Properties

Label 162.8.c.r.109.2
Level $162$
Weight $8$
Character 162.109
Analytic conductor $50.606$
Analytic rank $0$
Dimension $8$
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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 2x^{6} + 518x^{5} + 53377x^{4} + 11940x^{3} + 3528x^{2} + 1563408x + 346406544 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{18} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.2
Root \(11.0098 + 11.0098i\) of defining polynomial
Character \(\chi\) \(=\) 162.109
Dual form 162.8.c.r.55.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 + 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(5.62316 - 9.73960i) q^{5} +(-719.735 - 1246.62i) q^{7} -512.000 q^{8} +89.9705 q^{10} +(2216.31 + 3838.77i) q^{11} +(3615.49 - 6262.21i) q^{13} +(5757.88 - 9972.94i) q^{14} +(-2048.00 - 3547.24i) q^{16} -13221.1 q^{17} +13506.6 q^{19} +(359.882 + 623.334i) q^{20} +(-17730.5 + 30710.1i) q^{22} +(-32869.3 + 56931.3i) q^{23} +(38999.3 + 67548.7i) q^{25} +57847.8 q^{26} +92126.0 q^{28} +(74249.1 + 128603. i) q^{29} +(-69431.2 + 120258. i) q^{31} +(16384.0 - 28377.9i) q^{32} +(-52884.4 - 91598.4i) q^{34} -16188.7 q^{35} -121532. q^{37} +(54026.5 + 93576.6i) q^{38} +(-2879.06 + 4986.67i) q^{40} +(26393.4 - 45714.8i) q^{41} +(-375862. - 651012. i) q^{43} -283688. q^{44} -525909. q^{46} +(491796. + 851816. i) q^{47} +(-624264. + 1.08126e6i) q^{49} +(-311994. + 540390. i) q^{50} +(231391. + 400781. i) q^{52} +621759. q^{53} +49850.7 q^{55} +(368504. + 638268. i) q^{56} +(-593992. + 1.02883e6i) q^{58} +(407108. - 705132. i) q^{59} +(1.23477e6 + 2.13868e6i) q^{61} -1.11090e6 q^{62} +262144. q^{64} +(-40660.9 - 70426.8i) q^{65} +(-1.72741e6 + 2.99196e6i) q^{67} +(423075. - 732788. i) q^{68} +(-64754.9 - 112159. i) q^{70} -3.64076e6 q^{71} -5.55060e6 q^{73} +(-486126. - 841995. i) q^{74} +(-432212. + 748613. i) q^{76} +(3.19032e6 - 5.52579e6i) q^{77} +(1.02318e6 + 1.77220e6i) q^{79} -46064.9 q^{80} +422295. q^{82} +(5.13258e6 + 8.88989e6i) q^{83} +(-74344.3 + 128768. i) q^{85} +(3.00690e6 - 5.20810e6i) q^{86} +(-1.13475e6 - 1.96545e6i) q^{88} -8.12374e6 q^{89} -1.04088e7 q^{91} +(-2.10364e6 - 3.64360e6i) q^{92} +(-3.93437e6 + 6.81453e6i) q^{94} +(75949.9 - 131549. i) q^{95} +(6.64660e6 + 1.15122e7i) q^{97} -9.98823e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 32 q^{2} - 256 q^{4} + 528 q^{5} - 560 q^{7} - 4096 q^{8} + 8448 q^{10} + 2160 q^{11} - 13460 q^{13} + 4480 q^{14} - 16384 q^{16} - 45120 q^{17} + 73408 q^{19} + 33792 q^{20} - 17280 q^{22} + 62640 q^{23}+ \cdots - 23190336 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 5.62316 9.73960i 0.0201180 0.0348454i −0.855791 0.517322i \(-0.826929\pi\)
0.875909 + 0.482476i \(0.160262\pi\)
\(6\) 0 0
\(7\) −719.735 1246.62i −0.793102 1.37369i −0.924037 0.382303i \(-0.875131\pi\)
0.130935 0.991391i \(-0.458202\pi\)
\(8\) −512.000 −0.353553
\(9\) 0 0
\(10\) 89.9705 0.0284512
\(11\) 2216.31 + 3838.77i 0.502061 + 0.869596i 0.999997 + 0.00238204i \(0.000758226\pi\)
−0.497936 + 0.867214i \(0.665908\pi\)
\(12\) 0 0
\(13\) 3615.49 6262.21i 0.456420 0.790543i −0.542348 0.840154i \(-0.682465\pi\)
0.998769 + 0.0496105i \(0.0157980\pi\)
\(14\) 5757.88 9972.94i 0.560808 0.971348i
\(15\) 0 0
\(16\) −2048.00 3547.24i −0.125000 0.216506i
\(17\) −13221.1 −0.652674 −0.326337 0.945254i \(-0.605814\pi\)
−0.326337 + 0.945254i \(0.605814\pi\)
\(18\) 0 0
\(19\) 13506.6 0.451761 0.225881 0.974155i \(-0.427474\pi\)
0.225881 + 0.974155i \(0.427474\pi\)
\(20\) 359.882 + 623.334i 0.0100590 + 0.0174227i
\(21\) 0 0
\(22\) −17730.5 + 30710.1i −0.355011 + 0.614897i
\(23\) −32869.3 + 56931.3i −0.563304 + 0.975672i 0.433901 + 0.900961i \(0.357137\pi\)
−0.997205 + 0.0747111i \(0.976197\pi\)
\(24\) 0 0
\(25\) 38999.3 + 67548.7i 0.499191 + 0.864623i
\(26\) 57847.8 0.645476
\(27\) 0 0
\(28\) 92126.0 0.793102
\(29\) 74249.1 + 128603.i 0.565325 + 0.979171i 0.997019 + 0.0771513i \(0.0245824\pi\)
−0.431695 + 0.902020i \(0.642084\pi\)
\(30\) 0 0
\(31\) −69431.2 + 120258.i −0.418590 + 0.725019i −0.995798 0.0915783i \(-0.970809\pi\)
0.577208 + 0.816597i \(0.304142\pi\)
\(32\) 16384.0 28377.9i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −52884.4 91598.4i −0.230755 0.399679i
\(35\) −16188.7 −0.0638226
\(36\) 0 0
\(37\) −121532. −0.394442 −0.197221 0.980359i \(-0.563192\pi\)
−0.197221 + 0.980359i \(0.563192\pi\)
\(38\) 54026.5 + 93576.6i 0.159722 + 0.276646i
\(39\) 0 0
\(40\) −2879.06 + 4986.67i −0.00711279 + 0.0123197i
\(41\) 26393.4 45714.8i 0.0598070 0.103589i −0.834572 0.550899i \(-0.814285\pi\)
0.894379 + 0.447311i \(0.147618\pi\)
\(42\) 0 0
\(43\) −375862. 651012.i −0.720923 1.24868i −0.960630 0.277830i \(-0.910385\pi\)
0.239707 0.970845i \(-0.422949\pi\)
\(44\) −283688. −0.502061
\(45\) 0 0
