Properties

Label 11.3.d.a.7.1
Level $11$
Weight $3$
Character 11.7
Analytic conductor $0.300$
Analytic rank $0$
Dimension $4$
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] = [11,3,Mod(2,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 11.d (of order \(10\), degree \(4\), 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: \(0.299728290796\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 7.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 11.7
Dual form 11.3.d.a.8.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.80902 + 2.48990i) q^{2} +(1.11803 - 3.44095i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(6.54508 + 9.00854i) q^{6} +(-0.854102 + 0.277515i) q^{7} +(4.30902 + 1.40008i) q^{8} +(-3.30902 - 2.40414i) q^{9} +O(q^{10})\) \(q+(-1.80902 + 2.48990i) q^{2} +(1.11803 - 3.44095i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(6.54508 + 9.00854i) q^{6} +(-0.854102 + 0.277515i) q^{7} +(4.30902 + 1.40008i) q^{8} +(-3.30902 - 2.40414i) q^{9} -12.3107i q^{10} +(10.8713 + 1.67760i) q^{11} -19.7984 q^{12} +(-5.00000 + 6.88191i) q^{13} +(0.854102 - 2.62866i) q^{14} +(4.47214 + 13.7638i) q^{15} +(6.42705 - 4.66953i) q^{16} +(-14.5344 - 20.0049i) q^{17} +(11.9721 - 3.88998i) q^{18} +(11.2812 + 3.66547i) q^{19} +(17.7082 + 12.8658i) q^{20} +3.24920i q^{21} +(-23.8435 + 24.0337i) q^{22} -7.23607 q^{23} +(9.63525 - 13.2618i) q^{24} +(-2.78115 + 8.55951i) q^{25} +(-8.09017 - 24.8990i) q^{26} +(14.3713 - 10.4414i) q^{27} +(2.88854 + 3.97574i) q^{28} +(-3.29180 + 1.06957i) q^{29} +(-42.3607 - 13.7638i) q^{30} +(-26.7984 - 19.4702i) q^{31} +42.5730i q^{32} +(17.9271 - 35.5321i) q^{33} +76.1033 q^{34} +(2.11146 - 2.90617i) q^{35} +(-6.91641 + 21.2865i) q^{36} +(12.4377 + 38.2793i) q^{37} +(-29.5344 + 21.4580i) q^{38} +(18.0902 + 24.8990i) q^{39} +(-17.2361 + 5.60034i) q^{40} +(1.24265 + 0.403760i) q^{41} +(-8.09017 - 5.87785i) q^{42} -33.0625i q^{43} +(-9.65248 - 59.4145i) q^{44} +16.3607 q^{45} +(13.0902 - 18.0171i) q^{46} +(7.03444 - 21.6498i) q^{47} +(-8.88197 - 27.3359i) q^{48} +(-38.9894 + 28.3274i) q^{49} +(-16.2812 - 22.4091i) q^{50} +(-85.0861 + 27.6462i) q^{51} +(44.2705 + 14.3844i) q^{52} +(63.5410 + 46.1653i) q^{53} +54.6718i q^{54} +(-39.1246 + 20.1312i) q^{55} -4.06888 q^{56} +(25.2254 - 34.7198i) q^{57} +(3.29180 - 10.1311i) q^{58} +(9.66312 + 29.7400i) q^{59} +(64.0689 - 46.5488i) q^{60} +(-16.5066 - 22.7194i) q^{61} +(96.9574 - 31.5034i) q^{62} +(3.49342 + 1.13508i) q^{63} +(-80.2943 - 58.3372i) q^{64} -34.0260i q^{65} +(56.0410 + 108.915i) q^{66} -76.5066 q^{67} +(-79.5344 + 109.470i) q^{68} +(-8.09017 + 24.8990i) q^{69} +(3.41641 + 10.5146i) q^{70} +(50.4164 - 36.6297i) q^{71} +(-10.8926 - 14.9924i) q^{72} +(89.5344 - 29.0915i) q^{73} +(-117.812 - 38.2793i) q^{74} +(26.3435 + 19.1396i) q^{75} -64.9089i q^{76} +(-9.75078 + 1.58411i) q^{77} -94.7214 q^{78} +(38.7426 - 53.3247i) q^{79} +(-9.81966 + 30.2218i) q^{80} +(-31.2361 - 96.1347i) q^{81} +(-3.25329 + 2.36365i) q^{82} +(33.3303 + 45.8752i) q^{83} +(16.9098 - 5.49434i) q^{84} +(94.0689 + 30.5648i) q^{85} +(82.3222 + 59.8106i) q^{86} +12.5227i q^{87} +(44.4959 + 22.4496i) q^{88} -62.2968 q^{89} +(-29.5967 + 40.7364i) q^{90} +(2.36068 - 7.26543i) q^{91} +(12.2361 + 37.6587i) q^{92} +(-96.9574 + 70.4437i) q^{93} +(41.1803 + 56.6799i) q^{94} +(-45.1246 + 14.6619i) q^{95} +(146.492 + 47.5981i) q^{96} +(-58.5795 - 42.5605i) q^{97} -148.324i q^{98} +(-31.9402 - 31.6874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9} + q^{11} - 30 q^{12} - 20 q^{13} - 10 q^{14} + 19 q^{16} + 30 q^{18} + 25 q^{19} + 44 q^{20} - 35 q^{22} - 20 q^{23} + 5 q^{24} + 9 q^{25} - 10 q^{26} + 15 q^{27} - 60 q^{28} - 40 q^{29} - 80 q^{30} - 58 q^{31} + 65 q^{33} + 130 q^{34} + 80 q^{35} + 26 q^{36} + 90 q^{37} - 60 q^{38} + 50 q^{39} - 60 q^{40} - 80 q^{41} - 10 q^{42} + 24 q^{44} - 24 q^{45} + 30 q^{46} - 30 q^{47} - 40 q^{48} - 109 q^{49} - 45 q^{50} - 195 q^{51} + 110 q^{52} + 120 q^{53} - 76 q^{55} + 100 q^{56} + 45 q^{57} + 40 q^{58} + 23 q^{59} + 140 q^{60} + 10 q^{61} + 200 q^{62} + 90 q^{63} - 149 q^{64} + 90 q^{66} - 230 q^{67} - 260 q^{68} - 10 q^{69} - 40 q^{70} + 148 q^{71} - 95 q^{72} + 300 q^{73} - 270 q^{74} + 45 q^{75} - 200 q^{77} - 200 q^{78} + 70 q^{79} - 84 q^{80} - 116 q^{81} + 25 q^{82} + 225 q^{83} + 90 q^{84} + 260 q^{85} + 175 q^{86} + 55 q^{88} + 122 q^{89} - 20 q^{90} - 80 q^{91} + 40 q^{92} - 200 q^{93} + 120 q^{94} - 100 q^{95} + 340 q^{96} - 165 q^{97} + 31 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80902 + 2.48990i −0.904508 + 1.24495i 0.0644990 + 0.997918i \(0.479455\pi\)
−0.969007 + 0.247031i \(0.920545\pi\)
\(3\) 1.11803 3.44095i 0.372678 1.14698i −0.572354 0.820007i \(-0.693970\pi\)
0.945032 0.326978i \(-0.106030\pi\)
\(4\) −1.69098 5.20431i −0.422746 1.30108i
\(5\) −3.23607 + 2.35114i −0.647214 + 0.470228i −0.862321 0.506362i \(-0.830990\pi\)
0.215107 + 0.976590i \(0.430990\pi\)
\(6\) 6.54508 + 9.00854i 1.09085 + 1.50142i
\(7\) −0.854102 + 0.277515i −0.122015 + 0.0396449i −0.369388 0.929275i \(-0.620433\pi\)
0.247373 + 0.968920i \(0.420433\pi\)
\(8\) 4.30902 + 1.40008i 0.538627 + 0.175011i
\(9\) −3.30902 2.40414i −0.367669 0.267127i
\(10\) 12.3107i 1.23107i
\(11\) 10.8713 + 1.67760i 0.988302 + 0.152509i
\(12\) −19.7984 −1.64986
\(13\) −5.00000 + 6.88191i −0.384615 + 0.529378i −0.956800 0.290747i \(-0.906096\pi\)
0.572185 + 0.820125i \(0.306096\pi\)
\(14\) 0.854102 2.62866i 0.0610073 0.187761i
\(15\) 4.47214 + 13.7638i 0.298142 + 0.917588i
\(16\) 6.42705 4.66953i 0.401691 0.291845i
\(17\) −14.5344 20.0049i −0.854967 1.17676i −0.982746 0.184959i \(-0.940785\pi\)
0.127779 0.991803i \(-0.459215\pi\)
\(18\) 11.9721 3.88998i 0.665119 0.216110i
\(19\) 11.2812 + 3.66547i 0.593745 + 0.192919i 0.590449 0.807075i \(-0.298951\pi\)
0.00329617 + 0.999995i \(0.498951\pi\)
\(20\) 17.7082 + 12.8658i 0.885410 + 0.643288i
\(21\) 3.24920i 0.154724i
\(22\) −23.8435 + 24.0337i −1.08379 + 1.09244i
\(23\) −7.23607 −0.314612 −0.157306 0.987550i \(-0.550281\pi\)
−0.157306 + 0.987550i \(0.550281\pi\)
\(24\) 9.63525 13.2618i 0.401469 0.552575i
\(25\) −2.78115 + 8.55951i −0.111246 + 0.342380i
\(26\) −8.09017 24.8990i −0.311160 0.957653i
\(27\) 14.3713 10.4414i 0.532271 0.386718i
\(28\) 2.88854 + 3.97574i 0.103162 + 0.141991i
\(29\) −3.29180 + 1.06957i −0.113510 + 0.0368817i −0.365221 0.930921i \(-0.619007\pi\)
0.251711 + 0.967802i \(0.419007\pi\)
\(30\) −42.3607 13.7638i −1.41202 0.458794i
\(31\) −26.7984 19.4702i −0.864464 0.628070i 0.0646320 0.997909i \(-0.479413\pi\)
−0.929096 + 0.369840i \(0.879413\pi\)
\(32\) 42.5730i 1.33041i
\(33\) 17.9271 35.5321i 0.543244 1.07673i
\(34\) 76.1033 2.23833
\(35\) 2.11146 2.90617i 0.0603273 0.0830334i
\(36\) −6.91641 + 21.2865i −0.192122 + 0.591292i
\(37\) 12.4377 + 38.2793i 0.336154 + 1.03458i 0.966151 + 0.257978i \(0.0830561\pi\)
−0.629997 + 0.776598i \(0.716944\pi\)
\(38\) −29.5344 + 21.4580i −0.777222 + 0.564685i
\(39\) 18.0902 + 24.8990i 0.463851 + 0.638435i
\(40\) −17.2361 + 5.60034i −0.430902 + 0.140008i
\(41\) 1.24265 + 0.403760i 0.0303084 + 0.00984781i 0.324132 0.946012i \(-0.394928\pi\)
−0.293824 + 0.955860i \(0.594928\pi\)
\(42\) −8.09017 5.87785i −0.192623 0.139949i
\(43\) 33.0625i 0.768895i −0.923147 0.384447i \(-0.874392\pi\)
0.923147 0.384447i \(-0.125608\pi\)
\(44\) −9.65248 59.4145i −0.219374 1.35033i
\(45\) 16.3607 0.363571
\(46\) 13.0902 18.0171i 0.284569 0.391676i
\(47\) 7.03444 21.6498i 0.149669 0.460634i −0.847913 0.530136i \(-0.822141\pi\)
0.997582 + 0.0695019i \(0.0221410\pi\)
\(48\) −8.88197 27.3359i −0.185041 0.569498i
\(49\) −38.9894 + 28.3274i −0.795701 + 0.578111i
\(50\) −16.2812 22.4091i −0.325623 0.448182i
\(51\) −85.0861 + 27.6462i −1.66835 + 0.542081i
\(52\) 44.2705 + 14.3844i 0.851356 + 0.276622i
