Properties

Label 117.4.q.e.10.4
Level $117$
Weight $4$
Character 117.10
Analytic conductor $6.903$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,4,Mod(10,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.10");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.4
Root \(-2.04224i\) of defining polynomial
Character \(\chi\) \(=\) 117.10
Dual form 117.4.q.e.82.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.76863 - 1.02112i) q^{2} +(-1.91462 + 3.31622i) q^{4} +12.0825i q^{5} +(-25.7533 - 14.8686i) q^{7} +24.1582i q^{8} +O(q^{10})\) \(q+(1.76863 - 1.02112i) q^{2} +(-1.91462 + 3.31622i) q^{4} +12.0825i q^{5} +(-25.7533 - 14.8686i) q^{7} +24.1582i q^{8} +(12.3377 + 21.3694i) q^{10} +(-24.3038 + 14.0318i) q^{11} +(-40.9717 + 22.7667i) q^{13} -60.7308 q^{14} +(9.35146 + 16.1972i) q^{16} +(25.3278 - 43.8690i) q^{17} +(91.0612 + 52.5742i) q^{19} +(-40.0681 - 23.1333i) q^{20} +(-28.6563 + 49.6342i) q^{22} +(80.2961 + 139.077i) q^{23} -20.9857 q^{25} +(-49.2164 + 82.1030i) q^{26} +(98.6155 - 56.9357i) q^{28} +(70.0525 + 121.334i) q^{29} -223.593i q^{31} +(-134.294 - 77.5348i) q^{32} -103.451i q^{34} +(179.650 - 311.163i) q^{35} +(-197.759 + 114.176i) q^{37} +214.739 q^{38} -291.890 q^{40} +(-256.259 + 147.951i) q^{41} +(96.0517 - 166.366i) q^{43} -107.462i q^{44} +(284.029 + 163.984i) q^{46} -36.9300i q^{47} +(270.653 + 468.785i) q^{49} +(-37.1160 + 21.4289i) q^{50} +(2.94589 - 179.461i) q^{52} -149.102 q^{53} +(-169.538 - 293.649i) q^{55} +(359.200 - 622.152i) q^{56} +(247.794 + 143.064i) q^{58} +(380.070 + 219.433i) q^{59} +(-143.073 + 247.809i) q^{61} +(-228.316 - 395.454i) q^{62} -466.313 q^{64} +(-275.077 - 495.038i) q^{65} +(465.166 - 268.564i) q^{67} +(96.9863 + 167.985i) q^{68} -733.777i q^{70} +(-88.9656 - 51.3643i) q^{71} -75.5209i q^{73} +(-233.175 + 403.871i) q^{74} +(-348.696 + 201.319i) q^{76} +834.535 q^{77} +17.5526 q^{79} +(-195.702 + 112.989i) q^{80} +(-302.152 + 523.342i) q^{82} +1463.08i q^{83} +(530.045 + 306.022i) q^{85} -392.322i q^{86} +(-338.983 - 587.135i) q^{88} +(290.036 - 167.453i) q^{89} +(1393.66 + 22.8773i) q^{91} -614.946 q^{92} +(-37.7100 - 65.3156i) q^{94} +(-635.225 + 1100.24i) q^{95} +(-648.442 - 374.378i) q^{97} +(957.374 + 552.740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.76863 1.02112i 0.625307 0.361021i −0.153626 0.988129i \(-0.549095\pi\)
0.778932 + 0.627108i \(0.215762\pi\)
\(3\) 0 0
\(4\) −1.91462 + 3.31622i −0.239328 + 0.414528i
\(5\) 12.0825i 1.08069i 0.841444 + 0.540344i \(0.181706\pi\)
−0.841444 + 0.540344i \(0.818294\pi\)
\(6\) 0 0
\(7\) −25.7533 14.8686i −1.39055 0.802832i −0.397170 0.917745i \(-0.630008\pi\)
−0.993375 + 0.114914i \(0.963341\pi\)
\(8\) 24.1582i 1.06765i
\(9\) 0 0
\(10\) 12.3377 + 21.3694i 0.390151 + 0.675761i
\(11\) −24.3038 + 14.0318i −0.666169 + 0.384613i −0.794624 0.607102i \(-0.792332\pi\)
0.128454 + 0.991715i \(0.458998\pi\)
\(12\) 0 0
\(13\) −40.9717 + 22.7667i −0.874115 + 0.485719i
\(14\) −60.7308 −1.15936
\(15\) 0 0
\(16\) 9.35146 + 16.1972i 0.146117 + 0.253081i
\(17\) 25.3278 43.8690i 0.361347 0.625871i −0.626836 0.779151i \(-0.715650\pi\)
0.988183 + 0.153280i \(0.0489838\pi\)
\(18\) 0 0
\(19\) 91.0612 + 52.5742i 1.09952 + 0.634808i 0.936095 0.351748i \(-0.114413\pi\)
0.163425 + 0.986556i \(0.447746\pi\)
\(20\) −40.0681 23.1333i −0.447975 0.258639i
\(21\) 0 0
\(22\) −28.6563 + 49.6342i −0.277707 + 0.481002i
\(23\) 80.2961 + 139.077i 0.727951 + 1.26085i 0.957748 + 0.287610i \(0.0928607\pi\)
−0.229796 + 0.973239i \(0.573806\pi\)
\(24\) 0 0
\(25\) −20.9857 −0.167886
\(26\) −49.2164 + 82.1030i −0.371235 + 0.619297i
\(27\) 0 0
\(28\) 98.6155 56.9357i 0.665592 0.384280i
\(29\) 70.0525 + 121.334i 0.448566 + 0.776939i 0.998293 0.0584051i \(-0.0186015\pi\)
−0.549727 + 0.835344i \(0.685268\pi\)
\(30\) 0 0
\(31\) 223.593i 1.29544i −0.761880 0.647718i \(-0.775724\pi\)
0.761880 0.647718i \(-0.224276\pi\)
\(32\) −134.294 77.5348i −0.741878 0.428323i
\(33\) 0 0
\(34\) 103.451i 0.521815i
\(35\) 179.650 311.163i 0.867610 1.50274i
\(36\) 0 0
\(37\) −197.759 + 114.176i −0.878684 + 0.507308i −0.870224 0.492656i \(-0.836026\pi\)
−0.00845956 + 0.999964i \(0.502693\pi\)
\(38\) 214.739 0.916716
\(39\) 0 0
\(40\) −291.890 −1.15380
\(41\) −256.259 + 147.951i −0.976119 + 0.563563i −0.901096 0.433619i \(-0.857236\pi\)
−0.0750227 + 0.997182i \(0.523903\pi\)
\(42\) 0 0
\(43\) 96.0517 166.366i 0.340645 0.590015i −0.643907 0.765103i \(-0.722688\pi\)
0.984553 + 0.175088i \(0.0560211\pi\)
\(44\) 107.462i 0.368194i
\(45\) 0 0
\(46\) 284.029 + 163.984i 0.910386 + 0.525611i
\(47\) 36.9300i 0.114613i −0.998357 0.0573063i \(-0.981749\pi\)
0.998357 0.0573063i \(-0.0182512\pi\)
\(48\) 0 0
\(49\) 270.653 + 468.785i 0.789077 + 1.36672i
\(50\) −37.1160 + 21.4289i −0.104980 + 0.0606102i
\(51\) 0 0
\(52\) 2.94589 179.461i 0.00785618 0.478591i
\(53\) −149.102 −0.386429 −0.193214 0.981157i \(-0.561891\pi\)
−0.193214 + 0.981157i \(0.561891\pi\)
\(54\) 0 0
\(55\) −169.538 293.649i −0.415647 0.719921i
\(56\) 359.200 622.152i 0.857144 1.48462i
\(57\) 0 0
\(58\) 247.794 + 143.064i 0.560983 + 0.323884i
\(59\) 380.070 + 219.433i 0.838659 + 0.484200i 0.856808 0.515635i \(-0.172444\pi\)
−0.0181492 + 0.999835i \(0.505777\pi\)
\(60\) 0 0
\(61\) −143.073 + 247.809i −0.300305 + 0.520143i −0.976205 0.216850i \(-0.930422\pi\)
0.675900 + 0.736993i \(0.263755\pi\)
\(62\) −228.316 395.454i −0.467679 0.810044i
\(63\) 0 0
\(64\) −466.313 −0.910768
\(65\) −275.077 495.038i −0.524910 0.944645i
\(66\) 0 0
\(67\) 465.166 268.564i 0.848195 0.489706i −0.0118462 0.999930i \(-0.503771\pi\)
0.860042 + 0.510224i \(0.170438\pi\)
\(68\) 96.9863 + 167.985i 0.172961 + 0.299576i
\(69\) 0 0
\(70\) 733.777i 1.25290i
\(71\) −88.9656 51.3643i −0.148708 0.0858567i 0.423800 0.905756i \(-0.360696\pi\)
−0.572508 + 0.819899i \(0.694029\pi\)
\(72\) 0 0
\(73\) 75.5209i 0.121083i −0.998166 0.0605414i \(-0.980717\pi\)
