Properties

Label 162.8.c.h.55.1
Level $162$
Weight $8$
Character 162.55
Analytic conductor $50.606$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,8,Mod(55,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.55");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 162.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(50.6063741284\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 162.55
Dual form 162.8.c.h.109.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-82.5000 - 142.894i) q^{5} +(254.000 - 439.941i) q^{7} -512.000 q^{8} +O(q^{10})\) \(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-82.5000 - 142.894i) q^{5} +(254.000 - 439.941i) q^{7} -512.000 q^{8} -1320.00 q^{10} +(1512.00 - 2618.86i) q^{11} +(-2519.50 - 4363.90i) q^{13} +(-2032.00 - 3519.53i) q^{14} +(-2048.00 + 3547.24i) q^{16} +3189.00 q^{17} +1508.00 q^{19} +(-5280.00 + 9145.23i) q^{20} +(-12096.0 - 20950.9i) q^{22} +(-37800.0 - 65471.5i) q^{23} +(25450.0 - 44080.7i) q^{25} -40312.0 q^{26} -32512.0 q^{28} +(-41332.5 + 71590.0i) q^{29} +(87446.0 + 151461. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(12756.0 - 22094.0i) q^{34} -83820.0 q^{35} -323569. q^{37} +(6032.00 - 10447.7i) q^{38} +(42240.0 + 73161.8i) q^{40} +(-154059. - 266838. i) q^{41} +(-168340. + 291573. i) q^{43} -193536. q^{44} -604800. q^{46} +(-191598. + 331857. i) q^{47} +(282740. + 489719. i) q^{49} +(-203600. - 352646. i) q^{50} +(-161248. + 279290. i) q^{52} -760206. q^{53} -498960. q^{55} +(-130048. + 225250. i) q^{56} +(330660. + 572720. i) q^{58} +(-1.11283e6 - 1.92748e6i) q^{59} +(-1.12241e6 + 1.94407e6i) q^{61} +1.39914e6 q^{62} +262144. q^{64} +(-415718. + 720044. i) q^{65} +(-736594. - 1.27582e6i) q^{67} +(-102048. - 176752. i) q^{68} +(-335280. + 580722. i) q^{70} +5.00689e6 q^{71} -5.89830e6 q^{73} +(-1.29428e6 + 2.24175e6i) q^{74} +(-48256.0 - 83581.8i) q^{76} +(-768096. - 1.33038e6i) q^{77} +(-3.51438e6 + 6.08709e6i) q^{79} +675840. q^{80} -2.46494e6 q^{82} +(-1.32560e6 + 2.29600e6i) q^{83} +(-263092. - 455690. i) q^{85} +(1.34672e6 + 2.33259e6i) q^{86} +(-774144. + 1.34086e6i) q^{88} +6.77090e6 q^{89} -2.55981e6 q^{91} +(-2.41920e6 + 4.19018e6i) q^{92} +(1.53278e6 + 2.65486e6i) q^{94} +(-124410. - 215484. i) q^{95} +(-8.08819e6 + 1.40092e7i) q^{97} +4.52383e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 8 q^{2} - 64 q^{4} - 165 q^{5} + 508 q^{7} - 1024 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 8 q^{2} - 64 q^{4} - 165 q^{5} + 508 q^{7} - 1024 q^{8} - 2640 q^{10} + 3024 q^{11} - 5039 q^{13} - 4064 q^{14} - 4096 q^{16} + 6378 q^{17} + 3016 q^{19} - 10560 q^{20} - 24192 q^{22} - 75600 q^{23} + 50900 q^{25} - 80624 q^{26} - 65024 q^{28} - 82665 q^{29} + 174892 q^{31} + 32768 q^{32} + 25512 q^{34} - 167640 q^{35} - 647138 q^{37} + 12064 q^{38} + 84480 q^{40} - 308118 q^{41} - 336680 q^{43} - 387072 q^{44} - 1209600 q^{46} - 383196 q^{47} + 565479 q^{49} - 407200 q^{50} - 322496 q^{52} - 1520412 q^{53} - 997920 q^{55} - 260096 q^{56} + 661320 q^{58} - 2225664 q^{59} - 2244815 q^{61} + 2798272 q^{62} + 524288 q^{64} - 831435 q^{65} - 1473188 q^{67} - 204096 q^{68} - 670560 q^{70} + 10013784 q^{71} - 11796602 q^{73} - 2588552 q^{74} - 96512 q^{76} - 1536192 q^{77} - 7028768 q^{79} + 1351680 q^{80} - 4929888 q^{82} - 2651196 q^{83} - 526185 q^{85} + 2693440 q^{86} - 1548288 q^{88} + 13541802 q^{89} - 5119624 q^{91} - 4838400 q^{92} + 3065568 q^{94} - 248820 q^{95} - 16176386 q^{97} + 9047664 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 6.92820i 0.353553 0.612372i
\(3\) 0 0
\(4\) −32.0000 55.4256i −0.250000 0.433013i
\(5\) −82.5000 142.894i −0.295161 0.511234i 0.679861 0.733341i \(-0.262040\pi\)
−0.975022 + 0.222107i \(0.928707\pi\)
\(6\) 0 0
\(7\) 254.000 439.941i 0.279892 0.484787i −0.691466 0.722409i \(-0.743035\pi\)
0.971358 + 0.237622i \(0.0763680\pi\)
\(8\) −512.000 −0.353553
\(9\) 0 0
\(10\) −1320.00 −0.417421
\(11\) 1512.00 2618.86i 0.342513 0.593250i −0.642385 0.766382i \(-0.722055\pi\)
0.984899 + 0.173131i \(0.0553885\pi\)
\(12\) 0 0
\(13\) −2519.50 4363.90i −0.318063 0.550901i 0.662021 0.749485i \(-0.269699\pi\)
−0.980084 + 0.198585i \(0.936366\pi\)
\(14\) −2032.00 3519.53i −0.197914 0.342796i
\(15\) 0 0
\(16\) −2048.00 + 3547.24i −0.125000 + 0.216506i
\(17\) 3189.00 0.157428 0.0787142 0.996897i \(-0.474919\pi\)
0.0787142 + 0.996897i \(0.474919\pi\)
\(18\) 0 0
\(19\) 1508.00 0.0504387 0.0252193 0.999682i \(-0.491972\pi\)
0.0252193 + 0.999682i \(0.491972\pi\)
\(20\) −5280.00 + 9145.23i −0.147580 + 0.255617i
\(21\) 0 0
\(22\) −12096.0 20950.9i −0.242193 0.419491i
\(23\) −37800.0 65471.5i −0.647805 1.12203i −0.983646 0.180113i \(-0.942354\pi\)
0.335841 0.941919i \(-0.390980\pi\)
\(24\) 0 0
\(25\) 25450.0 44080.7i 0.325760 0.564233i
\(26\) −40312.0 −0.449808
\(27\) 0 0
\(28\) −32512.0 −0.279892
\(29\) −41332.5 + 71590.0i −0.314701 + 0.545079i −0.979374 0.202056i \(-0.935238\pi\)
