Properties

Label 605.2.j.j.9.2
Level $605$
Weight $2$
Character 605.9
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(9,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: 16.0.343361479062744140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + 168 x^{7} + 54 x^{6} + 189 x^{5} + 648 x^{4} - 1944 x^{3} + 2187 x^{2} - 2187 x + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 9.2
Root \(-0.144291 - 1.72603i\) of defining polynomial
Character \(\chi\) \(=\) 605.9
Dual form 605.2.j.j.269.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.753510 - 0.244830i) q^{2} +(1.48377 + 2.04223i) q^{3} +(-1.11020 - 0.806607i) q^{4} +(-0.228670 - 2.22434i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-2.03615 + 2.80252i) q^{7} +(1.57045 + 2.16154i) q^{8} +(-1.04209 + 3.20723i) q^{9} +O(q^{10})\) \(q+(-0.753510 - 0.244830i) q^{2} +(1.48377 + 2.04223i) q^{3} +(-1.11020 - 0.806607i) q^{4} +(-0.228670 - 2.22434i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-2.03615 + 2.80252i) q^{7} +(1.57045 + 2.16154i) q^{8} +(-1.04209 + 3.20723i) q^{9} +(-0.372281 + 1.73205i) q^{10} -3.46410i q^{12} +(2.22040 - 1.61321i) q^{14} +(4.20333 - 3.76741i) q^{15} +(0.193976 + 0.596996i) q^{16} +(-4.80158 + 1.56013i) q^{17} +(1.57045 - 2.16154i) q^{18} +(-3.23607 + 2.35114i) q^{19} +(-1.54030 + 2.65391i) q^{20} -8.74456 q^{21} +2.52434i q^{23} +(-2.08418 + 6.41446i) q^{24} +(-4.89542 + 1.01728i) q^{25} +(-0.893769 + 0.290403i) q^{27} +(4.52106 - 1.46898i) q^{28} +(2.22040 + 1.61321i) q^{29} +(-4.08963 + 1.80968i) q^{30} +(-0.733075 + 2.25617i) q^{31} -5.84096i q^{32} +4.00000 q^{34} +(6.69937 + 3.88824i) q^{35} +(3.74390 - 2.72010i) q^{36} +(-6.48745 + 8.92921i) q^{37} +(3.01404 - 0.979321i) q^{38} +(4.44890 - 3.98751i) q^{40} +(-2.22040 + 1.61321i) q^{41} +(6.58911 + 2.14093i) q^{42} +3.46410i q^{43} +(7.37228 + 1.58457i) q^{45} +(0.618034 - 1.90211i) q^{46} +(-3.89893 - 5.36641i) q^{47} +(-0.931389 + 1.28195i) q^{48} +(-1.54508 - 4.75528i) q^{49} +(3.93781 + 0.432013i) q^{50} +(-10.3106 - 7.49107i) q^{51} +(3.01404 + 0.979321i) q^{53} +0.744563 q^{54} -9.25544 q^{56} +(-9.60315 - 3.12025i) q^{57} +(-1.27813 - 1.75919i) q^{58} +(-1.31685 - 0.956749i) q^{59} +(-7.70536 + 0.792137i) q^{60} +(-3.32025 - 10.2187i) q^{61} +(1.10476 - 1.52057i) q^{62} +(-6.86646 - 9.45088i) q^{63} +(-1.04209 + 3.20723i) q^{64} -0.644810i q^{67} +(6.58911 + 2.14093i) q^{68} +(-5.15528 + 3.74553i) q^{69} +(-4.09608 - 4.57004i) q^{70} +(2.19923 + 6.76852i) q^{71} +(-8.56912 + 2.78428i) q^{72} +(-4.07230 + 5.60503i) q^{73} +(7.07450 - 5.13992i) q^{74} +(-9.34120 - 8.48817i) q^{75} +5.48913 q^{76} +(3.93829 - 12.1208i) q^{79} +(1.28357 - 0.567984i) q^{80} +(6.26548 + 4.55214i) q^{81} +(2.06805 - 0.671952i) q^{82} +(6.30860 - 2.04979i) q^{83} +(9.70820 + 7.05342i) q^{84} +(4.56824 + 10.3236i) q^{85} +(0.848116 - 2.61023i) q^{86} +6.92820i q^{87} +4.37228 q^{89} +(-5.16713 - 2.99895i) q^{90} +(2.03615 - 2.80252i) q^{92} +(-5.69534 + 1.85053i) q^{93} +(1.62402 + 4.99822i) q^{94} +(5.96974 + 6.66049i) q^{95} +(11.9286 - 8.66664i) q^{96} +(-3.90781 - 1.26972i) q^{97} +3.96143i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35} + 30 q^{36} + 28 q^{40} + 12 q^{41} + 72 q^{45} - 8 q^{46} + 20 q^{49} - 18 q^{50} - 28 q^{51} - 80 q^{54} - 240 q^{56} - 18 q^{59} + 18 q^{60} + 20 q^{61} + 2 q^{64} - 14 q^{69} - 24 q^{70} + 6 q^{71} + 12 q^{74} - 15 q^{75} - 96 q^{76} - 28 q^{79} - 6 q^{80} + 8 q^{81} + 48 q^{84} + 2 q^{85} + 12 q^{86} + 24 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.753510 0.244830i −0.532812 0.173121i 0.0302400 0.999543i \(-0.490373\pi\)
−0.563052 + 0.826422i \(0.690373\pi\)
\(3\) 1.48377 + 2.04223i 0.856654 + 1.17908i 0.982357 + 0.187015i \(0.0598814\pi\)
−0.125703 + 0.992068i \(0.540119\pi\)
\(4\) −1.11020 0.806607i −0.555099 0.403303i
\(5\) −0.228670 2.22434i −0.102264 0.994757i
\(6\) −0.618034 1.90211i −0.252311 0.776534i
\(7\) −2.03615 + 2.80252i −0.769592 + 1.05925i 0.226764 + 0.973950i \(0.427186\pi\)
−0.996355 + 0.0853021i \(0.972814\pi\)
\(8\) 1.57045 + 2.16154i 0.555239 + 0.764221i
\(9\) −1.04209 + 3.20723i −0.347364 + 1.06908i
\(10\) −0.372281 + 1.73205i −0.117726 + 0.547723i
\(11\) 0 0
\(12\) 3.46410i 1.00000i
\(13\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(14\) 2.22040 1.61321i 0.593426 0.431149i
\(15\) 4.20333 3.76741i 1.08530 0.972741i
\(16\) 0.193976 + 0.596996i 0.0484939 + 0.149249i
\(17\) −4.80158 + 1.56013i −1.16455 + 0.378386i −0.826607 0.562779i \(-0.809732\pi\)
−0.337946 + 0.941166i \(0.609732\pi\)
\(18\) 1.57045 2.16154i 0.370159 0.509481i
\(19\) −3.23607 + 2.35114i −0.742405 + 0.539389i −0.893463 0.449136i \(-0.851732\pi\)
0.151058 + 0.988525i \(0.451732\pi\)
\(20\) −1.54030 + 2.65391i −0.344422 + 0.593433i
\(21\) −8.74456 −1.90822
\(22\) 0 0
\(23\) 2.52434i 0.526361i 0.964747 + 0.263180i \(0.0847714\pi\)
−0.964747 + 0.263180i \(0.915229\pi\)
\(24\) −2.08418 + 6.41446i −0.425432 + 1.30935i
\(25\) −4.89542 + 1.01728i −0.979084 + 0.203457i
\(26\) 0 0
\(27\) −0.893769 + 0.290403i −0.172006 + 0.0558881i
\(28\) 4.52106 1.46898i 0.854400 0.277611i
\(29\) 2.22040 + 1.61321i 0.412318 + 0.299566i 0.774539 0.632526i \(-0.217982\pi\)
−0.362222 + 0.932092i \(0.617982\pi\)
\(30\) −4.08963 + 1.80968i −0.746661 + 0.330400i
\(31\) −0.733075 + 2.25617i −0.131664 + 0.405221i −0.995056 0.0993129i \(-0.968336\pi\)
0.863392 + 0.504534i \(0.168336\pi\)
\(32\) 5.84096i 1.03255i
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 6.69937 + 3.88824i 1.13240 + 0.657233i
\(36\) 3.74390 2.72010i 0.623984 0.453351i
\(37\) −6.48745 + 8.92921i −1.06653 + 1.46795i −0.192991 + 0.981200i \(0.561819\pi\)
−0.873540 + 0.486753i \(0.838181\pi\)
\(38\) 3.01404 0.979321i 0.488942 0.158867i
\(39\) 0 0
\(40\) 4.44890 3.98751i 0.703433 0.630481i
\(41\) −2.22040 + 1.61321i −0.346768 + 0.251942i −0.747512 0.664248i \(-0.768752\pi\)
0.400744 + 0.916190i \(0.368752\pi\)
\(42\) 6.58911 + 2.14093i 1.01672 + 0.330353i
\(43\) 3.46410i 0.528271i 0.964486 + 0.264135i \(0.0850865\pi\)
−0.964486 + 0.264135i \(0.914913\pi\)
\(44\) 0 0
\(45\) 7.37228 + 1.58457i 1.09899 + 0.236214i
\(46\) 0.618034 1.90211i 0.0911241 0.280451i
\(47\) −3.89893 5.36641i −0.568717 0.782772i 0.423685 0.905810i \(-0.360736\pi\)
−0.992402 + 0.123038i \(0.960736\pi\)
\(48\) −0.931389 + 1.28195i −0.134434 + 0.185033i
\(49\) −1.54508 4.75528i −0.220726 0.679326i
\(50\) 3.93781 + 0.432013i 0.556890 + 0.0610959i
\(51\) −10.3106 7.49107i −1.44377 1.04896i
\(52\) 0 0
\(53\) 3.01404 + 0.979321i 0.414010 + 0.134520i 0.508613 0.860995i \(-0.330158\pi\)
−0.0946033 + 0.995515i \(0.530158\pi\)
\(54\) 0.744563 0.101322
\(55\) 0 0
\(56\) −9.25544 −1.23681
\(57\) −9.60315 3.12025i −1.27197 0.413288i
\(58\) −1.27813 1.75919i −0.167826 0.230993i
\(59\) −1.31685 0.956749i −0.171440 0.124558i 0.498757 0.866742i \(-0.333790\pi\)
−0.670196 + 0.742184i \(0.733790\pi\)
\(60\) −7.70536 + 0.792137i −0.994757 + 0.102264i
\(61\) −3.32025 10.2187i −0.425115 1.30837i −0.902884 0.429884i \(-0.858555\pi\)
0.477770 0.878485i \(-0.341445\pi\)
\(62\) 1.10476 1.52057i 0.140304 0.193113i
\(63\) −6.86646 9.45088i −0.865093 1.19070i
