Properties

Label 1305.4.a.b.1.1
Level $1305$
Weight $4$
Character 1305.1
Self dual yes
Analytic conductor $76.997$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1305,4,Mod(1,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1305.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1305.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(76.9974925575\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 145)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1305.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -7.00000 q^{4} +5.00000 q^{5} -14.0000 q^{7} +15.0000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} -7.00000 q^{4} +5.00000 q^{5} -14.0000 q^{7} +15.0000 q^{8} -5.00000 q^{10} -62.0000 q^{11} +42.0000 q^{13} +14.0000 q^{14} +41.0000 q^{16} +114.000 q^{17} -70.0000 q^{19} -35.0000 q^{20} +62.0000 q^{22} -62.0000 q^{23} +25.0000 q^{25} -42.0000 q^{26} +98.0000 q^{28} +29.0000 q^{29} +142.000 q^{31} -161.000 q^{32} -114.000 q^{34} -70.0000 q^{35} +146.000 q^{37} +70.0000 q^{38} +75.0000 q^{40} -162.000 q^{41} +352.000 q^{43} +434.000 q^{44} +62.0000 q^{46} +444.000 q^{47} -147.000 q^{49} -25.0000 q^{50} -294.000 q^{52} +238.000 q^{53} -310.000 q^{55} -210.000 q^{56} -29.0000 q^{58} -840.000 q^{59} +2.00000 q^{61} -142.000 q^{62} -167.000 q^{64} +210.000 q^{65} -154.000 q^{67} -798.000 q^{68} +70.0000 q^{70} -892.000 q^{71} -38.0000 q^{73} -146.000 q^{74} +490.000 q^{76} +868.000 q^{77} +1050.00 q^{79} +205.000 q^{80} +162.000 q^{82} +778.000 q^{83} +570.000 q^{85} -352.000 q^{86} -930.000 q^{88} -1410.00 q^{89} -588.000 q^{91} +434.000 q^{92} -444.000 q^{94} -350.000 q^{95} +466.000 q^{97} +147.000 q^{98} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.353553 −0.176777 0.984251i \(-0.556567\pi\)
−0.176777 + 0.984251i \(0.556567\pi\)
\(3\) 0 0
\(4\) −7.00000 −0.875000
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −14.0000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 15.0000 0.662913
\(9\) 0 0
\(10\) −5.00000 −0.158114
\(11\) −62.0000 −1.69943 −0.849714 0.527244i \(-0.823225\pi\)
−0.849714 + 0.527244i \(0.823225\pi\)
\(12\) 0 0
\(13\) 42.0000 0.896054 0.448027 0.894020i \(-0.352127\pi\)
0.448027 + 0.894020i \(0.352127\pi\)
\(14\) 14.0000 0.267261
\(15\) 0 0
\(16\) 41.0000 0.640625
\(17\) 114.000 1.62642 0.813208 0.581974i \(-0.197719\pi\)
0.813208 + 0.581974i \(0.197719\pi\)
\(18\) 0 0
\(19\) −70.0000 −0.845216 −0.422608 0.906313i \(-0.638885\pi\)
−0.422608 + 0.906313i \(0.638885\pi\)
\(20\) −35.0000 −0.391312
\(21\) 0 0
\(22\) 62.0000 0.600838
\(23\) −62.0000 −0.562082 −0.281041 0.959696i \(-0.590680\pi\)
−0.281041 + 0.959696i \(0.590680\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −42.0000 −0.316803
\(27\) 0 0
\(28\) 98.0000 0.661438
\(29\) 29.0000 0.185695
\(30\) 0 0
\(31\) 142.000 0.822708 0.411354 0.911476i \(-0.365056\pi\)
0.411354 + 0.911476i \(0.365056\pi\)
\(32\) −161.000 −0.889408
\(33\) 0 0
\(34\) −114.000 −0.575025
\(35\) −70.0000 −0.338062
\(36\) 0 0
\(37\) 146.000 0.648710 0.324355 0.945936i \(-0.394853\pi\)
0.324355 + 0.945936i \(0.394853\pi\)
\(38\) 70.0000 0.298829
\(39\) 0 0
\(40\) 75.0000 0.296464
\(41\) −162.000 −0.617077 −0.308538 0.951212i \(-0.599840\pi\)
−0.308538 + 0.951212i \(0.599840\pi\)
\(42\) 0 0
\(43\) 352.000 1.24836 0.624180 0.781280i \(-0.285433\pi\)
0.624180 + 0.781280i \(0.285433\pi\)
\(44\) 434.000 1.48700
\(45\) 0 0
\(46\) 62.0000 0.198726
\(47\) 444.000 1.37796 0.688979 0.724781i \(-0.258059\pi\)
0.688979 + 0.724781i \(0.258059\pi\)
\(48\) 0 0
\(49\) −147.000 −0.428571
\(50\) −25.0000 −0.0707107
\(51\) 0 0
\(52\) −294.000 −0.784047
\(53\) 238.000 0.616827 0.308413 0.951252i \(-0.400202\pi\)
0.308413 + 0.951252i \(0.400202\pi\)
\(54\) 0 0
\(55\) −310.000 −0.760007
\(56\) −210.000 −0.501115
\(57\) 0 0
\(58\) −29.0000 −0.0656532
\(59\) −840.000 −1.85354 −0.926769 0.375633i \(-0.877425\pi\)
−0.926769 + 0.375633i \(0.877425\pi\)
\(60\) 0 0
\(61\) 2.00000 0.00419793 0.00209897 0.999998i \(-0.499332\pi\)
0.00209897 + 0.999998i \(0.499332\pi\)
\(62\) −142.000 −0.290871
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 210.000 0.400728
\(66\) 0 0
\(67\) −154.000 −0.280807 −0.140404 0.990094i \(-0.544840\pi\)
−0.140404 + 0.990094i \(0.544840\pi\)
\(68\) −798.000 −1.42311
\(69\) 0 0
\(70\) 70.0000 0.119523
\(71\) −892.000 −1.49100 −0.745499 0.666506i \(-0.767789\pi\)
−0.745499 + 0.666506i \(0.767789\pi\)
\(72\) 0 0
\(73\) −38.0000 −0.0609255 −0.0304628 0.999536i \(-0.509698\pi\)