\(53\) 63.5410 + 46.1653i 1.19889 + 0.871043i 0.994175 0.107780i \(-0.0343741\pi\)
0.204712 + 0.978822i \(0.434374\pi\)
\(54\) 54.6718i 1.01244i
\(55\) −39.1246 + 20.1312i −0.711357 + 0.366022i
\(56\) −4.06888 −0.0726586
\(57\) 25.2254 34.7198i 0.442551 0.609120i
\(58\) 3.29180 10.1311i 0.0567551 0.174674i
\(59\) 9.66312 + 29.7400i 0.163782 + 0.504068i 0.998944 0.0459347i \(-0.0146266\pi\)
−0.835163 + 0.550003i \(0.814627\pi\)
\(60\) 64.0689 46.5488i 1.06781 0.775813i
\(61\) −16.5066 22.7194i −0.270600 0.372448i 0.651992 0.758226i \(-0.273933\pi\)
−0.922592 + 0.385777i \(0.873933\pi\)
\(62\) 96.9574 31.5034i 1.56383 0.508119i
\(63\) 3.49342 + 1.13508i 0.0554511 + 0.0180172i
\(64\) −80.2943 58.3372i −1.25460 0.911519i
\(65\) 34.0260i 0.523477i
\(66\) 56.0410 + 108.915i 0.849106 + 1.65022i
\(67\) −76.5066 −1.14189 −0.570945 0.820989i \(-0.693423\pi\)
−0.570945 + 0.820989i \(0.693423\pi\)
\(68\) −79.5344 + 109.470i −1.16962 + 1.60985i
\(69\) −8.09017 + 24.8990i −0.117249 + 0.360855i
\(70\) 3.41641 + 10.5146i 0.0488058 + 0.150209i
\(71\) 50.4164 36.6297i 0.710090 0.515911i −0.173113 0.984902i \(-0.555382\pi\)
0.883203 + 0.468991i \(0.155382\pi\)
\(72\) −10.8926 14.9924i −0.151286 0.208228i
\(73\) 89.5344 29.0915i 1.22650 0.398514i 0.377054 0.926191i \(-0.376937\pi\)
0.849445 + 0.527677i \(0.176937\pi\)
\(74\) −117.812 38.2793i −1.59205 0.517288i
\(75\) 26.3435 + 19.1396i 0.351246 + 0.255195i
\(76\) 64.9089i 0.854064i
\(77\) −9.75078 + 1.58411i −0.126633 + 0.0205729i
\(78\) −94.7214 −1.21438
\(79\) 38.7426 53.3247i 0.490413 0.674996i −0.490051 0.871694i \(-0.663022\pi\)
0.980464 + 0.196698i \(0.0630218\pi\)
\(80\) −9.81966 + 30.2218i −0.122746 + 0.377773i
\(81\) −31.2361 96.1347i −0.385630 1.18685i
\(82\) −3.25329 + 2.36365i −0.0396743 + 0.0288250i
\(83\) 33.3303 + 45.8752i 0.401570 + 0.552714i 0.961137 0.276071i \(-0.0890326\pi\)
−0.559567 + 0.828785i \(0.689033\pi\)
\(84\) 16.9098 5.49434i 0.201308 0.0654088i
\(85\) 94.0689 + 30.5648i 1.10669 + 0.359586i
\(86\) 82.3222 + 59.8106i 0.957235 + 0.695472i
\(87\) 12.5227i 0.143939i
\(88\) 44.4959 + 22.4496i 0.505636 + 0.255109i
\(89\) −62.2968 −0.699964 −0.349982 0.936756i \(-0.613812\pi\)
−0.349982 + 0.936756i \(0.613812\pi\)
\(90\) −29.5967 + 40.7364i −0.328853 + 0.452627i
\(91\) 2.36068 7.26543i 0.0259415 0.0798398i
\(92\) 12.2361 + 37.6587i 0.133001 + 0.409334i
\(93\) −96.9574 + 70.4437i −1.04255 + 0.757459i
\(94\) 41.1803 + 56.6799i 0.438089 + 0.602977i
\(95\) −45.1246 + 14.6619i −0.474996 + 0.154336i
\(96\) 146.492 + 47.5981i 1.52596 + 0.495813i
\(97\) −58.5795 42.5605i −0.603913 0.438768i 0.243353 0.969938i \(-0.421753\pi\)
−0.847266 + 0.531170i \(0.821753\pi\)
\(98\) 148.324i 1.51351i
\(99\) −31.9402 31.6874i −0.322628 0.320075i
\(100\) 49.2492 0.492492
\(101\) −37.8409 + 52.0836i −0.374663 + 0.515679i −0.954161 0.299295i \(-0.903249\pi\)
0.579498 + 0.814974i \(0.303249\pi\)
\(102\) 85.0861 261.868i 0.834177 2.56733i
\(103\) −10.0770 31.0139i −0.0978351 0.301105i 0.890147 0.455673i \(-0.150601\pi\)
−0.987982 + 0.154568i \(0.950601\pi\)
\(104\) −31.1803 + 22.6538i −0.299811 + 0.217825i
\(105\) −7.63932 10.5146i −0.0727554 0.100139i
\(106\) −229.894 + 74.6969i −2.16881 + 0.704688i
\(107\) −5.13932 1.66987i −0.0480310 0.0156062i 0.284903 0.958556i \(-0.408039\pi\)
−0.332934 + 0.942950i \(0.608039\pi\)
\(108\) −78.6418 57.1366i −0.728165 0.529043i
\(109\) 137.002i 1.25690i 0.777850 + 0.628450i \(0.216310\pi\)
−0.777850 + 0.628450i \(0.783690\pi\)
\(110\) 20.6525 133.834i 0.187750 1.21667i
\(111\) 145.623 1.31192
\(112\) −4.19350 + 5.77185i −0.0374419 + 0.0515344i
\(113\) −14.3713 + 44.2304i −0.127180 + 0.391419i −0.994292 0.106694i \(-0.965974\pi\)
0.867112 + 0.498113i \(0.165974\pi\)
\(114\) 40.8156 + 125.617i 0.358032 + 1.10191i
\(115\) 23.4164 17.0130i 0.203621 0.147939i
\(116\) 11.1327 + 15.3229i 0.0959719 + 0.132094i
\(117\) 33.0902 10.7516i 0.282822 0.0918944i
\(118\) −91.5304 29.7400i −0.775681 0.252034i
\(119\) 17.9656 + 13.0527i 0.150971 + 0.109687i
\(120\) 65.5699i 0.546416i
\(121\) 115.371 + 36.4754i 0.953482 + 0.301450i
\(122\) 86.4296 0.708439
\(123\) 2.77864 3.82447i 0.0225906 0.0310933i
\(124\) −56.0132 + 172.391i −0.451719 + 1.39025i
\(125\) −42.0263 129.344i −0.336210 1.03475i
\(126\) −9.14590 + 6.64488i −0.0725865 + 0.0527372i
\(127\) 49.0395 + 67.4970i 0.386138 + 0.531473i 0.957197 0.289436i \(-0.0934676\pi\)
−0.571060 + 0.820908i \(0.693468\pi\)
\(128\) 128.550 41.7685i 1.00430 0.326316i
\(129\) −113.766 36.9650i −0.881910 0.286550i
\(130\) 84.7214 + 61.5537i 0.651703 + 0.473490i
\(131\) 85.0901i 0.649543i −0.945793 0.324771i \(-0.894713\pi\)
0.945793 0.324771i \(-0.105287\pi\)
\(132\) −215.235 33.2137i −1.63056 0.251619i
\(133\) −10.6525 −0.0800938
\(134\) 138.402 190.494i 1.03285 1.42159i
\(135\) −21.9574 + 67.5780i −0.162648 + 0.500578i
\(136\) −34.6205 106.551i −0.254563 0.783464i
\(137\) −47.5238 + 34.5281i −0.346889 + 0.252030i −0.747563 0.664191i \(-0.768776\pi\)
0.400674 + 0.916221i \(0.368776\pi\)
\(138\) −47.3607 65.1864i −0.343193 0.472365i
\(139\) 153.108 49.7479i 1.10150 0.357899i 0.298820 0.954310i \(-0.403407\pi\)
0.802679 + 0.596411i \(0.203407\pi\)
\(140\) −18.6950 6.07439i −0.133536 0.0433885i
\(141\) −66.6312 48.4104i −0.472562 0.343336i
\(142\) 191.795i 1.35067i
\(143\) −65.9017 + 66.4275i −0.460851 + 0.464528i
\(144\) −32.4934 −0.225649
\(145\) 8.13777 11.2007i 0.0561225 0.0772460i
\(146\) −89.5344 + 275.559i −0.613250 + 1.88739i
\(147\) 53.8820 + 165.832i 0.366544 + 1.12811i
\(148\) 178.185 129.459i 1.20396 0.874725i
\(149\) −151.103 207.976i −1.01412 1.39581i −0.916248 0.400612i \(-0.868798\pi\)
−0.0978685 0.995199i \(-0.531202\pi\)
\(150\) −95.3115 + 30.9686i −0.635410 + 0.206457i
\(151\) −274.087 89.0563i −1.81515 0.589777i −0.999944 0.0106004i \(-0.996626\pi\)
−0.815202 0.579176i \(-0.803374\pi\)
\(152\) 43.4787 + 31.5891i 0.286044 + 0.207823i
\(153\) 101.140i 0.661043i
\(154\) 13.6950 27.1441i 0.0889289 0.176261i
\(155\) 132.498 0.854829
\(156\) 98.9919 136.251i 0.634563 0.873401i
\(157\) 85.4803 263.081i 0.544460 1.67568i −0.177809 0.984065i \(-0.556901\pi\)
0.722270 0.691612i \(-0.243099\pi\)
\(158\) 62.6869 + 192.930i 0.396753 + 1.22108i
\(159\) 229.894 167.027i 1.44587 1.05049i
\(160\) −100.095 137.769i −0.625595 0.861058i
\(161\) 6.18034 2.00811i 0.0383872 0.0124728i
\(162\) 295.872 + 96.1347i 1.82637 + 0.593424i
\(163\) 56.1180 + 40.7721i 0.344282 + 0.250136i 0.746466 0.665423i \(-0.231749\pi\)
−0.402184 + 0.915559i \(0.631749\pi\)
\(164\) 7.14987i 0.0435967i
\(165\) 25.5279 + 157.133i 0.154714 + 0.952323i
\(166\) −174.520 −1.05132
\(167\) −169.864 + 233.798i −1.01715 + 1.39999i −0.102968 + 0.994685i \(0.532834\pi\)
−0.914182 + 0.405303i \(0.867166\pi\)
\(168\) −4.54915 + 14.0008i −0.0270783 + 0.0833384i
\(169\) 29.8632 + 91.9095i 0.176705 + 0.543843i
\(170\) −246.276 + 178.930i −1.44868 + 1.05253i
\(171\) −28.5172 39.2506i −0.166767 0.229536i
\(172\) −172.067 + 55.9081i −1.00039 + 0.325047i
\(173\) 174.241 + 56.6144i 1.00717 + 0.327251i 0.765729 0.643164i \(-0.222379\pi\)
0.241445 + 0.970414i \(0.422379\pi\)
\(174\) −31.1803 22.6538i −0.179197 0.130194i
\(175\) 8.08250i 0.0461857i
\(176\) 77.7041 39.9819i 0.441501 0.227170i
\(177\) 113.138 0.639196
\(178\) 112.696 155.113i 0.633124 0.871420i
\(179\) 0.633702 1.95033i 0.00354024 0.0108957i −0.949271 0.314460i \(-0.898177\pi\)
0.952811 + 0.303564i \(0.0981766\pi\)
\(180\) −27.6656 85.1461i −0.153698 0.473034i
\(181\) 58.9787 42.8505i 0.325849 0.236743i −0.412818 0.910814i \(-0.635455\pi\)
0.738667 + 0.674070i \(0.235455\pi\)
\(182\) 13.8197 + 19.0211i 0.0759322 + 0.104512i
\(183\) −96.6312 + 31.3974i −0.528039 + 0.171570i
\(184\) −31.1803 10.1311i −0.169458 0.0550604i
