Properties

Label 54.9.f.a.5.19
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

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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 5.19
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.27231 + 8.66680i) q^{2} +(24.9903 + 77.0486i) q^{3} +(-22.2270 + 126.055i) q^{4} +(56.2230 + 154.472i) q^{5} +(-486.028 + 776.907i) q^{6} +(-208.662 - 1183.38i) q^{7} +(-1254.14 + 724.077i) q^{8} +(-5311.97 + 3850.93i) q^{9} +O(q^{10})\) \(q+(7.27231 + 8.66680i) q^{2} +(24.9903 + 77.0486i) q^{3} +(-22.2270 + 126.055i) q^{4} +(56.2230 + 154.472i) q^{5} +(-486.028 + 776.907i) q^{6} +(-208.662 - 1183.38i) q^{7} +(-1254.14 + 724.077i) q^{8} +(-5311.97 + 3850.93i) q^{9} +(-929.903 + 1610.64i) q^{10} +(-7030.57 + 19316.3i) q^{11} +(-10267.8 + 1437.60i) q^{12} +(-12002.7 - 10071.5i) q^{13} +(8738.66 - 10414.3i) q^{14} +(-10496.8 + 8192.20i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-41860.0 - 24167.9i) q^{17} +(-72005.6 - 18032.6i) q^{18} +(28549.2 + 49448.6i) q^{19} +(-20721.6 + 3653.78i) q^{20} +(85963.1 - 45650.0i) q^{21} +(-218539. + 79541.8i) q^{22} +(-167772. - 29582.8i) q^{23} +(-87130.4 - 78534.7i) q^{24} +(278536. - 233719. i) q^{25} -177268. i q^{26} +(-429457. - 313044. i) q^{27} +153809. q^{28} +(91695.1 + 109278. i) q^{29} +(-147336. - 31397.4i) q^{30} +(-9132.60 + 51793.5i) q^{31} +(-63398.2 - 174185. i) q^{32} +(-1.66399e6 - 58974.7i) q^{33} +(-94960.6 - 538548. i) q^{34} +(171067. - 98765.4i) q^{35} +(-367362. - 755197. i) q^{36} +(-578940. + 1.00275e6i) q^{37} +(-220943. + 607035. i) q^{38} +(476040. - 1.17648e6i) q^{39} +(-182361. - 153019. i) q^{40} +(-444007. + 529147. i) q^{41} +(1.02079e6 + 413044. i) q^{42} +(-1.88806e6 - 687198. i) q^{43} +(-2.27866e6 - 1.31558e6i) q^{44} +(-893515. - 604037. i) q^{45} +(-963705. - 1.66919e6i) q^{46} +(-4.94303e6 + 871590. i) q^{47} +(47005.3 - 1.32627e6i) q^{48} +(4.06030e6 - 1.47783e6i) q^{49} +(4.05120e6 + 714335. i) q^{50} +(816007. - 3.82921e6i) q^{51} +(1.53634e6 - 1.28915e6i) q^{52} +7.65492e6i q^{53} +(-410053. - 5.99857e6i) q^{54} -3.37910e6 q^{55} +(1.11855e6 + 1.33303e6i) q^{56} +(-3.09649e6 + 3.43541e6i) q^{57} +(-280255. + 1.58941e6i) q^{58} +(6.88653e6 + 1.89206e7i) q^{59} +(-799359. - 1.50526e6i) q^{60} +(384284. + 2.17938e6i) q^{61} +(-515299. + 297508. i) q^{62} +(5.66552e6 + 5.48253e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(880925. - 2.42032e6i) q^{65} +(-1.15899e7 - 1.48504e7i) q^{66} +(6.08818e6 + 5.10859e6i) q^{67} +(3.97691e6 - 4.73950e6i) q^{68} +(-1.91337e6 - 1.36659e7i) q^{69} +(2.10003e6 + 764349. i) q^{70} +(2.24866e7 + 1.29826e7i) q^{71} +(3.87357e6 - 8.67588e6i) q^{72} +(1.62215e7 + 2.80964e7i) q^{73} +(-1.29009e7 + 2.27478e6i) q^{74} +(2.49684e7 + 1.56201e7i) q^{75} +(-6.86782e6 + 2.49968e6i) q^{76} +(2.43255e7 + 4.28925e6i) q^{77} +(1.36582e7 - 4.42997e6i) q^{78} +(-2.94656e7 + 2.47245e7i) q^{79} -2.69329e6i q^{80} +(1.33873e7 - 4.09121e7i) q^{81} -7.81498e6 q^{82} +(5.66217e7 + 6.74791e7i) q^{83} +(3.84374e6 + 1.18508e7i) q^{84} +(1.37975e6 - 7.82497e6i) q^{85} +(-7.77476e6 - 2.13610e7i) q^{86} +(-6.12822e6 + 9.79586e6i) q^{87} +(-5.16921e6 - 2.93160e7i) q^{88} +(7.08084e7 - 4.08813e7i) q^{89} +(-1.26285e6 - 1.21367e7i) q^{90} +(-9.41384e6 + 1.63052e7i) q^{91} +(7.45815e6 - 2.04911e7i) q^{92} +(-4.21884e6 + 590682. i) q^{93} +(-4.35012e7 - 3.65018e7i) q^{94} +(-6.03328e6 + 7.19018e6i) q^{95} +(1.18364e7 - 9.23767e6i) q^{96} +(-3.69947e7 - 1.34650e7i) q^{97} +(4.23358e7 + 2.44426e7i) q^{98} +(-3.70397e7 - 1.29682e8i) 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
\(3\) 24.9903 + 77.0486i 0.308522 + 0.951217i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) 56.2230 + 154.472i 0.0899569 + 0.247154i 0.976510 0.215472i \(-0.0691292\pi\)
−0.886553 + 0.462627i \(0.846907\pi\)
\(6\) −486.028 + 776.907i −0.375021 + 0.599466i
\(7\) −208.662 1183.38i −0.0869061 0.492869i −0.996929 0.0783109i \(-0.975047\pi\)
0.910023 0.414558i \(-0.136064\pi\)
\(8\) −1254.14 + 724.077i −0.306186 + 0.176777i
\(9\) −5311.97 + 3850.93i −0.809628 + 0.586943i
\(10\) −929.903 + 1610.64i −0.0929903 + 0.161064i
\(11\) −7030.57 + 19316.3i −0.480197 + 1.31933i 0.429127 + 0.903244i \(0.358821\pi\)
−0.909325 + 0.416087i \(0.863401\pi\)
\(12\) −10267.8 + 1437.60i −0.495170 + 0.0693289i
\(13\) −12002.7 10071.5i −0.420248 0.352630i 0.408010 0.912978i \(-0.366223\pi\)
−0.828257 + 0.560348i \(0.810667\pi\)
\(14\) 8738.66 10414.3i 0.227474 0.271093i
\(15\) −10496.8 + 8192.20i −0.207344 + 0.161821i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) −41860.0 24167.9i −0.501191 0.289363i 0.228014 0.973658i \(-0.426777\pi\)
−0.729205 + 0.684295i \(0.760110\pi\)
\(18\) −72005.6 18032.6i −0.685924 0.171778i
\(19\) 28549.2 + 49448.6i 0.219068 + 0.379437i 0.954523 0.298136i \(-0.0963650\pi\)
−0.735455 + 0.677573i \(0.763032\pi\)
\(20\) −20721.6 + 3653.78i −0.129510 + 0.0228362i
\(21\) 85963.1 45650.0i 0.442013 0.234728i
\(22\) −218539. + 79541.8i −0.932908 + 0.339551i
\(23\) −167772. 29582.8i −0.599528 0.105713i −0.134356 0.990933i \(-0.542896\pi\)
−0.465172 + 0.885220i \(0.654008\pi\)
\(24\) −87130.4 78534.7i −0.262618 0.236710i
\(25\) 278536. 233719.i 0.713051 0.598321i
\(26\) 177268.i 0.387915i
\(27\) −429457. 313044.i −0.808099 0.589047i
\(28\) 153809. 0.250236
\(29\) 91695.1 + 109278.i 0.129644 + 0.154504i 0.826961 0.562259i \(-0.190067\pi\)
−0.697317 + 0.716763i \(0.745623\pi\)
\(30\) −147336. 31397.4i −0.181896 0.0387622i
\(31\) −9132.60 + 51793.5i −0.00988889 + 0.0560827i −0.989353 0.145536i \(-0.953509\pi\)
0.979464 + 0.201619i \(0.0646203\pi\)
\(32\) −63398.2 174185.i −0.0604612 0.166116i
\(33\) −1.66399e6 58974.7i −1.40312 0.0497290i
\(34\) −94960.6 538548.i −0.0710604 0.403004i
\(35\) 171067. 98765.4i 0.113997 0.0658162i
\(36\) −367362. 755197.i −0.218718 0.449625i
\(37\) −578940. + 1.00275e6i −0.308906 + 0.535042i −0.978123 0.208025i \(-0.933296\pi\)
0.669217 + 0.743067i \(0.266630\pi\)
\(38\) −220943. + 607035.i −0.105961 + 0.291125i
\(39\) 476040. 1.17648e6i 0.205772 0.508541i
\(40\) −182361. 153019.i −0.0712347 0.0597730i
\(41\) −444007. + 529147.i −0.157128 + 0.187258i −0.838865 0.544339i \(-0.816780\pi\)
0.681737 + 0.731597i \(0.261225\pi\)
\(42\) 1.02079e6 + 413044.i 0.328050 + 0.132739i
\(43\) −1.88806e6 687198.i −0.552258 0.201006i 0.0507913 0.998709i \(-0.483826\pi\)
−0.603050 + 0.797704i \(0.706048\pi\)
