Properties

Label 201.4.f.a.38.20
Level $201$
Weight $4$
Character 201.38
Analytic conductor $11.859$
Analytic rank $0$
Dimension $132$
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] = [201,4,Mod(38,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.38");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.f (of order \(6\), degree \(2\), 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: \(11.8593839112\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(66\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 38.20
Character \(\chi\) \(=\) 201.38
Dual form 201.4.f.a.164.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38906 + 2.40592i) q^{2} +(-3.61547 + 3.73207i) q^{3} +(0.141034 + 0.244278i) q^{4} +10.9301 q^{5} +(-3.95695 - 13.8826i) q^{6} +(2.00045 - 1.15496i) q^{7} -23.0086 q^{8} +(-0.856687 - 26.9864i) q^{9} +O(q^{10})\) \(q+(-1.38906 + 2.40592i) q^{2} +(-3.61547 + 3.73207i) q^{3} +(0.141034 + 0.244278i) q^{4} +10.9301 q^{5} +(-3.95695 - 13.8826i) q^{6} +(2.00045 - 1.15496i) q^{7} -23.0086 q^{8} +(-0.856687 - 26.9864i) q^{9} +(-15.1826 + 26.2970i) q^{10} +(-18.3727 - 31.8225i) q^{11} +(-1.42157 - 0.356832i) q^{12} +(-16.5662 - 9.56448i) q^{13} +6.41723i q^{14} +(-39.5175 + 40.7919i) q^{15} +(30.8319 - 53.4025i) q^{16} +(-107.618 - 62.1332i) q^{17} +(66.1171 + 35.4246i) q^{18} +(-27.5352 + 47.6924i) q^{19} +(1.54152 + 2.66999i) q^{20} +(-2.92218 + 11.6415i) q^{21} +102.083 q^{22} +(-100.451 - 57.9956i) q^{23} +(83.1868 - 85.8695i) q^{24} -5.53261 q^{25} +(46.0227 - 26.5712i) q^{26} +(103.812 + 94.3714i) q^{27} +(0.564263 + 0.325777i) q^{28} +(152.435 - 88.0084i) q^{29} +(-43.2500 - 151.738i) q^{30} +(-7.32049 + 4.22648i) q^{31} +(-6.37946 - 11.0495i) q^{32} +(185.190 + 46.4851i) q^{33} +(298.975 - 172.613i) q^{34} +(21.8651 - 12.6238i) q^{35} +(6.47137 - 4.01527i) q^{36} +(172.841 - 299.369i) q^{37} +(-76.4961 - 132.495i) q^{38} +(95.5899 - 27.2459i) q^{39} -251.486 q^{40} +(200.399 + 347.102i) q^{41} +(-23.9495 - 23.2013i) q^{42} -97.5694i q^{43} +(5.18236 - 8.97611i) q^{44} +(-9.36369 - 294.964i) q^{45} +(279.066 - 161.119i) q^{46} +(-316.170 + 182.541i) q^{47} +(87.8297 + 308.142i) q^{48} +(-168.832 + 292.426i) q^{49} +(7.68512 - 13.3110i) q^{50} +(620.975 - 176.996i) q^{51} -5.39567i q^{52} -222.675 q^{53} +(-371.252 + 118.677i) q^{54} +(-200.816 - 347.824i) q^{55} +(-46.0274 + 26.5739i) q^{56} +(-78.4385 - 275.194i) q^{57} +488.995i q^{58} +826.051i q^{59} +(-15.5379 - 3.90022i) q^{60} +(-489.306 - 282.501i) q^{61} -23.4833i q^{62} +(-32.8820 - 52.9955i) q^{63} +528.757 q^{64} +(-181.070 - 104.541i) q^{65} +(-369.079 + 380.982i) q^{66} +(-308.545 - 453.391i) q^{67} -35.0516i q^{68} +(579.623 - 165.210i) q^{69} +70.1410i q^{70} +(-561.555 + 324.214i) q^{71} +(19.7111 + 620.918i) q^{72} +(33.9814 - 58.8576i) q^{73} +(480.171 + 831.681i) q^{74} +(20.0030 - 20.6481i) q^{75} -15.5336 q^{76} +(-73.5074 - 42.4395i) q^{77} +(-67.2283 + 267.828i) q^{78} +(432.403 - 249.648i) q^{79} +(336.997 - 583.695i) q^{80} +(-727.532 + 46.2378i) q^{81} -1113.47 q^{82} +(266.538 + 153.886i) q^{83} +(-3.25590 + 0.928028i) q^{84} +(-1176.28 - 679.123i) q^{85} +(234.744 + 135.530i) q^{86} +(-222.672 + 887.091i) q^{87} +(422.730 + 732.190i) q^{88} -1425.34i q^{89} +(722.668 + 387.195i) q^{90} -44.1864 q^{91} -32.7174i q^{92} +(10.6935 - 42.6013i) q^{93} -1014.24i q^{94} +(-300.963 + 521.284i) q^{95} +(64.3025 + 16.1408i) q^{96} +(-912.164 - 526.638i) q^{97} +(-469.035 - 812.393i) q^{98} +(-843.035 + 523.076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q - 258 q^{4} - 23 q^{6} - 66 q^{7} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 132 q - 258 q^{4} - 23 q^{6} - 66 q^{7} - 70 q^{9} - 18 q^{10} + 114 q^{12} - 180 q^{13} - 188 q^{15} - 738 q^{16} + 159 q^{18} - 208 q^{19} + 96 q^{21} - 324 q^{22} + 736 q^{24} + 2508 q^{25} + 1704 q^{28} - 843 q^{30} + 612 q^{31} + 146 q^{33} - 762 q^{34} + 221 q^{36} - 238 q^{37} - 394 q^{39} - 864 q^{40} - 3462 q^{46} + 951 q^{48} + 2316 q^{49} - 309 q^{51} - 376 q^{54} - 96 q^{55} - 1113 q^{57} + 122 q^{60} + 1728 q^{61} - 534 q^{63} + 900 q^{64} - 1214 q^{67} - 372 q^{69} + 578 q^{73} - 184 q^{76} - 4686 q^{78} + 4476 q^{79} + 666 q^{81} + 1368 q^{82} + 1161 q^{84} - 1908 q^{85} - 462 q^{87} + 2562 q^{88} - 1160 q^{90} - 3636 q^{91} - 1828 q^{93} - 3900 q^{96} + 1074 q^{97} + 906 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38906 + 2.40592i −0.491106 + 0.850621i −0.999948 0.0102393i \(-0.996741\pi\)
0.508841 + 0.860860i \(0.330074\pi\)
\(3\) −3.61547 + 3.73207i −0.695798 + 0.718237i
\(4\) 0.141034 + 0.244278i 0.0176293 + 0.0305348i
\(5\) 10.9301 0.977619 0.488810 0.872391i \(-0.337431\pi\)
0.488810 + 0.872391i \(0.337431\pi\)
\(6\) −3.95695 13.8826i −0.269237 0.944592i
\(7\) 2.00045 1.15496i 0.108014 0.0623620i −0.445020 0.895521i \(-0.646803\pi\)
0.553034 + 0.833159i \(0.313470\pi\)
\(8\) −23.0086 −1.01684
\(9\) −0.856687 26.9864i −0.0317292 0.999497i
\(10\) −15.1826 + 26.2970i −0.480115 + 0.831583i
\(11\) −18.3727 31.8225i −0.503599 0.872259i −0.999991 0.00416065i \(-0.998676\pi\)
0.496392 0.868098i \(-0.334658\pi\)
\(12\) −1.42157 0.356832i −0.0341976 0.00858405i
\(13\) −16.5662 9.56448i −0.353433 0.204055i 0.312763 0.949831i \(-0.398745\pi\)
−0.666196 + 0.745777i \(0.732079\pi\)
\(14\) 6.41723i 0.122505i
\(15\) −39.5175 + 40.7919i −0.680226 + 0.702162i
\(16\) 30.8319 53.4025i 0.481749 0.834414i
\(17\) −107.618 62.1332i −1.53536 0.886442i −0.999101 0.0423901i \(-0.986503\pi\)
−0.536261 0.844052i \(-0.680164\pi\)
\(18\) 66.1171 + 35.4246i 0.865775 + 0.463870i
\(19\) −27.5352 + 47.6924i −0.332474 + 0.575863i −0.982996 0.183625i \(-0.941217\pi\)
0.650522 + 0.759487i \(0.274550\pi\)
\(20\) 1.54152 + 2.66999i 0.0172347 + 0.0298514i
\(21\) −2.92218 + 11.6415i −0.0303654 + 0.120971i
\(22\) 102.083 0.989282
\(23\) −100.451 57.9956i −0.910676 0.525779i −0.0300276 0.999549i \(-0.509560\pi\)
−0.880649 + 0.473770i \(0.842893\pi\)
\(24\) 83.1868 85.8695i 0.707518 0.730335i
\(25\) −5.53261 −0.0442609
\(26\) 46.0227 26.5712i 0.347146 0.200425i
\(27\) 103.812 + 94.3714i 0.739953 + 0.672659i
\(28\) 0.564263 + 0.325777i 0.00380842 + 0.00219879i
\(29\) 152.435 88.0084i 0.976086 0.563543i 0.0749996 0.997184i \(-0.476104\pi\)
0.901086 + 0.433640i \(0.142771\pi\)
\(30\) −43.2500 151.738i −0.263211 0.923451i
\(31\) −7.32049 + 4.22648i −0.0424128 + 0.0244871i −0.521056 0.853522i \(-0.674462\pi\)
0.478644 + 0.878009i \(0.341129\pi\)
\(32\) −6.37946 11.0495i −0.0352419 0.0610407i
\(33\) 185.190 + 46.4851i 0.976892 + 0.245213i
\(34\) 298.975 172.613i 1.50805 0.870674i
\(35\) 21.8651 12.6238i 0.105597 0.0609662i
\(36\) 6.47137 4.01527i 0.0299600 0.0185892i
\(37\) 172.841 299.369i 0.767968 1.33016i −0.170695 0.985324i \(-0.554601\pi\)
0.938663 0.344836i \(-0.112065\pi\)
\(38\) −76.4961 132.495i −0.326561 0.565620i
\(39\) 95.5899 27.2459i 0.392478 0.111868i
\(40\) −251.486 −0.994086
\(41\) 200.399 + 347.102i 0.763344 + 1.32215i 0.941118 + 0.338080i \(0.109777\pi\)
−0.177773 + 0.984071i \(0.556889\pi\)
\(42\) −23.9495 23.2013i −0.0879879 0.0852391i
\(43\) 97.5694i 0.346028i −0.984919 0.173014i \(-0.944649\pi\)
0.984919 0.173014i \(-0.0553506\pi\)
\(44\) 5.18236 8.97611i 0.0177561 0.0307545i
\(45\) −9.36369 294.964i −0.0310190 0.977127i
\(46\) 279.066 161.119i 0.894478 0.516427i
\(47\) −316.170 + 182.541i −0.981238 + 0.566518i −0.902644 0.430389i \(-0.858376\pi\)
−0.0785941 + 0.996907i \(0.525043\pi\)
\(48\) 87.8297 + 308.142i 0.264107 + 0.926594i
\(49\) −168.832 + 292.426i −0.492222 + 0.852553i
\(50\) 7.68512 13.3110i 0.0217368 0.0376492i
