Properties

Label 507.2.j.i.316.4
Level $507$
Weight $2$
Character 507.316
Analytic conductor $4.048$
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] = [507,2,Mod(316,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.316");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.4
Root \(0.385418 - 0.222521i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.i.361.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.77441 + 1.02446i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.09903 + 1.90358i) q^{4} +3.35690i q^{5} +(1.77441 - 1.02446i) q^{6} +(-1.94594 + 1.12349i) q^{7} +0.405813i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.77441 + 1.02446i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.09903 + 1.90358i) q^{4} +3.35690i q^{5} +(1.77441 - 1.02446i) q^{6} +(-1.94594 + 1.12349i) q^{7} +0.405813i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.43900 + 5.95652i) q^{10} +(4.27730 + 2.46950i) q^{11} +2.19806 q^{12} -4.60388 q^{14} +(2.90716 + 1.67845i) q^{15} +(1.78232 - 3.08707i) q^{16} +(0.455927 + 0.789689i) q^{17} -2.04892i q^{18} +(-3.29257 + 1.90097i) q^{19} +(-6.39011 + 3.68933i) q^{20} +2.24698i q^{21} +(5.05980 + 8.76383i) q^{22} +(1.01357 - 1.75556i) q^{23} +(0.351445 + 0.202907i) q^{24} -6.26875 q^{25} -1.00000 q^{27} +(-4.27730 - 2.46950i) q^{28} +(1.96950 - 3.41127i) q^{29} +(3.43900 + 5.95652i) q^{30} -8.82908i q^{31} +(7.02805 - 4.05765i) q^{32} +(4.27730 - 2.46950i) q^{33} +1.86831i q^{34} +(-3.77144 - 6.53232i) q^{35} +(1.09903 - 1.90358i) q^{36} +(7.62270 + 4.40097i) q^{37} -7.78986 q^{38} -1.36227 q^{40} +(-6.00935 - 3.46950i) q^{41} +(-2.30194 + 3.98707i) q^{42} +(-1.14310 - 1.97991i) q^{43} +10.8562i q^{44} +(2.90716 - 1.67845i) q^{45} +(3.59700 - 2.07673i) q^{46} -3.80194i q^{47} +(-1.78232 - 3.08707i) q^{48} +(-0.975541 + 1.68969i) q^{49} +(-11.1234 - 6.42208i) q^{50} +0.911854 q^{51} +0.542877 q^{53} +(-1.77441 - 1.02446i) q^{54} +(-8.28986 + 14.3585i) q^{55} +(-0.455927 - 0.789689i) q^{56} +3.80194i q^{57} +(6.98942 - 4.03534i) q^{58} +(4.08226 - 2.35690i) q^{59} +7.37867i q^{60} +(-1.83997 - 3.18692i) q^{61} +(9.04503 - 15.6665i) q^{62} +(1.94594 + 1.12349i) q^{63} +9.49827 q^{64} +10.1196 q^{66} +(1.31732 + 0.760553i) q^{67} +(-1.00216 + 1.73578i) q^{68} +(-1.01357 - 1.75556i) q^{69} -15.4547i q^{70} +(2.05999 - 1.18933i) q^{71} +(0.351445 - 0.202907i) q^{72} -7.41119i q^{73} +(9.01722 + 15.6183i) q^{74} +(-3.13437 + 5.42890i) q^{75} +(-7.23728 - 4.17845i) q^{76} -11.0978 q^{77} -3.74094 q^{79} +(10.3630 + 5.98307i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.10872 - 12.3127i) q^{82} +2.30798i q^{83} +(-4.27730 + 2.46950i) q^{84} +(-2.65090 + 1.53050i) q^{85} -4.68425i q^{86} +(-1.96950 - 3.41127i) q^{87} +(-1.00216 + 1.73578i) q^{88} +(-8.71101 - 5.02930i) q^{89} +6.87800 q^{90} +4.45580 q^{92} +(-7.64621 - 4.41454i) q^{93} +(3.89493 - 6.74621i) q^{94} +(-6.38135 - 11.0528i) q^{95} -8.11529i q^{96} +(-13.9684 + 8.06465i) q^{97} +(-3.46203 + 1.99880i) q^{98} -4.93900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9} - 2 q^{10} + 44 q^{12} - 20 q^{14} - 22 q^{16} - 2 q^{17} + 18 q^{22} - 44 q^{25} - 12 q^{27} + 4 q^{29} + 2 q^{30} - 8 q^{35} + 22 q^{36} + 12 q^{40} - 10 q^{42} - 30 q^{43} + 22 q^{48} - 30 q^{49} - 4 q^{51} - 68 q^{53} - 6 q^{55} + 2 q^{56} + 26 q^{61} - 4 q^{62} + 36 q^{66} + 26 q^{68} - 30 q^{74} - 22 q^{75} - 60 q^{77} + 12 q^{79} - 6 q^{81} - 6 q^{82} - 4 q^{87} + 26 q^{88} + 4 q^{90} + 28 q^{92} - 42 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.77441 + 1.02446i 1.25470 + 0.724402i 0.972039 0.234818i \(-0.0754495\pi\)
0.282661 + 0.959220i \(0.408783\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 1.09903 + 1.90358i 0.549516 + 0.951789i
\(5\) 3.35690i 1.50125i 0.660729 + 0.750625i \(0.270247\pi\)
−0.660729 + 0.750625i \(0.729753\pi\)
\(6\) 1.77441 1.02446i 0.724402 0.418234i
\(7\) −1.94594 + 1.12349i −0.735497 + 0.424639i −0.820430 0.571747i \(-0.806266\pi\)
0.0849330 + 0.996387i \(0.472932\pi\)
\(8\) 0.405813i 0.143477i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −3.43900 + 5.95652i −1.08751 + 1.88362i
\(11\) 4.27730 + 2.46950i 1.28965 + 0.744582i 0.978593 0.205807i \(-0.0659820\pi\)
0.311062 + 0.950390i \(0.399315\pi\)
\(12\) 2.19806 0.634526
\(13\) 0 0
\(14\) −4.60388 −1.23044
\(15\) 2.90716 + 1.67845i 0.750625 + 0.433373i
\(16\) 1.78232 3.08707i 0.445581 0.771769i
\(17\) 0.455927 + 0.789689i 0.110579 + 0.191528i 0.916004 0.401170i \(-0.131396\pi\)
−0.805425 + 0.592698i \(0.798063\pi\)
\(18\) 2.04892i 0.482934i
\(19\) −3.29257 + 1.90097i −0.755368 + 0.436112i −0.827630 0.561274i \(-0.810312\pi\)
0.0722619 + 0.997386i \(0.476978\pi\)
\(20\) −6.39011 + 3.68933i −1.42887 + 0.824960i
\(21\) 2.24698i 0.490331i
\(22\) 5.05980 + 8.76383i 1.07875 + 1.86846i
\(23\) 1.01357 1.75556i 0.211345 0.366060i −0.740791 0.671736i \(-0.765549\pi\)
0.952136 + 0.305676i \(0.0988824\pi\)
\(24\) 0.351445 + 0.202907i 0.0717383 + 0.0414181i
\(25\) −6.26875 −1.25375
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −4.27730 2.46950i −0.808334 0.466692i
\(29\) 1.96950 3.41127i 0.365727 0.633458i −0.623165 0.782090i \(-0.714154\pi\)
0.988893 + 0.148632i \(0.0474870\pi\)
\(30\) 3.43900 + 5.95652i 0.627873 + 1.08751i
\(31\) 8.82908i 1.58575i −0.609384 0.792875i \(-0.708583\pi\)
0.609384 0.792875i \(-0.291417\pi\)
\(32\) 7.02805 4.05765i 1.24240 0.717297i
\(33\) 4.27730 2.46950i 0.744582 0.429885i
\(34\) 1.86831i 0.320413i
\(35\) −3.77144 6.53232i −0.637489 1.10416i
\(36\) 1.09903 1.90358i 0.183172 0.317263i
\(37\) 7.62270 + 4.40097i 1.25316 + 0.723515i 0.971737 0.236068i \(-0.0758587\pi\)
0.281428 + 0.959582i \(0.409192\pi\)
\(38\) −7.78986 −1.26368
\(39\) 0 0
\(40\) −1.36227 −0.215394
\(41\) −6.00935 3.46950i −0.938503 0.541845i −0.0490123 0.998798i \(-0.515607\pi\)
−0.889491 + 0.456953i \(0.848941\pi\)
\(42\) −2.30194 + 3.98707i −0.355197 + 0.615219i
\(43\) −1.14310 1.97991i −0.174322 0.301934i 0.765605 0.643311i \(-0.222440\pi\)
−0.939926 + 0.341377i \(0.889107\pi\)
\(44\) 10.8562i 1.63664i
\(45\) 2.90716 1.67845i 0.433373 0.250208i
\(46\) 3.59700 2.07673i 0.530349 0.306197i
\(47\) 3.80194i 0.554570i −0.960788 0.277285i \(-0.910565\pi\)
0.960788 0.277285i \(-0.0894346\pi\)
\(48\) −1.78232 3.08707i −0.257256 0.445581i
\(49\) −0.975541 + 1.68969i −0.139363 + 0.241384i
\(50\) −11.1234 6.42208i −1.57308 0.908219i
\(51\) 0.911854 0.127685
\(52\) 0 0
\(53\) 0.542877 0.0745698 0.0372849 0.999305i \(-0.488129\pi\)
0.0372849 + 0.999305i \(0.488129\pi\)
\(54\) −1.77441 1.02446i −0.241467 0.139411i
\(55\) −8.28986 + 14.3585i −1.11780 + 1.93609i
\(56\) −0.455927 0.789689i −0.0609258 0.105527i
\(57\) 3.80194i 0.503579i
\(58\) 6.98942 4.03534i 0.917756 0.529867i
\(59\) 4.08226 2.35690i 0.531465 0.306842i −0.210148 0.977670i \(-0.567394\pi\)
0.741613 + 0.670828i \(0.234061\pi\)
\(60\) 7.37867i 0.952582i
\(61\) −1.83997 3.18692i −0.235584 0.408043i 0.723858 0.689949i \(-0.242367\pi\)
