Properties

Label 150.3.k.a.13.2
Level $150$
Weight $3$
Character 150.13
Analytic conductor $4.087$
Analytic rank $0$
Dimension $32$
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] = [150,3,Mod(13,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.k (of order \(20\), degree \(8\), 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: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 150.13
Dual form 150.3.k.a.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.39680 - 0.221232i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(1.90211 - 0.618034i) q^{4} +(1.98098 - 4.59083i) q^{5} +(-0.756934 + 2.32960i) q^{6} +(3.83711 - 3.83711i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\) \(q+(1.39680 - 0.221232i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(1.90211 - 0.618034i) q^{4} +(1.98098 - 4.59083i) q^{5} +(-0.756934 + 2.32960i) q^{6} +(3.83711 - 3.83711i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(1.75141 - 6.85074i) q^{10} +(10.4992 + 7.62811i) q^{11} +(-0.541905 + 3.42145i) q^{12} +(-0.104266 - 0.0165142i) q^{13} +(4.51079 - 6.20857i) q^{14} +(5.52716 + 6.66712i) q^{15} +(3.23607 - 2.35114i) q^{16} +(3.65779 + 7.17883i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(-3.30085 - 1.07251i) q^{19} +(0.930770 - 9.95659i) q^{20} +(2.90444 + 8.93894i) q^{21} +(16.3529 + 8.33220i) q^{22} +(-0.273325 - 1.72571i) q^{23} +4.89898i q^{24} +(-17.1514 - 18.1887i) q^{25} -0.149293 q^{26} +(5.13218 - 0.812857i) q^{27} +(4.92715 - 9.67008i) q^{28} +(-43.2716 + 14.0598i) q^{29} +(9.19533 + 8.08986i) q^{30} +(-3.47861 + 10.7061i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-20.0281 + 10.2048i) q^{33} +(6.69740 + 9.21818i) q^{34} +(-10.0143 - 25.2168i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(4.05555 - 25.6057i) q^{37} +(-4.84792 - 0.767834i) q^{38} +(0.107474 - 0.147925i) q^{39} +(-0.902613 - 14.1133i) q^{40} +(-51.0770 + 37.1096i) q^{41} +(6.03450 + 11.8434i) q^{42} +(-51.7744 - 51.7744i) q^{43} +(24.6851 + 8.02067i) q^{44} +(-14.6354 + 3.28731i) q^{45} +(-0.763562 - 2.35000i) q^{46} +(59.7583 + 30.4484i) q^{47} +(1.08381 + 6.84291i) q^{48} +19.5532i q^{49} +(-27.9810 - 21.6116i) q^{50} -13.9551 q^{51} +(-0.208533 + 0.0330284i) q^{52} +(-28.3235 + 55.5880i) q^{53} +(6.98881 - 2.27080i) q^{54} +(55.8181 - 33.0888i) q^{55} +(4.74293 - 14.5972i) q^{56} +(4.25075 - 4.25075i) q^{57} +(-57.3314 + 29.2118i) q^{58} +(39.9991 + 55.0540i) q^{59} +(14.6338 + 9.26564i) q^{60} +(35.3844 + 25.7082i) q^{61} +(-2.49041 + 15.7238i) q^{62} +(-16.0790 - 2.54667i) q^{63} +(4.70228 - 6.47214i) q^{64} +(-0.282364 + 0.445955i) q^{65} +(-25.7177 + 18.6850i) q^{66} +(-1.08774 - 2.13481i) q^{67} +(11.3943 + 11.3943i) q^{68} +(2.87815 + 0.935168i) q^{69} +(-19.5667 - 33.0074i) q^{70} +(-4.80591 - 14.7911i) q^{71} +(-7.56044 - 3.85224i) q^{72} +(-16.2922 - 102.865i) q^{73} -36.6634i q^{74} +(41.5568 - 12.1668i) q^{75} -6.94145 q^{76} +(69.5564 - 11.0167i) q^{77} +(0.117394 - 0.230399i) q^{78} +(31.5603 - 10.2545i) q^{79} +(-4.38308 - 19.5138i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-63.1346 + 63.1346i) q^{82} +(-89.8383 + 45.7749i) q^{83} +(11.0491 + 15.2078i) q^{84} +(40.2028 - 2.57116i) q^{85} +(-83.7728 - 60.8645i) q^{86} +(12.3279 - 77.8355i) q^{87} +(36.2546 + 5.74216i) q^{88} +(-60.8866 + 83.8032i) q^{89} +(-19.7154 + 7.82953i) q^{90} +(-0.463448 + 0.336715i) q^{91} +(-1.58644 - 3.11356i) q^{92} +(-13.7870 - 13.7870i) q^{93} +(90.2067 + 29.3099i) q^{94} +(-11.4627 + 13.0290i) q^{95} +(3.02774 + 9.31841i) q^{96} +(-60.6542 - 30.9048i) q^{97} +(4.32579 + 27.3119i) q^{98} -38.9331i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} + 20 q^{10} + 32 q^{11} - 16 q^{13} - 60 q^{14} + 32 q^{16} + 148 q^{17} - 96 q^{18} + 180 q^{19} + 40 q^{20} - 36 q^{21} + 48 q^{22} + 48 q^{23} - 160 q^{25} - 8 q^{26} - 56 q^{28} - 200 q^{29} - 120 q^{30} + 120 q^{31} + 128 q^{32} - 156 q^{33} - 100 q^{34} - 180 q^{35} - 48 q^{36} + 444 q^{37} + 32 q^{38} - 120 q^{39} - 304 q^{41} - 24 q^{42} + 216 q^{43} + 40 q^{44} + 60 q^{45} - 16 q^{46} + 32 q^{47} + 40 q^{50} + 24 q^{51} - 32 q^{52} - 340 q^{53} + 80 q^{55} + 72 q^{56} - 24 q^{57} - 192 q^{58} - 560 q^{59} + 312 q^{61} + 40 q^{62} + 24 q^{63} - 520 q^{65} - 108 q^{66} + 688 q^{67} - 16 q^{68} + 180 q^{69} + 80 q^{70} + 212 q^{71} + 48 q^{72} - 376 q^{73} + 120 q^{75} - 64 q^{76} - 176 q^{77} - 48 q^{78} + 440 q^{79} + 80 q^{80} + 72 q^{81} - 256 q^{82} - 96 q^{83} - 240 q^{85} + 408 q^{86} + 264 q^{87} + 184 q^{88} - 560 q^{89} - 516 q^{91} + 216 q^{92} + 48 q^{93} + 80 q^{94} + 520 q^{95} - 716 q^{97} - 108 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{19}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39680 0.221232i 0.698401 0.110616i
\(3\) −0.786335 + 1.54327i −0.262112 + 0.514423i
\(4\) 1.90211 0.618034i 0.475528 0.154508i
\(5\) 1.98098 4.59083i 0.396197 0.918166i
\(6\) −0.756934 + 2.32960i −0.126156 + 0.388267i
\(7\) 3.83711 3.83711i 0.548158 0.548158i −0.377749 0.925908i \(-0.623302\pi\)
0.925908 + 0.377749i \(0.123302\pi\)
\(8\) 2.52015 1.28408i 0.315018 0.160510i
\(9\) −1.76336 2.42705i −0.195928 0.269672i
\(10\) 1.75141 6.85074i 0.175141 0.685074i
\(11\) 10.4992 + 7.62811i 0.954472 + 0.693464i 0.951860 0.306532i \(-0.0991687\pi\)
0.00261153 + 0.999997i \(0.499169\pi\)
\(12\) −0.541905 + 3.42145i −0.0451587 + 0.285121i
\(13\) −0.104266 0.0165142i −0.00802050 0.00127032i 0.152423 0.988315i \(-0.451292\pi\)
−0.160443 + 0.987045i \(0.551292\pi\)
\(14\) 4.51079 6.20857i 0.322199 0.443469i
\(15\) 5.52716 + 6.66712i 0.368478 + 0.444475i
\(16\) 3.23607 2.35114i 0.202254 0.146946i
\(17\) 3.65779 + 7.17883i 0.215164 + 0.422284i 0.973210 0.229918i \(-0.0738457\pi\)
−0.758046 + 0.652201i \(0.773846\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) −3.30085 1.07251i −0.173729 0.0564480i 0.220861 0.975305i \(-0.429113\pi\)
−0.394590 + 0.918857i \(0.629113\pi\)
\(20\) 0.930770 9.95659i 0.0465385 0.497829i
\(21\) 2.90444 + 8.93894i 0.138307 + 0.425664i
\(22\) 16.3529 + 8.33220i 0.743312 + 0.378737i
\(23\) −0.273325 1.72571i −0.0118837 0.0750307i 0.981034 0.193837i \(-0.0620933\pi\)
−0.992917 + 0.118806i \(0.962093\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −17.1514 18.1887i −0.686056 0.727549i
\(26\) −0.149293 −0.00574204
\(27\) 5.13218 0.812857i 0.190081 0.0301058i
\(28\) 4.92715 9.67008i 0.175970 0.345360i
\(29\) −43.2716 + 14.0598i −1.49213 + 0.484821i −0.937710 0.347419i \(-0.887058\pi\)
−0.554415 + 0.832240i \(0.687058\pi\)
\(30\) 9.19533 + 8.08986i 0.306511 + 0.269662i
\(31\) −3.47861 + 10.7061i −0.112213 + 0.345357i −0.991356 0.131202i \(-0.958116\pi\)
0.879142 + 0.476559i \(0.158116\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) −20.0281 + 10.2048i −0.606912 + 0.309237i
\(34\) 6.69740 + 9.21818i 0.196982 + 0.271123i
\(35\) −10.0143 25.2168i −0.286121 0.720479i
\(36\) −4.85410 3.52671i −0.134836 0.0979642i
\(37\) 4.05555 25.6057i 0.109609 0.692047i −0.870288 0.492544i \(-0.836067\pi\)
0.979897 0.199503i \(-0.0639328\pi\)
\(38\) −4.84792 0.767834i −0.127577 0.0202062i
\(39\) 0.107474 0.147925i 0.00275575 0.00379296i
\(40\) −0.902613 14.1133i −0.0225653 0.352833i
\(41\) −51.0770 + 37.1096i −1.24578 + 0.905112i −0.997969 0.0636964i \(-0.979711\pi\)
−0.247811 + 0.968808i \(0.579711\pi\)
\(42\) 6.03450 + 11.8434i 0.143679 + 0.281985i
\(43\) −51.7744 51.7744i −1.20406 1.20406i −0.972922 0.231135i \(-0.925756\pi\)
−0.231135 0.972922i \(-0.574244\pi\)
\(44\) 24.6851 + 8.02067i 0.561024 + 0.182288i
\(45\) −14.6354 + 3.28731i −0.325230 + 0.0730514i
\(46\) −0.763562 2.35000i −0.0165992 0.0510870i
\(47\) 59.7583 + 30.4484i 1.27145 + 0.647838i 0.953821 0.300376i \(-0.0971123\pi\)
0.317632 + 0.948214i \(0.397112\pi\)
\(48\) 1.08381 + 6.84291i 0.0225794 + 0.142561i
\(49\) 19.5532i 0.399045i
\(50\) −27.9810 21.6116i −0.559621 0.432232i
\(51\) −13.9551 −0.273630
\(52\) −0.208533 + 0.0330284i −0.00401025 + 0.000635161i
\(53\) −28.3235 + 55.5880i −0.534406 + 1.04883i 0.453131 + 0.891444i \(0.350307\pi\)
