Properties

Label 147.4.g.d.80.5
Level $147$
Weight $4$
Character 147.80
Analytic conductor $8.673$
Analytic rank $0$
Dimension $12$
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] = [147,4,Mod(68,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.68");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.g (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: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 80.5
Root \(-2.59957 + 1.49740i\) of defining polynomial
Character \(\chi\) \(=\) 147.80
Dual form 147.4.g.d.68.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.24076 - 1.29370i) q^{2} +(-2.59358 - 4.50260i) q^{3} +(-0.652660 + 1.13044i) q^{4} +(8.05907 + 13.9587i) q^{5} +(-11.6366 - 6.73392i) q^{6} +24.0767i q^{8} +(-13.5467 + 23.3556i) q^{9} +O(q^{10})\) \(q+(2.24076 - 1.29370i) q^{2} +(-2.59358 - 4.50260i) q^{3} +(-0.652660 + 1.13044i) q^{4} +(8.05907 + 13.9587i) q^{5} +(-11.6366 - 6.73392i) q^{6} +24.0767i q^{8} +(-13.5467 + 23.3556i) q^{9} +(36.1169 + 20.8521i) q^{10} +(30.8296 + 17.7995i) q^{11} +(6.78264 + 0.00678109i) q^{12} +7.40831i q^{13} +(41.9486 - 72.4897i) q^{15} +(25.9268 + 44.9065i) q^{16} +(14.4601 - 25.0457i) q^{17} +(-0.139688 + 69.8599i) q^{18} +(-30.4580 + 17.5849i) q^{19} -21.0393 q^{20} +92.1090 q^{22} +(48.0017 - 27.7138i) q^{23} +(108.407 - 62.4446i) q^{24} +(-67.3971 + 116.735i) q^{25} +(9.58416 + 16.6003i) q^{26} +(140.295 + 0.420792i) q^{27} -68.1510i q^{29} +(0.216652 - 216.701i) q^{30} +(154.734 + 89.3356i) q^{31} +(-50.6165 - 29.2234i) q^{32} +(0.184935 - 184.977i) q^{33} -74.8285i q^{34} +(-17.5608 - 30.5571i) q^{36} +(116.838 + 202.370i) q^{37} +(-45.4994 + 78.8072i) q^{38} +(33.3566 - 19.2140i) q^{39} +(-336.079 + 194.035i) q^{40} -370.068 q^{41} -187.068 q^{43} +(-40.2425 + 23.2340i) q^{44} +(-435.189 - 0.870180i) q^{45} +(71.7068 - 124.200i) q^{46} +(87.3726 + 151.334i) q^{47} +(134.953 - 233.206i) q^{48} +348.768i q^{50} +(-150.274 - 0.150240i) q^{51} +(-8.37465 - 4.83511i) q^{52} +(-235.715 - 136.090i) q^{53} +(314.913 - 180.558i) q^{54} +573.789i q^{55} +(158.173 + 91.5321i) q^{57} +(-88.1672 - 152.710i) q^{58} +(48.4354 - 83.8926i) q^{59} +(54.5671 + 94.7315i) q^{60} +(333.882 - 192.767i) q^{61} +462.295 q^{62} -566.055 q^{64} +(-103.411 + 59.7041i) q^{65} +(-238.892 - 414.730i) q^{66} +(509.009 - 881.630i) q^{67} +(18.8751 + 32.6926i) q^{68} +(-249.280 - 144.254i) q^{69} -125.333i q^{71} +(-562.326 - 326.160i) q^{72} +(-195.346 - 112.783i) q^{73} +(523.613 + 302.308i) q^{74} +(700.411 + 0.700251i) q^{75} -45.9079i q^{76} +(49.8870 - 86.2076i) q^{78} +(532.154 + 921.718i) q^{79} +(-417.891 + 723.809i) q^{80} +(-361.972 - 632.785i) q^{81} +(-829.234 + 478.758i) q^{82} +601.040 q^{83} +466.140 q^{85} +(-419.175 + 242.011i) q^{86} +(-306.856 + 176.755i) q^{87} +(-428.552 + 742.274i) q^{88} +(-752.606 - 1303.55i) q^{89} +(-976.280 + 561.055i) q^{90} +72.3506i q^{92} +(0.928190 - 928.402i) q^{93} +(391.562 + 226.069i) q^{94} +(-490.926 - 283.436i) q^{95} +(-0.303630 + 303.699i) q^{96} -327.463i q^{97} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9} - 30 q^{10} + 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} - 300 q^{19} - 268 q^{22} - 414 q^{24} - 42 q^{25} - 822 q^{30} + 930 q^{31} + 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} - 2298 q^{40} - 1012 q^{43} - 2367 q^{45} + 608 q^{46} - 1341 q^{51} + 3000 q^{52} + 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} - 2358 q^{61} - 548 q^{64} - 2934 q^{66} + 792 q^{67} - 2712 q^{72} + 2904 q^{73} + 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} - 5040 q^{82} + 348 q^{85} - 1638 q^{87} - 554 q^{88} - 1479 q^{93} + 1356 q^{94} + 4410 q^{96} - 3354 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24076 1.29370i 0.792229 0.457393i −0.0485179 0.998822i \(-0.515450\pi\)
0.840747 + 0.541429i \(0.182116\pi\)
\(3\) −2.59358 4.50260i −0.499134 0.866525i
\(4\) −0.652660 + 1.13044i −0.0815825 + 0.141305i
\(5\) 8.05907 + 13.9587i 0.720825 + 1.24851i 0.960670 + 0.277694i \(0.0895701\pi\)
−0.239845 + 0.970811i \(0.577097\pi\)
\(6\) −11.6366 6.73392i −0.791771 0.458185i
\(7\) 0 0
\(8\) 24.0767i 1.06405i
\(9\) −13.5467 + 23.3556i −0.501731 + 0.865024i
\(10\) 36.1169 + 20.8521i 1.14212 + 0.659401i
\(11\) 30.8296 + 17.7995i 0.845043 + 0.487886i 0.858975 0.512017i \(-0.171102\pi\)
−0.0139322 + 0.999903i \(0.504435\pi\)
\(12\) 6.78264 + 0.00678109i 0.163165 + 0.000163128i
\(13\) 7.40831i 0.158054i 0.996872 + 0.0790268i \(0.0251813\pi\)
−0.996872 + 0.0790268i \(0.974819\pi\)
\(14\) 0 0
\(15\) 41.9486 72.4897i 0.722073 1.24778i
\(16\) 25.9268 + 44.9065i 0.405106 + 0.701664i
\(17\) 14.4601 25.0457i 0.206300 0.357322i −0.744246 0.667905i \(-0.767191\pi\)
0.950546 + 0.310584i \(0.100524\pi\)
\(18\) −0.139688 + 69.8599i −0.00182915 + 0.914785i
\(19\) −30.4580 + 17.5849i −0.367765 + 0.212329i −0.672482 0.740114i \(-0.734772\pi\)
0.304716 + 0.952443i \(0.401438\pi\)
\(20\) −21.0393 −0.235227
\(21\) 0 0
\(22\) 92.1090 0.892623
\(23\) 48.0017 27.7138i 0.435175 0.251249i −0.266374 0.963870i \(-0.585825\pi\)
0.701549 + 0.712621i \(0.252492\pi\)
\(24\) 108.407 62.4446i 0.922024 0.531102i
\(25\) −67.3971 + 116.735i −0.539177 + 0.933881i
\(26\) 9.58416 + 16.6003i 0.0722927 + 0.125215i
\(27\) 140.295 + 0.420792i 0.999996 + 0.00299931i
\(28\) 0 0
\(29\) 68.1510i 0.436390i −0.975905 0.218195i \(-0.929983\pi\)
0.975905 0.218195i \(-0.0700169\pi\)
\(30\) 0.216652 216.701i 0.00131850 1.31880i
\(31\) 154.734 + 89.3356i 0.896484 + 0.517585i 0.876058 0.482206i \(-0.160164\pi\)
0.0204262 + 0.999791i \(0.493498\pi\)
\(32\) −50.6165 29.2234i −0.279619 0.161438i
\(33\) 0.184935 184.977i 0.000975549 0.975771i
\(34\) 74.8285i 0.377440i
\(35\) 0 0
\(36\) −17.5608 30.5571i −0.0812998 0.141468i
\(37\) 116.838 + 202.370i 0.519137 + 0.899172i 0.999753 + 0.0222405i \(0.00707996\pi\)
−0.480615 + 0.876931i \(0.659587\pi\)
\(38\) −45.4994 + 78.8072i −0.194236 + 0.336427i
\(39\) 33.3566 19.2140i 0.136957 0.0788899i
\(40\) −336.079 + 194.035i −1.32847 + 0.766992i
\(41\) −370.068 −1.40963 −0.704816 0.709390i \(-0.748970\pi\)
−0.704816 + 0.709390i \(0.748970\pi\)
\(42\) 0 0
\(43\) −187.068 −0.663432 −0.331716 0.943379i \(-0.607628\pi\)
−0.331716 + 0.943379i \(0.607628\pi\)
\(44\) −40.2425 + 23.2340i −0.137881 + 0.0796059i
\(45\) −435.189 0.870180i −1.44165 0.00288264i
\(46\) 71.7068 124.200i 0.229839 0.398093i
\(47\) 87.3726 + 151.334i 0.271162 + 0.469666i 0.969160 0.246434i \(-0.0792588\pi\)
−0.697998 + 0.716100i \(0.745925\pi\)
\(48\) 134.953 233.206i 0.405807 0.701259i
\(49\) 0 0
\(50\) 348.768i 0.986464i
\(51\) −150.274 0.150240i −0.412599 0.000412505i
\(52\) −8.37465 4.83511i −0.0223338 0.0128944i
\(53\) −235.715 136.090i −0.610905 0.352706i 0.162415 0.986723i \(-0.448072\pi\)
−0.773319 + 0.634017i \(0.781405\pi\)
\(54\) 314.913 180.558i 0.793597 0.455015i
\(55\) 573.789i 1.40672i
\(56\) 0 0
\(57\) 158.173 + 91.5321i 0.367553 + 0.212697i
\(58\) −88.1672 152.710i −0.199602 0.345721i
