Properties

Label 2200.2.a.u.1.1
Level $2200$
Weight $2$
Character 2200.1
Self dual yes
Analytic conductor $17.567$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2200,2,Mod(1,2200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2200.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2200.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(17.5670884447\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1229.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 7x + 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.75153\) of defining polynomial
Character \(\chi\) \(=\) 2200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.75153 q^{3} -3.57093 q^{7} +4.57093 q^{9} +O(q^{10})\) \(q-2.75153 q^{3} -3.57093 q^{7} +4.57093 q^{9} +1.00000 q^{11} -1.00000 q^{13} -0.751532 q^{17} -2.50306 q^{19} +9.82552 q^{21} -5.75153 q^{23} -4.32246 q^{27} -4.07399 q^{29} -6.14186 q^{31} -2.75153 q^{33} +2.81940 q^{37} +2.75153 q^{39} +1.18060 q^{41} -7.68367 q^{43} +9.82552 q^{47} +5.75153 q^{49} +2.06786 q^{51} -14.2159 q^{53} +6.88726 q^{57} -9.82552 q^{59} +7.07399 q^{61} -16.3225 q^{63} +14.6449 q^{67} +15.8255 q^{69} +5.81940 q^{71} +14.7128 q^{73} -3.57093 q^{77} -3.89339 q^{79} -1.81940 q^{81} +5.57706 q^{83} +11.2097 q^{87} +7.42907 q^{89} +3.57093 q^{91} +16.8995 q^{93} +0.609675 q^{97} +4.57093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} - 3 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{3} - 3 q^{7} + 6 q^{9} + 3 q^{11} - 3 q^{13} + 5 q^{17} + 7 q^{19} - 10 q^{23} + 2 q^{27} + 10 q^{29} - 3 q^{31} - q^{33} + 8 q^{37} + q^{39} + 4 q^{41} - 9 q^{43} + 10 q^{49} + 13 q^{51} - 5 q^{53} + 27 q^{57} - q^{61} - 34 q^{63} + 14 q^{67} + 18 q^{69} + 17 q^{71} + 21 q^{73} - 3 q^{77} + 11 q^{79} - 5 q^{81} - 20 q^{83} + 25 q^{87} + 30 q^{89} + 3 q^{91} - q^{93} + 10 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −2.75153 −1.58860 −0.794299 0.607527i \(-0.792162\pi\)
−0.794299 + 0.607527i \(0.792162\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.57093 −1.34968 −0.674842 0.737962i \(-0.735788\pi\)
−0.674842 + 0.737962i \(0.735788\pi\)
\(8\) 0 0
\(9\) 4.57093 1.52364
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.751532 −0.182273 −0.0911367 0.995838i \(-0.529050\pi\)
−0.0911367 + 0.995838i \(0.529050\pi\)
\(18\) 0 0
\(19\) −2.50306 −0.574242 −0.287121 0.957894i \(-0.592698\pi\)
−0.287121 + 0.957894i \(0.592698\pi\)
\(20\) 0 0
\(21\) 9.82552 2.14411
\(22\) 0 0
\(23\) −5.75153 −1.19928 −0.599639 0.800271i \(-0.704689\pi\)
−0.599639 + 0.800271i \(0.704689\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.32246 −0.831858
\(28\) 0 0
\(29\) −4.07399 −0.756521 −0.378261 0.925699i \(-0.623478\pi\)
−0.378261 + 0.925699i \(0.623478\pi\)
\(30\) 0 0
\(31\) −6.14186 −1.10311 −0.551555 0.834138i \(-0.685965\pi\)
−0.551555 + 0.834138i \(0.685965\pi\)
\(32\) 0 0
\(33\) −2.75153 −0.478980
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.81940 0.463506 0.231753 0.972775i \(-0.425554\pi\)
0.231753 + 0.972775i \(0.425554\pi\)
\(38\) 0 0
\(39\) 2.75153 0.440598
\(40\) 0 0
\(41\) 1.18060 0.184379 0.0921896 0.995741i \(-0.470613\pi\)
0.0921896 + 0.995741i \(0.470613\pi\)
\(42\) 0 0
\(43\) −7.68367 −1.17175 −0.585874 0.810402i \(-0.699249\pi\)
−0.585874 + 0.810402i \(0.699249\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.82552 1.43320 0.716600 0.697484i \(-0.245697\pi\)
0.716600 + 0.697484i \(0.245697\pi\)
\(48\) 0 0
\(49\) 5.75153 0.821647
\(50\) 0 0
\(51\) 2.06786 0.289559
\(52\) 0 0
\(53\) −14.2159 −1.95270 −0.976349 0.216202i \(-0.930633\pi\)
−0.976349 + 0.216202i \(0.930633\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 6.88726 0.912240
\(58\) 0 0
\(59\) −9.82552 −1.27917 −0.639587 0.768719i \(-0.720895\pi\)
−0.639587 + 0.768719i \(0.720895\pi\)
\(60\) 0 0
\(61\) 7.07399 0.905732 0.452866 0.891579i \(-0.350402\pi\)
0.452866 + 0.891579i \(0.350402\pi\)
\(62\) 0 0
\(63\) −16.3225 −2.05644
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 14.6449 1.78916 0.894581 0.446906i \(-0.147474\pi\)
0.894581 + 0.446906i \(0.147474\pi\)
\(68\) 0 0
\(69\) 15.8255 1.90517
