Properties

Label 495.4.a.d.1.2
Level $495$
Weight $4$
Character 495.1
Self dual yes
Analytic conductor $29.206$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 495.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.2059454528\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \( x^{2} - x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 495.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56155 q^{2} -1.43845 q^{4} +5.00000 q^{5} +6.24621 q^{7} -24.1771 q^{8} +O(q^{10})\) \(q+2.56155 q^{2} -1.43845 q^{4} +5.00000 q^{5} +6.24621 q^{7} -24.1771 q^{8} +12.8078 q^{10} +11.0000 q^{11} -49.1231 q^{13} +16.0000 q^{14} -50.4233 q^{16} -82.7083 q^{17} -130.354 q^{19} -7.19224 q^{20} +28.1771 q^{22} +185.693 q^{23} +25.0000 q^{25} -125.831 q^{26} -8.98485 q^{28} +8.90720 q^{29} +5.26137 q^{31} +64.2547 q^{32} -211.862 q^{34} +31.2311 q^{35} -416.894 q^{37} -333.909 q^{38} -120.885 q^{40} +298.479 q^{41} -513.633 q^{43} -15.8229 q^{44} +475.663 q^{46} -557.295 q^{47} -303.985 q^{49} +64.0388 q^{50} +70.6610 q^{52} +168.064 q^{53} +55.0000 q^{55} -151.015 q^{56} +22.8163 q^{58} -618.773 q^{59} +786.405 q^{61} +13.4773 q^{62} +567.978 q^{64} -245.616 q^{65} -339.015 q^{67} +118.972 q^{68} +80.0000 q^{70} -1120.71 q^{71} -123.430 q^{73} -1067.90 q^{74} +187.508 q^{76} +68.7083 q^{77} -309.835 q^{79} -252.116 q^{80} +764.570 q^{82} +1021.22 q^{83} -413.542 q^{85} -1315.70 q^{86} -265.948 q^{88} +141.879 q^{89} -306.833 q^{91} -267.110 q^{92} -1427.54 q^{94} -651.771 q^{95} +798.345 q^{97} -778.673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - 7 q^{4} + 10 q^{5} - 4 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - 7 q^{4} + 10 q^{5} - 4 q^{7} - 3 q^{8} + 5 q^{10} + 22 q^{11} - 90 q^{13} + 32 q^{14} - 39 q^{16} + 16 q^{17} - 170 q^{19} - 35 q^{20} + 11 q^{22} + 124 q^{23} + 50 q^{25} - 62 q^{26} + 48 q^{28} + 158 q^{29} + 60 q^{31} - 123 q^{32} - 366 q^{34} - 20 q^{35} - 372 q^{37} - 272 q^{38} - 15 q^{40} - 38 q^{41} - 516 q^{43} - 77 q^{44} + 572 q^{46} - 224 q^{47} - 542 q^{49} + 25 q^{50} + 298 q^{52} - 472 q^{53} + 110 q^{55} - 368 q^{56} - 210 q^{58} - 248 q^{59} + 72 q^{61} - 72 q^{62} + 769 q^{64} - 450 q^{65} - 744 q^{67} - 430 q^{68} + 160 q^{70} - 2060 q^{71} - 486 q^{73} - 1138 q^{74} + 408 q^{76} - 44 q^{77} + 642 q^{79} - 195 q^{80} + 1290 q^{82} + 286 q^{83} + 80 q^{85} - 1312 q^{86} - 33 q^{88} - 244 q^{89} + 112 q^{91} + 76 q^{92} - 1948 q^{94} - 850 q^{95} - 168 q^{97} - 407 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56155 0.905646 0.452823 0.891601i \(-0.350417\pi\)
0.452823 + 0.891601i \(0.350417\pi\)
\(3\) 0 0
\(4\) −1.43845 −0.179806
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 6.24621 0.337264 0.168632 0.985679i \(-0.446065\pi\)
0.168632 + 0.985679i \(0.446065\pi\)
\(8\) −24.1771 −1.06849
\(9\) 0 0
\(10\) 12.8078 0.405017
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −49.1231 −1.04802 −0.524011 0.851711i \(-0.675565\pi\)
−0.524011 + 0.851711i \(0.675565\pi\)
\(14\) 16.0000 0.305441
\(15\) 0 0
\(16\) −50.4233 −0.787864
\(17\) −82.7083 −1.17998 −0.589992 0.807409i \(-0.700869\pi\)
−0.589992 + 0.807409i \(0.700869\pi\)
\(18\) 0 0
\(19\) −130.354 −1.57396 −0.786981 0.616977i \(-0.788357\pi\)
−0.786981 + 0.616977i \(0.788357\pi\)
\(20\) −7.19224 −0.0804116
\(21\) 0 0
\(22\) 28.1771 0.273062
\(23\) 185.693 1.68347 0.841733 0.539895i \(-0.181536\pi\)
0.841733 + 0.539895i \(0.181536\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −125.831 −0.949137
\(27\) 0 0
\(28\) −8.98485 −0.0606420
\(29\) 8.90720 0.0570354 0.0285177 0.999593i \(-0.490921\pi\)
0.0285177 + 0.999593i \(0.490921\pi\)
\(30\) 0 0
\(31\) 5.26137 0.0304829 0.0152414 0.999884i \(-0.495148\pi\)
0.0152414 + 0.999884i \(0.495148\pi\)
\(32\) 64.2547 0.354961
\(33\) 0 0
\(34\) −211.862 −1.06865
\(35\) 31.2311 0.150829
\(36\) 0 0
\(37\) −416.894 −1.85235 −0.926175 0.377094i \(-0.876923\pi\)
−0.926175 + 0.377094i \(0.876923\pi\)
\(38\) −333.909 −1.42545
\(39\) 0 0
\(40\) −120.885 −0.477842
\(41\) 298.479 1.13694 0.568471 0.822703i \(-0.307535\pi\)
0.568471 + 0.822703i \(0.307535\pi\)
\(42\) 0 0
\(43\) −513.633 −1.82159 −0.910793 0.412863i \(-0.864529\pi\)
−0.910793 + 0.412863i \(0.864529\pi\)
\(44\) −15.8229 −0.0542135
\(45\) 0 0
\(46\) 475.663 1.52462
\(47\) −557.295 −1.72957 −0.864786 0.502140i \(-0.832546\pi\)
−0.864786 + 0.502140i \(0.832546\pi\)
\(48\) 0 0
\(49\) −303.985 −0.886253
\(50\) 64.0388 0.181129
\(51\) 0 0
\(52\) 70.6610 0.188441
\(53\) 168.064 0.435574 0.217787 0.975996i \(-0.430116\pi\)
0.217787 + 0.975996i \(0.430116\pi\)
\(54\) 0 0
