Properties

Label 216.3.x.a.101.64
Level $216$
Weight $3$
Character 216.101
Analytic conductor $5.886$
Analytic rank $0$
Dimension $420$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [216,3,Mod(5,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.x (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.88557371018\)
Analytic rank: \(0\)
Dimension: \(420\)
Relative dimension: \(70\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 101.64
Character \(\chi\) \(=\) 216.101
Dual form 216.3.x.a.77.64

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.84234 - 0.778309i) q^{2} +(1.68752 + 2.48038i) q^{3} +(2.78847 - 2.86783i) q^{4} +(0.0158330 + 0.0897932i) q^{5} +(5.03950 + 3.25630i) q^{6} +(4.80570 + 4.03246i) q^{7} +(2.90527 - 7.45382i) q^{8} +(-3.30455 + 8.37138i) q^{9} +O(q^{10})\) \(q+(1.84234 - 0.778309i) q^{2} +(1.68752 + 2.48038i) q^{3} +(2.78847 - 2.86783i) q^{4} +(0.0158330 + 0.0897932i) q^{5} +(5.03950 + 3.25630i) q^{6} +(4.80570 + 4.03246i) q^{7} +(2.90527 - 7.45382i) q^{8} +(-3.30455 + 8.37138i) q^{9} +(0.0990567 + 0.153107i) q^{10} +(1.16979 - 6.63419i) q^{11} +(11.8189 + 2.07694i) q^{12} +(-3.44076 + 9.45340i) q^{13} +(11.9923 + 3.68886i) q^{14} +(-0.196003 + 0.190800i) q^{15} +(-0.448872 - 15.9937i) q^{16} +(8.06265 - 4.65498i) q^{17} +(0.427396 + 17.9949i) q^{18} +(-16.7972 - 9.69785i) q^{19} +(0.301661 + 0.204980i) q^{20} +(-1.89231 + 18.7248i) q^{21} +(-3.00830 - 13.1329i) q^{22} +(0.477626 + 0.569213i) q^{23} +(23.3910 - 5.37231i) q^{24} +(23.4845 - 8.54766i) q^{25} +(1.01861 + 20.0944i) q^{26} +(-26.3407 + 5.93033i) q^{27} +(24.9649 - 2.53752i) q^{28} +(-5.36461 + 1.95256i) q^{29} +(-0.212604 + 0.504070i) q^{30} +(-8.84587 + 7.42257i) q^{31} +(-13.2750 - 29.1166i) q^{32} +(18.4293 - 8.29381i) q^{33} +(11.2312 - 14.8513i) q^{34} +(-0.285999 + 0.495365i) q^{35} +(14.7930 + 32.8202i) q^{36} +(-45.0507 + 26.0100i) q^{37} +(-38.4941 - 4.79340i) q^{38} +(-29.2543 + 7.41843i) q^{39} +(0.715302 + 0.142857i) q^{40} +(16.1245 - 44.3018i) q^{41} +(11.0874 + 35.9703i) q^{42} +(-33.2309 - 5.85950i) q^{43} +(-15.7638 - 21.8540i) q^{44} +(-0.804014 - 0.164183i) q^{45} +(1.32298 + 0.676946i) q^{46} +(-12.2731 + 14.6265i) q^{47} +(38.9129 - 28.1031i) q^{48} +(-1.67476 - 9.49803i) q^{49} +(36.6138 - 34.0259i) q^{50} +(25.1520 + 12.1431i) q^{51} +(17.5163 + 36.2280i) q^{52} -31.3696 q^{53} +(-43.9130 + 31.4269i) q^{54} +0.614227 q^{55} +(44.0191 - 24.1054i) q^{56} +(-4.29123 - 58.0287i) q^{57} +(-8.36377 + 7.77261i) q^{58} +(-10.4833 - 59.4537i) q^{59} +(0.000632880 + 1.09414i) q^{60} +(38.9052 - 46.3654i) q^{61} +(-10.5201 + 20.5598i) q^{62} +(-49.6379 + 26.9048i) q^{63} +(-47.1188 - 43.3107i) q^{64} +(-0.903329 - 0.159281i) q^{65} +(27.4980 - 29.6238i) q^{66} +(-25.7894 + 70.8557i) q^{67} +(9.13280 - 36.1026i) q^{68} +(-0.605859 + 2.14525i) q^{69} +(-0.141362 + 1.13523i) q^{70} +(22.9941 - 13.2757i) q^{71} +(52.7981 + 48.9526i) q^{72} +(-11.2424 + 19.4724i) q^{73} +(-62.7550 + 82.9827i) q^{74} +(60.8320 + 43.8261i) q^{75} +(-74.6502 + 21.1292i) q^{76} +(32.3737 - 27.1648i) q^{77} +(-48.1228 + 36.4362i) q^{78} +(-136.839 + 49.8053i) q^{79} +(1.42902 - 0.293534i) q^{80} +(-59.1599 - 55.3273i) q^{81} +(-4.77353 - 94.1690i) q^{82} +(30.3624 - 11.0510i) q^{83} +(48.4229 + 57.6404i) q^{84} +(0.545641 + 0.650270i) q^{85} +(-65.7833 + 15.0687i) q^{86} +(-13.8960 - 10.0113i) q^{87} +(-46.0515 - 27.9935i) q^{88} +(95.4963 + 55.1348i) q^{89} +(-1.60906 + 0.323290i) q^{90} +(-54.6557 + 31.5555i) q^{91} +(2.96425 + 0.217483i) q^{92} +(-33.3384 - 9.41537i) q^{93} +(-11.2274 + 36.4994i) q^{94} +(0.604853 - 1.66182i) q^{95} +(49.8182 - 82.0618i) q^{96} +(-16.2700 + 92.2716i) q^{97} +(-10.4779 - 16.1952i) q^{98} +(51.6717 + 31.7157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 51 q^{12} + 39 q^{14} - 12 q^{15} - 6 q^{16} - 18 q^{17} - 27 q^{18} + 57 q^{20} - 6 q^{22} - 12 q^{23} + 126 q^{24} - 12 q^{25} - 12 q^{28} + 87 q^{30} - 12 q^{31} + 84 q^{32} - 36 q^{33} - 18 q^{34} - 36 q^{36} - 108 q^{38} - 12 q^{39} + 69 q^{40} - 84 q^{41} + 114 q^{42} - 657 q^{44} - 3 q^{46} - 12 q^{47} - 453 q^{48} - 12 q^{49} + 153 q^{50} + 21 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 66 q^{57} + 129 q^{58} + 210 q^{60} - 900 q^{62} + 468 q^{63} - 3 q^{64} - 12 q^{65} - 855 q^{66} + 279 q^{68} + 153 q^{70} - 18 q^{71} - 156 q^{72} - 6 q^{73} + 423 q^{74} - 54 q^{76} + 642 q^{78} - 12 q^{79} - 12 q^{81} - 12 q^{82} + 192 q^{84} + 606 q^{86} - 588 q^{87} + 186 q^{88} - 18 q^{89} - 534 q^{90} - 735 q^{92} + 345 q^{94} - 162 q^{95} - 486 q^{96} - 12 q^{97} - 1548 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84234 0.778309i 0.921172 0.389155i
\(3\) 1.68752 + 2.48038i 0.562507 + 0.826793i
\(4\) 2.78847 2.86783i 0.697117 0.716957i
\(5\) 0.0158330 + 0.0897932i 0.00316659 + 0.0179586i 0.986350 0.164662i \(-0.0526532\pi\)
−0.983184 + 0.182620i \(0.941542\pi\)
\(6\) 5.03950 + 3.25630i 0.839916 + 0.542717i
\(7\) 4.80570 + 4.03246i 0.686528 + 0.576066i 0.917906 0.396798i \(-0.129879\pi\)
−0.231378 + 0.972864i \(0.574323\pi\)
\(8\) 2.90527 7.45382i 0.363158 0.931727i
\(9\) −3.30455 + 8.37138i −0.367172 + 0.930153i
\(10\) 0.0990567 + 0.153107i 0.00990567 + 0.0153107i
\(11\) 1.16979 6.63419i 0.106344 0.603108i −0.884331 0.466861i \(-0.845385\pi\)
0.990675 0.136247i \(-0.0435041\pi\)
\(12\) 11.8189 + 2.07694i 0.984908 + 0.173079i
\(13\) −3.44076 + 9.45340i −0.264674 + 0.727184i 0.734164 + 0.678973i \(0.237574\pi\)
−0.998837 + 0.0482119i \(0.984648\pi\)
\(14\) 11.9923 + 3.68886i 0.856589 + 0.263490i
\(15\) −0.196003 + 0.190800i −0.0130668 + 0.0127200i
\(16\) −0.448872 15.9937i −0.0280545 0.999606i
\(17\) 8.06265 4.65498i 0.474274 0.273822i −0.243753 0.969837i \(-0.578379\pi\)
0.718027 + 0.696015i \(0.245045\pi\)
\(18\) 0.427396 + 17.9949i 0.0237442 + 0.999718i
\(19\) −16.7972 9.69785i −0.884062 0.510413i −0.0120664 0.999927i \(-0.503841\pi\)
−0.871996 + 0.489514i \(0.837174\pi\)
\(20\) 0.301661 + 0.204980i 0.0150831 + 0.0102490i
\(21\) −1.89231 + 18.7248i −0.0901100 + 0.891657i
\(22\) −3.00830 13.1329i −0.136741 0.596951i
\(23\) 0.477626 + 0.569213i 0.0207664 + 0.0247484i 0.776328 0.630330i \(-0.217080\pi\)
−0.755561 + 0.655078i \(0.772636\pi\)
\(24\) 23.3910 5.37231i 0.974624 0.223846i
\(25\) 23.4845 8.54766i 0.939380 0.341906i
\(26\) 1.01861 + 20.0944i 0.0391772 + 0.772861i
\(27\) −26.3407 + 5.93033i −0.975581 + 0.219642i
\(28\) 24.9649 2.53752i 0.891605 0.0906258i
\(29\) −5.36461 + 1.95256i −0.184987 + 0.0673296i −0.432853 0.901465i \(-0.642493\pi\)
0.247866 + 0.968794i \(0.420271\pi\)
\(30\) −0.212604 + 0.504070i −0.00708678 + 0.0168023i
\(31\) −8.84587 + 7.42257i −0.285351 + 0.239438i −0.774216 0.632922i \(-0.781855\pi\)
0.488865 + 0.872359i \(0.337411\pi\)
\(32\) −13.2750 29.1166i −0.414844 0.909892i
\(33\) 18.4293 8.29381i 0.558465 0.251328i
\(34\) 11.2312 14.8513i 0.330329 0.436803i
\(35\) −0.285999 + 0.495365i −0.00817140 + 0.0141533i
\(36\) 14.7930 + 32.8202i 0.410917 + 0.911673i
\(37\) −45.0507 + 26.0100i −1.21759 + 0.702973i −0.964401 0.264445i \(-0.914811\pi\)
−0.253184 + 0.967418i \(0.581478\pi\)
\(38\) −38.4941 4.79340i −1.01300 0.126142i
\(39\) −29.2543 + 7.41843i −0.750111 + 0.190216i
\(40\) 0.715302 + 0.142857i 0.0178825 + 0.00357143i
\(41\) 16.1245 44.3018i 0.393281 1.08053i −0.572213 0.820105i \(-0.693915\pi\)
0.965494 0.260426i \(-0.0838630\pi\)
\(42\) 11.0874 + 35.9703i 0.263986 + 0.856437i
\(43\) −33.2309 5.85950i −0.772811 0.136268i −0.226683 0.973969i \(-0.572788\pi\)
−0.546129 + 0.837701i \(0.683899\pi\)
\(44\) −15.7638 21.8540i −0.358268 0.496681i
\(45\) −0.804014 0.164183i −0.0178670 0.00364850i
\(46\) 1.32298 + 0.676946i 0.0287604 + 0.0147162i
\(47\) −12.2731 + 14.6265i −0.261130 + 0.311203i −0.880640 0.473786i \(-0.842887\pi\)
0.619510 + 0.784989i \(0.287331\pi\)
\(48\) 38.9129 28.1031i 0.810686 0.585481i
\(49\) −1.67476 9.49803i −0.0341787 0.193837i
\(50\) 36.6138 34.0259i 0.732277 0.680519i
\(51\) 25.1520 + 12.1431i 0.493176 + 0.238099i
\(52\) 17.5163 + 36.2280i 0.336851 + 0.696693i
\(53\) −31.3696 −0.591879 −0.295940 0.955207i \(-0.595633\pi\)
