Properties

Label 1620.4.i.q.541.1
Level $1620$
Weight $4$
Character 1620.541
Analytic conductor $95.583$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1620,4,Mod(541,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.541");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.i (of order \(3\), degree \(2\), not minimal)

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: no
Analytic conductor: \(95.5830942093\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-23})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} - 6x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 540)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(2.32666 - 0.765945i\) of defining polynomial
Character \(\chi\) \(=\) 1620.541
Dual form 1620.4.i.q.1081.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.50000 + 4.33013i) q^{5} +(-14.9599 + 25.9114i) q^{7} +O(q^{10})\) \(q+(2.50000 + 4.33013i) q^{5} +(-14.9599 + 25.9114i) q^{7} +(-7.95994 + 13.7870i) q^{11} +(-20.9599 - 36.3037i) q^{13} -36.9199 q^{17} -10.9199 q^{19} +(57.3397 + 99.3153i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-72.7997 + 126.093i) q^{29} +(23.2196 + 40.2174i) q^{31} -149.599 q^{35} +74.0000 q^{37} +(-167.639 - 290.360i) q^{41} +(-42.2003 + 73.0931i) q^{43} +(-127.599 + 221.009i) q^{47} +(-276.099 - 478.218i) q^{49} -399.638 q^{53} -79.5994 q^{55} +(-1.28045 - 2.21780i) q^{59} +(-284.260 + 492.352i) q^{61} +(104.800 - 181.518i) q^{65} +(-384.760 - 666.423i) q^{67} +441.837 q^{71} +966.317 q^{73} +(-238.160 - 412.506i) q^{77} +(-251.620 + 435.819i) q^{79} +(635.378 - 1100.51i) q^{83} +(-92.2997 - 159.868i) q^{85} -0.240385 q^{89} +1254.24 q^{91} +(-27.2997 - 47.2844i) q^{95} +(3.35897 - 5.81791i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 10 q^{5} - 10 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 10 q^{5} - 10 q^{7} + 18 q^{11} - 34 q^{13} - 48 q^{17} + 56 q^{19} + 30 q^{23} - 50 q^{25} - 42 q^{29} - 256 q^{31} - 100 q^{35} + 296 q^{37} - 222 q^{41} - 418 q^{43} - 12 q^{47} - 606 q^{49} + 96 q^{53} + 180 q^{55} - 354 q^{59} - 838 q^{61} + 170 q^{65} - 1240 q^{67} - 924 q^{71} + 1772 q^{73} - 1152 q^{77} - 1156 q^{79} + 1146 q^{83} - 120 q^{85} - 300 q^{89} + 2824 q^{91} + 140 q^{95} - 784 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −14.9599 + 25.9114i −0.807761 + 1.39908i 0.106651 + 0.994297i \(0.465987\pi\)
−0.914411 + 0.404786i \(0.867346\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −7.95994 + 13.7870i −0.218183 + 0.377904i −0.954252 0.299002i \(-0.903346\pi\)
0.736070 + 0.676906i \(0.236680\pi\)
\(12\) 0 0
\(13\) −20.9599 36.3037i −0.447172 0.774525i 0.551028 0.834487i \(-0.314236\pi\)
−0.998201 + 0.0599613i \(0.980902\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −36.9199 −0.526728 −0.263364 0.964696i \(-0.584832\pi\)
−0.263364 + 0.964696i \(0.584832\pi\)
\(18\) 0 0
\(19\) −10.9199 −0.131852 −0.0659261 0.997825i \(-0.521000\pi\)
−0.0659261 + 0.997825i \(0.521000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 57.3397 + 99.3153i 0.519833 + 0.900377i 0.999734 + 0.0230548i \(0.00733923\pi\)
−0.479901 + 0.877323i \(0.659327\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −72.7997 + 126.093i −0.466157 + 0.807408i −0.999253 0.0386469i \(-0.987695\pi\)
0.533096 + 0.846055i \(0.321029\pi\)
\(30\) 0 0
\(31\) 23.2196 + 40.2174i 0.134528 + 0.233009i 0.925417 0.378951i \(-0.123715\pi\)
−0.790889 + 0.611959i \(0.790382\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −149.599 −0.722483
\(36\) 0 0
\(37\) 74.0000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −167.639 290.360i −0.638558 1.10601i −0.985749 0.168221i \(-0.946198\pi\)
0.347191 0.937794i \(-0.387135\pi\)
\(42\) 0 0
\(43\) −42.2003 + 73.0931i −0.149663 + 0.259223i −0.931103 0.364757i \(-0.881152\pi\)
0.781440 + 0.623980i \(0.214485\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −127.599 + 221.009i −0.396006 + 0.685902i −0.993229 0.116173i \(-0.962937\pi\)
0.597223 + 0.802075i \(0.296271\pi\)
\(48\) 0 0
\(49\) −276.099 478.218i −0.804954 1.39422i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −399.638 −1.03574 −0.517872 0.855458i \(-0.673276\pi\)
−0.517872 + 0.855458i \(0.673276\pi\)
\(54\) 0 0
\(55\) −79.5994 −0.195149
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.28045 2.21780i −0.00282543 0.00489379i 0.864609 0.502445i \(-0.167566\pi\)
−0.867435 + 0.497551i \(0.834233\pi\)
\(60\) 0 0
\(61\) −284.260 + 492.352i −0.596651 + 1.03343i 0.396661 + 0.917965i \(0.370169\pi\)
−0.993312 + 0.115465i \(0.963164\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 104.800 181.518i 0.199982 0.346378i
\(66\) 0 0
\(67\) −384.760 666.423i −0.701580 1.21517i −0.967912 0.251291i \(-0.919145\pi\)
