Properties

Label 60.4.e.a.11.8
Level $60$
Weight $4$
Character 60.11
Analytic conductor $3.540$
Analytic rank $0$
Dimension $24$
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] = [60,4,Mod(11,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.11");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 60.e (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.54011460034\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.8
Character \(\chi\) \(=\) 60.11
Dual form 60.4.e.a.11.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.91554 + 2.08103i) q^{2} +(-2.09257 - 4.75617i) q^{3} +(-0.661378 - 7.97261i) q^{4} +5.00000i q^{5} +(13.9062 + 4.75594i) q^{6} +32.2690i q^{7} +(17.8582 + 13.8955i) q^{8} +(-18.2423 + 19.9053i) q^{9} +O(q^{10})\) \(q+(-1.91554 + 2.08103i) q^{2} +(-2.09257 - 4.75617i) q^{3} +(-0.661378 - 7.97261i) q^{4} +5.00000i q^{5} +(13.9062 + 4.75594i) q^{6} +32.2690i q^{7} +(17.8582 + 13.8955i) q^{8} +(-18.2423 + 19.9053i) q^{9} +(-10.4052 - 9.57772i) q^{10} -32.4750 q^{11} +(-36.5351 + 19.8289i) q^{12} +44.9257 q^{13} +(-67.1527 - 61.8126i) q^{14} +(23.7808 - 10.4629i) q^{15} +(-63.1252 + 10.5458i) q^{16} +79.2204i q^{17} +(-6.47961 - 76.0921i) q^{18} +69.0323i q^{19} +(39.8631 - 3.30689i) q^{20} +(153.477 - 67.5252i) q^{21} +(62.2073 - 67.5815i) q^{22} -72.8705 q^{23} +(28.7200 - 114.014i) q^{24} -25.0000 q^{25} +(-86.0572 + 93.4918i) q^{26} +(132.846 + 45.1100i) q^{27} +(257.268 - 21.3420i) q^{28} -219.925i q^{29} +(-23.7797 + 69.5308i) q^{30} +28.4726i q^{31} +(98.9729 - 151.566i) q^{32} +(67.9564 + 154.457i) q^{33} +(-164.860 - 151.750i) q^{34} -161.345 q^{35} +(170.762 + 132.274i) q^{36} -152.826 q^{37} +(-143.658 - 132.234i) q^{38} +(-94.0104 - 213.674i) q^{39} +(-69.4777 + 89.2908i) q^{40} -104.817i q^{41} +(-153.469 + 448.737i) q^{42} +96.6054i q^{43} +(21.4783 + 258.911i) q^{44} +(-99.5264 - 91.2113i) q^{45} +(139.587 - 151.646i) q^{46} +103.880 q^{47} +(182.252 + 278.166i) q^{48} -698.285 q^{49} +(47.8886 - 52.0258i) q^{50} +(376.785 - 165.775i) q^{51} +(-29.7129 - 358.175i) q^{52} +544.398i q^{53} +(-348.348 + 190.047i) q^{54} -162.375i q^{55} +(-448.395 + 576.264i) q^{56} +(328.329 - 144.455i) q^{57} +(457.671 + 421.276i) q^{58} +431.052 q^{59} +(-99.1446 - 182.676i) q^{60} +183.375 q^{61} +(-59.2524 - 54.5406i) q^{62} +(-642.322 - 588.659i) q^{63} +(125.827 + 496.298i) q^{64} +224.629i q^{65} +(-451.602 - 154.449i) q^{66} -290.222i q^{67} +(631.593 - 52.3946i) q^{68} +(152.487 + 346.584i) q^{69} +(309.063 - 335.763i) q^{70} +489.128 q^{71} +(-602.368 + 101.985i) q^{72} -292.966 q^{73} +(292.745 - 318.036i) q^{74} +(52.3144 + 118.904i) q^{75} +(550.368 - 45.6564i) q^{76} -1047.93i q^{77} +(624.744 + 213.664i) q^{78} +656.389i q^{79} +(-52.7291 - 315.626i) q^{80} +(-63.4397 - 726.234i) q^{81} +(218.127 + 200.781i) q^{82} -392.339 q^{83} +(-639.858 - 1178.95i) q^{84} -396.102 q^{85} +(-201.039 - 185.052i) q^{86} +(-1046.00 + 460.210i) q^{87} +(-579.944 - 451.258i) q^{88} -336.343i q^{89} +(380.461 - 32.3981i) q^{90} +1449.71i q^{91} +(48.1949 + 580.968i) q^{92} +(135.421 - 59.5811i) q^{93} +(-198.986 + 216.177i) q^{94} -345.161 q^{95} +(-927.983 - 153.568i) q^{96} +1039.74 q^{97} +(1337.60 - 1453.15i) q^{98} +(592.417 - 646.424i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.91554 + 2.08103i −0.677247 + 0.735755i
\(3\) −2.09257 4.75617i −0.402716 0.915325i
\(4\) −0.661378 7.97261i −0.0826723 0.996577i
\(5\) 5.00000i 0.447214i
\(6\) 13.9062 + 4.75594i 0.946194 + 0.323601i
\(7\) 32.2690i 1.74236i 0.490964 + 0.871180i \(0.336645\pi\)
−0.490964 + 0.871180i \(0.663355\pi\)
\(8\) 17.8582 + 13.8955i 0.789226 + 0.614102i
\(9\) −18.2423 + 19.9053i −0.675639 + 0.737232i
\(10\) −10.4052 9.57772i −0.329040 0.302874i
\(11\) −32.4750 −0.890144 −0.445072 0.895495i \(-0.646822\pi\)
−0.445072 + 0.895495i \(0.646822\pi\)
\(12\) −36.5351 + 19.8289i −0.878898 + 0.477010i
\(13\) 44.9257 0.958473 0.479237 0.877686i \(-0.340914\pi\)
0.479237 + 0.877686i \(0.340914\pi\)
\(14\) −67.1527 61.8126i −1.28195 1.18001i
\(15\) 23.7808 10.4629i 0.409346 0.180100i
\(16\) −63.1252 + 10.5458i −0.986331 + 0.164779i
\(17\) 79.2204i 1.13022i 0.825015 + 0.565111i \(0.191167\pi\)
−0.825015 + 0.565111i \(0.808833\pi\)
\(18\) −6.47961 76.0921i −0.0848478 0.996394i
\(19\) 69.0323i 0.833531i 0.909014 + 0.416765i \(0.136836\pi\)
−0.909014 + 0.416765i \(0.863164\pi\)
\(20\) 39.8631 3.30689i 0.445683 0.0369722i
\(21\) 153.477 67.5252i 1.59483 0.701676i
\(22\) 62.2073 67.5815i 0.602847 0.654928i
\(23\) −72.8705 −0.660632 −0.330316 0.943870i \(-0.607155\pi\)
−0.330316 + 0.943870i \(0.607155\pi\)
\(24\) 28.7200 114.014i 0.244269 0.969708i
\(25\) −25.0000 −0.200000
\(26\) −86.0572 + 93.4918i −0.649123 + 0.705202i
\(27\) 132.846 + 45.1100i 0.946898 + 0.321534i
\(28\) 257.268 21.3420i 1.73640 0.144045i
\(29\) 219.925i 1.40824i −0.710079 0.704122i \(-0.751341\pi\)
0.710079 0.704122i \(-0.248659\pi\)
\(30\) −23.7797 + 69.5308i −0.144719 + 0.423151i
\(31\) 28.4726i 0.164962i 0.996593 + 0.0824812i \(0.0262844\pi\)
−0.996593 + 0.0824812i \(0.973716\pi\)
\(32\) 98.9729 151.566i 0.546753 0.837294i
\(33\) 67.9564 + 154.457i 0.358475 + 0.814771i
\(34\) −164.860 151.750i −0.831566 0.765439i
\(35\) −161.345 −0.779207
\(36\) 170.762 + 132.274i 0.790565 + 0.612378i
\(37\) −152.826 −0.679039 −0.339520 0.940599i \(-0.610265\pi\)
−0.339520 + 0.940599i \(0.610265\pi\)
\(38\) −143.658 132.234i −0.613275 0.564506i
\(39\) −94.0104 213.674i −0.385993 0.877314i
\(40\) −69.4777 + 89.2908i −0.274635 + 0.352953i
\(41\) 104.817i 0.399259i −0.979871 0.199629i \(-0.936026\pi\)
0.979871 0.199629i \(-0.0639738\pi\)
\(42\) −153.469 + 448.737i −0.563829 + 1.64861i
\(43\) 96.6054i 0.342609i 0.985218 + 0.171305i \(0.0547982\pi\)
−0.985218 + 0.171305i \(0.945202\pi\)
\(44\) 21.4783 + 258.911i 0.0735902 + 0.887097i
\(45\) −99.5264 91.2113i −0.329700 0.302155i
\(46\) 139.587 151.646i 0.447411 0.486064i
\(47\) 103.880 0.322391 0.161196 0.986922i \(-0.448465\pi\)
0.161196 + 0.986922i \(0.448465\pi\)
\(48\) 182.252 + 278.166i 0.548037 + 0.836454i
\(49\) −698.285 −2.03582
\(50\) 47.8886 52.0258i 0.135449 0.147151i
\(51\) 376.785 165.775i 1.03452 0.455158i
\(52\) −29.7129 358.175i −0.0792391 0.955192i
\(53\) 544.398i 1.41092i 0.708750 + 0.705460i \(0.249260\pi\)
−0.708750 + 0.705460i \(0.750740\pi\)
\(54\) −348.348 + 190.047i −0.877855 + 0.478927i
\(55\) 162.375i 0.398084i
\(56\) −448.395 + 576.264i −1.06999 + 1.37512i
\(57\) 328.329 144.455i 0.762952 0.335676i
\(58\) 457.671 + 421.276i 1.03612 + 0.953729i
\(59\) 431.052 0.951156 0.475578 0.879674i \(-0.342239\pi\)
0.475578 + 0.879674i \(0.342239\pi\)
\(60\) −99.1446 182.676i −0.213325 0.393055i
\(61\) 183.375 0.384898 0.192449 0.981307i \(-0.438357\pi\)
0.192449 + 0.981307i \(0.438357\pi\)
\(62\) −59.2524 54.5406i −0.121372 0.111720i
\(63\) −642.322 588.659i −1.28452 1.17721i
\(64\) 125.827 + 496.298i 0.245757 + 0.969332i
\(65\) 224.629i 0.428642i
\(66\) −451.602 154.449i −0.842248 0.288051i
\(67\) 290.222i 0.529198i −0.964359 0.264599i \(-0.914760\pi\)
0.964359 0.264599i \(-0.0852395\pi\)
