Properties

Label 99.8.j.a.8.7
Level $99$
Weight $8$
Character 99.8
Analytic conductor $30.926$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,8,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.9261175229\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 8.7
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.3691 + 8.26015i) q^{2} +(21.4727 - 66.0862i) q^{4} +(-96.0085 + 132.144i) q^{5} +(553.787 + 179.936i) q^{7} +(-254.099 - 782.037i) q^{8} +O(q^{10})\) \(q+(-11.3691 + 8.26015i) q^{2} +(21.4727 - 66.0862i) q^{4} +(-96.0085 + 132.144i) q^{5} +(553.787 + 179.936i) q^{7} +(-254.099 - 782.037i) q^{8} -2295.41i q^{10} +(-941.608 + 4312.84i) q^{11} +(2811.59 + 3869.82i) q^{13} +(-7782.37 + 2528.65i) q^{14} +(16544.3 + 12020.1i) q^{16} +(-8274.08 - 6011.47i) q^{17} +(15935.6 - 5177.79i) q^{19} +(6671.35 + 9182.33i) q^{20} +(-24919.4 - 56811.0i) q^{22} +96735.9i q^{23} +(15897.5 + 48927.3i) q^{25} +(-63930.7 - 20772.3i) q^{26} +(23782.6 - 32733.9i) q^{28} +(-59666.6 + 183635. i) q^{29} +(-19373.3 + 14075.5i) q^{31} -182130. q^{32} +143725. q^{34} +(-76945.8 + 55904.4i) q^{35} +(51007.7 - 156985. i) q^{37} +(-138405. + 190498. i) q^{38} +(127737. + 41504.4i) q^{40} +(-153264. - 471699. i) q^{41} -644342. i q^{43} +(264800. + 154835. i) q^{44} +(-799053. - 1.09980e6i) q^{46} +(-37230.0 + 12096.8i) q^{47} +(-391957. - 284774. i) q^{49} +(-584887. - 424945. i) q^{50} +(316114. - 102712. i) q^{52} +(-909358. - 1.25162e6i) q^{53} +(-479515. - 538497. i) q^{55} -478804. i q^{56} +(-838496. - 2.58062e6i) q^{58} +(998790. + 324527. i) q^{59} +(-549479. + 756292. i) q^{61} +(103991. - 320053. i) q^{62} +(-47008.8 + 34153.9i) q^{64} -781312. q^{65} -1.07170e6 q^{67} +(-574942. + 417720. i) q^{68} +(413028. - 1.27117e6i) q^{70} +(102165. - 140618. i) q^{71} +(-317538. - 103174. i) q^{73} +(716811. + 2.20612e6i) q^{74} -1.16430e6i q^{76} +(-1.29749e6 + 2.21896e6i) q^{77} +(661388. + 910322. i) q^{79} +(-3.17679e6 + 1.03220e6i) q^{80} +(5.63879e6 + 4.09682e6i) q^{82} +(-6.31646e6 - 4.58918e6i) q^{83} +(1.58876e6 - 516221. i) q^{85} +(5.32236e6 + 7.32560e6i) q^{86} +(3.61206e6 - 359516. i) q^{88} -4.24767e6i q^{89} +(860701. + 2.64897e6i) q^{91} +(6.39290e6 + 2.07718e6i) q^{92} +(323351. - 445055. i) q^{94} +(-845738. + 2.60291e6i) q^{95} +(-6.98825e6 + 5.07726e6i) q^{97} +6.80849e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.3691 + 8.26015i −1.00490 + 0.730101i −0.963133 0.269026i \(-0.913298\pi\)
−0.0417652 + 0.999127i \(0.513298\pi\)
\(3\) 0 0
\(4\) 21.4727 66.0862i 0.167755 0.516298i
\(5\) −96.0085 + 132.144i −0.343490 + 0.472774i −0.945457 0.325747i \(-0.894384\pi\)
0.601966 + 0.798521i \(0.294384\pi\)
\(6\) 0 0
\(7\) 553.787 + 179.936i 0.610239 + 0.198279i 0.597802 0.801644i \(-0.296041\pi\)
0.0124370 + 0.999923i \(0.496041\pi\)
\(8\) −254.099 782.037i −0.175464 0.540023i
\(9\) 0 0
\(10\) 2295.41i 0.725873i
\(11\) −941.608 + 4312.84i −0.213302 + 0.976986i
\(12\) 0 0
\(13\) 2811.59 + 3869.82i 0.354936 + 0.488528i 0.948729 0.316090i \(-0.102370\pi\)
−0.593793 + 0.804618i \(0.702370\pi\)
\(14\) −7782.37 + 2528.65i −0.757991 + 0.246286i
\(15\) 0 0
\(16\) 16544.3 + 12020.1i 1.00978 + 0.733651i
\(17\) −8274.08 6011.47i −0.408459 0.296763i 0.364519 0.931196i \(-0.381234\pi\)
−0.772978 + 0.634433i \(0.781234\pi\)
\(18\) 0 0
\(19\) 15935.6 5177.79i 0.533005 0.173184i −0.0301344 0.999546i \(-0.509594\pi\)
0.563139 + 0.826362i \(0.309594\pi\)
\(20\) 6671.35 + 9182.33i 0.186470 + 0.256654i
\(21\) 0 0
\(22\) −24919.4 56811.0i −0.498952 1.13750i
\(23\) 96735.9i 1.65783i 0.559374 + 0.828915i \(0.311042\pi\)
−0.559374 + 0.828915i \(0.688958\pi\)
\(24\) 0 0
\(25\) 15897.5 + 48927.3i 0.203487 + 0.626270i
\(26\) −63930.7 20772.3i −0.713350 0.231781i
\(27\) 0 0
\(28\) 23782.6 32733.9i 0.204742 0.281803i
\(29\) −59666.6 + 183635.i −0.454295 + 1.39818i 0.417665 + 0.908601i \(0.362849\pi\)
−0.871960 + 0.489577i \(0.837151\pi\)
\(30\) 0 0
\(31\) −19373.3 + 14075.5i −0.116799 + 0.0848591i −0.644651 0.764477i \(-0.722997\pi\)
0.527853 + 0.849336i \(0.322997\pi\)
\(32\) −182130. −0.982556
\(33\) 0 0
\(34\) 143725. 0.627127
\(35\) −76945.8 + 55904.4i −0.303352 + 0.220398i
\(36\) 0 0
\(37\) 51007.7 156985.i 0.165550 0.509511i −0.833526 0.552480i \(-0.813682\pi\)
0.999076 + 0.0429690i \(0.0136817\pi\)
\(38\) −138405. + 190498.i −0.409174 + 0.563179i
\(39\) 0 0
\(40\) 127737. + 41504.4i 0.315579 + 0.102538i
\(41\) −153264. 471699.i −0.347294 1.06886i −0.960344 0.278817i \(-0.910058\pi\)
0.613050 0.790044i \(-0.289942\pi\)
\(42\) 0 0
\(43\) 644342.i 1.23588i −0.786225 0.617941i \(-0.787967\pi\)
0.786225 0.617941i \(-0.212033\pi\)
\(44\) 264800. + 154835.i 0.468634 + 0.274022i
\(45\) 0 0
\(46\) −799053. 1.09980e6i −1.21038 1.66595i
\(47\) −37230.0 + 12096.8i −0.0523059 + 0.0169952i −0.335053 0.942199i \(-0.608754\pi\)
0.282747 + 0.959194i \(0.408754\pi\)
\(48\) 0 0
\(49\) −391957. 284774.i −0.475940 0.345791i
\(50\) −584887. 424945.i −0.661724 0.480771i
\(51\) 0 0
