Properties

Label 225.4.k.a.124.1
Level $225$
Weight $4$
Character 225.124
Analytic conductor $13.275$
Analytic rank $0$
Dimension $8$
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] = [225,4,Mod(49,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not 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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.303595776.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.1
Root \(-0.396143 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.4.k.a.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.92048 - 1.68614i) q^{2} +(4.97494 - 1.50000i) q^{3} +(1.68614 + 2.92048i) q^{4} +(-17.0584 - 4.00772i) q^{6} +(1.40965 + 0.813859i) q^{7} +15.6060i q^{8} +(22.5000 - 14.9248i) q^{9} +O(q^{10})\) \(q+(-2.92048 - 1.68614i) q^{2} +(4.97494 - 1.50000i) q^{3} +(1.68614 + 2.92048i) q^{4} +(-17.0584 - 4.00772i) q^{6} +(1.40965 + 0.813859i) q^{7} +15.6060i q^{8} +(22.5000 - 14.9248i) q^{9} +(16.4307 - 28.4588i) q^{11} +(12.7692 + 12.0000i) q^{12} +(-28.5977 + 16.5109i) q^{13} +(-2.74456 - 4.75372i) q^{14} +(39.8030 - 68.9408i) q^{16} -110.307i q^{17} +(-90.8762 + 5.64947i) q^{18} +54.3070 q^{19} +(8.23369 + 1.93443i) q^{21} +(-95.9711 + 55.4090i) q^{22} +(-58.4026 + 33.7188i) q^{23} +(23.4090 + 77.6387i) q^{24} +111.359 q^{26} +(89.5489 - 108.000i) q^{27} +5.48913i q^{28} +(137.259 - 237.740i) q^{29} +(3.00000 + 5.19615i) q^{31} +(-124.366 + 71.8030i) q^{32} +(39.0535 - 166.227i) q^{33} +(-185.993 + 322.150i) q^{34} +(81.5258 + 40.5455i) q^{36} +347.723i q^{37} +(-158.603 - 91.5693i) q^{38} +(-117.505 + 125.037i) q^{39} +(-145.668 - 252.305i) q^{41} +(-20.7846 - 19.5326i) q^{42} +(-174.408 - 100.694i) q^{43} +110.818 q^{44} +227.418 q^{46} +(-417.507 - 241.048i) q^{47} +(94.6062 - 402.681i) q^{48} +(-170.175 - 294.752i) q^{49} +(-165.461 - 548.771i) q^{51} +(-96.4394 - 55.6793i) q^{52} -175.228i q^{53} +(-443.629 + 164.420i) q^{54} +(-12.7011 + 21.9989i) q^{56} +(270.174 - 81.4605i) q^{57} +(-801.728 + 462.878i) q^{58} +(-91.6209 - 158.692i) q^{59} +(-218.297 + 378.102i) q^{61} -20.2337i q^{62} +(43.8637 - 2.72686i) q^{63} -152.568 q^{64} +(-394.337 + 419.613i) q^{66} +(720.100 - 415.750i) q^{67} +(322.150 - 185.993i) q^{68} +(-239.971 + 255.353i) q^{69} -118.951 q^{71} +(232.916 + 351.134i) q^{72} +183.318i q^{73} +(586.310 - 1015.52i) q^{74} +(91.5693 + 158.603i) q^{76} +(46.3229 - 26.7446i) q^{77} +(554.002 - 167.038i) q^{78} +(-319.147 + 552.778i) q^{79} +(283.500 - 671.617i) q^{81} +982.470i q^{82} +(1294.40 + 747.322i) q^{83} +(8.23369 + 27.3081i) q^{84} +(339.569 + 588.151i) q^{86} +(326.247 - 1388.63i) q^{87} +(444.127 + 256.417i) q^{88} +1437.27 q^{89} -53.7501 q^{91} +(-196.950 - 113.709i) q^{92} +(22.7190 + 21.3505i) q^{93} +(812.880 + 1407.95i) q^{94} +(-511.011 + 543.765i) q^{96} +(-772.294 - 445.884i) q^{97} +1147.76i q^{98} +(-55.0516 - 885.548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + 74 q^{11} + 24 q^{14} + 238 q^{16} - 140 q^{19} - 72 q^{21} - 54 q^{24} - 304 q^{26} + 650 q^{29} + 24 q^{31} - 902 q^{34} + 342 q^{36} + 1128 q^{39} - 476 q^{41} + 404 q^{44} - 984 q^{46} - 1258 q^{49} - 462 q^{51} - 1998 q^{54} + 312 q^{56} - 170 q^{59} + 494 q^{61} - 2852 q^{64} - 1776 q^{66} + 3078 q^{69} + 1576 q^{71} + 968 q^{74} + 790 q^{76} - 1680 q^{79} + 2268 q^{81} - 72 q^{84} + 2774 q^{86} + 4260 q^{89} - 2544 q^{91} + 1264 q^{94} + 48 q^{96} + 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.92048 1.68614i −1.03255 0.596141i −0.114833 0.993385i \(-0.536633\pi\)
−0.917713 + 0.397244i \(0.869967\pi\)
\(3\) 4.97494 1.50000i 0.957427 0.288675i
\(4\) 1.68614 + 2.92048i 0.210768 + 0.365060i
\(5\) 0 0
\(6\) −17.0584 4.00772i −1.16068 0.272691i
\(7\) 1.40965 + 0.813859i 0.0761137 + 0.0439443i 0.537574 0.843217i \(-0.319341\pi\)
−0.461460 + 0.887161i \(0.652674\pi\)
\(8\) 15.6060i 0.689693i
\(9\) 22.5000 14.9248i 0.833333 0.552771i
\(10\) 0 0
\(11\) 16.4307 28.4588i 0.450368 0.780060i −0.548041 0.836451i \(-0.684626\pi\)
0.998409 + 0.0563918i \(0.0179596\pi\)
\(12\) 12.7692 + 12.0000i 0.307178 + 0.288675i
\(13\) −28.5977 + 16.5109i −0.610121 + 0.352253i −0.773013 0.634391i \(-0.781251\pi\)
0.162892 + 0.986644i \(0.447918\pi\)
\(14\) −2.74456 4.75372i −0.0523939 0.0907490i
\(15\) 0 0
\(16\) 39.8030 68.9408i 0.621922 1.07720i
\(17\) 110.307i 1.57373i −0.617126 0.786864i \(-0.711703\pi\)
0.617126 0.786864i \(-0.288297\pi\)
\(18\) −90.8762 + 5.64947i −1.18998 + 0.0739774i
\(19\) 54.3070 0.655731 0.327865 0.944724i \(-0.393671\pi\)
0.327865 + 0.944724i \(0.393671\pi\)
\(20\) 0 0
\(21\) 8.23369 + 1.93443i 0.0855590 + 0.0201013i
\(22\) −95.9711 + 55.4090i −0.930051 + 0.536965i
\(23\) −58.4026 + 33.7188i −0.529469 + 0.305689i −0.740800 0.671725i \(-0.765553\pi\)
0.211331 + 0.977415i \(0.432220\pi\)
\(24\) 23.4090 + 77.6387i 0.199097 + 0.660331i
\(25\) 0 0
\(26\) 111.359 0.839970
\(27\) 89.5489 108.000i 0.638285 0.769800i
\(28\) 5.48913i 0.0370481i
\(29\) 137.259 237.740i 0.878912 1.52232i 0.0263757 0.999652i \(-0.491603\pi\)
0.852536 0.522668i \(-0.175063\pi\)
\(30\) 0 0
\(31\) 3.00000 + 5.19615i 0.0173812 + 0.0301050i 0.874585 0.484872i \(-0.161134\pi\)
−0.857204 + 0.514977i \(0.827800\pi\)
\(32\) −124.366 + 71.8030i −0.687034 + 0.396659i
\(33\) 39.0535 166.227i 0.206010 0.876860i
\(34\) −185.993 + 322.150i −0.938164 + 1.62495i
\(35\) 0 0
\(36\) 81.5258 + 40.5455i 0.377434 + 0.187711i
\(37\) 347.723i 1.54501i 0.635010 + 0.772504i \(0.280996\pi\)
−0.635010 + 0.772504i \(0.719004\pi\)
\(38\) −158.603 91.5693i −0.677072 0.390908i
\(39\) −117.505 + 125.037i −0.482459 + 0.513383i
\(40\) 0 0
\(41\) −145.668 252.305i −0.554868 0.961060i −0.997914 0.0645606i \(-0.979435\pi\)
0.443046 0.896499i \(-0.353898\pi\)
\(42\) −20.7846 19.5326i −0.0763604 0.0717607i
\(43\) −174.408 100.694i −0.618533 0.357110i 0.157765 0.987477i \(-0.449571\pi\)
−0.776297 + 0.630367i \(0.782905\pi\)
\(44\) 110.818 0.379692
\(45\) 0 0
\(46\) 227.418 0.728935
\(47\) −417.507 241.048i −1.29574 0.748094i −0.316071 0.948735i \(-0.602364\pi\)
−0.979665 + 0.200642i \(0.935697\pi\)
\(48\) 94.6062 402.681i 0.284484 1.21087i
\(49\) −170.175 294.752i −0.496138 0.859336i
\(50\) 0 0
\(51\) −165.461 548.771i −0.454296 1.50673i
\(52\) −96.4394 55.6793i −0.257187 0.148487i
\(53\) 175.228i 0.454140i −0.973878 0.227070i \(-0.927085\pi\)
0.973878 0.227070i \(-0.0729147\pi\)
\(54\) −443.629 + 164.420i −1.11797 + 0.414347i
\(55\) 0 0
\(56\) −12.7011 + 21.9989i −0.0303081 + 0.0524951i
\(57\) 270.174 81.4605i 0.627815 0.189293i
\(58\) −801.728 + 462.878i −1.81503 + 1.04791i
\(59\) −91.6209 158.692i −0.202170 0.350169i 0.747057 0.664760i \(-0.231466\pi\)
−0.949227 + 0.314591i \(0.898133\pi\)
\(60\) 0 0