\(64\) −1.04209 + 3.20723i −0.130262 + 0.400904i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.644810i 0.0787761i −0.999224 0.0393880i \(-0.987459\pi\)
0.999224 0.0393880i \(-0.0125408\pi\)
\(68\) 6.58911 + 2.14093i 0.799047 + 0.259626i
\(69\) −5.15528 + 3.74553i −0.620623 + 0.450909i
\(70\) −4.09608 4.57004i −0.489575 0.546224i
\(71\) 2.19923 + 6.76852i 0.261000 + 0.803276i 0.992588 + 0.121528i \(0.0387796\pi\)
−0.731588 + 0.681747i \(0.761220\pi\)
\(72\) −8.56912 + 2.78428i −1.00988 + 0.328130i
\(73\) −4.07230 + 5.60503i −0.476626 + 0.656020i −0.977852 0.209297i \(-0.932883\pi\)
0.501226 + 0.865316i \(0.332883\pi\)
\(74\) 7.07450 5.13992i 0.822394 0.597504i
\(75\) −9.34120 8.48817i −1.07863 0.980130i
\(76\) 5.48913 0.629646
\(77\) 0 0
\(78\) 0 0
\(79\) 3.93829 12.1208i 0.443092 1.36370i −0.441471 0.897276i \(-0.645543\pi\)
0.884563 0.466421i \(-0.154457\pi\)
\(80\) 1.28357 0.567984i 0.143507 0.0635026i
\(81\) 6.26548 + 4.55214i 0.696165 + 0.505793i
\(82\) 2.06805 0.671952i 0.228378 0.0742046i
\(83\) 6.30860 2.04979i 0.692458 0.224993i 0.0584167 0.998292i \(-0.481395\pi\)
0.634042 + 0.773299i \(0.281395\pi\)
\(84\) 9.70820 + 7.05342i 1.05925 + 0.769592i
\(85\) 4.56824 + 10.3236i 0.495495 + 1.11975i
\(86\) 0.848116 2.61023i 0.0914548 0.281469i
\(87\) 6.92820i 0.742781i
\(88\) 0 0
\(89\) 4.37228 0.463461 0.231730 0.972780i \(-0.425561\pi\)
0.231730 + 0.972780i \(0.425561\pi\)
\(90\) −5.16713 2.99895i −0.544664 0.316117i
\(91\) 0 0
\(92\) 2.03615 2.80252i 0.212283 0.292183i
\(93\) −5.69534 + 1.85053i −0.590580 + 0.191891i
\(94\) 1.62402 + 4.99822i 0.167505 + 0.515527i
\(95\) 5.96974 + 6.66049i 0.612483 + 0.683352i
\(96\) 11.9286 8.66664i 1.21746 0.884535i
\(97\) −3.90781 1.26972i −0.396778 0.128921i 0.103830 0.994595i \(-0.466890\pi\)
−0.500608 + 0.865674i \(0.666890\pi\)
\(98\) 3.96143i 0.400165i
\(99\) 0 0
\(100\) 6.25544 + 2.81929i 0.625544 + 0.281929i
\(101\) −1.85410 + 5.70634i −0.184490 + 0.567802i −0.999939 0.0110267i \(-0.996490\pi\)
0.815449 + 0.578829i \(0.196490\pi\)
\(102\) 5.93507 + 8.16893i 0.587660 + 0.808844i
\(103\) 6.10844 8.40755i 0.601883 0.828421i −0.393996 0.919112i \(-0.628908\pi\)
0.995879 + 0.0906914i \(0.0289077\pi\)
\(104\) 0 0
\(105\) 1.99962 + 19.4509i 0.195143 + 1.89822i
\(106\) −2.03134 1.47586i −0.197301 0.143348i
\(107\) 3.89893 + 5.36641i 0.376923 + 0.518791i 0.954766 0.297358i \(-0.0961053\pi\)
−0.577843 + 0.816148i \(0.696105\pi\)
\(108\) 1.22650 + 0.398515i 0.118020 + 0.0383471i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) −27.8614 −2.64449
\(112\) −2.06805 0.671952i −0.195413 0.0634935i
\(113\) 9.45499 + 13.0137i 0.889451 + 1.22422i 0.973713 + 0.227780i \(0.0731468\pi\)
−0.0842619 + 0.996444i \(0.526853\pi\)
\(114\) 6.47214 + 4.70228i 0.606171 + 0.440409i
\(115\) 5.61500 0.577241i 0.523601 0.0538280i
\(116\) −1.16385 3.58198i −0.108061 0.332578i
\(117\) 0 0
\(118\) 0.758020 + 1.04332i 0.0697814 + 0.0960458i
\(119\) 5.40444 16.6331i 0.495424 1.52476i
\(120\) 14.7446 + 3.16915i 1.34599 + 0.289302i
\(121\) 0 0
\(122\) 8.51278i 0.770711i
\(123\) −6.58911 2.14093i −0.594120 0.193041i
\(124\) 2.63370 1.91350i 0.236514 0.171837i
\(125\) 3.38223 + 10.6565i 0.302516 + 0.953144i
\(126\) 2.86009 + 8.80244i 0.254797 + 0.784184i
\(127\) 11.1102 3.60991i 0.985868 0.320328i 0.228663 0.973506i \(-0.426564\pi\)
0.757205 + 0.653178i \(0.226564\pi\)
\(128\) −5.29601 + 7.28933i −0.468106 + 0.644292i
\(129\) −7.07450 + 5.13992i −0.622875 + 0.452545i
\(130\) 0 0
\(131\) −8.74456 −0.764016 −0.382008 0.924159i \(-0.624767\pi\)
−0.382008 + 0.924159i \(0.624767\pi\)
\(132\) 0 0
\(133\) 13.8564i 1.20150i
\(134\) −0.157869 + 0.485871i −0.0136378 + 0.0419728i
\(135\) 0.850335 + 1.92164i 0.0731852 + 0.165389i
\(136\) −10.9129 7.92871i −0.935776 0.679881i
\(137\) 2.12027 0.688918i 0.181147 0.0588582i −0.217039 0.976163i \(-0.569640\pi\)
0.398186 + 0.917305i \(0.369640\pi\)
\(138\) 4.80158 1.56013i 0.408737 0.132807i
\(139\) −14.7514 10.7175i −1.25119 0.909046i −0.252904 0.967491i \(-0.581386\pi\)
−0.998291 + 0.0584456i \(0.981386\pi\)
\(140\) −4.30135 9.72048i −0.363531 0.821531i
\(141\) 5.17435 15.9250i 0.435759 1.34113i
\(142\) 5.63858i 0.473179i
\(143\) 0 0
\(144\) −2.11684 −0.176404
\(145\) 3.08060 5.30782i 0.255830 0.440791i
\(146\) 4.44080 3.22643i 0.367523 0.267021i
\(147\) 7.41884 10.2112i 0.611896 0.842202i
\(148\) 14.4047 4.68038i 1.18406 0.384725i
\(149\) 3.55033 + 10.9268i 0.290855 + 0.895159i 0.984582 + 0.174921i \(0.0559672\pi\)
−0.693728 + 0.720237i \(0.744033\pi\)
\(150\) 4.96052 + 8.68293i 0.405025 + 0.708958i
\(151\) 17.9874 13.0686i 1.46380 1.06351i 0.481443 0.876478i \(-0.340113\pi\)
0.982354 0.187033i \(-0.0598871\pi\)
\(152\) −10.1642 3.30254i −0.824424 0.267872i
\(153\) 17.0256i 1.37643i
\(154\) 0 0
\(155\) 5.18614 + 1.11469i 0.416561 + 0.0895342i
\(156\) 0 0
\(157\) −3.17318 4.36750i −0.253247 0.348565i 0.663398 0.748267i \(-0.269114\pi\)
−0.916645 + 0.399702i \(0.869114\pi\)
\(158\) −5.93507 + 8.16893i −0.472169 + 0.649885i
\(159\) 2.47214 + 7.60845i 0.196053 + 0.603390i
\(160\) −12.9923 + 1.33566i −1.02713 + 0.105593i
\(161\) −7.07450 5.13992i −0.557549 0.405083i
\(162\) −3.60660 4.96406i −0.283361 0.390013i
\(163\) 3.29456 + 1.07047i 0.258050 + 0.0838454i 0.435185 0.900341i \(-0.356683\pi\)
−0.177135 + 0.984187i \(0.556683\pi\)
\(164\) 3.76631 0.294100
\(165\) 0 0
\(166\) −5.25544 −0.407901
\(167\) 21.2744 + 6.91246i 1.64626 + 0.534902i 0.977924 0.208959i \(-0.0670074\pi\)
0.668335 + 0.743861i \(0.267007\pi\)
\(168\) −13.7329 18.9018i −1.05952 1.45830i
\(169\) −10.5172 7.64121i −0.809017 0.587785i
\(170\) −0.914681 8.89738i −0.0701529 0.682398i
\(171\) −4.16837 12.8289i −0.318763 0.981052i
\(172\) 2.79417 3.84584i 0.213053 0.293243i
\(173\) 1.10476 + 1.52057i 0.0839932 + 0.115607i 0.848946 0.528480i \(-0.177238\pi\)
−0.764953 + 0.644086i \(0.777238\pi\)
\(174\) 1.69623 5.22047i 0.128591 0.395763i
\(175\) 7.11684 15.7908i 0.537983 1.19368i
\(176\) 0 0
\(177\) 4.10891i 0.308845i
\(178\) −3.29456 1.07047i −0.246937 0.0802348i
\(179\) −12.8321 + 9.32310i −0.959120 + 0.696841i −0.952946 0.303140i \(-0.901965\pi\)
−0.00617360 + 0.999981i \(0.501965\pi\)
\(180\) −6.90657 7.70572i −0.514785 0.574351i
\(181\) 2.12701 + 6.54627i 0.158100 + 0.486580i 0.998462 0.0554448i \(-0.0176577\pi\)
−0.840362 + 0.542025i \(0.817658\pi\)
\(182\) 0 0
\(183\) 15.9424 21.9429i 1.17850 1.62207i
\(184\) −5.45647 + 3.96435i −0.402256 + 0.292256i
\(185\) 21.3451 + 12.3885i 1.56933 + 0.910820i
\(186\) 4.74456 0.347888
\(187\) 0 0
\(188\) 9.10268i 0.663881i
\(189\) 1.00599 3.09610i 0.0731747 0.225208i
\(190\) −2.86757 6.48032i −0.208035 0.470132i
\(191\) 11.0251 + 8.01017i 0.797745 + 0.579596i 0.910252 0.414055i \(-0.135888\pi\)
−0.112507 + 0.993651i \(0.535888\pi\)
\(192\) −8.09613 + 2.63059i −0.584288 + 0.189847i
\(193\) −22.2203 + 7.21983i −1.59946 + 0.519695i −0.966973 0.254880i \(-0.917964\pi\)
−0.632483 + 0.774575i \(0.717964\pi\)
\(194\) 2.63370 + 1.91350i 0.189089 + 0.137381i
\(195\) 0 0
\(196\) −2.12029 + 6.52559i −0.151449 + 0.466113i
\(197\) 1.87953i 0.133911i −0.997756 0.0669554i \(-0.978671\pi\)
