Properties

Label 2205.4.a.ca.1.6
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 1.6
Root \(4.10376\) of defining polynomial
Character \(\chi\) \(=\) 2205.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.51797 q^{2} +22.4480 q^{4} +5.00000 q^{5} +79.7239 q^{8} +O(q^{10})\) \(q+5.51797 q^{2} +22.4480 q^{4} +5.00000 q^{5} +79.7239 q^{8} +27.5899 q^{10} -34.5211 q^{11} +68.8935 q^{13} +260.330 q^{16} +91.4346 q^{17} +11.8278 q^{19} +112.240 q^{20} -190.486 q^{22} +0.104165 q^{23} +25.0000 q^{25} +380.152 q^{26} -190.863 q^{29} +159.802 q^{31} +798.703 q^{32} +504.534 q^{34} -177.908 q^{37} +65.2657 q^{38} +398.619 q^{40} -145.247 q^{41} +8.25729 q^{43} -774.930 q^{44} +0.574782 q^{46} -260.529 q^{47} +137.949 q^{50} +1546.52 q^{52} -353.107 q^{53} -172.605 q^{55} -1053.18 q^{58} -240.495 q^{59} +778.188 q^{61} +881.783 q^{62} +2324.58 q^{64} +344.467 q^{65} +151.945 q^{67} +2052.53 q^{68} +311.449 q^{71} +639.888 q^{73} -981.690 q^{74} +265.512 q^{76} +391.186 q^{79} +1301.65 q^{80} -801.472 q^{82} -493.205 q^{83} +457.173 q^{85} +45.5635 q^{86} -2752.15 q^{88} -473.850 q^{89} +2.33831 q^{92} -1437.59 q^{94} +59.1392 q^{95} +839.005 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} + 14 q^{4} + 30 q^{5} + 66 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.51797 1.95090 0.975449 0.220225i \(-0.0706790\pi\)
0.975449 + 0.220225i \(0.0706790\pi\)
\(3\) 0 0
\(4\) 22.4480 2.80600
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) 79.7239 3.52333
\(9\) 0 0
\(10\) 27.5899 0.872468
\(11\) −34.5211 −0.946227 −0.473113 0.881002i \(-0.656870\pi\)
−0.473113 + 0.881002i \(0.656870\pi\)
\(12\) 0 0
\(13\) 68.8935 1.46982 0.734908 0.678167i \(-0.237225\pi\)
0.734908 + 0.678167i \(0.237225\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 260.330 4.06766
\(17\) 91.4346 1.30448 0.652239 0.758013i \(-0.273830\pi\)
0.652239 + 0.758013i \(0.273830\pi\)
\(18\) 0 0
\(19\) 11.8278 0.142815 0.0714077 0.997447i \(-0.477251\pi\)
0.0714077 + 0.997447i \(0.477251\pi\)
\(20\) 112.240 1.25488
\(21\) 0 0
\(22\) −190.486 −1.84599
\(23\) 0.104165 0.000944348 0 0.000472174 1.00000i \(-0.499850\pi\)
0.000472174 1.00000i \(0.499850\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 380.152 2.86746
\(27\) 0 0
\(28\) 0 0
\(29\) −190.863 −1.22215 −0.611076 0.791572i \(-0.709263\pi\)
−0.611076 + 0.791572i \(0.709263\pi\)
\(30\) 0 0
\(31\) 159.802 0.925847 0.462924 0.886398i \(-0.346800\pi\)
0.462924 + 0.886398i \(0.346800\pi\)
\(32\) 798.703 4.41225
\(33\) 0 0
\(34\) 504.534 2.54491
\(35\) 0 0
\(36\) 0 0
\(37\) −177.908 −0.790482 −0.395241 0.918577i \(-0.629339\pi\)
−0.395241 + 0.918577i \(0.629339\pi\)
\(38\) 65.2657 0.278618
\(39\) 0 0
\(40\) 398.619 1.57568
\(41\) −145.247 −0.553264 −0.276632 0.960976i \(-0.589218\pi\)
−0.276632 + 0.960976i \(0.589218\pi\)
\(42\) 0 0
\(43\) 8.25729 0.0292843 0.0146421 0.999893i \(-0.495339\pi\)
0.0146421 + 0.999893i \(0.495339\pi\)
\(44\) −774.930 −2.65512
\(45\) 0 0
\(46\) 0.574782 0.00184233
\(47\) −260.529 −0.808553 −0.404277 0.914637i \(-0.632477\pi\)
−0.404277 + 0.914637i \(0.632477\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 137.949 0.390180
\(51\) 0 0
\(52\) 1546.52 4.12431
\(53\) −353.107 −0.915151 −0.457576 0.889171i \(-0.651282\pi\)
−0.457576 + 0.889171i \(0.651282\pi\)
\(54\) 0 0
\(55\) −172.605 −0.423165
\(56\) 0 0
\(57\) 0 0
\(58\) −1053.18 −2.38429
\(59\) −240.495 −0.530673 −0.265337 0.964156i \(-0.585483\pi\)
−0.265337 + 0.964156i \(0.585483\pi\)
\(60\) 0 0
\(61\) 778.188 1.63339 0.816695 0.577069i \(-0.195804\pi\)
0.816695 + 0.577069i \(0.195804\pi\)
\(62\) 881.783 1.80623
\(63\) 0 0
\(64\) 2324.58 4.54020
\(65\) 344.467 0.657322
\(66\) 0 0
\(67\) 151.945 0.277059 0.138530 0.990358i \(-0.455762\pi\)
0.138530 + 0.990358i \(0.455762\pi\)
\(68\) 2052.53 3.66037
\(69\) 0 0
\(70\) 0 0
\(71\) 311.449 0.520594 0.260297 0.965529i \(-0.416180\pi\)
0.260297 + 0.965529i \(0.416180\pi\)
\(72\) 0 0
\(73\) 639.888 1.02593 0.512967 0.858408i \(-0.328546\pi\)
0.512967 + 0.858408i \(0.328546\pi\)
\(74\) −981.690 −1.54215
\(75\) 0 0
\(76\) 265.512 0.400740
\(77\) 0 0
\(78\) 0 0
\(79\) 391.186 0.557112 0.278556 0.960420i \(-0.410144\pi\)
0.278556 + 0.960420i \(0.410144\pi\)
\(80\) 1301.65 1.81911
\(81\) 0 0
\(82\) −801.472 −1.07936
\(83\) −493.205 −0.652245 −0.326122 0.945328i \(-0.605742\pi\)