\(46\) −525909. −0.796633
\(47\) 491796. + 851816.i 0.690944 + 1.19675i 0.971529 + 0.236921i \(0.0761382\pi\)
−0.280585 + 0.959829i \(0.590528\pi\)
\(48\) 0 0
\(49\) −624264. + 1.08126e6i −0.758023 + 1.31293i
\(50\) −311994. + 540390.i −0.352981 + 0.611381i
\(51\) 0 0
\(52\) 231391. + 400781.i 0.228210 + 0.395272i
\(53\) 621759. 0.573663 0.286831 0.957981i \(-0.407398\pi\)
0.286831 + 0.957981i \(0.407398\pi\)
\(54\) 0 0
\(55\) 49850.7 0.0404019
\(56\) 368504. + 638268.i 0.280404 + 0.485674i
\(57\) 0 0
\(58\) −593992. + 1.02883e6i −0.399745 + 0.692378i
\(59\) 407108. 705132.i 0.258064 0.446980i −0.707659 0.706554i \(-0.750249\pi\)
0.965723 + 0.259574i \(0.0835821\pi\)
\(60\) 0 0
\(61\) 1.23477e6 + 2.13868e6i 0.696514 + 1.20640i 0.969668 + 0.244428i \(0.0786001\pi\)
−0.273153 + 0.961971i \(0.588067\pi\)
\(62\) −1.11090e6 −0.591975
\(63\) 0 0
\(64\) 262144. 0.125000
\(65\) −40660.9 70426.8i −0.0183646 0.0318083i
\(66\) 0 0
\(67\) −1.72741e6 + 2.99196e6i −0.701671 + 1.21533i 0.266209 + 0.963915i \(0.414229\pi\)
−0.967880 + 0.251414i \(0.919105\pi\)
\(68\) 423075. 732788.i 0.163168 0.282616i
\(69\) 0 0
\(70\) −64754.9 112159.i −0.0225647 0.0390832i
\(71\) −3.64076e6 −1.20722 −0.603612 0.797278i \(-0.706272\pi\)
−0.603612 + 0.797278i \(0.706272\pi\)
\(72\) 0 0
\(73\) −5.55060e6 −1.66997 −0.834987 0.550269i \(-0.814525\pi\)
−0.834987 + 0.550269i \(0.814525\pi\)
\(74\) −486126. 841995.i −0.139456 0.241545i
\(75\) 0 0
\(76\) −432212. + 748613.i −0.112940 + 0.195618i
\(77\) 3.19032e6 5.52579e6i 0.796372 1.37936i
\(78\) 0 0
\(79\) 1.02318e6 + 1.77220e6i 0.233484 + 0.404407i 0.958831 0.283977i \(-0.0916539\pi\)
−0.725347 + 0.688384i \(0.758321\pi\)
\(80\) −46064.9 −0.0100590
\(81\) 0 0
\(82\) 422295. 0.0845799
\(83\) 5.13258e6 + 8.88989e6i 0.985286 + 1.70657i 0.640657 + 0.767827i \(0.278662\pi\)
0.344630 + 0.938739i \(0.388005\pi\)
\(84\) 0 0
\(85\) −74344.3 + 128768.i −0.0131305 + 0.0227427i
\(86\) 3.00690e6 5.20810e6i 0.509770 0.882947i
\(87\) 0 0
\(88\) −1.13475e6 1.96545e6i −0.177506 0.307449i
\(89\) −8.12374e6 −1.22149 −0.610747 0.791826i \(-0.709131\pi\)
−0.610747 + 0.791826i \(0.709131\pi\)
\(90\) 0 0
\(91\) −1.04088e7 −1.44795
\(92\) −2.10364e6 3.64360e6i −0.281652 0.487836i
\(93\) 0 0
\(94\) −3.93437e6 + 6.81453e6i −0.488571 + 0.846230i
\(95\) 75949.9 131549.i 0.00908854 0.0157418i
\(96\) 0 0
\(97\) 6.64660e6 + 1.15122e7i 0.739432 + 1.28073i 0.952751 + 0.303752i \(0.0982394\pi\)
−0.213319 + 0.976983i \(0.568427\pi\)
\(98\) −9.98823e6 −1.07201
\(99\) 0 0
\(100\) −4.99191e6 −0.499191
\(101\) −6.68327e6 1.15758e7i −0.645452 1.11796i −0.984197 0.177078i \(-0.943336\pi\)
0.338745 0.940878i \(-0.389998\pi\)
\(102\) 0 0
\(103\) −6.76614e6 + 1.17193e7i −0.610114 + 1.05675i 0.381107 + 0.924531i \(0.375543\pi\)
−0.991221 + 0.132217i \(0.957790\pi\)
\(104\) −1.85113e6 + 3.20625e6i −0.161369 + 0.279499i
\(105\) 0 0
\(106\) 2.48704e6 + 4.30767e6i 0.202820 + 0.351295i
\(107\) 1.89550e7 1.49583 0.747914 0.663796i \(-0.231056\pi\)
0.747914 + 0.663796i \(0.231056\pi\)
\(108\) 0 0
\(109\) −1.33257e7 −0.985589 −0.492794 0.870146i \(-0.664025\pi\)
−0.492794 + 0.870146i \(0.664025\pi\)
\(110\) 199403. + 345376.i 0.0142842 + 0.0247410i
\(111\) 0 0
\(112\) −2.94803e6 + 5.10614e6i −0.198276 + 0.343423i
\(113\) 1.02134e7 1.76901e7i 0.665878 1.15333i −0.313168 0.949698i \(-0.601390\pi\)
0.979046 0.203637i \(-0.0652762\pi\)
\(114\) 0 0
\(115\) 369659. + 640267.i 0.0226651 + 0.0392572i
\(116\) −9.50388e6 −0.565325
\(117\) 0 0
\(118\) 6.51373e6 0.364958
\(119\) 9.51568e6 + 1.64816e7i 0.517637 + 0.896574i
\(120\) 0 0
\(121\) −80510.7 + 139449.i −0.00413147 + 0.00715592i
\(122\) −9.87812e6 + 1.71094e7i −0.492510 + 0.853052i
\(123\) 0 0
\(124\) −4.44360e6 7.69653e6i −0.209295 0.362509i
\(125\) 1.75581e6 0.0804069
\(126\) 0 0
\(127\) 1.13846e7 0.493178 0.246589 0.969120i \(-0.420690\pi\)
0.246589 + 0.969120i \(0.420690\pi\)
\(128\) 1.04858e6 + 1.81619e6i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 325287. 563414.i 0.0129857 0.0224919i
\(131\) 2.64090e6 4.57417e6i 0.102636 0.177772i −0.810134 0.586245i \(-0.800605\pi\)
0.912770 + 0.408474i \(0.133939\pi\)
\(132\) 0 0
\(133\) −9.72118e6 1.68376e7i −0.358293 0.620582i
\(134\) −2.76385e7 −0.992312
\(135\) 0 0
\(136\) 6.76920e6 0.230755
\(137\) 2.45057e7 + 4.24451e7i 0.814226 + 1.41028i 0.909882 + 0.414866i \(0.136172\pi\)
−0.0956566 + 0.995414i \(0.530495\pi\)
\(138\) 0 0
\(139\) 9.43972e6 1.63501e7i 0.298131 0.516378i −0.677577 0.735452i \(-0.736970\pi\)
0.975708 + 0.219073i \(0.0703034\pi\)
\(140\) 518039. 897270.i 0.0159557 0.0276360i
\(141\) 0 0
\(142\) −1.45630e7 2.52239e7i −0.426818 0.739270i
\(143\) 3.20522e7 0.916604
\(144\) 0 0
\(145\) 1.67006e6 0.0454929
\(146\) −2.22024e7 3.84557e7i −0.590425 1.02265i
\(147\) 0 0
