Properties

Label 16.28.e.a.5.1
Level $16$
Weight $28$
Character 16.5
Analytic conductor $73.897$
Analytic rank $0$
Dimension $106$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,28,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 28, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 28);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 28 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), degree \(2\), 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: \(73.8968919741\)
Analytic rank: \(0\)
Dimension: \(106\)
Relative dimension: \(53\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 16.5
Dual form 16.28.e.a.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11581.2 + 305.932i) q^{2} +(-2.33243e6 + 2.33243e6i) q^{3} +(1.34031e8 - 7.08611e6i) q^{4} +(-3.25506e9 - 3.25506e9i) q^{5} +(2.62988e10 - 2.77259e10i) q^{6} -4.57721e11i q^{7} +(-1.55007e12 + 1.23070e11i) q^{8} -3.25487e12i q^{9} +O(q^{10})\) \(q+(-11581.2 + 305.932i) q^{2} +(-2.33243e6 + 2.33243e6i) q^{3} +(1.34031e8 - 7.08611e6i) q^{4} +(-3.25506e9 - 3.25506e9i) q^{5} +(2.62988e10 - 2.77259e10i) q^{6} -4.57721e11i q^{7} +(-1.55007e12 + 1.23070e11i) q^{8} -3.25487e12i q^{9} +(3.86933e13 + 3.67017e13i) q^{10} +(7.31216e13 + 7.31216e13i) q^{11} +(-2.96089e14 + 3.29145e14i) q^{12} +(-1.05155e15 + 1.05155e15i) q^{13} +(1.40031e14 + 5.30096e15i) q^{14} +1.51844e16 q^{15} +(1.79140e16 - 1.89951e15i) q^{16} -3.52795e16 q^{17} +(9.95769e14 + 3.76953e16i) q^{18} +(-1.46140e17 + 1.46140e17i) q^{19} +(-4.59343e17 - 4.13212e17i) q^{20} +(1.06760e18 + 1.06760e18i) q^{21} +(-8.69206e17 - 8.24465e17i) q^{22} -2.95092e18i q^{23} +(3.32837e18 - 3.90248e18i) q^{24} +1.37403e19i q^{25} +(1.18565e19 - 1.24999e19i) q^{26} +(-1.01944e19 - 1.01944e19i) q^{27} +(-3.24346e18 - 6.13486e19i) q^{28} +(-3.27394e19 + 3.27394e19i) q^{29} +(-1.75854e20 + 4.64539e18i) q^{30} -7.52814e18 q^{31} +(-2.06884e20 + 2.74791e19i) q^{32} -3.41102e20 q^{33} +(4.08579e20 - 1.07931e19i) q^{34} +(-1.48991e21 + 1.48991e21i) q^{35} +(-2.30644e19 - 4.36253e20i) q^{36} +(-2.52539e20 - 2.52539e20i) q^{37} +(1.64777e21 - 1.73718e21i) q^{38} -4.90532e21i q^{39} +(5.44616e21 + 4.64496e21i) q^{40} +3.98696e21i q^{41} +(-1.26907e22 - 1.20375e22i) q^{42} +(1.03084e22 + 1.03084e22i) q^{43} +(1.03187e22 + 9.28238e21i) q^{44} +(-1.05948e22 + 1.05948e22i) q^{45} +(9.02779e20 + 3.41752e22i) q^{46} -2.78056e22 q^{47} +(-3.73526e22 + 4.62136e22i) q^{48} -1.43796e23 q^{49} +(-4.20358e21 - 1.59129e23i) q^{50} +(8.22869e22 - 8.22869e22i) q^{51} +(-1.33488e23 + 1.48391e23i) q^{52} +(-3.83935e21 - 3.83935e21i) q^{53} +(1.21182e23 + 1.14945e23i) q^{54} -4.76030e23i q^{55} +(5.63316e22 + 7.09498e23i) q^{56} -6.81723e23i q^{57} +(3.69145e23 - 3.89177e23i) q^{58} +(-5.02923e23 - 5.02923e23i) q^{59} +(2.03517e24 - 1.07598e23i) q^{60} +(-1.45871e24 + 1.45871e24i) q^{61} +(8.71849e22 - 2.30310e21i) q^{62} -1.48982e24 q^{63} +(2.38756e24 - 3.81533e23i) q^{64} +6.84570e24 q^{65} +(3.95037e24 - 1.04354e23i) q^{66} +(-3.20060e24 + 3.20060e24i) q^{67} +(-4.72853e24 + 2.49994e23i) q^{68} +(6.88281e24 + 6.88281e24i) q^{69} +(1.67991e25 - 1.77108e25i) q^{70} +2.21358e24i q^{71} +(4.00577e23 + 5.04527e24i) q^{72} -8.58412e24i q^{73} +(3.00196e24 + 2.84744e24i) q^{74} +(-3.20482e25 - 3.20482e25i) q^{75} +(-1.85516e25 + 2.06228e25i) q^{76} +(3.34693e25 - 3.34693e25i) q^{77} +(1.50069e24 + 5.68095e25i) q^{78} +2.53654e25 q^{79} +(-6.44941e25 - 5.21280e25i) q^{80} +7.23759e25 q^{81} +(-1.21974e24 - 4.61738e25i) q^{82} +(-4.74091e25 + 4.74091e25i) q^{83} +(1.50657e26 + 1.35526e26i) q^{84} +(1.14837e26 + 1.14837e26i) q^{85} +(-1.22537e26 - 1.16230e26i) q^{86} -1.52725e26i q^{87} +(-1.22342e26 - 1.04344e26i) q^{88} -7.83314e25i q^{89} +(1.19459e26 - 1.25942e26i) q^{90} +(4.81315e26 + 4.81315e26i) q^{91} +(-2.09105e25 - 3.95513e26i) q^{92} +(1.75589e25 - 1.75589e25i) q^{93} +(3.22022e26 - 8.50660e24i) q^{94} +9.51389e26 q^{95} +(4.18450e26 - 5.46636e26i) q^{96} -7.63225e26 q^{97} +(1.66533e27 - 4.39918e25i) q^{98} +(2.38002e26 - 2.38002e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11581.2 + 305.932i −0.999651 + 0.0264070i
\(3\) −2.33243e6 + 2.33243e6i −0.844641 + 0.844641i −0.989458 0.144818i \(-0.953740\pi\)
0.144818 + 0.989458i \(0.453740\pi\)
\(4\) 1.34031e8 7.08611e6i 0.998605 0.0527956i
\(5\) −3.25506e9 3.25506e9i −1.19252 1.19252i −0.976359 0.216157i \(-0.930648\pi\)
−0.216157 0.976359i \(-0.569352\pi\)
\(6\) 2.62988e10 2.77259e10i 0.822042 0.866650i
\(7\) 4.57721e11i 1.78557i −0.450481 0.892786i \(-0.648748\pi\)
0.450481 0.892786i \(-0.351252\pi\)
\(8\) −1.55007e12 + 1.23070e11i −0.996863 + 0.0791474i
\(9\) 3.25487e12i 0.426835i
\(10\) 3.86933e13 + 3.67017e13i 1.22359 + 1.16061i
\(11\) 7.31216e13 + 7.31216e13i 0.638623 + 0.638623i 0.950216 0.311593i \(-0.100863\pi\)
−0.311593 + 0.950216i \(0.600863\pi\)
\(12\) −2.96089e14 + 3.29145e14i −0.798869 + 0.888056i
\(13\) −1.05155e15 + 1.05155e15i −0.962928 + 0.962928i −0.999337 0.0364094i \(-0.988408\pi\)
0.0364094 + 0.999337i \(0.488408\pi\)
\(14\) 1.40031e14 + 5.30096e15i 0.0471516 + 1.78495i
\(15\) 1.51844e16 2.01449
\(16\) 1.79140e16 1.89951e15i 0.994425 0.105444i
\(17\) −3.52795e16 −0.863896 −0.431948 0.901898i \(-0.642174\pi\)
−0.431948 + 0.901898i \(0.642174\pi\)
\(18\) 9.95769e14 + 3.76953e16i 0.0112714 + 0.426686i
\(19\) −1.46140e17 + 1.46140e17i −0.797251 + 0.797251i −0.982661 0.185410i \(-0.940639\pi\)
0.185410 + 0.982661i \(0.440639\pi\)
\(20\) −4.59343e17 4.13212e17i −1.25381 1.12789i
\(21\) 1.06760e18 + 1.06760e18i 1.50817 + 1.50817i
\(22\) −8.69206e17 8.24465e17i −0.655264 0.621536i
\(23\) 2.95092e18i 1.22076i −0.792108 0.610381i \(-0.791016\pi\)
0.792108 0.610381i \(-0.208984\pi\)
\(24\) 3.32837e18 3.90248e18i 0.775140 0.908842i
\(25\) 1.37403e19i 1.84419i
\(26\) 1.18565e19 1.24999e19i 0.937164 0.988020i
\(27\) −1.01944e19 1.01944e19i −0.484118 0.484118i
\(28\) −3.24346e18 6.13486e19i −0.0942704 1.78308i
\(29\) −3.27394e19 + 3.27394e19i −0.592512 + 0.592512i −0.938309 0.345797i \(-0.887608\pi\)
0.345797 + 0.938309i \(0.387608\pi\)
\(30\) −1.75854e20 + 4.64539e18i −2.01379 + 0.0531968i