−0.295940 + 0.955207i \(0.595633\pi\)
\(54\) −43.9130 + 31.4269i −0.813203 + 0.581980i
\(55\) 0.614227 0.0111678
\(56\) 44.0191 24.1054i 0.786055 0.430454i
\(57\) −4.29123 58.0287i −0.0752847 1.01805i
\(58\) −8.36377 + 7.77261i −0.144203 + 0.134011i
\(59\) −10.4833 59.4537i −0.177683 1.00769i −0.935001 0.354644i \(-0.884602\pi\)
0.757319 0.653046i \(-0.226509\pi\)
\(60\) 0.000632880 1.09414i 1.05480e−5 0.0182357i
\(61\) 38.9052 46.3654i 0.637791 0.760089i −0.346229 0.938150i \(-0.612538\pi\)
0.984019 + 0.178061i \(0.0569824\pi\)
\(62\) −10.5201 + 20.5598i −0.169679 + 0.331609i
\(63\) −49.6379 + 26.9048i −0.787903 + 0.427061i
\(64\) −47.1188 43.3107i −0.736232 0.676729i
\(65\) −0.903329 0.159281i −0.0138974 0.00245048i
\(66\) 27.4980 29.6238i 0.416637 0.448845i
\(67\) −25.7894 + 70.8557i −0.384916 + 1.05755i 0.584343 + 0.811506i \(0.301352\pi\)
−0.969259 + 0.246041i \(0.920870\pi\)
\(68\) 9.13280 36.1026i 0.134306 0.530920i
\(69\) −0.605859 + 2.14525i −0.00878057 + 0.0310906i
\(70\) −0.141362 + 1.13523i −0.00201946 + 0.0162176i
\(71\) 22.9941 13.2757i 0.323861 0.186981i −0.329251 0.944242i \(-0.606796\pi\)
0.653112 + 0.757261i \(0.273463\pi\)
\(72\) 52.7981 + 48.9526i 0.733307 + 0.679897i
\(73\) −11.2424 + 19.4724i −0.154005 + 0.266745i −0.932696 0.360663i \(-0.882551\pi\)
0.778691 + 0.627407i \(0.215884\pi\)
\(74\) −62.7550 + 82.9827i −0.848041 + 1.12139i
\(75\) 60.8320 + 43.8261i 0.811093 + 0.584348i
\(76\) −74.6502 + 21.1292i −0.982239 + 0.278016i
\(77\) 32.3737 27.1648i 0.420438 0.352789i
\(78\) −48.1228 + 36.4362i −0.616959 + 0.467131i
\(79\) −136.839 + 49.8053i −1.73214 + 0.630446i −0.998779 0.0493963i \(-0.984270\pi\)
−0.733358 + 0.679843i \(0.762048\pi\)
\(80\) 1.42902 0.293534i 0.0178627 0.00366917i
\(81\) −59.1599 55.3273i −0.730369 0.683053i
\(82\) −4.77353 94.1690i −0.0582138 1.14840i
\(83\) 30.3624 11.0510i 0.365812 0.133145i −0.152573 0.988292i \(-0.548756\pi\)
0.518385 + 0.855148i \(0.326534\pi\)
\(84\) 48.4229 + 57.6404i 0.576463 + 0.686195i
\(85\) 0.545641 + 0.650270i 0.00641931 + 0.00765023i
\(86\) −65.7833 + 15.0687i −0.764922 + 0.175217i
\(87\) −13.8960 10.0113i −0.159724 0.115072i
\(88\) −46.0515 27.9935i −0.523312 0.318108i
\(89\) 95.4963 + 55.1348i 1.07299 + 0.619492i 0.928997 0.370086i \(-0.120672\pi\)
0.143995 + 0.989578i \(0.454005\pi\)
\(90\) −1.60906 + 0.323290i −0.0178784 + 0.00359212i
\(91\) −54.6557 + 31.5555i −0.600612 + 0.346763i
\(92\) 2.96425 + 0.217483i 0.0322201 + 0.00236395i
\(93\) −33.3384 9.41537i −0.358477 0.101241i
\(94\) −11.2274 + 36.4994i −0.119440 + 0.388292i
\(95\) 0.604853 1.66182i 0.00636687 0.0174928i
\(96\) 49.8182 82.0618i 0.518940 0.854811i
\(97\) −16.2700 + 92.2716i −0.167732 + 0.951254i 0.778471 + 0.627680i \(0.215995\pi\)
−0.946203 + 0.323574i \(0.895116\pi\)
\(98\) −10.4779 16.1952i −0.106917 0.165257i
\(99\) 51.6717 + 31.7157i 0.521936 + 0.320361i
\(100\) 40.9726 91.1844i 0.409726 0.911844i
\(101\) 112.985 + 94.8059i 1.11867 + 0.938673i 0.998536 0.0540854i \(-0.0172243\pi\)
0.120130 + 0.992758i \(0.461669\pi\)
\(102\) 55.7897 + 2.79569i 0.546958 + 0.0274087i
\(103\) 34.4629 + 195.449i 0.334592 + 1.89756i 0.431227 + 0.902244i \(0.358081\pi\)
−0.0966350 + 0.995320i \(0.530808\pi\)
\(104\) 60.4676 + 53.1114i 0.581419 + 0.510687i
\(105\) −1.71132 + 0.126553i −0.0162983 + 0.00120526i
\(106\) −57.7936 + 24.4152i −0.545223 + 0.230332i
\(107\) −96.8594 −0.905228 −0.452614 0.891707i \(-0.649508\pi\)
−0.452614 + 0.891707i \(0.649508\pi\)
\(108\) −56.4430 + 92.0771i −0.522620 + 0.852565i
\(109\) 127.296i 1.16785i −0.811807 0.583926i \(-0.801516\pi\)
0.811807 0.583926i \(-0.198484\pi\)
\(110\) 1.13162 0.478058i 0.0102874 0.00434598i
\(111\) −140.539 67.8502i −1.26611 0.611263i
\(112\) 62.3368 78.6709i 0.556579 0.702419i
\(113\) 210.930 37.1926i 1.86663 0.329138i 0.877903 0.478839i \(-0.158942\pi\)
0.988731 + 0.149702i \(0.0478313\pi\)
\(114\) −53.0702 103.569i −0.465528 0.908499i
\(115\) −0.0435492 + 0.0519000i −0.000378689 + 0.000451304i
\(116\) −9.35945 + 20.8294i −0.0806849 + 0.179564i
\(117\) −67.7678 60.0431i −0.579212 0.513189i
\(118\) −65.5872 101.375i −0.555823 0.859110i
\(119\) 57.5177 + 10.1419i 0.483342 + 0.0852262i
\(120\) 0.852746 + 2.01529i 0.00710622 + 0.0167941i
\(121\) 71.0588 + 25.8633i 0.587262 + 0.213746i
\(122\) 35.5902 115.701i 0.291723 0.948372i
\(123\) 137.096 34.7652i 1.11460 0.282644i
\(124\) −3.37980 + 46.0660i −0.0272565 + 0.371500i
\(125\) 2.27908 + 3.94749i 0.0182327 + 0.0315799i
\(126\) −70.5099 + 88.2016i −0.559602 + 0.700013i
\(127\) 39.7238 68.8036i 0.312786 0.541760i −0.666179 0.745792i \(-0.732071\pi\)
0.978964 + 0.204032i \(0.0654046\pi\)
\(128\) −120.518 43.1202i −0.941549 0.336876i
\(129\) −41.5440 92.3132i −0.322047 0.715606i
\(130\) −1.78821 + 0.409618i −0.0137555 + 0.00315091i
\(131\) 116.464 97.7247i 0.889037 0.745990i −0.0789801 0.996876i \(-0.525166\pi\)
0.968017 + 0.250886i \(0.0807219\pi\)
\(132\) 27.6044 75.9792i 0.209124 0.575600i
\(133\) −41.6159 114.339i −0.312902 0.859691i
\(134\) 7.63473 + 150.613i 0.0569756 + 1.12398i
\(135\) −0.949555 2.27132i −0.00703374 0.0168246i
\(136\) −11.2732 73.6215i −0.0828911 0.541335i
\(137\) −68.8364 189.127i −0.502456 1.38049i −0.888870 0.458160i \(-0.848509\pi\)
0.386414 0.922326i \(-0.373714\pi\)
\(138\) 0.553468 + 4.42384i 0.00401064 + 0.0320568i
\(139\) −11.2356 13.3900i −0.0808315 0.0963313i 0.724113 0.689681i \(-0.242249\pi\)
−0.804944 + 0.593350i \(0.797805\pi\)
\(140\) 0.623122 + 2.20151i 0.00445087 + 0.0157250i
\(141\) −56.9905 5.75941i −0.404188 0.0408469i
\(142\) 32.0305 42.3549i 0.225567 0.298274i
\(143\) 58.6907 + 33.8851i 0.410424 + 0.236959i
\(144\) 135.373 + 49.0943i 0.940088 + 0.340933i
\(145\) −0.260264 0.450791i −0.00179493 0.00310890i
\(146\) −5.55681 + 44.6248i −0.0380604 + 0.305650i
\(147\) 20.7325 20.1821i 0.141037 0.137294i
\(148\) −51.0302 + 201.726i −0.344798 + 1.36301i
\(149\) 117.852 + 42.8946i 0.790953 + 0.287883i 0.705732 0.708479i \(-0.250618\pi\)
0.0852206 + 0.996362i \(0.472840\pi\)
\(150\) 146.184 + 33.3967i 0.974559 + 0.222645i
\(151\) −19.8744 + 112.713i −0.131619 + 0.746447i 0.845536 + 0.533918i \(0.179281\pi\)
−0.977155 + 0.212529i \(0.931830\pi\)
\(152\) −121.086 + 97.0283i −0.796621 + 0.638344i
\(153\) 12.3251 + 82.8781i 0.0805562 + 0.541687i
\(154\) 38.5010 75.2437i 0.250006 0.488595i
\(155\) −0.806553 0.676778i −0.00520357 0.00436631i
\(156\) −60.3001 + 104.582i −0.386539 + 0.670401i
\(157\) 282.859 49.8757i 1.80165 0.317680i 0.830657 0.556784i \(-0.187965\pi\)
0.970994 + 0.239104i \(0.0768538\pi\)
\(158\) −213.340 + 198.261i −1.35026 + 1.25482i
\(159\) −52.9368 77.8084i −0.332936 0.489361i
\(160\) 2.40429 1.65301i 0.0150268 0.0103313i
\(161\) 4.66147i 0.0289533i
\(162\) −152.055 55.8873i −0.938609 0.344983i
\(163\) 226.336i 1.38857i 0.719701 + 0.694284i \(0.244279\pi\)
−0.719701 + 0.694284i \(0.755721\pi\)
\(164\) −82.0871 169.777i −0.500531 1.03522i
\(165\) 1.03652 + 1.52351i 0.00628194 + 0.00923342i
\(166\) 47.3369 43.9911i 0.285162 0.265007i
\(167\) 170.846 30.1248i 1.02303 0.180388i 0.363128 0.931739i \(-0.381709\pi\)
0.659902 + 0.751351i \(0.270598\pi\)
\(168\) 134.074 + 68.5055i 0.798057 + 0.407771i
\(169\) 51.9336 + 43.5774i 0.307299 + 0.257855i
\(170\) 1.51137 + 0.773344i 0.00889041 + 0.00454908i
\(171\) 136.692 108.568i 0.799366 0.634903i
\(172\) −109.467 + 78.9614i −0.636438 + 0.459078i
\(173\) −38.7423 + 219.718i −0.223944 + 1.27005i 0.640751 + 0.767749i \(0.278623\pi\)
−0.864694 + 0.502299i \(0.832488\pi\)
\(174\) −33.3930 7.62887i −0.191914 0.0438441i
\(175\) 147.328 + 53.6228i 0.841871 + 0.306416i
\(176\) −106.630 15.7313i −0.605854 0.0893825i
\(177\) 129.777 126.332i 0.733202 0.713739i
\(178\) 218.849 + 27.2517i 1.22949 + 0.153099i
\(179\) −130.256 225.610i −0.727686 1.26039i −0.957859 0.287240i \(-0.907262\pi\)
0.230172 0.973150i \(-0.426071\pi\)
\(180\) −2.71282 + 1.84796i −0.0150712 + 0.0102664i
\(181\) 244.458 + 141.138i 1.35060 + 0.779768i 0.988333 0.152307i \(-0.0486703\pi\)
0.362265 + 0.932075i \(0.382004\pi\)
\(182\) −76.1347 + 100.675i −0.418322 + 0.553160i