−0.959442 + 0.281905i \(0.909034\pi\)
\(62\) 9.04503 15.6665i 1.14872 1.98964i
\(63\) 1.94594 + 1.12349i 0.245166 + 0.141546i
\(64\) 9.49827 1.18728
\(65\) 0 0
\(66\) 10.1196 1.24564
\(67\) 1.31732 + 0.760553i 0.160936 + 0.0929164i 0.578305 0.815821i \(-0.303714\pi\)
−0.417369 + 0.908737i \(0.637048\pi\)
\(68\) −1.00216 + 1.73578i −0.121529 + 0.210495i
\(69\) −1.01357 1.75556i −0.122020 0.211345i
\(70\) 15.4547i 1.84719i
\(71\) 2.05999 1.18933i 0.244475 0.141148i −0.372757 0.927929i \(-0.621587\pi\)
0.617232 + 0.786781i \(0.288254\pi\)
\(72\) 0.351445 0.202907i 0.0414181 0.0239128i
\(73\) 7.41119i 0.867414i −0.901054 0.433707i \(-0.857205\pi\)
0.901054 0.433707i \(-0.142795\pi\)
\(74\) 9.01722 + 15.6183i 1.04823 + 1.81559i
\(75\) −3.13437 + 5.42890i −0.361926 + 0.626875i
\(76\) −7.23728 4.17845i −0.830173 0.479301i
\(77\) −11.0978 −1.26472
\(78\) 0 0
\(79\) −3.74094 −0.420888 −0.210444 0.977606i \(-0.567491\pi\)
−0.210444 + 0.977606i \(0.567491\pi\)
\(80\) 10.3630 + 5.98307i 1.15862 + 0.668928i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −7.10872 12.3127i −0.785027 1.35971i
\(83\) 2.30798i 0.253334i 0.991945 + 0.126667i \(0.0404279\pi\)
−0.991945 + 0.126667i \(0.959572\pi\)
\(84\) −4.27730 + 2.46950i −0.466692 + 0.269445i
\(85\) −2.65090 + 1.53050i −0.287531 + 0.166006i
\(86\) 4.68425i 0.505116i
\(87\) −1.96950 3.41127i −0.211153 0.365727i
\(88\) −1.00216 + 1.73578i −0.106830 + 0.185035i
\(89\) −8.71101 5.02930i −0.923365 0.533105i −0.0386580 0.999253i \(-0.512308\pi\)
−0.884707 + 0.466147i \(0.845642\pi\)
\(90\) 6.87800 0.725005
\(91\) 0 0
\(92\) 4.45580 0.464549
\(93\) −7.64621 4.41454i −0.792875 0.457767i
\(94\) 3.89493 6.74621i 0.401731 0.695819i
\(95\) −6.38135 11.0528i −0.654713 1.13400i
\(96\) 8.11529i 0.828264i
\(97\) −13.9684 + 8.06465i −1.41827 + 0.818841i −0.996147 0.0876961i \(-0.972050\pi\)
−0.422127 + 0.906537i \(0.638716\pi\)
\(98\) −3.46203 + 1.99880i −0.349718 + 0.201910i
\(99\) 4.93900i 0.496388i
\(100\) −6.88955 11.9331i −0.688955 1.19331i
\(101\) −4.97434 + 8.61582i −0.494966 + 0.857306i −0.999983 0.00580325i \(-0.998153\pi\)
0.505017 + 0.863109i \(0.331486\pi\)
\(102\) 1.61801 + 0.934157i 0.160207 + 0.0924953i
\(103\) 10.9879 1.08267 0.541336 0.840806i \(-0.317919\pi\)
0.541336 + 0.840806i \(0.317919\pi\)
\(104\) 0 0
\(105\) −7.54288 −0.736109
\(106\) 0.963288 + 0.556155i 0.0935628 + 0.0540185i
\(107\) 4.93631 8.54994i 0.477211 0.826554i −0.522448 0.852671i \(-0.674981\pi\)
0.999659 + 0.0261171i \(0.00831428\pi\)
\(108\) −1.09903 1.90358i −0.105754 0.183172i
\(109\) 20.2446i 1.93908i 0.244934 + 0.969540i \(0.421234\pi\)
−0.244934 + 0.969540i \(0.578766\pi\)
\(110\) −29.4193 + 16.9852i −2.80502 + 1.61948i
\(111\) 7.62270 4.40097i 0.723515 0.417721i
\(112\) 8.00969i 0.756844i
\(113\) −4.84601 8.39354i −0.455874 0.789598i 0.542864 0.839821i \(-0.317340\pi\)
−0.998738 + 0.0502233i \(0.984007\pi\)
\(114\) −3.89493 + 6.74621i −0.364793 + 0.631841i
\(115\) 5.89324 + 3.40246i 0.549547 + 0.317281i
\(116\) 8.65817 0.803891
\(117\) 0 0
\(118\) 9.65817 0.889107
\(119\) −1.77441 1.02446i −0.162660 0.0939120i
\(120\) −0.681136 + 1.17976i −0.0621790 + 0.107697i
\(121\) 6.69687 + 11.5993i 0.608806 + 1.05448i
\(122\) 7.53989i 0.682630i
\(123\) −6.00935 + 3.46950i −0.541845 + 0.312834i
\(124\) 16.8068 9.70344i 1.50930 0.871395i
\(125\) 4.25906i 0.380942i
\(126\) 2.30194 + 3.98707i 0.205073 + 0.355197i
\(127\) 6.90581 11.9612i 0.612792 1.06139i −0.377976 0.925815i \(-0.623380\pi\)
0.990768 0.135571i \(-0.0432869\pi\)
\(128\) 2.79777 + 1.61529i 0.247290 + 0.142773i
\(129\) −2.28621 −0.201289
\(130\) 0 0
\(131\) 2.99462 0.261641 0.130821 0.991406i \(-0.458239\pi\)
0.130821 + 0.991406i \(0.458239\pi\)
\(132\) 9.40177 + 5.42812i 0.818319 + 0.472457i
\(133\) 4.27144 7.39835i 0.370381 0.641518i
\(134\) 1.55831 + 2.69907i 0.134618 + 0.233164i
\(135\) 3.35690i 0.288916i
\(136\) −0.320466 + 0.185021i −0.0274797 + 0.0158654i
\(137\) −19.9354 + 11.5097i −1.70319 + 0.983339i −0.760706 + 0.649096i \(0.775147\pi\)
−0.942487 + 0.334243i \(0.891519\pi\)
\(138\) 4.15346i 0.353566i
\(139\) −0.491271 0.850906i −0.0416690 0.0721729i 0.844439 0.535652i \(-0.179934\pi\)
−0.886108 + 0.463479i \(0.846601\pi\)
\(140\) 8.28986 14.3585i 0.700621 1.21351i
\(141\) −3.29257 1.90097i −0.277285 0.160090i
\(142\) 4.87369 0.408991
\(143\) 0 0
\(144\) −3.56465 −0.297054
\(145\) 11.4513 + 6.61141i 0.950978 + 0.549048i
\(146\) 7.59246 13.1505i 0.628356 1.08835i
\(147\) 0.975541 + 1.68969i 0.0804613 + 0.139363i
\(148\) 19.3472i 1.59033i
\(149\) 8.88461 5.12953i 0.727855 0.420228i −0.0897817 0.995961i \(-0.528617\pi\)
0.817637 + 0.575734i \(0.195284\pi\)
\(150\) −11.1234 + 6.42208i −0.908219 + 0.524360i
\(151\) 20.1685i 1.64129i 0.571438 + 0.820646i \(0.306386\pi\)
−0.571438 + 0.820646i \(0.693614\pi\)
\(152\) −0.771438 1.33617i −0.0625719 0.108378i
\(153\) 0.455927 0.789689i 0.0368595 0.0638425i
\(154\) −19.6922 11.3693i −1.58684 0.916162i
\(155\) 29.6383 2.38061
\(156\) 0 0
\(157\) 10.4383 0.833070 0.416535 0.909120i \(-0.363244\pi\)
0.416535 + 0.909120i \(0.363244\pi\)
\(158\) −6.63798 3.83244i −0.528089 0.304892i
\(159\) 0.271438 0.470145i 0.0215265 0.0372849i
\(160\) 13.6211 + 23.5924i 1.07684 + 1.86515i
\(161\) 4.55496i 0.358981i
\(162\) −1.77441 + 1.02446i −0.139411 + 0.0804891i
\(163\) 9.56657 5.52326i 0.749312 0.432615i −0.0761335 0.997098i \(-0.524258\pi\)
0.825445 + 0.564482i \(0.190924\pi\)
\(164\) 15.2524i 1.19101i
\(165\) 8.28986 + 14.3585i 0.645364 + 1.11780i
\(166\) −2.36443 + 4.09531i −0.183515 + 0.317858i
\(167\) 7.02339 + 4.05496i 0.543487 + 0.313782i 0.746491 0.665396i \(-0.231737\pi\)
−0.203004 + 0.979178i \(0.565071\pi\)
\(168\) −0.911854 −0.0703511
\(169\) 0 0
\(170\) −6.27173 −0.481020
\(171\) 3.29257 + 1.90097i 0.251789 + 0.145371i
\(172\) 2.51261 4.35198i 0.191585 0.331835i
\(173\) −9.02811 15.6371i −0.686394 1.18887i −0.972996 0.230820i \(-0.925859\pi\)
0.286602 0.958050i \(-0.407474\pi\)
\(174\) 8.07069i 0.611837i
\(175\) 12.1986 7.04288i 0.922129 0.532391i
\(176\) 15.2471 8.80290i 1.14929 0.663543i
\(177\) 4.71379i 0.354310i
\(178\) −10.3046 17.8481i −0.772364 1.33777i
\(179\) −9.93512 + 17.2081i −0.742585 + 1.28620i 0.208729 + 0.977974i \(0.433067\pi\)
−0.951314 + 0.308222i \(0.900266\pi\)
\(180\) 6.39011 + 3.68933i 0.476291 + 0.274987i
\(181\) 10.0828 0.749446 0.374723 0.927137i \(-0.377738\pi\)
0.374723 + 0.927137i \(0.377738\pi\)
\(182\) 0 0
\(183\) −3.67994 −0.272029
\(184\) 0.712430 + 0.411322i 0.0525210 + 0.0303230i
\(185\) −14.7736 + 25.5886i −1.08618 + 1.88131i
\(186\) −9.04503 15.6665i −0.663214 1.14872i
\(187\) 4.50365i 0.329339i
\(188\) 7.23728 4.17845i 0.527833 0.304745i
\(189\) 1.94594 1.12349i 0.141546 0.0817219i
\(190\) 26.1497i 1.89710i
\(191\) 3.29374 + 5.70493i 0.238327 + 0.412794i 0.960234 0.279196i \(-0.0900678\pi\)
−0.721908 + 0.691990i \(0.756734\pi\)
\(192\) 4.74914 8.22574i 0.342739 0.593642i
