Properties

Label 43.8.c.a.6.18
Level $43$
Weight $8$
Character 43.6
Analytic conductor $13.433$
Analytic rank $0$
Dimension $50$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,8,Mod(6,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.6");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.4325560958\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(25\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.18
Character \(\chi\) \(=\) 43.6
Dual form 43.8.c.a.36.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+11.0451 q^{2} +(-18.5527 + 32.1342i) q^{3} -6.00588 q^{4} +(52.2320 - 90.4684i) q^{5} +(-204.916 + 354.925i) q^{6} +(-372.866 - 645.822i) q^{7} -1480.11 q^{8} +(405.097 + 701.648i) q^{9} +O(q^{10})\) \(q+11.0451 q^{2} +(-18.5527 + 32.1342i) q^{3} -6.00588 q^{4} +(52.2320 - 90.4684i) q^{5} +(-204.916 + 354.925i) q^{6} +(-372.866 - 645.822i) q^{7} -1480.11 q^{8} +(405.097 + 701.648i) q^{9} +(576.907 - 999.232i) q^{10} -2764.67 q^{11} +(111.425 - 192.994i) q^{12} +(-5341.64 - 9251.98i) q^{13} +(-4118.34 - 7133.17i) q^{14} +(1938.09 + 3356.86i) q^{15} -15579.2 q^{16} +(-14846.3 - 25714.5i) q^{17} +(4474.33 + 7749.77i) q^{18} +(16702.5 - 28929.5i) q^{19} +(-313.699 + 543.342i) q^{20} +27670.6 q^{21} -30536.0 q^{22} +(-51542.4 + 89274.0i) q^{23} +(27460.0 - 47562.0i) q^{24} +(33606.1 + 58207.5i) q^{25} +(-58998.9 - 102189. i) q^{26} -111212. q^{27} +(2239.39 + 3878.73i) q^{28} +(47771.6 + 82742.9i) q^{29} +(21406.3 + 37076.9i) q^{30} +(22861.2 - 39596.8i) q^{31} +17380.3 q^{32} +(51292.0 - 88840.3i) q^{33} +(-163979. - 284020. i) q^{34} -77902.0 q^{35} +(-2432.96 - 4214.01i) q^{36} +(-45598.3 + 78978.6i) q^{37} +(184480. - 319530. i) q^{38} +396406. q^{39} +(-77308.9 + 133903. i) q^{40} -824298. q^{41} +305625. q^{42} +(-59757.9 + 517926. i) q^{43} +16604.3 q^{44} +84636.0 q^{45} +(-569290. + 986040. i) q^{46} +1.28435e6 q^{47} +(289035. - 500624. i) q^{48} +(133714. - 231599. i) q^{49} +(371183. + 642908. i) q^{50} +1.10175e6 q^{51} +(32081.2 + 55566.3i) q^{52} +(152213. - 263641. i) q^{53} -1.22835e6 q^{54} +(-144404. + 250115. i) q^{55} +(551881. + 955887. i) q^{56} +(619751. + 1.07344e6i) q^{57} +(527642. + 913903. i) q^{58} -850229. q^{59} +(-11639.9 - 20160.9i) q^{60} +(41989.7 + 72728.3i) q^{61} +(252504. - 437350. i) q^{62} +(302093. - 523241. i) q^{63} +2.18610e6 q^{64} -1.11602e6 q^{65} +(566525. - 981250. i) q^{66} +(-602192. + 1.04303e6i) q^{67} +(89165.1 + 154438. i) q^{68} +(-1.91250e6 - 3.31254e6i) q^{69} -860435. q^{70} +(-2.89614e6 - 5.01625e6i) q^{71} +(-599587. - 1.03851e6i) q^{72} +(-1.71385e6 - 2.96848e6i) q^{73} +(-503638. + 872326. i) q^{74} -2.49394e6 q^{75} +(-100313. + 173747. i) q^{76} +(1.03085e6 + 1.78548e6i) q^{77} +4.37835e6 q^{78} +(-1.08113e6 - 1.87256e6i) q^{79} +(-813731. + 1.40942e6i) q^{80} +(1.17733e6 - 2.03920e6i) q^{81} -9.10445e6 q^{82} +(-1.63863e6 + 2.83820e6i) q^{83} -166186. q^{84} -3.10181e6 q^{85} +(-660032. + 5.72054e6i) q^{86} -3.54517e6 q^{87} +4.09201e6 q^{88} +(4.99320e6 - 8.64847e6i) q^{89} +934813. q^{90} +(-3.98343e6 + 6.89950e6i) q^{91} +(309557. - 536169. i) q^{92} +(848273. + 1.46925e6i) q^{93} +1.41858e7 q^{94} +(-1.74481e6 - 3.02209e6i) q^{95} +(-322451. + 558501. i) q^{96} +252617. q^{97} +(1.47688e6 - 2.55804e6i) q^{98} +(-1.11996e6 - 1.93982e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9} + 1667 q^{10} - 4594 q^{11} - 8448 q^{12} + 2972 q^{13} - 15928 q^{14} - 2485 q^{15} + 185846 q^{16} + 25298 q^{17} + 13249 q^{18} + 3269 q^{19} + 2705 q^{20} - 85260 q^{21} + 150968 q^{22} - 19120 q^{23} - 55070 q^{24} - 296876 q^{25} - 139545 q^{26} - 274154 q^{27} - 118970 q^{28} - 231057 q^{29} + 240447 q^{30} - 177637 q^{31} + 1254274 q^{32} - 344986 q^{33} + 104923 q^{34} - 518850 q^{35} + 816168 q^{36} + 885140 q^{37} + 200956 q^{38} - 59884 q^{39} + 160425 q^{40} + 2202852 q^{41} - 349786 q^{42} + 1009342 q^{43} - 1012518 q^{44} + 775768 q^{45} - 1277532 q^{46} - 2784982 q^{47} - 2238049 q^{48} - 1241240 q^{49} - 5126146 q^{50} - 2477574 q^{51} - 268404 q^{52} - 398258 q^{53} + 6491644 q^{54} - 2551752 q^{55} - 4471819 q^{56} + 2094777 q^{57} - 2294852 q^{58} + 5664766 q^{59} + 1374965 q^{60} + 2652290 q^{61} - 5621243 q^{62} - 3210173 q^{63} + 5395148 q^{64} + 22093214 q^{65} - 284525 q^{66} + 5696184 q^{67} + 2422800 q^{68} + 4199245 q^{69} - 8874170 q^{70} - 16652990 q^{71} + 5916954 q^{72} + 108058 q^{73} + 8260200 q^{74} - 3594466 q^{75} - 7386456 q^{76} - 8874183 q^{77} - 27627308 q^{78} - 7378370 q^{79} + 7523523 q^{80} - 14862361 q^{81} + 7898428 q^{82} + 18099816 q^{83} + 47917640 q^{84} + 5843026 q^{85} + 14578342 q^{86} - 24244628 q^{87} + 23110740 q^{88} - 20405960 q^{89} + 32640076 q^{90} + 10283016 q^{91} - 27186571 q^{92} - 19267997 q^{93} - 52636002 q^{94} + 1708621 q^{95} + 8113092 q^{96} + 53505940 q^{97} - 3752059 q^{98} + 10929650 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.0451 0.976258 0.488129 0.872772i \(-0.337680\pi\)
0.488129 + 0.872772i \(0.337680\pi\)
\(3\) −18.5527 + 32.1342i −0.396718 + 0.687136i −0.993319 0.115402i \(-0.963184\pi\)
0.596601 + 0.802538i \(0.296518\pi\)
\(4\) −6.00588 −0.0469209
\(5\) 52.2320 90.4684i 0.186871 0.323670i −0.757335 0.653027i \(-0.773499\pi\)
0.944205 + 0.329357i \(0.106832\pi\)
\(6\) −204.916 + 354.925i −0.387299 + 0.670822i
\(7\) −372.866 645.822i −0.410875 0.711656i 0.584111 0.811674i \(-0.301443\pi\)
−0.994986 + 0.100018i \(0.968110\pi\)
\(8\) −1480.11 −1.02206
\(9\) 405.097 + 701.648i 0.185229 + 0.320827i
\(10\) 576.907 999.232i 0.182434 0.315985i
\(11\) −2764.67 −0.626280 −0.313140 0.949707i \(-0.601381\pi\)
−0.313140 + 0.949707i \(0.601381\pi\)
\(12\) 111.425 192.994i 0.0186144 0.0322411i
\(13\) −5341.64 9251.98i −0.674330 1.16797i −0.976664 0.214772i \(-0.931099\pi\)
0.302334 0.953202i \(-0.402234\pi\)
\(14\) −4118.34 7133.17i −0.401119 0.694759i
\(15\) 1938.09 + 3356.86i 0.148270 + 0.256811i
\(16\) −15579.2 −0.950877
\(17\) −14846.3 25714.5i −0.732904 1.26943i −0.955637 0.294547i \(-0.904831\pi\)
0.222733 0.974879i \(-0.428502\pi\)
\(18\) 4474.33 + 7749.77i 0.180832 + 0.313210i
\(19\) 16702.5 28929.5i 0.558655 0.967618i −0.438955 0.898509i \(-0.644651\pi\)
0.997609 0.0691088i \(-0.0220156\pi\)
\(20\) −313.699 + 543.342i −0.00876815 + 0.0151869i
\(21\) 27670.6 0.652006
\(22\) −30536.0 −0.611411
\(23\) −51542.4 + 89274.0i −0.883318 + 1.52995i −0.0356880 + 0.999363i \(0.511362\pi\)
−0.847630 + 0.530588i \(0.821971\pi\)
\(24\) 27460.0 47562.0i 0.405472 0.702297i
\(25\) 33606.1 + 58207.5i 0.430159 + 0.745057i
\(26\) −58998.9 102189.i −0.658320 1.14024i
\(27\) −111212. −1.08737
\(28\) 2239.39 + 3878.73i 0.0192786 + 0.0333915i
\(29\) 47771.6 + 82742.9i 0.363728 + 0.629996i 0.988571 0.150755i \(-0.0481703\pi\)
−0.624843 + 0.780751i \(0.714837\pi\)
\(30\) 21406.3 + 37076.9i 0.144750 + 0.250714i
\(31\) 22861.2 39596.8i 0.137827 0.238723i −0.788847 0.614590i \(-0.789322\pi\)
0.926674 + 0.375867i \(0.122655\pi\)
\(32\) 17380.3 0.0937631
\(33\) 51292.0 88840.3i 0.248457 0.430340i
\(34\) −163979. 284020.i −0.715503 1.23929i
\(35\) −77902.0 −0.307122
\(36\) −2432.96 4214.01i −0.00869114 0.0150535i
\(37\) −45598.3 + 78978.6i −0.147993 + 0.256332i −0.930486 0.366328i \(-0.880615\pi\)
0.782492 + 0.622660i \(0.213948\pi\)
\(38\) 184480. 319530.i 0.545391 0.944645i
\(39\) 396406. 1.07008
\(40\) −77308.9 + 133903.i −0.190994 + 0.330811i
\(41\) −824298. −1.86784 −0.933922 0.357476i \(-0.883637\pi\)
−0.933922 + 0.357476i \(0.883637\pi\)
\(42\) 305625. 0.636525
\(43\) −59757.9 + 517926.i −0.114619 + 0.993410i
\(44\) 16604.3 0.0293856
\(45\) 84636.0 0.138456
\(46\) −569290. + 986040.i −0.862346 + 1.49363i
\(47\) 1.28435e6 1.80443 0.902216 0.431284i \(-0.141939\pi\)