\(183\) 180.657 + 18.2570i 0.987198 + 0.0997653i
\(184\) 5.63044 1.90643i 0.0306002 0.0103610i
\(185\) −3.04881 3.63343i −0.0164800 0.0196402i
\(186\) −68.7488 + 8.60119i −0.369617 + 0.0462429i
\(187\) −21.4504 58.9345i −0.114708 0.315158i
\(188\) 7.72316 + 75.9829i 0.0410807 + 0.404164i
\(189\) −150.499 77.7183i −0.796292 0.411208i
\(190\) −0.179062 3.53241i −0.000942430 0.0185916i
\(191\) −38.4531 105.649i −0.201325 0.553136i 0.797409 0.603439i \(-0.206203\pi\)
−0.998734 + 0.0503035i \(0.983981\pi\)
\(192\) 27.9128 189.960i 0.145379 0.989376i
\(193\) −46.1834 + 38.7525i −0.239292 + 0.200790i −0.754545 0.656248i \(-0.772142\pi\)
0.515253 + 0.857038i \(0.327698\pi\)
\(194\) 41.8409 + 182.659i 0.215675 + 0.941542i
\(195\) −1.12931 2.50939i −0.00579132 0.0128687i
\(196\) −31.9087 21.6820i −0.162800 0.110623i
\(197\) −140.618 + 243.558i −0.713799 + 1.23634i 0.249622 + 0.968343i \(0.419694\pi\)
−0.963421 + 0.267993i \(0.913640\pi\)
\(198\) 119.882 + 18.2148i 0.605463 + 0.0919939i
\(199\) −108.873 188.573i −0.547098 0.947602i −0.998472 0.0552668i \(-0.982399\pi\)
0.451373 0.892335i \(-0.350934\pi\)
\(200\) 4.51603 199.882i 0.0225802 0.999412i
\(201\) −219.269 + 55.6030i −1.09089 + 0.276632i
\(202\) 281.946 + 86.7278i 1.39577 + 0.429345i
\(203\) −33.6543 12.2492i −0.165785 0.0603407i
\(204\) 104.960 38.2710i 0.514509 0.187603i
\(205\) 4.23330 + 0.746445i 0.0206502 + 0.00364119i
\(206\) 215.612 + 333.262i 1.04666 + 1.61778i
\(207\) −6.34344 + 2.11740i −0.0306446 + 0.0102290i
\(208\) 152.739 + 50.7871i 0.734324 + 0.244169i
\(209\) −83.9865 + 100.091i −0.401849 + 0.478905i
\(210\) −3.05435 + 1.56509i −0.0145445 + 0.00745281i
\(211\) 170.678 30.0952i 0.808902 0.142631i 0.246123 0.969239i \(-0.420843\pi\)
0.562779 + 0.826607i \(0.309732\pi\)
\(212\) −87.4732 + 89.9626i −0.412609 + 0.424352i
\(213\) 71.7317 + 34.6312i 0.336769 + 0.162588i
\(214\) −178.448 + 75.3865i −0.833871 + 0.352273i
\(215\) 3.07668i 0.0143102i
\(216\) −32.3231 + 213.568i −0.149644 + 0.988740i
\(217\) −72.4418 −0.333833
\(218\) −99.0755 234.523i −0.454475 1.07579i
\(219\) −67.2705 + 4.97467i −0.307171 + 0.0227154i
\(220\) 1.71275 1.76150i 0.00778524 0.00800680i
\(221\) 16.2637 + 92.2361i 0.0735915 + 0.417358i
\(222\) −311.729 15.6211i −1.40418 0.0703654i
\(223\) −101.720 85.3535i −0.456145 0.382751i 0.385565 0.922681i \(-0.374006\pi\)
−0.841710 + 0.539929i \(0.818451\pi\)
\(224\) 53.6156 193.456i 0.239355 0.863644i
\(225\) −6.05005 + 224.844i −0.0268891 + 0.999306i
\(226\) 359.658 232.690i 1.59141 1.02960i
\(227\) −30.0632 + 170.497i −0.132437 + 0.751088i 0.844173 + 0.536071i \(0.180092\pi\)
−0.976610 + 0.215017i \(0.931019\pi\)
\(228\) −178.382 149.505i −0.782378 0.655722i
\(229\) 43.6299 119.872i 0.190524 0.523460i −0.807246 0.590216i \(-0.799043\pi\)
0.997769 + 0.0667561i \(0.0212649\pi\)
\(230\) −0.0398385 + 0.129512i −0.000173211 + 0.000563097i
\(231\) 122.010 + 34.4580i 0.528183 + 0.149169i
\(232\) −1.03161 + 45.6595i −0.00444658 + 0.196808i
\(233\) −332.368 + 191.893i −1.42647 + 0.823574i −0.996840 0.0794303i \(-0.974690\pi\)
−0.429632 + 0.903004i \(0.641357\pi\)
\(234\) −171.584 57.8758i −0.733264 0.247332i
\(235\) −1.50769 0.870463i −0.00641568 0.00370410i
\(236\) −199.735 135.721i −0.846336 0.575087i
\(237\) −354.454 255.365i −1.49559 1.07749i
\(238\) 113.861 26.0816i 0.478407 0.109587i
\(239\) −193.217 230.267i −0.808439 0.963460i 0.191398 0.981513i \(-0.438698\pi\)
−0.999837 + 0.0180522i \(0.994254\pi\)
\(240\) 3.13957 + 3.04916i 0.0130816 + 0.0127049i
\(241\) −59.4335 + 21.6320i −0.246612 + 0.0897594i −0.462369 0.886688i \(-0.653000\pi\)
0.215757 + 0.976447i \(0.430778\pi\)
\(242\) 151.044 7.65661i 0.624150 0.0316389i
\(243\) 37.3991 240.105i 0.153906 0.988086i
\(244\) −24.4821 240.862i −0.100336 0.987140i
\(245\) 0.826342 0.300764i 0.00337283 0.00122761i
\(246\) 225.519 170.752i 0.916745 0.694115i
\(247\) 149.473 125.422i 0.605152 0.507783i
\(248\) 29.6269 + 87.5001i 0.119463 + 0.352823i
\(249\) 78.6478 + 56.6614i 0.315855 + 0.227556i
\(250\) 7.27122 + 5.49880i 0.0290849 + 0.0219952i
\(251\) 18.9371 32.8000i 0.0754466 0.130677i −0.825834 0.563914i \(-0.809295\pi\)
0.901280 + 0.433236i \(0.142628\pi\)
\(252\) −61.2554 + 217.376i −0.243077 + 0.862604i
\(253\) 4.33499 2.50281i 0.0171343 0.00989251i
\(254\) 19.6344 157.677i 0.0773009 0.620777i
\(255\) −0.692134 + 2.45074i −0.00271425 + 0.00961074i
\(256\) −255.597 + 14.3582i −0.998426 + 0.0560869i
\(257\) −41.1816 + 113.145i −0.160240 + 0.440255i −0.993666 0.112376i \(-0.964154\pi\)
0.833426 + 0.552631i \(0.186376\pi\)
\(258\) −148.387 137.739i −0.575142 0.533871i
\(259\) −321.384 56.6687i −1.24087 0.218798i
\(260\) −2.97570 + 2.14644i −0.0114450 + 0.00825554i
\(261\) 1.38203 51.3615i 0.00529512 0.196787i
\(262\) 138.506 270.687i 0.528651 1.03316i
\(263\) −241.678 + 288.021i −0.918928 + 1.09514i 0.0762538 + 0.997088i \(0.475704\pi\)
−0.995182 + 0.0980473i \(0.968740\pi\)
\(264\) −8.27846 161.465i −0.0313578 0.611609i
\(265\) −0.496674 2.81678i −0.00187424 0.0106293i
\(266\) −165.662 178.262i −0.622789 0.670156i
\(267\) 24.3968 + 329.908i 0.0913736 + 1.23561i
\(268\) 131.289 + 271.538i 0.489885 + 1.01320i
\(269\) −142.107 −0.528278 −0.264139 0.964485i \(-0.585088\pi\)
−0.264139 + 0.964485i \(0.585088\pi\)
\(270\) −3.51720 3.44551i −0.0130267 0.0127611i
\(271\) 143.794 0.530607 0.265303 0.964165i \(-0.414528\pi\)
0.265303 + 0.964165i \(0.414528\pi\)
\(272\) −78.0694 126.862i −0.287020 0.466405i
\(273\) −170.502 82.3162i −0.624550 0.301525i
\(274\) −274.019 294.860i −1.00007 1.07613i
\(275\) −29.2349 165.800i −0.106309 0.602907i
\(276\) 4.46279 + 7.71947i 0.0161695 + 0.0279691i
\(277\) −12.7030 + 15.1388i −0.0458592 + 0.0546528i −0.788486 0.615052i \(-0.789135\pi\)
0.742627 + 0.669705i \(0.233579\pi\)
\(278\) −31.1214 15.9243i −0.111948 0.0572817i
\(279\) −32.9055 98.5804i −0.117941 0.353335i
\(280\) 2.86146 + 3.57095i 0.0102195 + 0.0127534i
\(281\) −13.1397 2.31689i −0.0467607 0.00824517i 0.150219 0.988653i \(-0.452002\pi\)
−0.196980 + 0.980408i \(0.563113\pi\)
\(282\) −109.479 + 33.7454i −0.388223 + 0.119665i
\(283\) −37.6450 + 103.429i −0.133021 + 0.365473i −0.988264 0.152754i \(-0.951186\pi\)
0.855243 + 0.518227i \(0.173408\pi\)
\(284\) 26.0461 102.962i 0.0917116 0.362542i
\(285\) 5.14264 1.30409i 0.0180444 0.00457575i
\(286\) 134.502 + 16.7485i 0.470285 + 0.0585612i
\(287\) 256.135 147.879i 0.892455 0.515259i
\(288\) 287.614 14.9131i 0.998658 0.0517815i
\(289\) −101.162 + 175.218i −0.350043 + 0.606292i
\(290\) −0.830351 0.627946i −0.00286328 0.00216533i
\(291\) −256.324 + 115.355i −0.880840 + 0.396407i
\(292\) 24.4944 + 86.5393i 0.0838848 + 0.296367i
\(293\) 19.8199 16.6309i 0.0676448 0.0567607i −0.608338 0.793678i \(-0.708164\pi\)
0.675983 + 0.736917i \(0.263719\pi\)
\(294\) 22.4885 53.3188i 0.0764915 0.181356i
\(295\) 5.17256 1.88266i 0.0175341 0.00638189i
\(296\) 62.9897 + 411.365i 0.212803 + 1.38975i
\(297\) 8.52997 + 181.686i 0.0287205 + 0.611738i
\(298\) 250.509 12.6986i 0.840635 0.0426127i
\(299\) −7.02439 + 2.55667i −0.0234929 + 0.00855073i
\(300\) 295.314 52.2480i 0.984380 0.174160i
\(301\) −136.069 162.161i −0.452058 0.538742i
\(302\) 51.1104 + 223.126i 0.169240 + 0.738826i
\(303\) −44.4896 + 440.233i −0.146830 + 1.45292i
\(304\) −147.565 + 273.002i −0.485411 + 0.898033i
\(305\) 4.77929 + 2.75932i 0.0156698 + 0.00904696i
\(306\) 87.2119 + 143.097i 0.285006 + 0.467638i
\(307\) −210.510 + 121.538i −0.685701 + 0.395890i −0.802000 0.597324i \(-0.796230\pi\)
0.116298 + 0.993214i \(0.462897\pi\)
\(308\) 12.3692 168.590i 0.0401599 0.547372i
\(309\) −426.631 + 415.305i −1.38068 + 1.34403i
\(310\) −2.01269 0.619112i −0.00649255 0.00199713i
\(311\) 70.5333 193.789i 0.226795 0.623115i −0.773143 0.634232i \(-0.781317\pi\)
0.999938 + 0.0111171i \(0.00353874\pi\)
\(312\) −29.6961 + 239.609i −0.0951797 + 0.767978i
\(313\) 38.6125 218.982i 0.123363 0.699624i −0.858904 0.512136i \(-0.828854\pi\)
0.982267 0.187488i \(-0.0600346\pi\)
\(314\) 482.306 312.040i 1.53600 0.993759i
\(315\) −3.20179 4.03116i −0.0101644 0.0127973i
\(316\) −238.738 + 531.311i −0.755500 + 1.68136i