\(68\) 631.593 52.3946i 1.12635 0.0934379i
\(69\) 152.487 + 346.584i 0.266047 + 0.604693i
\(70\) 309.063 335.763i 0.527716 0.573306i
\(71\) 489.128 0.817589 0.408794 0.912627i \(-0.365949\pi\)
0.408794 + 0.912627i \(0.365949\pi\)
\(72\) −602.368 + 101.985i −0.985969 + 0.166931i
\(73\) −292.966 −0.469713 −0.234856 0.972030i \(-0.575462\pi\)
−0.234856 + 0.972030i \(0.575462\pi\)
\(74\) 292.745 318.036i 0.459878 0.499607i
\(75\) 52.3144 + 118.904i 0.0805432 + 0.183065i
\(76\) 550.368 45.6564i 0.830677 0.0689099i
\(77\) 1047.93i 1.55095i
\(78\) 624.744 + 213.664i 0.906901 + 0.310163i
\(79\) 656.389i 0.934805i 0.884045 + 0.467402i \(0.154810\pi\)
−0.884045 + 0.467402i \(0.845190\pi\)
\(80\) −52.7291 315.626i −0.0736912 0.441100i
\(81\) −63.4397 726.234i −0.0870228 0.996206i
\(82\) 218.127 + 200.781i 0.293757 + 0.270397i
\(83\) −392.339 −0.518853 −0.259426 0.965763i \(-0.583533\pi\)
−0.259426 + 0.965763i \(0.583533\pi\)
\(84\) −639.858 1178.95i −0.831122 1.53136i
\(85\) −396.102 −0.505450
\(86\) −201.039 185.052i −0.252076 0.232031i
\(87\) −1046.00 + 460.210i −1.28900 + 0.567122i
\(88\) −579.944 451.258i −0.702525 0.546639i
\(89\) 336.343i 0.400588i −0.979736 0.200294i \(-0.935810\pi\)
0.979736 0.200294i \(-0.0641897\pi\)
\(90\) 380.461 32.3981i 0.445601 0.0379451i
\(91\) 1449.71i 1.67000i
\(92\) 48.1949 + 580.968i 0.0546160 + 0.658371i
\(93\) 135.421 59.5811i 0.150994 0.0664330i
\(94\) −198.986 + 216.177i −0.218339 + 0.237201i
\(95\) −345.161 −0.372766
\(96\) −927.983 153.568i −0.986582 0.163265i
\(97\) 1039.74 1.08834 0.544171 0.838974i \(-0.316844\pi\)
0.544171 + 0.838974i \(0.316844\pi\)
\(98\) 1337.60 1453.15i 1.37875 1.49786i
\(99\) 592.417 646.424i 0.601416 0.656243i
\(100\) 16.5345 + 199.315i 0.0165345 + 0.199315i
\(101\) 308.323i 0.303755i 0.988399 + 0.151877i \(0.0485319\pi\)
−0.988399 + 0.151877i \(0.951468\pi\)
\(102\) −376.767 + 1101.65i −0.365740 + 1.06941i
\(103\) 264.352i 0.252887i −0.991974 0.126443i \(-0.959644\pi\)
0.991974 0.126443i \(-0.0403562\pi\)
\(104\) 802.290 + 624.267i 0.756452 + 0.588601i
\(105\) 337.626 + 767.383i 0.313799 + 0.713228i
\(106\) −1132.91 1042.82i −1.03809 0.955542i
\(107\) 1561.77 1.41104 0.705522 0.708688i \(-0.250713\pi\)
0.705522 + 0.708688i \(0.250713\pi\)
\(108\) 271.783 1088.97i 0.242151 0.970238i
\(109\) 2178.35 1.91420 0.957100 0.289757i \(-0.0935744\pi\)
0.957100 + 0.289757i \(0.0935744\pi\)
\(110\) 337.907 + 311.037i 0.292893 + 0.269602i
\(111\) 319.800 + 726.867i 0.273460 + 0.621542i
\(112\) −340.303 2036.98i −0.287103 1.71854i
\(113\) 1715.85i 1.42844i 0.699920 + 0.714221i \(0.253219\pi\)
−0.699920 + 0.714221i \(0.746781\pi\)
\(114\) −328.313 + 959.973i −0.269731 + 0.788682i
\(115\) 364.352i 0.295444i
\(116\) −1753.38 + 145.454i −1.40342 + 0.116423i
\(117\) −819.547 + 894.258i −0.647582 + 0.706617i
\(118\) −825.699 + 897.033i −0.644168 + 0.699818i
\(119\) −2556.36 −1.96925
\(120\) 570.069 + 143.600i 0.433666 + 0.109240i
\(121\) −276.374 −0.207644
\(122\) −351.263 + 381.610i −0.260671 + 0.283191i
\(123\) −498.525 + 219.337i −0.365451 + 0.160788i
\(124\) 227.001 18.8312i 0.164398 0.0136378i
\(125\) 125.000i 0.0894427i
\(126\) 2455.41 209.090i 1.73608 0.147835i
\(127\) 1396.37i 0.975652i −0.872941 0.487826i \(-0.837790\pi\)
0.872941 0.487826i \(-0.162210\pi\)
\(128\) −1273.84 688.830i −0.879629 0.475660i
\(129\) 459.472 202.154i 0.313599 0.137974i
\(130\) −467.459 430.286i −0.315376 0.290297i
\(131\) 1510.54 1.00745 0.503727 0.863863i \(-0.331962\pi\)
0.503727 + 0.863863i \(0.331962\pi\)
\(132\) 1186.48 643.944i 0.782346 0.424607i
\(133\) −2227.60 −1.45231
\(134\) 603.961 + 555.933i 0.389360 + 0.358398i
\(135\) −225.550 + 664.231i −0.143794 + 0.423466i
\(136\) −1100.81 + 1414.73i −0.694071 + 0.892000i
\(137\) 541.789i 0.337870i 0.985627 + 0.168935i \(0.0540327\pi\)
−0.985627 + 0.168935i \(0.945967\pi\)
\(138\) −1013.35 346.567i −0.625086 0.213781i
\(139\) 713.800i 0.435566i 0.975997 + 0.217783i \(0.0698825\pi\)
−0.975997 + 0.217783i \(0.930117\pi\)
\(140\) 106.710 + 1286.34i 0.0644188 + 0.776540i
\(141\) −217.376 494.069i −0.129832 0.295093i
\(142\) −936.946 + 1017.89i −0.553710 + 0.601545i
\(143\) −1458.96 −0.853179
\(144\) 941.628 1448.90i 0.544924 0.838486i
\(145\) 1099.63 0.629786
\(146\) 561.189 609.671i 0.318112 0.345594i
\(147\) 1461.21 + 3321.16i 0.819857 + 1.86343i
\(148\) 101.076 + 1218.42i 0.0561377 + 0.676715i
\(149\) 109.018i 0.0599405i −0.999551 0.0299702i \(-0.990459\pi\)
0.999551 0.0299702i \(-0.00954126\pi\)
\(150\) −347.654 118.898i −0.189239 0.0647201i
\(151\) 3186.38i 1.71725i −0.512607 0.858623i \(-0.671320\pi\)
0.512607 0.858623i \(-0.328680\pi\)
\(152\) −959.241 + 1232.79i −0.511873 + 0.657845i
\(153\) −1576.90 1445.16i −0.833236 0.763622i
\(154\) 2180.78 + 2007.36i 1.14112 + 1.05038i
\(155\) −142.363 −0.0737734
\(156\) −1641.37 + 890.828i −0.842400 + 0.457201i
\(157\) −1029.37 −0.523266 −0.261633 0.965167i \(-0.584261\pi\)
−0.261633 + 0.965167i \(0.584261\pi\)
\(158\) −1365.97 1257.34i −0.687788 0.633094i
\(159\) 2589.25 1139.19i 1.29145 0.568200i
\(160\) 757.832 + 494.864i 0.374449 + 0.244515i
\(161\) 2351.45i 1.15106i
\(162\) 1632.84 + 1259.11i 0.791900 + 0.610650i
\(163\) 224.555i 0.107905i −0.998544 0.0539524i \(-0.982818\pi\)
0.998544 0.0539524i \(-0.0171819\pi\)
\(164\) −835.662 + 69.3234i −0.397892 + 0.0330076i
\(165\) −772.283 + 339.782i −0.364377 + 0.160315i
\(166\) 751.542 816.469i 0.351392 0.381749i
\(167\) −959.236 −0.444479 −0.222239 0.974992i \(-0.571337\pi\)
−0.222239 + 0.974992i \(0.571337\pi\)
\(168\) 3679.11 + 926.766i 1.68958 + 0.425604i
\(169\) −178.681 −0.0813294
\(170\) 758.751 824.300i 0.342315 0.371888i
\(171\) −1374.11 1259.30i −0.614506 0.563166i
\(172\) 770.198 63.8927i 0.341436 0.0283243i
\(173\) 1819.46i 0.799600i −0.916602 0.399800i \(-0.869080\pi\)
0.916602 0.399800i \(-0.130920\pi\)
\(174\) 1045.95 3058.31i 0.455709 1.33247i
\(175\) 806.724i 0.348472i
\(176\) 2049.99 342.476i 0.877976 0.146677i
\(177\) −902.008 2050.16i −0.383046 0.870617i
\(178\) 699.941 + 644.280i 0.294735 + 0.271297i
\(179\) 797.802 0.333131 0.166566 0.986030i \(-0.446732\pi\)
0.166566 + 0.986030i \(0.446732\pi\)
\(180\) −661.368 + 853.810i −0.273864 + 0.353552i
\(181\) 1893.23 0.777472 0.388736 0.921349i \(-0.372912\pi\)
0.388736 + 0.921349i \(0.372912\pi\)
\(182\) −3016.88 2776.98i −1.22872 1.13101i
\(183\) −383.726 872.164i −0.155005 0.352307i
\(184\) −1301.33 1012.58i −0.521388 0.405696i
\(185\) 764.131i 0.303676i
\(186\) −135.414 + 395.945i −0.0533820 + 0.156086i
\(187\) 2572.68i 1.00606i
\(188\) −68.7037 828.192i −0.0266528 0.321288i
\(189\) −1455.65 + 4286.80i −0.560228 + 1.64984i
\(190\) 661.172 718.291i 0.252455 0.274265i
\(191\) −2169.17 −0.821759 −0.410879 0.911690i \(-0.634778\pi\)
−0.410879 + 0.911690i \(0.634778\pi\)
\(192\) 2097.17 1637.00i 0.788283 0.615313i
\(193\) 4329.69 1.61481 0.807405 0.589998i \(-0.200872\pi\)
0.807405 + 0.589998i \(0.200872\pi\)
\(194\) −1991.66 + 2163.72i −0.737077 + 0.800754i
\(195\) 1068.37 470.052i 0.392347 0.172621i
\(196\) 461.831 + 5567.16i 0.168306 + 2.02885i