\(31\) −7.52814e18 −0.0553739 −0.0276869 0.999617i \(-0.508814\pi\)
−0.0276869 + 0.999617i \(0.508814\pi\)
\(32\) −2.06884e20 + 2.74791e19i −0.991294 + 0.131667i
\(33\) −3.41102e20 −1.07881
\(34\) 4.08579e20 1.07931e19i 0.863595 0.0228129i
\(35\) −1.48991e21 + 1.48991e21i −2.12932 + 2.12932i
\(36\) −2.30644e19 4.36253e20i −0.0225350 0.426240i
\(37\) −2.52539e20 2.52539e20i −0.170453 0.170453i 0.616725 0.787178i \(-0.288459\pi\)
−0.787178 + 0.616725i \(0.788459\pi\)
\(38\) 1.64777e21 1.73718e21i 0.775920 0.818026i
\(39\) 4.90532e21i 1.62666i
\(40\) 5.44616e21 + 4.64496e21i 1.28316 + 1.09439i
\(41\) 3.98696e21i 0.673070i 0.941671 + 0.336535i \(0.109255\pi\)
−0.941671 + 0.336535i \(0.890745\pi\)
\(42\) −1.26907e22 1.20375e22i −1.54747 1.46781i
\(43\) 1.03084e22 + 1.03084e22i 0.914884 + 0.914884i 0.996651 0.0817674i \(-0.0260565\pi\)
−0.0817674 + 0.996651i \(0.526056\pi\)
\(44\) 1.03187e22 + 9.28238e21i 0.671449 + 0.604016i
\(45\) −1.05948e22 + 1.05948e22i −0.509008 + 0.509008i
\(46\) 9.02779e20 + 3.41752e22i 0.0322367 + 1.22034i
\(47\) −2.78056e22 −0.742695 −0.371348 0.928494i \(-0.621104\pi\)
−0.371348 + 0.928494i \(0.621104\pi\)
\(48\) −3.73526e22 + 4.62136e22i −0.750870 + 0.928994i
\(49\) −1.43796e23 −2.18827
\(50\) −4.20358e21 1.59129e23i −0.0486995 1.84354i
\(51\) 8.22869e22 8.22869e22i 0.729682 0.729682i
\(52\) −1.33488e23 + 1.48391e23i −0.910746 + 1.01242i
\(53\) −3.83935e21 3.83935e21i −0.0202550 0.0202550i 0.696907 0.717162i \(-0.254559\pi\)
−0.717162 + 0.696907i \(0.754559\pi\)
\(54\) 1.21182e23 + 1.14945e23i 0.496733 + 0.471165i
\(55\) 4.76030e23i 1.52313i
\(56\) 5.63316e22 + 7.09498e23i 0.141323 + 1.77997i
\(57\) 6.81723e23i 1.34678i
\(58\) 3.69145e23 3.89177e23i 0.576659 0.607952i
\(59\) −5.02923e23 5.02923e23i −0.623734 0.623734i 0.322750 0.946484i \(-0.395393\pi\)
−0.946484 + 0.322750i \(0.895393\pi\)
\(60\) 2.03517e24 1.07598e23i 2.01168 0.106356i
\(61\) −1.45871e24 + 1.45871e24i −1.15350 + 1.15350i −0.167651 + 0.985846i \(0.553618\pi\)
−0.985846 + 0.167651i \(0.946382\pi\)
\(62\) 8.71849e22 2.30310e21i 0.0553546 0.00146226i
\(63\) −1.48982e24 −0.762145
\(64\) 2.38756e24 3.81533e23i 0.987471 0.157798i
\(65\) 6.84570e24 2.29661
\(66\) 3.95037e24 1.04354e23i 1.07844 0.0284882i
\(67\) −3.20060e24 + 3.20060e24i −0.713216 + 0.713216i −0.967207 0.253991i \(-0.918257\pi\)
0.253991 + 0.967207i \(0.418257\pi\)
\(68\) −4.72853e24 + 2.49994e23i −0.862692 + 0.0456100i
\(69\) 6.88281e24 + 6.88281e24i 1.03111 + 1.03111i
\(70\) 1.67991e25 1.77108e25i 2.07235 2.18481i
\(71\) 2.21358e24i 0.225480i 0.993625 + 0.112740i \(0.0359627\pi\)
−0.993625 + 0.112740i \(0.964037\pi\)
\(72\) 4.00577e23 + 5.04527e24i 0.0337829 + 0.425496i
\(73\) 8.58412e24i 0.600948i −0.953790 0.300474i \(-0.902855\pi\)
0.953790 0.300474i \(-0.0971449\pi\)
\(74\) 3.00196e24 + 2.84744e24i 0.174895 + 0.165893i
\(75\) −3.20482e25 3.20482e25i −1.55767 1.55767i
\(76\) −1.85516e25 + 2.06228e25i −0.754048 + 0.838231i
\(77\) 3.34693e25 3.34693e25i 1.14031 1.14031i
\(78\) 1.50069e24 + 5.68095e25i 0.0429551 + 1.62609i
\(79\) 2.53654e25 0.611329 0.305665 0.952139i \(-0.401121\pi\)
0.305665 + 0.952139i \(0.401121\pi\)
\(80\) −6.44941e25 5.21280e25i −1.31161 1.06012i
\(81\) 7.23759e25 1.24465
\(82\) −1.21974e24 4.61738e25i −0.0177738 0.672835i
\(83\) −4.74091e25 + 4.74091e25i −0.586554 + 0.586554i −0.936696 0.350143i \(-0.886133\pi\)
0.350143 + 0.936696i \(0.386133\pi\)
\(84\) 1.50657e26 + 1.35526e26i 1.58569 + 1.42644i
\(85\) 1.14837e26 + 1.14837e26i 1.03021 + 1.03021i
\(86\) −1.22537e26 1.16230e26i −0.938724 0.890406i
\(87\) 1.52725e26i 1.00092i
\(88\) −1.22342e26 1.04344e26i −0.687165 0.586074i
\(89\) 7.83314e25i 0.377721i −0.982004 0.188860i \(-0.939521\pi\)
0.982004 0.188860i \(-0.0604794\pi\)
\(90\) 1.19459e26 1.25942e26i 0.495389 0.522272i
\(91\) 4.81315e26 + 4.81315e26i 1.71938 + 1.71938i
\(92\) −2.09105e25 3.95513e26i −0.0644509 1.21906i
\(93\) 1.75589e25 1.75589e25i 0.0467710 0.0467710i
\(94\) 3.22022e26 8.50660e24i 0.742436 0.0196124i
\(95\) 9.51389e26 1.90147
\(96\) 4.18450e26 5.46636e26i 0.726076 0.948498i
\(97\) −7.63225e26 −1.15142 −0.575711 0.817653i \(-0.695275\pi\)
−0.575711 + 0.817653i \(0.695275\pi\)
\(98\) 1.66533e27 4.39918e25i 2.18750 0.0577856i
\(99\) 2.38002e26 2.38002e26i 0.272587 0.272587i
\(100\) 9.73650e25 + 1.84161e27i 0.0973650 + 1.84161i
\(101\) 5.79920e26 + 5.79920e26i 0.507025 + 0.507025i 0.913612 0.406587i \(-0.133281\pi\)
−0.406587 + 0.913612i \(0.633281\pi\)
\(102\) −9.27807e26 + 9.78156e26i −0.710159 + 0.748696i
\(103\) 1.50880e27i 1.01235i 0.862432 + 0.506173i \(0.168940\pi\)
−0.862432 + 0.506173i \(0.831060\pi\)
\(104\) 1.50055e27 1.75938e27i 0.883694 1.03612i
\(105\) 6.95022e27i 3.59702i
\(106\) 4.56388e25 + 4.32897e25i 0.0207829 + 0.0197131i
\(107\) −2.05125e27 2.05125e27i −0.822882 0.822882i 0.163638 0.986520i \(-0.447677\pi\)
−0.986520 + 0.163638i \(0.947677\pi\)
\(108\) −1.43860e27 1.29412e27i −0.509002 0.457884i
\(109\) 8.30595e26 8.30595e26i 0.259497 0.259497i −0.565353 0.824849i \(-0.691260\pi\)
0.824849 + 0.565353i \(0.191260\pi\)
\(110\) 1.45633e26 + 5.51300e27i 0.0402215 + 1.52260i
\(111\) 1.17806e27 0.287943
\(112\) −8.69446e26 8.19960e27i −0.188278 1.77562i
\(113\) −3.54387e26 −0.0680642 −0.0340321 0.999421i \(-0.510835\pi\)
−0.0340321 + 0.999421i \(0.510835\pi\)
\(114\) 2.08561e26 + 7.89516e27i 0.0355645 + 1.34631i
\(115\) −9.60541e27 + 9.60541e27i −1.45578 + 1.45578i
\(116\) −4.15608e27 + 4.62007e27i −0.560404 + 0.622968i
\(117\) 3.42265e27 + 3.42265e27i 0.411011 + 0.411011i
\(118\) 5.97831e27 + 5.67059e27i 0.639988 + 0.607046i
\(119\) 1.61482e28i 1.54255i
\(120\) −2.35368e28 + 1.86874e27i −2.00817 + 0.159442i
\(121\) 2.41646e27i 0.184322i
\(122\) 1.64474e28 1.73399e28i 1.12263 1.18356i
\(123\) −9.29931e27 9.29931e27i −0.568502 0.568502i
\(124\) −1.00900e27 + 5.33452e25i −0.0552966 + 0.00292350i
\(125\) 2.04733e28 2.04733e28i 1.00671 1.00671i
\(126\) 1.72540e28 4.55784e26i 0.761879 0.0201260i
\(127\) −2.55876e28 −1.01550 −0.507749 0.861505i \(-0.669522\pi\)
−0.507749 + 0.861505i \(0.669522\pi\)
\(128\) −2.75341e28 + 5.14904e27i −0.982960 + 0.183819i