\(51\) 620.975 176.996i 1.70498 0.485970i
\(52\) 5.39567i 0.0143893i
\(53\) −222.675 −0.577109 −0.288555 0.957463i \(-0.593175\pi\)
−0.288555 + 0.957463i \(0.593175\pi\)
\(54\) −371.252 + 118.677i −0.935573 + 0.299072i
\(55\) −200.816 347.824i −0.492328 0.852737i
\(56\) −46.0274 + 26.5739i −0.109833 + 0.0634124i
\(57\) −78.4385 275.194i −0.182271 0.639480i
\(58\) 488.995i 1.10704i
\(59\) 826.051i 1.82276i 0.411568 + 0.911379i \(0.364981\pi\)
−0.411568 + 0.911379i \(0.635019\pi\)
\(60\) −15.5379 3.90022i −0.0334322 0.00839194i
\(61\) −489.306 282.501i −1.02704 0.592959i −0.110901 0.993831i \(-0.535374\pi\)
−0.916134 + 0.400872i \(0.868707\pi\)
\(62\) 23.4833i 0.0481030i
\(63\) −32.8820 52.9955i −0.0657578 0.105981i
\(64\) 528.757 1.03273
\(65\) −181.070 104.541i −0.345523 0.199488i
\(66\) −369.079 + 380.982i −0.688341 + 0.710539i
\(67\) −308.545 453.391i −0.562608 0.826724i
\(68\) 35.0516i 0.0625092i
\(69\) 579.623 165.210i 1.01128 0.288245i
\(70\) 70.1410i 0.119764i
\(71\) −561.555 + 324.214i −0.938652 + 0.541931i −0.889537 0.456862i \(-0.848973\pi\)
−0.0491143 + 0.998793i \(0.515640\pi\)
\(72\) 19.7111 + 620.918i 0.0322636 + 1.01633i
\(73\) 33.9814 58.8576i 0.0544826 0.0943666i −0.837498 0.546441i \(-0.815982\pi\)
0.891980 + 0.452074i \(0.149316\pi\)
\(74\) 480.171 + 831.681i 0.754308 + 1.30650i
\(75\) 20.0030 20.6481i 0.0307966 0.0317898i
\(76\) −15.5336 −0.0234451
\(77\) −73.5074 42.4395i −0.108792 0.0628108i
\(78\) −67.2283 + 267.828i −0.0975911 + 0.388789i
\(79\) 432.403 249.648i 0.615813 0.355540i −0.159424 0.987210i \(-0.550964\pi\)
0.775237 + 0.631671i \(0.217630\pi\)
\(80\) 336.997 583.695i 0.470967 0.815739i
\(81\) −727.532 + 46.2378i −0.997987 + 0.0634264i
\(82\) −1113.47 −1.49953
\(83\) 266.538 + 153.886i 0.352486 + 0.203508i 0.665780 0.746148i \(-0.268099\pi\)
−0.313293 + 0.949656i \(0.601432\pi\)
\(84\) −3.25590 + 0.928028i −0.00422914 + 0.00120543i
\(85\) −1176.28 679.123i −1.50100 0.866603i
\(86\) 234.744 + 135.530i 0.294339 + 0.169936i
\(87\) −222.672 + 887.091i −0.274401 + 1.09317i
\(88\) 422.730 + 732.190i 0.512081 + 0.886951i
\(89\) 1425.34i 1.69759i −0.528720 0.848796i \(-0.677328\pi\)
0.528720 0.848796i \(-0.322672\pi\)
\(90\) 722.668 + 387.195i 0.846398 + 0.453488i
\(91\) −44.1864 −0.0509010
\(92\) 32.7174i 0.0370764i
\(93\) 10.6935 42.6013i 0.0119233 0.0475005i
\(94\) 1014.24i 1.11288i
\(95\) −300.963 + 521.284i −0.325033 + 0.562974i
\(96\) 64.3025 + 16.1408i 0.0683629 + 0.0171600i
\(97\) −912.164 526.638i −0.954806 0.551258i −0.0602357 0.998184i \(-0.519185\pi\)
−0.894571 + 0.446926i \(0.852519\pi\)
\(98\) −469.035 812.393i −0.483467 0.837389i
\(99\) −843.035 + 523.076i −0.855841 + 0.531021i
\(100\) −0.780286 1.35150i −0.000780286 0.00135150i
\(101\) 409.539 + 709.342i 0.403471 + 0.698833i 0.994142 0.108080i \(-0.0344701\pi\)
−0.590671 + 0.806913i \(0.701137\pi\)
\(102\) −436.732 + 1739.87i −0.423950 + 1.68895i
\(103\) 585.028 + 1013.30i 0.559656 + 0.969352i 0.997525 + 0.0703137i \(0.0224000\pi\)
−0.437869 + 0.899039i \(0.644267\pi\)
\(104\) 381.163 + 220.065i 0.359386 + 0.207492i
\(105\) −31.9398 + 127.243i −0.0296857 + 0.118264i
\(106\) 309.309 535.738i 0.283422 0.490901i
\(107\) 698.436i 0.631031i −0.948920 0.315515i \(-0.897823\pi\)
0.948920 0.315515i \(-0.102177\pi\)
\(108\) −8.41179 + 38.6687i −0.00749467 + 0.0344528i
\(109\) 1283.25i 1.12764i 0.825896 + 0.563822i \(0.190670\pi\)
−0.825896 + 0.563822i \(0.809330\pi\)
\(110\) 1115.78 0.967141
\(111\) 492.364 + 1727.41i 0.421019 + 1.47711i
\(112\) 142.439i 0.120171i
\(113\) −590.645 1023.03i −0.491710 0.851666i 0.508245 0.861213i \(-0.330294\pi\)
−0.999954 + 0.00954665i \(0.996961\pi\)
\(114\) 771.051 + 193.544i 0.633469 + 0.159009i
\(115\) −1097.94 633.899i −0.890294 0.514012i
\(116\) 42.9971 + 24.8244i 0.0344153 + 0.0198697i
\(117\) −243.919 + 455.255i −0.192738 + 0.359729i
\(118\) −1987.41 1147.43i −1.55048 0.895168i
\(119\) −287.045 −0.221121
\(120\) 909.242 938.564i 0.691683 0.713989i
\(121\) −9.61475 + 16.6532i −0.00722370 + 0.0125118i
\(122\) 1359.35 784.820i 1.00877 0.582412i
\(123\) −2019.95 507.034i −1.48075 0.371688i
\(124\) −2.06488 1.19216i −0.00149541 0.000863377i
\(125\) −1426.74 −1.02089
\(126\) 173.178 5.49756i 0.122444 0.00388699i
\(127\) 566.100 + 980.514i 0.395538 + 0.685091i 0.993170 0.116679i \(-0.0372250\pi\)
−0.597632 + 0.801771i \(0.703892\pi\)
\(128\) −683.439 + 1183.75i −0.471937 + 0.817420i
\(129\) 364.136 + 352.760i 0.248530 + 0.240766i
\(130\) 503.034 290.427i 0.339377 0.195939i
\(131\) 397.928i 0.265398i 0.991156 + 0.132699i \(0.0423644\pi\)
−0.991156 + 0.132699i \(0.957636\pi\)
\(132\) 14.7628 + 51.7938i 0.00973436 + 0.0341521i
\(133\) 127.208i 0.0829350i
\(134\) 1519.41 112.547i 0.979529 0.0725569i
\(135\) 1134.68 + 1031.49i 0.723392 + 0.657604i
\(136\) 2476.13 + 1429.59i 1.56122 + 0.901373i
\(137\) 883.595 0.551026 0.275513 0.961297i \(-0.411152\pi\)
0.275513 + 0.961297i \(0.411152\pi\)
\(138\) −407.649 + 1624.01i −0.251459 + 1.00178i
\(139\) 821.876i 0.501515i −0.968050 0.250758i \(-0.919320\pi\)
0.968050 0.250758i \(-0.0806798\pi\)
\(140\) 6.16746 + 3.56078i 0.00372318 + 0.00214958i
\(141\) 461.850 1839.94i 0.275849 1.09894i
\(142\) 1801.41i 1.06458i
\(143\) 702.903i 0.411047i
\(144\) −1467.55 786.294i −0.849279 0.455031i
\(145\) 1666.13 961.942i 0.954240 0.550931i
\(146\) 94.4044 + 163.513i 0.0535135 + 0.0926880i
\(147\) −480.945 1687.35i −0.269848 0.946737i
\(148\) 97.5056 0.0541548
\(149\) 122.637i 0.0674283i −0.999432 0.0337141i \(-0.989266\pi\)
0.999432 0.0337141i \(-0.0107336\pi\)
\(150\) 21.8923 + 76.8070i 0.0119166 + 0.0418084i
\(151\) −210.923 + 365.330i −0.113673 + 0.196888i −0.917249 0.398315i \(-0.869595\pi\)
0.803575 + 0.595203i \(0.202928\pi\)
\(152\) 633.546 1097.33i 0.338075 0.585562i
\(153\) −1584.56 + 2957.45i −0.837280 + 1.56272i
\(154\) 204.212 117.902i 0.106856 0.0616936i
\(155\) −80.0137 + 46.1960i −0.0414636 + 0.0239390i
\(156\) 20.1370 + 19.5079i 0.0103349 + 0.0100121i
\(157\) 1188.40 2058.37i 0.604106 1.04634i −0.388086 0.921623i \(-0.626864\pi\)
0.992192 0.124719i \(-0.0398029\pi\)
\(158\) 1387.10i 0.698431i
\(159\) 805.076 831.039i 0.401552 0.414501i
\(160\) −69.7282 120.773i −0.0344531 0.0596746i
\(161\) −267.930 −0.131154
\(162\) 899.340 1814.61i 0.436166 0.880057i
\(163\) −980.158 1697.68i −0.470993 0.815785i 0.528456 0.848961i \(-0.322771\pi\)
−0.999450 + 0.0331761i \(0.989438\pi\)
\(164\) −56.5262 + 97.9063i −0.0269144 + 0.0466171i
\(165\) 2024.15 + 508.088i 0.955028 + 0.239725i
\(166\) −740.474 + 427.513i −0.346216 + 0.199888i
\(167\) −1350.43 + 779.669i −0.625743 + 0.361273i −0.779102 0.626898i \(-0.784324\pi\)
0.153358 + 0.988171i \(0.450991\pi\)
\(168\) 67.2352 267.855i 0.0308768 0.123009i
\(169\) −915.541 1585.76i −0.416723 0.721786i
\(170\) 3267.83 1886.68i 1.47430 0.851188i
\(171\) 1310.64 + 702.219i 0.586122 + 0.314035i
\(172\) 23.8341 13.7606i 0.0105659 0.00610021i
\(173\) −3241.85 1871.68i −1.42470 0.822551i −0.428004 0.903777i \(-0.640783\pi\)
−0.996696 + 0.0812258i \(0.974117\pi\)
\(174\) −1824.97 1767.95i −0.795116 0.770276i
\(175\) −11.0677 + 6.38994i −0.00478080 + 0.00276019i
\(176\) −2265.87 −0.970433
\(177\) −3082.88 2986.57i −1.30917 1.26827i
\(178\) 3429.25 + 1979.88i 1.44401 + 0.833698i
\(179\) 1239.37 0.517514 0.258757 0.965942i \(-0.416687\pi\)
0.258757 + 0.965942i \(0.416687\pi\)
\(180\) 70.7328 43.8874i 0.0292895 0.0181732i
\(181\) −465.378 806.059i −0.191112 0.331016i 0.754507 0.656292i \(-0.227876\pi\)
−0.945619 + 0.325276i \(0.894543\pi\)
\(182\) 61.3774 106.309i 0.0249978 0.0432974i
