Properties

Label 1764.4.k.p.1549.1
Level $1764$
Weight $4$
Character 1764.1549
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 1549.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1549
Dual form 1764.4.k.p.361.1

$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

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

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 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 22.0000 + 38.1051i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 0 0
\(13\) 44.0000 0.938723 0.469362 0.883006i \(-0.344484\pi\)
0.469362 + 0.883006i \(0.344484\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −36.0000 62.3538i −0.513605 0.889590i −0.999875 0.0157814i \(-0.994976\pi\)
0.486271 0.873808i \(-0.338357\pi\)
\(18\) 0 0
\(19\) 50.0000 86.6025i 0.603726 1.04568i −0.388526 0.921438i \(-0.627016\pi\)
0.992251 0.124246i \(-0.0396511\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −60.0000 + 103.923i −0.543951 + 0.942150i 0.454721 + 0.890634i \(0.349739\pi\)
−0.998672 + 0.0515165i \(0.983595\pi\)
\(24\) 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 −0.912080 0.410012i \(-0.865525\pi\)
0.100960 0.994891i \(-0.467809\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 15.0000 25.9808i 0.0666482 0.115438i −0.830776 0.556607i \(-0.812103\pi\)
0.897424 + 0.441169i \(0.145436\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 120.000 0.457094 0.228547 0.973533i \(-0.426603\pi\)
0.228547 + 0.973533i \(0.426603\pi\)
\(42\) 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 \(-0.876936\pi\)
0.789636 + 0.613576i \(0.210270\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 55.0000 + 95.2628i 0.142544 + 0.246893i 0.928454 0.371448i \(-0.121138\pi\)
−0.785910 + 0.618341i \(0.787805\pi\)
\(54\) 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 −0.985452 0.169955i \(-0.945638\pi\)
0.345540 0.938404i \(-0.387696\pi\)
\(60\) 0 0
\(61\) 190.000 329.090i 0.398803 0.690748i −0.594775 0.803892i \(-0.702759\pi\)
0.993579 + 0.113144i \(0.0360923\pi\)
\(62\) 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 0.835677 + 0.549221i \(0.185076\pi\)
0.0578010 + 0.998328i \(0.481591\pi\)
\(68\) 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 −0.999885 0.0151432i \(-0.995180\pi\)
0.486828 0.873498i \(-0.338154\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 244.000 422.620i 0.347496 0.601880i −0.638308 0.769781i \(-0.720366\pi\)
0.985804 + 0.167901i \(0.0536989\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 660.000 0.872824 0.436412 0.899747i \(-0.356249\pi\)
0.436412 + 0.899747i \(0.356249\pi\)
\(84\) 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 \(-0.894364\pi\)
0.754875 + 0.655869i \(0.227697\pi\)
\(90\) 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 \(-0.541433\pi\)
−0.129797 + 0.991541i \(0.541433\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −110.000 190.526i −0.108370 0.187703i 0.806740 0.590907i \(-0.201230\pi\)
−0.915110 + 0.403204i \(0.867897\pi\)
\(102\) 0 0
\(103\) 668.000 1157.01i 0.639029 1.10683i −0.346617 0.938007i \(-0.612670\pi\)
0.985646 0.168824i \(-0.0539970\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 50.0000 86.6025i 0.0451746 0.0782447i −0.842554 0.538612i \(-0.818949\pi\)
0.887729 + 0.460367i \(0.152282\pi\)
\(108\) 0 0
\(109\) −341.000 590.629i −0.299650 0.519009i 0.676406 0.736529i \(-0.263537\pi\)
−0.976056 + 0.217520i \(0.930203\pi\)
\(110\) 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 \(-0.801435\pi\)
0.911702 + 0.410852i \(0.134769\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 595.000 + 1030.57i 0.371053 + 0.642683i 0.989728 0.142964i \(-0.0456634\pi\)
−0.618675 + 0.785647i \(0.712330\pi\)
\(138\) 0 0
\(139\) −2220.00 −1.35466 −0.677331 0.735679i \(-0.736863\pi\)
−0.677331 + 0.735679i \(0.736863\pi\)
\(140\) 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 −0.316021 0.948752i \(-0.602347\pi\)