\(317\) 11.3747 + 9.54451i 0.0358824 + 0.0301089i 0.660552 0.750780i \(-0.270322\pi\)
−0.624670 + 0.780889i \(0.714767\pi\)
\(318\) −158.087 102.149i −0.497129 0.321223i
\(319\) 6.67819 + 37.8739i 0.0209348 + 0.118727i
\(320\) 3.14297 4.91669i 0.00982179 0.0153647i
\(321\) −163.452 240.248i −0.509197 0.748436i
\(322\) 3.62807 + 8.58804i 0.0112673 + 0.0266709i
\(323\) −180.573 −0.559050
\(324\) −323.635 + 15.3819i −0.998872 + 0.0474751i
\(325\) 251.419i 0.773596i
\(326\) 176.160 + 416.990i 0.540367 + 1.27911i
\(327\) 315.742 214.814i 0.965571 0.656924i
\(328\) −283.371 248.898i −0.863937 0.758835i
\(329\) −117.962 + 20.7999i −0.358547 + 0.0632215i
\(330\) 3.09539 + 2.00011i 0.00937997 + 0.00606093i
\(331\) −133.336 + 158.903i −0.402827 + 0.480071i −0.928880 0.370381i \(-0.879227\pi\)
0.526052 + 0.850452i \(0.323672\pi\)
\(332\) 52.9722 117.889i 0.159555 0.355089i
\(333\) −68.8674 463.087i −0.206809 1.39065i
\(334\) 291.311 188.471i 0.872189 0.564285i
\(335\) −6.77069 1.19385i −0.0202110 0.00356374i
\(336\) 300.328 + 21.8600i 0.893834 + 0.0650596i
\(337\) −224.249 81.6199i −0.665427 0.242196i −0.0128494 0.999917i \(-0.504090\pi\)
−0.652578 + 0.757722i \(0.726312\pi\)
\(338\) 129.596 + 39.8643i 0.383421 + 0.117942i
\(339\) 448.200 + 460.422i 1.32212 + 1.35818i
\(340\) 3.38637 + 0.248453i 0.00995990 + 0.000730744i
\(341\) 38.8949 + 67.3680i 0.114061 + 0.197560i
\(342\) 167.333 306.409i 0.489278 0.895932i
\(343\) 183.950 318.611i 0.536298 0.928895i
\(344\) −140.220 + 230.674i −0.407617 + 0.670563i
\(345\) −0.202222 0.0204363i −0.000586150 5.92358e-5i
\(346\) 99.6321 + 434.950i 0.287954 + 1.25708i
\(347\) 98.2213 82.4175i 0.283058 0.237514i −0.490193 0.871614i \(-0.663074\pi\)
0.773251 + 0.634100i \(0.218629\pi\)
\(348\) −67.4591 + 11.9351i −0.193848 + 0.0342963i
\(349\) −180.467 495.830i −0.517099 1.42072i −0.873702 0.486461i \(-0.838288\pi\)
0.356604 0.934256i \(-0.383935\pi\)
\(350\) 313.163 15.8746i 0.894752 0.0453560i
\(351\) 34.5700 269.414i 0.0984901 0.767560i
\(352\) −208.694 + 54.0088i −0.592880 + 0.153434i
\(353\) −90.1021 247.554i −0.255247 0.701285i −0.999445 0.0333255i \(-0.989390\pi\)
0.744198 0.667959i \(-0.232832\pi\)
\(354\) 140.769 333.753i 0.397651 0.942806i
\(355\) 1.55613 + 1.85452i 0.00438347 + 0.00522401i
\(356\) 424.406 120.125i 1.19215 0.337430i
\(357\) 71.9064 + 159.780i 0.201419 + 0.447564i
\(358\) −415.570 314.272i −1.16081 0.877854i
\(359\) 454.091 + 262.170i 1.26488 + 0.730278i 0.974014 0.226487i \(-0.0727241\pi\)
0.290864 + 0.956765i \(0.406057\pi\)
\(360\) −3.55966 + 5.51598i −0.00988795 + 0.0153222i
\(361\) 7.59678 + 13.1580i 0.0210437 + 0.0364488i
\(362\) 560.225 + 69.7609i 1.54758 + 0.192710i
\(363\) 55.7624 + 219.897i 0.153615 + 0.605778i
\(364\) −61.9100 + 244.735i −0.170083 + 0.672348i
\(365\) −1.92649 0.701184i −0.00527805 0.00192105i
\(366\) 347.042 106.971i 0.948203 0.292271i
\(367\) 28.6991 162.761i 0.0781992 0.443490i −0.920419 0.390934i \(-0.872152\pi\)
0.998618 0.0525559i \(-0.0167368\pi\)
\(368\) 8.88943 7.89452i 0.0241561 0.0214525i
\(369\) 317.583 + 281.382i 0.860657 + 0.762553i
\(370\) −8.44489 4.32111i −0.0228240 0.0116787i
\(371\) −150.753 126.497i −0.406342 0.340961i
\(372\) −119.965 + 69.3542i −0.322486 + 0.186436i
\(373\) 552.028 97.3375i 1.47997 0.260958i 0.625403 0.780302i \(-0.284934\pi\)
0.854566 + 0.519343i \(0.173823\pi\)
\(374\) −85.3883 91.8826i −0.228311 0.245675i
\(375\) −5.94526 + 12.3144i −0.0158540 + 0.0328385i
\(376\) 73.3669 + 133.976i 0.195125 + 0.356318i
\(377\) 57.4321i 0.152340i
\(378\) −337.760 26.0491i −0.893545 0.0689129i
\(379\) 586.224i 1.54677i 0.633940 + 0.773383i \(0.281437\pi\)
−0.633940 + 0.773383i \(0.718563\pi\)
\(380\) −3.07920 6.36855i −0.00810315 0.0167593i
\(381\) 237.694 17.5775i 0.623868 0.0461351i
\(382\) −153.071 164.713i −0.400710 0.431187i
\(383\) −531.424 + 93.7043i −1.38753 + 0.244659i −0.817009 0.576625i \(-0.804370\pi\)
−0.570520 + 0.821284i \(0.693258\pi\)
\(384\) −96.4227 371.697i −0.251101 0.967961i
\(385\) 2.95179 + 2.47684i 0.00766698 + 0.00643336i
\(386\) −54.9244 + 107.340i −0.142291 + 0.278084i
\(387\) 158.865 258.825i 0.410505 0.668799i
\(388\) 219.251 + 303.956i 0.565079 + 0.783392i
\(389\) −54.4757 + 308.947i −0.140040 + 0.794208i 0.831176 + 0.556009i \(0.187668\pi\)
−0.971216 + 0.238199i \(0.923443\pi\)
\(390\) −4.03365 3.74421i −0.0103427 0.00960053i
\(391\) 6.50061 + 2.36603i 0.0166256 + 0.00605122i
\(392\) −75.6622 15.1110i −0.193016 0.0385484i
\(393\) 438.929 + 123.962i 1.11687 + 0.315424i
\(394\) −69.5040 + 558.163i −0.176406 + 1.41666i
\(395\) −6.63874 11.4986i −0.0168069 0.0291105i
\(396\) 235.040 59.7471i 0.593536 0.150876i
\(397\) −158.354 91.4259i −0.398877 0.230292i 0.287122 0.957894i \(-0.407301\pi\)
−0.685999 + 0.727602i \(0.740635\pi\)
\(398\) −347.349 262.680i −0.872736 0.659999i
\(399\) 213.376 296.172i 0.534777 0.742287i
\(400\) −147.250 371.767i −0.368126 0.929418i
\(401\) 351.664 + 419.097i 0.876968 + 1.04513i 0.998618 + 0.0525568i \(0.0167371\pi\)
−0.121650 + 0.992573i \(0.538818\pi\)
\(402\) −360.693 + 273.099i −0.897246 + 0.679351i
\(403\) −39.7320 109.163i −0.0985906 0.270875i
\(404\) 586.943 59.6589i 1.45283 0.147671i
\(405\) 4.03134 6.18815i 0.00995392 0.0152794i
\(406\) −71.5365 + 3.62626i −0.176198 + 0.00893169i
\(407\) 119.856 + 329.301i 0.294486 + 0.809092i
\(408\) 163.585 152.200i 0.400945 0.373038i
\(409\) 87.3255 73.2748i 0.213510 0.179156i −0.529760 0.848147i \(-0.677718\pi\)
0.743270 + 0.668991i \(0.233274\pi\)
\(410\) 8.38016 1.91961i 0.0204394 0.00468197i
\(411\) 352.943 489.895i 0.858741 1.19196i
\(412\) 656.613 + 446.170i 1.59372 + 1.08294i
\(413\) 189.365 327.990i 0.458511 0.794164i
\(414\) −10.0388 + 8.83813i −0.0242483 + 0.0213481i
\(415\) 1.47303 + 2.55137i 0.00354948 + 0.00614787i
\(416\) 320.926 25.3111i 0.771458 0.0608440i
\(417\) 14.2521 50.4645i 0.0341777 0.121018i
\(418\) −76.8302 + 249.770i −0.183804 + 0.597536i
\(419\) 144.532 + 52.6055i 0.344946 + 0.125550i 0.508683 0.860954i \(-0.330133\pi\)
−0.163737 + 0.986504i \(0.552355\pi\)
\(420\) −4.40904 + 5.26066i −0.0104977 + 0.0125254i
\(421\) 17.6517 + 3.11247i 0.0419281 + 0.00739305i 0.194573 0.980888i \(-0.437668\pi\)
−0.152645 + 0.988281i \(0.548779\pi\)
\(422\) 291.025 188.286i 0.689633 0.446176i
\(423\) −81.8872 151.077i −0.193587 0.357156i
\(424\) −91.1370 + 233.823i −0.214946 + 0.551470i
\(425\) 149.558 178.237i 0.351902 0.419380i
\(426\) 159.108 + 7.97311i 0.373494 + 0.0187162i
\(427\) 373.933 65.9346i 0.875722 0.154413i
\(428\) −270.089 + 277.776i −0.631050 + 0.649009i
\(429\) 14.9939 + 202.757i 0.0349508 + 0.472627i
\(430\) −2.39461 5.66831i −0.00556886 0.0131821i
\(431\) 498.923i 1.15759i −0.815472 0.578797i \(-0.803522\pi\)
0.815472 0.578797i \(-0.196478\pi\)
\(432\) 106.672 + 418.623i 0.246925 + 0.969035i
\(433\) −38.6641 −0.0892936 −0.0446468 0.999003i \(-0.514216\pi\)
−0.0446468 + 0.999003i \(0.514216\pi\)
\(434\) −133.463 + 56.3821i −0.307518 + 0.129913i
\(435\) 0.678931 1.40627i 0.00156076 0.00323281i
\(436\) −365.063 354.961i −0.837299 0.814130i
\(437\) −2.50263 14.1931i −0.00572684 0.0324785i
\(438\) −120.064 + 61.5223i −0.274118 + 0.140462i
\(439\) −239.442 200.915i −0.545425 0.457666i 0.327963 0.944690i \(-0.393638\pi\)
−0.873388 + 0.487025i \(0.838082\pi\)
\(440\) 1.78449 4.57833i 0.00405566 0.0104053i
\(441\) 85.0459 + 17.3667i 0.192848 + 0.0393802i
\(442\) 101.752 + 157.273i 0.230207 + 0.355820i
\(443\) 71.2504 404.081i 0.160836 0.912147i −0.792418 0.609978i \(-0.791178\pi\)
0.953254 0.302169i \(-0.0977106\pi\)
\(444\) −586.470 + 213.842i −1.32088 + 0.481626i
\(445\) −3.43874 + 9.44787i −0.00772751 + 0.0212312i
\(446\) −253.835 78.0807i −0.569138 0.175069i
\(447\) 92.4827 + 364.703i 0.206896 + 0.815890i
\(448\) −51.7904 398.143i −0.115604 0.888712i
\(449\) −709.114 + 409.407i −1.57932 + 0.911820i −0.584365 + 0.811491i \(0.698656\pi\)
−0.994954 + 0.100330i \(0.968010\pi\)
\(450\) 163.852 + 418.949i 0.364115 + 0.930997i
\(451\) −275.044 158.797i −0.609854 0.352099i
\(452\) 481.509 708.620i 1.06529 1.56774i
\(453\) −313.111 + 140.910i −0.691193 + 0.311060i
