Properties

Label 99.8.j.a.8.15
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 8.15
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.51130 - 1.09802i) q^{2} +(-38.4758 + 118.416i) q^{4} +(76.1409 - 104.799i) q^{5} +(-748.574 - 243.227i) q^{7} +(145.766 + 448.620i) q^{8} +O(q^{10})\) \(q+(1.51130 - 1.09802i) q^{2} +(-38.4758 + 118.416i) q^{4} +(76.1409 - 104.799i) q^{5} +(-748.574 - 243.227i) q^{7} +(145.766 + 448.620i) q^{8} -241.988i q^{10} +(2321.23 + 3754.87i) q^{11} +(-2631.03 - 3621.30i) q^{13} +(-1398.39 + 454.365i) q^{14} +(-12180.7 - 8849.78i) q^{16} +(-16295.6 - 11839.4i) q^{17} +(17290.8 - 5618.11i) q^{19} +(9480.33 + 13048.6i) q^{20} +(7631.02 + 3125.97i) q^{22} -10616.6i q^{23} +(18956.6 + 58342.3i) q^{25} +(-7952.56 - 2583.94i) q^{26} +(57604.0 - 79285.1i) q^{28} +(53775.6 - 165504. i) q^{29} +(108254. - 78650.8i) q^{31} -88504.5 q^{32} -37627.5 q^{34} +(-82487.1 + 59930.4i) q^{35} +(154847. - 476569. i) q^{37} +(19962.7 - 27476.4i) q^{38} +(58113.7 + 18882.3i) q^{40} +(-82675.1 - 254448. i) q^{41} -458712. i q^{43} +(-533949. + 130400. i) q^{44} +(-11657.3 - 16044.9i) q^{46} +(-375838. + 122117. i) q^{47} +(-165056. - 119920. i) q^{49} +(92710.4 + 67358.0i) q^{50} +(530052. - 172224. i) q^{52} +(-484241. - 666501. i) q^{53} +(570248. + 42636.8i) q^{55} -371280. i q^{56} +(-100457. - 309174. i) q^{58} +(-1.72820e6 - 561527. i) q^{59} +(1.36409e6 - 1.87751e6i) q^{61} +(77243.2 - 237730. i) q^{62} +(1.42537e6 - 1.03559e6i) q^{64} -579838. q^{65} +3.01286e6 q^{67} +(2.02897e6 - 1.47413e6i) q^{68} +(-58857.8 + 181146. i) q^{70} +(-876758. + 1.20675e6i) q^{71} +(-3.44663e6 - 1.11988e6i) q^{73} +(-289265. - 890266. i) q^{74} +2.26367e6i q^{76} +(-824329. - 3.37539e6i) q^{77} +(-1.07213e6 - 1.47565e6i) q^{79} +(-1.85490e6 + 602692. i) q^{80} +(-404337. - 293768. i) q^{82} +(5.79033e6 + 4.20692e6i) q^{83} +(-2.48152e6 + 806296. i) q^{85} +(-503677. - 693252. i) q^{86} +(-1.34616e6 + 1.58868e6i) q^{88} +1.02936e7i q^{89} +(1.08872e6 + 3.35075e6i) q^{91} +(1.25718e6 + 408482. i) q^{92} +(-433917. + 597236. i) q^{94} +(727763. - 2.23982e6i) q^{95} +(-5.23658e6 + 3.80460e6i) q^{97} -381124. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.51130 1.09802i 0.133581 0.0970526i −0.518988 0.854782i \(-0.673691\pi\)
0.652569 + 0.757729i \(0.273691\pi\)
\(3\) 0 0
\(4\) −38.4758 + 118.416i −0.300592 + 0.925128i
\(5\) 76.1409 104.799i 0.272410 0.374940i −0.650791 0.759257i \(-0.725563\pi\)
0.923202 + 0.384316i \(0.125563\pi\)
\(6\) 0 0
\(7\) −748.574 243.227i −0.824882 0.268020i −0.133994 0.990982i \(-0.542780\pi\)
−0.690888 + 0.722962i \(0.742780\pi\)
\(8\) 145.766 + 448.620i 0.100656 + 0.309788i
\(9\) 0 0
\(10\) 241.988i 0.0765232i
\(11\) 2321.23 + 3754.87i 0.525828 + 0.850591i
\(12\) 0 0
\(13\) −2631.03 3621.30i −0.332142 0.457154i 0.609984 0.792414i \(-0.291176\pi\)
−0.942126 + 0.335260i \(0.891176\pi\)
\(14\) −1398.39 + 454.365i −0.136201 + 0.0442544i
\(15\) 0 0
\(16\) −12180.7 8849.78i −0.743449 0.540147i
\(17\) −16295.6 11839.4i −0.804450 0.584467i 0.107767 0.994176i \(-0.465630\pi\)
−0.912216 + 0.409709i \(0.865630\pi\)
\(18\) 0 0
\(19\) 17290.8 5618.11i 0.578331 0.187911i −0.00522159 0.999986i \(-0.501662\pi\)
0.583553 + 0.812075i \(0.301662\pi\)
\(20\) 9480.33 + 13048.6i 0.264983 + 0.364718i
\(21\) 0 0
\(22\) 7631.02 + 3125.97i 0.152793 + 0.0625901i
\(23\) 10616.6i 0.181944i −0.995853 0.0909721i \(-0.971003\pi\)
0.995853 0.0909721i \(-0.0289974\pi\)
\(24\) 0 0
\(25\) 18956.6 + 58342.3i 0.242644 + 0.746781i
\(26\) −7952.56 2583.94i −0.0887360 0.0288321i
\(27\) 0 0
\(28\) 57604.0 79285.1i 0.495906 0.682556i
\(29\) 53775.6 165504.i 0.409442 1.26013i −0.507686 0.861542i \(-0.669499\pi\)
0.917129 0.398591i \(-0.130501\pi\)
\(30\) 0 0
\(31\) 108254. 78650.8i 0.652644 0.474173i −0.211527 0.977372i \(-0.567844\pi\)
0.864171 + 0.503199i \(0.167844\pi\)
\(32\) −88504.5 −0.477464
\(33\) 0 0
\(34\) −37627.5 −0.164184
\(35\) −82487.1 + 59930.4i −0.325198 + 0.236270i
\(36\) 0 0
\(37\) 154847. 476569.i 0.502569 1.54675i −0.302249 0.953229i \(-0.597737\pi\)
0.804819 0.593521i \(-0.202263\pi\)
\(38\) 19962.7 27476.4i 0.0590171 0.0812300i
\(39\) 0 0
\(40\) 58113.7 + 18882.3i 0.143572 + 0.0466492i
\(41\) −82675.1 254448.i −0.187340 0.576574i 0.812640 0.582765i \(-0.198029\pi\)
−0.999981 + 0.00619105i \(0.998029\pi\)
\(42\) 0 0
\(43\) 458712.i 0.879833i −0.898039 0.439917i \(-0.855008\pi\)
0.898039 0.439917i \(-0.144992\pi\)
\(44\) −533949. + 130400.i −0.944965 + 0.230777i
\(45\) 0 0
\(46\) −11657.3 16044.9i −0.0176582 0.0243044i
\(47\) −375838. + 122117.i −0.528030 + 0.171567i −0.560887 0.827893i \(-0.689540\pi\)
0.0328564 + 0.999460i \(0.489540\pi\)
\(48\) 0 0
\(49\) −165056. 119920.i −0.200422 0.145615i
\(50\) 92710.4 + 67358.0i 0.104890 + 0.0762069i
\(51\) 0 0
\(52\) 530052. 172224.i 0.522765 0.169857i
\(53\) −484241. 666501.i −0.446782 0.614943i 0.524920 0.851152i \(-0.324095\pi\)
−0.971702 + 0.236208i \(0.924095\pi\)