0.664673 + 0.747135i \(0.268571\pi\)
\(30\) 0 0
\(31\) 87446.0 + 151461.i 0.527198 + 0.913134i 0.999498 + 0.0316960i \(0.0100908\pi\)
−0.472299 + 0.881438i \(0.656576\pi\)
\(32\) 16384.0 + 28377.9i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 12756.0 22094.0i 0.0556594 0.0964049i
\(35\) −83820.0 −0.330453
\(36\) 0 0
\(37\) −323569. −1.05017 −0.525087 0.851049i \(-0.675967\pi\)
−0.525087 + 0.851049i \(0.675967\pi\)
\(38\) 6032.00 10447.7i 0.0178328 0.0308873i
\(39\) 0 0
\(40\) 42240.0 + 73161.8i 0.104355 + 0.180748i
\(41\) −154059. 266838.i −0.349095 0.604650i 0.636994 0.770869i \(-0.280178\pi\)
−0.986089 + 0.166219i \(0.946844\pi\)
\(42\) 0 0
\(43\) −168340. + 291573.i −0.322885 + 0.559253i −0.981082 0.193593i \(-0.937986\pi\)
0.658197 + 0.752846i \(0.271319\pi\)
\(44\) −193536. −0.342513
\(45\) 0 0
\(46\) −604800. −0.916135
\(47\) −191598. + 331857.i −0.269184 + 0.466240i −0.968651 0.248425i \(-0.920087\pi\)
0.699468 + 0.714664i \(0.253420\pi\)
\(48\) 0 0
\(49\) 282740. + 489719.i 0.343321 + 0.594649i
\(50\) −203600. 352646.i −0.230347 0.398973i
\(51\) 0 0
\(52\) −161248. + 279290.i −0.159031 + 0.275450i
\(53\) −760206. −0.701400 −0.350700 0.936488i \(-0.614056\pi\)
−0.350700 + 0.936488i \(0.614056\pi\)
\(54\) 0 0
\(55\) −498960. −0.404386
\(56\) −130048. + 225250.i −0.0989568 + 0.171398i
\(57\) 0 0
\(58\) 330660. + 572720.i 0.222527 + 0.385429i
\(59\) −1.11283e6 1.92748e6i −0.705420 1.22182i −0.966540 0.256516i \(-0.917425\pi\)
0.261120 0.965306i \(-0.415908\pi\)
\(60\) 0 0
\(61\) −1.12241e6 + 1.94407e6i −0.633135 + 1.09662i 0.353772 + 0.935332i \(0.384899\pi\)
−0.986907 + 0.161290i \(0.948435\pi\)
\(62\) 1.39914e6 0.745571
\(63\) 0 0
\(64\) 262144. 0.125000
\(65\) −415718. + 720044.i −0.187759 + 0.325209i
\(66\) 0 0
\(67\) −736594. 1.27582e6i −0.299203 0.518235i 0.676751 0.736212i \(-0.263388\pi\)
−0.975954 + 0.217977i \(0.930054\pi\)
\(68\) −102048. 176752.i −0.0393571 0.0681685i
\(69\) 0 0
\(70\) −335280. + 580722.i −0.116833 + 0.202360i
\(71\) 5.00689e6 1.66021 0.830107 0.557604i \(-0.188279\pi\)
0.830107 + 0.557604i \(0.188279\pi\)
\(72\) 0 0
\(73\) −5.89830e6 −1.77459 −0.887293 0.461207i \(-0.847417\pi\)
−0.887293 + 0.461207i \(0.847417\pi\)
\(74\) −1.29428e6 + 2.24175e6i −0.371292 + 0.643097i
\(75\) 0 0
\(76\) −48256.0 83581.8i −0.0126097 0.0218406i
\(77\) −768096. 1.33038e6i −0.191733 0.332092i
\(78\) 0 0
\(79\) −3.51438e6 + 6.08709e6i −0.801963 + 1.38904i 0.116359 + 0.993207i \(0.462878\pi\)
−0.918322 + 0.395834i \(0.870456\pi\)
\(80\) 675840. 0.147580
\(81\) 0 0
\(82\) −2.46494e6 −0.493695
\(83\) −1.32560e6 + 2.29600e6i −0.254471 + 0.440757i −0.964752 0.263162i \(-0.915235\pi\)
0.710281 + 0.703919i \(0.248568\pi\)
\(84\) 0 0
\(85\) −263092. 455690.i −0.0464667 0.0804828i
\(86\) 1.34672e6 + 2.33259e6i 0.228314 + 0.395452i
\(87\) 0 0
\(88\) −774144. + 1.34086e6i −0.121097 + 0.209746i
\(89\) 6.77090e6 1.01808 0.509039 0.860743i \(-0.330001\pi\)
0.509039 + 0.860743i \(0.330001\pi\)
\(90\) 0 0
\(91\) −2.55981e6 −0.356093
\(92\) −2.41920e6 + 4.19018e6i −0.323903 + 0.561016i
\(93\) 0 0
\(94\) 1.53278e6 + 2.65486e6i 0.190341 + 0.329681i
\(95\) −124410. 215484.i −0.0148875 0.0257860i
\(96\) 0 0
\(97\) −8.08819e6 + 1.40092e7i −0.899809 + 1.55852i −0.0720719 + 0.997399i \(0.522961\pi\)
−0.827737 + 0.561116i \(0.810372\pi\)
\(98\) 4.52383e6 0.485529
\(99\) 0 0
\(100\) −3.25760e6 −0.325760
\(101\) 1.35081e6 2.33967e6i 0.130457 0.225959i −0.793396 0.608706i \(-0.791689\pi\)
0.923853 + 0.382748i \(0.125022\pi\)
\(102\) 0 0
\(103\) −1.03446e6 1.79173e6i −0.0932787 0.161563i 0.815610 0.578602i \(-0.196401\pi\)
−0.908889 + 0.417038i \(0.863068\pi\)
\(104\) 1.28998e6 + 2.23432e6i 0.112452 + 0.194773i
\(105\) 0 0
\(106\) −3.04082e6 + 5.26686e6i −0.247982 + 0.429518i
\(107\) 9.15450e6 0.722423 0.361211 0.932484i \(-0.382363\pi\)
0.361211 + 0.932484i \(0.382363\pi\)
\(108\) 0 0
\(109\) 8.68645e6 0.642465 0.321233 0.947000i \(-0.395903\pi\)
0.321233 + 0.947000i \(0.395903\pi\)
\(110\) −1.99584e6 + 3.45690e6i −0.142972 + 0.247635i
\(111\) 0 0
\(112\) 1.04038e6 + 1.80200e6i 0.0699730 + 0.121197i
\(113\) −1.24888e7 2.16312e7i −0.814227 1.41028i −0.909882 0.414867i \(-0.863828\pi\)
0.0956551 0.995415i \(-0.469505\pi\)
\(114\) 0 0
\(115\) −6.23700e6 + 1.08028e7i −0.382414 + 0.662360i
\(116\) 5.29056e6 0.314701
\(117\) 0 0
\(118\) −1.78053e7 −0.997614
\(119\) 810006. 1.40297e6i 0.0440630 0.0763193i
\(120\) 0 0
\(121\) 5.17130e6 + 8.95695e6i 0.265369 + 0.459633i
\(122\) 8.97926e6 + 1.55525e7i 0.447694 + 0.775429i
\(123\) 0 0
\(124\) 5.59654e6 9.69350e6i 0.263599 0.456567i
\(125\) −2.12891e7 −0.974929
\(126\) 0 0
\(127\) −4.98659e6 −0.216018 −0.108009 0.994150i \(-0.534448\pi\)
−0.108009 + 0.994150i \(0.534448\pi\)
\(128\) 1.04858e6 1.81619e6i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 3.32574e6 + 5.76035e6i 0.132766 + 0.229957i