−0.987537 + 0.157387i \(0.949693\pi\)
\(54\) 6.98881 2.27080i 0.129422 0.0420519i
\(55\) 55.8181 33.0888i 1.01487 0.601615i
\(56\) 4.74293 14.5972i 0.0846951 0.260665i
\(57\) 4.25075 4.25075i 0.0745746 0.0745746i
\(58\) −57.3314 + 29.2118i −0.988473 + 0.503652i
\(59\) 39.9991 + 55.0540i 0.677950 + 0.933118i 0.999907 0.0136359i \(-0.00434057\pi\)
−0.321957 + 0.946754i \(0.604341\pi\)
\(60\) 14.6338 + 9.26564i 0.243897 + 0.154427i
\(61\) 35.3844 + 25.7082i 0.580071 + 0.421447i 0.838750 0.544517i \(-0.183287\pi\)
−0.258678 + 0.965963i \(0.583287\pi\)
\(62\) −2.49041 + 15.7238i −0.0401679 + 0.253610i
\(63\) −16.0790 2.54667i −0.255223 0.0404233i
\(64\) 4.70228 6.47214i 0.0734732 0.101127i
\(65\) −0.282364 + 0.445955i −0.00434406 + 0.00686084i
\(66\) −25.7177 + 18.6850i −0.389661 + 0.283106i
\(67\) −1.08774 2.13481i −0.0162349 0.0318629i 0.882747 0.469849i \(-0.155692\pi\)
−0.898982 + 0.437986i \(0.855692\pi\)
\(68\) 11.3943 + 11.3943i 0.167563 + 0.167563i
\(69\) 2.87815 + 0.935168i 0.0417123 + 0.0135532i
\(70\) −19.5667 33.0074i −0.279524 0.471534i
\(71\) −4.80591 14.7911i −0.0676889 0.208325i 0.911491 0.411321i \(-0.134932\pi\)
−0.979180 + 0.202995i \(0.934932\pi\)
\(72\) −7.56044 3.85224i −0.105006 0.0535033i
\(73\) −16.2922 102.865i −0.223181 1.40911i −0.803784 0.594921i \(-0.797183\pi\)
0.580603 0.814187i \(-0.302817\pi\)
\(74\) 36.6634i 0.495451i
\(75\) 41.5568 12.1668i 0.554091 0.162224i
\(76\) −6.94145 −0.0913348
\(77\) 69.5564 11.0167i 0.903330 0.143073i
\(78\) 0.117394 0.230399i 0.00150506 0.00295384i
\(79\) 31.5603 10.2545i 0.399497 0.129804i −0.102376 0.994746i \(-0.532645\pi\)
0.501873 + 0.864941i \(0.332645\pi\)
\(80\) −4.38308 19.5138i −0.0547885 0.243923i
\(81\) −2.78115 + 8.55951i −0.0343352 + 0.105673i
\(82\) −63.1346 + 63.1346i −0.769934 + 0.769934i
\(83\) −89.8383 + 45.7749i −1.08239 + 0.551505i −0.901844 0.432062i \(-0.857786\pi\)
−0.180545 + 0.983567i \(0.557786\pi\)
\(84\) 11.0491 + 15.2078i 0.131537 + 0.181046i
\(85\) 40.2028 2.57116i 0.472974 0.0302489i
\(86\) −83.7728 60.8645i −0.974102 0.707727i
\(87\) 12.3279 77.8355i 0.141700 0.894661i
\(88\) 36.2546 + 5.74216i 0.411984 + 0.0652519i
\(89\) −60.8866 + 83.8032i −0.684119 + 0.941609i −0.999974 0.00719814i \(-0.997709\pi\)
0.315855 + 0.948808i \(0.397709\pi\)
\(90\) −19.7154 + 7.82953i −0.219060 + 0.0869948i
\(91\) −0.463448 + 0.336715i −0.00509284 + 0.00370016i
\(92\) −1.58644 3.11356i −0.0172439 0.0338431i
\(93\) −13.7870 13.7870i −0.148247 0.148247i
\(94\) 90.2067 + 29.3099i 0.959645 + 0.311808i
\(95\) −11.4627 + 13.0290i −0.120660 + 0.137148i
\(96\) 3.02774 + 9.31841i 0.0315389 + 0.0970668i
\(97\) −60.6542 30.9048i −0.625301 0.318607i 0.112473 0.993655i \(-0.464123\pi\)
−0.737774 + 0.675048i \(0.764123\pi\)
\(98\) 4.32579 + 27.3119i 0.0441407 + 0.278693i
\(99\) 38.9331i 0.393264i
\(100\) −43.8651 23.9969i −0.438651 0.239969i
\(101\) 60.0539 0.594593 0.297297 0.954785i \(-0.403915\pi\)
0.297297 + 0.954785i \(0.403915\pi\)
\(102\) −19.4925 + 3.08731i −0.191103 + 0.0302678i
\(103\) 55.5180 108.960i 0.539009 1.05787i −0.447519 0.894274i \(-0.647692\pi\)
0.986528 0.163591i \(-0.0523077\pi\)
\(104\) −0.283972 + 0.0922682i −0.00273050 + 0.000887194i
\(105\) 46.7908 + 4.37413i 0.445627 + 0.0416584i
\(106\) −27.2645 + 83.9115i −0.257212 + 0.791618i
\(107\) 133.194 133.194i 1.24480 1.24480i 0.286818 0.957985i \(-0.407402\pi\)
0.957985 0.286818i \(-0.0925975\pi\)
\(108\) 9.25961 4.71801i 0.0857371 0.0436853i
\(109\) 86.0632 + 118.456i 0.789571 + 1.08675i 0.994161 + 0.107903i \(0.0344136\pi\)
−0.204591 + 0.978848i \(0.565586\pi\)
\(110\) 70.6465 58.5672i 0.642241 0.532430i
\(111\) 36.3275 + 26.3935i 0.327275 + 0.237779i
\(112\) 3.39556 21.4387i 0.0303175 0.191417i
\(113\) 101.376 + 16.0563i 0.897128 + 0.142091i 0.587935 0.808908i \(-0.299941\pi\)
0.309193 + 0.950999i \(0.399941\pi\)
\(114\) 4.99706 6.87786i 0.0438338 0.0603321i
\(115\) −8.46387 2.16381i −0.0735989 0.0188157i
\(116\) −73.6181 + 53.4867i −0.634639 + 0.461092i
\(117\) 0.143778 + 0.282180i 0.00122887 + 0.00241180i
\(118\) 68.0505 + 68.0505i 0.576699 + 0.576699i
\(119\) 41.5813 + 13.5106i 0.349423 + 0.113534i
\(120\) 22.4904 + 9.70480i 0.187420 + 0.0808734i
\(121\) 14.6539 + 45.1001i 0.121107 + 0.372728i
\(122\) 55.1124 + 28.0812i 0.451741 + 0.230174i
\(123\) −17.1065 108.006i −0.139077 0.878098i
\(124\) 22.5141i 0.181565i
\(125\) −117.478 + 42.7075i −0.939824 + 0.341660i
\(126\) −23.0227 −0.182719
\(127\) 69.8635 11.0653i 0.550106 0.0871282i 0.124807 0.992181i \(-0.460169\pi\)
0.425299 + 0.905053i \(0.360169\pi\)
\(128\) 5.13632 10.0806i 0.0401275 0.0787546i
\(129\) 120.614 39.1898i 0.934991 0.303797i
\(130\) −0.295747 + 0.685379i −0.00227498 + 0.00527214i
\(131\) 34.2300 105.349i 0.261298 0.804192i −0.731225 0.682136i \(-0.761051\pi\)
0.992523 0.122056i \(-0.0389488\pi\)
\(132\) −31.7888 + 31.7888i −0.240824 + 0.240824i
\(133\) −16.7811 + 8.55039i −0.126174 + 0.0642887i
\(134\) −1.99165 2.74127i −0.0148630 0.0204572i
\(135\) 6.43508 25.1712i 0.0476673 0.186453i
\(136\) 18.4364 + 13.3948i 0.135561 + 0.0984912i
\(137\) 31.3499 197.935i 0.228831 1.44478i −0.559141 0.829072i \(-0.688869\pi\)
0.787972 0.615711i \(-0.211131\pi\)
\(138\) 4.22710 + 0.669507i 0.0306311 + 0.00485150i
\(139\) −130.858 + 180.111i −0.941427 + 1.29576i 0.0138042 + 0.999905i \(0.495606\pi\)
−0.955232 + 0.295859i \(0.904394\pi\)
\(140\) −34.6331 41.7760i −0.247379 0.298400i
\(141\) −93.9800 + 68.2805i −0.666525 + 0.484259i
\(142\) −9.98517 19.5970i −0.0703181 0.138007i
\(143\) −0.968741 0.968741i −0.00677441 0.00677441i
\(144\) −11.4127 3.70820i −0.0792547 0.0257514i
\(145\) −21.1743 + 226.505i −0.146030 + 1.56210i
\(146\) −45.5140 140.078i −0.311739 0.959435i
\(147\) −30.1758 15.3754i −0.205278 0.104594i
\(148\) −8.11110 51.2115i −0.0548047 0.346023i
\(149\) 166.223i 1.11559i −0.829978 0.557797i \(-0.811647\pi\)
0.829978 0.557797i \(-0.188353\pi\)
\(150\) 55.3550 26.1883i 0.369033 0.174589i
\(151\) −7.28196 −0.0482249 −0.0241124 0.999709i \(-0.507676\pi\)
−0.0241124 + 0.999709i \(0.507676\pi\)
\(152\) −9.69583 + 1.53567i −0.0637884 + 0.0101031i
\(153\) 10.9734 21.5365i 0.0717215 0.140761i
\(154\) 94.7193 30.7762i 0.615061 0.199845i
\(155\) 42.2586 + 37.1783i 0.272636 + 0.239860i
\(156\) 0.113005 0.347794i 0.000724391 0.00222945i
\(157\) −190.713 + 190.713i −1.21474 + 1.21474i −0.245284 + 0.969451i \(0.578881\pi\)
−0.969451 + 0.245284i \(0.921119\pi\)
\(158\) 41.8148 21.3057i 0.264651 0.134846i
\(159\) −63.5155 87.4216i −0.399469 0.549821i
\(160\) −10.4394 26.2873i −0.0652461 0.164295i
\(161\) −7.67050 5.57294i −0.0476428 0.0346145i
\(162\) −1.99109 + 12.5712i −0.0122907 + 0.0776001i
\(163\) 144.723 + 22.9219i 0.887871 + 0.140625i 0.583678 0.811985i \(-0.301613\pi\)
0.304193 + 0.952610i \(0.401613\pi\)
\(164\) −74.2192 + 102.154i −0.452556 + 0.622890i
\(165\) 7.17324 + 112.161i 0.0434742 + 0.679764i
\(166\) −115.359 + 83.8136i −0.694937 + 0.504901i
\(167\) 102.484 + 201.137i 0.613678 + 1.20441i 0.963529 + 0.267605i \(0.0862324\pi\)
−0.349851 + 0.936806i \(0.613768\pi\)
\(168\) 18.7979 + 18.7979i 0.111892 + 0.111892i
\(169\) −160.718 52.2204i −0.950994 0.308997i
\(170\) 55.5865 12.4855i 0.326980 0.0734443i
\(171\) 3.21754 + 9.90256i 0.0188160 + 0.0579097i
\(172\) −130.479 66.4824i −0.758600 0.386526i
\(173\) −5.66415 35.7620i −0.0327408 0.206717i 0.965895 0.258934i \(-0.0833712\pi\)
−0.998636 + 0.0522170i \(0.983371\pi\)
\(174\) 111.448i 0.640506i
\(175\) −135.604 3.98032i −0.774879 0.0227447i
\(176\) 51.9108 0.294948
\(177\) −116.416 + 18.4384i −0.657716 + 0.104172i
\(178\) −66.5066 + 130.527i −0.373633 + 0.733296i
\(179\) −265.756 + 86.3494i −1.48467 + 0.482399i −0.935505 0.353314i \(-0.885055\pi\)
−0.549167 + 0.835713i \(0.685055\pi\)
\(180\) −25.8064 + 15.2980i −0.143369 + 0.0849888i
\(181\) −36.6493 + 112.795i −0.202482 + 0.623177i 0.797325 + 0.603550i \(0.206248\pi\)
−0.999807 + 0.0196265i \(0.993752\pi\)
