Properties

Label 363.3.h.k.269.1
Level $363$
Weight $3$
Character 363.269
Analytic conductor $9.891$
Analytic rank $0$
Dimension $16$
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,3,Mod(245,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.245");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.h (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: \(9.89103359628\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: 16.0.23612624896000000000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} - 5 x^{14} + 20 x^{13} + 19 x^{12} + 88 x^{11} - 497 x^{10} + 10 x^{9} + 3711 x^{8} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{16} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 269.1
Root \(-0.241376 + 0.447303i\) of defining polynomial
Character \(\chi\) \(=\) 363.269
Dual form 363.3.h.k.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.51626 + 0.817582i) q^{2} +(-0.853491 + 2.87603i) q^{3} +(2.42705 - 1.76336i) q^{4} +(-2.68999 - 0.874032i) q^{5} +(-0.203788 - 7.93464i) q^{6} +(6.05413 - 4.39858i) q^{7} +(1.55513 - 2.14046i) q^{8} +(-7.54311 - 4.90933i) q^{9} +7.48331 q^{10} +(3.00000 + 8.48528i) q^{12} +(6.93741 + 21.3512i) q^{13} +(-11.6376 + 16.0177i) q^{14} +(4.80963 - 6.99053i) q^{15} +(-5.87132 + 18.0701i) q^{16} +(20.1301 + 6.54066i) q^{17} +(22.9942 + 6.18604i) q^{18} +(-12.1083 - 8.79716i) q^{19} +(-8.06998 + 2.62210i) q^{20} +(7.48331 + 21.1660i) q^{21} +31.1127i q^{23} +(4.82873 + 6.29947i) q^{24} +(-13.7533 - 9.99235i) q^{25} +(-34.9127 - 48.0532i) q^{26} +(20.5574 - 17.5041i) q^{27} +(6.93741 - 21.3512i) q^{28} +(-12.4411 - 17.1237i) q^{29} +(-6.38694 + 21.5222i) q^{30} +(9.27051 + 28.5317i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(-20.1301 + 6.54066i) q^{35} +(-26.9644 + 1.38598i) q^{36} +(8.09017 - 5.87785i) q^{37} +(37.6599 + 12.2364i) q^{38} +(-67.3276 + 1.72920i) q^{39} +(-6.05413 + 4.39858i) q^{40} +(24.8821 - 34.2473i) q^{41} +(-36.1349 - 47.1409i) q^{42} -14.9666 q^{43} +(16.0000 + 19.7990i) q^{45} +(-25.4372 - 78.2876i) q^{46} +(-21.6126 + 29.7472i) q^{47} +(-46.9590 - 32.3087i) q^{48} +(2.16312 - 6.65740i) q^{49} +(42.7764 + 13.8989i) q^{50} +(-35.9920 + 52.3123i) q^{51} +(54.4872 + 39.5872i) q^{52} +(-40.3499 + 13.1105i) q^{53} +(-37.4166 + 60.8523i) q^{54} -19.7990i q^{56} +(35.6352 - 27.3154i) q^{57} +(45.3050 + 32.9160i) q^{58} +(19.9501 + 27.4589i) q^{59} +(-0.653574 - 25.4475i) q^{60} +(-30.0621 + 92.5217i) q^{61} +(-46.6540 - 64.2137i) q^{62} +(-67.2610 + 3.45725i) q^{63} +(8.96149 + 27.5806i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(60.3902 - 19.6220i) q^{68} +(-89.4811 - 26.5544i) q^{69} +(45.3050 - 32.9160i) q^{70} +(-61.8699 - 20.1027i) q^{71} +(-22.2388 + 8.51104i) q^{72} +(-60.5413 + 43.9858i) q^{73} +(-15.5513 + 21.4046i) q^{74} +(40.4766 - 31.0265i) q^{75} -44.8999 q^{76} +(168.000 - 59.3970i) q^{78} +(6.93741 + 21.3512i) q^{79} +(31.5876 - 43.4767i) q^{80} +(32.7969 + 74.0632i) q^{81} +(-34.6099 + 106.518i) q^{82} +(20.1301 + 6.54066i) q^{83} +(55.4856 + 38.1752i) q^{84} +(-48.4330 - 35.1887i) q^{85} +(37.6599 - 12.2364i) q^{86} +(59.8665 - 21.1660i) q^{87} +62.2254i q^{89} +(-56.4474 - 36.7381i) q^{90} +(135.915 + 98.7479i) q^{91} +(54.8628 + 75.5121i) q^{92} +(-89.9703 + 2.31073i) q^{93} +(30.0621 - 92.5217i) q^{94} +(24.8821 + 34.2473i) q^{95} +(114.139 + 33.8719i) q^{96} +(22.8673 + 70.3782i) q^{97} +18.5203i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} + 12 q^{4} + 28 q^{9} + 48 q^{12} + 32 q^{15} + 76 q^{16} - 68 q^{25} - 92 q^{27} - 120 q^{31} - 896 q^{34} - 84 q^{36} + 40 q^{37} + 224 q^{42} + 256 q^{45} - 76 q^{48} - 28 q^{49} + 224 q^{58}+ \cdots - 296 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51626 + 0.817582i −1.25813 + 0.408791i −0.860828 0.508897i \(-0.830053\pi\)
−0.397302 + 0.917688i \(0.630053\pi\)
\(3\) −0.853491 + 2.87603i −0.284497 + 0.958677i
\(4\) 2.42705 1.76336i 0.606763 0.440839i
\(5\) −2.68999 0.874032i −0.537999 0.174806i 0.0273993 0.999625i \(-0.491277\pi\)
−0.565398 + 0.824818i \(0.691277\pi\)
\(6\) −0.203788 7.93464i −0.0339646 1.32244i
\(7\) 6.05413 4.39858i 0.864876 0.628369i −0.0643314 0.997929i \(-0.520491\pi\)
0.929207 + 0.369560i \(0.120491\pi\)
\(8\) 1.55513 2.14046i 0.194392 0.267557i
\(9\) −7.54311 4.90933i −0.838123 0.545481i
\(10\) 7.48331 0.748331
\(11\) 0 0
\(12\) 3.00000 + 8.48528i 0.250000 + 0.707107i
\(13\) 6.93741 + 21.3512i 0.533647 + 1.64240i 0.746554 + 0.665325i \(0.231707\pi\)
−0.212907 + 0.977073i \(0.568293\pi\)
\(14\) −11.6376 + 16.0177i −0.831254 + 1.14412i
\(15\) 4.80963 6.99053i 0.320642 0.466035i
\(16\) −5.87132 + 18.0701i −0.366958 + 1.12938i
\(17\) 20.1301 + 6.54066i 1.18412 + 0.384745i 0.833896 0.551921i \(-0.186105\pi\)
0.350225 + 0.936665i \(0.386105\pi\)
\(18\) 22.9942 + 6.18604i 1.27746 + 0.343669i
\(19\) −12.1083 8.79716i −0.637277 0.463009i 0.221637 0.975129i \(-0.428860\pi\)
−0.858914 + 0.512121i \(0.828860\pi\)
\(20\) −8.06998 + 2.62210i −0.403499 + 0.131105i
\(21\) 7.48331 + 21.1660i 0.356348 + 1.00791i
\(22\) 0 0
\(23\) 31.1127i 1.35273i 0.736568 + 0.676363i \(0.236445\pi\)
−0.736568 + 0.676363i \(0.763555\pi\)
\(24\) 4.82873 + 6.29947i 0.201197 + 0.262478i
\(25\) −13.7533 9.99235i −0.550132 0.399694i
\(26\) −34.9127 48.0532i −1.34279 1.84820i
\(27\) 20.5574 17.5041i 0.761384 0.648301i
\(28\) 6.93741 21.3512i 0.247765 0.762542i
\(29\) −12.4411 17.1237i −0.429002 0.590471i 0.538722 0.842484i \(-0.318907\pi\)
−0.967724 + 0.252013i \(0.918907\pi\)
\(30\) −6.38694 + 21.5222i −0.212898 + 0.717408i
\(31\) 9.27051 + 28.5317i 0.299049 + 0.920377i 0.981831 + 0.189756i \(0.0607696\pi\)
−0.682783 + 0.730622i \(0.739230\pi\)
\(32\) 39.6863i 1.24020i
\(33\) 0 0
\(34\) −56.0000 −1.64706
\(35\) −20.1301 + 6.54066i −0.575145 + 0.186876i
\(36\) −26.9644 + 1.38598i −0.749011 + 0.0384995i
\(37\) 8.09017 5.87785i 0.218653 0.158861i −0.473067 0.881026i \(-0.656853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(38\) 37.6599 + 12.2364i 0.991050 + 0.322012i
\(39\) −67.3276 + 1.72920i −1.72635 + 0.0443383i
\(40\) −6.05413 + 4.39858i −0.151353 + 0.109965i
\(41\) 24.8821 34.2473i 0.606881 0.835301i −0.389435 0.921054i \(-0.627330\pi\)
0.996316 + 0.0857534i \(0.0273297\pi\)
\(42\) −36.1349 47.1409i −0.860355 1.12240i
\(43\) −14.9666 −0.348061 −0.174031 0.984740i \(-0.555679\pi\)
−0.174031 + 0.984740i \(0.555679\pi\)
\(44\) 0 0
\(45\) 16.0000 + 19.7990i 0.355556 + 0.439978i
\(46\) −25.4372 78.2876i −0.552982 1.70190i
\(47\) −21.6126 + 29.7472i −0.459843 + 0.632919i −0.974476 0.224491i \(-0.927928\pi\)
0.514634 + 0.857410i \(0.327928\pi\)
\(48\) −46.9590 32.3087i −0.978312 0.673099i
\(49\) 2.16312 6.65740i 0.0441453 0.135865i
\(50\) 42.7764 + 13.8989i 0.855528 + 0.277978i
\(51\) −35.9920 + 52.3123i −0.705725 + 1.02573i
\(52\) 54.4872 + 39.5872i 1.04783 + 0.761293i
\(53\) −40.3499 + 13.1105i −0.761319 + 0.247368i −0.663845 0.747870i \(-0.731076\pi\)
−0.0974744 + 0.995238i \(0.531076\pi\)
\(54\) −37.4166 + 60.8523i −0.692900 + 1.12689i
\(55\) 0 0
\(56\) 19.7990i 0.353553i
\(57\) 35.6352 27.3154i 0.625179 0.479218i
\(58\) 45.3050 + 32.9160i 0.781120 + 0.567517i
\(59\) 19.9501 + 27.4589i 0.338137 + 0.465406i 0.943896 0.330242i \(-0.107130\pi\)
−0.605759 + 0.795648i \(0.707130\pi\)
\(60\) −0.653574 25.4475i −0.0108929 0.424124i
\(61\) −30.0621 + 92.5217i −0.492822 + 1.51675i 0.327502 + 0.944850i \(0.393793\pi\)
−0.820324 + 0.571899i \(0.806207\pi\)
