Properties

Label 121.4.c.a.9.1
Level $121$
Weight $4$
Character 121.9
Analytic conductor $7.139$
Analytic rank $0$
Dimension $4$
CM discriminant -11
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [121,4,Mod(3,121)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(121, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("121.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 121.c (of order \(5\), degree \(4\), 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: \(7.13923111069\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{5}]$

Embedding invariants

Embedding label 9.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 121.9
Dual form 121.4.c.a.27.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.47214 + 4.70228i) q^{3} +(6.47214 + 4.70228i) q^{4} +(5.56231 + 17.1190i) q^{5} +(11.4336 - 35.1891i) q^{9} +O(q^{10})\) \(q+(-6.47214 + 4.70228i) q^{3} +(6.47214 + 4.70228i) q^{4} +(5.56231 + 17.1190i) q^{5} +(11.4336 - 35.1891i) q^{9} -64.0000 q^{12} +(-116.498 - 84.6411i) q^{15} +(19.7771 + 60.8676i) q^{16} +(-44.4984 + 136.952i) q^{20} -108.000 q^{23} +(-160.994 + 116.969i) q^{25} +(24.7214 + 76.0845i) q^{27} +(105.066 - 323.359i) q^{31} +(239.469 - 173.984i) q^{36} +(351.113 + 255.099i) q^{37} +666.000 q^{45} +(29.1246 - 21.1603i) q^{47} +(-414.217 - 300.946i) q^{48} +(-105.993 - 326.212i) q^{49} +(-228.055 + 701.880i) q^{53} +(582.492 + 423.205i) q^{59} +(-355.988 - 1095.62i) q^{60} +(-158.217 + 486.941i) q^{64} -416.000 q^{67} +(698.991 - 507.846i) q^{69} +(189.118 + 582.047i) q^{71} +(491.955 - 1514.08i) q^{75} +(-931.988 + 677.129i) q^{80} +(290.437 + 211.015i) q^{81} +1674.00 q^{89} +(-698.991 - 507.846i) q^{92} +(840.526 + 2586.87i) q^{93} +(-10.5066 + 32.3359i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{3} + 8 q^{4} - 18 q^{5} - 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{3} + 8 q^{4} - 18 q^{5} - 37 q^{9} - 256 q^{12} - 144 q^{15} - 64 q^{16} + 144 q^{20} - 432 q^{23} - 199 q^{25} - 80 q^{27} - 340 q^{31} + 296 q^{36} + 434 q^{37} + 2664 q^{45} + 36 q^{47} - 512 q^{48} + 343 q^{49} + 738 q^{53} + 720 q^{59} + 1152 q^{60} + 512 q^{64} - 1664 q^{67} + 864 q^{69} - 612 q^{71} - 1592 q^{75} - 1152 q^{80} + 359 q^{81} + 6696 q^{89} - 864 q^{92} - 2720 q^{93} + 34 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

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 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(3\) −6.47214 + 4.70228i −1.24556 + 0.904955i −0.997956 0.0639059i \(-0.979644\pi\)
−0.247607 + 0.968860i \(0.579644\pi\)
\(4\) 6.47214 + 4.70228i 0.809017 + 0.587785i
\(5\) 5.56231 + 17.1190i 0.497508 + 1.53117i 0.813012 + 0.582247i \(0.197826\pi\)
−0.315504 + 0.948924i \(0.602174\pi\)
\(6\) 0 0
\(7\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(8\) 0 0
\(9\) 11.4336 35.1891i 0.423468 1.30330i
\(10\) 0 0
\(11\) 0 0
\(12\) −64.0000 −1.53960
\(13\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(14\) 0 0
\(15\) −116.498 84.6411i −2.00532 1.45695i
\(16\) 19.7771 + 60.8676i 0.309017 + 0.951057i
\(17\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(18\) 0 0
\(19\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(20\) −44.4984 + 136.952i −0.497508 + 1.53117i
\(21\) 0 0
\(22\) 0 0
\(23\) −108.000 −0.979111 −0.489556 0.871972i \(-0.662841\pi\)
−0.489556 + 0.871972i \(0.662841\pi\)
\(24\) 0 0
\(25\) −160.994 + 116.969i −1.28796 + 0.935754i
\(26\) 0 0
\(27\) 24.7214 + 76.0845i 0.176208 + 0.542314i
\(28\) 0 0
\(29\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(30\) 0 0
\(31\) 105.066 323.359i 0.608722 1.87345i 0.139885 0.990168i \(-0.455327\pi\)
0.468837 0.883285i \(-0.344673\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 239.469 173.984i 1.10865 0.805483i
\(37\) 351.113 + 255.099i 1.56007 + 1.13346i 0.935950 + 0.352132i \(0.114543\pi\)
