Properties

Label 288.3.u.a.235.1
Level $288$
Weight $3$
Character 288.235
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
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] = [288,3,Mod(19,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 7, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), 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: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 235.1
Character \(\chi\) \(=\) 288.235
Dual form 288.3.u.a.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.93931 - 0.488972i) q^{2} +(3.52181 + 1.89653i) q^{4} +(1.85856 - 4.48696i) q^{5} +(-5.27676 + 5.27676i) q^{7} +(-5.90252 - 5.40002i) q^{8} +O(q^{10})\) \(q+(-1.93931 - 0.488972i) q^{2} +(3.52181 + 1.89653i) q^{4} +(1.85856 - 4.48696i) q^{5} +(-5.27676 + 5.27676i) q^{7} +(-5.90252 - 5.40002i) q^{8} +(-5.79831 + 7.79280i) q^{10} +(-6.20050 + 14.9693i) q^{11} +(-4.22532 - 10.2008i) q^{13} +(12.8134 - 7.65307i) q^{14} +(8.80634 + 13.3585i) q^{16} -2.84356i q^{17} +(-12.4276 + 5.14768i) q^{19} +(15.0551 - 12.2774i) q^{20} +(19.3443 - 25.9983i) q^{22} +(1.43918 + 1.43918i) q^{23} +(0.999126 + 0.999126i) q^{25} +(3.20628 + 21.8486i) q^{26} +(-28.5913 + 8.57623i) q^{28} +(-36.9596 + 15.3092i) q^{29} +4.73823i q^{31} +(-10.5463 - 30.2122i) q^{32} +(-1.39042 + 5.51453i) q^{34} +(13.8694 + 33.4838i) q^{35} +(-6.68390 + 16.1364i) q^{37} +(26.6180 - 3.90618i) q^{38} +(-35.1998 + 16.4481i) q^{40} +(-40.4523 + 40.4523i) q^{41} +(-24.5000 + 59.1482i) q^{43} +(-50.2268 + 40.9598i) q^{44} +(-2.08729 - 3.49473i) q^{46} +16.5262 q^{47} -6.68842i q^{49} +(-1.44907 - 2.42615i) q^{50} +(4.46539 - 43.9389i) q^{52} +(46.9950 + 19.4659i) q^{53} +(55.6428 + 55.6428i) q^{55} +(59.6408 - 2.65160i) q^{56} +(79.1617 - 11.6170i) q^{58} +(-50.0578 - 20.7346i) q^{59} +(-54.3116 + 22.4966i) q^{61} +(2.31686 - 9.18889i) q^{62} +(5.67958 + 63.7475i) q^{64} -53.6237 q^{65} +(-25.5017 - 61.5665i) q^{67} +(5.39290 - 10.0145i) q^{68} +(-10.5245 - 71.7170i) q^{70} +(-7.12641 + 7.12641i) q^{71} +(55.3669 - 55.3669i) q^{73} +(20.8524 - 28.0251i) q^{74} +(-53.5304 - 5.44015i) q^{76} +(-46.2711 - 111.708i) q^{77} +11.0986 q^{79} +(76.3059 - 14.6862i) q^{80} +(98.2293 - 58.6693i) q^{82} +(29.9476 - 12.4047i) q^{83} +(-12.7589 - 5.28492i) q^{85} +(76.4348 - 102.727i) q^{86} +(117.433 - 54.8740i) q^{88} +(-16.7667 - 16.7667i) q^{89} +(76.1234 + 31.5313i) q^{91} +(2.33907 + 7.79797i) q^{92} +(-32.0494 - 8.08086i) q^{94} +65.3294i q^{95} -67.8301 q^{97} +(-3.27045 + 12.9709i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93931 0.488972i −0.969653 0.244486i
\(3\) 0 0
\(4\) 3.52181 + 1.89653i 0.880453 + 0.474133i
\(5\) 1.85856 4.48696i 0.371712 0.897391i −0.621749 0.783217i \(-0.713578\pi\)
0.993461 0.114175i \(-0.0364224\pi\)
\(6\) 0 0
\(7\) −5.27676 + 5.27676i −0.753823 + 0.753823i −0.975190 0.221367i \(-0.928948\pi\)
0.221367 + 0.975190i \(0.428948\pi\)
\(8\) −5.90252 5.40002i −0.737816 0.675002i
\(9\) 0 0
\(10\) −5.79831 + 7.79280i −0.579831 + 0.779280i
\(11\) −6.20050 + 14.9693i −0.563682 + 1.36085i 0.343120 + 0.939292i \(0.388516\pi\)
−0.906802 + 0.421557i \(0.861484\pi\)
\(12\) 0 0
\(13\) −4.22532 10.2008i −0.325025 0.784680i −0.998947 0.0458772i \(-0.985392\pi\)
0.673922 0.738802i \(-0.264608\pi\)
\(14\) 12.8134 7.65307i 0.915246 0.546648i
\(15\) 0 0
\(16\) 8.80634 + 13.3585i 0.550396 + 0.834903i
\(17\) 2.84356i 0.167268i −0.996497 0.0836341i \(-0.973347\pi\)
0.996497 0.0836341i \(-0.0266527\pi\)
\(18\) 0 0
\(19\) −12.4276 + 5.14768i −0.654084 + 0.270931i −0.684947 0.728593i \(-0.740175\pi\)
0.0308626 + 0.999524i \(0.490175\pi\)
\(20\) 15.0551 12.2774i 0.752757 0.613871i
\(21\) 0 0
\(22\) 19.3443 25.9983i 0.879284 1.18174i
\(23\) 1.43918 + 1.43918i 0.0625730 + 0.0625730i 0.737701 0.675128i \(-0.235912\pi\)
−0.675128 + 0.737701i \(0.735912\pi\)
\(24\) 0 0
\(25\) 0.999126 + 0.999126i 0.0399650 + 0.0399650i
\(26\) 3.20628 + 21.8486i 0.123318 + 0.840331i
\(27\) 0 0
\(28\) −28.5913 + 8.57623i −1.02112 + 0.306294i
\(29\) −36.9596 + 15.3092i −1.27447 + 0.527902i −0.914320 0.404993i \(-0.867274\pi\)
−0.360148 + 0.932895i \(0.617274\pi\)
\(30\) 0 0
\(31\) 4.73823i 0.152846i 0.997075 + 0.0764231i \(0.0243500\pi\)
−0.997075 + 0.0764231i \(0.975650\pi\)
\(32\) −10.5463 30.2122i −0.329572 0.944131i
\(33\) 0 0
\(34\) −1.39042 + 5.51453i −0.0408947 + 0.162192i
\(35\) 13.8694 + 33.4838i 0.396269 + 0.956679i
\(36\) 0 0
\(37\) −6.68390 + 16.1364i −0.180646 + 0.436118i −0.988100 0.153812i \(-0.950845\pi\)
0.807454 + 0.589930i \(0.200845\pi\)
\(38\) 26.6180 3.90618i 0.700473 0.102794i
\(39\) 0 0
\(40\) −35.1998 + 16.4481i −0.879996 + 0.411203i
\(41\) −40.4523 + 40.4523i −0.986641 + 0.986641i −0.999912 0.0132711i \(-0.995776\pi\)
0.0132711 + 0.999912i \(0.495776\pi\)
\(42\) 0 0
\(43\) −24.5000 + 59.1482i −0.569767 + 1.37554i 0.331984 + 0.943285i \(0.392282\pi\)
−0.901751 + 0.432255i \(0.857718\pi\)
\(44\) −50.2268 + 40.9598i −1.14152 + 0.930904i
\(45\) 0 0
\(46\) −2.08729 3.49473i −0.0453759 0.0759723i
\(47\) 16.5262 0.351622 0.175811 0.984424i \(-0.443745\pi\)
0.175811 + 0.984424i \(0.443745\pi\)
\(48\) 0 0
\(49\) 6.68842i 0.136498i
\(50\) −1.44907 2.42615i −0.0289813 0.0485231i
\(51\) 0 0
\(52\) 4.46539 43.9389i 0.0858729 0.844979i
\(53\) 46.9950 + 19.4659i 0.886697 + 0.367282i 0.779090 0.626912i \(-0.215681\pi\)
0.107607 + 0.994194i \(0.465681\pi\)
\(54\) 0 0
\(55\) 55.6428 + 55.6428i 1.01169 + 1.01169i
\(56\) 59.6408 2.65160i 1.06501 0.0473500i
\(57\) 0 0
\(58\) 79.1617 11.6170i 1.36486 0.200292i
\(59\) −50.0578 20.7346i −0.848437 0.351434i −0.0842623 0.996444i \(-0.526853\pi\)
−0.764174 + 0.645010i \(0.776853\pi\)
\(60\) 0 0
\(61\) −54.3116 + 22.4966i −0.890353 + 0.368796i −0.780503 0.625152i \(-0.785037\pi\)
−0.109850 + 0.993948i \(0.535037\pi\)
\(62\) 2.31686 9.18889i 0.0373687 0.148208i
\(63\) 0 0
\(64\) 5.67958 + 63.7475i 0.0887435 + 0.996055i
\(65\) −53.6237 −0.824980
\(66\) 0 0
\(67\) −25.5017 61.5665i −0.380622 0.918904i −0.991846 0.127445i \(-0.959322\pi\)
0.611223 0.791458i \(-0.290678\pi\)
\(68\) 5.39290 10.0145i 0.0793073 0.147272i
\(69\) 0 0
\(70\) −10.5245 71.7170i −0.150349 1.02453i
\(71\) −7.12641 + 7.12641i −0.100372 + 0.100372i −0.755510 0.655138i \(-0.772611\pi\)