\(193\) 9.41131 + 5.43362i 0.677441 + 0.391121i 0.798890 0.601477i \(-0.205421\pi\)
−0.121449 + 0.992598i \(0.538754\pi\)
\(194\) −33.0476 −2.37268
\(195\) 0 0
\(196\) −4.28860 −0.306329
\(197\) −8.00346 4.62080i −0.570223 0.329218i 0.187015 0.982357i \(-0.440119\pi\)
−0.757238 + 0.653139i \(0.773452\pi\)
\(198\) 5.05980 8.76383i 0.359585 0.622819i
\(199\) −0.782323 1.35502i −0.0554574 0.0960551i 0.836964 0.547258i \(-0.184328\pi\)
−0.892421 + 0.451203i \(0.850995\pi\)
\(200\) 2.54394i 0.179884i
\(201\) 1.31732 0.760553i 0.0929164 0.0536453i
\(202\) −17.6531 + 10.1920i −1.24207 + 0.717108i
\(203\) 8.85086i 0.621208i
\(204\) 1.00216 + 1.73578i 0.0701649 + 0.121529i
\(205\) 11.6468 20.1728i 0.813444 1.40893i
\(206\) 19.4971 + 11.2567i 1.35843 + 0.784289i
\(207\) −2.02715 −0.140896
\(208\) 0 0
\(209\) −18.7778 −1.29889
\(210\) −13.3842 7.72737i −0.923597 0.533239i
\(211\) −11.6223 + 20.1304i −0.800112 + 1.38583i 0.119430 + 0.992843i \(0.461893\pi\)
−0.919542 + 0.392991i \(0.871440\pi\)
\(212\) 0.596638 + 1.03341i 0.0409773 + 0.0709747i
\(213\) 2.37867i 0.162984i
\(214\) 17.5181 10.1141i 1.19751 0.691385i
\(215\) 6.64637 3.83728i 0.453278 0.261700i
\(216\) 0.405813i 0.0276121i
\(217\) 9.91939 + 17.1809i 0.673372 + 1.16631i
\(218\) −20.7397 + 35.9223i −1.40467 + 2.43296i
\(219\) −6.41828 3.70560i −0.433707 0.250401i
\(220\) −36.4432 −2.45700
\(221\) 0 0
\(222\) 18.0344 1.21039
\(223\) −9.29985 5.36927i −0.622764 0.359553i 0.155180 0.987886i \(-0.450404\pi\)
−0.777944 + 0.628333i \(0.783738\pi\)
\(224\) −9.11745 + 15.7919i −0.609185 + 1.05514i
\(225\) 3.13437 + 5.42890i 0.208958 + 0.361926i
\(226\) 19.8582i 1.32094i
\(227\) −6.04125 + 3.48792i −0.400972 + 0.231501i −0.686903 0.726749i \(-0.741030\pi\)
0.285931 + 0.958250i \(0.407697\pi\)
\(228\) −7.23728 + 4.17845i −0.479301 + 0.276724i
\(229\) 16.8049i 1.11050i 0.831683 + 0.555250i \(0.187378\pi\)
−0.831683 + 0.555250i \(0.812622\pi\)
\(230\) 6.97136 + 12.0748i 0.459678 + 0.796186i
\(231\) −5.54892 + 9.61101i −0.365092 + 0.632358i
\(232\) 1.38434 + 0.799249i 0.0908864 + 0.0524733i
\(233\) −8.69202 −0.569433 −0.284717 0.958612i \(-0.591900\pi\)
−0.284717 + 0.958612i \(0.591900\pi\)
\(234\) 0 0
\(235\) 12.7627 0.832547
\(236\) 8.97307 + 5.18060i 0.584097 + 0.337229i
\(237\) −1.87047 + 3.23975i −0.121500 + 0.210444i
\(238\) −2.09903 3.63563i −0.136060 0.235663i
\(239\) 22.9191i 1.48252i −0.671220 0.741258i \(-0.734229\pi\)
0.671220 0.741258i \(-0.265771\pi\)
\(240\) 10.3630 5.98307i 0.668928 0.386206i
\(241\) −19.0354 + 10.9901i −1.22618 + 0.707933i −0.966228 0.257690i \(-0.917039\pi\)
−0.259948 + 0.965623i \(0.583705\pi\)
\(242\) 27.4426i 1.76408i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 4.04437 7.00505i 0.258914 0.448452i
\(245\) −5.67210 3.27479i −0.362377 0.209219i
\(246\) −14.2174 −0.906471
\(247\) 0 0
\(248\) 3.58296 0.227518
\(249\) 1.99877 + 1.15399i 0.126667 + 0.0731311i
\(250\) 4.36323 7.55734i 0.275955 0.477968i
\(251\) 13.3218 + 23.0741i 0.840868 + 1.45643i 0.889162 + 0.457592i \(0.151288\pi\)
−0.0482946 + 0.998833i \(0.515379\pi\)
\(252\) 4.93900i 0.311128i
\(253\) 8.67072 5.00604i 0.545123 0.314727i
\(254\) 24.5075 14.1494i 1.53774 0.887815i
\(255\) 3.06100i 0.191687i
\(256\) −6.18867 10.7191i −0.386792 0.669943i
\(257\) 11.5722 20.0436i 0.721853 1.25029i −0.238404 0.971166i \(-0.576624\pi\)
0.960256 0.279119i \(-0.0900425\pi\)
\(258\) −4.05668 2.34213i −0.252558 0.145814i
\(259\) −19.7778 −1.22893
\(260\) 0 0
\(261\) −3.93900 −0.243818
\(262\) 5.31370 + 3.06787i 0.328282 + 0.189533i
\(263\) 9.26420 16.0461i 0.571255 0.989443i −0.425182 0.905108i \(-0.639790\pi\)
0.996437 0.0843352i \(-0.0268766\pi\)
\(264\) 1.00216 + 1.73578i 0.0616784 + 0.106830i
\(265\) 1.82238i 0.111948i
\(266\) 15.1586 8.75182i 0.929434 0.536609i
\(267\) −8.71101 + 5.02930i −0.533105 + 0.307788i
\(268\) 3.34349i 0.204236i
\(269\) −4.87920 8.45102i −0.297490 0.515268i 0.678071 0.734996i \(-0.262816\pi\)
−0.975561 + 0.219729i \(0.929483\pi\)
\(270\) 3.43900 5.95652i 0.209291 0.362503i
\(271\) −19.7471 11.4010i −1.19955 0.692560i −0.239094 0.970996i \(-0.576850\pi\)
−0.960455 + 0.278437i \(0.910184\pi\)
\(272\) 3.25044 0.197087
\(273\) 0 0
\(274\) −47.1648 −2.84933
\(275\) −26.8133 15.4807i −1.61690 0.933520i
\(276\) 2.22790 3.85883i 0.134104 0.232274i
\(277\) −11.9852 20.7590i −0.720123 1.24729i −0.960950 0.276721i \(-0.910752\pi\)
0.240828 0.970568i \(-0.422581\pi\)
\(278\) 2.01315i 0.120741i
\(279\) −7.64621 + 4.41454i −0.457767 + 0.264292i
\(280\) 2.65090 1.53050i 0.158422 0.0914648i
\(281\) 4.12498i 0.246076i 0.992402 + 0.123038i \(0.0392637\pi\)
−0.992402 + 0.123038i \(0.960736\pi\)
\(282\) −3.89493 6.74621i −0.231940 0.401731i
\(283\) −7.82789 + 13.5583i −0.465320 + 0.805957i −0.999216 0.0395927i \(-0.987394\pi\)
0.533896 + 0.845550i \(0.320727\pi\)
\(284\) 4.52798 + 2.61423i 0.268686 + 0.155126i
\(285\) −12.7627 −0.755998
\(286\) 0 0
\(287\) 15.5918 0.920354
\(288\) −7.02805 4.05765i −0.414132 0.239099i
\(289\) 8.08426 14.0024i 0.475545 0.823668i
\(290\) 13.5462 + 23.4628i 0.795462 + 1.37778i
\(291\) 16.1293i 0.945516i
\(292\) 14.1078 8.14513i 0.825595 0.476658i
\(293\) −19.5677 + 11.2974i −1.14315 + 0.660001i −0.947210 0.320614i \(-0.896111\pi\)
−0.195945 + 0.980615i \(0.562777\pi\)
\(294\) 3.99761i 0.233145i
\(295\) 7.91185 + 13.7037i 0.460646 + 0.797862i
\(296\) −1.78597 + 3.09339i −0.103807 + 0.179800i
\(297\) −4.27730 2.46950i −0.248194 0.143295i
\(298\) 21.0200 1.21765
\(299\) 0 0
\(300\) −13.7791 −0.795537
\(301\) 4.44883 + 2.56853i 0.256426 + 0.148048i
\(302\) −20.6618 + 35.7873i −1.18895 + 2.05933i
\(303\) 4.97434 + 8.61582i 0.285769 + 0.494966i
\(304\) 13.5526i 0.777293i
\(305\) 10.6982 6.17659i 0.612575 0.353670i
\(306\) 1.61801 0.934157i 0.0924953 0.0534022i
\(307\) 6.55496i 0.374111i 0.982349 + 0.187056i \(0.0598945\pi\)
−0.982349 + 0.187056i \(0.940106\pi\)
\(308\) −12.1969 21.1256i −0.694981 1.20374i
\(309\) 5.49396 9.51582i 0.312540 0.541336i
\(310\) 52.5907 + 30.3632i 2.98695 + 1.72452i
\(311\) 12.0392 0.682682 0.341341 0.939940i \(-0.389119\pi\)
0.341341 + 0.939940i \(0.389119\pi\)
\(312\) 0 0
\(313\) −33.8950 −1.91586 −0.957929 0.287005i \(-0.907340\pi\)
−0.957929 + 0.287005i \(0.907340\pi\)
\(314\) 18.5219 + 10.6936i 1.04525 + 0.603477i
\(315\) −3.77144 + 6.53232i −0.212496 + 0.368055i
\(316\) −4.11141 7.12117i −0.231285 0.400597i
\(317\) 4.49827i 0.252648i −0.991989 0.126324i \(-0.959682\pi\)
0.991989 0.126324i \(-0.0403179\pi\)
\(318\) 0.963288 0.556155i 0.0540185 0.0311876i
\(319\) 16.8483 9.72737i 0.943323 0.544628i
\(320\) 31.8847i 1.78241i
\(321\) −4.93631 8.54994i −0.275518 0.477211i
\(322\) −4.66637 + 8.08238i −0.260046 + 0.450414i
\(323\) −3.00235 1.73341i −0.167055 0.0964493i
\(324\) −2.19806 −0.122115
\(325\) 0 0
\(326\) 22.6334 1.25355
\(327\) 17.5323 + 10.1223i 0.969540 + 0.559764i
\(328\) 1.40797 2.43867i 0.0777421 0.134653i
\(329\) 4.27144 + 7.39835i 0.235492 + 0.407884i
