Properties

Label 2205.4.a.bz.1.3
Level $2205$
Weight $4$
Character 2205.1
Self dual yes
Analytic conductor $130.099$
Analytic rank $1$
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: \(1\)
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 \(-0.709009\pi\)
−0.610443 + 0.792060i \(0.709009\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 54.1990 0.846859
\(17\) −36.9686 −0.527423 −0.263712 0.964602i \(-0.584947\pi\)
−0.263712 + 0.964602i \(0.584947\pi\)
\(18\) 0 0
\(19\) −30.7659 −0.371484 −0.185742 0.982599i \(-0.559469\pi\)
−0.185742 + 0.982599i \(0.559469\pi\)
\(20\) 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 \(-0.768513\pi\)
−0.747014 + 0.664809i \(0.768513\pi\)
\(32\) −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 \(-0.330159\pi\)
0.508611 + 0.860996i \(0.330159\pi\)
\(42\) 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 \(-0.660644\pi\)
−0.483524 + 0.875331i \(0.660644\pi\)
\(48\) 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 \(-0.465246\pi\)
0.108967 + 0.994045i \(0.465246\pi\)
\(60\) 0 0
\(61\) −82.1682 −0.172468 −0.0862340 0.996275i \(-0.527483\pi\)
−0.0862340 + 0.996275i \(0.527483\pi\)
\(62\) 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 \(-0.268385\pi\)
0.665109 + 0.746747i \(0.268385\pi\)
\(74\) −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 \(-0.367108\pi\)
0.405469 + 0.914109i \(0.367108\pi\)
\(84\) 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 \(-0.587864\pi\)
−0.272542 + 0.962144i \(0.587864\pi\)
\(90\) 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 \(-0.235268\pi\)
0.739063 + 0.673636i \(0.235268\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −189.611 −0.189611
\(101\) 1823.79 1.79677 0.898386 0.439208i \(-0.144741\pi\)
0.898386 + 0.439208i \(0.144741\pi\)
\(102\) 0 0
\(103\) −407.775 −0.390090 −0.195045 0.980794i \(-0.562485\pi\)
−0.195045 + 0.980794i \(0.562485\pi\)
\(104\) −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 \(-0.701895\pi\)
−0.592591 + 0.805504i \(0.701895\pi\)
\(132\) 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 \(-0.731894\pi\)
−0.665763 + 0.746163i \(0.731894\pi\)
\(140\) 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 \(-0.709691\pi\)
−0.612140 + 0.790749i \(0.709691\pi\)
\(158\) 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 \(-0.409773\pi\)
0.279677 + 0.960094i \(0.409773\pi\)
\(168\) 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 \(-0.247488\pi\)
0.712665 + 0.701505i \(0.247488\pi\)
\(174\) 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 \(-0.481002\pi\)
0.0596491 + 0.998219i \(0.481002\pi\)
\(182\) 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 \(-0.756895\pi\)
−0.722256 + 0.691626i \(0.756895\pi\)
\(200\) 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 \(-0.750974\pi\)
−0.709267 + 0.704940i \(0.750974\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1275.66 0.375468
\(227\) 3685.02 1.07746 0.538730 0.842479i \(-0.318904\pi\)
0.538730 + 0.842479i \(0.318904\pi\)
\(228\) 0 0
\(229\) −3356.78 −0.968656 −0.484328 0.874887i \(-0.660936\pi\)
−0.484328 + 0.874887i \(0.660936\pi\)
\(230\) −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 \(-0.771640\pi\)
−0.753509 + 0.657438i \(0.771640\pi\)
\(242\) −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 \(-0.485354\pi\)
0.0459970 + 0.998942i \(0.485354\pi\)
\(252\) 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 \(-0.775636\pi\)
−0.761702 + 0.647928i \(0.775636\pi\)
\(258\) 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 \(-0.464517\pi\)
0.111243 + 0.993793i \(0.464517\pi\)
\(270\) 0 0
\(271\) −3884.42 −0.870708 −0.435354 0.900259i \(-0.643377\pi\)
−0.435354 + 0.900259i \(0.643377\pi\)