\(197\) 2110.47i 0.763274i 0.924312 + 0.381637i \(0.124640\pi\)
−0.924312 + 0.381637i \(0.875360\pi\)
\(198\) 210.425 + 2471.09i 0.0755267 + 0.886934i
\(199\) 1465.10i 0.521899i 0.965352 + 0.260950i \(0.0840357\pi\)
−0.965352 + 0.260950i \(0.915964\pi\)
\(200\) −446.454 347.389i −0.157845 0.122820i
\(201\) −1380.34 + 607.311i −0.484388 + 0.213116i
\(202\) −641.629 590.606i −0.223489 0.205717i
\(203\) 7096.75 2.45367
\(204\) −1570.85 2894.32i −0.539126 0.993349i
\(205\) 524.083 0.178554
\(206\) 550.124 + 506.377i 0.186063 + 0.171267i
\(207\) 1329.32 1450.51i 0.446349 0.487039i
\(208\) −2835.94 + 473.779i −0.945371 + 0.157936i
\(209\) 2241.82i 0.741962i
\(210\) −2243.68 767.346i −0.737281 0.252152i
\(211\) 2400.96i 0.783361i 0.920101 + 0.391681i \(0.128106\pi\)
−0.920101 + 0.391681i \(0.871894\pi\)
\(212\) 4340.27 360.053i 1.40609 0.116644i
\(213\) −1023.54 2326.37i −0.329256 0.748359i
\(214\) −2991.63 + 3250.08i −0.955625 + 1.03818i
\(215\) −483.027 −0.153219
\(216\) 1745.56 + 2651.55i 0.549862 + 0.835256i
\(217\) −918.782 −0.287424
\(218\) −4172.72 + 4533.21i −1.29639 + 1.40838i
\(219\) 613.052 + 1393.39i 0.189161 + 0.429940i
\(220\) −1294.55 + 107.391i −0.396722 + 0.0329105i
\(221\) 3559.03i 1.08329i
\(222\) −2125.22 726.832i −0.642503 0.219738i
\(223\) 1227.21i 0.368521i 0.982877 + 0.184260i \(0.0589890\pi\)
−0.982877 + 0.184260i \(0.941011\pi\)
\(224\) 4890.89 + 3193.75i 1.45887 + 0.952640i
\(225\) 456.057 497.632i 0.135128 0.147446i
\(226\) −3570.74 3286.79i −1.05098 0.967408i
\(227\) −6004.46 −1.75564 −0.877820 0.478991i \(-0.841003\pi\)
−0.877820 + 0.478991i \(0.841003\pi\)
\(228\) −1368.83 2522.10i −0.397602 0.732589i
\(229\) −3410.62 −0.984192 −0.492096 0.870541i \(-0.663769\pi\)
−0.492096 + 0.870541i \(0.663769\pi\)
\(230\) 758.228 + 697.933i 0.217374 + 0.200088i
\(231\) −4984.15 + 2192.88i −1.41962 + 0.624593i
\(232\) 3055.98 3927.46i 0.864806 1.11142i
\(233\) 6319.33i 1.77679i 0.459076 + 0.888397i \(0.348181\pi\)
−0.459076 + 0.888397i \(0.651819\pi\)
\(234\) −291.101 3418.49i −0.0813243 0.955017i
\(235\) 519.398i 0.144178i
\(236\) −285.088 3436.61i −0.0786342 0.947900i
\(237\) 3121.90 1373.54i 0.855650 0.376461i
\(238\) 4896.82 5319.86i 1.33367 1.44889i
\(239\) −3563.80 −0.964533 −0.482266 0.876025i \(-0.660186\pi\)
−0.482266 + 0.876025i \(0.660186\pi\)
\(240\) −1390.83 + 911.259i −0.374074 + 0.245090i
\(241\) −2833.81 −0.757435 −0.378718 0.925512i \(-0.623635\pi\)
−0.378718 + 0.925512i \(0.623635\pi\)
\(242\) 529.408 575.144i 0.140626 0.152775i
\(243\) −3321.34 + 1821.43i −0.876807 + 0.480843i
\(244\) −121.280 1461.98i −0.0318204 0.383581i
\(245\) 3491.43i 0.910445i
\(246\) 498.501 1457.60i 0.129200 0.377776i
\(247\) 3101.32i 0.798917i
\(248\) −395.643 + 508.469i −0.101304 + 0.130193i
\(249\) 820.998 + 1866.03i 0.208950 + 0.474919i
\(250\) 260.129 + 239.443i 0.0658080 + 0.0605748i
\(251\) 3865.84 0.972149 0.486075 0.873917i \(-0.338428\pi\)
0.486075 + 0.873917i \(0.338428\pi\)
\(252\) −4268.33 + 5510.31i −1.06698 + 1.37745i
\(253\) 2366.47 0.588058
\(254\) 2905.89 + 2674.81i 0.717841 + 0.660757i
\(255\) 828.873 + 1883.93i 0.203553 + 0.462651i
\(256\) 3873.57 1331.41i 0.945696 0.325052i
\(257\) 2960.51i 0.718566i 0.933229 + 0.359283i \(0.116979\pi\)
−0.933229 + 0.359283i \(0.883021\pi\)
\(258\) −459.449 + 1343.41i −0.110869 + 0.324174i
\(259\) 4931.54i 1.18313i
\(260\) 1790.88 148.564i 0.427175 0.0354368i
\(261\) 4377.67 + 4011.93i 1.03820 + 0.951465i
\(262\) −2893.50 + 3143.48i −0.682295 + 0.741239i
\(263\) 6555.46 1.53699 0.768493 0.639859i \(-0.221007\pi\)
0.768493 + 0.639859i \(0.221007\pi\)
\(264\) −932.683 + 3702.60i −0.217434 + 0.863179i
\(265\) −2721.99 −0.630983
\(266\) 4267.06 4635.70i 0.983573 1.06855i
\(267\) −1599.70 + 703.823i −0.366668 + 0.161323i
\(268\) −2313.83 + 191.946i −0.527386 + 0.0437500i
\(269\) 8701.31i 1.97222i −0.166083 0.986112i \(-0.553112\pi\)
0.166083 0.986112i \(-0.446888\pi\)
\(270\) −950.233 1741.74i −0.214183 0.392589i
\(271\) 2026.32i 0.454207i −0.973871 0.227104i \(-0.927074\pi\)
0.973871 0.227104i \(-0.0729256\pi\)
\(272\) −835.444 5000.80i −0.186236 1.11477i
\(273\) 6895.04 3033.62i 1.52860 0.672538i
\(274\) −1127.48 1037.82i −0.248589 0.228821i
\(275\) 811.875 0.178029
\(276\) 2662.33 1444.94i 0.580628 0.315128i
\(277\) 6200.10 1.34487 0.672433 0.740158i \(-0.265249\pi\)
0.672433 + 0.740158i \(0.265249\pi\)
\(278\) −1485.44 1367.31i −0.320470 0.294986i
\(279\) −566.755 519.405i −0.121616 0.111455i
\(280\) −2881.32 2241.97i −0.614971 0.478513i
\(281\) 8199.53i 1.74072i 0.492413 + 0.870361i \(0.336115\pi\)
−0.492413 + 0.870361i \(0.663885\pi\)
\(282\) 1444.57 + 494.045i 0.305045 + 0.104326i
\(283\) 7615.89i 1.59971i 0.600194 + 0.799854i \(0.295090\pi\)
−0.600194 + 0.799854i \(0.704910\pi\)
\(284\) −323.498 3899.63i −0.0675919 0.814790i
\(285\) 722.276 + 1641.64i 0.150119 + 0.341202i
\(286\) 2794.71 3036.15i 0.577813 0.627731i
\(287\) 3382.32 0.695652
\(288\) 1211.48 + 4735.00i 0.247872 + 0.968793i
\(289\) −1362.87 −0.277400
\(290\) −2106.38 + 2288.35i −0.426521 + 0.463368i
\(291\) −2175.72 4945.16i −0.438293 0.996186i
\(292\) 193.761 + 2335.70i 0.0388322 + 0.468105i
\(293\) 9294.47i 1.85320i −0.376044 0.926602i \(-0.622716\pi\)
0.376044 0.926602i \(-0.377284\pi\)
\(294\) −9710.46 3321.00i −1.92628 0.658792i
\(295\) 2155.26i 0.425370i
\(296\) −2729.19 2123.60i −0.535916 0.417000i
\(297\) −4314.18 1464.95i −0.842875 0.286212i
\(298\) 226.871 + 208.830i 0.0441016 + 0.0405945i
\(299\) −3273.76 −0.633198
\(300\) 913.378 495.723i 0.175780 0.0954019i
\(301\) −3117.36 −0.596948
\(302\) 6630.96 + 6103.66i 1.26347 + 1.16300i
\(303\) 1466.43 645.188i 0.278034 0.122327i
\(304\) −728.002 4357.67i −0.137348 0.822137i
\(305\) 916.876i 0.172132i
\(306\) 6028.05 513.317i 1.12615 0.0958967i
\(307\) 1982.97i 0.368646i −0.982866 0.184323i \(-0.940991\pi\)
0.982866 0.184323i \(-0.0590092\pi\)
\(308\) −8354.78 + 693.081i −1.54564 + 0.128221i
\(309\) −1257.30 + 553.176i −0.231474 + 0.101842i
\(310\) 272.703 296.262i 0.0499629 0.0542792i
\(311\) 326.148 0.0594668 0.0297334 0.999558i \(-0.490534\pi\)
0.0297334 + 0.999558i \(0.490534\pi\)
\(312\) 1290.27 5122.15i 0.234125 0.929439i
\(313\) 1059.90 0.191403 0.0957014 0.995410i \(-0.469491\pi\)
0.0957014 + 0.995410i \(0.469491\pi\)
\(314\) 1971.80 2142.15i 0.354380 0.384996i
\(315\) 2943.29 3211.61i 0.526463 0.574457i
\(316\) 5233.14 434.122i 0.931605 0.0772824i
\(317\) 1007.99i 0.178595i 0.996005 + 0.0892974i \(0.0284621\pi\)
−0.996005 + 0.0892974i \(0.971538\pi\)
\(318\) −2589.12 + 7570.48i −0.456575 + 1.33500i
\(319\) 7142.07i 1.25354i
\(320\) −2481.49 + 629.137i −0.433498 + 0.109906i
\(321\) −3268.11 7428.02i −0.568250 1.29156i
\(322\) 4893.45 + 4504.31i 0.846898 + 0.779552i
\(323\) −5468.76 −0.942074
\(324\) −5748.03 + 986.095i −0.985602 + 0.169084i
\(325\) −1123.14 −0.191695
\(326\) 467.305 + 430.145i 0.0793916 + 0.0730783i
\(327\) −4558.35 10360.6i −0.770880 1.75212i
\(328\) 1456.48 1871.83i 0.245186 0.315105i
\(329\) 3352.09i 0.561722i
\(330\) 772.246 2258.01i 0.128820 0.376665i