0.624122 + 0.781327i \(0.285457\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 666.000 2.20625
\(46\) 0 0
\(47\) 29.1246 21.1603i 0.0903885 0.0656711i −0.541673 0.840589i \(-0.682209\pi\)
0.632062 + 0.774918i \(0.282209\pi\)
\(48\) −414.217 300.946i −1.24556 0.904955i
\(49\) −105.993 326.212i −0.309017 0.951057i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −228.055 + 701.880i −0.591051 + 1.81907i −0.0175748 + 0.999846i \(0.505595\pi\)
−0.573476 + 0.819222i \(0.694405\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 582.492 + 423.205i 1.28532 + 0.933841i 0.999700 0.0245007i \(-0.00779958\pi\)
0.285623 + 0.958342i \(0.407800\pi\)
\(60\) −355.988 1095.62i −0.765963 2.35739i
\(61\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −158.217 + 486.941i −0.309017 + 0.951057i
\(65\) 0 0
\(66\) 0 0
\(67\) −416.000 −0.758545 −0.379272 0.925285i \(-0.623826\pi\)
−0.379272 + 0.925285i \(0.623826\pi\)
\(68\) 0 0
\(69\) 698.991 507.846i 1.21954 0.886051i
\(70\) 0 0
\(71\) 189.118 + 582.047i 0.316116 + 0.972905i 0.975293 + 0.220917i \(0.0709049\pi\)
−0.659177 + 0.751988i \(0.729095\pi\)
\(72\) 0 0
\(73\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(74\) 0 0
\(75\) 491.955 1514.08i 0.757414 2.33108i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(80\) −931.988 + 677.129i −1.30249 + 0.946316i
\(81\) 290.437 + 211.015i 0.398405 + 0.289458i
\(82\) 0 0
\(83\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1674.00 1.99375 0.996874 0.0790026i \(-0.0251735\pi\)
0.996874 + 0.0790026i \(0.0251735\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −698.991 507.846i −0.792118 0.575507i
\(93\) 840.526 + 2586.87i 0.937188 + 2.88437i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.5066 + 32.3359i −0.0109977 + 0.0338476i −0.956405 0.292044i \(-0.905665\pi\)
0.945407 + 0.325892i \(0.105665\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1592.00 −1.59200
\(101\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(102\) 0 0
\(103\) −948.168 688.884i −0.907046 0.659008i 0.0332199 0.999448i \(-0.489424\pi\)
−0.940266 + 0.340440i \(0.889424\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(108\) −197.771 + 608.676i −0.176208 + 0.542314i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −3472.00 −2.96890
\(112\) 0 0
\(113\) −1732.91 + 1259.04i −1.44264 + 1.04814i −0.455163 + 0.890408i \(0.650419\pi\)
−0.987481 + 0.157735i \(0.949581\pi\)
\(114\) 0 0
\(115\) −600.729 1848.85i −0.487115 1.49919i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 2200.53 1598.78i 1.59365 1.15786i
\(125\) −1077.61 782.930i −0.771075 0.560219i
\(126\) 0 0
\(127\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1164.98 + 846.411i −0.742710 + 0.539611i
\(136\) 0 0
\(137\) 372.674 + 1146.97i 0.232407 + 0.715275i 0.997455 + 0.0713013i \(0.0227152\pi\)
−0.765048 + 0.643973i \(0.777285\pi\)
\(138\) 0 0
\(139\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(140\) 0 0
\(141\) −88.9969 + 273.904i −0.0531553 + 0.163595i
\(142\) 0 0
\(143\) 0 0
\(144\) 2368.00 1.37037
\(145\) 0 0
\(146\) 0 0
\(147\) 2219.94 + 1612.88i 1.24556 + 0.904955i
\(148\) 1072.91 + 3302.07i 0.595895 + 1.83398i
\(149\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6120.00 3.17142
\(156\) 0 0
\(157\) 1079.23 784.106i 0.548610 0.398589i −0.278663 0.960389i \(-0.589891\pi\)
0.827273 + 0.561800i \(0.189891\pi\)
\(158\) 0 0
\(159\) −1824.44 5615.04i −0.909982 2.80064i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1152.02 3545.54i 0.553576 1.70373i −0.146100 0.989270i \(-0.546672\pi\)
0.699676 0.714460i \(-0.253328\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(168\) 0 0
\(169\) 1777.41 + 1291.36i 0.809017 + 0.587785i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5760.00 −2.44603
\(178\) 0 0
