Properties

Label 99.8.j.a.8.4
Level $99$
Weight $8$
Character 99.8
Analytic conductor $30.926$
Analytic rank $0$
Dimension $112$
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 8.4
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-14.7879 + 10.7440i) q^{2} +(63.6930 - 196.027i) q^{4} +(194.917 - 268.280i) q^{5} +(-72.5991 - 23.5889i) q^{7} +(441.228 + 1357.96i) q^{8} +O(q^{10})\) \(q+(-14.7879 + 10.7440i) q^{2} +(63.6930 - 196.027i) q^{4} +(194.917 - 268.280i) q^{5} +(-72.5991 - 23.5889i) q^{7} +(441.228 + 1357.96i) q^{8} +6061.48i q^{10} +(4373.83 - 597.324i) q^{11} +(5506.28 + 7578.75i) q^{13} +(1327.03 - 431.177i) q^{14} +(229.262 + 166.569i) q^{16} +(-9949.29 - 7228.58i) q^{17} +(-20612.9 + 6697.54i) q^{19} +(-40175.3 - 55296.5i) q^{20} +(-58261.9 + 55825.6i) q^{22} -88301.0i q^{23} +(-9839.67 - 30283.4i) q^{25} +(-162852. - 52913.9i) q^{26} +(-9248.11 + 12728.9i) q^{28} +(21088.6 - 64904.1i) q^{29} +(39589.7 - 28763.6i) q^{31} -187944. q^{32} +224793. q^{34} +(-20479.2 + 14879.0i) q^{35} +(12353.9 - 38021.3i) q^{37} +(232862. - 320508. i) q^{38} +(450317. + 146317. i) q^{40} +(129634. + 398974. i) q^{41} +273270. i q^{43} +(161491. - 895433. i) q^{44} +(948707. + 1.30578e6i) q^{46} +(1.12068e6 - 364132. i) q^{47} +(-661546. - 480641. i) q^{49} +(470873. + 342109. i) q^{50} +(1.83635e6 - 596666. i) q^{52} +(431286. + 593614. i) q^{53} +(692283. - 1.28984e6i) q^{55} -108995. i q^{56} +(385475. + 1.18637e6i) q^{58} +(-1.86916e6 - 607326. i) q^{59} +(1.39569e6 - 1.92100e6i) q^{61} +(-276411. + 850705. i) q^{62} +(2.74995e6 - 1.99795e6i) q^{64} +3.10649e6 q^{65} -369220. q^{67} +(-2.05070e6 + 1.48992e6i) q^{68} +(142984. - 440058. i) q^{70} +(2.08693e6 - 2.87241e6i) q^{71} +(-1.18339e6 - 384506. i) q^{73} +(225814. + 694984. i) q^{74} +4.46727e6i q^{76} +(-331626. - 59808.5i) q^{77} +(2.54246e6 + 3.49939e6i) q^{79} +(89374.2 - 29039.4i) q^{80} +(-6.20360e6 - 4.50718e6i) q^{82} +(-2.09707e6 - 1.52361e6i) q^{83} +(-3.87857e6 + 1.26022e6i) q^{85} +(-2.93601e6 - 4.04107e6i) q^{86} +(2.74100e6 + 5.67593e6i) q^{88} -6.18536e6i q^{89} +(-220977. - 680097. i) q^{91} +(-1.73094e7 - 5.62416e6i) q^{92} +(-1.26603e7 + 1.74254e7i) q^{94} +(-2.22099e6 + 6.83550e6i) q^{95} +(-7.39031e6 + 5.36938e6i) q^{97} +1.49469e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −14.7879 + 10.7440i −1.30708 + 0.949646i −0.999998 0.00203905i \(-0.999351\pi\)
−0.307077 + 0.951685i \(0.599351\pi\)
\(3\) 0 0
\(4\) 63.6930 196.027i 0.497601 1.53146i
\(5\) 194.917 268.280i 0.697356 0.959828i −0.302621 0.953111i \(-0.597862\pi\)
0.999977 0.00671741i \(-0.00213823\pi\)
\(6\) 0 0
\(7\) −72.5991 23.5889i −0.0799997 0.0259935i 0.268744 0.963212i \(-0.413392\pi\)
−0.348743 + 0.937218i \(0.613392\pi\)
\(8\) 441.228 + 1357.96i 0.304683 + 0.937719i
\(9\) 0 0
\(10\) 6061.48i 1.91681i
\(11\) 4373.83 597.324i 0.990803 0.135312i
\(12\) 0 0
\(13\) 5506.28 + 7578.75i 0.695115 + 0.956744i 0.999991 + 0.00435150i \(0.00138513\pi\)
−0.304876 + 0.952392i \(0.598615\pi\)
\(14\) 1327.03 431.177i 0.129250 0.0419959i
\(15\) 0 0
\(16\) 229.262 + 166.569i 0.0139931 + 0.0101665i
\(17\) −9949.29 7228.58i −0.491157 0.356847i 0.314472 0.949267i \(-0.398173\pi\)
−0.805629 + 0.592420i \(0.798173\pi\)
\(18\) 0 0
\(19\) −20612.9 + 6697.54i −0.689448 + 0.224015i −0.632727 0.774375i \(-0.718065\pi\)
−0.0567209 + 0.998390i \(0.518065\pi\)
\(20\) −40175.3 55296.5i −1.12293 1.54558i
\(21\) 0 0
\(22\) −58261.9 + 55825.6i −1.16656 + 1.11777i
\(23\) 88301.0i 1.51328i −0.653834 0.756638i \(-0.726840\pi\)
0.653834 0.756638i \(-0.273160\pi\)
\(24\) 0 0
\(25\) −9839.67 30283.4i −0.125948 0.387628i
\(26\) −162852. 52913.9i −1.81713 0.590423i
\(27\) 0 0
\(28\) −9248.11 + 12728.9i −0.0796159 + 0.109582i
\(29\) 21088.6 64904.1i 0.160567 0.494173i −0.838116 0.545493i \(-0.816343\pi\)
0.998682 + 0.0513193i \(0.0163426\pi\)
\(30\) 0 0
\(31\) 39589.7 28763.6i 0.238680 0.173411i −0.462015 0.886872i \(-0.652873\pi\)
0.700695 + 0.713461i \(0.252873\pi\)
\(32\) −187944. −1.01392
\(33\) 0 0
\(34\) 224793. 0.980858
\(35\) −20479.2 + 14879.0i −0.0807375 + 0.0586592i
\(36\) 0 0
\(37\) 12353.9 38021.3i 0.0400956 0.123402i −0.929005 0.370067i \(-0.879335\pi\)
0.969101 + 0.246665i \(0.0793348\pi\)
\(38\) 232862. 320508.i 0.688425 0.947536i
\(39\) 0 0
\(40\) 450317. + 146317.i 1.11252 + 0.361480i
\(41\) 129634. + 398974.i 0.293749 + 0.904067i 0.983639 + 0.180153i \(0.0576592\pi\)
−0.689889 + 0.723915i \(0.742341\pi\)
\(42\) 0 0
\(43\) 273270.i 0.524145i 0.965048 + 0.262073i \(0.0844060\pi\)
−0.965048 + 0.262073i \(0.915594\pi\)
\(44\) 161491. 895433.i 0.285800 1.58471i
\(45\) 0 0
\(46\) 948707. + 1.30578e6i 1.43708 + 1.97797i
\(47\) 1.12068e6 364132.i 1.57449 0.511583i 0.613860 0.789415i \(-0.289616\pi\)
0.960630 + 0.277832i \(0.0896158\pi\)
\(48\) 0 0
\(49\) −661546. 480641.i −0.803293 0.583626i
\(50\) 470873. + 342109.i 0.532732 + 0.387053i
\(51\) 0 0
\(52\) 1.83635e6 596666.i 1.81110 0.588464i