\(182\) −0.572854 + 0.572854i −0.00314755 + 0.00314755i
\(183\) −67.4987 + 34.3923i −0.368845 + 0.187936i
\(184\) −2.90476 3.99806i −0.0157867 0.0217286i
\(185\) −109.517 69.3429i −0.591986 0.374826i
\(186\) −22.3078 16.2076i −0.119934 0.0871375i
\(187\) −16.3570 + 103.274i −0.0874705 + 0.552267i
\(188\) 132.485 + 20.9836i 0.704708 + 0.111615i
\(189\) 16.5737 22.8118i 0.0876916 0.120697i
\(190\) −13.1286 + 20.7349i −0.0690981 + 0.109131i
\(191\) 268.636 195.176i 1.40647 1.02186i 0.412650 0.910889i \(-0.364603\pi\)
0.993823 0.110973i \(-0.0353969\pi\)
\(192\) 6.29068 + 12.3461i 0.0327639 + 0.0643029i
\(193\) −157.194 157.194i −0.814476 0.814476i 0.170825 0.985301i \(-0.445357\pi\)
−0.985301 + 0.170825i \(0.945357\pi\)
\(194\) −91.5590 29.7493i −0.471954 0.153347i
\(195\) −0.466196 0.786433i −0.00239075 0.00403299i
\(196\) 12.0845 + 37.1924i 0.0616558 + 0.189757i
\(197\) −258.292 131.607i −1.31113 0.668054i −0.348102 0.937457i \(-0.613174\pi\)
−0.963028 + 0.269403i \(0.913174\pi\)
\(198\) −8.61325 54.3819i −0.0435012 0.274656i
\(199\) 330.142i 1.65901i −0.558501 0.829504i \(-0.688623\pi\)
0.558501 0.829504i \(-0.311377\pi\)
\(200\) −66.5798 23.8145i −0.332899 0.119072i
\(201\) 4.14992 0.0206464
\(202\) 83.8834 13.2858i 0.415264 0.0657714i
\(203\) −112.089 + 219.987i −0.552162 + 1.08368i
\(204\) −26.5442 + 8.62473i −0.130119 + 0.0422781i
\(205\) 69.1810 + 307.999i 0.337469 + 1.50243i
\(206\) 53.4422 164.478i 0.259428 0.798437i
\(207\) −3.70641 + 3.70641i −0.0179053 + 0.0179053i
\(208\) −0.376240 + 0.191704i −0.00180885 + 0.000921654i
\(209\) −26.4751 36.4398i −0.126675 0.174353i
\(210\) 66.3252 4.24181i 0.315834 0.0201991i
\(211\) −0.959337 0.696999i −0.00454662 0.00330331i 0.585510 0.810665i \(-0.300894\pi\)
−0.590056 + 0.807362i \(0.700894\pi\)
\(212\) −19.5192 + 123.240i −0.0920719 + 0.581319i
\(213\) 26.6057 + 4.21392i 0.124909 + 0.0197837i
\(214\) 156.579 215.512i 0.731677 1.00707i
\(215\) −340.252 + 135.123i −1.58257 + 0.628480i
\(216\) 11.8901 8.63864i 0.0550466 0.0399937i
\(217\) 27.7325 + 54.4282i 0.127800 + 0.250821i
\(218\) 146.419 + 146.419i 0.671649 + 0.671649i
\(219\) 171.559 + 55.7430i 0.783376 + 0.254534i
\(220\) 85.7223 97.4361i 0.389647 0.442891i
\(221\) −0.262833 0.808916i −0.00118929 0.00366025i
\(222\) 56.5814 + 28.8297i 0.254871 + 0.129863i
\(223\) 1.76173 + 11.1231i 0.00790014 + 0.0498795i 0.991323 0.131445i \(-0.0419616\pi\)
−0.983423 + 0.181324i \(0.941962\pi\)
\(224\) 30.6969i 0.137040i
\(225\) −13.9009 + 73.7005i −0.0617819 + 0.327558i
\(226\) 145.154 0.642273
\(227\) 147.933 23.4302i 0.651686 0.103217i 0.178167 0.984000i \(-0.442983\pi\)
0.473519 + 0.880783i \(0.342983\pi\)
\(228\) 5.45830 10.7125i 0.0239399 0.0469847i
\(229\) 42.0859 13.6745i 0.183781 0.0597142i −0.215681 0.976464i \(-0.569197\pi\)
0.399462 + 0.916750i \(0.369197\pi\)
\(230\) −12.3011 1.14994i −0.0534828 0.00499972i
\(231\) −37.6930 + 116.007i −0.163173 + 0.502195i
\(232\) −90.9970 + 90.9970i −0.392228 + 0.392228i
\(233\) −80.2406 + 40.8846i −0.344380 + 0.175471i −0.617622 0.786475i \(-0.711904\pi\)
0.273242 + 0.961945i \(0.411904\pi\)
\(234\) 0.263257 + 0.362342i 0.00112503 + 0.00154847i
\(235\) 258.163 214.022i 1.09857 0.910733i
\(236\) 110.108 + 79.9981i 0.466559 + 0.338975i
\(237\) −8.99140 + 56.7695i −0.0379384 + 0.239534i
\(238\) 61.0698 + 9.67251i 0.256596 + 0.0406408i
\(239\) −215.012 + 295.939i −0.899633 + 1.23824i 0.0709524 + 0.997480i \(0.477396\pi\)
−0.970585 + 0.240758i \(0.922604\pi\)
\(240\) 33.5616 + 8.58011i 0.139840 + 0.0357505i
\(241\) 382.121 277.627i 1.58556 1.15198i 0.675618 0.737252i \(-0.263877\pi\)
0.909946 0.414727i \(-0.136123\pi\)
\(242\) 30.4462 + 59.7540i 0.125811 + 0.246917i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 83.1936 + 27.0312i 0.340957 + 0.110784i
\(245\) 89.7653 + 38.7346i 0.366389 + 0.158100i
\(246\) −47.7887 147.079i −0.194263 0.597881i
\(247\) 0.326457 + 0.166338i 0.00132169 + 0.000673433i
\(248\) 4.98082 + 31.4477i 0.0200840 + 0.126805i
\(249\) 174.639i 0.701362i
\(250\) −154.645 + 85.6438i −0.618581 + 0.342575i
\(251\) 100.019 0.398481 0.199241 0.979951i \(-0.436152\pi\)
0.199241 + 0.979951i \(0.436152\pi\)
\(252\) −32.1581 + 5.09334i −0.127611 + 0.0202117i
\(253\) 10.2942 20.2035i 0.0406884 0.0798556i
\(254\) 95.1375 30.9120i 0.374557 0.121701i
\(255\) −27.6449 + 64.0655i −0.108411 + 0.251237i
\(256\) 4.94427 15.2169i 0.0193136 0.0594410i
\(257\) 129.713 129.713i 0.504718 0.504718i −0.408182 0.912900i \(-0.633837\pi\)
0.912900 + 0.408182i \(0.133837\pi\)
\(258\) 159.804 81.4240i 0.619394 0.315597i
\(259\) −82.6904 113.814i −0.319268 0.439435i
\(260\) −0.261473 + 1.02277i −0.00100567 + 0.00393372i
\(261\) 110.427 + 80.2300i 0.423093 + 0.307395i
\(262\) 24.5060 154.725i 0.0935343 0.590552i
\(263\) 454.363 + 71.9641i 1.72762 + 0.273628i 0.939662 0.342105i \(-0.111140\pi\)
0.787955 + 0.615733i \(0.211140\pi\)
\(264\) −37.3699 + 51.4353i −0.141553 + 0.194831i
\(265\) 199.087 + 240.147i 0.751270 + 0.906217i
\(266\) −21.5482 + 15.6557i −0.0810084 + 0.0588561i
\(267\) −81.4536 159.862i −0.305070 0.598733i
\(268\) −3.38839 3.38839i −0.0126433 0.0126433i
\(269\) −140.238 45.5661i −0.521331 0.169391i 0.0365185 0.999333i \(-0.488373\pi\)
−0.557849 + 0.829942i \(0.688373\pi\)
\(270\) 3.41987 36.5828i 0.0126662 0.135492i
\(271\) −58.1538 178.979i −0.214590 0.660439i −0.999182 0.0404279i \(-0.987128\pi\)
0.784593 0.620012i \(-0.212872\pi\)
\(272\) 28.7153 + 14.6312i 0.105571 + 0.0537911i
\(273\) −0.155216 0.979996i −0.000568557 0.00358973i
\(274\) 283.412i 1.03435i
\(275\) −41.3303 321.800i −0.150292 1.17018i
\(276\) 6.05254 0.0219295
\(277\) −169.401 + 26.8306i −0.611558 + 0.0968612i −0.454528 0.890733i \(-0.650192\pi\)
−0.157030 + 0.987594i \(0.550192\pi\)
\(278\) −142.937 + 280.530i −0.514162 + 1.00910i
\(279\) 32.1182 10.4358i 0.115119 0.0374044i
\(280\) −57.6177 50.6909i −0.205777 0.181039i
\(281\) 151.657 466.753i 0.539706 1.66104i −0.193550 0.981090i \(-0.562000\pi\)
0.733256 0.679953i \(-0.238000\pi\)
\(282\) −116.166 + 116.166i −0.411935 + 0.411935i
\(283\) −175.683 + 89.5151i −0.620789 + 0.316308i −0.735947 0.677039i \(-0.763263\pi\)
0.115158 + 0.993347i \(0.463263\pi\)
\(284\) −18.2828 25.1641i −0.0643760 0.0886060i
\(285\) −11.0938 27.9351i −0.0389256 0.0980180i
\(286\) −1.56746 1.13882i −0.00548062 0.00398190i
\(287\) −53.5944 + 338.381i −0.186740 + 1.17903i
\(288\) −16.7616 2.65478i −0.0582001 0.00921799i
\(289\) 131.714 181.289i 0.455757 0.627296i
\(290\) 20.5338 + 321.067i 0.0708061 + 1.10713i
\(291\) 95.3889 69.3041i 0.327797 0.238159i
\(292\) −94.5636 185.592i −0.323848 0.635587i
\(293\) 128.886 + 128.886i 0.439884 + 0.439884i 0.891973 0.452089i \(-0.149321\pi\)
−0.452089 + 0.891973i \(0.649321\pi\)
\(294\) −45.5512 14.8005i −0.154936 0.0503417i
\(295\) 331.981 74.5677i 1.12536 0.252772i
\(296\) −22.6592 69.7378i −0.0765513 0.235601i
\(297\) 60.0843 + 30.6145i 0.202304 + 0.103079i
\(298\) −36.7739 232.181i −0.123402 0.779132i
\(299\) 0.184447i 0.000616879i
\(300\) 71.5263 48.8261i 0.238421 0.162754i
\(301\) −397.328 −1.32003
\(302\) −10.1715 + 1.61100i −0.0336803 + 0.00533444i
\(303\) −47.2225 + 92.6793i −0.155850 + 0.305872i
\(304\) −13.2034 + 4.29005i −0.0434323 + 0.0141120i
\(305\) 188.118 111.516i 0.616780 0.365626i
\(306\) 10.5631 32.5099i 0.0345199 0.106241i
\(307\) −110.355 + 110.355i −0.359463 + 0.359463i −0.863615 0.504152i \(-0.831805\pi\)
0.504152 + 0.863615i \(0.331805\pi\)
\(308\) 125.495 63.9432i 0.407453 0.207608i
\(309\) 124.499 + 171.358i 0.402910 + 0.554557i
\(310\) 67.2520 + 42.5817i 0.216942 + 0.137360i
\(311\) 18.9026 + 13.7335i 0.0607800 + 0.0441593i 0.617760 0.786366i \(-0.288040\pi\)
−0.556980 + 0.830526i \(0.688040\pi\)
\(312\) 0.0809026 0.510799i 0.000259303 0.00163718i
\(313\) 523.164 + 82.8610i 1.67145 + 0.264732i 0.919098 0.394029i \(-0.128919\pi\)
0.752353 + 0.658761i \(0.228919\pi\)
\(314\) −224.197 + 308.581i −0.714003 + 0.982742i
\(315\) −43.5437 + 68.7712i −0.138234 + 0.218321i
