Properties

Label 429.2.n.c.157.1
Level $429$
Weight $2$
Character 429.157
Analytic conductor $3.426$
Analytic rank $0$
Dimension $28$
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] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 157.1
Character \(\chi\) \(=\) 429.157
Dual form 429.2.n.c.235.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.05353 + 1.49197i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.37295 - 4.22550i) q^{4} +(-3.43019 - 2.49218i) q^{5} +(2.05353 + 1.49197i) q^{6} +(0.899200 - 2.76745i) q^{7} +(1.91620 + 5.89746i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-2.05353 + 1.49197i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.37295 - 4.22550i) q^{4} +(-3.43019 - 2.49218i) q^{5} +(2.05353 + 1.49197i) q^{6} +(0.899200 - 2.76745i) q^{7} +(1.91620 + 5.89746i) q^{8} +(-0.809017 + 0.587785i) q^{9} +10.7623 q^{10} +(3.13933 - 1.06986i) q^{11} -4.44296 q^{12} +(-0.809017 + 0.587785i) q^{13} +(2.28244 + 7.02462i) q^{14} +(-1.31022 + 4.03243i) q^{15} +(-5.54497 - 4.02866i) q^{16} +(-0.626709 - 0.455331i) q^{17} +(0.784377 - 2.41407i) q^{18} +(-2.41669 - 7.43781i) q^{19} +(-15.2402 + 11.0726i) q^{20} -2.90987 q^{21} +(-4.85049 + 6.88079i) q^{22} -3.36268 q^{23} +(5.01668 - 3.64483i) q^{24} +(4.01016 + 12.3420i) q^{25} +(0.784377 - 2.41407i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-10.4593 - 7.59915i) q^{28} +(-0.289444 + 0.890816i) q^{29} +(-3.32572 - 10.2355i) q^{30} +(-3.28474 + 2.38651i) q^{31} +4.99548 q^{32} +(-1.98761 - 2.65507i) q^{33} +1.96631 q^{34} +(-9.98142 + 7.25192i) q^{35} +(1.37295 + 4.22550i) q^{36} +(-1.44029 + 4.43274i) q^{37} +(16.0598 + 11.6681i) q^{38} +(0.809017 + 0.587785i) q^{39} +(8.12459 - 25.0049i) q^{40} +(-0.615421 - 1.89407i) q^{41} +(5.97550 - 4.34145i) q^{42} +3.54317 q^{43} +(-0.210571 - 14.7341i) q^{44} +4.23995 q^{45} +(6.90536 - 5.01703i) q^{46} +(-1.43367 - 4.41239i) q^{47} +(-2.11799 + 6.51850i) q^{48} +(-1.18712 - 0.862491i) q^{49} +(-26.6490 - 19.3616i) q^{50} +(-0.239382 + 0.736741i) q^{51} +(1.37295 + 4.22550i) q^{52} +(-6.46262 + 4.69537i) q^{53} -2.53830 q^{54} +(-13.4348 - 4.15394i) q^{55} +18.0440 q^{56} +(-6.32698 + 4.59682i) q^{57} +(-0.734694 - 2.26116i) q^{58} +(2.90367 - 8.93657i) q^{59} +(15.2402 + 11.0726i) q^{60} +(4.52572 + 3.28813i) q^{61} +(3.18470 - 9.80150i) q^{62} +(0.899200 + 2.76745i) q^{63} +(0.831591 - 0.604186i) q^{64} +4.23995 q^{65} +(8.04291 + 2.48681i) q^{66} -13.2680 q^{67} +(-2.78444 + 2.02302i) q^{68} +(1.03913 + 3.19810i) q^{69} +(9.67742 - 29.7840i) q^{70} +(8.27322 + 6.01084i) q^{71} +(-5.01668 - 3.64483i) q^{72} +(-0.616317 + 1.89683i) q^{73} +(-3.65587 - 11.2516i) q^{74} +(10.4987 - 7.62779i) q^{75} -34.7465 q^{76} +(-0.137912 - 9.64997i) q^{77} -2.53830 q^{78} +(-5.01552 + 3.64399i) q^{79} +(8.98017 + 27.6381i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.08969 + 2.97133i) q^{82} +(13.9807 + 10.1576i) q^{83} +(-3.99511 + 12.2957i) q^{84} +(1.01497 + 3.12374i) q^{85} +(-7.27598 + 5.28631i) q^{86} +0.936659 q^{87} +(12.3251 + 16.4640i) q^{88} +1.56195 q^{89} +(-8.70685 + 6.32589i) q^{90} +(0.899200 + 2.76745i) q^{91} +(-4.61679 + 14.2090i) q^{92} +(3.28474 + 2.38651i) q^{93} +(9.52725 + 6.92195i) q^{94} +(-10.2466 + 31.5359i) q^{95} +(-1.54369 - 4.75098i) q^{96} +(-7.32906 + 5.32487i) q^{97} +3.72459 q^{98} +(-1.91092 + 2.71079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05353 + 1.49197i −1.45206 + 1.05499i −0.466718 + 0.884406i \(0.654564\pi\)
−0.985344 + 0.170579i \(0.945436\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 1.37295 4.22550i 0.686475 2.11275i
\(5\) −3.43019 2.49218i −1.53403 1.11454i −0.953946 0.299978i \(-0.903021\pi\)
−0.580082 0.814558i \(-0.696979\pi\)
\(6\) 2.05353 + 1.49197i 0.838349 + 0.609096i
\(7\) 0.899200 2.76745i 0.339866 1.04600i −0.624410 0.781097i \(-0.714660\pi\)
0.964275 0.264902i \(-0.0853396\pi\)
\(8\) 1.91620 + 5.89746i 0.677479 + 2.08507i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 10.7623 3.40332
\(11\) 3.13933 1.06986i 0.946544 0.322576i
\(12\) −4.44296 −1.28257
\(13\) −0.809017 + 0.587785i −0.224381 + 0.163022i
\(14\) 2.28244 + 7.02462i 0.610007 + 1.87741i
\(15\) −1.31022 + 4.03243i −0.338296 + 1.04117i
\(16\) −5.54497 4.02866i −1.38624 1.00716i
\(17\) −0.626709 0.455331i −0.151999 0.110434i 0.509186 0.860656i \(-0.329946\pi\)
−0.661186 + 0.750222i \(0.729946\pi\)
\(18\) 0.784377 2.41407i 0.184879 0.569001i
\(19\) −2.41669 7.43781i −0.554427 1.70635i −0.697452 0.716632i \(-0.745683\pi\)
0.143025 0.989719i \(-0.454317\pi\)
\(20\) −15.2402 + 11.0726i −3.40781 + 2.47592i
\(21\) −2.90987 −0.634986
\(22\) −4.85049 + 6.88079i −1.03413 + 1.46699i
\(23\) −3.36268 −0.701168 −0.350584 0.936531i \(-0.614017\pi\)
−0.350584 + 0.936531i \(0.614017\pi\)
\(24\) 5.01668 3.64483i 1.02403 0.743998i
\(25\) 4.01016 + 12.3420i 0.802033 + 2.46840i
\(26\) 0.784377 2.41407i 0.153829 0.473437i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) −10.4593 7.59915i −1.97663 1.43610i
\(29\) −0.289444 + 0.890816i −0.0537483 + 0.165420i −0.974327 0.225136i \(-0.927717\pi\)
0.920579 + 0.390556i \(0.127717\pi\)
\(30\) −3.32572 10.2355i −0.607191 1.86874i
\(31\) −3.28474 + 2.38651i −0.589957 + 0.428629i −0.842300 0.539009i \(-0.818799\pi\)
0.252343 + 0.967638i \(0.418799\pi\)
\(32\) 4.99548 0.883084
\(33\) −1.98761 2.65507i −0.345998 0.462189i
\(34\) 1.96631 0.337219
\(35\) −9.98142 + 7.25192i −1.68717 + 1.22580i
\(36\) 1.37295 + 4.22550i 0.228825 + 0.704251i
\(37\) −1.44029 + 4.43274i −0.236781 + 0.728738i 0.760099 + 0.649808i \(0.225151\pi\)
−0.996880 + 0.0789307i \(0.974849\pi\)
\(38\) 16.0598 + 11.6681i 2.60524 + 1.89282i
\(39\) 0.809017 + 0.587785i 0.129546 + 0.0941210i
\(40\) 8.12459 25.0049i 1.28461 3.95363i
\(41\) −0.615421 1.89407i −0.0961126 0.295804i 0.891429 0.453160i \(-0.149703\pi\)
−0.987542 + 0.157355i \(0.949703\pi\)
\(42\) 5.97550 4.34145i 0.922040 0.669901i
\(43\) 3.54317 0.540328 0.270164 0.962814i \(-0.412922\pi\)
0.270164 + 0.962814i \(0.412922\pi\)
\(44\) −0.210571 14.7341i −0.0317448 2.22125i
\(45\) 4.23995 0.632054
\(46\) 6.90536 5.01703i 1.01814 0.739721i
\(47\) −1.43367 4.41239i −0.209123 0.643613i −0.999519 0.0310171i \(-0.990125\pi\)
0.790396 0.612596i \(-0.209875\pi\)
\(48\) −2.11799 + 6.51850i −0.305705 + 0.940865i
\(49\) −1.18712 0.862491i −0.169588 0.123213i
\(50\) −26.6490 19.3616i −3.76873 2.73814i
\(51\) −0.239382 + 0.736741i −0.0335201 + 0.103164i
\(52\) 1.37295 + 4.22550i 0.190394 + 0.585972i
\(53\) −6.46262 + 4.69537i −0.887710 + 0.644959i −0.935280 0.353909i \(-0.884852\pi\)
0.0475702 + 0.998868i \(0.484852\pi\)
\(54\) −2.53830 −0.345419
\(55\) −13.4348 4.15394i −1.81155 0.560117i
\(56\) 18.0440 2.41123
\(57\) −6.32698 + 4.59682i −0.838029 + 0.608864i
\(58\) −0.734694 2.26116i −0.0964700 0.296904i
\(59\) 2.90367 8.93657i 0.378025 1.16344i −0.563389 0.826192i \(-0.690503\pi\)
0.941415 0.337251i \(-0.109497\pi\)
\(60\) 15.2402 + 11.0726i 1.96750 + 1.42947i
\(61\) 4.52572 + 3.28813i 0.579459 + 0.421001i 0.838529 0.544857i \(-0.183416\pi\)
−0.259070 + 0.965858i \(0.583416\pi\)
\(62\) 3.18470 9.80150i 0.404458 1.24479i
\(63\) 0.899200 + 2.76745i 0.113289 + 0.348666i
\(64\) 0.831591 0.604186i 0.103949 0.0755233i
\(65\) 4.23995 0.525901
\(66\) 8.04291 + 2.48681i 0.990013 + 0.306105i
\(67\) −13.2680 −1.62095 −0.810474 0.585775i \(-0.800790\pi\)
−0.810474 + 0.585775i \(0.800790\pi\)
\(68\) −2.78444 + 2.02302i −0.337663 + 0.245327i
