Properties

Label 54.9.f.a.5.1
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.f (of order \(18\), degree \(6\), 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: \(21.9984449433\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(-80.6183 + 7.85385i) q^{3} +(-22.2270 + 126.055i) q^{4} +(208.139 + 571.857i) q^{5} +(654.349 + 641.588i) q^{6} +(-808.155 - 4583.27i) q^{7} +(1254.14 - 724.077i) q^{8} +(6437.63 - 1266.33i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(-80.6183 + 7.85385i) q^{3} +(-22.2270 + 126.055i) q^{4} +(208.139 + 571.857i) q^{5} +(654.349 + 641.588i) q^{6} +(-808.155 - 4583.27i) q^{7} +(1254.14 - 724.077i) q^{8} +(6437.63 - 1266.33i) q^{9} +(3442.52 - 5962.62i) q^{10} +(-2304.87 + 6332.57i) q^{11} +(801.881 - 10336.9i) q^{12} +(-28817.9 - 24181.1i) q^{13} +(-33845.2 + 40335.1i) q^{14} +(-21271.1 - 44467.4i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-25788.7 - 14889.1i) q^{17} +(-57791.5 - 46584.6i) q^{18} +(36420.7 + 63082.5i) q^{19} +(-76711.9 + 13526.4i) q^{20} +(101148. + 363149. i) q^{21} +(71644.8 - 26076.6i) q^{22} +(453226. + 79916.0i) q^{23} +(-95419.8 + 68223.7i) q^{24} +(15537.9 - 13037.9i) q^{25} +425611. i q^{26} +(-509046. + 152649. i) q^{27} +595709. q^{28} +(-488689. - 582397. i) q^{29} +(-230701. + 507733. i) q^{30} +(-266191. + 1.50964e6i) q^{31} +(63398.2 + 174185. i) q^{32} +(136079. - 528623. i) q^{33} +(58502.5 + 331784. i) q^{34} +(2.45277e6 - 1.41611e6i) q^{35} +(16538.4 + 839645. i) q^{36} +(-1.42819e6 + 2.47370e6i) q^{37} +(281861. - 774407. i) q^{38} +(2.51316e6 + 1.72311e6i) q^{39} +(675103. + 566479. i) q^{40} +(-2.69268e6 + 3.20902e6i) q^{41} +(2.41176e6 - 3.51756e6i) q^{42} +(2.67475e6 + 973529. i) q^{43} +(-747024. - 431294. i) q^{44} +(2.06408e6 + 3.41783e6i) q^{45} +(-2.60338e6 - 4.50919e6i) q^{46} +(-390402. + 68838.4i) q^{47} +(1.28520e6 + 330840. i) q^{48} +(-1.49361e7 + 5.43631e6i) q^{49} +(-225993. - 39848.7i) q^{50} +(2.19598e6 + 997795. i) q^{51} +(3.68869e6 - 3.09518e6i) q^{52} -34340.3i q^{53} +(5.02492e6 + 3.30169e6i) q^{54} -4.10105e6 q^{55} +(-4.33218e6 - 5.16289e6i) q^{56} +(-3.43162e6 - 4.79956e6i) q^{57} +(-1.49362e6 + 8.47075e6i) q^{58} +(5.31298e6 + 1.45973e7i) q^{59} +(6.07815e6 - 1.69296e6i) q^{60} +(-669659. - 3.79782e6i) q^{61} +(1.50196e7 - 8.67158e6i) q^{62} +(-1.10065e7 - 2.84820e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(7.82999e6 - 2.15127e7i) q^{65} +(-5.57108e6 + 2.66494e6i) q^{66} +(5.68875e6 + 4.77343e6i) q^{67} +(2.45006e6 - 2.91987e6i) q^{68} +(-3.71660e7 - 2.88312e6i) q^{69} +(-3.01104e7 - 1.09593e7i) q^{70} +(-2.44321e7 - 1.41059e7i) q^{71} +(7.15677e6 - 6.24950e6i) q^{72} +(6.47054e6 + 1.12073e7i) q^{73} +(3.18253e7 - 5.61166e6i) q^{74} +(-1.15024e6 + 1.17312e6i) q^{75} +(-8.76141e6 + 3.18889e6i) q^{76} +(3.08866e7 + 5.44614e6i) q^{77} +(-3.34268e6 - 3.43121e7i) q^{78} +(5.72766e6 - 4.80607e6i) q^{79} -9.97060e6i q^{80} +(3.98395e7 - 1.63043e7i) q^{81} +4.73939e7 q^{82} +(2.51217e7 + 2.99388e7i) q^{83} +(-4.80251e7 + 4.67861e6i) q^{84} +(3.14681e6 - 1.78464e7i) q^{85} +(-1.10142e7 - 3.02613e7i) q^{86} +(4.39714e7 + 4.31138e7i) q^{87} +(1.69465e6 + 9.61082e6i) q^{88} +(-2.94822e7 + 1.70215e7i) q^{89} +(1.46110e7 - 4.27445e7i) q^{90} +(-8.75391e7 + 1.51622e8i) q^{91} +(-2.01477e7 + 5.53553e7i) q^{92} +(9.60337e6 - 1.23796e8i) q^{93} +(3.43573e6 + 2.88292e6i) q^{94} +(-2.84936e7 + 3.39573e7i) q^{95} +(-6.47908e6 - 1.35446e7i) q^{96} +(-1.27634e8 - 4.64551e7i) q^{97} +(1.55736e8 + 8.99140e7i) q^{98} +(-6.81877e6 + 4.36855e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.27231 8.66680i −0.454519 0.541675i
\(3\) −80.6183 + 7.85385i −0.995288 + 0.0969611i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) 208.139 + 571.857i 0.333022 + 0.914971i 0.987321 + 0.158735i \(0.0507415\pi\)
−0.654299 + 0.756236i \(0.727036\pi\)
\(6\) 654.349 + 641.588i 0.504899 + 0.495052i
\(7\) −808.155 4583.27i −0.336591 1.90890i −0.410926 0.911669i \(-0.634795\pi\)
0.0743355 0.997233i \(-0.476316\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) 6437.63 1266.33i 0.981197 0.193008i
\(10\) 3442.52 5962.62i 0.344252 0.596262i
\(11\) −2304.87 + 6332.57i −0.157425 + 0.432523i −0.993182 0.116578i \(-0.962807\pi\)
0.835756 + 0.549101i \(0.185030\pi\)
\(12\) 801.881 10336.9i 0.0386710 0.498502i
\(13\) −28817.9 24181.1i −1.00899 0.846646i −0.0207890 0.999784i \(-0.506618\pi\)
−0.988205 + 0.153137i \(0.951062\pi\)
\(14\) −33845.2 + 40335.1i −0.881018 + 1.04996i
\(15\) −21271.1 44467.4i −0.420169 0.878369i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) −25788.7 14889.1i −0.308769 0.178268i 0.337606 0.941287i \(-0.390383\pi\)
−0.646376 + 0.763019i \(0.723716\pi\)
\(18\) −57791.5 46584.6i −0.550521 0.443764i
\(19\) 36420.7 + 63082.5i 0.279469 + 0.484055i 0.971253 0.238050i \(-0.0765082\pi\)
−0.691784 + 0.722105i \(0.743175\pi\)
\(20\) −76711.9 + 13526.4i −0.479449 + 0.0845399i
\(21\) 101148. + 363149.i 0.520094 + 1.86727i
\(22\) 71644.8 26076.6i 0.305840 0.111317i
\(23\) 453226. + 79916.0i 1.61958 + 0.285576i 0.908611 0.417643i \(-0.137144\pi\)
0.710973 + 0.703220i \(0.248255\pi\)
\(24\) −95419.8 + 68223.7i −0.287603 + 0.205632i
\(25\) 15537.9 13037.9i 0.0397771 0.0333769i
\(26\) 425611.i 0.931364i
\(27\) −509046. + 152649.i −0.957860 + 0.287237i
\(28\) 595709. 0.969175
\(29\) −488689. 582397.i −0.690941 0.823432i 0.300528 0.953773i \(-0.402837\pi\)
−0.991469 + 0.130341i \(0.958393\pi\)
\(30\) −230701. + 507733.i −0.284816 + 0.626831i
\(31\) −266191. + 1.50964e6i −0.288235 + 1.63466i 0.405261 + 0.914201i \(0.367181\pi\)
−0.693496 + 0.720461i \(0.743930\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) 136079. 528623.i 0.114746 0.445749i
\(34\) 58502.5 + 331784.i 0.0437783 + 0.248279i
\(35\) 2.45277e6 1.41611e6i 1.63450 0.943677i
\(36\) 16538.4 + 839645.i 0.00984656 + 0.499903i
\(37\) −1.42819e6 + 2.47370e6i −0.762042 + 1.31990i 0.179754 + 0.983712i \(0.442470\pi\)
−0.941796 + 0.336184i \(0.890863\pi\)
\(38\) 281861. 774407.i 0.135176 0.371394i
\(39\) 2.51316e6 + 1.72311e6i 1.08633 + 0.744824i
\(40\) 675103. + 566479.i 0.263712 + 0.221281i
\(41\) −2.69268e6 + 3.20902e6i −0.952906 + 1.13563i 0.0377562 + 0.999287i \(0.487979\pi\)
−0.990662 + 0.136342i \(0.956465\pi\)
\(42\) 2.41176e6 3.51756e6i 0.775062 1.13043i
\(43\) 2.67475e6 + 973529.i 0.782365 + 0.284757i 0.702158 0.712021i \(-0.252220\pi\)
0.0802063 + 0.996778i \(0.474442\pi\)
\(44\) −747024. 431294.i −0.199308 0.115070i