\(185\) −130.249 94.6316i −0.704050 0.511522i
\(186\) 368.848i 1.98305i
\(187\) −124.448 241.863i −0.665499 1.29339i
\(188\) −124.567 −0.662592
\(189\) −9.37694 + 12.9063i −0.0496134 + 0.0682870i
\(190\) 45.1246 138.879i 0.237498 0.730944i
\(191\) −32.0770 98.7229i −0.167942 0.516874i 0.831299 0.555826i \(-0.187598\pi\)
−0.999241 + 0.0389523i \(0.987598\pi\)
\(192\) −290.508 + 211.066i −1.51306 + 1.09930i
\(193\) 202.207 + 278.314i 1.04770 + 1.44204i 0.890784 + 0.454428i \(0.150156\pi\)
0.156919 + 0.987611i \(0.449844\pi\)
\(194\) 211.943 68.8644i 1.09249 0.354971i
\(195\) −117.082 38.0423i −0.600421 0.195089i
\(196\) 213.355 + 155.012i 1.08855 + 0.790875i
\(197\) 99.0718i 0.502903i 0.967870 + 0.251451i \(0.0809078\pi\)
−0.967870 + 0.251451i \(0.919092\pi\)
\(198\) 136.679 22.2048i 0.690297 0.112146i
\(199\) −153.469 −0.771201 −0.385601 0.922666i \(-0.626006\pi\)
−0.385601 + 0.922666i \(0.626006\pi\)
\(200\) −23.9681 + 32.9892i −0.119840 + 0.164946i
\(201\) −85.5370 + 263.256i −0.425557 + 1.30973i
\(202\) −61.2279 188.440i −0.303109 0.932872i
\(203\) 2.51471 1.82704i 0.0123877 0.00900021i
\(204\) 287.758 + 396.065i 1.41058 + 1.94150i
\(205\) −4.97058 + 1.61504i −0.0242467 + 0.00787825i
\(206\) 95.4508 + 31.0139i 0.463354 + 0.150553i
\(207\) 23.9443 + 17.3965i 0.115673 + 0.0840412i
\(208\) 67.5780i 0.324894i
\(209\) 116.492 + 58.7737i 0.557377 + 0.281214i
\(210\) 40.0000 0.190476
\(211\) −196.035 + 269.820i −0.929078 + 1.27877i 0.0311405 + 0.999515i \(0.490086\pi\)
−0.960218 + 0.279251i \(0.909914\pi\)
\(212\) 132.812 408.752i 0.626469 1.92807i
\(213\) −69.6738 214.434i −0.327107 1.00673i
\(214\) 13.4549 9.77557i 0.0628734 0.0456802i
\(215\) 77.7345 + 106.992i 0.361556 + 0.497639i
\(216\) 76.5451 24.8710i 0.354375 0.115144i
\(217\) 28.2918 + 9.19256i 0.130377 + 0.0423620i
\(218\) −341.122 247.839i −1.56478 1.13688i
\(219\) 340.609i 1.55529i
\(220\) 170.928 + 169.575i 0.776946 + 0.770796i
\(221\) 210.344 0.951785
\(222\) −263.435 + 362.587i −1.18664 + 1.63327i
\(223\) 35.2198 108.395i 0.157936 0.486078i −0.840510 0.541796i \(-0.817745\pi\)
0.998447 + 0.0557176i \(0.0177446\pi\)
\(224\) −11.8146 36.3617i −0.0527439 0.162329i
\(225\) 29.7812 21.6373i 0.132361 0.0961657i
\(226\) −84.1312 115.797i −0.372262 0.512375i
\(227\) −37.1058 + 12.0564i −0.163462 + 0.0531120i −0.389605 0.920982i \(-0.627388\pi\)
0.226143 + 0.974094i \(0.427388\pi\)
\(228\) −223.348 72.5703i −0.979599 0.318291i
\(229\) −108.575 78.8847i −0.474129 0.344475i 0.324919 0.945742i \(-0.394663\pi\)
−0.799048 + 0.601267i \(0.794663\pi\)
\(230\) 89.0813i 0.387310i
\(231\) −5.45085 + 35.3231i −0.0235968 + 0.152914i
\(232\) −15.6819 −0.0675944
\(233\) 157.139 216.283i 0.674415 0.928253i −0.325435 0.945564i \(-0.605511\pi\)
0.999850 + 0.0173116i \(0.00551073\pi\)
\(234\) −33.0902 + 101.841i −0.141411 + 0.435218i
\(235\) 28.1378 + 86.5991i 0.119735 + 0.368507i
\(236\) 138.436 100.580i 0.586594 0.426185i
\(237\) −140.172 192.930i −0.591444 0.814053i
\(238\) −65.0000 + 21.1198i −0.273109 + 0.0887386i
\(239\) 104.751 + 34.0356i 0.438288 + 0.142408i 0.519846 0.854260i \(-0.325990\pi\)
−0.0815577 + 0.996669i \(0.525990\pi\)
\(240\) 93.0132 + 67.5780i 0.387555 + 0.281575i
\(241\) 191.103i 0.792960i 0.918043 + 0.396480i \(0.129768\pi\)
−0.918043 + 0.396480i \(0.870232\pi\)
\(242\) −299.529 + 221.278i −1.23772 + 0.914373i
\(243\) −205.843 −0.847090
\(244\) −90.3262 + 124.323i −0.370189 + 0.509522i
\(245\) 59.5704 183.339i 0.243145 0.748322i
\(246\) 4.49593 + 13.8371i 0.0182762 + 0.0562482i
\(247\) −81.6312 + 59.3085i −0.330491 + 0.240116i
\(248\) −88.2148 121.417i −0.355705 0.489586i
\(249\) 195.119 63.3980i 0.783610 0.254610i
\(250\) 398.079 + 129.344i 1.59232 + 0.517375i
\(251\) 345.559 + 251.063i 1.37673 + 1.00025i 0.997177 + 0.0750826i \(0.0239221\pi\)
0.379553 + 0.925170i \(0.376078\pi\)
\(252\) 20.1003i 0.0797629i
\(253\) −78.6656 12.1392i −0.310931 0.0479811i
\(254\) −256.774 −1.01092
\(255\) 210.344 289.514i 0.824880 1.13535i
\(256\) −5.87132 + 18.0701i −0.0229349 + 0.0705862i
\(257\) 8.73917 + 26.8964i 0.0340046 + 0.104655i 0.966618 0.256221i \(-0.0824776\pi\)
−0.932614 + 0.360877i \(0.882478\pi\)
\(258\) 297.844 216.397i 1.15444 0.838747i
\(259\) −21.2461 29.2428i −0.0820313 0.112906i
\(260\) −177.082 + 57.5374i −0.681085 + 0.221298i
\(261\) 13.4640 + 4.37472i 0.0515862 + 0.0167614i
\(262\) 211.866 + 153.929i 0.808648 + 0.587517i
\(263\) 94.5506i 0.359508i −0.983712 0.179754i \(-0.942470\pi\)
0.983712 0.179754i \(-0.0575302\pi\)
\(264\) 126.996 128.009i 0.481045 0.484883i
\(265\) −314.164 −1.18552
\(266\) 19.2705 26.5236i 0.0724455 0.0997127i
\(267\) −69.6500 + 214.361i −0.260861 + 0.802848i
\(268\) 129.371 + 398.164i 0.482729 + 1.48569i
\(269\) −189.305 + 137.538i −0.703736 + 0.511294i −0.881147 0.472843i \(-0.843228\pi\)
0.177411 + 0.984137i \(0.443228\pi\)
\(270\) −128.541 176.922i −0.476078 0.655265i
\(271\) 136.400 44.3191i 0.503322 0.163539i −0.0463413 0.998926i \(-0.514756\pi\)
0.549663 + 0.835387i \(0.314756\pi\)
\(272\) −186.827 60.7038i −0.686865 0.223176i
\(273\) −22.3607 16.2460i −0.0819073 0.0595091i
\(274\) 180.791i 0.659822i
\(275\) −44.5942 + 88.3875i −0.162161 + 0.321409i
\(276\) 143.262 0.519067
\(277\) 228.695 314.772i 0.825614 1.13636i −0.163110 0.986608i \(-0.552152\pi\)
0.988724 0.149752i \(-0.0478476\pi\)
\(278\) −153.108 + 471.219i −0.550749 + 1.69503i
\(279\) 41.8673 + 128.854i 0.150062 + 0.461843i
\(280\) 13.1672 9.56652i 0.0470257 0.0341661i
\(281\) −59.3860 81.7379i −0.211338 0.290882i 0.690167 0.723650i \(-0.257537\pi\)
−0.901505 + 0.432768i \(0.857537\pi\)
\(282\) 241.074 78.3297i 0.854872 0.277765i
\(283\) −2.01626 0.655123i −0.00712460 0.00231492i 0.305453 0.952207i \(-0.401192\pi\)
−0.312577 + 0.949892i \(0.601192\pi\)
\(284\) −275.885 200.443i −0.971428 0.705783i
\(285\) 171.664i 0.602331i
\(286\) −46.1803 284.257i −0.161470 0.993905i
\(287\) −1.17340 −0.00408849
\(288\) 102.352 140.875i 0.355387 0.489149i
\(289\) −99.6418 + 306.666i −0.344781 + 1.06113i
\(290\) 13.1672 + 40.5244i 0.0454041 + 0.139739i
\(291\) −211.943 + 153.985i −0.728325 + 0.529159i
\(292\) −302.802 416.772i −1.03699 1.42730i
\(293\) −447.100 + 145.272i −1.52594 + 0.495808i −0.947456 0.319886i \(-0.896355\pi\)
−0.578483 + 0.815694i \(0.696355\pi\)
\(294\) −510.377 165.832i −1.73598 0.564053i
\(295\) −101.193 73.5214i −0.343029 0.249225i
\(296\) 182.360i 0.616081i
\(297\) 173.752 89.4023i 0.585023 0.301018i
\(298\) 791.187 2.65499
\(299\) 36.1803 49.7980i 0.121004 0.166548i
\(300\) 55.0623 169.464i 0.183541 0.564881i
\(301\) 9.17531 + 28.2387i 0.0304828 + 0.0938163i
\(302\) 717.569 521.345i 2.37606 1.72631i
\(303\) 136.910 + 188.440i 0.451848 + 0.621915i
\(304\) 89.6205 29.1195i 0.294804 0.0957878i
\(305\) 106.833 + 34.7121i 0.350272 + 0.113810i
\(306\) −251.827 182.963i −0.822965 0.597919i
\(307\) 99.4185i 0.323839i −0.986804 0.161919i \(-0.948232\pi\)
0.986804 0.161919i \(-0.0517685\pi\)
\(308\) 24.7326 + 48.0674i 0.0803006 + 0.156063i
\(309\) −117.984 −0.381824
\(310\) −239.692 + 329.908i −0.773200 + 1.06422i
\(311\) 104.823 322.611i 0.337051 1.03734i −0.628652 0.777686i \(-0.716393\pi\)
0.965703 0.259649i \(-0.0836068\pi\)
\(312\) 43.0902 + 132.618i 0.138110 + 0.425057i
\(313\) −312.595 + 227.114i −0.998707 + 0.725603i −0.961810 0.273716i \(-0.911747\pi\)
−0.0368962 + 0.999319i \(0.511747\pi\)
\(314\) 500.410 + 688.756i 1.59366 + 2.19349i
\(315\) −13.9737 + 4.54033i −0.0443609 + 0.0144137i
\(316\) −343.031 111.458i −1.08554 0.352714i
\(317\) 204.740 + 148.752i 0.645866 + 0.469249i 0.861860 0.507145i \(-0.169299\pi\)
−0.215994 + 0.976395i \(0.569299\pi\)
\(318\) 874.567i 2.75021i
\(319\) −37.5805 + 6.10532i −0.117807 + 0.0191389i
\(320\) 396.997 1.24062
\(321\) −11.4919 + 15.8172i −0.0358002 + 0.0492748i