\(316\) 53.6935 39.0106i 0.169916 0.123451i
\(317\) −11.0750 21.7360i −0.0349370 0.0685678i 0.872878 0.487938i \(-0.162251\pi\)
−0.907815 + 0.419370i \(0.862251\pi\)
\(318\) −108.059 108.059i −0.339808 0.339808i
\(319\) −561.567 182.464i −1.76040 0.571988i
\(320\) −20.3973 34.4086i −0.0637416 0.107527i
\(321\) 100.819 + 310.289i 0.314078 + 0.966632i
\(322\) −11.9471 6.08734i −0.0371027 0.0189048i
\(323\) −4.37447 27.6193i −0.0135432 0.0855086i
\(324\) 18.0000i 0.0555556i
\(325\) 1.48794 + 2.17971i 0.00457829 + 0.00670681i
\(326\) 207.220 0.635646
\(327\) −250.484 + 39.6727i −0.766005 + 0.121323i
\(328\) −81.0698 + 159.109i −0.247164 + 0.485087i
\(329\) 346.133 112.465i 1.05208 0.341840i
\(330\) 34.8332 + 155.080i 0.105555 + 0.469939i
\(331\) 2.96801 9.13460i 0.00896680 0.0275970i −0.946473 0.322783i \(-0.895382\pi\)
0.955440 + 0.295186i \(0.0953816\pi\)
\(332\) −142.592 + 142.592i −0.429494 + 0.429494i
\(333\) −69.2978 + 35.3090i −0.208101 + 0.106033i
\(334\) 187.648 + 258.275i 0.561820 + 0.773279i
\(335\) −11.9554 + 0.764602i −0.0356876 + 0.00228239i
\(336\) 30.4157 + 22.0983i 0.0905228 + 0.0657687i
\(337\) 36.5189 230.571i 0.108365 0.684187i −0.872370 0.488845i \(-0.837418\pi\)
0.980735 0.195342i \(-0.0625817\pi\)
\(338\) −236.044 37.3857i −0.698355 0.110609i
\(339\) −104.494 + 143.824i −0.308243 + 0.424260i
\(340\) 74.8812 29.7373i 0.220239 0.0874627i
\(341\) −118.190 + 85.8698i −0.346597 + 0.251818i
\(342\) 6.68503 + 13.1201i 0.0195469 + 0.0383629i
\(343\) 263.046 + 263.046i 0.766898 + 0.766898i
\(344\) −196.962 63.9967i −0.572563 0.186037i
\(345\) 9.99477 11.3605i 0.0289704 0.0329291i
\(346\) −15.8234 48.6994i −0.0457324 0.140750i
\(347\) −140.354 71.5141i −0.404479 0.206092i 0.239902 0.970797i \(-0.422885\pi\)
−0.644381 + 0.764705i \(0.722885\pi\)
\(348\) −24.6559 155.671i −0.0708502 0.447330i
\(349\) 3.44211i 0.00986278i −0.999988 0.00493139i \(-0.998430\pi\)
0.999988 0.00493139i \(-0.00156972\pi\)
\(350\) −190.292 + 24.4402i −0.543693 + 0.0698290i
\(351\) −0.548538 −0.00156279
\(352\) 72.5092 11.4843i 0.205992 0.0326259i
\(353\) 42.7528 83.9071i 0.121113 0.237697i −0.822488 0.568782i \(-0.807415\pi\)
0.943601 + 0.331085i \(0.107415\pi\)
\(354\) −158.531 + 51.5097i −0.447827 + 0.145508i
\(355\) −77.4238 7.23779i −0.218095 0.0203881i
\(356\) −64.0200 + 197.033i −0.179831 + 0.553464i
\(357\) −53.5473 + 53.5473i −0.149992 + 0.149992i
\(358\) −352.106 + 179.407i −0.983535 + 0.501136i
\(359\) 32.6765 + 44.9754i 0.0910210 + 0.125280i 0.852099 0.523381i \(-0.175329\pi\)
−0.761078 + 0.648661i \(0.775329\pi\)
\(360\) −32.6621 + 27.0775i −0.0907280 + 0.0752152i
\(361\) −282.310 205.110i −0.782022 0.568172i
\(362\) −26.2380 + 165.660i −0.0724807 + 0.457625i
\(363\) −81.1244 12.8488i −0.223483 0.0353963i
\(364\) −0.673430 + 0.926897i −0.00185008 + 0.00254642i
\(365\) −504.510 128.979i −1.38222 0.353367i
\(366\) −86.6736 + 62.9721i −0.236813 + 0.172055i
\(367\) 56.5884 + 111.061i 0.154192 + 0.302619i 0.955161 0.296087i \(-0.0956819\pi\)
−0.800969 + 0.598706i \(0.795682\pi\)
\(368\) −4.94187 4.94187i −0.0134290 0.0134290i
\(369\) 180.134 + 58.5290i 0.488167 + 0.158615i
\(370\) −168.315 72.6295i −0.454906 0.196296i
\(371\) 104.617 + 321.978i 0.281986 + 0.867864i
\(372\) −34.7452 17.7036i −0.0934012 0.0475903i
\(373\) −76.2040 481.133i −0.204300 1.28990i −0.850192 0.526473i \(-0.823514\pi\)
0.645892 0.763429i \(-0.276486\pi\)
\(374\) 147.872i 0.395379i
\(375\) 26.4678 214.882i 0.0705807 0.573020i
\(376\) 189.698 0.504515
\(377\) 4.74397 0.751370i 0.0125835 0.00199302i
\(378\) 18.1035 35.5301i 0.0478929 0.0939951i
\(379\) 21.8703 7.10610i 0.0577053 0.0187496i −0.280022 0.959994i \(-0.590342\pi\)
0.337727 + 0.941244i \(0.390342\pi\)
\(380\) −13.7509 + 31.8670i −0.0361866 + 0.0838605i
\(381\) −37.8594 + 116.519i −0.0993684 + 0.305824i
\(382\) 332.053 332.053i 0.869249 0.869249i
\(383\) −569.717 + 290.285i −1.48751 + 0.757925i −0.993745 0.111669i \(-0.964380\pi\)
−0.493767 + 0.869594i \(0.664380\pi\)
\(384\) 11.5182 + 15.8534i 0.0299953 + 0.0412850i
\(385\) 87.2146 341.145i 0.226532 0.886092i
\(386\) −254.345 184.792i −0.658925 0.478737i
\(387\) −34.3624 + 216.956i −0.0887918 + 0.560610i
\(388\) −134.471 21.2982i −0.346576 0.0548922i
\(389\) 242.288 333.481i 0.622849 0.857279i −0.374707 0.927143i \(-0.622257\pi\)
0.997556 + 0.0698647i \(0.0222568\pi\)
\(390\) −0.825167 0.995354i −0.00211581 0.00255219i
\(391\) 11.3888 8.27443i 0.0291273 0.0211622i
\(392\) 25.1078 + 49.2769i 0.0640506 + 0.125706i
\(393\) 135.666 + 135.666i 0.345206 + 0.345206i
\(394\) −389.899 126.686i −0.989591 0.321538i
\(395\) 15.4435 165.202i 0.0390975 0.418232i
\(396\) −24.0620 74.0552i −0.0607626 0.187008i
\(397\) −80.1470 40.8370i −0.201882 0.102864i 0.350127 0.936702i \(-0.386138\pi\)
−0.552009 + 0.833838i \(0.686138\pi\)
\(398\) −73.0380 461.144i −0.183513 1.15865i
\(399\) 32.6212i 0.0817574i
\(400\) −98.2673 18.5346i −0.245668 0.0463364i
\(401\) −486.484 −1.21318 −0.606588 0.795016i \(-0.707462\pi\)
−0.606588 + 0.795016i \(0.707462\pi\)
\(402\) 5.79662 0.918094i 0.0144194 0.00228382i
\(403\) 0.539504 1.05884i 0.00133872 0.00262739i
\(404\) 114.229 37.1154i 0.282746 0.0918697i
\(405\) 33.7858 + 29.7241i 0.0834217 + 0.0733927i
\(406\) −107.898 + 332.076i −0.265759 + 0.817921i
\(407\) 237.903 237.903i 0.584529 0.584529i
\(408\) −35.1689 + 17.9195i −0.0861983 + 0.0439202i
\(409\) 308.424 + 424.509i 0.754093 + 1.03792i 0.997682 + 0.0680417i \(0.0216751\pi\)
−0.243589 + 0.969878i \(0.578325\pi\)
\(410\) 164.771 + 414.909i 0.401882 + 1.01197i
\(411\) 280.816 + 204.025i 0.683250 + 0.496410i
\(412\) 38.2604 241.566i 0.0928650 0.586326i
\(413\) 364.729 + 57.7674i 0.883121 + 0.139873i
\(414\) −4.35714 + 5.99709i −0.0105245 + 0.0144857i
\(415\) 32.1764 + 503.112i 0.0775334 + 1.21232i
\(416\) −0.483122 + 0.351009i −0.00116135 + 0.000843772i
\(417\) −175.061 343.577i −0.419811 0.823926i
\(418\) −45.0421 45.0421i −0.107756 0.107756i
\(419\) 87.5034 + 28.4316i 0.208839 + 0.0678558i 0.411568 0.911379i \(-0.364981\pi\)
−0.202730 + 0.979235i \(0.564981\pi\)
\(420\) 91.7047 20.5982i 0.218345 0.0490433i
\(421\) 92.8058 + 285.627i 0.220441 + 0.678448i 0.998722 + 0.0505324i \(0.0160918\pi\)
−0.778281 + 0.627916i \(0.783908\pi\)
\(422\) −1.49420 0.761334i −0.00354076 0.00180411i
\(423\) −31.4754 198.728i −0.0744099 0.469805i
\(424\) 176.460i 0.416178i
\(425\) 67.8374 189.657i 0.159617 0.446253i
\(426\) 38.0951 0.0894251
\(427\) 234.419 37.1283i 0.548990 0.0869515i
\(428\) 171.032 335.668i 0.399606 0.784272i
\(429\) 2.25678 0.733273i 0.00526057 0.00170926i
\(430\) −445.371 + 264.015i −1.03575 + 0.613988i
\(431\) −66.0338 + 203.231i −0.153211 + 0.471534i −0.997975 0.0636042i \(-0.979740\pi\)
0.844764 + 0.535138i \(0.179740\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) 61.8453 31.5118i 0.142830 0.0727755i −0.381115 0.924528i \(-0.624460\pi\)
0.523945 + 0.851752i \(0.324460\pi\)
\(434\) 50.7781 + 69.8901i 0.117000 + 0.161037i
\(435\) −332.908 210.786i −0.765305 0.484566i
\(436\) 236.912 + 172.126i 0.543375 + 0.394785i
\(437\) −0.948635 + 5.98945i −0.00217079 + 0.0137058i
\(438\) 251.967 + 39.9076i 0.575266 + 0.0911132i
\(439\) 77.6968 106.941i 0.176986 0.243600i −0.711303 0.702886i \(-0.751895\pi\)
0.888289 + 0.459286i \(0.151895\pi\)
\(440\) 98.1811 155.063i 0.223139 0.352417i
\(441\) 47.4566 34.4792i 0.107611 0.0781842i
\(442\) −0.546083 1.07175i −0.00123548 0.00242477i
\(443\) 253.592 + 253.592i 0.572441 + 0.572441i 0.932810 0.360369i \(-0.117349\pi\)
−0.360369 + 0.932810i \(0.617349\pi\)
\(444\) 85.4111 + 27.7517i 0.192367 + 0.0625039i
\(445\) 264.111 + 445.533i 0.593507 + 1.00120i
\(446\) 4.92158 + 15.1471i 0.0110349 + 0.0339621i
\(447\) 256.527 + 130.707i 0.573887 + 0.292410i
\(448\) −6.79112 42.8775i −0.0151588 0.0957086i
\(449\) 224.503i 0.500006i −0.968245 0.250003i \(-0.919568\pi\)
0.968245 0.250003i \(-0.0804316\pi\)
\(450\) −3.11197 + 106.020i −0.00691548 + 0.235601i
\(451\) −819.343 −1.81672