\(148\) 3.88901e6 6.73596e6i 0.0986105 0.170798i
\(149\) −1.44249e7 + 2.49846e7i −0.357240 + 0.618758i −0.987499 0.157627i \(-0.949615\pi\)
0.630259 + 0.776385i \(0.282949\pi\)
\(150\) 0 0
\(151\) 1.79766e7 + 3.11364e7i 0.424902 + 0.735952i 0.996411 0.0846435i \(-0.0269751\pi\)
−0.571509 + 0.820596i \(0.693642\pi\)
\(152\) −6.91539e6 −0.159722
\(153\) 0 0
\(154\) 5.10451e7 1.12624
\(155\) 780845. + 1.35246e6i 0.0168424 + 0.0291719i
\(156\) 0 0
\(157\) 2.89045e7 5.00641e7i 0.596097 1.03247i −0.397294 0.917691i \(-0.630051\pi\)
0.993391 0.114779i \(-0.0366159\pi\)
\(158\) −8.18545e6 + 1.41776e7i −0.165098 + 0.285959i
\(159\) 0 0
\(160\) −184260. 319147.i −0.00355640 0.00615986i
\(161\) 9.46287e7 1.78703
\(162\) 0 0
\(163\) 3.23536e7 0.585148 0.292574 0.956243i \(-0.405488\pi\)
0.292574 + 0.956243i \(0.405488\pi\)
\(164\) 1.68918e6 + 2.92574e6i 0.0299035 + 0.0517944i
\(165\) 0 0
\(166\) −4.10606e7 + 7.11191e7i −0.696703 + 1.20672i
\(167\) −4.33872e7 + 7.51489e7i −0.720866 + 1.24858i 0.239788 + 0.970825i \(0.422922\pi\)
−0.960653 + 0.277751i \(0.910411\pi\)
\(168\) 0 0
\(169\) 5.23077e6 + 9.05996e6i 0.0833608 + 0.144385i
\(170\) −1.18951e6 −0.0185693
\(171\) 0 0
\(172\) 4.81103e7 0.720923
\(173\) −5.38618e6 9.32914e6i −0.0790897 0.136987i 0.823768 0.566927i \(-0.191868\pi\)
−0.902857 + 0.429940i \(0.858535\pi\)
\(174\) 0 0
\(175\) 5.61382e7 9.72343e7i 0.791818 1.37147i
\(176\) 9.07802e6 1.57236e7i 0.125515 0.217399i
\(177\) 0 0
\(178\) −3.24950e7 5.62829e7i −0.431863 0.748009i
\(179\) 3.61175e7 0.470687 0.235343 0.971912i \(-0.424379\pi\)
0.235343 + 0.971912i \(0.424379\pi\)
\(180\) 0 0
\(181\) 2.78118e7 0.348621 0.174310 0.984691i \(-0.444230\pi\)
0.174310 + 0.984691i \(0.444230\pi\)
\(182\) −4.16351e7 7.21140e7i −0.511928 0.886686i
\(183\) 0 0
\(184\) 1.68291e7 2.91488e7i 0.199158 0.344952i
\(185\) −683391. + 1.18367e6i −0.00793539 + 0.0137445i
\(186\) 0 0
\(187\) −2.93021e7 5.07527e7i −0.327682 0.567563i
\(188\) −6.29499e7 −0.690944
\(189\) 0 0
\(190\) 1.21520e6 0.0128531
\(191\) −4.73127e7 8.19480e7i −0.491316 0.850984i 0.508634 0.860983i \(-0.330151\pi\)
−0.999950 + 0.00999867i \(0.996817\pi\)
\(192\) 0 0
\(193\) 6.11115e7 1.05848e8i 0.611889 1.05982i −0.379033 0.925383i \(-0.623743\pi\)
0.990922 0.134439i \(-0.0429234\pi\)
\(194\) −5.31728e7 + 9.20980e7i −0.522858 + 0.905616i
\(195\) 0 0
\(196\) −3.99529e7 6.92005e7i −0.379011 0.656467i
\(197\) 1.37768e8 1.28385 0.641926 0.766766i \(-0.278136\pi\)
0.641926 + 0.766766i \(0.278136\pi\)
\(198\) 0 0
\(199\) −1.62646e8 −1.46305 −0.731524 0.681815i \(-0.761191\pi\)
−0.731524 + 0.681815i \(0.761191\pi\)
\(200\) −1.99676e7 3.45849e7i −0.176491 0.305691i
\(201\) 0 0
\(202\) 5.34662e7 9.26061e7i 0.456404 0.790514i
\(203\) 1.06879e8 1.85120e8i 0.896721 1.55317i
\(204\) 0 0
\(205\) −296829. 514123.i −0.00240640 0.00416800i
\(206\) −1.08258e8 −0.862831
\(207\) 0 0
\(208\) −2.96181e7 −0.228210
\(209\) 2.99349e7 + 5.18488e7i 0.226812 + 0.392850i
\(210\) 0 0
\(211\) 7.77889e7 1.34734e8i 0.570071 0.987392i −0.426487 0.904494i \(-0.640249\pi\)
0.996558 0.0828986i \(-0.0264178\pi\)
\(212\) −1.98963e7 + 3.44614e7i −0.143416 + 0.248403i
\(213\) 0 0
\(214\) 7.58202e7 + 1.31324e8i 0.528855 + 0.916003i
\(215\) −8.45413e6 −0.0580142
\(216\) 0 0
\(217\) 1.99888e8 1.32794
\(218\) −5.33026e7 9.23228e7i −0.348458 0.603547i
\(219\) 0 0
\(220\) −1.59522e6 + 2.76301e6i −0.0101005 + 0.0174946i
\(221\) −4.78007e7 + 8.27932e7i −0.297894 + 0.515967i
\(222\) 0 0
\(223\) 6.19714e7 + 1.07338e8i 0.374218 + 0.648164i 0.990210 0.139588i \(-0.0445779\pi\)
−0.615992 + 0.787752i \(0.711245\pi\)
\(224\) −4.71685e7 −0.280404
\(225\) 0 0
\(226\) 1.63414e8 0.941694
\(227\) −6.88520e7 1.19255e8i −0.390685 0.676685i 0.601855 0.798605i \(-0.294428\pi\)
−0.992540 + 0.121920i \(0.961095\pi\)
\(228\) 0 0
\(229\) −1.17560e8 + 2.03621e8i −0.646899 + 1.12046i 0.336960 + 0.941519i \(0.390601\pi\)
−0.983859 + 0.178944i \(0.942732\pi\)
\(230\) −2.95727e6 + 5.12214e6i −0.0160267 + 0.0277590i
\(231\) 0 0
\(232\) −3.80155e7 6.58448e7i −0.199872 0.346189i
\(233\) 1.44039e8 0.745992 0.372996 0.927833i \(-0.378330\pi\)
0.372996 + 0.927833i \(0.378330\pi\)
\(234\) 0 0
\(235\) 1.10618e7 0.0556017
\(236\) 2.60549e7 + 4.51284e7i 0.129032 + 0.223490i
\(237\) 0 0
\(238\) −7.61254e7 + 1.31853e8i −0.366025 + 0.633974i
\(239\) 3.65693e7 6.33399e7i 0.173270 0.300113i −0.766291 0.642494i \(-0.777900\pi\)
0.939561 + 0.342381i \(0.111233\pi\)
\(240\) 0 0
\(241\) 6.14199e7 + 1.06382e8i 0.282650 + 0.489564i 0.972037 0.234829i \(-0.0754531\pi\)
−0.689386 + 0.724394i \(0.742120\pi\)
\(242\) −1.28817e6 −0.00584278
\(243\) 0 0
\(244\) −1.58050e8 −0.696514
\(245\) 7.02067e6 + 1.21602e7i 0.0304998 + 0.0528273i
\(246\) 0 0
\(247\) 4.88330e7 8.45812e7i 0.206193 0.357137i
\(248\) 3.55488e7 6.15723e7i 0.147994 0.256333i