0.655138 + 0.755510i \(0.272611\pi\)
\(72\) 0 0
\(73\) 55.3669 55.3669i 0.758451 0.758451i −0.217590 0.976040i \(-0.569819\pi\)
0.976040 + 0.217590i \(0.0698194\pi\)
\(74\) 20.8524 28.0251i 0.281789 0.378718i
\(75\) 0 0
\(76\) −53.5304 5.44015i −0.704348 0.0715809i
\(77\) −46.2711 111.708i −0.600923 1.45076i
\(78\) 0 0
\(79\) 11.0986 0.140489 0.0702446 0.997530i \(-0.477622\pi\)
0.0702446 + 0.997530i \(0.477622\pi\)
\(80\) 76.3059 14.6862i 0.953824 0.183578i
\(81\) 0 0
\(82\) 98.2293 58.6693i 1.19792 0.715480i
\(83\) 29.9476 12.4047i 0.360814 0.149454i −0.194909 0.980821i \(-0.562441\pi\)
0.555724 + 0.831367i \(0.312441\pi\)
\(84\) 0 0
\(85\) −12.7589 5.28492i −0.150105 0.0621755i
\(86\) 76.4348 102.727i 0.888777 1.19450i
\(87\) 0 0
\(88\) 117.433 54.8740i 1.33447 0.623569i
\(89\) −16.7667 16.7667i −0.188390 0.188390i 0.606610 0.795000i \(-0.292529\pi\)
−0.795000 + 0.606610i \(0.792529\pi\)
\(90\) 0 0
\(91\) 76.1234 + 31.5313i 0.836521 + 0.346498i
\(92\) 2.33907 + 7.79797i 0.0254247 + 0.0847606i
\(93\) 0 0
\(94\) −32.0494 8.08086i −0.340951 0.0859666i
\(95\) 65.3294i 0.687678i
\(96\) 0 0
\(97\) −67.8301 −0.699280 −0.349640 0.936884i \(-0.613696\pi\)
−0.349640 + 0.936884i \(0.613696\pi\)
\(98\) −3.27045 + 12.9709i −0.0333719 + 0.132356i
\(99\) 0 0
\(100\) 1.62386 + 5.41361i 0.0162386 + 0.0541361i
\(101\) 45.6943 110.316i 0.452419 1.09224i −0.518981 0.854786i \(-0.673689\pi\)
0.971400 0.237450i \(-0.0763115\pi\)
\(102\) 0 0
\(103\) 61.7093 61.7093i 0.599120 0.599120i −0.340959 0.940078i \(-0.610752\pi\)
0.940078 + 0.340959i \(0.110752\pi\)
\(104\) −30.1446 + 83.0275i −0.289852 + 0.798341i
\(105\) 0 0
\(106\) −81.6193 60.7296i −0.769993 0.572921i
\(107\) −7.13652 + 17.2291i −0.0666965 + 0.161020i −0.953713 0.300718i \(-0.902774\pi\)
0.887017 + 0.461737i \(0.152774\pi\)
\(108\) 0 0
\(109\) −75.1681 181.472i −0.689616 1.66488i −0.745554 0.666445i \(-0.767815\pi\)
0.0559384 0.998434i \(-0.482185\pi\)
\(110\) −80.7006 135.116i −0.733642 1.22833i
\(111\) 0 0
\(112\) −116.958 24.0204i −1.04427 0.214468i
\(113\) 156.784i 1.38747i 0.720232 + 0.693734i \(0.244035\pi\)
−0.720232 + 0.693734i \(0.755965\pi\)
\(114\) 0 0
\(115\) 9.13234 3.78274i 0.0794116 0.0328934i
\(116\) −159.199 16.1790i −1.37241 0.139474i
\(117\) 0 0
\(118\) 86.9387 + 64.6876i 0.736769 + 0.548200i
\(119\) 15.0048 + 15.0048i 0.126091 + 0.126091i
\(120\) 0 0
\(121\) −100.075 100.075i −0.827066 0.827066i
\(122\) 116.327 17.0710i 0.953499 0.139926i
\(123\) 0 0
\(124\) −8.98621 + 16.6872i −0.0724694 + 0.134574i
\(125\) 118.514 49.0901i 0.948111 0.392720i
\(126\) 0 0
\(127\) 192.971i 1.51946i 0.650240 + 0.759729i \(0.274668\pi\)
−0.650240 + 0.759729i \(0.725332\pi\)
\(128\) 20.1563 126.403i 0.157471 0.987524i
\(129\) 0 0
\(130\) 103.993 + 26.2205i 0.799944 + 0.201696i
\(131\) −18.2599 44.0834i −0.139389 0.336515i 0.838734 0.544541i \(-0.183296\pi\)
−0.978123 + 0.208026i \(0.933296\pi\)
\(132\) 0 0
\(133\) 38.4144 92.7406i 0.288830 0.697297i
\(134\) 19.3513 + 131.866i 0.144413 + 0.984074i
\(135\) 0 0
\(136\) −15.3553 + 16.7842i −0.112906 + 0.123413i
\(137\) 27.8671 27.8671i 0.203409 0.203409i −0.598050 0.801459i \(-0.704057\pi\)
0.801459 + 0.598050i \(0.204057\pi\)
\(138\) 0 0
\(139\) 33.3447 80.5013i 0.239890 0.579146i −0.757381 0.652973i \(-0.773521\pi\)
0.997271 + 0.0738274i \(0.0235214\pi\)
\(140\) −14.6574 + 144.227i −0.104696 + 1.03020i
\(141\) 0 0
\(142\) 17.3049 10.3357i 0.121866 0.0727865i
\(143\) 178.899 1.25104
\(144\) 0 0
\(145\) 194.289i 1.33992i
\(146\) −134.446 + 80.3005i −0.920864 + 0.550004i
\(147\) 0 0
\(148\) −54.1426 + 44.1531i −0.365828 + 0.298331i
\(149\) 125.860 + 52.1327i 0.844695 + 0.349884i 0.762703 0.646749i \(-0.223872\pi\)
0.0819919 + 0.996633i \(0.473872\pi\)
\(150\) 0 0
\(151\) 106.254 + 106.254i 0.703672 + 0.703672i 0.965197 0.261525i \(-0.0842254\pi\)
−0.261525 + 0.965197i \(0.584225\pi\)
\(152\) 101.152 + 36.7250i 0.665472 + 0.241612i
\(153\) 0 0
\(154\) 35.1116 + 239.262i 0.227997 + 1.55365i
\(155\) 21.2603 + 8.80629i 0.137163 + 0.0568147i
\(156\) 0 0
\(157\) 209.345 86.7136i 1.33341 0.552316i 0.401783 0.915735i \(-0.368391\pi\)
0.931626 + 0.363419i \(0.118391\pi\)
\(158\) −21.5237 5.42692i −0.136226 0.0343476i
\(159\) 0 0
\(160\) −155.162 8.83036i −0.969760 0.0551897i
\(161\) −15.1884 −0.0943380
\(162\) 0 0
\(163\) −0.176018 0.424946i −0.00107987 0.00260703i 0.923339 0.383987i \(-0.125449\pi\)
−0.924419 + 0.381380i \(0.875449\pi\)
\(164\) −219.184 + 65.7464i −1.33649 + 0.400893i
\(165\) 0 0
\(166\) −64.1431 + 9.41298i −0.386404 + 0.0567047i
\(167\) −96.7499 + 96.7499i −0.579341 + 0.579341i −0.934722 0.355381i \(-0.884351\pi\)
0.355381 + 0.934722i \(0.384351\pi\)
\(168\) 0 0
\(169\) 33.2974 33.2974i 0.197026 0.197026i
\(170\) 22.1593 + 16.4878i 0.130349 + 0.0969872i
\(171\) 0 0
\(172\) −198.461 + 161.844i −1.15384 + 0.940954i
\(173\) −102.242 246.834i −0.590994 1.42678i −0.882544 0.470229i \(-0.844171\pi\)
0.291551 0.956555i \(-0.405829\pi\)
\(174\) 0 0
\(175\) −10.5443 −0.0602531
\(176\) −254.571 + 48.9960i −1.44643 + 0.278386i
\(177\) 0 0
\(178\) 24.3174 + 40.7143i 0.136614 + 0.228732i
\(179\) −269.771 + 111.743i −1.50710 + 0.624262i −0.974957 0.222393i \(-0.928613\pi\)
−0.532144 + 0.846654i \(0.678613\pi\)
\(180\) 0 0
\(181\) −33.2079 13.7552i −0.183469 0.0759954i 0.289058 0.957312i \(-0.406658\pi\)
−0.472527 + 0.881316i \(0.656658\pi\)
\(182\) −132.209 98.3711i −0.726421 0.540500i
\(183\) 0 0
\(184\) −0.723195 16.2664i −0.00393041 0.0884043i
\(185\) 59.9808 + 59.9808i 0.324220 + 0.324220i
\(186\) 0 0
\(187\) 42.5662 + 17.6315i 0.227627 + 0.0942861i
\(188\) 58.2023 + 31.3425i 0.309587 + 0.166715i
\(189\) 0 0
\(190\) 31.9442 126.694i 0.168127 0.666809i
\(191\) 47.7299i 0.249895i −0.992163 0.124947i \(-0.960124\pi\)
0.992163 0.124947i \(-0.0398762\pi\)
\(192\) 0 0
\(193\) −302.171 −1.56565 −0.782827 0.622240i \(-0.786223\pi\)
−0.782827 + 0.622240i \(0.786223\pi\)
\(194\) 131.543 + 33.1670i 0.678059 + 0.170964i
\(195\) 0 0
\(196\) 12.6848 23.5554i 0.0647183 0.120180i
\(197\) −18.2996 + 44.1791i −0.0928913 + 0.224259i −0.963495 0.267725i \(-0.913728\pi\)
0.870604 + 0.491984i \(0.163728\pi\)
\(198\) 0 0