\(454\) 77.3125 + 337.513i 0.170292 + 0.743420i
\(455\) −3.69883 4.40809i −0.00812930 0.00968812i
\(456\) −445.002 136.603i −0.975883 0.299567i
\(457\) 640.017 232.947i 1.40048 0.509731i 0.472156 0.881515i \(-0.343476\pi\)
0.928319 + 0.371784i \(0.121254\pi\)
\(458\) −12.9163 254.804i −0.0282015 0.556340i
\(459\) −184.770 + 170.429i −0.402549 + 0.371306i
\(460\) 0.0274044 + 0.269613i 5.95748e−5 + 0.000586116i
\(461\) 291.510 106.101i 0.632343 0.230154i −0.00590777 0.999983i \(-0.501881\pi\)
0.638251 + 0.769829i \(0.279658\pi\)
\(462\) 251.604 31.4782i 0.544597 0.0681347i
\(463\) −71.4292 + 59.9362i −0.154275 + 0.129452i −0.716658 0.697425i \(-0.754329\pi\)
0.562383 + 0.826877i \(0.309885\pi\)
\(464\) 33.6367 + 84.9235i 0.0724928 + 0.183025i
\(465\) 0.317592 3.14263i 0.000682993 0.00675835i
\(466\) −462.985 + 612.218i −0.993529 + 1.31377i
\(467\) 6.25150 10.8279i 0.0133865 0.0231861i −0.859255 0.511548i \(-0.829072\pi\)
0.872641 + 0.488362i \(0.162405\pi\)
\(468\) −361.162 + 26.9180i −0.771713 + 0.0575171i
\(469\) −409.659 + 236.516i −0.873472 + 0.504300i
\(470\) −3.45517 0.430247i −0.00735142 0.000915419i
\(471\) 601.041 + 617.432i 1.27610 + 1.31090i
\(472\) −473.614 94.5883i −1.00342 0.200399i
\(473\) −77.7461 + 213.606i −0.164368 + 0.451597i
\(474\) −851.780 194.595i −1.79700 0.410538i
\(475\) −477.367 84.1727i −1.00498 0.177206i
\(476\) 189.472 136.670i 0.398049 0.287123i
\(477\) 103.662 262.607i 0.217322 0.550538i
\(478\) −535.191 273.849i −1.11965 0.572905i
\(479\) −298.537 + 355.783i −0.623251 + 0.742761i −0.981626 0.190816i \(-0.938886\pi\)
0.358375 + 0.933578i \(0.383331\pi\)
\(480\) 8.15737 + 3.17406i 0.0169945 + 0.00661261i
\(481\) −90.8747 515.376i −0.188929 1.07147i
\(482\) −92.6605 + 86.1112i −0.192242 + 0.178654i
\(483\) −11.5622 + 7.86633i −0.0239383 + 0.0162864i
\(484\) 272.317 131.665i 0.562638 0.272036i
\(485\) −8.54297 −0.0176144
\(486\) −117.974 471.464i −0.242744 0.970090i
\(487\) −407.942 −0.837663 −0.418831 0.908064i \(-0.637560\pi\)
−0.418831 + 0.908064i \(0.637560\pi\)
\(488\) −232.570 424.696i −0.476577 0.870280i
\(489\) −561.400 + 381.947i −1.14806 + 0.781079i
\(490\) 1.28832 1.19726i 0.00262923 0.00244339i
\(491\) −88.2990 500.768i −0.179835 1.01989i −0.932414 0.361393i \(-0.882301\pi\)
0.752579 0.658502i \(-0.228810\pi\)
\(492\) 282.586 490.108i 0.574362 0.996155i
\(493\) −34.1639 + 40.7149i −0.0692979 + 0.0825861i
\(494\) 177.763 347.407i 0.359844 0.703254i
\(495\) −2.02974 + 5.14192i −0.00410049 + 0.0103877i
\(496\) 122.685 + 138.146i 0.247349 + 0.278521i
\(497\) 164.036 + 28.9240i 0.330053 + 0.0581973i
\(498\) 188.996 + 43.1775i 0.379511 + 0.0867019i
\(499\) −99.3941 + 273.083i −0.199187 + 0.547261i −0.998564 0.0535682i \(-0.982941\pi\)
0.799378 + 0.600829i \(0.205163\pi\)
\(500\) 17.6759 + 4.47143i 0.0353517 + 0.00894286i
\(501\) 363.027 + 372.927i 0.724605 + 0.744365i
\(502\) 9.36011 75.1678i 0.0186456 0.149737i
\(503\) −615.153 + 355.159i −1.22297 + 0.706081i −0.965550 0.260219i \(-0.916205\pi\)
−0.257418 + 0.966300i \(0.582872\pi\)
\(504\) 56.3324 + 448.158i 0.111771 + 0.889202i
\(505\) −6.72404 + 11.6464i −0.0133149 + 0.0230621i
\(506\) 6.03858 7.98499i 0.0119340 0.0157806i
\(507\) −20.4496 + 202.353i −0.0403345 + 0.399118i
\(508\) −86.5483 305.778i −0.170371 0.601924i
\(509\) 335.998 281.936i 0.660114 0.553901i −0.250007 0.968244i \(-0.580433\pi\)
0.910121 + 0.414343i \(0.135989\pi\)
\(510\) 0.632283 + 5.05380i 0.00123977 + 0.00990942i
\(511\) −132.549 + 48.2439i −0.259391 + 0.0944107i
\(512\) −459.723 + 225.386i −0.897896 + 0.440208i
\(513\) 499.960 + 155.835i 0.974582 + 0.303772i
\(514\) 12.1915 + 240.505i 0.0237188 + 0.467908i
\(515\) −17.0044 + 6.18908i −0.0330182 + 0.0120176i
\(516\) −380.583 138.271i −0.737563 0.267968i
\(517\) 82.6783 + 98.5322i 0.159919 + 0.190585i
\(518\) −636.206 + 145.733i −1.22820 + 0.281338i
\(519\) −610.363 + 274.684i −1.17604 + 0.529255i
\(520\) −3.81166 + 6.27049i −0.00733012 + 0.0120586i
\(521\) −327.212 188.916i −0.628046 0.362603i 0.151949 0.988388i \(-0.451445\pi\)
−0.779995 + 0.625786i \(0.784778\pi\)
\(522\) −37.4290 95.7013i −0.0717030 0.183336i
\(523\) 512.125 295.676i 0.979207 0.565345i 0.0771761 0.997017i \(-0.475410\pi\)
0.902031 + 0.431672i \(0.142076\pi\)
\(524\) 44.4981 606.501i 0.0849200 1.15744i
\(525\) 115.613 + 455.918i 0.220216 + 0.868414i
\(526\) −221.085 + 718.734i −0.420314 + 1.36641i
\(527\) −36.7693 + 101.023i −0.0697710 + 0.191694i
\(528\) −140.921 291.030i −0.266896 0.551194i
\(529\) 91.7640 520.420i 0.173467 0.983780i
\(530\) −3.10737 4.80291i −0.00586296 0.00906209i
\(531\) 532.352 + 108.708i 1.00255 + 0.204723i
\(532\) −443.949 199.483i −0.834491 0.374968i
\(533\) 363.322 + 304.863i 0.681654 + 0.571976i
\(534\) 301.718 + 588.816i 0.565014 + 1.10265i
\(535\) −1.53357 8.69732i −0.00286649 0.0162567i
\(536\) 453.221 + 398.084i 0.845561 + 0.742694i
\(537\) 339.788 703.805i 0.632753 1.31062i
\(538\) −261.810 + 110.603i −0.486635 + 0.205582i
\(539\) −64.9708 −0.120540
\(540\) −9.16156 3.61035i −0.0169659 0.00668583i
\(541\) 36.7562i 0.0679412i 0.999423 + 0.0339706i \(0.0108153\pi\)
−0.999423 + 0.0339706i \(0.989185\pi\)
\(542\) 264.919 111.917i 0.488780 0.206488i
\(543\) 62.4525 + 844.522i 0.115014 + 1.55529i
\(544\) −242.569 172.962i −0.445898 0.317944i
\(545\) 11.4303 2.01547i 0.0209730 0.00369811i
\(546\) −378.191 18.9516i −0.692658 0.0347099i
\(547\) 574.438 684.589i 1.05016 1.25153i 0.0832209 0.996531i \(-0.473479\pi\)
0.966940 0.255002i \(-0.0820763\pi\)
\(548\) −734.331 329.963i −1.34002 0.602122i
\(549\) 259.578 + 478.907i 0.472820 + 0.872326i
\(550\) −182.904 282.706i −0.332553 0.514011i
\(551\) 109.046 + 19.2277i 0.197906 + 0.0348961i
\(552\) 14.2301 + 10.7485i 0.0257792 + 0.0194719i
\(553\) −858.444 312.448i −1.55234 0.565005i
\(554\) −11.6206 + 37.7778i −0.0209758 + 0.0681910i
\(555\) 3.86735 13.6937i 0.00696820 0.0246733i
\(556\) −69.7304 5.11602i −0.125414 0.00920148i
\(557\) −405.373 702.126i −0.727779 1.26055i −0.957820 0.287369i \(-0.907219\pi\)
0.230041 0.973181i \(-0.426114\pi\)
\(558\) −137.349 156.008i −0.246146 0.279585i
\(559\) 169.732 293.984i 0.303634 0.525910i
\(560\) 8.05110 + 4.35183i 0.0143770 + 0.00777112i
\(561\) 109.982 152.658i 0.196046 0.272118i
\(562\) −26.0112 + 5.95827i −0.0462833 + 0.0106019i
\(563\) 381.155 319.827i 0.677007 0.568077i −0.238123 0.971235i \(-0.576532\pi\)
0.915130 + 0.403158i \(0.132088\pi\)
\(564\) −175.433 + 147.379i −0.311052 + 0.261310i
\(565\) 6.67929 + 18.3512i 0.0118217 + 0.0324800i
\(566\) 11.1445 + 219.851i 0.0196899 + 0.388430i
\(567\) −61.1995 504.446i −0.107936 0.889675i
\(568\) −32.1503 209.963i −0.0566027 0.369654i
\(569\) −143.082 393.114i −0.251462 0.690886i −0.999625 0.0273713i \(-0.991286\pi\)
0.748163 0.663514i \(-0.230936\pi\)
\(570\) 8.45953 6.40515i 0.0148413 0.0112371i
\(571\) −444.304 529.501i −0.778115 0.927322i 0.220731 0.975335i \(-0.429156\pi\)
−0.998847 + 0.0480130i \(0.984711\pi\)
\(572\) 260.834 73.8272i 0.456003 0.129069i
\(573\) 197.159 273.663i 0.344082 0.477596i
\(574\) 356.793 471.797i 0.621590 0.821946i
\(575\) 16.0823 + 9.28510i 0.0279691 + 0.0161480i
\(576\) 518.277 251.327i 0.899786 0.436332i
\(577\) 331.076 + 573.440i 0.573788 + 0.993830i 0.996172 + 0.0874130i \(0.0278600\pi\)
−0.422384 + 0.906417i \(0.638807\pi\)
\(578\) −50.0020 + 401.548i −0.0865086 + 0.694720i
\(579\) −174.056 49.1567i −0.300615 0.0848994i
\(580\) −2.01853 0.510624i −0.00348022 0.000880386i
\(581\) 190.475 + 69.3273i 0.327840 + 0.119324i
\(582\) −382.456 + 412.022i −0.657142 + 0.707942i
\(583\) −36.6957 + 208.112i −0.0629429 + 0.356967i
\(584\) 112.481 + 140.371i 0.192605 + 0.240361i
\(585\) 4.31850 7.03575i 0.00738205 0.0120269i
\(586\) 23.5712 46.0659i 0.0402238 0.0786107i
\(587\) 816.508 + 685.132i 1.39099 + 1.16718i 0.964939 + 0.262474i \(0.0845383\pi\)
0.426046 + 0.904701i \(0.359906\pi\)
\(588\) −0.0669439 115.735i −0.000113850 0.196828i
\(589\) 220.569 38.8922i 0.374480 0.0660309i
\(590\) 8.06435 7.49435i 0.0136684 0.0127023i
\(591\) −841.413 + 62.2226i −1.42371 + 0.105284i
\(592\) 436.218 + 708.852i 0.736855 + 1.19738i