−0.0304628 + 0.999536i \(0.509698\pi\)
\(74\) −146.000 −0.229353
\(75\) 0 0
\(76\) 490.000 0.739564
\(77\) 868.000 1.28465
\(78\) 0 0
\(79\) 1050.00 1.49537 0.747685 0.664054i \(-0.231165\pi\)
0.747685 + 0.664054i \(0.231165\pi\)
\(80\) 205.000 0.286496
\(81\) 0 0
\(82\) 162.000 0.218170
\(83\) 778.000 1.02887 0.514437 0.857528i \(-0.328001\pi\)
0.514437 + 0.857528i \(0.328001\pi\)
\(84\) 0 0
\(85\) 570.000 0.727355
\(86\) −352.000 −0.441362
\(87\) 0 0
\(88\) −930.000 −1.12657
\(89\) −1410.00 −1.67932 −0.839661 0.543110i \(-0.817246\pi\)
−0.839661 + 0.543110i \(0.817246\pi\)
\(90\) 0 0
\(91\) −588.000 −0.677353
\(92\) 434.000 0.491822
\(93\) 0 0
\(94\) −444.000 −0.487182
\(95\) −350.000 −0.377992
\(96\) 0 0
\(97\) 466.000 0.487785 0.243892 0.969802i \(-0.421576\pi\)
0.243892 + 0.969802i \(0.421576\pi\)
\(98\) 147.000 0.151523
\(99\) 0 0
\(100\) −175.000 −0.175000
\(101\) 878.000 0.864993 0.432496 0.901636i \(-0.357633\pi\)
0.432496 + 0.901636i \(0.357633\pi\)
\(102\) 0 0
\(103\) 1062.00 1.01594 0.507971 0.861374i \(-0.330396\pi\)
0.507971 + 0.861374i \(0.330396\pi\)
\(104\) 630.000 0.594006
\(105\) 0 0
\(106\) −238.000 −0.218081
\(107\) −1826.00 −1.64978 −0.824888 0.565296i \(-0.808762\pi\)
−0.824888 + 0.565296i \(0.808762\pi\)
\(108\) 0 0
\(109\) −1270.00 −1.11600 −0.558000 0.829841i \(-0.688431\pi\)
−0.558000 + 0.829841i \(0.688431\pi\)
\(110\) 310.000 0.268703
\(111\) 0 0
\(112\) −574.000 −0.484267
\(113\) −82.0000 −0.0682647 −0.0341324 0.999417i \(-0.510867\pi\)
−0.0341324 + 0.999417i \(0.510867\pi\)
\(114\) 0 0
\(115\) −310.000 −0.251371
\(116\) −203.000 −0.162483
\(117\) 0 0
\(118\) 840.000 0.655324
\(119\) −1596.00 −1.22945
\(120\) 0 0
\(121\) 2513.00 1.88805
\(122\) −2.00000 −0.00148419
\(123\) 0 0
\(124\) −994.000 −0.719870
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 296.000 0.206817 0.103408 0.994639i \(-0.467025\pi\)
0.103408 + 0.994639i \(0.467025\pi\)
\(128\) 1455.00 1.00473
\(129\) 0 0
\(130\) −210.000 −0.141679
\(131\) 198.000 0.132056 0.0660280 0.997818i \(-0.478967\pi\)
0.0660280 + 0.997818i \(0.478967\pi\)
\(132\) 0 0
\(133\) 980.000 0.638923
\(134\) 154.000 0.0992804
\(135\) 0 0
\(136\) 1710.00 1.07817
\(137\) −166.000 −0.103521 −0.0517604 0.998660i \(-0.516483\pi\)
−0.0517604 + 0.998660i \(0.516483\pi\)
\(138\) 0 0
\(139\) −80.0000 −0.0488166 −0.0244083 0.999702i \(-0.507770\pi\)
−0.0244083 + 0.999702i \(0.507770\pi\)
\(140\) 490.000 0.295804
\(141\) 0 0
\(142\) 892.000 0.527148
\(143\) −2604.00 −1.52278
\(144\) 0 0
\(145\) 145.000 0.0830455
\(146\) 38.0000 0.0215404
\(147\) 0 0
\(148\) −1022.00 −0.567621
\(149\) −3150.00 −1.73193 −0.865967 0.500102i \(-0.833296\pi\)
−0.865967 + 0.500102i \(0.833296\pi\)
\(150\) 0 0
\(151\) −1868.00 −1.00673 −0.503363 0.864075i \(-0.667904\pi\)
−0.503363 + 0.864075i \(0.667904\pi\)
\(152\) −1050.00 −0.560304
\(153\) 0 0
\(154\) −868.000 −0.454191
\(155\) 710.000 0.367926
\(156\) 0 0
\(157\) −354.000 −0.179951 −0.0899754 0.995944i \(-0.528679\pi\)
−0.0899754 + 0.995944i \(0.528679\pi\)
\(158\) −1050.00 −0.528693
\(159\) 0 0
\(160\) −805.000 −0.397755
\(161\) 868.000 0.424894
\(162\) 0 0
\(163\) −2268.00 −1.08984 −0.544919 0.838489i \(-0.683439\pi\)
−0.544919 + 0.838489i \(0.683439\pi\)
\(164\) 1134.00 0.539942
\(165\) 0 0
\(166\) −778.000 −0.363762
\(167\) −2046.00 −0.948049 −0.474025 0.880512i \(-0.657199\pi\)
−0.474025 + 0.880512i \(0.657199\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) −570.000 −0.257159
\(171\) 0 0
\(172\) −2464.00 −1.09232
\(173\) 2118.00 0.930801 0.465400 0.885100i \(-0.345910\pi\)
0.465400 + 0.885100i \(0.345910\pi\)
\(174\) 0 0
\(175\) −350.000 −0.151186
\(176\) −2542.00 −1.08870
\(177\) 0 0
\(178\) 1410.00 0.593730
\(179\) −1260.00 −0.526127 −0.263064 0.964778i \(-0.584733\pi\)
−0.263064 + 0.964778i \(0.584733\pi\)
\(180\) 0 0
\(181\) 1342.00 0.551105 0.275553 0.961286i \(-0.411139\pi\)
0.275553 + 0.961286i \(0.411139\pi\)
\(182\) 588.000 0.239481
\(183\) 0 0
\(184\) −930.000 −0.372611
\(185\) 730.000 0.290112
\(186\) 0 0
\(187\) −7068.00 −2.76398
\(188\) −3108.00 −1.20571
\(189\) 0 0
\(190\) 350.000 0.133640
\(191\) −1622.00 −0.614470 −0.307235 0.951634i \(-0.599404\pi\)
−0.307235 + 0.951634i \(0.599404\pi\)
\(192\) 0 0
\(193\) −4058.00 −1.51348 −0.756739 0.653717i \(-0.773209\pi\)
−0.756739 + 0.653717i \(0.773209\pi\)
\(194\) −466.000 −0.172458
\(195\) 0 0
\(196\) 1029.00 0.375000
\(197\) −266.000 −0.0962016 −0.0481008 0.998842i \(-0.515317\pi\)