\(70\) 0 0
\(71\) 5.81940 0.690635 0.345318 0.938486i \(-0.387771\pi\)
0.345318 + 0.938486i \(0.387771\pi\)
\(72\) 0 0
\(73\) 14.7128 1.72200 0.861001 0.508604i \(-0.169838\pi\)
0.861001 + 0.508604i \(0.169838\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.57093 −0.406945
\(78\) 0 0
\(79\) −3.89339 −0.438041 −0.219020 0.975720i \(-0.570286\pi\)
−0.219020 + 0.975720i \(0.570286\pi\)
\(80\) 0 0
\(81\) −1.81940 −0.202155
\(82\) 0 0
\(83\) 5.57706 0.612162 0.306081 0.952006i \(-0.400982\pi\)
0.306081 + 0.952006i \(0.400982\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 11.2097 1.20181
\(88\) 0 0
\(89\) 7.42907 0.787480 0.393740 0.919222i \(-0.371181\pi\)
0.393740 + 0.919222i \(0.371181\pi\)
\(90\) 0 0
\(91\) 3.57093 0.374335
\(92\) 0 0
\(93\) 16.8995 1.75240
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.609675 0.0619031 0.0309515 0.999521i \(-0.490146\pi\)
0.0309515 + 0.999521i \(0.490146\pi\)
\(98\) 0 0
\(99\) 4.57093 0.459396
\(100\) 0 0
\(101\) 0.248468 0.0247235 0.0123617 0.999924i \(-0.496065\pi\)
0.0123617 + 0.999924i \(0.496065\pi\)
\(102\) 0 0
\(103\) −17.5771 −1.73192 −0.865959 0.500114i \(-0.833291\pi\)
−0.865959 + 0.500114i \(0.833291\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −14.7868 −1.42949 −0.714746 0.699384i \(-0.753458\pi\)
−0.714746 + 0.699384i \(0.753458\pi\)
\(108\) 0 0
\(109\) 3.42907 0.328445 0.164223 0.986423i \(-0.447488\pi\)
0.164223 + 0.986423i \(0.447488\pi\)
\(110\) 0 0
\(111\) −7.75766 −0.736325
\(112\) 0 0
\(113\) 14.1867 1.33458 0.667288 0.744800i \(-0.267455\pi\)
0.667288 + 0.744800i \(0.267455\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −4.57093 −0.422583
\(118\) 0 0
\(119\) 2.68367 0.246011
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −3.24847 −0.292904
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 18.8995 1.67706 0.838531 0.544855i \(-0.183415\pi\)
0.838531 + 0.544855i \(0.183415\pi\)
\(128\) 0 0
\(129\) 21.1419 1.86144
\(130\) 0 0
\(131\) 20.5322 1.79391 0.896953 0.442127i \(-0.145776\pi\)
0.896953 + 0.442127i \(0.145776\pi\)
\(132\) 0 0
\(133\) 8.93826 0.775046
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.29334 0.281369 0.140685 0.990054i \(-0.455070\pi\)
0.140685 + 0.990054i \(0.455070\pi\)
\(138\) 0 0
\(139\) 18.4256 1.56284 0.781418 0.624008i \(-0.214497\pi\)
0.781418 + 0.624008i \(0.214497\pi\)
\(140\) 0 0
\(141\) −27.0352 −2.27678
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −15.8255 −1.30527
\(148\) 0 0
\(149\) 8.36121 0.684977 0.342488 0.939522i \(-0.388730\pi\)
0.342488 + 0.939522i \(0.388730\pi\)
\(150\) 0 0
\(151\) 5.04487 0.410546 0.205273 0.978705i \(-0.434192\pi\)
0.205273 + 0.978705i \(0.434192\pi\)
\(152\) 0 0
\(153\) −3.43520 −0.277719
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.2837 −0.980347 −0.490174 0.871625i \(-0.663067\pi\)
−0.490174 + 0.871625i \(0.663067\pi\)
\(158\) 0 0
\(159\) 39.1154 3.10205
\(160\) 0 0
\(161\) 20.5383 1.61865
\(162\) 0 0
\(163\) 12.0801 0.946188 0.473094 0.881012i \(-0.343137\pi\)
0.473094 + 0.881012i \(0.343137\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20.8317 1.61200 0.806001 0.591914i \(-0.201628\pi\)
0.806001 + 0.591914i \(0.201628\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −11.4413 −0.874940
\(172\) 0 0
\(173\) −2.50306 −0.190304 −0.0951522 0.995463i \(-0.530334\pi\)
−0.0951522 + 0.995463i \(0.530334\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 27.0352 2.03209
\(178\) 0 0
\(179\) −11.5709 −0.864852 −0.432426 0.901669i \(-0.642342\pi\)
−0.432426 + 0.901669i \(0.642342\pi\)
\(180\) 0 0
\(181\) −18.4413 −1.37073 −0.685367 0.728198i \(-0.740358\pi\)
−0.685367 + 0.728198i \(0.740358\pi\)
\(182\) 0 0
\(183\) −19.4643 −1.43884
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.751532 −0.0549575
\(188\) 0 0
\(189\) 15.4352 1.12275
\(190\) 0 0
\(191\) 3.29334 0.238298 0.119149 0.992876i \(-0.461983\pi\)
0.119149 + 0.992876i \(0.461983\pi\)
\(192\) 0 0
\(193\) 23.0061 1.65602 0.828009 0.560715i \(-0.189474\pi\)
0.828009 + 0.560715i \(0.189474\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.2546 −0.944351 −0.472175 0.881505i \(-0.656531\pi\)