\(54\) 0 0
\(55\) 570248. + 42636.8i 0.462162 + 0.0345553i
\(56\) 371280.i 0.282516i
\(57\) 0 0
\(58\) −100457. 309174.i −0.0676053 0.208068i
\(59\) −1.72820e6 561527.i −1.09550 0.355949i −0.295131 0.955457i \(-0.595363\pi\)
−0.800369 + 0.599508i \(0.795363\pi\)
\(60\) 0 0
\(61\) 1.36409e6 1.87751e6i 0.769465 1.05908i −0.226902 0.973918i \(-0.572860\pi\)
0.996367 0.0851602i \(-0.0271402\pi\)
\(62\) 77243.2 237730.i 0.0411613 0.126682i
\(63\) 0 0
\(64\) 1.42537e6 1.03559e6i 0.679669 0.493808i
\(65\) −579838. −0.261884
\(66\) 0 0
\(67\) 3.01286e6 1.22382 0.611910 0.790927i \(-0.290401\pi\)
0.611910 + 0.790927i \(0.290401\pi\)
\(68\) 2.02897e6 1.47413e6i 0.782518 0.568532i
\(69\) 0 0
\(70\) −58857.8 + 181146.i −0.0205098 + 0.0631226i
\(71\) −876758. + 1.20675e6i −0.290721 + 0.400143i −0.929248 0.369457i \(-0.879544\pi\)
0.638527 + 0.769599i \(0.279544\pi\)
\(72\) 0 0
\(73\) −3.44663e6 1.11988e6i −1.03697 0.336931i −0.259425 0.965763i \(-0.583533\pi\)
−0.777541 + 0.628832i \(0.783533\pi\)
\(74\) −289265. 890266.i −0.0829821 0.255393i
\(75\) 0 0
\(76\) 2.26367e6i 0.591515i
\(77\) −824329. 3.37539e6i −0.205771 0.842570i
\(78\) 0 0
\(79\) −1.07213e6 1.47565e6i −0.244653 0.336736i 0.668977 0.743283i \(-0.266733\pi\)
−0.913630 + 0.406547i \(0.866733\pi\)
\(80\) −1.85490e6 + 602692.i −0.405046 + 0.131607i
\(81\) 0 0
\(82\) −404337. 293768.i −0.0809832 0.0588378i
\(83\) 5.79033e6 + 4.20692e6i 1.11155 + 0.807590i 0.982907 0.184101i \(-0.0589373\pi\)
0.128645 + 0.991691i \(0.458937\pi\)
\(84\) 0 0
\(85\) −2.48152e6 + 806296.i −0.438280 + 0.142406i
\(86\) −503677. 693252.i −0.0853901 0.117529i
\(87\) 0 0
\(88\) −1.34616e6 + 1.58868e6i −0.210575 + 0.248512i
\(89\) 1.02936e7i 1.54775i 0.633337 + 0.773876i \(0.281685\pi\)
−0.633337 + 0.773876i \(0.718315\pi\)
\(90\) 0 0
\(91\) 1.08872e6 + 3.35075e6i 0.151451 + 0.466119i
\(92\) 1.25718e6 + 408482.i 0.168322 + 0.0546910i
\(93\) 0 0
\(94\) −433917. + 597236.i −0.0538840 + 0.0741649i
\(95\) 727763. 2.23982e6i 0.0870878 0.268029i
\(96\) 0 0
\(97\) −5.23658e6 + 3.80460e6i −0.582568 + 0.423260i −0.839649 0.543129i \(-0.817239\pi\)
0.257081 + 0.966390i \(0.417239\pi\)
\(98\) −381124. −0.0409049
\(99\) 0 0
\(100\) −7.63805e6 −0.763805
\(101\) 2.67456e6 1.94319e6i 0.258302 0.187668i −0.451096 0.892475i \(-0.648967\pi\)
0.709398 + 0.704808i \(0.248967\pi\)
\(102\) 0 0
\(103\) 1.78103e6 5.48145e6i 0.160598 0.494271i −0.838087 0.545537i \(-0.816326\pi\)
0.998685 + 0.0512663i \(0.0163257\pi\)
\(104\) 1.24108e6 1.70819e6i 0.108189 0.148909i
\(105\) 0 0
\(106\) −1.46367e6 475575.i −0.119364 0.0387836i
\(107\) −815012. 2.50835e6i −0.0643163 0.197945i 0.913735 0.406312i \(-0.133185\pi\)
−0.978051 + 0.208367i \(0.933185\pi\)
\(108\) 0 0
\(109\) 1.77871e7i 1.31556i 0.753209 + 0.657782i \(0.228505\pi\)
−0.753209 + 0.657782i \(0.771495\pi\)
\(110\) 908632. 561709.i 0.0650899 0.0402381i
\(111\) 0 0
\(112\) 6.96564e6 + 9.58738e6i 0.468487 + 0.644817i
\(113\) 6.43549e6 2.09102e6i 0.419573 0.136327i −0.0916191 0.995794i \(-0.529204\pi\)
0.511192 + 0.859467i \(0.329204\pi\)
\(114\) 0 0
\(115\) −1.11261e6 808358.i −0.0682182 0.0495634i
\(116\) 1.75294e7 + 1.27358e7i 1.04271 + 0.757573i
\(117\) 0 0
\(118\) −3.22840e6 + 1.04897e6i −0.180884 + 0.0587729i
\(119\) 9.31879e6 + 1.28262e7i 0.506927 + 0.697725i
\(120\) 0 0
\(121\) −8.71095e6 + 1.74318e7i −0.447009 + 0.894529i
\(122\) 4.33529e6i 0.216152i
\(123\) 0 0
\(124\) 5.14840e6 + 1.58451e7i 0.242491 + 0.746311i
\(125\) 1.71825e7 + 5.58293e6i 0.786866 + 0.255668i
\(126\) 0 0
\(127\) 5.32956e6 7.33550e6i 0.230876 0.317773i −0.677824 0.735225i \(-0.737077\pi\)
0.908699 + 0.417452i \(0.137077\pi\)
\(128\) 4.51778e6 1.39043e7i 0.190410 0.586022i
\(129\) 0 0
\(130\) −876310. + 636676.i −0.0349829 + 0.0254166i
\(131\) −3.16408e7 −1.22970 −0.614849 0.788645i \(-0.710783\pi\)
−0.614849 + 0.788645i \(0.710783\pi\)
\(132\) 0 0
\(133\) −1.43099e7 −0.527419
\(134\) 4.55335e6 3.30820e6i 0.163480 0.118775i
\(135\) 0 0
\(136\) 2.93608e6 9.03631e6i 0.100088 0.308039i
\(137\) −3.50383e7 + 4.82261e7i −1.16418 + 1.60236i −0.469756 + 0.882796i \(0.655658\pi\)
−0.694427 + 0.719564i \(0.744342\pi\)
\(138\) 0 0
\(139\) −4.30744e7 1.39957e7i −1.36040 0.442021i −0.464225 0.885717i \(-0.653667\pi\)
−0.896177 + 0.443696i \(0.853667\pi\)
\(140\) −3.92298e6 1.20737e7i −0.120828 0.371870i
\(141\) 0 0
\(142\) 2.78647e6i 0.0816668i
\(143\) 7.49029e6 1.82850e7i 0.214202 0.522902i
\(144\) 0 0
\(145\) −1.32502e7 1.82373e7i −0.360939 0.496789i
\(146\) −6.43855e6 + 2.09201e6i −0.171219 + 0.0556326i
\(147\) 0 0
\(148\) 5.04757e7 + 3.66728e7i 1.27987 + 0.929882i
\(149\) −8.08561e6 5.87454e6i −0.200245 0.145486i 0.483144 0.875541i \(-0.339495\pi\)
−0.683389 + 0.730055i \(0.739495\pi\)
\(150\) 0 0
\(151\) 9.81677e6 3.18966e6i 0.232033 0.0753920i −0.190693 0.981650i \(-0.561073\pi\)
0.422726 + 0.906258i \(0.361073\pi\)
\(152\) 5.04080e6 + 6.93806e6i 0.116425 + 0.160245i
\(153\) 0 0
\(154\) −4.95207e6 4.19609e6i −0.109261 0.0925811i
