Properties

Label 38.3.f.a.33.4
Level $38$
Weight $3$
Character 38.33
Analytic conductor $1.035$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,3,Mod(3,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([13]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 38.f (of order \(18\), degree \(6\), 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: \(1.03542500457\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 33.4
Character \(\chi\) \(=\) 38.33
Dual form 38.3.f.a.15.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.483690 + 1.32893i) q^{2} +(3.82266 + 0.674039i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(-6.81117 - 5.71525i) q^{5} +(0.953235 + 5.40606i) q^{6} +(2.55329 + 4.42243i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(5.70119 + 2.07506i) q^{9} +O(q^{10})\) \(q+(0.483690 + 1.32893i) q^{2} +(3.82266 + 0.674039i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(-6.81117 - 5.71525i) q^{5} +(0.953235 + 5.40606i) q^{6} +(2.55329 + 4.42243i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(5.70119 + 2.07506i) q^{9} +(4.30065 - 11.8160i) q^{10} +(2.70464 - 4.68458i) q^{11} +(-6.72319 + 3.88163i) q^{12} +(-12.3403 + 2.17592i) q^{13} +(-4.64208 + 5.53221i) q^{14} +(-22.1845 - 26.4385i) q^{15} +(0.694593 - 3.93923i) q^{16} +(24.2154 - 8.81367i) q^{17} +8.58014i q^{18} +(-8.05172 + 17.2096i) q^{19} +17.7827 q^{20} +(6.77948 + 18.6265i) q^{21} +(7.53367 + 1.32839i) q^{22} +(6.41312 - 5.38124i) q^{23} +(-8.41034 - 7.05711i) q^{24} +(9.38676 + 53.2349i) q^{25} +(-8.86051 - 15.3469i) q^{26} +(-9.85929 - 5.69226i) q^{27} +(-9.59723 - 3.49311i) q^{28} +(-16.1666 + 44.4173i) q^{29} +(24.4044 - 42.2696i) q^{30} +(19.0672 - 11.0085i) q^{31} +(5.57091 - 0.982302i) q^{32} +(13.4965 - 16.0845i) q^{33} +(23.4254 + 27.9174i) q^{34} +(7.88439 - 44.7146i) q^{35} +(-11.4024 + 4.15013i) q^{36} -16.7436i q^{37} +(-26.7648 - 2.37604i) q^{38} -48.6394 q^{39} +(8.60131 + 23.6319i) q^{40} +(-5.00714 - 0.882894i) q^{41} +(-21.4740 + 18.0188i) q^{42} +(28.8313 + 24.1924i) q^{43} +(1.87863 + 10.6542i) q^{44} +(-26.9723 - 46.7173i) q^{45} +(10.2532 + 5.91971i) q^{46} +(-42.1962 - 15.3582i) q^{47} +(5.31039 - 14.5902i) q^{48} +(11.4614 - 19.8518i) q^{49} +(-66.2050 + 38.2235i) q^{50} +(98.5079 - 17.3696i) q^{51} +(16.1091 - 19.1981i) q^{52} +(-18.1611 - 21.6435i) q^{53} +(2.79576 - 15.8556i) q^{54} +(-45.1953 + 16.4498i) q^{55} -14.4436i q^{56} +(-42.3789 + 60.3593i) q^{57} -66.8469 q^{58} +(-14.4265 - 39.6364i) q^{59} +(67.9773 + 11.9862i) q^{60} +(37.9655 - 31.8568i) q^{61} +(23.8521 + 20.0143i) q^{62} +(5.37997 + 30.5113i) q^{63} +(4.00000 + 6.92820i) q^{64} +(96.4878 + 55.7072i) q^{65} +(27.9033 + 10.1560i) q^{66} +(-8.84321 + 24.2965i) q^{67} +(-25.7695 + 44.6340i) q^{68} +(28.1424 - 16.2480i) q^{69} +(63.2360 - 11.1502i) q^{70} +(38.5613 - 45.9555i) q^{71} +(-11.0304 - 13.1455i) q^{72} +(5.90643 - 33.4970i) q^{73} +(22.2510 - 8.09869i) q^{74} +209.826i q^{75} +(-9.78827 - 36.7177i) q^{76} +27.6229 q^{77} +(-23.5264 - 64.6382i) q^{78} +(71.9176 + 12.6810i) q^{79} +(-27.2447 + 22.8610i) q^{80} +(-75.6808 - 63.5037i) q^{81} +(-1.24860 - 7.08117i) q^{82} +(-35.5483 - 61.5715i) q^{83} +(-34.3325 - 19.8219i) q^{84} +(-215.307 - 78.3655i) q^{85} +(-18.2045 + 50.0163i) q^{86} +(-91.7383 + 158.895i) q^{87} +(-13.2500 + 7.64989i) q^{88} +(-51.5470 + 9.08913i) q^{89} +(49.0377 - 58.4408i) q^{90} +(-41.1312 - 49.0182i) q^{91} +(-2.90747 + 16.4891i) q^{92} +(80.3078 - 29.2296i) q^{93} -63.5042i q^{94} +(153.199 - 71.1999i) q^{95} +21.9578 q^{96} +(14.8523 + 40.8063i) q^{97} +(31.9253 + 5.62929i) q^{98} +(25.1405 - 21.0954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25} + 48 q^{26} + 126 q^{27} + 72 q^{28} - 210 q^{29} - 108 q^{31} - 132 q^{33} - 24 q^{34} - 66 q^{35} - 12 q^{36} + 84 q^{38} + 120 q^{39} + 54 q^{41} + 72 q^{42} + 90 q^{43} - 48 q^{44} - 144 q^{45} - 360 q^{46} - 246 q^{47} - 48 q^{48} + 54 q^{49} - 432 q^{50} - 342 q^{51} + 36 q^{52} - 174 q^{53} - 42 q^{55} - 12 q^{57} + 48 q^{58} + 228 q^{59} + 132 q^{60} + 12 q^{61} + 204 q^{62} + 174 q^{63} + 96 q^{64} + 630 q^{65} + 696 q^{66} + 72 q^{67} - 48 q^{68} + 702 q^{69} + 528 q^{70} + 432 q^{71} + 96 q^{72} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 708 q^{78} - 246 q^{79} - 642 q^{81} - 384 q^{82} - 126 q^{83} - 540 q^{84} - 684 q^{85} - 12 q^{86} - 324 q^{87} - 12 q^{89} - 336 q^{90} + 372 q^{91} - 132 q^{92} - 168 q^{93} - 570 q^{95} + 72 q^{97} + 384 q^{98} - 204 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.483690 + 1.32893i 0.241845 + 0.664463i
\(3\) 3.82266 + 0.674039i 1.27422 + 0.224680i 0.769524 0.638617i \(-0.220493\pi\)
0.504696 + 0.863297i \(0.331604\pi\)
\(4\) −1.53209 + 1.28558i −0.383022 + 0.321394i
\(5\) −6.81117 5.71525i −1.36223 1.14305i −0.975285 0.220949i \(-0.929084\pi\)
−0.386949 0.922101i \(-0.626471\pi\)
\(6\) 0.953235 + 5.40606i 0.158872 + 0.901010i
\(7\) 2.55329 + 4.42243i 0.364756 + 0.631775i 0.988737 0.149664i \(-0.0478192\pi\)
−0.623981 + 0.781439i \(0.714486\pi\)
\(8\) −2.44949 1.41421i −0.306186 0.176777i
\(9\) 5.70119 + 2.07506i 0.633465 + 0.230563i
\(10\) 4.30065 11.8160i 0.430065 1.18160i
\(11\) 2.70464 4.68458i 0.245877 0.425871i −0.716501 0.697586i \(-0.754258\pi\)
0.962378 + 0.271715i \(0.0875909\pi\)
\(12\) −6.72319 + 3.88163i −0.560266 + 0.323469i
\(13\) −12.3403 + 2.17592i −0.949253 + 0.167379i −0.626777 0.779199i \(-0.715626\pi\)
−0.322476 + 0.946578i \(0.604515\pi\)
\(14\) −4.64208 + 5.53221i −0.331577 + 0.395158i
\(15\) −22.1845 26.4385i −1.47897 1.76257i
\(16\) 0.694593 3.93923i 0.0434120 0.246202i
\(17\) 24.2154 8.81367i 1.42443 0.518451i 0.489103 0.872226i \(-0.337324\pi\)
0.935331 + 0.353775i \(0.115102\pi\)
\(18\) 8.58014i 0.476675i
\(19\) −8.05172 + 17.2096i −0.423774 + 0.905768i
\(20\) 17.7827 0.889135
\(21\) 6.77948 + 18.6265i 0.322832 + 0.886974i
\(22\) 7.53367 + 1.32839i 0.342439 + 0.0603813i
\(23\) 6.41312 5.38124i 0.278831 0.233967i −0.492637 0.870235i \(-0.663967\pi\)
0.771468 + 0.636268i \(0.219523\pi\)
\(24\) −8.41034 7.05711i −0.350431 0.294046i
\(25\) 9.38676 + 53.2349i 0.375470 + 2.12940i
\(26\) −8.86051 15.3469i −0.340789 0.590264i
\(27\) −9.85929 5.69226i −0.365159 0.210825i
\(28\) −9.59723 3.49311i −0.342758 0.124754i
\(29\) −16.1666 + 44.4173i −0.557468 + 1.53163i 0.265830 + 0.964020i \(0.414354\pi\)
−0.823297 + 0.567610i \(0.807868\pi\)
\(30\) 24.4044 42.2696i 0.813479 1.40899i
\(31\) 19.0672 11.0085i 0.615072 0.355112i −0.159876 0.987137i \(-0.551109\pi\)
0.774948 + 0.632025i \(0.217776\pi\)
\(32\) 5.57091 0.982302i 0.174091 0.0306970i
\(33\) 13.4965 16.0845i 0.408986 0.487410i
\(34\) 23.4254 + 27.9174i 0.688984 + 0.821099i
\(35\) 7.88439 44.7146i 0.225268 1.27756i
\(36\) −11.4024 + 4.15013i −0.316733 + 0.115281i
\(37\) 16.7436i 0.452529i −0.974066 0.226265i \(-0.927349\pi\)
0.974066 0.226265i \(-0.0726514\pi\)
\(38\) −26.7648 2.37604i −0.704337 0.0625273i
\(39\) −48.6394 −1.24716
\(40\) 8.60131 + 23.6319i 0.215033 + 0.590798i
\(41\) −5.00714 0.882894i −0.122125 0.0215340i 0.112251 0.993680i \(-0.464194\pi\)
−0.234377 + 0.972146i \(0.575305\pi\)
\(42\) −21.4740 + 18.0188i −0.511286 + 0.429020i
\(43\) 28.8313 + 24.1924i 0.670496 + 0.562613i 0.913212 0.407484i \(-0.133594\pi\)
−0.242716 + 0.970097i \(0.578038\pi\)
\(44\) 1.87863 + 10.6542i 0.0426960 + 0.242141i
\(45\) −26.9723 46.7173i −0.599384 1.03816i
\(46\) 10.2532 + 5.91971i 0.222896 + 0.128689i
\(47\) −42.1962 15.3582i −0.897791 0.326769i −0.148424 0.988924i \(-0.547420\pi\)
−0.749367 + 0.662155i \(0.769642\pi\)
\(48\) 5.31039 14.5902i 0.110633 0.303962i
\(49\) 11.4614 19.8518i 0.233907 0.405138i
\(50\) −66.2050 + 38.2235i −1.32410 + 0.764470i
\(51\) 98.5079 17.3696i 1.93153 0.340581i
\(52\) 16.1091 19.1981i 0.309790 0.369194i
\(53\) −18.1611 21.6435i −0.342662 0.408368i 0.567000 0.823718i \(-0.308104\pi\)