\(330\) 33.9705i 1.87001i
\(331\) −9.71085 + 5.60656i −0.533757 + 0.308165i −0.742545 0.669796i \(-0.766381\pi\)
0.208788 + 0.977961i \(0.433048\pi\)
\(332\) −4.39342 + 2.53654i −0.241120 + 0.139211i
\(333\) 8.80194i 0.482343i
\(334\) 8.30827 + 14.3904i 0.454609 + 0.787405i
\(335\) −2.55310 + 4.42209i −0.139491 + 0.241605i
\(336\) 6.93659 + 4.00484i 0.378422 + 0.218482i
\(337\) −7.04892 −0.383979 −0.191989 0.981397i \(-0.561494\pi\)
−0.191989 + 0.981397i \(0.561494\pi\)
\(338\) 0 0
\(339\) −9.69202 −0.526398
\(340\) −5.82685 3.36413i −0.316005 0.182446i
\(341\) 21.8034 37.7646i 1.18072 2.04507i
\(342\) 3.89493 + 6.74621i 0.210614 + 0.364793i
\(343\) 20.1129i 1.08599i
\(344\) 0.803475 0.463887i 0.0433205 0.0250111i
\(345\) 5.89324 3.40246i 0.317281 0.183182i
\(346\) 36.9957i 1.98890i
\(347\) 1.35205 + 2.34182i 0.0725819 + 0.125716i 0.900032 0.435823i \(-0.143543\pi\)
−0.827450 + 0.561539i \(0.810209\pi\)
\(348\) 4.32908 7.49819i 0.232063 0.401945i
\(349\) −0.359835 0.207751i −0.0192615 0.0111207i 0.490338 0.871532i \(-0.336873\pi\)
−0.509600 + 0.860412i \(0.670207\pi\)
\(350\) 28.8605 1.54266
\(351\) 0 0
\(352\) 40.0814 2.13635
\(353\) 27.8576 + 16.0836i 1.48271 + 0.856044i 0.999807 0.0196301i \(-0.00624884\pi\)
0.482904 + 0.875674i \(0.339582\pi\)
\(354\) 4.82908 8.36422i 0.256663 0.444553i
\(355\) 3.99247 + 6.91516i 0.211898 + 0.367018i
\(356\) 22.1094i 1.17180i
\(357\) −1.77441 + 1.02446i −0.0939120 + 0.0542201i
\(358\) −35.2580 + 20.3562i −1.86344 + 1.07586i
\(359\) 22.3521i 1.17970i −0.807513 0.589850i \(-0.799187\pi\)
0.807513 0.589850i \(-0.200813\pi\)
\(360\) 0.681136 + 1.17976i 0.0358990 + 0.0621790i
\(361\) −2.27263 + 3.93632i −0.119612 + 0.207175i
\(362\) 17.8910 + 10.3294i 0.940331 + 0.542900i
\(363\) 13.3937 0.702989
\(364\) 0 0
\(365\) 24.8786 1.30221
\(366\) −6.52974 3.76995i −0.341315 0.197058i
\(367\) 1.15130 1.99411i 0.0600974 0.104092i −0.834411 0.551142i \(-0.814192\pi\)
0.894509 + 0.447050i \(0.147526\pi\)
\(368\) −3.61303 6.25795i −0.188342 0.326218i
\(369\) 6.93900i 0.361230i
\(370\) −52.4290 + 30.2699i −2.72565 + 1.57366i
\(371\) −1.05641 + 0.609916i −0.0548459 + 0.0316653i
\(372\) 19.4069i 1.00620i
\(373\) 9.63802 + 16.6935i 0.499038 + 0.864359i 0.999999 0.00111058i \(-0.000353507\pi\)
−0.500961 + 0.865470i \(0.667020\pi\)
\(374\) −4.61380 + 7.99134i −0.238574 + 0.413222i
\(375\) −3.68846 2.12953i −0.190471 0.109968i
\(376\) 1.54288 0.0795678
\(377\) 0 0
\(378\) 4.60388 0.236798
\(379\) 6.35614 + 3.66972i 0.326493 + 0.188501i 0.654283 0.756250i \(-0.272971\pi\)
−0.327790 + 0.944751i \(0.606304\pi\)
\(380\) 14.0266 24.2948i 0.719550 1.24630i
\(381\) −6.90581 11.9612i −0.353796 0.612792i
\(382\) 13.4972i 0.690577i
\(383\) 16.5325 9.54503i 0.844770 0.487728i −0.0141126 0.999900i \(-0.504492\pi\)
0.858883 + 0.512172i \(0.171159\pi\)
\(384\) 2.79777 1.61529i 0.142773 0.0824301i
\(385\) 37.2543i 1.89865i
\(386\) 11.1330 + 19.2830i 0.566657 + 0.981479i
\(387\) −1.14310 + 1.97991i −0.0581072 + 0.100645i
\(388\) −30.7034 17.7266i −1.55873 0.899932i
\(389\) 23.9879 1.21624 0.608118 0.793847i \(-0.291925\pi\)
0.608118 + 0.793847i \(0.291925\pi\)
\(390\) 0 0
\(391\) 1.84846 0.0934807
\(392\) −0.685697 0.395888i −0.0346329 0.0199953i
\(393\) 1.49731 2.59342i 0.0755294 0.130821i
\(394\) −9.46764 16.3984i −0.476973 0.826141i
\(395\) 12.5579i 0.631859i
\(396\) 9.40177 5.42812i 0.472457 0.272773i
\(397\) 3.82601 2.20895i 0.192022 0.110864i −0.400907 0.916119i \(-0.631305\pi\)
0.592929 + 0.805255i \(0.297972\pi\)
\(398\) 3.20583i 0.160694i
\(399\) −4.27144 7.39835i −0.213839 0.370381i
\(400\) −11.1729 + 19.3521i −0.558647 + 0.967605i
\(401\) −17.6745 10.2044i −0.882624 0.509583i −0.0111015 0.999938i \(-0.503534\pi\)
−0.871523 + 0.490355i \(0.836867\pi\)
\(402\) 3.11662 0.155443
\(403\) 0 0
\(404\) −21.8678 −1.08797
\(405\) −2.90716 1.67845i −0.144458 0.0834027i
\(406\) −9.06734 + 15.7051i −0.450004 + 0.779430i
\(407\) 21.7364 + 37.6485i 1.07743 + 1.86617i
\(408\) 0.370042i 0.0183198i
\(409\) −19.1817 + 11.0746i −0.948475 + 0.547602i −0.892607 0.450836i \(-0.851126\pi\)
−0.0558682 + 0.998438i \(0.517793\pi\)
\(410\) 41.3323 23.8632i 2.04126 1.17852i
\(411\) 23.0194i 1.13546i
\(412\) 12.0761 + 20.9164i 0.594945 + 1.03047i
\(413\) −5.29590 + 9.17276i −0.260594 + 0.451362i
\(414\) −3.59700 2.07673i −0.176783 0.102066i
\(415\) −7.74764 −0.380317
\(416\) 0 0
\(417\) −0.982542 −0.0481153
\(418\) −33.3196 19.2371i −1.62971 0.940915i
\(419\) −7.37800 + 12.7791i −0.360439 + 0.624299i −0.988033 0.154242i \(-0.950706\pi\)
0.627594 + 0.778541i \(0.284040\pi\)
\(420\) −8.28986 14.3585i −0.404504 0.700621i
\(421\) 8.47219i 0.412909i 0.978456 + 0.206455i \(0.0661926\pi\)
−0.978456 + 0.206455i \(0.933807\pi\)
\(422\) −41.2455 + 23.8131i −2.00780 + 1.15920i
\(423\) −3.29257 + 1.90097i −0.160090 + 0.0924283i
\(424\) 0.220306i 0.0106990i
\(425\) −2.85809 4.95036i −0.138638 0.240128i
\(426\) 2.43685 4.22074i 0.118066 0.204496i
\(427\) 7.16095 + 4.13437i 0.346543 + 0.200076i
\(428\) 21.7006 1.04894
\(429\) 0 0
\(430\) 15.7245 0.758305
\(431\) −2.07137 1.19591i −0.0997744 0.0576048i 0.449283 0.893390i \(-0.351680\pi\)
−0.549057 + 0.835785i \(0.685013\pi\)
\(432\) −1.78232 + 3.08707i −0.0857521 + 0.148527i
\(433\) −5.21432 9.03147i −0.250584 0.434025i 0.713102 0.701060i \(-0.247289\pi\)
−0.963687 + 0.267035i \(0.913956\pi\)
\(434\) 40.6480i 1.95117i
\(435\) 11.4513 6.61141i 0.549048 0.316993i
\(436\) −38.5371 + 22.2494i −1.84559 + 1.06555i
\(437\) 7.70709i 0.368680i
\(438\) −7.59246 13.1505i −0.362782 0.628356i
\(439\) −16.2751 + 28.1893i −0.776767 + 1.34540i 0.157028 + 0.987594i \(0.449809\pi\)
−0.933796 + 0.357807i \(0.883525\pi\)
\(440\) −5.82685 3.36413i −0.277784 0.160379i
\(441\) 1.95108 0.0929087
\(442\) 0 0
\(443\) 9.58211 0.455260 0.227630 0.973748i \(-0.426902\pi\)
0.227630 + 0.973748i \(0.426902\pi\)
\(444\) 16.7552 + 9.67360i 0.795165 + 0.459089i
\(445\) 16.8828 29.2419i 0.800324 1.38620i
\(446\) −11.0012 19.0546i −0.520922 0.902263i
\(447\) 10.2591i 0.485237i
\(448\) −18.4831 + 10.6712i −0.873243 + 0.504167i
\(449\) 24.5897 14.1969i 1.16046 0.669992i 0.209045 0.977906i \(-0.432964\pi\)
0.951414 + 0.307914i \(0.0996311\pi\)
\(450\) 12.8442i 0.605479i
\(451\) −17.1359 29.6802i −0.806896 1.39759i
\(452\) 10.6518 18.4495i 0.501020 0.867792i
\(453\) 17.4665 + 10.0843i 0.820646 + 0.473800i
\(454\) −14.2929 −0.670800
\(455\) 0 0
\(456\) −1.54288 −0.0722518
\(457\) −4.32639 2.49784i −0.202380 0.116844i 0.395385 0.918515i \(-0.370611\pi\)
−0.597765 + 0.801671i \(0.703944\pi\)
\(458\) −17.2159 + 29.8189i −0.804448 + 1.39335i
\(459\) −0.455927 0.789689i −0.0212808 0.0368595i
\(460\) 14.9576i 0.697404i
\(461\) 1.17137 0.676292i 0.0545562 0.0314981i −0.472474 0.881345i \(-0.656639\pi\)
0.527030 + 0.849847i \(0.323306\pi\)
\(462\) −19.6922 + 11.3693i −0.916162 + 0.528946i
\(463\) 3.36467i 0.156369i 0.996939 + 0.0781846i \(0.0249124\pi\)
−0.996939 + 0.0781846i \(0.975088\pi\)