\(155\) 1.73334e7i 0.373872i
\(156\) 0 0
\(157\) −1.66182e7 5.11457e7i −0.342717 1.05478i −0.962795 0.270235i \(-0.912899\pi\)
0.620077 0.784541i \(-0.287101\pi\)
\(158\) −3.24061e6 1.05294e6i −0.0653622 0.0212375i
\(159\) 0 0
\(160\) −6.73881e6 + 9.27518e6i −0.130066 + 0.179020i
\(161\) −2.58224e6 + 7.94732e6i −0.0487647 + 0.150082i
\(162\) 0 0
\(163\) 5.03543e7 3.65845e7i 0.910709 0.661669i −0.0304852 0.999535i \(-0.509705\pi\)
0.941194 + 0.337866i \(0.109705\pi\)
\(164\) 3.33118e7 0.589718
\(165\) 0 0
\(166\) 1.33702e7 0.226861
\(167\) −7.01670e6 + 5.09793e6i −0.116580 + 0.0847006i −0.644548 0.764564i \(-0.722954\pi\)
0.527967 + 0.849265i \(0.322954\pi\)
\(168\) 0 0
\(169\) 1.31989e7 4.06219e7i 0.210345 0.647376i
\(170\) −2.86500e6 + 3.94333e6i −0.0447253 + 0.0615590i
\(171\) 0 0
\(172\) 5.43190e7 + 1.76493e7i 0.813958 + 0.264471i
\(173\) −2.17751e7 6.70170e7i −0.319742 0.984064i −0.973758 0.227584i \(-0.926917\pi\)
0.654016 0.756480i \(-0.273083\pi\)
\(174\) 0 0
\(175\) 4.82843e7i 0.681040i
\(176\) 4.95562e6 6.62792e7i 0.0685179 0.916396i
\(177\) 0 0
\(178\) 1.13026e7 + 1.55567e7i 0.150213 + 0.206751i
\(179\) −3.78019e7 + 1.22826e7i −0.492638 + 0.160068i −0.544792 0.838571i \(-0.683391\pi\)
0.0521539 + 0.998639i \(0.483391\pi\)
\(180\) 0 0
\(181\) 3.59027e7 + 2.60849e7i 0.450041 + 0.326974i 0.789612 0.613606i \(-0.210282\pi\)
−0.339571 + 0.940580i \(0.610282\pi\)
\(182\) 5.32460e6 + 3.86855e6i 0.0654692 + 0.0475661i
\(183\) 0 0
\(184\) 4.76282e6 1.54754e6i 0.0563640 0.0183138i
\(185\) −3.81538e7 5.25142e7i −0.443034 0.609784i
\(186\) 0 0
\(187\) 6.62975e6 8.86699e7i 0.0741398 0.991587i
\(188\) 4.92040e7i 0.540067i
\(189\) 0 0
\(190\) −1.35951e6 4.18415e6i −0.0143796 0.0442558i
\(191\) 3.55882e7 + 1.15633e7i 0.369564 + 0.120079i 0.487910 0.872894i \(-0.337759\pi\)
−0.118346 + 0.992972i \(0.537759\pi\)
\(192\) 0 0
\(193\) 6.21348e7 8.55213e7i 0.622135 0.856295i −0.375371 0.926875i \(-0.622485\pi\)
0.997506 + 0.0705793i \(0.0224848\pi\)
\(194\) −3.73651e6 + 1.14998e7i −0.0367417 + 0.113079i
\(195\) 0 0
\(196\) 2.05512e7 1.49313e7i 0.194958 0.141645i
\(197\) −1.41140e8 −1.31528 −0.657639 0.753334i \(-0.728445\pi\)
−0.657639 + 0.753334i \(0.728445\pi\)
\(198\) 0 0
\(199\) −4.26963e7 −0.384065 −0.192032 0.981389i \(-0.561508\pi\)
−0.192032 + 0.981389i \(0.561508\pi\)
\(200\) −2.34103e7 + 1.70086e7i −0.206920 + 0.150336i
\(201\) 0 0
\(202\) 1.90841e6 5.87348e6i 0.0162908 0.0501378i
\(203\) −8.05101e7 + 1.10813e8i −0.675483 + 0.929722i
\(204\) 0 0
\(205\) −3.29608e7 1.07096e7i −0.267214 0.0868232i
\(206\) −3.32709e6 1.02397e7i −0.0265173 0.0816119i
\(207\) 0 0
\(208\) 6.73939e7i 0.519277i
\(209\) 6.12311e7 + 5.18837e7i 0.463938 + 0.393114i
\(210\) 0 0
\(211\) −4.49365e7 6.18498e7i −0.329314 0.453262i 0.611968 0.790882i \(-0.290378\pi\)
−0.941282 + 0.337620i \(0.890378\pi\)
\(212\) 9.75561e7 3.16979e7i 0.703200 0.228484i
\(213\) 0 0
\(214\) −3.98596e6 2.89597e6i −0.0278026 0.0201997i
\(215\) −4.80726e7 3.49268e7i −0.329885 0.239676i
\(216\) 0 0
\(217\) −1.00166e8 + 3.25458e7i −0.665442 + 0.216215i
\(218\) 1.95306e7 + 2.68816e7i 0.127679 + 0.175735i
\(219\) 0 0
\(220\) −2.69896e7 + 6.58861e7i −0.170890 + 0.417172i
\(221\) 9.01611e7i 0.561884i
\(222\) 0 0
\(223\) 2.91371e7 + 8.96746e7i 0.175946 + 0.541505i 0.999675 0.0254775i \(-0.00811063\pi\)
−0.823730 + 0.566983i \(0.808111\pi\)
\(224\) 6.62522e7 + 2.15266e7i 0.393851 + 0.127970i
\(225\) 0 0
\(226\) 7.42998e6 1.02265e7i 0.0428162 0.0589314i
\(227\) 4.97553e7 1.53131e8i 0.282325 0.868906i −0.704863 0.709343i \(-0.748992\pi\)
0.987188 0.159562i \(-0.0510083\pi\)
\(228\) 0 0
\(229\) −1.55227e8 + 1.12779e8i −0.854169 + 0.620590i −0.926292 0.376806i \(-0.877022\pi\)
0.0721234 + 0.997396i \(0.477022\pi\)
\(230\) −2.56909e6 −0.0139229
\(231\) 0 0
\(232\) 8.20873e7 0.431586
\(233\) −6.72870e7 + 4.88869e7i −0.348486 + 0.253190i −0.748234 0.663435i \(-0.769098\pi\)
0.399747 + 0.916625i \(0.369098\pi\)
\(234\) 0 0
\(235\) −1.58189e7 + 4.86856e7i −0.0795132 + 0.244717i
\(236\) 1.32988e8 1.83042e8i 0.658597 0.906481i
\(237\) 0 0
\(238\) 2.81670e7 + 9.15202e6i 0.135432 + 0.0440045i
\(239\) 1.14700e8 + 3.53009e8i 0.543462 + 1.67260i 0.724619 + 0.689150i \(0.242016\pi\)
−0.181157 + 0.983454i \(0.557984\pi\)
\(240\) 0 0
\(241\) 2.20890e8i 1.01652i −0.861204 0.508260i \(-0.830289\pi\)
0.861204 0.508260i \(-0.169711\pi\)
\(242\) 5.97573e6 + 3.59096e7i 0.0271042 + 0.162876i
\(243\) 0 0
\(244\) 1.69843e8 + 2.33769e8i 0.748487 + 1.03020i
\(245\) −2.51350e7 + 8.16686e6i −0.109194 + 0.0354792i
\(246\) 0 0
\(247\) −6.58374e7 4.78337e7i −0.277993 0.201973i
\(248\) 5.10640e7 + 3.71001e7i 0.212586 + 0.154452i
\(249\) 0 0
\(250\) 3.20981e7 1.04293e7i 0.129924 0.0422149i
\(251\) −1.13608e8 1.56368e8i −0.453473 0.624152i 0.519666 0.854369i \(-0.326056\pi\)
−0.973139 + 0.230217i \(0.926056\pi\)
\(252\) 0 0
\(253\) 3.98640e7 2.46436e7i 0.154760 0.0956714i
\(254\) 1.69381e7i 0.0648556i
\(255\) 0 0