\(183\) 2823.38 804.748i 1.14049 0.325075i
\(184\) 2311.24 + 1334.39i 0.926016 + 0.534635i
\(185\) 1889.17 3272.13i 0.750780 1.30039i
\(186\) 87.6414 + 84.9034i 0.0345494 + 0.0334700i
\(187\) 4566.23i 1.78564i
\(188\) −89.1815 51.4890i −0.0345970 0.0199746i
\(189\) 316.667 + 68.8860i 0.121874 + 0.0265118i
\(190\) −836.111 1448.19i −0.319252 0.552960i
\(191\) −579.893 + 1004.40i −0.219684 + 0.380503i −0.954711 0.297534i \(-0.903836\pi\)
0.735027 + 0.678037i \(0.237169\pi\)
\(192\) −1911.71 + 1973.36i −0.718571 + 0.741744i
\(193\) 1619.99 0.604193 0.302096 0.953277i \(-0.402314\pi\)
0.302096 + 0.953277i \(0.402314\pi\)
\(194\) 2534.10 1463.06i 0.937823 0.541452i
\(195\) 1044.81 297.801i 0.383694 0.109364i
\(196\) −95.2443 −0.0347100
\(197\) 721.356 + 1249.42i 0.260886 + 0.451867i 0.966477 0.256751i \(-0.0826521\pi\)
−0.705592 + 0.708618i \(0.749319\pi\)
\(198\) −87.4534 2754.86i −0.0313891 0.988784i
\(199\) −686.796 + 1189.57i −0.244652 + 0.423749i −0.962034 0.272931i \(-0.912007\pi\)
0.717382 + 0.696680i \(0.245340\pi\)
\(200\) 127.297 0.0450064
\(201\) 2807.62 + 487.713i 0.985245 + 0.171147i
\(202\) −2275.49 −0.792589
\(203\) 203.292 352.113i 0.0702873 0.121741i
\(204\) 130.815 + 126.728i 0.0448965 + 0.0434938i
\(205\) 2190.39 + 3793.86i 0.746260 + 1.29256i
\(206\) −3250.55 −1.09940
\(207\) −1479.04 + 2760.50i −0.496619 + 0.926900i
\(208\) −1021.53 + 589.783i −0.340532 + 0.196606i
\(209\) 2023.59 0.669735
\(210\) −261.771 253.593i −0.0860187 0.0833313i
\(211\) 253.871 439.718i 0.0828305 0.143467i −0.821634 0.570015i \(-0.806937\pi\)
0.904465 + 0.426549i \(0.140271\pi\)
\(212\) −31.4048 54.3947i −0.0101740 0.0176219i
\(213\) 820.298 3267.95i 0.263878 1.05125i
\(214\) 1680.38 + 970.168i 0.536768 + 0.309903i
\(215\) 1066.44i 0.338283i
\(216\) −2388.57 2171.35i −0.752416 0.683989i
\(217\) −9.76284 + 16.9097i −0.00305412 + 0.00528990i
\(218\) −3087.40 1782.51i −0.959197 0.553793i
\(219\) 96.8016 + 339.619i 0.0298687 + 0.104792i
\(220\) 56.6438 98.1099i 0.0173587 0.0300662i
\(221\) 1188.54 + 2058.62i 0.361765 + 0.626596i
\(222\) −4839.94 1214.89i −1.46322 0.367288i
\(223\) 282.812 0.0849259 0.0424630 0.999098i \(-0.486480\pi\)
0.0424630 + 0.999098i \(0.486480\pi\)
\(224\) −25.5236 14.7360i −0.00761324 0.00439550i
\(225\) 4.73972 + 149.305i 0.00140436 + 0.0442386i
\(226\) 3281.76 0.965927
\(227\) −5078.39 + 2932.01i −1.48486 + 0.857287i −0.999852 0.0172198i \(-0.994518\pi\)
−0.485013 + 0.874507i \(0.661185\pi\)
\(228\) 56.1614 57.9725i 0.0163131 0.0168391i
\(229\) −905.273 522.660i −0.261232 0.150822i 0.363664 0.931530i \(-0.381525\pi\)
−0.624896 + 0.780708i \(0.714859\pi\)
\(230\) 3050.22 1761.04i 0.874458 0.504869i
\(231\) 424.152 120.896i 0.120810 0.0344345i
\(232\) −3507.31 + 2024.95i −0.992527 + 0.573036i
\(233\) −937.878 1624.45i −0.263701 0.456744i 0.703521 0.710674i \(-0.251610\pi\)
−0.967223 + 0.253930i \(0.918277\pi\)
\(234\) −756.489 1219.23i −0.211339 0.340612i
\(235\) −3455.78 + 1995.19i −0.959277 + 0.553839i
\(236\) −201.786 + 116.501i −0.0556575 + 0.0321339i
\(237\) −631.639 + 2516.36i −0.173120 + 0.689683i
\(238\) 398.723 690.608i 0.108594 0.188090i
\(239\) −724.999 1255.73i −0.196219 0.339861i 0.751081 0.660210i \(-0.229533\pi\)
−0.947299 + 0.320350i \(0.896200\pi\)
\(240\) 959.989 + 3368.03i 0.258196 + 0.905856i
\(241\) −6146.20 −1.64279 −0.821394 0.570361i \(-0.806803\pi\)
−0.821394 + 0.570361i \(0.806803\pi\)
\(242\) −26.7109 46.2646i −0.00709521 0.0122893i
\(243\) 2457.81 2882.37i 0.648842 0.760923i
\(244\) 159.369i 0.0418137i
\(245\) −1845.35 + 3196.25i −0.481206 + 0.833473i
\(246\) 4025.71 4155.53i 1.04337 1.07702i
\(247\) 912.306 526.720i 0.235015 0.135686i
\(248\) 168.434 97.2453i 0.0431272 0.0248995i
\(249\) −1537.97 + 438.368i −0.391426 + 0.111568i
\(250\) 1981.82 3432.61i 0.501365 0.868390i
\(251\) 504.097 873.122i 0.126766 0.219566i −0.795656 0.605749i \(-0.792874\pi\)
0.922422 + 0.386184i \(0.126207\pi\)
\(252\) 8.30816 15.5065i 0.00207684 0.00387626i
\(253\) 4262.15i 1.05913i
\(254\) −3145.39 −0.777004
\(255\) 6787.33 1934.59i 1.66682 0.475093i
\(256\) 216.356 + 374.739i 0.0528212 + 0.0914891i
\(257\) 1395.74 805.832i 0.338771 0.195589i −0.320958 0.947094i \(-0.604005\pi\)
0.659728 + 0.751504i \(0.270671\pi\)
\(258\) −1354.52 + 386.078i −0.326855 + 0.0931634i
\(259\) 798.496i 0.191568i
\(260\) 58.9753i 0.0140673i
\(261\) −2505.62 4038.28i −0.594230 0.957714i
\(262\) −957.383 552.745i −0.225753 0.130339i
\(263\) 6665.32i 1.56274i 0.624067 + 0.781371i \(0.285479\pi\)
−0.624067 + 0.781371i \(0.714521\pi\)
\(264\) −4260.95 1069.56i −0.993347 0.249343i
\(265\) −2433.86 −0.564193
\(266\) −306.053 176.700i −0.0705463 0.0407299i
\(267\) 5319.47 + 5153.28i 1.21927 + 1.18118i
\(268\) 67.2381 139.314i 0.0153255 0.0317536i
\(269\) 2929.49i 0.663994i −0.943280 0.331997i \(-0.892278\pi\)
0.943280 0.331997i \(-0.107722\pi\)
\(270\) −4057.82 + 1297.15i −0.914634 + 0.292379i
\(271\) 2223.95i 0.498506i −0.968438 0.249253i \(-0.919815\pi\)
0.968438 0.249253i \(-0.0801850\pi\)
\(272\) −6636.14 + 3831.37i −1.47932 + 0.854085i
\(273\) 159.755 164.907i 0.0354168 0.0365590i
\(274\) −1227.37 + 2125.86i −0.270613 + 0.468715i
\(275\) 101.649 + 176.062i 0.0222897 + 0.0386069i
\(276\) 122.104 + 118.289i 0.0266296 + 0.0257977i
\(277\) 4490.48 0.974031 0.487016 0.873393i \(-0.338085\pi\)
0.487016 + 0.873393i \(0.338085\pi\)
\(278\) 1977.37 + 1141.63i 0.426600 + 0.246297i
\(279\) 120.329 + 193.933i 0.0258205 + 0.0416145i
\(280\) −503.085 + 290.456i −0.107375 + 0.0619932i
\(281\) 1642.13 2844.26i 0.348617 0.603823i −0.637387 0.770544i \(-0.719985\pi\)
0.986004 + 0.166721i \(0.0533180\pi\)
\(282\) 3785.22 + 3666.96i 0.799313 + 0.774341i
\(283\) 3678.48 0.772660 0.386330 0.922361i \(-0.373743\pi\)
0.386330 + 0.922361i \(0.373743\pi\)
\(284\) −158.397 91.4503i −0.0330955 0.0191077i
\(285\) −857.342 3007.90i −0.178191 0.625168i
\(286\) −1691.13 976.373i −0.349645 0.201868i
\(287\) 801.777 + 462.906i 0.164904 + 0.0952073i
\(288\) −292.722 + 181.625i −0.0598918 + 0.0371609i
\(289\) 5264.57 + 9118.50i 1.07156 + 1.85599i
\(290\) 5344.78i 1.08226i
\(291\) 5263.36 1500.21i 1.06029 0.302213i
\(292\) 19.1702 0.00384195
\(293\) 9043.84i 1.80323i 0.432539 + 0.901615i \(0.357618\pi\)
−0.432539 + 0.901615i \(0.642382\pi\)
\(294\) 4727.69 + 1186.71i 0.937839 + 0.235410i
\(295\) 9028.84i 1.78196i
\(296\) −3976.81 + 6888.04i −0.780904 + 1.35256i
\(297\) 1095.82 5037.44i 0.214093 0.984181i
\(298\) 295.055 + 170.350i 0.0573559 + 0.0331144i
\(299\) 1109.40 + 1921.53i 0.214575 + 0.371655i
\(300\) 7.86498 + 1.97421i 0.00151362 + 0.000379938i
\(301\) −112.689 195.183i −0.0215790 0.0373759i
\(302\) −585.969 1014.93i −0.111651 0.193386i
\(303\) −4127.99 1036.18i −0.782663 0.196459i
\(304\) 1697.93 + 2940.90i 0.320339 + 0.554843i
\(305\) −5348.17 3087.76i −1.00405 0.579688i
\(306\) −4914.34 7920.38i −0.918085 1.47967i
\(307\) −4603.49 + 7973.47i −0.855814 + 1.48231i 0.0200738 + 0.999799i \(0.493610\pi\)
−0.875888 + 0.482515i \(0.839723\pi\)
\(308\) 23.9417i 0.00442923i
\(309\) −5896.86 1480.19i −1.08563 0.272508i
\(310\) 256.675i 0.0470264i
\(311\) 4580.44 0.835154 0.417577 0.908641i \(-0.362879\pi\)
0.417577 + 0.908641i \(0.362879\pi\)
\(312\) −2199.38 + 626.890i −0.399088 + 0.113752i
\(313\) 9152.26i 1.65277i −0.563107 0.826384i \(-0.690394\pi\)
0.563107 0.826384i \(-0.309606\pi\)
\(314\) 3301.51 + 5718.39i 0.593360 + 1.02773i
\(315\) −359.404 579.247i −0.0642860 0.103609i
\(316\) 121.967 + 70.4178i 0.0217126 + 0.0125358i
\(317\) 5243.50 + 3027.34i 0.929036 + 0.536379i 0.886507 0.462716i \(-0.153125\pi\)