−0.326122 + 0.945328i \(0.605742\pi\)
\(84\) 0 0
\(85\) 457.173 0.583381
\(86\) 45.5635 0.0571307
\(87\) 0 0
\(88\) −2752.15 −3.33387
\(89\) −473.850 −0.564359 −0.282180 0.959362i \(-0.591057\pi\)
−0.282180 + 0.959362i \(0.591057\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.33831 0.00264984
\(93\) 0 0
\(94\) −1437.59 −1.57741
\(95\) 59.1392 0.0638690
\(96\) 0 0
\(97\) 839.005 0.878227 0.439114 0.898431i \(-0.355293\pi\)
0.439114 + 0.898431i \(0.355293\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 561.201 0.561201
\(101\) −887.440 −0.874293 −0.437146 0.899390i \(-0.644011\pi\)
−0.437146 + 0.899390i \(0.644011\pi\)
\(102\) 0 0
\(103\) 619.087 0.592238 0.296119 0.955151i \(-0.404308\pi\)
0.296119 + 0.955151i \(0.404308\pi\)
\(104\) 5492.46 5.17865
\(105\) 0 0
\(106\) −1948.44 −1.78537
\(107\) 2151.30 1.94368 0.971841 0.235639i \(-0.0757183\pi\)
0.971841 + 0.235639i \(0.0757183\pi\)
\(108\) 0 0
\(109\) −407.076 −0.357714 −0.178857 0.983875i \(-0.557240\pi\)
−0.178857 + 0.983875i \(0.557240\pi\)
\(110\) −952.432 −0.825553
\(111\) 0 0
\(112\) 0 0
\(113\) 349.581 0.291025 0.145513 0.989356i \(-0.453517\pi\)
0.145513 + 0.989356i \(0.453517\pi\)
\(114\) 0 0
\(115\) 0.520827 0.000422325 0
\(116\) −4284.50 −3.42936
\(117\) 0 0
\(118\) −1327.04 −1.03529
\(119\) 0 0
\(120\) 0 0
\(121\) −139.296 −0.104655
\(122\) 4294.02 3.18658
\(123\) 0 0
\(124\) 3587.24 2.59793
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1183.78 0.827114 0.413557 0.910478i \(-0.364286\pi\)
0.413557 + 0.910478i \(0.364286\pi\)
\(128\) 6437.36 4.44522
\(129\) 0 0
\(130\) 1900.76 1.28237
\(131\) −223.357 −0.148968 −0.0744840 0.997222i \(-0.523731\pi\)
−0.0744840 + 0.997222i \(0.523731\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 838.426 0.540515
\(135\) 0 0
\(136\) 7289.52 4.59611
\(137\) −2036.66 −1.27010 −0.635050 0.772471i \(-0.719021\pi\)
−0.635050 + 0.772471i \(0.719021\pi\)
\(138\) 0 0
\(139\) 2687.00 1.63963 0.819815 0.572629i \(-0.194076\pi\)
0.819815 + 0.572629i \(0.194076\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1718.57 1.01563
\(143\) −2378.28 −1.39078
\(144\) 0 0
\(145\) −954.316 −0.546563
\(146\) 3530.88 2.00149
\(147\) 0 0
\(148\) −3993.68 −2.21810
\(149\) −673.500 −0.370304 −0.185152 0.982710i \(-0.559278\pi\)
−0.185152 + 0.982710i \(0.559278\pi\)
\(150\) 0 0
\(151\) −2125.18 −1.14533 −0.572664 0.819790i \(-0.694090\pi\)
−0.572664 + 0.819790i \(0.694090\pi\)
\(152\) 942.961 0.503186
\(153\) 0 0
\(154\) 0 0
\(155\) 799.010 0.414052
\(156\) 0 0
\(157\) −2813.03 −1.42997 −0.714983 0.699142i \(-0.753565\pi\)
−0.714983 + 0.699142i \(0.753565\pi\)
\(158\) 2158.55 1.08687
\(159\) 0 0
\(160\) 3993.52 1.97322
\(161\) 0 0
\(162\) 0 0
\(163\) −1344.42 −0.646032 −0.323016 0.946394i \(-0.604697\pi\)
−0.323016 + 0.946394i \(0.604697\pi\)
\(164\) −3260.52 −1.55246
\(165\) 0 0
\(166\) −2721.49 −1.27246
\(167\) −1451.24 −0.672456 −0.336228 0.941781i \(-0.609151\pi\)
−0.336228 + 0.941781i \(0.609151\pi\)
\(168\) 0 0
\(169\) 2549.31 1.16036
\(170\) 2522.67 1.13812
\(171\) 0 0
\(172\) 185.360 0.0821718
\(173\) 1979.16 0.869784 0.434892 0.900483i \(-0.356787\pi\)
0.434892 + 0.900483i \(0.356787\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −8986.87 −3.84893
\(177\) 0 0
\(178\) −2614.69 −1.10101
\(179\) 4358.66 1.82001 0.910005 0.414598i \(-0.136078\pi\)
0.910005 + 0.414598i \(0.136078\pi\)
\(180\) 0 0
\(181\) −377.923 −0.155198 −0.0775988 0.996985i \(-0.524725\pi\)
−0.0775988 + 0.996985i \(0.524725\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 8.30447 0.00332725
\(185\) −889.538 −0.353514
\(186\) 0 0
\(187\) −3156.42 −1.23433
\(188\) −5848.36 −2.26880
\(189\) 0 0
\(190\) 326.328 0.124602
\(191\) 2425.95 0.919033 0.459517 0.888169i \(-0.348023\pi\)
0.459517 + 0.888169i \(0.348023\pi\)
\(192\) 0 0
\(193\) −622.923 −0.232326 −0.116163 0.993230i \(-0.537060\pi\)
−0.116163 + 0.993230i \(0.537060\pi\)
\(194\) 4629.61 1.71333
\(195\) 0 0
\(196\) 0 0
\(197\) −2842.29 −1.02794 −0.513971 0.857807i \(-0.671826\pi\)
−0.513971 + 0.857807i \(0.671826\pi\)
\(198\) 0 0
\(199\) −867.364 −0.308974 −0.154487 0.987995i \(-0.549372\pi\)
−0.154487 + 0.987995i \(0.549372\pi\)
\(200\) 1993.10 0.704666
\(201\) 0 0
\(202\) −4896.87 −1.70566
\(203\) 0 0
\(204\) 0 0
\(205\) −726.237 −0.247427
\(206\) 3416.11 1.15540
\(207\) 0 0
\(208\) 17935.0 5.97871