\(61\) −218.297 + 378.102i −0.458199 + 0.793623i −0.998866 0.0476132i \(-0.984839\pi\)
0.540667 + 0.841237i \(0.318172\pi\)
\(62\) 20.2337i 0.0414465i
\(63\) 43.8637 2.72686i 0.0877192 0.00545321i
\(64\) −152.568 −0.297984
\(65\) 0 0
\(66\) −394.337 + 419.613i −0.735447 + 0.782587i
\(67\) 720.100 415.750i 1.31305 0.758089i 0.330448 0.943824i \(-0.392800\pi\)
0.982600 + 0.185736i \(0.0594668\pi\)
\(68\) 322.150 185.993i 0.574506 0.331691i
\(69\) −239.971 + 255.353i −0.418683 + 0.445520i
\(70\) 0 0
\(71\) −118.951 −0.198829 −0.0994146 0.995046i \(-0.531697\pi\)
−0.0994146 + 0.995046i \(0.531697\pi\)
\(72\) 232.916 + 351.134i 0.381242 + 0.574744i
\(73\) 183.318i 0.293914i 0.989143 + 0.146957i \(0.0469479\pi\)
−0.989143 + 0.146957i \(0.953052\pi\)
\(74\) 586.310 1015.52i 0.921042 1.59529i
\(75\) 0 0
\(76\) 91.5693 + 158.603i 0.138207 + 0.239381i
\(77\) 46.3229 26.7446i 0.0685583 0.0395822i
\(78\) 554.002 167.038i 0.804210 0.242478i
\(79\) −319.147 + 552.778i −0.454517 + 0.787246i −0.998660 0.0517463i \(-0.983521\pi\)
0.544144 + 0.838992i \(0.316855\pi\)
\(80\) 0 0
\(81\) 283.500 671.617i 0.388889 0.921285i
\(82\) 982.470i 1.32312i
\(83\) 1294.40 + 747.322i 1.71179 + 0.988304i 0.932145 + 0.362085i \(0.117935\pi\)
0.779647 + 0.626219i \(0.215398\pi\)
\(84\) 8.23369 + 27.3081i 0.0106949 + 0.0354709i
\(85\) 0 0
\(86\) 339.569 + 588.151i 0.425776 + 0.737465i
\(87\) 326.247 1388.63i 0.402038 1.71123i
\(88\) 444.127 + 256.417i 0.538002 + 0.310615i
\(89\) 1437.27 1.71180 0.855900 0.517142i \(-0.173004\pi\)
0.855900 + 0.517142i \(0.173004\pi\)
\(90\) 0 0
\(91\) −53.7501 −0.0619181
\(92\) −196.950 113.709i −0.223190 0.128859i
\(93\) 22.7190 + 21.3505i 0.0253318 + 0.0238059i
\(94\) 812.880 + 1407.95i 0.891938 + 1.54488i
\(95\) 0 0
\(96\) −511.011 + 543.765i −0.543279 + 0.578102i
\(97\) −772.294 445.884i −0.808398 0.466729i 0.0380011 0.999278i \(-0.487901\pi\)
−0.846399 + 0.532549i \(0.821234\pi\)
\(98\) 1147.76i 1.18307i
\(99\) −55.0516 885.548i −0.0558878 0.899000i
\(100\) 0 0
\(101\) 76.8720 133.146i 0.0757332 0.131174i −0.825672 0.564151i \(-0.809204\pi\)
0.901405 + 0.432977i \(0.142537\pi\)
\(102\) −442.080 + 1881.66i −0.429142 + 1.82659i
\(103\) 117.168 67.6469i 0.112086 0.0647131i −0.442909 0.896567i \(-0.646053\pi\)
0.554995 + 0.831854i \(0.312720\pi\)
\(104\) −257.668 446.294i −0.242947 0.420796i
\(105\) 0 0
\(106\) −295.459 + 511.750i −0.270732 + 0.468921i
\(107\) 718.783i 0.649414i 0.945815 + 0.324707i \(0.105266\pi\)
−0.945815 + 0.324707i \(0.894734\pi\)
\(108\) 466.404 + 79.4226i 0.415553 + 0.0707634i
\(109\) 2010.56 1.76676 0.883378 0.468661i \(-0.155264\pi\)
0.883378 + 0.468661i \(0.155264\pi\)
\(110\) 0 0
\(111\) 521.584 + 1729.90i 0.446005 + 1.47923i
\(112\) 112.216 64.7881i 0.0946735 0.0546598i
\(113\) −196.367 + 113.372i −0.163474 + 0.0943820i −0.579505 0.814969i \(-0.696754\pi\)
0.416031 + 0.909351i \(0.363421\pi\)
\(114\) −926.392 217.647i −0.761093 0.178812i
\(115\) 0 0
\(116\) 925.755 0.740985
\(117\) −397.026 + 798.310i −0.313718 + 0.630801i
\(118\) 617.943i 0.482087i
\(119\) 89.7744 155.494i 0.0691564 0.119782i
\(120\) 0 0
\(121\) 125.564 + 217.483i 0.0943381 + 0.163398i
\(122\) 1275.07 736.160i 0.946223 0.546302i
\(123\) −1103.15 1036.70i −0.808680 0.759968i
\(124\) −10.1168 + 17.5229i −0.00732677 + 0.0126903i
\(125\) 0 0
\(126\) −132.701 65.9967i −0.0938250 0.0466623i
\(127\) 1132.24i 0.791100i −0.918444 0.395550i \(-0.870554\pi\)
0.918444 0.395550i \(-0.129446\pi\)
\(128\) 1440.50 + 831.675i 0.994717 + 0.574300i
\(129\) −1018.71 239.336i −0.695289 0.163352i
\(130\) 0 0
\(131\) −388.753 673.339i −0.259278 0.449083i 0.706770 0.707443i \(-0.250151\pi\)
−0.966049 + 0.258360i \(0.916818\pi\)
\(132\) 551.312 166.227i 0.363527 0.109608i
\(133\) 76.5537 + 44.1983i 0.0499101 + 0.0288156i
\(134\) −2804.05 −1.80771
\(135\) 0 0
\(136\) 1721.45 1.08539
\(137\) 540.087 + 311.819i 0.336808 + 0.194456i 0.658860 0.752266i \(-0.271039\pi\)
−0.322052 + 0.946722i \(0.604372\pi\)
\(138\) 1131.39 341.127i 0.697902 0.210425i
\(139\) 641.341 + 1110.83i 0.391351 + 0.677840i 0.992628 0.121201i \(-0.0386745\pi\)
−0.601277 + 0.799041i \(0.705341\pi\)
\(140\) 0 0
\(141\) −2438.64 572.937i −1.45653 0.342198i
\(142\) 347.394 + 200.568i 0.205300 + 0.118530i
\(143\) 1085.14i 0.634574i
\(144\) −133.361 2145.22i −0.0771766 1.24145i
\(145\) 0 0
\(146\) 309.099 535.376i 0.175214 0.303480i
\(147\) −1288.74 1211.11i −0.723085 0.679529i
\(148\) −1015.52 + 586.310i −0.564021 + 0.325638i
\(149\) 762.156 + 1320.09i 0.419049 + 0.725814i 0.995844 0.0910749i \(-0.0290303\pi\)
−0.576795 + 0.816889i \(0.695697\pi\)
\(150\) 0 0
\(151\) −1581.28 + 2738.86i −0.852203 + 1.47606i 0.0270124 + 0.999635i \(0.491401\pi\)
−0.879216 + 0.476424i \(0.841933\pi\)
\(152\) 847.514i 0.452253i
\(153\) −1646.31 2481.91i −0.869911 1.31144i
\(154\) −180.380 −0.0943861
\(155\) 0 0
\(156\) −563.299 132.342i −0.289103 0.0679220i
\(157\) 2068.67 1194.35i 1.05158 0.607131i 0.128490 0.991711i \(-0.458987\pi\)
0.923092 + 0.384580i \(0.125654\pi\)
\(158\) 1864.12 1076.25i 0.938619 0.541912i
\(159\) −262.842 871.749i −0.131099 0.434806i
\(160\) 0 0
\(161\) −109.769 −0.0537331
\(162\) −1960.40 + 1483.42i −0.950761 + 0.719436i
\(163\) 2544.79i 1.22284i −0.791305 0.611422i \(-0.790598\pi\)
0.791305 0.611422i \(-0.209402\pi\)
\(164\) 491.235 850.844i 0.233896 0.405120i
\(165\) 0 0
\(166\) −2520.18 4365.08i −1.17834 2.04094i
\(167\) 1190.40 687.279i 0.551593 0.318462i −0.198171 0.980167i \(-0.563500\pi\)
0.749764 + 0.661705i \(0.230167\pi\)
\(168\) −30.1887 + 128.495i −0.0138637 + 0.0590094i
\(169\) −553.282 + 958.313i −0.251835 + 0.436191i
\(170\) 0 0
\(171\) 1221.91 810.522i 0.546442 0.362469i
\(172\) 679.139i 0.301069i
\(173\) −2044.21 1180.23i −0.898372 0.518675i −0.0217005 0.999765i \(-0.506908\pi\)
−0.876672 + 0.481089i \(0.840241\pi\)
\(174\) −3294.23 + 3505.38i −1.43526 + 1.52725i
\(175\) 0 0
\(176\) −1307.98 2265.49i −0.560187 0.970272i
\(177\) −693.846 652.052i −0.294648 0.276899i
\(178\) −4197.52 2423.44i −1.76751 1.02047i
\(179\) −1305.11 −0.544963 −0.272482 0.962161i \(-0.587844\pi\)
−0.272482 + 0.962161i \(0.587844\pi\)
\(180\) 0 0
\(181\) 3099.43 1.27281 0.636406 0.771355i \(-0.280420\pi\)
0.636406 + 0.771355i \(0.280420\pi\)
\(182\) 156.976 + 90.6303i 0.0639332 + 0.0369119i
\(183\) −518.863 + 2208.48i −0.209593 + 0.892107i
\(184\) −526.214 911.429i −0.210832 0.365171i
\(185\) 0 0
\(186\) −30.3505 100.661i −0.0119646 0.0396820i
\(187\) −3139.21 1812.42i −1.22760 0.708756i
\(188\) 1625.76i 0.630696i
\(189\) 214.129 79.3616i 0.0824105 0.0305434i
\(190\) 0 0
\(191\) −190.356 + 329.706i −0.0721135 + 0.124904i −0.899827 0.436246i \(-0.856308\pi\)