0.0425295 + 0.999095i \(0.486458\pi\)
\(318\) 881.115 + 3091.31i 0.155379 + 0.545132i
\(319\) −5601.30 3233.91i −0.983111 0.567600i
\(320\) 5779.37 1.00961
\(321\) 2606.61 + 2525.18i 0.453230 + 0.439070i
\(322\) 372.171 644.619i 0.0644108 0.111563i
\(323\) 5926.57 3421.70i 1.02094 0.589439i
\(324\) −113.902 171.199i −0.0195305 0.0293551i
\(325\) 91.6541 + 52.9165i 0.0156432 + 0.00903163i
\(326\) 5445.99 0.925231
\(327\) −4789.18 4639.56i −0.809916 0.784613i
\(328\) −4610.90 7986.31i −0.776202 1.34442i
\(329\) −421.655 + 730.328i −0.0706583 + 0.122384i
\(330\) −4034.08 + 4164.17i −0.672935 + 0.694637i
\(331\) 2773.13 1601.07i 0.460499 0.265869i −0.251755 0.967791i \(-0.581008\pi\)
0.712254 + 0.701922i \(0.247674\pi\)
\(332\) 86.8126i 0.0143508i
\(333\) −8226.95 4407.88i −1.35386 0.725376i
\(334\) 4332.02i 0.709694i
\(335\) −3372.43 4955.61i −0.550016 0.808221i
\(336\) 531.591 + 514.983i 0.0863115 + 0.0836150i
\(337\) −951.133 549.137i −0.153743 0.0887638i 0.421155 0.906989i \(-0.361625\pi\)
−0.574898 + 0.818225i \(0.694958\pi\)
\(338\) 5086.96 0.818622
\(339\) 5953.47 + 1494.40i 0.953829 + 0.239424i
\(340\) 383.118i 0.0611102i
\(341\) 268.995 + 155.304i 0.0427181 + 0.0246633i
\(342\) −3510.03 + 2177.86i −0.554973 + 0.344343i
\(343\) 1572.28i 0.247508i
\(344\) 2244.93i 0.351856i
\(345\) 6335.34 1805.76i 0.988648 0.281794i
\(346\) 9006.23 5199.75i 1.39936 0.807920i
\(347\) −4072.89 7054.44i −0.630098 1.09136i −0.987531 0.157423i \(-0.949681\pi\)
0.357433 0.933939i \(-0.383652\pi\)
\(348\) −248.101 + 70.7162i −0.0382173 + 0.0108931i
\(349\) 1767.30 0.271064 0.135532 0.990773i \(-0.456726\pi\)
0.135532 + 0.990773i \(0.456726\pi\)
\(350\) 35.5040i 0.00542220i
\(351\) −817.161 2556.29i −0.124264 0.388731i
\(352\) −234.416 + 406.021i −0.0354955 + 0.0614801i
\(353\) −302.770 + 524.412i −0.0456510 + 0.0790698i −0.887948 0.459944i \(-0.847870\pi\)
0.842297 + 0.539014i \(0.181203\pi\)
\(354\) 11467.7 3268.65i 1.72176 0.490753i
\(355\) −6137.86 + 3543.69i −0.917644 + 0.529802i
\(356\) 348.179 201.021i 0.0518356 0.0299273i
\(357\) 1037.81 1071.27i 0.153856 0.158817i
\(358\) −1721.56 + 2981.83i −0.254154 + 0.440208i
\(359\) 4675.54i 0.687370i −0.939085 0.343685i \(-0.888325\pi\)
0.939085 0.343685i \(-0.111675\pi\)
\(360\) 215.445 + 6786.71i 0.0315415 + 0.993586i
\(361\) 1913.12 + 3313.62i 0.278921 + 0.483106i
\(362\) 2585.75 0.375425
\(363\) −27.3891 96.0922i −0.00396021 0.0138940i
\(364\) −6.23178 10.7938i −0.000897346 0.00155425i
\(365\) 371.421 643.320i 0.0532632 0.0922546i
\(366\) −1985.69 + 7910.68i −0.283589 + 1.12978i
\(367\) −10843.5 + 6260.52i −1.54231 + 0.890453i −0.543618 + 0.839333i \(0.682946\pi\)
−0.998692 + 0.0511208i \(0.983721\pi\)
\(368\) −6194.22 + 3576.24i −0.877435 + 0.506587i
\(369\) 9195.35 5705.42i 1.29727 0.804911i
\(370\) 5248.33 + 9090.37i 0.737426 + 1.27726i
\(371\) −445.450 + 257.181i −0.0623359 + 0.0359897i
\(372\) 11.9147 3.39605i 0.00166062 0.000473325i
\(373\) −1482.55 + 855.951i −0.205800 + 0.118819i −0.599358 0.800481i \(-0.704577\pi\)
0.393558 + 0.919300i \(0.371244\pi\)
\(374\) −10986.0 6342.76i −1.51891 0.876941i
\(375\) 5158.33 5324.68i 0.710333 0.733241i
\(376\) 7274.62 4200.00i 0.997766 0.576060i
\(377\) −3367.02 −0.459974
\(378\) −605.603 + 666.188i −0.0824044 + 0.0906482i
\(379\) −2697.83 1557.59i −0.365641 0.211103i 0.305911 0.952060i \(-0.401039\pi\)
−0.671553 + 0.740957i \(0.734372\pi\)
\(380\) −169.784 −0.0229204
\(381\) −5706.07 1432.30i −0.767272 0.192596i
\(382\) −1611.01 2790.35i −0.215776 0.373735i
\(383\) 7286.93 12621.3i 0.972180 1.68387i 0.283237 0.959050i \(-0.408592\pi\)
0.688943 0.724815i \(-0.258075\pi\)
\(384\) −1946.88 6830.46i −0.258728 0.907722i
\(385\) −803.445 463.869i −0.106357 0.0614051i
\(386\) −2250.26 + 3897.56i −0.296723 + 0.513939i
\(387\) −2633.05 + 83.5865i −0.345854 + 0.0109792i
\(388\) 297.096i 0.0388730i
\(389\) −3226.65 1862.91i −0.420559 0.242810i 0.274757 0.961514i \(-0.411403\pi\)
−0.695317 + 0.718704i \(0.744736\pi\)
\(390\) −734.813 + 2927.39i −0.0954070 + 0.380087i
\(391\) 7206.91 + 12482.7i 0.932145 + 1.61452i
\(392\) 3884.58 6728.29i 0.500513 0.866914i
\(393\) −1485.10 1438.70i −0.190619 0.184663i
\(394\) −4008.02 −0.512490
\(395\) 4726.22 2728.68i 0.602030 0.347582i
\(396\) −246.673 132.164i −0.0313024 0.0167714i
\(397\) −7680.12 −0.970917 −0.485458 0.874260i \(-0.661347\pi\)
−0.485458 + 0.874260i \(0.661347\pi\)
\(398\) −1908.00 3304.75i −0.240300 0.416212i
\(399\) −474.750 459.918i −0.0595670 0.0577061i
\(400\) −170.581 + 295.455i −0.0213226 + 0.0369319i
\(401\) −6014.43 −0.748993 −0.374496 0.927228i \(-0.622184\pi\)
−0.374496 + 0.927228i \(0.622184\pi\)
\(402\) −5073.35 + 6077.45i −0.629442 + 0.754019i
\(403\) 161.696 0.0199868
\(404\) −115.518 + 200.083i −0.0142258 + 0.0246398i
\(405\) −7952.01 + 505.385i −0.975651 + 0.0620068i
\(406\) 564.770 + 978.210i 0.0690371 + 0.119576i
\(407\) −12702.2 −1.54699
\(408\) −14287.7 + 4072.43i −1.73370 + 0.494155i
\(409\) 7455.67 4304.54i 0.901368 0.520405i 0.0237240 0.999719i \(-0.492448\pi\)
0.877644 + 0.479314i \(0.159114\pi\)
\(410\) −12170.3 −1.46597
\(411\) −3194.62 + 3297.64i −0.383403 + 0.395768i
\(412\) −165.018 + 285.819i −0.0197326 + 0.0341779i
\(413\) 954.056 + 1652.47i 0.113671 + 0.196884i
\(414\) −4587.08 7392.95i −0.544548 0.877641i
\(415\) 2913.29 + 1681.99i 0.344597 + 0.198953i
\(416\) 244.065i 0.0287651i
\(417\) 3067.30 + 2971.47i 0.360207 + 0.348954i
\(418\) −2810.88 + 4868.59i −0.328911 + 0.569691i
\(419\) 569.415 + 328.752i 0.0663907 + 0.0383307i 0.532828 0.846224i \(-0.321129\pi\)
−0.466437 + 0.884554i \(0.654463\pi\)
\(420\) −35.5874 + 10.1435i −0.00413449 + 0.00117845i
\(421\) 6462.55 11193.5i 0.748137 1.29581i −0.200578 0.979678i \(-0.564282\pi\)
0.948715 0.316133i \(-0.102385\pi\)
\(422\) 705.284 + 1221.59i 0.0813571 + 0.140915i
\(423\) 5196.98 + 8375.92i 0.597366 + 0.962768i
\(424\) 5123.43 0.586830
\(425\) 595.408 + 343.759i 0.0679565 + 0.0392347i
\(426\) 6722.98 + 6512.94i 0.764623 + 0.740735i
\(427\) −1305.11 −0.147912
\(428\) 170.613 98.5032i 0.0192684 0.0111246i
\(429\) −2623.28 2541.33i −0.295229 0.286006i
\(430\) 2565.78 + 1481.35i 0.287751 + 0.166133i
\(431\) 12741.0 7356.04i 1.42393 0.822106i 0.427298 0.904111i \(-0.359465\pi\)
0.996632 + 0.0820043i \(0.0261321\pi\)
\(432\) 8240.41 2634.19i 0.917748 0.293374i
\(433\) 12252.8 7074.15i 1.35989 0.785132i 0.370280 0.928920i \(-0.379262\pi\)
0.989608 + 0.143789i \(0.0459285\pi\)
\(434\) −27.1223 46.9772i −0.00299980 0.00519580i
\(435\) −2433.83 + 9696.00i −0.268260 + 1.06871i
\(436\) −313.470 + 180.982i −0.0344323 + 0.0198795i
\(437\) 5531.90 3193.85i 0.605553 0.349616i
\(438\) −951.560 238.854i −0.103807 0.0260568i
\(439\) −2915.82 + 5050.35i −0.317003 + 0.549066i −0.979861 0.199679i \(-0.936010\pi\)
0.662858 + 0.748745i \(0.269343\pi\)
\(440\) 4620.49 + 8002.92i 0.500621 + 0.867100i
\(441\) 8036.16 + 4305.66i 0.867742 + 0.464923i
\(442\) −6603.82 −0.710660
\(443\) −6824.66 11820.7i −0.731940 1.26776i −0.956053 0.293194i \(-0.905282\pi\)
0.224113 0.974563i \(-0.428052\pi\)
\(444\) −352.529 + 363.898i −0.0376808 + 0.0388960i
\(445\) 15579.1i 1.65960i
\(446\) −392.842 + 680.423i −0.0417077 + 0.0722398i
\(447\) 457.690 + 443.391i 0.0484295 + 0.0469165i
\(448\) 1057.75 610.693i 0.111549 0.0644030i
\(449\) 7412.97 4279.88i 0.779153 0.449844i −0.0569769 0.998375i \(-0.518146\pi\)
0.836130 + 0.548531i \(0.184813\pi\)
\(450\) −365.800 195.990i −0.0383200 0.0205313i
\(451\) 7363.77 12754.4i 0.768839 1.33167i
\(452\) 166.602 288.563i 0.0173369 0.0300285i
