Properties

Label 8016.2.a.be.1.11
Level 8016
Weight 2
Character 8016.1
Self dual yes
Analytic conductor 64.008
Analytic rank 0
Dimension 11
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-3.01685\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +4.01685 q^{5} +4.41557 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +4.01685 q^{5} +4.41557 q^{7} +1.00000 q^{9} -3.91880 q^{11} +1.33293 q^{13} +4.01685 q^{15} +5.36767 q^{17} -4.32150 q^{19} +4.41557 q^{21} -2.96332 q^{23} +11.1351 q^{25} +1.00000 q^{27} +0.641815 q^{29} +4.50410 q^{31} -3.91880 q^{33} +17.7367 q^{35} -3.58361 q^{37} +1.33293 q^{39} -8.78387 q^{41} -6.83087 q^{43} +4.01685 q^{45} +11.1340 q^{47} +12.4973 q^{49} +5.36767 q^{51} -1.90890 q^{53} -15.7412 q^{55} -4.32150 q^{57} +6.60930 q^{59} +0.00823330 q^{61} +4.41557 q^{63} +5.35420 q^{65} -4.03013 q^{67} -2.96332 q^{69} +2.34031 q^{71} +4.99602 q^{73} +11.1351 q^{75} -17.3037 q^{77} -1.33451 q^{79} +1.00000 q^{81} -14.1756 q^{83} +21.5611 q^{85} +0.641815 q^{87} +12.3702 q^{89} +5.88567 q^{91} +4.50410 q^{93} -17.3588 q^{95} +13.3417 q^{97} -3.91880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + O(q^{10}) \) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + q^{11} + 10q^{13} + 10q^{15} + 17q^{17} - 2q^{19} + q^{21} + 3q^{23} + 21q^{25} + 11q^{27} + 17q^{29} + 15q^{31} + q^{33} - 11q^{35} + 4q^{37} + 10q^{39} + 16q^{41} - 10q^{43} + 10q^{45} + 16q^{47} + 22q^{49} + 17q^{51} + 42q^{53} + 5q^{55} - 2q^{57} + 2q^{59} + 12q^{61} + q^{63} + 10q^{65} + q^{67} + 3q^{69} + 9q^{71} + 24q^{73} + 21q^{75} + 22q^{77} + 30q^{79} + 11q^{81} - 16q^{83} + 25q^{85} + 17q^{87} + 37q^{89} - q^{91} + 15q^{93} - 5q^{95} + 4q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 4.01685 1.79639 0.898195 0.439597i \(-0.144879\pi\)
0.898195 + 0.439597i \(0.144879\pi\)
\(6\) 0 0
\(7\) 4.41557 1.66893 0.834465 0.551062i \(-0.185777\pi\)
0.834465 + 0.551062i \(0.185777\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.91880 −1.18156 −0.590781 0.806832i \(-0.701180\pi\)
−0.590781 + 0.806832i \(0.701180\pi\)
\(12\) 0 0
\(13\) 1.33293 0.369690 0.184845 0.982768i \(-0.440822\pi\)
0.184845 + 0.982768i \(0.440822\pi\)
\(14\) 0 0
\(15\) 4.01685 1.03715
\(16\) 0 0
\(17\) 5.36767 1.30185 0.650926 0.759141i \(-0.274381\pi\)
0.650926 + 0.759141i \(0.274381\pi\)
\(18\) 0 0
\(19\) −4.32150 −0.991420 −0.495710 0.868488i \(-0.665092\pi\)
−0.495710 + 0.868488i \(0.665092\pi\)
\(20\) 0 0
\(21\) 4.41557 0.963557
\(22\) 0 0
\(23\) −2.96332 −0.617894 −0.308947 0.951079i \(-0.599977\pi\)
−0.308947 + 0.951079i \(0.599977\pi\)
\(24\) 0 0
\(25\) 11.1351 2.22702
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0.641815 0.119182 0.0595910 0.998223i \(-0.481020\pi\)
0.0595910 + 0.998223i \(0.481020\pi\)
\(30\) 0 0
\(31\) 4.50410 0.808960 0.404480 0.914547i \(-0.367453\pi\)
0.404480 + 0.914547i \(0.367453\pi\)
\(32\) 0 0
\(33\) −3.91880 −0.682175
\(34\) 0 0
\(35\) 17.7367 2.99805
\(36\) 0 0
\(37\) −3.58361 −0.589141 −0.294571 0.955630i \(-0.595177\pi\)
−0.294571 + 0.955630i \(0.595177\pi\)
\(38\) 0 0
\(39\) 1.33293 0.213440
\(40\) 0 0
\(41\) −8.78387 −1.37181 −0.685905 0.727691i \(-0.740594\pi\)
−0.685905 + 0.727691i \(0.740594\pi\)
\(42\) 0 0
\(43\) −6.83087 −1.04170 −0.520849 0.853649i \(-0.674385\pi\)
−0.520849 + 0.853649i \(0.674385\pi\)
\(44\) 0 0
\(45\) 4.01685 0.598797
\(46\) 0 0
\(47\) 11.1340 1.62406 0.812031 0.583615i \(-0.198362\pi\)
0.812031 + 0.583615i \(0.198362\pi\)
\(48\) 0 0
\(49\) 12.4973 1.78532
\(50\) 0 0
\(51\) 5.36767 0.751625
\(52\) 0 0
\(53\) −1.90890 −0.262208 −0.131104 0.991369i \(-0.541852\pi\)
−0.131104 + 0.991369i \(0.541852\pi\)
\(54\) 0 0
\(55\) −15.7412 −2.12255
\(56\) 0 0
\(57\) −4.32150 −0.572397
\(58\) 0 0
\(59\) 6.60930 0.860458 0.430229 0.902720i \(-0.358433\pi\)
0.430229 + 0.902720i \(0.358433\pi\)
\(60\) 0 0
\(61\) 0.00823330 0.00105417 0.000527083 1.00000i \(-0.499832\pi\)
0.000527083 1.00000i \(0.499832\pi\)
\(62\) 0 0
\(63\) 4.41557 0.556310
\(64\) 0 0
\(65\) 5.35420 0.664107
\(66\) 0 0
\(67\) −4.03013 −0.492359 −0.246179 0.969224i \(-0.579175\pi\)
−0.246179 + 0.969224i \(0.579175\pi\)
\(68\) 0 0