\(45\) 2.06408e6 + 3.41783e6i 0.503357 + 0.833490i
\(46\) −2.60338e6 4.50919e6i −0.581443 1.00709i
\(47\) −390402. + 68838.4i −0.0800056 + 0.0141072i −0.213508 0.976941i \(-0.568489\pi\)
0.133502 + 0.991049i \(0.457378\pi\)
\(48\) 1.28520e6 + 330840.i 0.242107 + 0.0623237i
\(49\) −1.49361e7 + 5.43631e6i −2.59092 + 0.943018i
\(50\) −225993. 39848.7i −0.0361589 0.00637579i
\(51\) 2.19598e6 + 997795.i 0.324599 + 0.147489i
\(52\) 3.68869e6 3.09518e6i 0.504497 0.423323i
\(53\) 34340.3i 0.00435212i −0.999998 0.00217606i \(-0.999307\pi\)
0.999998 0.00217606i \(-0.000692662\pi\)
\(54\) 5.02492e6 + 3.30169e6i 0.590955 + 0.388294i
\(55\) −4.10105e6 −0.448172
\(56\) −4.33218e6 5.16289e6i −0.440509 0.524978i
\(57\) −3.43162e6 4.79956e6i −0.325087 0.454676i
\(58\) −1.49362e6 + 8.47075e6i −0.131986 + 0.748531i
\(59\) 5.31298e6 + 1.45973e7i 0.438460 + 1.20466i 0.940494 + 0.339811i \(0.110363\pi\)
−0.502034 + 0.864848i \(0.667415\pi\)
\(60\) 6.07815e6 1.69296e6i 0.468993 0.130629i
\(61\) −669659. 3.79782e6i −0.0483653 0.274293i 0.951029 0.309103i \(-0.100029\pi\)
−0.999394 + 0.0348094i \(0.988918\pi\)
\(62\) 1.50196e7 8.67158e6i 1.01646 0.586856i
\(63\) −1.10065e7 2.84820e7i −0.698696 1.80804i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) 7.82999e6 2.15127e7i 0.438639 1.20515i
\(66\) −5.57108e6 + 2.66494e6i −0.293605 + 0.140447i
\(67\) 5.68875e6 + 4.77343e6i 0.282304 + 0.236882i 0.772934 0.634487i \(-0.218789\pi\)
−0.490629 + 0.871368i \(0.663233\pi\)
\(68\) 2.45006e6 2.91987e6i 0.114588 0.136561i
\(69\) −3.71660e7 2.88312e6i −1.63964 0.127194i
\(70\) −3.01104e7 1.09593e7i −1.25408 0.456447i
\(71\) −2.44321e7 1.41059e7i −0.961452 0.555094i −0.0648322 0.997896i \(-0.520651\pi\)
−0.896620 + 0.442802i \(0.853985\pi\)
\(72\) 7.15677e6 6.24950e6i 0.266310 0.232549i
\(73\) 6.47054e6 + 1.12073e7i 0.227850 + 0.394648i 0.957171 0.289524i \(-0.0934970\pi\)
−0.729321 + 0.684172i \(0.760164\pi\)
\(74\) 3.18253e7 5.61166e6i 1.06132 0.187139i
\(75\) −1.15024e6 + 1.17312e6i −0.0363534 + 0.0370765i
\(76\) −8.76141e6 + 3.18889e6i −0.262615 + 0.0955841i
\(77\) 3.08866e7 + 5.44614e6i 0.878631 + 0.154926i
\(78\) −3.34268e6 3.43121e7i −0.0903061 0.926976i
\(79\) 5.72766e6 4.80607e6i 0.147051 0.123391i −0.566294 0.824203i \(-0.691623\pi\)
0.713346 + 0.700812i \(0.247179\pi\)
\(80\) 9.97060e6i 0.243423i
\(81\) 3.98395e7 1.63043e7i 0.925495 0.378759i
\(82\) 4.73939e7 1.04826
\(83\) 2.51217e7 + 2.99388e7i 0.529341 + 0.630844i 0.962763 0.270347i \(-0.0871384\pi\)
−0.433422 + 0.901191i \(0.642694\pi\)
\(84\) −4.80251e7 + 4.67861e6i −0.964608 + 0.0939722i
\(85\) 3.14681e6 1.78464e7i 0.0602830 0.341882i
\(86\) −1.10142e7 3.02613e7i −0.201354 0.553215i
\(87\) 4.39714e7 + 4.31138e7i 0.767526 + 0.752557i
\(88\) 1.69465e6 + 9.61082e6i 0.0282585 + 0.160262i
\(89\) −2.94822e7 + 1.70215e7i −0.469894 + 0.271293i −0.716195 0.697900i \(-0.754118\pi\)
0.246301 + 0.969193i \(0.420785\pi\)
\(90\) 1.46110e7 4.27445e7i 0.222695 0.651494i
\(91\) −8.75391e7 + 1.51622e8i −1.27655 + 2.21104i
\(92\) −2.01477e7 + 5.53553e7i −0.281238 + 0.772694i
\(93\) 9.60337e6 1.23796e8i 0.128378 1.65491i
\(94\) 3.43573e6 + 2.88292e6i 0.0440056 + 0.0369251i
\(95\) −2.84936e7 + 3.39573e7i −0.349826 + 0.416907i
\(96\) −6.47908e6 1.35446e7i −0.0762831 0.159471i
\(97\) −1.27634e8 4.64551e7i −1.44172 0.524743i −0.501454 0.865184i \(-0.667201\pi\)
−0.940266 + 0.340441i \(0.889424\pi\)
\(98\) 1.55736e8 + 8.99140e7i 1.68843 + 0.974817i
\(99\) −6.81877e6 + 4.36855e7i −0.0709848 + 0.454775i
\(100\) 1.29813e6 + 2.24843e6i 0.0129813 + 0.0224843i
\(101\) 1.52432e8 2.68778e7i 1.46484 0.258291i 0.616337 0.787482i \(-0.288616\pi\)
0.848503 + 0.529191i \(0.177505\pi\)
\(102\) −7.32215e6 2.62884e7i −0.0676454 0.242864i
\(103\) 8.46933e6 3.08258e6i 0.0752489 0.0273884i −0.304121 0.952633i \(-0.598363\pi\)
0.379370 + 0.925245i \(0.376141\pi\)
\(104\) −5.36506e7 9.46004e6i −0.458607 0.0808649i
\(105\) −1.86616e8 + 1.33428e8i −1.53530 + 1.09771i
\(106\) −297621. + 249734.i −0.00235744 + 0.00197812i
\(107\) 1.30990e7i 0.0999319i 0.998751 + 0.0499659i \(0.0159113\pi\)
−0.998751 + 0.0499659i \(0.984089\pi\)
\(108\) −7.92775e6 6.75609e7i −0.0582713 0.496593i
\(109\) −3.69259e7 −0.261592 −0.130796 0.991409i \(-0.541753\pi\)
−0.130796 + 0.991409i \(0.541753\pi\)
\(110\) 2.98241e7 + 3.55430e7i 0.203703 + 0.242764i
\(111\) 9.57103e7 2.10642e8i 0.630473 1.38757i
\(112\) −1.32408e7 + 7.50923e7i −0.0841477 + 0.477225i
\(113\) 1.96169e7 + 5.38970e7i 0.120314 + 0.330561i 0.985200 0.171408i \(-0.0548316\pi\)
−0.864886 + 0.501968i \(0.832609\pi\)
\(114\) −1.66411e7 + 6.46451e7i −0.0985286 + 0.382751i
\(115\) 4.86334e7 + 2.75814e8i 0.278063 + 1.57697i
\(116\) 8.42764e7 4.86570e7i 0.465451 0.268728i
\(117\) −2.16140e8 1.19176e8i −1.15343 0.635983i
\(118\) 8.78742e7 1.52203e8i 0.453245 0.785044i
\(119\) −4.73996e7 + 1.30229e8i −0.236367 + 0.649413i
\(120\) −5.88747e7 4.03664e7i −0.283925 0.194668i
\(121\) 1.29419e8 + 1.08596e8i 0.603751 + 0.506607i
\(122\) −2.80450e7 + 3.34228e7i −0.126595 + 0.150870i
\(123\) 1.91877e8 2.79853e8i 0.838304 1.22267i
\(124\) −1.84382e8 6.71096e7i −0.779888 0.283856i
\(125\) 2.16559e8 + 1.25031e8i 0.887027 + 0.512125i
\(126\) −1.66805e8 + 3.02522e8i −0.661802 + 1.20026i
\(127\) 7.79555e7 + 1.35023e8i 0.299662 + 0.519030i 0.976059 0.217508i \(-0.0697927\pi\)
−0.676396 + 0.736538i \(0.736459\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) −2.23280e8 5.74772e7i −0.806289 0.207557i
\(130\) −2.43389e8 + 8.85862e7i −0.852171 + 0.310165i
\(131\) 2.07082e8 + 3.65141e7i 0.703164 + 0.123987i 0.513787 0.857918i \(-0.328242\pi\)
0.189377 + 0.981904i \(0.439353\pi\)
\(132\) 6.36112e7 + 2.89032e7i 0.209526 + 0.0952030i
\(133\) 2.59691e8 2.17906e8i 0.829946 0.696408i
\(134\) 8.40171e7i 0.260585i
\(135\) −1.93246e8 2.59329e8i −0.581802 0.780757i
\(136\) −4.31235e7 −0.126054
\(137\) 1.86230e8 + 2.21940e8i 0.528649 + 0.630019i 0.962603 0.270916i \(-0.0873265\pi\)
−0.433954 + 0.900935i \(0.642882\pi\)
\(138\) 2.45295e8 + 3.43077e8i 0.676352 + 0.945966i
\(139\) −5.40792e7 + 3.06699e8i −0.144868 + 0.821585i 0.822606 + 0.568612i \(0.192519\pi\)
−0.967473 + 0.252973i \(0.918592\pi\)
\(140\) 1.23990e8 + 3.40660e8i 0.322757 + 0.886766i
\(141\) 3.09329e7 8.61580e6i 0.0782608 0.0217981i
\(142\) 5.54250e7 + 3.14331e8i 0.136318 + 0.773096i
\(143\) 2.19550e8 1.26757e8i 0.525035 0.303129i
\(144\) −1.06209e8 1.65780e7i −0.247009 0.0385551i