0.266331 0.963881i \(-0.414188\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 441.837 0.738540 0.369270 0.929322i \(-0.379608\pi\)
0.369270 + 0.929322i \(0.379608\pi\)
\(72\) 0 0
\(73\) 966.317 1.54930 0.774650 0.632390i \(-0.217926\pi\)
0.774650 + 0.632390i \(0.217926\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −238.160 412.506i −0.352479 0.610511i
\(78\) 0 0
\(79\) −251.620 + 435.819i −0.358348 + 0.620677i −0.987685 0.156456i \(-0.949993\pi\)
0.629337 + 0.777132i \(0.283326\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 635.378 1100.51i 0.840263 1.45538i −0.0494095 0.998779i \(-0.515734\pi\)
0.889672 0.456599i \(-0.150933\pi\)
\(84\) 0 0
\(85\) −92.2997 159.868i −0.117780 0.204001i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.240385 −0.000286301 −0.000143150 1.00000i \(-0.500046\pi\)
−0.000143150 1.00000i \(0.500046\pi\)
\(90\) 0 0
\(91\) 1254.24 1.44483
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −27.2997 47.2844i −0.0294830 0.0510661i
\(96\) 0 0
\(97\) 3.35897 5.81791i 0.00351600 0.00608989i −0.864262 0.503042i \(-0.832214\pi\)
0.867778 + 0.496952i \(0.165547\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 597.679 1035.21i 0.588825 1.01987i −0.405562 0.914068i \(-0.632924\pi\)
0.994387 0.105807i \(-0.0337426\pi\)
\(102\) 0 0
\(103\) 228.077 + 395.041i 0.218185 + 0.377908i 0.954253 0.299000i \(-0.0966529\pi\)
−0.736068 + 0.676908i \(0.763320\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1516.47 1.37012 0.685061 0.728485i \(-0.259775\pi\)
0.685061 + 0.728485i \(0.259775\pi\)
\(108\) 0 0
\(109\) −1485.55 −1.30541 −0.652706 0.757611i \(-0.726366\pi\)
−0.652706 + 0.757611i \(0.726366\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −881.478 1526.76i −0.733827 1.27103i −0.955236 0.295844i \(-0.904399\pi\)
0.221409 0.975181i \(-0.428934\pi\)
\(114\) 0 0
\(115\) −286.699 + 496.577i −0.232476 + 0.402661i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 552.319 956.644i 0.425471 0.736937i
\(120\) 0 0
\(121\) 538.779 + 933.192i 0.404793 + 0.701121i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 698.481 0.488033 0.244016 0.969771i \(-0.421535\pi\)
0.244016 + 0.969771i \(0.421535\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 590.436 + 1022.66i 0.393791 + 0.682066i 0.992946 0.118567i \(-0.0378300\pi\)
−0.599155 + 0.800633i \(0.704497\pi\)
\(132\) 0 0
\(133\) 163.361 282.949i 0.106505 0.184472i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 982.976 1702.56i 0.613002 1.06175i −0.377729 0.925916i \(-0.623295\pi\)
0.990731 0.135835i \(-0.0433717\pi\)
\(138\) 0 0
\(139\) −1566.15 2712.66i −0.955679 1.65529i −0.732806 0.680438i \(-0.761790\pi\)
−0.222874 0.974847i \(-0.571544\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 667.359 0.390261
\(144\) 0 0
\(145\) −727.997 −0.416944
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1726.44 2990.28i −0.949230 1.64411i −0.747052 0.664766i \(-0.768531\pi\)
−0.202178 0.979349i \(-0.564802\pi\)
\(150\) 0 0
\(151\) −322.000 + 557.720i −0.173536 + 0.300574i −0.939654 0.342127i \(-0.888853\pi\)
0.766117 + 0.642701i \(0.222186\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −116.098 + 201.087i −0.0601626 + 0.104205i
\(156\) 0 0
\(157\) 761.559 + 1319.06i 0.387128 + 0.670525i 0.992062 0.125751i \(-0.0401339\pi\)
−0.604934 + 0.796275i \(0.706801\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3431.20 −1.67960
\(162\) 0 0
\(163\) 3805.67 1.82873 0.914364 0.404892i \(-0.132691\pi\)
0.914364 + 0.404892i \(0.132691\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1551.14 2686.66i −0.718748 1.24491i −0.961496 0.274819i \(-0.911382\pi\)
0.242748 0.970089i \(-0.421951\pi\)
\(168\) 0 0
\(169\) 219.862 380.812i 0.100074 0.173333i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1614.45 + 2796.31i −0.709505 + 1.22890i 0.255536 + 0.966800i \(0.417748\pi\)
−0.965041 + 0.262099i \(0.915585\pi\)
\(174\) 0 0
\(175\) −373.998 647.784i −0.161552 0.279816i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −313.276 −0.130812 −0.0654059 0.997859i \(-0.520834\pi\)
−0.0654059 + 0.997859i \(0.520834\pi\)
\(180\) 0 0
\(181\) −542.526 −0.222793 −0.111397 0.993776i \(-0.535532\pi\)
−0.111397 + 0.993776i \(0.535532\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 185.000 + 320.429i 0.0735215 + 0.127343i
\(186\) 0 0
\(187\) 293.880 509.015i 0.114923 0.199053i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2284.84 3957.46i 0.865577 1.49922i −0.000896169 1.00000i \(-0.500285\pi\)
0.866473 0.499224i \(-0.166381\pi\)
\(192\) 0 0
\(193\) 2366.48 + 4098.86i 0.882604 + 1.52872i 0.848435 + 0.529300i \(0.177545\pi\)