\(59\) 48.4354 83.8926i 0.106877 0.185117i −0.807626 0.589695i \(-0.799248\pi\)
0.914504 + 0.404578i \(0.132581\pi\)
\(60\) 54.5671 + 94.7315i 0.117410 + 0.203830i
\(61\) 333.882 192.767i 0.700807 0.404611i −0.106841 0.994276i \(-0.534073\pi\)
0.807648 + 0.589665i \(0.200740\pi\)
\(62\) 462.295 0.946960
\(63\) 0 0
\(64\) −566.055 −1.10558
\(65\) −103.411 + 59.7041i −0.197331 + 0.113929i
\(66\) −238.892 414.730i −0.445538 0.773480i
\(67\) 509.009 881.630i 0.928140 1.60759i 0.141708 0.989908i \(-0.454741\pi\)
0.786432 0.617677i \(-0.211926\pi\)
\(68\) 18.8751 + 32.6926i 0.0336609 + 0.0583023i
\(69\) −249.280 144.254i −0.434924 0.251684i
\(70\) 0 0
\(71\) 125.333i 0.209497i −0.994499 0.104749i \(-0.966596\pi\)
0.994499 0.104749i \(-0.0334038\pi\)
\(72\) −562.326 326.160i −0.920427 0.533866i
\(73\) −195.346 112.783i −0.313199 0.180825i 0.335158 0.942162i \(-0.391210\pi\)
−0.648357 + 0.761337i \(0.724544\pi\)
\(74\) 523.613 + 302.308i 0.822551 + 0.474900i
\(75\) 700.411 + 0.700251i 1.07835 + 0.00107811i
\(76\) 45.9079i 0.0692894i
\(77\) 0 0
\(78\) 49.8870 86.2076i 0.0724178 0.125142i
\(79\) 532.154 + 921.718i 0.757874 + 1.31268i 0.943933 + 0.330138i \(0.107095\pi\)
−0.186059 + 0.982539i \(0.559572\pi\)
\(80\) −417.891 + 723.809i −0.584021 + 1.01155i
\(81\) −361.972 632.785i −0.496533 0.868018i
\(82\) −829.234 + 478.758i −1.11675 + 0.644756i
\(83\) 601.040 0.794852 0.397426 0.917634i \(-0.369904\pi\)
0.397426 + 0.917634i \(0.369904\pi\)
\(84\) 0 0
\(85\) 466.140 0.594824
\(86\) −419.175 + 242.011i −0.525590 + 0.303450i
\(87\) −306.856 + 176.755i −0.378143 + 0.217817i
\(88\) −428.552 + 742.274i −0.519134 + 0.899166i
\(89\) −752.606 1303.55i −0.896360 1.55254i −0.832112 0.554607i \(-0.812869\pi\)
−0.0642474 0.997934i \(-0.520465\pi\)
\(90\) −976.280 + 561.055i −1.14343 + 0.657116i
\(91\) 0 0
\(92\) 72.3506i 0.0819900i
\(93\) 0.928190 928.402i 0.00103493 1.03517i
\(94\) 391.562 + 226.069i 0.429645 + 0.248055i
\(95\) −490.926 283.436i −0.530189 0.306105i
\(96\) −0.303630 + 303.699i −0.000322803 + 0.322876i
\(97\) 327.463i 0.342771i −0.985204 0.171386i \(-0.945176\pi\)
0.985204 0.171386i \(-0.0548244\pi\)
\(98\) 0 0
\(99\) −833.358 + 478.920i −0.846017 + 0.486195i
\(100\) −87.9747 152.377i −0.0879747 0.152377i
\(101\) 547.845 948.895i 0.539729 0.934837i −0.459190 0.888338i \(-0.651860\pi\)
0.998918 0.0464990i \(-0.0148064\pi\)
\(102\) −336.922 + 194.073i −0.327062 + 0.188393i
\(103\) −179.848 + 103.835i −0.172048 + 0.0993318i −0.583551 0.812076i \(-0.698337\pi\)
0.411503 + 0.911408i \(0.365004\pi\)
\(104\) −178.367 −0.168177
\(105\) 0 0
\(106\) −704.242 −0.645302
\(107\) 1561.25 901.391i 1.41058 0.814399i 0.415138 0.909759i \(-0.363733\pi\)
0.995443 + 0.0953593i \(0.0304000\pi\)
\(108\) −92.0409 + 158.321i −0.0820059 + 0.141060i
\(109\) −141.825 + 245.647i −0.124627 + 0.215860i −0.921587 0.388172i \(-0.873107\pi\)
0.796960 + 0.604032i \(0.206440\pi\)
\(110\) 742.313 + 1285.72i 0.643425 + 1.11444i
\(111\) 608.160 1050.94i 0.520036 0.898652i
\(112\) 0 0
\(113\) 1037.39i 0.863627i −0.901963 0.431814i \(-0.857874\pi\)
0.901963 0.431814i \(-0.142126\pi\)
\(114\) 472.843 + 0.472735i 0.388472 + 0.000388383i
\(115\) 773.697 + 446.694i 0.627371 + 0.362213i
\(116\) 77.0406 + 44.4794i 0.0616641 + 0.0356018i
\(117\) −173.026 100.358i −0.136720 0.0793003i
\(118\) 250.644i 0.195540i
\(119\) 0 0
\(120\) 1745.31 + 1009.98i 1.32770 + 0.768320i
\(121\) −31.8573 55.1785i −0.0239349 0.0414564i
\(122\) 498.767 863.890i 0.370133 0.641090i
\(123\) 959.799 + 1666.27i 0.703595 + 1.22148i
\(124\) −201.977 + 116.611i −0.146275 + 0.0844518i
\(125\) −157.864 −0.112958
\(126\) 0 0
\(127\) 1645.81 1.14994 0.574968 0.818176i \(-0.305015\pi\)
0.574968 + 0.818176i \(0.305015\pi\)
\(128\) −863.461 + 498.520i −0.596249 + 0.344245i
\(129\) 485.175 + 842.291i 0.331142 + 0.574881i
\(130\) −154.479 + 267.565i −0.104221 + 0.180516i
\(131\) −314.185 544.184i −0.209545 0.362943i 0.742026 0.670371i \(-0.233865\pi\)
−0.951571 + 0.307428i \(0.900532\pi\)
\(132\) 208.985 + 120.936i 0.137802 + 0.0797437i
\(133\) 0 0
\(134\) 2634.03i 1.69810i
\(135\) 1124.78 + 1961.74i 0.717077 + 1.25066i
\(136\) 603.016 + 348.151i 0.380207 + 0.219513i
\(137\) 432.079 + 249.461i 0.269453 + 0.155569i 0.628639 0.777697i \(-0.283612\pi\)
−0.359186 + 0.933266i \(0.616946\pi\)
\(138\) −745.199 0.745029i −0.459678 0.000459573i
\(139\) 1216.65i 0.742410i 0.928551 + 0.371205i \(0.121055\pi\)
−0.928551 + 0.371205i \(0.878945\pi\)
\(140\) 0 0
\(141\) 454.788 785.900i 0.271631 0.469395i
\(142\) −162.144 280.841i −0.0958226 0.165970i
\(143\) −131.864 + 228.395i −0.0771121 + 0.133562i
\(144\) −1400.04 2.79945i −0.810211 0.00162005i
\(145\) 951.300 549.233i 0.544835 0.314561i
\(146\) −583.631 −0.330833
\(147\) 0 0
\(148\) −305.022 −0.169410
\(149\) −2010.18 + 1160.58i −1.10524 + 0.638111i −0.937592 0.347736i \(-0.886950\pi\)
−0.167648 + 0.985847i \(0.553617\pi\)
\(150\) 1570.36 904.555i 0.854795 0.492377i
\(151\) −488.726 + 846.497i −0.263390 + 0.456205i −0.967141 0.254242i \(-0.918174\pi\)
0.703750 + 0.710447i \(0.251507\pi\)
\(152\) −423.386 733.326i −0.225929 0.391320i
\(153\) 389.070 + 677.012i 0.205585 + 0.357733i
\(154\) 0 0
\(155\) 2879.85i 1.49235i
\(156\) −0.0502364 + 50.2479i −2.57829e−5 + 0.0257888i
\(157\) 143.752 + 82.9950i 0.0730740 + 0.0421893i 0.536092 0.844160i \(-0.319900\pi\)
−0.463018 + 0.886349i \(0.653233\pi\)
\(158\) 2384.86 + 1376.90i 1.20082 + 0.693293i
\(159\) −1.41397 + 1414.29i −0.000705251 + 0.705412i
\(160\) 942.055i 0.465475i
\(161\) 0 0
\(162\) −1629.73 949.635i −0.790393 0.460558i
\(163\) −488.511 846.127i −0.234743 0.406587i 0.724455 0.689322i \(-0.242092\pi\)
−0.959198 + 0.282735i \(0.908758\pi\)
\(164\) 241.528 418.340i 0.115001 0.199188i
\(165\) 2583.54 1488.16i 1.21896 0.702142i
\(166\) 1346.79 777.568i 0.629704 0.363560i
\(167\) −1.00709 −0.000466651 −0.000233326 1.00000i \(-0.500074\pi\)
−0.000233326 1.00000i \(0.500074\pi\)
\(168\) 0 0
\(169\) 2142.12 0.975019
\(170\) 1044.51 603.048i 0.471236 0.272068i
\(171\) 1.89874 949.584i 0.000849123 0.424658i
\(172\) 122.092 211.469i 0.0541245 0.0937463i
\(173\) 1978.27 + 3426.47i 0.869395 + 1.50584i 0.862616 + 0.505860i \(0.168825\pi\)
0.00677983 + 0.999977i \(0.497842\pi\)
\(174\) −458.923 + 793.046i −0.199948 + 0.345521i
\(175\) 0 0
\(176\) 1845.93i 0.790582i
\(177\) −503.356 0.503241i −0.213754 0.000213706i
\(178\) −3372.82 1947.30i −1.42024 0.819978i
\(179\) −2423.54 1399.23i −1.01198 0.584266i −0.100208 0.994967i \(-0.531951\pi\)
−0.911770 + 0.410701i \(0.865284\pi\)
\(180\) 285.014 491.387i 0.118020 0.203477i
\(181\) 1506.74i 0.618758i −0.950939 0.309379i \(-0.899879\pi\)
0.950939 0.309379i \(-0.100121\pi\)
\(182\) 0 0
\(183\) −1733.90 1003.38i −0.700403 0.405312i
\(184\) 667.255 + 1155.72i 0.267341 + 0.463048i
\(185\) −1883.21 + 3261.82i −0.748414 + 1.29629i
\(186\) −1199.00 2081.53i −0.472660 0.820565i
\(187\) 891.599 514.765i 0.348664 0.201301i
\(188\) −228.098 −0.0884882
\(189\) 0 0
\(190\) −1466.73 −0.560041