\(129\) −4.80872e28 −1.54550
\(130\) −7.92814e28 + 2.09432e27i −2.29581 + 0.0606467i
\(131\) 2.79898e28 2.79898e28i 0.730866 0.730866i −0.239925 0.970791i \(-0.577123\pi\)
0.970791 + 0.239925i \(0.0771229\pi\)
\(132\) −4.57181e28 + 2.41709e27i −1.07731 + 0.0569566i
\(133\) 6.68913e28 + 6.68913e28i 1.42355 + 1.42355i
\(134\) 3.60876e28 3.80459e28i 0.694134 0.731801i
\(135\) 6.63669e28i 1.15464i
\(136\) 5.46855e28 4.34184e27i 0.861186 0.0683752i
\(137\) 3.84396e28i 0.548342i −0.961681 0.274171i \(-0.911597\pi\)
0.961681 0.274171i \(-0.0884034\pi\)
\(138\) −8.18169e28 7.76055e28i −1.05797 1.00352i
\(139\) 4.45967e28 + 4.45967e28i 0.523122 + 0.523122i 0.918513 0.395391i \(-0.129391\pi\)
−0.395391 + 0.918513i \(0.629391\pi\)
\(140\) −1.89136e29 + 2.10251e29i −2.01393 + 2.23877i
\(141\) 6.48546e28 6.48546e28i 0.627310 0.627310i
\(142\) −6.77204e26 2.56359e28i −0.00595425 0.225401i
\(143\) −1.53782e29 −1.22989
\(144\) −6.18267e27 5.83077e28i −0.0450072 0.424456i
\(145\) 2.13137e29 1.41316
\(146\) 2.62615e27 + 9.94144e28i 0.0158693 + 0.600739i
\(147\) 3.35395e29 3.35395e29i 1.84830 1.84830i
\(148\) −3.56374e28 3.20584e28i −0.179215 0.161216i
\(149\) −1.57873e29 1.57873e29i −0.724924 0.724924i 0.244680 0.969604i \(-0.421317\pi\)
−0.969604 + 0.244680i \(0.921317\pi\)
\(150\) 3.80961e29 + 3.61352e29i 1.59826 + 1.51600i
\(151\) 2.28490e29i 0.876353i 0.898889 + 0.438176i \(0.144375\pi\)
−0.898889 + 0.438176i \(0.855625\pi\)
\(152\) 2.08541e29 2.44512e29i 0.731650 0.857851i
\(153\) 1.14830e29i 0.368741i
\(154\) −3.77375e29 + 3.97854e29i −1.10980 + 1.17002i
\(155\) 2.45046e28 + 2.45046e28i 0.0660342 + 0.0660342i
\(156\) −3.47597e28 6.57463e29i −0.0858803 1.62439i
\(157\) 2.21273e29 2.21273e29i 0.501515 0.501515i −0.410394 0.911908i \(-0.634609\pi\)
0.911908 + 0.410394i \(0.134609\pi\)
\(158\) −2.93761e29 + 7.76007e27i −0.611116 + 0.0161434i
\(159\) 1.79100e28 0.0342165
\(160\) 7.62866e29 + 5.83974e29i 1.33915 + 1.02512i
\(161\) −1.35070e30 −2.17976
\(162\) −8.38199e29 + 2.21421e28i −1.24421 + 0.0328674i
\(163\) 5.65042e29 5.65042e29i 0.771877 0.771877i −0.206557 0.978434i \(-0.566226\pi\)
0.978434 + 0.206557i \(0.0662260\pi\)
\(164\) 2.82520e28 + 5.34375e29i 0.0355351 + 0.672131i
\(165\) 1.11031e30 + 1.11031e30i 1.28650 + 1.28650i
\(166\) 5.34551e29 5.63558e29i 0.570860 0.601838i
\(167\) 3.86533e29i 0.380640i −0.981722 0.190320i \(-0.939047\pi\)
0.981722 0.190320i \(-0.0609526\pi\)
\(168\) −1.78625e30 1.52347e30i −1.62280 1.38407i
\(169\) 1.01897e30i 0.854459i
\(170\) −1.36508e30 1.29482e30i −1.05706 1.00265i
\(171\) 4.75667e29 + 4.75667e29i 0.340295 + 0.340295i
\(172\) 1.45468e30 + 1.30859e30i 0.961910 + 0.865306i
\(173\) 1.26544e30 1.26544e30i 0.773781 0.773781i −0.204984 0.978765i \(-0.565714\pi\)
0.978765 + 0.204984i \(0.0657144\pi\)
\(174\) 4.67233e28 + 1.76873e30i 0.0264313 + 1.00057i
\(175\) 6.28921e30 3.29293
\(176\) 1.44879e30 + 1.17100e30i 0.702401 + 0.567724i
\(177\) 2.34607e30 1.05366
\(178\) 2.39641e28 + 9.07172e29i 0.00997448 + 0.377589i
\(179\) 2.23221e30 2.23221e30i 0.861427 0.861427i −0.130077 0.991504i \(-0.541522\pi\)
0.991504 + 0.130077i \(0.0415224\pi\)
\(180\) −1.34495e30 + 1.49510e30i −0.481424 + 0.535171i
\(181\) 3.53051e30 + 3.53051e30i 1.17267 + 1.17267i 0.981570 + 0.191103i \(0.0612063\pi\)
0.191103 + 0.981570i \(0.438794\pi\)
\(182\) −5.72146e30 5.42696e30i −1.76418 1.67337i
\(183\) 6.80469e30i 1.94858i
\(184\) 3.63169e29 + 4.57412e30i 0.0966202 + 1.21693i
\(185\) 1.64406e30i 0.406536i
\(186\) −1.97981e29 + 2.08725e29i −0.0455196 + 0.0479898i
\(187\) −2.57969e30 2.57969e30i −0.551704 0.551704i
\(188\) −3.72679e30 + 1.97033e29i −0.741659 + 0.0392111i
\(189\) −4.66620e30 + 4.66620e30i −0.864428 + 0.864428i
\(190\) −1.10182e31 + 2.91060e29i −1.90081 + 0.0502121i
\(191\) 1.31825e30 0.211860 0.105930 0.994374i \(-0.466218\pi\)
0.105930 + 0.994374i \(0.466218\pi\)
\(192\) −4.67892e30 + 6.45872e30i −0.700776 + 0.967341i
\(193\) 7.20451e30 1.00596 0.502980 0.864298i \(-0.332237\pi\)
0.502980 + 0.864298i \(0.332237\pi\)
\(194\) 8.83906e30 2.33495e29i 1.15102 0.0304056i
\(195\) −1.59671e31 + 1.59671e31i −1.93981 + 1.93981i
\(196\) −1.92731e31 + 1.01896e30i −2.18522 + 0.115531i
\(197\) −6.67235e29 6.67235e29i −0.0706293 0.0706293i 0.670910 0.741539i \(-0.265904\pi\)
−0.741539 + 0.670910i \(0.765904\pi\)
\(198\) −2.68353e30 + 2.82916e30i −0.265293 + 0.279690i
\(199\) 5.07434e30i 0.468666i −0.972156 0.234333i \(-0.924709\pi\)
0.972156 0.234333i \(-0.0752905\pi\)
\(200\) −1.69101e30 2.12983e31i −0.145963 1.83840i
\(201\) 1.49303e31i 1.20482i
\(202\) −6.89358e30 6.53875e30i −0.520237 0.493459i
\(203\) 1.49855e31 + 1.49855e31i 1.05797 + 1.05797i
\(204\) 1.04459e31 1.16121e31i 0.690140 0.767188i
\(205\) 1.29778e31 1.29778e31i 0.802646 0.802646i
\(206\) −4.61589e29 1.74737e31i −0.0267330 1.01199i
\(207\) −9.60486e30 −0.521065
\(208\) −1.68400e31 + 2.08348e31i −0.856025 + 1.05909i
\(209\) −2.13720e31 −1.01829
\(210\) 2.12629e30 + 8.04919e31i 0.0949867 + 3.59577i
\(211\) −2.32488e31 + 2.32488e31i −0.974064 + 0.974064i −0.999672 0.0256082i \(-0.991848\pi\)
0.0256082 + 0.999672i \(0.491848\pi\)
\(212\) −5.41796e29 4.87384e29i −0.0212962 0.0191574i
\(213\) −5.16302e30 5.16302e30i −0.190449 0.190449i
\(214\) 2.43835e31 + 2.31284e31i 0.844325 + 0.800865i
\(215\) 6.71088e31i 2.18203i
\(216\) 1.70566e31 + 1.45474e31i 0.520916 + 0.444283i
\(217\) 3.44579e30i 0.0988740i
\(218\) −9.36518e30 + 9.87339e30i −0.252554 + 0.266259i
\(219\) 2.00219e31 + 2.00219e31i 0.507585 + 0.507585i
\(220\) −3.37320e30 6.38026e31i −0.0804149 1.52101i
\(221\) 3.70980e31 3.70980e31i 0.831870 0.831870i
\(222\) −1.36433e31 + 3.60406e29i −0.287843 + 0.00760372i
\(223\) 9.24558e31 1.83577 0.917885 0.396846i \(-0.129895\pi\)
0.917885 + 0.396846i \(0.129895\pi\)
\(224\) 1.25777e31 + 9.46952e31i 0.235101 + 1.77003i
\(225\) 4.47228e31 0.787164
\(226\) 4.10423e30 1.08418e29i 0.0680405 0.00179737i
\(227\) 4.20968e29 4.20968e29i 0.00657506 0.00657506i −0.703812 0.710387i \(-0.748520\pi\)
0.710387 + 0.703812i \(0.248520\pi\)
\(228\) −4.83076e30 9.13717e31i −0.0711042 1.34490i