0.827714 + 0.561150i \(0.189641\pi\)
\(192\) −759.016 + 228.852i −0.285298 + 0.0860207i
\(193\) 1338.91 773.020i 0.499362 0.288307i −0.229088 0.973406i \(-0.573574\pi\)
0.728450 + 0.685099i \(0.240241\pi\)
\(194\) 1503.65 + 2604.39i 0.556472 + 0.963838i
\(195\) 0 0
\(196\) 573.879 993.987i 0.209140 0.362240i
\(197\) 4284.60i 1.54957i 0.632226 + 0.774784i \(0.282141\pi\)
−0.632226 + 0.774784i \(0.717859\pi\)
\(198\) −1332.38 + 2679.05i −0.478224 + 0.961576i
\(199\) 1402.85 0.499727 0.249863 0.968281i \(-0.419614\pi\)
0.249863 + 0.968281i \(0.419614\pi\)
\(200\) 0 0
\(201\) 2958.83 3148.48i 1.03831 1.10486i
\(202\) −449.007 + 259.234i −0.156396 + 0.0902953i
\(203\) 386.974 223.420i 0.133795 0.0772463i
\(204\) 1323.68 1408.53i 0.454296 0.483415i
\(205\) 0 0
\(206\) −456.249 −0.154312
\(207\) −810.813 + 1630.32i −0.272248 + 0.547416i
\(208\) 2628.73i 0.876296i
\(209\) 892.303 1545.51i 0.295320 0.511509i
\(210\) 0 0
\(211\) 1075.23 + 1862.35i 0.350814 + 0.607628i 0.986392 0.164409i \(-0.0525716\pi\)
−0.635578 + 0.772036i \(0.719238\pi\)
\(212\) 511.750 295.459i 0.165789 0.0957180i
\(213\) −591.773 + 178.426i −0.190365 + 0.0573971i
\(214\) 1211.97 2099.19i 0.387142 0.670550i
\(215\) 0 0
\(216\) 1685.44 + 1397.50i 0.530926 + 0.440220i
\(217\) 9.76631i 0.00305521i
\(218\) −5871.79 3390.08i −1.82426 1.05324i
\(219\) 274.977 + 911.994i 0.0848456 + 0.281401i
\(220\) 0 0
\(221\) 1821.27 + 3154.52i 0.554351 + 0.960164i
\(222\) 1393.58 5931.60i 0.421310 1.79326i
\(223\) 2215.42 + 1279.07i 0.665272 + 0.384095i 0.794283 0.607548i \(-0.207847\pi\)
−0.129011 + 0.991643i \(0.541180\pi\)
\(224\) −233.750 −0.0697236
\(225\) 0 0
\(226\) 764.646 0.225060
\(227\) −3537.32 2042.27i −1.03427 0.597138i −0.116067 0.993241i \(-0.537029\pi\)
−0.918206 + 0.396104i \(0.870362\pi\)
\(228\) 693.456 + 651.684i 0.201426 + 0.189293i
\(229\) −1370.95 2374.56i −0.395612 0.685221i 0.597567 0.801819i \(-0.296134\pi\)
−0.993179 + 0.116598i \(0.962801\pi\)
\(230\) 0 0
\(231\) 190.337 202.537i 0.0542132 0.0576881i
\(232\) 3710.17 + 2142.07i 1.04993 + 0.606179i
\(233\) 5084.70i 1.42966i 0.699300 + 0.714828i \(0.253495\pi\)
−0.699300 + 0.714828i \(0.746505\pi\)
\(234\) 2505.57 1662.01i 0.699975 0.464311i
\(235\) 0 0
\(236\) 308.971 535.154i 0.0852217 0.147608i
\(237\) −758.567 + 3228.76i −0.207908 + 0.884938i
\(238\) −524.369 + 302.745i −0.142814 + 0.0824538i
\(239\) 738.236 + 1278.66i 0.199801 + 0.346066i 0.948464 0.316885i \(-0.102637\pi\)
−0.748663 + 0.662951i \(0.769304\pi\)
\(240\) 0 0
\(241\) −881.728 + 1527.20i −0.235673 + 0.408197i −0.959468 0.281818i \(-0.909063\pi\)
0.723795 + 0.690015i \(0.242396\pi\)
\(242\) 846.874i 0.224955i
\(243\) 402.970 3766.50i 0.106381 0.994325i
\(244\) −1472.32 −0.386294
\(245\) 0 0
\(246\) 1473.70 + 4887.73i 0.381951 + 1.26679i
\(247\) −1553.05 + 896.657i −0.400075 + 0.230983i
\(248\) −81.0910 + 46.8179i −0.0207632 + 0.0119877i
\(249\) 7560.54 + 1776.28i 1.92422 + 0.452077i
\(250\) 0 0
\(251\) 1705.16 0.428801 0.214400 0.976746i \(-0.431220\pi\)
0.214400 + 0.976746i \(0.431220\pi\)
\(252\) 81.9242 + 123.505i 0.0204791 + 0.0308734i
\(253\) 2216.09i 0.550690i
\(254\) −1909.11 + 3306.68i −0.471607 + 0.816848i
\(255\) 0 0
\(256\) −2194.37 3800.76i −0.535735 0.927920i
\(257\) −197.970 + 114.298i −0.0480507 + 0.0277421i −0.523833 0.851821i \(-0.675498\pi\)
0.475782 + 0.879563i \(0.342165\pi\)
\(258\) 2571.56 + 2416.66i 0.620537 + 0.583158i
\(259\) −282.997 + 490.166i −0.0678942 + 0.117596i
\(260\) 0 0
\(261\) −459.892 7397.73i −0.109068 1.75444i
\(262\) 2621.97i 0.618266i
\(263\) 1116.10 + 644.380i 0.261679 + 0.151081i 0.625100 0.780544i \(-0.285058\pi\)
−0.363421 + 0.931625i \(0.618391\pi\)
\(264\) 2594.13 + 609.468i 0.604764 + 0.142084i
\(265\) 0 0
\(266\) −149.049 258.161i −0.0343563 0.0595069i
\(267\) 7150.32 2155.90i 1.63892 0.494154i
\(268\) 2428.38 + 1402.03i 0.553496 + 0.319561i
\(269\) −973.981 −0.220761 −0.110380 0.993889i \(-0.535207\pi\)
−0.110380 + 0.993889i \(0.535207\pi\)
\(270\) 0 0
\(271\) −4021.83 −0.901508 −0.450754 0.892648i \(-0.648845\pi\)
−0.450754 + 0.892648i \(0.648845\pi\)
\(272\) −7604.65 4390.55i −1.69522 0.978736i
\(273\) −267.403 + 80.6252i −0.0592820 + 0.0178742i
\(274\) −1051.54 1821.32i −0.231847 0.401570i
\(275\) 0 0
\(276\) −1150.38 270.271i −0.250886 0.0589435i
\(277\) −2926.45 1689.59i −0.634777 0.366489i 0.147823 0.989014i \(-0.452773\pi\)
−0.782600 + 0.622525i \(0.786107\pi\)
\(278\) 4325.56i 0.933201i
\(279\) 145.052 + 72.1390i 0.0311255 + 0.0154797i
\(280\) 0 0
\(281\) −366.654 + 635.063i −0.0778388 + 0.134821i −0.902317 0.431073i \(-0.858135\pi\)
0.824478 + 0.565893i \(0.191469\pi\)
\(282\) 6155.95 + 5785.14i 1.29993 + 1.22163i
\(283\) 5983.39 3454.51i 1.25680 0.725617i 0.284353 0.958720i \(-0.408221\pi\)
0.972452 + 0.233103i \(0.0748879\pi\)
\(284\) −200.568 347.394i −0.0419068 0.0725847i
\(285\) 0 0
\(286\) 1829.70 3169.13i 0.378295 0.655227i
\(287\) 474.214i 0.0975331i
\(288\) −1726.60 + 3471.71i −0.353267 + 0.710322i
\(289\) −7254.64 −1.47662
\(290\) 0 0
\(291\) −4510.94 1059.81i −0.908715 0.213494i
\(292\) −535.376 + 309.099i −0.107296 + 0.0619475i
\(293\) −4026.57 + 2324.74i −0.802850 + 0.463525i −0.844467 0.535608i \(-0.820082\pi\)
0.0416170 + 0.999134i \(0.486749\pi\)
\(294\) 1721.64 + 5710.02i 0.341523 + 1.13271i
\(295\) 0 0
\(296\) −5426.55 −1.06558
\(297\) −1602.20 4322.97i −0.313027 0.844593i
\(298\) 5140.41i 0.999248i
\(299\) 1113.45 1928.56i 0.215360 0.373014i
\(300\) 0 0
\(301\) −163.902 283.886i −0.0313859 0.0543619i
\(302\) 9236.19 5332.52i 1.75988 1.01607i
\(303\) 182.714 777.702i 0.0346424 0.147452i
\(304\) 2161.58 3743.97i 0.407813 0.706353i
\(305\) 0 0
\(306\) 623.176 + 10024.3i 0.116420 + 1.87271i
\(307\) 7361.42i 1.36853i 0.729234 + 0.684264i \(0.239877\pi\)
−0.729234 + 0.684264i \(0.760123\pi\)
\(308\) 156.214 + 90.1902i 0.0288997 + 0.0166853i
\(309\) 481.433 512.291i 0.0886335 0.0943146i
\(310\) 0 0
\(311\) 1354.60 + 2346.24i 0.246986 + 0.427792i 0.962688 0.270614i \(-0.0872266\pi\)
−0.715702 + 0.698405i \(0.753893\pi\)
\(312\) −1951.32 1833.78i −0.354077 0.332749i
\(313\) 5407.22 + 3121.86i 0.976467 + 0.563763i 0.901202 0.433400i \(-0.142686\pi\)
0.0752653 + 0.997164i \(0.476020\pi\)
\(314\) −8055.37 −1.44774
\(315\) 0 0
\(316\) −2152.50 −0.383189
\(317\) 1804.82 + 1042.02i 0.319776 + 0.184623i 0.651293 0.758827i \(-0.274227\pi\)
−0.331517 + 0.943449i \(0.607560\pi\)
\(318\) −702.266 + 2989.12i −0.123840 + 0.527111i
\(319\) −4510.54 7812.48i −0.791667 1.37121i
\(320\) 0 0
\(321\) 1078.17 + 3575.90i 0.187470 + 0.621767i
\(322\) 320.579 + 185.087i 0.0554819 + 0.0320325i
\(323\) 5990.45i 1.03194i
\(324\) 2439.46 304.483i 0.418289 0.0522091i
\(325\) 0 0