\(256\) 6.12491e7 + 1.88505e8i 0.228171 + 0.702237i
\(257\) −7.04482e7 2.28900e7i −0.258883 0.0841163i 0.176700 0.984265i \(-0.443458\pi\)
−0.435583 + 0.900148i \(0.643458\pi\)
\(258\) 0 0
\(259\) −2.31829e8 + 3.19085e8i −0.829121 + 1.14119i
\(260\) 2.23097e7 6.86623e7i 0.0787204 0.242277i
\(261\) 0 0
\(262\) −4.78188e7 + 3.47424e7i −0.164265 + 0.119345i
\(263\) 4.24969e8 1.44050 0.720248 0.693716i \(-0.244028\pi\)
0.720248 + 0.693716i \(0.244028\pi\)
\(264\) 0 0
\(265\) −1.06719e8 −0.352275
\(266\) −2.16266e7 + 1.57126e7i −0.0704534 + 0.0511874i
\(267\) 0 0
\(268\) −1.15922e8 + 3.56772e8i −0.367871 + 1.13219i
\(269\) 1.03034e8 1.41815e8i 0.322738 0.444210i −0.616563 0.787306i \(-0.711475\pi\)
0.939301 + 0.343095i \(0.111475\pi\)
\(270\) 0 0
\(271\) −1.30621e8 4.24415e7i −0.398678 0.129538i 0.102814 0.994701i \(-0.467215\pi\)
−0.501492 + 0.865162i \(0.667215\pi\)
\(272\) 9.37148e7 + 2.88425e8i 0.282369 + 0.869043i
\(273\) 0 0
\(274\) 1.11357e8i 0.327032i
\(275\) −1.75065e8 + 2.06605e8i −0.507616 + 0.599069i
\(276\) 0 0
\(277\) −7.78378e7 1.07135e8i −0.220045 0.302866i 0.684695 0.728829i \(-0.259935\pi\)
−0.904740 + 0.425963i \(0.859935\pi\)
\(278\) −8.04660e7 + 2.61450e7i −0.224624 + 0.0729847i
\(279\) 0 0
\(280\) −3.89097e7 2.82696e7i −0.105927 0.0769602i
\(281\) 3.31967e8 + 2.41188e8i 0.892531 + 0.648461i 0.936537 0.350570i \(-0.114012\pi\)
−0.0440060 + 0.999031i \(0.514012\pi\)
\(282\) 0 0
\(283\) −1.97701e8 + 6.42368e7i −0.518508 + 0.168473i −0.556568 0.830802i \(-0.687882\pi\)
0.0380601 + 0.999275i \(0.487882\pi\)
\(284\) −1.09165e8 1.50253e8i −0.282795 0.389233i
\(285\) 0 0
\(286\) −8.75735e6 3.58587e7i −0.0221356 0.0906388i
\(287\) 2.10582e8i 0.525817i
\(288\) 0 0
\(289\) −1.42772e6 4.39406e6i −0.00347936 0.0107084i
\(290\) −4.00500e7 1.30130e7i −0.0964294 0.0313318i
\(291\) 0 0
\(292\) 2.65224e8 3.65049e8i 0.623408 0.858047i
\(293\) −4.07420e7 + 1.25391e8i −0.0946249 + 0.291225i −0.987156 0.159761i \(-0.948928\pi\)
0.892531 + 0.450986i \(0.148928\pi\)
\(294\) 0 0
\(295\) −1.90434e8 + 1.38359e8i −0.431885 + 0.313783i
\(296\) 2.36370e8 0.529750
\(297\) 0 0
\(298\) −1.86702e7 −0.0408688
\(299\) −3.84459e7 + 2.79326e7i −0.0831766 + 0.0604313i
\(300\) 0 0
\(301\) −1.11571e8 + 3.43380e8i −0.235813 + 0.725759i
\(302\) 1.13338e7 1.55996e7i 0.0236783 0.0325904i
\(303\) 0 0
\(304\) −2.60332e8 8.45871e7i −0.531460 0.172682i
\(305\) −9.28980e7 2.85911e8i −0.187481 0.577007i
\(306\) 0 0
\(307\) 7.15899e8i 1.41211i −0.708159 0.706053i \(-0.750474\pi\)
0.708159 0.706053i \(-0.249526\pi\)
\(308\) 4.31418e8 + 3.22566e7i 0.841338 + 0.0629059i
\(309\) 0 0
\(310\) −1.90325e7 2.61960e7i −0.0362853 0.0499424i
\(311\) −3.44217e8 + 1.11843e8i −0.648889 + 0.210837i −0.614924 0.788586i \(-0.710813\pi\)
−0.0339648 + 0.999423i \(0.510813\pi\)
\(312\) 0 0
\(313\) −2.13191e7 1.54892e7i −0.0392974 0.0285512i 0.567963 0.823054i \(-0.307732\pi\)
−0.607261 + 0.794503i \(0.707732\pi\)
\(314\) −8.12744e7 5.90493e7i −0.148149 0.107637i
\(315\) 0 0
\(316\) 2.15992e8 7.01802e7i 0.385065 0.125115i
\(317\) −4.50308e8 6.19796e8i −0.793967 1.09280i −0.993603 0.112932i \(-0.963976\pi\)
0.199636 0.979870i \(-0.436024\pi\)
\(318\) 0 0
\(319\) 7.46273e8 1.82253e8i 1.28715 0.314346i
\(320\) 2.28228e8i 0.389354i
\(321\) 0 0
\(322\) 4.82381e6 + 1.48462e7i 0.00805183 + 0.0247810i
\(323\) −3.48279e8 1.13163e8i −0.575066 0.186850i
\(324\) 0 0
\(325\) 1.61400e8 2.22148e8i 0.260802 0.358963i
\(326\) 3.59298e7 1.10580e8i 0.0574371 0.176773i
\(327\) 0 0
\(328\) 1.02099e8 7.41795e7i 0.159759 0.116071i
\(329\) 3.11045e8 0.481546
\(330\) 0 0
\(331\) 4.24184e8 0.642920 0.321460 0.946923i \(-0.395826\pi\)
0.321460 + 0.946923i \(0.395826\pi\)
\(332\) −7.20956e8 + 5.23805e8i −1.08125 + 0.785573i
\(333\) 0 0
\(334\) −5.00669e6 + 1.54090e7i −0.00735256 + 0.0226288i
\(335\) 2.29402e8 3.15745e8i 0.333381 0.458860i
\(336\) 0 0
\(337\) 1.35872e8 + 4.41475e7i 0.193386 + 0.0628350i 0.404109 0.914711i \(-0.367582\pi\)
−0.210723 + 0.977546i \(0.567582\pi\)
\(338\) −2.46564e7 7.58846e7i −0.0347313 0.106892i
\(339\) 0 0
\(340\) 3.24876e8i 0.448271i
\(341\) 5.46605e8 + 2.23911e8i 0.746506 + 0.305799i
\(342\) 0 0
\(343\) 4.75396e8 + 6.54327e8i 0.636102 + 0.875519i
\(344\) 2.05787e8 6.68644e7i 0.272561 0.0885606i
\(345\) 0 0
\(346\) −1.06495e8 7.73732e7i −0.138218 0.100421i
\(347\) −7.58602e8 5.51157e8i −0.974678 0.708145i −0.0181648 0.999835i \(-0.505782\pi\)
−0.956513 + 0.291690i \(0.905782\pi\)
\(348\) 0 0
\(349\) 1.00888e9 3.27805e8i 1.27043 0.412788i 0.405230 0.914215i \(-0.367192\pi\)
0.865200 + 0.501427i \(0.167192\pi\)
\(350\) −5.30173e7 7.29721e7i −0.0660967 0.0909743i
\(351\) 0 0
\(352\) −2.05439e8 3.32323e8i −0.251064 0.406126i
\(353\) 4.08464e8i 0.494245i 0.968984 + 0.247122i \(0.0794849\pi\)
−0.968984 + 0.247122i \(0.920515\pi\)
\(354\) 0 0
\(355\) 5.97095e7 + 1.83767e8i 0.0708344 + 0.218006i
\(356\) −1.21893e9 3.96054e8i −1.43187 0.465242i
\(357\) 0 0