0.902216 + 0.431284i \(0.141939\pi\)
\(48\) 289035. 500624.i 0.377230 0.653382i
\(49\) 133714. 231599.i 0.162364 0.281223i
\(50\) 371183. + 642908.i 0.419946 + 0.727367i
\(51\) 1.10175e6 1.16302
\(52\) 32081.2 + 55566.3i 0.0316402 + 0.0548024i
\(53\) 152213. 263641.i 0.140438 0.243247i −0.787223 0.616668i \(-0.788482\pi\)
0.927662 + 0.373421i \(0.121815\pi\)
\(54\) −1.22835e6 −1.06156
\(55\) −144404. + 250115.i −0.117033 + 0.202708i
\(56\) 551881. + 955887.i 0.419940 + 0.727358i
\(57\) 619751. + 1.07344e6i 0.443257 + 0.767743i
\(58\) 527642. + 913903.i 0.355093 + 0.615038i
\(59\) −850229. −0.538957 −0.269478 0.963006i \(-0.586851\pi\)
−0.269478 + 0.963006i \(0.586851\pi\)
\(60\) −11639.9 20160.9i −0.00695697 0.0120498i
\(61\) 41989.7 + 72728.3i 0.0236858 + 0.0410250i 0.877625 0.479347i \(-0.159127\pi\)
−0.853940 + 0.520372i \(0.825793\pi\)
\(62\) 252504. 437350.i 0.134554 0.233055i
\(63\) 302093. 523241.i 0.152212 0.263639i
\(64\) 2.18610e6 1.04241
\(65\) −1.11602e6 −0.504050
\(66\) 566525. 981250.i 0.242558 0.420122i
\(67\) −602192. + 1.04303e6i −0.244609 + 0.423676i −0.962022 0.272973i \(-0.911993\pi\)
0.717412 + 0.696649i \(0.245326\pi\)
\(68\) 89165.1 + 154438.i 0.0343885 + 0.0595627i
\(69\) −1.91250e6 3.31254e6i −0.700856 1.21392i
\(70\) −860435. −0.299830
\(71\) −2.89614e6 5.01625e6i −0.960317 1.66332i −0.721703 0.692203i \(-0.756640\pi\)
−0.238614 0.971114i \(-0.576693\pi\)
\(72\) −599587. 1.03851e6i −0.189316 0.327906i
\(73\) −1.71385e6 2.96848e6i −0.515636 0.893108i −0.999835 0.0181502i \(-0.994222\pi\)
0.484199 0.874958i \(-0.339111\pi\)
\(74\) −503638. + 872326.i −0.144480 + 0.250246i
\(75\) −2.49394e6 −0.682607
\(76\) −100313. + 173747.i −0.0262126 + 0.0454015i
\(77\) 1.03085e6 + 1.78548e6i 0.257323 + 0.445696i
\(78\) 4.37835e6 1.04467
\(79\) −1.08113e6 1.87256e6i −0.246707 0.427309i 0.715903 0.698200i \(-0.246015\pi\)
−0.962610 + 0.270891i \(0.912682\pi\)
\(80\) −813731. + 1.40942e6i −0.177691 + 0.307770i
\(81\) 1.17733e6 2.03920e6i 0.246151 0.426346i
\(82\) −9.10445e6 −1.82350
\(83\) −1.63863e6 + 2.83820e6i −0.314564 + 0.544840i −0.979345 0.202198i \(-0.935192\pi\)
0.664781 + 0.747038i \(0.268525\pi\)
\(84\) −166186. −0.0305927
\(85\) −3.10181e6 −0.547833
\(86\) −660032. + 5.72054e6i −0.111897 + 0.969824i
\(87\) −3.54517e6 −0.577191
\(88\) 4.09201e6 0.640099
\(89\) 4.99320e6 8.64847e6i 0.750782 1.30039i −0.196663 0.980471i \(-0.563010\pi\)
0.947444 0.319921i \(-0.103656\pi\)
\(90\) 934813. 0.135169
\(91\) −3.98343e6 + 6.89950e6i −0.554130 + 0.959782i
\(92\) 309557. 536169.i 0.0414461 0.0717867i
\(93\) 848273. + 1.46925e6i 0.109357 + 0.189411i
\(94\) 1.41858e7 1.76159
\(95\) −1.74481e6 3.02209e6i −0.208792 0.361639i
\(96\) −322451. + 558501.i −0.0371975 + 0.0644280i
\(97\) 252617. 0.0281036 0.0140518 0.999901i \(-0.495527\pi\)
0.0140518 + 0.999901i \(0.495527\pi\)
\(98\) 1.47688e6 2.55804e6i 0.158509 0.274546i
\(99\) −1.11996e6 1.93982e6i −0.116005 0.200927i
\(100\) −201834. 349588.i −0.0201834 0.0349588i
\(101\) −6.23389e6 1.07974e7i −0.602052 1.04279i −0.992510 0.122164i \(-0.961017\pi\)
0.390458 0.920621i \(-0.372317\pi\)
\(102\) 1.21690e7 1.13541
\(103\) 9.32383e6 + 1.61493e7i 0.840744 + 1.45621i 0.889266 + 0.457390i \(0.151216\pi\)
−0.0485221 + 0.998822i \(0.515451\pi\)
\(104\) 7.90620e6 + 1.36939e7i 0.689209 + 1.19374i
\(105\) 1.44529e6 2.50332e6i 0.121841 0.211034i
\(106\) 1.68121e6 2.91193e6i 0.137104 0.237471i
\(107\) −7.76267e6 −0.612587 −0.306294 0.951937i \(-0.599089\pi\)
−0.306294 + 0.951937i \(0.599089\pi\)
\(108\) 667925. 0.0510205
\(109\) −84719.8 + 146739.i −0.00626602 + 0.0108531i −0.869141 0.494564i \(-0.835328\pi\)
0.862875 + 0.505417i \(0.168661\pi\)
\(110\) −1.59496e6 + 2.76255e6i −0.114255 + 0.197895i
\(111\) −1.69194e6 2.93053e6i −0.117423 0.203383i
\(112\) 5.80894e6 + 1.00614e7i 0.390691 + 0.676697i
\(113\) −1.72759e6 −0.112633 −0.0563165 0.998413i \(-0.517936\pi\)
−0.0563165 + 0.998413i \(0.517936\pi\)
\(114\) 6.84521e6 + 1.18563e7i 0.432733 + 0.749515i
\(115\) 5.38432e6 + 9.32591e6i 0.330133 + 0.571806i
\(116\) −286911. 496944.i −0.0170665 0.0295600i
\(117\) 4.32776e6 7.49590e6i 0.249812 0.432686i
\(118\) −9.39086e6 −0.526161
\(119\) −1.10713e7 + 1.91761e7i −0.602263 + 1.04315i
\(120\) −2.86857e6 4.96852e6i −0.151542 0.262478i
\(121\) −1.18438e7 −0.607773
\(122\) 463780. + 803290.i 0.0231234 + 0.0400510i
\(123\) 1.52929e7 2.64881e7i 0.741008 1.28346i
\(124\) −137302. + 237814.i −0.00646696 + 0.0112011i
\(125\) 1.51825e7 0.695278
\(126\) 3.33665e6 5.77925e6i 0.148598 0.257380i
\(127\) −8.33152e6 −0.360920 −0.180460 0.983582i \(-0.557759\pi\)
−0.180460 + 0.983582i \(0.557759\pi\)
\(128\) 2.19210e7 0.923902
\(129\) −1.55345e7 1.15292e7i −0.637136 0.472862i
\(130\) −1.23265e7 −0.492083
\(131\) −1.07491e7 −0.417755 −0.208877 0.977942i \(-0.566981\pi\)
−0.208877 + 0.977942i \(0.566981\pi\)
\(132\) −308053. + 533564.i −0.0116578 + 0.0201919i
\(133\) −2.49111e7 −0.918148
\(134\) −6.65126e6 + 1.15203e7i −0.238802 + 0.413617i
\(135\) −5.80882e6 + 1.00612e7i −0.203198 + 0.351949i
\(136\) 2.19741e7 + 3.80603e7i 0.749075 + 1.29744i
\(137\) 2.64037e7 0.877290 0.438645 0.898661i \(-0.355459\pi\)
0.438645 + 0.898661i \(0.355459\pi\)
\(138\) −2.11237e7 3.65873e7i −0.684216 1.18510i
\(139\) 2.49981e7 4.32981e7i 0.789507 1.36747i −0.136762 0.990604i \(-0.543670\pi\)
0.926269 0.376862i \(-0.122997\pi\)
\(140\) 467870. 0.0144104
\(141\) −2.38281e7 + 4.12715e7i −0.715851 + 1.23989i
\(142\) −3.19881e7 5.54050e7i −0.937517 1.62383i
\(143\) 1.47679e7 + 2.55787e7i 0.422320 + 0.731479i
\(144\) −6.31107e6 1.09311e7i −0.176130 0.305067i
\(145\) 9.98083e6 0.271881
\(146\) −1.89297e7 3.27871e7i −0.503394 0.871904i
\(147\) 4.96150e6 + 8.59357e6i 0.128826 + 0.223133i
\(148\) 273858. 474336.i 0.00694399 0.0120273i
\(149\) 8.06615e6 1.39710e7i 0.199763 0.345999i −0.748689 0.662922i \(-0.769316\pi\)
0.948451 + 0.316923i \(0.102650\pi\)
\(150\) −2.75457e7 −0.666400
\(151\) 3.40064e7 0.803789 0.401894 0.915686i \(-0.368352\pi\)
0.401894 + 0.915686i \(0.368352\pi\)
\(152\) −2.47215e7 + 4.28188e7i −0.570981 + 0.988968i
\(153\) 1.20284e7 2.08338e7i 0.271511 0.470270i
\(154\) 1.13858e7 + 1.97208e7i 0.251213 + 0.435114i
\(155\) −2.38817e6 4.13644e6i −0.0515116 0.0892207i
\(156\) −2.38077e6 −0.0502090
\(157\) −9.84695e6 1.70554e7i −0.203073 0.351733i 0.746444 0.665448i \(-0.231760\pi\)
−0.949517 + 0.313715i \(0.898426\pi\)
\(158\) −1.19411e7 2.06827e7i −0.240850 0.417164i
\(159\) 5.64791e6 + 9.78247e6i 0.111429 + 0.193001i
\(160\) 907807. 1.57237e6i 0.0175216 0.0303483i
\(161\) 7.68735e7 1.45173
\(162\) 1.30037e7 2.25231e7i 0.240307 0.416223i
\(163\) −2.01087e7 3.48294e7i −0.363687 0.629925i 0.624877 0.780723i \(-0.285149\pi\)
−0.988565 + 0.150798i \(0.951816\pi\)
\(164\) 4.95063e6 0.0876410
\(165\) −5.35816e6 9.28061e6i −0.0928586 0.160836i
\(166\) −1.80989e7 + 3.13482e7i −0.307095 + 0.531905i
\(167\) −5.26506e7 + 9.11936e7i −0.874774 + 1.51515i −0.0177708 + 0.999842i \(0.505657\pi\)
−0.857003 + 0.515311i \(0.827676\pi\)
\(168\) −4.09555e7 −0.666392
\(169\) −2.56919e7 + 4.44997e7i −0.409442 + 0.709175i
\(170\) −3.42597e7 −0.534826
\(171\) 2.70645e7 0.413917
\(172\) 358899. 3.11060e6i 0.00537802 0.0466117i
\(173\) −8.17472e7 −1.20036 −0.600180 0.799865i \(-0.704904\pi\)
−0.600180 + 0.799865i \(0.704904\pi\)
\(174\) −3.91567e7 −0.563487
\(175\) 2.50612e7 4.34072e7i 0.353482 0.612250i
\(176\) 4.30713e7 0.595516
\(177\) 1.57740e7 2.73214e7i 0.213814 0.370336i
\(178\) 5.51503e7 9.55232e7i 0.732956 1.26952i
\(179\) 4.42662e7 + 7.66713e7i 0.576882 + 0.999188i 0.995834 + 0.0911802i \(0.0290639\pi\)
−0.418953 + 0.908008i \(0.637603\pi\)
\(180\) −508314. −0.00649648