−0.472175 + 0.881505i \(0.656531\pi\)
\(198\) 0 0
\(199\) 1.65455 0.117288 0.0586439 0.998279i \(-0.481322\pi\)
0.0586439 + 0.998279i \(0.481322\pi\)
\(200\) 0 0
\(201\) −40.2960 −2.84226
\(202\) 0 0
\(203\) 14.5479 1.02107
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −26.2898 −1.82727
\(208\) 0 0
\(209\) −2.50306 −0.173141
\(210\) 0 0
\(211\) −20.9674 −1.44345 −0.721727 0.692178i \(-0.756651\pi\)
−0.721727 + 0.692178i \(0.756651\pi\)
\(212\) 0 0
\(213\) −16.0123 −1.09714
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 21.9321 1.48885
\(218\) 0 0
\(219\) −40.4827 −2.73557
\(220\) 0 0
\(221\) 0.751532 0.0505535
\(222\) 0 0
\(223\) 12.8317 0.859271 0.429636 0.903002i \(-0.358642\pi\)
0.429636 + 0.903002i \(0.358642\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.42907 −0.625829 −0.312915 0.949781i \(-0.601305\pi\)
−0.312915 + 0.949781i \(0.601305\pi\)
\(228\) 0 0
\(229\) −4.97701 −0.328890 −0.164445 0.986386i \(-0.552583\pi\)
−0.164445 + 0.986386i \(0.552583\pi\)
\(230\) 0 0
\(231\) 9.82552 0.646472
\(232\) 0 0
\(233\) 3.93214 0.257603 0.128801 0.991670i \(-0.458887\pi\)
0.128801 + 0.991670i \(0.458887\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 10.7128 0.695870
\(238\) 0 0
\(239\) 27.7189 1.79299 0.896494 0.443056i \(-0.146106\pi\)
0.896494 + 0.443056i \(0.146106\pi\)
\(240\) 0 0
\(241\) 12.1189 0.780645 0.390322 0.920678i \(-0.372364\pi\)
0.390322 + 0.920678i \(0.372364\pi\)
\(242\) 0 0
\(243\) 17.9735 1.15300
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.50306 0.159266
\(248\) 0 0
\(249\) −15.3455 −0.972478
\(250\) 0 0
\(251\) 14.1189 0.891175 0.445587 0.895238i \(-0.352995\pi\)
0.445587 + 0.895238i \(0.352995\pi\)
\(252\) 0 0
\(253\) −5.75153 −0.361596
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.6062 0.848730 0.424365 0.905491i \(-0.360497\pi\)
0.424365 + 0.905491i \(0.360497\pi\)
\(258\) 0 0
\(259\) −10.0679 −0.625587
\(260\) 0 0
\(261\) −18.6219 −1.15267
\(262\) 0 0
\(263\) −28.6959 −1.76947 −0.884733 0.466098i \(-0.845660\pi\)
−0.884733 + 0.466098i \(0.845660\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −20.4413 −1.25099
\(268\) 0 0
\(269\) −4.39033 −0.267683 −0.133841 0.991003i \(-0.542731\pi\)
−0.133841 + 0.991003i \(0.542731\pi\)
\(270\) 0 0
\(271\) 18.8317 1.14394 0.571971 0.820274i \(-0.306179\pi\)
0.571971 + 0.820274i \(0.306179\pi\)
\(272\) 0 0
\(273\) −9.82552 −0.594668
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 22.1092 1.32842 0.664208 0.747548i \(-0.268769\pi\)
0.664208 + 0.747548i \(0.268769\pi\)
\(278\) 0 0
\(279\) −28.0740 −1.68075
\(280\) 0 0
\(281\) −8.18673 −0.488379 −0.244190 0.969727i \(-0.578522\pi\)
−0.244190 + 0.969727i \(0.578522\pi\)
\(282\) 0 0
\(283\) −23.8934 −1.42031 −0.710157 0.704043i \(-0.751376\pi\)
−0.710157 + 0.704043i \(0.751376\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.21585 −0.248854
\(288\) 0 0
\(289\) −16.4352 −0.966776
\(290\) 0 0
\(291\) −1.67754 −0.0983391
\(292\) 0 0
\(293\) 6.99387 0.408586 0.204293 0.978910i \(-0.434510\pi\)
0.204293 + 0.978910i \(0.434510\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −4.32246 −0.250815
\(298\) 0 0
\(299\) 5.75153 0.332620
\(300\) 0 0
\(301\) 27.4378 1.58149
\(302\) 0 0
\(303\) −0.683667 −0.0392757
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 11.0352 0.629815 0.314907 0.949122i \(-0.398027\pi\)
0.314907 + 0.949122i \(0.398027\pi\)
\(308\) 0 0
\(309\) 48.3638 2.75132
\(310\) 0 0
\(311\) 23.6449 1.34078 0.670390 0.742009i \(-0.266127\pi\)
0.670390 + 0.742009i \(0.266127\pi\)
\(312\) 0 0
\(313\) 3.50306 0.198005 0.0990024 0.995087i \(-0.468435\pi\)
0.0990024 + 0.995087i \(0.468435\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.10048 −0.0618092 −0.0309046 0.999522i \(-0.509839\pi\)
−0.0309046 + 0.999522i \(0.509839\pi\)
\(318\) 0 0
\(319\) −4.07399 −0.228100
\(320\) 0 0
\(321\) 40.6863 2.27089
\(322\) 0 0
\(323\) 1.88113 0.104669
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −9.43520 −0.521768
\(328\) 0 0
\(329\) −35.0862 −1.93437
\(330\) 0 0