\(331\) 3283.67i 0.545278i 0.962116 + 0.272639i \(0.0878965\pi\)
−0.962116 + 0.272639i \(0.912104\pi\)
\(332\) 259.484 + 3127.97i 0.0428947 + 0.517077i
\(333\) 2787.89 3042.05i 0.458786 0.500610i
\(334\) 1837.46 1996.20i 0.301022 0.327028i
\(335\) 1451.11 0.236664
\(336\) −8976.12 + 5881.08i −1.45740 + 0.954878i
\(337\) −10806.5 −1.74678 −0.873391 0.487019i \(-0.838084\pi\)
−0.873391 + 0.487019i \(0.838084\pi\)
\(338\) 342.271 371.840i 0.0550801 0.0598385i
\(339\) 8160.89 3590.55i 1.30749 0.575257i
\(340\) 261.973 + 3157.97i 0.0417867 + 0.503720i
\(341\) 924.649i 0.146840i
\(342\) 5252.81 447.302i 0.830525 0.0707232i
\(343\) 11464.7i 1.80477i
\(344\) −1342.39 + 1725.19i −0.210397 + 0.270396i
\(345\) −1732.92 + 762.434i −0.270427 + 0.118980i
\(346\) 3786.35 + 3485.25i 0.588310 + 0.541527i
\(347\) 4257.61 0.658676 0.329338 0.944212i \(-0.393174\pi\)
0.329338 + 0.944212i \(0.393174\pi\)
\(348\) 4360.88 + 8034.99i 0.671746 + 1.23770i
\(349\) −1701.82 −0.261022 −0.130511 0.991447i \(-0.541662\pi\)
−0.130511 + 0.991447i \(0.541662\pi\)
\(350\) 1678.82 + 1545.32i 0.256390 + 0.236002i
\(351\) 5968.21 + 2026.60i 0.907576 + 0.308182i
\(352\) −3214.14 + 4922.12i −0.486689 + 0.745312i
\(353\) 3808.94i 0.574305i 0.957885 + 0.287152i \(0.0927086\pi\)
−0.957885 + 0.287152i \(0.907291\pi\)
\(354\) 5994.27 + 2050.06i 0.899978 + 0.307795i
\(355\) 2445.64i 0.365637i
\(356\) −2681.53 + 222.450i −0.399216 + 0.0331175i
\(357\) 5349.37 + 12158.5i 0.793050 + 1.80251i
\(358\) −1528.22 + 1660.25i −0.225612 + 0.245103i
\(359\) −3187.87 −0.468660 −0.234330 0.972157i \(-0.575290\pi\)
−0.234330 + 0.972157i \(0.575290\pi\)
\(360\) −509.926 3011.84i −0.0746540 0.440939i
\(361\) 2093.55 0.305226
\(362\) −3626.56 + 3939.86i −0.526541 + 0.572029i
\(363\) 578.334 + 1314.48i 0.0836217 + 0.190062i
\(364\) 11557.9 958.804i 1.66429 0.138063i
\(365\) 1464.83i 0.210062i
\(366\) 2550.04 + 872.122i 0.364188 + 0.124553i
\(367\) 10714.8i 1.52400i 0.647576 + 0.762001i \(0.275783\pi\)
−0.647576 + 0.762001i \(0.724217\pi\)
\(368\) 4599.96 768.479i 0.651602 0.108858i
\(369\) 2086.40 + 1912.09i 0.294346 + 0.269755i
\(370\) 1590.18 + 1463.73i 0.223431 + 0.205664i
\(371\) −17567.1 −2.45833
\(372\) −564.581 1040.25i −0.0786887 0.144985i
\(373\) −13485.1 −1.87194 −0.935969 0.352082i \(-0.885474\pi\)
−0.935969 + 0.352082i \(0.885474\pi\)
\(374\) 5353.83 + 4928.09i 0.740214 + 0.681351i
\(375\) −594.521 + 261.572i −0.0818691 + 0.0360200i
\(376\) 1855.10 + 1443.46i 0.254440 + 0.197981i
\(377\) 9880.29i 1.34976i
\(378\) −6132.61 11240.8i −0.834464 1.52954i
\(379\) 14560.5i 1.97341i −0.162534 0.986703i \(-0.551967\pi\)
0.162534 0.986703i \(-0.448033\pi\)
\(380\) 228.282 + 2751.84i 0.0308174 + 0.371490i
\(381\) −6641.37 + 2922.01i −0.893038 + 0.392911i
\(382\) 4155.15 4514.12i 0.556534 0.604614i
\(383\) 12768.6 1.70352 0.851759 0.523934i \(-0.175536\pi\)
0.851759 + 0.523934i \(0.175536\pi\)
\(384\) −610.587 + 7500.02i −0.0811429 + 0.996702i
\(385\) 5239.67 0.693606
\(386\) −8293.72 + 9010.23i −1.09363 + 1.18810i
\(387\) −1922.96 1762.30i −0.252582 0.231480i
\(388\) −687.658 8289.41i −0.0899757 1.08462i
\(389\) 1614.55i 0.210439i −0.994449 0.105220i \(-0.966445\pi\)
0.994449 0.105220i \(-0.0335545\pi\)
\(390\) −1068.32 + 3123.72i −0.138709 + 0.405579i
\(391\) 5772.82i 0.746660i
\(392\) −12470.1 9703.06i −1.60672 1.25020i
\(393\) −3160.92 7184.38i −0.405718 0.922147i
\(394\) −4391.96 4042.70i −0.561583 0.516925i
\(395\) −3281.95 −0.418057
\(396\) −5545.50 4295.59i −0.703717 0.545104i
\(397\) −3366.61 −0.425605 −0.212803 0.977095i \(-0.568259\pi\)
−0.212803 + 0.977095i \(0.568259\pi\)
\(398\) −3048.91 2806.46i −0.383990 0.353455i
\(399\) 4661.42 + 10594.8i 0.584869 + 1.32934i
\(400\) 1578.13 263.646i 0.197266 0.0329557i
\(401\) 2084.43i 0.259580i 0.991542 + 0.129790i \(0.0414303\pi\)
−0.991542 + 0.129790i \(0.958570\pi\)
\(402\) 1380.28 4035.87i 0.171249 0.500724i
\(403\) 1279.15i 0.158112i
\(404\) 2458.14 203.918i 0.302715 0.0251121i
\(405\) 3631.17 317.198i 0.445517 0.0389178i
\(406\) −13594.1 + 14768.6i −1.66174 + 1.80530i
\(407\) 4963.03 0.604443
\(408\) 9032.22 + 2275.21i 1.09598 + 0.276078i
\(409\) 9008.16 1.08906 0.544529 0.838742i \(-0.316708\pi\)
0.544529 + 0.838742i \(0.316708\pi\)
\(410\) −1003.90 + 1090.63i −0.120925 + 0.131372i
\(411\) 2576.84 1133.73i 0.309260 0.136066i
\(412\) −2107.57 + 174.836i −0.252021 + 0.0209067i
\(413\) 13909.6i 1.65726i
\(414\) 472.172 + 5544.87i 0.0560532 + 0.658250i
\(415\) 1961.69i 0.232038i
\(416\) 4446.43 6809.23i 0.524048 0.802524i
\(417\) 3394.95 1493.68i 0.398685 0.175410i
\(418\) 4665.30 + 4294.31i 0.545903 + 0.502492i
\(419\) −8794.29 −1.02537 −0.512684 0.858577i \(-0.671349\pi\)
−0.512684 + 0.858577i \(0.671349\pi\)
\(420\) 5894.75 3199.29i 0.684844 0.371689i
\(421\) 4897.05 0.566906 0.283453 0.958986i \(-0.408520\pi\)
0.283453 + 0.958986i \(0.408520\pi\)
\(422\) −4996.48 4599.15i −0.576362 0.530529i
\(423\) −1895.00 + 2067.75i −0.217820 + 0.237677i
\(424\) −7564.71 + 9721.94i −0.866449 + 1.11354i
\(425\) 1980.51i 0.226044i
\(426\) 6801.88 + 2326.26i 0.773597 + 0.264572i
\(427\) 5917.33i 0.670631i
\(428\) −1032.92 12451.4i −0.116654 1.40621i
\(429\) 3052.99 + 6939.07i 0.343589 + 0.780936i
\(430\) 925.260 1005.19i 0.103767 0.112732i
\(431\) 11897.9 1.32970 0.664848 0.746978i \(-0.268496\pi\)
0.664848 + 0.746978i \(0.268496\pi\)
\(432\) −8861.65 1446.60i −0.986936 0.161111i
\(433\) 1169.38 0.129785 0.0648925 0.997892i \(-0.479330\pi\)
0.0648925 + 0.997892i \(0.479330\pi\)
\(434\) 1759.97 1912.01i 0.194657 0.211474i
\(435\) −2301.05 5230.00i −0.253625 0.576459i
\(436\) −1440.71 17367.1i −0.158251 1.90765i
\(437\) 5030.41i 0.550657i
\(438\) −4074.02 1393.33i −0.444439 0.151999i
\(439\) 6786.60i 0.737829i 0.929463 + 0.368915i \(0.120270\pi\)
−0.929463 + 0.368915i \(0.879730\pi\)
\(440\) 2256.29 2899.72i 0.244465 0.314179i
\(441\) 12738.3 13899.6i 1.37548 1.50087i
\(442\) −7406.45 6817.48i −0.797034 0.733653i
\(443\) −9083.87 −0.974238 −0.487119 0.873336i \(-0.661952\pi\)
−0.487119 + 0.873336i \(0.661952\pi\)
\(444\) 5583.52 3030.38i 0.596806 0.323908i
\(445\) 1681.72 0.179148
\(446\) −2553.86 2350.78i −0.271141 0.249580i
\(447\) −518.510 + 228.129i −0.0548650 + 0.0241390i
\(448\) −16015.0 + 4060.32i −1.68892 + 0.428196i
\(449\) 3214.97i 0.337914i 0.985623 + 0.168957i \(0.0540400\pi\)
−0.985623 + 0.168957i \(0.945960\pi\)
\(450\) 161.990 + 1902.30i 0.0169696 + 0.199279i
\(451\) 3403.92i 0.355398i
\(452\) 13679.8 1134.83i 1.42355 0.118093i
\(453\) −15155.0 + 6667.75i −1.57184 + 0.691563i
\(454\) 11501.8 12495.5i 1.18900 1.29172i
\(455\) −7248.53 −0.746849
\(456\) 7870.63 + 1982.61i 0.808281 + 0.203606i
\(457\) 12339.4 1.26304 0.631522 0.775358i \(-0.282431\pi\)
0.631522 + 0.775358i \(0.282431\pi\)
\(458\) 6533.19 7097.60i 0.666541 0.724125i
\(459\) −3573.63 + 10524.1i −0.363405 + 1.07020i
\(460\) −2904.84 + 240.975i −0.294432 + 0.0244250i
\(461\) 12038.7i 1.21626i −0.793837 0.608130i \(-0.791920\pi\)
0.793837 0.608130i \(-0.208080\pi\)
\(462\) 4983.91 14572.7i 0.501889 1.46750i
