Properties

Label 882.2.l.a.227.8
Level $882$
Weight $2$
Character 882.227
Analytic conductor $7.043$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(227,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.227");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.l (of order \(6\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 227.8
Root \(1.62181 + 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 882.227
Dual form 882.2.l.a.509.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(1.94556 - 3.36980i) q^{5} +(1.10050 + 1.33750i) q^{6} -1.00000i q^{8} +(0.577806 - 2.94383i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(1.94556 - 3.36980i) q^{5} +(1.10050 + 1.33750i) q^{6} -1.00000i q^{8} +(0.577806 - 2.94383i) q^{9} +(3.36980 + 1.94556i) q^{10} +(-3.41614 + 1.97231i) q^{11} +(-1.33750 + 1.10050i) q^{12} +(2.46687 - 1.42425i) q^{13} +(-1.10628 - 6.64819i) q^{15} +1.00000 q^{16} +(-0.371058 + 0.642692i) q^{17} +(2.94383 + 0.577806i) q^{18} +(1.54563 - 0.892369i) q^{19} +(-1.94556 + 3.36980i) q^{20} +(-1.97231 - 3.41614i) q^{22} +(5.41535 + 3.12656i) q^{23} +(-1.10050 - 1.33750i) q^{24} +(-5.07039 - 8.78217i) q^{25} +(1.42425 + 2.46687i) q^{26} +(-2.46687 - 4.57324i) q^{27} +(-2.50079 - 1.44383i) q^{29} +(6.64819 - 1.10628i) q^{30} +3.51174i q^{31} +1.00000i q^{32} +(-2.39856 + 6.39742i) q^{33} +(-0.642692 - 0.371058i) q^{34} +(-0.577806 + 2.94383i) q^{36} +(-1.50079 - 2.59944i) q^{37} +(0.892369 + 1.54563i) q^{38} +(1.73205 - 4.61971i) q^{39} +(-3.36980 - 1.94556i) q^{40} +(-5.24705 - 9.08816i) q^{41} +(0.471521 - 0.816699i) q^{43} +(3.41614 - 1.97231i) q^{44} +(-8.79598 - 7.67448i) q^{45} +(-3.12656 + 5.41535i) q^{46} -2.18525 q^{47} +(1.33750 - 1.10050i) q^{48} +(8.78217 - 5.07039i) q^{50} +(0.210992 + 1.26795i) q^{51} +(-2.46687 + 1.42425i) q^{52} +(4.57324 - 2.46687i) q^{54} +15.3490i q^{55} +(1.08523 - 2.89450i) q^{57} +(1.44383 - 2.50079i) q^{58} -0.0211346 q^{59} +(1.10628 + 6.64819i) q^{60} +2.46911i q^{61} -3.51174 q^{62} -1.00000 q^{64} -11.0838i q^{65} +(-6.39742 - 2.39856i) q^{66} +13.4493 q^{67} +(0.371058 - 0.642692i) q^{68} +(10.6838 - 1.77782i) q^{69} +1.94304i q^{71} +(-2.94383 - 0.577806i) q^{72} +(4.20443 + 2.42743i) q^{73} +(2.59944 - 1.50079i) q^{74} +(-16.4464 - 6.16618i) q^{75} +(-1.54563 + 0.892369i) q^{76} +(4.61971 + 1.73205i) q^{78} +3.63613 q^{79} +(1.94556 - 3.36980i) q^{80} +(-8.33228 - 3.40192i) q^{81} +(9.08816 - 5.24705i) q^{82} +(-4.02998 + 6.98012i) q^{83} +(1.44383 + 2.50079i) q^{85} +(0.816699 + 0.471521i) q^{86} +(-4.93374 + 0.820992i) q^{87} +(1.97231 + 3.41614i) q^{88} +(4.63323 + 8.02499i) q^{89} +(7.67448 - 8.79598i) q^{90} +(-5.41535 - 3.12656i) q^{92} +(3.86466 + 4.69694i) q^{93} -2.18525i q^{94} -6.94462i q^{95} +(1.10050 + 1.33750i) q^{96} +(16.2983 + 9.40980i) q^{97} +(3.83228 + 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.33750 1.10050i 0.772205 0.635373i
\(4\) −1.00000 −0.500000
\(5\) 1.94556 3.36980i 0.870080 1.50702i 0.00816625 0.999967i \(-0.497401\pi\)
0.861913 0.507056i \(-0.169266\pi\)
\(6\) 1.10050 + 1.33750i 0.449277 + 0.546032i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.577806 2.94383i 0.192602 0.981277i
\(10\) 3.36980 + 1.94556i 1.06563 + 0.615239i
\(11\) −3.41614 + 1.97231i −1.03001 + 0.594674i −0.916986 0.398919i \(-0.869385\pi\)
−0.113019 + 0.993593i \(0.536052\pi\)
\(12\) −1.33750 + 1.10050i −0.386103 + 0.317687i
\(13\) 2.46687 1.42425i 0.684186 0.395015i −0.117244 0.993103i \(-0.537406\pi\)
0.801430 + 0.598088i \(0.204073\pi\)
\(14\) 0 0
\(15\) −1.10628 6.64819i −0.285641 1.71656i
\(16\) 1.00000 0.250000
\(17\) −0.371058 + 0.642692i −0.0899949 + 0.155876i −0.907509 0.420033i \(-0.862018\pi\)
0.817514 + 0.575909i \(0.195352\pi\)
\(18\) 2.94383 + 0.577806i 0.693868 + 0.136190i
\(19\) 1.54563 0.892369i 0.354591 0.204723i −0.312114 0.950045i \(-0.601037\pi\)
0.666706 + 0.745321i \(0.267704\pi\)
\(20\) −1.94556 + 3.36980i −0.435040 + 0.753511i
\(21\) 0 0
\(22\) −1.97231 3.41614i −0.420498 0.728324i
\(23\) 5.41535 + 3.12656i 1.12918 + 0.651932i 0.943728 0.330722i \(-0.107292\pi\)
0.185451 + 0.982654i \(0.440626\pi\)
\(24\) −1.10050 1.33750i −0.224638 0.273016i
\(25\) −5.07039 8.78217i −1.01408 1.75643i
\(26\) 1.42425 + 2.46687i 0.279318 + 0.483793i
\(27\) −2.46687 4.57324i −0.474749 0.880121i
\(28\) 0 0
\(29\) −2.50079 1.44383i −0.464385 0.268113i 0.249501 0.968374i \(-0.419733\pi\)
−0.713886 + 0.700262i \(0.753067\pi\)
\(30\) 6.64819 1.10628i 1.21379 0.201979i
\(31\) 3.51174i 0.630726i 0.948971 + 0.315363i \(0.102126\pi\)
−0.948971 + 0.315363i \(0.897874\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.39856 + 6.39742i −0.417536 + 1.11365i
\(34\) −0.642692 0.371058i −0.110221 0.0636360i
\(35\) 0 0
\(36\) −0.577806 + 2.94383i −0.0963009 + 0.490638i
\(37\) −1.50079 2.59944i −0.246728 0.427346i 0.715888 0.698215i \(-0.246022\pi\)
−0.962616 + 0.270870i \(0.912689\pi\)
\(38\) 0.892369 + 1.54563i 0.144761 + 0.250734i
\(39\) 1.73205 4.61971i 0.277350 0.739746i
\(40\) −3.36980 1.94556i −0.532813 0.307620i
\(41\) −5.24705 9.08816i −0.819452 1.41933i −0.906087 0.423092i \(-0.860945\pi\)
0.0866345 0.996240i \(-0.472389\pi\)
\(42\) 0 0
\(43\) 0.471521 0.816699i 0.0719063 0.124545i −0.827830 0.560978i \(-0.810425\pi\)
0.899737 + 0.436433i \(0.143758\pi\)
\(44\) 3.41614 1.97231i 0.515003 0.297337i
\(45\) −8.79598 7.67448i −1.31123 1.14404i
\(46\) −3.12656 + 5.41535i −0.460985 + 0.798450i
\(47\) −2.18525 −0.318752 −0.159376 0.987218i \(-0.550948\pi\)
−0.159376 + 0.987218i \(0.550948\pi\)
\(48\) 1.33750 1.10050i 0.193051 0.158843i
\(49\) 0 0
\(50\) 8.78217 5.07039i 1.24199 0.717061i
\(51\) 0.210992 + 1.26795i 0.0295447 + 0.177548i
\(52\) −2.46687 + 1.42425i −0.342093 + 0.197507i
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 4.57324 2.46687i 0.622340 0.335698i
\(55\) 15.3490i 2.06965i
\(56\) 0 0
\(57\) 1.08523 2.89450i 0.143742 0.383386i
\(58\) 1.44383 2.50079i 0.189584 0.328370i
\(59\) −0.0211346 −0.00275149 −0.00137575 0.999999i \(-0.500438\pi\)
−0.00137575 + 0.999999i \(0.500438\pi\)
\(60\) 1.10628 + 6.64819i 0.142821 + 0.858278i
\(61\) 2.46911i 0.316138i 0.987428 + 0.158069i \(0.0505268\pi\)
−0.987428 + 0.158069i \(0.949473\pi\)
\(62\) −3.51174 −0.445991
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 11.0838i 1.37478i
\(66\) −6.39742 2.39856i −0.787468 0.295242i
\(67\) 13.4493 1.64309 0.821544 0.570144i \(-0.193113\pi\)
0.821544 + 0.570144i \(0.193113\pi\)
\(68\) 0.371058 0.642692i 0.0449974 0.0779379i
\(69\) 10.6838 1.77782i 1.28618 0.214025i
\(70\) 0 0
\(71\) 1.94304i 0.230597i 0.993331 + 0.115298i \(0.0367824\pi\)
−0.993331 + 0.115298i \(0.963218\pi\)
\(72\) −2.94383 0.577806i −0.346934 0.0680950i
\(73\) 4.20443 + 2.42743i 0.492092 + 0.284109i 0.725442 0.688284i \(-0.241636\pi\)
−0.233350 + 0.972393i \(0.574969\pi\)
\(74\) 2.59944 1.50079i 0.302179 0.174463i
\(75\) −16.4464 6.16618i −1.89907 0.712009i
\(76\) −1.54563 + 0.892369i −0.177296 + 0.102362i
\(77\) 0 0