\(331\) −12.3225 −0.677304 −0.338652 0.940912i \(-0.609971\pi\)
−0.338652 + 0.940912i \(0.609971\pi\)
\(332\) 0 0
\(333\) 12.8873 0.706218
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 10.0000 0.544735 0.272367 0.962193i \(-0.412193\pi\)
0.272367 + 0.962193i \(0.412193\pi\)
\(338\) 0 0
\(339\) −39.0352 −2.12010
\(340\) 0 0
\(341\) −6.14186 −0.332600
\(342\) 0 0
\(343\) 4.45819 0.240720
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.5709 −0.835891 −0.417946 0.908472i \(-0.637250\pi\)
−0.417946 + 0.908472i \(0.637250\pi\)
\(348\) 0 0
\(349\) −12.1541 −0.650595 −0.325297 0.945612i \(-0.605464\pi\)
−0.325297 + 0.945612i \(0.605464\pi\)
\(350\) 0 0
\(351\) 4.32246 0.230716
\(352\) 0 0
\(353\) 18.0061 0.958370 0.479185 0.877714i \(-0.340932\pi\)
0.479185 + 0.877714i \(0.340932\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.38420 −0.390813
\(358\) 0 0
\(359\) −7.35508 −0.388186 −0.194093 0.980983i \(-0.562176\pi\)
−0.194093 + 0.980983i \(0.562176\pi\)
\(360\) 0 0
\(361\) −12.7347 −0.670246
\(362\) 0 0
\(363\) −2.75153 −0.144418
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −28.5322 −1.48937 −0.744684 0.667417i \(-0.767400\pi\)
−0.744684 + 0.667417i \(0.767400\pi\)
\(368\) 0 0
\(369\) 5.39645 0.280928
\(370\) 0 0
\(371\) 50.7638 2.63552
\(372\) 0 0
\(373\) −18.0510 −0.934645 −0.467323 0.884087i \(-0.654781\pi\)
−0.467323 + 0.884087i \(0.654781\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.07399 0.209821
\(378\) 0 0
\(379\) −2.32246 −0.119297 −0.0596484 0.998219i \(-0.518998\pi\)
−0.0596484 + 0.998219i \(0.518998\pi\)
\(380\) 0 0
\(381\) −52.0026 −2.66418
\(382\) 0 0
\(383\) 5.67141 0.289796 0.144898 0.989447i \(-0.453715\pi\)
0.144898 + 0.989447i \(0.453715\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −35.1215 −1.78533
\(388\) 0 0
\(389\) −26.7347 −1.35550 −0.677751 0.735292i \(-0.737045\pi\)
−0.677751 + 0.735292i \(0.737045\pi\)
\(390\) 0 0
\(391\) 4.32246 0.218596
\(392\) 0 0
\(393\) −56.4950 −2.84979
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9.89339 −0.496535 −0.248267 0.968692i \(-0.579861\pi\)
−0.248267 + 0.968692i \(0.579861\pi\)
\(398\) 0 0
\(399\) −24.5939 −1.23124
\(400\) 0 0
\(401\) −27.2572 −1.36116 −0.680580 0.732673i \(-0.738272\pi\)
−0.680580 + 0.732673i \(0.738272\pi\)
\(402\) 0 0
\(403\) 6.14186 0.305948
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.81940 0.139752
\(408\) 0 0
\(409\) −2.03875 −0.100809 −0.0504047 0.998729i \(-0.516051\pi\)
−0.0504047 + 0.998729i \(0.516051\pi\)
\(410\) 0 0
\(411\) −9.06174 −0.446982
\(412\) 0 0
\(413\) 35.0862 1.72648
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −50.6986 −2.48272
\(418\) 0 0
\(419\) 0.310204 0.0151545 0.00757723 0.999971i \(-0.497588\pi\)
0.00757723 + 0.999971i \(0.497588\pi\)
\(420\) 0 0
\(421\) −8.28109 −0.403595 −0.201798 0.979427i \(-0.564678\pi\)
−0.201798 + 0.979427i \(0.564678\pi\)
\(422\) 0 0
\(423\) 44.9118 2.18369
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −25.2607 −1.22245
\(428\) 0 0
\(429\) 2.75153 0.132845
\(430\) 0 0
\(431\) 4.45819 0.214743 0.107372 0.994219i \(-0.465757\pi\)
0.107372 + 0.994219i \(0.465757\pi\)
\(432\) 0 0
\(433\) −22.9348 −1.10217 −0.551087 0.834448i \(-0.685787\pi\)
−0.551087 + 0.834448i \(0.685787\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 14.3965 0.688676
\(438\) 0 0
\(439\) −0.964753 −0.0460451 −0.0230226 0.999735i \(-0.507329\pi\)
−0.0230226 + 0.999735i \(0.507329\pi\)
\(440\) 0 0
\(441\) 26.2898 1.25190
\(442\) 0 0
\(443\) 36.5092 1.73460 0.867302 0.497782i \(-0.165852\pi\)
0.867302 + 0.497782i \(0.165852\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −23.0061 −1.08815
\(448\) 0 0
\(449\) 8.68017 0.409642 0.204821 0.978799i \(-0.434339\pi\)
0.204821 + 0.978799i \(0.434339\pi\)
\(450\) 0 0
\(451\) 1.18060 0.0555924
\(452\) 0 0
\(453\) −13.8811 −0.652193
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −11.4934 −0.537640 −0.268820 0.963190i \(-0.586634\pi\)
−0.268820 + 0.963190i \(0.586634\pi\)
\(458\) 0 0
\(459\) 3.24847 0.151625
\(460\) 0 0
\(461\) 25.0571 1.16703 0.583513 0.812103i \(-0.301678\pi\)
