Properties

Label 847.2.f.u.323.2
Level $847$
Weight $2$
Character 847.323
Analytic conductor $6.763$
Analytic rank $0$
Dimension $12$
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] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + 376 x^{3} + 136 x^{2} + 48 x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 323.2
Root \(0.112275 + 0.345546i\) of defining polynomial
Character \(\chi\) \(=\) 847.323
Dual form 847.2.f.u.729.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.10296 + 0.801344i) q^{2} +(0.112275 - 0.345546i) q^{3} +(-0.0436753 - 0.134419i) q^{4} +(-2.54139 + 1.84643i) q^{5} +(0.400735 - 0.291151i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.902127 - 2.77646i) q^{8} +(2.32025 + 1.68576i) q^{9} +O(q^{10})\) \(q+(1.10296 + 0.801344i) q^{2} +(0.112275 - 0.345546i) q^{3} +(-0.0436753 - 0.134419i) q^{4} +(-2.54139 + 1.84643i) q^{5} +(0.400735 - 0.291151i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.902127 - 2.77646i) q^{8} +(2.32025 + 1.68576i) q^{9} -4.28267 q^{10} -0.0513514 q^{12} +(3.86549 + 2.80844i) q^{13} +(0.421292 - 1.29660i) q^{14} +(0.352692 + 1.08548i) q^{15} +(2.99122 - 2.17325i) q^{16} +(3.86549 - 2.80844i) q^{17} +(1.20826 + 3.71865i) q^{18} +(-2.16600 + 6.66627i) q^{19} +(0.359191 + 0.260967i) q^{20} -0.363328 q^{21} +5.14134 q^{23} +(-0.858108 - 0.623452i) q^{24} +(1.50429 - 4.62974i) q^{25} +(2.01293 + 6.19518i) q^{26} +(1.72483 - 1.25316i) q^{27} +(-0.114343 + 0.0830753i) q^{28} +(2.16600 + 6.66627i) q^{29} +(-0.480835 + 1.47986i) q^{30} +(2.94213 + 2.13758i) q^{31} -0.797984 q^{32} +6.51399 q^{34} +(2.54139 + 1.84643i) q^{35} +(0.125260 - 0.385512i) q^{36} +(-3.04938 - 9.38502i) q^{37} +(-7.73098 + 5.61689i) q^{38} +(1.40444 - 1.02039i) q^{39} +(2.83388 + 8.72180i) q^{40} +(-0.995650 + 3.06430i) q^{41} +(-0.400735 - 0.291151i) q^{42} +4.28267 q^{43} -9.00933 q^{45} +(5.67067 + 4.11998i) q^{46} +(-0.240418 + 0.739929i) q^{47} +(-0.415119 - 1.27760i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(5.36918 - 3.90094i) q^{50} +(-0.536449 - 1.65102i) q^{51} +(0.208681 - 0.642253i) q^{52} +(-1.84672 - 1.34172i) q^{53} +2.90663 q^{54} -2.91934 q^{56} +(2.06031 + 1.49691i) q^{57} +(-2.95297 + 9.08831i) q^{58} +(-0.112275 - 0.345546i) q^{59} +(0.130504 - 0.0948168i) q^{60} +(-2.60665 + 1.89384i) q^{61} +(1.53210 + 4.71532i) q^{62} +(0.886258 - 2.72762i) q^{63} +(-6.86258 - 4.98596i) q^{64} -15.0093 q^{65} -6.59465 q^{67} +(-0.546333 - 0.396934i) q^{68} +(0.577241 - 1.77657i) q^{69} +(1.32342 + 4.07306i) q^{70} +(12.2647 - 8.91082i) q^{71} +(6.77362 - 4.92132i) q^{72} +(-0.995650 - 3.06430i) q^{73} +(4.15730 - 12.7949i) q^{74} +(-1.43089 - 1.03960i) q^{75} +0.990671 q^{76} +2.36672 q^{78} +(3.00738 + 2.18499i) q^{79} +(-3.58912 + 11.0462i) q^{80} +(2.41941 + 7.44616i) q^{81} +(-3.55371 + 2.58192i) q^{82} +(-1.25884 + 0.914603i) q^{83} +(0.0158685 + 0.0488381i) q^{84} +(-4.63814 + 14.2747i) q^{85} +(4.72360 + 3.43189i) q^{86} +2.54669 q^{87} -5.58532 q^{89} +(-9.93689 - 7.21957i) q^{90} +(1.47649 - 4.54416i) q^{91} +(-0.224549 - 0.691091i) q^{92} +(1.06896 - 0.776644i) q^{93} +(-0.858108 + 0.623452i) q^{94} +(-6.80414 - 20.9410i) q^{95} +(-0.0895933 + 0.275740i) q^{96} +(-4.97599 - 3.61527i) q^{97} -1.36333 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9} + 16 q^{10} + 8 q^{12} + 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} + 8 q^{17} - 18 q^{18} + 14 q^{20} + 4 q^{21} + 28 q^{23} + 20 q^{24} - 2 q^{25} + 12 q^{26} + 19 q^{27} + 8 q^{28} - 8 q^{30} + 13 q^{31} - 136 q^{32} - 48 q^{34} + q^{35} - 18 q^{36} + 17 q^{37} - 16 q^{38} - 20 q^{39} - 36 q^{40} + 16 q^{41} - 12 q^{42} - 16 q^{43} - 24 q^{45} - 4 q^{47} - 36 q^{48} - 3 q^{49} + 22 q^{50} - 20 q^{51} + 10 q^{53} - 32 q^{54} + 24 q^{56} + 16 q^{57} + 16 q^{58} - q^{59} + 30 q^{60} - 16 q^{61} + 4 q^{62} + 4 q^{63} - 34 q^{64} - 96 q^{65} - 12 q^{67} + 7 q^{69} + 4 q^{70} - 5 q^{71} + 2 q^{72} + 16 q^{73} - 32 q^{74} - 20 q^{75} + 96 q^{76} + 112 q^{78} + 28 q^{79} + 56 q^{80} - 15 q^{81} - 28 q^{82} + 8 q^{83} + 2 q^{84} + 24 q^{85} - 12 q^{86} + 64 q^{87} - 84 q^{89} - 20 q^{90} - 8 q^{91} - 2 q^{92} - 17 q^{93} + 20 q^{94} + 24 q^{95} + 20 q^{96} + 11 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10296 + 0.801344i 0.779907 + 0.566636i 0.904951 0.425515i \(-0.139907\pi\)
−0.125044 + 0.992151i \(0.539907\pi\)
\(3\) 0.112275 0.345546i 0.0648218 0.199501i −0.913400 0.407063i \(-0.866553\pi\)
0.978222 + 0.207562i \(0.0665529\pi\)
\(4\) −0.0436753 0.134419i −0.0218376 0.0672093i
\(5\) −2.54139 + 1.84643i −1.13655 + 0.825749i −0.986634 0.162950i \(-0.947899\pi\)
−0.149912 + 0.988699i \(0.547899\pi\)
\(6\) 0.400735 0.291151i 0.163599 0.118862i
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) 0.902127 2.77646i 0.318950 0.981627i
\(9\) 2.32025 + 1.68576i 0.773418 + 0.561921i
\(10\) −4.28267 −1.35430
\(11\) 0 0
\(12\) −0.0513514 −0.0148239
\(13\) 3.86549 + 2.80844i 1.07209 + 0.778922i 0.976287 0.216478i \(-0.0694570\pi\)
0.0958065 + 0.995400i \(0.469457\pi\)
\(14\) 0.421292 1.29660i 0.112595 0.346532i
\(15\) 0.352692 + 1.08548i 0.0910647 + 0.280268i
\(16\) 2.99122 2.17325i 0.747805 0.543312i
\(17\) 3.86549 2.80844i 0.937519 0.681147i −0.0103032 0.999947i \(-0.503280\pi\)
0.947822 + 0.318800i \(0.103280\pi\)
\(18\) 1.20826 + 3.71865i 0.284790 + 0.876493i
\(19\) −2.16600 + 6.66627i −0.496915 + 1.52935i 0.317036 + 0.948413i \(0.397312\pi\)
−0.813951 + 0.580933i \(0.802688\pi\)
\(20\) 0.359191 + 0.260967i 0.0803175 + 0.0583541i
\(21\) −0.363328 −0.0792847
\(22\) 0 0
\(23\) 5.14134 1.07204 0.536021 0.844204i \(-0.319927\pi\)
0.536021 + 0.844204i \(0.319927\pi\)
\(24\) −0.858108 0.623452i −0.175161 0.127262i
\(25\) 1.50429 4.62974i 0.300858 0.925947i
\(26\) 2.01293 + 6.19518i 0.394769 + 1.21497i
\(27\) 1.72483 1.25316i 0.331944 0.241171i
\(28\) −0.114343 + 0.0830753i −0.0216089 + 0.0156998i
\(29\) 2.16600 + 6.66627i 0.402216 + 1.23789i 0.923197 + 0.384326i \(0.125566\pi\)
−0.520981 + 0.853568i \(0.674434\pi\)
\(30\) −0.480835 + 1.47986i −0.0877881 + 0.270184i
\(31\) 2.94213 + 2.13758i 0.528422 + 0.383921i 0.819767 0.572697i \(-0.194103\pi\)
−0.291345 + 0.956618i \(0.594103\pi\)
\(32\) −0.797984 −0.141065
\(33\) 0 0
\(34\) 6.51399 1.11714
\(35\) 2.54139 + 1.84643i 0.429574 + 0.312104i
\(36\) 0.125260 0.385512i 0.0208767 0.0642519i
\(37\) −3.04938 9.38502i −0.501315 1.54289i −0.806879 0.590716i \(-0.798845\pi\)
0.305565 0.952171i \(-0.401155\pi\)
\(38\) −7.73098 + 5.61689i −1.25413 + 0.911179i
\(39\) 1.40444 1.02039i 0.224891 0.163393i
\(40\) 2.83388 + 8.72180i 0.448076 + 1.37904i
\(41\) −0.995650 + 3.06430i −0.155494 + 0.478563i −0.998211 0.0597953i \(-0.980955\pi\)
0.842716 + 0.538358i \(0.180955\pi\)
\(42\) −0.400735 0.291151i −0.0618347 0.0449256i
\(43\) 4.28267 0.653101 0.326551 0.945180i \(-0.394114\pi\)
0.326551 + 0.945180i \(0.394114\pi\)
\(44\) 0 0
\(45\) −9.00933 −1.34303
\(46\) 5.67067 + 4.11998i 0.836094 + 0.607458i
\(47\) −0.240418 + 0.739929i −0.0350685 + 0.107930i −0.967059 0.254554i \(-0.918071\pi\)
0.931990 + 0.362484i \(0.118071\pi\)
\(48\) −0.415119 1.27760i −0.0599172 0.184406i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 5.36918 3.90094i 0.759317 0.551676i
\(51\) −0.536449 1.65102i −0.0751179 0.231189i
\(52\) 0.208681 0.642253i 0.0289388 0.0890645i