\(69\) 1.03913 + 3.19810i 0.125096 + 0.385006i
\(70\) 9.67742 29.7840i 1.15667 3.55987i
\(71\) 8.27322 + 6.01084i 0.981850 + 0.713356i 0.958121 0.286362i \(-0.0924461\pi\)
0.0237289 + 0.999718i \(0.492446\pi\)
\(72\) −5.01668 3.64483i −0.591221 0.429547i
\(73\) −0.616317 + 1.89683i −0.0721345 + 0.222007i −0.980624 0.195901i \(-0.937237\pi\)
0.908489 + 0.417908i \(0.137237\pi\)
\(74\) −3.65587 11.2516i −0.424987 1.30797i
\(75\) 10.4987 7.62779i 1.21229 0.880781i
\(76\) −34.7465 −3.98570
\(77\) −0.137912 9.64997i −0.0157165 1.09972i
\(78\) −2.53830 −0.287406
\(79\) −5.01552 + 3.64399i −0.564290 + 0.409981i −0.833027 0.553233i \(-0.813394\pi\)
0.268736 + 0.963214i \(0.413394\pi\)
\(80\) 8.98017 + 27.6381i 1.00401 + 3.09003i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 4.08969 + 2.97133i 0.451631 + 0.328129i
\(83\) 13.9807 + 10.1576i 1.53459 + 1.11494i 0.953620 + 0.301013i \(0.0973247\pi\)
0.580965 + 0.813929i \(0.302675\pi\)
\(84\) −3.99511 + 12.2957i −0.435902 + 1.34157i
\(85\) 1.01497 + 3.12374i 0.110089 + 0.338818i
\(86\) −7.27598 + 5.28631i −0.784589 + 0.570038i
\(87\) 0.936659 0.100420
\(88\) 12.3251 + 16.4640i 1.31386 + 1.75507i
\(89\) 1.56195 0.165566 0.0827831 0.996568i \(-0.473619\pi\)
0.0827831 + 0.996568i \(0.473619\pi\)
\(90\) −8.70685 + 6.32589i −0.917782 + 0.666808i
\(91\) 0.899200 + 2.76745i 0.0942618 + 0.290108i
\(92\) −4.61679 + 14.2090i −0.481334 + 1.48139i
\(93\) 3.28474 + 2.38651i 0.340612 + 0.247469i
\(94\) 9.52725 + 6.92195i 0.982661 + 0.713945i
\(95\) −10.2466 + 31.5359i −1.05128 + 3.23552i
\(96\) −1.54369 4.75098i −0.157552 0.484895i
\(97\) −7.32906 + 5.32487i −0.744153 + 0.540659i −0.894009 0.448049i \(-0.852119\pi\)
0.149856 + 0.988708i \(0.452119\pi\)
\(98\) 3.72459 0.376241
\(99\) −1.91092 + 2.71079i −0.192055 + 0.272445i
\(100\) 57.6570 5.76570
\(101\) 2.49382 1.81187i 0.248144 0.180287i −0.456760 0.889590i \(-0.650990\pi\)
0.704904 + 0.709303i \(0.250990\pi\)
\(102\) −0.607622 1.87007i −0.0601635 0.185164i
\(103\) −2.54026 + 7.81813i −0.250300 + 0.770343i 0.744420 + 0.667712i \(0.232726\pi\)
−0.994719 + 0.102631i \(0.967274\pi\)
\(104\) −5.01668 3.64483i −0.491926 0.357405i
\(105\) 9.98142 + 7.25192i 0.974087 + 0.707715i
\(106\) 6.26580 19.2841i 0.608588 1.87304i
\(107\) −5.82809 17.9370i −0.563423 1.73404i −0.672592 0.740013i \(-0.734819\pi\)
0.109169 0.994023i \(-0.465181\pi\)
\(108\) 3.59443 2.61150i 0.345874 0.251292i
\(109\) −10.7130 −1.02612 −0.513061 0.858352i \(-0.671488\pi\)
−0.513061 + 0.858352i \(0.671488\pi\)
\(110\) 33.7863 11.5141i 3.22139 1.09783i
\(111\) 4.66086 0.442389
\(112\) −16.1351 + 11.7229i −1.52463 + 1.10771i
\(113\) 1.34981 + 4.15430i 0.126980 + 0.390804i 0.994257 0.107023i \(-0.0341317\pi\)
−0.867277 + 0.497826i \(0.834132\pi\)
\(114\) 6.13428 18.8794i 0.574528 1.76822i
\(115\) 11.5346 + 8.38041i 1.07561 + 0.781477i
\(116\) 3.36675 + 2.44609i 0.312595 + 0.227114i
\(117\) 0.309017 0.951057i 0.0285686 0.0879252i
\(118\) 7.37038 + 22.6837i 0.678498 + 2.08820i
\(119\) −1.82364 + 1.32495i −0.167173 + 0.121458i
\(120\) −26.2917 −2.40010
\(121\) 8.71078 6.71731i 0.791889 0.610664i
\(122\) −14.1995 −1.28556
\(123\) −1.61119 + 1.17060i −0.145276 + 0.105550i
\(124\) 5.57440 + 17.1562i 0.500596 + 1.54068i
\(125\) 10.4518 32.1674i 0.934838 2.87714i
\(126\) −5.97550 4.34145i −0.532340 0.386768i
\(127\) 0.116965 + 0.0849802i 0.0103790 + 0.00754078i 0.592963 0.805230i \(-0.297958\pi\)
−0.582584 + 0.812771i \(0.697958\pi\)
\(128\) −3.89364 + 11.9834i −0.344152 + 1.05919i
\(129\) −1.09490 3.36975i −0.0964004 0.296690i
\(130\) −8.70685 + 6.32589i −0.763641 + 0.554818i
\(131\) 4.28002 0.373947 0.186974 0.982365i \(-0.440132\pi\)
0.186974 + 0.982365i \(0.440132\pi\)
\(132\) −13.9479 + 4.75336i −1.21401 + 0.413727i
\(133\) −22.7569 −1.97327
\(134\) 27.2462 19.7956i 2.35372 1.71008i
\(135\) −1.31022 4.03243i −0.112765 0.347056i
\(136\) 1.48439 4.56850i 0.127286 0.391745i
\(137\) −9.44724 6.86382i −0.807132 0.586416i 0.105866 0.994380i \(-0.466239\pi\)
−0.912998 + 0.407965i \(0.866239\pi\)
\(138\) −6.90536 5.01703i −0.587823 0.427078i
\(139\) 7.07374 21.7707i 0.599987 1.84657i 0.0718412 0.997416i \(-0.477113\pi\)
0.528146 0.849154i \(-0.322887\pi\)
\(140\) 16.9391 + 52.1330i 1.43161 + 4.40605i
\(141\) −3.75340 + 2.72701i −0.316093 + 0.229655i
\(142\) −25.9573 −2.17829
\(143\) −1.91092 + 2.71079i −0.159799 + 0.226688i
\(144\) 6.85396 0.571163
\(145\) 3.21292 2.33432i 0.266818 0.193855i
\(146\) −1.56440 4.81472i −0.129470 0.398469i
\(147\) −0.453438 + 1.39554i −0.0373990 + 0.115102i
\(148\) 16.7531 + 12.1719i 1.37710 + 1.00052i
\(149\) −7.61950 5.53589i −0.624214 0.453518i 0.230177 0.973149i \(-0.426070\pi\)
−0.854391 + 0.519631i \(0.826070\pi\)
\(150\) −10.1790 + 31.3277i −0.831111 + 2.55790i
\(151\) −0.881867 2.71411i −0.0717653 0.220871i 0.908740 0.417362i \(-0.137045\pi\)
−0.980506 + 0.196491i \(0.937045\pi\)
\(152\) 39.2333 28.5047i 3.18224 2.31203i
\(153\) 0.774655 0.0626272
\(154\) 14.6807 + 19.6107i 1.18301 + 1.58028i
\(155\) 17.2149 1.38273
\(156\) 3.59443 2.61150i 0.287785 0.209088i
\(157\) 1.20738 + 3.71595i 0.0963597 + 0.296565i 0.987606 0.156956i \(-0.0501680\pi\)
−0.891246 + 0.453520i \(0.850168\pi\)
\(158\) 4.86277 14.9661i 0.386861 1.19064i
\(159\) 6.46262 + 4.69537i 0.512519 + 0.372367i
\(160\) −17.1354 12.4496i −1.35468 0.984229i
\(161\) −3.02372 + 9.30606i −0.238303 + 0.733421i
\(162\) 0.784377 + 2.41407i 0.0616265 + 0.189667i
\(163\) 3.63845 2.64349i 0.284985 0.207054i −0.436104 0.899896i \(-0.643642\pi\)
0.721089 + 0.692842i \(0.243642\pi\)
\(164\) −8.84835 −0.690940
\(165\) 0.200950 + 14.0609i 0.0156439 + 1.09464i
\(166\) −43.8647 −3.40456
\(167\) −11.4583 + 8.32495i −0.886670 + 0.644204i −0.935008 0.354627i \(-0.884608\pi\)
0.0483375 + 0.998831i \(0.484608\pi\)
\(168\) −5.57590 17.1609i −0.430190 1.32399i
\(169\) 0.309017 0.951057i 0.0237705 0.0731582i
\(170\) −6.74480 4.90039i −0.517303 0.375843i
\(171\) 6.32698 + 4.59682i 0.483836 + 0.351528i
\(172\) 4.86459 14.9717i 0.370921 1.14158i
\(173\) −5.76564 17.7448i −0.438353 1.34911i −0.889611 0.456719i \(-0.849025\pi\)
0.451258 0.892394i \(-0.350975\pi\)
\(174\) −1.92345 + 1.39747i −0.145817 + 0.105942i
\(175\) 37.7619 2.85453
\(176\) −21.7176 6.71492i −1.63703 0.506156i
\(177\) −9.39647 −0.706282
\(178\) −3.20750 + 2.33039i −0.240413 + 0.174670i
\(179\) 4.58270 + 14.1041i 0.342527 + 1.05419i 0.962895 + 0.269878i \(0.0869834\pi\)
−0.620368 + 0.784311i \(0.713017\pi\)
\(180\) 5.82124 17.9159i 0.433889 1.33537i
\(181\) −10.3293 7.50464i −0.767767 0.557816i 0.133515 0.991047i \(-0.457373\pi\)
−0.901283 + 0.433231i \(0.857373\pi\)
\(182\) −5.97550 4.34145i −0.442934 0.321810i
\(183\) 1.72867 5.32030i 0.127787 0.393288i
\(184\) −6.44357 19.8313i −0.475026 1.46198i
\(185\) 15.9876 11.6157i 1.17543 0.854003i
\(186\) −10.3059 −0.755666
\(187\) −2.45459 0.758941i −0.179497 0.0554992i
\(188\) −20.6129 −1.50335
\(189\) 2.35414 1.71038i 0.171238 0.124412i
\(190\) −26.0090 80.0476i −1.88689 5.80726i
\(191\) −1.03127 + 3.17391i −0.0746199 + 0.229656i −0.981409 0.191928i \(-0.938526\pi\)
0.906789 + 0.421585i \(0.138526\pi\)
\(192\) −0.831591 0.604186i −0.0600149 0.0436034i
\(193\) −15.2261 11.0624i −1.09600 0.796291i −0.115598 0.993296i \(-0.536879\pi\)
−0.980403 + 0.197005i \(0.936879\pi\)
\(194\) 7.10584 21.8695i 0.510170 1.57014i
\(195\) −1.31022 4.03243i −0.0938265 0.288768i
\(196\) −5.27431 + 3.83201i −0.376737 + 0.273715i
