Properties

Label 273.3.w.c.116.2
Level $273$
Weight $3$
Character 273.116
Analytic conductor $7.439$
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] = [273,3,Mod(116,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.116");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 273.w (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.43871121704\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 16 x^{14} - 176 x^{13} + 344 x^{12} + 4576 x^{11} + 11040 x^{10} - 37664 x^{9} - 313120 x^{8} - 230912 x^{7} + 2040576 x^{6} + 9332224 x^{5} + \cdots + 97900608 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 116.2
Root \(-2.73864 - 4.07201i\) of defining polynomial
Character \(\chi\) \(=\) 273.116
Dual form 273.3.w.c.233.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70956 - 2.96105i) q^{2} +(0.447581 + 2.96642i) q^{3} +(-3.84521 + 6.66010i) q^{4} +(3.81256 + 6.60355i) q^{5} +(8.01856 - 6.39660i) q^{6} +(4.11804 - 5.66055i) q^{7} +12.6180 q^{8} +(-8.59934 + 2.65543i) q^{9} +O(q^{10})\) \(q+(-1.70956 - 2.96105i) q^{2} +(0.447581 + 2.96642i) q^{3} +(-3.84521 + 6.66010i) q^{4} +(3.81256 + 6.60355i) q^{5} +(8.01856 - 6.39660i) q^{6} +(4.11804 - 5.66055i) q^{7} +12.6180 q^{8} +(-8.59934 + 2.65543i) q^{9} +(13.0356 - 22.5784i) q^{10} +(-1.31613 + 2.27960i) q^{11} +(-21.4777 - 8.42558i) q^{12} -13.0000 q^{13} +(-23.8012 - 2.51665i) q^{14} +(-17.8825 + 14.2653i) q^{15} +(-6.19042 - 10.7221i) q^{16} +(23.8012 + 13.7416i) q^{17} +(22.5640 + 20.9234i) q^{18} +(-1.27488 + 0.736052i) q^{19} -58.6404 q^{20} +(18.6347 + 9.68229i) q^{21} +9.00000 q^{22} +(-28.1602 + 16.2583i) q^{23} +(5.64758 + 37.4303i) q^{24} +(-16.5712 + 28.7022i) q^{25} +(22.2243 + 38.4936i) q^{26} +(-11.7260 - 24.3208i) q^{27} +(21.8651 + 49.1925i) q^{28} +38.7082i q^{29} +(72.8115 + 28.5635i) q^{30} +(-13.6290 - 7.86870i) q^{31} +(4.07018 - 7.04976i) q^{32} +(-7.35133 - 2.88388i) q^{33} -93.9687i q^{34} +(53.0800 + 5.61249i) q^{35} +(15.3808 - 67.4831i) q^{36} +(-5.09952 + 2.94421i) q^{37} +(4.35897 + 2.51665i) q^{38} +(-5.81856 - 38.5635i) q^{39} +(48.1069 + 83.3235i) q^{40} -47.3245 q^{41} +(-3.18751 - 71.7308i) q^{42} -12.6904 q^{43} +(-10.1216 - 17.5311i) q^{44} +(-50.3208 - 46.6622i) q^{45} +(96.2831 + 55.5891i) q^{46} +(11.4237 + 19.7864i) q^{47} +(29.0356 - 23.1624i) q^{48} +(-15.0835 - 46.6207i) q^{49} +113.318 q^{50} +(-30.1105 + 76.7549i) q^{51} +(49.9877 - 86.5812i) q^{52} +(78.1152 + 45.0998i) q^{53} +(-51.9686 + 76.2993i) q^{54} -20.0712 q^{55} +(51.9614 - 71.4247i) q^{56} +(-2.75405 - 3.45239i) q^{57} +(114.617 - 66.1741i) q^{58} +(-18.1401 + 31.4196i) q^{59} +(-26.2463 - 173.952i) q^{60} +(32.6069 + 56.4768i) q^{61} +53.8081i q^{62} +(-20.3812 + 59.6121i) q^{63} -77.3562 q^{64} +(-49.5633 - 85.8461i) q^{65} +(4.02823 + 26.6978i) q^{66} +(8.13479 + 4.69662i) q^{67} +(-183.041 + 105.679i) q^{68} +(-60.8329 - 76.2581i) q^{69} +(-74.1247 - 166.767i) q^{70} +94.6770 q^{71} +(-108.506 + 33.5062i) q^{72} +(92.0638 + 53.1531i) q^{73} +(17.4359 + 10.0666i) q^{74} +(-92.5600 - 36.3108i) q^{75} -11.3211i q^{76} +(7.48391 + 16.8375i) q^{77} +(-104.241 + 83.1558i) q^{78} +(-18.4521 - 31.9599i) q^{79} +(47.2027 - 81.7574i) q^{80} +(66.8974 - 45.6699i) q^{81} +(80.9042 + 140.130i) q^{82} -11.2598 q^{83} +(-136.139 + 86.8787i) q^{84} +209.563i q^{85} +(21.6951 + 37.5769i) q^{86} +(-114.825 + 17.3251i) q^{87} +(-16.6069 + 28.7639i) q^{88} +(-77.0661 - 133.482i) q^{89} +(-52.1425 + 228.774i) q^{90} +(-53.5345 + 73.5871i) q^{91} -250.066i q^{92} +(17.2418 - 43.9512i) q^{93} +(39.0589 - 67.6521i) q^{94} +(-9.72111 - 5.61249i) q^{95} +(22.7343 + 8.91854i) q^{96} -22.6422i q^{97} +(-112.260 + 124.364i) q^{98} +(5.26450 - 23.0979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 24 q^{4} - 16 q^{9} + 96 q^{10} - 88 q^{12} - 208 q^{13} - 24 q^{16} + 144 q^{22} - 40 q^{25} + 264 q^{30} + 96 q^{36} + 432 q^{40} - 448 q^{42} - 128 q^{43} + 352 q^{48} - 504 q^{49} + 280 q^{51} + 312 q^{52} - 96 q^{55} + 184 q^{61} - 112 q^{64} - 448 q^{69} - 528 q^{75} + 80 q^{79} + 584 q^{81} + 544 q^{82} - 448 q^{87} + 72 q^{88} - 384 q^{90} - 88 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70956 2.96105i −0.854781 1.48052i −0.876848 0.480768i \(-0.840358\pi\)
0.0220666 0.999757i \(-0.492975\pi\)
\(3\) 0.447581 + 2.96642i 0.149194 + 0.988808i
\(4\) −3.84521 + 6.66010i −0.961302 + 1.66502i
\(5\) 3.81256 + 6.60355i 0.762512 + 1.32071i 0.941552 + 0.336868i \(0.109368\pi\)
−0.179040 + 0.983842i \(0.557299\pi\)
\(6\) 8.01856 6.39660i 1.33643 1.06610i
\(7\) 4.11804 5.66055i 0.588291 0.808649i
\(8\) 12.6180 1.57725
\(9\) −8.59934 + 2.65543i −0.955482 + 0.295048i
\(10\) 13.0356 22.5784i 1.30356 2.25784i
\(11\) −1.31613 + 2.27960i −0.119648 + 0.207236i −0.919628 0.392790i \(-0.871510\pi\)
0.799980 + 0.600026i \(0.204843\pi\)
\(12\) −21.4777 8.42558i −1.78981 0.702132i
\(13\) −13.0000 −1.00000
\(14\) −23.8012 2.51665i −1.70009 0.179761i
\(15\) −17.8825 + 14.2653i −1.19217 + 0.951020i
\(16\) −6.19042 10.7221i −0.386901 0.670132i
\(17\) 23.8012 + 13.7416i 1.40007 + 0.808331i 0.994399 0.105688i \(-0.0337046\pi\)
0.405671 + 0.914019i \(0.367038\pi\)
\(18\) 22.5640 + 20.9234i 1.25355 + 1.16241i
\(19\) −1.27488 + 0.736052i −0.0670989 + 0.0387396i −0.533174 0.846006i \(-0.679001\pi\)
0.466075 + 0.884745i \(0.345668\pi\)
\(20\) −58.6404 −2.93202
\(21\) 18.6347 + 9.68229i 0.887368 + 0.461061i
\(22\) 9.00000 0.409091
\(23\) −28.1602 + 16.2583i −1.22436 + 0.706882i −0.965843 0.259126i \(-0.916565\pi\)
−0.258512 + 0.966008i \(0.583232\pi\)
\(24\) 5.64758 + 37.4303i 0.235316 + 1.55960i
\(25\) −16.5712 + 28.7022i −0.662850 + 1.14809i
\(26\) 22.2243 + 38.4936i 0.854781 + 1.48052i
\(27\) −11.7260 24.3208i −0.434298 0.900769i
\(28\) 21.8651 + 49.1925i 0.780895 + 1.75687i
\(29\) 38.7082i 1.33477i 0.744715 + 0.667383i \(0.232586\pi\)
−0.744715 + 0.667383i \(0.767414\pi\)
\(30\) 72.8115 + 28.5635i 2.42705 + 0.952118i
\(31\) −13.6290 7.86870i −0.439645 0.253829i 0.263802 0.964577i \(-0.415023\pi\)
−0.703447 + 0.710748i \(0.748357\pi\)
\(32\) 4.07018 7.04976i 0.127193 0.220305i
\(33\) −7.35133 2.88388i −0.222767 0.0873904i
\(34\) 93.9687i 2.76378i
\(35\) 53.0800 + 5.61249i 1.51657 + 0.160357i
\(36\) 15.3808 67.4831i 0.427245 1.87453i
\(37\) −5.09952 + 2.94421i −0.137825 + 0.0795732i −0.567327 0.823493i \(-0.692022\pi\)
0.429502 + 0.903066i \(0.358689\pi\)
\(38\) 4.35897 + 2.51665i 0.114710 + 0.0662277i
\(39\) −5.81856 38.5635i −0.149194 0.988808i
\(40\) 48.1069 + 83.3235i 1.20267 + 2.08309i
\(41\) −47.3245 −1.15426 −0.577128 0.816654i \(-0.695827\pi\)
−0.577128 + 0.816654i \(0.695827\pi\)
\(42\) −3.18751 71.7308i −0.0758930 1.70788i
\(43\) −12.6904 −0.295126 −0.147563 0.989053i \(-0.547143\pi\)
−0.147563 + 0.989053i \(0.547143\pi\)
\(44\) −10.1216 17.5311i −0.230035 0.398433i
\(45\) −50.3208 46.6622i −1.11824 1.03694i
\(46\) 96.2831 + 55.5891i 2.09311 + 1.20846i
\(47\) 11.4237 + 19.7864i 0.243057 + 0.420987i 0.961583 0.274513i \(-0.0885165\pi\)
−0.718527 + 0.695499i \(0.755183\pi\)
\(48\) 29.0356 23.1624i 0.604909 0.482550i
\(49\) −15.0835 46.6207i −0.307827 0.951442i
\(50\) 113.318 2.26637
\(51\) −30.1105 + 76.7549i −0.590402 + 1.50500i
\(52\) 49.9877 86.5812i 0.961302 1.66502i
\(53\) 78.1152 + 45.0998i 1.47387 + 0.850940i 0.999567 0.0294208i \(-0.00936629\pi\)
0.474304 + 0.880361i \(0.342700\pi\)
\(54\) −51.9686 + 76.2993i −0.962382 + 1.41295i
\(55\) −20.0712 −0.364932
\(56\) 51.9614 71.4247i 0.927881 1.27544i
\(57\) −2.75405 3.45239i −0.0483167 0.0605682i
\(58\) 114.617 66.1741i 1.97615 1.14093i