−0.0481008 + 0.998842i \(0.515317\pi\)
\(198\) 0 0
\(199\) −2220.00 −0.790812 −0.395406 0.918506i \(-0.629396\pi\)
−0.395406 + 0.918506i \(0.629396\pi\)
\(200\) 375.000 0.132583
\(201\) 0 0
\(202\) −878.000 −0.305821
\(203\) −406.000 −0.140372
\(204\) 0 0
\(205\) −810.000 −0.275965
\(206\) −1062.00 −0.359190
\(207\) 0 0
\(208\) 1722.00 0.574035
\(209\) 4340.00 1.43638
\(210\) 0 0
\(211\) −3478.00 −1.13476 −0.567382 0.823454i \(-0.692044\pi\)
−0.567382 + 0.823454i \(0.692044\pi\)
\(212\) −1666.00 −0.539723
\(213\) 0 0
\(214\) 1826.00 0.583284
\(215\) 1760.00 0.558284
\(216\) 0 0
\(217\) −1988.00 −0.621909
\(218\) 1270.00 0.394565
\(219\) 0 0
\(220\) 2170.00 0.665006
\(221\) 4788.00 1.45736
\(222\) 0 0
\(223\) 6622.00 1.98853 0.994264 0.106950i \(-0.0341085\pi\)
0.994264 + 0.106950i \(0.0341085\pi\)
\(224\) 2254.00 0.672329
\(225\) 0 0
\(226\) 82.0000 0.0241352
\(227\) −3666.00 −1.07190 −0.535949 0.844250i \(-0.680046\pi\)
−0.535949 + 0.844250i \(0.680046\pi\)
\(228\) 0 0
\(229\) −350.000 −0.100998 −0.0504992 0.998724i \(-0.516081\pi\)
−0.0504992 + 0.998724i \(0.516081\pi\)
\(230\) 310.000 0.0888730
\(231\) 0 0
\(232\) 435.000 0.123100
\(233\) −2.00000 −0.000562336 0 −0.000281168 1.00000i \(-0.500089\pi\)
−0.000281168 1.00000i \(0.500089\pi\)
\(234\) 0 0
\(235\) 2220.00 0.616242
\(236\) 5880.00 1.62184
\(237\) 0 0
\(238\) 1596.00 0.434678
\(239\) −700.000 −0.189453 −0.0947264 0.995503i \(-0.530198\pi\)
−0.0947264 + 0.995503i \(0.530198\pi\)
\(240\) 0 0
\(241\) −1018.00 −0.272096 −0.136048 0.990702i \(-0.543440\pi\)
−0.136048 + 0.990702i \(0.543440\pi\)
\(242\) −2513.00 −0.667528
\(243\) 0 0
\(244\) −14.0000 −0.00367319
\(245\) −735.000 −0.191663
\(246\) 0 0
\(247\) −2940.00 −0.757359
\(248\) 2130.00 0.545384
\(249\) 0 0
\(250\) −125.000 −0.0316228
\(251\) −7102.00 −1.78595 −0.892977 0.450103i \(-0.851387\pi\)
−0.892977 + 0.450103i \(0.851387\pi\)
\(252\) 0 0
\(253\) 3844.00 0.955218
\(254\) −296.000 −0.0731208
\(255\) 0 0
\(256\) −119.000 −0.0290527
\(257\) −5906.00 −1.43349 −0.716743 0.697337i \(-0.754368\pi\)
−0.716743 + 0.697337i \(0.754368\pi\)
\(258\) 0 0
\(259\) −2044.00 −0.490378
\(260\) −1470.00 −0.350637
\(261\) 0 0
\(262\) −198.000 −0.0466889
\(263\) −6252.00 −1.46584 −0.732918 0.680317i \(-0.761842\pi\)
−0.732918 + 0.680317i \(0.761842\pi\)
\(264\) 0 0
\(265\) 1190.00 0.275853
\(266\) −980.000 −0.225893
\(267\) 0 0
\(268\) 1078.00 0.245706
\(269\) 7230.00 1.63874 0.819370 0.573266i \(-0.194324\pi\)
0.819370 + 0.573266i \(0.194324\pi\)
\(270\) 0 0
\(271\) −7838.00 −1.75692 −0.878459 0.477818i \(-0.841428\pi\)
−0.878459 + 0.477818i \(0.841428\pi\)
\(272\) 4674.00 1.04192
\(273\) 0 0
\(274\) 166.000 0.0366001
\(275\) −1550.00 −0.339886
\(276\) 0 0
\(277\) 5386.00 1.16828 0.584140 0.811653i \(-0.301432\pi\)
0.584140 + 0.811653i \(0.301432\pi\)
\(278\) 80.0000 0.0172593
\(279\) 0 0
\(280\) −1050.00 −0.224105
\(281\) −6502.00 −1.38034 −0.690172 0.723645i \(-0.742465\pi\)
−0.690172 + 0.723645i \(0.742465\pi\)
\(282\) 0 0
\(283\) −6478.00 −1.36070 −0.680348 0.732889i \(-0.738171\pi\)
−0.680348 + 0.732889i \(0.738171\pi\)
\(284\) 6244.00 1.30462
\(285\) 0 0
\(286\) 2604.00 0.538384
\(287\) 2268.00 0.466466
\(288\) 0 0
\(289\) 8083.00 1.64523
\(290\) −145.000 −0.0293610
\(291\) 0 0
\(292\) 266.000 0.0533098
\(293\) 6858.00 1.36740 0.683701 0.729762i \(-0.260369\pi\)
0.683701 + 0.729762i \(0.260369\pi\)
\(294\) 0 0
\(295\) −4200.00 −0.828927
\(296\) 2190.00 0.430038
\(297\) 0 0
\(298\) 3150.00 0.612331
\(299\) −2604.00 −0.503656
\(300\) 0 0
\(301\) −4928.00 −0.943672
\(302\) 1868.00 0.355932
\(303\) 0 0
\(304\) −2870.00 −0.541466
\(305\) 10.0000 0.00187737
\(306\) 0 0
\(307\) −3684.00 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) −6076.00 −1.12407
\(309\) 0 0
\(310\) −710.000 −0.130082
\(311\) 138.000 0.0251616 0.0125808 0.999921i \(-0.495995\pi\)
0.0125808 + 0.999921i \(0.495995\pi\)
\(312\) 0 0
\(313\) 8802.00 1.58952 0.794758 0.606927i \(-0.207598\pi\)
0.794758 + 0.606927i \(0.207598\pi\)
\(314\) 354.000 0.0636222
\(315\) 0 0
\(316\) −7350.00 −1.30845
\(317\) −5546.00 −0.982632 −0.491316 0.870981i \(-0.663484\pi\)
−0.491316 + 0.870981i \(0.663484\pi\)
\(318\) 0 0
\(319\) −1798.00 −0.315576
\(320\) −835.000 −0.145868
\(321\) 0 0
\(322\) −868.000 −0.150223
\(323\) −7980.00 −1.37467
\(324\) 0 0
\(325\) 1050.00 0.179211
\(326\) 2268.00 0.385316
\(327\) 0 0
\(328\) −2430.00 −0.409068
\(329\) −6216.00 −1.04164
\(330\) 0 0