\(131\) −1.11702e7 1.93474e7i −0.434123 0.751923i 0.563101 0.826388i \(-0.309608\pi\)
−0.997224 + 0.0744655i \(0.976275\pi\)
\(132\) 0 0
\(133\) 383032. 663431.i 0.0141174 0.0244520i
\(134\) −1.17855e7 −0.423137
\(135\) 0 0
\(136\) −1.63277e6 −0.0556594
\(137\) 6.43154e6 1.11398e7i 0.213694 0.370129i −0.739174 0.673515i \(-0.764784\pi\)
0.952868 + 0.303386i \(0.0981170\pi\)
\(138\) 0 0
\(139\) −2.20951e7 3.82699e7i −0.697822 1.20866i −0.969220 0.246196i \(-0.920819\pi\)
0.271398 0.962467i \(-0.412514\pi\)
\(140\) 2.68224e6 + 4.64578e6i 0.0826132 + 0.143090i
\(141\) 0 0
\(142\) 2.00276e7 3.46888e7i 0.586974 1.01667i
\(143\) −1.52379e7 −0.435763
\(144\) 0 0
\(145\) 1.36397e7 0.371550
\(146\) −2.35932e7 + 4.08646e7i −0.627411 + 1.08671i
\(147\) 0 0
\(148\) 1.03542e7 + 1.79340e7i 0.262543 + 0.454738i
\(149\) −1.31444e6 2.27667e6i −0.0325527 0.0563830i 0.849290 0.527927i \(-0.177030\pi\)
−0.881843 + 0.471544i \(0.843697\pi\)
\(150\) 0 0
\(151\) 2.76509e7 4.78928e7i 0.653568 1.13201i −0.328683 0.944440i \(-0.606605\pi\)
0.982251 0.187572i \(-0.0600619\pi\)
\(152\) −772096. −0.0178328
\(153\) 0 0
\(154\) −1.22895e7 −0.271152
\(155\) 1.44286e7 2.49911e7i 0.311217 0.539043i
\(156\) 0 0
\(157\) 1.11855e7 + 1.93739e7i 0.230679 + 0.399548i 0.958008 0.286741i \(-0.0925720\pi\)
−0.727329 + 0.686289i \(0.759239\pi\)
\(158\) 2.81151e7 + 4.86967e7i 0.567074 + 0.982200i
\(159\) 0 0
\(160\) 2.70336e6 4.68236e6i 0.0521776 0.0903742i
\(161\) −3.84048e7 −0.725262
\(162\) 0 0
\(163\) 5.23606e7 0.946995 0.473498 0.880795i \(-0.342991\pi\)
0.473498 + 0.880795i \(0.342991\pi\)
\(164\) −9.85978e6 + 1.70776e7i −0.174547 + 0.302325i
\(165\) 0 0
\(166\) 1.06048e7 + 1.83680e7i 0.179938 + 0.311662i
\(167\) −2.73979e7 4.74545e7i −0.455207 0.788442i 0.543493 0.839414i \(-0.317101\pi\)
−0.998700 + 0.0509718i \(0.983768\pi\)
\(168\) 0 0
\(169\) 1.86785e7 3.23521e7i 0.297672 0.515584i
\(170\) −4.20948e6 −0.0657139
\(171\) 0 0
\(172\) 2.15475e7 0.322885
\(173\) 6.18226e7 1.07080e8i 0.907791 1.57234i 0.0906639 0.995882i \(-0.471101\pi\)
0.817127 0.576458i \(-0.195566\pi\)
\(174\) 0 0
\(175\) −1.29286e7 2.23930e7i −0.182355 0.315849i
\(176\) 6.19315e6 + 1.07269e7i 0.0856283 + 0.148313i
\(177\) 0 0
\(178\) 2.70836e7 4.69102e7i 0.359945 0.623443i
\(179\) −9.87297e7 −1.28666 −0.643328 0.765591i \(-0.722447\pi\)
−0.643328 + 0.765591i \(0.722447\pi\)
\(180\) 0 0
\(181\) 9.19855e7 1.15304 0.576520 0.817083i \(-0.304410\pi\)
0.576520 + 0.817083i \(0.304410\pi\)
\(182\) −1.02392e7 + 1.77349e7i −0.125898 + 0.218061i
\(183\) 0 0
\(184\) 1.93536e7 + 3.35214e7i 0.229034 + 0.396698i
\(185\) 2.66944e7 + 4.62361e7i 0.309970 + 0.536884i
\(186\) 0 0
\(187\) 4.82177e6 8.35155e6i 0.0539213 0.0933945i
\(188\) 2.45245e7 0.269184
\(189\) 0 0
\(190\) −1.99056e6 −0.0210541
\(191\) 6.59893e7 1.14297e8i 0.685262 1.18691i −0.288092 0.957603i \(-0.593021\pi\)
0.973354 0.229306i \(-0.0736457\pi\)
\(192\) 0 0
\(193\) −7.39537e7 1.28092e8i −0.740473 1.28254i −0.952280 0.305225i \(-0.901268\pi\)
0.211807 0.977311i \(-0.432065\pi\)
\(194\) 6.47055e7 + 1.12073e8i 0.636261 + 1.10204i
\(195\) 0 0
\(196\) 1.80953e7 3.13420e7i 0.171660 0.297325i
\(197\) 2.69561e7 0.251203 0.125602 0.992081i \(-0.459914\pi\)
0.125602 + 0.992081i \(0.459914\pi\)
\(198\) 0 0
\(199\) 1.35831e8 1.22183 0.610916 0.791695i \(-0.290801\pi\)
0.610916 + 0.791695i \(0.290801\pi\)
\(200\) −1.30304e7 + 2.25693e7i −0.115174 + 0.199486i
\(201\) 0 0
\(202\) −1.08065e7 1.87173e7i −0.0922473 0.159777i
\(203\) 2.09969e7 + 3.63677e7i 0.176165 + 0.305126i
\(204\) 0 0
\(205\) −2.54197e7 + 4.40283e7i −0.206078 + 0.356938i
\(206\) −1.65513e7 −0.131916
\(207\) 0 0
\(208\) 2.06397e7 0.159031
\(209\) 2.28010e6 3.94924e6i 0.0172759 0.0299228i
\(210\) 0 0
\(211\) 1.09670e6 + 1.89954e6i 0.00803710 + 0.0139207i 0.870016 0.493024i \(-0.164108\pi\)
−0.861979 + 0.506944i \(0.830775\pi\)
\(212\) 2.43266e7 + 4.21349e7i 0.175350 + 0.303715i
\(213\) 0 0
\(214\) 3.66180e7 6.34242e7i 0.255415 0.442392i
\(215\) 5.55522e7 0.381212
\(216\) 0 0
\(217\) 8.88451e7 0.590234
\(218\) 3.47458e7 6.01815e7i 0.227146 0.393428i
\(219\) 0 0
\(220\) 1.59667e7 + 2.76552e7i 0.101097 + 0.175104i
\(221\) −8.03469e6 1.39165e7i −0.0500721 0.0867274i
\(222\) 0 0
\(223\) −9.97215e6 + 1.72723e7i −0.0602174 + 0.104300i −0.894562 0.446943i \(-0.852513\pi\)
0.834345 + 0.551242i \(0.185846\pi\)
\(224\) 1.66461e7 0.0989568
\(225\) 0 0
\(226\) −1.99820e8 −1.15149
\(227\) −6.29925e7 + 1.09106e8i −0.357436 + 0.619098i −0.987532 0.157420i \(-0.949682\pi\)
0.630096 + 0.776518i \(0.283016\pi\)
\(228\) 0 0
\(229\) −1.17523e7 2.03556e7i −0.0646693 0.112010i 0.831878 0.554959i \(-0.187266\pi\)
−0.896547 + 0.442948i \(0.853933\pi\)
\(230\) 4.98960e7 + 8.64224e7i 0.270407 + 0.468359i
\(231\) 0 0
\(232\) 2.11622e7 3.66541e7i 0.111264 0.192714i
\(233\) 1.27757e8 0.661665 0.330833 0.943689i \(-0.392670\pi\)