\(59\) −18.1401 + 31.4196i −0.307460 + 0.532536i −0.977806 0.209513i \(-0.932812\pi\)
0.670346 + 0.742048i \(0.266146\pi\)
\(60\) −26.2463 173.952i −0.437439 2.89920i
\(61\) 32.6069 + 56.4768i 0.534539 + 0.925848i 0.999186 + 0.0403523i \(0.0128480\pi\)
−0.464647 + 0.885496i \(0.653819\pi\)
\(62\) 53.8081i 0.867873i
\(63\) −20.3812 + 59.6121i −0.323511 + 0.946224i
\(64\) −77.3562 −1.20869
\(65\) −49.5633 85.8461i −0.762512 1.32071i
\(66\) 4.02823 + 26.6978i 0.0610338 + 0.404512i
\(67\) 8.13479 + 4.69662i 0.121415 + 0.0700989i 0.559477 0.828846i \(-0.311002\pi\)
−0.438063 + 0.898944i \(0.644335\pi\)
\(68\) −183.041 + 105.679i −2.69178 + 1.55410i
\(69\) −60.8329 76.2581i −0.881636 1.10519i
\(70\) −74.1247 166.767i −1.05892 2.38239i
\(71\) 94.6770 1.33348 0.666739 0.745291i \(-0.267689\pi\)
0.666739 + 0.745291i \(0.267689\pi\)
\(72\) −108.506 + 33.5062i −1.50703 + 0.465364i
\(73\) 92.0638 + 53.1531i 1.26115 + 0.728124i 0.973297 0.229551i \(-0.0737258\pi\)
0.287851 + 0.957675i \(0.407059\pi\)
\(74\) 17.4359 + 10.0666i 0.235620 + 0.136035i
\(75\) −92.5600 36.3108i −1.23413 0.484143i
\(76\) 11.3211i 0.148962i
\(77\) 7.48391 + 16.8375i 0.0971936 + 0.218668i
\(78\) −104.241 + 83.1558i −1.33643 + 1.06610i
\(79\) −18.4521 31.9599i −0.233571 0.404556i 0.725286 0.688448i \(-0.241708\pi\)
−0.958856 + 0.283892i \(0.908374\pi\)
\(80\) 47.2027 81.7574i 0.590033 1.02197i
\(81\) 66.8974 45.6699i 0.825893 0.563826i
\(82\) 80.9042 + 140.130i 0.986636 + 1.70890i
\(83\) −11.2598 −0.135660 −0.0678302 0.997697i \(-0.521608\pi\)
−0.0678302 + 0.997697i \(0.521608\pi\)
\(84\) −136.139 + 86.8787i −1.62071 + 1.03427i
\(85\) 209.563i 2.46545i
\(86\) 21.6951 + 37.5769i 0.252268 + 0.436941i
\(87\) −114.825 + 17.3251i −1.31983 + 0.199139i
\(88\) −16.6069 + 28.7639i −0.188714 + 0.326863i
\(89\) −77.0661 133.482i −0.865912 1.49980i −0.866139 0.499803i \(-0.833406\pi\)
0.000227621 1.00000i \(-0.499928\pi\)
\(90\) −52.1425 + 228.774i −0.579361 + 2.54194i
\(91\) −53.5345 + 73.5871i −0.588291 + 0.808649i
\(92\) 250.066i 2.71811i
\(93\) 17.2418 43.9512i 0.185396 0.472594i
\(94\) 39.0589 67.6521i 0.415521 0.719703i
\(95\) −9.72111 5.61249i −0.102327 0.0590788i
\(96\) 22.7343 + 8.91854i 0.236816 + 0.0929015i
\(97\) 22.6422i 0.233425i −0.993166 0.116712i \(-0.962764\pi\)
0.993166 0.116712i \(-0.0372355\pi\)
\(98\) −112.260 + 124.364i −1.14551 + 1.26902i
\(99\) 5.26450 23.0979i 0.0531768 0.233312i
\(100\) −127.440 220.732i −1.27440 2.20732i
\(101\) 23.4549 + 13.5417i 0.232227 + 0.134076i 0.611599 0.791168i \(-0.290527\pi\)
−0.379372 + 0.925244i \(0.623860\pi\)
\(102\) 278.751 42.0586i 2.73285 0.412339i
\(103\) −53.9644 93.4690i −0.523926 0.907466i −0.999612 0.0278513i \(-0.991134\pi\)
0.475686 0.879615i \(-0.342200\pi\)
\(104\) −164.034 −1.57725
\(105\) 7.10858 + 159.970i 0.0677008 + 1.52352i
\(106\) 308.404i 2.90947i
\(107\) 12.7306 7.35002i 0.118978 0.0686918i −0.439330 0.898326i \(-0.644784\pi\)
0.558308 + 0.829634i \(0.311451\pi\)
\(108\) 207.068 + 15.4219i 1.91729 + 0.142795i
\(109\) −125.211 72.2904i −1.14872 0.663215i −0.200146 0.979766i \(-0.564142\pi\)
−0.948575 + 0.316551i \(0.897475\pi\)
\(110\) 34.3131 + 59.4319i 0.311937 + 0.540290i
\(111\) −11.0162 13.8096i −0.0992452 0.124410i
\(112\) −86.1854 9.11293i −0.769512 0.0813655i
\(113\) 29.8000i 0.263717i −0.991269 0.131858i \(-0.957906\pi\)
0.991269 0.131858i \(-0.0420944\pi\)
\(114\) −5.51447 + 14.0570i −0.0483725 + 0.123307i
\(115\) −214.725 123.971i −1.86717 1.07801i
\(116\) −257.800 148.841i −2.22242 1.28311i
\(117\) 111.791 34.5206i 0.955482 0.295048i
\(118\) 124.047 1.05124
\(119\) 175.799 78.1392i 1.47730 0.656632i
\(120\) −225.641 + 179.999i −1.88034 + 1.50000i
\(121\) 57.0356 + 98.7886i 0.471369 + 0.816435i
\(122\) 111.487 193.101i 0.913828 1.58280i
\(123\) −21.1815 140.384i −0.172208 1.14134i
\(124\) 104.813 60.5136i 0.845263 0.488013i
\(125\) −62.0875 −0.496700
\(126\) 211.357 41.5609i 1.67744 0.329848i
\(127\) −35.1179 −0.276519 −0.138259 0.990396i \(-0.544151\pi\)
−0.138259 + 0.990396i \(0.544151\pi\)
\(128\) 115.965 + 200.857i 0.905973 + 1.56919i
\(129\) −5.67999 37.6452i −0.0440309 0.291823i
\(130\) −169.463 + 293.519i −1.30356 + 2.25784i
\(131\) 127.067 73.3622i 0.969977 0.560017i 0.0707481 0.997494i \(-0.477461\pi\)
0.899229 + 0.437477i \(0.144128\pi\)
\(132\) 47.4743 37.8714i 0.359654 0.286905i
\(133\) −1.08354 + 10.2476i −0.00814695 + 0.0770496i
\(134\) 32.1167i 0.239677i
\(135\) 115.897 170.158i 0.858498 1.26043i
\(136\) 300.323 + 173.392i 2.20826 + 1.27494i
\(137\) −46.2002 + 80.0212i −0.337228 + 0.584096i −0.983910 0.178664i \(-0.942823\pi\)
0.646682 + 0.762760i \(0.276156\pi\)
\(138\) −121.806 + 310.497i −0.882654 + 2.24998i
\(139\) 203.118 1.46128 0.730640 0.682763i \(-0.239222\pi\)
0.730640 + 0.682763i \(0.239222\pi\)
\(140\) −241.483 + 331.936i −1.72488 + 2.37097i
\(141\) −53.5818 + 42.7435i −0.380012 + 0.303145i
\(142\) −161.856 280.343i −1.13983 1.97425i
\(143\) 17.1096 29.6348i 0.119648 0.207236i
\(144\) 81.7053 + 75.7649i 0.567398 + 0.526145i
\(145\) −255.612 + 147.577i −1.76284 + 1.01778i
\(146\) 363.474i 2.48955i
\(147\) 131.546 65.6107i 0.894868 0.446331i
\(148\) 45.2844i 0.305975i
\(149\) −56.6732 98.1608i −0.380357 0.658798i 0.610756 0.791819i \(-0.290866\pi\)
−0.991113 + 0.133021i \(0.957532\pi\)
\(150\) 50.7192 + 336.150i 0.338128 + 2.24100i
\(151\) 108.637 + 62.7217i 0.719452 + 0.415376i 0.814551 0.580092i \(-0.196983\pi\)
−0.0950990 + 0.995468i \(0.530317\pi\)
\(152\) −16.0864 + 9.28750i −0.105832 + 0.0611020i
\(153\) −241.165 54.9665i −1.57624 0.359258i
\(154\) 37.0623 50.9449i 0.240664 0.330811i
\(155\) 120.000i 0.774191i
\(156\) 279.210 + 109.533i 1.78981 + 0.702132i
\(157\) −72.7383 + 125.986i −0.463302 + 0.802462i −0.999123 0.0418695i \(-0.986669\pi\)
0.535822 + 0.844331i \(0.320002\pi\)
\(158\) −63.0900 + 109.275i −0.399304 + 0.691614i
\(159\) −98.8223 + 251.909i −0.621524 + 1.58433i
\(160\) 62.0712 0.387945
\(161\) −23.9339 + 226.354i −0.148658 + 1.40593i
\(162\) −249.596 120.011i −1.54072 0.740807i
\(163\) 210.900 121.763i 1.29387 0.747014i 0.314528 0.949248i \(-0.398154\pi\)
0.979337 + 0.202234i \(0.0648203\pi\)
\(164\) 181.972 315.186i 1.10959 1.92186i
\(165\) −8.98351 59.5398i −0.0544455 0.360847i
\(166\) 19.2494 + 33.3409i 0.115960 + 0.200849i
\(167\) −67.4361 −0.403809 −0.201905 0.979405i \(-0.564713\pi\)
−0.201905 + 0.979405i \(0.564713\pi\)
\(168\) 235.133 + 122.171i 1.39960 + 0.727209i
\(169\) 169.000 1.00000
\(170\) 620.527 358.261i 3.65016 2.10742i
\(171\) 9.00859 9.71492i 0.0526818 0.0568124i
\(172\) 48.7973 84.5194i 0.283705 0.491392i
\(173\) 39.2307 22.6499i 0.226767 0.130924i −0.382313 0.924033i \(-0.624872\pi\)
0.609080 + 0.793109i \(0.291539\pi\)
\(174\) 247.601 + 310.384i 1.42299 + 1.78382i
\(175\) 94.2293 + 211.999i 0.538453 + 1.21142i
\(176\) 32.5895 0.185167
\(177\) −101.323 39.7485i −0.572447 0.224568i
\(178\) −263.499 + 456.393i −1.48033 + 2.56401i
\(179\) 98.2143 + 56.7040i 0.548683 + 0.316782i 0.748591 0.663032i \(-0.230731\pi\)
−0.199908 + 0.979815i \(0.564064\pi\)
\(180\) 504.269 155.715i 2.80149 0.865086i
\(181\) 108.047 0.596943 0.298471 0.954419i \(-0.403523\pi\)
0.298471 + 0.954419i \(0.403523\pi\)
\(182\) 309.416 + 32.7165i 1.70009 + 0.179761i
\(183\) −152.940 + 122.004i −0.835737 + 0.666687i
\(184\) −355.325 + 205.147i −1.93111 + 1.11493i
\(185\) −38.8844 22.4499i −0.210186 0.121351i
\(186\) −159.618 + 24.0835i −0.858160 + 0.129481i
\(187\) −62.6507 + 36.1714i −0.335031 + 0.193430i
\(188\) −175.706 −0.934604