−0.909662 + 0.415349i \(0.863659\pi\)
\(54\) 2.79576 15.8556i 0.0517734 0.293621i
\(55\) −45.1953 + 16.4498i −0.821734 + 0.299087i
\(56\) 14.4436i 0.257921i
\(57\) −42.3789 + 60.3593i −0.743490 + 1.05893i
\(58\) −66.8469 −1.15253
\(59\) −14.4265 39.6364i −0.244516 0.671803i −0.999864 0.0164790i \(-0.994754\pi\)
0.755348 0.655324i \(-0.227468\pi\)
\(60\) 67.9773 + 11.9862i 1.13295 + 0.199771i
\(61\) 37.9655 31.8568i 0.622385 0.522243i −0.276167 0.961110i \(-0.589064\pi\)
0.898552 + 0.438866i \(0.144620\pi\)
\(62\) 23.8521 + 20.0143i 0.384711 + 0.322811i
\(63\) 5.37997 + 30.5113i 0.0853964 + 0.484307i
\(64\) 4.00000 + 6.92820i 0.0625000 + 0.108253i
\(65\) 96.4878 + 55.7072i 1.48443 + 0.857034i
\(66\) 27.9033 + 10.1560i 0.422777 + 0.153878i
\(67\) −8.84321 + 24.2965i −0.131988 + 0.362635i −0.988028 0.154276i \(-0.950696\pi\)
0.856040 + 0.516910i \(0.172918\pi\)
\(68\) −25.7695 + 44.6340i −0.378963 + 0.656382i
\(69\) 28.1424 16.2480i 0.407860 0.235478i
\(70\) 63.2360 11.1502i 0.903371 0.159289i
\(71\) 38.5613 45.9555i 0.543116 0.647261i −0.422767 0.906238i \(-0.638941\pi\)
0.965883 + 0.258977i \(0.0833855\pi\)
\(72\) −11.0304 13.1455i −0.153200 0.182577i
\(73\) 5.90643 33.4970i 0.0809100 0.458863i −0.917254 0.398302i \(-0.869600\pi\)
0.998164 0.0605617i \(-0.0192892\pi\)
\(74\) 22.2510 8.09869i 0.300689 0.109442i
\(75\) 209.826i 2.79768i
\(76\) −9.78827 36.7177i −0.128793 0.483128i
\(77\) 27.6229 0.358740
\(78\) −23.5264 64.6382i −0.301620 0.828694i
\(79\) 71.9176 + 12.6810i 0.910350 + 0.160519i 0.609162 0.793046i \(-0.291506\pi\)
0.301188 + 0.953565i \(0.402617\pi\)
\(80\) −27.2447 + 22.8610i −0.340559 + 0.285763i
\(81\) −75.6808 63.5037i −0.934331 0.783997i
\(82\) −1.24860 7.08117i −0.0152268 0.0863557i
\(83\) −35.5483 61.5715i −0.428293 0.741825i 0.568429 0.822732i \(-0.307551\pi\)
−0.996722 + 0.0809077i \(0.974218\pi\)
\(84\) −34.3325 19.8219i −0.408720 0.235975i
\(85\) −215.307 78.3655i −2.53303 0.921947i
\(86\) −18.2045 + 50.0163i −0.211680 + 0.581585i
\(87\) −91.7383 + 158.895i −1.05446 + 1.82638i
\(88\) −13.2500 + 7.64989i −0.150568 + 0.0869305i
\(89\) −51.5470 + 9.08913i −0.579180 + 0.102125i −0.455561 0.890205i \(-0.650561\pi\)
−0.123619 + 0.992330i \(0.539450\pi\)
\(90\) 49.0377 58.4408i 0.544863 0.649343i
\(91\) −41.1312 49.0182i −0.451991 0.538662i
\(92\) −2.90747 + 16.4891i −0.0316030 + 0.179229i
\(93\) 80.3078 29.2296i 0.863525 0.314297i
\(94\) 63.5042i 0.675576i
\(95\) 153.199 71.1999i 1.61262 0.749472i
\(96\) 21.9578 0.228727
\(97\) 14.8523 + 40.8063i 0.153116 + 0.420683i 0.992407 0.123000i \(-0.0392515\pi\)
−0.839290 + 0.543683i \(0.817029\pi\)
\(98\) 31.9253 + 5.62929i 0.325769 + 0.0574418i
\(99\) 25.1405 21.0954i 0.253944 0.213085i
\(100\) −82.8189 69.4933i −0.828189 0.694933i
\(101\) 5.17443 + 29.3457i 0.0512320 + 0.290551i 0.999650 0.0264728i \(-0.00842754\pi\)
−0.948418 + 0.317024i \(0.897316\pi\)
\(102\) 70.7302 + 122.508i 0.693433 + 1.20106i
\(103\) 39.3922 + 22.7431i 0.382449 + 0.220807i 0.678883 0.734246i \(-0.262464\pi\)
−0.296435 + 0.955053i \(0.595798\pi\)
\(104\) 33.3046 + 12.1219i 0.320237 + 0.116557i
\(105\) 60.2787 165.614i 0.574083 1.57728i
\(106\) 19.9783 34.6035i 0.188475 0.326448i
\(107\) −162.047 + 93.5580i −1.51446 + 0.874373i −0.514603 + 0.857429i \(0.672061\pi\)
−0.999856 + 0.0169446i \(0.994606\pi\)
\(108\) 22.4231 3.95380i 0.207622 0.0366093i
\(109\) −36.0310 + 42.9401i −0.330560 + 0.393946i −0.905567 0.424202i \(-0.860555\pi\)
0.575008 + 0.818148i \(0.304999\pi\)
\(110\) −43.7210 52.1047i −0.397464 0.473679i
\(111\) 11.2858 64.0051i 0.101674 0.576622i
\(112\) 19.1945 6.98621i 0.171379 0.0623769i
\(113\) 125.823i 1.11348i 0.830687 + 0.556739i \(0.187948\pi\)
−0.830687 + 0.556739i \(0.812052\pi\)
\(114\) −100.711 27.1233i −0.883432 0.237924i
\(115\) −74.4360 −0.647270
\(116\) −32.3331 88.8345i −0.278734 0.765815i
\(117\) −74.8695 13.2015i −0.639910 0.112833i
\(118\) 45.6959 38.3434i 0.387253 0.324944i
\(119\) 100.807 + 84.5868i 0.847115 + 0.710814i
\(120\) 16.9511 + 96.1344i 0.141259 + 0.801120i
\(121\) 45.8698 + 79.4488i 0.379089 + 0.656602i
\(122\) 60.6989 + 35.0445i 0.497532 + 0.287250i
\(123\) −18.5455 6.75001i −0.150776 0.0548782i
\(124\) −15.0605 + 41.3783i −0.121456 + 0.333696i
\(125\) 129.174 223.737i 1.03340 1.78989i
\(126\) −37.9451 + 21.9076i −0.301151 + 0.173870i
\(127\) 1.58597 0.279649i 0.0124880 0.00220196i −0.167401 0.985889i \(-0.553537\pi\)
0.179889 + 0.983687i \(0.442426\pi\)
\(128\) −7.27231 + 8.66680i −0.0568149 + 0.0677094i
\(129\) 93.9059 + 111.913i 0.727953 + 0.867541i
\(130\) −27.3607 + 155.170i −0.210467 + 1.19362i
\(131\) 182.652 66.4799i 1.39429 0.507480i 0.467812 0.883828i \(-0.345043\pi\)
0.926478 + 0.376348i \(0.122820\pi\)
\(132\) 41.9937i 0.318134i
\(133\) −96.6665 + 8.33293i −0.726816 + 0.0626536i
\(134\) −36.5656 −0.272878
\(135\) 34.6206 + 95.1193i 0.256449 + 0.704587i
\(136\) −71.7797 12.6567i −0.527792 0.0930640i
\(137\) −139.253 + 116.847i −1.01644 + 0.852898i −0.989177 0.146730i \(-0.953125\pi\)
−0.0272675 + 0.999628i \(0.508681\pi\)
\(138\) 35.2045 + 29.5401i 0.255105 + 0.214059i
\(139\) −26.6261 151.004i −0.191555 1.08636i −0.917241 0.398334i \(-0.869589\pi\)
0.725686 0.688026i \(-0.241523\pi\)
\(140\) 45.4044 + 78.6427i 0.324317 + 0.561734i
\(141\) −150.950 87.1509i −1.07057 0.618091i
\(142\) 79.7232 + 29.0169i 0.561431 + 0.204344i
\(143\) −23.1828 + 63.6941i −0.162117 + 0.445414i
\(144\) 12.1342 21.0170i 0.0842650 0.145951i
\(145\) 363.969 210.138i 2.51013 1.44923i
\(146\) 47.3720 8.35295i 0.324465 0.0572120i
\(147\) 57.1940 68.1612i 0.389075 0.463682i
\(148\) 21.5251 + 25.6527i 0.145440 + 0.173329i
\(149\) −21.9985 + 124.760i −0.147641 + 0.837312i 0.817568 + 0.575832i \(0.195322\pi\)
−0.965209 + 0.261480i \(0.915789\pi\)
\(150\) −278.844 + 101.491i −1.85896 + 0.676605i
\(151\) 155.504i 1.02983i −0.857242 0.514913i \(-0.827824\pi\)
0.857242 0.514913i \(-0.172176\pi\)
\(152\) 44.0606 30.7679i 0.289873 0.202420i
\(153\) 156.345 1.02186
\(154\) 13.3609 + 36.7088i 0.0867593 + 0.238369i
\(155\) −192.787 33.9935i −1.24378 0.219313i
\(156\) 74.5199 62.5296i 0.477692 0.400831i
\(157\) −82.4620 69.1938i −0.525236 0.440725i 0.341217 0.939985i \(-0.389161\pi\)
−0.866452 + 0.499260i \(0.833605\pi\)
\(158\) 17.9337 + 101.707i 0.113504 + 0.643714i
\(159\) −54.8351 94.9772i −0.344875 0.597341i
\(160\) −43.5586 25.1485i −0.272241 0.157178i
\(161\) 40.1727 + 14.6217i 0.249520 + 0.0908178i
\(162\) 47.7858 131.290i 0.294974 0.810434i
\(163\) −50.5731 + 87.5953i −0.310265 + 0.537394i −0.978420 0.206628i \(-0.933751\pi\)
0.668155 + 0.744022i \(0.267084\pi\)
\(164\) 8.80641 5.08438i 0.0536976 0.0310023i
\(165\) −183.854 + 32.4185i −1.11427 + 0.196476i
\(166\) 64.6296 77.0225i 0.389335 0.463991i
\(167\) −10.9883 13.0953i −0.0657980 0.0784150i 0.732141 0.681153i \(-0.238521\pi\)
−0.797939 + 0.602738i \(0.794077\pi\)
\(168\) 9.73553 55.2130i 0.0579496 0.328649i
\(169\) −11.2601 + 4.09834i −0.0666278 + 0.0242505i
\(170\) 324.032i 1.90607i
\(171\) −81.6153 + 81.4073i −0.477283 + 0.476066i
\(172\) −75.2733 −0.437635
\(173\) 75.4796 + 207.378i 0.436298 + 1.19872i 0.941883 + 0.335942i \(0.109055\pi\)
−0.505584 + 0.862777i \(0.668723\pi\)
\(174\) −255.533 45.0574i −1.46858 0.258950i
\(175\) −211.461 + 177.436i −1.20835 + 1.01392i
\(176\) −16.5750 13.9081i −0.0941762 0.0790232i
\(177\) −28.4310 161.240i −0.160627 0.910963i
\(178\) −37.0115 64.1059i −0.207930 0.360145i
\(179\) 8.87590 + 5.12450i 0.0495860 + 0.0286285i 0.524588 0.851356i \(-0.324219\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(180\) 101.383 + 36.9002i 0.563237 + 0.205001i
\(181\) −64.6251 + 177.556i −0.357045 + 0.980972i 0.623005 + 0.782218i \(0.285912\pi\)
−0.980049 + 0.198754i \(0.936310\pi\)
\(182\) 45.2469 78.3699i 0.248609 0.430604i
\(183\) 166.602 96.1877i 0.910394 0.525616i
\(184\) −23.3191 + 4.11179i −0.126734 + 0.0223467i