\(78\) 4.61971 + 1.73205i 0.523079 + 0.196116i
\(79\) 3.63613 0.409096 0.204548 0.978856i \(-0.434427\pi\)
0.204548 + 0.978856i \(0.434427\pi\)
\(80\) 1.94556 3.36980i 0.217520 0.376756i
\(81\) −8.33228 3.40192i −0.925809 0.377992i
\(82\) 9.08816 5.24705i 1.00362 0.579440i
\(83\) −4.02998 + 6.98012i −0.442347 + 0.766168i −0.997863 0.0653378i \(-0.979188\pi\)
0.555516 + 0.831506i \(0.312521\pi\)
\(84\) 0 0
\(85\) 1.44383 + 2.50079i 0.156605 + 0.271249i
\(86\) 0.816699 + 0.471521i 0.0880669 + 0.0508454i
\(87\) −4.93374 + 0.820992i −0.528952 + 0.0880196i
\(88\) 1.97231 + 3.41614i 0.210249 + 0.364162i
\(89\) 4.63323 + 8.02499i 0.491122 + 0.850647i 0.999948 0.0102218i \(-0.00325375\pi\)
−0.508826 + 0.860869i \(0.669920\pi\)
\(90\) 7.67448 8.79598i 0.808962 0.927178i
\(91\) 0 0
\(92\) −5.41535 3.12656i −0.564589 0.325966i
\(93\) 3.86466 + 4.69694i 0.400747 + 0.487050i
\(94\) 2.18525i 0.225392i
\(95\) 6.94462i 0.712503i
\(96\) 1.10050 + 1.33750i 0.112319 + 0.136508i
\(97\) 16.2983 + 9.40980i 1.65484 + 0.955421i 0.975043 + 0.222018i \(0.0712643\pi\)
0.679794 + 0.733403i \(0.262069\pi\)
\(98\) 0 0
\(99\) 3.83228 + 11.1962i 0.385159 + 1.12526i
\(100\) 5.07039 + 8.78217i 0.507039 + 0.878217i
\(101\) 4.14079 + 7.17206i 0.412024 + 0.713647i 0.995111 0.0987631i \(-0.0314886\pi\)
−0.583087 + 0.812410i \(0.698155\pi\)
\(102\) −1.26795 + 0.210992i −0.125546 + 0.0208913i
\(103\) 14.7646 + 8.52435i 1.45480 + 0.839929i 0.998748 0.0500247i \(-0.0159300\pi\)
0.456051 + 0.889953i \(0.349263\pi\)
\(104\) −1.42425 2.46687i −0.139659 0.241896i
\(105\) 0 0
\(106\) 0 0
\(107\) −12.4161 + 7.16846i −1.20031 + 0.693001i −0.960625 0.277848i \(-0.910379\pi\)
−0.239689 + 0.970850i \(0.577045\pi\)
\(108\) 2.46687 + 4.57324i 0.237374 + 0.440061i
\(109\) −5.63998 + 9.76874i −0.540212 + 0.935675i 0.458679 + 0.888602i \(0.348323\pi\)
−0.998891 + 0.0470733i \(0.985011\pi\)
\(110\) −15.3490 −1.46347
\(111\) −4.86799 1.82513i −0.462049 0.173234i
\(112\) 0 0
\(113\) −8.51501 + 4.91614i −0.801024 + 0.462472i −0.843829 0.536612i \(-0.819704\pi\)
0.0428049 + 0.999083i \(0.486371\pi\)
\(114\) 2.89450 + 1.08523i 0.271095 + 0.101641i
\(115\) 21.0718 12.1658i 1.96495 1.13447i
\(116\) 2.50079 + 1.44383i 0.232192 + 0.134056i
\(117\) −2.76737 8.08498i −0.255844 0.747457i
\(118\) 0.0211346i 0.00194560i
\(119\) 0 0
\(120\) −6.64819 + 1.10628i −0.606894 + 0.100989i
\(121\) 2.28001 3.94910i 0.207274 0.359009i
\(122\) −2.46911 −0.223543
\(123\) −17.0194 6.38103i −1.53459 0.575358i
\(124\) 3.51174i 0.315363i
\(125\) −20.0033 −1.78915
\(126\) 0 0
\(127\) 2.94462 0.261293 0.130646 0.991429i \(-0.458295\pi\)
0.130646 + 0.991429i \(0.458295\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −0.268117 1.61124i −0.0236064 0.141862i
\(130\) 11.0838 0.972115
\(131\) 7.53255 13.0468i 0.658122 1.13990i −0.322979 0.946406i \(-0.604684\pi\)
0.981101 0.193495i \(-0.0619823\pi\)
\(132\) 2.39856 6.39742i 0.208768 0.556824i
\(133\) 0 0
\(134\) 13.4493i 1.16184i
\(135\) −20.2104 0.584648i −1.73943 0.0503185i
\(136\) 0.642692 + 0.371058i 0.0551104 + 0.0318180i
\(137\) 13.6139 7.85997i 1.16311 0.671523i 0.211064 0.977472i \(-0.432307\pi\)
0.952048 + 0.305950i \(0.0989739\pi\)
\(138\) 1.77782 + 10.6838i 0.151338 + 0.909465i
\(139\) 2.86373 1.65337i 0.242898 0.140237i −0.373610 0.927586i \(-0.621880\pi\)
0.616508 + 0.787349i \(0.288547\pi\)
\(140\) 0 0
\(141\) −2.92277 + 2.40487i −0.246142 + 0.202526i
\(142\) −1.94304 −0.163056
\(143\) −5.61811 + 9.73085i −0.469810 + 0.813735i
\(144\) 0.577806 2.94383i 0.0481505 0.245319i
\(145\) −9.73085 + 5.61811i −0.808103 + 0.466559i
\(146\) −2.42743 + 4.20443i −0.200896 + 0.347961i
\(147\) 0 0
\(148\) 1.50079 + 2.59944i 0.123364 + 0.213673i
\(149\) −9.52765 5.50079i −0.780535 0.450642i 0.0560848 0.998426i \(-0.482138\pi\)
−0.836620 + 0.547784i \(0.815472\pi\)
\(150\) 6.16618 16.4464i 0.503467 1.34284i
\(151\) 0.719988 + 1.24706i 0.0585918 + 0.101484i 0.893834 0.448399i \(-0.148006\pi\)
−0.835242 + 0.549883i \(0.814672\pi\)
\(152\) −0.892369 1.54563i −0.0723807 0.125367i
\(153\) 1.67758 + 1.46368i 0.135624 + 0.118332i
\(154\) 0 0
\(155\) 11.8339 + 6.83228i 0.950518 + 0.548782i
\(156\) −1.73205 + 4.61971i −0.138675 + 0.369873i
\(157\) 16.6071i 1.32539i 0.748890 + 0.662695i \(0.230587\pi\)
−0.748890 + 0.662695i \(0.769413\pi\)
\(158\) 3.63613i 0.289275i
\(159\) 0 0
\(160\) 3.36980 + 1.94556i 0.266406 + 0.153810i
\(161\) 0 0
\(162\) 3.40192 8.33228i 0.267280 0.654646i
\(163\) 6.19773 + 10.7348i 0.485444 + 0.840813i 0.999860 0.0167274i \(-0.00532476\pi\)
−0.514416 + 0.857541i \(0.671991\pi\)
\(164\) 5.24705 + 9.08816i 0.409726 + 0.709666i
\(165\) 16.8915 + 20.5292i 1.31500 + 1.59820i
\(166\) −6.98012 4.02998i −0.541763 0.312787i
\(167\) −5.86087 10.1513i −0.453528 0.785534i 0.545074 0.838388i \(-0.316502\pi\)
−0.998602 + 0.0528541i \(0.983168\pi\)
\(168\) 0 0
\(169\) −2.44304 + 4.23147i −0.187926 + 0.325498i
\(170\) −2.50079 + 1.44383i −0.191802 + 0.110737i
\(171\) −1.73391 5.06568i −0.132595 0.387383i
\(172\) −0.471521 + 0.816699i −0.0359532 + 0.0622727i
\(173\) 16.7710 1.27507 0.637536 0.770420i \(-0.279954\pi\)
0.637536 + 0.770420i \(0.279954\pi\)
\(174\) −0.820992 4.93374i −0.0622393 0.374026i
\(175\) 0 0
\(176\) −3.41614 + 1.97231i −0.257501 + 0.148668i
\(177\) −0.0282675 + 0.0232586i −0.00212472 + 0.00174822i
\(178\) −8.02499 + 4.63323i −0.601499 + 0.347275i
\(179\) −5.00158 2.88766i −0.373835 0.215834i 0.301297 0.953530i \(-0.402580\pi\)
−0.675133 + 0.737696i \(0.735914\pi\)
\(180\) 8.79598 + 7.67448i 0.655614 + 0.572022i
\(181\) 5.53310i 0.411272i −0.978629 0.205636i \(-0.934074\pi\)
0.978629 0.205636i \(-0.0659263\pi\)
\(182\) 0 0
\(183\) 2.71726 + 3.30244i 0.200865 + 0.244123i
\(184\) 3.12656 5.41535i 0.230493 0.399225i
\(185\) −11.6795 −0.858692
\(186\) −4.69694 + 3.86466i −0.344396 + 0.283371i
\(187\) 2.92737i 0.214070i
\(188\) 2.18525 0.159376
\(189\) 0 0
\(190\) 6.94462 0.503816
\(191\) 6.21372i 0.449609i 0.974404 + 0.224805i \(0.0721744\pi\)
−0.974404 + 0.224805i \(0.927826\pi\)
\(192\) −1.33750 + 1.10050i −0.0965257 + 0.0794216i
\(193\) −7.80542 −0.561847 −0.280923 0.959730i \(-0.590641\pi\)
−0.280923 + 0.959730i \(0.590641\pi\)
\(194\) −9.40980 + 16.2983i −0.675584 + 1.17015i
\(195\) −12.1977 14.8246i −0.873497 1.06161i
\(196\) 0 0
\(197\) 12.7737i 0.910092i −0.890468 0.455046i \(-0.849623\pi\)
0.890468 0.455046i \(-0.150377\pi\)
\(198\) −11.1962 + 3.83228i −0.795676 + 0.272348i
\(199\) 1.56925 + 0.906005i 0.111241 + 0.0642250i 0.554588 0.832125i \(-0.312876\pi\)
−0.443347 + 0.896350i \(0.646209\pi\)
\(200\) −8.78217 + 5.07039i −0.620993 + 0.358530i
\(201\) 17.9884 14.8009i 1.26880 1.04397i
\(202\) −7.17206 + 4.14079i −0.504624 + 0.291345i
\(203\) 0 0
\(204\) −0.210992 1.26795i −0.0147724 0.0887742i
\(205\) −40.8338 −2.85195
\(206\) −8.52435 + 14.7646i −0.593919 + 1.02870i
\(207\) 12.3331 14.1353i 0.857208 0.982474i
\(208\) 2.46687 1.42425i 0.171047 0.0987537i
\(209\) −3.52006 + 6.09692i −0.243487 + 0.421732i