\(69\) −2.96332 −0.356741
\(70\) 0 0
\(71\) 2.34031 0.277744 0.138872 0.990310i \(-0.455652\pi\)
0.138872 + 0.990310i \(0.455652\pi\)
\(72\) 0 0
\(73\) 4.99602 0.584740 0.292370 0.956305i \(-0.405556\pi\)
0.292370 + 0.956305i \(0.405556\pi\)
\(74\) 0 0
\(75\) 11.1351 1.28577
\(76\) 0 0
\(77\) −17.3037 −1.97194
\(78\) 0 0
\(79\) −1.33451 −0.150144 −0.0750718 0.997178i \(-0.523919\pi\)
−0.0750718 + 0.997178i \(0.523919\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.1756 −1.55597 −0.777986 0.628281i \(-0.783759\pi\)
−0.777986 + 0.628281i \(0.783759\pi\)
\(84\) 0 0
\(85\) 21.5611 2.33863
\(86\) 0 0
\(87\) 0.641815 0.0688098
\(88\) 0 0
\(89\) 12.3702 1.31124 0.655621 0.755090i \(-0.272407\pi\)
0.655621 + 0.755090i \(0.272407\pi\)
\(90\) 0 0
\(91\) 5.88567 0.616986
\(92\) 0 0
\(93\) 4.50410 0.467053
\(94\) 0 0
\(95\) −17.3588 −1.78098
\(96\) 0 0
\(97\) 13.3417 1.35464 0.677321 0.735688i \(-0.263141\pi\)
0.677321 + 0.735688i \(0.263141\pi\)
\(98\) 0 0
\(99\) −3.91880 −0.393854
\(100\) 0 0
\(101\) 0.0616138 0.00613081 0.00306540 0.999995i \(-0.499024\pi\)
0.00306540 + 0.999995i \(0.499024\pi\)
\(102\) 0 0
\(103\) 1.58232 0.155910 0.0779552 0.996957i \(-0.475161\pi\)
0.0779552 + 0.996957i \(0.475161\pi\)
\(104\) 0 0
\(105\) 17.7367 1.73092
\(106\) 0 0
\(107\) 15.1136 1.46109 0.730544 0.682865i \(-0.239266\pi\)
0.730544 + 0.682865i \(0.239266\pi\)
\(108\) 0 0
\(109\) −13.1743 −1.26187 −0.630934 0.775836i \(-0.717328\pi\)
−0.630934 + 0.775836i \(0.717328\pi\)
\(110\) 0 0
\(111\) −3.58361 −0.340141
\(112\) 0 0
\(113\) 20.1380 1.89443 0.947213 0.320604i \(-0.103886\pi\)
0.947213 + 0.320604i \(0.103886\pi\)
\(114\) 0 0
\(115\) −11.9032 −1.10998
\(116\) 0 0
\(117\) 1.33293 0.123230
\(118\) 0 0
\(119\) 23.7013 2.17270
\(120\) 0 0
\(121\) 4.35696 0.396088
\(122\) 0 0
\(123\) −8.78387 −0.792015
\(124\) 0 0
\(125\) 24.6438 2.20421
\(126\) 0 0
\(127\) −18.1668 −1.61204 −0.806019 0.591889i \(-0.798382\pi\)
−0.806019 + 0.591889i \(0.798382\pi\)
\(128\) 0 0
\(129\) −6.83087 −0.601425
\(130\) 0 0
\(131\) −11.0441 −0.964932 −0.482466 0.875915i \(-0.660259\pi\)
−0.482466 + 0.875915i \(0.660259\pi\)
\(132\) 0 0
\(133\) −19.0819 −1.65461
\(134\) 0 0
\(135\) 4.01685 0.345716
\(136\) 0 0
\(137\) 14.8528 1.26896 0.634480 0.772939i \(-0.281214\pi\)
0.634480 + 0.772939i \(0.281214\pi\)
\(138\) 0 0
\(139\) 12.3986 1.05164 0.525818 0.850597i \(-0.323759\pi\)
0.525818 + 0.850597i \(0.323759\pi\)
\(140\) 0 0
\(141\) 11.1340 0.937652
\(142\) 0 0
\(143\) −5.22350 −0.436811
\(144\) 0 0
\(145\) 2.57808 0.214098
\(146\) 0 0
\(147\) 12.4973 1.03076
\(148\) 0 0
\(149\) −17.3220 −1.41908 −0.709538 0.704667i \(-0.751096\pi\)
−0.709538 + 0.704667i \(0.751096\pi\)
\(150\) 0 0
\(151\) 12.7672 1.03898 0.519490 0.854477i \(-0.326122\pi\)
0.519490 + 0.854477i \(0.326122\pi\)
\(152\) 0 0
\(153\) 5.36767 0.433951
\(154\) 0 0
\(155\) 18.0923 1.45321
\(156\) 0 0
\(157\) 1.00398 0.0801265 0.0400632 0.999197i \(-0.487244\pi\)
0.0400632 + 0.999197i \(0.487244\pi\)
\(158\) 0 0
\(159\) −1.90890 −0.151386
\(160\) 0 0
\(161\) −13.0847 −1.03122
\(162\) 0 0
\(163\) −9.70804 −0.760392 −0.380196 0.924906i \(-0.624143\pi\)
−0.380196 + 0.924906i \(0.624143\pi\)
\(164\) 0 0
\(165\) −15.7412 −1.22545
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −11.2233 −0.863330
\(170\) 0 0
\(171\) −4.32150 −0.330473
\(172\) 0 0
\(173\) 23.0933 1.75575 0.877876 0.478888i \(-0.158960\pi\)
0.877876 + 0.478888i \(0.158960\pi\)
\(174\) 0 0
\(175\) 49.1678 3.71674
\(176\) 0 0
\(177\) 6.60930 0.496786
\(178\) 0 0
\(179\) 18.0863 1.35183 0.675917 0.736978i \(-0.263748\pi\)
0.675917 + 0.736978i \(0.263748\pi\)
\(180\) 0 0
\(181\) −18.8159 −1.39858 −0.699289 0.714839i \(-0.746500\pi\)
−0.699289 + 0.714839i \(0.746500\pi\)
\(182\) 0 0
\(183\) 0.00823330 0.000608623 0
\(184\) 0 0
\(185\) −14.3948 −1.05833
\(186\) 0 0
\(187\) −21.0348 −1.53822
\(188\) 0 0
\(189\) 4.41557 0.321186
\(190\) 0 0
\(191\) −5.24773 −0.379712 −0.189856 0.981812i \(-0.560802\pi\)
−0.189856 + 0.981812i \(0.560802\pi\)
\(192\) 0 0
\(193\) 15.4295 1.11064 0.555321 0.831636i \(-0.312595\pi\)
0.555321 + 0.831636i \(0.312595\pi\)
\(194\) 0 0