\(199\) −94.2590 + 94.2590i −0.473663 + 0.473663i −0.903098 0.429435i \(-0.858713\pi\)
0.429435 + 0.903098i \(0.358713\pi\)
\(200\) −0.502066 11.2927i −0.00251033 0.0564633i
\(201\) 0 0
\(202\) −142.556 + 191.593i −0.705725 + 0.948479i
\(203\) 114.244 275.810i 0.562779 1.35867i
\(204\) 0 0
\(205\) 106.325 + 256.691i 0.518657 + 1.25215i
\(206\) −149.847 + 89.4992i −0.727414 + 0.434462i
\(207\) 0 0
\(208\) 99.0577 146.276i 0.476239 0.703249i
\(209\) 217.951i 1.04283i
\(210\) 0 0
\(211\) −267.734 + 110.899i −1.26888 + 0.525589i −0.912625 0.408799i \(-0.865948\pi\)
−0.356259 + 0.934387i \(0.615948\pi\)
\(212\) 128.590 + 157.683i 0.606555 + 0.743787i
\(213\) 0 0
\(214\) 22.2644 29.9229i 0.104039 0.139827i
\(215\) 219.861 + 219.861i 1.02261 + 1.02261i
\(216\) 0 0
\(217\) −25.0025 25.0025i −0.115219 0.115219i
\(218\) 57.0394 + 388.684i 0.261648 + 1.78296i
\(219\) 0 0
\(220\) 90.4353 + 301.492i 0.411069 + 1.37042i
\(221\) −29.0067 + 12.0150i −0.131252 + 0.0543663i
\(222\) 0 0
\(223\) 408.363i 1.83123i −0.402061 0.915613i \(-0.631706\pi\)
0.402061 0.915613i \(-0.368294\pi\)
\(224\) 215.073 + 103.772i 0.960146 + 0.463269i
\(225\) 0 0
\(226\) 76.6628 304.052i 0.339216 1.34536i
\(227\) −82.5132 199.204i −0.363494 0.877553i −0.994784 0.102005i \(-0.967474\pi\)
0.631290 0.775547i \(-0.282526\pi\)
\(228\) 0 0
\(229\) 22.6069 54.5778i 0.0987200 0.238331i −0.866802 0.498652i \(-0.833828\pi\)
0.965522 + 0.260321i \(0.0838284\pi\)
\(230\) −19.5600 + 2.87043i −0.0850437 + 0.0124801i
\(231\) 0 0
\(232\) 300.824 + 109.220i 1.29666 + 0.470775i
\(233\) −58.2826 + 58.2826i −0.250140 + 0.250140i −0.821028 0.570888i \(-0.806599\pi\)
0.570888 + 0.821028i \(0.306599\pi\)
\(234\) 0 0
\(235\) 30.7150 74.1525i 0.130702 0.315543i
\(236\) −136.970 167.960i −0.580383 0.711693i
\(237\) 0 0
\(238\) −21.7619 36.4358i −0.0914368 0.153091i
\(239\) 367.366 1.53710 0.768548 0.639792i \(-0.220979\pi\)
0.768548 + 0.639792i \(0.220979\pi\)
\(240\) 0 0
\(241\) 312.345i 1.29604i 0.761624 + 0.648020i \(0.224403\pi\)
−0.761624 + 0.648020i \(0.775597\pi\)
\(242\) 145.142 + 243.010i 0.599761 + 1.00417i
\(243\) 0 0
\(244\) −233.941 23.7748i −0.958773 0.0974375i
\(245\) −30.0106 12.4308i −0.122492 0.0507380i
\(246\) 0 0
\(247\) 105.021 + 105.021i 0.425187 + 0.425187i
\(248\) 25.5866 27.9675i 0.103172 0.112772i
\(249\) 0 0
\(250\) −253.838 + 37.2507i −1.01535 + 0.149003i
\(251\) −223.120 92.4192i −0.888923 0.368204i −0.108972 0.994045i \(-0.534756\pi\)
−0.779951 + 0.625841i \(0.784756\pi\)
\(252\) 0 0
\(253\) −30.4672 + 12.6199i −0.120424 + 0.0498811i
\(254\) 94.3574 374.230i 0.371486 1.47335i
\(255\) 0 0
\(256\) −100.897 + 235.278i −0.394127 + 0.919056i
\(257\) −178.176 −0.693293 −0.346646 0.937996i \(-0.612680\pi\)
−0.346646 + 0.937996i \(0.612680\pi\)
\(258\) 0 0
\(259\) −49.8784 120.417i −0.192581 0.464931i
\(260\) −188.853 101.699i −0.726357 0.391150i
\(261\) 0 0
\(262\) 13.8561 + 94.4198i 0.0528858 + 0.360381i
\(263\) 147.164 147.164i 0.559558 0.559558i −0.369623 0.929182i \(-0.620513\pi\)
0.929182 + 0.369623i \(0.120513\pi\)
\(264\) 0 0
\(265\) 174.686 174.686i 0.659191 0.659191i
\(266\) −119.845 + 161.069i −0.450544 + 0.605522i
\(267\) 0 0
\(268\) 26.9506 265.191i 0.100562 0.989517i
\(269\) 138.119 + 333.450i 0.513455 + 1.23959i 0.941861 + 0.336004i \(0.109076\pi\)
−0.428405 + 0.903587i \(0.640924\pi\)
\(270\) 0 0
\(271\) 218.643 0.806801 0.403400 0.915024i \(-0.367828\pi\)
0.403400 + 0.915024i \(0.367828\pi\)
\(272\) 37.9856 25.0414i 0.139653 0.0920638i
\(273\) 0 0
\(274\) −67.6690 + 40.4166i −0.246967 + 0.147506i
\(275\) −21.1513 + 8.76117i −0.0769139 + 0.0318588i
\(276\) 0 0
\(277\) 256.038 + 106.054i 0.924323 + 0.382867i 0.793522 0.608541i \(-0.208245\pi\)
0.130801 + 0.991409i \(0.458245\pi\)
\(278\) −104.028 + 139.812i −0.374203 + 0.502921i
\(279\) 0 0
\(280\) 98.9483 272.534i 0.353387 0.973336i
\(281\) 49.4126 + 49.4126i 0.175845 + 0.175845i 0.789542 0.613697i \(-0.210318\pi\)
−0.613697 + 0.789542i \(0.710318\pi\)
\(282\) 0 0
\(283\) 118.290 + 48.9975i 0.417987 + 0.173136i 0.581757 0.813363i \(-0.302365\pi\)
−0.163770 + 0.986499i \(0.552365\pi\)
\(284\) −38.6133 + 11.5824i −0.135962 + 0.0407832i
\(285\) 0 0
\(286\) −346.940 87.4765i −1.21308 0.305862i
\(287\) 426.914i 1.48751i
\(288\) 0 0
\(289\) 280.914 0.972021
\(290\) 95.0018 376.786i 0.327592 1.29926i
\(291\) 0 0
\(292\) 299.997 89.9869i 1.02739 0.308174i
\(293\) 100.203 241.910i 0.341988 0.825633i −0.655526 0.755172i \(-0.727553\pi\)
0.997515 0.0704605i \(-0.0224469\pi\)
\(294\) 0 0
\(295\) −186.071 + 186.071i −0.630748 + 0.630748i
\(296\) 126.589 59.1521i 0.427664 0.199838i
\(297\) 0 0
\(298\) −218.589 162.643i −0.733519 0.545782i
\(299\) 8.59983 20.7618i 0.0287620 0.0694376i
\(300\) 0 0
\(301\) −182.830 441.392i −0.607410 1.46642i
\(302\) −154.104 258.015i −0.510280 0.854355i
\(303\) 0 0
\(304\) −178.207 120.681i −0.586206 0.396978i
\(305\) 285.505i 0.936081i
\(306\) 0 0
\(307\) −371.163 + 153.741i −1.20900 + 0.500784i −0.893896 0.448274i \(-0.852039\pi\)
−0.315103 + 0.949058i \(0.602039\pi\)
\(308\) 48.9000 481.170i 0.158766 1.56224i
\(309\) 0 0
\(310\) −36.9241 27.4737i −0.119110 0.0886250i
\(311\) 312.733 + 312.733i 1.00557 + 1.00557i 0.999984 + 0.00558671i \(0.00177831\pi\)
0.00558671 + 0.999984i \(0.498222\pi\)
\(312\) 0 0
\(313\) 358.245 + 358.245i 1.14455 + 1.14455i 0.987607 + 0.156946i \(0.0501649\pi\)
0.156946 + 0.987607i \(0.449835\pi\)
\(314\) −448.385 + 65.8004i −1.42798 + 0.209555i
\(315\) 0 0
\(316\) 39.0874 + 21.0489i 0.123694 + 0.0666105i
\(317\) −164.720 + 68.2292i −0.519621 + 0.215234i −0.627051 0.778979i \(-0.715738\pi\)
0.107429 + 0.994213i \(0.465738\pi\)
\(318\) 0 0
\(319\) 648.185i 2.03193i
\(320\) 296.588 + 92.9944i 0.926838 + 0.290607i
\(321\) 0 0
\(322\) 29.4550 + 7.42670i 0.0914751 + 0.0230643i
\(323\) 14.6377 + 35.3386i 0.0453181 + 0.109407i
\(324\) 0 0
\(325\) 5.97029 14.4135i 0.0183701 0.0443494i
\(326\) 0.133567 + 0.910167i 0.000409714 + 0.00279192i
\(327\) 0 0
\(328\) 457.214 20.3275i 1.39394 0.0619740i
\(329\) −87.2050 + 87.2050i −0.265061 + 0.265061i
\(330\) 0 0
\(331\) 21.3130 51.4542i 0.0643898 0.155451i −0.888409 0.459052i \(-0.848189\pi\)
0.952799 + 0.303601i \(0.0981891\pi\)
\(332\) 128.996 + 13.1095i 0.388541 + 0.0394864i