\(53\) 431286. + 593614.i 0.397924 + 0.547695i 0.960221 0.279240i \(-0.0900825\pi\)
−0.562298 + 0.826935i \(0.690082\pi\)
\(54\) 0 0
\(55\) 692283. 1.28984e6i 0.561066 1.04536i
\(56\) 108995.i 0.0829370i
\(57\) 0 0
\(58\) 385475. + 1.18637e6i 0.259417 + 0.798403i
\(59\) −1.86916e6 607326.i −1.18485 0.384982i −0.350684 0.936494i \(-0.614051\pi\)
−0.834167 + 0.551512i \(0.814051\pi\)
\(60\) 0 0
\(61\) 1.39569e6 1.92100e6i 0.787288 1.08361i −0.207152 0.978309i \(-0.566420\pi\)
0.994440 0.105300i \(-0.0335804\pi\)
\(62\) −276411. + 850705.i −0.147294 + 0.453323i
\(63\) 0 0
\(64\) 2.74995e6 1.99795e6i 1.31128 0.952698i
\(65\) 3.10649e6 1.40305
\(66\) 0 0
\(67\) −369220. −0.149977 −0.0749884 0.997184i \(-0.523892\pi\)
−0.0749884 + 0.997184i \(0.523892\pi\)
\(68\) −2.05070e6 + 1.48992e6i −0.790897 + 0.574620i
\(69\) 0 0
\(70\) 142984. 440058.i 0.0498245 0.153344i
\(71\) 2.08693e6 2.87241e6i 0.691995 0.952449i −0.308005 0.951385i \(-0.599661\pi\)
0.999999 0.00106427i \(-0.000338768\pi\)
\(72\) 0 0
\(73\) −1.18339e6 384506.i −0.356039 0.115684i 0.125536 0.992089i \(-0.459935\pi\)
−0.481575 + 0.876405i \(0.659935\pi\)
\(74\) 225814. + 694984.i 0.0647799 + 0.199372i
\(75\) 0 0
\(76\) 4.46727e6i 1.16733i
\(77\) −331626. 59808.5i −0.0827811 0.0149295i
\(78\) 0 0
\(79\) 2.54246e6 + 3.49939e6i 0.580174 + 0.798542i 0.993714 0.111944i \(-0.0357078\pi\)
−0.413540 + 0.910486i \(0.635708\pi\)
\(80\) 89374.2 29039.4i 0.0195163 0.00634122i
\(81\) 0 0
\(82\) −6.20360e6 4.50718e6i −1.24250 0.902726i
\(83\) −2.09707e6 1.52361e6i −0.402569 0.292484i 0.368017 0.929819i \(-0.380037\pi\)
−0.770587 + 0.637335i \(0.780037\pi\)
\(84\) 0 0
\(85\) −3.87857e6 + 1.26022e6i −0.685023 + 0.222578i
\(86\) −2.93601e6 4.04107e6i −0.497752 0.685097i
\(87\) 0 0
\(88\) 2.74100e6 + 5.67593e6i 0.428765 + 0.887867i
\(89\) 6.18536e6i 0.930037i −0.885301 0.465018i \(-0.846048\pi\)
0.885301 0.465018i \(-0.153952\pi\)
\(90\) 0 0
\(91\) −220977. 680097.i −0.0307399 0.0946076i
\(92\) −1.73094e7 5.62416e6i −2.31752 0.753009i
\(93\) 0 0
\(94\) −1.26603e7 + 1.74254e7i −1.57215 + 2.16388i
\(95\) −2.22099e6 + 6.83550e6i −0.265775 + 0.817970i
\(96\) 0 0
\(97\) −7.39031e6 + 5.36938e6i −0.822170 + 0.597342i −0.917333 0.398120i \(-0.869663\pi\)
0.0951629 + 0.995462i \(0.469663\pi\)
\(98\) 1.49469e7 1.60420
\(99\) 0 0
\(100\) −6.56308e6 −0.656308
\(101\) 8.99227e6 6.53326e6i 0.868449 0.630965i −0.0617212 0.998093i \(-0.519659\pi\)
0.930170 + 0.367128i \(0.119659\pi\)
\(102\) 0 0
\(103\) 3.84333e6 1.18286e7i 0.346559 1.06660i −0.614185 0.789162i \(-0.710515\pi\)
0.960744 0.277437i \(-0.0894850\pi\)
\(104\) −7.86212e6 + 1.08213e7i −0.685367 + 0.943326i
\(105\) 0 0
\(106\) −1.27556e7 4.14455e6i −1.04023 0.337992i
\(107\) −470632. 1.44846e6i −0.0371397 0.114304i 0.930768 0.365611i \(-0.119140\pi\)
−0.967908 + 0.251306i \(0.919140\pi\)
\(108\) 0 0
\(109\) 2.42278e7i 1.79193i −0.444121 0.895967i \(-0.646484\pi\)
0.444121 0.895967i \(-0.353516\pi\)
\(110\) 3.62067e6 + 2.65119e7i 0.259367 + 1.89918i
\(111\) 0 0
\(112\) −12715.1 17500.8i −0.000855176 0.00117705i
\(113\) −1.43236e7 + 4.65400e6i −0.933848 + 0.303426i −0.736135 0.676834i \(-0.763351\pi\)
−0.197713 + 0.980260i \(0.563351\pi\)
\(114\) 0 0
\(115\) −2.36894e7 1.72114e7i −1.45249 1.05529i
\(116\) −1.13798e7 8.26787e6i −0.676908 0.491803i
\(117\) 0 0
\(118\) 3.41660e7 1.11012e7i 1.91429 0.621989i
\(119\) 551795. + 759481.i 0.0300168 + 0.0413145i
\(120\) 0 0
\(121\) 1.87736e7 5.22519e6i 0.963381 0.268135i
\(122\) 4.34028e7i 2.16400i
\(123\) 0 0
\(124\) −3.11685e6 9.59268e6i −0.146805 0.451819i
\(125\) 1.45969e7 + 4.74281e6i 0.668459 + 0.217196i
\(126\) 0 0
\(127\) −469790. + 646611.i −0.0203512 + 0.0280111i −0.819071 0.573692i \(-0.805511\pi\)
0.798720 + 0.601703i \(0.205511\pi\)
\(128\) −1.17658e7 + 3.62115e7i −0.495893 + 1.52620i
\(129\) 0 0
\(130\) −4.59384e7 + 3.33762e7i −1.83389 + 1.33240i
\(131\) 4.37657e7 1.70092 0.850460 0.526039i \(-0.176324\pi\)
0.850460 + 0.526039i \(0.176324\pi\)
\(132\) 0 0
\(133\) 1.65447e6 0.0609786
\(134\) 5.45998e6 3.96691e6i 0.196031 0.142425i
\(135\) 0 0
\(136\) 5.42623e6 1.67002e7i 0.184974 0.569293i
\(137\) 3.35338e7 4.61553e7i 1.11419 1.53355i 0.299102 0.954221i \(-0.403313\pi\)
0.815091 0.579333i \(-0.196687\pi\)
\(138\) 0 0
\(139\) 2.50224e7 + 8.13027e6i 0.790273 + 0.256775i 0.676220 0.736699i \(-0.263617\pi\)
0.114053 + 0.993475i \(0.463617\pi\)
\(140\) 1.61231e6 + 4.96217e6i 0.0496592 + 0.152835i
\(141\) 0 0
\(142\) 6.48987e7i 1.90207i
\(143\) 2.86105e7 + 2.98591e7i 0.818181 + 0.853887i
\(144\) 0 0
\(145\) −1.33020e7 1.83086e7i −0.362349 0.498731i
\(146\) 2.16309e7 7.02832e6i 0.575229 0.186903i
\(147\) 0 0
\(148\) −6.66634e6 4.84338e6i −0.169033 0.122810i
\(149\) −4.90229e7 3.56172e7i −1.21408 0.882081i −0.218485 0.975840i \(-0.570112\pi\)
−0.995595 + 0.0937595i \(0.970112\pi\)
\(150\) 0 0
\(151\) 6.61252e7 2.14854e7i 1.56296 0.507837i 0.605364 0.795949i \(-0.293028\pi\)
0.957597 + 0.288112i \(0.0930276\pi\)