\(195\) 5.35420 0.383422
\(196\) 0 0
\(197\) −4.27605 −0.304656 −0.152328 0.988330i \(-0.548677\pi\)
−0.152328 + 0.988330i \(0.548677\pi\)
\(198\) 0 0
\(199\) −8.93953 −0.633707 −0.316853 0.948475i \(-0.602626\pi\)
−0.316853 + 0.948475i \(0.602626\pi\)
\(200\) 0 0
\(201\) −4.03013 −0.284263
\(202\) 0 0
\(203\) 2.83398 0.198906
\(204\) 0 0
\(205\) −35.2835 −2.46431
\(206\) 0 0
\(207\) −2.96332 −0.205965
\(208\) 0 0
\(209\) 16.9351 1.17142
\(210\) 0 0
\(211\) −20.7250 −1.42677 −0.713383 0.700774i \(-0.752838\pi\)
−0.713383 + 0.700774i \(0.752838\pi\)
\(212\) 0 0
\(213\) 2.34031 0.160356
\(214\) 0 0
\(215\) −27.4386 −1.87130
\(216\) 0 0
\(217\) 19.8882 1.35010
\(218\) 0 0
\(219\) 4.99602 0.337600
\(220\) 0 0
\(221\) 7.15476 0.481281
\(222\) 0 0
\(223\) −10.2434 −0.685948 −0.342974 0.939345i \(-0.611434\pi\)
−0.342974 + 0.939345i \(0.611434\pi\)
\(224\) 0 0
\(225\) 11.1351 0.742340
\(226\) 0 0
\(227\) −17.0924 −1.13446 −0.567230 0.823559i \(-0.691985\pi\)
−0.567230 + 0.823559i \(0.691985\pi\)
\(228\) 0 0
\(229\) 24.4530 1.61590 0.807949 0.589252i \(-0.200578\pi\)
0.807949 + 0.589252i \(0.200578\pi\)
\(230\) 0 0
\(231\) −17.3037 −1.13850
\(232\) 0 0
\(233\) −19.7612 −1.29460 −0.647300 0.762236i \(-0.724102\pi\)
−0.647300 + 0.762236i \(0.724102\pi\)
\(234\) 0 0
\(235\) 44.7236 2.91745
\(236\) 0 0
\(237\) −1.33451 −0.0866854
\(238\) 0 0
\(239\) −13.5708 −0.877819 −0.438910 0.898531i \(-0.644635\pi\)
−0.438910 + 0.898531i \(0.644635\pi\)
\(240\) 0 0
\(241\) 19.3143 1.24414 0.622072 0.782960i \(-0.286291\pi\)
0.622072 + 0.782960i \(0.286291\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 50.1997 3.20714
\(246\) 0 0
\(247\) −5.76028 −0.366518
\(248\) 0 0
\(249\) −14.1756 −0.898341
\(250\) 0 0
\(251\) 10.8135 0.682540 0.341270 0.939965i \(-0.389143\pi\)
0.341270 + 0.939965i \(0.389143\pi\)
\(252\) 0 0
\(253\) 11.6126 0.730080
\(254\) 0 0
\(255\) 21.5611 1.35021
\(256\) 0 0
\(257\) −0.473302 −0.0295238 −0.0147619 0.999891i \(-0.504699\pi\)
−0.0147619 + 0.999891i \(0.504699\pi\)
\(258\) 0 0
\(259\) −15.8237 −0.983235
\(260\) 0 0
\(261\) 0.641815 0.0397274
\(262\) 0 0
\(263\) −5.76686 −0.355600 −0.177800 0.984067i \(-0.556898\pi\)
−0.177800 + 0.984067i \(0.556898\pi\)
\(264\) 0 0
\(265\) −7.66777 −0.471028
\(266\) 0 0
\(267\) 12.3702 0.757046
\(268\) 0 0
\(269\) −2.62828 −0.160249 −0.0801247 0.996785i \(-0.525532\pi\)
−0.0801247 + 0.996785i \(0.525532\pi\)
\(270\) 0 0
\(271\) −1.50936 −0.0916873 −0.0458437 0.998949i \(-0.514598\pi\)
−0.0458437 + 0.998949i \(0.514598\pi\)
\(272\) 0 0
\(273\) 5.88567 0.356217
\(274\) 0 0
\(275\) −43.6362 −2.63136
\(276\) 0 0
\(277\) −11.3632 −0.682751 −0.341375 0.939927i \(-0.610893\pi\)
−0.341375 + 0.939927i \(0.610893\pi\)
\(278\) 0 0
\(279\) 4.50410 0.269653
\(280\) 0 0
\(281\) −26.3821 −1.57382 −0.786911 0.617066i \(-0.788321\pi\)
−0.786911 + 0.617066i \(0.788321\pi\)
\(282\) 0 0
\(283\) −19.9376 −1.18517 −0.592584 0.805509i \(-0.701892\pi\)
−0.592584 + 0.805509i \(0.701892\pi\)
\(284\) 0 0
\(285\) −17.3588 −1.02825
\(286\) 0 0
\(287\) −38.7858 −2.28945
\(288\) 0 0
\(289\) 11.8119 0.694819
\(290\) 0 0
\(291\) 13.3417 0.782103
\(292\) 0 0
\(293\) −30.6368 −1.78982 −0.894911 0.446244i \(-0.852761\pi\)
−0.894911 + 0.446244i \(0.852761\pi\)
\(294\) 0 0
\(295\) 26.5486 1.54572
\(296\) 0 0
\(297\) −3.91880 −0.227392
\(298\) 0 0
\(299\) −3.94991 −0.228429
\(300\) 0 0
\(301\) −30.1622 −1.73852
\(302\) 0 0
\(303\) 0.0616138 0.00353962
\(304\) 0 0
\(305\) 0.0330719 0.00189369
\(306\) 0 0
\(307\) 0.699590 0.0399277 0.0199638 0.999801i \(-0.493645\pi\)
0.0199638 + 0.999801i \(0.493645\pi\)
\(308\) 0 0
\(309\) 1.58232 0.0900149
\(310\) 0 0
\(311\) −15.0625 −0.854118 −0.427059 0.904224i \(-0.640450\pi\)
−0.427059 + 0.904224i \(0.640450\pi\)
\(312\) 0 0
\(313\) −7.76381 −0.438836 −0.219418 0.975631i \(-0.570416\pi\)
−0.219418 + 0.975631i \(0.570416\pi\)
\(314\) 0 0
\(315\) 17.7367 0.999350
\(316\) 0 0
\(317\) 12.0203 0.675129 0.337565 0.941302i \(-0.390397\pi\)
0.337565 + 0.941302i \(0.390397\pi\)
\(318\) 0 0
\(319\) −2.51514 −0.140821
\(320\) 0 0
\(321\) 15.1136 0.843560
\(322\) 0 0
\(323\) −23.1964 −1.29068
\(324\) 0 0