\(272\) −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 \(-0.558601\pi\)
−0.183062 + 0.983101i \(0.558601\pi\)
\(284\) 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 \(-0.665713\pi\)
−0.497402 + 0.867520i \(0.665713\pi\)
\(294\) 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 \(-0.549451\pi\)
−0.154731 + 0.987957i \(0.549451\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −831.177 −0.152283
\(311\) 545.623 0.0994838 0.0497419 0.998762i \(-0.484160\pi\)
0.0497419 + 0.998762i \(0.484160\pi\)
\(312\) 0 0
\(313\) −213.564 −0.0385667 −0.0192833 0.999814i \(-0.506138\pi\)
−0.0192833 + 0.999814i \(0.506138\pi\)
\(314\) 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 \(-0.203167\pi\)
0.803128 + 0.595806i \(0.203167\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5500.49 −0.832889
\(353\) −7174.63 −1.08178 −0.540888 0.841095i \(-0.681912\pi\)
−0.540888 + 0.841095i \(0.681912\pi\)
\(354\) 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 \(-0.626766\pi\)
−0.387803 + 0.921742i \(0.626766\pi\)
\(368\) −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 \(-0.431088\pi\)
0.214806 + 0.976657i \(0.431088\pi\)
\(384\) 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 \(-0.387940\pi\)
0.344819 + 0.938669i \(0.387940\pi\)
\(398\) 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 \(-0.352408\pi\)
0.447237 + 0.894416i \(0.352408\pi\)
\(410\) 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 \(-0.460289\pi\)
0.124433 + 0.992228i \(0.460289\pi\)
\(420\) 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 \(-0.575284\pi\)
−0.234312 + 0.972161i \(0.575284\pi\)
\(434\) 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 \(-0.762736\pi\)
−0.734826 + 0.678256i \(0.762736\pi\)
\(440\) −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 \(-0.385185\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(462\) 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 \(-0.336205\pi\)
0.492166 + 0.870501i \(0.336205\pi\)
\(468\) 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 \(-0.577720\pi\)
−0.241744 + 0.970340i \(0.577720\pi\)
\(480\) 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 \(-0.660278\pi\)
−0.482519 + 0.875886i \(0.660278\pi\)
\(504\) 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 \(-0.605960\pi\)
−0.326770 + 0.945104i \(0.605960\pi\)
\(510\) 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 \(-0.885610\pi\)
−0.936120 + 0.351681i \(0.885610\pi\)
\(522\) 0 0
\(523\) −11286.7 −0.943655 −0.471828 0.881691i \(-0.656405\pi\)
−0.471828 + 0.881691i \(0.656405\pi\)
\(524\) 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 \(-0.186447\pi\)
0.833304 + 0.552815i \(0.186447\pi\)
\(564\) 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 \(-0.454984\pi\)
0.140950 + 0.990017i \(0.454984\pi\)
\(578\) 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 \(-0.253481\pi\)
0.699331 + 0.714798i \(0.253481\pi\)
\(588\) 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 \(-0.552930\pi\)
−0.165519 + 0.986207i \(0.552930\pi\)
\(594\) 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 \(-0.517005\pi\)
−0.0533958 + 0.998573i \(0.517005\pi\)
\(602\) 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 \(-0.407802\pi\)
0.285617 + 0.958344i \(0.407802\pi\)
\(608\) 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 \(-0.742192\pi\)
−0.689551 + 0.724237i \(0.742192\pi\)
\(620\) −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 \(-0.458680\pi\)
0.129447 + 0.991586i \(0.458680\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −733.205 −0.0446557
\(647\) −103.679 −0.00629989 −0.00314995 0.999995i \(-0.501003\pi\)
−0.00314995 + 0.999995i \(0.501003\pi\)
\(648\) 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 \(-0.370484\pi\)