\(189\) −185.957 33.7781i −0.983900 0.178720i
\(190\) 38.3796i 0.201998i
\(191\) 99.9100 57.6831i 0.523089 0.302006i −0.215108 0.976590i \(-0.569010\pi\)
0.738198 + 0.674584i \(0.235677\pi\)
\(192\) −34.6232 229.471i −0.180329 1.19516i
\(193\) 139.629 + 80.6149i 0.723466 + 0.417694i 0.816027 0.578013i \(-0.196172\pi\)
−0.0925608 + 0.995707i \(0.529505\pi\)
\(194\) −67.0446 + 38.7082i −0.345591 + 0.199527i
\(195\) 232.472 185.449i 1.19217 0.951020i
\(196\) 368.497 + 78.8083i 1.88009 + 0.402083i
\(197\) 5.26450 0.0267234 0.0133617 0.999911i \(-0.495747\pi\)
0.0133617 + 0.999911i \(0.495747\pi\)
\(198\) −77.3941 + 23.8989i −0.390879 + 0.120701i
\(199\) 150.499 260.671i 0.756275 1.30991i −0.188463 0.982080i \(-0.560351\pi\)
0.944738 0.327826i \(-0.106316\pi\)
\(200\) −209.096 + 362.165i −1.04548 + 1.81082i
\(201\) −10.2912 + 26.2334i −0.0512000 + 0.130514i
\(202\) 92.6015i 0.458423i
\(203\) 219.110 + 159.402i 1.07936 + 0.785231i
\(204\) −395.414 495.678i −1.93830 2.42979i
\(205\) −180.427 312.510i −0.880134 1.52444i
\(206\) −184.511 + 319.582i −0.895684 + 1.55137i
\(207\) 198.986 214.588i 0.961286 1.03666i
\(208\) 80.4754 + 139.387i 0.386901 + 0.670132i
\(209\) 3.87495i 0.0185404i
\(210\) 461.526 294.527i 2.19774 1.40251i
\(211\) 38.9533 0.184613 0.0923065 0.995731i \(-0.470576\pi\)
0.0923065 + 0.995731i \(0.470576\pi\)
\(212\) −600.738 + 346.836i −2.83367 + 1.63602i
\(213\) 42.3756 + 280.852i 0.198947 + 1.31855i
\(214\) −43.5276 25.1306i −0.203400 0.117433i
\(215\) −48.3830 83.8018i −0.225037 0.389776i
\(216\) −147.959 306.879i −0.684996 1.42074i
\(217\) −100.666 + 44.7439i −0.463898 + 0.206193i
\(218\) 494.340i 2.26761i
\(219\) −116.468 + 296.891i −0.531820 + 1.35566i
\(220\) 77.1781 133.676i 0.350810 0.607620i
\(221\) −309.416 178.641i −1.40007 0.808331i
\(222\) −22.0579 + 56.2279i −0.0993598 + 0.253279i
\(223\) 102.696i 0.460522i −0.973129 0.230261i \(-0.926042\pi\)
0.973129 0.230261i \(-0.0739580\pi\)
\(224\) −23.1443 52.0706i −0.103323 0.232458i
\(225\) 66.2850 290.824i 0.294600 1.29255i
\(226\) −88.2392 + 50.9449i −0.390439 + 0.225420i
\(227\) −62.7246 + 108.642i −0.276320 + 0.478600i −0.970467 0.241233i \(-0.922448\pi\)
0.694148 + 0.719833i \(0.255782\pi\)
\(228\) 33.5832 5.06711i 0.147295 0.0222242i
\(229\) 374.053 215.960i 1.63342 0.943056i 0.650393 0.759598i \(-0.274604\pi\)
0.983028 0.183458i \(-0.0587290\pi\)
\(230\) 847.747i 3.68586i
\(231\) −46.5974 + 29.7366i −0.201720 + 0.128730i
\(232\) 488.420i 2.10526i
\(233\) −116.689 + 67.3705i −0.500811 + 0.289144i −0.729049 0.684462i \(-0.760037\pi\)
0.228237 + 0.973606i \(0.426704\pi\)
\(234\) −293.332 272.005i −1.25355 1.16241i
\(235\) −87.1069 + 150.874i −0.370668 + 0.642015i
\(236\) −139.505 241.630i −0.591123 1.02386i
\(237\) 86.5479 69.0414i 0.365181 0.291314i
\(238\) −531.914 386.966i −2.23493 1.62591i
\(239\) −219.958 −0.920326 −0.460163 0.887834i \(-0.652209\pi\)
−0.460163 + 0.887834i \(0.652209\pi\)
\(240\) 263.654 + 103.430i 1.09856 + 0.430959i
\(241\) −112.644 65.0348i −0.467401 0.269854i 0.247750 0.968824i \(-0.420309\pi\)
−0.715151 + 0.698970i \(0.753642\pi\)
\(242\) 195.012 337.771i 0.805834 1.39575i
\(243\) 165.418 + 178.005i 0.680734 + 0.732531i
\(244\) −501.521 −2.05541
\(245\) 250.355 277.349i 1.02186 1.13204i
\(246\) −379.474 + 302.716i −1.54258 + 1.23055i
\(247\) 16.5734 9.56867i 0.0670989 0.0387396i
\(248\) −171.970 99.2872i −0.693429 0.400352i
\(249\) −5.03968 33.4014i −0.0202397 0.134142i
\(250\) 106.142 + 183.844i 0.424570 + 0.735377i
\(251\) 217.191i 0.865302i −0.901562 0.432651i \(-0.857578\pi\)
0.901562 0.432651i \(-0.142422\pi\)
\(252\) −318.652 364.962i −1.26449 1.44826i
\(253\) 85.5918i 0.338307i
\(254\) 60.0362 + 103.986i 0.236363 + 0.409393i
\(255\) −621.653 + 93.7965i −2.43786 + 0.367830i
\(256\) 241.785 418.784i 0.944473 1.63587i
\(257\) −363.383 + 209.799i −1.41394 + 0.816340i −0.995757 0.0920216i \(-0.970667\pi\)
−0.418185 + 0.908362i \(0.637334\pi\)
\(258\) −101.759 + 81.1755i −0.394414 + 0.314634i
\(259\) −4.33418 + 40.9904i −0.0167343 + 0.158264i
\(260\) 762.325 2.93202
\(261\) −102.787 332.865i −0.393820 1.27535i
\(262\) −434.458 250.835i −1.65824 0.957384i
\(263\) 296.339 + 171.091i 1.12676 + 0.650537i 0.943119 0.332456i \(-0.107877\pi\)
0.183644 + 0.982993i \(0.441211\pi\)
\(264\) −92.7590 36.3888i −0.351360 0.137836i
\(265\) 687.783i 2.59541i
\(266\) 32.1960 14.3105i 0.121038 0.0537988i
\(267\) 361.472 288.355i 1.35383 1.07998i
\(268\) −62.5599 + 36.1190i −0.233433 + 0.134772i
\(269\) 71.7141 + 41.4042i 0.266595 + 0.153919i 0.627339 0.778746i \(-0.284144\pi\)
−0.360744 + 0.932665i \(0.617477\pi\)
\(270\) −701.979 52.2817i −2.59992 0.193636i
\(271\) 451.032 260.403i 1.66432 0.960897i 0.693709 0.720255i \(-0.255975\pi\)
0.970614 0.240642i \(-0.0773580\pi\)
\(272\) 340.266i 1.25098i
\(273\) −242.252 125.870i −0.887368 0.461061i
\(274\) 315.929 1.15302
\(275\) −43.6197 75.5515i −0.158617 0.274733i
\(276\) 741.801 111.925i 2.68769 0.405525i
\(277\) −76.3685 + 132.274i −0.275699 + 0.477524i −0.970311 0.241860i \(-0.922243\pi\)
0.694612 + 0.719384i \(0.255576\pi\)
\(278\) −347.243 601.442i −1.24907 2.16346i
\(279\) 138.095 + 31.4748i 0.494965 + 0.112813i
\(280\) 669.763 + 70.8183i 2.39201 + 0.252923i
\(281\) −321.417 −1.14383 −0.571917 0.820312i \(-0.693800\pi\)
−0.571917 + 0.820312i \(0.693800\pi\)
\(282\) 218.167 + 85.5856i 0.773641 + 0.303495i
\(283\) 27.7973 48.1463i 0.0982236 0.170128i −0.812726 0.582646i \(-0.802017\pi\)
0.910949 + 0.412518i \(0.135351\pi\)
\(284\) −364.053 + 630.558i −1.28188 + 2.22027i
\(285\) 12.2980 31.3490i 0.0431510 0.109996i
\(286\) −117.000 −0.409091
\(287\) −194.884 + 267.882i −0.679038 + 0.933388i
\(288\) −16.2807 + 71.4314i −0.0565303 + 0.248026i
\(289\) 233.165 + 403.853i 0.806798 + 1.39741i
\(290\) 873.968 + 504.586i 3.01368 + 1.73995i
\(291\) 67.1663 10.1342i 0.230812 0.0348255i
\(292\) −708.009 + 408.769i −2.42469 + 1.39989i
\(293\) 506.781 1.72963 0.864813 0.502093i \(-0.167437\pi\)
0.864813 + 0.502093i \(0.167437\pi\)
\(294\) −419.162 277.347i −1.42572 0.943358i
\(295\) −276.641 −0.937767
\(296\) −64.3457 + 37.1500i −0.217384 + 0.125507i
\(297\) 70.8745 + 5.27856i 0.238635 + 0.0177729i
\(298\) −193.773 + 335.624i −0.650244 + 1.12626i
\(299\) 366.082 211.358i 1.22436 0.706882i
\(300\) 597.746 476.836i 1.99249 1.58945i
\(301\) −52.2596 + 71.8347i −0.173620 + 0.238653i
\(302\) 428.907i 1.42022i
\(303\) −29.6724 + 75.6382i −0.0979288 + 0.249631i
\(304\) 15.7841 + 9.11293i 0.0519213 + 0.0299768i
\(305\) −248.631 + 430.642i −0.815185 + 1.41194i
\(306\) 249.527 + 808.069i 0.815449 + 2.64075i
\(307\) 199.468i 0.649734i 0.945760 + 0.324867i \(0.105319\pi\)
−0.945760 + 0.324867i \(0.894681\pi\)
\(308\) −140.916 14.9000i −0.457520 0.0483766i
\(309\) 253.115 201.916i 0.819144 0.653451i
\(310\) −355.325 + 205.147i −1.14621 + 0.661764i
\(311\) −140.108 80.8915i −0.450509 0.260101i 0.257536 0.966269i \(-0.417089\pi\)
−0.708045 + 0.706167i \(0.750423\pi\)
\(312\) −73.4185 486.594i −0.235316 1.55960i
\(313\) −195.142 337.997i −0.623458 1.07986i −0.988837 0.149003i \(-0.952394\pi\)
0.365378 0.930859i \(-0.380940\pi\)
\(314\) 497.403 1.58409
\(315\) −471.356 + 92.6865i −1.49637 + 0.294243i
\(316\) 283.808 0.898128
\(317\) −22.9875 39.8155i −0.0725158 0.125601i 0.827488 0.561484i \(-0.189769\pi\)
−0.900003 + 0.435883i \(0.856436\pi\)
\(318\) 914.857 138.036i 2.87691 0.434075i
\(319\) −88.2392 50.9449i −0.276612 0.159702i
\(320\) −294.925 510.826i −0.921642 1.59633i
\(321\) 27.5013 + 34.4747i 0.0856737 + 0.107398i