\(52\) 316114. 102712.i 0.311769 0.101300i
\(53\) −909358. 1.25162e6i −0.839014 1.15480i −0.986178 0.165692i \(-0.947014\pi\)
0.147163 0.989112i \(-0.452986\pi\)
\(54\) 0 0
\(55\) −479515. 538497.i −0.388626 0.436429i
\(56\) 478804.i 0.364334i
\(57\) 0 0
\(58\) −838496. 2.58062e6i −0.564291 1.73671i
\(59\) 998790. + 324527.i 0.633129 + 0.205716i 0.607961 0.793967i \(-0.291988\pi\)
0.0251684 + 0.999683i \(0.491988\pi\)
\(60\) 0 0
\(61\) −549479. + 756292.i −0.309953 + 0.426614i −0.935367 0.353679i \(-0.884930\pi\)
0.625413 + 0.780294i \(0.284930\pi\)
\(62\) 103991. 320053.i 0.0554149 0.170550i
\(63\) 0 0
\(64\) −47008.8 + 34153.9i −0.0224155 + 0.0162858i
\(65\) −781312. −0.352881
\(66\) 0 0
\(67\) −1.07170e6 −0.435322 −0.217661 0.976024i \(-0.569843\pi\)
−0.217661 + 0.976024i \(0.569843\pi\)
\(68\) −574942. + 417720.i −0.221739 + 0.161103i
\(69\) 0 0
\(70\) 413028. 1.27117e6i 0.143925 0.442955i
\(71\) 102165. 140618.i 0.0338763 0.0466268i −0.791743 0.610855i \(-0.790826\pi\)
0.825619 + 0.564228i \(0.190826\pi\)
\(72\) 0 0
\(73\) −317538. 103174.i −0.0955357 0.0310414i 0.260859 0.965377i \(-0.415994\pi\)
−0.356395 + 0.934335i \(0.615994\pi\)
\(74\) 716811. + 2.20612e6i 0.205633 + 0.632875i
\(75\) 0 0
\(76\) 1.16430e6i 0.304242i
\(77\) −1.29749e6 + 2.21896e6i −0.323881 + 0.553901i
\(78\) 0 0
\(79\) 661388. + 910322.i 0.150925 + 0.207731i 0.877784 0.479056i \(-0.159021\pi\)
−0.726859 + 0.686786i \(0.759021\pi\)
\(80\) −3.17679e6 + 1.03220e6i −0.693703 + 0.225398i
\(81\) 0 0
\(82\) 5.63879e6 + 4.09682e6i 1.12937 + 0.820537i
\(83\) −6.31646e6 4.58918e6i −1.21255 0.880971i −0.217093 0.976151i \(-0.569657\pi\)
−0.995460 + 0.0951797i \(0.969657\pi\)
\(84\) 0 0
\(85\) 1.58876e6 516221.i 0.280604 0.0911736i
\(86\) 5.32236e6 + 7.32560e6i 0.902318 + 1.24193i
\(87\) 0 0
\(88\) 3.61206e6 359516.i 0.565022 0.0562379i
\(89\) 4.24767e6i 0.638683i −0.947640 0.319342i \(-0.896538\pi\)
0.947640 0.319342i \(-0.103462\pi\)
\(90\) 0 0
\(91\) 860701. + 2.64897e6i 0.119731 + 0.368495i
\(92\) 6.39290e6 + 2.07718e6i 0.855935 + 0.278110i
\(93\) 0 0
\(94\) 323351. 445055.i 0.0401539 0.0552671i
\(95\) −845738. + 2.60291e6i −0.101205 + 0.311478i
\(96\) 0 0
\(97\) −6.98825e6 + 5.07726e6i −0.777441 + 0.564844i −0.904210 0.427088i \(-0.859539\pi\)
0.126769 + 0.991932i \(0.459539\pi\)
\(98\) 6.80849e6 0.730734
\(99\) 0 0
\(100\) 3.57478e6 0.357478
\(101\) −7.06221e6 + 5.13099e6i −0.682049 + 0.495538i −0.874037 0.485860i \(-0.838507\pi\)
0.191988 + 0.981397i \(0.438507\pi\)
\(102\) 0 0
\(103\) −6.01719e6 + 1.85190e7i −0.542579 + 1.66989i 0.184097 + 0.982908i \(0.441064\pi\)
−0.726676 + 0.686980i \(0.758936\pi\)
\(104\) 2.31192e6 3.18209e6i 0.201538 0.277393i
\(105\) 0 0
\(106\) 2.06772e7 + 6.71843e6i 1.68625 + 0.547895i
\(107\) 56532.0 + 173988.i 0.00446119 + 0.0137301i 0.953262 0.302144i \(-0.0977023\pi\)
−0.948801 + 0.315874i \(0.897702\pi\)
\(108\) 0 0
\(109\) 4.17100e6i 0.308495i 0.988032 + 0.154247i \(0.0492953\pi\)
−0.988032 + 0.154247i \(0.950705\pi\)
\(110\) 9.89973e6 + 2.16138e6i 0.709167 + 0.154830i
\(111\) 0 0
\(112\) 6.99916e6 + 9.63352e6i 0.470742 + 0.647921i
\(113\) 1.32531e7 4.30620e6i 0.864060 0.280750i 0.156737 0.987640i \(-0.449903\pi\)
0.707323 + 0.706890i \(0.249903\pi\)
\(114\) 0 0
\(115\) −1.27831e7 9.28747e6i −0.783779 0.569449i
\(116\) 1.08545e7 + 7.88627e6i 0.645666 + 0.469104i
\(117\) 0 0
\(118\) −1.40360e7 + 4.56058e6i −0.786424 + 0.255525i
\(119\) −3.50040e6 4.81788e6i −0.190416 0.262085i
\(120\) 0 0
\(121\) −1.77139e7 8.12200e6i −0.909004 0.416787i
\(122\) 1.31372e7i 0.655001i
\(123\) 0 0
\(124\) 514200. + 1.58255e6i 0.0242190 + 0.0745384i
\(125\) −2.01281e7 6.54001e6i −0.921759 0.299498i
\(126\) 0 0
\(127\) −1.22194e7 + 1.68186e7i −0.529343 + 0.728578i −0.987030 0.160535i \(-0.948678\pi\)
0.457687 + 0.889113i \(0.348678\pi\)
\(128\) 7.45635e6 2.29483e7i 0.314262 0.967198i
\(129\) 0 0
\(130\) 8.88283e6 6.45376e6i 0.354609 0.257639i
\(131\) 3.41737e7 1.32814 0.664068 0.747672i \(-0.268828\pi\)
0.664068 + 0.747672i \(0.268828\pi\)
\(132\) 0 0
\(133\) 9.75660e6 0.359599
\(134\) 1.21843e7 8.85239e6i 0.437454 0.317829i
\(135\) 0 0
\(136\) −2.59876e6 + 7.99815e6i −0.0885889 + 0.272649i
\(137\) 1.54285e7 2.12355e7i 0.512628 0.705571i −0.471732 0.881742i \(-0.656371\pi\)
0.984360 + 0.176171i \(0.0563710\pi\)
\(138\) 0 0
\(139\) 4.24118e6 + 1.37804e6i 0.133948 + 0.0435222i 0.375224 0.926934i \(-0.377566\pi\)
−0.241276 + 0.970457i \(0.577566\pi\)
\(140\) 2.04227e6 + 6.28547e6i 0.0629022 + 0.193593i
\(141\) 0 0
\(142\) 2.44259e6i 0.0715883i
\(143\) −1.93373e7 + 8.48207e6i −0.552994 + 0.242564i
\(144\) 0 0
\(145\) −1.85378e7 2.55151e7i −0.504976 0.695040i
\(146\) 4.46236e6 1.44991e6i 0.118667 0.0385572i
\(147\) 0 0
\(148\) −9.27929e6 6.74180e6i −0.235288 0.170946i
\(149\) −1.11427e7 8.09563e6i −0.275955 0.200493i 0.441196 0.897411i \(-0.354554\pi\)
−0.717151 + 0.696918i \(0.754554\pi\)
\(150\) 0 0
\(151\) 3.32678e7 1.08094e7i 0.786330 0.255494i 0.111790 0.993732i \(-0.464342\pi\)