\(463\) 2481.97i 0.249130i 0.992211 + 0.124565i \(0.0397535\pi\)
−0.992211 + 0.124565i \(0.960247\pi\)
\(464\) 2319.29 + 13882.8i 0.232048 + 1.38899i
\(465\) 297.905 + 677.103i 0.0297098 + 0.0675267i
\(466\) −13150.7 12105.0i −1.30729 1.20333i
\(467\) −1596.67 −0.158212 −0.0791060 0.996866i \(-0.525207\pi\)
−0.0791060 + 0.996866i \(0.525207\pi\)
\(468\) 7671.61 + 5942.49i 0.757735 + 0.586948i
\(469\) 9365.16 0.922053
\(470\) −1080.88 994.930i −0.106080 0.0976440i
\(471\) 2154.03 + 4895.86i 0.210728 + 0.478958i
\(472\) 7697.79 + 5989.70i 0.750677 + 0.584107i
\(473\) 3137.26i 0.304971i
\(474\) −3121.75 + 9127.85i −0.302503 + 0.884506i
\(475\) 1725.81i 0.166706i
\(476\) 1690.72 + 20380.9i 0.162803 + 1.96251i
\(477\) −10836.4 9931.05i −1.04018 0.953273i
\(478\) 6826.63 7416.39i 0.653227 0.709660i
\(479\) 13673.9 1.30433 0.652166 0.758076i \(-0.273861\pi\)
0.652166 + 0.758076i \(0.273861\pi\)
\(480\) 767.838 4639.92i 0.0730143 0.441213i
\(481\) −6865.82 −0.650841
\(482\) 5428.29 5897.25i 0.512971 0.557287i
\(483\) −11183.9 + 4920.59i −1.05359 + 0.463550i
\(484\) 182.788 + 2203.43i 0.0171664 + 0.206933i
\(485\) 5198.68i 0.486721i
\(486\) 2571.73 10400.8i 0.240033 0.970765i
\(487\) 2712.51i 0.252393i 0.992005 + 0.126197i \(0.0402770\pi\)
−0.992005 + 0.126197i \(0.959723\pi\)
\(488\) 3274.74 + 2548.10i 0.303772 + 0.236367i
\(489\) −1068.02 + 469.898i −0.0987680 + 0.0434550i
\(490\) 7265.77 + 6687.98i 0.669865 + 0.616597i
\(491\) 7797.19 0.716664 0.358332 0.933594i \(-0.383346\pi\)
0.358332 + 0.933594i \(0.383346\pi\)
\(492\) 2078.40 + 3829.49i 0.190450 + 0.350908i
\(493\) 17422.5 1.59163
\(494\) −6453.95 5940.72i −0.587807 0.541064i
\(495\) 3232.12 + 2962.09i 0.293481 + 0.268961i
\(496\) −300.267 1797.34i −0.0271823 0.162707i
\(497\) 15783.6i 1.42453i
\(498\) −5455.92 1865.94i −0.490935 0.167901i
\(499\) 10440.3i 0.936617i −0.883565 0.468309i \(-0.844864\pi\)
0.883565 0.468309i \(-0.155136\pi\)
\(500\) −996.577 + 82.6723i −0.0891365 + 0.00739443i
\(501\) 2007.27 + 4562.29i 0.178999 + 0.406842i
\(502\) −7405.18 + 8044.93i −0.658386 + 0.715264i
\(503\) −14638.9 −1.29764 −0.648822 0.760940i \(-0.724738\pi\)
−0.648822 + 0.760940i \(0.724738\pi\)
\(504\) −3290.95 19437.8i −0.290855 1.71791i
\(505\) −1541.61 −0.135843
\(506\) −4533.07 + 4924.69i −0.398260 + 0.432667i
\(507\) 373.903 + 849.835i 0.0327527 + 0.0744428i
\(508\) −11132.7 + 923.528i −0.972312 + 0.0806593i
\(509\) 1254.81i 0.109270i 0.998506 + 0.0546351i \(0.0173996\pi\)
−0.998506 + 0.0546351i \(0.982600\pi\)
\(510\) −5508.25 1883.84i −0.478254 0.163564i
\(511\) 9453.70i 0.818409i
\(512\) −4649.28 + 10611.4i −0.401311 + 0.915942i
\(513\) −3114.05 + 9170.67i −0.268009 + 0.789269i
\(514\) −6160.91 5670.99i −0.528689 0.486647i
\(515\) 1321.76 0.113094
\(516\) −1915.58 3529.49i −0.163428 0.301118i
\(517\) −3373.49 −0.286975
\(518\) 10262.7 + 9446.58i 0.870495 + 0.801272i
\(519\) −8653.65 + 3807.35i −0.731894 + 0.322012i
\(520\) −3121.34 + 4011.45i −0.263230 + 0.338296i
\(521\) 2219.01i 0.186596i 0.995638 + 0.0932980i \(0.0297409\pi\)
−0.995638 + 0.0932980i \(0.970259\pi\)
\(522\) −16734.6 + 1425.03i −1.40317 + 0.119486i
\(523\) 11035.2i 0.922633i −0.887236 0.461317i \(-0.847377\pi\)
0.887236 0.461317i \(-0.152623\pi\)
\(524\) −999.037 12042.9i −0.0832885 1.00400i
\(525\) −3836.91 + 1688.13i −0.318965 + 0.140335i
\(526\) −12557.3 + 13642.1i −1.04092 + 1.13085i
\(527\) −2255.61 −0.186444
\(528\) −5918.63 9033.44i −0.487832 0.744564i
\(529\) −6856.90 −0.563565
\(530\) 5214.09 5664.54i 0.427331 0.464249i
\(531\) −7863.36 + 8580.21i −0.642638 + 0.701223i
\(532\) 1473.29 + 17759.8i 0.120066 + 1.44734i
\(533\) 4708.96i 0.382679i
\(534\) 1599.63 4677.24i 0.129630 0.379034i
\(535\) 7808.83i 0.631038i
\(536\) 4032.79 5182.83i 0.324982 0.417657i
\(537\) −1669.46 3794.48i −0.134157 0.304923i
\(538\) 18107.7 + 16667.7i 1.45107 + 1.33568i
\(539\) 22676.8 1.81217
\(540\) 5444.83 + 1358.92i 0.433904 + 0.108293i
\(541\) 4389.37 0.348824 0.174412 0.984673i \(-0.444198\pi\)
0.174412 + 0.984673i \(0.444198\pi\)
\(542\) 4216.83 + 3881.50i 0.334185 + 0.307611i
\(543\) −3961.72 9004.50i −0.313101 0.711640i
\(544\) 12007.1 + 7840.67i 0.946327 + 0.617952i
\(545\) 10891.7i 0.856057i
\(546\) −6894.71 + 20159.8i −0.540415 + 1.58015i
\(547\) 11409.4i 0.891826i −0.895076 0.445913i \(-0.852879\pi\)
0.895076 0.445913i \(-0.147121\pi\)
\(548\) 4319.47 358.327i 0.336713 0.0279324i
\(549\) −3345.18 + 3650.13i −0.260052 + 0.283759i
\(550\) −1555.18 + 1689.54i −0.120569 + 0.130986i
\(551\) 15181.9 1.17381
\(552\) −2092.84 + 8308.24i −0.161372 + 0.640620i
\(553\) −21181.0 −1.62877
\(554\) −11876.6 + 12902.6i −0.910806 + 0.989492i
\(555\) −3634.33 + 1599.00i −0.277962 + 0.122295i
\(556\) 5690.85 472.091i 0.434075 0.0360092i
\(557\) 9758.39i 0.742327i −0.928567 0.371164i \(-0.878959\pi\)
0.928567 0.371164i \(-0.121041\pi\)
\(558\) 2166.54 184.492i 0.164368 0.0139967i
\(559\) 4340.07i 0.328382i
\(560\) 10184.9 1701.51i 0.768556 0.128397i
\(561\) −12236.1 + 5383.53i −0.920871 + 0.405156i
\(562\) −17063.5 15706.6i −1.28075 1.17890i
\(563\) −7722.59 −0.578097 −0.289048 0.957315i \(-0.593339\pi\)
−0.289048 + 0.957315i \(0.593339\pi\)
\(564\) −3795.25 + 2059.82i −0.283349 + 0.153784i
\(565\) −8579.27 −0.638818
\(566\) −15848.9 14588.6i −1.17699 1.08340i
\(567\) 23434.8 2047.13i 1.73575 0.151625i
\(568\) 8734.92 + 6796.70i 0.645262 + 0.502083i
\(569\) 10040.4i 0.739744i −0.929083 0.369872i \(-0.879402\pi\)
0.929083 0.369872i \(-0.120598\pi\)
\(570\) −4799.87 1641.57i −0.352709 0.120627i
\(571\) 18510.6i 1.35664i 0.734764 + 0.678322i \(0.237293\pi\)
−0.734764 + 0.678322i \(0.762707\pi\)
\(572\) 964.926 + 11631.7i 0.0705342 + 0.850258i
\(573\) 4539.16 + 10317.0i 0.330936 + 0.752176i
\(574\) −6478.99 + 7038.72i −0.471129 + 0.511830i
\(575\) 1821.76 0.132126
\(576\) −12174.3 6548.97i −0.880665 0.473739i
\(577\) 21556.9 1.55533 0.777664 0.628680i \(-0.216404\pi\)
0.777664 + 0.628680i \(0.216404\pi\)
\(578\) 2610.63 2836.16i 0.187868 0.204098i
\(579\) −9060.21 20592.7i −0.650310 1.47807i
\(580\) −727.268 8766.89i −0.0520658 0.627630i
\(581\) 12660.4i 0.904028i
\(582\) 14458.7 + 4944.92i 1.02978 + 0.352188i
\(583\) 17679.3i 1.25592i
\(584\) −5231.83 4070.92i −0.370710 0.288452i
\(585\) −4471.29 4097.73i −0.316009 0.289608i
\(586\) 19342.1 + 17804.0i 1.36350 + 1.25508i
\(587\) 7143.54 0.502292 0.251146 0.967949i \(-0.419193\pi\)
0.251146 + 0.967949i \(0.419193\pi\)
\(588\) 25511.9 13846.2i 1.78928 0.971104i
\(589\) −1965.53 −0.137501
\(590\) −4485.16 4128.50i −0.312968 0.288081i
\(591\) 10037.8 4416.32i 0.698643 0.307383i
\(592\) 9647.17 1611.68i 0.669757 0.111891i
\(593\) 8287.65i 0.573918i 0.957943 + 0.286959i \(0.0926443\pi\)
−0.957943 + 0.286959i \(0.907356\pi\)
\(594\) 11312.6 6171.76i 0.781417 0.426314i
\(595\) 12781.8i 0.880676i
\(596\) −869.162 + 72.1024i −0.0597353 + 0.00495542i
\(597\) 6968.25 3065.82i 0.477707 0.210177i
\(598\) 6271.03 6812.79i 0.428832 0.465879i
\(599\) −26207.7 −1.78767 −0.893837 0.448393i \(-0.851997\pi\)
−0.893837 + 0.448393i \(0.851997\pi\)
\(600\) −718.001 + 2850.35i −0.0488538 + 0.193942i