0.0341696 + 0.999416i \(0.489121\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3335.06 −1.20616 −0.603079 0.797681i \(-0.706060\pi\)
−0.603079 + 0.797681i \(0.706060\pi\)
\(198\) 0 0
\(199\) −4861.26 −1.73169 −0.865844 0.500315i \(-0.833218\pi\)
−0.865844 + 0.500315i \(0.833218\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2178.16 3772.68i −0.753087 1.30438i
\(204\) 0 0
\(205\) 838.197 1451.80i 0.285572 0.494625i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 86.9215 150.552i 0.0287679 0.0498274i
\(210\) 0 0
\(211\) 1032.93 + 1789.09i 0.337015 + 0.583727i 0.983870 0.178886i \(-0.0572494\pi\)
−0.646855 + 0.762613i \(0.723916\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −422.003 −0.133862
\(216\) 0 0
\(217\) −1389.45 −0.434664
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 773.838 + 1340.33i 0.235538 + 0.407964i
\(222\) 0 0
\(223\) 2031.47 3518.62i 0.610034 1.05661i −0.381200 0.924493i \(-0.624489\pi\)
0.991234 0.132117i \(-0.0421776\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1346.93 + 2332.96i −0.393828 + 0.682131i −0.992951 0.118527i \(-0.962183\pi\)
0.599122 + 0.800657i \(0.295516\pi\)
\(228\) 0 0
\(229\) 1024.02 + 1773.66i 0.295499 + 0.511820i 0.975101 0.221762i \(-0.0711807\pi\)
−0.679602 + 0.733581i \(0.737847\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −799.923 −0.224913 −0.112456 0.993657i \(-0.535872\pi\)
−0.112456 + 0.993657i \(0.535872\pi\)
\(234\) 0 0
\(235\) −1275.99 −0.354198
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −536.926 929.984i −0.145317 0.251697i 0.784174 0.620541i \(-0.213087\pi\)
−0.929491 + 0.368844i \(0.879754\pi\)
\(240\) 0 0
\(241\) 2393.70 4146.00i 0.639799 1.10816i −0.345678 0.938353i \(-0.612351\pi\)
0.985477 0.169811i \(-0.0543156\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1380.50 2391.09i 0.359987 0.623515i
\(246\) 0 0
\(247\) 228.880 + 396.431i 0.0589606 + 0.102123i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5498.07 −1.38261 −0.691305 0.722563i \(-0.742964\pi\)
−0.691305 + 0.722563i \(0.742964\pi\)
\(252\) 0 0
\(253\) −1825.68 −0.453675
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3450.62 5976.64i −0.837524 1.45063i −0.891959 0.452116i \(-0.850669\pi\)
0.0544354 0.998517i \(-0.482664\pi\)
\(258\) 0 0
\(259\) −1107.04 + 1917.44i −0.265590 + 0.460015i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3232.15 5598.25i 0.757806 1.31256i −0.186161 0.982519i \(-0.559605\pi\)
0.943967 0.330039i \(-0.107062\pi\)
\(264\) 0 0
\(265\) −999.095 1730.48i −0.231600 0.401142i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5349.66 1.21254 0.606272 0.795257i \(-0.292664\pi\)
0.606272 + 0.795257i \(0.292664\pi\)
\(270\) 0 0
\(271\) −2189.80 −0.490852 −0.245426 0.969415i \(-0.578928\pi\)
−0.245426 + 0.969415i \(0.578928\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −198.998 344.675i −0.0436366 0.0755807i
\(276\) 0 0
\(277\) −651.954 + 1129.22i −0.141415 + 0.244939i −0.928030 0.372506i \(-0.878499\pi\)
0.786614 + 0.617445i \(0.211832\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2702.72 4681.25i 0.573776 0.993808i −0.422398 0.906410i \(-0.638812\pi\)
0.996173 0.0873979i \(-0.0278551\pi\)
\(282\) 0 0
\(283\) −643.800 1115.09i −0.135229 0.234224i 0.790456 0.612519i \(-0.209844\pi\)
−0.925685 + 0.378295i \(0.876510\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10031.5 2.06321
\(288\) 0 0
\(289\) −3549.92 −0.722557
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 778.726 + 1348.79i 0.155268 + 0.268933i 0.933157 0.359470i \(-0.117042\pi\)
−0.777888 + 0.628403i \(0.783709\pi\)
\(294\) 0 0
\(295\) 6.40225 11.0890i 0.00126357 0.00218857i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2403.67 4163.29i 0.464910 0.805248i
\(300\) 0 0
\(301\) −1262.63 2186.94i −0.241783 0.418780i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2842.60 −0.533661
\(306\) 0 0
\(307\) −2343.27 −0.435627 −0.217813 0.975990i \(-0.569892\pi\)
−0.217813 + 0.975990i \(0.569892\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3053.82 5289.37i −0.556804 0.964414i −0.997761 0.0668850i \(-0.978694\pi\)
0.440956 0.897529i \(-0.354639\pi\)
\(312\) 0 0
\(313\) 1040.89 1802.87i 0.187970 0.325573i −0.756604 0.653874i \(-0.773143\pi\)
0.944573 + 0.328301i \(0.106476\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1805.86 + 3127.85i −0.319960 + 0.554187i −0.980479 0.196622i \(-0.937003\pi\)
0.660519 + 0.750809i \(0.270336\pi\)
\(318\) 0 0
\(319\) −1158.96 2007.38i −0.203415 0.352325i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 403.160 0.0694503
\(324\) 0 0
\(325\) 1048.00 0.178869
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3817.76 6612.55i −0.639756 1.10809i