\(185\) −95.6938 + 114.043i −0.517264 + 0.616451i
\(186\) 77.6881 + 92.5850i 0.417678 + 0.497769i
\(187\) 24.2056 137.277i 0.129442 0.734100i
\(188\) 84.3923 30.7163i 0.448895 0.163385i
\(189\) 58.1360i 0.307598i
\(190\) 168.720 + 169.151i 0.888000 + 0.890269i
\(191\) 1.43003 0.00748707 0.00374354 0.999993i \(-0.498808\pi\)
0.00374354 + 0.999993i \(0.498808\pi\)
\(192\) 10.6208 + 29.1803i 0.0553165 + 0.151981i
\(193\) 59.7448 + 10.5346i 0.309559 + 0.0545835i 0.326269 0.945277i \(-0.394208\pi\)
−0.0167108 + 0.999860i \(0.505319\pi\)
\(194\) −47.0446 + 39.4751i −0.242498 + 0.203480i
\(195\) 331.291 + 277.986i 1.69893 + 1.42557i
\(196\) 7.96102 + 45.1492i 0.0406175 + 0.230353i
\(197\) −118.683 205.566i −0.602453 1.04348i −0.992448 0.122663i \(-0.960857\pi\)
0.389995 0.920817i \(-0.372477\pi\)
\(198\) 40.1944 + 23.2062i 0.203002 + 0.117203i
\(199\) 239.059 + 87.0105i 1.20130 + 0.437239i 0.863679 0.504042i \(-0.168154\pi\)
0.337624 + 0.941281i \(0.390377\pi\)
\(200\) 52.2928 143.673i 0.261464 0.718367i
\(201\) −50.1814 + 86.9167i −0.249659 + 0.432421i
\(202\) −36.4954 + 21.0706i −0.180670 + 0.104310i
\(203\) −237.710 + 41.9147i −1.17099 + 0.206476i
\(204\) −128.593 + 153.251i −0.630358 + 0.751231i
\(205\) 29.0585 + 34.6306i 0.141749 + 0.168930i
\(206\) −11.1703 + 63.3499i −0.0542248 + 0.307524i
\(207\) 47.7288 17.3719i 0.230574 0.0839221i
\(208\) 50.1226i 0.240974i
\(209\) 58.8427 + 84.2647i 0.281544 + 0.403180i
\(210\) 249.246 1.18688
\(211\) −23.9637 65.8396i −0.113572 0.312036i 0.869864 0.493291i \(-0.164206\pi\)
−0.983436 + 0.181255i \(0.941984\pi\)
\(212\) 55.6488 + 9.81238i 0.262494 + 0.0462848i
\(213\) 178.383 149.681i 0.837477 0.702726i
\(214\) −202.712 170.096i −0.947253 0.794839i
\(215\) −58.1098 329.557i −0.270278 1.53282i
\(216\) 16.1002 + 27.8863i 0.0745377 + 0.129103i
\(217\) 97.3684 + 56.2157i 0.448702 + 0.259058i
\(218\) −74.4920 27.1129i −0.341706 0.124371i
\(219\) 45.1566 124.067i 0.206194 0.566515i
\(220\) 48.0959 83.3045i 0.218618 0.378657i
\(221\) −279.647 + 161.454i −1.26537 + 0.730561i
\(222\) 90.5168 15.9606i 0.407733 0.0718944i
\(223\) −163.747 + 195.146i −0.734290 + 0.875092i −0.995935 0.0900715i \(-0.971290\pi\)
0.261646 + 0.965164i \(0.415735\pi\)
\(224\) 18.5683 + 22.1289i 0.0828943 + 0.0987895i
\(225\) −56.9502 + 322.981i −0.253112 + 1.43547i
\(226\) −167.210 + 60.8593i −0.739865 + 0.269289i
\(227\) 303.973i 1.33909i −0.742772 0.669544i \(-0.766489\pi\)
0.742772 0.669544i \(-0.233511\pi\)
\(228\) −12.6681 146.957i −0.0555620 0.644549i
\(229\) 397.312 1.73499 0.867493 0.497449i \(-0.165730\pi\)
0.867493 + 0.497449i \(0.165730\pi\)
\(230\) −36.0039 98.9200i −0.156539 0.430087i
\(231\) 105.593 + 18.6189i 0.457113 + 0.0806014i
\(232\) 102.415 85.9367i 0.441445 0.370417i
\(233\) −78.1429 65.5697i −0.335377 0.281415i 0.459509 0.888173i \(-0.348025\pi\)
−0.794887 + 0.606758i \(0.792470\pi\)
\(234\) −18.6698 105.881i −0.0797853 0.452485i
\(235\) 199.630 + 345.769i 0.849488 + 1.47136i
\(236\) 73.0582 + 42.1801i 0.309568 + 0.178729i
\(237\) 266.369 + 96.9505i 1.12392 + 0.409074i
\(238\) −63.6505 + 174.878i −0.267439 + 0.734783i
\(239\) −184.028 + 318.746i −0.769992 + 1.33366i 0.167575 + 0.985859i \(0.446406\pi\)
−0.937567 + 0.347805i \(0.886927\pi\)
\(240\) −119.556 + 69.0260i −0.498152 + 0.287608i
\(241\) −65.6864 + 11.5823i −0.272557 + 0.0480592i −0.308256 0.951303i \(-0.599745\pi\)
0.0356988 + 0.999363i \(0.488634\pi\)
\(242\) −83.3949 + 99.3862i −0.344607 + 0.410687i
\(243\) −180.638 215.276i −0.743365 0.885908i
\(244\) −17.2122 + 97.6150i −0.0705416 + 0.400062i
\(245\) −191.524 + 69.7089i −0.781729 + 0.284526i
\(246\) 27.9105i 0.113457i
\(247\) 61.9137 229.891i 0.250663 0.930733i
\(248\) −62.2734 −0.251102
\(249\) −94.3876 259.328i −0.379067 1.04148i
\(250\) 359.810 + 63.4442i 1.43924 + 0.253777i
\(251\) 274.637 230.448i 1.09417 0.918119i 0.0971526 0.995269i \(-0.469027\pi\)
0.997019 + 0.0771501i \(0.0245821\pi\)
\(252\) −47.4672 39.8297i −0.188362 0.158054i
\(253\) −7.86367 44.5971i −0.0310817 0.176273i
\(254\) 1.13875 + 1.97237i 0.00448327 + 0.00776525i
\(255\) −770.226 444.690i −3.02050 1.74388i
\(256\) −15.0351 5.47232i −0.0587308 0.0213763i
\(257\) 41.0267 112.720i 0.159637 0.438599i −0.833926 0.551876i \(-0.813912\pi\)
0.993564 + 0.113276i \(0.0361345\pi\)
\(258\) −103.302 + 178.925i −0.400397 + 0.693508i
\(259\) 74.0472 42.7512i 0.285897 0.165063i
\(260\) −219.444 + 38.6938i −0.844014 + 0.148822i
\(261\) −184.337 + 219.685i −0.706273 + 0.841704i
\(262\) 176.694 + 210.575i 0.674403 + 0.803723i
\(263\) 60.8083 344.861i 0.231210 1.31126i −0.619239 0.785203i \(-0.712559\pi\)
0.850449 0.526057i \(-0.176330\pi\)
\(264\) −55.8066 + 20.3119i −0.211389 + 0.0769391i
\(265\) 251.213i 0.947973i
\(266\) −57.8304 124.432i −0.217408 0.467790i
\(267\) −203.173 −0.760949
\(268\) −17.6864 48.5930i −0.0659941 0.181317i
\(269\) 115.424 + 20.3524i 0.429085 + 0.0756593i 0.384020 0.923325i \(-0.374539\pi\)
0.0450652 + 0.998984i \(0.485650\pi\)
\(270\) −109.661 + 92.0164i −0.406151 + 0.340802i
\(271\) −203.292 170.582i −0.750156 0.629455i 0.185388 0.982665i \(-0.440646\pi\)
−0.935544 + 0.353210i \(0.885090\pi\)
\(272\) −17.8993 101.512i −0.0658062 0.373205i
\(273\) −124.190 215.104i −0.454910 0.787927i
\(274\) −222.636 128.539i −0.812541 0.469121i
\(275\) 274.771 + 100.009i 0.999168 + 0.363667i
\(276\) −22.2286 + 61.0725i −0.0805383 + 0.221277i
\(277\) 17.2320 29.8467i 0.0622094 0.107750i −0.833243 0.552906i \(-0.813519\pi\)
0.895453 + 0.445157i \(0.146852\pi\)
\(278\) 187.794 108.423i 0.675519 0.390011i
\(279\) 131.549 23.1957i 0.471503 0.0831387i
\(280\) −82.5487 + 98.3777i −0.294817 + 0.351349i
\(281\) 124.089 + 147.883i 0.441597 + 0.526275i 0.940231 0.340538i \(-0.110609\pi\)
−0.498634 + 0.866813i \(0.666165\pi\)
\(282\) 42.8043 242.755i 0.151788 0.860833i
\(283\) 3.28173 1.19445i 0.0115962 0.00422068i −0.336216 0.941785i \(-0.609147\pi\)
0.347812 + 0.937564i \(0.386925\pi\)
\(284\) 119.981i 0.422470i
\(285\) 633.619 168.911i 2.22322 0.592671i
\(286\) −95.8581 −0.335168
\(287\) −8.88015 24.3980i −0.0309413 0.0850104i
\(288\) 33.7992 + 5.95971i 0.117358 + 0.0206934i
\(289\) 287.316 241.087i 0.994174 0.834211i
\(290\) 455.306 + 382.047i 1.57002 + 1.31740i
\(291\) 29.2702 + 166.000i 0.100585 + 0.570446i
\(292\) 34.0138 + 58.9136i 0.116486 + 0.201759i
\(293\) 406.052 + 234.434i 1.38584 + 0.800117i 0.992844 0.119422i \(-0.0381043\pi\)
0.392999 + 0.919539i \(0.371438\pi\)
\(294\) 118.245 + 43.0378i 0.402195 + 0.146387i
\(295\) −128.271 + 352.421i −0.434816 + 1.19465i
\(296\) −23.6790 + 41.0132i −0.0799966 + 0.138558i
\(297\) −53.3317 + 30.7911i −0.179568 + 0.103674i
\(298\) −176.437 + 31.1105i −0.592069 + 0.104398i
\(299\) −67.4305 + 80.3606i −0.225520 + 0.268764i
\(300\) −269.747 321.473i −0.899158 1.07158i
\(301\) −33.3742 + 189.275i −0.110878 + 0.628819i
\(302\) 206.653 75.2156i 0.684282 0.249058i
\(303\) 115.666i 0.381737i
\(304\) 62.1999 + 43.6712i 0.204605 + 0.143655i
\(305\) −440.659 −1.44478
\(306\) 75.6226 + 207.771i 0.247133 + 0.678991i
\(307\) 52.5650 + 9.26863i 0.171221 + 0.0301910i 0.258602 0.965984i \(-0.416738\pi\)
−0.0873801 + 0.996175i \(0.527849\pi\)
\(308\) −42.3208 + 35.5114i −0.137405 + 0.115297i
\(309\) 135.253 + 113.491i 0.437713 + 0.367285i
\(310\) −48.0740 272.641i −0.155078 0.879488i
\(311\) 220.320 + 381.606i 0.708426 + 1.22703i 0.965441 + 0.260622i \(0.0839275\pi\)
−0.257015 + 0.966407i \(0.582739\pi\)
\(312\) 119.142 + 68.7865i 0.381864 + 0.220470i
\(313\) −568.688 206.985i −1.81689 0.661295i −0.995911 0.0903411i \(-0.971204\pi\)
−0.820982 0.570954i \(-0.806574\pi\)
\(314\) 52.0675 143.054i 0.165820 0.455587i
\(315\) 137.736 238.566i 0.437257 0.757352i
\(316\) −126.487 + 73.0271i −0.400274 + 0.231098i
\(317\) 151.913 26.7863i 0.479220 0.0844994i 0.0711799 0.997463i \(-0.477324\pi\)