\(181\) −4.45452e7 7.71546e7i −0.558375 0.967134i −0.997632 0.0687730i \(-0.978092\pi\)
0.439257 0.898361i \(-0.355242\pi\)
\(182\) −4.39973e7 + 7.62056e7i −0.540974 + 0.936994i
\(183\) −3.11608e6 −0.0375864
\(184\) 7.62883e7 1.32135e8i 0.902808 1.56371i
\(185\) 4.76338e6 + 8.25041e6i 0.0553113 + 0.0958020i
\(186\) 9.36926e6 + 1.62280e7i 0.106760 + 0.184914i
\(187\) 4.10451e7 + 7.10922e7i 0.459003 + 0.795017i
\(188\) −7.71365e6 −0.0846657
\(189\) 4.14671e7 + 7.18231e7i 0.446773 + 0.773834i
\(190\) −1.92716e7 3.33793e7i −0.203835 0.353053i
\(191\) −1.64668e7 + 2.85213e7i −0.170999 + 0.296178i −0.938769 0.344547i \(-0.888033\pi\)
0.767771 + 0.640725i \(0.221366\pi\)
\(192\) −4.05580e7 + 7.02486e7i −0.413545 + 0.716281i
\(193\) 7.67845e7 0.768817 0.384408 0.923163i \(-0.374405\pi\)
0.384408 + 0.923163i \(0.374405\pi\)
\(194\) 2.79018e6 0.0274364
\(195\) 2.07051e7 3.58623e7i 0.199966 0.346351i
\(196\) −803069. + 1.39096e6i −0.00761828 + 0.0131952i
\(197\) 3.68118e7 + 6.37598e7i 0.343048 + 0.594176i 0.984997 0.172571i \(-0.0552074\pi\)
−0.641949 + 0.766747i \(0.721874\pi\)
\(198\) −1.23700e7 2.14255e7i −0.113251 0.196157i
\(199\) 8.03131e7 0.722438 0.361219 0.932481i \(-0.382361\pi\)
0.361219 + 0.932481i \(0.382361\pi\)
\(200\) −4.97407e7 8.61534e7i −0.439650 0.761496i
\(201\) −2.23445e7 3.87019e7i −0.194082 0.336160i
\(202\) −6.88539e7 1.19258e8i −0.587758 1.01803i
\(203\) 3.56248e7 6.17040e7i 0.298893 0.517699i
\(204\) −6.61700e6 −0.0545702
\(205\) −4.30547e7 + 7.45729e7i −0.349046 + 0.604565i
\(206\) 1.02983e8 + 1.78371e8i 0.820783 + 1.42164i
\(207\) −8.35186e7 −0.654466
\(208\) 8.32183e7 + 1.44138e8i 0.641205 + 1.11060i
\(209\) −4.61768e7 + 7.99806e7i −0.349874 + 0.606000i
\(210\) 1.59634e7 2.76494e7i 0.118948 0.206024i
\(211\) 7.49453e7 0.549232 0.274616 0.961554i \(-0.411449\pi\)
0.274616 + 0.961554i \(0.411449\pi\)
\(212\) −914173. + 1.58339e6i −0.00658950 + 0.0114134i
\(213\) 2.14924e8 1.52390
\(214\) −8.57394e7 −0.598043
\(215\) 4.37347e7 + 3.24585e7i 0.300118 + 0.222738i
\(216\) 1.64606e8 1.11136
\(217\) −3.40967e7 −0.226518
\(218\) −935738. + 1.62075e6i −0.00611725 + 0.0105954i
\(219\) 1.27186e8 0.818249
\(220\) 867273. 1.50216e6i 0.00549132 0.00951124i
\(221\) −1.58607e8 + 2.74715e8i −0.988438 + 1.71203i
\(222\) −1.86876e7 3.23680e7i −0.114636 0.198555i
\(223\) 1.51700e8 0.916048 0.458024 0.888940i \(-0.348557\pi\)
0.458024 + 0.888940i \(0.348557\pi\)
\(224\) −6.48051e6 1.12246e7i −0.0385249 0.0667271i
\(225\) −2.72275e7 + 4.71594e7i −0.159356 + 0.276013i
\(226\) −1.90814e7 −0.109959
\(227\) −1.17782e8 + 2.04004e8i −0.668326 + 1.15757i 0.310046 + 0.950721i \(0.399655\pi\)
−0.978372 + 0.206853i \(0.933678\pi\)
\(228\) −3.72215e6 6.44696e6i −0.0207980 0.0360232i
\(229\) −1.58555e8 2.74625e8i −0.872479 1.51118i −0.859424 0.511263i \(-0.829178\pi\)
−0.0130546 0.999915i \(-0.504156\pi\)
\(230\) 5.94703e7 + 1.03006e8i 0.322294 + 0.558230i
\(231\) −7.65001e7 −0.408338
\(232\) −7.07072e7 1.22468e8i −0.371754 0.643897i
\(233\) −1.18058e8 2.04482e8i −0.611434 1.05903i −0.990999 0.133870i \(-0.957260\pi\)
0.379565 0.925165i \(-0.376074\pi\)
\(234\) 4.78005e7 8.27929e7i 0.243880 0.422413i
\(235\) 6.70841e7 1.16193e8i 0.337196 0.584040i
\(236\) 5.10637e6 0.0252883
\(237\) 8.02311e7 0.391493
\(238\) −1.22284e8 + 2.11802e8i −0.587964 + 1.01838i
\(239\) −4.19494e7 + 7.26585e7i −0.198762 + 0.344266i −0.948127 0.317891i \(-0.897025\pi\)
0.749365 + 0.662157i \(0.230359\pi\)
\(240\) −3.01938e7 5.22971e7i −0.140987 0.244196i
\(241\) −1.35866e8 2.35327e8i −0.625247 1.08296i −0.988493 0.151266i \(-0.951665\pi\)
0.363246 0.931693i \(-0.381668\pi\)
\(242\) −1.30816e8 −0.593343
\(243\) −7.79249e7 1.34970e8i −0.348381 0.603414i
\(244\) −252185. 436797.i −0.00111136 0.00192493i
\(245\) −1.39683e7 2.41938e7i −0.0606822 0.105105i
\(246\) 1.68912e8 2.92564e8i 0.723415 1.25299i
\(247\) −3.56874e8 −1.50687
\(248\) −3.38371e7 + 5.86075e7i −0.140868 + 0.243990i
\(249\) −6.08021e7 1.05312e8i −0.249586 0.432296i
\(250\) 1.67692e8 0.678770
\(251\) 2.78091e7 + 4.81667e7i 0.111001 + 0.192260i 0.916174 0.400780i \(-0.131261\pi\)
−0.805173 + 0.593040i \(0.797928\pi\)
\(252\) −1.81434e6 + 3.14252e6i −0.00714193 + 0.0123702i
\(253\) 1.42498e8 2.46813e8i 0.553204 0.958178i
\(254\) −9.20225e7 −0.352351
\(255\) 5.75468e7 9.96739e7i 0.217335 0.376436i
\(256\) −3.77012e7 −0.140448
\(257\) −1.22993e8 −0.451974 −0.225987 0.974130i \(-0.572561\pi\)
−0.225987 + 0.974130i \(0.572561\pi\)
\(258\) −1.71580e8 1.27341e8i −0.622009 0.461635i
\(259\) 6.80082e7 0.243227
\(260\) 6.70266e6 0.0236505
\(261\) −3.87043e7 + 6.70378e7i −0.134746 + 0.233388i
\(262\) −1.18725e8 −0.407836
\(263\) 8.00894e7 1.38719e8i 0.271475 0.470208i −0.697765 0.716327i \(-0.745822\pi\)
0.969240 + 0.246119i \(0.0791552\pi\)
\(264\) −7.59177e7 + 1.31493e8i −0.253939 + 0.439835i
\(265\) −1.59008e7 2.75409e7i −0.0524877 0.0909113i
\(266\) −2.75146e8 −0.896349
\(267\) 1.85274e8 + 3.20904e8i 0.595697 + 1.03178i
\(268\) 3.61669e6 6.26429e6i 0.0114773 0.0198793i
\(269\) 1.54462e8 0.483825 0.241913 0.970298i \(-0.422225\pi\)
0.241913 + 0.970298i \(0.422225\pi\)
\(270\) −6.41589e7 + 1.11127e8i −0.198374 + 0.343593i
\(271\) −2.01138e8 3.48382e8i −0.613906 1.06332i −0.990575 0.136969i \(-0.956264\pi\)
0.376669 0.926348i \(-0.377069\pi\)
\(272\) 2.31293e8 + 4.00611e8i 0.696902 + 1.20707i
\(273\) −1.47806e8 2.56008e8i −0.439667 0.761526i
\(274\) 2.91631e8 0.856461
\(275\) −9.29098e7 1.60925e8i −0.269400 0.466614i
\(276\) 1.14862e7 + 1.98947e7i 0.0328848 + 0.0569582i
\(277\) 1.30297e7 2.25681e7i 0.0368346 0.0637994i −0.847020 0.531560i \(-0.821606\pi\)
0.883855 + 0.467761i \(0.154939\pi\)
\(278\) 2.76107e8 4.78231e8i 0.770762 1.33500i
\(279\) 3.70440e7 0.102118
\(280\) 1.15303e8 0.313898
\(281\) −2.77479e8 + 4.80608e8i −0.746034 + 1.29217i 0.203676 + 0.979038i \(0.434711\pi\)
−0.949710 + 0.313131i \(0.898622\pi\)
\(282\) −2.63184e8 + 4.55848e8i −0.698855 + 1.21045i
\(283\) 3.76405e7 + 6.51952e7i 0.0987194 + 0.170987i 0.911155 0.412064i \(-0.135192\pi\)
−0.812435 + 0.583051i \(0.801859\pi\)
\(284\) 1.73938e7 + 3.01270e7i 0.0450590 + 0.0780444i
\(285\) 1.29483e8 0.331327
\(286\) 1.63112e8 + 2.82519e8i 0.412293 + 0.714112i
\(287\) 3.07352e8 + 5.32350e8i 0.767450 + 1.32926i
\(288\) 7.04070e6 + 1.21948e7i 0.0173677 + 0.0300817i
\(289\) −2.35656e8 + 4.08168e8i −0.574296 + 0.994710i
\(290\) 1.10239e8 0.265426
\(291\) −4.68673e6 + 8.11765e6i −0.0111492 + 0.0193110i
\(292\) 1.02932e7 + 1.78283e7i 0.0241941 + 0.0419055i
\(293\) −1.35586e8 −0.314903 −0.157452 0.987527i \(-0.550328\pi\)
−0.157452 + 0.987527i \(0.550328\pi\)
\(294\) 5.48002e7 + 9.49168e7i 0.125767 + 0.217835i
\(295\) −4.44091e7 + 7.69189e7i −0.100715 + 0.174444i
\(296\) 6.74904e7 1.16897e8i 0.151259 0.261988i
\(297\) 3.07464e8 0.680999
\(298\) 8.90914e7 1.54311e8i 0.195020 0.337784i
\(299\) 1.10128e9 2.38259
\(300\) 1.49783e7 0.0320286
\(301\) 3.56770e8 1.54524e8i 0.754059 0.326598i
\(302\) 3.75604e8 0.784705
\(303\) 4.62621e8 0.955380
\(304\) −2.60211e8 + 4.50698e8i −0.531212 + 0.920086i
\(305\) 8.77281e6 0.0177047
\(306\) 1.32855e8 2.30111e8i 0.265064 0.459105i
\(307\) 9.06111e7 1.56943e8i 0.178730 0.309569i −0.762716 0.646734i \(-0.776135\pi\)
0.941446 + 0.337165i \(0.109468\pi\)
\(308\) −6.19116e6 1.07234e7i −0.0120738 0.0209125i
\(309\) −6.91928e8 −1.33415
\(310\) −2.63776e7 4.56873e7i −0.0502886 0.0871024i
\(311\) −2.18761e8 + 3.78904e8i −0.412390 + 0.714280i −0.995151 0.0983640i \(-0.968639\pi\)
0.582761 + 0.812644i \(0.301972\pi\)
\(312\) −5.86724e8 −1.09369
\(313\) −1.84956e8 + 3.20353e8i −0.340928 + 0.590505i −0.984605 0.174792i \(-0.944075\pi\)
0.643677 + 0.765297i \(0.277408\pi\)