\(322\) −6.18034 + 19.0211i −0.0191936 + 0.0590718i
\(323\) −90.6378 278.954i −0.280612 0.863636i
\(324\) −447.495 + 325.124i −1.38116 + 1.00347i
\(325\) −45.0000 61.9372i −0.138462 0.190576i
\(326\) −203.037 + 65.9707i −0.622813 + 0.202364i
\(327\) 471.418 + 153.173i 1.44165 + 0.468419i
\(328\) 4.78928 + 3.47962i 0.0146015 + 0.0106086i
\(329\) 20.4433i 0.0621376i
\(330\) −437.426 220.695i −1.32553 0.668773i
\(331\) 372.116 1.12422 0.562109 0.827063i \(-0.309990\pi\)
0.562109 + 0.827063i \(0.309990\pi\)
\(332\) 182.388 251.035i 0.549361 0.756131i
\(333\) 50.8723 156.569i 0.152770 0.470177i
\(334\) −274.846 845.889i −0.822892 2.53260i
\(335\) 247.580 179.878i 0.739046 0.536949i
\(336\) 15.1722 + 20.8828i 0.0451554 + 0.0621511i
\(337\) −78.1910 + 25.4058i −0.232021 + 0.0753881i −0.422720 0.906260i \(-0.638925\pi\)
0.190699 + 0.981649i \(0.438925\pi\)
\(338\) −282.868 91.9095i −0.836888 0.271921i
\(339\) 136.127 + 98.9021i 0.401555 + 0.291747i
\(340\) 541.248i 1.59191i
\(341\) −258.671 256.623i −0.758565 0.752561i
\(342\) 149.318 0.436603
\(343\) 51.3050 70.6152i 0.149577 0.205875i
\(344\) 46.2902 142.467i 0.134565 0.414147i
\(345\) −32.3607 99.5959i −0.0937991 0.288684i
\(346\) −456.169 + 331.426i −1.31841 + 0.957879i
\(347\) −134.861 185.620i −0.388647 0.534927i 0.569202 0.822198i \(-0.307252\pi\)
−0.957850 + 0.287270i \(0.907252\pi\)
\(348\) 65.1722 21.1757i 0.187276 0.0608498i
\(349\) 220.997 + 71.8062i 0.633229 + 0.205749i 0.608005 0.793933i \(-0.291970\pi\)
0.0252240 + 0.999682i \(0.491970\pi\)
\(350\) 20.1246 + 14.6214i 0.0574989 + 0.0417754i
\(351\) 151.109i 0.430510i
\(352\) −71.4205 + 462.825i −0.202899 + 1.31484i
\(353\) 34.6443 0.0981426 0.0490713 0.998795i \(-0.484374\pi\)
0.0490713 + 0.998795i \(0.484374\pi\)
\(354\) −204.668 + 281.702i −0.578159 + 0.795767i
\(355\) −77.0294 + 237.072i −0.216984 + 0.667809i
\(356\) 105.343 + 324.212i 0.295907 + 0.910708i
\(357\) 65.0000 47.2253i 0.182073 0.132284i
\(358\) 3.70976 + 5.10604i 0.0103624 + 0.0142627i
\(359\) −429.681 + 139.612i −1.19688 + 0.388891i −0.838613 0.544728i \(-0.816633\pi\)
−0.358269 + 0.933618i \(0.616633\pi\)
\(360\) 70.4984 + 22.9063i 0.195829 + 0.0636287i
\(361\) −178.226 129.489i −0.493702 0.358695i
\(362\) 224.368i 0.619802i
\(363\) 254.499 356.207i 0.701100 0.981286i
\(364\) −41.8034 −0.114845
\(365\) −221.341 + 304.650i −0.606415 + 0.834658i
\(366\) 96.6312 297.400i 0.264020 0.812569i
\(367\) 113.974 + 350.775i 0.310555 + 0.955790i 0.977546 + 0.210724i \(0.0675821\pi\)
−0.666991 + 0.745066i \(0.732418\pi\)
\(368\) −46.5066 + 33.7890i −0.126377 + 0.0918180i
\(369\) −3.14124 4.32355i −0.00851284 0.0117169i
\(370\) 471.246 153.117i 1.27364 0.413830i
\(371\) −67.0820 21.7963i −0.180814 0.0587501i
\(372\) 530.564 + 385.477i 1.42625 + 1.03623i
\(373\) 593.166i 1.59026i −0.606440 0.795129i \(-0.707403\pi\)
0.606440 0.795129i \(-0.292597\pi\)
\(374\) 827.344 + 127.671i 2.21215 + 0.341366i
\(375\) −492.053 −1.31214
\(376\) 60.6231 83.4405i 0.161232 0.221916i
\(377\) 9.09830 28.0017i 0.0241334 0.0742750i
\(378\) −15.1722 46.6953i −0.0401381 0.123532i
\(379\) 227.537 165.315i 0.600361 0.436188i −0.245646 0.969360i \(-0.579000\pi\)
0.846007 + 0.533172i \(0.179000\pi\)
\(380\) 152.610 + 210.050i 0.401605 + 0.552762i
\(381\) 287.082 93.2786i 0.753496 0.244826i
\(382\) 303.838 + 98.7229i 0.795387 + 0.258437i
\(383\) −515.795 374.747i −1.34672 0.978452i −0.999168 0.0407931i \(-0.987012\pi\)
−0.347556 0.937659i \(-0.612988\pi\)
\(384\) 489.034i 1.27353i
\(385\) 27.8297 28.0517i 0.0722850 0.0728617i
\(386\) −1058.77 −2.74292
\(387\) −79.4868 + 109.404i −0.205392 + 0.282698i
\(388\) −122.441 + 376.835i −0.315570 + 0.971225i
\(389\) 206.259 + 634.801i 0.530229 + 1.63188i 0.753737 + 0.657176i \(0.228249\pi\)
−0.223507 + 0.974702i \(0.571751\pi\)
\(390\) 306.525 222.703i 0.785961 0.571034i
\(391\) 105.172 + 144.757i 0.268983 + 0.370223i
\(392\) −207.667 + 67.4750i −0.529762 + 0.172130i
\(393\) −292.791 95.1336i −0.745016 0.242070i
\(394\) −246.679 179.223i −0.626088 0.454880i
\(395\) 263.652i 0.667473i
\(396\) −110.901 + 219.810i −0.280052 + 0.555075i
\(397\) −5.37384 −0.0135361 −0.00676805 0.999977i \(-0.502154\pi\)
−0.00676805 + 0.999977i \(0.502154\pi\)
\(398\) 277.628 382.122i 0.697558 0.960106i
\(399\) −11.9098 + 36.6547i −0.0298492 + 0.0918664i
\(400\) 22.0942 + 67.9991i 0.0552356 + 0.169998i
\(401\) 228.786 166.223i 0.570539 0.414521i −0.264762 0.964314i \(-0.585293\pi\)
0.835301 + 0.549793i \(0.185293\pi\)
\(402\) −500.742 689.212i −1.24563 1.71446i
\(403\) 267.984 87.0732i 0.664972 0.216063i
\(404\) 335.048 + 108.864i 0.829326 + 0.269464i
\(405\) 327.108 + 237.658i 0.807675 + 0.586810i
\(406\) 9.56652i 0.0235629i
\(407\) 70.9969 + 437.012i 0.174440 + 1.07374i
\(408\) −405.344 −0.993491
\(409\) −18.2554 + 25.1265i −0.0446343 + 0.0614339i −0.830751 0.556644i \(-0.812089\pi\)
0.786116 + 0.618078i \(0.212089\pi\)
\(410\) 4.97058 15.2979i 0.0121234 0.0373119i
\(411\) 65.6763 + 202.131i 0.159796 + 0.491802i
\(412\) −144.366 + 104.888i −0.350402 + 0.254582i
\(413\) −16.5066 22.7194i −0.0399675 0.0550105i
\(414\) −86.6312 + 28.1482i −0.209254 + 0.0679908i
\(415\) −215.718 70.0911i −0.519803 0.168894i
\(416\) −292.984 212.865i −0.704288 0.511695i
\(417\) 582.459i 1.39678i
\(418\) −357.076 + 183.730i −0.854250 + 0.439546i
\(419\) −245.156 −0.585098 −0.292549 0.956251i \(-0.594503\pi\)
−0.292549 + 0.956251i \(0.594503\pi\)
\(420\) −41.8034 + 57.5374i −0.0995319 + 0.136994i
\(421\) −23.9211 + 73.6215i −0.0568196 + 0.174873i −0.975439 0.220272i \(-0.929306\pi\)
0.918619 + 0.395145i \(0.129306\pi\)
\(422\) −317.192 976.216i −0.751640 2.31331i
\(423\) −75.3262 + 54.7277i −0.178076 + 0.129380i
\(424\) 209.164 + 287.890i 0.493312 + 0.678985i
\(425\) 211.655 68.7709i 0.498012 0.161814i
\(426\) 659.959 + 214.434i 1.54920 + 0.503366i
\(427\) 20.4033 + 14.8238i 0.0477828 + 0.0347162i
\(428\) 29.5703i 0.0690896i
\(429\) 154.894 + 301.033i 0.361057 + 0.701708i
\(430\) −407.023 −0.946566
\(431\) 264.193 363.631i 0.612978 0.843692i −0.383840 0.923399i \(-0.625399\pi\)
0.996818 + 0.0797077i \(0.0253987\pi\)
\(432\) 43.6089 134.215i 0.100947 0.310682i
\(433\) 44.6093 + 137.293i 0.103024 + 0.317075i 0.989262 0.146156i \(-0.0466901\pi\)
−0.886238 + 0.463231i \(0.846690\pi\)
\(434\) −74.0689 + 53.8142i −0.170666 + 0.123996i
\(435\) −29.4427 40.5244i −0.0676844 0.0931596i
\(436\) 713.002 231.668i 1.63533 0.531349i
\(437\) −81.6312 26.5236i −0.186799 0.0606947i
\(438\) 848.082 + 616.168i 1.93626 + 1.40678i
\(439\) 155.406i 0.354001i 0.984211 + 0.177000i \(0.0566394\pi\)
−0.984211 + 0.177000i \(0.943361\pi\)
\(440\) −196.774 + 31.9679i −0.447214 + 0.0726543i
\(441\) 197.120 0.446983
\(442\) −380.517 + 523.736i −0.860897 + 1.18492i
\(443\) 100.216 308.434i 0.226222 0.696240i −0.771943 0.635691i \(-0.780715\pi\)
0.998165 0.0605483i \(-0.0192849\pi\)
\(444\) −246.246 757.868i −0.554608 1.70691i
\(445\) 201.597 146.469i 0.453026 0.329143i
\(446\) 206.180 + 283.783i 0.462288 + 0.636285i
\(447\) −884.574 + 287.416i −1.97891 + 0.642988i
\(448\) 84.7690 + 27.5431i 0.189216 + 0.0614801i
\(449\) 316.651 + 230.060i 0.705236 + 0.512384i 0.881633 0.471935i \(-0.156444\pi\)
−0.176397 + 0.984319i \(0.556444\pi\)
\(450\) 113.294i 0.251765i
\(451\) 12.8319 + 6.47407i 0.0284520 + 0.0143549i
\(452\) 254.490 0.563032
\(453\) −612.877 + 843.553i −1.35293 + 1.86215i
\(454\) 37.1058 114.200i 0.0817309 0.251542i
\(455\) 9.44272 + 29.0617i 0.0207532 + 0.0638719i
\(456\) 157.307 114.291i 0.344973 0.250637i
\(457\) −30.7092 42.2675i −0.0671973 0.0924891i 0.774096 0.633069i \(-0.218205\pi\)
−0.841293 + 0.540580i \(0.818205\pi\)
\(458\) 392.830 127.638i 0.857707 0.278686i
\(459\) −417.758 135.738i −0.910149 0.295725i
