Properties

Label 2205.4.a.ca.1.3
Level $2205$
Weight $4$
Character 2205.1
Self dual yes
Analytic conductor $130.099$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(130.099211563\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.1163891200.1
Defining polynomial: \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2\cdot 7 \)
Twist minimal: no (minimal twist has level 245)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.05886\) of defining polynomial
Character \(\chi\) \(=\) 2205.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.644648 q^{2} -7.58443 q^{4} +5.00000 q^{5} +10.0465 q^{8} +O(q^{10})\) \(q-0.644648 q^{2} -7.58443 q^{4} +5.00000 q^{5} +10.0465 q^{8} -3.22324 q^{10} +47.7013 q^{11} +57.2256 q^{13} +54.1990 q^{16} +36.9686 q^{17} +30.7659 q^{19} -37.9221 q^{20} -30.7506 q^{22} -53.1282 q^{23} +25.0000 q^{25} -36.8904 q^{26} +195.663 q^{29} +257.870 q^{31} -115.311 q^{32} -23.8317 q^{34} +346.423 q^{37} -19.8332 q^{38} +50.2324 q^{40} -267.050 q^{41} -176.859 q^{43} -361.787 q^{44} +34.2490 q^{46} +311.598 q^{47} -16.1162 q^{50} -434.024 q^{52} +492.270 q^{53} +238.507 q^{55} -126.134 q^{58} -98.7653 q^{59} +82.1682 q^{61} -166.235 q^{62} -359.257 q^{64} +286.128 q^{65} +654.668 q^{67} -280.386 q^{68} -779.658 q^{71} -829.673 q^{73} -223.321 q^{74} -233.342 q^{76} -769.426 q^{79} +270.995 q^{80} +172.153 q^{82} -613.203 q^{83} +184.843 q^{85} +114.012 q^{86} +479.230 q^{88} +457.666 q^{89} +402.947 q^{92} -200.871 q^{94} +153.830 q^{95} -1412.11 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} + 14 q^{4} + 30 q^{5} + 66 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} + 14 q^{4} + 30 q^{5} + 66 q^{8} + 10 q^{10} + 16 q^{11} + 168 q^{13} + 298 q^{16} + 4 q^{17} + 308 q^{19} + 70 q^{20} - 236 q^{22} + 336 q^{23} + 150 q^{25} - 56 q^{26} - 176 q^{29} + 392 q^{31} + 770 q^{32} + 812 q^{34} - 140 q^{37} - 20 q^{38} + 330 q^{40} - 656 q^{41} - 388 q^{43} + 160 q^{44} - 388 q^{46} - 628 q^{47} + 50 q^{50} + 1520 q^{52} + 676 q^{53} + 80 q^{55} - 2012 q^{58} - 996 q^{59} + 740 q^{61} + 364 q^{62} + 1426 q^{64} + 840 q^{65} + 1768 q^{67} + 2940 q^{68} + 224 q^{71} + 2640 q^{73} - 928 q^{74} - 1340 q^{76} + 1636 q^{79} + 1490 q^{80} - 1756 q^{82} - 140 q^{83} + 20 q^{85} - 1180 q^{86} - 5652 q^{88} + 1904 q^{89} + 1952 q^{92} - 3332 q^{94} + 1540 q^{95} + 516 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.644648 −0.227917 −0.113959 0.993485i \(-0.536353\pi\)
−0.113959 + 0.993485i \(0.536353\pi\)
\(3\) 0 0
\(4\) −7.58443 −0.948054
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) 10.0465 0.443995
\(9\) 0 0
\(10\) −3.22324 −0.101928
\(11\) 47.7013 1.30750 0.653750 0.756711i \(-0.273195\pi\)
0.653750 + 0.756711i \(0.273195\pi\)
\(12\) 0 0
\(13\) 57.2256 1.22089 0.610443 0.792060i \(-0.290991\pi\)
0.610443 + 0.792060i \(0.290991\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 54.1990 0.846859
\(17\) 36.9686 0.527423 0.263712 0.964602i \(-0.415053\pi\)
0.263712 + 0.964602i \(0.415053\pi\)
\(18\) 0 0
\(19\) 30.7659 0.371484 0.185742 0.982599i \(-0.440531\pi\)
0.185742 + 0.982599i \(0.440531\pi\)
\(20\) −37.9221 −0.423982
\(21\) 0 0
\(22\) −30.7506 −0.298002
\(23\) −53.1282 −0.481652 −0.240826 0.970568i \(-0.577418\pi\)
−0.240826 + 0.970568i \(0.577418\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −36.8904 −0.278261
\(27\) 0 0
\(28\) 0 0
\(29\) 195.663 1.25288 0.626442 0.779468i \(-0.284510\pi\)
0.626442 + 0.779468i \(0.284510\pi\)
\(30\) 0 0
\(31\) 257.870 1.49403 0.747014 0.664809i \(-0.231487\pi\)
0.747014 + 0.664809i \(0.231487\pi\)
\(32\) −115.311 −0.637010
\(33\) 0 0
\(34\) −23.8317 −0.120209
\(35\) 0 0
\(36\) 0 0
\(37\) 346.423 1.53923 0.769616 0.638507i \(-0.220447\pi\)
0.769616 + 0.638507i \(0.220447\pi\)
\(38\) −19.8332 −0.0846676
\(39\) 0 0
\(40\) 50.2324 0.198561
\(41\) −267.050 −1.01722 −0.508611 0.860996i \(-0.669841\pi\)
−0.508611 + 0.860996i \(0.669841\pi\)
\(42\) 0 0
\(43\) −176.859 −0.627227 −0.313614 0.949551i \(-0.601540\pi\)
−0.313614 + 0.949551i \(0.601540\pi\)
\(44\) −361.787 −1.23958
\(45\) 0 0
\(46\) 34.2490 0.109777
\(47\) 311.598 0.967049 0.483524 0.875331i \(-0.339356\pi\)
0.483524 + 0.875331i \(0.339356\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −16.1162 −0.0455835
\(51\) 0 0
\(52\) −434.024 −1.15747
\(53\) 492.270 1.27582 0.637910 0.770111i \(-0.279799\pi\)
0.637910 + 0.770111i \(0.279799\pi\)
\(54\) 0 0
\(55\) 238.507 0.584731
\(56\) 0 0
\(57\) 0 0
\(58\) −126.134 −0.285554