\(325\) 14.8424 0.823306
\(326\) 0 0
\(327\) −13.1743 −0.728540
\(328\) 0 0
\(329\) 49.1630 2.71044
\(330\) 0 0
\(331\) 4.62791 0.254373 0.127186 0.991879i \(-0.459405\pi\)
0.127186 + 0.991879i \(0.459405\pi\)
\(332\) 0 0
\(333\) −3.58361 −0.196380
\(334\) 0 0
\(335\) −16.1884 −0.884469
\(336\) 0 0
\(337\) −4.04164 −0.220162 −0.110081 0.993923i \(-0.535111\pi\)
−0.110081 + 0.993923i \(0.535111\pi\)
\(338\) 0 0
\(339\) 20.1380 1.09375
\(340\) 0 0
\(341\) −17.6506 −0.955836
\(342\) 0 0
\(343\) 24.2736 1.31065
\(344\) 0 0
\(345\) −11.9032 −0.640847
\(346\) 0 0
\(347\) 37.0090 1.98675 0.993373 0.114933i \(-0.0366653\pi\)
0.993373 + 0.114933i \(0.0366653\pi\)
\(348\) 0 0
\(349\) −5.18184 −0.277378 −0.138689 0.990336i \(-0.544289\pi\)
−0.138689 + 0.990336i \(0.544289\pi\)
\(350\) 0 0
\(351\) 1.33293 0.0711468
\(352\) 0 0
\(353\) −28.9215 −1.53934 −0.769668 0.638444i \(-0.779578\pi\)
−0.769668 + 0.638444i \(0.779578\pi\)
\(354\) 0 0
\(355\) 9.40068 0.498937
\(356\) 0 0
\(357\) 23.7013 1.25441
\(358\) 0 0
\(359\) −32.0737 −1.69279 −0.846393 0.532559i \(-0.821230\pi\)
−0.846393 + 0.532559i \(0.821230\pi\)
\(360\) 0 0
\(361\) −0.324636 −0.0170861
\(362\) 0 0
\(363\) 4.35696 0.228681
\(364\) 0 0
\(365\) 20.0683 1.05042
\(366\) 0 0
\(367\) 2.98571 0.155853 0.0779264 0.996959i \(-0.475170\pi\)
0.0779264 + 0.996959i \(0.475170\pi\)
\(368\) 0 0
\(369\) −8.78387 −0.457270
\(370\) 0 0
\(371\) −8.42889 −0.437606
\(372\) 0 0
\(373\) −26.5306 −1.37370 −0.686852 0.726797i \(-0.741008\pi\)
−0.686852 + 0.726797i \(0.741008\pi\)
\(374\) 0 0
\(375\) 24.6438 1.27260
\(376\) 0 0
\(377\) 0.855498 0.0440604
\(378\) 0 0
\(379\) −11.6976 −0.600864 −0.300432 0.953803i \(-0.597131\pi\)
−0.300432 + 0.953803i \(0.597131\pi\)
\(380\) 0 0
\(381\) −18.1668 −0.930711
\(382\) 0 0
\(383\) 14.4782 0.739800 0.369900 0.929072i \(-0.379392\pi\)
0.369900 + 0.929072i \(0.379392\pi\)
\(384\) 0 0
\(385\) −69.5065 −3.54238
\(386\) 0 0
\(387\) −6.83087 −0.347233
\(388\) 0 0
\(389\) 33.9739 1.72255 0.861273 0.508143i \(-0.169668\pi\)
0.861273 + 0.508143i \(0.169668\pi\)
\(390\) 0 0
\(391\) −15.9061 −0.804406
\(392\) 0 0
\(393\) −11.0441 −0.557104
\(394\) 0 0
\(395\) −5.36051 −0.269716
\(396\) 0 0
\(397\) 21.9115 1.09971 0.549853 0.835262i \(-0.314684\pi\)
0.549853 + 0.835262i \(0.314684\pi\)
\(398\) 0 0
\(399\) −19.0819 −0.955290
\(400\) 0 0
\(401\) −15.2013 −0.759115 −0.379557 0.925168i \(-0.623924\pi\)
−0.379557 + 0.925168i \(0.623924\pi\)
\(402\) 0 0
\(403\) 6.00367 0.299064
\(404\) 0 0
\(405\) 4.01685 0.199599
\(406\) 0 0
\(407\) 14.0434 0.696106
\(408\) 0 0
\(409\) −22.8815 −1.13141 −0.565707 0.824606i \(-0.691397\pi\)
−0.565707 + 0.824606i \(0.691397\pi\)
\(410\) 0 0
\(411\) 14.8528 0.732635
\(412\) 0 0
\(413\) 29.1838 1.43604
\(414\) 0 0
\(415\) −56.9412 −2.79513
\(416\) 0 0
\(417\) 12.3986 0.607162
\(418\) 0 0
\(419\) 7.44289 0.363609 0.181804 0.983335i \(-0.441806\pi\)
0.181804 + 0.983335i \(0.441806\pi\)
\(420\) 0 0
\(421\) −12.2244 −0.595780 −0.297890 0.954600i \(-0.596283\pi\)
−0.297890 + 0.954600i \(0.596283\pi\)
\(422\) 0 0
\(423\) 11.1340 0.541354
\(424\) 0 0
\(425\) 59.7696 2.89925
\(426\) 0 0
\(427\) 0.0363547 0.00175933
\(428\) 0 0
\(429\) −5.22350 −0.252193
\(430\) 0 0
\(431\) −7.14112 −0.343976 −0.171988 0.985099i \(-0.555019\pi\)
−0.171988 + 0.985099i \(0.555019\pi\)
\(432\) 0 0
\(433\) −6.96710 −0.334818 −0.167409 0.985888i \(-0.553540\pi\)
−0.167409 + 0.985888i \(0.553540\pi\)
\(434\) 0 0
\(435\) 2.57808 0.123609
\(436\) 0 0
\(437\) 12.8060 0.612593
\(438\) 0 0
\(439\) 9.01824 0.430417 0.215209 0.976568i \(-0.430957\pi\)
0.215209 + 0.976568i \(0.430957\pi\)
\(440\) 0 0
\(441\) 12.4973 0.595108
\(442\) 0 0
\(443\) −24.8441 −1.18038 −0.590189 0.807265i \(-0.700947\pi\)
−0.590189 + 0.807265i \(0.700947\pi\)
\(444\) 0 0
\(445\) 49.6894 2.35550
\(446\) 0 0
\(447\) −17.3220 −0.819304
\(448\) 0 0
\(449\) −6.68633 −0.315548 −0.157774 0.987475i \(-0.550432\pi\)
−0.157774 + 0.987475i \(0.550432\pi\)
\(450\) 0 0
\(451\) 34.4222 1.62088
\(452\) 0 0
\(453\) 12.7672 0.599855
\(454\) 0 0
\(455\) 23.6419 1.10835
\(456\) 0 0
\(457\) −10.5537 −0.493683 −0.246842 0.969056i \(-0.579393\pi\)