\(249\) 0 0
\(250\) 7.02326e6 + 1.21646e7i 0.0284281 + 0.0492390i
\(251\) −7.30348e7 −0.291522 −0.145761 0.989320i \(-0.546563\pi\)
−0.145761 + 0.989320i \(0.546563\pi\)
\(252\) 0 0
\(253\) −2.91395e8 −1.13125
\(254\) 4.55383e7 + 7.88746e7i 0.174365 + 0.302009i
\(255\) 0 0
\(256\) −8.38861e6 + 1.45295e7i −0.0312500 + 0.0541266i
\(257\) 6.69979e7 1.16044e8i 0.246204 0.426438i −0.716265 0.697828i \(-0.754150\pi\)
0.962469 + 0.271390i \(0.0874834\pi\)
\(258\) 0 0
\(259\) 8.74705e7 + 1.51503e8i 0.312833 + 0.541842i
\(260\) 5.20460e6 0.0183646
\(261\) 0 0
\(262\) 4.22543e7 0.145150
\(263\) 1.90065e8 + 3.29202e8i 0.644253 + 1.11588i 0.984473 + 0.175534i \(0.0561651\pi\)
−0.340220 + 0.940346i \(0.610502\pi\)
\(264\) 0 0
\(265\) 3.49625e6 6.05568e6i 0.0115410 0.0199895i
\(266\) 7.77695e7 1.34701e8i 0.253351 0.438818i
\(267\) 0 0
\(268\) −1.10554e8 1.91485e8i −0.350835 0.607664i
\(269\) −5.57685e8 −1.74685 −0.873426 0.486958i \(-0.838107\pi\)
−0.873426 + 0.486958i \(0.838107\pi\)
\(270\) 0 0
\(271\) −9.65793e7 −0.294776 −0.147388 0.989079i \(-0.547087\pi\)
−0.147388 + 0.989079i \(0.547087\pi\)
\(272\) 2.70768e7 + 4.68984e7i 0.0815842 + 0.141308i
\(273\) 0 0
\(274\) −1.96045e8 + 3.39561e8i −0.575745 + 0.997219i
\(275\) −1.72869e8 + 2.99418e8i −0.501249 + 0.868188i
\(276\) 0 0
\(277\) −2.82900e8 4.89997e8i −0.799749 1.38521i −0.919779 0.392436i \(-0.871633\pi\)
0.120030 0.992770i \(-0.461701\pi\)
\(278\) 1.51035e8 0.421621
\(279\) 0 0
\(280\) 8.28863e6 0.0225647
\(281\) 1.99775e8 + 3.46020e8i 0.537117 + 0.930314i 0.999058 + 0.0434033i \(0.0138200\pi\)
−0.461940 + 0.886911i \(0.652847\pi\)
\(282\) 0 0
\(283\) −3.39361e8 + 5.87791e8i −0.890040 + 1.54160i −0.0502152 + 0.998738i \(0.515991\pi\)
−0.839825 + 0.542857i \(0.817343\pi\)
\(284\) 1.16504e8 2.01791e8i 0.301806 0.522743i
\(285\) 0 0
\(286\) 1.28209e8 + 2.22064e8i 0.324069 + 0.561303i
\(287\) −7.59851e7 −0.189732
\(288\) 0 0
\(289\) −2.35541e8 −0.574017
\(290\) 6.68023e6 + 1.15705e7i 0.0160842 + 0.0278586i
\(291\) 0 0
\(292\) 1.77619e8 3.07645e8i 0.417494 0.723120i
\(293\) 5.58695e7 9.67688e7i 0.129759 0.224750i −0.793824 0.608148i \(-0.791913\pi\)
0.923583 + 0.383398i \(0.125246\pi\)
\(294\) 0 0
\(295\) −4.57847e6 7.93014e6i −0.0103835 0.0179847i
\(296\) 6.22242e7 0.139456
\(297\) 0 0
\(298\) −2.30798e8 −0.505214
\(299\) 2.37677e8 + 4.11669e8i 0.514207 + 0.890633i
\(300\) 0 0
\(301\) −5.41042e8 + 9.37112e8i −1.14353 + 1.98065i
\(302\) −1.43813e8 + 2.49092e8i −0.300451 + 0.520397i
\(303\) 0 0
\(304\) −2.76616e7 4.79112e7i −0.0564702 0.0978092i
\(305\) 2.77731e7 0.0560500
\(306\) 0 0
\(307\) −1.53022e8 −0.301835 −0.150917 0.988546i \(-0.548223\pi\)
−0.150917 + 0.988546i \(0.548223\pi\)
\(308\) 2.04180e8 + 3.53651e8i 0.398186 + 0.689679i
\(309\) 0 0
\(310\) −6.24676e6 + 1.08197e7i −0.0119094 + 0.0206276i
\(311\) −1.14184e8 + 1.97772e8i −0.215250 + 0.372825i −0.953350 0.301867i \(-0.902390\pi\)
0.738100 + 0.674692i \(0.235723\pi\)
\(312\) 0 0
\(313\) 3.51372e8 + 6.08594e8i 0.647682 + 1.12182i 0.983675 + 0.179954i \(0.0575950\pi\)
−0.335993 + 0.941865i \(0.609072\pi\)
\(314\) 4.62472e8 0.843008
\(315\) 0 0
\(316\) −1.30967e8 −0.233484
\(317\) −5.20588e8 9.01686e8i −0.917883 1.58982i −0.802625 0.596484i \(-0.796564\pi\)
−0.115257 0.993336i \(-0.536769\pi\)
\(318\) 0 0
\(319\) −3.29118e8 + 5.70050e8i −0.567655 + 0.983208i
\(320\) 1.47408e6 2.55318e6i 0.00251475 0.00435568i
\(321\) 0 0
\(322\) 3.78515e8 + 6.55607e8i 0.631811 + 1.09433i
\(323\) −1.78572e8 −0.294853
\(324\) 0 0
\(325\) 5.64005e8 0.911363
\(326\) 1.29414e8 + 2.24152e8i 0.206881 + 0.358328i
\(327\) 0 0
\(328\) −1.35134e7 + 2.34060e7i −0.0211450 + 0.0366242i
\(329\) 7.07926e8 1.22616e9i 1.09598 1.89829i
\(330\) 0 0
\(331\) −1.60638e8 2.78233e8i −0.243472 0.421706i 0.718229 0.695807i \(-0.244953\pi\)
−0.961701 + 0.274101i \(0.911620\pi\)
\(332\) −6.56970e8 −0.985286
\(333\) 0 0
\(334\) −6.94196e8 −1.01946
\(335\) 1.94270e7 + 3.36485e7i 0.0282324 + 0.0489000i
\(336\) 0 0
\(337\) 4.56823e8 7.91241e8i 0.650194 1.12617i −0.332881 0.942969i \(-0.608021\pi\)
0.983075 0.183201i \(-0.0586459\pi\)
\(338\) −4.18462e7 + 7.24797e7i −0.0589450 + 0.102096i
\(339\) 0 0
\(340\) −4.75804e6 8.24116e6i −0.00656525 0.0113714i
\(341\) −6.15525e8 −0.840631
\(342\) 0 0
\(343\) 6.11754e8 0.818554
\(344\) 1.92441e8 + 3.33318e8i 0.254885 + 0.441473i
\(345\) 0 0
\(346\) 4.30895e7 7.46331e7i 0.0559248 0.0968646i
\(347\) −2.98992e8 + 5.17869e8i −0.384155 + 0.665376i −0.991652 0.128946i \(-0.958841\pi\)
0.607497 + 0.794322i \(0.292174\pi\)
\(348\) 0 0
\(349\) −3.25273e8 5.63390e8i −0.409599 0.709447i 0.585245 0.810856i \(-0.300998\pi\)
−0.994845 + 0.101409i \(0.967665\pi\)
\(350\) 8.98212e8 1.11980
\(351\) 0 0
\(352\) 1.45248e8 0.177506
