Properties

Label 99.3.l.a.26.3
Level $99$
Weight $3$
Character 99.26
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,3,Mod(26,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.26");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), 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: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 26.3
Character \(\chi\) \(=\) 99.26
Dual form 99.3.l.a.80.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15480 + 1.58945i) q^{2} +(0.0432885 + 0.133228i) q^{4} +(-5.65603 - 7.78486i) q^{5} +(-1.61633 - 4.97456i) q^{7} +(-7.73579 - 2.51351i) q^{8} +O(q^{10})\) \(q+(-1.15480 + 1.58945i) q^{2} +(0.0432885 + 0.133228i) q^{4} +(-5.65603 - 7.78486i) q^{5} +(-1.61633 - 4.97456i) q^{7} +(-7.73579 - 2.51351i) q^{8} +18.9052 q^{10} +(9.06319 + 6.23366i) q^{11} +(-13.9350 - 10.1244i) q^{13} +(9.77335 + 3.17555i) q^{14} +(12.4751 - 9.06367i) q^{16} +(-4.53667 - 6.24419i) q^{17} +(4.33521 - 13.3424i) q^{19} +(0.792322 - 1.09054i) q^{20} +(-20.3743 + 7.20684i) q^{22} +5.68512i q^{23} +(-20.8879 + 64.2864i) q^{25} +(32.1844 - 10.4574i) q^{26} +(0.592783 - 0.430682i) q^{28} +(-22.9057 + 7.44253i) q^{29} +(-12.1481 - 8.82612i) q^{31} -2.24031i q^{32} +15.1638 q^{34} +(-29.5842 + 40.7192i) q^{35} +(-2.36563 - 7.28065i) q^{37} +(16.2007 + 22.2984i) q^{38} +(24.1865 + 74.4385i) q^{40} +(17.3048 + 5.62267i) q^{41} -53.6955 q^{43} +(-0.438168 + 1.47732i) q^{44} +(-9.03621 - 6.56519i) q^{46} +(36.9117 + 11.9934i) q^{47} +(17.5081 - 12.7204i) q^{49} +(-78.0585 - 107.438i) q^{50} +(0.745630 - 2.29481i) q^{52} +(47.9715 - 66.0271i) q^{53} +(-2.73355 - 105.813i) q^{55} +42.5448i q^{56} +(14.6221 - 45.0022i) q^{58} +(-0.000412921 + 0.000134166i) q^{59} +(-3.86696 + 2.80951i) q^{61} +(28.0573 - 9.11638i) q^{62} +(53.4611 + 38.8418i) q^{64} +165.746i q^{65} +111.796 q^{67} +(0.635517 - 0.874715i) q^{68} +(-30.5571 - 94.0452i) q^{70} +(-58.5632 - 80.6053i) q^{71} +(-10.5980 - 32.6171i) q^{73} +(14.3041 + 4.64767i) q^{74} +1.96525 q^{76} +(16.3606 - 55.1611i) q^{77} +(49.9398 + 36.2834i) q^{79} +(-141.119 - 45.8523i) q^{80} +(-28.9205 + 21.0120i) q^{82} +(-38.3421 - 52.7733i) q^{83} +(-22.9506 + 70.6347i) q^{85} +(62.0076 - 85.3462i) q^{86} +(-54.4426 - 71.0027i) q^{88} +92.5976i q^{89} +(-27.8408 + 85.6851i) q^{91} +(-0.757419 + 0.246100i) q^{92} +(-61.6886 + 44.8194i) q^{94} +(-128.389 + 41.7160i) q^{95} +(42.4116 + 30.8138i) q^{97} +42.5178i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15480 + 1.58945i −0.577401 + 0.794724i −0.993407 0.114637i \(-0.963429\pi\)
0.416006 + 0.909362i \(0.363429\pi\)
\(3\) 0 0
\(4\) 0.0432885 + 0.133228i 0.0108221 + 0.0333071i
\(5\) −5.65603 7.78486i −1.13121 1.55697i −0.785758 0.618533i \(-0.787727\pi\)
−0.345448 0.938438i \(-0.612273\pi\)
\(6\) 0 0
\(7\) −1.61633 4.97456i −0.230905 0.710651i −0.997638 0.0686861i \(-0.978119\pi\)
0.766734 0.641965i \(-0.221881\pi\)
\(8\) −7.73579 2.51351i −0.966973 0.314189i
\(9\) 0 0
\(10\) 18.9052 1.89052
\(11\) 9.06319 + 6.23366i 0.823927 + 0.566696i
\(12\) 0 0
\(13\) −13.9350 10.1244i −1.07193 0.778800i −0.0956692 0.995413i \(-0.530499\pi\)
−0.976258 + 0.216613i \(0.930499\pi\)
\(14\) 9.77335 + 3.17555i 0.698097 + 0.226825i
\(15\) 0 0
\(16\) 12.4751 9.06367i 0.779692 0.566479i
\(17\) −4.53667 6.24419i −0.266863 0.367306i 0.654464 0.756093i \(-0.272894\pi\)
−0.921328 + 0.388787i \(0.872894\pi\)
\(18\) 0 0
\(19\) 4.33521 13.3424i 0.228169 0.702231i −0.769786 0.638302i \(-0.779637\pi\)
0.997954 0.0639288i \(-0.0203630\pi\)
\(20\) 0.792322 1.09054i 0.0396161 0.0545269i
\(21\) 0 0
\(22\) −20.3743 + 7.20684i −0.926104 + 0.327584i
\(23\) 5.68512i 0.247179i 0.992333 + 0.123590i \(0.0394407\pi\)
−0.992333 + 0.123590i \(0.960559\pi\)
\(24\) 0 0
\(25\) −20.8879 + 64.2864i −0.835516 + 2.57145i
\(26\) 32.1844 10.4574i 1.23786 0.402206i
\(27\) 0 0
\(28\) 0.592783 0.430682i 0.0211708 0.0153815i
\(29\) −22.9057 + 7.44253i −0.789853 + 0.256639i −0.676042 0.736863i \(-0.736306\pi\)
−0.113812 + 0.993502i \(0.536306\pi\)
\(30\) 0 0
\(31\) −12.1481 8.82612i −0.391874 0.284713i 0.374349 0.927288i \(-0.377866\pi\)
−0.766223 + 0.642575i \(0.777866\pi\)
\(32\) 2.24031i 0.0700097i
\(33\) 0 0
\(34\) 15.1638 0.445994
\(35\) −29.5842 + 40.7192i −0.845263 + 1.16340i
\(36\) 0 0
\(37\) −2.36563 7.28065i −0.0639359 0.196774i 0.913986 0.405746i \(-0.132988\pi\)
−0.977922 + 0.208972i \(0.932988\pi\)
\(38\) 16.2007 + 22.2984i 0.426335 + 0.586800i
\(39\) 0 0
\(40\) 24.1865 + 74.4385i 0.604663 + 1.86096i
\(41\) 17.3048 + 5.62267i 0.422068 + 0.137138i 0.512347 0.858778i \(-0.328776\pi\)
−0.0902795 + 0.995916i \(0.528776\pi\)
\(42\) 0 0
\(43\) −53.6955 −1.24873 −0.624366 0.781132i \(-0.714642\pi\)
−0.624366 + 0.781132i \(0.714642\pi\)
\(44\) −0.438168 + 1.47732i −0.00995836 + 0.0335754i
\(45\) 0 0
\(46\) −9.03621 6.56519i −0.196439 0.142722i
\(47\) 36.9117 + 11.9934i 0.785356 + 0.255178i 0.674125 0.738617i \(-0.264521\pi\)
0.111231 + 0.993795i \(0.464521\pi\)
\(48\) 0 0
\(49\) 17.5081 12.7204i 0.357309 0.259600i
\(50\) −78.0585 107.438i −1.56117 2.14877i
\(51\) 0 0
\(52\) 0.745630 2.29481i 0.0143390 0.0441310i
\(53\) 47.9715 66.0271i 0.905123 1.24580i −0.0636816 0.997970i \(-0.520284\pi\)
0.968805 0.247825i \(-0.0797158\pi\)
\(54\) 0 0
\(55\) −2.73355 105.813i −0.0497010 1.92388i
\(56\) 42.5448i 0.759728i
\(57\) 0 0
\(58\) 14.6221 45.0022i 0.252105 0.775899i
\(59\) −0.000412921 0 0.000134166i −6.99867e−6 0 2.27400e-6i −0.309020 0.951055i \(-0.600001\pi\)
0.309013 + 0.951058i \(0.400001\pi\)
\(60\) 0 0
\(61\) −3.86696 + 2.80951i −0.0633928 + 0.0460576i −0.619030 0.785367i \(-0.712474\pi\)
0.555638 + 0.831425i \(0.312474\pi\)
\(62\) 28.0573 9.11638i 0.452537 0.147038i
\(63\) 0 0
\(64\) 53.4611 + 38.8418i 0.835330 + 0.606903i
\(65\) 165.746i 2.54994i
\(66\) 0 0
\(67\) 111.796 1.66860 0.834298 0.551313i \(-0.185873\pi\)
0.834298 + 0.551313i \(0.185873\pi\)
\(68\) 0.635517 0.874715i 0.00934585 0.0128635i
\(69\) 0 0
\(70\) −30.5571 94.0452i −0.436530 1.34350i
\(71\) −58.5632 80.6053i −0.824834 1.13529i −0.988863 0.148831i \(-0.952449\pi\)
0.164029 0.986456i \(-0.447551\pi\)
\(72\) 0 0
