Properties

Label 882.2.l.c.227.21
Level $882$
Weight $2$
Character 882.227
Analytic conductor $7.043$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 227.21
Character \(\chi\) \(=\) 882.227
Dual form 882.2.l.c.509.9

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.45331 - 0.942282i) q^{3} -1.00000 q^{4} +(-0.724499 + 1.25487i) q^{5} +(0.942282 + 1.45331i) q^{6} -1.00000i q^{8} +(1.22421 - 2.73885i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(1.45331 - 0.942282i) q^{3} -1.00000 q^{4} +(-0.724499 + 1.25487i) q^{5} +(0.942282 + 1.45331i) q^{6} -1.00000i q^{8} +(1.22421 - 2.73885i) q^{9} +(-1.25487 - 0.724499i) q^{10} +(1.21051 - 0.698887i) q^{11} +(-1.45331 + 0.942282i) q^{12} +(3.03494 - 1.75222i) q^{13} +(0.129520 + 2.50640i) q^{15} +1.00000 q^{16} +(3.95277 - 6.84639i) q^{17} +(2.73885 + 1.22421i) q^{18} +(-3.61019 + 2.08434i) q^{19} +(0.724499 - 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(3.13371 + 1.80925i) q^{23} +(-0.942282 - 1.45331i) q^{24} +(1.45020 + 2.51182i) q^{25} +(1.75222 + 3.03494i) q^{26} +(-0.801614 - 5.13395i) q^{27} +(4.06467 + 2.34674i) q^{29} +(-2.50640 + 0.129520i) q^{30} -0.917280i q^{31} +1.00000i q^{32} +(1.10069 - 2.15634i) q^{33} +(6.84639 + 3.95277i) q^{34} +(-1.22421 + 2.73885i) q^{36} +(2.14176 + 3.70963i) q^{37} +(-2.08434 - 3.61019i) q^{38} +(2.75961 - 5.40629i) q^{39} +(1.25487 + 0.724499i) q^{40} +(0.343727 + 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +(-1.21051 + 0.698887i) q^{44} +(2.54996 + 3.52052i) q^{45} +(-1.80925 + 3.13371i) q^{46} +8.31745 q^{47} +(1.45331 - 0.942282i) q^{48} +(-2.51182 + 1.45020i) q^{50} +(-0.706641 - 13.6745i) q^{51} +(-3.03494 + 1.75222i) q^{52} +(-5.16176 - 2.98014i) q^{53} +(5.13395 - 0.801614i) q^{54} +2.02537i q^{55} +(-3.28268 + 6.43101i) q^{57} +(-2.34674 + 4.06467i) q^{58} +9.44130 q^{59} +(-0.129520 - 2.50640i) q^{60} -9.85957i q^{61} +0.917280 q^{62} -1.00000 q^{64} +5.07794i q^{65} +(2.15634 + 1.10069i) q^{66} -2.97079 q^{67} +(-3.95277 + 6.84639i) q^{68} +(6.25907 - 0.323442i) q^{69} -12.9436i q^{71} +(-2.73885 - 1.22421i) q^{72} +(-9.79071 - 5.65267i) q^{73} +(-3.70963 + 2.14176i) q^{74} +(4.47443 + 2.28395i) q^{75} +(3.61019 - 2.08434i) q^{76} +(5.40629 + 2.75961i) q^{78} +15.6342 q^{79} +(-0.724499 + 1.25487i) q^{80} +(-6.00262 - 6.70586i) q^{81} +(-0.595352 + 0.343727i) q^{82} +(-4.11183 + 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(-10.4182 - 6.01497i) q^{86} +(8.11851 - 0.419530i) q^{87} +(-0.698887 - 1.21051i) q^{88} +(-0.533417 - 0.923906i) q^{89} +(-3.52052 + 2.54996i) q^{90} +(-3.13371 - 1.80925i) q^{92} +(-0.864336 - 1.33309i) q^{93} +8.31745i q^{94} -6.04043i q^{95} +(0.942282 + 1.45331i) q^{96} +(-10.9670 - 6.33179i) q^{97} +(-0.432231 - 4.17099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.45331 0.942282i 0.839068 0.544027i
\(4\) −1.00000 −0.500000
\(5\) −0.724499 + 1.25487i −0.324006 + 0.561195i −0.981311 0.192430i \(-0.938363\pi\)
0.657305 + 0.753625i \(0.271696\pi\)
\(6\) 0.942282 + 1.45331i 0.384685 + 0.593311i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.22421 2.73885i 0.408070 0.912951i
\(10\) −1.25487 0.724499i −0.396825 0.229107i
\(11\) 1.21051 0.698887i 0.364982 0.210722i −0.306282 0.951941i \(-0.599085\pi\)
0.671264 + 0.741218i \(0.265752\pi\)
\(12\) −1.45331 + 0.942282i −0.419534 + 0.272013i
\(13\) 3.03494 1.75222i 0.841740 0.485979i −0.0161150 0.999870i \(-0.505130\pi\)
0.857855 + 0.513891i \(0.171796\pi\)
\(14\) 0 0
\(15\) 0.129520 + 2.50640i 0.0334418 + 0.647148i
\(16\) 1.00000 0.250000
\(17\) 3.95277 6.84639i 0.958687 1.66049i 0.232990 0.972479i \(-0.425149\pi\)
0.725697 0.688015i \(-0.241518\pi\)
\(18\) 2.73885 + 1.22421i 0.645554 + 0.288549i
\(19\) −3.61019 + 2.08434i −0.828235 + 0.478181i −0.853248 0.521506i \(-0.825371\pi\)
0.0250133 + 0.999687i \(0.492037\pi\)
\(20\) 0.724499 1.25487i 0.162003 0.280597i
\(21\) 0 0
\(22\) 0.698887 + 1.21051i 0.149003 + 0.258081i
\(23\) 3.13371 + 1.80925i 0.653424 + 0.377255i 0.789767 0.613407i \(-0.210202\pi\)
−0.136343 + 0.990662i \(0.543535\pi\)
\(24\) −0.942282 1.45331i −0.192342 0.296655i
\(25\) 1.45020 + 2.51182i 0.290040 + 0.502364i
\(26\) 1.75222 + 3.03494i 0.343639 + 0.595200i
\(27\) −0.801614 5.13395i −0.154271 0.988029i
\(28\) 0 0
\(29\) 4.06467 + 2.34674i 0.754791 + 0.435779i 0.827422 0.561580i \(-0.189806\pi\)
−0.0726316 + 0.997359i \(0.523140\pi\)
\(30\) −2.50640 + 0.129520i −0.457603 + 0.0236469i
\(31\) 0.917280i 0.164748i −0.996601 0.0823741i \(-0.973750\pi\)
0.996601 0.0823741i \(-0.0262502\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.10069 2.15634i 0.191606 0.375370i
\(34\) 6.84639 + 3.95277i 1.17415 + 0.677894i
\(35\) 0 0
\(36\) −1.22421 + 2.73885i −0.204035 + 0.456475i
\(37\) 2.14176 + 3.70963i 0.352103 + 0.609860i 0.986618 0.163051i \(-0.0521334\pi\)
−0.634515 + 0.772911i \(0.718800\pi\)
\(38\) −2.08434 3.61019i −0.338125 0.585650i
\(39\) 2.75961 5.40629i 0.441892 0.865699i
\(40\) 1.25487 + 0.724499i 0.198412 + 0.114553i
\(41\) 0.343727 + 0.595352i 0.0536811 + 0.0929784i 0.891617 0.452790i \(-0.149571\pi\)
−0.837936 + 0.545768i \(0.816238\pi\)
\(42\) 0 0
\(43\) −6.01497 + 10.4182i −0.917275 + 1.58877i −0.113739 + 0.993511i \(0.536283\pi\)
−0.803536 + 0.595256i \(0.797051\pi\)
\(44\) −1.21051 + 0.698887i −0.182491 + 0.105361i
\(45\) 2.54996 + 3.52052i 0.380126 + 0.524808i
\(46\) −1.80925 + 3.13371i −0.266759 + 0.462041i