\(322\) 711.162 316.097i 2.20858 0.981668i
\(323\) −40.4582 −0.125258
\(324\) 46.9318 + 621.153i 0.144851 + 1.91714i
\(325\) 215.426 373.129i 0.662850 1.14809i
\(326\) −721.094 416.324i −2.21194 1.27707i
\(327\) 158.402 403.784i 0.484410 1.23481i
\(328\) −597.140 −1.82055
\(329\) 159.045 + 16.8168i 0.483419 + 0.0511150i
\(330\) −160.942 + 128.388i −0.487704 + 0.389054i
\(331\) −42.8290 + 24.7274i −0.129393 + 0.0747050i −0.563299 0.826253i \(-0.690468\pi\)
0.433906 + 0.900958i \(0.357135\pi\)
\(332\) 43.2963 74.9915i 0.130411 0.225878i
\(333\) 36.0344 38.8597i 0.108211 0.116696i
\(334\) 115.286 + 199.682i 0.345168 + 0.597849i
\(335\) 71.6247i 0.213805i
\(336\) −11.5421 259.741i −0.0343516 0.773039i
\(337\) 111.882 0.331994 0.165997 0.986126i \(-0.446916\pi\)
0.165997 + 0.986126i \(0.446916\pi\)
\(338\) −288.916 500.417i −0.854781 1.48052i
\(339\) 88.3993 13.3379i 0.260765 0.0393449i
\(340\) −1395.71 805.814i −4.10503 2.37004i
\(341\) 35.8749 20.7124i 0.105205 0.0607402i
\(342\) −44.1671 10.0666i −0.129144 0.0294345i
\(343\) −326.013 106.605i −0.950475 0.310800i
\(344\) −160.128 −0.465487
\(345\) 271.645 692.452i 0.787377 2.00711i
\(346\) −134.135 77.4428i −0.387673 0.223823i
\(347\) 481.422 + 277.949i 1.38738 + 0.801006i 0.993020 0.117949i \(-0.0376320\pi\)
0.394363 + 0.918955i \(0.370965\pi\)
\(348\) 326.139 831.364i 0.937182 2.38898i
\(349\) 121.834i 0.349094i 0.984649 + 0.174547i \(0.0558461\pi\)
−0.984649 + 0.174547i \(0.944154\pi\)
\(350\) 466.649 641.444i 1.33328 1.83270i
\(351\) 152.439 + 316.170i 0.434298 + 0.900769i
\(352\) 10.7137 + 18.5567i 0.0304368 + 0.0527180i
\(353\) −177.017 + 306.603i −0.501465 + 0.868564i 0.498533 + 0.866871i \(0.333872\pi\)
−0.999999 + 0.00169298i \(0.999461\pi\)
\(354\) 55.5210 + 367.975i 0.156839 + 1.03948i
\(355\) 360.962 + 625.204i 1.01679 + 1.76114i
\(356\) 1185.34 3.32961
\(357\) 310.478 + 486.522i 0.869688 + 1.36281i
\(358\) 387.756i 1.08312i
\(359\) 230.318 + 398.922i 0.641554 + 1.11120i 0.985086 + 0.172063i \(0.0550431\pi\)
−0.343532 + 0.939141i \(0.611624\pi\)
\(360\) −634.947 588.783i −1.76374 1.63551i
\(361\) −179.416 + 310.758i −0.496998 + 0.860827i
\(362\) −184.713 319.931i −0.510256 0.883789i
\(363\) −267.521 + 213.408i −0.736972 + 0.587900i
\(364\) −284.246 639.502i −0.780895 1.75687i
\(365\) 810.597i 2.22081i
\(366\) 622.719 + 244.289i 1.70142 + 0.667457i
\(367\) −197.260 + 341.665i −0.537494 + 0.930967i 0.461544 + 0.887117i \(0.347296\pi\)
−0.999038 + 0.0438500i \(0.986038\pi\)
\(368\) 348.646 + 201.291i 0.947408 + 0.546986i
\(369\) 406.959 125.667i 1.10287 0.340561i
\(370\) 153.518i 0.414914i
\(371\) 576.971 256.452i 1.55518 0.691245i
\(372\) 226.421 + 283.834i 0.608659 + 0.762994i
\(373\) 8.71374 + 15.0926i 0.0233612 + 0.0404629i 0.877470 0.479632i \(-0.159230\pi\)
−0.854108 + 0.520095i \(0.825897\pi\)
\(374\) 214.211 + 123.675i 0.572756 + 0.330681i
\(375\) −27.7892 184.178i −0.0741046 0.491141i
\(376\) 144.144 + 249.664i 0.383361 + 0.664001i
\(377\) 503.207i 1.33477i
\(378\) 217.887 + 608.374i 0.576420 + 1.60945i
\(379\) 364.695i 0.962255i −0.876651 0.481128i \(-0.840227\pi\)
0.876651 0.481128i \(-0.159773\pi\)
\(380\) 74.7594 43.1624i 0.196735 0.113585i
\(381\) −15.7181 104.175i −0.0412549 0.273424i
\(382\) −341.605 197.226i −0.894254 0.516298i
\(383\) 189.775 + 328.701i 0.495497 + 0.858226i 0.999987 0.00519153i \(-0.00165252\pi\)
−0.504489 + 0.863418i \(0.668319\pi\)
\(384\) −543.922 + 433.900i −1.41646 + 1.12995i
\(385\) −82.6541 + 113.614i −0.214686 + 0.295102i
\(386\) 551.265i 1.42815i
\(387\) 109.129 33.6985i 0.281988 0.0870763i
\(388\) 150.799 + 87.0639i 0.388657 + 0.224391i
\(389\) −3.35580 1.93747i −0.00862675 0.00498065i 0.495680 0.868505i \(-0.334919\pi\)
−0.504307 + 0.863524i \(0.668252\pi\)
\(390\) −946.549 371.326i −2.42705 0.952118i
\(391\) −893.661 −2.28558
\(392\) −190.324 588.259i −0.485521 1.50066i
\(393\) 274.496 + 344.099i 0.698464 + 0.875570i
\(394\) −9.00000 15.5885i −0.0228426 0.0395646i
\(395\) 140.699 243.698i 0.356201 0.616958i
\(396\) 133.591 + 123.878i 0.337352 + 0.312824i
\(397\) −566.438 + 327.033i −1.42680 + 0.823761i −0.996867 0.0791018i \(-0.974795\pi\)
−0.429929 + 0.902863i \(0.641461\pi\)
\(398\) −1029.15 −2.58580
\(399\) −30.8837 + 1.37238i −0.0774028 + 0.00343955i
\(400\) 410.332 1.02583
\(401\) −49.3294 85.4410i −0.123016 0.213070i 0.797940 0.602737i \(-0.205923\pi\)
−0.920956 + 0.389667i \(0.872590\pi\)
\(402\) 95.2717 14.3748i 0.236994 0.0357583i
\(403\) 177.177 + 102.293i 0.439645 + 0.253829i
\(404\) −180.378 + 104.141i −0.446480 + 0.257775i
\(405\) 556.634 + 267.641i 1.37440 + 0.660841i
\(406\) 97.4152 921.302i 0.239939 2.26922i
\(407\) 15.4998i 0.0380830i
\(408\) −379.934 + 968.493i −0.931212 + 2.37376i
\(409\) 337.204 + 194.685i 0.824460 + 0.476002i 0.851952 0.523620i \(-0.175419\pi\)
−0.0274923 + 0.999622i \(0.508752\pi\)
\(410\) −616.904 + 1068.51i −1.50464 + 2.60612i
\(411\) −258.055 101.234i −0.627871 0.246310i
\(412\) 830.017 2.01460
\(413\) 103.150 + 232.070i 0.249759 + 0.561913i
\(414\) −975.585 222.356i −2.35648 0.537093i
\(415\) −42.9288 74.3548i −0.103443 0.179168i
\(416\) −52.9123 + 91.6469i −0.127193 + 0.220305i
\(417\) 90.9118 + 602.534i 0.218014 + 1.44493i
\(418\) −11.4739 + 6.62447i −0.0274496 + 0.0158480i
\(419\) 101.383i 0.241965i −0.992655 0.120983i \(-0.961395\pi\)
0.992655 0.120983i \(-0.0386045\pi\)
\(420\) −1092.75 567.773i −2.60178 1.35184i
\(421\) 89.7621i 0.213212i −0.994301 0.106606i \(-0.966002\pi\)
0.994301 0.106606i \(-0.0339983\pi\)
\(422\) −66.5932 115.343i −0.157804 0.273324i
\(423\) −150.777 139.815i −0.356448 0.330532i
\(424\) 985.657 + 569.069i 2.32466 + 1.34214i
\(425\) −788.831 + 455.432i −1.85607 + 1.07160i
\(426\) 759.173 605.611i 1.78210 1.42162i
\(427\) 453.966 + 48.0007i 1.06315 + 0.112414i
\(428\) 113.049i 0.264134i
\(429\) 95.5672 + 37.4905i 0.222767 + 0.0873904i
\(430\) −165.427 + 286.529i −0.384715 + 0.666346i
\(431\) 323.225 559.842i 0.749941 1.29894i −0.197909 0.980220i \(-0.563415\pi\)
0.947850 0.318716i \(-0.103252\pi\)
\(432\) −188.181 + 276.284i −0.435604 + 0.639545i
\(433\) −571.521 −1.31991 −0.659955 0.751305i \(-0.729425\pi\)
−0.659955 + 0.751305i \(0.729425\pi\)
\(434\) 304.583 + 221.584i 0.701805 + 0.510562i
\(435\) −552.184 692.200i −1.26939 1.59126i
\(436\) 962.922 555.943i 2.20854 1.27510i
\(437\) 23.9339 41.4547i 0.0547686 0.0948620i
\(438\) 1078.22 162.684i 2.46168 0.371425i
\(439\) −192.296 333.066i −0.438032 0.758694i 0.559506 0.828826i \(-0.310991\pi\)
−0.997538 + 0.0701329i \(0.977658\pi\)
\(440\) −253.259 −0.575588
\(441\) 253.507 + 360.854i 0.574845 + 0.818262i
\(442\) 1221.59i 2.76378i
\(443\) −429.496 + 247.970i −0.969517 + 0.559751i −0.899089 0.437766i \(-0.855770\pi\)
−0.0704282 + 0.997517i \(0.522437\pi\)
\(444\) 134.333 20.2684i 0.302551 0.0456496i
\(445\) 587.639 1017.82i 1.32054 2.28724i
\(446\) −304.089 + 175.566i −0.681814 + 0.393646i
\(447\) 265.821 212.052i 0.594677 0.474388i
\(448\) −318.556 + 437.878i −0.711062 + 0.977407i
\(449\) −568.342 −1.26580 −0.632898 0.774235i \(-0.718135\pi\)
−0.632898 + 0.774235i \(0.718135\pi\)
\(450\) −974.463 + 300.909i −2.16547 + 0.668687i
\(451\) 62.2850 107.881i 0.138104 0.239203i
\(452\) 198.471 + 114.587i 0.439094 + 0.253511i
\(453\) −137.435 + 350.337i −0.303389 + 0.773371i
\(454\) 428.926 0.944771
\(455\) −690.039 72.9623i −1.51657 0.160357i
\(456\) −34.7506 43.5622i −0.0762075 0.0955312i
\(457\) −178.846 + 103.257i −0.391349 + 0.225945i −0.682744 0.730657i \(-0.739214\pi\)
0.291396 + 0.956603i \(0.405880\pi\)
