Properties

Label 1764.4.k.a.361.1
Level $1764$
Weight $4$
Character 1764.361
Analytic conductor $104.079$
Analytic rank $0$
Dimension $2$
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] = [1764,4,Mod(361,1764)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1764.361");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.k (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: \(104.079369250\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 196)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1764.361
Dual form 1764.4.k.a.1549.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.0000 - 17.3205i) q^{5} +O(q^{10})\) \(q+(-10.0000 - 17.3205i) q^{5} +(22.0000 - 38.1051i) q^{11} -44.0000 q^{13} +(36.0000 - 62.3538i) q^{17} +(-50.0000 - 86.6025i) q^{19} +(-60.0000 - 103.923i) q^{23} +(-137.500 + 238.157i) q^{25} -218.000 q^{29} +(140.000 - 242.487i) q^{31} +(15.0000 + 25.9808i) q^{37} -120.000 q^{41} +220.000 q^{43} +(44.0000 + 76.2102i) q^{47} +(55.0000 - 95.2628i) q^{53} -880.000 q^{55} +(290.000 - 502.295i) q^{59} +(-190.000 - 329.090i) q^{61} +(440.000 + 762.102i) q^{65} +(490.000 - 848.705i) q^{67} +112.000 q^{71} +(320.000 - 554.256i) q^{73} +(244.000 + 422.620i) q^{79} -660.000 q^{83} -1440.00 q^{85} +(160.000 + 277.128i) q^{89} +(-1000.00 + 1732.05i) q^{95} +248.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 20 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 20 q^{5} + 44 q^{11} - 88 q^{13} + 72 q^{17} - 100 q^{19} - 120 q^{23} - 275 q^{25} - 436 q^{29} + 280 q^{31} + 30 q^{37} - 240 q^{41} + 440 q^{43} + 88 q^{47} + 110 q^{53} - 1760 q^{55} + 580 q^{59} - 380 q^{61} + 880 q^{65} + 980 q^{67} + 224 q^{71} + 640 q^{73} + 488 q^{79} - 1320 q^{83} - 2880 q^{85} + 320 q^{89} - 2000 q^{95} + 496 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) −10.0000 17.3205i −0.894427 1.54919i −0.834512 0.550990i \(-0.814250\pi\)
−0.0599153 0.998203i \(-0.519083\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 22.0000 38.1051i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) 0 0
\(13\) −44.0000 −0.938723 −0.469362 0.883006i \(-0.655516\pi\)
−0.469362 + 0.883006i \(0.655516\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 36.0000 62.3538i 0.513605 0.889590i −0.486271 0.873808i \(-0.661643\pi\)
0.999875 0.0157814i \(-0.00502359\pi\)
\(18\) 0 0
\(19\) −50.0000 86.6025i −0.603726 1.04568i −0.992251 0.124246i \(-0.960349\pi\)
0.388526 0.921438i \(-0.372984\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −60.0000 103.923i −0.543951 0.942150i −0.998672 0.0515165i \(-0.983595\pi\)
0.454721 0.890634i \(-0.349739\pi\)
\(24\) 0 0
\(25\) −137.500 + 238.157i −1.10000 + 1.90526i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −218.000 −1.39592 −0.697958 0.716138i \(-0.745908\pi\)
−0.697958 + 0.716138i \(0.745908\pi\)
\(30\) 0 0
\(31\) 140.000 242.487i 0.811121 1.40490i −0.100960 0.994891i \(-0.532191\pi\)
0.912080 0.410012i \(-0.134475\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 15.0000 + 25.9808i 0.0666482 + 0.115438i 0.897424 0.441169i \(-0.145436\pi\)
−0.830776 + 0.556607i \(0.812103\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −120.000 −0.457094 −0.228547 0.973533i \(-0.573397\pi\)
−0.228547 + 0.973533i \(0.573397\pi\)
\(42\) 0 0
\(43\) 220.000 0.780225 0.390113 0.920767i \(-0.372436\pi\)
0.390113 + 0.920767i \(0.372436\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 44.0000 + 76.2102i 0.136554 + 0.236519i 0.926190 0.377057i \(-0.123064\pi\)
−0.789636 + 0.613576i \(0.789730\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 55.0000 95.2628i 0.142544 0.246893i −0.785910 0.618341i \(-0.787805\pi\)
0.928454 + 0.371448i \(0.121138\pi\)
\(54\) 0 0
\(55\) −880.000 −2.15744
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 290.000 502.295i 0.639912 1.10836i −0.345540 0.938404i \(-0.612304\pi\)
0.985452 0.169955i \(-0.0543624\pi\)
\(60\) 0 0
\(61\) −190.000 329.090i −0.398803 0.690748i 0.594775 0.803892i \(-0.297241\pi\)
−0.993579 + 0.113144i \(0.963908\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 440.000 + 762.102i 0.839620 + 1.45426i
\(66\) 0 0
\(67\) 490.000 848.705i 0.893478 1.54755i 0.0578010 0.998328i \(-0.481591\pi\)
0.835677 0.549221i \(-0.185076\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 112.000 0.187211 0.0936053 0.995609i \(-0.470161\pi\)