0.330833 + 0.943689i \(0.392670\pi\)
\(234\) 0 0
\(235\) 6.32273e7 0.317810
\(236\) −7.12212e7 + 1.23359e8i −0.352710 + 0.610911i
\(237\) 0 0
\(238\) −6.48005e6 1.12238e7i −0.0311572 0.0539659i
\(239\) −4.67439e7 8.09628e7i −0.221479 0.383613i 0.733778 0.679389i \(-0.237755\pi\)
−0.955257 + 0.295776i \(0.904422\pi\)
\(240\) 0 0
\(241\) 6.73901e7 1.16723e8i 0.310125 0.537152i −0.668264 0.743924i \(-0.732963\pi\)
0.978389 + 0.206772i \(0.0662958\pi\)
\(242\) 8.27408e7 0.375289
\(243\) 0 0
\(244\) 1.43668e8 0.633135
\(245\) 4.66520e7 8.08037e7i 0.202670 0.351034i
\(246\) 0 0
\(247\) −3.79941e6 6.58076e6i −0.0160427 0.0277867i
\(248\) −4.47724e7 7.75480e7i −0.186393 0.322842i
\(249\) 0 0
\(250\) −8.51565e7 + 1.47495e8i −0.344689 + 0.597019i
\(251\) −1.31470e7 −0.0524771 −0.0262385 0.999656i \(-0.508353\pi\)
−0.0262385 + 0.999656i \(0.508353\pi\)
\(252\) 0 0
\(253\) −2.28614e8 −0.887527
\(254\) −1.99464e7 + 3.45481e7i −0.0763740 + 0.132284i
\(255\) 0 0
\(256\) −8.38861e6 1.45295e7i −0.0312500 0.0541266i
\(257\) −6.42355e7 1.11259e8i −0.236053 0.408855i 0.723525 0.690298i \(-0.242520\pi\)
−0.959578 + 0.281443i \(0.909187\pi\)
\(258\) 0 0
\(259\) −8.21865e7 + 1.42351e8i −0.293935 + 0.509111i
\(260\) 5.32118e7 0.187759
\(261\) 0 0
\(262\) −1.78724e8 −0.613942
\(263\) −4.88758e7 + 8.46554e7i −0.165672 + 0.286952i −0.936894 0.349614i \(-0.886313\pi\)
0.771222 + 0.636567i \(0.219646\pi\)
\(264\) 0 0
\(265\) 6.27170e7 + 1.08629e8i 0.207026 + 0.358579i
\(266\) −3.06426e6 5.30745e6i −0.00998250 0.0172902i
\(267\) 0 0
\(268\) −4.71420e7 + 8.16524e7i −0.149602 + 0.259118i
\(269\) −3.96851e7 −0.124307 −0.0621534 0.998067i \(-0.519797\pi\)
−0.0621534 + 0.998067i \(0.519797\pi\)
\(270\) 0 0
\(271\) −3.50733e8 −1.07049 −0.535246 0.844696i \(-0.679781\pi\)
−0.535246 + 0.844696i \(0.679781\pi\)
\(272\) −6.53107e6 + 1.13121e7i −0.0196786 + 0.0340843i
\(273\) 0 0
\(274\) −5.14523e7 8.91180e7i −0.151105 0.261721i
\(275\) −7.69608e7 1.33300e8i −0.223154 0.386514i
\(276\) 0 0
\(277\) −2.69801e8 + 4.67309e8i −0.762719 + 1.32107i 0.178726 + 0.983899i \(0.442803\pi\)
−0.941444 + 0.337169i \(0.890531\pi\)
\(278\) −3.53522e8 −0.986869
\(279\) 0 0
\(280\) 4.29158e7 0.116833
\(281\) −5.04259e7 + 8.73403e7i −0.135576 + 0.234824i −0.925817 0.377971i \(-0.876622\pi\)
0.790242 + 0.612796i \(0.209955\pi\)
\(282\) 0 0
\(283\) 1.27056e8 + 2.20068e8i 0.333229 + 0.577170i 0.983143 0.182838i \(-0.0585284\pi\)
−0.649914 + 0.760008i \(0.725195\pi\)
\(284\) −1.60221e8 2.77510e8i −0.415053 0.718894i
\(285\) 0 0
\(286\) −6.09517e7 + 1.05572e8i −0.154065 + 0.266849i
\(287\) −1.56524e8 −0.390836
\(288\) 0 0
\(289\) −4.00169e8 −0.975216
\(290\) 5.45589e7 9.44988e7i 0.131363 0.227527i
\(291\) 0 0
\(292\) 1.88746e8 + 3.26917e8i 0.443646 + 0.768418i
\(293\) −2.71542e8 4.70325e8i −0.630668 1.09235i −0.987415 0.158148i \(-0.949448\pi\)
0.356748 0.934201i \(-0.383886\pi\)
\(294\) 0 0
\(295\) −1.83617e8 + 3.18034e8i −0.416425 + 0.721269i
\(296\) 1.65667e8 0.371292
\(297\) 0 0
\(298\) −2.10310e7 −0.0460365
\(299\) −1.90474e8 + 3.29911e8i −0.412085 + 0.713752i
\(300\) 0 0
\(301\) 8.55167e7 + 1.48119e8i 0.180746 + 0.313061i
\(302\) −2.21208e8 3.83143e8i −0.462142 0.800454i
\(303\) 0 0
\(304\) −3.08838e6 + 5.34924e6i −0.00630484 + 0.0109203i
\(305\) 3.70394e8 0.747507
\(306\) 0 0
\(307\) −7.29877e8 −1.43968 −0.719839 0.694141i \(-0.755784\pi\)
−0.719839 + 0.694141i \(0.755784\pi\)
\(308\) −4.91581e7 + 8.51444e7i −0.0958667 + 0.166046i
\(309\) 0 0
\(310\) −1.15429e8 1.99928e8i −0.220063 0.381161i
\(311\) 3.19385e8 + 5.53191e8i 0.602078 + 1.04283i 0.992506 + 0.122197i \(0.0389939\pi\)
−0.390427 + 0.920634i \(0.627673\pi\)
\(312\) 0 0
\(313\) 3.18880e8 5.52317e8i 0.587790 1.01808i −0.406731 0.913548i \(-0.633331\pi\)
0.994521 0.104535i \(-0.0333354\pi\)
\(314\) 1.78968e8 0.326229
\(315\) 0 0
\(316\) 4.49841e8 0.801963
\(317\) −3.27189e8 + 5.66707e8i −0.576887 + 0.999198i 0.418947 + 0.908011i \(0.362399\pi\)
−0.995834 + 0.0911869i \(0.970934\pi\)
\(318\) 0 0
\(319\) 1.24989e8 + 2.16488e8i 0.215579 + 0.373393i
\(320\) −2.16269e7 3.74589e7i −0.0368951 0.0639042i
\(321\) 0 0
\(322\) −1.53619e8 + 2.66076e8i −0.256419 + 0.444130i
\(323\) 4.80901e6 0.00794049
\(324\) 0 0
\(325\) −2.56485e8 −0.414448
\(326\) 2.09442e8 3.62765e8i 0.334813 0.579914i
\(327\) 0 0
\(328\) 7.88782e7 + 1.36621e8i 0.123424 + 0.213776i
\(329\) 9.73318e7 + 1.68584e8i 0.150685 + 0.260993i
\(330\) 0 0
\(331\) −4.03844e8 + 6.99479e8i −0.612091 + 1.06017i 0.378796 + 0.925480i \(0.376338\pi\)
−0.990887 + 0.134693i \(0.956995\pi\)
\(332\) 1.69677e8 0.254471
\(333\) 0 0
\(334\) −4.38366e8 −0.643760
\(335\) −1.21538e8 + 2.10510e8i −0.176626 + 0.305926i
\(336\) 0 0
\(337\) 9.36402e7 + 1.62190e8i 0.133278 + 0.230844i 0.924938 0.380117i \(-0.124116\pi\)
−0.791660 + 0.610961i \(0.790783\pi\)
\(338\) −1.49428e8 2.58817e8i −0.210486 0.364573i
\(339\) 0 0