0.998166 0.0605414i \(-0.0192827\pi\)
\(74\) −233.175 + 403.871i −0.366298 + 0.634446i
\(75\) 0 0
\(76\) −348.696 + 201.319i −0.526291 + 0.303854i
\(77\) 834.535 1.23512
\(78\) 0 0
\(79\) 17.5526 0.0249978 0.0124989 0.999922i \(-0.496021\pi\)
0.0124989 + 0.999922i \(0.496021\pi\)
\(80\) −195.702 + 112.989i −0.273502 + 0.157906i
\(81\) 0 0
\(82\) −302.152 + 523.342i −0.406916 + 0.704799i
\(83\) 1463.08i 1.93487i 0.253122 + 0.967434i \(0.418543\pi\)
−0.253122 + 0.967434i \(0.581457\pi\)
\(84\) 0 0
\(85\) 530.045 + 306.022i 0.676371 + 0.390503i
\(86\) 392.322i 0.491920i
\(87\) 0 0
\(88\) −338.983 587.135i −0.410633 0.711236i
\(89\) 290.036 167.453i 0.345436 0.199438i −0.317237 0.948346i \(-0.602755\pi\)
0.662673 + 0.748909i \(0.269422\pi\)
\(90\) 0 0
\(91\) 1393.66 + 22.8773i 1.60545 + 0.0263538i
\(92\) −614.946 −0.696876
\(93\) 0 0
\(94\) −37.7100 65.3156i −0.0413776 0.0716680i
\(95\) −635.225 + 1100.24i −0.686029 + 1.18824i
\(96\) 0 0
\(97\) −648.442 374.378i −0.678756 0.391880i 0.120630 0.992697i \(-0.461508\pi\)
−0.799386 + 0.600818i \(0.794842\pi\)
\(98\) 957.374 + 552.740i 0.986830 + 0.569747i
\(99\) 0 0
\(100\) 40.1797 69.5933i 0.0401797 0.0695933i
\(101\) 392.001 + 678.966i 0.386194 + 0.668907i 0.991934 0.126755i \(-0.0404563\pi\)
−0.605740 + 0.795662i \(0.707123\pi\)
\(102\) 0 0
\(103\) −396.040 −0.378864 −0.189432 0.981894i \(-0.560665\pi\)
−0.189432 + 0.981894i \(0.560665\pi\)
\(104\) −550.002 989.801i −0.518578 0.933250i
\(105\) 0 0
\(106\) −263.707 + 152.251i −0.241636 + 0.139509i
\(107\) −718.296 1244.12i −0.648974 1.12406i −0.983368 0.181623i \(-0.941865\pi\)
0.334394 0.942433i \(-0.391468\pi\)
\(108\) 0 0
\(109\) 1977.92i 1.73807i 0.494746 + 0.869037i \(0.335261\pi\)
−0.494746 + 0.869037i \(0.664739\pi\)
\(110\) −599.703 346.239i −0.519813 0.300114i
\(111\) 0 0
\(112\) 556.175i 0.469228i
\(113\) 61.2026 106.006i 0.0509509 0.0882496i −0.839425 0.543475i \(-0.817108\pi\)
0.890376 + 0.455226i \(0.150441\pi\)
\(114\) 0 0
\(115\) −1680.39 + 970.173i −1.36258 + 0.786688i
\(116\) −536.496 −0.429417
\(117\) 0 0
\(118\) 896.273 0.699225
\(119\) −1304.55 + 753.180i −1.00494 + 0.580201i
\(120\) 0 0
\(121\) −271.718 + 470.629i −0.204146 + 0.353591i
\(122\) 584.379i 0.433665i
\(123\) 0 0
\(124\) 741.484 + 428.096i 0.536994 + 0.310034i
\(125\) 1256.75i 0.899256i
\(126\) 0 0
\(127\) 1154.80 + 2000.18i 0.806868 + 1.39754i 0.915022 + 0.403403i \(0.132173\pi\)
−0.108154 + 0.994134i \(0.534494\pi\)
\(128\) 249.616 144.116i 0.172369 0.0995170i
\(129\) 0 0
\(130\) −992.006 594.654i −0.669266 0.401190i
\(131\) 1444.26 0.963250 0.481625 0.876377i \(-0.340047\pi\)
0.481625 + 0.876377i \(0.340047\pi\)
\(132\) 0 0
\(133\) −1563.41 2707.91i −1.01929 1.76546i
\(134\) 548.472 949.982i 0.353588 0.612433i
\(135\) 0 0
\(136\) 1059.80 + 611.874i 0.668212 + 0.385792i
\(137\) −637.324 367.959i −0.397447 0.229466i 0.287935 0.957650i \(-0.407031\pi\)
−0.685382 + 0.728184i \(0.740365\pi\)
\(138\) 0 0
\(139\) 752.571 1303.49i 0.459225 0.795400i −0.539696 0.841860i \(-0.681461\pi\)
0.998920 + 0.0464599i \(0.0147940\pi\)
\(140\) 687.923 + 1191.52i 0.415286 + 0.719297i
\(141\) 0 0
\(142\) −209.797 −0.123984
\(143\) 676.309 1128.22i 0.395495 0.659767i
\(144\) 0 0
\(145\) −1466.02 + 846.406i −0.839629 + 0.484760i
\(146\) −77.1160 133.569i −0.0437134 0.0757139i
\(147\) 0 0
\(148\) 874.415i 0.485652i
\(149\) −370.523 213.921i −0.203721 0.117618i 0.394669 0.918823i \(-0.370859\pi\)
−0.598390 + 0.801205i \(0.704193\pi\)
\(150\) 0 0
\(151\) 1601.83i 0.863278i −0.902046 0.431639i \(-0.857935\pi\)
0.902046 0.431639i \(-0.142065\pi\)
\(152\) −1270.10 + 2199.87i −0.677753 + 1.17390i
\(153\) 0 0
\(154\) 1475.99 852.161i 0.772327 0.445903i
\(155\) 2701.55 1.39996
\(156\) 0 0
\(157\) −730.346 −0.371261 −0.185631 0.982620i \(-0.559433\pi\)
−0.185631 + 0.982620i \(0.559433\pi\)
\(158\) 31.0442 17.9234i 0.0156313 0.00902473i
\(159\) 0 0
\(160\) 936.811 1622.60i 0.462884 0.801738i
\(161\) 4775.58i 2.33769i
\(162\) 0 0
\(163\) −1644.03 949.180i −0.790001 0.456107i 0.0499619 0.998751i \(-0.484090\pi\)
−0.839963 + 0.542644i \(0.817423\pi\)
\(164\) 1133.08i 0.539505i
\(165\) 0 0
\(166\) 1493.98 + 2587.66i 0.698528 + 1.20989i
\(167\) −1236.25 + 713.751i −0.572839 + 0.330729i −0.758282 0.651926i \(-0.773961\pi\)
0.185444 + 0.982655i \(0.440628\pi\)
\(168\) 0 0
\(169\) 1160.36 1865.58i 0.528155 0.849148i
\(170\) 1249.94 0.563919
\(171\) 0 0
\(172\) 367.806 + 637.058i 0.163052 + 0.282414i
\(173\) 1022.20 1770.50i 0.449227 0.778084i −0.549109 0.835751i \(-0.685033\pi\)
0.998336 + 0.0576667i \(0.0183661\pi\)
\(174\) 0 0
\(175\) 540.450 + 312.029i 0.233453 + 0.134784i
\(176\) −454.552 262.436i −0.194677 0.112397i
\(177\) 0 0
\(178\) 341.979 592.325i 0.144002 0.249419i
\(179\) 1944.86 + 3368.59i 0.812098 + 1.40660i 0.911393 + 0.411537i \(0.135008\pi\)
−0.0992948 + 0.995058i \(0.531659\pi\)
\(180\) 0 0
\(181\) 2477.02 1.01721 0.508606 0.861000i \(-0.330161\pi\)
0.508606 + 0.861000i \(0.330161\pi\)
\(182\) 2488.24 1382.64i 1.01341 0.563121i
\(183\) 0 0
\(184\) −3359.84 + 1939.81i −1.34615 + 0.777198i
\(185\) −1379.53 2389.41i −0.548242 0.949583i
\(186\) 0 0
\(187\) 1421.58i 0.555914i
\(188\) 122.468 + 70.7070i 0.0475101 + 0.0274300i
\(189\) 0 0
\(190\) 2594.57i 0.990683i
\(191\) 1138.40 1971.78i 0.431267 0.746977i −0.565715 0.824601i \(-0.691400\pi\)
0.996983 + 0.0776235i \(0.0247332\pi\)
\(192\) 0 0
\(193\) 3396.92 1961.21i 1.26692 0.731456i 0.292515 0.956261i \(-0.405508\pi\)
0.974404 + 0.224805i \(0.0721744\pi\)
\(194\) −1529.14 −0.565907
\(195\) 0 0
\(196\) −2072.80 −0.755392
\(197\) −4384.88 + 2531.61i −1.58584 + 0.915584i −0.591855 + 0.806045i \(0.701604\pi\)
−0.993982 + 0.109539i \(0.965063\pi\)
\(198\) 0 0
\(199\) 1635.03 2831.95i 0.582433 1.00880i −0.412757 0.910841i \(-0.635434\pi\)
0.995190 0.0979624i \(-0.0312325\pi\)