\(47\) 8.31745 1.21322 0.606612 0.794998i \(-0.292528\pi\)
0.606612 + 0.794998i \(0.292528\pi\)
\(48\) 1.45331 0.942282i 0.209767 0.136007i
\(49\) 0 0
\(50\) −2.51182 + 1.45020i −0.355225 + 0.205089i
\(51\) −0.706641 13.6745i −0.0989495 1.91482i
\(52\) −3.03494 + 1.75222i −0.420870 + 0.242990i
\(53\) −5.16176 2.98014i −0.709022 0.409354i 0.101677 0.994818i \(-0.467579\pi\)
−0.810699 + 0.585463i \(0.800913\pi\)
\(54\) 5.13395 0.801614i 0.698642 0.109086i
\(55\) 2.02537i 0.273101i
\(56\) 0 0
\(57\) −3.28268 + 6.43101i −0.434802 + 0.851808i
\(58\) −2.34674 + 4.06467i −0.308142 + 0.533718i
\(59\) 9.44130 1.22915 0.614577 0.788857i \(-0.289327\pi\)
0.614577 + 0.788857i \(0.289327\pi\)
\(60\) −0.129520 2.50640i −0.0167209 0.323574i
\(61\) 9.85957i 1.26239i −0.775625 0.631194i \(-0.782565\pi\)
0.775625 0.631194i \(-0.217435\pi\)
\(62\) 0.917280 0.116495
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.07794i 0.629840i
\(66\) 2.15634 + 1.10069i 0.265427 + 0.135486i
\(67\) −2.97079 −0.362940 −0.181470 0.983396i \(-0.558086\pi\)
−0.181470 + 0.983396i \(0.558086\pi\)
\(68\) −3.95277 + 6.84639i −0.479343 + 0.830247i
\(69\) 6.25907 0.323442i 0.753504 0.0389378i
\(70\) 0 0
\(71\) 12.9436i 1.53612i −0.640377 0.768061i \(-0.721222\pi\)
0.640377 0.768061i \(-0.278778\pi\)
\(72\) −2.73885 1.22421i −0.322777 0.144275i
\(73\) −9.79071 5.65267i −1.14592 0.661595i −0.198027 0.980197i \(-0.563453\pi\)
−0.947889 + 0.318602i \(0.896787\pi\)
\(74\) −3.70963 + 2.14176i −0.431236 + 0.248974i
\(75\) 4.47443 + 2.28395i 0.516663 + 0.263728i
\(76\) 3.61019 2.08434i 0.414117 0.239091i
\(77\) 0 0
\(78\) 5.40629 + 2.75961i 0.612141 + 0.312465i
\(79\) 15.6342 1.75898 0.879491 0.475915i \(-0.157883\pi\)
0.879491 + 0.475915i \(0.157883\pi\)
\(80\) −0.724499 + 1.25487i −0.0810015 + 0.140299i
\(81\) −6.00262 6.70586i −0.666957 0.745096i
\(82\) −0.595352 + 0.343727i −0.0657457 + 0.0379583i
\(83\) −4.11183 + 7.12189i −0.451332 + 0.781729i −0.998469 0.0553135i \(-0.982384\pi\)
0.547137 + 0.837043i \(0.315718\pi\)
\(84\) 0 0
\(85\) 5.72755 + 9.92041i 0.621240 + 1.07602i
\(86\) −10.4182 6.01497i −1.12343 0.648611i
\(87\) 8.11851 0.419530i 0.870396 0.0449783i
\(88\) −0.698887 1.21051i −0.0745016 0.129041i
\(89\) −0.533417 0.923906i −0.0565421 0.0979338i 0.836369 0.548167i \(-0.184674\pi\)
−0.892911 + 0.450233i \(0.851341\pi\)
\(90\) −3.52052 + 2.54996i −0.371096 + 0.268790i
\(91\) 0 0
\(92\) −3.13371 1.80925i −0.326712 0.188627i
\(93\) −0.864336 1.33309i −0.0896274 0.138235i
\(94\) 8.31745i 0.857879i
\(95\) 6.04043i 0.619735i
\(96\) 0.942282 + 1.45331i 0.0961712 + 0.148328i
\(97\) −10.9670 6.33179i −1.11353 0.642895i −0.173787 0.984783i \(-0.555600\pi\)
−0.939741 + 0.341888i \(0.888934\pi\)
\(98\) 0 0
\(99\) −0.432231 4.17099i −0.0434409 0.419200i
\(100\) −1.45020 2.51182i −0.145020 0.251182i
\(101\) −8.77726 15.2027i −0.873370 1.51272i −0.858489 0.512831i \(-0.828597\pi\)
−0.0148801 0.999889i \(-0.504737\pi\)
\(102\) 13.6745 0.706641i 1.35398 0.0699679i
\(103\) 3.86082 + 2.22905i 0.380418 + 0.219635i 0.678000 0.735062i \(-0.262847\pi\)
−0.297582 + 0.954696i \(0.596180\pi\)
\(104\) −1.75222 3.03494i −0.171820 0.297600i
\(105\) 0 0
\(106\) 2.98014 5.16176i 0.289457 0.501355i
\(107\) −2.04566 + 1.18106i −0.197762 + 0.114178i −0.595611 0.803273i \(-0.703090\pi\)
0.397849 + 0.917451i \(0.369757\pi\)
\(108\) 0.801614 + 5.13395i 0.0771353 + 0.494014i
\(109\) −6.49776 + 11.2545i −0.622373 + 1.07798i 0.366670 + 0.930351i \(0.380498\pi\)
−0.989043 + 0.147630i \(0.952836\pi\)
\(110\) −2.02537 −0.193112
\(111\) 6.60815 + 3.37310i 0.627218 + 0.320161i
\(112\) 0 0
\(113\) 2.90616 1.67787i 0.273388 0.157841i −0.357038 0.934090i \(-0.616213\pi\)
0.630426 + 0.776249i \(0.282880\pi\)
\(114\) −6.43101 3.28268i −0.602319 0.307451i
\(115\) −4.54074 + 2.62160i −0.423427 + 0.244465i
\(116\) −4.06467 2.34674i −0.377395 0.217889i
\(117\) −1.08367 10.4573i −0.100186 0.966781i
\(118\) 9.44130i 0.869143i
\(119\) 0 0
\(120\) 2.50640 0.129520i 0.228802 0.0118235i
\(121\) −4.52311 + 7.83426i −0.411192 + 0.712206i
\(122\) 9.85957 0.892644
\(123\) 1.06053 + 0.541343i 0.0956248 + 0.0488113i
\(124\) 0.917280i 0.0823741i
\(125\) −11.4477 −1.02391
\(126\) 0 0
\(127\) −12.9075 −1.14535 −0.572677 0.819781i \(-0.694095\pi\)
−0.572677 + 0.819781i \(0.694095\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.07530 + 20.8087i 0.0946753 + 1.83211i
\(130\) −5.07794 −0.445364
\(131\) −4.12856 + 7.15088i −0.360714 + 0.624775i −0.988079 0.153951i \(-0.950800\pi\)
0.627364 + 0.778726i \(0.284134\pi\)
\(132\) −1.10069 + 2.15634i −0.0958030 + 0.187685i
\(133\) 0 0
\(134\) 2.97079i 0.256637i
\(135\) 7.02320 + 2.71362i 0.604461 + 0.233551i
\(136\) −6.84639 3.95277i −0.587073 0.338947i
\(137\) −11.3267 + 6.53946i −0.967703 + 0.558703i −0.898535 0.438902i \(-0.855368\pi\)
−0.0691676 + 0.997605i \(0.522034\pi\)
\(138\) 0.323442 + 6.25907i 0.0275332 + 0.532808i
\(139\) −10.6722 + 6.16162i −0.905207 + 0.522621i −0.878886 0.477032i \(-0.841713\pi\)
−0.0263210 + 0.999654i \(0.508379\pi\)
\(140\) 0 0
\(141\) 12.0878 7.83738i 1.01798 0.660026i
\(142\) 12.9436 1.08620
\(143\) 2.44921 4.24216i 0.204813 0.354747i
\(144\) 1.22421 2.73885i 0.102018 0.228238i
\(145\) −5.88971 + 3.40042i −0.489113 + 0.282390i
\(146\) 5.65267 9.79071i 0.467818 0.810285i
\(147\) 0 0
\(148\) −2.14176 3.70963i −0.176051 0.304930i