\(209\) −408.309 −0.135136
\(210\) 0 0
\(211\) −5975.92 −1.94976 −0.974880 0.222730i \(-0.928503\pi\)
−0.974880 + 0.222730i \(0.928503\pi\)
\(212\) −7926.57 −2.56792
\(213\) 0 0
\(214\) 11870.8 3.79192
\(215\) 41.2864 0.0130963
\(216\) 0 0
\(217\) 0 0
\(218\) −2246.24 −0.697864
\(219\) 0 0
\(220\) −3874.65 −1.18740
\(221\) 6299.25 1.91734
\(222\) 0 0
\(223\) −5181.58 −1.55598 −0.777992 0.628274i \(-0.783762\pi\)
−0.777992 + 0.628274i \(0.783762\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1928.98 0.567761
\(227\) −3753.06 −1.09735 −0.548677 0.836035i \(-0.684868\pi\)
−0.548677 + 0.836035i \(0.684868\pi\)
\(228\) 0 0
\(229\) −6258.14 −1.80589 −0.902947 0.429752i \(-0.858601\pi\)
−0.902947 + 0.429752i \(0.858601\pi\)
\(230\) 2.87391 0.000823913 0
\(231\) 0 0
\(232\) −15216.4 −4.30605
\(233\) −1779.96 −0.500469 −0.250234 0.968185i \(-0.580508\pi\)
−0.250234 + 0.968185i \(0.580508\pi\)
\(234\) 0 0
\(235\) −1302.64 −0.361596
\(236\) −5398.63 −1.48907
\(237\) 0 0
\(238\) 0 0
\(239\) −3519.46 −0.952532 −0.476266 0.879301i \(-0.658010\pi\)
−0.476266 + 0.879301i \(0.658010\pi\)
\(240\) 0 0
\(241\) 362.930 0.0970058 0.0485029 0.998823i \(-0.484555\pi\)
0.0485029 + 0.998823i \(0.484555\pi\)
\(242\) −768.629 −0.204171
\(243\) 0 0
\(244\) 17468.8 4.58330
\(245\) 0 0
\(246\) 0 0
\(247\) 814.861 0.209912
\(248\) 12740.0 3.26207
\(249\) 0 0
\(250\) 689.747 0.174494
\(251\) 5333.85 1.34131 0.670656 0.741768i \(-0.266012\pi\)
0.670656 + 0.741768i \(0.266012\pi\)
\(252\) 0 0
\(253\) −3.59590 −0.000893567 0
\(254\) 6532.06 1.61361
\(255\) 0 0
\(256\) 16924.5 4.13197
\(257\) 2438.78 0.591933 0.295966 0.955198i \(-0.404358\pi\)
0.295966 + 0.955198i \(0.404358\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7732.62 1.84445
\(261\) 0 0
\(262\) −1232.48 −0.290621
\(263\) −1526.25 −0.357843 −0.178921 0.983863i \(-0.557261\pi\)
−0.178921 + 0.983863i \(0.557261\pi\)
\(264\) 0 0
\(265\) −1765.54 −0.409268
\(266\) 0 0
\(267\) 0 0
\(268\) 3410.86 0.777430
\(269\) 7564.12 1.71447 0.857235 0.514925i \(-0.172180\pi\)
0.857235 + 0.514925i \(0.172180\pi\)
\(270\) 0 0
\(271\) 4282.68 0.959980 0.479990 0.877274i \(-0.340640\pi\)
0.479990 + 0.877274i \(0.340640\pi\)
\(272\) 23803.2 5.30617
\(273\) 0 0
\(274\) −11238.2 −2.47784
\(275\) −863.027 −0.189245
\(276\) 0 0
\(277\) −4008.41 −0.869465 −0.434732 0.900560i \(-0.643157\pi\)
−0.434732 + 0.900560i \(0.643157\pi\)
\(278\) 14826.8 3.19875
\(279\) 0 0
\(280\) 0 0
\(281\) −6935.44 −1.47236 −0.736181 0.676785i \(-0.763373\pi\)
−0.736181 + 0.676785i \(0.763373\pi\)
\(282\) 0 0
\(283\) −2666.64 −0.560124 −0.280062 0.959982i \(-0.590355\pi\)
−0.280062 + 0.959982i \(0.590355\pi\)
\(284\) 6991.41 1.46079
\(285\) 0 0
\(286\) −13123.3 −2.71327
\(287\) 0 0
\(288\) 0 0
\(289\) 3447.28 0.701665
\(290\) −5265.89 −1.06629
\(291\) 0 0
\(292\) 14364.2 2.87878
\(293\) −5939.10 −1.18418 −0.592092 0.805870i \(-0.701698\pi\)
−0.592092 + 0.805870i \(0.701698\pi\)
\(294\) 0 0
\(295\) −1202.47 −0.237324
\(296\) −14183.5 −2.78513
\(297\) 0 0
\(298\) −3716.36 −0.722425
\(299\) 7.17632 0.00138802
\(300\) 0 0
\(301\) 0 0
\(302\) −11726.7 −2.23442
\(303\) 0 0
\(304\) 3079.14 0.580924
\(305\) 3890.94 0.730474
\(306\) 0 0
\(307\) 10381.5 1.92998 0.964992 0.262278i \(-0.0844737\pi\)
0.964992 + 0.262278i \(0.0844737\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4408.91 0.807772
\(311\) −4240.54 −0.773181 −0.386590 0.922252i \(-0.626347\pi\)
−0.386590 + 0.922252i \(0.626347\pi\)
\(312\) 0 0
\(313\) −283.903 −0.0512688 −0.0256344 0.999671i \(-0.508161\pi\)
−0.0256344 + 0.999671i \(0.508161\pi\)
\(314\) −15522.2 −2.78972
\(315\) 0 0
\(316\) 8781.36 1.56326
\(317\) −1739.49 −0.308201 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(318\) 0 0
\(319\) 6588.80 1.15643
\(320\) 11622.9 2.03044
\(321\) 0 0
\(322\) 0 0
\(323\) 1081.47 0.186300
\(324\) 0 0
\(325\) 1722.34 0.293963
\(326\) −7418.48 −1.26034
\(327\) 0 0
\(328\) −11579.7 −1.94933
\(329\) 0 0
\(330\) 0 0
\(331\) 5606.96 0.931077 0.465538 0.885028i \(-0.345861\pi\)
0.465538 + 0.885028i \(0.345861\pi\)
\(332\) −11071.5 −1.83020
\(333\) 0 0
\(334\) −8007.89 −1.31189
\(335\) 759.723 0.123905
\(336\) 0 0
\(337\) −9427.44 −1.52387 −0.761937 0.647652i \(-0.775751\pi\)
−0.761937 + 0.647652i \(0.775751\pi\)
\(338\) 14067.0 2.26375
\(339\) 0 0
\(340\) 10262.6 1.63697