\(330\) 0 0
\(331\) −3186.87 + 5519.83i −0.529204 + 0.916608i 0.470216 + 0.882551i \(0.344176\pi\)
−0.999420 + 0.0340567i \(0.989157\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1923.80 3332.12i 0.313756 0.543442i
\(336\) 0 0
\(337\) 4773.58 + 8268.09i 0.771613 + 1.33647i 0.936678 + 0.350191i \(0.113883\pi\)
−0.165065 + 0.986283i \(0.552783\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −739.305 −0.117406
\(342\) 0 0
\(343\) 6259.20 0.985321
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4637.52 8032.42i −0.717450 1.24266i −0.962007 0.273025i \(-0.911976\pi\)
0.244557 0.969635i \(-0.421357\pi\)
\(348\) 0 0
\(349\) 2229.73 3862.01i 0.341991 0.592345i −0.642812 0.766024i \(-0.722232\pi\)
0.984802 + 0.173679i \(0.0555655\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4833.22 8371.38i 0.728743 1.26222i −0.228671 0.973504i \(-0.573438\pi\)
0.957415 0.288717i \(-0.0932286\pi\)
\(354\) 0 0
\(355\) 1104.59 + 1913.21i 0.165143 + 0.286035i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3789.49 −0.557108 −0.278554 0.960421i \(-0.589855\pi\)
−0.278554 + 0.960421i \(0.589855\pi\)
\(360\) 0 0
\(361\) −6739.76 −0.982615
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2415.79 + 4184.28i 0.346434 + 0.600041i
\(366\) 0 0
\(367\) −1908.41 + 3305.46i −0.271439 + 0.470146i −0.969231 0.246155i \(-0.920833\pi\)
0.697792 + 0.716301i \(0.254166\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5978.56 10355.2i 0.836634 1.44909i
\(372\) 0 0
\(373\) −1041.36 1803.69i −0.144557 0.250380i 0.784651 0.619938i \(-0.212842\pi\)
−0.929208 + 0.369558i \(0.879509\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6103.51 0.833811
\(378\) 0 0
\(379\) 8074.43 1.09434 0.547171 0.837021i \(-0.315705\pi\)
0.547171 + 0.837021i \(0.315705\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 686.369 + 1188.83i 0.0915713 + 0.158606i 0.908172 0.418596i \(-0.137478\pi\)
−0.816601 + 0.577202i \(0.804144\pi\)
\(384\) 0 0
\(385\) 1190.80 2062.53i 0.157633 0.273029i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5188.51 + 8986.77i −0.676267 + 1.17133i 0.299830 + 0.953993i \(0.403070\pi\)
−0.976097 + 0.217336i \(0.930263\pi\)
\(390\) 0 0
\(391\) −2116.98 3666.71i −0.273811 0.474254i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2516.20 −0.320516
\(396\) 0 0
\(397\) −1717.90 −0.217176 −0.108588 0.994087i \(-0.534633\pi\)
−0.108588 + 0.994087i \(0.534633\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2579.88 + 4468.49i 0.321280 + 0.556473i 0.980752 0.195255i \(-0.0625536\pi\)
−0.659472 + 0.751729i \(0.729220\pi\)
\(402\) 0 0
\(403\) 973.361 1685.91i 0.120314 0.208390i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −589.035 + 1020.24i −0.0717381 + 0.124254i
\(408\) 0 0
\(409\) 3801.65 + 6584.65i 0.459607 + 0.796063i 0.998940 0.0460296i \(-0.0146568\pi\)
−0.539333 + 0.842093i \(0.681324\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 76.6218 0.00912908
\(414\) 0 0
\(415\) 6353.78 0.751554
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3581.22 6202.86i −0.417552 0.723221i 0.578141 0.815937i \(-0.303778\pi\)
−0.995693 + 0.0927162i \(0.970445\pi\)
\(420\) 0 0
\(421\) −1293.60 + 2240.57i −0.149753 + 0.259380i −0.931136 0.364672i \(-0.881181\pi\)
0.781383 + 0.624052i \(0.214515\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 461.498 799.339i 0.0526728 0.0912320i
\(426\) 0 0
\(427\) −8505.01 14731.1i −0.963902 1.66953i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11053.4 −1.23532 −0.617661 0.786444i \(-0.711920\pi\)
−0.617661 + 0.786444i \(0.711920\pi\)
\(432\) 0 0
\(433\) −2510.68 −0.278650 −0.139325 0.990247i \(-0.544493\pi\)
−0.139325 + 0.990247i \(0.544493\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −626.143 1084.51i −0.0685411 0.118717i
\(438\) 0 0
\(439\) −3419.75 + 5923.17i −0.371789 + 0.643958i −0.989841 0.142180i \(-0.954589\pi\)
0.618052 + 0.786138i \(0.287922\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6153.48 + 10658.1i −0.659956 + 1.14308i 0.320670 + 0.947191i \(0.396092\pi\)
−0.980627 + 0.195887i \(0.937242\pi\)
\(444\) 0 0
\(445\) −0.600963 1.04090i −6.40188e−5 0.000110884i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1073.61 0.112844 0.0564219 0.998407i \(-0.482031\pi\)
0.0564219 + 0.998407i \(0.482031\pi\)
\(450\) 0 0
\(451\) 5337.60 0.557290
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3135.59 + 5431.01i 0.323074 + 0.559581i
\(456\) 0 0
\(457\) −3660.14 + 6339.56i −0.374648 + 0.648910i −0.990274 0.139128i \(-0.955570\pi\)
0.615626 + 0.788039i \(0.288903\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 86.5289 149.872i 0.00874198 0.0151415i −0.861621 0.507552i \(-0.830551\pi\)