0.979654 0.200694i \(-0.0643196\pi\)
\(150\) 0 0
\(151\) −1028.00 1780.55i −0.554023 0.959596i −0.997979 0.0635472i \(-0.979759\pi\)
0.443956 0.896049i \(-0.353575\pi\)
\(152\) 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 \(-0.0798354\pi\)
−0.699294 + 0.714834i \(0.746502\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 990.000 1714.73i 0.475723 0.823976i −0.523891 0.851786i \(-0.675520\pi\)
0.999613 + 0.0278098i \(0.00885328\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 488.000 0.226123 0.113062 0.993588i \(-0.463934\pi\)
0.113062 + 0.993588i \(0.463934\pi\)
\(168\) 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 0.177076 + 0.984197i \(0.443336\pi\)
−0.940878 + 0.338746i \(0.889997\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −42.0000 72.7461i −0.0175376 0.0303760i 0.857123 0.515111i \(-0.172249\pi\)
−0.874661 + 0.484735i \(0.838916\pi\)
\(180\) 0 0
\(181\) −2180.00 −0.895238 −0.447619 0.894224i \(-0.647728\pi\)
−0.447619 + 0.894224i \(0.647728\pi\)
\(182\) 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 −0.792549 0.609808i \(-0.791247\pi\)
0.924384 + 0.381464i \(0.124580\pi\)
\(192\) 0 0
\(193\) −1345.00 2329.61i −0.501633 0.868854i −0.999998 0.00188695i \(-0.999399\pi\)
0.498365 0.866967i \(-0.333934\pi\)
\(194\) 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 0.998372 + 0.0570369i \(0.0181653\pi\)
−0.449791 + 0.893134i \(0.648501\pi\)
\(200\) 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 \(-0.381837\pi\)
0.362752 + 0.931886i \(0.381837\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2486.00 + 4305.88i 0.726879 + 1.25899i 0.958196 + 0.286113i \(0.0923634\pi\)
−0.231316 + 0.972879i \(0.574303\pi\)
\(228\) 0 0
\(229\) −2230.00 + 3862.47i −0.643505 + 1.11458i 0.341140 + 0.940012i \(0.389187\pi\)
−0.984645 + 0.174570i \(0.944146\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2275.00 3940.42i 0.639658 1.10792i −0.345850 0.938290i \(-0.612410\pi\)
0.985508 0.169630i \(-0.0542572\pi\)
\(234\) 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 −0.983876 0.178853i \(-0.942761\pi\)
0.337046 0.941488i \(-0.390572\pi\)
\(242\) 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 \(-0.683734\pi\)
−0.545694 + 0.837985i \(0.683734\pi\)
\(252\) 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 \(-0.692840\pi\)
0.996621 + 0.0821323i \(0.0261730\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1280.00 2217.03i −0.300107 0.519801i 0.676053 0.736853i \(-0.263689\pi\)
−0.976160 + 0.217052i \(0.930356\pi\)
\(264\) 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 −0.935965 0.352094i \(-0.885470\pi\)
0.163060 0.986616i \(-0.447864\pi\)
\(270\) 0 0
\(271\) 1760.00 3048.41i 0.394511 0.683312i −0.598528 0.801102i \(-0.704247\pi\)
0.993039 + 0.117789i \(0.0375808\pi\)
\(272\) 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 0.760728 + 0.649070i \(0.224842\pi\)
0.181747 + 0.983345i \(0.441825\pi\)
\(278\) 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 −0.972310 0.233694i \(-0.924919\pi\)
0.283770 0.958892i \(-0.408415\pi\)
\(284\) 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 \(-0.579655\pi\)
−0.247640 + 0.968852i \(0.579655\pi\)
\(294\) 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 \(-0.509114\pi\)
−0.0286295 + 0.999590i \(0.509114\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −880.000 1524.20i −0.160451 0.277909i 0.774580 0.632476i \(-0.217961\pi\)
−0.935030 + 0.354567i \(0.884628\pi\)
\(312\) 0 0
\(313\) 12.0000 20.7846i 0.00216703 0.00375340i −0.864940 0.501876i \(-0.832644\pi\)
0.867107 + 0.498122i \(0.165977\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2445.00 + 4234.86i −0.433202 + 0.750327i −0.997147 0.0754850i \(-0.975949\pi\)
0.563945 + 0.825812i \(0.309283\pi\)
\(318\) 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 0.303796 + 0.952737i \(0.401746\pi\)
−0.976993 + 0.213273i \(0.931588\pi\)
\(332\) 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 −0.991571 0.129566i \(-0.958642\pi\)