\(145\) 2.31333e8 4.00680e8i 0.523317 0.906412i
\(146\) 5.00757e7 1.37582e8i 0.110209 0.302796i
\(147\) 1.16143e9 5.55572e8i 2.48728 1.18979i
\(148\) −2.80079e8 2.35014e8i −0.583758 0.489831i
\(149\) −1.85737e8 + 2.21353e8i −0.376838 + 0.449098i −0.920813 0.390003i \(-0.872474\pi\)
0.543976 + 0.839101i \(0.316918\pi\)
\(150\) 1.85322e7 + 1.43762e6i 0.0366067 + 0.00283974i
\(151\) −8.24893e8 3.00236e8i −1.58668 0.577505i −0.610038 0.792372i \(-0.708846\pi\)
−0.976643 + 0.214868i \(0.931068\pi\)
\(152\) 9.13532e7 + 5.27428e7i 0.171139 + 0.0988073i
\(153\) −1.84873e8 6.31937e7i −0.337371 0.115321i
\(154\) −1.77416e8 3.07294e8i −0.315435 0.546350i
\(155\) −9.18705e8 + 1.61992e8i −1.59166 + 0.280652i
\(156\) −2.73067e8 + 2.78498e8i −0.461074 + 0.470245i
\(157\) −4.67660e8 + 1.70214e8i −0.769717 + 0.280154i −0.696878 0.717190i \(-0.745428\pi\)
−0.0728391 + 0.997344i \(0.523206\pi\)
\(158\) −8.33066e7 1.46892e7i −0.133675 0.0235706i
\(159\) 269704. + 2.76846e6i 0.000421986 + 0.00433161i
\(160\) −8.64132e7 + 7.25093e7i −0.131856 + 0.110640i
\(161\) 2.14184e9i 3.18775i
\(162\) −4.31032e8 2.26711e8i −0.625820 0.329165i
\(163\) 6.53890e8 0.926306 0.463153 0.886278i \(-0.346718\pi\)
0.463153 + 0.886278i \(0.346718\pi\)
\(164\) −3.44664e8 4.10754e8i −0.476453 0.567814i
\(165\) 3.30620e8 3.22090e7i 0.446060 0.0434552i
\(166\) 7.67814e7 4.35449e8i 0.101117 0.573462i
\(167\) −4.24548e8 1.16644e9i −0.545834 1.49967i −0.839284 0.543693i \(-0.817026\pi\)
0.293450 0.955974i \(-0.405196\pi\)
\(168\) 3.89802e8 + 3.82200e8i 0.489336 + 0.479792i
\(169\) 1.04096e8 + 5.90356e8i 0.127610 + 0.723714i
\(170\) −1.77556e8 + 1.02512e8i −0.212589 + 0.122738i
\(171\) 3.14346e8 + 3.59982e8i 0.367641 + 0.421013i
\(172\) −1.82170e8 + 3.15528e8i −0.208144 + 0.360516i
\(173\) 1.56927e8 4.31152e8i 0.175191 0.481334i −0.820755 0.571280i \(-0.806447\pi\)
0.995947 + 0.0899458i \(0.0286694\pi\)
\(174\) 5.38853e7 6.94629e8i 0.0587860 0.757802i
\(175\) −7.23131e7 6.06779e7i −0.0771019 0.0646962i
\(176\) 7.09711e7 8.45800e7i 0.0739658 0.0881490i
\(177\) −5.42968e8 1.13508e9i −0.553199 1.15647i
\(178\) 3.61926e8 + 1.31730e8i 0.360529 + 0.131222i
\(179\) 3.92103e8 + 2.26381e8i 0.381933 + 0.220509i 0.678659 0.734453i \(-0.262561\pi\)
−0.296726 + 0.954963i \(0.595895\pi\)
\(180\) −4.76714e8 + 1.84220e8i −0.454117 + 0.175488i
\(181\) 6.48174e8 + 1.12267e9i 0.603917 + 1.04602i 0.992222 + 0.124484i \(0.0397276\pi\)
−0.388304 + 0.921531i \(0.626939\pi\)
\(182\) 1.95069e9 3.43960e8i 1.77788 0.313489i
\(183\) 8.38143e7 + 3.00915e8i 0.0747332 + 0.268311i
\(184\) 6.26274e8 2.27945e8i 0.546377 0.198865i
\(185\) −1.71186e9 3.01847e8i −1.46144 0.257692i
\(186\) −1.14275e9 + 8.17050e8i −0.954773 + 0.682648i
\(187\) 1.53726e8 1.28991e8i 0.125713 0.105486i
\(188\) 5.07423e7i 0.0406199i
\(189\) 1.11102e9 + 2.20973e9i 0.870714 + 1.73178i
\(190\) 5.01516e8 0.384831
\(191\) 1.23458e8 + 1.47132e8i 0.0927655 + 0.110554i 0.810430 0.585835i \(-0.199233\pi\)
−0.717665 + 0.696389i \(0.754789\pi\)
\(192\) −7.02704e7 + 1.54653e8i −0.0517092 + 0.113803i
\(193\) 2.02415e7 1.14795e8i 0.0145886 0.0827361i −0.976644 0.214863i \(-0.931070\pi\)
0.991233 + 0.132127i \(0.0421806\pi\)
\(194\) 5.25580e8 + 1.44402e9i 0.371049 + 1.01945i
\(195\) −4.62283e8 + 1.79581e9i −0.319720 + 1.24200i
\(196\) −3.53291e8 2.00361e9i −0.239391 1.35766i
\(197\) −1.96751e9 + 1.13594e9i −1.30633 + 0.754208i −0.981481 0.191559i \(-0.938646\pi\)
−0.324845 + 0.945767i \(0.605312\pi\)
\(198\) 4.28202e8 2.58597e8i 0.278604 0.168253i
\(199\) −2.53993e8 + 4.39928e8i −0.161960 + 0.280524i −0.935572 0.353137i \(-0.885115\pi\)
0.773611 + 0.633660i \(0.218448\pi\)
\(200\) 1.00463e7 2.76019e7i 0.00627893 0.0172512i
\(201\) −4.96107e8 3.40147e8i −0.303943 0.208393i
\(202\) −1.34148e9 1.12563e9i −0.805708 0.676069i
\(203\) −2.27435e9 + 2.71046e9i −1.33929 + 1.59610i
\(204\) −1.74587e8 + 2.54637e8i −0.100807 + 0.147028i
\(205\) −2.39555e9 8.71908e8i −1.35641 0.493691i
\(206\) −8.83078e7 5.09845e7i −0.0490377 0.0283119i
\(207\) 3.01890e9 5.94631e7i 1.64425 0.0323867i
\(208\) 3.08175e8 + 5.33775e8i 0.164644 + 0.285171i
\(209\) −4.83419e8 + 8.52398e7i −0.253360 + 0.0446743i
\(210\) 2.51352e9 + 6.47037e8i 1.29243 + 0.332699i
\(211\) 1.98173e9 7.21292e8i 0.999806 0.363900i 0.210296 0.977638i \(-0.432557\pi\)
0.789510 + 0.613738i \(0.210335\pi\)
\(212\) 4.32878e6 + 763281.i 0.00214300 + 0.000377869i
\(213\) 2.08046e9 + 9.45307e8i 1.01074 + 0.459256i
\(214\) 1.13527e8 9.52602e7i 0.0541306 0.0454210i
\(215\) 1.73220e9i 0.810671i
\(216\) −5.27884e8 + 5.60032e8i −0.242507 + 0.257275i
\(217\) 7.13424e9 3.21743
\(218\) 2.68537e8 + 3.20030e8i 0.118899 + 0.141698i
\(219\) −6.09665e8 8.52696e8i −0.265042 0.370696i
\(220\) 9.11539e7 5.16960e8i 0.0389121 0.220681i
\(221\) 3.83141e8 + 1.05267e9i 0.160616 + 0.441290i
\(222\) −2.52163e9 + 7.02354e8i −1.03817 + 0.289164i
\(223\) −1.07941e8 6.12162e8i −0.0436481 0.247541i 0.955175 0.296042i \(-0.0956667\pi\)
−0.998823 + 0.0485009i \(0.984556\pi\)
\(224\) 7.47102e8 4.31339e8i 0.296748 0.171328i
\(225\) 8.35172e7 1.03609e8i 0.0325871 0.0404267i
\(226\) 3.24455e8 5.61972e8i 0.124371 0.215417i
\(227\) −5.66505e8 + 1.55646e9i −0.213354 + 0.586184i −0.999492 0.0318660i \(-0.989855\pi\)
0.786138 + 0.618050i \(0.212077\pi\)
\(228\) 6.81285e8 3.25894e8i 0.252110 0.120597i
\(229\) 1.41138e8 + 1.18429e8i 0.0513217 + 0.0430640i 0.668088 0.744083i \(-0.267113\pi\)
−0.616766 + 0.787147i \(0.711558\pi\)
\(230\) 2.03675e9 2.42730e9i 0.727823 0.867386i
\(231\) −2.53280e9 1.96480e8i −0.889513 0.0690034i
\(232\) −1.03459e9 3.76558e8i −0.357120 0.129981i
\(233\) −1.64102e9 9.47443e8i −0.556788 0.321462i 0.195067 0.980790i \(-0.437508\pi\)
−0.751855 + 0.659328i \(0.770841\pi\)
\(234\) 5.38963e8 + 2.73993e9i 0.179761 + 0.913852i
\(235\) −1.20623e8 2.08926e8i −0.0395513 0.0685048i
\(236\) −1.95816e9 + 3.45276e8i −0.631248 + 0.111306i
\(237\) −4.24008e8 + 4.32442e8i −0.134394 + 0.137067i
\(238\) 1.47338e9 5.36266e8i 0.459205 0.167137i
\(239\) 6.53182e7 + 1.15174e7i 0.0200190 + 0.00352989i 0.183649 0.982992i \(-0.441209\pi\)
−0.163630 + 0.986522i \(0.552320\pi\)
\(240\) 7.83076e7 + 8.03813e8i 0.0236025 + 0.242276i
\(241\) −3.35963e9 + 2.81906e9i −0.995917 + 0.835674i −0.986414 0.164281i \(-0.947470\pi\)
−0.00950371 + 0.999955i \(0.503025\pi\)
\(242\) 1.91140e9i 0.557300i
\(243\) −3.08375e9 + 1.62732e9i −0.884410 + 0.466711i
\(244\) 4.93621e8 0.139262
\(245\) −6.21758e9 7.40982e9i −1.72567 2.05657i