\(229\) −9.87624e31 9.87624e31i −1.37029 1.37029i −0.860005 0.510286i \(-0.829539\pi\)
−0.510286 0.860005i \(-0.670461\pi\)
\(230\) 1.08304e32 1.14181e32i 1.41683 1.49371i
\(231\) 1.56130e32i 1.92630i
\(232\) 4.67189e31 5.47774e31i 0.543757 0.637549i
\(233\) 3.06787e30i 0.0336925i 0.999858 + 0.0168462i \(0.00536258\pi\)
−0.999858 + 0.0168462i \(0.994637\pi\)
\(234\) −4.06855e31 3.85913e31i −0.421722 0.400015i
\(235\) 9.05088e31 + 9.05088e31i 0.885675 + 0.885675i
\(236\) −7.09708e31 6.38433e31i −0.655795 0.589934i
\(237\) −5.91630e31 + 5.91630e31i −0.516354 + 0.516354i
\(238\) −4.94023e30 1.87015e32i −0.0407341 1.54201i
\(239\) −6.57096e31 −0.511985 −0.255992 0.966679i \(-0.582402\pi\)
−0.255992 + 0.966679i \(0.582402\pi\)
\(240\) 2.72013e32 2.88429e31i 2.00326 0.212416i
\(241\) −1.93403e32 −1.34658 −0.673292 0.739377i \(-0.735120\pi\)
−0.673292 + 0.739377i \(0.735120\pi\)
\(242\) 7.39272e29 + 2.79855e31i 0.00486740 + 0.184258i
\(243\) −9.10733e31 + 9.10733e31i −0.567161 + 0.567161i
\(244\) −1.85175e32 + 2.05848e32i −1.09099 + 1.21279i
\(245\) 4.68065e32 + 4.68065e32i 2.60954 + 2.60954i
\(246\) 1.10542e32 + 1.04852e32i 0.583316 + 0.553291i
\(247\) 3.07346e32i 1.53539i
\(248\) 1.16691e31 9.26487e29i 0.0552002 0.00438270i
\(249\) 2.21157e32i 0.990854i
\(250\) −2.30842e32 + 2.43369e32i −0.979770 + 1.03294i
\(251\) −2.66170e32 2.66170e32i −1.07044 1.07044i −0.997323 0.0731219i \(-0.976704\pi\)
−0.0731219 0.997323i \(-0.523296\pi\)
\(252\) −1.99682e32 + 1.05571e31i −0.761082 + 0.0402379i
\(253\) 2.15776e32 2.15776e32i 0.779607 0.779607i
\(254\) 2.96335e32 7.82805e30i 1.01514 0.0268163i
\(255\) −5.35698e32 −1.74031
\(256\) 3.17302e32 6.80555e31i 0.977763 0.209712i
\(257\) −6.34528e32 −1.85504 −0.927520 0.373772i \(-0.878064\pi\)
−0.927520 + 0.373772i \(0.878064\pi\)
\(258\) 5.56907e32 1.47114e31i 1.54496 0.0408120i
\(259\) −1.15592e32 + 1.15592e32i −0.304356 + 0.304356i
\(260\) 9.17533e32 4.85094e31i 2.29341 0.121251i
\(261\) 1.06562e32 + 1.06562e32i 0.252905 + 0.252905i
\(262\) −3.15593e32 + 3.32719e32i −0.711312 + 0.749912i
\(263\) 4.34305e31i 0.0929806i 0.998919 + 0.0464903i \(0.0148037\pi\)
−0.998919 + 0.0464903i \(0.985196\pi\)
\(264\) 5.28731e32 4.19794e31i 1.07543 0.0853853i
\(265\) 2.49946e31i 0.0483089i
\(266\) −7.95146e32 7.54217e32i −1.46064 1.38546i
\(267\) 1.82703e32 + 1.82703e32i 0.319038 + 0.319038i
\(268\) −4.06298e32 + 4.51658e32i −0.674567 + 0.749876i
\(269\) −1.89230e32 + 1.89230e32i −0.298768 + 0.298768i −0.840531 0.541763i \(-0.817757\pi\)
0.541763 + 0.840531i \(0.317757\pi\)
\(270\) −2.03037e31 7.68608e32i −0.0304905 1.15423i
\(271\) 8.92317e32 1.27478 0.637388 0.770543i \(-0.280015\pi\)
0.637388 + 0.770543i \(0.280015\pi\)
\(272\) −6.31996e32 + 6.70137e31i −0.859080 + 0.0910927i
\(273\) −2.24527e33 −2.90451
\(274\) 1.17599e31 + 4.45177e32i 0.0144801 + 0.548151i
\(275\) −1.00471e33 + 1.00471e33i −1.17774 + 1.17774i
\(276\) 9.71279e32 + 8.73735e32i 1.08411 + 0.975230i
\(277\) −7.99909e31 7.99909e31i −0.0850283 0.0850283i 0.663313 0.748342i \(-0.269150\pi\)
−0.748342 + 0.663313i \(0.769150\pi\)
\(278\) −5.30127e32 5.02839e32i −0.536753 0.509125i
\(279\) 2.45032e31i 0.0236355i
\(280\) 2.12610e33 2.49282e33i 1.95411 2.29117i
\(281\) 1.15405e33i 1.01085i −0.862870 0.505426i \(-0.831335\pi\)
0.862870 0.505426i \(-0.168665\pi\)
\(282\) −7.31252e32 + 7.70934e32i −0.610526 + 0.643657i
\(283\) −4.10239e32 4.10239e32i −0.326528 0.326528i 0.524737 0.851265i \(-0.324164\pi\)
−0.851265 + 0.524737i \(0.824164\pi\)
\(284\) 1.56857e31 + 2.96687e32i 0.0119043 + 0.225165i
\(285\) −2.21905e33 + 2.21905e33i −1.60606 + 1.60606i
\(286\) 1.78098e33 4.70467e31i 1.22947 0.0324779i
\(287\) 1.82492e33 1.20181
\(288\) 8.94409e31 + 6.73382e32i 0.0562001 + 0.423119i
\(289\) −4.23070e32 −0.253683
\(290\) −2.46838e33 + 6.52054e31i −1.41267 + 0.0373173i
\(291\) 1.78017e33 1.78017e33i 0.972537 0.972537i
\(292\) −6.08280e31 1.15053e33i −0.0317274 0.600110i
\(293\) −5.20348e32 5.20348e32i −0.259168 0.259168i 0.565548 0.824716i \(-0.308665\pi\)
−0.824716 + 0.565548i \(0.808665\pi\)
\(294\) −3.78167e33 + 3.98688e33i −1.79885 + 1.89646i
\(295\) 3.27409e33i 1.48763i
\(296\) 4.22532e32 + 3.60372e32i 0.183409 + 0.156427i
\(297\) 1.49086e33i 0.618338i
\(298\) 1.87665e33 + 1.78006e33i 0.743814 + 0.705528i
\(299\) 3.10303e33 + 3.10303e33i 1.17551 + 1.17551i
\(300\) −4.52254e33 4.06834e33i −1.63774 1.47326i
\(301\) 4.71836e33 4.71836e33i 1.63359 1.63359i
\(302\) −6.99024e31 2.64619e33i −0.0231419 0.876047i
\(303\) −2.70525e33 −0.856508
\(304\) −2.34035e33 + 2.89554e33i −0.708741 + 0.876872i
\(305\) 9.49639e33 2.75113
\(306\) −3.51302e31 1.32987e33i −0.00973736 0.368613i
\(307\) −3.95492e33 + 3.95492e33i −1.04899 + 1.04899i −0.0502504 + 0.998737i \(0.516002\pi\)
−0.998737 + 0.0502504i \(0.983998\pi\)
\(308\) 4.24874e33 4.72307e33i 1.07851 1.19892i
\(309\) −3.51917e33 3.51917e33i −0.855068 0.855068i
\(310\) −2.91289e32 2.76295e32i −0.0677549 0.0642674i
\(311\) 1.43621e33i 0.319854i −0.987129 0.159927i \(-0.948874\pi\)
0.987129 0.159927i \(-0.0511259\pi\)
\(312\) 6.03697e32 + 7.60358e33i 0.128746 + 1.62155i
\(313\) 1.23917e33i 0.253094i −0.991961 0.126547i \(-0.959610\pi\)
0.991961 0.126547i \(-0.0403895\pi\)
\(314\) −2.49491e33 + 2.63030e33i −0.488096 + 0.514583i
\(315\) 4.84947e33 + 4.84947e33i 0.908870 + 0.908870i
\(316\) 3.39973e33 1.79742e32i 0.610477 0.0322755i
\(317\) 7.03040e33 7.03040e33i 1.20971 1.20971i 0.238586 0.971121i \(-0.423316\pi\)
0.971121 0.238586i \(-0.0766838\pi\)
\(318\) −2.07420e32 + 5.47924e30i −0.0342045 + 0.000903555i
\(319\) −4.78791e33 −0.756783
\(320\) −9.01356e33 6.52974e33i −1.36575 0.989398i
\(321\) 9.56880e33 1.39008
\(322\) 1.56427e34 4.13221e32i 2.17900 0.0575610i
\(323\) 5.15574e33 5.15574e33i 0.688743 0.688743i
\(324\) 9.70058e33 5.12863e32i 1.24291 0.0657119i
\(325\) −1.44485e34 1.44485e34i −1.77582 1.77582i
\(326\) −6.37100e33 + 6.71673e33i −0.751225 + 0.791991i
\(327\) 3.87461e33i 0.438363i
\(328\) −4.90675e32 6.18005e33i −0.0532717 0.670958i
\(329\) 1.27272e34i 1.32614i
\(330\) −1.31984e34 1.25190e34i −1.32003 1.25208i