\(458\) −1278.93 738.393i −2.79243 1.61221i
\(459\) 55.1132 739.998i 0.120072 1.61220i
\(460\) 1651.32 953.391i 3.58983 2.07259i
\(461\) −223.957 −0.485807 −0.242903 0.970050i \(-0.578100\pi\)
−0.242903 + 0.970050i \(0.578100\pi\)
\(462\) 167.713 + 87.1406i 0.363014 + 0.188616i
\(463\) 779.264i 1.68307i −0.540199 0.841537i \(-0.681651\pi\)
0.540199 0.841537i \(-0.318349\pi\)
\(464\) 415.034 239.620i 0.894470 0.516422i
\(465\) 355.970 53.7096i 0.765526 0.115504i
\(466\) 398.975 + 230.348i 0.856168 + 0.494309i
\(467\) 125.682 72.5624i 0.269126 0.155380i −0.359364 0.933197i \(-0.617006\pi\)
0.628490 + 0.777817i \(0.283673\pi\)
\(468\) −199.951 + 877.281i −0.427245 + 1.87453i
\(469\) 60.0848 26.7065i 0.128113 0.0569435i
\(470\) 595.659 1.26736
\(471\) −406.286 159.384i −0.862602 0.338394i
\(472\) −228.892 + 396.452i −0.484940 + 0.839941i
\(473\) 16.7022 28.9290i 0.0353112 0.0611608i
\(474\) −352.394 138.242i −0.743447 0.291650i
\(475\) 48.7892i 0.102714i
\(476\) −155.570 + 1471.30i −0.326828 + 3.09097i
\(477\) −791.499 180.399i −1.65933 0.378196i
\(478\) 376.032 + 651.306i 0.786677 + 1.36257i
\(479\) −315.482 + 546.431i −0.658627 + 1.14077i 0.322345 + 0.946622i \(0.395529\pi\)
−0.980971 + 0.194153i \(0.937804\pi\)
\(480\) 27.7819 + 184.130i 0.0578790 + 0.383603i
\(481\) 66.2937 38.2747i 0.137825 0.0795732i
\(482\) 444.724i 0.922664i
\(483\) −682.175 + 30.3138i −1.41237 + 0.0627615i
\(484\) −877.255 −1.81251
\(485\) 149.519 86.3247i 0.308286 0.177989i
\(486\) 244.288 794.123i 0.502651 1.63400i
\(487\) 398.367 + 229.997i 0.818002 + 0.472273i 0.849727 0.527223i \(-0.176767\pi\)
−0.0317252 + 0.999497i \(0.510100\pi\)
\(488\) 411.433 + 712.623i 0.843101 + 1.46029i
\(489\) 455.596 + 571.120i 0.931690 + 1.16793i
\(490\) −1249.24 267.168i −2.54947 0.545240i
\(491\) 589.214i 1.20003i −0.799989 0.600015i \(-0.795161\pi\)
0.799989 0.600015i \(-0.204839\pi\)
\(492\) 1016.42 + 398.736i 2.06590 + 0.810440i
\(493\) −531.914 + 921.302i −1.07893 + 1.86877i
\(494\) −56.6666 32.7165i −0.114710 0.0662277i
\(495\) 172.600 53.2978i 0.348686 0.107672i
\(496\) 194.842i 0.392827i
\(497\) 389.883 535.923i 0.784474 1.07832i
\(498\) −90.2875 + 72.0245i −0.181300 + 0.144628i
\(499\) −217.184 + 125.391i −0.435238 + 0.251285i −0.701575 0.712595i \(-0.747520\pi\)
0.266338 + 0.963880i \(0.414186\pi\)
\(500\) 238.739 413.509i 0.477479 0.827018i
\(501\) −30.1831 200.044i −0.0602458 0.399290i
\(502\) −643.112 + 371.301i −1.28110 + 0.739644i
\(503\) 312.424i 0.621121i 0.950554 + 0.310560i \(0.100517\pi\)
−0.950554 + 0.310560i \(0.899483\pi\)
\(504\) −257.170 + 752.185i −0.510258 + 1.49243i
\(505\) 206.514i 0.408939i
\(506\) −253.441 + 146.325i −0.500873 + 0.289179i
\(507\) 75.6412 + 501.326i 0.149194 + 0.988808i
\(508\) 135.036 233.889i 0.265818 0.460411i
\(509\) 20.4403 + 35.4037i 0.0401578 + 0.0695554i 0.885406 0.464819i \(-0.153881\pi\)
−0.845248 + 0.534374i \(0.820547\pi\)
\(510\) 1340.49 + 1680.39i 2.62841 + 3.29489i
\(511\) 679.997 302.245i 1.33072 0.591478i
\(512\) −725.669 −1.41732
\(513\) 32.8506 + 22.3751i 0.0640363 + 0.0436161i
\(514\) 1242.45 + 717.330i 2.41722 + 1.39558i
\(515\) 411.485 712.713i 0.799000 1.38391i
\(516\) 272.561 + 106.924i 0.528219 + 0.207217i
\(517\) −60.1400 −0.116325
\(518\) 128.784 57.2419i 0.248618 0.110506i
\(519\) 84.7481 + 106.237i 0.163291 + 0.204696i
\(520\) −625.389 1083.21i −1.20267 2.08309i
\(521\) 356.672 + 205.924i 0.684590 + 0.395248i 0.801582 0.597884i \(-0.203992\pi\)
−0.116992 + 0.993133i \(0.537325\pi\)
\(522\) −809.910 + 873.411i −1.55155 + 1.67320i
\(523\) −22.1289 38.3284i −0.0423115 0.0732857i 0.844094 0.536195i \(-0.180139\pi\)
−0.886406 + 0.462909i \(0.846806\pi\)
\(524\) 1128.37i 2.15338i
\(525\) −586.704 + 374.411i −1.11753 + 0.713164i
\(526\) 1169.96i 2.22427i
\(527\) −216.257 374.569i −0.410356 0.710757i
\(528\) 14.5864 + 96.6742i 0.0276258 + 0.183095i
\(529\) 264.163 457.544i 0.499363 0.864923i
\(530\) 2036.56 1175.81i 3.84257 2.21851i
\(531\) 72.5605 318.358i 0.136649 0.599544i
\(532\) −64.0835 46.6207i −0.120458 0.0876328i
\(533\) 615.218 1.15426
\(534\) −1471.79 577.376i −2.75617 1.08123i
\(535\) 97.0725 + 56.0448i 0.181444 + 0.104757i
\(536\) 102.645 + 59.2620i 0.191501 + 0.110563i
\(537\) −124.249 + 316.725i −0.231377 + 0.589804i
\(538\) 283.132i 0.526268i
\(539\) 126.128 + 26.9743i 0.234004 + 0.0500450i
\(540\) 687.619 + 1426.18i 1.27337 + 2.64107i
\(541\) 570.140 329.171i 1.05386 0.608449i 0.130135 0.991496i \(-0.458459\pi\)
0.923729 + 0.383048i \(0.125126\pi\)
\(542\) −1542.13 890.351i −2.84526 1.64271i
\(543\) 48.3597 + 320.512i 0.0890601 + 0.590262i
\(544\) 193.750 111.862i 0.356159 0.205628i
\(545\) 1102.45i 2.02284i
\(546\) 41.4376 + 932.501i 0.0758930 + 1.70788i
\(547\) 188.044 0.343774 0.171887 0.985117i \(-0.445014\pi\)
0.171887 + 0.985117i \(0.445014\pi\)
\(548\) −355.299 615.396i −0.648356 1.12299i
\(549\) −430.368 399.078i −0.783912 0.726917i
\(550\) −149.141 + 258.320i −0.271166 + 0.469673i
\(551\) −28.4913 49.3483i −0.0517083 0.0895614i
\(552\) −767.589 962.224i −1.39056 1.74316i
\(553\) −256.897 27.1634i −0.464552 0.0491200i
\(554\) 522.227 0.942648
\(555\) 49.1921 125.396i 0.0886344 0.225939i
\(556\) −781.031 + 1352.78i −1.40473 + 2.43307i
\(557\) −89.8156 + 155.565i −0.161249 + 0.279291i −0.935317 0.353811i \(-0.884886\pi\)
0.774068 + 0.633102i \(0.218219\pi\)
\(558\) −142.884 462.715i −0.256064 0.829238i
\(559\) 164.975 0.295126
\(560\) −268.409 603.873i −0.479302 1.07834i
\(561\) −135.341 169.659i −0.241250 0.302423i
\(562\) 549.483 + 951.732i 0.977727 + 1.69347i
\(563\) −559.119 322.808i −0.993107 0.573371i −0.0869053 0.996217i \(-0.527698\pi\)
−0.906202 + 0.422846i \(0.861031\pi\)
\(564\) −78.6425 521.217i −0.139437 0.924144i
\(565\) 196.786 113.614i 0.348293 0.201087i
\(566\) −190.085 −0.335839
\(567\) 16.9691 566.746i 0.0299280 0.999552i
\(568\) 1194.63 2.10323
\(569\) 293.747 169.595i 0.516251 0.298058i −0.219148 0.975692i \(-0.570328\pi\)
0.735399 + 0.677634i \(0.236995\pi\)
\(570\) −113.850 + 17.1780i −0.199737 + 0.0301368i
\(571\) 236.817 410.179i 0.414740 0.718352i −0.580661 0.814146i \(-0.697206\pi\)
0.995401 + 0.0957941i \(0.0305390\pi\)
\(572\) 131.580 + 227.904i 0.230035 + 0.398433i
\(573\) 215.830 + 270.558i 0.376667 + 0.472177i
\(574\) 1126.38 + 119.099i 1.96233 + 0.207490i
\(575\) 1077.68i 1.87423i
\(576\) 665.213 205.414i 1.15488 0.356622i
\(577\) −428.206 247.225i −0.742125 0.428466i 0.0807167 0.996737i \(-0.474279\pi\)
−0.822841 + 0.568271i \(0.807612\pi\)
\(578\) 797.219 1380.82i 1.37927 2.38897i
\(579\) −176.643 + 450.281i −0.305082 + 0.777687i
\(580\) 2269.86i 3.91356i
\(581\) −46.3684 + 63.7367i −0.0798078 + 0.109702i
\(582\) −144.833 181.558i −0.248854 0.311955i
\(583\) −205.619 + 118.714i −0.352691 + 0.203626i
\(584\) 1161.66 + 670.685i 1.98914 + 1.14843i
\(585\) 654.170 + 606.608i 1.11824 + 1.03694i
\(586\) −866.373 1500.60i −1.47845 2.56076i
\(587\) −805.107 −1.37156 −0.685781 0.727808i \(-0.740539\pi\)
−0.685781 + 0.727808i \(0.740539\pi\)
\(588\) −68.8463 + 1128.39i −0.117086 + 1.91904i
\(589\) 23.1671 0.0393329
\(590\) 472.935 + 819.148i 0.801586 + 1.38839i
\(591\) 2.35629 + 15.6168i 0.00398696 + 0.0264243i
\(592\) 63.1363 + 36.4517i 0.106649 + 0.0615739i
\(593\) 234.927 + 406.905i 0.396167 + 0.686181i 0.993249 0.115999i \(-0.0370069\pi\)
−0.597083 + 0.802180i \(0.703674\pi\)
\(594\) −105.534 218.887i −0.177667 0.368497i
\(595\) 1186.24 + 862.989i 1.99368 + 1.45040i
\(596\) 871.681 1.46255
\(597\) 840.622 + 329.771i 1.40808 + 0.552381i