\(593\) 678.148i 1.14359i −0.820397 0.571794i \(-0.806248\pi\)
0.820397 0.571794i \(-0.193752\pi\)
\(594\) 157.123 + 328.090i 0.264517 + 0.552340i
\(595\) 5.32527i 0.00895004i
\(596\) 451.641 218.369i 0.757787 0.366391i
\(597\) 284.007 588.266i 0.475724 0.985369i
\(598\) −10.9515 + 10.1774i −0.0183135 + 0.0170191i
\(599\) −966.941 + 170.498i −1.61426 + 0.284637i −0.906623 0.421941i \(-0.861349\pi\)
−0.707635 + 0.706578i \(0.750238\pi\)
\(600\) 503.405 326.104i 0.839008 0.543507i
\(601\) 541.659 + 454.506i 0.901263 + 0.756249i 0.970437 0.241355i \(-0.0775919\pi\)
−0.0691738 + 0.997605i \(0.522036\pi\)
\(602\) −376.898 192.853i −0.626077 0.320353i
\(603\) −507.937 450.039i −0.842351 0.746333i
\(604\) 267.824 + 371.295i 0.443417 + 0.614726i
\(605\) −1.19728 + 6.79009i −0.00197897 + 0.0112233i
\(606\) 260.672 + 845.688i 0.430153 + 1.39553i
\(607\) 607.829 + 221.232i 1.00137 + 0.364467i 0.790111 0.612964i \(-0.210023\pi\)
0.211255 + 0.977431i \(0.432245\pi\)
\(608\) −59.3852 + 617.815i −0.0976731 + 1.01614i
\(609\) −26.4098 104.146i −0.0433658 0.171012i
\(610\) 10.9527 + 1.36386i 0.0179553 + 0.00223584i
\(611\) −96.0417 166.349i −0.157188 0.272257i
\(612\) 272.048 + 195.757i 0.444523 + 0.319864i
\(613\) 80.2722 + 46.3452i 0.130950 + 0.0756039i 0.564044 0.825745i \(-0.309245\pi\)
−0.433094 + 0.901349i \(0.642578\pi\)
\(614\) −293.238 + 387.757i −0.477587 + 0.631527i
\(615\) 5.29231 + 11.7598i 0.00860539 + 0.0191217i
\(616\) −108.427 320.229i −0.176018 0.519852i
\(617\) 500.074 + 595.965i 0.810492 + 0.965907i 0.999872 0.0159968i \(-0.00509217\pi\)
−0.189380 + 0.981904i \(0.560648\pi\)
\(618\) −462.765 + 1097.19i −0.748810 + 1.77538i
\(619\) 198.813 + 546.234i 0.321184 + 0.882445i 0.990257 + 0.139249i \(0.0444689\pi\)
−0.669074 + 0.743196i \(0.733309\pi\)
\(620\) −4.18993 + 0.425879i −0.00675796 + 0.000686902i
\(621\) −15.9566 12.1610i −0.0256950 0.0195829i
\(622\) −20.8808 411.922i −0.0335704 0.662254i
\(623\) 236.597 + 650.046i 0.379771 + 1.04341i
\(624\) 131.780 + 464.555i 0.211185 + 0.744480i
\(625\) 478.300 401.342i 0.765280 0.642146i
\(626\) −99.2984 433.494i −0.158624 0.692482i
\(627\) −389.993 39.4123i −0.621998 0.0628586i
\(628\) 645.709 950.268i 1.02820 1.51317i
\(629\) −242.152 + 419.419i −0.384979 + 0.666803i
\(630\) −9.03629 4.93482i −0.0143433 0.00783304i
\(631\) −224.402 388.675i −0.355629 0.615967i 0.631597 0.775297i \(-0.282400\pi\)
−0.987225 + 0.159330i \(0.949067\pi\)
\(632\) −26.3139 + 1164.67i −0.0416359 + 1.84283i
\(633\) 362.671 + 372.561i 0.572940 + 0.588564i
\(634\) 28.3847 + 8.73125i 0.0447708 + 0.0137717i
\(635\) 6.80704 + 2.47756i 0.0107198 + 0.00390167i
\(636\) −370.754 65.1528i −0.582946 0.102442i
\(637\) 95.5511 + 16.8482i 0.150002 + 0.0264493i
\(638\) 41.7811 + 64.5791i 0.0654877 + 0.101221i
\(639\) 35.1503 + 236.363i 0.0550083 + 0.369894i
\(640\) 1.96374 11.5044i 0.00306834 0.0179757i
\(641\) 455.126 542.398i 0.710024 0.846174i −0.283597 0.958944i \(-0.591528\pi\)
0.993621 + 0.112770i \(0.0359722\pi\)
\(642\) −488.122 315.403i −0.760315 0.491282i
\(643\) 846.253 149.217i 1.31610 0.232064i 0.528860 0.848709i \(-0.322620\pi\)
0.787241 + 0.616645i \(0.211509\pi\)
\(644\) 13.3683 + 12.9984i 0.0207582 + 0.0201838i
\(645\) 7.63134 5.19196i 0.0118315 0.00804956i
\(646\) −332.678 + 140.542i −0.514981 + 0.217557i
\(647\) 1280.16i 1.97861i −0.145855 0.989306i \(-0.546593\pi\)
0.145855 0.989306i \(-0.453407\pi\)
\(648\) −584.275 + 280.227i −0.901659 + 0.432448i
\(649\) −406.690 −0.626641
\(650\) 195.682 + 463.200i 0.301048 + 0.712616i
\(651\) −122.247 179.683i −0.187783 0.276011i
\(652\) 649.094 + 631.132i 0.995543 + 0.967995i
\(653\) −194.733 1104.39i −0.298213 1.69125i −0.653848 0.756626i \(-0.726847\pi\)
0.355635 0.934625i \(-0.384265\pi\)
\(654\) 414.513 641.507i 0.633813 0.980897i
\(655\) 10.6190 + 8.91039i 0.0162122 + 0.0136036i
\(656\) −715.787 238.005i −1.09114 0.362813i
\(657\) −125.859 158.462i −0.191567 0.241190i
\(658\) −201.138 + 130.131i −0.305681 + 0.197768i
\(659\) −211.896 + 1201.72i −0.321541 + 1.82355i 0.211402 + 0.977399i \(0.432197\pi\)
−0.532943 + 0.846151i \(0.678914\pi\)
\(660\) 7.25948 + 1.27571i 0.0109992 + 0.00193290i
\(661\) −375.073 + 1030.50i −0.567433 + 1.55901i 0.241065 + 0.970509i \(0.422503\pi\)
−0.808498 + 0.588499i \(0.799719\pi\)
\(662\) −121.975 + 396.532i −0.184252 + 0.598990i
\(663\) −201.335 + 195.990i −0.303673 + 0.295612i
\(664\) 5.83864 258.422i 0.00879313 0.389190i
\(665\) 9.60796 5.54716i 0.0144481 0.00834159i
\(666\) −487.303 799.567i −0.731686 1.20055i
\(667\) −3.67370 2.12101i −0.00550780 0.00317993i
\(668\) 390.006 573.959i 0.583842 0.859220i
\(669\) 40.0538 396.341i 0.0598712 0.592437i
\(670\) −13.4031 + 3.07019i −0.0200047 + 0.00458238i
\(671\) −262.086 312.342i −0.390591 0.465488i
\(672\) 570.322 193.475i 0.848694 0.287909i
\(673\) 878.553 319.767i 1.30543 0.475137i 0.406667 0.913577i \(-0.366691\pi\)
0.898761 + 0.438440i \(0.144469\pi\)
\(674\) −476.669 + 24.1629i −0.707225 + 0.0358500i
\(675\) −567.907 + 364.422i −0.841344 + 0.539884i
\(676\) 269.788 27.4222i 0.399094 0.0405653i
\(677\) −611.661 + 222.626i −0.903487 + 0.328842i −0.751649 0.659563i \(-0.770741\pi\)
−0.151838 + 0.988405i \(0.548519\pi\)
\(678\) 1184.09 + 499.418i 1.74644 + 0.736605i
\(679\) −450.270 + 377.821i −0.663137 + 0.556438i
\(680\) 6.43223 2.17790i 0.00945916 0.00320280i
\(681\) −473.629 + 213.149i −0.695491 + 0.312994i
\(682\) 124.091 + 93.8428i 0.181952 + 0.137599i
\(683\) −357.892 + 619.887i −0.524000 + 0.907594i 0.475610 + 0.879656i \(0.342227\pi\)
−0.999610 + 0.0279381i \(0.991106\pi\)
\(684\) 69.8046 694.748i 0.102054 1.01571i
\(685\) 15.8924 9.17548i 0.0232006 0.0133949i
\(686\) 90.9218 730.161i 0.132539 1.06438i
\(687\) 370.955 94.0681i 0.539963 0.136926i
\(688\) −78.7987 + 534.115i −0.114533 + 0.776330i
\(689\) 107.935 296.549i 0.156655 0.430405i
\(690\) −0.388468 + 0.119740i −0.000562997 + 0.000173537i
\(691\) 143.931 + 25.3789i 0.208294 + 0.0367278i 0.276821 0.960921i \(-0.410719\pi\)
−0.0685277 + 0.997649i \(0.521830\pi\)
\(692\) 522.083 + 723.784i 0.754455 + 1.04593i
\(693\) 120.426 + 360.780i 0.173775 + 0.520606i
\(694\) 116.811 228.288i 0.168316 0.328945i
\(695\) 1.02444 1.22088i 0.00147402 0.00175667i
\(696\) −114.994 + 74.4926i −0.165221 + 0.107030i
\(697\) −76.2172 432.249i −0.109350 0.620157i
\(698\) −718.392 773.031i −1.02922 1.10749i
\(699\) −1036.84 500.575i −1.48333 0.716131i
\(700\) 564.599 272.984i 0.806570 0.389978i
\(701\) −641.799 −0.915548 −0.457774 0.889069i \(-0.651353\pi\)
−0.457774 + 0.889069i \(0.651353\pi\)
\(702\) −145.997 523.259i −0.207973 0.745383i
\(703\) 1008.97 1.43523
\(704\) −342.450 + 261.931i −0.486435 + 0.372061i
\(705\) −0.385173 5.20855i −0.000546345 0.00738802i
\(706\) −358.672 385.952i −0.508035 0.546674i
\(707\) 160.672 + 911.217i 0.227259 + 1.28885i
\(708\) −0.419041 724.450i −0.000591865 1.02323i
\(709\) −522.751 + 622.991i −0.737308 + 0.878689i −0.996189 0.0872198i \(-0.972202\pi\)
0.258881 + 0.965909i \(0.416646\pi\)
\(710\) 4.31032 + 2.20552i 0.00607088 + 0.00310637i
\(711\) 35.2523 1310.11i 0.0495813 1.84263i
\(712\) 688.407 551.631i 0.966864 0.774762i
\(713\) −8.45004 1.48997i −0.0118514 0.00208972i
\(714\) 256.835 + 238.405i 0.359713 + 0.333900i
\(715\) −2.11340 + 5.80653i −0.00295581 + 0.00812102i
\(716\) −1010.22 255.555i −1.41093 0.356920i
\(717\) 245.092 867.831i 0.341829 1.21036i
\(718\) 1040.64 + 129.584i 1.44936 + 0.180479i
\(719\) 533.266 307.881i 0.741677 0.428208i −0.0810016 0.996714i \(-0.525812\pi\)
0.822679 + 0.568506i \(0.192479\pi\)
\(720\) −2.26499 + 12.9329i −0.00314582 + 0.0179623i
\(721\) −622.522 + 1078.24i −0.863414 + 1.49548i
\(722\) 24.2369 + 18.3289i 0.0335691 + 0.0253863i
\(723\) −153.951 110.913i −0.212933 0.153407i
\(724\) 1086.42 307.505i 1.50059 0.424731i
\(725\) −109.295 + 91.7097i −0.150752 + 0.126496i
\(726\) 273.882 + 361.726i 0.377248 + 0.498246i
\(727\) −1006.23 + 366.238i −1.38409 + 0.503766i −0.923414 0.383805i \(-0.874613\pi\)
−0.460671 + 0.887571i \(0.652391\pi\)
\(728\) 76.4194 + 499.071i 0.104972 + 0.685536i