\(314\) −1.08760e8 1.88379e8i −0.198252 0.343382i
\(315\) −3.15579e7 5.46598e7i −0.0568880 0.0985329i
\(316\) 6.49311e6 + 1.12464e7i 0.0115757 + 0.0200497i
\(317\) −9.16005e7 −0.161507 −0.0807534 0.996734i \(-0.525733\pi\)
−0.0807534 + 0.996734i \(0.525733\pi\)
\(318\) 6.23817e7 + 1.08048e8i 0.108783 + 0.188418i
\(319\) −1.32073e8 2.28757e8i −0.227796 0.394554i
\(320\) 1.14184e8 1.97773e8i 0.194797 0.337398i
\(321\) 1.44018e8 2.49447e8i 0.243024 0.420931i
\(322\) 8.49075e8 1.41726
\(323\) −9.91880e8 −1.63776
\(324\) −7.07091e6 + 1.22472e7i −0.0115496 + 0.0200045i
\(325\) 3.59024e8 6.21847e8i 0.580138 1.00483i
\(326\) −2.22103e8 3.84694e8i −0.355053 0.614969i
\(327\) −3.14356e6 5.44480e6i −0.00497169 0.00861122i
\(328\) 1.22005e9 1.90906
\(329\) −4.78890e8 8.29461e8i −0.741395 1.28413i
\(330\) −5.91814e7 1.02505e8i −0.0906539 0.157017i
\(331\) 1.13223e8 + 1.96108e8i 0.171608 + 0.297233i 0.938982 0.343966i \(-0.111771\pi\)
−0.767374 + 0.641199i \(0.778437\pi\)
\(332\) 9.84144e6 1.70459e7i 0.0147596 0.0255644i
\(333\) −7.38869e7 −0.109651
\(334\) −5.81531e8 + 1.00724e9i −0.854005 + 1.47918i
\(335\) 6.29073e7 + 1.08959e8i 0.0914206 + 0.158345i
\(336\) −4.31085e8 −0.619977
\(337\) 2.72754e8 + 4.72424e8i 0.388210 + 0.672399i 0.992209 0.124586i \(-0.0397602\pi\)
−0.603999 + 0.796985i \(0.706427\pi\)
\(338\) −2.83769e8 + 4.91503e8i −0.399721 + 0.692337i
\(339\) 3.20514e7 5.55146e7i 0.0446835 0.0773942i
\(340\) 1.86291e7 0.0257048
\(341\) −6.32037e7 + 1.09472e8i −0.0863181 + 0.149507i
\(342\) 2.98930e8 0.404090
\(343\) −8.13571e8 −1.08859
\(344\) 8.84481e7 7.66587e8i 0.117148 1.01533i
\(345\) −3.99574e8 −0.523878
\(346\) −9.02906e8 −1.17186
\(347\) 6.34249e8 1.09855e9i 0.814905 1.41146i −0.0944914 0.995526i \(-0.530122\pi\)
0.909396 0.415931i \(-0.136544\pi\)
\(348\) 2.12918e7 0.0270823
\(349\) −5.70035e8 + 9.87330e8i −0.717815 + 1.24329i 0.244048 + 0.969763i \(0.421524\pi\)
−0.961864 + 0.273529i \(0.911809\pi\)
\(350\) 2.76803e8 4.79437e8i 0.345090 0.597713i
\(351\) 5.94053e8 + 1.02893e9i 0.733248 + 1.27002i
\(352\) −4.80507e7 −0.0587220
\(353\) −3.62048e8 6.27085e8i −0.438081 0.758779i 0.559460 0.828857i \(-0.311008\pi\)
−0.997541 + 0.0700784i \(0.977675\pi\)
\(354\) 1.74226e8 3.01767e8i 0.208737 0.361544i
\(355\) −6.05083e8 −0.717821
\(356\) −2.99885e7 + 5.19417e7i −0.0352274 + 0.0610156i
\(357\) −4.10806e8 7.11537e8i −0.477857 0.827673i
\(358\) 4.88924e8 + 8.46842e8i 0.563185 + 0.975465i
\(359\) 6.82146e8 + 1.18151e9i 0.778120 + 1.34774i 0.933024 + 0.359814i \(0.117160\pi\)
−0.154904 + 0.987930i \(0.549507\pi\)
\(360\) −1.25270e8 −0.141511
\(361\) −1.11010e8 1.92275e8i −0.124190 0.215103i
\(362\) −4.92006e8 8.52180e8i −0.545118 0.944172i
\(363\) 2.19734e8 3.80590e8i 0.241115 0.417623i
\(364\) 2.39240e7 4.14375e7i 0.0260003 0.0450339i
\(365\) −3.58071e8 −0.385429
\(366\) −3.44174e7 −0.0366940
\(367\) −3.30814e8 + 5.72987e8i −0.349343 + 0.605081i −0.986133 0.165957i \(-0.946929\pi\)
0.636790 + 0.771038i \(0.280262\pi\)
\(368\) 8.02988e8 1.39082e9i 0.839927 1.45480i
\(369\) −3.33920e8 5.78367e8i −0.345980 0.599254i
\(370\) 5.26120e7 + 9.11266e7i 0.0539981 + 0.0935274i
\(371\) −2.27020e8 −0.230810
\(372\) −5.09463e6 8.82415e6i −0.00513112 0.00888736i
\(373\) −7.02768e8 1.21723e9i −0.701182 1.21448i −0.968052 0.250750i \(-0.919323\pi\)
0.266870 0.963733i \(-0.414011\pi\)
\(374\) 4.53347e8 + 7.85220e8i 0.448105 + 0.776141i
\(375\) −2.81676e8 + 4.87877e8i −0.275829 + 0.477750i
\(376\) −1.90098e9 −1.84425
\(377\) 5.10357e8 8.83965e8i 0.490546 0.849651i
\(378\) 4.58008e8 + 7.93293e8i 0.436166 + 0.755462i
\(379\) 1.61314e9 1.52207 0.761036 0.648710i \(-0.224691\pi\)
0.761036 + 0.648710i \(0.224691\pi\)
\(380\) 1.04791e7 + 1.81503e7i 0.00979673 + 0.0169684i
\(381\) 1.54572e8 2.67727e8i 0.143184 0.248001i
\(382\) −1.81877e8 + 3.15021e8i −0.166939 + 0.289146i
\(383\) 3.68576e7 0.0335221 0.0167610 0.999860i \(-0.494665\pi\)
0.0167610 + 0.999860i \(0.494665\pi\)
\(384\) −4.06694e8 + 7.04414e8i −0.366529 + 0.634846i
\(385\) 2.15373e8 0.192344
\(386\) 8.48092e8 0.750563
\(387\) −3.87610e8 + 1.67881e8i −0.339943 + 0.147236i
\(388\) −1.51719e6 −0.00131865
\(389\) −1.28154e9 −1.10385 −0.551924 0.833895i \(-0.686106\pi\)
−0.551924 + 0.833895i \(0.686106\pi\)
\(390\) 2.28690e8 3.96102e8i 0.195218 0.338128i
\(391\) 3.06085e9 2.58955
\(392\) −1.97911e8 + 3.42792e8i −0.165947 + 0.287428i
\(393\) 1.99424e8 3.45413e8i 0.165731 0.287054i
\(394\) 4.06589e8 + 7.04233e8i 0.334903 + 0.580069i
\(395\) −2.25877e8 −0.184409
\(396\) 6.72633e6 + 1.16504e7i 0.00544309 + 0.00942770i
\(397\) −8.21431e8 + 1.42276e9i −0.658877 + 1.14121i 0.322029 + 0.946730i \(0.395635\pi\)
−0.980907 + 0.194479i \(0.937698\pi\)
\(398\) 8.87066e8 0.705286
\(399\) 4.62168e8 8.00498e8i 0.364246 0.630892i
\(400\) −5.23556e8 9.06826e8i −0.409028 0.708458i
\(401\) −5.31697e8 9.20927e8i −0.411774 0.713214i 0.583310 0.812250i \(-0.301757\pi\)
−0.995084 + 0.0990361i \(0.968424\pi\)
\(402\) −2.46797e8 4.27466e8i −0.189474 0.328178i
\(403\) −4.88465e8 −0.371763
\(404\) 3.74400e7 + 6.48480e7i 0.0282489 + 0.0489285i
\(405\) −1.22989e8 2.13023e8i −0.0919968 0.159343i
\(406\) 3.93479e8 6.81526e8i 0.291797 0.505407i
\(407\) 1.26064e8 2.18350e8i 0.0926854 0.160536i
\(408\) −1.63071e9 −1.18869
\(409\) 2.39333e8 0.172970 0.0864849 0.996253i \(-0.472437\pi\)
0.0864849 + 0.996253i \(0.472437\pi\)
\(410\) −4.75543e8 + 8.23665e8i −0.340758 + 0.590211i
\(411\) −4.89859e8 + 8.48461e8i −0.348037 + 0.602817i
\(412\) −5.59978e7 9.69910e7i −0.0394485 0.0683268i
\(413\) 3.17021e8 + 5.49097e8i 0.221444 + 0.383552i
\(414\) −9.22471e8 −0.638927
\(415\) 1.71178e8 + 2.96489e8i 0.117566 + 0.203629i
\(416\) −9.28392e7 1.60802e8i −0.0632273 0.109513i
\(417\) 9.27565e8 + 1.60659e9i 0.626424 + 1.08500i
\(418\) −5.10027e8 + 8.83393e8i −0.341567 + 0.591612i
\(419\) −8.51849e8 −0.565736 −0.282868 0.959159i \(-0.591286\pi\)
−0.282868 + 0.959159i \(0.591286\pi\)
\(420\) −8.68024e6 + 1.50346e7i −0.00571688 + 0.00990193i
\(421\) −8.98651e8 1.55651e9i −0.586954 1.01663i −0.994629 0.103507i \(-0.966994\pi\)
0.407675 0.913127i \(-0.366340\pi\)
\(422\) 8.27778e8 0.536192
\(423\) 5.20286e8 + 9.01161e8i 0.334234 + 0.578910i
\(424\) −2.25292e8 + 3.90216e8i −0.143537 + 0.248614i
\(425\) 9.97854e8 1.72833e9i 0.630530 1.09211i
\(426\) 2.37386e9 1.48772
\(427\) 3.13130e7 5.42357e7i 0.0194638 0.0337123i
\(428\) 4.66217e7 0.0287432
\(429\) −1.09593e9 −0.670167
\(430\) 4.83054e8 + 3.58507e8i 0.292992 + 0.217450i
\(431\) −5.71866e8 −0.344052 −0.172026 0.985092i \(-0.555031\pi\)
−0.172026 + 0.985092i \(0.555031\pi\)
\(432\) 1.73259e9 1.03396
\(433\) 2.72097e8 4.71285e8i 0.161070 0.278982i −0.774182 0.632963i \(-0.781839\pi\)
0.935253 + 0.353980i \(0.115172\pi\)
\(434\) −3.76601e8 −0.221140
\(435\) −1.85171e8 + 3.20726e8i −0.107860 + 0.186819i
\(436\) 508817. 881296.i 0.000294008 0.000509236i
\(437\) 1.72177e9 + 2.98219e9i 0.986939 + 1.70943i
\(438\) 1.40478e9 0.798822
\(439\) −9.16116e8 1.58676e9i −0.516803 0.895128i −0.999810 0.0195119i \(-0.993789\pi\)
0.483007 0.875616i \(-0.339545\pi\)
\(440\) 2.13734e8 3.70197e8i 0.119616 0.207181i
\(441\) 2.16668e8 0.120298
\(442\) −1.75183e9 + 3.03426e9i −0.964970 + 1.67138i
\(443\) −3.00511e8 5.20500e8i −0.164228 0.284451i 0.772153 0.635437i \(-0.219180\pi\)
−0.936381 + 0.350986i \(0.885847\pi\)
\(444\) 1.01616e7 + 1.76004e7i 0.00550962 + 0.00954294i
\(445\) −5.21609e8 9.03453e8i −0.280598 0.486010i
\(446\) 1.67554e9 0.894299
\(447\) 2.99297e8 + 5.18398e8i 0.158499 + 0.274528i
\(448\) −8.15122e8 1.41183e9i −0.428302 0.741840i
\(449\) −4.19636e8 + 7.26831e8i −0.218782 + 0.378941i −0.954436 0.298416i \(-0.903542\pi\)
0.735654 + 0.677357i \(0.236875\pi\)