\(200\) 506.977i 0.179243i
\(201\) 0 0
\(202\) 1386.61 + 800.561i 0.482979 + 0.278848i
\(203\) 4166.34i 1.44049i
\(204\) 0 0
\(205\) −1787.61 3096.23i −0.609035 1.05488i
\(206\) −700.450 + 404.405i −0.236906 + 0.136778i
\(207\) 0 0
\(208\) −751.902 450.725i −0.250649 0.150251i
\(209\) −2950.84 −0.976622
\(210\) 0 0
\(211\) 1406.09 + 2435.42i 0.458764 + 0.794602i 0.998896 0.0469781i \(-0.0149591\pi\)
−0.540132 + 0.841580i \(0.681626\pi\)
\(212\) 285.474 494.455i 0.0924831 0.160185i
\(213\) 0 0
\(214\) −2540.80 1466.93i −0.811616 0.468587i
\(215\) 2010.12 + 1160.54i 0.637622 + 0.368131i
\(216\) 0 0
\(217\) −3324.53 + 5758.25i −1.04002 + 1.80136i
\(218\) 2019.69 + 3498.21i 0.627481 + 1.08683i
\(219\) 0 0
\(220\) 1298.41 0.397903
\(221\) −38.9700 + 2374.02i −0.0118616 + 0.722596i
\(222\) 0 0
\(223\) 794.783 458.868i 0.238666 0.137794i −0.375897 0.926661i \(-0.622665\pi\)
0.614564 + 0.788867i \(0.289332\pi\)
\(224\) 2305.68 + 3993.55i 0.687743 + 1.19121i
\(225\) 0 0
\(226\) 249.981i 0.0735774i
\(227\) 1157.35 + 668.194i 0.338396 + 0.195373i 0.659562 0.751650i \(-0.270742\pi\)
−0.321167 + 0.947023i \(0.604075\pi\)
\(228\) 0 0
\(229\) 164.820i 0.0475617i 0.999717 + 0.0237808i \(0.00757039\pi\)
−0.999717 + 0.0237808i \(0.992430\pi\)
\(230\) −1981.33 + 3431.76i −0.568022 + 0.983843i
\(231\) 0 0
\(232\) −2931.22 + 1692.34i −0.829500 + 0.478912i
\(233\) −4243.42 −1.19312 −0.596558 0.802570i \(-0.703465\pi\)
−0.596558 + 0.802570i \(0.703465\pi\)
\(234\) 0 0
\(235\) 446.205 0.123860
\(236\) −1455.38 + 840.264i −0.401429 + 0.231765i
\(237\) 0 0
\(238\) −1538.18 + 2664.20i −0.418929 + 0.725607i
\(239\) 2491.07i 0.674200i −0.941469 0.337100i \(-0.890554\pi\)
0.941469 0.337100i \(-0.109446\pi\)
\(240\) 0 0
\(241\) −2526.54 1458.70i −0.675306 0.389888i 0.122778 0.992434i \(-0.460820\pi\)
−0.798084 + 0.602546i \(0.794153\pi\)
\(242\) 1109.83i 0.294803i
\(243\) 0 0
\(244\) −547.861 948.922i −0.143743 0.248969i
\(245\) −5664.08 + 3270.16i −1.47700 + 0.852746i
\(246\) 0 0
\(247\) −4927.87 80.8921i −1.26944 0.0208382i
\(248\) 5401.60 1.38307
\(249\) 0 0
\(250\) 1283.29 + 2222.73i 0.324650 + 0.562310i
\(251\) 656.939 1137.85i 0.165202 0.286138i −0.771525 0.636199i \(-0.780506\pi\)
0.936727 + 0.350061i \(0.113839\pi\)
\(252\) 0 0
\(253\) −3902.99 2253.39i −0.969878 0.559959i
\(254\) 4084.85 + 2358.39i 1.00908 + 0.582593i
\(255\) 0 0
\(256\) 2159.57 3740.49i 0.527239 0.913205i
\(257\) 493.791 + 855.271i 0.119851 + 0.207589i 0.919709 0.392601i \(-0.128425\pi\)
−0.799857 + 0.600190i \(0.795091\pi\)
\(258\) 0 0
\(259\) 6790.57 1.62913
\(260\) 2168.33 + 35.5936i 0.517207 + 0.00849007i
\(261\) 0 0
\(262\) 2554.37 1474.77i 0.602326 0.347753i
\(263\) −3493.23 6050.44i −0.819017 1.41858i −0.906407 0.422405i \(-0.861186\pi\)
0.0873899 0.996174i \(-0.472147\pi\)
\(264\) 0 0
\(265\) 1801.52i 0.417609i
\(266\) −5530.22 3192.87i −1.27473 0.735968i
\(267\) 0 0
\(268\) 2056.79i 0.468801i
\(269\) −2952.17 + 5113.31i −0.669134 + 1.15897i 0.309013 + 0.951058i \(0.400001\pi\)
−0.978147 + 0.207916i \(0.933332\pi\)
\(270\) 0 0
\(271\) −1845.97 + 1065.77i −0.413781 + 0.238897i −0.692413 0.721501i \(-0.743452\pi\)
0.278632 + 0.960398i \(0.410119\pi\)
\(272\) 947.408 0.211195
\(273\) 0 0
\(274\) −1502.92 −0.331368
\(275\) 510.032 294.467i 0.111840 0.0645710i
\(276\) 0 0
\(277\) 2016.21 3492.17i 0.437336 0.757489i −0.560147 0.828393i \(-0.689255\pi\)
0.997483 + 0.0709046i \(0.0225886\pi\)
\(278\) 3073.86i 0.663159i
\(279\) 0 0
\(280\) 7517.12 + 4340.01i 1.60441 + 0.926305i
\(281\) 2298.29i 0.487916i 0.969786 + 0.243958i \(0.0784459\pi\)
−0.969786 + 0.243958i \(0.921554\pi\)
\(282\) 0 0
\(283\) 3328.40 + 5764.96i 0.699127 + 1.21092i 0.968770 + 0.247963i \(0.0797611\pi\)
−0.269643 + 0.962960i \(0.586906\pi\)
\(284\) 340.671 196.687i 0.0711800 0.0410958i
\(285\) 0 0
\(286\) 44.0914 2686.01i 0.00911601 0.555339i
\(287\) 8799.33 1.80978
\(288\) 0 0
\(289\) 1173.51 + 2032.57i 0.238857 + 0.413713i
\(290\) −1728.57 + 2993.96i −0.350017 + 0.606247i
\(291\) 0 0
\(292\) 250.444 + 144.594i 0.0501922 + 0.0289785i
\(293\) 6466.60 + 3733.49i 1.28936 + 0.744413i 0.978540 0.206055i \(-0.0660627\pi\)
0.310821 + 0.950468i \(0.399396\pi\)
\(294\) 0 0
\(295\) −2651.29 + 4592.18i −0.523269 + 0.906328i
\(296\) −2758.28 4777.49i −0.541628 0.938128i
\(297\) 0 0
\(298\) −873.759 −0.169851
\(299\) −6456.18 3870.14i −1.24873 0.748548i
\(300\) 0 0
\(301\) −4947.29 + 2856.32i −0.947365 + 0.546962i
\(302\) −1635.66 2833.05i −0.311662 0.539814i
\(303\) 0 0
\(304\) 1966.58i 0.371024i
\(305\) −2994.14 1728.67i −0.562112 0.324536i
\(306\) 0 0
\(307\) 3965.99i 0.737299i −0.929568 0.368650i \(-0.879820\pi\)
0.929568 0.368650i \(-0.120180\pi\)
\(308\) −1597.82 + 2767.50i −0.295598 + 0.511991i
\(309\) 0 0
\(310\) 4778.06 2758.61i 0.875405 0.505415i
\(311\) 7372.29 1.34419 0.672097 0.740463i \(-0.265394\pi\)
0.672097 + 0.740463i \(0.265394\pi\)
\(312\) 0 0
\(313\) 8249.55 1.48975 0.744875 0.667204i \(-0.232509\pi\)
0.744875 + 0.667204i \(0.232509\pi\)
\(314\) −1291.72 + 745.772i −0.232152 + 0.134033i
\(315\) 0 0
\(316\) −33.6067 + 58.2084i −0.00598267 + 0.0103623i
\(317\) 5575.26i 0.987817i −0.869514 0.493909i \(-0.835568\pi\)
0.869514 0.493909i \(-0.164432\pi\)
\(318\) 0 0
\(319\) −3405.08 1965.92i −0.597642 0.345049i
\(320\) 5634.21i 0.984256i
\(321\) 0 0
\(322\) −4876.44 8446.25i −0.843955 1.46177i
\(323\) 4612.76 2663.18i 0.794615 0.458771i
\(324\) 0 0
\(325\) 859.819 477.775i 0.146751 0.0815452i
\(326\) −3876.91 −0.658657
\(327\) 0 0
\(328\) −3574.23 6190.74i −0.601688 1.04215i
\(329\) −549.099 + 951.068i −0.0920146 + 0.159374i
\(330\) 0 0
\(331\) −3600.38 2078.68i −0.597870 0.345180i 0.170333 0.985387i \(-0.445516\pi\)
−0.768203 + 0.640206i \(0.778849\pi\)
\(332\) −4851.91 2801.25i −0.802057 0.463068i
\(333\) 0 0
\(334\) −1457.65 + 2524.73i −0.238800 + 0.413614i