\(59\) −98.7653 −0.217935 −0.108967 0.994045i \(-0.534754\pi\)
−0.108967 + 0.994045i \(0.534754\pi\)
\(60\) 0 0
\(61\) 82.1682 0.172468 0.0862340 0.996275i \(-0.472517\pi\)
0.0862340 + 0.996275i \(0.472517\pi\)
\(62\) −166.235 −0.340515
\(63\) 0 0
\(64\) −359.257 −0.701674
\(65\) 286.128 0.545997
\(66\) 0 0
\(67\) 654.668 1.19374 0.596869 0.802339i \(-0.296411\pi\)
0.596869 + 0.802339i \(0.296411\pi\)
\(68\) −280.386 −0.500026
\(69\) 0 0
\(70\) 0 0
\(71\) −779.658 −1.30322 −0.651608 0.758556i \(-0.725905\pi\)
−0.651608 + 0.758556i \(0.725905\pi\)
\(72\) 0 0
\(73\) −829.673 −1.33022 −0.665109 0.746747i \(-0.731615\pi\)
−0.665109 + 0.746747i \(0.731615\pi\)
\(74\) −223.321 −0.350818
\(75\) 0 0
\(76\) −233.342 −0.352186
\(77\) 0 0
\(78\) 0 0
\(79\) −769.426 −1.09579 −0.547894 0.836548i \(-0.684570\pi\)
−0.547894 + 0.836548i \(0.684570\pi\)
\(80\) 270.995 0.378727
\(81\) 0 0
\(82\) 172.153 0.231843
\(83\) −613.203 −0.810937 −0.405469 0.914109i \(-0.632892\pi\)
−0.405469 + 0.914109i \(0.632892\pi\)
\(84\) 0 0
\(85\) 184.843 0.235871
\(86\) 114.012 0.142956
\(87\) 0 0
\(88\) 479.230 0.580524
\(89\) 457.666 0.545084 0.272542 0.962144i \(-0.412136\pi\)
0.272542 + 0.962144i \(0.412136\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 402.947 0.456632
\(93\) 0 0
\(94\) −200.871 −0.220407
\(95\) 153.830 0.166132
\(96\) 0 0
\(97\) −1412.11 −1.47813 −0.739063 0.673636i \(-0.764732\pi\)
−0.739063 + 0.673636i \(0.764732\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −189.611 −0.189611
\(101\) −1823.79 −1.79677 −0.898386 0.439208i \(-0.855259\pi\)
−0.898386 + 0.439208i \(0.855259\pi\)
\(102\) 0 0
\(103\) 407.775 0.390090 0.195045 0.980794i \(-0.437515\pi\)
0.195045 + 0.980794i \(0.437515\pi\)
\(104\) 574.915 0.542068
\(105\) 0 0
\(106\) −317.341 −0.290782
\(107\) 370.109 0.334390 0.167195 0.985924i \(-0.446529\pi\)
0.167195 + 0.985924i \(0.446529\pi\)
\(108\) 0 0
\(109\) 975.570 0.857272 0.428636 0.903477i \(-0.358994\pi\)
0.428636 + 0.903477i \(0.358994\pi\)
\(110\) −153.753 −0.133270
\(111\) 0 0
\(112\) 0 0
\(113\) −1978.85 −1.64739 −0.823693 0.567036i \(-0.808090\pi\)
−0.823693 + 0.567036i \(0.808090\pi\)
\(114\) 0 0
\(115\) −265.641 −0.215401
\(116\) −1483.99 −1.18780
\(117\) 0 0
\(118\) 63.6689 0.0496711
\(119\) 0 0
\(120\) 0 0
\(121\) 944.416 0.709554
\(122\) −52.9695 −0.0393085
\(123\) 0 0
\(124\) −1955.80 −1.41642
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1392.38 0.972867 0.486433 0.873718i \(-0.338298\pi\)
0.486433 + 0.873718i \(0.338298\pi\)
\(128\) 1154.08 0.796933
\(129\) 0 0
\(130\) −184.452 −0.124442
\(131\) 1777.02 1.18518 0.592591 0.805504i \(-0.298105\pi\)
0.592591 + 0.805504i \(0.298105\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −422.031 −0.272074
\(135\) 0 0
\(136\) 371.404 0.234174
\(137\) 1980.48 1.23506 0.617532 0.786545i \(-0.288132\pi\)
0.617532 + 0.786545i \(0.288132\pi\)
\(138\) 0 0
\(139\) 2182.09 1.33153 0.665763 0.746163i \(-0.268106\pi\)
0.665763 + 0.746163i \(0.268106\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 502.605 0.297026
\(143\) 2729.74 1.59631
\(144\) 0 0
\(145\) 978.313 0.560307
\(146\) 534.847 0.303180
\(147\) 0 0
\(148\) −2627.42 −1.45928
\(149\) −670.154 −0.368464 −0.184232 0.982883i \(-0.558980\pi\)
−0.184232 + 0.982883i \(0.558980\pi\)
\(150\) 0 0
\(151\) 3348.84 1.80480 0.902401 0.430898i \(-0.141803\pi\)
0.902401 + 0.430898i \(0.141803\pi\)
\(152\) 309.089 0.164937
\(153\) 0 0
\(154\) 0 0
\(155\) 1289.35 0.668149
\(156\) 0 0
\(157\) 2408.41 1.22428 0.612140 0.790749i \(-0.290309\pi\)
0.612140 + 0.790749i \(0.290309\pi\)
\(158\) 496.009 0.249749
\(159\) 0 0
\(160\) −576.555 −0.284879
\(161\) 0 0
\(162\) 0 0
\(163\) −3811.03 −1.83131 −0.915654 0.401968i \(-0.868326\pi\)
−0.915654 + 0.401968i \(0.868326\pi\)
\(164\) 2025.42 0.964382
\(165\) 0 0
\(166\) 395.300 0.184827
\(167\) −1207.15 −0.559354 −0.279677 0.960094i \(-0.590227\pi\)
−0.279677 + 0.960094i \(0.590227\pi\)
\(168\) 0 0
\(169\) 1077.77 0.490564
\(170\) −119.159 −0.0537591
\(171\) 0 0
\(172\) 1341.38 0.594645
\(173\) −3243.28 −1.42533 −0.712665 0.701505i \(-0.752512\pi\)
−0.712665 + 0.701505i \(0.752512\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2585.36 1.10727
\(177\) 0 0
\(178\) −295.034 −0.124234
\(179\) −859.728 −0.358989 −0.179495 0.983759i \(-0.557446\pi\)
−0.179495 + 0.983759i \(0.557446\pi\)
\(180\) 0 0
\(181\) −290.504 −0.119298 −0.0596491 0.998219i \(-0.518998\pi\)
−0.0596491 + 0.998219i \(0.518998\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −533.751 −0.213851