0.583513 + 0.812103i \(0.301678\pi\)
\(462\) 0 0
\(463\) −32.7868 −1.52373 −0.761865 0.647735i \(-0.775716\pi\)
−0.761865 + 0.647735i \(0.775716\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 41.7603 1.93244 0.966218 0.257727i \(-0.0829734\pi\)
0.966218 + 0.257727i \(0.0829734\pi\)
\(468\) 0 0
\(469\) −52.2960 −2.41480
\(470\) 0 0
\(471\) 33.7990 1.55738
\(472\) 0 0
\(473\) −7.68367 −0.353295
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −64.9796 −2.97521
\(478\) 0 0
\(479\) 3.96125 0.180994 0.0904972 0.995897i \(-0.471154\pi\)
0.0904972 + 0.995897i \(0.471154\pi\)
\(480\) 0 0
\(481\) −2.81940 −0.128553
\(482\) 0 0
\(483\) −56.5118 −2.57138
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 22.7990 1.03312 0.516561 0.856250i \(-0.327212\pi\)
0.516561 + 0.856250i \(0.327212\pi\)
\(488\) 0 0
\(489\) −33.2388 −1.50311
\(490\) 0 0
\(491\) −22.4256 −1.01205 −0.506026 0.862518i \(-0.668886\pi\)
−0.506026 + 0.862518i \(0.668886\pi\)
\(492\) 0 0
\(493\) 3.06174 0.137894
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −20.7807 −0.932140
\(498\) 0 0
\(499\) −23.9321 −1.07135 −0.535675 0.844424i \(-0.679943\pi\)
−0.535675 + 0.844424i \(0.679943\pi\)
\(500\) 0 0
\(501\) −57.3190 −2.56082
\(502\) 0 0
\(503\) 23.0766 1.02894 0.514468 0.857510i \(-0.327989\pi\)
0.514468 + 0.857510i \(0.327989\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 33.0184 1.46640
\(508\) 0 0
\(509\) 21.2220 0.940648 0.470324 0.882494i \(-0.344137\pi\)
0.470324 + 0.882494i \(0.344137\pi\)
\(510\) 0 0
\(511\) −52.5383 −2.32416
\(512\) 0 0
\(513\) 10.8194 0.477688
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 9.82552 0.432126
\(518\) 0 0
\(519\) 6.88726 0.302317
\(520\) 0 0
\(521\) 16.1806 0.708885 0.354443 0.935078i \(-0.384671\pi\)
0.354443 + 0.935078i \(0.384671\pi\)
\(522\) 0 0
\(523\) −31.8899 −1.39445 −0.697224 0.716854i \(-0.745582\pi\)
−0.697224 + 0.716854i \(0.745582\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.61580 0.201068
\(528\) 0 0
\(529\) 10.0801 0.438266
\(530\) 0 0
\(531\) −44.9118 −1.94901
\(532\) 0 0
\(533\) −1.18060 −0.0511376
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 31.8378 1.37390
\(538\) 0 0
\(539\) 5.75153 0.247736
\(540\) 0 0
\(541\) 12.4739 0.536297 0.268148 0.963378i \(-0.413588\pi\)
0.268148 + 0.963378i \(0.413588\pi\)
\(542\) 0 0
\(543\) 50.7419 2.17754
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −12.1250 −0.518427 −0.259214 0.965820i \(-0.583463\pi\)
−0.259214 + 0.965820i \(0.583463\pi\)
\(548\) 0 0
\(549\) 32.3347 1.38001
\(550\) 0 0
\(551\) 10.1975 0.434427
\(552\) 0 0
\(553\) 13.9030 0.591216
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −28.3673 −1.20196 −0.600981 0.799263i \(-0.705223\pi\)
−0.600981 + 0.799263i \(0.705223\pi\)
\(558\) 0 0
\(559\) 7.68367 0.324985
\(560\) 0 0
\(561\) 2.06786 0.0873053
\(562\) 0 0
\(563\) −4.08012 −0.171957 −0.0859783 0.996297i \(-0.527402\pi\)
−0.0859783 + 0.996297i \(0.527402\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.49694 0.272846
\(568\) 0 0
\(569\) −23.0088 −0.964577 −0.482289 0.876012i \(-0.660194\pi\)
−0.482289 + 0.876012i \(0.660194\pi\)
\(570\) 0 0
\(571\) −34.5322 −1.44513 −0.722563 0.691305i \(-0.757036\pi\)
−0.722563 + 0.691305i \(0.757036\pi\)
\(572\) 0 0
\(573\) −9.06174 −0.378559
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 25.1710 1.04788 0.523941 0.851755i \(-0.324461\pi\)
0.523941 + 0.851755i \(0.324461\pi\)
\(578\) 0 0
\(579\) −63.3021 −2.63075
\(580\) 0 0
\(581\) −19.9153 −0.826225
\(582\) 0 0
\(583\) −14.2159 −0.588760
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.2546 −0.423252 −0.211626 0.977351i \(-0.567876\pi\)
−0.211626 + 0.977351i \(0.567876\pi\)
\(588\) 0 0
\(589\) 15.3735 0.633453
\(590\) 0 0
\(591\) 36.4704 1.50019
\(592\) 0 0
\(593\) 10.9091 0.447985 0.223992 0.974591i \(-0.428091\pi\)
0.223992 + 0.974591i \(0.428091\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.55254 −0.186323
\(598\) 0 0
\(599\) 29.2607 1.19556 0.597780 0.801660i \(-0.296049\pi\)
0.597780 + 0.801660i \(0.296049\pi\)
\(600\) 0 0
\(601\) −27.2220 −1.11041 −0.555204 0.831714i \(-0.687360\pi\)