0.674541 + 0.738238i \(0.264342\pi\)
\(152\) −8.09845e6 1.11466e7i −0.187046 0.257447i
\(153\) 0 0
\(154\) −3.57769e6 3.59451e7i −0.0789370 0.793080i
\(155\) 3.91144e6i 0.0843676i
\(156\) 0 0
\(157\) −3.81134e6 1.17301e7i −0.0786012 0.241910i 0.904033 0.427463i \(-0.140592\pi\)
−0.982634 + 0.185553i \(0.940592\pi\)
\(158\) −1.50388e7 4.88640e6i −0.303329 0.0985575i
\(159\) 0 0
\(160\) 1.74861e7 2.40675e7i 0.337499 0.464527i
\(161\) −1.74063e7 + 5.35711e7i −0.328712 + 1.01167i
\(162\) 0 0
\(163\) −6.74097e7 + 4.89760e7i −1.21917 + 0.885782i −0.996031 0.0890043i \(-0.971632\pi\)
−0.223143 + 0.974786i \(0.571632\pi\)
\(164\) −3.44638e7 −0.610112
\(165\) 0 0
\(166\) 1.09720e8 1.86169
\(167\) −5.11559e7 + 3.71669e7i −0.849940 + 0.617517i −0.925129 0.379652i \(-0.876044\pi\)
0.0751897 + 0.997169i \(0.476044\pi\)
\(168\) 0 0
\(169\) 1.23199e7 3.79167e7i 0.196337 0.604264i
\(170\) −1.37988e7 + 1.89924e7i −0.215412 + 0.296489i
\(171\) 0 0
\(172\) −4.25821e7 1.38358e7i −0.638083 0.207326i
\(173\) 2.72671e7 + 8.39195e7i 0.400385 + 1.23226i 0.924688 + 0.380726i \(0.124326\pi\)
−0.524303 + 0.851532i \(0.675674\pi\)
\(174\) 0 0
\(175\) 2.99558e7i 0.422521i
\(176\) −6.74191e7 + 6.00346e7i −0.932157 + 0.830056i
\(177\) 0 0
\(178\) 3.50864e7 + 4.82922e7i 0.466303 + 0.641811i
\(179\) −1.08952e8 + 3.54006e7i −1.41987 + 0.461344i −0.915561 0.402180i \(-0.868253\pi\)
−0.504309 + 0.863523i \(0.668253\pi\)
\(180\) 0 0
\(181\) −1.13448e8 8.24245e7i −1.42207 1.03319i −0.991426 0.130670i \(-0.958287\pi\)
−0.430642 0.902523i \(-0.641713\pi\)
\(182\) −3.16663e7 2.30069e7i −0.389356 0.282884i
\(183\) 0 0
\(184\) 7.56510e7 2.45805e7i 0.895267 0.290890i
\(185\) 1.58476e7 + 2.18123e7i 0.184019 + 0.253280i
\(186\) 0 0
\(187\) 3.37174e7 3.00243e7i 0.377058 0.335759i
\(188\) 2.72014e6i 0.0298565i
\(189\) 0 0
\(190\) −1.18852e7 3.65788e7i −0.125709 0.386893i
\(191\) −6.26551e6 2.03579e6i −0.0650639 0.0211405i 0.276304 0.961070i \(-0.410890\pi\)
−0.341368 + 0.939930i \(0.610890\pi\)
\(192\) 0 0
\(193\) 3.98230e7 5.48117e7i 0.398734 0.548811i −0.561691 0.827347i \(-0.689849\pi\)
0.960426 + 0.278536i \(0.0898491\pi\)
\(194\) 3.75113e7 1.15448e8i 0.368856 1.13522i
\(195\) 0 0
\(196\) −2.72360e7 + 1.97881e7i −0.258373 + 0.187719i
\(197\) 1.56103e8 1.45472 0.727362 0.686254i \(-0.240746\pi\)
0.727362 + 0.686254i \(0.240746\pi\)
\(198\) 0 0
\(199\) −6.32652e7 −0.569088 −0.284544 0.958663i \(-0.591842\pi\)
−0.284544 + 0.958663i \(0.591842\pi\)
\(200\) 3.42235e7 2.48648e7i 0.302495 0.219776i
\(201\) 0 0
\(202\) 3.79083e7 1.16670e8i 0.323597 0.995930i
\(203\) −6.60852e7 + 9.09585e7i −0.554457 + 0.763145i
\(204\) 0 0
\(205\) 7.70470e7 + 2.50341e7i 0.624622 + 0.202952i
\(206\) −8.45596e7 2.60248e8i −0.673950 2.07421i
\(207\) 0 0
\(208\) 9.78193e7i 0.753708i
\(209\) 7.32588e6 + 7.36031e7i 0.0555070 + 0.557679i
\(210\) 0 0
\(211\) −6.25161e7 8.60460e7i −0.458145 0.630583i 0.515978 0.856602i \(-0.327429\pi\)
−0.974123 + 0.226019i \(0.927429\pi\)
\(212\) −1.02241e8 + 3.32202e7i −0.736972 + 0.239457i
\(213\) 0 0
\(214\) −2.07988e6 1.51112e6i −0.0145074 0.0105403i
\(215\) 8.51461e7 + 6.18623e7i 0.584293 + 0.424513i
\(216\) 0 0
\(217\) −1.32614e7 + 4.30888e6i −0.0881007 + 0.0286257i
\(218\) −3.44531e7 4.74207e7i −0.225232 0.310006i
\(219\) 0 0
\(220\) −4.58837e7 + 2.01263e7i −0.290522 + 0.127434i
\(221\) 4.89210e7i 0.304876i
\(222\) 0 0
\(223\) −8.06598e7 2.48245e8i −0.487069 1.49904i −0.828962 0.559305i \(-0.811068\pi\)
0.341894 0.939739i \(-0.388932\pi\)
\(224\) −1.00861e8 3.27719e7i −0.599594 0.194820i
\(225\) 0 0
\(226\) −1.15107e8 + 1.58431e8i −0.663316 + 0.912977i
\(227\) 3.87366e7 1.19219e8i 0.219802 0.676480i −0.778976 0.627054i \(-0.784261\pi\)
0.998778 0.0494265i \(-0.0157394\pi\)
\(228\) 0 0
\(229\) −1.87732e8 + 1.36395e8i −1.03303 + 0.750542i −0.968913 0.247401i \(-0.920424\pi\)
−0.0641187 + 0.997942i \(0.520424\pi\)
\(230\) 2.22049e8 1.20337
\(231\) 0 0
\(232\) 1.58771e8 0.834761
\(233\) 7.32155e7 5.31942e7i 0.379191 0.275498i −0.381821 0.924236i \(-0.624703\pi\)
0.761012 + 0.648738i \(0.224703\pi\)
\(234\) 0 0
\(235\) 1.97588e6 6.08113e6i 0.00993168 0.0305666i
\(236\) 4.28934e7 5.90378e7i 0.212422 0.292373i
\(237\) 0 0
\(238\) 7.95929e7 + 2.58613e7i 0.382697 + 0.124346i
\(239\) −1.25334e7 3.85739e7i −0.0593850 0.182768i 0.916963 0.398971i \(-0.130633\pi\)
−0.976348 + 0.216203i \(0.930633\pi\)
\(240\) 0 0
\(241\) 3.17808e8i 1.46253i 0.682094 + 0.731265i \(0.261070\pi\)
−0.682094 + 0.731265i \(0.738930\pi\)
\(242\) 2.68481e8 5.39797e7i 1.21775 0.244837i
\(243\) 0 0
\(244\) 3.81817e7 + 5.25526e7i 0.168264 + 0.231595i
\(245\) 7.52625e7 2.44543e7i 0.326962 0.106236i
\(246\) 0 0
\(247\) 6.48416e7 + 4.71102e7i 0.273788 + 0.198918i
\(248\) 1.59303e7 + 1.15741e7i 0.0663198 + 0.0481842i
\(249\) 0 0
\(250\) 2.82860e8 9.19069e7i 1.14494 0.372013i
\(251\) 2.54923e8 + 3.50872e8i 1.01754 + 1.40052i 0.913914 + 0.405908i \(0.133045\pi\)
0.103627 + 0.994616i \(0.466955\pi\)