0.383578 0.923508i \(-0.374692\pi\)
\(348\) 0 0
\(349\) 6060.00 0.929468 0.464734 0.885450i \(-0.346150\pi\)
0.464734 + 0.885450i \(0.346150\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1512.00 + 2618.86i 0.227976 + 0.394867i 0.957208 0.289400i \(-0.0934558\pi\)
−0.729232 + 0.684267i \(0.760122\pi\)
\(354\) 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 −0.563766 0.825934i \(-0.690648\pi\)
0.997163 + 0.0752688i \(0.0239815\pi\)
\(360\) 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 \(-0.116843\pi\)
−0.777494 + 0.628890i \(0.783510\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1705.00 2953.15i 0.236680 0.409941i −0.723080 0.690765i \(-0.757274\pi\)
0.959760 + 0.280823i \(0.0906074\pi\)
\(374\) 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 \(-0.876785\pi\)
0.789928 + 0.613200i \(0.210118\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5889.00 + 10200.0i 0.767569 + 1.32947i 0.938878 + 0.344250i \(0.111867\pi\)
−0.171309 + 0.985217i \(0.554800\pi\)
\(390\) 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 \(-0.737150\pi\)
0.975584 + 0.219625i \(0.0704833\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2937.00 + 5087.03i −0.365753 + 0.633502i −0.988897 0.148605i \(-0.952522\pi\)
0.623144 + 0.782107i \(0.285855\pi\)
\(402\) 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 0.882372 + 0.470552i \(0.155945\pi\)
−0.0336764 + 0.999433i \(0.510722\pi\)
\(410\) 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 \(-0.653184\pi\)
−0.462881 + 0.886420i \(0.653184\pi\)
\(420\) 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 0.995449 + 0.0952980i \(0.0303804\pi\)
−0.415194 + 0.909733i \(0.636286\pi\)
\(432\) 0 0
\(433\) −6520.00 −0.723629 −0.361814 0.932250i \(-0.617843\pi\)
−0.361814 + 0.932250i \(0.617843\pi\)
\(434\) 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 0.362086 + 0.932145i \(0.382065\pi\)
−0.988304 + 0.152497i \(0.951269\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6690.00 11587.4i 0.717498 1.24274i −0.244491 0.969652i \(-0.578621\pi\)
0.961988 0.273091i \(-0.0880460\pi\)
\(444\) 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 −0.0520411 0.998645i \(-0.516573\pi\)
0.890872 0.454254i \(-0.150094\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9540.00 0.963822 0.481911 0.876220i \(-0.339943\pi\)
0.481911 + 0.876220i \(0.339943\pi\)
\(462\) 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 \(-0.696219\pi\)
0.995693 + 0.0927068i \(0.0295519\pi\)
\(468\) 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 0.971009 + 0.239043i \(0.0768336\pi\)
−0.278487 + 0.960440i \(0.589833\pi\)
\(480\) 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 0.999926 0.0121603i \(-0.00387083\pi\)
−0.510494 + 0.859881i \(0.670537\pi\)
\(488\) 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 0.0804114 + 0.996762i \(0.474377\pi\)
−0.903427 + 0.428743i \(0.858957\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −20944.0 −1.85655 −0.928277 0.371889i \(-0.878710\pi\)
−0.928277 + 0.371889i \(0.878710\pi\)
\(504\) 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 \(-0.836937\pi\)
0.860310 + 0.509772i \(0.170270\pi\)
\(510\) 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 −0.990584 0.136905i \(-0.956284\pi\)
0.376728 0.926324i \(-0.377049\pi\)
\(522\) 0 0
\(523\) 3410.00 5906.29i 0.285103 0.493813i −0.687531 0.726155i \(-0.741306\pi\)
0.972634 + 0.232342i \(0.0746388\pi\)
\(524\) 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 −0.999819 0.0190437i \(-0.993938\pi\)
0.516402 + 0.856347i \(0.327271\pi\)
\(542\) 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 0.658169 0.752870i \(-0.271331\pi\)
−0.981089 + 0.193556i \(0.937998\pi\)
\(558\) 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 −0.999152 0.0411740i \(-0.986890\pi\)
0.463918 0.885878i \(-0.346443\pi\)
\(564\) 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 −0.302859 0.953035i \(-0.597941\pi\)