\(197\) 7.88673 0.561907 0.280953 0.959721i \(-0.409349\pi\)
0.280953 + 0.959721i \(0.409349\pi\)
\(198\) −0.120301 8.41772i −0.00854942 0.598222i
\(199\) 6.64393 0.470976 0.235488 0.971877i \(-0.424331\pi\)
0.235488 + 0.971877i \(0.424331\pi\)
\(200\) −65.1023 + 47.2996i −4.60342 + 3.34458i
\(201\) 4.10005 + 12.6186i 0.289195 + 0.890050i
\(202\) −2.41787 + 7.44143i −0.170121 + 0.523577i
\(203\) 2.20502 + 1.60204i 0.154762 + 0.112441i
\(204\) 2.78444 + 2.02302i 0.194950 + 0.141639i
\(205\) −2.60935 + 8.03077i −0.182245 + 0.560893i
\(206\) −6.44794 19.8447i −0.449250 1.38265i
\(207\) 2.72047 1.97653i 0.189085 0.137379i
\(208\) 6.85396 0.475236
\(209\) −15.5442 20.7642i −1.07522 1.43629i
\(210\) −31.3168 −2.16106
\(211\) 7.65263 5.55996i 0.526829 0.382764i −0.292341 0.956314i \(-0.594434\pi\)
0.819170 + 0.573550i \(0.194434\pi\)
\(212\) 10.9675 + 33.7543i 0.753248 + 2.31826i
\(213\) 3.16009 9.72575i 0.216526 0.666397i
\(214\) 38.7297 + 28.1388i 2.64751 + 1.92353i
\(215\) −12.1537 8.83020i −0.828878 0.602215i
\(216\) −1.91620 + 5.89746i −0.130381 + 0.401271i
\(217\) 3.65090 + 11.2363i 0.247839 + 0.762771i
\(218\) 21.9995 15.9836i 1.48999 1.08254i
\(219\) 1.99444 0.134772
\(220\) −35.9978 + 51.0656i −2.42697 + 3.44284i
\(221\) 0.774655 0.0521089
\(222\) −9.57120 + 6.95388i −0.642377 + 0.466714i
\(223\) 4.18676 + 12.8855i 0.280366 + 0.862878i 0.987749 + 0.156048i \(0.0498755\pi\)
−0.707383 + 0.706830i \(0.750125\pi\)
\(224\) 4.49193 13.8248i 0.300130 0.923705i
\(225\) −10.4987 7.62779i −0.699916 0.508519i
\(226\) −8.96998 6.51707i −0.596674 0.433509i
\(227\) 8.05283 24.7840i 0.534485 1.64498i −0.210275 0.977642i \(-0.567436\pi\)
0.744760 0.667333i \(-0.232564\pi\)
\(228\) 10.7373 + 33.0459i 0.711092 + 2.18852i
\(229\) 22.2301 16.1511i 1.46901 1.06730i 0.488110 0.872782i \(-0.337687\pi\)
0.980899 0.194515i \(-0.0623134\pi\)
\(230\) −36.1900 −2.38630
\(231\) −9.13505 + 3.11317i −0.601042 + 0.204831i
\(232\) −5.80818 −0.381326
\(233\) 4.19683 3.04918i 0.274944 0.199758i −0.441765 0.897131i \(-0.645648\pi\)
0.716709 + 0.697372i \(0.245648\pi\)
\(234\) 0.784377 + 2.41407i 0.0512763 + 0.157812i
\(235\) −6.07870 + 18.7083i −0.396530 + 1.22039i
\(236\) −33.7749 24.5389i −2.19856 1.59735i
\(237\) 5.01552 + 3.64399i 0.325793 + 0.236702i
\(238\) 1.76810 5.44166i 0.114609 0.352730i
\(239\) −0.644556 1.98374i −0.0416929 0.128317i 0.928044 0.372472i \(-0.121490\pi\)
−0.969736 + 0.244154i \(0.921490\pi\)
\(240\) 23.5104 17.0813i 1.51759 1.10259i
\(241\) −7.72932 −0.497889 −0.248945 0.968518i \(-0.580084\pi\)
−0.248945 + 0.968518i \(0.580084\pi\)
\(242\) −7.86577 + 26.7904i −0.505631 + 1.72215i
\(243\) −1.00000 −0.0641500
\(244\) 20.1076 14.6090i 1.28726 0.935246i
\(245\) 1.92256 + 5.91702i 0.122828 + 0.378024i
\(246\) 1.56212 4.80772i 0.0995973 0.306529i
\(247\) 6.32698 + 4.59682i 0.402576 + 0.292489i
\(248\) −20.3685 14.7986i −1.29340 0.939713i
\(249\) 5.34017 16.4353i 0.338419 1.04155i
\(250\) 26.5298 + 81.6504i 1.67789 + 5.16402i
\(251\) −16.5162 + 11.9997i −1.04249 + 0.757415i −0.970770 0.240010i \(-0.922849\pi\)
−0.0717218 + 0.997425i \(0.522849\pi\)
\(252\) 12.9284 0.814415
\(253\) −10.5566 + 3.59761i −0.663686 + 0.226180i
\(254\) −0.366980 −0.0230263
\(255\) 2.65722 1.93058i 0.166401 0.120898i
\(256\) −9.24794 28.4622i −0.577996 1.77889i
\(257\) 3.06767 9.44131i 0.191356 0.588932i −0.808644 0.588298i \(-0.799798\pi\)
1.00000 0.000634216i \(-0.000201877\pi\)
\(258\) 7.27598 + 5.28631i 0.452983 + 0.329111i
\(259\) 10.9723 + 7.97184i 0.681786 + 0.495346i
\(260\) 5.82124 17.9159i 0.361018 1.11110i
\(261\) −0.289444 0.890816i −0.0179161 0.0551401i
\(262\) −8.78914 + 6.38568i −0.542995 + 0.394509i
\(263\) −11.0697 −0.682588 −0.341294 0.939957i \(-0.610865\pi\)
−0.341294 + 0.939957i \(0.610865\pi\)
\(264\) 11.8495 16.8095i 0.729289 1.03455i
\(265\) 33.8697 2.08060
\(266\) 46.7319 33.9527i 2.86531 2.08177i
\(267\) −0.482669 1.48550i −0.0295388 0.0909112i
\(268\) −18.2163 + 56.0641i −1.11274 + 3.42466i
\(269\) 1.26350 + 0.917984i 0.0770367 + 0.0559705i 0.625637 0.780114i \(-0.284839\pi\)
−0.548600 + 0.836085i \(0.684839\pi\)
\(270\) 8.70685 + 6.32589i 0.529882 + 0.384982i
\(271\) −0.622397 + 1.91554i −0.0378079 + 0.116361i −0.968179 0.250258i \(-0.919485\pi\)
0.930371 + 0.366619i \(0.119485\pi\)
\(272\) 1.64071 + 5.04959i 0.0994827 + 0.306176i
\(273\) 2.35414 1.71038i 0.142479 0.103517i
\(274\) 29.6408 1.79067
\(275\) 25.7935 + 34.4553i 1.55541 + 2.07773i
\(276\) 14.9403 0.899297
\(277\) 7.73303 5.61837i 0.464633 0.337575i −0.330713 0.943731i \(-0.607289\pi\)
0.795346 + 0.606156i \(0.207289\pi\)
\(278\) 17.9553 + 55.2606i 1.07689 + 3.31431i
\(279\) 1.25466 3.86145i 0.0751145 0.231179i
\(280\) −61.8943 44.9689i −3.69889 2.68740i
\(281\) −3.18700 2.31549i −0.190120 0.138130i 0.488653 0.872478i \(-0.337488\pi\)
−0.678774 + 0.734348i \(0.737488\pi\)
\(282\) 3.63909 11.2000i 0.216704 0.666948i
\(283\) −2.65674 8.17662i −0.157927 0.486050i 0.840519 0.541783i \(-0.182250\pi\)
−0.998446 + 0.0557331i \(0.982250\pi\)
\(284\) 36.7576 26.7059i 2.18116 1.58471i
\(285\) 33.1588 1.96416
\(286\) −0.120301 8.41772i −0.00711355 0.497750i
\(287\) −5.79514 −0.342076
\(288\) −4.04143 + 2.93627i −0.238143 + 0.173021i
\(289\) −5.06785 15.5972i −0.298109 0.917485i
\(290\) −3.11506 + 9.58718i −0.182923 + 0.562979i
\(291\) 7.32906 + 5.32487i 0.429637 + 0.312150i
\(292\) 7.16889 + 5.20850i 0.419527 + 0.304804i
\(293\) −8.27637 + 25.4721i −0.483511 + 1.48809i 0.350615 + 0.936520i \(0.385973\pi\)
−0.834126 + 0.551574i \(0.814027\pi\)
\(294\) −1.15096 3.54230i −0.0671255 0.206591i
\(295\) −32.2317 + 23.4177i −1.87660 + 1.36343i
\(296\) −28.9018 −1.67988
\(297\) 3.16862 + 0.979714i 0.183862 + 0.0568488i
\(298\) 23.9063 1.38485
\(299\) 2.72047 1.97653i 0.157329 0.114306i
\(300\) −17.8170 54.8351i −1.02866 3.16590i
\(301\) 3.18601 9.80554i 0.183639 0.565182i
\(302\) 5.86032 + 4.25777i 0.337223 + 0.245007i
\(303\) −2.49382 1.81187i −0.143266 0.104089i
\(304\) −16.5639 + 50.9784i −0.950005 + 2.92381i
\(305\) −7.32947 22.5578i −0.419684 1.29166i
\(306\) −1.59077 + 1.15577i −0.0909385 + 0.0660707i
\(307\) 17.0080 0.970700 0.485350 0.874320i \(-0.338692\pi\)
0.485350 + 0.874320i \(0.338692\pi\)
\(308\) −40.9653 12.6662i −2.33422 0.721722i
\(309\) 8.22046 0.467646
\(310\) −35.3512 + 25.6842i −2.00782 + 1.45876i
\(311\) −7.58929 23.3574i −0.430349 1.32448i −0.897778 0.440448i \(-0.854820\pi\)
0.467429 0.884031i \(-0.345180\pi\)
\(312\) −1.91620 + 5.89746i −0.108483 + 0.333878i
\(313\) −18.9782 13.7885i −1.07271 0.779372i −0.0963159 0.995351i \(-0.530706\pi\)
−0.976398 + 0.215978i \(0.930706\pi\)
\(314\) −8.02349 5.82941i −0.452792 0.328972i
\(315\) 3.81256 11.7339i 0.214814 0.661128i
\(316\) 8.51163 + 26.1961i 0.478817 + 1.47365i
\(317\) −24.3500 + 17.6913i −1.36763 + 0.993643i −0.369714 + 0.929146i \(0.620544\pi\)
−0.997918 + 0.0644969i \(0.979456\pi\)
\(318\) −20.2765 −1.13705
\(319\) 0.0443924 + 3.10623i 0.00248550 + 0.173915i
\(320\) −4.35826 −0.243634
\(321\) −15.2581 + 11.0857i −0.851626 + 0.618743i
\(322\) −7.67511 23.6216i −0.427717 1.31638i
\(323\) −1.87210 + 5.76174i −0.104167 + 0.320592i
\(324\) −3.59443 2.61150i −0.199690 0.145084i
\(325\) −10.4987 7.62779i −0.582366 0.423113i
\(326\) −3.52764 + 10.8569i −0.195378 + 0.601311i
\(327\) 3.31051 + 10.1887i 0.183071 + 0.563436i
\(328\) 9.99094 7.25884i 0.551657 0.400802i
\(329\) −13.5002 −0.744292