\(601\) 13315.0 0.903711 0.451855 0.892091i \(-0.350762\pi\)
0.451855 + 0.892091i \(0.350762\pi\)
\(602\) 5971.43 6487.31i 0.404282 0.439208i
\(603\) 5776.95 + 5294.30i 0.390142 + 0.357547i
\(604\) −25403.8 + 2107.40i −1.71137 + 0.141969i
\(605\) 1381.87i 0.0928613i
\(606\) −1466.36 + 4287.58i −0.0982953 + 0.287411i
\(607\) 4763.81i 0.318546i −0.987235 0.159273i \(-0.949085\pi\)
0.987235 0.159273i \(-0.0509149\pi\)
\(608\) 10463.0 + 6832.32i 0.697910 + 0.455735i
\(609\) −14850.5 33753.3i −0.988131 2.24590i
\(610\) −1908.05 1756.32i −0.126647 0.116576i
\(611\) 4666.86 0.309003
\(612\) −10478.8 + 13527.8i −0.692122 + 0.893514i
\(613\) 20511.4 1.35146 0.675731 0.737148i \(-0.263828\pi\)
0.675731 + 0.737148i \(0.263828\pi\)
\(614\) 4126.63 + 3798.47i 0.271233 + 0.249664i
\(615\) −1096.68 2492.63i −0.0719065 0.163435i
\(616\) 14561.6 18714.2i 0.952442 1.22405i
\(617\) 8679.39i 0.566320i 0.959073 + 0.283160i \(0.0913827\pi\)
−0.959073 + 0.283160i \(0.908617\pi\)
\(618\) 1257.24 3676.11i 0.0818343 0.239280i
\(619\) 20896.1i 1.35684i −0.734674 0.678420i \(-0.762665\pi\)
0.734674 0.678420i \(-0.237335\pi\)
\(620\) 94.1559 + 1135.01i 0.00609902 + 0.0735209i
\(621\) −9680.56 3287.19i −0.625551 0.212416i
\(622\) −624.752 + 678.725i −0.0402737 + 0.0437530i
\(623\) 10853.4 0.697968
\(624\) 8187.79 + 12496.8i 0.525279 + 0.801719i
\(625\) 625.000 0.0400000
\(626\) −2030.29 + 2205.68i −0.129627 + 0.140826i
\(627\) −10662.5 + 4691.18i −0.679136 + 0.298800i
\(628\) 680.803 + 8206.77i 0.0432596 + 0.521474i
\(629\) 12106.9i 0.767465i
\(630\) 1045.45 + 12277.1i 0.0661140 + 0.776397i
\(631\) 5444.29i 0.343477i 0.985143 + 0.171738i \(0.0549384\pi\)
−0.985143 + 0.171738i \(0.945062\pi\)
\(632\) −9120.89 + 11721.9i −0.574066 + 0.737773i
\(633\) 11419.4 5024.20i 0.717030 0.315472i
\(634\) −2097.66 1930.86i −0.131402 0.120953i
\(635\) 6981.85 0.436325
\(636\) −10794.8 19889.6i −0.673023 1.24006i
\(637\) −31371.0 −1.95128
\(638\) −14862.9 13680.9i −0.922298 0.848956i
\(639\) −8922.80 + 9736.22i −0.552395 + 0.602753i
\(640\) 3444.15 6369.19i 0.212722 0.393382i
\(641\) 2664.42i 0.164178i −0.996625 0.0820890i \(-0.973841\pi\)
0.996625 0.0820890i \(-0.0261592\pi\)
\(642\) 21718.2 + 7427.66i 1.33512 + 0.456615i
\(643\) 17860.6i 1.09542i 0.836668 + 0.547710i \(0.184500\pi\)
−0.836668 + 0.547710i \(0.815500\pi\)
\(644\) −18747.2 + 1555.20i −1.14712 + 0.0951607i
\(645\) 1010.77 + 2297.36i 0.0617039 + 0.140246i
\(646\) 10475.7 11380.7i 0.638017 0.693136i
\(647\) −21691.5 −1.31805 −0.659026 0.752120i \(-0.729031\pi\)
−0.659026 + 0.752120i \(0.729031\pi\)
\(648\) 8958.51 13850.7i 0.543092 0.839673i
\(649\) −13998.4 −0.846665
\(650\) 2151.43 2337.29i 0.129825 0.141040i
\(651\) 1922.62 + 4369.88i 0.115750 + 0.263086i
\(652\) −1790.29 + 148.516i −0.107535 + 0.00892074i
\(653\) 5849.05i 0.350522i 0.984522 + 0.175261i \(0.0560769\pi\)
−0.984522 + 0.175261i \(0.943923\pi\)
\(654\) 30292.4 + 10360.1i 1.81120 + 0.619437i
\(655\) 7552.69i 0.450547i
\(656\) 1105.38 + 6616.56i 0.0657892 + 0.393801i
\(657\) 5344.36 5831.56i 0.317356 0.346287i
\(658\) −6975.79 6421.07i −0.413290 0.380425i
\(659\) 8922.46 0.527420 0.263710 0.964602i \(-0.415054\pi\)
0.263710 + 0.964602i \(0.415054\pi\)
\(660\) 3219.72 + 5932.39i 0.189890 + 0.349876i
\(661\) −2789.76 −0.164159 −0.0820796 0.996626i \(-0.526156\pi\)
−0.0820796 + 0.996626i \(0.526156\pi\)
\(662\) −6833.43 6290.02i −0.401191 0.369288i
\(663\) 16927.3 7447.54i 0.991559 0.436257i
\(664\) −7006.45 5451.76i −0.409492 0.318629i
\(665\) 11138.0i 0.649493i
\(666\) 990.254 + 11628.9i 0.0576150 + 0.676591i
\(667\) 16026.0i 0.930331i
\(668\) 634.418 + 7647.62i 0.0367460 + 0.442957i
\(669\) 5836.82 2568.03i 0.337316 0.148409i
\(670\) −2779.66 + 3019.80i −0.160280 + 0.174127i
\(671\) −5955.11 −0.342615
\(672\) 4955.46 29945.1i 0.284466 1.71898i
\(673\) −18308.8 −1.04867 −0.524334 0.851513i \(-0.675686\pi\)
−0.524334 + 0.851513i \(0.675686\pi\)
\(674\) 20700.3 22488.6i 1.18300 1.28520i
\(675\) −3321.15 1127.75i −0.189380 0.0643068i
\(676\) 118.175 + 1424.55i 0.00672368 + 0.0810510i
\(677\) 10293.0i 0.584330i −0.956368 0.292165i \(-0.905624\pi\)
0.956368 0.292165i \(-0.0943756\pi\)
\(678\) −8160.49 + 23860.9i −0.462245 + 1.35158i
\(679\) 33551.2i 1.89628i
\(680\) −7073.65 5504.05i −0.398915 0.310398i
\(681\) 12564.8 + 28558.2i 0.707025 + 1.60698i
\(682\) 1924.22 + 1771.21i 0.108039 + 0.0994472i
\(683\) −21101.1 −1.18215 −0.591077 0.806615i \(-0.701297\pi\)
−0.591077 + 0.806615i \(0.701297\pi\)
\(684\) −9131.15 + 11788.1i −0.510436 + 0.658960i
\(685\) −2708.94 −0.151100
\(686\) 23858.4 + 21961.1i 1.32787 + 1.22227i
\(687\) 7136.97 + 16221.5i 0.396350 + 0.900856i
\(688\) −1018.78 6098.23i −0.0564546 0.337926i
\(689\) 24457.5i 1.35233i
\(690\) 1732.84 5066.74i 0.0956058 0.279547i
\(691\) 17707.2i 0.974841i −0.873167 0.487420i \(-0.837938\pi\)
0.873167 0.487420i \(-0.162062\pi\)
\(692\) −14505.8 + 1203.35i −0.796863 + 0.0661048i
\(693\) 20859.4 + 19116.7i 1.14341 + 1.04788i
\(694\) −8155.64 + 8860.22i −0.446086 + 0.484624i
\(695\) −3569.00 −0.194791
\(696\) −25074.5 6316.26i −1.36558 0.343990i
\(697\) 8303.61 0.451251
\(698\) 3259.92 3541.55i 0.176776 0.192048i
\(699\) 30055.8 13223.7i 1.62634 0.715544i
\(700\) −6431.70 + 533.550i −0.347279 + 0.0288090i
\(701\) 390.697i 0.0210505i 0.999945 + 0.0105253i \(0.00335035\pi\)
−0.999945 + 0.0105253i \(0.996650\pi\)
\(702\) −15649.8 + 8537.98i −0.841400 + 0.459039i
\(703\) 10549.9i 0.566000i
\(704\) −4086.24 16117.3i −0.218759 0.862844i
\(705\) 2470.34 1086.88i 0.131970 0.0580627i
\(706\) −7926.53 7296.20i −0.422548 0.388946i
\(707\) −9949.25 −0.529250
\(708\) −15748.5 + 8547.29i −0.835969 + 0.453710i
\(709\) 3068.89 0.162559 0.0812797 0.996691i \(-0.474099\pi\)
0.0812797 + 0.996691i \(0.474099\pi\)
\(710\) −5089.45 4684.73i −0.269019 0.247626i
\(711\) −13065.6 11974.0i −0.689168 0.631591i
\(712\) 4673.67 6006.47i 0.246002 0.316154i
\(713\) 2074.81i 0.108979i
\(714\) −35549.1 12157.9i −1.86329 0.637251i
\(715\) 7294.81i 0.381553i
\(716\) −527.649 6360.57i −0.0275407 0.331991i
\(717\) 7457.53 + 16950.1i 0.388433 + 0.882861i
\(718\) 6106.50 6634.05i 0.317399 0.344819i
\(719\) 4167.04 0.216139 0.108070 0.994143i \(-0.465533\pi\)
0.108070 + 0.994143i \(0.465533\pi\)
\(720\) 7244.52 + 4708.14i 0.374982 + 0.243697i
\(721\) 8530.35 0.440620
\(722\) −4010.28 + 4356.74i −0.206714 + 0.224572i
\(723\) 5929.96 + 13478.1i 0.305031 + 0.693299i
\(724\) −1252.14 15094.0i −0.0642754 0.774811i
\(725\) 5498.13i 0.281649i
\(726\) −3843.30 1314.42i −0.196472 0.0671938i
\(727\) 36845.2i 1.87966i −0.341640 0.939831i \(-0.610982\pi\)
0.341640 0.939831i \(-0.389018\pi\)
\(728\) −20144.5 + 25889.1i −1.02555 + 1.31801i
\(729\) 15613.2 + 11985.4i 0.793232 + 0.608920i
\(730\) 3048.35 + 2805.94i 0.154554 + 0.142264i
\(731\) −7653.12 −0.387224
\(732\) −6699.64 + 3636.13i −0.338286 + 0.183600i
\(733\) 8332.32 0.419865 0.209933 0.977716i \(-0.432676\pi\)
0.209933 + 0.977716i \(0.432676\pi\)
\(734\) −22297.8 20524.7i −1.12129 1.03213i
\(735\) −16605.8 + 7306.07i −0.833353 + 0.366651i