\(246\) −3.82082e9 + 3.72225e8i −1.04332 + 0.101640i
\(247\) 4.75835e8 2.69860e9i 0.127841 0.725020i
\(248\) 7.59259e8 + 2.08605e9i 0.200717 + 0.551464i
\(249\) −2.26040e9 2.21632e9i −0.588015 0.576547i
\(250\) −4.91271e8 2.78614e9i −0.125765 0.713251i
\(251\) 5.21406e9 3.01034e9i 1.31366 0.758439i 0.330956 0.943646i \(-0.392629\pi\)
0.982699 + 0.185207i \(0.0592956\pi\)
\(252\) 3.83496e9 7.54363e8i 0.950952 0.187059i
\(253\) −1.55070e9 + 2.68589e9i −0.378482 + 0.655550i
\(254\) 6.03300e8 1.65755e9i 0.144943 0.398229i
\(255\) −1.13527e8 + 1.46347e9i −0.0268497 + 0.346116i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) −5.51616e9 + 6.57390e9i −1.26446 + 1.50692i −0.493953 + 0.869489i \(0.664448\pi\)
−0.770505 + 0.637434i \(0.779996\pi\)
\(258\) 1.12562e9 + 2.35311e9i 0.254046 + 0.531085i
\(259\) 1.24918e10 + 4.54665e9i 2.77605 + 1.01040i
\(260\) 2.53776e9 + 1.46517e9i 0.555337 + 0.320624i
\(261\) −3.88351e9 3.13042e9i −0.836879 0.674591i
\(262\) −1.18950e9 2.06028e9i −0.252441 0.437241i
\(263\) −3.56775e9 + 6.29090e8i −0.745712 + 0.131489i −0.533577 0.845751i \(-0.679153\pi\)
−0.212135 + 0.977240i \(0.568042\pi\)
\(264\) −2.12101e8 7.61499e8i −0.0436644 0.156767i
\(265\) 1.96377e7 7.14755e6i 0.00398206 0.00144935i
\(266\) −3.77711e9 6.66006e8i −0.754454 0.133031i
\(267\) 2.24312e9 1.60380e9i 0.441375 0.315576i
\(268\) −7.28160e8 + 6.10999e8i −0.141152 + 0.118441i
\(269\) 2.99749e9i 0.572465i −0.958160 0.286233i \(-0.907597\pi\)
0.958160 0.286233i \(-0.0924030\pi\)
\(270\) −8.42209e8 + 3.56074e9i −0.158477 + 0.670017i
\(271\) −4.06312e9 −0.753325 −0.376663 0.926351i \(-0.622928\pi\)
−0.376663 + 0.926351i \(0.622928\pi\)
\(272\) 3.13607e8 + 3.73743e8i 0.0572942 + 0.0682806i
\(273\) 5.86644e9 1.29111e10i 1.05615 2.32440i
\(274\) 5.69190e8 3.22804e9i 0.100985 0.572712i
\(275\) 4.67503e7 + 1.28445e8i 0.00817436 + 0.0224589i
\(276\) 1.18952e9 4.62089e9i 0.204991 0.796323i
\(277\) 5.01418e8 + 2.84368e9i 0.0851689 + 0.483017i 0.997320 + 0.0731627i \(0.0233092\pi\)
−0.912151 + 0.409854i \(0.865580\pi\)
\(278\) 3.05138e9 1.76171e9i 0.510877 0.294955i
\(279\) 1.98065e8 + 1.00556e10i 0.0326882 + 1.65956i
\(280\) 2.05074e9 3.55199e9i 0.333640 0.577882i
\(281\) 1.18431e9 3.25387e9i 0.189951 0.521885i −0.807760 0.589512i \(-0.799320\pi\)
0.997711 + 0.0676261i \(0.0215425\pi\)
\(282\) −2.99625e8 2.05433e8i −0.0473786 0.0324843i
\(283\) −5.07471e9 4.25819e9i −0.791163 0.663864i 0.154870 0.987935i \(-0.450504\pi\)
−0.946033 + 0.324070i \(0.894949\pi\)
\(284\) 2.32117e9 2.76627e9i 0.356808 0.425227i
\(285\) 2.03041e9 2.96137e9i 0.307754 0.448862i
\(286\) −2.69521e9 9.80976e8i −0.402836 0.146620i
\(287\) 1.68839e10 + 9.74792e9i 2.48854 + 1.43676i
\(288\) 6.28710e8 + 1.04106e9i 0.0913861 + 0.151323i
\(289\) −3.04451e9 5.27324e9i −0.436441 0.755938i
\(290\) −5.15494e9 + 9.08954e8i −0.728838 + 0.128514i
\(291\) 1.06545e10 + 2.74271e9i 1.48581 + 0.382480i
\(292\) −1.55656e9 + 5.66542e8i −0.214109 + 0.0779293i
\(293\) 2.26858e9 + 4.00012e8i 0.307811 + 0.0542753i 0.325420 0.945570i \(-0.394494\pi\)
−0.0176092 + 0.999845i \(0.505605\pi\)
\(294\) −1.32613e10 6.02560e9i −1.77500 0.806512i
\(295\) −7.24172e9 + 6.07652e9i −0.956211 + 0.802356i
\(296\) 4.13648e9i 0.538845i
\(297\) 2.06619e8 3.57540e9i 0.0265549 0.459514i
\(298\) 3.26916e9 0.414545
\(299\) −1.11286e10 1.32625e10i −1.39237 1.65936i
\(300\) −1.22312e8 1.71069e8i −0.0151003 0.0211197i
\(301\) 2.30034e9 1.30459e10i 0.280237 1.58930i
\(302\) 3.39679e9 + 9.33259e9i 0.408357 + 1.12195i
\(303\) −1.20777e10 + 3.36402e9i −1.43289 + 0.399106i
\(304\) −2.07238e8 1.17530e9i −0.0242647 0.137612i
\(305\) 2.03243e9 1.17342e9i 0.234864 0.135599i
\(306\) 7.96765e8 + 2.06182e9i 0.0908750 + 0.235161i
\(307\) −3.93188e9 + 6.81021e9i −0.442636 + 0.766668i −0.997884 0.0650169i \(-0.979290\pi\)
0.555248 + 0.831685i \(0.312623\pi\)
\(308\) −1.37303e9 + 3.77237e9i −0.152573 + 0.419190i
\(309\) −6.58573e8 + 3.15030e8i −0.0722387 + 0.0345555i
\(310\) 8.08507e9 + 6.78418e9i 0.875461 + 0.734599i
\(311\) −1.55726e9 + 1.85588e9i −0.166464 + 0.198384i −0.842827 0.538184i \(-0.819111\pi\)
0.676363 + 0.736568i \(0.263555\pi\)
\(312\) 4.39952e9 + 3.41290e8i 0.464287 + 0.0360168i
\(313\) −7.11159e9 2.58841e9i −0.740951 0.269684i −0.0561581 0.998422i \(-0.517885\pi\)
−0.684793 + 0.728738i \(0.740107\pi\)
\(314\) 4.87618e9 + 2.81526e9i 0.501604 + 0.289601i
\(315\) 1.39968e10 1.22224e10i 1.42163 1.24140i
\(316\) 4.78523e8 + 8.28826e8i 0.0479904 + 0.0831219i
\(317\) 1.30171e10 2.29527e9i 1.28907 0.227298i 0.513245 0.858242i \(-0.328443\pi\)
0.775829 + 0.630944i \(0.217332\pi\)
\(318\) 2.20323e7 2.24706e7i 0.00215453 0.00219738i
\(319\) 4.81443e9 1.75231e9i 0.464925 0.169219i
\(320\) 1.25685e9 + 2.21616e8i 0.119862 + 0.0211350i
\(321\) −1.02878e8 1.05602e9i −0.00968950 0.0994610i
\(322\) −1.85629e10 + 1.55761e10i −1.72672 + 1.44889i
\(323\) 2.16909e9i 0.199282i
\(324\) 1.16973e9 + 5.38439e9i 0.106147 + 0.488603i
\(325\) −7.63039e8 −0.0683933
\(326\) −4.75529e9 5.66714e9i −0.421024 0.501757i
\(327\) 2.97691e9 2.90010e8i 0.260360 0.0253643i
\(328\) −1.05342e9 + 5.97426e9i −0.0910139 + 0.516165i
\(329\) 6.31010e8 + 1.73369e9i 0.0538583 + 0.147975i
\(330\) −2.68352e9 2.63118e9i −0.226282 0.221868i
\(331\) 3.15619e9 + 1.78997e10i 0.262937 + 1.49119i 0.774846 + 0.632150i \(0.217827\pi\)
−0.511909 + 0.859040i \(0.671062\pi\)
\(332\) −4.33233e9 + 2.50127e9i −0.356590 + 0.205877i
\(333\) −6.06165e9 + 1.77333e10i −0.492963 + 1.44216i
\(334\) −7.02182e9 + 1.21622e10i −0.564240 + 0.977293i
\(335\) −1.54567e9 + 4.24669e9i −0.122726 + 0.337187i
\(336\) 4.77688e8 6.15781e9i 0.0374789 0.483136i
\(337\) −1.14032e10 9.56846e9i −0.884115 0.741861i 0.0829057 0.996557i \(-0.473580\pi\)
−0.967021 + 0.254697i \(0.918024\pi\)
\(338\) 4.35948e9 5.19543e9i 0.334017 0.398066i
\(339\) −2.00478e9 4.19102e9i −0.151799 0.317337i
\(340\) 2.17970e9 + 7.93345e8i 0.163110 + 0.0593672i
\(341\) −8.94639e9 5.16520e9i −0.661653 0.382006i
\(342\) 8.33865e8 5.34228e9i 0.0609525 0.390501i
\(343\) 2.35722e10 + 4.08282e10i 1.70303 + 2.94974i
\(344\) 4.05942e9 7.15785e8i 0.289888 0.0511150i
\(345\) −6.08695e9 2.18537e10i −0.429658 1.54258i
\(346\) −4.87793e9 + 1.77542e9i −0.340354 + 0.123879i
\(347\) 2.42670e10 + 4.27893e9i 1.67378 + 0.295132i 0.928420 0.371531i \(-0.121167\pi\)
0.745359 + 0.666664i \(0.232278\pi\)
\(348\) −6.41208e9 + 4.58454e9i −0.437202 + 0.312593i