\(335\) 3244.91 + 5620.35i 0.529219 + 0.916634i
\(336\) 0 0
\(337\) −3225.18 −0.521326 −0.260663 0.965430i \(-0.583941\pi\)
−0.260663 + 0.965430i \(0.583941\pi\)
\(338\) 147.264 4484.39i 0.0236986 0.721653i
\(339\) 0 0
\(340\) −2029.67 + 1171.83i −0.323749 + 0.186916i
\(341\) 3137.41 + 5434.15i 0.498241 + 0.862979i
\(342\) 0 0
\(343\) 5897.11i 0.928321i
\(344\) 4019.11 + 2320.44i 0.629930 + 0.363690i
\(345\) 0 0
\(346\) 4175.15i 0.648721i
\(347\) 1645.25 2849.65i 0.254529 0.440856i −0.710239 0.703961i \(-0.751413\pi\)
0.964767 + 0.263104i \(0.0847464\pi\)
\(348\) 0 0
\(349\) −3889.77 + 2245.76i −0.596604 + 0.344449i −0.767704 0.640804i \(-0.778601\pi\)
0.171101 + 0.985254i \(0.445268\pi\)
\(350\) 1274.48 0.194639
\(351\) 0 0
\(352\) 4351.81 0.658955
\(353\) 5107.71 2948.94i 0.770130 0.444635i −0.0627907 0.998027i \(-0.520000\pi\)
0.832921 + 0.553392i \(0.186667\pi\)
\(354\) 0 0
\(355\) 620.607 1074.92i 0.0927843 0.160707i
\(356\) 1282.43i 0.190924i
\(357\) 0 0
\(358\) 6879.49 + 3971.87i 1.01562 + 0.586369i
\(359\) 9277.20i 1.36388i 0.731410 + 0.681938i \(0.238863\pi\)
−0.731410 + 0.681938i \(0.761137\pi\)
\(360\) 0 0
\(361\) 2098.59 + 3634.87i 0.305962 + 0.529942i
\(362\) 4380.94 2529.33i 0.636069 0.367234i
\(363\) 0 0
\(364\) −2744.21 + 4577.90i −0.395152 + 0.659195i
\(365\) 912.477 0.130853
\(366\) 0 0
\(367\) 3287.18 + 5693.56i 0.467546 + 0.809814i 0.999312 0.0370774i \(-0.0118048\pi\)
−0.531766 + 0.846891i \(0.678471\pi\)
\(368\) −1501.77 + 2601.14i −0.212732 + 0.368462i
\(369\) 0 0
\(370\) −4879.75 2817.33i −0.685638 0.395853i
\(371\) 3839.86 + 2216.94i 0.537347 + 0.310237i
\(372\) 0 0
\(373\) 2672.77 4629.38i 0.371021 0.642628i −0.618702 0.785626i \(-0.712341\pi\)
0.989723 + 0.142998i \(0.0456743\pi\)
\(374\) 1451.60 + 2514.25i 0.200697 + 0.347617i
\(375\) 0 0
\(376\) 892.162 0.122366
\(377\) −5632.55 3376.41i −0.769472 0.461258i
\(378\) 0 0
\(379\) 899.378 519.256i 0.121894 0.0703757i −0.437813 0.899066i \(-0.644247\pi\)
0.559707 + 0.828690i \(0.310914\pi\)
\(380\) −2432.43 4213.10i −0.328372 0.568756i
\(381\) 0 0
\(382\) 4649.80i 0.622786i
\(383\) −5844.97 3374.59i −0.779801 0.450219i 0.0565585 0.998399i \(-0.481987\pi\)
−0.836360 + 0.548181i \(0.815321\pi\)
\(384\) 0 0
\(385\) 10083.2i 1.33478i
\(386\) 4005.27 6937.33i 0.528142 0.914769i
\(387\) 0 0
\(388\) 2483.04 1433.59i 0.324890 0.187575i
\(389\) −1246.11 −0.162417 −0.0812083 0.996697i \(-0.525878\pi\)
−0.0812083 + 0.996697i \(0.525878\pi\)
\(390\) 0 0
\(391\) 8134.89 1.05217
\(392\) −11325.0 + 6538.50i −1.45918 + 0.842459i
\(393\) 0 0
\(394\) −5170.17 + 8954.99i −0.661090 + 1.14504i
\(395\) 212.079i 0.0270148i
\(396\) 0 0
\(397\) −7236.24 4177.85i −0.914802 0.528161i −0.0328293 0.999461i \(-0.510452\pi\)
−0.881973 + 0.471300i \(0.843785\pi\)
\(398\) 6678.25i 0.841082i
\(399\) 0 0
\(400\) −196.247 339.910i −0.0245309 0.0424887i
\(401\) −2843.73 + 1641.83i −0.354137 + 0.204461i −0.666506 0.745500i \(-0.732211\pi\)
0.312369 + 0.949961i \(0.398878\pi\)
\(402\) 0 0
\(403\) 5090.47 + 9160.98i 0.629217 + 1.13236i
\(404\) −3002.14 −0.369708
\(405\) 0 0
\(406\) −4254.34 7368.74i −0.520048 0.900749i
\(407\) 3204.18 5549.81i 0.390235 0.675906i
\(408\) 0 0
\(409\) 9464.72 + 5464.46i 1.14426 + 0.660636i 0.947481 0.319813i \(-0.103620\pi\)
0.196775 + 0.980449i \(0.436953\pi\)
\(410\) −6323.26 3650.74i −0.761667 0.439749i
\(411\) 0 0
\(412\) 758.267 1313.36i 0.0906726 0.157050i
\(413\) −6525.36 11302.3i −0.777462 1.34660i
\(414\) 0 0
\(415\) −17677.6 −2.09099
\(416\) 7267.47 + 119.297i 0.856531 + 0.0140601i
\(417\) 0 0
\(418\) −5218.96 + 3013.17i −0.610688 + 0.352581i
\(419\) 3651.47 + 6324.53i 0.425742 + 0.737407i 0.996489 0.0837185i \(-0.0266796\pi\)
−0.570747 + 0.821126i \(0.693346\pi\)
\(420\) 0 0
\(421\) 7580.99i 0.877612i −0.898582 0.438806i \(-0.855401\pi\)
0.898582 0.438806i \(-0.144599\pi\)
\(422\) 4973.71 + 2871.57i 0.573736 + 0.331247i
\(423\) 0 0
\(424\) 3602.03i 0.412571i
\(425\) −531.521 + 920.622i −0.0606649 + 0.105075i
\(426\) 0 0
\(427\) 7369.18 4254.60i 0.835175 0.482188i
\(428\) 5501.06 0.621270
\(429\) 0 0
\(430\) 4740.21 0.531612
\(431\) −8709.40 + 5028.37i −0.973357 + 0.561968i −0.900258 0.435357i \(-0.856622\pi\)
−0.0730993 + 0.997325i \(0.523289\pi\)
\(432\) 0 0
\(433\) 1366.69 2367.18i 0.151683 0.262723i −0.780163 0.625576i \(-0.784864\pi\)
0.931846 + 0.362853i \(0.118197\pi\)
\(434\) 13579.0i 1.50187i
\(435\) 0 0
\(436\) −6559.22 3786.97i −0.720481 0.415970i
\(437\) 16886.0i 1.84844i
\(438\) 0 0
\(439\) 3372.12 + 5840.68i 0.366611 + 0.634989i 0.989033 0.147692i \(-0.0471846\pi\)
−0.622422 + 0.782682i \(0.713851\pi\)
\(440\) 7094.03 4095.74i 0.768624 0.443765i
\(441\) 0 0
\(442\) 2355.24 + 4238.56i 0.253455 + 0.456126i
\(443\) −8655.69 −0.928317 −0.464158 0.885752i \(-0.653643\pi\)
−0.464158 + 0.885752i \(0.653643\pi\)
\(444\) 0 0
\(445\) 2023.24 + 3504.35i 0.215530 + 0.373308i
\(446\) 937.120 1623.14i 0.0994931 0.172327i
\(447\) 0 0
\(448\) 12009.1 + 6933.45i 1.26646 + 0.731193i
\(449\) −5648.62 3261.23i −0.593708 0.342777i 0.172854 0.984947i \(-0.444701\pi\)
−0.766562 + 0.642170i \(0.778034\pi\)
\(450\) 0 0
\(451\) 4152.03 7191.53i 0.433507 0.750856i
\(452\) 234.360 + 405.923i 0.0243879 + 0.0422411i
\(453\) 0 0
\(454\) 2729.23 0.282135
\(455\) −276.414 + 16838.9i −0.0284802 + 1.73499i
\(456\) 0 0
\(457\) −1343.40 + 775.613i −0.137509 + 0.0793909i −0.567176 0.823596i \(-0.691964\pi\)
0.429667 + 0.902987i \(0.358631\pi\)
\(458\) 168.301 + 291.507i 0.0171708 + 0.0297406i
\(459\) 0 0
\(460\) 7430.06i 0.753105i
\(461\) 6725.77 + 3883.12i 0.679501 + 0.392310i 0.799667 0.600444i \(-0.205009\pi\)
−0.120166 + 0.992754i \(0.538343\pi\)
\(462\) 0 0
\(463\) 2004.52i 0.201205i 0.994927 + 0.100603i \(0.0320771\pi\)
−0.994927 + 0.100603i \(0.967923\pi\)
\(464\) −1310.19 + 2269.31i −0.131086 + 0.227048i
\(465\) 0 0
\(466\) −7505.06 + 4333.05i −0.746063 + 0.430739i