0.997756 0.0669554i \(-0.0213285\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −9.88693 8.98407i −0.699112 0.635269i
\(201\) 1.31685 0.956749i 0.0928836 0.0674839i
\(202\) 2.79417 3.84584i 0.196597 0.270592i
\(203\) −9.04212 + 2.93796i −0.634632 + 0.206204i
\(204\) 5.40444 + 16.6331i 0.378386 + 1.16455i
\(205\) 4.09608 + 4.57004i 0.286083 + 0.319185i
\(206\) −6.66119 + 4.83964i −0.464107 + 0.337194i
\(207\) −8.09613 2.63059i −0.562720 0.182839i
\(208\) 0 0
\(209\) 0 0
\(210\) 3.25544 15.1460i 0.224647 1.04518i
\(211\) 6.64050 20.4374i 0.457151 1.40697i −0.411440 0.911437i \(-0.634974\pi\)
0.868591 0.495530i \(-0.165026\pi\)
\(212\) −2.55626 3.51838i −0.175564 0.241644i
\(213\) −10.5597 + 14.5342i −0.723542 + 0.995870i
\(214\) −1.62402 4.99822i −0.111016 0.341671i
\(215\) 7.70536 0.792137i 0.525501 0.0540233i
\(216\) −2.03134 1.47586i −0.138215 0.100419i
\(217\) −4.83032 6.64836i −0.327903 0.451320i
\(218\) −7.53510 2.44830i −0.510341 0.165820i
\(219\) −17.4891 −1.18181
\(220\) 0 0
\(221\) 0 0
\(222\) 20.9938 + 6.82131i 1.40901 + 0.457816i
\(223\) 4.45131 + 6.12670i 0.298081 + 0.410274i 0.931618 0.363439i \(-0.118397\pi\)
−0.633537 + 0.773713i \(0.718397\pi\)
\(224\) 16.3694 + 11.8931i 1.09373 + 0.794639i
\(225\) 1.83882 16.7608i 0.122588 1.11739i
\(226\) −3.93829 12.1208i −0.261971 0.806264i
\(227\) 5.76170 7.93031i 0.382418 0.526353i −0.573805 0.818992i \(-0.694533\pi\)
0.956223 + 0.292639i \(0.0945334\pi\)
\(228\) 8.14459 + 11.2101i 0.539389 + 0.742405i
\(229\) −6.29538 + 19.3752i −0.416010 + 1.28035i 0.495333 + 0.868703i \(0.335046\pi\)
−0.911344 + 0.411646i \(0.864954\pi\)
\(230\) −4.37228 0.939764i −0.288300 0.0619662i
\(231\) 0 0
\(232\) 7.33296i 0.481433i
\(233\) −16.1923 5.26119i −1.06079 0.344672i −0.273896 0.961759i \(-0.588312\pi\)
−0.786894 + 0.617088i \(0.788312\pi\)
\(234\) 0 0
\(235\) −11.0452 + 9.89970i −0.720508 + 0.645785i
\(236\) 0.690248 + 2.12436i 0.0449313 + 0.138284i
\(237\) 30.5970 9.94157i 1.98749 0.645774i
\(238\) −8.14459 + 11.2101i −0.527935 + 0.726641i
\(239\) 2.63370 1.91350i 0.170360 0.123774i −0.499338 0.866407i \(-0.666423\pi\)
0.669698 + 0.742633i \(0.266423\pi\)
\(240\) 3.06447 + 1.77859i 0.197811 + 0.114807i
\(241\) −5.25544 −0.338532 −0.169266 0.985570i \(-0.554140\pi\)
−0.169266 + 0.985570i \(0.554140\pi\)
\(242\) 0 0
\(243\) 22.3692i 1.43498i
\(244\) −4.55632 + 14.0229i −0.291689 + 0.897725i
\(245\) −10.2241 + 4.52419i −0.653192 + 0.289040i
\(246\) 4.44080 + 3.22643i 0.283135 + 0.205709i
\(247\) 0 0
\(248\) −6.02808 + 1.95864i −0.382783 + 0.124374i
\(249\) 13.5466 + 9.84221i 0.858483 + 0.623725i
\(250\) 0.0604866 8.85783i 0.00382551 0.560218i
\(251\) −1.50898 + 4.64416i −0.0952459 + 0.293137i −0.987318 0.158757i \(-0.949251\pi\)
0.892072 + 0.451894i \(0.149251\pi\)
\(252\) 16.0309i 1.00985i
\(253\) 0 0
\(254\) −9.25544 −0.580738
\(255\) −14.3050 + 24.6472i −0.895813 + 1.54347i
\(256\) 11.2317 8.16031i 0.701982 0.510020i
\(257\) 14.0797 19.3790i 0.878265 1.20883i −0.0986329 0.995124i \(-0.531447\pi\)
0.976898 0.213705i \(-0.0685530\pi\)
\(258\) 6.58911 2.14093i 0.410220 0.133289i
\(259\) −11.8149 36.3624i −0.734140 2.25945i
\(260\) 0 0
\(261\) −7.48781 + 5.44021i −0.463484 + 0.336741i
\(262\) 6.58911 + 2.14093i 0.407077 + 0.132267i
\(263\) 14.1514i 0.872610i 0.899799 + 0.436305i \(0.143713\pi\)
−0.899799 + 0.436305i \(0.856287\pi\)
\(264\) 0 0
\(265\) 1.48913 6.92820i 0.0914762 0.425596i
\(266\) −3.39247 + 10.4409i −0.208005 + 0.640175i
\(267\) 6.48745 + 8.92921i 0.397026 + 0.546459i
\(268\) −0.520108 + 0.715868i −0.0317707 + 0.0437286i
\(269\) −3.55033 10.9268i −0.216468 0.666219i −0.999046 0.0436672i \(-0.986096\pi\)
0.782578 0.622552i \(-0.213904\pi\)
\(270\) −0.170259 1.65616i −0.0103617 0.100791i
\(271\) −7.67686 5.57757i −0.466336 0.338813i 0.329675 0.944094i \(-0.393061\pi\)
−0.796012 + 0.605281i \(0.793061\pi\)
\(272\) −1.86278 2.56389i −0.112948 0.155459i
\(273\) 0 0
\(274\) −1.76631 −0.106707
\(275\) 0 0
\(276\) 8.74456 0.526361
\(277\) −7.81561 2.53945i −0.469595 0.152581i 0.0646543 0.997908i \(-0.479406\pi\)
−0.534249 + 0.845327i \(0.679406\pi\)
\(278\) 8.49133 + 11.6873i 0.509276 + 0.700958i
\(279\) −6.47214 4.70228i −0.387477 0.281518i
\(280\) 2.11644 + 20.5873i 0.126482 + 1.23033i
\(281\) 7.25854 + 22.3395i 0.433008 + 1.33266i 0.895114 + 0.445837i \(0.147094\pi\)
−0.462106 + 0.886825i \(0.652906\pi\)
\(282\) −7.79785 + 10.7328i −0.464355 + 0.639130i
\(283\) 2.79417 + 3.84584i 0.166096 + 0.228612i 0.883949 0.467583i \(-0.154875\pi\)
−0.717853 + 0.696195i \(0.754875\pi\)
\(284\) 3.01796 9.28831i 0.179083 0.551160i
\(285\) −4.74456 + 22.0742i −0.281044 + 1.30756i
\(286\) 0 0
\(287\) 9.50744i 0.561207i
\(288\) 18.7333 + 6.08682i 1.10387 + 0.358669i
\(289\) 6.86785 4.98978i 0.403991 0.293517i
\(290\) −3.62078 + 3.24527i −0.212620 + 0.190569i
\(291\) −3.20521 9.86463i −0.187893 0.578275i
\(292\) 9.04212 2.93796i 0.529150 0.171931i
\(293\) −5.93507 + 8.16893i −0.346731 + 0.477234i −0.946392 0.323020i \(-0.895302\pi\)
0.599661 + 0.800254i \(0.295302\pi\)
\(294\) −8.09017 + 5.87785i −0.471828 + 0.342803i
\(295\) −1.82701 + 3.14791i −0.106373 + 0.183279i
\(296\) −29.4891 −1.71402
\(297\) 0 0
\(298\) 9.10268i 0.527304i
\(299\) 0 0
\(300\) 3.52397 + 16.9582i 0.203457 + 0.979084i
\(301\) −9.70820 7.05342i −0.559572 0.406553i
\(302\) −16.7533 + 5.44348i −0.964044 + 0.313237i
\(303\) −14.4047 + 4.68038i −0.827530 + 0.268881i
\(304\) −2.03134 1.47586i −0.116505 0.0846461i
\(305\) −21.9706 + 9.72210i −1.25804 + 0.556686i
\(306\) −4.16837 + 12.8289i −0.238290 + 0.733381i
\(307\) 28.1176i 1.60475i 0.596817 + 0.802377i \(0.296432\pi\)
−0.596817 + 0.802377i \(0.703568\pi\)
\(308\) 0 0
\(309\) 26.2337 1.49238
\(310\) −3.63490 2.10965i −0.206448 0.119820i
\(311\) 14.1490 10.2798i 0.802316 0.582917i −0.109277 0.994011i \(-0.534853\pi\)
0.911593 + 0.411095i \(0.134853\pi\)
\(312\) 0 0
\(313\) −30.2643 + 9.83345i −1.71064 + 0.555820i −0.990439 0.137949i \(-0.955949\pi\)
−0.720198 + 0.693769i \(0.755949\pi\)
\(314\) 1.32172 + 4.06785i 0.0745892 + 0.229562i
\(315\) −19.4519 + 17.4345i −1.09599 + 0.982324i
\(316\) −14.1490 + 10.2798i −0.795943 + 0.578287i
\(317\) −3.34677 1.08743i −0.187973 0.0610763i 0.213518 0.976939i \(-0.431508\pi\)
−0.401491 + 0.915863i \(0.631508\pi\)
\(318\) 6.33830i 0.355434i
\(319\) 0 0
\(320\) 7.37228 + 1.58457i 0.412123 + 0.0885804i
\(321\) −5.17435 + 15.9250i −0.288804 + 0.888848i
\(322\) 4.07230 + 5.60503i 0.226940 + 0.312356i
\(323\) 11.8701 16.3379i 0.660473 0.909063i
\(324\) −3.28415 10.1076i −0.182453 0.561531i
\(325\) 0 0
\(326\) −2.22040 1.61321i −0.122976 0.0893476i
\(327\) 14.8377 + 20.4223i 0.820526 + 1.12936i
\(328\) −6.97406 2.26601i −0.385078 0.125119i
\(329\) 22.9783 1.26683
\(330\) 0 0
\(331\) 3.11684 0.171317 0.0856586 0.996325i \(-0.472701\pi\)
0.0856586 + 0.996325i \(0.472701\pi\)
\(332\) −8.65717 2.81288i −0.475124 0.154377i
\(333\) −21.8775 30.1118i −1.19888 1.65012i
\(334\) −14.3381 10.4172i −0.784544 0.570004i
\(335\) −1.43428 + 0.147449i −0.0783631 + 0.00805600i
\(336\) −1.69623 5.22047i −0.0925371 0.284800i
\(337\) 7.38657 10.1667i 0.402372 0.553818i −0.558965 0.829191i \(-0.688801\pi\)