\(152\) −1.81900e7 2.50364e7i −0.420127 0.578255i
\(153\) 0 0
\(154\) 5.54663e6 2.67856e6i 0.122379 0.0590988i
\(155\) 1.62276e7i 0.350021i
\(156\) 0 0
\(157\) −9.68557e6 2.98091e7i −0.199745 0.614752i −0.999888 0.0149434i \(-0.995243\pi\)
0.800143 0.599809i \(-0.204757\pi\)
\(158\) −7.51950e7 2.44323e7i −1.51666 0.492794i
\(159\) 0 0
\(160\) −3.66335e7 + 5.04217e7i −0.707063 + 0.973189i
\(161\) −2.08292e6 + 6.41058e6i −0.0393353 + 0.121062i
\(162\) 0 0
\(163\) 3.21683e6 2.33717e6i 0.0581797 0.0422701i −0.558315 0.829629i \(-0.688552\pi\)
0.616495 + 0.787359i \(0.288552\pi\)
\(164\) 8.64664e7 1.53071
\(165\) 0 0
\(166\) 4.73810e7 0.803944
\(167\) −8.53648e7 + 6.20211e7i −1.41831 + 1.03046i −0.426262 + 0.904600i \(0.640170\pi\)
−0.992048 + 0.125862i \(0.959830\pi\)
\(168\) 0 0
\(169\) −7.72790e6 + 2.37840e7i −0.123157 + 0.379037i
\(170\) 4.38159e7 6.03074e7i 0.684007 0.941455i
\(171\) 0 0
\(172\) 5.35682e7 + 1.74054e7i 0.802707 + 0.260815i
\(173\) −2.78623e7 8.57512e7i −0.409124 1.25915i −0.917402 0.397961i \(-0.869718\pi\)
0.508278 0.861193i \(-0.330282\pi\)
\(174\) 0 0
\(175\) 2.43066e6i 0.0342839i
\(176\) 1.10225e6 + 591599.i 0.0152400 + 0.00817962i
\(177\) 0 0
\(178\) 6.64556e7 + 9.14683e7i 0.883205 + 1.21563i
\(179\) −1.14626e8 + 3.72441e7i −1.49381 + 0.485369i −0.938206 0.346077i \(-0.887514\pi\)
−0.555606 + 0.831446i \(0.687514\pi\)
\(180\) 0 0
\(181\) −9.53899e7 6.93048e7i −1.19571 0.868737i −0.201858 0.979415i \(-0.564698\pi\)
−0.993856 + 0.110677i \(0.964698\pi\)
\(182\) 1.05748e7 + 7.68301e6i 0.130023 + 0.0944673i
\(183\) 0 0
\(184\) 1.19909e8 3.89609e7i 1.41903 0.461070i
\(185\) −7.79239e6 1.07253e7i −0.0904835 0.124540i
\(186\) 0 0
\(187\) −4.78343e7 2.56736e7i −0.534926 0.287106i
\(188\) 2.42876e8i 2.66583i
\(189\) 0 0
\(190\) −4.05970e7 1.24945e8i −0.429394 1.32154i
\(191\) −9.64312e7 3.13324e7i −1.00138 0.325370i −0.237966 0.971274i \(-0.576481\pi\)
−0.763419 + 0.645904i \(0.776481\pi\)
\(192\) 0 0
\(193\) −1.02374e7 + 1.40906e7i −0.102504 + 0.141084i −0.857188 0.515004i \(-0.827790\pi\)
0.754684 + 0.656089i \(0.227790\pi\)
\(194\) 5.15983e7 1.58803e8i 0.507375 1.56154i
\(195\) 0 0
\(196\) −1.36354e8 + 9.90673e7i −1.29352 + 0.939797i
\(197\) 1.27719e6 0.0119021 0.00595105 0.999982i \(-0.498106\pi\)
0.00595105 + 0.999982i \(0.498106\pi\)
\(198\) 0 0
\(199\) 1.89402e8 1.70372 0.851861 0.523768i \(-0.175474\pi\)
0.851861 + 0.523768i \(0.175474\pi\)
\(200\) 3.67822e7 2.67238e7i 0.325111 0.236207i
\(201\) 0 0
\(202\) −6.27830e7 + 1.93226e8i −0.535935 + 1.64944i
\(203\) −3.06203e6 + 4.21452e6i −0.0256906 + 0.0353600i
\(204\) 0 0
\(205\) 1.32305e8 + 4.29884e7i 1.07260 + 0.348508i
\(206\) 7.02515e7 + 2.16212e8i 0.559913 + 1.72323i
\(207\) 0 0
\(208\) 2.65469e6i 0.0204547i
\(209\) −8.61567e7 + 4.16065e7i −0.652795 + 0.315245i
\(210\) 0 0
\(211\) 9.01787e7 + 1.24120e8i 0.660869 + 0.909608i 0.999510 0.0313077i \(-0.00996719\pi\)
−0.338641 + 0.940916i \(0.609967\pi\)
\(212\) 1.43834e8 4.67346e7i 1.03678 0.336870i
\(213\) 0 0
\(214\) 2.25219e7 + 1.63631e7i 0.157093 + 0.114135i
\(215\) 7.33128e7 + 5.32649e7i 0.503089 + 0.365516i
\(216\) 0 0
\(217\) −3.55268e6 + 1.15434e6i −0.0236019 + 0.00766872i
\(218\) 2.60304e8 + 3.58278e8i 1.70170 + 2.34219i
\(219\) 0 0
\(220\) −2.08750e8 2.17860e8i −1.32174 1.37942i
\(221\) 1.15206e8i 0.717961i
\(222\) 0 0
\(223\) 4.53676e7 + 1.39627e8i 0.273955 + 0.843145i 0.989494 + 0.144573i \(0.0461809\pi\)
−0.715540 + 0.698572i \(0.753819\pi\)
\(224\) 1.36446e7 + 4.43339e6i 0.0811133 + 0.0263553i
\(225\) 0 0
\(226\) 1.61812e8 2.22715e8i 0.932463 1.28342i
\(227\) −2.81273e7 + 8.65669e7i −0.159602 + 0.491203i −0.998598 0.0529337i \(-0.983143\pi\)
0.838996 + 0.544137i \(0.183143\pi\)
\(228\) 0 0
\(229\) 5.17047e7 3.75657e7i 0.284515 0.206713i −0.436369 0.899768i \(-0.643736\pi\)
0.720885 + 0.693055i \(0.243736\pi\)
\(230\) 5.35235e8 2.90066
\(231\) 0 0
\(232\) 9.74422e7 0.512317
\(233\) −1.95276e8 + 1.41876e8i −1.01135 + 0.734792i −0.964493 0.264110i \(-0.914922\pi\)
−0.0468612 + 0.998901i \(0.514922\pi\)
\(234\) 0 0
\(235\) 1.20751e8 3.71632e8i 0.606948 1.86800i
\(236\) −2.38104e8 + 3.27723e8i −1.17917 + 1.62298i
\(237\) 0 0
\(238\) −1.63198e7 5.30261e6i −0.0784683 0.0254959i
\(239\) −6.81816e7 2.09841e8i −0.323054 0.994257i −0.972311 0.233689i \(-0.924920\pi\)
0.649258 0.760568i \(-0.275080\pi\)
\(240\) 0 0
\(241\) 3.16216e8i 1.45521i 0.685998 + 0.727603i \(0.259366\pi\)
−0.685998 + 0.727603i \(0.740634\pi\)
\(242\) −2.21482e8 + 2.78973e8i −1.00458 + 1.26534i
\(243\) 0 0
\(244\) −2.87672e8 3.95946e8i −1.26775 1.74491i
\(245\) −2.57893e8 + 8.37945e7i −1.12036 + 0.364028i
\(246\) 0 0
\(247\) −1.64259e8 1.19341e8i −0.693571 0.503909i
\(248\) 5.65280e7 + 4.10700e7i 0.235333 + 0.170979i
\(249\) 0 0
\(250\) −2.66814e8 + 8.66930e7i −1.07999 + 0.350909i
\(251\) −849631. 1.16942e6i −0.00339135 0.00466779i 0.807318 0.590117i \(-0.200918\pi\)
−0.810709 + 0.585449i \(0.800918\pi\)
\(252\) 0 0