0.0936053 + 0.995609i \(0.470161\pi\)
\(72\) 0 0
\(73\) 320.000 554.256i 0.513057 0.888641i −0.486828 0.873498i \(-0.661846\pi\)
0.999885 0.0151432i \(-0.00482042\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 244.000 + 422.620i 0.347496 + 0.601880i 0.985804 0.167901i \(-0.0536989\pi\)
−0.638308 + 0.769781i \(0.720366\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −660.000 −0.872824 −0.436412 0.899747i \(-0.643751\pi\)
−0.436412 + 0.899747i \(0.643751\pi\)
\(84\) 0 0
\(85\) −1440.00 −1.83753
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 160.000 + 277.128i 0.190561 + 0.330062i 0.945436 0.325807i \(-0.105636\pi\)
−0.754875 + 0.655869i \(0.772303\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1000.00 + 1732.05i −1.07998 + 1.87058i
\(96\) 0 0
\(97\) 248.000 0.259594 0.129797 0.991541i \(-0.458567\pi\)
0.129797 + 0.991541i \(0.458567\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 110.000 190.526i 0.108370 0.187703i −0.806740 0.590907i \(-0.798770\pi\)
0.915110 + 0.403204i \(0.132103\pi\)
\(102\) 0 0
\(103\) −668.000 1157.01i −0.639029 1.10683i −0.985646 0.168824i \(-0.946003\pi\)
0.346617 0.938007i \(-0.387330\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 50.0000 + 86.6025i 0.0451746 + 0.0782447i 0.887729 0.460367i \(-0.152282\pi\)
−0.842554 + 0.538612i \(0.818949\pi\)
\(108\) 0 0
\(109\) −341.000 + 590.629i −0.299650 + 0.519009i −0.976056 0.217520i \(-0.930203\pi\)
0.676406 + 0.736529i \(0.263537\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −370.000 −0.308024 −0.154012 0.988069i \(-0.549219\pi\)
−0.154012 + 0.988069i \(0.549219\pi\)
\(114\) 0 0
\(115\) −1200.00 + 2078.46i −0.973048 + 1.68537i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −302.500 523.945i −0.227273 0.393648i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3000.00 2.14663
\(126\) 0 0
\(127\) −160.000 −0.111793 −0.0558965 0.998437i \(-0.517802\pi\)
−0.0558965 + 0.998437i \(0.517802\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −150.000 259.808i −0.100042 0.173279i 0.811659 0.584131i \(-0.198565\pi\)
−0.911702 + 0.410852i \(0.865231\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 595.000 1030.57i 0.371053 0.642683i −0.618675 0.785647i \(-0.712330\pi\)
0.989728 + 0.142964i \(0.0456634\pi\)
\(138\) 0 0
\(139\) 2220.00 1.35466 0.677331 0.735679i \(-0.263137\pi\)
0.677331 + 0.735679i \(0.263137\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −968.000 + 1676.63i −0.566072 + 0.980465i
\(144\) 0 0
\(145\) 2180.00 + 3775.87i 1.24855 + 2.16254i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1207.00 + 2090.59i 0.663633 + 1.14945i 0.979654 + 0.200694i \(0.0643196\pi\)
−0.316021 + 0.948752i \(0.602347\pi\)
\(150\) 0 0
\(151\) −1028.00 + 1780.55i −0.554023 + 0.959596i 0.443956 + 0.896049i \(0.353575\pi\)
−0.997979 + 0.0635472i \(0.979759\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5600.00 −2.90195
\(156\) 0 0
\(157\) −530.000 + 917.987i −0.269418 + 0.466645i −0.968712 0.248189i \(-0.920165\pi\)
0.699294 + 0.714834i \(0.253498\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 990.000 + 1714.73i 0.475723 + 0.823976i 0.999613 0.0278098i \(-0.00885328\pi\)
−0.523891 + 0.851786i \(0.675520\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −488.000 −0.226123 −0.113062 0.993588i \(-0.536066\pi\)
−0.113062 + 0.993588i \(0.536066\pi\)
\(168\) 0 0
\(169\) −261.000 −0.118798
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1738.00 + 3010.30i 0.763802 + 1.32294i 0.940878 + 0.338746i \(0.110003\pi\)
−0.177076 + 0.984197i \(0.556664\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −42.0000 + 72.7461i −0.0175376 + 0.0303760i −0.874661 0.484735i \(-0.838916\pi\)
0.857123 + 0.515111i \(0.172249\pi\)
\(180\) 0 0
\(181\) 2180.00 0.895238 0.447619 0.894224i \(-0.352272\pi\)
0.447619 + 0.894224i \(0.352272\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 300.000 519.615i 0.119224 0.206502i
\(186\) 0 0
\(187\) −1584.00 2743.57i −0.619431 1.07289i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 348.000 + 602.754i 0.131835 + 0.228344i 0.924384 0.381464i \(-0.124580\pi\)
−0.792549 + 0.609808i \(0.791247\pi\)
\(192\) 0 0
\(193\) −1345.00 + 2329.61i −0.501633 + 0.868854i 0.498365 + 0.866967i \(0.333934\pi\)
−0.999998 + 0.00188695i \(0.999399\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5310.00 −1.92042 −0.960208 0.279287i \(-0.909902\pi\)