\(340\) −1.68379e7 + 2.91641e7i −0.0232334 + 0.0402414i
\(341\) 5.28873e8 0.722290
\(342\) 0 0
\(343\) 7.05623e8 0.944155
\(344\) 8.61901e7 1.49286e8i 0.114157 0.197726i
\(345\) 0 0
\(346\) −4.94581e8 8.56639e8i −0.641905 1.11181i
\(347\) 1.41278e8 + 2.44700e8i 0.181518 + 0.314399i 0.942398 0.334494i \(-0.108565\pi\)
−0.760879 + 0.648893i \(0.775232\pi\)
\(348\) 0 0
\(349\) 3.80306e8 6.58709e8i 0.478899 0.829478i −0.520808 0.853674i \(-0.674369\pi\)
0.999707 + 0.0241959i \(0.00770255\pi\)
\(350\) −2.06858e8 −0.257889
\(351\) 0 0
\(352\) 9.90904e7 0.121097
\(353\) −2.34447e8 + 4.06074e8i −0.283683 + 0.491353i −0.972289 0.233783i \(-0.924890\pi\)
0.688606 + 0.725135i \(0.258223\pi\)
\(354\) 0 0
\(355\) −4.13069e8 7.15456e8i −0.490030 0.848757i
\(356\) −2.16669e8 3.75281e8i −0.254520 0.440841i
\(357\) 0 0
\(358\) −3.94919e8 + 6.84020e8i −0.454901 + 0.787912i
\(359\) −1.53906e8 −0.175560 −0.0877802 0.996140i \(-0.527977\pi\)
−0.0877802 + 0.996140i \(0.527977\pi\)
\(360\) 0 0
\(361\) −8.91598e8 −0.997456
\(362\) 3.67942e8 6.37294e8i 0.407661 0.706090i
\(363\) 0 0
\(364\) 8.19140e7 + 1.41879e8i 0.0890232 + 0.154193i
\(365\) 4.86610e8 + 8.42833e8i 0.523788 + 0.907228i
\(366\) 0 0
\(367\) 3.74764e8 6.49110e8i 0.395755 0.685468i −0.597442 0.801912i \(-0.703816\pi\)
0.993197 + 0.116444i \(0.0371496\pi\)
\(368\) 3.09658e8 0.323903
\(369\) 0 0
\(370\) 4.27111e8 0.438364
\(371\) −1.93092e8 + 3.34446e8i −0.196316 + 0.340030i
\(372\) 0 0
\(373\) 2.70864e8 + 4.69150e8i 0.270253 + 0.468092i 0.968926 0.247349i \(-0.0795594\pi\)
−0.698674 + 0.715441i \(0.746226\pi\)
\(374\) −3.85741e7 6.68124e7i −0.0381281 0.0660399i
\(375\) 0 0
\(376\) 9.80982e7 1.69911e8i 0.0951707 0.164841i
\(377\) 4.16549e8 0.400379
\(378\) 0 0
\(379\) 1.32974e9 1.25467 0.627334 0.778750i \(-0.284146\pi\)
0.627334 + 0.778750i \(0.284146\pi\)
\(380\) −7.96224e6 + 1.37910e7i −0.00744377 + 0.0128930i
\(381\) 0 0
\(382\) −5.27914e8 9.14375e8i −0.484554 0.839271i
\(383\) 3.59974e8 + 6.23494e8i 0.327398 + 0.567070i 0.981995 0.188908i \(-0.0604949\pi\)
−0.654597 + 0.755978i \(0.727162\pi\)
\(384\) 0 0
\(385\) −1.26736e8 + 2.19513e8i −0.113184 + 0.196041i
\(386\) −1.18326e9 −1.04719
\(387\) 0 0
\(388\) 1.03529e9 0.899809
\(389\) 1.16034e9 2.00976e9i 0.999447 1.73109i 0.470930 0.882171i \(-0.343919\pi\)
0.528517 0.848922i \(-0.322748\pi\)
\(390\) 0 0
\(391\) −1.20544e8 2.08789e8i −0.101983 0.176640i
\(392\) −1.44763e8 2.50736e8i −0.121382 0.210240i
\(393\) 0 0
\(394\) 1.07824e8 1.86757e8i 0.0888138 0.153830i
\(395\) 1.15975e9 0.946833
\(396\) 0 0
\(397\) 1.18373e9 0.949477 0.474739 0.880127i \(-0.342543\pi\)
0.474739 + 0.880127i \(0.342543\pi\)
\(398\) 5.43322e8 9.41061e8i 0.431983 0.748216i
\(399\) 0 0
\(400\) 1.04243e8 + 1.80555e8i 0.0814400 + 0.141058i
\(401\) 6.33820e8 + 1.09781e9i 0.490863 + 0.850200i 0.999945 0.0105184i \(-0.00334816\pi\)
−0.509082 + 0.860718i \(0.670015\pi\)
\(402\) 0 0
\(403\) 4.40640e8 7.63212e8i 0.335364 0.580868i
\(404\) −1.72903e8 −0.130457
\(405\) 0 0
\(406\) 3.35951e8 0.249135
\(407\) −4.89236e8 + 8.47382e8i −0.359698 + 0.623016i
\(408\) 0 0
\(409\) 5.09744e8 + 8.82903e8i 0.368401 + 0.638089i 0.989316 0.145789i \(-0.0465721\pi\)
−0.620915 + 0.783878i \(0.713239\pi\)
\(410\) 2.03358e8 + 3.52226e8i 0.145719 + 0.252393i
\(411\) 0 0
\(412\) −6.62053e7 + 1.14671e8i −0.0466394 + 0.0807817i
\(413\) −1.13064e9 −0.789765
\(414\) 0 0
\(415\) 4.37447e8 0.300440
\(416\) 8.25590e7 1.42996e8i 0.0562261 0.0973864i
\(417\) 0 0
\(418\) −1.82408e7 3.15939e7i −0.0122159 0.0211586i
\(419\) 5.20643e8 + 9.01780e8i 0.345773 + 0.598896i 0.985494 0.169711i \(-0.0542834\pi\)
−0.639721 + 0.768607i \(0.720950\pi\)
\(420\) 0 0
\(421\) 9.79224e8 1.69607e9i 0.639580 1.10779i −0.345945 0.938255i \(-0.612442\pi\)
0.985525 0.169530i \(-0.0542251\pi\)
\(422\) 1.75472e7 0.0113662
\(423\) 0 0
\(424\) 3.89225e8 0.247982
\(425\) 8.11600e7 1.40573e8i 0.0512839 0.0888263i
\(426\) 0 0
\(427\) 5.70183e8 + 9.87586e8i 0.354419 + 0.613871i
\(428\) −2.92944e8 5.07394e8i −0.180606 0.312818i
\(429\) 0 0
\(430\) 2.22209e8 3.84877e8i 0.134779 0.233444i
\(431\) −2.84256e9 −1.71017 −0.855084 0.518489i \(-0.826495\pi\)
−0.855084 + 0.518489i \(0.826495\pi\)
\(432\) 0 0
\(433\) −8.41292e7 −0.0498011 −0.0249006 0.999690i \(-0.507927\pi\)
−0.0249006 + 0.999690i \(0.507927\pi\)
\(434\) 3.55381e8 6.15537e8i 0.208679 0.361443i
\(435\) 0 0
\(436\) −2.77966e8 4.81452e8i −0.160616 0.278196i
\(437\) −5.70024e7 9.87311e7i −0.0326744 0.0565938i
\(438\) 0 0
\(439\) 9.35233e8 1.61987e9i 0.527587 0.913807i −0.471896 0.881654i \(-0.656430\pi\)
0.999483 0.0321530i \(-0.0102364\pi\)
\(440\) 2.55468e8 0.142972
\(441\) 0 0
\(442\) −1.28555e8 −0.0708127
\(443\) −5.06663e8 + 8.77566e8i −0.276889 + 0.479587i −0.970610 0.240658i \(-0.922637\pi\)
0.693721 + 0.720244i \(0.255970\pi\)
\(444\) 0 0
\(445\) −5.58599e8 9.67522e8i −0.300497 0.520476i