\(210\) 0 0
\(211\) −1.88766 3.26953i −0.129952 0.225083i 0.793706 0.608302i \(-0.208149\pi\)
−0.923658 + 0.383218i \(0.874816\pi\)
\(212\) 0 0
\(213\) 2.13832 + 2.59882i 0.146515 + 0.178068i
\(214\) −7.16846 12.4161i −0.490026 0.848750i
\(215\) −1.83474 3.17787i −0.125128 0.216729i
\(216\) −4.57324 + 2.46687i −0.311170 + 0.167849i
\(217\) 0 0
\(218\) −9.76874 5.63998i −0.661622 0.381988i
\(219\) 8.29481 1.38029i 0.560511 0.0932712i
\(220\) 15.3490i 1.03483i
\(221\) 2.11392i 0.142197i
\(222\) 1.82513 4.86799i 0.122495 0.326718i
\(223\) 11.0662 + 6.38910i 0.741051 + 0.427846i 0.822451 0.568836i \(-0.192606\pi\)
−0.0814006 + 0.996681i \(0.525939\pi\)
\(224\) 0 0
\(225\) −28.7829 + 9.85197i −1.91886 + 0.656798i
\(226\) −4.91614 8.51501i −0.327017 0.566410i
\(227\) −9.99110 17.3051i −0.663133 1.14858i −0.979788 0.200039i \(-0.935893\pi\)
0.316655 0.948541i \(-0.397440\pi\)
\(228\) −1.08523 + 2.89450i −0.0718708 + 0.191693i
\(229\) −8.77402 5.06568i −0.579804 0.334750i 0.181252 0.983437i \(-0.441985\pi\)
−0.761055 + 0.648687i \(0.775318\pi\)
\(230\) 12.1658 + 21.0718i 0.802188 + 1.38943i
\(231\) 0 0
\(232\) −1.44383 + 2.50079i −0.0947921 + 0.164185i
\(233\) −6.33070 + 3.65503i −0.414738 + 0.239449i −0.692824 0.721107i \(-0.743634\pi\)
0.278085 + 0.960556i \(0.410300\pi\)
\(234\) 8.08498 2.76737i 0.528532 0.180909i
\(235\) −4.25153 + 7.36387i −0.277339 + 0.480366i
\(236\) 0.0211346 0.00137575
\(237\) 4.86332 4.00156i 0.315906 0.259929i
\(238\) 0 0
\(239\) 7.28317 4.20494i 0.471109 0.271995i −0.245595 0.969373i \(-0.578983\pi\)
0.716704 + 0.697378i \(0.245650\pi\)
\(240\) −1.10628 6.64819i −0.0714103 0.429139i
\(241\) 7.75277 4.47607i 0.499400 0.288329i −0.229066 0.973411i \(-0.573567\pi\)
0.728466 + 0.685082i \(0.240234\pi\)
\(242\) 3.94910 + 2.28001i 0.253858 + 0.146565i
\(243\) −14.8882 + 4.61960i −0.955080 + 0.296347i
\(244\) 2.46911i 0.158069i
\(245\) 0 0
\(246\) 6.38103 17.0194i 0.406840 1.08512i
\(247\) 2.54191 4.40271i 0.161738 0.280138i
\(248\) 3.51174 0.222995
\(249\) 2.29153 + 13.7709i 0.145220 + 0.872695i
\(250\) 20.0033i 1.26512i
\(251\) 12.6432 0.798033 0.399017 0.916944i \(-0.369352\pi\)
0.399017 + 0.916944i \(0.369352\pi\)
\(252\) 0 0
\(253\) −24.6661 −1.55075
\(254\) 2.94462i 0.184762i
\(255\) 4.68324 + 1.75587i 0.293276 + 0.109957i
\(256\) 1.00000 0.0625000
\(257\) −8.15329 + 14.1219i −0.508588 + 0.880900i 0.491362 + 0.870955i \(0.336499\pi\)
−0.999951 + 0.00994523i \(0.996834\pi\)
\(258\) 1.61124 0.268117i 0.100312 0.0166922i
\(259\) 0 0
\(260\) 11.0838i 0.687389i
\(261\) −5.69536 + 6.52765i −0.352534 + 0.404051i
\(262\) 13.0468 + 7.53255i 0.806032 + 0.465363i
\(263\) −20.5434 + 11.8608i −1.26676 + 0.731366i −0.974374 0.224934i \(-0.927783\pi\)
−0.292389 + 0.956300i \(0.594450\pi\)
\(264\) 6.39742 + 2.39856i 0.393734 + 0.147621i
\(265\) 0 0
\(266\) 0 0
\(267\) 15.0284 + 5.63455i 0.919725 + 0.344829i
\(268\) −13.4493 −0.821544
\(269\) −3.64144 + 6.30716i −0.222022 + 0.384554i −0.955422 0.295244i \(-0.904599\pi\)
0.733400 + 0.679798i \(0.237932\pi\)
\(270\) 0.584648 20.2104i 0.0355805 1.22996i
\(271\) −19.6483 + 11.3440i −1.19355 + 0.689097i −0.959110 0.283033i \(-0.908659\pi\)
−0.234441 + 0.972130i \(0.575326\pi\)
\(272\) −0.371058 + 0.642692i −0.0224987 + 0.0389689i
\(273\) 0 0
\(274\) 7.85997 + 13.6139i 0.474838 + 0.822444i
\(275\) 34.6423 + 20.0007i 2.08901 + 1.20609i
\(276\) −10.6838 + 1.77782i −0.643089 + 0.107012i
\(277\) −12.0838 20.9298i −0.726046 1.25755i −0.958542 0.284951i \(-0.908023\pi\)
0.232496 0.972597i \(-0.425311\pi\)
\(278\) 1.65337 + 2.86373i 0.0991628 + 0.171755i
\(279\) 10.3380 + 2.02910i 0.618917 + 0.121479i
\(280\) 0 0
\(281\) −4.11229 2.37423i −0.245319 0.141635i 0.372300 0.928112i \(-0.378569\pi\)
−0.617619 + 0.786478i \(0.711903\pi\)
\(282\) −2.40487 2.92277i −0.143208 0.174049i
\(283\) 29.3853i 1.74677i −0.487027 0.873387i \(-0.661919\pi\)
0.487027 0.873387i \(-0.338081\pi\)
\(284\) 1.94304i 0.115298i
\(285\) −7.64254 9.28842i −0.452705 0.550198i
\(286\) −9.73085 5.61811i −0.575398 0.332206i
\(287\) 0 0
\(288\) 2.94383 + 0.577806i 0.173467 + 0.0340475i
\(289\) 8.22463 + 14.2455i 0.483802 + 0.837969i
\(290\) −5.61811 9.73085i −0.329907 0.571415i
\(291\) 32.1544 5.35061i 1.88492 0.313658i
\(292\) −4.20443 2.42743i −0.246046 0.142055i
\(293\) 3.31206 + 5.73666i 0.193493 + 0.335139i 0.946405 0.322981i \(-0.104685\pi\)
−0.752913 + 0.658121i \(0.771352\pi\)
\(294\) 0 0
\(295\) −0.0411186 + 0.0712195i −0.00239402 + 0.00414656i
\(296\) −2.59944 + 1.50079i −0.151090 + 0.0872316i
\(297\) 17.4470 + 10.7574i 1.01238 + 0.624209i
\(298\) 5.50079 9.52765i 0.318652 0.551922i
\(299\) 17.8119 1.03009
\(300\) 16.4464 + 6.16618i 0.949533 + 0.356005i
\(301\) 0 0
\(302\) −1.24706 + 0.719988i −0.0717600 + 0.0414307i
\(303\) 13.4311 + 5.03569i 0.771599 + 0.289293i
\(304\) 1.54563 0.892369i 0.0886479 0.0511809i
\(305\) 8.32043 + 4.80380i 0.476426 + 0.275065i
\(306\) −1.46368 + 1.67758i −0.0836733 + 0.0959007i
\(307\) 21.7242i 1.23987i 0.784655 + 0.619933i \(0.212840\pi\)
−0.784655 + 0.619933i \(0.787160\pi\)
\(308\) 0 0
\(309\) 29.1287 4.84712i 1.65707 0.275743i
\(310\) −6.83228 + 11.8339i −0.388048 + 0.672118i
\(311\) −6.29800 −0.357127 −0.178563 0.983928i \(-0.557145\pi\)
−0.178563 + 0.983928i \(0.557145\pi\)
\(312\) −4.61971 1.73205i −0.261540 0.0980581i
\(313\) 22.2191i 1.25590i 0.778256 + 0.627948i \(0.216105\pi\)
−0.778256 + 0.627948i \(0.783895\pi\)
\(314\) −16.6071 −0.937192
\(315\) 0 0
\(316\) −3.63613 −0.204548
\(317\) 15.6614i 0.879632i −0.898088 0.439816i \(-0.855044\pi\)
0.898088 0.439816i \(-0.144956\pi\)
\(318\) 0 0
\(319\) 11.3907 0.637758
\(320\) −1.94556 + 3.36980i −0.108760 + 0.188378i
\(321\) −8.71769 + 23.2518i −0.486574 + 1.29779i
\(322\) 0 0
\(323\) 1.32448i 0.0736963i
\(324\) 8.33228 + 3.40192i 0.462905 + 0.188996i
\(325\) −25.0159 14.4430i −1.38763 0.801151i
\(326\) −10.7348 + 6.19773i −0.594545 + 0.343260i
\(327\) 3.20701 + 19.2725i 0.177348 + 1.06577i
\(328\) −9.08816 + 5.24705i −0.501810 + 0.289720i
\(329\) 0 0
\(330\) −20.5292 + 16.8915i −1.13010 + 0.929847i
\(331\) 1.27226 0.0699296 0.0349648 0.999389i \(-0.488868\pi\)
0.0349648 + 0.999389i \(0.488868\pi\)
\(332\) 4.02998 6.98012i 0.221174 0.383084i
\(333\) −8.51948 + 2.91610i −0.466865 + 0.159801i
\(334\) 10.1513 5.86087i 0.555456 0.320693i
\(335\) 26.1663 45.3214i 1.42962 2.47617i
\(336\) 0 0
\(337\) −3.78001 6.54717i −0.205910 0.356647i 0.744512 0.667609i \(-0.232682\pi\)
−0.950422 + 0.310962i \(0.899349\pi\)
\(338\) −4.23147 2.44304i −0.230162 0.132884i
\(339\) −5.97860 + 15.9461i −0.324713 + 0.866072i
\(340\) −1.44383 2.50079i −0.0783027 0.135624i
\(341\) −6.92623 11.9966i −0.375076 0.649651i
\(342\) 5.06568 1.73391i 0.273921 0.0937592i
\(343\) 0 0
\(344\) −0.816699 0.471521i −0.0440334 0.0254227i
\(345\) 14.7950 39.4612i 0.796537 2.12452i
\(346\) 16.7710i 0.901613i
\(347\) 22.1091i 1.18688i 0.804879 + 0.593439i \(0.202230\pi\)
−0.804879 + 0.593439i \(0.797770\pi\)