\(62\) −46.6540 64.2137i −0.752484 1.03571i
\(63\) −67.2610 + 3.45725i −1.06764 + 0.0548770i
\(64\) 8.96149 + 27.5806i 0.140023 + 0.430947i
\(65\) 63.4980i 0.976893i
\(66\) 0 0
\(67\) −42.0000 −0.626866 −0.313433 0.949610i \(-0.601479\pi\)
−0.313433 + 0.949610i \(0.601479\pi\)
\(68\) 60.3902 19.6220i 0.888091 0.288558i
\(69\) −89.4811 26.5544i −1.29683 0.384846i
\(70\) 45.3050 32.9160i 0.647214 0.470228i
\(71\) −61.8699 20.1027i −0.871407 0.283137i −0.161022 0.986951i \(-0.551479\pi\)
−0.710385 + 0.703814i \(0.751479\pi\)
\(72\) −22.2388 + 8.51104i −0.308872 + 0.118209i
\(73\) −60.5413 + 43.9858i −0.829333 + 0.602545i −0.919370 0.393393i \(-0.871301\pi\)
0.0900377 + 0.995938i \(0.471301\pi\)
\(74\) −15.5513 + 21.4046i −0.210153 + 0.289251i
\(75\) 40.4766 31.0265i 0.539688 0.413687i
\(76\) −44.8999 −0.590788
\(77\) 0 0
\(78\) 168.000 59.3970i 2.15385 0.761500i
\(79\) 6.93741 + 21.3512i 0.0878154 + 0.270268i 0.985315 0.170748i \(-0.0546183\pi\)
−0.897499 + 0.441016i \(0.854618\pi\)
\(80\) 31.5876 43.4767i 0.394846 0.543458i
\(81\) 32.7969 + 74.0632i 0.404900 + 0.914361i
\(82\) −34.6099 + 106.518i −0.422072 + 1.29900i
\(83\) 20.1301 + 6.54066i 0.242531 + 0.0788031i 0.427760 0.903892i \(-0.359303\pi\)
−0.185229 + 0.982695i \(0.559303\pi\)
\(84\) 55.4856 + 38.1752i 0.660543 + 0.454467i
\(85\) −48.4330 35.1887i −0.569800 0.413984i
\(86\) 37.6599 12.2364i 0.437906 0.142284i
\(87\) 59.8665 21.1660i 0.688121 0.243287i
\(88\) 0 0
\(89\) 62.2254i 0.699162i 0.936906 + 0.349581i \(0.113676\pi\)
−0.936906 + 0.349581i \(0.886324\pi\)
\(90\) −56.4474 36.7381i −0.627194 0.408201i
\(91\) 135.915 + 98.7479i 1.49357 + 1.08514i
\(92\) 54.8628 + 75.5121i 0.596334 + 0.820784i
\(93\) −89.9703 + 2.31073i −0.967423 + 0.0248466i
\(94\) 30.0621 92.5217i 0.319810 0.984274i
\(95\) 24.8821 + 34.2473i 0.261917 + 0.360498i
\(96\) 114.139 + 33.8719i 1.18895 + 0.352832i
\(97\) 22.8673 + 70.3782i 0.235745 + 0.725548i 0.997022 + 0.0771212i \(0.0245728\pi\)
−0.761277 + 0.648427i \(0.775427\pi\)
\(98\) 18.5203i 0.188982i
\(99\) 0 0
\(100\) −51.0000 −0.510000
\(101\) −140.911 + 45.7846i −1.39515 + 0.453313i −0.907620 0.419792i \(-0.862103\pi\)
−0.487533 + 0.873105i \(0.662103\pi\)
\(102\) 47.7955 161.058i 0.468583 1.57900i
\(103\) −27.5066 + 19.9847i −0.267054 + 0.194026i −0.713251 0.700909i \(-0.752778\pi\)
0.446197 + 0.894935i \(0.352778\pi\)
\(104\) 56.4899 + 18.3547i 0.543172 + 0.176487i
\(105\) −1.63030 63.4771i −0.0155267 0.604544i
\(106\) 90.8119 65.9787i 0.856716 0.622441i
\(107\) 24.8821 34.2473i 0.232543 0.320068i −0.676759 0.736205i \(-0.736616\pi\)
0.909302 + 0.416136i \(0.136616\pi\)
\(108\) 19.0277 78.7334i 0.176183 0.729013i
\(109\) 67.3498 0.617888 0.308944 0.951080i \(-0.400024\pi\)
0.308944 + 0.951080i \(0.400024\pi\)
\(110\) 0 0
\(111\) 10.0000 + 28.2843i 0.0900901 + 0.254813i
\(112\) 43.9370 + 135.224i 0.392294 + 1.20736i
\(113\) 69.8253 96.1063i 0.617923 0.850498i −0.379276 0.925283i \(-0.623827\pi\)
0.997200 + 0.0747850i \(0.0238271\pi\)
\(114\) −67.3348 + 97.8674i −0.590656 + 0.858486i
\(115\) 27.1935 83.6930i 0.236465 0.727765i
\(116\) −60.3902 19.6220i −0.520605 0.169155i
\(117\) 52.4903 195.112i 0.448635 1.66763i
\(118\) −72.6495 52.7830i −0.615674 0.447313i
\(119\) 150.640 48.9458i 1.26588 0.411309i
\(120\) −7.48331 21.1660i −0.0623610 0.176383i
\(121\) 0 0
\(122\) 257.387i 2.10973i
\(123\) 77.2597 + 100.792i 0.628128 + 0.819444i
\(124\) 72.8115 + 52.9007i 0.587190 + 0.426618i
\(125\) 69.8253 + 96.1063i 0.558603 + 0.768851i
\(126\) 166.420 63.6908i 1.32079 0.505482i
\(127\) 20.8122 64.0535i 0.163876 0.504358i −0.835076 0.550135i \(-0.814576\pi\)
0.998952 + 0.0457767i \(0.0145763\pi\)
\(128\) 48.2091 + 66.3542i 0.376634 + 0.518392i
\(129\) 12.7739 43.0445i 0.0990223 0.333678i
\(130\) 51.9149 + 159.777i 0.399345 + 1.22906i
\(131\) 232.826i 1.77730i 0.458587 + 0.888649i \(0.348356\pi\)
−0.458587 + 0.888649i \(0.651644\pi\)
\(132\) 0 0
\(133\) −112.000 −0.842105
\(134\) 105.683 34.3384i 0.788678 0.256257i
\(135\) −70.5984 + 29.1182i −0.522951 + 0.215691i
\(136\) 45.3050 32.9160i 0.333125 0.242029i
\(137\) −150.640 48.9458i −1.09956 0.357269i −0.297626 0.954682i \(-0.596195\pi\)
−0.801933 + 0.597414i \(0.796195\pi\)
\(138\) 246.868 6.34038i 1.78890 0.0459448i
\(139\) 72.6495 52.7830i 0.522659 0.379734i −0.294946 0.955514i \(-0.595302\pi\)
0.817604 + 0.575780i \(0.195302\pi\)
\(140\) −37.3232 + 51.3710i −0.266594 + 0.366936i
\(141\) −67.1077 87.5475i −0.475941 0.620904i
\(142\) 172.116 1.21209
\(143\) 0 0
\(144\) 133.000 107.480i 0.923611 0.746390i
\(145\) 18.4998 + 56.9364i 0.127585 + 0.392665i
\(146\) 116.376 160.177i 0.797093 1.09710i
\(147\) 17.3007 + 11.9032i 0.117692 + 0.0809743i
\(148\) 9.27051 28.5317i 0.0626386 0.192782i
\(149\) 20.1301 + 6.54066i 0.135101 + 0.0438970i 0.375787 0.926706i \(-0.377372\pi\)
−0.240686 + 0.970603i \(0.577372\pi\)
\(150\) −76.4829 + 111.164i −0.509886 + 0.741091i
\(151\) 54.4872 + 39.5872i 0.360842 + 0.262167i 0.753403 0.657559i \(-0.228411\pi\)
−0.392561 + 0.919726i \(0.628411\pi\)
\(152\) −37.6599 + 12.2364i −0.247763 + 0.0805030i
\(153\) −119.733 148.162i −0.782569 0.968380i
\(154\) 0 0
\(155\) 84.8528i 0.547438i
\(156\) −160.358 + 122.919i −1.02794 + 0.787945i
\(157\) −69.5755 50.5495i −0.443156 0.321972i 0.343732 0.939068i \(-0.388309\pi\)
−0.786888 + 0.617096i \(0.788309\pi\)
\(158\) −34.9127 48.0532i −0.220966 0.304134i
\(159\) −3.26787 127.237i −0.0205527 0.800234i
\(160\) −34.6871 + 106.756i −0.216794 + 0.667224i
\(161\) 136.852 + 188.360i 0.850011 + 1.16994i
\(162\) −143.078 159.548i −0.883200 0.984865i
\(163\) −4.32624 13.3148i −0.0265413 0.0816858i 0.936908 0.349575i \(-0.113674\pi\)
−0.963450 + 0.267889i \(0.913674\pi\)
\(164\) 126.996i 0.774366i
\(165\) 0 0
\(166\) −56.0000 −0.337349
\(167\) 80.5203 26.1626i 0.482157 0.156662i −0.0578456 0.998326i \(-0.518423\pi\)
0.540003 + 0.841663i \(0.318423\pi\)
\(168\) 56.9425 + 16.8983i 0.338943 + 0.100585i
\(169\) −271.021 + 196.908i −1.60367 + 1.16514i
\(170\) 150.640 + 48.9458i 0.886116 + 0.287916i
\(171\) 48.1457 + 125.801i 0.281554 + 0.735681i
\(172\) −36.3248 + 26.3915i −0.211191 + 0.153439i
\(173\) −111.970 + 154.113i −0.647223 + 0.890826i −0.998975 0.0452670i \(-0.985586\pi\)
0.351752 + 0.936093i \(0.385586\pi\)
\(174\) −133.335 + 102.205i −0.766291 + 0.587385i
\(175\) −127.216 −0.726951
\(176\) 0 0
\(177\) −96.0000 + 33.9411i −0.542373 + 0.191758i
\(178\) −50.8744 156.575i −0.285811 0.879636i
\(179\) −186.201 + 256.284i −1.04023 + 1.43175i −0.143245 + 0.989687i \(0.545754\pi\)
−0.896983 + 0.442064i \(0.854246\pi\)
\(180\) 73.7455 + 19.8395i 0.409697 + 0.110219i
\(181\) −80.9625 + 249.177i −0.447306 + 1.37667i 0.432628 + 0.901572i \(0.357586\pi\)
−0.879935 + 0.475095i \(0.842414\pi\)
\(182\) −422.732 137.354i −2.32270 0.754691i
\(183\) −240.438 165.426i −1.31387 0.903967i
\(184\) 66.5954 + 48.3844i 0.361932 + 0.262959i
\(185\) −26.8999 + 8.74032i −0.145405 + 0.0472450i
\(186\) 224.499 79.3725i 1.20699 0.426734i
\(187\) 0 0
\(188\) 110.309i 0.586748i
\(189\) 47.4635 196.396i 0.251130 1.03913i
\(190\) −90.6099 65.8319i −0.476894 0.346484i
\(191\) −34.9127 48.0532i −0.182789 0.251587i 0.707783 0.706430i \(-0.249695\pi\)
−0.890572 + 0.454843i \(0.849695\pi\)
\(192\) −86.9713 + 2.23371i −0.452976 + 0.0116339i
\(193\) 46.2494 142.341i 0.239634 0.737519i −0.756838 0.653602i \(-0.773257\pi\)
0.996473 0.0839167i \(-0.0267430\pi\)