\(446\) 7.97772e7 + 1.38178e8i 0.0425801 + 0.0737509i
\(447\) 0 0
\(448\) 6.65846e7 1.15328e8i 0.0349865 0.0605984i
\(449\) 1.65756e8 0.0864183 0.0432092 0.999066i \(-0.486242\pi\)
0.0432092 + 0.999066i \(0.486242\pi\)
\(450\) 0 0
\(451\) −9.31749e8 −0.478279
\(452\) −7.99282e8 + 1.38440e9i −0.407113 + 0.705141i
\(453\) 0 0
\(454\) 5.03940e8 + 8.72850e8i 0.252746 + 0.437768i
\(455\) 2.11184e8 + 3.65782e8i 0.105105 + 0.182047i
\(456\) 0 0
\(457\) 6.90398e8 1.19581e9i 0.338371 0.586076i −0.645756 0.763544i \(-0.723457\pi\)
0.984126 + 0.177469i \(0.0567908\pi\)
\(458\) −1.88037e8 −0.0914562
\(459\) 0 0
\(460\) 7.98336e8 0.382414
\(461\) 1.39246e9 2.41181e9i 0.661955 1.14654i −0.318146 0.948042i \(-0.603060\pi\)
0.980101 0.198498i \(-0.0636063\pi\)
\(462\) 0 0
\(463\) −1.39459e9 2.41551e9i −0.653001 1.13103i −0.982391 0.186837i \(-0.940176\pi\)
0.329390 0.944194i \(-0.393157\pi\)
\(464\) −1.69298e8 2.93233e8i −0.0786754 0.136270i
\(465\) 0 0
\(466\) 5.11027e8 8.85125e8i 0.233934 0.405186i
\(467\) −3.97258e9 −1.80494 −0.902471 0.430751i \(-0.858249\pi\)
−0.902471 + 0.430751i \(0.858249\pi\)
\(468\) 0 0
\(469\) −7.48380e8 −0.334979
\(470\) 2.52909e8 4.38052e8i 0.112363 0.194618i
\(471\) 0 0
\(472\) 5.69770e8 + 9.86871e8i 0.249404 + 0.431980i
\(473\) 5.09060e8 + 8.81718e8i 0.221185 + 0.383103i
\(474\) 0 0
\(475\) 3.83786e7 6.64737e7i 0.0164309 0.0284592i
\(476\) −1.03681e8 −0.0440630
\(477\) 0 0
\(478\) −7.47902e8 −0.313218
\(479\) −1.17233e9 + 2.03054e9i −0.487391 + 0.844186i −0.999895 0.0144991i \(-0.995385\pi\)
0.512504 + 0.858685i \(0.328718\pi\)
\(480\) 0 0
\(481\) 8.15232e8 + 1.41202e9i 0.334021 + 0.578541i
\(482\) −5.39121e8 9.33785e8i −0.219291 0.379824i
\(483\) 0 0
\(484\) 3.30963e8 5.73245e8i 0.132685 0.229817i
\(485\) 2.66910e9 1.06235
\(486\) 0 0
\(487\) 3.08381e9 1.20986 0.604931 0.796278i \(-0.293201\pi\)
0.604931 + 0.796278i \(0.293201\pi\)
\(488\) 5.74673e8 9.95362e8i 0.223847 0.387714i
\(489\) 0 0
\(490\) −3.73216e8 6.46429e8i −0.143309 0.248219i
\(491\) −1.85925e9 3.22032e9i −0.708848 1.22776i −0.965285 0.261200i \(-0.915882\pi\)
0.256436 0.966561i \(-0.417452\pi\)
\(492\) 0 0
\(493\) −1.31809e8 + 2.28300e8i −0.0495430 + 0.0858109i
\(494\) −6.07905e7 −0.0226877
\(495\) 0 0
\(496\) −7.16358e8 −0.263599
\(497\) 1.27175e9 2.20274e9i 0.464681 0.804850i
\(498\) 0 0
\(499\) −2.18213e8 3.77956e8i −0.0786192 0.136172i 0.824035 0.566539i \(-0.191718\pi\)
−0.902654 + 0.430366i \(0.858384\pi\)
\(500\) 6.81252e8 + 1.17996e9i 0.243732 + 0.422156i
\(501\) 0 0
\(502\) −5.25881e7 + 9.10853e7i −0.0185535 + 0.0321355i
\(503\) 5.04603e8 0.176792 0.0883958 0.996085i \(-0.471826\pi\)
0.0883958 + 0.996085i \(0.471826\pi\)
\(504\) 0 0
\(505\) −4.45766e8 −0.154024
\(506\) −9.14458e8 + 1.58389e9i −0.313788 + 0.543497i
\(507\) 0 0
\(508\) 1.59571e8 + 2.76385e8i 0.0540046 + 0.0935387i
\(509\) −2.30043e9 3.98446e9i −0.773208 1.33923i −0.935796 0.352541i \(-0.885318\pi\)
0.162589 0.986694i \(-0.448016\pi\)
\(510\) 0 0
\(511\) −1.49817e9 + 2.59490e9i −0.496692 + 0.860296i
\(512\) −1.34218e8 −0.0441942
\(513\) 0 0
\(514\) −1.02777e9 −0.333829
\(515\) −1.70686e8 + 2.95636e8i −0.0550645 + 0.0953745i
\(516\) 0 0
\(517\) 5.79392e8 + 1.00354e9i 0.184398 + 0.319386i
\(518\) 6.57492e8 + 1.13881e9i 0.207844 + 0.359996i
\(519\) 0 0
\(520\) 2.12847e8 3.68662e8i 0.0663830 0.114979i
\(521\) −7.14937e7 −0.0221481 −0.0110740 0.999939i \(-0.503525\pi\)
−0.0110740 + 0.999939i \(0.503525\pi\)
\(522\) 0 0
\(523\) −2.12182e9 −0.648563 −0.324281 0.945961i \(-0.605122\pi\)
−0.324281 + 0.945961i \(0.605122\pi\)
\(524\) −7.14895e8 + 1.23823e9i −0.217061 + 0.375961i
\(525\) 0 0
\(526\) 3.91007e8 + 6.77243e8i 0.117148 + 0.202906i
\(527\) 2.78865e8 + 4.83009e8i 0.0829960 + 0.143753i
\(528\) 0 0
\(529\) −1.15527e9 + 2.00098e9i −0.339303 + 0.587690i
\(530\) 1.00347e9 0.292779
\(531\) 0 0
\(532\) −4.90281e7 −0.0141174
\(533\) −7.76303e8 + 1.34460e9i −0.222068 + 0.384633i
\(534\) 0 0
\(535\) −7.55246e8 1.30812e9i −0.213231 0.369327i
\(536\) 3.77136e8 + 6.53219e8i 0.105784 + 0.183224i
\(537\) 0 0
\(538\) −1.58740e8 + 2.74946e8i −0.0439491 + 0.0761220i
\(539\) 1.71001e9 0.470368
\(540\) 0 0
\(541\) −2.11351e9 −0.573870 −0.286935 0.957950i \(-0.592636\pi\)
−0.286935 + 0.957950i \(0.592636\pi\)
\(542\) −1.40293e9 + 2.42995e9i −0.378476 + 0.655540i
\(543\) 0 0
\(544\) 5.22486e7 + 9.04972e7i 0.0139148 + 0.0241012i
\(545\) −7.16632e8 1.24124e9i −0.189631 0.328450i
\(546\) 0 0
\(547\) −3.12777e9 + 5.41745e9i −0.817107 + 1.41527i 0.0906987 + 0.995878i \(0.471090\pi\)
−0.907805 + 0.419392i \(0.862243\pi\)
\(548\) −8.23237e8 −0.213694
\(549\) 0 0
\(550\) −1.23137e9 −0.315588
\(551\) −6.23294e7 + 1.07958e8i −0.0158731 + 0.0274931i
\(552\) 0 0
\(553\) 1.78531e9 + 3.09224e9i 0.448926 + 0.777563i
\(554\) 2.15841e9 + 3.73847e9i 0.539324 + 0.934136i
\(555\) 0 0
\(556\) −1.41409e9 + 2.44927e9i −0.348911 + 0.604331i