\(348\) 4.93374 0.820992i 0.264476 0.0440098i
\(349\) −12.7682 7.37173i −0.683467 0.394600i 0.117693 0.993050i \(-0.462450\pi\)
−0.801160 + 0.598450i \(0.795783\pi\)
\(350\) 0 0
\(351\) −12.5989 7.76816i −0.672478 0.414634i
\(352\) −1.97231 3.41614i −0.105124 0.182081i
\(353\) 8.63881 + 14.9629i 0.459798 + 0.796393i 0.998950 0.0458154i \(-0.0145886\pi\)
−0.539152 + 0.842208i \(0.681255\pi\)
\(354\) −0.0232586 0.0282675i −0.00123618 0.00150240i
\(355\) 6.54767 + 3.78030i 0.347514 + 0.200638i
\(356\) −4.63323 8.02499i −0.245561 0.425324i
\(357\) 0 0
\(358\) 2.88766 5.00158i 0.152618 0.264342i
\(359\) −9.45088 + 5.45647i −0.498799 + 0.287982i −0.728217 0.685346i \(-0.759651\pi\)
0.229419 + 0.973328i \(0.426318\pi\)
\(360\) −7.67448 + 8.79598i −0.404481 + 0.463589i
\(361\) −7.90736 + 13.6959i −0.416177 + 0.720839i
\(362\) 5.53310 0.290813
\(363\) −1.29646 7.79106i −0.0680466 0.408925i
\(364\) 0 0
\(365\) 16.3599 9.44541i 0.856318 0.494395i
\(366\) −3.30244 + 2.71726i −0.172621 + 0.142033i
\(367\) −30.9407 + 17.8636i −1.61509 + 0.932472i −0.626923 + 0.779081i \(0.715686\pi\)
−0.988166 + 0.153391i \(0.950981\pi\)
\(368\) 5.41535 + 3.12656i 0.282295 + 0.162983i
\(369\) −29.7858 + 10.1952i −1.55059 + 0.530743i
\(370\) 11.6795i 0.607187i
\(371\) 0 0
\(372\) −3.86466 4.69694i −0.200373 0.243525i
\(373\) 16.0300 27.7648i 0.830003 1.43761i −0.0680328 0.997683i \(-0.521672\pi\)
0.898035 0.439923i \(-0.144994\pi\)
\(374\) 2.92737 0.151371
\(375\) −26.7544 + 22.0136i −1.38159 + 1.13678i
\(376\) 2.18525i 0.112696i
\(377\) −8.22549 −0.423634
\(378\) 0 0
\(379\) 34.8891 1.79214 0.896068 0.443918i \(-0.146412\pi\)
0.896068 + 0.443918i \(0.146412\pi\)
\(380\) 6.94462i 0.356251i
\(381\) 3.93842 3.24055i 0.201772 0.166018i
\(382\) −6.21372 −0.317922
\(383\) −8.76711 + 15.1851i −0.447978 + 0.775921i −0.998254 0.0590616i \(-0.981189\pi\)
0.550276 + 0.834983i \(0.314523\pi\)
\(384\) −1.10050 1.33750i −0.0561596 0.0682539i
\(385\) 0 0
\(386\) 7.80542i 0.397286i
\(387\) −2.13178 1.85997i −0.108364 0.0945477i
\(388\) −16.2983 9.40980i −0.827418 0.477710i
\(389\) 6.60060 3.81086i 0.334664 0.193218i −0.323246 0.946315i \(-0.604774\pi\)
0.657910 + 0.753097i \(0.271441\pi\)
\(390\) 14.8246 12.1977i 0.750672 0.617656i
\(391\) −4.01882 + 2.32027i −0.203241 + 0.117341i
\(392\) 0 0
\(393\) −4.28317 25.7396i −0.216057 1.29839i
\(394\) 12.7737 0.643532
\(395\) 7.07430 12.2530i 0.355947 0.616517i
\(396\) −3.83228 11.1962i −0.192579 0.562628i
\(397\) 32.6032 18.8234i 1.63631 0.944722i 0.654216 0.756307i \(-0.272999\pi\)
0.982090 0.188414i \(-0.0603348\pi\)
\(398\) −0.906005 + 1.56925i −0.0454139 + 0.0786592i
\(399\) 0 0
\(400\) −5.07039 8.78217i −0.253519 0.439108i
\(401\) −18.5689 10.7207i −0.927284 0.535368i −0.0413326 0.999145i \(-0.513160\pi\)
−0.885952 + 0.463778i \(0.846494\pi\)
\(402\) 14.8009 + 17.9884i 0.738202 + 0.897178i
\(403\) 5.00158 + 8.66299i 0.249146 + 0.431534i
\(404\) −4.14079 7.17206i −0.206012 0.356823i
\(405\) −27.6747 + 21.4595i −1.37517 + 1.06633i
\(406\) 0 0
\(407\) 10.2538 + 5.92004i 0.508262 + 0.293445i
\(408\) 1.26795 0.210992i 0.0627728 0.0104456i
\(409\) 29.5703i 1.46216i −0.682293 0.731079i \(-0.739017\pi\)
0.682293 0.731079i \(-0.260983\pi\)
\(410\) 40.8338i 2.01664i
\(411\) 9.55865 25.4947i 0.471493 1.25756i
\(412\) −14.7646 8.52435i −0.727400 0.419964i
\(413\) 0 0
\(414\) 14.1353 + 12.3331i 0.694714 + 0.606137i
\(415\) 15.6811 + 27.1605i 0.769755 + 1.33325i
\(416\) 1.42425 + 2.46687i 0.0698294 + 0.120948i
\(417\) 2.01070 5.36291i 0.0984642 0.262623i
\(418\) −6.09692 3.52006i −0.298210 0.172172i
\(419\) 3.56481 + 6.17443i 0.174152 + 0.301641i 0.939868 0.341539i \(-0.110948\pi\)
−0.765715 + 0.643180i \(0.777615\pi\)
\(420\) 0 0
\(421\) −2.31007 + 4.00115i −0.112586 + 0.195004i −0.916812 0.399319i \(-0.869247\pi\)
0.804226 + 0.594323i \(0.202580\pi\)
\(422\) 3.26953 1.88766i 0.159158 0.0918899i
\(423\) −1.26265 + 6.43301i −0.0613922 + 0.312784i
\(424\) 0 0
\(425\) 7.52564 0.365047
\(426\) −2.59882 + 2.13832i −0.125913 + 0.103602i
\(427\) 0 0
\(428\) 12.4161 7.16846i 0.600157 0.346501i
\(429\) 3.19458 + 19.1977i 0.154236 + 0.926875i
\(430\) 3.17787 1.83474i 0.153250 0.0884792i
\(431\) −3.47078 2.00385i −0.167181 0.0965223i 0.414075 0.910243i \(-0.364105\pi\)
−0.581256 + 0.813721i \(0.697439\pi\)
\(432\) −2.46687 4.57324i −0.118687 0.220030i
\(433\) 29.4125i 1.41348i −0.707475 0.706738i \(-0.750166\pi\)
0.707475 0.706738i \(-0.249834\pi\)
\(434\) 0 0
\(435\) −6.83228 + 18.2230i −0.327583 + 0.873726i
\(436\) 5.63998 9.76874i 0.270106 0.467838i
\(437\) 11.1602 0.533863
\(438\) 1.38029 + 8.29481i 0.0659527 + 0.396341i
\(439\) 21.3769i 1.02027i −0.860096 0.510133i \(-0.829596\pi\)
0.860096 0.510133i \(-0.170404\pi\)
\(440\) 15.3490 0.731733
\(441\) 0 0
\(442\) −2.11392 −0.100549
\(443\) 5.83386i 0.277175i −0.990350 0.138587i \(-0.955744\pi\)
0.990350 0.138587i \(-0.0442562\pi\)
\(444\) 4.86799 + 1.82513i 0.231024 + 0.0866171i
\(445\) 36.0569 1.70926
\(446\) −6.38910 + 11.0662i −0.302533 + 0.524002i
\(447\) −18.7968 + 3.12786i −0.889059 + 0.147943i
\(448\) 0 0
\(449\) 22.5823i 1.06573i 0.846202 + 0.532863i \(0.178884\pi\)
−0.846202 + 0.532863i \(0.821116\pi\)
\(450\) −9.85197 28.7829i −0.464427 1.35684i
\(451\) 35.8493 + 20.6976i 1.68808 + 0.974613i
\(452\) 8.51501 4.91614i 0.400512 0.231236i
\(453\) 2.33537 + 0.875590i 0.109725 + 0.0411388i
\(454\) 17.3051 9.99110i 0.812168 0.468906i
\(455\) 0 0
\(456\) −2.89450 1.08523i −0.135548 0.0508203i
\(457\) 39.8623 1.86468 0.932340 0.361584i \(-0.117764\pi\)
0.932340 + 0.361584i \(0.117764\pi\)
\(458\) 5.06568 8.77402i 0.236704 0.409983i
\(459\) 3.85454 + 0.111505i 0.179915 + 0.00520459i
\(460\) −21.0718 + 12.1658i −0.982476 + 0.567233i
\(461\) 3.68254 6.37834i 0.171513 0.297069i −0.767436 0.641125i \(-0.778468\pi\)
0.938949 + 0.344056i \(0.111801\pi\)
\(462\) 0 0
\(463\) −14.3457 24.8475i −0.666702 1.15476i −0.978821 0.204718i \(-0.934372\pi\)
0.312119 0.950043i \(-0.398961\pi\)
\(464\) −2.50079 1.44383i −0.116096 0.0670282i
\(465\) 23.3467 3.88498i 1.08268 0.180162i
\(466\) −3.65503 6.33070i −0.169316 0.293264i
\(467\) −6.83519 11.8389i −0.316295 0.547839i 0.663417 0.748250i \(-0.269106\pi\)
−0.979712 + 0.200411i \(0.935772\pi\)
\(468\) 2.76737 + 8.08498i 0.127922 + 0.373728i
\(469\) 0 0
\(470\) −7.36387 4.25153i −0.339670 0.196109i
\(471\) 18.2761 + 22.2119i 0.842117 + 1.02347i
\(472\) 0.0211346i 0.000972799i
\(473\) 3.71994i 0.171043i
\(474\) 4.00156 + 4.86332i 0.183798 + 0.223380i
\(475\) −15.6739 9.04931i −0.719166 0.415211i
\(476\) 0 0
\(477\) 0 0
\(478\) 4.20494 + 7.28317i 0.192329 + 0.333124i
\(479\) −5.20537 9.01596i −0.237839 0.411950i 0.722255 0.691627i \(-0.243106\pi\)
−0.960094 + 0.279677i \(0.909773\pi\)
\(480\) 6.64819 1.10628i 0.303447 0.0504947i
\(481\) −7.40449 4.27499i −0.337616 0.194923i
\(482\) 4.47607 + 7.75277i 0.203879 + 0.353129i
\(483\) 0 0
\(484\) −2.28001 + 3.94910i −0.103637 + 0.179504i
\(485\) 63.4184 36.6146i 2.87968 1.66258i