\(53\) −1.84672 1.34172i −0.253667 0.184300i 0.453684 0.891163i \(-0.350110\pi\)
−0.707350 + 0.706863i \(0.750110\pi\)
\(54\) 2.90663 0.395542
\(55\) 0 0
\(56\) −2.91934 −0.390114
\(57\) 2.06031 + 1.49691i 0.272895 + 0.198270i
\(58\) −2.95297 + 9.08831i −0.387744 + 1.19335i
\(59\) −0.112275 0.345546i −0.0146169 0.0449862i 0.943482 0.331424i \(-0.107529\pi\)
−0.958099 + 0.286437i \(0.907529\pi\)
\(60\) 0.130504 0.0948168i 0.0168480 0.0122408i
\(61\) −2.60665 + 1.89384i −0.333747 + 0.242481i −0.742019 0.670379i \(-0.766132\pi\)
0.408272 + 0.912860i \(0.366132\pi\)
\(62\) 1.53210 + 4.71532i 0.194577 + 0.598846i
\(63\) 0.886258 2.72762i 0.111658 0.343648i
\(64\) −6.86258 4.98596i −0.857823 0.623245i
\(65\) −15.0093 −1.86168
\(66\) 0 0
\(67\) −6.59465 −0.805665 −0.402832 0.915274i \(-0.631974\pi\)
−0.402832 + 0.915274i \(0.631974\pi\)
\(68\) −0.546333 0.396934i −0.0662526 0.0481354i
\(69\) 0.577241 1.77657i 0.0694917 0.213873i
\(70\) 1.32342 + 4.07306i 0.158179 + 0.486824i
\(71\) 12.2647 8.91082i 1.45555 1.05752i 0.471057 0.882103i \(-0.343873\pi\)
0.984494 0.175417i \(-0.0561274\pi\)
\(72\) 6.77362 4.92132i 0.798279 0.579984i
\(73\) −0.995650 3.06430i −0.116532 0.358649i 0.875731 0.482799i \(-0.160380\pi\)
−0.992263 + 0.124150i \(0.960380\pi\)
\(74\) 4.15730 12.7949i 0.483277 1.48737i
\(75\) −1.43089 1.03960i −0.165225 0.120043i
\(76\) 0.990671 0.113638
\(77\) 0 0
\(78\) 2.36672 0.267978
\(79\) 3.00738 + 2.18499i 0.338357 + 0.245831i 0.743968 0.668215i \(-0.232941\pi\)
−0.405611 + 0.914046i \(0.632941\pi\)
\(80\) −3.58912 + 11.0462i −0.401275 + 1.23500i
\(81\) 2.41941 + 7.44616i 0.268823 + 0.827351i
\(82\) −3.55371 + 2.58192i −0.392442 + 0.285126i
\(83\) −1.25884 + 0.914603i −0.138176 + 0.100391i −0.654726 0.755866i \(-0.727216\pi\)
0.516550 + 0.856257i \(0.327216\pi\)
\(84\) 0.0158685 + 0.0488381i 0.00173139 + 0.00532867i
\(85\) −4.63814 + 14.2747i −0.503077 + 1.54831i
\(86\) 4.72360 + 3.43189i 0.509359 + 0.370071i
\(87\) 2.54669 0.273034
\(88\) 0 0
\(89\) −5.58532 −0.592043 −0.296021 0.955181i \(-0.595660\pi\)
−0.296021 + 0.955181i \(0.595660\pi\)
\(90\) −9.93689 7.21957i −1.04744 0.761010i
\(91\) 1.47649 4.54416i 0.154778 0.476357i
\(92\) −0.224549 0.691091i −0.0234109 0.0720513i
\(93\) 1.06896 0.776644i 0.110846 0.0805342i
\(94\) −0.858108 + 0.623452i −0.0885071 + 0.0643042i
\(95\) −6.80414 20.9410i −0.698090 2.14850i
\(96\) −0.0895933 + 0.275740i −0.00914408 + 0.0281426i
\(97\) −4.97599 3.61527i −0.505235 0.367075i 0.305778 0.952103i \(-0.401084\pi\)
−0.811013 + 0.585028i \(0.801084\pi\)
\(98\) −1.36333 −0.137717
\(99\) 0 0
\(100\) −0.688023 −0.0688023
\(101\) 8.73469 + 6.34612i 0.869134 + 0.631463i 0.930354 0.366662i \(-0.119499\pi\)
−0.0612206 + 0.998124i \(0.519499\pi\)
\(102\) 0.731356 2.25088i 0.0724150 0.222871i
\(103\) −4.09159 12.5926i −0.403156 1.24079i −0.922425 0.386176i \(-0.873796\pi\)
0.519269 0.854611i \(-0.326204\pi\)
\(104\) 11.2847 8.19881i 1.10656 0.803959i
\(105\) 0.923360 0.670861i 0.0901107 0.0654693i
\(106\) −0.961671 2.95972i −0.0934057 0.287473i
\(107\) 4.33200 13.3325i 0.418791 1.28890i −0.490026 0.871708i \(-0.663013\pi\)
0.908816 0.417197i \(-0.136987\pi\)
\(108\) −0.243781 0.177117i −0.0234578 0.0170431i
\(109\) −15.5747 −1.49178 −0.745892 0.666067i \(-0.767976\pi\)
−0.745892 + 0.666067i \(0.767976\pi\)
\(110\) 0 0
\(111\) −3.58532 −0.340304
\(112\) −2.99122 2.17325i −0.282644 0.205353i
\(113\) 1.27686 3.92977i 0.120117 0.369682i −0.872863 0.487965i \(-0.837739\pi\)
0.992980 + 0.118284i \(0.0377392\pi\)
\(114\) 1.07290 + 3.30204i 0.100486 + 0.309264i
\(115\) −13.0662 + 9.49312i −1.21843 + 0.885238i
\(116\) 0.801470 0.582302i 0.0744146 0.0540654i
\(117\) 4.23455 + 13.0326i 0.391484 + 1.20486i
\(118\) 0.153067 0.471092i 0.0140910 0.0433676i
\(119\) −3.86549 2.80844i −0.354349 0.257450i
\(120\) 3.33195 0.304164
\(121\) 0 0
\(122\) −4.39263 −0.397690
\(123\) 0.947068 + 0.688085i 0.0853943 + 0.0620426i
\(124\) 0.158833 0.488836i 0.0142636 0.0438988i
\(125\) −0.128143 0.394384i −0.0114615 0.0352748i
\(126\) 3.16327 2.29825i 0.281806 0.204744i
\(127\) −17.8135 + 12.9422i −1.58069 + 1.14844i −0.664791 + 0.747030i \(0.731479\pi\)
−0.915899 + 0.401408i \(0.868521\pi\)
\(128\) −3.08047 9.48073i −0.272278 0.837986i
\(129\) 0.480835 1.47986i 0.0423352 0.130294i
\(130\) −16.5546 12.0276i −1.45194 1.05489i
\(131\) 15.0093 1.31137 0.655686 0.755034i \(-0.272380\pi\)
0.655686 + 0.755034i \(0.272380\pi\)
\(132\) 0 0
\(133\) 7.00933 0.607786
\(134\) −7.27361 5.28458i −0.628344 0.456519i
\(135\) −2.06960 + 6.36956i −0.178122 + 0.548204i
\(136\) −4.31037 13.2660i −0.369611 1.13755i
\(137\) 8.65434 6.28775i 0.739390 0.537198i −0.153130 0.988206i \(-0.548935\pi\)
0.892520 + 0.451008i \(0.148935\pi\)
\(138\) 2.06031 1.49691i 0.175385 0.127425i
\(139\) 1.26780 + 3.90190i 0.107534 + 0.330955i 0.990317 0.138826i \(-0.0443329\pi\)
−0.882783 + 0.469781i \(0.844333\pi\)
\(140\) 0.137199 0.422254i 0.0115954 0.0356870i
\(141\) 0.228687 + 0.166151i 0.0192589 + 0.0139924i
\(142\) 20.6680 1.73442
\(143\) 0 0
\(144\) 10.6040 0.883665
\(145\) −17.8135 12.9422i −1.47933 1.07479i
\(146\) 1.35740 4.17764i 0.112339 0.345744i
\(147\) 0.112275 + 0.345546i 0.00926025 + 0.0285001i
\(148\) −1.12834 + 0.819786i −0.0927489 + 0.0673860i
\(149\) −11.3413 + 8.23996i −0.929118 + 0.675044i −0.945777 0.324817i \(-0.894697\pi\)
0.0166586 + 0.999861i \(0.494697\pi\)
\(150\) −0.745130 2.29327i −0.0608396 0.187245i
\(151\) −2.11039 + 6.49511i −0.171741 + 0.528564i −0.999470 0.0325642i \(-0.989633\pi\)
0.827729 + 0.561129i \(0.189633\pi\)
\(152\) 16.5546 + 12.0276i 1.34276 + 0.975570i
\(153\) 13.7033 1.10785
\(154\) 0 0
\(155\) −11.4240 −0.917598
\(156\) −0.198498 0.144217i −0.0158926 0.0115466i
\(157\) −7.24418 + 22.2953i −0.578149 + 1.77936i 0.0470494 + 0.998893i \(0.485018\pi\)
−0.625198 + 0.780466i \(0.714982\pi\)
\(158\) 1.56608 + 4.81990i 0.124591 + 0.383450i
\(159\) −0.670966 + 0.487485i −0.0532110 + 0.0386601i
\(160\) 2.02799 1.47342i 0.160327 0.116484i
\(161\) −1.58876 4.88970i −0.125212 0.385362i
\(162\) −3.29844 + 10.1516i −0.259150 + 0.797582i
\(163\) 0.801470 + 0.582302i 0.0627760 + 0.0456094i 0.618731 0.785603i \(-0.287647\pi\)
−0.555955 + 0.831213i \(0.687647\pi\)
\(164\) 0.455384 0.0355595
\(165\) 0 0
\(166\) −2.12136 −0.164649
\(167\) −0.457373 0.332301i −0.0353926 0.0257142i 0.569948 0.821681i \(-0.306963\pi\)
−0.605341 + 0.795966i \(0.706963\pi\)
\(168\) −0.327768 + 1.00877i −0.0252879 + 0.0778280i
\(169\) 3.03744 + 9.34828i 0.233649 + 0.719098i
\(170\) −16.5546 + 12.0276i −1.26968 + 0.922478i
\(171\) −16.2634 + 11.8161i −1.24370 + 0.903598i
\(172\) −0.187047 0.575671i −0.0142622 0.0438945i
\(173\) −5.32765 + 16.3968i −0.405054 + 1.24663i 0.515796 + 0.856711i \(0.327496\pi\)
−0.920850 + 0.389917i \(0.872504\pi\)
\(174\) 2.80888 + 2.04077i 0.212941 + 0.154711i
\(175\) −4.86799 −0.367986
\(176\) 0 0
\(177\) −0.132007 −0.00992228
\(178\) −6.16036 4.47576i −0.461739 0.335473i
\(179\) 3.49848 10.7672i 0.261488 0.804778i −0.730993 0.682385i \(-0.760943\pi\)
0.992482 0.122394i \(-0.0390571\pi\)
\(180\) 0.393485 + 1.21102i 0.0293286 + 0.0902642i
\(181\) −12.0360 + 8.74467i −0.894629 + 0.649986i −0.937081 0.349112i \(-0.886483\pi\)
0.0424516 + 0.999099i \(0.486483\pi\)
\(182\) 5.26993 3.82883i 0.390633 0.283812i
\(183\) 0.361748 + 1.11335i 0.0267412 + 0.0823009i