\(185\) 1732.12 0.688366
\(186\) 0 0
\(187\) 1763.45 0.689605
\(188\) −2363.30 −0.916814
\(189\) 0 0
\(190\) −99.1660 −0.0378645
\(191\) −4895.61 −1.85463 −0.927315 0.374282i \(-0.877889\pi\)
−0.927315 + 0.374282i \(0.877889\pi\)
\(192\) 0 0
\(193\) −3548.73 −1.32354 −0.661770 0.749707i \(-0.730194\pi\)
−0.661770 + 0.749707i \(0.730194\pi\)
\(194\) 910.315 0.336891
\(195\) 0 0
\(196\) 0 0
\(197\) 650.107 0.235118 0.117559 0.993066i \(-0.462493\pi\)
0.117559 + 0.993066i \(0.462493\pi\)
\(198\) 0 0
\(199\) 4055.09 1.44451 0.722256 0.691626i \(-0.243105\pi\)
0.722256 + 0.691626i \(0.243105\pi\)
\(200\) 251.162 0.0887991
\(201\) 0 0
\(202\) 1175.70 0.409516
\(203\) 0 0
\(204\) 0 0
\(205\) −1335.25 −0.454916
\(206\) −262.871 −0.0889083
\(207\) 0 0
\(208\) 3101.57 1.03392
\(209\) 1467.58 0.485714
\(210\) 0 0
\(211\) −1569.67 −0.512134 −0.256067 0.966659i \(-0.582427\pi\)
−0.256067 + 0.966659i \(0.582427\pi\)
\(212\) −3733.59 −1.20955
\(213\) 0 0
\(214\) −238.590 −0.0762134
\(215\) −884.296 −0.280504
\(216\) 0 0
\(217\) 0 0
\(218\) −628.900 −0.195387
\(219\) 0 0
\(220\) −1808.94 −0.554357
\(221\) 2115.55 0.643924
\(222\) 0 0
\(223\) 4723.86 1.41853 0.709267 0.704940i \(-0.249026\pi\)
0.709267 + 0.704940i \(0.249026\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1275.66 0.375468
\(227\) −3685.02 −1.07746 −0.538730 0.842479i \(-0.681096\pi\)
−0.538730 + 0.842479i \(0.681096\pi\)
\(228\) 0 0
\(229\) 3356.78 0.968656 0.484328 0.874887i \(-0.339064\pi\)
0.484328 + 0.874887i \(0.339064\pi\)
\(230\) 171.245 0.0490937
\(231\) 0 0
\(232\) 1965.72 0.556275
\(233\) −2314.01 −0.650627 −0.325314 0.945606i \(-0.605470\pi\)
−0.325314 + 0.945606i \(0.605470\pi\)
\(234\) 0 0
\(235\) 1557.99 0.432477
\(236\) 749.079 0.206614
\(237\) 0 0
\(238\) 0 0
\(239\) −941.179 −0.254727 −0.127364 0.991856i \(-0.540652\pi\)
−0.127364 + 0.991856i \(0.540652\pi\)
\(240\) 0 0
\(241\) 5638.24 1.50702 0.753509 0.657438i \(-0.228360\pi\)
0.753509 + 0.657438i \(0.228360\pi\)
\(242\) −608.816 −0.161720
\(243\) 0 0
\(244\) −623.199 −0.163509
\(245\) 0 0
\(246\) 0 0
\(247\) 1760.60 0.453539
\(248\) 2590.69 0.663341
\(249\) 0 0
\(250\) −80.5810 −0.0203856
\(251\) −365.822 −0.0919940 −0.0459970 0.998942i \(-0.514646\pi\)
−0.0459970 + 0.998942i \(0.514646\pi\)
\(252\) 0 0
\(253\) −2534.28 −0.629759
\(254\) −897.598 −0.221733
\(255\) 0 0
\(256\) 2130.08 0.520039
\(257\) 6276.46 1.52340 0.761702 0.647928i \(-0.224364\pi\)
0.761702 + 0.647928i \(0.224364\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2170.12 −0.517635
\(261\) 0 0
\(262\) −1145.55 −0.270124
\(263\) 4225.97 0.990817 0.495408 0.868660i \(-0.335018\pi\)
0.495408 + 0.868660i \(0.335018\pi\)
\(264\) 0 0
\(265\) 2461.35 0.570564
\(266\) 0 0
\(267\) 0 0
\(268\) −4965.28 −1.13173
\(269\) −981.591 −0.222486 −0.111243 0.993793i \(-0.535483\pi\)
−0.111243 + 0.993793i \(0.535483\pi\)
\(270\) 0 0
\(271\) 3884.42 0.870708 0.435354 0.900259i \(-0.356623\pi\)
0.435354 + 0.900259i \(0.356623\pi\)
\(272\) 2003.66 0.446653
\(273\) 0 0
\(274\) −1276.71 −0.281493
\(275\) 1192.53 0.261500
\(276\) 0 0
\(277\) 3614.93 0.784116 0.392058 0.919941i \(-0.371763\pi\)
0.392058 + 0.919941i \(0.371763\pi\)
\(278\) −1406.68 −0.303478
\(279\) 0 0
\(280\) 0 0
\(281\) −72.6835 −0.0154304 −0.00771518 0.999970i \(-0.502456\pi\)
−0.00771518 + 0.999970i \(0.502456\pi\)
\(282\) 0 0
\(283\) 1743.04 0.366125 0.183062 0.983101i \(-0.441399\pi\)
0.183062 + 0.983101i \(0.441399\pi\)
\(284\) 5913.26 1.23552
\(285\) 0 0
\(286\) −1759.72 −0.363827
\(287\) 0 0
\(288\) 0 0
\(289\) −3546.32 −0.721825
\(290\) −630.668 −0.127704
\(291\) 0 0
\(292\) 6292.59 1.26112
\(293\) 4989.29 0.994804 0.497402 0.867520i \(-0.334287\pi\)
0.497402 + 0.867520i \(0.334287\pi\)
\(294\) 0 0
\(295\) −493.827 −0.0974634
\(296\) 3480.33 0.683412
\(297\) 0 0
\(298\) 432.013 0.0839794
\(299\) −3040.29 −0.588042
\(300\) 0 0
\(301\) 0 0
\(302\) −2158.82 −0.411346
\(303\) 0 0
\(304\) 1667.48 0.314594
\(305\) 410.841 0.0771301
\(306\) 0 0
\(307\) 1664.61 0.309461 0.154731 0.987957i \(-0.450549\pi\)
0.154731 + 0.987957i \(0.450549\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −831.177 −0.152283
\(311\) −545.623 −0.0994838 −0.0497419 0.998762i \(-0.515840\pi\)
−0.0497419 + 0.998762i \(0.515840\pi\)
\(312\) 0 0
\(313\) 213.564 0.0385667 0.0192833 0.999814i \(-0.493862\pi\)
0.0192833 + 0.999814i \(0.493862\pi\)
\(314\) −1552.58 −0.279035
\(315\) 0 0
\(316\) 5835.66 1.03887