\(326\) −4290.88 + 7432.02i −0.728987 + 1.26264i
\(327\) 10002.4 3015.83i 1.69154 0.510018i
\(328\) 3937.47 2273.30i 0.662836 0.382689i
\(329\) −392.358 679.583i −0.0657489 0.113880i
\(330\) 0 0
\(331\) 113.938 197.347i 0.0189203 0.0327709i −0.856410 0.516296i \(-0.827310\pi\)
0.875331 + 0.483525i \(0.160644\pi\)
\(332\) 5040.36i 0.833210i
\(333\) 5189.70 + 7823.76i 0.854035 + 1.28751i
\(334\) −4635.39 −0.759394
\(335\) 0 0
\(336\) 461.087 490.641i 0.0748641 0.0796627i
\(337\) −2959.62 + 1708.74i −0.478400 + 0.276205i −0.719750 0.694234i \(-0.755743\pi\)
0.241349 + 0.970438i \(0.422410\pi\)
\(338\) 3231.70 1865.82i 0.520063 0.300259i
\(339\) −806.853 + 858.570i −0.129269 + 0.137555i
\(340\) 0 0
\(341\) 197.168 0.0313116
\(342\) −4935.21 + 306.806i −0.780309 + 0.0485092i
\(343\) 1112.30i 0.175098i
\(344\) 1571.43 2721.80i 0.246296 0.426598i
\(345\) 0 0
\(346\) 3980.05 + 6893.65i 0.618407 + 1.07111i
\(347\) −3126.00 + 1804.80i −0.483610 + 0.279212i −0.721920 0.691977i \(-0.756740\pi\)
0.238310 + 0.971189i \(0.423407\pi\)
\(348\) 4605.57 1388.63i 0.709439 0.213904i
\(349\) −4400.42 + 7621.74i −0.674925 + 1.16900i 0.301566 + 0.953445i \(0.402491\pi\)
−0.976491 + 0.215559i \(0.930843\pi\)
\(350\) 0 0
\(351\) −777.715 + 4567.08i −0.118266 + 0.694509i
\(352\) 4719.09i 0.714570i
\(353\) −7370.30 4255.24i −1.11128 0.641597i −0.172119 0.985076i \(-0.555061\pi\)
−0.939160 + 0.343479i \(0.888395\pi\)
\(354\) 926.914 + 3074.23i 0.139166 + 0.461563i
\(355\) 0 0
\(356\) 2423.44 + 4197.52i 0.360792 + 0.624910i
\(357\) 213.381 908.234i 0.0316340 0.134647i
\(358\) 3811.55 + 2200.60i 0.562700 + 0.324875i
\(359\) −4320.35 −0.635152 −0.317576 0.948233i \(-0.602869\pi\)
−0.317576 + 0.948233i \(0.602869\pi\)
\(360\) 0 0
\(361\) −3909.75 −0.570017
\(362\) −9051.83 5226.08i −1.31424 0.758775i
\(363\) 950.898 + 893.619i 0.137491 + 0.129209i
\(364\) −90.6303 156.976i −0.0130503 0.0226038i
\(365\) 0 0
\(366\) 5239.14 5574.95i 0.748235 0.796195i
\(367\) 5716.10 + 3300.19i 0.813020 + 0.469397i 0.848003 0.529991i \(-0.177805\pi\)
−0.0349838 + 0.999388i \(0.511138\pi\)
\(368\) 5368.43i 0.760459i
\(369\) −7043.15 3502.79i −0.993636 0.494168i
\(370\) 0 0
\(371\) 142.611 247.010i 0.0199569 0.0345663i
\(372\) −24.0463 + 102.351i −0.00335146 + 0.0142651i
\(373\) −7455.14 + 4304.23i −1.03489 + 0.597492i −0.918381 0.395698i \(-0.870503\pi\)
−0.116506 + 0.993190i \(0.537169\pi\)
\(374\) 6112.00 + 10586.3i 0.845037 + 1.46365i
\(375\) 0 0
\(376\) 3761.78 6515.60i 0.515955 0.893660i
\(377\) 9065.10i 1.23840i
\(378\) −759.174 129.278i −0.103301 0.0175908i
\(379\) 7129.80 0.966314 0.483157 0.875534i \(-0.339490\pi\)
0.483157 + 0.875534i \(0.339490\pi\)
\(380\) 0 0
\(381\) −1698.36 5632.81i −0.228371 0.757421i
\(382\) 1111.86 641.934i 0.148921 0.0859796i
\(383\) 5133.33 2963.73i 0.684859 0.395404i −0.116824 0.993153i \(-0.537271\pi\)
0.801683 + 0.597749i \(0.203938\pi\)
\(384\) 8413.93 + 1976.78i 1.11815 + 0.262700i
\(385\) 0 0
\(386\) −5213.68 −0.687486
\(387\) −5427.01 + 337.379i −0.712844 + 0.0443151i
\(388\) 3007.30i 0.393485i
\(389\) 519.432 899.683i 0.0677024 0.117264i −0.830187 0.557485i \(-0.811766\pi\)
0.897890 + 0.440221i \(0.145100\pi\)
\(390\) 0 0
\(391\) 3719.42 + 6442.22i 0.481072 + 0.833240i
\(392\) 4599.89 2655.75i 0.592678 0.342183i
\(393\) −2944.03 2766.69i −0.377879 0.355117i
\(394\) 7224.43 12513.1i 0.923761 1.60000i
\(395\) 0 0
\(396\) 2493.40 1653.94i 0.316410 0.209882i
\(397\) 13441.4i 1.69926i −0.527382 0.849628i \(-0.676826\pi\)
0.527382 0.849628i \(-0.323174\pi\)
\(398\) −4097.01 2365.41i −0.515991 0.297907i
\(399\) 447.147 + 105.053i 0.0561037 + 0.0131810i
\(400\) 0 0
\(401\) −6537.70 11323.6i −0.814157 1.41016i −0.909931 0.414759i \(-0.863866\pi\)
0.0957739 0.995403i \(-0.469467\pi\)
\(402\) −13950.0 + 4206.08i −1.73075 + 0.521841i
\(403\) −171.586 99.0652i −0.0212092 0.0122451i
\(404\) 518.468 0.0638484
\(405\) 0 0
\(406\) −1506.87 −0.184199
\(407\) 9895.78 + 5713.33i 1.20520 + 0.695821i
\(408\) 8564.10 2582.17i 1.03918 0.313325i
\(409\) −2636.59 4566.71i −0.318756 0.552101i 0.661473 0.749969i \(-0.269932\pi\)
−0.980229 + 0.197868i \(0.936598\pi\)
\(410\) 0 0
\(411\) 3154.63 + 741.151i 0.378604 + 0.0889496i
\(412\) 395.123 + 228.124i 0.0472484 + 0.0272788i
\(413\) 298.266i 0.0355368i
\(414\) 5116.91 3394.18i 0.607446 0.402934i
\(415\) 0 0
\(416\) 2371.06 4106.80i 0.279449 0.484020i
\(417\) 4856.88 + 4564.32i 0.570366 + 0.536009i
\(418\) −5211.91 + 3009.10i −0.609863 + 0.352105i
\(419\) 6923.06 + 11991.1i 0.807192 + 1.39810i 0.914801 + 0.403905i \(0.132347\pi\)
−0.107609 + 0.994193i \(0.534319\pi\)
\(420\) 0 0
\(421\) −548.684 + 950.349i −0.0635184 + 0.110017i −0.896036 0.443982i \(-0.853565\pi\)
0.832517 + 0.553999i \(0.186899\pi\)
\(422\) 7251.94i 0.836538i
\(423\) −12991.5 + 807.637i −1.49330 + 0.0928338i
\(424\) 2734.60 0.313217
\(425\) 0 0
\(426\) 2029.12 + 476.722i 0.230777 + 0.0542189i
\(427\) −615.444 + 355.327i −0.0697504 + 0.0402704i
\(428\) −2099.19 + 1211.97i −0.237075 + 0.136875i
\(429\) 1627.71 + 5398.51i 0.183186 + 0.607558i
\(430\) 0 0
\(431\) 15912.8 1.77841 0.889205 0.457509i \(-0.151258\pi\)
0.889205 + 0.457509i \(0.151258\pi\)
\(432\) −3881.29 10472.3i −0.432266 1.16632i
\(433\) 3566.31i 0.395810i 0.980221 + 0.197905i \(0.0634138\pi\)
−0.980221 + 0.197905i \(0.936586\pi\)
\(434\) 16.4674 28.5223i 0.00182133 0.00315464i
\(435\) 0 0
\(436\) 3390.08 + 5871.79i 0.372375 + 0.644972i
\(437\) −3171.67 + 1831.17i −0.347189 + 0.200450i
\(438\) 734.686 3127.11i 0.0801476 0.341140i
\(439\) −290.411 + 503.007i −0.0315730 + 0.0546861i −0.881380 0.472408i \(-0.843385\pi\)
0.849807 + 0.527094i \(0.176718\pi\)
\(440\) 0 0
\(441\) −8228.06 4092.09i −0.888464 0.441863i
\(442\) 12283.6i 1.32188i
\(443\) 9346.82 + 5396.39i 1.00244 + 0.578759i 0.908969 0.416863i \(-0.136871\pi\)
0.0934706 + 0.995622i \(0.470204\pi\)
\(444\) −4172.67 + 4440.13i −0.446005 + 0.474593i
\(445\) 0 0
\(446\) −4313.40 7471.03i −0.457949 0.793191i
\(447\) 5771.82 + 5424.15i 0.610733 + 0.573945i
\(448\) −215.067 124.169i −0.0226807 0.0130947i
\(449\) −2894.01 −0.304180 −0.152090 0.988367i \(-0.548600\pi\)
−0.152090 + 0.988367i \(0.548600\pi\)
\(450\) 0 0
\(451\) −9573.74 −0.999578
\(452\) −662.203 382.323i −0.0689102 0.0397853i
\(453\) −3758.48 + 15997.6i −0.389821 + 1.65923i
\(454\) 6887.11 + 11928.8i 0.711956 + 1.23314i
\(455\) 0 0
\(456\) 1271.27 + 4216.33i 0.130554 + 0.432999i
\(457\) 2771.21 + 1599.96i 0.283658 + 0.163770i 0.635078 0.772448i \(-0.280968\pi\)
−0.351420 + 0.936218i \(0.614301\pi\)
\(458\) 9246.49i 0.943363i
\(459\) −11913.2 9877.87i −1.21146 1.00449i
\(460\) 0 0
\(461\) −3658.19 + 6336.17i −0.369585 + 0.640141i −0.989501 0.144528i \(-0.953834\pi\)