\(179\) 1630.98 1184.98i 0.681034 0.494800i −0.192667 0.981264i \(-0.561714\pi\)
0.873700 + 0.486464i \(0.161714\pi\)
\(180\) 4310.44 + 3131.72i 1.78490 + 1.29680i
\(181\) −633.485 1949.67i −0.260147 0.800649i −0.992772 0.120017i \(-0.961705\pi\)
0.732625 0.680632i \(-0.238295\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2414.04 + 7429.65i −0.959372 + 2.95264i
\(186\) 0 0
\(187\) 0 0
\(188\) 288.000 0.111726
\(189\) 0 0
\(190\) 0 0
\(191\) −4223.07 3068.24i −1.59985 1.16236i −0.887807 0.460215i \(-0.847772\pi\)
−0.712038 0.702141i \(-0.752228\pi\)
\(192\) −1265.73 3895.53i −0.475763 1.46425i
\(193\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 847.943 2609.70i 0.309017 0.951057i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 3940.00 1.40351 0.701757 0.712417i \(-0.252399\pi\)
0.701757 + 0.712417i \(0.252399\pi\)
\(200\) 0 0
\(201\) 2692.41 1956.15i 0.944815 0.686448i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1234.83 + 3800.42i −0.414622 + 1.27608i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(212\) −4776.44 + 3470.28i −1.54739 + 1.12425i
\(213\) −3960.95 2877.80i −1.27418 0.925744i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −540.423 + 392.641i −0.162284 + 0.117907i −0.665964 0.745984i \(-0.731979\pi\)
0.503679 + 0.863891i \(0.331979\pi\)
\(224\) 0 0
\(225\) 2275.29 + 7002.63i 0.674161 + 2.07485i
\(226\) 0 0
\(227\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(228\) 0 0
\(229\) 1022.85 3148.00i 0.295160 0.908408i −0.688008 0.725703i \(-0.741515\pi\)
0.983168 0.182705i \(-0.0584854\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(234\) 0 0
\(235\) 524.243 + 380.885i 0.145523 + 0.105728i
\(236\) 1779.94 + 5478.09i 0.490950 + 1.51099i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(240\) 2847.90 8764.94i 0.765963 2.35739i
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) −5032.00 −1.32841
\(244\) 0 0
\(245\) 4994.87 3628.99i 1.30249 0.946316i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 200.243 616.285i 0.0503555 0.154978i −0.922717 0.385479i \(-0.874036\pi\)
0.973072 + 0.230500i \(0.0740363\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −3313.73 + 2407.57i −0.809017 + 0.587785i
\(257\) 6509.35 + 4729.32i 1.57993 + 1.14789i 0.916774 + 0.399406i \(0.130784\pi\)
0.663156 + 0.748481i \(0.269216\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −13284.0 −3.07936
\(266\) 0 0
\(267\) −10834.4 + 7871.62i −2.48334 + 1.80425i
\(268\) −2692.41 1956.15i −0.613675 0.445861i
\(269\) 862.157 + 2653.45i 0.195415 + 0.601426i 0.999972 + 0.00754961i \(0.00240314\pi\)
−0.804556 + 0.593876i \(0.797597\pi\)
\(270\) 0 0
\(271\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 6912.00 1.50744
\(277\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(278\) 0 0
\(279\) −10177.4 7394.34i −2.18390 1.58669i
\(280\) 0 0
\(281\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(284\) −1512.95 + 4656.37i −0.316116 + 0.972905i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3974.70 2887.79i 0.809017 0.587785i
\(290\) 0 0
\(291\) −84.0526 258.687i −0.0169321 0.0521118i
\(292\) 0 0
\(293\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(294\) 0 0
\(295\) −4004.86 + 12325.7i −0.790413 + 2.43264i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 10303.6 7486.03i 1.98294 1.44069i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 9376.00 1.72616
\(310\) 0 0
\(311\) −7659.77 + 5565.15i −1.39661 + 1.01470i −0.401507 + 0.915856i \(0.631514\pi\)
−0.995103 + 0.0988411i \(0.968486\pi\)
\(312\) 0 0
\(313\) −3393.62 10444.5i −0.612840 1.88613i −0.429458 0.903087i \(-0.641295\pi\)
−0.183382 0.983042i \(-0.558705\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1852.25 5700.63i 0.328179 1.01003i −0.641807 0.766866i \(-0.721815\pi\)