\(450\) −3.00730e8 + 5.20880e8i −0.155573 + 0.269460i
\(451\) 2.27891e9 1.16979
\(452\) 1.03757e7 0.00528484
\(453\) −6.30910e8 + 1.09277e9i −0.318878 + 0.552312i
\(454\) −1.30091e9 + 2.25325e9i −0.652458 + 1.13009i
\(455\) 4.16124e8 + 7.20748e8i 0.207101 + 0.358710i
\(456\) −9.17299e8 1.58881e9i −0.453037 0.784683i
\(457\) 2.48808e9 1.21943 0.609715 0.792620i \(-0.291284\pi\)
0.609715 + 0.792620i \(0.291284\pi\)
\(458\) −1.75125e9 3.03326e9i −0.851764 1.47530i
\(459\) 1.65108e9 + 2.85976e9i 0.796939 + 1.38034i
\(460\) −3.23376e7 5.60103e7i −0.0154901 0.0268297i
\(461\) 1.95907e9 3.39321e9i 0.931315 1.61308i 0.150238 0.988650i \(-0.451996\pi\)
0.781077 0.624435i \(-0.214671\pi\)
\(462\) −8.44951e8 −0.398643
\(463\) −2.00052e9 + 3.46500e9i −0.936719 + 1.62245i −0.165180 + 0.986263i \(0.552821\pi\)
−0.771539 + 0.636182i \(0.780513\pi\)
\(464\) −7.44243e8 1.28907e9i −0.345861 0.599049i
\(465\) 1.77228e8 0.0817423
\(466\) −1.30396e9 2.25853e9i −0.596917 1.03389i
\(467\) −1.36969e9 + 2.37237e9i −0.622319 + 1.07789i 0.366734 + 0.930326i \(0.380476\pi\)
−0.989053 + 0.147562i \(0.952857\pi\)
\(468\) −2.59920e7 + 4.50195e7i −0.0117214 + 0.0203020i
\(469\) 8.98146e8 0.402015
\(470\) 7.40950e8 1.28336e9i 0.329190 0.570174i
\(471\) 7.30749e8 0.322252
\(472\) 1.25843e9 0.550848
\(473\) 1.65211e8 1.43189e9i 0.0717835 0.622153i
\(474\) 8.86160e8 0.382198
\(475\) 2.24522e9 0.961240
\(476\) 6.64932e7 1.15170e8i 0.0282587 0.0489456i
\(477\) 2.46644e8 0.104053
\(478\) −4.63335e8 + 8.02520e8i −0.194043 + 0.336092i
\(479\) 4.69951e8 8.13980e8i 0.195379 0.338407i −0.751645 0.659567i \(-0.770740\pi\)
0.947025 + 0.321160i \(0.104073\pi\)
\(480\) 3.36845e7 + 5.83432e7i 0.0139023 + 0.0240794i
\(481\) 9.74278e8 0.399186
\(482\) −1.50065e9 2.59921e9i −0.610402 1.05725i
\(483\) −1.42621e9 + 2.47027e9i −0.575928 + 0.997537i
\(484\) 7.11323e7 0.0285173
\(485\) 1.31947e7 2.28539e7i 0.00525174 0.00909629i
\(486\) −8.60688e8 1.49076e9i −0.340110 0.589087i
\(487\) 1.37796e9 + 2.38669e9i 0.540610 + 0.936364i 0.998869 + 0.0475455i \(0.0151399\pi\)
−0.458259 + 0.888819i \(0.651527\pi\)
\(488\) −6.21492e7 1.07646e8i −0.0242084 0.0419302i
\(489\) 1.49228e9 0.577126
\(490\) −1.54281e8 2.67222e8i −0.0592415 0.102609i
\(491\) −1.08341e9 1.87653e9i −0.413056 0.715434i 0.582166 0.813070i \(-0.302205\pi\)
−0.995222 + 0.0976359i \(0.968872\pi\)
\(492\) −9.18475e7 + 1.59085e8i −0.0347688 + 0.0602213i
\(493\) 1.41846e9 2.45685e9i 0.533156 0.923453i
\(494\) −3.94171e9 −1.47109
\(495\) −2.33990e8 −0.0867121
\(496\) −3.56159e8 + 6.16885e8i −0.131056 + 0.226996i
\(497\) −2.15974e9 + 3.74078e9i −0.789140 + 1.36683i
\(498\) −6.71565e8 1.16318e9i −0.243660 0.422032i
\(499\) 1.14778e8 + 1.98801e8i 0.0413528 + 0.0716252i 0.885961 0.463760i \(-0.153500\pi\)
−0.844608 + 0.535385i \(0.820167\pi\)
\(500\) −9.11843e7 −0.0326231
\(501\) −1.95362e9 3.38377e9i −0.694077 1.20218i
\(502\) 3.07154e8 + 5.32006e8i 0.108366 + 0.187695i
\(503\) 1.13680e9 + 1.96900e9i 0.398288 + 0.689855i 0.993515 0.113703i \(-0.0362711\pi\)
−0.595227 + 0.803558i \(0.702938\pi\)
\(504\) −4.47131e8 + 7.74453e8i −0.155571 + 0.269456i
\(505\) −1.30243e9 −0.450024
\(506\) 1.57390e9 2.72607e9i 0.540070 0.935429i
\(507\) −9.53307e8 1.65118e9i −0.324866 0.562685i
\(508\) 5.00381e7 0.0169347
\(509\) −2.33727e7 4.04827e7i −0.00785591 0.0136068i 0.862071 0.506788i \(-0.169167\pi\)
−0.869927 + 0.493181i \(0.835834\pi\)
\(510\) 6.35610e8 1.10091e9i 0.212175 0.367498i
\(511\) −1.27807e9 + 2.21369e9i −0.423724 + 0.733911i
\(512\) −3.22230e9 −1.06102
\(513\) −1.85751e9 + 3.21731e9i −0.607465 + 1.05216i
\(514\) −1.35847e9 −0.441244
\(515\) 1.94801e9 0.628442
\(516\) 9.32981e7 + 6.92429e7i 0.0298950 + 0.0221871i
\(517\) −3.55080e9 −1.13008
\(518\) 7.51157e8 0.237452
\(519\) 1.51663e9 2.62688e9i 0.476205 0.824811i
\(520\) 1.65182e9 0.515172
\(521\) −8.49681e8 + 1.47169e9i −0.263223 + 0.455916i −0.967097 0.254410i \(-0.918119\pi\)
0.703873 + 0.710325i \(0.251452\pi\)
\(522\) −4.27492e8 + 7.40438e8i −0.131547 + 0.227846i
\(523\) −3.08663e9 5.34621e9i −0.943472 1.63414i −0.758782 0.651345i \(-0.774205\pi\)
−0.184690 0.982797i \(-0.559128\pi\)
\(524\) 6.45576e7 0.0196014
\(525\) 9.29903e8 + 1.61064e9i 0.280466 + 0.485781i
\(526\) 8.84595e8 1.53216e9i 0.265030 0.459045i
\(527\) −1.35762e9 −0.404055
\(528\) −7.99087e8 + 1.38406e9i −0.236252 + 0.409200i
\(529\) −3.61082e9 6.25412e9i −1.06050 1.83684i
\(530\) −1.75625e8 3.04192e8i −0.0512415 0.0887529i
\(531\) −3.44425e8 5.96561e8i −0.0998306 0.172912i
\(532\) 1.49613e8 0.0430804
\(533\) 4.40310e9 + 7.62639e9i 1.25954 + 2.18159i
\(534\) 2.04637e9 + 3.54442e9i 0.581554 + 1.00728i
\(535\) −4.05459e8 + 7.02276e8i −0.114475 + 0.198276i
\(536\) 8.91308e8 1.54379e9i 0.250006 0.433024i
\(537\) −3.28503e9 −0.915438
\(538\) 1.70605e9 0.472338
\(539\) −3.69675e8 + 6.40295e8i −0.101685 + 0.176124i
\(540\) 3.48870e7 6.04261e7i 0.00953424 0.0165138i
\(541\) −2.98841e9 5.17608e9i −0.811428 1.40543i −0.911865 0.410491i \(-0.865357\pi\)
0.100437 0.994943i \(-0.467976\pi\)
\(542\) −2.22159e9 3.84791e9i −0.599331 1.03807i
\(543\) 3.30573e9 0.886071
\(544\) −2.58033e8 4.46926e8i −0.0687194 0.119025i
\(545\) 8.85016e6 + 1.53289e7i 0.00234187 + 0.00405624i
\(546\) −1.63254e9 2.82763e9i −0.429228 0.743445i
\(547\) 3.21128e9 5.56210e9i 0.838923 1.45306i −0.0518724 0.998654i \(-0.516519\pi\)
0.890796 0.454404i \(-0.150148\pi\)
\(548\) −1.58578e8 −0.0411632
\(549\) −3.40198e7 + 5.89240e7i −0.00877461 + 0.0151981i
\(550\) −1.02620e9 1.77743e9i −0.263004 0.455536i
\(551\) 3.19162e9 0.812794
\(552\) 2.83070e9 + 4.90292e9i 0.716320 + 1.24070i
\(553\) −8.06229e8 + 1.39643e9i −0.202731 + 0.351141i
\(554\) 1.43915e8 2.49267e8i 0.0359601 0.0622847i
\(555\) −3.53494e8 −0.0877720
\(556\) −1.50136e8 + 2.60043e8i −0.0370444 + 0.0641628i
\(557\) 6.07034e9 1.48840 0.744200 0.667957i \(-0.232831\pi\)
0.744200 + 0.667957i \(0.232831\pi\)
\(558\) 4.09155e8 0.0996937
\(559\) 5.11105e9 2.21369e9i 1.23757 0.536014i
\(560\) 1.21365e9 0.292035
\(561\) −3.04598e9 −0.728379
\(562\) −3.06479e9 + 5.30837e9i −0.728322 + 1.26149i
\(563\) 3.26161e9 0.770288 0.385144 0.922856i \(-0.374152\pi\)
0.385144 + 0.922856i \(0.374152\pi\)
\(564\) 1.43109e8 2.47872e8i 0.0335884 0.0581768i
\(565\) −9.02353e7 + 1.56292e8i −0.0210478 + 0.0364559i
\(566\) 4.15743e8 + 7.20087e8i 0.0963756 + 0.166927i
\(567\) −1.75595e9 −0.404548
\(568\) 4.28659e9 + 7.42459e9i 0.981506 + 1.70002i
\(569\) −1.73473e9 + 3.00465e9i −0.394766 + 0.683755i −0.993071 0.117513i \(-0.962508\pi\)
0.598305 + 0.801268i \(0.295841\pi\)
\(570\) 1.43016e9 0.323460
\(571\) 2.71842e9 4.70844e9i 0.611068 1.05840i −0.379992 0.924990i \(-0.624073\pi\)
0.991061 0.133412i \(-0.0425932\pi\)
\(572\) −8.86939e7 1.53622e8i −0.0198156 0.0343217i
\(573\) −6.11006e8 1.05829e9i −0.135676 0.234999i
\(574\) 3.39474e9 + 5.87986e9i 0.749229 + 1.29770i
\(575\) −6.92856e9 −1.51987
\(576\) 8.85583e8 + 1.53387e9i 0.193086 + 0.334434i
\(577\) 5.15636e8 + 8.93107e8i 0.111745 + 0.193548i 0.916474 0.400095i \(-0.131023\pi\)
−0.804729 + 0.593642i \(0.797689\pi\)
\(578\) −2.60284e9 + 4.50825e9i −0.560661 + 0.971093i
\(579\) −1.42456e9 + 2.46740e9i −0.305003 + 0.528282i
\(580\) −5.99436e7 −0.0127569
\(581\) 2.44396e9 0.516985
\(582\) −5.17653e7 + 8.96602e7i −0.0108845 + 0.0188525i
\(583\) −4.20818e8 + 7.28879e8i −0.0879538 + 0.152340i
\(584\) 2.53669e9 + 4.39367e9i 0.527013 + 0.912814i
\(585\) −4.52095e8 7.83051e8i −0.0933649 0.161713i
\(586\) −1.49756e9 −0.307427
\(587\) 4.76767e6 + 8.25784e6i 0.000972910 + 0.00168513i 0.866511 0.499157i \(-0.166357\pi\)
−0.865539 + 0.500842i \(0.833024\pi\)
\(588\) −2.97982e7 5.16119e7i −0.00604462 0.0104696i
\(589\) −7.63678e8 1.32273e9i −0.153995 0.266727i