\(194\) −115.080 158.394i −0.593195 0.816463i
\(195\) 182.622 + 54.1950i 0.936525 + 0.277923i
\(196\) −6.48936 19.9722i −0.0331090 0.101899i
\(197\) 232.826i 1.18186i 0.806723 + 0.590929i \(0.201239\pi\)
−0.806723 + 0.590929i \(0.798761\pi\)
\(198\) 0 0
\(199\) 222.000 1.11558 0.557789 0.829983i \(-0.311650\pi\)
0.557789 + 0.829983i \(0.311650\pi\)
\(200\) −42.7764 + 13.8989i −0.213882 + 0.0694945i
\(201\) 35.8466 120.793i 0.178341 0.600962i
\(202\) 317.135 230.412i 1.56997 1.14065i
\(203\) −150.640 48.9458i −0.742067 0.241112i
\(204\) 4.89090 + 190.431i 0.0239750 + 0.933487i
\(205\) −96.8661 + 70.3773i −0.472517 + 0.343304i
\(206\) 52.8745 72.7756i 0.256673 0.353279i
\(207\) 152.743 234.686i 0.737887 1.13375i
\(208\) −426.549 −2.05072
\(209\) 0 0
\(210\) 56.0000 + 158.392i 0.266667 + 0.754247i
\(211\) −120.249 370.087i −0.569898 1.75397i −0.652929 0.757419i \(-0.726460\pi\)
0.0830307 0.996547i \(-0.473540\pi\)
\(212\) −74.8128 + 102.971i −0.352891 + 0.485713i
\(213\) 110.621 160.782i 0.519350 0.754846i
\(214\) −34.6099 + 106.518i −0.161729 + 0.497749i
\(215\) 40.2601 + 13.0813i 0.187256 + 0.0608433i
\(216\) −5.49743 71.2234i −0.0254511 0.329738i
\(217\) 181.624 + 131.957i 0.836976 + 0.608099i
\(218\) −169.470 + 55.0640i −0.777384 + 0.252587i
\(219\) −74.8331 211.660i −0.341704 0.966484i
\(220\) 0 0
\(221\) 475.176i 2.15012i
\(222\) −48.2873 62.9947i −0.217510 0.283760i
\(223\) 37.2148 + 27.0381i 0.166882 + 0.121247i 0.668092 0.744079i \(-0.267111\pi\)
−0.501209 + 0.865326i \(0.667111\pi\)
\(224\) −174.563 240.266i −0.779301 1.07262i
\(225\) 54.6868 + 142.893i 0.243052 + 0.635079i
\(226\) −97.1238 + 298.916i −0.429751 + 1.32264i
\(227\) 124.411 + 171.237i 0.548065 + 0.754346i 0.989748 0.142825i \(-0.0456185\pi\)
−0.441683 + 0.897171i \(0.645619\pi\)
\(228\) 38.3216 129.133i 0.168077 0.566375i
\(229\) 36.4640 + 112.225i 0.159231 + 0.490064i 0.998565 0.0535527i \(-0.0170545\pi\)
−0.839334 + 0.543617i \(0.817055\pi\)
\(230\) 232.826i 1.01229i
\(231\) 0 0
\(232\) −56.0000 −0.241379
\(233\) 80.5203 26.1626i 0.345581 0.112286i −0.131084 0.991371i \(-0.541846\pi\)
0.476664 + 0.879085i \(0.341846\pi\)
\(234\) 27.4411 + 533.868i 0.117270 + 2.28149i
\(235\) 84.1378 61.1297i 0.358033 0.260126i
\(236\) 96.8398 + 31.4652i 0.410338 + 0.133327i
\(237\) −67.3276 + 1.72920i −0.284083 + 0.00729618i
\(238\) −339.031 + 246.321i −1.42450 + 1.03496i
\(239\) 24.8821 34.2473i 0.104109 0.143294i −0.753784 0.657123i \(-0.771773\pi\)
0.857893 + 0.513829i \(0.171773\pi\)
\(240\) 98.0805 + 127.954i 0.408669 + 0.533142i
\(241\) 149.666 0.621022 0.310511 0.950570i \(-0.399500\pi\)
0.310511 + 0.950570i \(0.399500\pi\)
\(242\) 0 0
\(243\) −241.000 + 31.1127i −0.991770 + 0.128036i
\(244\) 90.1864 + 277.565i 0.369616 + 1.13756i
\(245\) −11.6376 + 16.0177i −0.0475002 + 0.0653784i
\(246\) −276.811 190.452i −1.12525 0.774193i
\(247\) 103.830 319.555i 0.420363 1.29374i
\(248\) 75.4878 + 24.5275i 0.304386 + 0.0989011i
\(249\) −35.9920 + 52.3123i −0.144546 + 0.210090i
\(250\) −254.273 184.740i −1.01709 0.738962i
\(251\) 48.4199 15.7326i 0.192908 0.0626796i −0.210970 0.977493i \(-0.567662\pi\)
0.403878 + 0.914813i \(0.367662\pi\)
\(252\) −157.150 + 126.996i −0.623610 + 0.503953i
\(253\) 0 0
\(254\) 178.191i 0.701539i
\(255\) 142.541 109.262i 0.558984 0.428477i
\(256\) −269.403 195.732i −1.05235 0.764580i
\(257\) 56.5253 + 77.8004i 0.219943 + 0.302725i 0.904703 0.426044i \(-0.140093\pi\)
−0.684760 + 0.728769i \(0.740093\pi\)
\(258\) 3.05001 + 118.755i 0.0118218 + 0.460290i
\(259\) 23.1247 71.1706i 0.0892846 0.274790i
\(260\) −111.970 154.113i −0.430652 0.592742i
\(261\) 9.77858 + 190.243i 0.0374658 + 0.728900i
\(262\) −190.354 585.851i −0.726544 2.23607i
\(263\) 465.652i 1.77054i −0.465077 0.885270i \(-0.653973\pi\)
0.465077 0.885270i \(-0.346027\pi\)
\(264\) 0 0
\(265\) 120.000 0.452830
\(266\) 281.821 91.5692i 1.05948 0.344245i
\(267\) −178.962 53.1088i −0.670270 0.198909i
\(268\) −101.936 + 74.0609i −0.380359 + 0.276347i
\(269\) 352.389 + 114.498i 1.31000 + 0.425644i 0.879048 0.476733i \(-0.158179\pi\)
0.430949 + 0.902376i \(0.358179\pi\)
\(270\) 153.837 130.989i 0.569767 0.485144i
\(271\) 272.436 197.936i 1.00530 0.730392i 0.0420805 0.999114i \(-0.486601\pi\)
0.963218 + 0.268722i \(0.0866014\pi\)
\(272\) −236.380 + 325.350i −0.869045 + 1.19614i
\(273\) −400.004 + 306.615i −1.46522 + 1.12313i
\(274\) 419.066 1.52944
\(275\) 0 0
\(276\) −264.000 + 93.3381i −0.956522 + 0.338182i
\(277\) 6.93741 + 21.3512i 0.0250448 + 0.0770800i 0.962798 0.270223i \(-0.0870975\pi\)
−0.937753 + 0.347303i \(0.887097\pi\)
\(278\) −139.651 + 192.213i −0.502340 + 0.691412i
\(279\) 70.1431 260.730i 0.251409 0.934515i
\(280\) −17.3050 + 53.2592i −0.0618034 + 0.190211i
\(281\) 20.1301 + 6.54066i 0.0716373 + 0.0232764i 0.344616 0.938744i \(-0.388009\pi\)
−0.272979 + 0.962020i \(0.588009\pi\)
\(282\) 240.438 + 165.426i 0.852615 + 0.586617i
\(283\) −145.299 105.566i −0.513424 0.373025i 0.300697 0.953720i \(-0.402781\pi\)
−0.814121 + 0.580695i \(0.802781\pi\)
\(284\) −185.610 + 60.3082i −0.653555 + 0.212353i
\(285\) −119.733 + 42.3320i −0.420116 + 0.148533i
\(286\) 0 0
\(287\) 316.784i 1.10378i
\(288\) −194.833 + 299.358i −0.676504 + 1.03944i
\(289\) 128.634 + 93.4579i 0.445099 + 0.323384i
\(290\) −93.1004 128.142i −0.321036 0.441868i
\(291\) −221.927 + 5.69981i −0.762635 + 0.0195870i
\(292\) −69.3741 + 213.512i −0.237583 + 0.731204i
\(293\) −12.4411 17.1237i −0.0424610 0.0584425i 0.787259 0.616623i \(-0.211500\pi\)
−0.829720 + 0.558180i \(0.811500\pi\)
\(294\) −53.2648 15.8069i −0.181173 0.0537649i
\(295\) −29.6656 91.3014i −0.100561 0.309496i
\(296\) 26.4575i 0.0893835i
\(297\) 0 0
\(298\) −56.0000 −0.187919
\(299\) −664.292 + 215.842i −2.22171 + 0.721879i
\(300\) 43.5280 146.678i 0.145093 0.488925i
\(301\) −90.6099 + 65.8319i −0.301030 + 0.218711i
\(302\) −169.470 55.0640i −0.561158 0.182331i
\(303\) −11.4121 444.340i −0.0376637 1.46647i
\(304\) 230.057 167.146i 0.756766 0.549823i
\(305\) 161.734 222.608i 0.530275 0.729861i
\(306\) 422.414 + 274.923i 1.38044 + 0.898440i
\(307\) 149.666 0.487512 0.243756 0.969837i \(-0.421620\pi\)
0.243756 + 0.969837i \(0.421620\pi\)
\(308\) 0 0
\(309\) −34.0000 96.1665i −0.110032 0.311219i
\(310\) 69.3741 + 213.512i 0.223788 + 0.688747i
\(311\) 14.9626 20.5942i 0.0481112 0.0662193i −0.784284 0.620402i \(-0.786969\pi\)
0.832395 + 0.554183i \(0.186969\pi\)
\(312\) −101.002 + 146.801i −0.323725 + 0.470516i
\(313\) 122.989 378.520i 0.392935 1.20933i −0.537622 0.843186i \(-0.680677\pi\)
0.930558 0.366145i \(-0.119323\pi\)
\(314\) 216.398 + 70.3121i 0.689166 + 0.223924i
\(315\) 183.954 + 49.4883i 0.583980 + 0.157106i
\(316\) 54.4872 + 39.5872i 0.172428 + 0.125276i
\(317\) −395.429 + 128.483i −1.24741 + 0.405308i −0.856992 0.515329i \(-0.827670\pi\)
−0.390418 + 0.920638i \(0.627670\pi\)
\(318\) 112.250 + 317.490i 0.352987 + 0.998397i
\(319\) 0 0
\(320\) 82.0244i 0.256326i
\(321\) 77.2597 + 100.792i 0.240684 + 0.313992i
\(322\) −498.354 362.076i −1.54768 1.12446i
\(323\) −186.201 256.284i −0.576473 0.793447i
\(324\) 210.200 + 121.923i 0.648764 + 0.376304i
\(325\) 117.936 362.970i 0.362880 1.11683i
\(326\) 21.7719 + 29.9664i 0.0667849 + 0.0919215i
\(327\) −57.4825 + 193.700i −0.175787 + 0.592355i
\(328\) −34.6099 106.518i −0.105518 0.324751i
\(329\) 275.158i 0.836347i
\(330\) 0 0
\(331\) 178.000 0.537764 0.268882 0.963173i \(-0.413346\pi\)