0.976782 0.214234i \(-0.0687254\pi\)
\(570\) 0 0
\(571\) 7194.00 + 12460.4i 0.527250 + 0.913223i 0.999496 + 0.0317563i \(0.0101101\pi\)
−0.472246 + 0.881467i \(0.656557\pi\)
\(572\) 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 0.813719 + 0.581259i \(0.197440\pi\)
0.0965256 + 0.995331i \(0.469227\pi\)
\(578\) 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 \(-0.309022\pi\)
0.564623 + 0.825349i \(0.309022\pi\)
\(588\) 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 −0.0751340 0.997173i \(-0.523938\pi\)
0.901145 0.433519i \(-0.142728\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1584.00 + 2743.57i 0.108048 + 0.187144i 0.914979 0.403501i \(-0.132207\pi\)
−0.806932 + 0.590645i \(0.798873\pi\)
\(600\) 0 0
\(601\) 12320.0 0.836179 0.418089 0.908406i \(-0.362700\pi\)
0.418089 + 0.908406i \(0.362700\pi\)
\(602\) 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 \(-0.929819\pi\)
0.677295 + 0.735712i \(0.263152\pi\)
\(608\) 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 0.930702 0.365778i \(-0.119197\pi\)
−0.782124 + 0.623123i \(0.785864\pi\)
\(614\) 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 −0.923391 0.383860i \(-0.874595\pi\)
0.129263 0.991610i \(-0.458739\pi\)
\(620\) 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 0.991691 0.128641i \(-0.0410614\pi\)
−0.607252 + 0.794509i \(0.707728\pi\)
\(642\) 0 0
\(643\) −15996.0 −0.981059 −0.490529 0.871425i \(-0.663197\pi\)
−0.490529 + 0.871425i \(0.663197\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2940.00 + 5092.23i 0.178645 + 0.309422i 0.941417 0.337246i \(-0.109495\pi\)
−0.762772 + 0.646668i \(0.776162\pi\)
\(648\) 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 −0.956328 0.292294i \(-0.905581\pi\)
0.731299 + 0.682058i \(0.238915\pi\)
\(654\) 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 \(-0.178095\pi\)
−0.883415 + 0.468592i \(0.844761\pi\)
\(662\) 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 \(-0.974410\pi\)
0.567932 + 0.823076i \(0.307744\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 770.000 + 1333.68i 0.0431380 + 0.0747171i 0.886788 0.462176i \(-0.152931\pi\)
−0.843650 + 0.536893i \(0.819598\pi\)
\(684\) 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 \(-0.782473\pi\)
0.934546 + 0.355843i \(0.115806\pi\)
\(692\) 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 0.184988 + 0.982741i \(0.440775\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(710\) 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 \(-0.896149\pi\)
0.751185 + 0.660092i \(0.229483\pi\)
\(720\) 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 \(-0.326180\pi\)
0.519333 + 0.854572i \(0.326180\pi\)
\(728\) 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 −0.408256 0.912867i \(-0.633863\pi\)
0.994694 0.102874i \(-0.0328037\pi\)
\(734\) 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 0.823849 0.566810i \(-0.191823\pi\)
−0.902796 + 0.430069i \(0.858489\pi\)
\(740\) 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 −0.594760 0.803903i \(-0.702753\pi\)
0.993581 + 0.113126i \(0.0360863\pi\)
\(752\) 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 0.0518116 0.998657i \(-0.483500\pi\)
0.838956 0.544199i \(-0.183166\pi\)
\(762\) 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 \(-0.457181\pi\)
0.134115 + 0.990966i \(0.457181\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3678.00 6370.48i −0.171136 0.296417i 0.767681 0.640832i \(-0.221411\pi\)
−0.938817 + 0.344415i \(0.888077\pi\)
\(774\) 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 −0.858316 0.513122i \(-0.828489\pi\)
−0.0152188 0.999884i \(-0.504844\pi\)
\(788\) 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 \(-0.444461\pi\)
0.173598 + 0.984817i \(0.444461\pi\)
\(798\) 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 0.668897 + 0.743355i \(0.266767\pi\)
0.309316 + 0.950959i \(0.399900\pi\)
\(810\) 0 0
\(811\) −2740.00 −0.118637 −0.0593184 0.998239i \(-0.518893\pi\)