−0.246842 + 0.969056i \(0.579393\pi\)
\(458\) 0 0
\(459\) 5.36767 0.250542
\(460\) 0 0
\(461\) −17.5758 −0.818587 −0.409293 0.912403i \(-0.634225\pi\)
−0.409293 + 0.912403i \(0.634225\pi\)
\(462\) 0 0
\(463\) 0.242028 0.0112480 0.00562400 0.999984i \(-0.498210\pi\)
0.00562400 + 0.999984i \(0.498210\pi\)
\(464\) 0 0
\(465\) 18.0923 0.839010
\(466\) 0 0
\(467\) −32.1216 −1.48641 −0.743205 0.669064i \(-0.766695\pi\)
−0.743205 + 0.669064i \(0.766695\pi\)
\(468\) 0 0
\(469\) −17.7953 −0.821712
\(470\) 0 0
\(471\) 1.00398 0.0462611
\(472\) 0 0
\(473\) 26.7688 1.23083
\(474\) 0 0
\(475\) −48.1203 −2.20791
\(476\) 0 0
\(477\) −1.90890 −0.0874026
\(478\) 0 0
\(479\) −15.7450 −0.719405 −0.359703 0.933067i \(-0.617122\pi\)
−0.359703 + 0.933067i \(0.617122\pi\)
\(480\) 0 0
\(481\) −4.77671 −0.217799
\(482\) 0 0
\(483\) −13.0847 −0.595376
\(484\) 0 0
\(485\) 53.5915 2.43347
\(486\) 0 0
\(487\) −22.7962 −1.03299 −0.516496 0.856289i \(-0.672764\pi\)
−0.516496 + 0.856289i \(0.672764\pi\)
\(488\) 0 0
\(489\) −9.70804 −0.439013
\(490\) 0 0
\(491\) 2.40062 0.108338 0.0541692 0.998532i \(-0.482749\pi\)
0.0541692 + 0.998532i \(0.482749\pi\)
\(492\) 0 0
\(493\) 3.44505 0.155157
\(494\) 0 0
\(495\) −15.7412 −0.707515
\(496\) 0 0
\(497\) 10.3338 0.463535
\(498\) 0 0
\(499\) 15.1018 0.676049 0.338024 0.941137i \(-0.390241\pi\)
0.338024 + 0.941137i \(0.390241\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 35.3038 1.57412 0.787059 0.616878i \(-0.211603\pi\)
0.787059 + 0.616878i \(0.211603\pi\)
\(504\) 0 0
\(505\) 0.247494 0.0110133
\(506\) 0 0
\(507\) −11.2233 −0.498444
\(508\) 0 0
\(509\) −6.51112 −0.288601 −0.144300 0.989534i \(-0.546093\pi\)
−0.144300 + 0.989534i \(0.546093\pi\)
\(510\) 0 0
\(511\) 22.0603 0.975890
\(512\) 0 0
\(513\) −4.32150 −0.190799
\(514\) 0 0
\(515\) 6.35594 0.280076
\(516\) 0 0
\(517\) −43.6319 −1.91893
\(518\) 0 0
\(519\) 23.0933 1.01368
\(520\) 0 0
\(521\) −16.3745 −0.717380 −0.358690 0.933457i \(-0.616776\pi\)
−0.358690 + 0.933457i \(0.616776\pi\)
\(522\) 0 0
\(523\) −33.9619 −1.48505 −0.742526 0.669817i \(-0.766372\pi\)
−0.742526 + 0.669817i \(0.766372\pi\)
\(524\) 0 0
\(525\) 49.1678 2.14586
\(526\) 0 0
\(527\) 24.1765 1.05315
\(528\) 0 0
\(529\) −14.2188 −0.618207
\(530\) 0 0
\(531\) 6.60930 0.286819
\(532\) 0 0
\(533\) −11.7083 −0.507144
\(534\) 0 0
\(535\) 60.7092 2.62469
\(536\) 0 0
\(537\) 18.0863 0.780482
\(538\) 0 0
\(539\) −48.9743 −2.10947
\(540\) 0 0
\(541\) 8.99706 0.386814 0.193407 0.981119i \(-0.438046\pi\)
0.193407 + 0.981119i \(0.438046\pi\)
\(542\) 0 0
\(543\) −18.8159 −0.807470
\(544\) 0 0
\(545\) −52.9192 −2.26681
\(546\) 0 0
\(547\) 20.4728 0.875355 0.437677 0.899132i \(-0.355801\pi\)
0.437677 + 0.899132i \(0.355801\pi\)
\(548\) 0 0
\(549\) 0.00823330 0.000351389 0
\(550\) 0 0
\(551\) −2.77360 −0.118160
\(552\) 0 0
\(553\) −5.89260 −0.250579
\(554\) 0 0
\(555\) −14.3948 −0.611026
\(556\) 0 0
\(557\) 20.5319 0.869965 0.434983 0.900439i \(-0.356754\pi\)
0.434983 + 0.900439i \(0.356754\pi\)
\(558\) 0 0
\(559\) −9.10511 −0.385105
\(560\) 0 0
\(561\) −21.0348 −0.888091
\(562\) 0 0
\(563\) 19.3977 0.817514 0.408757 0.912643i \(-0.365962\pi\)
0.408757 + 0.912643i \(0.365962\pi\)
\(564\) 0 0
\(565\) 80.8915 3.40313
\(566\) 0 0
\(567\) 4.41557 0.185437
\(568\) 0 0
\(569\) 32.4646 1.36098 0.680492 0.732755i \(-0.261766\pi\)
0.680492 + 0.732755i \(0.261766\pi\)
\(570\) 0 0
\(571\) −26.5493 −1.11105 −0.555527 0.831499i \(-0.687483\pi\)
−0.555527 + 0.831499i \(0.687483\pi\)
\(572\) 0 0
\(573\) −5.24773 −0.219227
\(574\) 0 0
\(575\) −32.9968 −1.37606
\(576\) 0 0
\(577\) −2.82004 −0.117400 −0.0586999 0.998276i \(-0.518696\pi\)
−0.0586999 + 0.998276i \(0.518696\pi\)
\(578\) 0 0
\(579\) 15.4295 0.641230
\(580\) 0 0
\(581\) −62.5933 −2.59681
\(582\) 0 0
\(583\) 7.48059 0.309815
\(584\) 0 0
\(585\) 5.35420 0.221369
\(586\) 0 0
\(587\) 26.9907 1.11403 0.557013 0.830504i \(-0.311948\pi\)
0.557013 + 0.830504i \(0.311948\pi\)
\(588\) 0 0
\(589\) −19.4645 −0.802019
\(590\) 0 0
\(591\) −4.27605 −0.175893
\(592\) 0 0
\(593\) 37.1868 1.52708 0.763538 0.645762i \(-0.223460\pi\)
0.763538 + 0.645762i \(0.223460\pi\)
\(594\) 0 0