\(184\) 4.63814 14.2747i 0.341928 1.05235i
\(185\) 25.0785 + 18.2206i 1.84381 + 1.33960i
\(186\) 1.80137 0.132083
\(187\) 0 0
\(188\) 0.109961 0.00801970
\(189\) −1.72483 1.25316i −0.125463 0.0911542i
\(190\) 9.27628 28.5494i 0.672972 2.07119i
\(191\) 1.18951 + 3.66094i 0.0860699 + 0.264896i 0.984824 0.173558i \(-0.0555263\pi\)
−0.898754 + 0.438454i \(0.855526\pi\)
\(192\) −2.49337 + 1.81154i −0.179943 + 0.130737i
\(193\) 2.06031 1.49691i 0.148305 0.107750i −0.511159 0.859486i \(-0.670784\pi\)
0.659463 + 0.751737i \(0.270784\pi\)
\(194\) −2.59122 7.97497i −0.186039 0.572569i
\(195\) −1.68517 + 5.18641i −0.120677 + 0.371406i
\(196\) 0.114343 + 0.0830753i 0.00816738 + 0.00593395i
\(197\) −10.5467 −0.751420 −0.375710 0.926737i \(-0.622601\pi\)
−0.375710 + 0.926737i \(0.622601\pi\)
\(198\) 0 0
\(199\) 11.6846 0.828302 0.414151 0.910208i \(-0.364079\pi\)
0.414151 + 0.910208i \(0.364079\pi\)
\(200\) −11.4972 8.35322i −0.812976 0.590662i
\(201\) −0.740412 + 2.27875i −0.0522246 + 0.160731i
\(202\) 4.54854 + 13.9990i 0.320034 + 0.984965i
\(203\) 5.67067 4.11998i 0.398003 0.289166i
\(204\) −0.198498 + 0.144217i −0.0138977 + 0.0100972i
\(205\) −3.12767 9.62599i −0.218446 0.672308i
\(206\) 5.57817 17.1679i 0.388650 1.19614i
\(207\) 11.9292 + 8.66708i 0.829137 + 0.602404i
\(208\) 17.6660 1.22492
\(209\) 0 0
\(210\) 1.55602 0.107375
\(211\) −8.98982 6.53149i −0.618885 0.449646i 0.233647 0.972322i \(-0.424934\pi\)
−0.852532 + 0.522675i \(0.824934\pi\)
\(212\) −0.0996963 + 0.306834i −0.00684717 + 0.0210734i
\(213\) −1.70208 5.23847i −0.116625 0.358934i
\(214\) 15.4620 11.2338i 1.05696 0.767925i
\(215\) −10.8840 + 7.90766i −0.742280 + 0.539298i
\(216\) −1.92334 5.91944i −0.130867 0.402767i
\(217\) 1.12379 3.45868i 0.0762881 0.234791i
\(218\) −17.1782 12.4807i −1.16345 0.845298i
\(219\) −1.17064 −0.0791046
\(220\) 0 0
\(221\) 22.8294 1.53567
\(222\) −3.95445 2.87308i −0.265405 0.192828i
\(223\) 8.66505 26.6683i 0.580255 1.78584i −0.0372888 0.999305i \(-0.511872\pi\)
0.617544 0.786537i \(-0.288128\pi\)
\(224\) 0.246591 + 0.758928i 0.0164760 + 0.0507080i
\(225\) 11.2950 8.20629i 0.752999 0.547086i
\(226\) 4.55742 3.31116i 0.303155 0.220255i
\(227\) −7.11027 21.8832i −0.471925 1.45244i −0.850060 0.526686i \(-0.823434\pi\)
0.378134 0.925751i \(-0.376566\pi\)
\(228\) 0.111227 0.342322i 0.00736620 0.0226708i
\(229\) −10.8603 7.89043i −0.717666 0.521415i 0.167972 0.985792i \(-0.446278\pi\)
−0.885638 + 0.464377i \(0.846278\pi\)
\(230\) −22.0187 −1.45187
\(231\) 0 0
\(232\) 20.4626 1.34344
\(233\) 2.86178 + 2.07921i 0.187482 + 0.136213i 0.677567 0.735461i \(-0.263034\pi\)
−0.490085 + 0.871674i \(0.663034\pi\)
\(234\) −5.77308 + 17.7677i −0.377398 + 1.16151i
\(235\) −0.755233 2.32437i −0.0492659 0.151625i
\(236\) −0.0415442 + 0.0301836i −0.00270429 + 0.00196478i
\(237\) 1.09267 0.793869i 0.0709763 0.0515673i
\(238\) −2.01293 6.19518i −0.130479 0.401574i
\(239\) 6.80414 20.9410i 0.440123 1.35456i −0.447621 0.894223i \(-0.647729\pi\)
0.887744 0.460337i \(-0.152271\pi\)
\(240\) 3.41399 + 2.48041i 0.220372 + 0.160110i
\(241\) −0.315366 −0.0203145 −0.0101573 0.999948i \(-0.503233\pi\)
−0.0101573 + 0.999948i \(0.503233\pi\)
\(242\) 0 0
\(243\) 9.24065 0.592788
\(244\) 0.368413 + 0.267668i 0.0235852 + 0.0171357i
\(245\) 0.970726 2.98759i 0.0620174 0.190870i
\(246\) 0.493181 + 1.51786i 0.0314441 + 0.0967749i
\(247\) −27.0945 + 19.6853i −1.72398 + 1.25255i
\(248\) 8.58909 6.24034i 0.545408 0.396262i
\(249\) 0.174701 + 0.537675i 0.0110712 + 0.0340737i
\(250\) 0.174701 0.537675i 0.0110491 0.0340055i
\(251\) −15.0849 10.9598i −0.952152 0.691779i −0.000837449 1.00000i \(-0.500267\pi\)
−0.951315 + 0.308220i \(0.900267\pi\)
\(252\) −0.405351 −0.0255347
\(253\) 0 0
\(254\) −30.0187 −1.88354
\(255\) 4.41182 + 3.20538i 0.276279 + 0.200728i
\(256\) −1.04285 + 3.20956i −0.0651780 + 0.200597i
\(257\) −2.64107 8.12838i −0.164746 0.507035i 0.834272 0.551353i \(-0.185888\pi\)
−0.999017 + 0.0443186i \(0.985888\pi\)
\(258\) 1.71622 1.24690i 0.106847 0.0776289i
\(259\) −7.98337 + 5.80026i −0.496063 + 0.360411i
\(260\) 0.655536 + 2.01753i 0.0406546 + 0.125122i
\(261\) −6.21208 + 19.1188i −0.384518 + 1.18342i
\(262\) 16.5546 + 12.0276i 1.02275 + 0.743070i
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 7.17064 0.440489
\(266\) 7.73098 + 5.61689i 0.474017 + 0.344393i
\(267\) −0.627090 + 1.92998i −0.0383773 + 0.118113i
\(268\) 0.288023 + 0.886444i 0.0175938 + 0.0541482i
\(269\) −6.11295 + 4.44131i −0.372713 + 0.270792i −0.758335 0.651865i \(-0.773987\pi\)
0.385622 + 0.922657i \(0.373987\pi\)
\(270\) −7.38688 + 5.36688i −0.449551 + 0.326618i
\(271\) 4.33200 + 13.3325i 0.263150 + 0.809894i 0.992114 + 0.125341i \(0.0400025\pi\)
−0.728963 + 0.684553i \(0.759998\pi\)
\(272\) 5.45909 16.8013i 0.331006 1.01873i
\(273\) −1.40444 1.02039i −0.0850007 0.0617566i
\(274\) 14.5840 0.881052
\(275\) 0 0
\(276\) −0.264015 −0.0158918
\(277\) 4.86920 + 3.53768i 0.292562 + 0.212558i 0.724378 0.689403i \(-0.242127\pi\)
−0.431816 + 0.901962i \(0.642127\pi\)
\(278\) −1.72843 + 5.31957i −0.103665 + 0.319047i
\(279\) 3.22303 + 9.91947i 0.192958 + 0.593863i
\(280\) 7.41920 5.39037i 0.443382 0.322136i
\(281\) 16.7208 12.1484i 0.997479 0.724711i 0.0359331 0.999354i \(-0.488560\pi\)
0.961546 + 0.274643i \(0.0885597\pi\)
\(282\) 0.119087 + 0.366513i 0.00709155 + 0.0218256i
\(283\) 3.06420 9.43063i 0.182148 0.560593i −0.817740 0.575588i \(-0.804773\pi\)
0.999888 + 0.0149950i \(0.00477324\pi\)
\(284\) −1.73344 1.25942i −0.102861 0.0747329i
\(285\) −8.00000 −0.473879
\(286\) 0 0
\(287\) 3.22199 0.190188
\(288\) −1.85153 1.34521i −0.109102 0.0792674i
\(289\) 1.80137 5.54405i 0.105963 0.326121i
\(290\) −9.27628 28.5494i −0.544722 1.67648i
\(291\) −1.80792 + 1.31353i −0.105982 + 0.0770005i
\(292\) −0.368413 + 0.267668i −0.0215598 + 0.0156641i
\(293\) −8.28062 25.4851i −0.483759 1.48886i −0.833770 0.552112i \(-0.813822\pi\)
0.350011 0.936746i \(-0.386178\pi\)
\(294\) −0.153067 + 0.471092i −0.00892706 + 0.0274747i
\(295\) 0.923360 + 0.670861i 0.0537601 + 0.0390590i
\(296\) −28.8081 −1.67443
\(297\) 0 0
\(298\) −19.1120 −1.10713
\(299\) 19.8738 + 14.4391i 1.14933 + 0.835037i
\(300\) −0.0772475 + 0.237743i −0.00445989 + 0.0137261i
\(301\) −1.32342 4.07306i −0.0762806 0.234767i
\(302\) −7.53248 + 5.47267i −0.433446 + 0.314917i
\(303\) 3.17356 2.30572i 0.182316 0.132460i
\(304\) 8.00847 + 24.6475i 0.459317 + 1.41363i
\(305\) 3.12767 9.62599i 0.179090 0.551182i
\(306\) 15.1141 + 10.9811i 0.864017 + 0.627745i
\(307\) 11.8973 0.679015 0.339507 0.940603i \(-0.389740\pi\)
0.339507 + 0.940603i \(0.389740\pi\)
\(308\) 0 0
\(309\) −4.81070 −0.273671
\(310\) −12.6002 9.15456i −0.715642 0.519944i
\(311\) −6.56372 + 20.2011i −0.372195 + 1.14550i 0.573157 + 0.819445i \(0.305718\pi\)
−0.945352 + 0.326052i \(0.894282\pi\)
\(312\) −1.56608 4.81990i −0.0886618 0.272873i
\(313\) 10.2724 7.46332i 0.580629 0.421852i −0.258322 0.966059i \(-0.583170\pi\)
0.838951 + 0.544207i \(0.183170\pi\)
\(314\) −25.8562 + 18.7856i −1.45915 + 1.06014i
\(315\) 2.78404 + 8.56838i 0.156863 + 0.482774i
\(316\) 0.162355 0.499678i 0.00913320 0.0281091i
\(317\) 9.60141 + 6.97583i 0.539269 + 0.391802i 0.823813 0.566861i \(-0.191842\pi\)
−0.284545 + 0.958663i \(0.591842\pi\)
\(318\) −1.13069 −0.0634059
\(319\) 0 0
\(320\) 26.6468 1.48960