0.961337 + 0.275373i \(0.0888015\pi\)
\(338\) 6.05403 + 8.33266i 0.329296 + 0.453237i
\(339\) −12.5479 + 38.6186i −0.681510 + 2.09747i
\(340\) 3.25544 15.1460i 0.176551 0.821409i
\(341\) 0 0
\(342\) 10.6873i 0.577901i
\(343\) −6.58911 2.14093i −0.355779 0.115599i
\(344\) −7.48781 + 5.44021i −0.403715 + 0.293316i
\(345\) 9.51022 + 10.6106i 0.512013 + 0.571257i
\(346\) −0.460165 1.41624i −0.0247386 0.0761377i
\(347\) −27.8635 + 9.05339i −1.49579 + 0.486011i −0.938787 0.344499i \(-0.888049\pi\)
−0.557003 + 0.830511i \(0.688049\pi\)
\(348\) 5.58834 7.69168i 0.299566 0.412318i
\(349\) 6.05883 4.40200i 0.324322 0.235634i −0.413696 0.910415i \(-0.635762\pi\)
0.738017 + 0.674782i \(0.235762\pi\)
\(350\) −9.22868 + 10.1561i −0.493294 + 0.542868i
\(351\) 0 0
\(352\) 0 0
\(353\) 21.7244i 1.15627i −0.815941 0.578136i \(-0.803780\pi\)
0.815941 0.578136i \(-0.196220\pi\)
\(354\) −1.00599 + 3.09610i −0.0534675 + 0.164556i
\(355\) 14.5526 6.43960i 0.772373 0.341778i
\(356\) −4.85410 3.52671i −0.257267 0.186915i
\(357\) 41.9877 13.6426i 2.22222 0.722044i
\(358\) 11.9517 3.88335i 0.631668 0.205241i
\(359\) −5.26741 3.82700i −0.278003 0.201981i 0.440043 0.897977i \(-0.354963\pi\)
−0.718046 + 0.695996i \(0.754963\pi\)
\(360\) 8.15270 + 18.4240i 0.429685 + 0.971030i
\(361\) −0.927051 + 2.85317i −0.0487922 + 0.150167i
\(362\) 5.45343i 0.286626i
\(363\) 0 0
\(364\) 0 0
\(365\) 13.3987 + 7.77648i 0.701322 + 0.407040i
\(366\) −17.3851 + 12.6310i −0.908732 + 0.660232i
\(367\) −14.1119 + 19.4234i −0.736637 + 1.01389i 0.262168 + 0.965022i \(0.415563\pi\)
−0.998805 + 0.0488717i \(0.984437\pi\)
\(368\) −1.50702 + 0.489660i −0.0785588 + 0.0255253i
\(369\) −2.86009 8.80244i −0.148890 0.458237i
\(370\) −13.0507 14.5608i −0.678473 0.756979i
\(371\) −8.88159 + 6.45285i −0.461109 + 0.335015i
\(372\) 7.81561 + 2.53945i 0.405221 + 0.131664i
\(373\) 8.21782i 0.425503i 0.977106 + 0.212751i \(0.0682424\pi\)
−0.977106 + 0.212751i \(0.931758\pi\)
\(374\) 0 0
\(375\) −16.7446 + 22.7190i −0.864685 + 1.17321i
\(376\) 5.47665 16.8554i 0.282437 0.869251i
\(377\) 0 0
\(378\) −1.51604 + 2.08665i −0.0779767 + 0.107326i
\(379\) 1.96914 + 6.06040i 0.101148 + 0.311302i 0.988807 0.149199i \(-0.0476697\pi\)
−0.887659 + 0.460501i \(0.847670\pi\)
\(380\) −1.25520 12.2097i −0.0643904 0.626345i
\(381\) 23.8572 + 17.3333i 1.22224 + 0.888010i
\(382\) −6.34636 8.73501i −0.324708 0.446922i
\(383\) −5.41483 1.75938i −0.276685 0.0899003i 0.167388 0.985891i \(-0.446467\pi\)
−0.444073 + 0.895991i \(0.646467\pi\)
\(384\) −22.7446 −1.16068
\(385\) 0 0
\(386\) 18.5109 0.942179
\(387\) −11.1102 3.60991i −0.564762 0.183502i
\(388\) 3.31428 + 4.56171i 0.168257 + 0.231586i
\(389\) −7.97805 5.79639i −0.404503 0.293889i 0.366870 0.930272i \(-0.380429\pi\)
−0.771373 + 0.636384i \(0.780429\pi\)
\(390\) 0 0
\(391\) −3.93829 12.1208i −0.199168 0.612975i
\(392\) 7.85227 10.8077i 0.396599 0.545872i
\(393\) −12.9749 17.8584i −0.654497 0.900838i
\(394\) −0.460165 + 1.41624i −0.0231828 + 0.0713493i
\(395\) −27.8614 5.98844i −1.40186 0.301311i
\(396\) 0 0
\(397\) 23.3639i 1.17260i 0.810095 + 0.586299i \(0.199416\pi\)
−0.810095 + 0.586299i \(0.800584\pi\)
\(398\) −6.02808 1.95864i −0.302160 0.0981778i
\(399\) 28.2980 20.5597i 1.41667 1.02927i
\(400\) −1.55691 2.72522i −0.0778453 0.136261i
\(401\) 3.55033 + 10.9268i 0.177295 + 0.545659i 0.999731 0.0231995i \(-0.00738530\pi\)
−0.822436 + 0.568858i \(0.807385\pi\)
\(402\) −1.22650 + 0.398515i −0.0611724 + 0.0198761i
\(403\) 0 0
\(404\) 6.66119 4.83964i 0.331407 0.240781i
\(405\) 8.69280 14.9775i 0.431949 0.744240i
\(406\) 7.53262 0.373838
\(407\) 0 0
\(408\) 34.0511i 1.68578i
\(409\) 1.39394 4.29010i 0.0689257 0.212132i −0.910661 0.413155i \(-0.864427\pi\)
0.979586 + 0.201023i \(0.0644267\pi\)
\(410\) −1.96756 4.44641i −0.0971706 0.219593i
\(411\) 4.55292 + 3.30789i 0.224579 + 0.163166i
\(412\) −13.5632 + 4.40694i −0.668210 + 0.217114i
\(413\) 5.36261 1.74242i 0.263877 0.0857388i
\(414\) 5.45647 + 3.96435i 0.268171 + 0.194837i
\(415\) −6.00202 13.5638i −0.294628 0.665819i
\(416\) 0 0
\(417\) 46.0280i 2.25400i
\(418\) 0 0
\(419\) −22.9783 −1.12256 −0.561280 0.827626i \(-0.689691\pi\)
−0.561280 + 0.827626i \(0.689691\pi\)
\(420\) 13.4693 23.2073i 0.657233 1.13240i
\(421\) −25.4752 + 18.5088i −1.24159 + 0.902066i −0.997703 0.0677386i \(-0.978422\pi\)
−0.243884 + 0.969804i \(0.578422\pi\)
\(422\) −10.0074 + 13.7740i −0.487151 + 0.670506i
\(423\) 21.2744 6.91246i 1.03439 0.336095i
\(424\) 2.61656 + 8.05295i 0.127072 + 0.391086i
\(425\) 21.9186 12.5220i 1.06321 0.607408i
\(426\) 11.5153 8.36635i 0.557918 0.405351i
\(427\) 35.3986 + 11.5017i 1.71306 + 0.556606i
\(428\) 9.10268i 0.439995i
\(429\) 0 0
\(430\) −6.00000 1.28962i −0.289346 0.0621910i
\(431\) −9.80289 + 30.1702i −0.472189 + 1.45325i 0.377524 + 0.926000i \(0.376776\pi\)
−0.849712 + 0.527247i \(0.823224\pi\)
\(432\) −0.346739 0.477245i −0.0166825 0.0229615i
\(433\) 12.0758 16.6209i 0.580325 0.798749i −0.413406 0.910547i \(-0.635661\pi\)
0.993731 + 0.111798i \(0.0356608\pi\)
\(434\) 2.01197 + 6.19221i 0.0965777 + 0.297236i
\(435\) 15.4107 1.58427i 0.738887 0.0759602i
\(436\) −11.1020 8.06607i −0.531689 0.386295i
\(437\) −5.93507 8.16893i −0.283913 0.390773i
\(438\) 13.1782 + 4.28187i 0.629680 + 0.204595i
\(439\) −1.48913 −0.0710721 −0.0355360 0.999368i \(-0.511314\pi\)
−0.0355360 + 0.999368i \(0.511314\pi\)
\(440\) 0 0
\(441\) 16.8614 0.802924
\(442\) 0 0
\(443\) −8.87034 12.2090i −0.421443 0.580066i 0.544520 0.838748i \(-0.316712\pi\)
−0.965963 + 0.258682i \(0.916712\pi\)
\(444\) 30.9317 + 22.4732i 1.46795 + 1.06653i
\(445\) −0.999811 9.72546i −0.0473956 0.461031i
\(446\) −1.85410 5.70634i −0.0877943 0.270203i
\(447\) −17.0472 + 23.4635i −0.806305 + 1.10978i
\(448\) −6.86646 9.45088i −0.324410 0.446512i
\(449\) 6.75555 20.7914i 0.318814 0.981208i −0.655342 0.755332i \(-0.727476\pi\)
0.974156 0.225876i \(-0.0725245\pi\)
\(450\) −5.48913 + 12.1793i −0.258760 + 0.574136i
\(451\) 0 0
\(452\) 22.0742i 1.03828i
\(453\) 53.3784 + 17.3437i 2.50793 + 0.814877i
\(454\) −6.28308 + 4.56492i −0.294879 + 0.214242i
\(455\) 0 0
\(456\) −8.33674 25.6578i −0.390404 1.20154i
\(457\) −19.7673 + 6.42280i −0.924677 + 0.300446i −0.732384 0.680892i \(-0.761592\pi\)
−0.192293 + 0.981338i \(0.561592\pi\)
\(458\) 9.48726 13.0581i 0.443311 0.610165i
\(459\) 3.83843 2.78878i 0.179163 0.130169i
\(460\) −6.69937 3.88824i −0.312360 0.181290i
\(461\) 32.2337 1.50127 0.750636 0.660716i \(-0.229747\pi\)
0.750636 + 0.660716i \(0.229747\pi\)
\(462\) 0 0
\(463\) 20.1398i 0.935976i 0.883735 + 0.467988i \(0.155021\pi\)
−0.883735 + 0.467988i \(0.844979\pi\)
\(464\) −0.532379 + 1.63849i −0.0247151 + 0.0760651i
\(465\) 5.41857 + 12.2452i 0.251280 + 0.567860i
\(466\) 10.9129 + 7.92871i 0.505532 + 0.367290i
\(467\) 4.18832 1.36087i 0.193813 0.0629735i −0.210502 0.977593i \(-0.567510\pi\)
0.404315 + 0.914620i \(0.367510\pi\)
\(468\) 0 0
\(469\) 1.80709 + 1.31293i 0.0834437 + 0.0606254i
\(470\) 10.7464 4.75532i 0.495694 0.219347i
\(471\) 4.21120 12.9607i 0.194042 0.597199i
\(472\) 4.34896i 0.200177i
\(473\) 0 0
\(474\) −25.4891 −1.17075