\(55\) 55.0000 0.134840
\(56\) −151.015 −0.360362
\(57\) 0 0
\(58\) 22.8163 0.0516539
\(59\) −618.773 −1.36538 −0.682689 0.730709i \(-0.739190\pi\)
−0.682689 + 0.730709i \(0.739190\pi\)
\(60\) 0 0
\(61\) 786.405 1.65064 0.825319 0.564667i \(-0.190996\pi\)
0.825319 + 0.564667i \(0.190996\pi\)
\(62\) 13.4773 0.0276067
\(63\) 0 0
\(64\) 567.978 1.10933
\(65\) −245.616 −0.468690
\(66\) 0 0
\(67\) −339.015 −0.618169 −0.309084 0.951035i \(-0.600023\pi\)
−0.309084 + 0.951035i \(0.600023\pi\)
\(68\) 118.972 0.212168
\(69\) 0 0
\(70\) 80.0000 0.136598
\(71\) −1120.71 −1.87329 −0.936645 0.350280i \(-0.886087\pi\)
−0.936645 + 0.350280i \(0.886087\pi\)
\(72\) 0 0
\(73\) −123.430 −0.197896 −0.0989478 0.995093i \(-0.531548\pi\)
−0.0989478 + 0.995093i \(0.531548\pi\)
\(74\) −1067.90 −1.67757
\(75\) 0 0
\(76\) 187.508 0.283008
\(77\) 68.7083 0.101689
\(78\) 0 0
\(79\) −309.835 −0.441255 −0.220628 0.975358i \(-0.570811\pi\)
−0.220628 + 0.975358i \(0.570811\pi\)
\(80\) −252.116 −0.352343
\(81\) 0 0
\(82\) 764.570 1.02967
\(83\) 1021.22 1.35053 0.675263 0.737577i \(-0.264030\pi\)
0.675263 + 0.737577i \(0.264030\pi\)
\(84\) 0 0
\(85\) −413.542 −0.527705
\(86\) −1315.70 −1.64971
\(87\) 0 0
\(88\) −265.948 −0.322161
\(89\) 141.879 0.168979 0.0844894 0.996424i \(-0.473074\pi\)
0.0844894 + 0.996424i \(0.473074\pi\)
\(90\) 0 0
\(91\) −306.833 −0.353460
\(92\) −267.110 −0.302697
\(93\) 0 0
\(94\) −1427.54 −1.56638
\(95\) −651.771 −0.703898
\(96\) 0 0
\(97\) 798.345 0.835666 0.417833 0.908524i \(-0.362790\pi\)
0.417833 + 0.908524i \(0.362790\pi\)
\(98\) −778.673 −0.802631
\(99\) 0 0
\(100\) −35.9612 −0.0359612
\(101\) −241.400 −0.237823 −0.118912 0.992905i \(-0.537941\pi\)
−0.118912 + 0.992905i \(0.537941\pi\)
\(102\) 0 0
\(103\) 1168.38 1.11771 0.558853 0.829267i \(-0.311242\pi\)
0.558853 + 0.829267i \(0.311242\pi\)
\(104\) 1187.65 1.11980
\(105\) 0 0
\(106\) 430.506 0.394476
\(107\) 2106.82 1.90350 0.951748 0.306882i \(-0.0992857\pi\)
0.951748 + 0.306882i \(0.0992857\pi\)
\(108\) 0 0
\(109\) 493.792 0.433914 0.216957 0.976181i \(-0.430387\pi\)
0.216957 + 0.976181i \(0.430387\pi\)
\(110\) 140.885 0.122117
\(111\) 0 0
\(112\) −314.955 −0.265718
\(113\) −170.000 −0.141524 −0.0707622 0.997493i \(-0.522543\pi\)
−0.0707622 + 0.997493i \(0.522543\pi\)
\(114\) 0 0
\(115\) 928.466 0.752869
\(116\) −12.8125 −0.0102553
\(117\) 0 0
\(118\) −1585.02 −1.23655
\(119\) −516.614 −0.397966
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 2014.42 1.49489
\(123\) 0 0
\(124\) −7.56820 −0.00548100
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −948.182 −0.662500 −0.331250 0.943543i \(-0.607470\pi\)
−0.331250 + 0.943543i \(0.607470\pi\)
\(128\) 940.868 0.649702
\(129\) 0 0
\(130\) −629.157 −0.424467
\(131\) 1484.84 0.990312 0.495156 0.868804i \(-0.335111\pi\)
0.495156 + 0.868804i \(0.335111\pi\)
\(132\) 0 0
\(133\) −814.220 −0.530841
\(134\) −868.405 −0.559842
\(135\) 0 0
\(136\) 1999.65 1.26080
\(137\) −684.928 −0.427134 −0.213567 0.976928i \(-0.568508\pi\)
−0.213567 + 0.976928i \(0.568508\pi\)
\(138\) 0 0
\(139\) 830.483 0.506767 0.253384 0.967366i \(-0.418457\pi\)
0.253384 + 0.967366i \(0.418457\pi\)
\(140\) −44.9242 −0.0271199
\(141\) 0 0
\(142\) −2870.75 −1.69654
\(143\) −540.354 −0.315991
\(144\) 0 0
\(145\) 44.5360 0.0255070
\(146\) −316.172 −0.179223
\(147\) 0 0
\(148\) 599.680 0.333063
\(149\) 1213.64 0.667285 0.333642 0.942700i \(-0.391722\pi\)
0.333642 + 0.942700i \(0.391722\pi\)
\(150\) 0 0
\(151\) 30.8466 0.0166242 0.00831212 0.999965i \(-0.497354\pi\)
0.00831212 + 0.999965i \(0.497354\pi\)
\(152\) 3151.58 1.68176
\(153\) 0 0
\(154\) 176.000 0.0920941
\(155\) 26.3068 0.0136324
\(156\) 0 0
\(157\) 345.239 0.175497 0.0877485 0.996143i \(-0.472033\pi\)
0.0877485 + 0.996143i \(0.472033\pi\)
\(158\) −793.659 −0.399621
\(159\) 0 0
\(160\) 321.274 0.158743
\(161\) 1159.88 0.567772
\(162\) 0 0
\(163\) 1921.49 0.923331 0.461665 0.887054i \(-0.347252\pi\)
0.461665 + 0.887054i \(0.347252\pi\)
\(164\) −429.346 −0.204429
\(165\) 0 0
\(166\) 2615.91 1.22310
\(167\) −172.297 −0.0798369 −0.0399185 0.999203i \(-0.512710\pi\)
−0.0399185 + 0.999203i \(0.512710\pi\)
\(168\) 0 0
\(169\) 216.080 0.0983521
\(170\) −1059.31 −0.477913
\(171\) 0 0
\(172\) 738.833 0.327532
\(173\) 1025.29 0.450587 0.225293 0.974291i \(-0.427666\pi\)
0.225293 + 0.974291i \(0.427666\pi\)
\(174\) 0 0
\(175\) 156.155 0.0674527
\(176\) −554.656 −0.237550
\(177\) 0 0
\(178\) 363.430 0.153035
\(179\) −1658.29 −0.692437 −0.346219 0.938154i \(-0.612534\pi\)
−0.346219 + 0.938154i \(0.612534\pi\)
\(180\) 0 0
\(181\) −2021.81 −0.830275 −0.415137 0.909759i \(-0.636266\pi\)