0.408040 + 0.912964i \(0.366212\pi\)
\(318\) 99.6945 118.811i 0.313505 0.373620i
\(319\) 164.351 + 195.866i 0.515208 + 0.614001i
\(320\) 12.3517 70.0502i 0.0385992 0.218907i
\(321\) −682.513 + 248.414i −2.12621 + 0.773877i
\(322\) 60.4589i 0.187761i
\(323\) −43.2956 + 487.702i −0.134042 + 1.50991i
\(324\) 197.589 0.609841
\(325\) −231.670 636.509i −0.712832 1.95849i
\(326\) −140.869 24.8391i −0.432114 0.0761934i
\(327\) −166.678 + 139.859i −0.509718 + 0.427704i
\(328\) 11.0163 + 9.24381i 0.0335864 + 0.0281823i
\(329\) −39.8187 225.823i −0.121030 0.686393i
\(330\) −132.010 228.648i −0.400031 0.692874i
\(331\) 450.525 + 260.110i 1.36110 + 0.785832i 0.989771 0.142668i \(-0.0455683\pi\)
0.371331 + 0.928501i \(0.378902\pi\)
\(332\) 133.618 + 48.6329i 0.402463 + 0.146485i
\(333\) 34.7440 95.4583i 0.104336 0.286662i
\(334\) 12.0878 20.9367i 0.0361910 0.0626846i
\(335\) 199.093 114.947i 0.594308 0.343124i
\(336\) 78.0829 13.7681i 0.232390 0.0409766i
\(337\) −23.1102 + 27.5417i −0.0685763 + 0.0817260i −0.799242 0.601009i \(-0.794765\pi\)
0.730666 + 0.682735i \(0.239210\pi\)
\(338\) −10.8928 12.9815i −0.0322272 0.0384068i
\(339\) −84.8096 + 480.979i −0.250176 + 1.41882i
\(340\) 430.615 156.731i 1.26651 0.460973i
\(341\) 119.096i 0.349255i
\(342\) −147.661 69.0849i −0.431757 0.202003i
\(343\) 367.280 1.07079
\(344\) −36.4089 100.033i −0.105840 0.290793i
\(345\) −284.544 50.1728i −0.824765 0.145428i
\(346\) −239.082 + 200.614i −0.690988 + 0.579808i
\(347\) 26.1505 + 21.9429i 0.0753617 + 0.0632360i 0.679690 0.733499i \(-0.262114\pi\)
−0.604329 + 0.796735i \(0.706559\pi\)
\(348\) −63.7207 361.378i −0.183106 1.03844i
\(349\) −282.963 490.107i −0.810783 1.40432i −0.912317 0.409485i \(-0.865709\pi\)
0.101534 0.994832i \(-0.467625\pi\)
\(350\) −338.081 195.191i −0.965946 0.557689i
\(351\) 134.052 + 48.7911i 0.381916 + 0.139006i
\(352\) 10.4657 28.7542i 0.0297320 0.0816880i
\(353\) 105.283 182.356i 0.298253 0.516590i −0.677483 0.735538i \(-0.736929\pi\)
0.975736 + 0.218948i \(0.0702627\pi\)
\(354\) 200.525 115.773i 0.566454 0.327043i
\(355\) −525.295 + 92.6237i −1.47970 + 0.260912i
\(356\) 67.2898 80.1929i 0.189016 0.225261i
\(357\) 328.335 + 391.295i 0.919706 + 1.09606i
\(358\) −2.51691 + 14.2741i −0.00703047 + 0.0398718i
\(359\) −171.635 + 62.4700i −0.478092 + 0.174011i −0.569814 0.821773i \(-0.692985\pi\)
0.0917228 + 0.995785i \(0.470763\pi\)
\(360\) 152.578i 0.423828i
\(361\) −231.340 277.133i −0.640830 0.767683i
\(362\) −267.217 −0.738169
\(363\) 121.793 + 334.624i 0.335519 + 0.921830i
\(364\) 126.033 + 22.2231i 0.346245 + 0.0610524i
\(365\) −231.674 + 194.397i −0.634723 + 0.532595i
\(366\) 208.410 + 174.877i 0.569426 + 0.477805i
\(367\) 101.549 + 575.911i 0.276699 + 1.56924i 0.733512 + 0.679676i \(0.237880\pi\)
−0.456813 + 0.889563i \(0.651009\pi\)
\(368\) −16.7435 29.0005i −0.0454985 0.0788058i
\(369\) −26.7146 15.4237i −0.0723973 0.0417986i
\(370\) −197.841 72.0084i −0.534706 0.194617i
\(371\) 49.3464 135.578i 0.133009 0.365440i
\(372\) −85.4618 + 148.024i −0.229736 + 0.397914i
\(373\) 121.339 70.0550i 0.325305 0.187815i −0.328450 0.944521i \(-0.606526\pi\)
0.653755 + 0.756707i \(0.273193\pi\)
\(374\) 194.139 34.2319i 0.519087 0.0915290i
\(375\) 644.597 768.201i 1.71893 2.04854i
\(376\) 81.6394 + 97.2940i 0.217126 + 0.258761i
\(377\) 102.851 583.299i 0.272815 1.54721i
\(378\) 77.2584 28.1198i 0.204387 0.0743909i
\(379\) 656.903i 1.73325i −0.498957 0.866627i \(-0.666284\pi\)
0.498957 0.866627i \(-0.333716\pi\)
\(380\) −143.181 + 306.033i −0.376793 + 0.805350i
\(381\) 6.25113 0.0164072
\(382\) 0.691691 + 1.90040i 0.00181071 + 0.00497488i
\(383\) −553.246 97.5522i −1.44451 0.254706i −0.604207 0.796827i \(-0.706510\pi\)
−0.840300 + 0.542122i \(0.817621\pi\)
\(384\) −33.6414 + 28.2284i −0.0876077 + 0.0735116i
\(385\) −188.145 157.872i −0.488687 0.410057i
\(386\) 14.8982 + 84.4919i 0.0385964 + 0.218891i
\(387\) 114.172 + 197.752i 0.295019 + 0.510988i
\(388\) −75.2146 43.4251i −0.193852 0.111920i
\(389\) −90.7497 33.0302i −0.233290 0.0849105i 0.222730 0.974880i \(-0.428503\pi\)
−0.456020 + 0.889970i \(0.650725\pi\)
\(390\) −209.181 + 574.721i −0.536362 + 1.47364i
\(391\) 107.867 186.832i 0.275876 0.477831i
\(392\) −56.1493 + 32.4178i −0.143238 + 0.0826985i
\(393\) 743.027 131.016i 1.89065 0.333373i
\(394\) 215.776 257.151i 0.547654 0.652668i
\(395\) −417.368 497.400i −1.05663 1.25924i
\(396\) −11.3978 + 64.6400i −0.0287822 + 0.163232i
\(397\) −386.969 + 140.845i −0.974733 + 0.354774i −0.779790 0.626041i \(-0.784674\pi\)
−0.194943 + 0.980815i \(0.562452\pi\)
\(398\) 359.778i 0.903966i
\(399\) −375.140 33.3030i −0.940201 0.0834661i
\(400\) 216.225 0.540562
\(401\) 202.368 + 556.000i 0.504657 + 1.38653i 0.886681 + 0.462382i \(0.153005\pi\)
−0.382024 + 0.924152i \(0.624773\pi\)
\(402\) −139.778 24.6466i −0.347707 0.0613101i
\(403\) −211.342 + 177.337i −0.524421 + 0.440041i
\(404\) −45.6538 38.3080i −0.113004 0.0948219i
\(405\) 152.535 + 865.070i 0.376630 + 2.13597i
\(406\) −170.679 295.625i −0.420393 0.728141i
\(407\) −78.4366 45.2854i −0.192719 0.111266i
\(408\) −265.859 96.7646i −0.651614 0.237168i
\(409\) 229.898 631.639i 0.562097 1.54435i −0.254460 0.967083i \(-0.581898\pi\)
0.816557 0.577265i \(-0.195880\pi\)
\(410\) −31.9662 + 55.3671i −0.0779664 + 0.135042i
\(411\) −611.076 + 352.805i −1.48680 + 0.858406i
\(412\) −89.5903 + 15.7972i −0.217452 + 0.0383427i
\(413\) 138.454 165.003i 0.335240 0.399523i
\(414\) 46.1719 + 55.0255i 0.111526 + 0.132912i
\(415\) −109.771 + 622.541i −0.264508 + 1.50010i
\(416\) −66.6092 + 24.2438i −0.160118 + 0.0582783i
\(417\) 595.184i 1.42730i
\(418\) −83.5200 + 118.955i −0.199809 + 0.284583i
\(419\) −121.024 −0.288839 −0.144420 0.989517i \(-0.546131\pi\)
−0.144420 + 0.989517i \(0.546131\pi\)
\(420\) 120.557 + 331.229i 0.287042 + 0.788640i
\(421\) 262.699 + 46.3210i 0.623989 + 0.110026i 0.476698 0.879067i \(-0.341834\pi\)
0.147291 + 0.989093i \(0.452945\pi\)
\(422\) 75.9050 63.6918i 0.179870 0.150929i
\(423\) −208.699 175.119i −0.493379 0.413994i
\(424\) 13.8768 + 78.6992i 0.0327283 + 0.185611i
\(425\) 696.499 + 1206.37i 1.63882 + 2.83852i
\(426\) 285.196 + 164.658i 0.669475 + 0.386522i
\(427\) 237.821 + 86.5599i 0.556959 + 0.202716i
\(428\) 127.995 351.663i 0.299053 0.821642i
\(429\) −131.552 + 227.855i −0.306649 + 0.531131i
\(430\) 409.850 236.627i 0.953139 0.550295i
\(431\) 712.000 125.545i 1.65197 0.291287i 0.731426 0.681921i \(-0.238855\pi\)
0.920546 + 0.390634i \(0.127744\pi\)
\(432\) −29.2713 + 34.8842i −0.0677577 + 0.0807505i
\(433\) −69.8599 83.2558i −0.161339 0.192277i 0.679318 0.733844i \(-0.262276\pi\)
−0.840657 + 0.541567i \(0.817831\pi\)
\(434\) −27.6104 + 156.586i −0.0636184 + 0.360798i
\(435\) 1532.97 557.956i 3.52407 1.28266i
\(436\) 112.109i 0.257130i
\(437\) 40.9724 + 153.695i 0.0937584 + 0.351706i
\(438\) 186.717 0.426295
\(439\) 24.9171 + 68.4591i 0.0567587 + 0.155943i 0.964832 0.262869i \(-0.0846687\pi\)
−0.908073 + 0.418812i \(0.862447\pi\)
\(440\) 133.969 + 23.6223i 0.304475 + 0.0536872i
\(441\) 106.537 89.3955i 0.241582 0.202711i
\(442\) −349.823 293.536i −0.791454 0.664109i
\(443\) −78.6832 446.235i −0.177614 1.00730i −0.935083 0.354430i \(-0.884675\pi\)
0.757468 0.652872i \(-0.226436\pi\)
\(444\) 64.9924 + 112.570i 0.146379 + 0.253536i
\(445\) 403.042 + 232.697i 0.905713 + 0.522914i
\(446\) −338.537 123.217i −0.759051 0.276272i
\(447\) −168.185 + 462.086i −0.376254 + 1.03375i
\(448\) −20.4263 + 35.3794i −0.0455944 + 0.0789719i
\(449\) −453.771 + 261.985i −1.01063 + 0.583485i −0.911375 0.411577i \(-0.864978\pi\)
−0.0992513 + 0.995062i \(0.531645\pi\)
\(450\) −456.764 + 80.5397i −1.01503 + 0.178977i
\(451\) −17.6785 + 21.0684i −0.0391985 + 0.0467149i
\(452\) −161.755 192.772i −0.357865 0.426487i
\(453\) 104.816 594.439i 0.231381 1.31223i
\(454\) 403.958 147.029i 0.889775 0.323852i
\(455\) 568.947i 1.25043i