−0.960208 + 0.279287i \(0.909902\pi\)
\(198\) 0 0
\(199\) −1540.00 + 2667.36i −0.548581 + 0.950171i 0.449791 + 0.893134i \(0.351499\pi\)
−0.998372 + 0.0570369i \(0.981835\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1200.00 + 2078.46i 0.408837 + 0.708127i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4400.00 −1.45624
\(210\) 0 0
\(211\) −4.00000 −0.00130508 −0.000652539 1.00000i \(-0.500208\pi\)
−0.000652539 1.00000i \(0.500208\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2200.00 3810.51i −0.697855 1.20872i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1584.00 + 2743.57i −0.482133 + 0.835079i
\(222\) 0 0
\(223\) −2416.00 −0.725504 −0.362752 0.931886i \(-0.618163\pi\)
−0.362752 + 0.931886i \(0.618163\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2486.00 + 4305.88i −0.726879 + 1.25899i 0.231316 + 0.972879i \(0.425697\pi\)
−0.958196 + 0.286113i \(0.907637\pi\)
\(228\) 0 0
\(229\) 2230.00 + 3862.47i 0.643505 + 1.11458i 0.984645 + 0.174570i \(0.0558536\pi\)
−0.341140 + 0.940012i \(0.610813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2275.00 + 3940.42i 0.639658 + 1.10792i 0.985508 + 0.169630i \(0.0542572\pi\)
−0.345850 + 0.938290i \(0.612410\pi\)
\(234\) 0 0
\(235\) 880.000 1524.20i 0.244276 0.423099i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2112.00 0.571606 0.285803 0.958288i \(-0.407740\pi\)
0.285803 + 0.958288i \(0.407740\pi\)
\(240\) 0 0
\(241\) 2420.00 4191.56i 0.646829 1.12034i −0.337046 0.941488i \(-0.609428\pi\)
0.983876 0.178853i \(-0.0572388\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2200.00 + 3810.51i 0.566731 + 0.981608i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4340.00 1.09139 0.545694 0.837985i \(-0.316266\pi\)
0.545694 + 0.837985i \(0.316266\pi\)
\(252\) 0 0
\(253\) −5280.00 −1.31206
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1760.00 3048.41i −0.427182 0.739901i 0.569439 0.822033i \(-0.307160\pi\)
−0.996621 + 0.0821323i \(0.973827\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1280.00 + 2217.03i −0.300107 + 0.519801i −0.976160 0.217052i \(-0.930356\pi\)
0.676053 + 0.736853i \(0.263689\pi\)
\(264\) 0 0
\(265\) −2200.00 −0.509981
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3410.00 5906.29i 0.772905 1.33871i −0.163060 0.986616i \(-0.552136\pi\)
0.935965 0.352094i \(-0.114530\pi\)
\(270\) 0 0
\(271\) −1760.00 3048.41i −0.394511 0.683312i 0.598528 0.801102i \(-0.295753\pi\)
−0.993039 + 0.117789i \(0.962419\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6050.00 + 10478.9i 1.32665 + 2.29783i
\(276\) 0 0
\(277\) 4345.00 7525.76i 0.942476 1.63242i 0.181747 0.983345i \(-0.441825\pi\)
0.760728 0.649070i \(-0.224842\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3894.00 −0.826678 −0.413339 0.910577i \(-0.635638\pi\)
−0.413339 + 0.910577i \(0.635638\pi\)
\(282\) 0 0
\(283\) 3278.00 5677.66i 0.688540 1.19259i −0.283770 0.958892i \(-0.591585\pi\)
0.972310 0.233694i \(-0.0750815\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −135.500 234.693i −0.0275799 0.0477698i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2484.00 0.495279 0.247640 0.968852i \(-0.420345\pi\)
0.247640 + 0.968852i \(0.420345\pi\)
\(294\) 0 0
\(295\) −11600.0 −2.28942
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2640.00 + 4572.61i 0.510619 + 0.884418i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3800.00 + 6581.79i −0.713401 + 1.23565i
\(306\) 0 0
\(307\) 308.000 0.0572589 0.0286295 0.999590i \(-0.490886\pi\)
0.0286295 + 0.999590i \(0.490886\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 880.000 1524.20i 0.160451 0.277909i −0.774580 0.632476i \(-0.782039\pi\)
0.935030 + 0.354567i \(0.115372\pi\)
\(312\) 0 0
\(313\) −12.0000 20.7846i −0.00216703 0.00375340i 0.864940 0.501876i \(-0.167356\pi\)
−0.867107 + 0.498122i \(0.834023\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2445.00 4234.86i −0.433202 0.750327i 0.563945 0.825812i \(-0.309283\pi\)
−0.997147 + 0.0754850i \(0.975949\pi\)
\(318\) 0 0
\(319\) −4796.00 + 8306.92i −0.841769 + 1.45799i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7200.00 −1.24031
\(324\) 0 0
\(325\) 6050.00 10478.9i 1.03260 1.78851i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −4054.00 7021.73i −0.673196 1.16601i −0.976993 0.213273i \(-0.931588\pi\)