\(353\) −3.08623e7 5.34551e7i −0.0373437 0.0646811i 0.846750 0.531992i \(-0.178556\pi\)
−0.884093 + 0.467311i \(0.845223\pi\)
\(354\) 0 0
\(355\) −2.04726e7 + 3.54595e7i −0.0242869 + 0.0420662i
\(356\) 2.59960e8 4.50264e8i 0.305373 0.528922i
\(357\) 0 0
\(358\) 1.44470e8 + 2.50229e8i 0.166413 + 0.288235i
\(359\) −1.70542e9 −1.94537 −0.972683 0.232137i \(-0.925428\pi\)
−0.972683 + 0.232137i \(0.925428\pi\)
\(360\) 0 0
\(361\) −7.11443e8 −0.795912
\(362\) 1.11247e8 + 1.92686e8i 0.123256 + 0.213486i
\(363\) 0 0
\(364\) 3.33080e8 5.76912e8i 0.361988 0.626982i
\(365\) −3.12119e7 + 5.40606e7i −0.0335966 + 0.0581910i
\(366\) 0 0
\(367\) −1.21509e8 2.10460e8i −0.128315 0.222248i 0.794709 0.606991i \(-0.207624\pi\)
−0.923024 + 0.384743i \(0.874290\pi\)
\(368\) 2.69265e8 0.281652
\(369\) 0 0
\(370\) −1.09343e7 −0.0112223
\(371\) −4.47501e8 7.75095e8i −0.454973 0.788037i
\(372\) 0 0
\(373\) 3.29270e8 5.70313e8i 0.328528 0.569026i −0.653692 0.756760i \(-0.726781\pi\)
0.982220 + 0.187734i \(0.0601143\pi\)
\(374\) 2.34417e8 4.06022e8i 0.231706 0.401327i
\(375\) 0 0
\(376\) −2.51800e8 4.36130e8i −0.244286 0.423115i
\(377\) 1.07379e9 1.03210
\(378\) 0 0
\(379\) 1.55665e7 0.0146877 0.00734387 0.999973i \(-0.497662\pi\)
0.00734387 + 0.999973i \(0.497662\pi\)
\(380\) 4.86079e6 + 8.41914e6i 0.00454427 + 0.00787091i
\(381\) 0 0
\(382\) 3.78501e8 6.55584e8i 0.347413 0.601737i
\(383\) −4.33940e8 + 7.51606e8i −0.394670 + 0.683588i −0.993059 0.117617i \(-0.962474\pi\)
0.598389 + 0.801206i \(0.295808\pi\)
\(384\) 0 0
\(385\) −3.58793e7 6.21448e7i −0.0320429 0.0554999i
\(386\) 9.77784e8 0.865342
\(387\) 0 0
\(388\) −8.50765e8 −0.739432
\(389\) −8.92558e8 1.54596e9i −0.768799 1.33160i −0.938215 0.346054i \(-0.887521\pi\)
0.169416 0.985545i \(-0.445812\pi\)
\(390\) 0 0
\(391\) 4.34568e8 7.52694e8i 0.367654 0.636795i
\(392\) 3.19623e8 5.53604e8i 0.268002 0.464192i
\(393\) 0 0
\(394\) 5.51070e8 + 9.54481e8i 0.453910 + 0.786196i
\(395\) 2.30140e7 0.0187890
\(396\) 0 0
\(397\) 1.49554e9 1.19958 0.599792 0.800156i \(-0.295250\pi\)
0.599792 + 0.800156i \(0.295250\pi\)
\(398\) −6.50586e8 1.12685e9i −0.517266 0.895931i
\(399\) 0 0
\(400\) 1.59741e8 2.76679e8i 0.124798 0.216156i
\(401\) −5.21084e8 + 9.02543e8i −0.403554 + 0.698977i −0.994152 0.107989i \(-0.965559\pi\)
0.590598 + 0.806966i \(0.298892\pi\)
\(402\) 0 0
\(403\) 5.02055e8 + 8.69585e8i 0.382106 + 0.661827i
\(404\) 8.55458e8 0.645452
\(405\) 0 0
\(406\) 1.71007e9 1.26815
\(407\) −2.69352e8 4.66532e8i −0.198034 0.343005i
\(408\) 0 0
\(409\) −6.94223e8 + 1.20243e9i −0.501727 + 0.869017i 0.498271 + 0.867021i \(0.333968\pi\)
−0.999998 + 0.00199527i \(0.999365\pi\)
\(410\) 2.37463e6 4.11298e6i 0.00170158 0.00294722i
\(411\) 0 0
\(412\) −4.33033e8 7.50035e8i −0.305057 0.528374i
\(413\) −1.17204e9 −0.818685
\(414\) 0 0
\(415\) 1.15445e8 0.0792880
\(416\) −1.18472e8 2.05200e8i −0.0806845 0.139750i
\(417\) 0 0
\(418\) −2.39479e8 + 4.14790e8i −0.160380 + 0.277787i
\(419\) −5.35466e8 + 9.27454e8i −0.355617 + 0.615947i −0.987223 0.159342i \(-0.949063\pi\)
0.631606 + 0.775289i \(0.282396\pi\)
\(420\) 0 0
\(421\) −3.33942e8 5.78405e8i −0.218114 0.377785i 0.736117 0.676854i \(-0.236657\pi\)
−0.954231 + 0.299069i \(0.903324\pi\)
\(422\) 1.24462e9 0.806203
\(423\) 0 0
\(424\) −3.18341e8 −0.202820
\(425\) −5.15613e8 8.93068e8i −0.325809 0.564317i
\(426\) 0 0
\(427\) 1.77741e9 3.07856e9i 1.10481 1.91359i
\(428\) −6.06561e8 + 1.05059e9i −0.373957 + 0.647712i
\(429\) 0 0
\(430\) −3.38165e7 5.85719e7i −0.0205111 0.0355263i
\(431\) 8.88266e8 0.534408 0.267204 0.963640i \(-0.413900\pi\)
0.267204 + 0.963640i \(0.413900\pi\)
\(432\) 0 0
\(433\) 1.04197e9 0.616806 0.308403 0.951256i \(-0.400205\pi\)
0.308403 + 0.951256i \(0.400205\pi\)
\(434\) 7.99552e8 + 1.38487e9i 0.469497 + 0.813193i
\(435\) 0 0
\(436\) 4.26421e8 7.38583e8i 0.246397 0.426772i
\(437\) −4.43953e8 + 7.68949e8i −0.254479 + 0.440771i
\(438\) 0 0
\(439\) −1.36180e9 2.35870e9i −0.768223 1.33060i −0.938526 0.345209i \(-0.887808\pi\)
0.170303 0.985392i \(-0.445525\pi\)
\(440\) −2.55236e7 −0.0142842
\(441\) 0 0
\(442\) −7.64811e8 −0.421285
\(443\) 7.09330e8 + 1.22860e9i 0.387646 + 0.671422i 0.992132 0.125193i \(-0.0399550\pi\)
−0.604487 + 0.796615i \(0.706622\pi\)
\(444\) 0 0
\(445\) −4.56811e7 + 7.91220e7i −0.0245740 + 0.0425635i
\(446\) −4.95771e8 + 8.58701e8i −0.264612 + 0.458321i
\(447\) 0 0
\(448\) −1.88674e8 3.26793e8i −0.0991378 0.171712i
\(449\) 3.79133e9 1.97665 0.988324 0.152368i \(-0.0486899\pi\)
0.988324 + 0.152368i \(0.0486899\pi\)
\(450\) 0 0
\(451\) 2.33984e8 0.120107
\(452\) 6.53656e8 + 1.13217e9i 0.332939 + 0.576667i
\(453\) 0 0
\(454\) 5.50816e8 9.54042e8i 0.276256 0.478489i
\(455\) −5.85301e7 + 1.01377e8i −0.0291299 + 0.0504545i
\(456\) 0 0
\(457\) −9.36482e8 1.62204e9i −0.458979 0.794975i 0.539928 0.841711i \(-0.318451\pi\)