\(460\) −128.138 93.0975i −0.278560 0.202386i
\(461\) 339.293i 0.735994i 0.929827 + 0.367997i \(0.119956\pi\)
−0.929827 + 0.367997i \(0.880044\pi\)
\(462\) −78.0902 77.4721i −0.169026 0.167689i
\(463\) 676.869 1.46192 0.730960 0.682420i \(-0.239072\pi\)
0.730960 + 0.682420i \(0.239072\pi\)
\(464\) −16.1622 + 22.2453i −0.0348322 + 0.0479425i
\(465\) 148.138 455.921i 0.318576 0.980476i
\(466\) 254.256 + 782.519i 0.545613 + 1.67923i
\(467\) −298.435 + 216.825i −0.639046 + 0.464294i −0.859522 0.511098i \(-0.829239\pi\)
0.220476 + 0.975392i \(0.429239\pi\)
\(468\) −111.910 154.031i −0.239124 0.329125i
\(469\) 65.3444 21.2317i 0.139327 0.0452701i
\(470\) −266.525 86.5991i −0.567074 0.184253i
\(471\) −809.681 588.267i −1.71907 1.24898i
\(472\) 141.679i 0.300168i
\(473\) 55.4656 359.433i 0.117263 0.759900i
\(474\) 733.951 1.54842
\(475\) −62.7492 + 86.3669i −0.132104 + 0.181825i
\(476\) 37.5511 115.570i 0.0788888 0.242795i
\(477\) −99.2705 305.523i −0.208114 0.640510i
\(478\) −274.241 + 199.248i −0.573726 + 0.416836i
\(479\) −279.454 384.635i −0.583411 0.802997i 0.410653 0.911792i \(-0.365301\pi\)
−0.994064 + 0.108795i \(0.965301\pi\)
\(480\) −585.967 + 190.392i −1.22077 + 0.396651i
\(481\) −325.623 105.801i −0.676971 0.219961i
\(482\) −475.828 345.709i −0.987195 0.717239i
\(483\) 23.5114i 0.0486779i
\(484\) −5.26142 662.108i −0.0108707 1.36799i
\(485\) 289.633 0.597182
\(486\) 372.373 512.528i 0.766200 1.05458i
\(487\) −55.3626 + 170.389i −0.113681 + 0.349874i −0.991670 0.128807i \(-0.958885\pi\)
0.877989 + 0.478681i \(0.158885\pi\)
\(488\) −39.3181 121.009i −0.0805699 0.247969i
\(489\) 203.037 147.515i 0.415208 0.301667i
\(490\) 348.731 + 479.988i 0.711697 + 0.979567i
\(491\) 611.297 198.622i 1.24500 0.404526i 0.388876 0.921290i \(-0.372863\pi\)
0.856128 + 0.516764i \(0.172863\pi\)
\(492\) −24.6024 7.99379i −0.0500048 0.0162475i
\(493\) 69.2411 + 50.3066i 0.140448 + 0.102042i
\(494\) 310.543i 0.628631i
\(495\) 177.862 + 27.4467i 0.359318 + 0.0554478i
\(496\) −263.151 −0.530546
\(497\) −32.8955 + 45.2768i −0.0661881 + 0.0911001i
\(498\) −195.119 + 600.515i −0.391805 + 1.20585i
\(499\) −162.446 499.958i −0.325543 1.00192i −0.971195 0.238287i \(-0.923414\pi\)
0.645651 0.763632i \(-0.276586\pi\)
\(500\) −602.079 + 437.436i −1.20416 + 0.874872i
\(501\) 614.574 + 845.889i 1.22670 + 1.68840i
\(502\) −1250.24 + 406.229i −2.49053 + 0.809222i
\(503\) 609.941 + 198.182i 1.21261 + 0.394000i 0.844384 0.535738i \(-0.179967\pi\)
0.368222 + 0.929738i \(0.379967\pi\)
\(504\) 13.4640 + 9.78217i 0.0267143 + 0.0194091i
\(505\) 257.515i 0.509932i
\(506\) 172.533 173.909i 0.340974 0.343694i
\(507\) 349.644 0.689634
\(508\) 268.351 369.353i 0.528249 0.727073i
\(509\) −140.705 + 433.046i −0.276434 + 0.850778i 0.712402 + 0.701772i \(0.247607\pi\)
−0.988836 + 0.149006i \(0.952393\pi\)
\(510\) 340.344 + 1047.47i 0.667342 + 2.05387i
\(511\) −68.3982 + 49.6942i −0.133852 + 0.0972490i
\(512\) 283.422 + 390.097i 0.553559 + 0.761908i
\(513\) 200.398 65.1131i 0.390639 0.126926i
\(514\) −82.7786 26.8964i −0.161048 0.0523276i
\(515\) 105.528 + 76.6705i 0.204908 + 0.148875i
\(516\) 654.583i 1.26857i
\(517\) 112.793 223.561i 0.218169 0.432419i
\(518\) 111.246 0.214761
\(519\) 389.615 536.259i 0.750703 1.03325i
\(520\) 47.6393 146.619i 0.0916141 0.281959i
\(521\) −56.0044 172.364i −0.107494 0.330833i 0.882814 0.469723i \(-0.155646\pi\)
−0.990308 + 0.138891i \(0.955646\pi\)
\(522\) −35.2492 + 25.6101i −0.0675272 + 0.0490614i
\(523\) −201.474 277.305i −0.385227 0.530219i 0.571733 0.820440i \(-0.306271\pi\)
−0.956960 + 0.290220i \(0.906271\pi\)
\(524\) −442.835 + 143.886i −0.845106 + 0.274591i
\(525\) −27.8115 9.03651i −0.0529743 0.0172124i
\(526\) 235.421 + 171.044i 0.447569 + 0.325178i
\(527\) 819.088i 1.55425i
\(528\) −50.7001 312.078i −0.0960229 0.591056i
\(529\) −476.639 −0.901020
\(530\) 568.328 782.237i 1.07232 1.47592i
\(531\) 39.5238 121.642i 0.0744328 0.229080i
\(532\) 18.0132 + 55.4388i 0.0338593 + 0.104208i
\(533\) −8.99187 + 6.53298i −0.0168703 + 0.0122570i
\(534\) −407.738 561.203i −0.763554 1.05094i
\(535\) 20.5573 6.67947i 0.0384248 0.0124850i
\(536\) −329.668 107.116i −0.615053 0.199843i
\(537\) −6.00251 4.36108i −0.0111779 0.00812119i
\(538\) 720.159i 1.33859i
\(539\) −471.388 + 242.548i −0.874560 + 0.449996i
\(540\) 388.827 0.720049
\(541\) 179.366 246.876i 0.331545 0.456332i −0.610403 0.792091i \(-0.708993\pi\)
0.941948 + 0.335759i \(0.108993\pi\)
\(542\) −136.400 + 419.796i −0.251661 + 0.774532i
\(543\) −81.5066 250.851i −0.150104 0.461973i
\(544\) 851.671 618.775i 1.56557 1.13745i
\(545\) −322.111 443.348i −0.591030 0.813483i
\(546\) 80.9017 26.2866i 0.148172 0.0481439i
\(547\) 143.880 + 46.7494i 0.263034 + 0.0854651i 0.437565 0.899187i \(-0.355841\pi\)
−0.174531 + 0.984652i \(0.555841\pi\)
\(548\) 260.057 + 188.942i 0.474556 + 0.344785i
\(549\) 114.863i 0.209222i
\(550\) −139.404 270.930i −0.253462 0.492599i
\(551\) −41.0557 −0.0745113
\(552\) −69.7214 + 95.9632i −0.126307 + 0.173846i
\(553\) −18.2918 + 56.2964i −0.0330774 + 0.101802i
\(554\) 370.036 + 1138.85i 0.667936 + 2.05569i
\(555\) −471.246 + 342.380i −0.849092 + 0.616902i
\(556\) −517.807 712.701i −0.931308 1.28184i
\(557\) −103.677 + 33.6867i −0.186134 + 0.0604787i −0.400601 0.916253i \(-0.631199\pi\)
0.214467 + 0.976731i \(0.431199\pi\)
\(558\) −396.572 128.854i −0.710703 0.230921i
\(559\) 227.533 + 165.312i 0.407036 + 0.295729i
\(560\) 28.5376i 0.0509600i
\(561\) −971.378 + 157.810i −1.73151 + 0.281301i
\(562\) 310.949 0.553291
\(563\) −585.827 + 806.321i −1.04054 + 1.43219i −0.143817 + 0.989604i \(0.545938\pi\)
−0.896728 + 0.442583i \(0.854062\pi\)
\(564\) −139.271 + 428.631i −0.246934 + 0.759983i
\(565\) −57.4853 176.922i −0.101744 0.313135i
\(566\) 5.27864 3.83516i 0.00932622 0.00677590i
\(567\) 53.3576 + 73.4404i 0.0941051 + 0.129525i
\(568\) 268.530 87.2506i 0.472764 0.153610i
\(569\) 94.4665 + 30.6940i 0.166022 + 0.0539438i 0.390849 0.920455i \(-0.372182\pi\)
−0.224827 + 0.974399i \(0.572182\pi\)
\(570\) −427.426 310.543i −0.749871 0.544813i
\(571\) 930.127i 1.62894i 0.580202 + 0.814472i \(0.302973\pi\)
−0.580202 + 0.814472i \(0.697027\pi\)
\(572\) 457.148 + 230.645i 0.799209 + 0.403226i
\(573\) −375.564 −0.655435
\(574\) 2.12269 2.92164i 0.00369807 0.00508996i
\(575\) 20.1246 61.9372i 0.0349993 0.107717i
\(576\) 125.444 + 386.078i 0.217785 + 0.670274i
\(577\) 281.012 204.167i 0.487022 0.353842i −0.317016 0.948420i \(-0.602681\pi\)
0.804038 + 0.594578i \(0.202681\pi\)
\(578\) −583.313 802.862i −1.00919 1.38903i
\(579\) 1183.74 384.620i 2.04445 0.664283i
\(580\) −72.0526 23.4113i −0.124229 0.0403643i
\(581\) −41.1985 29.9325i −0.0709097 0.0515189i
\(582\) 806.278i 1.38536i
\(583\) 613.328 + 608.474i 1.05202 + 1.04369i
\(584\) 426.536 0.730370
\(585\) −81.8034 + 112.593i −0.139835 + 0.192466i
\(586\) 447.100 1376.03i 0.762970 2.34818i
\(587\) −196.347 604.294i −0.334492 1.02946i −0.966972 0.254884i \(-0.917963\pi\)
0.632479 0.774577i \(-0.282037\pi\)
\(588\) 771.926 560.837i 1.31280 0.953804i
\(589\) −230.949 317.874i −0.392104 0.539685i
\(590\) 366.122 118.960i 0.620545 0.201627i
\(591\) 340.902 + 110.766i 0.576822 + 0.187421i
\(592\) 258.684 + 187.945i 0.436966 + 0.317474i
\(593\) 341.152i 0.575299i −0.957736 0.287650i \(-0.907126\pi\)
0.957736 0.287650i \(-0.0928739\pi\)
\(594\) −91.7173 + 594.354i −0.154406 + 1.00060i
\(595\) −88.8266 −0.149288
\(596\) −826.858 + 1138.07i −1.38735 + 1.90952i
\(597\) −171.584 + 528.080i −0.287410 + 0.884556i
\(598\) 58.5410 + 180.171i 0.0978947 + 0.301289i
\(599\) 362.164 263.128i 0.604614 0.439278i −0.242899 0.970052i \(-0.578098\pi\)
0.847514 + 0.530773i \(0.178098\pi\)
\(600\) 86.7173 + 119.356i 0.144529 + 0.198927i
\(601\) −762.584 + 247.779i −1.26886 + 0.412277i −0.864643 0.502387i \(-0.832455\pi\)