\(358\) −4.36435e7 + 6.00701e7i −0.0502723 + 0.0691939i
\(359\) 2.30341e8 7.08915e8i 0.262748 0.808656i −0.729455 0.684028i \(-0.760226\pi\)
0.992204 0.124627i \(-0.0397736\pi\)
\(360\) 0 0
\(361\) −4.55750e8 + 3.31122e8i −0.509861 + 0.370435i
\(362\) 8.29016e7 0.0918508
\(363\) 0 0
\(364\) −4.38673e8 −0.476745
\(365\) −3.79792e8 + 2.75935e8i −0.408809 + 0.297017i
\(366\) 0 0
\(367\) 4.80010e8 1.47732e9i 0.506896 1.56007i −0.290663 0.956825i \(-0.593876\pi\)
0.797559 0.603241i \(-0.206124\pi\)
\(368\) −9.39545e7 + 1.29317e8i −0.0982767 + 0.135266i
\(369\) 0 0
\(370\) −1.15324e8 3.74710e7i −0.118362 0.0384582i
\(371\) 2.00380e8 + 6.16705e8i 0.203725 + 0.627002i
\(372\) 0 0
\(373\) 8.45725e8i 0.843817i −0.906638 0.421908i \(-0.861360\pi\)
0.906638 0.421908i \(-0.138640\pi\)
\(374\) −8.73422e7 1.41287e8i −0.0863323 0.139653i
\(375\) 0 0
\(376\) −1.09569e8 1.50808e8i −0.106299 0.146308i
\(377\) −7.40826e8 + 2.40709e8i −0.712068 + 0.231365i
\(378\) 0 0
\(379\) 6.05111e8 + 4.39639e8i 0.570950 + 0.414819i 0.835450 0.549566i \(-0.185207\pi\)
−0.264500 + 0.964386i \(0.585207\pi\)
\(380\) 2.37230e8 + 1.72358e8i 0.221783 + 0.161135i
\(381\) 0 0
\(382\) 6.64814e7 2.16011e7i 0.0610208 0.0198269i
\(383\) −1.18554e9 1.63176e9i −1.07826 1.48409i −0.861426 0.507884i \(-0.830428\pi\)
−0.216831 0.976209i \(-0.569572\pi\)
\(384\) 0 0
\(385\) −4.16502e8 1.70616e8i −0.371967 0.152373i
\(386\) 1.97474e8i 0.174765i
\(387\) 0 0
\(388\) −2.49045e8 7.66481e8i −0.216455 0.666179i
\(389\) 2.05746e9 + 6.68508e8i 1.77218 + 0.575815i 0.998341 0.0575720i \(-0.0183359\pi\)
0.773835 + 0.633387i \(0.218336\pi\)
\(390\) 0 0
\(391\) −1.25695e8 + 1.73004e8i −0.106340 + 0.146365i
\(392\) 2.97391e7 9.15276e7i 0.0249360 0.0767452i
\(393\) 0 0
\(394\) −2.13305e8 + 1.54975e8i −0.175697 + 0.127651i
\(395\) −2.36280e8 −0.192902
\(396\) 0 0
\(397\) −1.25920e9 −1.01002 −0.505009 0.863114i \(-0.668511\pi\)
−0.505009 + 0.863114i \(0.668511\pi\)
\(398\) −6.45270e7 + 4.68816e7i −0.0513039 + 0.0372745i
\(399\) 0 0
\(400\) 2.85413e8 8.78410e8i 0.222979 0.686257i
\(401\) −1.42744e9 + 1.96471e9i −1.10549 + 1.52157i −0.277583 + 0.960702i \(0.589533\pi\)
−0.827903 + 0.560871i \(0.810467\pi\)
\(402\) 0 0
\(403\) −5.69636e8 1.85086e8i −0.433541 0.140866i
\(404\) 1.27199e8 + 3.91478e8i 0.0959728 + 0.295374i
\(405\) 0 0
\(406\) 2.55873e8i 0.189751i
\(407\) 2.14889e9 5.24798e8i 1.57992 0.385844i
\(408\) 0 0
\(409\) 1.03507e9 + 1.42465e9i 0.748062 + 1.02962i 0.998114 + 0.0613862i \(0.0195521\pi\)
−0.250052 + 0.968232i \(0.580448\pi\)
\(410\) −6.15732e7 + 2.00063e7i −0.0441213 + 0.0143359i
\(411\) 0 0
\(412\) 5.80566e8 + 4.21806e8i 0.408989 + 0.297148i
\(413\) 1.15711e9 + 8.40689e8i 0.808256 + 0.587233i
\(414\) 0 0
\(415\) 8.81762e8 2.86502e8i 0.605596 0.196770i
\(416\) 2.32858e8 + 3.20501e8i 0.158586 + 0.218275i
\(417\) 0 0
\(418\) 1.49508e8 + 1.11786e7i 0.100126 + 0.00748633i
\(419\) 1.61169e9i 1.07037i −0.844735 0.535185i \(-0.820242\pi\)
0.844735 0.535185i \(-0.179758\pi\)
\(420\) 0 0
\(421\) 4.29271e8 + 1.32116e9i 0.280378 + 0.862915i 0.987746 + 0.156070i \(0.0498824\pi\)
−0.707368 + 0.706846i \(0.750118\pi\)
\(422\) −1.35825e8 4.41323e7i −0.0879806 0.0285866i
\(423\) 0 0
\(424\) 2.28420e8 3.14393e8i 0.145530 0.200305i
\(425\) 3.81832e8 1.17516e9i 0.241274 0.742565i
\(426\) 0 0
\(427\) −1.47778e9 + 1.07367e9i −0.918572 + 0.667382i
\(428\) 3.28388e8 0.202458
\(429\) 0 0
\(430\) −1.11003e8 −0.0673277
\(431\) −7.98960e8 + 5.80479e8i −0.480679 + 0.349233i −0.801588 0.597876i \(-0.796011\pi\)
0.320910 + 0.947110i \(0.396011\pi\)
\(432\) 0 0
\(433\) −6.41796e8 + 1.97525e9i −0.379918 + 1.16927i 0.560183 + 0.828369i \(0.310731\pi\)
−0.940101 + 0.340897i \(0.889269\pi\)
\(434\) −1.15645e8 + 1.59171e8i −0.0679065 + 0.0934652i
\(435\) 0 0
\(436\) −2.10628e9 6.84372e8i −1.21706 0.395448i
\(437\) −5.96453e7 1.83569e8i −0.0341894 0.105224i
\(438\) 0 0
\(439\) 1.94981e9i 1.09994i 0.835186 + 0.549968i \(0.185360\pi\)
−0.835186 + 0.549968i \(0.814640\pi\)
\(440\) 6.39947e7 + 2.62040e8i 0.0358146 + 0.146650i
\(441\) 0 0
\(442\) 9.89991e7 + 1.36261e8i 0.0545323 + 0.0750572i
\(443\) 1.79322e9 5.82651e8i 0.979986 0.318417i 0.225145 0.974325i \(-0.427714\pi\)
0.754840 + 0.655909i \(0.227714\pi\)
\(444\) 0 0
\(445\) 1.07876e9 + 7.83763e8i 0.580315 + 0.421623i
\(446\) 1.42500e8 + 1.03532e8i 0.0760576 + 0.0552590i
\(447\) 0 0
\(448\) −1.31888e9 + 4.28529e8i −0.692997 + 0.225168i
\(449\) −9.78518e8 1.34681e9i −0.510160 0.702175i 0.473786 0.880640i \(-0.342887\pi\)
−0.983946 + 0.178465i \(0.942887\pi\)
\(450\) 0 0
\(451\) 7.63511e8 9.01067e8i 0.391920 0.462529i
\(452\) 8.42521e8i 0.429137i
\(453\) 0 0
\(454\) −9.29464e7 2.86060e8i −0.0466162 0.143470i
\(455\) 4.34052e8 + 1.41032e8i 0.216024 + 0.0701904i
\(456\) 0 0
\(457\) 1.44984e8 1.99554e8i 0.0710583 0.0978033i −0.772009 0.635612i \(-0.780748\pi\)
0.843067 + 0.537809i \(0.180748\pi\)
\(458\) −1.10761e8 + 3.40887e8i −0.0538712 + 0.165799i
\(459\) 0 0
\(460\) 1.38531e8 1.00649e8i 0.0663584 0.0482122i