0.303796 0.952737i \(-0.401746\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −19600.0 −3.19660
\(336\) 0 0
\(337\) 2990.00 0.483311 0.241655 0.970362i \(-0.422310\pi\)
0.241655 + 0.970362i \(0.422310\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6160.00 10669.4i −0.978248 1.69438i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3930.00 + 6806.96i −0.607993 + 1.05307i 0.383578 + 0.923508i \(0.374692\pi\)
−0.991571 + 0.129566i \(0.958642\pi\)
\(348\) 0 0
\(349\) −6060.00 −0.929468 −0.464734 0.885450i \(-0.653850\pi\)
−0.464734 + 0.885450i \(0.653850\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1512.00 + 2618.86i −0.227976 + 0.394867i −0.957208 0.289400i \(-0.906544\pi\)
0.729232 + 0.684267i \(0.239878\pi\)
\(354\) 0 0
\(355\) −1120.00 1939.90i −0.167446 0.290025i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2948.00 + 5106.09i 0.433397 + 0.750665i 0.997163 0.0752688i \(-0.0239815\pi\)
−0.563766 + 0.825934i \(0.690648\pi\)
\(360\) 0 0
\(361\) −1570.50 + 2720.19i −0.228969 + 0.396586i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12800.0 −1.83557
\(366\) 0 0
\(367\) −1096.00 + 1898.33i −0.155888 + 0.270005i −0.933382 0.358885i \(-0.883157\pi\)
0.777494 + 0.628890i \(0.216490\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1705.00 + 2953.15i 0.236680 + 0.409941i 0.959760 0.280823i \(-0.0906074\pi\)
−0.723080 + 0.690765i \(0.757274\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9592.00 1.31038
\(378\) 0 0
\(379\) 5916.00 0.801806 0.400903 0.916120i \(-0.368696\pi\)
0.400903 + 0.916120i \(0.368696\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1020.00 + 1766.69i 0.136082 + 0.235702i 0.926010 0.377498i \(-0.123215\pi\)
−0.789928 + 0.613200i \(0.789882\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5889.00 10200.0i 0.767569 1.32947i −0.171309 0.985217i \(-0.554800\pi\)
0.938878 0.344250i \(-0.111867\pi\)
\(390\) 0 0
\(391\) −8640.00 −1.11750
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4880.00 8452.41i 0.621619 1.07668i
\(396\) 0 0
\(397\) −2354.00 4077.25i −0.297592 0.515444i 0.677993 0.735069i \(-0.262850\pi\)
−0.975584 + 0.219625i \(0.929517\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2937.00 5087.03i −0.365753 0.633502i 0.623144 0.782107i \(-0.285855\pi\)
−0.988897 + 0.148605i \(0.952522\pi\)
\(402\) 0 0
\(403\) −6160.00 + 10669.4i −0.761418 + 1.31881i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1320.00 0.160762
\(408\) 0 0
\(409\) −7020.00 + 12159.0i −0.848696 + 1.46998i 0.0336764 + 0.999433i \(0.489278\pi\)
−0.882372 + 0.470552i \(0.844055\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 6600.00 + 11431.5i 0.780678 + 1.35217i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7940.00 0.925762 0.462881 0.886420i \(-0.346816\pi\)
0.462881 + 0.886420i \(0.346816\pi\)
\(420\) 0 0
\(421\) 5214.00 0.603598 0.301799 0.953372i \(-0.402413\pi\)
0.301799 + 0.953372i \(0.402413\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9900.00 + 17147.3i 1.12993 + 1.95710i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5192.00 8992.81i 0.580255 1.00503i −0.415194 0.909733i \(-0.636286\pi\)
0.995449 0.0952980i \(-0.0303804\pi\)
\(432\) 0 0
\(433\) 6520.00 0.723629 0.361814 0.932250i \(-0.382157\pi\)
0.361814 + 0.932250i \(0.382157\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6000.00 + 10392.3i −0.656794 + 1.13760i
\(438\) 0 0
\(439\) 5760.00 + 9976.61i 0.626218 + 1.08464i 0.988304 + 0.152497i \(0.0487314\pi\)
−0.362086 + 0.932145i \(0.617935\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6690.00 + 11587.4i 0.717498 + 1.24274i 0.961988 + 0.273091i \(0.0880460\pi\)
−0.244491 + 0.969652i \(0.578621\pi\)
\(444\) 0 0
\(445\) 3200.00 5542.56i 0.340887 0.590433i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4098.00 −0.430727 −0.215364 0.976534i \(-0.569094\pi\)
−0.215364 + 0.976534i \(0.569094\pi\)
\(450\) 0 0
\(451\) −2640.00 + 4572.61i −0.275638 + 0.477419i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8195.00 + 14194.2i 0.838831 + 1.45290i 0.890872 + 0.454254i \(0.150094\pi\)
−0.0520411 + 0.998645i \(0.516573\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9540.00 −0.963822 −0.481911 0.876220i \(-0.660057\pi\)
−0.481911 + 0.876220i \(0.660057\pi\)
\(462\) 0 0
\(463\) −8920.00 −0.895351 −0.447676 0.894196i \(-0.647748\pi\)