0.870363 + 0.492410i \(0.163884\pi\)
\(462\) 0 0
\(463\) −7799.30 13508.8i −0.782860 1.35595i −0.930269 0.366878i \(-0.880427\pi\)
0.147409 0.989076i \(-0.452907\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1561.75 −0.154752 −0.0773760 0.997002i \(-0.524654\pi\)
−0.0773760 + 0.997002i \(0.524654\pi\)
\(468\) 0 0
\(469\) 23023.9 2.26684
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −671.824 1163.63i −0.0653076 0.113116i
\(474\) 0 0
\(475\) 136.498 236.422i 0.0131852 0.0228375i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2229.55 + 3861.69i −0.212674 + 0.368362i −0.952550 0.304381i \(-0.901550\pi\)
0.739877 + 0.672742i \(0.234884\pi\)
\(480\) 0 0
\(481\) −1551.04 2686.47i −0.147029 0.254662i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 33.5897 0.00314481
\(486\) 0 0
\(487\) 9005.17 0.837912 0.418956 0.908007i \(-0.362396\pi\)
0.418956 + 0.908007i \(0.362396\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10298.1 + 17836.8i 0.946530 + 1.63944i 0.752658 + 0.658412i \(0.228772\pi\)
0.193873 + 0.981027i \(0.437895\pi\)
\(492\) 0 0
\(493\) 2687.75 4655.33i 0.245538 0.425285i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6609.85 + 11448.6i −0.596564 + 1.03328i
\(498\) 0 0
\(499\) 4073.27 + 7055.12i 0.365420 + 0.632927i 0.988844 0.148958i \(-0.0475919\pi\)
−0.623423 + 0.781885i \(0.714259\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9277.97 0.822434 0.411217 0.911537i \(-0.365104\pi\)
0.411217 + 0.911537i \(0.365104\pi\)
\(504\) 0 0
\(505\) 5976.79 0.526661
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4999.88 + 8660.05i 0.435395 + 0.754126i 0.997328 0.0730568i \(-0.0232754\pi\)
−0.561933 + 0.827183i \(0.689942\pi\)
\(510\) 0 0
\(511\) −14456.0 + 25038.6i −1.25146 + 2.16760i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1140.38 + 1975.20i −0.0975754 + 0.169006i
\(516\) 0 0
\(517\) −2031.37 3518.43i −0.172803 0.299304i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −17101.2 −1.43804 −0.719018 0.694992i \(-0.755408\pi\)
−0.719018 + 0.694992i \(0.755408\pi\)
\(522\) 0 0
\(523\) 766.452 0.0640815 0.0320407 0.999487i \(-0.489799\pi\)
0.0320407 + 0.999487i \(0.489799\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −857.263 1484.82i −0.0708595 0.122732i
\(528\) 0 0
\(529\) −492.192 + 852.502i −0.0404531 + 0.0700667i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7027.42 + 12171.9i −0.571091 + 0.989159i
\(534\) 0 0
\(535\) 3791.19 + 6566.53i 0.306369 + 0.530646i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8790.93 0.702509
\(540\) 0 0
\(541\) −19609.4 −1.55837 −0.779183 0.626797i \(-0.784365\pi\)
−0.779183 + 0.626797i \(0.784365\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3713.88 6432.63i −0.291899 0.505584i
\(546\) 0 0
\(547\) 4409.93 7638.22i 0.344707 0.597051i −0.640593 0.767880i \(-0.721312\pi\)
0.985301 + 0.170830i \(0.0546448\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 794.963 1376.92i 0.0614638 0.106458i
\(552\) 0 0
\(553\) −7528.44 13039.6i −0.578919 1.00272i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3398.63 0.258536 0.129268 0.991610i \(-0.458737\pi\)
0.129268 + 0.991610i \(0.458737\pi\)
\(558\) 0 0
\(559\) 3538.06 0.267700
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8540.76 14793.0i −0.639343 1.10737i −0.985577 0.169227i \(-0.945873\pi\)
0.346234 0.938148i \(-0.387460\pi\)
\(564\) 0 0
\(565\) 4407.39 7633.82i 0.328177 0.568420i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4536.89 + 7858.13i −0.334264 + 0.578963i −0.983343 0.181758i \(-0.941821\pi\)
0.649079 + 0.760721i \(0.275155\pi\)
\(570\) 0 0
\(571\) 12443.6 + 21552.9i 0.911992 + 1.57962i 0.811247 + 0.584703i \(0.198789\pi\)
0.100744 + 0.994912i \(0.467878\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2866.99 −0.207933
\(576\) 0 0
\(577\) −15279.3 −1.10240 −0.551199 0.834374i \(-0.685830\pi\)
−0.551199 + 0.834374i \(0.685830\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 19010.4 + 32927.0i 1.35746 + 2.35119i
\(582\) 0 0
\(583\) 3181.09 5509.81i 0.225982 0.391412i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −184.519 + 319.597i −0.0129743 + 0.0224722i −0.872440 0.488722i \(-0.837463\pi\)
0.859465 + 0.511194i \(0.170797\pi\)
\(588\) 0 0
\(589\) −253.555 439.169i −0.0177377 0.0307227i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −7306.60 −0.505980 −0.252990 0.967469i \(-0.581414\pi\)
−0.252990 + 0.967469i \(0.581414\pi\)
\(594\) 0 0
\(595\) 5523.19 0.380552
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1777.47 + 3078.66i 0.121244 + 0.210001i 0.920259 0.391311i \(-0.127978\pi\)
−0.799014 + 0.601312i \(0.794645\pi\)