\(331\) −1.93968e33 1.93968e33i −0.186231 0.186231i 0.607833 0.794065i \(-0.292039\pi\)
−0.794065 + 0.607833i \(0.792039\pi\)
\(332\) −6.01832e33 + 6.69022e33i −0.554768 + 0.616703i
\(333\) −8.21982e32 + 8.21982e32i −0.0727554 + 0.0727554i
\(334\) 1.18253e32 + 4.47652e33i 0.0100516 + 0.380507i
\(335\) 2.08363e34 1.70104
\(336\) 2.11529e34 + 1.70971e34i 1.65879 + 1.34073i
\(337\) 1.39572e33 0.105147 0.0525733 0.998617i \(-0.483258\pi\)
0.0525733 + 0.998617i \(0.483258\pi\)
\(338\) 3.11735e32 + 1.18009e34i 0.0225637 + 0.854161i
\(339\) 8.26583e32 8.26583e32i 0.0574898 0.0574898i
\(340\) 1.62054e34 + 1.45779e34i 1.08316 + 0.974382i
\(341\) −5.50470e32 5.50470e32i −0.0353630 0.0353630i
\(342\) −5.65432e33 5.36327e33i −0.349163 0.331190i
\(343\) 3.57406e34i 2.12174i
\(344\) −1.72473e34 1.47100e34i −0.984425 0.839603i
\(345\) 4.48079e34i 2.45922i
\(346\) −1.42681e34 + 1.50424e34i −0.753078 + 0.793944i
\(347\) 1.00271e34 + 1.00271e34i 0.509010 + 0.509010i 0.914222 0.405213i \(-0.132803\pi\)
−0.405213 + 0.914222i \(0.632803\pi\)
\(348\) −1.08222e33 2.04698e34i −0.0528442 0.999523i
\(349\) −1.43790e34 + 1.43790e34i −0.675436 + 0.675436i −0.958964 0.283528i \(-0.908495\pi\)
0.283528 + 0.958964i \(0.408495\pi\)
\(350\) −7.28365e34 + 1.92407e33i −3.29178 + 0.0869564i
\(351\) 2.14398e34 0.932341
\(352\) −1.71370e34 1.31184e34i −0.717148 0.548977i
\(353\) −1.48507e34 −0.598118 −0.299059 0.954235i \(-0.596673\pi\)
−0.299059 + 0.954235i \(0.596673\pi\)
\(354\) −2.71703e34 + 7.17736e32i −1.05329 + 0.0278241i
\(355\) 7.20533e33 7.20533e33i 0.268888 0.268888i
\(356\) −5.55065e32 1.04988e34i −0.0199420 0.377194i
\(357\) −3.76645e34 3.76645e34i −1.30290 1.30290i
\(358\) −2.51687e34 + 2.65345e34i −0.838379 + 0.883875i
\(359\) 1.54110e33i 0.0494376i −0.999694 0.0247188i \(-0.992131\pi\)
0.999694 0.0247188i \(-0.00786904\pi\)
\(360\) 1.51188e34 1.77266e34i 0.467124 0.547698i
\(361\) 9.11314e33i 0.271219i
\(362\) −4.19676e34 3.98074e34i −1.20323 1.14130i
\(363\) 5.63623e33 + 5.63623e33i 0.155686 + 0.155686i
\(364\) 6.79216e34 + 6.11003e34i 1.80775 + 1.62620i
\(365\) −2.79418e34 + 2.79418e34i −0.716640 + 0.716640i
\(366\) 2.08177e33 + 7.88064e34i 0.0514562 + 1.94790i
\(367\) −4.83897e34 −1.15282 −0.576410 0.817161i \(-0.695547\pi\)
−0.576410 + 0.817161i \(0.695547\pi\)
\(368\) −5.60530e33 5.28626e34i −0.128722 1.21396i
\(369\) 1.29771e34 0.287290
\(370\) −5.02970e32 1.90402e34i −0.0107354 0.406394i
\(371\) −1.75735e33 + 1.75735e33i −0.0361668 + 0.0361668i
\(372\) 2.22900e33 2.47785e33i 0.0442365 0.0491751i
\(373\) 7.21823e34 + 7.21823e34i 1.38153 + 1.38153i 0.841901 + 0.539632i \(0.181437\pi\)
0.539632 + 0.841901i \(0.318563\pi\)
\(374\) 3.06651e34 + 2.90867e34i 0.566080 + 0.536943i
\(375\) 9.55051e34i 1.70061i
\(376\) 4.31005e34 3.42202e33i 0.740365 0.0587824i
\(377\) 6.88540e34i 1.14109i
\(378\) 5.26126e34 5.54677e34i 0.841299 0.886953i
\(379\) 2.71495e34 + 2.71495e34i 0.418921 + 0.418921i 0.884832 0.465911i \(-0.154273\pi\)
−0.465911 + 0.884832i \(0.654273\pi\)
\(380\) 1.27515e35 6.74164e33i 1.89882 0.100389i
\(381\) 5.96813e34 5.96813e34i 0.857731 0.857731i
\(382\) −1.52670e34 + 4.03296e32i −0.211786 + 0.00559459i
\(383\) 6.33334e34 0.848104 0.424052 0.905638i \(-0.360607\pi\)
0.424052 + 0.905638i \(0.360607\pi\)
\(384\) 5.22116e34 7.62311e34i 0.674987 0.985509i
\(385\) −2.17889e35 −2.71967
\(386\) −8.34368e34 + 2.20409e33i −1.00561 + 0.0265644i
\(387\) 3.35525e34 3.35525e34i 0.390505 0.390505i
\(388\) −1.02296e35 + 5.40830e33i −1.14982 + 0.0607900i
\(389\) −4.61855e34 4.61855e34i −0.501401 0.501401i 0.410472 0.911873i \(-0.365364\pi\)
−0.911873 + 0.410472i \(0.865364\pi\)
\(390\) 1.80034e35 1.89803e35i 1.88791 1.99036i
\(391\) 1.04107e35i 1.05461i
\(392\) 2.22894e35 1.76970e34i 2.18140 0.173196i
\(393\) 1.30569e35i 1.23464i
\(394\) 7.93151e33 + 7.52325e33i 0.0724698 + 0.0687396i
\(395\) −8.25658e34 8.25658e34i −0.729020 0.729020i
\(396\) 3.02130e34 3.35860e34i 0.257815 0.286598i
\(397\) 1.22128e35 1.22128e35i 1.00726 1.00726i 0.00728905 0.999973i \(-0.497680\pi\)
0.999973 0.00728905i \(-0.00232020\pi\)
\(398\) 1.55240e33 + 5.87669e34i 0.0123761 + 0.468502i
\(399\) −3.12039e35 −2.40478
\(400\) 2.60998e34 + 2.46143e35i 0.194458 + 1.83391i
\(401\) 1.65864e35 1.19482 0.597410 0.801936i \(-0.296197\pi\)
0.597410 + 0.801936i \(0.296197\pi\)
\(402\) 4.56767e33 + 1.72911e35i 0.0318158 + 1.20440i
\(403\) 7.91620e33 7.91620e33i 0.0533210 0.0533210i
\(404\) 8.18364e34 + 7.36176e34i 0.533087 + 0.479549i
\(405\) −2.35588e35 2.35588e35i −1.48426 1.48426i
\(406\) −1.78134e35 1.68965e35i −1.08554 1.02967i
\(407\) 3.69321e34i 0.217710i
\(408\) −1.17423e35 + 1.37677e35i −0.669640 + 0.785145i
\(409\) 1.49964e35i 0.827415i −0.910410 0.413707i \(-0.864234\pi\)
0.910410 0.413707i \(-0.135766\pi\)
\(410\) −1.46328e35 + 1.54269e35i −0.781170 + 0.823561i
\(411\) 8.96577e34 + 8.96577e34i 0.463152 + 0.463152i
\(412\) 1.06915e34 + 2.02225e35i 0.0534474 + 1.01093i
\(413\) −2.30199e35 + 2.30199e35i −1.11372 + 1.11372i
\(414\) 1.11236e35 2.93843e33i 0.520883 0.0137598i
\(415\) 3.08639e35 1.39895
\(416\) 1.88653e35 2.46444e35i 0.827759 1.08133i
\(417\) −2.08037e35 −0.883700
\(418\) 2.47513e35 6.53836e33i 1.01793 0.0268899i
\(419\) −3.00753e35 + 3.00753e35i −1.19763 + 1.19763i −0.222751 + 0.974875i \(0.571504\pi\)
−0.974875 + 0.222751i \(0.928496\pi\)
\(420\) −4.92501e34 9.31542e35i −0.189907 3.59201i
\(421\) 4.02468e34 + 4.02468e34i 0.150287 + 0.150287i 0.778246 0.627959i \(-0.216109\pi\)
−0.627959 + 0.778246i \(0.716109\pi\)
\(422\) 2.62136e35 2.76361e35i 0.948002 0.999446i
\(423\) 9.05036e34i 0.317008i
\(424\) 6.42375e33 + 5.47874e33i 0.0217946 + 0.0185884i
\(425\) 4.84749e35i 1.59319i
\(426\) 6.13735e34 + 5.82144e34i 0.195412 + 0.185354i
\(427\) 6.67683e35 + 6.67683e35i 2.05965 + 2.05965i
\(428\) −2.89466e35 2.60395e35i −0.865179 0.778290i
\(429\) 3.58685e35 3.58685e35i 1.03882 1.03882i
\(430\) 2.05307e34 + 7.77200e35i 0.0576208 + 2.18127i
\(431\) −2.02475e35 −0.550717 −0.275358 0.961342i \(-0.588796\pi\)
−0.275358 + 0.961342i \(0.588796\pi\)
\(432\) −2.01987e35 1.63258e35i −0.532467 0.430372i