−0.415137 + 0.909759i \(0.636266\pi\)
\(182\) −785.970 −0.320110
\(183\) 0 0
\(184\) −4489.52 −1.79876
\(185\) −2084.47 −0.828396
\(186\) 0 0
\(187\) −909.792 −0.355778
\(188\) 801.640 0.310987
\(189\) 0 0
\(190\) −1669.55 −0.637482
\(191\) −1440.22 −0.545607 −0.272803 0.962070i \(-0.587951\pi\)
−0.272803 + 0.962070i \(0.587951\pi\)
\(192\) 0 0
\(193\) −2798.05 −1.04356 −0.521782 0.853079i \(-0.674733\pi\)
−0.521782 + 0.853079i \(0.674733\pi\)
\(194\) 2045.00 0.756817
\(195\) 0 0
\(196\) 437.266 0.159354
\(197\) −458.943 −0.165982 −0.0829908 0.996550i \(-0.526447\pi\)
−0.0829908 + 0.996550i \(0.526447\pi\)
\(198\) 0 0
\(199\) −2371.04 −0.844615 −0.422308 0.906453i \(-0.638780\pi\)
−0.422308 + 0.906453i \(0.638780\pi\)
\(200\) −604.427 −0.213697
\(201\) 0 0
\(202\) −618.358 −0.215384
\(203\) 55.6363 0.0192360
\(204\) 0 0
\(205\) 1492.40 0.508456
\(206\) 2992.86 1.01225
\(207\) 0 0
\(208\) 2476.95 0.825699
\(209\) −1433.90 −0.474568
\(210\) 0 0
\(211\) 4319.87 1.40944 0.704721 0.709484i \(-0.251072\pi\)
0.704721 + 0.709484i \(0.251072\pi\)
\(212\) −241.752 −0.0783187
\(213\) 0 0
\(214\) 5396.73 1.72389
\(215\) −2568.16 −0.814638
\(216\) 0 0
\(217\) 32.8636 0.0102808
\(218\) 1264.87 0.392973
\(219\) 0 0
\(220\) −79.1146 −0.0242450
\(221\) 4062.89 1.23665
\(222\) 0 0
\(223\) −3837.73 −1.15244 −0.576219 0.817295i \(-0.695473\pi\)
−0.576219 + 0.817295i \(0.695473\pi\)
\(224\) 401.349 0.119715
\(225\) 0 0
\(226\) −435.464 −0.128171
\(227\) 5003.71 1.46303 0.731515 0.681825i \(-0.238813\pi\)
0.731515 + 0.681825i \(0.238813\pi\)
\(228\) 0 0
\(229\) −277.375 −0.0800412 −0.0400206 0.999199i \(-0.512742\pi\)
−0.0400206 + 0.999199i \(0.512742\pi\)
\(230\) 2378.31 0.681832
\(231\) 0 0
\(232\) −215.350 −0.0609415
\(233\) −2269.91 −0.638225 −0.319113 0.947717i \(-0.603385\pi\)
−0.319113 + 0.947717i \(0.603385\pi\)
\(234\) 0 0
\(235\) −2786.48 −0.773488
\(236\) 890.072 0.245503
\(237\) 0 0
\(238\) −1323.33 −0.360416
\(239\) 1617.11 0.437665 0.218832 0.975762i \(-0.429775\pi\)
0.218832 + 0.975762i \(0.429775\pi\)
\(240\) 0 0
\(241\) 5646.63 1.50926 0.754629 0.656151i \(-0.227817\pi\)
0.754629 + 0.656151i \(0.227817\pi\)
\(242\) 309.948 0.0823314
\(243\) 0 0
\(244\) −1131.20 −0.296794
\(245\) −1519.92 −0.396344
\(246\) 0 0
\(247\) 6403.40 1.64955
\(248\) −127.204 −0.0325705
\(249\) 0 0
\(250\) 320.194 0.0810034
\(251\) 6217.61 1.56355 0.781777 0.623558i \(-0.214313\pi\)
0.781777 + 0.623558i \(0.214313\pi\)
\(252\) 0 0
\(253\) 2042.62 0.507584
\(254\) −2428.82 −0.599991
\(255\) 0 0
\(256\) −2133.74 −0.520933
\(257\) −7712.75 −1.87202 −0.936008 0.351980i \(-0.885509\pi\)
−0.936008 + 0.351980i \(0.885509\pi\)
\(258\) 0 0
\(259\) −2604.01 −0.624730
\(260\) 353.305 0.0842732
\(261\) 0 0
\(262\) 3803.49 0.896871
\(263\) −206.347 −0.0483798 −0.0241899 0.999707i \(-0.507701\pi\)
−0.0241899 + 0.999707i \(0.507701\pi\)
\(264\) 0 0
\(265\) 840.322 0.194795
\(266\) −2085.67 −0.480753
\(267\) 0 0
\(268\) 487.655 0.111150
\(269\) −1712.47 −0.388146 −0.194073 0.980987i \(-0.562170\pi\)
−0.194073 + 0.980987i \(0.562170\pi\)
\(270\) 0 0
\(271\) −477.081 −0.106940 −0.0534698 0.998569i \(-0.517028\pi\)
−0.0534698 + 0.998569i \(0.517028\pi\)
\(272\) 4170.43 0.929666
\(273\) 0 0
\(274\) −1754.48 −0.386832
\(275\) 275.000 0.0603023
\(276\) 0 0
\(277\) 4283.48 0.929130 0.464565 0.885539i \(-0.346211\pi\)
0.464565 + 0.885539i \(0.346211\pi\)
\(278\) 2127.33 0.458952
\(279\) 0 0
\(280\) −755.076 −0.161159
\(281\) −3477.79 −0.738319 −0.369160 0.929366i \(-0.620354\pi\)
−0.369160 + 0.929366i \(0.620354\pi\)
\(282\) 0 0
\(283\) −6568.27 −1.37966 −0.689829 0.723973i \(-0.742314\pi\)
−0.689829 + 0.723973i \(0.742314\pi\)
\(284\) 1612.08 0.336829
\(285\) 0 0
\(286\) −1384.15 −0.286176
\(287\) 1864.36 0.383449
\(288\) 0 0
\(289\) 1927.67 0.392360
\(290\) 114.081 0.0231003
\(291\) 0 0
\(292\) 177.547 0.0355828
\(293\) −8352.29 −1.66534 −0.832672 0.553766i \(-0.813190\pi\)
−0.832672 + 0.553766i \(0.813190\pi\)
\(294\) 0 0
\(295\) −3093.86 −0.610616
\(296\) 10079.3 1.97921
\(297\) 0 0
\(298\) 3108.81 0.604324
\(299\) −9121.83 −1.76431
\(300\) 0 0
\(301\) −3208.26 −0.614355
\(302\) 79.0152 0.0150557
\(303\) 0 0
\(304\) 6572.89 1.24007
\(305\) 3932.03 0.738187
\(306\) 0 0
\(307\) 5383.89 1.00090 0.500448 0.865767i \(-0.333169\pi\)
0.500448 + 0.865767i \(0.333169\pi\)
\(308\) −98.8333 −0.0182843
\(309\) 0 0
\(310\) 67.3863 0.0123461
\(311\) 1790.41 0.326447 0.163223 0.986589i \(-0.447811\pi\)
0.163223 + 0.986589i \(0.447811\pi\)
\(312\) 0 0
\(313\) −809.076 −0.146108 −0.0730538 0.997328i \(-0.523274\pi\)
−0.0730538 + 0.997328i \(0.523274\pi\)