\(330\) −21.3911 28.5746i −1.17754 1.57298i
\(331\) 11.2054 0.615907 0.307953 0.951401i \(-0.400356\pi\)
0.307953 + 0.951401i \(0.400356\pi\)
\(332\) 62.1158 45.1298i 3.40905 2.47682i
\(333\) −1.44029 4.43274i −0.0789271 0.242913i
\(334\) 11.1093 34.1910i 0.607875 1.87085i
\(335\) 45.5119 + 33.0663i 2.48658 + 1.80660i
\(336\) 16.1351 + 11.7229i 0.880245 + 0.639535i
\(337\) 7.73245 23.7980i 0.421213 1.29636i −0.485360 0.874314i \(-0.661312\pi\)
0.906574 0.422047i \(-0.138688\pi\)
\(338\) 0.784377 + 2.41407i 0.0426645 + 0.131308i
\(339\) 3.53386 2.56750i 0.191933 0.139447i
\(340\) 14.5929 0.791410
\(341\) −7.75866 + 11.0063i −0.420155 + 0.596022i
\(342\) −19.8510 −1.07342
\(343\) 13.0246 9.46292i 0.703262 0.510950i
\(344\) 6.78941 + 20.8957i 0.366061 + 1.12662i
\(345\) 4.40584 13.5598i 0.237202 0.730034i
\(346\) 38.3147 + 27.8372i 2.05981 + 1.49654i
\(347\) 18.9220 + 13.7476i 1.01579 + 0.738011i 0.965415 0.260719i \(-0.0839597\pi\)
0.0503706 + 0.998731i \(0.483960\pi\)
\(348\) 1.28599 3.95786i 0.0689360 0.212163i
\(349\) 3.33327 + 10.2587i 0.178426 + 0.549138i 0.999773 0.0212900i \(-0.00677732\pi\)
−0.821348 + 0.570428i \(0.806777\pi\)
\(350\) −77.5450 + 56.3398i −4.14496 + 3.01149i
\(351\) −1.00000 −0.0533761
\(352\) 15.6825 5.34448i 0.835877 0.284862i
\(353\) 1.10779 0.0589615 0.0294807 0.999565i \(-0.490615\pi\)
0.0294807 + 0.999565i \(0.490615\pi\)
\(354\) 19.2959 14.0193i 1.02557 0.745117i
\(355\) −13.3986 41.2367i −0.711124 2.18862i
\(356\) 2.14448 6.60002i 0.113657 0.349800i
\(357\) 1.82364 + 1.32495i 0.0965175 + 0.0701240i
\(358\) −30.4536 22.1259i −1.60952 1.16939i
\(359\) 1.70698 5.25353i 0.0900907 0.277271i −0.895852 0.444352i \(-0.853434\pi\)
0.985943 + 0.167081i \(0.0534341\pi\)
\(360\) 8.12459 + 25.0049i 0.428204 + 1.31788i
\(361\) −34.1093 + 24.7819i −1.79523 + 1.30431i
\(362\) 32.4081 1.70333
\(363\) −9.08032 6.20869i −0.476593 0.325871i
\(364\) 12.9284 0.677634
\(365\) 6.84132 4.97051i 0.358091 0.260168i
\(366\) 4.38788 + 13.5045i 0.229358 + 0.705892i
\(367\) −5.87475 + 18.0806i −0.306659 + 0.943801i 0.672393 + 0.740194i \(0.265266\pi\)
−0.979053 + 0.203607i \(0.934734\pi\)
\(368\) 18.6460 + 13.5471i 0.971988 + 0.706191i
\(369\) 1.61119 + 1.17060i 0.0838754 + 0.0609390i
\(370\) −15.5007 + 47.7063i −0.805844 + 2.48013i
\(371\) 7.18303 + 22.1071i 0.372924 + 1.14774i
\(372\) 14.5940 10.6031i 0.756662 0.549747i
\(373\) 8.71301 0.451143 0.225571 0.974227i \(-0.427575\pi\)
0.225571 + 0.974227i \(0.427575\pi\)
\(374\) 6.17288 2.10368i 0.319192 0.108779i
\(375\) −33.8228 −1.74660
\(376\) 23.2747 16.9100i 1.20030 0.872069i
\(377\) −0.289444 0.890816i −0.0149071 0.0458793i
\(378\) −2.28244 + 7.02462i −0.117396 + 0.361308i
\(379\) −26.4936 19.2487i −1.36088 0.988740i −0.998388 0.0567553i \(-0.981925\pi\)
−0.362496 0.931985i \(-0.618075\pi\)
\(380\) 119.187 + 86.5945i 6.11417 + 4.44220i
\(381\) 0.0446768 0.137501i 0.00228886 0.00704438i
\(382\) −2.61766 8.05634i −0.133931 0.412198i
\(383\) −9.13555 + 6.63737i −0.466805 + 0.339154i −0.796195 0.605040i \(-0.793157\pi\)
0.329390 + 0.944194i \(0.393157\pi\)
\(384\) 12.6001 0.642995
\(385\) −23.5764 + 33.4449i −1.20156 + 1.70451i
\(386\) 47.7721 2.43154
\(387\) −2.86648 + 2.08262i −0.145711 + 0.105866i
\(388\) 12.4378 + 38.2797i 0.631436 + 1.94336i
\(389\) 2.58841 7.96630i 0.131238 0.403908i −0.863748 0.503924i \(-0.831889\pi\)
0.994986 + 0.100016i \(0.0318893\pi\)
\(390\) 8.70685 + 6.32589i 0.440888 + 0.320324i
\(391\) 2.10742 + 1.53113i 0.106577 + 0.0774327i
\(392\) 2.81175 8.65368i 0.142015 0.437077i
\(393\) −1.32260 4.07054i −0.0667163 0.205332i
\(394\) −16.1956 + 11.7668i −0.815923 + 0.592803i
\(395\) 26.2857 1.32258
\(396\) 8.83085 + 11.7964i 0.443767 + 0.592790i
\(397\) −9.15050 −0.459250 −0.229625 0.973279i \(-0.573750\pi\)
−0.229625 + 0.973279i \(0.573750\pi\)
\(398\) −13.6435 + 9.91258i −0.683886 + 0.496873i
\(399\) 7.03226 + 21.6431i 0.352054 + 1.08351i
\(400\) 27.4855 84.5917i 1.37427 4.22958i
\(401\) 8.53273 + 6.19939i 0.426104 + 0.309583i 0.780089 0.625668i \(-0.215174\pi\)
−0.353985 + 0.935251i \(0.615174\pi\)
\(402\) −27.2462 19.7956i −1.35892 0.987312i
\(403\) 1.25466 3.86145i 0.0624991 0.192352i
\(404\) −4.23216 13.0252i −0.210558 0.648030i
\(405\) −3.43019 + 2.49218i −0.170448 + 0.123837i
\(406\) −6.91828 −0.343348
\(407\) 0.220899 + 15.4567i 0.0109495 + 0.766163i
\(408\) −4.80360 −0.237814
\(409\) −18.0486 + 13.1131i −0.892447 + 0.648401i −0.936515 0.350628i \(-0.885968\pi\)
0.0440681 + 0.999029i \(0.485968\pi\)
\(410\) −6.62332 20.3845i −0.327102 1.00672i
\(411\) −3.60852 + 11.1059i −0.177995 + 0.547813i
\(412\) 29.5479 + 21.4678i 1.45572 + 1.05764i
\(413\) −22.1206 16.0715i −1.08848 0.790828i
\(414\) −2.63761 + 8.11773i −0.129632 + 0.398965i
\(415\) −22.6420 69.6850i −1.11145 3.42070i
\(416\) −4.04143 + 2.93627i −0.198147 + 0.143962i
\(417\) −22.8911 −1.12098
\(418\) 62.9002 + 19.4483i 3.07655 + 0.951246i
\(419\) −14.9132 −0.728556 −0.364278 0.931290i \(-0.618684\pi\)
−0.364278 + 0.931290i \(0.618684\pi\)
\(420\) 44.3470 32.2200i 2.16391 1.57217i
\(421\) −3.79331 11.6746i −0.184875 0.568986i 0.815072 0.579360i \(-0.196698\pi\)
−0.999946 + 0.0103746i \(0.996698\pi\)
\(422\) −7.41956 + 22.8351i −0.361179 + 1.11159i
\(423\) 3.75340 + 2.72701i 0.182497 + 0.132592i
\(424\) −40.0744 29.1158i −1.94619 1.41399i
\(425\) 3.10649 9.56081i 0.150687 0.463767i
\(426\) 8.02125 + 24.6869i 0.388631 + 1.19608i
\(427\) 13.1693 9.56803i 0.637305 0.463029i
\(428\) −83.7946 −4.05036
\(429\) 3.16862 + 0.979714i 0.152982 + 0.0473010i
\(430\) 38.1324 1.83891
\(431\) 4.68595 3.40455i 0.225714 0.163991i −0.469181 0.883102i \(-0.655451\pi\)
0.694895 + 0.719111i \(0.255451\pi\)
\(432\) −2.11799 6.51850i −0.101902 0.313622i
\(433\) 4.77298 14.6897i 0.229375 0.705943i −0.768443 0.639918i \(-0.778968\pi\)
0.997818 0.0660250i \(-0.0210317\pi\)
\(434\) −24.2615 17.6270i −1.16459 0.846124i
\(435\) −3.21292 2.33432i −0.154048 0.111922i
\(436\) −14.7084 + 45.2679i −0.704407 + 2.16794i
\(437\) 8.12656 + 25.0110i 0.388746 + 1.19644i
\(438\) −4.09564 + 2.97566i −0.195697 + 0.142182i
\(439\) −25.9386 −1.23798 −0.618990 0.785399i \(-0.712458\pi\)
−0.618990 + 0.785399i \(0.712458\pi\)
\(440\) −1.24608 87.1909i −0.0594045 4.15666i
\(441\) 1.46736 0.0698742
\(442\) −1.59077 + 1.15577i −0.0756654 + 0.0549742i
\(443\) 2.00121 + 6.15911i 0.0950806 + 0.292628i 0.987275 0.159024i \(-0.0508348\pi\)
−0.892194 + 0.451652i \(0.850835\pi\)
\(444\) 6.39913 19.6945i 0.303689 0.934659i
\(445\) −5.35778 3.89266i −0.253983 0.184530i
\(446\) −27.8225 20.2142i −1.31743 0.957171i
\(447\) −2.91039 + 8.95726i −0.137657 + 0.423664i
\(448\) −0.924291 2.84467i −0.0436686 0.134398i
\(449\) −20.3046 + 14.7522i −0.958235 + 0.696199i −0.952740 0.303786i \(-0.901749\pi\)
−0.00549499 + 0.999985i \(0.501749\pi\)
\(450\) 32.9399 1.55280
\(451\) −3.95841 5.28770i −0.186394 0.248988i
\(452\) 19.4072 0.912839
\(453\) −2.30876 + 1.67741i −0.108475 + 0.0788117i
\(454\) 20.4405 + 62.9093i 0.959319 + 2.95248i
\(455\) 3.81256 11.7339i 0.178736 0.550092i
\(456\) −39.2333 28.5047i −1.83727 1.33485i
\(457\) −4.61687 3.35435i −0.215968 0.156910i 0.474542 0.880233i \(-0.342614\pi\)
−0.690510 + 0.723323i \(0.742614\pi\)
\(458\) −21.5531 + 66.3336i −1.00711 + 3.09957i
\(459\) −0.239382 0.736741i −0.0111734 0.0343881i
\(460\) 51.2479 37.2338i 2.38945 1.73603i
\(461\) −10.0596 −0.468520 −0.234260 0.972174i \(-0.575267\pi\)
−0.234260 + 0.972174i \(0.575267\pi\)