\(598\) −1251.68 722.658i −2.09311 1.20846i
\(599\) −331.592 191.445i −0.553577 0.319608i 0.196987 0.980406i \(-0.436884\pi\)
−0.750563 + 0.660799i \(0.770218\pi\)
\(600\) −1167.92 458.169i −1.94654 0.763615i
\(601\) −136.830 −0.227671 −0.113836 0.993500i \(-0.536314\pi\)
−0.113836 + 0.993500i \(0.536314\pi\)
\(602\) 302.047 + 31.9374i 0.501739 + 0.0530521i
\(603\) −82.4254 18.7865i −0.136692 0.0311550i
\(604\) −835.466 + 482.356i −1.38322 + 0.798603i
\(605\) −434.904 + 753.275i −0.718849 + 1.24508i
\(606\) 274.695 41.4467i 0.453292 0.0683938i
\(607\) 163.797 + 283.705i 0.269847 + 0.467389i 0.968822 0.247757i \(-0.0796935\pi\)
−0.698975 + 0.715146i \(0.746360\pi\)
\(608\) 11.9835i 0.0197096i
\(609\) −374.784 + 721.317i −0.615409 + 1.18443i
\(610\) 1700.20 2.78722
\(611\) −148.508 257.223i −0.243057 0.420987i
\(612\) 1293.41 1394.82i 2.11342 2.27912i
\(613\) 606.899 + 350.393i 0.990047 + 0.571604i 0.905288 0.424798i \(-0.139655\pi\)
0.0847586 + 0.996402i \(0.472988\pi\)
\(614\) 590.635 341.003i 0.961946 0.555380i
\(615\) 846.280 675.098i 1.37606 1.09772i
\(616\) 94.4319 + 212.455i 0.153299 + 0.344894i
\(617\) −197.729 −0.320469 −0.160234 0.987079i \(-0.551225\pi\)
−0.160234 + 0.987079i \(0.551225\pi\)
\(618\) −1030.60 404.299i −1.66764 0.654205i
\(619\) 353.048 + 203.832i 0.570351 + 0.329293i 0.757290 0.653079i \(-0.226523\pi\)
−0.186938 + 0.982372i \(0.559856\pi\)
\(620\) 799.209 + 461.423i 1.28905 + 0.744231i
\(621\) 725.621 + 494.232i 1.16847 + 0.795864i
\(622\) 553.156i 0.889319i
\(623\) −1072.94 113.449i −1.72222 0.182102i
\(624\) −377.463 + 301.111i −0.604909 + 0.482550i
\(625\) 177.569 + 307.558i 0.284110 + 0.492093i
\(626\) −667.217 + 1155.65i −1.06584 + 1.84609i
\(627\) 11.4947 1.73435i 0.0183329 0.00276612i
\(628\) −559.388 968.889i −0.890745 1.54282i
\(629\) −161.833 −0.257286
\(630\) 1080.26 + 1237.26i 1.71470 + 1.96390i
\(631\) 974.420i 1.54425i 0.635472 + 0.772124i \(0.280806\pi\)
−0.635472 + 0.772124i \(0.719194\pi\)
\(632\) −232.828 403.270i −0.368399 0.638086i
\(633\) 17.4348 + 115.552i 0.0275431 + 0.182547i
\(634\) −78.5971 + 136.134i −0.123970 + 0.214723i
\(635\) −133.889 231.903i −0.210849 0.365201i
\(636\) −1297.74 1626.81i −2.04048 2.55787i
\(637\) 196.086 + 606.069i 0.307827 + 0.951442i
\(638\) 348.374i 0.546041i
\(639\) −814.160 + 251.408i −1.27412 + 0.393440i
\(640\) −884.244 + 1531.56i −1.38163 + 2.39306i
\(641\) 436.447 + 251.983i 0.680884 + 0.393109i 0.800188 0.599749i \(-0.204733\pi\)
−0.119304 + 0.992858i \(0.538066\pi\)
\(642\) 55.0660 140.369i 0.0857726 0.218644i
\(643\) 806.217i 1.25384i −0.779085 0.626919i \(-0.784316\pi\)
0.779085 0.626919i \(-0.215684\pi\)
\(644\) −1415.51 1029.78i −2.19800 1.59904i
\(645\) 226.936 181.033i 0.351839 0.280671i
\(646\) 69.1658 + 119.799i 0.107068 + 0.185447i
\(647\) 415.070 + 239.641i 0.641530 + 0.370387i 0.785204 0.619238i \(-0.212558\pi\)
−0.143674 + 0.989625i \(0.545892\pi\)
\(648\) 844.111 576.263i 1.30264 0.889294i
\(649\) −47.7494 82.7043i −0.0735738 0.127433i
\(650\) −1473.14 −2.26637
\(651\) −177.786 278.591i −0.273096 0.427943i
\(652\) 1872.82i 2.87242i
\(653\) 440.531 254.341i 0.674626 0.389496i −0.123201 0.992382i \(-0.539316\pi\)
0.797827 + 0.602886i \(0.205983\pi\)
\(654\) −1466.42 + 221.257i −2.24224 + 0.338314i
\(655\) 968.902 + 559.396i 1.47924 + 0.854039i
\(656\) 292.958 + 507.419i 0.446583 + 0.773504i
\(657\) −932.832 212.612i −1.41984 0.323611i
\(658\) −222.101 499.689i −0.337540 0.759405i
\(659\) 443.924i 0.673633i 0.941570 + 0.336817i \(0.109350\pi\)
−0.941570 + 0.336817i \(0.890650\pi\)
\(660\) 431.084 + 169.112i 0.653158 + 0.256230i
\(661\) −508.855 293.788i −0.769826 0.444459i 0.0629863 0.998014i \(-0.479938\pi\)
−0.832813 + 0.553555i \(0.813271\pi\)
\(662\) 146.438 + 84.5459i 0.221205 + 0.127713i
\(663\) 391.437 997.814i 0.590402 1.50500i
\(664\) −142.076 −0.213970
\(665\) −71.8016 + 31.9144i −0.107972 + 0.0479915i
\(666\) −176.668 40.2665i −0.265268 0.0604601i
\(667\) −629.329 1090.03i −0.943522 1.63423i
\(668\) 259.306 449.131i 0.388182 0.672352i
\(669\) 304.641 45.9650i 0.455368 0.0687070i
\(670\) 212.084 122.447i 0.316543 0.182756i
\(671\) −171.659 −0.255826
\(672\) 144.105 91.9617i 0.214441 0.136848i
\(673\) 986.044 1.46515 0.732574 0.680688i \(-0.238319\pi\)
0.732574 + 0.680688i \(0.238319\pi\)
\(674\) −191.269 331.288i −0.283783 0.491526i
\(675\) 892.376 + 66.4619i 1.32204 + 0.0984621i
\(676\) −649.840 + 1125.56i −0.961302 + 1.66502i
\(677\) 129.730 74.8998i 0.191625 0.110635i −0.401118 0.916026i \(-0.631378\pi\)
0.592743 + 0.805392i \(0.298045\pi\)
\(678\) −190.618 238.953i −0.281148 0.352438i
\(679\) −128.167 93.2413i −0.188759 0.137322i
\(680\) 2644.27i 3.88863i
\(681\) −350.353 137.441i −0.514468 0.201823i
\(682\) −122.661 70.8183i −0.179855 0.103839i
\(683\) 320.414 554.973i 0.469127 0.812552i −0.530250 0.847841i \(-0.677902\pi\)
0.999377 + 0.0352896i \(0.0112354\pi\)
\(684\) 30.0624 + 97.3539i 0.0439508 + 0.142330i
\(685\) −704.565 −1.02856
\(686\) 241.678 + 1147.59i 0.352301 + 1.67287i
\(687\) 808.047 + 1012.94i 1.17620 + 1.47444i
\(688\) 78.5589 + 136.068i 0.114185 + 0.197773i
\(689\) −1015.50 586.298i −1.47387 0.850940i
\(690\) −2514.78 + 379.436i −3.64461 + 0.549907i
\(691\) −666.727 + 384.935i −0.964873 + 0.557070i −0.897669 0.440670i \(-0.854741\pi\)
−0.0672037 + 0.997739i \(0.521408\pi\)
\(692\) 348.374i 0.503431i
\(693\) −109.067 124.918i −0.157384 0.180257i
\(694\) 1900.68i 2.73874i
\(695\) 774.399 + 1341.30i 1.11424 + 1.92993i
\(696\) −1448.86 + 218.608i −2.08170 + 0.314091i
\(697\) −1126.38 650.315i −1.61604 0.933021i
\(698\) 360.756 208.282i 0.516842 0.298399i
\(699\) −252.077 315.995i −0.360625 0.452068i
\(700\) −1774.27 187.605i −2.53467 0.268007i
\(701\) 1220.21i 1.74067i 0.492457 + 0.870337i \(0.336099\pi\)
−0.492457 + 0.870337i \(0.663901\pi\)
\(702\) 675.592 991.890i 0.962382 1.41295i
\(703\) 4.33418 7.50702i 0.00616526 0.0106785i
\(704\) 101.811 176.341i 0.144617 0.250484i
\(705\) −486.542 190.868i −0.690131 0.270734i
\(706\) 1210.49 1.71457
\(707\) 173.241 77.0023i 0.245037 0.108914i
\(708\) 654.337 521.980i 0.924204 0.737260i
\(709\) 612.879 353.846i 0.864427 0.499077i −0.00106550 0.999999i \(-0.500339\pi\)
0.865492 + 0.500922i \(0.167006\pi\)
\(710\) 1234.17 2137.65i 1.73827 3.01078i
\(711\) 243.543 + 225.836i 0.342536 + 0.317632i
\(712\) −972.420 1684.28i −1.36576 2.36556i
\(713\) 511.726 0.717708
\(714\) 909.832 1751.08i 1.27427 2.45249i
\(715\) 260.926 0.364932
\(716\) −755.309 + 436.078i −1.05490 + 0.609047i
\(717\) −98.4490 652.488i −0.137307 0.910026i
\(718\) 787.485 1363.96i 1.09678 1.89967i
\(719\) −1030.82 + 595.144i −1.43369 + 0.827739i −0.997400 0.0720695i \(-0.977040\pi\)
−0.436286 + 0.899808i \(0.643706\pi\)
\(720\) −188.811 + 828.404i −0.262237 + 1.15056i
\(721\) −751.313 79.4412i −1.04204 0.110182i
\(722\) 1226.89 1.69930
\(723\) 142.504 363.257i 0.197100 0.502430i
\(724\) −415.462 + 719.601i −0.573842 + 0.993924i
\(725\) −1111.01 641.444i −1.53243 0.884750i
\(726\) 1089.25 + 427.308i 1.50035 + 0.588579i
\(727\) −301.359 −0.414524 −0.207262 0.978285i \(-0.566455\pi\)
−0.207262 + 0.978285i \(0.566455\pi\)
\(728\) −675.498 + 928.521i −0.927881 + 1.27544i
\(729\) −454.000 + 570.373i −0.622771 + 0.782404i
\(730\) 2400.22 1385.77i 3.28797 1.89831i
\(731\) −302.047 174.387i −0.413197 0.238559i
\(732\) −224.471 1487.72i −0.306655 2.03241i
\(733\) −879.905 + 508.013i −1.20042 + 0.693060i −0.960648 0.277770i \(-0.910405\pi\)
−0.239768 + 0.970830i \(0.577071\pi\)
\(734\) 1348.92 1.83776