\(600\) 0 0
\(601\) −3555.62 + 6158.51i −0.241326 + 0.417988i −0.961092 0.276228i \(-0.910916\pi\)
0.719767 + 0.694216i \(0.244249\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2693.89 + 4665.96i −0.181029 + 0.313551i
\(606\) 0 0
\(607\) 125.486 + 217.347i 0.00839094 + 0.0145335i 0.870190 0.492716i \(-0.163996\pi\)
−0.861799 + 0.507249i \(0.830662\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10697.9 0.708332
\(612\) 0 0
\(613\) 8375.38 0.551841 0.275921 0.961180i \(-0.411017\pi\)
0.275921 + 0.961180i \(0.411017\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3870.15 6703.29i −0.252522 0.437382i 0.711697 0.702486i \(-0.247927\pi\)
−0.964220 + 0.265105i \(0.914593\pi\)
\(618\) 0 0
\(619\) 5650.14 9786.34i 0.366880 0.635454i −0.622196 0.782861i \(-0.713759\pi\)
0.989076 + 0.147407i \(0.0470928\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.59615 6.22871i 0.000231263 0.000400559i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2732.07 −0.173187
\(630\) 0 0
\(631\) −13549.6 −0.854835 −0.427417 0.904054i \(-0.640577\pi\)
−0.427417 + 0.904054i \(0.640577\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1746.20 + 3024.51i 0.109127 + 0.189014i
\(636\) 0 0
\(637\) −11574.0 + 20046.8i −0.719907 + 1.24691i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2031.81 3519.19i 0.125197 0.216848i −0.796613 0.604490i \(-0.793377\pi\)
0.921810 + 0.387642i \(0.126710\pi\)
\(642\) 0 0
\(643\) −1795.59 3110.06i −0.110126 0.190744i 0.805695 0.592331i \(-0.201792\pi\)
−0.915821 + 0.401587i \(0.868459\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11040.5 0.670860 0.335430 0.942065i \(-0.391118\pi\)
0.335430 + 0.942065i \(0.391118\pi\)
\(648\) 0 0
\(649\) 40.7692 0.00246584
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9428.86 + 16331.3i 0.565054 + 0.978701i 0.997045 + 0.0768236i \(0.0244778\pi\)
−0.431991 + 0.901878i \(0.642189\pi\)
\(654\) 0 0
\(655\) −2952.18 + 5113.32i −0.176109 + 0.305029i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12095.9 20950.7i 0.715005 1.23843i −0.247953 0.968772i \(-0.579758\pi\)
0.962958 0.269653i \(-0.0869090\pi\)
\(660\) 0 0
\(661\) −16333.4 28290.3i −0.961113 1.66470i −0.719714 0.694271i \(-0.755727\pi\)
−0.241399 0.970426i \(-0.577606\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1633.61 0.0952609
\(666\) 0 0
\(667\) −16697.3 −0.969296
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4525.38 7838.18i −0.260358 0.450953i
\(672\) 0 0
\(673\) 13870.4 24024.2i 0.794450 1.37603i −0.128738 0.991679i \(-0.541093\pi\)
0.923188 0.384349i \(-0.125574\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9472.98 + 16407.7i −0.537779 + 0.931460i 0.461245 + 0.887273i \(0.347403\pi\)
−0.999023 + 0.0441869i \(0.985930\pi\)
\(678\) 0 0
\(679\) 100.500 + 174.071i 0.00568017 + 0.00983835i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 19889.1 1.11425 0.557125 0.830428i \(-0.311904\pi\)
0.557125 + 0.830428i \(0.311904\pi\)
\(684\) 0 0
\(685\) 9829.76 0.548286
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8376.38 + 14508.3i 0.463156 + 0.802210i
\(690\) 0 0
\(691\) −2465.15 + 4269.76i −0.135714 + 0.235064i −0.925870 0.377842i \(-0.876666\pi\)
0.790156 + 0.612906i \(0.210000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7830.77 13563.3i 0.427393 0.740266i
\(696\) 0 0
\(697\) 6189.23 + 10720.1i 0.336347 + 0.582570i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8173.40 −0.440378 −0.220189 0.975457i \(-0.570667\pi\)
−0.220189 + 0.975457i \(0.570667\pi\)
\(702\) 0 0
\(703\) −808.070 −0.0433527
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 17882.5 + 30973.4i 0.951259 + 1.64763i
\(708\) 0 0
\(709\) −3849.24 + 6667.07i −0.203894 + 0.353155i −0.949780 0.312919i \(-0.898693\pi\)
0.745886 + 0.666074i \(0.232027\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2662.81 + 4612.12i −0.139864 + 0.242251i
\(714\) 0 0
\(715\) 1668.40 + 2889.75i 0.0872651 + 0.151148i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 30407.2 1.57719 0.788593 0.614915i \(-0.210810\pi\)
0.788593 + 0.614915i \(0.210810\pi\)
\(720\) 0 0
\(721\) −13648.1 −0.704966
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1819.99 3152.32i −0.0932315 0.161482i
\(726\) 0 0
\(727\) 7631.57 13218.3i 0.389325 0.674330i −0.603034 0.797715i \(-0.706042\pi\)
0.992359 + 0.123385i \(0.0393750\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1558.03 2698.59i 0.0788315 0.136540i
\(732\) 0 0
\(733\) 3532.12 + 6117.80i 0.177983 + 0.308276i 0.941190 0.337879i \(-0.109709\pi\)
−0.763206 + 0.646155i \(0.776376\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12250.6 0.612291
\(738\) 0 0