\(73\) −10.5980 32.6171i −0.145177 0.446810i 0.851856 0.523775i \(-0.175477\pi\)
−0.997034 + 0.0769653i \(0.975477\pi\)
\(74\) 14.3041 + 4.64767i 0.193298 + 0.0628063i
\(75\) 0 0
\(76\) 1.96525 0.0258585
\(77\) 16.3606 55.1611i 0.212475 0.716377i
\(78\) 0 0
\(79\) 49.9398 + 36.2834i 0.632150 + 0.459284i 0.857144 0.515076i \(-0.172236\pi\)
−0.224995 + 0.974360i \(0.572236\pi\)
\(80\) −141.119 45.8523i −1.76398 0.573153i
\(81\) 0 0
\(82\) −28.9205 + 21.0120i −0.352690 + 0.256244i
\(83\) −38.3421 52.7733i −0.461953 0.635823i 0.512960 0.858413i \(-0.328549\pi\)
−0.974912 + 0.222589i \(0.928549\pi\)
\(84\) 0 0
\(85\) −22.9506 + 70.6347i −0.270007 + 0.830996i
\(86\) 62.0076 85.3462i 0.721019 0.992397i
\(87\) 0 0
\(88\) −54.4426 71.0027i −0.618666 0.806849i
\(89\) 92.5976i 1.04042i 0.854038 + 0.520211i \(0.174147\pi\)
−0.854038 + 0.520211i \(0.825853\pi\)
\(90\) 0 0
\(91\) −27.8408 + 85.6851i −0.305943 + 0.941595i
\(92\) −0.757419 + 0.246100i −0.00823282 + 0.00267500i
\(93\) 0 0
\(94\) −61.6886 + 44.8194i −0.656261 + 0.476802i
\(95\) −128.389 + 41.7160i −1.35146 + 0.439116i
\(96\) 0 0
\(97\) 42.4116 + 30.8138i 0.437233 + 0.317668i 0.784534 0.620085i \(-0.212902\pi\)
−0.347302 + 0.937753i \(0.612902\pi\)
\(98\) 42.5178i 0.433855i
\(99\) 0 0
\(100\) −9.46897 −0.0946897
\(101\) 34.6336 47.6691i 0.342907 0.471971i −0.602381 0.798209i \(-0.705781\pi\)
0.945288 + 0.326238i \(0.105781\pi\)
\(102\) 0 0
\(103\) −29.8866 91.9816i −0.290161 0.893025i −0.984804 0.173670i \(-0.944437\pi\)
0.694642 0.719355i \(-0.255563\pi\)
\(104\) 82.3508 + 113.346i 0.791834 + 1.08987i
\(105\) 0 0
\(106\) 49.5491 + 152.497i 0.467445 + 1.43865i
\(107\) 17.4915 + 5.68333i 0.163472 + 0.0531152i 0.389610 0.920980i \(-0.372610\pi\)
−0.226138 + 0.974095i \(0.572610\pi\)
\(108\) 0 0
\(109\) 50.6495 0.464674 0.232337 0.972635i \(-0.425363\pi\)
0.232337 + 0.972635i \(0.425363\pi\)
\(110\) 171.342 + 117.849i 1.55765 + 1.07135i
\(111\) 0 0
\(112\) −65.2516 47.4081i −0.582604 0.423286i
\(113\) 9.35427 + 3.03939i 0.0827811 + 0.0268972i 0.350115 0.936707i \(-0.386143\pi\)
−0.267334 + 0.963604i \(0.586143\pi\)
\(114\) 0 0
\(115\) 44.2579 32.1552i 0.384851 0.279611i
\(116\) −1.98311 2.72952i −0.0170958 0.0235303i
\(117\) 0 0
\(118\) 0.000263592 0 0.000811253i 2.23383e−6 0 6.87502e-6i
\(119\) −23.7293 + 32.6606i −0.199406 + 0.274459i
\(120\) 0 0
\(121\) 43.2830 + 112.994i 0.357711 + 0.933832i
\(122\) 9.39077i 0.0769736i
\(123\) 0 0
\(124\) 0.650015 2.00054i 0.00524206 0.0161334i
\(125\) 389.812 126.657i 3.11849 1.01326i
\(126\) 0 0
\(127\) −174.328 + 126.656i −1.37266 + 0.997294i −0.375133 + 0.926971i \(0.622403\pi\)
−0.997524 + 0.0703233i \(0.977597\pi\)
\(128\) −114.951 + 37.3500i −0.898058 + 0.291797i
\(129\) 0 0
\(130\) −263.445 191.404i −2.02650 1.47234i
\(131\) 166.588i 1.27166i −0.771827 0.635832i \(-0.780657\pi\)
0.771827 0.635832i \(-0.219343\pi\)
\(132\) 0 0
\(133\) −73.3797 −0.551727
\(134\) −129.102 + 177.694i −0.963450 + 1.32607i
\(135\) 0 0
\(136\) 19.3999 + 59.7067i 0.142646 + 0.439020i
\(137\) 25.7144 + 35.3928i 0.187696 + 0.258342i 0.892487 0.451074i \(-0.148959\pi\)
−0.704790 + 0.709416i \(0.748959\pi\)
\(138\) 0 0
\(139\) −31.8516 98.0291i −0.229148 0.705245i −0.997844 0.0656308i \(-0.979094\pi\)
0.768696 0.639614i \(-0.220906\pi\)
\(140\) −6.70560 2.17878i −0.0478972 0.0155627i
\(141\) 0 0
\(142\) 195.747 1.37850
\(143\) −63.1840 178.626i −0.441846 1.24913i
\(144\) 0 0
\(145\) 187.495 + 136.223i 1.29307 + 0.939468i
\(146\) 64.0818 + 20.8214i 0.438917 + 0.142613i
\(147\) 0 0
\(148\) 0.867584 0.630337i 0.00586205 0.00425903i
\(149\) −53.1924 73.2130i −0.356996 0.491363i 0.592313 0.805708i \(-0.298215\pi\)
−0.949309 + 0.314345i \(0.898215\pi\)
\(150\) 0 0
\(151\) 74.2733 228.590i 0.491876 1.51384i −0.329892 0.944019i \(-0.607012\pi\)
0.821769 0.569821i \(-0.192988\pi\)
\(152\) −67.0724 + 92.3173i −0.441266 + 0.607351i
\(153\) 0 0
\(154\) 68.7825 + 89.7044i 0.446639 + 0.582496i
\(155\) 144.492i 0.932207i
\(156\) 0 0
\(157\) −9.14801 + 28.1547i −0.0582676 + 0.179329i −0.975954 0.217976i \(-0.930055\pi\)
0.917687 + 0.397305i \(0.130055\pi\)
\(158\) −115.341 + 37.4766i −0.730008 + 0.237194i
\(159\) 0 0
\(160\) −17.4405 + 12.6713i −0.109003 + 0.0791953i
\(161\) 28.2810 9.18905i 0.175658 0.0570748i
\(162\) 0 0
\(163\) −169.962 123.484i −1.04271 0.757573i −0.0718974 0.997412i \(-0.522905\pi\)
−0.970813 + 0.239839i \(0.922905\pi\)
\(164\) 2.54888i 0.0155420i
\(165\) 0 0
\(166\) 128.158 0.772036
\(167\) 8.96158 12.3346i 0.0536622 0.0738596i −0.781343 0.624102i \(-0.785465\pi\)
0.835005 + 0.550243i \(0.185465\pi\)
\(168\) 0 0
\(169\) 39.4581 + 121.440i 0.233480 + 0.718578i
\(170\) −85.7668 118.048i −0.504511 0.694399i
\(171\) 0 0
\(172\) −2.32440 7.15375i −0.0135139 0.0415916i
\(173\) −203.903 66.2520i −1.17863 0.382960i −0.346772 0.937950i \(-0.612722\pi\)
−0.831857 + 0.554990i \(0.812722\pi\)
\(174\) 0 0
\(175\) 353.558 2.02033
\(176\) 169.564 4.38046i 0.963431 0.0248890i
\(177\) 0 0
\(178\) −147.179 106.932i −0.826849 0.600741i
\(179\) −194.582 63.2234i −1.08705 0.353204i −0.289943 0.957044i \(-0.593636\pi\)
−0.797105 + 0.603840i \(0.793636\pi\)
\(180\) 0 0
\(181\) −110.640 + 80.3847i −0.611271 + 0.444114i −0.849862 0.527006i \(-0.823315\pi\)
0.238591 + 0.971120i \(0.423315\pi\)
\(182\) −104.042 143.201i −0.571657 0.786818i
\(183\) 0 0
\(184\) 14.2896 43.9789i 0.0776609 0.239016i
\(185\) −43.2988 + 59.5956i −0.234047 + 0.322139i
\(186\) 0 0
\(187\) −2.19257 84.8724i −0.0117250 0.453863i
\(188\) 5.43686i 0.0289195i
\(189\) 0 0
\(190\) 81.9581 252.241i 0.431358 1.32758i
\(191\) −232.753 + 75.6261i −1.21860 + 0.395948i −0.846573 0.532272i \(-0.821338\pi\)
−0.372030 + 0.928221i \(0.621338\pi\)
\(192\) 0 0
\(193\) 12.7310 9.24963i 0.0659639 0.0479256i −0.554315 0.832307i \(-0.687020\pi\)
0.620279 + 0.784382i \(0.287020\pi\)
\(194\) −97.9540 + 31.8272i −0.504918 + 0.164058i
\(195\) 0 0
\(196\) 2.45262 + 1.78193i 0.0125133 + 0.00909148i
\(197\) 95.4172i 0.484351i −0.970232 0.242176i \(-0.922139\pi\)
0.970232 0.242176i \(-0.0778610\pi\)
\(198\) 0 0
\(199\) −65.2214 −0.327746 −0.163873 0.986481i \(-0.552399\pi\)