\(456\) 189.168 87.9166i 0.414841 0.192800i
\(457\) −234.737 −0.513647 −0.256823 0.966458i \(-0.582676\pi\)
−0.256823 + 0.966458i \(0.582676\pi\)
\(458\) 192.176 + 527.998i 0.419597 + 1.15283i
\(459\) −288.916 50.9437i −0.629447 0.110988i
\(460\) 114.043 95.6931i 0.247919 0.208028i
\(461\) −244.641 205.279i −0.530676 0.445290i 0.337659 0.941268i \(-0.390365\pi\)
−0.868335 + 0.495979i \(0.834809\pi\)
\(462\) 26.3311 + 149.331i 0.0569938 + 0.323228i
\(463\) −347.408 601.728i −0.750341 1.29963i −0.947658 0.319288i \(-0.896556\pi\)
0.197317 0.980340i \(-0.436777\pi\)
\(464\) 163.741 + 94.5358i 0.352889 + 0.203741i
\(465\) −714.045 259.891i −1.53558 0.558906i
\(466\) 49.3403 135.561i 0.105881 0.290904i
\(467\) 217.856 377.338i 0.466501 0.808004i −0.532767 0.846262i \(-0.678848\pi\)
0.999268 + 0.0382582i \(0.0121809\pi\)
\(468\) 131.678 76.0245i 0.281364 0.162445i
\(469\) −130.029 + 22.9276i −0.277247 + 0.0488861i
\(470\) −362.942 + 432.538i −0.772218 + 0.920293i
\(471\) −268.585 320.087i −0.570244 0.679591i
\(472\) −20.7168 + 117.491i −0.0438916 + 0.248922i
\(473\) 191.310 69.6310i 0.404460 0.147211i
\(474\) 400.879i 0.845737i
\(475\) −991.731 267.090i −2.08785 0.562296i
\(476\) −263.188 −0.552915
\(477\) −58.6280 161.079i −0.122910 0.337692i
\(478\) −512.602 90.3856i −1.07239 0.189091i
\(479\) 84.4817 70.8886i 0.176371 0.147993i −0.550329 0.834948i \(-0.685498\pi\)
0.726700 + 0.686955i \(0.241053\pi\)
\(480\) −149.559 125.495i −0.311580 0.261447i
\(481\) 36.4328 + 206.621i 0.0757438 + 0.429564i
\(482\) −47.1638 81.6901i −0.0978502 0.169481i
\(483\) 143.711 + 82.9717i 0.297539 + 0.171784i
\(484\) −172.414 62.7536i −0.356227 0.129656i
\(485\) 132.057 362.823i 0.272282 0.748089i
\(486\) 198.713 344.181i 0.408874 0.708191i
\(487\) 387.961 223.989i 0.796635 0.459937i −0.0456583 0.998957i \(-0.514539\pi\)
0.842293 + 0.539020i \(0.181205\pi\)
\(488\) −138.048 + 24.3417i −0.282886 + 0.0498805i
\(489\) −252.367 + 300.759i −0.516087 + 0.615049i
\(490\) −185.276 220.803i −0.378114 0.450619i
\(491\) −41.6210 + 236.044i −0.0847678 + 0.480742i 0.912639 + 0.408767i \(0.134041\pi\)
−0.997406 + 0.0719749i \(0.977070\pi\)
\(492\) 37.0910 13.5000i 0.0753882 0.0274391i
\(493\) 1218.07i 2.47073i
\(494\) 335.455 28.9172i 0.679059 0.0585369i
\(495\) −291.801 −0.589498
\(496\) −30.1210 82.7567i −0.0607278 0.166848i
\(497\) 301.693 + 53.1966i 0.607028 + 0.107035i
\(498\) 298.973 250.868i 0.600348 0.503752i
\(499\) −346.239 290.529i −0.693865 0.582222i 0.226156 0.974091i \(-0.427384\pi\)
−0.920021 + 0.391869i \(0.871829\pi\)
\(500\) 89.7236 + 508.848i 0.179447 + 1.01770i
\(501\) −33.1777 57.4655i −0.0662230 0.114702i
\(502\) 439.087 + 253.507i 0.874676 + 0.504995i
\(503\) 410.210 + 149.304i 0.815528 + 0.296828i 0.715905 0.698198i \(-0.246014\pi\)
0.0996224 + 0.995025i \(0.468237\pi\)
\(504\) 29.9714 82.3456i 0.0594670 0.163384i
\(505\) 132.474 229.452i 0.262325 0.454360i
\(506\) 55.4627 32.0214i 0.109610 0.0632834i
\(507\) −45.8060 + 8.07683i −0.0903471 + 0.0159306i
\(508\) −2.07034 + 2.46733i −0.00407547 + 0.00485695i
\(509\) −56.1612 66.9303i −0.110336 0.131494i 0.708050 0.706163i \(-0.249575\pi\)
−0.818386 + 0.574669i \(0.805131\pi\)
\(510\) 218.410 1238.67i 0.428255 2.42876i
\(511\) 163.219 59.4069i 0.319411 0.116256i
\(512\) 22.6274i 0.0441942i
\(513\) 177.346 123.842i 0.345703 0.241407i
\(514\) 169.641 0.330040
\(515\) −138.325 380.043i −0.268591 0.737949i
\(516\) −287.744 50.7371i −0.557644 0.0983277i
\(517\) −186.072 + 156.133i −0.359907 + 0.301998i
\(518\) 92.6291 + 77.7250i 0.178821 + 0.150048i
\(519\) 148.752 + 843.614i 0.286613 + 1.62546i
\(520\) −157.564 272.909i −0.303007 0.524824i
\(521\) −718.337 414.732i −1.37877 0.796031i −0.386756 0.922182i \(-0.626404\pi\)
−0.992011 + 0.126151i \(0.959738\pi\)
\(522\) −381.107 138.711i −0.730089 0.265731i
\(523\) −332.878 + 914.574i −0.636477 + 1.74871i 0.0260404 + 0.999661i \(0.491710\pi\)
−0.662518 + 0.749046i \(0.730512\pi\)
\(524\) −194.374 + 336.666i −0.370943 + 0.642492i
\(525\) −927.941 + 535.747i −1.76751 + 1.02047i
\(526\) 487.708 85.9960i 0.927201 0.163490i
\(527\) 364.695 434.627i 0.692021 0.824719i
\(528\) −53.9861 64.3381i −0.102246 0.121853i
\(529\) −79.6896 + 451.942i −0.150642 + 0.854333i
\(530\) −333.843 + 121.509i −0.629893 + 0.229262i
\(531\) 255.910i 0.481940i
\(532\) 137.389 137.039i 0.258250 0.257592i
\(533\) 63.7107 0.119532
\(534\) −98.2728 270.002i −0.184031 0.505622i
\(535\) 1638.44 + 288.901i 3.06250 + 0.540002i
\(536\) 56.0218 47.0079i 0.104518 0.0877013i
\(537\) 30.4755 + 25.5720i 0.0567513 + 0.0476200i
\(538\) 28.7826 + 163.234i 0.0534992 + 0.303409i
\(539\) −61.9981 107.384i −0.115024 0.199228i
\(540\) −175.325 101.224i −0.324676 0.187452i
\(541\) 430.483 + 156.683i 0.795717 + 0.289617i 0.707710 0.706503i \(-0.249728\pi\)
0.0880063 + 0.996120i \(0.471950\pi\)
\(542\) 128.361 352.669i 0.236829 0.650681i
\(543\) −366.720 + 635.177i −0.675358 + 1.16975i
\(544\) 126.244 72.8870i 0.232066 0.133984i
\(545\) 490.827 86.5460i 0.900600 0.158800i
\(546\) 225.788 269.084i 0.413531 0.492827i
\(547\) 139.282 + 165.989i 0.254628 + 0.303454i 0.878182 0.478326i \(-0.158756\pi\)
−0.623554 + 0.781780i \(0.714312\pi\)
\(548\) 63.1321 358.040i 0.115205 0.653358i
\(549\) 282.553 102.841i 0.514669 0.187324i
\(550\) 413.524i 0.751861i
\(551\) −634.234 635.855i −1.15106 1.15400i
\(552\) −91.9125 −0.166508
\(553\) 127.546 + 350.429i 0.230643 + 0.633687i
\(554\) 47.9990 + 8.46351i 0.0866407 + 0.0152771i
\(555\) −442.675 + 371.448i −0.797612 + 0.669276i
\(556\) 234.921 + 197.122i 0.422519 + 0.354535i
\(557\) 50.3849 + 285.747i 0.0904576 + 0.513011i 0.996045 + 0.0888508i \(0.0283194\pi\)
−0.905587 + 0.424160i \(0.860569\pi\)
\(558\) 94.4544 + 163.600i 0.169273 + 0.293189i
\(559\) −408.428 235.806i −0.730640 0.421835i
\(560\) −170.665 62.1169i −0.304758 0.110923i
\(561\) 185.060 508.447i 0.329874 0.906322i
\(562\) −136.505 + 236.434i −0.242892 + 0.420702i
\(563\) 135.430 78.1905i 0.240550 0.138882i −0.374879 0.927074i \(-0.622316\pi\)
0.615430 + 0.788192i \(0.288983\pi\)
\(564\) 343.307 60.5344i 0.608701 0.107330i
\(565\) 719.110 857.002i 1.27276 1.51682i
\(566\) 3.17468 + 3.78344i 0.00560897 + 0.00668451i
\(567\) 87.6056 496.836i 0.154507 0.876254i
\(568\) −159.446 + 58.0337i −0.280715 + 0.102172i
\(569\) 469.455i 0.825053i 0.910946 + 0.412527i \(0.135354\pi\)
−0.910946 + 0.412527i \(0.864646\pi\)
\(570\) 530.945 + 760.332i 0.931483 + 1.33392i
\(571\) −112.970 −0.197846 −0.0989230 0.995095i \(-0.531540\pi\)
−0.0989230 + 0.995095i \(0.531540\pi\)
\(572\) −46.3655 127.388i −0.0810586 0.222707i
\(573\) 5.46652 + 0.963896i 0.00954018 + 0.00168219i
\(574\) 28.1279 23.6021i 0.0490033 0.0411187i
\(575\) 346.669 + 290.890i 0.602902 + 0.505895i
\(576\) 8.42830 + 47.7992i 0.0146325 + 0.0829848i
\(577\) −65.0229 112.623i −0.112691 0.195187i 0.804163 0.594409i \(-0.202614\pi\)
−0.916855 + 0.399221i \(0.869280\pi\)
\(578\) 459.359 + 265.211i 0.794739 + 0.458843i
\(579\) 221.284 + 80.5406i 0.382182 + 0.139103i
\(580\) −287.485 + 789.859i −0.495664 + 1.36183i
\(581\) 181.530 314.419i 0.312444 0.541169i
\(582\) −206.444 + 119.190i −0.354714 + 0.204794i
\(583\) −150.510 + 26.5390i −0.258165 + 0.0455214i
\(584\) −61.8397 + 73.6977i −0.105890 + 0.126195i
\(585\) 434.499 + 517.816i 0.742733 + 0.885155i
\(586\) −115.143 + 653.006i −0.196489 + 1.11435i
\(587\) −801.822 + 291.839i −1.36597 + 0.497171i −0.917894 0.396827i \(-0.870111\pi\)
−0.448072 + 0.893998i \(0.647889\pi\)
\(588\) 177.956i 0.302647i
\(589\) 35.9273 + 416.777i 0.0609972 + 0.707600i
\(590\) −530.385 −0.898957
\(591\) −315.127 865.805i −0.533210 1.46498i
\(592\) −65.9568 11.6300i −0.111414 0.0196452i
\(593\) 177.032 148.547i 0.298536 0.250501i −0.481199 0.876612i \(-0.659798\pi\)
0.779735 + 0.626110i \(0.215354\pi\)
\(594\) −66.7151 55.9806i −0.112315 0.0942434i