\(253\) −5.27443e7 3.86214e8i −0.204764 1.49936i
\(254\) 1.46094e7i 0.0559391i
\(255\) 0 0
\(256\) −8.06160e7 2.48110e8i −0.300318 0.924283i
\(257\) 2.83614e8 + 9.21519e7i 1.04223 + 0.338640i 0.779613 0.626261i \(-0.215416\pi\)
0.262613 + 0.964901i \(0.415416\pi\)
\(258\) 0 0
\(259\) −1.79376e6 + 2.46890e6i −0.00641528 + 0.00882987i
\(260\) 1.97862e8 6.08956e8i 0.698161 2.14872i
\(261\) 0 0
\(262\) −6.47201e8 + 4.70219e8i −2.22323 + 1.61527i
\(263\) −3.08584e8 −1.04599 −0.522996 0.852335i \(-0.675186\pi\)
−0.522996 + 0.852335i \(0.675186\pi\)
\(264\) 0 0
\(265\) 2.43320e8 0.803188
\(266\) −2.44660e7 + 1.77756e7i −0.0797035 + 0.0579080i
\(267\) 0 0
\(268\) −2.35167e7 + 7.23771e7i −0.0746286 + 0.229683i
\(269\) −2.57083e8 + 3.53845e8i −0.805269 + 1.10836i 0.186767 + 0.982404i \(0.440199\pi\)
−0.992036 + 0.125954i \(0.959801\pi\)
\(270\) 0 0
\(271\) 9.85469e7 + 3.20198e7i 0.300781 + 0.0977296i 0.455519 0.890226i \(-0.349454\pi\)
−0.154739 + 0.987955i \(0.549454\pi\)
\(272\) −1.07694e6 3.31448e6i −0.00324489 0.00998675i
\(273\) 0 0
\(274\) 1.04282e9i 3.06256i
\(275\) −6.11261e7 1.26577e8i −0.177240 0.367020i
\(276\) 0 0
\(277\) −7.39417e7 1.01772e8i −0.209031 0.287706i 0.691609 0.722272i \(-0.256902\pi\)
−0.900640 + 0.434566i \(0.856902\pi\)
\(278\) −4.57380e8 + 1.48612e8i −1.27679 + 0.414855i
\(279\) 0 0
\(280\) −2.92412e7 2.12450e7i −0.0796052 0.0578366i
\(281\) 1.30972e8 + 9.51567e7i 0.352133 + 0.255839i 0.749763 0.661706i \(-0.230167\pi\)
−0.397630 + 0.917546i \(0.630167\pi\)
\(282\) 0 0
\(283\) −2.04333e8 + 6.63917e7i −0.535901 + 0.174125i −0.564450 0.825467i \(-0.690912\pi\)
0.0285482 + 0.999592i \(0.490912\pi\)
\(284\) −4.30146e8 5.92046e8i −1.11430 1.53370i
\(285\) 0 0
\(286\) −7.43895e8 1.34161e8i −1.88031 0.339113i
\(287\) 3.20231e7i 0.0799607i
\(288\) 0 0
\(289\) −8.00657e7 2.46417e8i −0.195121 0.600521i
\(290\) 3.93415e8 + 1.27828e8i 0.947236 + 0.307775i
\(291\) 0 0
\(292\) −1.50747e8 + 2.07486e8i −0.354331 + 0.487695i
\(293\) 1.77785e8 5.47165e8i 0.412912 1.27081i −0.501193 0.865336i \(-0.667105\pi\)
0.914105 0.405478i \(-0.132895\pi\)
\(294\) 0 0
\(295\) −5.27264e8 + 3.83080e8i −1.19578 + 0.868785i
\(296\) 5.70824e7 0.127933
\(297\) 0 0
\(298\) 1.10762e9 2.42456
\(299\) 6.69211e8 4.86210e8i 1.44782 1.05190i
\(300\) 0 0
\(301\) 6.44612e6 1.98391e7i 0.0136244 0.0419315i
\(302\) −7.47012e8 + 1.02817e9i −1.56064 + 2.14804i
\(303\) 0 0
\(304\) −5.84136e6 1.89797e6i −0.0119249 0.00387465i
\(305\) −2.43323e8 7.48870e8i −0.491059 1.51132i
\(306\) 0 0
\(307\) 1.06336e8i 0.209746i 0.994486 + 0.104873i \(0.0334436\pi\)
−0.994486 + 0.104873i \(0.966556\pi\)
\(308\) −3.28463e7 + 6.11983e7i −0.0640560 + 0.119347i
\(309\) 0 0
\(310\) 1.74350e8 + 2.39972e8i 0.332396 + 0.457504i
\(311\) −2.88639e8 + 9.37846e7i −0.544119 + 0.176795i −0.568163 0.822916i \(-0.692346\pi\)
0.0240440 + 0.999711i \(0.492346\pi\)
\(312\) 0 0
\(313\) 6.64300e7 + 4.82642e7i 0.122450 + 0.0889652i 0.647325 0.762214i \(-0.275888\pi\)
−0.524875 + 0.851180i \(0.675888\pi\)
\(314\) 4.63498e8 + 3.36751e8i 0.844879 + 0.613840i
\(315\) 0 0
\(316\) 8.47911e8 2.75503e8i 1.51163 0.491158i
\(317\) 6.54888e8 + 9.01376e8i 1.15467 + 1.58927i 0.729197 + 0.684303i \(0.239894\pi\)
0.425477 + 0.904969i \(0.360106\pi\)
\(318\) 0 0
\(319\) 5.34692e7 2.96476e8i 0.0922224 0.511355i
\(320\) 1.12719e9i 1.92297i
\(321\) 0 0
\(322\) −3.80733e7 1.17178e8i −0.0635514 0.195591i
\(323\) 2.53497e8 + 8.23663e7i 0.418567 + 0.136001i
\(324\) 0 0
\(325\) 1.75330e8 2.41321e8i 0.283312 0.389946i
\(326\) −2.24595e7 + 6.91234e7i −0.0359037 + 0.110500i
\(327\) 0 0
\(328\) −4.84593e8 + 3.52077e8i −0.758260 + 0.550908i
\(329\) −8.99500e7 −0.139256
\(330\) 0 0
\(331\) 5.26497e8 0.797991 0.398996 0.916953i \(-0.369359\pi\)
0.398996 + 0.916953i \(0.369359\pi\)
\(332\) −4.32238e8 + 3.14039e8i −0.648246 + 0.470978i
\(333\) 0 0
\(334\) 5.96007e8 1.83432e9i 0.875263 2.69378i
\(335\) −7.19673e7 + 9.90545e7i −0.104587 + 0.143952i
\(336\) 0 0
\(337\) −5.61134e8 1.82324e8i −0.798661 0.259501i −0.118873 0.992909i \(-0.537928\pi\)
−0.679788 + 0.733409i \(0.737928\pi\)
\(338\) −1.41257e8 4.34744e8i −0.198976 0.612385i
\(339\) 0 0
\(340\) 8.40571e8i 1.15984i
\(341\) 1.55977e8 1.49455e8i 0.213020 0.204113i
\(342\) 0 0
\(343\) 7.36412e7 + 1.01358e8i 0.0985352 + 0.135622i
\(344\) −3.71090e8 + 1.20574e8i −0.491501 + 0.159698i
\(345\) 0 0
\(346\) 1.33334e9 + 9.68725e8i 1.73051 + 1.25729i
\(347\) 5.28779e8 + 3.84180e8i 0.679393 + 0.493608i 0.873156 0.487440i \(-0.162069\pi\)
−0.193763 + 0.981048i \(0.562069\pi\)
\(348\) 0 0
\(349\) 1.50436e9 4.88797e8i 1.89437 0.615517i 0.919321 0.393508i \(-0.128739\pi\)
0.975045 0.222009i \(-0.0712615\pi\)
\(350\) −2.61150e7 3.59442e7i −0.0325576 0.0448116i
\(351\) 0 0
\(352\) −8.22035e8 + 1.12264e8i −1.00460 + 0.137195i
\(353\) 3.80307e8i 0.460175i 0.973170 + 0.230088i \(0.0739012\pi\)
−0.973170 + 0.230088i \(0.926099\pi\)
\(354\) 0 0
\(355\) −3.63833e8 1.11976e9i −0.431621 1.32839i
\(356\) −1.21250e9 3.93964e8i −1.42431 0.462787i