−0.447676 + 0.894196i \(0.647748\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4214.00 7298.86i −0.417560 0.723236i 0.578133 0.815942i \(-0.303781\pi\)
−0.995693 + 0.0927068i \(0.970448\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4840.00 8383.13i 0.470494 0.814919i
\(474\) 0 0
\(475\) 27500.0 2.65639
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7260.00 + 12574.7i −0.692522 + 1.19948i 0.278487 + 0.960440i \(0.410167\pi\)
−0.971009 + 0.239043i \(0.923166\pi\)
\(480\) 0 0
\(481\) −660.000 1143.15i −0.0625643 0.108364i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2480.00 4295.49i −0.232188 0.402161i
\(486\) 0 0
\(487\) 5260.00 9110.59i 0.489432 0.847721i −0.510494 0.859881i \(-0.670537\pi\)
0.999926 + 0.0121603i \(0.00387083\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5436.00 0.499640 0.249820 0.968292i \(-0.419629\pi\)
0.249820 + 0.968292i \(0.419629\pi\)
\(492\) 0 0
\(493\) −7848.00 + 13593.1i −0.716950 + 1.24179i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −9174.00 15889.8i −0.823015 1.42550i −0.903427 0.428743i \(-0.858957\pi\)
0.0804114 0.996762i \(-0.474377\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 20944.0 1.85655 0.928277 0.371889i \(-0.121290\pi\)
0.928277 + 0.371889i \(0.121290\pi\)
\(504\) 0 0
\(505\) −4400.00 −0.387718
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 130.000 + 225.167i 0.0113205 + 0.0196077i 0.871630 0.490164i \(-0.163063\pi\)
−0.860310 + 0.509772i \(0.829730\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −13360.0 + 23140.2i −1.14313 + 1.97996i
\(516\) 0 0
\(517\) 3872.00 0.329382
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7300.00 12644.0i 0.613856 1.06323i −0.376728 0.926324i \(-0.622951\pi\)
0.990584 0.136905i \(-0.0437157\pi\)
\(522\) 0 0
\(523\) −3410.00 5906.29i −0.285103 0.493813i 0.687531 0.726155i \(-0.258694\pi\)
−0.972634 + 0.232342i \(0.925361\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10080.0 17459.1i −0.833191 1.44313i
\(528\) 0 0
\(529\) −1116.50 + 1933.83i −0.0917646 + 0.158941i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5280.00 0.429085
\(534\) 0 0
\(535\) 1000.00 1732.05i 0.0808108 0.139968i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −6083.00 10536.1i −0.483417 0.837303i 0.516402 0.856347i \(-0.327271\pi\)
−0.999819 + 0.0190437i \(0.993938\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 13640.0 1.07206
\(546\) 0 0
\(547\) 22660.0 1.77125 0.885623 0.464405i \(-0.153732\pi\)
0.885623 + 0.464405i \(0.153732\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 10900.0 + 18879.4i 0.842751 + 1.45969i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4245.00 + 7352.56i −0.322920 + 0.559314i −0.981089 0.193556i \(-0.937998\pi\)
0.658169 + 0.752870i \(0.271331\pi\)
\(558\) 0 0
\(559\) −9680.00 −0.732416
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7150.00 12384.2i 0.535234 0.927052i −0.463918 0.885878i \(-0.653557\pi\)
0.999152 0.0411740i \(-0.0131098\pi\)
\(564\) 0 0
\(565\) 3700.00 + 6408.59i 0.275505 + 0.477188i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9147.00 + 15843.1i 0.673923 + 1.16727i 0.976782 + 0.214234i \(0.0687254\pi\)
−0.302859 + 0.953035i \(0.597941\pi\)
\(570\) 0 0
\(571\) 7194.00 12460.4i 0.527250 0.913223i −0.472246 0.881467i \(-0.656557\pi\)
0.999496 0.0317563i \(-0.0101101\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 33000.0 2.39338
\(576\) 0 0
\(577\) −12616.0 + 21851.6i −0.910244 + 1.57659i −0.0965256 + 0.995331i \(0.530773\pi\)
−0.813719 + 0.581259i \(0.802560\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2420.00 4191.56i −0.171915 0.297765i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16060.0 −1.12925 −0.564623 0.825349i \(-0.690978\pi\)
−0.564623 + 0.825349i \(0.690978\pi\)
\(588\) 0 0
\(589\) −28000.0 −1.95878
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11928.0 20659.9i −0.826011 1.43069i −0.901145 0.433519i \(-0.857272\pi\)
0.0751340 0.997173i \(-0.476062\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1584.00 2743.57i 0.108048 0.187144i −0.806932 0.590645i \(-0.798873\pi\)
0.914979 + 0.403501i \(0.132207\pi\)
\(600\) 0 0
\(601\) −12320.0 −0.836179 −0.418089 0.908406i \(-0.637300\pi\)
−0.418089 + 0.908406i \(0.637300\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6050.00 + 10478.9i −0.406558 + 0.704179i
\(606\) 0 0
\(607\) 4464.00 + 7731.87i 0.298498 + 0.517013i 0.975792 0.218698i \(-0.0701811\pi\)