\(595\) −203.176 1152.27i −0.341473 1.93659i
\(596\) −126.684 219.423i −0.212557 0.368160i
\(597\) 855.195 + 493.747i 1.43249 + 0.827047i
\(598\) −139.409 50.7406i −0.233125 0.0848505i
\(599\) −128.583 + 353.278i −0.214662 + 0.589779i −0.999554 0.0298532i \(-0.990496\pi\)
0.784892 + 0.619632i \(0.212718\pi\)
\(600\) 296.739 513.967i 0.494565 0.856612i
\(601\) −663.945 + 383.329i −1.10473 + 0.637818i −0.937460 0.348092i \(-0.886830\pi\)
−0.167273 + 0.985911i \(0.553496\pi\)
\(602\) −267.675 + 47.1983i −0.444642 + 0.0784025i
\(603\) −100.834 + 120.169i −0.167220 + 0.199285i
\(604\) 199.912 + 238.246i 0.330980 + 0.394446i
\(605\) 141.643 803.297i 0.234121 1.32776i
\(606\) −153.712 + 55.9466i −0.253650 + 0.0923211i
\(607\) 504.411i 0.830990i −0.909596 0.415495i \(-0.863608\pi\)
0.909596 0.415495i \(-0.136392\pi\)
\(608\) −27.9504 + 103.782i −0.0459710 + 0.170695i
\(609\) −936.937 −1.53849
\(610\) −213.142 585.604i −0.349414 0.960006i
\(611\) 554.131 + 97.7082i 0.906925 + 0.159915i
\(612\) −239.535 + 200.994i −0.391397 + 0.328421i
\(613\) 736.614 + 618.093i 1.20165 + 1.00831i 0.999581 + 0.0289371i \(0.00921225\pi\)
0.202073 + 0.979370i \(0.435232\pi\)
\(614\) 13.1078 + 74.3381i 0.0213482 + 0.121072i
\(615\) 87.7386 + 151.968i 0.142664 + 0.247102i
\(616\) −67.6621 39.0647i −0.109841 0.0634168i
\(617\) −120.801 43.9680i −0.195788 0.0712609i 0.242265 0.970210i \(-0.422110\pi\)
−0.438053 + 0.898949i \(0.644332\pi\)
\(618\) −85.4006 + 234.636i −0.138189 + 0.379670i
\(619\) 371.077 642.724i 0.599478 1.03833i −0.393420 0.919359i \(-0.628708\pi\)
0.992898 0.118968i \(-0.0379585\pi\)
\(620\) 339.067 195.761i 0.546883 0.315743i
\(621\) −93.8602 + 16.5501i −0.151144 + 0.0266507i
\(622\) −400.560 + 477.368i −0.643986 + 0.767473i
\(623\) −171.810 204.756i −0.275779 0.328661i
\(624\) −33.7846 + 191.602i −0.0541419 + 0.307054i
\(625\) −888.635 + 323.437i −1.42182 + 0.517499i
\(626\) 855.860i 1.36719i
\(627\) 168.138 + 361.778i 0.268163 + 0.576998i
\(628\) 215.293 0.342823
\(629\) −147.572 405.452i −0.234614 0.644598i
\(630\) 383.658 + 67.6492i 0.608981 + 0.107380i
\(631\) 426.786 358.116i 0.676365 0.567538i −0.238577 0.971124i \(-0.576681\pi\)
0.914942 + 0.403586i \(0.132236\pi\)
\(632\) −158.228 132.769i −0.250360 0.210077i
\(633\) −47.2265 267.835i −0.0746075 0.423120i
\(634\) 109.076 + 188.924i 0.172044 + 0.297988i
\(635\) −12.4006 7.15948i −0.0195285 0.0112748i
\(636\) 206.113 + 75.0188i 0.324076 + 0.117954i
\(637\) −98.2413 + 269.916i −0.154225 + 0.423730i
\(638\) −180.797 + 313.149i −0.283381 + 0.490830i
\(639\) 315.206 181.984i 0.493280 0.284795i
\(640\) 99.0659 17.4680i 0.154791 0.0272937i
\(641\) −47.3994 + 56.4884i −0.0739460 + 0.0881254i −0.801749 0.597661i \(-0.796097\pi\)
0.727803 + 0.685786i \(0.240541\pi\)
\(642\) −660.249 786.854i −1.02843 1.22563i
\(643\) −61.7979 + 350.473i −0.0961087 + 0.545059i 0.898293 + 0.439396i \(0.144808\pi\)
−0.994402 + 0.105663i \(0.966304\pi\)
\(644\) −80.3454 + 29.2433i −0.124760 + 0.0454089i
\(645\) 1298.95i 2.01388i
\(646\) −669.061 + 178.360i −1.03570 + 0.276098i
\(647\) −23.7607 −0.0367245 −0.0183622 0.999831i \(-0.505845\pi\)
−0.0183622 + 0.999831i \(0.505845\pi\)
\(648\) 95.5715 + 262.581i 0.147487 + 0.405217i
\(649\) −224.698 39.6203i −0.346222 0.0610483i
\(650\) 733.817 615.746i 1.12895 0.947301i
\(651\) 334.315 + 280.524i 0.513541 + 0.430912i
\(652\) −35.1277 199.219i −0.0538769 0.305551i
\(653\) −558.832 967.926i −0.855792 1.48228i −0.875908 0.482478i \(-0.839737\pi\)
0.0201159 0.999798i \(-0.493596\pi\)
\(654\) −266.483 153.854i −0.407466 0.235251i
\(655\) −1624.02 591.096i −2.47943 0.902437i
\(656\) −6.95585 + 19.1110i −0.0106034 + 0.0291327i
\(657\) 103.182 178.717i 0.157050 0.272019i
\(658\) 280.843 162.145i 0.426812 0.246420i
\(659\) 1024.08 180.573i 1.55399 0.274011i 0.670304 0.742087i \(-0.266164\pi\)
0.883688 + 0.468076i \(0.155053\pi\)
\(660\) 240.005 286.027i 0.363644 0.433374i
\(661\) 245.426 + 292.488i 0.371296 + 0.442493i 0.919047 0.394148i \(-0.128960\pi\)
−0.547751 + 0.836641i \(0.684516\pi\)
\(662\) −127.754 + 724.527i −0.192981 + 1.09445i
\(663\) −1177.82 + 428.692i −1.77650 + 0.646594i
\(664\) 201.092i 0.302849i
\(665\) 706.037 + 495.716i 1.06171 + 0.745438i
\(666\) 143.662 0.215709
\(667\) 135.342 + 371.849i 0.202912 + 0.557495i
\(668\) 33.6700 + 5.93693i 0.0504042 + 0.00888762i
\(669\) −757.484 + 635.604i −1.13226 + 0.950081i
\(670\) 249.055 + 208.982i 0.371724 + 0.311913i
\(671\) −46.5527 264.014i −0.0693782 0.393463i
\(672\) 56.0647 + 97.1069i 0.0834296 + 0.144504i
\(673\) −564.575 325.958i −0.838893 0.484335i 0.0179948 0.999838i \(-0.494272\pi\)
−0.856888 + 0.515503i \(0.827605\pi\)
\(674\) −47.7790 17.3901i −0.0708887 0.0258014i
\(675\) 210.481 578.291i 0.311823 0.856727i
\(676\) 11.9827 20.7547i 0.0177260 0.0307023i
\(677\) −666.881 + 385.024i −0.985052 + 0.568720i −0.903792 0.427973i \(-0.859228\pi\)
−0.0812607 + 0.996693i \(0.525895\pi\)
\(678\) −680.207 + 119.939i −1.00326 + 0.176901i
\(679\) −142.541 + 169.873i −0.209927 + 0.250182i
\(680\) 416.568 + 496.446i 0.612600 + 0.730068i
\(681\) 204.890 1161.99i 0.300866 1.70629i
\(682\) 158.270 57.6055i 0.232067 0.0844656i
\(683\) 794.510i 1.16327i 0.813452 + 0.581633i \(0.197586\pi\)
−0.813452 + 0.581633i \(0.802414\pi\)
\(684\) 20.3867 229.646i 0.0298052 0.335740i
\(685\) 1616.29 2.35954
\(686\) 177.649 + 488.088i 0.258964 + 0.711498i
\(687\) 1518.79 + 267.803i 2.21076 + 0.389816i
\(688\) 115.325 96.7695i 0.167624 0.140653i
\(689\) 271.207 + 227.570i 0.393625 + 0.330290i
\(690\) −70.9550 402.406i −0.102833 0.583197i
\(691\) 235.437 + 407.789i 0.340719 + 0.590143i 0.984566 0.175011i \(-0.0559962\pi\)
−0.643847 + 0.765154i \(0.722663\pi\)
\(692\) −382.242 220.688i −0.552373 0.318913i
\(693\) 157.484 + 57.3194i 0.227249 + 0.0827119i
\(694\) −16.5117 + 45.3657i −0.0237921 + 0.0653684i
\(695\) −681.671 + 1180.69i −0.980822 + 1.69883i
\(696\) 449.424 259.475i 0.645724 0.372809i
\(697\) −129.031 + 22.7517i −0.185124 + 0.0326423i
\(698\) 514.449 613.096i 0.737033 0.878362i
\(699\) −254.517 303.322i −0.364116 0.433937i
\(700\) 95.8684 543.697i 0.136955 0.776710i
\(701\) 453.072 164.905i 0.646322 0.235242i 0.00200220 0.999998i \(-0.499363\pi\)
0.644320 + 0.764756i \(0.277140\pi\)
\(702\) 201.745i 0.287387i
\(703\) 288.150 + 134.815i 0.409886 + 0.191770i
\(704\) 43.2743 0.0614692
\(705\) 530.056 + 1456.32i 0.751852 + 2.06570i
\(706\) 293.262 + 51.7101i 0.415386 + 0.0732437i
\(707\) −116.567 + 97.8115i −0.164876 + 0.138347i
\(708\) 250.846 + 210.484i 0.354302 + 0.297294i
\(709\) 142.393 + 807.549i 0.200836 + 1.13900i 0.903859 + 0.427830i \(0.140722\pi\)
−0.703023 + 0.711167i \(0.748167\pi\)
\(710\) −377.170 653.277i −0.531225 0.920108i
\(711\) 383.702 + 221.531i 0.539665 + 0.311576i
\(712\) 139.118 + 50.6348i 0.195390 + 0.0711162i
\(713\) 63.0412 173.204i 0.0884168 0.242923i
\(714\) −361.189 + 625.598i −0.505867 + 0.876188i
\(715\) 521.930 301.336i 0.729972 0.421449i
\(716\) −20.1866 + 3.55944i −0.0281936 + 0.00497129i
\(717\) −918.324 + 1094.42i −1.28079 + 1.52638i
\(718\) −166.036 197.874i −0.231248 0.275590i
\(719\) −74.1833 + 420.714i −0.103176 + 0.585138i 0.888758 + 0.458377i \(0.151569\pi\)
−0.991933 + 0.126761i \(0.959542\pi\)
\(720\) −202.765 + 73.8005i −0.281618 + 0.102501i
\(721\) 232.279i 0.322162i
\(722\) 256.393 441.480i 0.355115 0.611468i
\(723\) −258.904 −0.358096
\(724\) −129.250 355.112i −0.178522 0.490486i
\(725\) −2516.30 443.692i −3.47076 0.611989i
\(726\) −385.781 + 323.708i −0.531378 + 0.445879i
\(727\) −661.153 554.773i −0.909426 0.763099i 0.0625833 0.998040i \(-0.480066\pi\)
−0.972010 + 0.234940i \(0.924511\pi\)
\(728\) 31.4282 + 178.238i 0.0431705 + 0.244832i
\(729\) −100.839 174.658i −0.138325 0.239586i
\(730\) −370.398 213.849i −0.507394 0.292944i
\(731\) 911.385 + 331.717i 1.24677 + 0.453785i