0.619915 + 0.784669i \(0.287167\pi\)
\(462\) −897.381 + 270.571i −0.0903678 + 0.0272469i
\(463\) 6072.55 3505.99i 0.609536 0.351916i −0.163248 0.986585i \(-0.552197\pi\)
0.772784 + 0.634669i \(0.218864\pi\)
\(464\) −10926.7 18925.6i −1.09323 1.89353i
\(465\) 0 0
\(466\) 8573.53 14849.8i 0.852277 1.47619i
\(467\) 8002.63i 0.792971i 0.918041 + 0.396485i \(0.129770\pi\)
−0.918041 + 0.396485i \(0.870230\pi\)
\(468\) −3000.89 + 186.555i −0.296402 + 0.0184263i
\(469\) 1353.45 0.133255
\(470\) 0 0
\(471\) 8500.00 9044.83i 0.831549 0.884849i
\(472\) 2476.54 1429.83i 0.241509 0.139435i
\(473\) −5731.28 + 3308.95i −0.557134 + 0.321661i
\(474\) 7659.52 8150.47i 0.742222 0.789797i
\(475\) 0 0
\(476\) 605.489 0.0583037
\(477\) −2615.25 3942.63i −0.251035 0.378450i
\(478\) 4979.08i 0.476439i
\(479\) −1589.42 + 2752.96i −0.151613 + 0.262601i −0.931820 0.362920i \(-0.881780\pi\)
0.780208 + 0.625520i \(0.215113\pi\)
\(480\) 0 0
\(481\) −5741.21 9944.06i −0.544234 0.942641i
\(482\) 5150.14 2973.44i 0.486686 0.280988i
\(483\) −546.096 + 164.654i −0.0514456 + 0.0155114i
\(484\) −423.437 + 733.414i −0.0397668 + 0.0688781i
\(485\) 0 0
\(486\) −7527.71 + 10320.5i −0.702601 + 0.963269i
\(487\) 13060.3i 1.21523i −0.794232 0.607615i \(-0.792126\pi\)
0.794232 0.607615i \(-0.207874\pi\)
\(488\) −5900.65 3406.74i −0.547356 0.316016i
\(489\) −3817.19 12660.2i −0.353005 1.17078i
\(490\) 0 0
\(491\) 2200.81 + 3811.91i 0.202283 + 0.350365i 0.949264 0.314481i \(-0.101831\pi\)
−0.746981 + 0.664846i \(0.768497\pi\)
\(492\) 1167.60 4969.75i 0.106991 0.455393i
\(493\) −26224.4 15140.7i −2.39572 1.38317i
\(494\) 6047.56 0.550794
\(495\) 0 0
\(496\) 477.636 0.0432389
\(497\) −167.679 96.8093i −0.0151336 0.00873741i
\(498\) −19085.3 17935.7i −1.71734 1.61389i
\(499\) 9362.60 + 16216.5i 0.839935 + 1.45481i 0.889948 + 0.456062i \(0.150740\pi\)
−0.0500129 + 0.998749i \(0.515926\pi\)
\(500\) 0 0
\(501\) 4891.26 5204.77i 0.436178 0.464136i
\(502\) −4979.90 2875.15i −0.442757 0.255626i
\(503\) 3811.68i 0.337882i −0.985626 0.168941i \(-0.945965\pi\)
0.985626 0.168941i \(-0.0540347\pi\)
\(504\) 42.5553 + 684.536i 0.00376104 + 0.0604993i
\(505\) 0 0
\(506\) 3736.64 6472.06i 0.328289 0.568613i
\(507\) −1315.07 + 5597.47i −0.115196 + 0.490320i
\(508\) 3306.68 1909.11i 0.288799 0.166738i
\(509\) 2247.74 + 3893.20i 0.195735 + 0.339024i 0.947141 0.320816i \(-0.103957\pi\)
−0.751406 + 0.659840i \(0.770624\pi\)
\(510\) 0 0
\(511\) −149.195 + 258.413i −0.0129158 + 0.0223709i
\(512\) 1493.27i 0.128894i
\(513\) 4863.13 5865.16i 0.418543 0.504782i
\(514\) 770.891 0.0661528
\(515\) 0 0
\(516\) −1018.71 3378.67i −0.0869111 0.288251i
\(517\) −13719.9 + 7921.16i −1.16712 + 0.673834i
\(518\) 1652.98 954.347i 0.140208 0.0809490i
\(519\) −11940.2 2805.23i −1.00985 0.237256i
\(520\) 0 0
\(521\) 12095.0 1.01706 0.508531 0.861043i \(-0.330189\pi\)
0.508531 + 0.861043i \(0.330189\pi\)
\(522\) −11130.5 + 22380.4i −0.933274 + 1.87656i
\(523\) 7385.38i 0.617476i 0.951147 + 0.308738i \(0.0999067\pi\)
−0.951147 + 0.308738i \(0.900093\pi\)
\(524\) 1310.98 2270.69i 0.109295 0.189304i
\(525\) 0 0
\(526\) −2173.03 3763.80i −0.180131 0.311995i
\(527\) 573.172 330.921i 0.0473772 0.0273532i
\(528\) −9905.37 9308.70i −0.816431 0.767253i
\(529\) −3809.59 + 6598.40i −0.313108 + 0.542320i
\(530\) 0 0
\(531\) −4429.92 2203.15i −0.362038 0.180054i
\(532\) 298.098i 0.0242936i
\(533\) 8331.56 + 4810.23i 0.677073 + 0.390908i
\(534\) −24517.5 5760.17i −1.98685 0.466792i
\(535\) 0 0
\(536\) 6488.18 + 11237.9i 0.522848 + 0.905600i
\(537\) −6492.83 + 1957.66i −0.521763 + 0.157317i
\(538\) 2844.49 + 1642.27i 0.227946 + 0.131605i
\(539\) −11184.4 −0.893778
\(540\) 0 0
\(541\) −5935.19 −0.471670 −0.235835 0.971793i \(-0.575783\pi\)
−0.235835 + 0.971793i \(0.575783\pi\)
\(542\) 11745.7 + 6781.37i 0.930849 + 0.537426i
\(543\) 15419.5 4649.15i 1.21862 0.367429i
\(544\) 7920.37 + 13718.5i 0.624234 + 1.08120i
\(545\) 0 0
\(546\) 916.892 + 215.416i 0.0718670 + 0.0168845i
\(547\) −8796.41 5078.61i −0.687582 0.396976i 0.115124 0.993351i \(-0.463274\pi\)
−0.802705 + 0.596376i \(0.796607\pi\)
\(548\) 2103.08i 0.163940i
\(549\) 731.413 + 11765.3i 0.0568596 + 0.914632i
\(550\) 0 0
\(551\) 7454.16 12911.0i 0.576330 0.998232i
\(552\) −3985.03 3744.98i −0.307272 0.288763i
\(553\) −899.768 + 519.481i −0.0691899 + 0.0399468i
\(554\) 5697.76 + 9868.81i 0.436958 + 0.756833i
\(555\) 0 0
\(556\) −2162.78 + 3746.05i −0.164968 + 0.285733i
\(557\) 5709.62i 0.434334i −0.976134 0.217167i \(-0.930318\pi\)
0.976134 0.217167i \(-0.0696817\pi\)
\(558\) −301.984 455.258i −0.0229104 0.0345387i
\(559\) 6650.20 0.503173
\(560\) 0 0
\(561\) −18336.0 4307.88i −1.37994 0.324204i
\(562\) 2141.61 1236.46i 0.160744 0.0928058i
\(563\) 11205.6 6469.56i 0.838828 0.484297i −0.0180378 0.999837i \(-0.505742\pi\)
0.856866 + 0.515540i \(0.172409\pi\)
\(564\) −2438.64 8088.06i −0.182066 0.603845i
\(565\) 0 0
\(566\) −23299.2 −1.73028
\(567\) 946.236 716.012i 0.0700850 0.0530330i
\(568\) 1856.34i 0.137131i
\(569\) −3062.71 + 5304.77i −0.225651 + 0.390839i −0.956515 0.291684i \(-0.905784\pi\)
0.730863 + 0.682524i \(0.239118\pi\)
\(570\) 0 0
\(571\) 9641.20 + 16699.0i 0.706605 + 1.22388i 0.966109 + 0.258134i \(0.0831076\pi\)
−0.259504 + 0.965742i \(0.583559\pi\)
\(572\) −3169.13 + 1829.70i −0.231658 + 0.133748i
\(573\) −452.450 + 1925.80i −0.0329867 + 0.140404i
\(574\) −799.592 + 1384.93i −0.0581434 + 0.100707i
\(575\) 0 0
\(576\) −3432.78 + 2277.05i −0.248320 + 0.164717i
\(577\) 4988.14i 0.359894i 0.983676 + 0.179947i \(0.0575927\pi\)
−0.983676 + 0.179947i \(0.942407\pi\)
\(578\) 21187.0 + 12232.3i 1.52468 + 0.880274i
\(579\) 5501.46 5854.09i 0.394876 0.420186i
\(580\) 0 0
\(581\) 1216.43 + 2106.92i 0.0868606 + 0.150447i
\(582\) 11387.1 + 10701.2i 0.811018 + 0.762165i
\(583\) −4986.78 2879.12i −0.354256 0.204530i
\(584\) −2860.85 −0.202710
\(585\) 0 0
\(586\) 15679.4 1.10531
\(587\) −13245.0 7647.00i −0.931311 0.537693i −0.0440852 0.999028i \(-0.514037\pi\)
−0.887226 + 0.461335i \(0.847371\pi\)
\(588\) 1364.03 5805.84i 0.0956661 0.407192i
\(589\) 162.921 + 282.188i 0.0113974 + 0.0197408i
\(590\) 0 0
\(591\) 6426.90 + 21315.6i 0.447322 + 1.48360i
\(592\) 23972.3 + 13840.4i 1.66428 + 0.960874i
\(593\) 11090.9i 0.768040i −0.923325 0.384020i \(-0.874539\pi\)
0.923325 0.384020i \(-0.125461\pi\)
\(594\) −2609.94 + 15326.7i −0.180281 + 1.05869i
\(595\) 0 0
\(596\) −2570.21 + 4451.73i −0.176644 + 0.305956i
\(597\) 6979.10 2104.28i 0.478452 0.144259i
\(598\) −6503.63 + 3754.88i −0.444738 + 0.256770i
\(599\) −14100.8 24423.3i −0.961840 1.66596i −0.717875 0.696172i \(-0.754885\pi\)
−0.243965 0.969784i \(-0.578448\pi\)
\(600\) 0 0