\(314\) 884.347 0.158938
\(315\) 0 0
\(316\) 445.682 0.0793403
\(317\) −10744.5 −1.90370 −0.951849 0.306567i \(-0.900820\pi\)
−0.951849 + 0.306567i \(0.900820\pi\)
\(318\) 0 0
\(319\) 97.9792 0.0171968
\(320\) 2839.89 0.496109
\(321\) 0 0
\(322\) 2971.09 0.514200
\(323\) 10781.4 1.85725
\(324\) 0 0
\(325\) −1228.08 −0.209605
\(326\) 4922.00 0.836210
\(327\) 0 0
\(328\) −7216.35 −1.21481
\(329\) −3480.98 −0.583322
\(330\) 0 0
\(331\) 3399.12 0.564449 0.282224 0.959348i \(-0.408928\pi\)
0.282224 + 0.959348i \(0.408928\pi\)
\(332\) −1468.97 −0.242832
\(333\) 0 0
\(334\) −441.349 −0.0723039
\(335\) −1695.08 −0.276453
\(336\) 0 0
\(337\) −11840.0 −1.91384 −0.956919 0.290356i \(-0.906226\pi\)
−0.956919 + 0.290356i \(0.906226\pi\)
\(338\) 553.499 0.0890721
\(339\) 0 0
\(340\) 594.858 0.0948844
\(341\) 57.8750 0.00919093
\(342\) 0 0
\(343\) −4041.20 −0.636165
\(344\) 12418.1 1.94634
\(345\) 0 0
\(346\) 2626.34 0.408072
\(347\) 2076.67 0.321272 0.160636 0.987014i \(-0.448645\pi\)
0.160636 + 0.987014i \(0.448645\pi\)
\(348\) 0 0
\(349\) 5837.37 0.895322 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(350\) 400.000 0.0610883
\(351\) 0 0
\(352\) 706.802 0.107025
\(353\) 2423.64 0.365431 0.182715 0.983166i \(-0.441511\pi\)
0.182715 + 0.983166i \(0.441511\pi\)
\(354\) 0 0
\(355\) −5603.54 −0.837761
\(356\) −204.085 −0.0303834
\(357\) 0 0
\(358\) −4247.79 −0.627103
\(359\) 3882.22 0.570740 0.285370 0.958417i \(-0.407884\pi\)
0.285370 + 0.958417i \(0.407884\pi\)
\(360\) 0 0
\(361\) 10133.2 1.47736
\(362\) −5178.96 −0.751935
\(363\) 0 0
\(364\) 441.363 0.0635542
\(365\) −617.150 −0.0885016
\(366\) 0 0
\(367\) 5666.65 0.805986 0.402993 0.915203i \(-0.367970\pi\)
0.402993 + 0.915203i \(0.367970\pi\)
\(368\) −9363.26 −1.32634
\(369\) 0 0
\(370\) −5339.48 −0.750233
\(371\) 1049.77 0.146903
\(372\) 0 0
\(373\) 174.771 0.0242608 0.0121304 0.999926i \(-0.496139\pi\)
0.0121304 + 0.999926i \(0.496139\pi\)
\(374\) −2330.48 −0.322209
\(375\) 0 0
\(376\) 13473.8 1.84802
\(377\) −437.550 −0.0597744
\(378\) 0 0
\(379\) 252.686 0.0342470 0.0171235 0.999853i \(-0.494549\pi\)
0.0171235 + 0.999853i \(0.494549\pi\)
\(380\) 937.538 0.126565
\(381\) 0 0
\(382\) −3689.21 −0.494126
\(383\) 11014.5 1.46950 0.734748 0.678340i \(-0.237300\pi\)
0.734748 + 0.678340i \(0.237300\pi\)
\(384\) 0 0
\(385\) 343.542 0.0454766
\(386\) −7167.35 −0.945099
\(387\) 0 0
\(388\) −1148.38 −0.150258
\(389\) −8099.40 −1.05567 −0.527835 0.849347i \(-0.676996\pi\)
−0.527835 + 0.849347i \(0.676996\pi\)
\(390\) 0 0
\(391\) −15358.4 −1.98646
\(392\) 7349.47 0.946949
\(393\) 0 0
\(394\) −1175.61 −0.150320
\(395\) −1549.18 −0.197335
\(396\) 0 0
\(397\) −424.353 −0.0536465 −0.0268232 0.999640i \(-0.508539\pi\)
−0.0268232 + 0.999640i \(0.508539\pi\)
\(398\) −6073.54 −0.764922
\(399\) 0 0
\(400\) −1260.58 −0.157573
\(401\) 5904.18 0.735263 0.367632 0.929972i \(-0.380169\pi\)
0.367632 + 0.929972i \(0.380169\pi\)
\(402\) 0 0
\(403\) −258.455 −0.0319468
\(404\) 347.241 0.0427620
\(405\) 0 0
\(406\) 142.515 0.0174210
\(407\) −4585.83 −0.558504
\(408\) 0 0
\(409\) 1370.47 0.165686 0.0828430 0.996563i \(-0.473600\pi\)
0.0828430 + 0.996563i \(0.473600\pi\)
\(410\) 3822.85 0.460481
\(411\) 0 0
\(412\) −1680.65 −0.200970
\(413\) −3864.98 −0.460493
\(414\) 0 0
\(415\) 5106.11 0.603973
\(416\) −3156.39 −0.372007
\(417\) 0 0
\(418\) −3673.00 −0.429790
\(419\) −1268.73 −0.147927 −0.0739635 0.997261i \(-0.523565\pi\)
−0.0739635 + 0.997261i \(0.523565\pi\)
\(420\) 0 0
\(421\) −12241.9 −1.41719 −0.708594 0.705617i \(-0.750670\pi\)
−0.708594 + 0.705617i \(0.750670\pi\)
\(422\) 11065.6 1.27646
\(423\) 0 0
\(424\) −4063.31 −0.465405
\(425\) −2067.71 −0.235997
\(426\) 0 0
\(427\) 4912.05 0.556700
\(428\) −3030.55 −0.342260
\(429\) 0 0
\(430\) −6578.48 −0.737774
\(431\) −8050.11 −0.899675 −0.449838 0.893110i \(-0.648518\pi\)
−0.449838 + 0.893110i \(0.648518\pi\)
\(432\) 0 0
\(433\) −16565.7 −1.83856 −0.919282 0.393600i \(-0.871230\pi\)
−0.919282 + 0.393600i \(0.871230\pi\)
\(434\) 84.1819 0.00931073
\(435\) 0 0
\(436\) −710.293 −0.0780203
\(437\) −24205.9 −2.64971
\(438\) 0 0
\(439\) 4705.80 0.511607 0.255804 0.966729i \(-0.417660\pi\)
0.255804 + 0.966729i \(0.417660\pi\)
\(440\) −1329.74 −0.144075
\(441\) 0 0
\(442\) 10407.3 1.11997
\(443\) −15094.0 −1.61882 −0.809408 0.587246i \(-0.800212\pi\)
−0.809408 + 0.587246i \(0.800212\pi\)
\(444\) 0 0
\(445\) 709.394 0.0755696
\(446\) −9830.56 −1.04370
\(447\) 0 0
\(448\) 3547.71 0.374138
\(449\) −973.478 −0.102319 −0.0511595 0.998690i \(-0.516292\pi\)
−0.0511595 + 0.998690i \(0.516292\pi\)
\(450\) 0 0