\(595\) 95.2048 3.90302
\(596\) 0 0
\(597\) −8.93953 −0.365871
\(598\) 0 0
\(599\) −28.6209 −1.16942 −0.584709 0.811243i \(-0.698791\pi\)
−0.584709 + 0.811243i \(0.698791\pi\)
\(600\) 0 0
\(601\) −16.6774 −0.680285 −0.340142 0.940374i \(-0.610475\pi\)
−0.340142 + 0.940374i \(0.610475\pi\)
\(602\) 0 0
\(603\) −4.03013 −0.164120
\(604\) 0 0
\(605\) 17.5013 0.711528
\(606\) 0 0
\(607\) 23.8248 0.967020 0.483510 0.875339i \(-0.339362\pi\)
0.483510 + 0.875339i \(0.339362\pi\)
\(608\) 0 0
\(609\) 2.83398 0.114839
\(610\) 0 0
\(611\) 14.8409 0.600399
\(612\) 0 0
\(613\) 33.8091 1.36554 0.682769 0.730635i \(-0.260776\pi\)
0.682769 + 0.730635i \(0.260776\pi\)
\(614\) 0 0
\(615\) −35.2835 −1.42277
\(616\) 0 0
\(617\) 1.75349 0.0705928 0.0352964 0.999377i \(-0.488762\pi\)
0.0352964 + 0.999377i \(0.488762\pi\)
\(618\) 0 0
\(619\) 43.9500 1.76650 0.883251 0.468901i \(-0.155350\pi\)
0.883251 + 0.468901i \(0.155350\pi\)
\(620\) 0 0
\(621\) −2.96332 −0.118914
\(622\) 0 0
\(623\) 54.6217 2.18837
\(624\) 0 0
\(625\) 43.3149 1.73260
\(626\) 0 0
\(627\) 16.9351 0.676322
\(628\) 0 0
\(629\) −19.2356 −0.766975
\(630\) 0 0
\(631\) −23.5677 −0.938215 −0.469108 0.883141i \(-0.655424\pi\)
−0.469108 + 0.883141i \(0.655424\pi\)
\(632\) 0 0
\(633\) −20.7250 −0.823744
\(634\) 0 0
\(635\) −72.9731 −2.89585
\(636\) 0 0
\(637\) 16.6581 0.660016
\(638\) 0 0
\(639\) 2.34031 0.0925813
\(640\) 0 0
\(641\) −45.5487 −1.79907 −0.899533 0.436854i \(-0.856093\pi\)
−0.899533 + 0.436854i \(0.856093\pi\)
\(642\) 0 0
\(643\) −2.60193 −0.102610 −0.0513050 0.998683i \(-0.516338\pi\)
−0.0513050 + 0.998683i \(0.516338\pi\)
\(644\) 0 0
\(645\) −27.4386 −1.08039
\(646\) 0 0
\(647\) 0.0801218 0.00314991 0.00157496 0.999999i \(-0.499499\pi\)
0.00157496 + 0.999999i \(0.499499\pi\)
\(648\) 0 0
\(649\) −25.9005 −1.01668
\(650\) 0 0
\(651\) 19.8882 0.779479
\(652\) 0 0
\(653\) 40.6905 1.59234 0.796171 0.605072i \(-0.206856\pi\)
0.796171 + 0.605072i \(0.206856\pi\)
\(654\) 0 0
\(655\) −44.3627 −1.73339
\(656\) 0 0
\(657\) 4.99602 0.194913
\(658\) 0 0
\(659\) −40.4684 −1.57642 −0.788212 0.615404i \(-0.788993\pi\)
−0.788212 + 0.615404i \(0.788993\pi\)
\(660\) 0 0
\(661\) −18.0618 −0.702523 −0.351262 0.936277i \(-0.614247\pi\)
−0.351262 + 0.936277i \(0.614247\pi\)
\(662\) 0 0
\(663\) 7.15476 0.277868
\(664\) 0 0
\(665\) −76.6491 −2.97233
\(666\) 0 0
\(667\) −1.90190 −0.0736419
\(668\) 0 0
\(669\) −10.2434 −0.396032
\(670\) 0 0
\(671\) −0.0322646 −0.00124556
\(672\) 0 0
\(673\) 33.2906 1.28326 0.641630 0.767015i \(-0.278259\pi\)
0.641630 + 0.767015i \(0.278259\pi\)
\(674\) 0 0
\(675\) 11.1351 0.428590
\(676\) 0 0
\(677\) 41.0968 1.57948 0.789738 0.613444i \(-0.210216\pi\)
0.789738 + 0.613444i \(0.210216\pi\)
\(678\) 0 0
\(679\) 58.9111 2.26080
\(680\) 0 0
\(681\) −17.0924 −0.654981
\(682\) 0 0
\(683\) 30.2871 1.15890 0.579451 0.815007i \(-0.303267\pi\)
0.579451 + 0.815007i \(0.303267\pi\)
\(684\) 0 0
\(685\) 59.6615 2.27955
\(686\) 0 0
\(687\) 24.4530 0.932939
\(688\) 0 0
\(689\) −2.54444 −0.0969355
\(690\) 0 0
\(691\) 35.2114 1.33951 0.669753 0.742584i \(-0.266400\pi\)
0.669753 + 0.742584i \(0.266400\pi\)
\(692\) 0 0
\(693\) −17.3037 −0.657314
\(694\) 0 0
\(695\) 49.8033 1.88915
\(696\) 0 0
\(697\) −47.1490 −1.78589
\(698\) 0 0
\(699\) −19.7612 −0.747437
\(700\) 0 0
\(701\) 13.6585 0.515876 0.257938 0.966162i \(-0.416957\pi\)
0.257938 + 0.966162i \(0.416957\pi\)
\(702\) 0 0
\(703\) 15.4866 0.584086
\(704\) 0 0
\(705\) 44.7236 1.68439
\(706\) 0 0
\(707\) 0.272060 0.0102319
\(708\) 0 0
\(709\) −28.6575 −1.07626 −0.538128 0.842863i \(-0.680868\pi\)
−0.538128 + 0.842863i \(0.680868\pi\)
\(710\) 0 0
\(711\) −1.33451 −0.0500479
\(712\) 0 0
\(713\) −13.3471 −0.499851
\(714\) 0 0
\(715\) −20.9820 −0.784683
\(716\) 0 0
\(717\) −13.5708 −0.506809
\(718\) 0 0
\(719\) 49.4611 1.84459 0.922295 0.386487i \(-0.126312\pi\)
0.922295 + 0.386487i \(0.126312\pi\)
\(720\) 0 0
\(721\) 6.98684 0.260204
\(722\) 0 0
\(723\) 19.3143 0.718307
\(724\) 0 0
\(725\) 7.14667 0.265421
\(726\) 0 0
\(727\) −14.4539 −0.536067 −0.268034 0.963410i \(-0.586374\pi\)
−0.268034 + 0.963410i \(0.586374\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −36.6659 −1.35614