\(461\) 3.53444e9 1.68022 0.840112 0.542413i \(-0.182489\pi\)
0.840112 + 0.542413i \(0.182489\pi\)
\(462\) 0 0
\(463\) 9.52975e8 0.446219 0.223110 0.974793i \(-0.428379\pi\)
0.223110 + 0.974793i \(0.428379\pi\)
\(464\) −2.11970e9 + 1.54005e9i −0.985057 + 0.715686i
\(465\) 0 0
\(466\) −4.80120e7 + 1.47766e8i −0.0219785 + 0.0676430i
\(467\) −2.18229e9 + 3.00366e9i −0.991523 + 1.36471i −0.0611385 + 0.998129i \(0.519473\pi\)
−0.930385 + 0.366585i \(0.880527\pi\)
\(468\) 0 0
\(469\) −2.25535e9 7.32808e8i −1.00951 0.328009i
\(470\) 2.95509e7 + 9.09482e7i 0.0131289 + 0.0404066i
\(471\) 0 0
\(472\) 8.57157e8i 0.375201i
\(473\) 1.72240e9 1.06478e9i 0.748378 0.462641i
\(474\) 0 0
\(475\) 6.55547e8 + 9.02283e8i 0.280657 + 0.386292i
\(476\) −1.87738e9 + 6.09998e8i −0.797863 + 0.259241i
\(477\) 0 0
\(478\) 5.60958e8 + 4.07560e8i 0.234927 + 0.170684i
\(479\) 3.77955e9 + 2.74600e9i 1.57132 + 1.14163i 0.925876 + 0.377828i \(0.123329\pi\)
0.645447 + 0.763805i \(0.276671\pi\)
\(480\) 0 0
\(481\) −2.13321e9 + 6.93121e8i −0.874028 + 0.283989i
\(482\) −2.42542e8 3.33831e8i −0.0986559 0.135788i
\(483\) 0 0
\(484\) −1.72905e9 1.70222e9i −0.693186 0.682429i
\(485\) 8.38474e8i 0.333729i
\(486\) 0 0
\(487\) 9.64691e8 + 2.96901e9i 0.378475 + 1.16483i 0.941104 + 0.338117i \(0.109790\pi\)
−0.562629 + 0.826709i \(0.690210\pi\)
\(488\) 1.04113e9 + 3.38283e8i 0.405540 + 0.131768i
\(489\) 0 0
\(490\) −2.90192e7 + 3.99415e7i −0.0111429 + 0.0153369i
\(491\) 1.36754e9 4.20885e9i 0.521379 1.60464i −0.249987 0.968249i \(-0.580426\pi\)
0.771366 0.636391i \(-0.219574\pi\)
\(492\) 0 0
\(493\) −2.83578e9 + 2.06032e9i −1.06588 + 0.774408i
\(494\) −1.52023e8 −0.0567367
\(495\) 0 0
\(496\) −2.01464e9 −0.741331
\(497\) 9.49834e8 6.90095e8i 0.347057 0.252151i
\(498\) 0 0
\(499\) 1.40472e8 4.32329e8i 0.0506102 0.155762i −0.922557 0.385860i \(-0.873905\pi\)
0.973167 + 0.230098i \(0.0739047\pi\)
\(500\) −1.32222e9 + 1.81988e9i −0.473052 + 0.651100i
\(501\) 0 0
\(502\) −3.43392e8 1.11575e8i −0.121151 0.0393644i
\(503\) −3.74294e8 1.15196e9i −0.131137 0.403598i 0.863832 0.503780i \(-0.168058\pi\)
−0.994969 + 0.100182i \(0.968058\pi\)
\(504\) 0 0
\(505\) 4.28248e8i 0.147971i
\(506\) 3.31872e7 8.10155e7i 0.0113879 0.0277998i
\(507\) 0 0
\(508\) 6.63585e8 + 9.13346e8i 0.224581 + 0.309109i
\(509\) −4.72487e9 + 1.53520e9i −1.58810 + 0.516005i −0.964127 0.265441i \(-0.914483\pi\)
−0.623973 + 0.781446i \(0.714483\pi\)
\(510\) 0 0
\(511\) 2.30767e9 + 1.67662e9i 0.765070 + 0.555856i
\(512\) 1.81349e9 + 1.31758e9i 0.597133 + 0.433843i
\(513\) 0 0
\(514\) −1.31602e8 + 4.27602e7i −0.0427457 + 0.0138889i
\(515\) −4.38841e8 6.04013e8i −0.141573 0.194859i
\(516\) 0 0
\(517\) −1.33094e9 1.12776e9i −0.423587 0.358923i
\(518\) 7.36787e8i 0.232910i
\(519\) 0 0
\(520\) −8.45204e7 2.60127e8i −0.0263603 0.0811285i
\(521\) −9.56364e8 3.10742e8i −0.296272 0.0962648i 0.157109 0.987581i \(-0.449783\pi\)
−0.453382 + 0.891316i \(0.649783\pi\)
\(522\) 0 0
\(523\) 3.06565e9 4.21950e9i 0.937058 1.28975i −0.0199838 0.999800i \(-0.506361\pi\)
0.957042 0.289950i \(-0.0936385\pi\)
\(524\) 1.21741e9 3.74679e9i 0.369638 1.13763i
\(525\) 0 0
\(526\) 6.42256e8 4.66627e8i 0.192424 0.139804i
\(527\) −2.69524e9 −0.802157
\(528\) 0 0
\(529\) 3.29211e9 0.966896
\(530\) −1.61285e8 + 1.17180e8i −0.0470574 + 0.0341892i
\(531\) 0 0
\(532\) 5.50585e8 1.69453e9i 0.158538 0.487930i
\(533\) −7.03911e8 + 9.68851e8i −0.201360 + 0.277148i
\(534\) 0 0
\(535\) −3.24929e8 1.05576e8i −0.0917381 0.0298075i
\(536\) 4.39172e8 + 1.35163e9i 0.123185 + 0.379124i
\(537\) 0 0
\(538\) 3.27459e8i 0.0906607i
\(539\) 6.71519e7 8.98126e8i 0.0184713 0.247045i
\(540\) 0 0
\(541\) 3.74274e8 + 5.15144e8i 0.101625 + 0.139874i 0.856801 0.515648i \(-0.172449\pi\)
−0.755176 + 0.655522i \(0.772449\pi\)
\(542\) −2.44010e8 + 7.92837e7i −0.0658280 + 0.0213888i
\(543\) 0 0
\(544\) 1.44223e9 + 1.04784e9i 0.384095 + 0.279062i
\(545\) 1.86407e9 + 1.35432e9i 0.493258 + 0.358373i
\(546\) 0 0
\(547\) 3.67370e9 1.19366e9i 0.959728 0.311834i 0.213066 0.977038i \(-0.431655\pi\)
0.746662 + 0.665203i \(0.231655\pi\)
\(548\) −4.36263e9 6.00465e9i −1.13244 1.55867i
\(549\) 0 0
\(550\) −3.77186e7 + 5.04469e8i −0.00966687 + 0.129290i
\(551\) 3.16382e9i 0.805713i
\(552\) 0 0
\(553\) 4.43647e8 + 1.36541e9i 0.111558 + 0.343340i
\(554\) −2.35273e8 7.64448e7i −0.0587878 0.0191013i
\(555\) 0 0
\(556\) 3.31464e9 4.56222e9i 0.817853 1.12568i
\(557\) 2.34200e9 7.20793e9i 0.574240 1.76733i −0.0645111 0.997917i \(-0.520549\pi\)
0.638752 0.769413i \(-0.279451\pi\)
\(558\) 0 0
\(559\) −1.66113e9 + 1.20688e9i −0.402220 + 0.292230i
\(560\) 1.53512e9 0.369389
\(561\) 0 0
\(562\) 7.66533e8 0.182160
\(563\) −6.74965e9 + 4.90391e9i −1.59405 + 1.15814i −0.696194 + 0.717854i \(0.745124\pi\)
−0.897855 + 0.440290i \(0.854876\pi\)
\(564\) 0 0
\(565\) 2.70868e8 8.33645e8i 0.0631812 0.194452i
\(566\) −2.28252e8 + 3.14161e8i −0.0529123 + 0.0728275i
\(567\) 0 0