\(433\) 2.11043e35 0.539242 0.269621 0.962966i \(-0.413102\pi\)
0.269621 + 0.962966i \(0.413102\pi\)
\(434\) −1.05418e33 3.99064e34i −0.00261097 0.0988395i
\(435\) −4.97128e35 + 4.97128e35i −1.19361 + 1.19361i
\(436\) 1.05439e35 1.17211e35i 0.245434 0.272835i
\(437\) 4.31247e35 + 4.31247e35i 0.973255 + 0.973255i
\(438\) −2.38003e35 2.25752e35i −0.520812 0.494005i
\(439\) 4.45130e34i 0.0944531i 0.998884 + 0.0472265i \(0.0150383\pi\)
−0.998884 + 0.0472265i \(0.984962\pi\)
\(440\) 5.85850e34 + 7.37879e35i 0.120552 + 1.51836i
\(441\) 4.68039e35i 0.934030i
\(442\) −4.18290e35 + 4.40989e35i −0.809612 + 0.853547i
\(443\) −4.85605e35 4.85605e35i −0.911660 0.911660i 0.0847429 0.996403i \(-0.472993\pi\)
−0.996403 + 0.0847429i \(0.972993\pi\)
\(444\) 1.57896e35 8.34786e33i 0.287542 0.0152021i
\(445\) −2.54974e35 + 2.54974e35i −0.450438 + 0.450438i
\(446\) −1.07075e36 + 2.82851e34i −1.83513 + 0.0484772i
\(447\) 7.36455e35 1.22460
\(448\) −1.74636e35 1.09284e36i −0.281760 1.76320i
\(449\) −4.71509e35 −0.738184 −0.369092 0.929393i \(-0.620331\pi\)
−0.369092 + 0.929393i \(0.620331\pi\)
\(450\) −5.17944e35 + 1.36821e34i −0.786889 + 0.0207867i
\(451\) −2.91533e35 + 2.91533e35i −0.429838 + 0.429838i
\(452\) −4.74987e34 + 2.51122e33i −0.0679693 + 0.00359349i
\(453\) −5.32938e35 5.32938e35i −0.740203 0.740203i
\(454\) −4.74653e33 + 5.00410e33i −0.00639914 + 0.00674640i
\(455\) 3.13342e36i 4.10077i
\(456\) 8.38995e34 + 1.05672e36i 0.106594 + 1.34256i
\(457\) 1.20700e36i 1.48881i −0.667728 0.744405i \(-0.732733\pi\)
0.667728 0.744405i \(-0.267267\pi\)
\(458\) 1.17400e36 + 1.11357e36i 1.40600 + 1.33363i
\(459\) 3.59653e35 + 3.59653e35i 0.418228 + 0.418228i
\(460\) −1.21935e36 + 1.35548e36i −1.37689 + 1.53061i
\(461\) −4.20312e35 + 4.20312e35i −0.460903 + 0.460903i −0.898951 0.438049i \(-0.855670\pi\)
0.438049 + 0.898951i \(0.355670\pi\)
\(462\) −4.77650e34 1.80817e36i −0.0508678 1.92563i
\(463\) 1.27380e36 1.31752 0.658762 0.752351i \(-0.271080\pi\)
0.658762 + 0.752351i \(0.271080\pi\)
\(464\) −5.24303e35 + 6.48681e35i −0.526732 + 0.651686i
\(465\) −1.14310e35 −0.111550
\(466\) −9.38560e32 3.55297e34i −0.000889718 0.0336807i
\(467\) 2.52284e35 2.52284e35i 0.232333 0.232333i −0.581333 0.813666i \(-0.697469\pi\)
0.813666 + 0.581333i \(0.197469\pi\)
\(468\) 4.82994e35 + 4.34487e35i 0.432138 + 0.388739i
\(469\) 1.46498e36 + 1.46498e36i 1.27350 + 1.27350i
\(470\) −1.07589e36 1.02051e36i −0.908755 0.861978i
\(471\) 1.03221e36i 0.847199i
\(472\) 8.41459e35 + 7.17670e35i 0.671144 + 0.572410i
\(473\) 1.50753e36i 1.16853i
\(474\) 6.67078e35 7.03278e35i 0.502538 0.529809i
\(475\) −2.00800e36 2.00800e36i −1.47028 1.47028i
\(476\) 1.14428e35 + 2.16435e36i 0.0814399 + 1.54040i
\(477\) −1.24966e34 + 1.24966e34i −0.00864557 + 0.00864557i
\(478\) 7.60996e35 2.01026e34i 0.511806 0.0135200i
\(479\) −1.59000e36 −1.03960 −0.519802 0.854287i \(-0.673994\pi\)
−0.519802 + 0.854287i \(0.673994\pi\)
\(480\) −3.14141e36 + 4.17253e35i −1.99696 + 0.265242i
\(481\) 5.31113e35 0.328268
\(482\) 2.23984e36 5.91681e34i 1.34611 0.0355593i
\(483\) 3.15041e36 3.15041e36i 1.84111 1.84111i
\(484\) −1.71233e34 3.23880e35i −0.00973140 0.184065i
\(485\) 2.48434e36 + 2.48434e36i 1.37309 + 1.37309i
\(486\) 1.02688e36 1.08260e36i 0.551986 0.581940i
\(487\) 2.21222e36i 1.15661i 0.815820 + 0.578307i \(0.196286\pi\)
−0.815820 + 0.578307i \(0.803714\pi\)
\(488\) 2.08158e36 2.44062e36i 1.05858 1.24118i
\(489\) 2.63584e36i 1.30392i
\(490\) −5.56395e36 5.27756e36i −2.67754 2.53972i
\(491\) 3.23979e35 + 3.23979e35i 0.151676 + 0.151676i 0.778866 0.627190i \(-0.215795\pi\)
−0.627190 + 0.778866i \(0.715795\pi\)
\(492\) −1.31229e36 1.18050e36i −0.597723 0.537695i
\(493\) 1.15503e36 1.15503e36i 0.511869 0.511869i
\(494\) 9.40269e34 + 3.55944e36i 0.0405451 + 1.53486i
\(495\) −1.54942e36 −0.650128
\(496\) −1.34859e35 + 1.42998e34i −0.0550652 + 0.00583884i
\(497\) 1.01320e36 0.402610
\(498\) 6.76589e34 + 2.56126e36i 0.0261655 + 0.990508i
\(499\) 1.92777e36 1.92777e36i 0.725600 0.725600i −0.244140 0.969740i \(-0.578506\pi\)
0.969740 + 0.244140i \(0.0785056\pi\)
\(500\) 2.59897e36 2.88912e36i 0.952152 1.05845i
\(501\) 9.01562e35 + 9.01562e35i 0.321504 + 0.321504i
\(502\) 3.16400e36 + 3.00114e36i 1.09834 + 1.04180i
\(503\) 4.17654e36i 1.41140i −0.708512 0.705698i \(-0.750633\pi\)
0.708512 0.705698i \(-0.249367\pi\)
\(504\) 2.30933e36 1.83352e35i 0.759754 0.0603218i
\(505\) 3.77535e36i 1.20927i
\(506\) −2.43293e36 + 2.56495e36i −0.758748 + 0.799922i
\(507\) 2.37668e36 + 2.37668e36i 0.721711 + 0.721711i
\(508\) −3.42952e36 + 1.81316e35i −1.01408 + 0.0536139i
\(509\) 3.84305e36 3.84305e36i 1.10659 1.10659i 0.112992 0.993596i \(-0.463957\pi\)
0.993596 0.112992i \(-0.0360434\pi\)
\(510\) 6.20402e36 1.63887e35i 1.73971 0.0459565i
\(511\) −3.92913e36 −1.07304
\(512\) −3.65392e36 + 8.85237e35i −0.971884 + 0.235459i
\(513\) 2.97962e36 0.771928
\(514\) 7.34859e36 1.94122e35i 1.85439 0.0489861i
\(515\) 4.91123e36 4.91123e36i 1.20724 1.20724i
\(516\) −6.44515e36 + 3.40751e35i −1.54334 + 0.0815954i
\(517\) −2.03319e36 2.03319e36i −0.474302 0.474302i
\(518\) 1.30333e36 1.37406e36i 0.296213 0.312287i
\(519\) 5.90309e36i 1.30713i
\(520\) −1.06113e37 + 8.42499e35i −2.28941 + 0.181771i
\(521\) 1.75125e36i 0.368163i 0.982911 + 0.184081i \(0.0589310\pi\)
−0.982911 + 0.184081i \(0.941069\pi\)
\(522\) −1.26672e36 1.20152e36i −0.259495 0.246138i
\(523\) −2.20670e36 2.20670e36i −0.440524 0.440524i 0.451664 0.892188i \(-0.350831\pi\)
−0.892188 + 0.451664i \(0.850831\pi\)
\(524\) 3.55315e36 3.94983e36i 0.691261 0.768434i
\(525\) −1.46691e37 + 1.46691e37i −2.78134 + 2.78134i
\(526\) −1.32868e34 5.02977e35i −0.00245534 0.0929482i
\(527\) 2.65589e35 0.0478373
\(528\) −6.11049e36 + 6.47927e35i −1.07280 + 0.113754i
\(529\) −2.86470e36 −0.490261
\(530\) −7.64664e33 2.89468e35i −0.00127569 0.0482921i
\(531\) −1.63695e36 + 1.63695e36i −0.266232 + 0.266232i
\(532\) 9.43948e36 + 8.49148e36i 1.49672 + 1.34641i
\(533\) −4.19248e36 4.19248e36i −0.648117 0.648117i
\(534\) −2.17181e36 2.06002e36i −0.327352 0.310502i
\(535\) 1.33539e37i 1.96260i
\(536\) 4.56724e36 5.35503e36i 0.654530 0.767428i