−0.555204 + 0.831714i \(0.687360\pi\)
\(602\) 0 0
\(603\) 66.9409 2.72604
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 32.7347 1.32866 0.664330 0.747440i \(-0.268717\pi\)
0.664330 + 0.747440i \(0.268717\pi\)
\(608\) 0 0
\(609\) −40.0291 −1.62206
\(610\) 0 0
\(611\) −9.82552 −0.397498
\(612\) 0 0
\(613\) 14.1894 0.573103 0.286551 0.958065i \(-0.407491\pi\)
0.286551 + 0.958065i \(0.407491\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −24.4766 −0.985390 −0.492695 0.870202i \(-0.663988\pi\)
−0.492695 + 0.870202i \(0.663988\pi\)
\(618\) 0 0
\(619\) 31.7603 1.27655 0.638277 0.769807i \(-0.279647\pi\)
0.638277 + 0.769807i \(0.279647\pi\)
\(620\) 0 0
\(621\) 24.8608 0.997628
\(622\) 0 0
\(623\) −26.5287 −1.06285
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 6.88726 0.275051
\(628\) 0 0
\(629\) −2.11887 −0.0844848
\(630\) 0 0
\(631\) −24.0219 −0.956296 −0.478148 0.878279i \(-0.658692\pi\)
−0.478148 + 0.878279i \(0.658692\pi\)
\(632\) 0 0
\(633\) 57.6924 2.29307
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.75153 −0.227884
\(638\) 0 0
\(639\) 26.6000 1.05228
\(640\) 0 0
\(641\) 16.0061 0.632204 0.316102 0.948725i \(-0.397626\pi\)
0.316102 + 0.948725i \(0.397626\pi\)
\(642\) 0 0
\(643\) 11.0836 0.437095 0.218548 0.975826i \(-0.429868\pi\)
0.218548 + 0.975826i \(0.429868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −29.0449 −1.14187 −0.570936 0.820995i \(-0.693420\pi\)
−0.570936 + 0.820995i \(0.693420\pi\)
\(648\) 0 0
\(649\) −9.82552 −0.385686
\(650\) 0 0
\(651\) −60.3470 −2.36518
\(652\) 0 0
\(653\) 50.3251 1.96937 0.984686 0.174335i \(-0.0557774\pi\)
0.984686 + 0.174335i \(0.0557774\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 67.2511 2.62372
\(658\) 0 0
\(659\) 26.7189 1.04082 0.520411 0.853916i \(-0.325779\pi\)
0.520411 + 0.853916i \(0.325779\pi\)
\(660\) 0 0
\(661\) −4.83165 −0.187930 −0.0939648 0.995576i \(-0.529954\pi\)
−0.0939648 + 0.995576i \(0.529954\pi\)
\(662\) 0 0
\(663\) −2.06786 −0.0803092
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 23.4317 0.907279
\(668\) 0 0
\(669\) −35.3067 −1.36504
\(670\) 0 0
\(671\) 7.07399 0.273088
\(672\) 0 0
\(673\) 20.7542 0.800014 0.400007 0.916512i \(-0.369008\pi\)
0.400007 + 0.916512i \(0.369008\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5.53568 −0.212754 −0.106377 0.994326i \(-0.533925\pi\)
−0.106377 + 0.994326i \(0.533925\pi\)
\(678\) 0 0
\(679\) −2.17710 −0.0835496
\(680\) 0 0
\(681\) 25.9444 0.994191
\(682\) 0 0
\(683\) 41.0256 1.56980 0.784901 0.619621i \(-0.212714\pi\)
0.784901 + 0.619621i \(0.212714\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 13.6944 0.522474
\(688\) 0 0
\(689\) 14.2159 0.541581
\(690\) 0 0
\(691\) 51.5180 1.95984 0.979918 0.199403i \(-0.0639002\pi\)
0.979918 + 0.199403i \(0.0639002\pi\)
\(692\) 0 0
\(693\) −16.3225 −0.620039
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.887261 −0.0336074
\(698\) 0 0
\(699\) −10.8194 −0.409227
\(700\) 0 0
\(701\) 19.2450 0.726872 0.363436 0.931619i \(-0.381603\pi\)
0.363436 + 0.931619i \(0.381603\pi\)
\(702\) 0 0
\(703\) −7.05713 −0.266165
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.887261 −0.0333689
\(708\) 0 0
\(709\) −8.99387 −0.337772 −0.168886 0.985636i \(-0.554017\pi\)
−0.168886 + 0.985636i \(0.554017\pi\)
\(710\) 0 0
\(711\) −17.7964 −0.667417
\(712\) 0 0
\(713\) 35.3251 1.32294
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −76.2695 −2.84834
\(718\) 0 0
\(719\) −10.6837 −0.398434 −0.199217 0.979955i \(-0.563840\pi\)
−0.199217 + 0.979955i \(0.563840\pi\)
\(720\) 0 0
\(721\) 62.7664 2.33754
\(722\) 0 0
\(723\) −33.3455 −1.24013
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.98424 −0.0735916 −0.0367958 0.999323i \(-0.511715\pi\)
−0.0367958 + 0.999323i \(0.511715\pi\)
\(728\) 0 0
\(729\) −43.9965 −1.62950
\(730\) 0 0
\(731\) 5.77452 0.213578
\(732\) 0 0
\(733\) 32.8765 1.21432 0.607161 0.794579i \(-0.292308\pi\)
0.607161 + 0.794579i \(0.292308\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 14.6449 0.539453
\(738\) 0 0
\(739\) 31.4352 1.15636 0.578181 0.815908i \(-0.303763\pi\)