0.969985 0.243163i \(-0.0781851\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −9216.00 −1.60997
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 887.497 + 2731.43i 0.152177 + 0.468353i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8120.00 1.34839 0.674193 0.738555i \(-0.264492\pi\)
0.674193 + 0.738555i \(0.264492\pi\)
\(332\) 0 0
\(333\) 12991.2 9438.66i 2.13788 1.55326i
\(334\) 0 0
\(335\) −2313.92 7121.51i −0.377382 1.16146i
\(336\) 0 0
\(337\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(338\) 0 0
\(339\) 5295.32 16297.3i 0.848384 2.61106i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 12581.8 + 9141.24i 1.96343 + 1.42651i
\(346\) 0 0
\(347\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8802.00 1.32715 0.663574 0.748111i \(-0.269039\pi\)
0.663574 + 0.748111i \(0.269039\pi\)
\(354\) 0 0
\(355\) −8912.13 + 6475.04i −1.33241 + 0.968055i
\(356\) 10834.4 + 7871.62i 1.61298 + 1.17190i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(360\) 0 0
\(361\) −2119.55 + 6523.30i −0.309017 + 0.951057i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8022.21 + 5828.48i 1.14102 + 0.829003i 0.987262 0.159105i \(-0.0508608\pi\)
0.153763 + 0.988108i \(0.450861\pi\)
\(368\) −2135.93 6573.70i −0.302562 0.931190i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −6724.21 + 20695.0i −0.937188 + 2.88437i
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 10656.0 1.46740
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 3955.42 + 12173.5i 0.536085 + 1.64990i 0.741293 + 0.671181i \(0.234213\pi\)
−0.205209 + 0.978718i \(0.565787\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4483.22 13797.9i 0.598125 1.84084i 0.0596113 0.998222i \(-0.481014\pi\)
0.538513 0.842617i \(-0.318986\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −220.053 + 159.878i −0.0287925 + 0.0209190i
\(389\) −11431.4 8305.41i −1.48996 1.08252i −0.974172 0.225807i \(-0.927498\pi\)
−0.515791 0.856715i \(-0.672502\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −2374.00 −0.300120 −0.150060 0.988677i \(-0.547947\pi\)
−0.150060 + 0.988677i \(0.547947\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −10303.6 7486.03i −1.28796 0.935754i
\(401\) −2808.96 8645.10i −0.349808 1.07660i −0.958959 0.283544i \(-0.908490\pi\)
0.609151 0.793054i \(-0.291510\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1996.87 + 6145.73i −0.245000 + 0.754034i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(410\) 0 0
\(411\) −7805.40 5670.95i −0.936768 0.680602i
\(412\) −2897.34 8917.11i −0.346461 1.06630i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16344.0 −1.90562 −0.952812 0.303560i \(-0.901825\pi\)
−0.952812 + 0.303560i \(0.901825\pi\)
\(420\) 0 0
\(421\) 9408.87 6835.94i 1.08922 0.791362i 0.109950 0.993937i \(-0.464931\pi\)
0.979267 + 0.202575i \(0.0649310\pi\)
\(422\) 0 0
\(423\) −411.611 1266.81i −0.0473125 0.145613i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(432\) −4142.17 + 3009.46i −0.461320 + 0.335168i
\(433\) 10745.4 + 7806.96i 1.19258 + 0.866464i 0.993535 0.113526i \(-0.0362145\pi\)
0.199050 + 0.979989i \(0.436214\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −12691.0 −1.37037
\(442\) 0 0
\(443\) 15086.5 10961.0i 1.61802 1.17556i 0.806711 0.590946i \(-0.201245\pi\)
0.811311 0.584615i \(-0.198755\pi\)
\(444\) −22471.3 16326.3i −2.40189 1.74507i
\(445\) 9311.30 + 28657.2i 0.991906 + 3.05277i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2096.99 6453.87i 0.220408 0.678345i −0.778318 0.627871i \(-0.783927\pi\)
0.998725 0.0504744i \(-0.0160733\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −17136.0 −1.78321
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 4805.83 14790.8i 0.487115 1.49919i
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 13268.0 1.33178 0.665892 0.746048i \(-0.268051\pi\)