\(252\) 0 0
\(253\) −4.17206e8 9.10872e7i −1.61968 0.353619i
\(254\) 2.92147e8i 1.11862i
\(255\) 0 0
\(256\) 1.02486e8 + 3.15419e8i 0.381789 + 1.17503i
\(257\) −1.42133e8 4.61818e7i −0.522311 0.169709i 0.0359830 0.999352i \(-0.488544\pi\)
−0.558294 + 0.829643i \(0.688544\pi\)
\(258\) 0 0
\(259\) 5.64948e7 7.77584e7i 0.202050 0.278098i
\(260\) −1.67769e7 + 5.16339e7i −0.0591976 + 0.182192i
\(261\) 0 0
\(262\) −3.88525e8 + 2.82280e8i −1.33464 + 0.969674i
\(263\) 4.14571e8 1.40525 0.702626 0.711559i \(-0.252011\pi\)
0.702626 + 0.711559i \(0.252011\pi\)
\(264\) 0 0
\(265\) 2.52701e8 0.834155
\(266\) −1.10924e8 + 8.05910e7i −0.361360 + 0.262543i
\(267\) 0 0
\(268\) −2.30123e7 + 7.08244e7i −0.0730276 + 0.224756i
\(269\) −3.44641e8 + 4.74358e8i −1.07953 + 1.48584i −0.219492 + 0.975614i \(0.570440\pi\)
−0.860038 + 0.510230i \(0.829560\pi\)
\(270\) 0 0
\(271\) −2.53903e8 8.24981e7i −0.774953 0.251797i −0.105269 0.994444i \(-0.533570\pi\)
−0.669684 + 0.742646i \(0.733570\pi\)
\(272\) −6.46302e7 1.98911e8i −0.194735 0.599333i
\(273\) 0 0
\(274\) 3.68871e8i 1.08330i
\(275\) −2.25985e8 + 2.24927e7i −0.655261 + 0.0652196i
\(276\) 0 0
\(277\) 3.50803e8 + 4.82839e8i 0.991710 + 1.36497i 0.930276 + 0.366860i \(0.119567\pi\)
0.0614338 + 0.998111i \(0.480433\pi\)
\(278\) −5.96014e7 + 1.93657e7i −0.166379 + 0.0540599i
\(279\) 0 0
\(280\) 6.32712e7 + 4.59692e7i 0.172248 + 0.125145i
\(281\) 2.94824e8 + 2.14202e8i 0.792666 + 0.575906i 0.908753 0.417333i \(-0.137035\pi\)
−0.116087 + 0.993239i \(0.537035\pi\)
\(282\) 0 0
\(283\) 6.84940e8 2.22550e8i 1.79639 0.583681i 0.796604 0.604502i \(-0.206628\pi\)
0.999783 + 0.0208207i \(0.00662791\pi\)
\(284\) −7.09912e6 9.77111e6i −0.0183904 0.0253122i
\(285\) 0 0
\(286\) 1.49785e8 2.56163e8i 0.378606 0.647493i
\(287\) 2.88799e8i 0.721121i
\(288\) 0 0
\(289\) −9.44790e7 2.90776e8i −0.230246 0.708626i
\(290\) 4.21518e8 + 1.36959e8i 1.01490 + 0.329761i
\(291\) 0 0
\(292\) −1.36368e7 + 1.87694e7i −0.0320533 + 0.0441175i
\(293\) −1.68663e6 + 5.19092e6i −0.00391727 + 0.0120561i −0.952996 0.302983i \(-0.902018\pi\)
0.949079 + 0.315039i \(0.102018\pi\)
\(294\) 0 0
\(295\) −1.38777e8 + 1.00827e8i −0.314731 + 0.228666i
\(296\) −1.35729e8 −0.304196
\(297\) 0 0
\(298\) 1.93554e8 0.423686
\(299\) −3.74351e8 + 2.71982e8i −0.809897 + 0.588424i
\(300\) 0 0
\(301\) 1.15940e8 3.56828e8i 0.245049 0.754182i
\(302\) −2.88939e8 + 3.97690e8i −0.603645 + 0.830846i
\(303\) 0 0
\(304\) 3.25881e8 + 1.05885e8i 0.665276 + 0.216161i
\(305\) −4.71852e7 1.45221e8i −0.0952261 0.293076i
\(306\) 0 0
\(307\) 9.15331e8i 1.80548i 0.430182 + 0.902742i \(0.358450\pi\)
−0.430182 + 0.902742i \(0.641550\pi\)
\(308\) 1.18782e8 + 1.33393e8i 0.231645 + 0.260139i
\(309\) 0 0
\(310\) 3.23091e7 + 4.44696e7i 0.0615969 + 0.0847809i
\(311\) −3.31026e8 + 1.07557e8i −0.624024 + 0.202758i −0.603926 0.797040i \(-0.706398\pi\)
−0.0200977 + 0.999798i \(0.506398\pi\)
\(312\) 0 0
\(313\) −6.39979e7 4.64972e7i −0.117967 0.0857081i 0.527237 0.849718i \(-0.323228\pi\)
−0.645204 + 0.764010i \(0.723228\pi\)
\(314\) 1.40224e8 + 1.01879e8i 0.255605 + 0.185708i
\(315\) 0 0
\(316\) 7.43615e7 2.41615e7i 0.132569 0.0430744i
\(317\) −2.01898e7 2.77888e7i −0.0355979 0.0489963i 0.790847 0.612014i \(-0.209640\pi\)
−0.826445 + 0.563018i \(0.809640\pi\)
\(318\) 0 0
\(319\) −7.35805e8 4.30244e8i −1.26910 0.742075i
\(320\) 9.49100e6i 0.0161915i
\(321\) 0 0
\(322\) −2.44611e8 7.52835e8i −0.408301 1.25662i
\(323\) −1.62979e8 5.29550e7i −0.269105 0.0874375i
\(324\) 0 0
\(325\) −1.44643e8 + 1.99084e8i −0.233725 + 0.321695i
\(326\) 3.61840e8 1.11363e9i 0.578435 1.78024i
\(327\) 0 0
\(328\) −3.29942e8 + 2.39717e8i −0.516272 + 0.375094i
\(329\) −2.27941e7 −0.0352889
\(330\) 0 0
\(331\) 2.47127e8 0.374561 0.187281 0.982306i \(-0.440033\pi\)
0.187281 + 0.982306i \(0.440033\pi\)
\(332\) −4.38913e8 + 3.18889e8i −0.658256 + 0.478251i
\(333\) 0 0
\(334\) 2.74593e8 8.45111e8i 0.403253 1.24108i
\(335\) 1.02892e8 1.41619e8i 0.149529 0.205809i
\(336\) 0 0
\(337\) −2.25479e8 7.32625e7i −0.320923 0.104274i 0.144125 0.989559i \(-0.453963\pi\)
−0.465049 + 0.885285i \(0.653963\pi\)
\(338\) 1.73131e8 + 5.32843e8i 0.243875 + 0.750570i
\(339\) 0 0
\(340\) 1.16080e8i 0.160170i
\(341\) −4.24634e7 9.68074e7i −0.0579928 0.132211i
\(342\) 0 0
\(343\) −4.47685e8 6.16185e8i −0.599022 0.824484i
\(344\) −5.03899e8 + 1.63727e8i −0.667405 + 0.216853i
\(345\) 0 0
\(346\) −1.00319e9 7.28861e8i −1.30202 0.945972i
\(347\) −7.12169e7 5.17421e7i −0.0915018 0.0664799i 0.541094 0.840962i \(-0.318010\pi\)
−0.632596 + 0.774482i \(0.718010\pi\)
\(348\) 0 0
\(349\) −8.28840e8 + 2.69306e8i −1.04371 + 0.339123i −0.780199 0.625532i \(-0.784882\pi\)
−0.263515 + 0.964655i \(0.584882\pi\)
\(350\) −2.47440e8 3.40572e8i −0.308483 0.424591i
\(351\) 0 0
\(352\) 1.71495e8 7.85498e8i 0.209582 0.959944i
\(353\) 1.37940e9i 1.66909i −0.550943 0.834543i \(-0.685732\pi\)
0.550943 0.834543i \(-0.314268\pi\)
\(354\) 0 0
\(355\) 8.77315e6 + 2.70010e7i 0.0104077 + 0.0320317i