\(467\) 18674.3 1.85042 0.925209 0.379458i \(-0.123889\pi\)
0.925209 + 0.379458i \(0.123889\pi\)
\(468\) 0 0
\(469\) −15972.7 −1.57261
\(470\) 789.173 455.629i 0.0774507 0.0447162i
\(471\) 0 0
\(472\) −5301.11 + 9181.80i −0.516957 + 0.895395i
\(473\) 5391.11i 0.524067i
\(474\) 0 0
\(475\) −1910.98 1103.31i −0.184594 0.106575i
\(476\) 5768.22i 0.555433i
\(477\) 0 0
\(478\) −2543.68 4405.79i −0.243400 0.421581i
\(479\) −8065.31 + 4656.51i −0.769340 + 0.444178i −0.832639 0.553816i \(-0.813171\pi\)
0.0632994 + 0.997995i \(0.479838\pi\)
\(480\) 0 0
\(481\) 5503.09 9180.28i 0.521662 0.870239i
\(482\) −5958.03 −0.563031
\(483\) 0 0
\(484\) −1040.47 1802.15i −0.0977155 0.169248i
\(485\) 4523.41 7834.77i 0.423500 0.733523i
\(486\) 0 0
\(487\) 3062.96 + 1768.40i 0.285002 + 0.164546i 0.635686 0.771948i \(-0.280717\pi\)
−0.350684 + 0.936494i \(0.614051\pi\)
\(488\) −5986.62 3456.38i −0.555331 0.320621i
\(489\) 0 0
\(490\) −6678.46 + 11567.4i −0.615718 + 1.06646i
\(491\) 1680.89 + 2911.39i 0.154496 + 0.267595i 0.932875 0.360199i \(-0.117291\pi\)
−0.778379 + 0.627794i \(0.783958\pi\)
\(492\) 0 0
\(493\) 7097.10 0.648351
\(494\) −8798.20 + 4888.88i −0.801315 + 0.445266i
\(495\) 0 0
\(496\) 3621.58 2090.92i 0.327851 0.189285i
\(497\) 1527.44 + 2645.60i 0.137857 + 0.238775i
\(498\) 0 0
\(499\) 4027.43i 0.361308i 0.983547 + 0.180654i \(0.0578214\pi\)
−0.983547 + 0.180654i \(0.942179\pi\)
\(500\) −4167.66 2406.20i −0.372767 0.215217i
\(501\) 0 0
\(502\) 2683.26i 0.238565i
\(503\) 883.336 1529.98i 0.0783022 0.135623i −0.824215 0.566277i \(-0.808383\pi\)
0.902518 + 0.430653i \(0.141717\pi\)
\(504\) 0 0
\(505\) −8203.57 + 4736.33i −0.722880 + 0.417355i
\(506\) −9203.96 −0.808628
\(507\) 0 0
\(508\) −8844.05 −0.772424
\(509\) 5903.06 3408.13i 0.514044 0.296784i −0.220450 0.975398i \(-0.570753\pi\)
0.734495 + 0.678615i \(0.237419\pi\)
\(510\) 0 0
\(511\) −1122.89 + 1944.91i −0.0972091 + 0.168371i
\(512\) 6514.89i 0.562344i
\(513\) 0 0
\(514\) 1746.67 + 1008.44i 0.149888 + 0.0865378i
\(515\) 4785.13i 0.409433i
\(516\) 0 0
\(517\) 518.194 + 897.538i 0.0440815 + 0.0763514i
\(518\) 12010.0 6933.99i 1.01871 0.588151i
\(519\) 0 0
\(520\) 11959.2 6645.37i 1.00855 0.560421i
\(521\) 5442.27 0.457640 0.228820 0.973469i \(-0.426513\pi\)
0.228820 + 0.973469i \(0.426513\pi\)
\(522\) 0 0
\(523\) −10364.3 17951.4i −0.866535 1.50088i −0.865515 0.500883i \(-0.833009\pi\)
−0.00101984 0.999999i \(-0.500325\pi\)
\(524\) −2765.22 + 4789.49i −0.230532 + 0.399294i
\(525\) 0 0
\(526\) −12356.5 7134.01i −1.02427 0.591365i
\(527\) −9808.81 5663.12i −0.810775 0.468101i
\(528\) 0 0
\(529\) −6811.41 + 11797.7i −0.559827 + 0.969648i
\(530\) −1839.57 3186.22i −0.150765 0.261133i
\(531\) 0 0
\(532\) 11973.4 0.975775
\(533\) 7130.99 11896.0i 0.579508 0.966738i
\(534\) 0 0
\(535\) 15032.1 8678.77i 1.21475 0.701339i
\(536\) 6488.01 + 11237.6i 0.522835 + 0.905577i
\(537\) 0 0
\(538\) 12058.1i 0.966285i
\(539\) −13155.8 7595.50i −1.05132 0.606979i
\(540\) 0 0
\(541\) 8577.44i 0.681651i 0.940127 + 0.340825i \(0.110706\pi\)
−0.940127 + 0.340825i \(0.889294\pi\)
\(542\) −2176.56 + 3769.92i −0.172493 + 0.298767i
\(543\) 0 0
\(544\) −6802.75 + 3927.57i −0.536150 + 0.309546i
\(545\) −23898.1 −1.87832
\(546\) 0 0
\(547\) 8723.99 0.681921 0.340961 0.940078i \(-0.389248\pi\)
0.340961 + 0.940078i \(0.389248\pi\)
\(548\) 2440.47 1409.01i 0.190240 0.109835i
\(549\) 0 0
\(550\) 601.373 1041.61i 0.0466230 0.0807533i
\(551\) 14731.8i 1.13901i
\(552\) 0 0
\(553\) −452.037 260.984i −0.0347606 0.0200690i
\(554\) 8235.17i 0.631550i
\(555\) 0 0
\(556\) 2881.78 + 4991.39i 0.219810 + 0.380723i
\(557\) 835.720 482.503i 0.0635738 0.0367043i −0.467876 0.883794i \(-0.654981\pi\)
0.531450 + 0.847090i \(0.321647\pi\)
\(558\) 0 0
\(559\) −147.788 + 9003.09i −0.0111820 + 0.681199i
\(560\) 6719.95 0.507089
\(561\) 0 0
\(562\) 2346.83 + 4064.83i 0.176148 + 0.305097i
\(563\) 7302.60 12648.5i 0.546657 0.946837i −0.451844 0.892097i \(-0.649234\pi\)
0.998501 0.0547402i \(-0.0174331\pi\)
\(564\) 0 0
\(565\) 1280.81 + 739.477i 0.0953702 + 0.0550620i
\(566\) 11773.4 + 6797.40i 0.874337 + 0.504799i
\(567\) 0 0
\(568\) 1240.87 2149.25i 0.0916650 0.158768i
\(569\) −3901.24 6757.15i −0.287432 0.497846i 0.685764 0.727824i \(-0.259468\pi\)
−0.973196 + 0.229977i \(0.926135\pi\)
\(570\) 0 0
\(571\) −11988.2 −0.878618 −0.439309 0.898336i \(-0.644777\pi\)
−0.439309 + 0.898336i \(0.644777\pi\)
\(572\) 2446.56 + 4402.91i 0.178839 + 0.321844i
\(573\) 0 0
\(574\) 15562.8 8985.18i 1.13167 0.653370i
\(575\) −1685.07 2918.63i −0.122213 0.211678i
\(576\) 0 0
\(577\) 5576.90i 0.402374i −0.979553 0.201187i \(-0.935520\pi\)
0.979553 0.201187i \(-0.0644798\pi\)
\(578\) 4151.01 + 2396.58i 0.298718 + 0.172465i
\(579\) 0 0
\(580\) 6482.19i 0.464066i
\(581\) 21754.1 37679.1i 1.55337 2.69052i
\(582\) 0 0
\(583\) 3623.74 2092.17i 0.257427 0.148626i
\(584\) 1824.45 0.129274
\(585\) 0 0
\(586\) 15249.4 1.07499
\(587\) 23169.7 13377.0i 1.62916 0.940593i 0.644810 0.764343i \(-0.276936\pi\)
0.984345 0.176251i \(-0.0563969\pi\)
\(588\) 0 0
\(589\) 11755.2 20360.6i 0.822353 1.42436i
\(590\) 10829.2i 0.755644i
\(591\) 0 0
\(592\) −3698.66 2135.42i −0.256781 0.148252i
\(593\) 3589.40i 0.248565i 0.992247 + 0.124283i \(0.0396629\pi\)
−0.992247 + 0.124283i \(0.960337\pi\)
\(594\) 0 0
\(595\) −9100.26 15762.1i −0.627016 1.08602i
\(596\) 1418.82 819.158i 0.0975122 0.0562987i
\(597\) 0 0
\(598\) −15370.5 252.310i −1.05108 0.0172537i
\(599\) 7462.78 0.509050 0.254525 0.967066i \(-0.418081\pi\)
0.254525 + 0.967066i \(0.418081\pi\)
\(600\) 0 0
\(601\) 8255.52 + 14299.0i 0.560316 + 0.970495i 0.997469 + 0.0711081i \(0.0226535\pi\)
−0.437153 + 0.899387i \(0.644013\pi\)
\(602\) −5833.30 + 10103.6i −0.394929 + 0.684037i
\(603\) 0 0
\(604\) 5312.02 + 3066.90i 0.357853 + 0.206606i
\(605\) −5686.35 3283.02i −0.382121 0.220618i
\(606\) 0 0