0.665892 + 0.746048i \(0.268051\pi\)
\(464\) 0 0
\(465\) −39609.5 + 28778.0i −3.95020 + 2.86999i
\(466\) 0 0
\(467\) 1290.45 + 3971.61i 0.127870 + 0.393542i 0.994413 0.105559i \(-0.0336633\pi\)
−0.866543 + 0.499102i \(0.833663\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −3297.83 + 10149.7i −0.322624 + 0.992935i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 22091.0 + 16050.1i 2.12050 + 1.54063i
\(478\) 0 0
\(479\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −612.000 −0.0572979
\(486\) 0 0
\(487\) −13497.6 + 9806.61i −1.25593 + 0.912484i −0.998550 0.0538268i \(-0.982858\pi\)
−0.257377 + 0.966311i \(0.582858\pi\)
\(488\) 0 0
\(489\) 9216.12 + 28364.3i 0.852285 + 2.62306i
\(490\) 0 0
\(491\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 21760.0 1.96986
\(497\) 0 0
\(498\) 0 0
\(499\) −3333.15 2421.68i −0.299023 0.217253i 0.428149 0.903708i \(-0.359166\pi\)
−0.727172 + 0.686455i \(0.759166\pi\)
\(500\) −3292.89 10134.5i −0.294525 0.906454i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −17576.0 −1.53960
\(508\) 0 0
\(509\) 18130.1 13172.3i 1.57878 1.14705i 0.660713 0.750638i \(-0.270254\pi\)
0.918071 0.396416i \(-0.129746\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6519.02 20063.5i 0.557791 1.71670i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −16237.0 11796.9i −1.36536 0.991995i −0.998083 0.0618848i \(-0.980289\pi\)
−0.367281 0.930110i \(-0.619711\pi\)
\(522\) 0 0
\(523\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −503.000 −0.0413413
\(530\) 0 0
\(531\) 21552.2 15658.6i 1.76137 1.27971i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4983.83 + 15338.6i −0.400499 + 1.23261i
\(538\) 0 0
\(539\) 0 0
\(540\) −11520.0 −0.918040
\(541\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(542\) 0 0
\(543\) 13267.9 + 9639.68i 1.04858 + 0.761838i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(548\) −2981.40 + 9175.79i −0.232407 + 0.715275i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −19312.3 59437.2i −1.47705 4.54589i
\(556\) 0 0
\(557\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(564\) −1863.98 + 1354.26i −0.139162 + 0.101107i
\(565\) −31192.5 22662.6i −2.32261 1.68748i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 41760.0 3.04459
\(574\) 0 0
\(575\) 17387.4 12632.7i 1.26105 0.916207i
\(576\) 15326.0 + 11135.0i 1.10865 + 0.805483i
\(577\) −6942.38 21366.4i −0.500892 1.54159i −0.807568 0.589774i \(-0.799217\pi\)
0.306676 0.951814i \(-0.400783\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21086.2 + 15320.0i 1.48266 + 1.07722i 0.976688 + 0.214666i \(0.0688662\pi\)
0.505972 + 0.862550i \(0.331134\pi\)
\(588\) 6783.54 + 20877.6i 0.475763 + 1.46425i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −8583.26 + 26416.5i −0.595895 + 1.83398i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −25500.2 + 18527.0i −1.74816 + 1.27012i
\(598\) 0 0
\(599\) 5573.43 + 17153.3i 0.380174 + 1.17006i 0.939921 + 0.341392i \(0.110898\pi\)
−0.559747 + 0.828663i \(0.689102\pi\)
\(600\) 0 0
\(601\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(602\) 0 0
\(603\) −4756.39 + 14638.7i −0.321219 + 0.988611i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3654.00 0.238419 0.119209 0.992869i \(-0.461964\pi\)
0.119209 + 0.992869i \(0.461964\pi\)
\(618\) 0 0
\(619\) −1501.54 + 1090.93i −0.0974989 + 0.0708371i −0.635467 0.772128i \(-0.719192\pi\)
0.537968 + 0.842965i \(0.319192\pi\)
\(620\) 39609.5 + 28778.0i 2.56573 + 1.86411i
\(621\) −2669.91 8217.13i −0.172528 0.530986i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −277.806 + 855.000i −0.0177796 + 0.0547200i
\(626\) 0 0
\(627\) 0 0
\(628\) 10672.0 0.678120
\(629\) 0 0
\(630\) 0 0
\(631\) 10442.8 + 7587.13i 0.658829 + 0.478667i 0.866267 0.499581i \(-0.166513\pi\)