\(557\) 6.50846e9 1.59583 0.797913 0.602773i \(-0.205938\pi\)
0.797913 + 0.602773i \(0.205938\pi\)
\(558\) 0 0
\(559\) 1.69653e9 0.410790
\(560\) 1.71663e8 2.97330e8i 0.0413066 0.0715451i
\(561\) 0 0
\(562\) 4.03408e8 + 6.98722e8i 0.0958665 + 0.166046i
\(563\) −8.66244e7 1.50038e8i −0.0204579 0.0354341i 0.855615 0.517612i \(-0.173179\pi\)
−0.876073 + 0.482178i \(0.839846\pi\)
\(564\) 0 0
\(565\) −2.06065e9 + 3.56915e9i −0.480656 + 0.832520i
\(566\) 2.03290e9 0.471257
\(567\) 0 0
\(568\) −2.56353e9 −0.586974
\(569\) 3.64441e9 6.31230e9i 0.829343 1.43646i −0.0692121 0.997602i \(-0.522049\pi\)
0.898555 0.438862i \(-0.144618\pi\)
\(570\) 0 0
\(571\) −2.14518e9 3.71556e9i −0.482212 0.835215i 0.517580 0.855635i \(-0.326833\pi\)
−0.999791 + 0.0204199i \(0.993500\pi\)
\(572\) 4.87614e8 + 8.44572e8i 0.108941 + 0.188691i
\(573\) 0 0
\(574\) −6.26096e8 + 1.08443e9i −0.138181 + 0.239337i
\(575\) −3.84804e9 −0.844116
\(576\) 0 0
\(577\) 6.28378e8 0.136178 0.0680888 0.997679i \(-0.478310\pi\)
0.0680888 + 0.997679i \(0.478310\pi\)
\(578\) −1.60068e9 + 2.77245e9i −0.344791 + 0.597196i
\(579\) 0 0
\(580\) −4.36471e8 7.55990e8i −0.0928876 0.160886i
\(581\) 6.73404e8 + 1.16637e9i 0.142449 + 0.246729i
\(582\) 0 0
\(583\) −1.14943e9 + 1.99087e9i −0.240239 + 0.416106i
\(584\) 3.01993e9 0.627411
\(585\) 0 0
\(586\) −4.34467e9 −0.891899
\(587\) −4.48401e9 + 7.76654e9i −0.915026 + 1.58487i −0.108163 + 0.994133i \(0.534497\pi\)
−0.806863 + 0.590738i \(0.798837\pi\)
\(588\) 0 0
\(589\) 1.31869e8 + 2.28403e8i 0.0265912 + 0.0460573i
\(590\) 1.46894e9 + 2.54428e9i 0.294457 + 0.510014i
\(591\) 0 0
\(592\) 6.62669e8 1.14778e9i 0.131272 0.227369i
\(593\) 7.57484e9 1.49170 0.745851 0.666112i \(-0.232043\pi\)
0.745851 + 0.666112i \(0.232043\pi\)
\(594\) 0 0
\(595\) −2.67302e8 −0.0520227
\(596\) −8.41239e7 + 1.45707e8i −0.0162764 + 0.0281915i
\(597\) 0 0
\(598\) 1.52379e9 + 2.63929e9i 0.291388 + 0.504699i
\(599\) −3.02973e9 5.24765e9i −0.575984 0.997633i −0.995934 0.0900859i \(-0.971286\pi\)
0.419950 0.907547i \(-0.362047\pi\)
\(600\) 0 0
\(601\) 3.27899e8 5.67937e8i 0.0616139 0.106718i −0.833573 0.552409i \(-0.813709\pi\)
0.895187 + 0.445691i \(0.147042\pi\)
\(602\) 1.36827e9 0.255613
\(603\) 0 0
\(604\) −3.53932e9 −0.653568
\(605\) 8.53264e8 1.47790e9i 0.156653 0.271332i
\(606\) 0 0
\(607\) −1.92806e9 3.33949e9i −0.349913 0.606066i 0.636321 0.771424i \(-0.280455\pi\)
−0.986234 + 0.165358i \(0.947122\pi\)
\(608\) 2.47071e7 + 4.27939e7i 0.00445819 + 0.00772181i
\(609\) 0 0
\(610\) 1.48158e9 2.56617e9i 0.264284 0.457752i
\(611\) 1.93092e9 0.342469
\(612\) 0 0
\(613\) −4.89889e9 −0.858986 −0.429493 0.903070i \(-0.641308\pi\)
−0.429493 + 0.903070i \(0.641308\pi\)
\(614\) −2.91951e9 + 5.05674e9i −0.509003 + 0.881619i
\(615\) 0 0
\(616\) 3.93265e8 + 6.81155e8i 0.0677880 + 0.117412i
\(617\) −3.32728e9 5.76302e9i −0.570284 0.987761i −0.996537 0.0831565i \(-0.973500\pi\)
0.426253 0.904604i \(-0.359833\pi\)
\(618\) 0 0
\(619\) −5.27657e9 + 9.13929e9i −0.894199 + 1.54880i −0.0594070 + 0.998234i \(0.518921\pi\)
−0.834792 + 0.550565i \(0.814412\pi\)
\(620\) −1.84686e9 −0.311217
\(621\) 0 0
\(622\) 5.11016e9 0.851468
\(623\) 1.71981e9 2.97880e9i 0.284952 0.493552i
\(624\) 0 0
\(625\) −2.31928e8 4.01712e8i −0.0379992 0.0658165i
\(626\) −2.55104e9 4.41853e9i −0.415631 0.719893i
\(627\) 0 0
\(628\) 7.15874e8 1.23993e9i 0.115339 0.199774i
\(629\) −1.03186e9 −0.165327
\(630\) 0 0
\(631\) 6.37775e9 1.01057 0.505283 0.862954i \(-0.331388\pi\)
0.505283 + 0.862954i \(0.331388\pi\)
\(632\) 1.79936e9 3.11659e9i 0.283537 0.491100i
\(633\) 0 0
\(634\) 2.61751e9 + 4.53366e9i 0.407921 + 0.706540i
\(635\) 4.11394e8 + 7.12555e8i 0.0637602 + 0.110436i
\(636\) 0 0
\(637\) 1.42472e9 2.46769e9i 0.218395 0.378271i
\(638\) 1.99983e9 0.304874
\(639\) 0 0
\(640\) −3.46030e8 −0.0521776
\(641\) 3.34351e8 5.79113e8i 0.0501418 0.0868481i −0.839865 0.542795i \(-0.817366\pi\)
0.890007 + 0.455947i \(0.150699\pi\)
\(642\) 0 0
\(643\) −1.62316e9 2.81140e9i −0.240782 0.417046i 0.720155 0.693813i \(-0.244070\pi\)
−0.960937 + 0.276767i \(0.910737\pi\)
\(644\) 1.22895e9 + 2.12861e9i 0.181316 + 0.314048i
\(645\) 0 0
\(646\) 1.92360e7 3.33178e7i 0.00280739 0.00486253i
\(647\) −7.46321e9 −1.08333 −0.541665 0.840595i \(-0.682206\pi\)
−0.541665 + 0.840595i \(0.682206\pi\)
\(648\) 0 0
\(649\) −6.73041e9 −0.966462
\(650\) −1.02594e9 + 1.77698e9i −0.146530 + 0.253797i
\(651\) 0 0
\(652\) −1.67554e9 2.90212e9i −0.236749 0.410061i
\(653\) −5.08150e9 8.80141e9i −0.714160 1.23696i −0.963283 0.268490i \(-0.913475\pi\)
0.249122 0.968472i \(-0.419858\pi\)
\(654\) 0 0
\(655\) −1.84309e9 + 3.19232e9i −0.256272 + 0.443876i
\(656\) 1.26205e9 0.174547
\(657\) 0 0
\(658\) 1.55731e9 0.213100
\(659\) −1.41534e9 + 2.45144e9i −0.192647 + 0.333674i −0.946127 0.323797i \(-0.895041\pi\)
0.753480 + 0.657471i \(0.228374\pi\)
\(660\) 0 0