\(321\) −4.12063 2.99381i −0.229991 0.167098i
\(322\) 2.16600 6.66627i 0.120707 0.371497i
\(323\) 10.3492 + 31.8515i 0.575843 + 1.77226i
\(324\) 0.895235 0.650426i 0.0497353 0.0361348i
\(325\) 18.8172 13.6715i 1.04379 0.758357i
\(326\) 0.417361 + 1.28451i 0.0231155 + 0.0711422i
\(327\) −1.74864 + 5.38176i −0.0967000 + 0.297612i
\(328\) 7.60970 + 5.52877i 0.420175 + 0.305275i
\(329\) 0.778008 0.0428930
\(330\) 0 0
\(331\) −11.8867 −0.653349 −0.326675 0.945137i \(-0.605928\pi\)
−0.326675 + 0.945137i \(0.605928\pi\)
\(332\) 0.177920 + 0.129266i 0.00976463 + 0.00709442i
\(333\) 8.74559 26.9162i 0.479255 1.47500i
\(334\) −0.238175 0.733027i −0.0130323 0.0401094i
\(335\) 16.7596 12.1766i 0.915675 0.665277i
\(336\) −1.08679 + 0.789603i −0.0592895 + 0.0430764i
\(337\) 0.306134 + 0.942184i 0.0166762 + 0.0513241i 0.959048 0.283242i \(-0.0914101\pi\)
−0.942372 + 0.334567i \(0.891410\pi\)
\(338\) −4.14103 + 12.7448i −0.225242 + 0.693224i
\(339\) −1.21456 0.882427i −0.0659657 0.0479269i
\(340\) 2.12136 0.115047
\(341\) 0 0
\(342\) −27.4066 −1.48198
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) 3.86351 11.8907i 0.208307 0.641102i
\(345\) 1.81331 + 5.58079i 0.0976253 + 0.300460i
\(346\) −19.0157 + 13.8157i −1.02229 + 0.742736i
\(347\) 12.2884 8.92805i 0.659676 0.479283i −0.206878 0.978367i \(-0.566330\pi\)
0.866553 + 0.499084i \(0.166330\pi\)
\(348\) −0.111227 0.342322i −0.00596241 0.0183504i
\(349\) −9.17882 + 28.2495i −0.491331 + 1.51216i 0.331266 + 0.943537i \(0.392524\pi\)
−0.822597 + 0.568624i \(0.807476\pi\)
\(350\) −5.36918 3.90094i −0.286995 0.208514i
\(351\) 10.1867 0.543728
\(352\) 0 0
\(353\) −6.71601 −0.357457 −0.178729 0.983898i \(-0.557198\pi\)
−0.178729 + 0.983898i \(0.557198\pi\)
\(354\) −0.145598 0.105783i −0.00773846 0.00562232i
\(355\) −14.7162 + 45.2918i −0.781055 + 2.40384i
\(356\) 0.243940 + 0.750771i 0.0129288 + 0.0397908i
\(357\) −1.40444 + 1.02039i −0.0743309 + 0.0540046i
\(358\) 12.4869 9.07226i 0.659953 0.479484i
\(359\) 5.48072 + 16.8679i 0.289261 + 0.890255i 0.985089 + 0.172046i \(0.0550378\pi\)
−0.695828 + 0.718209i \(0.744962\pi\)
\(360\) −8.12756 + 25.0141i −0.428360 + 1.31836i
\(361\) −24.3762 17.7104i −1.28296 0.932125i
\(362\) −20.2827 −1.06603
\(363\) 0 0
\(364\) −0.675305 −0.0353956
\(365\) 8.18835 + 5.94919i 0.428598 + 0.311395i
\(366\) −0.493181 + 1.51786i −0.0257790 + 0.0793396i
\(367\) −2.50283 7.70290i −0.130646 0.402088i 0.864241 0.503078i \(-0.167799\pi\)
−0.994887 + 0.100990i \(0.967799\pi\)
\(368\) 15.3789 11.1734i 0.801679 0.582454i
\(369\) −7.47584 + 5.43152i −0.389177 + 0.282754i
\(370\) 13.0595 + 40.1930i 0.678930 + 2.08953i
\(371\) −0.705385 + 2.17095i −0.0366217 + 0.112710i
\(372\) −0.151082 0.109768i −0.00783326 0.00569120i
\(373\) 0.565344 0.0292724 0.0146362 0.999893i \(-0.495341\pi\)
0.0146362 + 0.999893i \(0.495341\pi\)
\(374\) 0 0
\(375\) −0.150665 −0.00778030
\(376\) 1.83750 + 1.33502i 0.0947617 + 0.0688484i
\(377\) −10.3492 + 31.8515i −0.533010 + 1.64043i
\(378\) −0.898197 2.76437i −0.0461983 0.142184i
\(379\) 18.2320 13.2464i 0.936517 0.680419i −0.0110628 0.999939i \(-0.503521\pi\)
0.947580 + 0.319519i \(0.103521\pi\)
\(380\) −2.51769 + 1.82921i −0.129155 + 0.0938363i
\(381\) 2.47214 + 7.60845i 0.126651 + 0.389793i
\(382\) −1.62169 + 4.99106i −0.0829730 + 0.255365i
\(383\) −17.3059 12.5735i −0.884292 0.642476i 0.0500914 0.998745i \(-0.484049\pi\)
−0.934383 + 0.356269i \(0.884049\pi\)
\(384\) −3.62188 −0.184828
\(385\) 0 0
\(386\) 3.47197 0.176719
\(387\) 9.93689 + 7.21957i 0.505121 + 0.366992i
\(388\) −0.268632 + 0.826764i −0.0136377 + 0.0419726i
\(389\) 3.29990 + 10.1560i 0.167311 + 0.514932i 0.999199 0.0400122i \(-0.0127397\pi\)
−0.831888 + 0.554944i \(0.812740\pi\)
\(390\) −6.01476 + 4.36998i −0.304569 + 0.221283i
\(391\) 19.8738 14.4391i 1.00506 0.730219i
\(392\) 0.902127 + 2.77646i 0.0455643 + 0.140232i
\(393\) 1.68517 5.18641i 0.0850054 0.261620i
\(394\) −11.6325 8.45153i −0.586038 0.425782i
\(395\) −11.6774 −0.587553
\(396\) 0 0
\(397\) −23.9160 −1.20031 −0.600154 0.799885i \(-0.704894\pi\)
−0.600154 + 0.799885i \(0.704894\pi\)
\(398\) 12.8876 + 9.36341i 0.645999 + 0.469346i
\(399\) 0.786970 2.42204i 0.0393978 0.121254i
\(400\) −5.56190 17.1178i −0.278095 0.855888i
\(401\) −9.43210 + 6.85282i −0.471017 + 0.342214i −0.797837 0.602873i \(-0.794023\pi\)
0.326821 + 0.945086i \(0.394023\pi\)
\(402\) −2.64271 + 1.92004i −0.131806 + 0.0957628i
\(403\) 5.36949 + 16.5256i 0.267474 + 0.823199i
\(404\) 0.471547 1.45127i 0.0234603 0.0722035i
\(405\) −19.8975 14.4564i −0.988714 0.718343i
\(406\) 9.55602 0.474257
\(407\) 0 0
\(408\) −5.06794 −0.250900
\(409\) −26.5482 19.2884i −1.31272 0.953748i −0.999992 0.00390587i \(-0.998757\pi\)
−0.312729 0.949842i \(-0.601243\pi\)
\(410\) 4.26404 13.1234i 0.210586 0.648117i
\(411\) −1.20104 3.69642i −0.0592430 0.182331i
\(412\) −1.51398 + 1.09997i −0.0745884 + 0.0541917i
\(413\) −0.293939 + 0.213559i −0.0144638 + 0.0105086i
\(414\) 6.21208 + 19.1188i 0.305307 + 0.939638i
\(415\) 1.51047 4.64873i 0.0741458 0.228197i
\(416\) −3.08460 2.24109i −0.151235 0.109879i
\(417\) 1.49063 0.0729964
\(418\) 0 0
\(419\) 10.7967 0.527452 0.263726 0.964598i \(-0.415049\pi\)
0.263726 + 0.964598i \(0.415049\pi\)
\(420\) −0.130504 0.0948168i −0.00636795 0.00462659i
\(421\) −0.355982 + 1.09560i −0.0173495 + 0.0533963i −0.959356 0.282197i \(-0.908937\pi\)
0.942007 + 0.335593i \(0.108937\pi\)
\(422\) −4.68141 14.4079i −0.227887 0.701365i
\(423\) −1.80518 + 1.31154i −0.0877707 + 0.0637691i
\(424\) −5.39121 + 3.91695i −0.261820 + 0.190224i
\(425\) −7.18752 22.1209i −0.348646 1.07302i
\(426\) 2.32050 7.14175i 0.112428 0.346019i
\(427\) 2.60665 + 1.89384i 0.126144 + 0.0916493i
\(428\) −1.98134 −0.0957718
\(429\) 0 0
\(430\) −18.3413 −0.884495
\(431\) 25.8562 + 18.7856i 1.24545 + 0.904873i 0.997949 0.0640148i \(-0.0203905\pi\)
0.247501 + 0.968888i \(0.420391\pi\)
\(432\) 2.43591 7.49697i 0.117198 0.360698i
\(433\) −1.36998 4.21635i −0.0658369 0.202625i 0.912726 0.408571i \(-0.133973\pi\)
−0.978563 + 0.205946i \(0.933973\pi\)
\(434\) 4.01109 2.91423i 0.192538 0.139887i
\(435\) −6.47214 + 4.70228i −0.310315 + 0.225457i
\(436\) 0.680228 + 2.09353i 0.0325770 + 0.100262i
\(437\) −11.1361 + 34.2735i −0.532714 + 1.63952i
\(438\) −1.29116 0.938086i −0.0616942 0.0448235i
\(439\) −27.4720 −1.31117 −0.655583 0.755123i \(-0.727577\pi\)
−0.655583 + 0.755123i \(0.727577\pi\)
\(440\) 0 0
\(441\) −2.86799 −0.136571
\(442\) 25.1798 + 18.2942i 1.19768 + 0.870165i
\(443\) −2.40747 + 7.40942i −0.114382 + 0.352032i −0.991818 0.127662i \(-0.959253\pi\)
0.877435 + 0.479695i \(0.159253\pi\)
\(444\) 0.156590 + 0.481934i 0.00743142 + 0.0228716i
\(445\) 14.1945 10.3129i 0.672884 0.488879i
\(446\) 30.9277 22.4703i 1.46447 1.06400i
\(447\) 1.57394 + 4.84409i 0.0744448 + 0.229117i
\(448\) −2.62127 + 8.06745i −0.123844 + 0.381151i
\(449\) −16.5934 12.0558i −0.783092 0.568950i 0.122813 0.992430i \(-0.460808\pi\)
−0.905905 + 0.423480i \(0.860808\pi\)
\(450\) 19.0339 0.897268
\(451\) 0 0
\(452\) −0.584002 −0.0274691
\(453\) 2.00741 + 1.45847i 0.0943165 + 0.0685249i
\(454\) 9.69364 29.8339i 0.454945 1.40018i
\(455\) 4.63814 + 14.2747i 0.217439 + 0.669209i
\(456\) 6.01476 4.36998i 0.281667 0.204643i
\(457\) 6.92951 5.03458i 0.324149 0.235508i −0.413795 0.910370i \(-0.635797\pi\)
0.737944 + 0.674862i \(0.235797\pi\)