\(732\) −131.593 + 361.548i −0.179771 + 0.493917i
\(733\) 386.858 670.058i 0.527774 0.914132i −0.471702 0.881758i \(-0.656360\pi\)
0.999476 0.0323734i \(-0.0103066\pi\)
\(734\) −716.225 + 413.513i −0.975783 + 0.563369i
\(735\) −779.117 + 137.379i −1.06002 + 0.186911i
\(736\) 30.4409 36.2781i 0.0413599 0.0492909i
\(737\) 89.9012 + 107.140i 0.121983 + 0.145373i
\(738\) 7.57536 42.9620i 0.0102647 0.0582141i
\(739\) 862.926 314.079i 1.16769 0.425006i 0.315854 0.948808i \(-0.397709\pi\)
0.851840 + 0.523802i \(0.175487\pi\)
\(740\) 297.746i 0.402360i
\(741\) 391.631 837.064i 0.528516 1.12964i
\(742\) 204.042 0.274989
\(743\) −193.556 531.791i −0.260506 0.715736i −0.999133 0.0416212i \(-0.986748\pi\)
0.738627 0.674114i \(-0.235474\pi\)
\(744\) −238.050 41.9747i −0.319960 0.0564175i
\(745\) 862.868 724.032i 1.15821 0.971855i
\(746\) 151.788 + 127.365i 0.203469 + 0.170731i
\(747\) −74.9029 424.795i −0.100272 0.568669i
\(748\) 139.394 + 241.438i 0.186356 + 0.322778i
\(749\) −827.506 477.761i −1.10481 0.637865i
\(750\) 1332.67 + 485.051i 1.77689 + 0.646735i
\(751\) −156.364 + 429.606i −0.208207 + 0.572045i −0.999209 0.0397693i \(-0.987338\pi\)
0.791002 + 0.611814i \(0.209560\pi\)
\(752\) −89.8085 + 155.553i −0.119426 + 0.206852i
\(753\) 1205.18 695.809i 1.60050 0.924049i
\(754\) 824.909 145.454i 1.09404 0.192910i
\(755\) −888.743 + 1059.16i −1.17714 + 1.40287i
\(756\) 74.7382 + 89.0695i 0.0988600 + 0.117817i
\(757\) −252.597 + 1432.55i −0.333681 + 1.89240i 0.106201 + 0.994345i \(0.466131\pi\)
−0.439882 + 0.898056i \(0.644980\pi\)
\(758\) 872.975 317.737i 1.15168 0.419178i
\(759\) 175.780i 0.231594i
\(760\) −475.951 42.2524i −0.626251 0.0555952i
\(761\) 1394.79 1.83284 0.916422 0.400213i \(-0.131064\pi\)
0.916422 + 0.400213i \(0.131064\pi\)
\(762\) 3.02360 + 8.30728i 0.00396798 + 0.0109019i
\(763\) −281.897 49.7060i −0.369459 0.0651455i
\(764\) −2.19093 + 1.83841i −0.00286771 + 0.00240630i
\(765\) −1064.89 893.553i −1.39202 1.16804i
\(766\) −137.960 782.408i −0.180104 1.02142i
\(767\) 264.272 + 457.733i 0.344553 + 0.596784i
\(768\) −53.7855 31.0531i −0.0700332 0.0404337i
\(769\) 840.058 + 305.756i 1.09240 + 0.397602i 0.824511 0.565846i \(-0.191450\pi\)
0.267893 + 0.963449i \(0.413673\pi\)
\(770\) 118.797 326.391i 0.154281 0.423885i
\(771\) 232.809 403.237i 0.301957 0.523005i
\(772\) −105.077 + 60.6665i −0.136111 + 0.0785835i
\(773\) −1243.52 + 219.266i −1.60869 + 0.283656i −0.904539 0.426391i \(-0.859785\pi\)
−0.704155 + 0.710047i \(0.748674\pi\)
\(774\) −207.574 + 247.377i −0.268184 + 0.319609i
\(775\) 765.015 + 911.710i 0.987117 + 1.17640i
\(776\) 21.3283 120.959i 0.0274849 0.155875i
\(777\) 311.874 113.513i 0.401382 0.146091i
\(778\) 136.576i 0.175548i
\(779\) 55.5103 79.0620i 0.0712584 0.101492i
\(780\) −864.940 −1.10890
\(781\) −110.988 304.937i −0.142110 0.390444i
\(782\) 300.460 + 52.9792i 0.384220 + 0.0677484i
\(783\) 412.226 345.898i 0.526470 0.441760i
\(784\) −70.2397 58.9381i −0.0895915 0.0751762i
\(785\) 166.203 + 942.582i 0.211723 + 1.20074i
\(786\) 533.504 + 924.057i 0.678759 + 1.17564i
\(787\) 558.566 + 322.488i 0.709741 + 0.409769i 0.810965 0.585094i \(-0.198943\pi\)
−0.101224 + 0.994864i \(0.532276\pi\)
\(788\) 446.103 + 162.368i 0.566121 + 0.206051i
\(789\) 464.900 1277.30i 0.589226 1.61889i
\(790\) 459.131 795.239i 0.581179 1.00663i
\(791\) −556.443 + 321.263i −0.703468 + 0.406147i
\(792\) −91.4147 + 16.1189i −0.115423 + 0.0203521i
\(793\) −399.187 + 475.732i −0.503388 + 0.599915i
\(794\) −374.346 446.128i −0.471468 0.561874i
\(795\) −169.327 + 960.302i −0.212990 + 1.20793i
\(796\) −478.119 + 174.021i −0.600652 + 0.218619i
\(797\) 1189.87i 1.49294i −0.665420 0.746469i \(-0.731748\pi\)
0.665420 0.746469i \(-0.268252\pi\)
\(798\) −137.194 514.642i −0.171923 0.644914i
\(799\) −1157.16 −1.44826
\(800\) 104.586 + 287.347i 0.130732 + 0.359183i
\(801\) −312.740 55.1445i −0.390437 0.0688445i
\(802\) −641.000 + 537.863i −0.799252 + 0.670652i
\(803\) −140.945 118.267i −0.175523 0.147281i
\(804\) −34.8556 197.676i −0.0433528 0.245866i
\(805\) −190.057 329.188i −0.236095 0.408929i
\(806\) −337.891 195.081i −0.419220 0.242037i
\(807\) 427.508 + 155.600i 0.529750 + 0.192813i
\(808\) 28.8263 79.1997i 0.0356761 0.0980194i
\(809\) −18.1339 + 31.4088i −0.0224152 + 0.0388242i −0.877015 0.480462i \(-0.840469\pi\)
0.854600 + 0.519286i \(0.173802\pi\)
\(810\) −1075.83 + 621.133i −1.32819 + 0.766831i
\(811\) −1479.98 + 260.960i −1.82488 + 0.321775i −0.977775 0.209656i \(-0.932766\pi\)
−0.847102 + 0.531431i \(0.821655\pi\)
\(812\) 310.308 369.811i 0.382153 0.455433i
\(813\) −662.138 789.106i −0.814438 0.970610i
\(814\) 22.2420 126.141i 0.0273243 0.154964i
\(815\) 845.091 307.588i 1.03692 0.377409i
\(816\) 400.110i 0.490331i
\(817\) −648.483 + 301.385i −0.793736 + 0.368893i
\(818\) 950.600 1.16210
\(819\) −132.781 364.812i −0.162125 0.445436i
\(820\) −89.0405 15.7002i −0.108586 0.0191466i
\(821\) −250.228 + 209.966i −0.304784 + 0.255744i −0.782332 0.622861i \(-0.785970\pi\)
0.477548 + 0.878606i \(0.341526\pi\)
\(822\) −764.423 641.427i −0.929955 0.780325i
\(823\) −276.459 1567.88i −0.335917 1.90508i −0.417990 0.908451i \(-0.637265\pi\)
0.0820738 0.996626i \(-0.473846\pi\)
\(824\) −64.3272 111.418i −0.0780670 0.135216i
\(825\) 982.948 + 567.505i 1.19145 + 0.687885i
\(826\) 286.246 + 104.185i 0.346544 + 0.126132i
\(827\) −369.722 + 1015.80i −0.447064 + 1.22830i 0.487695 + 0.873014i \(0.337838\pi\)
−0.934759 + 0.355284i \(0.884384\pi\)
\(828\) −50.7920 + 87.9742i −0.0613429 + 0.106249i
\(829\) 647.255 373.693i 0.780766 0.450775i −0.0559357 0.998434i \(-0.517814\pi\)
0.836702 + 0.547659i \(0.184481\pi\)
\(830\) −880.406 + 155.239i −1.06073 + 0.187035i
\(831\) 85.9899 102.479i 0.103478 0.123320i
\(832\) −64.4364 76.7923i −0.0774476 0.0922984i
\(833\) 102.576 581.735i 0.123140 0.698362i
\(834\) 790.956 287.884i 0.948389 0.345185i
\(835\) 151.995i 0.182030i
\(836\) −198.481 53.4543i −0.237417 0.0639406i
\(837\) −250.653 −0.299466
\(838\) −58.5378 160.831i −0.0698542 0.191923i
\(839\) −621.162 109.528i −0.740360 0.130545i −0.209267 0.977859i \(-0.567108\pi\)
−0.531094 + 0.847313i \(0.678219\pi\)
\(840\) −381.866 + 320.424i −0.454603 + 0.381457i
\(841\) −1067.29 895.565i −1.26908 1.06488i
\(842\) 65.5078 + 371.513i 0.0778002 + 0.441227i
\(843\) 374.671 + 648.948i 0.444449 + 0.769808i
\(844\) 121.356 + 70.0650i 0.143787 + 0.0830154i
\(845\) 100.118 + 36.4398i 0.118482 + 0.0431240i
\(846\) 131.775 362.049i 0.155763 0.427954i
\(847\) −234.238 + 405.712i −0.276550 + 0.478999i
\(848\) −97.8734 + 56.5072i −0.115417 + 0.0666359i
\(849\) 13.3501 2.35398i 0.0157245 0.00277265i
\(850\) −1266.29 + 1509.11i −1.48975 + 1.77542i
\(851\) −90.1013 107.379i −0.105877 0.126179i
\(852\) −80.8721 + 458.648i −0.0949203 + 0.538320i
\(853\) −445.774 + 162.248i −0.522595 + 0.190209i −0.589829 0.807528i \(-0.700805\pi\)
0.0672338 + 0.997737i \(0.478583\pi\)
\(854\) 357.915i 0.419104i
\(855\) 1021.16 88.0269i 1.19434 0.102955i
\(856\) 529.244 0.618275
\(857\) 224.222 + 616.044i 0.261636 + 0.718838i 0.999058 + 0.0434057i \(0.0138208\pi\)
−0.737422 + 0.675433i \(0.763957\pi\)
\(858\) −366.433 64.6120i −0.427078 0.0753054i
\(859\) 1024.32 859.510i 1.19246 1.00059i 0.192648 0.981268i \(-0.438292\pi\)
0.999813 0.0193257i \(-0.00615196\pi\)
\(860\) 512.699 + 430.206i 0.596162 + 0.500239i
\(861\) −17.5006 99.2509i −0.0203259 0.115274i
\(862\) 511.227 + 885.471i 0.593070 + 1.02723i
\(863\) −278.578 160.837i −0.322801 0.186369i 0.329839 0.944037i \(-0.393005\pi\)
−0.652641 + 0.757668i \(0.726339\pi\)
\(864\) −60.5168 22.0263i −0.0700426 0.0254934i
\(865\) 671.116 1843.88i 0.775856 2.13165i
\(866\) 76.8503 133.109i 0.0887417 0.153705i
\(867\) 1260.82 727.932i 1.45423 0.839599i
\(868\) −221.446 + 39.0470i −0.255123 + 0.0449850i
\(869\) 253.917 302.606i 0.292194 0.348223i
\(870\) 1482.97 + 1767.33i 1.70456 + 2.03141i