−0.163873 + 0.986481i \(0.552399\pi\)
\(200\) 323.169 444.804i 1.61584 2.22402i
\(201\) 0 0
\(202\) 35.7726 + 110.097i 0.177092 + 0.545033i
\(203\) 74.0466 + 101.916i 0.364762 + 0.502051i
\(204\) 0 0
\(205\) −54.1047 166.517i −0.263926 0.812279i
\(206\) 180.713 + 58.7173i 0.877248 + 0.285035i
\(207\) 0 0
\(208\) −265.605 −1.27695
\(209\) 122.463 93.9005i 0.585946 0.449285i
\(210\) 0 0
\(211\) 222.580 + 161.714i 1.05488 + 0.766415i 0.973134 0.230238i \(-0.0739506\pi\)
0.0817453 + 0.996653i \(0.473951\pi\)
\(212\) 10.8733 + 3.53295i 0.0512891 + 0.0166649i
\(213\) 0 0
\(214\) −29.2326 + 21.2387i −0.136601 + 0.0992462i
\(215\) 303.703 + 418.011i 1.41257 + 1.94424i
\(216\) 0 0
\(217\) −24.2707 + 74.6974i −0.111846 + 0.344228i
\(218\) −58.4902 + 80.5048i −0.268304 + 0.369288i
\(219\) 0 0
\(220\) 13.9790 4.94469i 0.0635410 0.0224759i
\(221\) 132.944i 0.601558i
\(222\) 0 0
\(223\) 56.5219 173.956i 0.253461 0.780074i −0.740668 0.671872i \(-0.765491\pi\)
0.994129 0.108202i \(-0.0345094\pi\)
\(224\) −11.1445 + 3.62108i −0.0497525 + 0.0161656i
\(225\) 0 0
\(226\) −15.6333 + 11.3582i −0.0691738 + 0.0502577i
\(227\) 238.155 77.3812i 1.04914 0.340886i 0.266809 0.963749i \(-0.414031\pi\)
0.782331 + 0.622863i \(0.214031\pi\)
\(228\) 0 0
\(229\) 283.549 + 206.010i 1.23820 + 0.899608i 0.997477 0.0709854i \(-0.0226144\pi\)
0.240726 + 0.970593i \(0.422614\pi\)
\(230\) 107.479i 0.467298i
\(231\) 0 0
\(232\) 195.901 0.844400
\(233\) −214.372 + 295.058i −0.920052 + 1.26634i 0.0435636 + 0.999051i \(0.486129\pi\)
−0.963616 + 0.267292i \(0.913871\pi\)
\(234\) 0 0
\(235\) −115.407 355.187i −0.491095 1.51144i
\(236\) −3.57495e−5 0 4.92049e-5i −1.51481e−7 0 2.08495e-7i
\(237\) 0 0
\(238\) −24.5097 75.4331i −0.102982 0.316946i
\(239\) 230.931 + 75.0342i 0.966240 + 0.313951i 0.749297 0.662234i \(-0.230391\pi\)
0.216943 + 0.976184i \(0.430391\pi\)
\(240\) 0 0
\(241\) −418.345 −1.73587 −0.867935 0.496677i \(-0.834553\pi\)
−0.867935 + 0.496677i \(0.834553\pi\)
\(242\) −229.581 61.6893i −0.948682 0.254914i
\(243\) 0 0
\(244\) −0.541702 0.393569i −0.00222009 0.00161299i
\(245\) −198.053 64.3513i −0.808379 0.262658i
\(246\) 0 0
\(247\) −195.495 + 142.036i −0.791478 + 0.575043i
\(248\) 71.7906 + 98.8113i 0.289478 + 0.398433i
\(249\) 0 0
\(250\) −248.840 + 765.850i −0.995359 + 3.06340i
\(251\) 162.338 223.439i 0.646766 0.890197i −0.352188 0.935929i \(-0.614562\pi\)
0.998954 + 0.0457326i \(0.0145622\pi\)
\(252\) 0 0
\(253\) −35.4391 + 51.5254i −0.140076 + 0.203658i
\(254\) 423.348i 1.66672i
\(255\) 0 0
\(256\) −8.30108 + 25.5481i −0.0324261 + 0.0997972i
\(257\) 153.309 49.8130i 0.596532 0.193825i 0.00483877 0.999988i \(-0.498460\pi\)
0.591693 + 0.806163i \(0.298460\pi\)
\(258\) 0 0
\(259\) −32.3944 + 23.5359i −0.125075 + 0.0908722i
\(260\) −22.0821 + 7.17491i −0.0849311 + 0.0275958i
\(261\) 0 0
\(262\) 264.783 + 192.376i 1.01062 + 0.734260i
\(263\) 55.4784i 0.210944i 0.994422 + 0.105472i \(0.0336354\pi\)
−0.994422 + 0.105472i \(0.966365\pi\)
\(264\) 0 0
\(265\) −785.340 −2.96355
\(266\) 84.7390 116.633i 0.318568 0.438471i
\(267\) 0 0
\(268\) 4.83948 + 14.8944i 0.0180578 + 0.0555761i
\(269\) 34.2101 + 47.0861i 0.127175 + 0.175041i 0.867856 0.496815i \(-0.165497\pi\)
−0.740682 + 0.671856i \(0.765497\pi\)
\(270\) 0 0
\(271\) 131.612 + 405.060i 0.485653 + 1.49469i 0.831033 + 0.556223i \(0.187750\pi\)
−0.345380 + 0.938463i \(0.612250\pi\)
\(272\) −113.191 36.7779i −0.416142 0.135213i
\(273\) 0 0
\(274\) −85.9501 −0.313686
\(275\) −590.050 + 452.432i −2.14564 + 1.64521i
\(276\) 0 0
\(277\) 103.461 + 75.1686i 0.373504 + 0.271367i 0.758663 0.651484i \(-0.225853\pi\)
−0.385158 + 0.922851i \(0.625853\pi\)
\(278\) 192.594 + 62.5777i 0.692786 + 0.225100i
\(279\) 0 0
\(280\) 331.205 240.635i 1.18288 0.859409i
\(281\) 43.7302 + 60.1895i 0.155624 + 0.214198i 0.879709 0.475513i \(-0.157738\pi\)
−0.724085 + 0.689711i \(0.757738\pi\)
\(282\) 0 0
\(283\) 152.758 470.142i 0.539782 1.66128i −0.193301 0.981139i \(-0.561919\pi\)
0.733083 0.680139i \(-0.238081\pi\)
\(284\) 8.20379 11.2916i 0.0288866 0.0397590i
\(285\) 0 0
\(286\) 356.882 + 105.850i 1.24784 + 0.370104i
\(287\) 95.1718i 0.331609i
\(288\) 0 0
\(289\) 70.8974 218.200i 0.245320 0.755016i
\(290\) −433.038 + 140.703i −1.49324 + 0.485182i
\(291\) 0 0
\(292\) 3.88676 2.82389i 0.0133108 0.00967087i
\(293\) 12.9456 4.20629i 0.0441831 0.0143559i −0.286842 0.957978i \(-0.592606\pi\)
0.331025 + 0.943622i \(0.392606\pi\)
\(294\) 0 0
\(295\) 0.00337996 + 0.00245568i 1.14575e−5 + 8.32436e-6i
\(296\) 62.2676i 0.210363i
\(297\) 0 0
\(298\) 177.795 0.596628
\(299\) 57.5585 79.2225i 0.192503 0.264958i
\(300\) 0 0
\(301\) 86.7897 + 267.111i 0.288338 + 0.887413i
\(302\) 277.561 + 382.030i 0.919075 + 1.26500i
\(303\) 0 0
\(304\) −66.8490 205.740i −0.219898 0.676777i
\(305\) 43.7433 + 14.2131i 0.143421 + 0.0466002i
\(306\) 0 0
\(307\) −215.268 −0.701198 −0.350599 0.936526i \(-0.614022\pi\)
−0.350599 + 0.936526i \(0.614022\pi\)
\(308\) 8.05724 0.208148i 0.0261599 0.000675806i
\(309\) 0 0
\(310\) −229.663 166.860i −0.740847 0.538257i
\(311\) 85.6398 + 27.8260i 0.275369 + 0.0894728i 0.443446 0.896301i \(-0.353756\pi\)
−0.168077 + 0.985774i \(0.553756\pi\)
\(312\) 0 0
\(313\) −208.941 + 151.805i −0.667544 + 0.484999i −0.869202 0.494457i \(-0.835367\pi\)
0.201658 + 0.979456i \(0.435367\pi\)
\(314\) −34.1863 47.0534i −0.108873 0.149851i
\(315\) 0 0
\(316\) −2.67216 + 8.22405i −0.00845619 + 0.0260255i
\(317\) 61.7422 84.9808i 0.194770 0.268078i −0.700451 0.713701i \(-0.747018\pi\)
0.895221 + 0.445623i \(0.147018\pi\)
\(318\) 0 0
\(319\) −253.993 75.3335i −0.796218 0.236155i
\(320\) 635.878i 1.98712i
\(321\) 0 0
\(322\) −18.0534 + 55.5627i −0.0560665 + 0.172555i
\(323\) −102.980 + 33.4602i −0.318823 + 0.103592i
\(324\) 0 0
\(325\) 941.935 684.356i 2.89826 2.10571i
\(326\) 392.544 127.545i 1.20412 0.391244i
\(327\) 0 0
\(328\) −119.733 86.9915i −0.365041 0.265218i
\(329\) 203.005i 0.617036i
\(330\) 0 0
\(331\) 258.731 0.781664 0.390832 0.920462i \(-0.372187\pi\)
0.390832 + 0.920462i \(0.372187\pi\)
\(332\) 5.37113 7.39273i 0.0161781 0.0222673i