\(486\) −4.61960 14.8882i −0.209549 0.675344i
\(487\) −1.16925 + 2.02520i −0.0529838 + 0.0917707i −0.891301 0.453412i \(-0.850207\pi\)
0.838317 + 0.545183i \(0.183540\pi\)
\(488\) 2.46911 0.111772
\(489\) 20.1031 + 7.53716i 0.909092 + 0.340842i
\(490\) 0 0
\(491\) −29.3448 + 16.9422i −1.32431 + 0.764591i −0.984413 0.175871i \(-0.943726\pi\)
−0.339898 + 0.940462i \(0.610392\pi\)
\(492\) 17.0194 + 6.38103i 0.767295 + 0.287679i
\(493\) 1.85588 1.07149i 0.0835845 0.0482575i
\(494\) 4.40271 + 2.54191i 0.198087 + 0.114366i
\(495\) 45.1848 + 8.86872i 2.03090 + 0.398619i
\(496\) 3.51174i 0.157682i
\(497\) 0 0
\(498\) −13.7709 + 2.29153i −0.617088 + 0.102686i
\(499\) 8.30223 14.3799i 0.371659 0.643732i −0.618162 0.786051i \(-0.712123\pi\)
0.989821 + 0.142319i \(0.0454558\pi\)
\(500\) 20.0033 0.894576
\(501\) −19.0104 7.12751i −0.849324 0.318434i
\(502\) 12.6432i 0.564295i
\(503\) 35.3661 1.57690 0.788449 0.615100i \(-0.210885\pi\)
0.788449 + 0.615100i \(0.210885\pi\)
\(504\) 0 0
\(505\) 32.2246 1.43398
\(506\) 24.6661i 1.09654i
\(507\) 1.38916 + 8.34816i 0.0616950 + 0.370755i
\(508\) −2.94462 −0.130646
\(509\) 18.5291 32.0933i 0.821287 1.42251i −0.0834371 0.996513i \(-0.526590\pi\)
0.904724 0.425998i \(-0.140077\pi\)
\(510\) −1.75587 + 4.68324i −0.0777511 + 0.207377i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −7.89388 4.86718i −0.348523 0.214891i
\(514\) −14.1219 8.15329i −0.622891 0.359626i
\(515\) 57.4507 33.1692i 2.53158 1.46161i
\(516\) 0.268117 + 1.61124i 0.0118032 + 0.0709310i
\(517\) 7.46513 4.30999i 0.328316 0.189553i
\(518\) 0 0
\(519\) 22.4311 18.4564i 0.984618 0.810147i
\(520\) −11.0838 −0.486057
\(521\) 0.891547 1.54420i 0.0390594 0.0676528i −0.845835 0.533445i \(-0.820897\pi\)
0.884894 + 0.465792i \(0.154231\pi\)
\(522\) −6.52765 5.69536i −0.285707 0.249279i
\(523\) −20.8312 + 12.0269i −0.910886 + 0.525901i −0.880716 0.473644i \(-0.842938\pi\)
−0.0301702 + 0.999545i \(0.509605\pi\)
\(524\) −7.53255 + 13.0468i −0.329061 + 0.569950i
\(525\) 0 0
\(526\) −11.8608 20.5434i −0.517154 0.895737i
\(527\) −2.25696 1.30306i −0.0983149 0.0567621i
\(528\) −2.39856 + 6.39742i −0.104384 + 0.278412i
\(529\) 8.05069 + 13.9442i 0.350030 + 0.606270i
\(530\) 0 0
\(531\) −0.0122117 + 0.0622167i −0.000529942 + 0.00269998i
\(532\) 0 0
\(533\) −25.8876 14.9462i −1.12132 0.647392i
\(534\) −5.63455 + 15.0284i −0.243831 + 0.650344i
\(535\) 55.7866i 2.41187i
\(536\) 13.4493i 0.580920i
\(537\) −9.86747 + 1.64198i −0.425813 + 0.0708569i
\(538\) −6.30716 3.64144i −0.271921 0.156994i
\(539\) 0 0
\(540\) 20.2104 + 0.584648i 0.869716 + 0.0251592i
\(541\) −15.0016 25.9835i −0.644968 1.11712i −0.984309 0.176454i \(-0.943537\pi\)
0.339341 0.940664i \(-0.389796\pi\)
\(542\) −11.3440 19.6483i −0.487265 0.843968i
\(543\) −6.08917 7.40051i −0.261311 0.317586i
\(544\) −0.642692 0.371058i −0.0275552 0.0159090i
\(545\) 21.9458 + 38.0113i 0.940056 + 1.62822i
\(546\) 0 0
\(547\) −10.7816 + 18.6743i −0.460987 + 0.798454i −0.999010 0.0444765i \(-0.985838\pi\)
0.538023 + 0.842930i \(0.319171\pi\)
\(548\) −13.6139 + 7.85997i −0.581556 + 0.335761i
\(549\) 7.26865 + 1.42667i 0.310219 + 0.0608887i
\(550\) −20.0007 + 34.6423i −0.852835 + 1.47715i
\(551\) −5.15372 −0.219556
\(552\) −1.77782 10.6838i −0.0756692 0.454733i
\(553\) 0 0
\(554\) 20.9298 12.0838i 0.889221 0.513392i
\(555\) −15.6213 + 12.8533i −0.663087 + 0.545590i
\(556\) −2.86373 + 1.65337i −0.121449 + 0.0701187i
\(557\) −31.9976 18.4738i −1.35578 0.782762i −0.366731 0.930327i \(-0.619523\pi\)
−0.989052 + 0.147565i \(0.952856\pi\)
\(558\) −2.02910 + 10.3380i −0.0858987 + 0.437640i
\(559\) 2.68625i 0.113616i
\(560\) 0 0
\(561\) −3.22157 3.91535i −0.136015 0.165306i
\(562\) 2.37423 4.11229i 0.100151 0.173467i
\(563\) 15.1684 0.639273 0.319637 0.947540i \(-0.396439\pi\)
0.319637 + 0.947540i \(0.396439\pi\)
\(564\) 2.92277 2.40487i 0.123071 0.101263i
\(565\) 38.2585i 1.60955i
\(566\) 29.3853 1.23516
\(567\) 0 0
\(568\) 1.94304 0.0815282
\(569\) 36.7292i 1.53977i 0.638183 + 0.769885i \(0.279686\pi\)
−0.638183 + 0.769885i \(0.720314\pi\)
\(570\) 9.28842 7.64254i 0.389049 0.320111i
\(571\) 11.2277 0.469866 0.234933 0.972012i \(-0.424513\pi\)
0.234933 + 0.972012i \(0.424513\pi\)
\(572\) 5.61811 9.73085i 0.234905 0.406867i
\(573\) 6.83819 + 8.31085i 0.285670 + 0.347191i
\(574\) 0 0
\(575\) 63.4114i 2.64444i
\(576\) −0.577806 + 2.94383i −0.0240752 + 0.122660i
\(577\) −31.6545 18.2757i −1.31780 0.760829i −0.334422 0.942424i \(-0.608541\pi\)
−0.983374 + 0.181594i \(0.941874\pi\)
\(578\) −14.2455 + 8.22463i −0.592534 + 0.342100i
\(579\) −10.4397 + 8.58986i −0.433861 + 0.356982i
\(580\) 9.73085 5.61811i 0.404052 0.233279i
\(581\) 0 0
\(582\) 5.35061 + 32.1544i 0.221790 + 1.33284i
\(583\) 0 0
\(584\) 2.42743 4.20443i 0.100448 0.173981i
\(585\) −32.6289 6.40429i −1.34904 0.264785i
\(586\) −5.73666 + 3.31206i −0.236979 + 0.136820i
\(587\) −4.99738 + 8.65571i −0.206264 + 0.357259i −0.950535 0.310619i \(-0.899464\pi\)
0.744271 + 0.667878i \(0.232797\pi\)
\(588\) 0 0
\(589\) 3.13376 + 5.42784i 0.129124 + 0.223650i
\(590\) −0.0712195 0.0411186i −0.00293206 0.00169283i
\(591\) −14.0575 17.0849i −0.578248 0.702778i
\(592\) −1.50079 2.59944i −0.0616820 0.106836i
\(593\) 3.89111 + 6.73961i 0.159789 + 0.276763i 0.934792 0.355194i \(-0.115585\pi\)
−0.775004 + 0.631957i \(0.782252\pi\)
\(594\) −10.7574 + 17.4470i −0.441382 + 0.715860i
\(595\) 0 0
\(596\) 9.52765 + 5.50079i 0.390268 + 0.225321i
\(597\) 3.09592 0.515173i 0.126708 0.0210846i
\(598\) 17.8119i 0.728385i
\(599\) 25.0124i 1.02198i 0.859586 + 0.510990i \(0.170721\pi\)
−0.859586 + 0.510990i \(0.829279\pi\)
\(600\) −6.16618 + 16.4464i −0.251733 + 0.671421i
\(601\) −25.9925 15.0068i −1.06026 0.612139i −0.134753 0.990879i \(-0.543024\pi\)
−0.925503 + 0.378740i \(0.876357\pi\)
\(602\) 0 0
\(603\) 7.77106 39.5924i 0.316462 1.61233i
\(604\) −0.719988 1.24706i −0.0292959 0.0507420i
\(605\) −8.87179 15.3664i −0.360689 0.624732i
\(606\) −5.03569 + 13.4311i −0.204561 + 0.545603i
\(607\) 3.96882 + 2.29140i 0.161089 + 0.0930050i 0.578378 0.815769i \(-0.303686\pi\)
−0.417288 + 0.908774i \(0.637019\pi\)
\(608\) 0.892369 + 1.54563i 0.0361903 + 0.0626835i
\(609\) 0 0
\(610\) −4.80380 + 8.32043i −0.194500 + 0.336884i
\(611\) −5.39073 + 3.11234i −0.218085 + 0.125912i
\(612\) −1.67758 1.46368i −0.0678120 0.0591659i
\(613\) −15.2761 + 26.4590i −0.616996 + 1.06867i 0.373034 + 0.927818i \(0.378317\pi\)
−0.990031 + 0.140852i \(0.955016\pi\)
\(614\) −21.7242 −0.876717
\(615\) −54.6151 + 44.9375i −2.20229 + 1.81206i
\(616\) 0 0
\(617\) −28.2484 + 16.3092i −1.13724 + 0.656585i −0.945745 0.324909i \(-0.894666\pi\)
−0.191493 + 0.981494i \(0.561333\pi\)
\(618\) 4.84712 + 29.1287i 0.194980 + 1.17173i
\(619\) −17.3244 + 10.0023i −0.696327 + 0.402024i −0.805978 0.591946i \(-0.798360\pi\)
0.109651 + 0.993970i \(0.465027\pi\)
\(620\) −11.8339 6.83228i −0.475259 0.274391i
\(621\) 0.939542 32.4785i 0.0377025 1.30332i
\(622\) 6.29800i 0.252527i
\(623\) 0 0