\(458\) −5.65542 17.4056i −0.264261 0.813310i
\(459\) 3.14788 9.68817i 0.146930 0.452205i
\(460\) 1.84672 + 1.34172i 0.0861038 + 0.0625581i
\(461\) 9.66598 0.450189 0.225095 0.974337i \(-0.427731\pi\)
0.225095 + 0.974337i \(0.427731\pi\)
\(462\) 0 0
\(463\) 11.4240 0.530919 0.265459 0.964122i \(-0.414476\pi\)
0.265459 + 0.964122i \(0.414476\pi\)
\(464\) 20.9664 + 15.2330i 0.973343 + 0.707175i
\(465\) −1.28263 + 3.94752i −0.0594804 + 0.183062i
\(466\) 1.49026 + 4.58655i 0.0690349 + 0.212468i
\(467\) −14.7408 + 10.7098i −0.682124 + 0.495592i −0.874062 0.485815i \(-0.838523\pi\)
0.191937 + 0.981407i \(0.438523\pi\)
\(468\) 1.56688 1.13840i 0.0724290 0.0526228i
\(469\) 2.03786 + 6.27188i 0.0940996 + 0.289609i
\(470\) 1.02963 3.16888i 0.0474933 0.146169i
\(471\) 6.89071 + 5.00639i 0.317507 + 0.230682i
\(472\) −1.06068 −0.0488218
\(473\) 0 0
\(474\) 1.84132 0.0845749
\(475\) 27.6048 + 20.0560i 1.26659 + 0.920234i
\(476\) −0.208681 + 0.642253i −0.00956487 + 0.0294376i
\(477\) −2.02304 6.22627i −0.0926285 0.285081i
\(478\) 24.2856 17.6445i 1.11080 0.807042i
\(479\) −2.80888 + 2.04077i −0.128341 + 0.0932453i −0.650104 0.759845i \(-0.725275\pi\)
0.521763 + 0.853091i \(0.325275\pi\)
\(480\) −0.281443 0.866192i −0.0128460 0.0395361i
\(481\) 14.5699 44.8417i 0.664333 2.04461i
\(482\) −0.347835 0.252717i −0.0158434 0.0115109i
\(483\) −1.86799 −0.0849966
\(484\) 0 0
\(485\) 19.3213 0.877335
\(486\) 10.1920 + 7.40494i 0.462320 + 0.335895i
\(487\) −8.48602 + 26.1173i −0.384538 + 1.18349i 0.552277 + 0.833661i \(0.313759\pi\)
−0.936815 + 0.349826i \(0.886241\pi\)
\(488\) 2.90665 + 8.94574i 0.131578 + 0.404954i
\(489\) 0.291197 0.211567i 0.0131684 0.00956738i
\(490\) 3.46475 2.51729i 0.156522 0.113720i
\(491\) −1.93569 5.95743i −0.0873563 0.268855i 0.897830 0.440342i \(-0.145143\pi\)
−0.985186 + 0.171487i \(0.945143\pi\)
\(492\) 0.0511280 0.157356i 0.00230503 0.00709415i
\(493\) 27.0945 + 19.6853i 1.22027 + 0.886581i
\(494\) −45.6587 −2.05428
\(495\) 0 0
\(496\) 13.4461 0.603746
\(497\) −12.2647 8.91082i −0.550147 0.399705i
\(498\) −0.238175 + 0.733027i −0.0106729 + 0.0328477i
\(499\) −6.38678 19.6565i −0.285911 0.879945i −0.986124 0.166010i \(-0.946911\pi\)
0.700213 0.713934i \(-0.253089\pi\)
\(500\) −0.0474158 + 0.0344496i −0.00212050 + 0.00154063i
\(501\) −0.166177 + 0.120734i −0.00742422 + 0.00539401i
\(502\) −7.85540 24.1764i −0.350604 1.07905i
\(503\) 6.80414 20.9410i 0.303382 0.933712i −0.676895 0.736080i \(-0.736675\pi\)
0.980276 0.197633i \(-0.0633253\pi\)
\(504\) −6.77362 4.92132i −0.301721 0.219213i
\(505\) −33.9160 −1.50924
\(506\) 0 0
\(507\) 3.57128 0.158606
\(508\) 2.51769 + 1.82921i 0.111704 + 0.0811579i
\(509\) 6.62038 20.3754i 0.293443 0.903126i −0.690297 0.723527i \(-0.742520\pi\)
0.983740 0.179599i \(-0.0574801\pi\)
\(510\) 2.29743 + 7.07078i 0.101732 + 0.313099i
\(511\) −2.60665 + 1.89384i −0.115311 + 0.0837785i
\(512\) −19.8517 + 14.4231i −0.877332 + 0.637419i
\(513\) 4.61793 + 14.2125i 0.203887 + 0.627499i
\(514\) 3.60065 11.0817i 0.158818 0.488791i
\(515\) 33.6497 + 24.4479i 1.48278 + 1.07731i
\(516\) −0.219921 −0.00968149
\(517\) 0 0
\(518\) −13.4533 −0.591105
\(519\) 5.06769 + 3.68190i 0.222447 + 0.161617i
\(520\) −13.5403 + 41.6728i −0.593782 + 1.82747i
\(521\) 4.30932 + 13.2627i 0.188795 + 0.581051i 0.999993 0.00372050i \(-0.00118427\pi\)
−0.811198 + 0.584771i \(0.801184\pi\)
\(522\) −22.1724 + 16.1092i −0.970459 + 0.705080i
\(523\) 14.9517 10.8630i 0.653792 0.475007i −0.210769 0.977536i \(-0.567597\pi\)
0.864561 + 0.502529i \(0.167597\pi\)
\(524\) −0.655536 2.01753i −0.0286372 0.0881364i
\(525\) −0.546552 + 1.68211i −0.0238535 + 0.0734135i
\(526\) 17.6473 + 12.8215i 0.769458 + 0.559044i
\(527\) 17.3760 0.756912
\(528\) 0 0
\(529\) 3.43334 0.149276
\(530\) 7.90890 + 5.74615i 0.343541 + 0.249597i
\(531\) 0.322003 0.991022i 0.0139737 0.0430067i
\(532\) −0.306134 0.942184i −0.0132726 0.0408489i
\(533\) −12.4546 + 9.04878i −0.539468 + 0.391946i
\(534\) −2.23823 + 1.62617i −0.0968578 + 0.0703713i
\(535\) 13.6083 + 41.8820i 0.588337 + 1.81072i
\(536\) −5.94921 + 18.3098i −0.256967 + 0.790862i
\(537\) −3.32777 2.41777i −0.143604 0.104334i
\(538\) −10.3013 −0.444122
\(539\) 0 0
\(540\) 0.946578 0.0407342
\(541\) −30.3004 22.0145i −1.30271 0.946477i −0.302736 0.953074i \(-0.597900\pi\)
−0.999978 + 0.00659687i \(0.997900\pi\)
\(542\) −5.90594 + 18.1766i −0.253682 + 0.780753i
\(543\) 1.67035 + 5.14079i 0.0716814 + 0.220613i
\(544\) −3.08460 + 2.24109i −0.132251 + 0.0960860i
\(545\) 39.5814 28.7576i 1.69548 1.23184i
\(546\) −0.731356 2.25088i −0.0312991 0.0963289i
\(547\) −5.29367 + 16.2923i −0.226341 + 0.696606i 0.771812 + 0.635851i \(0.219351\pi\)
−0.998153 + 0.0607551i \(0.980649\pi\)
\(548\) −1.22317 0.888686i −0.0522513 0.0379628i
\(549\) −9.24065 −0.394381
\(550\) 0 0
\(551\) −49.1307 −2.09304
\(552\) −4.41182 3.20538i −0.187780 0.136430i
\(553\) 1.14872 3.53539i 0.0488484 0.150340i
\(554\) 2.53561 + 7.80380i 0.107728 + 0.331552i
\(555\) 9.11171 6.62005i 0.386771 0.281005i
\(556\) 0.469117 0.340833i 0.0198950 0.0144545i
\(557\) 7.59111 + 23.3630i 0.321646 + 0.989923i 0.972932 + 0.231091i \(0.0742296\pi\)
−0.651286 + 0.758832i \(0.725770\pi\)
\(558\) −4.39405 + 13.5235i −0.186015 + 0.572495i
\(559\) 16.5546 + 12.0276i 0.700186 + 0.508715i
\(560\) 11.6146 0.490807
\(561\) 0 0
\(562\) 28.1773 1.18859
\(563\) 12.1428 + 8.82226i 0.511758 + 0.371814i 0.813490 0.581579i \(-0.197565\pi\)
−0.301732 + 0.953393i \(0.597565\pi\)
\(564\) 0.0123458 0.0379964i 0.000519851 0.00159994i
\(565\) 4.01105 + 12.3447i 0.168746 + 0.519347i
\(566\) 10.9369 7.94609i 0.459710 0.333999i
\(567\) 6.33408 4.60198i 0.266007 0.193265i
\(568\) −13.6762 42.0911i −0.573842 1.76610i
\(569\) 3.73994 11.5104i 0.156786 0.482539i −0.841551 0.540178i \(-0.818357\pi\)
0.998338 + 0.0576384i \(0.0183571\pi\)
\(570\) −8.82365 6.41075i −0.369582 0.268517i
\(571\) 38.9439 1.62975 0.814877 0.579634i \(-0.196805\pi\)
0.814877 + 0.579634i \(0.196805\pi\)
\(572\) 0 0
\(573\) 1.39857 0.0584262
\(574\) 3.55371 + 2.58192i 0.148329 + 0.107767i
\(575\) 7.73407 23.8030i 0.322533 0.992655i
\(576\) −7.51779 23.1374i −0.313241 0.964058i
\(577\) −30.8645 + 22.4244i −1.28491 + 0.933540i −0.999689 0.0249227i \(-0.992066\pi\)
−0.285218 + 0.958463i \(0.592066\pi\)
\(578\) 6.42953 4.67132i 0.267433 0.194301i
\(579\) −0.285928 0.879997i −0.0118828 0.0365714i
\(580\) −0.961671 + 2.95972i −0.0399312 + 0.122896i
\(581\) 1.25884 + 0.914603i 0.0522256 + 0.0379441i
\(582\) −3.04664 −0.126287
\(583\) 0 0
\(584\) −9.40610 −0.389227
\(585\) −34.8255 25.3022i −1.43986 1.04612i
\(586\) 11.2892 34.7446i 0.466353 1.43529i
\(587\) −10.7528 33.0936i −0.443814 1.36592i −0.883779 0.467904i \(-0.845009\pi\)
0.439965 0.898015i \(-0.354991\pi\)
\(588\) 0.0415442 0.0301836i 0.00171325 0.00124475i
\(589\) −20.6224 + 14.9830i −0.849729 + 0.617364i
\(590\) 0.480835 + 1.47986i 0.0197957 + 0.0609248i
\(591\) −1.18413 + 3.64436i −0.0487084 + 0.149909i
\(592\) −29.5173 21.4456i −1.21316 0.881409i
\(593\) −18.5913 −0.763452 −0.381726 0.924276i \(-0.624670\pi\)
−0.381726 + 0.924276i \(0.624670\pi\)
\(594\) 0 0
\(595\) 15.0093 0.615322
\(596\) 1.60294 + 1.16460i 0.0656590 + 0.0477040i
\(597\) 1.31189 4.03757i 0.0536920 0.165247i
\(598\) 10.3492 + 31.8515i 0.423209 + 1.30250i