−0.404215 + 0.914664i \(0.632455\pi\)
\(602\) −86.9098 28.2387i −0.144368 0.0469082i
\(603\) 253.162 + 183.933i 0.419837 + 0.305029i
\(604\) 1577.03i 2.61097i
\(605\) −459.108 + 153.217i −0.758857 + 0.253252i
\(606\) −716.869 −1.18295
\(607\) 599.237 824.779i 0.987211 1.35878i 0.0543575 0.998522i \(-0.482689\pi\)
0.932853 0.360257i \(-0.117311\pi\)
\(608\) −156.050 + 480.273i −0.256661 + 0.789922i
\(609\) −3.47524 10.6957i −0.00570647 0.0175627i
\(610\) −279.692 + 203.208i −0.458511 + 0.333128i
\(611\) 113.820 + 156.659i 0.186284 + 0.256398i
\(612\) 526.362 171.025i 0.860068 0.279453i
\(613\) −711.597 231.212i −1.16084 0.377181i −0.335626 0.941995i \(-0.608948\pi\)
−0.825218 + 0.564814i \(0.808948\pi\)
\(614\) 247.542 + 179.850i 0.403163 + 0.292915i
\(615\) 18.9092i 0.0307467i
\(616\) −44.2341 6.82596i −0.0718087 0.0110811i
\(617\) 517.100 0.838088 0.419044 0.907966i \(-0.362365\pi\)
0.419044 + 0.907966i \(0.362365\pi\)
\(618\) 213.435 293.768i 0.345363 0.475352i
\(619\) −214.219 + 659.299i −0.346073 + 1.06510i 0.614934 + 0.788579i \(0.289183\pi\)
−0.961007 + 0.276525i \(0.910817\pi\)
\(620\) −224.053 689.563i −0.361375 1.11220i
\(621\) −103.992 + 75.5545i −0.167459 + 0.121666i
\(622\) 613.643 + 844.607i 0.986565 + 1.35789i
\(623\) 53.2078 17.2883i 0.0854058 0.0277500i
\(624\) 232.533 + 75.5545i 0.372649 + 0.121081i
\(625\) 258.076 + 187.503i 0.412922 + 0.300006i
\(626\) 1189.18i 1.89965i
\(627\) 332.480 335.132i 0.530271 0.534501i
\(628\) −1513.70 −2.41035
\(629\) 585.000 805.183i 0.930048 1.28010i
\(630\) 13.9737 43.0066i 0.0221805 0.0682644i
\(631\) −277.128 852.911i −0.439188 1.35168i −0.888733 0.458425i \(-0.848414\pi\)
0.449545 0.893258i \(-0.351586\pi\)
\(632\) 241.602 175.534i 0.382281 0.277744i
\(633\) 709.263 + 976.216i 1.12048 + 1.54221i
\(634\) −740.755 + 240.686i −1.16838 + 0.379631i
\(635\) −317.390 103.126i −0.499827 0.162404i
\(636\) −1258.01 913.997i −1.97800 1.43710i
\(637\) 409.958i 0.643577i
\(638\) 52.7821 104.616i 0.0827306 0.163975i
\(639\) −254.892 −0.398891
\(640\) −317.793 + 437.405i −0.496552 + 0.683445i
\(641\) 175.756 540.922i 0.274191 0.843872i −0.715242 0.698877i \(-0.753683\pi\)
0.989432 0.144995i \(-0.0463165\pi\)
\(642\) −18.5942 57.2272i −0.0289630 0.0891389i
\(643\) −534.364 + 388.238i −0.831048 + 0.603791i −0.919855 0.392257i \(-0.871694\pi\)
0.0888080 + 0.996049i \(0.471694\pi\)
\(644\) −20.9017 28.7687i −0.0324561 0.0446719i
\(645\) 455.066 147.860i 0.705528 0.229240i
\(646\) 858.533 + 278.954i 1.32900 + 0.431818i
\(647\) −28.5999 20.7790i −0.0442038 0.0321159i 0.565464 0.824773i \(-0.308697\pi\)
−0.609668 + 0.792657i \(0.708697\pi\)
\(648\) 457.979i 0.706758i
\(649\) 55.1591 + 339.524i 0.0849908 + 0.523150i
\(650\) 235.623 0.362497
\(651\) 63.2624 87.0732i 0.0971772 0.133753i
\(652\) 117.296 361.001i 0.179902 0.553682i
\(653\) 129.615 + 398.914i 0.198491 + 0.610894i 0.999918 + 0.0128008i \(0.00407473\pi\)
−0.801427 + 0.598093i \(0.795925\pi\)
\(654\) −1234.19 + 896.691i −1.88714 + 1.37109i
\(655\) 200.059 + 275.357i 0.305433 + 0.420393i
\(656\) 9.87192 3.20758i 0.0150487 0.00488960i
\(657\) −366.211 118.989i −0.557399 0.181110i
\(658\) −50.9017 36.9822i −0.0773582 0.0562040i
\(659\) 1281.39i 1.94445i −0.234058 0.972223i \(-0.575200\pi\)
0.234058 0.972223i \(-0.424800\pi\)
\(660\) 774.604 398.565i 1.17364 0.603886i
\(661\) 70.6950 0.106952 0.0534758 0.998569i \(-0.482970\pi\)
0.0534758 + 0.998569i \(0.482970\pi\)
\(662\) −673.165 + 926.532i −1.01687 + 1.39960i
\(663\) 235.172 723.786i 0.354709 1.09168i
\(664\) 79.3916 + 244.342i 0.119566 + 0.367986i
\(665\) 34.4721 25.0455i 0.0518378 0.0376624i
\(666\) 297.812 + 409.902i 0.447164 + 0.615469i
\(667\) 23.8197 7.73948i 0.0357116 0.0116034i
\(668\) 1503.99 + 488.677i 2.25149 + 0.731553i
\(669\) −333.607 242.380i −0.498665 0.362301i
\(670\) 941.852i 1.40575i
\(671\) −141.334 274.681i −0.210632 0.409360i
\(672\) −138.328 −0.205845
\(673\) −470.230 + 647.216i −0.698708 + 0.961689i 0.301259 + 0.953542i \(0.402593\pi\)
−0.999967 + 0.00814624i \(0.997407\pi\)
\(674\) 78.1910 240.647i 0.116010 0.357043i
\(675\) 49.4042 + 152.051i 0.0731914 + 0.225260i
\(676\) 427.827 310.835i 0.632880 0.459815i
\(677\) 550.202 + 757.288i 0.812706 + 1.11859i 0.990900 + 0.134598i \(0.0429743\pi\)
−0.178195 + 0.983995i \(0.557026\pi\)
\(678\) −492.513 + 160.027i −0.726420 + 0.236028i
\(679\) 61.8441 + 20.0944i 0.0910811 + 0.0295940i
\(680\) 362.551 + 263.409i 0.533163 + 0.387366i
\(681\) 141.159i 0.207282i
\(682\) 1106.91 179.828i 1.62303 0.263677i
\(683\) −241.319 −0.353322 −0.176661 0.984272i \(-0.556530\pi\)
−0.176661 + 0.984272i \(0.556530\pi\)
\(684\) −156.050 + 214.785i −0.228143 + 0.314013i
\(685\) 72.6099 223.470i 0.106000 0.326234i
\(686\) 83.0132 + 255.488i 0.121010 + 0.372432i
\(687\) −392.830 + 285.407i −0.571805 + 0.415440i
\(688\) −154.386 212.494i −0.224398 0.308858i
\(689\) −635.410 + 206.457i −0.922221 + 0.299648i
\(690\) 306.525 + 99.5959i 0.444239 + 0.144342i
\(691\) 736.915 + 535.400i 1.06645 + 0.774819i 0.975270 0.221015i \(-0.0709371\pi\)
0.0911771 + 0.995835i \(0.470937\pi\)
\(692\) 1002.54i 1.44876i
\(693\) 36.0739 + 18.2004i 0.0520547 + 0.0262632i
\(694\) 706.140 1.01749
\(695\) −378.505 + 520.967i −0.544611 + 0.749593i
\(696\) −17.5329 + 53.9607i −0.0251909 + 0.0775297i
\(697\) −9.98397 30.7275i −0.0143242 0.0440853i
\(698\) −578.577 + 420.361i −0.828907 + 0.602236i
\(699\) −568.533 782.519i −0.813352 1.11948i
\(700\) −42.0639 + 13.6674i −0.0600912 + 0.0195248i
\(701\) −410.902 133.510i −0.586165 0.190457i 0.000895496 1.00000i \(-0.499715\pi\)
−0.587061 + 0.809543i \(0.699715\pi\)
\(702\) −376.246 273.359i −0.535963 0.389400i
\(703\) 477.424i 0.679124i
\(704\) −775.039 768.905i −1.10091 1.09219i
\(705\) 329.443 0.467295
\(706\) −62.6722 + 86.2609i −0.0887708 + 0.122183i
\(707\) 17.8661 54.9861i 0.0252703 0.0777739i
\(708\) −191.314 588.804i −0.270218 0.831644i
\(709\) 708.956 515.087i 0.999938 0.726498i 0.0378633 0.999283i \(-0.487945\pi\)
0.962075 + 0.272785i \(0.0879448\pi\)
\(710\) −450.938 620.663i −0.635124 0.874173i
\(711\) −256.400 + 83.3095i −0.360619 + 0.117172i
\(712\) −268.438 87.2208i −0.377020 0.122501i
\(713\) 193.915 + 140.887i 0.271970 + 0.197598i
\(714\) 247.275i 0.346323i
\(715\) 57.0820 369.908i 0.0798350 0.517354i
\(716\) −11.2217 −0.0156728
\(717\) 234.230 322.390i 0.326680 0.449637i
\(718\) 429.681 1322.42i 0.598441 1.84181i
\(719\) 155.218 + 477.712i 0.215880 + 0.664411i 0.999090 + 0.0426534i \(0.0135811\pi\)
−0.783210 + 0.621758i \(0.786419\pi\)
\(720\) 105.151 76.3966i 0.146043 0.106106i
\(721\) 17.2136 + 23.6925i 0.0238746 + 0.0328606i
\(722\) 644.829 209.518i 0.893115 0.290191i
\(723\) 657.578 + 213.660i 0.909514 + 0.295519i
\(724\) −322.740 234.484i −0.445773 0.323873i
\(725\) 31.1508i 0.0429666i
\(726\) 426.525 + 1278.06i 0.587500 + 1.76042i
\(727\) −393.878 −0.541786 −0.270893 0.962609i \(-0.587319\pi\)
−0.270893 + 0.962609i \(0.587319\pi\)
\(728\) 20.3444 28.0017i 0.0279456 0.0384639i
\(729\) 50.9853 156.917i 0.0699387 0.215249i
\(730\) −358.138 1102.23i −0.490600 1.50991i
\(731\) −661.413 + 480.544i −0.904805 + 0.657380i
\(732\) 326.803 + 449.806i 0.446453 + 0.614489i
\(733\) −590.381 + 191.826i −0.805431 + 0.261700i −0.682661 0.730735i \(-0.739178\pi\)
−0.122769 + 0.992435i \(0.539178\pi\)
\(734\) −1079.57 350.775i −1.47081 0.477895i
\(735\) −564.259 409.958i −0.767700 0.557766i
\(736\) 308.061i 0.418562i
\(737\) −831.728 128.347i −1.12853 0.174148i
\(738\) 16.4477 0.0222869
\(739\) −499.618 + 687.666i −0.676074 + 0.930535i −0.999878 0.0155884i \(-0.995038\pi\)
0.323805 + 0.946124i \(0.395038\pi\)
\(740\) −272.243 + 837.878i −0.367896 + 1.13227i
\(741\) 112.812 + 347.198i 0.152242 + 0.468554i
