.0297 −2.71771
\(957\) −37.7143 −1.21913
\(958\) −42.8801 −1.38539
\(959\) 1.71238 0.0552955
\(960\) 77.9918 2.51718
\(961\) −11.0110 −0.355195
\(962\) −4.92822 −0.158892
\(963\) 46.5018 1.49850
\(964\) 17.9642 0.578586
\(965\) −15.9932 −0.514840
\(966\) −52.1400 −1.67758
\(967\) 32.9861 1.06076 0.530380 0.847760i \(-0.322049\pi\)
0.530380 + 0.847760i \(0.322049\pi\)
\(968\) 4.38074 0.140802
\(969\) −20.9142 −0.671860
\(970\) −1.14483 −0.0367583
\(971\) −16.3461 −0.524571 −0.262285 0.964990i \(-0.584476\pi\)
−0.262285 + 0.964990i \(0.584476\pi\)
\(972\) 69.6011 2.23246
\(973\) −30.5843 −0.980486
\(974\) 23.5711 0.755268
\(975\) −1.74021 −0.0557312
\(976\) −1.44567 −0.0462749
\(977\) 35.7362 1.14330 0.571651 0.820497i \(-0.306303\pi\)
0.571651 + 0.820497i \(0.306303\pi\)
\(978\) −116.872 −3.73716
\(979\) 35.9353 1.14850
\(980\) −28.0822 −0.897051
\(981\) −3.76795 −0.120301
\(982\) −95.0813 −3.03417
\(983\) 27.5874 0.879902 0.439951 0.898022i \(-0.354996\pi\)
0.439951 + 0.898022i \(0.354996\pi\)
\(984\) −50.5855 −1.61261
\(985\) −21.0551 −0.670871
\(986\) 27.1930 0.866001
\(987\) −34.6208 −1.10199
\(988\) −21.9492 −0.698298
\(989\) −54.8032 −1.74264
\(990\) −60.4927 −1.92258
\(991\) −47.8239 −1.51918 −0.759589 0.650404i \(-0.774600\pi\)
−0.759589 + 0.650404i \(0.774600\pi\)
\(992\) −26.5101 −0.841696
\(993\) −22.1866 −0.704069
\(994\) 10.8137 0.342989
\(995\) 2.69594 0.0854671
\(996\) −83.1479 −2.63464
\(997\) 9.60225 0.304106 0.152053 0.988372i \(-0.451411\pi\)
0.152053 + 0.988372i \(0.451411\pi\)
\(998\) −26.0897 −0.825854
\(999\) −1.99784 −0.0632088
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 4033.2.a.f.1.9 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.9 85 1.1 even 1 trivial