\(537\) 1.04129e37i 1.45519i
\(538\) 2.13362e36 2.24940e36i 0.290774 0.306553i
\(539\) −1.05146e37 1.05146e37i −1.39748 1.39748i
\(540\) 4.70283e35 + 8.89519e36i 0.0609598 + 1.15303i
\(541\) 5.57551e36 5.57551e36i 0.704890 0.704890i −0.260566 0.965456i \(-0.583909\pi\)
0.965456 + 0.260566i \(0.0839092\pi\)
\(542\) −1.03341e37 + 2.72988e35i −1.27433 + 0.0336630i
\(543\) −1.64693e37 −1.98097
\(544\) 7.29876e36 9.69446e35i 0.856375 0.113747i
\(545\) −5.40728e36 −0.618907
\(546\) 2.60029e37 6.86899e35i 2.90350 0.0766995i
\(547\) −3.06093e36 + 3.06093e36i −0.333445 + 0.333445i −0.853893 0.520448i \(-0.825765\pi\)
0.520448 + 0.853893i \(0.325765\pi\)
\(548\) −2.72387e35 5.15208e36i −0.0289500 0.547577i
\(549\) 4.74792e36 + 4.74792e36i 0.492353 + 0.492353i
\(550\) 1.13284e37 1.19431e37i 1.14623 1.20843i
\(551\) 9.56905e36i 0.944762i
\(552\) −1.15159e37 9.82175e36i −1.10948 0.946262i
\(553\) 1.16103e37i 1.09157i
\(554\) 9.50862e35 + 9.01918e35i 0.0872440 + 0.0827533i
\(555\) −3.83465e36 3.83465e36i −0.343377 0.343377i
\(556\) 6.29333e36 + 5.66130e36i 0.550011 + 0.494774i
\(557\) −1.01026e37 + 1.01026e37i −0.861765 + 0.861765i −0.991543 0.129778i \(-0.958573\pi\)
0.129778 + 0.991543i \(0.458573\pi\)
\(558\) −7.49629e33 2.83776e35i −0.000624144 0.0236273i
\(559\) −2.16795e37 −1.76193
\(560\) −2.38601e37 + 2.95203e37i −1.89293 + 2.34198i
\(561\) 1.20339e37 0.931983
\(562\) 3.53059e35 + 1.33652e37i 0.0266936 + 1.01050i
\(563\) −2.85063e36 + 2.85063e36i −0.210416 + 0.210416i −0.804444 0.594028i \(-0.797537\pi\)
0.594028 + 0.804444i \(0.297537\pi\)
\(564\) 8.23292e36 9.15206e36i 0.593316 0.659555i
\(565\) 1.15355e36 + 1.15355e36i 0.0811676 + 0.0811676i
\(566\) 4.87657e36 + 4.62555e36i 0.335037 + 0.317791i
\(567\) 3.31280e37i 2.22241i
\(568\) −2.72425e35 3.43119e36i −0.0178461 0.224772i
\(569\) 1.12984e37i 0.722775i 0.932416 + 0.361388i \(0.117697\pi\)
−0.932416 + 0.361388i \(0.882303\pi\)
\(570\) 2.50204e37 2.63781e37i 1.56309 1.64791i
\(571\) 9.87170e36 + 9.87170e36i 0.602288 + 0.602288i 0.940919 0.338631i \(-0.109964\pi\)
−0.338631 + 0.940919i \(0.609964\pi\)
\(572\) −2.06114e37 + 1.08971e36i −1.22818 + 0.0649331i
\(573\) −3.07474e36 + 3.07474e36i −0.178946 + 0.178946i
\(574\) −2.11347e37 + 5.58300e35i −1.20140 + 0.0317363i
\(575\) 4.05464e37 2.25131
\(576\) −1.24184e36 7.77121e36i −0.0673539 0.421488i
\(577\) 1.53120e37 0.811259 0.405629 0.914038i \(-0.367052\pi\)
0.405629 + 0.914038i \(0.367052\pi\)
\(578\) 4.89966e36 1.29431e35i 0.253595 0.00669901i
\(579\) −1.68040e37 + 1.68040e37i −0.849675 + 0.849675i
\(580\) 2.85669e37 1.51031e36i 1.41119 0.0746086i
\(581\) 2.17002e37 + 2.17002e37i 1.04733 + 1.04733i
\(582\) −2.00719e37 + 2.11611e37i −0.946516 + 0.997880i
\(583\) 5.61478e35i 0.0258707i
\(584\) 1.05645e36 + 1.33060e37i 0.0475635 + 0.599063i
\(585\) 2.22819e37i 0.980275i
\(586\) 6.18544e36 + 5.86706e36i 0.265921 + 0.252234i
\(587\) 1.22724e37 + 1.22724e37i 0.515604 + 0.515604i 0.916238 0.400634i \(-0.131210\pi\)
−0.400634 + 0.916238i \(0.631210\pi\)
\(588\) 4.25765e37 4.73298e37i 1.74814 1.94330i
\(589\) 1.10016e36 1.10016e36i 0.0441469 0.0441469i
\(590\) −1.00165e36 3.79179e37i −0.0392838 1.48711i
\(591\) 3.11256e36 0.119313
\(592\) −5.00367e36 4.04427e36i −0.187476 0.151530i
\(593\) −4.00738e36 −0.146765 −0.0733825 0.997304i \(-0.523379\pi\)
−0.0733825 + 0.997304i \(0.523379\pi\)
\(594\) 4.56102e35 + 1.72660e37i 0.0163285 + 0.618122i
\(595\) 5.25632e37 5.25632e37i 1.83951 1.83951i
\(596\) −2.22785e37 2.00411e37i −0.762186 0.685640i
\(597\) 1.18356e37 + 1.18356e37i 0.395854 + 0.395854i
\(598\) −3.68861e37 3.49875e37i −1.20614 1.14405i
\(599\) 2.52974e37i 0.808749i 0.914594 + 0.404374i \(0.132511\pi\)
−0.914594 + 0.404374i \(0.867489\pi\)
\(600\) 5.36210e37 + 4.57327e37i 1.67607 + 1.42950i
\(601\) 1.83437e37i 0.560637i −0.959907 0.280318i \(-0.909560\pi\)
0.959907 0.280318i \(-0.0904400\pi\)
\(602\) −5.32008e37 + 5.60878e37i −1.58988 + 1.67616i
\(603\) 1.04175e37 + 1.04175e37i 0.304426 + 0.304426i
\(604\) 1.61911e36 + 3.06247e37i 0.0462676 + 0.875131i
\(605\) −7.86573e36 + 7.86573e36i −0.219807 + 0.219807i
\(606\) 3.13300e37 8.27621e35i 0.856209 0.0226178i
\(607\) −2.15299e37 −0.575432 −0.287716 0.957716i \(-0.592896\pi\)
−0.287716 + 0.957716i \(0.592896\pi\)
\(608\) 2.62182e37 3.42498e37i 0.685339 0.895282i
\(609\) −6.99053e37 −1.78721
\(610\) −1.09980e38 + 2.90525e36i −2.75017 + 0.0726491i
\(611\) 2.92389e37 2.92389e37i 0.715162 0.715162i
\(612\) 8.13700e35 + 1.53908e37i 0.0194679 + 0.368227i
\(613\) −2.58608e37 2.58608e37i −0.605237 0.605237i 0.336460 0.941698i \(-0.390770\pi\)
−0.941698 + 0.336460i \(0.890770\pi\)
\(614\) 4.45928e37 4.70127e37i 1.02092 1.07632i
\(615\) 6.05397e37i 1.35589i
\(616\) −4.77606e37 + 5.59987e37i −1.04648 + 1.22698i
\(617\) 2.00824e37i 0.430493i −0.976560 0.215247i \(-0.930944\pi\)
0.976560 0.215247i \(-0.0690555\pi\)
\(618\) 4.18328e37 + 3.96796e37i 0.877350 + 0.832190i
\(619\) 1.73371e37 + 1.73371e37i 0.355755 + 0.355755i 0.862246 0.506490i \(-0.169057\pi\)
−0.506490 + 0.862246i \(0.669057\pi\)
\(620\) 3.45800e36 + 3.11072e36i 0.0694284 + 0.0624558i
\(621\) −3.00829e37 + 3.00829e37i −0.590993 + 0.590993i
\(622\) 4.39382e35 + 1.66330e37i 0.00844640 + 0.319743i
\(623\) −3.58539e37 −0.674448
\(624\) −9.31771e36 8.78738e37i −0.171521 1.61759i
\(625\) −3.09107e37 −0.556837
\(626\) 3.79102e35 + 1.43511e37i 0.00668347 + 0.253006i
\(627\) 4.98486e37 4.98486e37i 0.860085 0.860085i
\(628\) 2.80894e37 3.12253e37i 0.474337 0.527293i
\(629\) 8.90944e36 + 8.90944e36i 0.147254 + 0.147254i
\(630\) −5.76463e37 5.46791e37i −0.932554 0.884552i
\(631\) 5.73798e37i 0.908579i −0.890854 0.454290i \(-0.849893\pi\)
0.890854 0.454290i \(-0.150107\pi\)
\(632\) −3.93180e37 + 3.12171e36i −0.609412 + 0.0483851i
\(633\) 1.08452e38i 1.64547i
\(634\) −7.92697e37 + 8.35713e37i −1.17734 + 1.24123i
\(635\) 8.32892e37 + 8.32892e37i 1.21100 + 1.21100i
\(636\) 2.40049e36 1.26912e35i 0.0341687 0.00180648i
\(637\) 1.51209e38 1.51209e38i 2.10714 2.10714i
\(638\) 5.54497e37 1.46477e36i 0.756519 0.0199844i
\(639\) 7.20492e36 0.0962427