\(44\) −2.27866e6 1.31558e6i −0.607951 0.351001i
\(45\) −893515. 604037.i −0.217897 0.147304i
\(46\) −963705. 1.66919e6i −0.215235 0.372798i
\(47\) −4.94303e6 + 871590.i −1.01298 + 0.178616i −0.655413 0.755270i \(-0.727506\pi\)
−0.357569 + 0.933887i \(0.616394\pi\)
\(48\) 47005.3 1.32627e6i 0.00885486 0.249843i
\(49\) 4.06030e6 1.47783e6i 0.704326 0.256354i
\(50\) 4.05120e6 + 714335.i 0.648191 + 0.114294i
\(51\) 816007. 3.82921e6i 0.120618 0.566016i
\(52\) 1.53634e6 1.28915e6i 0.210124 0.176315i
\(53\) 7.65492e6i 0.970146i 0.874474 + 0.485073i \(0.161207\pi\)
−0.874474 + 0.485073i \(0.838793\pi\)
\(54\) −410053. 5.99857e6i −0.0482242 0.705460i
\(55\) −3.37910e6 −0.369276
\(56\) 1.11855e6 + 1.33303e6i 0.113737 + 0.135547i
\(57\) −3.09649e6 + 3.43541e6i −0.293339 + 0.325446i
\(58\) −280255. + 1.58941e6i −0.0247652 + 0.140450i
\(59\) 6.88653e6 + 1.89206e7i 0.568319 + 1.56144i 0.807128 + 0.590377i \(0.201021\pi\)
−0.238809 + 0.971067i \(0.576757\pi\)
\(60\) −799359. 1.50526e6i −0.0616789 0.116147i
\(61\) 384284. + 2.17938e6i 0.0277545 + 0.157403i 0.995535 0.0943911i \(-0.0300904\pi\)
−0.967781 + 0.251794i \(0.918979\pi\)
\(62\) −515299. + 297508.i −0.0348733 + 0.0201341i
\(63\) 5.66552e6 + 5.48253e6i 0.359648 + 0.348032i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) 880925. 2.42032e6i 0.0493498 0.135588i
\(66\) −1.15899e7 1.48504e7i −0.610809 0.782639i
\(67\) 6.08818e6 + 5.10859e6i 0.302126 + 0.253514i 0.781229 0.624245i \(-0.214593\pi\)
−0.479102 + 0.877759i \(0.659038\pi\)
\(68\) 3.97691e6 4.73950e6i 0.185999 0.221665i
\(69\) −1.91337e6 1.36659e7i −0.0844116 0.602896i
\(70\) 2.10003e6 + 764349.i 0.0874648 + 0.0318346i
\(71\) 2.24866e7 + 1.29826e7i 0.884892 + 0.510893i 0.872268 0.489028i \(-0.162648\pi\)
0.0126236 + 0.999920i \(0.495982\pi\)
\(72\) 3.87357e6 8.67588e6i 0.144139 0.322837i
\(73\) 1.62215e7 + 2.80964e7i 0.571213 + 0.989371i 0.996442 + 0.0842844i \(0.0268604\pi\)
−0.425228 + 0.905086i \(0.639806\pi\)
\(74\) −1.29009e7 + 2.27478e6i −0.430223 + 0.0758599i
\(75\) 2.49684e7 + 1.56201e7i 0.789125 + 0.493671i
\(76\) −6.86782e6 + 2.49968e6i −0.205857 + 0.0749256i
\(77\) 2.43255e7 + 4.28925e6i 0.691990 + 0.122016i
\(78\) 1.36582e7 4.42997e6i 0.368991 0.119680i
\(79\) −2.94656e7 + 2.47245e7i −0.756496 + 0.634775i −0.937212 0.348760i \(-0.886603\pi\)
0.180716 + 0.983535i \(0.442158\pi\)
\(80\) 2.69329e6i 0.0657541i
\(81\) 1.33873e7 4.09121e7i 0.310996 0.950411i
\(82\) −7.81498e6 −0.172851
\(83\) 5.66217e7 + 6.74791e7i 1.19308 + 1.42186i 0.881852 + 0.471526i \(0.156297\pi\)
0.311231 + 0.950334i \(0.399259\pi\)
\(84\) 3.84374e6 + 1.18508e7i 0.0772034 + 0.238029i
\(85\) 1.37975e6 7.82497e6i 0.0264317 0.149902i
\(86\) −7.77476e6 2.13610e7i −0.142132 0.390506i
\(87\) −6.12822e6 + 9.79586e6i −0.106969 + 0.170988i
\(88\) −5.16921e6 2.93160e7i −0.0861972 0.488849i
\(89\) 7.08084e7 4.08813e7i 1.12856 0.651575i 0.184988 0.982741i \(-0.440775\pi\)
0.943573 + 0.331166i \(0.107442\pi\)
\(90\) −1.26285e6 1.21367e7i −0.0192478 0.184982i
\(91\) −9.41384e6 + 1.63052e7i −0.137278 + 0.237773i
\(92\) 7.45815e6 2.04911e7i 0.104107 0.286031i
\(93\) −4.21884e6 + 590682.i −0.0563977 + 0.00789627i
\(94\) −4.35012e7 3.65018e7i −0.557172 0.467523i
\(95\) −6.03328e6 + 7.19018e6i −0.0740728 + 0.0882766i
\(96\) 1.18364e7 9.23767e6i 0.139359 0.108762i
\(97\) −3.69947e7 1.34650e7i −0.417881 0.152096i 0.124518 0.992217i \(-0.460262\pi\)
−0.542399 + 0.840121i \(0.682484\pi\)
\(98\) 4.23358e7 + 2.44426e7i 0.458990 + 0.264998i
\(99\) −3.70397e7 1.29682e8i −0.385591 1.35002i
\(100\) 2.32706e7 + 4.03058e7i 0.232706 + 0.403058i
\(101\) −7.13785e7 + 1.25860e7i −0.685934 + 0.120949i −0.505745 0.862683i \(-0.668782\pi\)
−0.180189 + 0.983632i \(0.557671\pi\)
\(102\) 3.91213e7 2.07751e7i 0.361420 0.191929i
\(103\) −1.93572e8 + 7.04544e7i −1.71986 + 0.625978i −0.997828 0.0658801i \(-0.979015\pi\)
−0.722033 + 0.691858i \(0.756792\pi\)
\(104\) 2.23455e7 + 3.94012e6i 0.191011 + 0.0336803i
\(105\) 1.18847e7 + 1.07123e7i 0.0977761 + 0.0881301i
\(106\) −6.63437e7 + 5.56689e7i −0.525504 + 0.440950i
\(107\) 2.19855e7i 0.167726i 0.996477 + 0.0838632i \(0.0267259\pi\)
−0.996477 + 0.0838632i \(0.973274\pi\)
\(108\) 4.90064e7 4.71773e7i 0.360212 0.346767i
\(109\) −2.30074e8 −1.62990 −0.814952 0.579529i \(-0.803236\pi\)
−0.814952 + 0.579529i \(0.803236\pi\)
\(110\) −2.45739e7 2.92860e7i −0.167843 0.200028i
\(111\) −9.17287e7 1.95474e7i −0.604245 0.128765i
\(112\) −3.41871e6 + 1.93885e7i −0.0217265 + 0.123217i
\(113\) −1.72375e7 4.73597e7i −0.105721 0.290466i 0.875541 0.483144i \(-0.160505\pi\)
−0.981262 + 0.192678i \(0.938283\pi\)
\(114\) −5.22926e7 1.85334e6i −0.309614 0.0109733i
\(115\) −4.86298e6 2.75793e7i −0.0278042 0.157686i
\(116\) −1.58132e7 + 9.12974e6i −0.0873348 + 0.0504227i
\(117\) 1.02542e8 + 7.27770e6i 0.547218 + 0.0388374i
\(118\) −1.13900e8 + 1.97280e8i −0.587483 + 1.01755i
\(119\) −1.98652e7 + 5.45791e7i −0.0990614 + 0.272169i
\(120\) 7.23264e6 1.78746e7i 0.0348796 0.0862010i
\(121\) −1.59483e8 1.33822e8i −0.744001 0.624291i
\(122\) −1.60936e7 + 1.91797e7i −0.0726465 + 0.0865768i
\(123\) −5.18659e7 2.09866e7i −0.226601 0.0916899i
\(124\) −6.32586e6 2.30243e6i −0.0267567 0.00973865i
\(125\) 1.07373e8 + 6.19919e7i 0.439800 + 0.253919i
\(126\) −6.31461e6 + 8.89726e7i −0.0250533 + 0.352999i
\(127\) −9.56569e7 1.65683e8i −0.367707 0.636887i 0.621500 0.783414i \(-0.286524\pi\)
−0.989207 + 0.146528i \(0.953190\pi\)
\(128\) 2.33661e7 4.12008e6i 0.0870455 0.0153485i
\(129\) 5.76444e6 1.62646e8i 0.0208160 0.587332i
\(130\) 2.73828e7 9.96653e6i 0.0958748 0.0348956i
\(131\) 3.80884e8 + 6.71600e7i 1.29332 + 0.228048i 0.777628 0.628725i \(-0.216423\pi\)
0.515695 + 0.856772i \(0.327534\pi\)
\(132\) 4.44196e7 2.08444e8i 0.146312 0.686585i
\(133\) 5.25593e7 4.41025e7i 0.167974 0.140947i
\(134\) 8.99163e7i 0.278881i
\(135\) 2.42110e7 8.39391e7i 0.0728917 0.252714i
\(136\) 6.99976e7 0.204610
\(137\) 9.85818e7 + 1.17485e8i 0.279843 + 0.333504i 0.887597 0.460622i \(-0.152374\pi\)
−0.607753 + 0.794126i \(0.707929\pi\)
\(138\) 1.04525e8 1.15966e8i 0.288207 0.319752i
\(139\) 5.39538e7 3.05987e8i 0.144532 0.819680i −0.823210 0.567737i \(-0.807819\pi\)
0.967742 0.251943i \(-0.0810697\pi\)
\(140\) 8.64762e6 + 2.37591e7i 0.0225105 + 0.0618470i
\(141\) −1.90683e8 3.59072e8i −0.482430 0.908459i
\(142\) 5.10115e7 + 2.89301e8i 0.125463 + 0.711535i
\(143\) 2.78929e8 1.61040e8i 0.667037 0.385114i
\(144\) 1.03362e8 2.95222e7i 0.240387 0.0686592i