\(452\) 202.751 32.1126i 0.448564 0.0710456i
\(453\) 5.72606 11.2380i 0.0126403 0.0248080i
\(454\) 201.449 65.4548i 0.443721 0.144174i
\(455\) 0.627716 + 2.79464i 0.00137960 + 0.00614206i
\(456\) 5.25422 16.1708i 0.0115224 0.0354623i
\(457\) 62.5335 62.5335i 0.136835 0.136835i −0.635372 0.772206i \(-0.719153\pi\)
0.772206 + 0.635372i \(0.219153\pi\)
\(458\) 55.7605 28.4114i 0.121748 0.0620336i
\(459\) 24.6078 + 33.8698i 0.0536118 + 0.0737903i
\(460\) −17.4365 + 1.11515i −0.0379055 + 0.00242424i
\(461\) −260.296 189.116i −0.564634 0.410231i 0.268518 0.963275i \(-0.413466\pi\)
−0.833152 + 0.553044i \(0.813466\pi\)
\(462\) −26.9852 + 170.378i −0.0584095 + 0.368783i
\(463\) −103.803 16.4409i −0.224198 0.0355094i 0.0433249 0.999061i \(-0.486205\pi\)
−0.267522 + 0.963552i \(0.586205\pi\)
\(464\) −106.973 + 147.236i −0.230546 + 0.317319i
\(465\) −90.6055 + 35.9819i −0.194851 + 0.0773804i
\(466\) −103.035 + 74.8595i −0.221106 + 0.160643i
\(467\) 9.37430 + 18.3981i 0.0200735 + 0.0393964i 0.900825 0.434181i \(-0.142962\pi\)
−0.880752 + 0.473578i \(0.842962\pi\)
\(468\) 0.447879 + 0.447879i 0.000957007 + 0.000957007i
\(469\) −12.3653 4.01773i −0.0263652 0.00856658i
\(470\) 313.255 356.061i 0.666500 0.757576i
\(471\) −144.357 444.287i −0.306491 0.943284i
\(472\) 171.497 + 87.3822i 0.363342 + 0.185132i
\(473\) −148.649 938.530i −0.314268 1.98421i
\(474\) 81.2849i 0.171487i
\(475\) 37.1066 + 78.4334i 0.0781192 + 0.165123i
\(476\) 87.4423 0.183702
\(477\) 184.859 29.2789i 0.387546 0.0613812i
\(478\) −234.858 + 460.936i −0.491336 + 0.964301i
\(479\) 475.382 154.461i 0.992447 0.322466i 0.232604 0.972572i \(-0.425275\pi\)
0.759844 + 0.650106i \(0.225275\pi\)
\(480\) 48.7771 + 4.55982i 0.101619 + 0.00949963i
\(481\) −0.845715 + 2.60284i −0.00175824 + 0.00541132i
\(482\) 472.327 472.327i 0.979932 0.979932i
\(483\) 14.6321 7.45544i 0.0302943 0.0154357i
\(484\) 55.7468 + 76.7288i 0.115179 + 0.158531i
\(485\) −262.034 + 217.231i −0.540276 + 0.447899i
\(486\) −17.8351 12.9580i −0.0366978 0.0266625i
\(487\) −14.4874 + 91.4696i −0.0297482 + 0.187823i −0.998088 0.0618144i \(-0.980311\pi\)
0.968339 + 0.249637i \(0.0803113\pi\)
\(488\) 122.185 + 19.3522i 0.250379 + 0.0396562i
\(489\) −149.175 + 205.322i −0.305062 + 0.419882i
\(490\) 133.954 + 34.2456i 0.273375 + 0.0698890i
\(491\) −30.9440 + 22.4821i −0.0630224 + 0.0457885i −0.618850 0.785509i \(-0.712401\pi\)
0.555828 + 0.831297i \(0.312401\pi\)
\(492\) −99.2899 194.867i −0.201809 0.396072i
\(493\) −259.212 259.212i −0.525784 0.525784i
\(494\) 0.492795 + 0.160119i 0.000997560 + 0.000324127i
\(495\) −178.735 77.1260i −0.361081 0.155810i
\(496\) 13.9145 + 42.8243i 0.0280533 + 0.0863393i
\(497\) −75.1958 38.3142i −0.151299 0.0770909i
\(498\) −38.6357 243.936i −0.0775817 0.489832i
\(499\) 763.633i 1.53033i 0.643836 + 0.765163i \(0.277342\pi\)
−0.643836 + 0.765163i \(0.722658\pi\)
\(500\) −197.062 + 153.840i −0.394123 + 0.307680i
\(501\) −390.995 −0.780429
\(502\) 139.707 22.1273i 0.278300 0.0440784i
\(503\) −182.277 + 357.739i −0.362380 + 0.711211i −0.998158 0.0606608i \(-0.980679\pi\)
0.635778 + 0.771872i \(0.280679\pi\)
\(504\) −43.7917 + 14.2288i −0.0868883 + 0.0282317i
\(505\) 118.966 275.697i 0.235576 0.545935i
\(506\) 9.90928 30.4976i 0.0195836 0.0602720i
\(507\) 206.968 206.968i 0.408221 0.408221i
\(508\) 126.049 64.2254i 0.248129 0.126428i
\(509\) 486.285 + 669.314i 0.955373 + 1.31496i 0.949099 + 0.314978i \(0.101997\pi\)
0.00627400 + 0.999980i \(0.498003\pi\)
\(510\) −24.4411 + 95.6027i −0.0479237 + 0.187456i
\(511\) −457.219 332.189i −0.894753 0.650076i
\(512\) 3.53971 22.3488i 0.00691349 0.0436501i
\(513\) −17.8124 2.82120i −0.0347220 0.00549942i
\(514\) 152.486 209.879i 0.296666 0.408325i
\(515\) −390.237 470.722i −0.757742 0.914023i
\(516\) 205.201 149.087i 0.397675 0.288928i
\(517\) 395.150 + 775.526i 0.764314 + 1.50005i
\(518\) −140.681 140.681i −0.271585 0.271585i
\(519\) 59.6444 + 19.3796i 0.114922 + 0.0373403i
\(520\) −0.138957 + 1.48645i −0.000267226 + 0.00285856i
\(521\) 225.602 + 694.332i 0.433017 + 1.33269i 0.895105 + 0.445856i \(0.147101\pi\)
−0.462088 + 0.886834i \(0.652899\pi\)
\(522\) 171.994 + 87.6355i 0.329491 + 0.167884i
\(523\) 49.8292 + 314.609i 0.0952756 + 0.601547i 0.988416 + 0.151769i \(0.0484969\pi\)
−0.893140 + 0.449778i \(0.851503\pi\)
\(524\) 221.541i 0.422789i
\(525\) 112.773 206.143i 0.214805 0.392654i
\(526\) 650.576 1.23684
\(527\) −89.5810 + 14.1882i −0.169983 + 0.0269227i
\(528\) −40.8193 + 80.1124i −0.0773093 + 0.151728i
\(529\) 500.206 162.527i 0.945568 0.307234i
\(530\) 331.213 + 291.394i 0.624930 + 0.549800i
\(531\) 63.0863 194.160i 0.118807 0.365649i
\(532\) −26.6351 + 26.6351i −0.0500660 + 0.0500660i
\(533\) 5.93845 3.02579i 0.0111416 0.00567691i
\(534\) −149.141 205.275i −0.279291 0.384410i
\(535\) −347.615 875.326i −0.649748 1.63612i
\(536\) −5.48254 3.98330i −0.0102286 0.00743152i
\(537\) 75.7129 478.033i 0.140992 0.890191i
\(538\) −205.965 32.6217i −0.382835 0.0606351i
\(539\) −149.154 + 205.293i −0.276723 + 0.380877i
\(540\) −3.31641 51.8556i −0.00614150 0.0960289i
\(541\) −580.484 + 421.746i −1.07298 + 0.779568i −0.976446 0.215761i \(-0.930777\pi\)
−0.0965371 + 0.995329i \(0.530777\pi\)
\(542\) −120.825 237.133i −0.222925 0.437515i
\(543\) −145.254 145.254i −0.267503 0.267503i
\(544\) 43.3465 + 14.0841i 0.0796810 + 0.0258899i
\(545\) 714.300 160.442i 1.31064 0.294389i
\(546\) −0.433612 1.33452i −0.000794162 0.00244418i
\(547\) 547.263 + 278.845i 1.00048 + 0.509771i 0.875928 0.482442i \(-0.160250\pi\)
0.124554 + 0.992213i \(0.460250\pi\)
\(548\) −62.6997 395.871i −0.114416 0.722392i
\(549\) 131.212i 0.239003i
\(550\) −128.922 440.347i −0.234405 0.800630i
\(551\) 157.913 0.286593
\(552\) 8.45420 1.33901i 0.0153156 0.00242575i
\(553\) 81.7523 160.448i 0.147834 0.290141i
\(554\) −230.685 + 74.9540i −0.416398 + 0.135296i
\(555\) 193.132 114.488i 0.347986 0.206285i
\(556\) −137.593 + 423.467i −0.247469 + 0.761631i
\(557\) −110.327 + 110.327i −0.198074 + 0.198074i −0.799174 0.601100i \(-0.794729\pi\)
0.601100 + 0.799174i \(0.294729\pi\)
\(558\) 42.5540 21.6824i 0.0762617 0.0388573i
\(559\) 4.54332 + 6.25335i 0.00812759 + 0.0111867i
\(560\) −91.6950 58.0582i −0.163741 0.103675i
\(561\) −146.517 106.451i −0.261172 0.189752i
\(562\) 108.575 685.513i 0.193193 1.21977i
\(563\) −210.554 33.3485i −0.373986 0.0592336i −0.0333879 0.999442i \(-0.510630\pi\)
−0.340598 + 0.940209i \(0.610630\pi\)
\(564\) −136.561 + 187.960i −0.242129 + 0.333262i
\(565\) 274.535 433.590i 0.485903 0.767416i
\(566\) −225.591 + 163.902i −0.398571 + 0.289579i
\(567\) 22.1722 + 43.5154i 0.0391044 + 0.0767467i
\(568\) −31.1045 31.1045i −0.0547615 0.0547615i
\(569\) 580.070 + 188.476i 1.01946 + 0.331241i 0.770613 0.637303i \(-0.219950\pi\)
0.248842 + 0.968544i \(0.419950\pi\)
\(570\) −21.6760 36.5656i −0.0380280 0.0641501i
\(571\) 127.570 + 392.619i 0.223414 + 0.687598i 0.998449 + 0.0556793i \(0.0177324\pi\)
−0.775034 + 0.631919i \(0.782268\pi\)
\(572\) −2.44137 1.24394i −0.00426813 0.00217472i
\(573\) 89.9706 + 568.052i 0.157017 + 0.991364i
\(574\) 484.509i 0.844092i
\(575\) −26.7005 + 34.5697i −0.0464356 + 0.0601212i
\(576\) −24.0000 −0.0416667
\(577\) −294.314 + 46.6148i −0.510077 + 0.0807883i −0.406168 0.913799i \(-0.633135\pi\)
−0.103909 + 0.994587i \(0.533135\pi\)
\(578\) 143.871 282.364i 0.248913 0.488518i
\(579\) 366.199 118.985i 0.632469 0.205502i
\(580\) 99.7118 + 443.924i 0.171917 + 0.765387i
\(581\) −169.076 + 520.363i −0.291009 + 0.895633i
\(582\) 117.907 117.907i 0.202590 0.202590i
\(583\) −721.405 + 367.574i −1.23740 + 0.630488i
\(584\) −173.145 238.314i −0.296482 0.408072i
\(585\) 1.58026 0.101065i 0.00270131 0.000172761i
\(586\) 208.542 + 151.515i 0.355874 + 0.258558i
\(587\) −141.441 + 893.022i −0.240955 + 1.52133i 0.509535 + 0.860450i \(0.329818\pi\)
−0.750490 + 0.660882i \(0.770182\pi\)
\(588\) −66.9003 10.5960i −0.113776 0.0180204i
\(589\) 22.9648 31.6083i 0.0389895 0.0536644i
\(590\) 447.215 177.601i 0.757991 0.301019i