\(356\) −2.80712e8 9.12088e7i −0.329751 0.107143i
\(357\) 0 0
\(358\) 9.46271e8 1.30243e9i 1.09000 1.50025i
\(359\) 4.09101e8 1.25908e9i 0.466659 1.43623i −0.390224 0.920720i \(-0.627602\pi\)
0.856884 0.515510i \(-0.172398\pi\)
\(360\) 0 0
\(361\) −4.96023e8 + 3.60382e8i −0.554916 + 0.403170i
\(362\) 1.97064e9 2.18337
\(363\) 0 0
\(364\) 1.93541e8 0.210339
\(365\) 4.41202e7 3.20552e7i 0.0474912 0.0345044i
\(366\) 0 0
\(367\) 2.92644e7 9.00667e7i 0.0309036 0.0951115i −0.934415 0.356186i \(-0.884077\pi\)
0.965319 + 0.261075i \(0.0840769\pi\)
\(368\) −1.16278e9 + 1.60043e9i −1.21627 + 1.67405i
\(369\) 0 0
\(370\) −3.60346e8 1.17084e8i −0.369840 0.120168i
\(371\) −2.78378e8 8.56760e8i −0.283026 0.871064i
\(372\) 0 0
\(373\) 2.71591e8i 0.270978i −0.990779 0.135489i \(-0.956739\pi\)
0.990779 0.135489i \(-0.0432606\pi\)
\(374\) −1.35332e8 + 6.19861e8i −0.133768 + 0.612694i
\(375\) 0 0
\(376\) 1.89202e7 + 2.60415e7i 0.0183556 + 0.0252643i
\(377\) −8.78393e8 + 2.85407e8i −0.844295 + 0.274328i
\(378\) 0 0
\(379\) 6.23522e8 + 4.53015e8i 0.588321 + 0.427440i 0.841714 0.539923i \(-0.181547\pi\)
−0.253393 + 0.967363i \(0.581547\pi\)
\(380\) 1.53856e8 + 1.11783e8i 0.143838 + 0.104504i
\(381\) 0 0
\(382\) 8.80493e7 2.86090e7i 0.0808173 0.0262591i
\(383\) −4.39609e8 6.05070e8i −0.399826 0.550313i 0.560874 0.827901i \(-0.310465\pi\)
−0.960700 + 0.277588i \(0.910465\pi\)
\(384\) 0 0
\(385\) −1.68654e8 3.84495e8i −0.150620 0.343382i
\(386\) 9.52105e8i 0.842616i
\(387\) 0 0
\(388\) 1.85480e8 + 5.70849e8i 0.161208 + 0.496147i
\(389\) −7.64506e8 2.48403e8i −0.658502 0.213960i −0.0393430 0.999226i \(-0.512527\pi\)
−0.619159 + 0.785265i \(0.712527\pi\)
\(390\) 0 0
\(391\) 5.81525e8 8.00400e8i 0.491983 0.677156i
\(392\) −1.23108e8 + 3.78886e8i −0.103225 + 0.317693i
\(393\) 0 0
\(394\) −1.77476e9 + 1.28944e9i −1.46185 + 1.06210i
\(395\) −1.83793e8 −0.150051
\(396\) 0 0
\(397\) 2.43762e9 1.95523 0.977617 0.210392i \(-0.0674742\pi\)
0.977617 + 0.210392i \(0.0674742\pi\)
\(398\) 7.19270e8 5.22580e8i 0.571875 0.415492i
\(399\) 0 0
\(400\) −3.25101e8 + 1.00056e9i −0.253985 + 0.781686i
\(401\) −2.00181e8 + 2.75526e8i −0.155031 + 0.213382i −0.879467 0.475961i \(-0.842100\pi\)
0.724436 + 0.689342i \(0.242100\pi\)
\(402\) 0 0
\(403\) −1.08940e8 3.53966e7i −0.0829121 0.0269398i
\(404\) 1.87443e8 + 5.76890e8i 0.141428 + 0.435270i
\(405\) 0 0
\(406\) 1.57999e9i 1.17169i
\(407\) 6.29023e8 + 3.67806e8i 0.462473 + 0.270420i
\(408\) 0 0
\(409\) 8.97339e8 + 1.23508e9i 0.648522 + 0.892614i 0.999034 0.0439440i \(-0.0139923\pi\)
−0.350512 + 0.936558i \(0.613992\pi\)
\(410\) −1.08274e9 + 3.51804e8i −0.775857 + 0.252091i
\(411\) 0 0
\(412\) 1.09464e9 + 7.95306e8i 0.771139 + 0.560265i
\(413\) 4.94723e8 + 3.59437e8i 0.345571 + 0.251072i
\(414\) 0 0
\(415\) 1.21287e9 3.94085e8i 0.833001 0.270658i
\(416\) −5.12076e8 7.04812e8i −0.348745 0.480006i
\(417\) 0 0
\(418\) −6.91262e8 7.76290e8i −0.462941 0.519885i
\(419\) 9.08467e8i 0.603337i 0.953413 + 0.301669i \(0.0975436\pi\)
−0.953413 + 0.301669i \(0.902456\pi\)
\(420\) 0 0
\(421\) 1.89744e8 + 5.83973e8i 0.123931 + 0.381422i 0.993705 0.112030i \(-0.0357352\pi\)
−0.869773 + 0.493451i \(0.835735\pi\)
\(422\) 1.42151e9 + 4.61875e8i 0.920779 + 0.299179i
\(423\) 0 0
\(424\) −7.47749e8 + 1.02919e9i −0.476404 + 0.655714i
\(425\) 1.62588e8 5.00396e8i 0.102737 0.316193i
\(426\) 0 0
\(427\) −4.40379e8 + 3.19954e8i −0.273734 + 0.198879i
\(428\) 1.27121e7 0.00783723
\(429\) 0 0
\(430\) −1.47903e9 −0.897092
\(431\) −1.81162e9 + 1.31622e9i −1.08993 + 0.791879i −0.979387 0.201993i \(-0.935258\pi\)
−0.110540 + 0.993872i \(0.535258\pi\)
\(432\) 0 0
\(433\) −4.63265e8 + 1.42578e9i −0.274234 + 0.844006i 0.715187 + 0.698933i \(0.246342\pi\)
−0.989421 + 0.145073i \(0.953658\pi\)
\(434\) 1.15178e8 1.58529e8i 0.0676326 0.0930883i
\(435\) 0 0
\(436\) 2.75646e8 + 8.95627e7i 0.159275 + 0.0517517i
\(437\) 5.00878e8 + 1.54155e9i 0.287109 + 0.883631i
\(438\) 0 0
\(439\) 1.24697e9i 0.703447i 0.936104 + 0.351723i \(0.114404\pi\)
−0.936104 + 0.351723i \(0.885596\pi\)
\(440\) −2.99280e8 + 5.11830e8i −0.167492 + 0.286445i
\(441\) 0 0
\(442\) 4.04095e8 + 5.56189e8i 0.222590 + 0.306369i
\(443\) 1.69610e9 5.51096e8i 0.926912 0.301172i 0.193613 0.981078i \(-0.437980\pi\)
0.733299 + 0.679906i \(0.237980\pi\)
\(444\) 0 0
\(445\) 5.61305e8 + 4.07812e8i 0.301953 + 0.219382i
\(446\) 2.96758e9 + 2.15607e9i 1.58391 + 1.15078i
\(447\) 0 0
\(448\) −3.21784e7 + 1.04554e7i −0.0169079 + 0.00549372i
\(449\) −8.62253e8 1.18679e9i −0.449544 0.618744i 0.522755 0.852483i \(-0.324904\pi\)
−0.972300 + 0.233738i \(0.924904\pi\)
\(450\) 0 0
\(451\) 2.17867e9 2.16848e8i 1.11834 0.111311i
\(452\) 9.68314e8i 0.493210i
\(453\) 0 0
\(454\) 5.44366e8 + 1.67539e9i 0.273021 + 0.840271i
\(455\) −4.32680e8 1.40586e8i −0.215341 0.0699686i
\(456\) 0 0
\(457\) −2.07808e8 + 2.86023e8i −0.101849 + 0.140183i −0.856899 0.515484i \(-0.827612\pi\)
0.755051 + 0.655667i \(0.227612\pi\)
\(458\) 1.00770e9 3.10139e9i 0.490121 1.50844i