\(317\) 2683.93 0.475535 0.237767 0.971322i \(-0.423584\pi\)
0.237767 + 0.971322i \(0.423584\pi\)
\(318\) 0 0
\(319\) 9333.37 1.63815
\(320\) −1796.28 −0.313798
\(321\) 0 0
\(322\) 0 0
\(323\) 1137.37 0.195929
\(324\) 0 0
\(325\) 1430.64 0.244177
\(326\) 2456.77 0.417387
\(327\) 0 0
\(328\) −2682.91 −0.451642
\(329\) 0 0
\(330\) 0 0
\(331\) −5067.52 −0.841500 −0.420750 0.907177i \(-0.638233\pi\)
−0.420750 + 0.907177i \(0.638233\pi\)
\(332\) 4650.80 0.768812
\(333\) 0 0
\(334\) 778.187 0.127487
\(335\) 3273.34 0.533856
\(336\) 0 0
\(337\) −9353.21 −1.51187 −0.755937 0.654644i \(-0.772818\pi\)
−0.755937 + 0.654644i \(0.772818\pi\)
\(338\) −694.782 −0.111808
\(339\) 0 0
\(340\) −1401.93 −0.223618
\(341\) 12300.7 1.95344
\(342\) 0 0
\(343\) 0 0
\(344\) −1776.81 −0.278486
\(345\) 0 0
\(346\) 2090.77 0.324858
\(347\) −2349.34 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(348\) 0 0
\(349\) −10472.6 −1.60626 −0.803128 0.595806i \(-0.796833\pi\)
−0.803128 + 0.595806i \(0.796833\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5500.49 −0.832889
\(353\) 7174.63 1.08178 0.540888 0.841095i \(-0.318088\pi\)
0.540888 + 0.841095i \(0.318088\pi\)
\(354\) 0 0
\(355\) −3898.29 −0.582816
\(356\) −3471.14 −0.516769
\(357\) 0 0
\(358\) 554.222 0.0818199
\(359\) 7534.13 1.10762 0.553811 0.832643i \(-0.313173\pi\)
0.553811 + 0.832643i \(0.313173\pi\)
\(360\) 0 0
\(361\) −5912.46 −0.862000
\(362\) 187.273 0.0271902
\(363\) 0 0
\(364\) 0 0
\(365\) −4148.36 −0.594891
\(366\) 0 0
\(367\) 5453.06 0.775606 0.387803 0.921742i \(-0.373234\pi\)
0.387803 + 0.921742i \(0.373234\pi\)
\(368\) −2879.49 −0.407891
\(369\) 0 0
\(370\) −1116.60 −0.156891
\(371\) 0 0
\(372\) 0 0
\(373\) 8231.29 1.14263 0.571314 0.820732i \(-0.306434\pi\)
0.571314 + 0.820732i \(0.306434\pi\)
\(374\) −1136.80 −0.157173
\(375\) 0 0
\(376\) 3130.46 0.429365
\(377\) 11196.9 1.52963
\(378\) 0 0
\(379\) 1670.06 0.226346 0.113173 0.993575i \(-0.463898\pi\)
0.113173 + 0.993575i \(0.463898\pi\)
\(380\) −1166.71 −0.157502
\(381\) 0 0
\(382\) 3155.95 0.422703
\(383\) −3220.14 −0.429612 −0.214806 0.976657i \(-0.568912\pi\)
−0.214806 + 0.976657i \(0.568912\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2287.68 0.301658
\(387\) 0 0
\(388\) 10710.1 1.40134
\(389\) −3522.23 −0.459085 −0.229543 0.973299i \(-0.573723\pi\)
−0.229543 + 0.973299i \(0.573723\pi\)
\(390\) 0 0
\(391\) −1964.07 −0.254034
\(392\) 0 0
\(393\) 0 0
\(394\) −419.090 −0.0535875
\(395\) −3847.13 −0.490051
\(396\) 0 0
\(397\) −5455.16 −0.689639 −0.344819 0.938669i \(-0.612060\pi\)
−0.344819 + 0.938669i \(0.612060\pi\)
\(398\) −2614.11 −0.329229
\(399\) 0 0
\(400\) 1354.97 0.169372
\(401\) 1161.80 0.144682 0.0723409 0.997380i \(-0.476953\pi\)
0.0723409 + 0.997380i \(0.476953\pi\)
\(402\) 0 0
\(403\) 14756.8 1.82404
\(404\) 13832.4 1.70344
\(405\) 0 0
\(406\) 0 0
\(407\) 16524.8 2.01255
\(408\) 0 0
\(409\) −7398.65 −0.894473 −0.447237 0.894416i \(-0.647592\pi\)
−0.447237 + 0.894416i \(0.647592\pi\)
\(410\) 860.765 0.103683
\(411\) 0 0
\(412\) −3092.74 −0.369826
\(413\) 0 0
\(414\) 0 0
\(415\) −3066.02 −0.362662
\(416\) −6598.74 −0.777716
\(417\) 0 0
\(418\) −946.069 −0.110703
\(419\) −2134.46 −0.248867 −0.124433 0.992228i \(-0.539711\pi\)
−0.124433 + 0.992228i \(0.539711\pi\)
\(420\) 0 0
\(421\) −3902.36 −0.451756 −0.225878 0.974156i \(-0.572525\pi\)
−0.225878 + 0.974156i \(0.572525\pi\)
\(422\) 1011.88 0.116724
\(423\) 0 0
\(424\) 4945.58 0.566459
\(425\) 924.214 0.105485
\(426\) 0 0
\(427\) 0 0
\(428\) −2807.06 −0.317020
\(429\) 0 0
\(430\) 570.059 0.0639319
\(431\) 3618.13 0.404360 0.202180 0.979348i \(-0.435197\pi\)
0.202180 + 0.979348i \(0.435197\pi\)
\(432\) 0 0
\(433\) 4222.37 0.468624 0.234312 0.972161i \(-0.424716\pi\)
0.234312 + 0.972161i \(0.424716\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7399.14 −0.812740
\(437\) −1634.54 −0.178926
\(438\) 0 0
\(439\) 13518.0 1.46965 0.734826 0.678256i \(-0.237264\pi\)
0.734826 + 0.678256i \(0.237264\pi\)
\(440\) 2396.15 0.259618
\(441\) 0 0
\(442\) −1363.78 −0.146762
\(443\) −16591.2 −1.77939 −0.889695 0.456555i \(-0.849083\pi\)
−0.889695 + 0.456555i \(0.849083\pi\)
\(444\) 0 0
\(445\) 2288.33 0.243769
\(446\) −3045.23 −0.323309
\(447\) 0 0
\(448\) 0 0
\(449\) −8354.32 −0.878095 −0.439048 0.898464i \(-0.644684\pi\)
−0.439048 + 0.898464i \(0.644684\pi\)
\(450\) 0 0
\(451\) −12738.6 −1.33002
\(452\) 15008.5 1.56181
\(453\) 0 0
\(454\) 2375.54 0.245572
\(455\) 0 0
\(456\) 0 0
\(457\) −1280.34 −0.131054 −0.0655269 0.997851i \(-0.520873\pi\)