\(149\) 0.538692 + 0.311014i 0.0441314 + 0.0254792i 0.521903 0.853005i \(-0.325222\pi\)
−0.477772 + 0.878484i \(0.658555\pi\)
\(150\) −2.28395 + 4.47443i −0.186484 + 0.365336i
\(151\) 10.5911 + 18.3443i 0.861889 + 1.49284i 0.870103 + 0.492870i \(0.164052\pi\)
−0.00821353 + 0.999966i \(0.502614\pi\)
\(152\) 2.08434 + 3.61019i 0.169063 + 0.292825i
\(153\) −13.9122 19.2075i −1.12474 1.55283i
\(154\) 0 0
\(155\) 1.15107 + 0.664569i 0.0924559 + 0.0533794i
\(156\) −2.75961 + 5.40629i −0.220946 + 0.432849i
\(157\) 15.0294i 1.19947i 0.800197 + 0.599737i \(0.204728\pi\)
−0.800197 + 0.599737i \(0.795272\pi\)
\(158\) 15.6342i 1.24379i
\(159\) −10.3098 + 0.532764i −0.817618 + 0.0422509i
\(160\) −1.25487 0.724499i −0.0992062 0.0572767i
\(161\) 0 0
\(162\) 6.70586 6.00262i 0.526862 0.471610i
\(163\) 1.51764 + 2.62863i 0.118871 + 0.205890i 0.919320 0.393510i \(-0.128739\pi\)
−0.800450 + 0.599400i \(0.795406\pi\)
\(164\) −0.343727 0.595352i −0.0268406 0.0464892i
\(165\) 1.90847 + 2.94349i 0.148574 + 0.229150i
\(166\) −7.12189 4.11183i −0.552766 0.319140i
\(167\) 3.05895 + 5.29826i 0.236709 + 0.409992i 0.959768 0.280794i \(-0.0905979\pi\)
−0.723059 + 0.690786i \(0.757265\pi\)
\(168\) 0 0
\(169\) −0.359433 + 0.622557i −0.0276487 + 0.0478890i
\(170\) −9.92041 + 5.72755i −0.760861 + 0.439283i
\(171\) 1.28908 + 12.4395i 0.0985782 + 0.951269i
\(172\) 6.01497 10.4182i 0.458637 0.794383i
\(173\) −2.29515 −0.174497 −0.0872484 0.996187i \(-0.527807\pi\)
−0.0872484 + 0.996187i \(0.527807\pi\)
\(174\) 0.419530 + 8.11851i 0.0318045 + 0.615463i
\(175\) 0 0
\(176\) 1.21051 0.698887i 0.0912454 0.0526806i
\(177\) 13.7211 8.89637i 1.03134 0.668692i
\(178\) 0.923906 0.533417i 0.0692497 0.0399813i
\(179\) −2.92364 1.68796i −0.218523 0.126164i 0.386743 0.922187i \(-0.373600\pi\)
−0.605266 + 0.796023i \(0.706933\pi\)
\(180\) −2.54996 3.52052i −0.190063 0.262404i
\(181\) 1.68857i 0.125511i 0.998029 + 0.0627553i \(0.0199888\pi\)
−0.998029 + 0.0627553i \(0.980011\pi\)
\(182\) 0 0
\(183\) −9.29049 14.3290i −0.686773 1.05923i
\(184\) 1.80925 3.13371i 0.133380 0.231020i
\(185\) −6.20681 −0.456334
\(186\) 1.33309 0.864336i 0.0977469 0.0633762i
\(187\) 11.0501i 0.808067i
\(188\) −8.31745 −0.606612
\(189\) 0 0
\(190\) 6.04043 0.438219
\(191\) 8.94832i 0.647478i 0.946146 + 0.323739i \(0.104940\pi\)
−0.946146 + 0.323739i \(0.895060\pi\)
\(192\) −1.45331 + 0.942282i −0.104883 + 0.0680033i
\(193\) 25.6055 1.84313 0.921564 0.388227i \(-0.126912\pi\)
0.921564 + 0.388227i \(0.126912\pi\)
\(194\) 6.33179 10.9670i 0.454596 0.787383i
\(195\) 4.78485 + 7.37981i 0.342650 + 0.528479i
\(196\) 0 0
\(197\) 23.5602i 1.67860i −0.543670 0.839299i \(-0.682966\pi\)
0.543670 0.839299i \(-0.317034\pi\)
\(198\) 4.17099 0.432231i 0.296419 0.0307173i
\(199\) −11.7989 6.81212i −0.836404 0.482898i 0.0196362 0.999807i \(-0.493749\pi\)
−0.856040 + 0.516909i \(0.827083\pi\)
\(200\) 2.51182 1.45020i 0.177613 0.102545i
\(201\) −4.31748 + 2.79932i −0.304531 + 0.197449i
\(202\) 15.2027 8.77726i 1.06965 0.617566i
\(203\) 0 0
\(204\) 0.706641 + 13.6745i 0.0494748 + 0.957409i
\(205\) −0.996120 −0.0695720
\(206\) −2.22905 + 3.86082i −0.155305 + 0.268996i
\(207\) 8.79159 6.36787i 0.611058 0.442598i
\(208\) 3.03494 1.75222i 0.210435 0.121495i
\(209\) −2.91344 + 5.04623i −0.201527 + 0.349055i
\(210\) 0 0
\(211\) −10.7961 18.6994i −0.743235 1.28732i −0.951015 0.309145i \(-0.899957\pi\)
0.207780 0.978176i \(-0.433376\pi\)
\(212\) 5.16176 + 2.98014i 0.354511 + 0.204677i
\(213\) −12.1965 18.8110i −0.835691 1.28891i
\(214\) −1.18106 2.04566i −0.0807359 0.139839i
\(215\) −8.71569 15.0960i −0.594405 1.02954i
\(216\) −5.13395 + 0.801614i −0.349321 + 0.0545429i
\(217\) 0 0
\(218\) −11.2545 6.49776i −0.762248 0.440084i
\(219\) −19.5553 + 1.01053i −1.32143 + 0.0682856i
\(220\) 2.02537i 0.136551i
\(221\) 27.7045i 1.86361i
\(222\) −3.37310 + 6.60815i −0.226388 + 0.443510i
\(223\) −14.5710 8.41256i −0.975745 0.563347i −0.0747620 0.997201i \(-0.523820\pi\)
−0.900983 + 0.433855i \(0.857153\pi\)
\(224\) 0 0
\(225\) 8.65486 0.896887i 0.576991 0.0597924i
\(226\) 1.67787 + 2.90616i 0.111610 + 0.193315i
\(227\) 6.11065 + 10.5840i 0.405578 + 0.702482i 0.994389 0.105789i \(-0.0337369\pi\)
−0.588810 + 0.808271i \(0.700404\pi\)
\(228\) 3.28268 6.43101i 0.217401 0.425904i
\(229\) 16.8458 + 9.72591i 1.11320 + 0.642706i 0.939656 0.342120i \(-0.111145\pi\)
0.173543 + 0.984826i \(0.444478\pi\)
\(230\) −2.62160 4.54074i −0.172863 0.299408i
\(231\) 0 0
\(232\) 2.34674 4.06467i 0.154071 0.266859i
\(233\) −24.7381 + 14.2825i −1.62065 + 0.935681i −0.633900 + 0.773415i \(0.718547\pi\)
−0.986747 + 0.162265i \(0.948120\pi\)
\(234\) 10.4573 1.08367i 0.683617 0.0708420i
\(235\) −6.02598 + 10.4373i −0.393092 + 0.680855i
\(236\) −9.44130 −0.614577
\(237\) 22.7213 14.7318i 1.47591 0.956933i
\(238\) 0 0
\(239\) −10.0020 + 5.77465i −0.646975 + 0.373531i −0.787296 0.616575i \(-0.788520\pi\)
0.140322 + 0.990106i \(0.455186\pi\)
\(240\) 0.129520 + 2.50640i 0.00836046 + 0.161787i
\(241\) 0.0299000 0.0172628i 0.00192603 0.00111199i −0.499037 0.866581i \(-0.666313\pi\)
0.500963 + 0.865469i \(0.332979\pi\)
\(242\) −7.83426 4.52311i −0.503606 0.290757i
\(243\) −15.0425 4.08953i −0.964975 0.262344i
\(244\) 9.85957i 0.631194i
\(245\) 0 0
\(246\) −0.541343 + 1.06053i −0.0345148 + 0.0676170i
\(247\) −7.30447 + 12.6517i −0.464772 + 0.805009i
\(248\) −0.917280 −0.0582473