\(732\) 0 0
\(733\) −23.5450 −0.869653 −0.434827 0.900514i \(-0.643190\pi\)
−0.434827 + 0.900514i \(0.643190\pi\)
\(734\) 0 0
\(735\) 50.1997 1.85164
\(736\) 0 0
\(737\) 15.7933 0.581752
\(738\) 0 0
\(739\) 12.1706 0.447704 0.223852 0.974623i \(-0.428137\pi\)
0.223852 + 0.974623i \(0.428137\pi\)
\(740\) 0 0
\(741\) −5.76028 −0.211609
\(742\) 0 0
\(743\) 22.7882 0.836017 0.418008 0.908443i \(-0.362728\pi\)
0.418008 + 0.908443i \(0.362728\pi\)
\(744\) 0 0
\(745\) −69.5800 −2.54921
\(746\) 0 0
\(747\) −14.1756 −0.518658
\(748\) 0 0
\(749\) 66.7353 2.43845
\(750\) 0 0
\(751\) 35.0391 1.27859 0.639297 0.768960i \(-0.279225\pi\)
0.639297 + 0.768960i \(0.279225\pi\)
\(752\) 0 0
\(753\) 10.8135 0.394065
\(754\) 0 0
\(755\) 51.2839 1.86641
\(756\) 0 0
\(757\) 0.874303 0.0317771 0.0158885 0.999874i \(-0.494942\pi\)
0.0158885 + 0.999874i \(0.494942\pi\)
\(758\) 0 0
\(759\) 11.6126 0.421512
\(760\) 0 0
\(761\) −21.2232 −0.769340 −0.384670 0.923054i \(-0.625685\pi\)
−0.384670 + 0.923054i \(0.625685\pi\)
\(762\) 0 0
\(763\) −58.1720 −2.10597
\(764\) 0 0
\(765\) 21.5611 0.779545
\(766\) 0 0
\(767\) 8.80977 0.318102
\(768\) 0 0
\(769\) −53.3473 −1.92375 −0.961876 0.273487i \(-0.911823\pi\)
−0.961876 + 0.273487i \(0.911823\pi\)
\(770\) 0 0
\(771\) −0.473302 −0.0170456
\(772\) 0 0
\(773\) 11.4161 0.410609 0.205305 0.978698i \(-0.434181\pi\)
0.205305 + 0.978698i \(0.434181\pi\)
\(774\) 0 0
\(775\) 50.1535 1.80157
\(776\) 0 0
\(777\) −15.8237 −0.567671
\(778\) 0 0
\(779\) 37.9595 1.36004
\(780\) 0 0
\(781\) −9.17120 −0.328172
\(782\) 0 0
\(783\) 0.641815 0.0229366
\(784\) 0 0
\(785\) 4.03285 0.143938
\(786\) 0 0
\(787\) 37.1510 1.32429 0.662145 0.749375i \(-0.269646\pi\)
0.662145 + 0.749375i \(0.269646\pi\)
\(788\) 0 0
\(789\) −5.76686 −0.205306
\(790\) 0 0
\(791\) 88.9209 3.16166
\(792\) 0 0
\(793\) 0.0109745 0.000389714 0
\(794\) 0 0
\(795\) −7.66777 −0.271948
\(796\) 0 0
\(797\) 12.4526 0.441093 0.220547 0.975376i \(-0.429216\pi\)
0.220547 + 0.975376i \(0.429216\pi\)
\(798\) 0 0
\(799\) 59.7637 2.11429
\(800\) 0 0
\(801\) 12.3702 0.437081
\(802\) 0 0
\(803\) −19.5784 −0.690906
\(804\) 0 0
\(805\) −52.5594 −1.85248
\(806\) 0 0
\(807\) −2.62828 −0.0925200
\(808\) 0 0
\(809\) 50.0293 1.75894 0.879469 0.475957i \(-0.157898\pi\)
0.879469 + 0.475957i \(0.157898\pi\)
\(810\) 0 0
\(811\) −40.8278 −1.43366 −0.716829 0.697249i \(-0.754407\pi\)
−0.716829 + 0.697249i \(0.754407\pi\)
\(812\) 0 0
\(813\) −1.50936 −0.0529357
\(814\) 0 0
\(815\) −38.9957 −1.36596
\(816\) 0 0
\(817\) 29.5196 1.03276
\(818\) 0 0
\(819\) 5.88567 0.205662
\(820\) 0 0
\(821\) −27.7502 −0.968490 −0.484245 0.874932i \(-0.660906\pi\)
−0.484245 + 0.874932i \(0.660906\pi\)
\(822\) 0 0
\(823\) 44.3295 1.54523 0.772614 0.634876i \(-0.218949\pi\)
0.772614 + 0.634876i \(0.218949\pi\)
\(824\) 0 0
\(825\) −43.6362 −1.51922
\(826\) 0 0
\(827\) 8.50957 0.295907 0.147953 0.988994i \(-0.452731\pi\)
0.147953 + 0.988994i \(0.452731\pi\)
\(828\) 0 0
\(829\) −1.03665 −0.0360045 −0.0180022 0.999838i \(-0.505731\pi\)
−0.0180022 + 0.999838i \(0.505731\pi\)
\(830\) 0 0
\(831\) −11.3632 −0.394186
\(832\) 0 0
\(833\) 67.0813 2.32423
\(834\) 0 0
\(835\) −4.01685 −0.139009
\(836\) 0 0
\(837\) 4.50410 0.155684
\(838\) 0 0
\(839\) 26.5492 0.916580 0.458290 0.888803i \(-0.348462\pi\)
0.458290 + 0.888803i \(0.348462\pi\)
\(840\) 0 0
\(841\) −28.5881 −0.985796
\(842\) 0 0
\(843\) −26.3821 −0.908647
\(844\) 0 0
\(845\) −45.0823 −1.55088
\(846\) 0 0
\(847\) 19.2385 0.661042
\(848\) 0 0
\(849\) −19.9376 −0.684257
\(850\) 0 0
\(851\) 10.6194 0.364027
\(852\) 0 0
\(853\) −37.6529 −1.28921 −0.644606 0.764515i \(-0.722978\pi\)
−0.644606 + 0.764515i \(0.722978\pi\)
\(854\) 0 0
\(855\) −17.3588 −0.593659
\(856\) 0 0
\(857\) 8.32877 0.284505 0.142253 0.989830i \(-0.454565\pi\)
0.142253 + 0.989830i \(0.454565\pi\)
\(858\) 0 0
\(859\) −6.27936 −0.214249 −0.107125 0.994246i \(-0.534164\pi\)
−0.107125 + 0.994246i \(0.534164\pi\)
\(860\) 0 0
\(861\) −38.7858 −1.32182
\(862\) 0 0
\(863\) −0.750794 −0.0255573 −0.0127787 0.999918i \(-0.504068\pi\)
−0.0127787 + 0.999918i \(0.504068\pi\)
\(864\) 0 0