−0.0593184 + 0.998239i \(0.518893\pi\)
\(812\) 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 −0.850160 0.526525i \(-0.823495\pi\)
0.881064 + 0.472997i \(0.156828\pi\)
\(822\) 0 0
\(823\) −18560.0 32146.9i −0.786101 1.36157i −0.928339 0.371734i \(-0.878763\pi\)
0.142239 0.989832i \(-0.454570\pi\)
\(824\) 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 \(-0.241638\pi\)
−0.958794 + 0.284101i \(0.908305\pi\)
\(830\) 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 \(-0.442315\pi\)
0.180232 + 0.983624i \(0.442315\pi\)
\(840\) 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 \(-0.505239\pi\)
−0.0164574 + 0.999865i \(0.505239\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 660.000 + 1143.15i 0.0263071 + 0.0455652i 0.878879 0.477044i \(-0.158292\pi\)
−0.852572 + 0.522610i \(0.824959\pi\)
\(858\) 0 0
\(859\) 21390.0 37048.6i 0.849613 1.47157i −0.0319414 0.999490i \(-0.510169\pi\)
0.881554 0.472083i \(-0.156498\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 14940.0 25876.8i 0.589297 1.02069i −0.405027 0.914305i \(-0.632738\pi\)
0.994325 0.106388i \(-0.0339286\pi\)
\(864\) 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 0.456448 + 0.889750i \(0.349121\pi\)
−0.998770 + 0.0495796i \(0.984212\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 20800.0 0.795425 0.397713 0.917510i \(-0.369804\pi\)
0.397713 + 0.917510i \(0.369804\pi\)
\(882\) 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 \(-0.904041\pi\)
0.734591 + 0.678510i \(0.237374\pi\)
\(888\) 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 0.972521 + 0.232816i \(0.0747940\pi\)
−0.284636 + 0.958636i \(0.591873\pi\)
\(908\) 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 0.171313 + 0.985217i \(0.445199\pi\)
−0.938879 + 0.344247i \(0.888134\pi\)
\(920\) 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 \(-0.783897\pi\)
0.932945 + 0.360020i \(0.117230\pi\)
\(930\) 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 \(-0.832816\pi\)
−0.865212 + 0.501407i \(0.832816\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 18450.0 + 31956.3i 0.639163 + 1.10706i 0.985617 + 0.168996i \(0.0540526\pi\)
−0.346453 + 0.938067i \(0.612614\pi\)
\(942\) 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 0.424339 + 0.905503i \(0.360506\pi\)
−0.996358 + 0.0852631i \(0.972827\pi\)
\(948\) 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 \(-0.838909\pi\)
0.857134 + 0.515093i \(0.172243\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19385.0 33575.8i −0.634781 1.09947i −0.986561 0.163390i \(-0.947757\pi\)
0.351780 0.936083i \(-0.385576\pi\)
\(978\) 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 \(-0.0377016\pi\)
−0.598832 + 0.800875i \(0.704368\pi\)
\(984\) 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 0.879113 0.476613i \(-0.158136\pi\)
−0.852316 + 0.523028i \(0.824802\pi\)
\(992\) 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 0.959097 + 0.283077i \(0.0913553\pi\)
−0.234396 + 0.972141i \(0.575311\pi\)
\(998\) 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.p.1549.1 2
3.2 odd 2 196.4.e.b.177.1 2
7.2 even 3 1764.4.a.a.1.1 1
7.3 odd 6 1764.4.k.a.361.1 2
7.4 even 3 inner 1764.4.k.p.361.1 2
7.5 odd 6 1764.4.a.m.1.1 1
7.6 odd 2 1764.4.k.a.1549.1 2
21.2 odd 6 196.4.a.c.1.1 yes 1
21.5 even 6 196.4.a.a.1.1 1
21.11 odd 6 196.4.e.b.165.1 2
21.17 even 6 196.4.e.e.165.1 2
21.20 even 2 196.4.e.e.177.1 2
84.23 even 6 784.4.a.f.1.1 1
84.47 odd 6 784.4.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
196.4.a.a.1.1 1 21.5 even 6
196.4.a.c.1.1 yes 1 21.2 odd 6
196.4.e.b.165.1 2 21.11 odd 6
196.4.e.b.177.1 2 3.2 odd 2
196.4.e.e.165.1 2 21.17 even 6
196.4.e.e.177.1 2 21.20 even 2
784.4.a.f.1.1 1 84.23 even 6
784.4.a.m.1.1 1 84.47 odd 6
1764.4.a.a.1.1 1 7.2 even 3
1764.4.a.m.1.1 1 7.5 odd 6
1764.4.k.a.361.1 2 7.3 odd 6
1764.4.k.a.1549.1 2 7.6 odd 2
1764.4.k.p.361.1 2 7.4 even 3 inner
1764.4.k.p.1549.1 2 1.1 even 1 trivial