\(249\) 0.735076 + 14.2248i 0.0465836 + 0.901460i
\(250\) 11.4477i 0.724014i
\(251\) 3.26317 0.205969 0.102985 0.994683i \(-0.467161\pi\)
0.102985 + 0.994683i \(0.467161\pi\)
\(252\) 0 0
\(253\) 5.05784 0.317984
\(254\) 12.9075i 0.809887i
\(255\) 17.6717 + 9.02045i 1.10665 + 0.564883i
\(256\) 1.00000 0.0625000
\(257\) 9.89851 17.1447i 0.617452 1.06946i −0.372497 0.928034i \(-0.621498\pi\)
0.989949 0.141425i \(-0.0451685\pi\)
\(258\) −20.8087 + 1.07530i −1.29549 + 0.0669455i
\(259\) 0 0
\(260\) 5.07794i 0.314920i
\(261\) 11.4034 8.25963i 0.705852 0.511258i
\(262\) −7.15088 4.12856i −0.441783 0.255063i
\(263\) 15.2576 8.80897i 0.940823 0.543184i 0.0506045 0.998719i \(-0.483885\pi\)
0.890218 + 0.455535i \(0.150552\pi\)
\(264\) −2.15634 1.10069i −0.132713 0.0677429i
\(265\) 7.47939 4.31823i 0.459455 0.265266i
\(266\) 0 0
\(267\) −1.64580 0.840091i −0.100721 0.0514127i
\(268\) 2.97079 0.181470
\(269\) −3.83672 + 6.64540i −0.233929 + 0.405177i −0.958961 0.283538i \(-0.908492\pi\)
0.725032 + 0.688715i \(0.241825\pi\)
\(270\) −2.71362 + 7.02320i −0.165146 + 0.427419i
\(271\) −6.09146 + 3.51690i −0.370030 + 0.213637i −0.673471 0.739213i \(-0.735198\pi\)
0.303442 + 0.952850i \(0.401864\pi\)
\(272\) 3.95277 6.84639i 0.239672 0.415123i
\(273\) 0 0
\(274\) −6.53946 11.3267i −0.395063 0.684269i
\(275\) 3.51096 + 2.02705i 0.211719 + 0.122236i
\(276\) −6.25907 + 0.323442i −0.376752 + 0.0194689i
\(277\) −8.65364 14.9885i −0.519947 0.900575i −0.999731 0.0231880i \(-0.992618\pi\)
0.479784 0.877387i \(-0.340715\pi\)
\(278\) −6.16162 10.6722i −0.369549 0.640078i
\(279\) −2.51229 1.12294i −0.150407 0.0672289i
\(280\) 0 0
\(281\) 14.3155 + 8.26508i 0.853994 + 0.493053i 0.861996 0.506915i \(-0.169214\pi\)
−0.00800273 + 0.999968i \(0.502547\pi\)
\(282\) 7.83738 + 12.0878i 0.466709 + 0.719819i
\(283\) 3.16284i 0.188011i 0.995572 + 0.0940057i \(0.0299672\pi\)
−0.995572 + 0.0940057i \(0.970033\pi\)
\(284\) 12.9436i 0.768061i
\(285\) −5.69178 8.77860i −0.337152 0.519999i
\(286\) 4.24216 + 2.44921i 0.250844 + 0.144825i
\(287\) 0 0
\(288\) 2.73885 + 1.22421i 0.161388 + 0.0721373i
\(289\) −22.7487 39.4019i −1.33816 2.31776i
\(290\) −3.40042 5.88971i −0.199680 0.345855i
\(291\) −21.9047 + 1.13194i −1.28408 + 0.0663556i
\(292\) 9.79071 + 5.65267i 0.572958 + 0.330797i
\(293\) 4.26045 + 7.37932i 0.248898 + 0.431104i 0.963220 0.268713i \(-0.0865982\pi\)
−0.714322 + 0.699817i \(0.753265\pi\)
\(294\) 0 0
\(295\) −6.84022 + 11.8476i −0.398253 + 0.689794i
\(296\) 3.70963 2.14176i 0.215618 0.124487i
\(297\) −4.55841 5.65444i −0.264506 0.328104i
\(298\) −0.311014 + 0.538692i −0.0180165 + 0.0312056i
\(299\) 12.6808 0.733351
\(300\) −4.47443 2.28395i −0.258332 0.131864i
\(301\) 0 0
\(302\) −18.3443 + 10.5911i −1.05559 + 0.609448i
\(303\) −27.0812 13.8235i −1.55578 0.794139i
\(304\) −3.61019 + 2.08434i −0.207059 + 0.119545i
\(305\) 12.3725 + 7.14325i 0.708446 + 0.409022i
\(306\) 19.2075 13.9122i 1.09802 0.795309i
\(307\) 25.0805i 1.43142i 0.698398 + 0.715710i \(0.253897\pi\)
−0.698398 + 0.715710i \(0.746103\pi\)
\(308\) 0 0
\(309\) 7.71136 0.398490i 0.438684 0.0226693i
\(310\) −0.664569 + 1.15107i −0.0377450 + 0.0653762i
\(311\) −3.57355 −0.202638 −0.101319 0.994854i \(-0.532306\pi\)
−0.101319 + 0.994854i \(0.532306\pi\)
\(312\) −5.40629 2.75961i −0.306071 0.156232i
\(313\) 13.6293i 0.770372i 0.922839 + 0.385186i \(0.125863\pi\)
−0.922839 + 0.385186i \(0.874137\pi\)
\(314\) −15.0294 −0.848157
\(315\) 0 0
\(316\) −15.6342 −0.879491
\(317\) 4.28994i 0.240947i −0.992717 0.120474i \(-0.961559\pi\)
0.992717 0.120474i \(-0.0384413\pi\)
\(318\) −0.532764 10.3098i −0.0298759 0.578143i
\(319\) 6.56042 0.367313
\(320\) 0.724499 1.25487i 0.0405007 0.0701494i
\(321\) −1.86008 + 3.64404i −0.103820 + 0.203391i
\(322\) 0 0
\(323\) 32.9557i 1.83370i
\(324\) 6.00262 + 6.70586i 0.333479 + 0.372548i
\(325\) 8.80254 + 5.08215i 0.488277 + 0.281907i
\(326\) −2.62863 + 1.51764i −0.145586 + 0.0840542i
\(327\) 1.16161 + 22.4789i 0.0642373 + 1.24309i
\(328\) 0.595352 0.343727i 0.0328728 0.0189791i
\(329\) 0 0
\(330\) −2.94349 + 1.90847i −0.162034 + 0.105058i
\(331\) 8.93923 0.491345 0.245672 0.969353i \(-0.420991\pi\)
0.245672 + 0.969353i \(0.420991\pi\)
\(332\) 4.11183 7.12189i 0.225666 0.390865i
\(333\) 12.7821 1.32458i 0.700454 0.0725867i
\(334\) −5.29826 + 3.05895i −0.289908 + 0.167379i
\(335\) 2.15234 3.72796i 0.117595 0.203680i
\(336\) 0 0
\(337\) 0.0729773 + 0.126400i 0.00397532 + 0.00688546i 0.868006 0.496553i \(-0.165401\pi\)
−0.864031 + 0.503439i \(0.832068\pi\)
\(338\) −0.622557 0.359433i −0.0338626 0.0195506i
\(339\) 2.64252 5.17688i 0.143522 0.281170i
\(340\) −5.72755 9.92041i −0.310620 0.538010i
\(341\) −0.641075 1.11037i −0.0347161 0.0601301i
\(342\) −12.4395 + 1.28908i −0.672649 + 0.0697053i
\(343\) 0 0
\(344\) 10.4182 + 6.01497i 0.561714 + 0.324306i
\(345\) −4.12882 + 8.08865i −0.222288 + 0.435479i
\(346\) 2.29515i 0.123388i
\(347\) 22.2844i 1.19629i −0.801389 0.598144i \(-0.795905\pi\)
0.801389 0.598144i \(-0.204095\pi\)
\(348\) −8.11851 + 0.419530i −0.435198 + 0.0224891i
\(349\) −2.79851 1.61572i −0.149801 0.0864876i 0.423226 0.906024i \(-0.360898\pi\)
−0.573027 + 0.819537i \(0.694231\pi\)
\(350\) 0 0
\(351\) −11.4287 14.1766i −0.610017 0.756691i
\(352\) 0.698887 + 1.21051i 0.0372508 + 0.0645203i
\(353\) −3.13232 5.42533i −0.166716 0.288761i 0.770547 0.637383i \(-0.219983\pi\)