\(349\) −1.55872e10 + 1.30792e10i −1.05067 + 0.881618i −0.993164 0.116727i \(-0.962760\pi\)
−0.0575079 + 0.998345i \(0.518315\pi\)
\(350\) 1.06799e9i 0.0711698i
\(351\) 1.83608e10 + 7.91024e9i 1.20966 + 0.521148i
\(352\) −1.24916e9 −0.0813670
\(353\) 6.55825e9 + 7.81582e9i 0.422366 + 0.503357i 0.934704 0.355428i \(-0.115665\pi\)
−0.512337 + 0.858784i \(0.671220\pi\)
\(354\) −5.88890e9 + 1.29605e10i −0.374991 + 0.825292i
\(355\) 2.98127e9 1.69076e10i 0.187710 1.06456i
\(356\) −1.49036e9 4.09473e9i −0.0927878 0.254932i
\(357\) 2.79848e9 1.08711e10i 0.172286 0.669272i
\(358\) −8.89497e8 5.04459e9i −0.0541517 0.307110i
\(359\) 1.49833e10 8.65060e9i 0.902047 0.520797i 0.0241833 0.999708i \(-0.492301\pi\)
0.877864 + 0.478910i \(0.158968\pi\)
\(360\) 5.06342e9 + 2.79188e9i 0.301463 + 0.166221i
\(361\) 5.83885e9 1.01132e10i 0.343794 0.595469i
\(362\) 5.01624e9 1.37820e10i 0.292108 0.802561i
\(363\) −1.12865e10 7.73837e9i −0.650028 0.445680i
\(364\) −1.71671e10 1.44049e10i −0.977892 0.820548i
\(365\) −5.06220e9 + 6.03290e9i −0.285212 + 0.339903i
\(366\) 1.99845e9 2.91475e9i 0.111370 0.162434i
\(367\) −2.63458e10 9.58908e9i −1.45227 0.528583i −0.509045 0.860740i \(-0.670001\pi\)
−0.943224 + 0.332158i \(0.892223\pi\)
\(368\) −6.53001e9 3.77010e9i −0.356060 0.205571i
\(369\) −1.32708e10 + 2.40683e10i −0.715802 + 1.29819i
\(370\) 9.83314e9 + 1.70315e10i 0.524669 + 0.908753i
\(371\) −1.57391e8 + 2.77523e7i −0.00830777 + 0.00146488i
\(372\) 1.53917e10 + 3.96216e9i 0.803736 + 0.206900i
\(373\) 1.95992e10 7.13352e9i 1.01252 0.368526i 0.218118 0.975922i \(-0.430008\pi\)
0.794399 + 0.607396i \(0.207786\pi\)
\(374\) −2.23588e9 3.94247e8i −0.114278 0.0201503i
\(375\) −1.84406e10 8.37893e9i −0.932504 0.423705i
\(376\) −4.39774e8 + 3.69014e8i −0.0220028 + 0.0184625i
\(377\) 2.86005e10i 1.41582i
\(378\) 1.10716e10 2.56989e10i 0.542305 1.25877i
\(379\) −9.38168e9 −0.454699 −0.227350 0.973813i \(-0.573006\pi\)
−0.227350 + 0.973813i \(0.573006\pi\)
\(380\) −3.64718e9 4.34654e9i −0.174913 0.208453i
\(381\) −7.34509e9 1.02731e10i −0.348576 0.487529i
\(382\) 3.77336e8 2.13998e9i 0.0177204 0.100498i
\(383\) −1.93666e9 5.32094e9i −0.0900034 0.247282i 0.886521 0.462688i \(-0.153115\pi\)
−0.976525 + 0.215405i \(0.930893\pi\)
\(384\) 1.85138e9 5.15667e8i 0.0851472 0.0237162i
\(385\) 3.31428e9 + 1.87962e10i 0.150851 + 0.855516i
\(386\) −1.14211e9 + 6.59398e8i −0.0514469 + 0.0297029i
\(387\) 1.84519e10 + 2.88011e9i 0.822614 + 0.128400i
\(388\) 8.69285e9 1.50564e10i 0.383562 0.664348i
\(389\) −6.25611e9 + 1.71885e10i −0.273216 + 0.750655i 0.724874 + 0.688881i \(0.241898\pi\)
−0.998090 + 0.0617737i \(0.980324\pi\)
\(390\) 1.89258e10 9.05321e9i 0.818082 0.391331i
\(391\) −1.04982e10 8.80906e9i −0.449168 0.376897i
\(392\) −1.47957e10 + 1.76328e10i −0.626600 + 0.746753i
\(393\) −1.69814e10 1.31732e9i −0.711873 0.0552231i
\(394\) 2.41533e10 + 8.79109e9i 1.00229 + 0.364802i
\(395\) 3.94053e9 + 2.27507e9i 0.161870 + 0.0934557i
\(396\) −5.35523e9 1.83054e9i −0.217770 0.0744386i
\(397\) −2.05364e10 3.55700e10i −0.826726 1.43193i −0.900593 0.434664i \(-0.856867\pi\)
0.0738664 0.997268i \(-0.476466\pi\)
\(398\) 5.65988e9 9.97990e8i 0.225567 0.0397735i
\(399\) −1.92244e10 + 1.96068e10i −0.758511 + 0.773599i
\(400\) −3.12280e8 + 1.13661e8i −0.0121985 + 0.00443987i
\(401\) 5.68533e9 + 1.00248e9i 0.219876 + 0.0387701i 0.282501 0.959267i \(-0.408836\pi\)
−0.0626247 + 0.998037i \(0.519947\pi\)
\(402\) 6.59858e8 + 6.77332e9i 0.0252666 + 0.259357i
\(403\) 4.41759e10 3.70680e10i 1.67481 1.40533i
\(404\) 1.98123e10i 0.743719i
\(405\) 1.76159e10 + 1.93889e10i 0.654763 + 0.720666i
\(406\) 4.00308e10 1.47330
\(407\) −1.23731e10 1.47456e10i −0.450920 0.537386i
\(408\) 3.47654e9 3.38685e8i 0.125461 0.0122224i
\(409\) −3.40118e9 + 1.92890e10i −0.121545 + 0.689314i 0.861756 + 0.507324i \(0.169365\pi\)
−0.983300 + 0.181990i \(0.941746\pi\)
\(410\) 9.86452e9 + 2.71025e10i 0.349092 + 0.959123i
\(411\) −1.67566e10 1.64298e10i −0.587245 0.575792i
\(412\) 2.00329e8 + 1.13612e9i 0.00695272 + 0.0394308i
\(413\) 6.26096e10 3.61477e10i 2.15199 1.24245i
\(414\) −2.24698e10 2.57318e10i −0.764887 0.875929i
\(415\) −1.18919e10 + 2.05974e10i −0.400922 + 0.694417i
\(416\) 2.38498e9 6.55268e9i 0.0796363 0.218799i
\(417\) 1.95101e9 2.51503e10i 0.0645232 0.831760i
\(418\) 4.25433e9 + 3.56981e9i 0.139356 + 0.116934i
\(419\) −4.21037e9 + 5.01772e9i −0.136604 + 0.162798i −0.830010 0.557749i \(-0.811665\pi\)
0.693405 + 0.720548i \(0.256110\pi\)
\(420\) −1.26714e10 2.64897e10i −0.407218 0.851293i
\(421\) −4.93249e10 1.79528e10i −1.57014 0.571483i −0.597107 0.802162i \(-0.703683\pi\)
−0.973030 + 0.230678i \(0.925905\pi\)
\(422\) −2.06631e10 1.19298e10i −0.651547 0.376171i
\(423\) −2.42609e9 + 9.37534e8i −0.0757785 + 0.0292837i
\(424\) −2.48651e7 4.30675e7i −0.000769353 0.00133256i
\(425\) −5.94825e8 + 1.04884e8i −0.0182320 + 0.00321479i
\(426\) −6.93697e9 2.49055e10i −0.210636 0.756236i
\(427\) −1.68653e10 + 6.13846e9i −0.507320 + 0.184649i
\(428\) −1.65120e9 2.91152e8i −0.0492068 0.00867649i
\(429\) −1.67042e10 + 1.19432e10i −0.493170 + 0.352609i
\(430\) 1.50127e10 1.25971e10i 0.439120 0.368466i
\(431\) 5.46765e9i 0.158450i −0.996857 0.0792248i \(-0.974755\pi\)
0.996857 0.0792248i \(-0.0252445\pi\)
\(432\) 8.69263e9 + 5.02339e8i 0.249584 + 0.0144232i
\(433\) 5.74008e10 1.63292 0.816462 0.577399i \(-0.195932\pi\)
0.816462 + 0.577399i \(0.195932\pi\)
\(434\) −5.18824e10 6.18310e10i −1.46238 1.74280i
\(435\) −1.55028e10 + 3.41190e10i −0.432965 + 0.952882i
\(436\) 8.20751e8 4.65471e9i 0.0227125 0.128809i
\(437\) 1.14655e10 + 3.15012e10i 0.314389 + 0.863777i
\(438\) −2.95648e9 + 1.14849e10i −0.0803300 + 0.312055i
\(439\) 4.09034e8 + 2.31975e9i 0.0110129 + 0.0624572i 0.989819 0.142332i \(-0.0454601\pi\)
−0.978806 + 0.204789i \(0.934349\pi\)
\(440\) −5.14329e9 + 2.96948e9i −0.137224 + 0.0792263i
\(441\) −8.92692e10 + 5.39110e10i −2.36019 + 1.42536i
\(442\) 6.33697e9 1.09760e10i 0.166032 0.287577i
\(443\) −9.87952e8 + 2.71438e9i −0.0256520 + 0.0704782i −0.951858 0.306540i \(-0.900829\pi\)
0.926206 + 0.377019i \(0.123051\pi\)
\(444\) 2.44252e10 + 1.67467e10i 0.628502 + 0.430922i
\(445\) −1.58703e10 1.33167e10i −0.404710 0.339592i
\(446\) −4.52051e9 + 5.38733e9i −0.114248 + 0.136155i
\(447\) 1.32354e10 1.93039e10i 0.331517 0.483520i
\(448\) −9.17149e9 3.33815e9i −0.227682 0.0828693i
\(449\) −1.65503e10 9.55529e9i −0.407211 0.235103i 0.282380 0.959303i \(-0.408876\pi\)