\(331\) 3082.00 0.511789 0.255894 0.966705i \(-0.417630\pi\)
0.255894 + 0.966705i \(0.417630\pi\)
\(332\) −5446.00 −0.900265
\(333\) 0 0
\(334\) 2046.00 0.335186
\(335\) −770.000 −0.125581
\(336\) 0 0
\(337\) −6414.00 −1.03677 −0.518387 0.855146i \(-0.673467\pi\)
−0.518387 + 0.855146i \(0.673467\pi\)
\(338\) 433.000 0.0696808
\(339\) 0 0
\(340\) −3990.00 −0.636436
\(341\) −8804.00 −1.39813
\(342\) 0 0
\(343\) 6860.00 1.07990
\(344\) 5280.00 0.827554
\(345\) 0 0
\(346\) −2118.00 −0.329088
\(347\) −1486.00 −0.229892 −0.114946 0.993372i \(-0.536670\pi\)
−0.114946 + 0.993372i \(0.536670\pi\)
\(348\) 0 0
\(349\) 1370.00 0.210127 0.105064 0.994466i \(-0.466495\pi\)
0.105064 + 0.994466i \(0.466495\pi\)
\(350\) 350.000 0.0534522
\(351\) 0 0
\(352\) 9982.00 1.51148
\(353\) −1122.00 −0.169173 −0.0845865 0.996416i \(-0.526957\pi\)
−0.0845865 + 0.996416i \(0.526957\pi\)
\(354\) 0 0
\(355\) −4460.00 −0.666795
\(356\) 9870.00 1.46941
\(357\) 0 0
\(358\) 1260.00 0.186014
\(359\) 4230.00 0.621869 0.310934 0.950431i \(-0.399358\pi\)
0.310934 + 0.950431i \(0.399358\pi\)
\(360\) 0 0
\(361\) −1959.00 −0.285610
\(362\) −1342.00 −0.194845
\(363\) 0 0
\(364\) 4116.00 0.592684
\(365\) −190.000 −0.0272467
\(366\) 0 0
\(367\) 4016.00 0.571208 0.285604 0.958348i \(-0.407806\pi\)
0.285604 + 0.958348i \(0.407806\pi\)
\(368\) −2542.00 −0.360084
\(369\) 0 0
\(370\) −730.000 −0.102570
\(371\) −3332.00 −0.466277
\(372\) 0 0
\(373\) 3802.00 0.527775 0.263888 0.964553i \(-0.414995\pi\)
0.263888 + 0.964553i \(0.414995\pi\)
\(374\) 7068.00 0.977213
\(375\) 0 0
\(376\) 6660.00 0.913466
\(377\) 1218.00 0.166393
\(378\) 0 0
\(379\) −4430.00 −0.600406 −0.300203 0.953875i \(-0.597054\pi\)
−0.300203 + 0.953875i \(0.597054\pi\)
\(380\) 2450.00 0.330743
\(381\) 0 0
\(382\) 1622.00 0.217248
\(383\) −8642.00 −1.15296 −0.576482 0.817110i \(-0.695575\pi\)
−0.576482 + 0.817110i \(0.695575\pi\)
\(384\) 0 0
\(385\) 4340.00 0.574511
\(386\) 4058.00 0.535095
\(387\) 0 0
\(388\) −3262.00 −0.426812
\(389\) −10.0000 −0.00130339 −0.000651697 1.00000i \(-0.500207\pi\)
−0.000651697 1.00000i \(0.500207\pi\)
\(390\) 0 0
\(391\) −7068.00 −0.914179
\(392\) −2205.00 −0.284105
\(393\) 0 0
\(394\) 266.000 0.0340124
\(395\) 5250.00 0.668750
\(396\) 0 0
\(397\) −7654.00 −0.967615 −0.483808 0.875174i \(-0.660747\pi\)
−0.483808 + 0.875174i \(0.660747\pi\)
\(398\) 2220.00 0.279594
\(399\) 0 0
\(400\) 1025.00 0.128125
\(401\) −8402.00 −1.04632 −0.523162 0.852233i \(-0.675248\pi\)
−0.523162 + 0.852233i \(0.675248\pi\)
\(402\) 0 0
\(403\) 5964.00 0.737191
\(404\) −6146.00 −0.756869
\(405\) 0 0
\(406\) 406.000 0.0496292
\(407\) −9052.00 −1.10243
\(408\) 0 0
\(409\) −790.000 −0.0955085 −0.0477543 0.998859i \(-0.515206\pi\)
−0.0477543 + 0.998859i \(0.515206\pi\)
\(410\) 810.000 0.0975684
\(411\) 0 0
\(412\) −7434.00 −0.888949
\(413\) 11760.0 1.40114
\(414\) 0 0
\(415\) 3890.00 0.460127
\(416\) −6762.00 −0.796958
\(417\) 0 0
\(418\) −4340.00 −0.507838
\(419\) 15220.0 1.77457 0.887286 0.461220i \(-0.152588\pi\)
0.887286 + 0.461220i \(0.152588\pi\)
\(420\) 0 0
\(421\) 4122.00 0.477183 0.238591 0.971120i \(-0.423314\pi\)
0.238591 + 0.971120i \(0.423314\pi\)
\(422\) 3478.00 0.401200
\(423\) 0 0
\(424\) 3570.00 0.408902
\(425\) 2850.00 0.325283
\(426\) 0 0
\(427\) −28.0000 −0.00317334
\(428\) 12782.0 1.44355
\(429\) 0 0
\(430\) −1760.00 −0.197383
\(431\) 12168.0 1.35989 0.679944 0.733264i \(-0.262004\pi\)
0.679944 + 0.733264i \(0.262004\pi\)
\(432\) 0 0
\(433\) 11822.0 1.31208 0.656038 0.754728i \(-0.272231\pi\)
0.656038 + 0.754728i \(0.272231\pi\)
\(434\) 1988.00 0.219878
\(435\) 0 0
\(436\) 8890.00 0.976500
\(437\) 4340.00 0.475081
\(438\) 0 0
\(439\) −6480.00 −0.704496 −0.352248 0.935907i \(-0.614583\pi\)
−0.352248 + 0.935907i \(0.614583\pi\)
\(440\) −4650.00 −0.503818
\(441\) 0 0
\(442\) −4788.00 −0.515253
\(443\) 5308.00 0.569279 0.284640 0.958635i \(-0.408126\pi\)
0.284640 + 0.958635i \(0.408126\pi\)
\(444\) 0 0
\(445\) −7050.00 −0.751016
\(446\) −6622.00 −0.703051
\(447\) 0 0
\(448\) 2338.00 0.246563
\(449\) −5210.00 −0.547606 −0.273803 0.961786i \(-0.588282\pi\)
−0.273803 + 0.961786i \(0.588282\pi\)
\(450\) 0 0
\(451\) 10044.0 1.04868
\(452\) 574.000 0.0597316
\(453\) 0 0
\(454\) 3666.00 0.378973
\(455\) −2940.00 −0.302922
\(456\) 0 0
\(457\) 5626.00 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(458\) 350.000 0.0357084
\(459\) 0 0
\(460\) 2170.00 0.219950
\(461\) 4278.00 0.432205 0.216102 0.976371i \(-0.430666\pi\)