\(357\) 0 0
\(358\) 1.29492e9 1.78230e9i 1.49160 2.05301i
\(359\) 4.32632e8 1.33150e9i 0.493501 1.51884i −0.325779 0.945446i \(-0.605626\pi\)
0.819280 0.573394i \(-0.194374\pi\)
\(360\) 0 0
\(361\) −3.43123e8 + 2.49293e8i −0.383861 + 0.278892i
\(362\) 2.15523e9 2.38788
\(363\) 0 0
\(364\) −1.47392e8 −0.160184
\(365\) −3.33818e8 + 2.42533e8i −0.359323 + 0.261063i
\(366\) 0 0
\(367\) −2.45330e8 + 7.55048e8i −0.259071 + 0.797340i 0.733929 + 0.679226i \(0.237685\pi\)
−0.993000 + 0.118113i \(0.962315\pi\)
\(368\) 1.47082e7 2.02441e7i 0.0153848 0.0211754i
\(369\) 0 0
\(370\) 2.30465e8 + 7.48828e7i 0.236537 + 0.0768557i
\(371\) −1.73083e7 5.32694e7i −0.0175973 0.0541589i
\(372\) 0 0
\(373\) 1.12986e9i 1.12731i 0.826010 + 0.563655i \(0.190605\pi\)
−0.826010 + 0.563655i \(0.809395\pi\)
\(374\) 9.83205e8 1.34274e8i 0.971837 0.132722i
\(375\) 0 0
\(376\) 9.88954e8 + 1.36118e9i 0.959441 + 1.32056i
\(377\) 6.08012e8 1.97555e8i 0.584409 0.189886i
\(378\) 0 0
\(379\) −2.95684e8 2.14827e8i −0.278991 0.202699i 0.439486 0.898249i \(-0.355161\pi\)
−0.718477 + 0.695551i \(0.755161\pi\)
\(380\) 1.19848e9 + 8.70746e8i 1.12044 + 0.814046i
\(381\) 0 0
\(382\) 1.76265e9 5.72719e8i 1.61787 0.525678i
\(383\) 4.78842e8 + 6.59069e8i 0.435508 + 0.599426i 0.969207 0.246249i \(-0.0791982\pi\)
−0.533698 + 0.845675i \(0.679198\pi\)
\(384\) 0 0
\(385\) −8.06850e7 + 7.73111e7i −0.0720577 + 0.0690445i
\(386\) 3.18361e8i 0.281750i
\(387\) 0 0
\(388\) 5.81831e8 + 1.79069e9i 0.505692 + 1.55636i
\(389\) −4.48316e7 1.45667e7i −0.0386154 0.0125469i 0.289646 0.957134i \(-0.406463\pi\)
−0.328261 + 0.944587i \(0.606463\pi\)
\(390\) 0 0
\(391\) −6.38291e8 + 8.78532e8i −0.540008 + 0.743257i
\(392\) 3.60800e8 1.11043e9i 0.302527 0.931084i
\(393\) 0 0
\(394\) −1.88869e7 + 1.37222e7i −0.0155570 + 0.0113028i
\(395\) 1.43438e9 1.17105
\(396\) 0 0
\(397\) −1.78256e9 −1.42980 −0.714902 0.699224i \(-0.753529\pi\)
−0.714902 + 0.699224i \(0.753529\pi\)
\(398\) −2.80085e9 + 2.03494e9i −2.22689 + 1.61793i
\(399\) 0 0
\(400\) 2.78840e6 8.58182e6i 0.00217844 0.00670455i
\(401\) −8.77578e8 + 1.20788e9i −0.679643 + 0.935448i −0.999930 0.0118727i \(-0.996221\pi\)
0.320287 + 0.947321i \(0.396221\pi\)
\(402\) 0 0
\(403\) 4.35984e8 + 1.41660e8i 0.331820 + 0.107815i
\(404\) −7.07951e8 2.17885e9i −0.534156 1.64396i
\(405\) 0 0
\(406\) 9.52223e7i 0.0706151i
\(407\) 3.13227e7 1.73678e8i 0.0230292 0.127692i
\(408\) 0 0
\(409\) 7.90411e7 + 1.08791e8i 0.0571244 + 0.0786250i 0.836623 0.547778i \(-0.184526\pi\)
−0.779499 + 0.626403i \(0.784526\pi\)
\(410\) −2.41837e9 + 7.85777e8i −1.73292 + 0.563061i
\(411\) 0 0
\(412\) −2.07392e9 1.50679e9i −1.46101 1.06148i
\(413\) 1.21373e8 + 8.81827e7i 0.0847807 + 0.0615968i
\(414\) 0 0
\(415\) −8.17511e8 + 2.65625e8i −0.561468 + 0.182432i
\(416\) −1.03487e9 1.42438e9i −0.704791 0.970062i
\(417\) 0 0
\(418\) 8.27053e8 1.54094e9i 0.553881 1.03197i
\(419\) 2.46822e9i 1.63921i −0.572930 0.819604i \(-0.694193\pi\)
0.572930 0.819604i \(-0.305807\pi\)
\(420\) 0 0
\(421\) −2.15144e8 6.62146e8i −0.140521 0.432480i 0.855887 0.517164i \(-0.173012\pi\)
−0.996408 + 0.0846833i \(0.973012\pi\)
\(422\) −2.66710e9 8.66593e8i −1.72761 0.561335i
\(423\) 0 0
\(424\) −6.15810e8 + 8.47590e8i −0.392343 + 0.540014i
\(425\) −1.21008e8 + 3.72425e8i −0.0764634 + 0.235330i
\(426\) 0 0
\(427\) −1.46640e8 + 1.06540e8i −0.0911496 + 0.0662240i
\(428\) −3.13913e8 −0.193533
\(429\) 0 0
\(430\) −1.65642e9 −1.00469
\(431\) 4.45542e8 3.23706e8i 0.268052 0.194751i −0.445637 0.895214i \(-0.647023\pi\)
0.713689 + 0.700463i \(0.247023\pi\)
\(432\) 0 0
\(433\) −3.42794e8 + 1.05501e9i −0.202920 + 0.624524i 0.796872 + 0.604148i \(0.206486\pi\)
−0.999792 + 0.0203762i \(0.993514\pi\)
\(434\) 4.01344e7 5.52402e7i 0.0235669 0.0324370i
\(435\) 0 0
\(436\) −4.74931e9 1.54314e9i −2.74427 0.891669i
\(437\) 5.91399e8 + 1.82014e9i 0.338997 + 1.04333i
\(438\) 0 0
\(439\) 1.80506e9i 1.01828i −0.860684 0.509139i \(-0.829964\pi\)
0.860684 0.509139i \(-0.170036\pi\)
\(440\) 2.05701e9 + 3.70980e8i 1.15120 + 0.207618i
\(441\) 0 0
\(442\) 1.23777e9 + 1.70365e9i 0.681809 + 0.938429i
\(443\) 1.17482e8 3.81722e7i 0.0642034 0.0208609i −0.276739 0.960945i \(-0.589254\pi\)
0.340943 + 0.940084i \(0.389254\pi\)
\(444\) 0 0
\(445\) −1.65941e9 1.20563e9i −0.892675 0.648567i
\(446\) −2.17104e9 1.57736e9i −1.15877 0.841895i
\(447\) 0 0
\(448\) −2.46773e8 + 8.01815e7i −0.129666 + 0.0421309i
\(449\) −1.68117e9 2.31393e9i −0.876494 1.20639i −0.977380 0.211492i \(-0.932168\pi\)
0.100886 0.994898i \(-0.467832\pi\)
\(450\) 0 0
\(451\) 8.05315e8 + 1.66761e9i 0.413379 + 0.856005i
\(452\) 3.10423e9i 1.58114i
\(453\) 0 0
\(454\) −5.14133e8 1.58234e9i −0.257858 0.793604i
\(455\) −2.25529e8 7.32787e7i −0.112244 0.0364702i
\(456\) 0 0
\(457\) −1.49764e9 + 2.06132e9i −0.734007 + 1.01027i 0.264935 + 0.964266i \(0.414650\pi\)
−0.998941 + 0.0460069i \(0.985350\pi\)
\(458\) −3.60996e8 + 1.11103e9i −0.175579 + 0.540378i
\(459\) 0 0