\(333\) 0 0
\(334\) 234.936 140.320i 0.703400 0.420119i
\(335\) −323.643 −0.966098
\(336\) 0 0
\(337\) 173.028i 0.513437i −0.966486 0.256718i \(-0.917359\pi\)
0.966486 0.256718i \(-0.0826413\pi\)
\(338\) −80.8553 + 48.2924i −0.239217 + 0.142877i
\(339\) 0 0
\(340\) −34.9115 42.8102i −0.102681 0.125912i
\(341\) −70.9282 29.3794i −0.208001 0.0861567i
\(342\) 0 0
\(343\) −223.268 223.268i −0.650927 0.650927i
\(344\) 464.013 216.823i 1.34888 0.630301i
\(345\) 0 0
\(346\) 77.5836 + 528.679i 0.224230 + 1.52798i
\(347\) −48.9563 20.2784i −0.141085 0.0584391i 0.311024 0.950402i \(-0.399328\pi\)
−0.452109 + 0.891963i \(0.649328\pi\)
\(348\) 0 0
\(349\) −222.227 + 92.0495i −0.636754 + 0.263752i −0.677620 0.735412i \(-0.736988\pi\)
0.0408656 + 0.999165i \(0.486988\pi\)
\(350\) 20.4486 + 5.15586i 0.0584246 + 0.0147310i
\(351\) 0 0
\(352\) 517.649 + 29.4597i 1.47059 + 0.0836924i
\(353\) 75.1997 0.213030 0.106515 0.994311i \(-0.466031\pi\)
0.106515 + 0.994311i \(0.466031\pi\)
\(354\) 0 0
\(355\) 18.7310 + 45.2208i 0.0527635 + 0.127382i
\(356\) −27.2507 90.8479i −0.0765469 0.255191i
\(357\) 0 0
\(358\) 577.808 84.7931i 1.61399 0.236852i
\(359\) −369.532 + 369.532i −1.02934 + 1.02934i −0.0297806 + 0.999556i \(0.509481\pi\)
−0.999556 + 0.0297806i \(0.990519\pi\)
\(360\) 0 0
\(361\) −127.319 + 127.319i −0.352684 + 0.352684i
\(362\) 57.6744 + 42.9132i 0.159322 + 0.118545i
\(363\) 0 0
\(364\) 208.292 + 255.418i 0.572231 + 0.701697i
\(365\) −145.526 351.332i −0.398702 0.962552i
\(366\) 0 0
\(367\) −482.888 −1.31577 −0.657885 0.753118i \(-0.728549\pi\)
−0.657885 + 0.753118i \(0.728549\pi\)
\(368\) −6.55131 + 31.8991i −0.0178025 + 0.0866824i
\(369\) 0 0
\(370\) −86.9922 145.650i −0.235114 0.393648i
\(371\) −350.698 + 145.264i −0.945278 + 0.391547i
\(372\) 0 0
\(373\) 459.056 + 190.147i 1.23071 + 0.509778i 0.900801 0.434233i \(-0.142980\pi\)
0.329913 + 0.944011i \(0.392980\pi\)
\(374\) −73.9276 55.0065i −0.197667 0.147076i
\(375\) 0 0
\(376\) −97.5465 89.2420i −0.259432 0.237346i
\(377\) 312.332 + 312.332i 0.828468 + 0.828468i
\(378\) 0 0
\(379\) 209.167 + 86.6398i 0.551891 + 0.228601i 0.641161 0.767407i \(-0.278453\pi\)
−0.0892693 + 0.996008i \(0.528453\pi\)
\(380\) −123.899 + 230.078i −0.326050 + 0.605468i
\(381\) 0 0
\(382\) −23.3386 + 92.5629i −0.0610958 + 0.242311i
\(383\) 243.083i 0.634682i 0.948312 + 0.317341i \(0.102790\pi\)
−0.948312 + 0.317341i \(0.897210\pi\)
\(384\) 0 0
\(385\) −587.227 −1.52527
\(386\) 586.002 + 147.753i 1.51814 + 0.382780i
\(387\) 0 0
\(388\) −238.885 128.642i −0.615683 0.331551i
\(389\) −100.024 + 241.479i −0.257131 + 0.620768i −0.998746 0.0500566i \(-0.984060\pi\)
0.741616 + 0.670825i \(0.234060\pi\)
\(390\) 0 0
\(391\) 4.09239 4.09239i 0.0104665 0.0104665i
\(392\) −36.1176 + 39.4786i −0.0921367 + 0.100711i
\(393\) 0 0
\(394\) 57.0908 76.7288i 0.144901 0.194743i
\(395\) 20.6275 49.7992i 0.0522215 0.126074i
\(396\) 0 0
\(397\) −177.617 428.806i −0.447399 1.08012i −0.973293 0.229566i \(-0.926269\pi\)
0.525894 0.850550i \(-0.323731\pi\)
\(398\) 228.887 136.707i 0.575093 0.343485i
\(399\) 0 0
\(400\) −4.54813 + 22.1454i −0.0113703 + 0.0553636i
\(401\) 539.233i 1.34472i 0.740224 + 0.672360i \(0.234719\pi\)
−0.740224 + 0.672360i \(0.765281\pi\)
\(402\) 0 0
\(403\) 48.3339 20.0206i 0.119935 0.0496788i
\(404\) 370.144 301.851i 0.916198 0.747156i
\(405\) 0 0
\(406\) −356.417 + 479.017i −0.877875 + 1.17984i
\(407\) −200.107 200.107i −0.491664 0.491664i
\(408\) 0 0
\(409\) 177.821 + 177.821i 0.434769 + 0.434769i 0.890247 0.455478i \(-0.150532\pi\)
−0.455478 + 0.890247i \(0.650532\pi\)
\(410\) −80.6817 549.791i −0.196785 1.34095i
\(411\) 0 0
\(412\) 334.362 100.295i 0.811559 0.243435i
\(413\) 373.554 154.731i 0.904490 0.374652i
\(414\) 0 0
\(415\) 157.428i 0.379345i
\(416\) −263.628 + 235.237i −0.633721 + 0.565474i
\(417\) 0 0
\(418\) −106.572 + 422.674i −0.254957 + 1.01118i
\(419\) −55.0604 132.927i −0.131409 0.317249i 0.844456 0.535625i \(-0.179924\pi\)
−0.975865 + 0.218376i \(0.929924\pi\)
\(420\) 0 0
\(421\) −292.384 + 705.877i −0.694498 + 1.67667i 0.0410159 + 0.999158i \(0.486941\pi\)
−0.735514 + 0.677509i \(0.763059\pi\)
\(422\) 573.445 84.1530i 1.35888 0.199415i
\(423\) 0 0
\(424\) −172.272 368.672i −0.406303 0.869509i
\(425\) 2.84107 2.84107i 0.00668488 0.00668488i
\(426\) 0 0
\(427\) 167.880 405.298i 0.393162 0.949176i
\(428\) −57.8090 + 47.1430i −0.135068 + 0.110147i
\(429\) 0 0
\(430\) −318.872 533.883i −0.741562 1.24159i
\(431\) −810.711 −1.88100 −0.940500 0.339794i \(-0.889643\pi\)
−0.940500 + 0.339794i \(0.889643\pi\)
\(432\) 0 0
\(433\) 753.072i 1.73920i 0.493759 + 0.869599i \(0.335622\pi\)
−0.493759 + 0.869599i \(0.664378\pi\)
\(434\) 36.2620 + 60.7131i 0.0835531 + 0.139892i
\(435\) 0 0
\(436\) 79.4389 781.669i 0.182199 1.79282i
\(437\) −25.2940 10.4771i −0.0578810 0.0239751i
\(438\) 0 0
\(439\) 504.938 + 504.938i 1.15020 + 1.15020i 0.986512 + 0.163689i \(0.0523392\pi\)
0.163689 + 0.986512i \(0.447661\pi\)
\(440\) −27.9608 628.905i −0.0635472 1.42933i
\(441\) 0 0
\(442\) 62.1278 9.11724i 0.140561 0.0206272i
\(443\) 697.291 + 288.827i 1.57402 + 0.651981i 0.987452 0.157919i \(-0.0504784\pi\)
0.586569 + 0.809899i \(0.300478\pi\)
\(444\) 0 0
\(445\) −106.394 + 44.0697i −0.239087 + 0.0990330i
\(446\) −199.678 + 791.942i −0.447709 + 1.77565i
\(447\) 0 0
\(448\) −366.350 306.410i −0.817746 0.683952i
\(449\) 294.056 0.654913 0.327457 0.944866i \(-0.393808\pi\)
0.327457 + 0.944866i \(0.393808\pi\)
\(450\) 0 0
\(451\) −354.719 856.368i −0.786517 1.89882i
\(452\) −297.345 + 552.163i −0.657843 + 1.22160i
\(453\) 0 0
\(454\) 62.6130 + 426.665i 0.137914 + 0.939791i
\(455\) 282.960 282.960i 0.621889 0.621889i
\(456\) 0 0
\(457\) 175.139 175.139i 0.383237 0.383237i −0.489030 0.872267i \(-0.662649\pi\)
0.872267 + 0.489030i \(0.162649\pi\)
\(458\) −70.5287 + 94.7890i −0.153993 + 0.206963i
\(459\) 0 0
\(460\) 39.3365 + 3.99766i 0.0855141 + 0.00869056i
\(461\) 107.290 + 259.020i 0.232732 + 0.561866i 0.996497 0.0836293i \(-0.0266512\pi\)
−0.763765 + 0.645495i \(0.776651\pi\)
\(462\) 0 0
\(463\) 53.7059 0.115996 0.0579978 0.998317i \(-0.481528\pi\)
0.0579978 + 0.998317i \(0.481528\pi\)
\(464\) −529.985 358.905i −1.14221 0.773502i