\(145\) −1.17250e7 + 2.03082e7i −0.0265240 + 0.0459409i
\(146\) −1.25538e8 + 3.44914e8i −0.276290 + 0.759100i
\(147\) 2.15332e8 + 2.75909e8i 0.461148 + 0.590876i
\(148\) −1.13534e8 9.52667e7i −0.236636 0.198561i
\(149\) 1.35261e8 1.61198e8i 0.274428 0.327050i −0.611174 0.791497i \(-0.709302\pi\)
0.885601 + 0.464447i \(0.153747\pi\)
\(150\) 4.62021e7 + 3.29990e8i 0.0912633 + 0.651833i
\(151\) 8.14285e8 + 2.96375e8i 1.56628 + 0.570078i 0.972164 0.234303i \(-0.0752809\pi\)
0.594113 + 0.804381i \(0.297503\pi\)
\(152\) −7.16092e7 4.13436e7i −0.134151 0.0774522i
\(153\) 3.15428e8 3.28210e7i 0.575618 0.0598944i
\(154\) 1.39729e8 + 2.42017e8i 0.248429 + 0.430292i
\(155\) −8.51409e6 + 1.50126e6i −0.0147507 + 0.00260094i
\(156\) 1.37721e8 + 8.61570e7i 0.232541 + 0.145476i
\(157\) −3.82829e8 + 1.39338e8i −0.630095 + 0.229336i −0.637272 0.770639i \(-0.719937\pi\)
0.00717787 + 0.999974i \(0.497715\pi\)
\(158\) −4.28566e8 7.55677e7i −0.687684 0.121257i
\(159\) −5.89801e8 + 1.91299e8i −0.922819 + 0.299311i
\(160\) 2.33422e7 1.95864e7i 0.0356174 0.0298865i
\(161\) 2.04711e8i 0.304676i
\(162\) 4.51934e8 1.81500e8i 0.656168 0.263522i
\(163\) 5.41974e8 0.767764 0.383882 0.923382i \(-0.374587\pi\)
0.383882 + 0.923382i \(0.374587\pi\)
\(164\) −5.68329e7 6.77309e7i −0.0785642 0.0936292i
\(165\) −8.44448e7 2.60355e8i −0.113930 0.351261i
\(166\) −1.73058e8 + 9.81458e8i −0.227907 + 1.29253i
\(167\) −7.66929e7 2.10712e8i −0.0986028 0.270909i 0.880577 0.473903i \(-0.157155\pi\)
−0.979180 + 0.202994i \(0.934933\pi\)
\(168\) −7.47555e7 + 1.19495e8i −0.0938439 + 0.150008i
\(169\) −9.90198e7 5.61569e8i −0.121388 0.688424i
\(170\) 7.78514e7 4.49475e7i 0.0932118 0.0538159i
\(171\) −3.42075e8 1.52729e8i −0.400071 0.178622i
\(172\) 1.28591e8 2.22726e8i 0.146925 0.254482i
\(173\) −4.92623e8 + 1.35347e9i −0.549959 + 1.51100i 0.283806 + 0.958882i \(0.408403\pi\)
−0.833765 + 0.552119i \(0.813819\pi\)
\(174\) −1.29465e8 + 1.81265e7i −0.141239 + 0.0197750i
\(175\) −3.34698e8 2.80845e8i −0.356862 0.299443i
\(176\) 2.16484e8 2.57996e8i 0.225619 0.268882i
\(177\) −1.28571e9 + 1.00343e9i −1.30993 + 1.02233i
\(178\) 8.69251e8 + 3.16381e8i 0.865895 + 0.315160i
\(179\) 8.54282e8 + 4.93220e8i 0.832126 + 0.480428i 0.854580 0.519319i \(-0.173815\pi\)
−0.0224537 + 0.999748i \(0.507148\pi\)
\(180\) 9.60023e7 9.92065e7i 0.0914516 0.0945039i
\(181\) 4.05549e8 + 7.02431e8i 0.377858 + 0.654469i 0.990750 0.135697i \(-0.0433274\pi\)
−0.612892 + 0.790166i \(0.709994\pi\)
\(182\) −2.09775e8 + 3.69889e7i −0.191191 + 0.0337121i
\(183\) −1.58315e8 + 8.40719e7i −0.141162 + 0.0749629i
\(184\) 2.31830e8 8.43793e7i 0.202255 0.0736147i
\(185\) −1.87447e8 3.30519e7i −0.160026 0.0282169i
\(186\) −3.58001e7 3.22683e7i −0.0299111 0.0269602i
\(187\) 7.61134e8 6.38667e8i 0.622436 0.522286i
\(188\) 6.42469e8i 0.514305i
\(189\) −2.80838e8 + 5.73530e8i −0.220094 + 0.449478i
\(190\) −1.06192e8 −0.0814848
\(191\) −1.00657e9 1.19958e9i −0.756327 0.901356i 0.241283 0.970455i \(-0.422432\pi\)
−0.997610 + 0.0690993i \(0.977987\pi\)
\(192\) 1.66139e8 + 3.54043e7i 0.122255 + 0.0260526i
\(193\) 2.98451e8 1.69260e9i 0.215102 1.21990i −0.665627 0.746284i \(-0.731836\pi\)
0.880729 0.473620i \(-0.157053\pi\)
\(194\) −1.52339e8 4.18547e8i −0.107548 0.295486i
\(195\) 2.08497e8 + 7.38948e6i 0.144199 + 0.00511064i
\(196\) 9.60400e7 + 5.44670e8i 0.0650770 + 0.369070i
\(197\) 3.80610e8 2.19745e8i 0.252706 0.145900i −0.368297 0.929708i \(-0.620059\pi\)
0.621003 + 0.783808i \(0.286726\pi\)
\(198\) 8.54564e8 1.26410e9i 0.556012 0.822474i
\(199\) 1.46631e9 2.53972e9i 0.935001 1.61947i 0.160370 0.987057i \(-0.448731\pi\)
0.774632 0.632413i \(-0.217935\pi\)
\(200\) −1.80092e8 + 4.94798e8i −0.112557 + 0.309249i
\(201\) −2.41464e8 + 5.96751e8i −0.147934 + 0.365602i
\(202\) −6.28167e8 5.27095e8i −0.377285 0.316580i
\(203\) 1.10184e8 1.31312e8i 0.0648834 0.0773251i
\(204\) 4.64556e8 + 1.87974e8i 0.268236 + 0.108537i
\(205\) −1.06702e8 3.88362e7i −0.0604165 0.0219898i
\(206\) −2.01833e9 1.16528e9i −1.12079 0.647087i
\(207\) 1.00512e9 4.88938e8i 0.547442 0.266301i
\(208\) 1.28356e8 + 2.22318e8i 0.0685743 + 0.118774i
\(209\) −1.15588e9 + 2.03813e8i −0.605799 + 0.106819i
\(210\) −6.41160e6 + 1.80906e8i −0.00329678 + 0.0930197i
\(211\) −7.05872e8 + 2.56916e8i −0.356120 + 0.129617i −0.513884 0.857860i \(-0.671794\pi\)
0.157764 + 0.987477i \(0.449571\pi\)
\(212\) −9.64944e8 1.70146e8i −0.477704 0.0842320i
\(213\) −4.38348e8 + 2.05700e9i −0.212961 + 0.999346i
\(214\) −1.90544e8 + 1.59885e8i −0.0908532 + 0.0762349i
\(215\) 3.30288e8i 0.154575i
\(216\) 7.65266e8 + 8.16406e7i 0.351558 + 0.0375052i
\(217\) 6.31969e7 0.0285008
\(218\) −1.67317e9 1.99401e9i −0.740823 0.882878i
\(219\) −1.75941e9 + 1.95198e9i −0.764874 + 0.848591i
\(220\) 7.51072e7 4.25954e8i 0.0320620 0.181833i
\(221\) 2.59027e8 + 7.11670e8i 0.108586 + 0.298339i
\(222\) −4.97666e8 9.37149e8i −0.204892 0.385831i
\(223\) 4.71306e8 + 2.67291e9i 0.190583 + 1.08085i 0.918570 + 0.395257i \(0.129345\pi\)
−0.727988 + 0.685590i \(0.759544\pi\)
\(224\) −1.92898e8 + 1.11370e8i −0.0766188 + 0.0442359i
\(225\) −5.79536e8 + 2.31413e9i −0.226126 + 0.902938i
\(226\) 2.85101e8 4.93809e8i 0.109286 0.189289i
\(227\) 1.18132e8 3.24565e8i 0.0444902 0.122236i −0.915458 0.402414i \(-0.868171\pi\)
0.959948 + 0.280178i \(0.0903935\pi\)
\(228\) −3.64226e8 4.66688e8i −0.134782 0.172698i
\(229\) −1.00726e9 8.45193e8i −0.366269 0.307336i 0.441014 0.897500i \(-0.354619\pi\)
−0.807284 + 0.590164i \(0.799063\pi\)
\(230\) 2.03659e8 2.42712e8i 0.0727768 0.0867320i
\(231\) 2.77422e8 + 1.98144e9i 0.0974300 + 0.695877i
\(232\) −1.94124e8 7.06554e7i −0.0670081 0.0243890i
\(233\) −3.40604e9 1.96648e9i −1.15565 0.667215i −0.205392 0.978680i \(-0.565847\pi\)
−0.950258 + 0.311465i \(0.899180\pi\)
\(234\) 6.82646e8 + 9.41641e8i 0.227684 + 0.314067i
\(235\) −4.12548e8 7.14554e8i −0.135271 0.234295i
\(236\) −2.53811e9 + 4.47537e8i −0.818205 + 0.144272i
\(237\) −2.64134e9 1.65241e9i −0.837205 0.523749i
\(238\) −6.17492e8 + 2.24749e8i −0.192452 + 0.0700470i
\(239\) 4.49635e9 + 7.92828e8i 1.37806 + 0.242989i 0.813098 0.582127i \(-0.197779\pi\)
0.564963 + 0.825116i \(0.308890\pi\)
\(240\) 2.07514e8 6.73060e7i 0.0625464 0.0202866i
\(241\) 6.86412e7 5.75968e7i 0.0203478 0.0170738i −0.632557 0.774514i \(-0.717995\pi\)
0.652905 + 0.757440i \(0.273550\pi\)
\(242\) 2.35541e9i 0.686760i
\(243\) 3.48677e9 + 9.07045e6i 0.999997 + 0.00260138i