\(591\) 406.209 295.128i 0.687324 0.499370i
\(592\) −47.0786 92.3970i −0.0795247 0.156076i
\(593\) −821.404 821.404i −1.38517 1.38517i −0.835159 0.550008i \(-0.814624\pi\)
−0.550008 0.835159i \(-0.685376\pi\)
\(594\) 90.6988 + 29.4698i 0.152692 + 0.0496125i
\(595\) 144.397 164.128i 0.242683 0.275846i
\(596\) −102.732 316.176i −0.172369 0.530496i
\(597\) 509.498 + 259.602i 0.853431 + 0.434845i
\(598\) 0.0408055 + 0.257636i 6.82366e−5 + 0.000430829i
\(599\) 260.320i 0.434590i 0.976106 + 0.217295i \(0.0697234\pi\)
−0.976106 + 0.217295i \(0.930277\pi\)
\(600\) 89.1062 84.0243i 0.148510 0.140041i
\(601\) 94.4332 0.157127 0.0785634 0.996909i \(-0.474967\pi\)
0.0785634 + 0.996909i \(0.474967\pi\)
\(602\) −554.989 + 87.9016i −0.921908 + 0.146016i
\(603\) −3.26322 + 6.40444i −0.00541165 + 0.0106210i
\(604\) −13.8511 + 4.50050i −0.0229323 + 0.00745115i
\(605\) 236.076 + 22.0690i 0.390208 + 0.0364777i
\(606\) −45.4568 + 139.902i −0.0750113 + 0.230861i
\(607\) −300.878 + 300.878i −0.495680 + 0.495680i −0.910090 0.414410i \(-0.863988\pi\)
0.414410 + 0.910090i \(0.363988\pi\)
\(608\) −17.4935 + 8.91337i −0.0287722 + 0.0146601i
\(609\) −251.360 345.967i −0.412741 0.568090i
\(610\) 238.093 197.383i 0.390316 0.323579i
\(611\) −5.72795 4.16160i −0.00937472 0.00681113i
\(612\) 7.56234 47.7467i 0.0123568 0.0780175i
\(613\) 481.056 + 76.1918i 0.784757 + 0.124293i 0.535939 0.844257i \(-0.319958\pi\)
0.248818 + 0.968550i \(0.419958\pi\)
\(614\) −129.730 + 178.558i −0.211287 + 0.290812i
\(615\) −529.725 135.425i −0.861341 0.220204i
\(616\) 161.146 117.080i 0.261601 0.190064i
\(617\) −349.395 685.727i −0.566281 1.11139i −0.979629 0.200815i \(-0.935641\pi\)
0.413348 0.910573i \(-0.364359\pi\)
\(618\) 211.810 + 211.810i 0.342735 + 0.342735i
\(619\) −1153.38 374.754i −1.86329 0.605419i −0.993760 0.111536i \(-0.964423\pi\)
−0.869528 0.493883i \(-0.835577\pi\)
\(620\) 103.358 + 44.6000i 0.166707 + 0.0719355i
\(621\) −2.80550 8.63446i −0.00451772 0.0139041i
\(622\) 29.4415 + 15.0012i 0.0473336 + 0.0241177i
\(623\) 87.9336 + 555.191i 0.141145 + 0.891157i
\(624\) 0.731384i 0.00117209i
\(625\) −36.6591 + 623.924i −0.0586545 + 0.998278i
\(626\) 749.088 1.19663
\(627\) 77.0546 12.2043i 0.122894 0.0194645i
\(628\) −244.891 + 480.626i −0.389954 + 0.765328i
\(629\) 198.653 64.5464i 0.315824 0.102617i
\(630\) −45.6075 + 105.693i −0.0723929 + 0.167767i
\(631\) 382.691 1177.80i 0.606484 1.86656i 0.120233 0.992746i \(-0.461636\pi\)
0.486251 0.873819i \(-0.338364\pi\)
\(632\) 66.3688 66.3688i 0.105014 0.105014i
\(633\) 1.83002 0.932440i 0.00289102 0.00147305i
\(634\) −20.2783 27.9107i −0.0319847 0.0440232i
\(635\) 87.5996 342.651i 0.137952 0.539608i
\(636\) −174.843 127.031i −0.274911 0.199734i
\(637\) 0.322905 2.03874i 0.000506915 0.00320054i
\(638\) −824.765 130.630i −1.29273 0.204749i
\(639\) −27.4242 + 37.7461i −0.0429173 + 0.0590706i
\(640\) −36.1033 43.5494i −0.0564114 0.0680460i
\(641\) −602.958 + 438.075i −0.940653 + 0.683424i −0.948578 0.316544i \(-0.897477\pi\)
0.00792497 + 0.999969i \(0.497477\pi\)
\(642\) 209.470 + 411.108i 0.326277 + 0.640355i
\(643\) 326.069 + 326.069i 0.507105 + 0.507105i 0.913637 0.406531i \(-0.133262\pi\)
−0.406531 + 0.913637i \(0.633262\pi\)
\(644\) −18.0344 5.85974i −0.0280038 0.00909897i
\(645\) 59.0205 631.352i 0.0915047 0.978840i
\(646\) −12.2205 37.6109i −0.0189172 0.0582212i
\(647\) 87.7162 + 44.6936i 0.135574 + 0.0690783i 0.520462 0.853885i \(-0.325760\pi\)
−0.384888 + 0.922963i \(0.625760\pi\)
\(648\) 3.98217 + 25.1424i 0.00614533 + 0.0388001i
\(649\) 883.140i 1.36077i
\(650\) 2.56058 + 2.71545i 0.00393936 + 0.00417761i
\(651\) −105.804 −0.162526
\(652\) 289.446 45.8437i 0.443936 0.0703125i
\(653\) −255.147 + 500.754i −0.390731 + 0.766852i −0.999652 0.0263786i \(-0.991602\pi\)
0.608921 + 0.793231i \(0.291602\pi\)
\(654\) −341.099 + 110.830i −0.521558 + 0.169465i
\(655\) −415.831 365.839i −0.634856 0.558533i
\(656\) −78.0387 + 240.178i −0.118961 + 0.366126i
\(657\) −220.929 + 220.929i −0.336270 + 0.336270i
\(658\) 458.598 233.667i 0.696958 0.355118i
\(659\) −571.682 786.853i −0.867499 1.19401i −0.979729 0.200328i \(-0.935799\pi\)
0.112230 0.993682i \(-0.464201\pi\)
\(660\) 82.9637 + 208.910i 0.125703 + 0.316530i
\(661\) −20.3488 14.7843i −0.0307849 0.0223665i 0.572286 0.820054i \(-0.306057\pi\)
−0.603071 + 0.797687i \(0.706057\pi\)
\(662\) 2.12486 13.4159i 0.00320976 0.0202656i
\(663\) 1.45505 + 0.230457i 0.00219464 + 0.000347597i
\(664\) −167.627 + 230.719i −0.252451 + 0.347468i
\(665\) 6.01029 + 93.9773i 0.00903803 + 0.141319i
\(666\) −88.9838 + 64.6505i −0.133609 + 0.0970729i
\(667\) 36.0903 + 70.8312i 0.0541084 + 0.106194i
\(668\) 319.246 + 319.246i 0.477913 + 0.477913i
\(669\) −18.5513 6.02768i −0.0277299 0.00900999i
\(670\) −16.5301 + 3.71290i −0.0246718 + 0.00554164i
\(671\) 175.402 + 539.831i 0.261404 + 0.804518i
\(672\) 47.3735 + 24.1380i 0.0704963 + 0.0359197i
\(673\) −43.2840 273.285i −0.0643151 0.406069i −0.998752 0.0499411i \(-0.984097\pi\)
0.934437 0.356128i \(-0.115903\pi\)
\(674\) 330.141i 0.489824i
\(675\) −102.809 79.4061i −0.152309 0.117639i
\(676\) −337.978 −0.499967
\(677\) −1008.64 + 159.752i −1.48986 + 0.235971i −0.847650 0.530556i \(-0.821983\pi\)
−0.642212 + 0.766527i \(0.721983\pi\)
\(678\) −114.139 + 224.011i −0.168347 + 0.330400i
\(679\) −351.322 + 114.151i −0.517411 + 0.168117i
\(680\) 98.0154 58.1032i 0.144140 0.0854460i
\(681\) −80.1655 + 246.724i −0.117717 + 0.362297i
\(682\) −146.090 + 146.090i −0.214209 + 0.214209i
\(683\) 118.823 60.5433i 0.173972 0.0886432i −0.364836 0.931072i \(-0.618875\pi\)
0.538808 + 0.842429i \(0.318875\pi\)
\(684\) 12.2402 + 16.8472i 0.0178951 + 0.0246305i
\(685\) −846.583 536.029i −1.23589 0.782524i
\(686\) 425.617 + 309.229i 0.620434 + 0.450771i
\(687\) −11.9901 + 75.7027i −0.0174529 + 0.110193i
\(688\) −289.275 45.8166i −0.420457 0.0665939i
\(689\) 3.87118 5.32823i 0.00561855 0.00773327i
\(690\) 11.4474 18.0796i 0.0165904 0.0262023i
\(691\) 795.522 577.980i 1.15126 0.836440i 0.162613 0.986690i \(-0.448008\pi\)
0.988648 + 0.150250i \(0.0480077\pi\)
\(692\) −32.8760 64.5228i −0.0475087 0.0932411i
\(693\) −149.391 149.391i −0.215571 0.215571i
\(694\) −211.868 68.8402i −0.305286 0.0991934i
\(695\) 567.631 + 957.546i 0.816735 + 1.37776i
\(696\) −68.8787 211.987i −0.0989637 0.304579i
\(697\) −453.232 230.933i −0.650262 0.331325i
\(698\) −0.761504 4.80795i −0.00109098 0.00688818i
\(699\) 155.982i 0.223150i
\(700\) −260.394 + 76.2368i −0.371991 + 0.108910i
\(701\) −333.026 −0.475072 −0.237536 0.971379i \(-0.576340\pi\)
−0.237536 + 0.971379i \(0.576340\pi\)
\(702\) −0.766199 + 0.121354i −0.00109145 + 0.000172869i
\(703\) −40.8492 + 80.1712i −0.0581070 + 0.114041i
\(704\) 98.7403 32.0827i 0.140256 0.0455720i
\(705\) 127.291 + 566.709i 0.180555 + 0.803842i
\(706\) 41.1543 126.660i 0.0582922 0.179405i
\(707\) 230.433 230.433i 0.325931 0.325931i
\(708\) −210.040 + 107.021i −0.296667 + 0.151159i
\(709\) 393.674 + 541.845i 0.555252 + 0.764239i 0.990713 0.135969i \(-0.0434147\pi\)
−0.435461 + 0.900208i \(0.643415\pi\)
\(710\) −109.747 + 7.01883i −0.154573 + 0.00988568i
\(711\) −80.5403 58.5159i −0.113277 0.0823009i
\(712\) −45.8332 + 289.380i −0.0643725 + 0.406432i
\(713\) 19.4263 + 3.07683i 0.0272459 + 0.00431532i
\(714\) −62.9486 + 86.6413i −0.0881633 + 0.121346i
\(715\) −6.36639 + 2.52826i −0.00890404 + 0.00353603i
\(716\) −452.131 + 328.493i −0.631469 + 0.458789i
\(717\) −287.642 564.529i −0.401174 0.787348i
\(718\) 55.5927 + 55.5927i 0.0774271 + 0.0774271i
\(719\) 470.195 + 152.775i 0.653956 + 0.212483i 0.617158 0.786839i \(-0.288284\pi\)
0.0367985 + 0.999323i \(0.488284\pi\)
\(720\) −39.6321 + 45.0477i −0.0550445 + 0.0625663i
\(721\) −205.063 631.120i −0.284415 0.875340i
\(722\) −439.708 224.042i −0.609014 0.310308i
\(723\) 127.978 + 808.023i 0.177010 + 1.11760i
\(724\) 237.199i 0.327623i
\(725\) 997.899 + 545.910i 1.37641 + 0.752980i
\(726\) −116.157 −0.159996