\(341\) −5516.53 −0.876062
\(342\) 0 0
\(343\) 0 0
\(344\) 658.303 0.103178
\(345\) 0 0
\(346\) 10920.9 1.69686
\(347\) −11634.2 −1.79988 −0.899939 0.436017i \(-0.856389\pi\)
−0.899939 + 0.436017i \(0.856389\pi\)
\(348\) 0 0
\(349\) −1317.10 −0.202013 −0.101006 0.994886i \(-0.532206\pi\)
−0.101006 + 0.994886i \(0.532206\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −27572.1 −4.17499
\(353\) −5848.82 −0.881874 −0.440937 0.897538i \(-0.645354\pi\)
−0.440937 + 0.897538i \(0.645354\pi\)
\(354\) 0 0
\(355\) 1557.24 0.232817
\(356\) −10637.0 −1.58359
\(357\) 0 0
\(358\) 24051.0 3.55065
\(359\) 12422.0 1.82621 0.913104 0.407727i \(-0.133679\pi\)
0.913104 + 0.407727i \(0.133679\pi\)
\(360\) 0 0
\(361\) −6719.10 −0.979604
\(362\) −2085.37 −0.302775
\(363\) 0 0
\(364\) 0 0
\(365\) 3199.44 0.458812
\(366\) 0 0
\(367\) −6590.78 −0.937427 −0.468713 0.883350i \(-0.655282\pi\)
−0.468713 + 0.883350i \(0.655282\pi\)
\(368\) 27.1174 0.00384128
\(369\) 0 0
\(370\) −4908.45 −0.689670
\(371\) 0 0
\(372\) 0 0
\(373\) 344.278 0.0477910 0.0238955 0.999714i \(-0.492393\pi\)
0.0238955 + 0.999714i \(0.492393\pi\)
\(374\) −17417.0 −2.40806
\(375\) 0 0
\(376\) −20770.4 −2.84880
\(377\) −13149.2 −1.79634
\(378\) 0 0
\(379\) 5241.23 0.710353 0.355177 0.934799i \(-0.384421\pi\)
0.355177 + 0.934799i \(0.384421\pi\)
\(380\) 1327.56 0.179217
\(381\) 0 0
\(382\) 13386.3 1.79294
\(383\) −7597.37 −1.01360 −0.506798 0.862065i \(-0.669171\pi\)
−0.506798 + 0.862065i \(0.669171\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3437.27 −0.453245
\(387\) 0 0
\(388\) 18834.0 2.46431
\(389\) −3101.84 −0.404291 −0.202146 0.979355i \(-0.564791\pi\)
−0.202146 + 0.979355i \(0.564791\pi\)
\(390\) 0 0
\(391\) 9.52432 0.00123188
\(392\) 0 0
\(393\) 0 0
\(394\) −15683.7 −2.00541
\(395\) 1955.93 0.249148
\(396\) 0 0
\(397\) −2932.06 −0.370669 −0.185335 0.982675i \(-0.559337\pi\)
−0.185335 + 0.982675i \(0.559337\pi\)
\(398\) −4786.09 −0.602777
\(399\) 0 0
\(400\) 6508.25 0.813531
\(401\) −89.2375 −0.0111130 −0.00555649 0.999985i \(-0.501769\pi\)
−0.00555649 + 0.999985i \(0.501769\pi\)
\(402\) 0 0
\(403\) 11009.3 1.36083
\(404\) −19921.3 −2.45327
\(405\) 0 0
\(406\) 0 0
\(407\) 6141.56 0.747975
\(408\) 0 0
\(409\) 147.388 0.0178188 0.00890940 0.999960i \(-0.497164\pi\)
0.00890940 + 0.999960i \(0.497164\pi\)
\(410\) −4007.36 −0.482706
\(411\) 0 0
\(412\) 13897.3 1.66182
\(413\) 0 0
\(414\) 0 0
\(415\) −2466.03 −0.291693
\(416\) 55025.4 6.48520
\(417\) 0 0
\(418\) −2253.04 −0.263636
\(419\) 3781.67 0.440923 0.220462 0.975396i \(-0.429244\pi\)
0.220462 + 0.975396i \(0.429244\pi\)
\(420\) 0 0
\(421\) −10899.2 −1.26175 −0.630874 0.775885i \(-0.717304\pi\)
−0.630874 + 0.775885i \(0.717304\pi\)
\(422\) −32975.0 −3.80378
\(423\) 0 0
\(424\) −28151.1 −3.22438
\(425\) 2285.86 0.260896
\(426\) 0 0
\(427\) 0 0
\(428\) 48292.4 5.45398
\(429\) 0 0
\(430\) 227.817 0.0255496
\(431\) 11283.4 1.26102 0.630512 0.776180i \(-0.282845\pi\)
0.630512 + 0.776180i \(0.282845\pi\)
\(432\) 0 0
\(433\) −8906.19 −0.988462 −0.494231 0.869331i \(-0.664550\pi\)
−0.494231 + 0.869331i \(0.664550\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −9138.07 −1.00375
\(437\) 1.23205 0.000134867 0
\(438\) 0 0
\(439\) 8149.49 0.886000 0.443000 0.896522i \(-0.353914\pi\)
0.443000 + 0.896522i \(0.353914\pi\)
\(440\) −13760.8 −1.49095
\(441\) 0 0
\(442\) 34759.1 3.74054
\(443\) 11472.8 1.23045 0.615223 0.788353i \(-0.289066\pi\)
0.615223 + 0.788353i \(0.289066\pi\)
\(444\) 0 0
\(445\) −2369.25 −0.252389
\(446\) −28591.8 −3.03557
\(447\) 0 0
\(448\) 0 0
\(449\) −1963.80 −0.206409 −0.103204 0.994660i \(-0.532910\pi\)
−0.103204 + 0.994660i \(0.532910\pi\)
\(450\) 0 0
\(451\) 5014.10 0.523514
\(452\) 7847.42 0.816618
\(453\) 0 0
\(454\) −20709.3 −2.14083
\(455\) 0 0
\(456\) 0 0
\(457\) 5589.85 0.572171 0.286086 0.958204i \(-0.407646\pi\)
0.286086 + 0.958204i \(0.407646\pi\)
\(458\) −34532.3 −3.52311
\(459\) 0 0
\(460\) 11.6915 0.00118505
\(461\) 18790.9 1.89844 0.949219 0.314618i \(-0.101876\pi\)
0.949219 + 0.314618i \(0.101876\pi\)
\(462\) 0 0
\(463\) −7892.22 −0.792187 −0.396094 0.918210i \(-0.629634\pi\)
−0.396094 + 0.918210i \(0.629634\pi\)
\(464\) −49687.4 −4.97130
\(465\) 0 0
\(466\) −9821.78 −0.976363
\(467\) −385.511 −0.0381998 −0.0190999 0.999818i \(-0.506080\pi\)
−0.0190999 + 0.999818i \(0.506080\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −7187.95 −0.705437