0.578181 + 0.815908i \(0.303763\pi\)
\(740\) 0 0
\(741\) −6.88726 −0.253010
\(742\) 0 0
\(743\) 28.3638 1.04057 0.520284 0.853993i \(-0.325826\pi\)
0.520284 + 0.853993i \(0.325826\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 25.4923 0.932716
\(748\) 0 0
\(749\) 52.8025 1.92936
\(750\) 0 0
\(751\) −17.4291 −0.635996 −0.317998 0.948091i \(-0.603011\pi\)
−0.317998 + 0.948091i \(0.603011\pi\)
\(752\) 0 0
\(753\) −38.8485 −1.41572
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 21.8838 0.795379 0.397689 0.917520i \(-0.369812\pi\)
0.397689 + 0.917520i \(0.369812\pi\)
\(758\) 0 0
\(759\) 15.8255 0.574430
\(760\) 0 0
\(761\) 32.7224 1.18619 0.593093 0.805134i \(-0.297907\pi\)
0.593093 + 0.805134i \(0.297907\pi\)
\(762\) 0 0
\(763\) −12.2450 −0.443298
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.82552 0.354779
\(768\) 0 0
\(769\) −9.54181 −0.344086 −0.172043 0.985089i \(-0.555037\pi\)
−0.172043 + 0.985089i \(0.555037\pi\)
\(770\) 0 0
\(771\) −37.4378 −1.34829
\(772\) 0 0
\(773\) 0.0556080 0.00200008 0.00100004 0.999999i \(-0.499682\pi\)
0.00100004 + 0.999999i \(0.499682\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 27.7021 0.993806
\(778\) 0 0
\(779\) −2.95513 −0.105878
\(780\) 0 0
\(781\) 5.81940 0.208234
\(782\) 0 0
\(783\) 17.6097 0.629318
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −22.0970 −0.787672 −0.393836 0.919181i \(-0.628852\pi\)
−0.393836 + 0.919181i \(0.628852\pi\)
\(788\) 0 0
\(789\) 78.9578 2.81097
\(790\) 0 0
\(791\) −50.6598 −1.80126
\(792\) 0 0
\(793\) −7.07399 −0.251205
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −35.7577 −1.26660 −0.633301 0.773906i \(-0.718300\pi\)
−0.633301 + 0.773906i \(0.718300\pi\)
\(798\) 0 0
\(799\) −7.38420 −0.261234
\(800\) 0 0
\(801\) 33.9578 1.19984
\(802\) 0 0
\(803\) 14.7128 0.519203
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12.0801 0.425240
\(808\) 0 0
\(809\) 24.9286 0.876444 0.438222 0.898867i \(-0.355608\pi\)
0.438222 + 0.898867i \(0.355608\pi\)
\(810\) 0 0
\(811\) 29.6123 1.03983 0.519914 0.854218i \(-0.325964\pi\)
0.519914 + 0.854218i \(0.325964\pi\)
\(812\) 0 0
\(813\) −51.8159 −1.81726
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 19.2327 0.672867
\(818\) 0 0
\(819\) 16.3225 0.570353
\(820\) 0 0
\(821\) 0.328589 0.0114678 0.00573392 0.999984i \(-0.498175\pi\)
0.00573392 + 0.999984i \(0.498175\pi\)
\(822\) 0 0
\(823\) 42.5797 1.48423 0.742117 0.670270i \(-0.233822\pi\)
0.742117 + 0.670270i \(0.233822\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 23.1867 0.806282 0.403141 0.915138i \(-0.367918\pi\)
0.403141 + 0.915138i \(0.367918\pi\)
\(828\) 0 0
\(829\) −36.2546 −1.25917 −0.629587 0.776930i \(-0.716776\pi\)
−0.629587 + 0.776930i \(0.716776\pi\)
\(830\) 0 0
\(831\) −60.8343 −2.11032
\(832\) 0 0
\(833\) −4.32246 −0.149764
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 26.5479 0.917631
\(838\) 0 0
\(839\) −13.6607 −0.471619 −0.235809 0.971799i \(-0.575774\pi\)
−0.235809 + 0.971799i \(0.575774\pi\)
\(840\) 0 0
\(841\) −12.4026 −0.427675
\(842\) 0 0
\(843\) 22.5261 0.775839
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −3.57093 −0.122699
\(848\) 0 0
\(849\) 65.7434 2.25631
\(850\) 0 0
\(851\) −16.2159 −0.555872
\(852\) 0 0
\(853\) −54.2476 −1.85740 −0.928701 0.370829i \(-0.879074\pi\)
−0.928701 + 0.370829i \(0.879074\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.41221 −0.219037 −0.109518 0.993985i \(-0.534931\pi\)
−0.109518 + 0.993985i \(0.534931\pi\)
\(858\) 0 0
\(859\) 51.5031 1.75726 0.878631 0.477501i \(-0.158457\pi\)
0.878631 + 0.477501i \(0.158457\pi\)
\(860\) 0 0
\(861\) 11.6000 0.395329
\(862\) 0 0
\(863\) 43.2837 1.47339 0.736697 0.676223i \(-0.236384\pi\)
0.736697 + 0.676223i \(0.236384\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 45.2220 1.53582
\(868\) 0 0
\(869\) −3.89339 −0.132074
\(870\) 0 0
\(871\) −14.6449 −0.496224
\(872\) 0 0
\(873\) 2.78678 0.0943182
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −10.2511 −0.346155 −0.173077 0.984908i \(-0.555371\pi\)
−0.173077 + 0.984908i \(0.555371\pi\)
\(878\) 0 0