\(453\) −600.849 2108.02i −0.0623186 0.218639i
\(454\) 16290.9i 1.68408i
\(455\) −482.962 −0.0497618
\(456\) 1804.76 + 6331.82i 0.185341 + 0.650251i
\(457\) 8285.86 + 14351.5i 0.848132 + 1.46901i 0.882873 + 0.469611i \(0.155606\pi\)
−0.0347414 + 0.999396i \(0.511061\pi\)
\(458\) 2514.95 1452.01i 0.256585 0.148140i
\(459\) −5308.48 16606.3i −0.539822 1.68870i
\(460\) 357.605i 0.0362466i
\(461\) 13991.0i 1.41351i 0.707460 + 0.706753i \(0.249841\pi\)
−0.707460 + 0.706753i \(0.750159\pi\)
\(462\) −298.306 + 1188.41i −0.0300399 + 0.119675i
\(463\) −3101.22 1790.49i −0.311287 0.179721i 0.336215 0.941785i \(-0.390853\pi\)
−0.647502 + 0.762064i \(0.724186\pi\)
\(464\) 10853.9i 1.08595i
\(465\) 116.881 465.637i 0.0116564 0.0464374i
\(466\) 5211.07 0.518022
\(467\) 15926.4 + 9195.13i 1.57813 + 0.911134i 0.995120 + 0.0986699i \(0.0314588\pi\)
0.583011 + 0.812464i \(0.301875\pi\)
\(468\) −145.610 + 4.62240i −0.0143821 + 0.000456561i
\(469\) −1140.88 550.628i −0.112326 0.0542125i
\(470\) 11085.8i 1.08797i
\(471\) 3385.35 + 11877.2i 0.331186 + 1.16193i
\(472\) 19006.2i 1.85346i
\(473\) −3104.90 + 1792.62i −0.301826 + 0.174259i
\(474\) −5176.77 5015.04i −0.501639 0.485967i
\(475\) 152.342 263.864i 0.0147156 0.0254882i
\(476\) −40.4832 70.1189i −0.00389820 0.00675188i
\(477\) 190.763 + 6009.20i 0.0183112 + 0.576818i
\(478\) 4028.26 0.385457
\(479\) 12307.3 + 7105.65i 1.17398 + 0.677798i 0.954614 0.297844i \(-0.0962676\pi\)
0.219367 + 0.975643i \(0.429601\pi\)
\(480\) 702.833 + 176.421i 0.0668329 + 0.0167760i
\(481\) −5726.61 + 3306.26i −0.542850 + 0.313415i
\(482\) 8537.44 14787.3i 0.806783 1.39739i
\(483\) 968.695 999.935i 0.0912571 0.0942000i
\(484\) −5.42403 −0.000509394
\(485\) −9970.06 5756.21i −0.933437 0.538920i
\(486\) 3520.71 + 9917.08i 0.328607 + 0.925613i
\(487\) 1756.22 + 1013.95i 0.163413 + 0.0943463i 0.579476 0.814989i \(-0.303257\pi\)
−0.416063 + 0.909336i \(0.636591\pi\)
\(488\) 11258.2 + 6499.93i 1.04433 + 0.602947i
\(489\) 9879.61 + 2479.91i 0.913643 + 0.229337i
\(490\) −5126.61 8879.55i −0.472646 0.818647i
\(491\) 854.119i 0.0785048i −0.999229 0.0392524i \(-0.987502\pi\)
0.999229 0.0392524i \(-0.0124976\pi\)
\(492\) −161.024 564.938i −0.0147551 0.0517670i
\(493\) −21873.0 −1.99819
\(494\) 2926.58i 0.266545i
\(495\) −9214.47 + 5717.28i −0.836686 + 0.519137i
\(496\) 521.243i 0.0471865i
\(497\) −748.907 + 1297.15i −0.0675917 + 0.117072i
\(498\) 1081.66 4309.16i 0.0973298 0.387747i
\(499\) −6829.44 3942.98i −0.612681 0.353731i 0.161333 0.986900i \(-0.448421\pi\)
−0.774014 + 0.633169i \(0.781754\pi\)
\(500\) −201.218 348.520i −0.0179975 0.0311726i
\(501\) 1972.65 7858.76i 0.175911 0.700805i
\(502\) 1400.44 + 2425.63i 0.124511 + 0.215660i
\(503\) 4763.75 + 8251.06i 0.422277 + 0.731405i 0.996162 0.0875312i \(-0.0278977\pi\)
−0.573885 + 0.818936i \(0.694564\pi\)
\(504\) 756.566 + 1219.35i 0.0668654 + 0.107766i
\(505\) 4476.30 + 7753.19i 0.394441 + 0.683192i
\(506\) −10254.4 5920.38i −0.900916 0.520144i
\(507\) 9228.30 + 2316.43i 0.808369 + 0.202911i
\(508\) −159.679 + 276.572i −0.0139461 + 0.0241553i
\(509\) 10901.0i 0.949273i −0.880182 0.474636i \(-0.842580\pi\)
0.880182 0.474636i \(-0.157420\pi\)
\(510\) −4773.53 + 19017.0i −0.414461 + 1.65115i
\(511\) 156.989i 0.0135906i
\(512\) −12137.1 −1.04764
\(513\) −7359.30 + 2352.53i −0.633375 + 0.202469i
\(514\) 4477.39i 0.384221i
\(515\) 6394.43 + 11075.5i 0.547130 + 0.947658i
\(516\) −34.8159 + 138.702i −0.00297032 + 0.0118333i
\(517\) 11617.8 + 6707.55i 0.988300 + 0.570596i
\(518\) 1921.12 + 1109.16i 0.162952 + 0.0940802i
\(519\) 18706.1 5331.78i 1.58209 0.450943i
\(520\) 4166.16 + 2405.33i 0.351343 + 0.202848i
\(521\) −7177.17 −0.603527 −0.301763 0.953383i \(-0.597575\pi\)
−0.301763 + 0.953383i \(0.597575\pi\)
\(522\) 13196.2 418.916i 1.10648 0.0351254i
\(523\) 1116.42 1933.69i 0.0933414 0.161672i −0.815574 0.578653i \(-0.803579\pi\)
0.908915 + 0.416981i \(0.136912\pi\)
\(524\) −97.2051 + 56.1214i −0.00810386 + 0.00467877i
\(525\) 16.1673 64.4081i 0.00134400 0.00535429i
\(526\) −16036.2 9258.52i −1.32930 0.767472i
\(527\) 1050.42 0.0868254
\(528\) 8192.19 8456.38i 0.675226 0.697001i
\(529\) 643.482 + 1114.54i 0.0528875 + 0.0916038i
\(530\) 3380.78 5855.68i 0.277079 0.479914i
\(531\) 22292.2 707.668i 1.82184 0.0578346i
\(532\) −31.0742 + 17.9407i −0.00253240 + 0.00146208i
\(533\) 7666.86i 0.623056i
\(534\) −19787.4 + 5640.00i −1.60353 + 0.457054i
\(535\) 7633.98i 0.616908i
\(536\) 7099.17 + 10431.9i 0.572084 + 0.840649i
\(537\) −4480.92 + 4625.42i −0.360086 + 0.371698i
\(538\) 7048.12 + 4069.24i 0.564807 + 0.326091i
\(539\) 12407.6 0.991530
\(540\) −91.9418 + 422.653i −0.00732693 + 0.0336817i
\(541\) 11178.6i 0.888365i −0.895936 0.444183i \(-0.853494\pi\)
0.895936 0.444183i \(-0.146506\pi\)
\(542\) 5350.63 + 3089.19i 0.424040 + 0.244819i
\(543\) 4690.83 + 1177.46i 0.370723 + 0.0930565i
\(544\) 1585.51i 0.124960i
\(545\) 14026.1i 1.10241i
\(546\) 174.843 + 613.422i 0.0137044 + 0.0480806i
\(547\) −13770.5 + 7950.41i −1.07639 + 0.621453i −0.929920 0.367762i \(-0.880124\pi\)
−0.146468 + 0.989215i \(0.546791\pi\)
\(548\) 124.617 + 215.843i 0.00971418 + 0.0168255i
\(549\) −7204.50 + 13446.6i −0.560074 + 1.04533i
\(550\) −564.786 −0.0437865
\(551\) 9693.33i 0.749455i
\(552\) −13336.3 + 3801.24i −1.02832 + 0.293100i
\(553\) 576.667 998.817i 0.0443443 0.0768066i
\(554\) −6237.54 + 10803.7i −0.478353 + 0.828532i
\(555\) 5381.59 + 18880.8i 0.411596 + 1.44405i
\(556\) 200.766 115.913i 0.0153137 0.00884134i
\(557\) −21407.7 + 12359.8i −1.62850 + 0.940214i −0.643958 + 0.765061i \(0.722709\pi\)
−0.984541 + 0.175154i \(0.943958\pi\)
\(558\) −633.731 + 20.1179i −0.0480788 + 0.00152627i
\(559\) −933.201 + 1616.35i −0.0706086 + 0.122298i
\(560\) 1556.87i 0.117482i
\(561\) −17041.5 16509.1i −1.28252 1.24245i
\(562\) 4562.04 + 7901.68i 0.342416 + 0.593082i
\(563\) 5379.26 0.402680 0.201340 0.979521i \(-0.435470\pi\)
0.201340 + 0.979521i \(0.435470\pi\)
\(564\) 514.594 146.675i 0.0384190 0.0109506i
\(565\) −6455.81 11181.8i −0.480705 0.832605i
\(566\) −5109.62 + 8850.12i −0.379458 + 0.657241i
\(567\) −1401.99 + 932.767i −0.103841 + 0.0690873i
\(568\) 12920.6 7459.69i 0.954462 0.551059i
\(569\) 1654.32 955.122i 0.121885 0.0703704i −0.437818 0.899064i \(-0.644249\pi\)
0.559703 + 0.828693i \(0.310915\pi\)
\(570\) 8427.67 + 2115.46i 0.619292 + 0.155450i
\(571\) 3347.28 + 5797.66i 0.245323 + 0.424911i 0.962222 0.272265i \(-0.0877728\pi\)
−0.716900 + 0.697176i \(0.754439\pi\)
\(572\) −171.704 + 99.1332i −0.0125512 + 0.00724645i
\(573\) −1651.92 5795.60i −0.120436 0.422539i
\(574\) −2227.43 + 1286.01i −0.161971 + 0.0935138i
\(575\) 555.758 + 320.867i 0.0403073 + 0.0232714i
\(576\) −452.979 14269.2i −0.0327676 1.03221i
\(577\) −21932.4 + 12662.7i −1.58243 + 0.913614i −0.587921 + 0.808918i \(0.700054\pi\)
−0.994504 + 0.104696i \(0.966613\pi\)
\(578\) −29251.2 −2.10500
\(579\) −5857.02 + 6045.90i −0.420396 + 0.433954i
\(580\) 469.963 + 271.333i 0.0336451 + 0.0194250i
\(581\) 710.928 0.0507646
\(582\) −3701.72 + 14747.1i −0.263645 + 1.05032i
\(583\) 4091.15 + 7086.08i 0.290631 + 0.503388i
\(584\) −781.864 + 1354.23i −0.0554003 + 0.0959561i
\(585\) −2666.06 + 4975.99i −0.188424 + 0.351678i
\(586\) −21758.7 12562.4i −1.53387 0.885578i
\(587\) −8672.94 + 15022.0i −0.609831 + 1.05626i 0.381437 + 0.924395i \(0.375429\pi\)
−0.991268 + 0.131863i \(0.957904\pi\)
\(588\) 344.353 355.458i 0.0241512 0.0249300i
\(589\) 465.509i 0.0325653i
\(590\) −21722.7 12541.6i −1.51578 0.875133i
\(591\) −7270.98 1825.11i −0.506071 0.127031i