\(739\) −20382.0 −1.01457 −0.507284 0.861779i \(-0.669350\pi\)
−0.507284 + 0.861779i \(0.669350\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15467.5 + 26790.5i 0.763724 + 1.32281i 0.940919 + 0.338633i \(0.109964\pi\)
−0.177195 + 0.984176i \(0.556702\pi\)
\(744\) 0 0
\(745\) 8632.19 14951.4i 0.424509 0.735270i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −22686.4 + 39293.9i −1.10673 + 1.91691i
\(750\) 0 0
\(751\) 14542.4 + 25188.2i 0.706606 + 1.22388i 0.966109 + 0.258135i \(0.0831080\pi\)
−0.259503 + 0.965742i \(0.583559\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3220.00 −0.155216
\(756\) 0 0
\(757\) 5538.75 0.265930 0.132965 0.991121i \(-0.457550\pi\)
0.132965 + 0.991121i \(0.457550\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12652.1 21914.0i −0.602677 1.04387i −0.992414 0.122941i \(-0.960767\pi\)
0.389737 0.920926i \(-0.372566\pi\)
\(762\) 0 0
\(763\) 22223.8 38492.7i 1.05446 1.82638i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −53.6763 + 92.9700i −0.00252691 + 0.00437673i
\(768\) 0 0
\(769\) 17531.9 + 30366.2i 0.822129 + 1.42397i 0.904094 + 0.427335i \(0.140547\pi\)
−0.0819641 + 0.996635i \(0.526119\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −32958.1 −1.53353 −0.766766 0.641927i \(-0.778135\pi\)
−0.766766 + 0.641927i \(0.778135\pi\)
\(774\) 0 0
\(775\) −1160.98 −0.0538110
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1830.60 + 3170.69i 0.0841952 + 0.145830i
\(780\) 0 0
\(781\) −3516.99 + 6091.61i −0.161137 + 0.279097i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3807.80 + 6595.30i −0.173129 + 0.299868i
\(786\) 0 0
\(787\) 1115.28 + 1931.73i 0.0505153 + 0.0874951i 0.890177 0.455614i \(-0.150580\pi\)
−0.839662 + 0.543109i \(0.817247\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 52747.4 2.37103
\(792\) 0 0
\(793\) 23832.3 1.06722
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 10976.9 + 19012.6i 0.487857 + 0.844993i 0.999902 0.0139654i \(-0.00444545\pi\)
−0.512046 + 0.858958i \(0.671112\pi\)
\(798\) 0 0
\(799\) 4710.95 8159.61i 0.208588 0.361284i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −7691.82 + 13322.6i −0.338031 + 0.585486i
\(804\) 0 0
\(805\) −8577.99 14857.5i −0.375571 0.650507i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −27001.6 −1.17345 −0.586727 0.809785i \(-0.699584\pi\)
−0.586727 + 0.809785i \(0.699584\pi\)
\(810\) 0 0
\(811\) −37870.0 −1.63970 −0.819850 0.572579i \(-0.805943\pi\)
−0.819850 + 0.572579i \(0.805943\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9514.17 + 16479.0i 0.408916 + 0.708264i
\(816\) 0 0
\(817\) 460.822 798.167i 0.0197333 0.0341791i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −18858.7 + 32664.3i −0.801674 + 1.38854i 0.116839 + 0.993151i \(0.462724\pi\)
−0.918513 + 0.395390i \(0.870609\pi\)
\(822\) 0 0
\(823\) 8679.38 + 15033.1i 0.367611 + 0.636721i 0.989192 0.146629i \(-0.0468424\pi\)
−0.621580 + 0.783350i \(0.713509\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −4418.15 −0.185773 −0.0928864 0.995677i \(-0.529609\pi\)
−0.0928864 + 0.995677i \(0.529609\pi\)
\(828\) 0 0
\(829\) −19161.9 −0.802797 −0.401399 0.915903i \(-0.631476\pi\)
−0.401399 + 0.915903i \(0.631476\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 10193.6 + 17655.8i 0.423992 + 0.734376i
\(834\) 0 0
\(835\) 7755.71 13433.3i 0.321434 0.556740i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2846.68 4930.60i 0.117138 0.202888i −0.801495 0.598002i \(-0.795961\pi\)
0.918632 + 0.395114i \(0.129295\pi\)
\(840\) 0 0
\(841\) 1594.91 + 2762.47i 0.0653948 + 0.113267i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2198.62 0.0895087
\(846\) 0 0
\(847\) −32240.4 −1.30790
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4243.14 + 7349.34i 0.170920 + 0.296042i
\(852\) 0 0
\(853\) 948.837 1643.43i 0.0380862 0.0659673i −0.846354 0.532621i \(-0.821207\pi\)
0.884440 + 0.466654i \(0.154541\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −11150.7 + 19313.6i −0.444459 + 0.769826i −0.998014 0.0629864i \(-0.979938\pi\)
0.553555 + 0.832813i \(0.313271\pi\)
\(858\) 0 0
\(859\) −14876.4 25766.7i −0.590892 1.02346i −0.994113 0.108353i \(-0.965442\pi\)
0.403220 0.915103i \(-0.367891\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18461.6 −0.728203 −0.364102 0.931359i \(-0.618624\pi\)
−0.364102 + 0.931359i \(0.618624\pi\)
\(864\) 0 0
\(865\) −16144.5 −0.634601
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −4005.76 6938.18i −0.156371 0.270842i
\(870\) 0 0
\(871\) −16129.1 + 27936.4i −0.627454 + 1.08678i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1869.99 3238.92i 0.0722483 0.125138i
\(876\) 0 0
\(877\) 13611.8 + 23576.3i 0.524102 + 0.907772i 0.999606 + 0.0280584i \(0.00893243\pi\)