\(244\) −2.83264e8 −0.0799158
\(245\) 4.56564e8 + 5.44112e8i 0.126718 + 0.151016i
\(246\) −1.95299e8 6.02133e8i −0.0533284 0.164419i
\(247\) 1.55352e8 8.81047e8i 0.0417379 0.236707i
\(248\) −2.60490e7 7.15690e7i −0.00688627 0.0189199i
\(249\) −3.78418e9 + 6.04895e9i −0.984406 + 1.57356i
\(250\) 2.43579e8 + 1.38141e9i 0.0623563 + 0.353640i
\(251\) 3.33550e9 1.92575e9i 0.840362 0.485183i −0.0170249 0.999855i \(-0.505419\pi\)
0.857387 + 0.514672i \(0.172086\pi\)
\(252\) −8.17030e8 + 5.92309e8i −0.202598 + 0.146874i
\(253\) 1.75097e9 3.03276e9i 0.427362 0.740213i
\(254\) 7.40292e8 2.03394e9i 0.177856 0.488655i
\(255\) 6.37383e8 8.92402e7i 0.150744 0.0211057i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 1.63458e9 1.94802e9i 0.374693 0.446541i −0.545439 0.838150i \(-0.683637\pi\)
0.920132 + 0.391609i \(0.128082\pi\)
\(258\) 1.45154e9 1.13285e9i 0.327605 0.255678i
\(259\) 1.30744e9 + 4.75869e8i 0.290551 + 0.105752i
\(260\) 2.85514e8 + 1.64842e8i 0.0624791 + 0.0360723i
\(261\) −9.07903e8 2.27369e8i −0.195649 0.0489971i
\(262\) 2.18784e9 + 3.78945e9i 0.464313 + 0.804213i
\(263\) −3.70152e9 + 6.52678e8i −0.773673 + 0.136419i −0.546527 0.837441i \(-0.684050\pi\)
−0.227146 + 0.973861i \(0.572939\pi\)
\(264\) 2.12958e9 1.13090e9i 0.438408 0.232813i
\(265\) −1.18247e9 + 4.30383e8i −0.239776 + 0.0872713i
\(266\) 7.64455e8 + 1.34794e8i 0.152695 + 0.0269243i
\(267\) 4.91937e9 + 4.43405e9i 0.967975 + 0.872481i
\(268\) −7.79287e8 + 6.53899e8i −0.151063 + 0.126757i
\(269\) 7.72684e9i 1.47568i −0.674974 0.737841i \(-0.735845\pi\)
0.674974 0.737841i \(-0.264155\pi\)
\(270\) 9.03554e8 4.00599e8i 0.170020 0.0753799i
\(271\) 3.95510e9 0.733297 0.366648 0.930360i \(-0.380505\pi\)
0.366648 + 0.930360i \(0.380505\pi\)
\(272\) 5.09044e8 + 6.06656e8i 0.0929994 + 0.110832i
\(273\) −1.49155e9 3.17850e8i −0.268527 0.0572231i
\(274\) −3.01304e8 + 1.70878e9i −0.0534567 + 0.303168i
\(275\) 2.55633e9 + 7.02347e9i 0.446978 + 1.22806i
\(276\) 1.76519e9 + 6.25613e7i 0.304197 + 0.0107813i
\(277\) 5.07004e8 + 2.87536e9i 0.0861177 + 0.488398i 0.997110 + 0.0759739i \(0.0242066\pi\)
−0.910992 + 0.412424i \(0.864682\pi\)
\(278\) 3.04430e9 1.75763e9i 0.509693 0.294271i
\(279\) −1.50941e8 3.10295e8i −0.0249110 0.0512103i
\(280\) −1.43028e8 + 2.47731e8i −0.0232695 + 0.0403040i
\(281\) −3.32680e9 + 9.14031e9i −0.533583 + 1.46601i 0.321196 + 0.947013i \(0.395915\pi\)
−0.854778 + 0.518993i \(0.826307\pi\)
\(282\) 1.72531e9 4.26389e9i 0.272816 0.674233i
\(283\) −6.48646e8 5.44279e8i −0.101126 0.0848547i 0.590823 0.806801i \(-0.298803\pi\)
−0.691949 + 0.721947i \(0.743248\pi\)
\(284\) −2.13634e9 + 2.54599e9i −0.328395 + 0.391366i
\(285\) −7.04767e8 2.85171e8i −0.106823 0.0432241i
\(286\) 3.42416e9 + 1.24629e9i 0.511788 + 0.186276i
\(287\) 7.18829e8 + 4.15016e8i 0.105949 + 0.0611698i
\(288\) 1.00754e9 + 6.81123e8i 0.146452 + 0.0990047i
\(289\) −2.31971e9 4.01785e9i −0.332538 0.575973i
\(290\) −2.61275e8 + 4.60698e7i −0.0369407 + 0.00651365i
\(291\) 1.12948e8 3.18688e9i 0.0157510 0.444420i
\(292\) −3.90225e9 + 1.42030e9i −0.536765 + 0.195366i
\(293\) 7.33194e9 + 1.29282e9i 0.994829 + 0.175415i 0.647285 0.762248i \(-0.275904\pi\)
0.347544 + 0.937664i \(0.387016\pi\)
\(294\) −8.25282e8 + 3.87274e9i −0.110462 + 0.518357i
\(295\) −2.53551e9 + 2.12754e9i −0.334794 + 0.280925i
\(296\) 1.67679e9i 0.218430i
\(297\) 9.06618e9 6.09465e9i 1.16520 0.783291i
\(298\) 2.38073e9 0.301888
\(299\) 1.71578e9 + 2.04479e9i 0.214673 + 0.255837i
\(300\) −2.52397e9 + 2.80022e9i −0.311601 + 0.345706i
\(301\) −4.19249e8 + 2.37768e9i −0.0510748 + 0.289659i
\(302\) 3.35310e9 + 9.21258e9i 0.403106 + 1.10752i
\(303\) −2.75350e9 5.18509e9i −0.326674 0.615157i
\(304\) −1.62448e8 9.21286e8i −0.0190204 0.107870i
\(305\) −3.15047e8 + 1.81892e8i −0.0364062 + 0.0210191i
\(306\) 2.57834e9 + 2.49507e9i 0.294073 + 0.284575i
\(307\) 7.60096e9 1.31652e10i 0.855687 1.48209i −0.0203192 0.999794i \(-0.506468\pi\)
0.876006 0.482300i \(-0.160198\pi\)
\(308\) −1.08137e9 + 2.97103e9i −0.120163 + 0.330144i
\(309\) −1.02658e10 1.31538e10i −1.12606 1.44283i
\(310\) −7.49283e7 6.28723e7i −0.00811332 0.00680789i
\(311\) −3.17153e9 + 3.77968e9i −0.339021 + 0.404030i −0.908438 0.418019i \(-0.862725\pi\)
0.569417 + 0.822049i \(0.307169\pi\)
\(312\) 2.54841e8 + 1.82016e9i 0.0268937 + 0.192084i
\(313\) −5.86324e9 2.13404e9i −0.610886 0.222344i 0.0180048 0.999838i \(-0.494269\pi\)
−0.628891 + 0.777494i \(0.716491\pi\)
\(314\) −3.99167e9 2.30459e9i −0.410616 0.237069i
\(315\) −5.28362e8 + 1.18341e9i −0.0536648 + 0.120196i
\(316\) −2.46173e9 4.26384e9i −0.246884 0.427615i
\(317\) 2.43346e9 4.29085e8i 0.240983 0.0424919i −0.0518518 0.998655i \(-0.516512\pi\)
0.292835 + 0.956163i \(0.405401\pi\)
\(318\) −5.94716e9 3.72050e9i −0.581569 0.363826i
\(319\) −2.75552e9 + 1.00293e9i −0.266097 + 0.0968515i
\(320\) 3.39503e8 + 5.98636e7i 0.0323776 + 0.00570904i
\(321\) −1.69395e9 + 5.49424e8i −0.159544 + 0.0517473i
\(322\) −1.77419e9 + 1.48872e9i −0.165035 + 0.138481i
\(323\) 2.75989e9i 0.253560i
\(324\) 4.85963e9 + 2.59690e9i 0.440984 + 0.235654i
\(325\) −5.69707e9 −0.510644
\(326\) 3.94140e9 + 4.69718e9i 0.348964 + 0.415879i
\(327\) −5.74962e9 1.77269e10i −0.502861 1.55039i
\(328\) 1.73703e8 9.85120e8i 0.0150076 0.0851126i
\(329\) 2.06284e9 + 5.66761e9i 0.176069 + 0.483745i
\(330\) 1.64234e9 2.62525e9i 0.138486 0.221368i
\(331\) 3.98804e9 + 2.26173e10i 0.332237 + 1.88421i 0.452974 + 0.891524i \(0.350363\pi\)
−0.120737 + 0.992684i \(0.538526\pi\)
\(332\) −9.76463e9 + 5.63761e9i −0.803718 + 0.464027i
\(333\) −7.86226e8 7.55606e9i −0.0639397 0.614495i
\(334\) 1.26847e9 2.19705e9i 0.101928 0.176544i
\(335\) −4.46836e8 + 1.22767e9i −0.0354788 + 0.0974771i
\(336\) −1.57929e9 + 2.21117e8i −0.123909 + 0.0173486i
\(337\) −9.34844e9 7.84427e9i −0.724802 0.608181i 0.203907 0.978990i \(-0.434636\pi\)
−0.928709 + 0.370809i \(0.879080\pi\)
\(338\) 4.14691e9 4.94209e9i 0.317729 0.378655i
\(339\) 3.21823e9 2.51166e9i 0.243679 0.190179i
\(340\) 9.55711e8 + 3.47850e8i 0.0715173 + 0.0260302i
\(341\) −9.36253e8 5.40546e8i −0.0692430 0.0399775i
\(342\) −1.16401e9 4.07539e9i −0.0850850 0.297896i
\(343\) −6.05965e9 1.04956e10i −0.437795 0.758283i
\(344\) 2.86547e9 5.05260e8i 0.204627 0.0360813i
\(345\) 2.00342e9 1.06390e9i 0.141415 0.0750973i
\(346\) −1.53128e10 + 5.57340e9i −1.06844 + 0.388880i
\(347\) 1.59239e10 + 2.80781e9i 1.09833 + 0.193665i 0.693306 0.720643i \(-0.256153\pi\)
0.405020 + 0.914308i \(0.367264\pi\)