\(592\) −10658.0 18460.2i −0.739936 1.28161i
\(593\) 9864.02 17085.0i 0.683080 1.18313i −0.290956 0.956737i \(-0.593973\pi\)
0.974036 0.226393i \(-0.0726934\pi\)
\(594\) 10597.5 + 9633.74i 0.732022 + 0.665450i
\(595\) −3137.44 −0.216172
\(596\) 29.9575 17.2960i 0.00205891 0.00118871i
\(597\) −1956.45 6864.01i −0.134124 0.470562i
\(598\) −6164.06 −0.421517
\(599\) 2467.54 + 4273.91i 0.168316 + 0.291531i 0.937828 0.347101i \(-0.112834\pi\)
−0.769512 + 0.638632i \(0.779501\pi\)
\(600\) −460.240 + 475.082i −0.0313154 + 0.0323253i
\(601\) −2859.44 + 4952.69i −0.194075 + 0.336147i −0.946597 0.322420i \(-0.895504\pi\)
0.752522 + 0.658567i \(0.228837\pi\)
\(602\) 626.125 0.0423903
\(603\) −11971.1 + 8714.93i −0.808457 + 0.588556i
\(604\) −118.989 −0.00801591
\(605\) −105.090 + 182.022i −0.00706203 + 0.0122318i
\(606\) 8226.98 8492.29i 0.551482 0.569267i
\(607\) −8683.79 15040.8i −0.580666 1.00574i −0.995401 0.0958005i \(-0.969459\pi\)
0.414735 0.909942i \(-0.363874\pi\)
\(608\) 702.640 0.0468681
\(609\) 579.111 + 2031.76i 0.0385333 + 0.135190i
\(610\) 14857.8 8578.17i 0.986190 0.569377i
\(611\) 6983.64 0.462402
\(612\) −945.916 + 30.0282i −0.0624778 + 0.00198337i
\(613\) −10020.8 + 17356.5i −0.660255 + 1.14360i 0.320293 + 0.947318i \(0.396218\pi\)
−0.980549 + 0.196277i \(0.937115\pi\)
\(614\) −12789.0 22151.2i −0.840591 1.45595i
\(615\) −22078.2 5541.93i −1.44761 0.363370i
\(616\) 1691.30 + 976.472i 0.110624 + 0.0638688i
\(617\) 19429.1i 1.26772i 0.773446 + 0.633862i \(0.218531\pi\)
−0.773446 + 0.633862i \(0.781469\pi\)
\(618\) 11752.3 12131.3i 0.764962 0.789631i
\(619\) 12804.4 22177.9i 0.831427 1.44007i −0.0654796 0.997854i \(-0.520858\pi\)
0.896907 0.442220i \(-0.145809\pi\)
\(620\) −22.5693 13.0304i −0.00146194 0.000844054i
\(621\) −4954.97 15500.4i −0.320187 1.00163i
\(622\) −6362.50 + 11020.2i −0.410150 + 0.710400i
\(623\) −1646.21 2851.32i −0.105865 0.183364i
\(624\) 1492.22 5944.78i 0.0957317 0.381381i
\(625\) −14902.8 −0.953780
\(626\) 22019.6 + 12713.0i 1.40588 + 0.811685i
\(627\) −7316.24 + 7552.18i −0.466001 + 0.481029i
\(628\) 670.419 0.0425997
\(629\) −37201.5 + 21478.3i −2.35822 + 1.36152i
\(630\) 1892.85 60.0889i 0.119703 0.00380000i
\(631\) 8911.60 + 5145.11i 0.562227 + 0.324602i 0.754039 0.656830i \(-0.228103\pi\)
−0.191812 + 0.981432i \(0.561436\pi\)
\(632\) −9948.98 + 5744.04i −0.626185 + 0.361528i
\(633\) 723.193 + 2537.26i 0.0454097 + 0.159316i
\(634\) −14567.1 + 8410.30i −0.912511 + 0.526838i
\(635\) 6187.54 + 10717.1i 0.386685 + 0.669758i
\(636\) 316.548 + 79.4577i 0.0197357 + 0.00495394i
\(637\) 5593.80 3229.58i 0.347935 0.200880i
\(638\) 15561.1 8984.18i 0.965624 0.557503i
\(639\) 9230.44 + 14876.6i 0.571441 + 0.920984i
\(640\) −7470.06 + 12938.5i −0.461375 + 0.799125i
\(641\) −7620.57 13199.2i −0.469570 0.813319i 0.529825 0.848107i \(-0.322258\pi\)
−0.999395 + 0.0347880i \(0.988924\pi\)
\(642\) −9696.10 + 2763.68i −0.596066 + 0.169897i
\(643\) 1679.90 0.103031 0.0515153 0.998672i \(-0.483595\pi\)
0.0515153 + 0.998672i \(0.483595\pi\)
\(644\) −37.7873 65.4495i −0.00231216 0.00400477i
\(645\) 3980.05 + 3855.70i 0.242968 + 0.235377i
\(646\) 19011.8i 1.15791i
\(647\) −563.660 + 976.288i −0.0342500 + 0.0593228i −0.882642 0.470045i \(-0.844238\pi\)
0.848392 + 0.529368i \(0.177571\pi\)
\(648\) 16739.5 1063.87i 1.01480 0.0644947i
\(649\) 26287.0 15176.8i 1.58992 0.917939i
\(650\) −254.626 + 147.008i −0.0153650 + 0.00887098i
\(651\) −27.8110 97.5723i −0.00167435 0.00587429i
\(652\) 276.471 478.862i 0.0166065 0.0287633i
\(653\) 4727.40 8188.10i 0.283304 0.490697i −0.688892 0.724864i \(-0.741903\pi\)
0.972196 + 0.234167i \(0.0752361\pi\)
\(654\) 17814.9 5077.77i 1.06516 0.303603i
\(655\) 4349.40i 0.259458i
\(656\) 24714.8 1.47096
\(657\) −1617.47 866.615i −0.0960478 0.0514610i
\(658\) −1171.41 2028.94i −0.0694015 0.120207i
\(659\) −9779.57 + 5646.24i −0.578085 + 0.333758i −0.760372 0.649488i \(-0.774983\pi\)
0.182287 + 0.983245i \(0.441650\pi\)
\(660\) 161.359 + 566.113i 0.00951650 + 0.0333877i
\(661\) 3774.15i 0.222084i −0.993816 0.111042i \(-0.964581\pi\)
0.993816 0.111042i \(-0.0354188\pi\)
\(662\) 8895.90i 0.522280i
\(663\) −11980.1 3007.15i −0.701760 0.176151i
\(664\) −6132.66 3540.69i −0.358424 0.206936i
\(665\) 1390.40i 0.0810789i
\(666\) 22032.7 13670.6i 1.28191 0.795382i
\(667\) −20416.4 −1.18520
\(668\) −380.912 219.920i −0.0220628 0.0127380i
\(669\) −1022.50 + 1055.47i −0.0590913 + 0.0609970i
\(670\) 16607.3 1230.16i 0.957606 0.0709330i
\(671\) 20761.2i 1.19445i
\(672\) 147.276 41.9780i 0.00845429 0.00240972i
\(673\) 1669.77i 0.0956388i 0.998856 + 0.0478194i \(0.0152272\pi\)
−0.998856 + 0.0478194i \(0.984773\pi\)
\(674\) 2642.36 1525.57i 0.151009 0.0871849i
\(675\) −574.354 522.120i −0.0327509 0.0297725i
\(676\) 258.245 447.293i 0.0146930 0.0254491i
\(677\) 15434.6 + 26733.6i 0.876220 + 1.51766i 0.855457 + 0.517873i \(0.173276\pi\)
0.0207628 + 0.999784i \(0.493391\pi\)
\(678\) −11865.1 + 12247.8i −0.672090 + 0.693764i
\(679\) −2432.98 −0.137510
\(680\) 27064.4 + 15625.6i 1.52628 + 0.881200i
\(681\) 7418.32 29553.5i 0.417431 1.66298i
\(682\) −747.299 + 431.453i −0.0419583 + 0.0242246i
\(683\) 15597.2 27015.1i 0.873807 1.51348i 0.0157791 0.999876i \(-0.494977\pi\)
0.858028 0.513603i \(-0.171690\pi\)
\(684\) 13.3075 + 419.197i 0.000743894 + 0.0234333i
\(685\) 9657.79 0.538694
\(686\) −3782.78 2183.99i −0.210535 0.121553i
\(687\) 5223.60 1488.88i 0.290091 0.0826846i
\(688\) −5210.45 3008.26i −0.288730 0.166699i
\(689\) 3688.87 + 2129.77i 0.203969 + 0.117762i
\(690\) −4455.65 + 17750.6i −0.245831 + 0.979355i
\(691\) 8944.01 + 15491.5i 0.492397 + 0.852856i 0.999962 0.00875736i \(-0.00278759\pi\)
−0.507565 + 0.861614i \(0.669454\pi\)
\(692\) 1055.88i 0.0580038i
\(693\) −1082.32 + 2020.06i −0.0593273 + 0.110730i
\(694\) 22629.9 1.23778
\(695\) 8983.20i 0.490291i
\(696\) 5123.35 20410.7i 0.279023 1.11159i
\(697\) 49805.8i 2.70664i
\(698\) −2454.88 + 4251.98i −0.133121 + 0.230573i
\(699\) 9453.44 + 2372.94i 0.511534 + 0.128402i
\(700\) −3.12185 1.80240i −0.000168564 9.73204e-5i
\(701\) −10071.8 17444.8i −0.542662 0.939918i −0.998750 0.0499836i \(-0.984083\pi\)
0.456088 0.889935i \(-0.349250\pi\)
\(702\) 7285.30 + 1584.81i 0.391689 + 0.0852061i
\(703\) 9518.41 + 16486.4i 0.510660 + 0.884488i
\(704\) −9714.71 16826.4i −0.520081 0.900806i
\(705\) 5048.07 20110.8i 0.269676 1.07435i
\(706\) −841.129 1456.88i −0.0448390 0.0776634i
\(707\) 1638.52 + 946.001i 0.0871612 + 0.0503225i
\(708\) 294.762 1174.29i 0.0156467 0.0623340i
\(709\) −3883.43 + 6726.29i −0.205705 + 0.356292i −0.950357 0.311161i \(-0.899282\pi\)
0.744652 + 0.667453i \(0.232616\pi\)
\(710\) 19689.6i 1.04076i
\(711\) −7107.54 11455.1i −0.374900 0.604222i
\(712\) 32795.0i 1.72619i
\(713\) 980.470 0.0514991
\(714\) 1135.83 + 3984.94i 0.0595339 + 0.208869i
\(715\) 7682.81i 0.401847i
\(716\) 174.794 + 302.752i 0.00912339 + 0.0158022i
\(717\) 7307.70 + 1834.33i 0.380629 + 0.0955430i
\(718\) 11249.0 + 6494.60i 0.584691 + 0.337572i
\(719\) −12808.2 7394.83i −0.664348 0.383561i 0.129584 0.991568i \(-0.458636\pi\)
−0.793932 + 0.608007i \(0.791969\pi\)
\(720\) −16040.5 8594.28i −0.830272 0.444847i
\(721\) 2340.64 + 1351.37i 0.120901 + 0.0698025i
\(722\) −10629.8 −0.547920
\(723\) 22221.4 22938.1i 1.14305 1.17991i
\(724\) 131.268 227.363i 0.00673833 0.0116711i
\(725\) −843.364 + 486.916i −0.0432024 + 0.0249429i
\(726\) 269.235 + 67.5816i 0.0137634 + 0.00345481i
\(727\) −17337.6 10009.8i −0.884477 0.510653i −0.0123450 0.999924i \(-0.503930\pi\)
−0.872132 + 0.489271i \(0.837263\pi\)
\(728\) 1016.66 0.0517583