\(742\) 175.623 127.598i 0.236689 0.171964i
\(743\) 238.416 + 328.152i 0.320883 + 0.441658i 0.938737 0.344635i \(-0.111997\pi\)
−0.617853 + 0.786293i \(0.711997\pi\)
\(744\) −516.418 + 167.794i −0.694111 + 0.225530i
\(745\) 977.961 + 317.759i 1.31270 + 0.426522i
\(746\) 1476.92 + 1073.05i 1.97979 + 1.43840i
\(747\) 231.933i 0.310486i
\(748\) −1048.29 + 1056.65i −1.40146 + 1.41264i
\(749\) 4.85292 0.00647919
\(750\) 890.132 1225.16i 1.18684 1.63355i
\(751\) −262.486 + 807.849i −0.349515 + 1.07570i 0.609606 + 0.792704i \(0.291327\pi\)
−0.959122 + 0.282993i \(0.908673\pi\)
\(752\) −55.8835 171.992i −0.0743132 0.228712i
\(753\) 1250.24 908.356i 1.66035 1.20632i
\(754\) 53.2624 + 73.3094i 0.0706398 + 0.0972273i
\(755\) 1096.35 356.225i 1.45212 0.471821i
\(756\) 83.0244 + 26.9763i 0.109821 + 0.0356829i
\(757\) −485.832 352.977i −0.641786 0.466284i 0.218678 0.975797i \(-0.429826\pi\)
−0.860463 + 0.509513i \(0.829826\pi\)
\(758\) 865.602i 1.14196i
\(759\) −129.721 + 257.113i −0.170911 + 0.338752i
\(760\) −214.971 −0.282856
\(761\) 205.275 282.537i 0.269744 0.371271i −0.652559 0.757738i \(-0.726305\pi\)
0.922303 + 0.386467i \(0.126305\pi\)
\(762\) −287.082 + 883.548i −0.376748 + 1.15951i
\(763\) −38.0201 117.014i −0.0498298 0.153360i
\(764\) −459.543 + 333.877i −0.601496 + 0.437012i
\(765\) −237.793 327.294i −0.310841 0.427836i
\(766\) 1866.16 606.354i 2.43625 0.791584i
\(767\) −252.984 82.1994i −0.329835 0.107170i
\(768\) 55.6140 + 40.4059i 0.0724140 + 0.0526119i
\(769\) 768.616i 0.999500i 0.866170 + 0.499750i \(0.166575\pi\)
−0.866170 + 0.499750i \(0.833425\pi\)
\(770\) 19.5016 + 120.039i 0.0253267 + 0.155895i
\(771\) 102.320 0.132711
\(772\) 1106.50 1522.97i 1.43329 1.97276i
\(773\) 2.15905 6.64488i 0.00279308 0.00859623i −0.949650 0.313312i \(-0.898561\pi\)
0.952443 + 0.304716i \(0.0985615\pi\)
\(774\) −128.612 395.828i −0.166166 0.511406i
\(775\) 241.185 175.231i 0.311207 0.226105i
\(776\) −192.832 265.410i −0.248495 0.342024i
\(777\) −124.377 + 40.4125i −0.160073 + 0.0520110i
\(778\) −1953.72 634.801i −2.51120 0.815939i
\(779\) 12.5385 + 9.10976i 0.0160956 + 0.0116942i
\(780\) 673.660i 0.863667i
\(781\) 609.543 313.634i 0.780465 0.401581i
\(782\) −550.689 −0.704206
\(783\) −36.1397 + 49.7420i −0.0461554 + 0.0635275i
\(784\) −118.311 + 364.124i −0.150907 + 0.464443i
\(785\) 341.921 + 1052.32i 0.435568 + 1.34054i
\(786\) 766.537 556.922i 0.975238 0.708552i
\(787\) −648.159 892.115i −0.823582 1.13356i −0.989084 0.147354i \(-0.952924\pi\)
0.165501 0.986210i \(-0.447076\pi\)
\(788\) 515.601 167.529i 0.654315 0.212600i
\(789\) −325.344 105.711i −0.412350 0.133981i
\(790\) −656.466 476.950i −0.830970 0.603735i
\(791\) 41.7655i 0.0528009i
\(792\) −93.2659 181.261i −0.117760 0.228864i
\(793\) 238.885 0.301243
\(794\) 9.72136 13.3803i 0.0122435 0.0168518i
\(795\) −351.246 + 1081.02i −0.441819 + 1.35978i
\(796\) 259.514 + 798.700i 0.326022 + 1.00339i
\(797\) 583.596 424.007i 0.732240 0.532004i −0.158031 0.987434i \(-0.550515\pi\)
0.890271 + 0.455430i \(0.150515\pi\)
\(798\) −69.7214 95.9632i −0.0873701 0.120255i
\(799\) −535.344 + 173.944i −0.670018 + 0.217702i
\(800\) −364.404 118.402i −0.455505 0.148003i
\(801\) 206.141 + 149.770i 0.257355 + 0.186979i
\(802\) 870.354i 1.08523i
\(803\) 1022.16 166.060i 1.27293 0.206800i
\(804\) 1514.71 1.88396
\(805\) −15.2786 + 21.0292i −0.0189797 + 0.0261233i
\(806\) −267.984 + 824.769i −0.332486 + 1.02329i
\(807\) 261.613 + 805.162i 0.324180 + 0.997722i
\(808\) −235.979 + 171.449i −0.292053 + 0.212189i
\(809\) −471.682 649.215i −0.583044 0.802491i 0.410981 0.911644i \(-0.365186\pi\)
−0.994025 + 0.109153i \(0.965186\pi\)
\(810\) −1183.49 + 384.539i −1.46110 + 0.474739i
\(811\) −471.598 153.232i −0.581502 0.188942i 0.00347122 0.999994i \(-0.498895\pi\)
−0.584973 + 0.811052i \(0.698895\pi\)
\(812\) −13.7608 9.99783i −0.0169468 0.0123126i
\(813\) 518.897i 0.638250i
\(814\) −1216.55 613.787i −1.49453 0.754038i
\(815\) −277.463 −0.340445
\(816\) −417.758 + 574.995i −0.511959 + 0.704651i
\(817\) 121.189 372.983i 0.148335 0.456527i
\(818\) −29.5379 90.9084i −0.0361099 0.111135i
\(819\) −25.2786 + 18.3660i −0.0308653 + 0.0224249i
\(820\) 16.8103 + 23.1375i 0.0205004 + 0.0282164i
\(821\) −276.921 + 89.9771i −0.337297 + 0.109595i −0.472768 0.881187i \(-0.656745\pi\)
0.135471 + 0.990781i \(0.456745\pi\)
\(822\) −622.095 202.131i −0.756806 0.245901i
\(823\) −869.681 631.860i −1.05672 0.767752i −0.0832414 0.996529i \(-0.526527\pi\)
−0.973479 + 0.228777i \(0.926527\pi\)
\(824\) 147.748i 0.179306i
\(825\) 254.280 + 252.267i 0.308218 + 0.305778i
\(826\) 86.4296 0.104636
\(827\) −268.497 + 369.554i −0.324664 + 0.446861i −0.939884 0.341494i \(-0.889067\pi\)
0.615220 + 0.788355i \(0.289067\pi\)
\(828\) 50.0476 154.031i 0.0604440 0.186027i
\(829\) 0.679973 + 2.09274i 0.000820233 + 0.00252442i 0.951466 0.307755i \(-0.0995776\pi\)
−0.950646 + 0.310279i \(0.899578\pi\)
\(830\) 564.758 410.321i 0.680431 0.494362i
\(831\) −827.426 1138.85i −0.995700 1.37046i
\(832\) 802.943 260.892i 0.965076 0.313572i
\(833\) 1133.38 + 368.257i 1.36060 + 0.442085i
\(834\) 1450.26 + 1053.68i 1.73892 + 1.26340i
\(835\) 1155.96i 1.38438i
\(836\) 108.891 705.645i 0.130252 0.844073i
\(837\) −588.423 −0.703015
\(838\) 443.491 610.413i 0.529226 0.728417i
\(839\) 448.822 1381.33i 0.534948 1.64640i −0.208813 0.977956i \(-0.566960\pi\)
0.743761 0.668446i \(-0.233040\pi\)
\(840\) −18.1966 56.0034i −0.0216626 0.0666707i
\(841\) −670.691 + 487.286i −0.797493 + 0.579412i
\(842\) −140.036 192.744i −0.166314 0.228912i
\(843\) −347.652 + 112.959i −0.412398 + 0.133996i
\(844\) 1735.72 + 563.969i 2.05654 + 0.668209i
\(845\) −312.731 227.213i −0.370096 0.268891i
\(846\) 286.558i 0.338721i
\(847\) −108.661 + 0.863474i −0.128290 + 0.00101945i
\(848\) 623.951 0.735792
\(849\) −4.50850 + 6.20541i −0.00531036 + 0.00730909i
\(850\) −211.655 + 651.407i −0.249006 + 0.766361i
\(851\) −90.0000 276.992i −0.105758 0.325489i
\(852\) −998.163 + 725.208i −1.17155 + 0.851183i
\(853\) 622.757 + 857.151i 0.730079 + 1.00487i 0.999128 + 0.0417407i \(0.0132903\pi\)
−0.269050 + 0.963126i \(0.586710\pi\)
\(854\) −73.8197 + 23.9855i −0.0864399 + 0.0280860i
\(855\) 184.567 + 59.9696i 0.215868 + 0.0701398i
\(856\) −19.8075 14.3910i −0.0231396 0.0168119i
\(857\) 951.067i 1.10976i 0.831929 + 0.554882i \(0.187237\pi\)
−0.831929 + 0.554882i \(0.812763\pi\)
\(858\) −1029.75 158.904i −1.20017 0.185203i
\(859\) 1146.23 1.33438 0.667188 0.744890i \(-0.267498\pi\)
0.667188 + 0.744890i \(0.267498\pi\)
\(860\) 425.374 585.477i 0.494621 0.680787i
\(861\) −1.31190 + 4.03760i −0.00152369 + 0.00468943i
\(862\) 427.474 + 1315.63i 0.495910 + 1.52625i
\(863\) −764.758 + 555.629i −0.886162 + 0.643834i −0.934874 0.354979i \(-0.884488\pi\)
0.0487126 + 0.998813i \(0.484488\pi\)
\(864\) 444.521 + 611.831i 0.514492 + 0.708137i
\(865\) −696.964 + 226.457i −0.805739 + 0.261801i
\(866\) −422.545 137.293i −0.487928 0.158537i
\(867\) 943.821 + 685.726i 1.08861 + 0.790918i
\(868\) 162.784i 0.187539i
\(869\) 510.641 514.715i 0.587619 0.592307i
\(870\) 154.164 0.177200
\(871\) 382.533 526.511i 0.439188 0.604491i
\(872\) −191.815 + 590.345i −0.219971 + 0.677001i
\(873\) 91.5191 + 281.667i 0.104833 + 0.322643i
\(874\) 213.713 155.272i 0.244523 0.177656i
\(875\) 71.7895 + 98.8098i 0.0820452 + 0.112925i
\(876\) −1772.64 + 575.964i −2.02356 + 0.657494i
\(877\) 150.931 + 49.0405i 0.172099 + 0.0559185i 0.393799 0.919196i \(-0.371161\pi\)
−0.221700 + 0.975115i \(0.571161\pi\)
\(878\) −386.946 281.133i −0.440713 0.320197i
\(879\) 1700.87i 1.93501i
\(880\) −157.453 + 312.078i −0.178924 + 0.354634i
\(881\) 402.370 0.456719 0.228360 0.973577i \(-0.426664\pi\)
0.228360 + 0.973577i \(0.426664\pi\)
\(882\) −356.593 + 490.808i −0.404300 + 0.556471i