\(471\) 0 0
\(472\) −19173.2 −1.86974
\(473\) −285.050 −0.0277096
\(474\) 0 0
\(475\) 295.696 0.0285631
\(476\) 0 0
\(477\) 0 0
\(478\) −19420.3 −1.85829
\(479\) −1694.46 −0.161632 −0.0808160 0.996729i \(-0.525753\pi\)
−0.0808160 + 0.996729i \(0.525753\pi\)
\(480\) 0 0
\(481\) −12256.7 −1.16186
\(482\) 2002.64 0.189248
\(483\) 0 0
\(484\) −3126.91 −0.293662
\(485\) 4195.03 0.392755
\(486\) 0 0
\(487\) 15711.2 1.46189 0.730945 0.682436i \(-0.239079\pi\)
0.730945 + 0.682436i \(0.239079\pi\)
\(488\) 62040.2 5.75498
\(489\) 0 0
\(490\) 0 0
\(491\) 2716.34 0.249667 0.124834 0.992178i \(-0.460160\pi\)
0.124834 + 0.992178i \(0.460160\pi\)
\(492\) 0 0
\(493\) −17451.5 −1.59427
\(494\) 4496.38 0.409518
\(495\) 0 0
\(496\) 41601.2 3.76603
\(497\) 0 0
\(498\) 0 0
\(499\) 4295.34 0.385342 0.192671 0.981263i \(-0.438285\pi\)
0.192671 + 0.981263i \(0.438285\pi\)
\(500\) 2806.00 0.250977
\(501\) 0 0
\(502\) 29432.0 2.61677
\(503\) −6515.26 −0.577537 −0.288769 0.957399i \(-0.593246\pi\)
−0.288769 + 0.957399i \(0.593246\pi\)
\(504\) 0 0
\(505\) −4437.20 −0.390996
\(506\) −19.8421 −0.00174326
\(507\) 0 0
\(508\) 26573.5 2.32088
\(509\) −14391.8 −1.25325 −0.626624 0.779321i \(-0.715564\pi\)
−0.626624 + 0.779321i \(0.715564\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 41890.2 3.61583
\(513\) 0 0
\(514\) 13457.1 1.15480
\(515\) 3095.44 0.264857
\(516\) 0 0
\(517\) 8993.73 0.765075
\(518\) 0 0
\(519\) 0 0
\(520\) 27462.3 2.31596
\(521\) −2913.36 −0.244984 −0.122492 0.992469i \(-0.539089\pi\)
−0.122492 + 0.992469i \(0.539089\pi\)
\(522\) 0 0
\(523\) 16870.2 1.41048 0.705242 0.708967i \(-0.250838\pi\)
0.705242 + 0.708967i \(0.250838\pi\)
\(524\) −5013.93 −0.418005
\(525\) 0 0
\(526\) −8421.82 −0.698115
\(527\) 14611.4 1.20775
\(528\) 0 0
\(529\) −12167.0 −0.999999
\(530\) −9742.18 −0.798441
\(531\) 0 0
\(532\) 0 0
\(533\) −10006.6 −0.813197
\(534\) 0 0
\(535\) 10756.5 0.869241
\(536\) 12113.6 0.976172
\(537\) 0 0
\(538\) 41738.6 3.34476
\(539\) 0 0
\(540\) 0 0
\(541\) −2229.59 −0.177186 −0.0885929 0.996068i \(-0.528237\pi\)
−0.0885929 + 0.996068i \(0.528237\pi\)
\(542\) 23631.7 1.87282
\(543\) 0 0
\(544\) 73029.1 5.75569
\(545\) −2035.38 −0.159975
\(546\) 0 0
\(547\) −1218.73 −0.0952639 −0.0476319 0.998865i \(-0.515167\pi\)
−0.0476319 + 0.998865i \(0.515167\pi\)
\(548\) −45719.1 −3.56391
\(549\) 0 0
\(550\) −4762.16 −0.369198
\(551\) −2257.50 −0.174542
\(552\) 0 0
\(553\) 0 0
\(554\) −22118.3 −1.69624
\(555\) 0 0
\(556\) 60317.9 4.60081
\(557\) 22734.5 1.72943 0.864714 0.502264i \(-0.167499\pi\)
0.864714 + 0.502264i \(0.167499\pi\)
\(558\) 0 0
\(559\) 568.873 0.0430425
\(560\) 0 0
\(561\) 0 0
\(562\) −38269.6 −2.87243
\(563\) −4302.11 −0.322047 −0.161023 0.986951i \(-0.551479\pi\)
−0.161023 + 0.986951i \(0.551479\pi\)
\(564\) 0 0
\(565\) 1747.91 0.130150
\(566\) −14714.4 −1.09275
\(567\) 0 0
\(568\) 24829.9 1.83422
\(569\) −14866.9 −1.09535 −0.547675 0.836691i \(-0.684487\pi\)
−0.547675 + 0.836691i \(0.684487\pi\)
\(570\) 0 0
\(571\) 16514.5 1.21035 0.605174 0.796093i \(-0.293103\pi\)
0.605174 + 0.796093i \(0.293103\pi\)
\(572\) −53387.6 −3.90253
\(573\) 0 0
\(574\) 0 0
\(575\) 2.60414 0.000188870 0
\(576\) 0 0
\(577\) 1867.97 0.134774 0.0673870 0.997727i \(-0.478534\pi\)
0.0673870 + 0.997727i \(0.478534\pi\)
\(578\) 19022.0 1.36888
\(579\) 0 0
\(580\) −21422.5 −1.53366
\(581\) 0 0
\(582\) 0 0
\(583\) 12189.6 0.865941
\(584\) 51014.3 3.61471
\(585\) 0 0
\(586\) −32771.8 −2.31022
\(587\) −3926.15 −0.276064 −0.138032 0.990428i \(-0.544078\pi\)
−0.138032 + 0.990428i \(0.544078\pi\)
\(588\) 0 0
\(589\) 1890.11 0.132225
\(590\) −6635.21 −0.462996
\(591\) 0 0
\(592\) −46314.7 −3.21541
\(593\) 7554.18 0.523125 0.261562 0.965187i \(-0.415762\pi\)
0.261562 + 0.965187i \(0.415762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −15118.8 −1.03907
\(597\) 0 0
\(598\) 39.5988 0.00270788
\(599\) −28210.9 −1.92432 −0.962160 0.272487i \(-0.912154\pi\)
−0.962160 + 0.272487i \(0.912154\pi\)
\(600\) 0 0
\(601\) −23181.4 −1.57336 −0.786679 0.617363i \(-0.788201\pi\)
−0.786679 + 0.617363i \(0.788201\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −47706.1 −3.21380
\(605\) −696.478 −0.0468031
\(606\) 0 0
\(607\) −24863.6 −1.66257 −0.831287 0.555844i \(-0.812395\pi\)
−0.831287 + 0.555844i \(0.812395\pi\)