\(607\) 5976.78 10352.1i 0.399654 0.692222i −0.594029 0.804444i \(-0.702464\pi\)
0.993683 + 0.112222i \(0.0357968\pi\)
\(608\) −8152.66 14120.8i −0.543806 0.941900i
\(609\) 0 0
\(610\) −7060.73 −0.468657
\(611\) 840.773 + 1513.08i 0.0556695 + 0.100185i
\(612\) 0 0
\(613\) 3962.63 2287.82i 0.261091 0.150741i −0.363741 0.931500i \(-0.618501\pi\)
0.624832 + 0.780759i \(0.285167\pi\)
\(614\) −4049.76 7014.38i −0.266181 0.461038i
\(615\) 0 0
\(616\) 20160.9i 1.31868i
\(617\) 16654.6 + 9615.51i 1.08669 + 0.627400i 0.932693 0.360671i \(-0.117452\pi\)
0.153996 + 0.988071i \(0.450786\pi\)
\(618\) 0 0
\(619\) 11715.6i 0.760727i −0.924837 0.380363i \(-0.875799\pi\)
0.924837 0.380363i \(-0.124201\pi\)
\(620\) −5172.45 + 8958.95i −0.335050 + 0.580323i
\(621\) 0 0
\(622\) 13038.9 7528.00i 0.840533 0.485282i
\(623\) −9959.17 −0.640459
\(624\) 0 0
\(625\) −17807.8 −1.13970
\(626\) 14590.4 8423.79i 0.931551 0.537831i
\(627\) 0 0
\(628\) 1398.34 2421.99i 0.0888531 0.153898i
\(629\) 11567.3i 0.733256i
\(630\) 0 0
\(631\) 7603.78 + 4390.04i 0.479717 + 0.276965i 0.720299 0.693664i \(-0.244005\pi\)
−0.240581 + 0.970629i \(0.577338\pi\)
\(632\) 424.040i 0.0266889i
\(633\) 0 0
\(634\) −5693.02 9860.60i −0.356623 0.617689i
\(635\) −24167.1 + 13952.9i −1.51030 + 0.871973i
\(636\) 0 0
\(637\) −21761.8 13045.0i −1.35359 0.811403i
\(638\) −8029.78 −0.498279
\(639\) 0 0
\(640\) 1741.28 + 3015.98i 0.107547 + 0.186277i
\(641\) −12495.9 + 21643.5i −0.769980 + 1.33364i 0.167593 + 0.985856i \(0.446401\pi\)
−0.937573 + 0.347789i \(0.886933\pi\)
\(642\) 0 0
\(643\) −2038.50 1176.93i −0.125024 0.0721827i 0.436184 0.899858i \(-0.356330\pi\)
−0.561208 + 0.827675i \(0.689663\pi\)
\(644\) 15836.9 + 9143.42i 0.969038 + 0.559474i
\(645\) 0 0
\(646\) 5438.85 9420.37i 0.331252 0.573745i
\(647\) 2955.40 + 5118.90i 0.179581 + 0.311043i 0.941737 0.336350i \(-0.109193\pi\)
−0.762156 + 0.647393i \(0.775859\pi\)
\(648\) 0 0
\(649\) −12316.2 −0.744918
\(650\) 1032.84 1722.99i 0.0623251 0.103971i
\(651\) 0 0
\(652\) 6295.38 3634.64i 0.378138 0.218318i
\(653\) 2962.17 + 5130.63i 0.177517 + 0.307469i 0.941029 0.338325i \(-0.109860\pi\)
−0.763512 + 0.645793i \(0.776527\pi\)
\(654\) 0 0
\(655\) 17450.2i 1.04097i
\(656\) −4792.79 2767.12i −0.285254 0.164692i
\(657\) 0 0
\(658\) 2242.79i 0.132877i
\(659\) −6419.77 + 11119.4i −0.379482 + 0.657282i −0.990987 0.133958i \(-0.957231\pi\)
0.611505 + 0.791241i \(0.290564\pi\)
\(660\) 0 0
\(661\) 8890.18 5132.75i 0.523129 0.302028i −0.215085 0.976595i \(-0.569003\pi\)
0.738214 + 0.674567i \(0.235670\pi\)
\(662\) −8490.35 −0.498469
\(663\) 0 0
\(664\) −35345.4 −2.06577
\(665\) 32718.2 18889.9i 1.90791 1.10153i
\(666\) 0 0
\(667\) −11249.9 + 19485.4i −0.653069 + 1.13115i
\(668\) 5466.25i 0.316610i
\(669\) 0 0
\(670\) 11478.1 + 6626.89i 0.661848 + 0.382118i
\(671\) 8030.27i 0.462004i
\(672\) 0 0
\(673\) 4931.41 + 8541.45i 0.282454 + 0.489225i 0.971989 0.235028i \(-0.0755181\pi\)
−0.689534 + 0.724253i \(0.742185\pi\)
\(674\) −5704.17 + 3293.30i −0.325989 + 0.188210i
\(675\) 0 0
\(676\) 3965.03 + 7419.88i 0.225593 + 0.422160i
\(677\) −32615.5 −1.85158 −0.925788 0.378043i \(-0.876597\pi\)
−0.925788 + 0.378043i \(0.876597\pi\)
\(678\) 0 0
\(679\) 11133.0 + 19282.9i 0.629227 + 1.08985i
\(680\) −7392.93 + 12804.9i −0.416921 + 0.722128i
\(681\) 0 0
\(682\) 11097.9 + 6407.35i 0.623107 + 0.359751i
\(683\) −18729.9 10813.7i −1.04931 0.605820i −0.126854 0.991921i \(-0.540488\pi\)
−0.922456 + 0.386102i \(0.873821\pi\)
\(684\) 0 0
\(685\) 4445.85 7700.44i 0.247981 0.429516i
\(686\) −6021.66 10429.8i −0.335143 0.580485i
\(687\) 0 0
\(688\) 3592.90 0.199096
\(689\) 6108.95 3394.56i 0.337783 0.187696i
\(690\) 0 0
\(691\) −12326.3 + 7116.57i −0.678601 + 0.391790i −0.799328 0.600896i \(-0.794811\pi\)
0.120727 + 0.992686i \(0.461477\pi\)
\(692\) 3914.25 + 6779.67i 0.215025 + 0.372434i
\(693\) 0 0
\(694\) 6719.98i 0.367561i
\(695\) 15749.4 + 9092.90i 0.859579 + 0.496278i
\(696\) 0 0
\(697\) 14989.1i 0.814566i
\(698\) −4586.39 + 7943.86i −0.248707 + 0.430773i
\(699\) 0 0
\(700\) −2069.52 + 1194.84i −0.111743 + 0.0645151i
\(701\) −28747.0 −1.54887 −0.774437 0.632651i \(-0.781967\pi\)
−0.774437 + 0.632651i \(0.781967\pi\)
\(702\) 0 0
\(703\) −24010.8 −1.28817
\(704\) 11333.2 6543.21i 0.606726 0.350293i
\(705\) 0 0
\(706\) 6022.45 10431.2i 0.321045 0.556066i
\(707\) 23314.1i 1.24019i
\(708\) 0 0
\(709\) 1575.00 + 909.324i 0.0834276 + 0.0481670i 0.541133 0.840937i \(-0.317995\pi\)
−0.457706 + 0.889104i \(0.651329\pi\)
\(710\) 2534.86i 0.133988i
\(711\) 0 0
\(712\) 4045.35 + 7006.75i 0.212930 + 0.368805i
\(713\) 31096.6 17953.6i 1.63335 0.943014i
\(714\) 0 0
\(715\) 13631.7 + 8171.47i 0.713002 + 0.427407i
\(716\) −14894.7 −0.777431
\(717\) 0 0
\(718\) 9473.15 + 16408.0i 0.492388 + 0.852841i
\(719\) −13070.9 + 22639.5i −0.677973 + 1.17428i 0.297617 + 0.954685i \(0.403808\pi\)
−0.975590 + 0.219599i \(0.929525\pi\)
\(720\) 0 0
\(721\) 10199.3 + 5888.58i 0.526827 + 0.304164i
\(722\) 7423.29 + 4285.84i 0.382640 + 0.220917i
\(723\) 0 0
\(724\) −4742.55 + 8214.34i −0.243447 + 0.421662i
\(725\) −1470.10 2546.29i −0.0753078 0.130437i
\(726\) 0 0
\(727\) 1340.10 0.0683652 0.0341826 0.999416i \(-0.489117\pi\)
0.0341826 + 0.999416i \(0.489117\pi\)
\(728\) −552.674 + 33668.4i −0.0281366 + 1.71406i
\(729\) 0 0
\(730\) 1613.84 931.750i 0.0818231 0.0472406i
\(731\) −4865.56 8427.39i −0.246182 0.426400i
\(732\) 0 0
\(733\) 32517.1i 1.63854i 0.573409 + 0.819269i \(0.305620\pi\)
−0.573409 + 0.819269i \(0.694380\pi\)
\(734\) 11627.6 + 6713.22i 0.584719 + 0.337588i
\(735\) 0 0
\(736\) 24903.0i 1.24719i
\(737\) −7536.86 + 13054.2i −0.376694 + 0.652454i
\(738\) 0 0
\(739\) −19200.2 + 11085.3i −0.955741 + 0.551797i −0.894860 0.446348i \(-0.852724\pi\)
−0.0608813 + 0.998145i \(0.519391\pi\)
\(740\) 10565.1 0.524838
\(741\) 0 0
\(742\) 9055.07 0.448008