\(465\) 0 0
\(466\) 141.526 84.5292i 0.303704 0.181393i
\(467\) −101.550 + 42.0634i −0.217452 + 0.0900716i −0.488750 0.872424i \(-0.662547\pi\)
0.271298 + 0.962495i \(0.412547\pi\)
\(468\) 0 0
\(469\) 459.438 + 190.306i 0.979613 + 0.405769i
\(470\) −95.8242 + 128.786i −0.203881 + 0.274012i
\(471\) 0 0
\(472\) 183.500 + 392.699i 0.388771 + 0.831990i
\(473\) −733.498 733.498i −1.55074 1.55074i
\(474\) 0 0
\(475\) −17.5599 7.27355i −0.0369682 0.0153127i
\(476\) 24.3870 + 81.3011i 0.0512332 + 0.170801i
\(477\) 0 0
\(478\) −712.435 179.632i −1.49045 0.375798i
\(479\) 40.7997i 0.0851769i −0.999093 0.0425884i \(-0.986440\pi\)
0.999093 0.0425884i \(-0.0135604\pi\)
\(480\) 0 0
\(481\) 192.846 0.400927
\(482\) 152.728 605.733i 0.316863 1.25671i
\(483\) 0 0
\(484\) −162.650 542.241i −0.336054 1.12033i
\(485\) −126.066 + 304.351i −0.259931 + 0.627528i
\(486\) 0 0
\(487\) −143.660 + 143.660i −0.294989 + 0.294989i −0.839047 0.544058i \(-0.816887\pi\)
0.544058 + 0.839047i \(0.316887\pi\)
\(488\) 442.057 + 160.497i 0.905855 + 0.328887i
\(489\) 0 0
\(490\) 52.1215 + 38.7815i 0.106370 + 0.0791459i
\(491\) −182.575 + 440.775i −0.371843 + 0.897709i 0.621595 + 0.783339i \(0.286485\pi\)
−0.993438 + 0.114370i \(0.963515\pi\)
\(492\) 0 0
\(493\) 43.5325 + 105.097i 0.0883012 + 0.213178i
\(494\) −152.316 255.021i −0.308332 0.516236i
\(495\) 0 0
\(496\) −63.2955 + 41.7265i −0.127612 + 0.0841261i
\(497\) 75.2087i 0.151325i
\(498\) 0 0
\(499\) −409.850 + 169.766i −0.821343 + 0.340211i −0.753470 0.657482i \(-0.771621\pi\)
−0.0678733 + 0.997694i \(0.521621\pi\)
\(500\) 510.485 + 51.8792i 1.02097 + 0.103758i
\(501\) 0 0
\(502\) 387.507 + 288.328i 0.771926 + 0.574359i
\(503\) −453.715 453.715i −0.902019 0.902019i 0.0935920 0.995611i \(-0.470165\pi\)
−0.995611 + 0.0935920i \(0.970165\pi\)
\(504\) 0 0
\(505\) −410.057 410.057i −0.811993 0.811993i
\(506\) 65.2560 9.57631i 0.128964 0.0189255i
\(507\) 0 0
\(508\) −365.976 + 679.608i −0.720425 + 1.33781i
\(509\) 71.5029 29.6175i 0.140477 0.0581876i −0.311337 0.950299i \(-0.600777\pi\)
0.451815 + 0.892112i \(0.350777\pi\)
\(510\) 0 0
\(511\) 584.316i 1.14348i
\(512\) 310.714 406.941i 0.606863 0.794807i
\(513\) 0 0
\(514\) 345.538 + 87.1231i 0.672253 + 0.169500i
\(515\) −162.197 391.578i −0.314945 0.760345i
\(516\) 0 0
\(517\) −102.471 + 247.387i −0.198203 + 0.478504i
\(518\) 37.8489 + 257.915i 0.0730674 + 0.497905i
\(519\) 0 0
\(520\) 316.515 + 289.569i 0.608683 + 0.556864i
\(521\) 565.729 565.729i 1.08585 1.08585i 0.0899020 0.995951i \(-0.471345\pi\)
0.995951 0.0899020i \(-0.0286554\pi\)
\(522\) 0 0
\(523\) −1.50925 + 3.64366i −0.00288576 + 0.00696685i −0.925316 0.379197i \(-0.876200\pi\)
0.922430 + 0.386164i \(0.126200\pi\)
\(524\) 19.2974 189.884i 0.0368271 0.362374i
\(525\) 0 0
\(526\) −357.355 + 213.437i −0.679381 + 0.405773i
\(527\) 13.4734 0.0255663
\(528\) 0 0
\(529\) 524.858i 0.992169i
\(530\) −424.185 + 253.353i −0.800350 + 0.478024i
\(531\) 0 0
\(532\) 311.174 253.761i 0.584913 0.476994i
\(533\) 583.571 + 241.723i 1.09488 + 0.453514i
\(534\) 0 0
\(535\) 64.0426 + 64.0426i 0.119706 + 0.119706i
\(536\) −181.936 + 501.108i −0.339433 + 0.934902i
\(537\) 0 0
\(538\) −104.808 714.198i −0.194811 1.32751i
\(539\) 100.121 + 41.4716i 0.185754 + 0.0769417i
\(540\) 0 0
\(541\) −746.681 + 309.286i −1.38019 + 0.571692i −0.944531 0.328421i \(-0.893483\pi\)
−0.435656 + 0.900113i \(0.643483\pi\)
\(542\) −424.016 106.910i −0.782317 0.197251i
\(543\) 0 0
\(544\) −85.9101 + 29.9890i −0.157923 + 0.0551268i
\(545\) −953.961 −1.75039
\(546\) 0 0
\(547\) 298.176 + 719.861i 0.545112 + 1.31602i 0.921076 + 0.389383i \(0.127312\pi\)
−0.375964 + 0.926634i \(0.622688\pi\)
\(548\) 150.993 45.2919i 0.275535 0.0826494i
\(549\) 0 0
\(550\) 45.3029 6.64819i 0.0823688 0.0120876i
\(551\) 380.512 380.512i 0.690585 0.690585i
\(552\) 0 0
\(553\) −58.5649 + 58.5649i −0.105904 + 0.105904i
\(554\) −444.678 330.867i −0.802667 0.597232i
\(555\) 0 0
\(556\) 270.107 220.271i 0.485804 0.396171i
\(557\) −83.4142 201.380i −0.149756 0.361544i 0.831143 0.556058i \(-0.187687\pi\)
−0.980900 + 0.194515i \(0.937687\pi\)
\(558\) 0 0
\(559\) 706.882 1.26455
\(560\) −325.152 + 480.144i −0.580629 + 0.857400i
\(561\) 0 0
\(562\) −71.6647 119.987i −0.127517 0.213501i
\(563\) 19.5811 8.11076i 0.0347800 0.0144063i −0.365226 0.930919i \(-0.619008\pi\)
0.400006 + 0.916513i \(0.369008\pi\)
\(564\) 0 0
\(565\) 703.482 + 291.392i 1.24510 + 0.515738i
\(566\) −205.443 152.862i −0.362973 0.270074i
\(567\) 0 0
\(568\) 80.5466 3.58106i 0.141807 0.00630468i
\(569\) 366.760 + 366.760i 0.644569 + 0.644569i 0.951675 0.307106i \(-0.0993606\pi\)
−0.307106 + 0.951675i \(0.599361\pi\)
\(570\) 0 0
\(571\) −121.285 50.2378i −0.212408 0.0879822i 0.273943 0.961746i \(-0.411672\pi\)
−0.486350 + 0.873764i \(0.661672\pi\)
\(572\) 630.049 + 339.287i 1.10148 + 0.593159i
\(573\) 0 0
\(574\) −208.749 + 827.917i −0.363674 + 1.44236i
\(575\) 2.87584i 0.00500147i
\(576\) 0 0
\(577\) 464.948 0.805802 0.402901 0.915244i \(-0.368002\pi\)
0.402901 + 0.915244i \(0.368002\pi\)
\(578\) −544.778 137.359i −0.942523 0.237645i
\(579\) 0 0
\(580\) −368.475 + 684.250i −0.635302 + 1.17974i
\(581\) −92.5696 + 223.483i −0.159328 + 0.384652i
\(582\) 0 0
\(583\) −582.785 + 582.785i −0.999631 + 0.999631i
\(584\) −625.787 + 27.8221i −1.07155 + 0.0476407i
\(585\) 0 0
\(586\) −312.611 + 420.142i −0.533465 + 0.716966i
\(587\) −159.551 + 385.190i −0.271807 + 0.656201i −0.999561 0.0296380i \(-0.990565\pi\)
0.727753 + 0.685839i \(0.240565\pi\)
\(588\) 0 0
\(589\) −24.3909 58.8849i −0.0414107 0.0999743i
\(590\) 451.831 269.865i 0.765815 0.457398i
\(591\) 0 0
\(592\) −274.418 + 52.8158i −0.463543 + 0.0892159i
\(593\) 470.422i 0.793292i 0.917972 + 0.396646i \(0.129826\pi\)
−0.917972 + 0.396646i \(0.870174\pi\)
\(594\) 0 0
\(595\) 95.2131 39.4385i 0.160022 0.0662833i
\(596\) 344.383 + 422.298i 0.577823 + 0.708554i
\(597\) 0 0
\(598\) −26.8296 + 36.0585i −0.0448656 + 0.0602984i
\(599\) 506.817 + 506.817i 0.846105 + 0.846105i 0.989645 0.143540i \(-0.0458485\pi\)
−0.143540 + 0.989645i \(0.545849\pi\)
\(600\) 0 0
\(601\) −261.398 261.398i −0.434939 0.434939i 0.455366 0.890305i \(-0.349509\pi\)
−0.890305 + 0.455366i \(0.849509\pi\)