\(451\) 3283.27 0.342801
\(452\) 244.536 0.0254469
\(453\) 0 0
\(454\) 12817.3 1.32499
\(455\) −1534.17 −0.158072
\(456\) 0 0
\(457\) 62.6577 0.00641358 0.00320679 0.999995i \(-0.498979\pi\)
0.00320679 + 0.999995i \(0.498979\pi\)
\(458\) −710.510 −0.0724890
\(459\) 0 0
\(460\) −1335.55 −0.135370
\(461\) 11866.2 1.19884 0.599419 0.800436i \(-0.295398\pi\)
0.599419 + 0.800436i \(0.295398\pi\)
\(462\) 0 0
\(463\) −13144.8 −1.31942 −0.659711 0.751519i \(-0.729321\pi\)
−0.659711 + 0.751519i \(0.729321\pi\)
\(464\) −449.131 −0.0449361
\(465\) 0 0
\(466\) −5814.48 −0.578006
\(467\) 10176.8 1.00840 0.504201 0.863586i \(-0.331787\pi\)
0.504201 + 0.863586i \(0.331787\pi\)
\(468\) 0 0
\(469\) −2117.56 −0.208486
\(470\) −7137.71 −0.700506
\(471\) 0 0
\(472\) 14960.1 1.45889
\(473\) −5649.96 −0.549229
\(474\) 0 0
\(475\) −3258.85 −0.314793
\(476\) 743.121 0.0715565
\(477\) 0 0
\(478\) 4142.30 0.396369
\(479\) −3431.25 −0.327302 −0.163651 0.986518i \(-0.552327\pi\)
−0.163651 + 0.986518i \(0.552327\pi\)
\(480\) 0 0
\(481\) 20479.1 1.94130
\(482\) 14464.1 1.36685
\(483\) 0 0
\(484\) −174.052 −0.0163460
\(485\) 3991.72 0.373721
\(486\) 0 0
\(487\) −2833.20 −0.263624 −0.131812 0.991275i \(-0.542079\pi\)
−0.131812 + 0.991275i \(0.542079\pi\)
\(488\) −19013.0 −1.76368
\(489\) 0 0
\(490\) −3893.37 −0.358948
\(491\) 2667.29 0.245159 0.122580 0.992459i \(-0.460883\pi\)
0.122580 + 0.992459i \(0.460883\pi\)
\(492\) 0 0
\(493\) −736.700 −0.0673008
\(494\) 16402.7 1.49391
\(495\) 0 0
\(496\) −265.295 −0.0240164
\(497\) −7000.18 −0.631793
\(498\) 0 0
\(499\) −11137.0 −0.999120 −0.499560 0.866279i \(-0.666505\pi\)
−0.499560 + 0.866279i \(0.666505\pi\)
\(500\) −179.806 −0.0160823
\(501\) 0 0
\(502\) 15926.7 1.41603
\(503\) −8780.30 −0.778319 −0.389159 0.921170i \(-0.627234\pi\)
−0.389159 + 0.921170i \(0.627234\pi\)
\(504\) 0 0
\(505\) −1207.00 −0.106358
\(506\) 5232.29 0.459691
\(507\) 0 0
\(508\) 1363.91 0.119121
\(509\) −13597.4 −1.18408 −0.592039 0.805910i \(-0.701677\pi\)
−0.592039 + 0.805910i \(0.701677\pi\)
\(510\) 0 0
\(511\) −770.969 −0.0667430
\(512\) −12992.6 −1.12148
\(513\) 0 0
\(514\) −19756.6 −1.69538
\(515\) 5841.89 0.499854
\(516\) 0 0
\(517\) −6130.25 −0.521486
\(518\) −6670.30 −0.565784
\(519\) 0 0
\(520\) 5938.27 0.500789
\(521\) −14001.3 −1.17736 −0.588682 0.808364i \(-0.700353\pi\)
−0.588682 + 0.808364i \(0.700353\pi\)
\(522\) 0 0
\(523\) −14749.8 −1.23320 −0.616602 0.787275i \(-0.711491\pi\)
−0.616602 + 0.787275i \(0.711491\pi\)
\(524\) −2135.86 −0.178064
\(525\) 0 0
\(526\) −528.568 −0.0438149
\(527\) −435.159 −0.0359693
\(528\) 0 0
\(529\) 22315.0 1.83406
\(530\) 2152.53 0.176415
\(531\) 0 0
\(532\) 1171.21 0.0954483
\(533\) −14662.2 −1.19154
\(534\) 0 0
\(535\) 10534.1 0.851269
\(536\) 8196.40 0.660505
\(537\) 0 0
\(538\) −4386.59 −0.351523
\(539\) −3343.83 −0.267215
\(540\) 0 0
\(541\) 1484.06 0.117939 0.0589694 0.998260i \(-0.481219\pi\)
0.0589694 + 0.998260i \(0.481219\pi\)
\(542\) −1222.07 −0.0968493
\(543\) 0 0
\(544\) −5314.40 −0.418847
\(545\) 2468.96 0.194052
\(546\) 0 0
\(547\) −16562.2 −1.29460 −0.647302 0.762234i \(-0.724103\pi\)
−0.647302 + 0.762234i \(0.724103\pi\)
\(548\) 985.233 0.0768012
\(549\) 0 0
\(550\) 704.427 0.0546125
\(551\) −1161.09 −0.0897716
\(552\) 0 0
\(553\) −1935.30 −0.148819
\(554\) 10972.3 0.841463
\(555\) 0 0
\(556\) −1194.61 −0.0911197
\(557\) 8821.52 0.671059 0.335529 0.942030i \(-0.391085\pi\)
0.335529 + 0.942030i \(0.391085\pi\)
\(558\) 0 0
\(559\) 25231.2 1.90906
\(560\) −1574.77 −0.118833
\(561\) 0 0
\(562\) −8908.55 −0.668656
\(563\) 5985.53 0.448064 0.224032 0.974582i \(-0.428078\pi\)
0.224032 + 0.974582i \(0.428078\pi\)
\(564\) 0 0
\(565\) −850.000 −0.0632916
\(566\) −16825.0 −1.24948
\(567\) 0 0
\(568\) 27095.5 2.00158
\(569\) 3453.08 0.254413 0.127206 0.991876i \(-0.459399\pi\)
0.127206 + 0.991876i \(0.459399\pi\)
\(570\) 0 0
\(571\) −21484.5 −1.57460 −0.787302 0.616568i \(-0.788523\pi\)
−0.787302 + 0.616568i \(0.788523\pi\)
\(572\) 777.271 0.0568170
\(573\) 0 0
\(574\) 4775.67 0.347269
\(575\) 4642.33 0.336693
\(576\) 0 0
\(577\) −13294.4 −0.959189 −0.479594 0.877490i \(-0.659216\pi\)
−0.479594 + 0.877490i \(0.659216\pi\)
\(578\) 4937.82 0.355340
\(579\) 0 0
\(580\) −64.0627 −0.00458631
\(581\) 6378.77 0.455483
\(582\) 0 0
\(583\) 1848.71 0.131330
\(584\) 2984.18 0.211449
\(585\) 0 0
\(586\) −21394.8 −1.50821
\(587\) −6695.73 −0.470805 −0.235402 0.971898i \(-0.575641\pi\)
−0.235402 + 0.971898i \(0.575641\pi\)
\(588\) 0 0
\(589\) −685.841 −0.0479789
\(590\) −7925.09 −0.553002
\(591\) 0 0
\(592\) 21021.2 1.45940