−0.0655269 + 0.997851i \(0.520873\pi\)
\(458\) −2163.94 −0.220774
\(459\) 0 0
\(460\) 2014.73 0.204212
\(461\) −6986.72 −0.705865 −0.352932 0.935649i \(-0.614815\pi\)
−0.352932 + 0.935649i \(0.614815\pi\)
\(462\) 0 0
\(463\) −5587.32 −0.560831 −0.280416 0.959879i \(-0.590472\pi\)
−0.280416 + 0.959879i \(0.590472\pi\)
\(464\) 10604.7 1.06102
\(465\) 0 0
\(466\) 1491.73 0.148289
\(467\) −9933.83 −0.984332 −0.492166 0.870501i \(-0.663795\pi\)
−0.492166 + 0.870501i \(0.663795\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1004.36 −0.0985691
\(471\) 0 0
\(472\) −992.243 −0.0967620
\(473\) −8436.41 −0.820099
\(474\) 0 0
\(475\) 769.148 0.0742967
\(476\) 0 0
\(477\) 0 0
\(478\) 606.729 0.0580568
\(479\) 5068.62 0.483489 0.241744 0.970340i \(-0.422280\pi\)
0.241744 + 0.970340i \(0.422280\pi\)
\(480\) 0 0
\(481\) 19824.3 1.87923
\(482\) −3634.68 −0.343476
\(483\) 0 0
\(484\) −7162.86 −0.672695
\(485\) −7060.56 −0.661038
\(486\) 0 0
\(487\) 264.353 0.0245975 0.0122988 0.999924i \(-0.496085\pi\)
0.0122988 + 0.999924i \(0.496085\pi\)
\(488\) 825.500 0.0765751
\(489\) 0 0
\(490\) 0 0
\(491\) 7459.47 0.685623 0.342812 0.939404i \(-0.388621\pi\)
0.342812 + 0.939404i \(0.388621\pi\)
\(492\) 0 0
\(493\) 7233.37 0.660800
\(494\) −1134.97 −0.103370
\(495\) 0 0
\(496\) 13976.3 1.26523
\(497\) 0 0
\(498\) 0 0
\(499\) 7206.67 0.646523 0.323261 0.946310i \(-0.395221\pi\)
0.323261 + 0.946310i \(0.395221\pi\)
\(500\) −948.054 −0.0847965
\(501\) 0 0
\(502\) 235.827 0.0209670
\(503\) 10886.7 0.965037 0.482519 0.875886i \(-0.339722\pi\)
0.482519 + 0.875886i \(0.339722\pi\)
\(504\) 0 0
\(505\) −9118.95 −0.803541
\(506\) 1633.72 0.143533
\(507\) 0 0
\(508\) −10560.4 −0.922330
\(509\) 7504.97 0.653540 0.326770 0.945104i \(-0.394040\pi\)
0.326770 + 0.945104i \(0.394040\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −10605.8 −0.915459
\(513\) 0 0
\(514\) −4046.11 −0.347210
\(515\) 2038.87 0.174453
\(516\) 0 0
\(517\) 14863.7 1.26442
\(518\) 0 0
\(519\) 0 0
\(520\) 2874.58 0.242420
\(521\) 22264.8 1.87224 0.936120 0.351681i \(-0.114390\pi\)
0.936120 + 0.351681i \(0.114390\pi\)
\(522\) 0 0
\(523\) 11286.7 0.943655 0.471828 0.881691i \(-0.343595\pi\)
0.471828 + 0.881691i \(0.343595\pi\)
\(524\) −13477.7 −1.12362
\(525\) 0 0
\(526\) −2724.27 −0.225824
\(527\) 9533.09 0.787985
\(528\) 0 0
\(529\) −9344.40 −0.768012
\(530\) −1586.70 −0.130042
\(531\) 0 0
\(532\) 0 0
\(533\) −15282.1 −1.24191
\(534\) 0 0
\(535\) 1850.54 0.149544
\(536\) 6577.10 0.530014
\(537\) 0 0
\(538\) 632.781 0.0507084
\(539\) 0 0
\(540\) 0 0
\(541\) 16406.8 1.30385 0.651924 0.758284i \(-0.273962\pi\)
0.651924 + 0.758284i \(0.273962\pi\)
\(542\) −2504.08 −0.198450
\(543\) 0 0
\(544\) −4262.88 −0.335974
\(545\) 4877.85 0.383384
\(546\) 0 0
\(547\) −8692.48 −0.679458 −0.339729 0.940523i \(-0.610335\pi\)
−0.339729 + 0.940523i \(0.610335\pi\)
\(548\) −15020.8 −1.17091
\(549\) 0 0
\(550\) −768.764 −0.0596004
\(551\) 6019.74 0.465426
\(552\) 0 0
\(553\) 0 0
\(554\) −2330.36 −0.178714
\(555\) 0 0
\(556\) −16549.9 −1.26236
\(557\) 13935.7 1.06010 0.530049 0.847967i \(-0.322174\pi\)
0.530049 + 0.847967i \(0.322174\pi\)
\(558\) 0 0
\(559\) −10120.9 −0.765773
\(560\) 0 0
\(561\) 0 0
\(562\) 46.8553 0.00351685
\(563\) −22263.6 −1.66661 −0.833304 0.552815i \(-0.813553\pi\)
−0.833304 + 0.552815i \(0.813553\pi\)
\(564\) 0 0
\(565\) −9894.26 −0.736734
\(566\) −1123.65 −0.0834462
\(567\) 0 0
\(568\) −7832.81 −0.578622
\(569\) −9525.66 −0.701822 −0.350911 0.936409i \(-0.614128\pi\)
−0.350911 + 0.936409i \(0.614128\pi\)
\(570\) 0 0
\(571\) 7669.99 0.562135 0.281068 0.959688i \(-0.409311\pi\)
0.281068 + 0.959688i \(0.409311\pi\)
\(572\) −20703.5 −1.51339
\(573\) 0 0
\(574\) 0 0
\(575\) −1328.20 −0.0963304
\(576\) 0 0
\(577\) −3907.15 −0.281901 −0.140950 0.990017i \(-0.545016\pi\)
−0.140950 + 0.990017i \(0.545016\pi\)
\(578\) 2286.13 0.164516
\(579\) 0 0
\(580\) −7419.95 −0.531201
\(581\) 0 0
\(582\) 0 0
\(583\) 23481.9 1.66813
\(584\) −8335.28 −0.590610
\(585\) 0 0
\(586\) −3216.34 −0.226733
\(587\) −19891.6 −1.39866 −0.699331 0.714798i \(-0.746519\pi\)
−0.699331 + 0.714798i \(0.746519\pi\)
\(588\) 0 0
\(589\) 7933.61 0.555007
\(590\) 318.344 0.0222136
\(591\) 0 0
\(592\) 18775.8 1.30351
\(593\) 4780.36 0.331038 0.165519 0.986207i \(-0.447070\pi\)
0.165519 + 0.986207i \(0.447070\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5082.74 0.349324
\(597\) 0 0
\(598\) 1959.92 0.134025
\(599\) −11085.6 −0.756170 −0.378085 0.925771i \(-0.623417\pi\)