\(590\) −4.90503e8 + 8.49576e8i −0.0983240 + 0.170302i
\(591\) −2.73183e9 −0.544373
\(592\) 7.10384e8 1.23042e9i 0.140724 0.243741i
\(593\) 3.23933e9 + 5.61068e9i 0.637916 + 1.10490i 0.985889 + 0.167399i \(0.0535367\pi\)
−0.347973 + 0.937505i \(0.613130\pi\)
\(594\) 3.39597e9 0.664831
\(595\) 1.15656e9 + 2.00321e9i 0.225091 + 0.389869i
\(596\) −4.84443e7 + 8.39080e7i −0.00937305 + 0.0162346i
\(597\) −1.49002e9 + 2.58080e9i −0.286604 + 0.496414i
\(598\) 1.21638e10 2.32602
\(599\) −1.99194e9 + 3.45014e9i −0.378688 + 0.655908i −0.990872 0.134808i \(-0.956958\pi\)
0.612183 + 0.790716i \(0.290291\pi\)
\(600\) 3.69129e9 0.697668
\(601\) 5.93997e9 1.11615 0.558077 0.829789i \(-0.311539\pi\)
0.558077 + 0.829789i \(0.311539\pi\)
\(602\) 3.94056e9 1.70673e9i 0.736156 0.318843i
\(603\) −9.75783e8 −0.181235
\(604\) −2.04239e8 −0.0377145
\(605\) −6.18624e8 + 1.07149e9i −0.113575 + 0.196718i
\(606\) 5.10970e9 0.932697
\(607\) −3.32807e8 + 5.76439e8i −0.0603993 + 0.104615i −0.894644 0.446780i \(-0.852571\pi\)
0.834245 + 0.551394i \(0.185904\pi\)
\(608\) 2.90294e8 5.02804e8i 0.0523812 0.0907269i
\(609\) 1.32187e9 + 2.28955e9i 0.237153 + 0.410761i
\(610\) 9.68966e7 0.0172844
\(611\) −6.86053e9 1.18828e10i −1.21678 2.10753i
\(612\) −7.22410e7 + 1.25125e8i −0.0127395 + 0.0220655i
\(613\) −4.44059e9 −0.778625 −0.389313 0.921106i \(-0.627287\pi\)
−0.389313 + 0.921106i \(0.627287\pi\)
\(614\) 1.00081e9 1.73345e9i 0.174486 0.302219i
\(615\) −1.59756e9 2.76705e9i −0.276945 0.479683i
\(616\) −1.52577e9 2.64271e9i −0.263000 0.455530i
\(617\) −4.02866e9 6.97784e9i −0.690498 1.19598i −0.971675 0.236321i \(-0.924058\pi\)
0.281177 0.959656i \(-0.409275\pi\)
\(618\) −7.64241e9 −1.30248
\(619\) 1.17104e9 + 2.02830e9i 0.198451 + 0.343728i 0.948026 0.318192i \(-0.103075\pi\)
−0.749575 + 0.661919i \(0.769742\pi\)
\(620\) 1.43431e7 + 2.48429e7i 0.00241697 + 0.00418632i
\(621\) 5.73212e9 9.92833e9i 0.960495 1.66363i
\(622\) −2.41623e9 + 4.18503e9i −0.402598 + 0.697321i
\(623\) −7.44717e9 −1.23391
\(624\) −6.17569e9 −1.01751
\(625\) −1.83247e9 + 3.17393e9i −0.300232 + 0.520016i
\(626\) −2.04286e9 + 3.53833e9i −0.332834 + 0.576485i
\(627\) −1.71341e9 2.96771e9i −0.277603 0.480822i
\(628\) 5.91396e7 + 1.02433e8i 0.00952839 + 0.0165037i
\(629\) 2.70786e9 0.433860
\(630\) −3.48559e8 6.03723e8i −0.0555373 0.0961935i
\(631\) −4.77830e8 8.27626e8i −0.0757130 0.131139i 0.825683 0.564134i \(-0.190790\pi\)
−0.901396 + 0.432995i \(0.857457\pi\)
\(632\) 1.60018e9 + 2.77160e9i 0.252150 + 0.436737i
\(633\) −1.39044e9 + 2.40831e9i −0.217890 + 0.377397i
\(634\) −1.01174e9 −0.157672
\(635\) −4.35172e8 + 7.53740e8i −0.0674455 + 0.116819i
\(636\) −3.39207e7 5.87524e7i −0.00522835 0.00905577i
\(637\) −2.85700e9 −0.437948
\(638\) −1.45876e9 2.52664e9i −0.222387 0.385186i
\(639\) 2.34643e9 4.06414e9i 0.355758 0.616191i
\(640\) 1.14498e9 1.98316e9i 0.172650 0.299039i
\(641\) 8.45274e9 1.26764 0.633818 0.773482i \(-0.281487\pi\)
0.633818 + 0.773482i \(0.281487\pi\)
\(642\) 1.59070e9 2.75516e9i 0.237254 0.410937i
\(643\) 1.82745e9 0.271086 0.135543 0.990771i \(-0.456722\pi\)
0.135543 + 0.990771i \(0.456722\pi\)
\(644\) −4.61693e8 −0.0681166
\(645\) −1.85442e9 + 8.03186e8i −0.272113 + 0.117857i
\(646\) −1.09554e10 −1.59888
\(647\) −3.92133e9 −0.569204 −0.284602 0.958646i \(-0.591861\pi\)
−0.284602 + 0.958646i \(0.591861\pi\)
\(648\) −1.74258e9 + 3.01823e9i −0.251582 + 0.435753i
\(649\) 2.35060e9 0.337538
\(650\) 3.96545e9 6.86836e9i 0.566364 0.980971i
\(651\) 6.32584e8 1.09567e9i 0.0898638 0.155649i
\(652\) 1.20771e8 + 2.09181e8i 0.0170646 + 0.0295567i
\(653\) −7.58044e9 −1.06536 −0.532682 0.846315i \(-0.678816\pi\)
−0.532682 + 0.846315i \(0.678816\pi\)
\(654\) −3.47209e7 6.01383e7i −0.00485365 0.00840677i
\(655\) −5.61445e8 + 9.72452e8i −0.0780662 + 0.135215i
\(656\) 1.28419e10 1.77609
\(657\) 1.38855e9 2.40504e9i 0.191022 0.330860i
\(658\) −5.28938e9 9.16148e9i −0.723793 1.25365i
\(659\) 1.02000e9 + 1.76669e9i 0.138836 + 0.240470i 0.927056 0.374923i \(-0.122331\pi\)
−0.788221 + 0.615393i \(0.788997\pi\)
\(660\) 3.21805e7 + 5.57382e7i 0.00435701 + 0.00754657i
\(661\) −8.89691e9 −1.19821 −0.599107 0.800669i \(-0.704477\pi\)
−0.599107 + 0.800669i \(0.704477\pi\)
\(662\) 1.25056e9 + 2.16603e9i 0.167533 + 0.290176i
\(663\) −5.88517e9 1.01934e10i −0.784263 1.35838i
\(664\) 2.42535e9 4.20084e9i 0.321504 0.556862i
\(665\) −1.30116e9 + 2.25367e9i −0.171575 + 0.297177i
\(666\) −8.16088e8 −0.107048
\(667\) −9.84905e9 −1.28515
\(668\) 3.16213e8 5.47698e8i 0.0410452 0.0710924i
\(669\) −2.81444e9 + 4.87475e9i −0.363413 + 0.629450i
\(670\) 6.94817e8 + 1.20346e9i 0.0892501 + 0.154586i
\(671\) −1.16088e8 2.01070e8i −0.0148339 0.0256932i
\(672\) 4.80923e8 0.0611341
\(673\) 4.63554e9 + 8.02899e9i 0.586202 + 1.01533i 0.994724 + 0.102584i \(0.0327109\pi\)
−0.408522 + 0.912748i \(0.633956\pi\)
\(674\) 3.01259e9 + 5.21797e9i 0.378993 + 0.656435i
\(675\) −3.73740e9 6.47337e9i −0.467742 0.810154i
\(676\) 1.54302e8 2.67260e8i 0.0192114 0.0332751i
\(677\) 4.13107e9 0.511684 0.255842 0.966719i \(-0.417647\pi\)
0.255842 + 0.966719i \(0.417647\pi\)
\(678\) 3.54010e8 6.13164e8i 0.0436227 0.0755566i
\(679\) −9.41923e7 1.63146e8i −0.0115471 0.0200001i
\(680\) 4.59101e9 0.559921
\(681\) −4.37034e9 7.56965e9i −0.530274 0.918461i
\(682\) −6.98091e8 + 1.20913e9i −0.0842688 + 0.145958i
\(683\) −1.62442e9 + 2.81358e9i −0.195086 + 0.337898i −0.946929 0.321444i \(-0.895832\pi\)
0.751843 + 0.659342i \(0.229165\pi\)
\(684\) −1.62546e8 −0.0194214
\(685\) 1.37912e9 2.38870e9i 0.163940 0.283952i
\(686\) −8.98597e9 −1.06275
\(687\) 1.17665e10 1.38451
\(688\) 9.30979e8 8.06886e9i 0.108988 0.944611i
\(689\) −3.25226e9 −0.378808
\(690\) −4.41333e9 −0.511440
\(691\) 1.75727e8 3.04368e8i 0.0202612 0.0350934i −0.855717 0.517444i \(-0.826884\pi\)
0.875978 + 0.482351i \(0.160217\pi\)
\(692\) 4.90964e8 0.0563220
\(693\) −8.35188e8 + 1.44659e9i −0.0953274 + 0.165112i
\(694\) 7.00534e9 1.21336e10i 0.795557 1.37795i
\(695\) −2.61140e9 4.52309e9i −0.295072 0.511079i
\(696\) 5.24723e9 0.589926
\(697\) 1.22378e10 + 2.11964e10i 1.36895 + 2.37109i
\(698\) −6.29609e9 + 1.09052e10i −0.700773 + 1.21377i
\(699\) 8.76116e9 0.970268
\(700\) −1.50514e8 + 2.60698e8i −0.0165857 + 0.0287273i
\(701\) 4.32657e9 + 7.49384e9i 0.474385 + 0.821658i 0.999570 0.0293298i \(-0.00933730\pi\)
−0.525185 + 0.850988i \(0.676004\pi\)
\(702\) 6.56138e9 + 1.13646e10i 0.715839 + 1.23987i
\(703\) 1.52321e9 + 2.63828e9i 0.165354 + 0.286402i
\(704\) −6.04385e9 −0.652844
\(705\) 2.48918e9 + 4.31138e9i 0.267543 + 0.463399i
\(706\) −3.99885e9 6.92622e9i −0.427680 0.740764i
\(707\) −4.64881e9 + 8.05197e9i −0.494736 + 0.856908i
\(708\) −9.47368e7 + 1.64089e8i −0.0100323 + 0.0173765i
\(709\) −8.86426e9 −0.934073 −0.467037 0.884238i \(-0.654678\pi\)
−0.467037 + 0.884238i \(0.654678\pi\)
\(710\) −6.68320e9 −0.700778
\(711\) 8.75921e8 1.51714e9i 0.0913948 0.158300i
\(712\) −7.39047e9 + 1.28007e10i −0.767347 + 1.32908i
\(713\) 2.35664e9 + 4.08183e9i 0.243490 + 0.421736i
\(714\) −4.53739e9 7.85900e9i −0.466512 0.808022i
\(715\) 3.08542e9 0.315677
\(716\) −2.65857e8 4.60479e8i −0.0270678 0.0468828i
\(717\) −1.55655e9 2.69602e9i −0.157705 0.273153i
\(718\) 7.53437e9 + 1.30499e10i 0.759646 + 1.31575i
\(719\) 3.44836e8 5.97274e8i 0.0345989 0.0599270i −0.848207 0.529664i \(-0.822318\pi\)
0.882806 + 0.469737i \(0.155651\pi\)
\(720\) −1.31856e9 −0.131655
\(721\) 6.95307e9 1.20431e10i 0.690881 1.19664i
\(722\) −1.22611e9 2.12369e9i −0.121241 0.209996i
\(723\) 1.00827e10 0.992187
\(724\) 2.67533e8 + 4.63381e8i 0.0261995 + 0.0453789i
\(725\) −3.21084e9 + 5.56134e9i −0.312922 + 0.541996i
\(726\) 2.42698e9 4.20365e9i 0.235390 0.407707i