\(593\) 10239.6 0.709088 0.354544 0.935039i \(-0.384636\pi\)
0.354544 + 0.935039i \(0.384636\pi\)
\(594\) 0 0
\(595\) −2583.07 −0.177976
\(596\) −1745.76 −0.119982
\(597\) 0 0
\(598\) −23366.0 −1.59784
\(599\) 23890.8 1.62963 0.814817 0.579719i \(-0.196838\pi\)
0.814817 + 0.579719i \(0.196838\pi\)
\(600\) 0 0
\(601\) −11343.8 −0.769920 −0.384960 0.922933i \(-0.625785\pi\)
−0.384960 + 0.922933i \(0.625785\pi\)
\(602\) −8218.12 −0.556388
\(603\) 0 0
\(604\) −44.3712 −0.00298914
\(605\) 605.000 0.0406558
\(606\) 0 0
\(607\) −26032.5 −1.74074 −0.870369 0.492399i \(-0.836120\pi\)
−0.870369 + 0.492399i \(0.836120\pi\)
\(608\) −8375.87 −0.558695
\(609\) 0 0
\(610\) 10072.1 0.668536
\(611\) 27376.1 1.81263
\(612\) 0 0
\(613\) −4568.13 −0.300987 −0.150493 0.988611i \(-0.548086\pi\)
−0.150493 + 0.988611i \(0.548086\pi\)
\(614\) 13791.1 0.906457
\(615\) 0 0
\(616\) −1661.17 −0.108653
\(617\) 12755.9 0.832308 0.416154 0.909294i \(-0.363378\pi\)
0.416154 + 0.909294i \(0.363378\pi\)
\(618\) 0 0
\(619\) −1138.94 −0.0739545 −0.0369772 0.999316i \(-0.511773\pi\)
−0.0369772 + 0.999316i \(0.511773\pi\)
\(620\) −37.8410 −0.00245118
\(621\) 0 0
\(622\) 4586.24 0.295645
\(623\) 886.205 0.0569904
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −2072.49 −0.132322
\(627\) 0 0
\(628\) −496.607 −0.0315554
\(629\) 34480.6 2.18574
\(630\) 0 0
\(631\) 7997.36 0.504548 0.252274 0.967656i \(-0.418822\pi\)
0.252274 + 0.967656i \(0.418822\pi\)
\(632\) 7490.91 0.471475
\(633\) 0 0
\(634\) −27522.7 −1.72408
\(635\) −4740.91 −0.296279
\(636\) 0 0
\(637\) 14932.7 0.928814
\(638\) 250.979 0.0155742
\(639\) 0 0
\(640\) 4704.34 0.290555
\(641\) 573.115 0.0353146 0.0176573 0.999844i \(-0.494379\pi\)
0.0176573 + 0.999844i \(0.494379\pi\)
\(642\) 0 0
\(643\) −16027.8 −0.983009 −0.491504 0.870875i \(-0.663553\pi\)
−0.491504 + 0.870875i \(0.663553\pi\)
\(644\) −1668.42 −0.102089
\(645\) 0 0
\(646\) 27617.1 1.68201
\(647\) 2622.74 0.159367 0.0796837 0.996820i \(-0.474609\pi\)
0.0796837 + 0.996820i \(0.474609\pi\)
\(648\) 0 0
\(649\) −6806.50 −0.411677
\(650\) −3145.79 −0.189827
\(651\) 0 0
\(652\) −2763.97 −0.166020
\(653\) −3102.00 −0.185897 −0.0929484 0.995671i \(-0.529629\pi\)
−0.0929484 + 0.995671i \(0.529629\pi\)
\(654\) 0 0
\(655\) 7424.19 0.442881
\(656\) −15050.3 −0.895755
\(657\) 0 0
\(658\) −8916.73 −0.528283
\(659\) 20840.2 1.23190 0.615948 0.787787i \(-0.288773\pi\)
0.615948 + 0.787787i \(0.288773\pi\)
\(660\) 0 0
\(661\) 18242.9 1.07348 0.536738 0.843749i \(-0.319657\pi\)
0.536738 + 0.843749i \(0.319657\pi\)
\(662\) 8707.03 0.511191
\(663\) 0 0
\(664\) −24690.2 −1.44302
\(665\) −4071.10 −0.237399
\(666\) 0 0
\(667\) 1654.01 0.0960171
\(668\) 247.841 0.0143551
\(669\) 0 0
\(670\) −4342.03 −0.250369
\(671\) 8650.46 0.497686
\(672\) 0 0
\(673\) −12746.6 −0.730084 −0.365042 0.930991i \(-0.618945\pi\)
−0.365042 + 0.930991i \(0.618945\pi\)
\(674\) −30328.7 −1.73326
\(675\) 0 0
\(676\) −310.819 −0.0176843
\(677\) 7683.11 0.436168 0.218084 0.975930i \(-0.430019\pi\)
0.218084 + 0.975930i \(0.430019\pi\)
\(678\) 0 0
\(679\) 4986.63 0.281840
\(680\) 9998.23 0.563845
\(681\) 0 0
\(682\) 148.250 0.00832373
\(683\) 21397.1 1.19874 0.599368 0.800473i \(-0.295418\pi\)
0.599368 + 0.800473i \(0.295418\pi\)
\(684\) 0 0
\(685\) −3424.64 −0.191020
\(686\) −10351.8 −0.576140
\(687\) 0 0
\(688\) 25899.0 1.43516
\(689\) −8255.84 −0.456491
\(690\) 0 0
\(691\) 26137.5 1.43895 0.719477 0.694516i \(-0.244381\pi\)
0.719477 + 0.694516i \(0.244381\pi\)
\(692\) −1474.83 −0.0810181
\(693\) 0 0
\(694\) 5319.50 0.290959
\(695\) 4152.41 0.226633
\(696\) 0 0
\(697\) −24686.7 −1.34157
\(698\) 14952.7 0.810845
\(699\) 0 0
\(700\) −224.621 −0.0121284
\(701\) −13382.4 −0.721036 −0.360518 0.932752i \(-0.617400\pi\)
−0.360518 + 0.932752i \(0.617400\pi\)
\(702\) 0 0
\(703\) 54343.9 2.91553
\(704\) 6247.76 0.334476
\(705\) 0 0
\(706\) 6208.27 0.330951
\(707\) −1507.83 −0.0802092
\(708\) 0 0
\(709\) 18164.6 0.962179 0.481090 0.876671i \(-0.340241\pi\)
0.481090 + 0.876671i \(0.340241\pi\)
\(710\) −14353.8 −0.758715
\(711\) 0 0
\(712\) −3430.21 −0.180552
\(713\) 977.000 0.0513169
\(714\) 0 0
\(715\) −2701.77 −0.141315
\(716\) 2385.36 0.124504
\(717\) 0 0
\(718\) 9944.50 0.516888
\(719\) −9665.62 −0.501344 −0.250672 0.968072i \(-0.580652\pi\)
−0.250672 + 0.968072i \(0.580652\pi\)
\(720\) 0 0
\(721\) 7297.94 0.376962
\(722\) 25956.7 1.33796
\(723\) 0 0
\(724\) 2908.26 0.149288
\(725\) 222.680 0.0114071
\(726\) 0 0
\(727\) −29779.6 −1.51921 −0.759605 0.650385i \(-0.774608\pi\)
−0.759605 + 0.650385i \(0.774608\pi\)
\(728\) 7418.33 0.377667
\(729\) 0 0
\(730\) −1580.86 −0.0801511