\(599\) −19.9569 + 14.4995i −0.815416 + 0.592434i −0.915396 0.402555i \(-0.868122\pi\)
0.0999801 + 0.994989i \(0.468122\pi\)
\(600\) −4.17726 + 3.03496i −0.170536 + 0.123902i
\(601\) −9.31025 28.6540i −0.379773 1.16882i −0.940201 0.340619i \(-0.889363\pi\)
0.560428 0.828203i \(-0.310637\pi\)
\(602\) 1.80425 5.55292i 0.0735359 0.226320i
\(603\) −15.3013 11.1170i −0.623116 0.452720i
\(604\) 0.965235 0.0392749
\(605\) 0 0
\(606\) 5.34797 0.217247
\(607\) 11.0501 + 8.02839i 0.448511 + 0.325862i 0.789008 0.614383i \(-0.210595\pi\)
−0.340497 + 0.940246i \(0.610595\pi\)
\(608\) 1.72843 5.31957i 0.0700973 0.215737i
\(609\) −0.786970 2.42204i −0.0318896 0.0981461i
\(610\) 11.1634 8.11069i 0.451993 0.328392i
\(611\) −3.00738 + 2.18499i −0.121666 + 0.0883953i
\(612\) −0.598495 1.84198i −0.0241927 0.0744575i
\(613\) −13.9144 + 42.8242i −0.561998 + 1.72965i 0.114709 + 0.993399i \(0.463406\pi\)
−0.676707 + 0.736252i \(0.736594\pi\)
\(614\) 13.1222 + 9.53383i 0.529569 + 0.384754i
\(615\) −3.67738 −0.148286
\(616\) 0 0
\(617\) −8.26401 −0.332697 −0.166348 0.986067i \(-0.553198\pi\)
−0.166348 + 0.986067i \(0.553198\pi\)
\(618\) −5.30599 3.85503i −0.213438 0.155072i
\(619\) 13.3032 40.9430i 0.534700 1.64564i −0.209595 0.977788i \(-0.567215\pi\)
0.744296 0.667850i \(-0.232785\pi\)
\(620\) 0.498947 + 1.53560i 0.0200382 + 0.0616712i
\(621\) 8.86793 6.44293i 0.355858 0.258546i
\(622\) −23.4275 + 17.0211i −0.939357 + 0.682483i
\(623\) 1.72596 + 5.31196i 0.0691491 + 0.212819i
\(624\) 1.98344 6.10440i 0.0794012 0.244372i
\(625\) 20.7453 + 15.0723i 0.829812 + 0.602894i
\(626\) 17.3107 0.691873
\(627\) 0 0
\(628\) 3.31330 0.132215
\(629\) −38.1446 27.7137i −1.52093 1.10502i
\(630\) −3.79555 + 11.6815i −0.151219 + 0.465403i
\(631\) 0.320955 + 0.987799i 0.0127770 + 0.0393237i 0.957242 0.289289i \(-0.0934189\pi\)
−0.944465 + 0.328613i \(0.893419\pi\)
\(632\) 8.77958 6.37874i 0.349233 0.253733i
\(633\) −3.26626 + 2.37307i −0.129822 + 0.0943212i
\(634\) 4.99989 + 15.3881i 0.198571 + 0.611138i
\(635\) 21.3741 65.7827i 0.848205 2.61051i
\(636\) 0.0948317 + 0.0688993i 0.00376032 + 0.00273203i
\(637\) −4.77801 −0.189312
\(638\) 0 0
\(639\) 43.4787 1.71999
\(640\) 25.3342 + 18.4064i 1.00142 + 0.727576i
\(641\) 10.3957 31.9948i 0.410607 1.26372i −0.505515 0.862818i \(-0.668698\pi\)
0.916122 0.400900i \(-0.131302\pi\)
\(642\) −2.14580 6.60408i −0.0846878 0.260642i
\(643\) 17.0147 12.3619i 0.670996 0.487507i −0.199363 0.979926i \(-0.563887\pi\)
0.870358 + 0.492419i \(0.163887\pi\)
\(644\) −0.587877 + 0.427118i −0.0231656 + 0.0168308i
\(645\) 1.51047 + 4.64873i 0.0594745 + 0.183044i
\(646\) −14.1093 + 43.4240i −0.555124 + 1.70850i
\(647\) −20.4115 14.8298i −0.802459 0.583021i 0.109176 0.994022i \(-0.465179\pi\)
−0.911634 + 0.411002i \(0.865179\pi\)
\(648\) 22.8566 0.897892
\(649\) 0 0
\(650\) 31.7101 1.24377
\(651\) −1.06896 0.776644i −0.0418958 0.0304391i
\(652\) 0.0432678 0.133165i 0.00169450 0.00521513i
\(653\) 6.37772 + 19.6286i 0.249580 + 0.768127i 0.994849 + 0.101364i \(0.0323207\pi\)
−0.745270 + 0.666763i \(0.767679\pi\)
\(654\) −6.24132 + 4.53458i −0.244055 + 0.177316i
\(655\) −38.1446 + 27.7137i −1.49043 + 1.08286i
\(656\) 3.68127 + 11.3298i 0.143729 + 0.442354i
\(657\) 2.85552 8.78838i 0.111404 0.342867i
\(658\) 0.858108 + 0.623452i 0.0334525 + 0.0243047i
\(659\) −18.5067 −0.720920 −0.360460 0.932775i \(-0.617380\pi\)
−0.360460 + 0.932775i \(0.617380\pi\)
\(660\) 0 0
\(661\) 16.8001 0.653446 0.326723 0.945120i \(-0.394056\pi\)
0.326723 + 0.945120i \(0.394056\pi\)
\(662\) −13.1104 9.52530i −0.509552 0.370211i
\(663\) 2.56316 7.88859i 0.0995448 0.306367i
\(664\) 1.40372 + 4.32022i 0.0544750 + 0.167657i
\(665\) −17.8135 + 12.9422i −0.690777 + 0.501879i
\(666\) 31.2151 22.6791i 1.20956 0.878798i
\(667\) 11.1361 + 34.2735i 0.431193 + 1.32708i
\(668\) −0.0246916 + 0.0759928i −0.000955345 + 0.00294025i
\(669\) −8.24225 5.98834i −0.318664 0.231523i
\(670\) 28.2427 1.09111
\(671\) 0 0
\(672\) 0.289930 0.0111843
\(673\) −14.2031 10.3192i −0.547490 0.397775i 0.279369 0.960184i \(-0.409875\pi\)
−0.826859 + 0.562409i \(0.809875\pi\)
\(674\) −0.417361 + 1.28451i −0.0160762 + 0.0494773i
\(675\) −3.20716 9.87063i −0.123444 0.379921i
\(676\) 1.12392 0.816577i 0.0432278 0.0314068i
\(677\) 2.95074 2.14384i 0.113406 0.0823945i −0.529637 0.848225i \(-0.677672\pi\)
0.643043 + 0.765830i \(0.277672\pi\)
\(678\) −0.632475 1.94656i −0.0242900 0.0747570i
\(679\) −1.90066 + 5.84963i −0.0729406 + 0.224488i
\(680\) 35.4490 + 25.7552i 1.35941 + 0.987668i
\(681\) −8.35994 −0.320354
\(682\) 0 0
\(683\) 27.4720 1.05119 0.525593 0.850736i \(-0.323844\pi\)
0.525593 + 0.850736i \(0.323844\pi\)
\(684\) 2.29861 + 1.67004i 0.0878895 + 0.0638555i
\(685\) −10.3842 + 31.9593i −0.396760 + 1.22110i
\(686\) 0.421292 + 1.29660i 0.0160850 + 0.0495045i
\(687\) −3.94584 + 2.86682i −0.150543 + 0.109376i
\(688\) 12.8104 9.30731i 0.488393 0.354838i
\(689\) −3.37033 10.3728i −0.128399 0.395173i
\(690\) −2.47214 + 7.60845i −0.0941126 + 0.289649i
\(691\) 4.81904 + 3.50124i 0.183325 + 0.133193i 0.675663 0.737211i \(-0.263858\pi\)
−0.492338 + 0.870404i \(0.663858\pi\)
\(692\) 2.43673 0.0926304
\(693\) 0 0
\(694\) 20.7080 0.786065
\(695\) −10.4266 7.57536i −0.395503 0.287350i
\(696\) 2.29743 7.07078i 0.0870840 0.268017i
\(697\) 4.75723 + 14.6412i 0.180193 + 0.554576i
\(698\) −32.7614 + 23.8026i −1.24004 + 0.900940i
\(699\) 1.03977 0.755435i 0.0393276 0.0285732i
\(700\) 0.212611 + 0.654349i 0.00803593 + 0.0247321i
\(701\) 2.27723 7.00859i 0.0860097 0.264711i −0.898797 0.438365i \(-0.855558\pi\)
0.984807 + 0.173655i \(0.0555576\pi\)
\(702\) 11.2355 + 8.16309i 0.424058 + 0.308096i
\(703\) 69.1680 2.60872
\(704\) 0 0
\(705\) −0.887968 −0.0334428
\(706\) −7.40746 5.38184i −0.278783 0.202548i
\(707\) 3.33635 10.2682i 0.125476 0.386177i
\(708\) 0.00576546 + 0.0177443i 0.000216679 + 0.000666870i
\(709\) 28.0858 20.4056i 1.05479 0.766347i 0.0816692 0.996659i \(-0.473975\pi\)
0.973117 + 0.230313i \(0.0739749\pi\)
\(710\) −52.5257 + 38.1621i −1.97125 + 1.43220i
\(711\) 3.29451 + 10.1395i 0.123554 + 0.380260i
\(712\) −5.03867 + 15.5074i −0.188832 + 0.581165i
\(713\) 15.1265 + 10.9900i 0.566491 + 0.411580i
\(714\) −2.36672 −0.0885722
\(715\) 0 0
\(716\) −1.60011 −0.0597989
\(717\) −6.47214 4.70228i −0.241706 0.175610i
\(718\) −7.47202 + 22.9965i −0.278853 + 0.858222i
\(719\) −1.25523 3.86319i −0.0468121 0.144073i 0.924918 0.380166i \(-0.124133\pi\)
−0.971730 + 0.236093i \(0.924133\pi\)
\(720\) −26.9489 + 19.5795i −1.00433 + 0.729685i
\(721\) −10.7119 + 7.78266i −0.398932 + 0.289841i
\(722\) −12.6938 39.0675i −0.472415 1.45394i
\(723\) −0.0354076 + 0.108973i −0.00131682 + 0.00405277i
\(724\) 1.70112 + 1.23594i 0.0632217 + 0.0459333i
\(725\) 34.1214 1.26724
\(726\) 0 0
\(727\) −30.5433 −1.13279 −0.566394 0.824135i \(-0.691662\pi\)
−0.566394 + 0.824135i \(0.691662\pi\)
\(728\) −11.2847 8.19881i −0.418239 0.303868i
\(729\) −6.22072 + 19.1454i −0.230397 + 0.709090i
\(730\) 4.26404 + 13.1234i 0.157819 + 0.485718i
\(731\) 16.5546 12.0276i 0.612295 0.444858i
\(732\) 0.133855 0.0972513i 0.00494742 0.00359451i
\(733\) −9.52822 29.3249i −0.351933 1.08314i −0.957767 0.287547i \(-0.907160\pi\)
0.605834 0.795591i \(-0.292840\pi\)
\(734\) 3.41217 10.5016i 0.125946 0.387621i
\(735\) −0.923360 0.670861i −0.0340587 0.0247451i
\(736\) −4.10270 −0.151228
\(737\) 0 0