\(460\) −4.88274e9 + 3.54752e9i −2.33890 + 1.69931i
\(461\) 1.43615e9 0.682726 0.341363 0.939932i \(-0.389112\pi\)
0.341363 + 0.939932i \(0.389112\pi\)
\(462\) 0 0
\(463\) 3.63234e9 1.70080 0.850399 0.526138i \(-0.176360\pi\)
0.850399 + 0.526138i \(0.176360\pi\)
\(464\) 1.56458e7 1.13674e7i 0.00727085 0.00528258i
\(465\) 0 0
\(466\) 1.36339e9 4.19610e9i 0.624124 1.92086i
\(467\) 1.00506e8 1.38334e8i 0.0456648 0.0628521i −0.785574 0.618768i \(-0.787632\pi\)
0.831239 + 0.555916i \(0.187632\pi\)
\(468\) 0 0
\(469\) 2.68051e7 + 8.70950e6i 0.0119981 + 0.00389842i
\(470\) 2.20718e9 + 6.79299e9i 0.980606 + 3.01800i
\(471\) 0 0
\(472\) 2.80621e9i 1.22835i
\(473\) 1.63231e8 + 1.19523e9i 0.0709230 + 0.519325i
\(474\) 0 0
\(475\) 4.05648e8 + 5.58327e8i 0.173669 + 0.239035i
\(476\) 1.84024e8 5.97931e7i 0.0782079 0.0254113i
\(477\) 0 0
\(478\) 3.26280e9 + 2.37056e9i 1.36645 + 0.992782i
\(479\) 1.95205e9 + 1.41825e9i 0.811551 + 0.589626i 0.914280 0.405083i \(-0.132757\pi\)
−0.102729 + 0.994709i \(0.532757\pi\)
\(480\) 0 0
\(481\) 3.56178e8 1.15729e8i 0.145935 0.0474171i
\(482\) −3.39743e9 4.67616e9i −1.38193 1.90206i
\(483\) 0 0
\(484\) 1.71468e8 4.01293e9i 0.0687425 1.60880i
\(485\) 3.02926e9i 1.20570i
\(486\) 0 0
\(487\) 1.16512e9 + 3.58586e9i 0.457107 + 1.40683i 0.868644 + 0.495436i \(0.164992\pi\)
−0.411538 + 0.911393i \(0.635008\pi\)
\(488\) 3.22446e9 + 1.04769e9i 1.25599 + 0.408097i
\(489\) 0 0
\(490\) 2.91340e9 4.00995e9i 1.11870 1.53976i
\(491\) −1.15909e9 + 3.56732e9i −0.441909 + 1.36006i 0.443929 + 0.896062i \(0.353584\pi\)
−0.885838 + 0.463994i \(0.846416\pi\)
\(492\) 0 0
\(493\) −6.78981e8 + 4.93309e8i −0.255208 + 0.185419i
\(494\) 3.71125e9 1.38508
\(495\) 0 0
\(496\) 1.38675e7 0.00510286
\(497\) −2.19266e8 + 1.59306e8i −0.0801168 + 0.0582083i
\(498\) 0 0
\(499\) −1.50366e9 + 4.62778e9i −0.541748 + 1.66733i 0.186852 + 0.982388i \(0.440172\pi\)
−0.728600 + 0.684940i \(0.759828\pi\)
\(500\) 1.85944e9 2.55930e9i 0.665253 0.915642i
\(501\) 0 0
\(502\) 2.51285e7 + 8.16473e6i 0.00886549 + 0.00288057i
\(503\) 9.71261e8 + 2.98923e9i 0.340289 + 1.04730i 0.964058 + 0.265693i \(0.0856007\pi\)
−0.623769 + 0.781609i \(0.714399\pi\)
\(504\) 0 0
\(505\) 3.68589e9i 1.27357i
\(506\) 4.92946e9 + 5.14459e9i 1.69150 + 1.76532i
\(507\) 0 0
\(508\) 9.68307e7 + 1.33276e8i 0.0327710 + 0.0451055i
\(509\) 3.07026e9 9.97588e8i 1.03196 0.335304i 0.256395 0.966572i \(-0.417465\pi\)
0.775565 + 0.631268i \(0.217465\pi\)
\(510\) 0 0
\(511\) 7.68429e7 + 5.58297e7i 0.0254760 + 0.0185094i
\(512\) −8.49894e7 6.17484e7i −0.0279847 0.0203320i
\(513\) 0 0
\(514\) −5.18413e9 + 1.68443e9i −1.68386 + 0.547118i
\(515\) −2.42424e9 3.33667e9i −0.782077 1.07644i
\(516\) 0 0
\(517\) 4.68417e9 2.26206e9i 1.49079 0.719925i
\(518\) 5.57820e7i 0.0176335i
\(519\) 0 0
\(520\) 1.37067e9 + 4.21850e9i 0.427487 + 1.31567i
\(521\) −1.64022e7 5.32940e6i −0.00508125 0.00165100i 0.306475 0.951879i \(-0.400850\pi\)
−0.311557 + 0.950228i \(0.600850\pi\)
\(522\) 0 0
\(523\) −2.28534e9 + 3.14550e9i −0.698546 + 0.961466i 0.301423 + 0.953491i \(0.402539\pi\)
−0.999968 + 0.00797495i \(0.997461\pi\)
\(524\) 2.78757e9 8.57924e9i 0.846380 2.60489i
\(525\) 0 0
\(526\) 4.56330e9 3.31543e9i 1.36719 0.993321i
\(527\) −6.01809e8 −0.179111
\(528\) 0 0
\(529\) −4.39225e9 −1.29001
\(530\) −3.59818e9 + 2.61423e9i −1.04983 + 0.762744i
\(531\) 0 0
\(532\) 1.05378e8 3.24320e8i 0.0303430 0.0933862i
\(533\) −2.30992e9 + 3.17933e9i −0.660771 + 0.909474i
\(534\) 0 0
\(535\) −4.80327e8 1.56068e8i −0.135612 0.0440630i
\(536\) −1.62911e8 5.01387e8i −0.0456954 0.140636i
\(537\) 0 0
\(538\) 7.99472e9i 2.21343i
\(539\) −3.18059e9 1.70709e9i −0.874876 0.469564i
\(540\) 0 0
\(541\) −1.06024e8 1.45930e8i −0.0287882 0.0396236i 0.794380 0.607421i \(-0.207796\pi\)
−0.823168 + 0.567797i \(0.807796\pi\)
\(542\) −1.80132e9 + 5.85284e8i −0.485952 + 0.157895i
\(543\) 0 0
\(544\) 1.86991e9 + 1.35857e9i 0.497995 + 0.361814i
\(545\) −6.49985e9 4.72242e9i −1.71995 1.24962i
\(546\) 0 0
\(547\) 4.64326e9 1.50869e9i 1.21302 0.394134i 0.368484 0.929634i \(-0.379877\pi\)
0.844535 + 0.535501i \(0.179877\pi\)
\(548\) −6.91180e9 9.51328e9i −1.79415 2.46944i
\(549\) 0 0
\(550\) 2.26387e9 + 1.21506e9i 0.580205 + 0.311408i
\(551\) 1.47910e9i 0.376676i
\(552\) 0 0
\(553\) −1.02033e8 3.14026e8i −0.0256569 0.0789638i
\(554\) 2.18688e9 + 7.10560e8i 0.546438 + 0.177548i
\(555\) 0 0
\(556\) 3.18750e9 4.38722e9i 0.786482 1.08250i
\(557\) −1.37870e8 + 4.24321e8i −0.0338047 + 0.104040i −0.966535 0.256534i \(-0.917419\pi\)
0.932730 + 0.360575i \(0.117419\pi\)
\(558\) 0 0
\(559\) −2.07104e9 + 1.50470e9i −0.501473 + 0.364341i
\(560\) −7.17349e6 −0.00172613
\(561\) 0 0
\(562\) −2.95916e9 −0.703221
\(563\) −1.07591e9 + 7.81691e8i −0.254094 + 0.184610i −0.707539 0.706674i \(-0.750195\pi\)
0.453445 + 0.891284i \(0.350195\pi\)
\(564\) 0 0
\(565\) −1.54333e9 + 4.74987e9i −0.359988 + 1.10793i
\(566\) 2.30833e9 3.17714e9i 0.535106 0.736511i
\(567\) 0 0