\(464\) −7.02057 12.1600i −0.325922 0.564513i
\(465\) 14.8192 25.6675i 0.687222 1.19030i
\(466\) −15.4232 8.90462i −0.714468 0.412498i
\(467\) −6.91079 −0.319793 −0.159897 0.987134i \(-0.551116\pi\)
−0.159897 + 0.987134i \(0.551116\pi\)
\(468\) 0 0
\(469\) −3.41789 −0.157824
\(470\) 22.6463 + 13.0749i 1.04460 + 0.603099i
\(471\) 5.21917 9.03987i 0.240487 0.416535i
\(472\) 0.956459 + 1.65664i 0.0440246 + 0.0762529i
\(473\) 11.2916i 0.519188i
\(474\) −6.63798 + 3.83244i −0.304892 + 0.176030i
\(475\) 20.6403 11.9167i 0.947043 0.546776i
\(476\) 4.50365i 0.206424i
\(477\) −0.271438 0.470145i −0.0124283 0.0215265i
\(478\) 23.4797 40.6681i 1.07394 1.86011i
\(479\) 3.04471 + 1.75786i 0.139116 + 0.0803189i 0.567943 0.823068i \(-0.307739\pi\)
−0.428826 + 0.903387i \(0.641073\pi\)
\(480\) 27.2422 1.24343
\(481\) 0 0
\(482\) −45.0355 −2.05131
\(483\) 3.94471 + 2.27748i 0.179490 + 0.103629i
\(484\) −14.7201 + 25.4960i −0.669097 + 1.15891i
\(485\) −27.0722 46.8904i −1.22928 2.12918i
\(486\) 2.04892i 0.0929408i
\(487\) −11.1266 + 6.42394i −0.504194 + 0.291096i −0.730444 0.682973i \(-0.760687\pi\)
0.226250 + 0.974069i \(0.427353\pi\)
\(488\) 1.29329 0.746684i 0.0585447 0.0338008i
\(489\) 11.0465i 0.499541i
\(490\) −6.70978 11.6217i −0.303117 0.525014i
\(491\) 14.3354 24.8297i 0.646948 1.12055i −0.336899 0.941541i \(-0.609378\pi\)
0.983848 0.179007i \(-0.0572885\pi\)
\(492\) −13.2089 7.62618i −0.595504 0.343815i
\(493\) 3.59179 0.161766
\(494\) 0 0
\(495\) 16.5797 0.745203
\(496\) −27.2560 15.7363i −1.22383 0.706580i
\(497\) −2.67241 + 4.62874i −0.119874 + 0.207628i
\(498\) 2.36443 + 4.09531i 0.105953 + 0.183515i
\(499\) 33.5555i 1.50215i −0.660215 0.751076i \(-0.729535\pi\)
0.660215 0.751076i \(-0.270465\pi\)
\(500\) 8.10745 4.68084i 0.362576 0.209334i
\(501\) 7.02339 4.05496i 0.313782 0.181162i
\(502\) 54.5907i 2.43650i
\(503\) −10.7817 18.6744i −0.480730 0.832650i 0.519025 0.854759i \(-0.326295\pi\)
−0.999756 + 0.0221094i \(0.992962\pi\)
\(504\) −0.455927 + 0.789689i −0.0203086 + 0.0351755i
\(505\) −28.9224 16.6984i −1.28703 0.743067i
\(506\) 20.5139 0.911955
\(507\) 0 0
\(508\) 30.3588 1.34695
\(509\) 7.69904 + 4.44504i 0.341254 + 0.197023i 0.660826 0.750539i \(-0.270206\pi\)
−0.319572 + 0.947562i \(0.603539\pi\)
\(510\) −3.13587 + 5.43148i −0.138859 + 0.240510i
\(511\) 8.32640 + 14.4217i 0.368338 + 0.637980i
\(512\) 31.8213i 1.40632i
\(513\) 3.29257 1.90097i 0.145371 0.0839298i
\(514\) 41.0677 23.7104i 1.81142 1.04582i
\(515\) 36.8853i 1.62536i
\(516\) −2.51261 4.35198i −0.110612 0.191585i
\(517\) 9.38889 16.2620i 0.412923 0.715203i
\(518\) −35.0940 20.2615i −1.54194 0.890240i
\(519\) −18.0562 −0.792580
\(520\) 0 0
\(521\) 19.3478 0.847642 0.423821 0.905746i \(-0.360688\pi\)
0.423821 + 0.905746i \(0.360688\pi\)
\(522\) −6.98942 4.03534i −0.305919 0.176622i
\(523\) 6.29739 10.9074i 0.275366 0.476947i −0.694862 0.719143i \(-0.744534\pi\)
0.970227 + 0.242196i \(0.0778678\pi\)
\(524\) 3.29118 + 5.70050i 0.143776 + 0.249027i
\(525\) 14.0858i 0.614753i
\(526\) 32.8771 18.9816i 1.43351 0.827636i
\(527\) 6.97223 4.02542i 0.303715 0.175350i
\(528\) 17.6058i 0.766194i
\(529\) 9.44534 + 16.3598i 0.410667 + 0.711296i
\(530\) −1.86695 + 3.23366i −0.0810953 + 0.140461i
\(531\) −4.08226 2.35690i −0.177155 0.102281i
\(532\) 18.7778 0.814120
\(533\) 0 0
\(534\) −20.6093 −0.891850
\(535\) 28.7013 + 16.5707i 1.24086 + 0.716413i
\(536\) −0.308643 + 0.534585i −0.0133313 + 0.0230905i
\(537\) 9.93512 + 17.2081i 0.428732 + 0.742585i
\(538\) 19.9941i 0.862009i
\(539\) −8.34537 + 4.81820i −0.359460 + 0.207535i
\(540\) 6.39011 3.68933i 0.274987 0.158764i
\(541\) 29.0019i 1.24689i −0.781867 0.623445i \(-0.785733\pi\)
0.781867 0.623445i \(-0.214267\pi\)
\(542\) −23.3596 40.4601i −1.00338 1.73791i
\(543\) 5.04138 8.73193i 0.216347 0.374723i
\(544\) 6.40856 + 3.69998i 0.274765 + 0.158635i
\(545\) −67.9590 −2.91104
\(546\) 0 0
\(547\) 27.7006 1.18439 0.592197 0.805793i \(-0.298261\pi\)
0.592197 + 0.805793i \(0.298261\pi\)
\(548\) −43.8192 25.2990i −1.87186 1.08072i
\(549\) −1.83997 + 3.18692i −0.0785280 + 0.136014i
\(550\) −31.7186 54.9383i −1.35249 2.34258i
\(551\) 14.9758i 0.637992i
\(552\) 0.712430 0.411322i 0.0303230 0.0175070i
\(553\) 7.27965 4.20291i 0.309562 0.178726i
\(554\) 49.1135i 2.08663i
\(555\) 14.7736 + 25.5886i 0.627104 + 1.08618i
\(556\) 1.07984 1.87034i 0.0457956 0.0793203i
\(557\) 5.89738 + 3.40485i 0.249880 + 0.144268i 0.619709 0.784831i \(-0.287251\pi\)
−0.369829 + 0.929100i \(0.620584\pi\)
\(558\) −18.0901 −0.765814
\(559\) 0 0
\(560\) −26.8877 −1.13621
\(561\) 3.90027 + 2.25182i 0.164670 + 0.0950721i
\(562\) −4.22587 + 7.31943i −0.178258 + 0.308751i
\(563\) −9.62618 16.6730i −0.405695 0.702684i 0.588707 0.808346i \(-0.299637\pi\)
−0.994402 + 0.105662i \(0.966304\pi\)
\(564\) 8.35690i 0.351889i
\(565\) 28.1762 16.2676i 1.18538 0.684381i
\(566\) −27.7798 + 16.0387i −1.16767 + 0.674157i
\(567\) 2.24698i 0.0943643i
\(568\) 0.482647 + 0.835969i 0.0202514 + 0.0350765i
\(569\) 3.92423 6.79697i 0.164512 0.284944i −0.771970 0.635659i \(-0.780728\pi\)
0.936482 + 0.350716i \(0.114062\pi\)
\(570\) −22.6463 13.0749i −0.948551 0.547646i
\(571\) −29.8568 −1.24947 −0.624735 0.780837i \(-0.714793\pi\)
−0.624735 + 0.780837i \(0.714793\pi\)
\(572\) 0 0
\(573\) 6.58748 0.275196
\(574\) 27.6663 + 15.9731i 1.15477 + 0.666706i
\(575\) −6.35384 + 11.0052i −0.264973 + 0.458947i
\(576\) −4.74914 8.22574i −0.197881 0.342739i
\(577\) 8.97823i 0.373769i 0.982382 + 0.186884i \(0.0598389\pi\)
−0.982382 + 0.186884i \(0.940161\pi\)
\(578\) 28.6897 16.5640i 1.19333 0.688971i
\(579\) 9.41131 5.43362i 0.391121 0.225814i
\(580\) 29.0646i 1.20684i
\(581\) −2.59299 4.49119i −0.107575 0.186326i
\(582\) −16.5238 + 28.6201i −0.684933 + 1.18634i
\(583\) 2.32205 + 1.34063i 0.0961693 + 0.0555234i
\(584\) 3.00756 0.124454
\(585\) 0 0
\(586\) −46.2948 −1.91242
\(587\) −20.6580 11.9269i −0.852648 0.492277i 0.00889531 0.999960i \(-0.497168\pi\)
−0.861543 + 0.507684i \(0.830502\pi\)
\(588\) −2.14430 + 3.71404i −0.0884295 + 0.153164i
\(589\) 16.7838 + 29.0704i 0.691565 + 1.19783i
\(590\) 32.4215i 1.33477i
\(591\) −8.00346 + 4.62080i −0.329218 + 0.190074i
\(592\) 27.1722 15.6879i 1.11677 0.644769i
\(593\) 11.9866i 0.492230i −0.969241 0.246115i \(-0.920846\pi\)
0.969241 0.246115i \(-0.0791541\pi\)
\(594\) −5.05980 8.76383i −0.207606 0.359585i
\(595\) 3.43900 5.95652i 0.140985 0.244194i
\(596\) 19.5289 + 11.2750i 0.799936 + 0.461843i
\(597\) −1.56465 −0.0640367
\(598\) 0 0
\(599\) 29.1142 1.18958 0.594788 0.803883i \(-0.297236\pi\)
0.594788 + 0.803883i \(0.297236\pi\)
\(600\) −2.20312 1.27197i −0.0899419 0.0519280i
\(601\) −18.5683 + 32.1612i −0.757417 + 1.31188i 0.186747 + 0.982408i \(0.440205\pi\)
−0.944164 + 0.329476i \(0.893128\pi\)
\(602\) 5.26271 + 9.11528i 0.214492 + 0.371511i
\(603\) 1.52111i 0.0619442i
\(604\) −38.3924 + 22.1658i −1.56216 + 0.901915i
\(605\) −38.9377 + 22.4807i −1.58304 + 0.913970i