\(624\) 1.73205 4.61971i 0.0693375 0.184937i
\(625\) −13.5657 + 23.4965i −0.542628 + 0.939859i
\(626\) −22.2191 −0.888052
\(627\) 2.00158 + 12.0284i 0.0799353 + 0.480369i
\(628\) 16.6071i 0.662695i
\(629\) 2.22752 0.0888171
\(630\) 0 0
\(631\) 6.09634 0.242692 0.121346 0.992610i \(-0.461279\pi\)
0.121346 + 0.992610i \(0.461279\pi\)
\(632\) 3.63613i 0.144637i
\(633\) −6.12285 2.29562i −0.243362 0.0912426i
\(634\) 15.6614 0.621994
\(635\) 5.72893 9.92279i 0.227345 0.393774i
\(636\) 0 0
\(637\) 0 0
\(638\) 11.3907i 0.450963i
\(639\) 5.71999 + 1.12270i 0.226279 + 0.0444134i
\(640\) −3.36980 1.94556i −0.133203 0.0769049i
\(641\) −28.9612 + 16.7207i −1.14390 + 0.660429i −0.947393 0.320074i \(-0.896292\pi\)
−0.196504 + 0.980503i \(0.562959\pi\)
\(642\) −23.2518 8.71769i −0.917674 0.344060i
\(643\) 16.6022 9.58527i 0.654726 0.378006i −0.135539 0.990772i \(-0.543276\pi\)
0.790264 + 0.612766i \(0.209943\pi\)
\(644\) 0 0
\(645\) −5.95121 2.23126i −0.234328 0.0878559i
\(646\) −1.32448 −0.0521111
\(647\) 22.3025 38.6290i 0.876800 1.51866i 0.0219681 0.999759i \(-0.493007\pi\)
0.854832 0.518904i \(-0.173660\pi\)
\(648\) −3.40192 + 8.33228i −0.133640 + 0.327323i
\(649\) 0.0721988 0.0416840i 0.00283405 0.00163624i
\(650\) 14.4430 25.0159i 0.566500 0.981206i
\(651\) 0 0
\(652\) −6.19773 10.7348i −0.242722 0.420407i
\(653\) 0.564755 + 0.326061i 0.0221006 + 0.0127598i 0.511010 0.859575i \(-0.329272\pi\)
−0.488909 + 0.872335i \(0.662605\pi\)
\(654\) −19.2725 + 3.20701i −0.753613 + 0.125404i
\(655\) −29.3100 50.7664i −1.14524 1.98361i
\(656\) −5.24705 9.08816i −0.204863 0.354833i
\(657\) 9.57529 10.9746i 0.373568 0.428158i
\(658\) 0 0
\(659\) 26.2738 + 15.1692i 1.02348 + 0.590908i 0.915111 0.403202i \(-0.132103\pi\)
0.108372 + 0.994110i \(0.465436\pi\)
\(660\) −16.8915 20.5292i −0.657501 0.799099i
\(661\) 12.8176i 0.498548i −0.968433 0.249274i \(-0.919808\pi\)
0.968433 0.249274i \(-0.0801919\pi\)
\(662\) 1.27226i 0.0494477i
\(663\) 2.32636 + 2.82736i 0.0903484 + 0.109806i
\(664\) 6.98012 + 4.02998i 0.270881 + 0.156393i
\(665\) 0 0
\(666\) −2.91610 8.51948i −0.112996 0.330123i
\(667\) −9.02843 15.6377i −0.349582 0.605494i
\(668\) 5.86087 + 10.1513i 0.226764 + 0.392767i
\(669\) 21.8323 3.63297i 0.844085 0.140459i
\(670\) 45.3214 + 26.1663i 1.75092 + 1.01089i
\(671\) −4.86986 8.43484i −0.187999 0.325623i
\(672\) 0 0
\(673\) 11.2246 19.4416i 0.432678 0.749420i −0.564425 0.825484i \(-0.690902\pi\)
0.997103 + 0.0760644i \(0.0242355\pi\)
\(674\) 6.54717 3.78001i 0.252188 0.145601i
\(675\) −27.6550 + 44.8526i −1.06444 + 1.72638i
\(676\) 2.44304 4.23147i 0.0939632 0.162749i
\(677\) −51.1807 −1.96703 −0.983516 0.180820i \(-0.942125\pi\)
−0.983516 + 0.180820i \(0.942125\pi\)
\(678\) −15.9461 5.97860i −0.612406 0.229607i
\(679\) 0 0
\(680\) 2.50079 1.44383i 0.0959009 0.0553684i
\(681\) −32.4073 12.1503i −1.24185 0.465602i
\(682\) 11.9966 6.92623i 0.459373 0.265219i
\(683\) −12.6107 7.28080i −0.482536 0.278592i 0.238937 0.971035i \(-0.423201\pi\)
−0.721473 + 0.692443i \(0.756534\pi\)
\(684\) 1.73391 + 5.06568i 0.0662977 + 0.193691i
\(685\) 61.1681i 2.33711i
\(686\) 0 0
\(687\) −17.3100 + 2.88045i −0.660419 + 0.109896i
\(688\) 0.471521 0.816699i 0.0179766 0.0311363i
\(689\) 0 0
\(690\) 39.4612 + 14.7950i 1.50226 + 0.563237i
\(691\) 24.4515i 0.930180i 0.885263 + 0.465090i \(0.153978\pi\)
−0.885263 + 0.465090i \(0.846022\pi\)
\(692\) −16.7710 −0.637536
\(693\) 0 0
\(694\) −22.1091 −0.839250
\(695\) 12.8669i 0.488071i
\(696\) 0.820992 + 4.93374i 0.0311196 + 0.187013i
\(697\) 7.78785 0.294986
\(698\) 7.37173 12.7682i 0.279024 0.483284i
\(699\) −4.44495 + 11.8555i −0.168123 + 0.448417i
\(700\) 0 0
\(701\) 2.21697i 0.0837337i 0.999123 + 0.0418669i \(0.0133305\pi\)
−0.999123 + 0.0418669i \(0.986669\pi\)
\(702\) 7.76816 12.5989i 0.293190 0.475514i
\(703\) −4.63932 2.67851i −0.174975 0.101022i
\(704\) 3.41614 1.97231i 0.128751 0.0743342i
\(705\) 2.41751 + 14.5280i 0.0910487 + 0.547155i
\(706\) −14.9629 + 8.63881i −0.563135 + 0.325126i
\(707\) 0 0
\(708\) 0.0282675 0.0232586i 0.00106236 0.000874112i
\(709\) −24.3923 −0.916072 −0.458036 0.888934i \(-0.651447\pi\)
−0.458036 + 0.888934i \(0.651447\pi\)
\(710\) −3.78030 + 6.54767i −0.141872 + 0.245730i
\(711\) 2.10098 10.7041i 0.0787927 0.401437i
\(712\) 8.02499 4.63323i 0.300749 0.173638i
\(713\) −10.9796 + 19.0173i −0.411190 + 0.712203i
\(714\) 0 0
\(715\) 21.8607 + 37.8639i 0.817544 + 1.41603i
\(716\) 5.00158 + 2.88766i 0.186918 + 0.107917i
\(717\) 5.11370 13.6392i 0.190975 0.509366i
\(718\) −5.45647 9.45088i −0.203634 0.352704i
\(719\) 1.11376 + 1.92909i 0.0415363 + 0.0719429i 0.886046 0.463597i \(-0.153441\pi\)
−0.844510 + 0.535540i \(0.820108\pi\)
\(720\) −8.79598 7.67448i −0.327807 0.286011i
\(721\) 0 0
\(722\) −13.6959 7.90736i −0.509710 0.294281i
\(723\) 5.44342 14.5186i 0.202443 0.539954i
\(724\) 5.53310i 0.205636i
\(725\) 29.2831i 1.08755i
\(726\) 7.79106 1.29646i 0.289153 0.0481162i
\(727\) 10.4880 + 6.05523i 0.388977 + 0.224576i 0.681717 0.731616i \(-0.261234\pi\)
−0.292740 + 0.956192i \(0.594567\pi\)
\(728\) 0 0
\(729\) −14.8291 + 22.5632i −0.549227 + 0.835673i
\(730\) 9.44541 + 16.3599i 0.349590 + 0.605508i
\(731\) 0.349924 + 0.606086i 0.0129424 + 0.0224169i
\(732\) −2.71726 3.30244i −0.100433 0.122062i
\(733\) −13.5673 7.83306i −0.501118 0.289321i 0.228057 0.973648i \(-0.426763\pi\)
−0.729175 + 0.684327i \(0.760096\pi\)
\(734\) −17.8636 30.9407i −0.659357 1.14204i
\(735\) 0 0
\(736\) −3.12656 + 5.41535i −0.115246 + 0.199613i
\(737\) −45.9446 + 26.5261i −1.69239 + 0.977102i
\(738\) −10.1952 29.7858i −0.375292 1.09643i
\(739\) 4.05227 7.01874i 0.149065 0.258188i −0.781817 0.623508i \(-0.785707\pi\)
0.930882 + 0.365319i \(0.119040\pi\)
\(740\) 11.6795 0.429346
\(741\) −1.44538 8.68599i −0.0530974 0.319088i
\(742\) 0 0
\(743\) −10.5429 + 6.08697i −0.386783 + 0.223309i −0.680765 0.732502i \(-0.738353\pi\)
0.293982 + 0.955811i \(0.405019\pi\)
\(744\) 4.69694 3.86466i 0.172198 0.141685i
\(745\) −37.0732 + 21.4042i −1.35826 + 0.784189i
\(746\) 27.7648 + 16.0300i 1.01654 + 0.586900i
\(747\) 18.2198 + 15.8967i 0.666626 + 0.581631i
\(748\) 2.92737i 0.107035i
\(749\) 0 0
\(750\) −22.0136 26.7544i −0.803824 0.976934i
\(751\) −17.3062 + 29.9752i −0.631511 + 1.09381i 0.355732 + 0.934588i \(0.384232\pi\)
−0.987243 + 0.159221i \(0.949102\pi\)
\(752\) −2.18525 −0.0796879
\(753\) 16.9103 13.9139i 0.616246 0.507049i
\(754\) 8.22549i 0.299555i
\(755\) 5.60311 0.203918
\(756\) 0 0
\(757\) −39.0553 −1.41949 −0.709744 0.704459i \(-0.751190\pi\)
−0.709744 + 0.704459i \(0.751190\pi\)
\(758\) 34.8891i 1.26723i
\(759\) −32.9909 + 27.1451i −1.19749 + 0.985303i
\(760\) −6.94462 −0.251908
\(761\) 5.11262 8.85532i 0.185332 0.321005i −0.758356 0.651840i \(-0.773997\pi\)
0.943688 + 0.330835i \(0.107330\pi\)
\(762\) 3.24055 + 3.93842i 0.117393 + 0.142674i
\(763\) 0 0
\(764\) 6.21372i 0.224805i
\(765\) 8.19615 2.80542i 0.296333 0.101430i
\(766\) −15.1851 8.76711i −0.548659 0.316769i