\(608\) 9446.93 0.630137
\(609\) 0 0
\(610\) 21470.1 1.42508
\(611\) −17948.7 −1.18843
\(612\) 0 0
\(613\) −12792.7 −0.842893 −0.421446 0.906853i \(-0.638477\pi\)
−0.421446 + 0.906853i \(0.638477\pi\)
\(614\) 57285.0 3.76520
\(615\) 0 0
\(616\) 0 0
\(617\) −19793.3 −1.29149 −0.645744 0.763554i \(-0.723453\pi\)
−0.645744 + 0.763554i \(0.723453\pi\)
\(618\) 0 0
\(619\) −20951.7 −1.36045 −0.680226 0.733002i \(-0.738118\pi\)
−0.680226 + 0.733002i \(0.738118\pi\)
\(620\) 17936.2 1.16183
\(621\) 0 0
\(622\) −23399.2 −1.50840
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −1566.57 −0.100020
\(627\) 0 0
\(628\) −63147.1 −4.01249
\(629\) −16266.9 −1.03117
\(630\) 0 0
\(631\) 23273.5 1.46831 0.734156 0.678981i \(-0.237578\pi\)
0.734156 + 0.678981i \(0.237578\pi\)
\(632\) 31186.9 1.96289
\(633\) 0 0
\(634\) −9598.47 −0.601268
\(635\) 5918.90 0.369896
\(636\) 0 0
\(637\) 0 0
\(638\) 36356.8 2.25608
\(639\) 0 0
\(640\) 32186.8 1.98796
\(641\) 22117.7 1.36287 0.681434 0.731880i \(-0.261357\pi\)
0.681434 + 0.731880i \(0.261357\pi\)
\(642\) 0 0
\(643\) 20269.9 1.24318 0.621591 0.783342i \(-0.286487\pi\)
0.621591 + 0.783342i \(0.286487\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5967.54 0.363451
\(647\) 3145.25 0.191117 0.0955583 0.995424i \(-0.469536\pi\)
0.0955583 + 0.995424i \(0.469536\pi\)
\(648\) 0 0
\(649\) 8302.13 0.502137
\(650\) 9503.81 0.573493
\(651\) 0 0
\(652\) −30179.6 −1.81277
\(653\) 5953.35 0.356773 0.178386 0.983961i \(-0.442912\pi\)
0.178386 + 0.983961i \(0.442912\pi\)
\(654\) 0 0
\(655\) −1116.79 −0.0666205
\(656\) −37812.3 −2.25049
\(657\) 0 0
\(658\) 0 0
\(659\) −26277.5 −1.55330 −0.776652 0.629930i \(-0.783084\pi\)
−0.776652 + 0.629930i \(0.783084\pi\)
\(660\) 0 0
\(661\) −24004.3 −1.41250 −0.706248 0.707964i \(-0.749614\pi\)
−0.706248 + 0.707964i \(0.749614\pi\)
\(662\) 30939.1 1.81644
\(663\) 0 0
\(664\) −39320.3 −2.29808
\(665\) 0 0
\(666\) 0 0
\(667\) −19.8814 −0.00115414
\(668\) −32577.4 −1.88691
\(669\) 0 0
\(670\) 4192.13 0.241725
\(671\) −26863.9 −1.54556
\(672\) 0 0
\(673\) 9205.36 0.527252 0.263626 0.964625i \(-0.415082\pi\)
0.263626 + 0.964625i \(0.415082\pi\)
\(674\) −52020.4 −2.97292
\(675\) 0 0
\(676\) 57227.1 3.25598
\(677\) 18773.1 1.06575 0.532873 0.846195i \(-0.321112\pi\)
0.532873 + 0.846195i \(0.321112\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 36447.6 2.05544
\(681\) 0 0
\(682\) −30440.1 −1.70911
\(683\) 10222.2 0.572684 0.286342 0.958127i \(-0.407561\pi\)
0.286342 + 0.958127i \(0.407561\pi\)
\(684\) 0 0
\(685\) −10183.3 −0.568006
\(686\) 0 0
\(687\) 0 0
\(688\) 2149.62 0.119118
\(689\) −24326.8 −1.34510
\(690\) 0 0
\(691\) 22355.1 1.23072 0.615361 0.788246i \(-0.289010\pi\)
0.615361 + 0.788246i \(0.289010\pi\)
\(692\) 44428.2 2.44062
\(693\) 0 0
\(694\) −64197.3 −3.51138
\(695\) 13435.0 0.733264
\(696\) 0 0
\(697\) −13280.6 −0.721722
\(698\) −7267.70 −0.394107
\(699\) 0 0
\(700\) 0 0
\(701\) −16217.3 −0.873779 −0.436890 0.899515i \(-0.643920\pi\)
−0.436890 + 0.899515i \(0.643920\pi\)
\(702\) 0 0
\(703\) −2104.26 −0.112893
\(704\) −80247.1 −4.29606
\(705\) 0 0
\(706\) −32273.7 −1.72045
\(707\) 0 0
\(708\) 0 0
\(709\) 3922.92 0.207798 0.103899 0.994588i \(-0.466868\pi\)
0.103899 + 0.994588i \(0.466868\pi\)
\(710\) 8592.83 0.454202
\(711\) 0 0
\(712\) −37777.1 −1.98842
\(713\) 16.6458 0.000874322 0
\(714\) 0 0
\(715\) −11891.4 −0.621976
\(716\) 97843.4 5.10695
\(717\) 0 0
\(718\) 68544.3 3.56275
\(719\) −23908.6 −1.24011 −0.620055 0.784558i \(-0.712890\pi\)
−0.620055 + 0.784558i \(0.712890\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −37075.8 −1.91111
\(723\) 0 0
\(724\) −8483.62 −0.435485
\(725\) −4771.58 −0.244430
\(726\) 0 0
\(727\) −26906.4 −1.37263 −0.686315 0.727305i \(-0.740773\pi\)
−0.686315 + 0.727305i \(0.740773\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 17654.4 0.895095
\(731\) 755.001 0.0382007
\(732\) 0 0
\(733\) 27637.5 1.39265 0.696325 0.717726i \(-0.254817\pi\)
0.696325 + 0.717726i \(0.254817\pi\)
\(734\) −36367.7 −1.82882
\(735\) 0 0
\(736\) 83.1973 0.00416670
\(737\) −5245.29 −0.262161
\(738\) 0 0
\(739\) −14038.9 −0.698821 −0.349410 0.936970i \(-0.613618\pi\)
−0.349410 + 0.936970i \(0.613618\pi\)
\(740\) −19968.4 −0.991963
\(741\) 0 0
\(742\) 0 0
\(743\) −17698.7 −0.873893 −0.436946 0.899488i \(-0.643940\pi\)
−0.436946 + 0.899488i \(0.643940\pi\)