\(568\) −6.69176e8 2.17428e8i −0.153222 0.0497848i
\(569\) 1.23554e9 + 3.80261e9i 0.281167 + 0.865344i 0.987521 + 0.157485i \(0.0503387\pi\)
−0.706354 + 0.707859i \(0.749661\pi\)
\(570\) 0 0
\(571\) 6.68412e9i 1.50251i −0.660011 0.751256i \(-0.729448\pi\)
0.660011 0.751256i \(-0.270552\pi\)
\(572\) 1.87705e9 + 1.59051e9i 0.419363 + 0.355344i
\(573\) 0 0
\(574\) 2.31224e8 + 3.18253e8i 0.0510319 + 0.0702394i
\(575\) 6.19397e8 2.01254e8i 0.135873 0.0441477i
\(576\) 0 0
\(577\) −2.41493e9 1.75455e9i −0.523347 0.380234i 0.294516 0.955646i \(-0.404841\pi\)
−0.817863 + 0.575413i \(0.804841\pi\)
\(578\) −6.98250e6 5.07309e6i −0.00150405 0.00109276i
\(579\) 0 0
\(580\) 2.66940e9 8.67342e8i 0.568089 0.184583i
\(581\) −3.31126e9 4.55755e9i −0.700449 0.964085i
\(582\) 0 0
\(583\) 1.37859e9 3.36536e9i 0.288134 0.703383i
\(584\) 1.70947e9i 0.355153i
\(585\) 0 0
\(586\) 7.61089e7 + 2.34239e8i 0.0156241 + 0.0480859i
\(587\) −8.01720e8 2.60495e8i −0.163602 0.0531576i 0.226071 0.974111i \(-0.427412\pi\)
−0.389673 + 0.920953i \(0.627412\pi\)
\(588\) 0 0
\(589\) 1.42992e9 1.96811e9i 0.288342 0.396868i
\(590\) −1.35882e8 + 4.18203e8i −0.0272384 + 0.0838311i
\(591\) 0 0
\(592\) −6.10367e9 + 4.43458e9i −1.20911 + 0.878468i
\(593\) 1.49654e9 0.294712 0.147356 0.989084i \(-0.452924\pi\)
0.147356 + 0.989084i \(0.452924\pi\)
\(594\) 0 0
\(595\) 2.05372e9 0.399697
\(596\) 1.00674e9 7.31441e8i 0.194785 0.141520i
\(597\) 0 0
\(598\) −2.74327e7 + 8.44291e7i −0.00524583 + 0.0161450i
\(599\) −1.29324e9 + 1.77999e9i −0.245859 + 0.338395i −0.914056 0.405589i \(-0.867066\pi\)
0.668197 + 0.743985i \(0.267066\pi\)
\(600\) 0 0
\(601\) −4.56672e9 1.48382e9i −0.858112 0.278818i −0.153272 0.988184i \(-0.548981\pi\)
−0.704840 + 0.709367i \(0.748981\pi\)
\(602\) 2.08422e8 + 6.41458e8i 0.0389365 + 0.119834i
\(603\) 0 0
\(604\) 1.28519e9i 0.237322i
\(605\) 1.16358e9 + 2.24018e9i 0.213625 + 0.411281i
\(606\) 0 0
\(607\) 9.84517e8 + 1.35507e9i 0.178675 + 0.245925i 0.888955 0.457994i \(-0.151432\pi\)
−0.710281 + 0.703919i \(0.751432\pi\)
\(608\) −1.53031e9 + 4.97228e8i −0.276132 + 0.0897208i
\(609\) 0 0
\(610\) −4.54334e8 3.30093e8i −0.0810440 0.0588819i
\(611\) 1.43107e9 + 1.03973e9i 0.253814 + 0.184407i
\(612\) 0 0
\(613\) 1.35669e9 4.40815e8i 0.237886 0.0772939i −0.187648 0.982236i \(-0.560086\pi\)
0.425534 + 0.904943i \(0.360086\pi\)
\(614\) −7.86075e8 1.08194e9i −0.137049 0.188631i
\(615\) 0 0
\(616\) 1.39411e9 8.61826e8i 0.240306 0.148555i
\(617\) 3.98821e9i 0.683566i 0.939779 + 0.341783i \(0.111031\pi\)
−0.939779 + 0.341783i \(0.888969\pi\)
\(618\) 0 0
\(619\) −2.71528e9 8.35677e9i −0.460148 1.41619i −0.864984 0.501800i \(-0.832671\pi\)
0.404836 0.914389i \(-0.367329\pi\)
\(620\) 2.05256e9 + 6.66917e8i 0.345879 + 0.112383i
\(621\) 0 0
\(622\) −3.97409e8 + 5.46986e8i −0.0662173 + 0.0911402i
\(623\) 2.50367e9 7.70551e9i 0.414829 1.27671i
\(624\) 0 0
\(625\) −1.98388e9 + 1.44138e9i −0.325040 + 0.236155i
\(626\) −4.92271e7 −0.00802037
\(627\) 0 0
\(628\) 6.69588e9 1.07882
\(629\) −8.16563e9 + 5.93268e9i −1.30832 + 0.950547i
\(630\) 0 0
\(631\) −9.47035e8 + 2.91468e9i −0.150059 + 0.461836i −0.997627 0.0688522i \(-0.978066\pi\)
0.847567 + 0.530688i \(0.178066\pi\)
\(632\) 5.05729e8 6.96077e8i 0.0796909 0.109685i
\(633\) 0 0
\(634\) −1.36110e9 4.42249e8i −0.212119 0.0689215i
\(635\) −3.62956e8 1.11706e9i −0.0562531 0.173129i
\(636\) 0 0
\(637\) 9.13230e8i 0.139988i
\(638\) 9.27725e8 1.09487e9i 0.141432 0.166912i
\(639\) 0 0
\(640\) −1.11317e9 1.53214e9i −0.167854 0.231031i
\(641\) −6.57373e9 + 2.13593e9i −0.985845 + 0.320321i −0.757196 0.653188i \(-0.773431\pi\)
−0.228650 + 0.973509i \(0.573431\pi\)
\(642\) 0 0
\(643\) 7.95504e9 + 5.77967e9i 1.18006 + 0.857363i 0.992178 0.124829i \(-0.0398381\pi\)
0.187881 + 0.982192i \(0.439838\pi\)
\(644\) −8.41738e8 6.11559e8i −0.124187 0.0902272i
\(645\) 0 0
\(646\) −6.50609e8 + 2.11396e8i −0.0949525 + 0.0308519i
\(647\) −4.38807e9 6.03966e9i −0.636954 0.876692i 0.361494 0.932374i \(-0.382267\pi\)
−0.998449 + 0.0556821i \(0.982267\pi\)
\(648\) 0 0
\(649\) −1.90309e9 7.79261e9i −0.273277 1.11899i
\(650\) 5.12953e8i 0.0732623i
\(651\) 0 0
\(652\) 2.39478e9 + 7.37038e9i 0.338376 + 1.04141i
\(653\) 8.37050e8 + 2.71974e8i 0.117640 + 0.0382236i 0.367245 0.930124i \(-0.380301\pi\)
−0.249605 + 0.968348i \(0.580301\pi\)
\(654\) 0 0
\(655\) −2.40916e9 + 3.31593e9i −0.334982 + 0.461063i
\(656\) −1.24477e9 + 3.83100e9i −0.172157 + 0.529845i
\(657\) 0 0
\(658\) 4.70083e8 3.41535e8i 0.0643256 0.0467353i
\(659\) 1.33640e10 1.81902 0.909509 0.415684i \(-0.136458\pi\)
0.909509 + 0.415684i \(0.136458\pi\)
\(660\) 0 0
\(661\) −1.33756e10 −1.80139 −0.900693 0.434455i \(-0.856941\pi\)
−0.900693 + 0.434455i \(0.856941\pi\)
\(662\) 6.41070e8 4.65765e8i 0.0858821 0.0623970i
\(663\) 0 0
\(664\) −1.04328e9 + 3.21088e9i −0.138297 + 0.425634i
\(665\) −1.08957e9 + 1.49966e9i −0.143674 + 0.197751i
\(666\) 0 0
\(667\) −1.75709e9 5.70915e8i −0.229274 0.0744956i
\(668\) −3.33705e8 1.02704e9i −0.0433157 0.133312i