−0.937263 + 0.348622i \(0.886650\pi\)
\(354\) 8.89637 + 13.7211i 0.472837 + 0.729270i
\(355\) 16.2425 + 9.37762i 0.862063 + 0.497712i
\(356\) 0.533417 + 0.923906i 0.0282711 + 0.0489669i
\(357\) 0 0
\(358\) 1.68796 2.92364i 0.0892116 0.154519i
\(359\) 10.4523 6.03463i 0.551651 0.318496i −0.198137 0.980174i \(-0.563489\pi\)
0.749787 + 0.661679i \(0.230156\pi\)
\(360\) 3.52052 2.54996i 0.185548 0.134395i
\(361\) −0.811015 + 1.40472i −0.0426850 + 0.0739326i
\(362\) −1.68857 −0.0887494
\(363\) 0.808603 + 15.6476i 0.0424406 + 0.821289i
\(364\) 0 0
\(365\) 14.1867 8.19071i 0.742567 0.428721i
\(366\) 14.3290 9.29049i 0.748989 0.485622i
\(367\) 14.7907 8.53940i 0.772067 0.445753i −0.0615446 0.998104i \(-0.519603\pi\)
0.833611 + 0.552351i \(0.186269\pi\)
\(368\) 3.13371 + 1.80925i 0.163356 + 0.0943136i
\(369\) 2.05138 0.212580i 0.106790 0.0110665i
\(370\) 6.20681i 0.322677i
\(371\) 0 0
\(372\) 0.864336 + 1.33309i 0.0448137 + 0.0691175i
\(373\) −1.93680 + 3.35463i −0.100284 + 0.173696i −0.911801 0.410631i \(-0.865308\pi\)
0.811518 + 0.584328i \(0.198642\pi\)
\(374\) 11.0501 0.571389
\(375\) −16.6370 + 10.7869i −0.859131 + 0.557035i
\(376\) 8.31745i 0.428939i
\(377\) 16.4480 0.847117
\(378\) 0 0
\(379\) 8.21884 0.422173 0.211087 0.977467i \(-0.432300\pi\)
0.211087 + 0.977467i \(0.432300\pi\)
\(380\) 6.04043i 0.309867i
\(381\) −18.7586 + 12.1625i −0.961030 + 0.623103i
\(382\) −8.94832 −0.457836
\(383\) −15.1513 + 26.2428i −0.774195 + 1.34095i 0.161050 + 0.986946i \(0.448512\pi\)
−0.935246 + 0.353999i \(0.884821\pi\)
\(384\) −0.942282 1.45331i −0.0480856 0.0741638i
\(385\) 0 0
\(386\) 25.6055i 1.30329i
\(387\) 21.1704 + 29.2282i 1.07615 + 1.48575i
\(388\) 10.9670 + 6.33179i 0.556764 + 0.321448i
\(389\) −18.2352 + 10.5281i −0.924562 + 0.533796i −0.885088 0.465424i \(-0.845902\pi\)
−0.0394744 + 0.999221i \(0.512568\pi\)
\(390\) −7.37981 + 4.78485i −0.373691 + 0.242290i
\(391\) 24.7737 14.3031i 1.25286 0.723338i
\(392\) 0 0
\(393\) 0.738068 + 14.2827i 0.0372306 + 0.720467i
\(394\) 23.5602 1.18695
\(395\) −11.3269 + 19.6189i −0.569921 + 0.987132i
\(396\) 0.432231 + 4.17099i 0.0217204 + 0.209600i
\(397\) −0.516521 + 0.298214i −0.0259235 + 0.0149669i −0.512906 0.858445i \(-0.671431\pi\)
0.486982 + 0.873412i \(0.338098\pi\)
\(398\) 6.81212 11.7989i 0.341461 0.591427i
\(399\) 0 0
\(400\) 1.45020 + 2.51182i 0.0725101 + 0.125591i
\(401\) 2.02316 + 1.16807i 0.101032 + 0.0583309i 0.549665 0.835385i \(-0.314755\pi\)
−0.448633 + 0.893716i \(0.648089\pi\)
\(402\) −2.79932 4.31748i −0.139618 0.215336i
\(403\) −1.60728 2.78389i −0.0800642 0.138675i
\(404\) 8.77726 + 15.2027i 0.436685 + 0.756360i
\(405\) 12.7639 2.67411i 0.634242 0.132878i
\(406\) 0 0
\(407\) 5.18523 + 2.99369i 0.257022 + 0.148392i
\(408\) −13.6745 + 0.706641i −0.676990 + 0.0349839i
\(409\) 9.64564i 0.476946i −0.971149 0.238473i \(-0.923353\pi\)
0.971149 0.238473i \(-0.0766469\pi\)
\(410\) 0.996120i 0.0491948i
\(411\) −10.2991 + 20.1768i −0.508019 + 0.995246i
\(412\) −3.86082 2.22905i −0.190209 0.109817i
\(413\) 0 0
\(414\) 6.36787 + 8.79159i 0.312964 + 0.432083i
\(415\) −5.95803 10.3196i −0.292468 0.506570i
\(416\) 1.75222 + 3.03494i 0.0859098 + 0.148800i
\(417\) −9.70407 + 19.0110i −0.475210 + 0.930971i
\(418\) −5.04623 2.91344i −0.246819 0.142501i
\(419\) 14.4297 + 24.9930i 0.704939 + 1.22099i 0.966714 + 0.255861i \(0.0823590\pi\)
−0.261775 + 0.965129i \(0.584308\pi\)
\(420\) 0 0
\(421\) 6.14672 10.6464i 0.299573 0.518875i −0.676466 0.736474i \(-0.736489\pi\)
0.976038 + 0.217599i \(0.0698226\pi\)
\(422\) 18.6994 10.7961i 0.910273 0.525546i
\(423\) 10.1823 22.7802i 0.495081 1.10761i
\(424\) −2.98014 + 5.16176i −0.144729 + 0.250677i
\(425\) 22.9292 1.11223
\(426\) 18.8110 12.1965i 0.911397 0.590923i
\(427\) 0 0
\(428\) 2.04566 1.18106i 0.0988808 0.0570889i
\(429\) −0.437848 8.47301i −0.0211395 0.409081i
\(430\) 15.0960 8.71569i 0.727995 0.420308i
\(431\) 24.0435 + 13.8815i 1.15814 + 0.668650i 0.950857 0.309631i \(-0.100206\pi\)
0.207280 + 0.978282i \(0.433539\pi\)
\(432\) −0.801614 5.13395i −0.0385677 0.247007i
\(433\) 21.3927i 1.02807i −0.857769 0.514035i \(-0.828150\pi\)
0.857769 0.514035i \(-0.171850\pi\)
\(434\) 0 0
\(435\) −5.35540 + 10.4916i −0.256772 + 0.503035i
\(436\) 6.49776 11.2545i 0.311186 0.538990i
\(437\) −15.0844 −0.721585
\(438\) −1.01053 19.5553i −0.0482852 0.934389i
\(439\) 2.63916i 0.125960i 0.998015 + 0.0629801i \(0.0200605\pi\)
−0.998015 + 0.0629801i \(0.979940\pi\)
\(440\) 2.02537 0.0965558
\(441\) 0 0
\(442\) 27.7045 1.31777
\(443\) 12.1750i 0.578452i −0.957261 0.289226i \(-0.906602\pi\)
0.957261 0.289226i \(-0.0933979\pi\)
\(444\) −6.60815 3.37310i −0.313609 0.160080i
\(445\) 1.54584 0.0732799
\(446\) 8.41256 14.5710i 0.398346 0.689956i
\(447\) 1.07595 0.0556003i 0.0508906 0.00262981i
\(448\) 0 0
\(449\) 14.2454i 0.672283i 0.941811 + 0.336142i \(0.109122\pi\)
−0.941811 + 0.336142i \(0.890878\pi\)
\(450\) 0.896887 + 8.65486i 0.0422796 + 0.407994i
\(451\) 0.832168 + 0.480452i 0.0391853 + 0.0226236i
\(452\) −2.90616 + 1.67787i −0.136694 + 0.0789204i
\(453\) 32.6776 + 16.6801i 1.53533 + 0.783700i
\(454\) −10.5840 + 6.11065i −0.496730 + 0.286787i
\(455\) 0 0
\(456\) 6.43101 + 3.28268i 0.301160 + 0.153726i
\(457\) −11.5631 −0.540900 −0.270450 0.962734i \(-0.587172\pi\)
−0.270450 + 0.962734i \(0.587172\pi\)
\(458\) −9.72591 + 16.8458i −0.454462 + 0.787151i
\(459\) −38.3176 14.8051i −1.78851 0.691044i