\(462\) 14.1143 20.0222i 0.656657 0.931518i
\(463\) 19.6675 0.914024 0.457012 0.889461i \(-0.348920\pi\)
0.457012 + 0.889461i \(0.348920\pi\)
\(464\) 5.19374 3.77348i 0.241113 0.175179i
\(465\) −5.31970 16.3723i −0.246695 0.759249i
\(466\) −4.06901 + 12.5231i −0.188493 + 0.580123i
\(467\) −18.8337 13.6835i −0.871522 0.633198i 0.0594731 0.998230i \(-0.481058\pi\)
−0.930995 + 0.365032i \(0.881058\pi\)
\(468\) −3.59443 2.61150i −0.166153 0.120717i
\(469\) −11.9306 + 36.7186i −0.550904 + 1.69551i
\(470\) −15.4295 47.4872i −0.711712 2.19042i
\(471\) 3.16097 2.29658i 0.145650 0.105821i
\(472\) 58.2671 2.68196
\(473\) 11.1232 3.79070i 0.511444 0.174297i
\(474\) −15.7362 −0.722789
\(475\) 82.1063 59.6537i 3.76729 2.73710i
\(476\) 3.09483 + 9.52491i 0.141851 + 0.436574i
\(477\) 2.46850 7.59727i 0.113025 0.347855i
\(478\) 4.28330 + 3.11200i 0.195914 + 0.142340i
\(479\) −1.58621 1.15245i −0.0724759 0.0526568i 0.550957 0.834533i \(-0.314263\pi\)
−0.623433 + 0.781877i \(0.714263\pi\)
\(480\) −6.54516 + 20.1439i −0.298744 + 0.919440i
\(481\) −1.44029 4.43274i −0.0656714 0.202116i
\(482\) 15.8724 11.5319i 0.722966 0.525266i
\(483\) 9.78497 0.445232
\(484\) −16.4245 46.0300i −0.746570 2.09227i
\(485\) 38.4106 1.74414
\(486\) 2.05353 1.49197i 0.0931498 0.0676773i
\(487\) 0.511393 + 1.57391i 0.0231734 + 0.0713205i 0.961974 0.273139i \(-0.0880620\pi\)
−0.938801 + 0.344460i \(0.888062\pi\)
\(488\) −10.7194 + 32.9909i −0.485245 + 1.49343i
\(489\) −3.63845 2.64349i −0.164536 0.119543i
\(490\) −12.7761 9.28235i −0.577163 0.419334i
\(491\) −6.40416 + 19.7100i −0.289016 + 0.889499i 0.696150 + 0.717896i \(0.254895\pi\)
−0.985166 + 0.171603i \(0.945105\pi\)
\(492\) 2.73429 + 8.41528i 0.123271 + 0.379390i
\(493\) 0.587013 0.426490i 0.0264377 0.0192081i
\(494\) −19.8510 −0.893137
\(495\) 13.3106 4.53617i 0.598267 0.203886i
\(496\) 27.8282 1.24952
\(497\) 24.0740 17.4908i 1.07987 0.784569i
\(498\) 13.5549 + 41.7178i 0.607411 + 1.86942i
\(499\) −4.11783 + 12.6734i −0.184339 + 0.567338i −0.999936 0.0112821i \(-0.996409\pi\)
0.815597 + 0.578620i \(0.196409\pi\)
\(500\) −121.574 88.3283i −5.43693 3.95016i
\(501\) 11.4583 + 8.32495i 0.511919 + 0.371931i
\(502\) 16.0132 49.2834i 0.714702 2.19963i
\(503\) −3.09643 9.52983i −0.138063 0.424914i 0.857991 0.513665i \(-0.171713\pi\)
−0.996054 + 0.0887508i \(0.971713\pi\)
\(504\) −14.5979 + 10.6060i −0.650242 + 0.472428i
\(505\) −13.0698 −0.581597
\(506\) 16.3106 23.1379i 0.725097 1.02861i
\(507\) −1.00000 −0.0444116
\(508\) 0.519672 0.377564i 0.0230567 0.0167517i
\(509\) −9.48804 29.2012i −0.420550 1.29432i −0.907192 0.420718i \(-0.861778\pi\)
0.486642 0.873602i \(-0.338222\pi\)
\(510\) −2.57629 + 7.92899i −0.114080 + 0.351102i
\(511\) 4.69519 + 3.41126i 0.207703 + 0.150905i
\(512\) 41.0684 + 29.8380i 1.81499 + 1.31866i
\(513\) 2.41669 7.43781i 0.106700 0.328387i
\(514\) 7.78665 + 23.9648i 0.343454 + 1.05704i
\(515\) 28.1978 20.4869i 1.24254 0.902759i
\(516\) −15.7421 −0.693009
\(517\) −9.22142 12.3181i −0.405558 0.541750i
\(518\) −34.4257 −1.51258
\(519\) −15.0946 + 10.9669i −0.662581 + 0.481393i
\(520\) 8.12459 + 25.0049i 0.356287 + 1.09654i
\(521\) −4.81093 + 14.8065i −0.210771 + 0.648686i 0.788656 + 0.614835i \(0.210777\pi\)
−0.999427 + 0.0338512i \(0.989223\pi\)
\(522\) 1.92345 + 1.39747i 0.0841873 + 0.0611656i
\(523\) −5.04532 3.66564i −0.220616 0.160287i 0.471988 0.881605i \(-0.343537\pi\)
−0.692604 + 0.721318i \(0.743537\pi\)
\(524\) 5.87625 18.0853i 0.256705 0.790058i
\(525\) −11.6691 35.9137i −0.509280 1.56740i
\(526\) 22.7320 16.5157i 0.991160 0.720120i
\(527\) 3.14523 0.137008
\(528\) 0.324839 + 22.7297i 0.0141368 + 0.989183i
\(529\) −11.6924 −0.508364
\(530\) −69.5524 + 50.5328i −3.02116 + 2.19500i
\(531\) 2.90367 + 8.93657i 0.126008 + 0.387814i
\(532\) −31.2440 + 96.1593i −1.35460 + 4.16903i
\(533\) 1.61119 + 1.17060i 0.0697885 + 0.0507043i
\(534\) 3.20750 + 2.33039i 0.138802 + 0.100846i
\(535\) −24.7108 + 76.0520i −1.06834 + 3.28802i
\(536\) −25.4242 78.2476i −1.09816 3.37978i
\(537\) 11.9977 8.71681i 0.517737 0.376158i
\(538\) −3.96423 −0.170910
\(539\) −4.64950 1.43759i −0.200268 0.0619214i
\(540\) −18.8379 −0.810655
\(541\) 11.0803 8.05029i 0.476378 0.346109i −0.323544 0.946213i \(-0.604874\pi\)
0.799922 + 0.600104i \(0.204874\pi\)
\(542\) −1.57983 4.86222i −0.0678595 0.208850i
\(543\) −3.94542 + 12.1428i −0.169314 + 0.521096i
\(544\) −3.13071 2.27460i −0.134228 0.0975225i
\(545\) 36.7477 + 26.6988i 1.57410 + 1.14365i
\(546\) −2.28244 + 7.02462i −0.0976793 + 0.300626i
\(547\) −10.8993 33.5447i −0.466022 1.43427i −0.857692 0.514164i \(-0.828102\pi\)
0.391670 0.920106i \(-0.371898\pi\)
\(548\) −41.9737 + 30.4957i −1.79303 + 1.30271i
\(549\) −5.59409 −0.238750
\(550\) −104.374 32.2717i −4.45053 1.37607i
\(551\) 7.32521 0.312065
\(552\) −16.8695 + 12.2564i −0.718013 + 0.521667i
\(553\) 5.57461 + 17.1569i 0.237057 + 0.729585i
\(554\) −7.49751 + 23.0750i −0.318539 + 0.980361i
\(555\) −15.9876 11.6157i −0.678638 0.493059i
\(556\) −82.2804 59.7802i −3.48947 2.53525i
\(557\) 0.118885 0.365889i 0.00503730 0.0155032i −0.948506 0.316758i \(-0.897406\pi\)
0.953544 + 0.301255i \(0.0974056\pi\)
\(558\) 3.18470 + 9.80150i 0.134819 + 0.414931i
\(559\) −2.86648 + 2.08262i −0.121239 + 0.0880854i
\(560\) 84.5621 3.57340
\(561\) 0.0367143 + 2.56898i 0.00155008 + 0.108462i
\(562\) 9.99923 0.421792
\(563\) 7.47112 5.42809i 0.314870 0.228767i −0.419113 0.907934i \(-0.637659\pi\)
0.733983 + 0.679167i \(0.237659\pi\)
\(564\) 6.36974 + 19.6041i 0.268215 + 0.825480i
\(565\) 5.72314 17.6140i 0.240774 0.741027i
\(566\) 17.6550 + 12.8271i 0.742095 + 0.539164i
\(567\) −2.35414 1.71038i −0.0988644 0.0718292i
\(568\) −19.5956 + 60.3089i −0.822212 + 2.53051i
\(569\) −2.91295 8.96514i −0.122117 0.375838i 0.871248 0.490844i \(-0.163311\pi\)
−0.993365 + 0.115005i \(0.963311\pi\)
\(570\) −68.0926 + 49.4721i −2.85208 + 2.07216i
\(571\) 9.23726 0.386567 0.193284 0.981143i \(-0.438086\pi\)
0.193284 + 0.981143i \(0.438086\pi\)
\(572\) 8.83085 + 11.7964i 0.369237 + 0.493232i
\(573\) 3.33725 0.139416
\(574\) 11.9005 8.64620i 0.496716 0.360885i
\(575\) −13.4849 41.5023i −0.562359 1.73076i
\(576\) −0.317640 + 0.977594i −0.0132350 + 0.0407331i
\(577\) −6.16974 4.48258i −0.256850 0.186612i 0.451907 0.892065i \(-0.350744\pi\)
−0.708757 + 0.705453i \(0.750744\pi\)
\(578\) 33.6776 + 24.4682i 1.40081 + 1.01774i
\(579\) −5.81586 + 17.8994i −0.241699 + 0.743873i
\(580\) −5.45251 16.7811i −0.226403 0.696797i
\(581\) 40.6822 29.5573i 1.68778 1.22624i
\(582\) −22.9950 −0.953173
\(583\) −15.2649 + 21.6544i −0.632208 + 0.896835i
\(584\) −12.3675 −0.511769
\(585\) −3.43019 + 2.49218i −0.141821 + 0.103039i
\(586\) −21.0079 64.6557i −0.867828 2.67090i
\(587\) −7.96326 + 24.5084i −0.328679 + 1.01157i 0.641074 + 0.767479i \(0.278489\pi\)
−0.969753 + 0.244090i \(0.921511\pi\)
\(588\) 5.27431 + 3.83201i 0.217509 + 0.158030i
\(589\) 25.6886 + 18.6639i 1.05848 + 0.769031i
\(590\) 31.2500 96.1777i 1.28654 3.95957i
\(591\) −2.43714 7.50073i −0.100250 0.308539i
\(592\) 25.8443 18.7770i 1.06220 0.771730i
\(593\) 23.7206 0.974088 0.487044 0.873377i \(-0.338075\pi\)
0.487044 + 0.873377i \(0.338075\pi\)
\(594\) −7.96856 + 2.71563i −0.326954 + 0.111424i
\(595\) 9.55747 0.391818
\(596\) −33.8531 + 24.5957i −1.38668 + 1.00748i
\(597\) −2.05309 6.31876i −0.0840273 0.258609i
\(598\) −2.63761 + 8.11773i −0.107860 + 0.331959i
\(599\) 5.28929 + 3.84289i 0.216114 + 0.157016i 0.690576 0.723260i \(-0.257357\pi\)