0.268882 + 0.963173i \(0.413346\pi\)
\(332\) 60.3902 19.6220i 0.181898 0.0591023i
\(333\) −89.8813 + 4.61994i −0.269914 + 0.0138737i
\(334\) −181.220 + 131.664i −0.542574 + 0.394203i
\(335\) 112.980 + 36.7093i 0.337253 + 0.109580i
\(336\) −426.408 + 10.9516i −1.26907 + 0.0325940i
\(337\) 205.840 149.552i 0.610802 0.443774i −0.238894 0.971046i \(-0.576785\pi\)
0.849697 + 0.527272i \(0.176785\pi\)
\(338\) 520.970 717.053i 1.54133 2.12146i
\(339\) 216.809 + 282.846i 0.639556 + 0.834353i
\(340\) −179.600 −0.528234
\(341\) 0 0
\(342\) −224.000 277.186i −0.654971 0.810485i
\(343\) 97.1238 + 298.916i 0.283160 + 0.871476i
\(344\) −23.2751 + 32.0354i −0.0676602 + 0.0931263i
\(345\) 217.494 + 149.641i 0.630418 + 0.433741i
\(346\) 155.745 479.332i 0.450129 1.38535i
\(347\) 462.992 + 150.435i 1.33427 + 0.433531i 0.887372 0.461054i \(-0.152529\pi\)
0.446898 + 0.894585i \(0.352529\pi\)
\(348\) 107.976 156.937i 0.310276 0.450968i
\(349\) 54.4872 + 39.5872i 0.156124 + 0.113430i 0.663104 0.748527i \(-0.269239\pi\)
−0.506981 + 0.861957i \(0.669239\pi\)
\(350\) 320.109 104.010i 0.914598 0.297171i
\(351\) 516.349 + 317.490i 1.47108 + 0.904530i
\(352\) 0 0
\(353\) 124.451i 0.352552i −0.984341 0.176276i \(-0.943595\pi\)
0.984341 0.176276i \(-0.0564051\pi\)
\(354\) 213.811 163.893i 0.603986 0.462973i
\(355\) 148.859 + 108.152i 0.419321 + 0.304655i
\(356\) 109.726 + 151.024i 0.308218 + 0.424225i
\(357\) 12.2001 + 475.019i 0.0341738 + 1.33059i
\(358\) 258.997 797.110i 0.723455 2.22656i
\(359\) −149.293 205.484i −0.415857 0.572379i 0.548777 0.835969i \(-0.315093\pi\)
−0.964635 + 0.263590i \(0.915093\pi\)
\(360\) 67.2610 3.45725i 0.186836 0.00960347i
\(361\) −42.3353 130.295i −0.117272 0.360927i
\(362\) 693.187i 1.91488i
\(363\) 0 0
\(364\) 504.000 1.38462
\(365\) 201.301 65.4066i 0.551509 0.179196i
\(366\) 740.253 + 219.677i 2.02255 + 0.600211i
\(367\) 114.880 83.4655i 0.313026 0.227426i −0.420168 0.907446i \(-0.638029\pi\)
0.733194 + 0.680020i \(0.238029\pi\)
\(368\) −562.209 182.673i −1.52774 0.496393i
\(369\) −355.820 + 136.177i −0.964282 + 0.369042i
\(370\) 60.5413 43.9858i 0.163625 0.118881i
\(371\) −186.616 + 256.855i −0.503008 + 0.692331i
\(372\) −214.288 + 164.258i −0.576043 + 0.441554i
\(373\) −426.549 −1.14356 −0.571781 0.820406i \(-0.693747\pi\)
−0.571781 + 0.820406i \(0.693747\pi\)
\(374\) 0 0
\(375\) −336.000 + 118.794i −0.896000 + 0.316784i
\(376\) 30.0621 + 92.5217i 0.0799525 + 0.246068i
\(377\) 279.301 384.425i 0.740852 1.01970i
\(378\) 41.1390 + 532.987i 0.108833 + 1.41002i
\(379\) −108.156 + 332.870i −0.285372 + 0.878284i 0.700915 + 0.713245i \(0.252775\pi\)
−0.986287 + 0.165040i \(0.947225\pi\)
\(380\) 120.780 + 39.2439i 0.317843 + 0.103274i
\(381\) 166.457 + 114.526i 0.436894 + 0.300592i
\(382\) 127.137 + 92.3702i 0.332819 + 0.241807i
\(383\) 492.269 159.948i 1.28530 0.417618i 0.414854 0.909888i \(-0.363832\pi\)
0.870443 + 0.492269i \(0.163832\pi\)
\(384\) −231.983 + 82.0183i −0.604122 + 0.213589i
\(385\) 0 0
\(386\) 395.980i 1.02585i
\(387\) 112.895 + 73.4761i 0.291718 + 0.189861i
\(388\) 179.602 + 130.488i 0.462891 + 0.336310i
\(389\) 257.689 + 354.678i 0.662439 + 0.911769i 0.999559 0.0296928i \(-0.00945289\pi\)
−0.337120 + 0.941462i \(0.609453\pi\)
\(390\) −503.834 + 12.9401i −1.29188 + 0.0331798i
\(391\) −203.497 + 626.301i −0.520454 + 1.60179i
\(392\) −10.8859 14.9832i −0.0277702 0.0382225i
\(393\) −669.615 198.715i −1.70386 0.505636i
\(394\) −190.354 585.851i −0.483133 1.48693i
\(395\) 63.4980i 0.160755i
\(396\) 0 0
\(397\) 442.000 1.11335 0.556675 0.830730i \(-0.312077\pi\)
0.556675 + 0.830730i \(0.312077\pi\)
\(398\) −558.610 + 181.503i −1.40354 + 0.456038i
\(399\) 95.5910 322.115i 0.239576 0.807307i
\(400\) 261.312 189.855i 0.653281 0.474637i
\(401\) 500.339 + 162.570i 1.24773 + 0.405411i 0.857106 0.515140i \(-0.172260\pi\)
0.390622 + 0.920551i \(0.372260\pi\)
\(402\) 8.55908 + 333.255i 0.0212912 + 0.828992i
\(403\) −544.872 + 395.872i −1.35204 + 0.982314i
\(404\) −261.262 + 359.597i −0.646689 + 0.890091i
\(405\) −23.4899 227.895i −0.0579998 0.562704i
\(406\) 419.066 1.03218
\(407\) 0 0
\(408\) 56.0000 + 158.392i 0.137255 + 0.388215i
\(409\) −69.3741 213.512i −0.169619 0.522033i 0.829728 0.558168i \(-0.188496\pi\)
−0.999347 + 0.0361345i \(0.988496\pi\)
\(410\) 186.201 256.284i 0.454148 0.625082i
\(411\) 269.339 391.470i 0.655326 0.952481i
\(412\) −31.5197 + 97.0078i −0.0765042 + 0.235456i
\(413\) 241.561 + 78.4879i 0.584893 + 0.190043i
\(414\) −192.464 + 715.411i −0.464890 + 1.72805i
\(415\) −48.4330 35.1887i −0.116706 0.0847919i
\(416\) 847.348 275.320i 2.03689 0.661827i
\(417\) 89.7998 + 253.992i 0.215347 + 0.609094i
\(418\) 0 0
\(419\) 684.479i 1.63360i −0.576919 0.816801i \(-0.695745\pi\)
0.576919 0.816801i \(-0.304255\pi\)
\(420\) −115.890 151.187i −0.275927 0.359970i
\(421\) 215.199 + 156.351i 0.511160 + 0.371380i 0.813264 0.581895i \(-0.197689\pi\)
−0.302103 + 0.953275i \(0.597689\pi\)
\(422\) 605.153 + 832.921i 1.43401 + 1.97375i
\(423\) 309.065 118.283i 0.730650 0.279628i
\(424\) −34.6871 + 106.756i −0.0818091 + 0.251783i
\(425\) −211.498 291.102i −0.497643 0.684946i
\(426\) −146.900 + 495.012i −0.344835 + 1.16200i
\(427\) 224.964 + 692.369i 0.526849 + 1.62147i
\(428\) 126.996i 0.296720i
\(429\) 0 0
\(430\) −112.000 −0.260465
\(431\) 523.382 170.057i 1.21434 0.394564i 0.369324 0.929301i \(-0.379589\pi\)
0.845019 + 0.534737i \(0.179589\pi\)
\(432\) 195.602 + 474.245i 0.452783 + 1.09779i
\(433\) −597.055 + 433.786i −1.37888 + 1.00181i −0.381895 + 0.924206i \(0.624728\pi\)
−0.996984 + 0.0776084i \(0.975272\pi\)
\(434\) −564.899 183.547i −1.30161 0.422919i
\(435\) −179.540 + 4.61119i −0.412736 + 0.0106004i
\(436\) 163.461 118.762i 0.374912 0.272389i
\(437\) 273.704 376.721i 0.626324 0.862061i
\(438\) 361.349 + 471.409i 0.824998 + 1.07628i
\(439\) −426.549 −0.971638 −0.485819 0.874060i \(-0.661479\pi\)
−0.485819 + 0.874060i \(0.661479\pi\)
\(440\) 0 0
\(441\) −49.0000 + 39.5980i −0.111111 + 0.0897913i
\(442\) −388.495 1195.67i −0.878948 2.70513i
\(443\) 69.8253 96.1063i 0.157619 0.216944i −0.722902 0.690950i \(-0.757192\pi\)
0.880522 + 0.474006i \(0.157192\pi\)
\(444\) 74.1457 + 51.0138i 0.166995 + 0.114896i
\(445\) 54.3870 167.386i 0.122218 0.376148i
\(446\) −115.748 37.6088i −0.259524 0.0843246i
\(447\) −35.9920 + 52.3123i −0.0805189 + 0.117030i
\(448\) 175.570 + 127.559i 0.391897 + 0.284730i
\(449\) −484.199 + 157.326i −1.07839 + 0.350391i −0.793751 0.608242i \(-0.791875\pi\)
−0.284643 + 0.958634i \(0.591875\pi\)
\(450\) −254.433 314.844i −0.565406 0.699654i
\(451\) 0 0
\(452\) 356.382i 0.788455i
\(453\) −160.358 + 122.919i −0.353992 + 0.271345i
\(454\) −453.050 329.160i −0.997906 0.725021i
\(455\) −279.301 384.425i −0.613849 0.844891i
\(456\) −3.05001 118.755i −0.00668863 0.260427i
\(457\) −208.122 + 640.535i −0.455410 + 1.40161i 0.415243 + 0.909711i \(0.363697\pi\)
−0.870653 + 0.491898i \(0.836303\pi\)
\(458\) −183.506 252.574i −0.400668 0.551472i
\(459\) 528.310 217.901i 1.15100 0.474730i
\(460\) −81.5805 251.079i −0.177349 0.545824i
\(461\) 698.478i 1.51514i −0.652755 0.757569i \(-0.726387\pi\)
0.652755 0.757569i \(-0.273613\pi\)
\(462\) 0 0
\(463\) 882.000 1.90497 0.952484 0.304589i \(-0.0985192\pi\)
0.952484 + 0.304589i \(0.0985192\pi\)
\(464\) 382.471 124.272i 0.824292 0.267829i
\(465\) 244.039 + 72.4211i 0.524816 + 0.155744i
\(466\) −181.220 + 131.664i −0.388884 + 0.282541i