\(743\) −26316.6 + 15193.9i −1.29941 + 0.750216i −0.980303 0.197502i \(-0.936717\pi\)
−0.319110 + 0.947718i \(0.603384\pi\)
\(744\) 0 0
\(745\) 2584.70 4476.83i 0.127109 0.220159i
\(746\) 10916.9i 0.535786i
\(747\) 0 0
\(748\) −4714.27 2721.78i −0.230442 0.133046i
\(749\) 42720.3i 2.08407i
\(750\) 0 0
\(751\) −8449.17 14634.4i −0.410539 0.711074i 0.584410 0.811459i \(-0.301326\pi\)
−0.994949 + 0.100385i \(0.967993\pi\)
\(752\) 598.163 345.350i 0.0290063 0.0167468i
\(753\) 0 0
\(754\) −13409.6 220.122i −0.647680 0.0106318i
\(755\) 19354.0 0.932934
\(756\) 0 0
\(757\) −16462.9 28514.6i −0.790428 1.36906i −0.925702 0.378253i \(-0.876525\pi\)
0.135275 0.990808i \(-0.456808\pi\)
\(758\) 1060.45 1836.75i 0.0508142 0.0880128i
\(759\) 0 0
\(760\) −26579.9 15345.9i −1.26862 0.732440i
\(761\) −14542.3 8396.01i −0.692718 0.399941i 0.111911 0.993718i \(-0.464303\pi\)
−0.804630 + 0.593777i \(0.797636\pi\)
\(762\) 0 0
\(763\) 29409.0 50937.8i 1.39538 2.41687i
\(764\) 4359.23 + 7550.41i 0.206429 + 0.357545i
\(765\) 0 0
\(766\) −13783.5 −0.650153
\(767\) −20567.9 337.626i −0.968270 0.0158944i
\(768\) 0 0
\(769\) 1335.04 770.783i 0.0626042 0.0361445i −0.468371 0.883532i \(-0.655159\pi\)
0.530975 + 0.847387i \(0.321826\pi\)
\(770\) 10296.2 + 17833.5i 0.481882 + 0.834645i
\(771\) 0 0
\(772\) 15019.9i 0.700231i
\(773\) 32970.6 + 19035.6i 1.53411 + 0.885721i 0.999166 + 0.0408357i \(0.0130020\pi\)
0.534948 + 0.844885i \(0.320331\pi\)
\(774\) 0 0
\(775\) 4692.26i 0.217485i
\(776\) 9044.30 15665.2i 0.418391 0.724674i
\(777\) 0 0
\(778\) −2203.91 + 1272.43i −0.101560 + 0.0586358i
\(779\) −31113.6 −1.43102
\(780\) 0 0
\(781\) 2882.93 0.132086
\(782\) 14387.6 8306.71i 0.657930 0.379856i
\(783\) 0 0
\(784\) −5062.01 + 8767.66i −0.230595 + 0.399401i
\(785\) 8824.38i 0.401217i
\(786\) 0 0
\(787\) −17363.6 10024.9i −0.786463 0.454065i 0.0522528 0.998634i \(-0.483360\pi\)
−0.838716 + 0.544569i \(0.816693\pi\)
\(788\) 19388.3i 0.876498i
\(789\) 0 0
\(790\) 216.558 + 375.090i 0.00975291 + 0.0168925i
\(791\) −3152.33 + 1820.00i −0.141699 + 0.0818100i
\(792\) 0 0
\(793\) 220.136 13410.5i 0.00985781 0.600529i
\(794\) −17064.4 −0.762709
\(795\) 0 0
\(796\) 6260.93 + 10844.2i 0.278785 + 0.482869i
\(797\) 11200.9 19400.6i 0.497813 0.862238i −0.502183 0.864761i \(-0.667470\pi\)
0.999997 + 0.00252302i \(0.000803104\pi\)
\(798\) 0 0
\(799\) −1620.08 935.355i −0.0717327 0.0414149i
\(800\) 2818.26 + 1627.12i 0.124551 + 0.0719093i
\(801\) 0 0
\(802\) −3353.01 + 5807.59i −0.147630 + 0.255702i
\(803\) 1059.69 + 1835.44i 0.0465700 + 0.0806617i
\(804\) 0 0
\(805\) 57700.7 2.52631
\(806\) 18357.7 + 11004.4i 0.802259 + 0.480911i
\(807\) 0 0
\(808\) −16402.6 + 9470.04i −0.714159 + 0.412320i
\(809\) −20983.2 36343.9i −0.911903 1.57946i −0.811373 0.584528i \(-0.801280\pi\)
−0.100530 0.994934i \(-0.532054\pi\)
\(810\) 0 0
\(811\) 13029.1i 0.564133i 0.959395 + 0.282067i \(0.0910199\pi\)
−0.959395 + 0.282067i \(0.908980\pi\)
\(812\) 13816.5 + 7976.97i 0.597124 + 0.344750i
\(813\) 0 0
\(814\) 13087.4i 0.563532i
\(815\) 11468.4 19863.9i 0.492909 0.853744i
\(816\) 0 0
\(817\) 17493.2 10099.7i 0.749092 0.432489i
\(818\) 22319.5 0.954014
\(819\) 0 0
\(820\) 13690.4 0.583036
\(821\) 7706.01 4449.07i 0.327578 0.189127i −0.327187 0.944960i \(-0.606101\pi\)
0.654765 + 0.755832i \(0.272767\pi\)
\(822\) 0 0
\(823\) 11361.8 19679.2i 0.481224 0.833504i −0.518544 0.855051i \(-0.673526\pi\)
0.999768 + 0.0215466i \(0.00685902\pi\)
\(824\) 9567.61i 0.404494i
\(825\) 0 0
\(826\) −23081.9 13326.4i −0.972304 0.561360i
\(827\) 19073.3i 0.801989i −0.916081 0.400994i \(-0.868665\pi\)
0.916081 0.400994i \(-0.131335\pi\)
\(828\) 0 0
\(829\) 21251.9 + 36809.4i 0.890361 + 1.54215i 0.839443 + 0.543448i \(0.182881\pi\)
0.0509178 + 0.998703i \(0.483785\pi\)
\(830\) −31265.2 + 18051.0i −1.30751 + 0.754891i
\(831\) 0 0
\(832\) 19105.6 10616.4i 0.796116 0.442377i
\(833\) 27420.2 1.14052
\(834\) 0 0
\(835\) −8623.86 14937.0i −0.357414 0.619060i
\(836\) 5649.74 9785.65i 0.233733 0.404837i
\(837\) 0 0
\(838\) 12916.2 + 7457.19i 0.532439 + 0.307404i
\(839\) −16824.5 9713.62i −0.692307 0.399704i 0.112168 0.993689i \(-0.464220\pi\)
−0.804476 + 0.593985i \(0.797554\pi\)
\(840\) 0 0
\(841\) 2379.80 4121.94i 0.0975768 0.169008i
\(842\) −7741.11 13408.0i −0.316836 0.548777i
\(843\) 0 0
\(844\) −10768.5 −0.439180
\(845\) 22540.8 + 14020.0i 0.917664 + 0.570770i
\(846\) 0 0
\(847\) 13995.2 8080.15i 0.567747 0.327789i
\(848\) −1394.32 2415.03i −0.0564637 0.0977979i
\(849\) 0 0
\(850\) 2170.99i 0.0876052i
\(851\) −31758.5 18335.8i −1.27928 0.738592i
\(852\) 0 0
\(853\) 26851.8i 1.07783i 0.842361 + 0.538914i \(0.181165\pi\)
−0.842361 + 0.538914i \(0.818835\pi\)
\(854\) 8688.92 15049.7i 0.348160 0.603031i
\(855\) 0 0
\(856\) 30055.8 17352.7i 1.20010 0.692878i
\(857\) 41539.4 1.65573 0.827864 0.560929i \(-0.189556\pi\)
0.827864 + 0.560929i \(0.189556\pi\)
\(858\) 0 0
\(859\) −11936.2 −0.474107 −0.237054 0.971497i \(-0.576182\pi\)
−0.237054 + 0.971497i \(0.576182\pi\)
\(860\) −7697.22 + 4443.99i −0.305201 + 0.176208i
\(861\) 0 0
\(862\) −10269.2 + 17786.7i −0.405765 + 0.702805i
\(863\) 41128.6i 1.62229i 0.584848 + 0.811143i \(0.301154\pi\)
−0.584848 + 0.811143i \(0.698846\pi\)
\(864\) 0 0
\(865\) 21392.0 + 12350.7i 0.840866 + 0.485474i
\(866\) 5582.22i 0.219043i
\(867\) 0 0
\(868\) −12730.4 22049.7i −0.497810 0.862232i
\(869\) −426.595 + 246.295i −0.0166528 + 0.00961448i
\(870\) 0 0
\(871\) −12944.3 + 21593.8i −0.503561 + 0.840044i
\(872\) −47782.9 −1.85566
\(873\) 0 0
\(874\) 17242.7 + 29865.2i 0.667325 + 1.15584i
\(875\) 18686.1 32365.4i 0.721951 1.25046i
\(876\) 0 0
\(877\) −5548.50 3203.43i −0.213637 0.123343i 0.389364 0.921084i \(-0.372695\pi\)
−0.603001 + 0.797741i \(0.706028\pi\)
\(878\) 11928.1 + 6886.68i 0.458489 + 0.264709i
\(879\) 0 0
\(880\) 3170.87 5492.10i 0.121466 0.210385i