\(602\) 138.736 + 945.393i 0.230459 + 1.57042i
\(603\) 0 0
\(604\) 172.694 + 575.723i 0.285916 + 0.953184i
\(605\) −635.027 + 263.037i −1.04963 + 0.434772i
\(606\) 0 0
\(607\) 812.089i 1.33787i −0.743319 0.668937i \(-0.766750\pi\)
0.743319 0.668937i \(-0.233250\pi\)
\(608\) 286.588 + 321.176i 0.471361 + 0.528250i
\(609\) 0 0
\(610\) 139.604 553.681i 0.228859 0.907674i
\(611\) −69.8287 168.581i −0.114286 0.275911i
\(612\) 0 0
\(613\) 105.168 253.898i 0.171563 0.414190i −0.814588 0.580040i \(-0.803037\pi\)
0.986151 + 0.165850i \(0.0530369\pi\)
\(614\) 794.973 116.662i 1.29474 0.190003i
\(615\) 0 0
\(616\) −330.110 + 909.225i −0.535894 + 1.47601i
\(617\) 508.739 508.739i 0.824536 0.824536i −0.162218 0.986755i \(-0.551865\pi\)
0.986755 + 0.162218i \(0.0518649\pi\)
\(618\) 0 0
\(619\) −6.64960 + 16.0536i −0.0107425 + 0.0259347i −0.929160 0.369678i \(-0.879468\pi\)
0.918417 + 0.395613i \(0.129468\pi\)
\(620\) 58.1733 + 71.3348i 0.0938278 + 0.115056i
\(621\) 0 0
\(622\) −453.567 759.402i −0.729207 1.22090i
\(623\) 176.948 0.284026
\(624\) 0 0
\(625\) 587.679i 0.940287i
\(626\) −519.575 869.919i −0.829992 1.38965i
\(627\) 0 0
\(628\) 901.730 + 91.6403i 1.43588 + 0.145924i
\(629\) 45.8847 + 19.0061i 0.0729487 + 0.0302163i
\(630\) 0 0
\(631\) −177.518 177.518i −0.281329 0.281329i 0.552310 0.833639i \(-0.313746\pi\)
−0.833639 + 0.552310i \(0.813746\pi\)
\(632\) −65.5100 59.9329i −0.103655 0.0948306i
\(633\) 0 0
\(634\) 352.804 51.7740i 0.556474 0.0816624i
\(635\) 865.853 + 358.648i 1.36355 + 0.564800i
\(636\) 0 0
\(637\) −68.2274 + 28.2607i −0.107107 + 0.0443654i
\(638\) −316.944 + 1257.03i −0.496777 + 1.97026i
\(639\) 0 0
\(640\) −529.703 325.368i −0.827662 0.508387i
\(641\) −334.058 −0.521151 −0.260575 0.965454i \(-0.583912\pi\)
−0.260575 + 0.965454i \(0.583912\pi\)
\(642\) 0 0
\(643\) −19.9758 48.2257i −0.0310665 0.0750011i 0.907585 0.419869i \(-0.137924\pi\)
−0.938651 + 0.344867i \(0.887924\pi\)
\(644\) −53.4908 28.8053i −0.0830602 0.0447287i
\(645\) 0 0
\(646\) −11.1075 75.6898i −0.0171942 0.117167i
\(647\) −443.581 + 443.581i −0.685596 + 0.685596i −0.961255 0.275659i \(-0.911104\pi\)
0.275659 + 0.961255i \(0.411104\pi\)
\(648\) 0 0
\(649\) 620.767 620.767i 0.956497 0.956497i
\(650\) −18.6260 + 25.0330i −0.0286554 + 0.0385123i
\(651\) 0 0
\(652\) 0.186019 1.83040i 0.000285305 0.00280737i
\(653\) 14.0746 + 33.9792i 0.0215538 + 0.0520355i 0.934290 0.356514i \(-0.116035\pi\)
−0.912736 + 0.408549i \(0.866035\pi\)
\(654\) 0 0
\(655\) −231.737 −0.353798
\(656\) −896.617 184.143i −1.36679 0.280706i
\(657\) 0 0
\(658\) 211.758 126.476i 0.321821 0.192213i
\(659\) 845.778 350.333i 1.28343 0.531613i 0.366407 0.930455i \(-0.380588\pi\)
0.917020 + 0.398842i \(0.130588\pi\)
\(660\) 0 0
\(661\) −1022.39 423.490i −1.54674 0.640680i −0.564017 0.825763i \(-0.690745\pi\)
−0.982723 + 0.185083i \(0.940745\pi\)
\(662\) −66.4921 + 89.3640i −0.100441 + 0.134991i
\(663\) 0 0
\(664\) −243.752 88.4985i −0.367096 0.133281i
\(665\) −344.727 344.727i −0.518387 0.518387i
\(666\) 0 0
\(667\) −75.2241 31.1588i −0.112780 0.0467149i
\(668\) −524.224 + 157.246i −0.784767 + 0.235398i
\(669\) 0 0
\(670\) 627.642 + 158.252i 0.936780 + 0.236197i
\(671\) 952.498i 1.41952i
\(672\) 0 0
\(673\) −441.074 −0.655385 −0.327693 0.944784i \(-0.606271\pi\)
−0.327693 + 0.944784i \(0.606271\pi\)
\(674\) −84.6059 + 335.555i −0.125528 + 0.497856i
\(675\) 0 0
\(676\) 180.417 54.1177i 0.266889 0.0800558i
\(677\) 3.12869 7.55333i 0.00462140 0.0111571i −0.921552 0.388255i \(-0.873078\pi\)
0.926173 + 0.377098i \(0.123078\pi\)
\(678\) 0 0
\(679\) 357.923 357.923i 0.527133 0.527133i
\(680\) 46.7712 + 100.093i 0.0687812 + 0.147195i
\(681\) 0 0
\(682\) 123.186 + 91.6576i 0.180624 + 0.134395i
\(683\) 198.853 480.073i 0.291146 0.702889i −0.708851 0.705358i \(-0.750786\pi\)
0.999997 + 0.00246964i \(0.000786112\pi\)
\(684\) 0 0
\(685\) −73.2458 176.831i −0.106928 0.258147i
\(686\) 323.813 + 542.157i 0.472031 + 0.790316i
\(687\) 0 0
\(688\) −1005.88 + 193.598i −1.46204 + 0.281392i
\(689\) 561.638i 0.815149i
\(690\) 0 0
\(691\) 260.304 107.822i 0.376707 0.156037i −0.186293 0.982494i \(-0.559647\pi\)
0.563000 + 0.826457i \(0.309647\pi\)
\(692\) 108.051 1063.21i 0.156143 1.53643i
\(693\) 0 0
\(694\) 85.0257 + 63.2642i 0.122515 + 0.0911588i
\(695\) −299.233 299.233i −0.430551 0.430551i
\(696\) 0 0
\(697\) 115.028 + 115.028i 0.165034 + 0.165034i
\(698\) 475.976 69.8494i 0.681914 0.100071i
\(699\) 0 0
\(700\) −37.1350 19.9976i −0.0530501 0.0285680i
\(701\) 487.328 201.858i 0.695189 0.287957i −0.00697111 0.999976i \(-0.502219\pi\)
0.702160 + 0.712019i \(0.252219\pi\)
\(702\) 0 0
\(703\) 234.943i 0.334200i
\(704\) −989.474 310.247i −1.40550 0.440692i
\(705\) 0 0
\(706\) −145.835 36.7705i −0.206565 0.0520829i
\(707\) 340.992 + 823.228i 0.482309 + 1.16440i
\(708\) 0 0
\(709\) 260.932 629.945i 0.368028 0.888498i −0.626046 0.779786i \(-0.715328\pi\)
0.994073 0.108711i \(-0.0346724\pi\)
\(710\) −14.2136 96.8558i −0.0200191 0.136417i
\(711\) 0 0
\(712\) 8.42537 + 189.507i 0.0118334 + 0.266161i
\(713\) −6.81917 + 6.81917i −0.00956405 + 0.00956405i
\(714\) 0 0
\(715\) 332.494 802.712i 0.465027 1.12267i
\(716\) −1162.01 118.092i −1.62291 0.164932i
\(717\) 0 0
\(718\) 897.326 535.945i 1.24976 0.746441i
\(719\) 349.854 0.486585 0.243292 0.969953i \(-0.421773\pi\)
0.243292 + 0.969953i \(0.421773\pi\)
\(720\) 0 0
\(721\) 651.251i 0.903261i
\(722\) 309.166 184.655i 0.428207 0.255755i
\(723\) 0 0
\(724\) −90.8650 111.423i −0.125504 0.153899i
\(725\) −52.2230 21.6315i −0.0720318 0.0298365i
\(726\) 0 0
\(727\) −58.3736 58.3736i −0.0802938 0.0802938i 0.665819 0.746113i \(-0.268082\pi\)
−0.746113 + 0.665819i \(0.768082\pi\)
\(728\) −279.050 597.182i −0.383311 0.820305i
\(729\) 0 0
\(730\) 110.429 + 752.498i 0.151272 + 1.03082i
\(731\) 168.191 + 69.6672i 0.230084 + 0.0953040i
\(732\) 0 0
\(733\) 327.632 135.710i 0.446975 0.185143i −0.147831 0.989013i \(-0.547229\pi\)
0.594805 + 0.803870i \(0.297229\pi\)
\(734\) 936.467 + 236.118i 1.27584 + 0.321687i
\(735\) 0 0
\(736\) 28.3027 58.6588i 0.0384548 0.0796994i
\(737\) 1079.73 1.46504
\(738\) 0 0
\(739\) 328.523 + 793.126i 0.444551 + 1.07324i 0.974334 + 0.225108i \(0.0722736\pi\)