\(467\) −505.719 164.318i −1.08291 0.351859i −0.287407 0.957809i \(-0.592793\pi\)
−0.795503 + 0.605950i \(0.792793\pi\)
\(468\) −216.656 566.106i −0.462939 1.20963i
\(469\) −254.273 + 184.740i −0.542161 + 0.393903i
\(470\) −161.734 + 222.608i −0.344115 + 0.473633i
\(471\) 204.764 156.958i 0.434743 0.333243i
\(472\) 89.7998 0.190254
\(473\) 0 0
\(474\) 168.000 59.3970i 0.354430 0.125310i
\(475\) 78.6240 + 241.980i 0.165524 + 0.509431i
\(476\) 279.301 384.425i 0.586767 0.807616i
\(477\) 368.727 + 99.1973i 0.773013 + 0.207961i
\(478\) −34.6099 + 106.518i −0.0724057 + 0.222842i
\(479\) −644.162 209.301i −1.34481 0.436954i −0.453864 0.891071i \(-0.649955\pi\)
−0.890942 + 0.454117i \(0.849955\pi\)
\(480\) −277.428 190.876i −0.577975 0.397659i
\(481\) 181.624 + 131.957i 0.377596 + 0.274340i
\(482\) −376.599 + 122.364i −0.781326 + 0.253868i
\(483\) −658.532 + 232.826i −1.36342 + 0.482042i
\(484\) 0 0
\(485\) 209.304i 0.431554i
\(486\) 580.981 275.325i 1.19543 0.566512i
\(487\) −283.156 205.725i −0.581429 0.422433i 0.257810 0.966196i \(-0.416999\pi\)
−0.839239 + 0.543763i \(0.816999\pi\)
\(488\) 151.288 + 208.230i 0.310017 + 0.426702i
\(489\) 41.9862 1.07834i 0.0858613 0.00220520i
\(490\) 16.1873 49.8194i 0.0330353 0.101672i
\(491\) −149.293 205.484i −0.304059 0.418501i 0.629458 0.777034i \(-0.283277\pi\)
−0.933517 + 0.358533i \(0.883277\pi\)
\(492\) 365.245 + 108.390i 0.742367 + 0.220305i
\(493\) −138.440 426.073i −0.280811 0.864246i
\(494\) 888.972i 1.79954i
\(495\) 0 0
\(496\) −570.000 −1.14919
\(497\) −462.992 + 150.435i −0.931573 + 0.302686i
\(498\) 47.7955 161.058i 0.0959749 0.323409i
\(499\) 79.2837 57.6030i 0.158885 0.115437i −0.505502 0.862825i \(-0.668693\pi\)
0.664387 + 0.747389i \(0.268693\pi\)
\(500\) 338.939 + 110.128i 0.677879 + 0.220256i
\(501\) 6.52120 + 253.908i 0.0130164 + 0.506803i
\(502\) −108.974 + 79.1745i −0.217080 + 0.157718i
\(503\) 298.586 410.968i 0.593610 0.817034i −0.401495 0.915861i \(-0.631509\pi\)
0.995105 + 0.0988277i \(0.0315093\pi\)
\(504\) −97.1998 + 149.346i −0.192857 + 0.296321i
\(505\) 419.066 0.829833
\(506\) 0 0
\(507\) −335.000 947.523i −0.660750 1.86888i
\(508\) −62.4367 192.160i −0.122907 0.378269i
\(509\) −94.7629 + 130.430i −0.186175 + 0.256248i −0.891894 0.452244i \(-0.850624\pi\)
0.705720 + 0.708491i \(0.250624\pi\)
\(510\) −269.339 + 391.470i −0.528116 + 0.767587i
\(511\) −173.050 + 532.592i −0.338649 + 1.04225i
\(512\) 525.898 + 170.875i 1.02714 + 0.333740i
\(513\) −402.901 + 31.0982i −0.785381 + 0.0606202i
\(514\) −205.840 149.552i −0.400468 0.290957i
\(515\) 91.4598 29.7171i 0.177592 0.0577031i
\(516\) −44.8999 126.996i −0.0870153 0.246116i
\(517\) 0 0
\(518\) 197.990i 0.382220i
\(519\) −347.669 453.562i −0.669882 0.873915i
\(520\) −135.915 98.7479i −0.261375 0.189900i
\(521\) −89.7754 123.565i −0.172314 0.237169i 0.714122 0.700021i \(-0.246826\pi\)
−0.886436 + 0.462852i \(0.846826\pi\)
\(522\) −180.145 470.706i −0.345105 0.901735i
\(523\) −4.62494 + 14.2341i −0.00884310 + 0.0272163i −0.955381 0.295377i \(-0.904555\pi\)
0.946538 + 0.322593i \(0.104555\pi\)
\(524\) 410.555 + 565.081i 0.783502 + 1.07840i
\(525\) 108.578 365.878i 0.206815 0.696911i
\(526\) 380.709 + 1171.70i 0.723781 + 2.22757i
\(527\) 634.980i 1.20490i
\(528\) 0 0
\(529\) −439.000 −0.829868
\(530\) −301.951 + 98.1099i −0.569719 + 0.185113i
\(531\) −15.6806 305.067i −0.0295303 0.574515i
\(532\) −271.830 + 197.496i −0.510958 + 0.371233i
\(533\) 903.838 + 293.675i 1.69576 + 0.550985i
\(534\) 493.736 12.6808i 0.924599 0.0237467i
\(535\) −96.8661 + 70.3773i −0.181058 + 0.131546i
\(536\) −65.3156 + 89.8992i −0.121857 + 0.167722i
\(537\) −578.159 754.255i −1.07665 1.40457i
\(538\) −980.314 −1.82215
\(539\) 0 0
\(540\) −120.000 + 195.161i −0.222222 + 0.361410i
\(541\) 159.561 + 491.077i 0.294936 + 0.907721i 0.983243 + 0.182301i \(0.0583544\pi\)
−0.688307 + 0.725420i \(0.741646\pi\)
\(542\) −523.690 + 720.797i −0.966218 + 1.32988i
\(543\) −647.539 445.521i −1.19252 0.820480i
\(544\) 259.574 798.887i 0.477159 1.46854i
\(545\) −181.171 58.8659i −0.332423 0.108011i
\(546\) 755.831 1098.56i 1.38431 2.01201i
\(547\) −544.872 395.872i −0.996109 0.723716i −0.0348585 0.999392i \(-0.511098\pi\)
−0.961250 + 0.275677i \(0.911098\pi\)
\(548\) −451.919 + 146.837i −0.824670 + 0.267951i
\(549\) 680.982 550.316i 1.24040 1.00240i
\(550\) 0 0
\(551\) 316.784i 0.574925i
\(552\) −195.994 + 150.235i −0.355061 + 0.272165i
\(553\) 135.915 + 98.7479i 0.245777 + 0.178568i
\(554\) −34.9127 48.0532i −0.0630192 0.0867386i
\(555\) −2.17858 84.8248i −0.00392537 0.152838i
\(556\) 83.2490 256.214i 0.149728 0.460817i
\(557\) 261.262 + 359.597i 0.469053 + 0.645596i 0.976355 0.216172i \(-0.0693573\pi\)
−0.507302 + 0.861768i \(0.669357\pi\)
\(558\) 36.6697 + 713.411i 0.0657163 + 1.27851i
\(559\) −103.830 319.555i −0.185742 0.571655i
\(560\) 402.154i 0.718132i
\(561\) 0 0
\(562\) −56.0000 −0.0996441
\(563\) 523.382 170.057i 0.929630 0.302055i 0.195219 0.980760i \(-0.437458\pi\)
0.734411 + 0.678704i \(0.237458\pi\)
\(564\) −317.251 94.1474i −0.562502 0.166928i
\(565\) −271.830 + 197.496i −0.481115 + 0.349550i
\(566\) 451.919 + 146.837i 0.798443 + 0.259430i
\(567\) 524.330 + 304.128i 0.924744 + 0.536382i
\(568\) −139.245 + 101.167i −0.245150 + 0.178112i
\(569\) −659.377 + 907.554i −1.15883 + 1.59500i −0.443389 + 0.896329i \(0.646224\pi\)
−0.715445 + 0.698669i \(0.753776\pi\)
\(570\) 266.669 204.410i 0.467841 0.358614i
\(571\) 808.198 1.41541 0.707704 0.706509i \(-0.249731\pi\)
0.707704 + 0.706509i \(0.249731\pi\)
\(572\) 0 0
\(573\) 168.000 59.3970i 0.293194 0.103660i
\(574\) 258.997 + 797.110i 0.451214 + 1.38869i
\(575\) 310.889 427.902i 0.540676 0.744177i
\(576\) 67.8050 252.039i 0.117717 0.437567i
\(577\) 95.7953 294.828i 0.166023 0.510966i −0.833087 0.553142i \(-0.813429\pi\)
0.999110 + 0.0421754i \(0.0134288\pi\)
\(578\) −400.085 129.996i −0.692189 0.224906i
\(579\) 369.904 + 254.502i 0.638867 + 0.439554i
\(580\) 145.299 + 105.566i 0.250516 + 0.182010i
\(581\) 150.640 48.9458i 0.259277 0.0842441i
\(582\) 553.765 195.786i 0.951487 0.336401i
\(583\) 0 0
\(584\) 197.990i 0.339024i
\(585\) −311.733 + 478.972i −0.532877 + 0.818756i
\(586\) 45.3050 + 32.9160i 0.0773122 + 0.0561706i
\(587\) −565.253 778.004i −0.962952 1.32539i −0.945528 0.325541i \(-0.894454\pi\)
−0.0174238 0.999848i \(-0.505546\pi\)
\(588\) 62.9792 1.61751i 0.107108 0.00275087i
\(589\) 138.748 427.023i 0.235566 0.724997i
\(590\) 149.293 + 205.484i 0.253039 + 0.348278i
\(591\) −669.615 198.715i −1.13302 0.336235i
\(592\) 58.7132 + 180.701i 0.0991778 + 0.305238i
\(593\) 232.826i 0.392624i −0.980541 0.196312i \(-0.937103\pi\)
0.980541 0.196312i \(-0.0628966\pi\)
\(594\) 0 0
\(595\) −448.000 −0.752941
\(596\) 60.3902 19.6220i 0.101326 0.0329228i
\(597\) −189.475 + 638.479i −0.317378 + 1.06948i
\(598\) 1495.06 1086.23i 2.50011 1.81643i
\(599\) −831.208 270.076i −1.38766 0.450878i −0.482480 0.875907i \(-0.660264\pi\)
−0.905180 + 0.425029i \(0.860264\pi\)
\(600\) −3.46439 134.889i −0.00577398 0.224815i
\(601\) 472.222 343.089i 0.785727 0.570864i −0.120965 0.992657i \(-0.538599\pi\)
0.906692 + 0.421793i \(0.138599\pi\)
\(602\) 174.175 239.731i 0.289327 0.398225i
\(603\) 316.810 + 206.192i 0.525391 + 0.341943i
\(604\) 202.049 0.334519
\(605\) 0 0
\(606\) 392.000 + 1108.74i 0.646865 + 1.82961i
\(607\) 261.309 + 804.227i 0.430493 + 1.32492i 0.897635 + 0.440739i \(0.145284\pi\)