\(879\) −19.2439 −0.649079
\(880\) 0 0
\(881\) 8.19023 0.275936 0.137968 0.990437i \(-0.455943\pi\)
0.137968 + 0.990437i \(0.455943\pi\)
\(882\) 0 0
\(883\) −6.76116 −0.227531 −0.113766 0.993508i \(-0.536291\pi\)
−0.113766 + 0.993508i \(0.536291\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 10.3225 0.346594 0.173297 0.984870i \(-0.444558\pi\)
0.173297 + 0.984870i \(0.444558\pi\)
\(888\) 0 0
\(889\) −67.4888 −2.26350
\(890\) 0 0
\(891\) −1.81940 −0.0609521
\(892\) 0 0
\(893\) −24.5939 −0.823004
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −15.8255 −0.528399
\(898\) 0 0
\(899\) 25.0219 0.834527
\(900\) 0 0
\(901\) 10.6837 0.355925
\(902\) 0 0
\(903\) −75.4961 −2.51235
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −11.9348 −0.396287 −0.198144 0.980173i \(-0.563491\pi\)
−0.198144 + 0.980173i \(0.563491\pi\)
\(908\) 0 0
\(909\) 1.13573 0.0376698
\(910\) 0 0
\(911\) −7.35508 −0.243685 −0.121842 0.992549i \(-0.538880\pi\)
−0.121842 + 0.992549i \(0.538880\pi\)
\(912\) 0 0
\(913\) 5.57706 0.184574
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −73.3190 −2.42121
\(918\) 0 0
\(919\) −25.0184 −0.825280 −0.412640 0.910894i \(-0.635393\pi\)
−0.412640 + 0.910894i \(0.635393\pi\)
\(920\) 0 0
\(921\) −30.3638 −1.00052
\(922\) 0 0
\(923\) −5.81940 −0.191548
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −80.3435 −2.63883
\(928\) 0 0
\(929\) 4.42557 0.145198 0.0725992 0.997361i \(-0.476871\pi\)
0.0725992 + 0.997361i \(0.476871\pi\)
\(930\) 0 0
\(931\) −14.3965 −0.471825
\(932\) 0 0
\(933\) −65.0598 −2.12996
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 40.3612 1.31854 0.659272 0.751905i \(-0.270865\pi\)
0.659272 + 0.751905i \(0.270865\pi\)
\(938\) 0 0
\(939\) −9.63879 −0.314550
\(940\) 0 0
\(941\) 13.2704 0.432601 0.216301 0.976327i \(-0.430601\pi\)
0.216301 + 0.976327i \(0.430601\pi\)
\(942\) 0 0
\(943\) −6.79028 −0.221122
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.81940 0.156609 0.0783047 0.996929i \(-0.475049\pi\)
0.0783047 + 0.996929i \(0.475049\pi\)
\(948\) 0 0
\(949\) −14.7128 −0.477597
\(950\) 0 0
\(951\) 3.02801 0.0981900
\(952\) 0 0
\(953\) −16.0123 −0.518688 −0.259344 0.965785i \(-0.583506\pi\)
−0.259344 + 0.965785i \(0.583506\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 11.2097 0.362359
\(958\) 0 0
\(959\) −11.7603 −0.379760
\(960\) 0 0
\(961\) 6.72241 0.216852
\(962\) 0 0
\(963\) −67.5893 −2.17804
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −50.6211 −1.62786 −0.813932 0.580960i \(-0.802677\pi\)
−0.813932 + 0.580960i \(0.802677\pi\)
\(968\) 0 0
\(969\) −5.17600 −0.166277
\(970\) 0 0
\(971\) 27.5249 0.883318 0.441659 0.897183i \(-0.354390\pi\)
0.441659 + 0.897183i \(0.354390\pi\)
\(972\) 0 0
\(973\) −65.7964 −2.10934
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −48.1215 −1.53954 −0.769772 0.638320i \(-0.779630\pi\)
−0.769772 + 0.638320i \(0.779630\pi\)
\(978\) 0 0
\(979\) 7.42907 0.237434
\(980\) 0 0
\(981\) 15.6740 0.500434
\(982\) 0 0
\(983\) −12.8960 −0.411319 −0.205660 0.978624i \(-0.565934\pi\)
−0.205660 + 0.978624i \(0.565934\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 96.5409 3.07293
\(988\) 0 0
\(989\) 44.1929 1.40525
\(990\) 0 0
\(991\) 1.53218 0.0486714 0.0243357 0.999704i \(-0.492253\pi\)
0.0243357 + 0.999704i \(0.492253\pi\)
\(992\) 0 0
\(993\) 33.9056 1.07596
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −31.9831 −1.01292 −0.506458 0.862265i \(-0.669046\pi\)
−0.506458 + 0.862265i \(0.669046\pi\)
\(998\) 0 0
\(999\) −12.1867 −0.385571
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 2200.2.a.u.1.1 3
4.3 odd 2 4400.2.a.bz.1.3 3
5.2 odd 4 2200.2.b.m.1849.6 6
5.3 odd 4 2200.2.b.m.1849.1 6
5.4 even 2 2200.2.a.v.1.3 yes 3
20.3 even 4 4400.2.b.bb.4049.6 6
20.7 even 4 4400.2.b.bb.4049.1 6
20.19 odd 2 4400.2.a.by.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2200.2.a.u.1.1 3 1.1 even 1 trivial
2200.2.a.v.1.3 yes 3 5.4 even 2
2200.2.b.m.1849.1 6 5.3 odd 4
2200.2.b.m.1849.6 6 5.2 odd 4
4400.2.a.by.1.1 3 20.19 odd 2
4400.2.a.bz.1.3 3 4.3 odd 2
4400.2.b.bb.4049.1 6 20.7 even 4
4400.2.b.bb.4049.6 6 20.3 even 4