\(661\) −1.98137e9 3.43184e9i −0.266846 0.462192i 0.701199 0.712965i \(-0.252648\pi\)
−0.968046 + 0.250774i \(0.919315\pi\)
\(662\) 3.23075e9 + 5.59583e9i 0.432814 + 0.749655i
\(663\) 0 0
\(664\) 6.78706e8 1.17555e9i 0.0899691 0.155831i
\(665\) −1.26401e8 −0.0166676
\(666\) 0 0
\(667\) 6.24947e9 0.815461
\(668\) −1.75346e9 + 3.03709e9i −0.227604 + 0.394221i
\(669\) 0 0
\(670\) 9.72304e8 + 1.68408e9i 0.124894 + 0.216322i
\(671\) 3.39416e9 + 5.87886e9i 0.433714 + 0.751215i
\(672\) 0 0
\(673\) 5.93077e9 1.02724e10i 0.749995 1.29903i −0.197829 0.980237i \(-0.563389\pi\)
0.947824 0.318794i \(-0.103278\pi\)
\(674\) 1.49824e9 0.188483
\(675\) 0 0
\(676\) −2.39085e9 −0.297672
\(677\) 4.93418e9 8.54625e9i 0.611159 1.05856i −0.379886 0.925033i \(-0.624037\pi\)
0.991045 0.133526i \(-0.0426299\pi\)
\(678\) 0 0
\(679\) 4.10880e9 + 7.11665e9i 0.503699 + 0.872432i
\(680\) 1.34703e8 + 2.33313e8i 0.0164285 + 0.0284550i
\(681\) 0 0
\(682\) 2.11549e9 3.66414e9i 0.255368 0.442310i
\(683\) −1.36287e10 −1.63674 −0.818372 0.574689i \(-0.805123\pi\)
−0.818372 + 0.574689i \(0.805123\pi\)
\(684\) 0 0
\(685\) −2.12241e9 −0.252297
\(686\) 2.82249e9 4.88870e9i 0.333809 0.578175i
\(687\) 0 0
\(688\) −6.89521e8 1.19428e9i −0.0807212 0.139813i
\(689\) 1.91534e9 + 3.31746e9i 0.223089 + 0.386402i
\(690\) 0 0
\(691\) 1.08135e9 1.87295e9i 0.124679 0.215950i −0.796929 0.604074i \(-0.793543\pi\)
0.921607 + 0.388124i \(0.126877\pi\)
\(692\) −7.91329e9 −0.907791
\(693\) 0 0
\(694\) 2.26045e9 0.256706
\(695\) −3.64569e9 + 6.31453e9i −0.411940 + 0.713500i
\(696\) 0 0
\(697\) −4.91294e8 8.50946e8i −0.0549575 0.0951892i
\(698\) −3.04245e9 5.26968e9i −0.338633 0.586530i
\(699\) 0 0
\(700\) −8.27430e8 + 1.43315e9i −0.0911776 + 0.157924i
\(701\) −2.93914e9 −0.322260 −0.161130 0.986933i \(-0.551514\pi\)
−0.161130 + 0.986933i \(0.551514\pi\)
\(702\) 0 0
\(703\) −4.87942e8 −0.0529693
\(704\) 3.96362e8 6.86519e8i 0.0428142 0.0741563i
\(705\) 0 0
\(706\) 1.87557e9 + 3.24859e9i 0.200594 + 0.347439i
\(707\) −6.86210e8 1.18855e9i −0.0730279 0.126488i
\(708\) 0 0
\(709\) 6.54572e9 1.13375e10i 0.689756 1.19469i −0.282160 0.959367i \(-0.591051\pi\)
0.971917 0.235326i \(-0.0756157\pi\)
\(710\) −6.60910e9 −0.693007
\(711\) 0 0
\(712\) −3.46670e9 −0.359945
\(713\) 6.61092e9 1.14504e10i 0.683044 1.18307i
\(714\) 0 0
\(715\) 1.25713e9 + 2.17741e9i 0.128620 + 0.222777i
\(716\) 3.15935e9 + 5.47216e9i 0.321664 + 0.557138i
\(717\) 0 0
\(718\) −6.15626e8 + 1.06630e9i −0.0620699 + 0.107508i
\(719\) 3.03015e9 0.304027 0.152014 0.988378i \(-0.451424\pi\)
0.152014 + 0.988378i \(0.451424\pi\)
\(720\) 0 0
\(721\) −1.05101e9 −0.104432
\(722\) −3.56639e9 + 6.17717e9i −0.352654 + 0.610815i
\(723\) 0 0
\(724\) −2.94354e9 5.09836e9i −0.288260 0.499281i
\(725\) 2.10382e9 + 3.64393e9i 0.205034 + 0.355130i
\(726\) 0 0
\(727\) 5.34238e9 9.25328e9i 0.515661 0.893151i −0.484174 0.874972i \(-0.660880\pi\)
0.999835 0.0181794i \(-0.00578701\pi\)
\(728\) 1.31062e9 0.125898
\(729\) 0 0
\(730\) 7.78576e9 0.740749
\(731\) −5.36836e8 + 9.29828e8i −0.0508313 + 0.0880424i
\(732\) 0 0
\(733\) 8.38524e9 + 1.45237e10i 0.786414 + 1.36211i 0.928150 + 0.372205i \(0.121398\pi\)
−0.141736 + 0.989904i \(0.545268\pi\)
\(734\) −2.99811e9 5.19288e9i −0.279841 0.484699i
\(735\) 0 0
\(736\) 1.23863e9 2.14537e9i 0.114517 0.198349i
\(737\) −4.45492e9 −0.409924
\(738\) 0 0
\(739\) 1.68052e10 1.53175 0.765877 0.642987i \(-0.222305\pi\)
0.765877 + 0.642987i \(0.222305\pi\)
\(740\) 1.70844e9 2.95911e9i 0.154985 0.268442i
\(741\) 0 0
\(742\) 1.54474e9 + 2.67557e9i 0.138817 + 0.240437i
\(743\) 1.03917e10 + 1.79989e10i 0.929448 + 1.60985i 0.784246 + 0.620450i \(0.213050\pi\)
0.145203 + 0.989402i \(0.453617\pi\)
\(744\) 0 0
\(745\) −2.16882e8 + 3.75651e8i −0.0192166 + 0.0332841i
\(746\) 4.33382e9 0.382195
\(747\) 0 0
\(748\) −6.17186e8 −0.0539213
\(749\) 2.32524e9 4.02744e9i 0.202200 0.350221i
\(750\) 0 0
\(751\) −5.03006e9 8.71232e9i −0.433344 0.750575i 0.563814 0.825901i \(-0.309333\pi\)
−0.997159 + 0.0753269i \(0.976000\pi\)
\(752\) −7.84785e8 1.35929e9i −0.0672959 0.116560i
\(753\) 0 0
\(754\) 1.66620e9 2.88594e9i 0.141555 0.245181i
\(755\) −9.12481e9 −0.771631
\(756\) 0 0
\(757\) 6.59893e9 0.552889 0.276445 0.961030i \(-0.410844\pi\)
0.276445 + 0.961030i \(0.410844\pi\)
\(758\) 5.31896e9 9.21270e9i 0.443592 0.768325i
\(759\) 0 0
\(760\) 6.36979e7 + 1.10328e8i 0.00526354 + 0.00911671i
\(761\) −3.03962e9 5.26478e9i −0.250019 0.433046i 0.713511 0.700644i \(-0.247104\pi\)
−0.963531 + 0.267597i \(0.913770\pi\)
\(762\) 0 0
\(763\) 2.20636e9 3.82153e9i 0.179821 0.311459i
\(764\) −8.44663e9 −0.685262
\(765\) 0 0
\(766\) 5.75959e9 0.463011
\(767\) −5.60756e9 + 9.71258e9i −0.448735 + 0.777232i
\(768\) 0 0
\(769\) −2.42525e9 4.20065e9i −0.192315 0.333100i 0.753702 0.657216i \(-0.228266\pi\)
−0.946017 + 0.324117i \(0.894933\pi\)
\(770\) 1.01389e9 + 1.75610e9i 0.0800335 + 0.138622i
\(771\) 0 0
\(772\)