−0.474461 + 0.880276i \(0.657357\pi\)
\(600\) 65.1023 + 47.2996i 2.65779 + 1.93100i
\(601\) −1.92550 + 5.92609i −0.0785430 + 0.241730i −0.982617 0.185646i \(-0.940562\pi\)
0.904074 + 0.427377i \(0.140562\pi\)
\(602\) 8.08705 + 24.8894i 0.329604 + 1.01442i
\(603\) 10.7341 7.79875i 0.437125 0.317590i
\(604\) −12.6792 −0.515911
\(605\) −46.6204 + 1.33281i −1.89539 + 0.0541866i
\(606\) 7.82438 0.317844
\(607\) −23.4618 + 17.0460i −0.952287 + 0.691877i −0.951347 0.308122i \(-0.900299\pi\)
−0.000940390 1.00000i \(0.500299\pi\)
\(608\) −12.0725 37.1554i −0.489606 1.50685i
\(609\) 0.842244 2.59216i 0.0341294 0.105040i
\(610\) 48.7069 + 35.3876i 1.97209 + 1.43280i
\(611\) 3.75340 + 2.72701i 0.151846 + 0.110323i
\(612\) 1.06356 3.27331i 0.0429920 0.132316i
\(613\) −3.60379 11.0913i −0.145556 0.447975i 0.851526 0.524312i \(-0.175677\pi\)
−0.997082 + 0.0763372i \(0.975677\pi\)
\(614\) −34.9265 + 25.3756i −1.40952 + 1.02407i
\(615\) 8.44405 0.340497
\(616\) 56.6460 19.3046i 2.28233 0.777805i
\(617\) 35.3625 1.42364 0.711820 0.702362i \(-0.247871\pi\)
0.711820 + 0.702362i \(0.247871\pi\)
\(618\) −16.8809 + 12.2647i −0.679051 + 0.493359i
\(619\) 7.03025 + 21.6369i 0.282570 + 0.869660i 0.987117 + 0.160003i \(0.0511503\pi\)
−0.704547 + 0.709657i \(0.748850\pi\)
\(620\) 23.6352 72.7416i 0.949212 2.92137i
\(621\) −2.72047 1.97653i −0.109169 0.0793156i
\(622\) 50.4335 + 36.6421i 2.02220 + 1.46921i
\(623\) 1.40450 4.32262i 0.0562703 0.173182i
\(624\) −2.11799 6.51850i −0.0847874 0.260949i
\(625\) −63.5248 + 46.1535i −2.54099 + 1.84614i
\(626\) 59.5444 2.37987
\(627\) −14.9445 + 21.1999i −0.596826 + 0.846644i
\(628\) 17.3594 0.692716
\(629\) 2.92100 2.12223i 0.116468 0.0846190i
\(630\) 9.67742 + 29.7840i 0.385558 + 1.18662i
\(631\) −10.3091 + 31.7283i −0.410400 + 1.26308i 0.505901 + 0.862592i \(0.331160\pi\)
−0.916301 + 0.400491i \(0.868840\pi\)
\(632\) −31.1010 22.5962i −1.23713 0.898829i
\(633\) −7.65263 5.55996i −0.304165 0.220989i
\(634\) 23.6084 72.6591i 0.937608 2.88566i
\(635\) −0.189427 0.582997i −0.00751719 0.0231355i
\(636\) 28.7132 20.8613i 1.13855 0.827206i
\(637\) 1.46736 0.0581388
\(638\) −4.72557 6.31249i −0.187087 0.249914i
\(639\) −10.2263 −0.404545
\(640\) 43.2207 31.4017i 1.70845 1.24126i
\(641\) 14.3083 + 44.0364i 0.565144 + 1.73933i 0.667523 + 0.744589i \(0.267355\pi\)
−0.102379 + 0.994745i \(0.532645\pi\)
\(642\) 14.7934 45.5295i 0.583850 1.79691i
\(643\) −32.1592 23.3650i −1.26824 0.921427i −0.269105 0.963111i \(-0.586728\pi\)
−0.999131 + 0.0416837i \(0.986728\pi\)
\(644\) 35.1714 + 25.5535i 1.38595 + 1.00695i
\(645\) −4.64231 + 14.2876i −0.182791 + 0.562572i
\(646\) −4.75195 14.6250i −0.186963 0.575413i
\(647\) 13.5189 9.82207i 0.531484 0.386146i −0.289429 0.957200i \(-0.593465\pi\)
0.820913 + 0.571054i \(0.193465\pi\)
\(648\) 6.20095 0.243597
\(649\) −0.445340 31.1614i −0.0174811 1.22319i
\(650\) 32.9399 1.29201
\(651\) 9.55818 6.94443i 0.374615 0.272174i
\(652\) −6.17466 19.0037i −0.241818 0.744241i
\(653\) 9.29381 28.6034i 0.363695 1.11934i −0.587099 0.809515i \(-0.699730\pi\)
0.950794 0.309823i \(-0.100270\pi\)
\(654\) −21.9995 15.9836i −0.860248 0.625007i
\(655\) −14.6813 10.6666i −0.573646 0.416778i
\(656\) −4.21807 + 12.9819i −0.164688 + 0.506858i
\(657\) −0.616317 1.89683i −0.0240448 0.0740023i
\(658\) 27.7231 20.1420i 1.08076 0.785217i
\(659\) −8.53745 −0.332572 −0.166286 0.986078i \(-0.553177\pi\)
−0.166286 + 0.986078i \(0.553177\pi\)
\(660\) 59.6902 + 18.4558i 2.32344 + 0.718390i
\(661\) −7.46076 −0.290190 −0.145095 0.989418i \(-0.546349\pi\)
−0.145095 + 0.989418i \(0.546349\pi\)
\(662\) −23.0107 + 16.7182i −0.894335 + 0.649772i
\(663\) −0.239382 0.736741i −0.00929681 0.0286126i
\(664\) −33.1141 + 101.915i −1.28508 + 3.95506i
\(665\) 78.0604 + 56.7142i 3.02705 + 2.19928i
\(666\) 9.57120 + 6.95388i 0.370876 + 0.269458i
\(667\) 0.973306 2.99553i 0.0376866 0.115987i
\(668\) 19.4454 + 59.8468i 0.752366 + 2.31554i
\(669\) 10.9611 7.96369i 0.423780 0.307894i
\(670\) −142.794 −5.51661
\(671\) 17.7256 + 5.48061i 0.684288 + 0.211577i
\(672\) −14.5362 −0.560746
\(673\) 18.8649 13.7062i 0.727190 0.528334i −0.161483 0.986875i \(-0.551628\pi\)
0.888673 + 0.458541i \(0.151628\pi\)
\(674\) 19.6273 + 60.4065i 0.756014 + 2.32677i
\(675\) −4.01016 + 12.3420i −0.154351 + 0.475044i
\(676\) −3.59443 2.61150i −0.138247 0.100442i
\(677\) 22.9295 + 16.6592i 0.881251 + 0.640266i 0.933582 0.358364i \(-0.116665\pi\)
−0.0523313 + 0.998630i \(0.516665\pi\)
\(678\) −3.42623 + 10.5448i −0.131584 + 0.404972i
\(679\) 8.14604 + 25.0709i 0.312617 + 0.962135i
\(680\) −16.4773 + 11.9714i −0.631874 + 0.459084i
\(681\) −26.0595 −0.998602
\(682\) −0.488442 34.1774i −0.0187034 1.30872i
\(683\) 7.36889 0.281963 0.140981 0.990012i \(-0.454974\pi\)
0.140981 + 0.990012i \(0.454974\pi\)
\(684\) 28.1105 20.4235i 1.07483 0.780911i
\(685\) 15.3000 + 47.0884i 0.584581 + 1.79916i
\(686\) −12.6279 + 38.8647i −0.482136 + 1.48386i
\(687\) −22.2301 16.1511i −0.848133 0.616205i
\(688\) −19.6467 14.2742i −0.749025 0.544198i
\(689\) 2.46850 7.59727i 0.0940425 0.289433i
\(690\) 11.1833 + 34.4188i 0.425742 + 1.31030i
\(691\) 11.2321 8.16063i 0.427291 0.310445i −0.353274 0.935520i \(-0.614932\pi\)
0.780565 + 0.625075i \(0.214932\pi\)
\(692\) −82.8967 −3.15126
\(693\) 5.78368 + 7.72593i 0.219704 + 0.293484i
\(694\) −59.3679 −2.25357
\(695\) −78.5209 + 57.0487i −2.97847 + 2.16398i
\(696\) 1.79483 + 5.52391i 0.0680327 + 0.209383i
\(697\) −0.476739 + 1.46725i −0.0180578 + 0.0555762i
\(698\) −22.1507 16.0935i −0.838418 0.609146i
\(699\) −4.19683 3.04918i −0.158739 0.115330i
\(700\) 51.8452 159.563i 1.95956 6.03092i
\(701\) −5.29491 16.2961i −0.199986 0.615494i −0.999882 0.0153553i \(-0.995112\pi\)
0.799896 0.600139i \(-0.204888\pi\)
\(702\) 2.05353 1.49197i 0.0775054 0.0563109i
\(703\) 36.4506 1.37476
\(704\) 1.96424 2.78643i 0.0740302 0.105018i
\(705\) 19.6711 0.740855
\(706\) −2.27487 + 1.65279i −0.0856157 + 0.0622035i
\(707\) −2.77181 8.53076i −0.104245 0.320832i
\(708\) −12.9009 + 39.7048i −0.484845 + 1.49220i
\(709\) −8.06019 5.85607i −0.302707 0.219929i 0.426054 0.904698i \(-0.359903\pi\)
−0.728761 + 0.684768i \(0.759903\pi\)
\(710\) 89.0385 + 64.6902i 3.34155 + 2.42778i
\(711\) 1.91576 5.89610i 0.0718465 0.221121i
\(712\) 2.99301 + 9.21153i 0.112168 + 0.345217i
\(713\) 11.0455 8.02506i 0.413659 0.300541i
\(714\) −5.72170 −0.214129
\(715\) 13.3106 4.53617i 0.497788 0.169643i
\(716\) 65.8887 2.46238
\(717\) −1.68747 + 1.22602i −0.0630197 + 0.0457865i
\(718\) 4.33281 + 13.3350i 0.161699 + 0.497659i
\(719\) −8.97751 + 27.6299i −0.334805 + 1.03042i 0.632013 + 0.774957i \(0.282229\pi\)
−0.966818 + 0.255466i \(0.917771\pi\)
\(720\) −23.5104 17.0813i −0.876180 0.636582i
\(721\) 19.3521 + 14.0601i 0.720710 + 0.523626i
\(722\) 33.0705 101.780i 1.23076 3.78788i
\(723\) 2.38849 + 7.35102i 0.0888290 + 0.273387i
\(724\) −45.8924 + 33.3428i −1.70558 + 1.23918i
\(725\) −12.1552 −0.451432
\(726\) 27.9099 0.797906i 1.03583 0.0296131i
\(727\) −8.86626 −0.328831 −0.164416 0.986391i \(-0.552574\pi\)
−0.164416 + 0.986391i \(0.552574\pi\)
\(728\) −14.5979 + 10.6060i −0.541034 + 0.393084i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −6.63296 + 20.4142i −0.245497 + 0.755562i
\(731\) −2.22053 1.61331i −0.0821294 0.0596705i
\(732\) −20.1076 14.6090i −0.743197 0.539964i
\(733\) 7.21724 22.2124i 0.266575 0.820433i −0.724752 0.689010i \(-0.758045\pi\)