\(865\) 92.7624 3.15402
\(866\) 0 0
\(867\) 11.8119 0.401154
\(868\) 0 0
\(869\) 5.22965 0.177404
\(870\) 0 0
\(871\) −5.37190 −0.182020
\(872\) 0 0
\(873\) 13.3417 0.451547
\(874\) 0 0
\(875\) 108.816 3.67866
\(876\) 0 0
\(877\) −2.08436 −0.0703839 −0.0351920 0.999381i \(-0.511204\pi\)
−0.0351920 + 0.999381i \(0.511204\pi\)
\(878\) 0 0
\(879\) −30.6368 −1.03335
\(880\) 0 0
\(881\) −27.7826 −0.936018 −0.468009 0.883724i \(-0.655029\pi\)
−0.468009 + 0.883724i \(0.655029\pi\)
\(882\) 0 0
\(883\) 5.29815 0.178297 0.0891484 0.996018i \(-0.471585\pi\)
0.0891484 + 0.996018i \(0.471585\pi\)
\(884\) 0 0
\(885\) 26.5486 0.892421
\(886\) 0 0
\(887\) 48.2315 1.61946 0.809728 0.586805i \(-0.199615\pi\)
0.809728 + 0.586805i \(0.199615\pi\)
\(888\) 0 0
\(889\) −80.2166 −2.69038
\(890\) 0 0
\(891\) −3.91880 −0.131285
\(892\) 0 0
\(893\) −48.1156 −1.61013
\(894\) 0 0
\(895\) 72.6500 2.42842
\(896\) 0 0
\(897\) −3.94991 −0.131884
\(898\) 0 0
\(899\) 2.89080 0.0964135
\(900\) 0 0
\(901\) −10.2464 −0.341356
\(902\) 0 0
\(903\) −30.1622 −1.00374
\(904\) 0 0
\(905\) −75.5809 −2.51239
\(906\) 0 0
\(907\) 23.6247 0.784445 0.392222 0.919870i \(-0.371706\pi\)
0.392222 + 0.919870i \(0.371706\pi\)
\(908\) 0 0
\(909\) 0.0616138 0.00204360
\(910\) 0 0
\(911\) 31.1298 1.03138 0.515688 0.856777i \(-0.327536\pi\)
0.515688 + 0.856777i \(0.327536\pi\)
\(912\) 0 0
\(913\) 55.5512 1.83848
\(914\) 0 0
\(915\) 0.0330719 0.00109332
\(916\) 0 0
\(917\) −48.7662 −1.61040
\(918\) 0 0
\(919\) −33.7448 −1.11314 −0.556569 0.830801i \(-0.687883\pi\)
−0.556569 + 0.830801i \(0.687883\pi\)
\(920\) 0 0
\(921\) 0.699590 0.0230523
\(922\) 0 0
\(923\) 3.11948 0.102679
\(924\) 0 0
\(925\) −39.9038 −1.31203
\(926\) 0 0
\(927\) 1.58232 0.0519702
\(928\) 0 0
\(929\) −21.5423 −0.706779 −0.353390 0.935476i \(-0.614971\pi\)
−0.353390 + 0.935476i \(0.614971\pi\)
\(930\) 0 0
\(931\) −54.0070 −1.77001
\(932\) 0 0
\(933\) −15.0625 −0.493125
\(934\) 0 0
\(935\) −84.4937 −2.76324
\(936\) 0 0
\(937\) 52.7027 1.72172 0.860861 0.508841i \(-0.169926\pi\)
0.860861 + 0.508841i \(0.169926\pi\)
\(938\) 0 0
\(939\) −7.76381 −0.253362
\(940\) 0 0
\(941\) 55.8970 1.82219 0.911094 0.412198i \(-0.135239\pi\)
0.911094 + 0.412198i \(0.135239\pi\)
\(942\) 0 0
\(943\) 26.0294 0.847633
\(944\) 0 0
\(945\) 17.7367 0.576975
\(946\) 0 0
\(947\) 9.46512 0.307575 0.153788 0.988104i \(-0.450853\pi\)
0.153788 + 0.988104i \(0.450853\pi\)
\(948\) 0 0
\(949\) 6.65937 0.216172
\(950\) 0 0
\(951\) 12.0203 0.389786
\(952\) 0 0
\(953\) −20.4719 −0.663151 −0.331575 0.943429i \(-0.607580\pi\)
−0.331575 + 0.943429i \(0.607580\pi\)
\(954\) 0 0
\(955\) −21.0794 −0.682112
\(956\) 0 0
\(957\) −2.51514 −0.0813030
\(958\) 0 0
\(959\) 65.5836 2.11781
\(960\) 0 0
\(961\) −10.7131 −0.345584
\(962\) 0 0
\(963\) 15.1136 0.487030
\(964\) 0 0
\(965\) 61.9782 1.99515
\(966\) 0 0
\(967\) −60.8243 −1.95598 −0.977988 0.208660i \(-0.933090\pi\)
−0.977988 + 0.208660i \(0.933090\pi\)
\(968\) 0 0
\(969\) −23.1964 −0.745176
\(970\) 0 0
\(971\) −45.6775 −1.46586 −0.732930 0.680304i \(-0.761848\pi\)
−0.732930 + 0.680304i \(0.761848\pi\)
\(972\) 0 0
\(973\) 54.7469 1.75511
\(974\) 0 0
\(975\) 14.8424 0.475336
\(976\) 0 0
\(977\) −56.6492 −1.81237 −0.906183 0.422885i \(-0.861018\pi\)
−0.906183 + 0.422885i \(0.861018\pi\)
\(978\) 0 0
\(979\) −48.4765 −1.54931
\(980\) 0 0
\(981\) −13.1743 −0.420623
\(982\) 0 0
\(983\) 39.9879 1.27542 0.637708 0.770278i \(-0.279883\pi\)
0.637708 + 0.770278i \(0.279883\pi\)
\(984\) 0 0
\(985\) −17.1762 −0.547281
\(986\) 0 0
\(987\) 49.1630 1.56488
\(988\) 0 0
\(989\) 20.2420 0.643659
\(990\) 0 0
\(991\) −13.6527 −0.433692 −0.216846 0.976206i \(-0.569577\pi\)
−0.216846 + 0.976206i \(0.569577\pi\)
\(992\) 0 0
\(993\) 4.62791 0.146862
\(994\) 0 0
\(995\) −35.9088 −1.13838
\(996\) 0 0
\(997\) 16.9689 0.537410 0.268705 0.963223i \(-0.413404\pi\)
0.268705 + 0.963223i \(0.413404\pi\)
\(998\) 0 0
\(999\) −3.58361 −0.113380
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 8016.2.a.be.1.11 11
4.3 odd 2 4008.2.a.k.1.11 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.k.1.11 11 4.3 odd 2
8016.2.a.be.1.11 11 1.1 even 1 trivial