\(348\) −1.09861e9 9.90228e8i −0.0749077 0.0675178i
\(349\) −1.98769e10 + 1.66787e10i −1.33982 + 1.12424i −0.358146 + 0.933666i \(0.616591\pi\)
−0.981673 + 0.190575i \(0.938965\pi\)
\(350\) 4.94315e9i 0.329406i
\(351\) 2.00183e9 + 8.08262e9i 0.131886 + 0.532505i
\(352\) 3.81034e9 0.248195
\(353\) −1.67764e10 1.99934e10i −1.08044 1.28762i −0.955351 0.295474i \(-0.904522\pi\)
−0.125090 0.992145i \(-0.539922\pi\)
\(354\) −1.80466e10 3.84573e9i −1.14916 0.244887i
\(355\) −7.41184e8 + 4.20346e9i −0.0466673 + 0.264663i
\(356\) 3.57945e9 + 9.83445e9i 0.222852 + 0.612280i
\(357\) −4.70168e9 1.66635e8i −0.289454 0.0102587i
\(358\) 1.93797e9 + 1.09907e10i 0.117982 + 0.669106i
\(359\) −3.47299e9 + 2.00513e9i −0.209086 + 0.120716i −0.600887 0.799334i \(-0.705186\pi\)
0.391800 + 0.920050i \(0.371852\pi\)
\(360\) 1.55796e9 + 1.10572e8i 0.0927570 + 0.00658320i
\(361\) 6.86167e9 1.18848e10i 0.404018 0.699781i
\(362\) −3.13855e9 + 8.62311e9i −0.182766 + 0.502145i
\(363\) 6.32529e9 1.56322e10i 0.364296 0.900314i
\(364\) −1.84612e9 1.54908e9i −0.105161 0.0882406i
\(365\) −3.42807e9 + 4.08542e9i −0.193143 + 0.230179i
\(366\) −1.87995e9 7.60687e8i −0.104766 0.0423918i
\(367\) −1.90736e9 6.94222e8i −0.105140 0.0382678i 0.288914 0.957355i \(-0.406706\pi\)
−0.394055 + 0.919087i \(0.628928\pi\)
\(368\) 2.41724e9 + 1.39559e9i 0.131804 + 0.0760971i
\(369\) 3.20843e8 4.52066e9i 0.0173056 0.243835i
\(370\) −1.07672e9 1.86493e9i −0.0574506 0.0995074i
\(371\) 9.05866e9 1.59729e9i 0.478155 0.0843116i
\(372\) 1.93135e7 5.44937e8i 0.00100853 0.0284561i
\(373\) −2.03253e10 + 7.39780e9i −1.05003 + 0.382179i −0.808674 0.588257i \(-0.799814\pi\)
−0.241355 + 0.970437i \(0.577592\pi\)
\(374\) 1.10704e10 + 1.95201e9i 0.565818 + 0.0997691i
\(375\) −2.09310e9 + 9.82215e9i −0.105844 + 0.496685i
\(376\) 5.56815e9 4.67223e9i 0.278586 0.233762i
\(377\) 2.23513e9i 0.110646i
\(378\) −7.01301e9 + 1.73692e9i −0.343509 + 0.0850770i
\(379\) 1.49378e10 0.723988 0.361994 0.932180i \(-0.382096\pi\)
0.361994 + 0.932180i \(0.382096\pi\)
\(380\) −7.72260e8 9.20343e8i −0.0370364 0.0441383i
\(381\) 1.03751e10 1.15107e10i 0.492372 0.546263i
\(382\) 3.07646e9 1.74475e10i 0.144477 0.819367i
\(383\) 4.58187e8 + 1.25886e9i 0.0212935 + 0.0585035i 0.949884 0.312603i \(-0.101201\pi\)
−0.928590 + 0.371106i \(0.878979\pi\)
\(384\) 9.01372e8 + 1.69736e9i 0.0414552 + 0.0780639i
\(385\) 7.05089e8 + 3.99876e9i 0.0320923 + 0.182005i
\(386\) 1.68399e10 9.72251e9i 0.758560 0.437955i
\(387\) 1.26757e10 3.62042e9i 0.565103 0.161404i
\(388\) 2.51961e9 4.36409e9i 0.111175 0.192560i
\(389\) −9.48685e9 + 2.60649e10i −0.414308 + 1.13830i 0.540568 + 0.841300i \(0.318209\pi\)
−0.954877 + 0.297003i \(0.904013\pi\)
\(390\) 1.45221e9 + 1.86074e9i 0.0627728 + 0.0804317i
\(391\) 6.30800e9 + 5.29304e9i 0.269889 + 0.226463i
\(392\) −4.02211e9 + 4.79337e9i −0.170337 + 0.203000i
\(393\) 4.34380e9 + 3.10249e10i 0.182096 + 1.30059i
\(394\) 4.67241e9 + 1.70062e9i 0.193890 + 0.0705702i
\(395\) −5.47588e9 3.16150e9i −0.224940 0.129869i
\(396\) 1.71704e10 1.78662e9i 0.698232 0.0726526i
\(397\) 2.37511e9 + 4.11381e9i 0.0956141 + 0.165608i 0.909865 0.414905i \(-0.136185\pi\)
−0.814251 + 0.580513i \(0.802852\pi\)
\(398\) 3.26746e10 5.76142e9i 1.30220 0.229614i
\(399\) 4.71150e9 + 2.94748e9i 0.185895 + 0.116295i
\(400\) −5.59800e9 + 2.03750e9i −0.218672 + 0.0795900i
\(401\) 1.10159e10 + 1.94239e9i 0.426031 + 0.0751207i 0.382553 0.923934i \(-0.375045\pi\)
0.0434779 + 0.999054i \(0.486156\pi\)
\(402\) −6.92792e9 + 2.24703e9i −0.265277 + 0.0860410i
\(403\) 6.31252e8 5.29683e8i 0.0239322 0.0200815i
\(404\) 9.27740e9i 0.348258i
\(405\) 7.07243e9 2.32239e8i 0.262875 0.00863209i
\(406\) 1.93935e9 0.0713759
\(407\) −1.52993e10 1.82329e10i −0.557561 0.664476i
\(408\) 1.74926e9 + 5.39322e9i 0.0631268 + 0.194629i
\(409\) −6.92317e9 + 3.92632e10i −0.247407 + 1.40311i 0.567429 + 0.823422i \(0.307938\pi\)
−0.814836 + 0.579691i \(0.803173\pi\)
\(410\) −4.39382e8 1.20719e9i −0.0155491 0.0427209i
\(411\) −6.58848e9 + 1.05316e10i −0.230897 + 0.369085i
\(412\) −4.57864e9 2.59668e10i −0.158909 0.901216i
\(413\) 2.09532e10 1.20974e10i 0.720197 0.415806i
\(414\) 1.15471e10 + 5.15550e9i 0.393071 + 0.175497i
\(415\) −7.24016e9 + 1.25403e10i −0.244093 + 0.422782i
\(416\) −9.93347e8 + 2.72920e9i −0.0331687 + 0.0911301i
\(417\) 2.49242e10 3.48965e9i 0.824285 0.115408i
\(418\) −1.01723e10 8.53561e9i −0.333208 0.279595i
\(419\) 1.71314e10 2.04164e10i 0.555822 0.662403i −0.412834 0.910806i \(-0.635461\pi\)
0.968657 + 0.248403i \(0.0799056\pi\)
\(420\) −1.61450e9 + 1.26003e9i −0.0518849 + 0.0404935i
\(421\) 3.16228e10 + 1.15098e10i 1.00663 + 0.366385i 0.792139 0.610340i \(-0.208967\pi\)
0.214495 + 0.976725i \(0.431189\pi\)
\(422\) −7.35996e9 4.24928e9i −0.232074 0.133988i
\(423\) 2.29008e10 2.36651e10i 0.715302 0.739176i
\(424\) −5.54275e9 9.60033e9i −0.171499 0.297045i
\(425\) −1.73080e10 + 3.05187e9i −0.530507 + 0.0935426i
\(426\) −2.10154e10 + 1.11601e10i −0.638116 + 0.338866i
\(427\) 2.49885e9 9.09506e8i 0.0751672 0.0273586i
\(428\) −2.77139e9 4.88671e8i −0.0825891 0.0145627i
\(429\) 1.93784e10 + 1.74667e10i 0.572123 + 0.515681i
\(430\) 2.86254e9 2.40196e9i 0.0837294 0.0702573i
\(431\) 1.93140e10i 0.559709i −0.960042 0.279855i \(-0.909714\pi\)
0.960042 0.279855i \(-0.0902863\pi\)
\(432\) 4.85769e9 + 7.22613e9i 0.139475 + 0.207477i
\(433\) 2.04852e10 0.582759 0.291380 0.956607i \(-0.405886\pi\)
0.291380 + 0.956607i \(0.405886\pi\)
\(434\) 4.59588e8 + 5.47716e8i 0.0129542 + 0.0154382i
\(435\) −1.85773e9 3.95883e8i −0.0518830 0.0110563i
\(436\) 5.11385e9 2.90021e10i 0.141515 0.802571i
\(437\) −3.32693e9 9.14067e9i −0.0912259 0.250641i
\(438\) −2.97124e10 1.05306e9i −0.807311 0.0286125i
\(439\) 4.30405e9 + 2.44095e10i 0.115883 + 0.657205i 0.986309 + 0.164906i \(0.0527321\pi\)
−0.870426 + 0.492299i \(0.836157\pi\)
\(440\) 4.23786e9 2.44673e9i 0.113067 0.0652793i
\(441\) −1.58772e10 + 2.34861e10i −0.419777 + 0.620950i
\(442\) −4.28418e9 + 7.42042e9i −0.112248 + 0.194419i
\(443\) −2.16534e10 + 5.94923e10i −0.562227 + 1.54471i 0.254137 + 0.967168i \(0.418209\pi\)
−0.816364 + 0.577538i \(0.804014\pi\)
\(444\) 4.50291e9 1.11284e10i 0.115867 0.286353i
\(445\) 1.02961e10 + 8.63942e9i 0.262561 + 0.220315i
\(446\) −1.97381e10 + 2.35229e10i −0.498845 + 0.594500i
\(447\) 1.58003e10 + 6.39329e9i 0.395763 + 0.160138i
\(448\) −2.36803e9 8.61894e8i −0.0587863 0.0213964i