\(568\) 4.82143e9 + 1.56658e9i 1.10397 + 0.358701i
\(569\) 5.16896e8 + 1.59084e9i 0.117628 + 0.362021i 0.992486 0.122358i \(-0.0390455\pi\)
−0.874858 + 0.484379i \(0.839046\pi\)
\(570\) 0 0
\(571\) 1.64546e9i 0.369881i −0.982750 0.184940i \(-0.940791\pi\)
0.982750 0.184940i \(-0.0592092\pi\)
\(572\) 7.67547e9 3.70661e9i 1.71482 0.828115i
\(573\) 0 0
\(574\) 3.44056e8 + 4.73553e8i 0.0759343 + 0.104515i
\(575\) −2.67406e9 + 8.68853e8i −0.586588 + 0.190594i
\(576\) 0 0
\(577\) 1.48214e9 + 1.07684e9i 0.321200 + 0.233365i 0.736687 0.676234i \(-0.236389\pi\)
−0.415488 + 0.909599i \(0.636389\pi\)
\(578\) 3.83151e9 + 2.78375e9i 0.825319 + 0.599630i
\(579\) 0 0
\(580\) −4.43621e9 + 1.44141e9i −0.944092 + 0.306754i
\(581\) 1.16305e8 + 1.60081e8i 0.0246027 + 0.0338628i
\(582\) 0 0
\(583\) 2.24095e9 + 2.33875e9i 0.468374 + 0.488814i
\(584\) 1.77665e9i 0.369111i
\(585\) 0 0
\(586\) 3.24969e9 + 1.00015e10i 0.667115 + 2.05317i
\(587\) −5.54757e8 1.80251e8i −0.113206 0.0367828i 0.251866 0.967762i \(-0.418956\pi\)
−0.365072 + 0.930979i \(0.618956\pi\)
\(588\) 0 0
\(589\) −6.23413e8 + 8.58055e8i −0.125711 + 0.173026i
\(590\) 3.68130e9 1.13299e10i 0.737936 2.27113i
\(591\) 0 0
\(592\) 9.16544e6 6.65908e6i 0.00181563 0.00131913i
\(593\) −6.34419e9 −1.24935 −0.624676 0.780884i \(-0.714769\pi\)
−0.624676 + 0.780884i \(0.714769\pi\)
\(594\) 0 0
\(595\) 3.11308e8 0.0605872
\(596\) −1.01044e10 + 7.34124e9i −1.95500 + 1.42039i
\(597\) 0 0
\(598\) −4.67235e9 + 1.43800e10i −0.893473 + 2.74983i
\(599\) 4.39871e9 6.05430e9i 0.836241 1.15099i −0.150488 0.988612i \(-0.548085\pi\)
0.986729 0.162375i \(-0.0519155\pi\)
\(600\) 0 0
\(601\) −2.91754e9 9.47966e8i −0.548222 0.178128i 0.0217930 0.999763i \(-0.493063\pi\)
−0.570015 + 0.821634i \(0.693063\pi\)
\(602\) 1.17827e8 + 3.62636e8i 0.0220120 + 0.0677459i
\(603\) 0 0
\(604\) 1.43308e10i 2.64631i
\(605\) 2.25747e9 6.05506e9i 0.414457 1.11167i
\(606\) 0 0
\(607\) 2.70175e9 + 3.71864e9i 0.490325 + 0.674875i 0.980448 0.196779i \(-0.0630480\pi\)
−0.490123 + 0.871653i \(0.663048\pi\)
\(608\) 3.87407e9 1.25876e9i 0.699045 0.227134i
\(609\) 0 0
\(610\) 1.16441e10 + 8.45993e9i 2.07707 + 1.50908i
\(611\) 8.93045e9 + 6.48835e9i 1.58391 + 1.15077i
\(612\) 0 0
\(613\) −2.67774e9 + 8.70050e8i −0.469522 + 0.152557i −0.534216 0.845348i \(-0.679393\pi\)
0.0646934 + 0.997905i \(0.479393\pi\)
\(614\) −1.14247e9 1.57248e9i −0.199185 0.274154i
\(615\) 0 0
\(616\) −6.51053e7 4.76725e8i −0.0112223 0.0821742i
\(617\) 7.32574e9i 1.25561i −0.778373 0.627803i \(-0.783954\pi\)
0.778373 0.627803i \(-0.216046\pi\)
\(618\) 0 0
\(619\) −1.50954e8 4.64590e8i −0.0255816 0.0787322i 0.937451 0.348118i \(-0.113179\pi\)
−0.963032 + 0.269386i \(0.913179\pi\)
\(620\) −3.18105e9 1.03359e9i −0.536044 0.174171i
\(621\) 0 0
\(622\) 3.26074e9 4.48802e9i 0.543312 0.747805i
\(623\) −1.45906e8 + 4.49052e8i −0.0241749 + 0.0744026i
\(624\) 0 0
\(625\) 6.13013e9 4.45380e9i 1.00436 0.729711i
\(626\) −1.50091e9 −0.244537
\(627\) 0 0
\(628\) −6.46029e9 −1.04086
\(629\) −3.97752e8 + 2.88984e8i −0.0637288 + 0.0463017i
\(630\) 0 0
\(631\) 1.30938e9 4.02987e9i 0.207474 0.638539i −0.792129 0.610354i \(-0.791027\pi\)
0.999603 0.0281853i \(-0.00897286\pi\)
\(632\) −3.63023e9 + 4.99659e9i −0.572038 + 0.787343i
\(633\) 0 0
\(634\) −1.93688e10 6.29330e9i −3.01849 0.980767i
\(635\) 8.19028e7 + 2.52071e8i 0.0126938 + 0.0390674i
\(636\) 0 0
\(637\) 7.66024e9i 1.17423i
\(638\) 2.39465e9 + 4.95872e9i 0.365064 + 0.755958i
\(639\) 0 0
\(640\) 7.42147e9 + 1.02148e10i 1.11908 + 1.54028i
\(641\) −9.19294e9 + 2.98697e9i −1.37864 + 0.447948i −0.902222 0.431271i \(-0.858065\pi\)
−0.476418 + 0.879219i \(0.658065\pi\)
\(642\) 0 0
\(643\) 1.04351e10 + 7.58156e9i 1.54796 + 1.12466i 0.945087 + 0.326818i \(0.105977\pi\)
0.602871 + 0.797839i \(0.294023\pi\)
\(644\) 1.12398e9 + 8.16617e8i 0.165828 + 0.120481i
\(645\) 0 0
\(646\) −4.63363e9 + 1.50556e9i −0.676250 + 0.219727i
\(647\) −9.00612e8 1.23959e9i −0.130729 0.179933i 0.738634 0.674106i \(-0.235471\pi\)
−0.869364 + 0.494173i \(0.835471\pi\)
\(648\) 0 0
\(649\) −8.53814e9 1.53985e9i −1.22605 0.221117i
\(650\) 5.45238e9i 0.778734i
\(651\) 0 0
\(652\) −2.53257e8 7.79446e8i −0.0357846 0.110134i
\(653\) 1.09247e10 + 3.54965e9i 1.53537 + 0.498872i 0.950094 0.311963i \(-0.100986\pi\)
0.585276 + 0.810834i \(0.300986\pi\)
\(654\) 0 0
\(655\) 8.53067e9 1.17415e10i 1.18615 1.63259i
\(656\) −3.67363e7 + 1.13063e8i −0.00508080 + 0.0156371i
\(657\) 0 0
\(658\) 1.33017e9 9.66424e8i 0.182019 0.132244i
\(659\) 1.09359e7 0.00148852 0.000744262 1.00000i \(-0.499763\pi\)
0.000744262 1.00000i \(0.499763\pi\)
\(660\) 0 0
\(661\) −3.76410e9 −0.506939 −0.253469 0.967343i \(-0.581572\pi\)
−0.253469 + 0.967343i \(0.581572\pi\)
\(662\) −7.78577e9 + 5.65669e9i −1.04303 + 0.757809i
\(663\) 0 0
\(664\) 1.14372e9 3.52001e9i 0.151611 0.466612i
\(665\) 3.22483e8 4.43860e8i 0.0425238 0.0585289i
\(666\) 0 0
\(667\) −5.73110e9 1.86215e9i −0.747821 0.242982i