0.991326 0.131423i \(-0.0419545\pi\)
\(734\) −14.9119 45.8940i −0.550407 1.69398i
\(735\) 5.03332 3.65692i 0.185657 0.134887i
\(736\) −16.7982 −0.619190
\(737\) −41.6527 + 14.1950i −1.53430 + 0.522879i
\(738\) −5.05513 −0.186082
\(739\) −6.32918 + 4.59842i −0.232823 + 0.169156i −0.698080 0.716020i \(-0.745962\pi\)
0.465257 + 0.885176i \(0.345962\pi\)
\(740\) −27.1320 83.5036i −0.997391 3.06965i
\(741\) 2.41669 7.43781i 0.0887794 0.273235i
\(742\) −47.7337 34.6806i −1.75236 1.27316i
\(743\) −28.7485 20.8870i −1.05468 0.766269i −0.0815823 0.996667i \(-0.525997\pi\)
−0.973097 + 0.230398i \(0.925997\pi\)
\(744\) −7.78009 + 23.9447i −0.285232 + 0.877854i
\(745\) 12.3399 + 37.9783i 0.452099 + 1.39142i
\(746\) −17.8924 + 12.9996i −0.655087 + 0.475949i
\(747\) −17.2811 −0.632284
\(748\) −6.57693 + 9.32989i −0.240476 + 0.341134i
\(749\) −54.8805 −2.00529
\(750\) 69.4560 50.4627i 2.53617 1.84264i
\(751\) 10.7353 + 33.0399i 0.391738 + 1.20564i 0.931473 + 0.363810i \(0.118524\pi\)
−0.539735 + 0.841835i \(0.681476\pi\)
\(752\) −9.82633 + 30.2423i −0.358329 + 1.10282i
\(753\) 16.5162 + 11.9997i 0.601883 + 0.437294i
\(754\) 1.92345 + 1.39747i 0.0700481 + 0.0508929i
\(755\) −3.73907 + 11.5077i −0.136079 + 0.418807i
\(756\) −3.99511 12.2957i −0.145301 0.447189i
\(757\) 26.0420 18.9206i 0.946514 0.687683i −0.00346582 0.999994i \(-0.501103\pi\)
0.949980 + 0.312311i \(0.101103\pi\)
\(758\) 83.1239 3.01920
\(759\) 6.68369 + 8.92817i 0.242603 + 0.324072i
\(760\) −205.617 −7.45849
\(761\) −19.4476 + 14.1295i −0.704974 + 0.512194i −0.881548 0.472094i \(-0.843498\pi\)
0.176574 + 0.984287i \(0.443498\pi\)
\(762\) 0.113403 + 0.349018i 0.00410815 + 0.0126436i
\(763\) −9.63315 + 29.6478i −0.348744 + 1.07332i
\(764\) 11.9955 + 8.71525i 0.433982 + 0.315307i
\(765\) −2.65722 1.93058i −0.0960718 0.0698003i
\(766\) 8.85732 27.2600i 0.320028 0.984944i
\(767\) 2.90367 + 8.93657i 0.104845 + 0.322681i
\(768\) −24.2114 + 17.5906i −0.873654 + 0.634747i
\(769\) 17.7925 0.641613 0.320807 0.947145i \(-0.396046\pi\)
0.320807 + 0.947145i \(0.396046\pi\)
\(770\) −1.48424 103.855i −0.0534883 3.74269i
\(771\) −9.92718 −0.357519
\(772\) −67.6491 + 49.1499i −2.43474 + 1.76894i
\(773\) −4.33107 13.3297i −0.155778 0.479435i 0.842461 0.538757i \(-0.181106\pi\)
−0.998239 + 0.0593223i \(0.981106\pi\)
\(774\) 2.77918 8.55343i 0.0998955 0.307447i
\(775\) −42.6267 30.9701i −1.53119 1.11248i
\(776\) −45.4472 33.0193i −1.63146 1.18532i
\(777\) 4.19105 12.8987i 0.150353 0.462739i
\(778\) 6.57015 + 20.2209i 0.235551 + 0.724953i
\(779\) −12.6005 + 9.15477i −0.451458 + 0.328004i
\(780\) −18.8379 −0.674505
\(781\) 32.4031 + 10.0188i 1.15948 + 0.358501i
\(782\) −6.61206 −0.236447
\(783\) −0.757773 + 0.550554i −0.0270806 + 0.0196752i
\(784\) 3.10785 + 9.56497i 0.110995 + 0.341606i
\(785\) 5.11925 15.7554i 0.182714 0.562335i
\(786\) 8.78914 + 6.38568i 0.313498 + 0.227770i
\(787\) 28.7442 + 20.8839i 1.02462 + 0.744431i 0.967225 0.253920i \(-0.0817201\pi\)
0.0573965 + 0.998351i \(0.481720\pi\)
\(788\) 10.8281 33.3254i 0.385735 1.18717i
\(789\) 3.42073 + 10.5279i 0.121781 + 0.374804i
\(790\) −53.9783 + 39.2175i −1.92046 + 1.39530i
\(791\) 12.7106 0.451936
\(792\) −19.6485 6.07516i −0.698178 0.215872i
\(793\) −5.59409 −0.198652
\(794\) 18.7908 13.6523i 0.666860 0.484502i
\(795\) −10.4663 32.2120i −0.371202 1.14244i
\(796\) 9.12178 28.0740i 0.323313 0.995055i
\(797\) −30.5386 22.1876i −1.08173 0.785926i −0.103750 0.994603i \(-0.533084\pi\)
−0.977984 + 0.208678i \(0.933084\pi\)
\(798\) −46.7319 33.9527i −1.65429 1.20191i
\(799\) −1.11060 + 3.41808i −0.0392903 + 0.120923i
\(800\) 20.0327 + 61.6543i 0.708262 + 2.17981i
\(801\) −1.26364 + 0.918091i −0.0446486 + 0.0324391i
\(802\) −26.7715 −0.945335
\(803\) 0.0945254 + 6.61415i 0.00333573 + 0.233408i
\(804\) 58.9493 2.07898
\(805\) 33.5643 24.3859i 1.18299 0.859490i
\(806\) 3.18470 + 9.80150i 0.112176 + 0.345243i
\(807\) 0.482613 1.48533i 0.0169888 0.0522861i
\(808\) 15.4641 + 11.2353i 0.544024 + 0.395256i
\(809\) 8.96242 + 6.51158i 0.315102 + 0.228935i 0.734083 0.679060i \(-0.237612\pi\)
−0.418981 + 0.907995i \(0.637612\pi\)
\(810\) 3.32572 10.2355i 0.116854 0.359639i
\(811\) −3.48859 10.7368i −0.122501 0.377019i 0.870937 0.491395i \(-0.163513\pi\)
−0.993437 + 0.114376i \(0.963513\pi\)
\(812\) 9.79682 7.11781i 0.343801 0.249786i
\(813\) 2.01412 0.0706383
\(814\) −23.5147 31.4113i −0.824190 1.10096i
\(815\) −19.0686 −0.667945
\(816\) 4.29544 3.12082i 0.150370 0.109251i
\(817\) −8.56274 26.3534i −0.299572 0.921988i
\(818\) 17.4989 53.8561i 0.611836 1.88304i
\(819\) −2.35414 1.71038i −0.0822602 0.0597655i
\(820\) 30.3515 + 22.0517i 1.05992 + 0.770078i
\(821\) −7.03946 + 21.6652i −0.245679 + 0.756121i 0.749845 + 0.661613i \(0.230128\pi\)
−0.995524 + 0.0945082i \(0.969872\pi\)
\(822\) −9.15951 28.1901i −0.319475 0.983242i
\(823\) 37.1408 26.9844i 1.29465 0.940616i 0.294758 0.955572i \(-0.404761\pi\)
0.999888 + 0.0149563i \(0.00476092\pi\)
\(824\) −50.9747 −1.77579
\(825\) 24.7983 35.1784i 0.863367 1.22475i
\(826\) 69.4035 2.41486
\(827\) 31.2959 22.7378i 1.08826 0.790671i 0.109160 0.994024i \(-0.465184\pi\)
0.979105 + 0.203353i \(0.0651841\pi\)
\(828\) −4.61679 14.2090i −0.160445 0.493798i
\(829\) 15.3511 47.2458i 0.533166 1.64092i −0.214413 0.976743i \(-0.568784\pi\)
0.747579 0.664173i \(-0.231216\pi\)
\(830\) 150.464 + 109.319i 5.22269 + 3.79451i
\(831\) −7.73303 5.61837i −0.268256 0.194899i
\(832\) −0.317640 + 0.977594i −0.0110122 + 0.0338920i
\(833\) 0.351258 + 1.08106i 0.0121704 + 0.0374566i
\(834\) 47.0075 34.1529i 1.62774 1.18262i
\(835\) 60.0514 2.07817
\(836\) −109.081 + 37.1740i −3.77264 + 1.28569i
\(837\) −4.06017 −0.140340
\(838\) 30.6246 22.2501i 1.05791 0.768616i
\(839\) −16.3528 50.3288i −0.564561 1.73754i −0.669251 0.743037i \(-0.733385\pi\)
0.104689 0.994505i \(-0.466615\pi\)
\(840\) −23.6415 + 72.7611i −0.815710 + 2.51050i
\(841\) 22.7517 + 16.5301i 0.784542 + 0.570003i
\(842\) 25.2079 + 18.3146i 0.868721 + 0.631163i
\(843\) −1.21732 + 3.74654i −0.0419269 + 0.129038i
\(844\) −12.9870 39.9698i −0.447030 1.37582i
\(845\) −3.43019 + 2.49218i −0.118002 + 0.0857336i
\(846\) −11.7763 −0.404879
\(847\) −10.7571 30.1469i −0.369618 1.03586i
\(848\) 54.7511 1.88016
\(849\) −6.95545 + 5.05343i −0.238710 + 0.173433i
\(850\) 7.88521 + 24.2682i 0.270460 + 0.832392i
\(851\) 4.84322 14.9059i 0.166023 0.510968i
\(852\) −36.7576 26.7059i −1.25929 0.914930i
\(853\) −21.5047 15.6241i −0.736306 0.534958i 0.155246 0.987876i \(-0.450383\pi\)
−0.891552 + 0.452918i \(0.850383\pi\)
\(854\) −12.7682 + 39.2964i −0.436918 + 1.34469i
\(855\) −10.2466 31.5359i −0.350428 1.07851i
\(856\) 94.6150 68.7418i 3.23387 2.34955i
\(857\) 0.463785 0.0158426 0.00792130 0.999969i \(-0.497479\pi\)
0.00792130 + 0.999969i \(0.497479\pi\)
\(858\) −7.96856 + 2.71563i −0.272042 + 0.0927102i
\(859\) 35.7585 1.22006 0.610032 0.792376i \(-0.291156\pi\)
0.610032 + 0.792376i \(0.291156\pi\)
\(860\) −53.9985 + 39.2322i −1.84133 + 1.33781i
\(861\) 1.79080 + 5.51151i 0.0610302 + 0.187832i
\(862\) −4.54324 + 13.9826i −0.154743 + 0.476251i
\(863\) −3.78032 2.74656i −0.128684 0.0934941i 0.521582 0.853201i \(-0.325342\pi\)
−0.650265 + 0.759707i \(0.725342\pi\)
\(864\) 4.04143 + 2.93627i 0.137492 + 0.0998939i
\(865\) −24.4460 + 75.2371i −0.831189 + 2.55814i
\(866\) 12.1152 + 37.2869i 0.411693 + 1.26706i
\(867\) −13.2678 + 9.63962i −0.450598 + 0.327379i
\(868\) 52.4916 1.78168