\(735\) 934.789 + 618.523i 1.27182 + 0.841528i
\(736\) 264.697i 0.359642i
\(737\) −21.4128 + 12.3627i −0.0290540 + 0.0167744i
\(738\) −1067.83 990.191i −1.44692 1.34172i
\(739\) −930.201 537.052i −1.25873 0.726728i −0.285902 0.958259i \(-0.592293\pi\)
−0.972828 + 0.231531i \(0.925627\pi\)
\(740\) 299.038 172.649i 0.404105 0.233310i
\(741\) 35.8027 + 44.8811i 0.0483167 + 0.0605682i
\(742\) −1745.73 1270.02i −2.35274 1.71162i
\(743\) −530.788 −0.714385 −0.357192 0.934031i \(-0.616266\pi\)
−0.357192 + 0.934031i \(0.616266\pi\)
\(744\) 217.557 554.576i 0.292416 0.745399i
\(745\) 432.140 748.488i 0.580054 1.00468i
\(746\) 29.7934 51.6036i 0.0399375 0.0691738i
\(747\) 96.8270 29.8997i 0.129621 0.0400263i
\(748\) 556.347i 0.743779i
\(749\) 10.8200 102.330i 0.0144459 0.136622i
\(750\) −497.852 + 397.149i −0.663803 + 0.529532i
\(751\) 259.436 + 449.356i 0.345454 + 0.598344i 0.985436 0.170046i \(-0.0543916\pi\)
−0.639982 + 0.768390i \(0.721058\pi\)
\(752\) 141.435 244.972i 0.188078 0.325760i
\(753\) 644.280 97.2105i 0.855617 0.129098i
\(754\) −1490.02 + 860.264i −1.97615 + 1.14093i
\(755\) 956.522i 1.26692i
\(756\) 940.009 1108.61i 1.24340 1.46641i
\(757\) 216.211 0.285616 0.142808 0.989750i \(-0.454387\pi\)
0.142808 + 0.989750i \(0.454387\pi\)
\(758\) −1079.88 + 623.468i −1.42464 + 0.822518i
\(759\) 253.902 38.3093i 0.334521 0.0504734i
\(760\) −122.661 70.8183i −0.161396 0.0931820i
\(761\) −316.996 549.052i −0.416551 0.721488i 0.579039 0.815300i \(-0.303428\pi\)
−0.995590 + 0.0938121i \(0.970095\pi\)
\(762\) −281.595 + 224.635i −0.369547 + 0.294797i
\(763\) −924.825 + 411.066i −1.21209 + 0.538750i
\(764\) 887.214i 1.16127i
\(765\) −556.481 1802.11i −0.727426 2.35569i
\(766\) 648.866 1123.87i 0.847084 1.46719i
\(767\) 235.822 408.455i 0.307460 0.532536i
\(768\) 1350.51 + 529.797i 1.75848 + 0.689840i
\(769\) 819.151i 1.06522i 0.846362 + 0.532608i \(0.178788\pi\)
−0.846362 + 0.532608i \(0.821212\pi\)
\(770\) 477.720 + 50.5124i 0.620415 + 0.0656005i
\(771\) −784.997 984.046i −1.01815 1.27632i
\(772\) −1073.81 + 619.962i −1.39094 + 0.803059i
\(773\) 568.343 984.399i 0.735244 1.27348i −0.219373 0.975641i \(-0.570401\pi\)
0.954616 0.297838i \(-0.0962656\pi\)
\(774\) −286.346 265.527i −0.369956 0.343058i
\(775\) 451.699 260.788i 0.582837 0.336501i
\(776\) 285.699i 0.368169i
\(777\) −123.535 + 5.48952i −0.158989 + 0.00706502i
\(778\) 13.2489i 0.0170295i
\(779\) 60.3330 34.8333i 0.0774493 0.0447154i
\(780\) 341.202 + 2261.38i 0.437439 + 2.89920i
\(781\) −124.607 + 215.825i −0.159548 + 0.276345i
\(782\) 1527.77 + 2646.17i 1.95367 + 3.38385i
\(783\) 941.414 453.894i 1.20232 0.579686i
\(784\) −406.499 + 450.329i −0.518493 + 0.574399i
\(785\) −1109.28 −1.41309
\(786\) 549.626 1401.06i 0.699270 1.78251i
\(787\) −930.596 537.280i −1.18246 0.682694i −0.225878 0.974156i \(-0.572525\pi\)
−0.956582 + 0.291462i \(0.905858\pi\)
\(788\) −20.2431 + 35.0621i −0.0256892 + 0.0444951i
\(789\) −374.893 + 955.643i −0.475150 + 1.21121i
\(790\) −962.137 −1.21790
\(791\) −168.684 122.717i −0.213254 0.155142i
\(792\) 66.4275 291.449i 0.0838731 0.367992i
\(793\) −423.889 734.198i −0.534539 0.925848i
\(794\) 1936.72 + 1118.17i 2.43920 + 1.40827i
\(795\) −2040.26 + 307.839i −2.56636 + 0.387219i
\(796\) 1157.40 + 2004.67i 1.45402 + 2.51843i
\(797\) 119.200i 0.149561i 0.997200 + 0.0747803i \(0.0238256\pi\)
−0.997200 + 0.0747803i \(0.976174\pi\)
\(798\) 56.8613 + 89.1020i 0.0712548 + 0.111657i
\(799\) 627.919i 0.785881i
\(800\) 134.896 + 233.647i 0.168620 + 0.292058i
\(801\) 1017.17 + 943.217i 1.26988 + 1.17755i
\(802\) −168.663 + 292.133i −0.210303 + 0.364256i
\(803\) −242.335 + 139.912i −0.301787 + 0.174237i
\(804\) −135.145 169.413i −0.168091 0.210713i
\(805\) −1585.99 + 704.940i −1.97017 + 0.875702i
\(806\) 699.506i 0.867873i
\(807\) −90.7244 + 231.266i −0.112422 + 0.286575i
\(808\) 295.954 + 170.869i 0.366279 + 0.211471i
\(809\) 348.228 + 201.050i 0.430443 + 0.248516i 0.699535 0.714598i \(-0.253390\pi\)
−0.269092 + 0.963114i \(0.586724\pi\)
\(810\) −159.103 2105.77i −0.196424 2.59971i
\(811\) 1280.62i 1.57906i −0.613712 0.789530i \(-0.710324\pi\)
0.613712 0.789530i \(-0.289676\pi\)
\(812\) −1904.15 + 846.358i −2.34502 + 1.04231i
\(813\) 974.339 + 1221.40i 1.19845 + 1.50234i
\(814\) −45.8957 + 26.4979i −0.0563829 + 0.0325527i
\(815\) 1608.14 + 928.459i 1.97318 + 1.13921i
\(816\) 1009.37 152.296i 1.23698 0.186638i
\(817\) 16.1787 9.34080i 0.0198026 0.0114331i
\(818\) 1331.30i 1.62751i
\(819\) 264.956 774.958i 0.323511 0.946224i
\(820\) 2775.12 3.38430
\(821\) −404.665 700.900i −0.492893 0.853716i 0.507074 0.861903i \(-0.330727\pi\)
−0.999966 + 0.00818719i \(0.997394\pi\)
\(822\) 141.404 + 937.179i 0.172024 + 1.14012i
\(823\) 36.0687 62.4728i 0.0438259 0.0759087i −0.843280 0.537474i \(-0.819379\pi\)
0.887106 + 0.461565i \(0.152712\pi\)
\(824\) −680.922 1179.39i −0.826362 1.43130i
\(825\) 204.595 163.210i 0.247993 0.197830i
\(826\) 510.829 702.172i 0.618437 0.850087i
\(827\) −645.671 −0.780739 −0.390370 0.920658i \(-0.627653\pi\)
−0.390370 + 0.920658i \(0.627653\pi\)
\(828\) 664.033 + 2150.40i 0.801972 + 2.59710i
\(829\) 468.985 812.306i 0.565724 0.979863i −0.431258 0.902229i \(-0.641930\pi\)
0.996982 0.0776340i \(-0.0247366\pi\)
\(830\) −146.779 + 254.228i −0.176842 + 0.306299i
\(831\) −426.562 167.338i −0.513312 0.201369i
\(832\) 1005.63 1.20869
\(833\) 281.637 1316.90i 0.338100 1.58091i
\(834\) 1628.71 1299.26i 1.95289 1.55787i
\(835\) −257.104 445.318i −0.307909 0.533315i
\(836\) 25.8075 + 14.9000i 0.0308703 + 0.0178229i
\(837\) −31.5588 + 423.736i −0.0377047 + 0.506256i
\(838\) −300.201 + 173.321i −0.358235 + 0.206827i
\(839\) −743.899 −0.886650 −0.443325 0.896361i \(-0.646201\pi\)
−0.443325 + 0.896361i \(0.646201\pi\)
\(840\) 89.6960 + 2018.50i 0.106781 + 2.40297i
\(841\) −657.327 −0.781601
\(842\) −265.790 + 153.454i −0.315665 + 0.182249i
\(843\) −143.860 953.459i −0.170653 1.13103i
\(844\) −149.784 + 259.433i −0.177469 + 0.307385i
\(845\) 644.323 + 1116.00i 0.762512 + 1.32071i
\(846\) −156.236 + 685.482i −0.184676 + 0.810262i
\(847\) 794.072 + 83.9624i 0.937511 + 0.0991291i
\(848\) 1116.75i 1.31692i
\(849\) 155.264 + 60.9092i 0.182879 + 0.0717422i
\(850\) 2697.11 + 1557.18i 3.17307 + 1.83197i
\(851\) 95.7355 165.819i 0.112498 0.194852i
\(852\) −2033.44 797.709i −2.38667 0.936278i
\(853\) 857.426i 1.00519i 0.864522 + 0.502594i \(0.167621\pi\)
−0.864522 + 0.502594i \(0.832379\pi\)
\(854\) −633.950 1426.27i −0.742330 1.67011i
\(855\) 98.4987 + 22.4499i 0.115203 + 0.0262572i
\(856\) 160.635 92.7425i 0.187657 0.108344i
\(857\) 604.822 + 349.194i 0.705744 + 0.407461i 0.809483 0.587143i \(-0.199747\pi\)
−0.103739 + 0.994605i \(0.533081\pi\)
\(858\) −52.3670 347.072i −0.0610338 0.404512i
\(859\) −50.3096 87.1388i −0.0585676 0.101442i 0.835255 0.549863i \(-0.185320\pi\)
−0.893823 + 0.448421i \(0.851987\pi\)
\(860\) 744.171 0.865315
\(861\) −881.879 458.209i −1.02425 0.532183i
\(862\) −2210.29 −2.56414
\(863\) 426.398 + 738.543i 0.494088 + 0.855785i 0.999977 0.00681331i \(-0.00216876\pi\)
−0.505889 + 0.862599i \(0.668835\pi\)
\(864\) −219.183 16.3242i −0.253684 0.0188937i
\(865\) 299.139 + 172.708i 0.345826 + 0.199663i
\(866\) 977.051 + 1692.30i 1.12823 + 1.95416i
\(867\) −1093.64 + 872.422i −1.26141 + 1.00625i
\(868\) 89.0823 842.494i 0.102629 0.970615i
\(869\) 97.1411 0.111785
\(870\) −1105.64 + 2818.40i −1.27085 + 3.23954i
\(871\) −105.752 61.0561i −0.121415 0.0700989i
\(872\) −1579.91 912.160i −1.81182 1.04605i
\(873\) 60.1248 + 194.708i 0.0688714 + 0.223033i