−0.378085 + 0.925771i \(0.623417\pi\)
\(600\) 0 0
\(601\) 1573.44 0.106792 0.0533958 0.998573i \(-0.482995\pi\)
0.0533958 + 0.998573i \(0.482995\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −25399.1 −1.71105
\(605\) 4722.08 0.317322
\(606\) 0 0
\(607\) −8542.73 −0.571233 −0.285617 0.958344i \(-0.592198\pi\)
−0.285617 + 0.958344i \(0.592198\pi\)
\(608\) −3547.65 −0.236639
\(609\) 0 0
\(610\) −264.848 −0.0175793
\(611\) 17831.4 1.18066
\(612\) 0 0
\(613\) 15068.2 0.992817 0.496409 0.868089i \(-0.334652\pi\)
0.496409 + 0.868089i \(0.334652\pi\)
\(614\) −1073.09 −0.0705316
\(615\) 0 0
\(616\) 0 0
\(617\) −2524.58 −0.164725 −0.0823627 0.996602i \(-0.526247\pi\)
−0.0823627 + 0.996602i \(0.526247\pi\)
\(618\) 0 0
\(619\) 21238.9 1.37910 0.689551 0.724237i \(-0.257808\pi\)
0.689551 + 0.724237i \(0.257808\pi\)
\(620\) −9778.99 −0.633441
\(621\) 0 0
\(622\) 351.735 0.0226741
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −137.674 −0.00879002
\(627\) 0 0
\(628\) −18266.4 −1.16068
\(629\) 12806.8 0.811827
\(630\) 0 0
\(631\) −8885.83 −0.560601 −0.280300 0.959912i \(-0.590434\pi\)
−0.280300 + 0.959912i \(0.590434\pi\)
\(632\) −7730.02 −0.486525
\(633\) 0 0
\(634\) −1730.19 −0.108383
\(635\) 6961.92 0.435079
\(636\) 0 0
\(637\) 0 0
\(638\) −6016.74 −0.373362
\(639\) 0 0
\(640\) 5770.41 0.356399
\(641\) −3655.63 −0.225255 −0.112628 0.993637i \(-0.535927\pi\)
−0.112628 + 0.993637i \(0.535927\pi\)
\(642\) 0 0
\(643\) −4221.22 −0.258894 −0.129447 0.991586i \(-0.541320\pi\)
−0.129447 + 0.991586i \(0.541320\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −733.205 −0.0446557
\(647\) 103.679 0.00629989 0.00314995 0.999995i \(-0.498997\pi\)
0.00314995 + 0.999995i \(0.498997\pi\)
\(648\) 0 0
\(649\) −4711.24 −0.284949
\(650\) −922.259 −0.0556523
\(651\) 0 0
\(652\) 28904.5 1.73618
\(653\) −4476.11 −0.268245 −0.134122 0.990965i \(-0.542821\pi\)
−0.134122 + 0.990965i \(0.542821\pi\)
\(654\) 0 0
\(655\) 8885.09 0.530029
\(656\) −14473.8 −0.861445
\(657\) 0 0
\(658\) 0 0
\(659\) −12022.0 −0.710641 −0.355321 0.934745i \(-0.615628\pi\)
−0.355321 + 0.934745i \(0.615628\pi\)
\(660\) 0 0
\(661\) −13451.0 −0.791504 −0.395752 0.918357i \(-0.629516\pi\)
−0.395752 + 0.918357i \(0.629516\pi\)
\(662\) 3266.77 0.191792
\(663\) 0 0
\(664\) −6160.53 −0.360053
\(665\) 0 0
\(666\) 0 0
\(667\) −10395.2 −0.603454
\(668\) 9155.55 0.530297
\(669\) 0 0
\(670\) −2110.15 −0.121675
\(671\) 3919.53 0.225502
\(672\) 0 0
\(673\) 9774.83 0.559869 0.279935 0.960019i \(-0.409687\pi\)
0.279935 + 0.960019i \(0.409687\pi\)
\(674\) 6029.53 0.344583
\(675\) 0 0
\(676\) −8174.27 −0.465081
\(677\) 23857.4 1.35438 0.677190 0.735808i \(-0.263198\pi\)
0.677190 + 0.735808i \(0.263198\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1857.02 0.104726
\(681\) 0 0
\(682\) −7929.65 −0.445223
\(683\) −11919.4 −0.667763 −0.333881 0.942615i \(-0.608358\pi\)
−0.333881 + 0.942615i \(0.608358\pi\)
\(684\) 0 0
\(685\) 9902.40 0.552338
\(686\) 0 0
\(687\) 0 0
\(688\) −9585.59 −0.531173
\(689\) 28170.5 1.55763
\(690\) 0 0
\(691\) 8203.58 0.451634 0.225817 0.974170i \(-0.427495\pi\)
0.225817 + 0.974170i \(0.427495\pi\)
\(692\) 24598.4 1.35129
\(693\) 0 0
\(694\) 1514.50 0.0828380
\(695\) 10910.4 0.595477
\(696\) 0 0
\(697\) −9872.44 −0.536507
\(698\) 6751.12 0.366094
\(699\) 0 0
\(700\) 0 0
\(701\) −449.084 −0.0241964 −0.0120982 0.999927i \(-0.503851\pi\)
−0.0120982 + 0.999927i \(0.503851\pi\)
\(702\) 0 0
\(703\) 10658.0 0.571800
\(704\) −17137.0 −0.917438
\(705\) 0 0
\(706\) −4625.11 −0.246556
\(707\) 0 0
\(708\) 0 0
\(709\) 1897.64 0.100518 0.0502590 0.998736i \(-0.483995\pi\)
0.0502590 + 0.998736i \(0.483995\pi\)
\(710\) 2513.02 0.132834
\(711\) 0 0
\(712\) 4597.93 0.242015
\(713\) −13700.2 −0.719601
\(714\) 0 0
\(715\) 13648.7 0.713891
\(716\) 6520.54 0.340341
\(717\) 0 0
\(718\) −4856.86 −0.252446
\(719\) 6494.70 0.336873 0.168436 0.985713i \(-0.446128\pi\)
0.168436 + 0.985713i \(0.446128\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3811.45 0.196465
\(723\) 0 0
\(724\) 2203.31 0.113101
\(725\) 4891.57 0.250577
\(726\) 0 0
\(727\) 18311.2 0.934148 0.467074 0.884218i \(-0.345308\pi\)
0.467074 + 0.884218i \(0.345308\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2674.23 0.135586
\(731\) −6538.23 −0.330814
\(732\) 0 0
\(733\) −21233.3 −1.06994 −0.534972 0.844870i \(-0.679678\pi\)
−0.534972 + 0.844870i \(0.679678\pi\)
\(734\) −3515.30 −0.176774
\(735\) 0 0
\(736\) 6126.27 0.306817