\(727\) −1.64120e10 −1.58413 −0.792066 0.610436i \(-0.790994\pi\)
−0.792066 + 0.610436i \(0.790994\pi\)
\(728\) 5.89590e9 1.02120e10i 0.566357 0.980959i
\(729\) 1.09325e10 1.04514
\(730\) −3.95493e9 −0.376278
\(731\) 1.42054e10 6.15264e9i 1.34506 0.582573i
\(732\) 1.87148e7 0.00176359
\(733\) 1.94484e10 1.82398 0.911988 0.410216i \(-0.134547\pi\)
0.911988 + 0.410216i \(0.134547\pi\)
\(734\) −3.65387e9 + 6.32869e9i −0.341049 + 0.590715i
\(735\) 1.03660e9 0.0962950
\(736\) −8.95821e8 + 1.55161e9i −0.0828226 + 0.143453i
\(737\) 1.66486e9 2.88362e9i 0.153194 0.265340i
\(738\) −3.68818e9 6.38812e9i −0.337765 0.585027i
\(739\) 1.34814e9 0.122880 0.0614399 0.998111i \(-0.480431\pi\)
0.0614399 + 0.998111i \(0.480431\pi\)
\(740\) −2.86083e7 4.95510e7i −0.00259526 0.00449512i
\(741\) 6.62097e9 1.14679e10i 0.597803 1.03542i
\(742\) −2.50746e9 −0.225330
\(743\) −5.82248e9 + 1.00848e10i −0.520771 + 0.902002i 0.478937 + 0.877849i \(0.341022\pi\)
−0.999708 + 0.0241528i \(0.992311\pi\)
\(744\) −1.25554e9 2.17465e9i −0.111770 0.193591i
\(745\) −8.42622e8 1.45946e9i −0.0746596 0.129314i
\(746\) −7.76213e9 1.34444e10i −0.684534 1.18565i
\(747\) −2.65522e9 −0.233066
\(748\) −2.46512e8 4.26971e8i −0.0215369 0.0373029i
\(749\) 2.89443e9 + 5.01330e9i 0.251696 + 0.435951i
\(750\) −3.11114e9 + 5.38865e9i −0.269281 + 0.466408i
\(751\) −5.47687e9 + 9.48622e9i −0.471838 + 0.817247i −0.999481 0.0322191i \(-0.989743\pi\)
0.527643 + 0.849466i \(0.323076\pi\)
\(752\) −2.00091e10 −1.71579
\(753\) −2.06373e9 −0.176145
\(754\) 5.63695e9 9.76348e9i 0.478899 0.829478i
\(755\) 1.77622e9 3.07651e9i 0.150205 0.260162i
\(756\) −2.49046e8 4.31361e8i −0.0209630 0.0363090i
\(757\) −2.67071e9 4.62580e9i −0.223764 0.387571i 0.732184 0.681107i \(-0.238501\pi\)
−0.955948 + 0.293536i \(0.905168\pi\)
\(758\) 1.78173e10 1.48593
\(759\) 5.28742e9 + 9.15808e9i 0.438932 + 0.760253i
\(760\) 2.58250e9 + 4.47302e9i 0.213399 + 0.369618i
\(761\) 5.38218e9 + 9.32220e9i 0.442702 + 0.766783i 0.997889 0.0649430i \(-0.0206865\pi\)
−0.555187 + 0.831726i \(0.687353\pi\)
\(762\) 1.70726e9 2.95707e9i 0.139784 0.242113i
\(763\) 1.26356e8 0.0102982
\(764\) 9.88976e7 1.71296e8i 0.00802341 0.0138970i
\(765\) −1.25653e9 2.17638e9i −0.101475 0.175760i
\(766\) 4.07095e8 0.0327262
\(767\) 4.54161e9 + 7.86630e9i 0.363435 + 0.629487i
\(768\) 6.99459e8 1.21150e9i 0.0557183 0.0965069i
\(769\) 9.28006e9 1.60735e10i 0.735882 1.27459i −0.218453 0.975848i \(-0.570101\pi\)
0.954335 0.298738i \(-0.0965657\pi\)
\(770\) 2.37882e9 0.187778
\(771\) 2.28185e9 3.95227e9i 0.179306 0.310568i
\(772\) −4.61158e8 −0.0360736
\(773\) −1.96237e10 −1.52810 −0.764051 0.645156i \(-0.776792\pi\)
−0.764051 + 0.645156i \(0.776792\pi\)
\(774\) −4.28119e9 + 1.85426e9i −0.331872 + 0.143740i
\(775\) 3.07311e9 0.237149
\(776\) −3.73901e8 −0.0287237
\(777\) −1.26173e9 + 2.18539e9i −0.0964926 + 0.167130i
\(778\) −1.41547e10 −1.07764
\(779\) −1.37678e10 + 2.38466e10i −1.04348 + 1.80736i
\(780\) −1.24352e8 + 2.15384e8i −0.00938259 + 0.0162511i
\(781\) 8.00685e9 + 1.38683e10i 0.601427 + 1.04170i
\(782\) 3.38074e10 2.52807
\(783\) −5.31277e9 9.20200e9i −0.395508 0.685040i
\(784\) −2.08315e9 + 3.60813e9i −0.154388 + 0.267409i
\(785\) −2.05730e9 −0.151794
\(786\) 2.20266e9 3.81511e9i 0.161796 0.280239i
\(787\) −1.51245e9 2.61965e9i −0.110604 0.191572i 0.805410 0.592718i \(-0.201945\pi\)
−0.916014 + 0.401147i \(0.868612\pi\)
\(788\) −2.21087e8 3.82934e8i −0.0160961 0.0278793i
\(789\) 2.97174e9 + 5.14721e9i 0.215398 + 0.373080i
\(790\) −2.49484e9 −0.180031
\(791\) 6.44158e8 + 1.11571e9i 0.0462780 + 0.0801559i
\(792\) 1.65766e9 + 2.87115e9i 0.118565 + 0.205361i
\(793\) 4.48587e8 7.76976e8i 0.0319441 0.0553288i
\(794\) −9.07279e9 + 1.57145e10i −0.643234 + 1.11411i
\(795\) 1.18001e9 0.0832913
\(796\) −4.82351e8 −0.0338975
\(797\) −4.51436e9 + 7.81910e9i −0.315858 + 0.547082i −0.979619 0.200862i \(-0.935626\pi\)
0.663762 + 0.747944i \(0.268959\pi\)
\(798\) 5.10469e9 8.84158e9i 0.355598 0.615914i
\(799\) −1.90678e10 3.30265e10i −1.32248 2.29059i
\(800\) 5.84085e8 + 1.01166e9i 0.0403330 + 0.0698589i
\(801\) 8.09091e9 0.556267
\(802\) −5.87265e9 1.01717e10i −0.401998 0.696280i
\(803\) 4.73823e9 + 8.20686e9i 0.322933 + 0.559336i
\(804\) 1.34199e8 + 2.32439e8i 0.00910650 + 0.0157729i
\(805\) 4.01525e9 6.95463e9i 0.271286 0.469881i
\(806\) −5.39515e9 −0.362936
\(807\) −2.86568e9 + 4.96351e9i −0.191942 + 0.332454i
\(808\) 9.22683e9 + 1.59813e10i 0.615336 + 1.06579i
\(809\) 1.72660e9 0.114649 0.0573246 0.998356i \(-0.481743\pi\)
0.0573246 + 0.998356i \(0.481743\pi\)
\(810\) −1.35842e9 2.35285e9i −0.0898125 0.155560i
\(811\) −1.06571e10 + 1.84587e10i −0.701564 + 1.21515i 0.266353 + 0.963876i \(0.414181\pi\)
−0.967917 + 0.251270i \(0.919152\pi\)
\(812\) −2.13958e8 + 3.70587e8i −0.0140244 + 0.0242909i
\(813\) 1.49266e10 0.974191
\(814\) 1.39239e9 2.41169e9i 0.0904848 0.156724i
\(815\) −4.20128e9 −0.271850
\(816\) −1.71644e10 −1.10589
\(817\) 1.39853e10 + 1.03794e10i 0.897209 + 0.665880i
\(818\) 2.64345e9 0.168863
\(819\) −6.45469e9 −0.410565
\(820\) 2.58581e8 4.47876e8i 0.0163775 0.0283667i
\(821\) 1.36364e10 0.860004 0.430002 0.902828i \(-0.358513\pi\)
0.430002 + 0.902828i \(0.358513\pi\)
\(822\) −5.41054e9 + 9.37134e9i −0.339774 + 0.588505i
\(823\) 3.41248e9 5.91058e9i 0.213388 0.369599i −0.739385 0.673283i \(-0.764883\pi\)
0.952773 + 0.303684i \(0.0982168\pi\)
\(824\) −1.38003e10 2.39028e10i −0.859295 1.48834i
\(825\) 6.89490e9 0.427503
\(826\) 3.50153e9 + 6.06483e9i 0.216186 + 0.374445i
\(827\) 1.17149e10 2.02908e10i 0.720226 1.24747i −0.240683 0.970604i \(-0.577371\pi\)
0.960909 0.276865i \(-0.0892954\pi\)
\(828\) 5.01602e8 0.0307081
\(829\) 1.27488e9 2.20817e9i 0.0777195 0.134614i −0.824546 0.565795i \(-0.808569\pi\)
0.902266 + 0.431181i \(0.141903\pi\)
\(830\) 1.89068e9 + 3.27475e9i 0.114774 + 0.198795i
\(831\) 4.83472e8 + 8.37399e8i 0.0292259 + 0.0506208i
\(832\) −1.16774e10 2.02258e10i −0.702931 1.21751i
\(833\) −7.94062e9 −0.475989
\(834\) 1.02450e10 + 1.77449e10i 0.611551 + 1.05924i
\(835\) 5.50009e9 + 9.52644e9i 0.326939 + 0.566276i
\(836\) 2.77332e8 4.80354e8i 0.0164164 0.0284341i
\(837\) −2.54244e9 + 4.40363e9i −0.149869 + 0.259581i
\(838\) −9.40876e9 −0.552304
\(839\) 7.44172e9 0.435017 0.217509 0.976058i \(-0.430207\pi\)
0.217509 + 0.976058i \(0.430207\pi\)
\(840\) −2.13919e9 + 3.70518e9i −0.124529 + 0.215691i
\(841\) 4.06068e9 7.03330e9i 0.235403 0.407731i
\(842\) −9.92569e9 1.71918e10i −0.573018 0.992497i
\(843\) −1.02960e10 1.78331e10i −0.591931 1.02525i
\(844\) −4.50112e8 −0.0257705
\(845\) 2.68388e9 + 4.64861e9i 0.153026 + 0.265048i
\(846\) 5.74660e9 + 9.95341e9i 0.326298 + 0.565166i
\(847\) 4.41614e9 + 7.64898e9i 0.249719 + 0.432525i
\(848\) −2.37135e9 + 4.10730e9i −0.133540 + 0.231298i
\(849\) −2.79333e9 −0.156655
\(850\) 1.10214e10 1.90896e10i 0.615560 1.06618i
\(851\) −4.70049e9 8.14149e9i −0.261451 0.452846i
\(852\) −1.29081e9 −0.0715028
\(853\) −1.74866e10 3.02877e10i −0.964681 1.67088i −0.710471 0.703727i \(-0.751518\pi\)
−0.254210 0.967149i \(-0.581815\pi\)
\(854\) 3.45855e8 5.99039e8i 0.0190017 0.0329119i
\(855\) 1.41363e9 2.44848e9i 0.0773490 0.133972i
\(856\) 1.14896e10 0.626104
\(857\) −5.86990e8 + 1.01670e9i −0.0318565 + 0.0551771i −0.881514 0.472158i \(-0.843475\pi\)
0.849658 + 0.527335i \(0.176809\pi\)
\(858\) −1.21047e10 −0.654256
\(859\) −1.16759e10 −0.628513 −0.314257 0.949338i \(-0.601755\pi\)
−0.314257 + 0.949338i \(0.601755\pi\)
\(860\) −2.62665e8 1.94942e8i −0.0140818 0.0104511i
\(861\) −2.28088e10 −1.21785
\(862\) −6.31631e9 −0.335883
\(863\) −5.86365e9 + 1.01561e10i −0.310549 + 0.537887i −0.978481 0.206335i \(-0.933846\pi\)
0.667932 + 0.744222i \(0.267180\pi\)