−0.207438 + 0.978248i \(0.566513\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 14595.5 44920.3i 0.909982 2.80064i
\(637\) 0 0
\(638\) 0 0
\(639\) 22644.0 1.40185
\(640\) 0 0
\(641\) 3713.39 2697.93i 0.228814 0.166243i −0.467471 0.884008i \(-0.654835\pi\)
0.696285 + 0.717765i \(0.254835\pi\)
\(642\) 0 0
\(643\) −3142.08 9670.34i −0.192709 0.593097i −0.999996 0.00293742i \(-0.999065\pi\)
0.807287 0.590159i \(-0.200935\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10112.3 31122.4i 0.614458 1.89111i 0.205071 0.978747i \(-0.434258\pi\)
0.409387 0.912361i \(-0.365742\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 24128.1 17530.1i 1.44928 1.05296i
\(653\) −26488.8 19245.3i −1.58742 1.15333i −0.907502 0.420047i \(-0.862014\pi\)
−0.679922 0.733284i \(-0.737986\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −23582.0 −1.38765 −0.693823 0.720146i \(-0.744075\pi\)
−0.693823 + 0.720146i \(0.744075\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1651.39 5082.45i 0.0954354 0.293720i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(674\) 0 0
\(675\) −12879.6 9357.54i −0.734421 0.533588i
\(676\) 5431.28 + 16715.8i 0.309017 + 0.951057i
\(677\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −35352.0 −1.98054 −0.990268 0.139170i \(-0.955556\pi\)
−0.990268 + 0.139170i \(0.955556\pi\)
\(684\) 0 0
\(685\) −17562.1 + 12759.6i −0.979584 + 0.711709i
\(686\) 0 0
\(687\) 8182.77 + 25184.0i 0.454428 + 1.39859i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −9371.87 + 28843.6i −0.515952 + 1.58794i 0.265592 + 0.964086i \(0.414433\pi\)
−0.781544 + 0.623851i \(0.785567\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −5184.00 −0.276937
\(706\) 0 0
\(707\) 0 0
\(708\) −37279.5 27085.1i −1.97888 1.43774i
\(709\) −10368.8 31911.8i −0.549234 1.69037i −0.710705 0.703491i \(-0.751624\pi\)
0.161471 0.986877i \(-0.448376\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −11347.1 + 34922.8i −0.596006 + 1.83432i
\(714\) 0 0
\(715\) 0 0
\(716\) 16128.0 0.841804
\(717\) 0 0
\(718\) 0 0
\(719\) −18319.4 13309.8i −0.950205 0.690365i 0.000650107 1.00000i \(-0.499793\pi\)
−0.950855 + 0.309635i \(0.899793\pi\)
\(720\) 13171.5 + 40537.8i 0.681770 + 2.09827i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 5067.88 15597.3i 0.260147 0.800649i
\(725\) 0 0
\(726\) 0 0
\(727\) −33284.0 −1.69799 −0.848993 0.528405i \(-0.822790\pi\)
−0.848993 + 0.528405i \(0.822790\pi\)
\(728\) 0 0
\(729\) 24726.0 17964.5i 1.25621 0.912690i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(734\) 0 0
\(735\) −15263.0 + 46974.6i −0.765963 + 2.35739i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(740\) −50560.3 + 36734.2i −2.51167 + 1.82483i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −32079.1 + 23306.9i −1.55870 + 1.13246i −0.621637 + 0.783306i \(0.713532\pi\)
−0.937064 + 0.349157i \(0.886468\pi\)
\(752\) 1863.98 + 1354.26i 0.0903885 + 0.0656711i
\(753\) 1601.94 + 4930.28i 0.0775273 + 0.238605i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 9711.17 29887.9i 0.466259 1.43500i −0.391132 0.920335i \(-0.627916\pi\)
0.857392 0.514665i \(-0.172084\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −12904.5 39716.1i −0.611087 1.88073i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 10125.9 31164.2i 0.475763 1.46425i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) −64368.0 −3.00669
\(772\) 0 0
\(773\) −26081.1 + 18949.0i −1.21355 + 0.881693i −0.995548 0.0942558i \(-0.969953\pi\)
−0.217999 + 0.975949i \(0.569953\pi\)
\(774\) 0 0
\(775\) 20908.1 + 64348.5i 0.969085 + 2.98254i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 17759.5 12903.1i 0.809017 0.587785i
\(785\) 19426.1 + 14113.9i 0.883246 + 0.641716i
\(786\) 0 0
\(787\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0