−0.467142 + 0.884182i \(0.654716\pi\)
\(608\) −349.127 + 480.532i −0.574221 + 0.790348i
\(609\) 269.339 391.470i 0.442265 0.642807i
\(610\) −224.964 + 692.369i −0.368794 + 1.13503i
\(611\) −785.073 255.086i −1.28490 0.417489i
\(612\) −551.861 148.465i −0.901733 0.242590i
\(613\) −478.276 347.488i −0.780222 0.566865i 0.124824 0.992179i \(-0.460164\pi\)
−0.905046 + 0.425314i \(0.860164\pi\)
\(614\) −376.599 + 122.364i −0.613354 + 0.199291i
\(615\) −119.733 338.656i −0.194688 0.550660i
\(616\) 0 0
\(617\) 435.578i 0.705961i 0.935631 + 0.352980i \(0.114832\pi\)
−0.935631 + 0.352980i \(0.885168\pi\)
\(618\) 164.177 + 214.182i 0.265658 + 0.346573i
\(619\) 677.956 + 492.564i 1.09524 + 0.795742i 0.980277 0.197628i \(-0.0633237\pi\)
0.114967 + 0.993369i \(0.463324\pi\)
\(620\) −149.626 205.942i −0.241332 0.332165i
\(621\) 544.601 + 639.595i 0.876974 + 1.02994i
\(622\) −20.8122 + 64.0535i −0.0334602 + 0.102980i
\(623\) 273.704 + 376.721i 0.439331 + 0.604688i
\(624\) 364.056 1226.77i 0.583422 1.96597i
\(625\) 27.5025 + 84.6440i 0.0440040 + 0.135430i
\(626\) 1053.01i 1.68212i
\(627\) 0 0
\(628\) −258.000 −0.410828
\(629\) 201.301 65.4066i 0.320033 0.103985i
\(630\) −503.336 + 25.8717i −0.798945 + 0.0410662i
\(631\) −205.490 + 149.297i −0.325658 + 0.236605i −0.738586 0.674159i \(-0.764506\pi\)
0.412928 + 0.910764i \(0.364506\pi\)
\(632\) 56.4899 + 18.3547i 0.0893827 + 0.0290422i
\(633\) 1167.01 29.9727i 1.84362 0.0473503i
\(634\) 889.957 646.592i 1.40372 1.01986i
\(635\) −111.970 + 154.113i −0.176330 + 0.242698i
\(636\) −232.296 303.049i −0.365245 0.476492i
\(637\) 157.150 0.246703
\(638\) 0 0
\(639\) 368.000 + 455.377i 0.575900 + 0.712640i
\(640\) −71.6866 220.629i −0.112010 0.344732i
\(641\) 69.8253 96.1063i 0.108932 0.149932i −0.751070 0.660222i \(-0.770462\pi\)
0.860002 + 0.510290i \(0.170462\pi\)
\(642\) −276.811 190.452i −0.431169 0.296654i
\(643\) −135.349 + 416.563i −0.210497 + 0.647843i 0.788946 + 0.614463i \(0.210627\pi\)
−0.999443 + 0.0333799i \(0.989373\pi\)
\(644\) 664.292 + 215.842i 1.03151 + 0.335158i
\(645\) −71.9839 + 104.625i −0.111603 + 0.162209i
\(646\) 678.062 + 492.641i 1.04963 + 0.762602i
\(647\) 314.729 102.262i 0.486444 0.158055i −0.0555189 0.998458i \(-0.517681\pi\)
0.541963 + 0.840402i \(0.317681\pi\)
\(648\) 209.533 + 44.9778i 0.323353 + 0.0694101i
\(649\) 0 0
\(650\) 1009.75i 1.55346i
\(651\) −534.528 + 409.731i −0.821088 + 0.629388i
\(652\) −33.9787 24.6870i −0.0521146 0.0378635i
\(653\) 367.414 + 505.702i 0.562656 + 0.774429i 0.991661 0.128873i \(-0.0411359\pi\)
−0.429005 + 0.903302i \(0.641136\pi\)
\(654\) −13.7251 534.397i −0.0209863 0.817120i
\(655\) 203.497 626.301i 0.310683 0.956185i
\(656\) 472.761 + 650.699i 0.720672 + 0.991919i
\(657\) 672.610 34.5725i 1.02376 0.0526218i
\(658\) −224.964 692.369i −0.341891 1.05223i
\(659\) 465.652i 0.706604i 0.935509 + 0.353302i \(0.114941\pi\)
−0.935509 + 0.353302i \(0.885059\pi\)
\(660\) 0 0
\(661\) −394.000 −0.596067 −0.298033 0.954555i \(-0.596331\pi\)
−0.298033 + 0.954555i \(0.596331\pi\)
\(662\) −447.894 + 145.530i −0.676577 + 0.219833i
\(663\) −1366.62 405.558i −2.06127 0.611702i
\(664\) 45.3050 32.9160i 0.0682303 0.0495723i
\(665\) 301.279 + 97.8916i 0.453052 + 0.147205i
\(666\) 222.388 85.1104i 0.333915 0.127793i
\(667\) 532.763 387.075i 0.798746 0.580323i
\(668\) 149.293 205.484i 0.223492 0.307611i
\(669\) −109.525 + 83.9541i −0.163714 + 0.125492i
\(670\) −314.299 −0.469103
\(671\) 0 0
\(672\) 840.000 296.985i 1.25000 0.441942i
\(673\) −272.872 839.813i −0.405456 1.24786i −0.920514 0.390709i \(-0.872230\pi\)
0.515059 0.857155i \(-0.327770\pi\)
\(674\) −395.677 + 544.602i −0.587058 + 0.808016i
\(675\) −457.639 + 35.3232i −0.677983 + 0.0523306i
\(676\) −310.562 + 955.812i −0.459411 + 1.41392i
\(677\) −865.593 281.248i −1.27857 0.415433i −0.410495 0.911863i \(-0.634644\pi\)
−0.868077 + 0.496430i \(0.834644\pi\)
\(678\) −776.798 534.453i −1.14572 0.788279i
\(679\) 448.006 + 325.495i 0.659802 + 0.479374i
\(680\) −150.640 + 48.9458i −0.221529 + 0.0719791i
\(681\) −598.665 + 211.660i −0.879097 + 0.310808i
\(682\) 0 0
\(683\) 435.578i 0.637742i −0.947798 0.318871i \(-0.896696\pi\)
0.947798 0.318871i \(-0.103304\pi\)
\(684\) 338.685 + 220.428i 0.495153 + 0.322264i
\(685\) 362.440 + 263.328i 0.529109 + 0.384420i
\(686\) −488.777 672.744i −0.712503 0.980677i
\(687\) −353.883 + 9.08889i −0.515114 + 0.0132298i
\(688\) 87.8739 270.448i 0.127724 0.393093i
\(689\) −559.848 770.565i −0.812552 1.11838i
\(690\) −669.615 198.715i −0.970457 0.287993i
\(691\) 131.641 + 405.150i 0.190508 + 0.586324i 1.00000 0.000807501i \(-0.000257036\pi\)
−0.809491 + 0.587132i \(0.800257\pi\)
\(692\) 571.482i 0.825841i
\(693\) 0 0
\(694\) −1288.00 −1.85591
\(695\) −241.561 + 78.4879i −0.347570 + 0.112932i
\(696\) 47.7955 161.058i 0.0686717 0.231405i
\(697\) 724.879 526.656i 1.04000 0.755603i
\(698\) −169.470 55.0640i −0.242793 0.0788883i
\(699\) 6.52120 + 253.908i 0.00932933 + 0.363245i
\(700\) −308.761 + 224.328i −0.441087 + 0.320468i
\(701\) 161.734 222.608i 0.230719 0.317557i −0.677924 0.735132i \(-0.737120\pi\)
0.908642 + 0.417575i \(0.137120\pi\)
\(702\) −1558.84 376.730i −2.22057 0.536652i
\(703\) −149.666 −0.212897
\(704\) 0 0
\(705\) 104.000 + 294.156i 0.147518 + 0.417243i
\(706\) 101.749 + 313.150i 0.144120 + 0.443556i
\(707\) −651.703 + 896.992i −0.921786 + 1.26873i
\(708\) −173.147 + 251.659i −0.244557 + 0.355451i
\(709\) −12.9787 + 39.9444i −0.0183057 + 0.0563390i −0.959792 0.280712i \(-0.909429\pi\)
0.941486 + 0.337051i \(0.109429\pi\)
\(710\) −462.992 150.435i −0.652101 0.211880i
\(711\) 52.4903 195.112i 0.0738260 0.274419i
\(712\) 133.191 + 96.7688i 0.187066 + 0.135911i
\(713\) −887.698 + 288.431i −1.24502 + 0.404531i
\(714\) −419.066 1185.30i −0.586927 1.66008i
\(715\) 0 0
\(716\) 950.352i 1.32731i
\(717\) 77.2597 + 100.792i 0.107754 + 0.140574i
\(718\) 543.659 + 394.992i 0.757186 + 0.550128i
\(719\) −254.364 350.102i −0.353774 0.486928i 0.594627 0.804002i \(-0.297300\pi\)
−0.948401 + 0.317073i \(0.897300\pi\)
\(720\) −451.710 + 172.875i −0.627376 + 0.240104i
\(721\) −78.6240 + 241.980i −0.109049 + 0.335617i
\(722\) 213.053 + 293.243i 0.295088 + 0.406153i
\(723\) −127.739 + 430.445i −0.176679 + 0.595359i
\(724\) 242.887 + 747.530i 0.335480 + 1.03250i
\(725\) 359.822i 0.496306i
\(726\) 0 0
\(727\) 1102.00 1.51582 0.757909 0.652360i \(-0.226221\pi\)
0.757909 + 0.652360i \(0.226221\pi\)
\(728\) 422.732 137.354i 0.580675 0.188673i
\(729\) 116.210 719.678i 0.159410 0.987212i
\(730\) −453.050 + 329.160i −0.620616 + 0.450904i
\(731\) −301.279 97.8916i −0.412147 0.133915i
\(732\) −875.259 + 22.4795i −1.19571 + 0.0307097i
\(733\) −393.518 + 285.908i −0.536860 + 0.390052i −0.822918 0.568161i \(-0.807655\pi\)
0.286058 + 0.958212i \(0.407655\pi\)
\(734\) −220.829 + 303.945i −0.300857 + 0.414094i
\(735\) −36.1349 47.1409i −0.0491631 0.0641373i
\(736\) 1234.75 1.67765
\(737\) 0 0
\(738\) 784.000 633.568i 1.06233 0.858493i
\(739\) −323.746 996.388i −0.438087 1.34829i −0.889890 0.456175i \(-0.849219\pi\)
0.451804 0.892117i \(-0.350781\pi\)
\(740\) −49.8752 + 68.6474i −0.0673990 + 0.0927667i
\(741\) 830.432 + 571.355i 1.12069 + 0.771059i
\(742\) 259.574 798.887i 0.349831 1.07667i
\(743\) 241.561 + 78.4879i 0.325116 + 0.105636i 0.467027 0.884243i \(-0.345325\pi\)
−0.141912 + 0.989879i \(0.545325\pi\)
\(744\) −134.970 + 196.171i −0.181411 + 0.263671i