\(731\) 42481.7 2.14944
\(732\) 0 0
\(733\) 35029.5 1.76513 0.882567 0.470187i \(-0.155814\pi\)
0.882567 + 0.470187i \(0.155814\pi\)
\(734\) 14515.4 0.729937
\(735\) 0 0
\(736\) 11931.7 0.597564
\(737\) −3729.17 −0.186385
\(738\) 0 0
\(739\) 23297.3 1.15968 0.579842 0.814729i \(-0.303114\pi\)
0.579842 + 0.814729i \(0.303114\pi\)
\(740\) 2998.40 0.148950
\(741\) 0 0
\(742\) 2689.03 0.133042
\(743\) −21570.4 −1.06506 −0.532530 0.846411i \(-0.678759\pi\)
−0.532530 + 0.846411i \(0.678759\pi\)
\(744\) 0 0
\(745\) 6068.21 0.298419
\(746\) 447.684 0.0219717
\(747\) 0 0
\(748\) 1308.69 0.0639710
\(749\) 13159.6 0.641980
\(750\) 0 0
\(751\) 28554.8 1.38746 0.693729 0.720236i \(-0.255966\pi\)
0.693729 + 0.720236i \(0.255966\pi\)
\(752\) 28100.7 1.36267
\(753\) 0 0
\(754\) −1120.81 −0.0541344
\(755\) 154.233 0.00743458
\(756\) 0 0
\(757\) 7812.81 0.375114 0.187557 0.982254i \(-0.439943\pi\)
0.187557 + 0.982254i \(0.439943\pi\)
\(758\) 647.268 0.0310156
\(759\) 0 0
\(760\) 15757.9 0.752105
\(761\) −2875.13 −0.136956 −0.0684778 0.997653i \(-0.521814\pi\)
−0.0684778 + 0.997653i \(0.521814\pi\)
\(762\) 0 0
\(763\) 3084.33 0.146344
\(764\) 2071.69 0.0981033
\(765\) 0 0
\(766\) 28214.3 1.33084
\(767\) 30396.0 1.43095
\(768\) 0 0
\(769\) −27657.7 −1.29696 −0.648479 0.761233i \(-0.724594\pi\)
−0.648479 + 0.761233i \(0.724594\pi\)
\(770\) 880.000 0.0411857
\(771\) 0 0
\(772\) 4024.84 0.187639
\(773\) 3929.35 0.182832 0.0914160 0.995813i \(-0.470861\pi\)
0.0914160 + 0.995813i \(0.470861\pi\)
\(774\) 0 0
\(775\) 131.534 0.00609658
\(776\) −19301.6 −0.892898
\(777\) 0 0
\(778\) −20747.0 −0.956064
\(779\) −38908.0 −1.78950
\(780\) 0 0
\(781\) −12327.8 −0.564818
\(782\) −39341.3 −1.79903
\(783\) 0 0
\(784\) 15327.9 0.698247
\(785\) 1726.19 0.0784847
\(786\) 0 0
\(787\) −21125.7 −0.956860 −0.478430 0.878126i \(-0.658794\pi\)
−0.478430 + 0.878126i \(0.658794\pi\)
\(788\) 660.166 0.0298445
\(789\) 0 0
\(790\) −3968.30 −0.178716
\(791\) −1061.86 −0.0477310
\(792\) 0 0
\(793\) −38630.7 −1.72991
\(794\) −1087.00 −0.0485847
\(795\) 0 0
\(796\) 3410.61 0.151867
\(797\) −11696.3 −0.519828 −0.259914 0.965632i \(-0.583694\pi\)
−0.259914 + 0.965632i \(0.583694\pi\)
\(798\) 0 0
\(799\) 46093.0 2.04087
\(800\) 1606.37 0.0709921
\(801\) 0 0
\(802\) 15123.9 0.665888
\(803\) −1357.73 −0.0596678
\(804\) 0 0
\(805\) 5799.39 0.253915
\(806\) −662.045 −0.0289324
\(807\) 0 0
\(808\) 5836.34 0.254111
\(809\) −14310.2 −0.621902 −0.310951 0.950426i \(-0.600648\pi\)
−0.310951 + 0.950426i \(0.600648\pi\)
\(810\) 0 0
\(811\) 21697.9 0.939477 0.469739 0.882806i \(-0.344348\pi\)
0.469739 + 0.882806i \(0.344348\pi\)
\(812\) −80.0299 −0.00345874
\(813\) 0 0
\(814\) −11746.9 −0.505807
\(815\) 9607.46 0.412926
\(816\) 0 0
\(817\) 66954.1 2.86711
\(818\) 3510.54 0.150053
\(819\) 0 0
\(820\) −2146.73 −0.0914233
\(821\) −3613.00 −0.153587 −0.0767934 0.997047i \(-0.524468\pi\)
−0.0767934 + 0.997047i \(0.524468\pi\)
\(822\) 0 0
\(823\) −4763.98 −0.201776 −0.100888 0.994898i \(-0.532168\pi\)
−0.100888 + 0.994898i \(0.532168\pi\)
\(824\) −28248.0 −1.19425
\(825\) 0 0
\(826\) −9900.36 −0.417043
\(827\) 33571.7 1.41161 0.705806 0.708405i \(-0.250585\pi\)
0.705806 + 0.708405i \(0.250585\pi\)
\(828\) 0 0
\(829\) 17980.5 0.753303 0.376652 0.926355i \(-0.377075\pi\)
0.376652 + 0.926355i \(0.377075\pi\)
\(830\) 13079.6 0.546986
\(831\) 0 0
\(832\) −27900.9 −1.16261
\(833\) 25142.1 1.04576
\(834\) 0 0
\(835\) −861.486 −0.0357041
\(836\) 2062.58 0.0853301
\(837\) 0 0
\(838\) −3249.91 −0.133969
\(839\) 40139.5 1.65169 0.825847 0.563895i \(-0.190698\pi\)
0.825847 + 0.563895i \(0.190698\pi\)
\(840\) 0 0
\(841\) −24309.7 −0.996747
\(842\) −31358.4 −1.28347
\(843\) 0 0
\(844\) −6213.91 −0.253426
\(845\) 1080.40 0.0439844
\(846\) 0 0
\(847\) 755.792 0.0306603
\(848\) −8474.36 −0.343173
\(849\) 0 0
\(850\) −5296.54 −0.213729
\(851\) −77414.4 −3.11837
\(852\) 0 0
\(853\) −15369.2 −0.616919 −0.308459 0.951237i \(-0.599813\pi\)
−0.308459 + 0.951237i \(0.599813\pi\)
\(854\) 12582.5 0.504173
\(855\) 0 0
\(856\) −50936.8 −2.03386
\(857\) −10324.9 −0.411541 −0.205770 0.978600i \(-0.565970\pi\)
−0.205770 + 0.978600i \(0.565970\pi\)
\(858\) 0 0
\(859\) −27112.5 −1.07691 −0.538455 0.842655i \(-0.680992\pi\)
−0.538455 + 0.842655i \(0.680992\pi\)
\(860\) 3694.17 0.146477
\(861\) 0 0
\(862\) −20620.8 −0.814787
\(863\) −30463.6 −1.20161 −0.600807 0.799394i \(-0.705154\pi\)
−0.600807 + 0.799394i \(0.705154\pi\)
\(864\) 0 0
\(865\) 5126.46 0.201508
\(866\) −42434.0 −1.66509
\(867\) 0 0
\(868\) −47.2726 −0.00184854
\(869\) −3408.19 −0.133044
\(870\) 0 0
\(871\) 16653.5 0.647855