\(475\) 13.4501 14.8018i 0.617134 0.679154i
\(476\) −19.4164 + 14.1068i −0.889950 + 0.646586i
\(477\) −6.28181 + 8.64617i −0.287624 + 0.395881i
\(478\) −2.45300 + 0.797029i −0.112198 + 0.0364553i
\(479\) 5.40444 + 16.6331i 0.246935 + 0.759988i 0.995312 + 0.0967144i \(0.0308334\pi\)
−0.748377 + 0.663273i \(0.769167\pi\)
\(480\) −22.0053 24.5515i −1.00440 1.12062i
\(481\) 0 0
\(482\) 3.96002 + 1.28669i 0.180374 + 0.0586071i
\(483\) 22.0742i 1.00441i
\(484\) 0 0
\(485\) −1.93070 + 8.98266i −0.0876687 + 0.407882i
\(486\) 5.47665 16.8554i 0.248426 0.764576i
\(487\) −13.3539 18.3801i −0.605124 0.832881i 0.391042 0.920373i \(-0.372115\pi\)
−0.996165 + 0.0874917i \(0.972115\pi\)
\(488\) 16.8738 23.2248i 0.763843 1.05134i
\(489\) 2.70222 + 8.31657i 0.122199 + 0.376088i
\(490\) 8.81160 0.905863i 0.398067 0.0409227i
\(491\) 23.8572 + 17.3333i 1.07666 + 0.782240i 0.977098 0.212792i \(-0.0682555\pi\)
0.0995629 + 0.995031i \(0.468256\pi\)
\(492\) 5.58834 + 7.69168i 0.251942 + 0.346768i
\(493\) −13.1782 4.28187i −0.593517 0.192846i
\(494\) 0 0
\(495\) 0 0
\(496\) −1.48913 −0.0668637
\(497\) −23.4468 7.61834i −1.05173 0.341729i
\(498\) −7.79785 10.7328i −0.349430 0.480949i
\(499\) −16.1803 11.7557i −0.724331 0.526258i 0.163434 0.986554i \(-0.447743\pi\)
−0.887765 + 0.460297i \(0.847743\pi\)
\(500\) 4.84064 14.5589i 0.216480 0.651096i
\(501\) 17.4494 + 53.7037i 0.779581 + 2.39930i
\(502\) 2.27406 3.12997i 0.101496 0.139698i
\(503\) −0.173369 0.238623i −0.00773016 0.0106397i 0.805134 0.593092i \(-0.202093\pi\)
−0.812865 + 0.582453i \(0.802093\pi\)
\(504\) 9.64502 29.6843i 0.429623 1.32224i
\(505\) 13.1168 + 2.81929i 0.583692 + 0.125457i
\(506\) 0 0
\(507\) 32.8164i 1.45743i
\(508\) −15.2463 4.95382i −0.676444 0.219790i
\(509\) 22.9537 16.6768i 1.01740 0.739187i 0.0516541 0.998665i \(-0.483551\pi\)
0.965749 + 0.259478i \(0.0835507\pi\)
\(510\) 16.8133 15.0696i 0.744507 0.667295i
\(511\) −7.41641 22.8254i −0.328083 1.00973i
\(512\) 6.67716 2.16954i 0.295091 0.0958810i
\(513\) 2.20952 3.04114i 0.0975526 0.134270i
\(514\) −15.3537 + 11.1551i −0.677224 + 0.492032i
\(515\) −20.0981 11.6647i −0.885629 0.514009i
\(516\) 12.0000 0.528271
\(517\) 0 0
\(518\) 30.2921i 1.33096i
\(519\) −1.46615 + 4.51235i −0.0643569 + 0.198070i
\(520\) 0 0
\(521\) −15.0525 10.9363i −0.659464 0.479129i 0.207018 0.978337i \(-0.433624\pi\)
−0.866482 + 0.499209i \(0.833624\pi\)
\(522\) 6.97406 2.26601i 0.305246 0.0991806i
\(523\) −8.65717 + 2.81288i −0.378552 + 0.122999i −0.492111 0.870532i \(-0.663775\pi\)
0.113560 + 0.993531i \(0.463775\pi\)
\(524\) 9.70820 + 7.05342i 0.424105 + 0.308130i
\(525\) 42.8083 8.89570i 1.86831 0.388240i
\(526\) 3.46468 10.6632i 0.151067 0.464937i
\(527\) 11.9769i 0.521721i
\(528\) 0 0
\(529\) 16.6277 0.722944
\(530\) −2.81830 + 4.85589i −0.122419 + 0.210926i
\(531\) 4.44080 3.22643i 0.192714 0.140015i
\(532\) −11.1767 + 15.3834i −0.484570 + 0.666954i
\(533\) 0 0
\(534\) −2.70222 8.31657i −0.116936 0.359893i
\(535\) 11.0452 9.89970i 0.477525 0.428001i
\(536\) 1.39379 1.01264i 0.0602024 0.0437396i
\(537\) −38.0799 12.3729i −1.64327 0.533930i
\(538\) 9.10268i 0.392445i
\(539\) 0 0
\(540\) 0.605969 2.81929i 0.0260768 0.121323i
\(541\) 0.0722135 0.222250i 0.00310470 0.00955529i −0.949492 0.313791i \(-0.898401\pi\)
0.952597 + 0.304235i \(0.0984010\pi\)
\(542\) 4.41903 + 6.08228i 0.189814 + 0.261256i
\(543\) −10.2130 + 14.0570i −0.438282 + 0.603244i
\(544\) 9.11264 + 28.0458i 0.390701 + 1.20245i
\(545\) −2.28670 22.2434i −0.0979516 0.952805i
\(546\) 0 0
\(547\) −5.35042 7.36423i −0.228768 0.314872i 0.679167 0.733984i \(-0.262341\pi\)
−0.907934 + 0.419112i \(0.862341\pi\)
\(548\) −2.90961 0.945389i −0.124292 0.0403850i
\(549\) 36.2337 1.54642
\(550\) 0 0
\(551\) −10.9783 −0.467689
\(552\) −16.1923 5.26119i −0.689189 0.223931i
\(553\) 25.9498 + 35.7169i 1.10350 + 1.51884i
\(554\) 5.26741 + 3.82700i 0.223791 + 0.162593i
\(555\) 6.37108 + 61.9734i 0.270437 + 2.63062i
\(556\) 7.73215 + 23.7971i 0.327916 + 1.00922i
\(557\) −18.9100 + 26.0274i −0.801242 + 1.10281i 0.191375 + 0.981517i \(0.438705\pi\)
−0.992616 + 0.121297i \(0.961295\pi\)
\(558\) 3.72556 + 5.12779i 0.157715 + 0.217077i
\(559\) 0 0
\(560\) −1.02175 + 4.75372i −0.0431768 + 0.200881i
\(561\) 0 0
\(562\) 18.6101i 0.785021i
\(563\) −11.6712 3.79220i −0.491883 0.159822i 0.0525644 0.998618i \(-0.483261\pi\)
−0.544447 + 0.838795i \(0.683261\pi\)
\(564\) −18.5898 + 13.5063i −0.782772 + 0.568717i
\(565\) 26.7848 24.0070i 1.12685 1.00998i
\(566\) −1.16385 3.58198i −0.0489205 0.150562i
\(567\) −25.5149 + 8.29029i −1.07153 + 0.348160i
\(568\) −11.1767 + 15.3834i −0.468963 + 0.645472i
\(569\) 31.3450 22.7735i 1.31405 0.954714i 0.314065 0.949401i \(-0.398309\pi\)
0.999986 0.00531266i \(-0.00169108\pi\)
\(570\) 8.97951 15.4715i 0.376110 0.648031i
\(571\) 21.4891 0.899292 0.449646 0.893207i \(-0.351550\pi\)
0.449646 + 0.893207i \(0.351550\pi\)
\(572\) 0 0
\(573\) 34.4010i 1.43712i
\(574\) −2.32771 + 7.16395i −0.0971567 + 0.299018i
\(575\) −2.56797 12.3577i −0.107092 0.515351i
\(576\) −9.20037 6.68446i −0.383349 0.278519i
\(577\) −30.2643 + 9.83345i −1.25992 + 0.409372i −0.861465 0.507817i \(-0.830453\pi\)
−0.398453 + 0.917189i \(0.630453\pi\)
\(578\) −6.39664 + 2.07839i −0.266065 + 0.0864498i
\(579\) −47.7144 34.6665i −1.98294 1.44069i
\(580\) −7.70141 + 3.40791i −0.319784 + 0.141506i
\(581\) −7.10067 + 21.8536i −0.294585 + 0.906641i
\(582\) 8.21782i 0.340640i
\(583\) 0 0
\(584\) −18.5109 −0.765985
\(585\) 0 0
\(586\) 6.47214 4.70228i 0.267361 0.194249i
\(587\) −16.4626 + 22.6588i −0.679482 + 0.935227i −0.999928 0.0120400i \(-0.996167\pi\)
0.320445 + 0.947267i \(0.396167\pi\)
\(588\) −16.4728 + 5.35233i −0.679326 + 0.220726i
\(589\) −2.93230 9.02469i −0.120823 0.371856i
\(590\) 2.14738 1.92467i 0.0884061 0.0792376i
\(591\) 3.83843 2.78878i 0.157892 0.114715i
\(592\) −6.58911 2.14093i −0.270811 0.0879918i
\(593\) 43.5586i 1.78874i 0.447333 + 0.894368i \(0.352374\pi\)
−0.447333 + 0.894368i \(0.647626\pi\)
\(594\) 0 0
\(595\) −38.2337 8.21782i −1.56743 0.336898i
\(596\) 4.87206 14.9947i 0.199567 0.614205i
\(597\) 11.8701 + 16.3379i 0.485813 + 0.668664i
\(598\) 0 0
\(599\) 10.8089 + 33.2663i 0.441639 + 1.35922i 0.886128 + 0.463440i \(0.153385\pi\)
−0.444490 + 0.895784i \(0.646615\pi\)
\(600\) 3.67763 33.5217i 0.150139 1.36852i
\(601\) 24.6486 + 17.9083i 1.00544 + 0.730494i 0.963247 0.268616i \(-0.0865662\pi\)
0.0421910 + 0.999110i \(0.486566\pi\)
\(602\) 5.58834 + 7.69168i 0.227764 + 0.313490i
\(603\) 2.06805 + 0.671952i 0.0842177 + 0.0273640i
\(604\) −30.5109 −1.24147
\(605\) 0 0
\(606\) 12.0000 0.487467
\(607\) −3.29456 1.07047i −0.133722 0.0434489i 0.241391 0.970428i \(-0.422396\pi\)
−0.375113 + 0.926979i \(0.622396\pi\)
\(608\) 13.7329 + 18.9018i 0.556944 + 0.766567i
\(609\) −19.4164 14.1068i −0.786793 0.571638i
\(610\) 18.9354 1.94662i 0.766670 0.0788163i
\(611\) 0 0
\(612\) −13.7329 + 18.9018i −0.555121 + 0.764058i
\(613\) 25.9498 + 35.7169i 1.04810 + 1.44259i 0.890442 + 0.455097i \(0.150395\pi\)
0.157661 + 0.987493i \(0.449605\pi\)
\(614\) 6.88403 21.1869i 0.277817 0.855032i
\(615\) −3.25544 + 15.1460i −0.131272 + 0.610747i