−0.998907 + 0.0467359i \(0.985118\pi\)
\(458\) −1.88097e9 −0.914854
\(459\) 0 0
\(460\) −4.73163e7 −0.0226651
\(461\) 2.73697e8 + 4.74057e8i 0.130112 + 0.225360i 0.923719 0.383070i \(-0.125133\pi\)
−0.793608 + 0.608430i \(0.791800\pi\)
\(462\) 0 0
\(463\) 5.61388e8 9.72353e8i 0.262863 0.455292i −0.704138 0.710063i \(-0.748667\pi\)
0.967002 + 0.254770i \(0.0819999\pi\)
\(464\) 3.04124e8 5.26758e8i 0.141331 0.244793i
\(465\) 0 0
\(466\) 5.76156e8 + 9.97931e8i 0.263748 + 0.456825i
\(467\) −2.32612e9 −1.05687 −0.528436 0.848973i \(-0.677221\pi\)
−0.528436 + 0.848973i \(0.677221\pi\)
\(468\) 0 0
\(469\) 4.97310e9 2.22599
\(470\) 4.42472e7 + 7.66384e7i 0.0196582 + 0.0340489i
\(471\) 0 0
\(472\) −2.08439e8 + 3.61028e8i −0.0912395 + 0.158031i
\(473\) 1.66606e9 2.88570e9i 0.723895 1.25382i
\(474\) 0 0
\(475\) 5.26748e8 + 9.12355e8i 0.225515 + 0.390603i
\(476\) −1.21801e9 −0.517637
\(477\) 0 0
\(478\) 5.85109e8 0.245041
\(479\) −8.84067e8 1.53125e9i −0.367545 0.636607i 0.621636 0.783306i \(-0.286468\pi\)
−0.989181 + 0.146699i \(0.953135\pi\)
\(480\) 0 0
\(481\) −4.39396e8 + 7.61056e8i −0.180031 + 0.311823i
\(482\) −4.91359e8 + 8.51059e8i −0.199864 + 0.346174i
\(483\) 0 0
\(484\) −5.15268e6 8.92471e6i −0.00206573 0.00357796i
\(485\) 1.49500e8 0.0595037
\(486\) 0 0
\(487\) −1.97414e9 −0.774509 −0.387254 0.921973i \(-0.626577\pi\)
−0.387254 + 0.921973i \(0.626577\pi\)
\(488\) −6.32200e8 1.09500e9i −0.246255 0.426526i
\(489\) 0 0
\(490\) −5.61654e7 + 9.72813e7i −0.0215666 + 0.0373545i
\(491\) −1.75190e9 + 3.03438e9i −0.667920 + 1.15687i 0.310564 + 0.950552i \(0.399482\pi\)
−0.978485 + 0.206320i \(0.933851\pi\)
\(492\) 0 0
\(493\) −9.81654e8 1.70027e9i −0.368973 0.639079i
\(494\) 7.81328e8 0.291601
\(495\) 0 0
\(496\) 5.68780e8 0.209295
\(497\) 2.62038e9 + 4.53863e9i 0.957452 + 1.65836i
\(498\) 0 0
\(499\) −4.37327e8 + 7.57473e8i −0.157563 + 0.272907i −0.933989 0.357301i \(-0.883697\pi\)
0.776426 + 0.630208i \(0.217030\pi\)
\(500\) −5.61861e7 + 9.73171e7i −0.0201017 + 0.0348172i
\(501\) 0 0
\(502\) −2.92139e8 5.06000e8i −0.103069 0.178520i
\(503\) 2.61478e9 0.916111 0.458055 0.888924i \(-0.348546\pi\)
0.458055 + 0.888924i \(0.348546\pi\)
\(504\) 0 0
\(505\) −1.50324e8 −0.0519409
\(506\) −1.16558e9 2.01884e9i −0.399959 0.692748i
\(507\) 0 0
\(508\) −3.64306e8 + 6.30997e8i −0.123294 + 0.213552i
\(509\) 4.26286e8 7.38349e8i 0.143281 0.248170i −0.785449 0.618926i \(-0.787568\pi\)
0.928730 + 0.370756i \(0.120901\pi\)
\(510\) 0 0
\(511\) 3.99496e9 + 6.91947e9i 1.32446 + 2.29403i
\(512\) −1.34218e8 −0.0441942
\(513\) 0 0
\(514\) 1.07197e9 0.348185
\(515\) 7.60942e7 + 1.31799e8i 0.0245486 + 0.0425194i
\(516\) 0 0
\(517\) −2.17995e9 + 3.77578e9i −0.693793 + 1.20168i
\(518\) −6.99764e8 + 1.21203e9i −0.221206 + 0.383140i
\(519\) 0 0
\(520\) 2.08184e7 + 3.60585e7i 0.00649285 + 0.0112459i
\(521\) 2.66940e9 0.826954 0.413477 0.910515i \(-0.364314\pi\)
0.413477 + 0.910515i \(0.364314\pi\)
\(522\) 0 0
\(523\) −4.41770e9 −1.35033 −0.675165 0.737667i \(-0.735928\pi\)
−0.675165 + 0.737667i \(0.735928\pi\)
\(524\) 1.69017e8 + 2.92747e8i 0.0513182 + 0.0888858i
\(525\) 0 0
\(526\) −1.52052e9 + 2.63362e9i −0.455556 + 0.789046i
\(527\) 9.17956e8 1.58995e9i 0.273203 0.473201i
\(528\) 0 0
\(529\) −4.58369e8 7.93919e8i −0.134623 0.233175i
\(530\) 5.59400e7 0.0163214
\(531\) 0 0
\(532\) 1.24431e9 0.358293
\(533\) −1.90850e8 3.30562e8i −0.0545943 0.0945601i
\(534\) 0 0
\(535\) 1.06587e8 1.84614e8i 0.0300931 0.0521228i
\(536\) 8.84433e8 1.53188e9i 0.248078 0.429684i
\(537\) 0 0
\(538\) −2.23074e9 3.86375e9i −0.617605 1.06972i
\(539\) −5.53426e9 −1.52230
\(540\) 0 0
\(541\) −3.86240e9 −1.04874 −0.524368 0.851492i \(-0.675699\pi\)
−0.524368 + 0.851492i \(0.675699\pi\)
\(542\) −3.86317e8 6.69121e8i −0.104219 0.180513i
\(543\) 0 0
\(544\) −2.16614e8 + 3.75187e8i −0.0576888 + 0.0999199i
\(545\) −7.49323e7 + 1.29786e8i −0.0198281 + 0.0343433i
\(546\) 0 0
\(547\) 1.08461e9 + 1.87859e9i 0.283346 + 0.490769i 0.972207 0.234124i \(-0.0752223\pi\)
−0.688861 + 0.724894i \(0.741889\pi\)
\(548\) −3.13673e9 −0.814226
\(549\) 0 0
\(550\) −2.76591e9 −0.708873
\(551\) 1.00285e9 + 1.73699e9i 0.255392 + 0.442352i
\(552\) 0 0
\(553\) 1.47284e9 2.55103e9i 0.370354 0.641472i
\(554\) 2.26320e9 3.91998e9i 0.565508 0.979489i
\(555\) 0 0
\(556\) 6.04142e8 + 1.04640e9i 0.149066 + 0.258189i
\(557\) −2.25645e8 −0.0553265 −0.0276632 0.999617i \(-0.508807\pi\)
−0.0276632 + 0.999617i \(0.508807\pi\)
\(558\) 0 0
\(559\) −5.43570e9 −1.31618
\(560\) 3.31545e7 + 5.74253e7i 0.00797783 + 0.0138180i
\(561\) 0 0
\(562\) −1.59820e9 + 2.76816e9i −0.379799 + 0.657831i
\(563\) 3.90401e8 6.76194e8i 0.0922001 0.159695i −0.816237 0.577718i \(-0.803943\pi\)
0.908437 + 0.418023i \(0.137277\pi\)
\(564\) 0 0