\(601\) −10572.0 + 18311.3i −0.717539 + 1.24281i 0.244433 + 0.969666i \(0.421398\pi\)
−0.961972 + 0.273148i \(0.911935\pi\)
\(602\) 1105.45i 0.0748416i
\(603\) 9997.26 20101.7i 0.675157 1.35755i
\(604\) −10665.0 −0.718467
\(605\) 0 0
\(606\) −1844.93 + 1963.18i −0.123672 + 0.131599i
\(607\) 7620.14 4399.49i 0.509542 0.294184i −0.223103 0.974795i \(-0.571619\pi\)
0.732645 + 0.680611i \(0.238285\pi\)
\(608\) −6753.97 + 3899.41i −0.450509 + 0.260102i
\(609\) 1590.04 1691.96i 0.105799 0.112581i
\(610\) 0 0
\(611\) 15919.6 1.05407
\(612\) 4472.45 8992.87i 0.295406 0.593979i
\(613\) 19539.8i 1.28745i 0.765257 + 0.643724i \(0.222612\pi\)
−0.765257 + 0.643724i \(0.777388\pi\)
\(614\) 12412.4 21498.9i 0.815836 1.41307i
\(615\) 0 0
\(616\) 417.375 + 722.914i 0.0272995 + 0.0472842i
\(617\) 2835.26 1636.94i 0.184997 0.106808i −0.404641 0.914475i \(-0.632604\pi\)
0.589638 + 0.807667i \(0.299270\pi\)
\(618\) −2269.81 + 684.373i −0.147743 + 0.0445462i
\(619\) 4693.24 8128.92i 0.304745 0.527834i −0.672460 0.740134i \(-0.734762\pi\)
0.977205 + 0.212300i \(0.0680954\pi\)
\(620\) 0 0
\(621\) −1588.26 + 9326.96i −0.102632 + 0.602702i
\(622\) 9136.21i 0.588953i
\(623\) 2026.04 + 1169.73i 0.130291 + 0.0752238i
\(624\) 3943.09 + 13077.8i 0.252965 + 0.838989i
\(625\) 0 0
\(626\) −10527.8 18234.7i −0.672165 1.16422i
\(627\) 2120.88 9027.29i 0.135087 0.574984i
\(628\) 6976.15 + 4027.68i 0.443278 + 0.255927i
\(629\) 38356.3 2.43142
\(630\) 0 0
\(631\) 9647.08 0.608628 0.304314 0.952572i \(-0.401573\pi\)
0.304314 + 0.952572i \(0.401573\pi\)
\(632\) −8626.64 4980.59i −0.542958 0.313477i
\(633\) 8142.72 + 7652.23i 0.511286 + 0.480488i
\(634\) −3513.97 6086.37i −0.220122 0.381263i
\(635\) 0 0
\(636\) 2102.74 2237.52i 0.131099 0.139502i
\(637\) 9733.23 + 5619.48i 0.605408 + 0.349532i
\(638\) 30421.6i 1.88778i
\(639\) −2676.40 + 1775.32i −0.165691 + 0.109907i
\(640\) 0 0
\(641\) 3501.88 6065.44i 0.215782 0.373745i −0.737732 0.675093i \(-0.764103\pi\)
0.953514 + 0.301348i \(0.0974367\pi\)
\(642\) 2880.68 12261.3i 0.177089 0.753761i
\(643\) −5446.34 + 3144.44i −0.334032 + 0.192853i −0.657630 0.753341i \(-0.728441\pi\)
0.323598 + 0.946195i \(0.395108\pi\)
\(644\) −185.087 320.579i −0.0113252 0.0196158i
\(645\) 0 0
\(646\) −10100.7 + 17495.0i −0.615183 + 1.06553i
\(647\) 5900.85i 0.358557i 0.983798 + 0.179279i \(0.0573764\pi\)
−0.983798 + 0.179279i \(0.942624\pi\)
\(648\) 10481.2 + 4424.29i 0.635404 + 0.268214i
\(649\) −6021.58 −0.364203
\(650\) 0 0
\(651\) 14.6495 + 48.5868i 0.000881963 + 0.00292514i
\(652\) 7432.02 4290.88i 0.446412 0.257736i
\(653\) −6828.74 + 3942.57i −0.409233 + 0.236271i −0.690460 0.723370i \(-0.742592\pi\)
0.281227 + 0.959641i \(0.409259\pi\)
\(654\) −34296.9 8057.75i −2.05064 0.481778i
\(655\) 0 0
\(656\) −23192.2 −1.38034
\(657\) 2735.98 + 4124.65i 0.162467 + 0.244928i
\(658\) 2646.28i 0.156782i
\(659\) 14378.9 24905.0i 0.849959 1.47217i −0.0312845 0.999511i \(-0.509960\pi\)
0.881244 0.472662i \(-0.156707\pi\)
\(660\) 0 0
\(661\) −4130.11 7153.57i −0.243030 0.420940i 0.718546 0.695479i \(-0.244808\pi\)
−0.961576 + 0.274539i \(0.911475\pi\)
\(662\) −665.509 + 384.232i −0.0390721 + 0.0225583i
\(663\) 13792.5 + 12961.7i 0.807926 + 0.759260i
\(664\) −11662.7 + 20200.4i −0.681626 + 1.18061i
\(665\) 0 0
\(666\) −1964.45 31599.7i −0.114296 1.83853i
\(667\) 18512.9i 1.07470i
\(668\) 4014.37 + 2317.70i 0.232516 + 0.134243i
\(669\) 12940.2 + 3040.18i 0.747828 + 0.175695i
\(670\) 0 0
\(671\) 7173.56 + 12425.0i 0.412716 + 0.714845i
\(672\) −1162.89 + 350.625i −0.0667553 + 0.0201275i
\(673\) −697.118 402.481i −0.0399285 0.0230528i 0.479903 0.877322i \(-0.340672\pi\)
−0.519831 + 0.854269i \(0.674005\pi\)
\(674\) 11524.7 0.658627
\(675\) 0 0
\(676\) −3731.65 −0.212315
\(677\) 1180.63 + 681.636i 0.0670240 + 0.0386963i 0.533137 0.846029i \(-0.321013\pi\)
−0.466114 + 0.884725i \(0.654346\pi\)
\(678\) 3804.07 1146.97i 0.215478 0.0649692i
\(679\) −725.774 1257.08i −0.0410201 0.0710489i
\(680\) 0 0
\(681\) −20661.3 4854.19i −1.16262 0.273147i
\(682\) −575.827 332.454i −0.0323307 0.0186661i
\(683\) 11434.6i 0.640604i −0.947315 0.320302i \(-0.896216\pi\)
0.947315 0.320302i \(-0.103784\pi\)
\(684\) 4427.42 + 2201.91i 0.247495 + 0.123088i
\(685\) 0 0
\(686\) −1875.50 + 3248.46i −0.104383 + 0.180797i
\(687\) −10382.3 9756.87i −0.576576 0.541845i
\(688\) −13883.9 + 8015.86i −0.769358 + 0.444189i
\(689\) 2893.17 + 5011.12i 0.159972 + 0.277080i
\(690\) 0 0
\(691\) 9765.29 16914.0i 0.537611 0.931170i −0.461421 0.887181i \(-0.652660\pi\)
0.999032 0.0439884i \(-0.0140065\pi\)
\(692\) 7960.10i 0.437280i
\(693\) 643.109 1293.11i 0.0352521 0.0708822i
\(694\) 12172.6 0.665799
\(695\) 0 0
\(696\) 21671.0 + 5091.40i 1.18022 + 0.277283i
\(697\) −27831.0 + 16068.3i −1.51245 + 0.873212i
\(698\) 25702.7 14839.4i 1.39378 0.804701i
\(699\) 7627.06 + 25296.1i 0.412706 + 1.36879i
\(700\) 0 0
\(701\) −11041.4 −0.594903 −0.297452 0.954737i \(-0.596137\pi\)
−0.297452 + 0.954737i \(0.596137\pi\)
\(702\) 9972.04 12026.7i 0.536140 0.646609i
\(703\) 18883.8i 1.01311i
\(704\) −2506.80 + 4341.90i −0.134203 + 0.232446i
\(705\) 0 0
\(706\) 14349.9 + 24854.7i 0.764964 + 1.32496i
\(707\) 216.725 125.126i 0.0115287 0.00665608i
\(708\) 734.382 3125.82i 0.0389827 0.165926i
\(709\) 1969.54 3411.34i 0.104327 0.180699i −0.809136 0.587621i \(-0.800065\pi\)
0.913463 + 0.406922i \(0.133398\pi\)
\(710\) 0 0
\(711\) 1069.31 + 17200.7i 0.0564027 + 0.907282i
\(712\) 22430.0i 1.18062i
\(713\) −350.416 202.313i −0.0184056 0.0106265i
\(714\) −2154.59 + 2292.69i −0.112932 + 0.120170i
\(715\) 0 0
\(716\) −2200.60 3811.55i −0.114861 0.198944i
\(717\) 5590.67 + 5253.91i 0.291196 + 0.273655i
\(718\) 12617.5 + 7284.72i 0.655824 + 0.378640i
\(719\) 23298.2 1.20845 0.604225 0.796814i \(-0.293483\pi\)
0.604225 + 0.796814i \(0.293483\pi\)
\(720\) 0 0
\(721\) 220.220 0.0113751
\(722\) 11418.3 + 6592.38i 0.588569 + 0.339810i
\(723\) −2095.75 + 8920.31i −0.107803 + 0.458852i
\(724\) 5226.08 + 9051.83i 0.268267 + 0.464653i
\(725\) 0 0
\(726\) −1270.31 4213.15i −0.0649389 0.215378i
\(727\) −8231.12 4752.24i −0.419911 0.242436i 0.275128 0.961408i \(-0.411280\pi\)
−0.695039 + 0.718972i \(0.744613\pi\)
\(728\) 838.823i 0.0427044i
\(729\) −3645.00 19342.6i −0.185185 0.982704i
\(730\) 0 0
\(731\) −11107.3 + 19238.4i −0.561994 + 0.973402i
\(732\) −7324.70 + 2208.48i −0.369848 + 0.111513i
\(733\) 6340.01 3660.40i 0.319473 0.184448i −0.331685 0.943390i \(-0.607617\pi\)
0.651157 + 0.758943i \(0.274284\pi\)
\(734\) −11129.2 19276.3i −0.559653 0.969348i
\(735\) 0 0
\(736\) 4842.22 8386.96i 0.242509 0.420037i
\(737\) 27324.3i 1.36567i
\(738\) 14663.2 + 22105.6i 0.731381 + 1.10260i
\(739\) 1274.52 0.0634424 0.0317212 0.999497i \(-0.489901\pi\)