−0.677295 + 0.735712i \(0.736848\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1936.00 3353.25i −0.128187 0.222026i
\(612\) 0 0
\(613\) 2255.00 3905.77i 0.148578 0.257345i −0.782124 0.623123i \(-0.785864\pi\)
0.930702 + 0.365778i \(0.119197\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5830.00 −0.380400 −0.190200 0.981745i \(-0.560914\pi\)
−0.190200 + 0.981745i \(0.560914\pi\)
\(618\) 0 0
\(619\) 12230.0 21183.0i 0.794128 1.37547i −0.129263 0.991610i \(-0.541261\pi\)
0.923391 0.383860i \(-0.125405\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12812.5 22191.9i −0.820000 1.42028i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2160.00 0.136923
\(630\) 0 0
\(631\) 15216.0 0.959967 0.479984 0.877277i \(-0.340643\pi\)
0.479984 + 0.877277i \(0.340643\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1600.00 + 2771.28i 0.0999907 + 0.173189i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6239.00 10806.3i 0.384439 0.665869i −0.607252 0.794509i \(-0.707728\pi\)
0.991691 + 0.128641i \(0.0410614\pi\)
\(642\) 0 0
\(643\) 15996.0 0.981059 0.490529 0.871425i \(-0.336803\pi\)
0.490529 + 0.871425i \(0.336803\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2940.00 + 5092.23i −0.178645 + 0.309422i −0.941417 0.337246i \(-0.890505\pi\)
0.762772 + 0.646668i \(0.223838\pi\)
\(648\) 0 0
\(649\) −12760.0 22101.0i −0.771762 1.33673i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3755.00 6503.85i −0.225030 0.389763i 0.731299 0.682058i \(-0.238915\pi\)
−0.956328 + 0.292294i \(0.905581\pi\)
\(654\) 0 0
\(655\) −3000.00 + 5196.15i −0.178961 + 0.309970i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 16508.0 0.975812 0.487906 0.872896i \(-0.337761\pi\)
0.487906 + 0.872896i \(0.337761\pi\)
\(660\) 0 0
\(661\) 610.000 1056.55i 0.0358945 0.0621711i −0.847520 0.530763i \(-0.821905\pi\)
0.883415 + 0.468592i \(0.155239\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 13080.0 + 22655.2i 0.759310 + 1.31516i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −16720.0 −0.961950
\(672\) 0 0
\(673\) −13090.0 −0.749751 −0.374875 0.927075i \(-0.622315\pi\)
−0.374875 + 0.927075i \(0.622315\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7554.00 + 13083.9i 0.428839 + 0.742770i 0.996770 0.0803053i \(-0.0255895\pi\)
−0.567932 + 0.823076i \(0.692256\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 770.000 1333.68i 0.0431380 0.0747171i −0.843650 0.536893i \(-0.819598\pi\)
0.886788 + 0.462176i \(0.152931\pi\)
\(684\) 0 0
\(685\) −23800.0 −1.32752
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2420.00 + 4191.56i −0.133809 + 0.231765i
\(690\) 0 0
\(691\) −2890.00 5005.63i −0.159104 0.275576i 0.775442 0.631419i \(-0.217527\pi\)
−0.934546 + 0.355843i \(0.884194\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −22200.0 38451.5i −1.21165 2.09863i
\(696\) 0 0
\(697\) −4320.00 + 7482.46i −0.234766 + 0.406626i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 10406.0 0.560669 0.280335 0.959902i \(-0.409555\pi\)
0.280335 + 0.959902i \(0.409555\pi\)
\(702\) 0 0
\(703\) 1500.00 2598.08i 0.0804745 0.139386i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −14321.0 24804.7i −0.758585 1.31391i −0.943572 0.331166i \(-0.892558\pi\)
0.184988 0.982741i \(-0.440775\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −33600.0 −1.76484
\(714\) 0 0
\(715\) 38720.0 2.02524
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3780.00 + 6547.15i 0.196064 + 0.339593i 0.947249 0.320499i \(-0.103851\pi\)
−0.751185 + 0.660092i \(0.770517\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 29975.0 51918.2i 1.53551 2.65958i
\(726\) 0 0
\(727\) −20360.0 −1.03867 −0.519333 0.854572i \(-0.673820\pi\)
−0.519333 + 0.854572i \(0.673820\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 7920.00 13717.8i 0.400727 0.694080i
\(732\) 0 0
\(733\) −11638.0 20157.6i −0.586438 1.01574i −0.994694 0.102874i \(-0.967196\pi\)
0.408256 0.912867i \(-0.366137\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21560.0 37343.0i −1.07758 1.86641i
\(738\) 0 0
\(739\) −1586.00 + 2747.03i −0.0789472 + 0.136740i −0.902796 0.430069i \(-0.858489\pi\)
0.823849 + 0.566810i \(0.191823\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6600.00 0.325882 0.162941 0.986636i \(-0.447902\pi\)
0.162941 + 0.986636i \(0.447902\pi\)
\(744\) 0 0