\(191\) 3184.51 1838.58i 1.20640 0.696518i 0.244433 0.969666i \(-0.421398\pi\)
0.961972 + 0.273148i \(0.0880650\pi\)
\(192\) 1468.11 + 2548.71i 0.551830 + 0.958009i
\(193\) 64.7335 112.122i 0.0241431 0.0418171i −0.853701 0.520763i \(-0.825648\pi\)
0.877845 + 0.478946i \(0.158981\pi\)
\(194\) −423.640 733.766i −0.156781 0.271553i
\(195\) 537.026 + 310.769i 0.197217 + 0.114126i
\(196\) 0 0
\(197\) 3044.81i 1.10119i 0.834774 + 0.550593i \(0.185598\pi\)
−0.834774 + 0.550593i \(0.814402\pi\)
\(198\) −1247.78 + 2151.27i −0.447856 + 0.772140i
\(199\) −3458.29 1996.64i −1.23192 0.711248i −0.264488 0.964389i \(-0.585203\pi\)
−0.967429 + 0.253141i \(0.918536\pi\)
\(200\) −2810.59 1622.70i −0.993695 0.573710i
\(201\) −5289.78 5.28857i −1.85628 0.00185586i
\(202\) 2835.00i 0.987473i
\(203\) 0 0
\(204\) 98.2476 169.778i 0.0337191 0.0582687i
\(205\) −2982.40 5165.67i −1.01610 1.75993i
\(206\) −268.664 + 465.339i −0.0908674 + 0.157387i
\(207\) −2.99240 + 1496.54i −0.00100476 + 0.502496i
\(208\) −332.682 + 192.074i −0.110901 + 0.0640285i
\(209\) −1252.01 −0.414370
\(210\) 0 0
\(211\) −4383.67 −1.43026 −0.715129 0.698992i \(-0.753632\pi\)
−0.715129 + 0.698992i \(0.753632\pi\)
\(212\) 307.683 177.641i 0.0996783 0.0575493i
\(213\) −564.324 + 325.061i −0.181534 + 0.104567i
\(214\) 2332.27 4039.60i 0.745002 1.29038i
\(215\) −1507.59 2611.23i −0.478219 0.828299i
\(216\) −10.1313 + 3377.85i −0.00319141 + 1.06404i
\(217\) 0 0
\(218\) 733.916i 0.228014i
\(219\) −1.17181 + 1172.07i −0.000361568 + 0.361650i
\(220\) −648.634 374.489i −0.198777 0.114764i
\(221\) 185.546 + 107.125i 0.0564759 + 0.0326064i
\(222\) 3.14096 3141.68i 0.000949583 0.949799i
\(223\) 4851.53i 1.45687i 0.685114 + 0.728436i \(0.259753\pi\)
−0.685114 + 0.728436i \(0.740247\pi\)
\(224\) 0 0
\(225\) −1813.42 3155.48i −0.537308 0.934958i
\(226\) −1342.08 2324.55i −0.395017 0.684190i
\(227\) 1184.05 2050.83i 0.346203 0.599642i −0.639368 0.768901i \(-0.720804\pi\)
0.985572 + 0.169259i \(0.0541374\pi\)
\(228\) −206.705 + 119.066i −0.0600410 + 0.0345847i
\(229\) 3737.27 2157.72i 1.07845 0.622646i 0.147975 0.988991i \(-0.452724\pi\)
0.930479 + 0.366345i \(0.119391\pi\)
\(230\) 2311.56 0.662695
\(231\) 0 0
\(232\) 1640.85 0.464340
\(233\) −4826.98 + 2786.86i −1.35719 + 0.783576i −0.989245 0.146270i \(-0.953273\pi\)
−0.367949 + 0.929846i \(0.619940\pi\)
\(234\) −517.544 1.03485i −0.144585 0.000289104i
\(235\) −1408.28 + 2439.22i −0.390920 + 0.677094i
\(236\) 63.2237 + 109.507i 0.0174386 + 0.0302046i
\(237\) 2769.94 4786.62i 0.759186 1.31192i
\(238\) 0 0
\(239\) 4683.70i 1.26763i −0.773485 0.633814i \(-0.781488\pi\)
0.773485 0.633814i \(-0.218512\pi\)
\(240\) 4342.85 + 4.34186i 1.16804 + 0.00116778i
\(241\) 1896.77 + 1095.10i 0.506977 + 0.292703i 0.731590 0.681745i \(-0.238778\pi\)
−0.224613 + 0.974448i \(0.572112\pi\)
\(242\) −142.769 82.4279i −0.0379238 0.0218953i
\(243\) −1910.37 + 3270.99i −0.504323 + 0.863515i
\(244\) 503.245i 0.132037i
\(245\) 0 0
\(246\) 4306.34 + 2492.01i 1.11611 + 0.645872i
\(247\) −130.275 225.642i −0.0335594 0.0581266i
\(248\) −2150.90 + 3725.47i −0.550736 + 0.953902i
\(249\) −1558.84 2706.24i −0.396738 0.688759i
\(250\) −353.735 + 204.229i −0.0894887 + 0.0516663i
\(251\) −2240.70 −0.563473 −0.281736 0.959492i \(-0.590910\pi\)
−0.281736 + 0.959492i \(0.590910\pi\)
\(252\) 0 0
\(253\) 1973.16 0.490323
\(254\) 3687.86 2129.19i 0.911012 0.525973i
\(255\) −1208.97 2098.84i −0.296897 0.515429i
\(256\) 974.345 1687.61i 0.237877 0.412015i
\(257\) 555.785 + 962.648i 0.134898 + 0.233651i 0.925559 0.378604i \(-0.123596\pi\)
−0.790660 + 0.612255i \(0.790263\pi\)
\(258\) 2176.84 + 1259.70i 0.525287 + 0.303975i
\(259\) 0 0
\(260\) 155.866i 0.0371784i
\(261\) 1591.71 + 923.223i 0.377488 + 0.218950i
\(262\) −1408.03 812.924i −0.332016 0.191689i
\(263\) 1782.86 + 1029.34i 0.418007 + 0.241337i 0.694224 0.719759i \(-0.255748\pi\)
−0.276217 + 0.961095i \(0.589081\pi\)
\(264\) 4453.64 + 4.45262i 1.03827 + 0.00103803i
\(265\) 4387.04i 1.01696i
\(266\) 0 0
\(267\) −3917.42 + 6769.54i −0.897912 + 1.55164i
\(268\) 664.420 + 1150.81i 0.151440 + 0.262302i
\(269\) 2414.62 4182.24i 0.547294 0.947940i −0.451165 0.892441i \(-0.648991\pi\)
0.998459 0.0554999i \(-0.0176752\pi\)
\(270\) 5058.26 + 2940.65i 1.14013 + 0.662824i
\(271\) 191.772 110.720i 0.0429865 0.0248183i −0.478353 0.878168i \(-0.658766\pi\)
0.521339 + 0.853350i \(0.325433\pi\)
\(272\) 1499.62 0.334293
\(273\) 0 0
\(274\) 1290.91 0.284624
\(275\) −4155.65 + 2399.27i −0.911255 + 0.526113i
\(276\) 325.766 187.647i 0.0710463 0.0409240i
\(277\) −1233.58 + 2136.62i −0.267576 + 0.463455i −0.968235 0.250041i \(-0.919556\pi\)
0.700660 + 0.713496i \(0.252889\pi\)
\(278\) 1573.99 + 2726.22i 0.339573 + 0.588158i
\(279\) −4182.63 + 2403.70i −0.897517 + 0.515792i
\(280\) 0 0
\(281\) 4174.76i 0.886282i −0.896452 0.443141i \(-0.853864\pi\)
0.896452 0.443141i \(-0.146136\pi\)
\(282\) 2.34884 2349.37i 0.000495997 0.496111i
\(283\) 5628.39 + 3249.55i 1.18224 + 0.682565i 0.956531 0.291630i \(-0.0941977\pi\)
0.225706 + 0.974195i \(0.427531\pi\)
\(284\) 141.681 + 81.7998i 0.0296030 + 0.0170913i
\(285\) −2.94488 + 2945.55i −0.000612069 + 0.612209i
\(286\) 682.372i 0.141082i
\(287\) 0 0
\(288\) 1368.22 786.299i 0.279942 0.160879i
\(289\) 2038.31 + 3530.46i 0.414881 + 0.718595i
\(290\) 1421.09 2461.40i 0.287756 0.498408i
\(291\) −1474.43 + 849.300i −0.297020 + 0.171089i
\(292\) 254.989 147.218i 0.0511030 0.0295043i
\(293\) −5637.32 −1.12401 −0.562007 0.827133i \(-0.689970\pi\)
−0.562007 + 0.827133i \(0.689970\pi\)
\(294\) 0 0
\(295\) 1561.38 0.308159
\(296\) −4872.38 + 2813.07i −0.956762 + 0.552387i
\(297\) 4317.76 + 2510.16i 0.843576 + 0.490418i
\(298\) −3002.90 + 5201.17i −0.583735 + 1.01106i
\(299\) 205.312 + 355.611i 0.0397108 + 0.0687810i
\(300\) −457.922 + 791.315i −0.0881270 + 0.152289i
\(301\) 0 0
\(302\) 2529.06i 0.481892i
\(303\) −5693.37 5.69207i −1.07946 0.00107921i
\(304\) −1579.36 911.841i −0.297968 0.172032i
\(305\) 5381.56 + 3107.05i 1.01032 + 0.583308i
\(306\) 1747.67 + 1013.68i 0.326495 + 0.189373i
\(307\) 3442.95i 0.640064i 0.947407 + 0.320032i \(0.103694\pi\)
−0.947407 + 0.320032i \(0.896306\pi\)
\(308\) 0 0
\(309\) 933.976 + 540.477i 0.171948 + 0.0995037i
\(310\) 3725.67 + 6453.05i 0.682593 + 1.18228i
\(311\) 75.7324 131.172i 0.0138083 0.0239167i −0.859039 0.511911i \(-0.828938\pi\)
0.872847 + 0.487994i \(0.162271\pi\)
\(312\) 462.609 + 803.116i 0.0839426 + 0.145729i
\(313\) −8335.31 + 4812.40i −1.50524 + 0.869050i −0.505257 + 0.862969i \(0.668602\pi\)
−0.999982 + 0.00608123i \(0.998064\pi\)
\(314\) 429.484 0.0771885
\(315\) 0 0
\(316\) −1389.26 −0.247317
\(317\) 7866.93 4541.98i 1.39385 0.804741i 0.400112 0.916466i \(-0.368971\pi\)
0.993739 + 0.111726i \(0.0356377\pi\)
\(318\) 1826.50 + 3170.91i 0.322092 + 0.559170i
\(319\) 1213.05 2101.07i 0.212909 0.368768i
\(320\) −4561.87 7901.39i −0.796926 1.38032i
\(321\) −8107.83 4691.87i −1.40977 0.815809i
\(322\) 0 0
\(323\) 1017.12i 0.175214i
\(324\) 951.570 + 3.80543i 0.163164 + 0.000652509i