\(668\) 6.72067e9 + 2.06841e10i 0.872358 + 2.68484i
\(669\) 0 0
\(670\) 2.23802e9i 0.287477i
\(671\) 4.95704e9 9.23580e9i 0.633422 1.18017i
\(672\) 0 0
\(673\) −3.59607e9 4.94957e9i −0.454753 0.625914i 0.518657 0.854982i \(-0.326432\pi\)
−0.973410 + 0.229068i \(0.926432\pi\)
\(674\) 1.02569e10 3.33266e9i 1.29034 0.419258i
\(675\) 0 0
\(676\) 4.17009e9 + 3.02975e9i 0.519197 + 0.377219i
\(677\) 6.01956e9 + 4.37347e9i 0.745597 + 0.541708i 0.894459 0.447150i \(-0.147561\pi\)
−0.148862 + 0.988858i \(0.547561\pi\)
\(678\) 0 0
\(679\) 6.63188e8 2.15483e8i 0.0813004 0.0264161i
\(680\) −3.42267e9 4.71090e9i −0.417430 0.574543i
\(681\) 0 0
\(682\) −7.00827e8 + 3.88594e9i −0.0845990 + 0.469085i
\(683\) 6.55957e9i 0.787777i 0.919158 + 0.393888i \(0.128870\pi\)
−0.919158 + 0.393888i \(0.871130\pi\)
\(684\) 0 0
\(685\) −5.84624e9 1.79929e10i −0.694960 2.13887i
\(686\) −2.17799e9 7.07673e8i −0.257586 0.0836947i
\(687\) 0 0
\(688\) −4.55182e7 + 6.26504e7i −0.00532875 + 0.00733439i
\(689\) −2.12407e9 + 6.53722e9i −0.247401 + 0.761422i
\(690\) 0 0
\(691\) 3.46227e9 2.51548e9i 0.399197 0.290034i −0.370017 0.929025i \(-0.620648\pi\)
0.769214 + 0.638992i \(0.220648\pi\)
\(692\) −1.85842e10 −2.13192
\(693\) 0 0
\(694\) −1.19472e10 −1.35677
\(695\) 7.05848e9 5.12829e9i 0.797562 0.579463i
\(696\) 0 0
\(697\) 1.59424e9 4.90658e9i 0.178336 0.548863i
\(698\) −1.69947e10 + 2.33912e10i −1.89156 + 2.60350i
\(699\) 0 0
\(700\) 4.76474e8 + 1.54816e8i 0.0525044 + 0.0170597i
\(701\) −1.74200e9 5.36131e9i −0.191000 0.587838i −1.00000 2.93357e-5i \(-0.999991\pi\)
0.809000 0.587809i \(-0.200009\pi\)
\(702\) 0 0
\(703\) 8.66470e8i 0.0940611i
\(704\) 1.08344e10 1.03813e10i 1.17031 1.12137i
\(705\) 0 0
\(706\) −4.08603e9 5.62393e9i −0.437003 0.601483i
\(707\) −8.06943e8 + 2.62192e8i −0.0858766 + 0.0279030i
\(708\) 0 0
\(709\) −7.18831e9 5.22261e9i −0.757469 0.550334i 0.140664 0.990057i \(-0.455076\pi\)
−0.898133 + 0.439724i \(0.855076\pi\)
\(710\) 1.74110e10 + 1.26499e10i 1.82566 + 1.32642i
\(711\) 0 0
\(712\) 8.39948e9 2.72916e9i 0.872113 0.283367i
\(713\) −2.53986e9 3.49581e9i −0.262419 0.361189i
\(714\) 0 0
\(715\) 1.35873e10 1.85558e9i 1.39015 0.189850i
\(716\) 2.48419e10i 2.52923i
\(717\) 0 0
\(718\) 7.90800e9 + 2.43383e10i 0.797317 + 2.45389i
\(719\) 1.28303e10 + 4.16881e9i 1.28732 + 0.418274i 0.871151 0.491015i \(-0.163374\pi\)
0.416164 + 0.909289i \(0.363374\pi\)
\(720\) 0 0
\(721\) −5.58045e8 + 7.68083e8i −0.0554492 + 0.0763193i
\(722\) 2.39564e9 7.37303e9i 0.236887 0.729064i
\(723\) 0 0
\(724\) −1.96613e10 + 1.42848e10i −1.92543 + 1.39890i
\(725\) −2.17302e9 −0.211778
\(726\) 0 0
\(727\) −3.88356e9 −0.374852 −0.187426 0.982279i \(-0.560014\pi\)
−0.187426 + 0.982279i \(0.560014\pi\)
\(728\) 8.26045e8 6.00157e8i 0.0793494 0.0576507i
\(729\) 0 0
\(730\) 2.33068e9 7.17309e9i 0.221744 0.682459i
\(731\) 1.97535e9 2.71884e9i 0.187040 0.257438i
\(732\) 0 0
\(733\) −6.86357e9 2.23011e9i −0.643704 0.209152i −0.0310677 0.999517i \(-0.509891\pi\)
−0.612636 + 0.790365i \(0.709891\pi\)
\(734\) −4.48434e9 1.38014e10i −0.418564 1.28821i
\(735\) 0 0
\(736\) 1.65957e10i 1.53434i
\(737\) −1.61491e9 + 2.20544e8i −0.148597 + 0.0202936i
\(738\) 0 0
\(739\) −1.29510e9 1.78255e9i −0.118045 0.162475i 0.745905 0.666052i \(-0.232017\pi\)
−0.863950 + 0.503577i \(0.832017\pi\)
\(740\) −2.59877e9 + 8.44390e8i −0.235752 + 0.0766006i
\(741\) 0 0
\(742\) 8.28280e8 + 6.01781e8i 0.0744327 + 0.0540785i
\(743\) −6.12290e9 4.44855e9i −0.547641 0.397885i 0.279274 0.960212i \(-0.409906\pi\)
−0.826915 + 0.562327i \(0.809906\pi\)
\(744\) 0 0
\(745\) −1.91108e10 + 6.20947e9i −1.69329 + 0.550184i
\(746\) −1.21392e10 1.67082e10i −1.07055 1.47348i
\(747\) 0 0
\(748\) −8.07943e9 + 7.74157e9i −0.705870 + 0.676353i
\(749\) 1.16258e8i 0.0101097i
\(750\) 0 0
\(751\) 5.75420e9 + 1.77096e10i 0.495730 + 1.52570i 0.815816 + 0.578312i \(0.196288\pi\)
−0.320086 + 0.947389i \(0.603712\pi\)
\(752\) 3.17583e8 + 1.03189e8i 0.0272330 + 0.00884852i
\(753\) 0 0
\(754\) −6.86866e9 + 9.45390e9i −0.583542 + 0.803177i
\(755\) 7.12483e9 2.19280e10i 0.602504 1.85432i
\(756\) 0 0
\(757\) 1.80582e10 1.31200e10i 1.51300 1.09926i 0.548174 0.836364i \(-0.315323\pi\)
0.964825 0.262894i \(-0.0846770\pi\)
\(758\) 6.68063e9 0.557154
\(759\) 0 0
\(760\) −1.02623e10 −0.848003
\(761\) −1.01033e10 + 7.34046e9i −0.831029 + 0.603778i −0.919850 0.392270i \(-0.871690\pi\)
0.0888215 + 0.996048i \(0.471690\pi\)
\(762\) 0 0
\(763\) −5.71508e8 + 1.75892e9i −0.0465786 + 0.143354i
\(764\) −1.22840e10 + 1.69074e10i −0.996581 + 1.37168i
\(765\) 0 0
\(766\) −1.41621e10 4.60154e9i −1.13848 0.369916i
\(767\) −5.68934e9 1.75100e10i −0.455279 1.40121i
\(768\) 0 0
\(769\) 1.17360e10i 0.930630i 0.885145 + 0.465315i \(0.154059\pi\)
−0.885145 + 0.465315i \(0.845941\pi\)
\(770\) 3.62528e8 2.01015e9i 0.0286170 0.158676i
\(771\) 0 0
\(772\) 2.11008e9 + 2.90428e9i 0.165059 + 0.227184i
\(773\) −4.38016e9 + 1.42320e9i −0.341084 + 0.110825i −0.474550 0.880228i \(-0.657389\pi\)
0.133466 +