\(333\) 0 0
\(334\) 9.25629 + 28.4879i 0.0277135 + 0.0852933i
\(335\) −632.321 870.316i −1.88753 2.59796i
\(336\) 0 0
\(337\) −113.715 349.979i −0.337433 1.03851i −0.965511 0.260362i \(-0.916158\pi\)
0.628078 0.778150i \(-0.283842\pi\)
\(338\) −238.588 77.5221i −0.705883 0.229355i
\(339\) 0 0
\(340\) −10.4040 −0.0306001
\(341\) −55.0817 155.720i −0.161530 0.456657i
\(342\) 0 0
\(343\) −298.926 217.183i −0.871505 0.633186i
\(344\) 415.377 + 134.964i 1.20749 + 0.392337i
\(345\) 0 0
\(346\) 340.772 247.585i 0.984889 0.715564i
\(347\) 245.149 + 337.419i 0.706482 + 0.972388i 0.999866 + 0.0163937i \(0.00521852\pi\)
−0.293384 + 0.955995i \(0.594781\pi\)
\(348\) 0 0
\(349\) 86.4724 266.135i 0.247772 0.762564i −0.747396 0.664379i \(-0.768696\pi\)
0.995168 0.0981851i \(-0.0313037\pi\)
\(350\) −408.290 + 561.963i −1.16654 + 1.60561i
\(351\) 0 0
\(352\) 13.9653 20.3044i 0.0396742 0.0576828i
\(353\) 333.271i 0.944111i 0.881569 + 0.472056i \(0.156488\pi\)
−0.881569 + 0.472056i \(0.843512\pi\)
\(354\) 0 0
\(355\) −296.266 + 911.812i −0.834551 + 2.56848i
\(356\) −12.3366 + 4.00841i −0.0346534 + 0.0112596i
\(357\) 0 0
\(358\) 325.194 236.267i 0.908363 0.659964i
\(359\) 472.450 153.508i 1.31602 0.427600i 0.434891 0.900483i \(-0.356787\pi\)
0.881125 + 0.472883i \(0.156787\pi\)
\(360\) 0 0
\(361\) 132.830 + 96.5064i 0.367949 + 0.267331i
\(362\) 268.685i 0.742224i
\(363\) 0 0
\(364\) −12.6209 −0.0346727
\(365\) −193.977 + 266.987i −0.531445 + 0.731471i
\(366\) 0 0
\(367\) 51.0462 + 157.104i 0.139090 + 0.428076i 0.996204 0.0870514i \(-0.0277444\pi\)
−0.857113 + 0.515128i \(0.827744\pi\)
\(368\) 51.5281 + 70.9223i 0.140022 + 0.192724i
\(369\) 0 0
\(370\) −44.7227 137.642i −0.120872 0.372006i
\(371\) −405.994 131.915i −1.09432 0.355567i
\(372\) 0 0
\(373\) 393.501 1.05496 0.527481 0.849567i \(-0.323136\pi\)
0.527481 + 0.849567i \(0.323136\pi\)
\(374\) 137.432 + 94.5259i 0.367466 + 0.252743i
\(375\) 0 0
\(376\) −255.396 185.556i −0.679245 0.493500i
\(377\) 394.544 + 128.195i 1.04654 + 0.340040i
\(378\) 0 0
\(379\) −153.017 + 111.173i −0.403739 + 0.293334i −0.771062 0.636760i \(-0.780274\pi\)
0.367323 + 0.930093i \(0.380274\pi\)
\(380\) −11.1155 15.2992i −0.0292513 0.0402610i
\(381\) 0 0
\(382\) 148.580 457.282i 0.388953 1.19707i
\(383\) −275.626 + 379.367i −0.719651 + 0.990514i 0.279885 + 0.960034i \(0.409704\pi\)
−0.999535 + 0.0304804i \(0.990296\pi\)
\(384\) 0 0
\(385\) −521.957 + 184.628i −1.35573 + 0.479553i
\(386\) 30.9168i 0.0800954i
\(387\) 0 0
\(388\) −2.26934 + 6.98431i −0.00584881 + 0.0180008i
\(389\) −432.711 + 140.596i −1.11237 + 0.361430i −0.806850 0.590756i \(-0.798830\pi\)
−0.305518 + 0.952186i \(0.598830\pi\)
\(390\) 0 0
\(391\) 35.4990 25.7915i 0.0907903 0.0659630i
\(392\) −167.412 + 54.3954i −0.427071 + 0.138764i
\(393\) 0 0
\(394\) 151.661 + 110.188i 0.384926 + 0.279665i
\(395\) 593.994i 1.50378i
\(396\) 0 0
\(397\) 168.638 0.424782 0.212391 0.977185i \(-0.431875\pi\)
0.212391 + 0.977185i \(0.431875\pi\)
\(398\) 75.3178 103.666i 0.189241 0.260468i
\(399\) 0 0
\(400\) 322.092 + 991.298i 0.805231 + 2.47825i
\(401\) −41.0252 56.4664i −0.102307 0.140814i 0.754794 0.655962i \(-0.227737\pi\)
−0.857101 + 0.515148i \(0.827737\pi\)
\(402\) 0 0
\(403\) 79.9253 + 245.985i 0.198326 + 0.610384i
\(404\) 7.85011 + 2.55066i 0.0194310 + 0.00631350i
\(405\) 0 0
\(406\) −247.500 −0.609606
\(407\) 23.9450 80.7325i 0.0588328 0.198360i
\(408\) 0 0
\(409\) −448.126 325.583i −1.09566 0.796046i −0.115317 0.993329i \(-0.536788\pi\)
−0.980347 + 0.197283i \(0.936788\pi\)
\(410\) 327.151 + 106.298i 0.797929 + 0.259263i
\(411\) 0 0
\(412\) 10.9608 7.96349i 0.0266039 0.0193289i
\(413\) 0.00133484 + 0.00183724i 3.23205e−6 + 4.44853e-6i
\(414\) 0 0
\(415\) −193.969 + 596.975i −0.467395 + 1.43849i
\(416\) −22.6818 + 31.2188i −0.0545235 + 0.0750452i
\(417\) 0 0
\(418\) 7.82980 + 303.085i 0.0187316 + 0.725083i
\(419\) 307.485i 0.733855i −0.930250 0.366927i \(-0.880410\pi\)
0.930250 0.366927i \(-0.119590\pi\)
\(420\) 0 0
\(421\) −1.09596 + 3.37301i −0.00260322 + 0.00801189i −0.952350 0.305008i \(-0.901341\pi\)
0.949746 + 0.313020i \(0.101341\pi\)
\(422\) −514.071 + 167.032i −1.21818 + 0.395810i
\(423\) 0 0
\(424\) −537.057 + 390.195i −1.26664 + 0.920271i
\(425\) 496.178 161.218i 1.16748 0.379337i
\(426\) 0 0
\(427\) 20.2264 + 14.6953i 0.0473686 + 0.0344153i
\(428\) 2.57638i 0.00601959i
\(429\) 0 0
\(430\) −1015.12 −2.36076
\(431\) −69.9030 + 96.2132i −0.162188 + 0.223232i −0.882374 0.470548i \(-0.844056\pi\)
0.720187 + 0.693781i \(0.244056\pi\)
\(432\) 0 0
\(433\) 61.6340 + 189.690i 0.142342 + 0.438083i 0.996660 0.0816680i \(-0.0260247\pi\)
−0.854318 + 0.519751i \(0.826025\pi\)
\(434\) −90.6999 124.838i −0.208986 0.287644i
\(435\) 0 0
\(436\) 2.19254 + 6.74795i 0.00502876 + 0.0154769i
\(437\) 75.8532 + 24.6462i 0.173577 + 0.0563986i
\(438\) 0 0
\(439\) −7.94474 −0.0180973 −0.00904867 0.999959i \(-0.502880\pi\)
−0.00904867 + 0.999959i \(0.502880\pi\)
\(440\) −244.817 + 825.421i −0.556402 + 1.87596i
\(441\) 0 0
\(442\) −211.308 153.524i −0.478073 0.347340i
\(443\) 446.341 + 145.025i 1.00754 + 0.327370i 0.765875 0.642989i \(-0.222306\pi\)
0.241666 + 0.970359i \(0.422306\pi\)
\(444\) 0 0
\(445\) 720.859 523.735i 1.61991 1.17693i
\(446\) 211.223 + 290.724i 0.473595 + 0.651847i
\(447\) 0 0
\(448\) 106.810 328.727i 0.238415 0.733765i
\(449\) 434.087 597.469i 0.966786 1.33067i 0.0231324 0.999732i \(-0.492636\pi\)
0.943654 0.330935i \(-0.107364\pi\)
\(450\) 0 0
\(451\) 121.787 + 158.831i 0.270037 + 0.352176i
\(452\) 1.37782i 0.00304828i
\(453\) 0 0
\(454\) −152.028 + 467.895i −0.334864 + 1.03060i
\(455\) 824.515 267.901i 1.81212 0.588794i
\(456\) 0 0
\(457\) 146.584 106.500i 0.320753 0.233041i −0.415744 0.909482i \(-0.636479\pi\)
0.736497 + 0.676441i \(0.236479\pi\)
\(458\) −654.885 + 212.785i −1.42988 + 0.464596i
\(459\) 0 0
\(460\) 6.19984 + 4.50445i 0.0134779 + 0.00979228i
\(461\) 561.409i 1.21781i 0.793244 + 0.608903i \(0.208390\pi\)
−0.793244 + 0.608903i \(0.791610\pi\)
\(462\) 0 0
\(463\) 379.155 0.818909 0.409454 0.912331i \(-0.365719\pi\)
0.409454 + 0.912331i \(0.365719\pi\)