\(640\) 1.06385e38 + 7.28647e37i 1.39140 + 0.952988i
\(641\) −6.74215e37 −0.863406 −0.431703 0.902016i \(-0.642087\pi\)
−0.431703 + 0.902016i \(0.642087\pi\)
\(642\) −1.10818e38 + 2.92740e36i −1.38959 + 0.0367079i
\(643\) −9.60356e37 + 9.60356e37i −1.17919 + 1.17919i −0.199241 + 0.979951i \(0.563848\pi\)
−0.979951 + 0.199241i \(0.936152\pi\)
\(644\) −1.81035e38 + 9.57119e36i −2.17672 + 0.115082i
\(645\) 1.56527e38 + 1.56527e38i 1.84303 + 1.84303i
\(646\) −5.81323e37 + 6.12869e37i −0.670315 + 0.706690i
\(647\) 4.86931e37i 0.549869i 0.961463 + 0.274934i \(0.0886562\pi\)
−0.961463 + 0.274934i \(0.911344\pi\)
\(648\) −1.12187e38 + 8.90729e36i −1.24074 + 0.0985106i
\(649\) 7.35491e37i 0.796662i
\(650\) 1.71752e38 + 1.62911e38i 1.82209 + 1.72830i
\(651\) −8.03707e36 8.03707e36i −0.0835130 0.0835130i
\(652\) 7.17289e37 7.97368e37i 0.730049 0.811552i
\(653\) 9.96444e37 9.96444e37i 0.993401 0.993401i −0.00657695 0.999978i \(-0.502094\pi\)
0.999978 + 0.00657695i \(0.00209352\pi\)
\(654\) −1.18537e36 4.48726e37i −0.0115759 0.438210i
\(655\) −1.82217e38 −1.74314
\(656\) 7.57327e36 + 7.14223e37i 0.0709711 + 0.669317i
\(657\) −2.79402e37 −0.256506
\(658\) −3.89365e36 1.47396e38i −0.0350193 1.32567i
\(659\) 1.08343e36 1.08343e36i 0.00954661 0.00954661i −0.702317 0.711864i \(-0.747851\pi\)
0.711864 + 0.702317i \(0.247851\pi\)
\(660\) 1.56683e38 + 1.40947e38i 1.35263 + 1.21679i
\(661\) 1.01016e38 + 1.01016e38i 0.854419 + 0.854419i 0.990674 0.136255i \(-0.0435066\pi\)
−0.136255 + 0.990674i \(0.543507\pi\)
\(662\) 2.30572e37 + 2.18704e37i 0.191084 + 0.181248i
\(663\) 1.73057e38i 1.40526i
\(664\) 6.76527e37 7.93219e37i 0.538289 0.631138i
\(665\) 4.35471e38i 3.39521i
\(666\) 9.26807e36 9.77101e36i 0.0708088 0.0746513i
\(667\) 9.66111e37 + 9.66111e37i 0.723316 + 0.723316i
\(668\) −2.73902e36 5.18073e37i −0.0200961 0.380109i
\(669\) −2.15647e38 + 2.15647e38i −1.55057 + 1.55057i
\(670\) −2.41309e38 + 6.37448e36i −1.70045 + 0.0449195i
\(671\) −2.13327e38 −1.47330
\(672\) −2.50207e38 1.91533e38i −1.69361 1.29646i
\(673\) −3.17797e37 −0.210837 −0.105418 0.994428i \(-0.533618\pi\)
−0.105418 + 0.994428i \(0.533618\pi\)
\(674\) −1.61641e37 + 4.26995e35i −0.105110 + 0.00277661i
\(675\) 1.40074e38 1.40074e38i 0.892804 0.892804i
\(676\) −7.22054e36 1.36573e38i −0.0451117 0.853267i
\(677\) −3.46930e36 3.46930e36i −0.0212468 0.0212468i 0.696404 0.717650i \(-0.254782\pi\)
−0.717650 + 0.696404i \(0.754782\pi\)
\(678\) −9.31995e36 + 9.82570e36i −0.0559516 + 0.0589879i
\(679\) 3.49344e38i 2.05595i
\(680\) −1.92138e38 1.63872e38i −1.10852 0.945440i
\(681\) 1.96376e36i 0.0111071i
\(682\) 6.54350e36 + 6.20669e36i 0.0362845 + 0.0344168i
\(683\) −3.49900e37 3.49900e37i −0.190223 0.190223i 0.605569 0.795793i \(-0.292945\pi\)
−0.795793 + 0.605569i \(0.792945\pi\)
\(684\) 6.71245e37 + 6.03833e37i 0.357787 + 0.321854i
\(685\) −1.25123e38 + 1.25123e38i −0.653906 + 0.653906i
\(686\) −1.09342e37 4.13919e38i −0.0560288 2.12100i
\(687\) 4.60713e38 2.31481
\(688\) 2.04245e38 + 1.65083e38i 1.00625 + 0.813315i
\(689\) 8.07451e36 0.0390083
\(690\) 1.37082e37 + 5.18930e38i 0.0649406 + 2.45836i
\(691\) −1.58069e38 + 1.58069e38i −0.734333 + 0.734333i −0.971475 0.237142i \(-0.923789\pi\)
0.237142 + 0.971475i \(0.423789\pi\)
\(692\) 1.60640e38 1.78574e38i 0.731849 0.813554i
\(693\) −1.08938e38 1.08938e38i −0.486723 0.486723i
\(694\) −1.19193e38 1.13058e38i −0.522274 0.495391i
\(695\) 2.90330e38i 1.24766i
\(696\) 1.87958e37 + 2.36733e38i 0.0792202 + 0.997779i
\(697\) 1.40658e38i 0.581462i
\(698\) 1.62127e38 1.70924e38i 0.657364 0.693036i
\(699\) −7.15561e36 7.15561e36i −0.0284580 0.0284580i
\(700\) 8.42946e38 4.45660e37i 3.28834 0.173852i
\(701\) −2.09073e38 + 2.09073e38i −0.800026 + 0.800026i −0.983099 0.183073i \(-0.941395\pi\)
0.183073 + 0.983099i \(0.441395\pi\)
\(702\) −2.48299e38 + 6.55912e36i −0.932016 + 0.0246204i
\(703\) 7.38120e37 0.271788
\(704\) 2.02480e38 + 1.46684e38i 0.731395 + 0.529848i
\(705\) −4.22211e38 −1.49615
\(706\) 1.71988e38 4.54329e36i 0.597910 0.0157945i
\(707\) 2.65442e38 2.65442e38i 0.905330 0.905330i
\(708\) 3.14445e38 1.66245e37i 1.05219 0.0556288i
\(709\) −1.35313e38 1.35313e38i −0.444236 0.444236i 0.449197 0.893433i \(-0.351710\pi\)
−0.893433 + 0.449197i \(0.851710\pi\)
\(710\) −8.12421e37 + 8.56507e37i −0.261694 + 0.275895i
\(711\) 8.25611e37i 0.260937i
\(712\) 9.64023e36 + 1.21419e38i 0.0298956 + 0.376536i
\(713\) 2.22149e37i 0.0675983i
\(714\) 4.47722e38 + 4.24677e38i 1.33685 + 1.26804i
\(715\) 5.00569e38 + 5.00569e38i 1.46667 + 1.46667i
\(716\) 2.83366e38 3.15002e38i 0.814746 0.905705i
\(717\) 1.53263e38 1.53263e38i 0.432443 0.432443i
\(718\) 4.71473e35 + 1.78478e37i 0.00130550 + 0.0494203i
\(719\) −4.16658e38 −1.13224 −0.566122 0.824321i \(-0.691557\pi\)
−0.566122 + 0.824321i \(0.691557\pi\)
\(720\) −1.69670e38 + 2.09920e38i −0.452498 + 0.559842i
\(721\) 6.90609e38 1.80762
\(722\) 2.78800e36 + 1.05541e38i 0.00716210 + 0.271125i
\(723\) 4.51100e38 4.51100e38i 1.13738 1.13738i
\(724\) 4.98214e38 + 4.48179e38i 1.23295 + 1.10913i
\(725\) −4.49847e38 4.49847e38i −1.09270 1.09270i
\(726\) −6.69986e37 6.35500e37i −0.159743 0.151520i
\(727\) 9.24040e37i 0.216260i 0.994137 + 0.108130i \(0.0344863\pi\)
−0.994137 + 0.108130i \(0.965514\pi\)
\(728\) −8.05306e38 6.86835e38i −1.85007 1.57790i
\(729\) 1.27065e38i 0.286552i
\(730\) 3.15052e38 3.32148e38i 0.697466 0.735315i
\(731\) −3.63674e38 3.63674e38i −0.790365 0.790365i
\(732\) −4.82188e37 9.12036e38i −0.102877 1.94586i
\(733\) −2.10372e38 + 2.10372e38i −0.440640 + 0.440640i −0.892227 0.451587i \(-0.850858\pi\)
0.451587 + 0.892227i \(0.350858\pi\)
\(734\) 5.60411e38 1.48039e37i 1.15242 0.0304425i
\(735\) −2.18346e39 −4.40825
\(736\) 8.10884e37 + 6.10498e38i 0.160734 + 1.21013i
\(737\) −4.68065e38 −0.910952
\(738\) −1.50290e38 + 3.97009e36i −0.287190 + 0.00758647i
\(739\) 4.09334e37 4.09334e37i 0.0768030 0.0768030i −0.667662 0.744465i \(-0.732705\pi\)
0.744465 + 0.667662i \(0.232705\pi\)
\(740\) 1.16500e37 + 2.20354e38i 0.0214633 + 0.405969i
\(741\) 7.16864e38 + 7.16864e38i 1.29685 + 1.29685i
\(742\) 1.98146e37 2.08899e37i 0.0351992 0.0371093i