0.216102 + 0.976371i \(0.430666\pi\)
\(462\) 0 0
\(463\) 9642.00 0.967822 0.483911 0.875117i \(-0.339216\pi\)
0.483911 + 0.875117i \(0.339216\pi\)
\(464\) 1189.00 0.118961
\(465\) 0 0
\(466\) 2.00000 0.000198816 0
\(467\) 2204.00 0.218392 0.109196 0.994020i \(-0.465172\pi\)
0.109196 + 0.994020i \(0.465172\pi\)
\(468\) 0 0
\(469\) 2156.00 0.212270
\(470\) −2220.00 −0.217874
\(471\) 0 0
\(472\) −12600.0 −1.22873
\(473\) −21824.0 −2.12150
\(474\) 0 0
\(475\) −1750.00 −0.169043
\(476\) 11172.0 1.07577
\(477\) 0 0
\(478\) 700.000 0.0669817
\(479\) −11870.0 −1.13226 −0.566132 0.824315i \(-0.691561\pi\)
−0.566132 + 0.824315i \(0.691561\pi\)
\(480\) 0 0
\(481\) 6132.00 0.581279
\(482\) 1018.00 0.0962005
\(483\) 0 0
\(484\) −17591.0 −1.65205
\(485\) 2330.00 0.218144
\(486\) 0 0
\(487\) 12626.0 1.17482 0.587411 0.809289i \(-0.300147\pi\)
0.587411 + 0.809289i \(0.300147\pi\)
\(488\) 30.0000 0.00278286
\(489\) 0 0
\(490\) 735.000 0.0677631
\(491\) −922.000 −0.0847439 −0.0423720 0.999102i \(-0.513491\pi\)
−0.0423720 + 0.999102i \(0.513491\pi\)
\(492\) 0 0
\(493\) 3306.00 0.302018
\(494\) 2940.00 0.267767
\(495\) 0 0
\(496\) 5822.00 0.527047
\(497\) 12488.0 1.12709
\(498\) 0 0
\(499\) 18060.0 1.62019 0.810097 0.586296i \(-0.199414\pi\)
0.810097 + 0.586296i \(0.199414\pi\)
\(500\) −875.000 −0.0782624
\(501\) 0 0
\(502\) 7102.00 0.631430
\(503\) −13272.0 −1.17648 −0.588240 0.808687i \(-0.700179\pi\)
−0.588240 + 0.808687i \(0.700179\pi\)
\(504\) 0 0
\(505\) 4390.00 0.386837
\(506\) −3844.00 −0.337721
\(507\) 0 0
\(508\) −2072.00 −0.180965
\(509\) −2410.00 −0.209865 −0.104933 0.994479i \(-0.533463\pi\)
−0.104933 + 0.994479i \(0.533463\pi\)
\(510\) 0 0
\(511\) 532.000 0.0460554
\(512\) −11521.0 −0.994455
\(513\) 0 0
\(514\) 5906.00 0.506814
\(515\) 5310.00 0.454343
\(516\) 0 0
\(517\) −27528.0 −2.34174
\(518\) 2044.00 0.173375
\(519\) 0 0
\(520\) 3150.00 0.265647
\(521\) 4018.00 0.337873 0.168936 0.985627i \(-0.445967\pi\)
0.168936 + 0.985627i \(0.445967\pi\)
\(522\) 0 0
\(523\) −3618.00 −0.302493 −0.151247 0.988496i \(-0.548329\pi\)
−0.151247 + 0.988496i \(0.548329\pi\)
\(524\) −1386.00 −0.115549
\(525\) 0 0
\(526\) 6252.00 0.518251
\(527\) 16188.0 1.33807
\(528\) 0 0
\(529\) −8323.00 −0.684063
\(530\) −1190.00 −0.0975289
\(531\) 0 0
\(532\) −6860.00 −0.559058
\(533\) −6804.00 −0.552934
\(534\) 0 0
\(535\) −9130.00 −0.737802
\(536\) −2310.00 −0.186151
\(537\) 0 0
\(538\) −7230.00 −0.579382
\(539\) 9114.00 0.728326
\(540\) 0 0
\(541\) 20522.0 1.63089 0.815443 0.578837i \(-0.196493\pi\)
0.815443 + 0.578837i \(0.196493\pi\)
\(542\) 7838.00 0.621164
\(543\) 0 0
\(544\) −18354.0 −1.44655
\(545\) −6350.00 −0.499090
\(546\) 0 0
\(547\) 20026.0 1.56536 0.782678 0.622427i \(-0.213853\pi\)
0.782678 + 0.622427i \(0.213853\pi\)
\(548\) 1162.00 0.0905806
\(549\) 0 0
\(550\) 1550.00 0.120168
\(551\) −2030.00 −0.156953
\(552\) 0 0
\(553\) −14700.0 −1.13039
\(554\) −5386.00 −0.413049
\(555\) 0 0
\(556\) 560.000 0.0427146
\(557\) −9186.00 −0.698785 −0.349393 0.936976i \(-0.613612\pi\)
−0.349393 + 0.936976i \(0.613612\pi\)
\(558\) 0 0
\(559\) 14784.0 1.11860
\(560\) −2870.00 −0.216571
\(561\) 0 0
\(562\) 6502.00 0.488025
\(563\) 17068.0 1.27767 0.638837 0.769342i \(-0.279416\pi\)
0.638837 + 0.769342i \(0.279416\pi\)
\(564\) 0 0
\(565\) −410.000 −0.0305289
\(566\) 6478.00 0.481079
\(567\) 0 0
\(568\) −13380.0 −0.988402
\(569\) 15270.0 1.12505 0.562523 0.826781i \(-0.309831\pi\)
0.562523 + 0.826781i \(0.309831\pi\)
\(570\) 0 0
\(571\) 15492.0 1.13541 0.567706 0.823232i \(-0.307831\pi\)
0.567706 + 0.823232i \(0.307831\pi\)
\(572\) 18228.0 1.33243
\(573\) 0 0
\(574\) −2268.00 −0.164921
\(575\) −1550.00 −0.112416
\(576\) 0 0
\(577\) −14554.0 −1.05007 −0.525035 0.851080i \(-0.675948\pi\)
−0.525035 + 0.851080i \(0.675948\pi\)
\(578\) −8083.00 −0.581676
\(579\) 0 0
\(580\) −1015.00 −0.0726648
\(581\) −10892.0 −0.777756
\(582\) 0 0
\(583\) −14756.0 −1.04825
\(584\) −570.000 −0.0403883
\(585\) 0 0
\(586\) −6858.00 −0.483449
\(587\) −13226.0 −0.929975 −0.464988 0.885317i \(-0.653941\pi\)
−0.464988 + 0.885317i \(0.653941\pi\)
\(588\) 0 0
\(589\) −9940.00 −0.695366
\(590\) 4200.00 0.293070
\(591\) 0 0
\(592\) 5986.00 0.415580
\(593\) −4642.00 −0.321457 −0.160729 0.986999i \(-0.551384\pi\)
−0.160729 + 0.986999i \(0.551384\pi\)
\(594\) 0 0
\(595\) −7980.00 −0.549829
\(596\) 22050.0 1.51544
\(597\) 0 0
\(598\) 2604.00 0.178069
\(599\) −16530.0 −1.12754 −0.563771 0.825931i \(-0.690650\pi\)