\(325\) −864.811 499.299i −0.147603 0.0852188i
\(326\) −2189.27 1263.98i −0.371941 0.214740i
\(327\) 1473.88 + 1.47355i 0.249254 + 0.000249197i
\(328\) 8910.00i 1.49992i
\(329\) 0 0
\(330\) 3863.85 6676.95i 0.644539 1.11380i
\(331\) 702.788 + 1217.26i 0.116703 + 0.202136i 0.918459 0.395516i \(-0.129434\pi\)
−0.801756 + 0.597651i \(0.796101\pi\)
\(332\) −392.275 + 679.440i −0.0648460 + 0.112317i
\(333\) −6309.25 12.6156i −1.03827 0.00207607i
\(334\) −2.25664 + 1.30287i −0.000369695 + 0.000213443i
\(335\) 16408.6 2.67611
\(336\) 0 0
\(337\) 7983.35 1.29045 0.645223 0.763994i \(-0.276764\pi\)
0.645223 + 0.763994i \(0.276764\pi\)
\(338\) 4799.97 2771.27i 0.772438 0.445967i
\(339\) −4670.97 + 2690.56i −0.748354 + 0.431066i
\(340\) −304.231 + 526.944i −0.0485272 + 0.0840516i
\(341\) 3180.25 + 5508.36i 0.505045 + 0.874764i
\(342\) −1224.23 2130.25i −0.193563 0.336815i
\(343\) 0 0
\(344\) 4503.97i 0.705924i
\(345\) 4.64112 4642.18i 0.000724260 0.724425i
\(346\) 8865.68 + 5118.60i 1.37752 + 0.795312i
\(347\) 2268.41 + 1309.67i 0.350935 + 0.202612i 0.665097 0.746757i \(-0.268390\pi\)
−0.314162 + 0.949369i \(0.601724\pi\)
\(348\) 0.462138 462.243i 7.11873e−5 0.0712036i
\(349\) 6032.33i 0.925224i 0.886561 + 0.462612i \(0.153088\pi\)
−0.886561 + 0.462612i \(0.846912\pi\)
\(350\) 0 0
\(351\) −3.11736 + 1039.35i −0.000474052 + 0.158053i
\(352\) −1040.32 1801.89i −0.157527 0.272845i
\(353\) 2658.15 4604.06i 0.400791 0.694190i −0.593031 0.805180i \(-0.702069\pi\)
0.993822 + 0.110990i \(0.0354020\pi\)
\(354\) −1128.55 + 650.066i −0.169440 + 0.0976005i
\(355\) 1749.49 1010.07i 0.261558 0.151011i
\(356\) 1964.78 0.292509
\(357\) 0 0
\(358\) −7240.77 −1.06896
\(359\) 1612.51 930.982i 0.237061 0.136867i −0.376764 0.926309i \(-0.622963\pi\)
0.613825 + 0.789442i \(0.289630\pi\)
\(360\) 20.9510 10477.9i 0.00306727 1.53398i
\(361\) −2811.04 + 4868.87i −0.409832 + 0.709851i
\(362\) −1949.28 3376.25i −0.283016 0.490198i
\(363\) −165.822 + 286.550i −0.0239763 + 0.0414325i
\(364\) 0 0
\(365\) 3635.70i 0.521373i
\(366\) −5183.34 5.18215i −0.740266 0.000740097i
\(367\) 1675.89 + 967.574i 0.238367 + 0.137621i 0.614426 0.788975i \(-0.289388\pi\)
−0.376059 + 0.926596i \(0.622721\pi\)
\(368\) 2489.06 + 1437.06i 0.352585 + 0.203565i
\(369\) 5013.21 8643.18i 0.707255 1.21937i
\(370\) 9745.28i 1.36928i
\(371\) 0 0
\(372\) 1048.90 + 606.980i 0.146190 + 0.0845980i
\(373\) −3871.04 6704.83i −0.537359 0.930732i −0.999045 0.0436892i \(-0.986089\pi\)
0.461687 0.887043i \(-0.347244\pi\)
\(374\) 1331.91 2306.93i 0.184148 0.318953i
\(375\) 409.432 + 710.797i 0.0563812 + 0.0978810i
\(376\) −3643.61 + 2103.64i −0.499747 + 0.288529i
\(377\) 504.884 0.0689730
\(378\) 0 0
\(379\) −3722.15 −0.504470 −0.252235 0.967666i \(-0.581166\pi\)
−0.252235 + 0.967666i \(0.581166\pi\)
\(380\) 640.815 369.975i 0.0865082 0.0499455i
\(381\) −4268.53 7410.41i −0.573972 0.996448i
\(382\) 4757.15 8239.63i 0.637165 1.10360i
\(383\) −3546.73 6143.12i −0.473184 0.819578i 0.526345 0.850271i \(-0.323562\pi\)
−0.999529 + 0.0306926i \(0.990229\pi\)
\(384\) 4484.08 + 2594.87i 0.595905 + 0.344841i
\(385\) 0 0
\(386\) 334.984i 0.0441716i
\(387\) 2534.16 4369.09i 0.332864 0.573885i
\(388\) 370.177 + 213.722i 0.0484353 + 0.0279641i
\(389\) −6173.12 3564.05i −0.804601 0.464537i 0.0404765 0.999180i \(-0.487112\pi\)
−0.845077 + 0.534644i \(0.820446\pi\)
\(390\) 1605.39 + 1.60502i 0.208441 + 0.000208394i
\(391\) 1602.98i 0.207330i
\(392\) 0 0
\(393\) −1635.38 + 2826.03i −0.209908 + 0.362733i
\(394\) 3939.08 + 6822.69i 0.503675 + 0.872391i
\(395\) −8577.33 + 14856.4i −1.09259 + 1.89242i
\(396\) 2.50870 1254.63i 0.000318351 0.159211i
\(397\) −7738.99 + 4468.11i −0.978360 + 0.564857i −0.901775 0.432206i \(-0.857735\pi\)
−0.0765855 + 0.997063i \(0.524402\pi\)
\(398\) −10332.3 −1.30128
\(399\) 0 0
\(400\) −6989.56 −0.873695
\(401\) −7719.60 + 4456.91i −0.961343 + 0.555032i −0.896586 0.442869i \(-0.853961\pi\)
−0.0647568 + 0.997901i \(0.520627\pi\)
\(402\) −11860.0 + 6831.56i −1.47145 + 0.847580i
\(403\) −661.826 + 1146.32i −0.0818062 + 0.141692i
\(404\) 715.112 + 1238.61i 0.0880648 + 0.152533i
\(405\) 5915.71 10152.3i 0.725812 1.24561i
\(406\) 0 0
\(407\) 8318.63i 1.01312i
\(408\) 3.61727 3618.09i 0.000438925 0.439025i
\(409\) 2680.13 + 1547.37i 0.324019 + 0.187073i 0.653183 0.757200i \(-0.273433\pi\)
−0.329163 + 0.944273i \(0.606767\pi\)
\(410\) −13365.7 7716.69i −1.60996 0.929513i
\(411\) 2.59188 2592.47i 0.000311066 0.311137i
\(412\) 271.076i 0.0324149i
\(413\) 0 0
\(414\) 1929.38 + 3357.26i 0.229043 + 0.398552i
\(415\) 4843.82 + 8389.74i 0.572949 + 0.992377i
\(416\) 216.496 374.983i 0.0255159 0.0441948i
\(417\) 5478.09 3155.48i 0.643317 0.370562i
\(418\) −2805.45 + 1619.73i −0.328276 + 0.189530i
\(419\) −7234.25 −0.843476 −0.421738 0.906718i \(-0.638580\pi\)
−0.421738 + 0.906718i \(0.638580\pi\)
\(420\) 0 0
\(421\) 406.124 0.0470148 0.0235074 0.999724i \(-0.492517\pi\)
0.0235074 + 0.999724i \(0.492517\pi\)
\(422\) −9822.77 + 5671.18i −1.13309 + 0.654191i
\(423\) −4718.11 9.43408i −0.542323 0.00108440i
\(424\) 3276.60 5675.23i 0.375296 0.650032i
\(425\) 1949.14 + 3376.01i 0.222464 + 0.385319i
\(426\) −843.982 + 1458.45i −0.0959885 + 0.165874i
\(427\) 0 0
\(428\) 2353.21i 0.265763i
\(429\) 1370.37 + 1.37006i 0.154224 + 0.000154189i
\(430\) −6756.31 3900.76i −0.757717 0.437468i
\(431\) 10590.4 + 6114.37i 1.18358 + 0.683338i 0.956839 0.290618i \(-0.0938609\pi\)
0.226737 + 0.973956i \(0.427194\pi\)
\(432\) 3618.52 + 6311.09i 0.403000 + 0.702876i
\(433\) 3252.79i 0.361014i 0.983574 + 0.180507i \(0.0577738\pi\)
−0.983574 + 0.180507i \(0.942226\pi\)
\(434\) 0 0
\(435\) −4940.24 2858.84i −0.544521 0.315105i
\(436\) −185.126 320.648i −0.0203348 0.0352208i
\(437\) −974.689 + 1688.21i −0.106695 + 0.184801i
\(438\) 1513.69 + 2627.85i 0.165130 + 0.286675i
\(439\) 13036.8 7526.81i 1.41734 0.818303i 0.421278 0.906932i \(-0.361582\pi\)
0.996065 + 0.0886287i \(0.0282485\pi\)
\(440\) −13814.9 −1.49682
\(441\) 0 0
\(442\) 554.353 0.0596558
\(443\) 204.373 117.995i 0.0219189 0.0126549i −0.489001 0.872283i \(-0.662638\pi\)
0.510919 + 0.859629i \(0.329305\pi\)
\(444\) 791.098 + 1373.39i 0.0845583 + 0.146798i
\(445\) 12130.6 21010.8i 1.29224 2.23822i
\(446\) 6276.44 + 10871.1i 0.666364 + 1.15418i
\(447\) 10439.2 + 6040.99i 1.10460 + 0.639215i
\(448\) 0 0
\(449\) 5874.66i 0.617466i 0.951149 + 0.308733i \(0.0999049\pi\)
−0.951149 + 0.308733i \(0.900095\pi\)
\(450\) −8145.69 4724.66i −0.853315 0.494939i
\(451\) −11409.0 6587.02i −1.19120 0.687739i
\(452\) 1172.71 + 677.066i 0.122035 + 0.0704568i
\(453\) 5078.98 + 5.07782i 0.526780 + 0.000526660i
\(454\) 6127.24i 0.633405i
\(455\) 0 0
\(456\) −2203.79 + 3808.27i −0.226320 + 0.391094i
\(457\) −153.883 266.533i −0.0157513 0.0272821i 0.858042 0.513579i \(-0.171681\pi\)
−0.873794 + 0.486297i \(0.838347\pi\)
\(458\) 5582.89 9669.85i 0.569588 0.986556i
\(459\) 2039.23 3507.71i 0.207370 0.356701i
\(460\) −1009.92 + 583.079i −0.102365 + 0.0591004i