\(565\) −1.14863e8 1.98948e8i −0.0267923 0.0464056i
\(566\) −5.42978e9 −1.25871
\(567\) 0 0
\(568\) 1.86407e9 0.426818
\(569\) −3.34607e8 5.79557e8i −0.0761452 0.131887i 0.825439 0.564492i \(-0.190928\pi\)
−0.901584 + 0.432605i \(0.857595\pi\)
\(570\) 0 0
\(571\) 6.68261e8 1.15746e9i 0.150217 0.260184i −0.781090 0.624418i \(-0.785336\pi\)
0.931307 + 0.364235i \(0.118669\pi\)
\(572\) −1.02567e9 + 1.77651e9i −0.229151 + 0.396901i
\(573\) 0 0
\(574\) −3.03940e8 5.26440e8i −0.0670805 0.116187i
\(575\) −5.12751e9 −1.12478
\(576\) 0 0
\(577\) −7.13624e9 −1.54651 −0.773257 0.634092i \(-0.781374\pi\)
−0.773257 + 0.634092i \(0.781374\pi\)
\(578\) −9.42165e8 1.63188e9i −0.202946 0.351512i
\(579\) 0 0
\(580\) −5.34418e7 + 9.25639e7i −0.0113732 + 0.0196990i
\(581\) 7.38819e9 1.27967e10i 1.56287 2.70696i
\(582\) 0 0
\(583\) 1.37801e9 + 2.38679e9i 0.288014 + 0.498855i
\(584\) 2.84191e9 0.590425
\(585\) 0 0
\(586\) 8.93912e8 0.183507
\(587\) 1.42735e9 + 2.47224e9i 0.291271 + 0.504496i 0.974111 0.226072i \(-0.0725885\pi\)
−0.682839 + 0.730568i \(0.739255\pi\)
\(588\) 0 0
\(589\) −9.37781e8 + 1.62428e9i −0.189103 + 0.327535i
\(590\) 3.66277e7 6.34411e7i 0.00734223 0.0127171i
\(591\) 0 0
\(592\) 2.48897e8 + 4.31102e8i 0.0493052 + 0.0853992i
\(593\) 6.55017e9 1.28991 0.644957 0.764219i \(-0.276875\pi\)
0.644957 + 0.764219i \(0.276875\pi\)
\(594\) 0 0
\(595\) 2.14033e8 0.0416553
\(596\) −9.23192e8 1.59902e9i −0.178620 0.309379i
\(597\) 0 0
\(598\) −1.90142e9 + 3.29335e9i −0.363599 + 0.629773i
\(599\) −3.75708e9 + 6.50744e9i −0.714259 + 1.23713i 0.248985 + 0.968507i \(0.419903\pi\)
−0.963244 + 0.268626i \(0.913430\pi\)
\(600\) 0 0
\(601\) 1.70371e9 + 2.95092e9i 0.320137 + 0.554493i 0.980516 0.196439i \(-0.0629378\pi\)
−0.660379 + 0.750932i \(0.729604\pi\)
\(602\) −8.65667e9 −1.61720
\(603\) 0 0
\(604\) −2.30101e9 −0.424902
\(605\) 905448. + 1.56828e6i 0.000166234 + 0.000287926i
\(606\) 0 0
\(607\) −2.47151e9 + 4.28078e9i −0.448540 + 0.776895i −0.998291 0.0584338i \(-0.981389\pi\)
0.549751 + 0.835329i \(0.314723\pi\)
\(608\) 2.21292e8 3.83290e8i 0.0399304 0.0691616i
\(609\) 0 0
\(610\) 1.11093e8 + 1.92418e8i 0.0198167 + 0.0343235i
\(611\) 7.11233e9 1.26144
\(612\) 0 0
\(613\) 4.05250e9 0.710577 0.355288 0.934757i \(-0.384383\pi\)
0.355288 + 0.934757i \(0.384383\pi\)
\(614\) −6.12087e8 1.06017e9i −0.106715 0.184835i
\(615\) 0 0
\(616\) −1.63344e9 + 2.82920e9i −0.281560 + 0.487676i
\(617\) 3.07794e9 5.33115e9i 0.527549 0.913741i −0.471936 0.881633i \(-0.656445\pi\)
0.999484 0.0321082i \(-0.0102221\pi\)
\(618\) 0 0
\(619\) −1.82063e8 3.15342e8i −0.0308534 0.0534397i 0.850186 0.526482i \(-0.176489\pi\)
−0.881040 + 0.473042i \(0.843156\pi\)
\(620\) −9.99482e7 −0.0168424
\(621\) 0 0
\(622\) −1.82694e9 −0.304410
\(623\) 5.84694e9 + 1.01272e10i 0.968770 + 1.67796i
\(624\) 0 0
\(625\) −3.03694e9 + 5.26014e9i −0.497573 + 0.861822i
\(626\) −2.81098e9 + 4.86875e9i −0.457981 + 0.793246i
\(627\) 0 0
\(628\) 1.84989e9 + 3.20410e9i 0.298048 + 0.516235i
\(629\) 1.60678e9 0.257442
\(630\) 0 0
\(631\) 3.22087e9 0.510353 0.255177 0.966894i \(-0.417866\pi\)
0.255177 + 0.966894i \(0.417866\pi\)
\(632\) −5.23869e8 9.07368e8i −0.0825492 0.142979i
\(633\) 0 0
\(634\) 4.16471e9 7.21349e9i 0.649041 1.12417i
\(635\) 6.40172e7 1.10881e8i 0.00992176 0.0171850i
\(636\) 0 0
\(637\) 4.51404e9 + 7.81855e9i 0.691954 + 1.19850i
\(638\) −5.26590e9 −0.802786
\(639\) 0 0
\(640\) 2.35852e7 0.00355640
\(641\) −6.22206e9 1.07769e10i −0.933106 1.61619i −0.777978 0.628292i \(-0.783754\pi\)
−0.155128 0.987894i \(-0.549579\pi\)
\(642\) 0 0
\(643\) 2.41505e8 4.18298e8i 0.0358251 0.0620509i −0.847557 0.530704i \(-0.821927\pi\)
0.883382 + 0.468654i \(0.155261\pi\)
\(644\) −3.02812e9 + 5.24485e9i −0.446758 + 0.773808i
\(645\) 0 0
\(646\) −7.14289e8 1.23719e9i −0.104246 0.180560i
\(647\) −4.60241e9 −0.668068 −0.334034 0.942561i \(-0.608410\pi\)
−0.334034 + 0.942561i \(0.608410\pi\)
\(648\) 0 0
\(649\) 3.60912e9 0.518256
\(650\) 2.25602e9 + 3.90754e9i 0.322215 + 0.558094i
\(651\) 0 0
\(652\) −1.03531e9 + 1.79322e9i −0.146287 + 0.253376i
\(653\) 2.84182e9 4.92218e9i 0.399393 0.691769i −0.594258 0.804275i \(-0.702554\pi\)
0.993651 + 0.112505i \(0.0358875\pi\)
\(654\) 0 0
\(655\) −2.97003e7 5.14425e7i −0.00412969 0.00715282i
\(656\) −2.16215e8 −0.0299035
\(657\) 0 0
\(658\) 1.13268e10 1.54995
\(659\) 2.25571e9 + 3.90700e9i 0.307032 + 0.531796i 0.977712 0.209952i \(-0.0673307\pi\)
−0.670679 + 0.741747i \(0.733997\pi\)
\(660\) 0 0
\(661\) −4.88093e8 + 8.45401e8i −0.0657351 + 0.113856i −0.897020 0.441990i \(-0.854273\pi\)
0.831285 + 0.555847i \(0.187606\pi\)
\(662\) 1.28510e9 2.22586e9i 0.172161 0.298191i
\(663\) 0 0
\(664\) −2.62788e9 4.55162e9i −0.348351 0.603362i
\(665\) −2.18655e8 −0.0288326
\(666\) 0 0
\(667\) −9.76206e9 −1.27380