\(744\) 0 0
\(745\) −3367.50 −0.165605
\(746\) 1899.72 0.0932354
\(747\) 0 0
\(748\) −70855.4 −3.46354
\(749\) 0 0
\(750\) 0 0
\(751\) 17199.7 0.835719 0.417859 0.908512i \(-0.362780\pi\)
0.417859 + 0.908512i \(0.362780\pi\)
\(752\) −67823.4 −3.28892
\(753\) 0 0
\(754\) −72557.1 −3.50448
\(755\) −10625.9 −0.512206
\(756\) 0 0
\(757\) −19200.7 −0.921879 −0.460939 0.887432i \(-0.652487\pi\)
−0.460939 + 0.887432i \(0.652487\pi\)
\(758\) 28921.0 1.38583
\(759\) 0 0
\(760\) 4714.80 0.225031
\(761\) 27918.7 1.32990 0.664949 0.746889i \(-0.268453\pi\)
0.664949 + 0.746889i \(0.268453\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 54457.7 2.57881
\(765\) 0 0
\(766\) −41922.1 −1.97742
\(767\) −16568.5 −0.779992
\(768\) 0 0
\(769\) −7436.29 −0.348712 −0.174356 0.984683i \(-0.555784\pi\)
−0.174356 + 0.984683i \(0.555784\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −13983.4 −0.651908
\(773\) −4989.84 −0.232176 −0.116088 0.993239i \(-0.537035\pi\)
−0.116088 + 0.993239i \(0.537035\pi\)
\(774\) 0 0
\(775\) 3995.05 0.185169
\(776\) 66888.7 3.09429
\(777\) 0 0
\(778\) −17115.9 −0.788731
\(779\) −1717.96 −0.0790146
\(780\) 0 0
\(781\) −10751.5 −0.492600
\(782\) 52.5550 0.00240328
\(783\) 0 0
\(784\) 0 0
\(785\) −14065.2 −0.639500
\(786\) 0 0
\(787\) −2870.69 −0.130024 −0.0650122 0.997884i \(-0.520709\pi\)
−0.0650122 + 0.997884i \(0.520709\pi\)
\(788\) −63803.8 −2.88441
\(789\) 0 0
\(790\) 10792.8 0.486063
\(791\) 0 0
\(792\) 0 0
\(793\) 53612.1 2.40078
\(794\) −16179.0 −0.723138
\(795\) 0 0
\(796\) −19470.6 −0.866982
\(797\) −4676.61 −0.207847 −0.103923 0.994585i \(-0.533140\pi\)
−0.103923 + 0.994585i \(0.533140\pi\)
\(798\) 0 0
\(799\) −23821.3 −1.05474
\(800\) 19967.6 0.882451
\(801\) 0 0
\(802\) −492.410 −0.0216803
\(803\) −22089.6 −0.970766
\(804\) 0 0
\(805\) 0 0
\(806\) 60749.1 2.65483
\(807\) 0 0
\(808\) −70750.2 −3.08042
\(809\) 15376.9 0.668261 0.334131 0.942527i \(-0.391557\pi\)
0.334131 + 0.942527i \(0.391557\pi\)
\(810\) 0 0
\(811\) 36422.9 1.57704 0.788522 0.615007i \(-0.210847\pi\)
0.788522 + 0.615007i \(0.210847\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 33889.0 1.45922
\(815\) −6722.10 −0.288914
\(816\) 0 0
\(817\) 97.6658 0.00418225
\(818\) 813.285 0.0347627
\(819\) 0 0
\(820\) −16302.6 −0.694282
\(821\) 25479.0 1.08310 0.541550 0.840669i \(-0.317838\pi\)
0.541550 + 0.840669i \(0.317838\pi\)
\(822\) 0 0
\(823\) −17933.3 −0.759557 −0.379779 0.925077i \(-0.624000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(824\) 49356.1 2.08665
\(825\) 0 0
\(826\) 0 0
\(827\) −13021.6 −0.547529 −0.273764 0.961797i \(-0.588269\pi\)
−0.273764 + 0.961797i \(0.588269\pi\)
\(828\) 0 0
\(829\) −11397.6 −0.477509 −0.238754 0.971080i \(-0.576739\pi\)
−0.238754 + 0.971080i \(0.576739\pi\)
\(830\) −13607.5 −0.569063
\(831\) 0 0
\(832\) 160149. 6.67326
\(833\) 0 0
\(834\) 0 0
\(835\) −7256.19 −0.300731
\(836\) −9165.75 −0.379191
\(837\) 0 0
\(838\) 20867.2 0.860196
\(839\) 37681.2 1.55053 0.775267 0.631633i \(-0.217615\pi\)
0.775267 + 0.631633i \(0.217615\pi\)
\(840\) 0 0
\(841\) 12039.8 0.493656
\(842\) −60141.7 −2.46154
\(843\) 0 0
\(844\) −134148. −5.47104
\(845\) 12746.6 0.518929
\(846\) 0 0
\(847\) 0 0
\(848\) −91924.4 −3.72252
\(849\) 0 0
\(850\) 12613.3 0.508981
\(851\) −18.5318 −0.000746490 0
\(852\) 0 0
\(853\) 21771.6 0.873911 0.436956 0.899483i \(-0.356057\pi\)
0.436956 + 0.899483i \(0.356057\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 171510. 6.84823
\(857\) −29860.2 −1.19021 −0.595103 0.803649i \(-0.702889\pi\)
−0.595103 + 0.803649i \(0.702889\pi\)
\(858\) 0 0
\(859\) 18530.6 0.736039 0.368019 0.929818i \(-0.380036\pi\)
0.368019 + 0.929818i \(0.380036\pi\)
\(860\) 926.799 0.0367484
\(861\) 0 0
\(862\) 62261.4 2.46013
\(863\) 21296.5 0.840024 0.420012 0.907519i \(-0.362026\pi\)
0.420012 + 0.907519i \(0.362026\pi\)
\(864\) 0 0
\(865\) 9895.79 0.388979
\(866\) −49144.1 −1.92839
\(867\) 0 0
\(868\) 0 0
\(869\) −13504.2 −0.527155
\(870\) 0 0
\(871\) 10468.0 0.407226
\(872\) −32453.7 −1.26035
\(873\) 0 0
\(874\) 6.79843 0.000263112 0
\(875\) 0 0
\(876\) 0 0
\(877\) −18793.4 −0.723614 −0.361807 0.932253i \(-0.617840\pi\)
−0.361807 + 0.932253i \(0.617840\pi\)
\(878\) 44968.7 1.72850
\(879\) 0 0
\(880\) −44934.4 −1.72129
\(881\) −1638.62 −0.0626634 −0.0313317 0.999509i \(-0.509975\pi\)