\(459\) 0 0
\(460\) −8.88261e8 + 6.45359e8i −0.425489 + 0.309136i
\(461\) 3.51925e9 1.67300 0.836501 0.547966i \(-0.184598\pi\)
0.836501 + 0.547966i \(0.184598\pi\)
\(462\) 0 0
\(463\) −3.06454e8 −0.143493 −0.0717467 0.997423i \(-0.522857\pi\)
−0.0717467 + 0.997423i \(0.522857\pi\)
\(464\) −3.19446e9 + 2.32091e9i −1.48452 + 1.07856i
\(465\) 0 0
\(466\) −3.93004e8 + 1.20954e9i −0.179906 + 0.553695i
\(467\) 1.77136e9 2.43807e9i 0.804819 1.10774i −0.187283 0.982306i \(-0.559968\pi\)
0.992102 0.125432i \(-0.0400318\pi\)
\(468\) 0 0
\(469\) −5.93493e8 1.92837e8i −0.265650 0.0863150i
\(470\) 2.77670e7 + 8.54581e7i 0.0123364 + 0.0379674i
\(471\) 0 0
\(472\) 8.63553e8i 0.378000i
\(473\) 2.77894e9 + 6.06717e8i 1.20744 + 0.263616i
\(474\) 0 0
\(475\) 5.06671e8 + 6.97373e8i 0.216919 + 0.298564i
\(476\) −3.93558e8 + 1.27875e8i −0.167257 + 0.0543451i
\(477\) 0 0
\(478\) 4.61120e8 + 3.35023e8i 0.193115 + 0.140306i
\(479\) −7.86161e8 5.71180e8i −0.326842 0.237464i 0.412248 0.911072i \(-0.364744\pi\)
−0.739089 + 0.673607i \(0.764744\pi\)
\(480\) 0 0
\(481\) 7.50919e8 2.43988e8i 0.307670 0.0999681i
\(482\) −2.62514e9 3.61319e9i −1.06779 1.46969i
\(483\) 0 0
\(484\) −9.17117e8 + 9.96244e8i −0.367677 + 0.399399i
\(485\) 1.41092e9i 0.561573i
\(486\) 0 0
\(487\) −2.09606e7 6.45101e7i −0.00822341 0.0253091i 0.946861 0.321644i \(-0.104235\pi\)
−0.955084 + 0.296335i \(0.904235\pi\)
\(488\) 7.31071e8 + 2.37539e8i 0.284767 + 0.0925265i
\(489\) 0 0
\(490\) −6.53672e8 + 8.99703e8i −0.251000 + 0.345472i
\(491\) 3.36942e8 1.03700e9i 0.128461 0.395361i −0.866055 0.499949i \(-0.833352\pi\)
0.994516 + 0.104587i \(0.0333522\pi\)
\(492\) 0 0
\(493\) 1.59760e9 1.16073e9i 0.600488 0.436280i
\(494\) −1.12633e9 −0.420359
\(495\) 0 0
\(496\) −4.89707e8 −0.180198
\(497\) 8.18797e7 5.94891e7i 0.0299177 0.0217365i
\(498\) 0 0
\(499\) 4.30751e8 1.32572e9i 0.155194 0.477638i −0.842987 0.537935i \(-0.819205\pi\)
0.998180 + 0.0602969i \(0.0192048\pi\)
\(500\) −8.64409e8 + 1.18976e9i −0.309260 + 0.425660i
\(501\) 0 0
\(502\) −5.79651e9 1.88340e9i −2.04505 0.664477i
\(503\) 8.78845e8 + 2.70481e9i 0.307910 + 0.947651i 0.978575 + 0.205890i \(0.0660089\pi\)
−0.670665 + 0.741761i \(0.733991\pi\)
\(504\) 0 0
\(505\) 1.42585e9i 0.492668i
\(506\) 5.49566e9 2.41060e9i 1.88579 0.827178i
\(507\) 0 0
\(508\) 8.49092e8 + 1.16867e9i 0.287363 + 0.395522i
\(509\) −2.15677e9 + 7.00776e8i −0.724921 + 0.235541i −0.648156 0.761508i \(-0.724459\pi\)
−0.0767657 + 0.997049i \(0.524459\pi\)
\(510\) 0 0
\(511\) −1.57284e8 1.14273e8i −0.0521447 0.0378853i
\(512\) −1.27190e9 9.24087e8i −0.418800 0.304276i
\(513\) 0 0
\(514\) 1.99740e9 6.48994e8i 0.648774 0.210799i
\(515\) −1.86948e9 2.57312e9i −0.603109 0.830108i
\(516\) 0 0
\(517\) −1.71153e7 1.71957e8i −0.00544712 0.0547273i
\(518\) 1.35070e9i 0.426977i
\(519\) 0 0
\(520\) 1.98531e8 + 6.11015e8i 0.0619179 + 0.190564i
\(521\) 3.08986e9 + 1.00396e9i 0.957209 + 0.311016i 0.745641 0.666347i \(-0.232143\pi\)
0.211567 + 0.977363i \(0.432143\pi\)
\(522\) 0 0
\(523\) 3.13065e9 4.30897e9i 0.956926 1.31710i 0.00854483 0.999963i \(-0.497280\pi\)
0.948381 0.317132i \(-0.102720\pi\)
\(524\) 7.33802e8 2.25841e9i 0.222802 0.685714i
\(525\) 0 0
\(526\) −4.71331e9 + 3.42442e9i −1.41214 + 1.02598i
\(527\) 2.44911e8 0.0728904
\(528\) 0 0
\(529\) −5.95301e9 −1.74840
\(530\) −2.87299e9 + 2.08735e9i −0.838241 + 0.609017i
\(531\) 0 0
\(532\) 2.09501e8 6.44777e8i 0.0603246 0.185660i
\(533\) 1.39448e9 1.91933e9i 0.398901 0.549041i
\(534\) 0 0
\(535\) −2.84190e7 9.23390e6i −0.00802363 0.00260704i
\(536\) 2.72318e8 + 8.38108e8i 0.0763834 + 0.235084i
\(537\) 0 0
\(538\) 8.23983e9i 2.28129i
\(539\) 1.59725e9 1.42230e9i 0.439352 0.391229i
\(540\) 0 0
\(541\) 2.66374e9 + 3.66632e9i 0.723271 + 0.995497i 0.999409 + 0.0343793i \(0.0109454\pi\)
−0.276138 + 0.961118i \(0.589055\pi\)
\(542\) 3.56810e9 1.15935e9i 0.962586 0.312763i
\(543\) 0 0
\(544\) 1.50696e9 + 1.09487e9i 0.401334 + 0.291586i
\(545\) −5.51175e8 4.00452e8i −0.145848 0.105965i
\(546\) 0 0
\(547\) −1.48712e9 + 4.83195e8i −0.388499 + 0.126231i −0.496753 0.867892i \(-0.665474\pi\)
0.108253 + 0.994123i \(0.465474\pi\)
\(548\) −1.07208e9 1.47559e9i −0.278289 0.383032i
\(549\) 0 0
\(550\) 2.38345e9 2.12239e9i 0.610854 0.543946i
\(551\) 3.23528e9i 0.823912i
\(552\) 0 0
\(553\) 2.02468e8 + 6.23132e8i 0.0509118 + 0.156690i
\(554\) −7.97665e9 2.59177e9i −1.99313 0.647609i
\(555\) 0 0
\(556\) 1.82139e8 2.50693e8i 0.0449409 0.0618558i
\(557\) −1.91100e9 + 5.88145e9i −0.468562 + 1.44209i 0.385884 + 0.922547i \(0.373897\pi\)
−0.854446 + 0.519540i \(0.826103\pi\)
\(558\) 0 0
\(559\) 2.49349e9 1.81163e9i 0.603763 0.438659i
\(560\) −1.94499e9 −0.468016
\(561\) 0 0
\(562\) −5.12123e9 −1.21702
\(563\) −2.59975e9 + 1.88883e9i −0.613978 + 0.446081i −0.850813 0.525469i \(-0.823890\pi\)
0.236835 + 0.971550i \(0.423890\pi\)
\(564\) 0 0
\(565\) −7.03373e8 + 2.16476e9i −0.164065 + 0.504940i
\(566\) −5.94886e9 + 8.18791e9i −1.37904 + 1.89808i
\(567\) 0 0