−0.689591 + 0.724199i \(0.742210\pi\)
\(450\) −1.50532e9 + 2.96502e7i −0.0367096 + 0.000723067i
\(451\) −1.41150e10 2.44479e10i −0.341174 0.590930i
\(452\) −7.23003e9 + 1.27485e9i −0.173215 + 0.0305426i
\(453\) 6.88595e10 + 1.77260e10i 1.63520 + 0.420937i
\(454\) 1.76093e10 6.40927e9i 0.414495 0.150864i
\(455\) −1.04926e11 1.85014e10i −2.44816 0.431676i
\(456\) −7.77898e9 3.53456e9i −0.179913 0.0817479i
\(457\) 1.70069e10 1.42705e10i 0.389907 0.327171i −0.426670 0.904407i \(-0.640313\pi\)
0.816577 + 0.577237i \(0.195869\pi\)
\(458\) 2.08446e9i 0.0473731i
\(459\) 1.54005e10 + 3.64261e9i 0.346963 + 0.0820658i
\(460\) −3.58488e10 −0.800651
\(461\) 1.08079e10 + 1.28803e10i 0.239297 + 0.285183i 0.872305 0.488963i \(-0.162625\pi\)
−0.633008 + 0.774145i \(0.718180\pi\)
\(462\) 1.67164e10 + 2.33801e10i 0.366924 + 0.513191i
\(463\) 3.11709e9 1.76779e10i 0.0678305 0.384686i −0.931927 0.362647i \(-0.881873\pi\)
0.999757 0.0220390i \(-0.00701580\pi\)
\(464\) 4.26027e9 + 1.17050e10i 0.0919105 + 0.252522i
\(465\) 7.27922e10 2.02749e10i 1.55694 0.433658i
\(466\) 3.72270e9 + 2.11125e10i 0.0789432 + 0.447709i
\(467\) 1.26576e10 7.30789e9i 0.266125 0.153647i −0.361000 0.932566i \(-0.617565\pi\)
0.627125 + 0.778918i \(0.284231\pi\)
\(468\) 1.98269e10 2.45967e10i 0.413306 0.512736i
\(469\) 1.72805e10 2.99308e10i 0.357163 0.618624i
\(470\) −9.33509e8 + 2.56480e9i −0.0191305 + 0.0525607i
\(471\) 3.63651e10 1.73953e10i 0.738926 0.353467i
\(472\) 1.72328e10 + 1.44600e10i 0.347206 + 0.291340i
\(473\) −1.23299e10 + 1.46942e10i −0.246328 + 0.293562i
\(474\) 6.83141e9 + 5.29942e8i 0.135331 + 0.0104982i
\(475\) 1.38836e9 + 5.05323e8i 0.0272727 + 0.00992646i
\(476\) −1.53626e10 8.86958e9i −0.299251 0.172773i
\(477\) −4.34861e7 2.21070e8i −0.000839996 0.00427029i
\(478\) −3.75196e8 6.49858e8i −0.00718698 0.0124482i
\(479\) −9.35117e9 + 1.64886e9i −0.177633 + 0.0313215i −0.261757 0.965134i \(-0.584302\pi\)
0.0841240 + 0.996455i \(0.473191\pi\)
\(480\) 6.39701e9 6.52426e9i 0.120507 0.122904i
\(481\) 1.00974e11 3.67516e10i 1.88638 0.686587i
\(482\) 4.88646e10 + 8.61614e9i 0.905328 + 0.159634i
\(483\) 1.68217e10 + 1.72672e11i 0.309088 + 3.17273i
\(484\) −1.65657e10 + 1.39003e10i −0.301876 + 0.253304i
\(485\) 8.26577e10i 1.49388i
\(486\) 3.65296e10 + 1.48918e10i 0.654787 + 0.266934i
\(487\) −1.09510e11 −1.94687 −0.973435 0.228964i \(-0.926466\pi\)
−0.973435 + 0.228964i \(0.926466\pi\)
\(488\) −3.58976e9 4.27811e9i −0.0632975 0.0754350i
\(489\) −5.27155e10 + 5.13555e9i −0.921941 + 0.0898156i
\(490\) −1.90033e10 + 1.07773e11i −0.329644 + 1.86950i
\(491\) −1.59722e10 4.38833e10i −0.274814 0.755045i −0.997929 0.0643180i \(-0.979513\pi\)
0.723116 0.690727i \(-0.242709\pi\)
\(492\) 3.10122e10 + 3.04074e10i 0.529264 + 0.518942i
\(493\) 3.93129e9 + 2.22954e10i 0.0665498 + 0.377423i
\(494\) −2.68486e10 + 1.55011e10i −0.450831 + 0.260288i
\(495\) −2.64011e10 + 5.19328e9i −0.439745 + 0.0865009i
\(496\) 1.25578e10 2.17507e10i 0.207485 0.359374i
\(497\) −4.49062e10 + 1.23379e11i −0.736005 + 2.02216i
\(498\) −2.77004e9 + 3.57082e10i −0.0450369 + 0.580565i
\(499\) −1.51236e10 1.26902e10i −0.243923 0.204676i 0.512627 0.858611i \(-0.328672\pi\)
−0.756550 + 0.653936i \(0.773117\pi\)
\(500\) −2.05742e10 + 2.45194e10i −0.329188 + 0.392311i
\(501\) 4.33873e10 + 9.07018e10i 0.688672 + 1.43968i
\(502\) −6.40083e10 2.32971e10i −1.00791 0.366849i
\(503\) 1.03427e11 + 5.97137e10i 1.61571 + 0.932828i 0.988014 + 0.154367i \(0.0493337\pi\)
0.627692 + 0.778462i \(0.284000\pi\)
\(504\) −3.44269e10 2.77509e10i −0.533551 0.430085i
\(505\) 4.70972e10 + 8.15748e10i 0.724152 + 1.25427i
\(506\) 3.45552e10 6.09302e9i 0.527123 0.0929459i
\(507\) −1.30286e10 4.67760e10i −0.197181 0.707931i
\(508\) −1.87531e10 + 6.82556e9i −0.281590 + 0.102491i
\(509\) −4.55739e10 8.03591e9i −0.678962 0.119719i −0.176476 0.984305i \(-0.556470\pi\)
−0.502486 + 0.864586i \(0.667581\pi\)
\(510\) 1.35092e10 9.65886e9i 0.199686 0.142773i
\(511\) 4.61370e10 3.87135e10i 0.676652 0.567778i
\(512\) 3.03700e9i 0.0441942i
\(513\) −2.81693e10 2.65523e10i −0.406731 0.383383i
\(514\) 9.70900e10 1.39098
\(515\) 3.52559e9 + 4.20164e9i 0.0501191 + 0.0597296i
\(516\) 1.22081e10 2.68681e10i 0.172207 0.378999i
\(517\) 4.63900e8 2.63091e9i 0.00649326 0.0368251i
\(518\) −5.14395e10 1.41329e11i −0.714460 1.96296i
\(519\) −9.26496e9 + 3.59913e10i −0.127695 + 0.496053i
\(520\) −5.75698e9 3.26494e10i −0.0787374 0.446542i
\(521\) −1.06319e11 + 6.13835e10i −1.44298 + 0.833106i −0.998048 0.0624566i \(-0.980106\pi\)
−0.444935 + 0.895563i \(0.646773\pi\)
\(522\) 1.11136e9 + 5.64230e10i 0.0149683 + 0.759931i
\(523\) 8.51271e9 1.47445e10i 0.113779 0.197071i −0.803512 0.595288i \(-0.797038\pi\)
0.917291 + 0.398218i \(0.130371\pi\)
\(524\) −9.20560e9 + 2.52922e10i −0.122103 + 0.335476i
\(525\) 6.30632e9 + 4.32382e9i 0.0830116 + 0.0569154i
\(526\) 3.13980e10 + 2.63460e10i 0.410165 + 0.344169i
\(527\) 2.93420e10 3.49684e10i 0.380406 0.453350i
\(528\) −5.05729e9 + 7.37610e9i −0.0650702 + 0.0949054i
\(529\) 1.25439e11 + 4.56560e10i 1.60181 + 0.583009i
\(530\) −2.04758e8 1.18217e8i −0.00259500 0.00149823i
\(531\) 5.26880e10 + 8.72440e10i 0.662725 + 1.09738i
\(532\) 2.16961e10 + 3.75788e10i 0.270855 + 0.469134i
\(533\) 1.55195e11 2.73650e10i 1.92295 0.339068i
\(534\) −3.02125e10 7.77737e9i −0.371553 0.0956462i
\(535\) −7.49077e9 + 2.72642e9i −0.0914347 + 0.0332795i
\(536\) 1.05908e10 + 1.86745e9i 0.128313 + 0.0226250i
\(537\) −3.33886e10 1.51709e10i −0.401515 0.182438i
\(538\) −2.59787e10 + 2.17987e10i −0.310090 + 0.260197i
\(539\) 1.07114e11i 1.26909i
\(540\) 3.69851e10 1.85956e10i 0.434962 0.218693i
\(541\) −4.41827e10 −0.515778 −0.257889 0.966175i \(-0.583027\pi\)
−0.257889 + 0.966175i \(0.583027\pi\)
\(542\) 2.95483e10 + 3.52143e10i 0.342401 + 0.408058i
\(543\) −6.10720e10 8.54172e10i −0.702495 0.982530i
\(544\) 9.58504e8 5.43595e9i 0.0109446 0.0620697i
\(545\) −7.68571e9 2.11163e10i −0.0871161 0.239349i
\(546\) −1.54560e11 + 4.30499e10i −1.73911 + 0.484397i
\(547\) −1.14275e10 6.48085e10i −0.127644 0.723907i −0.979702 0.200459i \(-0.935757\pi\)
0.852058 0.523448i \(-0.175355\pi\)
\(548\) −3.21161e10 + 1.85422e10i −0.356123 + 0.205608i
\(549\) −9.12031e9 2.36010e10i −0.100397 0.259801i
\(550\) 7.73228e8 1.33927e9i 0.00845001 0.0146358i
\(551\) 1.89407e10 5.20391e10i 0.205489 0.564577i
\(552\) −4.86989e10 + 2.32952e10i −0.524521 + 0.250905i
\(553\) −2.66564e10 2.23674e10i −0.285037 0.239174i