−0.475504 + 0.879714i \(0.657734\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −24637.3 −0.942169 −0.471085 0.882088i \(-0.656137\pi\)
−0.471085 + 0.882088i \(0.656137\pi\)
\(882\) 0 0
\(883\) 37662.2 1.43537 0.717686 0.696367i \(-0.245201\pi\)
0.717686 + 0.696367i \(0.245201\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1190.86 2062.63i −0.0450792 0.0780794i 0.842605 0.538531i \(-0.181021\pi\)
−0.887685 + 0.460452i \(0.847687\pi\)
\(888\) 0 0
\(889\) −10449.2 + 18098.6i −0.394214 + 0.682798i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1393.37 2413.39i 0.0522142 0.0904377i
\(894\) 0 0
\(895\) −783.189 1356.52i −0.0292504 0.0506632i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6761.50 −0.250844
\(900\) 0 0
\(901\) 14754.6 0.545556
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1356.31 2349.20i −0.0498181 0.0862875i
\(906\) 0 0
\(907\) −17432.9 + 30194.7i −0.638204 + 1.10540i 0.347622 + 0.937635i \(0.386989\pi\)
−0.985827 + 0.167768i \(0.946344\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −26570.6 + 46021.5i −0.966325 + 1.67372i −0.260311 + 0.965525i \(0.583825\pi\)
−0.706013 + 0.708198i \(0.749508\pi\)
\(912\) 0 0
\(913\) 10115.1 + 17519.9i 0.366662 + 0.635077i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −35331.5 −1.27236
\(918\) 0 0
\(919\) −9861.81 −0.353984 −0.176992 0.984212i \(-0.556637\pi\)
−0.176992 + 0.984212i \(0.556637\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −9260.87 16040.3i −0.330255 0.572018i
\(924\) 0 0
\(925\) −925.000 + 1602.15i −0.0328798 + 0.0569495i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −10341.6 + 17912.2i −0.365228 + 0.632593i −0.988813 0.149163i \(-0.952342\pi\)
0.623585 + 0.781756i \(0.285676\pi\)
\(930\) 0 0
\(931\) 3014.97 + 5222.08i 0.106135 + 0.183831i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2938.80 0.102790
\(936\) 0 0
\(937\) 6795.89 0.236939 0.118470 0.992958i \(-0.462201\pi\)
0.118470 + 0.992958i \(0.462201\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3321.58 5753.15i −0.115070 0.199306i 0.802738 0.596332i \(-0.203376\pi\)
−0.917808 + 0.397025i \(0.870042\pi\)
\(942\) 0 0
\(943\) 19224.8 33298.3i 0.663887 1.14989i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 13217.1 22892.7i 0.453535 0.785545i −0.545068 0.838392i \(-0.683496\pi\)
0.998603 + 0.0528466i \(0.0168294\pi\)
\(948\) 0 0
\(949\) −20253.9 35080.9i −0.692804 1.19997i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −8451.56 −0.287275 −0.143637 0.989630i \(-0.545880\pi\)
−0.143637 + 0.989630i \(0.545880\pi\)
\(954\) 0 0
\(955\) 22848.4 0.774196
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 29410.5 + 50940.5i 0.990318 + 1.71528i
\(960\) 0 0
\(961\) 13817.2 23932.1i 0.463805 0.803333i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −11832.4 + 20494.3i −0.394713 + 0.683662i
\(966\) 0 0
\(967\) 7662.42 + 13271.7i 0.254816 + 0.441354i 0.964845 0.262818i \(-0.0846518\pi\)
−0.710030 + 0.704172i \(0.751318\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1686.74 0.0557468 0.0278734 0.999611i \(-0.491126\pi\)
0.0278734 + 0.999611i \(0.491126\pi\)
\(972\) 0 0
\(973\) 93718.2 3.08784
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4850.53 + 8401.36i 0.158835 + 0.275111i 0.934449 0.356097i \(-0.115893\pi\)
−0.775614 + 0.631208i \(0.782559\pi\)
\(978\) 0 0
\(979\) 1.91345 3.31419i 6.24659e−5 0.000108194i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 18228.1 31572.1i 0.591442 1.02441i −0.402597 0.915377i \(-0.631892\pi\)
0.994038 0.109030i \(-0.0347744\pi\)
\(984\) 0 0
\(985\) −8337.65 14441.2i −0.269705 0.467143i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9679.02 −0.311198
\(990\) 0 0
\(991\) −13556.5 −0.434547 −0.217274 0.976111i \(-0.569716\pi\)
−0.217274 + 0.976111i \(0.569716\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −12153.2 21049.9i −0.387217 0.670680i
\(996\) 0 0
\(997\) −30926.6 + 53566.5i −0.982404 + 1.70157i −0.329456 + 0.944171i \(0.606865\pi\)
−0.652948 + 0.757403i \(0.726468\pi\)
\(998\) 0 0
\(999\) 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 1620.4.i.q.541.1 4
3.2 odd 2 1620.4.i.n.541.1 4
9.2 odd 6 540.4.a.i.1.2 yes 2
9.4 even 3 inner 1620.4.i.q.1081.1 4
9.5 odd 6 1620.4.i.n.1081.1 4
9.7 even 3 540.4.a.f.1.2 2
36.7 odd 6 2160.4.a.v.1.1 2
36.11 even 6 2160.4.a.ba.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
540.4.a.f.1.2 2 9.7 even 3
540.4.a.i.1.2 yes 2 9.2 odd 6
1620.4.i.n.541.1 4 3.2 odd 2
1620.4.i.n.1081.1 4 9.5 odd 6
1620.4.i.q.541.1 4 1.1 even 1 trivial
1620.4.i.q.1081.1 4 9.4 even 3 inner
2160.4.a.v.1.1 2 36.7 odd 6
2160.4.a.ba.1.1 2 36.11 even 6