\(460\) 4.54074 2.62160i 0.211713 0.122233i
\(461\) −11.0041 + 19.0597i −0.512513 + 0.887698i 0.487382 + 0.873189i \(0.337952\pi\)
−0.999895 + 0.0145095i \(0.995381\pi\)
\(462\) 0 0
\(463\) 6.47862 + 11.2213i 0.301087 + 0.521498i 0.976382 0.216049i \(-0.0693171\pi\)
−0.675295 + 0.737547i \(0.735984\pi\)
\(464\) 4.06467 + 2.34674i 0.188698 + 0.108945i
\(465\) 2.29907 0.118806i 0.106617 0.00550949i
\(466\) −14.2825 24.7381i −0.661626 1.14597i
\(467\) −1.42545 2.46895i −0.0659619 0.114249i 0.831158 0.556036i \(-0.187678\pi\)
−0.897120 + 0.441786i \(0.854345\pi\)
\(468\) 1.08367 + 10.4573i 0.0500928 + 0.483390i
\(469\) 0 0
\(470\) −10.4373 6.02598i −0.481437 0.277958i
\(471\) 14.1619 + 21.8423i 0.652546 + 1.00644i
\(472\) 9.44130i 0.434571i
\(473\) 16.8151i 0.773161i
\(474\) 14.7318 + 22.7213i 0.676654 + 1.04362i
\(475\) −10.4710 6.04544i −0.480443 0.277384i
\(476\) 0 0
\(477\) −14.4813 + 10.4890i −0.663051 + 0.480257i
\(478\) −5.77465 10.0020i −0.264126 0.457480i
\(479\) 16.6352 + 28.8130i 0.760081 + 1.31650i 0.942808 + 0.333336i \(0.108174\pi\)
−0.182727 + 0.983164i \(0.558492\pi\)
\(480\) −2.50640 + 0.129520i −0.114401 + 0.00591174i
\(481\) 13.0002 + 7.50567i 0.592758 + 0.342229i
\(482\) 0.0172628 + 0.0299000i 0.000786298 + 0.00136191i
\(483\) 0 0
\(484\) 4.52311 7.83426i 0.205596 0.356103i
\(485\) 15.8911 9.17475i 0.721579 0.416604i
\(486\) 4.08953 15.0425i 0.185505 0.682340i
\(487\) 5.22500 9.04997i 0.236767 0.410093i −0.723017 0.690830i \(-0.757245\pi\)
0.959785 + 0.280737i \(0.0905788\pi\)
\(488\) −9.85957 −0.446322
\(489\) 4.68250 + 2.39016i 0.211750 + 0.108087i
\(490\) 0 0
\(491\) 2.03404 1.17436i 0.0917952 0.0529980i −0.453400 0.891307i \(-0.649789\pi\)
0.545195 + 0.838309i \(0.316456\pi\)
\(492\) −1.06053 0.541343i −0.0478124 0.0244056i
\(493\) 32.1334 18.5522i 1.44722 0.835550i
\(494\) −12.6517 7.30447i −0.569228 0.328644i
\(495\) 5.54719 + 2.47948i 0.249328 + 0.111444i
\(496\) 0.917280i 0.0411871i
\(497\) 0 0
\(498\) −14.2248 + 0.735076i −0.637429 + 0.0329396i
\(499\) −17.3895 + 30.1195i −0.778462 + 1.34834i 0.154366 + 0.988014i \(0.450667\pi\)
−0.932828 + 0.360322i \(0.882667\pi\)
\(500\) 11.4477 0.511956
\(501\) 9.43806 + 4.81762i 0.421661 + 0.215235i
\(502\) 3.26317i 0.145642i
\(503\) 17.8290 0.794956 0.397478 0.917612i \(-0.369886\pi\)
0.397478 + 0.917612i \(0.369886\pi\)
\(504\) 0 0
\(505\) 25.4365 1.13191
\(506\) 5.05784i 0.224849i
\(507\) 0.0642563 + 1.24345i 0.00285372 + 0.0552237i
\(508\) 12.9075 0.572677
\(509\) −7.78061 + 13.4764i −0.344869 + 0.597331i −0.985330 0.170660i \(-0.945410\pi\)
0.640461 + 0.767991i \(0.278743\pi\)
\(510\) −9.02045 + 17.6717i −0.399432 + 0.782517i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 13.5949 + 16.8637i 0.600229 + 0.744550i
\(514\) 17.1447 + 9.89851i 0.756222 + 0.436605i
\(515\) −5.59433 + 3.22989i −0.246516 + 0.142326i
\(516\) −1.07530 20.8087i −0.0473376 0.916053i
\(517\) 10.0683 5.81295i 0.442805 0.255653i
\(518\) 0 0
\(519\) −3.33556 + 2.16267i −0.146415 + 0.0949309i
\(520\) 5.07794 0.222682
\(521\) 14.8188 25.6669i 0.649222 1.12449i −0.334087 0.942542i \(-0.608428\pi\)
0.983309 0.181944i \(-0.0582389\pi\)
\(522\) 8.25963 + 11.4034i 0.361514 + 0.499113i
\(523\) −19.2353 + 11.1055i −0.841101 + 0.485610i −0.857638 0.514253i \(-0.828069\pi\)
0.0165371 + 0.999863i \(0.494736\pi\)
\(524\) 4.12856 7.15088i 0.180357 0.312388i
\(525\) 0 0
\(526\) 8.80897 + 15.2576i 0.384089 + 0.665262i
\(527\) −6.28006 3.62579i −0.273564 0.157942i
\(528\) 1.10069 2.15634i 0.0479015 0.0938425i
\(529\) −4.95323 8.57925i −0.215358 0.373011i
\(530\) 4.31823 + 7.47939i 0.187572 + 0.324884i
\(531\) 11.5581 25.8583i 0.501581 1.12216i
\(532\) 0 0
\(533\) 2.08638 + 1.20457i 0.0903711 + 0.0521758i
\(534\) 0.840091 1.64580i 0.0363543 0.0712207i
\(535\) 3.42272i 0.147977i
\(536\) 2.97079i 0.128319i
\(537\) −5.83948 + 0.301759i −0.251992 + 0.0130219i
\(538\) −6.64540 3.83672i −0.286503 0.165413i
\(539\) 0 0
\(540\) −7.02320 2.71362i −0.302231 0.116776i
\(541\) −11.0171 19.0822i −0.473662 0.820406i 0.525884 0.850557i \(-0.323735\pi\)
−0.999545 + 0.0301502i \(0.990401\pi\)
\(542\) −3.51690 6.09146i −0.151064 0.261650i
\(543\) 1.59111 + 2.45402i 0.0682811 + 0.105312i
\(544\) 6.84639 + 3.95277i 0.293537 + 0.169473i
\(545\) −9.41525 16.3077i −0.403305 0.698545i
\(546\) 0 0
\(547\) −14.5256 + 25.1592i −0.621072 + 1.07573i 0.368215 + 0.929741i \(0.379969\pi\)
−0.989286 + 0.145987i \(0.953364\pi\)
\(548\) 11.3267 6.53946i 0.483851 0.279352i
\(549\) −27.0039 12.0702i −1.15250 0.515143i
\(550\) −2.02705 + 3.51096i −0.0864338 + 0.149708i
\(551\) −19.5657 −0.833525
\(552\) −0.323442 6.25907i −0.0137666 0.266404i
\(553\) 0 0
\(554\) 14.9885 8.65364i 0.636802 0.367658i
\(555\) −9.02040 + 5.84856i −0.382895 + 0.248258i
\(556\) 10.6722 6.16162i 0.452603 0.261311i
\(557\) 14.9946 + 8.65716i 0.635344 + 0.366816i 0.782819 0.622250i \(-0.213781\pi\)
−0.147475 + 0.989066i \(0.547115\pi\)
\(558\) 1.12294 2.51229i 0.0475380 0.106354i
\(559\) 42.1583i 1.78311i
\(560\) 0 0
\(561\) −10.4123 16.0593i −0.439610 0.678023i
\(562\) −8.26508 + 14.3155i −0.348641 + 0.603865i
\(563\) −20.7668 −0.875216 −0.437608 0.899166i \(-0.644174\pi\)
−0.437608 + 0.899166i \(0.644174\pi\)
\(564\) −12.0878 + 7.83738i −0.508989 + 0.330013i
\(565\) 4.86247i 0.204566i
\(566\) −3.16284 −0.132944
\(567\) 0 0
\(568\) −12.9436 −0.543101