\(606\) 20.3840i 0.828045i
\(607\) 7.11625 + 12.3257i 0.288840 + 0.500285i 0.973533 0.228546i \(-0.0733972\pi\)
−0.684693 + 0.728831i \(0.740064\pi\)
\(608\) −15.4269 + 26.7202i −0.625644 + 1.08365i
\(609\) 7.66507 + 4.42543i 0.310604 + 0.179327i
\(610\) 25.3106 1.02480
\(611\) 0 0
\(612\) 2.00431 0.0810195
\(613\) −26.2526 15.1570i −1.06033 0.612184i −0.134810 0.990872i \(-0.543042\pi\)
−0.925525 + 0.378687i \(0.876376\pi\)
\(614\) −6.71528 + 11.6312i −0.271007 + 0.469398i
\(615\) −11.6468 20.1728i −0.469642 0.813444i
\(616\) 4.50365i 0.181457i
\(617\) −21.6192 + 12.4819i −0.870358 + 0.502501i −0.867467 0.497494i \(-0.834254\pi\)
−0.00289086 + 0.999996i \(0.500920\pi\)
\(618\) 19.4971 11.2567i 0.784289 0.452810i
\(619\) 35.6122i 1.43138i −0.698420 0.715688i \(-0.746113\pi\)
0.698420 0.715688i \(-0.253887\pi\)
\(620\) 32.5734 + 56.4188i 1.30818 + 2.26584i
\(621\) −1.01357 + 1.75556i −0.0406733 + 0.0704482i
\(622\) 21.3626 + 12.3337i 0.856561 + 0.494536i
\(623\) 22.6015 0.905509
\(624\) 0 0
\(625\) −17.0465 −0.681861
\(626\) −60.1438 34.7240i −2.40383 1.38785i
\(627\) −9.38889 + 16.2620i −0.374956 + 0.649443i
\(628\) 11.4721 + 19.8702i 0.457785 + 0.792907i
\(629\) 8.02608i 0.320021i
\(630\) −13.3842 + 7.72737i −0.533239 + 0.307866i
\(631\) −20.6832 + 11.9415i −0.823385 + 0.475382i −0.851582 0.524221i \(-0.824357\pi\)
0.0281972 + 0.999602i \(0.491023\pi\)
\(632\) 1.51812i 0.0603877i
\(633\) 11.6223 + 20.1304i 0.461945 + 0.800112i
\(634\) 4.60829 7.98180i 0.183019 0.316998i
\(635\) 40.1526 + 23.1821i 1.59341 + 0.919953i
\(636\) 1.19328 0.0473165
\(637\) 0 0
\(638\) 39.8611 1.57812
\(639\) −2.05999 1.18933i −0.0814918 0.0470493i
\(640\) −5.42237 + 9.39182i −0.214338 + 0.371244i
\(641\) −12.3288 21.3542i −0.486960 0.843440i 0.512927 0.858432i \(-0.328561\pi\)
−0.999888 + 0.0149922i \(0.995228\pi\)
\(642\) 20.2282i 0.798343i
\(643\) 41.4103 23.9083i 1.63306 0.942850i 0.649923 0.760000i \(-0.274801\pi\)
0.983141 0.182850i \(-0.0585323\pi\)
\(644\) −8.67072 + 5.00604i −0.341674 + 0.197266i
\(645\) 7.67456i 0.302186i
\(646\) −3.55161 6.15156i −0.139736 0.242030i
\(647\) −2.69471 + 4.66737i −0.105940 + 0.183493i −0.914122 0.405440i \(-0.867118\pi\)
0.808182 + 0.588933i \(0.200452\pi\)
\(648\) −0.351445 0.202907i −0.0138060 0.00797092i
\(649\) 23.2814 0.913876
\(650\) 0 0
\(651\) 19.8388 0.777543
\(652\) 21.0279 + 12.1405i 0.823517 + 0.475458i
\(653\) 2.51895 4.36295i 0.0985741 0.170735i −0.812521 0.582933i \(-0.801905\pi\)
0.911095 + 0.412197i \(0.135239\pi\)
\(654\) 20.7397 + 35.9223i 0.810988 + 1.40467i
\(655\) 10.0526i 0.392789i
\(656\) −21.4212 + 12.3675i −0.836358 + 0.482871i
\(657\) −6.41828 + 3.70560i −0.250401 + 0.144569i
\(658\) 17.5036i 0.682363i
\(659\) 21.9906 + 38.0888i 0.856632 + 1.48373i 0.875122 + 0.483902i \(0.160781\pi\)
−0.0184899 + 0.999829i \(0.505886\pi\)
\(660\) −18.2216 + 31.5608i −0.709276 + 1.22850i
\(661\) −33.0989 19.1097i −1.28740 0.743280i −0.309210 0.950994i \(-0.600064\pi\)
−0.978190 + 0.207714i \(0.933398\pi\)
\(662\) −22.9748 −0.892940
\(663\) 0 0
\(664\) −0.936608 −0.0363474
\(665\) 24.8355 + 14.3388i 0.963079 + 0.556034i
\(666\) 9.01722 15.6183i 0.349410 0.605196i
\(667\) −3.99247 6.91516i −0.154589 0.267756i
\(668\) 17.8261i 0.689713i
\(669\) −9.29985 + 5.36927i −0.359553 + 0.207588i
\(670\) −9.06051 + 5.23109i −0.350038 + 0.202094i
\(671\) 18.1752i 0.701647i
\(672\) 9.11745 + 15.7919i 0.351713 + 0.609185i
\(673\) −3.33244 + 5.77195i −0.128456 + 0.222492i −0.923079 0.384611i \(-0.874335\pi\)
0.794623 + 0.607104i \(0.207669\pi\)
\(674\) −12.5077 7.22132i −0.481779 0.278155i
\(675\) 6.26875 0.241284
\(676\) 0 0
\(677\) 4.80194 0.184553 0.0922767 0.995733i \(-0.470586\pi\)
0.0922767 + 0.995733i \(0.470586\pi\)
\(678\) −17.1977 9.92908i −0.660472 0.381324i
\(679\) 18.1211 31.3867i 0.695424 1.20451i
\(680\) −0.621097 1.07577i −0.0238180 0.0412539i
\(681\) 6.97584i 0.267315i
\(682\) 77.3766 44.6734i 2.96290 1.71063i
\(683\) −9.75063 + 5.62953i −0.373098 + 0.215408i −0.674811 0.737991i \(-0.735775\pi\)
0.301713 + 0.953399i \(0.402441\pi\)
\(684\) 8.35690i 0.319534i
\(685\) −38.6368 66.9209i −1.47624 2.55692i
\(686\) 20.6048 35.6886i 0.786696 1.36260i
\(687\) 14.5535 + 8.40246i 0.555250 + 0.320574i
\(688\) −8.14952 −0.310698
\(689\) 0 0
\(690\) 13.9427 0.530790
\(691\) 21.4033 + 12.3572i 0.814219 + 0.470090i 0.848419 0.529325i \(-0.177555\pi\)
−0.0341997 + 0.999415i \(0.510888\pi\)
\(692\) 19.8443 34.3714i 0.754369 1.30660i
\(693\) 5.54892 + 9.61101i 0.210786 + 0.365092i
\(694\) 5.54048i 0.210314i
\(695\) 2.85640 1.64914i 0.108350 0.0625556i
\(696\) 1.38434 0.799249i 0.0524733 0.0302955i
\(697\) 6.32736i 0.239666i
\(698\) −0.425665 0.737273i −0.0161116 0.0279062i
\(699\) −4.34601 + 7.52751i −0.164381 + 0.284717i
\(700\) 26.8133 + 15.4807i 1.01345 + 0.585115i
\(701\) −25.8920 −0.977927 −0.488964 0.872304i \(-0.662625\pi\)
−0.488964 + 0.872304i \(0.662625\pi\)
\(702\) 0 0
\(703\) −33.4644 −1.26213
\(704\) 40.6270 + 23.4560i 1.53119 + 0.884031i
\(705\) 6.38135 11.0528i 0.240336 0.416274i
\(706\) 32.9540 + 57.0779i 1.24024 + 2.14816i
\(707\) 22.3545i 0.840728i
\(708\) 8.97307 5.18060i 0.337229 0.194699i
\(709\) −0.0737525 + 0.0425810i −0.00276983 + 0.00159916i −0.501384 0.865225i \(-0.667176\pi\)
0.498614 + 0.866824i \(0.333842\pi\)
\(710\) 16.3605i 0.613998i
\(711\) 1.87047 + 3.23975i 0.0701481 + 0.121500i
\(712\) 2.04096 3.53504i 0.0764881 0.132481i
\(713\) −15.5000 8.94893i −0.580479 0.335140i
\(714\) −4.19806 −0.157109
\(715\) 0 0
\(716\) −43.6760 −1.63225
\(717\) −19.8486 11.4596i −0.741258 0.427966i
\(718\) 22.8988 39.6619i 0.854576 1.48017i
\(719\) 13.5254 + 23.4267i 0.504413 + 0.873669i 0.999987 + 0.00510319i \(0.00162440\pi\)
−0.495574 + 0.868566i \(0.665042\pi\)
\(720\) 11.9661i 0.445952i
\(721\) −21.3818 + 12.3448i −0.796302 + 0.459745i
\(722\) −8.06519 + 4.65644i −0.300155 + 0.173295i
\(723\) 21.9801i 0.817451i
\(724\) 11.0813 + 19.1933i 0.411832 + 0.713315i
\(725\) −12.3463 + 21.3844i −0.458530 + 0.794198i
\(726\) 23.7660 + 13.7213i 0.882040 + 0.509246i
\(727\) 47.1584 1.74901 0.874503 0.485019i \(-0.161187\pi\)
0.874503 + 0.485019i \(0.161187\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 44.1449 + 25.4871i 1.63388 + 0.943320i
\(731\) 1.04234 1.80539i 0.0385525 0.0667749i
\(732\) −4.04437 7.00505i −0.149484 0.258914i
\(733\) 9.68186i 0.357608i −0.983885 0.178804i \(-0.942777\pi\)
0.983885 0.178804i \(-0.0572227\pi\)
\(734\) 4.08577 2.35892i 0.150809 0.0870693i
\(735\) −5.67210 + 3.27479i −0.209219 + 0.120792i
\(736\) 16.4509i 0.606388i
\(737\) 3.75637 + 6.50623i 0.138368 + 0.239660i
\(738\) −7.10872 + 12.3127i −0.261676 + 0.453235i
\(739\) 31.4488 + 18.1570i 1.15686 + 0.667915i 0.950550 0.310571i \(-0.100520\pi\)
0.206313 + 0.978486i \(0.433854\pi\)
\(740\) −64.9466 −2.38748
\(741\) 0 0
\(742\) −2.49934 −0.0917535
\(743\) 36.1597 + 20.8768i 1.32657 + 0.765896i 0.984768 0.173876i \(-0.0556292\pi\)