−0.529783 + 0.848134i \(0.677726\pi\)
\(740\) 97.4857 + 324.996i 0.131737 + 0.439184i
\(741\) 0 0
\(742\) 751.141 110.230i 1.01232 0.148558i
\(743\) −79.8532 + 79.8532i −0.107474 + 0.107474i −0.758799 0.651325i \(-0.774214\pi\)
0.651325 + 0.758799i \(0.274214\pi\)
\(744\) 0 0
\(745\) 467.835 467.835i 0.627966 0.627966i
\(746\) −797.274 593.219i −1.06873 0.795200i
\(747\) 0 0
\(748\) 116.472 + 142.823i 0.155711 + 0.190940i
\(749\) −53.2561 128.572i −0.0711029 0.171658i
\(750\) 0 0
\(751\) −729.615 −0.971524 −0.485762 0.874091i \(-0.661458\pi\)
−0.485762 + 0.874091i \(0.661458\pi\)
\(752\) 145.536 + 220.765i 0.193532 + 0.293570i
\(753\) 0 0
\(754\) −452.986 758.429i −0.600778 1.00587i
\(755\) 674.239 279.279i 0.893032 0.369906i
\(756\) 0 0
\(757\) 565.974 + 234.434i 0.747654 + 0.309688i 0.723784 0.690027i \(-0.242401\pi\)
0.0238700 + 0.999715i \(0.492401\pi\)
\(758\) −363.274 270.298i −0.479253 0.356593i
\(759\) 0 0
\(760\) 352.780 385.608i 0.464184 0.507379i
\(761\) −186.563 186.563i −0.245155 0.245155i 0.573824 0.818979i \(-0.305459\pi\)
−0.818979 + 0.573824i \(0.805459\pi\)
\(762\) 0 0
\(763\) 1354.23 + 560.940i 1.77487 + 0.735176i
\(764\) 90.5213 168.096i 0.118483 0.220021i
\(765\) 0 0
\(766\) 118.861 471.413i 0.155171 0.615421i
\(767\) 598.241i 0.779976i
\(768\) 0 0
\(769\) 134.178 0.174484 0.0872420 0.996187i \(-0.472195\pi\)
0.0872420 + 0.996187i \(0.472195\pi\)
\(770\) 1138.81 + 287.137i 1.47898 + 0.372906i
\(771\) 0 0
\(772\) −1064.19 573.077i −1.37849 0.742328i
\(773\) 155.016 374.241i 0.200538 0.484141i −0.791334 0.611384i \(-0.790613\pi\)
0.991872 + 0.127243i \(0.0406130\pi\)
\(774\) 0 0
\(775\) −4.73409 + 4.73409i −0.00610851 + 0.00610851i
\(776\) 400.369 + 366.284i 0.515940 + 0.472016i
\(777\) 0 0
\(778\) 312.053 419.393i 0.401097 0.539065i
\(779\) 294.489 710.960i 0.378035 0.912657i
\(780\) 0 0
\(781\) −62.4903 150.865i −0.0800132 0.193169i
\(782\) −9.93746 + 5.93534i −0.0127078 + 0.00758994i
\(783\) 0 0
\(784\) 89.3469 58.9005i 0.113963 0.0751282i
\(785\) 1100.49i 1.40189i
\(786\) 0 0
\(787\) 464.245 192.297i 0.589892 0.244341i −0.0677120 0.997705i \(-0.521570\pi\)
0.657604 + 0.753364i \(0.271570\pi\)
\(788\) −148.235 + 120.885i −0.188115 + 0.153407i
\(789\) 0 0
\(790\) −64.3534 + 86.4895i −0.0814600 + 0.109480i
\(791\) −827.311 827.311i −1.04590 1.04590i
\(792\) 0 0
\(793\) 458.968 + 458.968i 0.578774 + 0.578774i
\(794\) 134.780 + 918.436i 0.169749 + 1.15672i
\(795\) 0 0
\(796\) −510.728 + 153.198i −0.641618 + 0.192459i
\(797\) −1426.93 + 591.055i −1.79038 + 0.741600i −0.800564 + 0.599247i \(0.795467\pi\)
−0.989816 + 0.142353i \(0.954533\pi\)
\(798\) 0 0
\(799\) 46.9933i 0.0588152i
\(800\) 19.6487 40.7228i 0.0245609 0.0509035i
\(801\) 0 0
\(802\) 263.669 1045.74i 0.328765 1.30391i
\(803\) 485.503 + 1172.11i 0.604612 + 1.45966i
\(804\) 0 0
\(805\) −28.2286 + 68.1498i −0.0350665 + 0.0846581i
\(806\) −103.524 + 15.1921i −0.128441 + 0.0188488i
\(807\) 0 0
\(808\) −865.419 + 404.391i −1.07106 + 0.500485i
\(809\) 950.297 950.297i 1.17466 1.17466i 0.193570 0.981086i \(-0.437993\pi\)
0.981086 0.193570i \(-0.0620067\pi\)
\(810\) 0 0
\(811\) −580.036 + 1400.33i −0.715210 + 1.72667i −0.0286586 + 0.999589i \(0.509124\pi\)
−0.686552 + 0.727081i \(0.740876\pi\)
\(812\) 925.428 754.683i 1.13969 0.929412i
\(813\) 0 0
\(814\) 290.222 + 485.916i 0.356538 + 0.596948i
\(815\) −2.23385 −0.00274092
\(816\) 0 0
\(817\) 861.189i 1.05409i
\(818\) −257.899 431.798i −0.315280 0.527870i
\(819\) 0 0
\(820\) −112.366 + 1105.66i −0.137031 + 1.34837i
\(821\) −646.816 267.920i −0.787839 0.326334i −0.0477645 0.998859i \(-0.515210\pi\)
−0.740074 + 0.672525i \(0.765210\pi\)
\(822\) 0 0
\(823\) −262.313 262.313i −0.318728 0.318728i 0.529551 0.848278i \(-0.322361\pi\)
−0.848278 + 0.529551i \(0.822361\pi\)
\(824\) −697.472 + 31.0092i −0.846447 + 0.0376326i
\(825\) 0 0
\(826\) −800.096 + 117.414i −0.968639 + 0.142148i
\(827\) −893.204 369.977i −1.08005 0.447373i −0.229525 0.973303i \(-0.573717\pi\)
−0.850528 + 0.525930i \(0.823717\pi\)
\(828\) 0 0
\(829\) −161.439 + 66.8701i −0.194739 + 0.0806635i −0.477922 0.878402i \(-0.658610\pi\)
0.283183 + 0.959066i \(0.408610\pi\)
\(830\) −76.9780 + 305.302i −0.0927446 + 0.367833i
\(831\) 0 0
\(832\) 626.279 327.290i 0.752740 0.393378i
\(833\) −19.0189 −0.0228318
\(834\) 0 0
\(835\) 254.297 + 613.928i 0.304548 + 0.735243i
\(836\) 413.351 767.583i 0.494439 0.918162i
\(837\) 0 0
\(838\) 41.7811 + 284.710i 0.0498582 + 0.339749i
\(839\) −552.802 + 552.802i −0.658882 + 0.658882i −0.955116 0.296234i \(-0.904269\pi\)
0.296234 + 0.955116i \(0.404269\pi\)
\(840\) 0 0
\(841\) 536.963 536.963i 0.638481 0.638481i
\(842\) 912.175 1225.94i 1.08334 1.45599i
\(843\) 0 0
\(844\) −1153.23 117.200i −1.36639 0.138863i
\(845\) −87.5188 211.289i −0.103573 0.250046i
\(846\) 0 0
\(847\) 1056.14 1.24692
\(848\) 153.819 + 799.204i 0.181390 + 0.942457i
\(849\) 0 0
\(850\) −6.89891 + 4.12051i −0.00811637 + 0.00484765i
\(851\) −32.8425 + 13.6038i −0.0385928 + 0.0159857i
\(852\) 0 0
\(853\) −653.395 270.645i −0.765997 0.317286i −0.0347472 0.999396i \(-0.511063\pi\)
−0.731250 + 0.682110i \(0.761063\pi\)
\(854\) −523.750 + 703.909i −0.613290 + 0.824249i
\(855\) 0 0
\(856\) 135.161 63.1578i 0.157898 0.0737824i
\(857\) 26.5894 + 26.5894i 0.0310261 + 0.0310261i 0.722450 0.691424i \(-0.243016\pi\)
−0.691424 + 0.722450i \(0.743016\pi\)
\(858\) 0 0
\(859\) 149.594 + 61.9638i 0.174149 + 0.0721349i 0.468054 0.883700i \(-0.344955\pi\)
−0.293906 + 0.955834i \(0.594955\pi\)
\(860\) 357.336 + 1191.28i 0.415507 + 1.38521i
\(861\) 0 0
\(862\) 1572.22 + 396.414i 1.82392 + 0.459878i
\(863\) 448.190i 0.519339i −0.965698 0.259670i \(-0.916386\pi\)
0.965698 0.259670i \(-0.0836137\pi\)
\(864\) 0 0
\(865\) −1297.55 −1.50006
\(866\) 368.231 1460.44i 0.425209 1.68642i
\(867\) 0 0
\(868\) −40.6362 135.472i −0.0468159 0.156074i
\(869\) −68.8172 + 166.139i −0.0791913 + 0.191185i
\(870\) 0 0
\(871\) −520.277 + 520.277i −0.597333 + 0.597333i
\(872\) −536.270 + 1477.05i −0.614988 + 1.69387i
\(873\) 0 0
\(874\) 43.9298 + 32.6864i 0.0502629 + 0.0373986i
\(875\) −366.333 + 884.406i −0.418666 + 1.01075i
\(876\) 0 0
\(877\) −285.210 688.559i −0.325211 0.785130i −0.998935 0.0461461i \(-0.985306\pi\)