\(461\) 4752.26 0.480119 0.240060 0.970758i \(-0.422833\pi\)
0.240060 + 0.970758i \(0.422833\pi\)
\(462\) 0 0
\(463\) −9529.43 −0.956523 −0.478261 0.878218i \(-0.658733\pi\)
−0.478261 + 0.878218i \(0.658733\pi\)
\(464\) 3060.42 1766.94i 0.306199 0.176784i
\(465\) 12966.8 7469.10i 1.29316 0.744884i
\(466\) −7210.74 + 12489.4i −0.716805 + 1.24154i
\(467\) 3269.28 + 5662.56i 0.323949 + 0.561097i 0.981299 0.192489i \(-0.0616559\pi\)
−0.657350 + 0.753586i \(0.728323\pi\)
\(468\) 226.376 130.096i 0.0223595 0.0128497i
\(469\) 0 0
\(470\) 7287.61i 0.715218i
\(471\) 0.862312 862.509i 8.43593e−5 0.0843786i
\(472\) 2019.85 + 1166.16i 0.196973 + 0.113723i
\(473\) −5767.23 3329.71i −0.560629 0.323679i
\(474\) 14.3059 14309.2i 0.00138627 1.38659i
\(475\) 4740.69i 0.457932i
\(476\) 0 0
\(477\) 6371.64 3661.70i 0.611609 0.351484i
\(478\) −6059.32 10495.0i −0.579805 1.00425i
\(479\) −3671.28 + 6358.85i −0.350199 + 0.606562i −0.986284 0.165057i \(-0.947219\pi\)
0.636085 + 0.771619i \(0.280553\pi\)
\(480\) −4241.69 + 2443.29i −0.403345 + 0.232334i
\(481\) −1499.22 + 865.574i −0.142117 + 0.0820515i
\(482\) 5666.94 0.535523
\(483\) 0 0
\(484\) 83.1680 0.00781066
\(485\) 4570.96 2639.05i 0.427952 0.247078i
\(486\) −48.9940 + 9800.97i −0.00457287 + 0.914775i
\(487\) −3508.78 + 6077.39i −0.326485 + 0.565489i −0.981812 0.189857i \(-0.939198\pi\)
0.655327 + 0.755345i \(0.272531\pi\)
\(488\) 4641.19 + 8038.77i 0.430526 + 0.745693i
\(489\) −2542.77 + 4394.06i −0.235150 + 0.406352i
\(490\) 0 0
\(491\) 224.222i 0.0206089i 0.999947 + 0.0103045i \(0.00328007\pi\)
−0.999947 + 0.0103045i \(0.996720\pi\)
\(492\) −2510.04 2.50946i −0.230002 0.000229950i
\(493\) −1706.89 985.471i −0.155932 0.0900272i
\(494\) −583.829 337.074i −0.0531735 0.0306997i
\(495\) −13401.2 7772.96i −1.21685 0.705795i
\(496\) 9264.74i 0.838708i
\(497\) 0 0
\(498\) −6994.07 4047.36i −0.629341 0.364189i
\(499\) 10396.1 + 18006.6i 0.932651 + 1.61540i 0.778770 + 0.627309i \(0.215844\pi\)
0.153881 + 0.988089i \(0.450823\pi\)
\(500\) 103.031 178.456i 0.00921540 0.0159615i
\(501\) 2.61196 + 4.53451i 0.000232922 + 0.000404365i
\(502\) −5020.87 + 2898.80i −0.446399 + 0.257729i
\(503\) 7341.52 0.650780 0.325390 0.945580i \(-0.394504\pi\)
0.325390 + 0.945580i \(0.394504\pi\)
\(504\) 0 0
\(505\) 17660.5 1.55620
\(506\) 4421.38 2552.69i 0.388448 0.224270i
\(507\) −5555.74 9645.09i −0.486665 0.844878i
\(508\) −1074.15 + 1860.49i −0.0938146 + 0.162492i
\(509\) −9956.11 17244.5i −0.866988 1.50167i −0.865060 0.501669i \(-0.832720\pi\)
−0.00192778 0.999998i \(-0.500614\pi\)
\(510\) −5424.29 3138.95i −0.470964 0.272539i
\(511\) 0 0
\(512\) 13018.4i 1.12370i
\(513\) −4280.52 + 2454.27i −0.368400 + 0.211225i
\(514\) 2490.76 + 1438.04i 0.213741 + 0.123403i
\(515\) −2898.81 1673.63i −0.248032 0.143202i
\(516\) −1268.81 1.26852i −0.108249 0.000108224i
\(517\) 6220.75i 0.529184i
\(518\) 0 0
\(519\) 10297.2 17794.2i 0.870900 1.50497i
\(520\) −1437.47 2489.78i −0.121226 0.209969i
\(521\) −3745.90 + 6488.08i −0.314992 + 0.545582i −0.979436 0.201756i \(-0.935335\pi\)
0.664444 + 0.747338i \(0.268668\pi\)
\(522\) 4761.02 + 9.51987i 0.399203 + 0.000798225i
\(523\) −249.515 + 144.058i −0.0208614 + 0.0120444i −0.510394 0.859940i \(-0.670501\pi\)
0.489533 + 0.871985i \(0.337167\pi\)
\(524\) 820.223 0.0683809
\(525\) 0 0
\(526\) 5326.62 0.441543
\(527\) 4474.94 2583.61i 0.369889 0.213555i
\(528\) 8311.49 4787.57i 0.685059 0.394606i
\(529\) −4547.39 + 7876.32i −0.373748 + 0.647351i
\(530\) −5675.53 9830.30i −0.465149 0.805662i
\(531\) 1303.23 + 2267.71i 0.106507 + 0.185330i
\(532\) 0 0
\(533\) 2741.58i 0.222797i
\(534\) −20.2323 + 20236.9i −0.00163958 + 1.63996i
\(535\) 25164.5 + 14528.7i 2.03356 + 1.17408i
\(536\) 21226.7 + 12255.2i 1.71055 + 0.987586i
\(537\) −14.5379 + 14541.2i −0.00116826 + 1.16853i
\(538\) 12495.2i 1.00131i
\(539\) 0 0
\(540\) −2951.72 8.85317i −0.235226 0.000705518i
\(541\) −7400.87 12818.7i −0.588149 1.01870i −0.994475 0.104975i \(-0.966524\pi\)
0.406326 0.913728i \(-0.366810\pi\)
\(542\) 286.478 496.194i 0.0227034 0.0393235i
\(543\) −6784.24 + 3907.85i −0.536169 + 0.308843i
\(544\) −1463.84 + 845.149i −0.115371 + 0.0666093i
\(545\) −4571.90 −0.359337
\(546\) 0 0
\(547\) −4036.80 −0.315541 −0.157771 0.987476i \(-0.550431\pi\)
−0.157771 + 0.987476i \(0.550431\pi\)
\(548\) −564.001 + 325.626i −0.0439652 + 0.0253833i
\(549\) −20.8141 + 10409.4i −0.00161807 + 0.809221i
\(550\) −6207.88 + 10752.4i −0.481282 + 0.833604i
\(551\) 1198.43 + 2075.74i 0.0926585 + 0.160489i
\(552\) 3473.16 6001.82i 0.267803 0.462780i
\(553\) 0 0
\(554\) 6383.53i 0.489549i
\(555\) 19570.9 + 19.5664i 1.49683 + 0.00149649i
\(556\) −1375.35 794.059i −0.104906 0.0605676i
\(557\) −14891.1 8597.36i −1.13277 0.654007i −0.188142 0.982142i \(-0.560246\pi\)
−0.944631 + 0.328135i \(0.893580\pi\)
\(558\) −6262.59 + 10797.2i −0.475119 + 0.819143i
\(559\) 1385.86i 0.104858i
\(560\) 0 0
\(561\) −4630.21 2679.43i −0.348463 0.201650i
\(562\) −5400.90 9354.64i −0.405380 0.702138i
\(563\) 9453.63 16374.2i 0.707678 1.22573i −0.258038 0.966135i \(-0.583076\pi\)
0.965716 0.259600i \(-0.0835907\pi\)
\(564\) 591.591 + 1027.04i 0.0441675 + 0.0766773i
\(565\) 14480.7 8360.43i 1.07824 0.622524i
\(566\) 16815.8 1.24880
\(567\) 0 0
\(568\) 3017.60 0.222915
\(569\) 6255.57 3611.66i 0.460891 0.266096i −0.251528 0.967850i \(-0.580933\pi\)
0.712419 + 0.701754i \(0.247600\pi\)
\(570\) 3804.07 + 6604.09i 0.279535 + 0.485289i
\(571\) 4965.17 8599.93i 0.363898 0.630290i −0.624700 0.780865i \(-0.714779\pi\)
0.988599 + 0.150574i \(0.0481122\pi\)
\(572\) −172.125 298.129i −0.0125820 0.0217926i
\(573\) −16537.7 9570.08i −1.20571 0.697724i
\(574\) 0 0
\(575\) 7471.31i 0.541870i
\(576\) 7668.19 13220.6i 0.554701 0.956349i
\(577\) −7254.16 4188.19i −0.523388 0.302178i 0.214932 0.976629i \(-0.431047\pi\)
−0.738320 + 0.674451i \(0.764380\pi\)
\(578\) 9134.73 + 5273.94i 0.657361 + 0.379528i
\(579\) −672.730 0.672576i −0.0482862 4.82752e-5i
\(580\) 1433.85i 0.102651i
\(581\) 0 0
\(582\) −2205.11 + 3810.56i −0.157053 + 0.271397i
\(583\) −4844.67 8391.21i −0.344161 0.596104i
\(584\) 2715.44 4703.27i 0.192407 0.333258i
\(585\) 6.44656 3224.01i 0.000455611 0.227857i
\(586\) −12631.9 + 7293.03i −0.890476 + 0.514116i
\(587\) −21277.2 −1.49609 −0.748043 0.663650i \(-0.769006\pi\)
−0.748043 + 0.663650i \(0.769006\pi\)
\(588\) 0 0
\(589\) −6283.84 −0.439594
\(590\) 3498.67 2019.96i 0.244132 0.140950i
\(591\) 13709.5 7896.94i 0.954204 0.549639i
\(592\) −6058.48 + 10493.6i −0.420611 + 0.728520i
\(593\) −1424.49 2467.29i −0.0986454 0.170859i 0.812479 0.582991i \(-0.198118\pi\)
−0.911124 + 0.412132i \(0.864784\pi\)
\(594\) 12922.5 + 38.7587i 0.892619 + 0.00267725i
\(595\) 0 0
\(596\) 3029.86i 0.208235i
\(597\) −20.7450 + 20749.7i −0.00142217 + 1.42249i
\(598\) 920.111 + 531.227i 0.0629200 + 0.0363269i
\(599\) −3844.40 2219.57i −0.262234 0.151401i 0.363119 0.931743i \(-0.381712\pi\)
−0.625353 + 0.780342i \(0.715045\pi\)
\(600\) −16.8597 + 16863.5i −0.00114716 + 1.14742i