\(464\) −218.294 + 300.456i −0.470462 + 0.647535i
\(465\) 0 0
\(466\) −221.422 681.467i −0.475155 1.46238i
\(467\) 268.209 + 369.158i 0.574324 + 0.790489i 0.993059 0.117619i \(-0.0375263\pi\)
−0.418735 + 0.908109i \(0.637526\pi\)
\(468\) 0 0
\(469\) −180.699 556.136i −0.385287 1.18579i
\(470\) 697.825 + 226.737i 1.48473 + 0.482419i
\(471\) 0 0
\(472\) 0.00353150 7.48199e−6
\(473\) −486.652 334.719i −1.02886 0.707651i
\(474\) 0 0
\(475\) 767.181 + 557.389i 1.61512 + 1.17345i
\(476\) −5.37853 1.74759i −0.0112994 0.00367141i
\(477\) 0 0
\(478\) −385.943 + 280.404i −0.807412 + 0.586619i
\(479\) 316.414 + 435.507i 0.660573 + 0.909201i 0.999500 0.0316118i \(-0.0100640\pi\)
−0.338927 + 0.940813i \(0.610064\pi\)
\(480\) 0 0
\(481\) −40.7471 + 125.407i −0.0847134 + 0.260721i
\(482\) 483.106 664.938i 1.00229 1.37954i
\(483\) 0 0
\(484\) −13.1803 + 10.6578i −0.0272320 + 0.0220203i
\(485\) 504.452i 1.04011i
\(486\) 0 0
\(487\) 60.1626 185.162i 0.123537 0.380208i −0.870095 0.492885i \(-0.835942\pi\)
0.993632 + 0.112676i \(0.0359424\pi\)
\(488\) 36.9757 12.0141i 0.0757700 0.0246192i
\(489\) 0 0
\(490\) 330.995 240.482i 0.675500 0.490780i
\(491\) 193.879 62.9950i 0.394865 0.128299i −0.104853 0.994488i \(-0.533437\pi\)
0.499717 + 0.866188i \(0.333437\pi\)
\(492\) 0 0
\(493\) 150.388 + 109.264i 0.305048 + 0.221630i
\(494\) 474.752i 0.961037i
\(495\) 0 0
\(496\) −231.546 −0.466826
\(497\) −306.318 + 421.611i −0.616335 + 0.848312i
\(498\) 0 0
\(499\) −264.246 813.267i −0.529552 1.62979i −0.755135 0.655569i \(-0.772429\pi\)
0.225584 0.974224i \(-0.427571\pi\)
\(500\) 33.7487 + 46.4511i 0.0674974 + 0.0929022i
\(501\) 0 0
\(502\) 167.677 + 516.057i 0.334018 + 1.02800i
\(503\) 258.957 + 84.1401i 0.514824 + 0.167277i 0.554895 0.831920i \(-0.312758\pi\)
−0.0400708 + 0.999197i \(0.512758\pi\)
\(504\) 0 0
\(505\) −566.986 −1.12274
\(506\) −40.9718 115.830i −0.0809719 0.228914i
\(507\) 0 0
\(508\) −24.4206 17.7426i −0.0480720 0.0349264i
\(509\) −897.352 291.567i −1.76297 0.572824i −0.765468 0.643473i \(-0.777493\pi\)
−0.997501 + 0.0706498i \(0.977493\pi\)
\(510\) 0 0
\(511\) −145.126 + 105.440i −0.284004 + 0.206341i
\(512\) −315.197 433.831i −0.615619 0.847327i
\(513\) 0 0
\(514\) −97.8660 + 301.200i −0.190401 + 0.585993i
\(515\) −547.024 + 752.914i −1.06218 + 1.46197i
\(516\) 0 0
\(517\) 259.776 + 338.793i 0.502468 + 0.655306i
\(518\) 78.6685i 0.151870i
\(519\) 0 0
\(520\) 416.605 1282.18i 0.801163 2.46573i
\(521\) −308.494 + 100.236i −0.592119 + 0.192391i −0.589722 0.807606i \(-0.700763\pi\)
−0.00239665 + 0.999997i \(0.500763\pi\)
\(522\) 0 0
\(523\) −98.0023 + 71.2028i −0.187385 + 0.136143i −0.677523 0.735502i \(-0.736946\pi\)
0.490138 + 0.871645i \(0.336946\pi\)
\(524\) 22.1942 7.21135i 0.0423554 0.0137621i
\(525\) 0 0
\(526\) −88.1801 64.0666i −0.167643 0.121800i
\(527\) 115.896i 0.219917i
\(528\) 0 0
\(529\) 496.679 0.938902
\(530\) 906.913 1248.26i 1.71116 2.35520i
\(531\) 0 0
\(532\) −3.17649 9.77624i −0.00597085 0.0183764i
\(533\) −184.217 253.553i −0.345623 0.475709i
\(534\) 0 0
\(535\) −54.6885 168.314i −0.102221 0.314605i
\(536\) −864.830 281.000i −1.61349 0.524254i
\(537\) 0 0
\(538\) −114.347 −0.212540
\(539\) 237.974 6.14776i 0.441510 0.0114059i
\(540\) 0 0
\(541\) 482.965 + 350.895i 0.892727 + 0.648604i 0.936588 0.350433i \(-0.113966\pi\)
−0.0438604 + 0.999038i \(0.513966\pi\)
\(542\) −795.808 258.574i −1.46828 0.477073i
\(543\) 0 0
\(544\) −13.9889 + 10.1635i −0.0257149 + 0.0186830i
\(545\) −286.475 394.299i −0.525643 0.723485i
\(546\) 0 0
\(547\) −104.567 + 321.823i −0.191164 + 0.588343i 0.808836 + 0.588035i \(0.200098\pi\)
−1.00000 0.000308188i \(0.999902\pi\)
\(548\) −3.60219 + 4.95798i −0.00657333 + 0.00904742i
\(549\) 0 0
\(550\) −37.7256 1460.32i −0.0685920 2.65513i
\(551\) 337.882i 0.613217i
\(552\) 0 0
\(553\) 99.7746 307.075i 0.180424 0.555289i
\(554\) −238.953 + 77.6406i −0.431324 + 0.140146i
\(555\) 0 0
\(556\) 11.6814 8.48706i 0.0210098 0.0152645i
\(557\) −454.284 + 147.606i −0.815590 + 0.265001i −0.686964 0.726692i \(-0.741057\pi\)
−0.128627 + 0.991693i \(0.541057\pi\)
\(558\) 0 0
\(559\) 748.249 + 543.635i 1.33855 + 0.972513i
\(560\) 776.116i 1.38592i
\(561\) 0 0
\(562\) −146.168 −0.260085
\(563\) 277.409 381.820i 0.492733 0.678189i −0.488156 0.872756i \(-0.662330\pi\)
0.980889 + 0.194567i \(0.0623303\pi\)
\(564\) 0 0
\(565\) −29.2468 90.0125i −0.0517643 0.159314i
\(566\) 570.861 + 785.722i 1.00859 + 1.38820i
\(567\) 0 0
\(568\) 250.430 + 770.745i 0.440898 + 1.35694i
\(569\) −122.262 39.7253i −0.214871 0.0698159i 0.199603 0.979877i \(-0.436035\pi\)
−0.414475 + 0.910061i \(0.636035\pi\)
\(570\) 0 0
\(571\) 266.234 0.466259 0.233130 0.972446i \(-0.425103\pi\)
0.233130 + 0.972446i \(0.425103\pi\)
\(572\) 21.0629 16.1503i 0.0368232 0.0282348i
\(573\) 0 0
\(574\) 151.271 + 109.905i 0.263538 + 0.191471i
\(575\) −365.476 118.750i −0.635610 0.206522i
\(576\) 0 0
\(577\) −583.296 + 423.789i −1.01091 + 0.734470i −0.964400 0.264448i \(-0.914810\pi\)
−0.0465112 + 0.998918i \(0.514810\pi\)
\(578\) 264.945 + 364.665i 0.458382 + 0.630908i
\(579\) 0 0
\(580\) −10.0324 + 30.8765i −0.0172972 + 0.0532353i
\(581\) −200.551 + 276.034i −0.345182 + 0.475102i
\(582\) 0 0
\(583\) 846.366 299.379i 1.45174 0.513514i
\(584\) 278.957i 0.477667i
\(585\) 0 0
\(586\) −8.26396 + 25.4339i −0.0141023 + 0.0434025i
\(587\) 391.709 127.274i 0.667307 0.216821i 0.0442770 0.999019i \(-0.485902\pi\)
0.623030 + 0.782198i \(0.285902\pi\)
\(588\) 0 0
\(589\) −170.426 + 123.822i −0.289348 + 0.210224i
\(590\) −0.00780637 + 0.00253644i −1.32311e−5 + 4.29906e-6i
\(591\) 0 0
\(592\) −95.5008 69.3854i −0.161319 0.117205i
\(593\) 750.336i 1.26532i 0.774429 + 0.632661i \(0.218037\pi\)
−0.774429 + 0.632661i \(0.781963\pi\)
\(594\) 0 0
\(595\) 388.472 0.652895
\(596\) 7.45143 10.2560i 0.0125024 0.0172081i
\(597\) 0 0
\(598\) 59.4514 + 182.973i 0.0994171 + 0.305974i
\(599\) −319.528 439.793i −0.533436 0.734211i 0.454213 0.890893i \(-0.349920\pi\)
−0.987649 + 0.156682i \(0.949920\pi\)
\(600\) 0 0
\(601\) −227.497 700.163i −0.378530 1.16500i −0.941066 0.338224i \(-0.890174\pi\)