\(745\) −48.4330 35.1887i −0.0650108 0.0472331i
\(746\) 1073.31 348.739i 1.43875 0.467478i
\(747\) −119.733 148.162i −0.160285 0.198343i
\(748\) 0 0
\(749\) 316.784i 0.422942i
\(750\) 748.339 573.624i 0.997786 0.764832i
\(751\) −283.156 205.725i −0.377039 0.273935i 0.383085 0.923713i \(-0.374862\pi\)
−0.760124 + 0.649779i \(0.774862\pi\)
\(752\) −410.639 565.197i −0.546063 0.751591i
\(753\) 3.92145 + 152.685i 0.00520776 + 0.202769i
\(754\) −388.495 + 1195.67i −0.515246 + 1.58576i
\(755\) −111.970 154.113i −0.148304 0.204123i
\(756\) −231.119 560.357i −0.305713 0.741213i
\(757\) 90.8510 + 279.611i 0.120015 + 0.369367i 0.992960 0.118451i \(-0.0377930\pi\)
−0.872945 + 0.487818i \(0.837793\pi\)
\(758\) 926.013i 1.22165i
\(759\) 0 0
\(760\) 112.000 0.147368
\(761\) 744.813 242.004i 0.978729 0.318008i 0.224394 0.974498i \(-0.427960\pi\)
0.754335 + 0.656490i \(0.227960\pi\)
\(762\) −512.483 152.084i −0.672549 0.199586i
\(763\) 407.745 296.244i 0.534397 0.388262i
\(764\) −169.470 55.0640i −0.221819 0.0720733i
\(765\) 192.583 + 503.206i 0.251742 + 0.657785i
\(766\) −1107.91 + 804.941i −1.44635 + 1.05084i
\(767\) −447.878 + 616.452i −0.583935 + 0.803718i
\(768\) 792.865 607.754i 1.03238 0.791347i
\(769\) −838.131 −1.08990 −0.544949 0.838469i \(-0.683451\pi\)
−0.544949 + 0.838469i \(0.683451\pi\)
\(770\) 0 0
\(771\) −272.000 + 96.1665i −0.352789 + 0.124730i
\(772\) −138.748 427.023i −0.179726 0.553139i
\(773\) −241.064 + 331.796i −0.311855 + 0.429231i −0.935959 0.352110i \(-0.885464\pi\)
0.624104 + 0.781341i \(0.285464\pi\)
\(774\) −344.146 92.5842i −0.444633 0.119618i
\(775\) 157.599 485.039i 0.203353 0.625857i
\(776\) 186.203 + 60.5011i 0.239953 + 0.0779653i
\(777\) 184.952 + 127.251i 0.238033 + 0.163772i
\(778\) −938.390 681.780i −1.20616 0.876324i
\(779\) −602.559 + 195.783i −0.773503 + 0.251326i
\(780\) 538.799 190.494i 0.690768 0.244223i
\(781\) 0 0
\(782\) 1742.31i 2.22802i
\(783\) −555.491 134.247i −0.709439 0.171452i
\(784\) 107.599 + 78.1754i 0.137244 + 0.0997136i
\(785\) 142.976 + 196.789i 0.182135 + 0.250687i
\(786\) 1847.39 47.4471i 2.35037 0.0603652i
\(787\) 97.1238 298.916i 0.123410 0.379817i −0.870198 0.492702i \(-0.836009\pi\)
0.993608 + 0.112885i \(0.0360091\pi\)
\(788\) 410.555 + 565.081i 0.521009 + 0.717108i
\(789\) 1339.23 + 397.430i 1.69738 + 0.503713i
\(790\) 51.9149 + 159.777i 0.0657150 + 0.202250i
\(791\) 888.972i 1.12386i
\(792\) 0 0
\(793\) −2184.00 −2.75410
\(794\) −1112.19 + 361.371i −1.40074 + 0.455128i
\(795\) −102.419 + 345.124i −0.128829 + 0.434118i
\(796\) 538.805 391.465i 0.676891 0.491790i
\(797\) 234.029 + 76.0408i 0.293638 + 0.0954088i 0.452132 0.891951i \(-0.350664\pi\)
−0.158494 + 0.987360i \(0.550664\pi\)
\(798\) 22.8242 + 888.679i 0.0286018 + 1.11363i
\(799\) −629.629 + 457.453i −0.788022 + 0.572531i
\(800\) −396.559 + 545.817i −0.495699 + 0.682271i
\(801\) 305.485 469.373i 0.381380 0.585984i
\(802\) −1391.90 −1.73553
\(803\) 0 0
\(804\) −126.000 356.382i −0.156716 0.443261i
\(805\) −203.497 626.301i −0.252792 0.778013i
\(806\) 1047.38 1441.59i 1.29948 1.78858i
\(807\) −630.061 + 915.759i −0.780745 + 1.13477i
\(808\) −121.135 + 372.814i −0.149919 + 0.461404i
\(809\) 241.561 + 78.4879i 0.298592 + 0.0970184i 0.454482 0.890756i \(-0.349824\pi\)
−0.155890 + 0.987774i \(0.549824\pi\)
\(810\) 245.430 + 554.238i 0.303000 + 0.684245i
\(811\) 787.037 + 571.816i 0.970452 + 0.705075i 0.955555 0.294814i \(-0.0952578\pi\)
0.0148976 + 0.999889i \(0.495258\pi\)
\(812\) −451.919 + 146.837i −0.556550 + 0.180834i
\(813\) 336.749 + 952.470i 0.414206 + 1.17155i
\(814\) 0 0
\(815\) 39.5980i 0.0485865i
\(816\) −733.967 957.520i −0.899469 1.17343i
\(817\) 181.220 + 131.664i 0.221811 + 0.161155i
\(818\) 349.127 + 480.532i 0.426805 + 0.587447i
\(819\) −540.434 1412.12i −0.659871 1.72420i
\(820\) −110.999 + 341.619i −0.135364 + 0.416608i
\(821\) −286.145 393.844i −0.348532 0.479713i 0.598377 0.801215i \(-0.295812\pi\)
−0.946909 + 0.321502i \(0.895812\pi\)
\(822\) −357.669 + 1205.25i −0.435120 + 1.46624i
\(823\) 321.996 + 991.001i 0.391246 + 1.20413i 0.931847 + 0.362853i \(0.118197\pi\)
−0.540600 + 0.841280i \(0.681803\pi\)
\(824\) 89.9555i 0.109169i
\(825\) 0 0
\(826\) −672.000 −0.813559
\(827\) 1187.67 385.899i 1.43612 0.466625i 0.515437 0.856927i \(-0.327630\pi\)
0.920687 + 0.390303i \(0.127630\pi\)
\(828\) −43.1217 838.935i −0.0520793 1.01321i
\(829\) −953.022 + 692.411i −1.14960 + 0.835236i −0.988428 0.151689i \(-0.951529\pi\)
−0.161176 + 0.986926i \(0.551529\pi\)
\(830\) 150.640 + 48.9458i 0.181494 + 0.0589708i
\(831\) −67.3276 + 1.72920i −0.0810200 + 0.00208086i
\(832\) −526.709 + 382.677i −0.633064 + 0.459948i
\(833\) 87.0875 119.866i 0.104547 0.143896i
\(834\) −433.619 565.691i −0.519927 0.678287i
\(835\) −239.466 −0.286786
\(836\) 0 0
\(837\) 690.000 + 424.264i 0.824373 + 0.506887i
\(838\) 559.618 + 1722.33i 0.667802 + 2.05528i
\(839\) 600.165 826.057i 0.715334 0.984573i −0.284332 0.958726i \(-0.591772\pi\)
0.999666 0.0258470i \(-0.00822826\pi\)
\(840\) −138.405 95.2258i −0.164768 0.113364i
\(841\) 121.444 373.765i 0.144404 0.444430i
\(842\) −669.325 217.477i −0.794923 0.258286i
\(843\) −35.9920 + 52.3123i −0.0426951 + 0.0620549i
\(844\) −944.444 686.179i −1.11901 0.813008i
\(845\) 901.148 292.801i 1.06645 0.346510i
\(846\) −680.982 + 550.316i −0.804943 + 0.650492i
\(847\) 0 0
\(848\) 806.102i 0.950592i
\(849\) 427.622 327.785i 0.503678 0.386084i
\(850\) 770.184 + 559.572i 0.906099 + 0.658319i
\(851\) 182.876 + 251.707i 0.214895 + 0.295778i
\(852\) −15.0322 585.291i −0.0176434 0.686962i
\(853\) −182.685 + 562.247i −0.214168 + 0.659141i 0.785044 + 0.619440i \(0.212640\pi\)
−0.999212 + 0.0397007i \(0.987360\pi\)
\(854\) −1132.14 1558.25i −1.32569 1.82465i
\(855\) −19.5572 380.486i −0.0228739 0.445013i
\(856\) −34.6099 106.518i −0.0404321 0.124437i
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 706.000 0.821886 0.410943 0.911661i \(-0.365200\pi\)
0.410943 + 0.911661i \(0.365200\pi\)
\(860\) 120.780 39.2439i 0.140442 0.0456325i
\(861\) 911.080 + 270.372i 1.05817 + 0.314021i
\(862\) −1177.93 + 855.815i −1.36651 + 0.992825i
\(863\) 470.749 + 152.956i 0.545480 + 0.177237i 0.568777 0.822491i \(-0.307417\pi\)
−0.0232978 + 0.999729i \(0.507417\pi\)
\(864\) −694.674 815.845i −0.804021 0.944265i
\(865\) 435.897 316.698i 0.503927 0.366125i
\(866\) 1147.69 1579.66i 1.32528 1.82409i
\(867\) −378.575 + 290.189i −0.436650 + 0.334705i
\(868\) 673.498 0.775920
\(869\) 0 0
\(870\) 448.000 158.392i 0.514943 0.182060i
\(871\) −291.371 896.749i −0.334525 1.02956i
\(872\) 104.738 144.159i 0.120112 0.165320i
\(873\) 173.020 643.133i 0.198190 0.736693i
\(874\) −380.709 + 1171.70i −0.435594 + 1.34062i
\(875\) 845.463 + 274.708i 0.966243 + 0.313952i
\(876\) −554.856 381.752i −0.633397 0.435790i
\(877\) −78.7037 57.1816i −0.0897419 0.0652013i 0.542010 0.840372i \(-0.317664\pi\)
−0.631751 + 0.775171i \(0.717664\pi\)
\(878\) 1073.31 348.739i 1.22245 0.397197i
\(879\) 59.8665 21.1660i 0.0681075 0.0240796i
\(880\) 0 0
\(881\) 1493.41i 1.69513i 0.530692 + 0.847565i \(0.321932\pi\)
−0.530692 + 0.847565i \(0.678068\pi\)
\(882\) 90.9221 139.700i 0.103086 0.158390i
\(883\) −69.5755 50.5495i −0.0787944 0.0572475i 0.547691 0.836681i \(-0.315507\pi\)
−0.626485 + 0.779433i \(0.715507\pi\)
\(884\) 837.904 + 1153.28i 0.947855 + 1.30461i
\(885\) 287.905 7.39435i 0.325316 0.00835520i
\(886\) −97.1238 + 298.916i −0.109621 + 0.337377i