\(568\) −1.35928e8 4.41657e7i −0.0311236 0.0101127i
\(569\) 2.04087e8 + 6.28116e8i 0.0464433 + 0.142938i 0.971589 0.236674i \(-0.0760574\pi\)
−0.925146 + 0.379612i \(0.876057\pi\)
\(570\) 0 0
\(571\) 8.42572e9i 1.89400i −0.321230 0.947001i \(-0.604096\pi\)
0.321230 0.947001i \(-0.395904\pi\)
\(572\) 1.45323e8 + 1.46006e9i 0.0324675 + 0.326201i
\(573\) 0 0
\(574\) 2.38552e9 + 3.28339e9i 0.526492 + 0.724653i
\(575\) −4.73303e9 + 1.53785e9i −1.03825 + 0.337348i
\(576\) 0 0
\(577\) 6.21811e9 + 4.51772e9i 1.34755 + 0.979049i 0.999130 + 0.0417088i \(0.0132802\pi\)
0.348415 + 0.937340i \(0.386720\pi\)
\(578\) 3.47600e9 + 2.52546e9i 0.748743 + 0.543993i
\(579\) 0 0
\(580\) −2.08425e9 + 6.77215e8i −0.443560 + 0.144121i
\(581\) −2.67222e9 3.67799e9i −0.565269 0.778026i
\(582\) 0 0
\(583\) 6.25431e9 2.74337e9i 1.30719 0.573383i
\(584\) 2.74543e8i 0.0570381i
\(585\) 0 0
\(586\) −2.37023e7 7.29480e7i −0.00486573 0.0149752i
\(587\) −1.12760e9 3.66380e8i −0.230103 0.0747650i 0.191696 0.981454i \(-0.438601\pi\)
−0.421799 + 0.906689i \(0.638601\pi\)
\(588\) 0 0
\(589\) −2.35845e8 + 3.24613e8i −0.0475580 + 0.0654579i
\(590\) 7.44922e8 2.29263e9i 0.149324 0.459571i
\(591\) 0 0
\(592\) 2.73087e9 1.98410e9i 0.540973 0.393040i
\(593\) 2.53649e9 0.499507 0.249754 0.968309i \(-0.419650\pi\)
0.249754 + 0.968309i \(0.419650\pi\)
\(594\) 0 0
\(595\) 9.72724e8 0.189313
\(596\) −7.74272e8 + 5.62542e8i −0.149807 + 0.108841i
\(597\) 0 0
\(598\) 2.00943e9 6.18439e9i 0.384254 1.18261i
\(599\) −2.86306e9 + 3.94066e9i −0.544297 + 0.749160i −0.989225 0.146406i \(-0.953229\pi\)
0.444928 + 0.895567i \(0.353229\pi\)
\(600\) 0 0
\(601\) −8.96163e9 2.91181e9i −1.68394 0.547145i −0.698270 0.715835i \(-0.746046\pi\)
−0.985669 + 0.168690i \(0.946046\pi\)
\(602\) 1.62931e9 + 5.01451e9i 0.304380 + 0.936787i
\(603\) 0 0
\(604\) 2.43065e9i 0.448841i
\(605\) 2.77396e9 1.56101e9i 0.509280 0.286591i
\(606\) 0 0
\(607\) −2.53882e9 3.49438e9i −0.460756 0.634176i 0.513909 0.857845i \(-0.328197\pi\)
−0.974665 + 0.223668i \(0.928197\pi\)
\(608\) −2.90236e9 + 9.43033e8i −0.523707 + 0.170163i
\(609\) 0 0
\(610\) 1.73600e9 + 1.26128e9i 0.309668 + 0.224987i
\(611\) −1.51488e8 1.10062e8i −0.0268679 0.0195207i
\(612\) 0 0
\(613\) −4.21404e9 + 1.36923e9i −0.738903 + 0.240084i −0.654199 0.756322i \(-0.726994\pi\)
−0.0847034 + 0.996406i \(0.526994\pi\)
\(614\) −7.56077e9 1.04065e10i −1.31819 1.81433i
\(615\) 0 0
\(616\) 2.06500e9 + 4.50845e8i 0.355949 + 0.0777132i
\(617\) 6.98347e9i 1.19694i 0.801144 + 0.598471i \(0.204225\pi\)
−0.801144 + 0.598471i \(0.795775\pi\)
\(618\) 0 0
\(619\) 2.60161e9 + 8.00694e9i 0.440885 + 1.35690i 0.886934 + 0.461896i \(0.152831\pi\)
−0.446049 + 0.895009i \(0.647169\pi\)
\(620\) −2.58492e8 8.39892e7i −0.0435588 0.0141531i
\(621\) 0 0
\(622\) 2.87504e9 3.95715e9i 0.479047 0.659351i
\(623\) 7.64309e8 2.35230e9i 0.126637 0.389749i
\(624\) 0 0
\(625\) −4.54874e8 + 3.30485e8i −0.0745266 + 0.0541467i
\(626\) 1.11167e9 0.181120
\(627\) 0 0
\(628\) −8.57038e8 −0.138083
\(629\) −1.36576e9 + 9.92279e8i −0.218824 + 0.158985i
\(630\) 0 0
\(631\) 2.06046e8 6.34145e8i 0.0326484 0.100481i −0.933404 0.358826i \(-0.883177\pi\)
0.966053 + 0.258345i \(0.0831771\pi\)
\(632\) 5.43848e8 7.48542e8i 0.0856974 0.117952i
\(633\) 0 0
\(634\) 4.59080e8 + 1.49164e8i 0.0715445 + 0.0232462i
\(635\) −1.04931e9 3.22945e9i −0.162629 0.500520i
\(636\) 0 0
\(637\) 2.31747e9i 0.355244i
\(638\) 1.19193e10 1.18636e9i 1.81710 0.180860i
\(639\) 0 0
\(640\) 2.31661e9 + 3.18854e9i 0.349320 + 0.480798i
\(641\) 5.82066e9 1.89125e9i 0.872910 0.283626i 0.161899 0.986807i \(-0.448238\pi\)
0.711010 + 0.703182i \(0.248238\pi\)
\(642\) 0 0
\(643\) 1.74840e9 + 1.27029e9i 0.259360 + 0.188436i 0.709865 0.704338i \(-0.248756\pi\)
−0.450505 + 0.892774i \(0.648756\pi\)
\(644\) 3.16655e9 + 2.30063e9i 0.467181 + 0.339427i
\(645\) 0 0
\(646\) 2.29034e9 7.44177e8i 0.334261 0.108608i
\(647\) −7.47669e9 1.02908e10i −1.08529 1.49377i −0.853565 0.520986i \(-0.825564\pi\)
−0.231721 0.972782i \(-0.574436\pi\)
\(648\) 0 0
\(649\) −2.34010e9 + 4.00204e9i −0.336030 + 0.574679i
\(650\) 3.45818e9i 0.493914i
\(651\) 0 0
\(652\) 1.78917e9 + 5.50649e9i 0.252804 + 0.778052i
\(653\) 1.30518e10 + 4.24078e9i 1.83431 + 0.596005i 0.998926 + 0.0463434i \(0.0147568\pi\)
0.835388 + 0.549661i \(0.185243\pi\)
\(654\) 0 0
\(655\) −3.28097e9 + 4.51586e9i −0.456202 + 0.627908i
\(656\) 3.13424e9 9.64619e9i 0.433479 1.33411i
\(657\) 0 0
\(658\) 2.59149e8 1.88283e8i 0.0354617 0.0257644i
\(659\) −5.43787e9 −0.740167 −0.370083 0.928999i \(-0.620671\pi\)
−0.370083 + 0.928999i \(0.620671\pi\)
\(660\) 0 0
\(661\) −8.82241e9 −1.18818 −0.594090 0.804399i \(-0.702488\pi\)
−0.594090 + 0.804399i \(0.702488\pi\)
\(662\) −2.80962e9 + 2.04131e9i −0.376396 + 0.273467i
\(663\) 0 0
\(664\) −1.98390e9 + 6.10582e9i −0.262985 + 0.809386i
\(665\) −9.36717e8 + 1.28928e9i −0.123519 + 0.170009i
\(666\) 0 0
\(667\) −1.77641e10 5.77190e9i −2.31794 0.753145i
\(668\) 1.35777e9 + 4.17877e9i 0.176241 + 0.542414i