\(736\) −7212.20 + 11044.7i −0.361203 + 0.553143i
\(737\) 9424.96i 0.471062i
\(738\) −7975.72 + 679.171i −0.397819 + 0.0338762i
\(739\) 29386.0i 1.46276i 0.681970 + 0.731381i \(0.261124\pi\)
−0.681970 + 0.731381i \(0.738876\pi\)
\(740\) −6092.12 + 505.379i −0.302636 + 0.0251056i
\(741\) 14750.4 6489.75i 0.731269 0.321737i
\(742\) 33650.6 36557.8i 1.66490 1.80873i
\(743\) −15195.8 −0.750311 −0.375155 0.926962i \(-0.622411\pi\)
−0.375155 + 0.926962i \(0.622411\pi\)
\(744\) 3246.27 + 817.735i 0.159965 + 0.0402952i
\(745\) 545.092 0.0268062
\(746\) 25831.3 28062.9i 1.26777 1.37729i
\(747\) 7157.15 7809.61i 0.350557 0.382515i
\(748\) −20511.0 + 1701.52i −1.00262 + 0.0831732i
\(749\) 50396.6i 2.45854i
\(750\) 594.492 1738.27i 0.0289437 0.0846301i
\(751\) 4230.63i 0.205563i 0.994704 + 0.102782i \(0.0327742\pi\)
−0.994704 + 0.102782i \(0.967226\pi\)
\(752\) −6557.42 + 1095.50i −0.317984 + 0.0531232i
\(753\) −8089.55 18386.6i −0.391500 0.889833i
\(754\) 20561.2 + 18926.1i 0.993096 + 0.914124i
\(755\) 15931.9 0.767976
\(756\) 35139.8 + 8770.16i 1.69050 + 0.421915i
\(757\) 15946.8 0.765649 0.382825 0.923821i \(-0.374951\pi\)
0.382825 + 0.923821i \(0.374951\pi\)
\(758\) 30300.8 + 27891.2i 1.45194 + 1.33648i
\(759\) −4952.01 11255.3i −0.236820 0.538264i
\(760\) −6163.94 4796.21i −0.294197 0.228917i
\(761\) 6461.80i 0.307806i −0.988086 0.153903i \(-0.950816\pi\)
0.988086 0.153903i \(-0.0491843\pi\)
\(762\) 6641.05 19418.1i 0.315722 0.923156i
\(763\) 70293.0i 3.33523i
\(764\) 1434.64 + 17294.0i 0.0679367 + 0.818946i
\(765\) 7225.79 7884.51i 0.341502 0.372634i
\(766\) −24458.9 + 26571.9i −1.15370 + 1.25337i
\(767\) 19365.3 0.911657
\(768\) −14438.2 15637.3i −0.678375 0.734715i
\(769\) −28578.2 −1.34013 −0.670064 0.742304i \(-0.733733\pi\)
−0.670064 + 0.742304i \(0.733733\pi\)
\(770\) −10036.8 + 10903.9i −0.469743 + 0.510325i
\(771\) 14080.7 6195.09i 0.657722 0.289378i
\(772\) −2863.56 34519.0i −0.133500 1.60928i
\(773\) 31061.7i 1.44530i −0.691216 0.722648i \(-0.742925\pi\)
0.691216 0.722648i \(-0.257075\pi\)
\(774\) 7350.91 625.966i 0.341374 0.0290696i
\(775\) 711.816i 0.0329925i
\(776\) 18567.8 + 14447.7i 0.858948 + 0.668353i
\(777\) −23455.2 + 10319.6i −1.08295 + 0.476466i
\(778\) 3359.92 + 3092.74i 0.154832 + 0.142519i
\(779\) 7235.73 0.332794
\(780\) −4454.14 8206.83i −0.204466 0.376733i
\(781\) −15884.4 −0.727771
\(782\) 12013.4 + 11058.1i 0.549360 + 0.505674i
\(783\) 9920.82 29216.2i 0.452799 1.33346i
\(784\) 44079.4 7364.00i 2.00799 0.335459i
\(785\) 5146.85i 0.234011i
\(786\) 21005.8 + 7184.03i 0.953246 + 0.326013i
\(787\) 14851.0i 0.672657i 0.941745 + 0.336328i \(0.109185\pi\)
−0.941745 + 0.336328i \(0.890815\pi\)
\(788\) 16826.0 1395.82i 0.760661 0.0631016i
\(789\) −13717.8 31178.9i −0.618969 1.40684i
\(790\) 6286.71 6829.83i 0.283128 0.307588i
\(791\) −55368.8 −2.48886
\(792\) 19561.9 3311.97i 0.877654 0.148593i
\(793\) 8238.26 0.368915
\(794\) 6448.89 7006.02i 0.288240 0.313141i
\(795\) 5695.96 + 12946.2i 0.254107 + 0.577554i
\(796\) 11680.7 968.983i 0.520113 0.0431466i
\(797\) 19580.3i 0.870226i −0.900376 0.435113i \(-0.856708\pi\)
0.900376 0.435113i \(-0.143292\pi\)
\(798\) −30977.3 10594.3i −1.37417 0.469969i
\(799\) 8229.38i 0.364374i
\(800\) −2474.32 + 3789.16i −0.109351 + 0.167459i
\(801\) 6695.00 + 6135.66i 0.295326 + 0.270653i
\(802\) −4337.76 3992.82i −0.190987 0.175800i
\(803\) 9514.06 0.418112
\(804\) 5754.79 + 10603.3i 0.252432 + 0.465111i
\(805\) 11757.3 0.514769
\(806\) −2661.96 2450.27i −0.116332 0.107081i
\(807\) −41384.9 + 18208.1i −1.80523 + 0.794246i
\(808\) −4284.31 + 5506.07i −0.186537 + 0.239731i
\(809\) 22199.3i 0.964754i 0.875964 + 0.482377i \(0.160226\pi\)
−0.875964 + 0.482377i \(0.839774\pi\)
\(810\) −6295.57 + 8164.19i −0.273091 + 0.354149i
\(811\) 16803.2i 0.727547i 0.931488 + 0.363773i \(0.118512\pi\)
−0.931488 + 0.363773i \(0.881488\pi\)
\(812\) −4693.64 56579.7i −0.202850 2.44527i
\(813\) −9637.51 + 4240.22i −0.415747 + 0.182917i
\(814\) −9506.90 + 10328.2i −0.409357 + 0.444722i
\(815\) 1122.77 0.0482565
\(816\) −22036.4 + 14438.1i −0.945378 + 0.619403i
\(817\) −6668.89 −0.285575
\(818\) −17255.5 + 18746.3i −0.737562 + 0.801280i
\(819\) −28856.8 26445.9i −1.23118 1.12832i
\(820\) −346.617 4178.31i −0.0147615 0.177943i
\(821\) 3573.41i 0.151904i −0.997111 0.0759519i \(-0.975800\pi\)
0.997111 0.0759519i \(-0.0241995\pi\)
\(822\) −2576.71 + 7534.19i −0.109335 + 0.319690i
\(823\) 9176.02i 0.388646i −0.980938 0.194323i \(-0.937749\pi\)
0.980938 0.194323i \(-0.0622510\pi\)
\(824\) 3673.31 4720.83i 0.155298 0.199585i
\(825\) −1698.91 3861.41i −0.0716951 0.162954i
\(826\) −28946.3 26644.5i −1.21933 1.12237i
\(827\) 14278.9 0.600394 0.300197 0.953877i \(-0.402948\pi\)
0.300197 + 0.953877i \(0.402948\pi\)
\(828\) −12443.5 9638.84i −0.522273 0.404557i
\(829\) 20720.7 0.868105 0.434052 0.900888i \(-0.357083\pi\)
0.434052 + 0.900888i \(0.357083\pi\)
\(830\) 4082.35 + 3757.71i 0.170723 + 0.157147i
\(831\) −12974.2 29488.7i −0.541599 1.23099i
\(832\) 5652.89 + 22296.5i 0.235551 + 0.929078i
\(833\) 55318.4i 2.30092i
\(834\) −3394.79 + 9926.21i −0.140949 + 0.412130i
\(835\) 4796.18i 0.198777i
\(836\) −17873.2 + 1482.69i −0.739422 + 0.0613397i
\(837\) −1284.40 + 3782.48i −0.0530411 + 0.156203i
\(838\) 16845.9 18301.2i 0.694428 0.754420i
\(839\) 26785.4 1.10219 0.551094 0.834443i \(-0.314211\pi\)
0.551094 + 0.834443i \(0.314211\pi\)
\(840\) −4633.83 + 18395.5i −0.190336 + 0.755603i
\(841\) −23978.1 −0.983150
\(842\) −9380.51 + 10190.9i −0.383935 + 0.417104i
\(843\) 38998.4 17158.1i 1.59333 0.701017i
\(844\) 19142.0 1587.95i 0.780680 0.0647622i
\(845\) 893.403i 0.0363716i
\(846\) −673.100 7904.42i −0.0273542 0.321229i
\(847\) 8918.31i 0.361791i
\(848\) −5741.12 34365.2i −0.232489 1.39163i
\(849\) 36222.4 15936.8i 1.46425 0.644229i
\(850\) 4121.50 + 3793.75i 0.166313 + 0.153088i
\(851\) 11136.5 0.448595
\(852\) −17870.3 + 9698.87i −0.718577 + 0.389998i
\(853\) −20065.4 −0.805425 −0.402713 0.915326i \(-0.631933\pi\)
−0.402713 + 0.915326i \(0.631933\pi\)
\(854\) −12314.1 11334.9i −0.493421 0.454183i
\(855\) 6296.52 6870.53i 0.251856 0.274815i
\(856\) 27890.3 + 21701.6i 1.11363 + 0.866525i
\(857\) 1780.43i 0.0709664i −0.999370 0.0354832i \(-0.988703\pi\)
0.999370 0.0354832i \(-0.0112970\pi\)
\(858\) −20288.6 6938.74i −0.807272 0.276089i
\(859\) 27394.4i 1.08811i −0.839050 0.544054i \(-0.816889\pi\)
0.839050 0.544054i \(-0.183111\pi\)
\(860\) 319.464 + 3850.99i 0.0126670 + 0.152695i
\(861\) −7077.76 16086.9i −0.280150 0.636748i
\(862\) −22790.9 + 24759.8i −0.900534 + 0.978332i
\(863\) 39367.0 1.55280 0.776400 0.630240i \(-0.217043\pi\)
0.776400 + 0.630240i \(0.217043\pi\)
\(864\) 19985.3 15670.3i 0.786938 0.617032i
\(865\) 9097.29 0.357592
\(866\) −2240.00 + 2433.52i −0.0878965 + 0.0954900i
\(867\) 2851.90 + 6482.02i 0.111713 + 0.253911i
\(868\) 607.662 + 7325.09i 0.0237620 + 0.286440i
\(869\) 21316.2i 0.832110i
\(870\) 15291.6 + 5229.75i 0.595899 + 0.203799i
\(871\) 13038.4i 0.507222i
\(872\) 38901.3 + 30269.3i 1.51074 + 1.17552i
\(873\) −18967.1 + 20696.2i −0.735327 + 0.802361i