\(729\) 1871.06 + 19593.9i 0.0950597 + 0.995472i
\(730\) 1031.85 + 1787.22i 0.0523158 + 0.0906136i
\(731\) −6062.30 + 10500.2i −0.306734 + 0.531278i
\(732\) 594.776 + 576.194i 0.0300322 + 0.0290939i
\(733\) 27509.5 15882.6i 1.38620 0.800325i 0.393319 0.919402i \(-0.371327\pi\)
0.992885 + 0.119077i \(0.0379936\pi\)
\(734\) 34784.9i 1.74923i
\(735\) −5256.79 18442.9i −0.263809 0.925549i
\(736\) 1479.92i 0.0741178i
\(737\) −8759.22 + 18148.7i −0.437788 + 0.907077i
\(738\) 953.892 + 30048.4i 0.0475789 + 1.49878i
\(739\) −3012.45 1739.24i −0.149952 0.0865750i 0.423147 0.906061i \(-0.360926\pi\)
−0.573099 + 0.819486i \(0.694259\pi\)
\(740\) 1065.75 0.0529428
\(741\) −1332.66 + 5309.13i −0.0660683 + 0.263206i
\(742\) 1428.96i 0.0706990i
\(743\) −3572.25 2062.44i −0.176384 0.101835i 0.409209 0.912441i \(-0.365805\pi\)
−0.585593 + 0.810606i \(0.699138\pi\)
\(744\) −246.042 + 980.194i −0.0121241 + 0.0483006i
\(745\) 1340.44i 0.0659192i
\(746\) 4755.86i 0.233411i
\(747\) 3924.49 7324.74i 0.192222 0.358766i
\(748\) −1115.43 + 643.993i −0.0545242 + 0.0314796i
\(749\) −806.665 1397.18i −0.0393523 0.0681602i
\(750\) 5645.53 + 19806.8i 0.274861 + 0.964323i
\(751\) −35785.7 −1.73880 −0.869399 0.494110i \(-0.835494\pi\)
−0.869399 + 0.494110i \(0.835494\pi\)
\(752\) 22512.4i 1.09168i
\(753\) 1436.00 + 5038.07i 0.0694964 + 0.243822i
\(754\) 4676.99 8100.78i 0.225896 0.391264i
\(755\) −2305.42 + 3993.10i −0.111129 + 0.192482i
\(756\) 27.8334 + 87.0700i 0.00133901 + 0.00418877i
\(757\) 8648.00 4992.93i 0.415214 0.239724i −0.277813 0.960635i \(-0.589610\pi\)
0.693028 + 0.720911i \(0.256276\pi\)
\(758\) 7494.88 4327.17i 0.359137 0.207348i
\(759\) −15906.6 15409.7i −0.760705 0.736939i
\(760\) 6924.73 11994.0i 0.330508 0.572457i
\(761\) 26099.6i 1.24325i −0.783316 0.621623i \(-0.786473\pi\)
0.783316 0.621623i \(-0.213527\pi\)
\(762\) 11372.1 11738.8i 0.540638 0.558073i
\(763\) 1482.10 + 2567.08i 0.0703221 + 0.121801i
\(764\) −327.139 −0.0154914
\(765\) −17319.4 + 32325.2i −0.818541 + 1.52774i
\(766\) 20244.0 + 35063.6i 0.954887 + 1.65391i
\(767\) 7900.75 13684.5i 0.371942 0.644223i
\(768\) −2180.78 547.405i −0.102464 0.0257198i
\(769\) 20982.9 12114.5i 0.983955 0.568087i 0.0804932 0.996755i \(-0.474350\pi\)
0.903462 + 0.428668i \(0.141017\pi\)
\(770\) 2232.06 1288.68i 0.104465 0.0603128i
\(771\) −2038.85 + 8122.48i −0.0952365 + 0.379408i
\(772\) 228.473 + 395.727i 0.0106515 + 0.0184489i
\(773\) −2242.05 + 1294.45i −0.104322 + 0.0602303i −0.551253 0.834338i \(-0.685850\pi\)
0.446931 + 0.894568i \(0.352517\pi\)
\(774\) 3456.35 6451.01i 0.160512 0.299582i
\(775\) 40.5014 23.3835i 0.00187723 0.00108382i
\(776\) 20987.6 + 12117.2i 0.970889 + 0.560543i
\(777\) 2980.04 + 2886.94i 0.137591 + 0.133293i
\(778\) 8964.01 5175.37i 0.413079 0.238491i
\(779\) −22072.2 −1.01517
\(780\) 220.100 + 213.224i 0.0101036 + 0.00978799i
\(781\) 20634.6 + 11913.4i 0.945408 + 0.545831i
\(782\) −40043.2 −1.83113
\(783\) 24130.1 + 5249.15i 1.10133 + 0.239577i
\(784\) 10410.8 + 18032.1i 0.474255 + 0.821434i
\(785\) 12989.3 22498.2i 0.590585 1.02292i
\(786\) 5524.28 1574.58i 0.250693 0.0714549i
\(787\) −20050.3 11576.0i −0.908152 0.524322i −0.0283162 0.999599i \(-0.509015\pi\)
−0.879836 + 0.475277i \(0.842348\pi\)
\(788\) −203.471 + 352.423i −0.00919844 + 0.0159322i
\(789\) −24875.4 24098.3i −1.12242 1.08735i
\(790\) 15161.2i 0.682799i
\(791\) −2363.11 1364.34i −0.106223 0.0613279i
\(792\) 19397.0 12035.2i 0.870257 0.539966i
\(793\) 5403.94 + 9359.91i 0.241992 + 0.419143i
\(794\) 10668.1 18477.7i 0.476823 0.825882i
\(795\) 8799.57 9083.35i 0.392564 0.405224i
\(796\) −387.446 −0.0172521
\(797\) 19473.9 11243.3i 0.865496 0.499695i −0.000352611 1.00000i \(-0.500112\pi\)
0.865849 + 0.500305i \(0.166779\pi\)
\(798\) 1765.98 503.358i 0.0783397 0.0223292i
\(799\) 45367.4 2.00874
\(800\) 35.2951 + 61.1328i 0.00155984 + 0.00270172i
\(801\) −38464.8 + 1221.07i −1.69674 + 0.0538632i
\(802\) 8354.39 14470.2i 0.367835 0.637109i
\(803\) −2497.33 −0.109749
\(804\) 276.833 + 754.624i 0.0121432 + 0.0331014i
\(805\) −2928.51 −0.128219
\(806\) −224.606 + 389.029i −0.00981564 + 0.0170012i
\(807\) 10933.1 + 10591.5i 0.476905 + 0.462006i
\(808\) −9422.89 16320.9i −0.410267 0.710604i
\(809\) 10634.0 0.462141 0.231070 0.972937i \(-0.425777\pi\)
0.231070 + 0.972937i \(0.425777\pi\)
\(810\) 9829.89 19833.9i 0.426404 0.860361i
\(811\) −26581.6 + 15346.9i −1.15093 + 0.664492i −0.949114 0.314931i \(-0.898018\pi\)
−0.201819 + 0.979423i \(0.564685\pi\)
\(812\) 114.685 0.00495645
\(813\) 8299.92 + 8040.62i 0.358045 + 0.346860i
\(814\) 17644.1 30560.5i 0.759737 1.31590i
\(815\) −10713.2 18555.9i −0.460452 0.797527i
\(816\) 9693.82 38618.8i 0.415872 1.65677i
\(817\) 4653.32 + 2686.60i 0.199265 + 0.115045i
\(818\) 23917.0i 1.02230i
\(819\) 37.8539 + 1192.43i 0.00161505 + 0.0508753i
\(820\) −617.838 + 1070.13i −0.0263120 + 0.0455737i
\(821\) −13214.0 7629.13i −0.561721 0.324310i 0.192115 0.981372i \(-0.438465\pi\)
−0.753836 + 0.657062i \(0.771799\pi\)
\(822\) −3496.35 12266.6i −0.148357 0.520495i
\(823\) 2212.65 3832.42i 0.0937159 0.162321i −0.815356 0.578960i \(-0.803459\pi\)
0.909072 + 0.416639i \(0.136792\pi\)
\(824\) −13460.7 23314.5i −0.569083 0.985680i
\(825\) −1024.58 257.184i −0.0432381 0.0108533i
\(826\) −5300.96 −0.223298
\(827\) −6737.03 3889.63i −0.283276 0.163550i 0.351629 0.936139i \(-0.385628\pi\)
−0.634906 + 0.772590i \(0.718961\pi\)
\(828\) −882.926 + 28.0286i −0.0370577 + 0.00117640i
\(829\) −11747.1 −0.492151 −0.246076 0.969251i \(-0.579141\pi\)
−0.246076 + 0.969251i \(0.579141\pi\)
\(830\) −8093.47 + 4672.76i −0.338468 + 0.195415i
\(831\) −16235.2 + 16758.8i −0.677729 + 0.699585i
\(832\) −8759.47 5057.28i −0.365000 0.210733i
\(833\) 36338.7 20980.2i 1.51148 0.872652i
\(834\) −11409.8 + 3252.13i −0.473727 + 0.135026i
\(835\) −14760.3 + 8521.87i −0.611739 + 0.353187i
\(836\) 285.395 + 494.319i 0.0118069 + 0.0204502i
\(837\) −1158.82 252.083i −0.0478549 0.0104101i
\(838\) −1581.90 + 913.310i −0.0652098 + 0.0376489i
\(839\) −4739.10 + 2736.12i −0.195008 + 0.112588i −0.594325 0.804225i \(-0.702581\pi\)
0.399317 + 0.916813i \(0.369247\pi\)
\(840\) 734.888 2927.69i 0.0301858 0.120256i
\(841\) 3296.47 5709.66i 0.135162 0.234108i
\(842\) 17953.7 + 31096.8i 0.734829 + 1.27276i
\(843\) 4677.88 + 16411.9i 0.191121 + 0.670529i
\(844\) 143.218 0.00584096
\(845\) −10007.0 17332.6i −0.407397 0.705632i
\(846\) −27370.7 + 868.887i −1.11232 + 0.0353108i
\(847\) 44.4186i 0.00180194i
\(848\) −6865.51 + 11891.4i −0.278022 + 0.481548i
\(849\) −13299.4 + 13728.3i −0.537616 + 0.554953i
\(850\) −1654.11 + 955.002i −0.0667477 + 0.0385368i
\(851\) −34724.1 + 20048.0i −1.39874 + 0.807563i
\(852\) 913.978 260.511i 0.0367516 0.0104753i
\(853\) −9511.17 + 16473.8i −0.381778 + 0.661258i −0.991316 0.131498i \(-0.958021\pi\)
0.609539 + 0.792756i \(0.291355\pi\)
\(854\) 1812.87 3139.98i 0.0726407 0.125817i
\(855\) 14325.4 + 7675.34i 0.573004 + 0.307007i
\(856\) 16070.0i 0.641660i
\(857\) 42620.8 1.69883 0.849415 0.527725i \(-0.176955\pi\)
0.849415 + 0.527725i \(0.176955\pi\)
\(858\) 9758.12 2781.35i 0.388271 0.110669i
\(859\) 17196.6 + 29785.4i 0.683050 + 1.18308i 0.974045 + 0.226353i \(0.0726802\pi\)
−0.290995 + 0.956724i \(0.593986\pi\)
\(860\) 260.509 150.405i 0.0103294 0.00596368i
\(861\) −4626.40 + 1318.66i −0.183121 + 0.0521950i
\(862\) 40871.9i 1.61497i
\(863\) 14740.9i 0.581445i −0.956807 0.290722i \(-0.906104\pi\)
0.956807 0.290722i \(-0.0938956\pi\)
\(864\) 380.494 1749.12i 0.0149823 0.0688730i
\(865\) −35433.8 20457.7i −1.39281 0.804142i
\(866\) 39305.6i 1.54233i