\(669\) 0 0
\(670\) 7.29076e8i 0.0936506i
\(671\) 1.02162e10 + 7.63852e8i 1.30545 + 0.0976069i
\(672\) 0 0
\(673\) 8.27950e9 + 1.13958e10i 1.04701 + 1.44109i 0.891371 + 0.453275i \(0.149744\pi\)
0.155641 + 0.987814i \(0.450256\pi\)
\(674\) 2.53819e8 8.24707e7i 0.0319311 0.0103750i
\(675\) 0 0
\(676\) 4.30246e9 + 3.12592e9i 0.535677 + 0.389192i
\(677\) 3.39800e9 + 2.46879e9i 0.420885 + 0.305791i 0.777994 0.628272i \(-0.216237\pi\)
−0.357109 + 0.934063i \(0.616237\pi\)
\(678\) 0 0
\(679\) 4.84535e9 1.57435e9i 0.593992 0.193000i
\(680\) −7.23441e8 9.95731e8i −0.0882312 0.121440i
\(681\) 0 0
\(682\) 1.07195e9 2.61788e8i 0.129398 0.0316013i
\(683\) 3.47316e9i 0.417112i −0.978010 0.208556i \(-0.933124\pi\)
0.978010 0.208556i \(-0.0668763\pi\)
\(684\) 0 0
\(685\) 2.38620e9 + 7.34396e9i 0.283654 + 0.872998i
\(686\) 1.43693e9 + 4.66888e8i 0.169943 + 0.0552177i
\(687\) 0 0
\(688\) −4.05950e9 + 5.58742e9i −0.475240 + 0.654111i
\(689\) −1.13955e9 + 3.50716e9i −0.132729 + 0.408497i
\(690\) 0 0
\(691\) −9.07512e9 + 6.59346e9i −1.04636 + 0.760222i −0.971516 0.236974i \(-0.923844\pi\)
−0.0748392 + 0.997196i \(0.523844\pi\)
\(692\) 8.77372e9 1.00650
\(693\) 0 0
\(694\) −1.75166e9 −0.198926
\(695\) −4.74646e9 + 3.44851e9i −0.536319 + 0.389659i
\(696\) 0 0
\(697\) −1.66528e9 + 5.12520e9i −0.186283 + 0.573319i
\(698\) 1.16478e9 1.60319e9i 0.129644 0.178439i
\(699\) 0 0
\(700\) 5.71765e9 + 1.85778e9i 0.630049 + 0.204715i
\(701\) 3.73182e9 + 1.14854e10i 0.409174 + 1.25931i 0.917359 + 0.398060i \(0.130317\pi\)
−0.508185 + 0.861248i \(0.669683\pi\)
\(702\) 0 0
\(703\) 9.11020e9i 0.988972i
\(704\) 7.19712e9 + 2.94823e9i 0.777418 + 0.318462i
\(705\) 0 0
\(706\) 4.48503e8 + 6.17312e8i 0.0479677 + 0.0660219i
\(707\) −2.47474e9 + 8.04093e8i −0.263368 + 0.0855733i
\(708\) 0 0
\(709\) −1.45744e10 1.05889e10i −1.53577 1.11581i −0.952917 0.303231i \(-0.901935\pi\)
−0.582858 0.812574i \(-0.698065\pi\)
\(710\) 2.92020e8 + 2.12165e8i 0.0306202 + 0.0222469i
\(711\) 0 0
\(712\) −4.61791e9 + 1.50045e9i −0.479474 + 0.155791i
\(713\) −8.35004e8 1.14928e9i −0.0862731 0.118745i
\(714\) 0 0
\(715\) −1.34594e9 2.17722e9i −0.137706 0.222757i
\(716\) 4.94894e9i 0.503868i
\(717\) 0 0
\(718\) −4.30293e8 1.32430e9i −0.0433839 0.133522i
\(719\) −1.25173e10 4.06711e9i −1.25591 0.408070i −0.395876 0.918304i \(-0.629559\pi\)
−0.860036 + 0.510234i \(0.829559\pi\)
\(720\) 0 0
\(721\) −2.66647e9 + 3.67008e9i −0.264949 + 0.364671i
\(722\) −3.25196e8 + 1.00085e9i −0.0321562 + 0.0989666i
\(723\) 0 0
\(724\) −4.47026e9 + 3.24783e9i −0.437772 + 0.318060i
\(725\) 1.06753e10 1.04039
\(726\) 0 0
\(727\) 2.85229e8 0.0275311 0.0137656 0.999905i \(-0.495618\pi\)
0.0137656 + 0.999905i \(0.495618\pi\)
\(728\) −1.34452e9 + 9.76848e8i −0.129153 + 0.0938355i
\(729\) 0 0
\(730\) −2.70996e8 + 8.34041e8i −0.0257830 + 0.0793520i
\(731\) −5.43089e9 + 7.47498e9i −0.514233 + 0.707782i
\(732\) 0 0
\(733\) −8.72039e9 2.83343e9i −0.817847 0.265735i −0.129929 0.991523i \(-0.541475\pi\)
−0.687918 + 0.725789i \(0.741475\pi\)
\(734\) −8.96693e8 2.75974e9i −0.0836965 0.257591i
\(735\) 0 0
\(736\) 9.39617e8i 0.0868717i
\(737\) 6.99355e9 + 1.13129e10i 0.643519 + 1.04097i
\(738\) 0 0
\(739\) 8.51714e8 + 1.17228e9i 0.0776315 + 0.106851i 0.846067 0.533077i \(-0.178964\pi\)
−0.768435 + 0.639928i \(0.778964\pi\)
\(740\) 7.68654e9 2.49751e9i 0.697301 0.226567i
\(741\) 0 0
\(742\) 9.79992e8 + 7.12006e8i 0.0880661 + 0.0639838i
\(743\) −9.40407e9 6.83246e9i −0.841114 0.611105i 0.0815674 0.996668i \(-0.474007\pi\)
−0.922682 + 0.385563i \(0.874007\pi\)
\(744\) 0 0
\(745\) −1.23129e9 + 4.00071e8i −0.109097 + 0.0354479i
\(746\) −9.28627e8 1.27815e9i −0.0818946 0.112718i
\(747\) 0 0
\(748\) 1.02449e10 + 4.19672e9i 0.895058 + 0.366652i
\(749\) 2.07592e9i 0.180520i
\(750\) 0 0
\(751\) −6.90746e8 2.12590e9i −0.0595084 0.183148i 0.916883 0.399155i \(-0.130697\pi\)
−0.976392 + 0.216007i \(0.930697\pi\)
\(752\) 5.65868e9 + 1.83862e9i 0.485235 + 0.157662i
\(753\) 0 0
\(754\) −8.55307e8 + 1.17723e9i −0.0726645 + 0.100014i
\(755\) 4.13185e8 1.27165e9i 0.0349406 0.107536i
\(756\) 0 0
\(757\) −6.89701e9 + 5.01097e9i −0.577864 + 0.419842i −0.837953 0.545742i \(-0.816248\pi\)
0.260090 + 0.965584i \(0.416248\pi\)
\(758\) 1.39724e9 0.116528
\(759\) 0 0
\(760\) 1.11091e9 0.0917979
\(761\) −7.44429e9 + 5.40859e9i −0.612318 + 0.444875i −0.850230 0.526412i \(-0.823537\pi\)
0.237912 + 0.971287i \(0.423537\pi\)
\(762\) 0 0
\(763\) 4.32629e9 1.33149e10i 0.352598 1.08518i
\(764\) −2.73857e9 + 3.76932e9i −0.222176 + 0.305799i
\(765\) 0 0
\(766\) −3.58343e9 1.16433e9i −0.288070 0.0935997i
\(767\) 2.51349e9 + 7.73573e9i 0.201138 + 0.619038i
\(768\) 0 0
\(769\) 4.77791e9i 0.378875i −0.981893 0.189437i \(-0.939334\pi\)
0.981893 0.189437i \(-0.0606664\pi\)
\(770\) −8.16801e8 + 1.99477e8i −0.0644761 + 0.0157462i
\(771\) 0 0
\(772\) 7.73643e9 + 1.06483e10i 0.605174 + 0.832950i
\(773\) 8.98078e9 2.91803e9i 0.699336 0.227228i 0.0622946