\(767\) −0.0521363 + 0.0301009i −0.00188253 + 0.00108688i
\(768\) 1.33750 1.10050i 0.0482628 0.0397108i
\(769\) −26.6746 + 15.4006i −0.961910 + 0.555359i −0.896760 0.442517i \(-0.854086\pi\)
−0.0651494 + 0.997876i \(0.520752\pi\)
\(770\) 0 0
\(771\) 4.63613 + 27.8607i 0.166966 + 1.00338i
\(772\) 7.80542 0.280923
\(773\) 17.8916 30.9892i 0.643518 1.11461i −0.341124 0.940018i \(-0.610808\pi\)
0.984642 0.174587i \(-0.0558590\pi\)
\(774\) 1.85997 2.13178i 0.0668553 0.0766251i
\(775\) 30.8406 17.8059i 1.10783 0.639605i
\(776\) 9.40980 16.2983i 0.337792 0.585073i
\(777\) 0 0
\(778\) 3.81086 + 6.60060i 0.136626 + 0.236643i
\(779\) −16.2200 9.36461i −0.581141 0.335522i
\(780\) 12.1977 + 14.8246i 0.436749 + 0.530805i
\(781\) −3.83228 6.63771i −0.137130 0.237516i
\(782\) −2.32027 4.01882i −0.0829727 0.143713i
\(783\) −0.433877 + 14.9985i −0.0155055 + 0.536001i
\(784\) 0 0
\(785\) 55.9626 + 32.3100i 1.99739 + 1.15319i
\(786\) 25.7396 4.28317i 0.918101 0.152775i
\(787\) 15.3413i 0.546857i 0.961892 + 0.273429i \(0.0881578\pi\)
−0.961892 + 0.273429i \(0.911842\pi\)
\(788\) 12.7737i 0.455046i
\(789\) −14.4241 + 38.4718i −0.513511 + 1.36963i
\(790\) 12.2530 + 7.07430i 0.435944 + 0.251692i
\(791\) 0 0
\(792\) 11.1962 3.83228i 0.397838 0.136174i
\(793\) 3.51663 + 6.09098i 0.124879 + 0.216297i
\(794\) 18.8234 + 32.6032i 0.668019 + 1.15704i
\(795\) 0 0
\(796\) −1.56925 0.906005i −0.0556205 0.0321125i
\(797\) −17.5200 30.3455i −0.620590 1.07489i −0.989376 0.145379i \(-0.953560\pi\)
0.368786 0.929514i \(-0.379774\pi\)
\(798\) 0 0
\(799\) 0.810856 1.40444i 0.0286860 0.0496857i
\(800\) 8.78217 5.07039i 0.310496 0.179265i
\(801\) 26.3013 9.00256i 0.929312 0.318090i
\(802\) 10.7207 18.5689i 0.378562 0.655689i
\(803\) −19.1506 −0.675809
\(804\) −17.9884 + 14.8009i −0.634401 + 0.521987i
\(805\) 0 0
\(806\) −8.66299 + 5.00158i −0.305141 + 0.176173i
\(807\) 2.07060 + 12.4432i 0.0728885 + 0.438022i
\(808\) 7.17206 4.14079i 0.252312 0.145673i
\(809\) 23.6360 + 13.6462i 0.830997 + 0.479777i 0.854194 0.519954i \(-0.174051\pi\)
−0.0231967 + 0.999731i \(0.507384\pi\)
\(810\) −21.4595 27.6747i −0.754011 0.972391i
\(811\) 27.7628i 0.974883i 0.873156 + 0.487442i \(0.162070\pi\)
−0.873156 + 0.487442i \(0.837930\pi\)
\(812\) 0 0
\(813\) −13.7956 + 36.7955i −0.483833 + 1.29047i
\(814\) −5.92004 + 10.2538i −0.207497 + 0.359396i
\(815\) 48.2322 1.68950
\(816\) 0.210992 + 1.26795i 0.00738618 + 0.0443871i
\(817\) 1.68308i 0.0588836i
\(818\) 29.5703 1.03390
\(819\) 0 0
\(820\) 40.8338 1.42598
\(821\) 44.4523i 1.55140i 0.631104 + 0.775698i \(0.282602\pi\)
−0.631104 + 0.775698i \(0.717398\pi\)
\(822\) 25.4947 + 9.55865i 0.889231 + 0.333396i
\(823\) −51.1153 −1.78177 −0.890884 0.454231i \(-0.849914\pi\)
−0.890884 + 0.454231i \(0.849914\pi\)
\(824\) 8.52435 14.7646i 0.296960 0.514349i
\(825\) 68.3448 11.3728i 2.37946 0.395951i
\(826\) 0 0
\(827\) 14.5414i 0.505653i 0.967512 + 0.252826i \(0.0813601\pi\)
−0.967512 + 0.252826i \(0.918640\pi\)
\(828\) −12.3331 + 14.1353i −0.428604 + 0.491237i
\(829\) 24.2211 + 13.9841i 0.841234 + 0.485686i 0.857683 0.514178i \(-0.171903\pi\)
−0.0164497 + 0.999865i \(0.505236\pi\)
\(830\) −27.1605 + 15.6811i −0.942754 + 0.544299i
\(831\) −39.1953 14.6953i −1.35967 0.509775i
\(832\) −2.46687 + 1.42425i −0.0855233 + 0.0493769i
\(833\) 0 0
\(834\) 5.36291 + 2.01070i 0.185703 + 0.0696247i
\(835\) −45.6107 −1.57842
\(836\) 3.52006 6.09692i 0.121744 0.210866i
\(837\) 16.0600 8.66299i 0.555116 0.299437i
\(838\) −6.17443 + 3.56481i −0.213292 + 0.123144i
\(839\) −0.499354 + 0.864906i −0.0172396 + 0.0298599i −0.874517 0.484996i \(-0.838821\pi\)
0.857277 + 0.514856i \(0.172154\pi\)
\(840\) 0 0
\(841\) −10.3307 17.8933i −0.356231 0.617011i
\(842\) −4.00115 2.31007i −0.137889 0.0796102i
\(843\) −8.11303 + 1.35004i −0.279428 + 0.0464978i
\(844\) 1.88766 + 3.26953i 0.0649760 + 0.112542i
\(845\) 9.50616 + 16.4651i 0.327022 + 0.566418i
\(846\) −6.43301 1.26265i −0.221172 0.0434108i
\(847\) 0 0
\(848\) 0 0
\(849\) −32.3385 39.3028i −1.10985 1.34887i
\(850\) 7.52564i 0.258127i
\(851\) 18.7692i 0.643400i
\(852\) −2.13832 2.59882i −0.0732575 0.0890340i
\(853\) 8.48739 + 4.90020i 0.290603 + 0.167780i 0.638214 0.769859i \(-0.279674\pi\)
−0.347611 + 0.937639i \(0.613007\pi\)
\(854\) 0 0
\(855\) −20.4438 4.01264i −0.699163 0.137229i
\(856\) 7.16846 + 12.4161i 0.245013 + 0.424375i
\(857\) 3.85002 + 6.66842i 0.131514 + 0.227789i 0.924260 0.381763i \(-0.124683\pi\)
−0.792746 + 0.609552i \(0.791349\pi\)
\(858\) −19.1977 + 3.19458i −0.655400 + 0.109061i
\(859\) 16.4022 + 9.46979i 0.559634 + 0.323105i 0.752999 0.658022i \(-0.228607\pi\)
−0.193364 + 0.981127i \(0.561940\pi\)
\(860\) 1.83474 + 3.17787i 0.0625642 + 0.108364i
\(861\) 0 0
\(862\) 2.00385 3.47078i 0.0682515 0.118215i
\(863\) −15.1156 + 8.72700i −0.514541 + 0.297070i −0.734698 0.678394i \(-0.762676\pi\)
0.220157 + 0.975464i \(0.429343\pi\)
\(864\) 4.57324 2.46687i 0.155585 0.0839245i
\(865\) 32.6289 56.5149i 1.10942 1.92156i
\(866\) 29.4125 0.999479
\(867\) 26.6776 + 10.0021i 0.906018 + 0.339690i
\(868\) 0 0
\(869\) −12.4215 + 7.17157i −0.421371 + 0.243279i
\(870\) −18.2230 6.83228i −0.617818 0.231636i
\(871\) 33.1776 19.1551i 1.12418 0.649045i
\(872\) 9.76874 + 5.63998i 0.330811 + 0.190994i
\(873\) 37.1181 42.5423i 1.25626 1.43984i
\(874\) 11.1602i 0.377498i
\(875\) 0 0
\(876\) −8.29481 + 1.38029i −0.280256 + 0.0466356i
\(877\) −0.196152 + 0.339746i −0.00662360 + 0.0114724i −0.869318 0.494253i \(-0.835442\pi\)
0.862695 + 0.505725i \(0.168775\pi\)
\(878\) 21.3769 0.721436
\(879\) 10.7431 + 4.02786i 0.362355 + 0.135856i
\(880\) 15.3490i 0.517414i
\(881\) 37.0259 1.24744 0.623718 0.781650i \(-0.285622\pi\)
0.623718 + 0.781650i \(0.285622\pi\)
\(882\) 0 0
\(883\) −29.9586 −1.00819 −0.504094 0.863649i \(-0.668174\pi\)
−0.504094 + 0.863649i \(0.668174\pi\)
\(884\) 2.11392i 0.0710987i
\(885\) 0.0233809 + 0.140507i 0.000785940 + 0.00472309i
\(886\) 5.83386 0.195992
\(887\) −14.4930 + 25.1026i −0.486626 + 0.842861i −0.999882 0.0153745i \(-0.995106\pi\)
0.513256 + 0.858236i \(0.328439\pi\)
\(888\) −1.82513 + 4.86799i −0.0612475 + 0.163359i
\(889\) 0 0
\(890\) 36.0569i 1.20863i
\(891\) 35.1739 4.81239i 1.17837 0.161221i
\(892\) −11.0662 6.38910i −0.370525 0.213923i
\(893\) −3.37759 + 1.95005i −0.113027 + 0.0652560i
\(894\) −3.12786 18.7968i −0.104611 0.628660i
\(895\) −19.4617 + 11.2362i −0.650533 + 0.375586i
\(896\) 0 0
\(897\) 23.8235 19.6020i 0.795442 0.654492i
\(898\) −22.5823 −0.753582
\(899\) 5.07035 8.78211i 0.169106 0.292900i
\(900\) 28.7829 9.85197i 0.959430 0.328399i
\(901\) 0 0
\(902\) −20.6976 + 35.8493i −0.689156 + 1.19365i
\(903\) 0 0
\(904\) 4.91614 + 8.51501i 0.163508 + 0.283205i
\(905\) −18.6455 10.7650i −0.619796 0.357839i
\(906\) −0.875590 + 2.33537i −0.0290895 + 0.0775874i
\(907\) 1.94773 + 3.37357i 0.0646733 + 0.112017i 0.896549 0.442945i \(-0.146066\pi\)
−0.831876 + 0.554962i \(0.812733\pi\)
\(908\) 9.99110 + 17.3051i 0.331566 + 0.574290i