\(883\) 244.512 752.530i 0.276910 0.852243i −0.711797 0.702385i \(-0.752118\pi\)
0.988708 0.149858i \(-0.0478816\pi\)
\(884\) −355.689 1094.70i −0.402363 1.23835i
\(885\) −366.122 + 266.003i −0.413697 + 0.300568i
\(886\) 586.677 + 807.491i 0.662163 + 0.911390i
\(887\) 805.659 261.775i 0.908297 0.295124i 0.182640 0.983180i \(-0.441536\pi\)
0.725657 + 0.688056i \(0.241536\pi\)
\(888\) 627.492 + 203.885i 0.706635 + 0.229600i
\(889\) −60.6161 44.0402i −0.0681846 0.0495390i
\(890\) 766.920i 0.861707i
\(891\) −178.302 1097.51i −0.200114 1.23178i
\(892\) −623.680 −0.699192
\(893\) 158.713 218.450i 0.177730 0.244625i
\(894\) 884.574 2722.44i 0.989457 3.04523i
\(895\) 2.53481 + 7.80134i 0.00283219 + 0.00871658i
\(896\) −98.2035 + 71.3491i −0.109602 + 0.0796306i
\(897\) −130.902 180.171i −0.145933 0.200859i
\(898\) −1145.65 + 372.245i −1.27578 + 0.414527i
\(899\) 109.039 + 35.4291i 0.121290 + 0.0394094i
\(900\) −162.967 118.402i −0.181074 0.131558i
\(901\) 1942.12i 2.15552i
\(902\) −39.3328 + 20.2383i −0.0436062 + 0.0224372i
\(903\) 107.426 0.118966
\(904\) −123.853 + 170.468i −0.137005 + 0.188571i
\(905\) −90.1115 + 277.335i −0.0995707 + 0.306447i
\(906\) −991.656 3052.00i −1.09454 3.36866i
\(907\) −345.216 + 250.814i −0.380613 + 0.276532i −0.761598 0.648049i \(-0.775585\pi\)
0.380985 + 0.924581i \(0.375585\pi\)
\(908\) 125.491 + 172.723i 0.138206 + 0.190224i
\(909\) 250.433 81.3705i 0.275503 0.0895165i
\(910\) −89.4427 29.0617i −0.0982887 0.0319359i
\(911\) −113.353 82.3554i −0.124427 0.0904011i 0.523831 0.851822i \(-0.324502\pi\)
−0.648258 + 0.761421i \(0.724502\pi\)
\(912\) 340.937i 0.373834i
\(913\) 285.384 + 554.639i 0.312579 + 0.607491i
\(914\) 160.795 0.175925
\(915\) 238.885 328.798i 0.261077 0.359342i
\(916\) −226.941 + 698.453i −0.247752 + 0.762503i
\(917\) 23.6137 + 72.6756i 0.0257511 + 0.0792537i
\(918\) 1093.71 794.624i 1.19140 0.865603i
\(919\) 611.124 + 841.140i 0.664988 + 0.915278i 0.999634 0.0270664i \(-0.00861655\pi\)
−0.334645 + 0.942344i \(0.608617\pi\)
\(920\) 124.721 40.5244i 0.135567 0.0440483i
\(921\) −342.095 111.153i −0.371438 0.120688i
\(922\) −844.805 613.787i −0.916275 0.665713i
\(923\) 530.109i 0.574333i
\(924\) 193.050 31.3628i 0.208928 0.0339424i
\(925\) −362.243 −0.391614
\(926\) −1224.47 + 1685.34i −1.32232 + 1.82002i
\(927\) −41.2167 + 126.852i −0.0444625 + 0.136841i
\(928\) −45.5348 140.142i −0.0490677 0.151015i
\(929\) −1329.96 + 966.270i −1.43160 + 1.04012i −0.441884 + 0.897072i \(0.645690\pi\)
−0.989716 + 0.143046i \(0.954310\pi\)
\(930\) 867.214 + 1193.62i 0.932488 + 1.28346i
\(931\) −543.678 + 176.652i −0.583972 + 0.189744i
\(932\) −1391.32 452.068i −1.49284 0.485052i
\(933\) −992.895 721.381i −1.06420 0.773184i
\(934\) 1135.31i 1.21554i
\(935\) 971.378 + 490.090i 1.03891 + 0.524160i
\(936\) 157.639 0.168418
\(937\) −426.456 + 586.966i −0.455129 + 0.626431i −0.973490 0.228731i \(-0.926542\pi\)
0.518361 + 0.855162i \(0.326542\pi\)
\(938\) −65.3444 + 201.109i −0.0696636 + 0.214402i
\(939\) 431.996 + 1329.55i 0.460060 + 1.41592i
\(940\) 403.108 292.875i 0.428839 0.311570i
\(941\) −107.800 148.374i −0.114559 0.157677i 0.747887 0.663826i \(-0.231069\pi\)
−0.862446 + 0.506149i \(0.831069\pi\)
\(942\) 2929.45 951.837i 3.10982 1.01044i
\(943\) −8.99187 2.92164i −0.00953539 0.00309823i
\(944\) 200.977 + 146.018i 0.212900 + 0.154681i
\(945\) 63.8120i 0.0675259i
\(946\) 794.613 + 788.324i 0.839971 + 0.833323i
\(947\) −926.439 −0.978288 −0.489144 0.872203i \(-0.662691\pi\)
−0.489144 + 0.872203i \(0.662691\pi\)
\(948\) −767.041 + 1055.74i −0.809115 + 1.11365i
\(949\) −247.467 + 761.625i −0.260766 + 0.802556i
\(950\) −101.530 312.478i −0.106874 0.328925i
\(951\) 740.755 538.190i 0.778922 0.565920i
\(952\) 59.1390 + 81.3978i 0.0621207 + 0.0855019i
\(953\) 237.606 77.2030i 0.249325 0.0810105i −0.181688 0.983356i \(-0.558156\pi\)
0.431013 + 0.902346i \(0.358156\pi\)
\(954\) 940.304 + 305.523i 0.985643 + 0.320255i
\(955\) 335.915 + 244.056i 0.351743 + 0.255556i
\(956\) 602.709i 0.630449i
\(957\) −21.0081 + 136.139i −0.0219521 + 0.142256i
\(958\) 1463.24 1.52739
\(959\) 31.0081 42.6790i 0.0323338 0.0445037i
\(960\) 443.856 1366.05i 0.462350 1.42297i
\(961\) 42.1004 + 129.572i 0.0438090 + 0.134830i
\(962\) 852.492 619.372i 0.886167 0.643838i
\(963\) 12.9915 + 17.8813i 0.0134907 + 0.0185683i
\(964\) 994.562 323.153i 1.03170 0.335221i
\(965\) −1308.71 425.225i −1.35618 0.440648i
\(966\) 58.5410 + 42.5325i 0.0606015 + 0.0440295i
\(967\) 554.026i 0.572933i −0.958090 0.286466i \(-0.907519\pi\)
0.958090 0.286466i \(-0.0924806\pi\)
\(968\) 446.068 + 318.703i 0.460814 + 0.329239i
\(969\) −1061.21 −1.09516
\(970\) −523.951 + 721.157i −0.540156 + 0.743461i
\(971\) −352.634 + 1085.30i −0.363166 + 1.11771i 0.587955 + 0.808893i \(0.299933\pi\)
−0.951121 + 0.308817i \(0.900067\pi\)
\(972\) 348.077 + 1071.27i 0.358104 + 1.10213i
\(973\) −116.964 + 84.9796i −0.120210 + 0.0873377i
\(974\) −324.098 446.083i −0.332750 0.457991i
\(975\) −263.435 + 85.5951i −0.270189 + 0.0877898i
\(976\) −212.177 68.9406i −0.217395 0.0706358i
\(977\) −104.116 75.6451i −0.106568 0.0774258i 0.533225 0.845973i \(-0.320980\pi\)
−0.639793 + 0.768547i \(0.720980\pi\)
\(978\) 772.398i 0.789773i
\(979\) −677.249 104.509i −0.691776 0.106751i
\(980\) −1054.89 −1.07641
\(981\) 329.373 453.343i 0.335752 0.462123i
\(982\) −611.297 + 1881.38i −0.622502 + 1.91586i
\(983\) −412.497 1269.53i −0.419630 1.29149i −0.908043 0.418876i \(-0.862424\pi\)
0.488413 0.872613i \(-0.337576\pi\)
\(984\) 17.3278 12.5894i 0.0176095 0.0127941i
\(985\) −232.932 320.603i −0.236479 0.325485i
\(986\) −250.517 + 81.3978i −0.254074 + 0.0825535i
\(987\) 70.3444 + 22.8563i 0.0712709 + 0.0231573i
\(988\) 446.697 + 324.544i 0.452122 + 0.328486i
\(989\) 239.242i 0.241903i
\(990\) −390.095 + 393.207i −0.394036 + 0.397179i
\(991\) 762.024 0.768944 0.384472 0.923137i \(-0.374383\pi\)
0.384472 + 0.923137i \(0.374383\pi\)
\(992\) 828.904 1140.89i 0.835588 1.15009i
\(993\) 416.039 1280.44i 0.418972 1.28946i
\(994\) −53.2260 163.813i −0.0535473 0.164802i
\(995\) 496.636 360.827i 0.499132 0.362641i
\(996\) −659.886 908.255i −0.662536 0.911903i
\(997\) 1146.56 372.540i 1.15001 0.373661i 0.328864 0.944377i \(-0.393334\pi\)
0.821147 + 0.570716i \(0.193334\pi\)
\(998\) 1538.71 + 499.958i 1.54180 + 0.500960i
\(999\) 578.435 + 420.257i 0.579014 + 0.420678i
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 11.3.d.a.7.1 4
3.2 odd 2 99.3.k.a.73.1 4
4.3 odd 2 176.3.n.a.161.1 4
5.2 odd 4 275.3.q.d.249.1 8
5.3 odd 4 275.3.q.d.249.2 8
5.4 even 2 275.3.x.e.51.1 4
11.2 odd 10 121.3.d.a.94.1 4
11.3 even 5 121.3.d.d.118.1 4
11.4 even 5 121.3.d.a.112.1 4
11.5 even 5 121.3.b.b.120.1 4
11.6 odd 10 121.3.b.b.120.4 4
11.7 odd 10 121.3.d.c.112.1 4
11.8 odd 10 inner 11.3.d.a.8.1 yes 4
11.9 even 5 121.3.d.c.94.1 4
11.10 odd 2 121.3.d.d.40.1 4
33.5 odd 10 1089.3.c.e.604.4 4
33.8 even 10 99.3.k.a.19.1 4
33.17 even 10 1089.3.c.e.604.1 4
44.19 even 10 176.3.n.a.129.1 4
55.8 even 20 275.3.q.d.74.1 8
55.19 odd 10 275.3.x.e.151.1 4
55.52 even 20 275.3.q.d.74.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.3.d.a.7.1 4 1.1 even 1 trivial
11.3.d.a.8.1 yes 4 11.8 odd 10 inner
99.3.k.a.19.1 4 33.8 even 10
99.3.k.a.73.1 4 3.2 odd 2
121.3.b.b.120.1 4 11.5 even 5
121.3.b.b.120.4 4 11.6 odd 10
121.3.d.a.94.1 4 11.2 odd 10
121.3.d.a.112.1 4 11.4 even 5
121.3.d.c.94.1 4 11.9 even 5
121.3.d.c.112.1 4 11.7 odd 10
121.3.d.d.40.1 4 11.10 odd 2
121.3.d.d.118.1 4 11.3 even 5
176.3.n.a.129.1 4 44.19 even 10
176.3.n.a.161.1 4 4.3 odd 2
275.3.q.d.74.1 8 55.8 even 20
275.3.q.d.74.2 8 55.52 even 20
275.3.q.d.249.1 8 5.2 odd 4
275.3.q.d.249.2 8 5.3 odd 4
275.3.x.e.51.1 4 5.4 even 2
275.3.x.e.151.1 4 55.19 odd 10
1089.3.c.e.604.1 4 33.17 even 10
1089.3.c.e.604.4 4 33.5 odd 10