\(869\) −11.8468 + 16.8056i −0.401875 + 0.570091i
\(870\) 10.0806 0.341763
\(871\) 10.7341 7.79875i 0.363710 0.264251i
\(872\) −20.5283 63.1796i −0.695176 2.13953i
\(873\) 2.79945 8.61582i 0.0947471 0.291601i
\(874\) −54.0039 39.2361i −1.82671 1.32718i
\(875\) −79.6234 57.8498i −2.69176 1.95568i
\(876\) 2.73827 8.42753i 0.0925176 0.284740i
\(877\) −14.7163 45.2921i −0.496934 1.52941i −0.813920 0.580976i \(-0.802671\pi\)
0.316986 0.948430i \(-0.397329\pi\)
\(878\) 53.2655 38.6997i 1.79763 1.30605i
\(879\) 26.7829 0.903365
\(880\) 57.7607 + 77.1576i 1.94711 + 2.60098i
\(881\) 33.2974 1.12182 0.560909 0.827877i \(-0.310452\pi\)
0.560909 + 0.827877i \(0.310452\pi\)
\(882\) −3.01326 + 2.18926i −0.101462 + 0.0737162i
\(883\) 7.72739 + 23.7825i 0.260047 + 0.800344i 0.992793 + 0.119841i \(0.0382385\pi\)
−0.732746 + 0.680503i \(0.761762\pi\)
\(884\) 1.06356 3.27331i 0.0357715 0.110093i
\(885\) 32.2317 + 23.4177i 1.08346 + 0.787177i
\(886\) −13.2988 9.66212i −0.446781 0.324605i
\(887\) 9.68079 29.7944i 0.325049 1.00040i −0.646369 0.763025i \(-0.723713\pi\)
0.971418 0.237374i \(-0.0762865\pi\)
\(888\) 8.93114 + 27.4872i 0.299710 + 0.922411i
\(889\) 0.340354 0.247282i 0.0114151 0.00829356i
\(890\) 16.8101 0.563476
\(891\) −0.0473944 3.31629i −0.00158777 0.111100i
\(892\) 60.1960 2.01551
\(893\) −29.3538 + 21.3268i −0.982286 + 0.713673i
\(894\) −7.38744 22.7362i −0.247073 0.760413i
\(895\) 19.4304 59.8006i 0.649487 1.99891i
\(896\) 29.6623 + 21.5509i 0.990948 + 0.719966i
\(897\) −2.72047 1.97653i −0.0908337 0.0659946i
\(898\) 19.6862 60.5880i 0.656938 2.02185i
\(899\) −1.17519 3.61686i −0.0391947 0.120629i
\(900\) −46.6455 + 33.8899i −1.55485 + 1.12966i
\(901\) 6.18813 0.206157
\(902\) 16.0178 + 4.95259i 0.533335 + 0.164903i
\(903\) −10.3102 −0.343101
\(904\) −21.9133 + 15.9209i −0.728825 + 0.529522i
\(905\) 16.7284 + 51.4847i 0.556071 + 1.71141i
\(906\) 2.23844 6.88922i 0.0743673 0.228879i
\(907\) 39.9052 + 28.9928i 1.32503 + 0.962692i 0.999855 + 0.0170385i \(0.00542379\pi\)
0.325177 + 0.945653i \(0.394576\pi\)
\(908\) −93.6690 68.0545i −3.10851 2.25847i
\(909\) −0.952554 + 2.93166i −0.0315942 + 0.0972370i
\(910\) 9.67742 + 29.7840i 0.320803 + 0.987331i
\(911\) 5.09260 3.69999i 0.168726 0.122586i −0.500218 0.865900i \(-0.666747\pi\)
0.668944 + 0.743313i \(0.266747\pi\)
\(912\) 53.6019 1.77494
\(913\) 54.7574 + 16.9306i 1.81220 + 0.560320i
\(914\) 14.4855 0.479137
\(915\) −19.1888 + 13.9415i −0.634362 + 0.460891i
\(916\) −37.7259 116.108i −1.24650 3.83632i
\(917\) 3.84860 11.8448i 0.127092 0.391149i
\(918\) 1.59077 + 1.15577i 0.0525034 + 0.0381459i
\(919\) −5.87612 4.26925i −0.193835 0.140830i 0.486635 0.873606i \(-0.338224\pi\)
−0.680470 + 0.732776i \(0.738224\pi\)
\(920\) −27.3204 + 84.0836i −0.900727 + 2.77215i
\(921\) −5.25577 16.1756i −0.173184 0.533004i
\(922\) 20.6576 15.0086i 0.680320 0.494282i
\(923\) −10.2263 −0.336601
\(924\) 0.612735 + 42.8744i 0.0201575 + 1.41046i
\(925\) −60.4848 −1.98873
\(926\) −40.3876 + 29.3433i −1.32722 + 0.964282i
\(927\) −2.54026 7.81813i −0.0834332 0.256781i
\(928\) −1.44591 + 4.45005i −0.0474643 + 0.146080i
\(929\) 8.07166 + 5.86440i 0.264822 + 0.192405i 0.712270 0.701905i \(-0.247667\pi\)
−0.447448 + 0.894310i \(0.647667\pi\)
\(930\) 35.3512 + 25.6842i 1.15921 + 0.842217i
\(931\) −3.54615 + 10.9139i −0.116220 + 0.357690i
\(932\) −7.12227 21.9201i −0.233298 0.718017i
\(933\) −19.8690 + 14.4357i −0.650483 + 0.472603i
\(934\) 59.0910 1.93352
\(935\) 6.52829 + 8.72059i 0.213498 + 0.285194i
\(936\) 6.20095 0.202685
\(937\) 24.2072 17.5876i 0.790815 0.574561i −0.117390 0.993086i \(-0.537453\pi\)
0.908205 + 0.418525i \(0.137453\pi\)
\(938\) −30.2834 93.2029i −0.988790 3.04318i
\(939\) −7.24905 + 22.3103i −0.236564 + 0.728068i
\(940\) 70.7063 + 51.3711i 2.30618 + 1.67554i
\(941\) −5.50383 3.99877i −0.179420 0.130356i 0.494450 0.869206i \(-0.335369\pi\)
−0.673870 + 0.738850i \(0.735369\pi\)
\(942\) −3.06470 + 9.43218i −0.0998533 + 0.307317i
\(943\) 2.06947 + 6.36916i 0.0673911 + 0.207408i
\(944\) −52.1031 + 37.8551i −1.69581 + 1.23208i
\(945\) −12.3377 −0.401346
\(946\) −17.1861 + 24.3798i −0.558768 + 0.792655i
\(947\) −25.6645 −0.833985 −0.416993 0.908910i \(-0.636916\pi\)
−0.416993 + 0.908910i \(0.636916\pi\)
\(948\) 22.2837 16.1901i 0.723742 0.525830i
\(949\) −0.616317 1.89683i −0.0200065 0.0615737i
\(950\) −79.6056 + 245.001i −2.58275 + 7.94888i
\(951\) 24.3500 + 17.6913i 0.789603 + 0.573680i
\(952\) −11.3083 8.21599i −0.366505 0.266282i
\(953\) 1.19456 3.67647i 0.0386955 0.119093i −0.929843 0.367957i \(-0.880057\pi\)
0.968538 + 0.248864i \(0.0800574\pi\)
\(954\) 6.26580 + 19.2841i 0.202863 + 0.624347i
\(955\) 11.4474 8.31703i 0.370429 0.269133i
\(956\) −9.26725 −0.299724
\(957\) 2.94048 1.00210i 0.0950523 0.0323932i
\(958\) 4.97675 0.160792
\(959\) −27.4903 + 19.9728i −0.887707 + 0.644957i
\(960\) 1.34678 + 4.14495i 0.0434670 + 0.133778i
\(961\) −4.48540 + 13.8046i −0.144690 + 0.445311i
\(962\) 9.57120 + 6.95388i 0.308588 + 0.224202i
\(963\) 15.2581 + 11.0857i 0.491687 + 0.357231i
\(964\) −10.6120 + 32.6603i −0.341788 + 1.05192i
\(965\) 24.6590 + 75.8925i 0.793800 + 2.44307i
\(966\) −20.0937 + 14.5989i −0.646504 + 0.469713i
\(967\) −12.4272 −0.399632 −0.199816 0.979833i \(-0.564034\pi\)
−0.199816 + 0.979833i \(0.564034\pi\)
\(968\) 56.3067 + 38.4998i 1.80976 + 1.23743i
\(969\) 6.05825 0.194619
\(970\) −78.8772 + 57.3076i −2.53259 + 1.84004i
\(971\) 12.8549 + 39.5632i 0.412532 + 1.26964i 0.914440 + 0.404722i \(0.132632\pi\)
−0.501908 + 0.864921i \(0.667368\pi\)
\(972\) −1.37295 + 4.22550i −0.0440374 + 0.135533i
\(973\) −53.8888 39.1525i −1.72760 1.25517i
\(974\) −3.39839 2.46907i −0.108891 0.0791142i
\(975\) −4.01016 + 12.3420i −0.128428 + 0.395261i
\(976\) −11.8482 36.4651i −0.379253 1.16722i
\(977\) 22.4162 16.2863i 0.717157 0.521045i −0.168317 0.985733i \(-0.553833\pi\)
0.885475 + 0.464688i \(0.153833\pi\)
\(978\) 11.4157 0.365033
\(979\) 4.90347 1.67107i 0.156716 0.0534077i
\(980\) 27.6420 0.882990
\(981\) 8.66702 6.29696i 0.276717 0.201046i
\(982\) −16.2557 50.0298i −0.518739 1.59652i
\(983\) 13.8777 42.7113i 0.442631 1.36228i −0.442429 0.896803i \(-0.645883\pi\)
0.885061 0.465476i \(-0.154117\pi\)
\(984\) −9.99094 7.25884i −0.318499 0.231403i
\(985\) −27.0530 19.6552i −0.861980 0.626265i
\(986\) −0.569135 + 1.75162i −0.0181249 + 0.0557828i
\(987\) 4.17180 + 12.8395i 0.132790 + 0.408685i
\(988\) 28.1105 20.4235i 0.894314 0.649757i
\(989\) −11.9145 −0.378860
\(990\) −20.5658 + 29.1742i −0.653625 + 0.927217i
\(991\) −27.2762 −0.866456 −0.433228 0.901284i \(-0.642626\pi\)
−0.433228 + 0.901284i \(0.642626\pi\)
\(992\) −16.4089 + 11.9217i −0.520982 + 0.378515i
\(993\) −3.46267 10.6570i −0.109885 0.338190i
\(994\) −23.3408 + 71.8356i −0.740325 + 2.27849i
\(995\) −22.7900 16.5579i −0.722490 0.524920i
\(996\) −62.1158 45.1298i −1.96821 1.42999i
\(997\) −12.0855 + 37.1952i −0.382750 + 1.17798i 0.555349 + 0.831618i \(0.312585\pi\)
−0.938099 + 0.346367i \(0.887415\pi\)
\(998\) −10.4523 32.1688i −0.330861 1.01829i
\(999\) −3.77072 + 2.73959i −0.119300 + 0.0866766i
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 429.2.n.c.157.1 28
11.2 odd 10 4719.2.a.bo.1.2 14
11.4 even 5 inner 429.2.n.c.235.1 yes 28
11.9 even 5 4719.2.a.bp.1.13 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.c.157.1 28 1.1 even 1 trivial
429.2.n.c.235.1 yes 28 11.4 even 5 inner
4719.2.a.bo.1.2 14 11.2 odd 10
4719.2.a.bp.1.13 14 11.9 even 5