\(554\) 2.09992e10 2.50258e10i 0.222927 0.265674i
\(555\) 1.40378e11 + 1.08897e10i 1.47954 + 0.114775i
\(556\) −3.74590e10 1.36340e10i −0.391974 0.142667i
\(557\) −1.45491e11 8.39991e10i −1.51152 0.872678i −0.999909 0.0134620i \(-0.995715\pi\)
−0.511613 0.859216i \(-0.670952\pi\)
\(558\) 8.57097e10 7.48442e10i 0.884084 0.772008i
\(559\) −5.35396e10 9.27333e10i −0.548312 0.949705i
\(560\) −4.56980e10 + 8.05779e9i −0.464670 + 0.0819339i
\(561\) −1.13800e10 + 1.16064e10i −0.114893 + 0.117178i
\(562\) −3.68134e10 + 1.33990e10i −0.369029 + 0.134315i
\(563\) −4.17694e10 7.36508e9i −0.415743 0.0733067i −0.0381357 0.999273i \(-0.512142\pi\)
−0.377607 + 0.925966i \(0.623253\pi\)
\(564\) 3.98523e8 + 4.09076e9i 0.00393855 + 0.0404285i
\(565\) −2.67383e10 + 2.24361e10i −0.262386 + 0.220168i
\(566\) 7.49484e10i 0.730293i
\(567\) −1.06924e11 1.69419e11i −1.03453 1.63919i
\(568\) −4.08550e10 −0.392511
\(569\) 4.96494e9 + 5.91699e9i 0.0473658 + 0.0564484i 0.789207 0.614127i \(-0.210492\pi\)
−0.741841 + 0.670575i \(0.766047\pi\)
\(570\) −4.04314e10 + 3.93883e9i −0.383018 + 0.0373136i
\(571\) −1.20307e9 + 6.82293e9i −0.0113174 + 0.0641839i −0.989943 0.141464i \(-0.954819\pi\)
0.978626 + 0.205648i \(0.0659302\pi\)
\(572\) 1.10985e10 + 3.04928e10i 0.103676 + 0.284848i
\(573\) −1.11085e10 1.08919e10i −0.103048 0.101038i
\(574\) −3.83016e10 2.17219e11i −0.352833 2.00102i
\(575\) 8.08412e9 4.66737e9i 0.0739540 0.0426973i
\(576\) 4.45046e9 1.30198e10i 0.0404310 0.118281i
\(577\) 3.42329e9 5.92932e9i 0.0308845 0.0534936i −0.850170 0.526508i \(-0.823501\pi\)
0.881055 + 0.473015i \(0.156834\pi\)
\(578\) −2.35615e10 + 6.47348e10i −0.211102 + 0.579998i
\(579\) −7.30252e8 + 9.41358e9i −0.00649769 + 0.0837608i
\(580\) 4.53660e10 + 3.80666e10i 0.400884 + 0.336382i
\(581\) 1.16916e11 1.39335e11i 1.02605 1.22280i
\(582\) −5.37125e10 1.12287e11i −0.468148 0.978669i
\(583\) 2.17462e8 + 7.91498e7i 0.00188239 + 0.000685134i
\(584\) 1.62299e10 + 9.37035e9i 0.139529 + 0.0805572i
\(585\) 2.31644e10 1.48406e11i 0.197787 1.26715i
\(586\) −1.30310e10 2.25703e10i −0.110506 0.191403i
\(587\) 1.17881e11 2.07856e10i 0.992867 0.175069i 0.346462 0.938064i \(-0.387383\pi\)
0.646405 + 0.762995i \(0.276272\pi\)
\(588\) 4.42178e10 + 1.58753e11i 0.369903 + 1.32805i
\(589\) −1.04927e11 + 3.81903e10i −0.871819 + 0.317316i
\(590\) 1.05328e11 + 1.85722e10i 0.869233 + 0.153269i
\(591\) 1.49696e11 1.07030e11i 1.22704 0.877317i
\(592\) 3.58501e10 3.00818e10i 0.291879 0.244916i
\(593\) 1.43481e11i 1.16031i 0.814506 + 0.580155i \(0.197008\pi\)
−0.814506 + 0.580155i \(0.802992\pi\)
\(594\) −3.24899e10 + 2.42107e10i −0.260977 + 0.194474i
\(595\) −8.43382e10 −0.672910
\(596\) −2.37744e10 2.83332e10i −0.188419 0.224549i
\(597\) 1.70213e10 3.74611e10i 0.133997 0.294906i
\(598\) −3.40131e10 + 1.92898e11i −0.265976 + 1.50842i
\(599\) 3.73399e10 + 1.02591e11i 0.290046 + 0.796894i 0.996059 + 0.0886950i \(0.0282696\pi\)
−0.706013 + 0.708199i \(0.749508\pi\)
\(600\) −5.93133e8 + 2.30412e9i −0.00457665 + 0.0177787i
\(601\) 1.76969e9 + 1.00364e10i 0.0135644 + 0.0769275i 0.990839 0.135052i \(-0.0431201\pi\)
−0.977274 + 0.211979i \(0.932009\pi\)
\(602\) −1.29795e11 + 7.49370e10i −0.988260 + 0.570572i
\(603\) 4.26668e10 + 2.35258e10i 0.322716 + 0.177940i
\(604\) 5.61813e10 9.73088e10i 0.422128 0.731147i
\(605\) −3.51640e10 + 9.66124e10i −0.262468 + 0.721126i
\(606\) 1.16988e11 + 8.02109e10i 0.867464 + 0.594761i
\(607\) −6.80673e10 5.71152e10i −0.501399 0.420724i 0.356691 0.934222i \(-0.383905\pi\)
−0.858090 + 0.513499i \(0.828349\pi\)
\(608\) −8.67902e9 + 1.03433e10i −0.0635121 + 0.0756908i
\(609\) 1.62067e11 2.36376e11i 1.17822 1.71844i
\(610\) −2.49503e10 9.08116e9i −0.180201 0.0655876i
\(611\) 1.29151e10 + 7.45656e9i 0.0926690 + 0.0535025i
\(612\) 1.20751e10 2.18996e10i 0.0860764 0.156110i
\(613\) 4.78807e10 + 8.29318e10i 0.339093 + 0.587326i 0.984262 0.176713i \(-0.0565466\pi\)
−0.645170 + 0.764039i \(0.723213\pi\)
\(614\) 8.76166e10 1.54492e10i 0.616472 0.108701i
\(615\) 1.99973e11 + 5.14775e10i 1.39788 + 0.359846i
\(616\) 4.26795e10 1.55341e10i 0.296412 0.107885i
\(617\) −1.02462e11 1.80668e10i −0.707004 0.124664i −0.191427 0.981507i \(-0.561311\pi\)
−0.515577 + 0.856843i \(0.672423\pi\)
\(618\) 7.51965e9 + 3.41673e9i 0.0515518 + 0.0234238i
\(619\) −8.74309e10 + 7.33632e10i −0.595528 + 0.499708i −0.890005 0.455951i \(-0.849299\pi\)
0.294477 + 0.955659i \(0.404855\pi\)
\(620\) 1.19408e11i 0.808105i
\(621\) −2.42912e11 + 2.85038e10i −1.63336 + 0.191662i
\(622\) 2.74094e10 0.183121
\(623\) 1.01841e11 + 1.21369e11i 0.676034 + 0.805666i
\(624\) −2.90368e10 4.06117e10i −0.191518 0.267863i
\(625\) −2.50493e10 + 1.42062e11i −0.164163 + 0.931016i
\(626\) 2.92845e10 + 8.04585e10i 0.190695 + 0.523931i
\(627\) 3.83030e10 1.06686e10i 0.247835 0.0690298i
\(628\) −1.10618e10 6.27344e10i −0.0711190 0.403336i
\(629\) 7.36624e10 4.25290e10i 0.470590 0.271695i
\(630\) −2.07718e11 3.24222e10i −1.31859 0.205817i
\(631\) −8.73812e10 + 1.51349e11i −0.551189 + 0.954688i 0.447000 + 0.894534i \(0.352492\pi\)
−0.998189 + 0.0601538i \(0.980841\pi\)
\(632\) 3.70331e9 1.01748e10i 0.0232125 0.0637757i
\(633\) −1.54099e11 + 7.37136e10i −0.959811 + 0.459127i
\(634\) −1.14557e11 9.61249e10i −0.709031 0.594948i
\(635\) −6.09882e10 + 7.26829e10i −0.375103 + 0.447031i
\(636\) −3.54974e8 2.75369e7i −0.00216954 0.000168301i
\(637\) 5.61884e11 + 2.04509e11i 3.41263 + 1.24209i
\(638\) −5.01990e10 2.89824e10i −0.302979 0.174925i
\(639\) −1.75148e11 5.98694e10i −1.05051 0.359089i
\(640\) −7.21948e9 1.25045e10i −0.0430315 0.0745327i
\(641\) 7.99764e9 1.41020e9i 0.0473729 0.00835312i −0.149911 0.988699i \(-0.547899\pi\)
0.197284 + 0.980346i \(0.436788\pi\)
\(642\) −8.40418e9 + 8.57134e9i −0.0494715 + 0.0504555i
\(643\) 1.09381e11 3.98115e10i 0.639880 0.232897i −0.00164564 0.999999i \(-0.500524\pi\)
0.641526 + 0.767101i \(0.278302\pi\)
\(644\) 2.69991e11 + 4.76067e10i 1.56966 + 0.276773i
\(645\) −1.36044e10 1.39647e11i −0.0786035 0.806851i
\(646\) −1.87991e10 + 1.57743e10i −0.107946 + 0.0905774i
\(647\) 2.68470e11i 1.53207i −0.642800 0.766034i \(-0.722227\pi\)
0.642800 0.766034i \(-0.277773\pi\)
\(648\) 3.81587e10 4.92948e10i 0.216418 0.279577i
\(649\) −1.04684e11 −0.590067
\(650\) 5.54906e9 + 6.61311e9i 0.0310861 + 0.0370469i
\(651\) −5.75150e11 + 5.60312e10i −3.20227 + 0.311965i
\(652\) −1.45340e10 + 8.24264e10i −0.0804257 + 0.456117i
\(653\) 1.68626e10 + 4.63295e10i 0.0927408 + 0.254803i 0.977387 0.211461i \(-0.0678220\pi\)