\(737\) 31228.5 1.56081
\(738\) 0 0
\(739\) −22023.5 −1.09628 −0.548138 0.836388i \(-0.684663\pi\)
−0.548138 + 0.836388i \(0.684663\pi\)
\(740\) −13137.1 −0.652608
\(741\) 0 0
\(742\) 0 0
\(743\) −9436.77 −0.465951 −0.232975 0.972483i \(-0.574846\pi\)
−0.232975 + 0.972483i \(0.574846\pi\)
\(744\) 0 0
\(745\) −3350.77 −0.164782
\(746\) −5306.29 −0.260425
\(747\) 0 0
\(748\) −13374.8 −0.653783
\(749\) 0 0
\(750\) 0 0
\(751\) −39161.8 −1.90284 −0.951421 0.307893i \(-0.900376\pi\)
−0.951421 + 0.307893i \(0.900376\pi\)
\(752\) 16888.3 0.818954
\(753\) 0 0
\(754\) −7218.07 −0.348629
\(755\) 16744.2 0.807132
\(756\) 0 0
\(757\) 20340.6 0.976607 0.488303 0.872674i \(-0.337616\pi\)
0.488303 + 0.872674i \(0.337616\pi\)
\(758\) −1076.60 −0.0515883
\(759\) 0 0
\(760\) 1545.44 0.0737621
\(761\) 3307.90 0.157570 0.0787852 0.996892i \(-0.474896\pi\)
0.0787852 + 0.996892i \(0.474896\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 37130.4 1.75829
\(765\) 0 0
\(766\) 2075.85 0.0979160
\(767\) −5651.91 −0.266074
\(768\) 0 0
\(769\) −17234.0 −0.808159 −0.404079 0.914724i \(-0.632408\pi\)
−0.404079 + 0.914724i \(0.632408\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 26915.1 1.25479
\(773\) −8726.33 −0.406034 −0.203017 0.979175i \(-0.565075\pi\)
−0.203017 + 0.979175i \(0.565075\pi\)
\(774\) 0 0
\(775\) 6446.75 0.298806
\(776\) −14186.7 −0.656281
\(777\) 0 0
\(778\) 2270.60 0.104634
\(779\) −8216.03 −0.377882
\(780\) 0 0
\(781\) −37190.7 −1.70395
\(782\) 1266.14 0.0578989
\(783\) 0 0
\(784\) 0 0
\(785\) 12042.0 0.547515
\(786\) 0 0
\(787\) 10642.1 0.482018 0.241009 0.970523i \(-0.422522\pi\)
0.241009 + 0.970523i \(0.422522\pi\)
\(788\) −4930.69 −0.222904
\(789\) 0 0
\(790\) 2480.05 0.111691
\(791\) 0 0
\(792\) 0 0
\(793\) 4702.12 0.210564
\(794\) 3516.66 0.157181
\(795\) 0 0
\(796\) −30755.5 −1.36947
\(797\) 29234.1 1.29928 0.649640 0.760242i \(-0.274920\pi\)
0.649640 + 0.760242i \(0.274920\pi\)
\(798\) 0 0
\(799\) 11519.3 0.510044
\(800\) −2882.78 −0.127402
\(801\) 0 0
\(802\) −748.950 −0.0329755
\(803\) −39576.5 −1.73926
\(804\) 0 0
\(805\) 0 0
\(806\) −9512.93 −0.415730
\(807\) 0 0
\(808\) −18322.7 −0.797758
\(809\) −36211.2 −1.57369 −0.786846 0.617150i \(-0.788287\pi\)
−0.786846 + 0.617150i \(0.788287\pi\)
\(810\) 0 0
\(811\) 27995.2 1.21214 0.606069 0.795412i \(-0.292746\pi\)
0.606069 + 0.795412i \(0.292746\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −10652.7 −0.458694
\(815\) −19055.2 −0.818985
\(816\) 0 0
\(817\) −5441.23 −0.233005
\(818\) 4769.52 0.203866
\(819\) 0 0
\(820\) 10127.1 0.431285
\(821\) −44805.7 −1.90467 −0.952333 0.305060i \(-0.901323\pi\)
−0.952333 + 0.305060i \(0.901323\pi\)
\(822\) 0 0
\(823\) −15850.9 −0.671360 −0.335680 0.941976i \(-0.608966\pi\)
−0.335680 + 0.941976i \(0.608966\pi\)
\(824\) 4096.70 0.173198
\(825\) 0 0
\(826\) 0 0
\(827\) 45013.9 1.89273 0.946363 0.323104i \(-0.104726\pi\)
0.946363 + 0.323104i \(0.104726\pi\)
\(828\) 0 0
\(829\) −5655.83 −0.236954 −0.118477 0.992957i \(-0.537801\pi\)
−0.118477 + 0.992957i \(0.537801\pi\)
\(830\) 1976.50 0.0826571
\(831\) 0 0
\(832\) −20558.7 −0.856664
\(833\) 0 0
\(834\) 0 0
\(835\) −6035.75 −0.250151
\(836\) −11130.7 −0.460483
\(837\) 0 0
\(838\) 1375.97 0.0567211
\(839\) −22037.0 −0.906797 −0.453398 0.891308i \(-0.649789\pi\)
−0.453398 + 0.891308i \(0.649789\pi\)
\(840\) 0 0
\(841\) 13894.9 0.569719
\(842\) 2515.65 0.102963
\(843\) 0 0
\(844\) 11905.0 0.485530
\(845\) 5388.85 0.219387
\(846\) 0 0
\(847\) 0 0
\(848\) 26680.5 1.08044
\(849\) 0 0
\(850\) −595.793 −0.0240418
\(851\) −18404.8 −0.741374
\(852\) 0 0
\(853\) 44486.7 1.78569 0.892846 0.450362i \(-0.148705\pi\)
0.892846 + 0.450362i \(0.148705\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 3718.29 0.148468
\(857\) −38559.6 −1.53696 −0.768478 0.639877i \(-0.778985\pi\)
−0.768478 + 0.639877i \(0.778985\pi\)
\(858\) 0 0
\(859\) −8426.01 −0.334682 −0.167341 0.985899i \(-0.553518\pi\)
−0.167341 + 0.985899i \(0.553518\pi\)
\(860\) 6706.88 0.265933
\(861\) 0 0
\(862\) −2332.42 −0.0921608
\(863\) 20054.3 0.791029 0.395514 0.918460i \(-0.370566\pi\)
0.395514 + 0.918460i \(0.370566\pi\)
\(864\) 0 0
\(865\) −16216.4 −0.637427
\(866\) −2721.94 −0.106808
\(867\) 0 0
\(868\) 0 0
\(869\) −36702.6 −1.43274
\(870\) 0 0
\(871\) 37463.8 1.45742
\(872\) 9801.04 0.380625
\(873\) 0 0
\(874\) 1053.70 0.0407803
\(875\) 0 0
\(876\) 0 0
\(877\) 47082.1 1.81283 0.906414 0.422391i \(-0.138809\pi\)
0.906414 + 0.422391i \(0.138809\pi\)
\(878\) −8714.32 −0.334959