\(449\) −8.94403e7 5.16384e7i −0.00220063 0.00127054i 0.498899 0.866660i \(-0.333738\pi\)
−0.501100 + 0.865389i \(0.667071\pi\)
\(450\) −2.42707e10 + 1.18064e10i −0.591878 + 0.287916i
\(451\) −7.09956e9 1.22968e10i −0.171603 0.297225i
\(452\) 6.35308e9 1.12022e9i 0.152206 0.0268380i
\(453\) −2.48609e9 + 7.01460e10i −0.0590370 + 1.66575i
\(454\) 3.67203e9 1.33651e9i 0.0864337 0.0314593i
\(455\) −3.04797e9 5.37440e8i −0.0711157 0.0125396i
\(456\) 1.39593e9 6.55058e9i 0.0322853 0.151503i
\(457\) −1.19344e10 + 1.00142e10i −0.273613 + 0.229588i −0.769261 0.638935i \(-0.779375\pi\)
0.495648 + 0.868524i \(0.334931\pi\)
\(458\) 1.48762e10i 0.338089i
\(459\) 1.04114e10 + 2.34831e10i 0.234563 + 0.529059i
\(460\) 3.58461e9 0.0800591
\(461\) −4.01010e10 4.77905e10i −0.887874 1.05813i −0.997937 0.0642027i \(-0.979550\pi\)
0.110063 0.993925i \(-0.464895\pi\)
\(462\) −1.51552e10 + 1.68140e10i −0.332656 + 0.369065i
\(463\) 9.35146e9 5.30348e10i 0.203496 1.15408i −0.696293 0.717757i \(-0.745169\pi\)
0.899789 0.436325i \(-0.143720\pi\)
\(464\) −7.99374e8 2.19626e9i −0.0172456 0.0473819i
\(465\) −3.28440e8 6.18481e8i −0.00702496 0.0132286i
\(466\) −7.72671e9 4.38203e10i −0.163852 0.929249i
\(467\) −5.47144e10 + 3.15893e10i −1.15036 + 0.664161i −0.948975 0.315352i \(-0.897878\pi\)
−0.201385 + 0.979512i \(0.564544\pi\)
\(468\) −3.19660e9 + 1.27643e10i −0.0666354 + 0.266080i
\(469\) 4.77502e9 8.27058e9i 0.0986925 0.170940i
\(470\) 3.19272e9 8.77194e9i 0.0654289 0.179765i
\(471\) −2.03028e10 2.60143e10i −0.412546 0.528602i
\(472\) −2.23366e10 1.87426e10i −0.450038 0.377627i
\(473\) 2.65483e10 3.16390e10i 0.530386 0.632089i
\(474\) −4.88760e9 3.49088e10i −0.0968238 0.691547i
\(475\) 1.95090e10 + 7.10071e9i 0.383232 + 0.139485i
\(476\) −6.43845e9 3.71724e9i −0.125416 0.0724090i
\(477\) −2.94786e10 4.06627e10i −0.569420 0.785457i
\(478\) 2.58276e10 + 4.47347e10i 0.494734 + 0.856905i
\(479\) −7.87848e10 + 1.38919e10i −1.49658 + 0.263888i −0.861182 0.508296i \(-0.830276\pi\)
−0.635399 + 0.772184i \(0.719164\pi\)
\(480\) 2.09243e9 + 1.30901e9i 0.0394173 + 0.0246592i
\(481\) 1.70480e10 6.20498e9i 0.318489 0.115920i
\(482\) 9.98360e8 + 1.76038e8i 0.0184969 + 0.00326150i
\(483\) −1.57727e10 + 5.11579e9i −0.289813 + 0.0939992i
\(484\) 2.04139e10 1.71293e10i 0.372001 0.312146i
\(485\) 6.47167e9i 0.116963i
\(486\) 2.52783e10 + 3.02851e10i 0.453109 + 0.542856i
\(487\) −2.08030e10 −0.369837 −0.184918 0.982754i \(-0.559202\pi\)
−0.184918 + 0.982754i \(0.559202\pi\)
\(488\) −2.05999e9 2.45500e9i −0.0363233 0.0432884i
\(489\) 1.35441e10 + 4.17583e10i 0.236872 + 0.730310i
\(490\) −1.39544e9 + 7.91391e9i −0.0242061 + 0.137280i
\(491\) −2.25741e10 6.20218e10i −0.388404 1.06713i −0.967720 0.252029i \(-0.918902\pi\)
0.579315 0.815104i \(-0.303320\pi\)
\(492\) 3.79830e9 6.07151e9i 0.0648229 0.103618i
\(493\) −1.19734e9 6.79044e9i −0.0202689 0.114950i
\(494\) 8.76564e9 5.06084e9i 0.147189 0.0849797i
\(495\) 1.79497e10 1.30127e10i 0.298976 0.216744i
\(496\) 4.30838e8 7.46233e8i 0.00711848 0.0123296i
\(497\) 1.06713e10 2.93191e10i 0.174901 0.480535i
\(498\) −7.99447e10 + 1.11931e10i −1.29979 + 0.181984i
\(499\) 7.65321e10 + 6.42181e10i 1.23436 + 1.03575i 0.997944 + 0.0640979i \(0.0204170\pi\)
0.236415 + 0.971652i \(0.424027\pi\)
\(500\) −1.02010e10 + 1.21571e10i −0.163216 + 0.194513i
\(501\) 1.43185e10 1.11748e10i 0.227272 0.177374i
\(502\) 4.09470e10 + 1.49035e10i 0.644773 + 0.234678i
\(503\) 1.60623e10 + 9.27356e9i 0.250920 + 0.144869i 0.620185 0.784455i \(-0.287057\pi\)
−0.369265 + 0.929324i \(0.620391\pi\)
\(504\) −1.10751e10 2.77358e9i −0.171643 0.0429852i
\(505\) −5.95729e9 1.03183e10i −0.0915975 0.158651i
\(506\) 3.90180e10 6.87992e9i 0.595199 0.104950i
\(507\) 4.07936e10 2.16631e10i 0.617390 0.327860i
\(508\) 2.30114e10 8.37545e9i 0.345531 0.125763i
\(509\) −9.18979e10 1.62041e10i −1.36910 0.241409i −0.559712 0.828687i \(-0.689088\pi\)
−0.809385 + 0.587278i \(0.800200\pi\)
\(510\) 5.40867e9 + 4.87509e9i 0.0799485 + 0.0720613i
\(511\) 2.98639e10 2.50588e10i 0.437988 0.367516i
\(512\) 3.03700e9i 0.0441942i
\(513\) 3.21895e9 3.01732e10i 0.0464777 0.435664i
\(514\) 2.87703e10 0.412185
\(515\) −2.17664e10 2.59402e10i −0.309427 0.368760i
\(516\) 2.03742e10 + 4.34176e9i 0.287397 + 0.0612445i
\(517\) 1.79164e10 1.01609e11i 0.250778 1.42223i
\(518\) 5.38385e9 + 1.47920e10i 0.0747780 + 0.205451i
\(519\) −1.16594e11 4.13228e9i −1.60696 0.0569536i
\(520\) 6.47698e8 + 3.67328e9i 0.00885848 + 0.0502389i
\(521\) 5.92996e10 3.42366e10i 0.804824 0.464665i −0.0403314 0.999186i \(-0.512841\pi\)
0.845155 + 0.534521i \(0.179508\pi\)
\(522\) −4.63199e9 9.52212e9i −0.0623858 0.128248i
\(523\) −1.94700e10 + 3.37230e10i −0.260231 + 0.450733i −0.966303 0.257407i \(-0.917132\pi\)
0.706072 + 0.708140i \(0.250465\pi\)
\(524\) −1.69318e10 + 4.65197e10i −0.224583 + 0.617037i
\(525\) 1.32745e10 3.28064e10i 0.174735 0.431838i
\(526\) −3.25753e10 2.73339e10i −0.425544 0.357074i
\(527\) 1.63403e9 1.94736e9i 0.0211845 0.0252466i
\(528\) 2.52882e10 + 1.02324e10i 0.325374 + 0.131657i
\(529\) −4.63158e10 1.68576e10i −0.591434 0.215264i
\(530\) −1.23293e10 7.11833e9i −0.156256 0.0902142i
\(531\) −1.09443e11 7.39860e10i −1.37661 0.930618i
\(532\) 4.39112e9 + 7.60564e9i 0.0548187 + 0.0949488i
\(533\) 1.06586e10 1.87939e9i 0.132066 0.0232867i
\(534\) −2.65391e9 + 7.48810e10i −0.0326378 + 0.920888i
\(535\) −3.39614e9 + 1.23609e9i −0.0414543 + 0.0150881i
\(536\) −1.13344e10 1.99857e9i −0.137322 0.0242136i
\(537\) −1.66532e10 + 7.81470e10i −0.200262 + 0.939756i
\(538\) 6.69670e10 5.61920e10i 0.799341 0.670727i
\(539\) 8.88200e10i 1.05234i
\(540\) 1.00428e10 + 4.91764e9i 0.118109 + 0.0578338i
\(541\) 4.75003e10 0.554507 0.277254 0.960797i \(-0.410576\pi\)
0.277254 + 0.960797i \(0.410576\pi\)
\(542\) 2.87627e10 + 3.42780e10i 0.333298 + 0.397209i
\(543\) −4.39865e10 + 4.88009e10i −0.505965 + 0.561343i
\(544\) −1.55583e9 + 8.82358e9i −0.0177651 + 0.100751i
\(545\) −1.29355e10 3.55399e10i −0.146621 0.402838i
\(546\) −8.09228e9 1.52385e10i −0.0910543 0.171463i
\(547\) −3.70895e9 2.10345e10i −0.0414287 0.234954i 0.957061 0.289885i \(-0.0936171\pi\)
−0.998490 + 0.0549313i \(0.982506\pi\)
\(548\) −1.70008e10 + 9.81543e9i −0.188516 + 0.108840i
\(549\) −1.04340e10 1.00970e10i −0.114858 0.111148i
\(550\) −4.22806e10 + 7.32321e10i −0.462051 + 0.800296i
\(551\) −2.78582e9 + 7.65398e9i −0.0302237 + 0.0830388i
\(552\) 1.22948e10 + 1.57535e10i 0.132424 + 0.169676i