\(881\) 1469.04 + 2544.45i 0.0561783 + 0.0973037i 0.892747 0.450559i \(-0.148775\pi\)
−0.836569 + 0.547862i \(0.815442\pi\)
\(882\) 0 0
\(883\) −3022.06 −0.115176 −0.0575881 0.998340i \(-0.518341\pi\)
−0.0575881 + 0.998340i \(0.518341\pi\)
\(884\) −7798.16 4674.58i −0.296697 0.177854i
\(885\) 0 0
\(886\) −15308.8 + 8838.51i −0.580483 + 0.335142i
\(887\) −5030.22 8712.59i −0.190415 0.329809i 0.754973 0.655756i \(-0.227650\pi\)
−0.945388 + 0.325948i \(0.894317\pi\)
\(888\) 0 0
\(889\) 68681.5i 2.59112i
\(890\) 7156.74 + 4131.94i 0.269544 + 0.155621i
\(891\) 0 0
\(892\) 3514.24i 0.131912i
\(893\) 1941.57 3362.89i 0.0727570 0.126019i
\(894\) 0 0
\(895\) −40700.9 + 23498.7i −1.52009 + 0.877624i
\(896\) −8571.24 −0.319582
\(897\) 0 0
\(898\) −13320.5 −0.494999
\(899\) 27129.5 15663.2i 1.00647 0.581088i
\(900\) 0 0
\(901\) −3776.42 + 6540.95i −0.139635 + 0.241854i
\(902\) 16958.9i 0.626020i
\(903\) 0 0
\(904\) 2560.91 + 1478.54i 0.0942197 + 0.0543978i
\(905\) 29928.4i 1.09929i
\(906\) 0 0
\(907\) −21579.3 37376.5i −0.789999 1.36832i −0.925967 0.377606i \(-0.876748\pi\)
0.135967 0.990713i \(-0.456586\pi\)
\(908\) −4431.76 + 2558.68i −0.161975 + 0.0935163i
\(909\) 0 0
\(910\) 16705.7 + 30064.1i 0.608558 + 1.09518i
\(911\) 32665.9 1.18800 0.594001 0.804464i \(-0.297547\pi\)
0.594001 + 0.804464i \(0.297547\pi\)
\(912\) 0 0
\(913\) −20529.7 35558.4i −0.744176 1.28895i
\(914\) −1583.99 + 2743.55i −0.0573235 + 0.0992873i
\(915\) 0 0
\(916\) −546.581 315.568i −0.0197156 0.0113828i
\(917\) −37194.4 21474.2i −1.33944 0.773327i
\(918\) 0 0
\(919\) −9494.97 + 16445.8i −0.340816 + 0.590311i −0.984585 0.174909i \(-0.944037\pi\)
0.643768 + 0.765221i \(0.277370\pi\)
\(920\) −23437.6 40595.2i −0.839909 1.45476i
\(921\) 0 0
\(922\) 15860.6 0.566529
\(923\) 4814.47 + 79.0305i 0.171690 + 0.00281833i
\(924\) 0 0
\(925\) 4150.10 2396.06i 0.147518 0.0851698i
\(926\) 2046.86 + 3545.27i 0.0726393 + 0.125815i
\(927\) 0 0
\(928\) 21726.0i 0.768525i
\(929\) 4846.98 + 2798.40i 0.171178 + 0.0988295i 0.583141 0.812371i \(-0.301823\pi\)
−0.411963 + 0.911200i \(0.635157\pi\)
\(930\) 0 0
\(931\) 56917.6i 2.00365i
\(932\) 8124.55 14072.1i 0.285546 0.494579i
\(933\) 0 0
\(934\) 33028.1 19068.8i 1.15708 0.668040i
\(935\) −17176.1 −0.600770
\(936\) 0 0
\(937\) 40294.4 1.40487 0.702433 0.711750i \(-0.252097\pi\)
0.702433 + 0.711750i \(0.252097\pi\)
\(938\) −28249.9 + 16310.1i −0.983360 + 0.567743i
\(939\) 0 0
\(940\) −854.314 + 1479.72i −0.0296432 + 0.0513436i
\(941\) 43648.8i 1.51213i 0.654499 + 0.756063i \(0.272880\pi\)
−0.654499 + 0.756063i \(0.727120\pi\)
\(942\) 0 0
\(943\) −41153.1 23759.8i −1.42113 0.820492i
\(944\) 8208.10i 0.282999i
\(945\) 0 0
\(946\) 5504.98 + 9534.90i 0.189199 + 0.327702i
\(947\) 9081.62 5243.28i 0.311629 0.179919i −0.336026 0.941853i \(-0.609083\pi\)
0.647655 + 0.761933i \(0.275750\pi\)
\(948\) 0 0
\(949\) 1719.36 + 3094.22i 0.0588122 + 0.105840i
\(950\) −4506.44 −0.153903
\(951\) 0 0
\(952\) −18195.5 31515.5i −0.619452 1.07292i
\(953\) −16529.4 + 28629.7i −0.561846 + 0.973145i 0.435490 + 0.900194i \(0.356575\pi\)
−0.997335 + 0.0729517i \(0.976758\pi\)
\(954\) 0 0
\(955\) 23823.9 + 13754.7i 0.807249 + 0.466065i
\(956\) 8260.93 + 4769.45i 0.279475 + 0.161355i
\(957\) 0 0
\(958\) −9509.73 + 16471.3i −0.320715 + 0.555495i
\(959\) 10942.1 + 18952.3i 0.368445 + 0.638166i
\(960\) 0 0
\(961\) −20202.8 −0.678152
\(962\) 358.769 21855.9i 0.0120241 0.732497i
\(963\) 0 0
\(964\) 9674.74 5585.71i 0.323239 0.186622i
\(965\) 23696.2 + 41043.1i 0.790476 + 1.36914i
\(966\) 0 0
\(967\) 53634.9i 1.78364i 0.452389 + 0.891821i \(0.350572\pi\)
−0.452389 + 0.891821i \(0.649428\pi\)
\(968\) −11369.5 6564.21i −0.377511 0.217956i
\(969\) 0 0
\(970\) 18475.8i 0.611569i
\(971\) −2043.40 + 3539.27i −0.0675344 + 0.116973i −0.897815 0.440372i \(-0.854847\pi\)
0.830281 + 0.557345i \(0.188180\pi\)
\(972\) 0 0
\(973\) −38762.3 + 22379.4i −1.27715 + 0.737360i
\(974\) 7223.00 0.237618
\(975\) 0 0
\(976\) −5351.76 −0.175518
\(977\) 12454.3 7190.48i 0.407827 0.235459i −0.282028 0.959406i \(-0.591007\pi\)
0.689856 + 0.723947i \(0.257674\pi\)
\(978\) 0 0
\(979\) −4699.32 + 8139.46i −0.153413 + 0.265718i
\(980\) 25044.5i 0.816343i
\(981\) 0 0
\(982\) 5945.76 + 3432.79i 0.193215 + 0.111553i
\(983\) 12916.5i 0.419099i 0.977798 + 0.209549i \(0.0671997\pi\)
−0.977798 + 0.209549i \(0.932800\pi\)
\(984\) 0 0
\(985\) −30588.1 52980.1i −0.989460 1.71379i
\(986\) 12552.2 7247.00i 0.405418 0.234068i
\(987\) 0 0
\(988\) 9703.27 16187.0i 0.312451 0.521233i
\(989\) 30850.3 0.991893
\(990\) 0 0
\(991\) 2919.49 + 5056.71i 0.0935829 + 0.162090i 0.909016 0.416761i \(-0.136835\pi\)
−0.815433 + 0.578851i \(0.803501\pi\)
\(992\) −17336.2 + 30027.2i −0.554865 + 0.961055i
\(993\) 0 0
\(994\) 5402.95 + 3119.40i 0.172406 + 0.0995385i
\(995\) 34217.0 + 19755.2i 1.09020 + 0.629428i
\(996\) 0 0
\(997\) −22145.1 + 38356.4i −0.703452 + 1.21841i 0.263796 + 0.964579i \(0.415026\pi\)
−0.967247 + 0.253835i \(0.918308\pi\)
\(998\) 4112.50 + 7123.05i 0.130440 + 0.225928i
\(999\) 0 0
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 117.4.q.e.10.4 10
3.2 odd 2 39.4.j.c.10.2 yes 10
12.11 even 2 624.4.bv.h.49.2 10
13.2 odd 12 1521.4.a.bk.1.7 10
13.4 even 6 inner 117.4.q.e.82.4 10
13.11 odd 12 1521.4.a.bk.1.4 10
39.2 even 12 507.4.a.r.1.4 10
39.11 even 12 507.4.a.r.1.7 10
39.17 odd 6 39.4.j.c.4.2 10
39.23 odd 6 507.4.b.i.337.7 10
39.29 odd 6 507.4.b.i.337.4 10
156.95 even 6 624.4.bv.h.433.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.j.c.4.2 10 39.17 odd 6
39.4.j.c.10.2 yes 10 3.2 odd 2
117.4.q.e.10.4 10 1.1 even 1 trivial
117.4.q.e.82.4 10 13.4 even 6 inner
507.4.a.r.1.4 10 39.2 even 12
507.4.a.r.1.7 10 39.11 even 12
507.4.b.i.337.4 10 39.29 odd 6
507.4.b.i.337.7 10 39.23 odd 6
624.4.bv.h.49.2 10 12.11 even 2
624.4.bv.h.433.4 10 156.95 even 6
1521.4.a.bk.1.4 10 13.11 odd 12
1521.4.a.bk.1.7 10 13.2 odd 12