\(871\) 56.2603 319.068i 0.0645928 0.366324i
\(872\) 148.984 54.2257i 0.170853 0.0621855i
\(873\) 263.464i 0.301791i
\(874\) −184.432 + 128.790i −0.211020 + 0.147357i
\(875\) 1319.28 1.50775
\(876\) 90.3132 + 248.133i 0.103097 + 0.283257i
\(877\) −1422.91 250.898i −1.62248 0.286087i −0.712791 0.701377i \(-0.752569\pi\)
−0.909689 + 0.415290i \(0.863680\pi\)
\(878\) −78.9249 + 66.2259i −0.0898917 + 0.0754281i
\(879\) 1394.18 + 1169.86i 1.58610 + 1.33090i
\(880\) 33.4070 + 189.461i 0.0379626 + 0.215296i
\(881\) 437.607 + 757.958i 0.496716 + 0.860338i 0.999993 0.00378748i \(-0.00120559\pi\)
−0.503276 + 0.864125i \(0.667872\pi\)
\(882\) 170.331 + 98.3407i 0.193119 + 0.111497i
\(883\) 373.459 + 135.928i 0.422943 + 0.153939i 0.544719 0.838619i \(-0.316637\pi\)
−0.121775 + 0.992558i \(0.538859\pi\)
\(884\) 220.882 606.869i 0.249867 0.686503i
\(885\) −727.881 + 1260.73i −0.822465 + 1.42455i
\(886\) 554.955 320.403i 0.626360 0.361629i
\(887\) 331.705 58.4885i 0.373962 0.0659396i 0.0164916 0.999864i \(-0.494750\pi\)
0.357471 + 0.933924i \(0.383639\pi\)
\(888\) −118.161 + 140.819i −0.133065 + 0.158580i
\(889\) 5.28617 + 6.29981i 0.00594620 + 0.00708640i
\(890\) −114.289 + 648.166i −0.128415 + 0.728277i
\(891\) −502.178 + 182.778i −0.563611 + 0.205138i
\(892\) 509.489i 0.571176i
\(893\) 604.059 602.519i 0.676438 0.674714i
\(894\) −695.427 −0.777883
\(895\) −31.1675 85.6319i −0.0348240 0.0956781i
\(896\) −56.8966 10.0324i −0.0635007 0.0111969i
\(897\) −311.930 + 261.741i −0.347748 + 0.291795i
\(898\) −567.643 476.309i −0.632119 0.530411i
\(899\) 180.715 + 1024.88i 0.201018 + 1.14003i
\(900\) −327.963 568.049i −0.364403 0.631165i
\(901\) −630.536 364.040i −0.699818 0.404040i
\(902\) −36.5493 13.3029i −0.0405203 0.0147482i
\(903\) −255.157 + 701.038i −0.282566 + 0.776343i
\(904\) 177.941 308.202i 0.196837 0.340932i
\(905\) 1454.95 840.016i 1.60768 0.928194i
\(906\) 840.663 148.232i 0.927884 0.163611i
\(907\) 1053.26 1255.23i 1.16126 1.38394i 0.251989 0.967730i \(-0.418915\pi\)
0.909271 0.416205i \(-0.136640\pi\)
\(908\) 390.780 + 465.714i 0.430375 + 0.512901i
\(909\) −31.3937 + 178.042i −0.0345365 + 0.195866i
\(910\) −756.088 + 275.194i −0.830866 + 0.302411i
\(911\) 396.810i 0.435577i 0.975996 + 0.217788i \(0.0698843\pi\)
−0.975996 + 0.217788i \(0.930116\pi\)
\(912\) 208.333 + 208.865i 0.228435 + 0.229019i
\(913\) −384.582 −0.421229
\(914\) −113.540 311.948i −0.124223 0.341299i
\(915\) −1684.49 297.021i −1.84098 0.324614i
\(916\) −608.717 + 510.774i −0.664538 + 0.557614i
\(917\) 760.366 + 638.023i 0.829188 + 0.695772i
\(918\) −72.0453 408.589i −0.0784807 0.445086i
\(919\) −267.955 464.111i −0.291572 0.505018i 0.682610 0.730783i \(-0.260845\pi\)
−0.974182 + 0.225766i \(0.927512\pi\)
\(920\) 182.330 + 105.268i 0.198185 + 0.114422i
\(921\) 194.691 + 70.8617i 0.211391 + 0.0769399i
\(922\) 154.470 424.401i 0.167537 0.460305i
\(923\) −375.861 + 651.011i −0.407217 + 0.705320i
\(924\) −185.714 + 107.222i −0.200989 + 0.116041i
\(925\) 891.343 157.168i 0.963615 0.169911i
\(926\) 631.614 752.729i 0.682089 0.812882i
\(927\) 177.389 + 211.404i 0.191358 + 0.228052i
\(928\) −46.4313 + 263.325i −0.0500338 + 0.283756i
\(929\) −41.9597 + 15.2721i −0.0451665 + 0.0164393i −0.364505 0.931202i \(-0.618762\pi\)
0.319338 + 0.947641i \(0.396539\pi\)
\(930\) 1074.62i 1.15551i
\(931\) 249.357 + 357.087i 0.267838 + 0.383552i
\(932\) 204.017 0.218902
\(933\) 584.993 + 1607.26i 0.627002 + 1.72267i
\(934\) 606.829 + 107.000i 0.649710 + 0.114561i
\(935\) −949.439 + 796.674i −1.01544 + 0.852058i
\(936\) 164.722 + 138.218i 0.175985 + 0.147669i
\(937\) −285.568 1619.53i −0.304768 1.72843i −0.624594 0.780949i \(-0.714736\pi\)
0.319826 0.947476i \(-0.396375\pi\)
\(938\) −93.3626 161.709i −0.0995337 0.172397i
\(939\) −2034.38 1174.55i −2.16654 1.25085i
\(940\) −750.362 273.110i −0.798258 0.290542i
\(941\) −545.476 + 1498.68i −0.579677 + 1.59265i 0.209049 + 0.977905i \(0.432963\pi\)
−0.788726 + 0.614745i \(0.789259\pi\)
\(942\) 295.460 511.752i 0.313652 0.543262i
\(943\) −36.8625 + 21.2825i −0.0390906 + 0.0225690i
\(944\) −166.157 + 29.2980i −0.176014 + 0.0310360i
\(945\) −332.262 + 395.974i −0.351600 + 0.419020i
\(946\) 185.069 + 220.557i 0.195633 + 0.233146i
\(947\) 35.7341 202.658i 0.0377340 0.214000i −0.960111 0.279620i \(-0.909791\pi\)
0.997845 + 0.0656202i \(0.0209026\pi\)
\(948\) −532.739 + 193.901i −0.561961 + 0.204537i
\(949\) 426.215i 0.449120i
\(950\) −124.746 1447.13i −0.131312 1.52329i
\(951\) 598.766 0.629617
\(952\) −127.301 349.757i −0.133720 0.367392i
\(953\) 161.981 + 28.5616i 0.169970 + 0.0299702i 0.257985 0.966149i \(-0.416941\pi\)
−0.0880155 + 0.996119i \(0.528053\pi\)
\(954\) 185.705 155.825i 0.194659 0.163338i
\(955\) −9.74019 8.17299i −0.0101991 0.00855810i
\(956\) −127.825 724.929i −0.133708 0.758294i
\(957\) 496.239 + 859.511i 0.518536 + 0.898130i
\(958\) 135.069 + 77.9819i 0.140990 + 0.0814007i
\(959\) −872.300 317.491i −0.909593 0.331065i
\(960\) 94.4331 259.453i 0.0983678 0.270263i
\(961\) −238.127 + 412.448i −0.247791 + 0.429186i
\(962\) −256.961 + 148.357i −0.267111 + 0.154217i
\(963\) −1118.00 + 197.134i −1.16096 + 0.204708i
\(964\) 85.7474 102.190i 0.0889496 0.106006i
\(965\) −346.724 413.210i −0.359300 0.428197i
\(966\) −40.7516 + 231.114i −0.0421860 + 0.239248i
\(967\) −130.875 + 47.6346i −0.135341 + 0.0492602i −0.408803 0.912623i \(-0.634054\pi\)
0.273462 + 0.961883i \(0.411831\pi\)
\(968\) 259.479i 0.268057i
\(969\) −494.234 + 1835.14i −0.510046 + 1.89385i
\(970\) 546.040 0.562927
\(971\) −80.4039 220.908i −0.0828053 0.227506i 0.891380 0.453258i \(-0.149738\pi\)
−0.974185 + 0.225752i \(0.927516\pi\)
\(972\) 553.506 + 97.5981i 0.569451 + 0.100410i
\(973\) 599.820 503.309i 0.616465 0.517275i
\(974\) 485.318 + 407.230i 0.498273 + 0.418101i
\(975\) −456.566 2589.32i −0.468273 2.65571i
\(976\) −99.1209 171.682i −0.101558 0.175904i
\(977\) 186.217 + 107.512i 0.190601 + 0.110043i 0.592264 0.805744i \(-0.298234\pi\)
−0.401663 + 0.915788i \(0.631568\pi\)
\(978\) −521.753 189.903i −0.533490 0.194175i
\(979\) −96.8375 + 266.059i −0.0989147 + 0.271766i
\(980\) 203.815 353.018i 0.207975 0.360223i
\(981\) −294.523 + 170.043i −0.300227 + 0.173336i
\(982\) −333.817 + 58.8610i −0.339936 + 0.0599399i
\(983\) 426.057 507.756i 0.433426 0.516537i −0.504482 0.863422i \(-0.668316\pi\)
0.937907 + 0.346886i \(0.112761\pi\)
\(984\) 35.8811 + 42.7614i 0.0364645 + 0.0434567i
\(985\) −366.486 + 2078.45i −0.372067 + 2.11010i
\(986\) −1618.72 + 589.167i −1.64171 + 0.597532i
\(987\) 890.086i 0.901809i
\(988\) 200.685 + 431.808i 0.203123 + 0.437053i
\(989\) 315.084 0.318588
\(990\) −141.141 387.783i −0.142567 0.391700i
\(991\) 251.249 + 44.3020i 0.253531 + 0.0447044i 0.298969 0.954263i \(-0.403357\pi\)
−0.0454380 + 0.998967i \(0.514468\pi\)
\(992\) 95.4083 80.0571i 0.0961778 0.0807027i
\(993\) 1546.88 + 1297.99i 1.55778 + 1.30714i
\(994\) 75.2314 + 426.658i 0.0756855 + 0.429234i
\(995\) −1130.99 1958.93i −1.13667 1.96877i
\(996\) 477.996 + 275.971i 0.479915 + 0.277079i
\(997\) −1394.81 507.668i −1.39900 0.509196i −0.471121 0.882069i \(-0.656150\pi\)
−0.927882 + 0.372873i \(0.878373\pi\)
\(998\) 218.619 600.651i 0.219057 0.601855i
\(999\) −95.3088 + 165.080i −0.0954043 + 0.165245i
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 38.3.f.a.33.4 yes 24
3.2 odd 2 342.3.z.b.109.2 24
4.3 odd 2 304.3.z.c.33.1 24
19.2 odd 18 722.3.b.f.721.14 24
19.15 odd 18 inner 38.3.f.a.15.4 24
19.17 even 9 722.3.b.f.721.11 24
57.53 even 18 342.3.z.b.91.2 24
76.15 even 18 304.3.z.c.129.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.3.f.a.15.4 24 19.15 odd 18 inner
38.3.f.a.33.4 yes 24 1.1 even 1 trivial
304.3.z.c.33.1 24 4.3 odd 2
304.3.z.c.129.1 24 76.15 even 18
342.3.z.b.91.2 24 57.53 even 18
342.3.z.b.109.2 24 3.2 odd 2
722.3.b.f.721.11 24 19.17 even 9
722.3.b.f.721.14 24 19.2 odd 18