0.395752 + 0.918357i \(0.370484\pi\)
\(662\) 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 \(-0.736802\pi\)
−0.677190 + 0.735808i \(0.736802\pi\)
\(678\) 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 \(-0.572505\pi\)
−0.225817 + 0.974170i \(0.572505\pi\)
\(692\) −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 \(-0.553872\pi\)
−0.168436 + 0.985713i \(0.553872\pi\)
\(720\) 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 \(-0.654692\pi\)
−0.467074 + 0.884218i \(0.654692\pi\)
\(728\) 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 \(-0.320322\pi\)
0.534972 + 0.844870i \(0.320322\pi\)
\(734\) 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 \(-0.525104\pi\)
−0.0787852 + 0.996892i \(0.525104\pi\)
\(762\) 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 \(-0.367592\pi\)
0.404079 + 0.914724i \(0.367592\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 26915.1 1.25479
\(773\) 8726.33 0.406034 0.203017 0.979175i \(-0.434925\pi\)
0.203017 + 0.979175i \(0.434925\pi\)
\(774\) 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 \(-0.577478\pi\)
−0.241009 + 0.970523i \(0.577478\pi\)
\(788\) −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 \(-0.725080\pi\)
−0.649640 + 0.760242i \(0.725080\pi\)
\(798\) 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 \(-0.707254\pi\)
−0.606069 + 0.795412i \(0.707254\pi\)
\(812\) 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 \(-0.462199\pi\)
0.118477 + 0.992957i \(0.462199\pi\)
\(830\) 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 \(-0.350211\pi\)
0.453398 + 0.891308i \(0.350211\pi\)
\(840\) 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 \(-0.851295\pi\)
−0.892846 + 0.450362i \(0.851295\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 3718.29 0.148468
\(857\) 38559.6 1.53696 0.768478 0.639877i \(-0.221015\pi\)
0.768478 + 0.639877i \(0.221015\pi\)
\(858\) 0 0
\(859\) 8426.01 0.334682 0.167341 0.985899i \(-0.446482\pi\)
0.167341 + 0.985899i \(0.446482\pi\)
\(860\) −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 \(-0.442060\pi\)
0.181021 + 0.983479i \(0.442060\pi\)
\(882\) 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 \(-0.379877\pi\)
0.368484 + 0.929634i \(0.379877\pi\)
\(888\) 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 \(-0.393821\pi\)
0.327420 + 0.944879i \(0.393821\pi\)
\(930\) 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 \(-0.422423\pi\)
0.241309 + 0.970448i \(0.422423\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −11816.5 −0.410012
\(941\) 53393.2 1.84970 0.924850 0.380333i \(-0.124191\pi\)
0.924850 + 0.380333i \(0.124191\pi\)
\(942\) 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 \(-0.440077\pi\)
0.187143 + 0.982333i \(0.440077\pi\)
\(972\) 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 \(-0.919053\pi\)
−0.967839 + 0.251570i \(0.919053\pi\)
\(984\) 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 \(-0.553947\pi\)
−0.168669 + 0.985673i \(0.553947\pi\)
\(998\) −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.bz.1.3 6
3.2 odd 2 245.4.a.o.1.4 6
7.6 odd 2 2205.4.a.ca.1.3 6
15.14 odd 2 1225.4.a.bj.1.3 6
21.2 odd 6 245.4.e.q.116.3 12
21.5 even 6 245.4.e.p.116.3 12
21.11 odd 6 245.4.e.q.226.3 12
21.17 even 6 245.4.e.p.226.3 12
21.20 even 2 245.4.a.p.1.4 yes 6
105.104 even 2 1225.4.a.bi.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.4 6 3.2 odd 2
245.4.a.p.1.4 yes 6 21.20 even 2
245.4.e.p.116.3 12 21.5 even 6
245.4.e.p.226.3 12 21.17 even 6
245.4.e.q.116.3 12 21.2 odd 6
245.4.e.q.226.3 12 21.11 odd 6
1225.4.a.bi.1.3 6 105.104 even 2
1225.4.a.bj.1.3 6 15.14 odd 2
2205.4.a.bz.1.3 6 1.1 even 1 trivial
2205.4.a.ca.1.3 6 7.6 odd 2