\(872\) −11938.4 −0.463631
\(873\) 0 0
\(874\) −62004.6 −2.39970
\(875\) 780.776 0.0301658
\(876\) 0 0
\(877\) −5086.12 −0.195833 −0.0979167 0.995195i \(-0.531218\pi\)
−0.0979167 + 0.995195i \(0.531218\pi\)
\(878\) 12054.2 0.463335
\(879\) 0 0
\(880\) −2773.28 −0.106236
\(881\) 10625.5 0.406338 0.203169 0.979144i \(-0.434876\pi\)
0.203169 + 0.979144i \(0.434876\pi\)
\(882\) 0 0
\(883\) 13112.2 0.499728 0.249864 0.968281i \(-0.419614\pi\)
0.249864 + 0.968281i \(0.419614\pi\)
\(884\) −5844.25 −0.222357
\(885\) 0 0
\(886\) −38664.0 −1.46607
\(887\) 14442.8 0.546719 0.273360 0.961912i \(-0.411865\pi\)
0.273360 + 0.961912i \(0.411865\pi\)
\(888\) 0 0
\(889\) −5922.54 −0.223437
\(890\) 1817.15 0.0684393
\(891\) 0 0
\(892\) 5520.38 0.207215
\(893\) 72645.8 2.72228
\(894\) 0 0
\(895\) −8291.44 −0.309667
\(896\) 5876.86 0.219121
\(897\) 0 0
\(898\) −2493.61 −0.0926648
\(899\) 46.8641 0.00173860
\(900\) 0 0
\(901\) −13900.3 −0.513970
\(902\) 8410.27 0.310456
\(903\) 0 0
\(904\) 4110.10 0.151217
\(905\) −10109.0 −0.371310
\(906\) 0 0
\(907\) −44981.9 −1.64675 −0.823374 0.567499i \(-0.807911\pi\)
−0.823374 + 0.567499i \(0.807911\pi\)
\(908\) −7197.57 −0.263062
\(909\) 0 0
\(910\) −3929.85 −0.143157
\(911\) −6841.96 −0.248830 −0.124415 0.992230i \(-0.539705\pi\)
−0.124415 + 0.992230i \(0.539705\pi\)
\(912\) 0 0
\(913\) 11233.4 0.407199
\(914\) 160.501 0.00580843
\(915\) 0 0
\(916\) 398.989 0.0143919
\(917\) 9274.61 0.333996
\(918\) 0 0
\(919\) −4753.54 −0.170625 −0.0853127 0.996354i \(-0.527189\pi\)
−0.0853127 + 0.996354i \(0.527189\pi\)
\(920\) −22447.6 −0.804430
\(921\) 0 0
\(922\) 30395.9 1.08572
\(923\) 55052.7 1.96325
\(924\) 0 0
\(925\) −10422.3 −0.370470
\(926\) −33671.2 −1.19493
\(927\) 0 0
\(928\) 572.330 0.0202453
\(929\) 7507.93 0.265153 0.132576 0.991173i \(-0.457675\pi\)
0.132576 + 0.991173i \(0.457675\pi\)
\(930\) 0 0
\(931\) 39625.7 1.39493
\(932\) 3265.14 0.114757
\(933\) 0 0
\(934\) 26068.3 0.913256
\(935\) −4548.96 −0.159109
\(936\) 0 0
\(937\) 8540.47 0.297764 0.148882 0.988855i \(-0.452433\pi\)
0.148882 + 0.988855i \(0.452433\pi\)
\(938\) −5424.24 −0.188814
\(939\) 0 0
\(940\) 4008.20 0.139078
\(941\) −9101.13 −0.315290 −0.157645 0.987496i \(-0.550390\pi\)
−0.157645 + 0.987496i \(0.550390\pi\)
\(942\) 0 0
\(943\) 55425.5 1.91400
\(944\) 31200.6 1.07573
\(945\) 0 0
\(946\) −14472.7 −0.497407
\(947\) −47540.0 −1.63130 −0.815650 0.578546i \(-0.803620\pi\)
−0.815650 + 0.578546i \(0.803620\pi\)
\(948\) 0 0
\(949\) 6063.26 0.207399
\(950\) −8347.73 −0.285091
\(951\) 0 0
\(952\) 12490.2 0.425221
\(953\) −47370.7 −1.61016 −0.805082 0.593164i \(-0.797879\pi\)
−0.805082 + 0.593164i \(0.797879\pi\)
\(954\) 0 0
\(955\) −7201.12 −0.244003
\(956\) −2326.12 −0.0786947
\(957\) 0 0
\(958\) −8789.33 −0.296420
\(959\) −4278.20 −0.144057
\(960\) 0 0
\(961\) −29763.3 −0.999071
\(962\) 52458.4 1.75813
\(963\) 0 0
\(964\) −8122.38 −0.271374
\(965\) −13990.2 −0.466696
\(966\) 0 0
\(967\) −36171.6 −1.20290 −0.601448 0.798912i \(-0.705409\pi\)
−0.601448 + 0.798912i \(0.705409\pi\)
\(968\) −2925.43 −0.0971351
\(969\) 0 0
\(970\) 10225.0 0.338459
\(971\) 31713.2 1.04812 0.524060 0.851681i \(-0.324417\pi\)
0.524060 + 0.851681i \(0.324417\pi\)
\(972\) 0 0
\(973\) 5187.37 0.170914
\(974\) −7257.40 −0.238750
\(975\) 0 0
\(976\) −39653.1 −1.30048
\(977\) −22800.5 −0.746626 −0.373313 0.927706i \(-0.621778\pi\)
−0.373313 + 0.927706i \(0.621778\pi\)
\(978\) 0 0
\(979\) 1560.67 0.0509490
\(980\) 2186.33 0.0712651
\(981\) 0 0
\(982\) 6832.41 0.222027
\(983\) 44597.4 1.44704 0.723518 0.690305i \(-0.242524\pi\)
0.723518 + 0.690305i \(0.242524\pi\)
\(984\) 0 0
\(985\) −2294.72 −0.0742292
\(986\) −1887.10 −0.0609507
\(987\) 0 0
\(988\) −9210.95 −0.296599
\(989\) −95378.1 −3.06658
\(990\) 0 0
\(991\) −34788.1 −1.11512 −0.557558 0.830138i \(-0.688261\pi\)
−0.557558 + 0.830138i \(0.688261\pi\)
\(992\) 338.068 0.0108202
\(993\) 0 0
\(994\) −17931.3 −0.572180
\(995\) −11855.2 −0.377723
\(996\) 0 0
\(997\) −20360.5 −0.646765 −0.323383 0.946268i \(-0.604820\pi\)
−0.323383 + 0.946268i \(0.604820\pi\)
\(998\) −28528.0 −0.904849
\(999\) 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 495.4.a.d.1.2 2
3.2 odd 2 165.4.a.c.1.1 2
5.4 even 2 2475.4.a.n.1.1 2
15.2 even 4 825.4.c.j.199.1 4
15.8 even 4 825.4.c.j.199.4 4
15.14 odd 2 825.4.a.m.1.2 2
33.32 even 2 1815.4.a.n.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.4.a.c.1.1 2 3.2 odd 2
495.4.a.d.1.2 2 1.1 even 1 trivial
825.4.a.m.1.2 2 15.14 odd 2
825.4.c.j.199.1 4 15.2 even 4
825.4.c.j.199.4 4 15.8 even 4
1815.4.a.n.1.2 2 33.32 even 2
2475.4.a.n.1.1 2 5.4 even 2