\(887\) −149.293 205.484i −0.168312 0.231662i 0.716526 0.697560i \(-0.245731\pi\)
−0.884838 + 0.465899i \(0.845731\pi\)
\(888\) 76.0926 + 22.5812i 0.0856899 + 0.0254293i
\(889\) −155.745 479.332i −0.175191 0.539182i
\(890\) 465.652i 0.523205i
\(891\) 0 0
\(892\) 138.000 0.154709
\(893\) 523.382 170.057i 0.586094 0.190433i
\(894\) 47.7955 161.058i 0.0534625 0.180154i
\(895\) 724.879 526.656i 0.809921 0.588442i
\(896\) 583.729 + 189.665i 0.651483 + 0.211680i
\(897\) −53.7999 2094.74i −0.0599776 2.33528i
\(898\) 1089.74 791.745i 1.21352 0.881676i
\(899\) 373.232 513.710i 0.415164 0.571424i
\(900\) 384.698 + 250.376i 0.427443 + 0.278195i
\(901\) −897.998 −0.996668
\(902\) 0 0
\(903\) −112.000 316.784i −0.124031 0.350813i
\(904\) −97.1238 298.916i −0.107438 0.330660i
\(905\) 435.577 599.520i 0.481301 0.662453i
\(906\) 303.007 440.403i 0.334444 0.486096i
\(907\) −298.510 + 918.721i −0.329118 + 1.01292i 0.640429 + 0.768018i \(0.278757\pi\)
−0.969547 + 0.244905i \(0.921243\pi\)
\(908\) 603.902 + 196.220i 0.665090 + 0.216101i
\(909\) 1287.67 + 346.418i 1.41658 + 0.381098i
\(910\) 1017.09 + 738.962i 1.11769 + 0.812046i
\(911\) 1379.97 448.378i 1.51478 0.492183i 0.570494 0.821302i \(-0.306752\pi\)
0.944288 + 0.329119i \(0.106752\pi\)
\(912\) 284.366 + 804.308i 0.311805 + 0.881917i
\(913\) 0 0
\(914\) 1781.91i 1.94957i
\(915\) 502.188 + 655.145i 0.548839 + 0.716006i
\(916\) 286.392 + 208.076i 0.312655 + 0.227157i
\(917\) 1024.10 + 1409.56i 1.11680 + 1.53714i
\(918\) −1151.21 + 980.232i −1.25404 + 1.06779i
\(919\) 122.561 377.204i 0.133363 0.410450i −0.861968 0.506962i \(-0.830768\pi\)
0.995332 + 0.0965115i \(0.0307685\pi\)
\(920\) −136.852 188.360i −0.148752 0.204739i
\(921\) −127.739 + 430.445i −0.138696 + 0.467367i
\(922\) 571.063 + 1757.55i 0.619375 + 1.90624i
\(923\) 1460.45i 1.58229i
\(924\) 0 0
\(925\) −170.000 −0.183784
\(926\) −2219.34 + 721.107i −2.39670 + 0.778734i
\(927\) 305.597 15.7078i 0.329662 0.0169448i
\(928\) −679.574 + 493.740i −0.732300 + 0.532047i
\(929\) −1452.60 471.977i −1.56361 0.508049i −0.605843 0.795584i \(-0.707164\pi\)
−0.957770 + 0.287535i \(0.907164\pi\)
\(930\) −673.276 + 17.2920i −0.723953 + 0.0185935i
\(931\) −84.7578 + 61.5801i −0.0910395 + 0.0661441i
\(932\) 149.293 205.484i 0.160185 0.220476i
\(933\) 46.4592 + 60.6098i 0.0497955 + 0.0649623i
\(934\) 1406.86 1.50628
\(935\) 0 0
\(936\) −336.000 415.779i −0.358974 0.444208i
\(937\) 388.495 + 1195.67i 0.414616 + 1.27606i 0.912594 + 0.408867i \(0.134076\pi\)
−0.497978 + 0.867190i \(0.665924\pi\)
\(938\) 488.777 672.744i 0.521085 0.717211i
\(939\) 983.667 + 676.783i 1.04757 + 0.720749i
\(940\) 96.4133 296.730i 0.102567 0.315670i
\(941\) 462.992 + 150.435i 0.492021 + 0.159867i 0.544510 0.838754i \(-0.316716\pi\)
−0.0524893 + 0.998621i \(0.516716\pi\)
\(942\) −386.914 + 562.357i −0.410736 + 0.596982i
\(943\) 1065.53 + 774.150i 1.12993 + 0.820944i
\(944\) −613.319 + 199.279i −0.649702 + 0.211101i
\(945\) −299.333 + 486.818i −0.316754 + 0.515152i
\(946\) 0 0
\(947\) 435.578i 0.459955i 0.973196 + 0.229978i \(0.0738653\pi\)
−0.973196 + 0.229978i \(0.926135\pi\)
\(948\) −160.358 + 122.919i −0.169154 + 0.129662i
\(949\) −1359.15 987.479i −1.43219 1.04055i
\(950\) −395.677 544.602i −0.416502 0.573266i
\(951\) −32.0251 1246.93i −0.0336752 1.31117i
\(952\) 129.498 398.555i 0.136028 0.418650i
\(953\) 945.521 + 1301.40i 0.992152 + 1.36558i 0.930018 + 0.367513i \(0.119791\pi\)
0.0621339 + 0.998068i \(0.480209\pi\)
\(954\) −1008.92 + 51.8587i −1.05756 + 0.0543593i
\(955\) 51.9149 + 159.777i 0.0543611 + 0.167306i
\(956\) 126.996i 0.132841i
\(957\) 0 0
\(958\) 1792.00 1.87056
\(959\) −1127.28 + 366.277i −1.17548 + 0.381936i
\(960\) 235.905 + 70.0071i 0.245734 + 0.0729240i
\(961\) 49.3500 35.8549i 0.0513528 0.0373100i
\(962\) −564.899 183.547i −0.587213 0.190797i
\(963\) −355.820 + 136.177i −0.369491 + 0.141409i
\(964\) 363.248 263.915i 0.376813 0.273771i
\(965\) −248.821 + 342.473i −0.257846 + 0.354895i
\(966\) 1466.68 1124.25i 1.51830 1.16382i
\(967\) 1055.15 1.09116 0.545578 0.838060i \(-0.316310\pi\)
0.545578 + 0.838060i \(0.316310\pi\)
\(968\) 0 0
\(969\) 896.000 316.784i 0.924665 0.326918i
\(970\) 171.123 + 526.662i 0.176415 + 0.542951i
\(971\) −149.626 + 205.942i −0.154094 + 0.212093i −0.879084 0.476667i \(-0.841845\pi\)
0.724989 + 0.688760i \(0.241845\pi\)
\(972\) −530.057 + 500.481i −0.545326 + 0.514898i
\(973\) 207.659 639.110i 0.213422 0.656845i
\(974\) 880.691 + 286.154i 0.904200 + 0.293792i
\(975\) 943.255 + 648.979i 0.967441 + 0.665620i
\(976\) −1495.37 1086.45i −1.53214 1.11317i
\(977\) −1371.90 + 445.756i −1.40419 + 0.456250i −0.910544 0.413411i \(-0.864337\pi\)
−0.493649 + 0.869661i \(0.664337\pi\)
\(978\) −104.766 + 37.0405i −0.107123 + 0.0378737i
\(979\) 0 0
\(980\) 59.3970i 0.0606092i
\(981\) −508.027 330.643i −0.517866 0.337047i
\(982\) 543.659 + 394.992i 0.553625 + 0.402232i
\(983\) 403.989 + 556.044i 0.410976 + 0.565660i 0.963456 0.267866i \(-0.0863185\pi\)
−0.552480 + 0.833526i \(0.686318\pi\)
\(984\) 335.889 8.62674i 0.341351 0.00876701i
\(985\) 203.497 626.301i 0.206596 0.635838i
\(986\) 696.700 + 958.925i 0.706592 + 0.972541i
\(987\) −791.363 234.845i −0.801787 0.237938i
\(988\) −311.489 958.665i −0.315272 0.970309i
\(989\) 465.652i 0.470831i
\(990\) 0 0
\(991\) 574.000 0.579213 0.289606 0.957146i \(-0.406476\pi\)
0.289606 + 0.957146i \(0.406476\pi\)
\(992\) 1132.32 367.912i 1.14145 0.370879i
\(993\) −151.921 + 511.933i −0.152992 + 0.515542i
\(994\) 1042.01 757.067i 1.04830 0.761637i
\(995\) −597.179 194.035i −0.600180 0.195010i
\(996\) 4.89090 + 190.431i 0.00491054 + 0.191196i
\(997\) 1071.58 778.549i 1.07481 0.780892i 0.0980354 0.995183i \(-0.468744\pi\)
0.976770 + 0.214291i \(0.0687442\pi\)
\(998\) −152.403 + 209.765i −0.152709 + 0.210185i
\(999\) 63.4258 262.445i 0.0634893 0.262707i
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 363.3.h.k.269.1 16
3.2 odd 2 inner 363.3.h.k.269.4 16
11.2 odd 10 inner 363.3.h.k.251.2 16
11.3 even 5 363.3.b.i.122.3 yes 4
11.4 even 5 inner 363.3.h.k.245.2 16
11.5 even 5 inner 363.3.h.k.323.3 16
11.6 odd 10 inner 363.3.h.k.323.1 16
11.7 odd 10 inner 363.3.h.k.245.4 16
11.8 odd 10 363.3.b.i.122.1 4
11.9 even 5 inner 363.3.h.k.251.4 16
11.10 odd 2 inner 363.3.h.k.269.3 16
33.2 even 10 inner 363.3.h.k.251.3 16
33.5 odd 10 inner 363.3.h.k.323.2 16
33.8 even 10 363.3.b.i.122.4 yes 4
33.14 odd 10 363.3.b.i.122.2 yes 4
33.17 even 10 inner 363.3.h.k.323.4 16
33.20 odd 10 inner 363.3.h.k.251.1 16
33.26 odd 10 inner 363.3.h.k.245.3 16
33.29 even 10 inner 363.3.h.k.245.1 16
33.32 even 2 inner 363.3.h.k.269.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.3.b.i.122.1 4 11.8 odd 10
363.3.b.i.122.2 yes 4 33.14 odd 10
363.3.b.i.122.3 yes 4 11.3 even 5
363.3.b.i.122.4 yes 4 33.8 even 10
363.3.h.k.245.1 16 33.29 even 10 inner
363.3.h.k.245.2 16 11.4 even 5 inner
363.3.h.k.245.3 16 33.26 odd 10 inner
363.3.h.k.245.4 16 11.7 odd 10 inner
363.3.h.k.251.1 16 33.20 odd 10 inner
363.3.h.k.251.2 16 11.2 odd 10 inner
363.3.h.k.251.3 16 33.2 even 10 inner
363.3.h.k.251.4 16 11.9 even 5 inner
363.3.h.k.269.1 16 1.1 even 1 trivial
363.3.h.k.269.2 16 33.32 even 2 inner
363.3.h.k.269.3 16 11.10 odd 2 inner
363.3.h.k.269.4 16 3.2 odd 2 inner
363.3.h.k.323.1 16 11.6 odd 10 inner
363.3.h.k.323.2 16 33.5 odd 10 inner
363.3.h.k.323.3 16 11.5 even 5 inner
363.3.h.k.323.4 16 33.17 even 10 inner