\(727\) 990.760 156.921i 1.36281 0.215847i 0.568159 0.822919i \(-0.307656\pi\)
0.794647 + 0.607072i \(0.207656\pi\)
\(728\) −0.735589 + 1.44368i −0.00101043 + 0.00198307i
\(729\) 25.6785 8.34346i 0.0352243 0.0114451i
\(730\) −733.234 68.5448i −1.00443 0.0938970i
\(731\) 182.299 561.060i 0.249384 0.767524i
\(732\) −107.134 + 107.134i −0.146359 + 0.146359i
\(733\) 358.456 182.643i 0.489026 0.249171i −0.192048 0.981385i \(-0.561513\pi\)
0.681074 + 0.732214i \(0.261513\pi\)
\(734\) 103.613 + 142.611i 0.141162 + 0.194293i
\(735\) −130.363 + 108.074i −0.177365 + 0.147039i
\(736\) −7.99612 5.80952i −0.0108643 0.00789337i
\(737\) 4.86418 30.7112i 0.00659997 0.0416706i
\(738\) 264.560 + 41.9021i 0.358482 + 0.0567780i
\(739\) 632.639 870.754i 0.856075 1.17829i −0.126416 0.991977i \(-0.540347\pi\)
0.982491 0.186309i \(-0.0596525\pi\)
\(740\) −251.171 64.2125i −0.339420 0.0867736i
\(741\) −0.513408 + 0.373013i −0.000692859 + 0.000503391i
\(742\) 217.361 + 426.595i 0.292939 + 0.574925i
\(743\) −693.867 693.867i −0.933872 0.933872i 0.0640733 0.997945i \(-0.479591\pi\)
−0.997945 + 0.0640733i \(0.979591\pi\)
\(744\) −52.4488 17.0417i −0.0704957 0.0229054i
\(745\) −763.103 329.286i −1.02430 0.441995i
\(746\) −212.884 655.189i −0.285367 0.878270i
\(747\) 269.515 + 137.325i 0.360796 + 0.183835i
\(748\) 32.7140 + 206.548i 0.0437352 + 0.276133i
\(749\) 1022.16i 1.36470i
\(750\) −10.5686 306.004i −0.0140914 0.408005i
\(751\) 937.116 1.24782 0.623912 0.781494i \(-0.285542\pi\)
0.623912 + 0.781494i \(0.285542\pi\)
\(752\) 264.970 41.9672i 0.352354 0.0558074i
\(753\) −78.6483 + 154.356i −0.104447 + 0.204988i
\(754\) 6.46015 2.09903i 0.00856784 0.00278386i
\(755\) −14.4254 + 33.4302i −0.0191066 + 0.0442784i
\(756\) 17.4266 53.6336i 0.0230511 0.0709440i
\(757\) −862.862 + 862.862i −1.13984 + 1.13984i −0.151366 + 0.988478i \(0.548367\pi\)
−0.988478 + 0.151366i \(0.951633\pi\)
\(758\) 28.9764 14.7642i 0.0382275 0.0194779i
\(759\) 23.0847 + 31.7734i 0.0304146 + 0.0418621i
\(760\) −12.1573 + 47.5540i −0.0159965 + 0.0625711i
\(761\) 231.102 + 167.905i 0.303682 + 0.220638i 0.729181 0.684321i \(-0.239901\pi\)
−0.425499 + 0.904959i \(0.639901\pi\)
\(762\) −27.1043 + 171.130i −0.0355700 + 0.224580i
\(763\) 784.762 + 124.294i 1.02852 + 0.162902i
\(764\) 390.352 537.273i 0.510931 0.703237i
\(765\) −77.1321 93.0403i −0.100826 0.121621i
\(766\) −731.562 + 531.511i −0.955042 + 0.693878i
\(767\) −3.26139 6.40084i −0.00425214 0.00834529i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) −1283.93 417.175i −1.66961 0.542490i −0.686761 0.726883i \(-0.740968\pi\)
−0.982853 + 0.184393i \(0.940968\pi\)
\(770\) 46.3494 495.807i 0.0601941 0.643906i
\(771\) 98.1838 + 302.179i 0.127346 + 0.391931i
\(772\) −396.152 201.849i −0.513150 0.261463i
\(773\) 52.5151 + 331.567i 0.0679367 + 0.428935i 0.998091 + 0.0617657i \(0.0196732\pi\)
−0.930154 + 0.367170i \(0.880327\pi\)
\(774\) 310.647i 0.401352i
\(775\) 254.393 120.353i 0.328249 0.155294i
\(776\) −192.542 −0.248121
\(777\) 240.667 38.1179i 0.309739 0.0490578i
\(778\) 264.652 519.409i 0.340170 0.667621i
\(779\) 208.398 67.7127i 0.267520 0.0869226i
\(780\) −1.37280 1.20776i −0.00176000 0.00154841i
\(781\) 62.3698 191.954i 0.0798589 0.245780i
\(782\) 14.0773 14.0773i 0.0180017 0.0180017i
\(783\) −210.649 + 107.331i −0.269028 + 0.137077i
\(784\) 45.9723 + 63.2755i 0.0586381 + 0.0807085i
\(785\) 497.732 + 1253.33i 0.634054 + 1.59660i
\(786\) 219.512 + 159.485i 0.279277 + 0.202907i
\(787\) 233.750 1475.84i 0.297014 1.87527i −0.161926 0.986803i \(-0.551770\pi\)
0.458939 0.888468i \(-0.348230\pi\)
\(788\) −572.639 90.6971i −0.726699 0.115098i
\(789\) −468.341 + 644.617i −0.593589 + 0.817005i
\(790\) −14.9763 234.171i −0.0189574 0.296419i
\(791\) 450.599 327.379i 0.569657 0.413880i
\(792\) −49.9932 98.1172i −0.0631228 0.123885i
\(793\) −3.26485 3.26485i −0.00411709 0.00411709i
\(794\) −120.984 39.3101i −0.152373 0.0495089i
\(795\) −527.161 + 118.408i −0.663095 + 0.148941i
\(796\) −204.039 627.968i −0.256331 0.788905i
\(797\) 476.396 + 242.736i 0.597736 + 0.304562i 0.726557 0.687106i \(-0.241119\pi\)
−0.128821 + 0.991668i \(0.541119\pi\)
\(798\) −7.21684 45.5654i −0.00904366 0.0570994i
\(799\) 540.368i 0.676306i
\(800\) −141.360 4.14929i −0.176701 0.00518661i
\(801\) 310.759 0.387964
\(802\) −679.522 + 107.626i −0.847284 + 0.134197i
\(803\) 613.610 1204.28i 0.764147 1.49972i
\(804\) 7.89361 2.56479i 0.00981793 0.00319004i
\(805\) −40.7796 + 24.1740i −0.0506578 + 0.0300298i
\(806\) 0.519333 1.59834i 0.000644333 0.00198305i
\(807\) 180.595 180.595i 0.223785 0.223785i
\(808\) 151.345 77.1140i 0.187308 0.0954381i
\(809\) −246.192 338.855i −0.304317 0.418856i 0.629282 0.777177i \(-0.283349\pi\)
−0.933598 + 0.358321i \(0.883349\pi\)
\(810\) 53.7680 + 34.0441i 0.0663802 + 0.0420298i
\(811\) 754.843 + 548.426i 0.930756 + 0.676234i 0.946178 0.323647i \(-0.104909\pi\)
−0.0154219 + 0.999881i \(0.504909\pi\)
\(812\) −77.2465 + 487.715i −0.0951311 + 0.600634i
\(813\) 321.941 + 50.9905i 0.395992 + 0.0627189i
\(814\) 279.672 384.935i 0.343577 0.472894i
\(815\) 391.924 618.991i 0.480889 0.759498i
\(816\) −45.1597 + 32.8104i −0.0553427 + 0.0402088i
\(817\) 115.371 + 226.429i 0.141213 + 0.277146i
\(818\) 524.722 + 524.722i 0.641470 + 0.641470i
\(819\) 1.63445 + 0.531065i 0.00199566 + 0.000648431i
\(820\) 321.944 + 543.093i 0.392615 + 0.662309i
\(821\) 215.923 + 664.543i 0.263000 + 0.809431i 0.992147 + 0.125074i \(0.0399169\pi\)
−0.729147 + 0.684357i \(0.760083\pi\)
\(822\) 437.381 + 222.857i 0.532094 + 0.271115i
\(823\) 88.1338 + 556.455i 0.107088 + 0.676130i 0.981575 + 0.191079i \(0.0611988\pi\)
−0.874486 + 0.485051i \(0.838801\pi\)
\(824\) 345.885i 0.419763i
\(825\) 529.123 + 189.258i 0.641361 + 0.229404i
\(826\) 522.234 0.632245
\(827\) −740.501 + 117.284i −0.895406 + 0.141818i −0.587143 0.809483i \(-0.699747\pi\)
−0.308262 + 0.951301i \(0.599747\pi\)
\(828\) −4.75932 + 9.34069i −0.00574797 + 0.0112810i
\(829\) 452.818 147.129i 0.546222 0.177478i −0.0228906 0.999738i \(-0.507287\pi\)
0.569112 + 0.822260i \(0.307287\pi\)
\(830\) 156.248 + 695.629i 0.188251 + 0.838107i
\(831\) 91.7995 282.530i 0.110469 0.339988i
\(832\) −0.597172 + 0.597172i −0.000717755 + 0.000717755i
\(833\) −140.369 + 71.5215i −0.168510 + 0.0858602i
\(834\) −320.536 441.180i −0.384336 0.528993i
\(835\) 1126.40 72.0388i 1.34899 0.0862741i
\(836\) −72.8796 52.9501i −0.0871765 0.0633375i
\(837\) −9.15036 + 57.7731i −0.0109323 + 0.0690240i
\(838\) 128.515 + 20.3548i 0.153359 + 0.0242897i
\(839\) 399.399 549.726i 0.476042 0.655216i −0.501696 0.865044i \(-0.667290\pi\)
0.977738 + 0.209828i \(0.0672904\pi\)
\(840\) 123.536 49.0596i 0.147067 0.0584043i
\(841\) 994.373 722.454i 1.18237 0.859042i
\(842\) 192.821 + 378.432i 0.229004 + 0.449445i
\(843\) 601.072 + 601.072i 0.713015 + 0.713015i
\(844\) −2.25554 0.732868i −0.00267244 0.000868327i
\(845\) −558.115 + 634.381i −0.660491 + 0.750746i
\(846\) −87.9298 270.620i −0.103936 0.319882i
\(847\) 229.282 + 116.825i 0.270700 + 0.137928i
\(848\) 39.0385 + 246.479i 0.0460359 + 0.290659i
\(849\) 341.515i 0.402256i
\(850\) 52.7971 279.922i 0.0621143 0.329320i
\(851\) −45.2964 −0.0532273
\(852\) 53.2113 8.42785i 0.0624546 0.00989184i
\(853\) 745.125 1462.39i 0.873535 1.71441i 0.193676 0.981066i \(-0.437959\pi\)
0.679859 0.733343i \(-0.262041\pi\)
\(854\) 319.223 103.722i 0.373797 0.121454i
\(855\) 51.8349 + 4.84567i 0.0606256 + 0.00566745i
\(856\) 164.637 506.700i 0.192333 0.591939i
\(857\) 356.131 356.131i 0.415555 0.415555i −0.468113 0.883668i \(-0.655066\pi\)
0.883668 + 0.468113i \(0.155066\pi\)
\(858\) 2.99006 1.52351i 0.00348491 0.00177565i
\(859\) −403.777 555.751i −0.470054 0.646974i 0.506501 0.862239i \(-0.330938\pi\)
−0.976556 + 0.215265i \(0.930938\pi\)
\(860\) −563.687 + 467.307i −0.655450 + 0.543380i
\(861\) −480.070 348.792i −0.557573 0.405101i
\(862\) −47.2750 + 298.483i −0.0548434 + 0.346267i
\(863\) 995.377 + 157.652i 1.15339 + 0.182679i 0.703695 0.710502i \(-0.251532\pi\)
0.449697 + 0.893181i \(0.351532\pi\)