\(616\) 0 0
\(617\) 3.75906i 0.151334i −0.997133 0.0756669i \(-0.975891\pi\)
0.997133 0.0756669i \(-0.0241086\pi\)
\(618\) −19.7673 6.42280i −0.795159 0.258363i
\(619\) −2.52158 + 1.83203i −0.101351 + 0.0736357i −0.637306 0.770610i \(-0.719951\pi\)
0.535956 + 0.844246i \(0.319951\pi\)
\(620\) −4.85853 5.42071i −0.195123 0.217701i
\(621\) −0.733075 2.25617i −0.0294173 0.0905371i
\(622\) −13.1782 + 4.28187i −0.528399 + 0.171687i
\(623\) −8.90261 + 12.2534i −0.356676 + 0.490922i
\(624\) 0 0
\(625\) 22.9303 9.96006i 0.917211 0.398402i
\(626\) 25.2119 1.00767
\(627\) 0 0
\(628\) 7.40830i 0.295624i
\(629\) 17.2193 52.9955i 0.686578 2.11307i
\(630\) 18.9257 8.37468i 0.754016 0.333655i
\(631\) 13.4345 + 9.76074i 0.534819 + 0.388569i 0.822157 0.569260i \(-0.192770\pi\)
−0.287338 + 0.957829i \(0.592770\pi\)
\(632\) 32.3845 10.5224i 1.28819 0.418557i
\(633\) 51.5908 16.7629i 2.05055 0.666265i
\(634\) 2.25559 + 1.63878i 0.0895809 + 0.0650843i
\(635\) −10.5703 23.8874i −0.419468 0.947941i
\(636\) 3.39247 10.4409i 0.134520 0.414010i
\(637\) 0 0
\(638\) 0 0
\(639\) −24.0000 −0.949425
\(640\) 17.4250 + 10.1133i 0.688785 + 0.399763i
\(641\) 15.8792 11.5369i 0.627189 0.455680i −0.228236 0.973606i \(-0.573296\pi\)
0.855425 + 0.517926i \(0.173296\pi\)
\(642\) 7.79785 10.7328i 0.307757 0.423591i
\(643\) 37.2383 12.0995i 1.46854 0.477156i 0.537871 0.843027i \(-0.319229\pi\)
0.930665 + 0.365871i \(0.119229\pi\)
\(644\) 3.70820 + 11.4127i 0.146124 + 0.449723i
\(645\) 13.0507 + 14.5608i 0.513871 + 0.573330i
\(646\) −12.9443 + 9.40456i −0.509286 + 0.370018i
\(647\) 39.0259 + 12.6803i 1.53426 + 0.498513i 0.949787 0.312897i \(-0.101299\pi\)
0.584478 + 0.811410i \(0.301299\pi\)
\(648\) 20.6920i 0.812860i
\(649\) 0 0
\(650\) 0 0
\(651\) 6.41042 19.7293i 0.251244 0.773250i
\(652\) −2.79417 3.84584i −0.109428 0.150615i
\(653\) −15.0433 + 20.7054i −0.588691 + 0.810263i −0.994615 0.103644i \(-0.966950\pi\)
0.405924 + 0.913907i \(0.366950\pi\)
\(654\) −6.18034 19.0211i −0.241670 0.743785i
\(655\) 1.99962 + 19.4509i 0.0781317 + 0.760010i
\(656\) −1.39379 1.01264i −0.0544182 0.0395371i
\(657\) −13.7329 18.9018i −0.535772 0.737428i
\(658\) −17.3143 5.62577i −0.674983 0.219315i
\(659\) 32.7446 1.27555 0.637774 0.770224i \(-0.279856\pi\)
0.637774 + 0.770224i \(0.279856\pi\)
\(660\) 0 0
\(661\) 35.3505 1.37498 0.687488 0.726196i \(-0.258713\pi\)
0.687488 + 0.726196i \(0.258713\pi\)
\(662\) −2.34857 0.763097i −0.0912799 0.0296586i
\(663\) 0 0
\(664\) 14.3381 + 10.4172i 0.556425 + 0.404266i
\(665\) −30.8214 + 3.16855i −1.19520 + 0.122871i
\(666\) 9.11264 + 28.0458i 0.353108 + 1.08675i
\(667\) −4.07230 + 5.60503i −0.157680 + 0.217028i
\(668\) −18.0431 24.8342i −0.698110 0.960866i
\(669\) −5.90743 + 18.1812i −0.228394 + 0.702926i
\(670\) 1.11684 + 0.240051i 0.0431474 + 0.00927397i
\(671\) 0 0
\(672\) 51.0767i 1.97033i
\(673\) −1.22650 0.398515i −0.0472782 0.0153616i 0.285282 0.958443i \(-0.407913\pi\)
−0.332561 + 0.943082i \(0.607913\pi\)
\(674\) −8.05498 + 5.85228i −0.310266 + 0.225422i
\(675\) 4.07995 2.33086i 0.157037 0.0897149i
\(676\) 5.51276 + 16.9665i 0.212029 + 0.652559i
\(677\) 41.3222 13.4264i 1.58814 0.516019i 0.624004 0.781421i \(-0.285505\pi\)
0.964138 + 0.265403i \(0.0855049\pi\)
\(678\) 18.9100 26.0274i 0.726233 0.999575i
\(679\) 11.5153 8.36635i 0.441916 0.321071i
\(680\) −15.1407 + 26.0872i −0.580620 + 1.00040i
\(681\) 24.7446 0.948214
\(682\) 0 0
\(683\) 44.4434i 1.70058i −0.526314 0.850290i \(-0.676427\pi\)
0.526314 0.850290i \(-0.323573\pi\)
\(684\) −5.72017 + 17.6049i −0.218716 + 0.673140i
\(685\) −2.01723 4.55868i −0.0770745 0.174178i
\(686\) 4.44080 + 3.22643i 0.169550 + 0.123186i
\(687\) −48.9095 + 15.8917i −1.86601 + 0.606305i
\(688\) −2.06805 + 0.671952i −0.0788438 + 0.0256179i
\(689\) 0 0
\(690\) −4.56824 10.3236i −0.173910 0.393013i
\(691\) 4.98710 15.3487i 0.189718 0.583893i −0.810279 0.586044i \(-0.800685\pi\)
0.999998 + 0.00215105i \(0.000684700\pi\)
\(692\) 2.57924i 0.0980480i
\(693\) 0 0
\(694\) 23.2119 0.881113
\(695\) −20.4662 + 35.2629i −0.776327 + 1.33760i
\(696\) −14.9756 + 10.8804i −0.567649 + 0.412421i
\(697\) 8.14459 11.2101i 0.308498 0.424612i
\(698\) −5.64313 + 1.83356i −0.213596 + 0.0694014i
\(699\) −13.2810 40.8747i −0.502334 1.54602i
\(700\) −20.6381 + 11.7905i −0.780047 + 0.445638i
\(701\) −28.7113 + 20.8600i −1.08441 + 0.787871i −0.978447 0.206499i \(-0.933793\pi\)
−0.105964 + 0.994370i \(0.533793\pi\)
\(702\) 0 0
\(703\) 44.1485i 1.66509i
\(704\) 0 0
\(705\) −36.6060 7.86797i −1.37866 0.296325i
\(706\) −5.31878 + 16.3695i −0.200175 + 0.616075i
\(707\) −12.2169 16.8151i −0.459463 0.632397i
\(708\) −3.31428 + 4.56171i −0.124558 + 0.171440i
\(709\) −12.7058 39.1044i −0.477176 1.46860i −0.843000 0.537914i \(-0.819213\pi\)
0.365823 0.930684i \(-0.380787\pi\)
\(710\) −12.5422 + 1.28938i −0.470699 + 0.0483894i
\(711\) 34.7701 + 25.2620i 1.30398 + 0.947398i
\(712\) 6.86646 + 9.45088i 0.257332 + 0.354187i
\(713\) −5.69534 1.85053i −0.213292 0.0693029i
\(714\) −34.9783 −1.30903
\(715\) 0 0
\(716\) 21.7663 0.813445
\(717\) 7.81561 + 2.53945i 0.291879 + 0.0948374i
\(718\) 3.03208 + 4.17330i 0.113156 + 0.155746i
\(719\) 17.2729 + 12.5495i 0.644172 + 0.468018i 0.861281 0.508129i \(-0.169663\pi\)
−0.217109 + 0.976147i \(0.569663\pi\)
\(720\) 0.484059 + 4.70859i 0.0180398 + 0.175479i
\(721\) 11.1246 + 34.2380i 0.414302 + 1.27509i
\(722\) 1.39708 1.92292i 0.0519941 0.0715637i
\(723\) −7.79785 10.7328i −0.290005 0.399158i
\(724\) 2.91886 8.98332i 0.108479 0.333863i
\(725\) −12.5109 5.63858i −0.464642 0.209412i
\(726\) 0 0
\(727\) 15.7908i 0.585650i −0.956166 0.292825i \(-0.905405\pi\)
0.956166 0.292825i \(-0.0945953\pi\)
\(728\) 0 0
\(729\) −26.8866 + 19.5343i −0.995801 + 0.723492i
\(730\) −8.19216 9.14007i −0.303206 0.338289i
\(731\) −5.40444 16.6331i −0.199890 0.615199i
\(732\) −35.3986 + 11.5017i −1.30837 + 0.425115i
\(733\) 17.8052 24.5068i 0.657651 0.905179i −0.341750 0.939791i \(-0.611020\pi\)
0.999401 + 0.0346121i \(0.0110196\pi\)
\(734\) 15.3889 11.1807i 0.568015 0.412687i
\(735\) −24.4096 14.1671i −0.900362 0.522560i
\(736\) 14.7446 0.543492
\(737\) 0 0
\(738\) 7.33296i 0.269930i
\(739\) 0.230083 0.708121i 0.00846372 0.0260487i −0.946735 0.322012i \(-0.895641\pi\)
0.955199 + 0.295964i \(0.0956407\pi\)
\(740\) −13.7047 30.9708i −0.503795 1.13851i
\(741\) 0 0
\(742\) 8.27222 2.68781i 0.303683 0.0986725i
\(743\) 20.7133 6.73017i 0.759898 0.246906i 0.0966632 0.995317i \(-0.469183\pi\)
0.663235 + 0.748411i \(0.269183\pi\)
\(744\) −12.9443 9.40456i −0.474560 0.344788i
\(745\) 23.4931 10.3958i 0.860722 0.380873i
\(746\) 2.01197 6.19221i 0.0736635 0.226713i
\(747\) 22.3692i 0.818446i
\(748\) 0 0
\(749\) −22.9783 −0.839607
\(750\) 18.1795 13.0194i 0.663821 0.475403i
\(751\) −17.4972 + 12.7125i −0.638482 + 0.463884i −0.859328 0.511425i \(-0.829118\pi\)
0.220847 + 0.975309i \(0.429118\pi\)
\(752\) 2.44743 3.36860i 0.0892485 0.122840i
\(753\) −11.7234 + 3.80917i −0.427225 + 0.138814i
\(754\) 0 0
\(755\) −33.1823 37.0218i −1.20763 1.34736i
\(756\) −3.61418 + 2.62586i −0.131447 + 0.0955015i
\(757\) −37.8516 12.2987i −1.37574 0.447005i −0.474473 0.880270i \(-0.657361\pi\)