\(601\) 7868.29i 0.534033i −0.963692 0.267017i \(-0.913962\pi\)
0.963692 0.267017i \(-0.0860379\pi\)
\(602\) 0 0
\(603\) 13695.6 + 23831.4i 0.924924 + 1.60944i
\(604\) −637.943 1104.95i −0.0429761 0.0744367i
\(605\) 513.480 889.374i 0.0345057 0.0597656i
\(606\) −12764.8 + 7352.78i −0.855670 + 0.492881i
\(607\) 15144.9 8743.92i 1.01271 0.584686i 0.100724 0.994914i \(-0.467884\pi\)
0.911983 + 0.410228i \(0.134551\pi\)
\(608\) 2055.57 0.137112
\(609\) 0 0
\(610\) 16078.4 1.06720
\(611\) −1121.13 + 647.284i −0.0742324 + 0.0428581i
\(612\) −1019.25 2.03804i −0.0673216 0.000134613i
\(613\) −6422.07 + 11123.3i −0.423140 + 0.732900i −0.996245 0.0865820i \(-0.972406\pi\)
0.573105 + 0.819482i \(0.305739\pi\)
\(614\) 4454.16 + 7714.83i 0.292761 + 0.507077i
\(615\) −15523.8 + 26826.1i −1.01786 + 1.75892i
\(616\) 0 0
\(617\) 23625.5i 1.54153i −0.637117 0.770767i \(-0.719873\pi\)
0.637117 0.770767i \(-0.280127\pi\)
\(618\) 2792.03 + 2.79140i 0.181735 + 0.000181693i
\(619\) −16529.1 9543.05i −1.07328 0.619657i −0.144202 0.989548i \(-0.546062\pi\)
−0.929075 + 0.369891i \(0.879395\pi\)
\(620\) −3255.49 1879.56i −0.210877 0.121750i
\(621\) 6746.08 3867.92i 0.435927 0.249942i
\(622\) 391.901i 0.0252633i
\(623\) 0 0
\(624\) 1727.67 + 999.772i 0.110836 + 0.0641393i
\(625\) 7152.40 + 12388.3i 0.457754 + 0.792853i
\(626\) −12451.6 + 21566.9i −0.794996 + 1.37697i
\(627\) 3247.18 + 5637.29i 0.206826 + 0.359062i
\(628\) −187.642 + 108.335i −0.0119231 + 0.00688382i
\(629\) 6757.98 0.428391
\(630\) 0 0
\(631\) 32.3893 0.00204342 0.00102171 0.999999i \(-0.499675\pi\)
0.00102171 + 0.999999i \(0.499675\pi\)
\(632\) −22191.9 + 12812.5i −1.39675 + 0.806414i
\(633\) 11369.4 + 19737.9i 0.713891 + 1.23935i
\(634\) 11751.9 20355.0i 0.736166 1.27508i
\(635\) 13263.7 + 22973.4i 0.828902 + 1.43570i
\(636\) −1597.85 924.648i −0.0996207 0.0576489i
\(637\) 0 0
\(638\) 6277.32i 0.389532i
\(639\) 2927.23 + 1697.85i 0.181220 + 0.105111i
\(640\) −13917.4 8035.20i −0.859583 0.496280i
\(641\) 18742.7 + 10821.1i 1.15490 + 0.666784i 0.950078 0.312014i \(-0.101004\pi\)
0.204827 + 0.978798i \(0.434337\pi\)
\(642\) −24237.6 24.2321i −1.49000 0.00148966i
\(643\) 19867.3i 1.21849i −0.792982 0.609246i \(-0.791472\pi\)
0.792982 0.609246i \(-0.208528\pi\)
\(644\) 0 0
\(645\) −7847.24 + 13560.5i −0.479046 + 0.827820i
\(646\) 1315.85 + 2279.12i 0.0801417 + 0.138809i
\(647\) 11212.2 19420.1i 0.681294 1.18004i −0.293293 0.956023i \(-0.594751\pi\)
0.974586 0.224012i \(-0.0719156\pi\)
\(648\) 15235.4 8715.08i 0.923613 0.528335i
\(649\) 2986.49 1724.25i 0.180632 0.104288i
\(650\) −2583.78 −0.155914
\(651\) 0 0
\(652\) 1275.33 0.0766038
\(653\) −17358.5 + 10021.9i −1.04026 + 0.600594i −0.919907 0.392137i \(-0.871736\pi\)
−0.120353 + 0.992731i \(0.538403\pi\)
\(654\) 3304.53 1903.47i 0.197580 0.113810i
\(655\) 5064.07 8771.22i 0.302091 0.523237i
\(656\) −9594.67 16618.5i −0.571050 0.989088i
\(657\) 5280.41 3034.59i 0.313559 0.180199i
\(658\) 0 0
\(659\) 13217.9i 0.781327i −0.920533 0.390664i \(-0.872246\pi\)
0.920533 0.390664i \(-0.127754\pi\)
\(660\) −3.89091 + 3891.80i −0.000229475 + 0.229527i
\(661\) −8470.90 4890.68i −0.498457 0.287784i 0.229619 0.973281i \(-0.426252\pi\)
−0.728076 + 0.685496i \(0.759585\pi\)
\(662\) 3149.56 + 1818.40i 0.184911 + 0.106758i
\(663\) 1.11302 1113.28i 6.51979e−5 0.0652128i
\(664\) 14471.0i 0.845761i
\(665\) 0 0
\(666\) −14153.8 + 8134.03i −0.823499 + 0.473254i
\(667\) −1888.72 3271.36i −0.109642 0.189906i
\(668\) 0.657286 1.13845i 3.80706e−5 6.59402e-5i
\(669\) 21844.5 12582.8i 1.26242 0.727174i
\(670\) 36767.7 21227.8i 2.12009 1.22403i
\(671\) 13724.6 0.789617
\(672\) 0 0
\(673\) −4670.73 −0.267524 −0.133762 0.991014i \(-0.542706\pi\)
−0.133762 + 0.991014i \(0.542706\pi\)
\(674\) 17888.8 10328.1i 1.02233 0.590242i
\(675\) −9504.63 + 16349.1i −0.541975 + 0.932260i
\(676\) −1398.07 + 2421.53i −0.0795445 + 0.137775i
\(677\) −13521.0 23419.1i −0.767584 1.32949i −0.938870 0.344273i \(-0.888125\pi\)
0.171286 0.985221i \(-0.445208\pi\)
\(678\) −6985.73 + 12071.8i −0.395701 + 0.683795i
\(679\) 0 0
\(680\) 11223.1i 0.632921i
\(681\) −12305.0 12.3022i −0.692406 0.000692248i
\(682\) 14252.4 + 8228.61i 0.800222 + 0.462009i
\(683\) −11596.9 6695.45i −0.649694 0.375101i 0.138645 0.990342i \(-0.455725\pi\)
−0.788339 + 0.615241i \(0.789059\pi\)
\(684\) 1072.21 + 621.902i 0.0599370 + 0.0347646i
\(685\) 8041.69i 0.448551i
\(686\) 0 0
\(687\) −19408.2 11231.2i −1.07783 0.623724i
\(688\) −4850.07 8400.57i −0.268761 0.465507i
\(689\) 1008.20 1746.25i 0.0557464 0.0965557i
\(690\) −5995.21 10408.0i −0.330773 0.574241i
\(691\) −26837.3 + 15494.6i −1.47748 + 0.853025i −0.999676 0.0254396i \(-0.991901\pi\)
−0.477807 + 0.878465i \(0.658568\pi\)
\(692\) −5164.56 −0.283710
\(693\) 0 0
\(694\) 6777.28 0.370694
\(695\) −16982.9 + 9805.07i −0.926903 + 0.535147i
\(696\) −4255.66 7388.07i −0.231768 0.402362i
\(697\) −5351.23 + 9268.60i −0.290807 + 0.503692i
\(698\) 7804.05 + 13517.0i 0.423191 + 0.732989i
\(699\) 25067.3 + 14506.0i 1.35641 + 0.784933i
\(700\) 0 0
\(701\) 2892.67i 0.155855i −0.996959 0.0779277i \(-0.975170\pi\)
0.996959 0.0779277i \(-0.0248303\pi\)
\(702\) 1337.63 + 2332.97i 0.0719168 + 0.125431i
\(703\) −7117.31 4109.18i −0.381841 0.220456i
\(704\) −17451.2 10075.5i −0.934259 0.539395i
\(705\) 14635.3 + 14.6320i 0.781841 + 0.000781662i
\(706\) 13755.5i 0.733277i
\(707\) 0 0
\(708\) 329.089 568.685i 0.0174688 0.0301871i
\(709\) −7965.19 13796.1i −0.421917 0.730781i 0.574210 0.818708i \(-0.305309\pi\)
−0.996127 + 0.0879267i \(0.971976\pi\)
\(710\) 2613.46 4526.64i 0.138143 0.239270i
\(711\) −28736.3 57.4595i −1.51574 0.00303080i
\(712\) 31385.2 18120.2i 1.65198 0.953770i
\(713\) 9903.30 0.520171
\(714\) 0 0
\(715\) −4250.81 −0.222337
\(716\) 3163.50 1826.45i 0.165119 0.0953317i
\(717\) −21088.8 + 12147.5i −1.09843 + 0.632716i
\(718\) 2408.83 4172.22i 0.125204 0.216860i
\(719\) −5938.87 10286.4i −0.308042 0.533545i 0.669892 0.742459i \(-0.266341\pi\)
−0.977934 + 0.208914i \(0.933007\pi\)
\(720\) −11244.0 19565.4i −0.581997 1.01272i
\(721\) 0 0
\(722\) 14546.6i 0.749819i
\(723\) 11.3780 11380.6i 0.000585273 0.585407i
\(724\) 1703.28 + 983.389i 0.0874336 + 0.0504798i
\(725\) 7955.61 + 4593.18i 0.407537 + 0.235291i
\(726\) −0.856420 + 856.615i −4.37806e−5 + 0.0437906i
\(727\) 16795.8i 0.856839i 0.903580 + 0.428419i \(0.140929\pi\)
−0.903580 + 0.428419i \(0.859071\pi\)
\(728\) 0 0
\(729\) 19682.6 + 118.070i 0.999982 + 0.00599859i
\(730\) −4703.52 8146.74i −0.238473 0.413047i
\(731\) −2705.03 + 4685.24i −0.136866 + 0.237059i
\(732\) 2265.91 1305.20i 0.114413 0.0659040i
\(733\) −22048.4 + 12729.7i −1.11102 + 0.641447i −0.939093 0.343663i \(-0.888332\pi\)
−0.171926 + 0.985110i \(0.554999\pi\)
\(734\) 5007.02 0.251788
\(735\) 0 0
\(736\) −3239.57 −0.162245
\(737\) 31385.1 18120.2i 1.56864 0.905653i
\(738\) 51.6941 25852.9i 0.00257843 1.28951i
\(739\) 9319.48 16141.8i 0.463901 0.803499i −0.535251 0.844693i \(-0.679783\pi\)
0.999151 + 0.0411940i \(0.0131162\pi\)