0.562535 0.826773i \(-0.309826\pi\)
\(602\) −524.785 170.513i −0.871735 0.283244i
\(603\) 0 0
\(604\) 33.6698 0.0557447
\(605\) 634.830 976.048i 1.04931 1.61330i
\(606\) 0 0
\(607\) −452.759 328.949i −0.745896 0.541925i 0.148656 0.988889i \(-0.452505\pi\)
−0.894552 + 0.446964i \(0.852505\pi\)
\(608\) −29.8911 9.71220i −0.0491630 0.0159740i
\(609\) 0 0
\(610\) −73.1058 + 53.1145i −0.119846 + 0.0870729i
\(611\) −392.941 540.837i −0.643112 0.885168i
\(612\) 0 0
\(613\) −33.9655 + 104.535i −0.0554086 + 0.170530i −0.974931 0.222508i \(-0.928576\pi\)
0.919522 + 0.393038i \(0.128576\pi\)
\(614\) 248.592 342.157i 0.404872 0.557259i
\(615\) 0 0
\(616\) −265.210 + 385.592i −0.430535 + 0.625961i
\(617\) 61.1594i 0.0991238i 0.998771 + 0.0495619i \(0.0157825\pi\)
−0.998771 + 0.0495619i \(0.984217\pi\)
\(618\) 0 0
\(619\) 25.2833 77.8139i 0.0408454 0.125709i −0.928555 0.371196i \(-0.878948\pi\)
0.969400 + 0.245487i \(0.0789478\pi\)
\(620\) −19.2504 + 6.25484i −0.0310491 + 0.0100885i
\(621\) 0 0
\(622\) −143.125 + 103.986i −0.230105 + 0.167181i
\(623\) 460.632 149.668i 0.739377 0.240238i
\(624\) 0 0
\(625\) −1823.67 1324.97i −2.91786 2.11995i
\(626\) 507.406i 0.810553i
\(627\) 0 0
\(628\) −4.14700 −0.00660351
\(629\) −34.7297 + 47.8014i −0.0552142 + 0.0759958i
\(630\) 0 0
\(631\) 2.87142 + 8.83732i 0.00455058 + 0.0140053i 0.953306 0.302006i \(-0.0976563\pi\)
−0.948755 + 0.316011i \(0.897656\pi\)
\(632\) −295.125 406.205i −0.466970 0.642729i
\(633\) 0 0
\(634\) 63.7726 + 196.272i 0.100588 + 0.309577i
\(635\) 1972.00 + 640.743i 3.10552 + 1.00904i
\(636\) 0 0
\(637\) −372.763 −0.585185
\(638\) 413.051 316.714i 0.647415 0.496417i
\(639\) 0 0
\(640\) 940.933 + 683.628i 1.47021 + 1.06817i
\(641\) −331.957 107.859i −0.517874 0.168268i 0.0384062 0.999262i \(-0.487772\pi\)
−0.556280 + 0.830995i \(0.687772\pi\)
\(642\) 0 0
\(643\) −733.104 + 532.631i −1.14013 + 0.828353i −0.987137 0.159874i \(-0.948891\pi\)
−0.152993 + 0.988227i \(0.548891\pi\)
\(644\) 2.44848 + 3.37005i 0.00380199 + 0.00523299i
\(645\) 0 0
\(646\) 65.7381 202.321i 0.101762 0.313191i
\(647\) −33.2345 + 45.7434i −0.0513671 + 0.0707007i −0.833928 0.551874i \(-0.813913\pi\)
0.782561 + 0.622574i \(0.213913\pi\)
\(648\) 0 0
\(649\) −0.00457873 0.00135804i −7.05506e−6 2.09250e-6i
\(650\) 2287.45i 3.51916i
\(651\) 0 0
\(652\) 9.09423 27.9892i 0.0139482 0.0429282i
\(653\) 540.720 175.691i 0.828055 0.269051i 0.135829 0.990732i \(-0.456630\pi\)
0.692226 + 0.721681i \(0.256630\pi\)
\(654\) 0 0
\(655\) −1296.86 + 942.227i −1.97995 + 1.43851i
\(656\) 266.840 86.7017i 0.406769 0.132167i
\(657\) 0 0
\(658\) 322.666 + 234.430i 0.490374 + 0.356277i
\(659\) 380.801i 0.577847i 0.957352 + 0.288923i \(0.0932973\pi\)
−0.957352 + 0.288923i \(0.906703\pi\)
\(660\) 0 0
\(661\) 350.773 0.530671 0.265335 0.964156i \(-0.414517\pi\)
0.265335 + 0.964156i \(0.414517\pi\)
\(662\) −298.783 + 411.239i −0.451333 + 0.621207i
\(663\) 0 0
\(664\) 163.960 + 504.616i 0.246927 + 0.759965i
\(665\) 415.038 + 571.250i 0.624117 + 0.859023i
\(666\) 0 0
\(667\) −42.3117 130.222i −0.0634358 0.195235i
\(668\) 2.03125 + 0.659992i 0.00304079 + 0.000988011i
\(669\) 0 0
\(670\) 2113.53 3.15452
\(671\) −52.5606 + 1.35784i −0.0783317 + 0.00202360i
\(672\) 0 0
\(673\) 390.671 + 283.839i 0.580491 + 0.421752i 0.838901 0.544284i \(-0.183198\pi\)
−0.258410 + 0.966035i \(0.583198\pi\)
\(674\) 687.591 + 223.412i 1.02017 + 0.331472i
\(675\) 0 0
\(676\) −14.4711 + 10.5139i −0.0214070 + 0.0155531i
\(677\) 499.429 + 687.405i 0.737709 + 1.01537i 0.998747 + 0.0500409i \(0.0159352\pi\)
−0.261038 + 0.965328i \(0.584065\pi\)
\(678\) 0 0
\(679\) 84.7340 260.784i 0.124792 0.384071i
\(680\) 355.082 488.728i 0.522179 0.718718i
\(681\) 0 0
\(682\) 311.117 + 92.2763i 0.456184 + 0.135302i
\(683\) 831.602i 1.21757i −0.793334 0.608786i \(-0.791657\pi\)
0.793334 0.608786i \(-0.208343\pi\)
\(684\) 0 0
\(685\) 130.087 400.366i 0.189908 0.584475i
\(686\) 690.402 224.325i 1.00642 0.327004i
\(687\) 0 0
\(688\) −669.855 + 486.678i −0.973626 + 0.707381i
\(689\) −1336.97 + 434.408i −1.94045 + 0.630491i
\(690\) 0 0
\(691\) −736.820 535.331i −1.06631 0.774719i −0.0910643 0.995845i \(-0.529027\pi\)
−0.975245 + 0.221126i \(0.929027\pi\)
\(692\) 30.0336i 0.0434011i
\(693\) 0 0
\(694\) −819.409 −1.18070
\(695\) −582.989 + 802.415i −0.838833 + 1.15455i
\(696\) 0 0
\(697\) −43.3971 133.563i −0.0622627 0.191625i
\(698\) 323.149 + 444.776i 0.462964 + 0.637216i
\(699\) 0 0
\(700\) 15.3050 + 47.1039i 0.0218643 + 0.0672913i
\(701\) −856.342 278.242i −1.22160 0.396922i −0.373936 0.927454i \(-0.621992\pi\)
−0.847665 + 0.530532i \(0.821992\pi\)
\(702\) 0 0
\(703\) −107.397 −0.152769
\(704\) 242.402 + 685.289i 0.344321 + 0.973422i
\(705\) 0 0
\(706\) −529.718 384.862i −0.750308 0.545131i
\(707\) −293.112 95.2379i −0.414586 0.134707i
\(708\) 0 0
\(709\) 746.154 542.113i 1.05240 0.764616i 0.0797356 0.996816i \(-0.474592\pi\)
0.972668 + 0.232200i \(0.0745924\pi\)
\(710\) −1107.15 1523.86i −1.55937 2.14628i
\(711\) 0 0
\(712\) 232.745 716.315i 0.326889 1.00606i
\(713\) 50.1776 69.0635i 0.0703753 0.0968632i
\(714\) 0 0
\(715\) −1033.21 + 1502.19i −1.44504 + 2.10097i
\(716\) 28.6606i 0.0400288i
\(717\) 0 0
\(718\) −301.593 + 928.206i −0.420045 + 1.29277i
\(719\) 9.82994 3.19394i 0.0136717 0.00444220i −0.302173 0.953253i \(-0.597712\pi\)
0.315845 + 0.948811i \(0.397712\pi\)
\(720\) 0 0
\(721\) −409.261 + 297.346i −0.567630 + 0.412407i
\(722\) −306.784 + 99.6802i −0.424909 + 0.138061i
\(723\) 0 0
\(724\) −15.4989 11.2606i −0.0214074 0.0155534i
\(725\) 1627.99i 2.24550i
\(726\) 0 0
\(727\) 119.809 0.164799 0.0823995 0.996599i \(-0.473742\pi\)
0.0823995 + 0.996599i \(0.473742\pi\)
\(728\) 430.741 592.864i 0.591677 0.814373i
\(729\) 0 0
\(730\) −200.357 616.635i −0.274461 0.844705i
\(731\) 243.599 + 335.285i 0.333240 + 0.458666i
\(732\) 0 0
\(733\) 393.151 + 1210.00i 0.536359 + 1.65074i 0.740693 + 0.671843i \(0.234497\pi\)
−0.204334 + 0.978901i \(0.565503\pi\)
\(734\) −308.657 100.289i −0.420514 0.136633i
\(735\) 0 0
\(736\) 12.7364 0.0173049
\(737\) 1013.23 + 696.898i 1.37480 + 0.945588i
\(738\) 0 0