0.673723 0.738984i \(-0.264694\pi\)
\(878\) −732.329 1226.13i −0.834088 1.39650i
\(879\) 0 0
\(880\) −253.292 + 1233.31i −0.287832 + 1.40149i
\(881\) 140.757i 0.159770i −0.996804 0.0798849i \(-0.974545\pi\)
0.996804 0.0798849i \(-0.0254553\pi\)
\(882\) 0 0
\(883\) −644.358 + 266.902i −0.729737 + 0.302267i −0.716444 0.697645i \(-0.754231\pi\)
−0.0132930 + 0.999912i \(0.504231\pi\)
\(884\) −124.943 12.6976i −0.141338 0.0143638i
\(885\) 0 0
\(886\) −1211.03 901.080i −1.36685 1.01702i
\(887\) 251.938 + 251.938i 0.284034 + 0.284034i 0.834715 0.550682i \(-0.185632\pi\)
−0.550682 + 0.834715i \(0.685632\pi\)
\(888\) 0 0
\(889\) −1018.26 1018.26i −1.14540 1.14540i
\(890\) 227.878 33.4411i 0.256043 0.0375743i
\(891\) 0 0
\(892\) 774.474 1438.18i 0.868244 1.61231i
\(893\) −205.381 + 85.0718i −0.229990 + 0.0952651i
\(894\) 0 0
\(895\) 1418.13i 1.58450i
\(896\) 560.639 + 773.358i 0.625713 + 0.863123i
\(897\) 0 0
\(898\) −570.264 143.785i −0.635038 0.160117i
\(899\) −72.5384 175.123i −0.0806878 0.194798i
\(900\) 0 0
\(901\) 55.3526 133.633i 0.0614346 0.148316i
\(902\) 269.170 + 1834.21i 0.298414 + 2.03349i
\(903\) 0 0
\(904\) 846.635 925.420i 0.936544 1.02369i
\(905\) −123.438 + 123.438i −0.136395 + 0.136395i
\(906\) 0 0
\(907\) 17.5960 42.4804i 0.0194002 0.0468362i −0.913883 0.405979i \(-0.866931\pi\)
0.933283 + 0.359142i \(0.116931\pi\)
\(908\) 87.2013 858.050i 0.0960366 0.944989i
\(909\) 0 0
\(910\) −687.104 + 410.386i −0.755060 + 0.450974i
\(911\) −425.886 −0.467493 −0.233747 0.972298i \(-0.575099\pi\)
−0.233747 + 0.972298i \(0.575099\pi\)
\(912\) 0 0
\(913\) 525.211i 0.575258i
\(914\) −425.287 + 254.011i −0.465303 + 0.277911i
\(915\) 0 0
\(916\) 183.126 149.338i 0.199919 0.163033i
\(917\) 328.971 + 136.264i 0.358747 + 0.148598i
\(918\) 0 0
\(919\) 339.201 + 339.201i 0.369098 + 0.369098i 0.867148 0.498050i \(-0.165951\pi\)
−0.498050 + 0.867148i \(0.665951\pi\)
\(920\) −74.3307 26.9871i −0.0807942 0.0293338i
\(921\) 0 0
\(922\) −81.4139 554.781i −0.0883015 0.601714i
\(923\) 102.807 + 42.5839i 0.111383 + 0.0461364i
\(924\) 0 0
\(925\) −22.8003 + 9.44420i −0.0246490 + 0.0102099i
\(926\) −104.152 26.2607i −0.112475 0.0283593i
\(927\) 0 0
\(928\) 852.309 + 955.174i 0.918437 + 1.02928i
\(929\) 674.156 0.725679 0.362839 0.931852i \(-0.381807\pi\)
0.362839 + 0.931852i \(0.381807\pi\)
\(930\) 0 0
\(931\) 34.4298 + 83.1210i 0.0369816 + 0.0892814i
\(932\) −315.795 + 94.7257i −0.338836 + 0.101637i
\(933\) 0 0
\(934\) 217.505 31.9188i 0.232874 0.0341743i
\(935\) 158.224 158.224i 0.169223 0.169223i
\(936\) 0 0
\(937\) −810.809 + 810.809i −0.865325 + 0.865325i −0.991951 0.126626i \(-0.959585\pi\)
0.126626 + 0.991951i \(0.459585\pi\)
\(938\) −797.937 593.713i −0.850680 0.632956i
\(939\) 0 0
\(940\) 248.805 202.899i 0.264686 0.215850i
\(941\) 372.431 + 899.128i 0.395782 + 0.955503i 0.988655 + 0.150206i \(0.0479938\pi\)
−0.592873 + 0.805296i \(0.702006\pi\)
\(942\) 0 0
\(943\) −116.436 −0.123474
\(944\) −163.844 851.291i −0.173563 0.901791i
\(945\) 0 0
\(946\) 1063.82 + 1781.14i 1.12454 + 1.88281i
\(947\) −647.322 + 268.130i −0.683551 + 0.283136i −0.697310 0.716769i \(-0.745620\pi\)
0.0137596 + 0.999905i \(0.495620\pi\)
\(948\) 0 0
\(949\) −798.732 330.846i −0.841656 0.348625i
\(950\) 30.4975 + 22.6919i 0.0321026 + 0.0238863i
\(951\) 0 0
\(952\) −7.53998 169.592i −0.00792014 0.178143i
\(953\) 584.883 + 584.883i 0.613728 + 0.613728i 0.943916 0.330187i \(-0.107112\pi\)
−0.330187 + 0.943916i \(0.607112\pi\)
\(954\) 0 0
\(955\) −214.162 88.7089i −0.224254 0.0928889i
\(956\) 1293.79 + 696.721i 1.35334 + 0.728788i
\(957\) 0 0
\(958\) −19.9499 + 79.1232i −0.0208245 + 0.0825920i
\(959\) 294.096i 0.306669i
\(960\) 0 0
\(961\) 938.549 0.976638
\(962\) −373.987 94.2962i −0.388760 0.0980210i
\(963\) 0 0
\(964\) −592.373 + 1100.02i −0.614495 + 1.14110i
\(965\) −561.603 + 1355.83i −0.581972 + 1.40500i
\(966\) 0 0
\(967\) 177.502 177.502i 0.183560 0.183560i −0.609345 0.792905i \(-0.708568\pi\)
0.792905 + 0.609345i \(0.208568\pi\)
\(968\) 50.2882 + 1131.10i 0.0519506 + 1.16849i
\(969\) 0 0
\(970\) 393.300 528.587i 0.405464 0.544935i
\(971\) −130.414 + 314.847i −0.134309 + 0.324250i −0.976698 0.214620i \(-0.931149\pi\)
0.842389 + 0.538870i \(0.181149\pi\)
\(972\) 0 0
\(973\) 248.834 + 600.738i 0.255739 + 0.617408i
\(974\) 348.846 208.355i 0.358158 0.213916i
\(975\) 0 0
\(976\) −778.806 527.406i −0.797957 0.540375i
\(977\) 73.1425i 0.0748644i −0.999299 0.0374322i \(-0.988082\pi\)
0.999299 0.0374322i \(-0.0119178\pi\)
\(978\) 0 0
\(979\) 354.949 147.025i 0.362563 0.150179i
\(980\) −82.1165 100.695i −0.0837923 0.102750i
\(981\) 0 0
\(982\) 569.595 765.524i 0.580036 0.779556i
\(983\) 614.269 + 614.269i 0.624892 + 0.624892i 0.946778 0.321886i \(-0.104317\pi\)
−0.321886 + 0.946778i \(0.604317\pi\)
\(984\) 0 0
\(985\) 164.219 + 164.219i 0.166720 + 0.166720i
\(986\) −33.0335 225.101i −0.0335025 0.228297i
\(987\) 0 0
\(988\) 170.689 + 569.041i 0.172762 + 0.575953i
\(989\) −120.385 + 49.8650i −0.121724 + 0.0504197i
\(990\) 0 0
\(991\) 763.403i 0.770336i −0.922847 0.385168i \(-0.874144\pi\)
0.922847 0.385168i \(-0.125856\pi\)
\(992\) 143.152 49.9708i 0.144307 0.0503738i
\(993\) 0 0
\(994\) −36.7749 + 145.853i −0.0369969 + 0.146733i
\(995\) 247.750 + 598.122i 0.248995 + 0.601128i
\(996\) 0 0
\(997\) −752.731 + 1817.25i −0.754996 + 1.82272i −0.225923 + 0.974145i \(0.572540\pi\)
−0.529073 + 0.848576i \(0.677460\pi\)
\(998\) 877.835 128.822i 0.879595 0.129080i
\(999\) 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 288.3.u.a.235.1 28
3.2 odd 2 32.3.h.a.11.7 yes 28
12.11 even 2 128.3.h.a.79.7 28
24.5 odd 2 256.3.h.b.159.7 28
24.11 even 2 256.3.h.a.159.1 28
32.3 odd 8 inner 288.3.u.a.163.1 28
96.29 odd 8 128.3.h.a.47.7 28
96.35 even 8 32.3.h.a.3.7 28
96.77 odd 8 256.3.h.a.95.1 28
96.83 even 8 256.3.h.b.95.7 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.3.7 28 96.35 even 8
32.3.h.a.11.7 yes 28 3.2 odd 2
128.3.h.a.47.7 28 96.29 odd 8
128.3.h.a.79.7 28 12.11 even 2
256.3.h.a.95.1 28 96.77 odd 8
256.3.h.a.159.1 28 24.11 even 2
256.3.h.b.95.7 28 96.83 even 8
256.3.h.b.159.7 28 24.5 odd 2
288.3.u.a.163.1 28 32.3 odd 8 inner
288.3.u.a.235.1 28 1.1 even 1 trivial