−0.563771 + 0.825931i \(0.690650\pi\)
\(600\) 0 0
\(601\) −23198.0 −1.57449 −0.787243 0.616643i \(-0.788492\pi\)
−0.787243 + 0.616643i \(0.788492\pi\)
\(602\) 4928.00 0.333638
\(603\) 0 0
\(604\) 13076.0 0.880886
\(605\) 12565.0 0.844363
\(606\) 0 0
\(607\) 7196.00 0.481181 0.240590 0.970627i \(-0.422659\pi\)
0.240590 + 0.970627i \(0.422659\pi\)
\(608\) 11270.0 0.751742
\(609\) 0 0
\(610\) −10.0000 −0.000663751 0
\(611\) 18648.0 1.23473
\(612\) 0 0
\(613\) 9282.00 0.611577 0.305788 0.952100i \(-0.401080\pi\)
0.305788 + 0.952100i \(0.401080\pi\)
\(614\) 3684.00 0.242140
\(615\) 0 0
\(616\) 13020.0 0.851608
\(617\) 7974.00 0.520294 0.260147 0.965569i \(-0.416229\pi\)
0.260147 + 0.965569i \(0.416229\pi\)
\(618\) 0 0
\(619\) −15890.0 −1.03178 −0.515891 0.856654i \(-0.672539\pi\)
−0.515891 + 0.856654i \(0.672539\pi\)
\(620\) −4970.00 −0.321935
\(621\) 0 0
\(622\) −138.000 −0.00889597
\(623\) 19740.0 1.26945
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −8802.00 −0.561979
\(627\) 0 0
\(628\) 2478.00 0.157457
\(629\) 16644.0 1.05507
\(630\) 0 0
\(631\) −19788.0 −1.24841 −0.624206 0.781260i \(-0.714577\pi\)
−0.624206 + 0.781260i \(0.714577\pi\)
\(632\) 15750.0 0.991300
\(633\) 0 0
\(634\) 5546.00 0.347413
\(635\) 1480.00 0.0924914
\(636\) 0 0
\(637\) −6174.00 −0.384023
\(638\) 1798.00 0.111573
\(639\) 0 0
\(640\) 7275.00 0.449328
\(641\) 9878.00 0.608670 0.304335 0.952565i \(-0.401566\pi\)
0.304335 + 0.952565i \(0.401566\pi\)
\(642\) 0 0
\(643\) −23918.0 −1.46693 −0.733463 0.679729i \(-0.762097\pi\)
−0.733463 + 0.679729i \(0.762097\pi\)
\(644\) −6076.00 −0.371783
\(645\) 0 0
\(646\) 7980.00 0.486020
\(647\) −28646.0 −1.74063 −0.870317 0.492492i \(-0.836086\pi\)
−0.870317 + 0.492492i \(0.836086\pi\)
\(648\) 0 0
\(649\) 52080.0 3.14995
\(650\) −1050.00 −0.0633606
\(651\) 0 0
\(652\) 15876.0 0.953608
\(653\) 23578.0 1.41298 0.706492 0.707721i \(-0.250277\pi\)
0.706492 + 0.707721i \(0.250277\pi\)
\(654\) 0 0
\(655\) 990.000 0.0590573
\(656\) −6642.00 −0.395315
\(657\) 0 0
\(658\) 6216.00 0.368275
\(659\) −22770.0 −1.34597 −0.672984 0.739657i \(-0.734988\pi\)
−0.672984 + 0.739657i \(0.734988\pi\)
\(660\) 0 0
\(661\) −1298.00 −0.0763787 −0.0381894 0.999271i \(-0.512159\pi\)
−0.0381894 + 0.999271i \(0.512159\pi\)
\(662\) −3082.00 −0.180945
\(663\) 0 0
\(664\) 11670.0 0.682054
\(665\) 4900.00 0.285735
\(666\) 0 0
\(667\) −1798.00 −0.104376
\(668\) 14322.0 0.829543
\(669\) 0 0
\(670\) 770.000 0.0443995
\(671\) −124.000 −0.00713408
\(672\) 0 0
\(673\) 1362.00 0.0780108 0.0390054 0.999239i \(-0.487581\pi\)
0.0390054 + 0.999239i \(0.487581\pi\)
\(674\) 6414.00 0.366555
\(675\) 0 0
\(676\) 3031.00 0.172451
\(677\) −12326.0 −0.699744 −0.349872 0.936798i \(-0.613775\pi\)
−0.349872 + 0.936798i \(0.613775\pi\)
\(678\) 0 0
\(679\) −6524.00 −0.368731
\(680\) 8550.00 0.482173
\(681\) 0 0
\(682\) 8804.00 0.494315
\(683\) 22538.0 1.26265 0.631327 0.775517i \(-0.282511\pi\)
0.631327 + 0.775517i \(0.282511\pi\)
\(684\) 0 0
\(685\) −830.000 −0.0462959
\(686\) −6860.00 −0.381802
\(687\) 0 0
\(688\) 14432.0 0.799731
\(689\) 9996.00 0.552710
\(690\) 0 0
\(691\) −21148.0 −1.16427 −0.582133 0.813094i \(-0.697782\pi\)
−0.582133 + 0.813094i \(0.697782\pi\)
\(692\) −14826.0 −0.814451
\(693\) 0 0
\(694\) 1486.00 0.0812792
\(695\) −400.000 −0.0218315
\(696\) 0 0
\(697\) −18468.0 −1.00362
\(698\) −1370.00 −0.0742912
\(699\) 0 0
\(700\) 2450.00 0.132288
\(701\) 24498.0 1.31994 0.659969 0.751293i \(-0.270569\pi\)
0.659969 + 0.751293i \(0.270569\pi\)
\(702\) 0 0
\(703\) −10220.0 −0.548300
\(704\) 10354.0 0.554305
\(705\) 0 0
\(706\) 1122.00 0.0598117
\(707\) −12292.0 −0.653873
\(708\) 0 0
\(709\) 17890.0 0.947635 0.473817 0.880623i \(-0.342876\pi\)
0.473817 + 0.880623i \(0.342876\pi\)
\(710\) 4460.00 0.235748
\(711\) 0 0
\(712\) −21150.0 −1.11324
\(713\) −8804.00 −0.462430
\(714\) 0 0
\(715\) −13020.0 −0.681008
\(716\) 8820.00 0.460362
\(717\) 0 0
\(718\) −4230.00 −0.219864
\(719\) 25140.0 1.30398 0.651992 0.758226i \(-0.273934\pi\)
0.651992 + 0.758226i \(0.273934\pi\)
\(720\) 0 0
\(721\) −14868.0 −0.767980
\(722\) 1959.00 0.100978
\(723\) 0 0
\(724\) −9394.00 −0.482217
\(725\) 725.000 0.0371391
\(726\) 0 0
\(727\) −9944.00 −0.507294 −0.253647 0.967297i \(-0.581630\pi\)
−0.253647 + 0.967297i \(0.581630\pi\)
\(728\) −8820.00 −0.449026
\(729\) 0 0
\(730\) 190.000 0.00963317
\(731\) 40128.0 2.03035
\(732\) 0 0
\(733\) −25318.0 −1.27577 −0.637887 0.770130i \(-0.720191\pi\)
−0.637887 + 0.770130i \(0.720191\pi\)