\(738\) −12.5980 −0.463740
\(739\) −17.9796 13.0630i −0.661392 0.480529i 0.205741 0.978607i \(-0.434040\pi\)
−0.867133 + 0.498077i \(0.834040\pi\)
\(740\) 1.35388 4.16680i 0.0497695 0.153175i
\(741\) 3.76015 + 11.5725i 0.138132 + 0.425128i
\(742\) −2.51769 + 1.82921i −0.0924272 + 0.0671523i
\(743\) 25.2004 18.3091i 0.924511 0.671697i −0.0201316 0.999797i \(-0.506409\pi\)
0.944643 + 0.328101i \(0.106409\pi\)
\(744\) −1.19199 3.66855i −0.0437003 0.134496i
\(745\) 13.6083 41.8820i 0.498569 1.53444i
\(746\) 0.623550 + 0.453036i 0.0228298 + 0.0165868i
\(747\) −4.46264 −0.163280
\(748\) 0 0
\(749\) −14.0187 −0.512231
\(750\) −0.166177 0.120734i −0.00606791 0.00440860i
\(751\) 3.70491 11.4026i 0.135194 0.416085i −0.860426 0.509575i \(-0.829802\pi\)
0.995620 + 0.0934905i \(0.0298025\pi\)
\(752\) 0.888909 + 2.73578i 0.0324152 + 0.0997636i
\(753\) −5.48078 + 3.98202i −0.199731 + 0.145113i
\(754\) −36.9387 + 26.8375i −1.34523 + 0.977365i
\(755\) −6.62944 20.4033i −0.241270 0.742553i
\(756\) −0.0931160 + 0.286582i −0.00338660 + 0.0104229i
\(757\) 9.26592 + 6.73209i 0.336776 + 0.244682i 0.743300 0.668958i \(-0.233259\pi\)
−0.406524 + 0.913640i \(0.633259\pi\)
\(758\) 30.7240 1.11595
\(759\) 0 0
\(760\) −64.2800 −2.33168
\(761\) −6.38318 4.63765i −0.231390 0.168115i 0.466049 0.884759i \(-0.345677\pi\)
−0.697439 + 0.716644i \(0.745677\pi\)
\(762\) −3.37033 + 10.3728i −0.122094 + 0.375768i
\(763\) 4.81284 + 14.8124i 0.174236 + 0.536245i
\(764\) 0.440146 0.319785i 0.0159239 0.0115694i
\(765\) −34.8255 + 25.3022i −1.25912 + 0.914802i
\(766\) −9.01198 27.7360i −0.325616 1.00214i
\(767\) 0.536449 1.65102i 0.0193700 0.0596149i
\(768\) 0.991963 + 0.720703i 0.0357944 + 0.0260061i
\(769\) −48.8153 −1.76033 −0.880163 0.474672i \(-0.842567\pi\)
−0.880163 + 0.474672i \(0.842567\pi\)
\(770\) 0 0
\(771\) −3.10525 −0.111833
\(772\) −0.291197 0.211567i −0.0104804 0.00761445i
\(773\) −0.987642 + 3.03965i −0.0355230 + 0.109329i −0.967246 0.253842i \(-0.918306\pi\)
0.931723 + 0.363170i \(0.118306\pi\)
\(774\) 5.17459 + 15.9257i 0.185997 + 0.572439i
\(775\) 14.3223 10.4057i 0.514471 0.373785i
\(776\) −14.5266 + 10.5542i −0.521476 + 0.378874i
\(777\) 1.10792 + 3.40984i 0.0397466 + 0.122327i
\(778\) −4.49884 + 13.8460i −0.161291 + 0.496404i
\(779\) −18.2708 13.2745i −0.654621 0.475610i
\(780\) 0.770750 0.0275973
\(781\) 0 0
\(782\) 33.4906 1.19762
\(783\) 12.0899 + 8.78383i 0.432058 + 0.313908i
\(784\) −1.14254 + 3.51639i −0.0408052 + 0.125585i
\(785\) −22.7564 70.0370i −0.812211 2.49973i
\(786\) 6.01476 4.36998i 0.214539 0.155872i
\(787\) 34.3681 24.9699i 1.22509 0.890080i 0.228578 0.973526i \(-0.426592\pi\)
0.996512 + 0.0834455i \(0.0265925\pi\)
\(788\) 0.460629 + 1.41767i 0.0164092 + 0.0505024i
\(789\) 1.79639 5.52873i 0.0639533 0.196828i
\(790\) −12.8796 9.35760i −0.458237 0.332928i
\(791\) −4.13201 −0.146917
\(792\) 0 0
\(793\) −15.3947 −0.546682
\(794\) −26.3782 19.1649i −0.936129 0.680137i
\(795\) 0.805081 2.47778i 0.0285533 0.0878779i
\(796\) −0.510329 1.57063i −0.0180881 0.0556696i
\(797\) 23.3471 16.9627i 0.826998 0.600850i −0.0917101 0.995786i \(-0.529233\pi\)
0.918709 + 0.394936i \(0.129233\pi\)
\(798\) 2.80888 2.04077i 0.0994334 0.0722426i
\(799\) 1.14872 + 3.53539i 0.0406387 + 0.125073i
\(800\) −1.20040 + 3.69445i −0.0424406 + 0.130619i
\(801\) −12.9594 9.41553i −0.457897 0.332681i
\(802\) −15.8947 −0.561260
\(803\) 0 0
\(804\) 0.338644 0.0119431
\(805\) 13.0662 + 9.49312i 0.460522 + 0.334589i
\(806\) −7.32038 + 22.5298i −0.257849 + 0.793579i
\(807\) 0.848349 + 2.61095i 0.0298633 + 0.0919097i
\(808\) 25.4996 18.5265i 0.897071 0.651760i
\(809\) 23.8282 17.3122i 0.837756 0.608665i −0.0839869 0.996467i \(-0.526765\pi\)
0.921743 + 0.387802i \(0.126765\pi\)
\(810\) −10.3615 31.8895i −0.364067 1.12048i
\(811\) −0.766764 + 2.35986i −0.0269247 + 0.0828657i −0.963616 0.267291i \(-0.913872\pi\)
0.936691 + 0.350156i \(0.113872\pi\)
\(812\) −0.801470 0.582302i −0.0281261 0.0204348i
\(813\) 5.09337 0.178632
\(814\) 0 0
\(815\) −3.11203 −0.109010
\(816\) −5.19271 3.77273i −0.181781 0.132072i
\(817\) −9.27628 + 28.5494i −0.324536 + 0.998818i
\(818\) −13.8248 42.5484i −0.483373 1.48767i
\(819\) 11.0862 8.05459i 0.387383 0.281450i
\(820\) −1.15731 + 0.840835i −0.0404150 + 0.0293632i
\(821\) −4.33200 13.3325i −0.151188 0.465309i 0.846567 0.532283i \(-0.178666\pi\)
−0.997755 + 0.0669738i \(0.978666\pi\)
\(822\) 1.63741 5.03944i 0.0571113 0.175771i
\(823\) 34.6205 + 25.1533i 1.20679 + 0.876787i 0.994936 0.100513i \(-0.0320484\pi\)
0.211859 + 0.977300i \(0.432048\pi\)
\(824\) −38.6540 −1.34658
\(825\) 0 0
\(826\) −0.495336 −0.0172349
\(827\) −7.41920 5.39037i −0.257991 0.187441i 0.451270 0.892388i \(-0.350971\pi\)
−0.709261 + 0.704946i \(0.750971\pi\)
\(828\) 0.644005 1.98204i 0.0223807 0.0688808i
\(829\) 9.02246 + 27.7683i 0.313363 + 0.964433i 0.976423 + 0.215866i \(0.0692575\pi\)
−0.663060 + 0.748566i \(0.730743\pi\)
\(830\) 5.39121 3.91695i 0.187132 0.135959i
\(831\) 1.76912 1.28534i 0.0613700 0.0445879i
\(832\) −12.5245 38.5463i −0.434208 1.33635i
\(833\) −1.47649 + 4.54416i −0.0511572 + 0.157446i
\(834\) 1.64410 + 1.19451i 0.0569304 + 0.0413624i
\(835\) 1.77594 0.0614588
\(836\) 0 0
\(837\) 7.75341 0.267997
\(838\) 11.9082 + 8.65185i 0.411363 + 0.298873i
\(839\) 6.09771 18.7668i 0.210516 0.647902i −0.788925 0.614489i \(-0.789362\pi\)
0.999442 0.0334134i \(-0.0106378\pi\)
\(840\) −1.02963 3.16888i −0.0355256 0.109337i
\(841\) −16.2861 + 11.8325i −0.561589 + 0.408018i
\(842\) −1.27059 + 0.923135i −0.0437873 + 0.0318133i
\(843\) −2.32050 7.14175i −0.0799222 0.245975i
\(844\) −0.485321 + 1.49366i −0.0167054 + 0.0514140i
\(845\) −24.9803 18.1492i −0.859348 0.624353i
\(846\) −3.04202 −0.104587
\(847\) 0 0
\(848\) −8.43984 −0.289825
\(849\) −2.91468 2.11764i −0.100032 0.0726773i
\(850\) 9.79895 30.1581i 0.336101 1.03441i
\(851\) −15.6779 48.2515i −0.537431 1.65404i
\(852\) −0.629809 + 0.457583i −0.0215769 + 0.0156765i
\(853\) −22.9378 + 16.6653i −0.785375 + 0.570609i −0.906587 0.422018i \(-0.861322\pi\)
0.121212 + 0.992627i \(0.461322\pi\)
\(854\) 1.35740 + 4.17764i 0.0464492 + 0.142956i
\(855\) 19.5142 60.0586i 0.667372 2.05396i
\(856\) −33.1092 24.0553i −1.13165 0.822192i
\(857\) −13.2033 −0.451017 −0.225509 0.974241i \(-0.572404\pi\)
−0.225509 + 0.974241i \(0.572404\pi\)
\(858\) 0 0
\(859\) −20.8260 −0.710573 −0.355286 0.934757i \(-0.615617\pi\)
−0.355286 + 0.934757i \(0.615617\pi\)
\(860\) 1.53830 + 1.11764i 0.0524555 + 0.0381111i
\(861\) 0.361748 1.11335i 0.0123283 0.0379427i
\(862\) 13.4645 + 41.4395i 0.458603 + 1.41143i
\(863\) −28.2702 + 20.5395i −0.962330 + 0.699174i −0.953691 0.300789i \(-0.902750\pi\)
−0.00863946 + 0.999963i \(0.502750\pi\)
\(864\) −1.37639 + 1.00000i −0.0468256 + 0.0340208i
\(865\) −16.7360 51.5080i −0.569039 1.75132i
\(866\) 1.86773 5.74827i 0.0634680 0.195334i
\(867\) −1.71347 1.24491i −0.0581926 0.0422794i
\(868\) −0.513993 −0.0174461
\(869\) 0 0
\(870\) −10.9066 −0.369769
\(871\) −25.4915 18.5207i −0.863748 0.627550i
\(872\) −14.0503 + 43.2425i −0.475804 + 1.46437i
\(873\) −5.45108 16.7767i −0.184491 0.567805i
\(874\) −39.7476 + 28.8783i −1.34448 + 0.976823i
\(875\) −0.335483 + 0.243743i −0.0113414 + 0.00824000i
\(876\) 0.0511280 + 0.157356i 0.00172746 + 0.00531656i
\(877\) 8.18317 25.1852i 0.276326 0.850444i −0.712539 0.701632i \(-0.752455\pi\)