0.341803 + 0.939772i \(0.388963\pi\)
\(744\) 1.79148 3.10293i 0.0656788 0.113759i
\(745\) 17.2193 + 29.8247i 0.630866 + 1.09269i
\(746\) 39.4950i 1.44602i
\(747\) 1.99877 1.15399i 0.0731311 0.0422223i
\(748\) −8.57304 + 4.94965i −0.313462 + 0.180977i
\(749\) 22.1836i 0.810571i
\(750\) −4.36323 7.55734i −0.159323 0.275955i
\(751\) −11.0963 + 19.2194i −0.404911 + 0.701327i −0.994311 0.106515i \(-0.966031\pi\)
0.589400 + 0.807841i \(0.299364\pi\)
\(752\) −11.7369 6.77628i −0.427999 0.247106i
\(753\) 26.6437 0.970950
\(754\) 0 0
\(755\) −67.7036 −2.46399
\(756\) 4.27730 + 2.46950i 0.155564 + 0.0898149i
\(757\) −4.61865 + 7.99973i −0.167868 + 0.290755i −0.937670 0.347527i \(-0.887021\pi\)
0.769802 + 0.638282i \(0.220355\pi\)
\(758\) 7.51895 + 13.0232i 0.273101 + 0.473024i
\(759\) 10.0121i 0.363416i
\(760\) 4.48538 2.58964i 0.162702 0.0939360i
\(761\) 6.49669 3.75086i 0.235505 0.135969i −0.377604 0.925967i \(-0.623252\pi\)
0.613109 + 0.789998i \(0.289919\pi\)
\(762\) 28.2989i 1.02516i
\(763\) −22.7446 39.3948i −0.823409 1.42619i
\(764\) −7.23985 + 12.5398i −0.261929 + 0.453673i
\(765\) 2.65090 + 1.53050i 0.0958436 + 0.0553353i
\(766\) 39.1140 1.41325
\(767\) 0 0
\(768\) −12.3773 −0.446629
\(769\) −4.45141 2.57002i −0.160522 0.0926774i 0.417587 0.908637i \(-0.362876\pi\)
−0.578109 + 0.815959i \(0.696209\pi\)
\(770\) 38.1655 66.1045i 1.37539 2.38224i
\(771\) −11.5722 20.0436i −0.416762 0.721853i
\(772\) 23.8869i 0.859708i
\(773\) −7.36271 + 4.25086i −0.264818 + 0.152893i −0.626531 0.779397i \(-0.715526\pi\)
0.361712 + 0.932290i \(0.382192\pi\)
\(774\) −4.05668 + 2.34213i −0.145814 + 0.0841860i
\(775\) 55.3473i 1.98813i
\(776\) −3.27274 5.66855i −0.117485 0.203489i
\(777\) −9.88889 + 17.1281i −0.354762 + 0.614466i
\(778\) 42.5645 + 24.5746i 1.52601 + 0.881043i
\(779\) 26.3817 0.945221
\(780\) 0 0
\(781\) 11.7482 0.420385
\(782\) 3.27994 + 1.89367i 0.117290 + 0.0677176i
\(783\) −1.96950 + 3.41127i −0.0703842 + 0.121909i
\(784\) 3.47746 + 6.02314i 0.124195 + 0.215112i
\(785\) 35.0404i 1.25065i
\(786\) 5.31370 3.06787i 0.189533 0.109427i
\(787\) 6.74248 3.89277i 0.240343 0.138762i −0.374991 0.927028i \(-0.622354\pi\)
0.615335 + 0.788266i \(0.289021\pi\)
\(788\) 20.3136i 0.723643i
\(789\) −9.26420 16.0461i −0.329814 0.571255i
\(790\) 12.8651 22.2830i 0.457719 0.792793i
\(791\) 18.8601 + 10.8889i 0.670588 + 0.387164i
\(792\) 2.00431 0.0712201
\(793\) 0 0
\(794\) 9.05190 0.321240
\(795\) 1.57823 + 0.911190i 0.0559740 + 0.0323166i
\(796\) 1.71960 2.97843i 0.0609494 0.105568i
\(797\) 10.6920 + 18.5191i 0.378731 + 0.655981i 0.990878 0.134763i \(-0.0430273\pi\)
−0.612147 + 0.790744i \(0.709694\pi\)
\(798\) 17.5036i 0.619622i
\(799\) 3.00235 1.73341i 0.106215 0.0613235i
\(800\) −44.0571 + 25.4364i −1.55765 + 0.899312i
\(801\) 10.0586i 0.355403i
\(802\) −20.9080 36.2137i −0.738286 1.27875i
\(803\) 18.3019 31.6999i 0.645861 1.11866i
\(804\) 2.89554 + 1.67174i 0.102118 + 0.0589578i
\(805\) −15.2905 −0.538920
\(806\) 0 0
\(807\) −9.75840 −0.343512
\(808\) −3.49641 2.01865i −0.123003 0.0710160i
\(809\) −1.14310 + 1.97991i −0.0401894 + 0.0696101i −0.885420 0.464791i \(-0.846129\pi\)
0.845231 + 0.534401i \(0.179463\pi\)
\(810\) −3.43900 5.95652i −0.120834 0.209291i
\(811\) 17.8079i 0.625320i 0.949865 + 0.312660i \(0.101220\pi\)
−0.949865 + 0.312660i \(0.898780\pi\)
\(812\) −16.8483 + 9.72737i −0.591259 + 0.341364i
\(813\) −19.7471 + 11.4010i −0.692560 + 0.399849i
\(814\) 89.0721i 3.12198i
\(815\) 18.5410 + 32.1140i 0.649463 + 1.12490i
\(816\) 1.62522 2.81496i 0.0568940 0.0985434i
\(817\) 7.52751 + 4.34601i 0.263354 + 0.152048i
\(818\) −45.3818 −1.58674
\(819\) 0 0
\(820\) 51.2006 1.78800
\(821\) −12.0424 6.95271i −0.420284 0.242651i 0.274915 0.961469i \(-0.411350\pi\)
−0.695199 + 0.718817i \(0.744684\pi\)
\(822\) −23.5824 + 40.8459i −0.822531 + 1.42466i
\(823\) −3.62415 6.27722i −0.126330 0.218810i 0.795922 0.605399i \(-0.206987\pi\)
−0.922252 + 0.386589i \(0.873653\pi\)
\(824\) 4.45904i 0.155338i
\(825\) −26.8133 + 15.4807i −0.933520 + 0.538968i
\(826\) −18.7942 + 10.8509i −0.653935 + 0.377550i
\(827\) 54.1191i 1.88191i −0.338536 0.940953i \(-0.609932\pi\)
0.338536 0.940953i \(-0.390068\pi\)
\(828\) −2.22790 3.85883i −0.0774248 0.134104i
\(829\) −2.89589 + 5.01582i −0.100578 + 0.174207i −0.911923 0.410361i \(-0.865403\pi\)
0.811345 + 0.584568i \(0.198736\pi\)
\(830\) −13.7475 7.93714i −0.477184 0.275502i
\(831\) −23.9705 −0.831526
\(832\) 0 0
\(833\) −1.77910 −0.0616422
\(834\) −1.74344 1.00657i −0.0603703 0.0348548i
\(835\) −13.6121 + 23.5768i −0.471065 + 0.815909i
\(836\) −20.6374 35.7450i −0.713758 1.23627i
\(837\) 8.82908i 0.305178i
\(838\) −26.1833 + 15.1169i −0.904486 + 0.522205i
\(839\) 4.58431 2.64675i 0.158268 0.0913760i −0.418774 0.908090i \(-0.637540\pi\)
0.577042 + 0.816714i \(0.304207\pi\)
\(840\) 3.06100i 0.105614i
\(841\) 6.74214 + 11.6777i 0.232487 + 0.402680i
\(842\) −8.67941 + 15.0332i −0.299112 + 0.518077i
\(843\) 3.57234 + 2.06249i 0.123038 + 0.0710360i
\(844\) −51.0930 −1.75870
\(845\) 0 0
\(846\) −7.78986 −0.267821
\(847\) −26.0634 15.0477i −0.895550 0.517046i
\(848\) 0.967582 1.67590i 0.0332269 0.0575507i
\(849\) 7.82789 + 13.5583i 0.268652 + 0.465320i
\(850\) 11.7120i 0.401718i
\(851\) 15.4523 8.92141i 0.529699 0.305822i
\(852\) 4.52798 2.61423i 0.155126 0.0895620i
\(853\) 13.5961i 0.465522i 0.972534 + 0.232761i \(0.0747760\pi\)
−0.972534 + 0.232761i \(0.925224\pi\)
\(854\) 8.47099 + 14.6722i 0.289871 + 0.502072i
\(855\) −6.38135 + 11.0528i −0.218238 + 0.377999i
\(856\) 3.46968 + 2.00322i 0.118591 + 0.0684687i
\(857\) 23.8323 0.814097 0.407048 0.913407i \(-0.366558\pi\)
0.407048 + 0.913407i \(0.366558\pi\)
\(858\) 0 0
\(859\) −26.9861 −0.920754 −0.460377 0.887723i \(-0.652286\pi\)
−0.460377 + 0.887723i \(0.652286\pi\)
\(860\) 14.6091 + 8.43458i 0.498167 + 0.287617i
\(861\) 7.79590 13.5029i 0.265683 0.460177i
\(862\) −2.45031 4.24407i −0.0834580 0.144553i
\(863\) 27.0291i 0.920080i −0.887898 0.460040i \(-0.847835\pi\)
0.887898 0.460040i \(-0.152165\pi\)
\(864\) −7.02805 + 4.05765i −0.239099 + 0.138044i
\(865\) 52.4922 30.3064i 1.78479 1.03045i
\(866\) 21.3674i 0.726095i
\(867\) −8.08426 14.0024i −0.274556 0.475545i
\(868\) −21.8034 + 37.7646i −0.740057 + 1.28182i
\(869\) −16.0011 9.23825i −0.542801 0.313386i
\(870\) 27.0925 0.918520
\(871\) 0 0
\(872\) −8.21552 −0.278213
\(873\) 13.9684 + 8.06465i 0.472758 + 0.272947i
\(874\) −7.89559 + 13.6756i −0.267072 + 0.462583i
\(875\) 4.78501 + 8.28788i 0.161763 + 0.280182i
\(876\) 16.2903i 0.550397i
\(877\) 35.4014 20.4390i 1.19542 0.690176i 0.235889 0.971780i \(-0.424200\pi\)
0.959531 + 0.281604i \(0.0908664\pi\)
\(878\) −57.7575 + 33.3463i −1.94922 + 1.12538i
\(879\) 22.5948i 0.762103i
\(880\) 29.5504 + 51.1828i 0.996144 + 1.72537i
\(881\) −11.2482 + 19.4824i −0.378961 + 0.656379i −0.990911 0.134517i \(-0.957052\pi\)
0.611951 + 0.790896i \(0.290385\pi\)
\(882\) 3.46203 + 1.99880i 0.116573 + 0.0673032i