\(569\) 14.7604i 0.618789i −0.950934 0.309394i \(-0.899874\pi\)
0.950934 0.309394i \(-0.100126\pi\)
\(570\) 8.77860 5.69178i 0.367695 0.238403i
\(571\) −22.2416 −0.930781 −0.465390 0.885106i \(-0.654086\pi\)
−0.465390 + 0.885106i \(0.654086\pi\)
\(572\) −2.44921 + 4.24216i −0.102407 + 0.177373i
\(573\) 8.43184 + 13.0047i 0.352245 + 0.543278i
\(574\) 0 0
\(575\) 10.4951i 0.437676i
\(576\) −1.22421 + 2.73885i −0.0510088 + 0.114119i
\(577\) 16.2104 + 9.35911i 0.674850 + 0.389625i 0.797912 0.602774i \(-0.205938\pi\)
−0.123062 + 0.992399i \(0.539271\pi\)
\(578\) 39.4019 22.7487i 1.63890 0.946222i
\(579\) 37.2128 24.1276i 1.54651 1.00271i
\(580\) 5.88971 3.40042i 0.244557 0.141195i
\(581\) 0 0
\(582\) −1.13194 21.9047i −0.0469205 0.907980i
\(583\) −8.33113 −0.345040
\(584\) −5.65267 + 9.79071i −0.233909 + 0.405142i
\(585\) 13.9077 + 6.21646i 0.575013 + 0.257019i
\(586\) −7.37932 + 4.26045i −0.304837 + 0.175998i
\(587\) 10.7433 18.6079i 0.443423 0.768031i −0.554518 0.832172i \(-0.687097\pi\)
0.997941 + 0.0641405i \(0.0204306\pi\)
\(588\) 0 0
\(589\) 1.91193 + 3.31155i 0.0787796 + 0.136450i
\(590\) −11.8476 6.84022i −0.487758 0.281607i
\(591\) −22.2004 34.2403i −0.913202 1.40846i
\(592\) 2.14176 + 3.70963i 0.0880257 + 0.152465i
\(593\) 7.04746 + 12.2066i 0.289404 + 0.501263i 0.973668 0.227972i \(-0.0732094\pi\)
−0.684263 + 0.729235i \(0.739876\pi\)
\(594\) 5.65444 4.55841i 0.232005 0.187034i
\(595\) 0 0
\(596\) −0.538692 0.311014i −0.0220657 0.0127396i
\(597\) −23.5664 + 1.21781i −0.964509 + 0.0498417i
\(598\) 12.6808i 0.518558i
\(599\) 19.1707i 0.783296i 0.920115 + 0.391648i \(0.128095\pi\)
−0.920115 + 0.391648i \(0.871905\pi\)
\(600\) 2.28395 4.47443i 0.0932420 0.182668i
\(601\) −34.6795 20.0222i −1.41460 0.816723i −0.418787 0.908084i \(-0.637545\pi\)
−0.995818 + 0.0913619i \(0.970878\pi\)
\(602\) 0 0
\(603\) −3.63688 + 8.13656i −0.148105 + 0.331346i
\(604\) −10.5911 18.3443i −0.430945 0.746418i
\(605\) −6.55399 11.3518i −0.266457 0.461518i
\(606\) 13.8235 27.0812i 0.561541 1.10010i
\(607\) −39.6529 22.8936i −1.60946 0.929223i −0.989490 0.144599i \(-0.953811\pi\)
−0.619971 0.784625i \(-0.712856\pi\)
\(608\) −2.08434 3.61019i −0.0845313 0.146413i
\(609\) 0 0
\(610\) −7.14325 + 12.3725i −0.289222 + 0.500947i
\(611\) 25.2429 14.5740i 1.02122 0.589601i
\(612\) 13.9122 + 19.2075i 0.562369 + 0.776416i
\(613\) 22.6481 39.2276i 0.914748 1.58439i 0.107477 0.994208i \(-0.465723\pi\)
0.807270 0.590182i \(-0.200944\pi\)
\(614\) −25.0805 −1.01217
\(615\) −1.44767 + 0.938625i −0.0583756 + 0.0378490i
\(616\) 0 0
\(617\) −28.6323 + 16.5308i −1.15269 + 0.665506i −0.949542 0.313641i \(-0.898451\pi\)
−0.203149 + 0.979148i \(0.565118\pi\)
\(618\) 0.398490 + 7.71136i 0.0160296 + 0.310196i
\(619\) 9.35801 5.40285i 0.376130 0.217159i −0.300003 0.953938i \(-0.596988\pi\)
0.676133 + 0.736779i \(0.263654\pi\)
\(620\) −1.15107 0.664569i −0.0462279 0.0266897i
\(621\) 6.77656 17.5386i 0.271934 0.703801i
\(622\) 3.57355i 0.143286i
\(623\) 0 0
\(624\) 2.75961 5.40629i 0.110473 0.216425i
\(625\) 1.04283 1.80623i 0.0417131 0.0722491i
\(626\) −13.6293 −0.544736
\(627\) 0.520840 + 10.0790i 0.0208003 + 0.402517i
\(628\) 15.0294i 0.599737i
\(629\) 33.8635 1.35022
\(630\) 0 0
\(631\) −30.0554 −1.19648 −0.598242 0.801315i \(-0.704134\pi\)
−0.598242 + 0.801315i \(0.704134\pi\)
\(632\) 15.6342i 0.621894i
\(633\) −33.3102 17.0030i −1.32396 0.675810i
\(634\) 4.28994 0.170375
\(635\) 9.35146 16.1972i 0.371101 0.642767i
\(636\) 10.3098 0.532764i 0.408809 0.0211255i
\(637\) 0 0
\(638\) 6.56042i 0.259730i
\(639\) −35.4506 15.8457i −1.40240 0.626845i
\(640\) 1.25487 + 0.724499i 0.0496031 + 0.0286384i
\(641\) 9.66957 5.58273i 0.381925 0.220505i −0.296730 0.954961i \(-0.595896\pi\)
0.678655 + 0.734457i \(0.262563\pi\)
\(642\) −3.64404 1.86008i −0.143819 0.0734117i
\(643\) 4.40588 2.54373i 0.173751 0.100315i −0.410602 0.911814i \(-0.634682\pi\)
0.584353 + 0.811499i \(0.301348\pi\)
\(644\) 0 0
\(645\) −26.8913 13.7265i −1.05884 0.540482i
\(646\) −32.9557 −1.29662
\(647\) −6.45711 + 11.1840i −0.253855 + 0.439690i −0.964584 0.263776i \(-0.915032\pi\)
0.710729 + 0.703466i \(0.248365\pi\)
\(648\) −6.70586 + 6.00262i −0.263431 + 0.235805i
\(649\) 11.4288 6.59840i 0.448618 0.259010i
\(650\) −5.08215 + 8.80254i −0.199338 + 0.345264i
\(651\) 0 0
\(652\) −1.51764 2.62863i −0.0594353 0.102945i
\(653\) 31.5843 + 18.2352i 1.23599 + 0.713598i 0.968272 0.249900i \(-0.0803977\pi\)
0.267716 + 0.963498i \(0.413731\pi\)
\(654\) −22.4789 + 1.16161i −0.878995 + 0.0454227i
\(655\) −5.98228 10.3616i −0.233747 0.404862i
\(656\) 0.343727 + 0.595352i 0.0134203 + 0.0232446i
\(657\) −27.4677 + 19.8952i −1.07162 + 0.776187i
\(658\) 0 0
\(659\) 2.04111 + 1.17844i 0.0795104 + 0.0459054i 0.539228 0.842160i \(-0.318716\pi\)
−0.459718 + 0.888065i \(0.652049\pi\)
\(660\) −1.90847 2.94349i −0.0742871 0.114575i
\(661\) 7.76114i 0.301873i 0.988543 + 0.150937i \(0.0482290\pi\)
−0.988543 + 0.150937i \(0.951771\pi\)
\(662\) 8.93923i 0.347433i
\(663\) −26.1054 40.2632i −1.01385 1.56369i
\(664\) 7.12189 + 4.11183i 0.276383 + 0.159570i
\(665\) 0 0
\(666\) 1.32458 + 12.7821i 0.0513266 + 0.495296i
\(667\) 8.49167 + 14.7080i 0.328799 + 0.569497i
\(668\) −3.05895 5.29826i −0.118354 0.204996i
\(669\) −29.1031 + 1.50392i −1.12519 + 0.0581450i
\(670\) 3.72796 + 2.15234i 0.144024 + 0.0831520i
\(671\) −6.89072 11.9351i −0.266013 0.460749i
\(672\) 0 0