\(864\) −1.93290e9 −0.101955
\(865\) −4.26982e9 + 7.39554e9i −0.224312 + 0.388520i
\(866\) 3.00533e9 5.20539e9i 0.157246 0.272358i
\(867\) −8.74409e9 1.51452e10i −0.455667 0.789239i
\(868\) 2.04780e8 0.0106284
\(869\) 2.98895e9 + 5.17702e9i 0.154508 + 0.267615i
\(870\) −2.04523e9 + 3.54244e9i −0.105299 + 0.182384i
\(871\) 1.28668e10 0.659790
\(872\) 1.25394e8 2.17189e8i 0.00640428 0.0110925i
\(873\) 1.02334e8 + 1.77248e8i 0.00520562 + 0.00901639i
\(874\) 1.90171e10 + 3.29386e10i 0.963507 + 1.66884i
\(875\) −5.66103e9 9.80520e9i −0.285672 0.494798i
\(876\) −7.63865e8 −0.0383930
\(877\) 4.01010e9 + 6.94569e9i 0.200750 + 0.347710i 0.948770 0.315966i \(-0.102329\pi\)
−0.748020 + 0.663676i \(0.768995\pi\)
\(878\) −1.01186e10 1.75259e10i −0.504532 0.873876i
\(879\) 2.51548e9 4.35693e9i 0.124928 0.216381i
\(880\) 2.24970e9 3.89659e9i 0.111284 0.192750i
\(881\) −1.23728e10 −0.609611 −0.304806 0.952415i \(-0.598591\pi\)
−0.304806 + 0.952415i \(0.598591\pi\)
\(882\) 2.39312e9 0.117442
\(883\) 6.26221e9 1.08465e10i 0.306101 0.530183i −0.671405 0.741091i \(-0.734309\pi\)
0.977506 + 0.210908i \(0.0676420\pi\)
\(884\) 9.52575e8 1.64991e9i 0.0463784 0.0803298i
\(885\) −1.64782e9 2.85410e9i −0.0799111 0.138410i
\(886\) −3.31917e9 5.74897e9i −0.160329 0.277697i
\(887\) −1.40949e10 −0.678155 −0.339078 0.940758i \(-0.610115\pi\)
−0.339078 + 0.940758i \(0.610115\pi\)
\(888\) 2.50425e9 + 4.33750e9i 0.120014 + 0.207871i
\(889\) 3.10654e9 + 5.38068e9i 0.148293 + 0.256851i
\(890\) −5.76122e9 9.97873e9i −0.273936 0.474471i
\(891\) −3.25493e9 + 5.63771e9i −0.154159 + 0.267012i
\(892\) −9.11092e8 −0.0429818
\(893\) 2.14518e10 3.71556e10i 1.00805 1.74600i
\(894\) 3.30577e9 + 5.72576e9i 0.154736 + 0.268010i
\(895\) 9.24844e9 0.431209
\(896\) −8.17360e9 1.41571e10i −0.379608 0.657500i
\(897\) −2.04317e10 + 3.53888e10i −0.945217 + 1.63716i
\(898\) −4.63492e9 + 8.02792e9i −0.213587 + 0.369944i
\(899\) 4.36847e9 0.200526
\(900\) 1.63525e8 2.83234e8i 0.00747713 0.0129508i
\(901\) −9.03919e9 −0.411711
\(902\) 2.51708e10 1.14202
\(903\) −1.65354e9 + 1.43313e10i −0.0747321 + 0.647709i
\(904\) 2.55702e9 0.115118
\(905\) −9.30674e9 −0.417376
\(906\) −6.96846e9 + 1.20697e10i −0.311307 + 0.539199i
\(907\) −2.19464e10 −0.976648 −0.488324 0.872662i \(-0.662392\pi\)
−0.488324 + 0.872662i \(0.662392\pi\)
\(908\) 7.07384e8 1.22523e9i 0.0313585 0.0543145i
\(909\) 5.05066e9 8.74799e9i 0.223036 0.386309i
\(910\) 4.59613e9 + 7.96073e9i 0.202184 + 0.350194i
\(911\) 2.56463e10 1.12386 0.561928 0.827186i \(-0.310060\pi\)
0.561928 + 0.827186i \(0.310060\pi\)
\(912\) −9.65521e9 1.67233e10i −0.421483 0.730030i
\(913\) 4.53028e9 7.84667e9i 0.197005 0.341223i
\(914\) 2.74811e10 1.19048
\(915\) −1.62759e8 + 2.81907e8i −0.00702379 + 0.0121656i
\(916\) 9.52260e8 + 1.64936e9i 0.0409375 + 0.0709059i
\(917\) 4.00796e9 + 6.94199e9i 0.171645 + 0.297298i
\(918\) 1.82364e10 + 3.15864e10i 0.778018 + 1.34757i
\(919\) −9.88803e9 −0.420248 −0.210124 0.977675i \(-0.567387\pi\)
−0.210124 + 0.977675i \(0.567387\pi\)
\(920\) −7.96937e9 1.38034e10i −0.337417 0.584423i
\(921\) 3.36215e9 + 5.82342e9i 0.141811 + 0.245623i
\(922\) 2.16381e10 3.74783e10i 0.909203 1.57479i
\(923\) −3.09402e10 + 5.35900e10i −1.29514 + 2.24325i
\(924\) 4.59450e8 0.0191596
\(925\) −6.12953e9 −0.254643
\(926\) −2.20959e10 + 3.82713e10i −0.914479 + 1.58392i
\(927\) −7.55410e9 + 1.30841e10i −0.311461 + 0.539466i
\(928\) 8.30285e8 + 1.43810e9i 0.0341043 + 0.0590704i
\(929\) −9.47111e9 1.64044e10i −0.387566 0.671284i 0.604555 0.796563i \(-0.293351\pi\)
−0.992122 + 0.125279i \(0.960017\pi\)
\(930\) 1.95750e9 0.0798016
\(931\) −4.46671e9 7.73656e9i −0.181411 0.314213i
\(932\) 7.09042e8 + 1.22810e9i 0.0286891 + 0.0496909i
\(933\) −8.11719e9 1.40594e10i −0.327205 0.566735i
\(934\) −1.51283e10 + 2.62031e10i −0.607543 + 1.05230i
\(935\) 8.57546e9 0.343097
\(936\) −6.40555e9 + 1.10947e10i −0.255324 + 0.442233i
\(937\) 2.09388e10 + 3.62670e10i 0.831500 + 1.44020i 0.896849 + 0.442338i \(0.145851\pi\)
−0.0653487 + 0.997862i \(0.520816\pi\)
\(938\) 9.92011e9 0.392470
\(939\) −6.86285e9 1.18868e10i −0.270505 0.468528i
\(940\) −4.02899e8 + 6.97841e8i −0.0158215 + 0.0274037i
\(941\) −1.10130e10 + 1.90751e10i −0.430865 + 0.746281i −0.996948 0.0780676i \(-0.975125\pi\)
0.566083 + 0.824349i \(0.308458\pi\)
\(942\) 8.07119e9 0.314601
\(943\) 4.24863e10 7.35884e10i 1.64990 2.85771i
\(944\) 1.32459e10 0.512482
\(945\) 8.66363e9 0.333956
\(946\) 1.82477e9 1.58154e10i 0.0700792 0.607381i
\(947\) 3.79143e10 1.45070 0.725351 0.688379i \(-0.241677\pi\)
0.725351 + 0.688379i \(0.241677\pi\)
\(948\) −4.81858e8 −0.0183692
\(949\) −1.83095e10 + 3.17131e10i −0.695418 + 1.20450i
\(950\) 2.47987e10 0.938418
\(951\) 1.69943e9 2.94351e9i 0.0640726 0.110977i
\(952\) 1.63868e10 2.83828e10i 0.615552 1.06617i
\(953\) 2.09653e10 + 3.63129e10i 0.784648 + 1.35905i 0.929209 + 0.369555i \(0.120490\pi\)
−0.144561 + 0.989496i \(0.546177\pi\)
\(954\) 2.72420e9 0.101583
\(955\) 1.72019e9 + 2.97945e9i 0.0639093 + 0.110694i
\(956\) 2.51943e8 4.36378e8i 0.00932610 0.0161533i
\(957\) 9.80121e9 0.361483
\(958\) 5.19066e9 8.99048e9i 0.190741 0.330372i
\(959\) −9.84504e9 1.70521e10i −0.360456 0.624328i
\(960\) 4.23685e9 + 7.33844e9i 0.154559 + 0.267704i
\(961\) 1.27110e10 + 2.20162e10i 0.462008 + 0.800221i
\(962\) 1.07610e10 0.389708
\(963\) −3.14463e9 5.44666e9i −0.113469 0.196534i
\(964\) 8.15996e8 + 1.41335e9i 0.0293372 + 0.0508135i
\(965\) 4.01060e9 6.94657e9i 0.143669 0.248843i
\(966\) −1.57526e10 + 2.72843e10i −0.562254 + 0.973853i
\(967\) −5.94040e9 −0.211263 −0.105631 0.994405i \(-0.533686\pi\)
−0.105631 + 0.994405i \(0.533686\pi\)
\(968\) 1.75301e10 0.621183
\(969\) 1.84020e10 3.18732e10i 0.649729 1.12536i
\(970\) 1.45737e8 2.52423e8i 0.00512705 0.00888032i
\(971\) 1.32430e9 + 2.29375e9i 0.0464214 + 0.0804042i 0.888302 0.459259i \(-0.151885\pi\)
−0.841881 + 0.539663i \(0.818552\pi\)
\(972\) 4.68008e8 + 8.10613e8i 0.0163464 + 0.0283127i
\(973\) −3.72838e10 −1.29755
\(974\) 1.52197e10 + 2.63612e10i 0.527775 + 0.914133i
\(975\) 1.33217e10 + 2.30738e10i 0.460302 + 0.797267i
\(976\) −6.54165e8 1.13305e9i −0.0225223 0.0390098i
\(977\) 6.52055e9 1.12939e10i 0.223693 0.387448i −0.732233 0.681054i \(-0.761522\pi\)
0.955927 + 0.293606i \(0.0948552\pi\)
\(978\) 1.64824e10 0.563423
\(979\) −1.38045e10 + 2.39102e10i −0.470200 + 0.814410i
\(980\) 8.38918e7 + 1.45305e8i 0.00284727 + 0.00493161i
\(981\) −1.37279e8 −0.00464261
\(982\) −1.19664e10 2.07264e10i −0.403249 0.698448i
\(983\) −2.61333e9 + 4.52643e9i −0.0877521 + 0.151991i −0.906561 0.422076i \(-0.861302\pi\)
0.818809 + 0.574067i \(0.194635\pi\)
\(984\) −2.26352e10 + 3.92053e10i −0.757358 + 1.31178i
\(985\) 7.69100e9 0.256422
\(986\) 1.56671e10 2.71362e10i 0.520497 0.901528i
\(987\) 3.55387e10 1.17650
\(988\) 2.14334e9 0.0707038
\(989\) −4.31573e10 3.20300e10i −1.41862 1.05286i
\(990\) −2.58445e9 −0.0846534
\(991\) −3.99304e10 −1.30330 −0.651652 0.758518i \(-0.725924\pi\)
−0.651652 + 0.758518i \(0.725924\pi\)
\(992\) 3.97335e8 6.88204e8i 0.0129231 0.0223834i
\(993\) −8.40235e9 −0.272319
\(994\) −2.38545e10 + 4.13172e10i −0.770404 + 1.33438i
\(995\) 4.19491e9 7.26580e9i 0.135003 0.233831i
\(996\) 3.65170e8 + 6.32493e8i 0.0117108 + 0.0202837i
\(997\) 5.75235e10 1.83828 0.919142 0.393927i \(-0.128884\pi\)
0.919142 + 0.393927i \(0.128884\pi\)
\(998\) 1.26773e9 + 2.19577e9i 0.0403710 + 0.0699246i
\(999\) 5.07107e9 8.78336e9i 0.160924 0.278728i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 43.8.c.a.6.18 50
43.36 even 3 inner 43.8.c.a.36.18 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.8.c.a.6.18 50 1.1 even 1 trivial
43.8.c.a.36.18 yes 50 43.36 even 3 inner