−0.901266 + 0.433266i \(0.857361\pi\)
\(758\) 5.04868i 0.183376i
\(759\) 0 0
\(760\) −5.02175 + 23.3639i −0.182158 + 0.847496i
\(761\) −6.56829 + 20.2151i −0.238100 + 0.732798i 0.758595 + 0.651563i \(0.225886\pi\)
−0.996695 + 0.0812347i \(0.974114\pi\)
\(762\) −13.7329 18.9018i −0.497491 0.684738i
\(763\) −20.3615 + 28.0252i −0.737135 + 1.01458i
\(764\) −5.77895 17.7858i −0.209075 0.643467i
\(765\) −37.8707 + 3.89324i −1.36922 + 0.140760i
\(766\) 3.64937 + 2.65143i 0.131857 + 0.0957999i
\(767\) 0 0
\(768\) 33.3305 + 10.8297i 1.20271 + 0.390785i
\(769\) −51.2119 −1.84675 −0.923375 0.383900i \(-0.874581\pi\)
−0.923375 + 0.383900i \(0.874581\pi\)
\(770\) 0 0
\(771\) 60.4674 2.17768
\(772\) 30.4926 + 9.90763i 1.09745 + 0.356584i
\(773\) −18.1520 24.9840i −0.652881 0.898613i 0.346339 0.938109i \(-0.387425\pi\)
−0.999220 + 0.0394963i \(0.987425\pi\)
\(774\) 7.48781 + 5.44021i 0.269144 + 0.195544i
\(775\) 1.29354 11.7907i 0.0464654 0.423533i
\(776\) −3.39247 10.4409i −0.121782 0.374808i
\(777\) 56.7299 78.0821i 2.03518 2.80118i
\(778\) 4.59240 + 6.32090i 0.164646 + 0.226615i
\(779\) 3.39247 10.4409i 0.121548 0.374085i
\(780\) 0 0
\(781\) 0 0
\(782\) 10.0974i 0.361081i
\(783\) −2.45300 0.797029i −0.0876632 0.0284835i
\(784\) 2.53918 1.84482i 0.0906848 0.0658864i
\(785\) −8.98922 + 8.05696i −0.320839 + 0.287565i
\(786\) 5.40444 + 16.6331i 0.192770 + 0.593285i
\(787\) 4.52106 1.46898i 0.161158 0.0523635i −0.227327 0.973819i \(-0.572999\pi\)
0.388485 + 0.921455i \(0.372999\pi\)
\(788\) −1.51604 + 2.08665i −0.0540067 + 0.0743338i
\(789\) −28.9004 + 20.9973i −1.02888 + 0.747525i
\(790\) 19.5277 + 11.3337i 0.694764 + 0.403234i
\(791\) −55.7228 −1.98128
\(792\) 0 0
\(793\) 0 0
\(794\) 5.72017 17.6049i 0.203001 0.624774i
\(795\) 16.3585 7.23871i 0.580177 0.256731i
\(796\) −8.88159 6.45285i −0.314800 0.228715i
\(797\) 29.7032 9.65116i 1.05214 0.341862i 0.268633 0.963242i \(-0.413428\pi\)
0.783509 + 0.621381i \(0.213428\pi\)
\(798\) −26.3565 + 8.56373i −0.933008 + 0.303153i
\(799\) 27.0933 + 19.6844i 0.958491 + 0.696385i
\(800\) 5.94191 + 28.5940i 0.210078 + 1.01095i
\(801\) −4.55632 + 14.0229i −0.160990 + 0.495475i
\(802\) 9.10268i 0.321427i
\(803\) 0 0
\(804\) −2.23369 −0.0787761
\(805\) −9.81524 + 16.9115i −0.345942 + 0.596051i
\(806\) 0 0
\(807\) 17.0472 23.4635i 0.600090 0.825953i
\(808\) −15.2463 + 4.95382i −0.536362 + 0.174275i
\(809\) −6.56829 20.2151i −0.230929 0.710726i −0.997635 0.0687282i \(-0.978106\pi\)
0.766707 0.641998i \(-0.221894\pi\)
\(810\) −10.2171 + 9.15746i −0.358991 + 0.321760i
\(811\) 27.6956 20.1221i 0.972525 0.706581i 0.0164996 0.999864i \(-0.494748\pi\)
0.956026 + 0.293283i \(0.0947478\pi\)
\(812\) 12.4083 + 4.03171i 0.435447 + 0.141485i
\(813\) 23.9538i 0.840095i
\(814\) 0 0
\(815\) 1.62772 7.57301i 0.0570165 0.265271i
\(816\) 2.47214 7.60845i 0.0865421 0.266349i
\(817\) −8.14459 11.2101i −0.284943 0.392191i
\(818\) −2.10069 + 2.89135i −0.0734489 + 0.101094i
\(819\) 0 0
\(820\) −0.861244 8.37758i −0.0300759 0.292558i
\(821\) −14.5623 10.5801i −0.508228 0.369249i 0.303923 0.952697i \(-0.401703\pi\)
−0.812151 + 0.583447i \(0.801703\pi\)
\(822\) −2.62080 3.60722i −0.0914108 0.125816i
\(823\) 31.8757 + 10.3570i 1.11112 + 0.361024i 0.806371 0.591410i \(-0.201428\pi\)
0.304746 + 0.952434i \(0.401428\pi\)
\(824\) 27.7663 0.967285
\(825\) 0 0
\(826\) −4.46738 −0.155440
\(827\) 17.1382 + 5.56855i 0.595955 + 0.193638i 0.591436 0.806352i \(-0.298561\pi\)
0.00451961 + 0.999990i \(0.498561\pi\)
\(828\) 6.86646 + 9.45088i 0.238626 + 0.328441i
\(829\) 25.3631 + 18.4274i 0.880897 + 0.640009i 0.933489 0.358607i \(-0.116748\pi\)
−0.0525914 + 0.998616i \(0.516748\pi\)
\(830\) 1.20176 + 11.6899i 0.0417138 + 0.405763i
\(831\) −6.41042 19.7293i −0.222375 0.684400i
\(832\) 0 0
\(833\) 14.8377 + 20.4223i 0.514095 + 0.707592i
\(834\) −11.2690 + 34.6825i −0.390215 + 1.20096i
\(835\) 10.5109 48.9022i 0.363744 1.69233i
\(836\) 0 0
\(837\) 2.22938i 0.0770588i
\(838\) 17.3143 + 5.62577i 0.598114 + 0.194339i
\(839\) 5.75765 4.18318i 0.198776 0.144419i −0.483945 0.875098i \(-0.660796\pi\)
0.682721 + 0.730679i \(0.260796\pi\)
\(840\) −38.9037 + 34.8690i −1.34231 + 1.20310i
\(841\) −6.63378 20.4167i −0.228751 0.704024i
\(842\) 23.7274 7.70949i 0.817699 0.265686i
\(843\) −34.8524 + 47.9702i −1.20038 + 1.65218i
\(844\) −23.8572 + 17.3333i −0.821199 + 0.596636i
\(845\) −14.5917 + 25.1412i −0.501970 + 0.864885i
\(846\) −17.7228 −0.609323
\(847\) 0 0
\(848\) 1.98933i 0.0683140i
\(849\) −3.70820 + 11.4127i −0.127265 + 0.391682i
\(850\) −19.5817 + 4.06913i −0.671646 + 0.139570i
\(851\) −22.5404 16.3765i −0.772673 0.561380i
\(852\) 23.4468 7.61834i 0.803276 0.261000i
\(853\) 23.4468 7.61834i 0.802805 0.260847i 0.121257 0.992621i \(-0.461307\pi\)
0.681547 + 0.731774i \(0.261307\pi\)
\(854\) −23.8572 17.3333i −0.816377 0.593132i
\(855\) −27.5828 + 12.2055i −0.943311 + 0.417419i
\(856\) −5.47665 + 16.8554i −0.187188 + 0.576106i
\(857\) 10.6873i 0.365070i 0.983199 + 0.182535i \(0.0584303\pi\)
−0.983199 + 0.182535i \(0.941570\pi\)
\(858\) 0 0
\(859\) −11.1168 −0.379302 −0.189651 0.981852i \(-0.560736\pi\)
−0.189651 + 0.981852i \(0.560736\pi\)
\(860\) −9.19342 5.33576i −0.313493 0.181948i
\(861\) 19.4164 14.1068i 0.661709 0.480760i
\(862\) 14.7731 20.3335i 0.503175 0.692561i
\(863\) 22.5009 7.31097i 0.765938 0.248868i 0.100113 0.994976i \(-0.468080\pi\)
0.665825 + 0.746108i \(0.268080\pi\)
\(864\) 1.69623 + 5.22047i 0.0577070 + 0.177604i
\(865\) 3.12965 2.80507i 0.106411 0.0953754i
\(866\) −13.1685 + 9.56749i −0.447485 + 0.325117i
\(867\) 20.3806 + 6.62205i 0.692161 + 0.224897i
\(868\) 11.2772i 0.382772i
\(869\) 0 0
\(870\) −12.0000 2.57924i −0.406838 0.0874444i
\(871\) 0 0
\(872\) 15.7045 + 21.6154i 0.531823 + 0.731991i
\(873\) 8.14459 11.2101i 0.275653 0.379403i
\(874\) 2.47214 + 7.60845i 0.0836212 + 0.257360i
\(875\) −36.7517 12.2194i −1.24243 0.413092i
\(876\) 19.4164 + 14.1068i 0.656020 + 0.476626i
\(877\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(878\) 1.12207 + 0.364583i 0.0378680 + 0.0123041i
\(879\) −25.4891 −0.859727
\(880\) 0 0
\(881\) 21.8614 0.736530 0.368265 0.929721i \(-0.379952\pi\)
0.368265 + 0.929721i \(0.379952\pi\)
\(882\) −12.7052 4.12818i −0.427807 0.139003i
\(883\) 14.2530 + 19.6176i 0.479653 + 0.660185i 0.978438 0.206540i \(-0.0662204\pi\)
−0.498785 + 0.866726i \(0.666220\pi\)
\(884\) 0 0
\(885\) −9.13964 + 0.939586i −0.307226 + 0.0315839i
\(886\) 3.69476 + 11.3713i 0.124128 + 0.382027i
\(887\) 8.31796 11.4487i 0.279290 0.384409i −0.646209 0.763161i \(-0.723646\pi\)
0.925498 + 0.378751i \(0.123646\pi\)
\(888\) −43.7550 60.2236i −1.46832 2.02097i
\(889\) −12.5051 + 38.4868i −0.419408 + 1.29080i
\(890\) −1.62772 + 7.57301i −0.0545613 + 0.253848i
\(891\) 0 0
\(892\) 10.3923i 0.347960i
\(893\) 25.2344 + 8.19915i 0.844436 + 0.274374i
\(894\) 18.5898 13.5063i 0.621736 0.451717i
\(895\) 23.6721 + 26.4112i 0.791272 + 0.882829i
\(896\) −9.64502 29.6843i −0.322217 0.991683i
\(897\) 0 0
\(898\) −10.1807 + 14.0126i −0.339736 + 0.467606i
\(899\) −5.26741 + 3.82700i −0.175678 + 0.127637i