\(864\) 17.2773 23.7801i 0.0199969 0.0275233i
\(865\) −175.398 44.8409i −0.202772 0.0518392i
\(866\) 79.4143 57.6979i 0.0917024 0.0666257i
\(867\) 176.206 + 345.823i 0.203236 + 0.398874i
\(868\) 86.3889 + 86.3889i 0.0995264 + 0.0995264i
\(869\) 409.580 + 133.081i 0.471323 + 0.153142i
\(870\) −511.639 220.777i −0.588091 0.253767i
\(871\) 0.0781602 + 0.240552i 8.97362e−5 + 0.000276180i
\(872\) 368.999 + 188.014i 0.423163 + 0.215613i
\(873\) 31.9473 + 201.707i 0.0365948 + 0.231050i
\(874\) 8.57594i 0.00981229i
\(875\) −286.902 + 614.649i −0.327888 + 0.702456i
\(876\) 360.776 0.411845
\(877\) 180.016 28.5117i 0.205263 0.0325105i −0.0529561 0.998597i \(-0.516864\pi\)
0.258219 + 0.966086i \(0.416864\pi\)
\(878\) 84.8685 166.564i 0.0966611 0.189708i
\(879\) −300.254 + 97.5583i −0.341585 + 0.110988i
\(880\) 102.835 238.314i 0.116858 0.270811i
\(881\) −7.55400 + 23.2488i −0.00857435 + 0.0263891i −0.955252 0.295793i \(-0.904416\pi\)
0.946678 + 0.322182i \(0.104416\pi\)
\(882\) 58.6596 58.6596i 0.0665075 0.0665075i
\(883\) 790.605 402.833i 0.895362 0.456210i 0.0551566 0.998478i \(-0.482434\pi\)
0.840206 + 0.542268i \(0.182434\pi\)
\(884\) −0.999875 1.37621i −0.00113108 0.00155680i
\(885\) −145.970 + 570.971i −0.164938 + 0.645165i
\(886\) 410.320 + 298.115i 0.463115 + 0.336473i
\(887\) −90.0023 + 568.252i −0.101468 + 0.640645i 0.883569 + 0.468302i \(0.155134\pi\)
−0.985037 + 0.172344i \(0.944866\pi\)
\(888\) 125.442 + 19.8680i 0.141263 + 0.0223739i
\(889\) 225.615 310.532i 0.253785 0.349305i
\(890\) 467.477 + 563.892i 0.525255 + 0.633586i
\(891\) −94.4927 + 68.6530i −0.106052 + 0.0770516i
\(892\) 10.2255 + 20.0687i 0.0114636 + 0.0224985i
\(893\) −164.597 164.597i −0.184319 0.184319i
\(894\) 387.235 + 125.820i 0.433148 + 0.140738i
\(895\) −130.044 + 1391.10i −0.145300 + 1.55430i
\(896\) −18.9717 58.3889i −0.0211738 0.0651662i
\(897\) −0.284651 0.145037i −0.000317337 0.000161691i
\(898\) −49.6671 313.586i −0.0553086 0.349205i
\(899\) 512.178i 0.569719i
\(900\) 19.1083 + 148.778i 0.0212314 + 0.165309i
\(901\) −502.658 −0.557889
\(902\) −1144.46 + 181.265i −1.26880 + 0.200959i
\(903\) 312.433 613.184i 0.345994 0.679052i
\(904\) 276.099 89.7099i 0.305419 0.0992366i
\(905\) 445.221 + 391.696i 0.491957 + 0.432813i
\(906\) 5.51196 16.9641i 0.00608384 0.0187241i
\(907\) −247.466 + 247.466i −0.272840 + 0.272840i −0.830242 0.557403i \(-0.811798\pi\)
0.557403 + 0.830242i \(0.311798\pi\)
\(908\) 266.904 135.994i 0.293947 0.149774i
\(909\) −105.896 145.754i −0.116498 0.160345i
\(910\) 1.49506 + 3.76469i 0.00164292 + 0.00413702i
\(911\) −612.110 444.724i −0.671910 0.488171i 0.198754 0.980049i \(-0.436311\pi\)
−0.870664 + 0.491878i \(0.836311\pi\)
\(912\) 3.76160 23.7498i 0.00412457 0.0260415i
\(913\) −1292.41 204.697i −1.41556 0.224203i
\(914\) 73.5125 101.181i 0.0804295 0.110702i
\(915\) 24.1752 + 378.005i 0.0264210 + 0.413121i
\(916\) 71.6009 52.0211i 0.0781669 0.0567916i
\(917\) −272.892 535.581i −0.297592 0.584057i
\(918\) 41.8653 + 41.8653i 0.0456049 + 0.0456049i
\(919\) −819.374 266.231i −0.891593 0.289696i −0.172830 0.984952i \(-0.555291\pi\)
−0.718763 + 0.695255i \(0.755291\pi\)
\(920\) −24.1087 + 5.41516i −0.0262051 + 0.00588604i
\(921\) −83.5316 257.084i −0.0906966 0.279135i
\(922\) −405.421 206.572i −0.439719 0.224048i
\(923\) 0.256833 + 1.62158i 0.000278259 + 0.00175686i
\(924\) 243.954i 0.264019i
\(925\) −535.294 + 365.409i −0.578696 + 0.395036i
\(926\) −148.630 −0.160508
\(927\) −362.350 + 57.3905i −0.390884 + 0.0619100i
\(928\) −116.847 + 229.326i −0.125913 + 0.247118i
\(929\) −1328.79 + 431.752i −1.43035 + 0.464749i −0.918875 0.394549i \(-0.870901\pi\)
−0.511475 + 0.859298i \(0.670901\pi\)
\(930\) −118.598 + 70.3044i −0.127524 + 0.0755961i
\(931\) 20.9710 64.5422i 0.0225253 0.0693257i
\(932\) −127.359 + 127.359i −0.136651 + 0.136651i
\(933\) −36.0583 + 18.3726i −0.0386477 + 0.0196920i
\(934\) 17.1643 + 23.6246i 0.0183772 + 0.0252940i
\(935\) 441.710 + 279.676i 0.472417 + 0.299119i
\(936\) 0.724684 + 0.526514i 0.000774235 + 0.000562514i
\(937\) −60.6837 + 383.142i −0.0647638 + 0.408902i 0.933914 + 0.357497i \(0.116370\pi\)
−0.998678 + 0.0514049i \(0.983630\pi\)
\(938\) −18.1607 2.87637i −0.0193611 0.00306650i
\(939\) −539.259 + 742.226i −0.574291 + 0.790443i
\(940\) 358.783 566.648i 0.381684 0.602817i
\(941\) −624.224 + 453.525i −0.663363 + 0.481961i −0.867797 0.496919i \(-0.834465\pi\)
0.204434 + 0.978880i \(0.434465\pi\)
\(942\) −299.929 588.644i −0.318396 0.624888i
\(943\) 78.0008 + 78.0008i 0.0827156 + 0.0827156i
\(944\) 258.879 + 84.1150i 0.274237 + 0.0891049i
\(945\) −71.8926 121.277i −0.0760768 0.128335i
\(946\) −415.265 1278.06i −0.438970 1.35101i
\(947\) −1105.64 563.350i −1.16752 0.594879i −0.240775 0.970581i \(-0.577402\pi\)
−0.926741 + 0.375702i \(0.877402\pi\)
\(948\) 17.9828 + 113.539i 0.0189692 + 0.119767i
\(949\) 10.9944i 0.0115853i
\(950\) 69.1826 + 101.347i 0.0728238 + 0.106681i
\(951\) 42.2531 0.0444302
\(952\) 122.140 19.3450i 0.128298 0.0203204i
\(953\) 100.299 196.847i 0.105245 0.206555i −0.832378 0.554208i \(-0.813021\pi\)
0.937623 + 0.347653i \(0.113021\pi\)
\(954\) 251.735 81.7935i 0.263873 0.0857375i
\(955\) −363.854 1619.90i −0.380999 1.69623i
\(956\) −226.077 + 695.794i −0.236482 + 0.727818i
\(957\) 723.171 723.171i 0.755664 0.755664i
\(958\) 629.843 320.921i 0.657456 0.334991i
\(959\) −639.206 879.792i −0.666534 0.917406i
\(960\) 69.1408 4.42188i 0.0720216 0.00460613i
\(961\) 674.946 + 490.377i 0.702337 + 0.510278i
\(962\) −0.605465 + 3.82276i −0.000629382 + 0.00397376i
\(963\) −558.137 88.4002i −0.579581 0.0917967i
\(964\) 555.254 764.242i 0.575990 0.792782i
\(965\) −1033.05 + 410.251i −1.07052 + 0.425131i
\(966\) 18.7888 13.6509i 0.0194501 0.0141313i
\(967\) −721.489 1416.00i −0.746111 1.46433i −0.880826 0.473441i \(-0.843012\pi\)
0.134714 0.990884i \(-0.456988\pi\)
\(968\) 94.8420 + 94.8420i 0.0979773 + 0.0979773i
\(969\) 46.0638 + 14.9670i 0.0475374 + 0.0154458i
\(970\) −317.951 + 361.399i −0.327785 + 0.372576i
\(971\) 55.4940 + 170.793i 0.0571514 + 0.175894i 0.975557 0.219746i \(-0.0705228\pi\)
−0.918406 + 0.395640i \(0.870523\pi\)
\(972\) −27.7788 14.1540i −0.0285790 0.0145618i
\(973\) 188.988 + 1193.22i 0.194232 + 1.22634i
\(974\) 130.970i 0.134466i
\(975\) −4.53391 + 0.582311i −0.00465016 + 0.000597242i
\(976\) 174.950 0.179252
\(977\) −107.860 + 17.0833i −0.110399 + 0.0174854i −0.211389 0.977402i \(-0.567799\pi\)
0.100991 + 0.994887i \(0.467799\pi\)
\(978\) −162.945 + 319.797i −0.166610 + 0.326991i
\(979\) −1278.52 + 415.416i −1.30595 + 0.424327i
\(980\) 194.683 + 18.1995i 0.198656 + 0.0185709i
\(981\) 135.738 417.760i 0.138367 0.425851i
\(982\) −38.2489 + 38.2489i −0.0389500 + 0.0389500i
\(983\) −279.983 + 142.658i −0.284825 + 0.145126i −0.590567 0.806989i \(-0.701096\pi\)
0.305741 + 0.952115i \(0.401096\pi\)
\(984\) −181.799 250.225i −0.184755 0.254294i
\(985\) −1115.86 + 925.066i −1.13285 + 0.939153i
\(986\) −419.413 304.722i −0.425368 0.309048i
\(987\) −98.6119 + 622.611i −0.0999108 + 0.630812i
\(988\) 0.723760 + 0.114632i 0.000732551 + 0.000116025i
\(989\) −75.1962 + 103.499i −0.0760325 + 0.104650i
\(990\) −266.721 68.1878i −0.269415 0.0688765i
\(991\) −1177.17 + 855.264i −1.18786 + 0.863032i −0.993037 0.117807i \(-0.962414\pi\)
−0.194825 + 0.980838i \(0.562414\pi\)
\(992\) 28.9098 + 56.7387i 0.0291430 + 0.0571963i
\(993\) 11.7633 + 11.7633i 0.0118462 + 0.0118462i
\(994\) −113.510 36.8816i −0.114195 0.0371043i
\(995\) −1515.63 654.007i −1.52324 0.657294i
\(996\) −107.933 332.183i −0.108366 0.333517i
\(997\) −1065.53 542.917i −1.06874 0.544551i −0.171089 0.985256i \(-0.554729\pi\)
−0.897652 + 0.440705i \(0.854729\pi\)
\(998\) 168.940 + 1066.64i 0.169278 + 1.06878i
\(999\) 134.710i 0.134845i
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 150.3.k.a.13.2 32
25.2 odd 20 inner 150.3.k.a.127.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.k.a.13.2 32 1.1 even 1 trivial
150.3.k.a.127.2 yes 32 25.2 odd 20 inner