\(740\) −2458.19 4257.72i −0.122115 0.211509i
\(741\) −678.099 + 1171.79i −0.0336175 + 0.0580930i
\(742\) 0 0
\(743\) 14043.3i 0.693401i 0.937976 + 0.346700i \(0.112698\pi\)
−0.937976 + 0.346700i \(0.887302\pi\)
\(744\) 22352.8 + 22.3477i 1.10147 + 0.00110122i
\(745\) −32400.4 18706.4i −1.59337 0.919932i
\(746\) −17348.1 10016.0i −0.851422 0.491569i
\(747\) −8142.12 + 14037.7i −0.398802 + 0.687566i
\(748\) 1343.87i 0.0656907i
\(749\) 0 0
\(750\) 1837.00 + 1063.04i 0.0894370 + 0.0517557i
\(751\) −8115.13 14055.8i −0.394308 0.682961i 0.598705 0.800970i \(-0.295682\pi\)
−0.993013 + 0.118009i \(0.962349\pi\)
\(752\) −4530.58 + 7847.20i −0.219699 + 0.380529i
\(753\) 5811.43 + 10089.0i 0.281248 + 0.488263i
\(754\) 1131.32 653.170i 0.0546424 0.0315478i
\(755\) −15754.7 −0.759433
\(756\) 0 0
\(757\) −33345.7 −1.60102 −0.800508 0.599322i \(-0.795437\pi\)
−0.800508 + 0.599322i \(0.795437\pi\)
\(758\) −8340.45 + 4815.36i −0.399655 + 0.230741i
\(759\) −5117.55 8884.35i −0.244737 0.424877i
\(760\) 6824.19 11819.9i 0.325710 0.564146i
\(761\) 5394.02 + 9342.71i 0.256942 + 0.445037i 0.965421 0.260695i \(-0.0839517\pi\)
−0.708479 + 0.705732i \(0.750618\pi\)
\(762\) −19151.6 11082.7i −0.910486 0.526884i
\(763\) 0 0
\(764\) 4799.87i 0.227295i
\(765\) −6314.68 + 10887.0i −0.298441 + 0.514537i
\(766\) −15894.7 9176.84i −0.749740 0.432862i
\(767\) 621.503 + 358.825i 0.0292584 + 0.0168923i
\(768\) −10125.7 10.1234i −0.475754 0.000475646i
\(769\) 35799.6i 1.67876i −0.543543 0.839381i \(-0.682918\pi\)
0.543543 0.839381i \(-0.317082\pi\)
\(770\) 0 0
\(771\) 2892.94 4999.17i 0.135132 0.233516i
\(772\) 84.4979 + 146.355i 0.00393931 + 0.00682308i
\(773\) −18306.3 + 31707.5i −0.851788 + 1.47534i 0.0278053 + 0.999613i \(0.491148\pi\)
−0.879593 + 0.475727i \(0.842185\pi\)
\(774\) 26.1312 13068.5i 0.00121352 0.606898i
\(775\) −20857.2 + 12041.9i −0.966727 + 0.558140i
\(776\) 7884.22 0.364725
\(777\) 0 0
\(778\) −18443.3 −0.849904
\(779\) 11271.5 6507.62i 0.518414 0.299306i
\(780\) −701.801 + 404.250i −0.0322160 + 0.0185570i
\(781\) 2230.86 3863.97i 0.102211 0.177034i
\(782\) −2073.78 3591.89i −0.0948314 0.164253i
\(783\) 28.6773 9561.27i 0.00130887 0.436388i
\(784\) 0 0
\(785\) 2675.45i 0.121644i
\(786\) −8.44622 + 8448.15i −0.000383291 + 0.383378i
\(787\) 34874.9 + 20135.0i 1.57961 + 0.911990i 0.994913 + 0.100742i \(0.0321216\pi\)
0.584701 + 0.811249i \(0.301212\pi\)
\(788\) −3441.97 1987.22i −0.155603 0.0898374i
\(789\) 10.6947 10697.2i 0.000482563 0.482673i
\(790\) 44386.1i 1.99897i
\(791\) 0 0
\(792\) −11530.8 20064.5i −0.517335 0.900203i
\(793\) 1428.08 + 2473.51i 0.0639503 + 0.110765i
\(794\) −11560.8 + 20023.9i −0.516723 + 0.894991i
\(795\) −19753.1 + 11378.1i −0.881219 + 0.507598i
\(796\) 4514.17 2606.26i 0.201006 0.116051i
\(797\) −11444.6 −0.508645 −0.254323 0.967119i \(-0.581852\pi\)
−0.254323 + 0.967119i \(0.581852\pi\)
\(798\) 0 0
\(799\) 5053.68 0.223762
\(800\) 6822.81 3939.15i 0.301528 0.174087i
\(801\) 40640.6 + 81.2628i 1.79272 + 0.00358462i
\(802\) −11531.9 + 19973.8i −0.507736 + 0.879424i
\(803\) −4014.95 6954.10i −0.176444 0.305610i
\(804\) 3458.40 5976.32i 0.151702 0.262150i
\(805\) 0 0
\(806\) 3424.83i 0.149670i
\(807\) −25093.5 25.0877i −1.09459 0.00109434i
\(808\) 22846.2 + 13190.3i 0.994712 + 0.574297i
\(809\) 2702.86 + 1560.50i 0.117463 + 0.0678172i 0.557580 0.830123i \(-0.311730\pi\)
−0.440117 + 0.897940i \(0.645063\pi\)
\(810\) 121.581 30402.1i 0.00527399 1.31879i
\(811\) 3571.23i 0.154628i −0.997007 0.0773138i \(-0.975366\pi\)
0.997007 0.0773138i \(-0.0246343\pi\)
\(812\) 0 0
\(813\) −995.903 576.313i −0.0429617 0.0248612i
\(814\) 10761.8 + 18640.1i 0.463394 + 0.802622i
\(815\) 7873.89 13638.0i 0.338418 0.586157i
\(816\) −3889.37 6752.17i −0.166857 0.289673i
\(817\) 5697.71 3289.58i 0.243987 0.140866i
\(818\) 8007.37 0.342263
\(819\) 0 0
\(820\) 7785.98 0.331583
\(821\) −24420.3 + 14099.1i −1.03809 + 0.599344i −0.919293 0.393574i \(-0.871238\pi\)
−0.118801 + 0.992918i \(0.537905\pi\)
\(822\) −3348.08 5812.47i −0.142066 0.246634i
\(823\) 5700.86 9874.18i 0.241457 0.418217i −0.719672 0.694314i \(-0.755708\pi\)
0.961130 + 0.276097i \(0.0890412\pi\)
\(824\) −2500.00 4330.13i −0.105694 0.183067i
\(825\) 21580.9 + 12488.5i 0.910729 + 0.527024i
\(826\) 0 0
\(827\) 18948.2i 0.796726i 0.917228 + 0.398363i \(0.130422\pi\)
−0.917228 + 0.398363i \(0.869578\pi\)
\(828\) −1689.80 980.115i −0.0709233 0.0411369i
\(829\) −663.246 382.925i −0.0277871 0.0160429i 0.486042 0.873935i \(-0.338440\pi\)
−0.513829 + 0.857893i \(0.671773\pi\)
\(830\) 21707.7 + 12532.9i 0.907813 + 0.524126i
\(831\) 12819.7 + 12.8168i 0.535151 + 0.000535029i
\(832\) 4193.51i 0.174740i
\(833\) 0 0
\(834\) 8192.83 14157.7i 0.340161 0.587819i
\(835\) −8.11618 14.0576i −0.000336374 0.000582617i
\(836\) 817.136 1415.32i 0.0338053 0.0585525i
\(837\) 21670.9 + 12598.5i 0.894928 + 0.520272i
\(838\) −16210.2 + 9358.98i −0.668225 + 0.385800i
\(839\) −5355.68 −0.220380 −0.110190 0.993911i \(-0.535146\pi\)
−0.110190 + 0.993911i \(0.535146\pi\)
\(840\) 0 0
\(841\) 19744.4 0.809564
\(842\) 910.026 525.404i 0.0372465 0.0215043i
\(843\) −18797.3 + 10827.6i −0.767986 + 0.442374i
\(844\) 2861.05 4955.48i 0.116684 0.202103i
\(845\) 17263.5 + 29901.2i 0.702818 + 1.21732i
\(846\) −10584.4 + 6082.70i −0.430140 + 0.247196i
\(847\) 0 0
\(848\) 14113.5i 0.571533i
\(849\) 33.7626 33770.3i 0.00136482 1.36513i
\(850\) 8735.11 + 5043.22i 0.352485 + 0.203507i
\(851\) 11216.8 + 6476.05i 0.451832 + 0.260865i
\(852\) 0.849894 850.088i 3.41748e−5 0.0341826i
\(853\) 8591.74i 0.344872i 0.985021 + 0.172436i \(0.0551638\pi\)
−0.985021 + 0.172436i \(0.944836\pi\)
\(854\) 0 0
\(855\) 13270.3 7626.26i 0.530800 0.305044i
\(856\) 21702.5 + 37589.8i 0.866560 + 1.50093i
\(857\) 20273.3 35114.5i 0.808080 1.39964i −0.106112 0.994354i \(-0.533840\pi\)
0.914192 0.405281i \(-0.132826\pi\)
\(858\) 3072.45 1769.78i 0.122251 0.0704189i
\(859\) 8352.92 4822.56i 0.331779 0.191553i −0.324852 0.945765i \(-0.605314\pi\)
0.656631 + 0.754212i \(0.271981\pi\)
\(860\) 3935.78 0.156057
\(861\) 0 0
\(862\) 31640.7 1.25022
\(863\) 9951.19 5745.32i 0.392517 0.226620i −0.290733 0.956804i \(-0.593899\pi\)
0.683250 + 0.730184i \(0.260566\pi\)
\(864\) −7088.97 4121.22i −0.279134 0.162276i
\(865\) −31886.1 + 55228.3i −1.25336 + 2.17089i
\(866\) 4208.14 + 7288.72i 0.165125 + 0.286006i
\(867\) 10609.7 18334.2i 0.415599 0.718180i
\(868\) 0 0
\(869\) 37888.3i 1.47902i
\(870\) −14768.4 14.7650i −0.575512 0.000575381i
\(871\) 6531.39 + 3770.90i 0.254085 + 0.146696i
\(872\) −5914.37 3414.66i −0.229686 0.132609i
\(873\) 7648.11 + 4436.05i 0.296506 + 0.171979i
\(874\) 5043.84i 0.195206i
\(875\) 0 0
\(876\) −1324.19 766.290i −0.0510735 0.0295554i
\(877\) 14714.7 + 25486.6i 0.566568 + 0.981324i 0.996902 + 0.0786543i \(0.0250623\pi\)
−0.430334 + 0.902670i \(0.641604\pi\)
\(878\) 19474.9 33731.6i 0.748573 1.29657i
\(879\) 14620.8 + 25382.6i 0.561033 + 0.973986i
\(880\) −25766.8 + 14876.5i −0.987046 + 0.569871i