\(900\) −15.5609 + 17.1247i −0.518695 + 0.570822i
\(901\) −16.0000 −0.533037
\(902\) 0 0
\(903\) 30.2921i 1.00806i
\(904\) −13.2810 + 40.8747i −0.441720 + 1.35947i
\(905\) 14.0748 6.22815i 0.467861 0.207031i
\(906\) −35.9749 26.1373i −1.19518 0.868353i
\(907\) −18.9258 + 6.14936i −0.628420 + 0.204186i −0.605875 0.795560i \(-0.707177\pi\)
−0.0225451 + 0.999746i \(0.507177\pi\)
\(908\) −12.7933 + 4.15679i −0.424560 + 0.137948i
\(909\) −16.3694 11.8931i −0.542939 0.394468i
\(910\) 0 0
\(911\) −9.42838 + 29.0176i −0.312376 + 0.961395i 0.664445 + 0.747337i \(0.268668\pi\)
−0.976821 + 0.214058i \(0.931332\pi\)
\(912\) 6.33830i 0.209882i
\(913\) 0 0
\(914\) 16.4674 0.544692
\(915\) −52.4541 30.4438i −1.73408 1.00644i
\(916\) 22.6173 16.4324i 0.747296 0.542942i
\(917\) 17.8052 24.5068i 0.587980 0.809285i
\(918\) −3.57507 + 1.16161i −0.117995 + 0.0383389i
\(919\) 1.92632 + 5.92859i 0.0635433 + 0.195566i 0.977788 0.209596i \(-0.0672150\pi\)
−0.914245 + 0.405162i \(0.867215\pi\)
\(920\) 10.0658 + 11.2305i 0.331860 + 0.370260i
\(921\) −57.4226 + 41.7200i −1.89214 + 1.37472i
\(922\) −24.2884 7.89178i −0.799896 0.259902i
\(923\) 0 0
\(924\) 0 0
\(925\) 22.6753 50.3118i 0.745558 1.65424i
\(926\) 4.93083 15.1755i 0.162037 0.498699i
\(927\) 20.5994 + 28.3526i 0.676573 + 0.931222i
\(928\) 9.42272 12.9693i 0.309316 0.425737i
\(929\) 16.3712 + 50.3853i 0.537121 + 1.65309i 0.739021 + 0.673682i \(0.235288\pi\)
−0.201900 + 0.979406i \(0.564712\pi\)
\(930\) −1.08494 10.5535i −0.0355766 0.346064i
\(931\) 16.1803 + 11.7557i 0.530289 + 0.385278i
\(932\) 13.7329 + 18.9018i 0.449837 + 0.619147i
\(933\) 41.9877 + 13.6426i 1.37461 + 0.446639i
\(934\) −3.48913 −0.114168
\(935\) 0 0
\(936\) 0 0
\(937\) 24.6733 + 8.01686i 0.806043 + 0.261899i 0.682921 0.730492i \(-0.260709\pi\)
0.123122 + 0.992392i \(0.460709\pi\)
\(938\) −1.04022 1.43174i −0.0339643 0.0467478i
\(939\) −64.9874 47.2161i −2.12078 1.54084i
\(940\) 20.2475 2.08151i 0.660401 0.0678915i
\(941\) −3.23460 9.95507i −0.105445 0.324526i 0.884390 0.466749i \(-0.154575\pi\)
−0.989835 + 0.142223i \(0.954575\pi\)
\(942\) −6.34636 + 8.73501i −0.206775 + 0.284602i
\(943\) −4.07230 5.60503i −0.132612 0.182525i
\(944\) 0.315738 0.971741i 0.0102764 0.0316275i
\(945\) −7.11684 1.52967i −0.231511 0.0497602i
\(946\) 0 0
\(947\) 56.1802i 1.82561i 0.408393 + 0.912806i \(0.366089\pi\)
−0.408393 + 0.912806i \(0.633911\pi\)
\(948\) −41.9877 13.6426i −1.36370 0.443092i
\(949\) 0 0
\(950\) −13.7587 + 7.86032i −0.446392 + 0.255022i
\(951\) −2.74505 8.44838i −0.0890142 0.273958i
\(952\) 44.4407 14.4397i 1.44033 0.467992i
\(953\) −24.4983 + 33.7190i −0.793578 + 1.09227i 0.200075 + 0.979781i \(0.435881\pi\)
−0.993653 + 0.112486i \(0.964119\pi\)
\(954\) 6.85025 4.97700i 0.221785 0.161136i
\(955\) 15.2963 26.3552i 0.494976 0.852835i
\(956\) −4.46738 −0.144485
\(957\) 0 0
\(958\) 13.8564i 0.447680i
\(959\) −2.38648 + 7.34483i −0.0770635 + 0.237177i
\(960\) 7.70269 + 17.4071i 0.248603 + 0.561810i
\(961\) 20.5266 + 14.9135i 0.662149 + 0.481079i
\(962\) 0 0
\(963\) −21.2744 + 6.91246i −0.685557 + 0.222751i
\(964\) 5.83458 + 4.23907i 0.187919 + 0.136531i
\(965\) 21.1405 + 47.7747i 0.680537 + 1.53792i
\(966\) −5.40444 + 16.6331i −0.173885 + 0.535163i
\(967\) 46.3229i 1.48965i 0.667262 + 0.744823i \(0.267466\pi\)
−0.667262 + 0.744823i \(0.732534\pi\)
\(968\) 0 0
\(969\) 50.9783 1.63766
\(970\) 3.65403 6.29583i 0.117324 0.202147i
\(971\) −43.7639 + 31.7963i −1.40445 + 1.02039i −0.410348 + 0.911929i \(0.634593\pi\)
−0.994100 + 0.108463i \(0.965407\pi\)
\(972\) 18.0431 24.8342i 0.578734 0.796559i
\(973\) 60.0719 19.5185i 1.92582 0.625736i
\(974\) 5.56231 + 17.1190i 0.178228 + 0.548529i
\(975\) 0 0
\(976\) 5.45647 3.96435i 0.174657 0.126896i
\(977\) −26.0237 8.45562i −0.832573 0.270519i −0.138444 0.990370i \(-0.544210\pi\)
−0.694129 + 0.719851i \(0.744210\pi\)
\(978\) 6.92820i 0.221540i
\(979\) 0 0
\(980\) 15.0000 + 3.22405i 0.479157 + 0.102989i
\(981\) −10.4209 + 32.0723i −0.332714 + 1.02399i
\(982\) −13.7329 18.9018i −0.438235 0.603179i
\(983\) 4.79804 6.60394i 0.153034 0.210633i −0.725616 0.688100i \(-0.758445\pi\)
0.878650 + 0.477467i \(0.158445\pi\)
\(984\) −5.72017 17.6049i −0.182353 0.561223i
\(985\) −4.18072 + 0.429792i −0.133209 + 0.0136943i
\(986\) 8.88159 + 6.45285i 0.282847 + 0.205501i
\(987\) 34.0944 + 46.9269i 1.08524 + 1.49370i
\(988\) 0 0
\(989\) −8.74456 −0.278061
\(990\) 0 0
\(991\) −26.9783 −0.856992 −0.428496 0.903544i \(-0.640956\pi\)
−0.428496 + 0.903544i \(0.640956\pi\)
\(992\) 13.1782 + 4.28187i 0.418409 + 0.135949i
\(993\) 4.62467 + 6.36532i 0.146760 + 0.201997i
\(994\) 15.8022 + 11.4810i 0.501216 + 0.364155i
\(995\) −1.82936 17.7948i −0.0579947 0.564132i
\(996\) −7.10067 21.8536i −0.224993 0.692458i
\(997\) −12.9749 + 17.8584i −0.410919 + 0.565582i −0.963442 0.267916i \(-0.913665\pi\)
0.552523 + 0.833498i \(0.313665\pi\)
\(998\) 9.31389 + 12.8195i 0.294826 + 0.405793i
\(999\) 3.20521 9.86463i 0.101408 0.312103i
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 605.2.j.j.9.2 16
5.4 even 2 inner 605.2.j.j.9.3 16
11.2 odd 10 605.2.j.i.124.2 16
11.3 even 5 inner 605.2.j.j.444.2 16
11.4 even 5 605.2.b.c.364.2 4
11.5 even 5 inner 605.2.j.j.269.3 16
11.6 odd 10 605.2.j.i.269.2 16
11.7 odd 10 55.2.b.a.34.3 yes 4
11.8 odd 10 605.2.j.i.444.3 16
11.9 even 5 inner 605.2.j.j.124.3 16
11.10 odd 2 605.2.j.i.9.3 16
33.29 even 10 495.2.c.a.199.2 4
44.7 even 10 880.2.b.h.529.4 4
55.4 even 10 605.2.b.c.364.3 4
55.7 even 20 275.2.a.h.1.2 4
55.9 even 10 inner 605.2.j.j.124.2 16
55.14 even 10 inner 605.2.j.j.444.3 16
55.18 even 20 275.2.a.h.1.3 4
55.19 odd 10 605.2.j.i.444.2 16
55.24 odd 10 605.2.j.i.124.3 16
55.29 odd 10 55.2.b.a.34.2 4
55.37 odd 20 3025.2.a.ba.1.3 4
55.39 odd 10 605.2.j.i.269.3 16
55.48 odd 20 3025.2.a.ba.1.2 4
55.49 even 10 inner 605.2.j.j.269.2 16
55.54 odd 2 605.2.j.i.9.2 16
165.29 even 10 495.2.c.a.199.3 4
165.62 odd 20 2475.2.a.bi.1.3 4
165.128 odd 20 2475.2.a.bi.1.2 4
220.7 odd 20 4400.2.a.cc.1.4 4
220.139 even 10 880.2.b.h.529.1 4
220.183 odd 20 4400.2.a.cc.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.b.a.34.2 4 55.29 odd 10
55.2.b.a.34.3 yes 4 11.7 odd 10
275.2.a.h.1.2 4 55.7 even 20
275.2.a.h.1.3 4 55.18 even 20
495.2.c.a.199.2 4 33.29 even 10
495.2.c.a.199.3 4 165.29 even 10
605.2.b.c.364.2 4 11.4 even 5
605.2.b.c.364.3 4 55.4 even 10
605.2.j.i.9.2 16 55.54 odd 2
605.2.j.i.9.3 16 11.10 odd 2
605.2.j.i.124.2 16 11.2 odd 10
605.2.j.i.124.3 16 55.24 odd 10
605.2.j.i.269.2 16 11.6 odd 10
605.2.j.i.269.3 16 55.39 odd 10
605.2.j.i.444.2 16 55.19 odd 10
605.2.j.i.444.3 16 11.8 odd 10
605.2.j.j.9.2 16 1.1 even 1 trivial
605.2.j.j.9.3 16 5.4 even 2 inner
605.2.j.j.124.2 16 55.9 even 10 inner
605.2.j.j.124.3 16 11.9 even 5 inner
605.2.j.j.269.2 16 55.49 even 10 inner
605.2.j.j.269.3 16 11.5 even 5 inner
605.2.j.j.444.2 16 11.3 even 5 inner
605.2.j.j.444.3 16 55.14 even 10 inner
880.2.b.h.529.1 4 220.139 even 10
880.2.b.h.529.4 4 44.7 even 10
2475.2.a.bi.1.2 4 165.128 odd 20
2475.2.a.bi.1.3 4 165.62 odd 20
3025.2.a.ba.1.2 4 55.48 odd 20
3025.2.a.ba.1.3 4 55.37 odd 20
4400.2.a.cc.1.1 4 220.183 odd 20
4400.2.a.cc.1.4 4 220.7 odd 20