\(909\) 23.5059 8.04573i 0.779642 0.266860i
\(910\) 0 0
\(911\) 1.32768 + 0.766538i 0.0439881 + 0.0253966i 0.521833 0.853048i \(-0.325248\pi\)
−0.477845 + 0.878444i \(0.658582\pi\)
\(912\) 1.08523 2.89450i 0.0359354 0.0958466i
\(913\) 31.7935i 1.05221i
\(914\) 39.8623i 1.31853i
\(915\) 16.4151 2.73154i 0.542668 0.0903020i
\(916\) 8.77402 + 5.06568i 0.289902 + 0.167375i
\(917\) 0 0
\(918\) −0.111505 + 3.85454i −0.00368020 + 0.127219i
\(919\) −14.1266 24.4679i −0.465992 0.807122i 0.533254 0.845955i \(-0.320969\pi\)
−0.999246 + 0.0388335i \(0.987636\pi\)
\(920\) −12.1658 21.0718i −0.401094 0.694715i
\(921\) 23.9074 + 29.0561i 0.787777 + 0.957430i
\(922\) 6.37834 + 3.68254i 0.210059 + 0.121278i
\(923\) 2.76737 + 4.79323i 0.0910892 + 0.157771i
\(924\) 0 0
\(925\) −15.2192 + 26.3603i −0.500403 + 0.866723i
\(926\) 24.8475 14.3457i 0.816539 0.471429i
\(927\) 33.6253 38.5391i 1.10440 1.26579i
\(928\) 1.44383 2.50079i 0.0473961 0.0820924i
\(929\) −3.28726 −0.107851 −0.0539257 0.998545i \(-0.517173\pi\)
−0.0539257 + 0.998545i \(0.517173\pi\)
\(930\) 3.88498 + 23.3467i 0.127393 + 0.765568i
\(931\) 0 0
\(932\) 6.33070 3.65503i 0.207369 0.119725i
\(933\) −8.42356 + 6.93093i −0.275775 + 0.226909i
\(934\) 11.8389 6.83519i 0.387380 0.223654i
\(935\) −9.86466 5.69536i −0.322609 0.186258i
\(936\) −8.08498 + 2.76737i −0.264266 + 0.0904544i
\(937\) 35.5084i 1.16001i −0.814613 0.580005i \(-0.803051\pi\)
0.814613 0.580005i \(-0.196949\pi\)
\(938\) 0 0
\(939\) 24.4520 + 29.7180i 0.797962 + 0.969809i
\(940\) 4.25153 7.36387i 0.138670 0.240183i
\(941\) −12.4988 −0.407450 −0.203725 0.979028i \(-0.565305\pi\)
−0.203725 + 0.979028i \(0.565305\pi\)
\(942\) −22.2119 + 18.2761i −0.723704 + 0.595466i
\(943\) 65.6208i 2.13691i
\(944\) −0.0211346 −0.000687873
\(945\) 0 0
\(946\) −3.71994 −0.120946
\(947\) 36.1154i 1.17359i −0.809734 0.586796i \(-0.800389\pi\)
0.809734 0.586796i \(-0.199611\pi\)
\(948\) −4.86332 + 4.00156i −0.157953 + 0.129964i
\(949\) 13.8290 0.448910
\(950\) 9.04931 15.6739i 0.293598 0.508527i
\(951\) −17.2354 20.9471i −0.558895 0.679257i
\(952\) 0 0
\(953\) 45.2925i 1.46717i −0.679599 0.733584i \(-0.737846\pi\)
0.679599 0.733584i \(-0.262154\pi\)
\(954\) 0 0
\(955\) 20.9390 + 12.0892i 0.677571 + 0.391196i
\(956\) −7.28317 + 4.20494i −0.235554 + 0.135997i
\(957\) 15.2351 12.5355i 0.492480 0.405215i
\(958\) 9.01596 5.20537i 0.291293 0.168178i
\(959\) 0 0
\(960\) 1.10628 + 6.64819i 0.0357052 + 0.214569i
\(961\) 18.6677 0.602184
\(962\) 4.27499 7.40449i 0.137831 0.238730i
\(963\) 13.9286 + 40.6930i 0.448844 + 1.31131i
\(964\) −7.75277 + 4.47607i −0.249700 + 0.144164i
\(965\) −15.1859 + 26.3028i −0.488851 + 0.846716i
\(966\) 0 0
\(967\) 12.0000 + 20.7845i 0.385893 + 0.668385i 0.991893 0.127079i \(-0.0405602\pi\)
−0.606000 + 0.795465i \(0.707227\pi\)
\(968\) −3.94910 2.28001i −0.126929 0.0732824i
\(969\) 1.45759 + 1.77150i 0.0468246 + 0.0569086i
\(970\) 36.6146 + 63.4184i 1.17562 + 2.03624i
\(971\) 16.6813 + 28.8928i 0.535328 + 0.927215i 0.999147 + 0.0412855i \(0.0131453\pi\)
−0.463819 + 0.885930i \(0.653521\pi\)
\(972\) 14.8882 4.61960i 0.477540 0.148174i
\(973\) 0 0
\(974\) −2.02520 1.16925i −0.0648917 0.0374652i
\(975\) −49.3533 + 8.21257i −1.58057 + 0.263013i
\(976\) 2.46911i 0.0790344i
\(977\) 34.5077i 1.10400i −0.833844 0.552000i \(-0.813865\pi\)
0.833844 0.552000i \(-0.186135\pi\)
\(978\) −7.53716 + 20.1031i −0.241012 + 0.642825i
\(979\) −31.6555 18.2763i −1.01172 0.584114i
\(980\) 0 0
\(981\) 25.4987 + 22.2476i 0.814111 + 0.710311i
\(982\) −16.9422 29.3448i −0.540648 0.936429i
\(983\) −1.20651 2.08973i −0.0384817 0.0666522i 0.846143 0.532956i \(-0.178919\pi\)
−0.884625 + 0.466304i \(0.845585\pi\)
\(984\) −6.38103 + 17.0194i −0.203420 + 0.542560i
\(985\) −43.0450 24.8521i −1.37153 0.791852i
\(986\) 1.07149 + 1.85588i 0.0341232 + 0.0591032i
\(987\) 0 0
\(988\) −2.54191 + 4.40271i −0.0808688 + 0.140069i
\(989\) 5.10691 2.94847i 0.162390 0.0937560i
\(990\) −8.86872 + 45.1848i −0.281866 + 1.43607i
\(991\) −24.2991 + 42.0873i −0.771887 + 1.33695i 0.164641 + 0.986354i \(0.447353\pi\)
−0.936528 + 0.350594i \(0.885980\pi\)
\(992\) −3.51174 −0.111498
\(993\) 1.70164 1.40012i 0.0540000 0.0444314i
\(994\) 0 0
\(995\) 6.10612 3.52537i 0.193577 0.111762i
\(996\) −2.29153 13.7709i −0.0726099 0.436347i
\(997\) −38.8449 + 22.4271i −1.23023 + 0.710274i −0.967078 0.254481i \(-0.918095\pi\)
−0.263152 + 0.964754i \(0.584762\pi\)
\(998\) 14.3799 + 8.30223i 0.455187 + 0.262802i
\(999\) −8.18564 + 13.2760i −0.258982 + 0.420033i
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 882.2.l.a.227.8 16
3.2 odd 2 2646.2.l.b.521.1 16
7.2 even 3 882.2.t.b.803.7 16
7.3 odd 6 126.2.m.a.83.4 yes 16
7.4 even 3 126.2.m.a.83.1 yes 16
7.5 odd 6 882.2.t.b.803.6 16
7.6 odd 2 inner 882.2.l.a.227.5 16
9.4 even 3 2646.2.t.a.2285.1 16
9.5 odd 6 882.2.t.b.815.6 16
21.2 odd 6 2646.2.t.a.1979.4 16
21.5 even 6 2646.2.t.a.1979.1 16
21.11 odd 6 378.2.m.a.251.5 16
21.17 even 6 378.2.m.a.251.8 16
21.20 even 2 2646.2.l.b.521.4 16
28.3 even 6 1008.2.cc.b.209.2 16
28.11 odd 6 1008.2.cc.b.209.7 16
63.4 even 3 378.2.m.a.125.8 16
63.5 even 6 inner 882.2.l.a.509.4 16
63.11 odd 6 1134.2.d.a.1133.8 16
63.13 odd 6 2646.2.t.a.2285.4 16
63.23 odd 6 inner 882.2.l.a.509.1 16
63.25 even 3 1134.2.d.a.1133.9 16
63.31 odd 6 378.2.m.a.125.5 16
63.32 odd 6 126.2.m.a.41.4 yes 16
63.38 even 6 1134.2.d.a.1133.1 16
63.40 odd 6 2646.2.l.b.1097.5 16
63.41 even 6 882.2.t.b.815.7 16
63.52 odd 6 1134.2.d.a.1133.16 16
63.58 even 3 2646.2.l.b.1097.8 16
63.59 even 6 126.2.m.a.41.1 16
84.11 even 6 3024.2.cc.b.2897.1 16
84.59 odd 6 3024.2.cc.b.2897.8 16
252.31 even 6 3024.2.cc.b.881.1 16
252.59 odd 6 1008.2.cc.b.545.7 16
252.67 odd 6 3024.2.cc.b.881.8 16
252.95 even 6 1008.2.cc.b.545.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.1 16 63.59 even 6
126.2.m.a.41.4 yes 16 63.32 odd 6
126.2.m.a.83.1 yes 16 7.4 even 3
126.2.m.a.83.4 yes 16 7.3 odd 6
378.2.m.a.125.5 16 63.31 odd 6
378.2.m.a.125.8 16 63.4 even 3
378.2.m.a.251.5 16 21.11 odd 6
378.2.m.a.251.8 16 21.17 even 6
882.2.l.a.227.5 16 7.6 odd 2 inner
882.2.l.a.227.8 16 1.1 even 1 trivial
882.2.l.a.509.1 16 63.23 odd 6 inner
882.2.l.a.509.4 16 63.5 even 6 inner
882.2.t.b.803.6 16 7.5 odd 6
882.2.t.b.803.7 16 7.2 even 3
882.2.t.b.815.6 16 9.5 odd 6
882.2.t.b.815.7 16 63.41 even 6
1008.2.cc.b.209.2 16 28.3 even 6
1008.2.cc.b.209.7 16 28.11 odd 6
1008.2.cc.b.545.2 16 252.95 even 6
1008.2.cc.b.545.7 16 252.59 odd 6
1134.2.d.a.1133.1 16 63.38 even 6
1134.2.d.a.1133.8 16 63.11 odd 6
1134.2.d.a.1133.9 16 63.25 even 3
1134.2.d.a.1133.16 16 63.52 odd 6
2646.2.l.b.521.1 16 3.2 odd 2
2646.2.l.b.521.4 16 21.20 even 2
2646.2.l.b.1097.5 16 63.40 odd 6
2646.2.l.b.1097.8 16 63.58 even 3
2646.2.t.a.1979.1 16 21.5 even 6
2646.2.t.a.1979.4 16 21.2 odd 6
2646.2.t.a.2285.1 16 9.4 even 3
2646.2.t.a.2285.4 16 63.13 odd 6
3024.2.cc.b.881.1 16 252.31 even 6
3024.2.cc.b.881.8 16 252.67 odd 6
3024.2.cc.b.2897.1 16 84.11 even 6
3024.2.cc.b.2897.8 16 84.59 odd 6