\(874\) 10468.4 + 9635.98i 0.405149 + 0.372931i
\(875\) 4033.62 0.155841
\(876\) 10703.5 5809.19i 0.412830 0.224058i
\(877\) −32232.4 −1.24106 −0.620530 0.784183i \(-0.713082\pi\)
−0.620530 + 0.784183i \(0.713082\pi\)
\(878\) −14123.1 13000.0i −0.542862 0.499693i
\(879\) −44206.0 + 19449.4i −1.69628 + 0.746315i
\(880\) 1712.38 + 10249.9i 0.0655958 + 0.392643i
\(881\) 35922.0i 1.37372i 0.726791 + 0.686858i \(0.241011\pi\)
−0.726791 + 0.686858i \(0.758989\pi\)
\(882\) 4524.62 + 53134.0i 0.172735 + 2.02848i
\(883\) 33930.5i 1.29315i −0.762851 0.646575i \(-0.776201\pi\)
0.762851 0.646575i \(-0.223799\pi\)
\(884\) 28374.8 2353.87i 1.07958 0.0895578i
\(885\) 10250.8 4510.04i 0.389352 0.171303i
\(886\) 17400.5 18903.8i 0.659800 0.716801i
\(887\) −6145.77 −0.232643 −0.116322 0.993212i \(-0.537110\pi\)
−0.116322 + 0.993212i \(0.537110\pi\)
\(888\) −4389.17 + 17424.3i −0.165868 + 0.658470i
\(889\) 45059.4 1.69994
\(890\) −3221.40 + 3499.70i −0.121328 + 0.131809i
\(891\) 2060.20 + 23584.5i 0.0774628 + 0.886767i
\(892\) 9784.08 811.651i 0.367259 0.0304665i
\(893\) 7171.04i 0.268723i
\(894\) 518.485 1516.03i 0.0193968 0.0567153i
\(895\) 3989.01i 0.148981i
\(896\) 22227.8 41105.4i 0.828771 1.53263i
\(897\) 6850.58 + 15570.5i 0.254999 + 0.579582i
\(898\) −6690.44 6158.41i −0.248622 0.228852i
\(899\) 6261.85 0.232307
\(900\) −4269.05 3306.84i −0.158113 0.122476i
\(901\) −43127.4 −1.59465
\(902\) −7083.66 6520.36i −0.261486 0.240692i
\(903\) 6523.30 + 14826.7i 0.240401 + 0.546402i
\(904\) −23842.7 + 30642.0i −0.877209 + 1.12736i
\(905\) 9466.13i 0.347696i
\(906\) 15154.2 44310.3i 0.555702 1.62485i
\(907\) 16054.2i 0.587731i −0.955847 0.293866i \(-0.905058\pi\)
0.955847 0.293866i \(-0.0949418\pi\)
\(908\) 3971.22 + 47871.3i 0.145143 + 1.74963i
\(909\) −6137.24 5624.50i −0.223938 0.205229i
\(910\) 13884.9 15084.4i 0.505801 0.549498i
\(911\) 5066.28 0.184252 0.0921259 0.995747i \(-0.470634\pi\)
0.0921259 + 0.995747i \(0.470634\pi\)
\(912\) −19202.4 + 12581.3i −0.697210 + 0.456806i
\(913\) 12741.2 0.461853
\(914\) −23636.6 + 25678.6i −0.855393 + 0.929291i
\(915\) 4360.82 1918.63i 0.157556 0.0693202i
\(916\) 2255.71 + 27191.5i 0.0813654 + 0.980823i
\(917\) 48743.5i 1.75535i
\(918\) −15055.6 27596.2i −0.541294 0.992170i
\(919\) 3167.51i 0.113696i 0.998383 + 0.0568480i \(0.0181050\pi\)
−0.998383 + 0.0568480i \(0.981895\pi\)
\(920\) 5062.88 6506.66i 0.181433 0.233172i
\(921\) −9431.36 + 4149.52i −0.337431 + 0.148460i
\(922\) 25052.8 + 23060.6i 0.894871 + 0.823709i
\(923\) 21974.4 0.783637
\(924\) 20779.4 + 38286.4i 0.739818 + 1.36313i
\(925\) 3820.65 0.135808
\(926\) −5165.06 4754.33i −0.183299 0.168722i
\(927\) 5261.99 + 4822.37i 0.186436 + 0.170860i
\(928\) −33333.3 21766.6i −1.17911 0.769961i
\(929\) 11889.1i 0.419880i −0.977714 0.209940i \(-0.932673\pi\)
0.977714 0.209940i \(-0.0673269\pi\)
\(930\) −1979.72 677.070i −0.0698040 0.0238731i
\(931\) 48204.2i 1.69692i
\(932\) 50381.6 4179.47i 1.77071 0.146892i
\(933\) −682.490 1551.22i −0.0239482 0.0544315i
\(934\) 3058.49 3322.72i 0.107149 0.116405i
\(935\) 12863.4 0.449923
\(936\) −27061.8 + 4581.75i −0.945024 + 0.159999i
\(937\) −34124.2 −1.18974 −0.594871 0.803822i \(-0.702797\pi\)
−0.594871 + 0.803822i \(0.702797\pi\)
\(938\) −17939.4 + 19489.2i −0.624458 + 0.678405i
\(939\) −2217.92 5041.06i −0.0770810 0.175196i
\(940\) 4140.96 343.518i 0.143684 0.0119195i
\(941\) 35775.5i 1.23937i 0.784851 + 0.619685i \(0.212740\pi\)
−0.784851 + 0.619685i \(0.787260\pi\)
\(942\) −14314.6 4895.62i −0.495111 0.169329i
\(943\) 7638.03i 0.263763i
\(944\) −27210.2 + 4545.80i −0.938154 + 0.156730i
\(945\) −21434.0 7278.26i −0.737830 0.250542i
\(946\) 6528.74 + 6009.56i 0.224384 + 0.206541i
\(947\) −1532.43 −0.0525841 −0.0262921 0.999654i \(-0.508370\pi\)
−0.0262921 + 0.999654i \(0.508370\pi\)
\(948\) −13015.5 23981.3i −0.445911 0.821598i
\(949\) −13161.7 −0.450207
\(950\) 3591.46 + 3305.86i 0.122655 + 0.112901i
\(951\) 4794.18 2109.30i 0.163472 0.0719230i
\(952\) −45651.8 35522.0i −1.55419 1.20932i
\(953\) 50714.5i 1.72382i −0.507060 0.861911i \(-0.669268\pi\)
0.507060 0.861911i \(-0.330732\pi\)
\(954\) 41424.4 3527.49i 1.40583 0.119713i
\(955\) 10845.9i 0.367502i
\(956\) 2357.02 + 28412.8i 0.0797401 + 0.961231i
\(957\) 33968.9 14945.3i 1.14740 0.504821i
\(958\) −26192.9 + 28455.7i −0.883355 + 0.959669i
\(959\) −17483.0 −0.588690
\(960\) 8184.98 + 10485.9i 0.275176 + 0.352531i
\(961\) 28980.3 0.972787
\(962\) 13151.8 14288.0i 0.440780 0.478860i
\(963\) −28490.1 + 31087.4i −0.953356 + 1.04027i
\(964\) 1874.22 + 22592.9i 0.0626189 + 0.754842i
\(965\) 21648.5i 0.722165i
\(966\) 11183.4 32699.7i 0.372483 1.08912i
\(967\) 45357.2i 1.50837i −0.656664 0.754183i \(-0.728033\pi\)
0.656664 0.754183i \(-0.271967\pi\)
\(968\) −4935.54 3840.37i −0.163878 0.127515i
\(969\) 11443.8 + 26010.3i 0.379388 + 0.862304i
\(970\) −10818.6 9958.30i −0.358108 0.329631i
\(971\) −33985.9 −1.12323 −0.561616 0.827398i \(-0.689820\pi\)
−0.561616 + 0.827398i \(0.689820\pi\)
\(972\) 16718.2 + 25275.1i 0.551684 + 0.834053i
\(973\) −23033.6 −0.758913
\(974\) −5644.82 5195.93i −0.185700 0.170933i
\(975\) 2350.26 + 5341.86i 0.0771985 + 0.175463i
\(976\) −11575.6 + 1933.84i −0.379637 + 0.0634230i
\(977\) 24747.5i 0.810382i −0.914232 0.405191i \(-0.867205\pi\)
0.914232 0.405191i \(-0.132795\pi\)
\(978\) 1067.97 3122.69i 0.0349181 0.102099i
\(979\) 10922.7i 0.356581i
\(980\) −27835.8 + 2309.15i −0.907329 + 0.0752686i
\(981\) −39738.0 + 43360.6i −1.29331 + 1.41121i
\(982\) −14935.9 + 16226.2i −0.485359 + 0.527290i
\(983\) −37535.3 −1.21789 −0.608947 0.793211i \(-0.708408\pi\)
−0.608947 + 0.793211i \(0.708408\pi\)
\(984\) −11950.5 3010.34i −0.387164 0.0975265i
\(985\) −10552.4 −0.341346
\(986\) −33373.7 + 36256.9i −1.07792 + 1.17105i
\(987\) 15943.1 7014.49i 0.514158 0.226214i
\(988\) 24725.7 2051.15i 0.796182 0.0660483i
\(989\) 7039.68i 0.226339i
\(990\) −12355.5 + 1052.13i −0.396649 + 0.0337766i
\(991\) 41257.7i 1.32250i 0.750167 + 0.661248i \(0.229973\pi\)
−0.750167 + 0.661248i \(0.770027\pi\)
\(992\) 4315.49 + 2818.02i 0.138122 + 0.0901937i
\(993\) 15617.7 6871.33i 0.499107 0.219592i
\(994\) −32846.2 30234.3i −1.04811 0.964761i
\(995\) −7325.48 −0.233400
\(996\) 14334.1 7779.65i 0.456019 0.247498i
\(997\) 27189.9 0.863704 0.431852 0.901945i \(-0.357860\pi\)
0.431852 + 0.901945i \(0.357860\pi\)
\(998\) 21726.6 + 19998.9i 0.689121 + 0.634321i
\(999\) −20302.4 6893.99i −0.642981 0.218334i
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 60.4.e.a.11.8 yes 24
3.2 odd 2 inner 60.4.e.a.11.17 yes 24
4.3 odd 2 inner 60.4.e.a.11.18 yes 24
8.3 odd 2 960.4.h.d.191.7 24
8.5 even 2 960.4.h.d.191.18 24
12.11 even 2 inner 60.4.e.a.11.7 24
24.5 odd 2 960.4.h.d.191.8 24
24.11 even 2 960.4.h.d.191.17 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.4.e.a.11.7 24 12.11 even 2 inner
60.4.e.a.11.8 yes 24 1.1 even 1 trivial
60.4.e.a.11.17 yes 24 3.2 odd 2 inner
60.4.e.a.11.18 yes 24 4.3 odd 2 inner
960.4.h.d.191.7 24 8.3 odd 2
960.4.h.d.191.8 24 24.5 odd 2
960.4.h.d.191.17 24 24.11 even 2
960.4.h.d.191.18 24 8.5 even 2