\(734\) −4016.00 −0.201953
\(735\) 0 0
\(736\) 9982.00 0.499920
\(737\) 9548.00 0.477212
\(738\) 0 0
\(739\) −7830.00 −0.389758 −0.194879 0.980827i \(-0.562431\pi\)
−0.194879 + 0.980827i \(0.562431\pi\)
\(740\) −5110.00 −0.253848
\(741\) 0 0
\(742\) 3332.00 0.164854
\(743\) 30008.0 1.48168 0.740839 0.671683i \(-0.234428\pi\)
0.740839 + 0.671683i \(0.234428\pi\)
\(744\) 0 0
\(745\) −15750.0 −0.774544
\(746\) −3802.00 −0.186597
\(747\) 0 0
\(748\) 49476.0 2.41848
\(749\) 25564.0 1.24711
\(750\) 0 0
\(751\) 15562.0 0.756146 0.378073 0.925776i \(-0.376587\pi\)
0.378073 + 0.925776i \(0.376587\pi\)
\(752\) 18204.0 0.882755
\(753\) 0 0
\(754\) −1218.00 −0.0588288
\(755\) −9340.00 −0.450222
\(756\) 0 0
\(757\) −6914.00 −0.331960 −0.165980 0.986129i \(-0.553079\pi\)
−0.165980 + 0.986129i \(0.553079\pi\)
\(758\) 4430.00 0.212276
\(759\) 0 0
\(760\) −5250.00 −0.250576
\(761\) 13018.0 0.620108 0.310054 0.950719i \(-0.399653\pi\)
0.310054 + 0.950719i \(0.399653\pi\)
\(762\) 0 0
\(763\) 17780.0 0.843616
\(764\) 11354.0 0.537661
\(765\) 0 0
\(766\) 8642.00 0.407635
\(767\) −35280.0 −1.66087
\(768\) 0 0
\(769\) 18450.0 0.865181 0.432590 0.901591i \(-0.357600\pi\)
0.432590 + 0.901591i \(0.357600\pi\)
\(770\) −4340.00 −0.203120
\(771\) 0 0
\(772\) 28406.0 1.32429
\(773\) 1838.00 0.0855217 0.0427608 0.999085i \(-0.486385\pi\)
0.0427608 + 0.999085i \(0.486385\pi\)
\(774\) 0 0
\(775\) 3550.00 0.164542
\(776\) 6990.00 0.323359
\(777\) 0 0
\(778\) 10.0000 0.000460819 0
\(779\) 11340.0 0.521563
\(780\) 0 0
\(781\) 55304.0 2.53384
\(782\) 7068.00 0.323211
\(783\) 0 0
\(784\) −6027.00 −0.274554
\(785\) −1770.00 −0.0804764
\(786\) 0 0
\(787\) −5274.00 −0.238879 −0.119440 0.992841i \(-0.538110\pi\)
−0.119440 + 0.992841i \(0.538110\pi\)
\(788\) 1862.00 0.0841764
\(789\) 0 0
\(790\) −5250.00 −0.236439
\(791\) 1148.00 0.0516033
\(792\) 0 0
\(793\) 84.0000 0.00376157
\(794\) 7654.00 0.342104
\(795\) 0 0
\(796\) 15540.0 0.691961
\(797\) −21926.0 −0.974478 −0.487239 0.873269i \(-0.661996\pi\)
−0.487239 + 0.873269i \(0.661996\pi\)
\(798\) 0 0
\(799\) 50616.0 2.24113
\(800\) −4025.00 −0.177882
\(801\) 0 0
\(802\) 8402.00 0.369931
\(803\) 2356.00 0.103539
\(804\) 0 0
\(805\) 4340.00 0.190019
\(806\) −5964.00 −0.260636
\(807\) 0 0
\(808\) 13170.0 0.573415
\(809\) −35010.0 −1.52149 −0.760745 0.649050i \(-0.775166\pi\)
−0.760745 + 0.649050i \(0.775166\pi\)
\(810\) 0 0
\(811\) −2888.00 −0.125045 −0.0625224 0.998044i \(-0.519914\pi\)
−0.0625224 + 0.998044i \(0.519914\pi\)
\(812\) 2842.00 0.122826
\(813\) 0 0
\(814\) 9052.00 0.389770
\(815\) −11340.0 −0.487390
\(816\) 0 0
\(817\) −24640.0 −1.05513
\(818\) 790.000 0.0337674
\(819\) 0 0
\(820\) 5670.00 0.241469
\(821\) −3542.00 −0.150568 −0.0752842 0.997162i \(-0.523986\pi\)
−0.0752842 + 0.997162i \(0.523986\pi\)
\(822\) 0 0
\(823\) −11468.0 −0.485722 −0.242861 0.970061i \(-0.578086\pi\)
−0.242861 + 0.970061i \(0.578086\pi\)
\(824\) 15930.0 0.673480
\(825\) 0 0
\(826\) −11760.0 −0.495379
\(827\) −16616.0 −0.698664 −0.349332 0.936999i \(-0.613591\pi\)
−0.349332 + 0.936999i \(0.613591\pi\)
\(828\) 0 0
\(829\) 33970.0 1.42319 0.711596 0.702588i \(-0.247972\pi\)
0.711596 + 0.702588i \(0.247972\pi\)
\(830\) −3890.00 −0.162679
\(831\) 0 0
\(832\) −7014.00 −0.292268
\(833\) −16758.0 −0.697035
\(834\) 0 0
\(835\) −10230.0 −0.423981
\(836\) −30380.0 −1.25684
\(837\) 0 0
\(838\) −15220.0 −0.627406
\(839\) 43410.0 1.78627 0.893134 0.449790i \(-0.148501\pi\)
0.893134 + 0.449790i \(0.148501\pi\)
\(840\) 0 0
\(841\) 841.000 0.0344828
\(842\) −4122.00 −0.168710
\(843\) 0 0
\(844\) 24346.0 0.992919
\(845\) −2165.00 −0.0881400
\(846\) 0 0
\(847\) −35182.0 −1.42723
\(848\) 9758.00 0.395155
\(849\) 0 0
\(850\) −2850.00 −0.115005
\(851\) −9052.00 −0.364628
\(852\) 0 0
\(853\) 82.0000 0.00329147 0.00164574 0.999999i \(-0.499476\pi\)
0.00164574 + 0.999999i \(0.499476\pi\)
\(854\) 28.0000 0.00112194
\(855\) 0 0
\(856\) −27390.0 −1.09366
\(857\) −29306.0 −1.16811 −0.584057 0.811713i \(-0.698536\pi\)
−0.584057 + 0.811713i \(0.698536\pi\)
\(858\) 0 0
\(859\) −490.000 −0.0194628 −0.00973142 0.999953i \(-0.503098\pi\)
−0.00973142 + 0.999953i \(0.503098\pi\)
\(860\) −12320.0 −0.488498
\(861\) 0 0
\(862\) −12168.0 −0.480793
\(863\) −31642.0 −1.24810 −0.624048 0.781386i \(-0.714513\pi\)
−0.624048 + 0.781386i \(0.714513\pi\)
\(864\) 0 0
\(865\) 10590.0 0.416267
\(866\) −11822.0 −0.463889
\(867\) 0 0
\(868\) 13916.0 0.544170
\(869\) −65100.0 −2.54127
\(870\) 0 0