\(883\) 4.16315 0.140101 0.0700505 0.997543i \(-0.477684\pi\)
0.0700505 + 0.997543i \(0.477684\pi\)
\(884\) 0 0
\(885\) 15.8237 0.531908
\(886\) 17.0026 + 9.81647i 0.571214 + 0.329791i
\(887\) 13.1501 22.7766i 0.441537 0.764765i −0.556266 0.831004i \(-0.687767\pi\)
0.997804 + 0.0662389i \(0.0211000\pi\)
\(888\) 1.78597 + 3.09339i 0.0599333 + 0.103807i
\(889\) 31.0344i 1.04086i
\(890\) 59.9143 34.5916i 2.00833 1.15951i
\(891\) −4.27730 + 2.46950i −0.143295 + 0.0827314i
\(892\) 23.6040i 0.790320i
\(893\) 7.22737 + 12.5182i 0.241855 + 0.418904i
\(894\) 10.5100 18.2038i 0.351506 0.608827i
\(895\) −57.7659 33.3512i −1.93090 1.11481i
\(896\) −7.25906 −0.242508
\(897\) 0 0
\(898\) 58.1764 1.94137
\(899\) −30.1184 17.3889i −1.00451 0.579952i
\(900\) −6.88955 + 11.9331i −0.229652 + 0.397768i
\(901\) 0.247512 + 0.428703i 0.00824582 + 0.0142822i
\(902\) 70.2199i 2.33807i
\(903\) 4.44883 2.56853i 0.148048 0.0854754i
\(904\) 3.40621 1.96658i 0.113289 0.0654073i
\(905\) 33.8468i 1.12511i
\(906\) 20.6618 + 35.7873i 0.686443 + 1.18895i
\(907\) −28.9557 + 50.1527i −0.961458 + 1.66529i −0.242613 + 0.970123i \(0.578005\pi\)
−0.718845 + 0.695171i \(0.755329\pi\)
\(908\) −13.2790 7.66666i −0.440681 0.254427i
\(909\) 9.94869 0.329977
\(910\) 0 0
\(911\) −0.286799 −0.00950208 −0.00475104 0.999989i \(-0.501512\pi\)
−0.00475104 + 0.999989i \(0.501512\pi\)
\(912\) 11.7369 + 6.77628i 0.388646 + 0.224385i
\(913\) −5.69955 + 9.87192i −0.188628 + 0.326713i
\(914\) −5.11788 8.86442i −0.169284 0.293209i
\(915\) 12.3532i 0.408383i
\(916\) −31.9895 + 18.4691i −1.05696 + 0.610237i
\(917\) −5.82736 + 3.36443i −0.192436 + 0.111103i
\(918\) 1.86831i 0.0616635i
\(919\) 15.5620 + 26.9541i 0.513342 + 0.889134i 0.999880 + 0.0154747i \(0.00492596\pi\)
−0.486539 + 0.873659i \(0.661741\pi\)
\(920\) −1.38076 + 2.39155i −0.0455224 + 0.0788472i
\(921\) 5.67676 + 3.27748i 0.187056 + 0.107997i
\(922\) 2.77133 0.0912690
\(923\) 0 0
\(924\) −24.3937 −0.802495
\(925\) −47.7848 27.5886i −1.57115 0.907107i
\(926\) −3.44696 + 5.97031i −0.113274 + 0.196197i
\(927\) −5.49396 9.51582i −0.180445 0.312540i
\(928\) 31.9661i 1.04934i
\(929\) 6.60493 3.81336i 0.216701 0.125112i −0.387721 0.921777i \(-0.626738\pi\)
0.604422 + 0.796665i \(0.293404\pi\)
\(930\) 52.5907 30.3632i 1.72452 0.995650i
\(931\) 7.41789i 0.243112i
\(932\) −9.55280 16.5459i −0.312912 0.541980i
\(933\) 6.01961 10.4263i 0.197073 0.341341i
\(934\) −12.2626 7.07982i −0.401245 0.231659i
\(935\) −15.1183 −0.494421
\(936\) 0 0
\(937\) −5.67324 −0.185337 −0.0926683 0.995697i \(-0.529540\pi\)
−0.0926683 + 0.995697i \(0.529540\pi\)
\(938\) −6.06476 3.50149i −0.198021 0.114328i
\(939\) −16.9475 + 29.3539i −0.553061 + 0.957929i
\(940\) 14.0266 + 24.2948i 0.457498 + 0.792409i
\(941\) 41.5394i 1.35415i 0.735916 + 0.677073i \(0.236752\pi\)
−0.735916 + 0.677073i \(0.763248\pi\)
\(942\) 18.5219 10.6936i 0.603477 0.348418i
\(943\) −12.1818 + 7.03319i −0.396695 + 0.229032i
\(944\) 16.8030i 0.546891i
\(945\) 3.77144 + 6.53232i 0.122685 + 0.212496i
\(946\) 11.5678 20.0360i 0.376100 0.651425i
\(947\) −40.9725 23.6555i −1.33143 0.768700i −0.345909 0.938268i \(-0.612429\pi\)
−0.985518 + 0.169568i \(0.945763\pi\)
\(948\) −8.22282 −0.267065
\(949\) 0 0
\(950\) 48.8327 1.58434
\(951\) −3.89562 2.24914i −0.126324 0.0729332i
\(952\) 0.415739 0.720081i 0.0134742 0.0233380i
\(953\) −17.1717 29.7423i −0.556247 0.963449i −0.997805 0.0662159i \(-0.978907\pi\)
0.441558 0.897233i \(-0.354426\pi\)
\(954\) 1.11231i 0.0360123i
\(955\) −19.1508 + 11.0567i −0.619707 + 0.357788i
\(956\) 43.6284 25.1889i 1.41104 0.814666i
\(957\) 19.4547i 0.628882i
\(958\) 3.60172 + 6.23836i 0.116366 + 0.201552i
\(959\) 25.8620 44.7944i 0.835129 1.44649i
\(960\) 27.6130 + 15.9424i 0.891205 + 0.514537i
\(961\) −46.9527 −1.51460
\(962\) 0 0
\(963\) −9.87263 −0.318141
\(964\) −41.8409 24.1569i −1.34761 0.778040i
\(965\) −18.2401 + 31.5928i −0.587170 + 1.01701i
\(966\) 4.66637 + 8.08238i 0.150138 + 0.260046i
\(967\) 48.5096i 1.55996i 0.625802 + 0.779982i \(0.284772\pi\)
−0.625802 + 0.779982i \(0.715228\pi\)
\(968\) −4.70715 + 2.71768i −0.151294 + 0.0873494i
\(969\) −3.00235 + 1.73341i −0.0964493 + 0.0556850i
\(970\) 110.937i 3.56198i
\(971\) −20.7325 35.9098i −0.665338 1.15240i −0.979194 0.202928i \(-0.934954\pi\)
0.313856 0.949471i \(-0.398379\pi\)
\(972\) −1.09903 + 1.90358i −0.0352514 + 0.0610573i
\(973\) 1.91197 + 1.10388i 0.0612949 + 0.0353886i
\(974\) −26.3242 −0.843483
\(975\) 0 0
\(976\) −13.1177 −0.419887
\(977\) 1.81586 + 1.04838i 0.0580944 + 0.0335408i 0.528766 0.848768i \(-0.322655\pi\)
−0.470671 + 0.882309i \(0.655988\pi\)
\(978\) 11.3167 19.6011i 0.361868 0.626774i
\(979\) −24.8397 43.0237i −0.793881 1.37504i
\(980\) 14.3964i 0.459876i
\(981\) 17.5323 10.1223i 0.559764 0.323180i
\(982\) 50.8740 29.3721i 1.62345 0.937301i
\(983\) 25.2336i 0.804826i −0.915458 0.402413i \(-0.868172\pi\)
0.915458 0.402413i \(-0.131828\pi\)
\(984\) −1.40797 2.43867i −0.0448844 0.0777421i
\(985\) 15.5115 26.8668i 0.494239 0.856047i
\(986\) 6.37333 + 3.67964i 0.202968 + 0.117184i
\(987\) 8.54288 0.271923
\(988\) 0 0
\(989\) −4.63448 −0.147368
\(990\) 29.4193 + 16.9852i 0.935006 + 0.539826i
\(991\) −6.02446 + 10.4347i −0.191373 + 0.331468i −0.945706 0.325025i \(-0.894627\pi\)
0.754332 + 0.656493i \(0.227961\pi\)
\(992\) −35.8253 62.0512i −1.13745 1.97013i
\(993\) 11.2131i 0.355838i
\(994\) −9.48392 + 5.47554i −0.300812 + 0.173674i
\(995\) 4.54867 2.62618i 0.144203 0.0832554i
\(996\) 5.07308i 0.160747i
\(997\) 0.717013 + 1.24190i 0.0227080 + 0.0393314i 0.877156 0.480205i \(-0.159438\pi\)
−0.854448 + 0.519537i \(0.826105\pi\)
\(998\) 34.3763 59.5415i 1.08816 1.88475i
\(999\) −7.62270 4.40097i −0.241172 0.139240i
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 507.2.j.i.316.4 12
13.2 odd 12 507.2.e.i.484.3 6
13.3 even 3 inner 507.2.j.i.361.3 12
13.4 even 6 507.2.b.f.337.4 6
13.5 odd 4 507.2.e.i.22.3 6
13.6 odd 12 507.2.a.l.1.1 yes 3
13.7 odd 12 507.2.a.i.1.3 3
13.8 odd 4 507.2.e.l.22.1 6
13.9 even 3 507.2.b.f.337.3 6
13.10 even 6 inner 507.2.j.i.361.4 12
13.11 odd 12 507.2.e.l.484.1 6
13.12 even 2 inner 507.2.j.i.316.3 12
39.17 odd 6 1521.2.b.k.1351.3 6
39.20 even 12 1521.2.a.s.1.1 3
39.32 even 12 1521.2.a.n.1.3 3
39.35 odd 6 1521.2.b.k.1351.4 6
52.7 even 12 8112.2.a.cg.1.2 3
52.19 even 12 8112.2.a.cp.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.a.i.1.3 3 13.7 odd 12
507.2.a.l.1.1 yes 3 13.6 odd 12
507.2.b.f.337.3 6 13.9 even 3
507.2.b.f.337.4 6 13.4 even 6
507.2.e.i.22.3 6 13.5 odd 4
507.2.e.i.484.3 6 13.2 odd 12
507.2.e.l.22.1 6 13.8 odd 4
507.2.e.l.484.1 6 13.11 odd 12
507.2.j.i.316.3 12 13.12 even 2 inner
507.2.j.i.316.4 12 1.1 even 1 trivial
507.2.j.i.361.3 12 13.3 even 3 inner
507.2.j.i.361.4 12 13.10 even 6 inner
1521.2.a.n.1.3 3 39.32 even 12
1521.2.a.s.1.1 3 39.20 even 12
1521.2.b.k.1351.3 6 39.17 odd 6
1521.2.b.k.1351.4 6 39.35 odd 6
8112.2.a.cg.1.2 3 52.7 even 12
8112.2.a.cp.1.2 3 52.19 even 12