\(739\) 136.706 + 99.3227i 0.184988 + 0.134402i 0.676425 0.736511i \(-0.263528\pi\)
−0.491437 + 0.870913i \(0.663528\pi\)
\(740\) −9.81416 3.18882i −0.0132624 0.00430921i
\(741\) 0 0
\(742\) 678.515 492.970i 0.914441 0.664380i
\(743\) −566.208 779.319i −0.762057 1.04888i −0.997040 0.0768822i \(-0.975503\pi\)
0.234983 0.971999i \(-0.424497\pi\)
\(744\) 0 0
\(745\) −269.095 + 828.190i −0.361202 + 1.11167i
\(746\) −454.416 + 625.450i −0.609137 + 0.838405i
\(747\) 0 0
\(748\) 11.2125 3.96611i 0.0149900 0.00530229i
\(749\) 96.1986i 0.128436i
\(750\) 0 0
\(751\) −127.573 + 392.629i −0.169871 + 0.522808i −0.999362 0.0357111i \(-0.988630\pi\)
0.829491 + 0.558519i \(0.188630\pi\)
\(752\) 569.180 184.938i 0.756889 0.245928i
\(753\) 0 0
\(754\) −659.380 + 479.067i −0.874509 + 0.635368i
\(755\) −2199.63 + 714.704i −2.91342 + 0.946627i
\(756\) 0 0
\(757\) −729.792 530.225i −0.964058 0.700429i −0.00996868 0.999950i \(-0.503173\pi\)
−0.954090 + 0.299521i \(0.903173\pi\)
\(758\) 371.596i 0.490233i
\(759\) 0 0
\(760\) 1098.04 1.44479
\(761\) −571.395 + 786.458i −0.750848 + 1.03345i 0.247073 + 0.968997i \(0.420531\pi\)
−0.997921 + 0.0644566i \(0.979469\pi\)
\(762\) 0 0
\(763\) −81.8665 251.959i −0.107295 0.330222i
\(764\) −20.1511 27.7356i −0.0263757 0.0363031i
\(765\) 0 0
\(766\) −284.691 876.187i −0.371659 1.14385i
\(767\) 0.00711243 + 0.00231097i 9.27305e−6 + 3.01300e-6i
\(768\) 0 0
\(769\) 1404.29 1.82613 0.913064 0.407817i \(-0.133710\pi\)
0.913064 + 0.407817i \(0.133710\pi\)
\(770\) 309.300 1042.83i 0.401689 1.35433i
\(771\) 0 0
\(772\) 1.78342 + 1.29573i 0.00231013 + 0.00167841i
\(773\) 138.598 + 45.0331i 0.179298 + 0.0582576i 0.397290 0.917693i \(-0.369951\pi\)
−0.217992 + 0.975951i \(0.569951\pi\)
\(774\) 0 0
\(775\) 821.147 596.599i 1.05955 0.769805i
\(776\) −250.636 344.971i −0.322985 0.444550i
\(777\) 0 0
\(778\) 276.225 850.133i 0.355045 1.09272i
\(779\) 150.040 206.512i 0.192605 0.265099i
\(780\) 0 0
\(781\) −28.3035 1095.60i −0.0362401 1.40282i
\(782\) 86.2080i 0.110240i
\(783\) 0 0
\(784\) 103.122 317.376i 0.131533 0.404816i
\(785\) 270.921 88.0277i 0.345123 0.112137i
\(786\) 0 0
\(787\) 740.082 537.701i 0.940383 0.683228i −0.00812966 0.999967i \(-0.502588\pi\)
0.948513 + 0.316739i \(0.102588\pi\)
\(788\) 12.7123 4.13047i 0.0161323 0.00524171i
\(789\) 0 0
\(790\) 944.124 + 685.946i 1.19509 + 0.868286i
\(791\) 51.4460i 0.0650392i
\(792\) 0 0
\(793\) 82.3310 0.103822
\(794\) −194.744 + 268.042i −0.245269 + 0.337584i
\(795\) 0 0
\(796\) −2.82334 8.68934i −0.00354691 0.0109163i
\(797\) −219.280 301.813i −0.275132 0.378687i 0.648982 0.760804i \(-0.275195\pi\)
−0.924114 + 0.382117i \(0.875195\pi\)
\(798\) 0 0
\(799\) −92.5677 284.894i −0.115854 0.356563i
\(800\) 144.021 + 46.7954i 0.180027 + 0.0584942i
\(801\) 0 0
\(802\) 137.126 0.170981
\(803\) 107.273 361.680i 0.133590 0.450410i
\(804\) 0 0
\(805\) −231.494 168.190i −0.287570 0.208932i
\(806\) −483.278 157.027i −0.599600 0.194822i
\(807\) 0 0
\(808\) −387.735 + 281.706i −0.479870 + 0.348646i
\(809\) 927.680 + 1276.84i 1.14670 + 1.57830i 0.751546 + 0.659680i \(0.229308\pi\)
0.395153 + 0.918615i \(0.370692\pi\)
\(810\) 0 0
\(811\) 222.549 684.936i 0.274413 0.844558i −0.714960 0.699165i \(-0.753555\pi\)
0.989374 0.145393i \(-0.0464447\pi\)
\(812\) −10.3728 + 14.2769i −0.0127744 + 0.0175824i
\(813\) 0 0
\(814\) 100.668 + 131.289i 0.123671 + 0.161289i
\(815\) 2021.56i 2.48044i
\(816\) 0 0
\(817\) −232.781 + 716.426i −0.284921 + 0.876898i
\(818\) 1034.99 336.290i 1.26527 0.411113i
\(819\) 0 0
\(820\) 19.8427 14.4166i 0.0241984 0.0175812i
\(821\) 887.035 288.215i 1.08043 0.351054i 0.285890 0.958263i \(-0.407711\pi\)
0.794542 + 0.607209i \(0.207711\pi\)
\(822\) 0 0
\(823\) −403.890 293.443i −0.490753 0.356553i 0.314721 0.949184i \(-0.398089\pi\)
−0.805474 + 0.592631i \(0.798089\pi\)
\(824\) 786.670i 0.954697i
\(825\) 0 0
\(826\) −0.00446168 −5.40155e−6
\(827\) 428.774 590.156i 0.518469 0.713611i −0.466850 0.884337i \(-0.654611\pi\)
0.985319 + 0.170726i \(0.0546112\pi\)
\(828\) 0 0
\(829\) −457.435 1407.84i −0.551792 1.69824i −0.704269 0.709934i \(-0.748725\pi\)
0.152477 0.988307i \(-0.451275\pi\)
\(830\) −724.866 997.692i −0.873332 1.20204i
\(831\) 0 0
\(832\) −351.734 1082.52i −0.422757 1.30111i
\(833\) −158.857 51.6158i −0.190705 0.0619638i
\(834\) 0 0
\(835\) −146.710 −0.175700
\(836\) 17.8114 + 12.2507i 0.0213055 + 0.0146539i
\(837\) 0 0
\(838\) 488.732 + 355.085i 0.583212 + 0.423729i
\(839\) −932.042 302.839i −1.11090 0.360952i −0.304609 0.952477i \(-0.598526\pi\)
−0.806286 + 0.591525i \(0.798526\pi\)
\(840\) 0 0
\(841\) −211.101 + 153.374i −0.251012 + 0.182371i
\(842\) −4.09561 5.63712i −0.00486414 0.00669492i
\(843\) 0 0
\(844\) −11.9097 + 36.6542i −0.0141110 + 0.0434292i
\(845\) 722.214 994.042i 0.854691 1.17638i
\(846\) 0 0
\(847\) 492.134 397.949i 0.581032 0.469834i
\(848\) 1258.49i 1.48407i
\(849\) 0 0
\(850\) −316.740 + 974.825i −0.372635 + 1.14685i
\(851\) 41.3914 13.4489i 0.0486385 0.0158036i
\(852\) 0 0
\(853\) 1124.90 817.288i 1.31876 0.958134i 0.318812 0.947818i \(-0.396716\pi\)
0.999947 0.0103159i \(-0.00328372\pi\)
\(854\) −46.7150 + 15.1786i −0.0547014 + 0.0177735i
\(855\) 0 0
\(856\) −121.025 87.9300i −0.141385 0.102722i
\(857\) 1044.64i 1.21895i 0.792804 + 0.609477i \(0.208621\pi\)
−0.792804 + 0.609477i \(0.791379\pi\)
\(858\) 0 0
\(859\) 480.571 0.559454 0.279727 0.960080i \(-0.409756\pi\)
0.279727 + 0.960080i \(0.409756\pi\)
\(860\) −42.5441 + 58.5569i −0.0494699 + 0.0680894i
\(861\) 0 0
\(862\) −72.2018 222.214i −0.0837608 0.257789i
\(863\) −383.286 527.547i −0.444132 0.611295i 0.526992 0.849870i \(-0.323320\pi\)
−0.971124 + 0.238575i \(0.923320\pi\)
\(864\) 0 0
\(865\) 637.518 + 1962.08i 0.737014 + 2.26830i
\(866\) −372.678 121.090i −0.430344 0.139827i
\(867\) 0 0
\(868\) −11.0024 −0.0126756
\(869\) 226.436 + 640.151i 0.260571 + 0.736653i
\(870\) 0 0
\(871\) −1557.88 1131.87i −1.78861 1.29950i
\(872\) −391.814 127.308i −0.449328 0.145995i
\(873\) 0 0
\(874\) −126.769 + 92.1032i −0.145045 + 0.105381i
\(875\) −1260.13 1734.42i −1.44015 1.98219i
\(876\) 0 0