\(879\) 0 0
\(880\) 12926.8 0.495185
\(881\) −9467.24 −0.362042 −0.181021 0.983479i \(-0.557940\pi\)
−0.181021 + 0.983479i \(0.557940\pi\)
\(882\) 0 0
\(883\) −3049.49 −0.116221 −0.0581106 0.998310i \(-0.518508\pi\)
−0.0581106 + 0.998310i \(0.518508\pi\)
\(884\) −16045.2 −0.610475
\(885\) 0 0
\(886\) 10695.5 0.405554
\(887\) −19468.6 −0.736968 −0.368484 0.929634i \(-0.620123\pi\)
−0.368484 + 0.929634i \(0.620123\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −1475.17 −0.0555592
\(891\) 0 0
\(892\) −35827.8 −1.34485
\(893\) 9586.61 0.359243
\(894\) 0 0
\(895\) −4298.64 −0.160545
\(896\) 0 0
\(897\) 0 0
\(898\) 5385.60 0.200133
\(899\) 50455.6 1.87184
\(900\) 0 0
\(901\) 18198.5 0.672898
\(902\) 8211.92 0.303134
\(903\) 0 0
\(904\) −19880.5 −0.731432
\(905\) −1452.52 −0.0533518
\(906\) 0 0
\(907\) −32014.2 −1.17201 −0.586006 0.810307i \(-0.699301\pi\)
−0.586006 + 0.810307i \(0.699301\pi\)
\(908\) 27948.8 1.02149
\(909\) 0 0
\(910\) 0 0
\(911\) −20921.1 −0.760866 −0.380433 0.924809i \(-0.624225\pi\)
−0.380433 + 0.924809i \(0.624225\pi\)
\(912\) 0 0
\(913\) −29250.6 −1.06030
\(914\) 825.366 0.0298694
\(915\) 0 0
\(916\) −25459.2 −0.918337
\(917\) 0 0
\(918\) 0 0
\(919\) 43467.4 1.56024 0.780118 0.625632i \(-0.215159\pi\)
0.780118 + 0.625632i \(0.215159\pi\)
\(920\) −2668.75 −0.0956372
\(921\) 0 0
\(922\) 4503.97 0.160879
\(923\) −44616.4 −1.59108
\(924\) 0 0
\(925\) 8660.58 0.307847
\(926\) 3601.85 0.127823
\(927\) 0 0
\(928\) −22562.1 −0.798099
\(929\) −18542.1 −0.654840 −0.327420 0.944879i \(-0.606179\pi\)
−0.327420 + 0.944879i \(0.606179\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 17550.5 0.616830
\(933\) 0 0
\(934\) 6403.82 0.224346
\(935\) 8817.25 0.308401
\(936\) 0 0
\(937\) −13842.5 −0.482619 −0.241309 0.970448i \(-0.577577\pi\)
−0.241309 + 0.970448i \(0.577577\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −11816.5 −0.410012
\(941\) −53393.2 −1.84970 −0.924850 0.380333i \(-0.875809\pi\)
−0.924850 + 0.380333i \(0.875809\pi\)
\(942\) 0 0
\(943\) 14187.9 0.489947
\(944\) −5352.98 −0.184560
\(945\) 0 0
\(946\) 5438.52 0.186915
\(947\) −22344.2 −0.766727 −0.383364 0.923598i \(-0.625234\pi\)
−0.383364 + 0.923598i \(0.625234\pi\)
\(948\) 0 0
\(949\) −47478.5 −1.62404
\(950\) −495.830 −0.0169335
\(951\) 0 0
\(952\) 0 0
\(953\) 8902.63 0.302607 0.151304 0.988487i \(-0.451653\pi\)
0.151304 + 0.988487i \(0.451653\pi\)
\(954\) 0 0
\(955\) −24478.1 −0.829416
\(956\) 7138.31 0.241495
\(957\) 0 0
\(958\) −3267.48 −0.110196
\(959\) 0 0
\(960\) 0 0
\(961\) 36706.0 1.23212
\(962\) −12779.7 −0.428309
\(963\) 0 0
\(964\) −42762.8 −1.42873
\(965\) −17743.6 −0.591905
\(966\) 0 0
\(967\) −2225.57 −0.0740119 −0.0370059 0.999315i \(-0.511782\pi\)
−0.0370059 + 0.999315i \(0.511782\pi\)
\(968\) 9488.05 0.315039
\(969\) 0 0
\(970\) 4551.58 0.150662
\(971\) −11324.8 −0.374285 −0.187143 0.982333i \(-0.559923\pi\)
−0.187143 + 0.982333i \(0.559923\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −170.415 −0.00560621
\(975\) 0 0
\(976\) 4453.43 0.146056
\(977\) 57695.9 1.88931 0.944654 0.328067i \(-0.106397\pi\)
0.944654 + 0.328067i \(0.106397\pi\)
\(978\) 0 0
\(979\) 21831.3 0.712697
\(980\) 0 0
\(981\) 0 0
\(982\) −4808.73 −0.156266
\(983\) 59657.3 1.93568 0.967839 0.251570i \(-0.0809469\pi\)
0.967839 + 0.251570i \(0.0809469\pi\)
\(984\) 0 0
\(985\) 3250.54 0.105148
\(986\) −4662.98 −0.150608
\(987\) 0 0
\(988\) −13353.1 −0.429980
\(989\) 9396.20 0.302105
\(990\) 0 0
\(991\) 2890.60 0.0926568 0.0463284 0.998926i \(-0.485248\pi\)
0.0463284 + 0.998926i \(0.485248\pi\)
\(992\) −29735.3 −0.951710
\(993\) 0 0
\(994\) 0 0
\(995\) 20275.5 0.646005
\(996\) 0 0
\(997\) 10619.6 0.337337 0.168669 0.985673i \(-0.446053\pi\)
0.168669 + 0.985673i \(0.446053\pi\)
\(998\) −4645.77 −0.147354
\(999\) 0 0
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 2205.4.a.ca.1.3 6
3.2 odd 2 245.4.a.p.1.4 yes 6
7.6 odd 2 2205.4.a.bz.1.3 6
15.14 odd 2 1225.4.a.bi.1.3 6
21.2 odd 6 245.4.e.p.116.3 12
21.5 even 6 245.4.e.q.116.3 12
21.11 odd 6 245.4.e.p.226.3 12
21.17 even 6 245.4.e.q.226.3 12
21.20 even 2 245.4.a.o.1.4 6
105.104 even 2 1225.4.a.bj.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.4 6 21.20 even 2
245.4.a.p.1.4 yes 6 3.2 odd 2
245.4.e.p.116.3 12 21.2 odd 6
245.4.e.p.226.3 12 21.11 odd 6
245.4.e.q.116.3 12 21.5 even 6
245.4.e.q.226.3 12 21.17 even 6
1225.4.a.bi.1.3 6 15.14 odd 2
1225.4.a.bj.1.3 6 105.104 even 2
2205.4.a.bz.1.3 6 7.6 odd 2
2205.4.a.ca.1.3 6 1.1 even 1 trivial