\(553\) 3.54068e10 + 2.97098e10i 0.378605 + 0.317687i
\(554\) −2.12331e10 + 2.53046e10i −0.225411 + 0.268634i
\(555\) −2.13775e9 1.52685e10i −0.0225312 0.160925i
\(556\) 3.73721e10 + 1.36023e10i 0.391065 + 0.142336i
\(557\) 1.16865e11 + 6.74719e10i 1.21412 + 0.700974i 0.963655 0.267150i \(-0.0860820\pi\)
0.250469 + 0.968125i \(0.419415\pi\)
\(558\) 1.59157e9 3.56474e9i 0.0164168 0.0367698i
\(559\) 1.57407e10 + 2.72637e10i 0.161205 + 0.279215i
\(560\) −3.18718e9 + 5.61985e8i −0.0324081 + 0.00571443i
\(561\) 6.82294e10 + 4.26838e10i 0.688842 + 0.430935i
\(562\) −1.03411e11 + 3.76385e10i −1.03662 + 0.377300i
\(563\) −1.10609e11 1.95033e10i −1.10092 0.194122i −0.406472 0.913663i \(-0.633241\pi\)
−0.694450 + 0.719541i \(0.744352\pi\)
\(564\) 4.95013e10 1.60555e10i 0.489215 0.158674i
\(565\) 6.34658e9 5.32541e9i 0.0622796 0.0522588i
\(566\) 9.57986e9i 0.0933455i
\(567\) −5.12079e10 7.30551e9i −0.495456 0.0706835i
\(568\) −3.76017e10 −0.361256
\(569\) 3.43285e10 + 4.09111e10i 0.327496 + 0.390294i 0.904519 0.426434i \(-0.140230\pi\)
−0.577023 + 0.816728i \(0.695786\pi\)
\(570\) −2.65376e9 8.18193e9i −0.0251399 0.0775097i
\(571\) 3.28001e9 1.86018e10i 0.0308553 0.174989i −0.965486 0.260456i \(-0.916127\pi\)
0.996341 + 0.0854668i \(0.0272382\pi\)
\(572\) 1.41002e10 + 3.87400e10i 0.131717 + 0.361889i
\(573\) 6.72716e10 1.07533e11i 0.624041 0.997520i
\(574\) 1.63068e9 + 9.24807e9i 0.0150218 + 0.0851929i
\(575\) −5.36447e10 + 3.09718e10i −0.490744 + 0.283331i
\(576\) 1.42401e9 + 1.36855e10i 0.0129367 + 0.124329i
\(577\) −4.71495e10 + 8.16654e10i −0.425377 + 0.736775i −0.996456 0.0841209i \(-0.973192\pi\)
0.571079 + 0.820895i \(0.306525\pi\)
\(578\) 1.79523e10 4.93235e10i 0.160845 0.441919i
\(579\) 1.37871e11 1.93034e10i 1.22676 0.171759i
\(580\) −2.29935e9 1.92938e9i −0.0203186 0.0170493i
\(581\) 6.80385e10 8.10852e10i 0.597105 0.711602i
\(582\) 2.84415e10 2.21971e10i 0.247891 0.193466i
\(583\) −1.47865e11 5.38184e10i −1.27994 0.465862i
\(584\) −4.06879e10 2.34912e10i −0.349795 0.201954i
\(585\) 4.64105e9 + 1.62491e10i 0.0396272 + 0.138741i
\(586\) 4.21156e10 + 7.29463e10i 0.357151 + 0.618604i
\(587\) 1.35705e11 2.39284e10i 1.14299 0.201540i 0.430078 0.902792i \(-0.358486\pi\)
0.712914 + 0.701251i \(0.247375\pi\)
\(588\) −3.95660e10 + 2.10112e10i −0.330988 + 0.175769i
\(589\) −2.82184e9 + 1.02707e9i −0.0234462 + 0.00853371i
\(590\) −3.68780e10 6.50259e9i −0.304340 0.0536634i
\(591\) 2.64426e10 + 2.38340e10i 0.216748 + 0.195365i
\(592\) 1.45324e10 1.21941e10i 0.118318 0.0992806i
\(593\) 1.85271e11i 1.49827i 0.662418 + 0.749134i \(0.269530\pi\)
−0.662418 + 0.749134i \(0.730470\pi\)
\(594\) 1.18753e11 + 3.42526e10i 0.953893 + 0.275136i
\(595\) −9.54780e9 −0.0761790
\(596\) 1.73134e10 + 2.06333e10i 0.137214 + 0.163525i
\(597\) 2.32325e11 + 4.95085e10i 1.82894 + 0.389747i
\(598\) −5.24408e9 + 2.97406e10i −0.0410076 + 0.232566i
\(599\) −1.46519e10 4.02556e10i −0.113811 0.312694i 0.869689 0.493600i \(-0.164319\pi\)
−0.983500 + 0.180906i \(0.942097\pi\)
\(600\) −4.26240e10 1.51067e9i −0.328889 0.0116564i
\(601\) −1.29415e10 7.33947e10i −0.0991940 0.562557i −0.993381 0.114864i \(-0.963357\pi\)
0.894187 0.447693i \(-0.147754\pi\)
\(602\) −2.36558e10 + 1.36577e10i −0.180116 + 0.103990i
\(603\) −5.20131e10 3.69150e9i −0.393408 0.0279212i
\(604\) −5.54588e10 + 9.60575e10i −0.416699 + 0.721744i
\(605\) 1.17051e10 3.21595e10i 0.0873683 0.240043i
\(606\) 2.49138e10 6.15716e10i 0.184735 0.456552i
\(607\) 1.81599e11 + 1.52380e11i 1.33770 + 1.12247i 0.982210 + 0.187787i \(0.0601315\pi\)
0.355493 + 0.934679i \(0.384313\pi\)
\(608\) 6.80324e9 8.10778e9i 0.0497853 0.0593318i
\(609\) 1.28709e10 + 5.20799e9i 0.0935709 + 0.0378617i
\(610\) −3.86754e9 1.40767e9i −0.0279329 0.0101667i
\(611\) 6.81079e10 + 3.93221e10i 0.488689 + 0.282145i
\(612\) −2.87374e9 + 4.04909e10i −0.0204853 + 0.288637i
\(613\) −1.24032e11 2.14830e11i −0.878401 1.52143i −0.853096 0.521755i \(-0.825278\pi\)
−0.0253051 0.999680i \(-0.508056\pi\)
\(614\) 1.69377e11 2.98658e10i 1.19174 0.210136i
\(615\) 3.25771e8 9.19174e9i 0.00227726 0.0642536i
\(616\) −3.36133e10 + 1.22343e10i −0.233447 + 0.0849679i
\(617\) 2.11361e11 + 3.72687e10i 1.45843 + 0.257160i 0.845922 0.533307i \(-0.179051\pi\)
0.612505 + 0.790467i \(0.290162\pi\)
\(618\) 3.93448e10 1.84630e11i 0.269732 1.26575i
\(619\) −6.25832e10 + 5.25135e10i −0.426280 + 0.357691i −0.830546 0.556950i \(-0.811971\pi\)
0.404266 + 0.914641i \(0.367527\pi\)
\(620\) 1.10662e9i 0.00748910i
\(621\) 6.27903e10 + 6.52247e10i 0.422208 + 0.438577i
\(622\) −5.58221e10 −0.372945
\(623\) −6.31530e10 7.52628e10i −0.419220 0.499607i
\(624\) −1.39217e10 + 1.54454e10i −0.0918233 + 0.101873i
\(625\) 2.11245e10 1.19803e11i 0.138441 0.785141i
\(626\) −2.41440e10 6.63350e10i −0.157221 0.431962i
\(627\) −4.45893e10 8.39657e10i −0.288510 0.543290i
\(628\) −9.05521e9 5.13547e10i −0.0582184 0.330173i
\(629\) 4.84689e10 2.79835e10i 0.309642 0.178772i
\(630\) −1.40988e10 + 4.02688e9i −0.0894991 + 0.0255627i
\(631\) 3.76596e10 6.52284e10i 0.237552 0.411452i −0.722459 0.691413i \(-0.756988\pi\)
0.960011 + 0.279961i \(0.0903217\pi\)
\(632\) 1.90514e10 5.23434e10i 0.119415 0.328090i
\(633\) −3.74350e10 4.79660e10i −0.233165 0.298757i
\(634\) 2.14157e10 + 1.79699e10i 0.132548 + 0.111221i
\(635\) 2.02151e10 2.40915e10i 0.124332 0.148173i
\(636\) −1.10047e10 7.85995e10i −0.0672592 0.480387i
\(637\) −6.36183e10 2.31552e10i −0.386389 0.140634i
\(638\) −2.87311e10 1.65879e10i −0.173408 0.100117i
\(639\) −1.69443e11 + 1.76310e10i −1.01630 + 0.105748i
\(640\) 1.95015e9 + 3.37776e9i 0.0116238 + 0.0201330i
\(641\) 2.97266e11 5.24160e10i 1.76081 0.310479i 0.802597 0.596522i \(-0.203451\pi\)
0.958217 + 0.286043i \(0.0923400\pi\)
\(642\) −1.70807e10 1.06856e10i −0.100546 0.0629010i
\(643\) −1.11349e11 + 4.05279e10i −0.651394 + 0.237088i −0.646517 0.762900i \(-0.723775\pi\)
−0.00487779 + 0.999988i \(0.501553\pi\)
\(644\) −2.58049e10 4.55011e9i −0.150024 0.0264532i
\(645\) 2.54482e10 8.25400e9i 0.147034 0.0476898i
\(646\) 2.39194e10 2.00708e10i 0.137347 0.115248i
\(647\) 2.81950e11i 1.60900i 0.593955 + 0.804499i \(0.297566\pi\)
−0.593955 + 0.804499i \(0.702434\pi\)
\(648\) 1.28339e10 + 6.10029e10i 0.0727880 + 0.345980i
\(649\) −4.13892e11 −2.33297
\(650\) −4.14309e10 4.93754e10i −0.232098 0.276603i
\(651\) 1.57931e9 + 4.86924e9i 0.00879313 + 0.0271105i
\(652\) −1.20464e10 + 6.83187e10i −0.0666604 + 0.378050i