\(881\) −22330.5 −0.853956 −0.426978 0.904262i \(-0.640422\pi\)
−0.426978 + 0.904262i \(0.640422\pi\)
\(882\) 0 0
\(883\) 15519.2 0.591463 0.295732 0.955271i \(-0.404437\pi\)
0.295732 + 0.955271i \(0.404437\pi\)
\(884\) −242.197 + 139.832i −0.00921489 + 0.00532022i
\(885\) −4049.55 7030.25i −0.153813 0.267027i
\(886\) 305.301 528.797i 0.0115765 0.0200511i
\(887\) 19107.9 + 33095.9i 0.723316 + 1.25282i 0.959663 + 0.281152i \(0.0907165\pi\)
−0.236347 + 0.971669i \(0.575950\pi\)
\(888\) 25303.0 + 14642.5i 0.956209 + 0.553343i
\(889\) 0 0
\(890\) 62773.6i 2.36424i
\(891\) 103.783 25951.4i 0.00390218 0.975764i
\(892\) −5484.36 3166.40i −0.205863 0.118855i
\(893\) −5322.39 3072.88i −0.199448 0.115151i
\(894\) 31207.0 + 31.1999i 1.16747 + 0.00116720i
\(895\) 45106.0i 1.68461i
\(896\) 0 0
\(897\) 1068.68 1846.74i 0.0397795 0.0687413i
\(898\) 7600.07 + 13163.7i 0.282425 + 0.489174i
\(899\) 6088.31 10545.3i 0.225869 0.391217i
\(900\) 4750.63 + 9.49910i 0.175949 + 0.000351818i
\(901\) −6816.94 + 3935.76i −0.252059 + 0.145526i
\(902\) −34086.6 −1.25827
\(903\) 0 0
\(904\) 24977.0 0.918941
\(905\) 21032.2 12142.9i 0.772522 0.446016i
\(906\) 11387.4 6559.32i 0.417571 0.240529i
\(907\) 4432.30 7676.97i 0.162262 0.281047i −0.773417 0.633897i \(-0.781454\pi\)
0.935680 + 0.352850i \(0.114788\pi\)
\(908\) 1545.56 + 2677.00i 0.0564883 + 0.0978405i
\(909\) 14740.5 + 25649.7i 0.537858 + 0.935915i
\(910\) 0 0
\(911\) 15145.0i 0.550798i −0.961330 0.275399i \(-0.911190\pi\)
0.961330 0.275399i \(-0.0888100\pi\)
\(912\) −9.47397 + 9476.13i −0.000343985 + 0.344064i
\(913\) 18529.8 + 10698.2i 0.671684 + 0.387797i
\(914\) −689.630 398.158i −0.0249573 0.0144091i
\(915\) 32.2820 32289.3i 0.00116635 1.16662i
\(916\) 5633.02i 0.203188i
\(917\) 0 0
\(918\) 31.4872 10498.1i 0.00113206 0.377439i
\(919\) 2244.07 + 3886.84i 0.0805495 + 0.139516i 0.903486 0.428617i \(-0.140999\pi\)
−0.822937 + 0.568133i \(0.807666\pi\)
\(920\) −10754.9 + 18628.0i −0.385412 + 0.667552i
\(921\) 15502.2 8929.55i 0.554631 0.319477i
\(922\) 10648.7 6148.02i 0.380364 0.219603i
\(923\) 928.506 0.0331118
\(924\) 0 0
\(925\) −31498.2 −1.11963
\(926\) −21353.2 + 12328.3i −0.757785 + 0.437507i
\(927\) 11.2116 5607.08i 0.000397236 0.198663i
\(928\) −1991.61 + 3449.56i −0.0704501 + 0.122023i
\(929\) −8911.93 15435.9i −0.314737 0.545141i 0.664644 0.747160i \(-0.268583\pi\)
−0.979382 + 0.202019i \(0.935250\pi\)
\(930\) 19392.6 33511.6i 0.683774 1.18160i
\(931\) 0 0
\(932\) 7275.49i 0.255704i
\(933\) −787.033 0.786854i −0.0276166 2.76103e-5i
\(934\) 14651.4 + 8458.97i 0.513284 + 0.296345i
\(935\) 14370.9 + 8297.05i 0.502652 + 0.290206i
\(936\) 2416.29 4165.89i 0.0843793 0.145477i
\(937\) 51270.5i 1.78755i 0.448516 + 0.893775i \(0.351953\pi\)
−0.448516 + 0.893775i \(0.648047\pi\)
\(938\) 0 0
\(939\) 43286.5 + 25049.2i 1.50437 + 0.870554i
\(940\) −1838.26 3183.96i −0.0637845 0.110478i
\(941\) −5422.48 + 9392.01i −0.187851 + 0.325367i −0.944533 0.328415i \(-0.893486\pi\)
0.756683 + 0.653782i \(0.226819\pi\)
\(942\) −1113.90 1933.79i −0.0385274 0.0668857i
\(943\) −17763.9 + 10256.0i −0.613437 + 0.354168i
\(944\) 5023.10 0.173186
\(945\) 0 0
\(946\) −17230.6 −0.592195
\(947\) −36916.8 + 21313.9i −1.26677 + 0.731372i −0.974376 0.224926i \(-0.927786\pi\)
−0.292397 + 0.956297i \(0.594453\pi\)
\(948\) 3603.16 + 6255.29i 0.123444 + 0.214306i
\(949\) 835.531 1447.18i 0.0285801 0.0495021i
\(950\) −6133.05 10622.8i −0.209455 0.362787i
\(951\) −40854.2 23641.7i −1.39305 0.806134i
\(952\) 0 0
\(953\) 33229.0i 1.12948i 0.825269 + 0.564739i \(0.191023\pi\)
−0.825269 + 0.564739i \(0.808977\pi\)
\(954\) 9540.17 16448.0i 0.323768 0.558201i
\(955\) 51328.4 + 29634.5i 1.73921 + 1.00413i
\(956\) 5294.64 + 3056.86i 0.179122 + 0.103416i
\(957\) −12606.4 12.6035i −0.425817 0.000425720i
\(958\) 18998.2i 0.640715i
\(959\) 0 0
\(960\) −23745.2 + 41033.1i −0.798306 + 1.37952i
\(961\) 1066.19 + 1846.70i 0.0357891 + 0.0619885i
\(962\) −2239.59 + 3879.09i −0.0750596 + 0.130007i
\(963\) −97.3279 + 48675.0i −0.00325685 + 1.62880i
\(964\) −2475.89 + 1429.45i −0.0827209 + 0.0477589i
\(965\) 2086.77 0.0696118
\(966\) 0 0
\(967\) −16853.4 −0.560464 −0.280232 0.959932i \(-0.590411\pi\)
−0.280232 + 0.959932i \(0.590411\pi\)
\(968\) 1328.51 767.018i 0.0441116 0.0254679i
\(969\) 4579.68 2637.98i 0.151827 0.0874552i
\(970\) 6828.29 11826.9i 0.226024 0.391485i
\(971\) 634.824 + 1099.55i 0.0209809 + 0.0363400i 0.876325 0.481720i \(-0.159988\pi\)
−0.855344 + 0.518060i \(0.826654\pi\)
\(972\) −2450.84 4294.41i −0.0808751 0.141711i
\(973\) 0 0
\(974\) 18157.3i 0.597328i
\(975\) −5.18768 + 5188.86i −0.000170399 + 0.170438i
\(976\) 17313.0 + 9995.66i 0.567803 + 0.327821i
\(977\) −49580.5 28625.3i −1.62356 0.937364i −0.985957 0.167001i \(-0.946592\pi\)
−0.637605 0.770363i \(-0.720075\pi\)
\(978\) −13.1326 + 13135.6i −0.000429382 + 0.429480i
\(979\) 53583.9i 1.74929i
\(980\) 0 0
\(981\) −3816.00 6640.13i −0.124195 0.216109i
\(982\) 290.077 + 502.428i 0.00942640 + 0.0163270i
\(983\) −30733.8 + 53232.4i −0.997207 + 1.72721i −0.433924 + 0.900950i \(0.642871\pi\)
−0.563283 + 0.826264i \(0.690462\pi\)
\(984\) −40118.1 + 23108.8i −1.29971 + 0.748659i
\(985\) −42501.6 + 24538.3i −1.37484 + 0.793762i
\(986\) −5099.63 −0.164711
\(987\) 0 0
\(988\) 340.100 0.0109514
\(989\) −8979.57 + 5184.36i −0.288710 + 0.166687i
\(990\) −40084.8 80.1514i −1.28685 0.00257311i
\(991\) 25996.6 45027.4i 0.833308 1.44333i −0.0620930 0.998070i \(-0.519778\pi\)
0.895401 0.445261i \(-0.146889\pi\)
\(992\) −5221.39 9043.71i −0.167116 0.289454i
\(993\) 3658.12 6321.44i 0.116905 0.202019i
\(994\) 0 0
\(995\) 64364.3i 2.05074i
\(996\) 4076.64 + 4.07571i 0.129692 + 0.000129662i
\(997\) −29417.3 16984.1i −0.934460 0.539510i −0.0462403 0.998930i \(-0.514724\pi\)
−0.888219 + 0.459420i \(0.848057\pi\)
\(998\) 46590.3 + 26898.9i 1.47775 + 0.853177i
\(999\) 16306.7 + 28440.7i 0.516438 + 0.900725i
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 147.4.g.d.80.5 12
3.2 odd 2 inner 147.4.g.d.80.2 12
7.2 even 3 21.4.g.a.5.2 12
7.3 odd 6 147.4.c.a.146.10 12
7.4 even 3 147.4.c.a.146.9 12
7.5 odd 6 inner 147.4.g.d.68.2 12
7.6 odd 2 21.4.g.a.17.5 yes 12
21.2 odd 6 21.4.g.a.5.5 yes 12
21.5 even 6 inner 147.4.g.d.68.5 12
21.11 odd 6 147.4.c.a.146.4 12
21.17 even 6 147.4.c.a.146.3 12
21.20 even 2 21.4.g.a.17.2 yes 12
28.23 odd 6 336.4.bc.d.257.1 12
28.27 even 2 336.4.bc.d.17.2 12
84.23 even 6 336.4.bc.d.257.2 12
84.83 odd 2 336.4.bc.d.17.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.g.a.5.2 12 7.2 even 3
21.4.g.a.5.5 yes 12 21.2 odd 6
21.4.g.a.17.2 yes 12 21.20 even 2
21.4.g.a.17.5 yes 12 7.6 odd 2
147.4.c.a.146.3 12 21.17 even 6
147.4.c.a.146.4 12 21.11 odd 6
147.4.c.a.146.9 12 7.4 even 3
147.4.c.a.146.10 12 7.3 odd 6
147.4.g.d.68.2 12 7.5 odd 6 inner
147.4.g.d.68.5 12 21.5 even 6 inner
147.4.g.d.80.2 12 3.2 odd 2 inner
147.4.g.d.80.5 12 1.1 even 1 trivial
336.4.bc.d.17.1 12 84.83 odd 2
336.4.bc.d.17.2 12 28.27 even 2
336.4.bc.d.257.1 12 28.23 odd 6
336.4.bc.d.257.2 12 84.23 even 6