\(874\) −163.666 −0.187261
\(875\) −255.679 + 351.449i −0.292204 + 0.401656i
\(876\) −1529.47 1917.30i −1.74598 2.18870i
\(877\) −408.625 + 235.920i −0.465935 + 0.269008i −0.714537 0.699598i \(-0.753362\pi\)
0.248601 + 0.968606i \(0.420029\pi\)
\(878\) −657.484 + 1138.80i −0.748843 + 1.29703i
\(879\) 226.826 + 1503.33i 0.258050 + 1.71027i
\(880\) 124.249 + 215.206i 0.141192 + 0.244553i
\(881\) 702.898i 0.797842i −0.916985 0.398921i \(-0.869385\pi\)
0.916985 0.398921i \(-0.130615\pi\)
\(882\) 635.120 1367.55i 0.720091 1.55051i
\(883\) 936.948 1.06110 0.530548 0.847655i \(-0.321986\pi\)
0.530548 + 0.847655i \(0.321986\pi\)
\(884\) 2379.53 1373.82i 2.69178 1.55410i
\(885\) −123.819 820.635i −0.139909 0.927271i
\(886\) 1468.50 + 847.839i 1.65745 + 0.956929i
\(887\) 892.025 515.011i 1.00567 0.580621i 0.0957459 0.995406i \(-0.469476\pi\)
0.909920 + 0.414785i \(0.136143\pi\)
\(888\) −139.003 174.249i −0.156534 0.196226i
\(889\) −144.617 + 198.786i −0.162674 + 0.223607i
\(890\) −4018.42 −4.51508
\(891\) 16.0637 + 212.606i 0.0180288 + 0.238616i
\(892\) 683.968 + 394.889i 0.766780 + 0.442701i
\(893\) −29.1276 16.8168i −0.0326177 0.0188318i
\(894\) −1082.33 424.593i −1.21066 0.474936i
\(895\) 864.751i 0.966202i
\(896\) 1614.50 + 170.712i 1.80190 + 0.190527i
\(897\) 790.828 + 991.355i 0.881636 + 1.10519i
\(898\) 971.617 + 1682.89i 1.08198 + 1.87404i
\(899\) 304.583 527.554i 0.338802 0.586823i
\(900\) 1682.04 + 1559.74i 1.86893 + 1.73305i
\(901\) 1239.49 + 2146.86i 1.37568 + 2.38275i
\(902\) −425.920 −0.472195
\(903\) −236.483 122.872i −0.261885 0.136071i
\(904\) 376.016i 0.415947i
\(905\) 411.934 + 713.491i 0.455176 + 0.788388i
\(906\) 1272.32 191.971i 1.40433 0.211888i
\(907\) −454.488 + 787.196i −0.501089 + 0.867912i 0.498910 + 0.866654i \(0.333734\pi\)
−0.999999 + 0.00125790i \(0.999600\pi\)
\(908\) −482.378 835.503i −0.531253 0.920158i
\(909\) −237.656 54.1668i −0.261447 0.0595894i
\(910\) 963.621 + 2167.97i 1.05892 + 2.38239i
\(911\) 80.1743i 0.0880069i 0.999031 + 0.0440035i \(0.0140113\pi\)
−0.999031 + 0.0440035i \(0.985989\pi\)
\(912\) −19.9682 + 50.9010i −0.0218949 + 0.0558125i
\(913\) 14.8193 25.6679i 0.0162315 0.0281138i
\(914\) 611.498 + 353.049i 0.669035 + 0.386268i
\(915\) −1388.75 544.799i −1.51776 0.595408i
\(916\) 3321.64i 3.62625i
\(917\) 107.997 1021.38i 0.117772 1.11382i
\(918\) −2285.39 + 1101.88i −2.48953 + 1.20031i
\(919\) −395.033 684.217i −0.429851 0.744524i 0.567009 0.823712i \(-0.308101\pi\)
−0.996860 + 0.0791880i \(0.974767\pi\)
\(920\) −2709.39 1564.27i −2.94499 1.70029i
\(921\) −591.707 + 89.2782i −0.642462 + 0.0969362i
\(922\) 382.869 + 663.148i 0.415259 + 0.719249i
\(923\) −1230.80 −1.33348
\(924\) −18.8718 424.686i −0.0204240 0.459617i
\(925\) 195.157i 0.210980i
\(926\) −2307.44 + 1332.20i −2.49183 + 1.43866i
\(927\) 712.259 + 660.474i 0.768348 + 0.712485i
\(928\) 272.884 + 157.549i 0.294056 + 0.169773i
\(929\) −623.696 1080.27i −0.671363 1.16283i −0.977518 0.210853i \(-0.932376\pi\)
0.306155 0.951982i \(-0.400957\pi\)
\(930\) −767.589 962.224i −0.825365 1.03465i
\(931\) 53.5449 + 48.3335i 0.0575134 + 0.0519156i
\(932\) 1036.21i 1.11182i
\(933\) 177.249 451.826i 0.189977 0.484272i
\(934\) −429.722 248.100i −0.460088 0.265632i
\(935\) −477.720 275.812i −0.510930 0.294986i
\(936\) 1410.58 435.581i 1.50703 0.465364i
\(937\) −1128.28 −1.20414 −0.602072 0.798442i \(-0.705658\pi\)
−0.602072 + 0.798442i \(0.705658\pi\)
\(938\) −181.798 132.258i −0.193814 0.141000i
\(939\) 915.299 730.156i 0.974760 0.777589i
\(940\) −669.888 1160.28i −0.712647 1.23434i
\(941\) −190.627 + 330.176i −0.202579 + 0.350878i −0.949359 0.314194i \(-0.898266\pi\)
0.746780 + 0.665072i \(0.231599\pi\)
\(942\) 222.628 + 1475.51i 0.236336 + 1.56636i
\(943\) 1332.67 769.415i 1.41322 0.815922i
\(944\) 449.179 0.475826
\(945\) −485.918 1356.76i −0.514199 1.43572i
\(946\) −114.214 −0.120733
\(947\) 521.905 + 903.966i 0.551114 + 0.954557i 0.998195 + 0.0600635i \(0.0191303\pi\)
−0.447081 + 0.894494i \(0.647536\pi\)
\(948\) 127.027 + 841.896i 0.133995 + 0.888076i
\(949\) −1196.83 690.990i −1.26115 0.728124i
\(950\) −144.467 + 83.4082i −0.152071 + 0.0877981i
\(951\) 107.821 86.0113i 0.113376 0.0904430i
\(952\) 2218.23 985.960i 2.33008 1.03567i
\(953\) 645.739i 0.677586i −0.940861 0.338793i \(-0.889981\pi\)
0.940861 0.338793i \(-0.110019\pi\)
\(954\) 818.945 + 2652.07i 0.858433 + 2.77995i
\(955\) 761.826 + 439.841i 0.797724 + 0.460566i
\(956\) 845.784 1464.94i 0.884711 1.53236i
\(957\) 111.630 284.557i 0.116646 0.297342i
\(958\) 2157.35 2.25193
\(959\) 262.709 + 591.049i 0.273941 + 0.616318i
\(960\) 1383.32 1103.51i 1.44096 1.14949i
\(961\) −356.667 617.766i −0.371142 0.642836i
\(962\) −226.667 130.866i −0.235620 0.136035i
\(963\) −89.9574 + 97.0106i −0.0934137 + 0.100738i
\(964\) 866.276 500.144i 0.898626 0.518822i
\(965\) 1229.40i 1.27399i
\(966\) 1255.98 + 1968.13i 1.30019 + 2.03740i
\(967\) 354.180i 0.366267i 0.983088 + 0.183134i \(0.0586241\pi\)
−0.983088 + 0.183134i \(0.941376\pi\)
\(968\) 719.675 + 1246.51i 0.743466 + 1.28772i
\(969\) −18.1083 120.016i −0.0186876 0.123856i
\(970\) −511.223 295.155i −0.527034 0.304283i
\(971\) −804.917 + 464.719i −0.828957 + 0.478599i −0.853495 0.521100i \(-0.825522\pi\)
0.0245383 + 0.999699i \(0.492188\pi\)
\(972\) −1821.60 + 417.236i −1.87407 + 0.429255i
\(973\) 836.447 1149.76i 0.859658 1.18166i
\(974\) 1572.78i 1.61476i
\(975\) 1203.28 + 472.040i 1.23413 + 0.484143i
\(976\) 403.700 699.229i 0.413627 0.716423i
\(977\) 523.426 906.600i 0.535748 0.927943i −0.463379 0.886160i \(-0.653363\pi\)
0.999127 0.0417824i \(-0.0133036\pi\)
\(978\) 912.244 2325.41i 0.932765 2.37772i
\(979\) 405.715 0.414418
\(980\) 884.505 + 2733.85i 0.902556 + 2.78965i
\(981\) 1268.69 + 289.162i 1.29326 + 0.294762i
\(982\) −1744.69 + 1007.30i −1.77667 + 1.02576i
\(983\) −439.404 + 761.070i −0.447003 + 0.774232i −0.998189 0.0601503i \(-0.980842\pi\)
0.551186 + 0.834382i \(0.314175\pi\)
\(984\) −267.269 1771.37i −0.271614 1.80017i
\(985\) 20.0712 + 34.7644i 0.0203769 + 0.0352938i
\(986\) 3637.36 3.68901
\(987\) 21.2996 + 479.321i 0.0215802 + 0.485634i
\(988\) 147.174i 0.148962i
\(989\) 357.364 206.324i 0.361339 0.208619i
\(990\) −452.887 419.960i −0.457462 0.424202i
\(991\) −257.036 + 445.199i −0.259370 + 0.449242i −0.966073 0.258268i \(-0.916848\pi\)
0.706703 + 0.707510i \(0.250182\pi\)
\(992\) −110.945 + 64.0541i −0.111840 + 0.0645706i
\(993\) −92.5213 115.982i −0.0931735 0.116799i
\(994\) −2253.43 238.269i −2.26703 0.239707i
\(995\) 2295.14 2.30668
\(996\) 241.835 + 94.8705i 0.242806 + 0.0952516i
\(997\) 553.005 957.832i 0.554669 0.960714i −0.443261 0.896393i \(-0.646178\pi\)
0.997929 0.0643215i \(-0.0204883\pi\)
\(998\) 742.578 + 428.728i 0.744066 + 0.429587i
\(999\) 131.403 + 89.5003i 0.131534 + 0.0895899i
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 273.3.w.c.116.2 yes 16
3.2 odd 2 inner 273.3.w.c.116.7 yes 16
7.2 even 3 inner 273.3.w.c.233.1 yes 16
13.12 even 2 inner 273.3.w.c.116.8 yes 16
21.2 odd 6 inner 273.3.w.c.233.8 yes 16
39.38 odd 2 inner 273.3.w.c.116.1 16
91.51 even 6 inner 273.3.w.c.233.7 yes 16
273.233 odd 6 inner 273.3.w.c.233.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.3.w.c.116.1 16 39.38 odd 2 inner
273.3.w.c.116.2 yes 16 1.1 even 1 trivial
273.3.w.c.116.7 yes 16 3.2 odd 2 inner
273.3.w.c.116.8 yes 16 13.12 even 2 inner
273.3.w.c.233.1 yes 16 7.2 even 3 inner
273.3.w.c.233.2 yes 16 273.233 odd 6 inner
273.3.w.c.233.7 yes 16 91.51 even 6 inner
273.3.w.c.233.8 yes 16 21.2 odd 6 inner