\(653\) −2.57428e10 7.07278e10i −0.141580 0.388989i 0.848554 0.529108i \(-0.177474\pi\)
−0.990135 + 0.140120i \(0.955251\pi\)
\(654\) 1.11822e11 1.78746e11i 0.611249 0.977071i
\(655\) 1.10401e10 + 6.26116e10i 0.0599803 + 0.340165i
\(656\) 9.80106e9 5.65865e9i 0.0529246 0.0305561i
\(657\) −1.94365e11 8.67794e10i −1.04317 0.465753i
\(658\) −3.41184e10 + 5.90949e10i −0.182006 + 0.315243i
\(659\) −5.87850e10 + 1.61511e11i −0.311692 + 0.856366i 0.680624 + 0.732633i \(0.261709\pi\)
−0.992316 + 0.123733i \(0.960513\pi\)
\(660\) 3.46961e10 4.85782e9i 0.182854 0.0256015i
\(661\) 2.61437e11 + 2.19372e11i 1.36950 + 1.14915i 0.972919 + 0.231147i \(0.0742479\pi\)
0.396581 + 0.918000i \(0.370197\pi\)
\(662\) −1.67017e11 + 1.99044e11i −0.869621 + 1.03637i
\(663\) −4.83600e10 + 3.77425e10i −0.250284 + 0.195333i
\(664\) −1.19872e11 4.36297e10i −0.616657 0.224445i
\(665\) 9.76762e9 + 5.63934e9i 0.0499462 + 0.0288364i
\(666\) 5.97692e10 6.17641e10i 0.303795 0.313935i
\(667\) −1.21512e10 2.10464e10i −0.0613924 0.106335i
\(668\) 2.82660e10 4.98407e9i 0.141958 0.0250310i
\(669\) −1.94166e11 + 1.03110e11i −0.969322 + 0.514751i
\(670\) −1.38895e10 + 5.05537e9i −0.0689267 + 0.0250873i
\(671\) −4.47994e10 7.89934e9i −0.220995 0.0389673i
\(672\) −1.34015e10 1.20794e10i −0.0657166 0.0592334i
\(673\) −2.65403e11 + 2.22700e11i −1.29374 + 1.08557i −0.302545 + 0.953135i \(0.597836\pi\)
−0.991191 + 0.132438i \(0.957719\pi\)
\(674\) 1.38067e11i 0.669038i
\(675\) −1.92783e11 + 1.31784e10i −0.928655 + 0.0634815i
\(676\) 7.29897e10 0.349522
\(677\) −2.70334e10 3.22171e10i −0.128690 0.153367i 0.697851 0.716242i \(-0.254140\pi\)
−0.826542 + 0.562875i \(0.809695\pi\)
\(678\) 4.51720e10 + 9.62617e9i 0.213772 + 0.0455549i
\(679\) −8.21478e9 + 4.65883e10i −0.0386471 + 0.219178i
\(680\) 3.93548e9 + 1.08126e10i 0.0184061 + 0.0505704i
\(681\) 2.79594e10 + 9.90929e8i 0.129999 + 0.00460738i
\(682\) −2.12392e9 1.20453e10i −0.00981749 0.0556778i
\(683\) −1.38691e11 + 8.00730e10i −0.637330 + 0.367962i −0.783585 0.621284i \(-0.786611\pi\)
0.146256 + 0.989247i \(0.453278\pi\)
\(684\) 2.68556e10 3.97258e10i 0.122690 0.181488i
\(685\) −1.26056e10 + 2.18335e10i −0.0572532 + 0.0991655i
\(686\) 4.68958e10 1.28845e11i 0.211757 0.581797i
\(687\) 3.99492e10 9.87297e10i 0.179341 0.443222i
\(688\) 2.52176e10 + 2.11601e10i 0.112551 + 0.0944417i
\(689\) 7.70961e10 9.18796e10i 0.342102 0.407701i
\(690\) 2.37901e10 + 9.62623e9i 0.104954 + 0.0424678i
\(691\) −2.33564e11 8.50102e10i −1.02446 0.372871i −0.225488 0.974246i \(-0.572398\pi\)
−0.798967 + 0.601375i \(0.794620\pi\)
\(692\) −1.59663e11 9.21814e10i −0.696273 0.401993i
\(693\) −1.45734e11 + 7.08917e10i −0.631871 + 0.307371i
\(694\) 9.14688e10 + 1.58429e11i 0.394308 + 0.682961i
\(695\) 5.02998e10 8.86921e9i 0.215589 0.0380142i
\(696\) 5.92680e8 1.67227e10i 0.00252571 0.0712638i
\(697\) 3.13745e10 1.14194e10i 0.132937 0.0483851i
\(698\) −2.89101e11 5.09764e10i −1.21795 0.214757i
\(699\) 6.63965e10 3.11574e11i 0.278123 1.30512i
\(700\) 4.28413e10 3.59481e10i 0.178431 0.149722i
\(701\) 2.89329e10i 0.119817i 0.998204 + 0.0599087i \(0.0190810\pi\)
−0.998204 + 0.0599087i \(0.980919\pi\)
\(702\) −5.54926e10 + 7.61288e10i −0.228500 + 0.313473i
\(703\) −6.61130e10 −0.270686
\(704\) 2.77100e10 + 3.30235e10i 0.112809 + 0.134441i
\(705\) 4.47457e10 4.96432e10i 0.181132 0.200957i
\(706\) 5.12752e10 2.90796e11i 0.206390 1.17050i
\(707\) 2.97879e10 + 8.18416e10i 0.119224 + 0.327564i
\(708\) −9.79101e10 1.84373e11i −0.389668 0.733779i
\(709\) −7.70118e10 4.36756e11i −0.304770 1.72844i −0.624584 0.780957i \(-0.714732\pi\)
0.319814 0.947480i \(-0.396380\pi\)
\(710\) −4.18207e10 + 2.41452e10i −0.164573 + 0.0950161i
\(711\) 6.13076e10 2.44806e11i 0.239903 0.957952i
\(712\) −5.92024e10 + 1.02542e11i −0.230366 + 0.399006i
\(713\) 3.06440e9 8.41936e9i 0.0118573 0.0325777i
\(714\) −3.27479e10 4.19603e10i −0.126006 0.161453i
\(715\) 4.05583e10 + 3.40325e10i 0.155187 + 0.130218i
\(716\) −8.11612e10 + 9.67241e10i −0.308813 + 0.368030i
\(717\) 5.12789e10 + 3.66251e11i 0.194027 + 1.38580i
\(718\) −4.26347e10 1.55178e10i −0.160423 0.0583891i
\(719\) 3.87178e11 + 2.23537e11i 1.44875 + 0.836439i 0.998407 0.0564146i \(-0.0179669\pi\)
0.450347 + 0.892854i \(0.351300\pi\)
\(720\) 1.03717e10 + 1.43067e10i 0.0385939 + 0.0532364i
\(721\) 1.23765e11 + 2.14368e11i 0.457992 + 0.793265i
\(722\) 1.52903e11 2.69610e10i 0.562688 0.0992171i
\(723\) 6.15312e9 + 3.84935e9i 0.0225186 + 0.0140875i
\(724\) −9.75593e10 + 3.55087e10i −0.355070 + 0.129235i
\(725\) 5.10807e10 + 9.00690e9i 0.184886 + 0.0326004i
\(726\) 1.81481e11 5.88623e10i 0.653258 0.211881i
\(727\) 3.89046e11 3.26448e11i 1.39272 1.16863i 0.428492 0.903545i \(-0.359045\pi\)
0.964225 0.265084i \(-0.0853996\pi\)
\(728\) 2.72654e10i 0.0970703i
\(729\) 8.64366e10 + 2.68878e11i 0.306047 + 0.952017i
\(730\) −6.03375e10 −0.212469
\(731\) 6.24261e10 + 7.43965e10i 0.218623 + 0.260545i
\(732\) −7.07886e9 2.18251e10i −0.0246558 0.0760172i
\(733\) 3.86826e9 2.19380e10i 0.0133998 0.0759942i −0.977375 0.211516i \(-0.932160\pi\)
0.990774 + 0.135522i \(0.0432711\pi\)
\(734\) −7.85422e9 2.15793e10i −0.0270595 0.0743452i
\(735\) −3.05134e10 + 4.87752e10i −0.104554 + 0.167128i
\(736\) 5.48358e9 + 3.10989e10i 0.0186876 + 0.105983i
\(737\) −1.41483e11 + 8.16850e10i −0.479549 + 0.276868i
\(738\) 4.15129e10 3.00950e10i 0.139945 0.101454i
\(739\) 2.43839e11 4.22341e11i 0.817569 1.41607i −0.0898991 0.995951i \(-0.528654\pi\)
0.907468 0.420121i \(-0.138012\pi\)
\(740\) 8.33275e9 2.28940e10i 0.0277883 0.0763476i
\(741\) 7.17658e10 1.00479e10i 0.238037 0.0333276i
\(742\) 7.97208e10 + 6.68937e10i 0.263000 + 0.220683i
\(743\) −2.62697e11 + 3.13071e11i −0.861986 + 1.02728i 0.137338 + 0.990524i \(0.456145\pi\)
−0.999324 + 0.0367512i \(0.988299\pi\)
\(744\) 4.86332e9 3.79557e9i 0.0158723 0.0123875i
\(745\) 3.25053e10 + 1.18310e10i 0.105519 + 0.0384056i
\(746\) −2.11927e11 1.22356e11i −0.684276 0.395067i
\(747\) −5.60630e11 1.40401e11i −1.80050 0.450907i
\(748\) 6.35897e10 + 1.10141e11i 0.203133 + 0.351837i
\(749\) 2.60172e10 4.58753e9i 0.0826671 0.0145764i
\(750\) −1.00348e11 + 5.32892e10i −0.317150 + 0.168420i
\(751\) 3.90539e11 1.42145e11i 1.22774 0.446859i 0.354914 0.934899i \(-0.384510\pi\)
0.872822 + 0.488039i \(0.162288\pi\)
\(752\) 8.09866e10 + 1.42801e10i 0.253246 + 0.0446540i
\(753\) 2.31732e11 + 2.08871e11i 0.720785 + 0.649677i
\(754\) 1.93714e10 1.62546e10i 0.0599345 0.0502910i
\(755\) 1.42447e11i 0.438395i