−0.0313317 + 0.999509i \(0.509975\pi\)
\(882\) 0 0
\(883\) −35424.1 −1.35008 −0.675038 0.737783i \(-0.735873\pi\)
−0.675038 + 0.737783i \(0.735873\pi\)
\(884\) 141406. 5.38008
\(885\) 0 0
\(886\) 63306.5 2.40048
\(887\) 5131.41 0.194246 0.0971229 0.995272i \(-0.469036\pi\)
0.0971229 + 0.995272i \(0.469036\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −13073.5 −0.492386
\(891\) 0 0
\(892\) −116316. −4.36610
\(893\) −3081.49 −0.115474
\(894\) 0 0
\(895\) 21793.3 0.813933
\(896\) 0 0
\(897\) 0 0
\(898\) −10836.2 −0.402682
\(899\) −30500.3 −1.13153
\(900\) 0 0
\(901\) −32286.2 −1.19380
\(902\) 27667.7 1.02132
\(903\) 0 0
\(904\) 27870.0 1.02538
\(905\) −1889.61 −0.0694065
\(906\) 0 0
\(907\) −19934.6 −0.729787 −0.364893 0.931049i \(-0.618895\pi\)
−0.364893 + 0.931049i \(0.618895\pi\)
\(908\) −84248.8 −3.07918
\(909\) 0 0
\(910\) 0 0
\(911\) −48387.4 −1.75976 −0.879882 0.475193i \(-0.842378\pi\)
−0.879882 + 0.475193i \(0.842378\pi\)
\(912\) 0 0
\(913\) 17026.0 0.617172
\(914\) 30844.7 1.11625
\(915\) 0 0
\(916\) −140483. −5.06735
\(917\) 0 0
\(918\) 0 0
\(919\) −14431.7 −0.518019 −0.259009 0.965875i \(-0.583396\pi\)
−0.259009 + 0.965875i \(0.583396\pi\)
\(920\) 41.5224 0.00148799
\(921\) 0 0
\(922\) 103688. 3.70366
\(923\) 21456.8 0.765177
\(924\) 0 0
\(925\) −4447.69 −0.158096
\(926\) −43549.1 −1.54548
\(927\) 0 0
\(928\) −152443. −5.39244
\(929\) −5549.82 −0.196000 −0.0979998 0.995186i \(-0.531244\pi\)
−0.0979998 + 0.995186i \(0.531244\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −39956.7 −1.40432
\(933\) 0 0
\(934\) −2127.24 −0.0745239
\(935\) −15782.1 −0.552010
\(936\) 0 0
\(937\) 26231.9 0.914576 0.457288 0.889319i \(-0.348821\pi\)
0.457288 + 0.889319i \(0.348821\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −29241.8 −1.01464
\(941\) −2836.80 −0.0982753 −0.0491376 0.998792i \(-0.515647\pi\)
−0.0491376 + 0.998792i \(0.515647\pi\)
\(942\) 0 0
\(943\) −15.1298 −0.000522474 0
\(944\) −62607.9 −2.15860
\(945\) 0 0
\(946\) −1572.90 −0.0540586
\(947\) 40272.9 1.38193 0.690967 0.722886i \(-0.257185\pi\)
0.690967 + 0.722886i \(0.257185\pi\)
\(948\) 0 0
\(949\) 44084.1 1.50793
\(950\) 1631.64 0.0557236
\(951\) 0 0
\(952\) 0 0
\(953\) −17770.1 −0.604019 −0.302010 0.953305i \(-0.597657\pi\)
−0.302010 + 0.953305i \(0.597657\pi\)
\(954\) 0 0
\(955\) 12129.7 0.411004
\(956\) −79005.0 −2.67281
\(957\) 0 0
\(958\) −9349.97 −0.315328
\(959\) 0 0
\(960\) 0 0
\(961\) −4254.35 −0.142807
\(962\) −67632.0 −2.26668
\(963\) 0 0
\(964\) 8147.07 0.272199
\(965\) −3114.61 −0.103899
\(966\) 0 0
\(967\) −3530.14 −0.117396 −0.0586978 0.998276i \(-0.518695\pi\)
−0.0586978 + 0.998276i \(0.518695\pi\)
\(968\) −11105.2 −0.368734
\(969\) 0 0
\(970\) 23148.0 0.766226
\(971\) −17650.7 −0.583356 −0.291678 0.956517i \(-0.594214\pi\)
−0.291678 + 0.956517i \(0.594214\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 86693.8 2.85200
\(975\) 0 0
\(976\) 202586. 6.64407
\(977\) 14477.6 0.474085 0.237042 0.971499i \(-0.423822\pi\)
0.237042 + 0.971499i \(0.423822\pi\)
\(978\) 0 0
\(979\) 16357.8 0.534012
\(980\) 0 0
\(981\) 0 0
\(982\) 14988.7 0.487075
\(983\) 8764.09 0.284365 0.142183 0.989840i \(-0.454588\pi\)
0.142183 + 0.989840i \(0.454588\pi\)
\(984\) 0 0
\(985\) −14211.4 −0.459710
\(986\) −96296.9 −3.11026
\(987\) 0 0
\(988\) 18292.0 0.589015
\(989\) 0.860124 2.76546e−5 0
\(990\) 0 0
\(991\) 33624.1 1.07781 0.538903 0.842368i \(-0.318839\pi\)
0.538903 + 0.842368i \(0.318839\pi\)
\(992\) 127634. 4.08507
\(993\) 0 0
\(994\) 0 0
\(995\) −4336.82 −0.138177
\(996\) 0 0
\(997\) 16631.3 0.528302 0.264151 0.964481i \(-0.414908\pi\)
0.264151 + 0.964481i \(0.414908\pi\)
\(998\) 23701.6 0.751764
\(999\) 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.1.6 6
3.2 odd 2 245.4.a.p.1.1 yes 6
7.6 odd 2 2205.4.a.bz.1.6 6
15.14 odd 2 1225.4.a.bi.1.6 6
21.2 odd 6 245.4.e.p.116.6 12
21.5 even 6 245.4.e.q.116.6 12
21.11 odd 6 245.4.e.p.226.6 12
21.17 even 6 245.4.e.q.226.6 12
21.20 even 2 245.4.a.o.1.1 6
105.104 even 2 1225.4.a.bj.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.1 6 21.20 even 2
245.4.a.p.1.1 yes 6 3.2 odd 2
245.4.e.p.116.6 12 21.2 odd 6
245.4.e.p.226.6 12 21.11 odd 6
245.4.e.q.116.6 12 21.5 even 6
245.4.e.q.226.6 12 21.17 even 6
1225.4.a.bi.1.6 6 15.14 odd 2
1225.4.a.bj.1.6 6 105.104 even 2
2205.4.a.bz.1.6 6 7.6 odd 2
2205.4.a.ca.1.6 6 1.1 even 1 trivial