\(729\) 658.662 312.418i 0.903515 0.428557i
\(730\) −4.09499 + 0.207580i −0.00560958 + 0.000284356i
\(731\) −295.205 + 107.446i −0.403837 + 0.146985i
\(732\) 556.115 467.184i 0.759720 0.638230i
\(733\) −437.679 521.606i −0.597107 0.711604i 0.379848 0.925049i \(-0.375976\pi\)
−0.976955 + 0.213444i \(0.931532\pi\)
\(734\) −73.8045 322.198i −0.100551 0.438962i
\(735\) 2.14048 + 1.54210i 0.00291221 + 0.00209809i
\(736\) 10.2330 21.4631i 0.0139036 0.0291619i
\(737\) 439.902 + 253.978i 0.596882 + 0.344610i
\(738\) 804.099 + 271.225i 1.08956 + 0.367514i
\(739\) −221.814 + 128.064i −0.300154 + 0.173294i −0.642512 0.766276i \(-0.722108\pi\)
0.342358 + 0.939570i \(0.388774\pi\)
\(740\) −18.9216 1.38825i −0.0255697 0.00187601i
\(741\) 563.333 + 159.096i 0.760234 + 0.214704i
\(742\) −376.192 115.718i −0.506997 0.155954i
\(743\) −231.205 + 635.232i −0.311178 + 0.854955i 0.681241 + 0.732059i \(0.261441\pi\)
−0.992420 + 0.122896i \(0.960782\pi\)
\(744\) −167.037 + 221.144i −0.224513 + 0.297237i
\(745\) −1.98570 + 11.2615i −0.00266537 + 0.0151160i
\(746\) 941.268 608.978i 1.26175 0.816324i
\(747\) −7.82193 + 290.694i −0.0104711 + 0.389148i
\(748\) −228.828 102.821i −0.305919 0.137461i
\(749\) −465.477 390.581i −0.621464 0.521470i
\(750\) −1.36877 + 27.3147i −0.00182503 + 0.0364196i
\(751\) 192.670 + 1092.69i 0.256552 + 1.45498i 0.792058 + 0.610446i \(0.209010\pi\)
−0.535506 + 0.844531i \(0.679879\pi\)
\(752\) 239.442 + 189.727i 0.318407 + 0.252297i
\(753\) 113.313 8.37953i 0.150482 0.0111282i
\(754\) −44.6999 105.810i −0.0592837 0.140331i
\(755\) −10.4356 −0.0138220
\(756\) −642.545 + 214.890i −0.849927 + 0.284247i
\(757\) 217.071i 0.286751i 0.989668 + 0.143376i \(0.0457957\pi\)
−0.989668 + 0.143376i \(0.954204\pi\)
\(758\) 456.263 + 1080.03i 0.601931 + 1.42484i
\(759\) 13.5233 + 6.52887i 0.0178172 + 0.00860194i
\(760\) −10.6296 9.33649i −0.0139864 0.0122849i
\(761\) 732.595 129.176i 0.962674 0.169745i 0.329843 0.944036i \(-0.393004\pi\)
0.632831 + 0.774290i \(0.281893\pi\)
\(762\) 424.233 217.383i 0.556736 0.285279i
\(763\) 513.315 611.745i 0.672759 0.801763i
\(764\) −410.208 184.322i −0.536921 0.241259i
\(765\) −7.24675 + 2.41892i −0.00947288 + 0.00316198i
\(766\) −906.135 + 586.248i −1.18294 + 0.765336i
\(767\) 598.110 + 105.463i 0.779804 + 0.137500i
\(768\) −466.939 609.747i −0.607994 0.793942i
\(769\) −801.123 291.585i −1.04177 0.379174i −0.236221 0.971699i \(-0.575909\pi\)
−0.805552 + 0.592525i \(0.798131\pi\)
\(770\) 7.36596 + 2.26580i 0.00956618 + 0.00294259i
\(771\) −350.138 + 88.7894i −0.454135 + 0.115161i
\(772\) −17.6456 + 240.506i −0.0228570 + 0.311537i
\(773\) 132.004 + 228.637i 0.170768 + 0.295779i 0.938689 0.344766i \(-0.112042\pi\)
−0.767921 + 0.640545i \(0.778708\pi\)
\(774\) 91.2386 600.492i 0.117879 0.775829i
\(775\) −144.295 + 249.927i −0.186188 + 0.322486i
\(776\) 640.507 + 389.347i 0.825396 + 0.501736i
\(777\) −401.782 892.784i −0.517094 1.14901i
\(778\) 140.093 + 611.586i 0.180068 + 0.786100i
\(779\) −700.479 + 587.771i −0.899202 + 0.754520i
\(780\) −10.3455 3.75869i −0.0132635 0.00481883i
\(781\) −61.1750 168.077i −0.0783291 0.215207i
\(782\) 13.8179 0.700443i 0.0176699 0.000895707i
\(783\) 129.728 83.2456i 0.165681 0.106316i
\(784\) −151.157 + 31.0490i −0.192802 + 0.0396033i
\(785\) 8.95701 + 24.6092i 0.0114102 + 0.0313493i
\(786\) 905.140 113.242i 1.15158 0.144074i
\(787\) 156.151 + 186.093i 0.198412 + 0.236459i 0.856072 0.516856i \(-0.172898\pi\)
−0.657660 + 0.753315i \(0.728453\pi\)
\(788\) 306.373 + 1082.42i 0.388798 + 1.37363i
\(789\) −1122.24 113.412i −1.42235 0.143742i
\(790\) −21.1803 16.0175i −0.0268106 0.0202753i
\(791\) 1163.64 + 671.829i 1.47110 + 0.849341i
\(792\) 386.523 293.009i 0.488035 0.369960i
\(793\) 304.448 + 527.319i 0.383919 + 0.664967i
\(794\) −362.901 45.1894i −0.457054 0.0569136i
\(795\) 6.14853 5.98531i 0.00773399 0.00752869i
\(796\) −844.382 213.602i −1.06078 0.268344i
\(797\) −350.881 127.710i −0.440252 0.160239i 0.112378 0.993666i \(-0.464153\pi\)
−0.552630 + 0.833427i \(0.686376\pi\)
\(798\) 162.598 711.724i 0.203757 0.891885i
\(799\) −30.8678 + 175.060i −0.0386330 + 0.219099i
\(800\) −560.636 570.317i −0.700795 0.712897i
\(801\) −777.127 + 617.240i −0.970196 + 0.770586i
\(802\) 974.074 + 498.418i 1.21456 + 0.621469i
\(803\) 116.032 + 97.3625i 0.144498 + 0.121248i
\(804\) −451.965 + 783.873i −0.562146 + 0.974967i
\(805\) −0.418569 + 0.0738050i −0.000519961 + 9.16832e-5i
\(806\) −158.162 170.192i −0.196231 0.211156i
\(807\) −239.808 352.479i −0.297160 0.436776i
\(808\) 1034.92 566.736i 1.28084 0.701406i
\(809\) 480.285i 0.593677i 0.954928 + 0.296838i \(0.0959323\pi\)
−0.954928 + 0.296838i \(0.904068\pi\)
\(810\) 2.61082 14.5383i 0.00322324 0.0179486i
\(811\) 990.343i 1.22114i −0.791963 0.610569i \(-0.790941\pi\)
0.791963 0.610569i \(-0.209059\pi\)
\(812\) −128.973 + 62.3583i −0.158833 + 0.0767960i
\(813\) 242.656 + 356.665i 0.298470 + 0.438702i
\(814\) 477.113 + 513.401i 0.586134 + 0.630713i
\(815\) −20.3235 + 3.58358i −0.0249368 + 0.00439703i
\(816\) 182.923 407.724i 0.224170 0.499662i
\(817\) 501.361 + 420.691i 0.613660 + 0.514922i
\(818\) 103.853 202.964i 0.126960 0.248122i
\(819\) −83.5502 561.820i −0.102015 0.685983i
\(820\) 13.9451 10.0589i 0.0170062 0.0122670i
\(821\) 167.537 950.148i 0.204064 1.15731i −0.694841 0.719163i \(-0.744525\pi\)
0.898905 0.438143i \(-0.144364\pi\)
\(822\) 268.952 1177.25i 0.327192 1.43218i
\(823\) −273.922 99.6993i −0.332833 0.121141i 0.170197 0.985410i \(-0.445559\pi\)
−0.503031 + 0.864269i \(0.667782\pi\)
\(824\) 1556.97 + 310.951i 1.88952 + 0.377368i
\(825\) 361.911 352.304i 0.438680 0.427035i
\(826\) 93.5982 751.655i 0.113315 0.909994i
\(827\) 319.762 + 553.845i 0.386653 + 0.669703i 0.991997 0.126261i \(-0.0402976\pi\)
−0.605344 + 0.795964i \(0.706964\pi\)
\(828\) −11.6162 + 24.0962i −0.0140292 + 0.0291017i
\(829\) −536.488 309.742i −0.647151 0.373633i 0.140213 0.990121i \(-0.455221\pi\)
−0.787364 + 0.616489i \(0.788555\pi\)
\(830\) 4.69959 + 3.55402i 0.00566215 + 0.00428196i
\(831\) −58.9866 5.96113i −0.0709827 0.00717344i
\(832\) 571.557 296.412i 0.686968 0.356264i
\(833\) −57.7161 68.7833i −0.0692870 0.0825730i
\(834\) −13.0197 104.065i −0.0156111 0.124779i
\(835\) 5.41000 + 14.8639i 0.00647904 + 0.0178010i
\(836\) 52.8505 + 519.960i 0.0632183 + 0.621962i
\(837\) 188.988 247.974i 0.225792 0.296266i
\(838\) 307.222 15.5734i 0.366613 0.0185840i
\(839\) 371.108 + 1019.61i 0.442322 + 1.21527i 0.937961 + 0.346741i \(0.112712\pi\)
−0.495639 + 0.868529i \(0.665066\pi\)
\(840\) −4.02855 + 13.1236i −0.00479589 + 0.0156233i
\(841\) −619.277 + 519.635i −0.736358 + 0.617877i
\(842\) 34.9430 8.00424i 0.0415000 0.00950622i
\(843\) −16.4268 36.5013i −0.0194861 0.0432993i
\(844\) 389.624 573.396i 0.461640 0.679379i
\(845\) −3.09070 + 5.35324i −0.00365763 + 0.00633520i
\(846\) −268.449 214.603i −0.317316 0.253668i
\(847\) 237.194 + 410.833i 0.280040 + 0.485044i
\(848\) 14.0809 + 501.716i 0.0166049 + 0.591646i
\(849\) −320.070 + 81.1644i −0.376996 + 0.0956001i
\(850\) 136.815 444.776i 0.160959 0.523266i
\(851\) −36.3226 13.2203i −0.0426823 0.0155351i
\(852\) 299.338 109.146i 0.351336 0.128106i
\(853\) 883.681 + 155.817i 1.03597 + 0.182669i 0.665672 0.746244i \(-0.268145\pi\)
0.370296 + 0.928914i \(0.379256\pi\)
\(854\) 637.597 412.510i 0.746601 0.483033i
\(855\) 11.9129 + 10.5550i 0.0139333 + 0.0123450i
\(856\) −281.402 + 721.972i −0.328741 + 0.843425i
\(857\) 620.387 739.349i 0.723906 0.862717i −0.271098 0.962552i \(-0.587387\pi\)
0.995004 + 0.0998344i \(0.0318313\pi\)
\(858\) 185.431 + 361.878i 0.216121 + 0.421769i
\(859\) 64.8908 11.4420i 0.0755423 0.0133201i −0.135749 0.990743i \(-0.543344\pi\)
0.211292 + 0.977423i \(0.432233\pi\)
\(860\) −8.82340 8.57924i −0.0102598 0.00997586i
\(861\) 799.029 + 385.761i 0.928025 + 0.448039i
\(862\) −388.316 919.188i −0.450483 1.06634i
\(863\) 1476.76i 1.71119i −0.517646 0.855595i \(-0.673191\pi\)
0.517646 0.855595i \(-0.326809\pi\)
\(864\) 522.344 + 688.224i 0.604565 + 0.796556i
\(865\) −20.3426 −0.0235175
\(866\) −71.2326 + 30.0926i −0.0822548 + 0.0347490i