0.988865 0.148812i \(-0.0475450\pi\)
\(878\) −30.3004 22.0145i −1.02259 0.742954i
\(879\) −9.73599 −0.328387
\(880\) 0 0
\(881\) 17.2627 0.581595 0.290798 0.956785i \(-0.406079\pi\)
0.290798 + 0.956785i \(0.406079\pi\)
\(882\) −3.16327 2.29825i −0.106513 0.0773861i
\(883\) −13.7830 + 42.4196i −0.463834 + 1.42753i 0.396609 + 0.917988i \(0.370187\pi\)
−0.860443 + 0.509547i \(0.829813\pi\)
\(884\) −0.997078 3.06869i −0.0335354 0.103211i
\(885\) 0.335483 0.243743i 0.0112771 0.00819332i
\(886\) −8.59283 + 6.24305i −0.288682 + 0.209739i
\(887\) −9.51445 29.2825i −0.319464 0.983209i −0.973878 0.227072i \(-0.927085\pi\)
0.654414 0.756137i \(-0.272915\pi\)
\(888\) −3.23441 + 9.95450i −0.108540 + 0.334051i
\(889\) 17.8135 + 12.9422i 0.597445 + 0.434069i
\(890\) 23.9201 0.801803
\(891\) 0 0
\(892\) −3.96316 −0.132697
\(893\) −4.41182 3.20538i −0.147636 0.107264i
\(894\) −2.14580 + 6.60408i −0.0717661 + 0.220873i
\(895\) 10.9899 + 33.8234i 0.367351 + 1.13059i
\(896\) −8.06479 + 5.85941i −0.269426 + 0.195749i
\(897\) 7.22071 5.24615i 0.241092 0.175164i
\(898\) −8.64094 26.5941i −0.288352 0.887456i
\(899\) −7.87704 + 24.2430i −0.262714 + 0.808550i
\(900\) −1.59639 1.15984i −0.0532130 0.0386615i
\(901\) −10.9066 −0.363352
\(902\) 0 0
\(903\) −1.55602 −0.0517810
\(904\) −9.75897 7.09031i −0.324579 0.235820i
\(905\) 14.4418 44.4473i 0.480062 1.47748i
\(906\) 1.04535 + 3.21726i 0.0347294 + 0.106886i
\(907\) −19.2385 + 13.9776i −0.638804 + 0.464118i −0.859439 0.511238i \(-0.829187\pi\)
0.220635 + 0.975356i \(0.429187\pi\)
\(908\) −2.63096 + 1.91151i −0.0873116 + 0.0634356i
\(909\) 9.56864 + 29.4492i 0.317372 + 0.976769i
\(910\) −6.32330 + 19.4611i −0.209615 + 0.645130i
\(911\) −39.6645 28.8179i −1.31414 0.954781i −0.999985 0.00540957i \(-0.998278\pi\)
−0.314157 0.949371i \(-0.601722\pi\)
\(912\) 9.41600 0.311795
\(913\) 0 0
\(914\) 11.6774 0.386253
\(915\) −2.97506 2.16151i −0.0983524 0.0714572i
\(916\) −0.586297 + 1.80444i −0.0193718 + 0.0596203i
\(917\) −4.63814 14.2747i −0.153165 0.471393i
\(918\) 11.2355 8.16309i 0.370828 0.269422i
\(919\) −32.3607 + 23.5114i −1.06748 + 0.775570i −0.975458 0.220187i \(-0.929333\pi\)
−0.0920227 + 0.995757i \(0.529333\pi\)
\(920\) 14.5699 + 44.8417i 0.480357 + 1.47839i
\(921\) 1.33576 4.11106i 0.0440149 0.135464i
\(922\) 10.6611 + 7.74577i 0.351106 + 0.255093i
\(923\) 72.4346 2.38421
\(924\) 0 0
\(925\) −48.0373 −1.57946
\(926\) 12.6002 + 9.15456i 0.414067 + 0.300838i
\(927\) 11.7346 36.1155i 0.385416 1.18619i
\(928\) −1.72843 5.31957i −0.0567386 0.174624i
\(929\) 45.7774 33.2592i 1.50191 1.09120i 0.532295 0.846559i \(-0.321330\pi\)
0.969614 0.244641i \(-0.0786702\pi\)
\(930\) −4.57800 + 3.32611i −0.150119 + 0.109067i
\(931\) −2.16600 6.66627i −0.0709878 0.218478i
\(932\) 0.154495 0.475487i 0.00506065 0.0155751i
\(933\) 6.24345 + 4.53613i 0.204401 + 0.148506i
\(934\) −24.8408 −0.812814
\(935\) 0 0
\(936\) 40.0046 1.30759
\(937\) 13.6039 + 9.88380i 0.444419 + 0.322890i 0.787389 0.616457i \(-0.211433\pi\)
−0.342969 + 0.939347i \(0.611433\pi\)
\(938\) −2.77827 + 8.55064i −0.0907137 + 0.279188i
\(939\) −1.42559 4.38752i −0.0465224 0.143181i
\(940\) −0.279453 + 0.203035i −0.00911476 + 0.00662226i
\(941\) −5.87290 + 4.26691i −0.191451 + 0.139097i −0.679382 0.733785i \(-0.737752\pi\)
0.487931 + 0.872882i \(0.337752\pi\)
\(942\) 3.58830 + 11.0437i 0.116913 + 0.359822i
\(943\) −5.11897 + 15.7546i −0.166697 + 0.513040i
\(944\) −1.08679 0.789603i −0.0353722 0.0256994i
\(945\) 6.69735 0.217865
\(946\) 0 0
\(947\) −25.6040 −0.832017 −0.416009 0.909361i \(-0.636571\pi\)
−0.416009 + 0.909361i \(0.636571\pi\)
\(948\) −0.154433 0.112202i −0.00501576 0.00364416i
\(949\) 4.75723 14.6412i 0.154426 0.475275i
\(950\) 14.3750 + 44.2418i 0.466388 + 1.43539i
\(951\) 3.48846 2.53452i 0.113121 0.0821873i
\(952\) −11.2847 + 8.19881i −0.365739 + 0.265725i
\(953\) 2.20927 + 6.79943i 0.0715653 + 0.220255i 0.980442 0.196811i \(-0.0630584\pi\)
−0.908876 + 0.417066i \(0.863058\pi\)
\(954\) 2.75806 8.48845i 0.0892956 0.274824i
\(955\) −9.78268 7.10753i −0.316560 0.229994i
\(956\) −3.11203 −0.100650
\(957\) 0 0
\(958\) −4.73344 −0.152930
\(959\) −8.65434 6.28775i −0.279463 0.203042i
\(960\) 2.99175 9.20767i 0.0965584 0.297176i
\(961\) −5.49266 16.9047i −0.177183 0.545312i
\(962\) 52.0036 37.7829i 1.67666 1.21817i
\(963\) 32.5269 23.6321i 1.04816 0.761535i
\(964\) 0.0137737 + 0.0423911i 0.000443621 + 0.00136533i
\(965\) −2.47214 + 7.60845i −0.0795809 + 0.244925i
\(966\) −2.06031 1.49691i −0.0662895 0.0481621i
\(967\) 15.9600 0.513241 0.256620 0.966512i \(-0.417391\pi\)
0.256620 + 0.966512i \(0.417391\pi\)
\(968\) 0 0
\(969\) 12.1681 0.390895
\(970\) 21.3105 + 15.4830i 0.684240 + 0.497130i
\(971\) −9.41819 + 28.9862i −0.302244 + 0.930212i 0.678447 + 0.734649i \(0.262653\pi\)
−0.980691 + 0.195563i \(0.937347\pi\)
\(972\) −0.403588 1.24212i −0.0129451 0.0398409i
\(973\) 3.31916 2.41151i 0.106407 0.0773094i
\(974\) −30.2886 + 22.0060i −0.970510 + 0.705117i
\(975\) −2.61143 8.03715i −0.0836327 0.257395i
\(976\) −3.68127 + 11.3298i −0.117835 + 0.362658i
\(977\) −3.34286 2.42873i −0.106948 0.0777021i 0.533026 0.846099i \(-0.321055\pi\)
−0.639974 + 0.768397i \(0.721055\pi\)
\(978\) 0.490715 0.0156913
\(979\) 0 0
\(980\) −0.443984 −0.0141826
\(981\) −36.1372 26.2552i −1.15377 0.838265i
\(982\) 2.63898 8.12194i 0.0842131 0.259181i
\(983\) −7.73303 23.7998i −0.246645 0.759096i −0.995362 0.0962053i \(-0.969329\pi\)
0.748716 0.662891i \(-0.230671\pi\)
\(984\) 2.76482 2.00876i 0.0881392 0.0640369i
\(985\) 26.8033 19.4737i 0.854024 0.620485i
\(986\) 14.1093 + 43.4240i 0.449332 + 1.38290i
\(987\) 0.0873505 0.268837i 0.00278040 0.00855718i
\(988\) 3.82943 + 2.78224i 0.121830 + 0.0885150i
\(989\) 22.0187 0.700153
\(990\) 0 0
\(991\) −27.5747 −0.875938 −0.437969 0.898990i \(-0.644302\pi\)
−0.437969 + 0.898990i \(0.644302\pi\)
\(992\) −2.34777 1.70576i −0.0745418 0.0541578i
\(993\) −1.33457 + 4.10738i −0.0423513 + 0.130344i
\(994\) −6.38678 19.6565i −0.202576 0.623466i
\(995\) −29.6953 + 21.5749i −0.941403 + 0.683969i
\(996\) 0.0646434 0.0469662i 0.00204830 0.00148818i
\(997\) 7.31895 + 22.5254i 0.231794 + 0.713387i 0.997531 + 0.0702335i \(0.0223744\pi\)
−0.765737 + 0.643154i \(0.777626\pi\)
\(998\) 8.70727 26.7982i 0.275624 0.848283i
\(999\) −17.0206 12.3662i −0.538508 0.391249i
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 847.2.f.u.323.2 12
11.2 odd 10 847.2.f.t.148.2 12
11.3 even 5 inner 847.2.f.u.729.2 12
11.4 even 5 inner 847.2.f.u.372.2 12
11.5 even 5 847.2.a.i.1.2 3
11.6 odd 10 847.2.a.j.1.2 yes 3
11.7 odd 10 847.2.f.t.372.2 12
11.8 odd 10 847.2.f.t.729.2 12
11.9 even 5 inner 847.2.f.u.148.2 12
11.10 odd 2 847.2.f.t.323.2 12
33.5 odd 10 7623.2.a.ce.1.2 3
33.17 even 10 7623.2.a.bz.1.2 3
77.6 even 10 5929.2.a.y.1.2 3
77.27 odd 10 5929.2.a.t.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.i.1.2 3 11.5 even 5
847.2.a.j.1.2 yes 3 11.6 odd 10
847.2.f.t.148.2 12 11.2 odd 10
847.2.f.t.323.2 12 11.10 odd 2
847.2.f.t.372.2 12 11.7 odd 10
847.2.f.t.729.2 12 11.8 odd 10
847.2.f.u.148.2 12 11.9 even 5 inner
847.2.f.u.323.2 12 1.1 even 1 trivial
847.2.f.u.372.2 12 11.4 even 5 inner
847.2.f.u.729.2 12 11.3 even 5 inner
5929.2.a.t.1.2 3 77.27 odd 10
5929.2.a.y.1.2 3 77.6 even 10
7623.2.a.bz.1.2 3 33.17 even 10
7623.2.a.ce.1.2 3 33.5 odd 10