\(673\) 17.5783 30.4465i 0.677594 1.17363i −0.298109 0.954532i \(-0.596356\pi\)
0.975703 0.219096i \(-0.0703106\pi\)
\(674\) −0.126400 + 0.0729773i −0.00486876 + 0.00281098i
\(675\) 11.7331 9.45877i 0.451606 0.364068i
\(676\) 0.359433 0.622557i 0.0138244 0.0239445i
\(677\) 14.0615 0.540427 0.270213 0.962800i \(-0.412906\pi\)
0.270213 + 0.962800i \(0.412906\pi\)
\(678\) 5.17688 + 2.64252i 0.198817 + 0.101485i
\(679\) 0 0
\(680\) 9.92041 5.72755i 0.380430 0.219642i
\(681\) 18.8537 + 9.62380i 0.722477 + 0.368785i
\(682\) 1.11037 0.641075i 0.0425184 0.0245480i
\(683\) 29.1299 + 16.8182i 1.11462 + 0.643529i 0.940023 0.341110i \(-0.110803\pi\)
0.174601 + 0.984639i \(0.444136\pi\)
\(684\) −1.28908 12.4395i −0.0492891 0.475634i
\(685\) 18.9513i 0.724093i
\(686\) 0 0
\(687\) 33.6466 1.73871i 1.28370 0.0663360i
\(688\) −6.01497 + 10.4182i −0.229319 + 0.397192i
\(689\) −20.8875 −0.795751
\(690\) −8.08865 4.12882i −0.307930 0.157181i
\(691\) 4.40252i 0.167480i 0.996488 + 0.0837399i \(0.0266865\pi\)
−0.996488 + 0.0837399i \(0.973314\pi\)
\(692\) 2.29515 0.0872484
\(693\) 0 0
\(694\) 22.2844 0.845903
\(695\) 17.8563i 0.677330i
\(696\) −0.419530 8.11851i −0.0159022 0.307731i
\(697\) 5.43469 0.205853
\(698\) 1.61572 2.79851i 0.0611560 0.105925i
\(699\) −22.4939 + 44.0672i −0.850798 + 1.66677i
\(700\) 0 0
\(701\) 31.5424i 1.19134i −0.803229 0.595670i \(-0.796887\pi\)
0.803229 0.595670i \(-0.203113\pi\)
\(702\) 14.1766 11.4287i 0.535062 0.431347i
\(703\) −15.4643 8.92832i −0.583247 0.336738i
\(704\) −1.21051 + 0.698887i −0.0456227 + 0.0263403i
\(705\) 1.07727 + 20.8468i 0.0405724 + 0.785136i
\(706\) 5.42533 3.13232i 0.204185 0.117886i
\(707\) 0 0
\(708\) −13.7211 + 8.89637i −0.515672 + 0.334346i
\(709\) 4.34537 0.163194 0.0815970 0.996665i \(-0.473998\pi\)
0.0815970 + 0.996665i \(0.473998\pi\)
\(710\) −9.37762 + 16.2425i −0.351936 + 0.609571i
\(711\) 19.1395 42.8197i 0.717788 1.60586i
\(712\) −0.923906 + 0.533417i −0.0346248 + 0.0199907i
\(713\) 1.65959 2.87449i 0.0621520 0.107651i
\(714\) 0 0
\(715\) 3.54890 + 6.14688i 0.132721 + 0.229880i
\(716\) 2.92364 + 1.68796i 0.109261 + 0.0630821i
\(717\) −9.09462 + 17.8170i −0.339645 + 0.665389i
\(718\) 6.03463 + 10.4523i 0.225210 + 0.390076i
\(719\) −14.1500 24.5086i −0.527707 0.914016i −0.999478 0.0322946i \(-0.989719\pi\)
0.471771 0.881721i \(-0.343615\pi\)
\(720\) 2.54996 + 3.52052i 0.0950315 + 0.131202i
\(721\) 0 0
\(722\) −1.40472 0.811015i −0.0522782 0.0301829i
\(723\) 0.0271875 0.0532624i 0.00101112 0.00198085i
\(724\) 1.68857i 0.0627553i
\(725\) 13.6130i 0.505573i
\(726\) −15.6476 + 0.808603i −0.580739 + 0.0300101i
\(727\) 11.7770 + 6.79945i 0.436784 + 0.252178i 0.702233 0.711948i \(-0.252187\pi\)
−0.265448 + 0.964125i \(0.585520\pi\)
\(728\) 0 0
\(729\) −25.7148 + 8.23089i −0.952401 + 0.304848i
\(730\) 8.19071 + 14.1867i 0.303152 + 0.525074i
\(731\) 47.5516 + 82.3617i 1.75876 + 3.04626i
\(732\) 9.29049 + 14.3290i 0.343387 + 0.529615i
\(733\) −41.0236 23.6850i −1.51524 0.874825i −0.999840 0.0178757i \(-0.994310\pi\)
−0.515401 0.856949i \(-0.672357\pi\)
\(734\) 8.53940 + 14.7907i 0.315195 + 0.545934i
\(735\) 0 0
\(736\) −1.80925 + 3.13371i −0.0666898 + 0.115510i
\(737\) −3.59617 + 2.07625i −0.132466 + 0.0764796i
\(738\) 0.212580 + 2.05138i 0.00782518 + 0.0755122i
\(739\) −16.8601 + 29.2026i −0.620210 + 1.07424i 0.369236 + 0.929336i \(0.379619\pi\)
−0.989446 + 0.144900i \(0.953714\pi\)
\(740\) 6.20681 0.228167
\(741\) 1.30583 + 25.2697i 0.0479708 + 0.928306i
\(742\) 0 0
\(743\) 6.86253 3.96208i 0.251762 0.145355i −0.368809 0.929505i \(-0.620234\pi\)
0.620571 + 0.784151i \(0.286901\pi\)
\(744\) −1.33309 + 0.864336i −0.0488735 + 0.0316881i
\(745\) −0.780564 + 0.450659i −0.0285976 + 0.0165109i
\(746\) −3.35463 1.93680i −0.122822 0.0709112i
\(747\) 14.4721 + 19.9804i 0.529505 + 0.731044i
\(748\) 11.0501i 0.404033i
\(749\) 0 0
\(750\) −10.7869 16.6370i −0.393883 0.607497i
\(751\) −2.06865 + 3.58301i −0.0754861 + 0.130746i −0.901298 0.433201i \(-0.857384\pi\)
0.825811 + 0.563946i \(0.190718\pi\)
\(752\) 8.31745 0.303306
\(753\) 4.74239 3.07482i 0.172822 0.112053i
\(754\) 16.4480i 0.599002i
\(755\) −30.6929 −1.11703
\(756\) 0 0
\(757\) 35.2411 1.28086 0.640430 0.768017i \(-0.278756\pi\)
0.640430 + 0.768017i \(0.278756\pi\)
\(758\) 8.21884i 0.298522i
\(759\) 7.35061 4.76591i 0.266810 0.172992i
\(760\) −6.04043 −0.219109
\(761\) −4.93597 + 8.54935i −0.178929 + 0.309914i −0.941514 0.336974i \(-0.890596\pi\)
0.762585 + 0.646888i \(0.223930\pi\)
\(762\) −12.1625 18.7586i −0.440600 0.679551i
\(763\) 0 0
\(764\) 8.94832i 0.323739i
\(765\) 34.1823 3.54224i 1.23586 0.128070i
\(766\) −26.2428 15.1513i −0.948192 0.547439i
\(767\) 28.6538 16.5433i 1.03463 0.597343i
\(768\) 1.45331 0.942282i 0.0524417 0.0340017i
\(769\) −18.6213 + 10.7510i −0.671503 + 0.387692i −0.796646 0.604446i \(-0.793394\pi\)
0.125143 + 0.992139i \(0.460061\pi\)
\(770\) 0 0
\(771\) −1.76957 34.2438i −0.0637295 1.23326i
\(772\) −25.6055 −0.921564
\(773\) 3.69775 6.40468i 0.132999 0.230360i −0.791832 0.610738i \(-0.790873\pi\)
0.924831 + 0.380378i \(0.124206\pi\)
\(774\) −29.2282 + 21.1704i −1.05059 + 0.760955i
\(775\) 2.30404 1.33024i 0.0827637 0.0477836i
\(776\) −6.33179 + 10.9670i −0.227298 + 0.393691i
\(777\) 0 0
\(778\) −10.5281 18.2352i −0.377451 0.653764i
\(779\) −2.48184 1.43289i −0.0889211 0.0513386i
\(780\) −4.78485 7.37981i −0.171325 0.264239i