\(877\) −107.579 + 331.093i −0.122667 + 0.377530i −0.993469 0.114104i \(-0.963600\pi\)
0.870802 + 0.491634i \(0.163600\pi\)
\(878\) 9.17460 12.6278i 0.0104494 0.0143824i
\(879\) 0 0
\(880\) −993.160 1295.25i −1.12859 1.47188i
\(881\) 81.0204i 0.0919641i −0.998942 0.0459821i \(-0.985358\pi\)
0.998942 0.0459821i \(-0.0146417\pi\)
\(882\) 0 0
\(883\) 301.483 927.871i 0.341431 1.05082i −0.622036 0.782989i \(-0.713694\pi\)
0.963467 0.267827i \(-0.0863057\pi\)
\(884\) −17.7119 + 5.75496i −0.0200361 + 0.00651013i
\(885\) 0 0
\(886\) −745.945 + 541.961i −0.841924 + 0.611694i
\(887\) 1459.07 474.081i 1.64495 0.534477i 0.667314 0.744776i \(-0.267444\pi\)
0.977637 + 0.210299i \(0.0674437\pi\)
\(888\) 0 0
\(889\) 911.831 + 662.484i 1.02568 + 0.745201i
\(890\) 1750.58i 1.96694i
\(891\) 0 0
\(892\) 25.6227 0.0287250
\(893\) 320.040 440.497i 0.358387 0.493278i
\(894\) 0 0
\(895\) 608.375 + 1872.38i 0.679748 + 2.09205i
\(896\) 371.600 + 511.463i 0.414732 + 0.570829i
\(897\) 0 0
\(898\) 448.363 + 1379.92i 0.499290 + 1.53666i
\(899\) 343.950 + 111.756i 0.382592 + 0.124312i
\(900\) 0 0
\(901\) −629.917 −0.699131
\(902\) −393.094 + 10.1551i −0.435803 + 0.0112584i
\(903\) 0 0
\(904\) −64.7231 47.0241i −0.0715963 0.0520178i
\(905\) 1251.57 + 406.659i 1.38295 + 0.449346i
\(906\) 0 0
\(907\) −841.629 + 611.479i −0.927926 + 0.674178i −0.945484 0.325668i \(-0.894411\pi\)
0.0175578 + 0.999846i \(0.494411\pi\)
\(908\) 20.6187 + 28.3792i 0.0227078 + 0.0312547i
\(909\) 0 0
\(910\) −526.336 + 1619.90i −0.578392 + 1.78011i
\(911\) 219.624 302.287i 0.241080 0.331819i −0.671282 0.741202i \(-0.734256\pi\)
0.912362 + 0.409383i \(0.134256\pi\)
\(912\) 0 0
\(913\) −18.5307 717.307i −0.0202965 0.785659i
\(914\) 355.974i 0.389468i
\(915\) 0 0
\(916\) −15.1720 + 46.6946i −0.0165633 + 0.0509766i
\(917\) −828.702 + 269.262i −0.903710 + 0.293633i
\(918\) 0 0
\(919\) −3.84227 + 2.79157i −0.00418092 + 0.00303762i −0.589874 0.807495i \(-0.700822\pi\)
0.585693 + 0.810533i \(0.300822\pi\)
\(920\) −423.192 + 137.503i −0.459991 + 0.149460i
\(921\) 0 0
\(922\) −892.331 648.316i −0.967821 0.703163i
\(923\) 1716.16i 1.85932i
\(924\) 0 0
\(925\) 517.460 0.559416
\(926\) −437.849 + 602.647i −0.472839 + 0.650807i
\(927\) 0 0
\(928\) 16.6736 + 51.3159i 0.0179672 + 0.0552974i
\(929\) 290.209 + 399.438i 0.312388 + 0.429966i 0.936124 0.351670i \(-0.114386\pi\)
−0.623736 + 0.781635i \(0.714386\pi\)
\(930\) 0 0
\(931\) −93.8192 288.746i −0.100772 0.310146i
\(932\) −48.5899 15.7878i −0.0521351 0.0169397i
\(933\) 0 0
\(934\) −896.487 −0.959836
\(935\) −648.318 + 497.110i −0.693389 + 0.531668i
\(936\) 0 0
\(937\) 475.006 + 345.112i 0.506944 + 0.368316i 0.811663 0.584126i \(-0.198563\pi\)
−0.304719 + 0.952442i \(0.598563\pi\)
\(938\) 1092.62 + 355.014i 1.16484 + 0.378480i
\(939\) 0 0
\(940\) 42.3252 30.7511i 0.0450268 0.0327139i
\(941\) −626.791 862.704i −0.666090 0.916794i 0.333574 0.942724i \(-0.391745\pi\)
−0.999664 + 0.0259296i \(0.991745\pi\)
\(942\) 0 0
\(943\) −31.9656 + 98.3799i −0.0338977 + 0.104326i
\(944\) −0.00393518 + 0.00541632i −4.16863e−6 + 5.73762e-6i
\(945\) 0 0
\(946\) 1094.01 386.975i 1.15645 0.409064i
\(947\) 198.618i 0.209734i 0.994486 + 0.104867i \(0.0334416\pi\)
−0.994486 + 0.104867i \(0.966558\pi\)
\(948\) 0 0
\(949\) −182.546 + 561.819i −0.192356 + 0.592012i
\(950\) −1771.88 + 575.720i −1.86514 + 0.606021i
\(951\) 0 0
\(952\) 265.658 193.012i 0.279052 0.202743i
\(953\) 1059.71 344.322i 1.11198 0.361303i 0.305276 0.952264i \(-0.401251\pi\)
0.806700 + 0.590961i \(0.201251\pi\)
\(954\) 0 0
\(955\) 1905.20 + 1384.21i 1.99497 + 1.44943i
\(956\) 34.0147i 0.0355802i
\(957\) 0 0
\(958\) −1057.61 −1.10398
\(959\) 134.501 185.124i 0.140251 0.193039i
\(960\) 0 0
\(961\) −227.289 699.524i −0.236513 0.727913i
\(962\) −152.273 209.586i −0.158288 0.217864i
\(963\) 0 0
\(964\) −18.1095 55.7354i −0.0187858 0.0578168i
\(965\) −144.014 46.7930i −0.149237 0.0484902i
\(966\) 0 0
\(967\) −983.820 −1.01739 −0.508697 0.860945i \(-0.669873\pi\)
−0.508697 + 0.860945i \(0.669873\pi\)
\(968\) −50.8172 982.887i −0.0524971 1.01538i
\(969\) 0 0
\(970\) 801.801 + 582.542i 0.826599 + 0.600559i
\(971\) −110.243 35.8200i −0.113535 0.0368898i 0.251698 0.967806i \(-0.419011\pi\)
−0.365234 + 0.930916i \(0.619011\pi\)
\(972\) 0 0
\(973\) −436.169 + 316.895i −0.448272 + 0.325689i
\(974\) 224.829 + 309.450i 0.230830 + 0.317711i
\(975\) 0 0
\(976\) −22.7761 + 70.0978i −0.0233362 + 0.0718215i
\(977\) 67.1734 92.4562i 0.0687547 0.0946328i −0.773255 0.634095i \(-0.781373\pi\)
0.842009 + 0.539463i \(0.181373\pi\)
\(978\) 0 0
\(979\) −577.222 + 839.230i −0.589603 + 0.857232i
\(980\) 29.1719i 0.0297673i
\(981\) 0 0
\(982\) −123.764 + 380.907i −0.126033 + 0.387889i
\(983\) 970.714 315.404i 0.987502 0.320859i 0.229641 0.973275i \(-0.426245\pi\)
0.757861 + 0.652417i \(0.226245\pi\)
\(984\) 0 0
\(985\) −742.809 + 539.682i −0.754121 + 0.547901i
\(986\) −347.338 + 112.857i −0.352270 + 0.114459i
\(987\) 0 0
\(988\) −27.3858 19.8970i −0.0277185 0.0201386i
\(989\) 305.265i 0.308661i
\(990\) 0 0
\(991\) 544.638 0.549584 0.274792 0.961504i \(-0.411391\pi\)
0.274792 + 0.961504i \(0.411391\pi\)
\(992\) −19.7732 + 27.2155i −0.0199327 + 0.0274350i
\(993\) 0 0
\(994\) −316.392 973.755i −0.318302 0.979632i
\(995\) 368.894 + 507.739i 0.370748 + 0.510291i
\(996\) 0 0
\(997\) 386.146 + 1188.43i 0.387308 + 1.19201i 0.934792 + 0.355195i \(0.115585\pi\)
−0.547485 + 0.836816i \(0.684415\pi\)
\(998\) 1597.80 + 519.156i 1.60100 + 0.520196i
\(999\) 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 99.3.l.a.26.3 32
3.2 odd 2 inner 99.3.l.a.26.6 yes 32
11.3 even 5 inner 99.3.l.a.80.6 yes 32
11.5 even 5 1089.3.b.i.485.5 16
11.6 odd 10 1089.3.b.j.485.12 16
33.5 odd 10 1089.3.b.i.485.12 16
33.14 odd 10 inner 99.3.l.a.80.3 yes 32
33.17 even 10 1089.3.b.j.485.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.3.l.a.26.3 32 1.1 even 1 trivial
99.3.l.a.26.6 yes 32 3.2 odd 2 inner
99.3.l.a.80.3 yes 32 33.14 odd 10 inner
99.3.l.a.80.6 yes 32 11.3 even 5 inner
1089.3.b.i.485.5 16 11.5 even 5
1089.3.b.i.485.12 16 33.5 odd 10
1089.3.b.j.485.5 16 33.17 even 10
1089.3.b.j.485.12 16 11.6 odd 10