\(669\) 0 0
\(670\) 2.45999e9i 0.315988i
\(671\) −2.74437e9 3.08194e9i −0.350682 0.393818i
\(672\) 0 0
\(673\) −3.45488e9 4.75523e9i −0.436898 0.601339i 0.532621 0.846354i \(-0.321207\pi\)
−0.969519 + 0.245015i \(0.921207\pi\)
\(674\) 3.16866e9 1.02956e9i 0.398626 0.129521i
\(675\) 0 0
\(676\) −2.24123e9 1.62835e9i −0.279044 0.202737i
\(677\) 6.68179e9 + 4.85461e9i 0.827623 + 0.601303i 0.918886 0.394524i \(-0.129090\pi\)
−0.0912628 + 0.995827i \(0.529090\pi\)
\(678\) 0 0
\(679\) −4.78359e9 + 1.55428e9i −0.586421 + 0.190540i
\(680\) −8.07407e8 1.11130e9i −0.0984717 0.135535i
\(681\) 0 0
\(682\) 1.28242e9 + 7.49862e8i 0.154804 + 0.0905182i
\(683\) 2.99225e9i 0.359356i −0.983725 0.179678i \(-0.942494\pi\)
0.983725 0.179678i \(-0.0575056\pi\)
\(684\) 0 0
\(685\) 1.32489e9 + 4.07758e9i 0.157493 + 0.484714i
\(686\) 1.01796e10 + 3.30754e9i 1.20391 + 0.391175i
\(687\) 0 0
\(688\) 7.74508e9 1.06602e10i 0.906706 1.24797i
\(689\) 2.28682e9 7.03811e9i 0.266357 0.819764i
\(690\) 0 0
\(691\) 3.88085e9 2.81960e9i 0.447459 0.325098i −0.341132 0.940015i \(-0.610810\pi\)
0.788592 + 0.614917i \(0.210810\pi\)
\(692\) 6.13141e9 0.703379
\(693\) 0 0
\(694\) 1.23707e9 0.140487
\(695\) −5.89290e8 + 4.28144e8i −0.0665859 + 0.0483775i
\(696\) 0 0
\(697\) −1.56748e9 + 4.82422e9i −0.175343 + 0.539650i
\(698\) 7.19867e9 9.90812e9i 0.801232 1.10280i
\(699\) 0 0
\(700\) 1.97967e9 + 6.43233e8i 0.218147 + 0.0708802i
\(701\) 2.52074e9 + 7.75804e9i 0.276385 + 0.850626i 0.988850 + 0.148918i \(0.0475790\pi\)
−0.712464 + 0.701708i \(0.752421\pi\)
\(702\) 0 0
\(703\) 2.76577e9i 0.300242i
\(704\) −1.03036e8 2.34901e8i −0.0111297 0.0253735i
\(705\) 0 0
\(706\) 1.13941e10 + 1.56826e10i 1.21860 + 1.67726i
\(707\) −4.83421e9 + 1.57073e9i −0.514467 + 0.167161i
\(708\) 0 0
\(709\) 1.10246e10 + 8.00988e9i 1.16172 + 0.844042i 0.989995 0.141102i \(-0.0450647\pi\)
0.171729 + 0.985144i \(0.445065\pi\)
\(710\) −3.22775e8 2.34510e8i −0.0338451 0.0245899i
\(711\) 0 0
\(712\) −3.32183e9 + 1.07933e9i −0.344904 + 0.112066i
\(713\) −1.36161e9 1.87409e9i −0.140682 0.193632i
\(714\) 0 0
\(715\) 7.35689e8 3.36967e9i 0.0752702 0.344759i
\(716\) 7.96034e9i 0.810469i
\(717\) 0 0
\(718\) 5.74910e9 + 1.76939e10i 0.579648 + 1.78397i
\(719\) −8.63174e9 2.80462e9i −0.866059 0.281400i −0.157902 0.987455i \(-0.550473\pi\)
−0.708157 + 0.706055i \(0.750473\pi\)
\(720\) 0 0
\(721\) −6.66448e9 + 9.17287e9i −0.662206 + 0.911448i
\(722\) 2.66254e9 8.19446e9i 0.263279 0.810289i
\(723\) 0 0
\(724\) −7.88315e9 + 5.72744e9i −0.771995 + 0.560887i
\(725\) −9.93331e9 −0.968080
\(726\) 0 0
\(727\) 5.28447e9 0.510071 0.255036 0.966932i \(-0.417913\pi\)
0.255036 + 0.966932i \(0.417913\pi\)
\(728\) 1.85289e9 1.34620e9i 0.177987 0.129315i
\(729\) 0 0
\(730\) −2.36827e8 + 7.28880e8i −0.0225321 + 0.0693467i
\(731\) −3.87344e9 + 5.33134e9i −0.366764 + 0.504807i
\(732\) 0 0
\(733\) 8.64121e8 + 2.80770e8i 0.0810421 + 0.0263322i 0.349257 0.937027i \(-0.386434\pi\)
−0.268215 + 0.963359i \(0.586434\pi\)
\(734\) 4.11253e8 + 1.26571e9i 0.0383860 + 0.118140i
\(735\) 0 0
\(736\) 1.76185e10i 1.62891i
\(737\) 1.00912e9 4.62206e9i 0.0928552 0.425304i
\(738\) 0 0
\(739\) 2.79618e9 + 3.84861e9i 0.254865 + 0.350791i 0.917208 0.398410i \(-0.130438\pi\)
−0.662343 + 0.749201i \(0.730438\pi\)
\(740\) 1.78178e9 5.78936e8i 0.161638 0.0525194i
\(741\) 0 0
\(742\) 1.02419e10 + 7.44116e9i 0.920377 + 0.668693i
\(743\) 1.41027e10 + 1.02462e10i 1.26137 + 0.916439i 0.998824 0.0484811i \(-0.0154381\pi\)
0.262545 + 0.964920i \(0.415438\pi\)
\(744\) 0 0
\(745\) 2.13958e9 6.95193e8i 0.189576 0.0615968i
\(746\) 2.24338e9 + 3.08775e9i 0.197842 + 0.272306i
\(747\) 0 0
\(748\) −1.26019e9 2.87296e9i −0.110098 0.251000i
\(749\) 1.06524e8i 0.00926322i
\(750\) 0 0
\(751\) −4.59061e9 1.41285e10i −0.395486 1.21718i −0.928583 0.371126i \(-0.878972\pi\)
0.533097 0.846054i \(-0.321028\pi\)
\(752\) −7.61350e8 2.47377e8i −0.0652862 0.0212128i
\(753\) 0 0
\(754\) 7.62905e9 1.05005e10i 0.648143 0.892092i
\(755\) −1.76560e9 + 5.43395e9i −0.149306 + 0.459516i
\(756\) 0 0
\(757\) −1.68840e10 + 1.22669e10i −1.41462 + 1.02778i −0.421989 + 0.906601i \(0.638668\pi\)
−0.992631 + 0.121180i \(0.961332\pi\)
\(758\) −1.08309e10 −0.903278
\(759\) 0 0
\(760\) 2.25048e9 0.185963
\(761\) −1.04244e9 + 7.57377e8i −0.0857442 + 0.0622968i −0.629831 0.776732i \(-0.716876\pi\)
0.544087 + 0.839029i \(0.316876\pi\)
\(762\) 0 0
\(763\) −7.50515e8 + 2.30985e9i −0.0611679 + 0.188255i
\(764\) −2.69075e8 + 3.70350e8i −0.0218296 + 0.0300459i
\(765\) 0 0
\(766\) 9.99594e9 + 3.24788e9i 0.803568 + 0.261095i
\(767\) 1.55233e9 + 4.77758e9i 0.124222 + 0.382317i
\(768\) 0 0
\(769\) 1.52335e10i 1.20797i 0.796995 + 0.603986i \(0.206422\pi\)
−0.796995 + 0.603986i \(0.793578\pi\)
\(770\) 5.09343e9 + 2.97826e9i 0.402062 + 0.235096i
\(771\) 0 0
\(772\) −2.76719e9 3.80871e9i −0.216460 0.297932i
\(773\) −6.76997e9 + 2.19970e9i −0.527180 + 0.171291i −0.560501 0.828154i \(-0.689391\pi\)
0.0333215 + 0.999445i