\(745\) 24140.0 41811.7i 1.18714 2.05619i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8208.00 + 14216.7i 0.398820 + 0.690777i 0.993581 0.113126i \(-0.0360863\pi\)
−0.594760 + 0.803903i \(0.702753\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 41120.0 1.98213
\(756\) 0 0
\(757\) 36850.0 1.76927 0.884634 0.466286i \(-0.154408\pi\)
0.884634 + 0.466286i \(0.154408\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −18700.0 32389.4i −0.890768 1.54286i −0.838956 0.544199i \(-0.816834\pi\)
−0.0518116 0.998657i \(-0.516500\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12760.0 + 22101.0i −0.600700 + 1.04044i
\(768\) 0 0
\(769\) −5720.00 −0.268229 −0.134115 0.990966i \(-0.542819\pi\)
−0.134115 + 0.990966i \(0.542819\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3678.00 6370.48i 0.171136 0.296417i −0.767681 0.640832i \(-0.778589\pi\)
0.938817 + 0.344415i \(0.111923\pi\)
\(774\) 0 0
\(775\) 38500.0 + 66684.0i 1.78447 + 3.09079i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6000.00 + 10392.3i 0.275959 + 0.477976i
\(780\) 0 0
\(781\) 2464.00 4267.77i 0.112892 0.195535i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 21200.0 0.963899
\(786\) 0 0
\(787\) 19286.0 33404.3i 0.873535 1.51301i 0.0152188 0.999884i \(-0.495156\pi\)
0.858316 0.513122i \(-0.171511\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 8360.00 + 14479.9i 0.374366 + 0.648421i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7812.00 −0.347196 −0.173598 0.984817i \(-0.555539\pi\)
−0.173598 + 0.984817i \(0.555539\pi\)
\(798\) 0 0
\(799\) 6336.00 0.280540
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −14080.0 24387.3i −0.618770 1.07174i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 22509.0 38986.7i 0.978213 1.69431i 0.309316 0.950959i \(-0.399900\pi\)
0.668897 0.743355i \(-0.266767\pi\)
\(810\) 0 0
\(811\) 2740.00 0.118637 0.0593184 0.998239i \(-0.481107\pi\)
0.0593184 + 0.998239i \(0.481107\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 19800.0 34294.6i 0.850998 1.47397i
\(816\) 0 0
\(817\) −11000.0 19052.6i −0.471042 0.815869i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 727.000 + 1259.20i 0.0309044 + 0.0535279i 0.881064 0.472997i \(-0.156828\pi\)
−0.850160 + 0.526525i \(0.823495\pi\)
\(822\) 0 0
\(823\) −18560.0 + 32146.9i −0.786101 + 1.36157i 0.142239 + 0.989832i \(0.454570\pi\)
−0.928339 + 0.371734i \(0.878763\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7260.00 0.305266 0.152633 0.988283i \(-0.451225\pi\)
0.152633 + 0.988283i \(0.451225\pi\)
\(828\) 0 0
\(829\) 5570.00 9647.52i 0.233358 0.404189i −0.725436 0.688290i \(-0.758362\pi\)
0.958794 + 0.284101i \(0.0916951\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 4880.00 + 8452.41i 0.202251 + 0.350309i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −8760.00 −0.360463 −0.180232 0.983624i \(-0.557685\pi\)
−0.180232 + 0.983624i \(0.557685\pi\)
\(840\) 0 0
\(841\) 23135.0 0.948583
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2610.00 + 4520.65i 0.106256 + 0.184042i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1800.00 3117.69i 0.0725067 0.125585i
\(852\) 0 0
\(853\) 820.000 0.0329147 0.0164574 0.999865i \(-0.494761\pi\)
0.0164574 + 0.999865i \(0.494761\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −660.000 + 1143.15i −0.0263071 + 0.0455652i −0.878879 0.477044i \(-0.841708\pi\)
0.852572 + 0.522610i \(0.175041\pi\)
\(858\) 0 0
\(859\) −21390.0 37048.6i −0.849613 1.47157i −0.881554 0.472083i \(-0.843502\pi\)
0.0319414 0.999490i \(-0.489831\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 14940.0 + 25876.8i 0.589297 + 1.02069i 0.994325 + 0.106388i \(0.0339286\pi\)
−0.405027 + 0.914305i \(0.632738\pi\)
\(864\) 0 0
\(865\) 34760.0 60206.1i 1.36633 2.36655i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 21472.0 0.838191
\(870\) 0 0
\(871\) −21560.0 + 37343.0i −0.838729 + 1.45272i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −14085.0 24395.9i −0.542322 0.939330i −0.998770 0.0495796i \(-0.984212\pi\)
0.456448 0.889750i \(-0.349121\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −20800.0 −0.795425 −0.397713 0.917510i \(-0.630196\pi\)
−0.397713 + 0.917510i \(0.630196\pi\)
\(882\) 0 0
\(883\) −20900.0 −0.796536 −0.398268 0.917269i \(-0.630389\pi\)