0.0317212 + 0.999497i \(0.489901\pi\)
\(740\) 0 0
\(741\) −6381.37 + 6790.39i −0.316363 + 0.336641i
\(742\) −832.986 + 480.925i −0.0412128 + 0.0237942i
\(743\) 1681.09 970.576i 0.0830055 0.0479232i −0.457923 0.888992i \(-0.651406\pi\)
0.540928 + 0.841069i \(0.318073\pi\)
\(744\) −333.196 + 354.553i −0.0164187 + 0.0174711i
\(745\) 0 0
\(746\) 29030.1 1.42476
\(747\) 40277.6 2503.93i 1.97280 0.122642i
\(748\) 12224.0i 0.597531i
\(749\) −584.988 + 1013.23i −0.0285380 + 0.0494293i
\(750\) 0 0
\(751\) −8270.01 14324.1i −0.401834 0.695996i 0.592114 0.805854i \(-0.298294\pi\)
−0.993947 + 0.109858i \(0.964960\pi\)
\(752\) −33236.0 + 19188.8i −1.61169 + 0.930511i
\(753\) 8483.08 2557.75i 0.410545 0.123784i
\(754\) 15285.0 26474.4i 0.738260 1.27870i
\(755\) 0 0
\(756\) 592.826 + 491.545i 0.0285197 + 0.0236472i
\(757\) 21145.7i 1.01526i −0.861575 0.507631i \(-0.830521\pi\)
0.861575 0.507631i \(-0.169479\pi\)
\(758\) −20822.4 12021.8i −0.997764 0.576059i
\(759\) 3324.14 + 11024.9i 0.158970 + 0.527245i
\(760\) 0 0
\(761\) 10067.1 + 17436.7i 0.479543 + 0.830593i 0.999725 0.0234624i \(-0.00746901\pi\)
−0.520181 + 0.854056i \(0.674136\pi\)
\(762\) −4537.69 + 19314.2i −0.215726 + 0.918213i
\(763\) 2834.17 + 1636.31i 0.134474 + 0.0776388i
\(764\) −1283.87 −0.0607968
\(765\) 0 0
\(766\) −19989.1 −0.942865
\(767\) 5240.29 + 3025.48i 0.246696 + 0.142430i
\(768\) −16618.0 15617.0i −0.780795 0.733762i
\(769\) 1097.36 + 1900.68i 0.0514587 + 0.0891291i 0.890607 0.454773i \(-0.150280\pi\)
−0.839149 + 0.543902i \(0.816946\pi\)
\(770\) 0 0
\(771\) −813.442 + 865.581i −0.0379966 + 0.0404321i
\(772\) 4515.18 + 2606.84i 0.210499 + 0.121531i
\(773\) 8327.70i 0.387486i −0.981052 0.193743i \(-0.937937\pi\)
0.981052 0.193743i \(-0.0620628\pi\)
\(774\) 16418.4 + 8165.40i 0.762462 + 0.379198i
\(775\) 0 0
\(776\) 6958.46 12052.4i 0.321900 0.557547i
\(777\) −672.646 + 2863.04i −0.0310567 + 0.132189i
\(778\) −3033.98 + 1751.67i −0.139812 + 0.0807204i
\(779\) −7910.82 13701.9i −0.363844 0.630196i
\(780\) 0 0
\(781\) −1954.45 + 3385.20i −0.0895463 + 0.155099i
\(782\) 25085.8i 1.14715i
\(783\) −13384.5 36113.4i −0.610887 1.64826i
\(784\) −27093.9 −1.23424
\(785\) 0 0
\(786\) 3932.95 + 13044.1i 0.178478 + 0.591944i
\(787\) 16422.7 9481.64i 0.743845 0.429459i −0.0796209 0.996825i \(-0.525371\pi\)
0.823465 + 0.567366i \(0.192038\pi\)
\(788\) −12513.1 + 7224.43i −0.565686 + 0.326599i
\(789\) 6519.10 + 1531.60i 0.294152 + 0.0691084i
\(790\) 0 0
\(791\) −369.076 −0.0165902
\(792\) 13819.8 859.134i 0.620034 0.0385454i
\(793\) 14417.1i 0.645608i
\(794\) −22664.1 + 39255.4i −1.01300 + 1.75456i
\(795\) 0 0
\(796\) 2365.41 + 4097.01i 0.105326 + 0.182430i
\(797\) −29674.5 + 17132.6i −1.31885 + 0.761439i −0.983544 0.180670i \(-0.942173\pi\)
−0.335307 + 0.942109i \(0.608840\pi\)
\(798\) −1128.75 1060.76i −0.0500718 0.0470557i
\(799\) −26589.2 + 46053.9i −1.17730 + 2.03914i
\(800\) 0 0
\(801\) 32338.5 21451.0i 1.42650 0.946233i
\(802\) 44093.9i 1.94141i
\(803\) 5217.00 + 3012.04i 0.229270 + 0.132369i
\(804\) 14184.1 + 3332.42i 0.622181 + 0.146176i
\(805\) 0 0
\(806\) 334.076 + 578.636i 0.0145997 + 0.0252873i
\(807\) −4845.49 + 1460.97i −0.211362 + 0.0637282i
\(808\) 2077.88 + 1199.66i 0.0904696 + 0.0522327i
\(809\) −36425.5 −1.58300 −0.791502 0.611166i \(-0.790701\pi\)
−0.791502 + 0.611166i \(0.790701\pi\)
\(810\) 0 0
\(811\) 45174.0 1.95595 0.977973 0.208732i \(-0.0669335\pi\)
0.977973 + 0.208732i \(0.0669335\pi\)
\(812\) 1304.99 + 753.435i 0.0563991 + 0.0325620i
\(813\) −20008.3 + 6032.74i −0.863128 + 0.260243i
\(814\) −19267.0 33371.3i −0.829615 1.43694i
\(815\) 0 0
\(816\) −44418.5 10435.7i −1.90559 0.447700i
\(817\) −9471.56 5468.41i −0.405591 0.234168i
\(818\) 17782.7i 0.760093i
\(819\) −1209.38 + 802.210i −0.0515984 + 0.0342265i
\(820\) 0 0
\(821\) 3459.65 5992.29i 0.147068 0.254729i −0.783075 0.621928i \(-0.786350\pi\)
0.930143 + 0.367199i \(0.119683\pi\)
\(822\) −7963.34 7483.66i −0.337900 0.317546i
\(823\) −9871.42 + 5699.26i −0.418100 + 0.241390i −0.694264 0.719721i \(-0.744270\pi\)
0.276164 + 0.961110i \(0.410937\pi\)
\(824\) 1055.70 + 1828.52i 0.0446322 + 0.0773052i
\(825\) 0 0
\(826\) −502.919 + 871.080i −0.0211850 + 0.0366934i
\(827\) 34712.0i 1.45956i −0.683683 0.729779i \(-0.739623\pi\)
0.683683 0.729779i \(-0.260377\pi\)
\(828\) −6128.46 + 380.986i −0.257221 + 0.0159906i
\(829\) −2732.97 −0.114500 −0.0572498 0.998360i \(-0.518233\pi\)
−0.0572498 + 0.998360i \(0.518233\pi\)
\(830\) 0 0
\(831\) −17093.3 4015.91i −0.713549 0.167642i
\(832\) 4363.09 2519.03i 0.181806 0.104966i
\(833\) −32513.2 + 18771.5i −1.35236 + 0.780786i
\(834\) −6488.34 21519.4i −0.269392 0.893472i
\(835\) 0 0
\(836\) 6018.19 0.248975
\(837\) 829.831 + 141.310i 0.0342690 + 0.00583557i
\(838\) 46693.0i 1.92480i
\(839\) −4787.89 + 8292.87i −0.197016 + 0.341242i −0.947560 0.319579i \(-0.896458\pi\)
0.750544 + 0.660821i \(0.229792\pi\)
\(840\) 0 0
\(841\) −25485.8 44142.8i −1.04497 1.80995i
\(842\) 3204.85 1850.32i 0.131171 0.0757318i
\(843\) −871.484 + 3709.38i −0.0356056 + 0.151551i
\(844\) −3625.97 + 6280.37i −0.147880 + 0.256136i
\(845\) 0 0
\(846\) 39303.2 + 19546.8i 1.59725 + 0.794364i
\(847\) 408.766i 0.0165825i
\(848\) −12080.4 6974.60i −0.489200 0.282440i
\(849\) 24585.2 26161.1i 0.993832 1.05753i
\(850\) 0 0
\(851\) −11724.8 20307.9i −0.472292 0.818034i
\(852\) −1518.90 1427.41i −0.0610761 0.0573971i
\(853\) −7830.51 4520.95i −0.314316 0.181470i 0.334540 0.942381i \(-0.391419\pi\)
−0.648856 + 0.760911i \(0.724752\pi\)
\(854\) 2396.52 0.0960274
\(855\) 0 0
\(856\) −11217.3 −0.447896
\(857\) −2005.09 1157.64i −0.0799213 0.0461426i 0.459507 0.888174i \(-0.348026\pi\)
−0.539428 + 0.842032i \(0.681360\pi\)
\(858\) 4348.94 18510.8i 0.173043 0.736536i
\(859\) −15701.6 27195.9i −0.623667 1.08022i −0.988797 0.149266i \(-0.952309\pi\)
0.365130 0.930957i \(-0.381025\pi\)
\(860\) 0 0
\(861\) −711.322 2359.19i −0.0281554 0.0933808i
\(862\) −46473.2 26831.3i −1.83629 1.06018i
\(863\) 40883.5i 1.61262i −0.591493 0.806310i \(-0.701461\pi\)
0.591493 0.806310i \(-0.298539\pi\)
\(864\) −3382.15 + 19861.4i −0.133175 + 0.782060i
\(865\) 0 0
\(866\) 6013.30 10415.3i 0.235959 0.408692i
\(867\) −36091.4 + 10882.0i −1.41376 + 0.426264i
\(868\) −28.5223 + 16.4674i −0.00111534 + 0.000643939i
\(869\) 10487.6 + 18165.1i 0.409399 + 0.709100i
\(870\) 0 0
\(871\) −13728.8 + 23779.0i −0.534078 + 0.925051i
\(872\) 31376.7i 1.21852i
\(873\) −24031.4 + 1493.95i −0.931659 + 0.0579182i
\(874\) 12350.4 0.477985
\(875\) 0 0
\(876\) −2199.81 + 2340.81i −0.0848456 + 0.0902840i
\(877\) 24521.2 14157.3i 0.944154 0.545107i 0.0528937 0.998600i \(-0.483156\pi\)
0.891260 + 0.453493i \(0.149822\pi\)