\(867\) −53064.8 13320.0i −2.07863 0.521765i
\(868\) −5.50757 −0.000215368
\(869\) −15888.9 9173.44i −0.620245 0.358099i
\(870\) −19947.1 19323.9i −0.777321 0.753036i
\(871\) 774.955 + 10462.0i 0.0301474 + 0.406994i
\(872\) 29525.8i 1.14664i
\(873\) −13430.6 + 25067.2i −0.520685 + 0.971817i
\(874\) 17745.7i 0.686795i
\(875\) −2854.11 + 1647.82i −0.110270 + 0.0636647i
\(876\) −69.3092 + 71.5444i −0.00267322 + 0.00275943i
\(877\) 1649.50 2857.02i 0.0635117 0.110006i −0.832521 0.553993i \(-0.813103\pi\)
0.896033 + 0.443988i \(0.146437\pi\)
\(878\) −8100.49 14030.5i −0.311365 0.539300i
\(879\) −33752.2 32697.8i −1.29515 1.25469i
\(880\) −24766.2 −0.948714
\(881\) 21751.9 + 12558.5i 0.831827 + 0.480256i 0.854478 0.519488i \(-0.173877\pi\)
−0.0226507 + 0.999743i \(0.507211\pi\)
\(882\) −21521.8 + 13353.5i −0.821627 + 0.509793i
\(883\) −15877.7 + 9166.97i −0.605125 + 0.349369i −0.771055 0.636768i \(-0.780271\pi\)
0.165930 + 0.986138i \(0.446937\pi\)
\(884\) −335.250 + 580.670i −0.0127553 + 0.0220928i
\(885\) −33696.2 32643.5i −1.27987 1.23989i
\(886\) 37919.4 1.43784
\(887\) 28356.8 + 16371.8i 1.07343 + 0.619743i 0.929115 0.369790i \(-0.120570\pi\)
0.144310 + 0.989532i \(0.453904\pi\)
\(888\) −11328.6 39745.3i −0.428111 1.50199i
\(889\) 2264.91 + 1307.65i 0.0854473 + 0.0493330i
\(890\) 37482.1 + 21640.3i 1.41169 + 0.815039i
\(891\) 14838.2 + 22302.4i 0.557909 + 0.838561i
\(892\) 39.8861 + 69.0847i 0.00149718 + 0.00259319i
\(893\) 20105.2i 0.753411i
\(894\) −1702.52 + 485.269i −0.0636922 + 0.0181542i
\(895\) 13546.5 0.505932
\(896\) 3157.38i 0.117724i
\(897\) −11182.3 2806.90i −0.416238 0.104481i
\(898\) 23780.0i 0.883685i
\(899\) −743.933 + 1288.53i −0.0275990 + 0.0478029i
\(900\) −35.8035 + 22.2149i −0.00132606 + 0.000822775i
\(901\) 23963.8 + 13835.5i 0.886072 + 0.511574i
\(902\) 20457.4 + 35433.3i 0.755163 + 1.30798i
\(903\) 1135.86 + 285.116i 0.0418594 + 0.0105073i
\(904\) 13589.9 + 23538.4i 0.499992 + 0.866011i
\(905\) −5086.64 8810.32i −0.186835 0.323608i
\(906\) 5906.34 + 1482.57i 0.216584 + 0.0543655i
\(907\) −4612.61 7989.27i −0.168863 0.292480i 0.769157 0.639060i \(-0.220676\pi\)
−0.938021 + 0.346580i \(0.887343\pi\)
\(908\) −1432.45 827.026i −0.0523541 0.0302267i
\(909\) 18791.7 11659.7i 0.685679 0.425442i
\(910\) 670.862 1161.97i 0.0244383 0.0423284i
\(911\) 45233.0i 1.64504i −0.568733 0.822522i \(-0.692566\pi\)
0.568733 0.822522i \(-0.307434\pi\)
\(912\) −17114.5 4295.96i −0.621400 0.155980i
\(913\) 11309.2i 0.409946i
\(914\) −46038.2 −1.66609
\(915\) 30859.9 8795.99i 1.11497 0.317799i
\(916\) 294.851i 0.0106355i
\(917\) 459.591 + 796.035i 0.0165507 + 0.0286667i
\(918\) 47327.1 + 10295.3i 1.70155 + 0.370147i
\(919\) 12662.9 + 7310.94i 0.454528 + 0.262422i 0.709741 0.704463i \(-0.248812\pi\)
−0.255213 + 0.966885i \(0.582145\pi\)
\(920\) 25262.1 + 14585.1i 0.905291 + 0.522670i
\(921\) −13113.8 46008.4i −0.469178 1.64607i
\(922\) −33661.3 19434.3i −1.20236 0.694182i
\(923\) 12403.7 0.442334
\(924\) 89.3520 + 86.5605i 0.00318124 + 0.00308185i
\(925\) −956.259 + 1656.29i −0.0339909 + 0.0588740i
\(926\) 8615.54 4974.18i 0.305750 0.176525i
\(927\) 26844.1 16655.9i 0.951107 0.590131i
\(928\) −1944.91 1122.89i −0.0687982 0.0397206i
\(929\) −11466.9 −0.404970 −0.202485 0.979285i \(-0.564902\pi\)
−0.202485 + 0.979285i \(0.564902\pi\)
\(930\) 957.931 + 928.004i 0.0337761 + 0.0327209i
\(931\) −9297.66 16104.0i −0.327302 0.566905i
\(932\) 264.545 458.206i 0.00929772 0.0161041i
\(933\) −16560.5 + 17094.5i −0.581099 + 0.599839i
\(934\) −44245.5 + 25545.1i −1.55006 + 0.894928i
\(935\) 49909.4i 1.74568i
\(936\) 5612.22 10474.8i 0.195984 0.365789i
\(937\) 52258.1i 1.82198i 0.412424 + 0.910992i \(0.364682\pi\)
−0.412424 + 0.910992i \(0.635318\pi\)
\(938\) 2909.51 1980.00i 0.101278 0.0689225i
\(939\) 34156.9 + 33089.8i 1.18708 + 1.14999i
\(940\) −974.764 562.780i −0.0338227 0.0195275i
\(941\) −48460.8 −1.67883 −0.839413 0.543494i \(-0.817101\pi\)
−0.839413 + 0.543494i \(0.817101\pi\)
\(942\) −33278.0 8353.21i −1.15101 0.288920i
\(943\) 46489.1i 1.60540i
\(944\) 44113.2 + 25468.8i 1.52093 + 0.878112i
\(945\) 3461.20 + 752.932i 0.119146 + 0.0259184i
\(946\) 9960.20i 0.342319i
\(947\) 35357.9i 1.21328i 0.794976 + 0.606641i \(0.207483\pi\)
−0.794976 + 0.606641i \(0.792517\pi\)
\(948\) −703.773 + 200.596i −0.0241113 + 0.00687243i
\(949\) −1125.88 + 650.030i −0.0385119 + 0.0222348i
\(950\) 423.223 + 733.044i 0.0144539 + 0.0250348i
\(951\) −30256.0 + 8623.85i −1.03167 + 0.294056i
\(952\) 6604.50 0.224846
\(953\) 2417.80i 0.0821829i 0.999155 + 0.0410914i \(0.0130835\pi\)
−0.999155 + 0.0410914i \(0.986917\pi\)
\(954\) −14722.6 7888.17i −0.499647 0.267703i
\(955\) −6338.30 + 10978.3i −0.214767 + 0.371987i
\(956\) 204.499 354.203i 0.00691838 0.0119830i
\(957\) 32320.5 9212.31i 1.09172 0.311172i
\(958\) −34191.2 + 19740.3i −1.15310 + 0.665742i
\(959\) 1767.59 1020.52i 0.0595186 0.0343631i
\(960\) −20895.2 + 21569.0i −0.702488 + 0.725143i
\(961\) −14859.8 + 25737.9i −0.498801 + 0.863948i
\(962\) 18370.4i 0.615680i
\(963\) −18848.3 + 598.341i −0.630713 + 0.0200221i
\(964\) −866.824 1501.38i −0.0289611 0.0501621i
\(965\) 17706.6 0.590670
\(966\) 1060.19 + 3719.57i 0.0353116 + 0.123887i
\(967\) −20455.9 35430.6i −0.680265 1.17825i −0.974900 0.222644i \(-0.928531\pi\)
0.294635 0.955610i \(-0.404802\pi\)
\(968\) 221.221 383.167i 0.00734538 0.0127226i
\(969\) −8657.31 + 34489.4i −0.287010 + 1.14341i
\(970\) 27698.0 15991.4i 0.916834 0.529334i
\(971\) 10265.5 5926.79i 0.339275 0.195880i −0.320677 0.947189i \(-0.603910\pi\)
0.659951 + 0.751308i \(0.270577\pi\)
\(972\) 1050.74 + 193.877i 0.0346732 + 0.00639774i
\(973\) −949.234 1644.12i −0.0312755 0.0541707i
\(974\) −4878.99 + 2816.88i −0.160506 + 0.0926682i
\(975\) −528.861 + 150.741i −0.0173714 + 0.00495137i
\(976\) −30172.5 + 17420.1i −0.989547 + 0.571315i
\(977\) −35942.2 20751.2i −1.17696 0.679519i −0.221652 0.975126i \(-0.571145\pi\)
−0.955310 + 0.295606i \(0.904478\pi\)
\(978\) −19689.8 + 20324.8i −0.643774 + 0.664536i
\(979\) −45357.9 + 26187.4i −1.48074 + 0.854906i
\(980\) −1041.03 −0.0339332
\(981\) 34630.3 1099.35i 1.12708 0.0357792i
\(982\) 2054.94 + 1186.42i 0.0667778 + 0.0385542i
\(983\) 34758.5 1.12780 0.563898 0.825844i \(-0.309301\pi\)
0.563898 + 0.825844i \(0.309301\pi\)
\(984\) 46476.0 + 11666.1i 1.50569 + 0.377949i
\(985\) 7884.50 + 13656.4i 0.255047 + 0.441754i
\(986\) 30382.9 52624.6i 0.981326 1.69971i
\(987\) −1201.15 4214.13i −0.0387366 0.135904i
\(988\) 257.332 + 148.571i 0.00828627 + 0.00478408i
\(989\) −5658.60 + 9800.98i −0.181934 + 0.315119i
\(990\) −955.875 30110.9i −0.0306866 0.966654i
\(991\) 26902.2i 0.862338i −0.902271 0.431169i \(-0.858101\pi\)
0.902271 0.431169i \(-0.141899\pi\)
\(992\) 93.4015 + 53.9254i 0.00298942 + 0.00172594i
\(993\) −4050.89 + 16138.1i −0.129457 + 0.515738i
\(994\) −2080.55 3603.62i −0.0663894 0.114990i
\(995\) −7506.76 + 13002.1i −0.239176 + 0.414265i
\(996\) −323.991 313.869i −0.0103073 0.00998525i
\(997\) 37291.0 1.18457 0.592285 0.805728i \(-0.298226\pi\)
0.592285 + 0.805728i \(0.298226\pi\)
\(998\) 18973.0 10954.1i 0.601783 0.347439i
\(999\) 46194.9 14767.0i 1.46300 0.467674i
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 201.4.f.a.38.20 132
3.2 odd 2 inner 201.4.f.a.38.47 yes 132
67.30 odd 6 inner 201.4.f.a.164.47 yes 132
201.164 even 6 inner 201.4.f.a.164.20 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.4.f.a.38.20 132 1.1 even 1 trivial
201.4.f.a.38.47 yes 132 3.2 odd 2 inner
201.4.f.a.164.20 yes 132 201.164 even 6 inner
201.4.f.a.164.47 yes 132 67.30 odd 6 inner