\(668\) −2.77678e9 4.80953e9i −0.360433 0.624288i
\(669\) 0 0
\(670\) −1.55416e8 + 2.69188e8i −0.0199634 + 0.0345775i
\(671\) −5.47326e9 + 9.47996e9i −0.699386 + 1.21137i
\(672\) 0 0
\(673\) −6.26231e9 1.08466e10i −0.791921 1.37165i −0.924776 0.380513i \(-0.875748\pi\)
0.132854 0.991136i \(-0.457586\pi\)
\(674\) 7.30917e9 0.919514
\(675\) 0 0
\(676\) −6.69539e8 −0.0833608
\(677\) 5.22456e9 + 9.04920e9i 0.647126 + 1.12086i 0.983806 + 0.179237i \(0.0573627\pi\)
−0.336680 + 0.941619i \(0.609304\pi\)
\(678\) 0 0
\(679\) 9.56758e9 1.65715e10i 1.17289 2.03151i
\(680\) 3.80643e7 6.59293e7i 0.00464234 0.00804076i
\(681\) 0 0
\(682\) −2.46210e9 4.26448e9i −0.297208 0.514779i
\(683\) −1.12280e9 −0.134844 −0.0674218 0.997725i \(-0.521477\pi\)
−0.0674218 + 0.997725i \(0.521477\pi\)
\(684\) 0 0
\(685\) 5.51197e8 0.0655225
\(686\) 2.44702e9 + 4.23836e9i 0.289403 + 0.501260i
\(687\) 0 0
\(688\) −1.53953e9 + 2.66655e9i −0.180231 + 0.312169i
\(689\) 2.24796e9 3.89358e9i 0.261831 0.453505i
\(690\) 0 0
\(691\) −3.73022e9 6.46092e9i −0.430091 0.744940i 0.566789 0.823863i \(-0.308185\pi\)
−0.996881 + 0.0789226i \(0.974852\pi\)
\(692\) 6.89431e8 0.0790897
\(693\) 0 0
\(694\) −4.78387e9 −0.543277
\(695\) −1.06162e8 1.83878e8i −0.0119956 0.0207770i
\(696\) 0 0
\(697\) −3.48950e8 + 6.04399e8i −0.0390345 + 0.0676097i
\(698\) 2.60219e9 4.50712e9i 0.289631 0.501655i
\(699\) 0 0
\(700\) 3.59285e9 + 6.22299e9i 0.395909 + 0.685735i
\(701\) 1.79013e10 1.96278 0.981392 0.192014i \(-0.0615020\pi\)
0.981392 + 0.192014i \(0.0615020\pi\)
\(702\) 0 0
\(703\) −1.64148e9 −0.178194
\(704\) 5.80993e8 + 1.00631e9i 0.0627577 + 0.108700i
\(705\) 0 0
\(706\) 2.46898e8 4.27641e8i 0.0264060 0.0457365i
\(707\) −9.62036e9 + 1.66630e10i −1.02382 + 1.77331i
\(708\) 0 0
\(709\) −3.77521e9 6.53885e9i −0.397813 0.689032i 0.595643 0.803249i \(-0.296897\pi\)
−0.993456 + 0.114217i \(0.963564\pi\)
\(710\) −3.27561e8 −0.0343469
\(711\) 0 0
\(712\) 4.15936e9 0.431863
\(713\) −4.56431e9 7.90562e9i −0.471587 0.816812i
\(714\) 0 0
\(715\) 1.80235e8 3.12176e8i 0.0184403 0.0319395i
\(716\) −1.15576e9 + 2.00183e9i −0.117672 + 0.203813i
\(717\) 0 0
\(718\) −6.82169e9 1.18155e10i −0.687791 1.19129i
\(719\) 3.79868e9 0.381137 0.190569 0.981674i \(-0.438967\pi\)
0.190569 + 0.981674i \(0.438967\pi\)
\(720\) 0 0
\(721\) 1.94793e10 1.93553
\(722\) −2.84577e9 4.92902e9i −0.281397 0.487394i
\(723\) 0 0
\(724\) −8.89976e8 + 1.54148e9i −0.0871552 + 0.150957i
\(725\) −5.79132e9 + 1.00309e10i −0.564409 + 0.977586i
\(726\) 0 0
\(727\) 1.96762e9 + 3.40802e9i 0.189920 + 0.328952i 0.945224 0.326424i \(-0.105844\pi\)
−0.755303 + 0.655376i \(0.772510\pi\)
\(728\) 5.32929e9 0.511928
\(729\) 0 0
\(730\) −4.99390e8 −0.0475127
\(731\) 4.96931e9 + 8.60710e9i 0.470528 + 0.814978i
\(732\) 0 0
\(733\) 5.67457e9 9.82865e9i 0.532193 0.921785i −0.467100 0.884204i \(-0.654701\pi\)
0.999294 0.0375812i \(-0.0119653\pi\)
\(734\) 9.72073e8 1.68368e9i 0.0907325 0.157153i
\(735\) 0 0
\(736\) 1.07706e9 + 1.86552e9i 0.0995791 + 0.172476i
\(737\) −1.53139e10 −1.40913
\(738\) 0 0
\(739\) 1.61420e10 1.47130 0.735652 0.677359i \(-0.236876\pi\)
0.735652 + 0.677359i \(0.236876\pi\)
\(740\) −4.37370e7 7.57548e7i −0.00396770 0.00687225i
\(741\) 0 0
\(742\) 3.58001e9 6.20076e9i 0.321715 0.557226i
\(743\) −2.96574e9 + 5.13681e9i −0.265260 + 0.459444i −0.967632 0.252366i \(-0.918791\pi\)
0.702371 + 0.711811i \(0.252125\pi\)
\(744\) 0 0
\(745\) 1.62227e8 + 2.80985e8i 0.0143739 + 0.0248964i
\(746\) 5.26833e9 0.464608
\(747\) 0 0
\(748\) 3.75067e9 0.327682
\(749\) −1.36426e10 2.36297e10i −1.18634 2.05481i
\(750\) 0 0
\(751\) 1.67463e9 2.90054e9i 0.144271 0.249885i −0.784830 0.619711i \(-0.787250\pi\)
0.929101 + 0.369827i \(0.120583\pi\)
\(752\) 2.01440e9 3.48904e9i 0.172736 0.299187i
\(753\) 0 0
\(754\) 4.29514e9 + 7.43941e9i 0.364903 + 0.632031i
\(755\) 4.04342e8 0.0341928
\(756\) 0 0
\(757\) −3.71611e9 −0.311353 −0.155677 0.987808i \(-0.549756\pi\)
−0.155677 + 0.987808i \(0.549756\pi\)
\(758\) 6.22661e7 + 1.07848e8i 0.00519290 + 0.00899436i
\(759\) 0 0
\(760\) −3.88863e7 + 6.73531e7i −0.00321329 + 0.00556557i
\(761\) 7.21722e8 1.25006e9i 0.0593641 0.102822i −0.834816 0.550529i \(-0.814426\pi\)
0.894180 + 0.447707i \(0.147759\pi\)
\(762\) 0 0
\(763\) 9.59093e9 + 1.66120e10i 0.781673 + 1.35390i
\(764\) 6.05602e9 0.491316
\(765\) 0 0
\(766\) −6.94304e9 −0.558148
\(767\) −2.94379e9 5.09879e9i −0.235572 0.408022i
\(768\) 0 0
\(769\) −5.12495e9 + 8.87668e9i −0.406394 + 0.703895i −0.994483 0.104901i \(-0.966547\pi\)
0.588088 + 0.808797i \(0.299881\pi\)
\(770\) 2.87034e8 4.97158e8i 0.0226577 0.0392443i
\(771\) 0 0
\(772\) 3.91114e9 + 6.77429e9i 0.305944 + 0.529911i
\(773\) 2.47581e10 1.92792 0.963959 0.266049i \(-0.0857185\pi\)
0.963959 + 0.266049i \(0.0857185\pi\)
\(774\)