−0.398268 + 0.917269i \(0.630389\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 5820.00 + 10080.5i 0.220312 + 0.381591i 0.954903 0.296919i \(-0.0959592\pi\)
−0.734591 + 0.678510i \(0.762626\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4400.00 7621.02i 0.164883 0.285585i
\(894\) 0 0
\(895\) 1680.00 0.0627444
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −30520.0 + 52862.2i −1.13226 + 1.96113i
\(900\) 0 0
\(901\) −3960.00 6858.92i −0.146423 0.253611i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −21800.0 37758.7i −0.800725 1.38690i
\(906\) 0 0
\(907\) 18790.0 32545.2i 0.687885 1.19145i −0.284636 0.958636i \(-0.591873\pi\)
0.972521 0.232816i \(-0.0747940\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 40832.0 1.48499 0.742494 0.669852i \(-0.233643\pi\)
0.742494 + 0.669852i \(0.233643\pi\)
\(912\) 0 0
\(913\) −14520.0 + 25149.4i −0.526333 + 0.911635i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −21384.0 37038.2i −0.767566 1.32946i −0.938879 0.344247i \(-0.888134\pi\)
0.171313 0.985217i \(-0.445199\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4928.00 −0.175739
\(924\) 0 0
\(925\) −8250.00 −0.293252
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −4380.00 7586.38i −0.154686 0.267924i 0.778259 0.627944i \(-0.216103\pi\)
−0.932945 + 0.360020i \(0.882770\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −31680.0 + 54871.4i −1.10807 + 1.91924i
\(936\) 0 0
\(937\) 49632.0 1.73042 0.865212 0.501407i \(-0.167184\pi\)
0.865212 + 0.501407i \(0.167184\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −18450.0 + 31956.3i −0.639163 + 1.10706i 0.346453 + 0.938067i \(0.387386\pi\)
−0.985617 + 0.168996i \(0.945947\pi\)
\(942\) 0 0
\(943\) 7200.00 + 12470.8i 0.248637 + 0.430651i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −16670.0 28873.3i −0.572019 0.990766i −0.996358 0.0852631i \(-0.972827\pi\)
0.424339 0.905503i \(-0.360506\pi\)
\(948\) 0 0
\(949\) −14080.0 + 24387.3i −0.481619 + 0.834188i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5610.00 −0.190688 −0.0953440 0.995444i \(-0.530395\pi\)
−0.0953440 + 0.995444i \(0.530395\pi\)
\(954\) 0 0
\(955\) 6960.00 12055.1i 0.235833 0.408474i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −24304.5 42096.6i −0.815834 1.41307i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 53800.0 1.79470
\(966\) 0 0
\(967\) −25160.0 −0.836702 −0.418351 0.908285i \(-0.637392\pi\)
−0.418351 + 0.908285i \(0.637392\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 530.000 + 917.987i 0.0175165 + 0.0303394i 0.874651 0.484754i \(-0.161091\pi\)
−0.857134 + 0.515093i \(0.827757\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19385.0 + 33575.8i −0.634781 + 1.09947i 0.351780 + 0.936083i \(0.385576\pi\)
−0.986561 + 0.163390i \(0.947757\pi\)
\(978\) 0 0
\(979\) 14080.0 0.459651
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −12148.0 + 21041.0i −0.394162 + 0.682708i −0.992994 0.118166i \(-0.962298\pi\)
0.598832 + 0.800875i \(0.295632\pi\)
\(984\) 0 0
\(985\) 53100.0 + 91971.9i 1.71767 + 2.97509i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −13200.0 22863.1i −0.424404 0.735089i
\(990\) 0 0
\(991\) 836.000 1447.99i 0.0267976 0.0464148i −0.852316 0.523028i \(-0.824802\pi\)
0.879113 + 0.476613i \(0.158136\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 61600.0 1.96266
\(996\) 0 0
\(997\) −22814.0 + 39515.0i −0.724701 + 1.25522i 0.234396 + 0.972141i \(0.424689\pi\)
−0.959097 + 0.283077i \(0.908645\pi\)
\(998\) 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 1764.4.k.a.361.1 2
3.2 odd 2 196.4.e.e.165.1 2
7.2 even 3 inner 1764.4.k.a.1549.1 2
7.3 odd 6 1764.4.a.a.1.1 1
7.4 even 3 1764.4.a.m.1.1 1
7.5 odd 6 1764.4.k.p.1549.1 2
7.6 odd 2 1764.4.k.p.361.1 2
21.2 odd 6 196.4.e.e.177.1 2
21.5 even 6 196.4.e.b.177.1 2
21.11 odd 6 196.4.a.a.1.1 1
21.17 even 6 196.4.a.c.1.1 yes 1
21.20 even 2 196.4.e.b.165.1 2
84.11 even 6 784.4.a.m.1.1 1
84.59 odd 6 784.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
196.4.a.a.1.1 1 21.11 odd 6
196.4.a.c.1.1 yes 1 21.17 even 6
196.4.e.b.165.1 2 21.20 even 2
196.4.e.b.177.1 2 21.5 even 6
196.4.e.e.165.1 2 3.2 odd 2
196.4.e.e.177.1 2 21.2 odd 6
784.4.a.f.1.1 1 84.59 odd 6
784.4.a.m.1.1 1 84.11 even 6
1764.4.a.a.1.1 1 7.3 odd 6
1764.4.a.m.1.1 1 7.4 even 3
1764.4.k.a.361.1 2 1.1 even 1 trivial
1764.4.k.a.1549.1 2 7.2 even 3 inner
1764.4.k.p.361.1 2 7.6 odd 2
1764.4.k.p.1549.1 2 7.5 odd 6