\(878\) 1696.28 979.348i 0.0652013 0.0376440i
\(879\) −16544.8 + 17605.3i −0.634862 + 0.675554i
\(880\) 0 0
\(881\) 6479.51 0.247787 0.123893 0.992296i \(-0.460462\pi\)
0.123893 + 0.992296i \(0.460462\pi\)
\(882\) 17130.1 + 25824.5i 0.653968 + 0.985893i
\(883\) 17769.0i 0.677208i −0.940929 0.338604i \(-0.890045\pi\)
0.940929 0.338604i \(-0.109955\pi\)
\(884\) −6141.82 + 10637.9i −0.233678 + 0.404743i
\(885\) 0 0
\(886\) −18198.1 31520.1i −0.690044 1.19519i
\(887\) 22419.8 12944.1i 0.848684 0.489988i −0.0115224 0.999934i \(-0.503668\pi\)
0.860207 + 0.509945i \(0.170334\pi\)
\(888\) −26996.8 + 8139.83i −1.02022 + 0.307607i
\(889\) 921.481 1596.05i 0.0347643 0.0602136i
\(890\) 0 0
\(891\) −14455.3 19103.2i −0.543514 0.718273i
\(892\) 8626.80i 0.323819i
\(893\) −22673.5 13090.6i −0.849654 0.490548i
\(894\) −7710.62 25573.2i −0.288458 0.956707i
\(895\) 0 0
\(896\) 1353.73 + 2344.73i 0.0504744 + 0.0874242i
\(897\) 2646.52 11264.6i 0.0985115 0.419303i
\(898\) 8451.90 + 4879.71i 0.314080 + 0.181334i
\(899\) 1647.11 0.0611060
\(900\) 0 0
\(901\) −19328.9 −0.714694
\(902\) 27959.9 + 16142.7i 1.03211 + 0.595889i
\(903\) −1241.23 1166.46i −0.0457426 0.0429873i
\(904\) −1769.28 3064.49i −0.0650946 0.112747i
\(905\) 0 0
\(906\) 37950.7 40383.2i 1.39164 1.48084i
\(907\) −39134.2 22594.1i −1.43267 0.827150i −0.435343 0.900265i \(-0.643373\pi\)
−0.997324 + 0.0731143i \(0.976706\pi\)
\(908\) 13774.2i 0.503429i
\(909\) −257.562 4143.09i −0.00939802 0.151175i
\(910\) 0 0
\(911\) −6587.08 + 11409.2i −0.239560 + 0.414931i −0.960588 0.277975i \(-0.910337\pi\)
0.721028 + 0.692906i \(0.243670\pi\)
\(912\) 5137.78 21868.4i 0.186545 0.794007i
\(913\) 42535.8 24558.0i 1.54187 0.890200i
\(914\) −5395.51 9345.29i −0.195260 0.338200i
\(915\) 0 0
\(916\) 4623.24 8007.69i 0.166765 0.288845i
\(917\) 1265.56i 0.0455752i
\(918\) 18136.7 + 48935.4i 0.652069 + 1.75938i
\(919\) 54078.5 1.94112 0.970558 0.240867i \(-0.0774316\pi\)
0.970558 + 0.240867i \(0.0774316\pi\)
\(920\) 0 0
\(921\) 11042.1 + 36622.6i 0.395060 + 1.31027i
\(922\) 21367.3 12336.4i 0.763228 0.440650i
\(923\) 3401.72 1963.98i 0.121310 0.0700383i
\(924\) 912.440 + 214.370i 0.0324860 + 0.00763229i
\(925\) 0 0
\(926\) −23646.4 −0.839166
\(927\) 1626.66 3270.76i 0.0576338 0.115886i
\(928\) 39422.6i 1.39451i
\(929\) −22858.9 + 39592.8i −0.807294 + 1.39827i 0.107438 + 0.994212i \(0.465735\pi\)
−0.914732 + 0.404062i \(0.867598\pi\)
\(930\) 0 0
\(931\) −9241.71 16007.1i −0.325333 0.563493i
\(932\) −14849.8 + 8573.53i −0.521911 + 0.301325i
\(933\) 10258.4 + 9640.50i 0.359963 + 0.338281i
\(934\) 13493.6 23371.5i 0.472722 0.818779i
\(935\) 0 0
\(936\) −12458.4 6195.98i −0.435059 0.216369i
\(937\) 5055.54i 0.176262i 0.996109 + 0.0881309i \(0.0280894\pi\)
−0.996109 + 0.0881309i \(0.971911\pi\)
\(938\) −3952.72 2282.10i −0.137592 0.0794385i
\(939\) 31583.4 + 7420.23i 1.09764 + 0.257881i
\(940\) 0 0
\(941\) −14056.0 24345.7i −0.486942 0.843407i 0.512946 0.858421i \(-0.328554\pi\)
−0.999887 + 0.0150136i \(0.995221\pi\)
\(942\) −40075.0 + 12083.1i −1.38611 + 0.417927i
\(943\) 17014.8 + 9823.52i 0.587571 + 0.339234i
\(944\) −14587.1 −0.502935
\(945\) 0 0
\(946\) 22317.4 0.767022
\(947\) 26085.0 + 15060.2i 0.895090 + 0.516780i 0.875604 0.483030i \(-0.160464\pi\)
0.0194859 + 0.999810i \(0.493797\pi\)
\(948\) −10708.6 + 3228.76i −0.366876 + 0.110617i
\(949\) −3026.74 5242.46i −0.103532 0.179323i
\(950\) 0 0
\(951\) 10541.9 + 2476.73i 0.359458 + 0.0844514i
\(952\) 2426.63 + 1401.02i 0.0826130 + 0.0476967i
\(953\) 19362.7i 0.658154i 0.944303 + 0.329077i \(0.106738\pi\)
−0.944303 + 0.329077i \(0.893262\pi\)
\(954\) 989.946 + 15924.1i 0.0335961 + 0.540420i
\(955\) 0 0
\(956\) −2489.54 + 4312.01i −0.0842233 + 0.145879i
\(957\) −34158.4 32100.8i −1.15380 1.08430i
\(958\) 9283.74 5359.97i 0.313094 0.180765i
\(959\) 507.554 + 879.109i 0.0170905 + 0.0296016i
\(960\) 0 0
\(961\) 14877.5 25768.6i 0.499396 0.864979i
\(962\) 38721.9i 1.29776i
\(963\) 10727.7 + 16172.6i 0.358977 + 0.541179i
\(964\) −5946.87 −0.198689
\(965\) 0 0
\(966\) 1872.49 + 439.925i 0.0623669 + 0.0146525i
\(967\) 26608.2 15362.3i 0.884863 0.510876i 0.0126043 0.999921i \(-0.495988\pi\)
0.872259 + 0.489045i \(0.162654\pi\)
\(968\) −3394.04 + 1959.55i −0.112695 + 0.0650643i
\(969\) −8985.67 29802.1i −0.297896 0.988010i
\(970\) 0 0
\(971\) −49791.0 −1.64559 −0.822796 0.568336i \(-0.807587\pi\)
−0.822796 + 0.568336i \(0.807587\pi\)
\(972\) 11679.5 5173.98i 0.385410 0.170736i
\(973\) 2087.84i 0.0687906i
\(974\) −22021.4 + 38142.3i −0.724448 + 1.25478i
\(975\) 0 0
\(976\) 17377.8 + 30099.2i 0.569927 + 0.987143i
\(977\) 19391.9 11195.9i 0.635008 0.366622i −0.147681 0.989035i \(-0.547181\pi\)
0.782689 + 0.622413i \(0.213847\pi\)
\(978\) −10198.8 + 43410.2i −0.333458 + 1.41933i
\(979\) 23615.3 40903.0i 0.770939 1.33531i
\(980\) 0 0
\(981\) 45237.5 30007.2i 1.47230 0.976611i
\(982\) 14843.5i 0.482357i
\(983\) 21321.0 + 12309.7i 0.691794 + 0.399408i 0.804284 0.594245i \(-0.202549\pi\)
−0.112490 + 0.993653i \(0.535883\pi\)
\(984\) 16178.7 17215.7i 0.524144 0.557741i
\(985\) 0 0
\(986\) 51058.7 + 88436.2i 1.64913 + 2.85637i
\(987\) −2971.33 2792.35i −0.0958242 0.0900521i
\(988\) −5237.34 3023.78i −0.168646 0.0973676i
\(989\) 13581.1 0.436658
\(990\) 0 0
\(991\) 24540.3 0.786629 0.393314 0.919404i \(-0.371328\pi\)
0.393314 + 0.919404i \(0.371328\pi\)
\(992\) −746.199 430.818i −0.0238829 0.0137888i
\(993\) 270.815 1152.70i 0.00865465 0.0368375i
\(994\) 326.468 + 565.460i 0.0104175 + 0.0180436i
\(995\) 0 0
\(996\) 7560.54 + 25075.5i 0.240527 + 0.797737i
\(997\) 39799.1 + 22978.0i 1.26424 + 0.729912i 0.973893 0.227008i \(-0.0728945\pi\)
0.290351 + 0.956920i \(0.406228\pi\)
\(998\) 63146.7i 2.00288i
\(999\) 37554.1 + 31138.2i 1.18935 + 0.986155i
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 225.4.k.a.124.1 8
5.2 odd 4 45.4.e.a.16.2 4
5.3 odd 4 225.4.e.a.151.1 4
5.4 even 2 inner 225.4.k.a.124.4 8
9.4 even 3 inner 225.4.k.a.49.4 8
15.2 even 4 135.4.e.a.46.1 4
45.2 even 12 405.4.a.e.1.2 2
45.4 even 6 inner 225.4.k.a.49.1 8
45.7 odd 12 405.4.a.d.1.1 2
45.13 odd 12 225.4.e.a.76.1 4
45.22 odd 12 45.4.e.a.31.2 yes 4
45.32 even 12 135.4.e.a.91.1 4
45.38 even 12 2025.4.a.j.1.1 2
45.43 odd 12 2025.4.a.l.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.a.16.2 4 5.2 odd 4
45.4.e.a.31.2 yes 4 45.22 odd 12
135.4.e.a.46.1 4 15.2 even 4
135.4.e.a.91.1 4 45.32 even 12
225.4.e.a.76.1 4 45.13 odd 12
225.4.e.a.151.1 4 5.3 odd 4
225.4.k.a.49.1 8 45.4 even 6 inner
225.4.k.a.49.4 8 9.4 even 3 inner
225.4.k.a.124.1 8 1.1 even 1 trivial
225.4.k.a.124.4 8 5.4 even 2 inner
405.4.a.d.1.1 2 45.7 odd 12
405.4.a.e.1.2 2 45.2 even 12
2025.4.a.j.1.1 2 45.38 even 12
2025.4.a.l.1.2 2 45.43 odd 12