\(871\) −6468.00 −0.251619
\(872\) −19050.0 −0.739810
\(873\) 0 0
\(874\) −4340.00 −0.167966
\(875\) −1750.00 −0.0676123
\(876\) 0 0
\(877\) −7774.00 −0.299326 −0.149663 0.988737i \(-0.547819\pi\)
−0.149663 + 0.988737i \(0.547819\pi\)
\(878\) 6480.00 0.249077
\(879\) 0 0
\(880\) −12710.0 −0.486880
\(881\) −14682.0 −0.561463 −0.280732 0.959786i \(-0.590577\pi\)
−0.280732 + 0.959786i \(0.590577\pi\)
\(882\) 0 0
\(883\) 922.000 0.0351390 0.0175695 0.999846i \(-0.494407\pi\)
0.0175695 + 0.999846i \(0.494407\pi\)
\(884\) −33516.0 −1.27519
\(885\) 0 0
\(886\) −5308.00 −0.201271
\(887\) 9664.00 0.365823 0.182912 0.983129i \(-0.441448\pi\)
0.182912 + 0.983129i \(0.441448\pi\)
\(888\) 0 0
\(889\) −4144.00 −0.156339
\(890\) 7050.00 0.265524
\(891\) 0 0
\(892\) −46354.0 −1.73996
\(893\) −31080.0 −1.16467
\(894\) 0 0
\(895\) −6300.00 −0.235291
\(896\) −20370.0 −0.759502
\(897\) 0 0
\(898\) 5210.00 0.193608
\(899\) 4118.00 0.152773
\(900\) 0 0
\(901\) 27132.0 1.00322
\(902\) −10044.0 −0.370763
\(903\) 0 0
\(904\) −1230.00 −0.0452535
\(905\) 6710.00 0.246462
\(906\) 0 0
\(907\) −31904.0 −1.16798 −0.583988 0.811762i \(-0.698509\pi\)
−0.583988 + 0.811762i \(0.698509\pi\)
\(908\) 25662.0 0.937911
\(909\) 0 0
\(910\) 2940.00 0.107099
\(911\) 27518.0 1.00078 0.500391 0.865800i \(-0.333190\pi\)
0.500391 + 0.865800i \(0.333190\pi\)
\(912\) 0 0
\(913\) −48236.0 −1.74850
\(914\) −5626.00 −0.203601
\(915\) 0 0
\(916\) 2450.00 0.0883737
\(917\) −2772.00 −0.0998250
\(918\) 0 0
\(919\) −19420.0 −0.697069 −0.348535 0.937296i \(-0.613321\pi\)
−0.348535 + 0.937296i \(0.613321\pi\)
\(920\) −4650.00 −0.166637
\(921\) 0 0
\(922\) −4278.00 −0.152807
\(923\) −37464.0 −1.33602
\(924\) 0 0
\(925\) 3650.00 0.129742
\(926\) −9642.00 −0.342177
\(927\) 0 0
\(928\) −4669.00 −0.165159
\(929\) −39010.0 −1.37769 −0.688846 0.724907i \(-0.741883\pi\)
−0.688846 + 0.724907i \(0.741883\pi\)
\(930\) 0 0
\(931\) 10290.0 0.362235
\(932\) 14.0000 0.000492044 0
\(933\) 0 0
\(934\) −2204.00 −0.0772132
\(935\) −35340.0 −1.23609
\(936\) 0 0
\(937\) −18734.0 −0.653162 −0.326581 0.945169i \(-0.605897\pi\)
−0.326581 + 0.945169i \(0.605897\pi\)
\(938\) −2156.00 −0.0750489
\(939\) 0 0
\(940\) −15540.0 −0.539212
\(941\) 29298.0 1.01497 0.507485 0.861660i \(-0.330575\pi\)
0.507485 + 0.861660i \(0.330575\pi\)
\(942\) 0 0
\(943\) 10044.0 0.346848
\(944\) −34440.0 −1.18742
\(945\) 0 0
\(946\) 21824.0 0.750063
\(947\) 45044.0 1.54565 0.772826 0.634617i \(-0.218842\pi\)
0.772826 + 0.634617i \(0.218842\pi\)
\(948\) 0 0
\(949\) −1596.00 −0.0545926
\(950\) 1750.00 0.0597658
\(951\) 0 0
\(952\) −23940.0 −0.815021
\(953\) −30282.0 −1.02931 −0.514654 0.857398i \(-0.672080\pi\)
−0.514654 + 0.857398i \(0.672080\pi\)
\(954\) 0 0
\(955\) −8110.00 −0.274799
\(956\) 4900.00 0.165771
\(957\) 0 0
\(958\) 11870.0 0.400316
\(959\) 2324.00 0.0782543
\(960\) 0 0
\(961\) −9627.00 −0.323151
\(962\) −6132.00 −0.205513
\(963\) 0 0
\(964\) 7126.00 0.238084
\(965\) −20290.0 −0.676848
\(966\) 0 0
\(967\) −15364.0 −0.510934 −0.255467 0.966818i \(-0.582229\pi\)
−0.255467 + 0.966818i \(0.582229\pi\)
\(968\) 37695.0 1.25161
\(969\) 0 0
\(970\) −2330.00 −0.0771256
\(971\) −44462.0 −1.46947 −0.734734 0.678355i \(-0.762693\pi\)
−0.734734 + 0.678355i \(0.762693\pi\)
\(972\) 0 0
\(973\) 1120.00 0.0369019
\(974\) −12626.0 −0.415363
\(975\) 0 0
\(976\) 82.0000 0.00268930
\(977\) 18534.0 0.606914 0.303457 0.952845i \(-0.401859\pi\)
0.303457 + 0.952845i \(0.401859\pi\)
\(978\) 0 0
\(979\) 87420.0 2.85389
\(980\) 5145.00 0.167705
\(981\) 0 0
\(982\) 922.000 0.0299615
\(983\) −14272.0 −0.463078 −0.231539 0.972826i \(-0.574376\pi\)
−0.231539 + 0.972826i \(0.574376\pi\)
\(984\) 0 0
\(985\) −1330.00 −0.0430227
\(986\) −3306.00 −0.106779
\(987\) 0 0
\(988\) 20580.0 0.662689
\(989\) −21824.0 −0.701681
\(990\) 0 0
\(991\) −6508.00 −0.208611 −0.104305 0.994545i \(-0.533262\pi\)
−0.104305 + 0.994545i \(0.533262\pi\)
\(992\) −22862.0 −0.731723
\(993\) 0 0
\(994\) −12488.0 −0.398486
\(995\) −11100.0 −0.353662
\(996\) 0 0
\(997\) −39874.0 −1.26662 −0.633311 0.773897i \(-0.718305\pi\)
−0.633311 + 0.773897i \(0.718305\pi\)
\(998\) −18060.0 −0.572825
\(999\) 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 1305.4.a.b.1.1 1
3.2 odd 2 145.4.a.a.1.1 1
12.11 even 2 2320.4.a.f.1.1 1
15.14 odd 2 725.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.4.a.a.1.1 1 3.2 odd 2
725.4.a.a.1.1 1 15.14 odd 2
1305.4.a.b.1.1 1 1.1 even 1 trivial
2320.4.a.f.1.1 1 12.11 even 2