−0.884646 + 0.466264i \(0.845600\pi\)
\(654\) −2.41625e10 2.36912e10i −0.132078 0.129502i
\(655\) 2.22209e10 + 1.26021e11i 0.120725 + 0.684665i
\(656\) 5.94386e10 3.43169e10i 0.320962 0.185307i
\(657\) 5.58471e10 + 6.39547e10i 0.299736 + 0.343250i
\(658\) 1.04366e10 1.80768e10i 0.0556745 0.0964311i
\(659\) −5.50314e10 + 1.51198e11i −0.291789 + 0.801684i 0.704016 + 0.710184i \(0.251388\pi\)
−0.995805 + 0.0914998i \(0.970834\pi\)
\(660\) −3.28856e9 + 4.23923e10i −0.0173312 + 0.223415i
\(661\) −1.27976e10 1.07385e10i −0.0670384 0.0562519i 0.608653 0.793437i \(-0.291710\pi\)
−0.675691 + 0.737185i \(0.736155\pi\)
\(662\) 1.32180e11 1.57526e11i 0.688231 0.820201i
\(663\) −3.91557e10 8.18555e10i −0.202647 0.423637i
\(664\) 5.31841e10 + 1.93574e10i 0.273596 + 0.0995807i
\(665\) 1.78663e11 + 1.03151e11i 0.913583 + 0.527457i
\(666\) 1.97773e11 7.64271e10i 1.00524 0.388464i
\(667\) −1.74944e11 3.03012e11i −0.883884 1.53093i
\(668\) 1.56472e11 2.75902e10i 0.785833 0.138564i
\(669\) 1.35098e10 + 4.85037e10i 0.0674443 + 0.242142i
\(670\) 4.80458e10 1.74872e10i 0.238427 0.0867804i
\(671\) 2.55934e10 + 4.51281e9i 0.126252 + 0.0222616i
\(672\) −5.68424e10 + 4.06415e10i −0.278738 + 0.199293i
\(673\) 1.65026e11 1.38473e11i 0.804435 0.675001i −0.144838 0.989455i \(-0.546266\pi\)
0.949273 + 0.314455i \(0.101822\pi\)
\(674\) 1.68415e11i 0.816094i
\(675\) −5.91929e9 + 9.00872e9i −0.0285138 + 0.0433959i
\(676\) −7.67313e10 −0.367439
\(677\) 1.44588e11 + 1.72314e11i 0.688302 + 0.820286i 0.991149 0.132753i \(-0.0423817\pi\)
−0.302847 + 0.953039i \(0.597937\pi\)
\(678\) −2.17433e10 + 4.78535e10i −0.102898 + 0.226462i
\(679\) −1.09768e11 + 6.22526e11i −0.516413 + 2.92873i
\(680\) −8.97567e9 2.46605e10i −0.0419789 0.115336i
\(681\) 3.34465e10 1.29928e11i 0.155511 0.604109i
\(682\) 2.02952e10 + 1.15100e11i 0.0938113 + 0.532030i
\(683\) −2.85374e11 + 1.64761e11i −1.31139 + 0.757131i −0.982326 0.187177i \(-0.940066\pi\)
−0.329063 + 0.944308i \(0.606733\pi\)
\(684\) −5.23646e10 + 3.16238e10i −0.239229 + 0.144474i
\(685\) −8.81563e10 + 1.52691e11i −0.400397 + 0.693508i
\(686\) 1.82426e11 5.01211e11i 0.823740 2.26321i
\(687\) −1.23084e10 8.43904e9i −0.0552554 0.0378849i
\(688\) −3.57249e10 2.99768e10i −0.159447 0.133792i
\(689\) −8.30386e8 + 9.89615e8i −0.00368471 + 0.00439126i
\(690\) −1.45136e11 + 2.11681e11i −0.640291 + 0.933869i
\(691\) −2.25153e10 8.19488e9i −0.0987563 0.0359443i 0.292169 0.956367i \(-0.405623\pi\)
−0.390926 + 0.920422i \(0.627845\pi\)
\(692\) 5.08611e10 + 2.93647e10i 0.221800 + 0.128056i
\(693\) 2.05733e11 4.05231e9i 0.892013 0.0175699i
\(694\) −1.39393e11 2.41435e11i −0.600899 1.04079i
\(695\) −1.86644e11 + 3.29103e10i −0.799970 + 0.141056i
\(696\) 8.63640e10 + 2.22320e10i 0.368041 + 0.0947419i
\(697\) 1.17220e11 4.26647e10i 0.496674 0.180775i
\(698\) 2.26710e11 + 3.99752e10i 0.955102 + 0.168410i
\(699\) 1.39737e11 + 6.34930e10i 0.585334 + 0.265960i
\(700\) 9.25608e9 7.76677e9i 0.0385509 0.0323481i
\(701\) 4.21785e11i 1.74670i 0.487091 + 0.873351i \(0.338058\pi\)
−0.487091 + 0.873351i \(0.661942\pi\)
\(702\) −6.49693e10 2.16656e11i −0.267522 0.892116i
\(703\) −2.08063e11 −0.851869
\(704\) 9.08430e9 + 1.08262e10i 0.0369829 + 0.0440745i
\(705\) 1.13653e10 + 1.58959e10i 0.0460072 + 0.0643471i
\(706\) 2.00445e10 1.13678e11i 0.0806821 0.457571i
\(707\) −2.46377e11 6.76915e11i −0.986104 2.70930i
\(708\) 1.55152e11 4.32147e10i 0.617481 0.171988i
\(709\) −1.96979e10 1.11712e11i −0.0779533 0.442095i −0.998656 0.0518302i \(-0.983495\pi\)
0.920703 0.390265i \(-0.127617\pi\)
\(710\) −1.68216e11 + 9.71195e10i −0.661963 + 0.382185i
\(711\) 3.07865e10 3.81928e10i 0.120471 0.149453i
\(712\) −2.46498e10 + 4.26948e10i −0.0959167 + 0.166133i
\(713\) −2.41289e11 + 6.62937e11i −0.933642 + 2.56516i
\(714\) −1.14570e11 + 5.48045e10i −0.440835 + 0.210874i
\(715\) 1.18184e11 + 9.91678e10i 0.452203 + 0.379443i
\(716\) −3.72517e10 + 4.43949e10i −0.141741 + 0.168920i
\(717\) −5.35630e9 4.15511e8i −0.0202670 0.00157219i
\(718\) −1.83936e11 6.69473e10i −0.692101 0.251904i
\(719\) −1.50686e11 8.69985e10i −0.563841 0.325534i 0.190845 0.981620i \(-0.438877\pi\)
−0.754686 + 0.656086i \(0.772211\pi\)
\(720\) −1.26261e10 6.41871e10i −0.0469827 0.238846i
\(721\) −2.09729e10 3.63260e10i −0.0776098 0.134424i
\(722\) −1.30111e11 + 2.29421e10i −0.478812 + 0.0844274i
\(723\) 2.48707e11 2.53654e11i 0.910197 0.928301i
\(724\) −1.55926e11 + 5.67523e10i −0.567497 + 0.206552i
\(725\) −1.51864e10 2.67778e9i −0.0549672 0.00969220i
\(726\) 1.50118e10 + 1.54094e11i 0.0540364 + 0.554674i
\(727\) −2.31003e11 + 1.93835e11i −0.826953 + 0.693896i −0.954589 0.297925i \(-0.903705\pi\)
0.127636 + 0.991821i \(0.459261\pi\)
\(728\) 2.53540e11i 0.902655i
\(729\) 2.35826e11 1.55411e11i 0.834990 0.550265i
\(730\) 8.90998e10 0.313751
\(731\) −5.44833e10 6.49307e10i −0.190807 0.227395i
\(732\) −3.97949e10 + 3.87682e9i −0.138606 + 0.0135030i
\(733\) 5.67847e10 3.22042e11i 0.196705 1.11557i −0.713265 0.700895i \(-0.752784\pi\)
0.909970 0.414675i \(-0.136105\pi\)
\(734\) 1.08488e11 + 2.98069e11i 0.373764 + 1.02691i
\(735\) 5.59447e11 + 5.48536e11i 1.91694 + 1.87956i
\(736\) 1.48135e10 + 8.40117e10i 0.0504832 + 0.286305i
\(737\) −4.33399e10 + 2.50223e10i −0.146899 + 0.0848119i
\(738\) 3.05105e11 6.00163e10i 1.02855 0.202322i
\(739\) −1.78330e11 + 3.08877e11i −0.597925 + 1.03564i 0.395202 + 0.918594i \(0.370675\pi\)
−0.993127 + 0.117042i \(0.962659\pi\)
\(740\) 7.60990e10 2.09080e11i 0.253777 0.697246i
\(741\) −1.71667e10 + 2.21293e11i −0.0569395 + 0.733999i
\(742\) 1.38512e9 + 1.16225e9i 0.00456954 + 0.00383430i
\(743\) 3.85547e11 4.59477e11i 1.26509 1.50768i 0.496343 0.868127i \(-0.334676\pi\)
0.768749 0.639551i \(-0.220880\pi\)
\(744\) −7.75937e10 1.62211e11i −0.253241 0.529404i
\(745\) −1.65241e11 6.01430e10i −0.536406 0.195236i
\(746\) −2.04356e11 1.17985e11i −0.659831 0.380953i
\(747\) 1.99636e11 + 1.60923e11i 0.641147 + 0.516815i
\(748\) 1.28432e10 + 2.22451e10i 0.0410267 + 0.0710603i
\(749\) 6.00364e10 1.05860e10i 0.190760 0.0336362i
\(750\) 6.14874e10 + 2.20755e11i 0.194331 + 0.697696i
\(751\) 5.82770e11 2.12111e11i 1.83205 0.666812i 0.839749 0.542975i \(-0.182702\pi\)
0.992302 0.123838i \(-0.0395202\pi\)
\(752\) 6.39635e9 + 1.12785e9i 0.0200014 + 0.00352679i
\(753\) −3.96706e11 + 2.83639e11i −1.23393 + 0.882239i
\(754\) 2.47875e11 2.07992e11i 0.766915 0.643518i
\(755\) 5.34211e11i 1.64409i