\(867\) −605.322 + 44.7636i −0.698179 + 0.0516305i
\(868\) −202.002 + 207.751i −0.232721 + 0.239344i
\(869\) 170.345 + 966.076i 0.196024 + 1.11171i
\(870\) 0.156310 3.11926i 0.000179666 0.00358535i
\(871\) −581.092 487.594i −0.667155 0.559810i
\(872\) −948.840 369.828i −1.08812 0.424115i
\(873\) −718.675 441.118i −0.823225 0.505290i
\(874\) −15.6573 24.2008i −0.0179146 0.0276897i
\(875\) −4.96550 + 28.1607i −0.00567485 + 0.0321837i
\(876\) −173.315 + 206.792i −0.197849 + 0.236064i
\(877\) −114.015 + 313.254i −0.130006 + 0.357189i −0.987568 0.157192i \(-0.949756\pi\)
0.857562 + 0.514380i \(0.171978\pi\)
\(878\) −597.508 183.796i −0.680533 0.209335i
\(879\) 74.6974 + 21.0959i 0.0849800 + 0.0239999i
\(880\) −0.275709 9.82376i −0.000313306 0.0111634i
\(881\) −1221.07 + 704.984i −1.38600 + 0.800209i −0.992862 0.119269i \(-0.961945\pi\)
−0.393141 + 0.919478i \(0.628611\pi\)
\(882\) 170.201 34.1966i 0.192971 0.0387716i
\(883\) 416.367 + 240.390i 0.471537 + 0.272242i 0.716883 0.697193i \(-0.245568\pi\)
−0.245346 + 0.969436i \(0.578901\pi\)
\(884\) 309.868 + 210.556i 0.350530 + 0.238186i
\(885\) 13.3985 + 9.65288i 0.0151395 + 0.0109072i
\(886\) −183.232 799.911i −0.206808 0.902835i
\(887\) −175.437 209.078i −0.197787 0.235713i 0.658030 0.752991i \(-0.271390\pi\)
−0.855817 + 0.517278i \(0.826945\pi\)
\(888\) −914.045 + 850.426i −1.02933 + 0.957687i
\(889\) 468.348 170.465i 0.526826 0.191749i
\(890\) 1.01801 + 20.0826i 0.00114383 + 0.0225648i
\(891\) −436.256 + 327.757i −0.489625 + 0.367853i
\(892\) −528.423 + 53.7108i −0.592403 + 0.0602138i
\(893\) 348.000 126.662i 0.389698 0.141838i
\(894\) 454.237 + 599.928i 0.508095 + 0.671061i
\(895\) 18.1959 15.2682i 0.0203306 0.0170594i
\(896\) −405.294 693.207i −0.452337 0.773669i
\(897\) −18.1953 13.1087i −0.0202846 0.0146140i
\(898\) −987.788 + 1306.18i −1.09999 + 1.45454i
\(899\) 32.9617 57.0913i 0.0366648 0.0635053i
\(900\) 627.943 + 644.321i 0.697714 + 0.715912i
\(901\) −252.922 + 146.025i −0.280713 + 0.162070i
\(902\) −630.319 78.4891i −0.698802 0.0870168i
\(903\) 172.601 611.154i 0.191142 0.676804i
\(904\) 335.580 1680.29i 0.371217 1.85872i
\(905\) −8.80274 + 24.1853i −0.00972679 + 0.0267241i
\(906\) −467.186 + 503.302i −0.515658 + 0.555521i
\(907\) 185.139 + 32.6450i 0.204123 + 0.0359923i 0.274774 0.961509i \(-0.411397\pi\)
−0.0706518 + 0.997501i \(0.522508\pi\)
\(908\) 405.125 + 561.642i 0.446173 + 0.618548i
\(909\) −1167.02 + 632.552i −1.28385 + 0.695876i
\(910\) −10.2454 5.24240i −0.0112587 0.00576087i
\(911\) 632.066 753.267i 0.693816 0.826857i −0.297996 0.954567i \(-0.596318\pi\)
0.991812 + 0.127710i \(0.0407626\pi\)
\(912\) −926.167 + 94.6801i −1.01553 + 0.103816i
\(913\) −37.7969 214.357i −0.0413986 0.234783i
\(914\) 997.828 927.300i 1.09172 1.01455i
\(915\) 1.22098 + 16.5109i 0.00133440 + 0.0180447i
\(916\) −222.112 459.383i −0.242481 0.501510i
\(917\) 953.761 1.04009
\(918\) −207.764 + 457.798i −0.226322 + 0.498691i
\(919\) 23.3372 0.0253941 0.0126971 0.999919i \(-0.495958\pi\)
0.0126971 + 0.999919i \(0.495958\pi\)
\(920\) 0.260331 + 0.475391i 0.000282968 + 0.000516730i
\(921\) −656.701 317.047i −0.713030 0.344242i
\(922\) 454.483 422.360i 0.492931 0.458091i
\(923\) 46.3830 + 263.051i 0.0502524 + 0.284996i
\(924\) 439.041 253.819i 0.475153 0.274696i
\(925\) −835.667 + 995.910i −0.903424 + 1.07666i
\(926\) −84.9483 + 166.017i −0.0917368 + 0.179284i
\(927\) −1750.06 357.369i −1.88788 0.385511i
\(928\) 128.067 + 130.279i 0.138003 + 0.140387i
\(929\) −883.579 155.799i −0.951108 0.167706i −0.323493 0.946230i \(-0.604857\pi\)
−0.627614 + 0.778525i \(0.715968\pi\)
\(930\) −1.86083 6.03700i −0.00200089 0.00649140i
\(931\) −63.9793 + 175.782i −0.0687210 + 0.188809i
\(932\) −376.483 + 1488.26i −0.403951 + 1.59685i
\(933\) 599.696 152.073i 0.642760 0.162994i
\(934\) 3.08996 24.8144i 0.00330830 0.0265678i
\(935\) 4.95230 2.85921i 0.00529657 0.00305798i
\(936\) −644.434 + 330.688i −0.688498 + 0.353299i
\(937\) −916.756 + 1587.87i −0.978395 + 1.69463i −0.310152 + 0.950687i \(0.600380\pi\)
−0.668243 + 0.743943i \(0.732954\pi\)
\(938\) −570.649 + 754.586i −0.608368 + 0.804463i
\(939\) 608.318 273.764i 0.647836 0.291548i
\(940\) −6.70047 + 1.89652i −0.00712816 + 0.00201758i
\(941\) −140.849 + 118.186i −0.149680 + 0.125596i −0.714553 0.699582i \(-0.753370\pi\)
0.564873 + 0.825178i \(0.308925\pi\)
\(942\) 1587.88 + 669.726i 1.68565 + 0.710962i
\(943\) 32.9186 11.9814i 0.0349084 0.0127056i
\(944\) −946.179 + 194.354i −1.00231 + 0.205883i
\(945\) 4.59573 14.7443i 0.00486321 0.0156025i
\(946\) 23.0161 + 454.046i 0.0243299 + 0.479964i
\(947\) −158.285 + 57.6109i −0.167143 + 0.0608351i −0.424236 0.905551i \(-0.639457\pi\)
0.257093 + 0.966387i \(0.417235\pi\)
\(948\) −1720.73 + 304.437i −1.81511 + 0.321136i
\(949\) −145.398 173.278i −0.153212 0.182590i
\(950\) −944.988 + 216.464i −0.994724 + 0.227857i
\(951\) −4.47895 + 44.3201i −0.00470973 + 0.0466037i
\(952\) 242.700 399.261i 0.254937 0.419392i
\(953\) 502.309 + 290.008i 0.527081 + 0.304311i 0.739827 0.672797i \(-0.234907\pi\)
−0.212746 + 0.977108i \(0.568241\pi\)
\(954\) −13.4072 564.493i −0.0140537 0.591712i
\(955\) 8.87773 5.12556i 0.00929605 0.00536708i
\(956\) −1199.15 87.9797i −1.25434 0.0920289i
\(957\) −82.6720 + 80.4774i −0.0863867 + 0.0840935i
\(958\) −273.099 + 887.828i −0.285072 + 0.926752i
\(959\) 431.838 1186.47i 0.450300 1.23719i
\(960\) 17.4991 0.501251i 0.0182282 0.000522137i
\(961\) −143.721 + 815.082i −0.149554 + 0.848160i
\(962\) −568.544 878.771i −0.591002 0.913484i
\(963\) 320.077 810.846i 0.332375 0.842000i
\(964\) −103.692 + 230.765i −0.107564 + 0.239383i
\(965\) −4.21093 3.53339i −0.00436366 0.00366155i
\(966\) −15.1792 + 23.4915i −0.0157134 + 0.0243183i
\(967\) 55.6940 + 315.856i 0.0575946 + 0.326635i 0.999969 0.00792608i \(-0.00252298\pi\)
−0.942374 + 0.334561i \(0.891412\pi\)
\(968\) 399.225 454.519i 0.412422 0.469545i
\(969\) −304.721 447.890i −0.314469 0.462218i
\(970\) −15.7391 + 6.64907i −0.0162259 + 0.00685471i
\(971\) 1187.70 1.22317 0.611587 0.791177i \(-0.290532\pi\)
0.611587 + 0.791177i \(0.290532\pi\)
\(972\) −584.293 776.779i −0.601125 0.799155i
\(973\) 109.656i 0.112698i
\(974\) −751.570 + 317.505i −0.771632 + 0.325980i
\(975\) −623.614 + 424.274i −0.639604 + 0.435153i
\(976\) −759.018 601.426i −0.777683 0.616216i
\(977\) 845.269 149.044i 0.865168 0.152552i 0.276585 0.960989i \(-0.410797\pi\)
0.588583 + 0.808437i \(0.299686\pi\)
\(978\) −737.019 + 1140.62i −0.753599 + 1.16628i
\(979\) 477.485 569.045i 0.487727 0.581251i
\(980\) 1.44169 3.20848i 0.00147111 0.00327396i
\(981\) 1065.64 + 420.656i 1.08628 + 0.428803i
\(982\) −552.430 853.864i −0.562556 0.869515i
\(983\) −571.635 100.795i −0.581521 0.102538i −0.124853 0.992175i \(-0.539846\pi\)
−0.456668 + 0.889637i \(0.650957\pi\)
\(984\) 139.166 1122.89i 0.141429 1.14115i
\(985\) −24.0963 8.77033i −0.0244632 0.00890389i
\(986\) −31.2529 + 101.601i −0.0316966 + 0.103044i
\(987\) −250.655 257.490i −0.253956 0.260881i
\(988\) 57.1100 778.399i 0.0578037 0.787853i
\(989\) −12.5366 21.7141i −0.0126761 0.0219556i
\(990\) 0.262518 + 11.0530i 0.000265170 + 0.0111646i
\(991\) 631.173 1093.22i 0.636906 1.10315i −0.349202 0.937047i \(-0.613547\pi\)
0.986108 0.166106i \(-0.0531193\pi\)
\(992\) 333.549 + 159.027i 0.336239 + 0.160309i
\(993\) −619.148 62.5705i −0.623512 0.0630116i
\(994\) 324.723 74.3829i 0.326683 0.0748319i
\(995\) 15.2088 12.7617i 0.0152852 0.0128258i
\(996\) 381.802 67.5498i 0.383336 0.0678211i
\(997\) −138.735 381.172i −0.139153 0.382318i 0.850467 0.526028i \(-0.176319\pi\)
−0.989620 + 0.143709i \(0.954097\pi\)
\(998\) 29.4248 + 580.473i 0.0294838 + 0.581636i
\(999\) 1032.42 952.286i 1.03345 0.953240i
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 216.3.x.a.101.64 yes 420
8.5 even 2 inner 216.3.x.a.101.8 yes 420
27.23 odd 18 inner 216.3.x.a.77.8 420
216.77 odd 18 inner 216.3.x.a.77.64 yes 420
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.3.x.a.77.8 420 27.23 odd 18 inner
216.3.x.a.77.64 yes 420 216.77 odd 18 inner
216.3.x.a.101.8 yes 420 8.5 even 2 inner
216.3.x.a.101.64 yes 420 1.1 even 1 trivial